LMFDB - Embedded newform 10.38.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,38,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, 38, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 38 $
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:	$86.7140381246$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1222518952080 $ x^2 - x - 1222518952080
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.10568e6$ 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)

$f(q)$	$=$	\(q+262144. q^{2} -6.89815e8 q^{3} +6.87195e10 q^{4} +3.81470e12 q^{5} -1.80831e14 q^{6} +3.29617e15 q^{7} +1.80144e16 q^{8} +2.55614e16 q^{9} +1.00000e18 q^{10} -1.36311e19 q^{11} -4.74038e19 q^{12} -1.75195e20 q^{13} +8.64071e20 q^{14} -2.63144e21 q^{15} +4.72237e21 q^{16} -8.98224e20 q^{17} +6.70076e21 q^{18} +1.81344e23 q^{19} +2.62144e23 q^{20} -2.27375e24 q^{21} -3.57330e24 q^{22} -8.96395e24 q^{23} -1.24266e25 q^{24} +1.45519e25 q^{25} -4.59263e25 q^{26} +2.92980e26 q^{27} +2.26511e26 q^{28} +8.10751e26 q^{29} -6.89815e26 q^{30} +1.17491e27 q^{31} +1.23794e27 q^{32} +9.40292e27 q^{33} -2.35464e26 q^{34} +1.25739e28 q^{35} +1.75656e27 q^{36} +1.05137e29 q^{37} +4.75384e28 q^{38} +1.20852e29 q^{39} +6.87195e28 q^{40} -7.89765e29 q^{41} -5.96049e29 q^{42} -2.46365e30 q^{43} -9.36720e29 q^{44} +9.75088e28 q^{45} -2.34985e30 q^{46} -4.05145e30 q^{47} -3.25756e30 q^{48} -7.69740e30 q^{49} +3.81470e30 q^{50} +6.19609e29 q^{51} -1.20393e31 q^{52} -7.63383e31 q^{53} +7.68030e31 q^{54} -5.19984e31 q^{55} +5.93785e31 q^{56} -1.25094e32 q^{57} +2.12534e32 q^{58} +5.16782e30 q^{59} -1.80831e32 q^{60} -3.70977e32 q^{61} +3.07996e32 q^{62} +8.42545e31 q^{63} +3.24519e32 q^{64} -6.68315e32 q^{65} +2.46492e33 q^{66} -4.33067e33 q^{67} -6.17255e31 q^{68} +6.18347e33 q^{69} +3.29617e33 q^{70} -5.77653e31 q^{71} +4.60472e32 q^{72} -2.08780e34 q^{73} +2.75610e34 q^{74} -1.00381e34 q^{75} +1.24619e34 q^{76} -4.49303e34 q^{77} +3.16807e34 q^{78} +1.43759e35 q^{79} +1.80144e34 q^{80} -2.13612e35 q^{81} -2.07032e35 q^{82} -4.18848e35 q^{83} -1.56251e35 q^{84} -3.42645e33 q^{85} -6.45832e35 q^{86} -5.59269e35 q^{87} -2.45555e35 q^{88} -8.24770e35 q^{89} +2.55614e34 q^{90} -5.77472e35 q^{91} -6.15998e35 q^{92} -8.10471e35 q^{93} -1.06206e36 q^{94} +6.91774e35 q^{95} -8.53950e35 q^{96} +6.35165e36 q^{97} -2.01783e36 q^{98} -3.48428e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 524288 q^{2} - 185500908 q^{3} + 137438953472 q^{4} + 7629394531250 q^{5} - 48627950026752 q^{6} - 651580251842156 q^{7} + 36\!\cdots\!68 q^{8} - 17\!\cdots\!94 q^{9} + 20\!\cdots\!00 q^{10} - 15\!\cdots\!96 q^{11}+ \cdots + 78\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 524288 * q^2 - 185500908 * q^3 + 137438953472 * q^4 + 7629394531250 * q^5 - 48627950026752 * q^6 - 651580251842156 * q^7 + 36028797018963968 * q^8 - 170389465494380694 * q^9 + 2000000000000000000 * q^10 - 15811115630860522896 * q^11 - 12747525331812876288 * q^12 + 6429344487266558572 * q^13 - 170807853538910142464 * q^14 - 707629806518554687500 * q^15 + 9444732965739290427392 * q^16 - 30086486759205422032236 * q^17 - 44666576042558932647936 * q^18 - 282081097533425281034600 * q^19 + 524288000000000000000000 * q^20 - 4264653231690594841548576 * q^21 - 4144789095936300914049024 * q^22 - 14354648550540471611627508 * q^23 - 3341687280582754641641472 * q^24 + 29103830456733703613281250 * q^25 + 1685414081270004730298368 * q^26 - 32925375001813220927793720 * q^27 - 44776253958104060386082816 * q^28 - 578633540117083155511918020 * q^29 - 185500908000000000000000000 * q^30 + 2260671503635508838314765944 * q^31 + 2475880078570760549798248448 * q^32 + 8303484625710513647731806384 * q^33 - 7886991985005146153218473984 * q^34 - 2485581405037521362304687500 * q^35 - 11709074910100568840060534784 * q^36 + 23409156380578671012580292044 * q^37 - 73945867231802236871534182400 * q^38 + 212447831621391944006692317912 * q^39 + 137438953472000000000000000000 * q^40 - 334062590091523076172157550556 * q^41 - 1117953256768299294142909906944 * q^42 - 3080803860243335731086983683148 * q^43 - 1086531592765125666812467347456 * q^44 - 649984228112719322204589843750 * q^45 - 3762984989632881390158481457152 * q^46 - 5719254234797705932998464723196 * q^47 - 876003270481085632778462035968 * q^48 - 10674800935606385388910371290046 * q^49 + 7629394531250000000000000000000 * q^50 - 14100454968892791632477832162456 * q^51 + 441821188920444120019335380992 * q^52 - 127521008880356361721910167829028 * q^53 - 8631189504475324986895556935680 * q^54 - 60314619563524333557128906250000 * q^55 - 11737826317593230805849293717504 * q^56 - 358806426239077801832338373934000 * q^57 - 151685310740452646718516237434880 * q^58 - 474813416242254001125398669352840 * q^59 - 48627950026752000000000000000000 * q^60 + 1116767772034257845253589521824284 * q^61 + 592621470649026828911186003623936 * q^62 + 857818881631791694623438004627332 * q^63 + 649037107316853453566312041152512 * q^64 + 24526002835336908615112304687500 * q^65 + 2176708673722256889671006652727296 * q^66 + 7673276641697340174249928119756604 * q^67 - 2067527626917189033189303644061696 * q^68 + 3464864588816145116711925093270432 * q^69 - 651580251842156000000000000000000 * q^70 - 177124214726258022727480075167576 * q^71 - 3069463733233403518008828830416896 * q^72 - 25288395079691542643236189517864828 * q^73 + 6136569890230415133921848077582336 * q^74 - 2699393488001078367233276367187500 * q^75 - 19384465419613565582451456711065600 * q^76 - 36323966557789313174990868685716912 * q^77 + 55691924372558169769690350986723328 * q^78 - 29788166810476233766295293415728880 * q^79 + 36028797018963968000000000000000000 * q^80 - 289737451617349629538643532205001598 * q^81 - 87572503616952225280074068932952064 * q^82 - 576769245728275106339296629264281388 * q^83 - 293064738542269050163798974645927936 * q^84 - 114770838772603691224044799804687500 * q^85 - 807614247139629001890066250635149312 * q^86 - 1259955264138170284486514196753039720 * q^87 - 284827737853821102800887440331505664 * q^88 - 1798113862347037022073261713320951020 * q^89 - 170389465494380694000000000000000000 * q^90 - 1294478156334281614052853414115613416 * q^91 - 986443937122322059141704963103653888 * q^92 - 262906295189014461095003655420293376 * q^93 - 1499268182126809824099949536397492224 * q^94 - 1076053991445256351602935791015625000 * q^95 - 229639001336993712119077151956795392 * q^96 - 2415124428275029756982464505939910956 * q^97 - 2798335016463600291390520371457818624 * q^98 + 78754716927122895554836018489952112 * 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 $

$2$	262144.	0.707107
$2$	262144.	0.707107
$3$	−6.89815e8	−1.02799	−0.513996	−	0.857793i	$-0.671835\pi$
$3$	−6.89815e8	−1.02799	−0.513996	+	0.857793i	$0.671835\pi$
$4$	6.87195e10	0.500000
$5$	3.81470e12	0.447214
$5$	3.81470e12	0.447214
$6$	−1.80831e14	−0.726900
$7$	3.29617e15	0.765060	0.382530	−	0.923943i	$-0.375053\pi$
$7$	3.29617e15	0.765060	0.382530	+	0.923943i	$0.375053\pi$
$8$	1.80144e16	0.353553
$9$	2.55614e16	0.0567672
$10$	1.00000e18	0.316228
$11$	−1.36311e19	−0.739205	−0.369603	−	0.929190i	$-0.620506\pi$
$11$	−1.36311e19	−0.739205	−0.369603	+	0.929190i	$0.620506\pi$
$12$	−4.74038e19	−0.513996
$13$	−1.75195e20	−0.432085	−0.216043	−	0.976384i	$-0.569315\pi$
$13$	−1.75195e20	−0.432085	−0.216043	+	0.976384i	$0.569315\pi$
$14$	8.64071e20	0.540979
$15$	−2.63144e21	−0.459732
$16$	4.72237e21	0.250000
$17$	−8.98224e20	−0.0154910	−0.00774550	−	0.999970i	$-0.502465\pi$
$17$	−8.98224e20	−0.0154910	−0.00774550	+	0.999970i	$0.502465\pi$
$18$	6.70076e21	0.0401405
$19$	1.81344e23	0.399542	0.199771	−	0.979843i	$-0.435980\pi$
$19$	1.81344e23	0.399542	0.199771	+	0.979843i	$0.435980\pi$
$20$	2.62144e23	0.223607
$21$	−2.27375e24	−0.786475
$22$	−3.57330e24	−0.522697
$23$	−8.96395e24	−0.576149	−0.288074	−	0.957608i	$-0.593015\pi$
$23$	−8.96395e24	−0.576149	−0.288074	+	0.957608i	$0.593015\pi$
$24$	−1.24266e25	−0.363450
$25$	1.45519e25	0.200000
$26$	−4.59263e25	−0.305530
$27$	2.92980e26	0.969636
$28$	2.26511e26	0.382530
$29$	8.10751e26	0.715360	0.357680	−	0.933844i	$-0.383568\pi$
$29$	8.10751e26	0.715360	0.357680	+	0.933844i	$0.383568\pi$
$30$	−6.89815e26	−0.325080
$31$	1.17491e27	0.301865	0.150933	−	0.988544i	$-0.451772\pi$
$31$	1.17491e27	0.301865	0.150933	+	0.988544i	$0.451772\pi$
$32$	1.23794e27	0.176777
$33$	9.40292e27	0.759897
$34$	−2.35464e26	−0.0109538
$35$	1.25739e28	0.342145
$36$	1.75656e27	0.0283836
$37$	1.05137e29	1.02335	0.511673	−	0.859180i	$-0.329026\pi$
$37$	1.05137e29	1.02335	0.511673	+	0.859180i	$0.329026\pi$
$38$	4.75384e28	0.282519
$39$	1.20852e29	0.444180
$40$	6.87195e28	0.158114
$41$	−7.89765e29	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$41$	−7.89765e29	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$42$	−5.96049e29	−0.556122
$43$	−2.46365e30	−1.48735	−0.743675	−	0.668541i	$-0.766919\pi$
$43$	−2.46365e30	−1.48735	−0.743675	+	0.668541i	$0.766919\pi$
$44$	−9.36720e29	−0.369603
$45$	9.75088e28	0.0253871
$46$	−2.34985e30	−0.407399
$47$	−4.05145e30	−0.471846	−0.235923	−	0.971772i	$-0.575811\pi$
$47$	−4.05145e30	−0.471846	−0.235923	+	0.971772i	$0.575811\pi$
$48$	−3.25756e30	−0.256998
$49$	−7.69740e30	−0.414683
$50$	3.81470e30	0.141421
$51$	6.19609e29	0.0159246
$52$	−1.20393e31	−0.216043
$53$	−7.63383e31	−0.963027	−0.481514	−	0.876439i	$-0.659913\pi$
$53$	−7.63383e31	−0.963027	−0.481514	+	0.876439i	$0.659913\pi$
$54$	7.68030e31	0.685636
$55$	−5.19984e31	−0.330583
$56$	5.93785e31	0.270490
$57$	−1.25094e32	−0.410726
$58$	2.12534e32	0.505836
$59$	5.16782e30	0.00896489	0.00448245	−	0.999990i	$-0.498573\pi$
$59$	5.16782e30	0.00896489	0.00448245	+	0.999990i	$0.498573\pi$
$60$	−1.80831e32	−0.229866
$61$	−3.70977e32	−0.347332	−0.173666	−	0.984805i	$-0.555561\pi$
$61$	−3.70977e32	−0.347332	−0.173666	+	0.984805i	$0.555561\pi$
$62$	3.07996e32	0.213451
$63$	8.42545e31	0.0434303
$64$	3.24519e32	0.125000
$65$	−6.68315e32	−0.193234
$66$	2.46492e33	0.537328
$67$	−4.33067e33	−0.714778	−0.357389	−	0.933956i	$-0.616333\pi$
$67$	−4.33067e33	−0.714778	−0.357389	+	0.933956i	$0.616333\pi$
$68$	−6.17255e31	−0.00774550
$69$	6.18347e33	0.592276
$70$	3.29617e33	0.241933
$71$	−5.77653e31	−0.00326128	−0.00163064	−	0.999999i	$-0.500519\pi$
$71$	−5.77653e31	−0.00326128	−0.00163064	+	0.999999i	$0.500519\pi$
$72$	4.60472e32	0.0200702
$73$	−2.08780e34	−0.705043	−0.352522	−	0.935804i	$-0.614676\pi$
$73$	−2.08780e34	−0.705043	−0.352522	+	0.935804i	$0.614676\pi$
$74$	2.75610e34	0.723615
$75$	−1.00381e34	−0.205598
$76$	1.24619e34	0.199771
$77$	−4.49303e34	−0.565536
$78$	3.16807e34	0.314083
$79$	1.43759e35	1.12599	0.562994	−	0.826461i	$-0.309650\pi$
$79$	1.43759e35	1.12599	0.562994	+	0.826461i	$0.309650\pi$
$80$	1.80144e34	0.111803
$81$	−2.13612e35	−1.05354
$82$	−2.07032e35	−0.813732
$83$	−4.18848e35	−1.31556	−0.657782	−	0.753208i	$-0.728505\pi$
$83$	−4.18848e35	−1.31556	−0.657782	+	0.753208i	$0.728505\pi$
$84$	−1.56251e35	−0.393238
$85$	−3.42645e33	−0.00692779
$86$	−6.45832e35	−1.05172
$87$	−5.59269e35	−0.735384
$88$	−2.45555e35	−0.261349
$89$	−8.24770e35	−0.712226	−0.356113	−	0.934443i	$-0.615898\pi$
$89$	−8.24770e35	−0.712226	−0.356113	+	0.934443i	$0.615898\pi$
$90$	2.55614e34	0.0179514
$91$	−5.77472e35	−0.330571
$92$	−6.15998e35	−0.288074
$93$	−8.10471e35	−0.310315
$94$	−1.06206e36	−0.333645
$95$	6.91774e35	0.178681
$96$	−8.53950e35	−0.181725
$97$	6.35165e36	1.11586	0.557930	−	0.829888i	$-0.311596\pi$
$97$	6.35165e36	1.11586	0.557930	+	0.829888i	$0.311596\pi$
$98$	−2.01783e36	−0.293225
$99$	−3.48428e35	−0.0419626
$100$	1.00000e36	0.100000
$101$	−6.22694e36	−0.518000	−0.259000	−	0.965877i	$-0.583393\pi$
$101$	−6.22694e36	−0.518000	−0.259000	+	0.965877i	$0.583393\pi$
$102$	1.62427e35	0.0112604
$103$	−2.97899e37	−1.72417	−0.862085	−	0.506764i	$-0.830842\pi$
$103$	−2.97899e37	−1.72417	−0.862085	+	0.506764i	$0.830842\pi$
$104$	−3.15603e36	−0.152765
$105$	−8.67366e36	−0.351723
$106$	−2.00116e37	−0.680963
$107$	−5.21404e37	−1.49133	−0.745666	−	0.666320i	$-0.767869\pi$
$107$	−5.21404e37	−1.49133	−0.745666	+	0.666320i	$0.767869\pi$
$108$	2.01334e37	0.484818
$109$	−6.52849e37	−1.32563	−0.662815	−	0.748783i	$-0.730639\pi$
$109$	−6.52849e37	−1.32563	−0.662815	+	0.748783i	$0.730639\pi$
$110$	−1.36311e37	−0.233757
$111$	−7.25250e37	−1.05199
$112$	1.55657e37	0.191265
$113$	2.53181e37	0.263925	0.131963	−	0.991255i	$-0.457872\pi$
$113$	2.53181e37	0.263925	0.131963	+	0.991255i	$0.457872\pi$
$114$	−3.27927e37	−0.290427
$115$	−3.41948e37	−0.257661
$116$	5.57144e37	0.357680
$117$	−4.47822e36	−0.0245283
$118$	1.35471e36	0.00633914
$119$	−2.96070e36	−0.0118515
$120$	−4.74038e37	−0.162540
$121$	−1.54234e38	−0.453576
$122$	−9.72493e37	−0.245601
$123$	5.44792e38	1.18300
$124$	8.07392e37	0.150933
$125$	5.55112e37	0.0894427
$126$	2.20868e37	0.0307099
$127$	6.80429e38	0.817361	0.408681	−	0.912678i	$-0.365989\pi$
$127$	6.80429e38	0.817361	0.408681	+	0.912678i	$0.365989\pi$
$128$	8.50706e37	0.0883883
$129$	1.69947e39	1.52898
$130$	−1.75195e38	−0.136637
$131$	−1.33635e39	−0.904487	−0.452243	−	0.891895i	$-0.649376\pi$
$131$	−1.33635e39	−0.904487	−0.452243	+	0.891895i	$0.649376\pi$
$132$	6.46164e38	0.379948
$133$	5.97742e38	0.305674
$134$	−1.13526e39	−0.505424
$135$	1.11763e39	0.433634
$136$	−1.61810e37	−0.00547690
$137$	2.14881e39	0.635138	0.317569	−	0.948235i	$-0.397134\pi$
$137$	2.14881e39	0.635138	0.317569	+	0.948235i	$0.397134\pi$
$138$	1.62096e39	0.418802
$139$	6.21195e39	1.40428	0.702141	−	0.712038i	$-0.252228\pi$
$139$	6.21195e39	1.40428	0.702141	+	0.712038i	$0.252228\pi$
$140$	8.64071e38	0.171073
$141$	2.79475e39	0.485054
$142$	−1.51428e37	−0.00230607
$143$	2.38809e39	0.319400
$144$	1.20710e38	0.0141918
$145$	3.09277e39	0.319919
$146$	−5.47304e39	−0.498541
$147$	5.30978e39	0.426291
$148$	7.22494e39	0.511673
$149$	−1.54514e40	−0.966100	−0.483050	−	0.875593i	$-0.660471\pi$
$149$	−1.54514e40	−0.966100	−0.483050	+	0.875593i	$0.660471\pi$
$150$	−2.63144e39	−0.145380
$151$	−2.44879e40	−1.19640	−0.598202	−	0.801345i	$-0.704118\pi$
$151$	−2.44879e40	−1.19640	−0.598202	+	0.801345i	$0.704118\pi$
$152$	3.26681e39	0.141260
$153$	−2.29598e37	−0.000879381 0
$154$	−1.17782e40	−0.399895
$155$	4.48193e39	0.134998
$156$	8.30489e39	0.222090
$157$	−5.93872e40	−1.41107	−0.705536	−	0.708674i	$-0.749294\pi$
$157$	−5.93872e40	−1.41107	−0.705536	+	0.708674i	$0.749294\pi$
$158$	3.76855e40	0.796193
$159$	5.26593e40	0.989984
$160$	4.72237e39	0.0790569
$161$	−2.95467e40	−0.440788
$162$	−5.59971e40	−0.744969
$163$	1.27298e41	1.51131	0.755653	−	0.654972i	$-0.227320\pi$
$163$	1.27298e41	1.51131	0.755653	+	0.654972i	$0.227320\pi$
$164$	−5.42722e40	−0.575396
$165$	3.58693e40	0.339836
$166$	−1.09799e41	−0.930245
$167$	−1.13007e41	−0.856742	−0.428371	−	0.903603i	$-0.640912\pi$
$167$	−1.13007e41	−0.856742	−0.428371	+	0.903603i	$0.640912\pi$
$168$	−4.09602e40	−0.278061
$169$	−1.33708e41	−0.813302
$170$	−8.98224e38	−0.00489868
$171$	4.63541e39	0.0226809
$172$	−1.69301e41	−0.743675
$173$	2.46449e41	0.972464	0.486232	−	0.873830i	$-0.338371\pi$
$173$	2.46449e41	0.972464	0.486232	+	0.873830i	$0.338371\pi$
$174$	−1.46609e41	−0.519995
$175$	4.79655e40	0.153012
$176$	−6.43709e40	−0.184801
$177$	−3.56484e39	−0.00921584
$178$	−2.16208e41	−0.503620
$179$	−1.68898e41	−0.354685	−0.177343	−	0.984149i	$-0.556750\pi$
$179$	−1.68898e41	−0.354685	−0.177343	+	0.984149i	$0.556750\pi$
$180$	6.70076e39	0.0126935
$181$	−6.06854e41	−1.03760	−0.518801	−	0.854895i	$-0.673621\pi$
$181$	−6.06854e41	−1.03760	−0.518801	+	0.854895i	$0.673621\pi$
$182$	−1.51381e41	−0.233749
$183$	2.55905e41	0.357054
$184$	−1.61480e41	−0.203699
$185$	4.01065e41	0.457655
$186$	−2.12460e41	−0.219426
$187$	1.22437e40	0.0114510
$188$	−2.78414e41	−0.235923
$189$	9.65712e41	0.741829
$190$	1.81344e41	0.126346
$191$	1.09994e42	0.695429	0.347714	−	0.937600i	$-0.386958\pi$
$191$	1.09994e42	0.695429	0.347714	+	0.937600i	$0.386958\pi$
$192$	−2.23858e41	−0.128499
$193$	3.18819e42	1.66240	0.831198	−	0.555977i	$-0.187656\pi$
$193$	3.18819e42	1.66240	0.831198	+	0.555977i	$0.187656\pi$
$194$	1.66505e42	0.789032
$195$	4.61014e41	0.198643
$196$	−5.28961e41	−0.207342
$197$	2.35999e42	0.841948	0.420974	−	0.907073i	$-0.361688\pi$
$197$	2.35999e42	0.841948	0.420974	+	0.907073i	$0.361688\pi$
$198$	−9.13384e40	−0.0296720
$199$	5.36739e42	1.58848	0.794238	−	0.607606i	$-0.207870\pi$
$199$	5.36739e42	1.58848	0.794238	+	0.607606i	$0.207870\pi$
$200$	2.62144e41	0.0707107
$201$	2.98736e42	0.734786
$202$	−1.63236e42	−0.366281
$203$	2.67237e42	0.547293
$204$	4.25792e40	0.00796231
$205$	−3.01271e42	−0.514649
$206$	−7.80924e42	−1.21917
$207$	−2.29131e41	−0.0327063
$208$	−8.27334e41	−0.108021
$209$	−2.47192e42	−0.295344
$210$	−2.27375e42	−0.248705
$211$	6.79782e42	0.680996	0.340498	−	0.940245i	$-0.389404\pi$
$211$	6.79782e42	0.680996	0.340498	+	0.940245i	$0.389404\pi$
$212$	−5.24592e42	−0.481514
$213$	3.98474e40	0.00335257
$214$	−1.36683e43	−1.05453
$215$	−9.39810e42	−0.665163
$216$	5.27786e42	0.342818
$217$	3.87270e42	0.230945
$218$	−1.71140e43	−0.937363
$219$	1.44020e43	0.724778
$220$	−3.57330e42	−0.165291
$221$	1.57364e41	0.00669343
$222$	−1.90120e43	−0.743871
$223$	−3.83398e42	−0.138042	−0.0690208	−	0.997615i	$-0.521987\pi$
$223$	−3.83398e42	−0.138042	−0.0690208	+	0.997615i	$0.521987\pi$
$224$	4.08046e42	0.135245
$225$	3.71967e41	0.0113534
$226$	6.63700e42	0.186623
$227$	1.43677e42	0.0372313	0.0186157	−	0.999827i	$-0.494074\pi$
$227$	1.43677e42	0.0372313	0.0186157	+	0.999827i	$0.494074\pi$
$228$	−8.59641e42	−0.205363
$229$	2.80830e43	0.618710	0.309355	−	0.950947i	$-0.399887\pi$
$229$	2.80830e43	0.618710	0.309355	+	0.950947i	$0.399887\pi$
$230$	−8.96395e42	−0.182194
$231$	3.09936e43	0.581367
$232$	1.46052e43	0.252918
$233$	−1.02012e44	−1.63143	−0.815716	−	0.578453i	$-0.803657\pi$
$233$	−1.02012e44	−1.63143	−0.815716	+	0.578453i	$0.803657\pi$
$234$	−1.17394e42	−0.0173441
$235$	−1.54551e43	−0.211016
$236$	3.55130e41	0.00448245
$237$	−9.91671e43	−1.15751
$238$	−7.76129e41	−0.00838031
$239$	1.19632e43	0.119532	0.0597661	−	0.998212i	$-0.480965\pi$
$239$	1.19632e43	0.119532	0.0597661	+	0.998212i	$0.480965\pi$
$240$	−1.24266e43	−0.114933
$241$	−2.33793e43	−0.200224	−0.100112	−	0.994976i	$-0.531920\pi$
$241$	−2.33793e43	−0.200224	−0.100112	+	0.994976i	$0.531920\pi$
$242$	−4.04314e43	−0.320726
$243$	1.54287e43	0.113400
$244$	−2.54933e43	−0.173666
$245$	−2.93632e43	−0.185452
$246$	1.42814e44	0.836510
$247$	−3.17706e43	−0.172636
$248$	2.11653e43	0.106726
$249$	2.88928e44	1.35239
$250$	1.45519e43	0.0632456
$251$	1.57065e44	0.634040	0.317020	−	0.948419i	$-0.397318\pi$
$251$	1.57065e44	0.634040	0.317020	+	0.948419i	$0.397318\pi$
$252$	5.78993e42	0.0217152
$253$	1.22188e44	0.425892
$254$	1.78370e44	0.577962
$255$	2.36362e42	0.00712171
$256$	2.23007e43	0.0625000
$257$	−6.40421e44	−1.66995	−0.834973	−	0.550291i	$-0.814517\pi$
$257$	−6.40421e44	−1.66995	−0.834973	+	0.550291i	$0.814517\pi$
$258$	4.45505e44	1.08116
$259$	3.46548e44	0.782922
$260$	−4.59263e43	−0.0966172
$261$	2.07239e43	0.0406090
$262$	−3.50317e44	−0.639569
$263$	6.42820e44	1.09372	0.546862	−	0.837223i	$-0.315822\pi$
$263$	6.42820e44	1.09372	0.546862	+	0.837223i	$0.315822\pi$
$264$	1.69388e44	0.268664
$265$	−2.91207e44	−0.430679
$266$	1.56694e44	0.216144
$267$	5.68939e44	0.732162
$268$	−2.97601e44	−0.357389
$269$	−4.52122e44	−0.506803	−0.253401	−	0.967361i	$-0.581549\pi$
$269$	−4.52122e44	−0.506803	−0.253401	+	0.967361i	$0.581549\pi$
$270$	2.92980e44	0.306626
$271$	−5.63666e44	−0.550922	−0.275461	−	0.961312i	$-0.588830\pi$
$271$	−5.63666e44	−0.550922	−0.275461	+	0.961312i	$0.588830\pi$
$272$	−4.24174e42	−0.00387275
$273$	3.98349e44	0.339824
$274$	5.63298e44	0.449110
$275$	−1.98358e44	−0.147841
$276$	4.24925e44	0.296138
$277$	−8.72981e44	−0.569022	−0.284511	−	0.958673i	$-0.591831\pi$
$277$	−8.72981e44	−0.569022	−0.284511	+	0.958673i	$0.591831\pi$
$278$	1.62843e45	0.992977
$279$	3.00323e43	0.0171361
$280$	2.26511e44	0.120967
$281$	−3.74401e45	−1.87184	−0.935922	−	0.352206i	$-0.885432\pi$
$281$	−3.74401e45	−1.87184	−0.935922	+	0.352206i	$0.885432\pi$
$282$	7.32628e44	0.342985
$283$	1.09059e45	0.478204	0.239102	−	0.970994i	$-0.423147\pi$
$283$	1.09059e45	0.478204	0.239102	+	0.970994i	$0.423147\pi$
$284$	−3.96960e42	−0.00163064
$285$	−4.77197e44	−0.183682
$286$	6.26024e44	0.225850
$287$	−2.60320e45	−0.880424
$288$	3.16434e43	0.0100351
$289$	−3.36129e45	−0.999760
$290$	8.10751e44	0.226217
$291$	−4.38147e45	−1.14709
$292$	−1.43472e45	−0.352522
$293$	−1.50027e45	−0.346033	−0.173017	−	0.984919i	$-0.555351\pi$
$293$	−1.50027e45	−0.346033	−0.173017	+	0.984919i	$0.555351\pi$
$294$	1.39193e45	0.301433
$295$	1.97137e43	0.00400922
$296$	1.89398e45	0.361808
$297$	−3.99363e45	−0.716760
$298$	−4.05049e45	−0.683136
$299$	1.57044e45	0.248945
$300$	−6.89815e44	−0.102799
$301$	−8.12062e45	−1.13791
$302$	−6.41936e45	−0.845986
$303$	4.29544e45	0.532500
$304$	8.56375e44	0.0998856
$305$	−1.41516e45	−0.155332
$306$	−6.01878e42	−0.000621816 0
$307$	8.88941e45	0.864595	0.432298	−	0.901731i	$-0.357703\pi$
$307$	8.88941e45	0.864595	0.432298	+	0.901731i	$0.357703\pi$
$308$	−3.08758e45	−0.282768
$309$	2.05495e46	1.77243
$310$	1.17491e45	0.0954582
$311$	1.86301e46	1.42609	0.713045	−	0.701118i	$-0.247316\pi$
$311$	1.86301e46	1.42609	0.713045	+	0.701118i	$0.247316\pi$
$312$	2.17708e45	0.157041
$313$	−1.03471e46	−0.703476	−0.351738	−	0.936098i	$-0.614409\pi$
$313$	−1.03471e46	−0.703476	−0.351738	+	0.936098i	$0.614409\pi$
$314$	−1.55680e46	−0.997779
$315$	3.21405e44	0.0194226
$316$	9.87903e45	0.562994
$317$	3.08721e46	1.65947	0.829736	−	0.558157i	$-0.188491\pi$
$317$	3.08721e46	1.65947	0.829736	+	0.558157i	$0.188491\pi$
$318$	1.38043e46	0.700025
$319$	−1.10514e46	−0.528798
$320$	1.23794e45	0.0559017
$321$	3.59672e46	1.53308
$322$	−7.74549e45	−0.311684
$323$	−1.62888e44	−0.00618931
$324$	−1.46793e46	−0.526772
$325$	−2.54942e45	−0.0864170
$326$	3.33705e46	1.06865
$327$	4.50345e46	1.36274
$328$	−1.42271e46	−0.406866
$329$	−1.33543e46	−0.360990
$330$	9.40292e45	0.240301
$331$	−3.83499e46	−0.926716	−0.463358	−	0.886171i	$-0.653356\pi$
$331$	−3.83499e46	−0.926716	−0.463358	+	0.886171i	$0.653356\pi$
$332$	−2.87830e46	−0.657782
$333$	2.68744e45	0.0580925
$334$	−2.96241e46	−0.605808
$335$	−1.65202e46	−0.319658
$336$	−1.07375e46	−0.196619
$337$	3.97446e46	0.688850	0.344425	−	0.938814i	$-0.388074\pi$
$337$	3.97446e46	0.688850	0.344425	+	0.938814i	$0.388074\pi$
$338$	−3.50506e46	−0.575092
$339$	−1.74648e46	−0.271313
$340$	−2.35464e44	−0.00346389
$341$	−1.60153e46	−0.223141
$342$	1.21514e45	0.0160378
$343$	−8.65557e46	−1.08232
$344$	−4.43813e46	−0.525858
$345$	2.35881e46	0.264874
$346$	6.46050e46	0.687636
$347$	1.01071e47	1.01983	0.509917	−	0.860223i	$-0.329676\pi$
$347$	1.01071e47	1.01983	0.509917	+	0.860223i	$0.329676\pi$
$348$	−3.84326e46	−0.367692
$349$	6.03446e46	0.547480	0.273740	−	0.961804i	$-0.411739\pi$
$349$	6.03446e46	0.547480	0.273740	+	0.961804i	$0.411739\pi$
$350$	1.25739e46	0.108196
$351$	−5.13286e46	−0.418965
$352$	−1.68744e46	−0.130674
$353$	6.49991e46	0.477612	0.238806	−	0.971067i	$-0.423244\pi$
$353$	6.49991e46	0.477612	0.238806	+	0.971067i	$0.423244\pi$
$354$	−9.34502e44	−0.00651658
$355$	−2.20357e44	−0.00145849
$356$	−5.66777e46	−0.356113
$357$	2.04233e45	0.0121833
$358$	−4.42756e46	−0.250801
$359$	−1.34716e47	−0.724724	−0.362362	−	0.932038i	$-0.618030\pi$
$359$	−1.34716e47	−0.724724	−0.362362	+	0.932038i	$0.618030\pi$
$360$	1.75656e45	0.00897568
$361$	−1.73122e47	−0.840366
$362$	−1.59083e47	−0.733695
$363$	1.06393e47	0.466272
$364$	−3.96835e46	−0.165286
$365$	−7.96432e46	−0.315305
$366$	6.70841e46	0.252476
$367$	1.76042e47	0.629934	0.314967	−	0.949103i	$-0.398007\pi$
$367$	1.76042e47	0.629934	0.314967	+	0.949103i	$0.398007\pi$
$368$	−4.23311e46	−0.144037
$369$	−2.01875e46	−0.0653272
$370$	1.05137e47	0.323611
$371$	−2.51624e47	−0.736774
$372$	−5.56952e46	−0.155158
$373$	3.37762e47	0.895359	0.447679	−	0.894194i	$-0.352251\pi$
$373$	3.37762e47	0.895359	0.447679	+	0.894194i	$0.352251\pi$
$374$	3.20962e45	0.00809710
$375$	−3.82924e46	−0.0919464
$376$	−7.29844e46	−0.166823
$377$	−1.42039e47	−0.309096
$378$	2.53156e47	0.524553
$379$	−6.92554e47	−1.36656	−0.683279	−	0.730157i	$-0.739447\pi$
$379$	−6.92554e47	−1.36656	−0.683279	+	0.730157i	$0.739447\pi$
$380$	4.75384e46	0.0893404
$381$	−4.69370e47	−0.840240
$382$	2.88343e47	0.491743
$383$	2.21003e47	0.359105	0.179553	−	0.983748i	$-0.442535\pi$
$383$	2.21003e47	0.359105	0.179553	+	0.983748i	$0.442535\pi$
$384$	−5.86830e46	−0.0908625
$385$	−1.71395e47	−0.252916
$386$	8.35765e47	1.17549
$387$	−6.29743e46	−0.0844327
$388$	4.36482e47	0.557930
$389$	3.20256e47	0.390328	0.195164	−	0.980771i	$-0.437476\pi$
$389$	3.20256e47	0.390328	0.195164	+	0.980771i	$0.437476\pi$
$390$	1.20852e47	0.140462
$391$	8.05163e45	0.00892512
$392$	−1.38664e47	−0.146613
$393$	9.21837e47	0.929805
$394$	6.18657e47	0.595347
$395$	5.48396e47	0.503557
$396$	−2.39438e46	−0.0209813
$397$	2.55758e47	0.213897	0.106948	−	0.994265i	$-0.465892\pi$
$397$	2.55758e47	0.213897	0.106948	+	0.994265i	$0.465892\pi$
$398$	1.40703e48	1.12322
$399$	−4.12331e47	−0.314230
$400$	6.87195e46	0.0500000
$401$	2.29575e48	1.59498	0.797488	−	0.603334i	$-0.206161\pi$
$401$	2.29575e48	1.59498	0.797488	+	0.603334i	$0.206161\pi$
$402$	7.83119e47	0.519572
$403$	−2.05838e47	−0.130432
$404$	−4.27912e47	−0.259000
$405$	−8.14865e47	−0.471160
$406$	7.00546e47	0.386995
$407$	−1.43313e48	−0.756463
$408$	1.11619e46	0.00563020
$409$	−1.23961e48	−0.597592	−0.298796	−	0.954317i	$-0.596585\pi$
$409$	−1.23961e48	−0.597592	−0.298796	+	0.954317i	$0.596585\pi$
$410$	−7.89765e47	−0.363912
$411$	−1.48228e48	−0.652916
$412$	−2.04714e48	−0.862085
$413$	1.70340e46	0.00685868
$414$	−6.00652e46	−0.0231269
$415$	−1.59778e48	−0.588338
$416$	−2.16881e47	−0.0763826
$417$	−4.28510e48	−1.44359
$418$	−6.47998e47	−0.208840
$419$	3.37300e48	1.04006	0.520029	−	0.854149i	$-0.325921\pi$
$419$	3.37300e48	1.04006	0.520029	+	0.854149i	$0.325921\pi$
$420$	−5.96049e47	−0.175861
$421$	2.03580e48	0.574798	0.287399	−	0.957811i	$-0.407209\pi$
$421$	2.03580e48	0.574798	0.287399	+	0.957811i	$0.407209\pi$
$422$	1.78201e48	0.481537
$423$	−1.03561e47	−0.0267854
$424$	−1.37519e48	−0.340482
$425$	−1.30709e46	−0.00309820
$426$	1.04458e46	0.00237062
$427$	−1.22280e48	−0.265730
$428$	−3.58306e48	−0.745666
$429$	−1.64734e48	−0.328340
$430$	−2.46365e48	−0.470342
$431$	6.24281e48	1.14170	0.570848	−	0.821056i	$-0.306615\pi$
$431$	6.24281e48	1.14170	0.570848	+	0.821056i	$0.306615\pi$
$432$	1.38356e48	0.242409
$433$	−4.71991e48	−0.792333	−0.396166	−	0.918179i	$-0.629660\pi$
$433$	−4.71991e48	−0.792333	−0.396166	+	0.918179i	$0.629660\pi$
$434$	1.01521e48	0.163303
$435$	−2.13344e48	−0.328874
$436$	−4.48635e48	−0.662815
$437$	−1.62556e48	−0.230196
$438$	3.77539e48	0.512496
$439$	−7.57651e48	−0.985997	−0.492999	−	0.870030i	$-0.664099\pi$
$439$	−7.57651e48	−0.985997	−0.492999	+	0.870030i	$0.664099\pi$
$440$	−9.36720e47	−0.116879
$441$	−1.96756e47	−0.0235404
$442$	4.12521e46	0.00473297
$443$	8.83812e48	0.972503	0.486252	−	0.873819i	$-0.338364\pi$
$443$	8.83812e48	0.972503	0.486252	+	0.873819i	$0.338364\pi$
$444$	−4.98388e48	−0.525996
$445$	−3.14625e48	−0.318517
$446$	−1.00505e48	−0.0976101
$447$	1.06586e49	0.993143
$448$	1.06967e48	0.0956325
$449$	−2.01986e49	−1.73286	−0.866429	−	0.499300i	$-0.833590\pi$
$449$	−2.01986e49	−1.73286	−0.866429	+	0.499300i	$0.833590\pi$
$450$	9.75088e46	0.00802809
$451$	1.07653e49	0.850671
$452$	1.73985e48	0.131963
$453$	1.68921e49	1.22989
$454$	3.76640e47	0.0263265
$455$	−2.20288e48	−0.147836
$456$	−2.25350e48	−0.145214
$457$	6.61916e48	0.409594	0.204797	−	0.978804i	$-0.434347\pi$
$457$	6.61916e48	0.409594	0.204797	+	0.978804i	$0.434347\pi$
$458$	7.36180e48	0.437494
$459$	−2.63162e47	−0.0150206
$460$	−2.34985e48	−0.128831
$461$	2.46377e49	1.29758	0.648788	−	0.760969i	$-0.275276\pi$
$461$	2.46377e49	1.29758	0.648788	+	0.760969i	$0.275276\pi$
$462$	8.12478e48	0.411088
$463$	3.33469e49	1.62109	0.810546	−	0.585675i	$-0.199171\pi$
$463$	3.33469e49	1.62109	0.810546	+	0.585675i	$0.199171\pi$
$464$	3.82866e48	0.178840
$465$	−3.09170e48	−0.138777
$466$	−2.67420e49	−1.15360
$467$	9.90311e48	0.410591	0.205295	−	0.978700i	$-0.434184\pi$
$467$	9.90311e48	0.410591	0.205295	+	0.978700i	$0.434184\pi$
$468$	−3.07741e47	−0.0122641
$469$	−1.42746e49	−0.546848
$470$	−4.05145e48	−0.149211
$471$	4.09662e49	1.45057
$472$	9.30952e46	0.00316957
$473$	3.35822e49	1.09946
$474$	−2.59961e49	−0.818480
$475$	2.63891e48	0.0799084
$476$	−2.03457e47	−0.00592577
$477$	−1.95131e48	−0.0546684
$478$	3.13607e48	0.0845221
$479$	−3.54457e49	−0.919086	−0.459543	−	0.888156i	$-0.651987\pi$
$479$	−3.54457e49	−0.919086	−0.459543	+	0.888156i	$0.651987\pi$
$480$	−3.25756e48	−0.0812699
$481$	−1.84194e49	−0.442173
$482$	−6.12874e48	−0.141580
$483$	2.03818e49	0.453127
$484$	−1.05989e49	−0.226788
$485$	2.42296e49	0.499028
$486$	4.04453e48	0.0801857
$487$	−5.61975e49	−1.07258	−0.536292	−	0.844032i	$-0.680175\pi$
$487$	−5.61975e49	−1.07258	−0.536292	+	0.844032i	$0.680175\pi$
$488$	−6.68292e48	−0.122800
$489$	−8.78124e49	−1.55361
$490$	−7.69740e48	−0.131134
$491$	−6.73087e49	−1.10424	−0.552120	−	0.833764i	$-0.686181\pi$
$491$	−6.73087e49	−1.10424	−0.552120	+	0.833764i	$0.686181\pi$
$492$	3.74378e49	0.591502
$493$	−7.28236e47	−0.0110816
$494$	−8.32848e48	−0.122072
$495$	−1.32915e48	−0.0187662
$496$	5.54836e48	0.0754664
$497$	−1.90404e47	−0.00249507
$498$	7.57408e49	0.956284
$499$	−1.57170e50	−1.91209	−0.956045	−	0.293221i	$-0.905273\pi$
$499$	−1.57170e50	−1.91209	−0.956045	+	0.293221i	$0.905273\pi$
$500$	3.81470e48	0.0447214
$501$	7.79539e49	0.880724
$502$	4.11738e49	0.448334
$503$	8.33167e49	0.874429	0.437214	−	0.899357i	$-0.355965\pi$
$503$	8.33167e49	0.874429	0.437214	+	0.899357i	$0.355965\pi$
$504$	1.51779e48	0.0153549
$505$	−2.37539e49	−0.231657
$506$	3.20309e49	0.301151
$507$	9.22336e49	0.836068
$508$	4.67587e49	0.408681
$509$	−1.50351e50	−1.26715	−0.633575	−	0.773682i	$-0.718413\pi$
$509$	−1.50351e50	−1.26715	−0.633575	+	0.773682i	$0.718413\pi$
$510$	6.19609e47	0.00503581
$511$	−6.88173e49	−0.539400
$512$	5.84601e48	0.0441942
$513$	5.31303e49	0.387410
$514$	−1.67882e50	−1.18083
$515$	−1.13639e50	−0.771072
$516$	1.16786e50	0.764492
$517$	5.52256e49	0.348791
$518$	9.08456e49	0.553609
$519$	−1.70004e50	−0.999685
$520$	−1.20393e49	−0.0683187
$521$	5.18958e49	0.284207	0.142103	−	0.989852i	$-0.454613\pi$
$521$	5.18958e49	0.284207	0.142103	+	0.989852i	$0.454613\pi$
$522$	5.43264e48	0.0287149
$523$	−1.48076e50	−0.755445	−0.377723	−	0.925919i	$-0.623293\pi$
$523$	−1.48076e50	−0.755445	−0.377723	+	0.925919i	$0.623293\pi$
$524$	−9.18335e49	−0.452243
$525$	−3.30874e49	−0.157295
$526$	1.68511e50	0.773380
$527$	−1.05533e48	−0.00467620
$528$	4.44040e49	0.189974
$529$	−1.61711e50	−0.668053
$530$	−7.63383e49	−0.304536
$531$	1.32096e47	0.000508912 0
$532$	4.10765e49	0.152837
$533$	1.38363e50	0.497240
$534$	1.49144e50	0.517717
$535$	−1.98900e50	−0.666944
$536$	−7.80144e49	−0.252712
$537$	1.16508e50	0.364614
$538$	−1.18521e50	−0.358364
$539$	1.04924e50	0.306536
$540$	7.68030e49	0.216817
$541$	5.01469e50	1.36803	0.684013	−	0.729470i	$-0.260233\pi$
$541$	5.01469e50	1.36803	0.684013	+	0.729470i	$0.260233\pi$
$542$	−1.47762e50	−0.389561
$543$	4.18617e50	1.06665
$544$	−1.11195e48	−0.00273845
$545$	−2.49042e50	−0.592840
$546$	1.04425e50	0.240292
$547$	4.97650e50	1.10703	0.553513	−	0.832840i	$-0.313287\pi$
$547$	4.97650e50	1.10703	0.553513	+	0.832840i	$0.313287\pi$
$548$	1.47665e50	0.317569
$549$	−9.48266e48	−0.0197171
$550$	−5.19984e49	−0.104539
$551$	1.47025e50	0.285816
$552$	1.11392e50	0.209401
$553$	4.73853e50	0.861448
$554$	−2.28847e50	−0.402359
$555$	−2.76661e50	−0.470465
$556$	4.26882e50	0.702141
$557$	6.67759e49	0.106243	0.0531213	−	0.998588i	$-0.483083\pi$
$557$	6.67759e49	0.106243	0.0531213	+	0.998588i	$0.483083\pi$
$558$	7.87279e48	0.0121170
$559$	4.31620e50	0.642662
$560$	5.93785e49	0.0855363
$561$	−8.44592e48	−0.0117716
$562$	−9.81469e50	−1.32359
$563$	1.01553e51	1.32522	0.662610	−	0.748964i	$-0.269449\pi$
$563$	1.01553e51	1.32522	0.662610	+	0.748964i	$0.269449\pi$
$564$	1.92054e50	0.242527
$565$	9.65810e49	0.118031
$566$	2.85892e50	0.338142
$567$	−7.04101e50	−0.806025
$568$	−1.04061e48	−0.00115304
$569$	−4.88120e50	−0.523540	−0.261770	−	0.965130i	$-0.584306\pi$
$569$	−4.88120e50	−0.523540	−0.261770	+	0.965130i	$0.584306\pi$
$570$	−1.25094e50	−0.129883
$571$	−6.10676e49	−0.0613822	−0.0306911	−	0.999529i	$-0.509771\pi$
$571$	−6.10676e49	−0.0613822	−0.0306911	+	0.999529i	$0.509771\pi$
$572$	1.64108e50	0.159700
$573$	−7.58757e50	−0.714895
$574$	−6.82413e50	−0.622554
$575$	−1.30443e50	−0.115230
$576$	8.29513e48	0.00709590
$577$	−5.54304e50	−0.459193	−0.229597	−	0.973286i	$-0.573741\pi$
$577$	−5.54304e50	−0.459193	−0.229597	+	0.973286i	$0.573741\pi$
$578$	−8.81142e50	−0.706937
$579$	−2.19926e51	−1.70893
$580$	2.12534e50	0.159959
$581$	−1.38059e51	−1.00649
$582$	−1.14858e51	−0.811118
$583$	1.04057e51	0.711875
$584$	−3.76104e50	−0.249270
$585$	−1.70830e49	−0.0109694
$586$	−3.93286e50	−0.244682
$587$	7.00286e50	0.422154	0.211077	−	0.977469i	$-0.432303\pi$
$587$	7.00286e50	0.422154	0.211077	+	0.977469i	$0.432303\pi$
$588$	3.64885e50	0.213145
$589$	2.13064e50	0.120608
$590$	5.16782e48	0.00283495
$591$	−1.62796e51	−0.865515
$592$	4.96494e50	0.255837
$593$	3.03179e51	1.51421	0.757106	−	0.653292i	$-0.226613\pi$
$593$	3.03179e51	1.51421	0.757106	+	0.653292i	$0.226613\pi$
$594$	−1.04691e51	−0.506826
$595$	−1.12942e49	−0.00530017
$596$	−1.06181e51	−0.483050
$597$	−3.70251e51	−1.63294
$598$	4.11681e50	0.176031
$599$	3.37693e51	1.39999	0.699997	−	0.714145i	$-0.253184\pi$
$599$	3.37693e51	1.39999	0.699997	+	0.714145i	$0.253184\pi$
$600$	−1.80831e50	−0.0726900
$601$	3.37420e51	1.31521	0.657603	−	0.753365i	$-0.271571\pi$
$601$	3.37420e51	1.31521	0.657603	+	0.753365i	$0.271571\pi$
$602$	−2.12877e51	−0.804626
$603$	−1.10698e50	−0.0405759
$604$	−1.68280e51	−0.598202
$605$	−5.88355e50	−0.202845
$606$	1.12602e51	0.376534
$607$	5.86428e51	1.90206	0.951029	−	0.309101i	$-0.100028\pi$
$607$	5.86428e51	1.90206	0.951029	+	0.309101i	$0.100028\pi$
$608$	2.24494e50	0.0706298
$609$	−1.84344e51	−0.562613
$610$	−3.70977e50	−0.109836
$611$	7.09793e50	0.203878
$612$	−1.57779e48	−0.000439690 0
$613$	−6.86486e50	−0.185615	−0.0928075	−	0.995684i	$-0.529584\pi$
$613$	−6.86486e50	−0.185615	−0.0928075	+	0.995684i	$0.529584\pi$
$614$	2.33031e51	0.611361
$615$	2.07822e51	0.529055
$616$	−8.09392e50	−0.199947
$617$	−2.90878e51	−0.697326	−0.348663	−	0.937248i	$-0.613364\pi$
$617$	−2.90878e51	−0.697326	−0.348663	+	0.937248i	$0.613364\pi$
$618$	5.38693e51	1.25330
$619$	4.53284e51	1.02351	0.511756	−	0.859131i	$-0.328995\pi$
$619$	4.53284e51	1.02351	0.511756	+	0.859131i	$0.328995\pi$
$620$	3.07996e50	0.0674992
$621$	−2.62626e51	−0.558654
$622$	4.88376e51	1.00840
$623$	−2.71858e51	−0.544895
$624$	5.70708e50	0.111045
$625$	2.11758e50	0.0400000
$626$	−2.71244e51	−0.497433
$627$	1.70517e51	0.303611
$628$	−4.08106e51	−0.705536
$629$	−9.44363e49	−0.0158527
$630$	8.42545e49	0.0137339
$631$	−4.30708e50	−0.0681772	−0.0340886	−	0.999419i	$-0.510853\pi$
$631$	−4.30708e50	−0.0681772	−0.0340886	+	0.999419i	$0.510853\pi$
$632$	2.58973e51	0.398097
$633$	−4.68924e51	−0.700058
$634$	8.09293e51	1.17342
$635$	2.59563e51	0.365535
$636$	3.61872e51	0.494992
$637$	1.34854e51	0.179178
$638$	−2.89706e51	−0.373916
$639$	−1.47656e48	−0.000185133 0
$640$	3.24519e50	0.0395285
$641$	−3.95135e51	−0.467597	−0.233799	−	0.972285i	$-0.575116\pi$
$641$	−3.95135e51	−0.467597	−0.233799	+	0.972285i	$0.575116\pi$
$642$	9.42860e51	1.08405
$643$	−1.17106e52	−1.30821	−0.654103	−	0.756406i	$-0.726954\pi$
$643$	−1.17106e52	−1.30821	−0.654103	+	0.756406i	$0.726954\pi$
$644$	−2.03043e51	−0.220394
$645$	6.48295e51	0.683783
$646$	−4.27001e49	−0.00437650
$647$	2.47032e51	0.246051	0.123025	−	0.992404i	$-0.460740\pi$
$647$	2.47032e51	0.246051	0.123025	+	0.992404i	$0.460740\pi$
$648$	−3.84809e51	−0.372484
$649$	−7.04429e49	−0.00662690
$650$	−6.68315e50	−0.0611061
$651$	−2.67145e51	−0.237410
$652$	8.74788e51	0.755653
$653$	−1.97344e52	−1.65703	−0.828513	−	0.559970i	$-0.810812\pi$
$653$	−1.97344e52	−1.65703	−0.828513	+	0.559970i	$0.810812\pi$
$654$	1.18055e52	0.963601
$655$	−5.09778e51	−0.404499
$656$	−3.72956e51	−0.287698
$657$	−5.33669e50	−0.0400233
$658$	−3.50074e51	−0.255259
$659$	−1.00529e52	−0.712711	−0.356355	−	0.934351i	$-0.615981\pi$
$659$	−1.00529e52	−0.712711	−0.356355	+	0.934351i	$0.615981\pi$
$660$	2.46492e51	0.169918
$661$	1.30458e52	0.874468	0.437234	−	0.899348i	$-0.355958\pi$
$661$	1.30458e52	0.874468	0.437234	+	0.899348i	$0.355958\pi$
$662$	−1.00532e52	−0.655287
$663$	−1.08552e50	−0.00688079
$664$	−7.54530e51	−0.465122
$665$	2.28020e51	0.136701
$666$	7.04496e50	0.0410776
$667$	−7.26753e51	−0.412154
$668$	−7.76577e51	−0.428371
$669$	2.64474e51	0.141906
$670$	−4.33067e51	−0.226033
$671$	5.05681e51	0.256750
$672$	−2.81476e51	−0.139031
$673$	−2.06557e52	−0.992570	−0.496285	−	0.868160i	$-0.665303\pi$
$673$	−2.06557e52	−0.992570	−0.496285	+	0.868160i	$0.665303\pi$
$674$	1.04188e52	0.487091
$675$	4.26342e51	0.193927
$676$	−9.18832e51	−0.406651
$677$	−1.48357e52	−0.638876	−0.319438	−	0.947607i	$-0.603494\pi$
$677$	−1.48357e52	−0.638876	−0.319438	+	0.947607i	$0.603494\pi$
$678$	−4.57830e51	−0.191847
$679$	2.09361e52	0.853700
$680$	−6.17255e49	−0.00244934
$681$	−9.91105e50	−0.0382735
$682$	−4.19831e51	−0.157784
$683$	−1.63537e51	−0.0598183	−0.0299092	−	0.999553i	$-0.509522\pi$
$683$	−1.63537e51	−0.0598183	−0.0299092	+	0.999553i	$0.509522\pi$
$684$	3.18543e50	0.0113404
$685$	8.19706e51	0.284042
$686$	−2.26901e52	−0.765314
$687$	−1.93721e52	−0.636029
$688$	−1.16343e52	−0.371838
$689$	1.33741e52	0.416110
$690$	6.18347e51	0.187294
$691$	−2.87913e51	−0.0849018	−0.0424509	−	0.999099i	$-0.513517\pi$
$691$	−2.87913e51	−0.0849018	−0.0424509	+	0.999099i	$0.513517\pi$
$692$	1.69358e52	0.486232
$693$	−1.14848e51	−0.0321039
$694$	2.64951e52	0.721132
$695$	2.36967e52	0.628014
$696$	−1.00749e52	−0.259998
$697$	7.09386e50	0.0178269
$698$	1.58190e52	0.387127
$699$	7.03698e52	1.67710
$700$	3.29617e51	0.0765060
$701$	−4.36552e52	−0.986852	−0.493426	−	0.869788i	$-0.664256\pi$
$701$	−4.36552e52	−0.986852	−0.493426	+	0.869788i	$0.664256\pi$
$702$	−1.34555e52	−0.296253
$703$	1.90660e52	0.408870
$704$	−4.42353e51	−0.0924007
$705$	1.06611e52	0.216923
$706$	1.70391e52	0.337723
$707$	−2.05251e52	−0.396301
$708$	−2.44974e50	−0.00460792
$709$	6.12553e52	1.12251	0.561253	−	0.827645i	$-0.310320\pi$
$709$	6.12553e52	1.12251	0.561253	+	0.827645i	$0.310320\pi$
$710$	−5.77653e49	−0.00103131
$711$	3.67467e51	0.0639191
$712$	−1.48577e52	−0.251810
$713$	−1.05318e52	−0.173919
$714$	5.35385e50	0.00861489
$715$	9.10985e51	0.142840
$716$	−1.16066e52	−0.177343
$717$	−8.25238e51	−0.122878
$718$	−3.53150e52	−0.512457
$719$	6.31848e52	0.893569	0.446784	−	0.894642i	$-0.352569\pi$
$719$	6.31848e52	0.893569	0.446784	+	0.894642i	$0.352569\pi$
$720$	4.60472e50	0.00634677
$721$	−9.81924e52	−1.31909
$722$	−4.53828e52	−0.594228
$723$	1.61274e52	0.205829
$724$	−4.17027e52	−0.518801
$725$	1.17980e52	0.143072
$726$	2.78902e52	0.329704
$727$	5.46946e52	0.630316	0.315158	−	0.949039i	$-0.397943\pi$
$727$	5.46946e52	0.630316	0.315158	+	0.949039i	$0.397943\pi$
$728$	−1.04028e52	−0.116875
$729$	8.55432e52	0.936971
$730$	−2.08780e52	−0.222954
$731$	2.21291e51	0.0230405
$732$	1.75857e52	0.178527
$733$	3.01068e52	0.298017	0.149008	−	0.988836i	$-0.452392\pi$
$733$	3.01068e52	0.298017	0.149008	+	0.988836i	$0.452392\pi$
$734$	4.61485e52	0.445431
$735$	2.02552e52	0.190643
$736$	−1.10968e52	−0.101850
$737$	5.90316e52	0.528367
$738$	−5.29202e51	−0.0461933
$739$	1.55405e53	1.32295	0.661476	−	0.749967i	$-0.269930\pi$
$739$	1.55405e53	1.32295	0.661476	+	0.749967i	$0.269930\pi$
$740$	2.75610e52	0.228827
$741$	2.19159e52	0.177469
$742$	−6.59616e52	−0.520978
$743$	1.58003e53	1.21723	0.608613	−	0.793467i	$-0.291726\pi$
$743$	1.58003e53	1.21723	0.608613	+	0.793467i	$0.291726\pi$
$744$	−1.46002e52	−0.109713
$745$	−5.89424e52	−0.432053
$746$	8.85422e52	0.633114
$747$	−1.07063e52	−0.0746809
$748$	8.41384e50	0.00572551
$749$	−1.71863e53	−1.14096
$750$	−1.00381e52	−0.0650159
$751$	−7.41700e52	−0.468694	−0.234347	−	0.972153i	$-0.575295\pi$
$751$	−7.41700e52	−0.468694	−0.234347	+	0.972153i	$0.575295\pi$
$752$	−1.91324e52	−0.117961
$753$	−1.08346e53	−0.651788
$754$	−3.72348e52	−0.218564
$755$	−9.34139e52	−0.535048
$756$	6.63632e52	0.370915
$757$	−2.14270e53	−1.16866	−0.584329	−	0.811517i	$-0.698642\pi$
$757$	−2.14270e53	−1.16866	−0.584329	+	0.811517i	$0.698642\pi$
$758$	−1.81549e53	−0.966303
$759$	−8.42873e52	−0.437814
$760$	1.24619e52	0.0631732
$761$	−4.02061e53	−1.98919	−0.994594	−	0.103844i	$-0.966886\pi$
$761$	−4.02061e53	−1.98919	−0.994594	+	0.103844i	$0.966886\pi$
$762$	−1.23043e53	−0.594140
$763$	−2.15190e53	−1.01419
$764$	7.55875e52	0.347714
$765$	−8.75847e49	−0.000393271 0
$766$	5.79347e52	0.253926
$767$	−9.05375e50	−0.00387360
$768$	−1.53834e52	−0.0642495
$769$	−1.75938e53	−0.717335	−0.358667	−	0.933465i	$-0.616769\pi$
$769$	−1.75938e53	−0.717335	−0.358667	+	0.933465i	$0.616769\pi$
$770$	−4.49303e52	−0.178838
$771$	4.41772e53	1.71669
$772$	2.19091e53	0.831198
$773$	−2.25368e53	−0.834781	−0.417390	−	0.908727i	$-0.637055\pi$
$773$	−2.25368e53	−0.834781	−0.417390	+	0.908727i	$0.637055\pi$
$774$	−1.65083e52	−0.0597029
$775$	1.70972e52	0.0603731
$776$	1.14421e53	0.394516
$777$	−2.39054e53	−0.804837
$778$	8.39531e52	0.276003
$779$	−1.43219e53	−0.459790
$780$	3.16807e52	0.0993217
$781$	7.87402e50	0.00241075
$782$	2.11069e51	0.00631101
$783$	2.37534e53	0.693638
$784$	−3.63499e52	−0.103671
$785$	−2.26544e53	−0.631051
$786$	2.41654e53	0.657471
$787$	5.34066e53	1.41926	0.709631	−	0.704574i	$-0.248862\pi$
$787$	5.34066e53	1.41926	0.709631	+	0.704574i	$0.248862\pi$
$788$	1.62177e53	0.420974
$789$	−4.43427e53	−1.12434
$790$	1.43759e53	0.356068
$791$	8.34528e52	0.201918
$792$	−6.27673e51	−0.0148360
$793$	6.49932e52	0.150077
$794$	6.70453e52	0.151248
$795$	2.00879e53	0.442734
$796$	3.68844e53	0.794238
$797$	6.52917e53	1.37366	0.686830	−	0.726818i	$-0.259002\pi$
$797$	6.52917e53	1.37366	0.686830	+	0.726818i	$0.259002\pi$
$798$	−1.08090e53	−0.222194
$799$	3.63911e51	0.00730937
$800$	1.80144e52	0.0353553
$801$	−2.10822e52	−0.0404311
$802$	6.01818e53	1.12782
$803$	2.84589e53	0.521171
$804$	2.05290e53	0.367393
$805$	−1.12712e53	−0.197127
$806$	−5.39593e52	−0.0922291
$807$	3.11881e53	0.520989
$808$	−1.12175e53	−0.183141
$809$	−5.66679e53	−0.904252	−0.452126	−	0.891954i	$-0.649334\pi$
$809$	−5.66679e53	−0.904252	−0.452126	+	0.891954i	$0.649334\pi$
$810$	−2.13612e53	−0.333160
$811$	4.52502e53	0.689818	0.344909	−	0.938636i	$-0.387910\pi$
$811$	4.52502e53	0.689818	0.344909	+	0.938636i	$0.387910\pi$
$812$	1.83644e53	0.273647
$813$	3.88826e53	0.566343
$814$	−3.75685e53	−0.534900
$815$	4.85605e53	0.675877
$816$	2.92602e51	0.00398116
$817$	−4.46770e53	−0.594259
$818$	−3.24957e53	−0.422561
$819$	−1.47610e52	−0.0187656
$820$	−2.07032e53	−0.257325
$821$	−1.11490e54	−1.35484	−0.677419	−	0.735597i	$-0.736902\pi$
$821$	−1.11490e54	−1.35484	−0.677419	+	0.735597i	$0.736902\pi$
$822$	−3.88572e53	−0.461681
$823$	1.69605e54	1.97034	0.985171	−	0.171575i	$-0.0548855\pi$
$823$	1.69605e54	1.97034	0.985171	+	0.171575i	$0.0548855\pi$
$824$	−5.36647e53	−0.609586
$825$	1.36830e53	0.151979
$826$	4.46536e51	0.00484982
$827$	−4.68182e53	−0.497236	−0.248618	−	0.968602i	$-0.579976\pi$
$827$	−4.68182e53	−0.497236	−0.248618	+	0.968602i	$0.579976\pi$
$828$	−1.57457e52	−0.0163532
$829$	−6.57785e53	−0.668075	−0.334037	−	0.942560i	$-0.608411\pi$
$829$	−6.57785e53	−0.668075	−0.334037	+	0.942560i	$0.608411\pi$
$830$	−4.18848e53	−0.416018
$831$	6.02196e53	0.584950
$832$	−5.68540e52	−0.0540106
$833$	6.91398e51	0.00642386
$834$	−1.12331e54	−1.02077
$835$	−4.31087e53	−0.383147
$836$	−1.69869e53	−0.147672
$837$	3.44225e53	0.292700
$838$	8.84213e53	0.735432
$839$	−1.37838e54	−1.12143	−0.560714	−	0.828009i	$-0.689473\pi$
$839$	−1.37838e54	−1.12143	−0.560714	+	0.828009i	$0.689473\pi$
$840$	−1.56251e53	−0.124353
$841$	−6.27159e53	−0.488260
$842$	5.33672e53	0.406444
$843$	2.58267e54	1.92424
$844$	4.67143e53	0.340498
$845$	−5.10054e53	−0.363720
$846$	−2.71478e52	−0.0189401
$847$	−5.08380e53	−0.347013
$848$	−3.60497e53	−0.240757
$849$	−7.52308e53	−0.491590
$850$	−3.42645e51	−0.00219076
$851$	−9.42441e53	−0.589600
$852$	2.73829e51	0.00167628
$853$	3.21106e54	1.92350	0.961748	−	0.273937i	$-0.0883260\pi$
$853$	3.21106e54	1.92350	0.961748	+	0.273937i	$0.0883260\pi$
$854$	−3.20550e53	−0.187899
$855$	1.76827e52	0.0101432
$856$	−9.39278e53	−0.527265
$857$	−3.02093e54	−1.65957	−0.829784	−	0.558085i	$-0.811536\pi$
$857$	−3.02093e54	−1.65957	−0.829784	+	0.558085i	$0.811536\pi$
$858$	−4.31841e53	−0.232172
$859$	−1.03473e54	−0.544444	−0.272222	−	0.962235i	$-0.587758\pi$
$859$	−1.03473e54	−0.544444	−0.272222	+	0.962235i	$0.587758\pi$
$860$	−6.45832e53	−0.332582
$861$	1.79573e54	0.905069
$862$	1.63651e54	0.807301
$863$	−2.58733e54	−1.24926	−0.624629	−	0.780921i	$-0.714750\pi$
$863$	−2.58733e54	−1.24926	−0.624629	+	0.780921i	$0.714750\pi$
$864$	3.62692e53	0.171409
$865$	9.40127e53	0.434899
$866$	−1.23730e54	−0.560264
$867$	2.31867e54	1.02775
$868$	2.66130e53	0.115473
$869$	−1.95959e54	−0.832336
$870$	−5.59269e53	−0.232549
$871$	7.58711e53	0.308845
$872$	−1.17607e54	−0.468681
$873$	1.62357e53	0.0633442
$874$	−4.26132e53	−0.162773
$875$	1.82974e53	0.0684291
$876$	9.89695e53	0.362389
$877$	−1.33643e54	−0.479132	−0.239566	−	0.970880i	$-0.577005\pi$
$877$	−1.33643e54	−0.479132	−0.239566	+	0.970880i	$0.577005\pi$
$878$	−1.98614e54	−0.697205
$879$	1.03491e54	0.355719
$880$	−2.45555e53	−0.0826457
$881$	1.19179e54	0.392776	0.196388	−	0.980526i	$-0.437079\pi$
$881$	1.19179e54	0.392776	0.196388	+	0.980526i	$0.437079\pi$
$882$	−5.15784e52	−0.0166456
$883$	2.32196e54	0.733805	0.366903	−	0.930259i	$-0.380418\pi$
$883$	2.32196e54	0.733805	0.366903	+	0.930259i	$0.380418\pi$
$884$	1.08140e52	0.00334672
$885$	−1.35988e52	−0.00412145
$886$	2.31686e54	0.687664
$887$	−2.27100e54	−0.660131	−0.330065	−	0.943958i	$-0.607071\pi$
$887$	−2.27100e54	−0.660131	−0.330065	+	0.943958i	$0.607071\pi$
$888$	−1.30649e54	−0.371935
$889$	2.24281e54	0.625330
$890$	−8.24770e53	−0.225226
$891$	2.91176e54	0.778786
$892$	−2.63469e53	−0.0690208
$893$	−7.34708e53	−0.188522
$894$	2.79409e54	0.702258
$895$	−6.44295e53	−0.158620
$896$	2.80407e53	0.0676224
$897$	−1.08331e54	−0.255914
$898$	−5.29493e54	−1.22532
$899$	9.52560e53	0.215942
$900$	2.55614e52	0.00567672
$901$	6.85688e52	0.0149183
$902$	2.82207e54	0.601515
$903$	5.60173e54	1.16976
$904$	4.56091e53	0.0933116
$905$	−2.31497e54	−0.464030
$906$	4.42817e54	0.869666
$907$	9.99936e53	0.192414	0.0962072	−	0.995361i	$-0.469329\pi$
$907$	9.99936e53	0.192414	0.0962072	+	0.995361i	$0.469329\pi$
$908$	9.87340e52	0.0186157
$909$	−1.59169e53	−0.0294054
$910$	−5.77472e53	−0.104536
$911$	8.26172e52	0.0146548	0.00732741	−	0.999973i	$-0.497668\pi$
$911$	8.26172e52	0.0146548	0.00732741	+	0.999973i	$0.497668\pi$
$912$	−5.90741e53	−0.102682
$913$	5.70935e54	0.972472
$914$	1.73517e54	0.289627
$915$	9.76202e53	0.159680
$916$	1.92985e54	0.309355
$917$	−4.40484e54	−0.691987
$918$	−6.89863e52	−0.0106212
$919$	5.97032e54	0.900867	0.450433	−	0.892810i	$-0.351269\pi$
$919$	5.97032e54	0.900867	0.450433	+	0.892810i	$0.351269\pi$
$920$	−6.15998e53	−0.0910971
$921$	−6.13205e54	−0.888797
$922$	6.45862e54	0.917524
$923$	1.01202e52	0.00140915
$924$	2.12986e54	0.290683
$925$	1.52994e54	0.204669
$926$	8.74170e54	1.14628
$927$	−7.61470e53	−0.0978763
$928$	1.00366e54	0.126459
$929$	−1.17859e55	−1.45571	−0.727853	−	0.685734i	$-0.759482\pi$
$929$	−1.17859e55	−1.45571	−0.727853	+	0.685734i	$0.759482\pi$
$930$	−8.10471e53	−0.0981303
$931$	−1.39588e54	−0.165683
$932$	−7.01025e54	−0.815716
$933$	−1.28513e55	−1.46601
$934$	2.59604e54	0.290332
$935$	4.67062e52	0.00512106
$936$	−8.06724e52	−0.00867205
$937$	−1.35568e54	−0.142881	−0.0714405	−	0.997445i	$-0.522760\pi$
$937$	−1.35568e54	−0.142881	−0.0714405	+	0.997445i	$0.522760\pi$
$938$	−3.74200e54	−0.386680
$939$	7.13761e54	0.723168
$940$	−1.06206e54	−0.105508
$941$	−1.66103e55	−1.61796	−0.808981	−	0.587835i	$-0.799980\pi$
$941$	−1.66103e55	−1.61796	−0.808981	+	0.587835i	$0.799980\pi$
$942$	1.07390e55	1.02571
$943$	7.07941e54	0.663027
$944$	2.44043e52	0.00224122
$945$	3.68390e54	0.331756
$946$	8.80338e54	0.777434
$947$	−5.07081e54	−0.439139	−0.219570	−	0.975597i	$-0.570465\pi$
$947$	−5.07081e54	−0.439139	−0.219570	+	0.975597i	$0.570465\pi$
$948$	−6.81471e54	−0.578753
$949$	3.65772e54	0.304639
$950$	6.91774e53	0.0565038
$951$	−2.12960e55	−1.70592
$952$	−5.33352e52	−0.00419015
$953$	−1.58180e55	−1.21880	−0.609401	−	0.792862i	$-0.708590\pi$
$953$	−1.58180e55	−1.21880	−0.609401	+	0.792862i	$0.708590\pi$
$954$	−5.11524e53	−0.0386564
$955$	4.19595e54	0.311005
$956$	8.22103e53	0.0597661
$957$	7.62342e54	0.543600
$958$	−9.29187e54	−0.649892
$959$	7.08284e54	0.485918
$960$	−8.53950e53	−0.0574665
$961$	−1.37685e55	−0.908877
$962$	−4.82854e54	−0.312663
$963$	−1.33278e54	−0.0846587
$964$	−1.60661e54	−0.100112
$965$	1.21620e55	0.743446
$966$	5.34296e54	0.320409
$967$	1.47153e55	0.865724	0.432862	−	0.901460i	$-0.357504\pi$
$967$	1.47153e55	0.865724	0.432862	+	0.901460i	$0.357504\pi$
$968$	−2.77843e54	−0.160363
$969$	1.12363e53	0.00636256
$970$	6.35165e54	0.352866
$971$	−3.18652e55	−1.73684	−0.868422	−	0.495825i	$-0.834866\pi$
$971$	−3.18652e55	−1.73684	−0.868422	+	0.495825i	$0.834866\pi$
$972$	1.06025e54	0.0566999
$973$	2.04756e55	1.07436
$974$	−1.47318e55	−0.758432
$975$	1.75863e54	0.0888360
$976$	−1.75189e54	−0.0868330
$977$	−1.74536e55	−0.848857	−0.424428	−	0.905462i	$-0.639525\pi$
$977$	−1.74536e55	−0.848857	−0.424428	+	0.905462i	$0.639525\pi$
$978$	−2.30195e55	−1.09857
$979$	1.12425e55	0.526481
$980$	−2.01783e54	−0.0927260
$981$	−1.66877e54	−0.0752523
$982$	−1.76446e55	−0.780816
$983$	−7.48657e54	−0.325119	−0.162560	−	0.986699i	$-0.551975\pi$
$983$	−7.48657e54	−0.325119	−0.162560	+	0.986699i	$0.551975\pi$
$984$	9.81410e54	0.418255
$985$	9.00265e54	0.376530
$986$	−1.90903e53	−0.00783590
$987$	9.21197e54	0.371095
$988$	−2.18326e54	−0.0863181
$989$	2.20841e55	0.856935
$990$	−3.48428e53	−0.0132697
$991$	−1.50174e55	−0.561349	−0.280674	−	0.959803i	$-0.590558\pi$
$991$	−1.50174e55	−0.561349	−0.280674	+	0.959803i	$0.590558\pi$
$992$	1.45447e54	0.0533628
$993$	2.64544e55	0.952656
$994$	−4.99133e52	−0.00176428
$995$	2.04750e55	0.710388
$996$	1.98550e55	0.676195
$997$	2.10810e55	0.704743	0.352371	−	0.935860i	$-0.385375\pi$
$997$	2.10810e55	0.704743	0.352371	+	0.935860i	$0.385375\pi$
$998$	−4.12010e55	−1.35205
$999$	3.08030e55	0.992273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.38.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.38.a.a.1.1	✓	2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+262144. q^{2} -6.89815e8 q^{3} +6.87195e10 q^{4} +3.81470e12 q^{5} -1.80831e14 q^{6} +3.29617e15 q^{7} +1.80144e16 q^{8} +2.55614e16 q^{9} +1.00000e18 q^{10} -1.36311e19 q^{11} -4.74038e19 q^{12} -1.75195e20 q^{13} +8.64071e20 q^{14} -2.63144e21 q^{15} +4.72237e21 q^{16} -8.98224e20 q^{17} +6.70076e21 q^{18} +1.81344e23 q^{19} +2.62144e23 q^{20} -2.27375e24 q^{21} -3.57330e24 q^{22} -8.96395e24 q^{23} -1.24266e25 q^{24} +1.45519e25 q^{25} -4.59263e25 q^{26} +2.92980e26 q^{27} +2.26511e26 q^{28} +8.10751e26 q^{29} -6.89815e26 q^{30} +1.17491e27 q^{31} +1.23794e27 q^{32} +9.40292e27 q^{33} -2.35464e26 q^{34} +1.25739e28 q^{35} +1.75656e27 q^{36} +1.05137e29 q^{37} +4.75384e28 q^{38} +1.20852e29 q^{39} +6.87195e28 q^{40} -7.89765e29 q^{41} -5.96049e29 q^{42} -2.46365e30 q^{43} -9.36720e29 q^{44} +9.75088e28 q^{45} -2.34985e30 q^{46} -4.05145e30 q^{47} -3.25756e30 q^{48} -7.69740e30 q^{49} +3.81470e30 q^{50} +6.19609e29 q^{51} -1.20393e31 q^{52} -7.63383e31 q^{53} +7.68030e31 q^{54} -5.19984e31 q^{55} +5.93785e31 q^{56} -1.25094e32 q^{57} +2.12534e32 q^{58} +5.16782e30 q^{59} -1.80831e32 q^{60} -3.70977e32 q^{61} +3.07996e32 q^{62} +8.42545e31 q^{63} +3.24519e32 q^{64} -6.68315e32 q^{65} +2.46492e33 q^{66} -4.33067e33 q^{67} -6.17255e31 q^{68} +6.18347e33 q^{69} +3.29617e33 q^{70} -5.77653e31 q^{71} +4.60472e32 q^{72} -2.08780e34 q^{73} +2.75610e34 q^{74} -1.00381e34 q^{75} +1.24619e34 q^{76} -4.49303e34 q^{77} +3.16807e34 q^{78} +1.43759e35 q^{79} +1.80144e34 q^{80} -2.13612e35 q^{81} -2.07032e35 q^{82} -4.18848e35 q^{83} -1.56251e35 q^{84} -3.42645e33 q^{85} -6.45832e35 q^{86} -5.59269e35 q^{87} -2.45555e35 q^{88} -8.24770e35 q^{89} +2.55614e34 q^{90} -5.77472e35 q^{91} -6.15998e35 q^{92} -8.10471e35 q^{93} -1.06206e36 q^{94} +6.91774e35 q^{95} -8.53950e35 q^{96} +6.35165e36 q^{97} -2.01783e36 q^{98} -3.48428e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 524288 q^{2} - 185500908 q^{3} + 137438953472 q^{4} + 7629394531250 q^{5} - 48627950026752 q^{6} - 651580251842156 q^{7} + 36\!\cdots\!68 q^{8} - 17\!\cdots\!94 q^{9} + 20\!\cdots\!00 q^{10} - 15\!\cdots\!96 q^{11}+ \cdots + 78\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 524288 * q^2 - 185500908 * q^3 + 137438953472 * q^4 + 7629394531250 * q^5 - 48627950026752 * q^6 - 651580251842156 * q^7 + 36028797018963968 * q^8 - 170389465494380694 * q^9 + 2000000000000000000 * q^10 - 15811115630860522896 * q^11 - 12747525331812876288 * q^12 + 6429344487266558572 * q^13 - 170807853538910142464 * q^14 - 707629806518554687500 * q^15 + 9444732965739290427392 * q^16 - 30086486759205422032236 * q^17 - 44666576042558932647936 * q^18 - 282081097533425281034600 * q^19 + 524288000000000000000000 * q^20 - 4264653231690594841548576 * q^21 - 4144789095936300914049024 * q^22 - 14354648550540471611627508 * q^23 - 3341687280582754641641472 * q^24 + 29103830456733703613281250 * q^25 + 1685414081270004730298368 * q^26 - 32925375001813220927793720 * q^27 - 44776253958104060386082816 * q^28 - 578633540117083155511918020 * q^29 - 185500908000000000000000000 * q^30 + 2260671503635508838314765944 * q^31 + 2475880078570760549798248448 * q^32 + 8303484625710513647731806384 * q^33 - 7886991985005146153218473984 * q^34 - 2485581405037521362304687500 * q^35 - 11709074910100568840060534784 * q^36 + 23409156380578671012580292044 * q^37 - 73945867231802236871534182400 * q^38 + 212447831621391944006692317912 * q^39 + 137438953472000000000000000000 * q^40 - 334062590091523076172157550556 * q^41 - 1117953256768299294142909906944 * q^42 - 3080803860243335731086983683148 * q^43 - 1086531592765125666812467347456 * q^44 - 649984228112719322204589843750 * q^45 - 3762984989632881390158481457152 * q^46 - 5719254234797705932998464723196 * q^47 - 876003270481085632778462035968 * q^48 - 10674800935606385388910371290046 * q^49 + 7629394531250000000000000000000 * q^50 - 14100454968892791632477832162456 * q^51 + 441821188920444120019335380992 * q^52 - 127521008880356361721910167829028 * q^53 - 8631189504475324986895556935680 * q^54 - 60314619563524333557128906250000 * q^55 - 11737826317593230805849293717504 * q^56 - 358806426239077801832338373934000 * q^57 - 151685310740452646718516237434880 * q^58 - 474813416242254001125398669352840 * q^59 - 48627950026752000000000000000000 * q^60 + 1116767772034257845253589521824284 * q^61 + 592621470649026828911186003623936 * q^62 + 857818881631791694623438004627332 * q^63 + 649037107316853453566312041152512 * q^64 + 24526002835336908615112304687500 * q^65 + 2176708673722256889671006652727296 * q^66 + 7673276641697340174249928119756604 * q^67 - 2067527626917189033189303644061696 * q^68 + 3464864588816145116711925093270432 * q^69 - 651580251842156000000000000000000 * q^70 - 177124214726258022727480075167576 * q^71 - 3069463733233403518008828830416896 * q^72 - 25288395079691542643236189517864828 * q^73 + 6136569890230415133921848077582336 * q^74 - 2699393488001078367233276367187500 * q^75 - 19384465419613565582451456711065600 * q^76 - 36323966557789313174990868685716912 * q^77 + 55691924372558169769690350986723328 * q^78 - 29788166810476233766295293415728880 * q^79 + 36028797018963968000000000000000000 * q^80 - 289737451617349629538643532205001598 * q^81 - 87572503616952225280074068932952064 * q^82 - 576769245728275106339296629264281388 * q^83 - 293064738542269050163798974645927936 * q^84 - 114770838772603691224044799804687500 * q^85 - 807614247139629001890066250635149312 * q^86 - 1259955264138170284486514196753039720 * q^87 - 284827737853821102800887440331505664 * q^88 - 1798113862347037022073261713320951020 * q^89 - 170389465494380694000000000000000000 * q^90 - 1294478156334281614052853414115613416 * q^91 - 986443937122322059141704963103653888 * q^92 - 262906295189014461095003655420293376 * q^93 - 1499268182126809824099949536397492224 * q^94 - 1076053991445256351602935791015625000 * q^95 - 229639001336993712119077151956795392 * q^96 - 2415124428275029756982464505939910956 * q^97 - 2798335016463600291390520371457818624 * q^98 + 78754716927122895554836018489952112 * q^99

Introduction

L-functions

Modular forms

Varieties

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