LMFDB - Embedded newform 21.14.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,14,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	21.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:	$22.5184950799$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+120.497 q^{2} +729.000 q^{3} +6327.63 q^{4} -62168.1 q^{5} +87842.6 q^{6} +117649. q^{7} -224652. q^{8} +531441. q^{9} +O(q^{10})$	\(q+120.497 q^{2} +729.000 q^{3} +6327.63 q^{4} -62168.1 q^{5} +87842.6 q^{6} +117649. q^{7} -224652. q^{8} +531441. q^{9} -7.49109e6 q^{10} -8.85265e6 q^{11} +4.61284e6 q^{12} -8.39684e6 q^{13} +1.41764e7 q^{14} -4.53205e7 q^{15} -7.89059e7 q^{16} +1.33892e8 q^{17} +6.40373e7 q^{18} -3.46327e8 q^{19} -3.93377e8 q^{20} +8.57661e7 q^{21} -1.06672e9 q^{22} +5.16232e8 q^{23} -1.63771e8 q^{24} +2.64417e9 q^{25} -1.01180e9 q^{26} +3.87420e8 q^{27} +7.44439e8 q^{28} +2.41001e9 q^{29} -5.46101e9 q^{30} -8.56433e9 q^{31} -7.66761e9 q^{32} -6.45358e9 q^{33} +1.61336e10 q^{34} -7.31401e9 q^{35} +3.36276e9 q^{36} -4.20316e9 q^{37} -4.17315e10 q^{38} -6.12130e9 q^{39} +1.39662e10 q^{40} +1.82419e10 q^{41} +1.03346e10 q^{42} -5.38398e9 q^{43} -5.60163e10 q^{44} -3.30387e10 q^{45} +6.22046e10 q^{46} -6.39708e10 q^{47} -5.75224e10 q^{48} +1.38413e10 q^{49} +3.18616e11 q^{50} +9.76070e10 q^{51} -5.31321e10 q^{52} +2.66663e11 q^{53} +4.66832e10 q^{54} +5.50352e11 q^{55} -2.64301e10 q^{56} -2.52472e11 q^{57} +2.90400e11 q^{58} -2.62371e10 q^{59} -2.86772e11 q^{60} -9.67948e9 q^{61} -1.03198e12 q^{62} +6.25235e10 q^{63} -2.77530e11 q^{64} +5.22016e11 q^{65} -7.77640e11 q^{66} -7.34892e11 q^{67} +8.47217e11 q^{68} +3.76333e11 q^{69} -8.81320e11 q^{70} +1.05215e12 q^{71} -1.19389e11 q^{72} -9.67631e11 q^{73} -5.06470e11 q^{74} +1.92760e12 q^{75} -2.19143e12 q^{76} -1.04150e12 q^{77} -7.37601e11 q^{78} -1.46116e12 q^{79} +4.90543e12 q^{80} +2.82430e11 q^{81} +2.19810e12 q^{82} +6.16621e11 q^{83} +5.42696e11 q^{84} -8.32379e12 q^{85} -6.48756e11 q^{86} +1.75689e12 q^{87} +1.98876e12 q^{88} +7.71766e11 q^{89} -3.98107e12 q^{90} -9.87880e11 q^{91} +3.26652e12 q^{92} -6.24340e12 q^{93} -7.70831e12 q^{94} +2.15305e13 q^{95} -5.58969e12 q^{96} -6.34908e12 q^{97} +1.66784e12 q^{98} -4.70466e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 144 q^{2} + 1458 q^{3} - 1312 q^{4} - 52560 q^{5} + 104976 q^{6} + 235298 q^{7} - 596736 q^{8} + 1062882 q^{9}+O(q^{10}) $ 2 * q + 144 * q^2 + 1458 * q^3 - 1312 * q^4 - 52560 * q^5 + 104976 * q^6 + 235298 * q^7 - 596736 * q^8 + 1062882 * q^9	\( 2 q + 144 q^{2} + 1458 q^{3} - 1312 q^{4} - 52560 q^{5} + 104976 q^{6} + 235298 q^{7} - 596736 q^{8} + 1062882 q^{9} - 7265280 q^{10} - 8593596 q^{11} - 956448 q^{12} - 37982012 q^{13} + 16941456 q^{14} - 38316240 q^{15} - 25067008 q^{16} + 16643088 q^{17} + 76527504 q^{18} - 211195304 q^{19} - 466778880 q^{20} + 171532242 q^{21} - 1060632672 q^{22} - 194997852 q^{23} - 435020544 q^{24} + 1515780950 q^{25} - 1707125472 q^{26} + 774840978 q^{27} - 154355488 q^{28} - 3481642548 q^{29} - 5296389120 q^{30} - 8393797520 q^{31} - 3354144768 q^{32} - 6264731484 q^{33} + 13377955584 q^{34} - 6183631440 q^{35} - 697250592 q^{36} - 22337946716 q^{37} - 38555551296 q^{38} - 27688886748 q^{39} + 10391162880 q^{40} - 12507403320 q^{41} + 12350321424 q^{42} + 26062746328 q^{43} - 57995302464 q^{44} - 27932538960 q^{45} + 45488879520 q^{46} + 29222658936 q^{47} - 18273848832 q^{48} + 27682574402 q^{49} + 292095486000 q^{50} + 12132811152 q^{51} + 172887632320 q^{52} + 523911868308 q^{53} + 55788550416 q^{54} + 552841085280 q^{55} - 70205393664 q^{56} - 153961376616 q^{57} + 151930661472 q^{58} - 94444581024 q^{59} - 340281803520 q^{60} + 461720554252 q^{61} - 1027971840384 q^{62} + 125047004418 q^{63} - 617200820224 q^{64} + 237758525280 q^{65} - 773201217888 q^{66} - 1237879942064 q^{67} + 1742952201984 q^{68} - 142153434108 q^{69} - 854752926720 q^{70} + 1961126619804 q^{71} - 317129976576 q^{72} - 2407791783284 q^{73} - 932684149728 q^{74} + 1105004312550 q^{75} - 3223782355328 q^{76} - 1011027975804 q^{77} - 1244494469088 q^{78} - 2622494223848 q^{79} + 5422719283200 q^{80} + 564859072962 q^{81} + 1475409286080 q^{82} + 4489561815912 q^{83} - 112525150752 q^{84} - 9450323756160 q^{85} + 90323285184 q^{86} - 2538117417492 q^{87} + 1892375536128 q^{88} + 520927840584 q^{89} - 3861067668480 q^{90} - 4468545729788 q^{91} + 8700054971328 q^{92} - 6119078392080 q^{93} - 5518028009280 q^{94} + 22828834751040 q^{95} - 2445171535872 q^{96} - 13027956631604 q^{97} + 1993145356944 q^{98} - 4566989251836 q^{99}+O(q^{100}) \) 2 * q + 144 * q^2 + 1458 * q^3 - 1312 * q^4 - 52560 * q^5 + 104976 * q^6 + 235298 * q^7 - 596736 * q^8 + 1062882 * q^9 - 7265280 * q^10 - 8593596 * q^11 - 956448 * q^12 - 37982012 * q^13 + 16941456 * q^14 - 38316240 * q^15 - 25067008 * q^16 + 16643088 * q^17 + 76527504 * q^18 - 211195304 * q^19 - 466778880 * q^20 + 171532242 * q^21 - 1060632672 * q^22 - 194997852 * q^23 - 435020544 * q^24 + 1515780950 * q^25 - 1707125472 * q^26 + 774840978 * q^27 - 154355488 * q^28 - 3481642548 * q^29 - 5296389120 * q^30 - 8393797520 * q^31 - 3354144768 * q^32 - 6264731484 * q^33 + 13377955584 * q^34 - 6183631440 * q^35 - 697250592 * q^36 - 22337946716 * q^37 - 38555551296 * q^38 - 27688886748 * q^39 + 10391162880 * q^40 - 12507403320 * q^41 + 12350321424 * q^42 + 26062746328 * q^43 - 57995302464 * q^44 - 27932538960 * q^45 + 45488879520 * q^46 + 29222658936 * q^47 - 18273848832 * q^48 + 27682574402 * q^49 + 292095486000 * q^50 + 12132811152 * q^51 + 172887632320 * q^52 + 523911868308 * q^53 + 55788550416 * q^54 + 552841085280 * q^55 - 70205393664 * q^56 - 153961376616 * q^57 + 151930661472 * q^58 - 94444581024 * q^59 - 340281803520 * q^60 + 461720554252 * q^61 - 1027971840384 * q^62 + 125047004418 * q^63 - 617200820224 * q^64 + 237758525280 * q^65 - 773201217888 * q^66 - 1237879942064 * q^67 + 1742952201984 * q^68 - 142153434108 * q^69 - 854752926720 * q^70 + 1961126619804 * q^71 - 317129976576 * q^72 - 2407791783284 * q^73 - 932684149728 * q^74 + 1105004312550 * q^75 - 3223782355328 * q^76 - 1011027975804 * q^77 - 1244494469088 * q^78 - 2622494223848 * q^79 + 5422719283200 * q^80 + 564859072962 * q^81 + 1475409286080 * q^82 + 4489561815912 * q^83 - 112525150752 * q^84 - 9450323756160 * q^85 + 90323285184 * q^86 - 2538117417492 * q^87 + 1892375536128 * q^88 + 520927840584 * q^89 - 3861067668480 * q^90 - 4468545729788 * q^91 + 8700054971328 * q^92 - 6119078392080 * q^93 - 5518028009280 * q^94 + 22828834751040 * q^95 - 2445171535872 * q^96 - 13027956631604 * q^97 + 1993145356944 * q^98 - 4566989251836 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	120.497	1.33132	0.665661	−	0.746255i	$-0.268150\pi$
$2$	120.497	1.33132	0.665661	+	0.746255i	$0.268150\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	6327.63	0.772416
$5$	−62168.1	−1.77935	−0.889677	−	0.456590i	$-0.849071\pi$
$5$	−62168.1	−1.77935	−0.889677	+	0.456590i	$0.849071\pi$
$6$	87842.6	0.768639
$7$	117649.	0.377964
$7$	117649.	0.377964
$8$	−224652.	−0.302988
$9$	531441.	0.333333
$10$	−7.49109e6	−2.36889
$11$	−8.85265e6	−1.50668	−0.753339	−	0.657632i	$-0.771558\pi$
$11$	−8.85265e6	−1.50668	−0.753339	+	0.657632i	$0.771558\pi$
$12$	4.61284e6	0.445954
$13$	−8.39684e6	−0.482485	−0.241243	−	0.970465i	$-0.577555\pi$
$13$	−8.39684e6	−0.482485	−0.241243	+	0.970465i	$0.577555\pi$
$14$	1.41764e7	0.503192
$15$	−4.53205e7	−1.02731
$16$	−7.89059e7	−1.17579
$17$	1.33892e8	1.34535	0.672675	−	0.739938i	$-0.265145\pi$
$17$	1.33892e8	1.34535	0.672675	+	0.739938i	$0.265145\pi$
$18$	6.40373e7	0.443774
$19$	−3.46327e8	−1.68884	−0.844418	−	0.535684i	$-0.820054\pi$
$19$	−3.46327e8	−1.68884	−0.844418	+	0.535684i	$0.820054\pi$
$20$	−3.93377e8	−1.37440
$21$	8.57661e7	0.218218
$22$	−1.06672e9	−2.00587
$23$	5.16232e8	0.727133	0.363567	−	0.931568i	$-0.381559\pi$
$23$	5.16232e8	0.727133	0.363567	+	0.931568i	$0.381559\pi$
$24$	−1.63771e8	−0.174930
$25$	2.64417e9	2.16610
$26$	−1.01180e9	−0.642343
$27$	3.87420e8	0.192450
$28$	7.44439e8	0.291946
$29$	2.41001e9	0.752370	0.376185	−	0.926545i	$-0.377236\pi$
$29$	2.41001e9	0.752370	0.376185	+	0.926545i	$0.377236\pi$
$30$	−5.46101e9	−1.36768
$31$	−8.56433e9	−1.73318	−0.866588	−	0.499025i	$-0.833692\pi$
$31$	−8.56433e9	−1.73318	−0.866588	+	0.499025i	$0.833692\pi$
$32$	−7.66761e9	−1.26237
$33$	−6.45358e9	−0.869881
$34$	1.61336e10	1.79109
$35$	−7.31401e9	−0.672533
$36$	3.36276e9	0.257472
$37$	−4.20316e9	−0.269318	−0.134659	−	0.990892i	$-0.542994\pi$
$37$	−4.20316e9	−0.269318	−0.134659	+	0.990892i	$0.542994\pi$
$38$	−4.17315e10	−2.24838
$39$	−6.12130e9	−0.278563
$40$	1.39662e10	0.539123
$41$	1.82419e10	0.599755	0.299877	−	0.953978i	$-0.403054\pi$
$41$	1.82419e10	0.599755	0.299877	+	0.953978i	$0.403054\pi$
$42$	1.03346e10	0.290518
$43$	−5.38398e9	−0.129885	−0.0649424	−	0.997889i	$-0.520686\pi$
$43$	−5.38398e9	−0.129885	−0.0649424	+	0.997889i	$0.520686\pi$
$44$	−5.60163e10	−1.16378
$45$	−3.30387e10	−0.593118
$46$	6.22046e10	0.968048
$47$	−6.39708e10	−0.865656	−0.432828	−	0.901476i	$-0.642484\pi$
$47$	−6.39708e10	−0.865656	−0.432828	+	0.901476i	$0.642484\pi$
$48$	−5.75224e10	−0.678843
$49$	1.38413e10	0.142857
$50$	3.18616e11	2.88378
$51$	9.76070e10	0.776739
$52$	−5.31321e10	−0.372679
$53$	2.66663e11	1.65260	0.826302	−	0.563227i	$-0.190440\pi$
$53$	2.66663e11	1.65260	0.826302	+	0.563227i	$0.190440\pi$
$54$	4.66832e10	0.256213
$55$	5.50352e11	2.68092
$56$	−2.64301e10	−0.114519
$57$	−2.52472e11	−0.975050
$58$	2.90400e11	1.00165
$59$	−2.62371e10	−0.0809801	−0.0404900	−	0.999180i	$-0.512892\pi$
$59$	−2.62371e10	−0.0809801	−0.0404900	+	0.999180i	$0.512892\pi$
$60$	−2.86772e11	−0.793511
$61$	−9.67948e9	−0.0240552	−0.0120276	−	0.999928i	$-0.503829\pi$
$61$	−9.67948e9	−0.0240552	−0.0120276	+	0.999928i	$0.503829\pi$
$62$	−1.03198e12	−2.30741
$63$	6.25235e10	0.125988
$64$	−2.77530e11	−0.504824
$65$	5.22016e11	0.858513
$66$	−7.77640e11	−1.15809
$67$	−7.34892e11	−0.992516	−0.496258	−	0.868175i	$-0.665293\pi$
$67$	−7.34892e11	−0.992516	−0.496258	+	0.868175i	$0.665293\pi$
$68$	8.47217e11	1.03917
$69$	3.76333e11	0.419810
$70$	−8.81320e11	−0.895357
$71$	1.05215e12	0.974758	0.487379	−	0.873191i	$-0.337953\pi$
$71$	1.05215e12	0.974758	0.487379	+	0.873191i	$0.337953\pi$
$72$	−1.19389e11	−0.100996
$73$	−9.67631e11	−0.748361	−0.374181	−	0.927356i	$-0.622076\pi$
$73$	−9.67631e11	−0.748361	−0.374181	+	0.927356i	$0.622076\pi$
$74$	−5.06470e11	−0.358548
$75$	1.92760e12	1.25060
$76$	−2.19143e12	−1.30448
$77$	−1.04150e12	−0.569471
$78$	−7.37601e11	−0.370857
$79$	−1.46116e12	−0.676272	−0.338136	−	0.941097i	$-0.609796\pi$
$79$	−1.46116e12	−0.676272	−0.338136	+	0.941097i	$0.609796\pi$
$80$	4.90543e12	2.09215
$81$	2.82430e11	0.111111
$82$	2.19810e12	0.798466
$83$	6.16621e11	0.207019	0.103510	−	0.994628i	$-0.466993\pi$
$83$	6.16621e11	0.207019	0.103510	+	0.994628i	$0.466993\pi$
$84$	5.42696e11	0.168555
$85$	−8.32379e12	−2.39386
$86$	−6.48756e11	−0.172918
$87$	1.75689e12	0.434381
$88$	1.98876e12	0.456505
$89$	7.71766e11	0.164608	0.0823040	−	0.996607i	$-0.473772\pi$
$89$	7.71766e11	0.164608	0.0823040	+	0.996607i	$0.473772\pi$
$90$	−3.98107e12	−0.789631
$91$	−9.87880e11	−0.182362
$92$	3.26652e12	0.561649
$93$	−6.24340e12	−1.00065
$94$	−7.70831e12	−1.15247
$95$	2.15305e13	3.00504
$96$	−5.58969e12	−0.728827
$97$	−6.34908e12	−0.773918	−0.386959	−	0.922097i	$-0.626474\pi$
$97$	−6.34908e12	−0.773918	−0.386959	+	0.922097i	$0.626474\pi$
$98$	1.66784e12	0.190189
$99$	−4.70466e12	−0.502226
$100$	1.67313e13	1.67313
$101$	−1.70983e13	−1.60274	−0.801372	−	0.598166i	$-0.795896\pi$
$101$	−1.70983e13	−1.60274	−0.801372	+	0.598166i	$0.795896\pi$
$102$	1.17614e13	1.03409
$103$	−6.95523e12	−0.573944	−0.286972	−	0.957939i	$-0.592649\pi$
$103$	−6.95523e12	−0.573944	−0.286972	+	0.957939i	$0.592649\pi$
$104$	1.88637e12	0.146187
$105$	−5.33192e12	−0.388287
$106$	3.21321e13	2.20015
$107$	−6.76864e12	−0.436020	−0.218010	−	0.975947i	$-0.569957\pi$
$107$	−6.76864e12	−0.436020	−0.218010	+	0.975947i	$0.569957\pi$
$108$	2.45145e12	0.148651
$109$	1.46131e13	0.834587	0.417293	−	0.908772i	$-0.362979\pi$
$109$	1.46131e13	0.834587	0.417293	+	0.908772i	$0.362979\pi$
$110$	6.63160e13	3.56916
$111$	−3.06410e12	−0.155491
$112$	−9.28320e12	−0.444407
$113$	−2.39073e13	−1.08024	−0.540120	−	0.841588i	$-0.681621\pi$
$113$	−2.39073e13	−1.08024	−0.540120	+	0.841588i	$0.681621\pi$
$114$	−3.04223e13	−1.29811
$115$	−3.20932e13	−1.29383
$116$	1.52496e13	0.581142
$117$	−4.46243e12	−0.160828
$118$	−3.16151e12	−0.107810
$119$	1.57522e13	0.508495
$120$	1.01813e13	0.311263
$121$	4.38466e13	1.27008
$122$	−1.16635e12	−0.0320251
$123$	1.32983e13	0.346269
$124$	−5.41919e13	−1.33873
$125$	−8.84941e13	−2.07491
$126$	7.53392e12	0.167731
$127$	7.20109e12	0.152291	0.0761455	−	0.997097i	$-0.475739\pi$
$127$	7.20109e12	0.152291	0.0761455	+	0.997097i	$0.475739\pi$
$128$	2.93714e13	0.590283
$129$	−3.92492e12	−0.0749891
$130$	6.29015e13	1.14296
$131$	−1.01331e14	−1.75178	−0.875891	−	0.482510i	$-0.839725\pi$
$131$	−1.01331e14	−1.75178	−0.875891	+	0.482510i	$0.839725\pi$
$132$	−4.08359e13	−0.671910
$133$	−4.07450e13	−0.638320
$134$	−8.85526e13	−1.32136
$135$	−2.40852e13	−0.342437
$136$	−3.00790e13	−0.407625
$137$	3.98660e13	0.515132	0.257566	−	0.966261i	$-0.417079\pi$
$137$	3.98660e13	0.515132	0.257566	+	0.966261i	$0.417079\pi$
$138$	4.53472e13	0.558902
$139$	1.00119e13	0.117739	0.0588697	−	0.998266i	$-0.481250\pi$
$139$	1.00119e13	0.117739	0.0588697	+	0.998266i	$0.481250\pi$
$140$	−4.62804e13	−0.519475
$141$	−4.66347e13	−0.499787
$142$	1.26781e14	1.29772
$143$	7.43343e13	0.726950
$144$	−4.19338e13	−0.391930
$145$	−1.49826e14	−1.33873
$146$	−1.16597e14	−0.996309
$147$	1.00903e13	0.0824786
$148$	−2.65960e13	−0.208025
$149$	9.06390e13	0.678585	0.339293	−	0.940681i	$-0.389812\pi$
$149$	9.06390e13	0.678585	0.339293	+	0.940681i	$0.389812\pi$
$150$	2.32271e14	1.66495
$151$	−9.81170e13	−0.673588	−0.336794	−	0.941578i	$-0.609343\pi$
$151$	−9.81170e13	−0.673588	−0.336794	+	0.941578i	$0.609343\pi$
$152$	7.78030e13	0.511697
$153$	7.11555e13	0.448450
$154$	−1.25499e14	−0.758149
$155$	5.32428e14	3.08393
$156$	−3.87333e13	−0.215166
$157$	6.51201e13	0.347030	0.173515	−	0.984831i	$-0.444487\pi$
$157$	6.51201e13	0.347030	0.173515	+	0.984831i	$0.444487\pi$
$158$	−1.76066e14	−0.900335
$159$	1.94397e14	0.954131
$160$	4.76681e14	2.24620
$161$	6.07342e13	0.274830
$162$	3.40320e13	0.147925
$163$	−1.08882e14	−0.454711	−0.227355	−	0.973812i	$-0.573008\pi$
$163$	−1.08882e14	−0.454711	−0.227355	+	0.973812i	$0.573008\pi$
$164$	1.15428e14	0.463260
$165$	4.01207e14	1.54783
$166$	7.43012e13	0.275609
$167$	−4.95063e14	−1.76605	−0.883026	−	0.469325i	$-0.844497\pi$
$167$	−4.95063e14	−1.76605	−0.883026	+	0.469325i	$0.844497\pi$
$168$	−1.92675e13	−0.0661174
$169$	−2.32368e14	−0.767208
$170$	−1.00300e15	−3.18699
$171$	−1.84052e14	−0.562946
$172$	−3.40678e13	−0.100325
$173$	−1.90395e14	−0.539953	−0.269977	−	0.962867i	$-0.587016\pi$
$173$	−1.90395e14	−0.539953	−0.269977	+	0.962867i	$0.587016\pi$
$174$	2.11701e14	0.578300
$175$	3.11084e14	0.818710
$176$	6.98526e14	1.77154
$177$	−1.91269e13	−0.0467539
$178$	9.29958e13	0.219146
$179$	−4.22937e14	−0.961017	−0.480508	−	0.876990i	$-0.659548\pi$
$179$	−4.22937e14	−0.961017	−0.480508	+	0.876990i	$0.659548\pi$
$180$	−2.09056e14	−0.458134
$181$	−7.29748e13	−0.154263	−0.0771316	−	0.997021i	$-0.524576\pi$
$181$	−7.29748e13	−0.154263	−0.0771316	+	0.997021i	$0.524576\pi$
$182$	−1.19037e14	−0.242783
$183$	−7.05634e12	−0.0138882
$184$	−1.15972e14	−0.220312
$185$	2.61302e14	0.479211
$186$	−7.52313e14	−1.33219
$187$	−1.18530e15	−2.02701
$188$	−4.04783e14	−0.668647
$189$	4.55796e13	0.0727393
$190$	2.59437e15	4.00067
$191$	−1.18436e13	−0.0176509	−0.00882545	−	0.999961i	$-0.502809\pi$
$191$	−1.18436e13	−0.0176509	−0.00882545	+	0.999961i	$0.502809\pi$
$192$	−2.02319e14	−0.291460
$193$	3.16578e14	0.440919	0.220459	−	0.975396i	$-0.429244\pi$
$193$	3.16578e14	0.440919	0.220459	+	0.975396i	$0.429244\pi$
$194$	−7.65048e14	−1.03033
$195$	3.80549e14	0.495662
$196$	8.75825e13	0.110345
$197$	−1.86843e14	−0.227743	−0.113872	−	0.993495i	$-0.536325\pi$
$197$	−1.86843e14	−0.227743	−0.113872	+	0.993495i	$0.536325\pi$
$198$	−5.66899e14	−0.668624
$199$	1.33329e15	1.52188	0.760940	−	0.648823i	$-0.224738\pi$
$199$	1.33329e15	1.52188	0.760940	+	0.648823i	$0.224738\pi$
$200$	−5.94018e14	−0.656303
$201$	−5.35737e14	−0.573029
$202$	−2.06030e15	−2.13377
$203$	2.83535e14	0.284369
$204$	6.17621e14	0.599965
$205$	−1.13406e15	−1.06718
$206$	−8.38088e14	−0.764104
$207$	2.74347e14	0.242378
$208$	6.62560e14	0.567301
$209$	3.06591e15	2.54453
$210$	−6.42482e14	−0.516935
$211$	−8.43170e14	−0.657777	−0.328889	−	0.944369i	$-0.606674\pi$
$211$	−8.43170e14	−0.657777	−0.328889	+	0.944369i	$0.606674\pi$
$212$	1.68734e15	1.27650
$213$	7.67015e14	0.562777
$214$	−8.15603e14	−0.580483
$215$	3.34712e14	0.231111
$216$	−8.70348e13	−0.0583100
$217$	−1.00758e15	−0.655079
$218$	1.76085e15	1.11110
$219$	−7.05403e14	−0.432067
$220$	3.48242e15	2.07078
$221$	−1.12427e15	−0.649112
$222$	−3.69217e14	−0.207008
$223$	−8.47823e14	−0.461661	−0.230831	−	0.972994i	$-0.574144\pi$
$223$	−8.47823e14	−0.461661	−0.230831	+	0.972994i	$0.574144\pi$
$224$	−9.02087e14	−0.477129
$225$	1.40522e15	0.722034
$226$	−2.88077e15	−1.43815
$227$	1.37679e15	0.667884	0.333942	−	0.942594i	$-0.391621\pi$
$227$	1.37679e15	0.667884	0.333942	+	0.942594i	$0.391621\pi$
$228$	−1.59755e15	−0.753144
$229$	−3.21542e15	−1.47336	−0.736678	−	0.676244i	$-0.763606\pi$
$229$	−3.21542e15	−1.47336	−0.736678	+	0.676244i	$0.763606\pi$
$230$	−3.86714e15	−1.72250
$231$	−7.59257e14	−0.328784
$232$	−5.41413e14	−0.227959
$233$	2.12539e15	0.870212	0.435106	−	0.900379i	$-0.356711\pi$
$233$	2.12539e15	0.870212	0.435106	+	0.900379i	$0.356711\pi$
$234$	−5.37711e14	−0.214114
$235$	3.97694e15	1.54031
$236$	−1.66019e14	−0.0625503
$237$	−1.06519e15	−0.390446
$238$	1.89810e15	0.676970
$239$	3.34982e15	1.16261	0.581306	−	0.813685i	$-0.302542\pi$
$239$	3.34982e15	1.16261	0.581306	+	0.813685i	$0.302542\pi$
$240$	3.57606e15	1.20790
$241$	4.30929e15	1.41676	0.708378	−	0.705833i	$-0.249427\pi$
$241$	4.30929e15	1.41676	0.708378	+	0.705833i	$0.249427\pi$
$242$	5.28341e15	1.69088
$243$	2.05891e14	0.0641500
$244$	−6.12482e13	−0.0185806
$245$	−8.60486e14	−0.254194
$246$	1.60241e15	0.460995
$247$	2.90805e15	0.814839
$248$	1.92399e15	0.525131
$249$	4.49517e14	0.119523
$250$	−1.06633e16	−2.76237
$251$	4.47376e15	1.12926	0.564630	−	0.825344i	$-0.309019\pi$
$251$	4.47376e15	1.12926	0.564630	+	0.825344i	$0.309019\pi$
$252$	3.95626e14	0.0973152
$253$	−4.57002e15	−1.09556
$254$	8.67713e14	0.202748
$255$	−6.06804e15	−1.38209
$256$	5.81271e15	1.29068
$257$	4.59239e14	0.0994200	0.0497100	−	0.998764i	$-0.484170\pi$
$257$	4.59239e14	0.0994200	0.0497100	+	0.998764i	$0.484170\pi$
$258$	−4.72943e14	−0.0998345
$259$	−4.94498e14	−0.101792
$260$	3.30312e15	0.663129
$261$	1.28078e15	0.250790
$262$	−1.22102e16	−2.33218
$263$	5.89580e12	0.00109858	0.000549288	−	1.00000i	$-0.499825\pi$
$263$	5.89580e12	0.00109858	0.000549288		1.00000i	$0.499825\pi$
$264$	1.44981e15	0.263563
$265$	−1.65779e16	−2.94057
$266$	−4.90967e15	−0.849809
$267$	5.62618e14	0.0950364
$268$	−4.65013e15	−0.766635
$269$	−8.08409e14	−0.130089	−0.0650446	−	0.997882i	$-0.520719\pi$
$269$	−8.08409e14	−0.130089	−0.0650446	+	0.997882i	$0.520719\pi$
$270$	−2.90220e15	−0.455894
$271$	9.26461e15	1.42078	0.710390	−	0.703808i	$-0.248519\pi$
$271$	9.26461e15	1.42078	0.710390	+	0.703808i	$0.248519\pi$
$272$	−1.05648e16	−1.58185
$273$	−7.20164e14	−0.105287
$274$	4.80375e15	0.685807
$275$	−2.34079e16	−3.26362
$276$	2.38130e15	0.324268
$277$	1.25747e16	1.67255	0.836277	−	0.548307i	$-0.184727\pi$
$277$	1.25747e16	1.67255	0.836277	+	0.548307i	$0.184727\pi$
$278$	1.20641e15	0.156749
$279$	−4.55144e15	−0.577725
$280$	1.64311e15	0.203769
$281$	1.20650e16	1.46196	0.730978	−	0.682401i	$-0.239064\pi$
$281$	1.20650e16	1.46196	0.730978	+	0.682401i	$0.239064\pi$
$282$	−5.61936e15	−0.665377
$283$	3.35155e15	0.387823	0.193911	−	0.981019i	$-0.437883\pi$
$283$	3.35155e15	0.387823	0.193911	+	0.981019i	$0.437883\pi$
$284$	6.65759e15	0.752918
$285$	1.56957e16	1.73496
$286$	8.95709e15	0.967804
$287$	2.14614e15	0.226686
$288$	−4.07488e15	−0.420789
$289$	8.02240e15	0.809969
$290$	−1.80536e16	−1.78228
$291$	−4.62848e15	−0.446822
$292$	−6.12281e15	−0.578046
$293$	1.86516e15	0.172217	0.0861086	−	0.996286i	$-0.472557\pi$
$293$	1.86516e15	0.172217	0.0861086	+	0.996286i	$0.472557\pi$
$294$	1.21585e15	0.109806
$295$	1.63111e15	0.144092
$296$	9.44248e14	0.0816000
$297$	−3.42970e15	−0.289960
$298$	1.09218e16	0.903415
$299$	−4.33472e15	−0.350831
$300$	1.21971e16	0.965983
$301$	−6.33420e14	−0.0490919
$302$	−1.18229e16	−0.896762
$303$	−1.24647e16	−0.925345
$304$	2.73272e16	1.98572
$305$	6.01755e14	0.0428026
$306$	8.57406e15	0.597031
$307$	−3.61080e15	−0.246152	−0.123076	−	0.992397i	$-0.539276\pi$
$307$	−3.61080e15	−0.246152	−0.123076	+	0.992397i	$0.539276\pi$
$308$	−6.59026e15	−0.439868
$309$	−5.07036e15	−0.331367
$310$	6.41562e16	4.10570
$311$	1.23260e16	0.772468	0.386234	−	0.922401i	$-0.373776\pi$
$311$	1.23260e16	0.772468	0.386234	+	0.922401i	$0.373776\pi$
$312$	1.37516e15	0.0844012
$313$	−1.17279e16	−0.704986	−0.352493	−	0.935814i	$-0.614666\pi$
$313$	−1.17279e16	−0.704986	−0.352493	+	0.935814i	$0.614666\pi$
$314$	7.84680e15	0.462008
$315$	−3.88697e15	−0.224178
$316$	−9.24568e15	−0.522363
$317$	−3.98896e15	−0.220788	−0.110394	−	0.993888i	$-0.535211\pi$
$317$	−3.98896e15	−0.220788	−0.110394	+	0.993888i	$0.535211\pi$
$318$	2.34243e16	1.27026
$319$	−2.13349e16	−1.13358
$320$	1.72535e16	0.898261
$321$	−4.93434e15	−0.251736
$322$	7.31831e15	0.365888
$323$	−4.63703e16	−2.27208
$324$	1.78711e15	0.0858240
$325$	−2.22027e16	−1.04511
$326$	−1.31200e16	−0.605366
$327$	1.06530e16	0.481849
$328$	−4.09807e15	−0.181718
$329$	−7.52610e15	−0.327187
$330$	4.83444e16	2.06066
$331$	−1.12346e16	−0.469543	−0.234772	−	0.972051i	$-0.575434\pi$
$331$	−1.12346e16	−0.469543	−0.234772	+	0.972051i	$0.575434\pi$
$332$	3.90175e15	0.159905
$333$	−2.23373e15	−0.0897725
$334$	−5.96538e16	−2.35118
$335$	4.56869e16	1.76604
$336$	−6.76745e15	−0.256578
$337$	−1.32912e16	−0.494276	−0.247138	−	0.968980i	$-0.579490\pi$
$337$	−1.32912e16	−0.494276	−0.247138	+	0.968980i	$0.579490\pi$
$338$	−2.79998e16	−1.02140
$339$	−1.74284e16	−0.623677
$340$	−5.26698e16	−1.84905
$341$	7.58170e16	2.61134
$342$	−2.21778e16	−0.749461
$343$	1.62841e15	0.0539949
$344$	1.20952e15	0.0393535
$345$	−2.33959e16	−0.746992
$346$	−2.29421e16	−0.718851
$347$	−6.45729e16	−1.98568	−0.992839	−	0.119464i	$-0.961882\pi$
$347$	−6.45729e16	−1.98568	−0.992839	+	0.119464i	$0.961882\pi$
$348$	1.11170e16	0.335523
$349$	2.58258e16	0.765048	0.382524	−	0.923946i	$-0.375055\pi$
$349$	2.58258e16	0.765048	0.382524	+	0.923946i	$0.375055\pi$
$350$	3.74848e16	1.08997
$351$	−3.25311e15	−0.0928544
$352$	6.78786e16	1.90198
$353$	−1.44237e16	−0.396771	−0.198386	−	0.980124i	$-0.563570\pi$
$353$	−1.44237e16	−0.396771	−0.198386	+	0.980124i	$0.563570\pi$
$354$	−2.30474e15	−0.0622444
$355$	−6.54099e16	−1.73444
$356$	4.88345e15	0.127146
$357$	1.14834e16	0.293580
$358$	−5.09628e16	−1.27942
$359$	−3.34023e16	−0.823498	−0.411749	−	0.911297i	$-0.635082\pi$
$359$	−3.34023e16	−0.823498	−0.411749	+	0.911297i	$0.635082\pi$
$360$	7.42220e15	0.179708
$361$	7.78893e16	1.85217
$362$	−8.79328e15	−0.205374
$363$	3.19642e16	0.733281
$364$	−6.25094e15	−0.140860
$365$	6.01558e16	1.33160
$366$	−8.50271e14	−0.0184897
$367$	7.66677e16	1.63788	0.818942	−	0.573876i	$-0.194561\pi$
$367$	7.66677e16	1.63788	0.818942	+	0.573876i	$0.194561\pi$
$368$	−4.07337e16	−0.854956
$369$	9.69447e15	0.199918
$370$	3.14863e16	0.637984
$371$	3.13726e16	0.624626
$372$	−3.95059e16	−0.772917
$373$	−3.05246e16	−0.586871	−0.293435	−	0.955979i	$-0.594799\pi$
$373$	−3.05246e16	−0.586871	−0.293435	+	0.955979i	$0.594799\pi$
$374$	−1.42825e17	−2.69860
$375$	−6.45122e16	−1.19795
$376$	1.43712e16	0.262283
$377$	−2.02364e16	−0.363007
$378$	5.49223e15	0.0968394
$379$	−2.35295e16	−0.407809	−0.203905	−	0.978991i	$-0.565363\pi$
$379$	−2.35295e16	−0.407809	−0.203905	+	0.978991i	$0.565363\pi$
$380$	1.36237e17	2.32114
$381$	5.24960e15	0.0879252
$382$	−1.42712e15	−0.0234990
$383$	4.05691e15	0.0656755	0.0328377	−	0.999461i	$-0.489546\pi$
$383$	4.05691e15	0.0656755	0.0328377	+	0.999461i	$0.489546\pi$
$384$	2.14118e16	0.340800
$385$	6.47484e16	1.01329
$386$	3.81469e16	0.587005
$387$	−2.86127e15	−0.0432950
$388$	−4.01746e16	−0.597786
$389$	1.06470e17	1.55796	0.778981	−	0.627048i	$-0.215737\pi$
$389$	1.06470e17	1.55796	0.778981	+	0.627048i	$0.215737\pi$
$390$	4.58552e16	0.659886
$391$	6.91191e16	0.978249
$392$	−3.10947e15	−0.0432840
$393$	−7.38705e16	−1.01139
$394$	−2.25141e16	−0.303200
$395$	9.08375e16	1.20333
$396$	−2.97693e16	−0.387927
$397$	−1.30666e17	−1.67504	−0.837521	−	0.546405i	$-0.815996\pi$
$397$	−1.30666e17	−1.67504	−0.837521	+	0.546405i	$0.815996\pi$
$398$	1.60658e17	2.02611
$399$	−2.97031e16	−0.368534
$400$	−2.08641e17	−2.54688
$401$	−3.24337e16	−0.389545	−0.194772	−	0.980848i	$-0.562397\pi$
$401$	−3.24337e16	−0.389545	−0.194772	+	0.980848i	$0.562397\pi$
$402$	−6.45549e16	−0.762886
$403$	7.19133e16	0.836232
$404$	−1.08192e17	−1.23799
$405$	−1.75581e16	−0.197706
$406$	3.41652e16	0.378586
$407$	3.72091e16	0.405775
$408$	−2.19276e16	−0.235342
$409$	1.35448e17	1.43077	0.715385	−	0.698731i	$-0.246251\pi$
$409$	1.35448e17	1.43077	0.715385	+	0.698731i	$0.246251\pi$
$410$	−1.36651e17	−1.42075
$411$	2.90623e16	0.297412
$412$	−4.40101e16	−0.443323
$413$	−3.08677e15	−0.0306076
$414$	3.30581e16	0.322683
$415$	−3.83341e16	−0.368361
$416$	6.43837e16	0.609073
$417$	7.29870e15	0.0679768
$418$	3.69434e17	3.38759
$419$	−1.38966e17	−1.25463	−0.627317	−	0.778764i	$-0.715847\pi$
$419$	−1.38966e17	−1.25463	−0.627317	+	0.778764i	$0.715847\pi$
$420$	−3.37384e16	−0.299919
$421$	−3.12023e15	−0.0273120	−0.0136560	−	0.999907i	$-0.504347\pi$
$421$	−3.12023e15	−0.0273120	−0.0136560	+	0.999907i	$0.504347\pi$
$422$	−1.01600e17	−0.875713
$423$	−3.39967e16	−0.288552
$424$	−5.99063e16	−0.500719
$425$	3.54032e17	2.91417
$426$	9.24233e16	0.749237
$427$	−1.13878e15	−0.00909199
$428$	−4.28294e16	−0.336789
$429$	5.41897e16	0.419705
$430$	4.03319e16	0.307683
$431$	2.52085e17	1.89428	0.947141	−	0.320818i	$-0.103958\pi$
$431$	2.52085e17	1.89428	0.947141	+	0.320818i	$0.103958\pi$
$432$	−3.05698e16	−0.226281
$433$	−2.06484e17	−1.50562	−0.752809	−	0.658239i	$-0.771302\pi$
$433$	−2.06484e17	−1.50562	−0.752809	+	0.658239i	$0.771302\pi$
$434$	−1.21411e17	−0.872120
$435$	−1.09223e17	−0.772918
$436$	9.24666e16	0.644648
$437$	−1.78785e17	−1.22801
$438$	−8.49993e16	−0.575219
$439$	8.35704e16	0.557228	0.278614	−	0.960403i	$-0.410125\pi$
$439$	8.35704e16	0.557228	0.278614	+	0.960403i	$0.410125\pi$
$440$	−1.23638e17	−0.812285
$441$	7.35583e15	0.0476190
$442$	−1.35471e17	−0.864176
$443$	2.34732e17	1.47553	0.737766	−	0.675057i	$-0.235881\pi$
$443$	2.34732e17	1.47553	0.737766	+	0.675057i	$0.235881\pi$
$444$	−1.93885e16	−0.120103
$445$	−4.79792e16	−0.292896
$446$	−1.02160e17	−0.614619
$447$	6.60758e16	0.391781
$448$	−3.26511e16	−0.190806
$449$	−1.54919e17	−0.892287	−0.446143	−	0.894961i	$-0.647203\pi$
$449$	−1.54919e17	−0.892287	−0.446143	+	0.894961i	$0.647203\pi$
$450$	1.69325e17	0.961259
$451$	−1.61489e17	−0.903638
$452$	−1.51276e17	−0.834394
$453$	−7.15273e16	−0.388896
$454$	1.65900e17	0.889168
$455$	6.14146e16	0.324487
$456$	5.67184e16	0.295428
$457$	−2.32608e17	−1.19445	−0.597227	−	0.802072i	$-0.703731\pi$
$457$	−2.32608e17	−1.19445	−0.597227	+	0.802072i	$0.703731\pi$
$458$	−3.87450e17	−1.96151
$459$	5.18724e16	0.258913
$460$	−2.03074e17	−0.999373
$461$	−6.40936e16	−0.310999	−0.155499	−	0.987836i	$-0.549699\pi$
$461$	−6.40936e16	−0.310999	−0.155499	+	0.987836i	$0.549699\pi$
$462$	−9.14885e16	−0.437717
$463$	−9.58259e16	−0.452071	−0.226035	−	0.974119i	$-0.572576\pi$
$463$	−9.58259e16	−0.452071	−0.226035	+	0.974119i	$0.572576\pi$
$464$	−1.90164e17	−0.884629
$465$	3.88140e17	1.78051
$466$	2.56104e17	1.15853
$467$	−2.01275e17	−0.897903	−0.448952	−	0.893556i	$-0.648202\pi$
$467$	−2.01275e17	−0.897903	−0.448952	+	0.893556i	$0.648202\pi$
$468$	−2.82366e16	−0.124226
$469$	−8.64594e16	−0.375136
$470$	4.79211e17	2.05065
$471$	4.74725e16	0.200358
$472$	5.89422e15	0.0245360
$473$	4.76625e16	0.195695
$474$	−1.28352e17	−0.519809
$475$	−9.15747e17	−3.65819
$476$	9.96742e16	0.392769
$477$	1.41715e17	0.550868
$478$	4.03644e17	1.54781
$479$	−4.24780e17	−1.60688	−0.803440	−	0.595385i	$-0.797000\pi$
$479$	−4.24780e17	−1.60688	−0.803440	+	0.595385i	$0.797000\pi$
$480$	3.47500e17	1.29684
$481$	3.52933e16	0.129942
$482$	5.19258e17	1.88616
$483$	4.42752e16	0.158673
$484$	2.77445e17	0.981030
$485$	3.94710e17	1.37707
$486$	2.48094e16	0.0854043
$487$	9.68500e16	0.328974	0.164487	−	0.986379i	$-0.447403\pi$
$487$	9.68500e16	0.328974	0.164487	+	0.986379i	$0.447403\pi$
$488$	2.17451e15	0.00728842
$489$	−7.93747e16	−0.262527
$490$	−1.03686e17	−0.338413
$491$	−5.43027e17	−1.74901	−0.874503	−	0.485019i	$-0.838813\pi$
$491$	−5.43027e17	−1.74901	−0.874503	+	0.485019i	$0.838813\pi$
$492$	8.41468e16	0.267463
$493$	3.22680e17	1.01220
$494$	3.50413e17	1.08481
$495$	2.92480e17	0.893639
$496$	6.75776e17	2.03785
$497$	1.23784e17	0.368424
$498$	5.41656e16	0.159123
$499$	−6.83876e17	−1.98301	−0.991503	−	0.130083i	$-0.958476\pi$
$499$	−6.83876e17	−1.98301	−0.991503	+	0.130083i	$0.958476\pi$
$500$	−5.59958e17	−1.60269
$501$	−3.60901e17	−1.01963
$502$	5.39077e17	1.50341
$503$	2.55026e17	0.702088	0.351044	−	0.936359i	$-0.385827\pi$
$503$	2.55026e17	0.702088	0.351044	+	0.936359i	$0.385827\pi$
$504$	−1.40460e16	−0.0381729
$505$	1.06297e18	2.85185
$506$	−5.50675e17	−1.45854
$507$	−1.69396e17	−0.442948
$508$	4.55658e16	0.117632
$509$	2.70096e17	0.688419	0.344210	−	0.938893i	$-0.388147\pi$
$509$	2.70096e17	0.688419	0.344210	+	0.938893i	$0.388147\pi$
$510$	−7.31183e17	−1.84001
$511$	−1.13841e17	−0.282854
$512$	4.59805e17	1.12803
$513$	−1.34174e17	−0.325017
$514$	5.53371e16	0.132360
$515$	4.32394e17	1.02125
$516$	−2.48355e16	−0.0579227
$517$	5.66311e17	1.30427
$518$	−5.95857e16	−0.135518
$519$	−1.38798e17	−0.311742
$520$	−1.17272e17	−0.260119
$521$	7.73924e17	1.69533	0.847663	−	0.530536i	$-0.178009\pi$
$521$	7.73924e17	1.69533	0.847663	+	0.530536i	$0.178009\pi$
$522$	1.54330e17	0.333882
$523$	−8.26672e16	−0.176633	−0.0883166	−	0.996092i	$-0.528149\pi$
$523$	−8.26672e16	−0.176633	−0.0883166	+	0.996092i	$0.528149\pi$
$524$	−6.41186e17	−1.35310
$525$	2.26780e17	0.472682
$526$	7.10428e14	0.00146256
$527$	−1.14669e18	−2.33173
$528$	5.09226e17	1.02280
$529$	−2.37541e17	−0.471278
$530$	−1.99759e18	−3.91484
$531$	−1.39435e16	−0.0269934
$532$	−2.57819e17	−0.493049
$533$	−1.53174e17	−0.289373
$534$	6.77940e16	0.126524
$535$	4.20793e17	0.775835
$536$	1.65095e17	0.300720
$537$	−3.08321e17	−0.554843
$538$	−9.74113e16	−0.173191
$539$	−1.22532e17	−0.215240
$540$	−1.52402e17	−0.264504
$541$	9.74821e17	1.67164	0.835820	−	0.549004i	$-0.184993\pi$
$541$	9.74821e17	1.67164	0.835820	+	0.549004i	$0.184993\pi$
$542$	1.11636e18	1.89151
$543$	−5.31987e16	−0.0890639
$544$	−1.02663e18	−1.69832
$545$	−9.08472e17	−1.48503
$546$	−8.67780e16	−0.140171
$547$	−6.51514e17	−1.03994	−0.519968	−	0.854186i	$-0.674056\pi$
$547$	−6.51514e17	−1.03994	−0.519968	+	0.854186i	$0.674056\pi$
$548$	2.52257e17	0.397896
$549$	−5.14407e15	−0.00801838
$550$	−2.82059e18	−4.34493
$551$	−8.34650e17	−1.27063
$552$	−8.45439e16	−0.127197
$553$	−1.71904e17	−0.255607
$554$	1.51522e18	2.22671
$555$	1.90489e17	0.276673
$556$	6.33518e16	0.0909437
$557$	6.82869e17	0.968899	0.484450	−	0.874819i	$-0.339020\pi$
$557$	6.82869e17	0.968899	0.484450	+	0.874819i	$0.339020\pi$
$558$	−5.48436e17	−0.769137
$559$	4.52084e16	0.0626676
$560$	5.77119e17	0.790757
$561$	−8.64080e17	−1.17030
$562$	1.45380e18	1.94633
$563$	2.71370e17	0.359135	0.179568	−	0.983746i	$-0.442530\pi$
$563$	2.71370e17	0.359135	0.179568	+	0.983746i	$0.442530\pi$
$564$	−2.95087e17	−0.386043
$565$	1.48627e18	1.92213
$566$	4.03853e17	0.516317
$567$	3.32276e16	0.0419961
$568$	−2.36367e17	−0.295340
$569$	−1.39031e18	−1.71744	−0.858721	−	0.512443i	$-0.828741\pi$
$569$	−1.39031e18	−1.71744	−0.858721	+	0.512443i	$0.828741\pi$
$570$	1.89129e18	2.30979
$571$	−3.55278e17	−0.428977	−0.214489	−	0.976727i	$-0.568808\pi$
$571$	−3.55278e17	−0.428977	−0.214489	+	0.976727i	$0.568808\pi$
$572$	4.70360e17	0.561508
$573$	−8.63398e15	−0.0101908
$574$	2.58604e17	0.301792
$575$	1.36500e18	1.57505
$576$	−1.47491e17	−0.168275
$577$	−5.50519e17	−0.621054	−0.310527	−	0.950564i	$-0.600506\pi$
$577$	−5.50519e17	−0.621054	−0.310527	+	0.950564i	$0.600506\pi$
$578$	9.66678e17	1.07833
$579$	2.30786e17	0.254565
$580$	−9.48040e17	−1.03406
$581$	7.25448e16	0.0782459
$582$	−5.57720e17	−0.594863
$583$	−2.36067e18	−2.48994
$584$	2.17380e17	0.226744
$585$	2.77420e17	0.286171
$586$	2.24747e17	0.229276
$587$	1.73228e18	1.74771	0.873857	−	0.486183i	$-0.161611\pi$
$587$	1.73228e18	1.74771	0.873857	+	0.486183i	$0.161611\pi$
$588$	6.38477e16	0.0637078
$589$	2.96606e18	2.92705
$590$	1.96545e17	0.191833
$591$	−1.36208e17	−0.131488
$592$	3.31654e17	0.316661
$593$	−2.01142e17	−0.189953	−0.0949767	−	0.995479i	$-0.530278\pi$
$593$	−2.01142e17	−0.189953	−0.0949767	+	0.995479i	$0.530278\pi$
$594$	−4.13270e17	−0.386030
$595$	−9.79285e17	−0.904793
$596$	5.73530e17	0.524150
$597$	9.71970e17	0.878658
$598$	−5.22322e17	−0.467069
$599$	−1.35928e18	−1.20236	−0.601182	−	0.799112i	$-0.705303\pi$
$599$	−1.35928e18	−1.20236	−0.601182	+	0.799112i	$0.705303\pi$
$600$	−4.33039e17	−0.378917
$601$	−1.34494e18	−1.16417	−0.582087	−	0.813127i	$-0.697764\pi$
$601$	−1.34494e18	−1.16417	−0.582087	+	0.813127i	$0.697764\pi$
$602$	−7.63255e16	−0.0653570
$603$	−3.90552e17	−0.330839
$604$	−6.20848e17	−0.520290
$605$	−2.72586e18	−2.25992
$606$	−1.50196e18	−1.23193
$607$	3.57044e17	0.289731	0.144866	−	0.989451i	$-0.453725\pi$
$607$	3.57044e17	0.289731	0.144866	+	0.989451i	$0.453725\pi$
$608$	2.65550e18	2.13193
$609$	2.06697e17	0.164181
$610$	7.25099e16	0.0569841
$611$	5.37152e17	0.417667
$612$	4.50246e17	0.346390
$613$	−2.40169e18	−1.82820	−0.914099	−	0.405490i	$-0.867101\pi$
$613$	−2.40169e18	−1.82820	−0.914099	+	0.405490i	$0.867101\pi$
$614$	−4.35092e17	−0.327707
$615$	−8.26731e17	−0.616135
$616$	2.33976e17	0.172543
$617$	1.59466e18	1.16363	0.581813	−	0.813322i	$-0.302343\pi$
$617$	1.59466e18	1.16363	0.581813	+	0.813322i	$0.302343\pi$
$618$	−6.10966e17	−0.441156
$619$	1.89842e18	1.35645	0.678224	−	0.734855i	$-0.262750\pi$
$619$	1.89842e18	1.35645	0.678224	+	0.734855i	$0.262750\pi$
$620$	3.36901e18	2.38208
$621$	1.99999e17	0.139937
$622$	1.48525e18	1.02840
$623$	9.07975e16	0.0622159
$624$	4.83007e17	0.327532
$625$	2.27377e18	1.52590
$626$	−1.41318e18	−0.938563
$627$	2.23505e18	1.46909
$628$	4.12056e17	0.268051
$629$	−5.62768e17	−0.362327
$630$	−4.68369e17	−0.298452
$631$	−3.61466e17	−0.227969	−0.113985	−	0.993483i	$-0.536361\pi$
$631$	−3.61466e17	−0.227969	−0.113985	+	0.993483i	$0.536361\pi$
$632$	3.28252e17	0.204902
$633$	−6.14671e17	−0.379768
$634$	−4.80659e17	−0.293939
$635$	−4.47678e17	−0.270980
$636$	1.23007e18	0.736986
$637$	−1.16223e17	−0.0689265
$638$	−2.57080e18	−1.50916
$639$	5.59154e17	0.324919
$640$	−1.82596e18	−1.05032
$641$	4.87935e17	0.277833	0.138917	−	0.990304i	$-0.455638\pi$
$641$	4.87935e17	0.277833	0.138917	+	0.990304i	$0.455638\pi$
$642$	−5.94575e17	−0.335142
$643$	1.41657e18	0.790436	0.395218	−	0.918587i	$-0.370669\pi$
$643$	1.41657e18	0.790436	0.395218	+	0.918587i	$0.370669\pi$
$644$	3.84303e17	0.212283
$645$	2.44005e17	0.133432
$646$	−5.58750e18	−3.02487
$647$	−3.25021e18	−1.74194	−0.870971	−	0.491335i	$-0.836509\pi$
$647$	−3.25021e18	−1.74194	−0.870971	+	0.491335i	$0.836509\pi$
$648$	−6.34483e16	−0.0336653
$649$	2.32268e17	0.122011
$650$	−2.67536e18	−1.39138
$651$	−7.34529e17	−0.378210
$652$	−6.88962e17	−0.351226
$653$	2.21933e18	1.12018	0.560088	−	0.828433i	$-0.310767\pi$
$653$	2.21933e18	1.12018	0.560088	+	0.828433i	$0.310767\pi$
$654$	1.28366e18	0.641496
$655$	6.29957e18	3.11704
$656$	−1.43939e18	−0.705186
$657$	−5.14239e17	−0.249454
$658$	−9.06875e17	−0.435591
$659$	−2.90788e18	−1.38300	−0.691498	−	0.722378i	$-0.743049\pi$
$659$	−2.90788e18	−1.38300	−0.691498	+	0.722378i	$0.743049\pi$
$660$	2.53869e18	1.19557
$661$	−3.72686e17	−0.173794	−0.0868968	−	0.996217i	$-0.527695\pi$
$661$	−3.72686e17	−0.173794	−0.0868968	+	0.996217i	$0.527695\pi$
$662$	−1.35374e18	−0.625113
$663$	−8.19591e17	−0.374765
$664$	−1.38525e17	−0.0627243
$665$	2.53304e18	1.13580
$666$	−2.69159e17	−0.119516
$667$	1.24412e18	0.547073
$668$	−3.13257e18	−1.36413
$669$	−6.18063e17	−0.266540
$670$	5.50515e18	2.35116
$671$	8.56890e16	0.0362434
$672$	−6.57621e17	−0.275471
$673$	−2.61068e18	−1.08307	−0.541535	−	0.840678i	$-0.682156\pi$
$673$	−2.61068e18	−1.08307	−0.541535	+	0.840678i	$0.682156\pi$
$674$	−1.60156e18	−0.658041
$675$	1.02441e18	0.416867
$676$	−1.47034e18	−0.592603
$677$	2.08092e18	0.830671	0.415336	−	0.909668i	$-0.363664\pi$
$677$	2.08092e18	0.830671	0.415336	+	0.909668i	$0.363664\pi$
$678$	−2.10008e18	−0.830314
$679$	−7.46963e17	−0.292513
$680$	1.86996e18	0.725309
$681$	1.00368e18	0.385603
$682$	9.13575e18	3.47653
$683$	−1.33429e18	−0.502940	−0.251470	−	0.967865i	$-0.580914\pi$
$683$	−1.33429e18	−0.502940	−0.251470	+	0.967865i	$0.580914\pi$
$684$	−1.16461e18	−0.434828
$685$	−2.47839e18	−0.916603
$686$	1.96220e17	0.0718846
$687$	−2.34404e18	−0.850642
$688$	4.24828e17	0.152717
$689$	−2.23912e18	−0.797357
$690$	−2.81915e18	−0.994486
$691$	4.13969e18	1.44664	0.723320	−	0.690513i	$-0.242615\pi$
$691$	4.13969e18	1.44664	0.723320	+	0.690513i	$0.242615\pi$
$692$	−1.20475e18	−0.417068
$693$	−5.53498e17	−0.189824
$694$	−7.78087e18	−2.64357
$695$	−6.22423e17	−0.209500
$696$	−3.94690e17	−0.131612
$697$	2.44243e18	0.806881
$698$	3.11194e18	1.01852
$699$	1.54941e18	0.502417
$700$	1.96842e18	0.632384
$701$	−2.80524e18	−0.892899	−0.446449	−	0.894809i	$-0.647312\pi$
$701$	−2.80524e18	−0.892899	−0.446449	+	0.894809i	$0.647312\pi$
$702$	−3.91991e17	−0.123619
$703$	1.45567e18	0.454833
$704$	2.45688e18	0.760608
$705$	2.89919e18	0.889298
$706$	−1.73802e18	−0.528230
$707$	−2.01160e18	−0.605781
$708$	−1.21028e17	−0.0361134
$709$	7.00429e17	0.207092	0.103546	−	0.994625i	$-0.466981\pi$
$709$	7.00429e17	0.207092	0.103546	+	0.994625i	$0.466981\pi$
$710$	−7.88173e18	−2.30910
$711$	−7.76520e17	−0.225424
$712$	−1.73379e17	−0.0498742
$713$	−4.42118e18	−1.26025
$714$	1.38372e18	0.390849
$715$	−4.62122e18	−1.29350
$716$	−2.67619e18	−0.742304
$717$	2.44202e18	0.671234
$718$	−4.02489e18	−1.09634
$719$	−2.05324e18	−0.554245	−0.277122	−	0.960835i	$-0.589381\pi$
$719$	−2.05324e18	−0.554245	−0.277122	+	0.960835i	$0.589381\pi$
$720$	2.60695e18	0.697382
$721$	−8.18276e17	−0.216931
$722$	9.38546e18	2.46583
$723$	3.14147e18	0.817964
$724$	−4.61758e17	−0.119155
$725$	6.37246e18	1.62971
$726$	3.85160e18	0.976233
$727$	3.69965e18	0.929367	0.464683	−	0.885477i	$-0.346168\pi$
$727$	3.69965e18	0.929367	0.464683	+	0.885477i	$0.346168\pi$
$728$	2.21929e17	0.0552536
$729$	1.50095e17	0.0370370
$730$	7.24862e18	1.77279
$731$	−7.20870e17	−0.174741
$732$	−4.46499e16	−0.0107275
$733$	−2.49172e18	−0.593366	−0.296683	−	0.954976i	$-0.595881\pi$
$733$	−2.49172e18	−0.593366	−0.296683	+	0.954976i	$0.595881\pi$
$734$	9.23826e18	2.18055
$735$	−6.27295e17	−0.146759
$736$	−3.95827e18	−0.917908
$737$	6.50574e18	1.49540
$738$	1.16816e18	0.266155
$739$	5.29988e18	1.19695	0.598476	−	0.801141i	$-0.295773\pi$
$739$	5.29988e18	1.19695	0.598476	+	0.801141i	$0.295773\pi$
$740$	1.65342e18	0.370150
$741$	2.11997e18	0.470448
$742$	3.78032e18	0.831577
$743$	1.38513e18	0.302039	0.151020	−	0.988531i	$-0.451744\pi$
$743$	1.38513e18	0.302039	0.151020	+	0.988531i	$0.451744\pi$
$744$	1.40259e18	0.303185
$745$	−5.63486e18	−1.20744
$746$	−3.67813e18	−0.781313
$747$	3.27698e17	0.0690064
$748$	−7.50011e18	−1.56570
$749$	−7.96323e17	−0.164800
$750$	−7.77356e18	−1.59486
$751$	2.08287e18	0.423646	0.211823	−	0.977308i	$-0.432060\pi$
$751$	2.08287e18	0.423646	0.211823	+	0.977308i	$0.432060\pi$
$752$	5.04767e18	1.01783
$753$	3.26137e18	0.651978
$754$	−2.43844e18	−0.483279
$755$	6.09975e18	1.19855
$756$	2.88411e17	0.0561850
$757$	−4.86420e17	−0.0939482	−0.0469741	−	0.998896i	$-0.514958\pi$
$757$	−4.86420e17	−0.0939482	−0.0469741	+	0.998896i	$0.514958\pi$
$758$	−2.83524e18	−0.542925
$759$	−3.33154e18	−0.632519
$760$	−4.83686e18	−0.910491
$761$	−9.27115e18	−1.73035	−0.865174	−	0.501473i	$-0.832792\pi$
$761$	−9.27115e18	−1.73035	−0.865174	+	0.501473i	$0.832792\pi$
$762$	6.32563e17	0.117057
$763$	1.71922e18	0.315444
$764$	−7.49419e16	−0.0136338
$765$	−4.42360e18	−0.797952
$766$	4.88847e17	0.0874351
$767$	2.20309e17	0.0390717
$768$	4.23746e18	0.745174
$769$	3.11593e18	0.543333	0.271667	−	0.962391i	$-0.412425\pi$
$769$	3.11593e18	0.543333	0.271667	+	0.962391i	$0.412425\pi$
$770$	7.80201e18	1.34902
$771$	3.34785e17	0.0574001
$772$	2.00319e18	0.340573
$773$	−3.42396e18	−0.577247	−0.288623	−	0.957443i	$-0.593198\pi$
$773$	−3.42396e18	−0.577247	−0.288623	+	0.957443i	$0.593198\pi$
$774$	−3.44775e17	−0.0576395
$775$	−2.26455e19	−3.75424
$776$	1.42633e18	0.234488
$777$	−3.60489e17	−0.0587699
$778$	1.28294e19	2.07415
$779$	−6.31764e18	−1.01289
$780$	2.40798e18	0.382857
$781$	−9.31428e18	−1.46865
$782$	8.32868e18	1.30236
$783$	9.33686e17	0.144794
$784$	−1.09216e18	−0.167970
$785$	−4.04839e18	−0.617490
$786$	−8.90120e18	−1.34649
$787$	−5.47651e17	−0.0821615	−0.0410807	−	0.999156i	$-0.513080\pi$
$787$	−5.47651e17	−0.0821615	−0.0410807	+	0.999156i	$0.513080\pi$
$788$	−1.18227e18	−0.175913
$789$	4.29804e15	0.000634263 0
$790$	1.09457e19	1.60202
$791$	−2.81267e18	−0.408292
$792$	1.05691e18	0.152168
$793$	8.12771e16	0.0116063
$794$	−1.57450e19	−2.23002
$795$	−1.20853e19	−1.69774
$796$	8.43658e18	1.17552
$797$	1.13843e18	0.157336	0.0786681	−	0.996901i	$-0.474933\pi$
$797$	1.13843e18	0.157336	0.0786681	+	0.996901i	$0.474933\pi$
$798$	−3.57915e18	−0.490638
$799$	−8.56515e18	−1.16461
$800$	−2.02745e19	−2.73441
$801$	4.10148e17	0.0548693
$802$	−3.90817e18	−0.518609
$803$	8.56610e18	1.12754
$804$	−3.38994e18	−0.442617
$805$	−3.77573e18	−0.489021
$806$	8.66537e18	1.11329
$807$	−5.89330e17	−0.0751071
$808$	3.84117e18	0.485612
$809$	−2.11984e18	−0.265851	−0.132925	−	0.991126i	$-0.542437\pi$
$809$	−2.11984e18	−0.265851	−0.132925	+	0.991126i	$0.542437\pi$
$810$	−2.11571e18	−0.263210
$811$	1.21142e18	0.149506	0.0747532	−	0.997202i	$-0.476183\pi$
$811$	1.21142e18	0.149506	0.0747532	+	0.997202i	$0.476183\pi$
$812$	1.79410e18	0.219651
$813$	6.75390e18	0.820288
$814$	4.48360e18	0.540217
$815$	6.76896e18	0.809091
$816$	−7.70177e18	−0.913281
$817$	1.86462e18	0.219354
$818$	1.63211e19	1.90481
$819$	−5.25000e17	−0.0607874
$820$	−7.17592e18	−0.824304
$821$	7.37978e18	0.841033	0.420516	−	0.907285i	$-0.361849\pi$
$821$	7.37978e18	0.841033	0.420516	+	0.907285i	$0.361849\pi$
$822$	3.50193e18	0.395951
$823$	4.81837e18	0.540507	0.270254	−	0.962789i	$-0.412892\pi$
$823$	4.81837e18	0.540507	0.270254	+	0.962789i	$0.412892\pi$
$824$	1.56251e18	0.173898
$825$	−1.70644e19	−1.88425
$826$	−3.71948e17	−0.0407485
$827$	1.09807e19	1.19356	0.596782	−	0.802403i	$-0.296446\pi$
$827$	1.09807e19	1.19356	0.596782	+	0.802403i	$0.296446\pi$
$828$	1.73596e18	0.187216
$829$	−1.41629e19	−1.51547	−0.757735	−	0.652562i	$-0.773694\pi$
$829$	−1.41629e19	−1.51547	−0.757735	+	0.652562i	$0.773694\pi$
$830$	−4.61917e18	−0.490406
$831$	9.16698e18	0.965650
$832$	2.33038e18	0.243570
$833$	1.85323e18	0.192193
$834$	8.79474e17	0.0904990
$835$	3.07771e19	3.14243
$836$	1.93999e19	1.96544
$837$	−3.31800e18	−0.333550
$838$	−1.67450e19	−1.67032
$839$	1.65151e18	0.163466	0.0817331	−	0.996654i	$-0.473954\pi$
$839$	1.65151e18	0.163466	0.0817331	+	0.996654i	$0.473954\pi$
$840$	1.19783e18	0.117646
$841$	−4.45250e18	−0.433940
$842$	−3.75980e17	−0.0363610
$843$	8.79535e18	0.844061
$844$	−5.33526e18	−0.508078
$845$	1.44459e19	1.36513
$846$	−4.09651e18	−0.384156
$847$	5.15851e18	0.480045
$848$	−2.10413e19	−1.94312
$849$	2.44328e18	0.223910
$850$	4.26600e19	3.87969
$851$	−2.16981e18	−0.195830
$852$	4.85338e18	0.434698
$853$	−1.91312e19	−1.70049	−0.850244	−	0.526389i	$-0.823546\pi$
$853$	−1.91312e19	−1.70049	−0.850244	+	0.526389i	$0.823546\pi$
$854$	−1.37220e17	−0.0121044
$855$	1.14422e19	1.00168
$856$	1.52059e18	0.132109
$857$	−1.30570e19	−1.12582	−0.562908	−	0.826519i	$-0.690318\pi$
$857$	−1.30570e19	−1.12582	−0.562908	+	0.826519i	$0.690318\pi$
$858$	6.52972e18	0.558762
$859$	−3.13411e18	−0.266170	−0.133085	−	0.991105i	$-0.542488\pi$
$859$	−3.13411e18	−0.266170	−0.133085	+	0.991105i	$0.542488\pi$
$860$	2.11793e18	0.178514
$861$	1.56453e18	0.130877
$862$	3.03756e19	2.52190
$863$	−6.30385e18	−0.519440	−0.259720	−	0.965684i	$-0.583630\pi$
$863$	−6.30385e18	−0.519440	−0.259720	+	0.965684i	$0.583630\pi$
$864$	−2.97059e18	−0.242942
$865$	1.18365e19	0.960768
$866$	−2.48808e19	−2.00446
$867$	5.84833e18	0.467636
$868$	−6.37562e18	−0.505993
$869$	1.29351e19	1.01892
$870$	−1.31611e19	−1.02900
$871$	6.17078e18	0.478875
$872$	−3.28287e18	−0.252870
$873$	−3.37416e18	−0.257973
$874$	−2.15431e19	−1.63487
$875$	−1.04112e19	−0.784243
$876$	−4.46353e18	−0.333735
$877$	−1.65893e19	−1.23120	−0.615602	−	0.788057i	$-0.711087\pi$
$877$	−1.65893e19	−1.23120	−0.615602	+	0.788057i	$0.711087\pi$
$878$	1.00700e19	0.741850
$879$	1.35970e18	0.0994297
$880$	−4.34260e19	−3.15219
$881$	−1.68653e19	−1.21521	−0.607606	−	0.794239i	$-0.707870\pi$
$881$	−1.68653e19	−1.21521	−0.607606	+	0.794239i	$0.707870\pi$
$882$	8.86358e17	0.0633962
$883$	−1.13346e19	−0.804751	−0.402376	−	0.915475i	$-0.631815\pi$
$883$	−1.13346e19	−0.804751	−0.402376	+	0.915475i	$0.631815\pi$
$884$	−7.11394e18	−0.501384
$885$	1.18908e18	0.0831917
$886$	2.82846e19	1.96441
$887$	1.74541e19	1.20336	0.601679	−	0.798738i	$-0.294499\pi$
$887$	1.74541e19	1.20336	0.601679	+	0.798738i	$0.294499\pi$
$888$	6.88357e17	0.0471118
$889$	8.47201e17	0.0575606
$890$	−5.78137e18	−0.389938
$891$	−2.50025e18	−0.167409
$892$	−5.36471e18	−0.356594
$893$	2.21548e19	1.46195
$894$	7.96197e18	0.521587
$895$	2.62932e19	1.70999
$896$	3.45552e18	0.223106
$897$	−3.16001e18	−0.202552
$898$	−1.86674e19	−1.18792
$899$	−2.06401e19	−1.30399
$900$	8.89171e18	0.557711
$901$	3.57039e19	2.22333
$902$	−1.94590e19	−1.20303
$903$	−4.61763e17	−0.0283432
$904$	5.37082e18	0.327300
$905$	4.53671e18	0.274489
$906$	−8.61886e18	−0.517746
$907$	3.65229e18	0.217830	0.108915	−	0.994051i	$-0.465262\pi$
$907$	3.65229e18	0.217830	0.108915	+	0.994051i	$0.465262\pi$
$908$	8.71185e18	0.515884
$909$	−9.08675e18	−0.534248
$910$	7.40030e18	0.431997
$911$	1.86374e19	1.08023	0.540114	−	0.841592i	$-0.318381\pi$
$911$	1.86374e19	1.08023	0.540114	+	0.841592i	$0.318381\pi$
$912$	1.99216e19	1.14645
$913$	−5.45873e18	−0.311911
$914$	−2.80287e19	−1.59020
$915$	4.38679e17	0.0247121
$916$	−2.03460e19	−1.13804
$917$	−1.19215e19	−0.662111
$918$	6.25049e18	0.344696
$919$	−3.06924e19	−1.68066	−0.840330	−	0.542075i	$-0.817639\pi$
$919$	−3.06924e19	−1.68066	−0.840330	+	0.542075i	$0.817639\pi$
$920$	7.20979e18	0.392014
$921$	−2.63227e18	−0.142116
$922$	−7.72312e18	−0.414039
$923$	−8.83470e18	−0.470307
$924$	−4.80430e18	−0.253958
$925$	−1.11139e19	−0.583370
$926$	−1.15468e19	−0.601851
$927$	−3.69630e18	−0.191315
$928$	−1.84790e19	−0.949766
$929$	−1.06009e19	−0.541054	−0.270527	−	0.962712i	$-0.587198\pi$
$929$	−1.06009e19	−0.541054	−0.270527	+	0.962712i	$0.587198\pi$
$930$	4.67699e19	2.37043
$931$	−4.79361e18	−0.241262
$932$	1.34487e19	0.672165
$933$	8.98568e18	0.445985
$934$	−2.42531e19	−1.19540
$935$	7.36876e19	3.60677
$936$	1.00249e18	0.0487291
$937$	2.98791e17	0.0144232	0.00721159	−	0.999974i	$-0.497704\pi$
$937$	2.98791e17	0.0144232	0.00721159	+	0.999974i	$0.497704\pi$
$938$	−1.04181e19	−0.499426
$939$	−8.54961e18	−0.407024
$940$	2.51646e19	1.18976
$941$	−1.71024e19	−0.803015	−0.401508	−	0.915856i	$-0.631514\pi$
$941$	−1.71024e19	−0.803015	−0.401508	+	0.915856i	$0.631514\pi$
$942$	5.72032e18	0.266741
$943$	9.41703e18	0.436102
$944$	2.07026e18	0.0952156
$945$	−2.83360e18	−0.129429
$946$	5.74321e18	0.260533
$947$	7.95034e18	0.358188	0.179094	−	0.983832i	$-0.442683\pi$
$947$	7.95034e18	0.358188	0.179094	+	0.983832i	$0.442683\pi$
$948$	−6.74010e18	−0.301587
$949$	8.12505e18	0.361073
$950$	−1.10345e20	−4.87023
$951$	−2.90795e18	−0.127472
$952$	−3.53877e18	−0.154068
$953$	3.00158e19	1.29791	0.648957	−	0.760825i	$-0.275205\pi$
$953$	3.00158e19	1.29791	0.648957	+	0.760825i	$0.275205\pi$
$954$	1.70763e19	0.733382
$955$	7.36294e17	0.0314072
$956$	2.11964e19	0.898019
$957$	−1.55532e19	−0.654472
$958$	−5.11850e19	−2.13927
$959$	4.69019e18	0.194702
$960$	1.25778e19	0.518611
$961$	4.89302e19	2.00390
$962$	4.25275e18	0.172994
$963$	−3.59713e18	−0.145340
$964$	2.72676e19	1.09432
$965$	−1.96811e19	−0.784551
$966$	5.33505e18	0.211245
$967$	−2.37954e18	−0.0935880	−0.0467940	−	0.998905i	$-0.514900\pi$
$967$	−2.37954e18	−0.0935880	−0.0467940	+	0.998905i	$0.514900\pi$
$968$	−9.85023e18	−0.384819
$969$	−3.38039e19	−1.31178
$970$	4.75616e19	1.83333
$971$	−3.56556e18	−0.136522	−0.0682610	−	0.997668i	$-0.521745\pi$
$971$	−3.56556e18	−0.136522	−0.0682610	+	0.997668i	$0.521745\pi$
$972$	1.30280e18	0.0495505
$973$	1.17789e18	0.0445013
$974$	1.16702e19	0.437970
$975$	−1.61857e19	−0.603396
$976$	7.63768e17	0.0282838
$977$	−3.71177e19	−1.36542	−0.682711	−	0.730689i	$-0.739199\pi$
$977$	−3.71177e19	−1.36542	−0.682711	+	0.730689i	$0.739199\pi$
$978$	−9.56444e18	−0.349508
$979$	−6.83217e18	−0.248011
$980$	−5.44484e18	−0.196343
$981$	7.76603e18	0.278196
$982$	−6.54333e19	−2.32849
$983$	2.18641e19	0.772919	0.386460	−	0.922306i	$-0.373698\pi$
$983$	2.18641e19	0.772919	0.386460	+	0.922306i	$0.373698\pi$
$984$	−2.98749e18	−0.104915
$985$	1.16157e19	0.405236
$986$	3.88821e19	1.34756
$987$	−5.48653e18	−0.188902
$988$	1.84011e19	0.629394
$989$	−2.77938e18	−0.0944436
$990$	3.52430e19	1.18972
$991$	2.88813e19	0.968587	0.484294	−	0.874906i	$-0.339077\pi$
$991$	2.88813e19	0.968587	0.484294	+	0.874906i	$0.339077\pi$
$992$	6.56680e19	2.18790
$993$	−8.19002e18	−0.271091
$994$	1.49156e19	0.490491
$995$	−8.28882e19	−2.70796
$996$	2.84437e18	0.0923211
$997$	1.73893e19	0.560741	0.280371	−	0.959892i	$-0.409543\pi$
$997$	1.73893e19	0.560741	0.280371	+	0.959892i	$0.409543\pi$
$998$	−8.24053e19	−2.64002
$999$	−1.62839e18	−0.0518302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.14.a.a.1.2	✓	2
3.2	odd	2		63.14.a.a.1.1		2
7.6	odd	2		147.14.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.14.a.a.1.2	✓	2	1.1	even	1	trivial
63.14.a.a.1.1		2	3.2	odd	2
147.14.a.c.1.2		2	7.6	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+120.497 q^{2} +729.000 q^{3} +6327.63 q^{4} -62168.1 q^{5} +87842.6 q^{6} +117649. q^{7} -224652. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+120.497 q^{2} +729.000 q^{3} +6327.63 q^{4} -62168.1 q^{5} +87842.6 q^{6} +117649. q^{7} -224652. q^{8} +531441. q^{9} -7.49109e6 q^{10} -8.85265e6 q^{11} +4.61284e6 q^{12} -8.39684e6 q^{13} +1.41764e7 q^{14} -4.53205e7 q^{15} -7.89059e7 q^{16} +1.33892e8 q^{17} +6.40373e7 q^{18} -3.46327e8 q^{19} -3.93377e8 q^{20} +8.57661e7 q^{21} -1.06672e9 q^{22} +5.16232e8 q^{23} -1.63771e8 q^{24} +2.64417e9 q^{25} -1.01180e9 q^{26} +3.87420e8 q^{27} +7.44439e8 q^{28} +2.41001e9 q^{29} -5.46101e9 q^{30} -8.56433e9 q^{31} -7.66761e9 q^{32} -6.45358e9 q^{33} +1.61336e10 q^{34} -7.31401e9 q^{35} +3.36276e9 q^{36} -4.20316e9 q^{37} -4.17315e10 q^{38} -6.12130e9 q^{39} +1.39662e10 q^{40} +1.82419e10 q^{41} +1.03346e10 q^{42} -5.38398e9 q^{43} -5.60163e10 q^{44} -3.30387e10 q^{45} +6.22046e10 q^{46} -6.39708e10 q^{47} -5.75224e10 q^{48} +1.38413e10 q^{49} +3.18616e11 q^{50} +9.76070e10 q^{51} -5.31321e10 q^{52} +2.66663e11 q^{53} +4.66832e10 q^{54} +5.50352e11 q^{55} -2.64301e10 q^{56} -2.52472e11 q^{57} +2.90400e11 q^{58} -2.62371e10 q^{59} -2.86772e11 q^{60} -9.67948e9 q^{61} -1.03198e12 q^{62} +6.25235e10 q^{63} -2.77530e11 q^{64} +5.22016e11 q^{65} -7.77640e11 q^{66} -7.34892e11 q^{67} +8.47217e11 q^{68} +3.76333e11 q^{69} -8.81320e11 q^{70} +1.05215e12 q^{71} -1.19389e11 q^{72} -9.67631e11 q^{73} -5.06470e11 q^{74} +1.92760e12 q^{75} -2.19143e12 q^{76} -1.04150e12 q^{77} -7.37601e11 q^{78} -1.46116e12 q^{79} +4.90543e12 q^{80} +2.82430e11 q^{81} +2.19810e12 q^{82} +6.16621e11 q^{83} +5.42696e11 q^{84} -8.32379e12 q^{85} -6.48756e11 q^{86} +1.75689e12 q^{87} +1.98876e12 q^{88} +7.71766e11 q^{89} -3.98107e12 q^{90} -9.87880e11 q^{91} +3.26652e12 q^{92} -6.24340e12 q^{93} -7.70831e12 q^{94} +2.15305e13 q^{95} -5.58969e12 q^{96} -6.34908e12 q^{97} +1.66784e12 q^{98} -4.70466e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 144 q^{2} + 1458 q^{3} - 1312 q^{4} - 52560 q^{5} + 104976 q^{6} + 235298 q^{7} - 596736 q^{8} + 1062882 q^{9}+O(q^{10}) \) 2 * q + 144 * q^2 + 1458 * q^3 - 1312 * q^4 - 52560 * q^5 + 104976 * q^6 + 235298 * q^7 - 596736 * q^8 + 1062882 * q^9	\( 2 q + 144 q^{2} + 1458 q^{3} - 1312 q^{4} - 52560 q^{5} + 104976 q^{6} + 235298 q^{7} - 596736 q^{8} + 1062882 q^{9} - 7265280 q^{10} - 8593596 q^{11} - 956448 q^{12} - 37982012 q^{13} + 16941456 q^{14} - 38316240 q^{15} - 25067008 q^{16} + 16643088 q^{17} + 76527504 q^{18} - 211195304 q^{19} - 466778880 q^{20} + 171532242 q^{21} - 1060632672 q^{22} - 194997852 q^{23} - 435020544 q^{24} + 1515780950 q^{25} - 1707125472 q^{26} + 774840978 q^{27} - 154355488 q^{28} - 3481642548 q^{29} - 5296389120 q^{30} - 8393797520 q^{31} - 3354144768 q^{32} - 6264731484 q^{33} + 13377955584 q^{34} - 6183631440 q^{35} - 697250592 q^{36} - 22337946716 q^{37} - 38555551296 q^{38} - 27688886748 q^{39} + 10391162880 q^{40} - 12507403320 q^{41} + 12350321424 q^{42} + 26062746328 q^{43} - 57995302464 q^{44} - 27932538960 q^{45} + 45488879520 q^{46} + 29222658936 q^{47} - 18273848832 q^{48} + 27682574402 q^{49} + 292095486000 q^{50} + 12132811152 q^{51} + 172887632320 q^{52} + 523911868308 q^{53} + 55788550416 q^{54} + 552841085280 q^{55} - 70205393664 q^{56} - 153961376616 q^{57} + 151930661472 q^{58} - 94444581024 q^{59} - 340281803520 q^{60} + 461720554252 q^{61} - 1027971840384 q^{62} + 125047004418 q^{63} - 617200820224 q^{64} + 237758525280 q^{65} - 773201217888 q^{66} - 1237879942064 q^{67} + 1742952201984 q^{68} - 142153434108 q^{69} - 854752926720 q^{70} + 1961126619804 q^{71} - 317129976576 q^{72} - 2407791783284 q^{73} - 932684149728 q^{74} + 1105004312550 q^{75} - 3223782355328 q^{76} - 1011027975804 q^{77} - 1244494469088 q^{78} - 2622494223848 q^{79} + 5422719283200 q^{80} + 564859072962 q^{81} + 1475409286080 q^{82} + 4489561815912 q^{83} - 112525150752 q^{84} - 9450323756160 q^{85} + 90323285184 q^{86} - 2538117417492 q^{87} + 1892375536128 q^{88} + 520927840584 q^{89} - 3861067668480 q^{90} - 4468545729788 q^{91} + 8700054971328 q^{92} - 6119078392080 q^{93} - 5518028009280 q^{94} + 22828834751040 q^{95} - 2445171535872 q^{96} - 13027956631604 q^{97} + 1993145356944 q^{98} - 4566989251836 q^{99}+O(q^{100}) \) 2 * q + 144 * q^2 + 1458 * q^3 - 1312 * q^4 - 52560 * q^5 + 104976 * q^6 + 235298 * q^7 - 596736 * q^8 + 1062882 * q^9 - 7265280 * q^10 - 8593596 * q^11 - 956448 * q^12 - 37982012 * q^13 + 16941456 * q^14 - 38316240 * q^15 - 25067008 * q^16 + 16643088 * q^17 + 76527504 * q^18 - 211195304 * q^19 - 466778880 * q^20 + 171532242 * q^21 - 1060632672 * q^22 - 194997852 * q^23 - 435020544 * q^24 + 1515780950 * q^25 - 1707125472 * q^26 + 774840978 * q^27 - 154355488 * q^28 - 3481642548 * q^29 - 5296389120 * q^30 - 8393797520 * q^31 - 3354144768 * q^32 - 6264731484 * q^33 + 13377955584 * q^34 - 6183631440 * q^35 - 697250592 * q^36 - 22337946716 * q^37 - 38555551296 * q^38 - 27688886748 * q^39 + 10391162880 * q^40 - 12507403320 * q^41 + 12350321424 * q^42 + 26062746328 * q^43 - 57995302464 * q^44 - 27932538960 * q^45 + 45488879520 * q^46 + 29222658936 * q^47 - 18273848832 * q^48 + 27682574402 * q^49 + 292095486000 * q^50 + 12132811152 * q^51 + 172887632320 * q^52 + 523911868308 * q^53 + 55788550416 * q^54 + 552841085280 * q^55 - 70205393664 * q^56 - 153961376616 * q^57 + 151930661472 * q^58 - 94444581024 * q^59 - 340281803520 * q^60 + 461720554252 * q^61 - 1027971840384 * q^62 + 125047004418 * q^63 - 617200820224 * q^64 + 237758525280 * q^65 - 773201217888 * q^66 - 1237879942064 * q^67 + 1742952201984 * q^68 - 142153434108 * q^69 - 854752926720 * q^70 + 1961126619804 * q^71 - 317129976576 * q^72 - 2407791783284 * q^73 - 932684149728 * q^74 + 1105004312550 * q^75 - 3223782355328 * q^76 - 1011027975804 * q^77 - 1244494469088 * q^78 - 2622494223848 * q^79 + 5422719283200 * q^80 + 564859072962 * q^81 + 1475409286080 * q^82 + 4489561815912 * q^83 - 112525150752 * q^84 - 9450323756160 * q^85 + 90323285184 * q^86 - 2538117417492 * q^87 + 1892375536128 * q^88 + 520927840584 * q^89 - 3861067668480 * q^90 - 4468545729788 * q^91 + 8700054971328 * q^92 - 6119078392080 * q^93 - 5518028009280 * q^94 + 22828834751040 * q^95 - 2445171535872 * q^96 - 13027956631604 * q^97 + 1993145356944 * q^98 - 4566989251836 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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