LMFDB - Embedded newform 10.22.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,22,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, 22, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
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:	$27.9477344287$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1179649}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 294912 $ x^2 - x - 294912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$543.558$ 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)

$f(q)$	$=$	\(q+1024.00 q^{2} -114848. q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} -1.17604e8 q^{6} -2.03949e8 q^{7} +1.07374e9 q^{8} +2.72970e9 q^{9} -1.00000e10 q^{10} -4.40105e10 q^{11} -1.20427e11 q^{12} -1.80893e11 q^{13} -2.08843e11 q^{14} +1.12156e12 q^{15} +1.09951e12 q^{16} +1.29311e13 q^{17} +2.79522e12 q^{18} +3.50261e13 q^{19} -1.02400e13 q^{20} +2.34231e13 q^{21} -4.50668e13 q^{22} -1.00465e14 q^{23} -1.23317e14 q^{24} +9.53674e13 q^{25} -1.85235e14 q^{26} +8.87849e14 q^{27} -2.13856e14 q^{28} +2.65416e15 q^{29} +1.14848e15 q^{30} +1.12512e15 q^{31} +1.12590e15 q^{32} +5.05452e15 q^{33} +1.32415e16 q^{34} +1.99169e15 q^{35} +2.86230e15 q^{36} +2.62794e16 q^{37} +3.58667e16 q^{38} +2.07752e16 q^{39} -1.04858e16 q^{40} -2.80940e16 q^{41} +2.39852e16 q^{42} +1.48308e17 q^{43} -4.61484e16 q^{44} -2.66573e16 q^{45} -1.02876e17 q^{46} -9.51528e16 q^{47} -1.26277e17 q^{48} -5.16951e17 q^{49} +9.76562e16 q^{50} -1.48511e18 q^{51} -1.89680e17 q^{52} +1.03378e18 q^{53} +9.09158e17 q^{54} +4.29790e17 q^{55} -2.18988e17 q^{56} -4.02268e18 q^{57} +2.71786e18 q^{58} -1.03132e18 q^{59} +1.17604e18 q^{60} -8.22371e18 q^{61} +1.15212e18 q^{62} -5.56719e17 q^{63} +1.15292e18 q^{64} +1.76653e18 q^{65} +5.17583e18 q^{66} -1.74709e19 q^{67} +1.35593e19 q^{68} +1.15382e19 q^{69} +2.03949e18 q^{70} +2.67322e19 q^{71} +2.93100e18 q^{72} +5.60167e19 q^{73} +2.69101e19 q^{74} -1.09528e19 q^{75} +3.67275e19 q^{76} +8.97588e18 q^{77} +2.12738e19 q^{78} -4.33055e19 q^{79} -1.07374e19 q^{80} -1.30521e20 q^{81} -2.87683e19 q^{82} -2.59402e20 q^{83} +2.45609e19 q^{84} -1.26280e20 q^{85} +1.51867e20 q^{86} -3.04825e20 q^{87} -4.72559e19 q^{88} +5.09045e20 q^{89} -2.72970e19 q^{90} +3.68929e19 q^{91} -1.05345e20 q^{92} -1.29218e20 q^{93} -9.74364e19 q^{94} -3.42052e20 q^{95} -1.29307e20 q^{96} +6.58070e20 q^{97} -5.29358e20 q^{98} -1.20136e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2048 q^{2} + 30972 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 31715328 q^{6} - 439959356 q^{7} + 2147483648 q^{8} + 13532817186 q^{9} - 20000000000 q^{10} + 105191777184 q^{11} + 32476495872 q^{12}+ \cdots + 14\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 2048 * q^2 + 30972 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 31715328 * q^6 - 439959356 * q^7 + 2147483648 * q^8 + 13532817186 * q^9 - 20000000000 * q^10 + 105191777184 * q^11 + 32476495872 * q^12 + 308456648932 * q^13 - 450518380544 * q^14 - 302460937500 * q^15 + 2199023255552 * q^16 + 18393996100404 * q^17 + 13857604798464 * q^18 + 23821216715800 * q^19 - 20480000000000 * q^20 - 10991999204616 * q^21 + 107716379836416 * q^22 - 82586042978868 * q^23 + 33255931772928 * q^24 + 190734863281250 * q^25 + 315859608506368 * q^26 + 937830505785480 * q^27 - 461330821677056 * q^28 - 167038888446420 * q^29 - 309720000000000 * q^30 + 5373084998145784 * q^31 + 2251799813685248 * q^32 + 26811195444517824 * q^33 + 18835452006813696 * q^34 + 4296478085937500 * q^35 + 14190187313627136 * q^36 + 83725084127912164 * q^37 + 24392925916979200 * q^38 + 92132195361143352 * q^39 - 20971520000000000 * q^40 - 63222375005514036 * q^41 - 11255807185526784 * q^42 - 113835841911164948 * q^43 + 110301572952489984 * q^44 - 132156417832031250 * q^45 - 84568108010360832 * q^46 + 13253549001226164 * q^47 + 34054074135478272 * q^48 - 1019795619700635846 * q^49 + 195312500000000000 * q^50 - 688515197556670056 * q^51 + 323440239110520832 * q^52 - 1445751023743904748 * q^53 + 960338437924331520 * q^54 - 1027263449062500000 * q^55 - 472402761397305344 * q^56 - 5656568844707914800 * q^57 - 171047821769134080 * q^58 - 817060118931432840 * q^59 - 317153280000000000 * q^60 - 4580997169825849436 * q^61 + 5502039038101282816 * q^62 - 3106370208073453308 * q^63 + 2305843009213693952 * q^64 - 3012271962226562500 * q^65 + 27454664135186251776 * q^66 - 28808031668773210556 * q^67 + 19287502854977224704 * q^68 + 14145335707649957352 * q^69 + 4399593560000000000 * q^70 + 51140957732016114984 * q^71 + 14530751809154187264 * q^72 + 14792322512082321412 * q^73 + 85734486146982055936 * q^74 + 2953720092773437500 * q^75 + 24978356138986700800 * q^76 - 26237463329898773952 * q^77 + 94343368049810792448 * q^78 + 25077766877525032720 * q^79 - 21474836480000000000 * q^80 - 236237497961757285078 * q^81 - 64739712005646372864 * q^82 - 120090321897786074868 * q^83 - 11525946557979426816 * q^84 - 179628868168007812500 * q^85 - 116567902117032906752 * q^86 - 716212291756398367320 * q^87 + 112948810703349743616 * q^88 + 104228468137266844980 * q^89 - 135328171860000000000 * q^90 - 78598912899601639096 * q^91 - 86597742602609491968 * q^92 + 490220677944452503824 * q^93 + 13571634177255591936 * q^94 - 232629069490234375000 * q^95 + 34871371914729750528 * q^96 - 260893520515229908796 * q^97 - 1044270714573451106304 * q^98 + 1491713506648872042912 * 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 $

$2$	1024.00	0.707107
$2$	1024.00	0.707107
$3$	−114848.	−1.12292	−0.561462	−	0.827503i	$-0.689761\pi$
$3$	−114848.	−1.12292	−0.561462	+	0.827503i	$0.689761\pi$
$4$	1.04858e6	0.500000
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	−1.17604e8	−0.794027
$7$	−2.03949e8	−0.272892	−0.136446	−	0.990647i	$-0.543568\pi$
$7$	−2.03949e8	−0.272892	−0.136446	+	0.990647i	$0.543568\pi$
$8$	1.07374e9	0.353553
$9$	2.72970e9	0.260957
$10$	−1.00000e10	−0.316228
$11$	−4.40105e10	−0.511603	−0.255802	−	0.966729i	$-0.582339\pi$
$11$	−4.40105e10	−0.511603	−0.255802	+	0.966729i	$0.582339\pi$
$12$	−1.20427e11	−0.561462
$13$	−1.80893e11	−0.363929	−0.181965	−	0.983305i	$-0.558246\pi$
$13$	−1.80893e11	−0.363929	−0.181965	+	0.983305i	$0.558246\pi$
$14$	−2.08843e11	−0.192964
$15$	1.12156e12	0.502187
$16$	1.09951e12	0.250000
$17$	1.29311e13	1.55569	0.777844	−	0.628458i	$-0.216314\pi$
$17$	1.29311e13	1.55569	0.777844	+	0.628458i	$0.216314\pi$
$18$	2.79522e12	0.184525
$19$	3.50261e13	1.31063	0.655313	−	0.755357i	$-0.272537\pi$
$19$	3.50261e13	1.31063	0.655313	+	0.755357i	$0.272537\pi$
$20$	−1.02400e13	−0.223607
$21$	2.34231e13	0.306437
$22$	−4.50668e13	−0.361758
$23$	−1.00465e14	−0.505677	−0.252838	−	0.967509i	$-0.581364\pi$
$23$	−1.00465e14	−0.505677	−0.252838	+	0.967509i	$0.581364\pi$
$24$	−1.23317e14	−0.397013
$25$	9.53674e13	0.200000
$26$	−1.85235e14	−0.257337
$27$	8.87849e14	0.829889
$28$	−2.13856e14	−0.136446
$29$	2.65416e15	1.17152	0.585758	−	0.810486i	$-0.300797\pi$
$29$	2.65416e15	1.17152	0.585758	+	0.810486i	$0.300797\pi$
$30$	1.14848e15	0.355100
$31$	1.12512e15	0.246548	0.123274	−	0.992373i	$-0.460661\pi$
$31$	1.12512e15	0.246548	0.123274	+	0.992373i	$0.460661\pi$
$32$	1.12590e15	0.176777
$33$	5.05452e15	0.574491
$34$	1.32415e16	1.10004
$35$	1.99169e15	0.122041
$36$	2.86230e15	0.130479
$37$	2.62794e16	0.898458	0.449229	−	0.893417i	$-0.351699\pi$
$37$	2.62794e16	0.898458	0.449229	+	0.893417i	$0.351699\pi$
$38$	3.58667e16	0.926753
$39$	2.07752e16	0.408665
$40$	−1.04858e16	−0.158114
$41$	−2.80940e16	−0.326876	−0.163438	−	0.986554i	$-0.552258\pi$
$41$	−2.80940e16	−0.326876	−0.163438	+	0.986554i	$0.552258\pi$
$42$	2.39852e16	0.216684
$43$	1.48308e17	1.04651	0.523257	−	0.852175i	$-0.324717\pi$
$43$	1.48308e17	1.04651	0.523257	+	0.852175i	$0.324717\pi$
$44$	−4.61484e16	−0.255802
$45$	−2.66573e16	−0.116704
$46$	−1.02876e17	−0.357567
$47$	−9.51528e16	−0.263872	−0.131936	−	0.991258i	$-0.542119\pi$
$47$	−9.51528e16	−0.263872	−0.131936	+	0.991258i	$0.542119\pi$
$48$	−1.26277e17	−0.280731
$49$	−5.16951e17	−0.925530
$50$	9.76562e16	0.141421
$51$	−1.48511e18	−1.74692
$52$	−1.89680e17	−0.181965
$53$	1.03378e18	0.811955	0.405978	−	0.913883i	$-0.366931\pi$
$53$	1.03378e18	0.811955	0.405978	+	0.913883i	$0.366931\pi$
$54$	9.09158e17	0.586820
$55$	4.29790e17	0.228796
$56$	−2.18988e17	−0.0964820
$57$	−4.02268e18	−1.47173
$58$	2.71786e18	0.828387
$59$	−1.03132e18	−0.262692	−0.131346	−	0.991337i	$-0.541930\pi$
$59$	−1.03132e18	−0.262692	−0.131346	+	0.991337i	$0.541930\pi$
$60$	1.17604e18	0.251093
$61$	−8.22371e18	−1.47606	−0.738031	−	0.674767i	$-0.764244\pi$
$61$	−8.22371e18	−1.47606	−0.738031	+	0.674767i	$0.764244\pi$
$62$	1.15212e18	0.174335
$63$	−5.56719e17	−0.0712132
$64$	1.15292e18	0.125000
$65$	1.76653e18	0.162754
$66$	5.17583e18	0.406227
$67$	−1.74709e19	−1.17092	−0.585462	−	0.810700i	$-0.699087\pi$
$67$	−1.74709e19	−1.17092	−0.585462	+	0.810700i	$0.699087\pi$
$68$	1.35593e19	0.777844
$69$	1.15382e19	0.567836
$70$	2.03949e18	0.0862961
$71$	2.67322e19	0.974591	0.487296	−	0.873237i	$-0.337983\pi$
$71$	2.67322e19	0.974591	0.487296	+	0.873237i	$0.337983\pi$
$72$	2.93100e18	0.0922623
$73$	5.60167e19	1.52555	0.762777	−	0.646662i	$-0.223836\pi$
$73$	5.60167e19	1.52555	0.762777	+	0.646662i	$0.223836\pi$
$74$	2.69101e19	0.635306
$75$	−1.09528e19	−0.224585
$76$	3.67275e19	0.655313
$77$	8.97588e18	0.139613
$78$	2.12738e19	0.288970
$79$	−4.33055e19	−0.514587	−0.257293	−	0.966333i	$-0.582831\pi$
$79$	−4.33055e19	−0.514587	−0.257293	+	0.966333i	$0.582831\pi$
$80$	−1.07374e19	−0.111803
$81$	−1.30521e20	−1.19286
$82$	−2.87683e19	−0.231137
$83$	−2.59402e20	−1.83507	−0.917535	−	0.397655i	$-0.869824\pi$
$83$	−2.59402e20	−1.83507	−0.917535	+	0.397655i	$0.869824\pi$
$84$	2.45609e19	0.153219
$85$	−1.26280e20	−0.695724
$86$	1.51867e20	0.739997
$87$	−3.04825e20	−1.31552
$88$	−4.72559e19	−0.180879
$89$	5.09045e20	1.73046	0.865230	−	0.501376i	$-0.167173\pi$
$89$	5.09045e20	1.73046	0.865230	+	0.501376i	$0.167173\pi$
$90$	−2.72970e19	−0.0825219
$91$	3.68929e19	0.0993135
$92$	−1.05345e20	−0.252838
$93$	−1.29218e20	−0.276854
$94$	−9.74364e19	−0.186586
$95$	−3.42052e20	−0.586130
$96$	−1.29307e20	−0.198507
$97$	6.58070e20	0.906085	0.453042	−	0.891489i	$-0.350339\pi$
$97$	6.58070e20	0.906085	0.453042	+	0.891489i	$0.350339\pi$
$98$	−5.29358e20	−0.654448
$99$	−1.20136e20	−0.133507
$100$	1.00000e20	0.100000
$101$	1.15672e21	1.04197	0.520984	−	0.853566i	$-0.325565\pi$
$101$	1.15672e21	1.04197	0.520984	+	0.853566i	$0.325565\pi$
$102$	−1.52076e21	−1.23526
$103$	2.10354e21	1.54226	0.771132	−	0.636675i	$-0.219691\pi$
$103$	2.10354e21	1.54226	0.771132	+	0.636675i	$0.219691\pi$
$104$	−1.94233e20	−0.128668
$105$	−2.28741e20	−0.137043
$106$	1.05859e21	0.574139
$107$	9.86090e20	0.484604	0.242302	−	0.970201i	$-0.422098\pi$
$107$	9.86090e20	0.484604	0.242302	+	0.970201i	$0.422098\pi$
$108$	9.30978e20	0.414944
$109$	1.78098e21	0.720576	0.360288	−	0.932841i	$-0.382678\pi$
$109$	1.78098e21	0.720576	0.360288	+	0.932841i	$0.382678\pi$
$110$	4.40105e20	0.161783
$111$	−3.01814e21	−1.00890
$112$	−2.24244e20	−0.0682231
$113$	3.61184e21	1.00093	0.500466	−	0.865756i	$-0.333162\pi$
$113$	3.61184e21	1.00093	0.500466	+	0.865756i	$0.333162\pi$
$114$	−4.11922e21	−1.04067
$115$	9.81104e20	0.226145
$116$	2.78309e21	0.585758
$117$	−4.93785e20	−0.0949700
$118$	−1.05607e21	−0.185751
$119$	−2.63728e21	−0.424535
$120$	1.20427e21	0.177550
$121$	−5.46332e21	−0.738262
$122$	−8.42108e21	−1.04373
$123$	3.22654e21	0.367057
$124$	1.17977e21	0.123274
$125$	−9.31323e20	−0.0894427
$126$	−5.70081e20	−0.0503553
$127$	1.58229e22	1.28632	0.643158	−	0.765734i	$-0.277624\pi$
$127$	1.58229e22	1.28632	0.643158	+	0.765734i	$0.277624\pi$
$128$	1.18059e21	0.0883883
$129$	−1.70328e22	−1.17516
$130$	1.80893e21	0.115085
$131$	−1.83709e22	−1.07840	−0.539202	−	0.842176i	$-0.681274\pi$
$131$	−1.83709e22	−1.07840	−0.539202	+	0.842176i	$0.681274\pi$
$132$	5.30005e21	0.287246
$133$	−7.14352e21	−0.357660
$134$	−1.78902e22	−0.827968
$135$	−8.67040e21	−0.371137
$136$	1.38847e22	0.550019
$137$	7.05876e21	0.258918	0.129459	−	0.991585i	$-0.458676\pi$
$137$	7.05876e21	0.258918	0.129459	+	0.991585i	$0.458676\pi$
$138$	1.18151e22	0.401521
$139$	−3.37498e22	−1.06320	−0.531601	−	0.846995i	$-0.678410\pi$
$139$	−3.37498e22	−1.06320	−0.531601	+	0.846995i	$0.678410\pi$
$140$	2.08843e21	0.0610206
$141$	1.09281e22	0.296308
$142$	2.73738e22	0.689140
$143$	7.96120e21	0.186187
$144$	3.00134e21	0.0652393
$145$	−2.59195e22	−0.523918
$146$	5.73611e22	1.07873
$147$	5.93708e22	1.03930
$148$	2.75560e22	0.449229
$149$	−5.68451e22	−0.863451	−0.431725	−	0.902005i	$-0.642095\pi$
$149$	−5.68451e22	−0.863451	−0.431725	+	0.902005i	$0.642095\pi$
$150$	−1.12156e22	−0.158805
$151$	1.33443e23	1.76213	0.881064	−	0.472997i	$-0.156828\pi$
$151$	1.33443e23	1.76213	0.881064	+	0.472997i	$0.156828\pi$
$152$	3.76090e22	0.463376
$153$	3.52981e22	0.405968
$154$	9.19131e21	0.0987210
$155$	−1.09875e22	−0.110259
$156$	2.17844e22	0.204332
$157$	−1.56723e22	−0.137463	−0.0687317	−	0.997635i	$-0.521895\pi$
$157$	−1.56723e22	−0.137463	−0.0687317	+	0.997635i	$0.521895\pi$
$158$	−4.43448e22	−0.363868
$159$	−1.18728e23	−0.911764
$160$	−1.09951e22	−0.0790569
$161$	2.04897e22	0.137995
$162$	−1.33654e23	−0.843478
$163$	1.20617e23	0.713575	0.356788	−	0.934185i	$-0.383872\pi$
$163$	1.20617e23	0.713575	0.356788	+	0.934185i	$0.383872\pi$
$164$	−2.94587e22	−0.163438
$165$	−4.93605e22	−0.256920
$166$	−2.65627e23	−1.29759
$167$	−3.63531e23	−1.66732	−0.833658	−	0.552281i	$-0.813758\pi$
$167$	−3.63531e23	−1.66732	−0.833658	+	0.552281i	$0.813758\pi$
$168$	2.51503e22	0.108342
$169$	−2.14342e23	−0.867555
$170$	−1.29311e23	−0.491952
$171$	9.56109e22	0.342017
$172$	1.55512e23	0.523257
$173$	5.25008e23	1.66219	0.831097	−	0.556127i	$-0.187713\pi$
$173$	5.25008e23	1.66219	0.831097	+	0.556127i	$0.187713\pi$
$174$	−3.12141e23	−0.930215
$175$	−1.94501e22	−0.0545785
$176$	−4.83901e22	−0.127901
$177$	1.18445e23	0.294983
$178$	5.21262e23	1.22362
$179$	−4.28059e23	−0.947428	−0.473714	−	0.880679i	$-0.657087\pi$
$179$	−4.28059e23	−0.947428	−0.473714	+	0.880679i	$0.657087\pi$
$180$	−2.79522e22	−0.0583518
$181$	4.13461e23	0.814346	0.407173	−	0.913351i	$-0.366515\pi$
$181$	4.13461e23	0.814346	0.407173	+	0.913351i	$0.366515\pi$
$182$	3.77783e22	0.0702252
$183$	9.44477e23	1.65750
$184$	−1.07874e23	−0.178784
$185$	−2.56635e23	−0.401803
$186$	−1.32319e23	−0.195765
$187$	−5.69105e23	−0.795895
$188$	−9.97749e22	−0.131936
$189$	−1.81076e23	−0.226470
$190$	−3.50261e23	−0.414456
$191$	7.69492e22	0.0861695	0.0430847	−	0.999071i	$-0.486281\pi$
$191$	7.69492e22	0.0861695	0.0430847	+	0.999071i	$0.486281\pi$
$192$	−1.32411e23	−0.140365
$193$	1.25195e24	1.25671	0.628355	−	0.777926i	$-0.283728\pi$
$193$	1.25195e24	1.25671	0.628355	+	0.777926i	$0.283728\pi$
$194$	6.73864e23	0.640699
$195$	−2.02883e23	−0.182760
$196$	−5.42062e23	−0.462765
$197$	9.01149e23	0.729292	0.364646	−	0.931146i	$-0.381190\pi$
$197$	9.01149e23	0.729292	0.364646	+	0.931146i	$0.381190\pi$
$198$	−1.23019e23	−0.0944034
$199$	−9.25260e23	−0.673452	−0.336726	−	0.941603i	$-0.609320\pi$
$199$	−9.25260e23	−0.673452	−0.336726	+	0.941603i	$0.609320\pi$
$200$	1.02400e23	0.0707107
$201$	2.00649e24	1.31486
$202$	1.18448e24	0.736783
$203$	−5.41312e23	−0.319698
$204$	−1.55725e24	−0.873459
$205$	2.74356e23	0.146184
$206$	2.15402e24	1.09055
$207$	−2.74240e23	−0.131960
$208$	−1.98894e23	−0.0909823
$209$	−1.54152e24	−0.670521
$210$	−2.34231e23	−0.0969040
$211$	−9.91626e23	−0.390285	−0.195143	−	0.980775i	$-0.562517\pi$
$211$	−9.91626e23	−0.390285	−0.195143	+	0.980775i	$0.562517\pi$
$212$	1.08400e24	0.405978
$213$	−3.07014e24	−1.09439
$214$	1.00976e24	0.342667
$215$	−1.44832e24	−0.468015
$216$	9.53321e23	0.293410
$217$	−2.29466e23	−0.0672809
$218$	1.82372e24	0.509524
$219$	−6.43340e24	−1.71308
$220$	4.50668e23	0.114398
$221$	−2.33915e24	−0.566160
$222$	−3.09057e24	−0.713400
$223$	−3.99965e24	−0.880687	−0.440343	−	0.897829i	$-0.645143\pi$
$223$	−3.99965e24	−0.880687	−0.440343	+	0.897829i	$0.645143\pi$
$224$	−2.29626e23	−0.0482410
$225$	2.60325e23	0.0521914
$226$	3.69852e24	0.707766
$227$	5.28899e24	0.966276	0.483138	−	0.875544i	$-0.339497\pi$
$227$	5.28899e24	0.966276	0.483138	+	0.875544i	$0.339497\pi$
$228$	−4.21808e24	−0.735866
$229$	−1.05761e24	−0.176219	−0.0881095	−	0.996111i	$-0.528083\pi$
$229$	−1.05761e24	−0.176219	−0.0881095	+	0.996111i	$0.528083\pi$
$230$	1.00465e24	0.159909
$231$	−1.03086e24	−0.156774
$232$	2.84988e24	0.414193
$233$	1.05916e25	1.47138	0.735691	−	0.677317i	$-0.236857\pi$
$233$	1.05916e25	1.47138	0.735691	+	0.677317i	$0.236857\pi$
$234$	−5.05636e23	−0.0671539
$235$	9.29226e23	0.118007
$236$	−1.08142e24	−0.131346
$237$	4.97355e24	0.577841
$238$	−2.70058e24	−0.300192
$239$	1.72062e25	1.83023	0.915115	−	0.403192i	$-0.132099\pi$
$239$	1.72062e25	1.83023	0.915115	+	0.403192i	$0.132099\pi$
$240$	1.23317e24	0.125547
$241$	−1.73077e25	−1.68679	−0.843394	−	0.537295i	$-0.819446\pi$
$241$	−1.73077e25	−1.68679	−0.843394	+	0.537295i	$0.819446\pi$
$242$	−5.59444e24	−0.522030
$243$	5.70290e24	0.509600
$244$	−8.62319e24	−0.738031
$245$	5.04835e24	0.413910
$246$	3.30398e24	0.259549
$247$	−6.33598e24	−0.476975
$248$	1.20809e24	0.0871677
$249$	2.97917e25	2.06064
$250$	−9.53674e23	−0.0632456
$251$	−9.29670e24	−0.591227	−0.295614	−	0.955308i	$-0.595524\pi$
$251$	−9.29670e24	−0.591227	−0.295614	+	0.955308i	$0.595524\pi$
$252$	−5.83763e23	−0.0356066
$253$	4.42152e24	0.258706
$254$	1.62027e25	0.909562
$255$	1.45031e25	0.781245
$256$	1.20893e24	0.0625000
$257$	9.32271e24	0.462641	0.231321	−	0.972878i	$-0.425695\pi$
$257$	9.32271e24	0.462641	0.231321	+	0.972878i	$0.425695\pi$
$258$	−1.74416e25	−0.830960
$259$	−5.35965e24	−0.245182
$260$	1.85235e24	0.0813771
$261$	7.24508e24	0.305716
$262$	−1.88118e25	−0.762547
$263$	−2.87230e25	−1.11865	−0.559325	−	0.828948i	$-0.688940\pi$
$263$	−2.87230e25	−1.11865	−0.559325	+	0.828948i	$0.688940\pi$
$264$	5.42725e24	0.203113
$265$	−1.00955e25	−0.363117
$266$	−7.31497e24	−0.252904
$267$	−5.84628e25	−1.94317
$268$	−1.83195e25	−0.585462
$269$	2.41759e25	0.742991	0.371495	−	0.928435i	$-0.378845\pi$
$269$	2.41759e25	0.742991	0.371495	+	0.928435i	$0.378845\pi$
$270$	−8.87849e24	−0.262434
$271$	−4.48847e25	−1.27621	−0.638103	−	0.769951i	$-0.720280\pi$
$271$	−4.48847e25	−1.27621	−0.638103	+	0.769951i	$0.720280\pi$
$272$	1.42179e25	0.388922
$273$	−4.23708e24	−0.111521
$274$	7.22817e24	0.183083
$275$	−4.19717e24	−0.102321
$276$	1.20987e25	0.283918
$277$	−1.57653e25	−0.356176	−0.178088	−	0.984015i	$-0.556991\pi$
$277$	−1.57653e25	−0.356176	−0.178088	+	0.984015i	$0.556991\pi$
$278$	−3.45598e25	−0.751798
$279$	3.07124e24	0.0643384
$280$	2.13856e24	0.0431481
$281$	9.40593e25	1.82804	0.914019	−	0.405671i	$-0.132962\pi$
$281$	9.40593e25	1.82804	0.914019	+	0.405671i	$0.132962\pi$
$282$	1.11904e25	0.209522
$283$	−4.41232e25	−0.795993	−0.397997	−	0.917387i	$-0.630294\pi$
$283$	−4.41232e25	−0.795993	−0.397997	+	0.917387i	$0.630294\pi$
$284$	2.80308e25	0.487296
$285$	3.92839e25	0.658179
$286$	8.15227e24	0.131654
$287$	5.72974e24	0.0892021
$288$	3.07337e24	0.0461312
$289$	9.81218e25	1.42016
$290$	−2.65416e25	−0.370466
$291$	−7.55780e25	−1.01746
$292$	5.87378e25	0.762777
$293$	2.98120e25	0.373492	0.186746	−	0.982408i	$-0.440206\pi$
$293$	2.98120e25	0.373492	0.186746	+	0.982408i	$0.440206\pi$
$294$	6.07957e25	0.734895
$295$	1.00715e25	0.117479
$296$	2.82173e25	0.317653
$297$	−3.90747e25	−0.424574
$298$	−5.82094e25	−0.610552
$299$	1.81734e25	0.184031
$300$	−1.14848e25	−0.112292
$301$	−3.02472e25	−0.285586
$302$	1.36645e26	1.24601
$303$	−1.32847e26	−1.17005
$304$	3.85116e25	0.327657
$305$	8.03097e25	0.660115
$306$	3.61453e25	0.287063
$307$	−4.58514e25	−0.351884	−0.175942	−	0.984401i	$-0.556297\pi$
$307$	−4.58514e25	−0.351884	−0.175942	+	0.984401i	$0.556297\pi$
$308$	9.41190e24	0.0698063
$309$	−2.41587e26	−1.73185
$310$	−1.12512e25	−0.0779652
$311$	−1.30419e26	−0.873691	−0.436845	−	0.899537i	$-0.643904\pi$
$311$	−1.30419e26	−0.873691	−0.436845	+	0.899537i	$0.643904\pi$
$312$	2.23072e25	0.144485
$313$	2.68379e26	1.68087	0.840434	−	0.541914i	$-0.182300\pi$
$313$	2.68379e26	1.68087	0.840434	+	0.541914i	$0.182300\pi$
$314$	−1.60485e25	−0.0972013
$315$	5.43671e24	0.0318475
$316$	−4.54091e25	−0.257293
$317$	1.49751e26	0.820820	0.410410	−	0.911901i	$-0.365386\pi$
$317$	1.49751e26	0.820820	0.410410	+	0.911901i	$0.365386\pi$
$318$	−1.21577e26	−0.644714
$319$	−1.16811e26	−0.599351
$320$	−1.12590e25	−0.0559017
$321$	−1.13250e26	−0.544173
$322$	2.09815e25	0.0975774
$323$	4.52926e26	2.03892
$324$	−1.36862e26	−0.596429
$325$	−1.72513e25	−0.0727859
$326$	1.23512e26	0.504574
$327$	−2.04541e26	−0.809151
$328$	−3.01657e25	−0.115568
$329$	1.94063e25	0.0720087
$330$	−5.05452e25	−0.181670
$331$	−2.76489e25	−0.0962685	−0.0481343	−	0.998841i	$-0.515328\pi$
$331$	−2.76489e25	−0.0962685	−0.0481343	+	0.998841i	$0.515328\pi$
$332$	−2.72002e26	−0.917535
$333$	7.17351e25	0.234459
$334$	−3.72255e26	−1.17897
$335$	1.70614e26	0.523653
$336$	2.57540e25	0.0766093
$337$	2.02980e25	0.0585247	0.0292624	−	0.999572i	$-0.490684\pi$
$337$	2.02980e25	0.0585247	0.0292624	+	0.999572i	$0.490684\pi$
$338$	−2.19486e26	−0.613454
$339$	−4.14812e26	−1.12397
$340$	−1.32415e26	−0.347862
$341$	−4.95171e25	−0.126135
$342$	9.79055e25	0.241843
$343$	2.19346e26	0.525462
$344$	1.59244e26	0.369999
$345$	−1.12678e26	−0.253944
$346$	5.37608e26	1.17535
$347$	2.67942e26	0.568304	0.284152	−	0.958779i	$-0.408288\pi$
$347$	2.67942e26	0.568304	0.284152	+	0.958779i	$0.408288\pi$
$348$	−3.19632e26	−0.657761
$349$	−5.63379e26	−1.12495	−0.562475	−	0.826814i	$-0.690151\pi$
$349$	−5.63379e26	−1.12495	−0.562475	+	0.826814i	$0.690151\pi$
$350$	−1.99169e25	−0.0385928
$351$	−1.60606e26	−0.302021
$352$	−4.95514e25	−0.0904395
$353$	1.00657e27	1.78324	0.891622	−	0.452781i	$-0.149568\pi$
$353$	1.00657e27	1.78324	0.891622	+	0.452781i	$0.149568\pi$
$354$	1.21288e26	0.208585
$355$	−2.61057e26	−0.435850
$356$	5.33773e26	0.865230
$357$	3.02887e26	0.476720
$358$	−4.38332e26	−0.669933
$359$	1.04937e27	1.55754	0.778768	−	0.627312i	$-0.215845\pi$
$359$	1.04937e27	1.55754	0.778768	+	0.627312i	$0.215845\pi$
$360$	−2.86230e25	−0.0412610
$361$	5.12617e26	0.717741
$362$	4.23384e26	0.575830
$363$	6.27452e26	0.829012
$364$	3.86850e25	0.0496568
$365$	−5.47038e26	−0.682248
$366$	9.67144e26	1.17203
$367$	−5.00538e26	−0.589445	−0.294723	−	0.955583i	$-0.595227\pi$
$367$	−5.00538e26	−0.589445	−0.294723	+	0.955583i	$0.595227\pi$
$368$	−1.10463e26	−0.126419
$369$	−7.66884e25	−0.0853008
$370$	−2.62794e26	−0.284117
$371$	−2.10838e26	−0.221576
$372$	−1.35495e26	−0.138427
$373$	5.47776e26	0.544077	0.272039	−	0.962286i	$-0.412302\pi$
$373$	5.47776e26	0.544077	0.272039	+	0.962286i	$0.412302\pi$
$374$	−5.82764e26	−0.562783
$375$	1.06961e26	0.100437
$376$	−1.02169e26	−0.0932930
$377$	−4.80120e26	−0.426349
$378$	−1.85421e26	−0.160139
$379$	−1.26713e27	−1.06441	−0.532205	−	0.846615i	$-0.678637\pi$
$379$	−1.26713e27	−1.06441	−0.532205	+	0.846615i	$0.678637\pi$
$380$	−3.58667e26	−0.293065
$381$	−1.81723e27	−1.44443
$382$	7.87959e25	0.0609310
$383$	−5.06606e26	−0.381139	−0.190570	−	0.981674i	$-0.561033\pi$
$383$	−5.06606e26	−0.381139	−0.190570	+	0.981674i	$0.561033\pi$
$384$	−1.35589e26	−0.0992534
$385$	−8.76551e25	−0.0624367
$386$	1.28200e27	0.888629
$387$	4.04836e26	0.273095
$388$	6.90036e26	0.453042
$389$	−1.46115e27	−0.933738	−0.466869	−	0.884327i	$-0.654618\pi$
$389$	−1.46115e27	−0.933738	−0.466869	+	0.884327i	$0.654618\pi$
$390$	−2.07752e26	−0.129231
$391$	−1.29913e27	−0.786675
$392$	−5.55072e26	−0.327224
$393$	2.10986e27	1.21097
$394$	9.22777e26	0.515687
$395$	4.22905e26	0.230130
$396$	−1.25971e26	−0.0667533
$397$	−3.60855e27	−1.86223	−0.931113	−	0.364730i	$-0.881161\pi$
$397$	−3.60855e27	−1.86223	−0.931113	+	0.364730i	$0.881161\pi$
$398$	−9.47466e26	−0.476202
$399$	8.20419e26	0.401625
$400$	1.04858e26	0.0500000
$401$	−3.67006e25	−0.0170474	−0.00852369	−	0.999964i	$-0.502713\pi$
$401$	−3.67006e25	−0.0170474	−0.00852369	+	0.999964i	$0.502713\pi$
$402$	2.05465e27	0.929745
$403$	−2.03526e26	−0.0897259
$404$	1.21291e27	0.520984
$405$	1.27462e27	0.533463
$406$	−5.54304e26	−0.226060
$407$	−1.15657e27	−0.459654
$408$	−1.59463e27	−0.617629
$409$	−2.39045e27	−0.902371	−0.451185	−	0.892430i	$-0.648999\pi$
$409$	−2.39045e27	−0.902371	−0.451185	+	0.892430i	$0.648999\pi$
$410$	2.80940e26	0.103367
$411$	−8.10684e26	−0.290745
$412$	2.20572e27	0.771132
$413$	2.10336e26	0.0716866
$414$	−2.80822e26	−0.0933098
$415$	2.53322e27	0.820668
$416$	−2.03668e26	−0.0643342
$417$	3.87610e27	1.19390
$418$	−1.57851e27	−0.474130
$419$	6.65037e27	1.94804	0.974021	−	0.226458i	$-0.0727145\pi$
$419$	6.65037e27	1.94804	0.974021	+	0.226458i	$0.0727145\pi$
$420$	−2.39852e26	−0.0685214
$421$	5.66789e26	0.157928	0.0789641	−	0.996877i	$-0.474839\pi$
$421$	5.66789e26	0.157928	0.0789641	+	0.996877i	$0.474839\pi$
$422$	−1.01543e27	−0.275973
$423$	−2.59739e26	−0.0688594
$424$	1.11001e27	0.287069
$425$	1.23321e27	0.311137
$426$	−3.14383e27	−0.773851
$427$	1.67721e27	0.402806
$428$	1.03399e27	0.242302
$429$	−9.14328e26	−0.209074
$430$	−1.48308e27	−0.330937
$431$	3.51896e27	0.766307	0.383153	−	0.923685i	$-0.374838\pi$
$431$	3.51896e27	0.766307	0.383153	+	0.923685i	$0.374838\pi$
$432$	9.76201e26	0.207472
$433$	1.55391e27	0.322332	0.161166	−	0.986927i	$-0.448474\pi$
$433$	1.55391e27	0.322332	0.161166	+	0.986927i	$0.448474\pi$
$434$	−2.34974e26	−0.0475748
$435$	2.97681e27	0.588320
$436$	1.86749e27	0.360288
$437$	−3.51890e27	−0.662753
$438$	−6.58781e27	−1.21133
$439$	5.58352e27	1.00238	0.501188	−	0.865338i	$-0.332897\pi$
$439$	5.58352e27	1.00238	0.501188	+	0.865338i	$0.332897\pi$
$440$	4.61484e26	0.0808916
$441$	−1.41112e27	−0.241524
$442$	−2.39529e27	−0.400336
$443$	−6.81633e27	−1.11253	−0.556265	−	0.831005i	$-0.687766\pi$
$443$	−6.81633e27	−1.11253	−0.556265	+	0.831005i	$0.687766\pi$
$444$	−3.16475e27	−0.504450
$445$	−4.97115e27	−0.773885
$446$	−4.09565e27	−0.622739
$447$	6.52855e27	0.969589
$448$	−2.35137e26	−0.0341115
$449$	−3.94071e27	−0.558455	−0.279227	−	0.960225i	$-0.590078\pi$
$449$	−3.94071e27	−0.558455	−0.279227	+	0.960225i	$0.590078\pi$
$450$	2.66573e26	0.0369049
$451$	1.23643e27	0.167231
$452$	3.78729e27	0.500466
$453$	−1.53256e28	−1.97873
$454$	5.41593e27	0.683261
$455$	−3.60282e26	−0.0444143
$456$	−4.31931e27	−0.520336
$457$	−2.47274e26	−0.0291111	−0.0145555	−	0.999894i	$-0.504633\pi$
$457$	−2.47274e26	−0.0291111	−0.0145555	+	0.999894i	$0.504633\pi$
$458$	−1.08299e27	−0.124606
$459$	1.14809e28	1.29105
$460$	1.02876e27	0.113073
$461$	−6.40047e27	−0.687625	−0.343813	−	0.939038i	$-0.611719\pi$
$461$	−6.40047e27	−0.687625	−0.343813	+	0.939038i	$0.611719\pi$
$462$	−1.05560e27	−0.110856
$463$	−8.60733e26	−0.0883625	−0.0441812	−	0.999024i	$-0.514068\pi$
$463$	−8.60733e26	−0.0883625	−0.0441812	+	0.999024i	$0.514068\pi$
$464$	2.91828e27	0.292879
$465$	1.26189e27	0.123813
$466$	1.08458e28	1.04042
$467$	−1.25054e28	−1.17292	−0.586461	−	0.809977i	$-0.699479\pi$
$467$	−1.25054e28	−1.17292	−0.586461	+	0.809977i	$0.699479\pi$
$468$	−5.17771e26	−0.0474850
$469$	3.56316e27	0.319536
$470$	9.51528e26	0.0834438
$471$	1.79993e27	0.154361
$472$	−1.10737e27	−0.0928756
$473$	−6.52710e27	−0.535400
$474$	5.09291e27	0.408596
$475$	3.34035e27	0.262125
$476$	−2.76539e27	−0.212268
$477$	2.82192e27	0.211886
$478$	1.76191e28	1.29417
$479$	9.68180e27	0.695718	0.347859	−	0.937547i	$-0.386909\pi$
$479$	9.68180e27	0.695718	0.347859	+	0.937547i	$0.386909\pi$
$480$	1.26277e27	0.0887749
$481$	−4.75377e27	−0.326975
$482$	−1.77231e28	−1.19274
$483$	−2.35320e27	−0.154958
$484$	−5.72871e27	−0.369131
$485$	−6.42646e27	−0.405213
$486$	5.83977e27	0.360342
$487$	−4.62318e27	−0.279182	−0.139591	−	0.990209i	$-0.544579\pi$
$487$	−4.62318e27	−0.279182	−0.139591	+	0.990209i	$0.544579\pi$
$488$	−8.83014e27	−0.521867
$489$	−1.38527e28	−0.801291
$490$	5.16951e27	0.292678
$491$	−2.14634e28	−1.18944	−0.594719	−	0.803934i	$-0.702737\pi$
$491$	−2.14634e28	−1.18944	−0.594719	+	0.803934i	$0.702737\pi$
$492$	3.38328e27	0.183529
$493$	3.43213e28	1.82251
$494$	−6.48804e27	−0.337272
$495$	1.17320e27	0.0597060
$496$	1.23708e27	0.0616369
$497$	−5.45200e27	−0.265958
$498$	3.05067e28	1.45709
$499$	2.68376e28	1.25513	0.627564	−	0.778565i	$-0.284052\pi$
$499$	2.68376e28	1.25513	0.627564	+	0.778565i	$0.284052\pi$
$500$	−9.76563e26	−0.0447214
$501$	4.17508e28	1.87227
$502$	−9.51982e27	−0.418061
$503$	−1.25016e27	−0.0537651	−0.0268826	−	0.999639i	$-0.508558\pi$
$503$	−1.25016e27	−0.0537651	−0.0268826	+	0.999639i	$0.508558\pi$
$504$	−5.97773e26	−0.0251777
$505$	−1.12961e28	−0.465983
$506$	4.52764e27	0.182933
$507$	2.46168e28	0.974198
$508$	1.65915e28	0.643158
$509$	−2.39131e28	−0.908029	−0.454014	−	0.890994i	$-0.650009\pi$
$509$	−2.39131e28	−0.908029	−0.454014	+	0.890994i	$0.650009\pi$
$510$	1.48511e28	0.552424
$511$	−1.14245e28	−0.416312
$512$	1.23794e27	0.0441942
$513$	3.10979e28	1.08767
$514$	9.54645e27	0.327137
$515$	−2.05423e28	−0.689722
$516$	−1.78602e28	−0.587578
$517$	4.18772e27	0.134998
$518$	−5.48828e27	−0.173370
$519$	−6.02961e28	−1.86652
$520$	1.89680e27	0.0575423
$521$	1.24898e28	0.371328	0.185664	−	0.982613i	$-0.440556\pi$
$521$	1.24898e28	0.371328	0.185664	+	0.982613i	$0.440556\pi$
$522$	7.41896e27	0.216174
$523$	−6.85611e28	−1.95799	−0.978995	−	0.203886i	$-0.934643\pi$
$523$	−6.85611e28	−1.95799	−0.978995	+	0.203886i	$0.934643\pi$
$524$	−1.92633e28	−0.539202
$525$	2.23380e27	0.0612874
$526$	−2.94123e28	−0.791005
$527$	1.45490e28	0.383551
$528$	5.55750e27	0.143623
$529$	−2.93783e28	−0.744291
$530$	−1.03378e28	−0.256763
$531$	−2.81520e27	−0.0685514
$532$	−7.49052e27	−0.178830
$533$	5.08202e27	0.118960
$534$	−5.98659e28	−1.37403
$535$	−9.62978e27	−0.216721
$536$	−1.87592e28	−0.413984
$537$	4.91617e28	1.06389
$538$	2.47561e28	0.525374
$539$	2.27513e28	0.473504
$540$	−9.09158e27	−0.185569
$541$	6.77012e28	1.35527	0.677634	−	0.735399i	$-0.263005\pi$
$541$	6.77012e28	1.35527	0.677634	+	0.735399i	$0.263005\pi$
$542$	−4.59619e28	−0.902413
$543$	−4.74851e28	−0.914449
$544$	1.45591e28	0.275009
$545$	−1.73923e28	−0.322251
$546$	−4.33877e27	−0.0788576
$547$	−1.66829e28	−0.297443	−0.148721	−	0.988879i	$-0.547516\pi$
$547$	−1.66829e28	−0.297443	−0.148721	+	0.988879i	$0.547516\pi$
$548$	7.40164e27	0.129459
$549$	−2.24483e28	−0.385189
$550$	−4.29790e27	−0.0723516
$551$	9.29649e28	1.53542
$552$	1.23891e28	0.200760
$553$	8.83209e27	0.140427
$554$	−1.61437e28	−0.251854
$555$	2.94740e28	0.451194
$556$	−3.53893e28	−0.531601
$557$	9.39997e28	1.38563	0.692815	−	0.721116i	$-0.256370\pi$
$557$	9.39997e28	1.38563	0.692815	+	0.721116i	$0.256370\pi$
$558$	3.14495e27	0.0454941
$559$	−2.68279e28	−0.380857
$560$	2.18988e27	0.0305103
$561$	6.53606e28	0.893729
$562$	9.63167e28	1.29262
$563$	5.21769e28	0.687290	0.343645	−	0.939100i	$-0.388338\pi$
$563$	5.21769e28	0.687290	0.343645	+	0.939100i	$0.388338\pi$
$564$	1.14589e28	0.148154
$565$	−3.52718e28	−0.447630
$566$	−4.51821e28	−0.562852
$567$	2.66197e28	0.325522
$568$	2.87035e28	0.344570
$569$	9.80844e27	0.115590	0.0577951	−	0.998328i	$-0.481593\pi$
$569$	9.80844e27	0.115590	0.0577951	+	0.998328i	$0.481593\pi$
$570$	4.02268e28	0.465403
$571$	4.43638e28	0.503906	0.251953	−	0.967740i	$-0.418927\pi$
$571$	4.43638e28	0.503906	0.251953	+	0.967740i	$0.418927\pi$
$572$	8.34793e27	0.0930937
$573$	−8.83745e27	−0.0967617
$574$	5.86725e27	0.0630754
$575$	−9.58110e27	−0.101135
$576$	3.14714e27	0.0326197
$577$	−1.56720e29	−1.59507	−0.797533	−	0.603276i	$-0.793862\pi$
$577$	−1.56720e29	−1.59507	−0.797533	+	0.603276i	$0.793862\pi$
$578$	1.00477e29	1.00421
$579$	−1.43784e29	−1.41119
$580$	−2.71786e28	−0.261959
$581$	5.29046e28	0.500776
$582$	−7.73919e28	−0.719456
$583$	−4.54973e28	−0.415399
$584$	6.01475e28	0.539365
$585$	4.82212e27	0.0424719
$586$	3.05275e28	0.264099
$587$	−1.20878e29	−1.02718	−0.513592	−	0.858035i	$-0.671685\pi$
$587$	−1.20878e29	−1.02718	−0.513592	+	0.858035i	$0.671685\pi$
$588$	6.22548e28	0.519650
$589$	3.94085e28	0.323132
$590$	1.03132e28	0.0830705
$591$	−1.03495e29	−0.818939
$592$	2.88945e28	0.224614
$593$	−3.14301e28	−0.240033	−0.120017	−	0.992772i	$-0.538295\pi$
$593$	−3.14301e28	−0.240033	−0.120017	+	0.992772i	$0.538295\pi$
$594$	−4.00125e28	−0.300219
$595$	2.57547e28	0.189858
$596$	−5.96064e28	−0.431725
$597$	1.06264e29	0.756235
$598$	1.86096e28	0.130129
$599$	1.87438e29	1.28788	0.643942	−	0.765075i	$-0.277298\pi$
$599$	1.87438e29	1.28788	0.643942	+	0.765075i	$0.277298\pi$
$600$	−1.17604e28	−0.0794027
$601$	−2.65601e29	−1.76217	−0.881085	−	0.472958i	$-0.843186\pi$
$601$	−2.65601e29	−1.76217	−0.881085	+	0.472958i	$0.843186\pi$
$602$	−3.09731e28	−0.201940
$603$	−4.76903e28	−0.305561
$604$	1.39925e29	0.881064
$605$	5.33528e28	0.330161
$606$	−1.36036e29	−0.827351
$607$	−2.33120e29	−1.39347	−0.696737	−	0.717326i	$-0.745366\pi$
$607$	−2.33120e29	−1.39347	−0.696737	+	0.717326i	$0.745366\pi$
$608$	3.94359e28	0.231688
$609$	6.21686e28	0.358996
$610$	8.22371e28	0.466772
$611$	1.72125e28	0.0960309
$612$	3.70128e28	0.202984
$613$	−5.29871e28	−0.285651	−0.142825	−	0.989748i	$-0.545619\pi$
$613$	−5.29871e28	−0.285651	−0.142825	+	0.989748i	$0.545619\pi$
$614$	−4.69519e28	−0.248820
$615$	−3.15092e28	−0.164153
$616$	9.63778e27	0.0493605
$617$	−9.06542e28	−0.456450	−0.228225	−	0.973608i	$-0.573292\pi$
$617$	−9.06542e28	−0.456450	−0.228225	+	0.973608i	$0.573292\pi$
$618$	−2.47385e29	−1.22460
$619$	1.52550e29	0.742441	0.371220	−	0.928545i	$-0.378939\pi$
$619$	1.52550e29	0.742441	0.371220	+	0.928545i	$0.378939\pi$
$620$	−1.15212e28	−0.0551297
$621$	−8.91979e28	−0.419655
$622$	−1.33549e29	−0.617793
$623$	−1.03819e29	−0.472229
$624$	2.28426e28	0.102166
$625$	9.09495e27	0.0400000
$626$	2.74820e29	1.18855
$627$	1.77040e29	0.752943
$628$	−1.64336e28	−0.0687317
$629$	3.39822e29	1.39772
$630$	5.56719e27	0.0225196
$631$	−3.07474e29	−1.22321	−0.611604	−	0.791164i	$-0.709475\pi$
$631$	−3.07474e29	−1.22321	−0.611604	+	0.791164i	$0.709475\pi$
$632$	−4.64989e28	−0.181934
$633$	1.13886e29	0.438260
$634$	1.53345e29	0.580407
$635$	−1.54521e29	−0.575258
$636$	−1.24495e29	−0.455882
$637$	9.35129e28	0.336827
$638$	−1.19614e29	−0.423806
$639$	7.29711e28	0.254327
$640$	−1.15292e28	−0.0395285
$641$	4.26974e29	1.44010	0.720049	−	0.693923i	$-0.244119\pi$
$641$	4.26974e29	1.44010	0.720049	+	0.693923i	$0.244119\pi$
$642$	−1.15968e29	−0.384788
$643$	−1.96406e29	−0.641120	−0.320560	−	0.947228i	$-0.603871\pi$
$643$	−1.96406e29	−0.641120	−0.320560	+	0.947228i	$0.603871\pi$
$644$	2.14850e28	0.0689976
$645$	1.66336e29	0.525545
$646$	4.63797e29	1.44174
$647$	4.70139e29	1.43791	0.718955	−	0.695057i	$-0.244621\pi$
$647$	4.70139e29	1.43791	0.718955	+	0.695057i	$0.244621\pi$
$648$	−1.40146e29	−0.421739
$649$	4.53889e28	0.134394
$650$	−1.76653e28	−0.0514674
$651$	2.63538e28	0.0755513
$652$	1.26476e29	0.356788
$653$	−3.28351e29	−0.911485	−0.455742	−	0.890112i	$-0.650626\pi$
$653$	−3.28351e29	−0.911485	−0.455742	+	0.890112i	$0.650626\pi$
$654$	−2.09450e29	−0.572156
$655$	1.79403e29	0.482277
$656$	−3.08897e28	−0.0817191
$657$	1.52909e29	0.398104
$658$	1.98720e28	0.0509179
$659$	−5.89725e28	−0.148714	−0.0743571	−	0.997232i	$-0.523690\pi$
$659$	−5.89725e28	−0.148714	−0.0743571	+	0.997232i	$0.523690\pi$
$660$	−5.17583e28	−0.128460
$661$	−2.99109e29	−0.730657	−0.365328	−	0.930879i	$-0.619043\pi$
$661$	−2.99109e29	−0.730657	−0.365328	+	0.930879i	$0.619043\pi$
$662$	−2.83125e28	−0.0680721
$663$	2.68647e29	0.635755
$664$	−2.78530e29	−0.648795
$665$	6.97609e28	0.159950
$666$	7.34567e28	0.165788
$667$	−2.66651e29	−0.592408
$668$	−3.81190e29	−0.833658
$669$	4.59352e29	0.988944
$670$	1.74709e29	0.370279
$671$	3.61930e29	0.755158
$672$	2.63720e28	0.0541710
$673$	−4.08136e29	−0.825366	−0.412683	−	0.910875i	$-0.635408\pi$
$673$	−4.08136e29	−0.825366	−0.412683	+	0.910875i	$0.635408\pi$
$674$	2.07852e28	0.0413832
$675$	8.46719e28	0.165978
$676$	−2.24754e29	−0.433778
$677$	−6.17392e28	−0.117322	−0.0586611	−	0.998278i	$-0.518683\pi$
$677$	−6.17392e28	−0.117322	−0.0586611	+	0.998278i	$0.518683\pi$
$678$	−4.24768e29	−0.794767
$679$	−1.34212e29	−0.247264
$680$	−1.35593e29	−0.245976
$681$	−6.07430e29	−1.08505
$682$	−5.07055e28	−0.0891906
$683$	8.86519e29	1.53557	0.767787	−	0.640706i	$-0.221358\pi$
$683$	8.86519e29	1.53557	0.767787	+	0.640706i	$0.221358\pi$
$684$	1.00255e29	0.171009
$685$	−6.89332e28	−0.115792
$686$	2.24610e29	0.371558
$687$	1.21464e29	0.197880
$688$	1.63066e29	0.261629
$689$	−1.87004e29	−0.295494
$690$	−1.15382e29	−0.179566
$691$	−3.58171e29	−0.548998	−0.274499	−	0.961587i	$-0.588512\pi$
$691$	−3.58171e29	−0.548998	−0.274499	+	0.961587i	$0.588512\pi$
$692$	5.50511e29	0.831097
$693$	2.45015e28	0.0364329
$694$	2.74372e29	0.401851
$695$	3.29588e29	0.475479
$696$	−3.27303e29	−0.465108
$697$	−3.63287e29	−0.508518
$698$	−5.76900e29	−0.795460
$699$	−1.21643e30	−1.65225
$700$	−2.03949e28	−0.0272892
$701$	−9.30503e29	−1.22653	−0.613265	−	0.789877i	$-0.710144\pi$
$701$	−9.30503e29	−1.22653	−0.613265	+	0.789877i	$0.710144\pi$
$702$	−1.64460e29	−0.213561
$703$	9.20465e29	1.17754
$704$	−5.07407e28	−0.0639504
$705$	−1.06720e29	−0.132513
$706$	1.03073e30	1.26094
$707$	−2.35912e29	−0.284345
$708$	1.24198e29	0.147492
$709$	−1.29300e30	−1.51290	−0.756452	−	0.654049i	$-0.773069\pi$
$709$	−1.29300e30	−1.51290	−0.756452	+	0.654049i	$0.773069\pi$
$710$	−2.67322e29	−0.308193
$711$	−1.18211e29	−0.134285
$712$	5.46583e29	0.611810
$713$	−1.13035e29	−0.124673
$714$	3.10156e29	0.337092
$715$	−7.77461e28	−0.0832655
$716$	−4.48852e29	−0.473714
$717$	−1.97609e30	−2.05521
$718$	1.07456e30	1.10134
$719$	−3.29773e29	−0.333090	−0.166545	−	0.986034i	$-0.553261\pi$
$719$	−3.29773e29	−0.333090	−0.166545	+	0.986034i	$0.553261\pi$
$720$	−2.93100e28	−0.0291759
$721$	−4.29013e29	−0.420872
$722$	5.24920e29	0.507519
$723$	1.98776e30	1.89413
$724$	4.33545e29	0.407173
$725$	2.53121e29	0.234303
$726$	6.42511e29	0.586200
$727$	1.06829e30	0.960677	0.480338	−	0.877083i	$-0.340514\pi$
$727$	1.06829e30	0.960677	0.480338	+	0.877083i	$0.340514\pi$
$728$	3.96135e28	0.0351126
$729$	7.10333e29	0.620616
$730$	−5.60167e29	−0.482422
$731$	1.91778e30	1.62805
$732$	9.90356e29	0.828752
$733$	1.28132e30	1.05698	0.528490	−	0.848939i	$-0.322758\pi$
$733$	1.28132e30	1.05698	0.528490	+	0.848939i	$0.322758\pi$
$734$	−5.12551e29	−0.416801
$735$	−5.79793e29	−0.464789
$736$	−1.13114e29	−0.0893919
$737$	7.68901e29	0.599049
$738$	−7.85289e28	−0.0603168
$739$	−1.68393e29	−0.127514	−0.0637569	−	0.997965i	$-0.520308\pi$
$739$	−1.68393e29	−0.127514	−0.0637569	+	0.997965i	$0.520308\pi$
$740$	−2.69101e29	−0.200901
$741$	7.27674e29	0.535607
$742$	−2.15898e29	−0.156678
$743$	5.78502e28	0.0413925	0.0206963	−	0.999786i	$-0.493412\pi$
$743$	5.78502e28	0.0413925	0.0206963	+	0.999786i	$0.493412\pi$
$744$	−1.38746e29	−0.0978827
$745$	5.55128e29	0.386147
$746$	5.60923e29	0.384721
$747$	−7.08090e29	−0.478875
$748$	−5.96750e29	−0.397947
$749$	−2.01112e29	−0.132245
$750$	1.09528e29	0.0710199
$751$	1.16126e30	0.742526	0.371263	−	0.928528i	$-0.378925\pi$
$751$	1.16126e30	0.742526	0.371263	+	0.928528i	$0.378925\pi$
$752$	−1.04622e29	−0.0659681
$753$	1.06771e30	0.663903
$754$	−4.91642e29	−0.301474
$755$	−1.30315e30	−0.788048
$756$	−1.89872e29	−0.113235
$757$	−2.47468e30	−1.45550	−0.727749	−	0.685843i	$-0.759434\pi$
$757$	−2.47468e30	−1.45550	−0.727749	+	0.685843i	$0.759434\pi$
$758$	−1.29754e30	−0.752652
$759$	−5.07803e29	−0.290507
$760$	−3.67275e29	−0.207228
$761$	8.23029e29	0.458011	0.229006	−	0.973425i	$-0.426453\pi$
$761$	8.23029e29	0.458011	0.229006	+	0.973425i	$0.426453\pi$
$762$	−1.86084e30	−1.02137
$763$	−3.63227e29	−0.196640
$764$	8.06870e28	0.0430847
$765$	−3.44708e29	−0.181554
$766$	−5.18765e29	−0.269506
$767$	1.86559e29	0.0956013
$768$	−1.38843e29	−0.0701827
$769$	−8.22507e29	−0.410122	−0.205061	−	0.978749i	$-0.565739\pi$
$769$	−8.22507e29	−0.410122	−0.205061	+	0.978749i	$0.565739\pi$
$770$	−8.97588e28	−0.0441494
$771$	−1.07069e30	−0.519511
$772$	1.31276e30	0.628355
$773$	−4.08869e30	−1.93063	−0.965316	−	0.261083i	$-0.915920\pi$
$773$	−4.08869e30	−1.93063	−0.965316	+	0.261083i	$0.915920\pi$
$774$	4.14552e29	0.193108
$775$	1.07300e29	0.0493095
$776$	7.06597e29	0.320349
$777$	6.15545e29	0.275321
$778$	−1.49622e30	−0.660252
$779$	−9.84024e29	−0.428413
$780$	−2.12738e29	−0.0913802
$781$	−1.17650e30	−0.498604
$782$	−1.33030e30	−0.556263
$783$	2.35649e30	0.972228
$784$	−5.68393e29	−0.231382
$785$	1.53050e29	0.0614755
$786$	2.16050e30	0.856282
$787$	2.27937e30	0.891414	0.445707	−	0.895179i	$-0.352952\pi$
$787$	2.27937e30	0.891414	0.445707	+	0.895179i	$0.352952\pi$
$788$	9.44924e29	0.364646
$789$	3.29878e30	1.25616
$790$	4.33055e29	0.162727
$791$	−7.36629e29	−0.273147
$792$	−1.28995e29	−0.0472017
$793$	1.48761e30	0.537182
$794$	−3.69516e30	−1.31679
$795$	1.15945e30	0.407753
$796$	−9.70205e29	−0.336726
$797$	3.26331e30	1.11775	0.558877	−	0.829250i	$-0.311232\pi$
$797$	3.26331e30	1.11775	0.558877	+	0.829250i	$0.311232\pi$
$798$	8.40109e29	0.283991
$799$	−1.23043e30	−0.410503
$800$	1.07374e29	0.0353553
$801$	1.38954e30	0.451576
$802$	−3.75814e28	−0.0120543
$803$	−2.46532e30	−0.780478
$804$	2.10396e30	0.657429
$805$	−2.00095e29	−0.0617134
$806$	−2.08411e29	−0.0634458
$807$	−2.77655e30	−0.834322
$808$	1.24202e30	0.368392
$809$	1.06157e30	0.310805	0.155403	−	0.987851i	$-0.450333\pi$
$809$	1.06157e30	0.310805	0.155403	+	0.987851i	$0.450333\pi$
$810$	1.30521e30	0.377215
$811$	−5.07809e30	−1.44871	−0.724355	−	0.689428i	$-0.757862\pi$
$811$	−5.07809e30	−1.44871	−0.724355	+	0.689428i	$0.757862\pi$
$812$	−5.67607e29	−0.159849
$813$	5.15491e30	1.43308
$814$	−1.18433e30	−0.325025
$815$	−1.17790e30	−0.319121
$816$	−1.63290e30	−0.436729
$817$	5.19464e30	1.37159
$818$	−2.44782e30	−0.638073
$819$	1.00707e29	0.0259166
$820$	2.87683e29	0.0730918
$821$	−3.24366e30	−0.813640	−0.406820	−	0.913508i	$-0.633362\pi$
$821$	−3.24366e30	−0.813640	−0.406820	+	0.913508i	$0.633362\pi$
$822$	−8.30141e29	−0.205588
$823$	1.47953e30	0.361764	0.180882	−	0.983505i	$-0.442105\pi$
$823$	1.47953e30	0.361764	0.180882	+	0.983505i	$0.442105\pi$
$824$	2.25865e30	0.545273
$825$	4.82037e29	0.114898
$826$	2.15384e29	0.0506901
$827$	1.06680e30	0.247898	0.123949	−	0.992289i	$-0.460444\pi$
$827$	1.06680e30	0.247898	0.123949	+	0.992289i	$0.460444\pi$
$828$	−2.87562e29	−0.0659800
$829$	1.37112e30	0.310637	0.155319	−	0.987864i	$-0.450360\pi$
$829$	1.37112e30	0.310637	0.155319	+	0.987864i	$0.450360\pi$
$830$	2.59402e30	0.580300
$831$	1.81061e30	0.399958
$832$	−2.08556e29	−0.0454912
$833$	−6.68475e30	−1.43983
$834$	3.96913e30	0.844212
$835$	3.55010e30	0.745647
$836$	−1.61640e30	−0.335260
$837$	9.98936e29	0.204607
$838$	6.80997e30	1.37747
$839$	7.78595e29	0.155529	0.0777645	−	0.996972i	$-0.475222\pi$
$839$	7.78595e29	0.155529	0.0777645	+	0.996972i	$0.475222\pi$
$840$	−2.45609e29	−0.0484520
$841$	1.91173e30	0.372450
$842$	5.80392e29	0.111672
$843$	−1.08025e31	−2.05275
$844$	−1.03980e30	−0.195143
$845$	2.09319e30	0.387983
$846$	−2.65973e29	−0.0486909
$847$	1.11424e30	0.201466
$848$	1.13665e30	0.202989
$849$	5.06746e30	0.893839
$850$	1.26280e30	0.220007
$851$	−2.64016e30	−0.454329
$852$	−3.21928e30	−0.547196
$853$	−5.07514e30	−0.852086	−0.426043	−	0.904703i	$-0.640093\pi$
$853$	−5.07514e30	−0.852086	−0.426043	+	0.904703i	$0.640093\pi$
$854$	1.71747e30	0.284827
$855$	−9.33700e29	−0.152955
$856$	1.05881e30	0.171333
$857$	−7.65635e30	−1.22384	−0.611918	−	0.790921i	$-0.709602\pi$
$857$	−7.65635e30	−1.22384	−0.611918	+	0.790921i	$0.709602\pi$
$858$	−9.36272e29	−0.147838
$859$	6.42591e30	1.00232	0.501160	−	0.865355i	$-0.332907\pi$
$859$	6.42591e30	1.00232	0.501160	+	0.865355i	$0.332907\pi$
$860$	−1.51867e30	−0.234008
$861$	−6.58049e29	−0.100167
$862$	3.60341e30	0.541861
$863$	−1.00027e31	−1.48594	−0.742972	−	0.669322i	$-0.766585\pi$
$863$	−1.00027e31	−1.48594	−0.742972	+	0.669322i	$0.766585\pi$
$864$	9.99629e29	0.146705
$865$	−5.12703e30	−0.743356
$866$	1.59121e30	0.227923
$867$	−1.12691e31	−1.59473
$868$	−2.40613e29	−0.0336405
$869$	1.90590e30	0.263264
$870$	3.04825e30	0.416005
$871$	3.16036e30	0.426134
$872$	1.91231e30	0.254762
$873$	1.79634e30	0.236449
$874$	−3.60335e30	−0.468637
$875$	1.89942e29	0.0244082
$876$	−6.74591e30	−0.856540
$877$	1.69135e30	0.212197	0.106098	−	0.994356i	$-0.466164\pi$
$877$	1.69135e30	0.212197	0.106098	+	0.994356i	$0.466164\pi$
$878$	5.71752e30	0.708787
$879$	−3.42385e30	−0.419403
$880$	4.72559e29	0.0571990
$881$	7.04503e30	0.842628	0.421314	−	0.906915i	$-0.361569\pi$
$881$	7.04503e30	0.842628	0.421314	+	0.906915i	$0.361569\pi$
$882$	−1.44499e30	−0.170783
$883$	−7.12748e30	−0.832431	−0.416216	−	0.909266i	$-0.636644\pi$
$883$	−7.12748e30	−0.832431	−0.416216	+	0.909266i	$0.636644\pi$
$884$	−2.45278e30	−0.283080
$885$	−1.15669e30	−0.131920
$886$	−6.97992e30	−0.786677
$887$	7.82765e30	0.871834	0.435917	−	0.899987i	$-0.356424\pi$
$887$	7.82765e30	0.871834	0.435917	+	0.899987i	$0.356424\pi$
$888$	−3.24070e30	−0.356700
$889$	−3.22706e30	−0.351026
$890$	−5.09045e30	−0.547219
$891$	5.74431e30	0.610270
$892$	−4.19394e30	−0.440343
$893$	−3.33283e30	−0.345838
$894$	6.68523e30	0.685603
$895$	4.18026e30	0.423703
$896$	−2.40780e29	−0.0241205
$897$	−2.08718e30	−0.206652
$898$	−4.03529e30	−0.394887
$899$	2.98625e30	0.288834
$900$	2.72970e29	0.0260957
$901$	1.33679e31	1.26315
$902$	1.26611e30	0.118250
$903$	3.47383e30	0.320691
$904$	3.87818e30	0.353883
$905$	−4.03770e30	−0.364187
$906$	−1.56935e31	−1.39918
$907$	4.42371e30	0.389862	0.194931	−	0.980817i	$-0.437552\pi$
$907$	4.42371e30	0.389862	0.194931	+	0.980817i	$0.437552\pi$
$908$	5.54591e30	0.483138
$909$	3.15751e30	0.271909
$910$	−3.68929e29	−0.0314057
$911$	1.34581e31	1.13251	0.566253	−	0.824231i	$-0.308392\pi$
$911$	1.34581e31	1.13251	0.566253	+	0.824231i	$0.308392\pi$
$912$	−4.42298e30	−0.367933
$913$	1.14164e31	0.938828
$914$	−2.53208e29	−0.0205846
$915$	−9.22341e30	−0.741259
$916$	−1.10898e30	−0.0881095
$917$	3.74672e30	0.294288
$918$	1.17564e31	0.912908
$919$	2.07587e31	1.59363	0.796815	−	0.604223i	$-0.206517\pi$
$919$	2.07587e31	1.59363	0.796815	+	0.604223i	$0.206517\pi$
$920$	1.05345e30	0.0799545
$921$	5.26594e30	0.395139
$922$	−6.55408e30	−0.486224
$923$	−4.83568e30	−0.354682
$924$	−1.08094e30	−0.0783871
$925$	2.50620e30	0.179692
$926$	−8.81390e29	−0.0624817
$927$	5.74203e30	0.402465
$928$	2.98832e30	0.207097
$929$	−2.58824e30	−0.177353	−0.0886767	−	0.996060i	$-0.528264\pi$
$929$	−2.58824e30	−0.177353	−0.0886767	+	0.996060i	$0.528264\pi$
$930$	1.29218e30	0.0875489
$931$	−1.81068e31	−1.21302
$932$	1.11061e31	0.735691
$933$	1.49784e31	0.981088
$934$	−1.28055e31	−0.829381
$935$	5.55767e30	0.355935
$936$	−5.30198e29	−0.0335770
$937$	−1.82163e31	−1.14076	−0.570381	−	0.821380i	$-0.693205\pi$
$937$	−1.82163e31	−1.14076	−0.570381	+	0.821380i	$0.693205\pi$
$938$	3.64867e30	0.225946
$939$	−3.08228e31	−1.88749
$940$	9.74364e29	0.0590037
$941$	1.59208e31	0.953394	0.476697	−	0.879068i	$-0.341834\pi$
$941$	1.59208e31	0.953394	0.476697	+	0.879068i	$0.341834\pi$
$942$	1.84313e30	0.109150
$943$	2.82247e30	0.165294
$944$	−1.13395e30	−0.0656730
$945$	1.76832e30	0.101281
$946$	−6.68375e30	−0.378585
$947$	6.90254e30	0.386664	0.193332	−	0.981133i	$-0.438071\pi$
$947$	6.90254e30	0.386664	0.193332	+	0.981133i	$0.438071\pi$
$948$	5.21514e30	0.288921
$949$	−1.01330e31	−0.555194
$950$	3.42052e30	0.185351
$951$	−1.71986e31	−0.921718
$952$	−2.83176e30	−0.150096
$953$	8.59868e30	0.450771	0.225386	−	0.974270i	$-0.427636\pi$
$953$	8.59868e30	0.450771	0.225386	+	0.974270i	$0.427636\pi$
$954$	2.88964e30	0.149826
$955$	−7.51457e29	−0.0385362
$956$	1.80420e31	0.915115
$957$	1.34155e31	0.673026
$958$	9.91416e30	0.491947
$959$	−1.43962e30	−0.0706567
$960$	1.29307e30	0.0627733
$961$	−1.95596e31	−0.939214
$962$	−4.86786e30	−0.231206
$963$	2.69173e30	0.126461
$964$	−1.81484e31	−0.843394
$965$	−1.22261e31	−0.562018
$966$	−2.40968e30	−0.109572
$967$	−2.71571e30	−0.122153	−0.0610766	−	0.998133i	$-0.519453\pi$
$967$	−2.71571e30	−0.122153	−0.0610766	+	0.998133i	$0.519453\pi$
$968$	−5.86620e30	−0.261015
$969$	−5.20177e31	−2.28956
$970$	−6.58070e30	−0.286529
$971$	−2.52216e30	−0.108635	−0.0543175	−	0.998524i	$-0.517298\pi$
$971$	−2.52216e30	−0.108635	−0.0543175	+	0.998524i	$0.517298\pi$
$972$	5.97992e30	0.254800
$973$	6.88323e30	0.290140
$974$	−4.73414e30	−0.197411
$975$	1.98128e30	0.0817329
$976$	−9.04207e30	−0.369016
$977$	−3.27075e30	−0.132055	−0.0660274	−	0.997818i	$-0.521032\pi$
$977$	−3.27075e30	−0.132055	−0.0660274	+	0.997818i	$0.521032\pi$
$978$	−1.41851e31	−0.566598
$979$	−2.24034e31	−0.885309
$980$	5.29358e30	0.206955
$981$	4.86154e30	0.188039
$982$	−2.19785e31	−0.841060
$983$	−1.41284e29	−0.00534910	−0.00267455	−	0.999996i	$-0.500851\pi$
$983$	−1.41284e29	−0.00534910	−0.00267455	+	0.999996i	$0.500851\pi$
$984$	3.46447e30	0.129774
$985$	−8.80029e30	−0.326149
$986$	3.51450e31	1.28871
$987$	−2.22877e30	−0.0808603
$988$	−6.64376e30	−0.238488
$989$	−1.48998e31	−0.529198
$990$	1.20136e30	0.0422185
$991$	2.73270e31	0.950209	0.475105	−	0.879929i	$-0.342410\pi$
$991$	2.73270e31	0.950209	0.475105	+	0.879929i	$0.342410\pi$
$992$	1.26677e30	0.0435839
$993$	3.17542e30	0.108102
$994$	−5.58285e30	−0.188061
$995$	9.03574e30	0.301177
$996$	3.12389e31	1.03032
$997$	2.01068e31	0.656213	0.328106	−	0.944641i	$-0.393590\pi$
$997$	2.01068e31	0.656213	0.328106	+	0.944641i	$0.393590\pi$
$998$	2.74817e31	0.887509
$999$	2.33322e31	0.745620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.a.d.1.1	✓	2
4.3	odd	2		80.22.a.c.1.2		2
5.2	odd	4		50.22.b.e.49.4		4
5.3	odd	4		50.22.b.e.49.1		4
5.4	even	2		50.22.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.a.d.1.1	✓	2	1.1	even	1	trivial
50.22.a.d.1.2		2	5.4	even	2
50.22.b.e.49.1		4	5.3	odd	4
50.22.b.e.49.4		4	5.2	odd	4
80.22.a.c.1.2		2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+1024.00 q^{2} -114848. q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} -1.17604e8 q^{6} -2.03949e8 q^{7} +1.07374e9 q^{8} +2.72970e9 q^{9} -1.00000e10 q^{10} -4.40105e10 q^{11} -1.20427e11 q^{12} -1.80893e11 q^{13} -2.08843e11 q^{14} +1.12156e12 q^{15} +1.09951e12 q^{16} +1.29311e13 q^{17} +2.79522e12 q^{18} +3.50261e13 q^{19} -1.02400e13 q^{20} +2.34231e13 q^{21} -4.50668e13 q^{22} -1.00465e14 q^{23} -1.23317e14 q^{24} +9.53674e13 q^{25} -1.85235e14 q^{26} +8.87849e14 q^{27} -2.13856e14 q^{28} +2.65416e15 q^{29} +1.14848e15 q^{30} +1.12512e15 q^{31} +1.12590e15 q^{32} +5.05452e15 q^{33} +1.32415e16 q^{34} +1.99169e15 q^{35} +2.86230e15 q^{36} +2.62794e16 q^{37} +3.58667e16 q^{38} +2.07752e16 q^{39} -1.04858e16 q^{40} -2.80940e16 q^{41} +2.39852e16 q^{42} +1.48308e17 q^{43} -4.61484e16 q^{44} -2.66573e16 q^{45} -1.02876e17 q^{46} -9.51528e16 q^{47} -1.26277e17 q^{48} -5.16951e17 q^{49} +9.76562e16 q^{50} -1.48511e18 q^{51} -1.89680e17 q^{52} +1.03378e18 q^{53} +9.09158e17 q^{54} +4.29790e17 q^{55} -2.18988e17 q^{56} -4.02268e18 q^{57} +2.71786e18 q^{58} -1.03132e18 q^{59} +1.17604e18 q^{60} -8.22371e18 q^{61} +1.15212e18 q^{62} -5.56719e17 q^{63} +1.15292e18 q^{64} +1.76653e18 q^{65} +5.17583e18 q^{66} -1.74709e19 q^{67} +1.35593e19 q^{68} +1.15382e19 q^{69} +2.03949e18 q^{70} +2.67322e19 q^{71} +2.93100e18 q^{72} +5.60167e19 q^{73} +2.69101e19 q^{74} -1.09528e19 q^{75} +3.67275e19 q^{76} +8.97588e18 q^{77} +2.12738e19 q^{78} -4.33055e19 q^{79} -1.07374e19 q^{80} -1.30521e20 q^{81} -2.87683e19 q^{82} -2.59402e20 q^{83} +2.45609e19 q^{84} -1.26280e20 q^{85} +1.51867e20 q^{86} -3.04825e20 q^{87} -4.72559e19 q^{88} +5.09045e20 q^{89} -2.72970e19 q^{90} +3.68929e19 q^{91} -1.05345e20 q^{92} -1.29218e20 q^{93} -9.74364e19 q^{94} -3.42052e20 q^{95} -1.29307e20 q^{96} +6.58070e20 q^{97} -5.29358e20 q^{98} -1.20136e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2048 q^{2} + 30972 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 31715328 q^{6} - 439959356 q^{7} + 2147483648 q^{8} + 13532817186 q^{9} - 20000000000 q^{10} + 105191777184 q^{11} + 32476495872 q^{12}+ \cdots + 14\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 2048 * q^2 + 30972 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 31715328 * q^6 - 439959356 * q^7 + 2147483648 * q^8 + 13532817186 * q^9 - 20000000000 * q^10 + 105191777184 * q^11 + 32476495872 * q^12 + 308456648932 * q^13 - 450518380544 * q^14 - 302460937500 * q^15 + 2199023255552 * q^16 + 18393996100404 * q^17 + 13857604798464 * q^18 + 23821216715800 * q^19 - 20480000000000 * q^20 - 10991999204616 * q^21 + 107716379836416 * q^22 - 82586042978868 * q^23 + 33255931772928 * q^24 + 190734863281250 * q^25 + 315859608506368 * q^26 + 937830505785480 * q^27 - 461330821677056 * q^28 - 167038888446420 * q^29 - 309720000000000 * q^30 + 5373084998145784 * q^31 + 2251799813685248 * q^32 + 26811195444517824 * q^33 + 18835452006813696 * q^34 + 4296478085937500 * q^35 + 14190187313627136 * q^36 + 83725084127912164 * q^37 + 24392925916979200 * q^38 + 92132195361143352 * q^39 - 20971520000000000 * q^40 - 63222375005514036 * q^41 - 11255807185526784 * q^42 - 113835841911164948 * q^43 + 110301572952489984 * q^44 - 132156417832031250 * q^45 - 84568108010360832 * q^46 + 13253549001226164 * q^47 + 34054074135478272 * q^48 - 1019795619700635846 * q^49 + 195312500000000000 * q^50 - 688515197556670056 * q^51 + 323440239110520832 * q^52 - 1445751023743904748 * q^53 + 960338437924331520 * q^54 - 1027263449062500000 * q^55 - 472402761397305344 * q^56 - 5656568844707914800 * q^57 - 171047821769134080 * q^58 - 817060118931432840 * q^59 - 317153280000000000 * q^60 - 4580997169825849436 * q^61 + 5502039038101282816 * q^62 - 3106370208073453308 * q^63 + 2305843009213693952 * q^64 - 3012271962226562500 * q^65 + 27454664135186251776 * q^66 - 28808031668773210556 * q^67 + 19287502854977224704 * q^68 + 14145335707649957352 * q^69 + 4399593560000000000 * q^70 + 51140957732016114984 * q^71 + 14530751809154187264 * q^72 + 14792322512082321412 * q^73 + 85734486146982055936 * q^74 + 2953720092773437500 * q^75 + 24978356138986700800 * q^76 - 26237463329898773952 * q^77 + 94343368049810792448 * q^78 + 25077766877525032720 * q^79 - 21474836480000000000 * q^80 - 236237497961757285078 * q^81 - 64739712005646372864 * q^82 - 120090321897786074868 * q^83 - 11525946557979426816 * q^84 - 179628868168007812500 * q^85 - 116567902117032906752 * q^86 - 716212291756398367320 * q^87 + 112948810703349743616 * q^88 + 104228468137266844980 * q^89 - 135328171860000000000 * q^90 - 78598912899601639096 * q^91 - 86597742602609491968 * q^92 + 490220677944452503824 * q^93 + 13571634177255591936 * q^94 - 232629069490234375000 * q^95 + 34871371914729750528 * q^96 - 260893520515229908796 * q^97 - 1044270714573451106304 * q^98 + 1491713506648872042912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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