LMFDB - Embedded newform 2.16.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,16,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	2.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:	$2.85387010200$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-128.000 q^{2} +6252.00 q^{3} +16384.0 q^{4} +90510.0 q^{5} -800256. q^{6} +56.0000 q^{7} -2.09715e6 q^{8} +2.47386e7 q^{9} +O(q^{10})$

\(q-128.000 q^{2} +6252.00 q^{3} +16384.0 q^{4} +90510.0 q^{5} -800256. q^{6} +56.0000 q^{7} -2.09715e6 q^{8} +2.47386e7 q^{9} -1.15853e7 q^{10} -9.58899e7 q^{11} +1.02433e8 q^{12} -5.97821e7 q^{13} -7168.00 q^{14} +5.65869e8 q^{15} +2.68435e8 q^{16} -1.35581e9 q^{17} -3.16654e9 q^{18} +3.78359e9 q^{19} +1.48292e9 q^{20} +350112. q^{21} +1.22739e10 q^{22} -1.16088e10 q^{23} -1.31114e10 q^{24} -2.23255e10 q^{25} +7.65211e9 q^{26} +6.49563e10 q^{27} +917504. q^{28} -2.89591e10 q^{29} -7.24312e10 q^{30} +2.53685e11 q^{31} -3.43597e10 q^{32} -5.99504e11 q^{33} +1.73544e11 q^{34} +5.06856e6 q^{35} +4.05317e11 q^{36} +8.17641e11 q^{37} -4.84300e11 q^{38} -3.73758e11 q^{39} -1.89813e11 q^{40} -6.82333e11 q^{41} -4.48143e7 q^{42} +3.66946e11 q^{43} -1.57106e12 q^{44} +2.23909e12 q^{45} +1.48593e12 q^{46} +6.95742e11 q^{47} +1.67826e12 q^{48} -4.74756e12 q^{49} +2.85767e12 q^{50} -8.47655e12 q^{51} -9.79471e11 q^{52} +1.29934e13 q^{53} -8.31441e12 q^{54} -8.67900e12 q^{55} -1.17441e8 q^{56} +2.36550e13 q^{57} +3.70677e12 q^{58} +9.20904e12 q^{59} +9.27119e12 q^{60} -4.23386e13 q^{61} -3.24717e13 q^{62} +1.38536e9 q^{63} +4.39805e12 q^{64} -5.41088e12 q^{65} +7.67365e13 q^{66} +3.00298e13 q^{67} -2.22137e13 q^{68} -7.25785e13 q^{69} -6.48776e8 q^{70} +1.15329e14 q^{71} -5.18806e13 q^{72} +4.37873e13 q^{73} -1.04658e14 q^{74} -1.39579e14 q^{75} +6.19904e13 q^{76} -5.36984e9 q^{77} +4.78410e13 q^{78} +7.96038e13 q^{79} +2.42961e13 q^{80} +5.11352e13 q^{81} +8.73387e13 q^{82} -3.41707e12 q^{83} +5.73624e9 q^{84} -1.22715e14 q^{85} -4.69690e13 q^{86} -1.81052e14 q^{87} +2.01096e14 q^{88} -3.77306e14 q^{89} -2.86604e14 q^{90} -3.34780e9 q^{91} -1.90199e14 q^{92} +1.58604e15 q^{93} -8.90549e13 q^{94} +3.42453e14 q^{95} -2.14817e14 q^{96} -1.66982e14 q^{97} +6.07688e14 q^{98} -2.37218e15 q^{99} +O(q^{100})\)

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 $

$2$	−128.000	−0.707107
$2$	−128.000	−0.707107
$3$	6252.00	1.65048	0.825239	−	0.564784i	$-0.191041\pi$
$3$	6252.00	1.65048	0.825239	+	0.564784i	$0.191041\pi$
$4$	16384.0	0.500000
$5$	90510.0	0.518109	0.259055	−	0.965863i	$-0.416589\pi$
$5$	90510.0	0.518109	0.259055	+	0.965863i	$0.416589\pi$
$6$	−800256.	−1.16706
$7$	56.0000	2.57012e−5 0	1.28506e−5	−	1.00000i	$-0.499996\pi$
$7$	56.0000	2.57012e−5 0	1.28506e−5		1.00000i	$0.499996\pi$
$8$	−2.09715e6	−0.353553
$9$	2.47386e7	1.72408
$10$	−1.15853e7	−0.366359
$11$	−9.58899e7	−1.48364	−0.741819	−	0.670600i	$-0.766037\pi$
$11$	−9.58899e7	−1.48364	−0.741819	+	0.670600i	$0.766037\pi$
$12$	1.02433e8	0.825239
$13$	−5.97821e7	−0.264239	−0.132119	−	0.991234i	$-0.542178\pi$
$13$	−5.97821e7	−0.264239	−0.132119	+	0.991234i	$0.542178\pi$
$14$	−7168.00	−1.81735e−5 0
$15$	5.65869e8	0.855128
$16$	2.68435e8	0.250000
$17$	−1.35581e9	−0.801370	−0.400685	−	0.916216i	$-0.631228\pi$
$17$	−1.35581e9	−0.801370	−0.400685	+	0.916216i	$0.631228\pi$
$18$	−3.16654e9	−1.21911
$19$	3.78359e9	0.971074	0.485537	−	0.874216i	$-0.338624\pi$
$19$	3.78359e9	0.971074	0.485537	+	0.874216i	$0.338624\pi$
$20$	1.48292e9	0.259055
$21$	350112.	4.24192e−5 0
$22$	1.22739e10	1.04909
$23$	−1.16088e10	−0.710936	−0.355468	−	0.934689i	$-0.615678\pi$
$23$	−1.16088e10	−0.710936	−0.355468	+	0.934689i	$0.615678\pi$
$24$	−1.31114e10	−0.583532
$25$	−2.23255e10	−0.731563
$26$	7.65211e9	0.186845
$27$	6.49563e10	1.19507
$28$	917504.	1.28506e−5 0
$29$	−2.89591e10	−0.311745	−0.155873	−	0.987777i	$-0.549819\pi$
$29$	−2.89591e10	−0.311745	−0.155873	+	0.987777i	$0.549819\pi$
$30$	−7.24312e10	−0.604667
$31$	2.53685e11	1.65609	0.828043	−	0.560665i	$-0.189454\pi$
$31$	2.53685e11	1.65609	0.828043	+	0.560665i	$0.189454\pi$
$32$	−3.43597e10	−0.176777
$33$	−5.99504e11	−2.44871
$34$	1.73544e11	0.566654
$35$	5.06856e6	1.33160e−5 0
$36$	4.05317e11	0.862038
$37$	8.17641e11	1.41596	0.707978	−	0.706234i	$-0.249607\pi$
$37$	8.17641e11	1.41596	0.707978	+	0.706234i	$0.249607\pi$
$38$	−4.84300e11	−0.686653
$39$	−3.73758e11	−0.436120
$40$	−1.89813e11	−0.183179
$41$	−6.82333e11	−0.547164	−0.273582	−	0.961849i	$-0.588209\pi$
$41$	−6.82333e11	−0.547164	−0.273582	+	0.961849i	$0.588209\pi$
$42$	−4.48143e7	−2.99949e−5 0
$43$	3.66946e11	0.205868	0.102934	−	0.994688i	$-0.467177\pi$
$43$	3.66946e11	0.205868	0.102934	+	0.994688i	$0.467177\pi$
$44$	−1.57106e12	−0.741819
$45$	2.23909e12	0.893260
$46$	1.48593e12	0.502707
$47$	6.95742e11	0.200315	0.100158	−	0.994972i	$-0.468065\pi$
$47$	6.95742e11	0.200315	0.100158	+	0.994972i	$0.468065\pi$
$48$	1.67826e12	0.412619
$49$	−4.74756e12	−1.00000
$50$	2.85767e12	0.517293
$51$	−8.47655e12	−1.32264
$52$	−9.79471e11	−0.132119
$53$	1.29934e13	1.51933	0.759666	−	0.650313i	$-0.225362\pi$
$53$	1.29934e13	1.51933	0.759666	+	0.650313i	$0.225362\pi$
$54$	−8.31441e12	−0.845042
$55$	−8.67900e12	−0.768687
$56$	−1.17441e8	−9.08673e−6 0
$57$	2.36550e13	1.60274
$58$	3.70677e12	0.220437
$59$	9.20904e12	0.481753	0.240876	−	0.970556i	$-0.422565\pi$
$59$	9.20904e12	0.481753	0.240876	+	0.970556i	$0.422565\pi$
$60$	9.27119e12	0.427564
$61$	−4.23386e13	−1.72490	−0.862448	−	0.506145i	$-0.831070\pi$
$61$	−4.23386e13	−1.72490	−0.862448	+	0.506145i	$0.831070\pi$
$62$	−3.24717e13	−1.17103
$63$	1.38536e9	4.43107e−5 0
$64$	4.39805e12	0.125000
$65$	−5.41088e12	−0.136905
$66$	7.67365e13	1.73150
$67$	3.00298e13	0.605329	0.302664	−	0.953097i	$-0.402124\pi$
$67$	3.00298e13	0.605329	0.302664	+	0.953097i	$0.402124\pi$
$68$	−2.22137e13	−0.400685
$69$	−7.25785e13	−1.17338
$70$	−6.48776e8	−9.41584e−6 0
$71$	1.15329e14	1.50487	0.752436	−	0.658665i	$-0.228879\pi$
$71$	1.15329e14	1.50487	0.752436	+	0.658665i	$0.228879\pi$
$72$	−5.18806e13	−0.609553
$73$	4.37873e13	0.463903	0.231951	−	0.972727i	$-0.425489\pi$
$73$	4.37873e13	0.463903	0.231951	+	0.972727i	$0.425489\pi$
$74$	−1.04658e14	−1.00123
$75$	−1.39579e14	−1.20743
$76$	6.19904e13	0.485537
$77$	−5.36984e9	−3.81312e−5 0
$78$	4.78410e13	0.308383
$79$	7.96038e13	0.466370	0.233185	−	0.972432i	$-0.425085\pi$
$79$	7.96038e13	0.466370	0.233185	+	0.972432i	$0.425085\pi$
$80$	2.42961e13	0.129527
$81$	5.11352e13	0.248360
$82$	8.73387e13	0.386903
$83$	−3.41707e12	−0.0138219	−0.00691095	−	0.999976i	$-0.502200\pi$
$83$	−3.41707e12	−0.0138219	−0.00691095	+	0.999976i	$0.502200\pi$
$84$	5.73624e9	2.12096e−5 0
$85$	−1.22715e14	−0.415198
$86$	−4.69690e13	−0.145570
$87$	−1.81052e14	−0.514529
$88$	2.01096e14	0.524545
$89$	−3.77306e14	−0.904209	−0.452105	−	0.891965i	$-0.649327\pi$
$89$	−3.77306e14	−0.904209	−0.452105	+	0.891965i	$0.649327\pi$
$90$	−2.86604e14	−0.631630
$91$	−3.34780e9	−6.79124e−6 0
$92$	−1.90199e14	−0.355468
$93$	1.58604e15	2.73333
$94$	−8.90549e13	−0.141644
$95$	3.42453e14	0.503123
$96$	−2.14817e14	−0.291766
$97$	−1.66982e14	−0.209837	−0.104919	−	0.994481i	$-0.533458\pi$
$97$	−1.66982e14	−0.209837	−0.104919	+	0.994481i	$0.533458\pi$
$98$	6.07688e14	0.707107
$99$	−2.37218e15	−2.55790
$100$	−3.65781e14	−0.365781
$101$	6.06802e13	0.0563167	0.0281583	−	0.999603i	$-0.491036\pi$
$101$	6.06802e13	0.0563167	0.0281583	+	0.999603i	$0.491036\pi$
$102$	1.08500e15	0.935250
$103$	5.87676e14	0.470825	0.235412	−	0.971896i	$-0.424356\pi$
$103$	5.87676e14	0.470825	0.235412	+	0.971896i	$0.424356\pi$
$104$	1.25372e14	0.0934225
$105$	3.16886e10	2.19778e−5 0
$106$	−1.66315e15	−1.07433
$107$	6.56968e14	0.395518	0.197759	−	0.980251i	$-0.436634\pi$
$107$	6.56968e14	0.395518	0.197759	+	0.980251i	$0.436634\pi$
$108$	1.06424e15	0.597535
$109$	−2.09023e15	−1.09520	−0.547602	−	0.836739i	$-0.684459\pi$
$109$	−2.09023e15	−1.09520	−0.547602	+	0.836739i	$0.684459\pi$
$110$	1.11091e15	0.543544
$111$	5.11189e15	2.33700
$112$	1.50324e10	6.42529e−6 0
$113$	−1.63296e15	−0.652959	−0.326480	−	0.945204i	$-0.605862\pi$
$113$	−1.63296e15	−0.652959	−0.326480	+	0.945204i	$0.605862\pi$
$114$	−3.02784e15	−1.13331
$115$	−1.05072e15	−0.368342
$116$	−4.74466e14	−0.155873
$117$	−1.47893e15	−0.455567
$118$	−1.17876e15	−0.340651
$119$	−7.59256e10	−2.05962e−5 0
$120$	−1.18671e15	−0.302333
$121$	5.01763e15	1.20118
$122$	5.41935e15	1.21969
$123$	−4.26595e15	−0.903082
$124$	4.15638e15	0.828043
$125$	−4.78283e15	−0.897139
$126$	−1.77326e11	−3.13324e−5 0
$127$	6.51334e15	1.08462	0.542308	−	0.840180i	$-0.317551\pi$
$127$	6.51334e15	1.08462	0.542308	+	0.840180i	$0.317551\pi$
$128$	−5.62950e14	−0.0883883
$129$	2.29414e15	0.339780
$130$	6.92593e14	0.0968061
$131$	−1.12636e16	−1.48642	−0.743212	−	0.669056i	$-0.766699\pi$
$131$	−1.12636e16	−1.48642	−0.743212	+	0.669056i	$0.766699\pi$
$132$	−9.82227e15	−1.22436
$133$	2.11881e11	2.49577e−5 0
$134$	−3.84381e15	−0.428032
$135$	5.87920e15	0.619177
$136$	2.84335e15	0.283327
$137$	5.10328e15	0.481332	0.240666	−	0.970608i	$-0.422634\pi$
$137$	5.10328e15	0.481332	0.240666	+	0.970608i	$0.422634\pi$
$138$	9.29005e15	0.829707
$139$	2.76682e15	0.234083	0.117041	−	0.993127i	$-0.462659\pi$
$139$	2.76682e15	0.234083	0.117041	+	0.993127i	$0.462659\pi$
$140$	8.30433e10	6.65801e−6 0
$141$	4.34978e15	0.330616
$142$	−1.47621e16	−1.06411
$143$	5.73251e15	0.392034
$144$	6.64072e15	0.431019
$145$	−2.62109e15	−0.161518
$146$	−5.60478e15	−0.328029
$147$	−2.96818e16	−1.65048
$148$	1.33962e16	0.707978
$149$	2.68469e16	1.34896	0.674478	−	0.738295i	$-0.264369\pi$
$149$	2.68469e16	1.34896	0.674478	+	0.738295i	$0.264369\pi$
$150$	1.78661e16	0.853780
$151$	−3.65479e16	−1.66164	−0.830818	−	0.556544i	$-0.812127\pi$
$151$	−3.65479e16	−1.66164	−0.830818	+	0.556544i	$0.812127\pi$
$152$	−7.93477e15	−0.343327
$153$	−3.35409e16	−1.38162
$154$	6.87339e11	2.69628e−5 0
$155$	2.29611e16	0.858033
$156$	−6.12365e15	−0.218060
$157$	2.99685e16	1.01723	0.508613	−	0.860995i	$-0.330158\pi$
$157$	2.99685e16	1.01723	0.508613	+	0.860995i	$0.330158\pi$
$158$	−1.01893e16	−0.329773
$159$	8.12346e16	2.50762
$160$	−3.10990e15	−0.0915897
$161$	−6.50095e11	−1.82719e−5 0
$162$	−6.54531e15	−0.175617
$163$	−4.29497e16	−1.10041	−0.550203	−	0.835031i	$-0.685450\pi$
$163$	−4.29497e16	−1.10041	−0.550203	+	0.835031i	$0.685450\pi$
$164$	−1.11793e16	−0.273582
$165$	−5.42611e16	−1.26870
$166$	4.37385e14	0.00977357
$167$	7.10064e15	0.151678	0.0758392	−	0.997120i	$-0.475836\pi$
$167$	7.10064e15	0.151678	0.0758392	+	0.997120i	$0.475836\pi$
$168$	−7.34238e11	−1.49974e−5 0
$169$	−4.76120e16	−0.930178
$170$	1.57075e16	0.293589
$171$	9.36008e16	1.67421
$172$	6.01204e15	0.102934
$173$	−5.69309e16	−0.933259	−0.466629	−	0.884453i	$-0.654532\pi$
$173$	−5.69309e16	−0.933259	−0.466629	+	0.884453i	$0.654532\pi$
$174$	2.31747e16	0.363827
$175$	−1.25023e12	−1.88020e−5 0
$176$	−2.57403e16	−0.370909
$177$	5.75749e16	0.795122
$178$	4.82952e16	0.639372
$179$	−2.65655e15	−0.0337225	−0.0168613	−	0.999858i	$-0.505367\pi$
$179$	−2.65655e15	−0.0337225	−0.0168613	+	0.999858i	$0.505367\pi$
$180$	3.66853e16	0.446630
$181$	5.17648e16	0.604569	0.302284	−	0.953218i	$-0.402251\pi$
$181$	5.17648e16	0.604569	0.302284	+	0.953218i	$0.402251\pi$
$182$	4.28518e11	4.80213e−6 0
$183$	−2.64701e17	−2.84690
$184$	2.43455e16	0.251354
$185$	7.40047e16	0.733620
$186$	−2.03013e17	−1.93276
$187$	1.30009e17	1.18894
$188$	1.13990e16	0.100158
$189$	3.63756e12	3.07147e−5 0
$190$	−4.38340e16	−0.355762
$191$	5.36753e16	0.418817	0.209408	−	0.977828i	$-0.432846\pi$
$191$	5.36753e16	0.418817	0.209408	+	0.977828i	$0.432846\pi$
$192$	2.74966e16	0.206310
$193$	1.14450e17	0.825913	0.412957	−	0.910751i	$-0.364496\pi$
$193$	1.14450e17	0.825913	0.412957	+	0.910751i	$0.364496\pi$
$194$	2.13737e16	0.148377
$195$	−3.38288e16	−0.225958
$196$	−7.77840e16	−0.500000
$197$	−2.07130e17	−1.28158	−0.640790	−	0.767716i	$-0.721393\pi$
$197$	−2.07130e17	−1.28158	−0.640790	+	0.767716i	$0.721393\pi$
$198$	3.03639e17	1.80871
$199$	−3.59838e16	−0.206399	−0.103200	−	0.994661i	$-0.532908\pi$
$199$	−3.59838e16	−0.206399	−0.103200	+	0.994661i	$0.532908\pi$
$200$	4.68200e16	0.258646
$201$	1.87746e17	0.999081
$202$	−7.76707e15	−0.0398219
$203$	−1.62171e12	−8.01222e−6 0
$204$	−1.38880e17	−0.661322
$205$	−6.17580e16	−0.283491
$206$	−7.52226e16	−0.332923
$207$	−2.87187e17	−1.22571
$208$	−1.60476e16	−0.0660597
$209$	−3.62809e17	−1.44072
$210$	−4.05615e12	−1.55406e−5 0
$211$	9.02699e16	0.333753	0.166876	−	0.985978i	$-0.446632\pi$
$211$	9.02699e16	0.333753	0.166876	+	0.985978i	$0.446632\pi$
$212$	2.12883e17	0.759666
$213$	7.21035e17	2.48376
$214$	−8.40919e16	−0.279673
$215$	3.32122e16	0.106662
$216$	−1.36223e17	−0.422521
$217$	1.42064e13	4.25633e−5 0
$218$	2.67549e17	0.774426
$219$	2.73758e17	0.765661
$220$	−1.42197e17	−0.384343
$221$	8.10535e16	0.211753
$222$	−6.54322e17	−1.65251
$223$	−3.22894e17	−0.788449	−0.394225	−	0.919014i	$-0.628987\pi$
$223$	−3.22894e17	−0.788449	−0.394225	+	0.919014i	$0.628987\pi$
$224$	−1.92415e12	−4.54337e−6 0
$225$	−5.52302e17	−1.26127
$226$	2.09018e17	0.461712
$227$	7.84856e17	1.67724	0.838621	−	0.544715i	$-0.183362\pi$
$227$	7.84856e17	1.67724	0.838621	+	0.544715i	$0.183362\pi$
$228$	3.87564e17	0.801368
$229$	−7.84092e17	−1.56892	−0.784460	−	0.620180i	$-0.787060\pi$
$229$	−7.84092e17	−1.56892	−0.784460	+	0.620180i	$0.787060\pi$
$230$	1.34492e17	0.260457
$231$	−3.35722e13	−6.29347e−5 0
$232$	6.07316e16	0.110219
$233$	−7.17048e17	−1.26002	−0.630012	−	0.776586i	$-0.716950\pi$
$233$	−7.17048e17	−1.26002	−0.630012	+	0.776586i	$0.716950\pi$
$234$	1.89303e17	0.322135
$235$	6.29716e16	0.103785
$236$	1.50881e17	0.240876
$237$	4.97683e17	0.769733
$238$	9.71848e12	1.45637e−5 0
$239$	6.93110e17	1.00651	0.503255	−	0.864138i	$-0.332136\pi$
$239$	6.93110e17	1.00651	0.503255	+	0.864138i	$0.332136\pi$
$240$	1.51899e17	0.213782
$241$	9.65566e17	1.31721	0.658604	−	0.752490i	$-0.271147\pi$
$241$	9.65566e17	1.31721	0.658604	+	0.752490i	$0.271147\pi$
$242$	−6.42257e17	−0.849364
$243$	−6.12355e17	−0.785157
$244$	−6.93676e17	−0.862448
$245$	−4.29702e17	−0.518109
$246$	5.46041e17	0.638575
$247$	−2.26191e17	−0.256595
$248$	−5.32017e17	−0.585515
$249$	−2.13635e16	−0.0228127
$250$	6.12202e17	0.634373
$251$	−8.46641e17	−0.851425	−0.425712	−	0.904859i	$-0.639976\pi$
$251$	−8.46641e17	−0.851425	−0.425712	+	0.904859i	$0.639976\pi$
$252$	2.26978e13	2.21554e−5 0
$253$	1.11317e18	1.05477
$254$	−8.33707e17	−0.766939
$255$	−7.67213e17	−0.685274
$256$	7.20576e16	0.0625000
$257$	1.40156e18	1.18063	0.590314	−	0.807174i	$-0.299004\pi$
$257$	1.40156e18	1.18063	0.590314	+	0.807174i	$0.299004\pi$
$258$	−2.93650e17	−0.240261
$259$	4.57879e13	3.63917e−5 0
$260$	−8.86519e16	−0.0684523
$261$	−7.16408e17	−0.537473
$262$	1.44174e18	1.05106
$263$	1.38804e18	0.983412	0.491706	−	0.870761i	$-0.336374\pi$
$263$	1.38804e18	0.983412	0.491706	+	0.870761i	$0.336374\pi$
$264$	1.25725e18	0.865750
$265$	1.17603e18	0.787181
$266$	−2.71208e13	−1.76478e−5 0
$267$	−2.35892e18	−1.49238
$268$	4.92008e17	0.302664
$269$	−2.85472e18	−1.70774	−0.853870	−	0.520486i	$-0.825751\pi$
$269$	−2.85472e18	−1.70774	−0.853870	+	0.520486i	$0.825751\pi$
$270$	−7.52537e17	−0.437824
$271$	−1.76158e18	−0.996858	−0.498429	−	0.866931i	$-0.666090\pi$
$271$	−1.76158e18	−0.996858	−0.498429	+	0.866931i	$0.666090\pi$
$272$	−3.63949e17	−0.200343
$273$	−2.09304e13	−1.12088e−5 0
$274$	−6.53220e17	−0.340353
$275$	2.14079e18	1.08537
$276$	−1.18913e18	−0.586692
$277$	3.96897e17	0.190581	0.0952905	−	0.995450i	$-0.469622\pi$
$277$	3.96897e17	0.190581	0.0952905	+	0.995450i	$0.469622\pi$
$278$	−3.54153e17	−0.165522
$279$	6.27582e18	2.85522
$280$	−1.06295e13	−4.70792e−6 0
$281$	3.36756e17	0.145217	0.0726086	−	0.997361i	$-0.476868\pi$
$281$	3.36756e17	0.145217	0.0726086	+	0.997361i	$0.476868\pi$
$282$	−5.56771e17	−0.233781
$283$	−4.56529e18	−1.86668	−0.933340	−	0.358992i	$-0.883120\pi$
$283$	−4.56529e18	−1.86668	−0.933340	+	0.358992i	$0.883120\pi$
$284$	1.88955e18	0.752436
$285$	2.14102e18	0.830393
$286$	−7.33761e17	−0.277210
$287$	−3.82107e13	−1.40628e−5 0
$288$	−8.50012e17	−0.304776
$289$	−1.02419e18	−0.357805
$290$	3.35499e17	0.114211
$291$	−1.04397e18	−0.346331
$292$	7.17412e17	0.231951
$293$	8.51076e17	0.268201	0.134101	−	0.990968i	$-0.457185\pi$
$293$	8.51076e17	0.268201	0.134101	+	0.990968i	$0.457185\pi$
$294$	3.79926e18	1.16706
$295$	8.33510e17	0.249601
$296$	−1.71472e18	−0.500616
$297$	−6.22866e18	−1.77305
$298$	−3.43641e18	−0.953855
$299$	6.94002e17	0.187857
$300$	−2.28686e18	−0.603714
$301$	2.05490e13	5.29104e−6 0
$302$	4.67814e18	1.17495
$303$	3.79373e17	0.0929494
$304$	1.01565e18	0.242769
$305$	−3.83207e18	−0.893685
$306$	4.29324e18	0.976955
$307$	3.96999e18	0.881560	0.440780	−	0.897615i	$-0.354702\pi$
$307$	3.96999e18	0.881560	0.440780	+	0.897615i	$0.354702\pi$
$308$	−8.79794e13	−1.90656e−5 0
$309$	3.67415e18	0.777085
$310$	−2.93902e18	−0.606721
$311$	3.18666e18	0.642144	0.321072	−	0.947055i	$-0.395957\pi$
$311$	3.18666e18	0.642144	0.321072	+	0.947055i	$0.395957\pi$
$312$	7.83827e17	0.154192
$313$	1.59866e18	0.307024	0.153512	−	0.988147i	$-0.450942\pi$
$313$	1.59866e18	0.307024	0.153512	+	0.988147i	$0.450942\pi$
$314$	−3.83597e18	−0.719288
$315$	1.25389e14	2.29578e−5 0
$316$	1.30423e18	0.233185
$317$	−4.92262e18	−0.859512	−0.429756	−	0.902945i	$-0.641400\pi$
$317$	−4.92262e18	−0.859512	−0.429756	+	0.902945i	$0.641400\pi$
$318$	−1.03980e19	−1.77316
$319$	2.77689e18	0.462517
$320$	3.98067e17	0.0647637
$321$	4.10736e18	0.652793
$322$	8.32122e13	1.29202e−5 0
$323$	−5.12985e18	−0.778190
$324$	8.37799e17	0.124180
$325$	1.33467e18	0.193307
$326$	5.49756e18	0.778104
$327$	−1.30681e19	−1.80761
$328$	1.43096e18	0.193452
$329$	3.89615e13	5.14833e−6 0
$330$	6.94542e18	0.897107
$331$	−6.42897e18	−0.811767	−0.405883	−	0.913925i	$-0.633036\pi$
$331$	−6.42897e18	−0.811767	−0.405883	+	0.913925i	$0.633036\pi$
$332$	−5.59853e16	−0.00691095
$333$	2.02273e19	2.44122
$334$	−9.08882e17	−0.107253
$335$	2.71800e18	0.313627
$336$	9.39825e13	1.06048e−5 0
$337$	1.44912e19	1.59912	0.799560	−	0.600586i	$-0.205066\pi$
$337$	1.44912e19	1.59912	0.799560	+	0.600586i	$0.205066\pi$
$338$	6.09433e18	0.657735
$339$	−1.02092e19	−1.07769
$340$	−2.01056e18	−0.207599
$341$	−2.43259e19	−2.45703
$342$	−1.19809e19	−1.18384
$343$	−5.31727e14	−5.14023e−5 0
$344$	−7.69541e17	−0.0727852
$345$	−6.56908e18	−0.607941
$346$	7.28715e18	0.659914
$347$	2.11500e19	1.87430	0.937149	−	0.348929i	$-0.113454\pi$
$347$	2.11500e19	1.87430	0.937149	+	0.348929i	$0.113454\pi$
$348$	−2.96636e18	−0.257264
$349$	−1.04783e19	−0.889409	−0.444705	−	0.895677i	$-0.646691\pi$
$349$	−1.04783e19	−0.889409	−0.444705	+	0.895677i	$0.646691\pi$
$350$	1.60029e14	1.32950e−5 0
$351$	−3.88323e18	−0.315784
$352$	3.29475e18	0.262273
$353$	1.39442e19	1.08663	0.543316	−	0.839528i	$-0.317168\pi$
$353$	1.39442e19	1.08663	0.543316	+	0.839528i	$0.317168\pi$
$354$	−7.36959e18	−0.562236
$355$	1.04384e19	0.779689
$356$	−6.18178e18	−0.452105
$357$	−4.74687e14	−3.39935e−5 0
$358$	3.40038e17	0.0238454
$359$	−1.03027e19	−0.707528	−0.353764	−	0.935335i	$-0.615098\pi$
$359$	−1.03027e19	−0.707528	−0.353764	+	0.935335i	$0.615098\pi$
$360$	−4.69571e18	−0.315815
$361$	−8.65550e17	−0.0570148
$362$	−6.62590e18	−0.427495
$363$	3.13702e19	1.98252
$364$	−5.48504e13	−3.39562e−6 0
$365$	3.96319e18	0.240353
$366$	3.38818e19	2.01306
$367$	−1.17900e19	−0.686310	−0.343155	−	0.939279i	$-0.611496\pi$
$367$	−1.17900e19	−0.686310	−0.343155	+	0.939279i	$0.611496\pi$
$368$	−3.11623e18	−0.177734
$369$	−1.68800e19	−0.943352
$370$	−9.47260e18	−0.518748
$371$	7.27629e14	3.90486e−5 0
$372$	2.59857e19	1.36667
$373$	−3.32551e19	−1.71413	−0.857063	−	0.515212i	$-0.827713\pi$
$373$	−3.32551e19	−1.71413	−0.857063	+	0.515212i	$0.827713\pi$
$374$	−1.66411e19	−0.840710
$375$	−2.99022e19	−1.48071
$376$	−1.45908e18	−0.0708221
$377$	1.73124e18	0.0823752
$378$	−4.65607e14	−2.17186e−5 0
$379$	−6.27237e18	−0.286839	−0.143419	−	0.989662i	$-0.545810\pi$
$379$	−6.27237e18	−0.286839	−0.143419	+	0.989662i	$0.545810\pi$
$380$	5.61075e18	0.251561
$381$	4.07214e19	1.79013
$382$	−6.87044e18	−0.296148
$383$	3.27919e19	1.38604	0.693020	−	0.720918i	$-0.256280\pi$
$383$	3.27919e19	1.38604	0.693020	+	0.720918i	$0.256280\pi$
$384$	−3.51956e18	−0.145883
$385$	−4.86024e14	−1.97561e−5 0
$386$	−1.46495e19	−0.584009
$387$	9.07772e18	0.354931
$388$	−2.73584e18	−0.104919
$389$	2.69074e19	1.01216	0.506081	−	0.862486i	$-0.331094\pi$
$389$	2.69074e19	1.01216	0.506081	+	0.862486i	$0.331094\pi$
$390$	4.33009e18	0.159776
$391$	1.57394e19	0.569723
$392$	9.95636e18	0.353553
$393$	−7.04201e19	−2.45331
$394$	2.65126e19	0.906214
$395$	7.20494e18	0.241631
$396$	−3.88658e19	−1.27895
$397$	6.98326e18	0.225491	0.112746	−	0.993624i	$-0.464035\pi$
$397$	6.98326e18	0.225491	0.112746	+	0.993624i	$0.464035\pi$
$398$	4.60592e18	0.145946
$399$	1.32468e15	4.11922e−5 0
$400$	−5.99296e18	−0.182891
$401$	1.22571e19	0.367118	0.183559	−	0.983009i	$-0.441238\pi$
$401$	1.22571e19	0.367118	0.183559	+	0.983009i	$0.441238\pi$
$402$	−2.40315e19	−0.706457
$403$	−1.51659e19	−0.437602
$404$	9.94185e17	0.0281583
$405$	4.62825e18	0.128678
$406$	2.07579e14	5.66550e−6 0
$407$	−7.84036e19	−2.10077
$408$	1.77766e19	0.467625
$409$	4.13285e19	1.06739	0.533697	−	0.845676i	$-0.320802\pi$
$409$	4.13285e19	1.06739	0.533697	+	0.845676i	$0.320802\pi$
$410$	7.90502e18	0.200458
$411$	3.19057e19	0.794428
$412$	9.62849e18	0.235412
$413$	5.15706e14	1.23816e−5 0
$414$	3.67599e19	0.866705
$415$	−3.09279e17	−0.00716126
$416$	2.05410e18	0.0467112
$417$	1.72982e19	0.386349
$418$	4.64395e19	1.01874
$419$	−6.58312e19	−1.41849	−0.709246	−	0.704961i	$-0.750964\pi$
$419$	−6.58312e19	−1.41849	−0.709246	+	0.704961i	$0.750964\pi$
$420$	5.19187e14	1.09889e−5 0
$421$	−6.81572e18	−0.141709	−0.0708543	−	0.997487i	$-0.522573\pi$
$421$	−6.81572e18	−0.141709	−0.0708543	+	0.997487i	$0.522573\pi$
$422$	−1.15545e19	−0.235999
$423$	1.72117e19	0.345359
$424$	−2.72491e19	−0.537165
$425$	3.02693e19	0.586253
$426$	−9.22925e19	−1.75628
$427$	−2.37096e15	−4.43319e−5 0
$428$	1.07638e19	0.197759
$429$	3.58396e19	0.647044
$430$	−4.25117e18	−0.0754214
$431$	−2.43444e19	−0.424444	−0.212222	−	0.977222i	$-0.568070\pi$
$431$	−2.43444e19	−0.424444	−0.212222	+	0.977222i	$0.568070\pi$
$432$	1.74366e19	0.298767
$433$	3.73209e19	0.628483	0.314241	−	0.949343i	$-0.398250\pi$
$433$	3.73209e19	0.628483	0.314241	+	0.949343i	$0.398250\pi$
$434$	−1.81842e15	−3.00968e−5 0
$435$	−1.63870e19	−0.266582
$436$	−3.42463e19	−0.547602
$437$	−4.39231e19	−0.690371
$438$	−3.50411e19	−0.541404
$439$	8.88153e19	1.34898	0.674488	−	0.738286i	$-0.264365\pi$
$439$	8.88153e19	1.34898	0.674488	+	0.738286i	$0.264365\pi$
$440$	1.82012e19	0.271772
$441$	−1.17448e20	−1.72408
$442$	−1.03748e19	−0.149732
$443$	−3.24463e19	−0.460402	−0.230201	−	0.973143i	$-0.573938\pi$
$443$	−3.24463e19	−0.460402	−0.230201	+	0.973143i	$0.573938\pi$
$444$	8.37533e19	1.16850
$445$	−3.41500e19	−0.468479
$446$	4.13304e19	0.557518
$447$	1.67847e20	2.22642
$448$	2.46291e14	3.21265e−6 0
$449$	1.40615e20	1.80378	0.901892	−	0.431961i	$-0.142178\pi$
$449$	1.40615e20	1.80378	0.901892	+	0.431961i	$0.142178\pi$
$450$	7.06947e19	0.891852
$451$	6.54289e19	0.811794
$452$	−2.67543e19	−0.326480
$453$	−2.28498e20	−2.74249
$454$	−1.00462e20	−1.18599
$455$	−3.03009e14	−3.51861e−6 0
$456$	−4.96082e19	−0.566653
$457$	−1.10893e20	−1.24605	−0.623023	−	0.782204i	$-0.714096\pi$
$457$	−1.10893e20	−1.24605	−0.623023	+	0.782204i	$0.714096\pi$
$458$	1.00364e20	1.10939
$459$	−8.80687e19	−0.957694
$460$	−1.72149e19	−0.184171
$461$	2.96124e19	0.311686	0.155843	−	0.987782i	$-0.450191\pi$
$461$	2.96124e19	0.311686	0.155843	+	0.987782i	$0.450191\pi$
$462$	4.29724e15	4.45016e−5 0
$463$	−1.33021e20	−1.35538	−0.677692	−	0.735346i	$-0.737020\pi$
$463$	−1.33021e20	−1.35538	−0.677692	+	0.735346i	$0.737020\pi$
$464$	−7.77365e18	−0.0779364
$465$	1.43553e20	1.41616
$466$	9.17821e19	0.890971
$467$	−7.07393e18	−0.0675747	−0.0337873	−	0.999429i	$-0.510757\pi$
$467$	−7.07393e18	−0.0675747	−0.0337873	+	0.999429i	$0.510757\pi$
$468$	−2.42307e19	−0.227784
$469$	1.68167e15	1.55576e−5 0
$470$	−8.06036e18	−0.0733872
$471$	1.87363e20	1.67891
$472$	−1.93127e19	−0.170325
$473$	−3.51864e19	−0.305433
$474$	−6.37034e19	−0.544284
$475$	−8.44707e19	−0.710402
$476$	−1.24397e15	−1.02981e−5 0
$477$	3.21438e20	2.61944
$478$	−8.87181e19	−0.711710
$479$	1.30964e19	0.103427	0.0517136	−	0.998662i	$-0.483532\pi$
$479$	1.30964e19	0.103427	0.0517136	+	0.998662i	$0.483532\pi$
$480$	−1.94431e19	−0.151167
$481$	−4.88803e19	−0.374150
$482$	−1.23592e20	−0.931406
$483$	−4.06440e15	−3.01573e−5 0
$484$	8.22089e19	0.600591
$485$	−1.51136e19	−0.108719
$486$	7.83815e19	0.555190
$487$	8.82232e19	0.615340	0.307670	−	0.951493i	$-0.400451\pi$
$487$	8.82232e19	0.615340	0.307670	+	0.951493i	$0.400451\pi$
$488$	8.87906e19	0.609843
$489$	−2.68521e20	−1.81619
$490$	5.50018e19	0.366359
$491$	−2.32523e20	−1.52530	−0.762651	−	0.646811i	$-0.776102\pi$
$491$	−2.32523e20	−1.52530	−0.762651	+	0.646811i	$0.776102\pi$
$492$	−6.98933e19	−0.451541
$493$	3.92632e19	0.249824
$494$	2.89525e19	0.181440
$495$	−2.14706e20	−1.32527
$496$	6.80981e19	0.414021
$497$	6.45841e15	3.86770e−5 0
$498$	2.73453e18	0.0161310
$499$	1.91680e20	1.11384	0.556919	−	0.830567i	$-0.311983\pi$
$499$	1.91680e20	1.11384	0.556919	+	0.830567i	$0.311983\pi$
$500$	−7.83619e19	−0.448569
$501$	4.43932e19	0.250342
$502$	1.08370e20	0.602048
$503$	2.64372e20	1.44696	0.723478	−	0.690348i	$-0.242542\pi$
$503$	2.64372e20	1.44696	0.723478	+	0.690348i	$0.242542\pi$
$504$	−2.90531e15	−1.56662e−5 0
$505$	5.49217e18	0.0291782
$506$	−1.42486e20	−0.745836
$507$	−2.97670e20	−1.53524
$508$	1.06715e20	0.542308
$509$	1.35342e20	0.677718	0.338859	−	0.940837i	$-0.389959\pi$
$509$	1.35342e20	0.677718	0.338859	+	0.940837i	$0.389959\pi$
$510$	9.82032e19	0.484562
$511$	2.45209e15	1.19228e−5 0
$512$	−9.22337e18	−0.0441942
$513$	2.45768e20	1.16050
$514$	−1.79400e20	−0.834830
$515$	5.31906e19	0.243939
$516$	3.75873e19	0.169890
$517$	−6.67146e19	−0.297195
$518$	−5.86085e15	−2.57328e−5 0
$519$	−3.55932e20	−1.54032
$520$	1.13474e19	0.0484031
$521$	1.16387e20	0.489352	0.244676	−	0.969605i	$-0.421318\pi$
$521$	1.16387e20	0.489352	0.244676	+	0.969605i	$0.421318\pi$
$522$	9.17002e19	0.380051
$523$	2.37253e20	0.969280	0.484640	−	0.874714i	$-0.338951\pi$
$523$	2.37253e20	0.969280	0.484640	+	0.874714i	$0.338951\pi$
$524$	−1.84543e20	−0.743212
$525$	−7.81643e15	−3.10323e−5 0
$526$	−1.77670e20	−0.695377
$527$	−3.43950e20	−1.32714
$528$	−1.60928e20	−0.612178
$529$	−1.31870e20	−0.494571
$530$	−1.50532e20	−0.556621
$531$	2.27819e20	0.830578
$532$	3.47146e15	1.24789e−5 0
$533$	4.07913e19	0.144582
$534$	3.01942e20	1.05527
$535$	5.94622e19	0.204921
$536$	−6.29770e19	−0.214016
$537$	−1.66087e19	−0.0556583
$538$	3.65404e20	1.20755
$539$	4.55243e20	1.48364
$540$	9.63248e19	0.309589
$541$	−2.01502e20	−0.638706	−0.319353	−	0.947636i	$-0.603466\pi$
$541$	−2.01502e20	−0.638706	−0.319353	+	0.947636i	$0.603466\pi$
$542$	2.25483e20	0.704885
$543$	3.23634e20	0.997827
$544$	4.65854e19	0.141664
$545$	−1.89187e20	−0.567435
$546$	2.67910e15	7.92581e−6 0
$547$	−2.12934e20	−0.621355	−0.310677	−	0.950515i	$-0.600556\pi$
$547$	−2.12934e20	−0.621355	−0.310677	+	0.950515i	$0.600556\pi$
$548$	8.36121e19	0.240666
$549$	−1.04740e21	−2.97385
$550$	−2.74021e20	−0.767475
$551$	−1.09569e20	−0.302728
$552$	1.52208e20	0.414854
$553$	4.45781e15	1.19863e−5 0
$554$	−5.08028e19	−0.134761
$555$	4.62677e20	1.21082
$556$	4.53316e19	0.117041
$557$	2.73616e20	0.696991	0.348495	−	0.937310i	$-0.386693\pi$
$557$	2.73616e20	0.696991	0.348495	+	0.937310i	$0.386693\pi$
$558$	−8.03305e20	−2.01894
$559$	−2.19368e19	−0.0543982
$560$	1.36058e15	3.32900e−6 0
$561$	8.12816e20	1.96232
$562$	−4.31048e19	−0.102684
$563$	−2.23411e20	−0.525159	−0.262580	−	0.964910i	$-0.584573\pi$
$563$	−2.23411e20	−0.525159	−0.262580	+	0.964910i	$0.584573\pi$
$564$	7.12667e19	0.165308
$565$	−1.47799e20	−0.338304
$566$	5.84357e20	1.31994
$567$	2.86357e15	6.38315e−6 0
$568$	−2.41862e20	−0.532053
$569$	−5.24953e20	−1.13967	−0.569834	−	0.821760i	$-0.692993\pi$
$569$	−5.24953e20	−1.13967	−0.569834	+	0.821760i	$0.692993\pi$
$570$	−2.74050e20	−0.587176
$571$	−1.54331e20	−0.326348	−0.163174	−	0.986597i	$-0.552173\pi$
$571$	−1.54331e20	−0.326348	−0.163174	+	0.986597i	$0.552173\pi$
$572$	9.39214e19	0.196017
$573$	3.35578e20	0.691248
$574$	4.89096e15	9.94387e−6 0
$575$	2.59173e20	0.520094
$576$	1.08802e20	0.215509
$577$	7.19413e20	1.40656	0.703282	−	0.710911i	$-0.251717\pi$
$577$	7.19413e20	1.40656	0.703282	+	0.710911i	$0.251717\pi$
$578$	1.31096e20	0.253007
$579$	7.15539e20	1.36315
$580$	−4.29439e19	−0.0807591
$581$	−1.91356e14	−3.55239e−7 0
$582$	1.33628e20	0.244893
$583$	−1.24593e21	−2.25414
$584$	−9.18287e19	−0.164014
$585$	−1.33858e20	−0.236034
$586$	−1.08938e20	−0.189647
$587$	−4.31990e20	−0.742485	−0.371243	−	0.928536i	$-0.621068\pi$
$587$	−4.31990e20	−0.742485	−0.371243	+	0.928536i	$0.621068\pi$
$588$	−4.86306e20	−0.825239
$589$	9.59842e20	1.60818
$590$	−1.06689e20	−0.176494
$591$	−1.29498e21	−2.11522
$592$	2.19484e20	0.353989
$593$	−4.19124e20	−0.667471	−0.333736	−	0.942667i	$-0.608309\pi$
$593$	−4.19124e20	−0.667471	−0.333736	+	0.942667i	$0.608309\pi$
$594$	7.97269e20	1.25374
$595$	−6.87203e15	−1.06711e−5 0
$596$	4.39860e20	0.674478
$597$	−2.24970e20	−0.340658
$598$	−8.88322e19	−0.132835
$599$	3.18808e20	0.470791	0.235396	−	0.971900i	$-0.424361\pi$
$599$	3.18808e20	0.470791	0.235396	+	0.971900i	$0.424361\pi$
$600$	2.92719e20	0.426890
$601$	−9.85641e20	−1.41958	−0.709791	−	0.704413i	$-0.751210\pi$
$601$	−9.85641e20	−1.41958	−0.709791	+	0.704413i	$0.751210\pi$
$602$	−2.63027e15	−3.74133e−6 0
$603$	7.42895e20	1.04363
$604$	−5.98801e20	−0.830818
$605$	4.54146e20	0.622344
$606$	−4.85597e19	−0.0657251
$607$	1.08297e21	1.44777	0.723886	−	0.689920i	$-0.242354\pi$
$607$	1.08297e21	1.44777	0.723886	+	0.689920i	$0.242354\pi$
$608$	−1.30003e20	−0.171663
$609$	−1.01389e16	−1.32240e−5 0
$610$	4.90505e20	0.631931
$611$	−4.15929e19	−0.0529310
$612$	−5.49535e20	−0.690812
$613$	1.47488e21	1.83148	0.915742	−	0.401767i	$-0.131604\pi$
$613$	1.47488e21	1.83148	0.915742	+	0.401767i	$0.131604\pi$
$614$	−5.08159e20	−0.623357
$615$	−3.86111e20	−0.467895
$616$	1.12614e16	1.34814e−5 0
$617$	−1.86048e20	−0.220032	−0.110016	−	0.993930i	$-0.535090\pi$
$617$	−1.86048e20	−0.220032	−0.110016	+	0.993930i	$0.535090\pi$
$618$	−4.70292e20	−0.549482
$619$	5.44499e20	0.628517	0.314258	−	0.949337i	$-0.398244\pi$
$619$	5.44499e20	0.628517	0.314258	+	0.949337i	$0.398244\pi$
$620$	3.76194e20	0.429017
$621$	−7.54068e20	−0.849618
$622$	−4.07892e20	−0.454065
$623$	−2.11291e16	−2.32392e−5 0
$624$	−1.00330e20	−0.109030
$625$	2.48427e20	0.266746
$626$	−2.04628e20	−0.217099
$627$	−2.26828e21	−2.37788
$628$	4.91004e20	0.508613
$629$	−1.10857e21	−1.13471
$630$	−1.60498e16	−1.62336e−5 0
$631$	−1.34412e20	−0.134344	−0.0671721	−	0.997741i	$-0.521398\pi$
$631$	−1.34412e20	−0.134344	−0.0671721	+	0.997741i	$0.521398\pi$
$632$	−1.66941e20	−0.164887
$633$	5.64367e20	0.550851
$634$	6.30095e20	0.607766
$635$	5.89522e20	0.561949
$636$	1.33095e21	1.25381
$637$	2.83819e20	0.264239
$638$	−3.55442e20	−0.327049
$639$	2.85307e21	2.59451
$640$	−5.09526e19	−0.0457948
$641$	−2.15011e20	−0.190997	−0.0954983	−	0.995430i	$-0.530444\pi$
$641$	−2.15011e20	−0.190997	−0.0954983	+	0.995430i	$0.530444\pi$
$642$	−5.25743e20	−0.461594
$643$	−1.36705e21	−1.18632	−0.593160	−	0.805085i	$-0.702120\pi$
$643$	−1.36705e21	−1.18632	−0.593160	+	0.805085i	$0.702120\pi$
$644$	−1.06512e16	−9.13593e−6 0
$645$	2.07643e20	0.176043
$646$	6.56621e20	0.550264
$647$	1.14998e20	0.0952597	0.0476298	−	0.998865i	$-0.484833\pi$
$647$	1.14998e20	0.0952597	0.0476298	+	0.998865i	$0.484833\pi$
$648$	−1.07238e20	−0.0878087
$649$	−8.83054e20	−0.714746
$650$	−1.70837e20	−0.136689
$651$	8.88183e16	7.02498e−5 0
$652$	−7.03687e20	−0.550203
$653$	−1.23391e21	−0.953751	−0.476876	−	0.878971i	$-0.658231\pi$
$653$	−1.23391e21	−0.953751	−0.476876	+	0.878971i	$0.658231\pi$
$654$	1.67272e21	1.27817
$655$	−1.01947e21	−0.770131
$656$	−1.83162e20	−0.136791
$657$	1.08324e21	0.799804
$658$	−4.98708e15	−3.64042e−6 0
$659$	1.63082e21	1.17697	0.588485	−	0.808508i	$-0.299725\pi$
$659$	1.63082e21	1.17697	0.588485	+	0.808508i	$0.299725\pi$
$660$	−8.89014e20	−0.634350
$661$	−1.38740e21	−0.978793	−0.489397	−	0.872061i	$-0.662783\pi$
$661$	−1.38740e21	−0.978793	−0.489397	+	0.872061i	$0.662783\pi$
$662$	8.22908e20	0.574006
$663$	5.06746e20	0.349494
$664$	7.16611e18	0.00488678
$665$	1.91774e16	1.29308e−5 0
$666$	−2.58909e21	−1.72620
$667$	3.36182e20	0.221631
$668$	1.16337e20	0.0758392
$669$	−2.01873e21	−1.30132
$670$	−3.47904e20	−0.221767
$671$	4.05985e21	2.55912
$672$	−1.20298e16	−7.49872e−6 0
$673$	−1.33937e21	−0.825631	−0.412816	−	0.910815i	$-0.635455\pi$
$673$	−1.33937e21	−0.825631	−0.412816	+	0.910815i	$0.635455\pi$
$674$	−1.85488e21	−1.13075
$675$	−1.45018e21	−0.874268
$676$	−7.80075e20	−0.465089
$677$	1.99408e21	1.17579	0.587893	−	0.808938i	$-0.299957\pi$
$677$	1.99408e21	1.17579	0.587893	+	0.808938i	$0.299957\pi$
$678$	1.30678e21	0.762045
$679$	−9.35100e15	−5.39306e−6 0
$680$	2.57352e20	0.146795
$681$	4.90692e21	2.76825
$682$	3.11371e21	1.73738
$683$	−1.25180e21	−0.690845	−0.345422	−	0.938447i	$-0.612264\pi$
$683$	−1.25180e21	−0.690845	−0.345422	+	0.938447i	$0.612264\pi$
$684$	1.53356e21	0.837103
$685$	4.61898e20	0.249383
$686$	6.80610e16	3.63469e−5 0
$687$	−4.90214e21	−2.58947
$688$	9.85012e19	0.0514669
$689$	−7.76772e20	−0.401466
$690$	8.40842e20	0.429879
$691$	−1.46431e21	−0.740539	−0.370269	−	0.928924i	$-0.620735\pi$
$691$	−1.46431e21	−0.740539	−0.370269	+	0.928924i	$0.620735\pi$
$692$	−9.32756e20	−0.466629
$693$	−1.32842e17	−6.57411e−5 0
$694$	−2.70720e21	−1.32533
$695$	2.50425e20	0.121281
$696$	3.79694e20	0.181913
$697$	9.25117e20	0.438481
$698$	1.34123e21	0.628907
$699$	−4.48298e21	−2.07964
$700$	−2.04838e16	−9.40100e−6 0
$701$	−2.97987e20	−0.135305	−0.0676523	−	0.997709i	$-0.521551\pi$
$701$	−2.97987e20	−0.135305	−0.0676523	+	0.997709i	$0.521551\pi$
$702$	4.97053e20	0.223293
$703$	3.09362e21	1.37500
$704$	−4.21728e20	−0.185455
$705$	3.93698e20	0.171295
$706$	−1.78486e21	−0.768365
$707$	3.39809e15	1.44740e−6 0
$708$	9.43307e20	0.397561
$709$	1.21881e21	0.508264	0.254132	−	0.967169i	$-0.418210\pi$
$709$	1.21881e21	0.508264	0.254132	+	0.967169i	$0.418210\pi$
$710$	−1.33612e21	−0.551323
$711$	1.96929e21	0.804057
$712$	7.91268e20	0.319686
$713$	−2.94499e21	−1.17737
$714$	6.07599e16	2.40370e−5 0
$715$	5.18849e20	0.203117
$716$	−4.35249e19	−0.0168613
$717$	4.33333e21	1.66122
$718$	1.31875e21	0.500298
$719$	−3.01856e21	−1.13327	−0.566634	−	0.823970i	$-0.691755\pi$
$719$	−3.01856e21	−1.13327	−0.566634	+	0.823970i	$0.691755\pi$
$720$	6.01051e20	0.223315
$721$	3.29099e16	1.21007e−5 0
$722$	1.10790e20	0.0403156
$723$	6.03672e21	2.17402
$724$	8.48115e20	0.302284
$725$	6.46527e20	0.228061
$726$	−4.01539e21	−1.40186
$727$	8.97710e20	0.310190	0.155095	−	0.987900i	$-0.450432\pi$
$727$	8.97710e20	0.310190	0.155095	+	0.987900i	$0.450432\pi$
$728$	7.02084e15	2.40107e−6 0
$729$	−4.56218e21	−1.54424
$730$	−5.07289e20	−0.169955
$731$	−4.97510e20	−0.164976
$732$	−4.33686e21	−1.42345
$733$	−8.52857e20	−0.277074	−0.138537	−	0.990357i	$-0.544240\pi$
$733$	−8.52857e20	−0.277074	−0.138537	+	0.990357i	$0.544240\pi$
$734$	1.50913e21	0.485294
$735$	−2.68650e21	−0.855128
$736$	3.98877e20	0.125677
$737$	−2.87955e21	−0.898089
$738$	2.16064e21	0.667051
$739$	2.19196e21	0.669883	0.334941	−	0.942239i	$-0.391284\pi$
$739$	2.19196e21	0.669883	0.334941	+	0.942239i	$0.391284\pi$
$740$	1.21249e21	0.366810
$741$	−1.41415e21	−0.423505
$742$	−9.31365e16	−2.76115e−5 0
$743$	1.89929e21	0.557410	0.278705	−	0.960377i	$-0.410095\pi$
$743$	1.89929e21	0.557410	0.278705	+	0.960377i	$0.410095\pi$
$744$	−3.32617e21	−0.966378
$745$	2.42992e21	0.698906
$746$	4.25666e21	1.21207
$747$	−8.45335e19	−0.0238300
$748$	2.13007e21	0.594472
$749$	3.67902e16	1.01653e−5 0
$750$	3.82749e21	1.04702
$751$	−4.40128e21	−1.19201	−0.596005	−	0.802981i	$-0.703246\pi$
$751$	−4.40128e21	−1.19201	−0.596005	+	0.802981i	$0.703246\pi$
$752$	1.86762e20	0.0500788
$753$	−5.29320e21	−1.40526
$754$	−2.21598e20	−0.0582481
$755$	−3.30795e21	−0.860909
$756$	5.95977e16	1.53573e−5 0
$757$	3.32600e21	0.848601	0.424300	−	0.905521i	$-0.360520\pi$
$757$	3.32600e21	0.848601	0.424300	+	0.905521i	$0.360520\pi$
$758$	8.02863e20	0.202825
$759$	6.95955e21	1.74088
$760$	−7.18176e20	−0.177881
$761$	6.66362e21	1.63428	0.817138	−	0.576443i	$-0.195560\pi$
$761$	6.66362e21	1.63428	0.817138	+	0.576443i	$0.195560\pi$
$762$	−5.21234e21	−1.26582
$763$	−1.17053e17	−2.81480e−5 0
$764$	8.79416e20	0.209408
$765$	−3.03579e21	−0.715832
$766$	−4.19736e21	−0.980079
$767$	−5.50536e20	−0.127298
$768$	4.50504e20	0.103155
$769$	1.77725e21	0.402997	0.201499	−	0.979489i	$-0.435419\pi$
$769$	1.77725e21	0.402997	0.201499	+	0.979489i	$0.435419\pi$
$770$	6.22111e16	1.39697e−5 0
$771$	8.76255e21	1.94860
$772$	1.87514e21	0.412957
$773$	−4.17145e21	−0.909790	−0.454895	−	0.890545i	$-0.650323\pi$
$773$	−4.17145e21	−0.909790	−0.454895	+	0.890545i	$0.650323\pi$
$774$	−1.16195e21	−0.250974
$775$	−5.66366e21	−1.21153
$776$	3.50187e20	0.0741886
$777$	2.86266e17	6.00637e−5 0
$778$	−3.44415e21	−0.715706
$779$	−2.58167e21	−0.531337
$780$	−5.54252e20	−0.112979
$781$	−1.10589e22	−2.23269
$782$	−2.01465e21	−0.402855
$783$	−1.88108e21	−0.372558
$784$	−1.27441e21	−0.250000
$785$	2.71245e21	0.527035
$786$	9.01377e21	1.73475
$787$	4.96836e21	0.947114	0.473557	−	0.880763i	$-0.342970\pi$
$787$	4.96836e21	0.947114	0.473557	+	0.880763i	$0.342970\pi$
$788$	−3.39361e21	−0.640790
$789$	8.67805e21	1.62310
$790$	−9.22232e20	−0.170859
$791$	−9.14455e16	−1.67818e−5 0
$792$	4.97483e21	0.904356
$793$	2.53109e21	0.455784
$794$	−8.93858e20	−0.159446
$795$	7.35254e21	1.29922
$796$	−5.89558e20	−0.103200
$797$	4.55056e21	0.789091	0.394546	−	0.918876i	$-0.370902\pi$
$797$	4.55056e21	0.789091	0.394546	+	0.918876i	$0.370902\pi$
$798$	−1.69559e17	−2.91273e−5 0
$799$	−9.43296e20	−0.160527
$800$	7.67099e20	0.129323
$801$	−9.33403e21	−1.55892
$802$	−1.56891e21	−0.259592
$803$	−4.19877e21	−0.688264
$804$	3.07603e21	0.499541
$805$	−5.88401e16	−9.46683e−6 0
$806$	1.94123e21	0.309431
$807$	−1.78477e22	−2.81859
$808$	−1.27256e20	−0.0199109
$809$	1.12040e22	1.73683	0.868417	−	0.495834i	$-0.165138\pi$
$809$	1.12040e22	1.73683	0.868417	+	0.495834i	$0.165138\pi$
$810$	−5.92416e20	−0.0909890
$811$	1.56431e21	0.238048	0.119024	−	0.992891i	$-0.462023\pi$
$811$	1.56431e21	0.238048	0.119024	+	0.992891i	$0.462023\pi$
$812$	−2.65701e16	−4.00611e−6 0
$813$	−1.10134e22	−1.64529
$814$	1.00357e22	1.48547
$815$	−3.88737e21	−0.570130
$816$	−2.27541e21	−0.330661
$817$	1.38837e21	0.199913
$818$	−5.29005e21	−0.754762
$819$	−8.28199e16	−1.17086e−5 0
$820$	−1.01184e21	−0.141745
$821$	5.31534e21	0.737831	0.368916	−	0.929463i	$-0.379729\pi$
$821$	5.31534e21	0.737831	0.368916	+	0.929463i	$0.379729\pi$
$822$	−4.08393e21	−0.561745
$823$	2.48380e21	0.338546	0.169273	−	0.985569i	$-0.445858\pi$
$823$	2.48380e21	0.338546	0.169273	+	0.985569i	$0.445858\pi$
$824$	−1.23245e21	−0.166462
$825$	1.33842e22	1.79139
$826$	−6.60104e16	−8.75511e−6 0
$827$	−6.01420e21	−0.790473	−0.395236	−	0.918580i	$-0.629337\pi$
$827$	−6.01420e21	−0.790473	−0.395236	+	0.918580i	$0.629337\pi$
$828$	−4.70526e21	−0.612853
$829$	−4.33653e21	−0.559736	−0.279868	−	0.960039i	$-0.590291\pi$
$829$	−4.33653e21	−0.559736	−0.279868	+	0.960039i	$0.590291\pi$
$830$	3.95877e19	0.00506378
$831$	2.48140e21	0.314550
$832$	−2.62925e20	−0.0330298
$833$	6.43681e21	0.801370
$834$	−2.21416e21	−0.273190
$835$	6.42679e20	0.0785861
$836$	−5.94426e21	−0.720361
$837$	1.64785e22	1.97914
$838$	8.42640e21	1.00303
$839$	7.92224e21	0.934616	0.467308	−	0.884095i	$-0.345224\pi$
$839$	7.92224e21	0.934616	0.467308	+	0.884095i	$0.345224\pi$
$840$	−6.64559e16	−7.77032e−6 0
$841$	−7.79056e21	−0.902815
$842$	8.72412e20	0.100203
$843$	2.10540e21	0.239678
$844$	1.47898e21	0.166876
$845$	−4.30936e21	−0.481934
$846$	−2.20309e21	−0.244205
$847$	2.80988e17	3.08718e−5 0
$848$	3.48788e21	0.379833
$849$	−2.85422e22	−3.08091
$850$	−3.87447e21	−0.414543
$851$	−9.49187e21	−1.00665
$852$	1.18134e22	1.24188
$853$	4.77976e21	0.498067	0.249034	−	0.968495i	$-0.419887\pi$
$853$	4.77976e21	0.498067	0.249034	+	0.968495i	$0.419887\pi$
$854$	3.03483e17	3.13474e−5 0
$855$	8.47181e21	0.867422
$856$	−1.37776e21	−0.139837
$857$	−1.38506e22	−1.39352	−0.696758	−	0.717306i	$-0.745375\pi$
$857$	−1.38506e22	−1.39352	−0.696758	+	0.717306i	$0.745375\pi$
$858$	−4.58747e21	−0.457529
$859$	1.13389e22	1.12104	0.560522	−	0.828140i	$-0.310601\pi$
$859$	1.13389e22	1.12104	0.560522	+	0.828140i	$0.310601\pi$
$860$	5.44149e20	0.0533310
$861$	−2.38893e17	−2.32103e−5 0
$862$	3.11609e21	0.300127
$863$	1.34506e22	1.28428	0.642142	−	0.766586i	$-0.278046\pi$
$863$	1.34506e22	1.28428	0.642142	+	0.766586i	$0.278046\pi$
$864$	−2.23188e21	−0.211261
$865$	−5.15281e21	−0.483530
$866$	−4.77708e21	−0.444404
$867$	−6.40324e21	−0.590550
$868$	2.32757e17	2.12817e−5 0
$869$	−7.63321e21	−0.691924
$870$	2.09754e21	0.188502
$871$	−1.79524e21	−0.159951
$872$	4.38353e21	0.387213
$873$	−4.13091e21	−0.361775
$874$	5.62216e21	0.488166
$875$	−2.67838e17	−2.30575e−5 0
$876$	4.48526e21	0.382831
$877$	8.71264e21	0.737315	0.368657	−	0.929565i	$-0.379818\pi$
$877$	8.71264e21	0.737315	0.368657	+	0.929565i	$0.379818\pi$
$878$	−1.13684e22	−0.953870
$879$	5.32093e21	0.442660
$880$	−2.32975e21	−0.192172
$881$	1.84288e22	1.50722	0.753611	−	0.657321i	$-0.228310\pi$
$881$	1.84288e22	1.50722	0.753611	+	0.657321i	$0.228310\pi$
$882$	1.50333e22	1.21911
$883$	6.38696e21	0.513558	0.256779	−	0.966470i	$-0.417339\pi$
$883$	6.38696e21	0.513558	0.256779	+	0.966470i	$0.417339\pi$
$884$	1.32798e21	0.105877
$885$	5.21110e21	0.411960
$886$	4.15312e21	0.325553
$887$	−1.26761e22	−0.985279	−0.492639	−	0.870234i	$-0.663968\pi$
$887$	−1.26761e22	−0.985279	−0.492639	+	0.870234i	$0.663968\pi$
$888$	−1.07204e22	−0.826256
$889$	3.64747e17	2.78759e−5 0
$890$	4.37120e21	0.331265
$891$	−4.90335e21	−0.368477
$892$	−5.29030e21	−0.394225
$893$	2.63240e21	0.194521
$894$	−2.14844e22	−1.57432
$895$	−2.40444e20	−0.0174720
$896$	−3.15252e16	−2.27168e−6 0
$897$	4.33890e21	0.310053
$898$	−1.79987e22	−1.27547
$899$	−7.34650e21	−0.516277
$900$	−9.04892e21	−0.630635
$901$	−1.76166e22	−1.21755
$902$	−8.37490e21	−0.574025
$903$	1.28472e17	8.73274e−6 0
$904$	3.42456e21	0.230856
$905$	4.68524e21	0.313233
$906$	2.92477e22	1.93923
$907$	1.29670e21	0.0852676	0.0426338	−	0.999091i	$-0.486425\pi$
$907$	1.29670e21	0.0852676	0.0426338	+	0.999091i	$0.486425\pi$
$908$	1.28591e22	0.838621
$909$	1.50114e21	0.0970942
$910$	3.87852e16	2.48803e−6 0
$911$	2.26280e22	1.43966	0.719828	−	0.694153i	$-0.244221\pi$
$911$	2.26280e22	1.43966	0.719828	+	0.694153i	$0.244221\pi$
$912$	6.34985e21	0.400684
$913$	3.27663e20	0.0205067
$914$	1.41943e22	0.881087
$915$	−2.39581e22	−1.47501
$916$	−1.28466e22	−0.784460
$917$	−6.30762e17	−3.82028e−5 0
$918$	1.12728e22	0.677192
$919$	−4.37047e21	−0.260412	−0.130206	−	0.991487i	$-0.541564\pi$
$919$	−4.37047e21	−0.260412	−0.130206	+	0.991487i	$0.541564\pi$
$920$	2.20351e21	0.130229
$921$	2.48204e22	1.45499
$922$	−3.79039e21	−0.220395
$923$	−6.89460e21	−0.397645
$924$	−5.50047e17	−3.14674e−5 0
$925$	−1.82543e22	−1.03586
$926$	1.70267e22	0.958401
$927$	1.45383e22	0.811737
$928$	9.95027e20	0.0551093
$929$	−2.43423e22	−1.33734	−0.668672	−	0.743557i	$-0.733137\pi$
$929$	−2.43423e22	−1.33734	−0.668672	+	0.743557i	$0.733137\pi$
$930$	−1.83747e22	−1.00138
$931$	−1.79628e22	−0.971074
$932$	−1.17481e22	−0.630012
$933$	1.99230e22	1.05984
$934$	9.05463e20	0.0477825
$935$	1.17671e22	0.616003
$936$	3.10153e21	0.161067
$937$	1.64776e22	0.848879	0.424439	−	0.905456i	$-0.360471\pi$
$937$	1.64776e22	0.848879	0.424439	+	0.905456i	$0.360471\pi$
$938$	−2.15254e17	−1.10009e−5 0
$939$	9.99480e21	0.506736
$940$	1.03173e21	0.0518926
$941$	−2.09383e22	−1.04477	−0.522384	−	0.852710i	$-0.674957\pi$
$941$	−2.09383e22	−1.04477	−0.522384	+	0.852710i	$0.674957\pi$
$942$	−2.39825e22	−1.18717
$943$	7.92110e21	0.388998
$944$	2.47203e21	0.120438
$945$	3.29235e17	1.59136e−5 0
$946$	4.50386e21	0.215974
$947$	−3.36036e22	−1.59868	−0.799338	−	0.600881i	$-0.794817\pi$
$947$	−3.36036e22	−1.59868	−0.799338	+	0.600881i	$0.794817\pi$
$948$	8.15404e21	0.384867
$949$	−2.61770e21	−0.122581
$950$	1.08122e22	0.502330
$951$	−3.07762e22	−1.41860
$952$	1.59228e17	7.28184e−6 0
$953$	3.45292e22	1.56671	0.783357	−	0.621572i	$-0.213506\pi$
$953$	3.45292e22	1.56671	0.783357	+	0.621572i	$0.213506\pi$
$954$	−4.11440e22	−1.85223
$955$	4.85815e21	0.216993
$956$	1.13559e22	0.503255
$957$	1.73611e22	0.763375
$958$	−1.67634e21	−0.0731340
$959$	2.85784e17	1.23708e−5 0
$960$	2.48872e21	0.106891
$961$	4.08910e22	1.74262
$962$	6.25668e21	0.264564
$963$	1.62525e22	0.681902
$964$	1.58198e22	0.658604
$965$	1.03588e22	0.427913
$966$	5.20243e17	2.13244e−5 0
$967$	1.34537e21	0.0547197	0.0273598	−	0.999626i	$-0.491290\pi$
$967$	1.34537e21	0.0547197	0.0273598	+	0.999626i	$0.491290\pi$
$968$	−1.05227e22	−0.424682
$969$	−3.20718e22	−1.28439
$970$	1.93454e21	0.0768756
$971$	1.50334e21	0.0592807	0.0296403	−	0.999561i	$-0.490564\pi$
$971$	1.50334e21	0.0592807	0.0296403	+	0.999561i	$0.490564\pi$
$972$	−1.00328e22	−0.392578
$973$	1.54942e17	6.01620e−6 0
$974$	−1.12926e22	−0.435111
$975$	8.34434e21	0.319049
$976$	−1.13652e22	−0.431224
$977$	−4.36133e22	−1.64214	−0.821068	−	0.570830i	$-0.806622\pi$
$977$	−4.36133e22	−1.64214	−0.821068	+	0.570830i	$0.806622\pi$
$978$	3.43707e22	1.28424
$979$	3.61799e22	1.34152
$980$	−7.04023e21	−0.259055
$981$	−5.17093e22	−1.88821
$982$	2.97630e22	1.07855
$983$	3.21986e21	0.115794	0.0578969	−	0.998323i	$-0.481561\pi$
$983$	3.21986e21	0.115794	0.0578969	+	0.998323i	$0.481561\pi$
$984$	8.94634e21	0.319288
$985$	−1.87473e22	−0.663999
$986$	−5.02569e21	−0.176652
$987$	2.43587e17	8.49721e−6 0
$988$	−3.70592e21	−0.128298
$989$	−4.25981e21	−0.146359
$990$	2.74824e22	0.937110
$991$	−4.85010e22	−1.64134	−0.820670	−	0.571402i	$-0.806400\pi$
$991$	−4.85010e22	−1.64134	−0.820670	+	0.571402i	$0.806400\pi$
$992$	−8.71656e21	−0.292757
$993$	−4.01939e22	−1.33980
$994$	−8.26676e17	−2.73488e−5 0
$995$	−3.25689e21	−0.106937
$996$	−3.50020e20	−0.0114064
$997$	5.35543e22	1.73213	0.866065	−	0.499931i	$-0.166641\pi$
$997$	5.35543e22	1.73213	0.866065	+	0.499931i	$0.166641\pi$
$998$	−2.45350e22	−0.787603
$999$	5.31110e22	1.69217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.16.a.a.1.1	✓	1
3.2	odd	2		18.16.a.e.1.1		1
4.3	odd	2		16.16.a.a.1.1		1
5.2	odd	4		50.16.b.a.49.1		2
5.3	odd	4		50.16.b.a.49.2		2
5.4	even	2		50.16.a.b.1.1		1
7.2	even	3		98.16.c.a.67.1		2
7.3	odd	6		98.16.c.d.79.1		2
7.4	even	3		98.16.c.a.79.1		2
7.5	odd	6		98.16.c.d.67.1		2
7.6	odd	2		98.16.a.a.1.1		1
8.3	odd	2		64.16.a.k.1.1		1
8.5	even	2		64.16.a.a.1.1		1
12.11	even	2		144.16.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.16.a.a.1.1	✓	1	1.1	even	1	trivial
16.16.a.a.1.1		1	4.3	odd	2
18.16.a.e.1.1		1	3.2	odd	2
50.16.a.b.1.1		1	5.4	even	2
50.16.b.a.49.1		2	5.2	odd	4
50.16.b.a.49.2		2	5.3	odd	4
64.16.a.a.1.1		1	8.5	even	2
64.16.a.k.1.1		1	8.3	odd	2
98.16.a.a.1.1		1	7.6	odd	2
98.16.c.a.67.1		2	7.2	even	3
98.16.c.a.79.1		2	7.4	even	3
98.16.c.d.67.1		2	7.5	odd	6
98.16.c.d.79.1		2	7.3	odd	6
144.16.a.d.1.1		1	12.11	even	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more