LMFDB - Embedded newform 3.38.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,38,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	3.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:	$26.0142114374$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 11777633936x^{2} - 35120319927360x + 11967042111800832000 $ x^4 - x^3 - 11777633936x^2 - 35120319927360x + 11967042111800832000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{10}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-35434.6$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+322000. q^{2} +3.87420e8 q^{3} -3.37552e10 q^{4} +1.53382e13 q^{5} +1.24749e14 q^{6} +2.48687e15 q^{7} -5.51245e16 q^{8} +1.50095e17 q^{9} +O(q^{10})$	\(q+322000. q^{2} +3.87420e8 q^{3} -3.37552e10 q^{4} +1.53382e13 q^{5} +1.24749e14 q^{6} +2.48687e15 q^{7} -5.51245e16 q^{8} +1.50095e17 q^{9} +4.93889e18 q^{10} -1.32093e18 q^{11} -1.30775e19 q^{12} +1.53342e20 q^{13} +8.00770e20 q^{14} +5.94233e21 q^{15} -1.31108e22 q^{16} +1.04822e23 q^{17} +4.83304e22 q^{18} -6.96548e23 q^{19} -5.17744e23 q^{20} +9.63463e23 q^{21} -4.25339e23 q^{22} +1.11946e25 q^{23} -2.13563e25 q^{24} +1.62501e26 q^{25} +4.93762e25 q^{26} +5.81497e25 q^{27} -8.39448e25 q^{28} +1.43220e27 q^{29} +1.91343e27 q^{30} +3.90372e26 q^{31} +3.35459e27 q^{32} -5.11755e26 q^{33} +3.37525e28 q^{34} +3.81440e28 q^{35} -5.06648e27 q^{36} -8.53226e28 q^{37} -2.24288e29 q^{38} +5.94080e28 q^{39} -8.45509e29 q^{40} +4.51987e29 q^{41} +3.10235e29 q^{42} -2.04528e30 q^{43} +4.45883e28 q^{44} +2.30218e30 q^{45} +3.60466e30 q^{46} -3.80345e30 q^{47} -5.07938e30 q^{48} -1.23776e31 q^{49} +5.23251e31 q^{50} +4.06100e31 q^{51} -5.17611e30 q^{52} +2.08682e31 q^{53} +1.87242e31 q^{54} -2.02607e31 q^{55} -1.37087e32 q^{56} -2.69857e32 q^{57} +4.61167e32 q^{58} -1.01104e33 q^{59} -2.00585e32 q^{60} -1.04937e33 q^{61} +1.25699e32 q^{62} +3.73265e32 q^{63} +2.88211e33 q^{64} +2.35199e33 q^{65} -1.64785e32 q^{66} +2.33599e33 q^{67} -3.53828e33 q^{68} +4.33702e33 q^{69} +1.22824e34 q^{70} +1.08272e33 q^{71} -8.27388e33 q^{72} -3.23026e34 q^{73} -2.74738e34 q^{74} +6.29560e34 q^{75} +2.35121e34 q^{76} -3.28498e33 q^{77} +1.91293e34 q^{78} -2.35299e35 q^{79} -2.01095e35 q^{80} +2.25284e34 q^{81} +1.45540e35 q^{82} -1.58763e35 q^{83} -3.25219e34 q^{84} +1.60777e36 q^{85} -6.58578e35 q^{86} +5.54863e35 q^{87} +7.28155e34 q^{88} -3.16700e35 q^{89} +7.41301e35 q^{90} +3.81342e35 q^{91} -3.77876e35 q^{92} +1.51238e35 q^{93} -1.22471e36 q^{94} -1.06838e37 q^{95} +1.29964e36 q^{96} +6.89438e36 q^{97} -3.98559e36 q^{98} -1.98265e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 60\!\cdots\!84 q^{9}+O(q^{10}) $ 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9	$ 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 31\!\cdots\!96 q^{99}+O(q^{100}) $ 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9 - 21511023001649316 * q^10 + 20953708852195292976 * q^11 + 134085826579099875588 * q^12 + 51830892788989874168 * q^13 - 1809002141673235613712 * q^14 - 1588358049236498806056 * q^15 + 55184727516616371757840 * q^16 + 81101770962322537501128 * q^17 + 65675708809825529383002 * q^18 - 544604242502813077907632 * q^19 - 3566083114449076353950376 * q^20 + 2559226120354571192186976 * q^21 + 23909208610123411045457976 * q^22 - 6105434608113226892697888 * q^23 + 54426423887751042218148264 * q^24 + 95396877753446381193398716 * q^25 + 428554172265180170762299788 * q^26 + 232598948012160238761560676 * q^27 + 2469833924959492064190244448 * q^28 + 4171186009659314742454127736 * q^29 - 8333811050189225811235524 * q^30 + 8995814656808409627856220864 * q^31 + 36517476440276920084276020384 * q^32 + 8117896129881129128260185264 * q^33 + 31219088393882932122099949524 * q^34 + 42129462142584542112964223040 * q^35 + 51947596501244070980142122532 * q^36 + 55519093704269258277039732824 * q^37 - 735180697664011480109320664568 * q^38 + 20080349829617030866215028152 * q^39 - 2663133991761021855901070923152 * q^40 - 869595339264691998704372818776 * q^41 - 700844494329092219676518145168 * q^42 - 509323958833633606104562745680 * q^43 + 2838804848354890092833187324336 * q^44 - 615362452142290444090131681384 * q^45 - 14832400342987743191058839458896 * q^46 + 4297748917019550924184843821120 * q^47 + 21379694119819270371828162383760 * q^48 + 40223006658016971616433785618020 * q^49 + 102764730674385833857211828709414 * q^50 + 31420487764988998054407847811592 * q^51 + 186771330756284408934646875520568 * q^52 - 125797679190958862093479980165288 * q^53 + 25444115222524214598246503127978 * q^54 - 324441401797069196184728188134624 * q^55 + 49261177652308793436687718380480 * q^56 - 210990841941914426518569886272048 * q^57 - 758216144723951752216603559669556 * q^58 - 1322751535061383229075407129388688 * q^59 - 1381573664014504126645791751653864 * q^60 - 1210012908287761061549313720873160 * q^61 - 3774869312329378363502064838581792 * q^62 + 991496635009340824662391221351264 * q^63 + 8553618714336434539515354532145728 * q^64 + 1596939597234927778869711846229968 * q^65 + 9262917291337022257579330290870264 * q^66 + 16212837695473169417262127089269648 * q^67 + 6364770984875237153325176447214984 * q^68 - 2365370461432749730136966298227232 * q^69 + 8205699211322075854652286498656160 * q^70 + 10892424995451680587530033164573088 * q^71 + 21085911757113789886414645113381096 * q^72 - 19472416597596703966438677461737048 * q^73 - 89115306434605413664690690272305412 * q^74 + 36958705028313418437226934124692124 * q^75 - 95475877084130734100913860795365168 * q^76 - 256189314900709292482321902951864192 * q^77 + 166030666981966339429833686631556332 * q^78 + 42564929886993357285736803130555520 * q^79 - 955034489632094448517301530341944736 * q^80 + 90113598179756697647360591499090564 * q^81 + 335470244295388111217009211756354948 * q^82 - 462964612731837394872969166562146224 * q^83 + 956864266956595720700203893073695072 * q^84 + 1847677353245070936584728247586996912 * q^85 - 363370083621183428400243233525783304 * q^86 + 1616002923572170440926487227549582904 * q^87 + 4210934419609684353108607591773010656 * q^88 - 314574774231571073544391076719446552 * q^89 - 3228689152297913406320288402251236 * q^90 + 2615056540536627234228451043107657024 * q^91 - 16598538663060910484079148451607722016 * q^92 + 3485162913294081237336365108822882496 * q^93 - 573809173038711993912694394480689248 * q^94 - 8958385060094338314910240959017780256 * q^95 + 14147618579538063674464137028143247776 * q^96 + 445047507548838106214452450407795848 * q^97 - 43086999614034505592591376853854433878 * q^98 + 3145039288289754558742704694209474096 * 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 $

$2$	322000.	0.868561	0.434281	−	0.900778i	$-0.357003\pi$
$2$	322000.	0.868561	0.434281	+	0.900778i	$0.357003\pi$
$3$	3.87420e8	0.577350
$3$	3.87420e8	0.577350
$4$	−3.37552e10	−0.245602
$5$	1.53382e13	1.79816	0.899081	−	0.437781i	$-0.144236\pi$
$5$	1.53382e13	1.79816	0.899081	+	0.437781i	$0.144236\pi$
$6$	1.24749e14	0.501464
$7$	2.48687e15	0.577216	0.288608	−	0.957447i	$-0.406807\pi$
$7$	2.48687e15	0.577216	0.288608	+	0.957447i	$0.406807\pi$
$8$	−5.51245e16	−1.08188
$9$	1.50095e17	0.333333
$10$	4.93889e18	1.56181
$11$	−1.32093e18	−0.0716333	−0.0358167	−	0.999358i	$-0.511403\pi$
$11$	−1.32093e18	−0.0716333	−0.0358167	+	0.999358i	$0.511403\pi$
$12$	−1.30775e19	−0.141798
$13$	1.53342e20	0.378190	0.189095	−	0.981959i	$-0.439445\pi$
$13$	1.53342e20	0.378190	0.189095	+	0.981959i	$0.439445\pi$
$14$	8.00770e20	0.501348
$15$	5.94233e21	1.03817
$16$	−1.31108e22	−0.694078
$17$	1.04822e23	1.80778	0.903890	−	0.427765i	$-0.140699\pi$
$17$	1.04822e23	1.80778	0.903890	+	0.427765i	$0.140699\pi$
$18$	4.83304e22	0.289520
$19$	−6.96548e23	−1.53465	−0.767325	−	0.641258i	$-0.778413\pi$
$19$	−6.96548e23	−1.53465	−0.767325	+	0.641258i	$0.778413\pi$
$20$	−5.17744e23	−0.441632
$21$	9.63463e23	0.333256
$22$	−4.25339e23	−0.0622179
$23$	1.11946e25	0.719521	0.359761	−	0.933045i	$-0.382858\pi$
$23$	1.11946e25	0.719521	0.359761	+	0.933045i	$0.382858\pi$
$24$	−2.13563e25	−0.624624
$25$	1.62501e26	2.23339
$26$	4.93762e25	0.328481
$27$	5.81497e25	0.192450
$28$	−8.39448e25	−0.141765
$29$	1.43220e27	1.26369	0.631845	−	0.775095i	$-0.282298\pi$
$29$	1.43220e27	1.26369	0.631845	+	0.775095i	$0.282298\pi$
$30$	1.91343e27	0.901714
$31$	3.90372e26	0.100297	0.0501484	−	0.998742i	$-0.484031\pi$
$31$	3.90372e26	0.100297	0.0501484	+	0.998742i	$0.484031\pi$
$32$	3.35459e27	0.479032
$33$	−5.11755e26	−0.0413575
$34$	3.37525e28	1.57017
$35$	3.81440e28	1.03793
$36$	−5.06648e27	−0.0818672
$37$	−8.53226e28	−0.830486	−0.415243	−	0.909711i	$-0.636303\pi$
$37$	−8.53226e28	−0.830486	−0.415243	+	0.909711i	$0.636303\pi$
$38$	−2.24288e29	−1.33294
$39$	5.94080e28	0.218348
$40$	−8.45509e29	−1.94540
$41$	4.51987e29	0.658605	0.329302	−	0.944225i	$-0.393186\pi$
$41$	4.51987e29	0.658605	0.329302	+	0.944225i	$0.393186\pi$
$42$	3.10235e29	0.289453
$43$	−2.04528e30	−1.23477	−0.617384	−	0.786662i	$-0.711808\pi$
$43$	−2.04528e30	−1.23477	−0.617384	+	0.786662i	$0.711808\pi$
$44$	4.45883e28	0.0175933
$45$	2.30218e30	0.599388
$46$	3.60466e30	0.624948
$47$	−3.80345e30	−0.442963	−0.221481	−	0.975165i	$-0.571089\pi$
$47$	−3.80345e30	−0.442963	−0.221481	+	0.975165i	$0.571089\pi$
$48$	−5.07938e30	−0.400726
$49$	−1.23776e31	−0.666821
$50$	5.23251e31	1.93984
$51$	4.06100e31	1.04372
$52$	−5.17611e30	−0.0928841
$53$	2.08682e31	0.263257	0.131629	−	0.991299i	$-0.457979\pi$
$53$	2.08682e31	0.263257	0.131629	+	0.991299i	$0.457979\pi$
$54$	1.87242e31	0.167155
$55$	−2.02607e31	−0.128808
$56$	−1.37087e32	−0.624480
$57$	−2.69857e32	−0.886031
$58$	4.61167e32	1.09759
$59$	−1.01104e33	−1.75390	−0.876952	−	0.480578i	$-0.840427\pi$
$59$	−1.01104e33	−1.75390	−0.876952	+	0.480578i	$0.840427\pi$
$60$	−2.00585e32	−0.254976
$61$	−1.04937e33	−0.982484	−0.491242	−	0.871023i	$-0.663457\pi$
$61$	−1.04937e33	−0.982484	−0.491242	+	0.871023i	$0.663457\pi$
$62$	1.25699e32	0.0871138
$63$	3.73265e32	0.192405
$64$	2.88211e33	1.11015
$65$	2.35199e33	0.680047
$66$	−1.64785e32	−0.0359215
$67$	2.33599e33	0.385557	0.192778	−	0.981242i	$-0.438250\pi$
$67$	2.33599e33	0.385557	0.192778	+	0.981242i	$0.438250\pi$
$68$	−3.53828e33	−0.443994
$69$	4.33702e33	0.415416
$70$	1.22824e34	0.901505
$71$	1.08272e33	0.0611275	0.0305637	−	0.999533i	$-0.490270\pi$
$71$	1.08272e33	0.0611275	0.0305637	+	0.999533i	$0.490270\pi$
$72$	−8.27388e33	−0.360627
$73$	−3.23026e34	−1.09085	−0.545424	−	0.838160i	$-0.683631\pi$
$73$	−3.23026e34	−1.09085	−0.545424	+	0.838160i	$0.683631\pi$
$74$	−2.74738e34	−0.721328
$75$	6.29560e34	1.28945
$76$	2.35121e34	0.376913
$77$	−3.28498e33	−0.0413479
$78$	1.91293e34	0.189649
$79$	−2.35299e35	−1.84297	−0.921486	−	0.388411i	$-0.873024\pi$
$79$	−2.35299e35	−1.84297	−0.921486	+	0.388411i	$0.873024\pi$
$80$	−2.01095e35	−1.24807
$81$	2.25284e34	0.111111
$82$	1.45540e35	0.572038
$83$	−1.58763e35	−0.498660	−0.249330	−	0.968419i	$-0.580210\pi$
$83$	−1.58763e35	−0.498660	−0.249330	+	0.968419i	$0.580210\pi$
$84$	−3.25219e34	−0.0818483
$85$	1.60777e36	3.25068
$86$	−6.58578e35	−1.07247
$87$	5.54863e35	0.729591
$88$	7.28155e34	0.0774987
$89$	−3.16700e35	−0.273484	−0.136742	−	0.990607i	$-0.543663\pi$
$89$	−3.16700e35	−0.273484	−0.136742	+	0.990607i	$0.543663\pi$
$90$	7.41301e35	0.520605
$91$	3.81342e35	0.218298
$92$	−3.77876e35	−0.176716
$93$	1.51238e35	0.0579064
$94$	−1.22471e36	−0.384740
$95$	−1.06838e37	−2.75955
$96$	1.29964e36	0.276569
$97$	6.89438e36	1.21121	0.605603	−	0.795767i	$-0.292932\pi$
$97$	6.89438e36	1.21121	0.605603	+	0.795767i	$0.292932\pi$
$98$	−3.98559e36	−0.579175
$99$	−1.98265e35	−0.0238778
$100$	−5.48524e36	−0.548524
$101$	8.14698e36	0.677721	0.338861	−	0.940837i	$-0.389958\pi$
$101$	8.14698e36	0.677721	0.338861	+	0.940837i	$0.389958\pi$
$102$	1.30764e37	0.906536
$103$	−1.09944e37	−0.636329	−0.318165	−	0.948036i	$-0.603066\pi$
$103$	−1.09944e37	−0.636329	−0.318165	+	0.948036i	$0.603066\pi$
$104$	−8.45291e36	−0.409157
$105$	1.47778e37	0.599249
$106$	6.71954e36	0.228655
$107$	2.26830e37	0.648783	0.324392	−	0.945923i	$-0.394840\pi$
$107$	2.26830e37	0.648783	0.324392	+	0.945923i	$0.394840\pi$
$108$	−1.96286e36	−0.0472661
$109$	3.74392e37	0.760216	0.380108	−	0.924942i	$-0.375887\pi$
$109$	3.74392e37	0.760216	0.380108	+	0.924942i	$0.375887\pi$
$110$	−6.52393e36	−0.111878
$111$	−3.30557e37	−0.479481
$112$	−3.26047e37	−0.400633
$113$	1.81279e37	0.188972	0.0944858	−	0.995526i	$-0.469879\pi$
$113$	1.81279e37	0.188972	0.0944858	+	0.995526i	$0.469879\pi$
$114$	−8.68938e37	−0.769572
$115$	1.71705e38	1.29382
$116$	−4.83442e37	−0.310364
$117$	2.30159e37	0.126063
$118$	−3.25554e38	−1.52337
$119$	2.60677e38	1.04348
$120$	−3.27568e38	−1.12318
$121$	−3.38295e38	−0.994869
$122$	−3.37896e38	−0.853348
$123$	1.75109e38	0.380245
$124$	−1.31771e37	−0.0246331
$125$	1.37646e39	2.21784
$126$	1.20191e38	0.167116
$127$	3.75363e38	0.450903	0.225451	−	0.974254i	$-0.427614\pi$
$127$	3.75363e38	0.450903	0.225451	+	0.974254i	$0.427614\pi$
$128$	4.66986e38	0.485198
$129$	−7.92382e38	−0.712894
$130$	7.57341e38	0.590663
$131$	1.53812e39	1.04105	0.520525	−	0.853846i	$-0.325736\pi$
$131$	1.53812e39	1.04105	0.520525	+	0.853846i	$0.325736\pi$
$132$	1.72744e37	0.0101575
$133$	−1.73222e39	−0.885825
$134$	7.52189e38	0.334879
$135$	8.91912e38	0.346057
$136$	−5.77823e39	−1.95580
$137$	−5.26351e39	−1.55577	−0.777885	−	0.628407i	$-0.783707\pi$
$137$	−5.26351e39	−1.55577	−0.777885	+	0.628407i	$0.783707\pi$
$138$	1.39652e39	0.360814
$139$	3.79319e39	0.857494	0.428747	−	0.903425i	$-0.358955\pi$
$139$	3.79319e39	0.857494	0.428747	+	0.903425i	$0.358955\pi$
$140$	−1.28756e39	−0.254917
$141$	−1.47353e39	−0.255745
$142$	3.48635e38	0.0530930
$143$	−2.02555e38	−0.0270910
$144$	−1.96786e39	−0.231359
$145$	2.19673e40	2.27232
$146$	−1.04014e40	−0.947468
$147$	−4.79534e39	−0.384989
$148$	2.88009e39	0.203969
$149$	−2.87234e40	−1.79593	−0.897967	−	0.440063i	$-0.854956\pi$
$149$	−2.87234e40	−1.79593	−0.897967	+	0.440063i	$0.854956\pi$
$150$	2.02718e40	1.11996
$151$	1.01312e39	0.0494982	0.0247491	−	0.999694i	$-0.492121\pi$
$151$	1.01312e39	0.0494982	0.0247491	+	0.999694i	$0.492121\pi$
$152$	3.83968e40	1.66031
$153$	1.57332e40	0.602593
$154$	−1.05776e39	−0.0359132
$155$	5.98759e39	0.180350
$156$	−2.00533e39	−0.0536267
$157$	−3.12964e40	−0.743620	−0.371810	−	0.928309i	$-0.621263\pi$
$157$	−3.12964e40	−0.743620	−0.371810	+	0.928309i	$0.621263\pi$
$158$	−7.57662e40	−1.60073
$159$	8.08475e39	0.151992
$160$	5.14533e40	0.861378
$161$	2.78395e40	0.415319
$162$	7.25413e39	0.0965068
$163$	−6.14970e40	−0.730102	−0.365051	−	0.930988i	$-0.618948\pi$
$163$	−6.14970e40	−0.730102	−0.365051	+	0.930988i	$0.618948\pi$
$164$	−1.52569e40	−0.161754
$165$	−7.84940e39	−0.0743676
$166$	−5.11216e40	−0.433117
$167$	−1.95759e41	−1.48411	−0.742055	−	0.670339i	$-0.766149\pi$
$167$	−1.95759e41	−1.48411	−0.742055	+	0.670339i	$0.766149\pi$
$168$	−5.31104e40	−0.360543
$169$	−1.40887e41	−0.856972
$170$	5.17702e41	2.82342
$171$	−1.04548e41	−0.511550
$172$	6.90388e40	0.303261
$173$	8.49345e40	0.335144	0.167572	−	0.985860i	$-0.446407\pi$
$173$	8.49345e40	0.335144	0.167572	+	0.985860i	$0.446407\pi$
$174$	1.78666e41	0.633695
$175$	4.04117e41	1.28915
$176$	1.73184e40	0.0497191
$177$	−3.91697e41	−1.01262
$178$	−1.01977e41	−0.237538
$179$	5.07222e41	1.06517	0.532583	−	0.846378i	$-0.321222\pi$
$179$	5.07222e41	1.06517	0.532583	+	0.846378i	$0.321222\pi$
$180$	−7.77107e40	−0.147211
$181$	2.84986e41	0.487270	0.243635	−	0.969867i	$-0.421660\pi$
$181$	2.84986e41	0.487270	0.243635	+	0.969867i	$0.421660\pi$
$182$	1.22792e41	0.189605
$183$	−4.06546e41	−0.567238
$184$	−6.17096e41	−0.778436
$185$	−1.30869e42	−1.49335
$186$	4.86985e40	0.0502952
$187$	−1.38462e41	−0.129497
$188$	1.28386e41	0.108792
$189$	1.44611e41	0.111085
$190$	−3.44017e42	−2.39684
$191$	1.34993e42	0.853483	0.426741	−	0.904374i	$-0.359661\pi$
$191$	1.34993e42	0.853483	0.426741	+	0.904374i	$0.359661\pi$
$192$	1.11659e42	0.640943
$193$	1.53006e42	0.797806	0.398903	−	0.916993i	$-0.369391\pi$
$193$	1.53006e42	0.797806	0.398903	+	0.916993i	$0.369391\pi$
$194$	2.21999e42	1.05201
$195$	9.11211e41	0.392626
$196$	4.17809e41	0.163772
$197$	−1.58341e42	−0.564896	−0.282448	−	0.959283i	$-0.591146\pi$
$197$	−1.58341e42	−0.564896	−0.282448	+	0.959283i	$0.591146\pi$
$198$	−6.38411e40	−0.0207393
$199$	3.81225e42	1.12823	0.564117	−	0.825695i	$-0.309217\pi$
$199$	3.81225e42	1.12823	0.564117	+	0.825695i	$0.309217\pi$
$200$	−8.95775e42	−2.41626
$201$	9.05012e41	0.222601
$202$	2.62332e42	0.588642
$203$	3.56169e42	0.729422
$204$	−1.37080e42	−0.256340
$205$	6.93266e42	1.18428
$206$	−3.54018e42	−0.552691
$207$	1.68025e42	0.239840
$208$	−2.01044e42	−0.262493
$209$	9.20091e41	0.109932
$210$	4.75844e42	0.520484
$211$	−1.03480e43	−1.03665	−0.518325	−	0.855184i	$-0.673444\pi$
$211$	−1.03480e43	−1.03665	−0.518325	+	0.855184i	$0.673444\pi$
$212$	−7.04410e41	−0.0646565
$213$	4.19468e41	0.0352920
$214$	7.30390e42	0.563508
$215$	−3.13708e43	−2.22031
$216$	−3.20547e42	−0.208208
$217$	9.70802e41	0.0578929
$218$	1.20554e43	0.660294
$219$	−1.25147e43	−0.629801
$220$	6.83904e41	0.0316356
$221$	1.60736e43	0.683684
$222$	−1.06439e43	−0.416459
$223$	−2.53188e43	−0.911598	−0.455799	−	0.890083i	$-0.650646\pi$
$223$	−2.53188e43	−0.911598	−0.455799	+	0.890083i	$0.650646\pi$
$224$	8.34241e42	0.276505
$225$	2.43905e43	0.744463
$226$	5.83718e42	0.164133
$227$	5.88632e43	1.52534	0.762668	−	0.646790i	$-0.223889\pi$
$227$	5.88632e43	1.52534	0.762668	+	0.646790i	$0.223889\pi$
$228$	9.10909e42	0.217611
$229$	2.71698e43	0.598590	0.299295	−	0.954161i	$-0.403249\pi$
$229$	2.71698e43	0.598590	0.299295	+	0.954161i	$0.403249\pi$
$230$	5.52889e43	1.12376
$231$	−1.27267e42	−0.0238722
$232$	−7.89492e43	−1.36716
$233$	−1.14243e43	−0.182703	−0.0913513	−	0.995819i	$-0.529119\pi$
$233$	−1.14243e43	−0.182703	−0.0913513	+	0.995819i	$0.529119\pi$
$234$	7.41110e42	0.109494
$235$	−5.83380e43	−0.796520
$236$	3.41279e43	0.430762
$237$	−9.11596e43	−1.06404
$238$	8.39379e43	0.906326
$239$	1.69778e43	0.169637	0.0848185	−	0.996396i	$-0.472969\pi$
$239$	1.69778e43	0.169637	0.0848185	+	0.996396i	$0.472969\pi$
$240$	−7.79085e43	−0.720571
$241$	−3.09126e43	−0.264740	−0.132370	−	0.991200i	$-0.542259\pi$
$241$	−3.09126e43	−0.264740	−0.132370	+	0.991200i	$0.542259\pi$
$242$	−1.08931e44	−0.864104
$243$	8.72796e42	0.0641500
$244$	3.54217e43	0.241300
$245$	−1.89850e44	−1.19905
$246$	5.63850e43	0.330266
$247$	−1.06810e44	−0.580390
$248$	−2.15190e43	−0.108509
$249$	−6.15080e43	−0.287902
$250$	4.43221e44	1.92633
$251$	2.54005e44	1.02537	0.512683	−	0.858578i	$-0.328652\pi$
$251$	2.54005e44	1.02537	0.512683	+	0.858578i	$0.328652\pi$
$252$	−1.25997e43	−0.0472551
$253$	−1.47873e43	−0.0515417
$254$	1.20867e44	0.391637
$255$	6.22884e44	1.87678
$256$	−2.45744e44	−0.688722
$257$	−3.66815e44	−0.956499	−0.478249	−	0.878224i	$-0.658729\pi$
$257$	−3.66815e44	−0.956499	−0.478249	+	0.878224i	$0.658729\pi$
$258$	−2.55147e44	−0.619192
$259$	−2.12186e44	−0.479370
$260$	−7.93922e43	−0.167021
$261$	2.14965e44	0.421230
$262$	4.95275e44	0.904216
$263$	−2.74111e44	−0.466385	−0.233192	−	0.972431i	$-0.574917\pi$
$263$	−2.74111e44	−0.466385	−0.233192	+	0.972431i	$0.574917\pi$
$264$	2.82102e43	0.0447439
$265$	3.20080e44	0.473380
$266$	−5.57775e44	−0.769393
$267$	−1.22696e44	−0.157896
$268$	−7.88521e43	−0.0946933
$269$	7.40366e44	0.829906	0.414953	−	0.909843i	$-0.363798\pi$
$269$	7.40366e44	0.829906	0.414953	+	0.909843i	$0.363798\pi$
$270$	2.87195e44	0.300571
$271$	−3.47586e44	−0.339727	−0.169863	−	0.985468i	$-0.554333\pi$
$271$	−3.47586e44	−0.339727	−0.169863	+	0.985468i	$0.554333\pi$
$272$	−1.37429e45	−1.25474
$273$	1.47740e44	0.126034
$274$	−1.69485e45	−1.35128
$275$	−2.14652e44	−0.159985
$276$	−1.46397e44	−0.102027
$277$	1.55336e45	1.01250	0.506252	−	0.862385i	$-0.331031\pi$
$277$	1.55336e45	1.01250	0.506252	+	0.862385i	$0.331031\pi$
$278$	1.22141e45	0.744786
$279$	5.85927e43	0.0334322
$280$	−2.10267e45	−1.12292
$281$	5.16475e44	0.258216	0.129108	−	0.991631i	$-0.458789\pi$
$281$	5.16475e44	0.258216	0.129108	+	0.991631i	$0.458789\pi$
$282$	−4.74477e44	−0.222130
$283$	2.81373e45	1.23377	0.616884	−	0.787054i	$-0.288395\pi$
$283$	2.81373e45	1.23377	0.616884	+	0.787054i	$0.288395\pi$
$284$	−3.65475e43	−0.0150130
$285$	−4.13912e45	−1.59323
$286$	−6.52225e43	−0.0235302
$287$	1.12403e45	0.380157
$288$	5.03506e44	0.159677
$289$	7.62546e45	2.26807
$290$	7.07347e45	1.97365
$291$	2.67102e45	0.699290
$292$	1.09038e45	0.267914
$293$	−3.48209e45	−0.803135	−0.401568	−	0.915829i	$-0.631534\pi$
$293$	−3.48209e45	−0.803135	−0.401568	+	0.915829i	$0.631534\pi$
$294$	−1.54410e45	−0.334387
$295$	−1.55075e46	−3.15380
$296$	4.70336e45	0.898487
$297$	−7.68117e43	−0.0137858
$298$	−9.24893e45	−1.55988
$299$	1.71661e45	0.272116
$300$	−2.12510e45	−0.316691
$301$	−5.08633e45	−0.712729
$302$	3.26226e44	0.0429922
$303$	3.15631e45	0.391283
$304$	9.13228e45	1.06517
$305$	−1.60954e46	−1.76667
$306$	5.06607e45	0.523389
$307$	2.84597e45	0.276803	0.138401	−	0.990376i	$-0.455804\pi$
$307$	2.84597e45	0.276803	0.138401	+	0.990376i	$0.455804\pi$
$308$	1.10885e44	0.0101551
$309$	−4.25944e45	−0.367385
$310$	1.92800e45	0.156645
$311$	8.10350e45	0.620306	0.310153	−	0.950687i	$-0.399620\pi$
$311$	8.10350e45	0.620306	0.310153	+	0.950687i	$0.399620\pi$
$312$	−3.27483e45	−0.236227
$313$	1.80984e46	1.23046	0.615232	−	0.788346i	$-0.289062\pi$
$313$	1.80984e46	1.23046	0.615232	+	0.788346i	$0.289062\pi$
$314$	−1.00774e46	−0.645879
$315$	5.72521e45	0.345976
$316$	7.94257e45	0.452637
$317$	−6.00023e45	−0.322531	−0.161266	−	0.986911i	$-0.551558\pi$
$317$	−6.00023e45	−0.322531	−0.161266	+	0.986911i	$0.551558\pi$
$318$	2.60329e45	0.132014
$319$	−1.89183e45	−0.0905223
$320$	4.42063e46	1.99622
$321$	8.78784e45	0.374575
$322$	8.96430e45	0.360730
$323$	−7.30132e46	−2.77431
$324$	−7.60452e44	−0.0272891
$325$	2.49182e46	0.844646
$326$	−1.98020e46	−0.634138
$327$	1.45047e46	0.438911
$328$	−2.49155e46	−0.712532
$329$	−9.45867e45	−0.255686
$330$	−2.52750e45	−0.0645928
$331$	1.64524e46	0.397567	0.198784	−	0.980043i	$-0.436301\pi$
$331$	1.64524e46	0.397567	0.198784	+	0.980043i	$0.436301\pi$
$332$	5.35908e45	0.122472
$333$	−1.28065e46	−0.276829
$334$	−6.30341e46	−1.28904
$335$	3.58299e46	0.693293
$336$	−1.26317e46	−0.231306
$337$	6.90318e46	1.19645	0.598227	−	0.801327i	$-0.295872\pi$
$337$	6.90318e46	1.19645	0.598227	+	0.801327i	$0.295872\pi$
$338$	−4.53655e46	−0.744333
$339$	7.02312e45	0.109103
$340$	−5.42708e46	−0.798373
$341$	−5.15654e44	−0.00718459
$342$	−3.36644e46	−0.444312
$343$	−7.69430e46	−0.962117
$344$	1.12745e47	1.33587
$345$	6.65220e46	0.746985
$346$	2.73489e46	0.291093
$347$	3.75519e46	0.378911	0.189455	−	0.981889i	$-0.439328\pi$
$347$	3.75519e46	0.378911	0.189455	+	0.981889i	$0.439328\pi$
$348$	−1.87295e46	−0.179189
$349$	−1.14417e47	−1.03805	−0.519026	−	0.854758i	$-0.673705\pi$
$349$	−1.14417e47	−1.03805	−0.519026	+	0.854758i	$0.673705\pi$
$350$	1.30126e47	1.11971
$351$	8.91682e45	0.0727827
$352$	−4.43118e45	−0.0343147
$353$	9.61675e46	0.706637	0.353318	−	0.935503i	$-0.385053\pi$
$353$	9.61675e46	0.706637	0.353318	+	0.935503i	$0.385053\pi$
$354$	−1.26126e47	−0.879519
$355$	1.66070e46	0.109917
$356$	1.06903e46	0.0671682
$357$	1.00992e47	0.602454
$358$	1.63325e47	0.925161
$359$	−3.14753e45	−0.0169326	−0.00846629	−	0.999964i	$-0.502695\pi$
$359$	−3.14753e45	−0.0169326	−0.00846629	+	0.999964i	$0.502695\pi$
$360$	−1.26906e47	−0.648466
$361$	2.79171e47	1.35515
$362$	9.17654e46	0.423224
$363$	−1.31062e47	−0.574388
$364$	−1.28723e46	−0.0536143
$365$	−4.95463e47	−1.96152
$366$	−1.30908e47	−0.492681
$367$	−6.18183e46	−0.221205	−0.110603	−	0.993865i	$-0.535278\pi$
$367$	−6.18183e46	−0.221205	−0.110603	+	0.993865i	$0.535278\pi$
$368$	−1.46770e47	−0.499404
$369$	6.78408e46	0.219535
$370$	−4.21399e47	−1.29706
$371$	5.18963e46	0.151957
$372$	−5.10507e45	−0.0142219
$373$	−6.43130e47	−1.70485	−0.852424	−	0.522852i	$-0.824868\pi$
$373$	−6.43130e47	−1.70485	−0.852424	+	0.522852i	$0.824868\pi$
$374$	−4.45847e46	−0.112476
$375$	5.33270e47	1.28047
$376$	2.09663e47	0.479233
$377$	2.19617e47	0.477915
$378$	4.65646e46	0.0964844
$379$	8.24615e47	1.62714	0.813572	−	0.581464i	$-0.197520\pi$
$379$	8.24615e47	1.62714	0.813572	+	0.581464i	$0.197520\pi$
$380$	3.60634e47	0.677751
$381$	1.45423e47	0.260329
$382$	4.34678e47	0.741302
$383$	−1.05734e48	−1.71806	−0.859032	−	0.511922i	$-0.828934\pi$
$383$	−1.05734e48	−1.71806	−0.859032	+	0.511922i	$0.828934\pi$
$384$	1.80920e47	0.280129
$385$	−5.03856e46	−0.0743503
$386$	4.92678e47	0.692944
$387$	−3.06985e47	−0.411590
$388$	−2.32721e47	−0.297474
$389$	−3.81308e46	−0.0464738	−0.0232369	−	0.999730i	$-0.507397\pi$
$389$	−3.81308e46	−0.0464738	−0.0232369	+	0.999730i	$0.507397\pi$
$390$	2.93409e47	0.341019
$391$	1.17343e48	1.30074
$392$	6.82309e47	0.721421
$393$	5.95900e47	0.601051
$394$	−5.09858e47	−0.490647
$395$	−3.60906e48	−3.31396
$396$	6.69247e45	0.00586442
$397$	−3.87592e47	−0.324153	−0.162077	−	0.986778i	$-0.551819\pi$
$397$	−3.87592e47	−0.324153	−0.162077	+	0.986778i	$0.551819\pi$
$398$	1.22754e48	0.979941
$399$	−6.71098e47	−0.511432
$400$	−2.13051e48	−1.55015
$401$	1.24335e48	0.863820	0.431910	−	0.901917i	$-0.357840\pi$
$401$	1.24335e48	0.863820	0.431910	+	0.901917i	$0.357840\pi$
$402$	2.91414e47	0.193343
$403$	5.98605e46	0.0379312
$404$	−2.75003e47	−0.166450
$405$	3.45545e47	0.199796
$406$	1.14686e48	0.633548
$407$	1.12705e47	0.0594905
$408$	−2.23860e48	−1.12918
$409$	1.71559e48	0.827053	0.413527	−	0.910492i	$-0.364297\pi$
$409$	1.71559e48	0.827053	0.413527	+	0.910492i	$0.364297\pi$
$410$	2.23231e48	1.02862
$411$	−2.03919e48	−0.898224
$412$	3.71118e47	0.156284
$413$	−2.51432e48	−1.01238
$414$	5.41039e47	0.208316
$415$	−2.43514e48	−0.896672
$416$	5.14400e47	0.181165
$417$	1.46956e48	0.495075
$418$	2.96269e47	0.0954827
$419$	2.35400e48	0.725851	0.362925	−	0.931818i	$-0.381778\pi$
$419$	2.35400e48	0.725851	0.362925	+	0.931818i	$0.381778\pi$
$420$	−4.98828e47	−0.147177
$421$	3.28974e48	0.928844	0.464422	−	0.885614i	$-0.346262\pi$
$421$	3.28974e48	0.928844	0.464422	+	0.885614i	$0.346262\pi$
$422$	−3.33206e48	−0.900393
$423$	−5.70878e47	−0.147654
$424$	−1.15035e48	−0.284813
$425$	1.70336e49	4.03748
$426$	1.35068e47	0.0306532
$427$	−2.60964e48	−0.567106
$428$	−7.65669e47	−0.159342
$429$	−7.84738e46	−0.0156410
$430$	−1.01014e49	−1.92848
$431$	−4.39374e48	−0.803534	−0.401767	−	0.915742i	$-0.631604\pi$
$431$	−4.39374e48	−0.803534	−0.401767	+	0.915742i	$0.631604\pi$
$432$	−7.62387e47	−0.133575
$433$	1.65722e48	0.278198	0.139099	−	0.990279i	$-0.455579\pi$
$433$	1.65722e48	0.278198	0.139099	+	0.990279i	$0.455579\pi$
$434$	3.12598e47	0.0502835
$435$	8.51060e48	1.31192
$436$	−1.26377e48	−0.186710
$437$	−7.79757e48	−1.10421
$438$	−4.02972e48	−0.547021
$439$	4.30529e48	0.560285	0.280142	−	0.959958i	$-0.409618\pi$
$439$	4.30529e48	0.560285	0.280142	+	0.959958i	$0.409618\pi$
$440$	1.11686e48	0.139355
$441$	−1.85781e48	−0.222274
$442$	5.17569e48	0.593822
$443$	−7.44863e48	−0.819611	−0.409805	−	0.912173i	$-0.634403\pi$
$443$	−7.44863e48	−0.819611	−0.409805	+	0.912173i	$0.634403\pi$
$444$	1.11580e48	0.117761
$445$	−4.85760e48	−0.491769
$446$	−8.15264e48	−0.791778
$447$	−1.11280e49	−1.03688
$448$	7.16741e48	0.640795
$449$	−1.42651e49	−1.22382	−0.611909	−	0.790928i	$-0.709598\pi$
$449$	−1.42651e49	−1.22382	−0.611909	+	0.790928i	$0.709598\pi$
$450$	7.85372e48	0.646612
$451$	−5.97043e47	−0.0471780
$452$	−6.11912e47	−0.0464118
$453$	3.92505e47	0.0285778
$454$	1.89539e49	1.32485
$455$	5.84910e48	0.392535
$456$	1.48757e49	0.958580
$457$	2.02914e49	1.25563	0.627817	−	0.778361i	$-0.283948\pi$
$457$	2.02914e49	1.25563	0.627817	+	0.778361i	$0.283948\pi$
$458$	8.74865e48	0.519912
$459$	6.09535e48	0.347907
$460$	−5.79594e48	−0.317763
$461$	1.29918e49	0.684232	0.342116	−	0.939658i	$-0.388856\pi$
$461$	1.29918e49	0.684232	0.342116	+	0.939658i	$0.388856\pi$
$462$	−4.09798e47	−0.0207345
$463$	−1.83380e49	−0.891463	−0.445731	−	0.895167i	$-0.647056\pi$
$463$	−1.83380e49	−0.891463	−0.445731	+	0.895167i	$0.647056\pi$
$464$	−1.87772e49	−0.877099
$465$	2.31972e48	0.104125
$466$	−3.67861e48	−0.158688
$467$	1.14081e49	0.472987	0.236494	−	0.971633i	$-0.424002\pi$
$467$	1.14081e49	0.472987	0.236494	+	0.971633i	$0.424002\pi$
$468$	−7.76906e47	−0.0309614
$469$	5.80931e48	0.222550
$470$	−1.87848e49	−0.691826
$471$	−1.21249e49	−0.429329
$472$	5.57330e49	1.89752
$473$	2.70167e48	0.0884506
$474$	−2.93534e49	−0.924184
$475$	−1.13189e50	−3.42747
$476$	−8.79922e48	−0.256281
$477$	3.13220e48	0.0877525
$478$	5.46685e48	0.147340
$479$	−2.24706e48	−0.0582649	−0.0291324	−	0.999576i	$-0.509274\pi$
$479$	−2.24706e48	−0.0582649	−0.0291324	+	0.999576i	$0.509274\pi$
$480$	1.99341e49	0.497317
$481$	−1.30836e49	−0.314082
$482$	−9.95383e48	−0.229943
$483$	1.07856e49	0.239785
$484$	1.14192e49	0.244341
$485$	1.05747e50	2.17794
$486$	2.81040e48	0.0557182
$487$	−6.62105e49	−1.26369	−0.631846	−	0.775094i	$-0.717702\pi$
$487$	−6.62105e49	−1.26369	−0.631846	+	0.775094i	$0.717702\pi$
$488$	5.78458e49	1.06293
$489$	−2.38252e49	−0.421524
$490$	−6.11317e49	−1.04145
$491$	1.27151e49	0.208599	0.104300	−	0.994546i	$-0.466740\pi$
$491$	1.27151e49	0.208599	0.104300	+	0.994546i	$0.466740\pi$
$492$	−5.91085e48	−0.0933890
$493$	1.50125e50	2.28447
$494$	−3.43929e49	−0.504104
$495$	−3.04102e48	−0.0429361
$496$	−5.11807e48	−0.0696138
$497$	2.69258e48	0.0352838
$498$	−1.98056e49	−0.250060
$499$	−1.07378e49	−0.130633	−0.0653166	−	0.997865i	$-0.520806\pi$
$499$	−1.07378e49	−0.130633	−0.0653166	+	0.997865i	$0.520806\pi$
$500$	−4.64629e49	−0.544704
$501$	−7.58409e49	−0.856851
$502$	8.17896e49	0.890593
$503$	8.93827e48	0.0938093	0.0469046	−	0.998899i	$-0.485064\pi$
$503$	8.93827e48	0.0938093	0.0469046	+	0.998899i	$0.485064\pi$
$504$	−2.05760e49	−0.208160
$505$	1.24960e50	1.21865
$506$	−4.76150e48	−0.0447671
$507$	−5.45825e49	−0.494773
$508$	−1.26705e49	−0.110743
$509$	1.92539e50	1.62270	0.811352	−	0.584558i	$-0.198732\pi$
$509$	1.92539e50	1.62270	0.811352	+	0.584558i	$0.198732\pi$
$510$	2.00568e50	1.63010
$511$	−8.03322e49	−0.629655
$512$	−1.43312e50	−1.08340
$513$	−4.05041e49	−0.295344
$514$	−1.18114e50	−0.830778
$515$	−1.68634e50	−1.14422
$516$	2.67470e49	0.175088
$517$	5.02409e48	0.0317309
$518$	−6.83238e49	−0.416362
$519$	3.29054e49	0.193495
$520$	−1.29652e50	−0.735731
$521$	−1.93636e50	−1.06045	−0.530223	−	0.847858i	$-0.677892\pi$
$521$	−1.93636e50	−1.06045	−0.530223	+	0.847858i	$0.677892\pi$
$522$	6.92188e49	0.365864
$523$	1.09154e50	0.556875	0.278438	−	0.960454i	$-0.410183\pi$
$523$	1.09154e50	0.556875	0.278438	+	0.960454i	$0.410183\pi$
$524$	−5.19197e49	−0.255684
$525$	1.56563e50	0.744291
$526$	−8.82635e49	−0.405084
$527$	4.09194e49	0.181314
$528$	6.70950e48	0.0287053
$529$	−1.16745e50	−0.482289
$530$	1.03066e50	0.411159
$531$	−1.51752e50	−0.584635
$532$	5.84716e49	0.217560
$533$	6.93088e49	0.249078
$534$	−3.95080e49	−0.137143
$535$	3.47915e50	1.16662
$536$	−1.28770e50	−0.417126
$537$	1.96508e50	0.614973
$538$	2.38397e50	0.720824
$539$	1.63500e49	0.0477666
$540$	−3.01067e49	−0.0849921
$541$	2.05140e50	0.559630	0.279815	−	0.960054i	$-0.409727\pi$
$541$	2.05140e50	0.559630	0.279815	+	0.960054i	$0.409727\pi$
$542$	−1.11922e50	−0.295073
$543$	1.10409e50	0.281326
$544$	3.51633e50	0.865984
$545$	5.74250e50	1.36699
$546$	4.75721e49	0.109468
$547$	−5.42161e50	−1.20604	−0.603021	−	0.797725i	$-0.706036\pi$
$547$	−5.42161e50	−1.20604	−0.603021	+	0.797725i	$0.706036\pi$
$548$	1.77671e50	0.382100
$549$	−1.57504e50	−0.327495
$550$	−6.91178e49	−0.138957
$551$	−9.97595e50	−1.93932
$552$	−2.39076e50	−0.449430
$553$	−5.85157e50	−1.06379
$554$	5.00182e50	0.879422
$555$	−5.07015e50	−0.862185
$556$	−1.28040e50	−0.210602
$557$	7.40435e50	1.17806	0.589028	−	0.808113i	$-0.299511\pi$
$557$	7.40435e50	1.17806	0.589028	+	0.808113i	$0.299511\pi$
$558$	1.88668e49	0.0290379
$559$	−3.13628e50	−0.466977
$560$	−5.00097e50	−0.720404
$561$	−5.36430e49	−0.0747653
$562$	1.66305e50	0.224276
$563$	−5.85968e50	−0.764660	−0.382330	−	0.924026i	$-0.624878\pi$
$563$	−5.85968e50	−0.764660	−0.382330	+	0.924026i	$0.624878\pi$
$564$	4.97395e49	0.0628114
$565$	2.78049e50	0.339802
$566$	9.06020e50	1.07160
$567$	5.60251e49	0.0641352
$568$	−5.96843e49	−0.0661327
$569$	−6.38178e50	−0.684486	−0.342243	−	0.939611i	$-0.611187\pi$
$569$	−6.38178e50	−0.684486	−0.342243	+	0.939611i	$0.611187\pi$
$570$	−1.33279e51	−1.38382
$571$	3.57695e50	0.359538	0.179769	−	0.983709i	$-0.442465\pi$
$571$	3.57695e50	0.359538	0.179769	+	0.983709i	$0.442465\pi$
$572$	6.83728e48	0.00665360
$573$	5.22991e50	0.492758
$574$	3.61938e50	0.330190
$575$	1.81913e51	1.60697
$576$	4.32589e50	0.370049
$577$	−1.18260e51	−0.979680	−0.489840	−	0.871812i	$-0.662945\pi$
$577$	−1.18260e51	−0.979680	−0.489840	+	0.871812i	$0.662945\pi$
$578$	2.45540e51	1.96996
$579$	5.92776e50	0.460614
$580$	−7.41513e50	−0.558086
$581$	−3.94822e50	−0.287835
$582$	8.60068e50	0.607376
$583$	−2.75654e49	−0.0188580
$584$	1.78066e51	1.18017
$585$	3.53022e50	0.226682
$586$	−1.12123e51	−0.697572
$587$	−2.16256e51	−1.30366	−0.651828	−	0.758367i	$-0.725998\pi$
$587$	−2.16256e51	−1.30366	−0.651828	+	0.758367i	$0.725998\pi$
$588$	1.61868e50	0.0945541
$589$	−2.71913e50	−0.153920
$590$	−4.99341e51	−2.73927
$591$	−6.13446e50	−0.326143
$592$	1.11864e51	0.576422
$593$	−1.31685e51	−0.657695	−0.328847	−	0.944383i	$-0.606660\pi$
$593$	−1.31685e51	−0.657695	−0.328847	+	0.944383i	$0.606660\pi$
$594$	−2.47333e49	−0.0119738
$595$	3.99832e51	1.87635
$596$	9.69566e50	0.441084
$597$	1.47694e51	0.651387
$598$	5.52746e50	0.236349
$599$	2.09368e51	0.867990	0.433995	−	0.900915i	$-0.357104\pi$
$599$	2.09368e51	0.867990	0.433995	+	0.900915i	$0.357104\pi$
$600$	−3.47042e51	−1.39503
$601$	4.42052e50	0.172304	0.0861521	−	0.996282i	$-0.472543\pi$
$601$	4.42052e50	0.172304	0.0861521	+	0.996282i	$0.472543\pi$
$602$	−1.63780e51	−0.619048
$603$	3.50620e50	0.128519
$604$	−3.41983e49	−0.0121568
$605$	−5.18883e51	−1.78894
$606$	1.01633e51	0.339853
$607$	4.41338e51	1.43146	0.715732	−	0.698375i	$-0.246093\pi$
$607$	4.41338e51	1.43146	0.715732	+	0.698375i	$0.246093\pi$
$608$	−2.33663e51	−0.735147
$609$	1.37987e51	0.421132
$610$	−5.18271e51	−1.53446
$611$	−5.83230e50	−0.167524
$612$	−5.31076e50	−0.147998
$613$	−3.52904e51	−0.954198	−0.477099	−	0.878850i	$-0.658312\pi$
$613$	−3.52904e51	−0.954198	−0.477099	+	0.878850i	$0.658312\pi$
$614$	9.16402e50	0.240420
$615$	2.68586e51	0.683743
$616$	1.81083e50	0.0447336
$617$	6.46795e51	1.55057	0.775284	−	0.631613i	$-0.217607\pi$
$617$	6.46795e51	1.55057	0.775284	+	0.631613i	$0.217607\pi$
$618$	−1.37154e51	−0.319096
$619$	−1.51171e51	−0.341344	−0.170672	−	0.985328i	$-0.554594\pi$
$619$	−1.51171e51	−0.341344	−0.170672	+	0.985328i	$0.554594\pi$
$620$	−2.02113e50	−0.0442942
$621$	6.50963e50	0.138472
$622$	2.60932e51	0.538773
$623$	−7.87590e50	−0.157860
$624$	−7.78884e50	−0.151551
$625$	9.28899e51	1.75464
$626$	5.82766e51	1.06873
$627$	3.56462e50	0.0634693
$628$	1.05642e51	0.182634
$629$	−8.94365e51	−1.50134
$630$	1.84352e51	0.300502
$631$	−7.44924e51	−1.17915	−0.589575	−	0.807714i	$-0.700705\pi$
$631$	−7.44924e51	−1.17915	−0.589575	+	0.807714i	$0.700705\pi$
$632$	1.29707e52	1.99388
$633$	−4.00904e51	−0.598510
$634$	−1.93207e51	−0.280138
$635$	5.75739e51	0.810797
$636$	−2.72903e50	−0.0373294
$637$	−1.89801e51	−0.252185
$638$	−6.09170e50	−0.0786241
$639$	1.62510e50	0.0203758
$640$	7.16271e51	0.872465
$641$	−2.96058e51	−0.350351	−0.175176	−	0.984537i	$-0.556049\pi$
$641$	−2.96058e51	−0.350351	−0.175176	+	0.984537i	$0.556049\pi$
$642$	2.82968e51	0.325341
$643$	−1.66529e52	−1.86032	−0.930159	−	0.367157i	$-0.880331\pi$
$643$	−1.66529e52	−1.86032	−0.930159	+	0.367157i	$0.880331\pi$
$644$	−9.39728e50	−0.102003
$645$	−1.21537e52	−1.28190
$646$	−2.35102e52	−2.40966
$647$	−3.47499e51	−0.346118	−0.173059	−	0.984911i	$-0.555365\pi$
$647$	−3.47499e51	−0.346118	−0.173059	+	0.984911i	$0.555365\pi$
$648$	−1.24187e51	−0.120209
$649$	1.33551e51	0.125638
$650$	8.02365e51	0.733627
$651$	3.76109e50	0.0334245
$652$	2.07585e51	0.179314
$653$	1.71299e51	0.143834	0.0719169	−	0.997411i	$-0.477088\pi$
$653$	1.71299e51	0.143834	0.0719169	+	0.997411i	$0.477088\pi$
$654$	4.67052e51	0.381221
$655$	2.35920e52	1.87198
$656$	−5.92590e51	−0.457123
$657$	−4.84844e51	−0.363616
$658$	−3.04569e51	−0.222078
$659$	7.36499e51	0.522146	0.261073	−	0.965319i	$-0.415924\pi$
$659$	7.36499e51	0.522146	0.261073	+	0.965319i	$0.415924\pi$
$660$	2.64958e50	0.0182648
$661$	1.02642e52	0.688017	0.344009	−	0.938967i	$-0.388215\pi$
$661$	1.02642e52	0.688017	0.344009	+	0.938967i	$0.388215\pi$
$662$	5.29765e51	0.345311
$663$	6.22724e51	0.394725
$664$	8.75173e51	0.539491
$665$	−2.65691e52	−1.59286
$666$	−4.12368e51	−0.240443
$667$	1.60329e52	0.909251
$668$	6.60788e51	0.364500
$669$	−9.80903e51	−0.526311
$670$	1.15372e52	0.602168
$671$	1.38614e51	0.0703786
$672$	3.23202e51	0.159640
$673$	−1.32994e52	−0.639077	−0.319539	−	0.947573i	$-0.603528\pi$
$673$	−1.32994e52	−0.639077	−0.319539	+	0.947573i	$0.603528\pi$
$674$	2.22282e52	1.03919
$675$	9.44936e51	0.429816
$676$	4.75567e51	0.210474
$677$	8.79193e51	0.378611	0.189306	−	0.981918i	$-0.439376\pi$
$677$	8.79193e51	0.378611	0.189306	+	0.981918i	$0.439376\pi$
$678$	2.26144e51	0.0947624
$679$	1.71454e52	0.699128
$680$	−8.86276e52	−3.51685
$681$	2.28048e52	0.880654
$682$	−1.66040e50	−0.00624025
$683$	2.88301e52	1.05454	0.527269	−	0.849698i	$-0.323216\pi$
$683$	2.88301e52	1.05454	0.527269	+	0.849698i	$0.323216\pi$
$684$	3.52905e51	0.125638
$685$	−8.07328e52	−2.79753
$686$	−2.47756e52	−0.835657
$687$	1.05261e52	0.345596
$688$	2.68151e52	0.857026
$689$	3.19997e51	0.0995614
$690$	2.14200e52	0.648802
$691$	−6.30524e52	−1.85933	−0.929667	−	0.368401i	$-0.879905\pi$
$691$	−6.30524e52	−1.85933	−0.929667	+	0.368401i	$0.879905\pi$
$692$	−2.86698e51	−0.0823119
$693$	−4.93057e50	−0.0137826
$694$	1.20917e52	0.329107
$695$	5.81807e52	1.54191
$696$	−3.05865e52	−0.789331
$697$	4.73780e52	1.19061
$698$	−3.68422e52	−0.901612
$699$	−4.42600e51	−0.105483
$700$	−1.36411e52	−0.316617
$701$	−4.33208e52	−0.979294	−0.489647	−	0.871921i	$-0.662874\pi$
$701$	−4.33208e52	−0.979294	−0.489647	+	0.871921i	$0.662874\pi$
$702$	2.87121e51	0.0632162
$703$	5.94313e52	1.27451
$704$	−3.80706e51	−0.0795235
$705$	−2.26014e52	−0.459871
$706$	3.09659e52	0.613757
$707$	2.02605e52	0.391192
$708$	1.32218e52	0.248700
$709$	−2.56002e52	−0.469124	−0.234562	−	0.972101i	$-0.575366\pi$
$709$	−2.56002e52	−0.469124	−0.234562	+	0.972101i	$0.575366\pi$
$710$	5.34743e51	0.0954698
$711$	−3.53171e52	−0.614324
$712$	1.74579e52	0.295877
$713$	4.37005e51	0.0721656
$714$	3.25193e52	0.523268
$715$	−3.10682e51	−0.0487141
$716$	−1.71214e52	−0.261606
$717$	6.57755e51	0.0979399
$718$	−1.01350e51	−0.0147070
$719$	6.18204e52	0.874274	0.437137	−	0.899395i	$-0.355992\pi$
$719$	6.18204e52	0.874274	0.437137	+	0.899395i	$0.355992\pi$
$720$	−3.01833e52	−0.416022
$721$	−2.73415e52	−0.367300
$722$	8.98931e52	1.17703
$723$	−1.19762e52	−0.152848
$724$	−9.61978e51	−0.119674
$725$	2.32733e53	2.82231
$726$	−4.22020e52	−0.498891
$727$	−3.15811e52	−0.363949	−0.181975	−	0.983303i	$-0.558249\pi$
$727$	−3.15811e52	−0.363949	−0.181975	+	0.983303i	$0.558249\pi$
$728$	−2.10213e52	−0.236172
$729$	3.38139e51	0.0370370
$730$	−1.59539e53	−1.70370
$731$	−2.14389e53	−2.23219
$732$	1.37231e52	0.139315
$733$	1.64324e53	1.62659	0.813296	−	0.581850i	$-0.197671\pi$
$733$	1.64324e53	1.62659	0.813296	+	0.581850i	$0.197671\pi$
$734$	−1.99055e52	−0.192130
$735$	−7.35518e52	−0.692274
$736$	3.75533e52	0.344674
$737$	−3.08569e51	−0.0276187
$738$	2.18447e52	0.190679
$739$	9.02443e52	0.768241	0.384120	−	0.923283i	$-0.374505\pi$
$739$	9.02443e52	0.768241	0.384120	+	0.923283i	$0.374505\pi$
$740$	4.41753e52	0.366769
$741$	−4.13805e52	−0.335088
$742$	1.67106e52	0.131984
$743$	5.81589e51	0.0448047	0.0224023	−	0.999749i	$-0.492869\pi$
$743$	5.81589e51	0.0448047	0.0224023	+	0.999749i	$0.492869\pi$
$744$	−8.33691e51	−0.0626478
$745$	−4.40565e53	−3.22938
$746$	−2.07088e53	−1.48076
$747$	−2.38295e52	−0.166220
$748$	4.67382e51	0.0318048
$749$	5.64095e52	0.374488
$750$	1.71713e53	1.11216
$751$	−2.03346e53	−1.28498	−0.642491	−	0.766293i	$-0.722099\pi$
$751$	−2.03346e53	−1.28498	−0.642491	+	0.766293i	$0.722099\pi$
$752$	4.98661e52	0.307451
$753$	9.84069e52	0.591995
$754$	7.07165e52	0.415098
$755$	1.55395e52	0.0890058
$756$	−4.88137e51	−0.0272828
$757$	8.46759e52	0.461834	0.230917	−	0.972973i	$-0.425827\pi$
$757$	8.46759e52	0.461834	0.230917	+	0.972973i	$0.425827\pi$
$758$	2.65526e53	1.41327
$759$	−5.72889e51	−0.0297576
$760$	5.88938e53	2.98551
$761$	−6.60711e52	−0.326885	−0.163443	−	0.986553i	$-0.552260\pi$
$761$	−6.60711e52	−0.326885	−0.163443	+	0.986553i	$0.552260\pi$
$762$	4.68263e52	0.226112
$763$	9.31064e52	0.438809
$764$	−4.55673e52	−0.209617
$765$	2.41318e53	1.08356
$766$	−3.40465e53	−1.49224
$767$	−1.55035e53	−0.663309
$768$	−9.52064e52	−0.397634
$769$	4.12388e53	1.68139	0.840696	−	0.541507i	$-0.182146\pi$
$769$	4.12388e53	1.68139	0.840696	+	0.541507i	$0.182146\pi$
$770$	−1.62241e52	−0.0645778
$771$	−1.42112e53	−0.552235
$772$	−5.16475e52	−0.195943
$773$	−1.80579e53	−0.668879	−0.334439	−	0.942417i	$-0.608547\pi$
$773$	−1.80579e53	−0.668879	−0.334439	+	0.942417i	$0.608547\pi$
$774$	−9.88490e52	−0.357491
$775$	6.34356e52	0.224002
$776$	−3.80049e53	−1.31038
$777$	−8.22052e52	−0.276764
$778$	−1.22781e52	−0.0403653
$779$	−3.14831e53	−1.01073
$780$	−3.07581e52	−0.0964295
$781$	−1.43020e51	−0.00437877
$782$	3.77846e53	1.12977
$783$	8.32820e52	0.243197
$784$	1.62280e53	0.462826
$785$	−4.80030e53	−1.33715
$786$	1.91880e53	0.522049
$787$	6.04656e53	1.60685	0.803425	−	0.595405i	$-0.203009\pi$
$787$	6.04656e53	1.60685	0.803425	+	0.595405i	$0.203009\pi$
$788$	5.34484e52	0.138739
$789$	−1.06196e53	−0.269267
$790$	−1.16212e54	−2.87838
$791$	4.50817e52	0.109078
$792$	1.09292e52	0.0258329
$793$	−1.60913e53	−0.371566
$794$	−1.24804e53	−0.281547
$795$	1.24006e53	0.273306
$796$	−1.28683e53	−0.277096
$797$	6.79705e53	1.43002	0.715009	−	0.699116i	$-0.246423\pi$
$797$	6.79705e53	1.43002	0.715009	+	0.699116i	$0.246423\pi$
$798$	−2.16093e53	−0.444210
$799$	−3.98684e53	−0.800779
$800$	5.45122e53	1.06987
$801$	−4.75349e52	−0.0911614
$802$	4.00359e53	0.750280
$803$	4.26694e52	0.0781411
$804$	−3.05489e52	−0.0546712
$805$	4.27007e53	0.746812
$806$	1.92751e52	0.0329456
$807$	2.86833e53	0.479147
$808$	−4.49098e53	−0.733214
$809$	1.11799e54	1.78397	0.891987	−	0.452061i	$-0.149311\pi$
$809$	1.11799e54	1.78397	0.891987	+	0.452061i	$0.149311\pi$
$810$	1.11265e53	0.173535
$811$	−9.12670e53	−1.39132	−0.695662	−	0.718369i	$-0.744889\pi$
$811$	−9.12670e53	−1.39132	−0.695662	+	0.718369i	$0.744889\pi$
$812$	−1.20226e53	−0.179147
$813$	−1.34662e53	−0.196141
$814$	3.62910e52	0.0516711
$815$	−9.43253e53	−1.31284
$816$	−5.32428e53	−0.724425
$817$	1.42463e54	1.89494
$818$	5.52421e53	0.718346
$819$	5.72374e52	0.0727659
$820$	−2.34014e53	−0.290861
$821$	4.11474e53	0.500027	0.250014	−	0.968242i	$-0.419565\pi$
$821$	4.11474e53	0.500027	0.250014	+	0.968242i	$0.419565\pi$
$822$	−6.56619e53	−0.780162
$823$	2.41018e53	0.279996	0.139998	−	0.990152i	$-0.455290\pi$
$823$	2.41018e53	0.279996	0.139998	+	0.990152i	$0.455290\pi$
$824$	6.06059e53	0.688432
$825$	−8.31605e52	−0.0923675
$826$	−8.09610e53	−0.879316
$827$	1.22285e54	1.29873	0.649367	−	0.760475i	$-0.275034\pi$
$827$	1.22285e54	1.29873	0.649367	+	0.760475i	$0.275034\pi$
$828$	−5.67172e52	−0.0589052
$829$	5.14834e53	0.522888	0.261444	−	0.965219i	$-0.415801\pi$
$829$	5.14834e53	0.522888	0.261444	+	0.965219i	$0.415801\pi$
$830$	−7.84113e53	−0.778815
$831$	6.01804e53	0.584570
$832$	4.41949e53	0.419846
$833$	−1.29744e54	−1.20547
$834$	4.73198e53	0.430002
$835$	−3.00258e54	−2.66867
$836$	−3.10579e52	−0.0269995
$837$	2.27000e52	0.0193021
$838$	7.57988e53	0.630446
$839$	−1.47001e54	−1.19598	−0.597990	−	0.801504i	$-0.704034\pi$
$839$	−1.47001e54	−1.19598	−0.597990	+	0.801504i	$0.704034\pi$
$840$	−8.14617e53	−0.648316
$841$	7.66718e53	0.596911
$842$	1.05929e54	0.806757
$843$	2.00093e53	0.149081
$844$	3.49300e53	0.254603
$845$	−2.16095e54	−1.54098
$846$	−1.83822e53	−0.128247
$847$	−8.41294e53	−0.574255
$848$	−2.73598e53	−0.182721
$849$	1.09010e54	0.712316
$850$	5.48480e54	3.50680
$851$	−9.55152e53	−0.597552
$852$	−1.41592e52	−0.00866777
$853$	−2.39398e54	−1.43405	−0.717024	−	0.697048i	$-0.754496\pi$
$853$	−2.39398e54	−1.43405	−0.717024	+	0.697048i	$0.754496\pi$
$854$	−8.40302e53	−0.492566
$855$	−1.60358e54	−0.919850
$856$	−1.25039e54	−0.701907
$857$	1.12045e54	0.615526	0.307763	−	0.951463i	$-0.400420\pi$
$857$	1.12045e54	0.615526	0.307763	+	0.951463i	$0.400420\pi$
$858$	−2.52685e52	−0.0135852
$859$	2.95876e54	1.55681	0.778405	−	0.627762i	$-0.216029\pi$
$859$	2.95876e54	1.55681	0.778405	+	0.627762i	$0.216029\pi$
$860$	1.05893e54	0.545313
$861$	4.35473e53	0.219484
$862$	−1.41478e54	−0.697919
$863$	−2.90233e52	−0.0140135	−0.00700675	−	0.999975i	$-0.502230\pi$
$863$	−2.90233e52	−0.0140135	−0.00700675	+	0.999975i	$0.502230\pi$
$864$	1.95068e53	0.0921897
$865$	1.30274e54	0.602643
$866$	5.33623e53	0.241632
$867$	2.95426e54	1.30947
$868$	−3.27697e52	−0.0142186
$869$	3.10813e53	0.132018
$870$	2.74041e54	1.13949
$871$	3.58207e53	0.145814
$872$	−2.06382e54	−0.822463
$873$	1.03481e54	0.403735
$874$	−2.51082e54	−0.959077
$875$	3.42308e54	1.28017
$876$	4.22436e53	0.154680
$877$	−9.87214e53	−0.353931	−0.176966	−	0.984217i	$-0.556628\pi$
$877$	−9.87214e53	−0.353931	−0.176966	+	0.984217i	$0.556628\pi$
$878$	1.38630e54	0.486642
$879$	−1.34903e54	−0.463690
$880$	2.65633e53	0.0894031
$881$	−3.43429e54	−1.13183	−0.565916	−	0.824463i	$-0.691477\pi$
$881$	−3.43429e54	−1.13183	−0.565916	+	0.824463i	$0.691477\pi$
$882$	−5.98215e53	−0.193058
$883$	−3.21368e54	−1.01561	−0.507807	−	0.861471i	$-0.669544\pi$
$883$	−3.21368e54	−1.01561	−0.507807	+	0.861471i	$0.669544\pi$
$884$	−5.42568e53	−0.167914
$885$	−6.00793e54	−1.82085
$886$	−2.39846e54	−0.711882
$887$	−3.18523e54	−0.925879	−0.462940	−	0.886390i	$-0.653205\pi$
$887$	−3.18523e54	−0.925879	−0.462940	+	0.886390i	$0.653205\pi$
$888$	1.82218e54	0.518742
$889$	9.33479e53	0.260269
$890$	−1.56414e54	−0.427132
$891$	−2.97584e52	−0.00795926
$892$	8.54643e53	0.223890
$893$	2.64929e54	0.679793
$894$	−3.58323e54	−0.900596
$895$	7.77987e54	1.91534
$896$	1.16133e54	0.280064
$897$	6.65048e53	0.157106
$898$	−4.59335e54	−1.06296
$899$	5.59090e53	0.126744
$900$	−8.23306e53	−0.182841
$901$	2.18743e54	0.475911
$902$	−1.92248e53	−0.0409770
$903$	−1.97055e54	−0.411494
$904$	−9.99291e53	−0.204445
$905$	4.37117e54	0.876192
$906$	1.26386e53	0.0248216
$907$	−1.66261e54	−0.319931	−0.159966	−	0.987123i	$-0.551138\pi$
$907$	−1.66261e54	−0.319931	−0.159966	+	0.987123i	$0.551138\pi$
$908$	−1.98694e54	−0.374625
$909$	1.22282e54	0.225907
$910$	1.88341e54	0.340940
$911$	1.12509e55	1.99570	0.997851	−	0.0655227i	$-0.0208715\pi$
$911$	1.12509e55	1.99570	0.997851	+	0.0655227i	$0.0208715\pi$
$912$	3.53803e54	0.614974
$913$	2.09715e53	0.0357207
$914$	6.53384e54	1.09060
$915$	−6.23569e54	−1.01999
$916$	−9.17122e53	−0.147015
$917$	3.82510e54	0.600912
$918$	1.96270e54	0.302179
$919$	−1.81936e54	−0.274525	−0.137263	−	0.990535i	$-0.543830\pi$
$919$	−1.81936e54	−0.274525	−0.137263	+	0.990535i	$0.543830\pi$
$920$	−9.46514e54	−1.39976
$921$	1.10259e54	0.159812
$922$	4.18336e54	0.594297
$923$	1.66027e53	0.0231178
$924$	4.29592e52	0.00586306
$925$	−1.38650e55	−1.85480
$926$	−5.90482e54	−0.774290
$927$	−1.65020e54	−0.212110
$928$	4.80444e54	0.605348
$929$	6.12532e52	0.00756550	0.00378275	−	0.999993i	$-0.498796\pi$
$929$	6.12532e52	0.00756550	0.00378275	+	0.999993i	$0.498796\pi$
$930$	7.46948e53	0.0904390
$931$	8.62160e54	1.02334
$932$	3.85630e53	0.0448721
$933$	3.13946e54	0.358134
$934$	3.67339e54	0.410818
$935$	−2.12376e54	−0.232857
$936$	−1.26874e54	−0.136386
$937$	−1.54519e55	−1.62855	−0.814274	−	0.580481i	$-0.802865\pi$
$937$	−1.54519e55	−1.62855	−0.814274	+	0.580481i	$0.802865\pi$
$938$	1.87059e54	0.193298
$939$	7.01168e54	0.710409
$940$	1.96922e54	0.195627
$941$	−1.06842e55	−1.04072	−0.520361	−	0.853946i	$-0.674203\pi$
$941$	−1.06842e55	−1.04072	−0.520361	+	0.853946i	$0.674203\pi$
$942$	−3.90420e54	−0.372899
$943$	5.05981e54	0.473880
$944$	1.32555e55	1.21735
$945$	2.21807e54	0.199750
$946$	8.69935e53	0.0768247
$947$	3.77859e54	0.327232	0.163616	−	0.986524i	$-0.447684\pi$
$947$	3.77859e54	0.327232	0.163616	+	0.986524i	$0.447684\pi$
$948$	3.07712e54	0.261330
$949$	−4.95335e54	−0.412548
$950$	−3.64469e55	−2.97697
$951$	−2.32461e54	−0.186213
$952$	−1.43697e55	−1.12892
$953$	5.53742e53	0.0426667	0.0213333	−	0.999772i	$-0.493209\pi$
$953$	5.53742e53	0.0426667	0.0213333	+	0.999772i	$0.493209\pi$
$954$	1.00857e54	0.0762184
$955$	2.07055e55	1.53470
$956$	−5.73090e53	−0.0416631
$957$	−7.32935e53	−0.0522631
$958$	−7.23551e53	−0.0506066
$959$	−1.30897e55	−0.898016
$960$	1.71264e55	1.15252
$961$	−1.49966e55	−0.989941
$962$	−4.21290e54	−0.272799
$963$	3.40459e54	0.216261
$964$	1.04346e54	0.0650206
$965$	2.34683e55	1.43459
$966$	3.47295e54	0.208268
$967$	1.91207e55	1.12490	0.562449	−	0.826832i	$-0.309859\pi$
$967$	1.91207e55	1.12490	0.562449	+	0.826832i	$0.309859\pi$
$968$	1.86483e55	1.07633
$969$	−2.82868e55	−1.60175
$970$	3.40506e55	1.89168
$971$	8.30735e54	0.452800	0.226400	−	0.974034i	$-0.427304\pi$
$971$	8.30735e54	0.452800	0.226400	+	0.974034i	$0.427304\pi$
$972$	−2.94615e53	−0.0157554
$973$	9.43317e54	0.494960
$974$	−2.13197e55	−1.09759
$975$	9.65383e54	0.487657
$976$	1.37580e55	0.681921
$977$	−3.32881e55	−1.61897	−0.809486	−	0.587140i	$-0.800254\pi$
$977$	−3.32881e55	−1.61897	−0.809486	+	0.587140i	$0.800254\pi$
$978$	−7.67171e54	−0.366120
$979$	4.18338e53	0.0195906
$980$	6.40844e54	0.294490
$981$	5.61943e54	0.253405
$982$	4.09426e54	0.181181
$983$	−5.66371e54	−0.245958	−0.122979	−	0.992409i	$-0.539245\pi$
$983$	−5.66371e54	−0.245958	−0.122979	+	0.992409i	$0.539245\pi$
$984$	−9.65279e54	−0.411380
$985$	−2.42867e55	−1.01578
$986$	4.83403e55	1.98420
$987$	−3.66448e54	−0.147620
$988$	3.60541e54	0.142545
$989$	−2.28960e55	−0.888442
$990$	−9.79207e53	−0.0372927
$991$	−3.93647e55	−1.47145	−0.735723	−	0.677283i	$-0.763157\pi$
$991$	−3.93647e55	−1.47145	−0.735723	+	0.677283i	$0.763157\pi$
$992$	1.30954e54	0.0480453
$993$	6.37398e54	0.229535
$994$	8.67009e53	0.0306461
$995$	5.84730e55	2.02875
$996$	2.07622e54	0.0707091
$997$	1.67431e53	0.00559727	0.00279863	−	0.999996i	$-0.499109\pi$
$997$	1.67431e53	0.00559727	0.00279863	+	0.999996i	$0.499109\pi$
$998$	−3.45755e54	−0.113463
$999$	−4.96149e54	−0.159827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.38.a.b.1.3	✓	4
3.2	odd	2		9.38.a.c.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.b.1.3	✓	4	1.1	even	1	trivial
9.38.a.c.1.2		4	3.2	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+322000. q^{2} +3.87420e8 q^{3} -3.37552e10 q^{4} +1.53382e13 q^{5} +1.24749e14 q^{6} +2.48687e15 q^{7} -5.51245e16 q^{8} +1.50095e17 q^{9} +O(q^{10})\)	\(q+322000. q^{2} +3.87420e8 q^{3} -3.37552e10 q^{4} +1.53382e13 q^{5} +1.24749e14 q^{6} +2.48687e15 q^{7} -5.51245e16 q^{8} +1.50095e17 q^{9} +4.93889e18 q^{10} -1.32093e18 q^{11} -1.30775e19 q^{12} +1.53342e20 q^{13} +8.00770e20 q^{14} +5.94233e21 q^{15} -1.31108e22 q^{16} +1.04822e23 q^{17} +4.83304e22 q^{18} -6.96548e23 q^{19} -5.17744e23 q^{20} +9.63463e23 q^{21} -4.25339e23 q^{22} +1.11946e25 q^{23} -2.13563e25 q^{24} +1.62501e26 q^{25} +4.93762e25 q^{26} +5.81497e25 q^{27} -8.39448e25 q^{28} +1.43220e27 q^{29} +1.91343e27 q^{30} +3.90372e26 q^{31} +3.35459e27 q^{32} -5.11755e26 q^{33} +3.37525e28 q^{34} +3.81440e28 q^{35} -5.06648e27 q^{36} -8.53226e28 q^{37} -2.24288e29 q^{38} +5.94080e28 q^{39} -8.45509e29 q^{40} +4.51987e29 q^{41} +3.10235e29 q^{42} -2.04528e30 q^{43} +4.45883e28 q^{44} +2.30218e30 q^{45} +3.60466e30 q^{46} -3.80345e30 q^{47} -5.07938e30 q^{48} -1.23776e31 q^{49} +5.23251e31 q^{50} +4.06100e31 q^{51} -5.17611e30 q^{52} +2.08682e31 q^{53} +1.87242e31 q^{54} -2.02607e31 q^{55} -1.37087e32 q^{56} -2.69857e32 q^{57} +4.61167e32 q^{58} -1.01104e33 q^{59} -2.00585e32 q^{60} -1.04937e33 q^{61} +1.25699e32 q^{62} +3.73265e32 q^{63} +2.88211e33 q^{64} +2.35199e33 q^{65} -1.64785e32 q^{66} +2.33599e33 q^{67} -3.53828e33 q^{68} +4.33702e33 q^{69} +1.22824e34 q^{70} +1.08272e33 q^{71} -8.27388e33 q^{72} -3.23026e34 q^{73} -2.74738e34 q^{74} +6.29560e34 q^{75} +2.35121e34 q^{76} -3.28498e33 q^{77} +1.91293e34 q^{78} -2.35299e35 q^{79} -2.01095e35 q^{80} +2.25284e34 q^{81} +1.45540e35 q^{82} -1.58763e35 q^{83} -3.25219e34 q^{84} +1.60777e36 q^{85} -6.58578e35 q^{86} +5.54863e35 q^{87} +7.28155e34 q^{88} -3.16700e35 q^{89} +7.41301e35 q^{90} +3.81342e35 q^{91} -3.77876e35 q^{92} +1.51238e35 q^{93} -1.22471e36 q^{94} -1.06838e37 q^{95} +1.29964e36 q^{96} +6.89438e36 q^{97} -3.98559e36 q^{98} -1.98265e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 60\!\cdots\!84 q^{9}+O(q^{10}) \) 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9	\( 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 31\!\cdots\!96 q^{99}+O(q^{100}) \) 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9 - 21511023001649316 * q^10 + 20953708852195292976 * q^11 + 134085826579099875588 * q^12 + 51830892788989874168 * q^13 - 1809002141673235613712 * q^14 - 1588358049236498806056 * q^15 + 55184727516616371757840 * q^16 + 81101770962322537501128 * q^17 + 65675708809825529383002 * q^18 - 544604242502813077907632 * q^19 - 3566083114449076353950376 * q^20 + 2559226120354571192186976 * q^21 + 23909208610123411045457976 * q^22 - 6105434608113226892697888 * q^23 + 54426423887751042218148264 * q^24 + 95396877753446381193398716 * q^25 + 428554172265180170762299788 * q^26 + 232598948012160238761560676 * q^27 + 2469833924959492064190244448 * q^28 + 4171186009659314742454127736 * q^29 - 8333811050189225811235524 * q^30 + 8995814656808409627856220864 * q^31 + 36517476440276920084276020384 * q^32 + 8117896129881129128260185264 * q^33 + 31219088393882932122099949524 * q^34 + 42129462142584542112964223040 * q^35 + 51947596501244070980142122532 * q^36 + 55519093704269258277039732824 * q^37 - 735180697664011480109320664568 * q^38 + 20080349829617030866215028152 * q^39 - 2663133991761021855901070923152 * q^40 - 869595339264691998704372818776 * q^41 - 700844494329092219676518145168 * q^42 - 509323958833633606104562745680 * q^43 + 2838804848354890092833187324336 * q^44 - 615362452142290444090131681384 * q^45 - 14832400342987743191058839458896 * q^46 + 4297748917019550924184843821120 * q^47 + 21379694119819270371828162383760 * q^48 + 40223006658016971616433785618020 * q^49 + 102764730674385833857211828709414 * q^50 + 31420487764988998054407847811592 * q^51 + 186771330756284408934646875520568 * q^52 - 125797679190958862093479980165288 * q^53 + 25444115222524214598246503127978 * q^54 - 324441401797069196184728188134624 * q^55 + 49261177652308793436687718380480 * q^56 - 210990841941914426518569886272048 * q^57 - 758216144723951752216603559669556 * q^58 - 1322751535061383229075407129388688 * q^59 - 1381573664014504126645791751653864 * q^60 - 1210012908287761061549313720873160 * q^61 - 3774869312329378363502064838581792 * q^62 + 991496635009340824662391221351264 * q^63 + 8553618714336434539515354532145728 * q^64 + 1596939597234927778869711846229968 * q^65 + 9262917291337022257579330290870264 * q^66 + 16212837695473169417262127089269648 * q^67 + 6364770984875237153325176447214984 * q^68 - 2365370461432749730136966298227232 * q^69 + 8205699211322075854652286498656160 * q^70 + 10892424995451680587530033164573088 * q^71 + 21085911757113789886414645113381096 * q^72 - 19472416597596703966438677461737048 * q^73 - 89115306434605413664690690272305412 * q^74 + 36958705028313418437226934124692124 * q^75 - 95475877084130734100913860795365168 * q^76 - 256189314900709292482321902951864192 * q^77 + 166030666981966339429833686631556332 * q^78 + 42564929886993357285736803130555520 * q^79 - 955034489632094448517301530341944736 * q^80 + 90113598179756697647360591499090564 * q^81 + 335470244295388111217009211756354948 * q^82 - 462964612731837394872969166562146224 * q^83 + 956864266956595720700203893073695072 * q^84 + 1847677353245070936584728247586996912 * q^85 - 363370083621183428400243233525783304 * q^86 + 1616002923572170440926487227549582904 * q^87 + 4210934419609684353108607591773010656 * q^88 - 314574774231571073544391076719446552 * q^89 - 3228689152297913406320288402251236 * q^90 + 2615056540536627234228451043107657024 * q^91 - 16598538663060910484079148451607722016 * q^92 + 3485162913294081237336365108822882496 * q^93 - 573809173038711993912694394480689248 * q^94 - 8958385060094338314910240959017780256 * q^95 + 14147618579538063674464137028143247776 * q^96 + 445047507548838106214452450407795848 * q^97 - 43086999614034505592591376853854433878 * q^98 + 3145039288289754558742704694209474096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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