LMFDB - Embedded newform 21.14.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q+23.5026 q^{2} +729.000 q^{3} -7639.63 q^{4} +9608.09 q^{5} +17133.4 q^{6} +117649. q^{7} -372084. q^{8} +531441. q^{9} +O(q^{10})$	\(q+23.5026 q^{2} +729.000 q^{3} -7639.63 q^{4} +9608.09 q^{5} +17133.4 q^{6} +117649. q^{7} -372084. q^{8} +531441. q^{9} +225815. q^{10} +259050. q^{11} -5.56929e6 q^{12} -2.95852e7 q^{13} +2.76505e6 q^{14} +7.00430e6 q^{15} +5.38389e7 q^{16} -1.17249e8 q^{17} +1.24902e7 q^{18} +1.35132e8 q^{19} -7.34023e7 q^{20} +8.57661e7 q^{21} +6.08834e6 q^{22} -7.11230e8 q^{23} -2.71249e8 q^{24} -1.12839e9 q^{25} -6.95328e8 q^{26} +3.87420e8 q^{27} -8.98795e8 q^{28} -5.89165e9 q^{29} +1.64619e8 q^{30} +1.70534e8 q^{31} +4.31347e9 q^{32} +1.88847e8 q^{33} -2.75564e9 q^{34} +1.13038e9 q^{35} -4.06001e9 q^{36} -1.81348e10 q^{37} +3.17594e9 q^{38} -2.15676e10 q^{39} -3.57502e9 q^{40} -3.07493e10 q^{41} +2.01572e9 q^{42} +3.14467e10 q^{43} -1.97904e9 q^{44} +5.10613e9 q^{45} -1.67157e10 q^{46} +9.31934e10 q^{47} +3.92486e10 q^{48} +1.38413e10 q^{49} -2.65200e10 q^{50} -8.54742e10 q^{51} +2.26020e11 q^{52} +2.57249e11 q^{53} +9.10538e9 q^{54} +2.48898e9 q^{55} -4.37753e10 q^{56} +9.85109e10 q^{57} -1.38469e11 q^{58} -6.82075e10 q^{59} -5.35102e10 q^{60} +4.71400e11 q^{61} +4.00798e9 q^{62} +6.25235e10 q^{63} -3.39671e11 q^{64} -2.84257e11 q^{65} +4.43840e9 q^{66} -5.02987e11 q^{67} +8.95736e11 q^{68} -5.18486e11 q^{69} +2.65669e10 q^{70} +9.08980e11 q^{71} -1.97741e11 q^{72} -1.44016e12 q^{73} -4.26214e11 q^{74} -8.22595e11 q^{75} -1.03235e12 q^{76} +3.04770e10 q^{77} -5.06894e11 q^{78} -1.16133e12 q^{79} +5.17289e11 q^{80} +2.82430e11 q^{81} -7.22687e11 q^{82} +3.87294e12 q^{83} -6.55221e11 q^{84} -1.12654e12 q^{85} +7.39079e11 q^{86} -4.29501e12 q^{87} -9.63883e10 q^{88} -2.50838e11 q^{89} +1.20007e11 q^{90} -3.48067e12 q^{91} +5.43353e12 q^{92} +1.24319e11 q^{93} +2.19029e12 q^{94} +1.29836e12 q^{95} +3.14452e12 q^{96} -6.67887e12 q^{97} +3.25306e11 q^{98} +1.37670e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	23.5026	0.259669	0.129835	−	0.991536i	$-0.458555\pi$
$2$	23.5026	0.259669	0.129835	+	0.991536i	$0.458555\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7639.63	−0.932572
$5$	9608.09	0.275000	0.137500	−	0.990502i	$-0.456093\pi$
$5$	9608.09	0.275000	0.137500	+	0.990502i	$0.456093\pi$
$6$	17133.4	0.149920
$7$	117649.	0.377964
$7$	117649.	0.377964
$8$	−372084.	−0.501829
$9$	531441.	0.333333
$10$	225815.	0.0714090
$11$	259050.	0.0440891	0.0220445	−	0.999757i	$-0.492982\pi$
$11$	259050.	0.0440891	0.0220445	+	0.999757i	$0.492982\pi$
$12$	−5.56929e6	−0.538421
$13$	−2.95852e7	−1.69997	−0.849987	−	0.526804i	$-0.823390\pi$
$13$	−2.95852e7	−1.69997	−0.849987	+	0.526804i	$0.823390\pi$
$14$	2.76505e6	0.0981458
$15$	7.00430e6	0.158771
$16$	5.38389e7	0.802262
$17$	−1.17249e8	−1.17812	−0.589060	−	0.808089i	$-0.700502\pi$
$17$	−1.17249e8	−1.17812	−0.589060	+	0.808089i	$0.700502\pi$
$18$	1.24902e7	0.0865564
$19$	1.35132e8	0.658959	0.329479	−	0.944163i	$-0.393127\pi$
$19$	1.35132e8	0.658959	0.329479	+	0.944163i	$0.393127\pi$
$20$	−7.34023e7	−0.256457
$21$	8.57661e7	0.218218
$22$	6.08834e6	0.0114486
$23$	−7.11230e8	−1.00180	−0.500898	−	0.865507i	$-0.666997\pi$
$23$	−7.11230e8	−1.00180	−0.500898	+	0.865507i	$0.666997\pi$
$24$	−2.71249e8	−0.289731
$25$	−1.12839e9	−0.924375
$26$	−6.95328e8	−0.441431
$27$	3.87420e8	0.192450
$28$	−8.98795e8	−0.352479
$29$	−5.89165e9	−1.83929	−0.919644	−	0.392752i	$-0.871523\pi$
$29$	−5.89165e9	−1.83929	−0.919644	+	0.392752i	$0.871523\pi$
$30$	1.64619e8	0.0412280
$31$	1.70534e8	0.0345111	0.0172555	−	0.999851i	$-0.494507\pi$
$31$	1.70534e8	0.0345111	0.0172555	+	0.999851i	$0.494507\pi$
$32$	4.31347e9	0.710152
$33$	1.88847e8	0.0254548
$34$	−2.75564e9	−0.305922
$35$	1.13038e9	0.103940
$36$	−4.06001e9	−0.310857
$37$	−1.81348e10	−1.16199	−0.580993	−	0.813908i	$-0.697336\pi$
$37$	−1.81348e10	−1.16199	−0.580993	+	0.813908i	$0.697336\pi$
$38$	3.17594e9	0.171111
$39$	−2.15676e10	−0.981480
$40$	−3.57502e9	−0.138003
$41$	−3.07493e10	−1.01097	−0.505486	−	0.862835i	$-0.668687\pi$
$41$	−3.07493e10	−1.01097	−0.505486	+	0.862835i	$0.668687\pi$
$42$	2.01572e9	0.0566645
$43$	3.14467e10	0.758631	0.379315	−	0.925267i	$-0.376160\pi$
$43$	3.14467e10	0.758631	0.379315	+	0.925267i	$0.376160\pi$
$44$	−1.97904e9	−0.0411162
$45$	5.10613e9	0.0916666
$46$	−1.67157e10	−0.260135
$47$	9.31934e10	1.26110	0.630550	−	0.776149i	$-0.282830\pi$
$47$	9.31934e10	1.26110	0.630550	+	0.776149i	$0.282830\pi$
$48$	3.92486e10	0.463186
$49$	1.38413e10	0.142857
$50$	−2.65200e10	−0.240032
$51$	−8.54742e10	−0.680188
$52$	2.26020e11	1.58535
$53$	2.57249e11	1.59427	0.797134	−	0.603803i	$-0.206349\pi$
$53$	2.57249e11	1.59427	0.797134	+	0.603803i	$0.206349\pi$
$54$	9.10538e9	0.0499734
$55$	2.48898e9	0.0121245
$56$	−4.37753e10	−0.189674
$57$	9.85109e10	0.380450
$58$	−1.38469e11	−0.477607
$59$	−6.82075e10	−0.210520	−0.105260	−	0.994445i	$-0.533568\pi$
$59$	−6.82075e10	−0.210520	−0.105260	+	0.994445i	$0.533568\pi$
$60$	−5.35102e10	−0.148065
$61$	4.71400e11	1.17151	0.585755	−	0.810488i	$-0.300798\pi$
$61$	4.71400e11	1.17151	0.585755	+	0.810488i	$0.300798\pi$
$62$	4.00798e9	0.00896147
$63$	6.25235e10	0.125988
$64$	−3.39671e11	−0.617857
$65$	−2.84257e11	−0.467492
$66$	4.43840e9	0.00660984
$67$	−5.02987e11	−0.679315	−0.339657	−	0.940549i	$-0.610311\pi$
$67$	−5.02987e11	−0.679315	−0.339657	+	0.940549i	$0.610311\pi$
$68$	8.95736e11	1.09868
$69$	−5.18486e11	−0.578387
$70$	2.65669e10	0.0269900
$71$	9.08980e11	0.842122	0.421061	−	0.907032i	$-0.361658\pi$
$71$	9.08980e11	0.842122	0.421061	+	0.907032i	$0.361658\pi$
$72$	−1.97741e11	−0.167276
$73$	−1.44016e12	−1.11381	−0.556907	−	0.830575i	$-0.688012\pi$
$73$	−1.44016e12	−1.11381	−0.556907	+	0.830575i	$0.688012\pi$
$74$	−4.26214e11	−0.301732
$75$	−8.22595e11	−0.533688
$76$	−1.03235e12	−0.614526
$77$	3.04770e10	0.0166641
$78$	−5.06894e11	−0.254860
$79$	−1.16133e12	−0.537503	−0.268752	−	0.963209i	$-0.586611\pi$
$79$	−1.16133e12	−0.537503	−0.268752	+	0.963209i	$0.586611\pi$
$80$	5.17289e11	0.220622
$81$	2.82430e11	0.111111
$82$	−7.22687e11	−0.262519
$83$	3.87294e12	1.30027	0.650135	−	0.759819i	$-0.274712\pi$
$83$	3.87294e12	1.30027	0.650135	+	0.759819i	$0.274712\pi$
$84$	−6.55221e11	−0.203504
$85$	−1.12654e12	−0.323983
$86$	7.39079e11	0.196993
$87$	−4.29501e12	−1.06191
$88$	−9.63883e10	−0.0221252
$89$	−2.50838e11	−0.0535006	−0.0267503	−	0.999642i	$-0.508516\pi$
$89$	−2.50838e11	−0.0535006	−0.0267503	+	0.999642i	$0.508516\pi$
$90$	1.20007e11	0.0238030
$91$	−3.48067e12	−0.642530
$92$	5.43353e12	0.934246
$93$	1.24319e11	0.0199250
$94$	2.19029e12	0.327469
$95$	1.29836e12	0.181213
$96$	3.14452e12	0.410007
$97$	−6.67887e12	−0.814117	−0.407059	−	0.913402i	$-0.633446\pi$
$97$	−6.67887e12	−0.814117	−0.407059	+	0.913402i	$0.633446\pi$
$98$	3.25306e11	0.0370956
$99$	1.37670e11	0.0146964
$100$	8.62046e12	0.862046
$101$	3.62249e12	0.339562	0.169781	−	0.985482i	$-0.445694\pi$
$101$	3.62249e12	0.339562	0.169781	+	0.985482i	$0.445694\pi$
$102$	−2.00886e12	−0.176624
$103$	−9.84940e10	−0.00812770	−0.00406385	−	0.999992i	$-0.501294\pi$
$103$	−9.84940e10	−0.00812770	−0.00406385	+	0.999992i	$0.501294\pi$
$104$	1.10082e13	0.853097
$105$	8.24049e11	0.0600098
$106$	6.04602e12	0.413982
$107$	1.91848e13	1.23584	0.617921	−	0.786240i	$-0.287975\pi$
$107$	1.91848e13	1.23584	0.617921	+	0.786240i	$0.287975\pi$
$108$	−2.95975e12	−0.179474
$109$	1.94275e12	0.110955	0.0554774	−	0.998460i	$-0.482332\pi$
$109$	1.94275e12	0.110955	0.0554774	+	0.998460i	$0.482332\pi$
$110$	5.84973e10	0.00314835
$111$	−1.32203e13	−0.670873
$112$	6.33409e12	0.303227
$113$	−8.72196e12	−0.394098	−0.197049	−	0.980394i	$-0.563136\pi$
$113$	−8.72196e12	−0.394098	−0.197049	+	0.980394i	$0.563136\pi$
$114$	2.31526e12	0.0987912
$115$	−6.83356e12	−0.275493
$116$	4.50100e13	1.71527
$117$	−1.57228e13	−0.566658
$118$	−1.60305e12	−0.0546656
$119$	−1.37942e13	−0.445288
$120$	−2.60619e12	−0.0796760
$121$	−3.44556e13	−0.998056
$122$	1.10791e13	0.304205
$123$	−2.24162e13	−0.583685
$124$	−1.30281e12	−0.0321841
$125$	−2.25703e13	−0.529203
$126$	1.46946e12	0.0327153
$127$	−2.06465e13	−0.436638	−0.218319	−	0.975877i	$-0.570057\pi$
$127$	−2.06465e13	−0.436638	−0.218319	+	0.975877i	$0.570057\pi$
$128$	−4.33190e13	−0.870591
$129$	2.29247e13	0.437996
$130$	−6.68077e12	−0.121393
$131$	−3.30684e13	−0.571676	−0.285838	−	0.958278i	$-0.592272\pi$
$131$	−3.30684e13	−0.571676	−0.285838	+	0.958278i	$0.592272\pi$
$132$	−1.44272e12	−0.0237385
$133$	1.58981e13	0.249063
$134$	−1.18215e13	−0.176397
$135$	3.72237e12	0.0529237
$136$	4.36263e13	0.591215
$137$	1.57774e13	0.203869	0.101935	−	0.994791i	$-0.467497\pi$
$137$	1.57774e13	0.203869	0.101935	+	0.994791i	$0.467497\pi$
$138$	−1.21858e13	−0.150189
$139$	−1.14454e14	−1.34597	−0.672984	−	0.739657i	$-0.734988\pi$
$139$	−1.14454e14	−1.34597	−0.672984	+	0.739657i	$0.734988\pi$
$140$	−8.63570e12	−0.0969316
$141$	6.79380e13	0.728096
$142$	2.13634e13	0.218673
$143$	−7.66403e12	−0.0749503
$144$	2.86122e13	0.267421
$145$	−5.66075e13	−0.505804
$146$	−3.38475e13	−0.289223
$147$	1.00903e13	0.0824786
$148$	1.38543e14	1.08364
$149$	−1.83854e14	−1.37646	−0.688228	−	0.725494i	$-0.741611\pi$
$149$	−1.83854e14	−1.37646	−0.688228	+	0.725494i	$0.741611\pi$
$150$	−1.93331e13	−0.138582
$151$	1.99626e14	1.37046	0.685231	−	0.728326i	$-0.259701\pi$
$151$	1.99626e14	1.37046	0.685231	+	0.728326i	$0.259701\pi$
$152$	−5.02803e13	−0.330685
$153$	−6.23107e13	−0.392707
$154$	7.16287e11	0.00432715
$155$	1.63850e12	0.00949054
$156$	1.64768e14	0.915301
$157$	1.86454e13	0.0993630	0.0496815	−	0.998765i	$-0.484179\pi$
$157$	1.86454e13	0.0993630	0.0496815	+	0.998765i	$0.484179\pi$
$158$	−2.72944e13	−0.139573
$159$	1.87535e14	0.920451
$160$	4.14442e13	0.195292
$161$	−8.36755e13	−0.378643
$162$	6.63782e12	0.0288521
$163$	−6.65747e13	−0.278029	−0.139014	−	0.990290i	$-0.544393\pi$
$163$	−6.65747e13	−0.278029	−0.139014	+	0.990290i	$0.544393\pi$
$164$	2.34913e14	0.942805
$165$	1.81446e12	0.00700007
$166$	9.10241e13	0.337640
$167$	5.40986e14	1.92987	0.964937	−	0.262483i	$-0.0845413\pi$
$167$	5.40986e14	1.92987	0.964937	+	0.262483i	$0.0845413\pi$
$168$	−3.19122e13	−0.109508
$169$	5.72407e14	1.88991
$170$	−2.64765e13	−0.0841283
$171$	7.18144e13	0.219653
$172$	−2.40241e14	−0.707478
$173$	−6.70280e14	−1.90089	−0.950445	−	0.310894i	$-0.899372\pi$
$173$	−6.70280e14	−1.90089	−0.950445	+	0.310894i	$0.899372\pi$
$174$	−1.00944e14	−0.275746
$175$	−1.32754e14	−0.349381
$176$	1.39470e13	0.0353710
$177$	−4.97232e13	−0.121544
$178$	−5.89535e12	−0.0138925
$179$	−3.35822e14	−0.763071	−0.381536	−	0.924354i	$-0.624605\pi$
$179$	−3.35822e14	−0.763071	−0.381536	+	0.924354i	$0.624605\pi$
$180$	−3.90090e13	−0.0854857
$181$	−5.20918e14	−1.10118	−0.550591	−	0.834775i	$-0.685597\pi$
$181$	−5.20918e14	−1.10118	−0.550591	+	0.834775i	$0.685597\pi$
$182$	−8.18046e13	−0.166845
$183$	3.43651e14	0.676371
$184$	2.64637e14	0.502730
$185$	−1.74241e14	−0.319546
$186$	2.92182e12	0.00517391
$187$	−3.03732e13	−0.0519422
$188$	−7.11963e14	−1.17607
$189$	4.55796e13	0.0727393
$190$	3.05147e13	0.0470556
$191$	−4.48195e14	−0.667959	−0.333979	−	0.942580i	$-0.608392\pi$
$191$	−4.48195e14	−0.667959	−0.333979	+	0.942580i	$0.608392\pi$
$192$	−2.47620e14	−0.356720
$193$	−3.73318e14	−0.519943	−0.259972	−	0.965616i	$-0.583713\pi$
$193$	−3.73318e14	−0.519943	−0.259972	+	0.965616i	$0.583713\pi$
$194$	−1.56971e14	−0.211401
$195$	−2.07223e14	−0.269907
$196$	−1.05742e14	−0.133225
$197$	1.45346e15	1.77162	0.885812	−	0.464044i	$-0.153602\pi$
$197$	1.45346e15	1.77162	0.885812	+	0.464044i	$0.153602\pi$
$198$	3.23559e12	0.00381619
$199$	9.97645e14	1.13876	0.569379	−	0.822075i	$-0.307184\pi$
$199$	9.97645e14	1.13876	0.569379	+	0.822075i	$0.307184\pi$
$200$	4.19855e14	0.463879
$201$	−3.66678e14	−0.392202
$202$	8.51380e13	0.0881738
$203$	−6.93147e14	−0.695186
$204$	6.52991e14	0.634324
$205$	−2.95442e14	−0.278017
$206$	−2.31486e12	−0.00211051
$207$	−3.77977e14	−0.333932
$208$	−1.59283e15	−1.36382
$209$	3.50058e13	0.0290529
$210$	1.93673e13	0.0155827
$211$	1.11790e15	0.872104	0.436052	−	0.899922i	$-0.356376\pi$
$211$	1.11790e15	0.872104	0.436052	+	0.899922i	$0.356376\pi$
$212$	−1.96529e15	−1.48677
$213$	6.62647e14	0.486200
$214$	4.50893e14	0.320910
$215$	3.02143e14	0.208623
$216$	−1.44153e14	−0.0965771
$217$	2.00631e13	0.0130440
$218$	4.56597e13	0.0288115
$219$	−1.04988e15	−0.643060
$220$	−1.90148e13	−0.0113069
$221$	3.46882e15	2.00277
$222$	−3.10710e14	−0.174205
$223$	−1.30675e15	−0.711556	−0.355778	−	0.934570i	$-0.615784\pi$
$223$	−1.30675e15	−0.711556	−0.355778	+	0.934570i	$0.615784\pi$
$224$	5.07475e14	0.268412
$225$	−5.99671e14	−0.308125
$226$	−2.04989e14	−0.102335
$227$	3.77064e15	1.82914	0.914570	−	0.404427i	$-0.132529\pi$
$227$	3.77064e15	1.82914	0.914570	+	0.404427i	$0.132529\pi$
$228$	−7.52587e14	−0.354797
$229$	−1.91905e15	−0.879338	−0.439669	−	0.898160i	$-0.644904\pi$
$229$	−1.91905e15	−0.879338	−0.439669	+	0.898160i	$0.644904\pi$
$230$	−1.60606e14	−0.0715372
$231$	2.22177e13	0.00962102
$232$	2.19219e15	0.923009
$233$	2.59898e15	1.06412	0.532059	−	0.846707i	$-0.321419\pi$
$233$	2.59898e15	1.06412	0.532059	+	0.846707i	$0.321419\pi$
$234$	−3.69526e14	−0.147144
$235$	8.95411e14	0.346802
$236$	5.21080e14	0.196325
$237$	−8.46613e14	−0.310328
$238$	−3.24199e14	−0.115627
$239$	4.85776e15	1.68597	0.842985	−	0.537937i	$-0.180796\pi$
$239$	4.85776e15	1.68597	0.842985	+	0.537937i	$0.180796\pi$
$240$	3.77104e14	0.127376
$241$	2.38391e15	0.783752	0.391876	−	0.920018i	$-0.371826\pi$
$241$	2.38391e15	0.783752	0.391876	+	0.920018i	$0.371826\pi$
$242$	−8.09796e14	−0.259164
$243$	2.05891e14	0.0641500
$244$	−3.60132e15	−1.09252
$245$	1.32988e14	0.0392857
$246$	−5.26839e14	−0.151565
$247$	−3.99789e15	−1.12021
$248$	−6.34528e13	−0.0173187
$249$	2.82337e15	0.750711
$250$	−5.30460e14	−0.137418
$251$	−2.23087e15	−0.563112	−0.281556	−	0.959545i	$-0.590851\pi$
$251$	−2.23087e15	−0.563112	−0.281556	+	0.959545i	$0.590851\pi$
$252$	−4.77656e14	−0.117493
$253$	−1.84244e14	−0.0441682
$254$	−4.85246e14	−0.113382
$255$	−8.21244e14	−0.187051
$256$	1.76447e15	0.391792
$257$	−5.17436e15	−1.12019	−0.560095	−	0.828429i	$-0.689235\pi$
$257$	−5.17436e15	−1.12019	−0.560095	+	0.828429i	$0.689235\pi$
$258$	5.38789e14	0.113734
$259$	−2.13354e15	−0.439190
$260$	2.17162e15	0.435970
$261$	−3.13106e15	−0.613096
$262$	−7.77193e14	−0.148447
$263$	−2.96009e15	−0.551559	−0.275780	−	0.961221i	$-0.588936\pi$
$263$	−2.96009e15	−0.551559	−0.275780	+	0.961221i	$0.588936\pi$
$264$	−7.02671e13	−0.0127740
$265$	2.47168e15	0.438423
$266$	3.73646e14	0.0646740
$267$	−1.82861e14	−0.0308886
$268$	3.84264e15	0.633510
$269$	−1.04968e15	−0.168915	−0.0844574	−	0.996427i	$-0.526916\pi$
$269$	−1.04968e15	−0.168915	−0.0844574	+	0.996427i	$0.526916\pi$
$270$	8.74853e13	0.0137427
$271$	−1.00071e16	−1.53465	−0.767324	−	0.641259i	$-0.778412\pi$
$271$	−1.00071e16	−1.53465	−0.767324	+	0.641259i	$0.778412\pi$
$272$	−6.31253e15	−0.945161
$273$	−2.53741e15	−0.370965
$274$	3.70810e14	0.0529386
$275$	−2.92309e14	−0.0407548
$276$	3.96104e15	0.539387
$277$	7.60534e15	1.01158	0.505790	−	0.862657i	$-0.331201\pi$
$277$	7.60534e15	1.01158	0.505790	+	0.862657i	$0.331201\pi$
$278$	−2.68996e15	−0.349506
$279$	9.06285e13	0.0115037
$280$	−4.20597e14	−0.0521602
$281$	4.18115e15	0.506646	0.253323	−	0.967382i	$-0.418477\pi$
$281$	4.18115e15	0.506646	0.253323	+	0.967382i	$0.418477\pi$
$282$	1.59672e15	0.189064
$283$	−5.89158e15	−0.681742	−0.340871	−	0.940110i	$-0.610722\pi$
$283$	−5.89158e15	−0.681742	−0.340871	+	0.940110i	$0.610722\pi$
$284$	−6.94427e15	−0.785340
$285$	9.46502e14	0.104624
$286$	−1.80125e14	−0.0194623
$287$	−3.61762e15	−0.382112
$288$	2.29235e15	0.236717
$289$	3.84265e15	0.387967
$290$	−1.33042e15	−0.131342
$291$	−4.86890e15	−0.470031
$292$	1.10023e16	1.03871
$293$	−6.27798e15	−0.579670	−0.289835	−	0.957077i	$-0.593600\pi$
$293$	−6.27798e15	−0.579670	−0.289835	+	0.957077i	$0.593600\pi$
$294$	2.37148e14	0.0214172
$295$	−6.55344e14	−0.0578930
$296$	6.74767e15	0.583119
$297$	1.00361e14	0.00848495
$298$	−4.32104e15	−0.357423
$299$	2.10419e16	1.70303
$300$	6.28432e15	0.497703
$301$	3.69968e15	0.286736
$302$	4.69173e15	0.355867
$303$	2.64080e15	0.196046
$304$	7.27533e15	0.528658
$305$	4.52926e15	0.322165
$306$	−1.46446e15	−0.101974
$307$	1.34213e16	0.914946	0.457473	−	0.889223i	$-0.348755\pi$
$307$	1.34213e16	0.914946	0.457473	+	0.889223i	$0.348755\pi$
$308$	−2.32833e14	−0.0155405
$309$	−7.18021e13	−0.00469253
$310$	3.85090e13	0.00246440
$311$	−2.13931e16	−1.34070	−0.670350	−	0.742045i	$-0.733856\pi$
$311$	−2.13931e16	−1.34070	−0.670350	+	0.742045i	$0.733856\pi$
$312$	8.02496e15	0.492536
$313$	−4.90021e15	−0.294562	−0.147281	−	0.989095i	$-0.547052\pi$
$313$	−4.90021e15	−0.294562	−0.147281	+	0.989095i	$0.547052\pi$
$314$	4.38216e14	0.0258015
$315$	6.00732e14	0.0346467
$316$	8.87217e15	0.501261
$317$	−1.85017e16	−1.02406	−0.512032	−	0.858966i	$-0.671107\pi$
$317$	−1.85017e16	−1.02406	−0.512032	+	0.858966i	$0.671107\pi$
$318$	4.40755e15	0.239013
$319$	−1.52623e15	−0.0810925
$320$	−3.26359e15	−0.169911
$321$	1.39857e16	0.713514
$322$	−1.96659e15	−0.0983219
$323$	−1.58440e16	−0.776333
$324$	−2.15766e15	−0.103619
$325$	3.33835e16	1.57141
$326$	−1.56468e15	−0.0721955
$327$	1.41627e15	0.0640597
$328$	1.14413e16	0.507336
$329$	1.09641e16	0.476651
$330$	4.26446e13	0.00181770
$331$	−1.95160e16	−0.815660	−0.407830	−	0.913058i	$-0.633714\pi$
$331$	−1.95160e16	−0.815660	−0.407830	+	0.913058i	$0.633714\pi$
$332$	−2.95878e16	−1.21259
$333$	−9.63757e15	−0.387329
$334$	1.27146e16	0.501129
$335$	−4.83275e15	−0.186811
$336$	4.61755e15	0.175068
$337$	−4.43667e16	−1.64992	−0.824960	−	0.565191i	$-0.808803\pi$
$337$	−4.43667e16	−1.64992	−0.824960	+	0.565191i	$0.808803\pi$
$338$	1.34530e16	0.490752
$339$	−6.35831e15	−0.227533
$340$	8.60631e15	0.302137
$341$	4.41767e13	0.00152156
$342$	1.68782e15	0.0570371
$343$	1.62841e15	0.0539949
$344$	−1.17008e16	−0.380703
$345$	−4.98167e15	−0.159056
$346$	−1.57533e16	−0.493602
$347$	−5.81713e15	−0.178882	−0.0894411	−	0.995992i	$-0.528508\pi$
$347$	−5.81713e15	−0.178882	−0.0894411	+	0.995992i	$0.528508\pi$
$348$	3.28123e16	0.990311
$349$	−4.32122e16	−1.28009	−0.640046	−	0.768337i	$-0.721085\pi$
$349$	−4.32122e16	−1.28009	−0.640046	+	0.768337i	$0.721085\pi$
$350$	−3.12005e15	−0.0907235
$351$	−1.14619e16	−0.327160
$352$	1.11740e15	0.0313100
$353$	3.37142e16	0.927421	0.463711	−	0.885987i	$-0.346518\pi$
$353$	3.37142e16	0.927421	0.463711	+	0.885987i	$0.346518\pi$
$354$	−1.16862e15	−0.0315612
$355$	8.73357e15	0.231583
$356$	1.91631e15	0.0498932
$357$	−1.00560e16	−0.257087
$358$	−7.89269e15	−0.198146
$359$	−6.90827e15	−0.170316	−0.0851580	−	0.996367i	$-0.527140\pi$
$359$	−6.90827e15	−0.170316	−0.0851580	+	0.996367i	$0.527140\pi$
$360$	−1.89991e15	−0.0460010
$361$	−2.37925e16	−0.565773
$362$	−1.22429e16	−0.285943
$363$	−2.51181e16	−0.576228
$364$	2.65910e16	0.599205
$365$	−1.38372e16	−0.306298
$366$	8.07668e15	0.175633
$367$	−4.51786e16	−0.965169	−0.482585	−	0.875849i	$-0.660302\pi$
$367$	−4.51786e16	−0.965169	−0.482585	+	0.875849i	$0.660302\pi$
$368$	−3.82918e16	−0.803702
$369$	−1.63414e16	−0.336991
$370$	−4.09511e15	−0.0829763
$371$	3.02651e16	0.602576
$372$	−9.49751e14	−0.0185815
$373$	9.05391e16	1.74072	0.870359	−	0.492417i	$-0.163887\pi$
$373$	9.05391e16	1.74072	0.870359	+	0.492417i	$0.163887\pi$
$374$	−7.13849e14	−0.0134878
$375$	−1.64537e16	−0.305535
$376$	−3.46758e16	−0.632857
$377$	1.74305e17	3.12674
$378$	1.07124e15	0.0188882
$379$	−9.91215e16	−1.71796	−0.858980	−	0.512009i	$-0.828901\pi$
$379$	−9.91215e16	−1.71796	−0.858980	+	0.512009i	$0.828901\pi$
$380$	−9.91896e15	−0.168995
$381$	−1.50513e16	−0.252093
$382$	−1.05337e16	−0.173448
$383$	4.90171e16	0.793515	0.396758	−	0.917923i	$-0.370135\pi$
$383$	4.90171e16	0.793515	0.396758	+	0.917923i	$0.370135\pi$
$384$	−3.15796e16	−0.502636
$385$	2.92825e14	0.00458262
$386$	−8.77393e15	−0.135013
$387$	1.67121e16	0.252877
$388$	5.10241e16	0.759223
$389$	8.57025e16	1.25407	0.627034	−	0.778992i	$-0.284269\pi$
$389$	8.57025e16	1.25407	0.627034	+	0.778992i	$0.284269\pi$
$390$	−4.87028e15	−0.0700865
$391$	8.33907e16	1.18024
$392$	−5.15012e15	−0.0716899
$393$	−2.41069e16	−0.330057
$394$	3.41600e16	0.460036
$395$	−1.11582e16	−0.147813
$396$	−1.05175e15	−0.0137054
$397$	7.06037e16	0.905084	0.452542	−	0.891743i	$-0.350517\pi$
$397$	7.06037e16	0.905084	0.452542	+	0.891743i	$0.350517\pi$
$398$	2.34472e16	0.295700
$399$	1.15897e16	0.143797
$400$	−6.07512e16	−0.741591
$401$	4.49264e16	0.539589	0.269795	−	0.962918i	$-0.413044\pi$
$401$	4.49264e16	0.539589	0.269795	+	0.962918i	$0.413044\pi$
$402$	−8.61787e15	−0.101843
$403$	−5.04526e15	−0.0586680
$404$	−2.76745e16	−0.316666
$405$	2.71361e15	0.0305555
$406$	−1.62907e16	−0.180518
$407$	−4.69781e15	−0.0512309
$408$	3.18036e16	0.341338
$409$	−9.23736e16	−0.975768	−0.487884	−	0.872909i	$-0.662231\pi$
$409$	−9.23736e16	−0.975768	−0.487884	+	0.872909i	$0.662231\pi$
$410$	−6.94364e15	−0.0721925
$411$	1.15017e16	0.117704
$412$	7.52458e14	0.00757967
$413$	−8.02454e15	−0.0795692
$414$	−8.88343e15	−0.0867118
$415$	3.72116e16	0.357574
$416$	−1.27615e17	−1.20724
$417$	−8.34369e16	−0.777095
$418$	8.22727e14	0.00754414
$419$	3.35566e16	0.302961	0.151480	−	0.988460i	$-0.451596\pi$
$419$	3.35566e16	0.302961	0.151480	+	0.988460i	$0.451596\pi$
$420$	−6.29543e15	−0.0559635
$421$	1.17203e17	1.02590	0.512950	−	0.858418i	$-0.328553\pi$
$421$	1.17203e17	1.02590	0.512950	+	0.858418i	$0.328553\pi$
$422$	2.62736e16	0.226459
$423$	4.95268e16	0.420366
$424$	−9.57184e16	−0.800050
$425$	1.32302e17	1.08902
$426$	1.55739e16	0.126251
$427$	5.54597e16	0.442789
$428$	−1.46565e17	−1.15251
$429$	−5.58708e15	−0.0432726
$430$	7.10114e15	0.0541730
$431$	1.12461e17	0.845083	0.422541	−	0.906344i	$-0.361138\pi$
$431$	1.12461e17	0.845083	0.422541	+	0.906344i	$0.361138\pi$
$432$	2.08583e16	0.154395
$433$	−1.26388e17	−0.921582	−0.460791	−	0.887509i	$-0.652434\pi$
$433$	−1.26388e17	−0.921582	−0.460791	+	0.887509i	$0.652434\pi$
$434$	4.71535e14	0.00338712
$435$	−4.12669e16	−0.292026
$436$	−1.48419e16	−0.103473
$437$	−9.61096e16	−0.660142
$438$	−2.46748e16	−0.166983
$439$	−1.00252e17	−0.668457	−0.334228	−	0.942492i	$-0.608476\pi$
$439$	−1.00252e17	−0.668457	−0.334228	+	0.942492i	$0.608476\pi$
$440$	−9.26108e14	−0.00608442
$441$	7.35583e15	0.0476190
$442$	8.15262e16	0.520059
$443$	−1.24694e17	−0.783831	−0.391915	−	0.920001i	$-0.628187\pi$
$443$	−1.24694e17	−0.783831	−0.391915	+	0.920001i	$0.628187\pi$
$444$	1.00998e17	0.625638
$445$	−2.41008e15	−0.0147127
$446$	−3.07119e16	−0.184769
$447$	−1.34030e17	−0.794697
$448$	−3.99619e16	−0.233528
$449$	7.36499e16	0.424200	0.212100	−	0.977248i	$-0.431970\pi$
$449$	7.36499e16	0.424200	0.212100	+	0.977248i	$0.431970\pi$
$450$	−1.40938e16	−0.0800106
$451$	−7.96559e15	−0.0445729
$452$	6.66325e16	0.367525
$453$	1.45527e17	0.791237
$454$	8.86198e16	0.474971
$455$	−3.34426e16	−0.176695
$456$	−3.66543e16	−0.190921
$457$	−1.34259e17	−0.689429	−0.344714	−	0.938708i	$-0.612024\pi$
$457$	−1.34259e17	−0.689429	−0.344714	+	0.938708i	$0.612024\pi$
$458$	−4.51026e16	−0.228337
$459$	−4.54245e16	−0.226729
$460$	5.22059e16	0.256917
$461$	−6.72631e13	−0.000326378 0	−0.000163189	−	1.00000i	$-0.500052\pi$
$461$	−6.72631e13	−0.000326378 0	−0.000163189		1.00000i	$0.500052\pi$
$462$	5.22173e14	0.00249828
$463$	−3.62159e17	−1.70853	−0.854265	−	0.519838i	$-0.825992\pi$
$463$	−3.62159e17	−1.70853	−0.854265	+	0.519838i	$0.825992\pi$
$464$	−3.17200e17	−1.47559
$465$	1.19447e15	0.00547937
$466$	6.10827e16	0.276319
$467$	−9.59455e16	−0.428021	−0.214010	−	0.976831i	$-0.568653\pi$
$467$	−9.59455e16	−0.428021	−0.214010	+	0.976831i	$0.568653\pi$
$468$	1.20116e17	0.528449
$469$	−5.91760e16	−0.256757
$470$	2.10445e16	0.0900538
$471$	1.35925e16	0.0573673
$472$	2.53789e16	0.105645
$473$	8.14627e15	0.0334473
$474$	−1.98976e16	−0.0805826
$475$	−1.52481e17	−0.609125
$476$	1.05382e17	0.415263
$477$	1.36713e17	0.531422
$478$	1.14170e17	0.437795
$479$	−1.93047e17	−0.730270	−0.365135	−	0.930955i	$-0.618977\pi$
$479$	−1.93047e17	−0.730270	−0.365135	+	0.930955i	$0.618977\pi$
$480$	3.02128e16	0.112752
$481$	5.36521e17	1.97535
$482$	5.60279e16	0.203516
$483$	−6.09994e16	−0.218610
$484$	2.63228e17	0.930759
$485$	−6.41712e16	−0.223882
$486$	4.83897e15	0.0166578
$487$	−4.96869e16	−0.168773	−0.0843867	−	0.996433i	$-0.526893\pi$
$487$	−4.96869e16	−0.168773	−0.0843867	+	0.996433i	$0.526893\pi$
$488$	−1.75400e17	−0.587898
$489$	−4.85329e16	−0.160520
$490$	3.12557e15	0.0102013
$491$	3.67185e17	1.18265	0.591323	−	0.806435i	$-0.298606\pi$
$491$	3.67185e17	1.18265	0.591323	+	0.806435i	$0.298606\pi$
$492$	1.71251e17	0.544329
$493$	6.90787e17	2.16690
$494$	−9.39607e16	−0.290885
$495$	1.32274e15	0.00404149
$496$	9.18134e15	0.0276869
$497$	1.06941e17	0.318292
$498$	6.63566e16	0.194937
$499$	2.08452e17	0.604438	0.302219	−	0.953239i	$-0.402273\pi$
$499$	2.08452e17	0.604438	0.302219	+	0.953239i	$0.402273\pi$
$500$	1.72429e17	0.493519
$501$	3.94379e17	1.11421
$502$	−5.24312e16	−0.146223
$503$	−5.91215e17	−1.62762	−0.813811	−	0.581129i	$-0.802611\pi$
$503$	−5.91215e17	−1.62762	−0.813811	+	0.581129i	$0.802611\pi$
$504$	−2.32640e16	−0.0632246
$505$	3.48053e16	0.0933794
$506$	−4.33021e15	−0.0114691
$507$	4.17285e17	1.09114
$508$	1.57732e17	0.407197
$509$	−4.35107e17	−1.10900	−0.554498	−	0.832185i	$-0.687090\pi$
$509$	−4.35107e17	−1.10900	−0.554498	+	0.832185i	$0.687090\pi$
$510$	−1.93014e16	−0.0485715
$511$	−1.69433e17	−0.420982
$512$	3.96339e17	0.972327
$513$	5.23527e16	0.126817
$514$	−1.21611e17	−0.290879
$515$	−9.46340e14	−0.00223512
$516$	−1.75136e17	−0.408462
$517$	2.41417e16	0.0556007
$518$	−5.01437e16	−0.114044
$519$	−4.88634e17	−1.09748
$520$	1.05768e17	0.234601
$521$	−6.24393e17	−1.36777	−0.683885	−	0.729590i	$-0.739711\pi$
$521$	−6.24393e17	−1.36777	−0.683885	+	0.729590i	$0.739711\pi$
$522$	−7.35881e16	−0.159202
$523$	−7.20990e17	−1.54052	−0.770262	−	0.637727i	$-0.779875\pi$
$523$	−7.20990e17	−1.54052	−0.770262	+	0.637727i	$0.779875\pi$
$524$	2.52631e17	0.533129
$525$	−9.67774e16	−0.201715
$526$	−6.95697e16	−0.143223
$527$	−1.99948e16	−0.0406582
$528$	1.01673e16	0.0204215
$529$	1.81137e15	0.00359374
$530$	5.80907e16	0.113845
$531$	−3.62482e16	−0.0701734
$532$	−1.21455e17	−0.232269
$533$	9.09722e17	1.71863
$534$	−4.29771e15	−0.00802082
$535$	1.84330e17	0.339856
$536$	1.87154e17	0.340900
$537$	−2.44815e17	−0.440559
$538$	−2.46702e16	−0.0438620
$539$	3.58558e15	0.00629844
$540$	−2.84375e16	−0.0493552
$541$	−7.96109e17	−1.36518	−0.682590	−	0.730801i	$-0.739147\pi$
$541$	−7.96109e17	−1.36518	−0.682590	+	0.730801i	$0.739147\pi$
$542$	−2.35193e17	−0.398501
$543$	−3.79749e17	−0.635767
$544$	−5.05748e17	−0.836645
$545$	1.86662e16	0.0305125
$546$	−5.96356e16	−0.0963281
$547$	8.09613e17	1.29229	0.646145	−	0.763215i	$-0.276380\pi$
$547$	8.09613e17	1.29229	0.646145	+	0.763215i	$0.276380\pi$
$548$	−1.20534e17	−0.190123
$549$	2.50521e17	0.390503
$550$	−6.87001e15	−0.0105828
$551$	−7.96148e17	−1.21202
$552$	1.92921e17	0.290252
$553$	−1.36630e17	−0.203157
$554$	1.78745e17	0.262676
$555$	−1.27021e17	−0.184490
$556$	8.74386e17	1.25521
$557$	9.80255e17	1.39085	0.695425	−	0.718599i	$-0.255216\pi$
$557$	9.80255e17	1.39085	0.695425	+	0.718599i	$0.255216\pi$
$558$	2.13000e15	0.00298716
$559$	−9.30357e17	−1.28965
$560$	6.08586e16	0.0833872
$561$	−2.21421e16	−0.0299889
$562$	9.82677e16	0.131560
$563$	−1.08025e18	−1.42961	−0.714806	−	0.699323i	$-0.753485\pi$
$563$	−1.08025e18	−1.42961	−0.714806	+	0.699323i	$0.753485\pi$
$564$	−5.19021e17	−0.679002
$565$	−8.38014e16	−0.108377
$566$	−1.38467e17	−0.177028
$567$	3.32276e16	0.0419961
$568$	−3.38217e17	−0.422602
$569$	7.85155e17	0.969897	0.484948	−	0.874543i	$-0.338838\pi$
$569$	7.85155e17	0.969897	0.484948	+	0.874543i	$0.338838\pi$
$570$	2.22452e16	0.0271675
$571$	−8.83772e17	−1.06710	−0.533551	−	0.845768i	$-0.679143\pi$
$571$	−8.83772e17	−1.06710	−0.533551	+	0.845768i	$0.679143\pi$
$572$	5.85504e16	0.0698965
$573$	−3.26734e17	−0.385646
$574$	−8.50234e16	−0.0992227
$575$	8.02543e17	0.926035
$576$	−1.80515e17	−0.205952
$577$	2.73967e17	0.309069	0.154534	−	0.987987i	$-0.450612\pi$
$577$	2.73967e17	0.309069	0.154534	+	0.987987i	$0.450612\pi$
$578$	9.03121e16	0.100743
$579$	−2.72149e17	−0.300189
$580$	4.32460e17	0.471698
$581$	4.55648e17	0.491456
$582$	−1.14432e17	−0.122053
$583$	6.66404e16	0.0702898
$584$	5.35861e17	0.558944
$585$	−1.51066e17	−0.155831
$586$	−1.47549e17	−0.150522
$587$	−6.62502e17	−0.668405	−0.334202	−	0.942501i	$-0.608467\pi$
$587$	−6.62502e17	−0.668405	−0.334202	+	0.942501i	$0.608467\pi$
$588$	−7.70861e16	−0.0769172
$589$	2.30445e16	0.0227414
$590$	−1.54023e16	−0.0150330
$591$	1.05957e18	1.02285
$592$	−9.76357e17	−0.932218
$593$	2.41078e17	0.227668	0.113834	−	0.993500i	$-0.463687\pi$
$593$	2.41078e17	0.227668	0.113834	+	0.993500i	$0.463687\pi$
$594$	2.35875e15	0.00220328
$595$	−1.32536e17	−0.122454
$596$	1.40458e18	1.28364
$597$	7.27283e17	0.657462
$598$	4.94538e17	0.442223
$599$	1.67007e18	1.47727	0.738637	−	0.674103i	$-0.235470\pi$
$599$	1.67007e18	1.47727	0.738637	+	0.674103i	$0.235470\pi$
$600$	3.06074e17	0.267821
$601$	2.36736e17	0.204918	0.102459	−	0.994737i	$-0.467329\pi$
$601$	2.36736e17	0.204918	0.102459	+	0.994737i	$0.467329\pi$
$602$	8.69519e16	0.0744564
$603$	−2.67308e17	−0.226438
$604$	−1.52507e18	−1.27805
$605$	−3.31053e17	−0.274465
$606$	6.20656e16	0.0509071
$607$	2.42336e18	1.96649	0.983243	−	0.182300i	$-0.0583541\pi$
$607$	2.42336e18	1.96649	0.983243	+	0.182300i	$0.0583541\pi$
$608$	5.82885e17	0.467961
$609$	−5.05304e17	−0.401366
$610$	1.06449e17	0.0836562
$611$	−2.75714e18	−2.14384
$612$	4.76031e17	0.366227
$613$	1.42410e18	1.08405	0.542023	−	0.840364i	$-0.317659\pi$
$613$	1.42410e18	1.08405	0.542023	+	0.840364i	$0.317659\pi$
$614$	3.15435e17	0.237583
$615$	−2.15377e17	−0.160513
$616$	−1.13400e16	−0.00836254
$617$	7.27155e17	0.530607	0.265304	−	0.964165i	$-0.414528\pi$
$617$	7.27155e17	0.530607	0.265304	+	0.964165i	$0.414528\pi$
$618$	−1.68754e15	−0.00121851
$619$	−8.24248e17	−0.588937	−0.294468	−	0.955661i	$-0.595143\pi$
$619$	−8.24248e17	−0.588937	−0.294468	+	0.955661i	$0.595143\pi$
$620$	−1.25175e16	−0.00885061
$621$	−2.75545e17	−0.192796
$622$	−5.02794e17	−0.348139
$623$	−2.95109e16	−0.0202213
$624$	−1.16118e18	−0.787405
$625$	1.16057e18	0.778845
$626$	−1.15167e17	−0.0764886
$627$	2.55192e16	0.0167737
$628$	−1.42444e17	−0.0926632
$629$	2.12628e18	1.36896
$630$	1.41187e16	0.00899668
$631$	−9.92218e17	−0.625772	−0.312886	−	0.949791i	$-0.601296\pi$
$631$	−9.92218e17	−0.625772	−0.312886	+	0.949791i	$0.601296\pi$
$632$	4.32114e17	0.269735
$633$	8.14951e17	0.503509
$634$	−4.34838e17	−0.265918
$635$	−1.98373e17	−0.120075
$636$	−1.43270e18	−0.858386
$637$	−4.09497e17	−0.242853
$638$	−3.58704e16	−0.0210572
$639$	4.83069e17	0.280707
$640$	−4.16213e17	−0.239412
$641$	−8.12150e17	−0.462444	−0.231222	−	0.972901i	$-0.574272\pi$
$641$	−8.12150e17	−0.462444	−0.231222	+	0.972901i	$0.574272\pi$
$642$	3.28701e17	0.185278
$643$	−3.30409e17	−0.184366	−0.0921829	−	0.995742i	$-0.529384\pi$
$643$	−3.30409e17	−0.184366	−0.0921829	+	0.995742i	$0.529384\pi$
$644$	6.39250e17	0.353112
$645$	2.20262e17	0.120449
$646$	−3.72374e17	−0.201590
$647$	−1.29484e18	−0.693968	−0.346984	−	0.937871i	$-0.612794\pi$
$647$	−1.29484e18	−0.693968	−0.346984	+	0.937871i	$0.612794\pi$
$648$	−1.05088e17	−0.0557588
$649$	−1.76691e16	−0.00928164
$650$	7.84599e17	0.408048
$651$	1.46260e16	0.00753094
$652$	5.08606e17	0.259282
$653$	−2.34172e18	−1.18195	−0.590976	−	0.806689i	$-0.701257\pi$
$653$	−2.34172e18	−1.18195	−0.590976	+	0.806689i	$0.701257\pi$
$654$	3.32860e16	0.0166343
$655$	−3.17725e17	−0.157211
$656$	−1.65551e18	−0.811065
$657$	−7.65360e17	−0.371271
$658$	2.57685e17	0.123772
$659$	−7.44565e17	−0.354117	−0.177059	−	0.984200i	$-0.556658\pi$
$659$	−7.44565e17	−0.354117	−0.177059	+	0.984200i	$0.556658\pi$
$660$	−1.38618e16	−0.00652807
$661$	3.30071e18	1.53921	0.769605	−	0.638521i	$-0.220453\pi$
$661$	3.30071e18	1.53921	0.769605	+	0.638521i	$0.220453\pi$
$662$	−4.58677e17	−0.211802
$663$	2.52877e18	1.15630
$664$	−1.44106e18	−0.652513
$665$	1.52750e17	0.0684922
$666$	−2.26508e17	−0.100577
$667$	4.19032e18	1.84259
$668$	−4.13293e18	−1.79975
$669$	−9.52617e17	−0.410817
$670$	−1.13582e17	−0.0485091
$671$	1.22116e17	0.0516507
$672$	3.69949e17	0.154968
$673$	−3.48728e18	−1.44674	−0.723368	−	0.690463i	$-0.757407\pi$
$673$	−3.48728e18	−1.44674	−0.723368	+	0.690463i	$0.757407\pi$
$674$	−1.04273e18	−0.428434
$675$	−4.37161e17	−0.177896
$676$	−4.37298e18	−1.76248
$677$	−2.99340e17	−0.119492	−0.0597460	−	0.998214i	$-0.519029\pi$
$677$	−2.99340e17	−0.119492	−0.0597460	+	0.998214i	$0.519029\pi$
$678$	−1.49437e17	−0.0590832
$679$	−7.85763e17	−0.307707
$680$	4.19166e17	0.162584
$681$	2.74880e18	1.05605
$682$	1.03827e15	0.000395103 0
$683$	3.10392e18	1.16997	0.584987	−	0.811043i	$-0.301100\pi$
$683$	3.10392e18	1.16997	0.584987	+	0.811043i	$0.301100\pi$
$684$	−5.48636e17	−0.204842
$685$	1.51591e17	0.0560640
$686$	3.82719e16	0.0140208
$687$	−1.39899e18	−0.507686
$688$	1.69306e18	0.608621
$689$	−7.61077e18	−2.71021
$690$	−1.17082e17	−0.0413020
$691$	2.91746e18	1.01952	0.509762	−	0.860315i	$-0.329733\pi$
$691$	2.91746e18	1.01952	0.509762	+	0.860315i	$0.329733\pi$
$692$	5.12069e18	1.77272
$693$	1.61967e16	0.00555470
$694$	−1.36718e17	−0.0464502
$695$	−1.09968e18	−0.370141
$696$	1.59811e18	0.532900
$697$	3.60531e18	1.19105
$698$	−1.01560e18	−0.332401
$699$	1.89466e18	0.614368
$700$	1.01419e18	0.325823
$701$	−6.03207e18	−1.91999	−0.959995	−	0.280017i	$-0.909660\pi$
$701$	−6.03207e18	−1.91999	−0.959995	+	0.280017i	$0.909660\pi$
$702$	−2.69384e17	−0.0849534
$703$	−2.45058e18	−0.765702
$704$	−8.79917e16	−0.0272408
$705$	6.52755e17	0.200226
$706$	7.92370e17	0.240823
$707$	4.26183e17	0.128342
$708$	3.79867e17	0.113348
$709$	2.92747e18	0.865550	0.432775	−	0.901502i	$-0.357535\pi$
$709$	2.92747e18	0.865550	0.432775	+	0.901502i	$0.357535\pi$
$710$	2.05261e17	0.0601351
$711$	−6.17181e17	−0.179168
$712$	9.33330e16	0.0268482
$713$	−1.21289e17	−0.0345731
$714$	−2.36341e17	−0.0667576
$715$	−7.36368e16	−0.0206113
$716$	2.56556e18	0.711619
$717$	3.54131e18	0.973395
$718$	−1.62362e17	−0.0442258
$719$	−1.13626e18	−0.306717	−0.153359	−	0.988171i	$-0.549009\pi$
$719$	−1.13626e18	−0.306717	−0.153359	+	0.988171i	$0.549009\pi$
$720$	2.74909e17	0.0735406
$721$	−1.15877e16	−0.00307198
$722$	−5.59184e17	−0.146914
$723$	1.73787e18	0.452499
$724$	3.97962e18	1.02693
$725$	6.64806e18	1.70019
$726$	−5.90341e17	−0.149629
$727$	3.99382e18	1.00326	0.501631	−	0.865082i	$-0.332734\pi$
$727$	3.99382e18	1.00326	0.501631	+	0.865082i	$0.332734\pi$
$728$	1.29510e18	0.322440
$729$	1.50095e17	0.0370370
$730$	−3.25210e17	−0.0795362
$731$	−3.68708e18	−0.893758
$732$	−2.62536e18	−0.630765
$733$	−4.89090e17	−0.116470	−0.0582348	−	0.998303i	$-0.518547\pi$
$733$	−4.89090e17	−0.116470	−0.0582348	+	0.998303i	$0.518547\pi$
$734$	−1.06181e18	−0.250625
$735$	9.69485e16	0.0226816
$736$	−3.06787e18	−0.711427
$737$	−1.30299e17	−0.0299503
$738$	−3.84065e17	−0.0875062
$739$	−6.39175e18	−1.44355	−0.721773	−	0.692129i	$-0.756673\pi$
$739$	−6.39175e18	−1.44355	−0.721773	+	0.692129i	$0.756673\pi$
$740$	1.33113e18	0.298000
$741$	−2.91446e18	−0.646755
$742$	7.11308e17	0.156471
$743$	3.62218e18	0.789846	0.394923	−	0.918714i	$-0.370771\pi$
$743$	3.62218e18	0.789846	0.394923	+	0.918714i	$0.370771\pi$
$744$	−4.62571e16	−0.00999895
$745$	−1.76649e18	−0.378525
$746$	2.12790e18	0.452011
$747$	2.05824e18	0.433423
$748$	2.32040e17	0.0484399
$749$	2.25707e18	0.467105
$750$	−3.86705e17	−0.0793381
$751$	2.50207e18	0.508909	0.254454	−	0.967085i	$-0.418104\pi$
$751$	2.50207e18	0.508909	0.254454	+	0.967085i	$0.418104\pi$
$752$	5.01743e18	1.01173
$753$	−1.62630e18	−0.325113
$754$	4.09663e18	0.811919
$755$	1.91803e18	0.376877
$756$	−3.48211e17	−0.0678346
$757$	−9.23796e18	−1.78424	−0.892119	−	0.451800i	$-0.850782\pi$
$757$	−9.23796e18	−1.78424	−0.892119	+	0.451800i	$0.850782\pi$
$758$	−2.32961e18	−0.446101
$759$	−1.34314e17	−0.0255005
$760$	−4.83098e17	−0.0909383
$761$	4.06749e18	0.759147	0.379574	−	0.925162i	$-0.376071\pi$
$761$	4.06749e18	0.759147	0.379574	+	0.925162i	$0.376071\pi$
$762$	−3.53744e17	−0.0654609
$763$	2.28563e17	0.0419369
$764$	3.42404e18	0.622920
$765$	−5.98687e17	−0.107994
$766$	1.15203e18	0.206051
$767$	2.01793e18	0.357879
$768$	1.28630e18	0.226201
$769$	−6.19100e18	−1.07954	−0.539771	−	0.841812i	$-0.681489\pi$
$769$	−6.19100e18	−1.07954	−0.539771	+	0.841812i	$0.681489\pi$
$770$	6.88215e15	0.00118997
$771$	−3.77211e18	−0.646742
$772$	2.85201e18	0.484884
$773$	−1.08111e19	−1.82265	−0.911324	−	0.411691i	$-0.864938\pi$
$773$	−1.08111e19	−1.82265	−0.911324	+	0.411691i	$0.864938\pi$
$774$	3.92777e17	0.0656644
$775$	−1.92428e17	−0.0319012
$776$	2.48510e18	0.408548
$777$	−1.55535e18	−0.253566
$778$	2.01423e18	0.325643
$779$	−4.15519e18	−0.666190
$780$	1.58311e18	0.251707
$781$	2.35471e17	0.0371284
$782$	1.95990e18	0.306471
$783$	−2.28255e18	−0.353971
$784$	7.45200e17	0.114609
$785$	1.79147e17	0.0273248
$786$	−5.66574e17	−0.0857058
$787$	8.42845e18	1.26448	0.632240	−	0.774772i	$-0.282136\pi$
$787$	8.42845e18	1.26448	0.632240	+	0.774772i	$0.282136\pi$
$788$	−1.11039e19	−1.65217
$789$	−2.15790e18	−0.318443
$790$	−2.62247e17	−0.0383826
$791$	−1.02613e18	−0.148955
$792$	−5.12247e16	−0.00737507
$793$	−1.39465e19	−1.99154
$794$	1.65937e18	0.235023
$795$	1.80185e18	0.253124
$796$	−7.62164e18	−1.06197
$797$	1.22403e19	1.69166	0.845831	−	0.533451i	$-0.179105\pi$
$797$	1.22403e19	1.69166	0.845831	+	0.533451i	$0.179105\pi$
$798$	2.72388e17	0.0373396
$799$	−1.09268e19	−1.48573
$800$	−4.86726e18	−0.656447
$801$	−1.33306e17	−0.0178335
$802$	1.05589e18	0.140115
$803$	−3.73073e17	−0.0491070
$804$	2.80128e18	0.365757
$805$	−8.03962e17	−0.104127
$806$	−1.18577e17	−0.0152343
$807$	−7.65218e17	−0.0975230
$808$	−1.34787e18	−0.170402
$809$	−6.22995e18	−0.781303	−0.390651	−	0.920539i	$-0.627750\pi$
$809$	−6.22995e18	−0.781303	−0.390651	+	0.920539i	$0.627750\pi$
$810$	6.37768e16	0.00793433
$811$	−4.70036e18	−0.580090	−0.290045	−	0.957013i	$-0.593670\pi$
$811$	−4.70036e18	−0.580090	−0.290045	+	0.957013i	$0.593670\pi$
$812$	5.29538e18	0.648311
$813$	−7.29519e18	−0.886030
$814$	−1.10411e17	−0.0133031
$815$	−6.39656e17	−0.0764578
$816$	−4.60184e18	−0.545689
$817$	4.24944e18	0.499906
$818$	−2.17102e18	−0.253377
$819$	−1.84977e18	−0.214177
$820$	2.25706e18	0.259271
$821$	7.35296e18	0.837976	0.418988	−	0.907992i	$-0.362385\pi$
$821$	7.35296e18	0.837976	0.418988	+	0.907992i	$0.362385\pi$
$822$	2.70320e17	0.0305641
$823$	1.27462e19	1.42983	0.714913	−	0.699213i	$-0.246466\pi$
$823$	1.27462e19	1.42983	0.714913	+	0.699213i	$0.246466\pi$
$824$	3.66481e16	0.00407872
$825$	−2.13093e17	−0.0235298
$826$	−1.88597e17	−0.0206617
$827$	1.42597e19	1.54998	0.774990	−	0.631974i	$-0.217755\pi$
$827$	1.42597e19	1.54998	0.774990	+	0.631974i	$0.217755\pi$
$828$	2.88760e18	0.311415
$829$	−1.00460e19	−1.07495	−0.537476	−	0.843279i	$-0.680622\pi$
$829$	−1.00460e19	−1.07495	−0.537476	+	0.843279i	$0.680622\pi$
$830$	8.74568e17	0.0928509
$831$	5.54429e18	0.584036
$832$	1.00492e19	1.05034
$833$	−1.62287e18	−0.168303
$834$	−1.96098e18	−0.201788
$835$	5.19784e18	0.530715
$836$	−2.67431e17	−0.0270939
$837$	6.60682e16	0.00664166
$838$	7.88666e17	0.0786696
$839$	−1.50849e19	−1.49311	−0.746553	−	0.665325i	$-0.768293\pi$
$839$	−1.50849e19	−1.49311	−0.746553	+	0.665325i	$0.768293\pi$
$840$	−3.06615e17	−0.0301147
$841$	2.44509e19	2.38298
$842$	2.75457e18	0.266395
$843$	3.04806e18	0.292512
$844$	−8.54036e18	−0.813299
$845$	5.49974e18	0.519725
$846$	1.16401e18	0.109156
$847$	−4.05367e18	−0.377230
$848$	1.38500e19	1.27902
$849$	−4.29496e18	−0.393604
$850$	3.10943e18	0.282786
$851$	1.28980e19	1.16407
$852$	−5.06237e18	−0.453416
$853$	3.74499e17	0.0332876	0.0166438	−	0.999861i	$-0.494702\pi$
$853$	3.74499e17	0.0332876	0.0166438	+	0.999861i	$0.494702\pi$
$854$	1.30345e18	0.114979
$855$	6.90000e17	0.0604045
$856$	−7.13837e18	−0.620182
$857$	−5.24592e18	−0.452321	−0.226160	−	0.974090i	$-0.572617\pi$
$857$	−5.24592e18	−0.452321	−0.226160	+	0.974090i	$0.572617\pi$
$858$	−1.31311e17	−0.0112366
$859$	−5.36762e18	−0.455855	−0.227927	−	0.973678i	$-0.573195\pi$
$859$	−5.36762e18	−0.455855	−0.227927	+	0.973678i	$0.573195\pi$
$860$	−2.30826e18	−0.194556
$861$	−2.63724e18	−0.220612
$862$	2.64312e18	0.219442
$863$	2.18145e19	1.79753	0.898763	−	0.438435i	$-0.144467\pi$
$863$	2.18145e19	1.79753	0.898763	+	0.438435i	$0.144467\pi$
$864$	1.67113e18	0.136669
$865$	−6.44012e18	−0.522744
$866$	−2.97044e18	−0.239306
$867$	2.80129e18	0.223993
$868$	−1.53275e17	−0.0121644
$869$	−3.00844e17	−0.0236980
$870$	−9.69878e17	−0.0758302
$871$	1.48810e19	1.15482
$872$	−7.22868e17	−0.0556803
$873$	−3.54943e18	−0.271372
$874$	−2.25882e18	−0.171419
$875$	−2.65537e18	−0.200020
$876$	8.02067e18	0.599700
$877$	1.01109e19	0.750400	0.375200	−	0.926944i	$-0.377574\pi$
$877$	1.01109e19	0.750400	0.375200	+	0.926944i	$0.377574\pi$
$878$	−2.35618e18	−0.173578
$879$	−4.57665e18	−0.334672
$880$	1.34004e17	0.00972701
$881$	−8.25495e18	−0.594800	−0.297400	−	0.954753i	$-0.596120\pi$
$881$	−8.25495e18	−0.594800	−0.297400	+	0.954753i	$0.596120\pi$
$882$	1.72881e17	0.0123652
$883$	−1.83774e19	−1.30479	−0.652393	−	0.757881i	$-0.726235\pi$
$883$	−1.83774e19	−1.30479	−0.652393	+	0.757881i	$0.726235\pi$
$884$	−2.65005e19	−1.86773
$885$	−4.77745e17	−0.0334245
$886$	−2.93064e18	−0.203537
$887$	−7.10051e18	−0.489537	−0.244769	−	0.969582i	$-0.578712\pi$
$887$	−7.10051e18	−0.489537	−0.244769	+	0.969582i	$0.578712\pi$
$888$	4.91905e18	0.336664
$889$	−2.42904e18	−0.165034
$890$	−5.66431e16	−0.00382042
$891$	7.31633e16	0.00489879
$892$	9.98305e18	0.663578
$893$	1.25934e19	0.831012
$894$	−3.15004e18	−0.206358
$895$	−3.22661e18	−0.209844
$896$	−5.09644e18	−0.329052
$897$	1.53395e19	0.983242
$898$	1.73096e18	0.110152
$899$	−1.00472e18	−0.0634759
$900$	4.58127e18	0.287349
$901$	−3.01621e19	−1.87824
$902$	−1.87212e17	−0.0115742
$903$	2.69706e18	0.165547
$904$	3.24530e18	0.197770
$905$	−5.00503e18	−0.302825
$906$	3.42027e18	0.205460
$907$	2.44574e19	1.45869	0.729346	−	0.684145i	$-0.239824\pi$
$907$	2.44574e19	1.45869	0.729346	+	0.684145i	$0.239824\pi$
$908$	−2.88063e19	−1.70580
$909$	1.92514e18	0.113187
$910$	−7.85986e17	−0.0458824
$911$	1.24193e19	0.719828	0.359914	−	0.932985i	$-0.382806\pi$
$911$	1.24193e19	0.719828	0.359914	+	0.932985i	$0.382806\pi$
$912$	5.30372e18	0.305221
$913$	1.00328e18	0.0573277
$914$	−3.15544e18	−0.179023
$915$	3.30183e18	0.186002
$916$	1.46608e19	0.820046
$917$	−3.89047e18	−0.216073
$918$	−1.06759e18	−0.0588746
$919$	5.55021e18	0.303920	0.151960	−	0.988387i	$-0.451442\pi$
$919$	5.55021e18	0.303920	0.151960	+	0.988387i	$0.451442\pi$
$920$	2.54266e18	0.138251
$921$	9.78414e18	0.528244
$922$	−1.58086e15	−8.47504e−5 0
$923$	−2.68923e19	−1.43159
$924$	−1.69735e17	−0.00897230
$925$	2.04631e19	1.07411
$926$	−8.51166e18	−0.443652
$927$	−5.23438e16	−0.00270923
$928$	−2.54134e19	−1.30618
$929$	8.99073e18	0.458874	0.229437	−	0.973324i	$-0.426312\pi$
$929$	8.99073e18	0.458874	0.229437	+	0.973324i	$0.426312\pi$
$930$	2.80731e16	0.00142282
$931$	1.87039e18	0.0941370
$932$	−1.98552e19	−0.992366
$933$	−1.55956e19	−0.774054
$934$	−2.25497e18	−0.111144
$935$	−2.91829e17	−0.0142841
$936$	5.85019e18	0.284366
$937$	−4.12823e19	−1.99277	−0.996385	−	0.0849571i	$-0.972925\pi$
$937$	−4.12823e19	−1.99277	−0.996385	+	0.0849571i	$0.972925\pi$
$938$	−1.39079e18	−0.0666718
$939$	−3.57225e18	−0.170065
$940$	−6.84061e18	−0.323418
$941$	−1.80121e18	−0.0845728	−0.0422864	−	0.999106i	$-0.513464\pi$
$941$	−1.80121e18	−0.0845728	−0.0422864	+	0.999106i	$0.513464\pi$
$942$	3.19459e17	0.0148965
$943$	2.18698e19	1.01279
$944$	−3.67221e18	−0.168892
$945$	4.37933e17	0.0200033
$946$	1.91458e17	0.00868524
$947$	−4.78830e18	−0.215728	−0.107864	−	0.994166i	$-0.534401\pi$
$947$	−4.78830e18	−0.215728	−0.107864	+	0.994166i	$0.534401\pi$
$948$	6.46781e18	0.289403
$949$	4.26074e19	1.89345
$950$	−3.58369e18	−0.158171
$951$	−1.34878e19	−0.591243
$952$	5.13259e18	0.223458
$953$	−3.24213e18	−0.140193	−0.0700966	−	0.997540i	$-0.522331\pi$
$953$	−3.24213e18	−0.140193	−0.0700966	+	0.997540i	$0.522331\pi$
$954$	3.21310e18	0.137994
$955$	−4.30630e18	−0.183688
$956$	−3.71115e19	−1.57229
$957$	−1.11262e18	−0.0468188
$958$	−4.53711e18	−0.189629
$959$	1.85620e18	0.0770554
$960$	−2.37916e18	−0.0980979
$961$	−2.43885e19	−0.998809
$962$	1.26096e19	0.512937
$963$	1.01956e19	0.411948
$964$	−1.82122e19	−0.730905
$965$	−3.58687e18	−0.142984
$966$	−1.43364e18	−0.0567662
$967$	8.51020e18	0.334709	0.167355	−	0.985897i	$-0.446478\pi$
$967$	8.51020e18	0.334709	0.167355	+	0.985897i	$0.446478\pi$
$968$	1.28204e19	0.500854
$969$	−1.15503e19	−0.448216
$970$	−1.50819e18	−0.0581353
$971$	7.36393e17	0.0281958	0.0140979	−	0.999901i	$-0.495512\pi$
$971$	7.36393e17	0.0281958	0.0140979	+	0.999901i	$0.495512\pi$
$972$	−1.57293e18	−0.0598245
$973$	−1.34654e19	−0.508728
$974$	−1.16777e18	−0.0438253
$975$	2.43366e19	0.907256
$976$	2.53797e19	0.939857
$977$	2.38064e19	0.875747	0.437874	−	0.899037i	$-0.355732\pi$
$977$	2.38064e19	0.875747	0.437874	+	0.899037i	$0.355732\pi$
$978$	−1.14065e18	−0.0416821
$979$	−6.49796e16	−0.00235879
$980$	−1.01598e18	−0.0366367
$981$	1.03246e18	0.0369849
$982$	8.62979e18	0.307097
$983$	5.22498e19	1.84708	0.923542	−	0.383497i	$-0.125281\pi$
$983$	5.22498e19	1.84708	0.923542	+	0.383497i	$0.125281\pi$
$984$	8.34071e18	0.292911
$985$	1.39649e19	0.487196
$986$	1.62353e19	0.562678
$987$	7.99284e18	0.275194
$988$	3.05424e19	1.04468
$989$	−2.23658e19	−0.759993
$990$	3.10879e16	0.00104945
$991$	1.22088e19	0.409443	0.204721	−	0.978820i	$-0.434371\pi$
$991$	1.22088e19	0.409443	0.204721	+	0.978820i	$0.434371\pi$
$992$	7.35591e17	0.0245081
$993$	−1.42272e19	−0.470922
$994$	2.51338e18	0.0826507
$995$	9.58547e18	0.313158
$996$	−2.15695e19	−0.700092
$997$	−3.57061e19	−1.15139	−0.575697	−	0.817663i	$-0.695269\pi$
$997$	−3.57061e19	−1.15139	−0.575697	+	0.817663i	$0.695269\pi$
$998$	4.89915e18	0.156954
$999$	−7.02579e18	−0.223624

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.14.a.a.1.1	✓	2	1.1	even	1	trivial
63.14.a.a.1.2		2	3.2	odd	2
147.14.a.c.1.1		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)

\(f(q)\)	\(=\)	\(q+23.5026 q^{2} +729.000 q^{3} -7639.63 q^{4} +9608.09 q^{5} +17133.4 q^{6} +117649. q^{7} -372084. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+23.5026 q^{2} +729.000 q^{3} -7639.63 q^{4} +9608.09 q^{5} +17133.4 q^{6} +117649. q^{7} -372084. q^{8} +531441. q^{9} +225815. q^{10} +259050. q^{11} -5.56929e6 q^{12} -2.95852e7 q^{13} +2.76505e6 q^{14} +7.00430e6 q^{15} +5.38389e7 q^{16} -1.17249e8 q^{17} +1.24902e7 q^{18} +1.35132e8 q^{19} -7.34023e7 q^{20} +8.57661e7 q^{21} +6.08834e6 q^{22} -7.11230e8 q^{23} -2.71249e8 q^{24} -1.12839e9 q^{25} -6.95328e8 q^{26} +3.87420e8 q^{27} -8.98795e8 q^{28} -5.89165e9 q^{29} +1.64619e8 q^{30} +1.70534e8 q^{31} +4.31347e9 q^{32} +1.88847e8 q^{33} -2.75564e9 q^{34} +1.13038e9 q^{35} -4.06001e9 q^{36} -1.81348e10 q^{37} +3.17594e9 q^{38} -2.15676e10 q^{39} -3.57502e9 q^{40} -3.07493e10 q^{41} +2.01572e9 q^{42} +3.14467e10 q^{43} -1.97904e9 q^{44} +5.10613e9 q^{45} -1.67157e10 q^{46} +9.31934e10 q^{47} +3.92486e10 q^{48} +1.38413e10 q^{49} -2.65200e10 q^{50} -8.54742e10 q^{51} +2.26020e11 q^{52} +2.57249e11 q^{53} +9.10538e9 q^{54} +2.48898e9 q^{55} -4.37753e10 q^{56} +9.85109e10 q^{57} -1.38469e11 q^{58} -6.82075e10 q^{59} -5.35102e10 q^{60} +4.71400e11 q^{61} +4.00798e9 q^{62} +6.25235e10 q^{63} -3.39671e11 q^{64} -2.84257e11 q^{65} +4.43840e9 q^{66} -5.02987e11 q^{67} +8.95736e11 q^{68} -5.18486e11 q^{69} +2.65669e10 q^{70} +9.08980e11 q^{71} -1.97741e11 q^{72} -1.44016e12 q^{73} -4.26214e11 q^{74} -8.22595e11 q^{75} -1.03235e12 q^{76} +3.04770e10 q^{77} -5.06894e11 q^{78} -1.16133e12 q^{79} +5.17289e11 q^{80} +2.82430e11 q^{81} -7.22687e11 q^{82} +3.87294e12 q^{83} -6.55221e11 q^{84} -1.12654e12 q^{85} +7.39079e11 q^{86} -4.29501e12 q^{87} -9.63883e10 q^{88} -2.50838e11 q^{89} +1.20007e11 q^{90} -3.48067e12 q^{91} +5.43353e12 q^{92} +1.24319e11 q^{93} +2.19029e12 q^{94} +1.29836e12 q^{95} +3.14452e12 q^{96} -6.67887e12 q^{97} +3.25306e11 q^{98} +1.37670e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 144 q^{2} + 1458 q^{3} - 1312 q^{4} - 52560 q^{5} + 104976 q^{6} + 235298 q^{7} - 596736 q^{8} + 1062882 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more