LMFDB - Embedded newform 3.26.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,26,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	3.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:	$11.8799033986$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 783420x + 148321440 $ x^3 - x^2 - 783420*x + 148321440
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$199.394$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10558.1 q^{2} +531441. q^{3} +7.79199e7 q^{4} -8.66156e8 q^{5} -5.61103e9 q^{6} -1.75156e10 q^{7} -4.68416e11 q^{8} +2.82430e11 q^{9} +O(q^{10})$	\(q-10558.1 q^{2} +531441. q^{3} +7.79199e7 q^{4} -8.66156e8 q^{5} -5.61103e9 q^{6} -1.75156e10 q^{7} -4.68416e11 q^{8} +2.82430e11 q^{9} +9.14500e12 q^{10} -8.03769e12 q^{11} +4.14098e13 q^{12} -2.74406e12 q^{13} +1.84932e14 q^{14} -4.60311e14 q^{15} +2.33105e15 q^{16} +3.84314e15 q^{17} -2.98193e15 q^{18} +5.80352e15 q^{19} -6.74908e16 q^{20} -9.30848e15 q^{21} +8.48630e16 q^{22} +1.28434e16 q^{23} -2.48936e17 q^{24} +4.52204e17 q^{25} +2.89722e16 q^{26} +1.50095e17 q^{27} -1.36481e18 q^{28} +1.23594e18 q^{29} +4.86003e18 q^{30} +3.64474e18 q^{31} -8.89410e18 q^{32} -4.27156e18 q^{33} -4.05764e19 q^{34} +1.51712e19 q^{35} +2.20069e19 q^{36} +3.54993e19 q^{37} -6.12744e19 q^{38} -1.45831e18 q^{39} +4.05722e20 q^{40} -2.62561e20 q^{41} +9.82803e19 q^{42} -7.82469e19 q^{43} -6.26295e20 q^{44} -2.44628e20 q^{45} -1.35602e20 q^{46} +1.42679e21 q^{47} +1.23882e21 q^{48} -1.03427e21 q^{49} -4.77443e21 q^{50} +2.04240e21 q^{51} -2.13817e20 q^{52} +3.15289e21 q^{53} -1.58472e21 q^{54} +6.96189e21 q^{55} +8.20457e21 q^{56} +3.08423e21 q^{57} -1.30493e22 q^{58} +5.95554e21 q^{59} -3.58674e22 q^{60} +1.46494e22 q^{61} -3.84817e22 q^{62} -4.94691e21 q^{63} +1.56881e22 q^{64} +2.37679e21 q^{65} +4.50997e22 q^{66} -6.68064e22 q^{67} +2.99457e23 q^{68} +6.82549e21 q^{69} -1.60180e23 q^{70} +1.43174e22 q^{71} -1.32295e23 q^{72} -6.25968e22 q^{73} -3.74807e23 q^{74} +2.40320e23 q^{75} +4.52210e23 q^{76} +1.40785e23 q^{77} +1.53970e22 q^{78} -3.24882e23 q^{79} -2.01905e24 q^{80} +7.97664e22 q^{81} +2.77216e24 q^{82} +1.01939e24 q^{83} -7.25316e23 q^{84} -3.32876e24 q^{85} +8.26142e23 q^{86} +6.56832e23 q^{87} +3.76498e24 q^{88} -8.94156e23 q^{89} +2.58282e24 q^{90} +4.80638e22 q^{91} +1.00075e24 q^{92} +1.93696e24 q^{93} -1.50643e25 q^{94} -5.02676e24 q^{95} -4.72669e24 q^{96} -8.14572e24 q^{97} +1.09200e25 q^{98} -2.27008e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9}+O(q^{10}) $ 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9	$ 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9} + 8363188874700 q^{10} - 5946998130780 q^{11} + 48226988914308 q^{12} + 248137774407690 q^{13} + 754361641264848 q^{14} - 86706060612750 q^{15} + 23\!\cdots\!16 q^{16}+ \cdots - 16\!\cdots\!80 q^{99}+O(q^{100}) $ 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9 + 8363188874700 * q^10 - 5946998130780 * q^11 + 48226988914308 * q^12 + 248137774407690 * q^13 + 754361641264848 * q^14 - 86706060612750 * q^15 + 2394637852352016 * q^16 + 6640885201245174 * q^17 - 1038775835177118 * q^18 - 4282718959080516 * q^19 - 84999590549092200 * q^20 - 5113829681644104 * q^21 - 67279455312049512 * q^22 - 54558955951564152 * q^23 - 142433006732403768 * q^24 + 285270827389168125 * q^25 + 914405315527228956 * q^26 + 450283905890997363 * q^27 + 2416760102519597472 * q^28 - 506350856671782 * q^29 + 4444541458759442700 * q^30 - 120595458951353856 * q^31 - 23423805952813711584 * q^32 - 3160478633619853980 * q^33 - 30744163051965656604 * q^34 - 12895712434403329200 * q^35 + 25629799215608757828 * q^36 + 71124029266471833426 * q^37 - 151631523417421211736 * q^38 + 131870586968997181290 * q^39 + 487276555770533818800 * q^40 - 178237898435247428226 * q^41 + 400898704995432085968 * q^42 + 233732145791955002244 * q^43 - 1709130121883010683088 * q^44 - 46079155558100472750 * q^45 - 727064486838202905936 * q^46 - 578974907441950806192 * q^47 + 1272608734891807735056 * q^48 + 1540848623287695627627 * q^49 - 7598435156177129081250 * q^50 + 3529238672234936515734 * q^51 + 1549295968705274668344 * q^52 + 9056010625929165756258 * q^53 - 552048068622362767038 * q^54 + 16758715188531155952600 * q^55 + 7112451608305863332160 * q^56 - 2276012446332708503556 * q^57 - 43337630795958244629252 * q^58 + 23769324802557802948596 * q^59 - 45172267401000107860200 * q^60 - 11371716695373075009318 * q^61 - 21881713022451611321088 * q^62 - 2717698759842624273864 * q^63 - 55686925877484831566784 * q^64 + 89289247460368023248700 * q^65 - 35755061010490904706792 * q^66 + 52213761253321486240524 * q^67 + 318831609976592944413384 * q^68 - 28994866109855204503032 * q^69 - 78749858107500801357600 * q^70 + 262955361870665606618136 * q^71 - 75694739530875390869688 * q^72 - 11752720924176446629602 * q^73 - 498161580663483575957172 * q^74 + 151604613778526897518125 * q^75 + 4571105415149082363216 * q^76 - 1386525122949230445864288 * q^77 + 485952475289106083605596 * q^78 - 500543105756664483755760 * q^79 - 1540345885402641092176800 * q^80 + 239299329230617529590083 * q^81 + 4108759898128895060824212 * q^82 - 59055829437561671377284 * q^83 + 1284365405643117400117152 * q^84 - 2357173046017457952925500 * q^85 + 2057662432276923640084440 * q^86 - 269095605620508497862 * q^87 + 4527751242141959006666592 * q^88 - 3359875059386549548018866 * q^89 + 2362011557384576987930700 * q^90 + 1253870789177107094217744 * q^91 - 1905611545816878301689504 * q^92 - 64089371300566444586496 * q^93 - 18037990008720502135322400 * q^94 - 5406514800597015344021400 * q^95 - 12448370859369271697912544 * q^96 - 12029431225244267569541466 * q^97 + 24058796570011739277032850 * q^98 - 1679607925529568818985180 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−10558.1	−1.82269	−0.911344	−	0.411645i	$-0.864954\pi$
$2$	−10558.1	−1.82269	−0.911344	+	0.411645i	$0.864954\pi$
$3$	531441.	0.577350
$3$	531441.	0.577350
$4$	7.79199e7	2.32219
$5$	−8.66156e8	−1.58661	−0.793307	−	0.608822i	$-0.791642\pi$
$5$	−8.66156e8	−1.58661	−0.793307	+	0.608822i	$0.791642\pi$
$6$	−5.61103e9	−1.05233
$7$	−1.75156e10	−0.478298	−0.239149	−	0.970983i	$-0.576868\pi$
$7$	−1.75156e10	−0.478298	−0.239149	+	0.970983i	$0.576868\pi$
$8$	−4.68416e11	−2.40995
$9$	2.82430e11	0.333333
$10$	9.14500e12	2.89190
$11$	−8.03769e12	−0.772187	−0.386093	−	0.922460i	$-0.626176\pi$
$11$	−8.03769e12	−0.772187	−0.386093	+	0.922460i	$0.626176\pi$
$12$	4.14098e13	1.34072
$13$	−2.74406e12	−0.0326664	−0.0163332	−	0.999867i	$-0.505199\pi$
$13$	−2.74406e12	−0.0326664	−0.0163332	+	0.999867i	$0.505199\pi$
$14$	1.84932e14	0.871788
$15$	−4.60311e14	−0.916032
$16$	2.33105e15	2.07039
$17$	3.84314e15	1.59983	0.799917	−	0.600110i	$-0.204877\pi$
$17$	3.84314e15	1.59983	0.799917	+	0.600110i	$0.204877\pi$
$18$	−2.98193e15	−0.607563
$19$	5.80352e15	0.601550	0.300775	−	0.953695i	$-0.402755\pi$
$19$	5.80352e15	0.601550	0.300775	+	0.953695i	$0.402755\pi$
$20$	−6.74908e16	−3.68442
$21$	−9.30848e15	−0.276145
$22$	8.48630e16	1.40746
$23$	1.28434e16	0.122203	0.0611013	−	0.998132i	$-0.480539\pi$
$23$	1.28434e16	0.122203	0.0611013	+	0.998132i	$0.480539\pi$
$24$	−2.48936e17	−1.39138
$25$	4.52204e17	1.51734
$26$	2.89722e16	0.0595408
$27$	1.50095e17	0.192450
$28$	−1.36481e18	−1.11070
$29$	1.23594e18	0.648670	0.324335	−	0.945942i	$-0.394859\pi$
$29$	1.23594e18	0.648670	0.324335	+	0.945942i	$0.394859\pi$
$30$	4.86003e18	1.66964
$31$	3.64474e18	0.831085	0.415542	−	0.909574i	$-0.363592\pi$
$31$	3.64474e18	0.831085	0.415542	+	0.909574i	$0.363592\pi$
$32$	−8.89410e18	−1.36373
$33$	−4.27156e18	−0.445822
$34$	−4.05764e19	−2.91600
$35$	1.51712e19	0.758874
$36$	2.20069e19	0.774064
$37$	3.54993e19	0.886541	0.443270	−	0.896388i	$-0.353818\pi$
$37$	3.54993e19	0.886541	0.443270	+	0.896388i	$0.353818\pi$
$38$	−6.12744e19	−1.09644
$39$	−1.45831e18	−0.0188600
$40$	4.05722e20	3.82365
$41$	−2.62561e20	−1.81732	−0.908661	−	0.417534i	$-0.862894\pi$
$41$	−2.62561e20	−1.81732	−0.908661	+	0.417534i	$0.862894\pi$
$42$	9.82803e19	0.503327
$43$	−7.82469e19	−0.298615	−0.149307	−	0.988791i	$-0.547704\pi$
$43$	−7.82469e19	−0.298615	−0.149307	+	0.988791i	$0.547704\pi$
$44$	−6.26295e20	−1.79317
$45$	−2.44628e20	−0.528871
$46$	−1.35602e20	−0.222737
$47$	1.42679e21	1.79117	0.895587	−	0.444886i	$-0.146756\pi$
$47$	1.42679e21	1.79117	0.895587	+	0.444886i	$0.146756\pi$
$48$	1.23882e21	1.19534
$49$	−1.03427e21	−0.771231
$50$	−4.77443e21	−2.76564
$51$	2.04240e21	0.923665
$52$	−2.13817e20	−0.0758578
$53$	3.15289e21	0.881578	0.440789	−	0.897611i	$-0.354699\pi$
$53$	3.15289e21	0.881578	0.440789	+	0.897611i	$0.354699\pi$
$54$	−1.58472e21	−0.350777
$55$	6.96189e21	1.22516
$56$	8.20457e21	1.15267
$57$	3.08423e21	0.347305
$58$	−1.30493e22	−1.18232
$59$	5.95554e21	0.435784	0.217892	−	0.975973i	$-0.430082\pi$
$59$	5.95554e21	0.435784	0.217892	+	0.975973i	$0.430082\pi$
$60$	−3.58674e22	−2.12720
$61$	1.46494e22	0.706637	0.353318	−	0.935503i	$-0.385053\pi$
$61$	1.46494e22	0.706637	0.353318	+	0.935503i	$0.385053\pi$
$62$	−3.84817e22	−1.51481
$63$	−4.94691e21	−0.159433
$64$	1.56881e22	0.415259
$65$	2.37679e21	0.0518290
$66$	4.50997e22	0.812595
$67$	−6.68064e22	−0.997431	−0.498716	−	0.866766i	$-0.666195\pi$
$67$	−6.68064e22	−0.997431	−0.498716	+	0.866766i	$0.666195\pi$
$68$	2.99457e23	3.71512
$69$	6.82549e21	0.0705537
$70$	−1.60180e23	−1.38319
$71$	1.43174e22	0.103546	0.0517732	−	0.998659i	$-0.483513\pi$
$71$	1.43174e22	0.103546	0.0517732	+	0.998659i	$0.483513\pi$
$72$	−1.32295e23	−0.803315
$73$	−6.25968e22	−0.319901	−0.159951	−	0.987125i	$-0.551134\pi$
$73$	−6.25968e22	−0.319901	−0.159951	+	0.987125i	$0.551134\pi$
$74$	−3.74807e23	−1.61589
$75$	2.40320e23	0.876039
$76$	4.52210e23	1.39691
$77$	1.40785e23	0.369335
$78$	1.53970e22	0.0343759
$79$	−3.24882e23	−0.618567	−0.309284	−	0.950970i	$-0.600089\pi$
$79$	−3.24882e23	−0.618567	−0.309284	+	0.950970i	$0.600089\pi$
$80$	−2.01905e24	−3.28491
$81$	7.97664e22	0.111111
$82$	2.77216e24	3.31241
$83$	1.01939e24	1.04681	0.523403	−	0.852085i	$-0.324662\pi$
$83$	1.01939e24	1.04681	0.523403	+	0.852085i	$0.324662\pi$
$84$	−7.25316e23	−0.641263
$85$	−3.32876e24	−2.53832
$86$	8.26142e23	0.544282
$87$	6.56832e23	0.374510
$88$	3.76498e24	1.86093
$89$	−8.94156e23	−0.383741	−0.191871	−	0.981420i	$-0.561455\pi$
$89$	−8.94156e23	−0.383741	−0.191871	+	0.981420i	$0.561455\pi$
$90$	2.58282e24	0.963968
$91$	4.80638e22	0.0156243
$92$	1.00075e24	0.283778
$93$	1.93696e24	0.479827
$94$	−1.50643e25	−3.26475
$95$	−5.02676e24	−0.954427
$96$	−4.72669e24	−0.787347
$97$	−8.14572e24	−1.19202	−0.596009	−	0.802978i	$-0.703248\pi$
$97$	−8.14572e24	−1.19202	−0.596009	+	0.802978i	$0.703248\pi$
$98$	1.09200e25	1.40571
$99$	−2.27008e24	−0.257396
$100$	3.52356e25	3.52356
$101$	1.52472e25	1.34640	0.673200	−	0.739460i	$-0.264919\pi$
$101$	1.52472e25	1.34640	0.673200	+	0.739460i	$0.264919\pi$
$102$	−2.15640e25	−1.68355
$103$	5.83804e24	0.403461	0.201731	−	0.979441i	$-0.435343\pi$
$103$	5.83804e24	0.403461	0.201731	+	0.979441i	$0.435343\pi$
$104$	1.28536e24	0.0787244
$105$	8.06260e24	0.438136
$106$	−3.32887e25	−1.60684
$107$	1.45692e23	0.00625372	0.00312686	−	0.999995i	$-0.499005\pi$
$107$	1.45692e23	0.00625372	0.00312686	+	0.999995i	$0.499005\pi$
$108$	1.16954e25	0.446906
$109$	3.43467e25	1.16965	0.584823	−	0.811161i	$-0.301164\pi$
$109$	3.43467e25	1.16965	0.584823	+	0.811161i	$0.301164\pi$
$110$	−7.35046e25	−2.23309
$111$	1.88658e25	0.511845
$112$	−4.08296e25	−0.990262
$113$	3.62034e25	0.785721	0.392860	−	0.919598i	$-0.371486\pi$
$113$	3.62034e25	0.785721	0.392860	+	0.919598i	$0.371486\pi$
$114$	−3.25637e25	−0.633029
$115$	−1.11244e25	−0.193888
$116$	9.63046e25	1.50634
$117$	−7.75004e23	−0.0108888
$118$	−6.28794e25	−0.794298
$119$	−6.73148e25	−0.765197
$120$	2.15617e26	2.20759
$121$	−4.37427e25	−0.403727
$122$	−1.54670e26	−1.28798
$123$	−1.39536e26	−1.04923
$124$	2.83998e26	1.92994
$125$	−1.33544e26	−0.820824
$126$	5.22302e25	0.290596
$127$	3.84962e26	1.94031	0.970155	−	0.242486i	$-0.0779630\pi$
$127$	3.84962e26	1.94031	0.970155	+	0.242486i	$0.0779630\pi$
$128$	1.32800e26	0.606837
$129$	−4.15836e25	−0.172405
$130$	−2.50944e25	−0.0944682
$131$	−3.67930e26	−1.25856	−0.629280	−	0.777179i	$-0.716650\pi$
$131$	−3.67930e26	−1.25856	−0.629280	+	0.777179i	$0.716650\pi$
$132$	−3.32839e26	−1.03529
$133$	−1.01652e26	−0.287720
$134$	7.05351e26	1.81801
$135$	−1.30005e26	−0.305344
$136$	−1.80019e27	−3.85552
$137$	−2.54551e26	−0.497471	−0.248735	−	0.968571i	$-0.580015\pi$
$137$	−2.54551e26	−0.497471	−0.248735	+	0.968571i	$0.580015\pi$
$138$	−7.20645e25	−0.128598
$139$	1.03188e27	1.68246	0.841232	−	0.540674i	$-0.181831\pi$
$139$	1.03188e27	1.68246	0.841232	+	0.540674i	$0.181831\pi$
$140$	1.18214e27	1.76225
$141$	7.58257e26	1.03414
$142$	−1.51165e26	−0.188733
$143$	2.20559e25	0.0252246
$144$	6.58357e26	0.690129
$145$	−1.07052e27	−1.02919
$146$	6.60906e26	0.583081
$147$	−5.49656e26	−0.445271
$148$	2.76610e27	2.05872
$149$	7.85762e26	0.537604	0.268802	−	0.963195i	$-0.413372\pi$
$149$	7.85762e26	0.537604	0.268802	+	0.963195i	$0.413372\pi$
$150$	−2.53733e27	−1.59675
$151$	−2.01098e27	−1.16465	−0.582327	−	0.812955i	$-0.697857\pi$
$151$	−2.01098e27	−1.16465	−0.582327	+	0.812955i	$0.697857\pi$
$152$	−2.71847e27	−1.44970
$153$	1.08542e27	0.533278
$154$	−1.48642e27	−0.673183
$155$	−3.15691e27	−1.31861
$156$	−1.13631e26	−0.0437965
$157$	1.56442e27	0.556684	0.278342	−	0.960482i	$-0.410215\pi$
$157$	1.56442e27	0.556684	0.278342	+	0.960482i	$0.410215\pi$
$158$	3.43015e27	1.12745
$159$	1.67558e27	0.508979
$160$	7.70368e27	2.16371
$161$	−2.24959e26	−0.0584493
$162$	−8.42185e26	−0.202521
$163$	6.67790e27	1.48695	0.743473	−	0.668766i	$-0.233177\pi$
$163$	6.67790e27	1.48695	0.743473	+	0.668766i	$0.233177\pi$
$164$	−2.04587e28	−4.22017
$165$	3.69984e27	0.707348
$166$	−1.07629e28	−1.90800
$167$	3.40414e27	0.559825	0.279912	−	0.960026i	$-0.409695\pi$
$167$	3.40414e27	0.559825	0.279912	+	0.960026i	$0.409695\pi$
$168$	4.36025e27	0.665495
$169$	−7.04888e27	−0.998933
$170$	3.51455e28	4.62657
$171$	1.63909e27	0.200517
$172$	−6.09699e27	−0.693441
$173$	4.73155e27	0.500526	0.250263	−	0.968178i	$-0.419483\pi$
$173$	4.73155e27	0.500526	0.250263	+	0.968178i	$0.419483\pi$
$174$	−6.93492e27	−0.682615
$175$	−7.92060e27	−0.725742
$176$	−1.87362e28	−1.59873
$177$	3.16502e27	0.251600
$178$	9.44063e27	0.699441
$179$	−1.47462e28	−1.01863	−0.509314	−	0.860581i	$-0.670101\pi$
$179$	−1.47462e28	−1.01863	−0.509314	+	0.860581i	$0.670101\pi$
$180$	−1.90614e28	−1.22814
$181$	2.35097e28	1.41340	0.706699	−	0.707515i	$-0.250184\pi$
$181$	2.35097e28	1.41340	0.706699	+	0.707515i	$0.250184\pi$
$182$	−5.07464e26	−0.0284782
$183$	7.78528e27	0.407977
$184$	−6.01604e27	−0.294502
$185$	−3.07480e28	−1.40660
$186$	−2.04507e28	−0.874575
$187$	−3.08900e28	−1.23537
$188$	1.11176e29	4.15945
$189$	−2.62899e27	−0.0920484
$190$	5.30732e28	1.73962
$191$	−6.06728e28	−1.86242	−0.931209	−	0.364486i	$-0.881245\pi$
$191$	−6.06728e28	−1.86242	−0.931209	+	0.364486i	$0.881245\pi$
$192$	8.33728e27	0.239750
$193$	2.50277e28	0.674457	0.337228	−	0.941423i	$-0.390511\pi$
$193$	2.50277e28	0.674457	0.337228	+	0.941423i	$0.390511\pi$
$194$	8.60036e28	2.17268
$195$	1.26312e27	0.0299235
$196$	−8.05905e28	−1.79095
$197$	4.77900e28	0.996573	0.498286	−	0.867013i	$-0.333963\pi$
$197$	4.77900e28	0.996573	0.498286	+	0.867013i	$0.333963\pi$
$198$	2.39678e28	0.469152
$199$	−1.61323e28	−0.296505	−0.148253	−	0.988950i	$-0.547365\pi$
$199$	−1.61323e28	−0.296505	−0.148253	+	0.988950i	$0.547365\pi$
$200$	−2.11820e29	−3.65672
$201$	−3.55037e28	−0.575867
$202$	−1.60983e29	−2.45407
$203$	−2.16483e28	−0.310258
$204$	1.59144e29	2.14493
$205$	2.27419e29	2.88339
$206$	−6.16389e28	−0.735384
$207$	3.62734e27	0.0407342
$208$	−6.39654e27	−0.0676322
$209$	−4.66469e28	−0.464509
$210$	−8.51261e28	−0.798585
$211$	6.22564e28	0.550368	0.275184	−	0.961392i	$-0.411261\pi$
$211$	6.22564e28	0.550368	0.275184	+	0.961392i	$0.411261\pi$
$212$	2.45673e29	2.04719
$213$	7.60886e27	0.0597826
$214$	−1.53824e27	−0.0113986
$215$	6.77740e28	0.473786
$216$	−7.03068e28	−0.463794
$217$	−6.38396e28	−0.397506
$218$	−3.62638e29	−2.13190
$219$	−3.32665e28	−0.184695
$220$	5.42470e29	2.84506
$221$	−1.05458e28	−0.0522609
$222$	−1.99188e29	−0.932933
$223$	−1.41853e29	−0.628100	−0.314050	−	0.949406i	$-0.601686\pi$
$223$	−1.41853e29	−0.628100	−0.314050	+	0.949406i	$0.601686\pi$
$224$	1.55785e29	0.652267
$225$	1.27716e29	0.505781
$226$	−3.82240e29	−1.43212
$227$	6.12049e28	0.217002	0.108501	−	0.994096i	$-0.465395\pi$
$227$	6.12049e28	0.217002	0.108501	+	0.994096i	$0.465395\pi$
$228$	2.40323e29	0.806509
$229$	−3.18136e28	−0.101081	−0.0505405	−	0.998722i	$-0.516094\pi$
$229$	−3.18136e28	−0.101081	−0.0505405	+	0.998722i	$0.516094\pi$
$230$	1.17453e29	0.353398
$231$	7.48187e28	0.213236
$232$	−5.78937e29	−1.56326
$233$	4.46157e29	1.14167	0.570833	−	0.821066i	$-0.306621\pi$
$233$	4.46157e29	1.14167	0.570833	+	0.821066i	$0.306621\pi$
$234$	8.18260e27	0.0198469
$235$	−1.23583e30	−2.84190
$236$	4.64055e29	1.01197
$237$	−1.72656e29	−0.357130
$238$	7.10719e29	1.39472
$239$	−4.81999e29	−0.897578	−0.448789	−	0.893638i	$-0.648145\pi$
$239$	−4.81999e29	−0.897578	−0.448789	+	0.893638i	$0.648145\pi$
$240$	−1.07301e30	−1.89654
$241$	5.78582e29	0.970849	0.485425	−	0.874278i	$-0.338665\pi$
$241$	5.78582e29	0.970849	0.485425	+	0.874278i	$0.338665\pi$
$242$	4.61841e29	0.735869
$243$	4.23912e28	0.0641500
$244$	1.14148e30	1.64095
$245$	8.95843e29	1.22365
$246$	1.47324e30	1.91242
$247$	−1.59252e28	−0.0196505
$248$	−1.70726e30	−2.00287
$249$	5.41748e29	0.604374
$250$	1.40998e30	1.49611
$251$	−6.06733e29	−0.612457	−0.306229	−	0.951958i	$-0.599067\pi$
$251$	−6.06733e29	−0.612457	−0.306229	+	0.951958i	$0.599067\pi$
$252$	−3.85463e29	−0.370233
$253$	−1.03231e29	−0.0943633
$254$	−4.06448e30	−3.53658
$255$	−1.76904e30	−1.46550
$256$	−1.92852e30	−1.52133
$257$	2.20115e30	1.65381	0.826905	−	0.562342i	$-0.190099\pi$
$257$	2.20115e30	1.65381	0.826905	+	0.562342i	$0.190099\pi$
$258$	4.39046e29	0.314241
$259$	−6.21791e29	−0.424030
$260$	1.85199e29	0.120357
$261$	3.49067e29	0.216223
$262$	3.88466e30	2.29396
$263$	5.93802e29	0.334345	0.167172	−	0.985928i	$-0.446536\pi$
$263$	5.93802e29	0.334345	0.167172	+	0.985928i	$0.446536\pi$
$264$	2.00087e30	1.07441
$265$	−2.73090e30	−1.39872
$266$	1.07325e30	0.524424
$267$	−4.75191e29	−0.221553
$268$	−5.20555e30	−2.31623
$269$	−1.29238e30	−0.548892	−0.274446	−	0.961603i	$-0.588494\pi$
$269$	−1.29238e30	−0.548892	−0.274446	+	0.961603i	$0.588494\pi$
$270$	1.37262e30	0.556547
$271$	3.40870e30	1.31969	0.659846	−	0.751401i	$-0.270621\pi$
$271$	3.40870e30	1.31969	0.659846	+	0.751401i	$0.270621\pi$
$272$	8.95856e30	3.31228
$273$	2.55430e28	0.00902069
$274$	2.68759e30	0.906735
$275$	−3.63467e30	−1.17167
$276$	5.31841e29	0.163839
$277$	−2.97949e29	−0.0877294	−0.0438647	−	0.999037i	$-0.513967\pi$
$277$	−2.97949e29	−0.0877294	−0.0438647	+	0.999037i	$0.513967\pi$
$278$	−1.08948e31	−3.06661
$279$	1.02938e30	0.277028
$280$	−7.10644e30	−1.82885
$281$	7.06888e30	1.73989	0.869945	−	0.493149i	$-0.164154\pi$
$281$	7.06888e30	1.73989	0.869945	+	0.493149i	$0.164154\pi$
$282$	−8.00578e30	−1.88491
$283$	5.39645e30	1.21556	0.607782	−	0.794104i	$-0.292060\pi$
$283$	5.39645e30	1.21556	0.607782	+	0.794104i	$0.292060\pi$
$284$	1.11561e30	0.240455
$285$	−2.67143e30	−0.551039
$286$	−2.32869e29	−0.0459766
$287$	4.59890e30	0.869221
$288$	−2.51196e30	−0.454575
$289$	8.99912e30	1.55947
$290$	1.13027e31	1.87589
$291$	−4.32897e30	−0.688212
$292$	−4.87753e30	−0.742873
$293$	−9.01982e30	−1.31629	−0.658146	−	0.752890i	$-0.728659\pi$
$293$	−9.01982e30	−1.31629	−0.658146	+	0.752890i	$0.728659\pi$
$294$	5.80334e30	0.811590
$295$	−5.15843e30	−0.691420
$296$	−1.66285e31	−2.13652
$297$	−1.20641e30	−0.148607
$298$	−8.29618e30	−0.979884
$299$	−3.52430e28	−0.00399193
$300$	1.87257e31	2.03433
$301$	1.37054e30	0.142827
$302$	2.12322e31	2.12280
$303$	8.10301e30	0.777345
$304$	1.35283e31	1.24544
$305$	−1.26886e31	−1.12116
$306$	−1.14600e31	−0.972000
$307$	−1.38074e31	−1.12430	−0.562149	−	0.827036i	$-0.690025\pi$
$307$	−1.38074e31	−1.12430	−0.562149	+	0.827036i	$0.690025\pi$
$308$	1.09699e31	0.857668
$309$	3.10258e30	0.232939
$310$	3.33311e31	2.40342
$311$	−9.77163e30	−0.676803	−0.338401	−	0.941002i	$-0.609886\pi$
$311$	−9.77163e30	−0.676803	−0.338401	+	0.941002i	$0.609886\pi$
$312$	6.83095e29	0.0454515
$313$	−1.56623e31	−1.00127	−0.500635	−	0.865658i	$-0.666900\pi$
$313$	−1.56623e31	−1.00127	−0.500635	+	0.865658i	$0.666900\pi$
$314$	−1.65174e31	−1.01466
$315$	4.28480e30	0.252958
$316$	−2.53147e31	−1.43643
$317$	3.12042e30	0.170205	0.0851024	−	0.996372i	$-0.472878\pi$
$317$	3.12042e30	0.170205	0.0851024	+	0.996372i	$0.472878\pi$
$318$	−1.76910e31	−0.927711
$319$	−9.93413e30	−0.500895
$320$	−1.35883e31	−0.658856
$321$	7.74267e28	0.00361059
$322$	2.37514e30	0.106535
$323$	2.23038e31	0.962380
$324$	6.21539e30	0.258021
$325$	−1.24087e30	−0.0495662
$326$	−7.05062e31	−2.71024
$327$	1.82533e31	0.675295
$328$	1.22988e32	4.37965
$329$	−2.49911e31	−0.856715
$330$	−3.90634e31	−1.28927
$331$	2.97950e31	0.946878	0.473439	−	0.880827i	$-0.343012\pi$
$331$	2.97950e31	0.946878	0.473439	+	0.880827i	$0.343012\pi$
$332$	7.94311e31	2.43089
$333$	1.00261e31	0.295514
$334$	−3.59414e31	−1.02039
$335$	5.78648e31	1.58254
$336$	−2.16985e31	−0.571728
$337$	−1.80278e30	−0.0457688	−0.0228844	−	0.999738i	$-0.507285\pi$
$337$	−1.80278e30	−0.0457688	−0.0228844	+	0.999738i	$0.507285\pi$
$338$	7.44231e31	1.82074
$339$	1.92399e31	0.453636
$340$	−2.59377e32	−5.89447
$341$	−2.92953e31	−0.641753
$342$	−1.73057e31	−0.365479
$343$	4.16054e31	0.847176
$344$	3.66521e31	0.719646
$345$	−5.91194e30	−0.111942
$346$	−4.99563e31	−0.912303
$347$	−7.20180e31	−1.26859	−0.634297	−	0.773089i	$-0.718710\pi$
$347$	−7.20180e31	−1.26859	−0.634297	+	0.773089i	$0.718710\pi$
$348$	5.11802e31	0.869685
$349$	4.42407e31	0.725277	0.362638	−	0.931930i	$-0.381876\pi$
$349$	4.42407e31	0.725277	0.362638	+	0.931930i	$0.381876\pi$
$350$	8.36268e31	1.32280
$351$	−4.11869e29	−0.00628666
$352$	7.14879e31	1.05305
$353$	−6.53342e31	−0.928874	−0.464437	−	0.885606i	$-0.653743\pi$
$353$	−6.53342e31	−0.928874	−0.464437	+	0.885606i	$0.653743\pi$
$354$	−3.34167e31	−0.458588
$355$	−1.24011e31	−0.164288
$356$	−6.96726e31	−0.891121
$357$	−3.57738e31	−0.441787
$358$	1.55692e32	1.85664
$359$	4.73870e31	0.545731	0.272866	−	0.962052i	$-0.412029\pi$
$359$	4.73870e31	0.545731	0.272866	+	0.962052i	$0.412029\pi$
$360$	1.14588e32	1.27455
$361$	−5.93956e31	−0.638138
$362$	−2.48218e32	−2.57618
$363$	−2.32466e31	−0.233092
$364$	3.74512e30	0.0362826
$365$	5.42186e31	0.507560
$366$	−8.21980e31	−0.743615
$367$	1.46367e32	1.27973	0.639864	−	0.768488i	$-0.278991\pi$
$367$	1.46367e32	1.27973	0.639864	+	0.768488i	$0.278991\pi$
$368$	2.99385e31	0.253007
$369$	−7.41550e31	−0.605774
$370$	3.24641e32	2.56379
$371$	−5.52246e31	−0.421657
$372$	1.50928e32	1.11425
$373$	−1.17636e32	−0.839805	−0.419902	−	0.907569i	$-0.637936\pi$
$373$	−1.17636e32	−0.839805	−0.419902	+	0.907569i	$0.637936\pi$
$374$	3.26141e32	2.25170
$375$	−7.09709e31	−0.473903
$376$	−6.68334e32	−4.31663
$377$	−3.39151e30	−0.0211898
$378$	2.77572e31	0.167776
$379$	7.75124e31	0.453295	0.226648	−	0.973977i	$-0.427223\pi$
$379$	7.75124e31	0.453295	0.226648	+	0.973977i	$0.427223\pi$
$380$	−3.91684e32	−2.21636
$381$	2.04584e32	1.12024
$382$	6.40592e32	3.39461
$383$	−5.85978e31	−0.300536	−0.150268	−	0.988645i	$-0.548014\pi$
$383$	−5.85978e31	−0.300536	−0.150268	+	0.988645i	$0.548014\pi$
$384$	7.05752e31	0.350358
$385$	−1.21941e32	−0.585993
$386$	−2.64246e32	−1.22932
$387$	−2.20992e31	−0.0995383
$388$	−6.34713e32	−2.76810
$389$	4.02764e31	0.170091	0.0850453	−	0.996377i	$-0.472897\pi$
$389$	4.02764e31	0.170091	0.0850453	+	0.996377i	$0.472897\pi$
$390$	−1.33362e31	−0.0545412
$391$	4.93589e31	0.195504
$392$	4.84471e32	1.85863
$393$	−1.95533e32	−0.726630
$394$	−5.04573e32	−1.81644
$395$	2.81398e32	0.981427
$396$	−1.76884e32	−0.597722
$397$	−1.44419e32	−0.472871	−0.236435	−	0.971647i	$-0.575979\pi$
$397$	−1.44419e32	−0.472871	−0.236435	+	0.971647i	$0.575979\pi$
$398$	1.70327e32	0.540437
$399$	−5.40220e31	−0.166115
$400$	1.05411e33	3.14149
$401$	3.72208e32	1.07518	0.537590	−	0.843207i	$-0.319335\pi$
$401$	3.72208e32	1.07518	0.537590	+	0.843207i	$0.319335\pi$
$402$	3.74853e32	1.04963
$403$	−1.00014e31	−0.0271486
$404$	1.18806e33	3.12660
$405$	−6.90902e31	−0.176290
$406$	2.28565e32	0.565503
$407$	−2.85333e32	−0.684575
$408$	−9.56696e32	−2.22598
$409$	8.68723e31	0.196038	0.0980189	−	0.995185i	$-0.468749\pi$
$409$	8.68723e31	0.196038	0.0980189	+	0.995185i	$0.468749\pi$
$410$	−2.40112e33	−5.25552
$411$	−1.35279e32	−0.287215
$412$	4.54900e32	0.936915
$413$	−1.04315e32	−0.208434
$414$	−3.82980e31	−0.0742458
$415$	−8.82955e32	−1.66088
$416$	2.44059e31	0.0445481
$417$	5.48385e32	0.971371
$418$	4.92504e32	0.846655
$419$	2.07673e32	0.346501	0.173251	−	0.984878i	$-0.444573\pi$
$419$	2.07673e32	0.346501	0.173251	+	0.984878i	$0.444573\pi$
$420$	6.28237e32	1.01744
$421$	3.45939e31	0.0543842	0.0271921	−	0.999630i	$-0.491343\pi$
$421$	3.45939e31	0.0543842	0.0271921	+	0.999630i	$0.491343\pi$
$422$	−6.57312e32	−1.00315
$423$	4.02969e32	0.597058
$424$	−1.47687e33	−2.12456
$425$	1.73788e33	2.42750
$426$	−8.03354e31	−0.108965
$427$	−2.56592e32	−0.337983
$428$	1.13523e31	0.0145223
$429$	1.17214e31	0.0145634
$430$	−7.15568e32	−0.863565
$431$	2.08566e32	0.244499	0.122250	−	0.992499i	$-0.460989\pi$
$431$	2.08566e32	0.244499	0.122250	+	0.992499i	$0.460989\pi$
$432$	3.49878e32	0.398446
$433$	1.06443e33	1.17766	0.588828	−	0.808258i	$-0.299590\pi$
$433$	1.06443e33	1.17766	0.588828	+	0.808258i	$0.299590\pi$
$434$	6.74028e32	0.724530
$435$	−5.68919e32	−0.594203
$436$	2.67629e33	2.71614
$437$	7.45367e31	0.0735110
$438$	3.51232e32	0.336642
$439$	−1.89482e33	−1.76506	−0.882532	−	0.470252i	$-0.844163\pi$
$439$	−1.89482e33	−1.76506	−0.882532	+	0.470252i	$0.844163\pi$
$440$	−3.26107e33	−2.95258
$441$	−2.92110e32	−0.257077
$442$	1.11344e32	0.0952554
$443$	−1.44571e33	−1.20236	−0.601182	−	0.799112i	$-0.705303\pi$
$443$	−1.44571e33	−1.20236	−0.601182	+	0.799112i	$0.705303\pi$
$444$	1.47002e33	1.18860
$445$	7.74479e32	0.608849
$446$	1.49771e33	1.14483
$447$	4.17586e32	0.310386
$448$	−2.74785e32	−0.198618
$449$	−1.46137e33	−1.02726	−0.513630	−	0.858012i	$-0.671700\pi$
$449$	−1.46137e33	−1.02726	−0.513630	+	0.858012i	$0.671700\pi$
$450$	−1.34844e33	−0.921881
$451$	2.11038e33	1.40331
$452$	2.82096e33	1.82460
$453$	−1.06872e33	−0.672413
$454$	−6.46210e32	−0.395526
$455$	−4.16307e31	−0.0247897
$456$	−1.44470e33	−0.836986
$457$	7.44617e32	0.419740	0.209870	−	0.977729i	$-0.432696\pi$
$457$	7.44617e32	0.419740	0.209870	+	0.977729i	$0.432696\pi$
$458$	3.35892e32	0.184239
$459$	5.76835e32	0.307888
$460$	−8.66809e32	−0.450246
$461$	−3.26259e33	−1.64931	−0.824653	−	0.565639i	$-0.808630\pi$
$461$	−3.26259e33	−1.64931	−0.824653	+	0.565639i	$0.808630\pi$
$462$	−7.89946e32	−0.388662
$463$	−1.31917e33	−0.631740	−0.315870	−	0.948802i	$-0.602296\pi$
$463$	−1.31917e33	−0.631740	−0.315870	+	0.948802i	$0.602296\pi$
$464$	2.88105e33	1.34300
$465$	−1.67771e33	−0.761300
$466$	−4.71059e33	−2.08090
$467$	−2.45701e33	−1.05669	−0.528343	−	0.849031i	$-0.677187\pi$
$467$	−2.45701e33	−1.05669	−0.528343	+	0.849031i	$0.677187\pi$
$468$	−6.03882e31	−0.0252859
$469$	1.17015e33	0.477069
$470$	1.30480e34	5.17990
$471$	8.31399e32	0.321402
$472$	−2.78967e33	−1.05021
$473$	6.28924e32	0.230587
$474$	1.82292e33	0.650936
$475$	2.62437e33	0.912758
$476$	−5.24516e33	−1.77694
$477$	8.90470e32	0.293859
$478$	5.08901e33	1.63601
$479$	1.21049e32	0.0379111	0.0189556	−	0.999820i	$-0.493966\pi$
$479$	1.21049e32	0.0379111	0.0189556	+	0.999820i	$0.493966\pi$
$480$	4.09405e33	1.24922
$481$	−9.74124e31	−0.0289601
$482$	−6.10875e33	−1.76956
$483$	−1.19552e32	−0.0337457
$484$	−3.40842e33	−0.937533
$485$	7.05547e33	1.89127
$486$	−4.47572e32	−0.116926
$487$	−1.89715e33	−0.483048	−0.241524	−	0.970395i	$-0.577647\pi$
$487$	−1.89715e33	−0.483048	−0.241524	+	0.970395i	$0.577647\pi$
$488$	−6.86201e33	−1.70296
$489$	3.54891e33	0.858489
$490$	−9.45844e33	−2.23033
$491$	−1.38187e31	−0.00317649	−0.00158824	−	0.999999i	$-0.500506\pi$
$491$	−1.38187e31	−0.00317649	−0.00158824	+	0.999999i	$0.500506\pi$
$492$	−1.08726e34	−2.43652
$493$	4.74991e33	1.03777
$494$	1.68141e32	0.0358167
$495$	1.96624e33	0.408388
$496$	8.49607e33	1.72067
$497$	−2.50777e32	−0.0495261
$498$	−5.71985e33	−1.10159
$499$	5.59006e33	1.04993	0.524964	−	0.851125i	$-0.324079\pi$
$499$	5.59006e33	1.04993	0.524964	+	0.851125i	$0.324079\pi$
$500$	−1.04058e34	−1.90611
$501$	1.80910e33	0.323215
$502$	6.40597e33	1.11632
$503$	−5.75382e33	−0.978039	−0.489020	−	0.872273i	$-0.662645\pi$
$503$	−5.75382e33	−0.978039	−0.489020	+	0.872273i	$0.662645\pi$
$504$	2.31721e33	0.384224
$505$	−1.32065e34	−2.13622
$506$	1.08993e33	0.171995
$507$	−3.74606e33	−0.576734
$508$	2.99962e34	4.50577
$509$	−2.37864e32	−0.0348624	−0.0174312	−	0.999848i	$-0.505549\pi$
$509$	−2.37864e32	−0.0348624	−0.0174312	+	0.999848i	$0.505549\pi$
$510$	1.86778e34	2.67115
$511$	1.09642e33	0.153008
$512$	1.59056e34	2.16608
$513$	8.71078e32	0.115768
$514$	−2.32400e34	−3.01438
$515$	−5.05666e33	−0.640137
$516$	−3.24019e33	−0.400359
$517$	−1.14681e34	−1.38312
$518$	6.56495e33	0.772875
$519$	2.51454e33	0.288979
$520$	−1.11333e33	−0.124905
$521$	1.58141e33	0.173210	0.0866051	−	0.996243i	$-0.472398\pi$
$521$	1.58141e33	0.173210	0.0866051	+	0.996243i	$0.472398\pi$
$522$	−3.68550e33	−0.394108
$523$	5.73737e33	0.599021	0.299511	−	0.954093i	$-0.403177\pi$
$523$	5.73737e33	0.599021	0.299511	+	0.954093i	$0.403177\pi$
$524$	−2.86691e34	−2.92262
$525$	−4.20933e33	−0.419007
$526$	−6.26944e33	−0.609406
$527$	1.40073e34	1.32960
$528$	−9.95721e33	−0.923025
$529$	−1.08808e34	−0.985067
$530$	2.88332e34	2.54944
$531$	1.68202e33	0.145261
$532$	−7.92070e33	−0.668141
$533$	7.20483e32	0.0593655
$534$	5.01714e33	0.403822
$535$	−1.26192e32	−0.00992223
$536$	3.12932e34	2.40376
$537$	−7.83671e33	−0.588105
$538$	1.36451e34	1.00046
$539$	8.31317e33	0.595535
$540$	−1.01300e34	−0.709068
$541$	2.93823e33	0.200965	0.100482	−	0.994939i	$-0.467961\pi$
$541$	2.93823e33	0.200965	0.100482	+	0.994939i	$0.467961\pi$
$542$	−3.59895e34	−2.40539
$543$	1.24940e34	0.816025
$544$	−3.41813e34	−2.18174
$545$	−2.97496e34	−1.85578
$546$	−2.69687e32	−0.0164419
$547$	1.26737e34	0.755197	0.377598	−	0.925969i	$-0.376750\pi$
$547$	1.26737e34	0.755197	0.377598	+	0.925969i	$0.376750\pi$
$548$	−1.98346e34	−1.15522
$549$	4.13742e33	0.235546
$550$	3.83754e34	2.13559
$551$	7.17283e33	0.390208
$552$	−3.19717e33	−0.170031
$553$	5.69048e33	0.295859
$554$	3.14579e33	0.159903
$555$	−1.63407e34	−0.812100
$556$	8.04043e34	3.90701
$557$	2.28469e34	1.08552	0.542760	−	0.839888i	$-0.317379\pi$
$557$	2.28469e34	1.08552	0.542760	+	0.839888i	$0.317379\pi$
$558$	−1.08684e34	−0.504936
$559$	2.14714e32	0.00975469
$560$	3.53648e34	1.57116
$561$	−1.64162e34	−0.713242
$562$	−7.46343e34	−3.17128
$563$	−1.35367e34	−0.562545	−0.281272	−	0.959628i	$-0.590756\pi$
$563$	−1.35367e34	−0.562545	−0.281272	+	0.959628i	$0.590756\pi$
$564$	5.90833e34	2.40146
$565$	−3.13578e34	−1.24664
$566$	−5.69765e34	−2.21559
$567$	−1.39715e33	−0.0531442
$568$	−6.70651e33	−0.249541
$569$	4.66336e34	1.69744	0.848722	−	0.528839i	$-0.177373\pi$
$569$	4.66336e34	1.69744	0.848722	+	0.528839i	$0.177373\pi$
$570$	2.82053e34	1.00437
$571$	2.45170e34	0.854115	0.427058	−	0.904224i	$-0.359550\pi$
$571$	2.45170e34	0.854115	0.427058	+	0.904224i	$0.359550\pi$
$572$	1.71859e33	0.0585764
$573$	−3.22440e34	−1.07527
$574$	−4.85558e34	−1.58432
$575$	5.80781e33	0.185423
$576$	4.43077e33	0.138420
$577$	3.10363e34	0.948794	0.474397	−	0.880311i	$-0.342666\pi$
$577$	3.10363e34	0.948794	0.474397	+	0.880311i	$0.342666\pi$
$578$	−9.50140e34	−2.84243
$579$	1.33007e34	0.389398
$580$	−8.34149e34	−2.38998
$581$	−1.78553e34	−0.500685
$582$	4.57059e34	1.25440
$583$	−2.53420e34	−0.680743
$584$	2.93214e34	0.770945
$585$	6.71275e32	0.0172763
$586$	9.52325e34	2.39919
$587$	−6.68767e34	−1.64930	−0.824648	−	0.565647i	$-0.808627\pi$
$587$	−6.68767e34	−1.64930	−0.824648	+	0.565647i	$0.808627\pi$
$588$	−4.28291e34	−1.03400
$589$	2.11523e34	0.499939
$590$	5.44634e34	1.26024
$591$	2.53976e34	0.575372
$592$	8.27507e34	1.83548
$593$	4.34492e34	0.943621	0.471811	−	0.881700i	$-0.343601\pi$
$593$	4.34492e34	0.943621	0.471811	+	0.881700i	$0.343601\pi$
$594$	1.27375e34	0.270865
$595$	5.83051e34	1.21407
$596$	6.12264e34	1.24842
$597$	−8.57336e33	−0.171187
$598$	3.72100e32	0.00727604
$599$	2.46556e34	0.472149	0.236075	−	0.971735i	$-0.424139\pi$
$599$	2.46556e34	0.472149	0.236075	+	0.971735i	$0.424139\pi$
$600$	−1.12570e35	−2.11121
$601$	2.24761e34	0.412848	0.206424	−	0.978463i	$-0.433817\pi$
$601$	2.24761e34	0.412848	0.206424	+	0.978463i	$0.433817\pi$
$602$	−1.44703e34	−0.260329
$603$	−1.88681e34	−0.332477
$604$	−1.56696e35	−2.70455
$605$	3.78880e34	0.640559
$606$	−8.55527e34	−1.41686
$607$	−9.53080e34	−1.54622	−0.773109	−	0.634273i	$-0.781299\pi$
$607$	−9.53080e34	−1.54622	−0.773109	+	0.634273i	$0.781299\pi$
$608$	−5.16171e34	−0.820349
$609$	−1.15048e34	−0.179127
$610$	1.33969e35	2.04352
$611$	−3.91521e33	−0.0585113
$612$	8.45756e34	1.23837
$613$	−6.51029e34	−0.933994	−0.466997	−	0.884259i	$-0.654664\pi$
$613$	−6.51029e34	−0.933994	−0.466997	+	0.884259i	$0.654664\pi$
$614$	1.45780e35	2.04925
$615$	1.20860e35	1.66473
$616$	−6.59458e34	−0.890078
$617$	−7.32055e34	−0.968231	−0.484115	−	0.875004i	$-0.660859\pi$
$617$	−7.32055e34	−0.968231	−0.484115	+	0.875004i	$0.660859\pi$
$618$	−3.27574e34	−0.424574
$619$	−5.88130e34	−0.747034	−0.373517	−	0.927623i	$-0.621848\pi$
$619$	−5.88130e34	−0.747034	−0.373517	+	0.927623i	$0.621848\pi$
$620$	−2.45986e35	−3.06207
$621$	1.92772e33	0.0235179
$622$	1.03170e35	1.23360
$623$	1.56616e34	0.183543
$624$	−3.39939e33	−0.0390475
$625$	−1.90969e34	−0.215012
$626$	1.65365e35	1.82500
$627$	−2.47901e34	−0.268184
$628$	1.21900e35	1.29273
$629$	1.36429e35	1.41832
$630$	−4.52395e34	−0.461064
$631$	−1.54670e35	−1.54539	−0.772695	−	0.634778i	$-0.781092\pi$
$631$	−1.54670e35	−1.54539	−0.772695	+	0.634778i	$0.781092\pi$
$632$	1.52180e35	1.49071
$633$	3.30856e34	0.317755
$634$	−3.29458e34	−0.310230
$635$	−3.33437e35	−3.07852
$636$	1.30561e35	1.18195
$637$	2.83811e33	0.0251934
$638$	1.04886e35	0.912975
$639$	4.04366e33	0.0345155
$640$	−1.15025e35	−0.962816
$641$	9.18519e34	0.753985	0.376993	−	0.926216i	$-0.376958\pi$
$641$	9.18519e34	0.753985	0.376993	+	0.926216i	$0.376958\pi$
$642$	−8.17481e32	−0.00658097
$643$	2.17111e35	1.71413	0.857066	−	0.515206i	$-0.172285\pi$
$643$	2.17111e35	1.71413	0.857066	+	0.515206i	$0.172285\pi$
$644$	−1.75287e34	−0.135730
$645$	3.60179e34	0.273541
$646$	−2.35486e35	−1.75412
$647$	−1.90634e35	−1.39283	−0.696413	−	0.717641i	$-0.745222\pi$
$647$	−1.90634e35	−1.39283	−0.696413	+	0.717641i	$0.745222\pi$
$648$	−3.73639e34	−0.267772
$649$	−4.78687e34	−0.336506
$650$	1.31013e34	0.0903438
$651$	−3.39270e34	−0.229500
$652$	5.20341e35	3.45298
$653$	1.49805e35	0.975241	0.487620	−	0.873056i	$-0.337865\pi$
$653$	1.49805e35	0.975241	0.487620	+	0.873056i	$0.337865\pi$
$654$	−1.92720e35	−1.23085
$655$	3.18685e35	1.99685
$656$	−6.12043e35	−3.76256
$657$	−1.76792e34	−0.106634
$658$	2.63859e35	1.56152
$659$	−1.23099e34	−0.0714802	−0.0357401	−	0.999361i	$-0.511379\pi$
$659$	−1.23099e34	−0.0714802	−0.0357401	+	0.999361i	$0.511379\pi$
$660$	2.88291e35	1.64260
$661$	9.08557e34	0.507965	0.253983	−	0.967209i	$-0.418259\pi$
$661$	9.08557e34	0.507965	0.253983	+	0.967209i	$0.418259\pi$
$662$	−3.14580e35	−1.72586
$663$	−5.60448e33	−0.0301729
$664$	−4.77501e35	−2.52275
$665$	8.80464e34	0.456500
$666$	−1.05857e35	−0.538629
$667$	1.58737e34	0.0792693
$668$	2.65250e35	1.30002
$669$	−7.53867e34	−0.362634
$670$	−6.10944e35	−2.88447
$671$	−1.17747e35	−0.545656
$672$	8.27905e34	0.376587
$673$	3.45077e33	0.0154073	0.00770367	−	0.999970i	$-0.497548\pi$
$673$	3.45077e33	0.0154073	0.00770367	+	0.999970i	$0.497548\pi$
$674$	1.90340e34	0.0834223
$675$	6.78733e34	0.292013
$676$	−5.49248e35	−2.31972
$677$	8.06730e34	0.334480	0.167240	−	0.985916i	$-0.446515\pi$
$677$	8.06730e34	0.334480	0.167240	+	0.985916i	$0.446515\pi$
$678$	−2.03138e35	−0.826837
$679$	1.42677e35	0.570140
$680$	1.55925e36	6.11721
$681$	3.25268e34	0.125286
$682$	3.09304e35	1.16972
$683$	2.23255e35	0.828976	0.414488	−	0.910055i	$-0.363961\pi$
$683$	2.23255e35	0.828976	0.414488	+	0.910055i	$0.363961\pi$
$684$	1.27717e35	0.465638
$685$	2.20481e35	0.789294
$686$	−4.39276e35	−1.54414
$687$	−1.69070e34	−0.0583591
$688$	−1.82397e35	−0.618249
$689$	−8.65173e33	−0.0287980
$690$	6.24191e34	0.204035
$691$	5.85416e34	0.187927	0.0939635	−	0.995576i	$-0.470046\pi$
$691$	5.85416e34	0.187927	0.0939635	+	0.995576i	$0.470046\pi$
$692$	3.68682e35	1.16232
$693$	3.97617e34	0.123112
$694$	7.60377e35	2.31225
$695$	−8.93773e35	−2.66942
$696$	−3.07671e35	−0.902549
$697$	−1.00906e36	−2.90742
$698$	−4.67099e35	−1.32195
$699$	2.37106e35	0.659141
$700$	−6.17172e35	−1.68531
$701$	2.70419e35	0.725374	0.362687	−	0.931911i	$-0.381859\pi$
$701$	2.70419e35	0.725374	0.362687	+	0.931911i	$0.381859\pi$
$702$	4.34857e33	0.0114586
$703$	2.06021e35	0.533298
$704$	−1.26096e35	−0.320658
$705$	−6.56769e35	−1.64077
$706$	6.89808e35	1.69305
$707$	−2.67064e35	−0.643980
$708$	2.46618e35	0.584263
$709$	1.94778e35	0.453380	0.226690	−	0.973967i	$-0.427210\pi$
$709$	1.94778e35	0.453380	0.226690	+	0.973967i	$0.427210\pi$
$710$	1.30933e35	0.299446
$711$	−9.17562e34	−0.206189
$712$	4.18838e35	0.924796
$713$	4.68107e34	0.101561
$714$	3.77705e35	0.805240
$715$	−1.91039e34	−0.0400217
$716$	−1.14902e36	−2.36545
$717$	−2.56154e35	−0.518217
$718$	−5.00319e35	−0.994698
$719$	8.86817e35	1.73270	0.866349	−	0.499439i	$-0.166460\pi$
$719$	8.86817e35	1.73270	0.866349	+	0.499439i	$0.166460\pi$
$720$	−5.70240e35	−1.09497
$721$	−1.02257e35	−0.192975
$722$	6.27107e35	1.16313
$723$	3.07482e35	0.560520
$724$	1.83187e36	3.28218
$725$	5.58899e35	0.984256
$726$	2.45441e35	0.424854
$727$	−9.02343e35	−1.53529	−0.767647	−	0.640873i	$-0.778572\pi$
$727$	−9.02343e35	−1.53529	−0.767647	+	0.640873i	$0.778572\pi$
$728$	−2.25139e34	−0.0376537
$729$	2.25284e34	0.0370370
$730$	−5.72448e35	−0.925124
$731$	−3.00714e35	−0.477734
$732$	6.06628e35	0.947401
$733$	3.06632e35	0.470780	0.235390	−	0.971901i	$-0.424363\pi$
$733$	3.06632e35	0.470780	0.235390	+	0.971901i	$0.424363\pi$
$734$	−1.54536e36	−2.33255
$735$	4.76088e35	0.706472
$736$	−1.14230e35	−0.166651
$737$	5.36969e35	0.770203
$738$	7.82939e35	1.10414
$739$	4.29197e35	0.595116	0.297558	−	0.954704i	$-0.403828\pi$
$739$	4.29197e35	0.595116	0.297558	+	0.954704i	$0.403828\pi$
$740$	−2.39588e36	−3.26639
$741$	−8.46332e33	−0.0113452
$742$	5.83069e35	0.768549
$743$	−1.95047e35	−0.252802	−0.126401	−	0.991979i	$-0.540343\pi$
$743$	−1.95047e35	−0.252802	−0.126401	+	0.991979i	$0.540343\pi$
$744$	−9.07306e35	−1.15636
$745$	−6.80592e35	−0.852970
$746$	1.24201e36	1.53070
$747$	2.87907e35	0.348935
$748$	−2.40694e36	−2.86877
$749$	−2.55187e33	−0.00299114
$750$	7.49321e35	0.863778
$751$	2.08963e35	0.236902	0.118451	−	0.992960i	$-0.462207\pi$
$751$	2.08963e35	0.236902	0.118451	+	0.992960i	$0.462207\pi$
$752$	3.32593e36	3.70843
$753$	−3.22443e35	−0.353602
$754$	3.58080e34	0.0386223
$755$	1.74183e36	1.84785
$756$	−2.04851e35	−0.213754
$757$	−1.28831e36	−1.32227	−0.661137	−	0.750265i	$-0.729926\pi$
$757$	−1.28831e36	−1.32227	−0.661137	+	0.750265i	$0.729926\pi$
$758$	−8.18387e35	−0.826216
$759$	−5.48611e34	−0.0544807
$760$	2.35462e36	2.30012
$761$	−2.73417e35	−0.262735	−0.131368	−	0.991334i	$-0.541937\pi$
$761$	−2.73417e35	−0.262735	−0.131368	+	0.991334i	$0.541937\pi$
$762$	−2.16003e36	−2.04185
$763$	−6.01602e35	−0.559439
$764$	−4.72762e36	−4.32489
$765$	−9.40141e35	−0.846107
$766$	6.18684e35	0.547784
$767$	−1.63424e34	−0.0142355
$768$	−1.02490e36	−0.878343
$769$	1.06271e34	0.00896056	0.00448028	−	0.999990i	$-0.498574\pi$
$769$	1.06271e34	0.00896056	0.00448028	+	0.999990i	$0.498574\pi$
$770$	1.28747e36	1.06808
$771$	1.16978e36	0.954828
$772$	1.95015e36	1.56622
$773$	6.61075e35	0.522405	0.261202	−	0.965284i	$-0.415881\pi$
$773$	6.61075e35	0.522405	0.261202	+	0.965284i	$0.415881\pi$
$774$	2.33327e35	0.181427
$775$	1.64816e36	1.26104
$776$	3.81559e36	2.87270
$777$	−3.30445e35	−0.244814
$778$	−4.25243e35	−0.310022
$779$	−1.52378e36	−1.09321
$780$	9.84223e34	0.0694882
$781$	−1.15079e35	−0.0799572
$782$	−5.21138e35	−0.356343
$783$	1.85509e35	0.124837
$784$	−2.41094e36	−1.59675
$785$	−1.35504e36	−0.883243
$786$	2.06447e36	1.32442
$787$	9.38912e35	0.592845	0.296422	−	0.955057i	$-0.404206\pi$
$787$	9.38912e35	0.592845	0.296422	+	0.955057i	$0.404206\pi$
$788$	3.72379e36	2.31423
$789$	3.15570e35	0.193034
$790$	−2.97104e36	−1.78884
$791$	−6.34122e35	−0.375809
$792$	1.06334e36	0.620310
$793$	−4.01988e34	−0.0230833
$794$	1.52479e36	0.861896
$795$	−1.45131e36	−0.807553
$796$	−1.25703e36	−0.688543
$797$	−1.30825e36	−0.705443	−0.352722	−	0.935728i	$-0.614744\pi$
$797$	−1.30825e36	−0.705443	−0.352722	+	0.935728i	$0.614744\pi$
$798$	5.70372e35	0.302776
$799$	5.48337e36	2.86558
$800$	−4.02194e36	−2.06924
$801$	−2.52536e35	−0.127914
$802$	−3.92982e36	−1.95972
$803$	5.03133e35	0.247024
$804$	−2.76644e36	−1.33727
$805$	1.94849e35	0.0927364
$806$	1.05596e35	0.0494834
$807$	−6.86824e35	−0.316903
$808$	−7.14206e36	−3.24475
$809$	3.36117e36	1.50361	0.751804	−	0.659387i	$-0.229184\pi$
$809$	3.36117e36	1.50361	0.751804	+	0.659387i	$0.229184\pi$
$810$	7.29464e35	0.321323
$811$	−2.22072e36	−0.963236	−0.481618	−	0.876381i	$-0.659951\pi$
$811$	−2.22072e36	−0.963236	−0.481618	+	0.876381i	$0.659951\pi$
$812$	−1.68683e36	−0.720478
$813$	1.81152e36	0.761925
$814$	3.01258e36	1.24777
$815$	−5.78411e36	−2.35921
$816$	4.76094e36	1.91234
$817$	−4.54108e35	−0.179632
$818$	−9.17210e35	−0.357316
$819$	1.35746e34	0.00520810
$820$	1.77204e37	6.69579
$821$	3.92309e36	1.45995	0.729976	−	0.683473i	$-0.239531\pi$
$821$	3.92309e36	1.45995	0.729976	+	0.683473i	$0.239531\pi$
$822$	1.42829e36	0.523503
$823$	−1.63151e36	−0.588969	−0.294485	−	0.955656i	$-0.595148\pi$
$823$	−1.63151e36	−0.588969	−0.294485	+	0.955656i	$0.595148\pi$
$824$	−2.73464e36	−0.972320
$825$	−1.93161e36	−0.676466
$826$	1.10137e36	0.379911
$827$	−4.43738e36	−1.50767	−0.753837	−	0.657061i	$-0.771799\pi$
$827$	−4.43738e36	−1.50767	−0.753837	+	0.657061i	$0.771799\pi$
$828$	2.82642e35	0.0945927
$829$	9.36913e35	0.308864	0.154432	−	0.988003i	$-0.450645\pi$
$829$	9.36913e35	0.308864	0.154432	+	0.988003i	$0.450645\pi$
$830$	9.32237e36	3.02726
$831$	−1.58342e35	−0.0506506
$832$	−4.30490e34	−0.0135650
$833$	−3.97486e36	−1.23384
$834$	−5.78993e36	−1.77051
$835$	−2.94852e36	−0.888225
$836$	−3.63472e36	−1.07868
$837$	5.47056e35	0.159942
$838$	−2.19264e36	−0.631564
$839$	−2.63649e36	−0.748173	−0.374087	−	0.927394i	$-0.622044\pi$
$839$	−2.63649e36	−0.748173	−0.374087	+	0.927394i	$0.622044\pi$
$840$	−3.77666e36	−1.05588
$841$	−2.10280e36	−0.579227
$842$	−3.65247e35	−0.0991254
$843$	3.75669e36	1.00453
$844$	4.85101e36	1.27806
$845$	6.10543e36	1.58492
$846$	−4.25460e36	−1.08825
$847$	7.66177e35	0.193102
$848$	7.34955e36	1.82521
$849$	2.86789e36	0.701806
$850$	−1.83488e37	−4.42457
$851$	4.55931e35	0.108338
$852$	5.92882e35	0.138827
$853$	5.93992e36	1.37062	0.685311	−	0.728251i	$-0.259666\pi$
$853$	5.93992e36	1.37062	0.685311	+	0.728251i	$0.259666\pi$
$854$	2.70913e36	0.616037
$855$	−1.41970e36	−0.318142
$856$	−6.82445e34	−0.0150711
$857$	−2.46464e36	−0.536405	−0.268203	−	0.963363i	$-0.586430\pi$
$857$	−2.46464e36	−0.536405	−0.268203	+	0.963363i	$0.586430\pi$
$858$	−1.23756e35	−0.0265446
$859$	−6.83001e35	−0.144380	−0.0721900	−	0.997391i	$-0.522999\pi$
$859$	−6.83001e35	−0.144380	−0.0721900	+	0.997391i	$0.522999\pi$
$860$	5.28094e36	1.10022
$861$	2.44404e36	0.501845
$862$	−2.20207e36	−0.445646
$863$	7.39949e36	1.47593	0.737967	−	0.674837i	$-0.235786\pi$
$863$	7.39949e36	1.47593	0.737967	+	0.674837i	$0.235786\pi$
$864$	−1.33496e36	−0.262449
$865$	−4.09826e36	−0.794142
$866$	−1.12384e37	−2.14650
$867$	4.78250e36	0.900361
$868$	−4.97438e36	−0.923086
$869$	2.61130e36	0.477649
$870$	6.00672e36	1.08305
$871$	1.83321e35	0.0325825
$872$	−1.60886e37	−2.81878
$873$	−2.30059e36	−0.397339
$874$	−7.86969e35	−0.133988
$875$	2.33910e36	0.392598
$876$	−2.59212e36	−0.428898
$877$	3.76381e36	0.613950	0.306975	−	0.951718i	$-0.400683\pi$
$877$	3.76381e36	0.613950	0.306975	+	0.951718i	$0.400683\pi$
$878$	2.00057e37	3.21716
$879$	−4.79350e36	−0.759962
$880$	1.62285e37	2.53656
$881$	7.87780e35	0.121396	0.0606982	−	0.998156i	$-0.480667\pi$
$881$	7.87780e35	0.121396	0.0606982	+	0.998156i	$0.480667\pi$
$882$	3.08413e36	0.468571
$883$	−5.36502e36	−0.803642	−0.401821	−	0.915718i	$-0.631623\pi$
$883$	−5.36502e36	−0.803642	−0.401821	+	0.915718i	$0.631623\pi$
$884$	−8.21729e35	−0.121360
$885$	−2.74140e36	−0.399192
$886$	1.52640e37	2.19153
$887$	−4.88027e36	−0.690873	−0.345437	−	0.938442i	$-0.612269\pi$
$887$	−4.88027e36	−0.690873	−0.345437	+	0.938442i	$0.612269\pi$
$888$	−8.83705e36	−1.23352
$889$	−6.74282e36	−0.928046
$890$	−8.17706e36	−1.10974
$891$	−6.41138e35	−0.0857986
$892$	−1.10532e37	−1.45857
$893$	8.28043e36	1.07748
$894$	−4.40893e36	−0.565737
$895$	1.27725e37	1.61617
$896$	−2.32606e36	−0.290249
$897$	−1.87296e34	−0.00230474
$898$	1.54293e37	1.87237
$899$	4.50470e36	0.539100
$900$	9.95159e36	1.17452
$901$	1.21170e37	1.41038
$902$	−2.22817e37	−2.55780
$903$	7.28360e35	0.0824611
$904$	−1.69582e37	−1.89354
$905$	−2.03630e37	−2.24252
$906$	1.12837e37	1.22560
$907$	−1.83038e37	−1.96087	−0.980436	−	0.196838i	$-0.936933\pi$
$907$	−1.83038e37	−1.96087	−0.980436	+	0.196838i	$0.936933\pi$
$908$	4.76908e36	0.503920
$909$	4.30627e36	0.448800
$910$	4.39543e35	0.0451839
$911$	−4.72782e36	−0.479381	−0.239691	−	0.970849i	$-0.577046\pi$
$911$	−4.72782e36	−0.479381	−0.239691	+	0.970849i	$0.577046\pi$
$912$	7.18949e36	0.719056
$913$	−8.19358e36	−0.808330
$914$	−7.86177e36	−0.765056
$915$	−6.74327e36	−0.647302
$916$	−2.47891e36	−0.234729
$917$	6.44450e36	0.601967
$918$	−6.09031e36	−0.561184
$919$	−1.78158e37	−1.61943	−0.809713	−	0.586826i	$-0.800377\pi$
$919$	−1.78158e37	−1.61943	−0.809713	+	0.586826i	$0.800377\pi$
$920$	5.21083e36	0.467261
$921$	−7.33781e36	−0.649114
$922$	3.44469e37	3.00617
$923$	−3.92879e34	−0.00338250
$924$	5.82986e36	0.495175
$925$	1.60529e37	1.34519
$926$	1.39280e37	1.15147
$927$	1.64884e36	0.134487
$928$	−1.09926e37	−0.884608
$929$	−6.06870e36	−0.481836	−0.240918	−	0.970545i	$-0.577448\pi$
$929$	−6.06870e36	−0.481836	−0.240918	+	0.970545i	$0.577448\pi$
$930$	1.77135e37	1.38761
$931$	−6.00243e36	−0.463934
$932$	3.47645e37	2.65117
$933$	−5.19304e36	−0.390752
$934$	2.59415e37	1.92601
$935$	2.67556e37	1.96006
$936$	3.63025e35	0.0262415
$937$	1.32075e37	0.942050	0.471025	−	0.882120i	$-0.343884\pi$
$937$	1.32075e37	0.942050	0.471025	+	0.882120i	$0.343884\pi$
$938$	−1.23546e37	−0.869548
$939$	−8.32359e36	−0.578084
$940$	−9.62954e37	−6.59945
$941$	6.25296e36	0.422879	0.211439	−	0.977391i	$-0.432185\pi$
$941$	6.25296e36	0.422879	0.211439	+	0.977391i	$0.432185\pi$
$942$	−8.77803e36	−0.585815
$943$	−3.37217e36	−0.222082
$944$	1.38827e37	0.902241
$945$	2.27712e36	0.146045
$946$	−6.64027e36	−0.420287
$947$	1.04311e37	0.651562	0.325781	−	0.945445i	$-0.394373\pi$
$947$	1.04311e37	0.651562	0.325781	+	0.945445i	$0.394373\pi$
$948$	−1.34533e37	−0.829324
$949$	1.71769e35	0.0104500
$950$	−2.77085e37	−1.66367
$951$	1.65832e36	0.0982678
$952$	3.15314e37	1.84408
$953$	−2.88829e37	−1.66717	−0.833583	−	0.552394i	$-0.813714\pi$
$953$	−2.88829e37	−1.66717	−0.833583	+	0.552394i	$0.813714\pi$
$954$	−9.40170e36	−0.535614
$955$	5.25521e37	2.95494
$956$	−3.75573e37	−2.08435
$957$	−5.27941e36	−0.289192
$958$	−1.27805e36	−0.0691002
$959$	4.45860e36	0.237939
$960$	−7.22139e36	−0.380391
$961$	−5.94867e36	−0.309298
$962$	1.02849e36	0.0527853
$963$	4.11477e34	0.00208457
$964$	4.50830e37	2.25450
$965$	−2.16779e37	−1.07010
$966$	1.26225e36	0.0615079
$967$	8.77630e36	0.422164	0.211082	−	0.977468i	$-0.432301\pi$
$967$	8.77630e36	0.422164	0.211082	+	0.977468i	$0.432301\pi$
$968$	2.04898e37	0.972961
$969$	1.18531e37	0.555630
$970$	−7.44926e37	−3.44720
$971$	1.71685e37	0.784316	0.392158	−	0.919898i	$-0.371729\pi$
$971$	1.71685e37	0.784316	0.392158	+	0.919898i	$0.371729\pi$
$972$	3.30311e36	0.148969
$973$	−1.80740e37	−0.804719
$974$	2.00304e37	0.880446
$975$	−6.59452e35	−0.0286171
$976$	3.41484e37	1.46301
$977$	2.24823e37	0.950950	0.475475	−	0.879729i	$-0.342276\pi$
$977$	2.24823e37	0.950950	0.475475	+	0.879729i	$0.342276\pi$
$978$	−3.74699e37	−1.56476
$979$	7.18695e36	0.296320
$980$	6.98040e37	2.84154
$981$	9.70053e36	0.389882
$982$	1.45899e35	0.00578975
$983$	−9.07200e36	−0.355455	−0.177727	−	0.984080i	$-0.556875\pi$
$983$	−9.07200e36	−0.355455	−0.177727	+	0.984080i	$0.556875\pi$
$984$	6.53608e37	2.52859
$985$	−4.13936e37	−1.58118
$986$	−5.01502e37	−1.89152
$987$	−1.32813e37	−0.494625
$988$	−1.24089e36	−0.0456323
$989$	−1.00495e36	−0.0364915
$990$	−2.07599e37	−0.744363
$991$	−4.66534e37	−1.65182	−0.825910	−	0.563802i	$-0.809338\pi$
$991$	−4.66534e37	−1.65182	−0.825910	+	0.563802i	$0.809338\pi$
$992$	−3.24167e37	−1.13337
$993$	1.58343e37	0.546680
$994$	2.64774e36	0.0902706
$995$	1.39731e37	0.470440
$996$	4.22130e37	1.40347
$997$	−4.58896e36	−0.150669	−0.0753346	−	0.997158i	$-0.524002\pi$
$997$	−4.58896e36	−0.150669	−0.0753346	+	0.997158i	$0.524002\pi$
$998$	−5.90206e37	−1.91369
$999$	5.32826e36	0.170615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.26.a.b.1.1	✓	3
3.2	odd	2		9.26.a.c.1.3		3
4.3	odd	2		48.26.a.i.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.26.a.b.1.1	✓	3	1.1	even	1	trivial
9.26.a.c.1.3		3	3.2	odd	2
48.26.a.i.1.1		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-10558.1 q^{2} +531441. q^{3} +7.79199e7 q^{4} -8.66156e8 q^{5} -5.61103e9 q^{6} -1.75156e10 q^{7} -4.68416e11 q^{8} +2.82430e11 q^{9} +O(q^{10})\)	\(q-10558.1 q^{2} +531441. q^{3} +7.79199e7 q^{4} -8.66156e8 q^{5} -5.61103e9 q^{6} -1.75156e10 q^{7} -4.68416e11 q^{8} +2.82430e11 q^{9} +9.14500e12 q^{10} -8.03769e12 q^{11} +4.14098e13 q^{12} -2.74406e12 q^{13} +1.84932e14 q^{14} -4.60311e14 q^{15} +2.33105e15 q^{16} +3.84314e15 q^{17} -2.98193e15 q^{18} +5.80352e15 q^{19} -6.74908e16 q^{20} -9.30848e15 q^{21} +8.48630e16 q^{22} +1.28434e16 q^{23} -2.48936e17 q^{24} +4.52204e17 q^{25} +2.89722e16 q^{26} +1.50095e17 q^{27} -1.36481e18 q^{28} +1.23594e18 q^{29} +4.86003e18 q^{30} +3.64474e18 q^{31} -8.89410e18 q^{32} -4.27156e18 q^{33} -4.05764e19 q^{34} +1.51712e19 q^{35} +2.20069e19 q^{36} +3.54993e19 q^{37} -6.12744e19 q^{38} -1.45831e18 q^{39} +4.05722e20 q^{40} -2.62561e20 q^{41} +9.82803e19 q^{42} -7.82469e19 q^{43} -6.26295e20 q^{44} -2.44628e20 q^{45} -1.35602e20 q^{46} +1.42679e21 q^{47} +1.23882e21 q^{48} -1.03427e21 q^{49} -4.77443e21 q^{50} +2.04240e21 q^{51} -2.13817e20 q^{52} +3.15289e21 q^{53} -1.58472e21 q^{54} +6.96189e21 q^{55} +8.20457e21 q^{56} +3.08423e21 q^{57} -1.30493e22 q^{58} +5.95554e21 q^{59} -3.58674e22 q^{60} +1.46494e22 q^{61} -3.84817e22 q^{62} -4.94691e21 q^{63} +1.56881e22 q^{64} +2.37679e21 q^{65} +4.50997e22 q^{66} -6.68064e22 q^{67} +2.99457e23 q^{68} +6.82549e21 q^{69} -1.60180e23 q^{70} +1.43174e22 q^{71} -1.32295e23 q^{72} -6.25968e22 q^{73} -3.74807e23 q^{74} +2.40320e23 q^{75} +4.52210e23 q^{76} +1.40785e23 q^{77} +1.53970e22 q^{78} -3.24882e23 q^{79} -2.01905e24 q^{80} +7.97664e22 q^{81} +2.77216e24 q^{82} +1.01939e24 q^{83} -7.25316e23 q^{84} -3.32876e24 q^{85} +8.26142e23 q^{86} +6.56832e23 q^{87} +3.76498e24 q^{88} -8.94156e23 q^{89} +2.58282e24 q^{90} +4.80638e22 q^{91} +1.00075e24 q^{92} +1.93696e24 q^{93} -1.50643e25 q^{94} -5.02676e24 q^{95} -4.72669e24 q^{96} -8.14572e24 q^{97} +1.09200e25 q^{98} -2.27008e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9}+O(q^{10}) \) 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9	\( 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9} + 8363188874700 q^{10} - 5946998130780 q^{11} + 48226988914308 q^{12} + 248137774407690 q^{13} + 754361641264848 q^{14} - 86706060612750 q^{15} + 23\!\cdots\!16 q^{16}+ \cdots - 16\!\cdots\!80 q^{99}+O(q^{100}) \) 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9 + 8363188874700 * q^10 - 5946998130780 * q^11 + 48226988914308 * q^12 + 248137774407690 * q^13 + 754361641264848 * q^14 - 86706060612750 * q^15 + 2394637852352016 * q^16 + 6640885201245174 * q^17 - 1038775835177118 * q^18 - 4282718959080516 * q^19 - 84999590549092200 * q^20 - 5113829681644104 * q^21 - 67279455312049512 * q^22 - 54558955951564152 * q^23 - 142433006732403768 * q^24 + 285270827389168125 * q^25 + 914405315527228956 * q^26 + 450283905890997363 * q^27 + 2416760102519597472 * q^28 - 506350856671782 * q^29 + 4444541458759442700 * q^30 - 120595458951353856 * q^31 - 23423805952813711584 * q^32 - 3160478633619853980 * q^33 - 30744163051965656604 * q^34 - 12895712434403329200 * q^35 + 25629799215608757828 * q^36 + 71124029266471833426 * q^37 - 151631523417421211736 * q^38 + 131870586968997181290 * q^39 + 487276555770533818800 * q^40 - 178237898435247428226 * q^41 + 400898704995432085968 * q^42 + 233732145791955002244 * q^43 - 1709130121883010683088 * q^44 - 46079155558100472750 * q^45 - 727064486838202905936 * q^46 - 578974907441950806192 * q^47 + 1272608734891807735056 * q^48 + 1540848623287695627627 * q^49 - 7598435156177129081250 * q^50 + 3529238672234936515734 * q^51 + 1549295968705274668344 * q^52 + 9056010625929165756258 * q^53 - 552048068622362767038 * q^54 + 16758715188531155952600 * q^55 + 7112451608305863332160 * q^56 - 2276012446332708503556 * q^57 - 43337630795958244629252 * q^58 + 23769324802557802948596 * q^59 - 45172267401000107860200 * q^60 - 11371716695373075009318 * q^61 - 21881713022451611321088 * q^62 - 2717698759842624273864 * q^63 - 55686925877484831566784 * q^64 + 89289247460368023248700 * q^65 - 35755061010490904706792 * q^66 + 52213761253321486240524 * q^67 + 318831609976592944413384 * q^68 - 28994866109855204503032 * q^69 - 78749858107500801357600 * q^70 + 262955361870665606618136 * q^71 - 75694739530875390869688 * q^72 - 11752720924176446629602 * q^73 - 498161580663483575957172 * q^74 + 151604613778526897518125 * q^75 + 4571105415149082363216 * q^76 - 1386525122949230445864288 * q^77 + 485952475289106083605596 * q^78 - 500543105756664483755760 * q^79 - 1540345885402641092176800 * q^80 + 239299329230617529590083 * q^81 + 4108759898128895060824212 * q^82 - 59055829437561671377284 * q^83 + 1284365405643117400117152 * q^84 - 2357173046017457952925500 * q^85 + 2057662432276923640084440 * q^86 - 269095605620508497862 * q^87 + 4527751242141959006666592 * q^88 - 3359875059386549548018866 * q^89 + 2362011557384576987930700 * q^90 + 1253870789177107094217744 * q^91 - 1905611545816878301689504 * q^92 - 64089371300566444586496 * q^93 - 18037990008720502135322400 * q^94 - 5406514800597015344021400 * q^95 - 12448370859369271697912544 * q^96 - 12029431225244267569541466 * q^97 + 24058796570011739277032850 * q^98 - 1679607925529568818985180 * q^99

Introduction

L-functions

Modular forms

Varieties

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