LMFDB - Embedded newform 10.28.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,28,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	10.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:	$46.1855574838$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{12929}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3232 $ x^2 - x - 3232
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-56.3529$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8192.00 q^{2} +1.45602e6 q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} -1.19278e10 q^{6} -3.42070e11 q^{7} -5.49756e11 q^{8} -5.50559e12 q^{9} +1.00000e13 q^{10} +1.20755e13 q^{11} +9.77122e13 q^{12} -1.02154e14 q^{13} +2.80224e15 q^{14} -1.77737e15 q^{15} +4.50360e15 q^{16} +1.63337e16 q^{17} +4.51018e16 q^{18} -2.21733e15 q^{19} -8.19200e16 q^{20} -4.98063e17 q^{21} -9.89228e16 q^{22} -1.90828e17 q^{23} -8.00458e17 q^{24} +1.49012e18 q^{25} +8.36847e17 q^{26} -1.91193e19 q^{27} -2.29560e19 q^{28} -6.52176e19 q^{29} +1.45602e19 q^{30} +4.50679e19 q^{31} -3.68935e19 q^{32} +1.75823e19 q^{33} -1.33806e20 q^{34} +4.17566e20 q^{35} -3.69474e20 q^{36} +2.51294e21 q^{37} +1.81644e19 q^{38} -1.48739e20 q^{39} +6.71089e20 q^{40} +6.73990e20 q^{41} +4.08013e21 q^{42} -1.21806e21 q^{43} +8.10376e20 q^{44} +6.72069e21 q^{45} +1.56326e21 q^{46} +4.88526e22 q^{47} +6.55735e21 q^{48} +5.12997e22 q^{49} -1.22070e22 q^{50} +2.37823e22 q^{51} -6.85545e21 q^{52} +9.75271e21 q^{53} +1.56626e23 q^{54} -1.47407e22 q^{55} +1.88055e23 q^{56} -3.22849e21 q^{57} +5.34263e23 q^{58} +1.09826e24 q^{59} -1.19278e23 q^{60} +9.88829e23 q^{61} -3.69197e23 q^{62} +1.88330e24 q^{63} +3.02231e23 q^{64} +1.24700e23 q^{65} -1.44034e23 q^{66} +8.13848e24 q^{67} +1.09614e24 q^{68} -2.77850e23 q^{69} -3.42070e24 q^{70} -1.38068e25 q^{71} +3.02673e24 q^{72} -2.27541e25 q^{73} -2.05860e25 q^{74} +2.16965e24 q^{75} -1.48803e23 q^{76} -4.13068e24 q^{77} +1.21847e24 q^{78} +2.55487e24 q^{79} -5.49756e24 q^{80} +1.41452e25 q^{81} -5.52132e24 q^{82} -9.67997e25 q^{83} -3.34244e25 q^{84} -1.99387e25 q^{85} +9.97833e24 q^{86} -9.49584e25 q^{87} -6.63860e24 q^{88} +3.24368e26 q^{89} -5.50559e25 q^{90} +3.49439e25 q^{91} -1.28062e25 q^{92} +6.56200e25 q^{93} -4.00200e26 q^{94} +2.70671e24 q^{95} -5.37178e25 q^{96} +4.91800e26 q^{97} -4.20247e26 q^{98} -6.64830e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16384 q^{2} - 2245644 q^{3} + 134217728 q^{4} - 2441406250 q^{5} + 18396315648 q^{6} - 120196732292 q^{7} - 1099511627776 q^{8} + 571163616594 q^{9} + 20000000000000 q^{10} + 7112122732704 q^{11}+ \cdots - 96\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 16384 * q^2 - 2245644 * q^3 + 134217728 * q^4 - 2441406250 * q^5 + 18396315648 * q^6 - 120196732292 * q^7 - 1099511627776 * q^8 + 571163616594 * q^9 + 20000000000000 * q^10 + 7112122732704 * q^11 - 150702617788416 * q^12 - 323114990355404 * q^13 + 984651630936064 * q^14 + 2741264648437500 * q^15 + 9007199254740992 * q^16 - 11949781720794252 * q^17 - 4678972347138048 * q^18 - 310800626187534200 * q^19 - 163840000000000000 * q^20 - 1319365315134326376 * q^21 - 58262509426311168 * q^22 - 1207992822578557644 * q^23 + 1234555844922703872 * q^24 + 2980232238769531250 * q^25 + 2646958000991469568 * q^26 - 13386024338103046440 * q^27 - 8066266160628236288 * q^28 - 85089627076663724580 * q^29 - 22456440000000000000 * q^30 - 169891626304914480056 * q^31 - 73786976294838206464 * q^32 + 35955214564003682112 * q^33 + 97892611856746512384 * q^34 + 146724526723632812500 * q^35 + 38330141467754889216 * q^36 + 1001687425876018532308 * q^37 + 2546078729728280166400 * q^38 + 669184707607358092488 * q^39 + 1342177280000000000000 * q^40 + 6829708525832119000044 * q^41 + 10808240661580401672192 * q^42 + 15331910221739375128036 * q^43 + 477286477220341088256 * q^44 - 697221211662597656250 * q^45 + 9895877202563544219648 * q^46 + 44654607958183509227628 * q^47 - 10113481481606790119424 * q^48 + 34815266426190611168346 * q^49 - 24414062500000000000000 * q^50 + 128478598882379942153544 * q^51 - 21683879944122118701056 * q^52 + 259350970067880627435396 * q^53 + 109658311377740156436480 * q^54 - 8681790445195312500000 * q^55 + 66078852387866511671296 * q^56 + 1139044611805451608251600 * q^57 + 697054225012029231759360 * q^58 + 2082093442621301023169640 * q^59 + 183963156480000000000000 * q^60 + 677925769536334246319284 * q^61 + 1391752202689859420618752 * q^62 + 3231569874371732206566876 * q^63 + 604462909807314587353088 * q^64 + 394427478461186523437500 * q^65 - 294545117708318163861504 * q^66 + 2453617552336948143390028 * q^67 - 801936276330467429449728 * q^68 + 3487358239126020846890568 * q^69 - 1201967322920000000000000 * q^70 - 23890193584108132090228776 * q^71 - 314000518903848052457472 * q^72 - 13919420706136886544146204 * q^73 - 8205823392776343816667136 * q^74 - 3346270322799682617187500 * q^75 - 20857476953934071123148800 * q^76 - 5231935501660614540408384 * q^77 - 5481961124719477493661696 * q^78 - 53659327270981104663051920 * q^79 - 10995116277760000000000000 * q^80 - 53416489016311609709962998 * q^81 - 55948972243616718848360448 * q^82 + 5756571261014435461903716 * q^83 - 88541107499666650498596864 * q^84 + 14587135889641420898437500 * q^85 - 125599008536488961048870912 * q^86 - 21398789661957929503788840 * q^87 - 3909930821389034194993152 * q^88 + 174438127411287409220344020 * q^89 + 5711636165940000000000000 * q^90 - 14081455302088161819283816 * q^91 - 81067026043400554247356416 * q^92 + 861329117078544091150519632 * q^93 - 365810548393439307592728576 * q^94 + 379395295639079833984375000 * q^95 + 82849640297322824658321408 * q^96 - 21732067184289340167295292 * q^97 - 285206662563353486691090432 * q^98 - 96644441211111069636758112 * q^99

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 $

$2$	−8192.00	−0.707107
$2$	−8192.00	−0.707107
$3$	1.45602e6	0.527268	0.263634	−	0.964623i	$-0.415079\pi$
$3$	1.45602e6	0.527268	0.263634	+	0.964623i	$0.415079\pi$
$4$	6.71089e7	0.500000
$5$	−1.22070e9	−0.447214
$5$	−1.22070e9	−0.447214
$6$	−1.19278e10	−0.372835
$7$	−3.42070e11	−1.33442	−0.667209	−	0.744871i	$-0.732511\pi$
$7$	−3.42070e11	−1.33442	−0.667209	+	0.744871i	$0.732511\pi$
$8$	−5.49756e11	−0.353553
$9$	−5.50559e12	−0.721988
$10$	1.00000e13	0.316228
$11$	1.20755e13	0.105464	0.0527321	−	0.998609i	$-0.483207\pi$
$11$	1.20755e13	0.105464	0.0527321	+	0.998609i	$0.483207\pi$
$12$	9.77122e13	0.263634
$13$	−1.02154e14	−0.0935451	−0.0467725	−	0.998906i	$-0.514894\pi$
$13$	−1.02154e14	−0.0935451	−0.0467725	+	0.998906i	$0.514894\pi$
$14$	2.80224e15	0.943576
$15$	−1.77737e15	−0.235802
$16$	4.50360e15	0.250000
$17$	1.63337e16	0.399968	0.199984	−	0.979799i	$-0.435911\pi$
$17$	1.63337e16	0.399968	0.199984	+	0.979799i	$0.435911\pi$
$18$	4.51018e16	0.510523
$19$	−2.21733e15	−0.0120964	−0.00604822	−	0.999982i	$-0.501925\pi$
$19$	−2.21733e15	−0.0120964	−0.00604822	+	0.999982i	$0.501925\pi$
$20$	−8.19200e16	−0.223607
$21$	−4.98063e17	−0.703596
$22$	−9.89228e16	−0.0745745
$23$	−1.90828e17	−0.0789434	−0.0394717	−	0.999221i	$-0.512567\pi$
$23$	−1.90828e17	−0.0789434	−0.0394717	+	0.999221i	$0.512567\pi$
$24$	−8.00458e17	−0.186418
$25$	1.49012e18	0.200000
$26$	8.36847e17	0.0661463
$27$	−1.91193e19	−0.907950
$28$	−2.29560e19	−0.667209
$29$	−6.52176e19	−1.18030	−0.590149	−	0.807294i	$-0.700931\pi$
$29$	−6.52176e19	−1.18030	−0.590149	+	0.807294i	$0.700931\pi$
$30$	1.45602e19	0.166737
$31$	4.50679e19	0.331501	0.165750	−	0.986168i	$-0.446995\pi$
$31$	4.50679e19	0.331501	0.165750	+	0.986168i	$0.446995\pi$
$32$	−3.68935e19	−0.176777
$33$	1.75823e19	0.0556080
$34$	−1.33806e20	−0.282820
$35$	4.17566e20	0.596770
$36$	−3.69474e20	−0.360994
$37$	2.51294e21	1.69613	0.848063	−	0.529895i	$-0.177769\pi$
$37$	2.51294e21	1.69613	0.848063	+	0.529895i	$0.177769\pi$
$38$	1.81644e19	0.00855347
$39$	−1.48739e20	−0.0493234
$40$	6.71089e20	0.158114
$41$	6.73990e20	0.113781	0.0568907	−	0.998380i	$-0.481881\pi$
$41$	6.73990e20	0.113781	0.0568907	+	0.998380i	$0.481881\pi$
$42$	4.08013e21	0.497518
$43$	−1.21806e21	−0.108104	−0.0540522	−	0.998538i	$-0.517214\pi$
$43$	−1.21806e21	−0.108104	−0.0540522	+	0.998538i	$0.517214\pi$
$44$	8.10376e20	0.0527321
$45$	6.72069e21	0.322883
$46$	1.56326e21	0.0558214
$47$	4.88526e22	1.30487	0.652434	−	0.757846i	$-0.273748\pi$
$47$	4.88526e22	1.30487	0.652434	+	0.757846i	$0.273748\pi$
$48$	6.55735e21	0.131817
$49$	5.12997e22	0.780671
$50$	−1.22070e22	−0.141421
$51$	2.37823e22	0.210891
$52$	−6.85545e21	−0.0467725
$53$	9.75271e21	0.0514519	0.0257259	−	0.999669i	$-0.491810\pi$
$53$	9.75271e21	0.0514519	0.0257259	+	0.999669i	$0.491810\pi$
$54$	1.56626e23	0.642018
$55$	−1.47407e22	−0.0471651
$56$	1.88055e23	0.471788
$57$	−3.22849e21	−0.00637807
$58$	5.34263e23	0.834597
$59$	1.09826e24	1.36208	0.681042	−	0.732245i	$-0.261527\pi$
$59$	1.09826e24	1.36208	0.681042	+	0.732245i	$0.261527\pi$
$60$	−1.19278e23	−0.117901
$61$	9.88829e23	0.781931	0.390966	−	0.920405i	$-0.372141\pi$
$61$	9.88829e23	0.781931	0.390966	+	0.920405i	$0.372141\pi$
$62$	−3.69197e23	−0.234407
$63$	1.88330e24	0.963434
$64$	3.02231e23	0.125000
$65$	1.24700e23	0.0418346
$66$	−1.44034e23	−0.0393208
$67$	8.13848e24	1.81357	0.906784	−	0.421597i	$-0.138530\pi$
$67$	8.13848e24	1.81357	0.906784	+	0.421597i	$0.138530\pi$
$68$	1.09614e24	0.199984
$69$	−2.77850e23	−0.0416244
$70$	−3.42070e24	−0.421980
$71$	−1.38068e25	−1.40638	−0.703192	−	0.711000i	$-0.748243\pi$
$71$	−1.38068e25	−1.40638	−0.703192	+	0.711000i	$0.748243\pi$
$72$	3.02673e24	0.255261
$73$	−2.27541e25	−1.59294	−0.796471	−	0.604676i	$-0.793302\pi$
$73$	−2.27541e25	−1.59294	−0.796471	+	0.604676i	$0.793302\pi$
$74$	−2.05860e25	−1.19934
$75$	2.16965e24	0.105454
$76$	−1.48803e23	−0.00604822
$77$	−4.13068e24	−0.140733
$78$	1.21847e24	0.0348769
$79$	2.55487e24	0.0615748	0.0307874	−	0.999526i	$-0.490199\pi$
$79$	2.55487e24	0.0615748	0.0307874	+	0.999526i	$0.490199\pi$
$80$	−5.49756e24	−0.111803
$81$	1.41452e25	0.243255
$82$	−5.52132e24	−0.0804556
$83$	−9.67997e25	−1.19762	−0.598811	−	0.800891i	$-0.704360\pi$
$83$	−9.67997e25	−1.19762	−0.598811	+	0.800891i	$0.704360\pi$
$84$	−3.34244e25	−0.351798
$85$	−1.99387e25	−0.178871
$86$	9.97833e24	0.0764414
$87$	−9.49584e25	−0.622334
$88$	−6.63860e24	−0.0372872
$89$	3.24368e26	1.56413	0.782064	−	0.623198i	$-0.214167\pi$
$89$	3.24368e26	1.56413	0.782064	+	0.623198i	$0.214167\pi$
$90$	−5.50559e25	−0.228313
$91$	3.49439e25	0.124828
$92$	−1.28062e25	−0.0394717
$93$	6.56200e25	0.174790
$94$	−4.00200e26	−0.922681
$95$	2.70671e24	0.00540969
$96$	−5.37178e25	−0.0932088
$97$	4.91800e26	0.741943	0.370971	−	0.928644i	$-0.379025\pi$
$97$	4.91800e26	0.741943	0.370971	+	0.928644i	$0.379025\pi$
$98$	−4.20247e26	−0.552018
$99$	−6.64830e25	−0.0761439
$100$	1.00000e26	0.100000
$101$	2.12114e27	1.85452	0.927259	−	0.374421i	$-0.122159\pi$
$101$	2.12114e27	1.85452	0.927259	+	0.374421i	$0.122159\pi$
$102$	−1.94825e26	−0.149122
$103$	3.47783e25	0.0233349	0.0116675	−	0.999932i	$-0.496286\pi$
$103$	3.47783e25	0.0233349	0.0116675	+	0.999932i	$0.496286\pi$
$104$	5.61599e25	0.0330732
$105$	6.07987e26	0.314658
$106$	−7.98942e25	−0.0363820
$107$	4.84969e27	1.94551	0.972754	−	0.231841i	$-0.0744750\pi$
$107$	4.84969e27	1.94551	0.972754	+	0.231841i	$0.0744750\pi$
$108$	−1.28308e27	−0.453975
$109$	−1.76094e27	−0.550158	−0.275079	−	0.961422i	$-0.588704\pi$
$109$	−1.76094e27	−0.550158	−0.275079	+	0.961422i	$0.588704\pi$
$110$	1.20755e26	0.0333507
$111$	3.65890e27	0.894314
$112$	−1.54055e27	−0.333604
$113$	3.51618e27	0.675324	0.337662	−	0.941268i	$-0.390364\pi$
$113$	3.51618e27	0.675324	0.337662	+	0.941268i	$0.390364\pi$
$114$	2.64478e25	0.00450997
$115$	2.32944e26	0.0353046
$116$	−4.37668e27	−0.590149
$117$	5.62419e26	0.0675384
$118$	−8.99696e27	−0.963138
$119$	−5.58729e27	−0.533725
$120$	9.77122e26	0.0833685
$121$	−1.29642e28	−0.988877
$122$	−8.10049e27	−0.552909
$123$	9.81346e26	0.0599933
$124$	3.02446e27	0.165750
$125$	−1.81899e27	−0.0894427
$126$	−1.54280e28	−0.681250
$127$	8.77438e27	0.348230	0.174115	−	0.984725i	$-0.444294\pi$
$127$	8.77438e27	0.348230	0.174115	+	0.984725i	$0.444294\pi$
$128$	−2.47588e27	−0.0883883
$129$	−1.77352e27	−0.0570001
$130$	−1.02154e27	−0.0295815
$131$	−3.38485e28	−0.883846	−0.441923	−	0.897053i	$-0.645703\pi$
$131$	−3.38485e28	−0.883846	−0.441923	+	0.897053i	$0.645703\pi$
$132$	1.17993e27	0.0278040
$133$	7.58484e26	0.0161417
$134$	−6.66705e28	−1.28239
$135$	2.33390e28	0.406048
$136$	−8.97957e27	−0.141410
$137$	1.01883e29	1.45337	0.726683	−	0.686973i	$-0.241061\pi$
$137$	1.01883e29	1.45337	0.726683	+	0.686973i	$0.241061\pi$
$138$	2.27615e27	0.0294329
$139$	−4.45983e28	−0.523141	−0.261571	−	0.965184i	$-0.584240\pi$
$139$	−4.45983e28	−0.523141	−0.261571	+	0.965184i	$0.584240\pi$
$140$	2.80224e28	0.298385
$141$	7.11306e28	0.688015
$142$	1.13105e29	0.994463
$143$	−1.23357e27	−0.00986566
$144$	−2.47950e28	−0.180497
$145$	7.96113e28	0.527846
$146$	1.86401e29	1.12638
$147$	7.46937e28	0.411623
$148$	1.68640e29	0.848063
$149$	−5.58786e28	−0.256585	−0.128292	−	0.991736i	$-0.540950\pi$
$149$	−5.58786e28	−0.256585	−0.128292	+	0.991736i	$0.540950\pi$
$150$	−1.77737e28	−0.0745670
$151$	−2.68196e29	−1.02864	−0.514320	−	0.857598i	$-0.671956\pi$
$151$	−2.68196e29	−1.02864	−0.514320	+	0.857598i	$0.671956\pi$
$152$	1.21899e27	0.00427673
$153$	−8.99269e28	−0.288772
$154$	3.38386e28	0.0995135
$155$	−5.50146e28	−0.148252
$156$	−9.98171e27	−0.0246617
$157$	−3.96402e28	−0.0898443	−0.0449222	−	0.998990i	$-0.514304\pi$
$157$	−3.96402e28	−0.0898443	−0.0449222	+	0.998990i	$0.514304\pi$
$158$	−2.09295e28	−0.0435400
$159$	1.42002e28	0.0271289
$160$	4.50360e28	0.0790569
$161$	6.52765e28	0.105343
$162$	−1.15877e29	−0.172007
$163$	−7.23256e29	−0.988005	−0.494003	−	0.869460i	$-0.664467\pi$
$163$	−7.23256e29	−0.988005	−0.494003	+	0.869460i	$0.664467\pi$
$164$	4.52307e28	0.0568907
$165$	−2.14628e28	−0.0248686
$166$	7.92983e29	0.846846
$167$	−9.65355e28	−0.0950637	−0.0475318	−	0.998870i	$-0.515136\pi$
$167$	−9.65355e28	−0.0950637	−0.0475318	+	0.998870i	$0.515136\pi$
$168$	2.73813e29	0.248759
$169$	−1.18210e30	−0.991249
$170$	1.63337e29	0.126481
$171$	1.22077e28	0.00873348
$172$	−8.17424e28	−0.0540522
$173$	−6.03771e29	−0.369190	−0.184595	−	0.982815i	$-0.559097\pi$
$173$	−6.03771e29	−0.369190	−0.184595	+	0.982815i	$0.559097\pi$
$174$	7.77900e29	0.440057
$175$	−5.09724e29	−0.266884
$176$	5.43834e28	0.0263661
$177$	1.59910e30	0.718184
$178$	−2.65722e30	−1.10601
$179$	−3.15544e30	−1.21771	−0.608854	−	0.793282i	$-0.708371\pi$
$179$	−3.15544e30	−1.21771	−0.608854	+	0.793282i	$0.708371\pi$
$180$	4.51018e29	0.161441
$181$	−2.41563e30	−0.802362	−0.401181	−	0.915999i	$-0.631400\pi$
$181$	−2.41563e30	−0.802362	−0.401181	+	0.915999i	$0.631400\pi$
$182$	−2.86261e29	−0.0882669
$183$	1.43976e30	0.412288
$184$	1.04909e29	0.0279107
$185$	−3.06755e30	−0.758531
$186$	−5.37559e29	−0.123595
$187$	1.97239e29	0.0421824
$188$	3.27844e30	0.652434
$189$	6.54016e30	1.21158
$190$	−2.21733e28	−0.00382523
$191$	1.23727e30	0.198845	0.0994227	−	0.995045i	$-0.468300\pi$
$191$	1.23727e30	0.198845	0.0994227	+	0.995045i	$0.468300\pi$
$192$	4.40056e29	0.0659086
$193$	9.55053e30	1.33353	0.666766	−	0.745267i	$-0.267678\pi$
$193$	9.55053e30	1.33353	0.666766	+	0.745267i	$0.267678\pi$
$194$	−4.02883e30	−0.524633
$195$	1.81566e29	0.0220581
$196$	3.44267e30	0.390336
$197$	−5.01468e30	−0.530822	−0.265411	−	0.964135i	$-0.585508\pi$
$197$	−5.01468e30	−0.530822	−0.265411	+	0.964135i	$0.585508\pi$
$198$	5.44629e29	0.0538419
$199$	1.64461e31	1.51896	0.759481	−	0.650530i	$-0.225453\pi$
$199$	1.64461e31	1.51896	0.759481	+	0.650530i	$0.225453\pi$
$200$	−8.19200e29	−0.0707107
$201$	1.18498e31	0.956237
$202$	−1.73764e31	−1.31134
$203$	2.23090e31	1.57501
$204$	1.59601e30	0.105445
$205$	−8.22741e29	−0.0508846
$206$	−2.84904e29	−0.0165003
$207$	1.05062e30	0.0569962
$208$	−4.60062e29	−0.0233863
$209$	−2.67755e28	−0.00127574
$210$	−4.98063e30	−0.222497
$211$	−1.40300e31	−0.587820	−0.293910	−	0.955833i	$-0.594957\pi$
$211$	−1.40300e31	−0.587820	−0.293910	+	0.955833i	$0.594957\pi$
$212$	6.54493e29	0.0257259
$213$	−2.01030e31	−0.741542
$214$	−3.97286e31	−1.37568
$215$	1.48689e30	0.0483458
$216$	1.05110e31	0.321009
$217$	−1.54164e31	−0.442361
$218$	1.44256e31	0.389021
$219$	−3.31305e31	−0.839908
$220$	−9.89228e29	−0.0235825
$221$	−1.66856e30	−0.0374150
$222$	−2.99737e31	−0.632376
$223$	1.89499e31	0.376264	0.188132	−	0.982144i	$-0.439757\pi$
$223$	1.89499e31	0.376264	0.188132	+	0.982144i	$0.439757\pi$
$224$	1.26202e31	0.235894
$225$	−8.20397e30	−0.144398
$226$	−2.88045e31	−0.477526
$227$	2.62637e31	0.410211	0.205106	−	0.978740i	$-0.434246\pi$
$227$	2.62637e31	0.410211	0.205106	+	0.978740i	$0.434246\pi$
$228$	−2.16660e29	−0.00318903
$229$	−1.17074e32	−1.62436	−0.812182	−	0.583405i	$-0.801720\pi$
$229$	−1.17074e32	−1.62436	−0.812182	+	0.583405i	$0.801720\pi$
$230$	−1.90828e30	−0.0249641
$231$	−6.01438e30	−0.0742043
$232$	3.58538e31	0.417299
$233$	4.74248e31	0.520835	0.260418	−	0.965496i	$-0.416140\pi$
$233$	4.74248e31	0.520835	0.260418	+	0.965496i	$0.416140\pi$
$234$	−4.60734e30	−0.0477569
$235$	−5.96345e31	−0.583554
$236$	7.37031e31	0.681042
$237$	3.71995e30	0.0324664
$238$	4.57711e31	0.377400
$239$	−4.45355e31	−0.347004	−0.173502	−	0.984834i	$-0.555508\pi$
$239$	−4.45355e31	−0.347004	−0.173502	+	0.984834i	$0.555508\pi$
$240$	−8.00458e30	−0.0589504
$241$	1.62097e32	1.12861	0.564307	−	0.825565i	$-0.309144\pi$
$241$	1.62097e32	1.12861	0.564307	+	0.825565i	$0.309144\pi$
$242$	1.06203e32	0.699242
$243$	1.66392e32	1.03621
$244$	6.63592e31	0.390966
$245$	−6.26218e31	−0.349127
$246$	−8.03918e30	−0.0424217
$247$	2.26510e29	0.00113156
$248$	−2.47764e31	−0.117203
$249$	−1.40943e32	−0.631468
$250$	1.49012e31	0.0632456
$251$	6.55019e31	0.263426	0.131713	−	0.991288i	$-0.457952\pi$
$251$	6.55019e31	0.263426	0.131713	+	0.991288i	$0.457952\pi$
$252$	1.26386e32	0.481717
$253$	−2.30435e30	−0.00832571
$254$	−7.18797e31	−0.246236
$255$	−2.90312e31	−0.0943131
$256$	2.02824e31	0.0625000
$257$	3.76002e32	1.09924	0.549621	−	0.835414i	$-0.314772\pi$
$257$	3.76002e32	1.09924	0.549621	+	0.835414i	$0.314772\pi$
$258$	1.45287e31	0.0403051
$259$	−8.59601e32	−2.26334
$260$	8.36847e30	0.0209173
$261$	3.59061e32	0.852161
$262$	2.77287e32	0.624973
$263$	1.47130e32	0.314992	0.157496	−	0.987520i	$-0.449658\pi$
$263$	1.47130e32	0.314992	0.157496	+	0.987520i	$0.449658\pi$
$264$	−9.66596e30	−0.0196604
$265$	−1.19052e31	−0.0230100
$266$	−6.21350e30	−0.0114139
$267$	4.72287e32	0.824715
$268$	5.46164e32	0.906784
$269$	−1.09666e33	−1.73148	−0.865738	−	0.500498i	$-0.833150\pi$
$269$	−1.09666e33	−1.73148	−0.865738	+	0.500498i	$0.833150\pi$
$270$	−1.91193e32	−0.287119
$271$	−7.97318e32	−1.13906	−0.569530	−	0.821971i	$-0.692875\pi$
$271$	−7.97318e32	−1.13906	−0.569530	+	0.821971i	$0.692875\pi$
$272$	7.35607e31	0.0999920
$273$	5.08792e31	0.0658180
$274$	−8.34627e32	−1.02768
$275$	1.79940e31	0.0210929
$276$	−1.86462e31	−0.0208122
$277$	−1.37742e33	−1.46416	−0.732081	−	0.681218i	$-0.761451\pi$
$277$	−1.37742e33	−1.46416	−0.732081	+	0.681218i	$0.761451\pi$
$278$	3.65350e32	0.369917
$279$	−2.48126e32	−0.239340
$280$	−2.29560e32	−0.210990
$281$	1.94855e33	1.70677	0.853387	−	0.521277i	$-0.174544\pi$
$281$	1.94855e33	1.70677	0.853387	+	0.521277i	$0.174544\pi$
$282$	−5.82702e32	−0.486500
$283$	2.07385e33	1.65067	0.825336	−	0.564642i	$-0.190986\pi$
$283$	2.07385e33	1.65067	0.825336	+	0.564642i	$0.190986\pi$
$284$	−9.26555e32	−0.703192
$285$	3.94103e30	0.00285236
$286$	1.01054e31	0.00697608
$287$	−2.30552e32	−0.151832
$288$	2.03120e32	0.127631
$289$	−1.40092e33	−0.840025
$290$	−6.52176e32	−0.373243
$291$	7.16073e32	0.391203
$292$	−1.52700e33	−0.796471
$293$	1.62146e33	0.807596	0.403798	−	0.914848i	$-0.367690\pi$
$293$	1.62146e33	0.807596	0.403798	+	0.914848i	$0.367690\pi$
$294$	−6.11891e32	−0.291062
$295$	−1.34065e33	−0.609142
$296$	−1.38150e33	−0.599671
$297$	−2.30876e32	−0.0957563
$298$	4.57758e32	0.181433
$299$	1.94939e31	0.00738476
$300$	1.45602e32	0.0527268
$301$	4.16661e32	0.144257
$302$	2.19706e33	0.727358
$303$	3.08843e33	0.977828
$304$	−9.98598e30	−0.00302411
$305$	−1.20707e33	−0.349690
$306$	7.36681e32	0.204193
$307$	4.28458e33	1.13642	0.568212	−	0.822882i	$-0.307635\pi$
$307$	4.28458e33	1.13642	0.568212	+	0.822882i	$0.307635\pi$
$308$	−2.77206e32	−0.0703667
$309$	5.06381e31	0.0123038
$310$	4.50679e32	0.104830
$311$	1.87537e33	0.417658	0.208829	−	0.977952i	$-0.433035\pi$
$311$	1.87537e33	0.417658	0.208829	+	0.977952i	$0.433035\pi$
$312$	8.17701e31	0.0174384
$313$	7.71677e33	1.57611	0.788056	−	0.615604i	$-0.211088\pi$
$313$	7.71677e33	1.57611	0.788056	+	0.615604i	$0.211088\pi$
$314$	3.24733e32	0.0635295
$315$	−2.29895e33	−0.430861
$316$	1.71454e32	0.0307874
$317$	−3.06539e32	−0.0527455	−0.0263728	−	0.999652i	$-0.508396\pi$
$317$	−3.06539e32	−0.0527455	−0.0263728	+	0.999652i	$0.508396\pi$
$318$	−1.16328e32	−0.0191831
$319$	−7.87538e32	−0.124479
$320$	−3.68935e32	−0.0559017
$321$	7.06127e33	1.02580
$322$	−5.34745e32	−0.0744891
$323$	−3.62174e31	−0.00483819
$324$	9.49268e32	0.121627
$325$	−1.52222e32	−0.0187090
$326$	5.92491e33	0.698625
$327$	−2.56398e33	−0.290081
$328$	−3.70530e32	−0.0402278
$329$	−1.67110e34	−1.74124
$330$	1.75823e32	0.0175848
$331$	−1.08931e34	−1.04586	−0.522930	−	0.852375i	$-0.675161\pi$
$331$	−1.08931e34	−1.04586	−0.522930	+	0.852375i	$0.675161\pi$
$332$	−6.49612e33	−0.598811
$333$	−1.38352e34	−1.22458
$334$	7.90819e32	0.0672202
$335$	−9.93467e33	−0.811052
$336$	−2.24308e33	−0.175899
$337$	−2.14689e34	−1.61736	−0.808680	−	0.588249i	$-0.799817\pi$
$337$	−2.14689e34	−1.61736	−0.808680	+	0.588249i	$0.799817\pi$
$338$	9.68375e33	0.700919
$339$	5.11964e33	0.356077
$340$	−1.33806e33	−0.0894356
$341$	5.44220e32	0.0349615
$342$	−1.00006e32	−0.00617550
$343$	4.93013e33	0.292676
$344$	6.69634e32	0.0382207
$345$	3.39172e32	0.0186150
$346$	4.94609e33	0.261057
$347$	2.88990e34	1.46702	0.733509	−	0.679680i	$-0.237881\pi$
$347$	2.88990e34	1.46702	0.733509	+	0.679680i	$0.237881\pi$
$348$	−6.37255e33	−0.311167
$349$	−4.64738e33	−0.218306	−0.109153	−	0.994025i	$-0.534814\pi$
$349$	−4.64738e33	−0.218306	−0.109153	+	0.994025i	$0.534814\pi$
$350$	4.17566e33	0.188715
$351$	1.95312e33	0.0849342
$352$	−4.45509e32	−0.0186436
$353$	−2.34595e34	−0.944845	−0.472422	−	0.881372i	$-0.656620\pi$
$353$	−2.34595e34	−0.944845	−0.472422	+	0.881372i	$0.656620\pi$
$354$	−1.30998e34	−0.507832
$355$	1.68539e34	0.628954
$356$	2.17679e34	0.782064
$357$	−8.13523e33	−0.281416
$358$	2.58493e34	0.861050
$359$	2.11955e34	0.679937	0.339968	−	0.940437i	$-0.389584\pi$
$359$	2.11955e34	0.679937	0.339968	+	0.940437i	$0.389584\pi$
$360$	−3.69474e33	−0.114156
$361$	−3.35957e34	−0.999854
$362$	1.97889e34	0.567356
$363$	−1.88762e34	−0.521404
$364$	2.34505e33	0.0624141
$365$	2.77759e34	0.712386
$366$	−1.17945e34	−0.291531
$367$	5.17652e34	1.23323	0.616617	−	0.787263i	$-0.288503\pi$
$367$	5.17652e34	1.23323	0.616617	+	0.787263i	$0.288503\pi$
$368$	−8.59412e32	−0.0197358
$369$	−3.71071e33	−0.0821488
$370$	2.51294e34	0.536362
$371$	−3.33611e33	−0.0686583
$372$	4.40369e33	0.0873950
$373$	2.59719e34	0.497089	0.248545	−	0.968620i	$-0.420048\pi$
$373$	2.59719e34	0.497089	0.248545	+	0.968620i	$0.420048\pi$
$374$	−1.61578e33	−0.0298274
$375$	−2.64849e33	−0.0471603
$376$	−2.68570e34	−0.461340
$377$	6.66225e33	0.110411
$378$	−5.35770e34	−0.856720
$379$	6.29669e34	0.971590	0.485795	−	0.874073i	$-0.338530\pi$
$379$	6.29669e34	0.971590	0.485795	+	0.874073i	$0.338530\pi$
$380$	1.81644e32	0.00270484
$381$	1.27757e34	0.183611
$382$	−1.01358e34	−0.140605
$383$	−5.45282e34	−0.730193	−0.365097	−	0.930970i	$-0.618964\pi$
$383$	−5.45282e34	−0.730193	−0.365097	+	0.930970i	$0.618964\pi$
$384$	−3.60494e33	−0.0466044
$385$	5.04234e33	0.0629379
$386$	−7.82379e34	−0.942950
$387$	6.70612e33	0.0780501
$388$	3.30042e34	0.370971
$389$	1.15416e35	1.25299	0.626495	−	0.779425i	$-0.284489\pi$
$389$	1.15416e35	1.25299	0.626495	+	0.779425i	$0.284489\pi$
$390$	−1.48739e33	−0.0155974
$391$	−3.11693e33	−0.0315748
$392$	−2.82023e34	−0.276009
$393$	−4.92842e34	−0.466024
$394$	4.10802e34	0.375348
$395$	−3.11874e33	−0.0275371
$396$	−4.46160e33	−0.0380720
$397$	−5.65268e34	−0.466211	−0.233106	−	0.972451i	$-0.574889\pi$
$397$	−5.65268e34	−0.466211	−0.233106	+	0.972451i	$0.574889\pi$
$398$	−1.34727e35	−1.07407
$399$	1.10437e33	0.00851101
$400$	6.71089e33	0.0500000
$401$	−3.91339e33	−0.0281906	−0.0140953	−	0.999901i	$-0.504487\pi$
$401$	−3.91339e33	−0.0281906	−0.0140953	+	0.999901i	$0.504487\pi$
$402$	−9.70738e34	−0.676161
$403$	−4.60388e33	−0.0310103
$404$	1.42347e35	0.927259
$405$	−1.72671e34	−0.108787
$406$	−1.82755e35	−1.11370
$407$	3.03451e34	0.178881
$408$	−1.30745e34	−0.0745611
$409$	−2.50975e34	−0.138473	−0.0692366	−	0.997600i	$-0.522056\pi$
$409$	−2.50975e34	−0.138473	−0.0692366	+	0.997600i	$0.522056\pi$
$410$	6.73990e33	0.0359808
$411$	1.48344e35	0.766314
$412$	2.33393e33	0.0116675
$413$	−3.75683e35	−1.81759
$414$	−8.60667e33	−0.0403024
$415$	1.18164e35	0.535593
$416$	3.76882e33	0.0165366
$417$	−6.49363e34	−0.275836
$418$	2.19345e32	0.000902085 0
$419$	4.06859e35	1.62015	0.810073	−	0.586329i	$-0.199427\pi$
$419$	4.06859e35	1.62015	0.810073	+	0.586329i	$0.199427\pi$
$420$	4.08013e34	0.157329
$421$	−2.35168e35	−0.878153	−0.439076	−	0.898450i	$-0.644694\pi$
$421$	−2.35168e35	−0.878153	−0.439076	+	0.898450i	$0.644694\pi$
$422$	1.14934e35	0.415652
$423$	−2.68962e35	−0.942099
$424$	−5.36161e33	−0.0181910
$425$	2.43392e34	0.0799936
$426$	1.64684e35	0.524349
$427$	−3.38249e35	−1.04342
$428$	3.25457e35	0.972754
$429$	−1.79610e33	−0.00520185
$430$	−1.21806e34	−0.0341856
$431$	5.93896e35	1.61535	0.807676	−	0.589626i	$-0.200725\pi$
$431$	5.93896e35	1.61535	0.807676	+	0.589626i	$0.200725\pi$
$432$	−8.61058e34	−0.226987
$433$	−5.11209e35	−1.30621	−0.653104	−	0.757269i	$-0.726533\pi$
$433$	−5.11209e35	−1.30621	−0.653104	+	0.757269i	$0.726533\pi$
$434$	1.26291e35	0.312796
$435$	1.15916e35	0.278316
$436$	−1.18175e35	−0.275079
$437$	4.23129e32	0.000954933 0
$438$	2.71405e35	0.593905
$439$	6.22583e35	1.32107	0.660536	−	0.750794i	$-0.270329\pi$
$439$	6.22583e35	1.32107	0.660536	+	0.750794i	$0.270329\pi$
$440$	8.10376e33	0.0166754
$441$	−2.82435e35	−0.563635
$442$	1.36688e34	0.0264564
$443$	7.89880e35	1.48290	0.741448	−	0.671010i	$-0.234139\pi$
$443$	7.89880e35	1.48290	0.741448	+	0.671010i	$0.234139\pi$
$444$	2.45545e35	0.447157
$445$	−3.95956e35	−0.699499
$446$	−1.55238e35	−0.266059
$447$	−8.13607e34	−0.135289
$448$	−1.03384e35	−0.166802
$449$	8.32672e35	1.30361	0.651806	−	0.758385i	$-0.274011\pi$
$449$	8.32672e35	1.30361	0.651806	+	0.758385i	$0.274011\pi$
$450$	6.72069e34	0.102105
$451$	8.13879e33	0.0119999
$452$	2.35967e35	0.337662
$453$	−3.90500e35	−0.542369
$454$	−2.15152e35	−0.290063
$455$	−4.26561e34	−0.0558249
$456$	1.77488e33	0.00225499
$457$	−3.61787e35	−0.446257	−0.223128	−	0.974789i	$-0.571627\pi$
$457$	−3.61787e35	−0.446257	−0.223128	+	0.974789i	$0.571627\pi$
$458$	9.59074e35	1.14860
$459$	−3.12290e35	−0.363151
$460$	1.56326e34	0.0176523
$461$	−4.32462e35	−0.474226	−0.237113	−	0.971482i	$-0.576201\pi$
$461$	−4.32462e35	−0.474226	−0.237113	+	0.971482i	$0.576201\pi$
$462$	4.92698e34	0.0524704
$463$	−5.74369e35	−0.594084	−0.297042	−	0.954864i	$-0.596000\pi$
$463$	−5.74369e35	−0.594084	−0.297042	+	0.954864i	$0.596000\pi$
$464$	−2.93714e35	−0.295075
$465$	−8.01026e34	−0.0781685
$466$	−3.88504e35	−0.368286
$467$	8.79293e35	0.809759	0.404879	−	0.914370i	$-0.367314\pi$
$467$	8.79293e35	0.809759	0.404879	+	0.914370i	$0.367314\pi$
$468$	3.77433e34	0.0337692
$469$	−2.78393e36	−2.42006
$470$	4.88526e35	0.412635
$471$	−5.77171e34	−0.0473721
$472$	−6.03776e35	−0.481569
$473$	−1.47087e34	−0.0114012
$474$	−3.04739e34	−0.0229572
$475$	−3.30408e33	−0.00241929
$476$	−3.74957e35	−0.266862
$477$	−5.36944e34	−0.0371476
$478$	3.64835e35	0.245369
$479$	−1.32449e36	−0.866001	−0.433000	−	0.901394i	$-0.642545\pi$
$479$	−1.32449e36	−0.866001	−0.433000	+	0.901394i	$0.642545\pi$
$480$	6.55735e34	0.0416842
$481$	−2.56707e35	−0.158664
$482$	−1.32790e36	−0.798050
$483$	9.50442e34	0.0555443
$484$	−8.70011e35	−0.494439
$485$	−6.00342e35	−0.331807
$486$	−1.36308e36	−0.732711
$487$	2.77661e36	1.45169	0.725844	−	0.687859i	$-0.241449\pi$
$487$	2.77661e36	1.45169	0.725844	+	0.687859i	$0.241449\pi$
$488$	−5.43615e35	−0.276454
$489$	−1.05308e36	−0.520944
$490$	5.12997e35	0.246870
$491$	3.83404e36	1.79497	0.897485	−	0.441046i	$-0.145392\pi$
$491$	3.83404e36	1.79497	0.897485	+	0.441046i	$0.145392\pi$
$492$	6.58570e34	0.0299967
$493$	−1.06525e36	−0.472082
$494$	−1.85557e33	−0.000800135 0
$495$	8.11560e34	0.0340526
$496$	2.02968e35	0.0828752
$497$	4.72288e36	1.87670
$498$	1.15460e36	0.446515
$499$	−1.37412e35	−0.0517210	−0.0258605	−	0.999666i	$-0.508233\pi$
$499$	−1.37412e35	−0.0517210	−0.0258605	+	0.999666i	$0.508233\pi$
$500$	−1.22070e35	−0.0447214
$501$	−1.40558e35	−0.0501241
$502$	−5.36591e35	−0.186270
$503$	4.60357e36	1.55570	0.777852	−	0.628447i	$-0.216309\pi$
$503$	4.60357e36	1.55570	0.777852	+	0.628447i	$0.216309\pi$
$504$	−1.03535e36	−0.340625
$505$	−2.58928e36	−0.829365
$506$	1.88772e34	0.00588716
$507$	−1.72116e36	−0.522654
$508$	5.88839e35	0.174115
$509$	1.03517e36	0.298071	0.149035	−	0.988832i	$-0.452383\pi$
$509$	1.03517e36	0.298071	0.149035	+	0.988832i	$0.452383\pi$
$510$	2.37823e35	0.0666895
$511$	7.78349e36	2.12565
$512$	−1.66153e35	−0.0441942
$513$	4.23939e34	0.0109830
$514$	−3.08021e36	−0.777281
$515$	−4.24540e34	−0.0104357
$516$	−1.19019e35	−0.0285000
$517$	5.89921e35	0.137617
$518$	7.04185e36	1.60042
$519$	−8.79106e35	−0.194662
$520$	−6.85545e34	−0.0147908
$521$	5.78940e36	1.21709	0.608547	−	0.793518i	$-0.291753\pi$
$521$	5.78940e36	1.21709	0.608547	+	0.793518i	$0.291753\pi$
$522$	−2.94143e36	−0.602569
$523$	−5.79695e36	−1.15725	−0.578625	−	0.815594i	$-0.696410\pi$
$523$	−5.79695e36	−1.15725	−0.578625	+	0.815594i	$0.696410\pi$
$524$	−2.27153e36	−0.441923
$525$	−7.42171e35	−0.140719
$526$	−1.20529e36	−0.222733
$527$	7.36128e35	0.132590
$528$	7.91836e34	0.0139020
$529$	−5.80680e36	−0.993768
$530$	9.75271e34	0.0162705
$531$	−6.04658e36	−0.983408
$532$	5.09010e34	0.00807085
$533$	−6.88509e34	−0.0106437
$534$	−3.86898e36	−0.583162
$535$	−5.92003e36	−0.870057
$536$	−4.47418e36	−0.641193
$537$	−4.59439e36	−0.642059
$538$	8.98384e36	1.22434
$539$	6.19472e35	0.0823329
$540$	1.56626e36	0.203024
$541$	4.55675e35	0.0576093	0.0288046	−	0.999585i	$-0.490830\pi$
$541$	4.55675e35	0.0576093	0.0288046	+	0.999585i	$0.490830\pi$
$542$	6.53163e36	0.805436
$543$	−3.51722e36	−0.423060
$544$	−6.02609e35	−0.0707051
$545$	2.14959e36	0.246038
$546$	−4.16802e35	−0.0465403
$547$	7.34964e36	0.800640	0.400320	−	0.916375i	$-0.368899\pi$
$547$	7.34964e36	0.800640	0.400320	+	0.916375i	$0.368899\pi$
$548$	6.83726e36	0.726683
$549$	−5.44409e36	−0.564545
$550$	−1.47407e35	−0.0149149
$551$	1.44609e35	0.0142774
$552$	1.52750e35	0.0147164
$553$	−8.73945e35	−0.0821665
$554$	1.12838e37	1.03532
$555$	−4.46643e36	−0.399949
$556$	−2.99294e36	−0.261571
$557$	−1.11649e37	−0.952381	−0.476191	−	0.879342i	$-0.657983\pi$
$557$	−1.11649e37	−0.952381	−0.476191	+	0.879342i	$0.657983\pi$
$558$	2.03264e36	0.169239
$559$	1.24430e35	0.0101126
$560$	1.88055e36	0.149192
$561$	2.87185e35	0.0222414
$562$	−1.59625e37	−1.20687
$563$	−1.14995e37	−0.848820	−0.424410	−	0.905470i	$-0.639518\pi$
$563$	−1.14995e37	−0.848820	−0.424410	+	0.905470i	$0.639518\pi$
$564$	4.77349e36	0.344008
$565$	−4.29221e36	−0.302014
$566$	−1.69890e37	−1.16720
$567$	−4.83865e36	−0.324603
$568$	7.59034e36	0.497232
$569$	4.14930e36	0.265436	0.132718	−	0.991154i	$-0.457630\pi$
$569$	4.14930e36	0.265436	0.132718	+	0.991154i	$0.457630\pi$
$570$	−3.22849e34	−0.00201692
$571$	1.01000e37	0.616220	0.308110	−	0.951351i	$-0.400304\pi$
$571$	1.01000e37	0.616220	0.308110	+	0.951351i	$0.400304\pi$
$572$	−8.27833e34	−0.00493283
$573$	1.80150e36	0.104845
$574$	1.88868e36	0.107361
$575$	−2.84355e35	−0.0157887
$576$	−1.66396e36	−0.0902485
$577$	−1.31282e37	−0.695557	−0.347779	−	0.937577i	$-0.613064\pi$
$577$	−1.31282e37	−0.695557	−0.347779	+	0.937577i	$0.613064\pi$
$578$	1.14763e37	0.593988
$579$	1.39058e37	0.703130
$580$	5.34263e36	0.263923
$581$	3.31123e37	1.59813
$582$	−5.86607e36	−0.276622
$583$	1.17769e35	0.00542633
$584$	1.25092e37	0.563190
$585$	−6.86547e35	−0.0302041
$586$	−1.32830e37	−0.571056
$587$	9.82196e36	0.412652	0.206326	−	0.978483i	$-0.433849\pi$
$587$	9.82196e36	0.412652	0.206326	+	0.978483i	$0.433849\pi$
$588$	5.01261e36	0.205812
$589$	−9.99306e34	−0.00400998
$590$	1.09826e37	0.430729
$591$	−7.30149e36	−0.279886
$592$	1.13173e37	0.424032
$593$	−1.06673e37	−0.390676	−0.195338	−	0.980736i	$-0.562580\pi$
$593$	−1.06673e37	−0.390676	−0.195338	+	0.980736i	$0.562580\pi$
$594$	1.89134e36	0.0677099
$595$	6.82042e36	0.238689
$596$	−3.74995e36	−0.128292
$597$	2.39459e37	0.800900
$598$	−1.59694e35	−0.00522182
$599$	1.34901e37	0.431274	0.215637	−	0.976474i	$-0.430817\pi$
$599$	1.34901e37	0.431274	0.215637	+	0.976474i	$0.430817\pi$
$600$	−1.19278e36	−0.0372835
$601$	3.52554e37	1.07751	0.538754	−	0.842463i	$-0.318895\pi$
$601$	3.52554e37	1.07751	0.538754	+	0.842463i	$0.318895\pi$
$602$	−3.41329e36	−0.102005
$603$	−4.48071e37	−1.30937
$604$	−1.79983e37	−0.514320
$605$	1.58254e37	0.442239
$606$	−2.53004e37	−0.691429
$607$	2.43922e37	0.651934	0.325967	−	0.945381i	$-0.394310\pi$
$607$	2.43922e37	0.651934	0.325967	+	0.945381i	$0.394310\pi$
$608$	8.18051e34	0.00213837
$609$	3.24825e37	0.830454
$610$	9.88829e36	0.247268
$611$	−4.99050e36	−0.122064
$612$	−6.03489e36	−0.144386
$613$	−5.62323e37	−1.31604	−0.658020	−	0.753000i	$-0.728606\pi$
$613$	−5.62323e37	−1.31604	−0.658020	+	0.753000i	$0.728606\pi$
$614$	−3.50993e37	−0.803573
$615$	−1.19793e36	−0.0268298
$616$	2.27087e36	0.0497568
$617$	4.80049e37	1.02905	0.514525	−	0.857476i	$-0.327968\pi$
$617$	4.80049e37	1.02905	0.514525	+	0.857476i	$0.327968\pi$
$618$	−4.14827e35	−0.00870007
$619$	2.24910e37	0.461513	0.230757	−	0.973011i	$-0.425880\pi$
$619$	2.24910e37	0.461513	0.230757	+	0.973011i	$0.425880\pi$
$620$	−3.69197e36	−0.0741259
$621$	3.64850e36	0.0716766
$622$	−1.53630e37	−0.295329
$623$	−1.10956e38	−2.08720
$624$	−6.69861e35	−0.0123308
$625$	2.22045e36	0.0400000
$626$	−6.32158e37	−1.11448
$627$	−3.89858e34	−0.000672658 0
$628$	−2.66021e36	−0.0449222
$629$	4.10457e37	0.678397
$630$	1.88330e37	0.304664
$631$	−1.02822e38	−1.62814	−0.814068	−	0.580770i	$-0.802751\pi$
$631$	−1.02822e38	−1.62814	−0.814068	+	0.580770i	$0.802751\pi$
$632$	−1.40455e36	−0.0217700
$633$	−2.04280e37	−0.309939
$634$	2.51117e36	0.0372967
$635$	−1.07109e37	−0.155733
$636$	9.52958e35	0.0135645
$637$	−5.24048e36	−0.0730279
$638$	6.45151e36	0.0880202
$639$	7.60143e37	1.01539
$640$	3.02231e36	0.0395285
$641$	6.67226e37	0.854456	0.427228	−	0.904144i	$-0.359490\pi$
$641$	6.67226e37	0.854456	0.427228	+	0.904144i	$0.359490\pi$
$642$	−5.78459e37	−0.725353
$643$	−2.92763e37	−0.359474	−0.179737	−	0.983715i	$-0.557525\pi$
$643$	−2.92763e37	−0.359474	−0.179737	+	0.983715i	$0.557525\pi$
$644$	4.38063e36	0.0526717
$645$	2.16494e36	0.0254912
$646$	2.96693e35	0.00342112
$647$	−6.89266e37	−0.778357	−0.389179	−	0.921162i	$-0.627241\pi$
$647$	−6.89266e37	−0.778357	−0.389179	+	0.921162i	$0.627241\pi$
$648$	−7.77640e36	−0.0860035
$649$	1.32621e37	0.143651
$650$	1.24700e36	0.0132293
$651$	−2.24467e37	−0.233243
$652$	−4.85369e37	−0.494003
$653$	−6.00351e37	−0.598518	−0.299259	−	0.954172i	$-0.596740\pi$
$653$	−6.00351e37	−0.598518	−0.299259	+	0.954172i	$0.596740\pi$
$654$	2.10041e37	0.205118
$655$	4.13189e37	0.395268
$656$	3.03538e36	0.0284454
$657$	1.25274e38	1.15009
$658$	1.36897e38	1.23124
$659$	−3.15651e37	−0.278134	−0.139067	−	0.990283i	$-0.544410\pi$
$659$	−3.15651e37	−0.278134	−0.139067	+	0.990283i	$0.544410\pi$
$660$	−1.44034e36	−0.0124343
$661$	−5.72052e37	−0.483855	−0.241928	−	0.970294i	$-0.577780\pi$
$661$	−5.72052e37	−0.483855	−0.241928	+	0.970294i	$0.577780\pi$
$662$	8.92363e37	0.739535
$663$	−2.42947e36	−0.0197278
$664$	5.32162e37	0.423423
$665$	−9.25883e35	−0.00721879
$666$	1.13338e38	0.865911
$667$	1.24453e37	0.0931768
$668$	−6.47839e36	−0.0475318
$669$	2.75916e37	0.198392
$670$	8.13848e37	0.573500
$671$	1.19407e37	0.0824658
$672$	1.83753e37	0.124379
$673$	2.84152e38	1.88516	0.942578	−	0.333987i	$-0.108394\pi$
$673$	2.84152e38	1.88516	0.942578	+	0.333987i	$0.108394\pi$
$674$	1.75873e38	1.14365
$675$	−2.84900e37	−0.181590
$676$	−7.93292e37	−0.495625
$677$	1.71997e37	0.105336	0.0526678	−	0.998612i	$-0.483228\pi$
$677$	1.71997e37	0.105336	0.0526678	+	0.998612i	$0.483228\pi$
$678$	−4.19401e37	−0.251784
$679$	−1.68230e38	−0.990062
$680$	1.09614e37	0.0632405
$681$	3.82406e37	0.216291
$682$	−4.45825e36	−0.0247215
$683$	−7.22090e37	−0.392565	−0.196283	−	0.980547i	$-0.562887\pi$
$683$	−7.22090e37	−0.392565	−0.196283	+	0.980547i	$0.562887\pi$
$684$	8.19247e35	0.00436674
$685$	−1.24369e38	−0.649965
$686$	−4.03876e37	−0.206953
$687$	−1.70463e38	−0.856475
$688$	−5.48564e36	−0.0270261
$689$	−9.96280e35	−0.00481307
$690$	−2.77850e36	−0.0131628
$691$	8.09519e37	0.376074	0.188037	−	0.982162i	$-0.439787\pi$
$691$	8.09519e37	0.376074	0.188037	+	0.982162i	$0.439787\pi$
$692$	−4.05184e37	−0.184595
$693$	2.27419e37	0.101608
$694$	−2.36741e38	−1.03734
$695$	5.44413e37	0.233956
$696$	5.22040e37	0.220028
$697$	1.10088e37	0.0455089
$698$	3.80714e37	0.154366
$699$	6.90517e37	0.274620
$700$	−3.42070e37	−0.133442
$701$	5.38842e37	0.206190	0.103095	−	0.994671i	$-0.467125\pi$
$701$	5.38842e37	0.206190	0.103095	+	0.994671i	$0.467125\pi$
$702$	−1.60000e37	−0.0600576
$703$	−5.57202e36	−0.0205171
$704$	3.64961e36	0.0131830
$705$	−8.68293e37	−0.307690
$706$	1.92180e38	0.668106
$707$	−7.25579e38	−2.47470
$708$	1.07314e38	0.359092
$709$	−6.64239e37	−0.218072	−0.109036	−	0.994038i	$-0.534776\pi$
$709$	−6.64239e37	−0.218072	−0.109036	+	0.994038i	$0.534776\pi$
$710$	−1.38068e38	−0.444738
$711$	−1.40661e37	−0.0444563
$712$	−1.78323e38	−0.553003
$713$	−8.60021e36	−0.0261698
$714$	6.66438e37	0.198991
$715$	1.50582e36	0.00441206
$716$	−2.11758e38	−0.608854
$717$	−6.48448e37	−0.182964
$718$	−1.73633e38	−0.480788
$719$	−2.15626e38	−0.585950	−0.292975	−	0.956120i	$-0.594645\pi$
$719$	−2.15626e38	−0.585950	−0.292975	+	0.956120i	$0.594645\pi$
$720$	3.02673e37	0.0807207
$721$	−1.18966e37	−0.0311385
$722$	2.75216e38	0.707003
$723$	2.36017e38	0.595082
$724$	−1.62111e38	−0.401181
$725$	−9.71818e37	−0.236060
$726$	1.54633e38	0.368688
$727$	7.29285e38	1.70680	0.853401	−	0.521255i	$-0.174536\pi$
$727$	7.29285e38	1.70680	0.853401	+	0.521255i	$0.174536\pi$
$728$	−1.92106e37	−0.0441334
$729$	1.34405e38	0.303106
$730$	−2.27541e38	−0.503733
$731$	−1.98954e37	−0.0432383
$732$	9.66207e37	0.206144
$733$	8.53218e38	1.78713	0.893566	−	0.448932i	$-0.148195\pi$
$733$	8.53218e38	1.78713	0.893566	+	0.448932i	$0.148195\pi$
$734$	−4.24060e38	−0.872029
$735$	−9.11788e37	−0.184084
$736$	7.04030e36	0.0139553
$737$	9.82766e37	0.191267
$738$	3.03981e37	0.0580880
$739$	6.54496e37	0.122802	0.0614012	−	0.998113i	$-0.480443\pi$
$739$	6.54496e37	0.122802	0.0614012	+	0.998113i	$0.480443\pi$
$740$	−2.05860e38	−0.379265
$741$	3.29804e35	0.000596637 0
$742$	2.73294e37	0.0485487
$743$	−1.95541e38	−0.341105	−0.170553	−	0.985349i	$-0.554555\pi$
$743$	−1.95541e38	−0.341105	−0.170553	+	0.985349i	$0.554555\pi$
$744$	−3.60750e37	−0.0617976
$745$	6.82112e37	0.114748
$746$	−2.12762e38	−0.351495
$747$	5.32939e38	0.864668
$748$	1.32365e37	0.0210912
$749$	−1.65893e39	−2.59612
$750$	2.16965e37	0.0333474
$751$	9.02110e38	1.36182	0.680911	−	0.732366i	$-0.261584\pi$
$751$	9.02110e38	1.36182	0.680911	+	0.732366i	$0.261584\pi$
$752$	2.20012e38	0.326217
$753$	9.53724e37	0.138896
$754$	−5.45772e37	−0.0780724
$755$	3.27388e38	0.460022
$756$	4.38902e38	0.605792
$757$	7.72330e38	1.04715	0.523575	−	0.851980i	$-0.324598\pi$
$757$	7.72330e38	1.04715	0.523575	+	0.851980i	$0.324598\pi$
$758$	−5.15825e38	−0.687018
$759$	−3.35519e36	−0.00438988
$760$	−1.48803e36	−0.00191261
$761$	−6.10975e38	−0.771490	−0.385745	−	0.922605i	$-0.626056\pi$
$761$	−6.10975e38	−0.771490	−0.385745	+	0.922605i	$0.626056\pi$
$762$	−1.04659e38	−0.129832
$763$	6.02366e38	0.734141
$764$	8.30321e37	0.0994227
$765$	1.09774e38	0.129143
$766$	4.46695e38	0.516325
$767$	−1.12192e38	−0.127416
$768$	2.95317e37	0.0329543
$769$	−7.47622e38	−0.819741	−0.409870	−	0.912144i	$-0.634426\pi$
$769$	−7.47622e38	−0.819741	−0.409870	+	0.912144i	$0.634426\pi$
$770$	−4.13068e37	−0.0445038
$771$	5.47468e38	0.579595
$772$	6.40925e38	0.666766
$773$	1.33482e39	1.36458	0.682288	−	0.731083i	$-0.260985\pi$
$773$	1.33482e39	1.36458	0.682288	+	0.731083i	$0.260985\pi$
$774$	−5.49366e37	−0.0551898
$775$	6.71565e37	0.0663002
$776$	−2.70370e38	−0.262316
$777$	−1.25160e39	−1.19339
$778$	−9.45491e38	−0.885998
$779$	−1.49446e36	−0.00137635
$780$	1.21847e37	0.0110290
$781$	−1.66724e38	−0.148323
$782$	2.55339e37	0.0223268
$783$	1.24692e39	1.07165
$784$	2.31033e38	0.195168
$785$	4.83889e37	0.0401796
$786$	4.03736e38	0.329529
$787$	−1.55203e38	−0.124521	−0.0622603	−	0.998060i	$-0.519831\pi$
$787$	−1.55203e38	−0.124521	−0.0622603	+	0.998060i	$0.519831\pi$
$788$	−3.36529e38	−0.265411
$789$	2.14225e38	0.166085
$790$	2.55487e37	0.0194717
$791$	−1.20278e39	−0.901164
$792$	3.65494e37	0.0269209
$793$	−1.01013e38	−0.0731458
$794$	4.63068e38	0.329661
$795$	−1.73342e37	−0.0121324
$796$	1.10368e39	0.759481
$797$	−1.19576e39	−0.809019	−0.404509	−	0.914534i	$-0.632558\pi$
$797$	−1.19576e39	−0.809019	−0.404509	+	0.914534i	$0.632558\pi$
$798$	−9.04701e36	−0.00601819
$799$	7.97946e38	0.521905
$800$	−5.49756e37	−0.0353553
$801$	−1.78583e39	−1.12928
$802$	3.20585e37	0.0199337
$803$	−2.74767e38	−0.167999
$804$	7.95229e38	0.478118
$805$	−7.96832e37	−0.0471110
$806$	3.77150e37	0.0219276
$807$	−1.59676e39	−0.912952
$808$	−1.16611e39	−0.655671
$809$	−2.75200e39	−1.52175	−0.760874	−	0.648899i	$-0.775230\pi$
$809$	−2.75200e39	−1.52175	−0.760874	+	0.648899i	$0.775230\pi$
$810$	1.41452e38	0.0769239
$811$	−2.91604e39	−1.55960	−0.779798	−	0.626032i	$-0.784678\pi$
$811$	−2.91604e39	−1.55960	−0.779798	+	0.626032i	$0.784678\pi$
$812$	1.49713e39	0.787506
$813$	−1.16092e39	−0.600590
$814$	−2.48587e38	−0.126488
$815$	8.82881e38	0.441849
$816$	1.07106e38	0.0527226
$817$	2.70084e36	0.00130768
$818$	2.05599e38	0.0979154
$819$	−1.92387e38	−0.0901245
$820$	−5.52132e37	−0.0254423
$821$	2.55103e38	0.115633	0.0578165	−	0.998327i	$-0.481586\pi$
$821$	2.55103e38	0.115633	0.0578165	+	0.998327i	$0.481586\pi$
$822$	−1.21524e39	−0.541866
$823$	−2.16576e39	−0.949977	−0.474989	−	0.879992i	$-0.657548\pi$
$823$	−2.16576e39	−0.949977	−0.474989	+	0.879992i	$0.657548\pi$
$824$	−1.91196e37	−0.00825014
$825$	2.61996e37	0.0111216
$826$	3.07759e39	1.28523
$827$	1.43961e39	0.591453	0.295727	−	0.955273i	$-0.404438\pi$
$827$	1.43961e39	0.591453	0.295727	+	0.955273i	$0.404438\pi$
$828$	7.05059e37	0.0284981
$829$	3.12334e39	1.24203	0.621016	−	0.783798i	$-0.286720\pi$
$829$	3.12334e39	1.24203	0.621016	+	0.783798i	$0.286720\pi$
$830$	−9.67997e38	−0.378721
$831$	−2.00555e39	−0.772006
$832$	−3.08742e37	−0.0116931
$833$	8.37917e38	0.312244
$834$	5.31958e38	0.195045
$835$	1.17841e38	0.0425138
$836$	−1.79687e36	−0.000637871 0
$837$	−8.61669e38	−0.300986
$838$	−3.33299e39	−1.14562
$839$	5.81719e39	1.96755	0.983777	−	0.179397i	$-0.0574145\pi$
$839$	5.81719e39	1.96755	0.983777	+	0.179397i	$0.0574145\pi$
$840$	−3.34244e38	−0.111248
$841$	1.20020e39	0.393105
$842$	1.92650e39	0.620948
$843$	2.83714e39	0.899928
$844$	−9.41537e38	−0.293910
$845$	1.44299e39	0.443300
$846$	2.20334e39	0.666164
$847$	4.43466e39	1.31958
$848$	4.39223e37	0.0128630
$849$	3.01958e39	0.870347
$850$	−1.99387e38	−0.0565640
$851$	−4.79538e38	−0.133898
$852$	−1.34909e39	−0.370771
$853$	−1.88847e39	−0.510854	−0.255427	−	0.966828i	$-0.582216\pi$
$853$	−1.88847e39	−0.510854	−0.255427	+	0.966828i	$0.582216\pi$
$854$	2.77094e39	0.737812
$855$	−1.49020e37	−0.00390573
$856$	−2.66614e39	−0.687841
$857$	−4.20096e39	−1.06686	−0.533429	−	0.845845i	$-0.679097\pi$
$857$	−4.20096e39	−1.06686	−0.533429	+	0.845845i	$0.679097\pi$
$858$	1.47137e37	0.00367826
$859$	7.26089e39	1.78683	0.893413	−	0.449236i	$-0.148304\pi$
$859$	7.26089e39	1.78683	0.893413	+	0.449236i	$0.148304\pi$
$860$	9.97833e37	0.0241729
$861$	−3.35689e38	−0.0800562
$862$	−4.86520e39	−1.14223
$863$	9.99655e38	0.231049	0.115525	−	0.993305i	$-0.463145\pi$
$863$	9.99655e38	0.231049	0.115525	+	0.993305i	$0.463145\pi$
$864$	7.05379e38	0.160504
$865$	7.37025e38	0.165107
$866$	4.18783e39	0.923628
$867$	−2.03977e39	−0.442919
$868$	−1.03458e39	−0.221180
$869$	3.08514e37	0.00649394
$870$	−9.49584e38	−0.196799
$871$	−8.31380e38	−0.169650
$872$	9.68089e38	0.194510
$873$	−2.70765e39	−0.535674
$874$	−3.46627e36	−0.000675240 0
$875$	6.22222e38	0.119354
$876$	−2.22335e39	−0.419954
$877$	−4.39906e39	−0.818211	−0.409105	−	0.912487i	$-0.634159\pi$
$877$	−4.39906e39	−0.818211	−0.409105	+	0.912487i	$0.634159\pi$
$878$	−5.10020e39	−0.934139
$879$	2.36089e39	0.425820
$880$	−6.63860e37	−0.0117913
$881$	−2.21444e39	−0.387338	−0.193669	−	0.981067i	$-0.562039\pi$
$881$	−2.21444e39	−0.387338	−0.193669	+	0.981067i	$0.562039\pi$
$882$	2.31371e39	0.398550
$883$	3.04198e38	0.0516044	0.0258022	−	0.999667i	$-0.491786\pi$
$883$	3.04198e38	0.0516044	0.0258022	+	0.999667i	$0.491786\pi$
$884$	−1.11975e38	−0.0187075
$885$	−1.95202e39	−0.321181
$886$	−6.47069e39	−1.04857
$887$	3.06989e39	0.489953	0.244977	−	0.969529i	$-0.421220\pi$
$887$	3.06989e39	0.489953	0.244977	+	0.969529i	$0.421220\pi$
$888$	−2.01150e39	−0.316188
$889$	−3.00145e39	−0.464684
$890$	3.24368e39	0.494621
$891$	1.70811e38	0.0256547
$892$	1.27171e39	0.188132
$893$	−1.08322e38	−0.0157842
$894$	6.66506e38	0.0956639
$895$	3.85185e39	0.544576
$896$	8.46925e38	0.117947
$897$	2.83835e37	0.00389375
$898$	−6.82125e39	−0.921793
$899$	−2.93922e39	−0.391270
$900$	−5.50559e38	−0.0721988
$901$	1.59298e38	0.0205791
$902$	−6.66730e37	−0.00848519
$903$	6.06669e38	0.0760619
$904$	−1.93304e39	−0.238763
$905$	2.94877e39	0.358827
$906$	3.19898e39	0.383513
$907$	−6.69307e39	−0.790546	−0.395273	−	0.918564i	$-0.629350\pi$
$907$	−6.69307e39	−0.790546	−0.395273	+	0.918564i	$0.629350\pi$
$908$	1.76253e39	0.205106
$909$	−1.16781e40	−1.33894
$910$	3.49439e38	0.0394741
$911$	−2.24684e39	−0.250077	−0.125039	−	0.992152i	$-0.539905\pi$
$911$	−2.24684e39	−0.250077	−0.125039	+	0.992152i	$0.539905\pi$
$912$	−1.45398e37	−0.00159452
$913$	−1.16891e39	−0.126306
$914$	2.96376e39	0.315551
$915$	−1.75752e39	−0.184381
$916$	−7.85673e39	−0.812182
$917$	1.15786e40	1.17942
$918$	2.55828e39	0.256787
$919$	−1.71198e40	−1.69332	−0.846662	−	0.532131i	$-0.821391\pi$
$919$	−1.71198e40	−1.69332	−0.846662	+	0.532131i	$0.821391\pi$
$920$	−1.28062e38	−0.0124820
$921$	6.23845e39	0.599200
$922$	3.54273e39	0.335328
$923$	1.41042e39	0.131560
$924$	−4.03618e38	−0.0371021
$925$	3.74457e39	0.339225
$926$	4.70523e39	0.420081
$927$	−1.91475e38	−0.0168475
$928$	2.40610e39	0.208649
$929$	1.02221e40	0.873632	0.436816	−	0.899551i	$-0.356106\pi$
$929$	1.02221e40	0.873632	0.436816	+	0.899551i	$0.356106\pi$
$930$	6.56200e38	0.0552735
$931$	−1.13749e38	−0.00944333
$932$	3.18262e39	0.260418
$933$	2.73058e39	0.220218
$934$	−7.20317e39	−0.572586
$935$	−2.40770e38	−0.0188645
$936$	−3.09193e38	−0.0238784
$937$	9.74565e39	0.741868	0.370934	−	0.928659i	$-0.379038\pi$
$937$	9.74565e39	0.741868	0.370934	+	0.928659i	$0.379038\pi$
$938$	2.28060e40	1.71124
$939$	1.12358e40	0.831034
$940$	−4.00200e39	−0.291777
$941$	2.57094e39	0.184771	0.0923853	−	0.995723i	$-0.470551\pi$
$941$	2.57094e39	0.184771	0.0923853	+	0.995723i	$0.470551\pi$
$942$	4.72819e38	0.0334971
$943$	−1.28616e38	−0.00898229
$944$	4.94613e39	0.340521
$945$	−7.98359e39	−0.541837
$946$	1.20494e38	0.00806183
$947$	−1.22271e39	−0.0806490	−0.0403245	−	0.999187i	$-0.512839\pi$
$947$	−1.22271e39	−0.0806490	−0.0403245	+	0.999187i	$0.512839\pi$
$948$	2.49642e38	0.0162332
$949$	2.32442e39	0.149012
$950$	2.70671e37	0.00171069
$951$	−4.46328e38	−0.0278111
$952$	3.07165e39	0.188700
$953$	7.65794e39	0.463829	0.231914	−	0.972736i	$-0.425501\pi$
$953$	7.65794e39	0.463829	0.231914	+	0.972736i	$0.425501\pi$
$954$	4.39865e38	0.0262673
$955$	−1.51035e39	−0.0889264
$956$	−2.98873e39	−0.173502
$957$	−1.14667e39	−0.0656340
$958$	1.08502e40	0.612355
$959$	−3.48512e40	−1.93940
$960$	−5.37178e38	−0.0294752
$961$	−1.64516e40	−0.890107
$962$	2.10294e39	0.112193
$963$	−2.67004e40	−1.40463
$964$	1.08781e40	0.564307
$965$	−1.16584e40	−0.596374
$966$	−7.78602e38	−0.0392757
$967$	−2.57889e37	−0.00128285	−0.000641425	−	1.00000i	$-0.500204\pi$
$967$	−2.57889e37	−0.00128285	−0.000641425		1.00000i	$0.500204\pi$
$968$	7.12713e39	0.349621
$969$	−5.27334e37	−0.00255102
$970$	4.91800e39	0.234623
$971$	3.64031e40	1.71269	0.856345	−	0.516404i	$-0.172730\pi$
$971$	3.64031e40	1.71269	0.856345	+	0.516404i	$0.172730\pi$
$972$	1.11664e40	0.518105
$973$	1.52558e40	0.698089
$974$	−2.27460e40	−1.02650
$975$	−2.21638e38	−0.00986467
$976$	4.45329e39	0.195483
$977$	9.13450e39	0.395465	0.197733	−	0.980256i	$-0.436642\pi$
$977$	9.13450e39	0.395465	0.197733	+	0.980256i	$0.436642\pi$
$978$	8.62682e39	0.368363
$979$	3.91691e39	0.164960
$980$	−4.20247e39	−0.174563
$981$	9.69503e39	0.397208
$982$	−3.14085e40	−1.26923
$983$	−1.10897e40	−0.442025	−0.221012	−	0.975271i	$-0.570936\pi$
$983$	−1.10897e40	−0.442025	−0.221012	+	0.975271i	$0.570936\pi$
$984$	−5.39501e38	−0.0212108
$985$	6.12143e39	0.237391
$986$	8.72651e39	0.333812
$987$	−2.43317e40	−0.918100
$988$	1.52008e37	0.000565781 0
$989$	2.32439e38	0.00853413
$990$	−6.64830e38	−0.0240788
$991$	4.45006e40	1.58991	0.794954	−	0.606670i	$-0.207495\pi$
$991$	4.45006e40	1.58991	0.794954	+	0.606670i	$0.207495\pi$
$992$	−1.66271e39	−0.0586017
$993$	−1.58606e40	−0.551449
$994$	−3.86898e40	−1.32703
$995$	−2.00758e40	−0.679300
$996$	−9.45850e39	−0.315734
$997$	2.41234e40	0.794427	0.397213	−	0.917726i	$-0.369977\pi$
$997$	2.41234e40	0.794427	0.397213	+	0.917726i	$0.369977\pi$
$998$	1.12568e39	0.0365723
$999$	−4.80457e40	−1.54000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.a.b.1.2	✓	2
5.2	odd	4		50.28.b.d.49.1		4
5.3	odd	4		50.28.b.d.49.4		4
5.4	even	2		50.28.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.b.1.2	✓	2	1.1	even	1	trivial
50.28.a.d.1.1		2	5.4	even	2
50.28.b.d.49.1		4	5.2	odd	4
50.28.b.d.49.4		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-8192.00 q^{2} +1.45602e6 q^{3} +6.71089e7 q^{4} -1.22070e9 q^{5} -1.19278e10 q^{6} -3.42070e11 q^{7} -5.49756e11 q^{8} -5.50559e12 q^{9} +1.00000e13 q^{10} +1.20755e13 q^{11} +9.77122e13 q^{12} -1.02154e14 q^{13} +2.80224e15 q^{14} -1.77737e15 q^{15} +4.50360e15 q^{16} +1.63337e16 q^{17} +4.51018e16 q^{18} -2.21733e15 q^{19} -8.19200e16 q^{20} -4.98063e17 q^{21} -9.89228e16 q^{22} -1.90828e17 q^{23} -8.00458e17 q^{24} +1.49012e18 q^{25} +8.36847e17 q^{26} -1.91193e19 q^{27} -2.29560e19 q^{28} -6.52176e19 q^{29} +1.45602e19 q^{30} +4.50679e19 q^{31} -3.68935e19 q^{32} +1.75823e19 q^{33} -1.33806e20 q^{34} +4.17566e20 q^{35} -3.69474e20 q^{36} +2.51294e21 q^{37} +1.81644e19 q^{38} -1.48739e20 q^{39} +6.71089e20 q^{40} +6.73990e20 q^{41} +4.08013e21 q^{42} -1.21806e21 q^{43} +8.10376e20 q^{44} +6.72069e21 q^{45} +1.56326e21 q^{46} +4.88526e22 q^{47} +6.55735e21 q^{48} +5.12997e22 q^{49} -1.22070e22 q^{50} +2.37823e22 q^{51} -6.85545e21 q^{52} +9.75271e21 q^{53} +1.56626e23 q^{54} -1.47407e22 q^{55} +1.88055e23 q^{56} -3.22849e21 q^{57} +5.34263e23 q^{58} +1.09826e24 q^{59} -1.19278e23 q^{60} +9.88829e23 q^{61} -3.69197e23 q^{62} +1.88330e24 q^{63} +3.02231e23 q^{64} +1.24700e23 q^{65} -1.44034e23 q^{66} +8.13848e24 q^{67} +1.09614e24 q^{68} -2.77850e23 q^{69} -3.42070e24 q^{70} -1.38068e25 q^{71} +3.02673e24 q^{72} -2.27541e25 q^{73} -2.05860e25 q^{74} +2.16965e24 q^{75} -1.48803e23 q^{76} -4.13068e24 q^{77} +1.21847e24 q^{78} +2.55487e24 q^{79} -5.49756e24 q^{80} +1.41452e25 q^{81} -5.52132e24 q^{82} -9.67997e25 q^{83} -3.34244e25 q^{84} -1.99387e25 q^{85} +9.97833e24 q^{86} -9.49584e25 q^{87} -6.63860e24 q^{88} +3.24368e26 q^{89} -5.50559e25 q^{90} +3.49439e25 q^{91} -1.28062e25 q^{92} +6.56200e25 q^{93} -4.00200e26 q^{94} +2.70671e24 q^{95} -5.37178e25 q^{96} +4.91800e26 q^{97} -4.20247e26 q^{98} -6.64830e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16384 q^{2} - 2245644 q^{3} + 134217728 q^{4} - 2441406250 q^{5} + 18396315648 q^{6} - 120196732292 q^{7} - 1099511627776 q^{8} + 571163616594 q^{9} + 20000000000000 q^{10} + 7112122732704 q^{11}+ \cdots - 96\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 16384 * q^2 - 2245644 * q^3 + 134217728 * q^4 - 2441406250 * q^5 + 18396315648 * q^6 - 120196732292 * q^7 - 1099511627776 * q^8 + 571163616594 * q^9 + 20000000000000 * q^10 + 7112122732704 * q^11 - 150702617788416 * q^12 - 323114990355404 * q^13 + 984651630936064 * q^14 + 2741264648437500 * q^15 + 9007199254740992 * q^16 - 11949781720794252 * q^17 - 4678972347138048 * q^18 - 310800626187534200 * q^19 - 163840000000000000 * q^20 - 1319365315134326376 * q^21 - 58262509426311168 * q^22 - 1207992822578557644 * q^23 + 1234555844922703872 * q^24 + 2980232238769531250 * q^25 + 2646958000991469568 * q^26 - 13386024338103046440 * q^27 - 8066266160628236288 * q^28 - 85089627076663724580 * q^29 - 22456440000000000000 * q^30 - 169891626304914480056 * q^31 - 73786976294838206464 * q^32 + 35955214564003682112 * q^33 + 97892611856746512384 * q^34 + 146724526723632812500 * q^35 + 38330141467754889216 * q^36 + 1001687425876018532308 * q^37 + 2546078729728280166400 * q^38 + 669184707607358092488 * q^39 + 1342177280000000000000 * q^40 + 6829708525832119000044 * q^41 + 10808240661580401672192 * q^42 + 15331910221739375128036 * q^43 + 477286477220341088256 * q^44 - 697221211662597656250 * q^45 + 9895877202563544219648 * q^46 + 44654607958183509227628 * q^47 - 10113481481606790119424 * q^48 + 34815266426190611168346 * q^49 - 24414062500000000000000 * q^50 + 128478598882379942153544 * q^51 - 21683879944122118701056 * q^52 + 259350970067880627435396 * q^53 + 109658311377740156436480 * q^54 - 8681790445195312500000 * q^55 + 66078852387866511671296 * q^56 + 1139044611805451608251600 * q^57 + 697054225012029231759360 * q^58 + 2082093442621301023169640 * q^59 + 183963156480000000000000 * q^60 + 677925769536334246319284 * q^61 + 1391752202689859420618752 * q^62 + 3231569874371732206566876 * q^63 + 604462909807314587353088 * q^64 + 394427478461186523437500 * q^65 - 294545117708318163861504 * q^66 + 2453617552336948143390028 * q^67 - 801936276330467429449728 * q^68 + 3487358239126020846890568 * q^69 - 1201967322920000000000000 * q^70 - 23890193584108132090228776 * q^71 - 314000518903848052457472 * q^72 - 13919420706136886544146204 * q^73 - 8205823392776343816667136 * q^74 - 3346270322799682617187500 * q^75 - 20857476953934071123148800 * q^76 - 5231935501660614540408384 * q^77 - 5481961124719477493661696 * q^78 - 53659327270981104663051920 * q^79 - 10995116277760000000000000 * q^80 - 53416489016311609709962998 * q^81 - 55948972243616718848360448 * q^82 + 5756571261014435461903716 * q^83 - 88541107499666650498596864 * q^84 + 14587135889641420898437500 * q^85 - 125599008536488961048870912 * q^86 - 21398789661957929503788840 * q^87 - 3909930821389034194993152 * q^88 + 174438127411287409220344020 * q^89 + 5711636165940000000000000 * q^90 - 14081455302088161819283816 * q^91 - 81067026043400554247356416 * q^92 + 861329117078544091150519632 * q^93 - 365810548393439307592728576 * q^94 + 379395295639079833984375000 * q^95 + 82849640297322824658321408 * q^96 - 21732067184289340167295292 * q^97 - 285206662563353486691090432 * q^98 - 96644441211111069636758112 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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