LMFDB - Embedded newform 10.38.a.a.1.2

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			1.2
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)

$f(q)$	$=$	\(q+262144. q^{2} +5.04314e8 q^{3} +6.87195e10 q^{4} +3.81470e12 q^{5} +1.32203e14 q^{6} -3.94775e15 q^{7} +1.80144e16 q^{8} -1.95951e17 q^{9} +1.00000e18 q^{10} -2.18005e18 q^{11} +3.46562e19 q^{12} +1.81624e20 q^{13} -1.03488e21 q^{14} +1.92381e21 q^{15} +4.72237e21 q^{16} -2.91883e22 q^{17} -5.13673e22 q^{18} -4.63426e23 q^{19} +2.62144e23 q^{20} -1.99091e24 q^{21} -5.71488e23 q^{22} -5.39070e24 q^{23} +9.08492e24 q^{24} +1.45519e25 q^{25} +4.76117e25 q^{26} -3.25906e26 q^{27} -2.71287e26 q^{28} -1.38938e27 q^{29} +5.04314e26 q^{30} +1.08576e27 q^{31} +1.23794e27 q^{32} -1.09943e27 q^{33} -7.65153e27 q^{34} -1.50595e28 q^{35} -1.34656e28 q^{36} -8.17276e28 q^{37} -1.21484e29 q^{38} +9.15957e28 q^{39} +6.87195e28 q^{40} +4.55702e29 q^{41} -5.21904e29 q^{42} -6.17149e29 q^{43} -1.49812e29 q^{44} -7.47493e29 q^{45} -1.41314e30 q^{46} -1.66780e30 q^{47} +2.38156e30 q^{48} -2.97740e30 q^{49} +3.81470e30 q^{50} -1.47201e31 q^{51} +1.24811e31 q^{52} -5.11828e31 q^{53} -8.54342e31 q^{54} -8.31624e30 q^{55} -7.11163e31 q^{56} -2.33712e32 q^{57} -3.64219e32 q^{58} -4.79981e32 q^{59} +1.32203e32 q^{60} +1.48774e33 q^{61} +2.84626e32 q^{62} +7.73564e32 q^{63} +3.24519e32 q^{64} +6.92841e32 q^{65} -2.88210e32 q^{66} +1.20039e34 q^{67} -2.00580e33 q^{68} -2.71861e33 q^{69} -3.94775e33 q^{70} -1.19359e32 q^{71} -3.52994e33 q^{72} -4.41041e33 q^{73} -2.14244e34 q^{74} +7.33874e33 q^{75} -3.18464e34 q^{76} +8.60630e33 q^{77} +2.40113e34 q^{78} -1.73547e35 q^{79} +1.80144e34 q^{80} -7.61254e34 q^{81} +1.19460e35 q^{82} -1.57921e35 q^{83} -1.36814e35 q^{84} -1.11344e35 q^{85} -1.61782e35 q^{86} -7.00687e35 q^{87} -3.92723e34 q^{88} -9.73344e35 q^{89} -1.95951e35 q^{90} -7.17007e35 q^{91} -3.70446e35 q^{92} +5.47565e35 q^{93} -4.37205e35 q^{94} -1.76783e36 q^{95} +6.24311e35 q^{96} -8.76678e36 q^{97} -7.80509e35 q^{98} +4.27183e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.04314e8	0.751551	0.375775	−	0.926711i	$-0.377376\pi$
$3$	5.04314e8	0.751551	0.375775	+	0.926711i	$0.377376\pi$
$4$	6.87195e10	0.500000
$5$	3.81470e12	0.447214
$5$	3.81470e12	0.447214
$6$	1.32203e14	0.531427
$7$	−3.94775e15	−0.916296	−0.458148	−	0.888876i	$-0.651487\pi$
$7$	−3.94775e15	−0.916296	−0.458148	+	0.888876i	$0.651487\pi$
$8$	1.80144e16	0.353553
$9$	−1.95951e17	−0.435172
$10$	1.00000e18	0.316228
$11$	−2.18005e18	−0.118223	−0.0591115	−	0.998251i	$-0.518827\pi$
$11$	−2.18005e18	−0.118223	−0.0591115	+	0.998251i	$0.518827\pi$
$12$	3.46562e19	0.375775
$13$	1.81624e20	0.447942	0.223971	−	0.974596i	$-0.428098\pi$
$13$	1.81624e20	0.447942	0.223971	+	0.974596i	$0.428098\pi$
$14$	−1.03488e21	−0.647919
$15$	1.92381e21	0.336104
$16$	4.72237e21	0.250000
$17$	−2.91883e22	−0.503388	−0.251694	−	0.967807i	$-0.580988\pi$
$17$	−2.91883e22	−0.503388	−0.251694	+	0.967807i	$0.580988\pi$
$18$	−5.13673e22	−0.307713
$19$	−4.63426e23	−1.02103	−0.510515	−	0.859869i	$-0.670545\pi$
$19$	−4.63426e23	−1.02103	−0.510515	+	0.859869i	$0.670545\pi$
$20$	2.62144e23	0.223607
$21$	−1.99091e24	−0.688643
$22$	−5.71488e23	−0.0835964
$23$	−5.39070e24	−0.346481	−0.173241	−	0.984880i	$-0.555424\pi$
$23$	−5.39070e24	−0.346481	−0.173241	+	0.984880i	$0.555424\pi$
$24$	9.08492e24	0.265713
$25$	1.45519e25	0.200000
$26$	4.76117e25	0.316743
$27$	−3.25906e26	−1.07860
$28$	−2.71287e26	−0.458148
$29$	−1.38938e27	−1.22591	−0.612956	−	0.790117i	$-0.710020\pi$
$29$	−1.38938e27	−1.22591	−0.612956	+	0.790117i	$0.710020\pi$
$30$	5.04314e26	0.237661
$31$	1.08576e27	0.278961	0.139480	−	0.990225i	$-0.455457\pi$
$31$	1.08576e27	0.278961	0.139480	+	0.990225i	$0.455457\pi$
$32$	1.23794e27	0.176777
$33$	−1.09943e27	−0.0888506
$34$	−7.65153e27	−0.355949
$35$	−1.50595e28	−0.409780
$36$	−1.34656e28	−0.217586
$37$	−8.17276e28	−0.795494	−0.397747	−	0.917495i	$-0.630208\pi$
$37$	−8.17276e28	−0.795494	−0.397747	+	0.917495i	$0.630208\pi$
$38$	−1.21484e29	−0.721977
$39$	9.15957e28	0.336651
$40$	6.87195e28	0.158114
$41$	4.55702e29	0.664018	0.332009	−	0.943276i	$-0.392274\pi$
$41$	4.55702e29	0.664018	0.332009	+	0.943276i	$0.392274\pi$
$42$	−5.21904e29	−0.486944
$43$	−6.17149e29	−0.372584	−0.186292	−	0.982494i	$-0.559647\pi$
$43$	−6.17149e29	−0.372584	−0.186292	+	0.982494i	$0.559647\pi$
$44$	−1.49812e29	−0.0591115
$45$	−7.47493e29	−0.194615
$46$	−1.41314e30	−0.244999
$47$	−1.66780e30	−0.194238	−0.0971191	−	0.995273i	$-0.530963\pi$
$47$	−1.66780e30	−0.194238	−0.0971191	+	0.995273i	$0.530963\pi$
$48$	2.38156e30	0.187888
$49$	−2.97740e30	−0.160402
$50$	3.81470e30	0.141421
$51$	−1.47201e31	−0.378322
$52$	1.24811e31	0.223971
$53$	−5.11828e31	−0.645684	−0.322842	−	0.946453i	$-0.604638\pi$
$53$	−5.11828e31	−0.645684	−0.322842	+	0.946453i	$0.604638\pi$
$54$	−8.54342e31	−0.762688
$55$	−8.31624e30	−0.0528710
$56$	−7.11163e31	−0.323959
$57$	−2.33712e32	−0.767355
$58$	−3.64219e32	−0.866851
$59$	−4.79981e32	−0.832649	−0.416325	−	0.909216i	$-0.636682\pi$
$59$	−4.79981e32	−0.832649	−0.416325	+	0.909216i	$0.636682\pi$
$60$	1.32203e32	0.168052
$61$	1.48774e33	1.39292	0.696460	−	0.717595i	$-0.254757\pi$
$61$	1.48774e33	1.39292	0.696460	+	0.717595i	$0.254757\pi$
$62$	2.84626e32	0.197255
$63$	7.73564e32	0.398746
$64$	3.24519e32	0.125000
$65$	6.92841e32	0.200326
$66$	−2.88210e32	−0.0628269
$67$	1.20039e34	1.98125	0.990627	−	0.136596i	$-0.0436162\pi$
$67$	1.20039e34	1.98125	0.990627	+	0.136596i	$0.0436162\pi$
$68$	−2.00580e33	−0.251694
$69$	−2.71861e33	−0.260398
$70$	−3.94775e33	−0.289758
$71$	−1.19359e32	−0.00673869	−0.00336934	−	0.999994i	$-0.501072\pi$
$71$	−1.19359e32	−0.00673869	−0.00336934	+	0.999994i	$0.501072\pi$
$72$	−3.52994e33	−0.153856
$73$	−4.41041e33	−0.148938	−0.0744691	−	0.997223i	$-0.523726\pi$
$73$	−4.41041e33	−0.148938	−0.0744691	+	0.997223i	$0.523726\pi$
$74$	−2.14244e34	−0.562499
$75$	7.33874e33	0.150310
$76$	−3.18464e34	−0.510515
$77$	8.60630e33	0.108327
$78$	2.40113e34	0.238048
$79$	−1.73547e35	−1.35930	−0.679651	−	0.733536i	$-0.737869\pi$
$79$	−1.73547e35	−1.35930	−0.679651	+	0.733536i	$0.737869\pi$
$80$	1.80144e34	0.111803
$81$	−7.61254e34	−0.375454
$82$	1.19460e35	0.469532
$83$	−1.57921e35	−0.496015	−0.248008	−	0.968758i	$-0.579776\pi$
$83$	−1.57921e35	−0.496015	−0.248008	+	0.968758i	$0.579776\pi$
$84$	−1.36814e35	−0.344321
$85$	−1.11344e35	−0.225122
$86$	−1.61782e35	−0.263456
$87$	−7.00687e35	−0.921335
$88$	−3.92723e34	−0.0417982
$89$	−9.73344e35	−0.840526	−0.420263	−	0.907402i	$-0.638062\pi$
$89$	−9.73344e35	−0.840526	−0.420263	+	0.907402i	$0.638062\pi$
$90$	−1.95951e35	−0.137613
$91$	−7.17007e35	−0.410447
$92$	−3.70446e35	−0.173241
$93$	5.47565e35	0.209653
$94$	−4.37205e35	−0.137347
$95$	−1.76783e36	−0.456618
$96$	6.24311e35	0.132857
$97$	−8.76678e36	−1.54015	−0.770075	−	0.637954i	$-0.779781\pi$
$97$	−8.76678e36	−1.54015	−0.770075	+	0.637954i	$0.779781\pi$
$98$	−7.80509e35	−0.113421
$99$	4.27183e35	0.0514473
$100$	1.00000e36	0.100000
$101$	−9.95992e36	−0.828534	−0.414267	−	0.910155i	$-0.635962\pi$
$101$	−9.95992e36	−0.828534	−0.414267	+	0.910155i	$0.635962\pi$
$102$	−3.85878e36	−0.267514
$103$	−1.38183e37	−0.799773	−0.399887	−	0.916565i	$-0.630951\pi$
$103$	−1.38183e37	−0.799773	−0.399887	+	0.916565i	$0.630951\pi$
$104$	3.27185e36	0.158371
$105$	−7.59470e36	−0.307970
$106$	−1.34173e37	−0.456568
$107$	1.66394e37	0.475924	0.237962	−	0.971275i	$-0.423521\pi$
$107$	1.66394e37	0.475924	0.237962	+	0.971275i	$0.423521\pi$
$108$	−2.23961e37	−0.539302
$109$	−2.15440e37	−0.437458	−0.218729	−	0.975786i	$-0.570191\pi$
$109$	−2.15440e37	−0.437458	−0.218729	+	0.975786i	$0.570191\pi$
$110$	−2.18005e36	−0.0373854
$111$	−4.12164e37	−0.597854
$112$	−1.86427e37	−0.229074
$113$	−7.20846e37	−0.751435	−0.375717	−	0.926734i	$-0.622604\pi$
$113$	−7.20846e37	−0.751435	−0.375717	+	0.926734i	$0.622604\pi$
$114$	−6.12663e37	−0.542602
$115$	−2.05639e37	−0.154951
$116$	−9.54778e37	−0.612956
$117$	−3.55894e37	−0.194932
$118$	−1.25824e38	−0.588772
$119$	1.15228e38	0.461253
$120$	3.46562e37	0.118831
$121$	−3.35287e38	−0.986023
$122$	3.90003e38	0.984944
$123$	2.29817e38	0.499043
$124$	7.46129e37	0.139480
$125$	5.55112e37	0.0894427
$126$	2.02785e38	0.281956
$127$	5.59928e38	0.672610	0.336305	−	0.941753i	$-0.390823\pi$
$127$	5.59928e38	0.672610	0.336305	+	0.941753i	$0.390823\pi$
$128$	8.50706e37	0.0883883
$129$	−3.11237e38	−0.280016
$130$	1.81624e38	0.141652
$131$	2.41935e39	1.63750	0.818748	−	0.574154i	$-0.194669\pi$
$131$	2.41935e39	1.63750	0.818748	+	0.574154i	$0.194669\pi$
$132$	−7.55524e37	−0.0444253
$133$	1.82949e39	0.935565
$134$	3.14676e39	1.40096
$135$	−1.24323e39	−0.482366
$136$	−5.25809e38	−0.177975
$137$	4.22583e39	1.24905	0.624527	−	0.781003i	$-0.285292\pi$
$137$	4.22583e39	1.24905	0.624527	+	0.781003i	$0.285292\pi$
$138$	−7.12666e38	−0.184129
$139$	1.36024e39	0.307497	0.153748	−	0.988110i	$-0.450866\pi$
$139$	1.36024e39	0.307497	0.153748	+	0.988110i	$0.450866\pi$
$140$	−1.03488e39	−0.204890
$141$	−8.41097e38	−0.145980
$142$	−3.12892e37	−0.00476497
$143$	−3.95950e38	−0.0529571
$144$	−9.25352e38	−0.108793
$145$	−5.30008e39	−0.548245
$146$	−1.15616e39	−0.105315
$147$	−1.50155e39	−0.120550
$148$	−5.61628e39	−0.397747
$149$	2.43718e39	0.152385	0.0761924	−	0.997093i	$-0.475724\pi$
$149$	2.43718e39	0.152385	0.0761924	+	0.997093i	$0.475724\pi$
$150$	1.92381e39	0.106285
$151$	2.40615e40	1.17557	0.587786	−	0.809017i	$-0.300000\pi$
$151$	2.40615e40	1.17557	0.587786	+	0.809017i	$0.300000\pi$
$152$	−8.34833e39	−0.360989
$153$	5.71946e39	0.219060
$154$	2.25609e39	0.0765990
$155$	4.14185e39	0.124755
$156$	6.29441e39	0.168326
$157$	3.62213e40	0.860638	0.430319	−	0.902677i	$-0.358401\pi$
$157$	3.62213e40	0.860638	0.430319	+	0.902677i	$0.358401\pi$
$158$	−4.54943e40	−0.961172
$159$	−2.58122e40	−0.485264
$160$	4.72237e39	0.0790569
$161$	2.12811e40	0.317479
$162$	−1.99558e40	−0.265486
$163$	−1.06162e41	−1.26037	−0.630186	−	0.776444i	$-0.717021\pi$
$163$	−1.06162e41	−1.26037	−0.630186	+	0.776444i	$0.717021\pi$
$164$	3.13156e40	0.332009
$165$	−4.19400e39	−0.0397352
$166$	−4.13980e40	−0.350736
$167$	−3.16742e40	−0.240133	−0.120066	−	0.992766i	$-0.538311\pi$
$167$	−3.16742e40	−0.240133	−0.120066	+	0.992766i	$0.538311\pi$
$168$	−3.58650e40	−0.243472
$169$	−1.31413e41	−0.799348
$170$	−2.91883e40	−0.159185
$171$	9.08086e40	0.444323
$172$	−4.24102e40	−0.186292
$173$	−3.69208e41	−1.45686	−0.728431	−	0.685119i	$-0.759750\pi$
$173$	−3.69208e41	−1.45686	−0.728431	+	0.685119i	$0.759750\pi$
$174$	−1.83681e41	−0.651482
$175$	−5.74473e40	−0.183259
$176$	−1.02950e40	−0.0295558
$177$	−2.42061e41	−0.625778
$178$	−2.55156e41	−0.594342
$179$	4.82779e41	1.01384	0.506918	−	0.861994i	$-0.330785\pi$
$179$	4.82779e41	1.01384	0.506918	+	0.861994i	$0.330785\pi$
$180$	−5.13673e40	−0.0973074
$181$	7.79879e41	1.33344	0.666720	−	0.745308i	$-0.267698\pi$
$181$	7.79879e41	1.33344	0.666720	+	0.745308i	$0.267698\pi$
$182$	−1.87959e41	−0.290230
$183$	7.50291e41	1.04685
$184$	−9.71102e40	−0.122500
$185$	−3.11766e41	−0.355756
$186$	1.43541e41	0.148247
$187$	6.36320e40	0.0595121
$188$	−1.14611e41	−0.0971191
$189$	1.28659e42	0.988320
$190$	−4.63426e41	−0.322878
$191$	3.29328e41	0.208214	0.104107	−	0.994566i	$-0.466801\pi$
$191$	3.29328e41	0.208214	0.104107	+	0.994566i	$0.466801\pi$
$192$	1.63659e41	0.0939438
$193$	−1.11821e41	−0.0583058	−0.0291529	−	0.999575i	$-0.509281\pi$
$193$	−1.11821e41	−0.0583058	−0.0291529	+	0.999575i	$0.509281\pi$
$194$	−2.29816e42	−1.08905
$195$	3.49410e41	0.150555
$196$	−2.04606e41	−0.0802011
$197$	4.09822e42	1.46208	0.731038	−	0.682337i	$-0.239036\pi$
$197$	4.09822e42	1.46208	0.731038	+	0.682337i	$0.239036\pi$
$198$	1.11983e41	0.0363788
$199$	5.54584e42	1.64129	0.820646	−	0.571437i	$-0.193614\pi$
$199$	5.54584e42	1.64129	0.820646	+	0.571437i	$0.193614\pi$
$200$	2.62144e41	0.0707107
$201$	6.05376e42	1.48901
$202$	−2.61093e42	−0.585862
$203$	5.48494e42	1.12330
$204$	−1.01156e42	−0.189161
$205$	1.73837e42	0.296958
$206$	−3.62239e42	−0.565525
$207$	1.05631e42	0.150779
$208$	8.57696e41	0.111985
$209$	1.01029e42	0.120709
$210$	−1.99091e42	−0.217768
$211$	−1.56109e43	−1.56388	−0.781939	−	0.623355i	$-0.785769\pi$
$211$	−1.56109e43	−1.56388	−0.781939	+	0.623355i	$0.785769\pi$
$212$	−3.51725e42	−0.322842
$213$	−6.01944e40	−0.00506447
$214$	4.36191e42	0.336529
$215$	−2.35424e42	−0.166625
$216$	−5.87099e42	−0.381344
$217$	−4.28631e42	−0.255610
$218$	−5.64764e42	−0.309330
$219$	−2.22424e42	−0.111935
$220$	−5.71488e41	−0.0264355
$221$	−5.30130e42	−0.225489
$222$	−1.08046e43	−0.422747
$223$	3.39504e42	0.122238	0.0611189	−	0.998130i	$-0.480533\pi$
$223$	3.39504e42	0.122238	0.0611189	+	0.998130i	$0.480533\pi$
$224$	−4.88707e42	−0.161980
$225$	−2.85146e42	−0.0870343
$226$	−1.88965e43	−0.531345
$227$	−5.49026e43	−1.42271	−0.711353	−	0.702835i	$-0.751917\pi$
$227$	−5.49026e43	−1.42271	−0.711353	+	0.702835i	$0.751917\pi$
$228$	−1.60606e43	−0.383678
$229$	5.12775e43	1.12972	0.564860	−	0.825187i	$-0.308930\pi$
$229$	5.12775e43	1.12972	0.564860	+	0.825187i	$0.308930\pi$
$230$	−5.39070e42	−0.109567
$231$	4.34028e42	0.0814135
$232$	−2.50289e43	−0.433426
$233$	9.95511e43	1.59207	0.796034	−	0.605252i	$-0.206928\pi$
$233$	9.95511e43	1.59207	0.796034	+	0.605252i	$0.206928\pi$
$234$	−9.32955e42	−0.137837
$235$	−6.36217e42	−0.0868659
$236$	−3.29841e43	−0.416325
$237$	−8.75223e43	−1.02158
$238$	3.02063e43	0.326155
$239$	−4.20147e43	−0.419798	−0.209899	−	0.977723i	$-0.567314\pi$
$239$	−4.20147e43	−0.419798	−0.209899	+	0.977723i	$0.567314\pi$
$240$	9.08492e42	0.0840259
$241$	9.20589e43	0.788407	0.394203	−	0.919023i	$-0.371021\pi$
$241$	9.20589e43	0.788407	0.394203	+	0.919023i	$0.371021\pi$
$242$	−8.78934e43	−0.697224
$243$	1.08359e44	0.796432
$244$	1.02237e44	0.696460
$245$	−1.13579e43	−0.0717341
$246$	6.02452e43	0.352877
$247$	−8.41693e43	−0.457362
$248$	1.95593e43	0.0986275
$249$	−7.96418e43	−0.372780
$250$	1.45519e43	0.0632456
$251$	−8.81367e43	−0.355789	−0.177895	−	0.984050i	$-0.556929\pi$
$251$	−8.81367e43	−0.355789	−0.177895	+	0.984050i	$0.556929\pi$
$252$	5.31589e43	0.199373
$253$	1.17520e43	0.0409621
$254$	1.46782e44	0.475607
$255$	−5.61526e43	−0.169191
$256$	2.23007e43	0.0625000
$257$	−1.46131e44	−0.381049	−0.190524	−	0.981682i	$-0.561019\pi$
$257$	−1.46131e44	−0.381049	−0.190524	+	0.981682i	$0.561019\pi$
$258$	−8.15890e43	−0.198001
$259$	3.22640e44	0.728908
$260$	4.76117e43	0.100163
$261$	2.72251e44	0.533482
$262$	6.34218e44	1.15788
$263$	−2.73688e44	−0.465666	−0.232833	−	0.972517i	$-0.574800\pi$
$263$	−2.73688e44	−0.465666	−0.232833	+	0.972517i	$0.574800\pi$
$264$	−1.98056e43	−0.0314134
$265$	−1.95247e44	−0.288759
$266$	4.79589e44	0.661544
$267$	−4.90872e44	−0.631698
$268$	8.24905e44	0.990627
$269$	1.32425e45	1.48440	0.742201	−	0.670177i	$-0.233782\pi$
$269$	1.32425e45	1.48440	0.742201	+	0.670177i	$0.233782\pi$
$270$	−3.25906e44	−0.341085
$271$	5.21202e44	0.509418	0.254709	−	0.967018i	$-0.418020\pi$
$271$	5.21202e44	0.509418	0.254709	+	0.967018i	$0.418020\pi$
$272$	−1.37838e44	−0.125847
$273$	−3.61597e44	−0.308472
$274$	1.10777e45	0.883214
$275$	−3.17239e43	−0.0236446
$276$	−1.86821e44	−0.130199
$277$	−1.63439e45	−1.06532	−0.532659	−	0.846330i	$-0.678807\pi$
$277$	−1.63439e45	−1.06532	−0.532659	+	0.846330i	$0.678807\pi$
$278$	3.56578e44	0.217433
$279$	−2.12756e44	−0.121396
$280$	−2.71287e44	−0.144879
$281$	1.81299e44	0.0906420	0.0453210	−	0.998972i	$-0.485569\pi$
$281$	1.81299e44	0.0906420	0.0453210	+	0.998972i	$0.485569\pi$
$282$	−2.20489e44	−0.103223
$283$	−3.63001e45	−1.59169	−0.795845	−	0.605500i	$-0.792973\pi$
$283$	−3.63001e45	−1.59169	−0.795845	+	0.605500i	$0.792973\pi$
$284$	−8.20228e42	−0.00336934
$285$	−8.91541e44	−0.343172
$286$	−1.03796e44	−0.0374463
$287$	−1.79900e45	−0.608437
$288$	−2.42575e44	−0.0769282
$289$	−2.51014e45	−0.746600
$290$	−1.38938e45	−0.387668
$291$	−4.42121e45	−1.15750
$292$	−3.03081e44	−0.0744691
$293$	1.89813e45	0.437800	0.218900	−	0.975747i	$-0.429753\pi$
$293$	1.89813e45	0.437800	0.218900	+	0.975747i	$0.429753\pi$
$294$	−3.93622e44	−0.0852420
$295$	−1.83098e45	−0.372372
$296$	−1.47227e45	−0.281250
$297$	7.10491e44	0.127516
$298$	6.38892e44	0.107752
$299$	−9.79081e44	−0.155204
$300$	5.04314e44	0.0751551
$301$	2.43635e45	0.341397
$302$	6.30757e45	0.831254
$303$	−5.02293e45	−0.622686
$304$	−2.18847e45	−0.255257
$305$	5.67529e45	0.622933
$306$	1.49932e45	0.154899
$307$	−1.42121e45	−0.138229	−0.0691143	−	0.997609i	$-0.522017\pi$
$307$	−1.42121e45	−0.138229	−0.0691143	+	0.997609i	$0.522017\pi$
$308$	5.91420e44	0.0541637
$309$	−6.96879e45	−0.601070
$310$	1.08576e45	0.0882151
$311$	1.48151e46	1.13406	0.567031	−	0.823696i	$-0.308092\pi$
$311$	1.48151e46	1.13406	0.567031	+	0.823696i	$0.308092\pi$
$312$	1.65004e45	0.119024
$313$	1.68494e46	1.14555	0.572775	−	0.819713i	$-0.305867\pi$
$313$	1.68494e46	1.14555	0.572775	+	0.819713i	$0.305867\pi$
$314$	9.49520e45	0.608563
$315$	2.95091e45	0.178325
$316$	−1.19261e46	−0.679651
$317$	9.92215e45	0.533347	0.266673	−	0.963787i	$-0.414076\pi$
$317$	9.92215e45	0.533347	0.266673	+	0.963787i	$0.414076\pi$
$318$	−6.76651e45	−0.343134
$319$	3.02893e45	0.144931
$320$	1.23794e45	0.0559017
$321$	8.39148e45	0.357681
$322$	5.57872e45	0.224492
$323$	1.35266e46	0.513975
$324$	−5.23130e45	−0.187727
$325$	2.64298e45	0.0895884
$326$	−2.78297e46	−0.891217
$327$	−1.08650e46	−0.328772
$328$	8.20920e45	0.234766
$329$	6.58407e45	0.177980
$330$	−1.09943e45	−0.0280970
$331$	4.31846e46	1.04354	0.521772	−	0.853085i	$-0.325271\pi$
$331$	4.31846e46	1.04354	0.521772	+	0.853085i	$0.325271\pi$
$332$	−1.08522e46	−0.248008
$333$	1.60146e46	0.346177
$334$	−8.30321e45	−0.169800
$335$	4.57914e46	0.886044
$336$	−9.40179e45	−0.172161
$337$	5.65717e45	0.0980497	0.0490248	−	0.998798i	$-0.484389\pi$
$337$	5.65717e45	0.0980497	0.0490248	+	0.998798i	$0.484389\pi$
$338$	−3.44493e46	−0.565224
$339$	−3.63533e46	−0.564741
$340$	−7.65153e45	−0.112561
$341$	−2.36702e45	−0.0329796
$342$	2.38049e46	0.314184
$343$	8.50326e46	1.06327
$344$	−1.11176e46	−0.131728
$345$	−1.03707e46	−0.116454
$346$	−9.67857e46	−1.03016
$347$	5.80965e46	0.586211	0.293106	−	0.956080i	$-0.405311\pi$
$347$	5.80965e46	0.586211	0.293106	+	0.956080i	$0.405311\pi$
$348$	−4.81508e46	−0.460668
$349$	−1.34423e47	−1.21956	−0.609780	−	0.792571i	$-0.708742\pi$
$349$	−1.34423e47	−1.21956	−0.609780	+	0.792571i	$0.708742\pi$
$350$	−1.50595e46	−0.129584
$351$	−5.91923e46	−0.483152
$352$	−2.69877e45	−0.0208991
$353$	−1.24862e47	−0.917484	−0.458742	−	0.888570i	$-0.651700\pi$
$353$	−1.24862e47	−0.917484	−0.458742	+	0.888570i	$0.651700\pi$
$354$	−6.34550e46	−0.442492
$355$	−4.55318e44	−0.00301363
$356$	−6.68877e46	−0.420263
$357$	5.81111e46	0.346655
$358$	1.26558e47	0.716890
$359$	−9.59735e46	−0.516302	−0.258151	−	0.966105i	$-0.583113\pi$
$359$	−9.59735e46	−0.516302	−0.258151	+	0.966105i	$0.583113\pi$
$360$	−1.34656e46	−0.0688067
$361$	8.75566e45	0.0425016
$362$	2.04441e47	0.942884
$363$	−1.69090e47	−0.741046
$364$	−4.92723e46	−0.205224
$365$	−1.68244e46	−0.0666072
$366$	1.96684e47	0.740235
$367$	1.16622e47	0.417310	0.208655	−	0.977989i	$-0.433091\pi$
$367$	1.16622e47	0.417310	0.208655	+	0.977989i	$0.433091\pi$
$368$	−2.54568e46	−0.0866204
$369$	−8.92952e46	−0.288962
$370$	−8.17276e46	−0.251557
$371$	2.02057e47	0.591638
$372$	3.76284e46	0.104827
$373$	−3.24328e47	−0.859749	−0.429874	−	0.902889i	$-0.641442\pi$
$373$	−3.24328e47	−0.859749	−0.429874	+	0.902889i	$0.641442\pi$
$374$	1.66807e46	0.0420814
$375$	2.79951e46	0.0672207
$376$	−3.00445e46	−0.0686735
$377$	−2.52346e47	−0.549138
$378$	3.37273e47	0.698848
$379$	−8.85067e46	−0.174643	−0.0873214	−	0.996180i	$-0.527831\pi$
$379$	−8.85067e46	−0.174643	−0.0873214	+	0.996180i	$0.527831\pi$
$380$	−1.21484e47	−0.228309
$381$	2.82380e47	0.505501
$382$	8.63313e46	0.147230
$383$	−1.64510e46	−0.0267310	−0.0133655	−	0.999911i	$-0.504255\pi$
$383$	−1.64510e46	−0.0267310	−0.0133655	+	0.999911i	$0.504255\pi$
$384$	4.29023e46	0.0664283
$385$	3.28304e46	0.0484454
$386$	−2.93131e46	−0.0412284
$387$	1.20931e47	0.162138
$388$	−6.02448e47	−0.770075
$389$	2.33292e47	0.284336	0.142168	−	0.989843i	$-0.454593\pi$
$389$	2.33292e47	0.284336	0.142168	+	0.989843i	$0.454593\pi$
$390$	9.15957e46	0.106458
$391$	1.57345e47	0.174415
$392$	−5.36362e46	−0.0567107
$393$	1.22011e48	1.23066
$394$	1.07432e48	1.03384
$395$	−6.62029e47	−0.607898
$396$	2.93558e46	0.0257237
$397$	−1.77175e48	−1.48176	−0.740879	−	0.671639i	$-0.765591\pi$
$397$	−1.77175e48	−1.48176	−0.740879	+	0.671639i	$0.765591\pi$
$398$	1.45381e48	1.16057
$399$	9.22637e47	0.703125
$400$	6.87195e46	0.0500000
$401$	9.35091e47	0.649656	0.324828	−	0.945773i	$-0.394694\pi$
$401$	9.35091e47	0.649656	0.324828	+	0.945773i	$0.394694\pi$
$402$	1.58696e48	1.05289
$403$	1.97200e47	0.124958
$404$	−6.84441e47	−0.414267
$405$	−2.90395e47	−0.167908
$406$	1.43784e48	0.794292
$407$	1.78171e47	0.0940458
$408$	−2.65173e47	−0.133757
$409$	−2.24904e48	−1.08422	−0.542108	−	0.840309i	$-0.682374\pi$
$409$	−2.24904e48	−1.08422	−0.542108	+	0.840309i	$0.682374\pi$
$410$	4.55702e47	0.209981
$411$	2.13115e48	0.938727
$412$	−9.49589e47	−0.399887
$413$	1.89484e48	0.762953
$414$	2.76906e47	0.106617
$415$	−6.02420e47	−0.221825
$416$	2.24840e47	0.0791857
$417$	6.85987e47	0.231099
$418$	2.64842e47	0.0853544
$419$	−5.89430e48	−1.81749	−0.908747	−	0.417348i	$-0.862960\pi$
$419$	−5.89430e48	−1.81749	−0.908747	+	0.417348i	$0.862960\pi$
$420$	−5.21904e47	−0.153985
$421$	−6.89314e48	−1.94625	−0.973125	−	0.230278i	$-0.926037\pi$
$421$	−6.89314e48	−1.94625	−0.973125	+	0.230278i	$0.926037\pi$
$422$	−4.09231e48	−1.10583
$423$	3.26807e47	0.0845269
$424$	−9.22027e47	−0.228284
$425$	−4.24745e47	−0.100678
$426$	−1.57796e46	−0.00358112
$427$	−5.87324e48	−1.27633
$428$	1.14345e48	0.237962
$429$	−1.99684e47	−0.0397999
$430$	−6.17149e47	−0.117821
$431$	−3.31632e47	−0.0606495	−0.0303247	−	0.999540i	$-0.509654\pi$
$431$	−3.31632e47	−0.0606495	−0.0303247	+	0.999540i	$0.509654\pi$
$432$	−1.53905e48	−0.269651
$433$	7.05114e48	1.18368	0.591838	−	0.806057i	$-0.298402\pi$
$433$	7.05114e48	1.18368	0.591838	+	0.806057i	$0.298402\pi$
$434$	−1.12363e48	−0.180744
$435$	−2.67291e48	−0.412034
$436$	−1.48049e48	−0.218729
$437$	2.49819e48	0.353768
$438$	−5.83070e47	−0.0791498
$439$	−4.37776e48	−0.569716	−0.284858	−	0.958570i	$-0.591946\pi$
$439$	−4.37776e48	−0.569716	−0.284858	+	0.958570i	$0.591946\pi$
$440$	−1.49812e47	−0.0186927
$441$	5.83425e47	0.0698025
$442$	−1.38970e48	−0.159445
$443$	1.23141e49	1.35498	0.677491	−	0.735531i	$-0.263067\pi$
$443$	1.23141e49	1.35498	0.677491	+	0.735531i	$0.263067\pi$
$444$	−2.83237e48	−0.298927
$445$	−3.71301e48	−0.375895
$446$	8.89990e47	0.0864351
$447$	1.22910e48	0.114525
$448$	−1.28112e48	−0.114537
$449$	1.51088e49	1.29621	0.648103	−	0.761553i	$-0.275563\pi$
$449$	1.51088e49	1.29621	0.648103	+	0.761553i	$0.275563\pi$
$450$	−7.47493e47	−0.0615426
$451$	−9.93455e47	−0.0785023
$452$	−4.95362e48	−0.375717
$453$	1.21346e49	0.883501
$454$	−1.43924e49	−1.00600
$455$	−2.73516e48	−0.183558
$456$	−4.21019e48	−0.271301
$457$	2.42148e49	1.49841	0.749207	−	0.662336i	$-0.230435\pi$
$457$	2.42148e49	1.49841	0.749207	+	0.662336i	$0.230435\pi$
$458$	1.34421e49	0.798832
$459$	9.51262e48	0.542957
$460$	−1.41314e48	−0.0774756
$461$	1.88635e49	0.993471	0.496736	−	0.867902i	$-0.334532\pi$
$461$	1.88635e49	0.993471	0.496736	+	0.867902i	$0.334532\pi$
$462$	1.13778e48	0.0575680
$463$	5.15519e48	0.250609	0.125304	−	0.992118i	$-0.460009\pi$
$463$	5.15519e48	0.250609	0.125304	+	0.992118i	$0.460009\pi$
$464$	−6.56118e48	−0.306478
$465$	2.08879e48	0.0937597
$466$	2.60967e49	1.12576
$467$	1.96969e49	0.816649	0.408324	−	0.912837i	$-0.366113\pi$
$467$	1.96969e49	0.816649	0.408324	+	0.912837i	$0.366113\pi$
$468$	−2.44569e48	−0.0974658
$469$	−4.73885e49	−1.81541
$470$	−1.66780e48	−0.0614235
$471$	1.82669e49	0.646813
$472$	−8.64657e48	−0.294386
$473$	1.34542e48	0.0440480
$474$	−2.29434e49	−0.722369
$475$	−6.74373e48	−0.204206
$476$	7.91840e48	0.230626
$477$	1.00293e49	0.280983
$478$	−1.10139e49	−0.296842
$479$	−6.22680e49	−1.61458	−0.807288	−	0.590158i	$-0.799065\pi$
$479$	−6.22680e49	−1.61458	−0.807288	+	0.590158i	$0.799065\pi$
$480$	2.38156e48	0.0594153
$481$	−1.48437e49	−0.356335
$482$	2.41327e49	0.557488
$483$	1.07324e49	0.238602
$484$	−2.30407e49	−0.493012
$485$	−3.34426e49	−0.688776
$486$	2.84056e49	0.563162
$487$	4.56184e49	0.870671	0.435335	−	0.900268i	$-0.356630\pi$
$487$	4.56184e49	0.870671	0.435335	+	0.900268i	$0.356630\pi$
$488$	2.68008e49	0.492472
$489$	−5.35390e49	−0.947233
$490$	−2.97740e48	−0.0507236
$491$	7.50460e49	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$491$	7.50460e49	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$492$	1.57929e49	0.249522
$493$	4.05537e49	0.617110
$494$	−2.20645e49	−0.323404
$495$	1.62957e48	0.0230080
$496$	5.12736e48	0.0697402
$497$	4.71199e47	0.00617463
$498$	−2.08776e49	−0.263596
$499$	−1.22644e50	−1.49206	−0.746030	−	0.665912i	$-0.768043\pi$
$499$	−1.22644e50	−1.49206	−0.746030	+	0.665912i	$0.768043\pi$
$500$	3.81470e48	0.0447214
$501$	−1.59738e49	−0.180472
$502$	−2.31045e49	−0.251581
$503$	−6.93196e48	−0.0727526	−0.0363763	−	0.999338i	$-0.511581\pi$
$503$	−6.93196e48	−0.0727526	−0.0363763	+	0.999338i	$0.511581\pi$
$504$	1.39353e49	0.140978
$505$	−3.79941e49	−0.370532
$506$	3.08072e48	0.0289646
$507$	−6.62737e49	−0.600750
$508$	3.84780e49	0.336305
$509$	−1.92494e50	−1.62233	−0.811165	−	0.584817i	$-0.801166\pi$
$509$	−1.92494e50	−1.62233	−0.811165	+	0.584817i	$0.801166\pi$
$510$	−1.47201e49	−0.119636
$511$	1.74112e49	0.136472
$512$	5.84601e48	0.0441942
$513$	1.51033e50	1.10129
$514$	−3.83075e49	−0.269442
$515$	−5.27128e49	−0.357670
$516$	−2.13881e49	−0.140008
$517$	3.63590e48	0.0229634
$518$	8.45781e49	0.515416
$519$	−1.86197e50	−1.09491
$520$	1.24811e49	0.0708258
$521$	−7.74303e49	−0.424046	−0.212023	−	0.977265i	$-0.568005\pi$
$521$	−7.74303e49	−0.424046	−0.212023	+	0.977265i	$0.568005\pi$
$522$	7.13690e49	0.377229
$523$	1.36453e50	0.696147	0.348074	−	0.937467i	$-0.386836\pi$
$523$	1.36453e50	0.696147	0.348074	+	0.937467i	$0.386836\pi$
$524$	1.66257e50	0.818748
$525$	−2.89715e49	−0.137729
$526$	−7.17458e49	−0.329276
$527$	−3.16915e49	−0.140426
$528$	−5.19192e48	−0.0222127
$529$	−2.13004e50	−0.879951
$530$	−5.11828e49	−0.204183
$531$	9.40527e49	0.362345
$532$	1.25721e50	0.467783
$533$	8.27666e49	0.297442
$534$	−1.28679e50	−0.446678
$535$	6.34742e49	0.212840
$536$	2.16244e50	0.700479
$537$	2.43473e50	0.761949
$538$	3.47143e50	1.04963
$539$	6.49090e48	0.0189632
$540$	−8.54342e49	−0.241183
$541$	−3.69295e49	−0.100745	−0.0503726	−	0.998730i	$-0.516041\pi$
$541$	−3.69295e49	−0.100745	−0.0503726	+	0.998730i	$0.516041\pi$
$542$	1.36630e50	0.360213
$543$	3.93304e50	1.00215
$544$	−3.61333e49	−0.0889873
$545$	−8.21840e49	−0.195637
$546$	−9.47904e49	−0.218123
$547$	−3.43870e50	−0.764942	−0.382471	−	0.923968i	$-0.624927\pi$
$547$	−3.43870e50	−0.764942	−0.382471	+	0.923968i	$0.624927\pi$
$548$	2.90397e50	0.624527
$549$	−2.91525e50	−0.606160
$550$	−8.31624e48	−0.0167193
$551$	6.43876e50	1.25169
$552$	−4.89741e49	−0.0920647
$553$	6.85120e50	1.24552
$554$	−4.28445e50	−0.753294
$555$	−1.57228e50	−0.267368
$556$	9.34747e49	0.153748
$557$	−1.65111e50	−0.262697	−0.131348	−	0.991336i	$-0.541931\pi$
$557$	−1.65111e50	−0.262697	−0.131348	+	0.991336i	$0.541931\pi$
$558$	−5.57726e49	−0.0858398
$559$	−1.12089e50	−0.166896
$560$	−7.11163e49	−0.102445
$561$	3.20905e49	0.0447264
$562$	4.75265e49	0.0640935
$563$	8.28221e50	1.08079	0.540395	−	0.841412i	$-0.318275\pi$
$563$	8.28221e50	1.08079	0.540395	+	0.841412i	$0.318275\pi$
$564$	−5.77998e49	−0.0729899
$565$	−2.74981e50	−0.336052
$566$	−9.51585e50	−1.12550
$567$	3.00524e50	0.344027
$568$	−2.15018e48	−0.00238249
$569$	5.31805e50	0.570394	0.285197	−	0.958469i	$-0.407941\pi$
$569$	5.31805e50	0.570394	0.285197	+	0.958469i	$0.407941\pi$
$570$	−2.33712e50	−0.242659
$571$	7.10776e50	0.714438	0.357219	−	0.934021i	$-0.383725\pi$
$571$	7.10776e50	0.714438	0.357219	+	0.934021i	$0.383725\pi$
$572$	−2.72095e49	−0.0264785
$573$	1.66085e50	0.156484
$574$	−4.71596e50	−0.430230
$575$	−7.84450e49	−0.0692963
$576$	−6.35897e49	−0.0543965
$577$	−1.53160e51	−1.26880	−0.634399	−	0.773006i	$-0.718752\pi$
$577$	−1.53160e51	−1.26880	−0.634399	+	0.773006i	$0.718752\pi$
$578$	−6.58018e50	−0.527926
$579$	−5.63928e49	−0.0438198
$580$	−3.64219e50	−0.274122
$581$	6.23432e50	0.454496
$582$	−1.15899e51	−0.818476
$583$	1.11581e50	0.0763348
$584$	−7.94509e49	−0.0526576
$585$	−1.35763e50	−0.0871761
$586$	4.97584e50	0.309571
$587$	−3.05746e51	−1.84313	−0.921565	−	0.388223i	$-0.873089\pi$
$587$	−3.05746e51	−1.84313	−0.921565	+	0.388223i	$0.873089\pi$
$588$	−1.03186e50	−0.0602752
$589$	−5.03169e50	−0.284827
$590$	−4.79981e50	−0.263307
$591$	2.06679e51	1.09882
$592$	−3.85948e50	−0.198874
$593$	−3.18854e51	−1.59250	−0.796252	−	0.604966i	$-0.793187\pi$
$593$	−3.18854e51	−1.59250	−0.796252	+	0.604966i	$0.793187\pi$
$594$	1.86251e50	0.0901674
$595$	4.39560e50	0.206278
$596$	1.67482e50	0.0761924
$597$	2.79685e51	1.23351
$598$	−2.56660e50	−0.109745
$599$	−2.67703e51	−1.10983	−0.554916	−	0.831906i	$-0.687250\pi$
$599$	−2.67703e51	−1.10983	−0.554916	+	0.831906i	$0.687250\pi$
$600$	1.32203e50	0.0531427
$601$	−1.40525e51	−0.547743	−0.273872	−	0.961766i	$-0.588304\pi$
$601$	−1.40525e51	−0.547743	−0.273872	+	0.961766i	$0.588304\pi$
$602$	6.38675e50	0.241404
$603$	−2.35218e51	−0.862186
$604$	1.65349e51	0.587786
$605$	−1.27902e51	−0.440963
$606$	−1.31673e51	−0.440305
$607$	2.84184e51	0.921741	0.460870	−	0.887467i	$-0.347537\pi$
$607$	2.84184e51	0.921741	0.460870	+	0.887467i	$0.347537\pi$
$608$	−5.73693e50	−0.180494
$609$	2.76613e51	0.844216
$610$	1.48774e51	0.440480
$611$	−3.02913e50	−0.0870074
$612$	3.93039e50	0.109530
$613$	5.74303e51	1.55282	0.776412	−	0.630226i	$-0.217038\pi$
$613$	5.74303e51	1.55282	0.776412	+	0.630226i	$0.217038\pi$
$614$	−3.72561e50	−0.0977424
$615$	8.76683e50	0.223179
$616$	1.55037e50	0.0382995
$617$	5.29231e51	1.26873	0.634366	−	0.773033i	$-0.281261\pi$
$617$	5.29231e51	1.26873	0.634366	+	0.773033i	$0.281261\pi$
$618$	−1.82683e51	−0.425021
$619$	1.88485e50	0.0425599	0.0212799	−	0.999774i	$-0.493226\pi$
$619$	1.88485e50	0.0425599	0.0212799	+	0.999774i	$0.493226\pi$
$620$	2.84626e50	0.0623775
$621$	1.75686e51	0.373716
$622$	3.88369e51	0.801903
$623$	3.84252e51	0.770171
$624$	4.32549e50	0.0841628
$625$	2.11758e50	0.0400000
$626$	4.41697e51	0.810026
$627$	5.09505e50	0.0907191
$628$	2.48911e51	0.430319
$629$	2.38549e51	0.400442
$630$	7.73564e50	0.126095
$631$	−5.48789e51	−0.868685	−0.434343	−	0.900748i	$-0.643019\pi$
$631$	−5.48789e51	−0.868685	−0.434343	+	0.900748i	$0.643019\pi$
$632$	−3.12635e51	−0.480586
$633$	−7.87281e51	−1.17533
$634$	2.60103e51	0.377133
$635$	2.13596e51	0.300800
$636$	−1.77380e51	−0.242632
$637$	−5.40769e50	−0.0718509
$638$	7.94016e50	0.102482
$639$	2.33885e49	0.00293249
$640$	3.24519e50	0.0395285
$641$	−1.26934e52	−1.50213	−0.751063	−	0.660231i	$-0.770458\pi$
$641$	−1.26934e52	−1.50213	−0.751063	+	0.660231i	$0.770458\pi$
$642$	2.19978e51	0.252918
$643$	−2.67003e50	−0.0298273	−0.0149136	−	0.999889i	$-0.504747\pi$
$643$	−2.67003e50	−0.0298273	−0.0149136	+	0.999889i	$0.504747\pi$
$644$	1.46243e51	0.158740
$645$	−1.18728e51	−0.125227
$646$	3.54591e51	0.363435
$647$	−7.38492e51	−0.735557	−0.367778	−	0.929913i	$-0.619882\pi$
$647$	−7.38492e51	−0.735557	−0.367778	+	0.929913i	$0.619882\pi$
$648$	−1.37135e51	−0.132743
$649$	1.04638e51	0.0984384
$650$	6.92841e50	0.0633486
$651$	−2.16165e51	−0.192104
$652$	−7.29540e51	−0.630186
$653$	−1.43531e52	−1.20518	−0.602592	−	0.798050i	$-0.705865\pi$
$653$	−1.43531e52	−1.20518	−0.602592	+	0.798050i	$0.705865\pi$
$654$	−2.84819e51	−0.232477
$655$	9.22909e51	0.732310
$656$	2.15199e51	0.166004
$657$	8.64224e50	0.0648137
$658$	1.72597e51	0.125851
$659$	1.21039e52	0.858112	0.429056	−	0.903278i	$-0.358846\pi$
$659$	1.21039e52	0.858112	0.429056	+	0.903278i	$0.358846\pi$
$660$	−2.88210e50	−0.0198676
$661$	−1.90863e52	−1.27937	−0.639683	−	0.768638i	$-0.720935\pi$
$661$	−1.90863e52	−1.27937	−0.639683	+	0.768638i	$0.720935\pi$
$662$	1.13206e52	0.737897
$663$	−2.67352e51	−0.169466
$664$	−2.84485e51	−0.175368
$665$	6.97894e51	0.418397
$666$	4.19813e51	0.244784
$667$	7.48975e51	0.424756
$668$	−2.17664e51	−0.120066
$669$	1.71217e51	0.0918678
$670$	1.20039e52	0.626527
$671$	−3.24336e51	−0.164675
$672$	−2.46462e51	−0.121736
$673$	−1.67548e52	−0.805120	−0.402560	−	0.915394i	$-0.631879\pi$
$673$	−1.67548e52	−0.805120	−0.402560	+	0.915394i	$0.631879\pi$
$674$	1.48299e51	0.0693316
$675$	−4.74255e51	−0.215721
$676$	−9.03067e51	−0.399674
$677$	−2.49877e52	−1.07606	−0.538029	−	0.842926i	$-0.680831\pi$
$677$	−2.49877e52	−1.07606	−0.538029	+	0.842926i	$0.680831\pi$
$678$	−9.52980e51	−0.399332
$679$	3.46090e52	1.41123
$680$	−2.00580e51	−0.0795927
$681$	−2.76882e52	−1.06923
$682$	−6.20499e50	−0.0233201
$683$	−4.73250e52	−1.73104	−0.865520	−	0.500874i	$-0.833012\pi$
$683$	−4.73250e52	−1.73104	−0.865520	+	0.500874i	$0.833012\pi$
$684$	6.24032e51	0.222162
$685$	1.61202e52	0.558594
$686$	2.22908e52	0.751847
$687$	2.58600e52	0.849041
$688$	−2.91441e51	−0.0931459
$689$	−9.29603e51	−0.289229
$690$	−2.71861e51	−0.0823452
$691$	1.73179e52	0.510683	0.255341	−	0.966851i	$-0.417812\pi$
$691$	1.73179e52	0.510683	0.255341	+	0.966851i	$0.417812\pi$
$692$	−2.53718e52	−0.728431
$693$	−1.68641e51	−0.0471410
$694$	1.52296e52	0.414514
$695$	5.18889e51	0.137517
$696$	−1.26225e52	−0.325741
$697$	−1.33012e52	−0.334259
$698$	−3.52382e52	−0.862359
$699$	5.02051e52	1.19652
$700$	−3.94775e51	−0.0916296
$701$	8.62925e51	0.195070	0.0975348	−	0.995232i	$-0.468904\pi$
$701$	8.62925e51	0.195070	0.0975348	+	0.995232i	$0.468904\pi$
$702$	−1.55169e52	−0.341640
$703$	3.78747e52	0.812223
$704$	−7.07468e50	−0.0147779
$705$	−3.20853e51	−0.0652841
$706$	−3.27318e52	−0.648759
$707$	3.93193e52	0.759183
$708$	−1.66343e52	−0.312889
$709$	2.82932e52	0.518473	0.259236	−	0.965814i	$-0.416529\pi$
$709$	2.82932e52	0.518473	0.259236	+	0.965814i	$0.416529\pi$
$710$	−1.19359e50	−0.00213096
$711$	3.40067e52	0.591530
$712$	−1.75342e52	−0.297171
$713$	−5.85301e51	−0.0966547
$714$	1.52335e52	0.245122
$715$	−1.51043e51	−0.0236831
$716$	3.31763e52	0.506918
$717$	−2.11886e52	−0.315500
$718$	−2.51589e52	−0.365081
$719$	1.27280e53	1.80001	0.900007	−	0.435875i	$-0.143561\pi$
$719$	1.27280e53	1.80001	0.900007	+	0.435875i	$0.143561\pi$
$720$	−3.52994e51	−0.0486537
$721$	5.45513e52	0.732829
$722$	2.29524e51	0.0300532
$723$	4.64266e52	0.592528
$724$	5.35929e52	0.666720
$725$	−2.02182e52	−0.245183
$726$	−4.43259e52	−0.523999
$727$	−5.42190e52	−0.624834	−0.312417	−	0.949945i	$-0.601139\pi$
$727$	−5.42190e52	−0.624834	−0.312417	+	0.949945i	$0.601139\pi$
$728$	−1.29164e52	−0.145115
$729$	8.89250e52	0.974012
$730$	−4.41041e51	−0.0470984
$731$	1.80135e52	0.187554
$732$	5.15596e52	0.523425
$733$	−4.67036e52	−0.462304	−0.231152	−	0.972918i	$-0.574249\pi$
$733$	−4.67036e52	−0.462304	−0.231152	+	0.972918i	$0.574249\pi$
$734$	3.05718e52	0.295083
$735$	−5.72795e51	−0.0539118
$736$	−6.67336e51	−0.0612498
$737$	−2.61692e52	−0.234230
$738$	−2.34082e52	−0.204327
$739$	−3.22372e52	−0.274432	−0.137216	−	0.990541i	$-0.543815\pi$
$739$	−3.22372e52	−0.274432	−0.137216	+	0.990541i	$0.543815\pi$
$740$	−2.14244e52	−0.177878
$741$	−4.24478e52	−0.343731
$742$	5.29679e52	0.418351
$743$	−5.43932e52	−0.419036	−0.209518	−	0.977805i	$-0.567190\pi$
$743$	−5.43932e52	−0.419036	−0.209518	+	0.977805i	$0.567190\pi$
$744$	9.86405e51	0.0741235
$745$	9.29710e51	0.0681485
$746$	−8.50207e52	−0.607934
$747$	3.09447e52	0.215852
$748$	4.37275e51	0.0297561
$749$	−6.56881e52	−0.436087
$750$	7.33874e51	0.0475322
$751$	−1.15095e53	−0.727304	−0.363652	−	0.931535i	$-0.618470\pi$
$751$	−1.15095e53	−0.727304	−0.363652	+	0.931535i	$0.618470\pi$
$752$	−7.87598e51	−0.0485595
$753$	−4.44486e52	−0.267394
$754$	−6.61510e52	−0.388299
$755$	9.17873e52	0.525731
$756$	8.84140e52	0.494160
$757$	−3.51043e53	−1.91464	−0.957318	−	0.289038i	$-0.906665\pi$
$757$	−3.51043e53	−1.91464	−0.957318	+	0.289038i	$0.906665\pi$
$758$	−2.32015e52	−0.123491
$759$	5.92671e51	0.0307851
$760$	−3.18464e52	−0.161439
$761$	−1.73091e53	−0.856363	−0.428182	−	0.903693i	$-0.640846\pi$
$761$	−1.73091e53	−0.856363	−0.428182	+	0.903693i	$0.640846\pi$
$762$	7.40242e52	0.357443
$763$	8.50504e52	0.400841
$764$	2.26312e52	0.104107
$765$	2.18180e52	0.0979668
$766$	−4.31254e51	−0.0189017
$767$	−8.71762e52	−0.372978
$768$	1.12466e52	0.0469719
$769$	−3.14722e53	−1.28319	−0.641594	−	0.767045i	$-0.721727\pi$
$769$	−3.14722e53	−1.28319	−0.641594	+	0.767045i	$0.721727\pi$
$770$	8.60630e51	0.0342561
$771$	−7.36961e52	−0.286377
$772$	−7.68426e51	−0.0291529
$773$	−1.31709e53	−0.487861	−0.243931	−	0.969793i	$-0.578437\pi$
$773$	−1.31709e53	−0.487861	−0.243931	+	0.969793i	$0.578437\pi$
$774$	3.17013e52	0.114649
$775$	1.57999e52	0.0557921
$776$	−1.57928e53	−0.544525
$777$	1.62712e53	0.547811
$778$	6.11560e52	0.201056
$779$	−2.11184e53	−0.677982
$780$	2.40113e52	0.0752775
$781$	2.60209e50	0.000796669 0
$782$	4.12471e52	0.123330
$783$	4.52808e53	1.32227
$784$	−1.40604e52	−0.0401006
$785$	1.38173e53	0.384889
$786$	3.19846e53	0.870208
$787$	2.46211e53	0.654296	0.327148	−	0.944973i	$-0.393912\pi$
$787$	2.46211e53	0.654296	0.327148	+	0.944973i	$0.393912\pi$
$788$	2.81628e53	0.731038
$789$	−1.38025e53	−0.349972
$790$	−1.73547e53	−0.429849
$791$	2.84572e53	0.688536
$792$	7.69545e51	0.0181894
$793$	2.70210e53	0.623948
$794$	−4.64453e53	−1.04776
$795$	−9.84658e52	−0.217017
$796$	3.81107e53	0.820646
$797$	−6.55944e53	−1.38003	−0.690013	−	0.723797i	$-0.742395\pi$
$797$	−6.55944e53	−1.38003	−0.690013	+	0.723797i	$0.742395\pi$
$798$	2.41864e53	0.497184
$799$	4.86803e52	0.0977772
$800$	1.80144e52	0.0353553
$801$	1.90728e53	0.365773
$802$	2.45129e53	0.459376
$803$	9.61493e51	0.0176079
$804$	4.16011e53	0.744506
$805$	8.11810e52	0.141981
$806$	5.16949e52	0.0883588
$807$	6.67837e53	1.11560
$808$	−1.79422e53	−0.292931
$809$	−1.13014e54	−1.80338	−0.901688	−	0.432387i	$-0.857671\pi$
$809$	−1.13014e54	−1.80338	−0.901688	+	0.432387i	$0.857671\pi$
$810$	−7.61254e52	−0.118729
$811$	4.98428e53	0.759831	0.379915	−	0.925021i	$-0.375953\pi$
$811$	4.98428e53	0.759831	0.379915	+	0.925021i	$0.375953\pi$
$812$	3.76922e53	0.561649
$813$	2.62850e53	0.382853
$814$	4.67063e52	0.0665004
$815$	−4.04976e53	−0.563655
$816$	−6.95135e52	−0.0945805
$817$	2.86003e53	0.380419
$818$	−5.89572e53	−0.766656
$819$	1.40498e53	0.178615
$820$	1.19460e53	0.148479
$821$	−6.32222e53	−0.768283	−0.384142	−	0.923274i	$-0.625503\pi$
$821$	−6.32222e53	−0.768283	−0.384142	+	0.923274i	$0.625503\pi$
$822$	5.58667e53	0.663780
$823$	1.53088e54	1.77846	0.889228	−	0.457465i	$-0.151243\pi$
$823$	1.53088e54	1.77846	0.889228	+	0.457465i	$0.151243\pi$
$824$	−2.48929e53	−0.282763
$825$	−1.59988e52	−0.0177701
$826$	4.96722e53	0.539489
$827$	1.35864e54	1.44295	0.721477	−	0.692439i	$-0.243464\pi$
$827$	1.35864e54	1.44295	0.721477	+	0.692439i	$0.243464\pi$
$828$	7.25892e52	0.0753895
$829$	−5.63827e53	−0.572648	−0.286324	−	0.958133i	$-0.592433\pi$
$829$	−5.63827e53	−0.572648	−0.286324	+	0.958133i	$0.592433\pi$
$830$	−1.57921e53	−0.156854
$831$	−8.24245e53	−0.800640
$832$	5.89404e52	0.0559927
$833$	8.69053e52	0.0807446
$834$	1.79827e53	0.163412
$835$	−1.20828e53	−0.107391
$836$	6.94268e52	0.0603546
$837$	−3.53856e53	−0.300888
$838$	−1.54516e54	−1.28516
$839$	−2.01357e54	−1.63821	−0.819106	−	0.573642i	$-0.805530\pi$
$839$	−2.01357e54	−1.63821	−0.819106	+	0.573642i	$0.805530\pi$
$840$	−1.36814e53	−0.108884
$841$	6.45914e53	0.502862
$842$	−1.80700e54	−1.37621
$843$	9.14319e52	0.0681220
$844$	−1.07277e54	−0.781939
$845$	−5.01303e53	−0.357479
$846$	8.56706e52	0.0597696
$847$	1.32363e54	0.903489
$848$	−2.41704e53	−0.161421
$849$	−1.83067e54	−1.19624
$850$	−1.11344e53	−0.0711899
$851$	4.40569e53	0.275624
$852$	−4.13653e51	−0.00253223
$853$	−5.77259e53	−0.345791	−0.172895	−	0.984940i	$-0.555312\pi$
$853$	−5.77259e53	−0.345791	−0.172895	+	0.984940i	$0.555312\pi$
$854$	−1.53963e54	−0.902500
$855$	3.46407e53	0.198707
$856$	2.99748e53	0.168264
$857$	−1.17381e54	−0.644842	−0.322421	−	0.946596i	$-0.604497\pi$
$857$	−1.17381e54	−0.644842	−0.322421	+	0.946596i	$0.604497\pi$
$858$	−5.23458e52	−0.0281428
$859$	3.05143e54	1.60557	0.802786	−	0.596267i	$-0.203350\pi$
$859$	3.05143e54	1.60557	0.802786	+	0.596267i	$0.203350\pi$
$860$	−1.61782e53	−0.0833123
$861$	−9.07261e53	−0.457271
$862$	−8.69353e52	−0.0428856
$863$	3.37124e54	1.62776	0.813879	−	0.581034i	$-0.197352\pi$
$863$	3.37124e54	1.62776	0.813879	+	0.581034i	$0.197352\pi$
$864$	−4.03451e53	−0.190672
$865$	−1.40842e54	−0.651528
$866$	1.84841e54	0.836986
$867$	−1.26590e54	−0.561108
$868$	−2.94553e53	−0.127805
$869$	3.78342e53	0.160701
$870$	−7.00687e53	−0.291352
$871$	2.18021e54	0.887487
$872$	−3.88103e53	−0.154665
$873$	1.71786e54	0.670229
$874$	6.54885e53	0.250152
$875$	−2.19144e53	−0.0819560
$876$	−1.52848e53	−0.0559673
$877$	4.59456e52	0.0164722	0.00823610	−	0.999966i	$-0.497378\pi$
$877$	4.59456e52	0.0164722	0.00823610	+	0.999966i	$0.497378\pi$
$878$	−1.14760e54	−0.402850
$879$	9.57256e53	0.329029
$880$	−3.92723e52	−0.0132177
$881$	−4.37096e54	−1.44053	−0.720266	−	0.693698i	$-0.755980\pi$
$881$	−4.37096e54	−1.44053	−0.720266	+	0.693698i	$0.755980\pi$
$882$	1.52941e53	0.0493578
$883$	5.60045e54	1.76991	0.884953	−	0.465680i	$-0.154190\pi$
$883$	5.60045e54	1.76991	0.884953	+	0.465680i	$0.154190\pi$
$884$	−3.64302e53	−0.112744
$885$	−9.23391e53	−0.279856
$886$	3.22806e54	0.958116
$887$	−3.86725e54	−1.12413	−0.562064	−	0.827094i	$-0.689992\pi$
$887$	−3.86725e54	−1.12413	−0.562064	+	0.827094i	$0.689992\pi$
$888$	−7.42489e53	−0.211373
$889$	−2.21045e54	−0.616310
$890$	−9.73344e53	−0.265798
$891$	1.65957e53	0.0443873
$892$	2.33306e53	0.0611189
$893$	7.72903e53	0.198323
$894$	3.22202e53	0.0809813
$895$	1.84166e54	0.453401
$896$	−3.35837e53	−0.0809899
$897$	−4.93765e53	−0.116643
$898$	3.96069e54	0.916556
$899$	−1.50854e54	−0.341981
$900$	−1.95951e53	−0.0435172
$901$	1.49394e54	0.325030
$902$	−2.60428e53	−0.0555095
$903$	1.22869e54	0.256577
$904$	−1.29856e54	−0.265672
$905$	2.97500e54	0.596332
$906$	3.18100e54	0.624730
$907$	2.47231e54	0.475739	0.237869	−	0.971297i	$-0.423551\pi$
$907$	2.47231e54	0.475739	0.237869	+	0.971297i	$0.423551\pi$
$908$	−3.77288e54	−0.711353
$909$	1.95166e54	0.360555
$910$	−7.17007e53	−0.129795
$911$	−7.75991e54	−1.37647	−0.688235	−	0.725488i	$-0.741614\pi$
$911$	−7.75991e54	−1.37647	−0.688235	+	0.725488i	$0.741614\pi$
$912$	−1.10367e54	−0.191839
$913$	3.44276e53	0.0586404
$914$	6.34777e54	1.05954
$915$	2.86213e54	0.468166
$916$	3.52376e54	0.564860
$917$	−9.55099e54	−1.50043
$918$	2.49368e54	0.383928
$919$	−3.05017e53	−0.0460243	−0.0230121	−	0.999735i	$-0.507326\pi$
$919$	−3.05017e53	−0.0460243	−0.0230121	+	0.999735i	$0.507326\pi$
$920$	−3.70446e53	−0.0547835
$921$	−7.16736e53	−0.103886
$922$	4.94496e54	0.702490
$923$	−2.16785e52	−0.00301854
$924$	2.98262e53	0.0407067
$925$	−1.18929e54	−0.159099
$926$	1.35140e54	0.177207
$927$	2.70771e54	0.348039
$928$	−1.71997e54	−0.216713
$929$	4.09018e54	0.505187	0.252593	−	0.967573i	$-0.418717\pi$
$929$	4.09018e54	0.505187	0.252593	+	0.967573i	$0.418717\pi$
$930$	5.47565e53	0.0662981
$931$	1.37981e54	0.163775
$932$	6.84110e54	0.796034
$933$	7.47146e54	0.852305
$934$	5.16342e54	0.577458
$935$	2.42737e53	0.0266146
$936$	−6.41122e53	−0.0689187
$937$	6.61227e54	0.696897	0.348448	−	0.937328i	$-0.386709\pi$
$937$	6.61227e54	0.696897	0.348448	+	0.937328i	$0.386709\pi$
$938$	−1.24226e55	−1.28369
$939$	8.49739e54	0.860938
$940$	−4.37205e53	−0.0434330
$941$	−1.99049e55	−1.93889	−0.969444	−	0.245314i	$-0.921109\pi$
$941$	−1.99049e55	−1.93889	−0.969444	+	0.245314i	$0.921109\pi$
$942$	4.78857e54	0.457366
$943$	−2.45655e54	−0.230070
$944$	−2.26665e54	−0.208162
$945$	4.90796e54	0.441990
$946$	3.52693e53	0.0311466
$947$	−2.25303e55	−1.95116	−0.975580	−	0.219644i	$-0.929510\pi$
$947$	−2.25303e55	−1.95116	−0.975580	+	0.219644i	$0.929510\pi$
$948$	−6.01448e54	−0.510792
$949$	−8.01038e53	−0.0667157
$950$	−1.76783e54	−0.144395
$951$	5.00389e54	0.400837
$952$	2.07576e54	0.163077
$953$	−1.62950e55	−1.25555	−0.627777	−	0.778393i	$-0.716035\pi$
$953$	−1.62950e55	−1.25555	−0.627777	+	0.778393i	$0.716035\pi$
$954$	2.62912e54	0.198685
$955$	1.25629e54	0.0931163
$956$	−2.88723e54	−0.209899
$957$	1.52753e54	0.108923
$958$	−1.63232e55	−1.14168
$959$	−1.66825e55	−1.14450
$960$	6.24311e53	0.0420130
$961$	−1.39701e55	−0.922181
$962$	−3.89119e54	−0.251967
$963$	−3.26050e54	−0.207109
$964$	6.32624e54	0.394203
$965$	−4.26562e53	−0.0260751
$966$	2.81343e54	0.168717
$967$	−4.18975e54	−0.246489	−0.123245	−	0.992376i	$-0.539330\pi$
$967$	−4.18975e54	−0.246489	−0.123245	+	0.992376i	$0.539330\pi$
$968$	−6.03999e54	−0.348612
$969$	6.82165e54	0.386278
$970$	−8.76678e54	−0.487038
$971$	−9.28589e54	−0.506137	−0.253068	−	0.967448i	$-0.581440\pi$
$971$	−9.28589e54	−0.506137	−0.253068	+	0.967448i	$0.581440\pi$
$972$	7.44637e54	0.398216
$973$	−5.36987e54	−0.281758
$974$	1.19586e55	0.615657
$975$	1.33289e54	0.0673302
$976$	7.02567e54	0.348230
$977$	1.35583e55	0.659409	0.329705	−	0.944084i	$-0.393051\pi$
$977$	1.35583e55	0.659409	0.329705	+	0.944084i	$0.393051\pi$
$978$	−1.40349e55	−0.669795
$979$	2.12194e54	0.0993696
$980$	−7.80509e53	−0.0358670
$981$	4.22157e54	0.190370
$982$	1.96728e55	0.870572
$983$	−1.34843e55	−0.585583	−0.292791	−	0.956176i	$-0.594584\pi$
$983$	−1.34843e55	−0.585583	−0.292791	+	0.956176i	$0.594584\pi$
$984$	4.14002e54	0.176438
$985$	1.56335e55	0.653860
$986$	1.06309e55	0.436363
$987$	3.32044e54	0.133761
$988$	−5.78407e54	−0.228681
$989$	3.32687e54	0.129093
$990$	4.27183e53	0.0162691
$991$	1.84939e55	0.691298	0.345649	−	0.938364i	$-0.387659\pi$
$991$	1.84939e55	0.691298	0.345649	+	0.938364i	$0.387659\pi$
$992$	1.34411e54	0.0493137
$993$	2.17786e55	0.784276
$994$	1.23522e53	0.00436612
$995$	2.11557e55	0.734008
$996$	−5.47294e54	−0.186390
$997$	−2.97900e54	−0.0995885	−0.0497943	−	0.998759i	$-0.515857\pi$
$997$	−2.97900e54	−0.0995885	−0.0497943	+	0.998759i	$0.515857\pi$
$998$	−3.21504e55	−1.05505
$999$	2.66355e55	0.858023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.38.a.a.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.38.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+262144. q^{2} +5.04314e8 q^{3} +6.87195e10 q^{4} +3.81470e12 q^{5} +1.32203e14 q^{6} -3.94775e15 q^{7} +1.80144e16 q^{8} -1.95951e17 q^{9} +1.00000e18 q^{10} -2.18005e18 q^{11} +3.46562e19 q^{12} +1.81624e20 q^{13} -1.03488e21 q^{14} +1.92381e21 q^{15} +4.72237e21 q^{16} -2.91883e22 q^{17} -5.13673e22 q^{18} -4.63426e23 q^{19} +2.62144e23 q^{20} -1.99091e24 q^{21} -5.71488e23 q^{22} -5.39070e24 q^{23} +9.08492e24 q^{24} +1.45519e25 q^{25} +4.76117e25 q^{26} -3.25906e26 q^{27} -2.71287e26 q^{28} -1.38938e27 q^{29} +5.04314e26 q^{30} +1.08576e27 q^{31} +1.23794e27 q^{32} -1.09943e27 q^{33} -7.65153e27 q^{34} -1.50595e28 q^{35} -1.34656e28 q^{36} -8.17276e28 q^{37} -1.21484e29 q^{38} +9.15957e28 q^{39} +6.87195e28 q^{40} +4.55702e29 q^{41} -5.21904e29 q^{42} -6.17149e29 q^{43} -1.49812e29 q^{44} -7.47493e29 q^{45} -1.41314e30 q^{46} -1.66780e30 q^{47} +2.38156e30 q^{48} -2.97740e30 q^{49} +3.81470e30 q^{50} -1.47201e31 q^{51} +1.24811e31 q^{52} -5.11828e31 q^{53} -8.54342e31 q^{54} -8.31624e30 q^{55} -7.11163e31 q^{56} -2.33712e32 q^{57} -3.64219e32 q^{58} -4.79981e32 q^{59} +1.32203e32 q^{60} +1.48774e33 q^{61} +2.84626e32 q^{62} +7.73564e32 q^{63} +3.24519e32 q^{64} +6.92841e32 q^{65} -2.88210e32 q^{66} +1.20039e34 q^{67} -2.00580e33 q^{68} -2.71861e33 q^{69} -3.94775e33 q^{70} -1.19359e32 q^{71} -3.52994e33 q^{72} -4.41041e33 q^{73} -2.14244e34 q^{74} +7.33874e33 q^{75} -3.18464e34 q^{76} +8.60630e33 q^{77} +2.40113e34 q^{78} -1.73547e35 q^{79} +1.80144e34 q^{80} -7.61254e34 q^{81} +1.19460e35 q^{82} -1.57921e35 q^{83} -1.36814e35 q^{84} -1.11344e35 q^{85} -1.61782e35 q^{86} -7.00687e35 q^{87} -3.92723e34 q^{88} -9.73344e35 q^{89} -1.95951e35 q^{90} -7.17007e35 q^{91} -3.70446e35 q^{92} +5.47565e35 q^{93} -4.37205e35 q^{94} -1.76783e36 q^{95} +6.24311e35 q^{96} -8.76678e36 q^{97} -7.80509e35 q^{98} +4.27183e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 524288 q^{2} - 185500908 q^{3} + 137438953472 q^{4} + 7629394531250 q^{5} - 48627950026752 q^{6} - 651580251842156 q^{7} + 36\!\cdots\!68 q^{8} - 17\!\cdots\!94 q^{9} + 20\!\cdots\!00 q^{10} - 15\!\cdots\!96 q^{11}+ \cdots + 78\!\cdots\!12 q^{99}+O(q^{100}) \) 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

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