LMFDB - Embedded newform 78.18.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,18,Mod(1,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("78.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	78.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:	$142.913228129$
Analytic rank:	$1$
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} - 13143327x^{2} + 23482672141x - 10722018405934 $ x^4 - x^3 - 13143327x^2 + 23482672141x - 10722018405934
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 53 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2086.69$ of defining polynomial
Character	$\chi$	$=$	78.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+256.000 q^{2} -6561.00 q^{3} +65536.0 q^{4} -805857. q^{5} -1.67962e6 q^{6} -4.19311e6 q^{7} +1.67772e7 q^{8} +4.30467e7 q^{9} +O(q^{10})$	\(q+256.000 q^{2} -6561.00 q^{3} +65536.0 q^{4} -805857. q^{5} -1.67962e6 q^{6} -4.19311e6 q^{7} +1.67772e7 q^{8} +4.30467e7 q^{9} -2.06299e8 q^{10} -7.67597e8 q^{11} -4.29982e8 q^{12} +8.15731e8 q^{13} -1.07344e9 q^{14} +5.28723e9 q^{15} +4.29497e9 q^{16} +4.06791e10 q^{17} +1.10200e10 q^{18} +7.46634e10 q^{19} -5.28127e10 q^{20} +2.75110e10 q^{21} -1.96505e11 q^{22} +1.02904e11 q^{23} -1.10075e11 q^{24} -1.13533e11 q^{25} +2.08827e11 q^{26} -2.82430e11 q^{27} -2.74799e11 q^{28} -1.74282e12 q^{29} +1.35353e12 q^{30} +4.67026e12 q^{31} +1.09951e12 q^{32} +5.03620e12 q^{33} +1.04139e13 q^{34} +3.37905e12 q^{35} +2.82111e12 q^{36} -2.46564e13 q^{37} +1.91138e13 q^{38} -5.35201e12 q^{39} -1.35200e13 q^{40} +7.63618e13 q^{41} +7.04281e12 q^{42} +5.20310e13 q^{43} -5.03052e13 q^{44} -3.46895e13 q^{45} +2.63433e13 q^{46} -9.94234e13 q^{47} -2.81793e13 q^{48} -2.15048e14 q^{49} -2.90645e13 q^{50} -2.66896e14 q^{51} +5.34597e13 q^{52} -1.08966e14 q^{53} -7.23020e13 q^{54} +6.18574e14 q^{55} -7.03487e13 q^{56} -4.89867e14 q^{57} -4.46162e14 q^{58} +9.18649e14 q^{59} +3.46504e14 q^{60} -2.78687e14 q^{61} +1.19559e15 q^{62} -1.80499e14 q^{63} +2.81475e14 q^{64} -6.57363e14 q^{65} +1.28927e15 q^{66} -6.43160e14 q^{67} +2.66595e15 q^{68} -6.75151e14 q^{69} +8.65036e14 q^{70} -8.67003e15 q^{71} +7.22204e14 q^{72} +5.62516e15 q^{73} -6.31205e15 q^{74} +7.44892e14 q^{75} +4.89314e15 q^{76} +3.21862e15 q^{77} -1.37011e15 q^{78} -6.45509e15 q^{79} -3.46113e15 q^{80} +1.85302e15 q^{81} +1.95486e16 q^{82} -5.26303e15 q^{83} +1.80296e15 q^{84} -3.27816e16 q^{85} +1.33199e16 q^{86} +1.14346e16 q^{87} -1.28781e16 q^{88} +1.67555e16 q^{89} -8.88052e15 q^{90} -3.42045e15 q^{91} +6.74389e15 q^{92} -3.06416e16 q^{93} -2.54524e16 q^{94} -6.01680e16 q^{95} -7.21390e15 q^{96} -8.27006e16 q^{97} -5.50524e16 q^{98} -3.30425e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1024 q^{2} - 26244 q^{3} + 262144 q^{4} - 518584 q^{5} - 6718464 q^{6} - 16826340 q^{7} + 67108864 q^{8} + 172186884 q^{9}+O(q^{10}) $ 4 * q + 1024 * q^2 - 26244 * q^3 + 262144 * q^4 - 518584 * q^5 - 6718464 * q^6 - 16826340 * q^7 + 67108864 * q^8 + 172186884 * q^9	\( 4 q + 1024 q^{2} - 26244 q^{3} + 262144 q^{4} - 518584 q^{5} - 6718464 q^{6} - 16826340 q^{7} + 67108864 q^{8} + 172186884 q^{9} - 132757504 q^{10} - 549884020 q^{11} - 1719926784 q^{12} + 3262922884 q^{13} - 4307543040 q^{14} + 3402429624 q^{15} + 17179869184 q^{16} - 16988107960 q^{17} + 44079842304 q^{18} - 10774690044 q^{19} - 33985921024 q^{20} + 110397616740 q^{21} - 140770309120 q^{22} - 261020574360 q^{23} - 440301256704 q^{24} + 348752894676 q^{25} + 835308258304 q^{26} - 1129718145924 q^{27} - 1102731018240 q^{28} + 5916347212968 q^{29} + 871021983744 q^{30} + 653877384884 q^{31} + 4398046511104 q^{32} + 3607789055220 q^{33} - 4348955637760 q^{34} + 22657981717760 q^{35} + 11284439629824 q^{36} + 22648713688872 q^{37} - 2758320651264 q^{38} - 21408037041924 q^{39} - 8700395782144 q^{40} + 16695856104776 q^{41} + 28261789885440 q^{42} - 131852373982632 q^{43} - 36037199134720 q^{44} - 22323340763064 q^{45} - 66821267036160 q^{46} - 392280969756004 q^{47} - 112717121716224 q^{48} - 320270218752756 q^{49} + 89280741037056 q^{50} + 111458976325560 q^{51} + 213838914125824 q^{52} - 74097065727976 q^{53} - 289207845356544 q^{54} - 663790840414456 q^{55} - 282299140669440 q^{56} + 70692741378684 q^{57} + 15\!\cdots\!08 q^{58}+ \cdots - 23\!\cdots\!20 q^{99}+O(q^{100}) \) 4 * q + 1024 * q^2 - 26244 * q^3 + 262144 * q^4 - 518584 * q^5 - 6718464 * q^6 - 16826340 * q^7 + 67108864 * q^8 + 172186884 * q^9 - 132757504 * q^10 - 549884020 * q^11 - 1719926784 * q^12 + 3262922884 * q^13 - 4307543040 * q^14 + 3402429624 * q^15 + 17179869184 * q^16 - 16988107960 * q^17 + 44079842304 * q^18 - 10774690044 * q^19 - 33985921024 * q^20 + 110397616740 * q^21 - 140770309120 * q^22 - 261020574360 * q^23 - 440301256704 * q^24 + 348752894676 * q^25 + 835308258304 * q^26 - 1129718145924 * q^27 - 1102731018240 * q^28 + 5916347212968 * q^29 + 871021983744 * q^30 + 653877384884 * q^31 + 4398046511104 * q^32 + 3607789055220 * q^33 - 4348955637760 * q^34 + 22657981717760 * q^35 + 11284439629824 * q^36 + 22648713688872 * q^37 - 2758320651264 * q^38 - 21408037041924 * q^39 - 8700395782144 * q^40 + 16695856104776 * q^41 + 28261789885440 * q^42 - 131852373982632 * q^43 - 36037199134720 * q^44 - 22323340763064 * q^45 - 66821267036160 * q^46 - 392280969756004 * q^47 - 112717121716224 * q^48 - 320270218752756 * q^49 + 89280741037056 * q^50 + 111458976325560 * q^51 + 213838914125824 * q^52 - 74097065727976 * q^53 - 289207845356544 * q^54 - 663790840414456 * q^55 - 282299140669440 * q^56 + 70692741378684 * q^57 + 1514584886519808 * q^58 + 972532690992940 * q^59 + 222981627838464 * q^60 + 4036496333495712 * q^61 + 167392610530304 * q^62 - 724318763431140 * q^63 + 1125899906842624 * q^64 - 423024900219064 * q^65 + 923593998136320 * q^66 + 3219563358634340 * q^67 - 1113332643266560 * q^68 + 1712555988375960 * q^69 + 5800443319746560 * q^70 - 5269779141375740 * q^71 + 2888816545234944 * q^72 + 1630484376609944 * q^73 + 5798070704351232 * q^74 - 2288167741969236 * q^75 - 706130086723584 * q^76 - 20097487159678912 * q^77 - 5480457482732544 * q^78 - 27965205092022016 * q^79 - 2227301320228864 * q^80 + 7412080755407364 * q^81 + 4274139162822656 * q^82 + 8598163018504788 * q^83 + 7235018210672640 * q^84 - 23034109274749936 * q^85 - 33754207739553792 * q^86 - 38817154064283048 * q^87 - 9225522978488320 * q^88 - 56353749364046152 * q^89 - 5714775235344384 * q^90 - 13725762459991140 * q^91 - 17106244361256960 * q^92 - 4290089522223924 * q^93 - 100423928257537024 * q^94 - 150775696530487936 * q^95 - 28855583159353344 * q^96 - 360024045001148952 * q^97 - 81989176000705536 * q^98 - 23670703991298420 * 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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	−6561.00	−0.577350
$3$	−6561.00	−0.577350
$4$	65536.0	0.500000
$5$	−805857.	−0.922599	−0.461300	−	0.887244i	$-0.652617\pi$
$5$	−805857.	−0.922599	−0.461300	+	0.887244i	$0.652617\pi$
$6$	−1.67962e6	−0.408248
$7$	−4.19311e6	−0.274918	−0.137459	−	0.990507i	$-0.543893\pi$
$7$	−4.19311e6	−0.274918	−0.137459	+	0.990507i	$0.543893\pi$
$8$	1.67772e7	0.353553
$9$	4.30467e7	0.333333
$10$	−2.06299e8	−0.652376
$11$	−7.67597e8	−1.07968	−0.539841	−	0.841767i	$-0.681515\pi$
$11$	−7.67597e8	−1.07968	−0.539841	+	0.841767i	$0.681515\pi$
$12$	−4.29982e8	−0.288675
$13$	8.15731e8	0.277350
$13$	8.15731e8	0.277350
$14$	−1.07344e9	−0.194396
$15$	5.28723e9	0.532663
$16$	4.29497e9	0.250000
$17$	4.06791e10	1.41435	0.707173	−	0.707040i	$-0.249970\pi$
$17$	4.06791e10	1.41435	0.707173	+	0.707040i	$0.249970\pi$
$18$	1.10200e10	0.235702
$19$	7.46634e10	1.00856	0.504280	−	0.863540i	$-0.331758\pi$
$19$	7.46634e10	1.00856	0.504280	+	0.863540i	$0.331758\pi$
$20$	−5.28127e10	−0.461300
$21$	2.75110e10	0.158724
$22$	−1.96505e11	−0.763450
$23$	1.02904e11	0.273996	0.136998	−	0.990571i	$-0.456255\pi$
$23$	1.02904e11	0.273996	0.136998	+	0.990571i	$0.456255\pi$
$24$	−1.10075e11	−0.204124
$25$	−1.13533e11	−0.148810
$26$	2.08827e11	0.196116
$27$	−2.82430e11	−0.192450
$28$	−2.74799e11	−0.137459
$29$	−1.74282e12	−0.646948	−0.323474	−	0.946237i	$-0.604851\pi$
$29$	−1.74282e12	−0.646948	−0.323474	+	0.946237i	$0.604851\pi$
$30$	1.35353e12	0.376650
$31$	4.67026e12	0.983483	0.491741	−	0.870741i	$-0.336361\pi$
$31$	4.67026e12	0.983483	0.491741	+	0.870741i	$0.336361\pi$
$32$	1.09951e12	0.176777
$33$	5.03620e12	0.623354
$34$	1.04139e13	1.00009
$35$	3.37905e12	0.253639
$36$	2.82111e12	0.166667
$37$	−2.46564e13	−1.15403	−0.577013	−	0.816735i	$-0.695782\pi$
$37$	−2.46564e13	−1.15403	−0.577013	+	0.816735i	$0.695782\pi$
$38$	1.91138e13	0.713160
$39$	−5.35201e12	−0.160128
$40$	−1.35200e13	−0.326188
$41$	7.63618e13	1.49353	0.746764	−	0.665089i	$-0.231606\pi$
$41$	7.63618e13	1.49353	0.746764	+	0.665089i	$0.231606\pi$
$42$	7.04281e12	0.112235
$43$	5.20310e13	0.678860	0.339430	−	0.940631i	$-0.389766\pi$
$43$	5.20310e13	0.678860	0.339430	+	0.940631i	$0.389766\pi$
$44$	−5.03052e13	−0.539841
$45$	−3.46895e13	−0.307533
$46$	2.63433e13	0.193744
$47$	−9.94234e13	−0.609056	−0.304528	−	0.952503i	$-0.598499\pi$
$47$	−9.94234e13	−0.609056	−0.304528	+	0.952503i	$0.598499\pi$
$48$	−2.81793e13	−0.144338
$49$	−2.15048e14	−0.924420
$50$	−2.90645e13	−0.105225
$51$	−2.66896e14	−0.816573
$52$	5.34597e13	0.138675
$53$	−1.08966e14	−0.240408	−0.120204	−	0.992749i	$-0.538355\pi$
$53$	−1.08966e14	−0.240408	−0.120204	+	0.992749i	$0.538355\pi$
$54$	−7.23020e13	−0.136083
$55$	6.18574e14	0.996113
$56$	−7.03487e13	−0.0971981
$57$	−4.89867e14	−0.582293
$58$	−4.46162e14	−0.457462
$59$	9.18649e14	0.814531	0.407265	−	0.913310i	$-0.366482\pi$
$59$	9.18649e14	0.814531	0.407265	+	0.913310i	$0.366482\pi$
$60$	3.46504e14	0.266332
$61$	−2.78687e14	−0.186128	−0.0930642	−	0.995660i	$-0.529666\pi$
$61$	−2.78687e14	−0.186128	−0.0930642	+	0.995660i	$0.529666\pi$
$62$	1.19559e15	0.695427
$63$	−1.80499e14	−0.0916392
$64$	2.81475e14	0.125000
$65$	−6.57363e14	−0.255883
$66$	1.28927e15	0.440778
$67$	−6.43160e14	−0.193501	−0.0967505	−	0.995309i	$-0.530845\pi$
$67$	−6.43160e14	−0.193501	−0.0967505	+	0.995309i	$0.530845\pi$
$68$	2.66595e15	0.707173
$69$	−6.75151e14	−0.158192
$70$	8.65036e14	0.179350
$71$	−8.67003e15	−1.59340	−0.796699	−	0.604376i	$-0.793423\pi$
$71$	−8.67003e15	−1.59340	−0.796699	+	0.604376i	$0.793423\pi$
$72$	7.22204e14	0.117851
$73$	5.62516e15	0.816376	0.408188	−	0.912898i	$-0.366161\pi$
$73$	5.62516e15	0.816376	0.408188	+	0.912898i	$0.366161\pi$
$74$	−6.31205e15	−0.816020
$75$	7.44892e14	0.0859157
$76$	4.89314e15	0.504280
$77$	3.21862e15	0.296823
$78$	−1.37011e15	−0.113228
$79$	−6.45509e15	−0.478710	−0.239355	−	0.970932i	$-0.576936\pi$
$79$	−6.45509e15	−0.478710	−0.239355	+	0.970932i	$0.576936\pi$
$80$	−3.46113e15	−0.230650
$81$	1.85302e15	0.111111
$82$	1.95486e16	1.05608
$83$	−5.26303e15	−0.256491	−0.128246	−	0.991742i	$-0.540935\pi$
$83$	−5.26303e15	−0.256491	−0.128246	+	0.991742i	$0.540935\pi$
$84$	1.80296e15	0.0793619
$85$	−3.27816e16	−1.30487
$86$	1.33199e16	0.480026
$87$	1.14346e16	0.373516
$88$	−1.28781e16	−0.381725
$89$	1.67555e16	0.451173	0.225586	−	0.974223i	$-0.427570\pi$
$89$	1.67555e16	0.451173	0.225586	+	0.974223i	$0.427570\pi$
$90$	−8.88052e15	−0.217459
$91$	−3.42045e15	−0.0762484
$92$	6.74389e15	0.136998
$93$	−3.06416e16	−0.567814
$94$	−2.54524e16	−0.430667
$95$	−6.01680e16	−0.930498
$96$	−7.21390e15	−0.102062
$97$	−8.27006e16	−1.07139	−0.535697	−	0.844410i	$-0.679951\pi$
$97$	−8.27006e16	−1.07139	−0.535697	+	0.844410i	$0.679951\pi$
$98$	−5.50524e16	−0.653664
$99$	−3.30425e16	−0.359894
$100$	−7.44052e15	−0.0744052
$101$	1.50491e17	1.38286	0.691429	−	0.722444i	$-0.256981\pi$
$101$	1.50491e17	1.38286	0.691429	+	0.722444i	$0.256981\pi$
$102$	−6.83253e16	−0.577404
$103$	−2.05013e17	−1.59465	−0.797325	−	0.603550i	$-0.793753\pi$
$103$	−2.05013e17	−1.59465	−0.797325	+	0.603550i	$0.793753\pi$
$104$	1.36857e16	0.0980581
$105$	−2.21699e16	−0.146438
$106$	−2.78954e16	−0.169994
$107$	−1.95456e17	−1.09973	−0.549865	−	0.835254i	$-0.685321\pi$
$107$	−1.95456e17	−1.09973	−0.549865	+	0.835254i	$0.685321\pi$
$108$	−1.85093e16	−0.0962250
$109$	−3.85353e17	−1.85239	−0.926197	−	0.377040i	$-0.876942\pi$
$109$	−3.85353e17	−1.85239	−0.926197	+	0.377040i	$0.876942\pi$
$110$	1.58355e17	0.704358
$111$	1.61771e17	0.666278
$112$	−1.80093e16	−0.0687294
$113$	6.33560e16	0.224193	0.112096	−	0.993697i	$-0.464243\pi$
$113$	6.33560e16	0.224193	0.112096	+	0.993697i	$0.464243\pi$
$114$	−1.25406e17	−0.411743
$115$	−8.29257e16	−0.252788
$116$	−1.14217e17	−0.323474
$117$	3.51145e16	0.0924500
$118$	2.35174e17	0.575960
$119$	−1.70572e17	−0.388829
$120$	8.87050e16	0.188325
$121$	8.37582e16	0.165711
$122$	−7.13438e16	−0.131613
$123$	−5.01010e17	−0.862289
$124$	3.06070e17	0.491741
$125$	7.06312e17	1.05989
$126$	−4.62079e16	−0.0647987
$127$	−8.20392e16	−0.107570	−0.0537848	−	0.998553i	$-0.517129\pi$
$127$	−8.20392e16	−0.107570	−0.0537848	+	0.998553i	$0.517129\pi$
$128$	7.20576e16	0.0883883
$129$	−3.41375e17	−0.391940
$130$	−1.68285e17	−0.180937
$131$	5.20040e17	0.523879	0.261940	−	0.965084i	$-0.415638\pi$
$131$	5.20040e17	0.523879	0.261940	+	0.965084i	$0.415638\pi$
$132$	3.30053e17	0.311677
$133$	−3.13072e17	−0.277271
$134$	−1.64649e17	−0.136826
$135$	2.27598e17	0.177554
$136$	6.82482e17	0.500047
$137$	2.34496e18	1.61440	0.807198	−	0.590280i	$-0.200983\pi$
$137$	2.34496e18	1.61440	0.807198	+	0.590280i	$0.200983\pi$
$138$	−1.72839e17	−0.111858
$139$	−6.40314e17	−0.389733	−0.194867	−	0.980830i	$-0.562427\pi$
$139$	−6.40314e17	−0.389733	−0.194867	+	0.980830i	$0.562427\pi$
$140$	2.21449e17	0.126819
$141$	6.52317e17	0.351638
$142$	−2.21953e18	−1.12670
$143$	−6.26152e17	−0.299450
$144$	1.84884e17	0.0833333
$145$	1.40446e18	0.596874
$146$	1.44004e18	0.577265
$147$	1.41093e18	0.533714
$148$	−1.61589e18	−0.577013
$149$	−5.67235e18	−1.91284	−0.956422	−	0.291987i	$-0.905684\pi$
$149$	−5.67235e18	−1.91284	−0.956422	+	0.291987i	$0.905684\pi$
$150$	1.90692e17	0.0607516
$151$	−1.02460e18	−0.308497	−0.154249	−	0.988032i	$-0.549296\pi$
$151$	−1.02460e18	−0.308497	−0.154249	+	0.988032i	$0.549296\pi$
$152$	1.25264e18	0.356580
$153$	1.75110e18	0.471449
$154$	8.23966e17	0.209886
$155$	−3.76357e18	−0.907361
$156$	−3.50749e17	−0.0800641
$157$	−1.61798e18	−0.349806	−0.174903	−	0.984586i	$-0.555961\pi$
$157$	−1.61798e18	−0.349806	−0.174903	+	0.984586i	$0.555961\pi$
$158$	−1.65250e18	−0.338499
$159$	7.14929e17	0.138799
$160$	−8.86050e17	−0.163094
$161$	−4.31486e17	−0.0753263
$162$	4.74373e17	0.0785674
$163$	−6.79263e18	−1.06769	−0.533843	−	0.845584i	$-0.679253\pi$
$163$	−6.79263e18	−1.06769	−0.533843	+	0.845584i	$0.679253\pi$
$164$	5.00445e18	0.746764
$165$	−4.05846e18	−0.575106
$166$	−1.34734e18	−0.181367
$167$	−1.26602e19	−1.61939	−0.809696	−	0.586849i	$-0.800368\pi$
$167$	−1.26602e19	−1.61939	−0.809696	+	0.586849i	$0.800368\pi$
$168$	4.61558e17	0.0561173
$169$	6.65417e17	0.0769231
$170$	−8.39208e18	−0.922686
$171$	3.21401e18	0.336187
$172$	3.40990e18	0.339430
$173$	−1.47094e19	−1.39381	−0.696904	−	0.717164i	$-0.745440\pi$
$173$	−1.47094e19	−1.39381	−0.696904	+	0.717164i	$0.745440\pi$
$174$	2.92727e18	0.264116
$175$	4.76057e17	0.0409106
$176$	−3.29680e18	−0.269920
$177$	−6.02726e18	−0.470270
$178$	4.28942e18	0.319027
$179$	3.94040e18	0.279441	0.139720	−	0.990191i	$-0.455380\pi$
$179$	3.94040e18	0.279441	0.139720	+	0.990191i	$0.455380\pi$
$180$	−2.27341e18	−0.153767
$181$	−8.05037e18	−0.519455	−0.259728	−	0.965682i	$-0.583633\pi$
$181$	−8.05037e18	−0.519455	−0.259728	+	0.965682i	$0.583633\pi$
$182$	−8.75634e17	−0.0539158
$183$	1.82846e18	0.107461
$184$	1.72644e18	0.0968722
$185$	1.98696e19	1.06470
$186$	−7.84425e18	−0.401505
$187$	−3.12252e19	−1.52704
$188$	−6.51581e18	−0.304528
$189$	1.18426e18	0.0529079
$190$	−1.54030e19	−0.657961
$191$	−2.39285e19	−0.977535	−0.488767	−	0.872414i	$-0.662553\pi$
$191$	−2.39285e19	−0.977535	−0.488767	+	0.872414i	$0.662553\pi$
$192$	−1.84676e18	−0.0721688
$193$	1.10048e19	0.411477	0.205738	−	0.978607i	$-0.434040\pi$
$193$	1.10048e19	0.411477	0.205738	+	0.978607i	$0.434040\pi$
$194$	−2.11714e19	−0.757590
$195$	4.31296e18	0.147734
$196$	−1.40934e19	−0.462210
$197$	−1.16260e19	−0.365148	−0.182574	−	0.983192i	$-0.558443\pi$
$197$	−1.16260e19	−0.365148	−0.182574	+	0.983192i	$0.558443\pi$
$198$	−8.45889e18	−0.254483
$199$	1.79803e19	0.518257	0.259129	−	0.965843i	$-0.416565\pi$
$199$	1.79803e19	0.518257	0.259129	+	0.965843i	$0.416565\pi$
$200$	−1.90477e18	−0.0526124
$201$	4.21977e18	0.111718
$202$	3.85256e19	0.977829
$203$	7.30783e18	0.177857
$204$	−1.74913e19	−0.408287
$205$	−6.15368e19	−1.37793
$206$	−5.24834e19	−1.12759
$207$	4.42966e18	0.0913320
$208$	3.50354e18	0.0693375
$209$	−5.73114e19	−1.08892
$210$	−5.67550e18	−0.103548
$211$	2.23706e19	0.391992	0.195996	−	0.980605i	$-0.437206\pi$
$211$	2.23706e19	0.391992	0.195996	+	0.980605i	$0.437206\pi$
$212$	−7.14123e18	−0.120204
$213$	5.68841e19	0.919949
$214$	−5.00366e19	−0.777626
$215$	−4.19296e19	−0.626316
$216$	−4.73838e18	−0.0680414
$217$	−1.95829e19	−0.270377
$218$	−9.86503e19	−1.30984
$219$	−3.69067e19	−0.471335
$220$	4.05389e19	0.498057
$221$	3.31832e19	0.392269
$222$	4.14134e19	0.471129
$223$	7.29878e19	0.799206	0.399603	−	0.916688i	$-0.369148\pi$
$223$	7.29878e19	0.799206	0.399603	+	0.916688i	$0.369148\pi$
$224$	−4.61037e18	−0.0485990
$225$	−4.88724e18	−0.0496034
$226$	1.62191e19	0.158528
$227$	−1.28127e20	−1.20621	−0.603103	−	0.797664i	$-0.706069\pi$
$227$	−1.28127e20	−1.20621	−0.603103	+	0.797664i	$0.706069\pi$
$228$	−3.21039e19	−0.291146
$229$	−1.36537e20	−1.19303	−0.596513	−	0.802604i	$-0.703447\pi$
$229$	−1.36537e20	−1.19303	−0.596513	+	0.802604i	$0.703447\pi$
$230$	−2.12290e19	−0.178748
$231$	−2.11173e19	−0.171371
$232$	−2.92397e19	−0.228731
$233$	−9.77395e19	−0.737131	−0.368566	−	0.929602i	$-0.620151\pi$
$233$	−9.77395e19	−0.737131	−0.368566	+	0.929602i	$0.620151\pi$
$234$	8.98932e18	0.0653720
$235$	8.01211e19	0.561914
$236$	6.02046e19	0.407265
$237$	4.23518e19	0.276383
$238$	−4.36664e19	−0.274943
$239$	2.27243e20	1.38073	0.690364	−	0.723462i	$-0.257450\pi$
$239$	2.27243e20	1.38073	0.690364	+	0.723462i	$0.257450\pi$
$240$	2.27085e19	0.133166
$241$	−1.74845e20	−0.989713	−0.494857	−	0.868975i	$-0.664779\pi$
$241$	−1.74845e20	−0.989713	−0.494857	+	0.868975i	$0.664779\pi$
$242$	2.14421e19	0.117175
$243$	−1.21577e19	−0.0641500
$244$	−1.82640e19	−0.0930642
$245$	1.73298e20	0.852870
$246$	−1.28259e20	−0.609731
$247$	6.09052e19	0.279724
$248$	7.83540e19	0.347714
$249$	3.45308e19	0.148085
$250$	1.80816e20	0.749457
$251$	9.00822e18	0.0360921	0.0180461	−	0.999837i	$-0.494255\pi$
$251$	9.00822e18	0.0360921	0.0180461	+	0.999837i	$0.494255\pi$
$252$	−1.18292e19	−0.0458196
$253$	−7.89885e19	−0.295828
$254$	−2.10020e19	−0.0760633
$255$	2.15080e20	0.753370
$256$	1.84467e19	0.0625000
$257$	1.87745e20	0.615371	0.307686	−	0.951488i	$-0.400446\pi$
$257$	1.87745e20	0.615371	0.307686	+	0.951488i	$0.400446\pi$
$258$	−8.73921e19	−0.277143
$259$	1.03387e20	0.317262
$260$	−4.30809e19	−0.127942
$261$	−7.50227e19	−0.215649
$262$	1.33130e20	0.370438
$263$	−7.95175e19	−0.214209	−0.107105	−	0.994248i	$-0.534158\pi$
$263$	−7.95175e19	−0.214209	−0.107105	+	0.994248i	$0.534158\pi$
$264$	8.44935e19	0.220389
$265$	8.78114e19	0.221800
$266$	−8.01463e19	−0.196060
$267$	−1.09933e20	−0.260485
$268$	−4.21501e19	−0.0967505
$269$	−8.20499e19	−0.182467	−0.0912334	−	0.995830i	$-0.529081\pi$
$269$	−8.20499e19	−0.182467	−0.0912334	+	0.995830i	$0.529081\pi$
$270$	5.82651e19	0.125550
$271$	5.01604e20	1.04742	0.523712	−	0.851896i	$-0.324547\pi$
$271$	5.01604e20	1.04742	0.523712	+	0.851896i	$0.324547\pi$
$272$	1.74715e20	0.353587
$273$	2.24415e19	0.0440221
$274$	6.00309e20	1.14155
$275$	8.71478e19	0.160668
$276$	−4.42467e19	−0.0790958
$277$	−2.96328e20	−0.513682	−0.256841	−	0.966454i	$-0.582682\pi$
$277$	−2.96328e20	−0.513682	−0.256841	+	0.966454i	$0.582682\pi$
$278$	−1.63920e20	−0.275583
$279$	2.01039e20	0.327828
$280$	5.66910e19	0.0896749
$281$	−4.44416e20	−0.682002	−0.341001	−	0.940063i	$-0.610766\pi$
$281$	−4.44416e20	−0.682002	−0.341001	+	0.940063i	$0.610766\pi$
$282$	1.66993e20	0.248646
$283$	1.16258e21	1.67973	0.839865	−	0.542796i	$-0.182634\pi$
$283$	1.16258e21	1.67973	0.839865	+	0.542796i	$0.182634\pi$
$284$	−5.68199e20	−0.796699
$285$	3.94763e20	0.537223
$286$	−1.60295e20	−0.211743
$287$	−3.20193e20	−0.410597
$288$	4.73304e19	0.0589256
$289$	8.27551e20	1.00038
$290$	3.59543e20	0.422054
$291$	5.42599e20	0.618569
$292$	3.68650e20	0.408188
$293$	1.24594e21	1.34005	0.670027	−	0.742336i	$-0.266282\pi$
$293$	1.24594e21	1.34005	0.670027	+	0.742336i	$0.266282\pi$
$294$	3.61199e20	0.377393
$295$	−7.40300e20	−0.751486
$296$	−4.13667e20	−0.408010
$297$	2.16792e20	0.207785
$298$	−1.45212e21	−1.35259
$299$	8.39417e19	0.0759928
$300$	4.88172e19	0.0429578
$301$	−2.18171e20	−0.186631
$302$	−2.62298e20	−0.218140
$303$	−9.87369e20	−0.798394
$304$	3.20677e20	0.252140
$305$	2.24582e20	0.171722
$306$	4.48282e20	0.333365
$307$	1.11058e21	0.803290	0.401645	−	0.915795i	$-0.368439\pi$
$307$	1.11058e21	0.803290	0.401645	+	0.915795i	$0.368439\pi$
$308$	2.10935e20	0.148412
$309$	1.34509e21	0.920672
$310$	−9.63473e20	−0.641601
$311$	−9.63223e20	−0.624113	−0.312057	−	0.950063i	$-0.601018\pi$
$311$	−9.63223e20	−0.624113	−0.312057	+	0.950063i	$0.601018\pi$
$312$	−8.97918e19	−0.0566139
$313$	8.08707e20	0.496208	0.248104	−	0.968733i	$-0.420192\pi$
$313$	8.08707e20	0.496208	0.248104	+	0.968733i	$0.420192\pi$
$314$	−4.14204e20	−0.247350
$315$	1.45457e20	0.0845463
$316$	−4.23041e20	−0.239355
$317$	8.64419e20	0.476124	0.238062	−	0.971250i	$-0.423488\pi$
$317$	8.64419e20	0.476124	0.238062	+	0.971250i	$0.423488\pi$
$318$	1.83022e20	0.0981460
$319$	1.33778e21	0.698498
$320$	−2.26829e20	−0.115325
$321$	1.28238e21	0.634929
$322$	−1.10460e20	−0.0532637
$323$	3.03724e21	1.42645
$324$	1.21440e20	0.0555556
$325$	−9.26126e19	−0.0412726
$326$	−1.73891e21	−0.754967
$327$	2.52830e21	1.06948
$328$	1.28114e21	0.528042
$329$	4.16893e20	0.167440
$330$	−1.03897e21	−0.406661
$331$	1.27575e21	0.486663	0.243332	−	0.969943i	$-0.421760\pi$
$331$	1.27575e21	0.486663	0.243332	+	0.969943i	$0.421760\pi$
$332$	−3.44918e20	−0.128246
$333$	−1.06138e21	−0.384676
$334$	−3.24102e21	−1.14508
$335$	5.18295e20	0.178524
$336$	1.18159e20	0.0396809
$337$	4.07274e21	1.33362	0.666811	−	0.745227i	$-0.267659\pi$
$337$	4.07274e21	1.33362	0.666811	+	0.745227i	$0.267659\pi$
$338$	1.70347e20	0.0543928
$339$	−4.15679e20	−0.129438
$340$	−2.14837e21	−0.652437
$341$	−3.58488e21	−1.06185
$342$	8.22788e20	0.237720
$343$	1.87717e21	0.529057
$344$	8.72935e20	0.240013
$345$	5.44075e20	0.145947
$346$	−3.76561e21	−0.985572
$347$	−3.94740e21	−1.00812	−0.504058	−	0.863670i	$-0.668160\pi$
$347$	−3.94740e21	−1.00812	−0.504058	+	0.863670i	$0.668160\pi$
$348$	7.49381e20	0.186758
$349$	−7.69003e21	−1.87030	−0.935151	−	0.354249i	$-0.884736\pi$
$349$	−7.69003e21	−1.87030	−0.935151	+	0.354249i	$0.884736\pi$
$350$	1.21871e20	0.0289282
$351$	−2.30386e20	−0.0533761
$352$	−8.43982e20	−0.190862
$353$	6.67263e20	0.147303	0.0736515	−	0.997284i	$-0.476535\pi$
$353$	6.67263e20	0.147303	0.0736515	+	0.997284i	$0.476535\pi$
$354$	−1.54298e21	−0.332531
$355$	6.98681e21	1.47007
$356$	1.09809e21	0.225586
$357$	1.11912e21	0.224490
$358$	1.00874e21	0.197594
$359$	6.85341e21	1.31100	0.655502	−	0.755194i	$-0.272457\pi$
$359$	6.85341e21	1.31100	0.655502	+	0.755194i	$0.272457\pi$
$360$	−5.81994e20	−0.108729
$361$	9.42353e19	0.0171950
$362$	−2.06090e21	−0.367310
$363$	−5.49537e20	−0.0956734
$364$	−2.24162e20	−0.0381242
$365$	−4.53308e21	−0.753188
$366$	4.68087e20	0.0759866
$367$	−4.89701e21	−0.776728	−0.388364	−	0.921506i	$-0.626960\pi$
$367$	−4.89701e21	−0.776728	−0.388364	+	0.921506i	$0.626960\pi$
$368$	4.41968e20	0.0684990
$369$	3.28713e21	0.497843
$370$	5.08661e21	0.752860
$371$	4.56908e20	0.0660923
$372$	−2.00813e21	−0.283907
$373$	−1.45779e21	−0.201451	−0.100726	−	0.994914i	$-0.532116\pi$
$373$	−1.45779e21	−0.201451	−0.100726	+	0.994914i	$0.532116\pi$
$374$	−7.99364e21	−1.07978
$375$	−4.63411e21	−0.611929
$376$	−1.66805e21	−0.215334
$377$	−1.42167e21	−0.179431
$378$	3.03170e20	0.0374115
$379$	−1.03983e22	−1.25466	−0.627332	−	0.778752i	$-0.715853\pi$
$379$	−1.03983e22	−1.25466	−0.627332	+	0.778752i	$0.715853\pi$
$380$	−3.94317e21	−0.465249
$381$	5.38259e20	0.0621054
$382$	−6.12570e21	−0.691221
$383$	5.28919e21	0.583713	0.291856	−	0.956462i	$-0.405727\pi$
$383$	5.28919e21	0.583713	0.291856	+	0.956462i	$0.405727\pi$
$384$	−4.72770e20	−0.0510310
$385$	−2.59375e21	−0.273849
$386$	2.81723e21	0.290958
$387$	2.23976e21	0.226287
$388$	−5.41987e21	−0.535697
$389$	7.13863e21	0.690308	0.345154	−	0.938546i	$-0.387827\pi$
$389$	7.13863e21	0.690308	0.345154	+	0.938546i	$0.387827\pi$
$390$	1.10412e21	0.104464
$391$	4.18603e21	0.387525
$392$	−3.60791e21	−0.326832
$393$	−3.41198e21	−0.302462
$394$	−2.97626e21	−0.258198
$395$	5.20188e21	0.441657
$396$	−2.16548e21	−0.179947
$397$	1.99489e22	1.62255	0.811277	−	0.584662i	$-0.198773\pi$
$397$	1.99489e22	1.62255	0.811277	+	0.584662i	$0.198773\pi$
$398$	4.60295e21	0.366463
$399$	2.05406e21	0.160083
$400$	−4.87622e20	−0.0372026
$401$	1.38267e22	1.03274	0.516370	−	0.856365i	$-0.327283\pi$
$401$	1.38267e22	1.03274	0.516370	+	0.856365i	$0.327283\pi$
$402$	1.08026e21	0.0789965
$403$	3.80968e21	0.272769
$404$	9.86256e21	0.691429
$405$	−1.49327e21	−0.102511
$406$	1.87080e21	0.125764
$407$	1.89262e22	1.24598
$408$	−4.47777e21	−0.288702
$409$	−3.67886e21	−0.232308	−0.116154	−	0.993231i	$-0.537057\pi$
$409$	−3.67886e21	−0.232308	−0.116154	+	0.993231i	$0.537057\pi$
$410$	−1.57534e22	−0.974343
$411$	−1.53853e22	−0.932072
$412$	−1.34358e22	−0.797325
$413$	−3.85199e21	−0.223929
$414$	1.13399e21	0.0645815
$415$	4.24125e21	0.236638
$416$	8.96905e20	0.0490290
$417$	4.20110e21	0.225013
$418$	−1.46717e22	−0.769986
$419$	−9.86443e21	−0.507286	−0.253643	−	0.967298i	$-0.581629\pi$
$419$	−9.86443e21	−0.507286	−0.253643	+	0.967298i	$0.581629\pi$
$420$	−1.45293e21	−0.0732192
$421$	−1.34405e22	−0.663772	−0.331886	−	0.943320i	$-0.607685\pi$
$421$	−1.34405e22	−0.663772	−0.331886	+	0.943320i	$0.607685\pi$
$422$	5.72688e21	0.277180
$423$	−4.27985e21	−0.203019
$424$	−1.82815e21	−0.0849969
$425$	−4.61843e21	−0.210469
$426$	1.45623e22	0.650502
$427$	1.16856e21	0.0511700
$428$	−1.28094e22	−0.549865
$429$	4.10819e21	0.172887
$430$	−1.07340e22	−0.442872
$431$	−6.77800e21	−0.274186	−0.137093	−	0.990558i	$-0.543776\pi$
$431$	−6.77800e21	−0.274186	−0.137093	+	0.990558i	$0.543776\pi$
$432$	−1.21303e21	−0.0481125
$433$	−2.54527e22	−0.989890	−0.494945	−	0.868924i	$-0.664812\pi$
$433$	−2.54527e22	−0.989890	−0.494945	+	0.868924i	$0.664812\pi$
$434$	−5.01322e21	−0.191185
$435$	−9.21469e21	−0.344605
$436$	−2.52545e22	−0.926197
$437$	7.68313e21	0.276342
$438$	−9.44811e21	−0.333284
$439$	−5.31922e22	−1.84034	−0.920172	−	0.391513i	$-0.871952\pi$
$439$	−5.31922e22	−1.84034	−0.920172	+	0.391513i	$0.871952\pi$
$440$	1.03779e22	0.352179
$441$	−9.25713e21	−0.308140
$442$	8.49490e21	0.277376
$443$	−2.65562e22	−0.850617	−0.425309	−	0.905048i	$-0.639834\pi$
$443$	−2.65562e22	−0.850617	−0.425309	+	0.905048i	$0.639834\pi$
$444$	1.06018e22	0.333139
$445$	−1.35026e22	−0.416252
$446$	1.86849e22	0.565124
$447$	3.72163e22	1.10438
$448$	−1.18025e21	−0.0343647
$449$	6.63996e22	1.89702	0.948509	−	0.316750i	$-0.102591\pi$
$449$	6.63996e22	1.89702	0.948509	+	0.316750i	$0.102591\pi$
$450$	−1.25113e21	−0.0350749
$451$	−5.86151e22	−1.61253
$452$	4.15210e21	0.112096
$453$	6.72242e21	0.178111
$454$	−3.28005e22	−0.852916
$455$	2.75639e21	0.0703468
$456$	−8.21860e21	−0.205872
$457$	7.51076e22	1.84670	0.923349	−	0.383961i	$-0.125440\pi$
$457$	7.51076e22	1.84670	0.923349	+	0.383961i	$0.125440\pi$
$458$	−3.49535e22	−0.843596
$459$	−1.14890e22	−0.272191
$460$	−5.43462e21	−0.126394
$461$	2.22823e22	0.508748	0.254374	−	0.967106i	$-0.418131\pi$
$461$	2.22823e22	0.508748	0.254374	+	0.967106i	$0.418131\pi$
$462$	−5.40604e21	−0.121178
$463$	−5.20096e22	−1.14458	−0.572288	−	0.820052i	$-0.693944\pi$
$463$	−5.20096e22	−1.14458	−0.572288	+	0.820052i	$0.693944\pi$
$464$	−7.48536e21	−0.161737
$465$	2.46928e22	0.523865
$466$	−2.50213e22	−0.521230
$467$	−4.02639e22	−0.823612	−0.411806	−	0.911271i	$-0.635102\pi$
$467$	−4.02639e22	−0.823612	−0.411806	+	0.911271i	$0.635102\pi$
$468$	2.30127e21	0.0462250
$469$	2.69684e21	0.0531969
$470$	2.05110e22	0.397333
$471$	1.06156e22	0.201961
$472$	1.54124e22	0.287980
$473$	−3.99388e22	−0.732952
$474$	1.08421e22	0.195432
$475$	−8.47678e21	−0.150084
$476$	−1.11786e22	−0.194414
$477$	−4.69065e21	−0.0801358
$478$	5.81742e22	0.976322
$479$	8.28768e22	1.36641	0.683205	−	0.730227i	$-0.260586\pi$
$479$	8.28768e22	1.36641	0.683205	+	0.730227i	$0.260586\pi$
$480$	5.81337e21	0.0941624
$481$	−2.01130e22	−0.320069
$482$	−4.47604e22	−0.699833
$483$	2.83098e21	0.0434897
$484$	5.48918e21	0.0828556
$485$	6.66449e22	0.988467
$486$	−3.11236e21	−0.0453609
$487$	−1.20478e22	−0.172549	−0.0862744	−	0.996271i	$-0.527496\pi$
$487$	−1.20478e22	−0.172549	−0.0862744	+	0.996271i	$0.527496\pi$
$488$	−4.67559e21	−0.0658063
$489$	4.45664e22	0.616428
$490$	4.43644e22	0.603070
$491$	−3.30788e22	−0.441934	−0.220967	−	0.975281i	$-0.570921\pi$
$491$	−3.30788e22	−0.441934	−0.220967	+	0.975281i	$0.570921\pi$
$492$	−3.28342e22	−0.431145
$493$	−7.08964e22	−0.915009
$494$	1.55917e22	0.197795
$495$	2.66276e22	0.332038
$496$	2.00586e22	0.245871
$497$	3.63544e22	0.438053
$498$	8.83987e21	0.104712
$499$	−1.05489e23	−1.22844	−0.614218	−	0.789137i	$-0.710528\pi$
$499$	−1.05489e23	−1.22844	−0.614218	+	0.789137i	$0.710528\pi$
$500$	4.62889e22	0.529946
$501$	8.30639e22	0.934957
$502$	2.30611e21	0.0255210
$503$	−9.96134e22	−1.08390	−0.541951	−	0.840410i	$-0.682314\pi$
$503$	−9.96134e22	−1.08390	−0.541951	+	0.840410i	$0.682314\pi$
$504$	−3.02828e21	−0.0323994
$505$	−1.21274e23	−1.27582
$506$	−2.02211e22	−0.209182
$507$	−4.36580e21	−0.0444116
$508$	−5.37652e21	−0.0537848
$509$	9.73878e22	0.958083	0.479042	−	0.877792i	$-0.340984\pi$
$509$	9.73878e22	0.958083	0.479042	+	0.877792i	$0.340984\pi$
$510$	5.50605e22	0.532713
$511$	−2.35869e22	−0.224436
$512$	4.72237e21	0.0441942
$513$	−2.10871e22	−0.194098
$514$	4.80627e22	0.435133
$515$	1.65211e23	1.47122
$516$	−2.23724e22	−0.195970
$517$	7.63171e22	0.657586
$518$	2.64671e22	0.224338
$519$	9.65084e22	0.804716
$520$	−1.10287e22	−0.0904683
$521$	6.69501e22	0.540295	0.270147	−	0.962819i	$-0.412928\pi$
$521$	6.69501e22	0.540295	0.270147	+	0.962819i	$0.412928\pi$
$522$	−1.92058e22	−0.152487
$523$	7.58425e22	0.592446	0.296223	−	0.955119i	$-0.404273\pi$
$523$	7.58425e22	0.592446	0.296223	+	0.955119i	$0.404273\pi$
$524$	3.40814e22	0.261940
$525$	−3.12341e21	−0.0236197
$526$	−2.03565e22	−0.151469
$527$	1.89982e23	1.39099
$528$	2.16303e22	0.155839
$529$	−1.30461e23	−0.924926
$530$	2.24797e22	0.156836
$531$	3.95448e22	0.271510
$532$	−2.05175e22	−0.138636
$533$	6.22907e22	0.414230
$534$	−2.81429e22	−0.184191
$535$	1.57509e23	1.01461
$536$	−1.07904e22	−0.0684130
$537$	−2.58530e22	−0.161335
$538$	−2.10048e22	−0.129023
$539$	1.65070e23	0.998079
$540$	1.49159e22	0.0887772
$541$	−9.87714e22	−0.578701	−0.289351	−	0.957223i	$-0.593439\pi$
$541$	−9.87714e22	−0.578701	−0.289351	+	0.957223i	$0.593439\pi$
$542$	1.28411e23	0.740640
$543$	5.28185e22	0.299908
$544$	4.47272e22	0.250023
$545$	3.10539e23	1.70902
$546$	5.74504e21	0.0311283
$547$	−1.34361e23	−0.716772	−0.358386	−	0.933573i	$-0.616673\pi$
$547$	−1.34361e23	−0.716772	−0.358386	+	0.933573i	$0.616673\pi$
$548$	1.53679e23	0.807198
$549$	−1.19965e22	−0.0620428
$550$	2.23098e22	0.113609
$551$	−1.30125e23	−0.652487
$552$	−1.13271e22	−0.0559292
$553$	2.70669e22	0.131606
$554$	−7.58598e22	−0.363228
$555$	−1.30364e23	−0.614707
$556$	−4.19636e22	−0.194867
$557$	1.43927e23	0.658225	0.329112	−	0.944291i	$-0.393251\pi$
$557$	1.43927e23	0.658225	0.329112	+	0.944291i	$0.393251\pi$
$558$	5.14661e22	0.231809
$559$	4.24433e22	0.188282
$560$	1.45129e22	0.0634097
$561$	2.04868e23	0.881639
$562$	−1.13770e23	−0.482248
$563$	−7.46677e22	−0.311754	−0.155877	−	0.987776i	$-0.549820\pi$
$563$	−7.46677e22	−0.311754	−0.155877	+	0.987776i	$0.549820\pi$
$564$	4.27503e22	0.175819
$565$	−5.10559e22	−0.206840
$566$	2.97621e23	1.18775
$567$	−7.76991e21	−0.0305464
$568$	−1.45459e23	−0.563352
$569$	1.01403e22	0.0386899	0.0193450	−	0.999813i	$-0.493842\pi$
$569$	1.01403e22	0.0386899	0.0193450	+	0.999813i	$0.493842\pi$
$570$	1.01059e23	0.379874
$571$	−4.12498e23	−1.52762	−0.763810	−	0.645441i	$-0.776674\pi$
$571$	−4.12498e23	−1.52762	−0.763810	+	0.645441i	$0.776674\pi$
$572$	−4.10355e22	−0.149725
$573$	1.56995e23	0.564380
$574$	−8.19695e22	−0.290336
$575$	−1.16830e22	−0.0407734
$576$	1.21166e22	0.0416667
$577$	3.23466e23	1.09606	0.548030	−	0.836459i	$-0.315378\pi$
$577$	3.23466e23	1.09606	0.548030	+	0.836459i	$0.315378\pi$
$578$	2.11853e23	0.707372
$579$	−7.22026e22	−0.237566
$580$	9.20430e22	0.298437
$581$	2.20685e22	0.0705139
$582$	1.38905e23	0.437395
$583$	8.36423e22	0.259563
$584$	9.43745e22	0.288633
$585$	−2.82973e22	−0.0852943
$586$	3.18961e23	0.947562
$587$	−5.75912e23	−1.68629	−0.843144	−	0.537687i	$-0.819298\pi$
$587$	−5.75912e23	−1.68629	−0.843144	+	0.537687i	$0.819298\pi$
$588$	9.24669e22	0.266857
$589$	3.48698e23	0.991902
$590$	−1.89517e23	−0.531381
$591$	7.62784e22	0.210818
$592$	−1.05899e23	−0.288507
$593$	−6.38225e23	−1.71399	−0.856996	−	0.515323i	$-0.827672\pi$
$593$	−6.38225e23	−1.71399	−0.856996	+	0.515323i	$0.827672\pi$
$594$	5.54988e22	0.146926
$595$	1.37457e23	0.358733
$596$	−3.71743e23	−0.956422
$597$	−1.17969e23	−0.299216
$598$	2.14891e22	0.0537350
$599$	−3.25286e23	−0.801931	−0.400966	−	0.916093i	$-0.631325\pi$
$599$	−3.25286e23	−0.801931	−0.400966	+	0.916093i	$0.631325\pi$
$600$	1.24972e22	0.0303758
$601$	−5.18841e23	−1.24337	−0.621687	−	0.783266i	$-0.713552\pi$
$601$	−5.18841e23	−1.24337	−0.621687	+	0.783266i	$0.713552\pi$
$602$	−5.58519e22	−0.131968
$603$	−2.76859e22	−0.0645004
$604$	−6.71483e22	−0.154249
$605$	−6.74972e22	−0.152885
$606$	−2.52767e23	−0.564550
$607$	−5.83325e23	−1.28472	−0.642358	−	0.766405i	$-0.722044\pi$
$607$	−5.83325e23	−1.28472	−0.642358	+	0.766405i	$0.722044\pi$
$608$	8.20933e22	0.178290
$609$	−4.79467e22	−0.102686
$610$	5.74929e22	0.121426
$611$	−8.11027e22	−0.168922
$612$	1.14760e23	0.235724
$613$	−5.92275e23	−1.19980	−0.599901	−	0.800074i	$-0.704793\pi$
$613$	−5.92275e23	−1.19980	−0.599901	+	0.800074i	$0.704793\pi$
$614$	2.84308e23	0.568012
$615$	4.03743e23	0.795548
$616$	5.39994e22	0.104943
$617$	−3.96688e23	−0.760370	−0.380185	−	0.924910i	$-0.624140\pi$
$617$	−3.96688e23	−0.760370	−0.380185	+	0.924910i	$0.624140\pi$
$618$	3.44344e23	0.651013
$619$	−7.80720e23	−1.45588	−0.727938	−	0.685643i	$-0.759521\pi$
$619$	−7.80720e23	−1.45588	−0.727938	+	0.685643i	$0.759521\pi$
$620$	−2.46649e23	−0.453680
$621$	−2.90630e22	−0.0527305
$622$	−2.46585e23	−0.441315
$623$	−7.02577e22	−0.124035
$624$	−2.29867e22	−0.0400320
$625$	−4.82568e23	−0.829045
$626$	2.07029e23	0.350872
$627$	3.76020e23	0.628691
$628$	−1.06036e23	−0.174903
$629$	−1.00300e24	−1.63219
$630$	3.72370e22	0.0597832
$631$	−1.01156e24	−1.60230	−0.801150	−	0.598464i	$-0.795778\pi$
$631$	−1.01156e24	−1.60230	−0.801150	+	0.598464i	$0.795778\pi$
$632$	−1.08298e23	−0.169249
$633$	−1.46774e23	−0.226317
$634$	2.21291e23	0.336671
$635$	6.61119e22	0.0992437
$636$	4.68536e22	0.0693997
$637$	−1.75422e23	−0.256388
$638$	3.42473e23	0.493913
$639$	−3.73216e23	−0.531133
$640$	−5.80681e22	−0.0815470
$641$	−1.13909e24	−1.57858	−0.789288	−	0.614023i	$-0.789550\pi$
$641$	−1.13909e24	−1.57858	−0.789288	+	0.614023i	$0.789550\pi$
$642$	3.28290e23	0.448963
$643$	4.64387e23	0.626740	0.313370	−	0.949631i	$-0.398542\pi$
$643$	4.64387e23	0.626740	0.313370	+	0.949631i	$0.398542\pi$
$644$	−2.82779e22	−0.0376632
$645$	2.75100e23	0.361604
$646$	7.77534e23	1.00866
$647$	7.13509e23	0.913509	0.456755	−	0.889593i	$-0.349012\pi$
$647$	7.13509e23	0.913509	0.456755	+	0.889593i	$0.349012\pi$
$648$	3.10885e22	0.0392837
$649$	−7.05152e23	−0.879433
$650$	−2.37088e22	−0.0291841
$651$	1.28483e23	0.156102
$652$	−4.45162e23	−0.533843
$653$	2.93959e23	0.347957	0.173978	−	0.984749i	$-0.444338\pi$
$653$	2.93959e23	0.347957	0.173978	+	0.984749i	$0.444338\pi$
$654$	6.47245e23	0.756237
$655$	−4.19078e23	−0.483330
$656$	3.27972e23	0.373382
$657$	2.42145e23	0.272125
$658$	1.06725e23	0.118398
$659$	1.23083e24	1.34794	0.673972	−	0.738757i	$-0.264587\pi$
$659$	1.23083e24	1.34794	0.673972	+	0.738757i	$0.264587\pi$
$660$	−2.65975e23	−0.287553
$661$	7.10384e23	0.758194	0.379097	−	0.925357i	$-0.376235\pi$
$661$	7.10384e23	0.758194	0.379097	+	0.925357i	$0.376235\pi$
$662$	3.26593e23	0.344123
$663$	−2.17715e23	−0.226477
$664$	−8.82990e22	−0.0906833
$665$	2.52291e23	0.255810
$666$	−2.71713e23	−0.272007
$667$	−1.79343e23	−0.177261
$668$	−8.29702e23	−0.809696
$669$	−4.78873e23	−0.461422
$670$	1.32684e23	0.126236
$671$	2.13919e23	0.200959
$672$	3.02486e22	0.0280587
$673$	1.27064e23	0.116384	0.0581922	−	0.998305i	$-0.481466\pi$
$673$	1.27064e23	0.116384	0.0581922	+	0.998305i	$0.481466\pi$
$674$	1.04262e24	0.943013
$675$	3.20652e22	0.0286386
$676$	4.36087e22	0.0384615
$677$	−7.04127e22	−0.0613263	−0.0306632	−	0.999530i	$-0.509762\pi$
$677$	−7.04127e22	−0.0613263	−0.0306632	+	0.999530i	$0.509762\pi$
$678$	−1.06414e23	−0.0915262
$679$	3.46773e23	0.294545
$680$	−5.49984e23	−0.461343
$681$	8.40642e23	0.696403
$682$	−9.17729e23	−0.750840
$683$	−2.08331e23	−0.168337	−0.0841683	−	0.996452i	$-0.526823\pi$
$683$	−2.08331e23	−0.168337	−0.0841683	+	0.996452i	$0.526823\pi$
$684$	2.10634e23	0.168093
$685$	−1.88970e24	−1.48944
$686$	4.80554e23	0.374100
$687$	8.95821e23	0.688793
$688$	2.23471e23	0.169715
$689$	−8.88873e22	−0.0666770
$690$	1.39283e23	0.103200
$691$	−2.58886e23	−0.189472	−0.0947361	−	0.995502i	$-0.530201\pi$
$691$	−2.58886e23	−0.189472	−0.0947361	+	0.995502i	$0.530201\pi$
$692$	−9.63996e23	−0.696904
$693$	1.38551e23	0.0989411
$694$	−1.01054e24	−0.712846
$695$	5.16002e23	0.359568
$696$	1.91841e23	0.132058
$697$	3.10633e24	2.11237
$698$	−1.96865e24	−1.32250
$699$	6.41269e23	0.425583
$700$	3.11989e22	0.0204553
$701$	−1.39628e24	−0.904420	−0.452210	−	0.891912i	$-0.649364\pi$
$701$	−1.39628e24	−0.904420	−0.452210	+	0.891912i	$0.649364\pi$
$702$	−5.89789e22	−0.0377426
$703$	−1.84093e24	−1.16391
$704$	−2.16059e23	−0.134960
$705$	−5.25675e23	−0.324421
$706$	1.70819e23	0.104159
$707$	−6.31023e23	−0.380172
$708$	−3.95002e23	−0.235135
$709$	−7.66376e23	−0.450764	−0.225382	−	0.974271i	$-0.572363\pi$
$709$	−7.66376e23	−0.450764	−0.225382	+	0.974271i	$0.572363\pi$
$710$	1.78862e24	1.03950
$711$	−2.77870e23	−0.159570
$712$	2.81111e23	0.159514
$713$	4.80587e23	0.269470
$714$	2.86495e23	0.158739
$715$	5.04590e23	0.276272
$716$	2.58238e23	0.139720
$717$	−1.49094e24	−0.797163
$718$	1.75447e24	0.927019
$719$	4.98613e23	0.260356	0.130178	−	0.991491i	$-0.458445\pi$
$719$	4.98613e23	0.260356	0.130178	+	0.991491i	$0.458445\pi$
$720$	−1.48990e23	−0.0768833
$721$	8.59643e23	0.438398
$722$	2.41242e22	0.0121587
$723$	1.14716e24	0.571411
$724$	−5.27589e23	−0.259728
$725$	1.97868e23	0.0962726
$726$	−1.40682e23	−0.0676513
$727$	−2.07358e24	−0.985549	−0.492774	−	0.870157i	$-0.664017\pi$
$727$	−2.07358e24	−0.985549	−0.492774	+	0.870157i	$0.664017\pi$
$728$	−5.73856e22	−0.0269579
$729$	7.97664e22	0.0370370
$730$	−1.16047e24	−0.532585
$731$	2.11657e24	0.960143
$732$	1.19830e23	0.0537306
$733$	−1.95493e24	−0.866460	−0.433230	−	0.901284i	$-0.642626\pi$
$733$	−1.95493e24	−0.866460	−0.433230	+	0.901284i	$0.642626\pi$
$734$	−1.25363e24	−0.549230
$735$	−1.13701e24	−0.492405
$736$	1.13144e23	0.0484361
$737$	4.93688e23	0.208919
$738$	8.41505e23	0.352028
$739$	−2.34288e24	−0.968883	−0.484442	−	0.874824i	$-0.660977\pi$
$739$	−2.34288e24	−0.968883	−0.484442	+	0.874824i	$0.660977\pi$
$740$	1.30217e24	0.532352
$741$	−3.99599e23	−0.161499
$742$	1.16968e23	0.0467343
$743$	3.80398e24	1.50256	0.751282	−	0.659981i	$-0.229436\pi$
$743$	3.80398e24	1.50256	0.751282	+	0.659981i	$0.229436\pi$
$744$	−5.14081e23	−0.200753
$745$	4.57110e24	1.76479
$746$	−3.73195e23	−0.142448
$747$	−2.26556e23	−0.0854970
$748$	−2.04637e24	−0.763521
$749$	8.19566e23	0.302335
$750$	−1.18633e24	−0.432699
$751$	1.01222e24	0.365037	0.182518	−	0.983202i	$-0.441575\pi$
$751$	1.01222e24	0.365037	0.182518	+	0.983202i	$0.441575\pi$
$752$	−4.27020e23	−0.152264
$753$	−5.91030e22	−0.0208378
$754$	−3.63948e23	−0.126877
$755$	8.25683e23	0.284619
$756$	7.76115e22	0.0264540
$757$	3.85347e24	1.29878	0.649392	−	0.760454i	$-0.275024\pi$
$757$	3.85347e24	1.29878	0.649392	+	0.760454i	$0.275024\pi$
$758$	−2.66196e24	−0.887182
$759$	5.18244e23	0.170796
$760$	−1.00945e24	−0.328981
$761$	5.70131e24	1.83741	0.918703	−	0.394950i	$-0.129238\pi$
$761$	5.70131e24	1.83741	0.918703	+	0.394950i	$0.129238\pi$
$762$	1.37794e23	0.0439151
$763$	1.61583e24	0.509256
$764$	−1.56818e24	−0.488767
$765$	−1.41114e24	−0.434958
$766$	1.35403e24	0.412747
$767$	7.49370e23	0.225910
$768$	−1.21029e23	−0.0360844
$769$	−5.23985e24	−1.54506	−0.772530	−	0.634978i	$-0.781009\pi$
$769$	−5.23985e24	−1.54506	−0.772530	+	0.634978i	$0.781009\pi$
$770$	−6.63999e23	−0.193641
$771$	−1.23180e24	−0.355285
$772$	7.21211e23	0.205738
$773$	1.33988e24	0.378043	0.189022	−	0.981973i	$-0.439468\pi$
$773$	1.33988e24	0.378043	0.189022	+	0.981973i	$0.439468\pi$
$774$	5.73379e23	0.160009
$775$	−5.30230e23	−0.146352
$776$	−1.38749e24	−0.378795
$777$	−6.78323e23	−0.183171
$778$	1.82749e24	0.488122
$779$	5.70143e24	1.50631
$780$	2.82654e23	0.0738671
$781$	6.65509e24	1.72036
$782$	1.07162e24	0.274022
$783$	4.92224e23	0.124505
$784$	−9.23626e23	−0.231105
$785$	1.30386e24	0.322731
$786$	−8.73468e23	−0.213873
$787$	2.33567e23	0.0565752	0.0282876	−	0.999600i	$-0.490995\pi$
$787$	2.33567e23	0.0565752	0.0282876	+	0.999600i	$0.490995\pi$
$788$	−7.61923e23	−0.182574
$789$	5.21714e23	0.123674
$790$	1.33168e24	0.312299
$791$	−2.65659e23	−0.0616345
$792$	−5.54362e23	−0.127242
$793$	−2.27333e23	−0.0516227
$794$	5.10691e24	1.14732
$795$	−5.76131e23	−0.128056
$796$	1.17836e24	0.259129
$797$	−3.16410e24	−0.688422	−0.344211	−	0.938892i	$-0.611854\pi$
$797$	−3.16410e24	−0.688422	−0.344211	+	0.938892i	$0.611854\pi$
$798$	5.25840e23	0.113195
$799$	−4.04446e24	−0.861415
$800$	−1.24831e23	−0.0263062
$801$	7.21271e23	0.150391
$802$	3.53964e24	0.730258
$803$	−4.31786e24	−0.881426
$804$	2.76547e23	0.0558589
$805$	3.47716e23	0.0694960
$806$	9.75277e23	0.192877
$807$	5.38329e23	0.105347
$808$	2.52481e24	0.488914
$809$	9.13565e24	1.75056	0.875280	−	0.483616i	$-0.160677\pi$
$809$	9.13565e24	1.75056	0.875280	+	0.483616i	$0.160677\pi$
$810$	−3.82277e23	−0.0724863
$811$	9.94095e23	0.186531	0.0932654	−	0.995641i	$-0.470270\pi$
$811$	9.94095e23	0.186531	0.0932654	+	0.995641i	$0.470270\pi$
$812$	4.78926e23	0.0889287
$813$	−3.29103e24	−0.604730
$814$	4.84511e24	0.881041
$815$	5.47389e24	0.985046
$816$	−1.14631e24	−0.204143
$817$	3.88481e24	0.684671
$818$	−9.41788e23	−0.164267
$819$	−1.47239e23	−0.0254161
$820$	−4.03287e24	−0.688964
$821$	−9.67652e24	−1.63607	−0.818036	−	0.575167i	$-0.804937\pi$
$821$	−9.67652e24	−1.63607	−0.818036	+	0.575167i	$0.804937\pi$
$822$	−3.93863e24	−0.659075
$823$	1.00831e24	0.166992	0.0834961	−	0.996508i	$-0.473391\pi$
$823$	1.00831e24	0.166992	0.0834961	+	0.996508i	$0.473391\pi$
$824$	−3.43955e24	−0.563794
$825$	−5.71777e23	−0.0927615
$826$	−9.86110e23	−0.158342
$827$	2.72386e24	0.432900	0.216450	−	0.976294i	$-0.430552\pi$
$827$	2.72386e24	0.432900	0.216450	+	0.976294i	$0.430552\pi$
$828$	2.90302e23	0.0456660
$829$	5.81792e22	0.00905845	0.00452923	−	0.999990i	$-0.498558\pi$
$829$	5.81792e22	0.00905845	0.00452923	+	0.999990i	$0.498558\pi$
$830$	1.08576e24	0.167329
$831$	1.94420e24	0.296574
$832$	2.29608e23	0.0346688
$833$	−8.74798e24	−1.30745
$834$	1.07548e24	0.159108
$835$	1.02024e25	1.49405
$836$	−3.75596e24	−0.544462
$837$	−1.31902e24	−0.189271
$838$	−2.52529e24	−0.358705
$839$	−6.40205e24	−0.900207	−0.450103	−	0.892976i	$-0.648613\pi$
$839$	−6.40205e24	−0.900207	−0.450103	+	0.892976i	$0.648613\pi$
$840$	−3.71950e23	−0.0517738
$841$	−4.21973e24	−0.581458
$842$	−3.44078e24	−0.469358
$843$	2.91581e24	0.393754
$844$	1.46608e24	0.195996
$845$	−5.36231e23	−0.0709692
$846$	−1.09564e24	−0.143556
$847$	−3.51207e23	−0.0455569
$848$	−4.68007e23	−0.0601019
$849$	−7.62771e24	−0.969792
$850$	−1.18232e24	−0.148824
$851$	−2.53724e24	−0.316199
$852$	3.72795e24	0.459975
$853$	−3.94833e24	−0.482333	−0.241166	−	0.970484i	$-0.577530\pi$
$853$	−3.94833e24	−0.482333	−0.241166	+	0.970484i	$0.577530\pi$
$854$	2.99152e23	0.0361826
$855$	−2.59004e24	−0.310166
$856$	−3.27920e24	−0.388813
$857$	7.75174e24	0.910043	0.455022	−	0.890480i	$-0.349631\pi$
$857$	7.75174e24	0.910043	0.455022	+	0.890480i	$0.349631\pi$
$858$	1.05170e24	0.122250
$859$	1.62583e25	1.87126	0.935631	−	0.352981i	$-0.114832\pi$
$859$	1.62583e25	1.87126	0.935631	+	0.352981i	$0.114832\pi$
$860$	−2.74789e24	−0.313158
$861$	2.10079e24	0.237059
$862$	−1.73517e24	−0.193879
$863$	2.28981e23	0.0253343	0.0126671	−	0.999920i	$-0.495968\pi$
$863$	2.28981e23	0.0253343	0.0126671	+	0.999920i	$0.495968\pi$
$864$	−3.10535e23	−0.0340207
$865$	1.18537e25	1.28593
$866$	−6.51589e24	−0.699958
$867$	−5.42956e24	−0.577567
$868$	−1.28339e24	−0.135188
$869$	4.95491e24	0.516854
$870$	−2.35896e24	−0.243673
$871$	−5.24646e23	−0.0536675
$872$	−6.46515e24	−0.654920
$873$	−3.55999e24	−0.357131
$874$	1.96688e24	0.195403
$875$	−2.96164e24	−0.291383
$876$	−2.41872e24	−0.235668
$877$	1.61333e25	1.55678	0.778391	−	0.627779i	$-0.216036\pi$
$877$	1.61333e25	1.55678	0.778391	+	0.627779i	$0.216036\pi$
$878$	−1.36172e25	−1.30132
$879$	−8.17461e24	−0.773681
$880$	2.65675e24	0.249028
$881$	9.25013e24	0.858722	0.429361	−	0.903133i	$-0.358739\pi$
$881$	9.25013e24	0.858722	0.429361	+	0.903133i	$0.358739\pi$
$882$	−2.36982e24	−0.217888
$883$	2.86370e23	0.0260772	0.0130386	−	0.999915i	$-0.495850\pi$
$883$	2.86370e23	0.0260772	0.0130386	+	0.999915i	$0.495850\pi$
$884$	2.17469e24	0.196135
$885$	4.85711e24	0.433870
$886$	−6.79839e24	−0.601477
$887$	1.07711e25	0.943864	0.471932	−	0.881635i	$-0.343557\pi$
$887$	1.07711e25	0.943864	0.471932	+	0.881635i	$0.343557\pi$
$888$	2.71407e24	0.235565
$889$	3.43999e23	0.0295728
$890$	−3.45666e24	−0.294335
$891$	−1.42237e24	−0.119965
$892$	4.78333e24	0.399603
$893$	−7.42329e24	−0.614270
$894$	9.52737e24	0.780915
$895$	−3.17540e24	−0.257812
$896$	−3.02145e23	−0.0242995
$897$	−5.50741e23	−0.0438745
$898$	1.69983e25	1.34139
$899$	−8.13943e24	−0.636263
$900$	−3.20290e23	−0.0248017
$901$	−4.43266e24	−0.340019
$902$	−1.50055e25	−1.14023
$903$	1.43142e24	0.107751
$904$	1.06294e24	0.0792640
$905$	6.48745e24	0.479249
$906$	1.72094e24	0.125943
$907$	−5.97007e24	−0.432830	−0.216415	−	0.976301i	$-0.569436\pi$
$907$	−5.97007e24	−0.432830	−0.216415	+	0.976301i	$0.569436\pi$
$908$	−8.39694e24	−0.603103
$909$	6.47813e24	0.460953
$910$	7.05636e23	0.0497427
$911$	−1.71616e25	−1.19854	−0.599269	−	0.800548i	$-0.704542\pi$
$911$	−1.71616e25	−1.19854	−0.599269	+	0.800548i	$0.704542\pi$
$912$	−2.10396e24	−0.145573
$913$	4.03989e24	0.276929
$914$	1.92275e25	1.30581
$915$	−1.47348e24	−0.0991437
$916$	−8.94811e24	−0.596513
$917$	−2.18058e24	−0.144024
$918$	−2.94118e24	−0.192468
$919$	−1.03631e25	−0.671906	−0.335953	−	0.941879i	$-0.609058\pi$
$919$	−1.03631e25	−0.671906	−0.335953	+	0.941879i	$0.609058\pi$
$920$	−1.39126e24	−0.0893742
$921$	−7.28649e24	−0.463780
$922$	5.70428e24	0.359739
$923$	−7.07241e24	−0.441929
$924$	−1.38395e24	−0.0856855
$925$	2.79933e24	0.171731
$926$	−1.33145e25	−0.809338
$927$	−8.82515e24	−0.531550
$928$	−1.91625e24	−0.114365
$929$	1.21363e25	0.717714	0.358857	−	0.933393i	$-0.383167\pi$
$929$	1.21363e25	0.717714	0.358857	+	0.933393i	$0.383167\pi$
$930$	6.32134e24	0.370428
$931$	−1.60562e25	−0.932334
$932$	−6.40546e24	−0.368566
$933$	6.31970e24	0.360332
$934$	−1.03076e25	−0.582382
$935$	2.51630e25	1.40885
$936$	5.89124e23	0.0326860
$937$	−1.98283e25	−1.09018	−0.545090	−	0.838377i	$-0.683505\pi$
$937$	−1.98283e25	−1.09018	−0.545090	+	0.838377i	$0.683505\pi$
$938$	6.90391e23	0.0376159
$939$	−5.30592e24	−0.286486
$940$	5.25082e24	0.280957
$941$	−4.91340e24	−0.260537	−0.130269	−	0.991479i	$-0.541584\pi$
$941$	−4.91340e24	−0.260537	−0.130269	+	0.991479i	$0.541584\pi$
$942$	2.71759e24	0.142808
$943$	7.85791e24	0.409221
$944$	3.94557e24	0.203633
$945$	−9.54342e23	−0.0488128
$946$	−1.02243e25	−0.518275
$947$	−2.81290e24	−0.141312	−0.0706561	−	0.997501i	$-0.522509\pi$
$947$	−2.81290e24	−0.141312	−0.0706561	+	0.997501i	$0.522509\pi$
$948$	2.77557e24	0.138192
$949$	4.58861e24	0.226422
$950$	−2.17006e24	−0.106126
$951$	−5.67145e24	−0.274891
$952$	−2.86172e24	−0.137472
$953$	1.28563e25	0.612104	0.306052	−	0.952015i	$-0.400992\pi$
$953$	1.28563e25	0.612104	0.306052	+	0.952015i	$0.400992\pi$
$954$	−1.20081e24	−0.0566646
$955$	1.92830e25	0.901873
$956$	1.48926e25	0.690364
$957$	−8.77720e24	−0.403278
$958$	2.12165e25	0.966198
$959$	−9.83266e24	−0.443826
$960$	1.48822e24	0.0665829
$961$	−7.38771e23	−0.0327613
$962$	−5.14893e24	−0.226323
$963$	−8.41372e24	−0.366577
$964$	−1.14587e25	−0.494857
$965$	−8.86831e24	−0.379628
$966$	7.24731e23	0.0307518
$967$	1.81478e24	0.0763308	0.0381654	−	0.999271i	$-0.487849\pi$
$967$	1.81478e24	0.0763308	0.0381654	+	0.999271i	$0.487849\pi$
$968$	1.40523e24	0.0585877
$969$	−1.99273e25	−0.823564
$970$	1.70611e25	0.698952
$971$	−2.75269e25	−1.11788	−0.558939	−	0.829209i	$-0.688791\pi$
$971$	−2.75269e25	−1.11788	−0.558939	+	0.829209i	$0.688791\pi$
$972$	−7.96765e23	−0.0320750
$973$	2.68491e24	0.107145
$974$	−3.08424e24	−0.122010
$975$	6.07631e23	0.0238287
$976$	−1.19695e24	−0.0465321
$977$	−2.63633e25	−1.01600	−0.508002	−	0.861356i	$-0.669616\pi$
$977$	−2.63633e25	−1.01600	−0.508002	+	0.861356i	$0.669616\pi$
$978$	1.14090e25	0.435881
$979$	−1.28615e25	−0.487123
$980$	1.13573e25	0.426435
$981$	−1.65882e25	−0.617465
$982$	−8.46817e24	−0.312494
$983$	−2.99106e25	−1.09426	−0.547130	−	0.837048i	$-0.684280\pi$
$983$	−2.99106e25	−1.09426	−0.547130	+	0.837048i	$0.684280\pi$
$984$	−8.40555e24	−0.304865
$985$	9.36892e24	0.336885
$986$	−1.81495e25	−0.647009
$987$	−2.73524e24	−0.0966716
$988$	3.99148e24	0.139862
$989$	5.35418e24	0.186005
$990$	6.81666e24	0.234786
$991$	−6.00747e24	−0.205147	−0.102574	−	0.994725i	$-0.532708\pi$
$991$	−6.00747e24	−0.205147	−0.102574	+	0.994725i	$0.532708\pi$
$992$	5.13501e24	0.173857
$993$	−8.37022e24	−0.280975
$994$	9.30671e24	0.309751
$995$	−1.44895e25	−0.478144
$996$	2.26301e24	0.0740426
$997$	−1.03089e25	−0.334428	−0.167214	−	0.985921i	$-0.553477\pi$
$997$	−1.03089e25	−0.334428	−0.167214	+	0.985921i	$0.553477\pi$
$998$	−2.70052e25	−0.868635
$999$	6.96371e24	0.222093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.18.a.d.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.18.a.d.1.2	✓	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	78.a (trivial)

\(f(q)\)	\(=\)	\(q+256.000 q^{2} -6561.00 q^{3} +65536.0 q^{4} -805857. q^{5} -1.67962e6 q^{6} -4.19311e6 q^{7} +1.67772e7 q^{8} +4.30467e7 q^{9} +O(q^{10})\)	\(q+256.000 q^{2} -6561.00 q^{3} +65536.0 q^{4} -805857. q^{5} -1.67962e6 q^{6} -4.19311e6 q^{7} +1.67772e7 q^{8} +4.30467e7 q^{9} -2.06299e8 q^{10} -7.67597e8 q^{11} -4.29982e8 q^{12} +8.15731e8 q^{13} -1.07344e9 q^{14} +5.28723e9 q^{15} +4.29497e9 q^{16} +4.06791e10 q^{17} +1.10200e10 q^{18} +7.46634e10 q^{19} -5.28127e10 q^{20} +2.75110e10 q^{21} -1.96505e11 q^{22} +1.02904e11 q^{23} -1.10075e11 q^{24} -1.13533e11 q^{25} +2.08827e11 q^{26} -2.82430e11 q^{27} -2.74799e11 q^{28} -1.74282e12 q^{29} +1.35353e12 q^{30} +4.67026e12 q^{31} +1.09951e12 q^{32} +5.03620e12 q^{33} +1.04139e13 q^{34} +3.37905e12 q^{35} +2.82111e12 q^{36} -2.46564e13 q^{37} +1.91138e13 q^{38} -5.35201e12 q^{39} -1.35200e13 q^{40} +7.63618e13 q^{41} +7.04281e12 q^{42} +5.20310e13 q^{43} -5.03052e13 q^{44} -3.46895e13 q^{45} +2.63433e13 q^{46} -9.94234e13 q^{47} -2.81793e13 q^{48} -2.15048e14 q^{49} -2.90645e13 q^{50} -2.66896e14 q^{51} +5.34597e13 q^{52} -1.08966e14 q^{53} -7.23020e13 q^{54} +6.18574e14 q^{55} -7.03487e13 q^{56} -4.89867e14 q^{57} -4.46162e14 q^{58} +9.18649e14 q^{59} +3.46504e14 q^{60} -2.78687e14 q^{61} +1.19559e15 q^{62} -1.80499e14 q^{63} +2.81475e14 q^{64} -6.57363e14 q^{65} +1.28927e15 q^{66} -6.43160e14 q^{67} +2.66595e15 q^{68} -6.75151e14 q^{69} +8.65036e14 q^{70} -8.67003e15 q^{71} +7.22204e14 q^{72} +5.62516e15 q^{73} -6.31205e15 q^{74} +7.44892e14 q^{75} +4.89314e15 q^{76} +3.21862e15 q^{77} -1.37011e15 q^{78} -6.45509e15 q^{79} -3.46113e15 q^{80} +1.85302e15 q^{81} +1.95486e16 q^{82} -5.26303e15 q^{83} +1.80296e15 q^{84} -3.27816e16 q^{85} +1.33199e16 q^{86} +1.14346e16 q^{87} -1.28781e16 q^{88} +1.67555e16 q^{89} -8.88052e15 q^{90} -3.42045e15 q^{91} +6.74389e15 q^{92} -3.06416e16 q^{93} -2.54524e16 q^{94} -6.01680e16 q^{95} -7.21390e15 q^{96} -8.27006e16 q^{97} -5.50524e16 q^{98} -3.30425e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1024 q^{2} - 26244 q^{3} + 262144 q^{4} - 518584 q^{5} - 6718464 q^{6} - 16826340 q^{7} + 67108864 q^{8} + 172186884 q^{9}+O(q^{10}) \) 4 * q + 1024 * q^2 - 26244 * q^3 + 262144 * q^4 - 518584 * q^5 - 6718464 * q^6 - 16826340 * q^7 + 67108864 * q^8 + 172186884 * q^9	\( 4 q + 1024 q^{2} - 26244 q^{3} + 262144 q^{4} - 518584 q^{5} - 6718464 q^{6} - 16826340 q^{7} + 67108864 q^{8} + 172186884 q^{9} - 132757504 q^{10} - 549884020 q^{11} - 1719926784 q^{12} + 3262922884 q^{13} - 4307543040 q^{14} + 3402429624 q^{15} + 17179869184 q^{16} - 16988107960 q^{17} + 44079842304 q^{18} - 10774690044 q^{19} - 33985921024 q^{20} + 110397616740 q^{21} - 140770309120 q^{22} - 261020574360 q^{23} - 440301256704 q^{24} + 348752894676 q^{25} + 835308258304 q^{26} - 1129718145924 q^{27} - 1102731018240 q^{28} + 5916347212968 q^{29} + 871021983744 q^{30} + 653877384884 q^{31} + 4398046511104 q^{32} + 3607789055220 q^{33} - 4348955637760 q^{34} + 22657981717760 q^{35} + 11284439629824 q^{36} + 22648713688872 q^{37} - 2758320651264 q^{38} - 21408037041924 q^{39} - 8700395782144 q^{40} + 16695856104776 q^{41} + 28261789885440 q^{42} - 131852373982632 q^{43} - 36037199134720 q^{44} - 22323340763064 q^{45} - 66821267036160 q^{46} - 392280969756004 q^{47} - 112717121716224 q^{48} - 320270218752756 q^{49} + 89280741037056 q^{50} + 111458976325560 q^{51} + 213838914125824 q^{52} - 74097065727976 q^{53} - 289207845356544 q^{54} - 663790840414456 q^{55} - 282299140669440 q^{56} + 70692741378684 q^{57} + 15\!\cdots\!08 q^{58}+ \cdots - 23\!\cdots\!20 q^{99}+O(q^{100}) \) 4 * q + 1024 * q^2 - 26244 * q^3 + 262144 * q^4 - 518584 * q^5 - 6718464 * q^6 - 16826340 * q^7 + 67108864 * q^8 + 172186884 * q^9 - 132757504 * q^10 - 549884020 * q^11 - 1719926784 * q^12 + 3262922884 * q^13 - 4307543040 * q^14 + 3402429624 * q^15 + 17179869184 * q^16 - 16988107960 * q^17 + 44079842304 * q^18 - 10774690044 * q^19 - 33985921024 * q^20 + 110397616740 * q^21 - 140770309120 * q^22 - 261020574360 * q^23 - 440301256704 * q^24 + 348752894676 * q^25 + 835308258304 * q^26 - 1129718145924 * q^27 - 1102731018240 * q^28 + 5916347212968 * q^29 + 871021983744 * q^30 + 653877384884 * q^31 + 4398046511104 * q^32 + 3607789055220 * q^33 - 4348955637760 * q^34 + 22657981717760 * q^35 + 11284439629824 * q^36 + 22648713688872 * q^37 - 2758320651264 * q^38 - 21408037041924 * q^39 - 8700395782144 * q^40 + 16695856104776 * q^41 + 28261789885440 * q^42 - 131852373982632 * q^43 - 36037199134720 * q^44 - 22323340763064 * q^45 - 66821267036160 * q^46 - 392280969756004 * q^47 - 112717121716224 * q^48 - 320270218752756 * q^49 + 89280741037056 * q^50 + 111458976325560 * q^51 + 213838914125824 * q^52 - 74097065727976 * q^53 - 289207845356544 * q^54 - 663790840414456 * q^55 - 282299140669440 * q^56 + 70692741378684 * q^57 + 1514584886519808 * q^58 + 972532690992940 * q^59 + 222981627838464 * q^60 + 4036496333495712 * q^61 + 167392610530304 * q^62 - 724318763431140 * q^63 + 1125899906842624 * q^64 - 423024900219064 * q^65 + 923593998136320 * q^66 + 3219563358634340 * q^67 - 1113332643266560 * q^68 + 1712555988375960 * q^69 + 5800443319746560 * q^70 - 5269779141375740 * q^71 + 2888816545234944 * q^72 + 1630484376609944 * q^73 + 5798070704351232 * q^74 - 2288167741969236 * q^75 - 706130086723584 * q^76 - 20097487159678912 * q^77 - 5480457482732544 * q^78 - 27965205092022016 * q^79 - 2227301320228864 * q^80 + 7412080755407364 * q^81 + 4274139162822656 * q^82 + 8598163018504788 * q^83 + 7235018210672640 * q^84 - 23034109274749936 * q^85 - 33754207739553792 * q^86 - 38817154064283048 * q^87 - 9225522978488320 * q^88 - 56353749364046152 * q^89 - 5714775235344384 * q^90 - 13725762459991140 * q^91 - 17106244361256960 * q^92 - 4290089522223924 * q^93 - 100423928257537024 * q^94 - 150775696530487936 * q^95 - 28855583159353344 * q^96 - 360024045001148952 * q^97 - 81989176000705536 * q^98 - 23670703991298420 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more