LMFDB - Embedded newform 47.20.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [47,20,Mod(1,47)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(47, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("47.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	47.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:	$107.543847381$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-480.216 q^{2} -36068.5 q^{3} -293681. q^{4} +5.02224e6 q^{5} +1.73207e7 q^{6} +6.92578e7 q^{7} +3.92802e8 q^{8} +1.38678e8 q^{9} +O(q^{10})$	\(q-480.216 q^{2} -36068.5 q^{3} -293681. q^{4} +5.02224e6 q^{5} +1.73207e7 q^{6} +6.92578e7 q^{7} +3.92802e8 q^{8} +1.38678e8 q^{9} -2.41176e9 q^{10} -4.10995e9 q^{11} +1.05926e10 q^{12} +1.56353e10 q^{13} -3.32587e10 q^{14} -1.81145e11 q^{15} -3.46563e10 q^{16} +9.99522e9 q^{17} -6.65953e10 q^{18} -1.56460e12 q^{19} -1.47494e12 q^{20} -2.49803e12 q^{21} +1.97366e12 q^{22} -9.33202e12 q^{23} -1.41678e13 q^{24} +6.14945e12 q^{25} -7.50831e12 q^{26} +3.69192e13 q^{27} -2.03397e13 q^{28} +3.05988e13 q^{29} +8.69887e13 q^{30} +1.26203e14 q^{31} -1.89299e14 q^{32} +1.48240e14 q^{33} -4.79986e12 q^{34} +3.47830e14 q^{35} -4.07270e13 q^{36} -1.07289e15 q^{37} +7.51344e14 q^{38} -5.63941e14 q^{39} +1.97275e15 q^{40} +3.48942e15 q^{41} +1.19959e15 q^{42} +4.53042e15 q^{43} +1.20701e15 q^{44} +6.96474e14 q^{45} +4.48138e15 q^{46} +1.11913e15 q^{47} +1.25000e15 q^{48} -6.60225e15 q^{49} -2.95307e15 q^{50} -3.60513e14 q^{51} -4.59178e15 q^{52} +2.70577e16 q^{53} -1.77292e16 q^{54} -2.06412e16 q^{55} +2.72046e16 q^{56} +5.64327e16 q^{57} -1.46940e16 q^{58} -2.54831e16 q^{59} +5.31988e16 q^{60} -1.33777e17 q^{61} -6.06047e16 q^{62} +9.60453e15 q^{63} +1.09074e17 q^{64} +7.85242e16 q^{65} -7.11871e16 q^{66} +2.78626e17 q^{67} -2.93540e15 q^{68} +3.36592e17 q^{69} -1.67033e17 q^{70} -6.03034e17 q^{71} +5.44729e16 q^{72} +4.95368e16 q^{73} +5.15217e17 q^{74} -2.21802e17 q^{75} +4.59491e17 q^{76} -2.84646e17 q^{77} +2.70814e17 q^{78} +9.43682e17 q^{79} -1.74052e17 q^{80} -1.49280e18 q^{81} -1.67568e18 q^{82} +1.80497e18 q^{83} +7.33622e17 q^{84} +5.01984e16 q^{85} -2.17558e18 q^{86} -1.10366e18 q^{87} -1.61439e18 q^{88} +3.40618e18 q^{89} -3.34458e17 q^{90} +1.08286e18 q^{91} +2.74063e18 q^{92} -4.55196e18 q^{93} -5.37424e17 q^{94} -7.85778e18 q^{95} +6.82773e18 q^{96} -6.45134e18 q^{97} +3.17051e18 q^{98} -5.69959e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) $ 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9	$ 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9} - 10197084160 q^{10} - 7963915630 q^{11} - 12629269764 q^{12} - 159160177690 q^{13} + 404118350082 q^{14} - 59651276056 q^{15} + 1400499411089 q^{16} - 2004886737784 q^{17} - 4449273908039 q^{18} - 1058821844658 q^{19} + 5114247081432 q^{20} + 2403861756792 q^{21} - 3900401557590 q^{22} - 17333732320340 q^{23} + 32877217250016 q^{24} + 85478486158774 q^{25} - 52056718761868 q^{26} - 137248515015920 q^{27} - 361374372214712 q^{28} - 66840103484258 q^{29} - 884984566401484 q^{30} - 481560705870844 q^{31} - 19\!\cdots\!67 q^{32}+ \cdots + 10\!\cdots\!22 q^{99}+O(q^{100}) $ 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9 - 10197084160 * q^10 - 7963915630 * q^11 - 12629269764 * q^12 - 159160177690 * q^13 + 404118350082 * q^14 - 59651276056 * q^15 + 1400499411089 * q^16 - 2004886737784 * q^17 - 4449273908039 * q^18 - 1058821844658 * q^19 + 5114247081432 * q^20 + 2403861756792 * q^21 - 3900401557590 * q^22 - 17333732320340 * q^23 + 32877217250016 * q^24 + 85478486158774 * q^25 - 52056718761868 * q^26 - 137248515015920 * q^27 - 361374372214712 * q^28 - 66840103484258 * q^29 - 884984566401484 * q^30 - 481560705870844 * q^31 - 1956224504349967 * q^32 - 1089319960511632 * q^33 - 1024355370607462 * q^34 - 368682962835736 * q^35 - 447128934368887 * q^36 - 2062248173433492 * q^37 - 1576879945450998 * q^38 - 2078450045289336 * q^39 - 6293443543679952 * q^40 + 1056258166827256 * q^41 + 3982705476758466 * q^42 - 3467551217747682 * q^43 - 3212244140107742 * q^44 + 4912736475062322 * q^45 + 5810353662475960 * q^46 + 38050436085494078 * q^47 + 57514374310072968 * q^48 + 47238885151375334 * q^49 + 14878200688182597 * q^50 - 29591098904130220 * q^51 - 21974217154008420 * q^52 - 72013726688940684 * q^53 + 172899128132785018 * q^54 + 93309162211316908 * q^55 + 475212376185711512 * q^56 + 64982196426903912 * q^57 + 191264232277219708 * q^58 + 76501047180767180 * q^59 + 400074650609834880 * q^60 - 93578930877721460 * q^61 + 57387957390004612 * q^62 - 383255174667133284 * q^63 + 259127393615024481 * q^64 - 901725390399661584 * q^65 - 254413721370645848 * q^66 - 1182341009802075686 * q^67 - 925231639360979526 * q^68 - 947344752044875104 * q^69 - 363789978732097444 * q^70 - 848931219817628416 * q^71 - 2149287430983690291 * q^72 - 2671220396145181732 * q^73 - 3011451157682875714 * q^74 - 17689756878445192 * q^75 - 3177271521326582258 * q^76 - 1684143788069292280 * q^77 - 224568865304519456 * q^78 + 707599882299569300 * q^79 - 715147860460459392 * q^80 + 3538237990220919930 * q^81 + 1087170674699769934 * q^82 + 3231397917214389292 * q^83 - 5938450004747482572 * q^84 - 1954320626223684628 * q^85 - 1629641946563167526 * q^86 + 7707422320592255560 * q^87 - 5131462381092863934 * q^88 - 6860870532479969712 * q^89 - 8661425364016769956 * q^90 - 2927652813879512704 * q^91 - 26818660612119538580 * q^92 - 19098581600812512 * q^93 - 1657432230665197927 * q^94 - 5345445300954569692 * q^95 - 59798491695034221784 * q^96 - 7217040872018076624 * q^97 - 44647529467669017809 * q^98 + 10120380184661285522 * 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 $

$2$	−480.216	−0.663211	−0.331605	−	0.943418i	$-0.607590\pi$
$2$	−480.216	−0.663211	−0.331605	+	0.943418i	$0.607590\pi$
$3$	−36068.5	−1.05798	−0.528989	−	0.848629i	$-0.677429\pi$
$3$	−36068.5	−1.05798	−0.528989	+	0.848629i	$0.677429\pi$
$4$	−293681.	−0.560151
$5$	5.02224e6	1.14996	0.574980	−	0.818167i	$-0.305010\pi$
$5$	5.02224e6	1.14996	0.574980	+	0.818167i	$0.305010\pi$
$6$	1.73207e7	0.701662
$7$	6.92578e7	0.648690	0.324345	−	0.945939i	$-0.394856\pi$
$7$	6.92578e7	0.648690	0.324345	+	0.945939i	$0.394856\pi$
$8$	3.92802e8	1.03471
$9$	1.38678e8	0.119317
$10$	−2.41176e9	−0.762666
$11$	−4.10995e9	−0.525540	−0.262770	−	0.964859i	$-0.584636\pi$
$11$	−4.10995e9	−0.525540	−0.262770	+	0.964859i	$0.584636\pi$
$12$	1.05926e10	0.592628
$13$	1.56353e10	0.408925	0.204463	−	0.978874i	$-0.434455\pi$
$13$	1.56353e10	0.408925	0.204463	+	0.978874i	$0.434455\pi$
$14$	−3.32587e10	−0.430218
$15$	−1.81145e11	−1.21663
$16$	−3.46563e10	−0.126079
$17$	9.99522e9	0.0204422	0.0102211	−	0.999948i	$-0.496746\pi$
$17$	9.99522e9	0.0204422	0.0102211	+	0.999948i	$0.496746\pi$
$18$	−6.65953e10	−0.0791325
$19$	−1.56460e12	−1.11235	−0.556177	−	0.831064i	$-0.687732\pi$
$19$	−1.56460e12	−1.11235	−0.556177	+	0.831064i	$0.687732\pi$
$20$	−1.47494e12	−0.644152
$21$	−2.49803e12	−0.686300
$22$	1.97366e12	0.348544
$23$	−9.33202e12	−1.08034	−0.540171	−	0.841555i	$-0.681640\pi$
$23$	−9.33202e12	−1.08034	−0.540171	+	0.841555i	$0.681640\pi$
$24$	−1.41678e13	−1.09470
$25$	6.14945e12	0.322409
$26$	−7.50831e12	−0.271203
$27$	3.69192e13	0.931743
$28$	−2.03397e13	−0.363365
$29$	3.05988e13	0.391673	0.195837	−	0.980637i	$-0.437258\pi$
$29$	3.05988e13	0.391673	0.195837	+	0.980637i	$0.437258\pi$
$30$	8.69887e13	0.806884
$31$	1.26203e14	0.857301	0.428651	−	0.903470i	$-0.358989\pi$
$31$	1.26203e14	0.857301	0.428651	+	0.903470i	$0.358989\pi$
$32$	−1.89299e14	−0.951092
$33$	1.48240e14	0.556009
$34$	−4.79986e12	−0.0135575
$35$	3.47830e14	0.745968
$36$	−4.07270e13	−0.0668358
$37$	−1.07289e15	−1.35718	−0.678590	−	0.734517i	$-0.737409\pi$
$37$	−1.07289e15	−1.35718	−0.678590	+	0.734517i	$0.737409\pi$
$38$	7.51344e14	0.737725
$39$	−5.63941e14	−0.432634
$40$	1.97275e15	1.18987
$41$	3.48942e15	1.66459	0.832295	−	0.554333i	$-0.187027\pi$
$41$	3.48942e15	1.66459	0.832295	+	0.554333i	$0.187027\pi$
$42$	1.19959e15	0.455161
$43$	4.53042e15	1.37464	0.687318	−	0.726356i	$-0.258788\pi$
$43$	4.53042e15	1.37464	0.687318	+	0.726356i	$0.258788\pi$
$44$	1.20701e15	0.294382
$45$	6.96474e14	0.137210
$46$	4.48138e15	0.716494
$47$	1.11913e15	0.145865
$47$	1.11913e15	0.145865
$48$	1.25000e15	0.133389
$49$	−6.60225e15	−0.579201
$50$	−2.95307e15	−0.213825
$51$	−3.60513e14	−0.0216274
$52$	−4.59178e15	−0.229060
$53$	2.70577e16	1.12634	0.563170	−	0.826341i	$-0.309582\pi$
$53$	2.70577e16	1.12634	0.563170	+	0.826341i	$0.309582\pi$
$54$	−1.77292e16	−0.617942
$55$	−2.06412e16	−0.604350
$56$	2.72046e16	0.671206
$57$	5.64327e16	1.17685
$58$	−1.46940e16	−0.259762
$59$	−2.54831e16	−0.382965	−0.191482	−	0.981496i	$-0.561329\pi$
$59$	−2.54831e16	−0.382965	−0.191482	+	0.981496i	$0.561329\pi$
$60$	5.31988e16	0.681498
$61$	−1.33777e17	−1.46470	−0.732351	−	0.680928i	$-0.761577\pi$
$61$	−1.33777e17	−1.46470	−0.732351	+	0.680928i	$0.761577\pi$
$62$	−6.06047e16	−0.568571
$63$	9.60453e15	0.0774000
$64$	1.09074e17	0.756854
$65$	7.85242e16	0.470247
$66$	−7.11871e16	−0.368751
$67$	2.78626e17	1.25116	0.625578	−	0.780162i	$-0.284863\pi$
$67$	2.78626e17	1.25116	0.625578	+	0.780162i	$0.284863\pi$
$68$	−2.93540e15	−0.0114507
$69$	3.36592e17	1.14298
$70$	−1.67033e17	−0.494734
$71$	−6.03034e17	−1.56095	−0.780473	−	0.625190i	$-0.785021\pi$
$71$	−6.03034e17	−1.56095	−0.780473	+	0.625190i	$0.785021\pi$
$72$	5.44729e16	0.123459
$73$	4.95368e16	0.0984829	0.0492414	−	0.998787i	$-0.484320\pi$
$73$	4.95368e16	0.0984829	0.0492414	+	0.998787i	$0.484320\pi$
$74$	5.15217e17	0.900096
$75$	−2.21802e17	−0.341101
$76$	4.59491e17	0.623086
$77$	−2.84646e17	−0.340912
$78$	2.70814e17	0.286927
$79$	9.43682e17	0.885866	0.442933	−	0.896555i	$-0.353938\pi$
$79$	9.43682e17	0.885866	0.442933	+	0.896555i	$0.353938\pi$
$80$	−1.74052e17	−0.144986
$81$	−1.49280e18	−1.10508
$82$	−1.67568e18	−1.10397
$83$	1.80497e18	1.05981	0.529906	−	0.848056i	$-0.322227\pi$
$83$	1.80497e18	1.05981	0.529906	+	0.848056i	$0.322227\pi$
$84$	7.33622e17	0.384432
$85$	5.01984e16	0.0235077
$86$	−2.17558e18	−0.911674
$87$	−1.10366e18	−0.414382
$88$	−1.61439e18	−0.543781
$89$	3.40618e18	1.03053	0.515267	−	0.857030i	$-0.327693\pi$
$89$	3.40618e18	1.03053	0.515267	+	0.857030i	$0.327693\pi$
$90$	−3.34458e17	−0.0909993
$91$	1.08286e18	0.265266
$92$	2.74063e18	0.605155
$93$	−4.55196e18	−0.907006
$94$	−5.37424e17	−0.0967392
$95$	−7.85778e18	−1.27916
$96$	6.82773e18	1.00623
$97$	−6.45134e18	−0.861626	−0.430813	−	0.902441i	$-0.641773\pi$
$97$	−6.45134e18	−0.861626	−0.430813	+	0.902441i	$0.641773\pi$
$98$	3.17051e18	0.384133
$99$	−5.69959e17	−0.0627060
$100$	−1.80598e18	−0.180598
$101$	−6.53695e18	−0.594733	−0.297366	−	0.954763i	$-0.596108\pi$
$101$	−6.53695e18	−0.594733	−0.297366	+	0.954763i	$0.596108\pi$
$102$	1.73124e17	0.0143435
$103$	1.88289e19	1.42191	0.710954	−	0.703239i	$-0.248263\pi$
$103$	1.88289e19	1.42191	0.710954	+	0.703239i	$0.248263\pi$
$104$	6.14156e18	0.423118
$105$	−1.25457e19	−0.789217
$106$	−1.29935e19	−0.747001
$107$	−1.44812e19	−0.761478	−0.380739	−	0.924683i	$-0.624330\pi$
$107$	−1.44812e19	−0.761478	−0.380739	+	0.924683i	$0.624330\pi$
$108$	−1.08424e19	−0.521917
$109$	−4.00460e18	−0.176607	−0.0883034	−	0.996094i	$-0.528144\pi$
$109$	−4.00460e18	−0.176607	−0.0883034	+	0.996094i	$0.528144\pi$
$110$	9.91221e18	0.400811
$111$	3.86974e19	1.43587
$112$	−2.40022e18	−0.0817861
$113$	−3.48901e19	−1.09259	−0.546294	−	0.837593i	$-0.683962\pi$
$113$	−3.48901e19	−1.09259	−0.546294	+	0.837593i	$0.683962\pi$
$114$	−2.70999e19	−0.780497
$115$	−4.68677e19	−1.24235
$116$	−8.98629e18	−0.219396
$117$	2.16827e18	0.0487918
$118$	1.22374e19	0.253986
$119$	6.92247e17	0.0132607
$120$	−7.11540e19	−1.25886
$121$	−4.42674e19	−0.723808
$122$	6.42420e19	0.971406
$123$	−1.25858e20	−1.76110
$124$	−3.70634e19	−0.480219
$125$	−6.49076e19	−0.779203
$126$	−4.61225e18	−0.0513325
$127$	4.36554e19	0.450715	0.225358	−	0.974276i	$-0.427645\pi$
$127$	4.36554e19	0.450715	0.225358	+	0.974276i	$0.427645\pi$
$128$	4.68679e19	0.449139
$129$	−1.63406e20	−1.45434
$130$	−3.77086e19	−0.311873
$131$	−1.45294e20	−1.11730	−0.558651	−	0.829403i	$-0.688681\pi$
$131$	−1.45294e20	−1.11730	−0.558651	+	0.829403i	$0.688681\pi$
$132$	−4.35351e19	−0.311449
$133$	−1.08360e20	−0.721573
$134$	−1.33801e20	−0.829780
$135$	1.85417e20	1.07147
$136$	3.92614e18	0.0211517
$137$	−3.61394e19	−0.181608	−0.0908040	−	0.995869i	$-0.528944\pi$
$137$	−3.61394e19	−0.181608	−0.0908040	+	0.995869i	$0.528944\pi$
$138$	−1.61637e20	−0.758035
$139$	2.48851e20	1.08968	0.544840	−	0.838540i	$-0.316590\pi$
$139$	2.48851e20	1.08968	0.544840	+	0.838540i	$0.316590\pi$
$140$	−1.02151e20	−0.417855
$141$	−4.03654e19	−0.154322
$142$	2.89587e20	1.03524
$143$	−6.42601e19	−0.214906
$144$	−4.80606e18	−0.0150434
$145$	1.53675e20	0.450409
$146$	−2.37884e19	−0.0653149
$147$	2.38134e20	0.612782
$148$	3.15086e20	0.760226
$149$	−2.84676e20	−0.644290	−0.322145	−	0.946690i	$-0.604404\pi$
$149$	−2.84676e20	−0.644290	−0.322145	+	0.946690i	$0.604404\pi$
$150$	1.06513e20	0.226222
$151$	−1.10401e20	−0.220135	−0.110068	−	0.993924i	$-0.535107\pi$
$151$	−1.10401e20	−0.220135	−0.110068	+	0.993924i	$0.535107\pi$
$152$	−6.14576e20	−1.15096
$153$	1.38612e18	0.00243911
$154$	1.36691e20	0.226097
$155$	6.33822e20	0.985862
$156$	1.65619e20	0.242340
$157$	1.31909e21	1.81647	0.908237	−	0.418457i	$-0.137429\pi$
$157$	1.31909e21	1.81647	0.908237	+	0.418457i	$0.137429\pi$
$158$	−4.53171e20	−0.587516
$159$	−9.75930e20	−1.19164
$160$	−9.50704e20	−1.09372
$161$	−6.46315e20	−0.700807
$162$	7.16866e20	0.732901
$163$	−6.39608e20	−0.616782	−0.308391	−	0.951260i	$-0.599791\pi$
$163$	−6.39608e20	−0.616782	−0.308391	+	0.951260i	$0.599791\pi$
$164$	−1.02478e21	−0.932422
$165$	7.44496e20	0.639389
$166$	−8.66777e20	−0.702879
$167$	6.19502e20	0.474500	0.237250	−	0.971449i	$-0.423754\pi$
$167$	6.19502e20	0.474500	0.237250	+	0.971449i	$0.423754\pi$
$168$	−9.81229e20	−0.710121
$169$	−1.21746e21	−0.832780
$170$	−2.41061e19	−0.0155906
$171$	−2.16975e20	−0.132723
$172$	−1.33050e21	−0.770005
$173$	−1.64075e21	−0.898680	−0.449340	−	0.893361i	$-0.648341\pi$
$173$	−1.64075e21	−0.898680	−0.449340	+	0.893361i	$0.648341\pi$
$174$	5.29993e20	0.274822
$175$	4.25898e20	0.209143
$176$	1.42436e20	0.0662595
$177$	9.19139e20	0.405168
$178$	−1.63570e21	−0.683461
$179$	8.49139e20	0.336415	0.168207	−	0.985752i	$-0.446202\pi$
$179$	8.49139e20	0.336415	0.168207	+	0.985752i	$0.446202\pi$
$180$	−2.04541e20	−0.0768585
$181$	−4.85769e21	−1.73174	−0.865871	−	0.500268i	$-0.833235\pi$
$181$	−4.85769e21	−1.73174	−0.865871	+	0.500268i	$0.833235\pi$
$182$	−5.20009e20	−0.175927
$183$	4.82515e21	1.54962
$184$	−3.66563e21	−1.11784
$185$	−5.38830e21	−1.56070
$186$	2.18592e21	0.601536
$187$	−4.10798e19	−0.0107432
$188$	−3.28667e20	−0.0817065
$189$	2.55694e21	0.604412
$190$	3.77343e21	0.848354
$191$	2.45075e21	0.524181	0.262091	−	0.965043i	$-0.415588\pi$
$191$	2.45075e21	0.524181	0.262091	+	0.965043i	$0.415588\pi$
$192$	−3.93414e21	−0.800734
$193$	7.67189e21	1.48630	0.743152	−	0.669123i	$-0.233330\pi$
$193$	7.67189e21	1.48630	0.743152	+	0.669123i	$0.233330\pi$
$194$	3.09804e21	0.571439
$195$	−2.83225e21	−0.497511
$196$	1.93895e21	0.324440
$197$	6.12997e21	0.977304	0.488652	−	0.872479i	$-0.337489\pi$
$197$	6.12997e21	0.977304	0.488652	+	0.872479i	$0.337489\pi$
$198$	2.73703e20	0.0415873
$199$	3.43476e21	0.497499	0.248750	−	0.968568i	$-0.419980\pi$
$199$	3.43476e21	0.497499	0.248750	+	0.968568i	$0.419980\pi$
$200$	2.41552e21	0.333599
$201$	−1.00496e22	−1.32370
$202$	3.13915e21	0.394433
$203$	2.11921e21	0.254075
$204$	1.05876e20	0.0121146
$205$	1.75247e22	1.91421
$206$	−9.04194e21	−0.943024
$207$	−1.29415e21	−0.128904
$208$	−5.41861e20	−0.0515568
$209$	6.43040e21	0.584586
$210$	6.02465e21	0.523417
$211$	−7.20440e21	−0.598294	−0.299147	−	0.954207i	$-0.596702\pi$
$211$	−7.20440e21	−0.598294	−0.299147	+	0.954207i	$0.596702\pi$
$212$	−7.94631e21	−0.630921
$213$	2.17506e22	1.65145
$214$	6.95408e21	0.505020
$215$	2.27529e22	1.58078
$216$	1.45019e22	0.964083
$217$	8.74054e21	0.556123
$218$	1.92307e21	0.117127
$219$	−1.78672e21	−0.104193
$220$	6.06191e21	0.338527
$221$	1.56278e20	0.00835933
$222$	−1.85831e22	−0.952282
$223$	−5.15334e21	−0.253042	−0.126521	−	0.991964i	$-0.540381\pi$
$223$	−5.15334e21	−0.253042	−0.126521	+	0.991964i	$0.540381\pi$
$224$	−1.31104e22	−0.616964
$225$	8.52794e20	0.0384689
$226$	1.67548e22	0.724616
$227$	2.14106e22	0.887940	0.443970	−	0.896042i	$-0.353570\pi$
$227$	2.14106e22	0.887940	0.443970	+	0.896042i	$0.353570\pi$
$228$	−1.65732e22	−0.659212
$229$	1.79886e20	0.00686373	0.00343187	−	0.999994i	$-0.498908\pi$
$229$	1.79886e20	0.00686373	0.00343187	+	0.999994i	$0.498908\pi$
$230$	2.25066e22	0.823940
$231$	1.02668e22	0.360678
$232$	1.20193e22	0.405268
$233$	−1.05106e22	−0.340210	−0.170105	−	0.985426i	$-0.554411\pi$
$233$	−1.05106e22	−0.340210	−0.170105	+	0.985426i	$0.554411\pi$
$234$	−1.04124e21	−0.0323593
$235$	5.62055e21	0.167739
$236$	7.48390e21	0.214518
$237$	−3.40372e22	−0.937227
$238$	−3.32428e20	−0.00879461
$239$	−6.59111e21	−0.167563	−0.0837816	−	0.996484i	$-0.526700\pi$
$239$	−6.59111e21	−0.167563	−0.0837816	+	0.996484i	$0.526700\pi$
$240$	6.27782e21	0.153392
$241$	−1.80397e22	−0.423708	−0.211854	−	0.977301i	$-0.567950\pi$
$241$	−1.80397e22	−0.423708	−0.211854	+	0.977301i	$0.567950\pi$
$242$	2.12579e22	0.480037
$243$	1.09334e22	0.237408
$244$	3.92878e22	0.820454
$245$	−3.31581e22	−0.666058
$246$	6.04392e22	1.16798
$247$	−2.44629e22	−0.454869
$248$	4.95727e22	0.887058
$249$	−6.51028e22	−1.12126
$250$	3.11697e22	0.516776
$251$	−1.05452e23	−1.68327	−0.841637	−	0.540044i	$-0.818408\pi$
$251$	−1.05452e23	−1.68327	−0.841637	+	0.540044i	$0.818408\pi$
$252$	−2.82066e21	−0.0433557
$253$	3.83541e22	0.567763
$254$	−2.09640e22	−0.298919
$255$	−1.81058e21	−0.0248706
$256$	−7.96929e22	−1.05473
$257$	−4.30271e22	−0.548753	−0.274377	−	0.961622i	$-0.588471\pi$
$257$	−4.30271e22	−0.548753	−0.274377	+	0.961622i	$0.588471\pi$
$258$	7.84700e22	0.964531
$259$	−7.43057e22	−0.880389
$260$	−2.30610e22	−0.263410
$261$	4.24338e21	0.0467334
$262$	6.97725e22	0.741007
$263$	−1.49814e23	−1.53452	−0.767262	−	0.641333i	$-0.778382\pi$
$263$	−1.49814e23	−1.53452	−0.767262	+	0.641333i	$0.778382\pi$
$264$	5.82288e22	0.575308
$265$	1.35890e23	1.29525
$266$	5.20364e22	0.478555
$267$	−1.22856e23	−1.09028
$268$	−8.18271e22	−0.700837
$269$	−1.76118e23	−1.45599	−0.727994	−	0.685583i	$-0.759547\pi$
$269$	−1.76118e23	−1.45599	−0.727994	+	0.685583i	$0.759547\pi$
$270$	−8.90402e22	−0.710609
$271$	2.42493e22	0.186849	0.0934244	−	0.995626i	$-0.470219\pi$
$271$	2.42493e22	0.186849	0.0934244	+	0.995626i	$0.470219\pi$
$272$	−3.46397e20	−0.00257733
$273$	−3.90573e22	−0.280645
$274$	1.73547e22	0.120444
$275$	−2.52739e22	−0.169438
$276$	−9.88507e22	−0.640241
$277$	1.92941e23	1.20744	0.603720	−	0.797196i	$-0.293684\pi$
$277$	1.92941e23	1.20744	0.603720	+	0.797196i	$0.293684\pi$
$278$	−1.19502e23	−0.722688
$279$	1.75016e22	0.102291
$280$	1.36628e23	0.771860
$281$	−2.13464e23	−1.16578	−0.582888	−	0.812553i	$-0.698077\pi$
$281$	−2.13464e23	−1.16578	−0.582888	+	0.812553i	$0.698077\pi$
$282$	1.93841e22	0.102348
$283$	−1.16392e23	−0.594224	−0.297112	−	0.954843i	$-0.596023\pi$
$283$	−1.16392e23	−0.594224	−0.297112	+	0.954843i	$0.596023\pi$
$284$	1.77099e23	0.874366
$285$	2.83419e23	1.35333
$286$	3.08587e22	0.142528
$287$	2.41670e23	1.07980
$288$	−2.62515e22	−0.113482
$289$	−2.38973e23	−0.999582
$290$	−7.37971e22	−0.298716
$291$	2.32690e23	0.911581
$292$	−1.45480e22	−0.0551653
$293$	8.82218e22	0.323842	0.161921	−	0.986804i	$-0.448231\pi$
$293$	8.82218e22	0.323842	0.161921	+	0.986804i	$0.448231\pi$
$294$	−1.14356e23	−0.406404
$295$	−1.27982e23	−0.440394
$296$	−4.21431e23	−1.40429
$297$	−1.51736e23	−0.489668
$298$	1.36706e23	0.427300
$299$	−1.45909e23	−0.441779
$300$	6.51389e22	0.191068
$301$	3.13767e23	0.891713
$302$	5.30161e22	0.145996
$303$	2.35778e23	0.629214
$304$	5.42231e22	0.140244
$305$	−6.71862e23	−1.68435
$306$	−6.65635e20	−0.00161764
$307$	−3.52429e23	−0.830342	−0.415171	−	0.909743i	$-0.636278\pi$
$307$	−3.52429e23	−0.830342	−0.415171	+	0.909743i	$0.636278\pi$
$308$	8.35949e22	0.190963
$309$	−6.79131e23	−1.50435
$310$	−3.04371e23	−0.653835
$311$	−6.97920e23	−1.45406	−0.727029	−	0.686607i	$-0.759099\pi$
$311$	−6.97920e23	−1.45406	−0.727029	+	0.686607i	$0.759099\pi$
$312$	−2.21517e23	−0.447650
$313$	−2.60143e23	−0.509965	−0.254982	−	0.966946i	$-0.582070\pi$
$313$	−2.60143e23	−0.509965	−0.254982	+	0.966946i	$0.582070\pi$
$314$	−6.33450e23	−1.20470
$315$	4.82363e22	0.0890069
$316$	−2.77141e23	−0.496219
$317$	−2.00931e23	−0.349128	−0.174564	−	0.984646i	$-0.555852\pi$
$317$	−2.00931e23	−0.349128	−0.174564	+	0.984646i	$0.555852\pi$
$318$	4.68657e23	0.790310
$319$	−1.25760e23	−0.205840
$320$	5.47797e23	0.870352
$321$	5.22314e23	0.805627
$322$	3.10371e23	0.464783
$323$	−1.56385e22	−0.0227390
$324$	4.38407e23	0.619013
$325$	9.61484e22	0.131841
$326$	3.07150e23	0.409057
$327$	1.44440e23	0.186846
$328$	1.37065e24	1.72237
$329$	7.75085e22	0.0946212
$330$	−3.57519e23	−0.424050
$331$	4.42372e23	0.509825	0.254913	−	0.966964i	$-0.417953\pi$
$331$	4.42372e23	0.509825	0.254913	+	0.966964i	$0.417953\pi$
$332$	−5.30086e23	−0.593655
$333$	−1.48786e23	−0.161935
$334$	−2.97495e23	−0.314694
$335$	1.39933e24	1.43878
$336$	8.65724e22	0.0865279
$337$	1.06653e24	1.03631	0.518154	−	0.855288i	$-0.326620\pi$
$337$	1.06653e24	1.03631	0.518154	+	0.855288i	$0.326620\pi$
$338$	5.84643e23	0.552309
$339$	1.25843e24	1.15593
$340$	−1.47423e22	−0.0131679
$341$	−5.18687e23	−0.450546
$342$	1.04195e23	0.0880234
$343$	−1.24672e24	−1.02441
$344$	1.77956e24	1.42235
$345$	1.69045e24	1.31438
$346$	7.87916e23	0.596014
$347$	−5.04477e23	−0.371288	−0.185644	−	0.982617i	$-0.559437\pi$
$347$	−5.04477e23	−0.371288	−0.185644	+	0.982617i	$0.559437\pi$
$348$	3.24122e23	0.232117
$349$	−9.11189e23	−0.634990	−0.317495	−	0.948260i	$-0.602842\pi$
$349$	−9.11189e23	−0.634990	−0.317495	+	0.948260i	$0.602842\pi$
$350$	−2.04523e23	−0.138706
$351$	5.77241e23	0.381013
$352$	7.78007e23	0.499837
$353$	−1.44784e24	−0.905440	−0.452720	−	0.891653i	$-0.649546\pi$
$353$	−1.44784e24	−0.905440	−0.452720	+	0.891653i	$0.649546\pi$
$354$	−4.41385e23	−0.268712
$355$	−3.02859e24	−1.79502
$356$	−1.00033e24	−0.577255
$357$	−2.49683e22	−0.0140295
$358$	−4.07770e23	−0.223114
$359$	−1.05154e24	−0.560312	−0.280156	−	0.959955i	$-0.590386\pi$
$359$	−1.05154e24	−0.560312	−0.280156	+	0.959955i	$0.590386\pi$
$360$	2.73576e23	0.141973
$361$	4.69539e23	0.237330
$362$	2.33274e24	1.14851
$363$	1.59666e24	0.765773
$364$	−3.18016e23	−0.148589
$365$	2.48786e23	0.113251
$366$	−2.31711e24	−1.02773
$367$	−3.42719e24	−1.48119	−0.740596	−	0.671951i	$-0.765457\pi$
$367$	−3.42719e24	−1.48119	−0.740596	+	0.671951i	$0.765457\pi$
$368$	3.23413e23	0.136208
$369$	4.83906e23	0.198614
$370$	2.58755e24	1.03507
$371$	1.87395e24	0.730645
$372$	1.33682e24	0.508061
$373$	1.38822e23	0.0514309	0.0257155	−	0.999669i	$-0.491814\pi$
$373$	1.38822e23	0.0514309	0.0257155	+	0.999669i	$0.491814\pi$
$374$	1.97272e22	0.00712500
$375$	2.34112e24	0.824380
$376$	4.39596e23	0.150928
$377$	4.78421e23	0.160165
$378$	−1.22788e24	−0.400853
$379$	−1.40980e24	−0.448834	−0.224417	−	0.974493i	$-0.572048\pi$
$379$	−1.40980e24	−0.448834	−0.224417	+	0.974493i	$0.572048\pi$
$380$	2.30768e24	0.716525
$381$	−1.57459e24	−0.476847
$382$	−1.17689e24	−0.347643
$383$	2.47927e24	0.714391	0.357196	−	0.934030i	$-0.383733\pi$
$383$	2.47927e24	0.714391	0.357196	+	0.934030i	$0.383733\pi$
$384$	−1.69046e24	−0.475179
$385$	−1.42956e24	−0.392036
$386$	−3.68416e24	−0.985733
$387$	6.28269e23	0.164018
$388$	1.89463e24	0.482641
$389$	4.53617e23	0.112763	0.0563817	−	0.998409i	$-0.482044\pi$
$389$	4.53617e23	0.112763	0.0563817	+	0.998409i	$0.482044\pi$
$390$	1.36009e24	0.329955
$391$	−9.32756e22	−0.0220846
$392$	−2.59338e24	−0.599305
$393$	5.24055e24	1.18208
$394$	−2.94371e24	−0.648158
$395$	4.73940e24	1.01871
$396$	1.67386e23	0.0351249
$397$	1.17709e24	0.241156	0.120578	−	0.992704i	$-0.461525\pi$
$397$	1.17709e24	0.241156	0.120578	+	0.992704i	$0.461525\pi$
$398$	−1.64943e24	−0.329947
$399$	3.90840e24	0.763408
$400$	−2.13117e23	−0.0406489
$401$	5.08179e24	0.946553	0.473276	−	0.880914i	$-0.343071\pi$
$401$	5.08179e24	0.946553	0.473276	+	0.880914i	$0.343071\pi$
$402$	4.82600e24	0.877889
$403$	1.97322e24	0.350572
$404$	1.91977e24	0.333140
$405$	−7.49721e24	−1.27080
$406$	−1.01768e24	−0.168505
$407$	4.40950e24	0.713252
$408$	−1.41610e23	−0.0223781
$409$	1.89681e24	0.292855	0.146427	−	0.989221i	$-0.453223\pi$
$409$	1.89681e24	0.292855	0.146427	+	0.989221i	$0.453223\pi$
$410$	−8.41566e24	−1.26953
$411$	1.30349e24	0.192137
$412$	−5.52968e24	−0.796484
$413$	−1.76490e24	−0.248425
$414$	6.21469e23	0.0854902
$415$	9.06502e24	1.21874
$416$	−2.95974e24	−0.388925
$417$	−8.97570e24	−1.15286
$418$	−3.08798e24	−0.387704
$419$	5.85993e23	0.0719216	0.0359608	−	0.999353i	$-0.488551\pi$
$419$	5.85993e23	0.0719216	0.0359608	+	0.999353i	$0.488551\pi$
$420$	3.68443e24	0.442081
$421$	−1.08173e25	−1.26893	−0.634466	−	0.772950i	$-0.718780\pi$
$421$	−1.08173e25	−1.26893	−0.634466	+	0.772950i	$0.718780\pi$
$422$	3.45967e24	0.396795
$423$	1.55199e23	0.0174042
$424$	1.06283e25	1.16543
$425$	6.14652e22	0.00659074
$426$	−1.04450e25	−1.09526
$427$	−9.26512e24	−0.950137
$428$	4.25284e24	0.426543
$429$	2.31777e24	0.227366
$430$	−1.09263e25	−1.04839
$431$	1.85652e25	1.74247	0.871234	−	0.490868i	$-0.163320\pi$
$431$	1.85652e25	1.74247	0.871234	+	0.490868i	$0.163320\pi$
$432$	−1.27948e24	−0.117473
$433$	−1.16609e25	−1.04737	−0.523683	−	0.851914i	$-0.675442\pi$
$433$	−1.16609e25	−1.04737	−0.523683	+	0.851914i	$0.675442\pi$
$434$	−4.19735e24	−0.368827
$435$	−5.54283e24	−0.476522
$436$	1.17607e24	0.0989265
$437$	1.46008e25	1.20172
$438$	8.58011e23	0.0691017
$439$	−4.41644e24	−0.348064	−0.174032	−	0.984740i	$-0.555680\pi$
$439$	−4.41644e24	−0.348064	−0.174032	+	0.984740i	$0.555680\pi$
$440$	−8.10788e24	−0.625326
$441$	−9.15587e23	−0.0691087
$442$	−7.50472e22	−0.00554400
$443$	1.29875e24	0.0939053	0.0469527	−	0.998897i	$-0.485049\pi$
$443$	1.29875e24	0.0939053	0.0469527	+	0.998897i	$0.485049\pi$
$444$	−1.13647e25	−0.804302
$445$	1.71067e25	1.18507
$446$	2.47472e24	0.167820
$447$	1.02678e25	0.681644
$448$	7.55423e24	0.490963
$449$	−2.89175e25	−1.84001	−0.920006	−	0.391904i	$-0.871817\pi$
$449$	−2.89175e25	−1.84001	−0.920006	+	0.391904i	$0.871817\pi$
$450$	−4.09525e23	−0.0255130
$451$	−1.43413e25	−0.874808
$452$	1.02465e25	0.612015
$453$	3.98198e24	0.232898
$454$	−1.02817e25	−0.588891
$455$	5.43841e24	0.305045
$456$	2.21668e25	1.21769
$457$	−3.48916e25	−1.87723	−0.938614	−	0.344969i	$-0.887889\pi$
$457$	−3.48916e25	−1.87723	−0.938614	+	0.344969i	$0.887889\pi$
$458$	−8.63841e22	−0.00455210
$459$	3.69015e23	0.0190469
$460$	1.37641e25	0.695904
$461$	−2.98213e25	−1.47696	−0.738478	−	0.674278i	$-0.764455\pi$
$461$	−2.98213e25	−1.47696	−0.738478	+	0.674278i	$0.764455\pi$
$462$	−4.93026e24	−0.239205
$463$	−1.34539e25	−0.639482	−0.319741	−	0.947505i	$-0.603596\pi$
$463$	−1.34539e25	−0.639482	−0.319741	+	0.947505i	$0.603596\pi$
$464$	−1.06044e24	−0.0493817
$465$	−2.28610e25	−1.04302
$466$	5.04737e24	0.225631
$467$	−7.87337e24	−0.344866	−0.172433	−	0.985021i	$-0.555163\pi$
$467$	−7.87337e24	−0.344866	−0.172433	+	0.985021i	$0.555163\pi$
$468$	−6.36778e23	−0.0273308
$469$	1.92970e25	0.811612
$470$	−2.69908e24	−0.111246
$471$	−4.75778e25	−1.92179
$472$	−1.00098e25	−0.396257
$473$	−1.86198e25	−0.722426
$474$	1.63452e25	0.621579
$475$	−9.62141e24	−0.358632
$476$	−2.03300e23	−0.00742797
$477$	3.75230e24	0.134392
$478$	3.16516e24	0.111130
$479$	1.93956e25	0.667599	0.333799	−	0.942644i	$-0.391669\pi$
$479$	1.93956e25	0.667599	0.333799	+	0.942644i	$0.391669\pi$
$480$	3.42905e25	1.15713
$481$	−1.67749e25	−0.554985
$482$	8.66294e24	0.281008
$483$	2.33116e25	0.741438
$484$	1.30005e25	0.405442
$485$	−3.24002e25	−0.990835
$486$	−5.25039e24	−0.157452
$487$	−3.37520e25	−0.992602	−0.496301	−	0.868151i	$-0.665309\pi$
$487$	−3.37520e25	−0.992602	−0.496301	+	0.868151i	$0.665309\pi$
$488$	−5.25479e25	−1.51554
$489$	2.30697e25	0.652542
$490$	1.59231e25	0.441737
$491$	−2.88469e24	−0.0784919	−0.0392459	−	0.999230i	$-0.512496\pi$
$491$	−2.88469e24	−0.0784919	−0.0392459	+	0.999230i	$0.512496\pi$
$492$	3.69622e25	0.986482
$493$	3.05842e23	0.00800666
$494$	1.17475e25	0.301674
$495$	−2.86247e24	−0.0721094
$496$	−4.37373e24	−0.108088
$497$	−4.17648e25	−1.01257
$498$	3.12634e25	0.743630
$499$	−5.62932e24	−0.131371	−0.0656857	−	0.997840i	$-0.520923\pi$
$499$	−5.62932e24	−0.131371	−0.0656857	+	0.997840i	$0.520923\pi$
$500$	1.90621e25	0.436472
$501$	−2.23445e25	−0.502011
$502$	5.06398e25	1.11637
$503$	−3.47147e24	−0.0750962	−0.0375481	−	0.999295i	$-0.511955\pi$
$503$	−3.47147e24	−0.0750962	−0.0375481	+	0.999295i	$0.511955\pi$
$504$	3.77267e24	0.0800865
$505$	−3.28301e25	−0.683919
$506$	−1.84182e25	−0.376546
$507$	4.39119e25	0.881063
$508$	−1.28207e25	−0.252469
$509$	−2.46679e25	−0.476775	−0.238388	−	0.971170i	$-0.576619\pi$
$509$	−2.46679e25	−0.476775	−0.238388	+	0.971170i	$0.576619\pi$
$510$	8.69472e23	0.0164945
$511$	3.43081e24	0.0638848
$512$	1.36976e25	0.250368
$513$	−5.77636e25	−1.03643
$514$	2.06623e25	0.363939
$515$	9.45634e25	1.63514
$516$	4.79891e25	0.814648
$517$	−4.59957e24	−0.0766578
$518$	3.56828e25	0.583883
$519$	5.91796e25	0.950784
$520$	3.08444e25	0.486569
$521$	7.74664e25	1.19993	0.599964	−	0.800027i	$-0.295182\pi$
$521$	7.74664e25	1.19993	0.599964	+	0.800027i	$0.295182\pi$
$522$	−2.03774e24	−0.0309941
$523$	6.19767e24	0.0925683	0.0462841	−	0.998928i	$-0.485262\pi$
$523$	6.19767e24	0.0925683	0.0462841	+	0.998928i	$0.485262\pi$
$524$	4.26701e25	0.625859
$525$	−1.53615e25	−0.221269
$526$	7.19433e25	1.01771
$527$	1.26143e24	0.0175251
$528$	−5.13744e24	−0.0701011
$529$	1.24711e25	0.167139
$530$	−6.52566e25	−0.859021
$531$	−3.53395e24	−0.0456943
$532$	3.18234e25	0.404190
$533$	5.45581e25	0.680692
$534$	5.89973e25	0.723087
$535$	−7.27279e25	−0.875669
$536$	1.09445e26	1.29458
$537$	−3.06272e25	−0.355919
$538$	8.45748e25	0.965627
$539$	2.71349e25	0.304393
$540$	−5.44534e25	−0.600184
$541$	−1.24290e26	−1.34605	−0.673027	−	0.739618i	$-0.735006\pi$
$541$	−1.24290e26	−1.34605	−0.673027	+	0.739618i	$0.735006\pi$
$542$	−1.16449e25	−0.123920
$543$	1.75210e26	1.83214
$544$	−1.89208e24	−0.0194424
$545$	−2.01121e25	−0.203091
$546$	1.87560e25	0.186127
$547$	1.03804e26	1.01236	0.506181	−	0.862427i	$-0.331057\pi$
$547$	1.03804e26	1.01236	0.506181	+	0.862427i	$0.331057\pi$
$548$	1.06134e25	0.101728
$549$	−1.85520e25	−0.174764
$550$	1.21369e25	0.112373
$551$	−4.78748e25	−0.435679
$552$	1.32214e26	1.18265
$553$	6.53573e25	0.574653
$554$	−9.26532e25	−0.800788
$555$	1.94348e26	1.65119
$556$	−7.30828e25	−0.610386
$557$	4.17806e25	0.343044	0.171522	−	0.985180i	$-0.445131\pi$
$557$	4.17806e25	0.343044	0.171522	+	0.985180i	$0.445131\pi$
$558$	−8.40453e24	−0.0678404
$559$	7.08343e25	0.562123
$560$	−1.20545e25	−0.0940508
$561$	1.48169e24	0.0113661
$562$	1.02509e26	0.773155
$563$	−1.89362e26	−1.40431	−0.702156	−	0.712023i	$-0.747779\pi$
$563$	−1.89362e26	−1.40431	−0.702156	+	0.712023i	$0.747779\pi$
$564$	1.18545e25	0.0864437
$565$	−1.75226e26	−1.25643
$566$	5.58931e25	0.394096
$567$	−1.03388e26	−0.716855
$568$	−2.36873e26	−1.61512
$569$	1.15772e25	0.0776311	0.0388156	−	0.999246i	$-0.487642\pi$
$569$	1.15772e25	0.0776311	0.0388156	+	0.999246i	$0.487642\pi$
$570$	−1.36102e26	−0.897540
$571$	−2.40311e26	−1.55859	−0.779294	−	0.626659i	$-0.784422\pi$
$571$	−2.40311e26	−1.55859	−0.779294	+	0.626659i	$0.784422\pi$
$572$	1.88720e25	0.120380
$573$	−8.83948e25	−0.554572
$574$	−1.16054e26	−0.716137
$575$	−5.73868e25	−0.348311
$576$	1.51262e25	0.0903057
$577$	1.76394e26	1.03589	0.517945	−	0.855414i	$-0.326697\pi$
$577$	1.76394e26	1.03589	0.517945	+	0.855414i	$0.326697\pi$
$578$	1.14758e26	0.662934
$579$	−2.76714e26	−1.57248
$580$	−4.51313e25	−0.252297
$581$	1.25008e26	0.687490
$582$	−1.11742e26	−0.604570
$583$	−1.11206e26	−0.591936
$584$	1.94581e25	0.101901
$585$	1.08896e25	0.0561087
$586$	−4.23655e25	−0.214776
$587$	6.33812e25	0.316154	0.158077	−	0.987427i	$-0.449471\pi$
$587$	6.33812e25	0.316154	0.158077	+	0.987427i	$0.449471\pi$
$588$	−6.99353e25	−0.343251
$589$	−1.97457e26	−0.953622
$590$	6.14592e25	0.292074
$591$	−2.21099e26	−1.03397
$592$	3.71823e25	0.171112
$593$	−3.00465e26	−1.36074	−0.680369	−	0.732870i	$-0.738181\pi$
$593$	−3.00465e26	−1.36074	−0.680369	+	0.732870i	$0.738181\pi$
$594$	7.28659e25	0.324753
$595$	3.47663e24	0.0152492
$596$	8.36038e25	0.360900
$597$	−1.23887e26	−0.526343
$598$	7.00677e25	0.292992
$599$	3.90875e26	1.60873	0.804365	−	0.594135i	$-0.202506\pi$
$599$	3.90875e26	1.60873	0.804365	+	0.594135i	$0.202506\pi$
$600$	−8.71241e25	−0.352940
$601$	2.71696e26	1.08337	0.541684	−	0.840582i	$-0.317787\pi$
$601$	2.71696e26	1.08337	0.541684	+	0.840582i	$0.317787\pi$
$602$	−1.50676e26	−0.591394
$603$	3.86393e25	0.149285
$604$	3.24225e25	0.123309
$605$	−2.22322e26	−0.832350
$606$	−1.13224e26	−0.417302
$607$	1.70006e26	0.616837	0.308419	−	0.951251i	$-0.400200\pi$
$607$	1.70006e26	0.616837	0.308419	+	0.951251i	$0.400200\pi$
$608$	2.96176e26	1.05795
$609$	−7.64367e25	−0.268805
$610$	3.22639e26	1.11708
$611$	1.74979e25	0.0596478
$612$	−4.07076e23	−0.00136627
$613$	5.99800e25	0.198213	0.0991064	−	0.995077i	$-0.468402\pi$
$613$	5.99800e25	0.198213	0.0991064	+	0.995077i	$0.468402\pi$
$614$	1.69242e26	0.550692
$615$	−6.32092e26	−2.02519
$616$	−1.11809e26	−0.352745
$617$	2.47012e26	0.767378	0.383689	−	0.923462i	$-0.374653\pi$
$617$	2.47012e26	0.767378	0.383689	+	0.923462i	$0.374653\pi$
$618$	3.26129e26	0.997699
$619$	2.07098e26	0.623899	0.311949	−	0.950099i	$-0.399018\pi$
$619$	2.07098e26	0.623899	0.311949	+	0.950099i	$0.399018\pi$
$620$	−1.86141e26	−0.552232
$621$	−3.44530e26	−1.00660
$622$	3.35152e26	0.964347
$623$	2.35904e26	0.668497
$624$	1.95441e25	0.0545460
$625$	−4.43274e26	−1.21846
$626$	1.24925e26	0.338214
$627$	−2.31935e26	−0.618479
$628$	−3.87392e26	−1.01750
$629$	−1.07237e25	−0.0277437
$630$	−2.31638e25	−0.0590303
$631$	−5.58580e26	−1.40219	−0.701095	−	0.713068i	$-0.747305\pi$
$631$	−5.58580e26	−1.40219	−0.701095	+	0.713068i	$0.747305\pi$
$632$	3.70680e26	0.916614
$633$	2.59852e26	0.632982
$634$	9.64904e25	0.231545
$635$	2.19248e26	0.518305
$636$	2.86612e26	0.667500
$637$	−1.03228e26	−0.236850
$638$	6.03917e25	0.136515
$639$	−8.36275e25	−0.186248
$640$	2.35382e26	0.516492
$641$	3.11704e26	0.673893	0.336947	−	0.941524i	$-0.390606\pi$
$641$	3.11704e26	0.673893	0.336947	+	0.941524i	$0.390606\pi$
$642$	−2.50824e26	−0.534300
$643$	−5.00441e26	−1.05039	−0.525193	−	0.850983i	$-0.676007\pi$
$643$	−5.00441e26	−1.05039	−0.525193	+	0.850983i	$0.676007\pi$
$644$	1.89810e26	0.392558
$645$	−8.20663e26	−1.67243
$646$	7.50985e24	0.0150807
$647$	3.39492e26	0.671799	0.335899	−	0.941898i	$-0.390960\pi$
$647$	3.39492e26	0.671799	0.335899	+	0.941898i	$0.390960\pi$
$648$	−5.86374e26	−1.14344
$649$	1.04734e26	0.201263
$650$	−4.61720e25	−0.0874383
$651$	−3.15258e26	−0.588366
$652$	1.87841e26	0.345492
$653$	−1.77635e26	−0.321998	−0.160999	−	0.986955i	$-0.551472\pi$
$653$	−1.77635e26	−0.321998	−0.160999	+	0.986955i	$0.551472\pi$
$654$	−6.93624e25	−0.123918
$655$	−7.29703e26	−1.28485
$656$	−1.20931e26	−0.209870
$657$	6.86966e24	0.0117507
$658$	−3.72208e25	−0.0627538
$659$	8.64080e26	1.43596	0.717980	−	0.696063i	$-0.245067\pi$
$659$	8.64080e26	1.43596	0.717980	+	0.696063i	$0.245067\pi$
$660$	−2.18644e26	−0.358155
$661$	1.11402e27	1.79878	0.899388	−	0.437150i	$-0.144012\pi$
$661$	1.11402e27	1.79878	0.899388	+	0.437150i	$0.144012\pi$
$662$	−2.12434e26	−0.338122
$663$	−5.63672e24	−0.00884398
$664$	7.08996e26	1.09660
$665$	−5.44212e26	−0.829780
$666$	7.14492e25	0.107397
$667$	−2.85549e26	−0.423141
$668$	−1.81936e26	−0.265792
$669$	1.85874e26	0.267713
$670$	−6.71980e26	−0.954214
$671$	5.49817e26	0.769759
$672$	4.72873e26	0.652734
$673$	−3.54302e26	−0.482203	−0.241102	−	0.970500i	$-0.577509\pi$
$673$	−3.54302e26	−0.482203	−0.241102	+	0.970500i	$0.577509\pi$
$674$	−5.12164e26	−0.687290
$675$	2.27033e26	0.300402
$676$	3.57544e26	0.466483
$677$	1.77192e23	0.000227956 0	0.000113978	−	1.00000i	$-0.499964\pi$
$677$	1.77192e23	0.000227956 0	0.000113978		1.00000i	$0.499964\pi$
$678$	−6.04320e26	−0.766628
$679$	−4.46806e26	−0.558928
$680$	1.97180e25	0.0243237
$681$	−7.72249e26	−0.939420
$682$	2.49082e26	0.298807
$683$	−1.17039e27	−1.38463	−0.692317	−	0.721594i	$-0.743410\pi$
$683$	−1.17039e27	−1.38463	−0.692317	+	0.721594i	$0.743410\pi$
$684$	6.37213e25	0.0743450
$685$	−1.81501e26	−0.208842
$686$	5.98695e26	0.679401
$687$	−6.48823e24	−0.00726168
$688$	−1.57008e26	−0.173313
$689$	4.23054e26	0.460589
$690$	−8.11780e26	−0.871710
$691$	−2.32944e26	−0.246723	−0.123362	−	0.992362i	$-0.539368\pi$
$691$	−2.32944e26	−0.246723	−0.123362	+	0.992362i	$0.539368\pi$
$692$	4.81857e26	0.503397
$693$	−3.94741e25	−0.0406768
$694$	2.42258e26	0.246242
$695$	1.24979e27	1.25309
$696$	−4.33518e26	−0.428765
$697$	3.48776e25	0.0340279
$698$	4.37568e26	0.421132
$699$	3.79103e26	0.359935
$700$	−1.25078e26	−0.117152
$701$	2.03088e27	1.87656	0.938281	−	0.345873i	$-0.112417\pi$
$701$	2.03088e27	1.87656	0.938281	+	0.345873i	$0.112417\pi$
$702$	−2.77200e26	−0.252692
$703$	1.67863e27	1.50966
$704$	−4.48289e26	−0.397757
$705$	−2.02725e26	−0.177464
$706$	6.95274e26	0.600497
$707$	−4.52734e26	−0.385797
$708$	−2.69933e26	−0.226955
$709$	−1.03046e27	−0.854853	−0.427427	−	0.904050i	$-0.640580\pi$
$709$	−1.03046e27	−0.854853	−0.427427	+	0.904050i	$0.640580\pi$
$710$	1.45437e27	1.19048
$711$	1.30868e26	0.105699
$712$	1.33795e27	1.06630
$713$	−1.17773e27	−0.926179
$714$	1.19902e25	0.00930450
$715$	−3.22730e26	−0.247134
$716$	−2.49376e26	−0.188443
$717$	2.37732e26	0.177278
$718$	5.04968e26	0.371605
$719$	3.94459e26	0.286469	0.143234	−	0.989689i	$-0.454250\pi$
$719$	3.94459e26	0.286469	0.143234	+	0.989689i	$0.454250\pi$
$720$	−2.41372e25	−0.0172993
$721$	1.30405e27	0.922377
$722$	−2.25480e26	−0.157400
$723$	6.50665e26	0.448274
$724$	1.42661e27	0.970038
$725$	1.88166e26	0.126279
$726$	−7.66742e26	−0.507869
$727$	7.50156e26	0.490427	0.245214	−	0.969469i	$-0.421142\pi$
$727$	7.50156e26	0.490427	0.245214	+	0.969469i	$0.421142\pi$
$728$	4.25351e26	0.274473
$729$	1.34067e27	0.853908
$730$	−1.19471e26	−0.0751095
$731$	4.52825e25	0.0281006
$732$	−1.41705e27	−0.868023
$733$	−2.95698e27	−1.78797	−0.893986	−	0.448094i	$-0.852103\pi$
$733$	−2.95698e27	−1.78797	−0.893986	+	0.448094i	$0.852103\pi$
$734$	1.64579e27	0.982342
$735$	1.19597e27	0.704675
$736$	1.76654e27	1.02750
$737$	−1.14514e27	−0.657532
$738$	−2.32379e26	−0.131723
$739$	5.18816e26	0.290329	0.145165	−	0.989408i	$-0.453629\pi$
$739$	5.18816e26	0.290329	0.145165	+	0.989408i	$0.453629\pi$
$740$	1.58244e27	0.874230
$741$	8.82340e26	0.481242
$742$	−8.99902e26	−0.484572
$743$	4.61194e26	0.245183	0.122591	−	0.992457i	$-0.460880\pi$
$743$	4.61194e26	0.245183	0.122591	+	0.992457i	$0.460880\pi$
$744$	−1.78802e27	−0.938487
$745$	−1.42971e27	−0.740908
$746$	−6.66645e25	−0.0341095
$747$	2.50310e26	0.126454
$748$	1.20643e25	0.00601781
$749$	−1.00293e27	−0.493963
$750$	−1.12424e27	−0.546738
$751$	3.32346e27	1.59592	0.797959	−	0.602712i	$-0.205913\pi$
$751$	3.32346e27	1.59592	0.797959	+	0.602712i	$0.205913\pi$
$752$	−3.87849e25	−0.0183905
$753$	3.80350e27	1.78087
$754$	−2.29745e26	−0.106223
$755$	−5.54458e26	−0.253147
$756$	−7.50924e26	−0.338562
$757$	−1.19670e27	−0.532812	−0.266406	−	0.963861i	$-0.585836\pi$
$757$	−1.19670e27	−0.532812	−0.266406	+	0.963861i	$0.585836\pi$
$758$	6.77009e26	0.297671
$759$	−1.38338e27	−0.600680
$760$	−3.08655e27	−1.32356
$761$	−3.87422e27	−1.64070	−0.820352	−	0.571859i	$-0.806223\pi$
$761$	−3.87422e27	−1.64070	−0.820352	+	0.571859i	$0.806223\pi$
$762$	7.56141e26	0.316250
$763$	−2.77350e26	−0.114563
$764$	−7.19737e26	−0.293621
$765$	6.96142e24	0.00280488
$766$	−1.19059e27	−0.473792
$767$	−3.98436e26	−0.156604
$768$	2.87441e27	1.11588
$769$	1.03364e26	0.0396343	0.0198171	−	0.999804i	$-0.493692\pi$
$769$	1.03364e26	0.0396343	0.0198171	+	0.999804i	$0.493692\pi$
$770$	6.86498e26	0.260002
$771$	1.55192e27	0.580569
$772$	−2.25308e27	−0.832555
$773$	1.99271e27	0.727343	0.363671	−	0.931527i	$-0.381523\pi$
$773$	1.99271e27	0.727343	0.363671	+	0.931527i	$0.381523\pi$
$774$	−3.01705e26	−0.108779
$775$	7.76079e26	0.276401
$776$	−2.53410e27	−0.891532
$777$	2.68010e27	0.931432
$778$	−2.17834e26	−0.0747860
$779$	−5.45954e27	−1.85161
$780$	8.31778e26	0.278682
$781$	2.47844e27	0.820339
$782$	4.47924e25	0.0146467
$783$	1.12968e27	0.364939
$784$	2.28810e26	0.0730251
$785$	6.62481e27	2.08887
$786$	−2.51659e27	−0.783969
$787$	5.22448e27	1.60799	0.803994	−	0.594637i	$-0.202704\pi$
$787$	5.22448e27	1.60799	0.803994	+	0.594637i	$0.202704\pi$
$788$	−1.80025e27	−0.547438
$789$	5.40359e27	1.62349
$790$	−2.27594e27	−0.675620
$791$	−2.41641e27	−0.708751
$792$	−2.23881e26	−0.0648825
$793$	−2.09164e27	−0.598953
$794$	−5.65255e26	−0.159937
$795$	−4.90136e27	−1.37034
$796$	−1.00872e27	−0.278675
$797$	8.96083e26	0.244621	0.122311	−	0.992492i	$-0.460970\pi$
$797$	8.96083e26	0.244621	0.122311	+	0.992492i	$0.460970\pi$
$798$	−1.87688e27	−0.506300
$799$	1.11860e25	0.00298180
$800$	−1.16408e27	−0.306640
$801$	4.72362e26	0.122961
$802$	−2.44035e27	−0.627764
$803$	−2.03593e26	−0.0517567
$804$	2.95139e27	0.741470
$805$	−3.24595e27	−0.805900
$806$	−9.47571e26	−0.232503
$807$	6.35233e27	1.54040
$808$	−2.56772e27	−0.615375
$809$	3.16153e27	0.748835	0.374418	−	0.927260i	$-0.377843\pi$
$809$	3.16153e27	0.748835	0.374418	+	0.927260i	$0.377843\pi$
$810$	3.60028e27	0.842808
$811$	8.01637e26	0.185472	0.0927362	−	0.995691i	$-0.470439\pi$
$811$	8.01637e26	0.185472	0.0927362	+	0.995691i	$0.470439\pi$
$812$	−6.22370e26	−0.142320
$813$	−8.74635e26	−0.197682
$814$	−2.11751e27	−0.473036
$815$	−3.21227e27	−0.709275
$816$	1.24940e25	0.00272676
$817$	−7.08827e27	−1.52908
$818$	−9.10877e26	−0.194224
$819$	1.50169e26	0.0316508
$820$	−5.14668e27	−1.07225
$821$	−6.29514e27	−1.29642	−0.648209	−	0.761462i	$-0.724482\pi$
$821$	−6.29514e27	−1.29642	−0.648209	+	0.761462i	$0.724482\pi$
$822$	−6.25958e26	−0.127428
$823$	−6.71943e27	−1.35218	−0.676089	−	0.736820i	$-0.736326\pi$
$823$	−6.71943e27	−1.35218	−0.676089	+	0.736820i	$0.736326\pi$
$824$	7.39602e27	1.47126
$825$	9.11593e26	0.179262
$826$	8.47535e26	0.164758
$827$	2.34291e27	0.450249	0.225125	−	0.974330i	$-0.427721\pi$
$827$	2.34291e27	0.450249	0.225125	+	0.974330i	$0.427721\pi$
$828$	3.80065e26	0.0722055
$829$	−4.44799e27	−0.835403	−0.417702	−	0.908584i	$-0.637164\pi$
$829$	−4.44799e27	−0.835403	−0.417702	+	0.908584i	$0.637164\pi$
$830$	−4.35317e27	−0.808283
$831$	−6.95909e27	−1.27745
$832$	1.70540e27	0.309496
$833$	−6.59910e25	−0.0118401
$834$	4.31027e27	0.764588
$835$	3.11129e27	0.545657
$836$	−1.88848e27	−0.327457
$837$	4.65931e27	0.798784
$838$	−2.81403e26	−0.0476992
$839$	9.52233e27	1.59590	0.797948	−	0.602727i	$-0.205919\pi$
$839$	9.52233e27	1.59590	0.797948	+	0.602727i	$0.205919\pi$
$840$	−4.92797e27	−0.816611
$841$	−5.16697e27	−0.846592
$842$	5.19464e27	0.841570
$843$	7.69934e27	1.23336
$844$	2.11579e27	0.335135
$845$	−6.11437e27	−0.957664
$846$	−7.45289e25	−0.0115427
$847$	−3.06586e27	−0.469527
$848$	−9.37719e26	−0.142008
$849$	4.19807e27	0.628676
$850$	−2.95165e25	−0.00437105
$851$	1.00122e28	1.46622
$852$	−6.38772e27	−0.925060
$853$	2.70415e27	0.387272	0.193636	−	0.981073i	$-0.437972\pi$
$853$	2.70415e27	0.387272	0.193636	+	0.981073i	$0.437972\pi$
$854$	4.44926e27	0.630141
$855$	−1.08970e27	−0.152626
$856$	−5.68822e27	−0.787908
$857$	−9.33540e27	−1.27884	−0.639418	−	0.768859i	$-0.720825\pi$
$857$	−9.33540e27	−1.27884	−0.639418	+	0.768859i	$0.720825\pi$
$858$	−1.11303e27	−0.150792
$859$	4.94694e27	0.662829	0.331414	−	0.943485i	$-0.392474\pi$
$859$	4.94694e27	0.662829	0.331414	+	0.943485i	$0.392474\pi$
$860$	−6.68208e27	−0.885475
$861$	−8.71668e27	−1.14241
$862$	−8.91529e27	−1.15562
$863$	3.87420e27	0.496683	0.248342	−	0.968673i	$-0.420114\pi$
$863$	3.87420e27	0.496683	0.248342	+	0.968673i	$0.420114\pi$
$864$	−6.98875e27	−0.886174
$865$	−8.24026e27	−1.03345
$866$	5.59976e27	0.694624
$867$	8.61939e27	1.05754
$868$	−2.56693e27	−0.311513
$869$	−3.87848e27	−0.465558
$870$	2.66175e27	0.316035
$871$	4.35640e27	0.511629
$872$	−1.57301e27	−0.182737
$873$	−8.94659e26	−0.102807
$874$	−7.01155e27	−0.796995
$875$	−4.49536e27	−0.505461
$876$	5.24725e26	0.0583637
$877$	2.78943e27	0.306916	0.153458	−	0.988155i	$-0.450959\pi$
$877$	2.78943e27	0.306916	0.153458	+	0.988155i	$0.450959\pi$
$878$	2.12084e27	0.230840
$879$	−3.18203e27	−0.342618
$880$	7.15346e26	0.0761958
$881$	−8.71087e27	−0.917889	−0.458945	−	0.888465i	$-0.651772\pi$
$881$	−8.71087e27	−0.917889	−0.458945	+	0.888465i	$0.651772\pi$
$882$	4.39679e26	0.0458337
$883$	1.65018e28	1.70178	0.850891	−	0.525342i	$-0.176063\pi$
$883$	1.65018e28	1.70178	0.850891	+	0.525342i	$0.176063\pi$
$884$	−4.58958e25	−0.00468249
$885$	4.61614e27	0.465927
$886$	−6.23681e26	−0.0622790
$887$	6.28798e26	0.0621208	0.0310604	−	0.999518i	$-0.490112\pi$
$887$	6.28798e26	0.0621208	0.0310604	+	0.999518i	$0.490112\pi$
$888$	1.52004e28	1.48570
$889$	3.02347e27	0.292375
$890$	−8.21489e27	−0.785953
$891$	6.13533e27	0.580764
$892$	1.51344e27	0.141742
$893$	−1.75099e27	−0.162253
$894$	−4.93078e27	−0.452074
$895$	4.26458e27	0.386864
$896$	3.24597e27	0.291352
$897$	5.26271e27	0.467392
$898$	1.38867e28	1.22032
$899$	3.86166e27	0.335782
$900$	−2.50449e26	−0.0215484
$901$	2.70447e26	0.0230249
$902$	6.88694e27	0.580182
$903$	−1.13171e28	−0.943413
$904$	−1.37049e28	−1.13051
$905$	−2.43965e28	−1.99143
$906$	−1.91221e27	−0.154461
$907$	2.65593e27	0.212299	0.106149	−	0.994350i	$-0.466148\pi$
$907$	2.65593e27	0.212299	0.106149	+	0.994350i	$0.466148\pi$
$908$	−6.28788e27	−0.497381
$909$	−9.06530e26	−0.0709619
$910$	−2.61161e27	−0.202309
$911$	1.69081e28	1.29619	0.648096	−	0.761558i	$-0.275565\pi$
$911$	1.69081e28	1.29619	0.648096	+	0.761558i	$0.275565\pi$
$912$	−1.95575e27	−0.148375
$913$	−7.41834e27	−0.556973
$914$	1.67555e28	1.24500
$915$	2.42331e28	1.78200
$916$	−5.28291e25	−0.00384473
$917$	−1.00627e28	−0.724783
$918$	−1.77207e26	−0.0126321
$919$	−7.13458e27	−0.503351	−0.251676	−	0.967812i	$-0.580982\pi$
$919$	−7.13458e27	−0.503351	−0.251676	+	0.967812i	$0.580982\pi$
$920$	−1.84097e28	−1.28547
$921$	1.27116e28	0.878483
$922$	1.43207e28	0.979533
$923$	−9.42860e27	−0.638309
$924$	−3.01515e27	−0.202034
$925$	−6.59767e27	−0.437566
$926$	6.46077e27	0.424111
$927$	2.61115e27	0.169658
$928$	−5.79232e27	−0.372517
$929$	−1.89698e28	−1.20758	−0.603788	−	0.797145i	$-0.706343\pi$
$929$	−1.89698e28	−1.20758	−0.603788	+	0.797145i	$0.706343\pi$
$930$	1.09782e28	0.691743
$931$	1.03299e28	0.644277
$932$	3.08677e27	0.190569
$933$	2.51729e28	1.53836
$934$	3.78092e27	0.228719
$935$	−2.06313e26	−0.0123542
$936$	8.51699e26	0.0504854
$937$	2.93499e28	1.72219	0.861095	−	0.508444i	$-0.169779\pi$
$937$	2.93499e28	1.72219	0.861095	+	0.508444i	$0.169779\pi$
$938$	−9.26674e27	−0.538270
$939$	9.38296e27	0.539532
$940$	−1.65065e27	−0.0939592
$941$	2.01655e28	1.13634	0.568169	−	0.822912i	$-0.307652\pi$
$941$	2.01655e28	1.13634	0.568169	+	0.822912i	$0.307652\pi$
$942$	2.28476e28	1.27455
$943$	−3.25634e28	−1.79833
$944$	8.83151e26	0.0482838
$945$	1.28416e28	0.695050
$946$	8.94151e27	0.479121
$947$	1.77114e28	0.939570	0.469785	−	0.882781i	$-0.344332\pi$
$947$	1.77114e28	0.939570	0.469785	+	0.882781i	$0.344332\pi$
$948$	9.99607e27	0.524989
$949$	7.74521e26	0.0402721
$950$	4.62035e27	0.237849
$951$	7.24730e27	0.369370
$952$	2.71916e26	0.0137209
$953$	1.54528e28	0.772011	0.386005	−	0.922497i	$-0.373855\pi$
$953$	1.54528e28	0.772011	0.386005	+	0.922497i	$0.373855\pi$
$954$	−1.80191e27	−0.0891301
$955$	1.23082e28	0.602787
$956$	1.93568e27	0.0938607
$957$	4.53596e27	0.217774
$958$	−9.31407e27	−0.442759
$959$	−2.50293e27	−0.117807
$960$	−1.97582e28	−0.920813
$961$	−5.74347e27	−0.265034
$962$	8.05556e27	0.368072
$963$	−2.00822e27	−0.0908575
$964$	5.29790e27	0.237341
$965$	3.85301e28	1.70919
$966$	−1.11946e28	−0.491730
$967$	−7.13621e27	−0.310396	−0.155198	−	0.987883i	$-0.549602\pi$
$967$	−7.13621e27	−0.310396	−0.155198	+	0.987883i	$0.549602\pi$
$968$	−1.73883e28	−0.748931
$969$	5.64057e26	0.0240573
$970$	1.55591e28	0.657133
$971$	−2.28987e28	−0.957699	−0.478849	−	0.877897i	$-0.658946\pi$
$971$	−2.28987e28	−0.957699	−0.478849	+	0.877897i	$0.658946\pi$
$972$	−3.21093e27	−0.132985
$973$	1.72349e28	0.706865
$974$	1.62083e28	0.658304
$975$	−3.46793e27	−0.139485
$976$	4.63623e27	0.184668
$977$	2.34889e28	0.926540	0.463270	−	0.886217i	$-0.346676\pi$
$977$	2.34889e28	0.926540	0.463270	+	0.886217i	$0.346676\pi$
$978$	−1.10785e28	−0.432773
$979$	−1.39992e28	−0.541586
$980$	9.73790e27	0.373094
$981$	−5.55349e26	−0.0210722
$982$	1.38527e27	0.0520567
$983$	5.31043e27	0.197638	0.0988192	−	0.995105i	$-0.468493\pi$
$983$	5.31043e27	0.197638	0.0988192	+	0.995105i	$0.468493\pi$
$984$	−4.94374e28	−1.82223
$985$	3.07862e28	1.12386
$986$	−1.46870e26	−0.00531011
$987$	−2.79562e27	−0.100107
$988$	7.18428e27	0.254796
$989$	−4.22780e28	−1.48508
$990$	1.37460e27	0.0478237
$991$	−1.56467e27	−0.0539167	−0.0269584	−	0.999637i	$-0.508582\pi$
$991$	−1.56467e27	−0.0539167	−0.0269584	+	0.999637i	$0.508582\pi$
$992$	−2.38901e28	−0.815373
$993$	−1.59557e28	−0.539384
$994$	2.00561e28	0.671547
$995$	1.72502e28	0.572104
$996$	1.91194e28	0.628074
$997$	−2.46710e28	−0.802753	−0.401377	−	0.915913i	$-0.631468\pi$
$997$	−2.46710e28	−0.802753	−0.401377	+	0.915913i	$0.631468\pi$
$998$	2.70329e27	0.0871269
$999$	−3.96101e28	−1.26454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.a.1.13	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.a.1.13	✓	34	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:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	47.a (trivial)

\(f(q)\)	\(=\)	\(q-480.216 q^{2} -36068.5 q^{3} -293681. q^{4} +5.02224e6 q^{5} +1.73207e7 q^{6} +6.92578e7 q^{7} +3.92802e8 q^{8} +1.38678e8 q^{9} +O(q^{10})\)	\(q-480.216 q^{2} -36068.5 q^{3} -293681. q^{4} +5.02224e6 q^{5} +1.73207e7 q^{6} +6.92578e7 q^{7} +3.92802e8 q^{8} +1.38678e8 q^{9} -2.41176e9 q^{10} -4.10995e9 q^{11} +1.05926e10 q^{12} +1.56353e10 q^{13} -3.32587e10 q^{14} -1.81145e11 q^{15} -3.46563e10 q^{16} +9.99522e9 q^{17} -6.65953e10 q^{18} -1.56460e12 q^{19} -1.47494e12 q^{20} -2.49803e12 q^{21} +1.97366e12 q^{22} -9.33202e12 q^{23} -1.41678e13 q^{24} +6.14945e12 q^{25} -7.50831e12 q^{26} +3.69192e13 q^{27} -2.03397e13 q^{28} +3.05988e13 q^{29} +8.69887e13 q^{30} +1.26203e14 q^{31} -1.89299e14 q^{32} +1.48240e14 q^{33} -4.79986e12 q^{34} +3.47830e14 q^{35} -4.07270e13 q^{36} -1.07289e15 q^{37} +7.51344e14 q^{38} -5.63941e14 q^{39} +1.97275e15 q^{40} +3.48942e15 q^{41} +1.19959e15 q^{42} +4.53042e15 q^{43} +1.20701e15 q^{44} +6.96474e14 q^{45} +4.48138e15 q^{46} +1.11913e15 q^{47} +1.25000e15 q^{48} -6.60225e15 q^{49} -2.95307e15 q^{50} -3.60513e14 q^{51} -4.59178e15 q^{52} +2.70577e16 q^{53} -1.77292e16 q^{54} -2.06412e16 q^{55} +2.72046e16 q^{56} +5.64327e16 q^{57} -1.46940e16 q^{58} -2.54831e16 q^{59} +5.31988e16 q^{60} -1.33777e17 q^{61} -6.06047e16 q^{62} +9.60453e15 q^{63} +1.09074e17 q^{64} +7.85242e16 q^{65} -7.11871e16 q^{66} +2.78626e17 q^{67} -2.93540e15 q^{68} +3.36592e17 q^{69} -1.67033e17 q^{70} -6.03034e17 q^{71} +5.44729e16 q^{72} +4.95368e16 q^{73} +5.15217e17 q^{74} -2.21802e17 q^{75} +4.59491e17 q^{76} -2.84646e17 q^{77} +2.70814e17 q^{78} +9.43682e17 q^{79} -1.74052e17 q^{80} -1.49280e18 q^{81} -1.67568e18 q^{82} +1.80497e18 q^{83} +7.33622e17 q^{84} +5.01984e16 q^{85} -2.17558e18 q^{86} -1.10366e18 q^{87} -1.61439e18 q^{88} +3.40618e18 q^{89} -3.34458e17 q^{90} +1.08286e18 q^{91} +2.74063e18 q^{92} -4.55196e18 q^{93} -5.37424e17 q^{94} -7.85778e18 q^{95} +6.82773e18 q^{96} -6.45134e18 q^{97} +3.17051e18 q^{98} -5.69959e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) \) 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9} - 10197084160 q^{10} - 7963915630 q^{11} - 12629269764 q^{12} - 159160177690 q^{13} + 404118350082 q^{14} - 59651276056 q^{15} + 1400499411089 q^{16} - 2004886737784 q^{17} - 4449273908039 q^{18} - 1058821844658 q^{19} + 5114247081432 q^{20} + 2403861756792 q^{21} - 3900401557590 q^{22} - 17333732320340 q^{23} + 32877217250016 q^{24} + 85478486158774 q^{25} - 52056718761868 q^{26} - 137248515015920 q^{27} - 361374372214712 q^{28} - 66840103484258 q^{29} - 884984566401484 q^{30} - 481560705870844 q^{31} - 19\!\cdots\!67 q^{32}+ \cdots + 10\!\cdots\!22 q^{99}+O(q^{100}) \) 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9 - 10197084160 * q^10 - 7963915630 * q^11 - 12629269764 * q^12 - 159160177690 * q^13 + 404118350082 * q^14 - 59651276056 * q^15 + 1400499411089 * q^16 - 2004886737784 * q^17 - 4449273908039 * q^18 - 1058821844658 * q^19 + 5114247081432 * q^20 + 2403861756792 * q^21 - 3900401557590 * q^22 - 17333732320340 * q^23 + 32877217250016 * q^24 + 85478486158774 * q^25 - 52056718761868 * q^26 - 137248515015920 * q^27 - 361374372214712 * q^28 - 66840103484258 * q^29 - 884984566401484 * q^30 - 481560705870844 * q^31 - 1956224504349967 * q^32 - 1089319960511632 * q^33 - 1024355370607462 * q^34 - 368682962835736 * q^35 - 447128934368887 * q^36 - 2062248173433492 * q^37 - 1576879945450998 * q^38 - 2078450045289336 * q^39 - 6293443543679952 * q^40 + 1056258166827256 * q^41 + 3982705476758466 * q^42 - 3467551217747682 * q^43 - 3212244140107742 * q^44 + 4912736475062322 * q^45 + 5810353662475960 * q^46 + 38050436085494078 * q^47 + 57514374310072968 * q^48 + 47238885151375334 * q^49 + 14878200688182597 * q^50 - 29591098904130220 * q^51 - 21974217154008420 * q^52 - 72013726688940684 * q^53 + 172899128132785018 * q^54 + 93309162211316908 * q^55 + 475212376185711512 * q^56 + 64982196426903912 * q^57 + 191264232277219708 * q^58 + 76501047180767180 * q^59 + 400074650609834880 * q^60 - 93578930877721460 * q^61 + 57387957390004612 * q^62 - 383255174667133284 * q^63 + 259127393615024481 * q^64 - 901725390399661584 * q^65 - 254413721370645848 * q^66 - 1182341009802075686 * q^67 - 925231639360979526 * q^68 - 947344752044875104 * q^69 - 363789978732097444 * q^70 - 848931219817628416 * q^71 - 2149287430983690291 * q^72 - 2671220396145181732 * q^73 - 3011451157682875714 * q^74 - 17689756878445192 * q^75 - 3177271521326582258 * q^76 - 1684143788069292280 * q^77 - 224568865304519456 * q^78 + 707599882299569300 * q^79 - 715147860460459392 * q^80 + 3538237990220919930 * q^81 + 1087170674699769934 * q^82 + 3231397917214389292 * q^83 - 5938450004747482572 * q^84 - 1954320626223684628 * q^85 - 1629641946563167526 * q^86 + 7707422320592255560 * q^87 - 5131462381092863934 * q^88 - 6860870532479969712 * q^89 - 8661425364016769956 * q^90 - 2927652813879512704 * q^91 - 26818660612119538580 * q^92 - 19098581600812512 * q^93 - 1657432230665197927 * q^94 - 5345445300954569692 * q^95 - 59798491695034221784 * q^96 - 7217040872018076624 * q^97 - 44647529467669017809 * q^98 + 10120380184661285522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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