LMFDB - Embedded newform 3.38.a.a.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:	$1$
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} - x^{2} - 2495042360x + 9241471873200 $ x^3 - x^2 - 2495042360*x + 9241471873200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-51708.0$ 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)

$f(q)$	$=$	$q+516864. q^{2} -3.87420e8 q^{3} +1.29709e11 q^{4} +3.13693e12 q^{5} -2.00244e14 q^{6} -3.10972e15 q^{7} -3.99525e15 q^{8} +1.50095e17 q^{9} +O(q^{10})$	\(q+516864. q^{2} -3.87420e8 q^{3} +1.29709e11 q^{4} +3.13693e12 q^{5} -2.00244e14 q^{6} -3.10972e15 q^{7} -3.99525e15 q^{8} +1.50095e17 q^{9} +1.62136e18 q^{10} +7.50440e18 q^{11} -5.02520e19 q^{12} -6.39538e20 q^{13} -1.60730e21 q^{14} -1.21531e21 q^{15} -1.98921e22 q^{16} -5.44751e22 q^{17} +7.75785e22 q^{18} +2.22938e23 q^{19} +4.06888e23 q^{20} +1.20477e24 q^{21} +3.87875e24 q^{22} -1.64570e25 q^{23} +1.54784e24 q^{24} -6.29193e25 q^{25} -3.30554e26 q^{26} -5.81497e25 q^{27} -4.03359e26 q^{28} +1.49927e27 q^{29} -6.28150e26 q^{30} -4.99985e27 q^{31} -9.73240e27 q^{32} -2.90736e27 q^{33} -2.81562e28 q^{34} -9.75497e27 q^{35} +1.94686e28 q^{36} +4.47694e28 q^{37} +1.15228e29 q^{38} +2.47770e29 q^{39} -1.25328e28 q^{40} +1.03254e30 q^{41} +6.22702e29 q^{42} -2.18835e30 q^{43} +9.73390e29 q^{44} +4.70836e29 q^{45} -8.50601e30 q^{46} +1.06681e31 q^{47} +7.70660e30 q^{48} -8.89176e30 q^{49} -3.25207e31 q^{50} +2.11048e31 q^{51} -8.29539e31 q^{52} -2.17162e31 q^{53} -3.00555e31 q^{54} +2.35408e31 q^{55} +1.24241e31 q^{56} -8.63707e31 q^{57} +7.74917e32 q^{58} +9.25373e32 q^{59} -1.57637e32 q^{60} +1.78286e33 q^{61} -2.58424e33 q^{62} -4.66752e32 q^{63} -2.29638e33 q^{64} -2.00618e33 q^{65} -1.50271e33 q^{66} +5.16951e33 q^{67} -7.06592e33 q^{68} +6.37577e33 q^{69} -5.04199e33 q^{70} +3.92232e33 q^{71} -5.99665e32 q^{72} -3.83796e34 q^{73} +2.31397e34 q^{74} +2.43762e34 q^{75} +2.89171e34 q^{76} -2.33366e34 q^{77} +1.28063e35 q^{78} -5.14706e34 q^{79} -6.24001e34 q^{80} +2.25284e34 q^{81} +5.33684e35 q^{82} -2.76468e35 q^{83} +1.56270e35 q^{84} -1.70885e35 q^{85} -1.13108e36 q^{86} -5.80847e35 q^{87} -2.99820e34 q^{88} -1.38448e36 q^{89} +2.43358e35 q^{90} +1.98878e36 q^{91} -2.13462e36 q^{92} +1.93704e36 q^{93} +5.51395e36 q^{94} +6.99340e35 q^{95} +3.77053e36 q^{96} +1.68983e36 q^{97} -4.59583e36 q^{98} +1.12637e36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 45\!\cdots\!63 q^{9}+O(q^{10}) $ 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9	$ 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 34\!\cdots\!20 q^{99}+O(q^{100}) $ 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9 + 10698950136741797880 * q^10 + 22673303357139628620 * q^11 - 131132770215589974672 * q^12 - 168270000203795091510 * q^13 + 797101803583223694528 * q^14 + 3730362592143228440310 * q^15 + 32071173863897028608256 * q^16 - 27168549617785276146906 * q^17 - 46665622870919402711868 * q^18 + 582035599719143813745204 * q^19 - 4066256929972106412494880 * q^20 + 1790612692538373730632816 * q^21 - 4486408000290444592999152 * q^22 - 17157197763697459349569272 * q^23 + 36178839725894735603677632 * q^24 - 24896488591542260192608275 * q^25 - 618603181238074545425686344 * q^26 - 174449211009120179071170507 * q^27 - 2033429672978753784958610688 * q^28 + 111201150055901033185229778 * q^29 - 4144992493763124201408763320 * q^30 - 11859842025407507592851987736 * q^31 - 27281435223830339470718352384 * q^32 - 8784102273868376561238795180 * q^33 - 18783445175675019452330905464 * q^34 + 47739964986924083632994534880 * q^35 + 50803521960848503410923854608 * q^36 + 60344578140045347560278093666 * q^37 - 372452605565029151271789397776 * q^38 + 65191245762984394008603948390 * q^39 + 1732463594119923393272610326400 * q^40 + 2087364862188523841295969725934 * q^41 - 308813570526994475930424384192 * q^42 + 2483325896102099669944761791244 * q^43 + 4284309379683814482835899511872 * q^44 - 1445218899595437120383607511590 * q^45 - 4327236604482200607954371165856 * q^46 - 11791379189662012541191082473632 * q^47 - 12425029861155006269057528957184 * q^48 - 22445324860908932271245865545973 * q^49 - 96691457712658313260807892933700 * q^50 + 10525652778343134781834358357034 * q^51 + 43220201443333906987967057359584 * q^52 - 115357757368640109037215455345382 * q^53 + 18079218432141178878219826663452 * q^54 - 129419469300146958823045789059480 * q^55 + 630552391741804501615596905794560 * q^56 - 225492516658598958982491855084756 * q^57 + 580965936186746161132050423512088 * q^58 + 1091721381032593697748326986744236 * q^59 + 1575351248209432222688802119596320 * q^60 + 294380981976352085651508270601002 * q^61 + 248838835694853996733454208986592 * q^62 - 693720044952823401986519854167024 * q^63 - 1064135955800023765084313699610624 * q^64 - 7515875365146923444942971038019860 * q^65 + 1738126381326036186247137444425328 * q^66 + 3824374619785575741360273276519444 * q^67 - 21329399470876894544665401157365216 * q^68 + 6647049947481376149267749297614008 * q^69 - 43059062291480572688803543269144960 * q^70 - 22149353642418626281921550104284744 * q^71 - 14016423778058764430102498387802048 * q^72 + 32759279450923542889398870347665278 * q^73 + 46478870171568672595185044851456728 * q^74 + 9645409784518223707985532085946475 * q^75 + 347061692957154720144564653376455616 * q^76 - 61122141948697926808926153780754368 * q^77 + 239659546972210465807272116553102216 * q^78 + 74649348023552719727334936629819640 * q^79 - 618088038723375449595358546989335040 * q^80 + 67585198634817523235520443624317923 * q^81 + 103937675337495441364448738414881512 * q^82 - 317656267631459020909914460046822604 * q^83 + 787792318252538877979265797505586432 * q^84 + 210972517320554825185658741373302580 * q^85 - 2655243937093032975138251645354123760 * q^86 - 43081603932019555612226948170121442 * q^87 - 1353962196634819912991147659264835328 * q^88 - 1604427814888922862357874180114447026 * q^89 + 1605855018835039028277517574319663480 * q^90 + 459759011513895387754487414763335904 * q^91 - 5426885178857894678398508472745540224 * q^92 + 4594745796946127015893929993303122904 * q^93 + 15155501875748762861069416648677456000 * q^94 - 10713376656166940710475311057833316200 * q^95 + 10569386975038174570781705261883595776 * q^96 + 2690787195739502167683294096108844614 * q^97 - 1675640263817086437903041451354198300 * q^98 + 3403141198368098368991272474406443020 * 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 $

$2$	516864.	1.39419	0.697094	−	0.716980i	$-0.254476\pi$
$2$	516864.	1.39419	0.697094	+	0.716980i	$0.254476\pi$
$3$	−3.87420e8	−0.577350
$3$	−3.87420e8	−0.577350
$4$	1.29709e11	0.943758
$5$	3.13693e12	0.367756	0.183878	−	0.982949i	$-0.441135\pi$
$5$	3.13693e12	0.367756	0.183878	+	0.982949i	$0.441135\pi$
$6$	−2.00244e14	−0.804934
$7$	−3.10972e15	−0.721785	−0.360892	−	0.932608i	$-0.617528\pi$
$7$	−3.10972e15	−0.721785	−0.360892	+	0.932608i	$0.617528\pi$
$8$	−3.99525e15	−0.0784114
$9$	1.50095e17	0.333333
$10$	1.62136e18	0.512721
$11$	7.50440e18	0.406960	0.203480	−	0.979079i	$-0.434775\pi$
$11$	7.50440e18	0.406960	0.203480	+	0.979079i	$0.434775\pi$
$12$	−5.02520e19	−0.544879
$13$	−6.39538e20	−1.57730	−0.788650	−	0.614843i	$-0.789219\pi$
$13$	−6.39538e20	−1.57730	−0.788650	+	0.614843i	$0.789219\pi$
$14$	−1.60730e21	−1.00630
$15$	−1.21531e21	−0.212324
$16$	−1.98921e22	−1.05308
$17$	−5.44751e22	−0.939492	−0.469746	−	0.882802i	$-0.655655\pi$
$17$	−5.44751e22	−0.939492	−0.469746	+	0.882802i	$0.655655\pi$
$18$	7.75785e22	0.464729
$19$	2.22938e23	0.491182	0.245591	−	0.969374i	$-0.421018\pi$
$19$	2.22938e23	0.491182	0.245591	+	0.969374i	$0.421018\pi$
$20$	4.06888e23	0.347073
$21$	1.20477e24	0.416722
$22$	3.87875e24	0.567378
$23$	−1.64570e25	−1.05775	−0.528877	−	0.848698i	$-0.677387\pi$
$23$	−1.64570e25	−1.05775	−0.528877	+	0.848698i	$0.677387\pi$
$24$	1.54784e24	0.0452708
$25$	−6.29193e25	−0.864756
$26$	−3.30554e26	−2.19905
$27$	−5.81497e25	−0.192450
$28$	−4.03359e26	−0.681190
$29$	1.49927e27	1.32287	0.661434	−	0.750004i	$-0.269948\pi$
$29$	1.49927e27	1.32287	0.661434	+	0.750004i	$0.269948\pi$
$30$	−6.28150e26	−0.296019
$31$	−4.99985e27	−1.28459	−0.642297	−	0.766456i	$-0.722018\pi$
$31$	−4.99985e27	−1.28459	−0.642297	+	0.766456i	$0.722018\pi$
$32$	−9.73240e27	−1.38978
$33$	−2.90736e27	−0.234958
$34$	−2.81562e28	−1.30983
$35$	−9.75497e27	−0.265440
$36$	1.94686e28	0.314586
$37$	4.47694e28	0.435762	0.217881	−	0.975975i	$-0.430086\pi$
$37$	4.47694e28	0.435762	0.217881	+	0.975975i	$0.430086\pi$
$38$	1.15228e29	0.684799
$39$	2.47770e29	0.910654
$40$	−1.25328e28	−0.0288362
$41$	1.03254e30	1.50455	0.752275	−	0.658849i	$-0.228956\pi$
$41$	1.03254e30	1.50455	0.752275	+	0.658849i	$0.228956\pi$
$42$	6.22702e29	0.580989
$43$	−2.18835e30	−1.32114	−0.660572	−	0.750763i	$-0.729686\pi$
$43$	−2.18835e30	−1.32114	−0.660572	+	0.750763i	$0.729686\pi$
$44$	9.73390e29	0.384072
$45$	4.70836e29	0.122585
$46$	−8.50601e30	−1.47471
$47$	1.06681e31	1.24244	0.621221	−	0.783635i	$-0.286637\pi$
$47$	1.06681e31	1.24244	0.621221	+	0.783635i	$0.286637\pi$
$48$	7.70660e30	0.607995
$49$	−8.89176e30	−0.479027
$50$	−3.25207e31	−1.20563
$51$	2.11048e31	0.542416
$52$	−8.29539e31	−1.48859
$53$	−2.17162e31	−0.273956	−0.136978	−	0.990574i	$-0.543739\pi$
$53$	−2.17162e31	−0.273956	−0.136978	+	0.990574i	$0.543739\pi$
$54$	−3.00555e31	−0.268311
$55$	2.35408e31	0.149662
$56$	1.24241e31	0.0565961
$57$	−8.63707e31	−0.283584
$58$	7.74917e32	1.84433
$59$	9.25373e32	1.60529	0.802647	−	0.596455i	$-0.203424\pi$
$59$	9.25373e32	1.60529	0.802647	+	0.596455i	$0.203424\pi$
$60$	−1.57637e32	−0.200382
$61$	1.78286e33	1.66923	0.834615	−	0.550833i	$-0.185690\pi$
$61$	1.78286e33	1.66923	0.834615	+	0.550833i	$0.185690\pi$
$62$	−2.58424e33	−1.79096
$63$	−4.66752e32	−0.240595
$64$	−2.29638e33	−0.884532
$65$	−2.00618e33	−0.580061
$66$	−1.50271e33	−0.327576
$67$	5.16951e33	0.853229	0.426615	−	0.904433i	$-0.359706\pi$
$67$	5.16951e33	0.853229	0.426615	+	0.904433i	$0.359706\pi$
$68$	−7.06592e33	−0.886654
$69$	6.37577e33	0.610695
$70$	−5.04199e33	−0.370074
$71$	3.92232e33	0.221444	0.110722	−	0.993851i	$-0.464684\pi$
$71$	3.92232e33	0.221444	0.110722	+	0.993851i	$0.464684\pi$
$72$	−5.99665e32	−0.0261371
$73$	−3.83796e34	−1.29607	−0.648034	−	0.761612i	$-0.724408\pi$
$73$	−3.83796e34	−1.29607	−0.648034	+	0.761612i	$0.724408\pi$
$74$	2.31397e34	0.607534
$75$	2.43762e34	0.499267
$76$	2.89171e34	0.463557
$77$	−2.33366e34	−0.293737
$78$	1.28063e35	1.26962
$79$	−5.14706e34	−0.403142	−0.201571	−	0.979474i	$-0.564605\pi$
$79$	−5.14706e34	−0.403142	−0.201571	+	0.979474i	$0.564605\pi$
$80$	−6.24001e34	−0.387276
$81$	2.25284e34	0.111111
$82$	5.33684e35	2.09763
$83$	−2.76468e35	−0.868361	−0.434180	−	0.900826i	$-0.642962\pi$
$83$	−2.76468e35	−0.868361	−0.434180	+	0.900826i	$0.642962\pi$
$84$	1.56270e35	0.393285
$85$	−1.70885e35	−0.345504
$86$	−1.13108e36	−1.84192
$87$	−5.80847e35	−0.763758
$88$	−2.99820e34	−0.0319103
$89$	−1.38448e36	−1.19556	−0.597780	−	0.801661i	$-0.703950\pi$
$89$	−1.38448e36	−1.19556	−0.597780	+	0.801661i	$0.703950\pi$
$90$	2.43358e35	0.170907
$91$	1.98878e36	1.13847
$92$	−2.13462e36	−0.998265
$93$	1.93704e36	0.741660
$94$	5.51395e36	1.73220
$95$	6.99340e35	0.180635
$96$	3.77053e36	0.802388
$97$	1.68983e36	0.296870	0.148435	−	0.988922i	$-0.452576\pi$
$97$	1.68983e36	0.296870	0.148435	+	0.988922i	$0.452576\pi$
$98$	−4.59583e36	−0.667853
$99$	1.12637e36	0.135653
$100$	−8.16120e36	−0.816120
$101$	−5.62367e36	−0.467815	−0.233908	−	0.972259i	$-0.575151\pi$
$101$	−5.62367e36	−0.467815	−0.233908	+	0.972259i	$0.575151\pi$
$102$	1.09083e37	0.756230
$103$	−1.48424e37	−0.859046	−0.429523	−	0.903056i	$-0.641318\pi$
$103$	−1.48424e37	−0.859046	−0.429523	+	0.903056i	$0.641318\pi$
$104$	2.55511e36	0.123678
$105$	3.77928e36	0.153252
$106$	−1.12243e37	−0.381945
$107$	4.70122e36	0.134465	0.0672327	−	0.997737i	$-0.478583\pi$
$107$	4.70122e36	0.134465	0.0672327	+	0.997737i	$0.478583\pi$
$108$	−7.54255e36	−0.181626
$109$	−3.33633e36	−0.0677453	−0.0338726	−	0.999426i	$-0.510784\pi$
$109$	−3.33633e36	−0.0677453	−0.0338726	+	0.999426i	$0.510784\pi$
$110$	1.21674e37	0.208657
$111$	−1.73446e37	−0.251587
$112$	6.18588e37	0.760096
$113$	−1.52031e38	−1.58483	−0.792414	−	0.609984i	$-0.791176\pi$
$113$	−1.52031e38	−1.58483	−0.792414	+	0.609984i	$0.791176\pi$
$114$	−4.46419e37	−0.395369
$115$	−5.16243e37	−0.388995
$116$	1.94469e38	1.24847
$117$	−9.59912e37	−0.525766
$118$	4.78292e38	2.23808
$119$	1.69402e38	0.678111
$120$	4.85547e36	0.0166486
$121$	−2.83723e38	−0.834384
$122$	9.21498e38	2.32722
$123$	−4.00028e38	−0.868653
$124$	−6.48527e38	−1.21235
$125$	−4.25615e38	−0.685775
$126$	−2.41247e38	−0.335434
$127$	−9.46165e38	−1.13658	−0.568288	−	0.822830i	$-0.692394\pi$
$127$	−9.46165e38	−1.13658	−0.568288	+	0.822830i	$0.692394\pi$
$128$	1.50697e38	0.156575
$129$	8.47811e38	0.762762
$130$	−1.03692e39	−0.808714
$131$	−7.30262e38	−0.494265	−0.247133	−	0.968982i	$-0.579488\pi$
$131$	−7.30262e38	−0.494265	−0.247133	+	0.968982i	$0.579488\pi$
$132$	−3.77111e38	−0.221744
$133$	−6.93274e38	−0.354527
$134$	2.67193e39	1.18956
$135$	−1.82412e38	−0.0707746
$136$	2.17642e38	0.0736669
$137$	2.73285e39	0.807765	0.403883	−	0.914811i	$-0.367660\pi$
$137$	2.73285e39	0.807765	0.403883	+	0.914811i	$0.367660\pi$
$138$	3.29540e39	0.851423
$139$	5.99229e39	1.35462	0.677312	−	0.735696i	$-0.263145\pi$
$139$	5.99229e39	1.35462	0.677312	+	0.735696i	$0.263145\pi$
$140$	−1.26531e39	−0.250512
$141$	−4.13304e39	−0.717325
$142$	2.02730e39	0.308734
$143$	−4.79935e39	−0.641897
$144$	−2.98570e39	−0.351026
$145$	4.70310e39	0.486492
$146$	−1.98370e40	−1.80696
$147$	3.44485e39	0.276566
$148$	5.80700e39	0.411254
$149$	−1.46862e40	−0.918255	−0.459127	−	0.888370i	$-0.651838\pi$
$149$	−1.46862e40	−0.918255	−0.459127	+	0.888370i	$0.651838\pi$
$150$	1.25992e40	0.696072
$151$	2.01471e40	0.984328	0.492164	−	0.870503i	$-0.336206\pi$
$151$	2.01471e40	0.984328	0.492164	+	0.870503i	$0.336206\pi$
$152$	−8.90692e38	−0.0385142
$153$	−8.17643e39	−0.313164
$154$	−1.20618e40	−0.409525
$155$	−1.56842e40	−0.472417
$156$	3.21380e40	0.859437
$157$	−5.21717e40	−1.23963	−0.619815	−	0.784748i	$-0.712792\pi$
$157$	−5.21717e40	−1.23963	−0.619815	+	0.784748i	$0.712792\pi$
$158$	−2.66033e40	−0.562056
$159$	8.41330e39	0.158168
$160$	−3.05298e40	−0.511099
$161$	5.11766e40	0.763471
$162$	1.16441e40	0.154910
$163$	1.10448e41	1.31125	0.655625	−	0.755086i	$-0.272405\pi$
$163$	1.10448e41	1.31125	0.655625	+	0.755086i	$0.272405\pi$
$164$	1.33930e41	1.41993
$165$	−9.12018e39	−0.0864073
$166$	−1.42896e41	−1.21066
$167$	8.68066e40	0.658109	0.329055	−	0.944311i	$-0.393270\pi$
$167$	8.68066e40	0.658109	0.329055	+	0.944311i	$0.393270\pi$
$168$	−4.81335e39	−0.0326758
$169$	2.44608e41	1.48787
$170$	−8.83241e40	−0.481697
$171$	3.34618e40	0.163727
$172$	−2.83849e41	−1.24684
$173$	−2.30699e41	−0.910316	−0.455158	−	0.890411i	$-0.650417\pi$
$173$	−2.30699e41	−0.910316	−0.455158	+	0.890411i	$0.650417\pi$
$174$	−3.00219e41	−1.06482
$175$	1.95661e41	0.624167
$176$	−1.49278e41	−0.428561
$177$	−3.58508e41	−0.926817
$178$	−7.15587e41	−1.66683
$179$	4.00112e41	0.840235	0.420118	−	0.907470i	$-0.361989\pi$
$179$	4.00112e41	0.840235	0.420118	+	0.907470i	$0.361989\pi$
$180$	6.10718e40	0.115691
$181$	8.60285e41	1.47092	0.735460	−	0.677569i	$-0.236966\pi$
$181$	8.60285e41	1.47092	0.735460	+	0.677569i	$0.236966\pi$
$182$	1.02793e42	1.58724
$183$	−6.90718e41	−0.963731
$184$	6.57497e40	0.0829400
$185$	1.40438e41	0.160254
$186$	1.00119e42	1.03401
$187$	−4.08803e41	−0.382336
$188$	1.38375e42	1.17257
$189$	1.80829e41	0.138907
$190$	3.61464e41	0.251839
$191$	−2.36146e42	−1.49301	−0.746507	−	0.665378i	$-0.768270\pi$
$191$	−2.36146e42	−1.49301	−0.746507	+	0.665378i	$0.768270\pi$
$192$	8.89663e41	0.510685
$193$	−2.73448e42	−1.42582	−0.712910	−	0.701255i	$-0.752623\pi$
$193$	−2.73448e42	−1.42582	−0.712910	+	0.701255i	$0.752623\pi$
$194$	8.73414e41	0.413893
$195$	7.77237e41	0.334898
$196$	−1.15334e42	−0.452086
$197$	−2.24211e42	−0.799893	−0.399947	−	0.916538i	$-0.630971\pi$
$197$	−2.24211e42	−0.799893	−0.399947	+	0.916538i	$0.630971\pi$
$198$	5.82180e41	0.189126
$199$	4.34264e42	1.28520	0.642602	−	0.766201i	$-0.277855\pi$
$199$	4.34264e42	1.28520	0.642602	+	0.766201i	$0.277855\pi$
$200$	2.51378e41	0.0678067
$201$	−2.00278e42	−0.492612
$202$	−2.90667e42	−0.652222
$203$	−4.66230e42	−0.954825
$204$	2.73748e42	0.511910
$205$	3.23901e42	0.553307
$206$	−7.67151e42	−1.19767
$207$	−2.47010e42	−0.352585
$208$	1.27217e43	1.66102
$209$	1.67302e42	0.199891
$210$	1.95337e42	0.213662
$211$	−1.99383e42	−0.199739	−0.0998696	−	0.995001i	$-0.531843\pi$
$211$	−1.99383e42	−0.199739	−0.0998696	+	0.995001i	$0.531843\pi$
$212$	−2.81679e42	−0.258548
$213$	−1.51959e42	−0.127851
$214$	2.42989e42	0.187470
$215$	−6.86469e42	−0.485858
$216$	2.32323e41	0.0150903
$217$	1.55481e43	0.927200
$218$	−1.72443e42	−0.0944496
$219$	1.48690e43	0.748285
$220$	3.05345e42	0.141245
$221$	3.48389e43	1.48186
$222$	−8.96478e42	−0.350760
$223$	−1.45882e43	−0.525245	−0.262622	−	0.964899i	$-0.584587\pi$
$223$	−1.45882e43	−0.525245	−0.262622	+	0.964899i	$0.584587\pi$
$224$	3.02650e43	1.00312
$225$	−9.44384e42	−0.288252
$226$	−7.85795e43	−2.20955
$227$	−1.02701e43	−0.266132	−0.133066	−	0.991107i	$-0.542482\pi$
$227$	−1.02701e43	−0.266132	−0.133066	+	0.991107i	$0.542482\pi$
$228$	−1.12031e43	−0.267635
$229$	−7.93768e43	−1.74879	−0.874394	−	0.485216i	$-0.838741\pi$
$229$	−7.93768e43	−1.74879	−0.874394	+	0.485216i	$0.838741\pi$
$230$	−2.66828e43	−0.542333
$231$	9.04107e42	0.169589
$232$	−5.98995e42	−0.103728
$233$	3.40755e43	0.544951	0.272476	−	0.962163i	$-0.412158\pi$
$233$	3.40755e43	0.544951	0.272476	+	0.962163i	$0.412158\pi$
$234$	−4.96144e43	−0.733017
$235$	3.34650e43	0.456916
$236$	1.20029e44	1.51501
$237$	1.99408e43	0.232754
$238$	8.75580e43	0.945414
$239$	4.85851e43	0.485447	0.242724	−	0.970095i	$-0.421959\pi$
$239$	4.85851e43	0.485447	0.242724	+	0.970095i	$0.421959\pi$
$240$	2.41751e43	0.223594
$241$	1.16789e44	1.00020	0.500100	−	0.865968i	$-0.333297\pi$
$241$	1.16789e44	1.00020	0.500100	+	0.865968i	$0.333297\pi$
$242$	−1.46646e44	−1.16329
$243$	−8.72796e42	−0.0641500
$244$	2.31254e44	1.57535
$245$	−2.78928e43	−0.176165
$246$	−2.06760e44	−1.21106
$247$	−1.42577e44	−0.774741
$248$	1.99756e43	0.100727
$249$	1.07109e44	0.501348
$250$	−2.19985e44	−0.956098
$251$	1.50654e44	0.608158	0.304079	−	0.952647i	$-0.401651\pi$
$251$	1.50654e44	0.608158	0.304079	+	0.952647i	$0.401651\pi$
$252$	−6.05421e43	−0.227063
$253$	−1.23500e44	−0.430464
$254$	−4.89039e44	−1.58460
$255$	6.62042e43	0.199477
$256$	3.93501e44	1.10283
$257$	−2.05457e44	−0.535746	−0.267873	−	0.963454i	$-0.586321\pi$
$257$	−2.05457e44	−0.535746	−0.267873	+	0.963454i	$0.586321\pi$
$258$	4.38203e44	1.06343
$259$	−1.39220e44	−0.314526
$260$	−2.60220e44	−0.547437
$261$	2.25032e44	0.440956
$262$	−3.77446e44	−0.689098
$263$	3.74763e44	0.637639	0.318819	−	0.947815i	$-0.396714\pi$
$263$	3.74763e44	0.637639	0.318819	+	0.947815i	$0.396714\pi$
$264$	1.16156e43	0.0184234
$265$	−6.81221e43	−0.100749
$266$	−3.58328e44	−0.494278
$267$	5.36375e44	0.690256
$268$	6.70533e44	0.805242
$269$	−6.18015e44	−0.692758	−0.346379	−	0.938095i	$-0.612589\pi$
$269$	−6.18015e44	−0.692758	−0.346379	+	0.938095i	$0.612589\pi$
$270$	−9.42819e43	−0.0986731
$271$	−8.98660e44	−0.878342	−0.439171	−	0.898403i	$-0.644728\pi$
$271$	−8.98660e44	−0.878342	−0.439171	+	0.898403i	$0.644728\pi$
$272$	1.08362e45	0.989359
$273$	−7.70495e44	−0.657296
$274$	1.41251e45	1.12618
$275$	−4.72171e44	−0.351921
$276$	8.26996e44	0.576348
$277$	5.14897e44	0.335617	0.167809	−	0.985820i	$-0.446331\pi$
$277$	5.14897e44	0.335617	0.167809	+	0.985820i	$0.446331\pi$
$278$	3.09719e45	1.88860
$279$	−7.50451e44	−0.428198
$280$	3.89735e43	0.0208135
$281$	−2.48686e45	−1.24333	−0.621663	−	0.783285i	$-0.713543\pi$
$281$	−2.48686e45	−1.24333	−0.621663	+	0.783285i	$0.713543\pi$
$282$	−2.13622e45	−1.00008
$283$	1.48025e45	0.649062	0.324531	−	0.945875i	$-0.394793\pi$
$283$	1.48025e45	0.649062	0.324531	+	0.945875i	$0.394793\pi$
$284$	5.08761e44	0.208989
$285$	−2.70939e44	−0.104290
$286$	−2.48061e45	−0.894925
$287$	−3.21092e45	−1.08596
$288$	−1.46078e45	−0.463259
$289$	−3.94555e44	−0.117354
$290$	2.43086e45	0.678261
$291$	−6.54676e44	−0.171398
$292$	−4.97819e45	−1.22317
$293$	1.29229e45	0.298064	0.149032	−	0.988832i	$-0.452384\pi$
$293$	1.29229e45	0.298064	0.149032	+	0.988832i	$0.452384\pi$
$294$	1.78052e45	0.385585
$295$	2.90283e45	0.590356
$296$	−1.78865e44	−0.0341687
$297$	−4.36379e44	−0.0783194
$298$	−7.59076e45	−1.28022
$299$	1.05249e46	1.66840
$300$	3.16182e45	0.471187
$301$	6.80515e45	0.953581
$302$	1.04133e46	1.37234
$303$	2.17873e45	0.270093
$304$	−4.43470e45	−0.517253
$305$	5.59272e45	0.613869
$306$	−4.22610e45	−0.436609
$307$	3.03724e45	0.295406	0.147703	−	0.989032i	$-0.452812\pi$
$307$	3.03724e45	0.295406	0.147703	+	0.989032i	$0.452812\pi$
$308$	−3.02697e45	−0.277217
$309$	5.75026e45	0.495970
$310$	−8.10658e45	−0.658637
$311$	−2.03519e46	−1.55789	−0.778947	−	0.627090i	$-0.784246\pi$
$311$	−2.03519e46	−1.55789	−0.778947	+	0.627090i	$0.784246\pi$
$312$	−9.89903e44	−0.0714056
$313$	1.26896e46	0.862736	0.431368	−	0.902176i	$-0.358031\pi$
$313$	1.26896e46	0.862736	0.431368	+	0.902176i	$0.358031\pi$
$314$	−2.69657e46	−1.72828
$315$	−1.46417e45	−0.0884802
$316$	−6.67621e45	−0.380469
$317$	−2.19161e46	−1.17806	−0.589029	−	0.808112i	$-0.700490\pi$
$317$	−2.19161e46	−1.17806	−0.589029	+	0.808112i	$0.700490\pi$
$318$	4.34853e45	0.220516
$319$	1.12511e46	0.538354
$320$	−7.20356e45	−0.325292
$321$	−1.82135e45	−0.0776336
$322$	2.64513e46	1.06442
$323$	−1.21446e46	−0.461461
$324$	2.92214e45	0.104862
$325$	4.02392e46	1.36398
$326$	5.70864e46	1.82813
$327$	1.29256e45	0.0391127
$328$	−4.12527e45	−0.117974
$329$	−3.31748e46	−0.896776
$330$	−4.71389e45	−0.120468
$331$	−6.51418e46	−1.57413	−0.787067	−	0.616867i	$-0.788402\pi$
$331$	−6.51418e46	−1.57413	−0.787067	+	0.616867i	$0.788402\pi$
$332$	−3.58604e46	−0.819523
$333$	6.71965e45	0.145254
$334$	4.48672e46	0.917528
$335$	1.62164e46	0.313780
$336$	−2.39654e46	−0.438842
$337$	−4.49138e46	−0.778443	−0.389221	−	0.921144i	$-0.627256\pi$
$337$	−4.49138e46	−0.778443	−0.389221	+	0.921144i	$0.627256\pi$
$338$	1.26429e47	2.07437
$339$	5.89001e46	0.915000
$340$	−2.21653e46	−0.326072
$341$	−3.75209e46	−0.522778
$342$	1.72952e46	0.228266
$343$	8.53739e46	1.06754
$344$	8.74299e45	0.103593
$345$	2.00003e46	0.224587
$346$	−1.19240e47	−1.26915
$347$	−3.07449e45	−0.0310226	−0.0155113	−	0.999880i	$-0.504938\pi$
$347$	−3.07449e45	−0.0310226	−0.0155113	+	0.999880i	$0.504938\pi$
$348$	−7.53412e46	−0.720803
$349$	−1.55130e47	−1.40742	−0.703711	−	0.710487i	$-0.748475\pi$
$349$	−1.55130e47	−1.40742	−0.703711	+	0.710487i	$0.748475\pi$
$350$	1.01130e47	0.870206
$351$	3.71889e46	0.303551
$352$	−7.30358e46	−0.565583
$353$	1.60772e47	1.18135	0.590675	−	0.806909i	$-0.298861\pi$
$353$	1.60772e47	1.18135	0.590675	+	0.806909i	$0.298861\pi$
$354$	−1.85300e47	−1.29216
$355$	1.23040e46	0.0814372
$356$	−1.79580e47	−1.12832
$357$	−6.56300e46	−0.391508
$358$	2.06804e47	1.17145
$359$	−3.06245e47	−1.64749	−0.823743	−	0.566963i	$-0.808118\pi$
$359$	−3.06245e47	−1.64749	−0.823743	+	0.566963i	$0.808118\pi$
$360$	−1.88111e45	−0.00961208
$361$	−1.56306e47	−0.758741
$362$	4.44650e47	2.05074
$363$	1.09920e47	0.481732
$364$	2.57963e47	1.07444
$365$	−1.20394e47	−0.476636
$366$	−3.57007e47	−1.34362
$367$	3.11125e47	1.11330	0.556651	−	0.830746i	$-0.312086\pi$
$367$	3.11125e47	1.11330	0.556651	+	0.830746i	$0.312086\pi$
$368$	3.27364e47	1.11390
$369$	1.54979e47	0.501517
$370$	7.25875e46	0.223424
$371$	6.75313e46	0.197737
$372$	2.51252e47	0.699948
$373$	2.77220e47	0.734872	0.367436	−	0.930049i	$-0.380236\pi$
$373$	2.77220e47	0.734872	0.367436	+	0.930049i	$0.380236\pi$
$374$	−2.11296e47	−0.533047
$375$	1.64892e47	0.395932
$376$	−4.26217e46	−0.0974216
$377$	−9.58838e47	−2.08656
$378$	9.34642e46	0.193663
$379$	−3.61039e47	−0.712408	−0.356204	−	0.934408i	$-0.615929\pi$
$379$	−3.61039e47	−0.712408	−0.356204	+	0.934408i	$0.615929\pi$
$380$	9.07108e46	0.170476
$381$	3.66564e47	0.656202
$382$	−1.22055e48	−2.08154
$383$	3.07589e47	0.499797	0.249898	−	0.968272i	$-0.419603\pi$
$383$	3.07589e47	0.499797	0.249898	+	0.968272i	$0.419603\pi$
$384$	−5.83833e46	−0.0903984
$385$	−7.32052e46	−0.108024
$386$	−1.41335e48	−1.98786
$387$	−3.28459e47	−0.440381
$388$	2.19187e47	0.280174
$389$	8.01241e47	0.976552	0.488276	−	0.872689i	$-0.337626\pi$
$389$	8.01241e47	0.976552	0.488276	+	0.872689i	$0.337626\pi$
$390$	4.01725e47	0.466911
$391$	8.96496e47	0.993753
$392$	3.55248e46	0.0375612
$393$	2.82919e47	0.285364
$394$	−1.15887e48	−1.11520
$395$	−1.61460e47	−0.148258
$396$	1.46101e47	0.128024
$397$	5.55598e47	0.464661	0.232331	−	0.972637i	$-0.425365\pi$
$397$	5.55598e47	0.464661	0.232331	+	0.972637i	$0.425365\pi$
$398$	2.24455e48	1.79181
$399$	2.68589e47	0.204686
$400$	1.25160e48	0.910656
$401$	−2.52389e48	−1.75347	−0.876736	−	0.480972i	$-0.840284\pi$
$401$	−2.52389e48	−1.75347	−0.876736	+	0.480972i	$0.840284\pi$
$402$	−1.03516e48	−0.686794
$403$	3.19759e48	2.02619
$404$	−7.29442e47	−0.441505
$405$	7.06700e46	0.0408618
$406$	−2.40978e48	−1.33121
$407$	3.35968e47	0.177338
$408$	−8.43188e46	−0.0425316
$409$	1.92635e48	0.928653	0.464326	−	0.885664i	$-0.346296\pi$
$409$	1.92635e48	0.928653	0.464326	+	0.885664i	$0.346296\pi$
$410$	1.67413e48	0.771414
$411$	−1.05876e48	−0.466363
$412$	−1.92520e48	−0.810731
$413$	−2.87765e48	−1.15868
$414$	−1.27671e48	−0.491569
$415$	−8.67260e47	−0.319345
$416$	6.22423e48	2.19209
$417$	−2.32153e48	−0.782092
$418$	8.64721e47	0.278686
$419$	1.97665e48	0.609494	0.304747	−	0.952433i	$-0.401428\pi$
$419$	1.97665e48	0.609494	0.304747	+	0.952433i	$0.401428\pi$
$420$	4.90207e47	0.144633
$421$	−3.96618e48	−1.11983	−0.559916	−	0.828549i	$-0.689167\pi$
$421$	−3.96618e48	−1.11983	−0.559916	+	0.828549i	$0.689167\pi$
$422$	−1.03054e48	−0.278474
$423$	1.60122e48	0.414148
$424$	8.67616e46	0.0214812
$425$	3.42753e48	0.812431
$426$	−7.85419e47	−0.178248
$427$	−5.54421e48	−1.20482
$428$	6.09791e47	0.126903
$429$	1.85937e48	0.370600
$430$	−3.54811e48	−0.677377
$431$	−9.76026e48	−1.78497	−0.892487	−	0.451074i	$-0.851041\pi$
$431$	−9.76026e48	−1.78497	−0.892487	+	0.451074i	$0.851041\pi$
$432$	1.15672e48	0.202665
$433$	−4.50754e48	−0.756683	−0.378341	−	0.925666i	$-0.623505\pi$
$433$	−4.50754e48	−0.756683	−0.378341	+	0.925666i	$0.623505\pi$
$434$	8.03627e48	1.29269
$435$	−1.82208e48	−0.280876
$436$	−4.32753e47	−0.0639352
$437$	−3.66888e48	−0.519550
$438$	7.68527e48	1.04325
$439$	1.11863e49	1.45577	0.727886	−	0.685699i	$-0.240503\pi$
$439$	1.11863e49	1.45577	0.727886	+	0.685699i	$0.240503\pi$
$440$	−9.40512e46	−0.0117352
$441$	−1.33460e48	−0.159676
$442$	1.80070e49	2.06599
$443$	1.43677e49	1.58095	0.790474	−	0.612496i	$-0.209834\pi$
$443$	1.43677e49	1.58095	0.790474	+	0.612496i	$0.209834\pi$
$444$	−2.24975e48	−0.237438
$445$	−4.34301e48	−0.439674
$446$	−7.54011e48	−0.732290
$447$	5.68973e48	0.530155
$448$	7.14108e48	0.638441
$449$	−9.50078e48	−0.815084	−0.407542	−	0.913187i	$-0.633614\pi$
$449$	−9.50078e48	−0.815084	−0.407542	+	0.913187i	$0.633614\pi$
$450$	−4.88118e48	−0.401877
$451$	7.74862e48	0.612292
$452$	−1.97199e49	−1.49569
$453$	−7.80541e48	−0.568302
$454$	−5.30824e48	−0.371037
$455$	6.23867e48	0.418679
$456$	3.45072e47	0.0222362
$457$	−1.14567e49	−0.708941	−0.354471	−	0.935067i	$-0.615339\pi$
$457$	−1.14567e49	−0.708941	−0.354471	+	0.935067i	$0.615339\pi$
$458$	−4.10270e49	−2.43814
$459$	3.16771e48	0.180805
$460$	−6.69615e48	−0.367118
$461$	1.13686e49	0.598741	0.299370	−	0.954137i	$-0.403223\pi$
$461$	1.13686e49	0.598741	0.299370	+	0.954137i	$0.403223\pi$
$462$	4.67300e48	0.236439
$463$	1.21451e49	0.590409	0.295204	−	0.955434i	$-0.404612\pi$
$463$	1.21451e49	0.590409	0.295204	+	0.955434i	$0.404612\pi$
$464$	−2.98236e49	−1.39308
$465$	6.07637e48	0.272750
$466$	1.76124e49	0.759764
$467$	4.37721e49	1.81483	0.907414	−	0.420237i	$-0.138053\pi$
$467$	4.37721e49	1.81483	0.907414	+	0.420237i	$0.138053\pi$
$468$	−1.24509e49	−0.496196
$469$	−1.60757e49	−0.615848
$470$	1.72969e49	0.637026
$471$	2.02124e49	0.715700
$472$	−3.69709e48	−0.125873
$473$	−1.64222e49	−0.537652
$474$	1.03067e49	0.324503
$475$	−1.40271e49	−0.424752
$476$	2.19730e49	0.639973
$477$	−3.25948e48	−0.0913185
$478$	2.51119e49	0.676805
$479$	3.52297e49	0.913486	0.456743	−	0.889599i	$-0.349016\pi$
$479$	3.52297e49	0.913486	0.456743	+	0.889599i	$0.349016\pi$
$480$	1.18279e49	0.295083
$481$	−2.86317e49	−0.687327
$482$	6.03640e49	1.39447
$483$	−1.98269e49	−0.440790
$484$	−3.68015e49	−0.787457
$485$	5.30089e48	0.109176
$486$	−4.51117e48	−0.0894372
$487$	−3.72470e49	−0.710894	−0.355447	−	0.934696i	$-0.615671\pi$
$487$	−3.72470e49	−0.710894	−0.355447	+	0.934696i	$0.615671\pi$
$488$	−7.12299e48	−0.130887
$489$	−4.27897e49	−0.757051
$490$	−1.44168e49	−0.245607
$491$	6.86626e49	1.12645	0.563226	−	0.826303i	$-0.309560\pi$
$491$	6.86626e49	1.12645	0.563226	+	0.826303i	$0.309560\pi$
$492$	−5.18873e49	−0.819798
$493$	−8.16728e49	−1.24282
$494$	−7.36930e49	−1.08013
$495$	3.53334e48	0.0498873
$496$	9.94575e49	1.35278
$497$	−1.21973e49	−0.159835
$498$	5.53610e49	0.698973
$499$	1.17556e50	1.43016	0.715080	−	0.699042i	$-0.246390\pi$
$499$	1.17556e50	1.43016	0.715080	+	0.699042i	$0.246390\pi$
$500$	−5.52061e49	−0.647206
$501$	−3.36307e49	−0.379960
$502$	7.78675e49	0.847886
$503$	−1.53249e49	−0.160838	−0.0804191	−	0.996761i	$-0.525626\pi$
$503$	−1.53249e49	−0.160838	−0.0804191	+	0.996761i	$0.525626\pi$
$504$	1.86479e48	0.0188654
$505$	−1.76411e49	−0.172042
$506$	−6.38325e49	−0.600147
$507$	−9.47660e49	−0.859024
$508$	−1.22726e50	−1.07265
$509$	−7.32055e49	−0.616971	−0.308486	−	0.951229i	$-0.599822\pi$
$509$	−7.32055e49	−0.616971	−0.308486	+	0.951229i	$0.599822\pi$
$510$	3.42185e49	0.278108
$511$	1.19350e50	0.935481
$512$	1.82675e50	1.38097
$513$	−1.29638e49	−0.0945280
$514$	−1.06193e50	−0.746930
$515$	−4.65596e49	−0.315919
$516$	1.09969e50	0.719863
$517$	8.00577e49	0.505624
$518$	−7.19579e49	−0.438508
$519$	8.93774e49	0.525571
$520$	8.01520e48	0.0454834
$521$	1.44081e50	0.789061	0.394530	−	0.918883i	$-0.370907\pi$
$521$	1.44081e50	0.789061	0.394530	+	0.918883i	$0.370907\pi$
$522$	1.16311e50	0.614775
$523$	−1.41522e50	−0.722007	−0.361003	−	0.932564i	$-0.617566\pi$
$523$	−1.41522e50	−0.722007	−0.361003	+	0.932564i	$0.617566\pi$
$524$	−9.47217e49	−0.466467
$525$	−7.58032e49	−0.360363
$526$	1.93701e50	0.888988
$527$	2.72368e50	1.20687
$528$	5.78335e49	0.247430
$529$	2.87681e49	0.118845
$530$	−3.52099e49	−0.140463
$531$	1.38893e50	0.535098
$532$	−8.99240e49	−0.334588
$533$	−6.60350e50	−2.37313
$534$	2.77233e50	0.962347
$535$	1.47474e49	0.0494504
$536$	−2.06535e49	−0.0669029
$537$	−1.55012e50	−0.485110
$538$	−3.19429e50	−0.965835
$539$	−6.67273e49	−0.194945
$540$	−2.36605e49	−0.0667942
$541$	−3.29954e50	−0.900127	−0.450064	−	0.892997i	$-0.648599\pi$
$541$	−3.29954e50	−0.900127	−0.450064	+	0.892997i	$0.648599\pi$
$542$	−4.64485e50	−1.22457
$543$	−3.33292e50	−0.849236
$544$	5.30174e50	1.30569
$545$	−1.04658e49	−0.0249137
$546$	−3.98241e50	−0.916394
$547$	9.95610e49	0.221474	0.110737	−	0.993850i	$-0.464679\pi$
$547$	9.95610e49	0.221474	0.110737	+	0.993850i	$0.464679\pi$
$548$	3.54475e50	0.762335
$549$	2.67598e50	0.556410
$550$	−2.44048e50	−0.490643
$551$	3.34244e50	0.649768
$552$	−2.54728e49	−0.0478854
$553$	1.60059e50	0.290982
$554$	2.66131e50	0.467913
$555$	−5.44087e49	−0.0925227
$556$	7.77254e50	1.27844
$557$	9.57323e50	1.52313	0.761565	−	0.648088i	$-0.224431\pi$
$557$	9.57323e50	1.52313	0.761565	+	0.648088i	$0.224431\pi$
$558$	−3.87881e50	−0.596988
$559$	1.39953e51	2.08384
$560$	1.94047e50	0.279530
$561$	1.58379e50	0.220742
$562$	−1.28537e51	−1.73343
$563$	3.20639e50	0.418419	0.209209	−	0.977871i	$-0.432911\pi$
$563$	3.20639e50	0.418419	0.209209	+	0.977871i	$0.432911\pi$
$564$	−5.36093e50	−0.676981
$565$	−4.76911e50	−0.582829
$566$	7.65088e50	0.904914
$567$	−7.00570e49	−0.0801983
$568$	−1.56706e49	−0.0173637
$569$	−1.54737e51	−1.65966	−0.829829	−	0.558018i	$-0.811562\pi$
$569$	−1.54737e51	−1.65966	−0.829829	+	0.558018i	$0.811562\pi$
$570$	−1.40038e50	−0.145399
$571$	−8.82178e50	−0.886723	−0.443362	−	0.896343i	$-0.646214\pi$
$571$	−8.82178e50	−0.886723	−0.443362	+	0.896343i	$0.646214\pi$
$572$	−6.22519e50	−0.605796
$573$	9.14879e50	0.861992
$574$	−1.65961e51	−1.51403
$575$	1.03546e51	0.914699
$576$	−3.44674e50	−0.294844
$577$	−4.93183e50	−0.408560	−0.204280	−	0.978913i	$-0.565485\pi$
$577$	−4.93183e50	−0.408560	−0.204280	+	0.978913i	$0.565485\pi$
$578$	−2.03931e50	−0.163613
$579$	1.05939e51	0.823198
$580$	6.10035e50	0.459131
$581$	8.59738e50	0.626769
$582$	−3.38378e50	−0.238961
$583$	−1.62967e50	−0.111489
$584$	1.53336e50	0.101626
$585$	−3.01117e50	−0.193354
$586$	6.67939e50	0.415557
$587$	−1.61018e51	−0.970666	−0.485333	−	0.874330i	$-0.661302\pi$
$587$	−1.61018e51	−0.970666	−0.485333	+	0.874330i	$0.661302\pi$
$588$	4.46828e50	0.261012
$589$	−1.11466e51	−0.630969
$590$	1.50037e51	0.823067
$591$	8.68640e50	0.461819
$592$	−8.90557e50	−0.458892
$593$	8.02157e49	0.0400634	0.0200317	−	0.999799i	$-0.493623\pi$
$593$	8.02157e49	0.0400634	0.0200317	+	0.999799i	$0.493623\pi$
$594$	−2.25549e50	−0.109192
$595$	5.31403e50	0.249379
$596$	−1.90493e51	−0.866611
$597$	−1.68243e51	−0.742012
$598$	5.43991e51	2.32606
$599$	−4.13904e51	−1.71595	−0.857973	−	0.513694i	$-0.828276\pi$
$599$	−4.13904e51	−1.71595	−0.857973	+	0.513694i	$0.828276\pi$
$600$	−9.73890e49	−0.0391482
$601$	1.01480e51	0.395551	0.197776	−	0.980247i	$-0.436628\pi$
$601$	1.01480e51	0.395551	0.197776	+	0.980247i	$0.436628\pi$
$602$	3.51733e51	1.32947
$603$	7.75916e50	0.284410
$604$	2.61327e51	0.928968
$605$	−8.90020e50	−0.306849
$606$	1.12610e51	0.376561
$607$	−1.59854e51	−0.518482	−0.259241	−	0.965813i	$-0.583472\pi$
$607$	−1.59854e51	−0.518482	−0.259241	+	0.965813i	$0.583472\pi$
$608$	−2.16972e51	−0.682633
$609$	1.80627e51	0.551269
$610$	2.89067e51	0.855849
$611$	−6.82265e51	−1.95970
$612$	−1.06056e51	−0.295551
$613$	3.62477e51	0.980081	0.490041	−	0.871700i	$-0.336982\pi$
$613$	3.62477e51	0.980081	0.490041	+	0.871700i	$0.336982\pi$
$614$	1.56984e51	0.411851
$615$	−1.25486e51	−0.319452
$616$	9.32355e49	0.0230323
$617$	2.49598e51	0.598364	0.299182	−	0.954196i	$-0.403286\pi$
$617$	2.49598e51	0.598364	0.299182	+	0.954196i	$0.403286\pi$
$618$	2.97210e51	0.691475
$619$	−2.35643e51	−0.532080	−0.266040	−	0.963962i	$-0.585715\pi$
$619$	−2.35643e51	−0.532080	−0.266040	+	0.963962i	$0.585715\pi$
$620$	−2.03438e51	−0.445847
$621$	9.56969e50	0.203565
$622$	−1.05192e52	−2.17200
$623$	4.30534e51	0.862936
$624$	−4.92866e51	−0.958990
$625$	3.24286e51	0.612558
$626$	6.55880e51	1.20282
$627$	−6.48160e50	−0.115407
$628$	−6.76715e51	−1.16991
$629$	−2.43882e51	−0.409395
$630$	−7.56776e50	−0.123358
$631$	−4.78740e51	−0.757804	−0.378902	−	0.925437i	$-0.623698\pi$
$631$	−4.78740e51	−0.757804	−0.378902	+	0.925437i	$0.623698\pi$
$632$	2.05638e50	0.0316109
$633$	7.72451e50	0.115319
$634$	−1.13276e52	−1.64243
$635$	−2.96805e51	−0.417982
$636$	1.09128e51	0.149273
$637$	5.68661e51	0.755569
$638$	5.81529e51	0.750566
$639$	5.88719e50	0.0738146
$640$	4.72727e50	0.0575813
$641$	5.92335e51	0.700961	0.350480	−	0.936570i	$-0.386018\pi$
$641$	5.92335e51	0.700961	0.350480	+	0.936570i	$0.386018\pi$
$642$	−9.41389e50	−0.108236
$643$	1.23332e52	1.37776	0.688879	−	0.724877i	$-0.258103\pi$
$643$	1.23332e52	1.37776	0.688879	+	0.724877i	$0.258103\pi$
$644$	6.63807e51	0.720532
$645$	2.65952e51	0.280510
$646$	−6.27709e51	−0.643364
$647$	2.91813e51	0.290654	0.145327	−	0.989384i	$-0.453577\pi$
$647$	2.91813e51	0.290654	0.145327	+	0.989384i	$0.453577\pi$
$648$	−9.00065e49	−0.00871237
$649$	6.94437e51	0.653290
$650$	2.07982e52	1.90164
$651$	−6.02367e51	−0.535319
$652$	1.43261e52	1.23750
$653$	1.85059e51	0.155387	0.0776936	−	0.996977i	$-0.475244\pi$
$653$	1.85059e51	0.155387	0.0776936	+	0.996977i	$0.475244\pi$
$654$	6.68079e50	0.0545305
$655$	−2.29078e51	−0.181769
$656$	−2.05394e52	−1.58441
$657$	−5.76057e51	−0.432022
$658$	−1.71468e52	−1.25027
$659$	−5.04387e51	−0.357588	−0.178794	−	0.983886i	$-0.557220\pi$
$659$	−5.04387e51	−0.357588	−0.178794	+	0.983886i	$0.557220\pi$
$660$	−1.18297e51	−0.0815476
$661$	1.90856e52	1.27932	0.639659	−	0.768659i	$-0.279075\pi$
$661$	1.90856e52	1.27932	0.639659	+	0.768659i	$0.279075\pi$
$662$	−3.36694e52	−2.19464
$663$	−1.34973e52	−0.855553
$664$	1.10456e51	0.0680894
$665$	−2.17475e51	−0.130380
$666$	3.47314e51	0.202511
$667$	−2.46734e52	−1.39927
$668$	1.12596e52	0.621096
$669$	5.65177e51	0.303250
$670$	8.38167e51	0.437468
$671$	1.33793e52	0.679310
$672$	−1.17253e52	−0.579151
$673$	−7.73202e51	−0.371548	−0.185774	−	0.982593i	$-0.559479\pi$
$673$	−7.73202e51	−0.371548	−0.185774	+	0.982593i	$0.559479\pi$
$674$	−2.32143e52	−1.08529
$675$	3.65874e51	0.166422
$676$	3.17278e52	1.40419
$677$	−4.47773e50	−0.0192827	−0.00964135	−	0.999954i	$-0.503069\pi$
$677$	−4.47773e50	−0.0192827	−0.00964135	+	0.999954i	$0.503069\pi$
$678$	3.04433e52	1.27568
$679$	−5.25491e51	−0.214276
$680$	6.82726e50	0.0270914
$681$	3.97885e51	0.153651
$682$	−1.93932e52	−0.728850
$683$	−3.49109e52	−1.27696	−0.638481	−	0.769637i	$-0.720437\pi$
$683$	−3.49109e52	−1.27696	−0.638481	+	0.769637i	$0.720437\pi$
$684$	4.34030e51	0.154519
$685$	8.57275e51	0.297060
$686$	4.41267e52	1.48835
$687$	3.07522e52	1.00966
$688$	4.35308e52	1.39127
$689$	1.38883e52	0.432110
$690$	1.03374e52	0.313116
$691$	−4.18261e52	−1.23340	−0.616700	−	0.787198i	$-0.711531\pi$
$691$	−4.18261e52	−1.23340	−0.616700	+	0.787198i	$0.711531\pi$
$692$	−2.99237e52	−0.859118
$693$	−3.50270e51	−0.0979124
$694$	−1.58909e51	−0.0432513
$695$	1.87974e52	0.498171
$696$	2.32063e51	0.0598873
$697$	−5.62479e52	−1.41351
$698$	−8.01808e52	−1.96221
$699$	−1.32015e52	−0.314628
$700$	2.53791e52	0.589063
$701$	5.92287e52	1.33890	0.669452	−	0.742856i	$-0.266529\pi$
$701$	5.92287e52	1.33890	0.669452	+	0.742856i	$0.266529\pi$
$702$	1.92216e52	0.423207
$703$	9.98079e51	0.214038
$704$	−1.72329e52	−0.359969
$705$	−1.29650e52	−0.263800
$706$	8.30973e52	1.64702
$707$	1.74880e52	0.337662
$708$	−4.65018e52	−0.874691
$709$	−9.83617e51	−0.180248	−0.0901241	−	0.995931i	$-0.528726\pi$
$709$	−9.83617e51	−0.180248	−0.0901241	+	0.995931i	$0.528726\pi$
$710$	6.35951e51	0.113539
$711$	−7.72546e51	−0.134381
$712$	5.53134e51	0.0937454
$713$	8.22824e52	1.35878
$714$	−3.39218e52	−0.545835
$715$	−1.50552e52	−0.236061
$716$	5.18982e52	0.792979
$717$	−1.88229e52	−0.280273
$718$	−1.58287e53	−2.29690
$719$	−8.07338e52	−1.14175	−0.570875	−	0.821037i	$-0.693396\pi$
$719$	−8.07338e52	−1.14175	−0.570875	+	0.821037i	$0.693396\pi$
$720$	−9.36592e51	−0.129092
$721$	4.61558e52	0.620046
$722$	−8.07891e52	−1.05783
$723$	−4.52465e52	−0.577466
$724$	1.11587e53	1.38819
$725$	−9.43328e52	−1.14396
$726$	5.68138e52	0.671624
$727$	9.90481e51	0.114146	0.0570728	−	0.998370i	$-0.481823\pi$
$727$	9.90481e51	0.114146	0.0570728	+	0.998370i	$0.481823\pi$
$728$	−7.94568e51	−0.0892690
$729$	3.38139e51	0.0370370
$730$	−6.22273e52	−0.664520
$731$	1.19211e53	1.24120
$732$	−8.95925e52	−0.909529
$733$	−8.81869e52	−0.872932	−0.436466	−	0.899721i	$-0.643770\pi$
$733$	−8.81869e52	−0.872932	−0.436466	+	0.899721i	$0.643770\pi$
$734$	1.60809e53	1.55215
$735$	1.08062e52	0.101709
$736$	1.60166e53	1.47004
$737$	3.87941e52	0.347230
$738$	8.01031e52	0.699209
$739$	−1.03605e53	−0.881978	−0.440989	−	0.897513i	$-0.645372\pi$
$739$	−1.03605e53	−0.881978	−0.440989	+	0.897513i	$0.645372\pi$
$740$	1.82161e52	0.151241
$741$	5.52373e52	0.447297
$742$	3.49045e52	0.275682
$743$	1.35827e53	1.04639	0.523195	−	0.852213i	$-0.324740\pi$
$743$	1.35827e53	1.04639	0.523195	+	0.852213i	$0.324740\pi$
$744$	−7.73897e51	−0.0581546
$745$	−4.60695e52	−0.337694
$746$	1.43285e53	1.02455
$747$	−4.14964e52	−0.289454
$748$	−5.30255e52	−0.360832
$749$	−1.46195e52	−0.0970550
$750$	8.52266e52	0.552004
$751$	2.26512e53	1.43137	0.715687	−	0.698421i	$-0.246114\pi$
$751$	2.26512e53	1.43137	0.715687	+	0.698421i	$0.246114\pi$
$752$	−2.12211e53	−1.30839
$753$	−5.83664e52	−0.351120
$754$	−4.95589e53	−2.90905
$755$	6.32001e52	0.361992
$756$	2.34552e52	0.131095
$757$	2.91830e52	0.159168	0.0795841	−	0.996828i	$-0.474641\pi$
$757$	2.91830e52	0.159168	0.0795841	+	0.996828i	$0.474641\pi$
$758$	−1.86608e53	−0.993230
$759$	4.78463e52	0.248528
$760$	−2.79404e51	−0.0141638
$761$	2.49523e52	0.123451	0.0617256	−	0.998093i	$-0.480340\pi$
$761$	2.49523e52	0.123451	0.0617256	+	0.998093i	$0.480340\pi$
$762$	1.89464e53	0.914868
$763$	1.03751e52	0.0488975
$764$	−3.06303e53	−1.40904
$765$	−2.56489e52	−0.115168
$766$	1.58982e53	0.696810
$767$	−5.91811e53	−2.53203
$768$	−1.52451e53	−0.636717
$769$	3.98900e53	1.62640	0.813199	−	0.581986i	$-0.197724\pi$
$769$	3.98900e53	1.62640	0.813199	+	0.581986i	$0.197724\pi$
$770$	−3.78371e52	−0.150605
$771$	7.95983e52	0.309313
$772$	−3.54687e53	−1.34563
$773$	−1.73601e52	−0.0643029	−0.0321515	−	0.999483i	$-0.510236\pi$
$773$	−1.73601e52	−0.0643029	−0.0321515	+	0.999483i	$0.510236\pi$
$774$	−1.69769e53	−0.613974
$775$	3.14587e53	1.11086
$776$	−6.75130e51	−0.0232780
$777$	5.39368e52	0.181592
$778$	4.14132e53	1.36150
$779$	2.30193e53	0.739008
$780$	1.00815e53	0.316063
$781$	2.94347e52	0.0901187
$782$	4.63366e53	1.38548
$783$	−8.71821e52	−0.254586
$784$	1.76876e53	0.504453
$785$	−1.63659e53	−0.455881
$786$	1.46230e53	0.397851
$787$	6.17560e53	1.64114	0.820572	−	0.571544i	$-0.193655\pi$
$787$	6.17560e53	1.64114	0.820572	+	0.571544i	$0.193655\pi$
$788$	−2.90822e53	−0.754906
$789$	−1.45191e53	−0.368141
$790$	−8.34526e52	−0.206699
$791$	4.72775e53	1.14390
$792$	−4.50013e51	−0.0106368
$793$	−1.14021e54	−2.63288
$794$	2.87169e53	0.647825
$795$	2.63919e52	0.0581673
$796$	5.63280e53	1.21292
$797$	−8.27498e53	−1.74096	−0.870478	−	0.492207i	$-0.836190\pi$
$797$	−8.27498e53	−1.74096	−0.870478	+	0.492207i	$0.836190\pi$
$798$	1.38824e53	0.285371
$799$	−5.81146e53	−1.16727
$800$	6.12355e53	1.20182
$801$	−2.07803e53	−0.398520
$802$	−1.30450e54	−2.44467
$803$	−2.88016e53	−0.527447
$804$	−2.59778e53	−0.464907
$805$	1.60537e53	0.280771
$806$	1.65272e54	2.82489
$807$	2.39432e53	0.399964
$808$	2.24680e52	0.0366821
$809$	−4.25983e53	−0.679742	−0.339871	−	0.940472i	$-0.610383\pi$
$809$	−4.25983e53	−0.679742	−0.339871	+	0.940472i	$0.610383\pi$
$810$	3.65267e52	0.0569689
$811$	3.53733e52	0.0539249	0.0269625	−	0.999636i	$-0.491417\pi$
$811$	3.53733e52	0.0539249	0.0269625	+	0.999636i	$0.491417\pi$
$812$	−6.04744e53	−0.901124
$813$	3.48159e53	0.507111
$814$	1.73649e53	0.247242
$815$	3.46466e53	0.482220
$816$	−4.19818e53	−0.571207
$817$	−4.87865e53	−0.648921
$818$	9.95659e53	1.29472
$819$	2.98506e53	0.379490
$820$	4.20130e53	0.522188
$821$	−1.14147e54	−1.38713	−0.693566	−	0.720393i	$-0.743961\pi$
$821$	−1.14147e54	−1.38713	−0.693566	+	0.720393i	$0.743961\pi$
$822$	−5.47235e53	−0.650198
$823$	−4.03065e52	−0.0468250	−0.0234125	−	0.999726i	$-0.507453\pi$
$823$	−4.03065e52	−0.0468250	−0.0234125	+	0.999726i	$0.507453\pi$
$824$	5.92992e52	0.0673589
$825$	1.82929e53	0.203182
$826$	−1.48735e54	−1.61541
$827$	6.45322e53	0.685369	0.342685	−	0.939450i	$-0.388664\pi$
$827$	6.45322e53	0.685369	0.342685	+	0.939450i	$0.388664\pi$
$828$	−3.20395e53	−0.332755
$829$	2.31995e52	0.0235625	0.0117812	−	0.999931i	$-0.496250\pi$
$829$	2.31995e52	0.0235625	0.0117812	+	0.999931i	$0.496250\pi$
$830$	−4.48255e53	−0.445226
$831$	−1.99482e53	−0.193769
$832$	1.46862e54	1.39517
$833$	4.84380e53	0.450042
$834$	−1.19992e54	−1.09038
$835$	2.72306e53	0.242023
$836$	2.17005e53	0.188649
$837$	2.90740e53	0.247220
$838$	1.02166e54	0.849749
$839$	8.80747e53	0.716564	0.358282	−	0.933613i	$-0.383363\pi$
$839$	8.80747e53	0.716564	0.358282	+	0.933613i	$0.383363\pi$
$840$	−1.50991e52	−0.0120167
$841$	9.63330e53	0.749979
$842$	−2.04997e54	−1.56126
$843$	9.63462e53	0.717835
$844$	−2.58618e53	−0.188506
$845$	7.67316e53	0.547174
$846$	8.27614e53	0.577399
$847$	8.82300e53	0.602245
$848$	4.31980e53	0.288497
$849$	−5.73480e53	−0.374736
$850$	1.77157e54	1.13268
$851$	−7.36769e53	−0.460929
$852$	−1.97104e53	−0.120660
$853$	5.96791e53	0.357491	0.178745	−	0.983895i	$-0.442796\pi$
$853$	5.96791e53	0.357491	0.178745	+	0.983895i	$0.442796\pi$
$854$	−2.86560e54	−1.67975
$855$	1.04967e53	0.0602116
$856$	−1.87825e52	−0.0105436
$857$	−5.15514e52	−0.0283202	−0.0141601	−	0.999900i	$-0.504507\pi$
$857$	−5.15514e52	−0.0283202	−0.0141601	+	0.999900i	$0.504507\pi$
$858$	9.61039e53	0.516685
$859$	−1.99312e53	−0.104872	−0.0524360	−	0.998624i	$-0.516699\pi$
$859$	−1.99312e53	−0.104872	−0.0524360	+	0.998624i	$0.516699\pi$
$860$	−8.90413e53	−0.458533
$861$	1.24398e54	0.626980
$862$	−5.04472e54	−2.48859
$863$	−1.31893e54	−0.636829	−0.318415	−	0.947952i	$-0.603150\pi$
$863$	−1.31893e54	−0.636829	−0.318415	+	0.947952i	$0.603150\pi$
$864$	5.65936e53	0.267463
$865$	−7.23685e53	−0.334774
$866$	−2.32979e54	−1.05496
$867$	1.52859e53	0.0677544
$868$	2.01674e54	0.875053
$869$	−3.86256e53	−0.164063
$870$	−9.41765e53	−0.391594
$871$	−3.30610e54	−1.34580
$872$	1.33295e52	0.00531200
$873$	2.53635e53	0.0989568
$874$	−1.89631e54	−0.724350
$875$	1.32354e54	0.494982
$876$	1.92865e54	0.706200
$877$	−1.88243e54	−0.674880	−0.337440	−	0.941347i	$-0.609561\pi$
$877$	−1.88243e54	−0.674880	−0.337440	+	0.941347i	$0.609561\pi$
$878$	5.78180e54	2.02962
$879$	−5.00660e53	−0.172087
$880$	−4.68275e53	−0.157606
$881$	1.05207e54	0.346728	0.173364	−	0.984858i	$-0.444536\pi$
$881$	1.05207e54	0.346728	0.173364	+	0.984858i	$0.444536\pi$
$882$	−6.89809e53	−0.222618
$883$	3.19393e54	1.00937	0.504687	−	0.863303i	$-0.331608\pi$
$883$	3.19393e54	1.00937	0.504687	+	0.863303i	$0.331608\pi$
$884$	4.51892e54	1.39852
$885$	−1.12462e54	−0.340842
$886$	7.42613e54	2.20414
$887$	−1.83622e54	−0.533751	−0.266875	−	0.963731i	$-0.585991\pi$
$887$	−1.83622e54	−0.533751	−0.266875	+	0.963731i	$0.585991\pi$
$888$	6.92959e52	0.0197273
$889$	2.94231e54	0.820362
$890$	−2.24474e54	−0.612988
$891$	1.69062e53	0.0452178
$892$	−1.89222e54	−0.495704
$893$	2.37832e54	0.610265
$894$	2.94082e54	0.739135
$895$	1.25512e54	0.309001
$896$	−4.68627e53	−0.113013
$897$	−4.07754e54	−0.963249
$898$	−4.91061e54	−1.13638
$899$	−7.49612e54	−1.69935
$900$	−1.22495e54	−0.272040
$901$	1.18299e54	0.257379
$902$	4.00498e54	0.853649
$903$	−2.63645e54	−0.550550
$904$	6.07403e53	0.124268
$905$	2.69865e54	0.540939
$906$	−4.03433e54	−0.792319
$907$	−8.28761e52	−0.0159476	−0.00797379	−	0.999968i	$-0.502538\pi$
$907$	−8.28761e52	−0.0159476	−0.00797379	+	0.999968i	$0.502538\pi$
$908$	−1.33213e54	−0.251164
$909$	−8.44083e53	−0.155938
$910$	3.22454e54	0.583717
$911$	4.90694e54	0.870404	0.435202	−	0.900333i	$-0.356677\pi$
$911$	4.90694e54	0.870404	0.435202	+	0.900333i	$0.356677\pi$
$912$	1.71809e54	0.298636
$913$	−2.07473e54	−0.353388
$914$	−5.92156e54	−0.988397
$915$	−2.16673e54	−0.354418
$916$	−1.02959e55	−1.65043
$917$	2.27091e54	0.356753
$918$	1.63728e54	0.252077
$919$	−4.20928e53	−0.0635142	−0.0317571	−	0.999496i	$-0.510110\pi$
$919$	−4.20928e53	−0.0635142	−0.0317571	+	0.999496i	$0.510110\pi$
$920$	2.06252e53	0.0305017
$921$	−1.17669e54	−0.170553
$922$	5.87600e54	0.834757
$923$	−2.50847e54	−0.349283
$924$	1.17271e54	0.160051
$925$	−2.81686e54	−0.376828
$926$	6.27736e54	0.823140
$927$	−2.22777e54	−0.286349
$928$	−1.45915e55	−1.83849
$929$	8.91667e54	1.10132	0.550658	−	0.834731i	$-0.314377\pi$
$929$	8.91667e54	1.10132	0.550658	+	0.834731i	$0.314377\pi$
$930$	3.14066e54	0.380265
$931$	−1.98231e54	−0.235289
$932$	4.41990e54	0.514302
$933$	7.88474e54	0.899450
$934$	2.26242e55	2.53021
$935$	−1.28239e54	−0.140606
$936$	3.83509e53	0.0412261
$937$	−4.22934e54	−0.445749	−0.222874	−	0.974847i	$-0.571544\pi$
$937$	−4.22934e54	−0.445749	−0.222874	+	0.974847i	$0.571544\pi$
$938$	−8.30897e54	−0.858607
$939$	−4.91621e54	−0.498101
$940$	4.34072e54	0.431218
$941$	−3.94717e54	−0.384484	−0.192242	−	0.981348i	$-0.561576\pi$
$941$	−3.94717e54	−0.384484	−0.192242	+	0.981348i	$0.561576\pi$
$942$	1.04471e55	0.997820
$943$	−1.69925e55	−1.59145
$944$	−1.84076e55	−1.69050
$945$	5.67249e53	0.0510840
$946$	−8.48806e54	−0.749588
$947$	1.89235e55	1.63881	0.819403	−	0.573218i	$-0.194305\pi$
$947$	1.89235e55	1.63881	0.819403	+	0.573218i	$0.194305\pi$
$948$	2.58650e54	0.219664
$949$	2.45452e55	2.04429
$950$	−7.25009e54	−0.592184
$951$	8.49074e54	0.680152
$952$	−6.76805e53	−0.0531716
$953$	−8.10408e54	−0.624432	−0.312216	−	0.950011i	$-0.601071\pi$
$953$	−8.10408e54	−0.624432	−0.312216	+	0.950011i	$0.601071\pi$
$954$	−1.68471e54	−0.127315
$955$	−7.40774e54	−0.549064
$956$	6.30194e54	0.458145
$957$	−4.35891e54	−0.310819
$958$	1.82089e55	1.27357
$959$	−8.49839e54	−0.583032
$960$	2.79081e54	0.187807
$961$	9.84956e54	0.650181
$962$	−1.47987e55	−0.958263
$963$	7.05628e53	0.0448218
$964$	1.51486e55	0.943947
$965$	−8.57787e54	−0.524354
$966$	−1.02478e55	−0.614544
$967$	5.03527e54	0.296233	0.148116	−	0.988970i	$-0.452679\pi$
$967$	5.03527e54	0.296233	0.148116	+	0.988970i	$0.452679\pi$
$968$	1.13355e54	0.0654252
$969$	4.70506e54	0.266425
$970$	2.73984e54	0.152212
$971$	3.61276e54	0.196917	0.0984585	−	0.995141i	$-0.468609\pi$
$971$	3.61276e54	0.196917	0.0984585	+	0.995141i	$0.468609\pi$
$972$	−1.13210e54	−0.0605421
$973$	−1.86343e55	−0.977746
$974$	−1.92516e55	−0.991120
$975$	−1.55895e55	−0.787493
$976$	−3.54649e55	−1.75783
$977$	3.31889e55	1.61415	0.807075	−	0.590449i	$-0.201049\pi$
$977$	3.31889e55	1.61415	0.807075	+	0.590449i	$0.201049\pi$
$978$	−2.21164e55	−1.05547
$979$	−1.03897e55	−0.486544
$980$	−3.61795e54	−0.166257
$981$	−5.00765e53	−0.0225818
$982$	3.54892e55	1.57048
$983$	−2.95416e55	−1.28290	−0.641451	−	0.767164i	$-0.721667\pi$
$983$	−2.95416e55	−1.28290	−0.641451	+	0.767164i	$0.721667\pi$
$984$	1.59821e54	0.0681123
$985$	−7.03334e54	−0.294165
$986$	−4.22137e55	−1.73273
$987$	1.28526e55	0.517754
$988$	−1.84936e55	−0.731168
$989$	3.60136e55	1.39745
$990$	1.82626e54	0.0695522
$991$	3.55938e55	1.33049	0.665245	−	0.746625i	$-0.268327\pi$
$991$	3.55938e55	1.33049	0.665245	+	0.746625i	$0.268327\pi$
$992$	4.86605e55	1.78530
$993$	2.52373e55	0.908827
$994$	−6.30435e54	−0.222839
$995$	1.36225e55	0.472641
$996$	1.38931e55	0.473152
$997$	9.42016e54	0.314918	0.157459	−	0.987526i	$-0.449670\pi$
$997$	9.42016e54	0.314918	0.157459	+	0.987526i	$0.449670\pi$
$998$	6.07605e55	1.99391
$999$	−2.60333e54	−0.0838624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.38.a.a.1.3	✓	3
3.2	odd	2		9.38.a.b.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.a.1.3	✓	3	1.1	even	1	trivial
9.38.a.b.1.1		3	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)

\(f(q)\)	\(=\)	\(q+516864. q^{2} -3.87420e8 q^{3} +1.29709e11 q^{4} +3.13693e12 q^{5} -2.00244e14 q^{6} -3.10972e15 q^{7} -3.99525e15 q^{8} +1.50095e17 q^{9} +O(q^{10})\)	\(q+516864. q^{2} -3.87420e8 q^{3} +1.29709e11 q^{4} +3.13693e12 q^{5} -2.00244e14 q^{6} -3.10972e15 q^{7} -3.99525e15 q^{8} +1.50095e17 q^{9} +1.62136e18 q^{10} +7.50440e18 q^{11} -5.02520e19 q^{12} -6.39538e20 q^{13} -1.60730e21 q^{14} -1.21531e21 q^{15} -1.98921e22 q^{16} -5.44751e22 q^{17} +7.75785e22 q^{18} +2.22938e23 q^{19} +4.06888e23 q^{20} +1.20477e24 q^{21} +3.87875e24 q^{22} -1.64570e25 q^{23} +1.54784e24 q^{24} -6.29193e25 q^{25} -3.30554e26 q^{26} -5.81497e25 q^{27} -4.03359e26 q^{28} +1.49927e27 q^{29} -6.28150e26 q^{30} -4.99985e27 q^{31} -9.73240e27 q^{32} -2.90736e27 q^{33} -2.81562e28 q^{34} -9.75497e27 q^{35} +1.94686e28 q^{36} +4.47694e28 q^{37} +1.15228e29 q^{38} +2.47770e29 q^{39} -1.25328e28 q^{40} +1.03254e30 q^{41} +6.22702e29 q^{42} -2.18835e30 q^{43} +9.73390e29 q^{44} +4.70836e29 q^{45} -8.50601e30 q^{46} +1.06681e31 q^{47} +7.70660e30 q^{48} -8.89176e30 q^{49} -3.25207e31 q^{50} +2.11048e31 q^{51} -8.29539e31 q^{52} -2.17162e31 q^{53} -3.00555e31 q^{54} +2.35408e31 q^{55} +1.24241e31 q^{56} -8.63707e31 q^{57} +7.74917e32 q^{58} +9.25373e32 q^{59} -1.57637e32 q^{60} +1.78286e33 q^{61} -2.58424e33 q^{62} -4.66752e32 q^{63} -2.29638e33 q^{64} -2.00618e33 q^{65} -1.50271e33 q^{66} +5.16951e33 q^{67} -7.06592e33 q^{68} +6.37577e33 q^{69} -5.04199e33 q^{70} +3.92232e33 q^{71} -5.99665e32 q^{72} -3.83796e34 q^{73} +2.31397e34 q^{74} +2.43762e34 q^{75} +2.89171e34 q^{76} -2.33366e34 q^{77} +1.28063e35 q^{78} -5.14706e34 q^{79} -6.24001e34 q^{80} +2.25284e34 q^{81} +5.33684e35 q^{82} -2.76468e35 q^{83} +1.56270e35 q^{84} -1.70885e35 q^{85} -1.13108e36 q^{86} -5.80847e35 q^{87} -2.99820e34 q^{88} -1.38448e36 q^{89} +2.43358e35 q^{90} +1.98878e36 q^{91} -2.13462e36 q^{92} +1.93704e36 q^{93} +5.51395e36 q^{94} +6.99340e35 q^{95} +3.77053e36 q^{96} +1.68983e36 q^{97} -4.59583e36 q^{98} +1.12637e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 45\!\cdots\!63 q^{9}+O(q^{10}) \) 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9	\( 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 34\!\cdots\!20 q^{99}+O(q^{100}) \) 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9 + 10698950136741797880 * q^10 + 22673303357139628620 * q^11 - 131132770215589974672 * q^12 - 168270000203795091510 * q^13 + 797101803583223694528 * q^14 + 3730362592143228440310 * q^15 + 32071173863897028608256 * q^16 - 27168549617785276146906 * q^17 - 46665622870919402711868 * q^18 + 582035599719143813745204 * q^19 - 4066256929972106412494880 * q^20 + 1790612692538373730632816 * q^21 - 4486408000290444592999152 * q^22 - 17157197763697459349569272 * q^23 + 36178839725894735603677632 * q^24 - 24896488591542260192608275 * q^25 - 618603181238074545425686344 * q^26 - 174449211009120179071170507 * q^27 - 2033429672978753784958610688 * q^28 + 111201150055901033185229778 * q^29 - 4144992493763124201408763320 * q^30 - 11859842025407507592851987736 * q^31 - 27281435223830339470718352384 * q^32 - 8784102273868376561238795180 * q^33 - 18783445175675019452330905464 * q^34 + 47739964986924083632994534880 * q^35 + 50803521960848503410923854608 * q^36 + 60344578140045347560278093666 * q^37 - 372452605565029151271789397776 * q^38 + 65191245762984394008603948390 * q^39 + 1732463594119923393272610326400 * q^40 + 2087364862188523841295969725934 * q^41 - 308813570526994475930424384192 * q^42 + 2483325896102099669944761791244 * q^43 + 4284309379683814482835899511872 * q^44 - 1445218899595437120383607511590 * q^45 - 4327236604482200607954371165856 * q^46 - 11791379189662012541191082473632 * q^47 - 12425029861155006269057528957184 * q^48 - 22445324860908932271245865545973 * q^49 - 96691457712658313260807892933700 * q^50 + 10525652778343134781834358357034 * q^51 + 43220201443333906987967057359584 * q^52 - 115357757368640109037215455345382 * q^53 + 18079218432141178878219826663452 * q^54 - 129419469300146958823045789059480 * q^55 + 630552391741804501615596905794560 * q^56 - 225492516658598958982491855084756 * q^57 + 580965936186746161132050423512088 * q^58 + 1091721381032593697748326986744236 * q^59 + 1575351248209432222688802119596320 * q^60 + 294380981976352085651508270601002 * q^61 + 248838835694853996733454208986592 * q^62 - 693720044952823401986519854167024 * q^63 - 1064135955800023765084313699610624 * q^64 - 7515875365146923444942971038019860 * q^65 + 1738126381326036186247137444425328 * q^66 + 3824374619785575741360273276519444 * q^67 - 21329399470876894544665401157365216 * q^68 + 6647049947481376149267749297614008 * q^69 - 43059062291480572688803543269144960 * q^70 - 22149353642418626281921550104284744 * q^71 - 14016423778058764430102498387802048 * q^72 + 32759279450923542889398870347665278 * q^73 + 46478870171568672595185044851456728 * q^74 + 9645409784518223707985532085946475 * q^75 + 347061692957154720144564653376455616 * q^76 - 61122141948697926808926153780754368 * q^77 + 239659546972210465807272116553102216 * q^78 + 74649348023552719727334936629819640 * q^79 - 618088038723375449595358546989335040 * q^80 + 67585198634817523235520443624317923 * q^81 + 103937675337495441364448738414881512 * q^82 - 317656267631459020909914460046822604 * q^83 + 787792318252538877979265797505586432 * q^84 + 210972517320554825185658741373302580 * q^85 - 2655243937093032975138251645354123760 * q^86 - 43081603932019555612226948170121442 * q^87 - 1353962196634819912991147659264835328 * q^88 - 1604427814888922862357874180114447026 * q^89 + 1605855018835039028277517574319663480 * q^90 + 459759011513895387754487414763335904 * q^91 - 5426885178857894678398508472745540224 * q^92 + 4594745796946127015893929993303122904 * q^93 + 15155501875748762861069416648677456000 * q^94 - 10713376656166940710475311057833316200 * q^95 + 10569386975038174570781705261883595776 * q^96 + 2690787195739502167683294096108844614 * q^97 - 1675640263817086437903041451354198300 * q^98 + 3403141198368098368991272474406443020 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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