Properties

Label 21.22.c.b.20.27
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,22,Mod(20,21)]
 
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([1, 1]))
 
N = Newforms(chi, 22, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.20");
 
S:= CuspForms(chi, 22);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(58.6902423003\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.27
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.28

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2822.55i q^{2} +(-20847.2 - 100129. i) q^{3} -5.86963e6 q^{4} +4.54821e6 q^{5} +(-2.82618e8 + 5.88423e7i) q^{6} +(2.96411e8 + 6.86066e8i) q^{7} +1.06480e10i q^{8} +(-9.59114e9 + 4.17481e9i) q^{9} +O(q^{10})\) \(q-2822.55i q^{2} +(-20847.2 - 100129. i) q^{3} -5.86963e6 q^{4} +4.54821e6 q^{5} +(-2.82618e8 + 5.88423e7i) q^{6} +(2.96411e8 + 6.86066e8i) q^{7} +1.06480e10i q^{8} +(-9.59114e9 + 4.17481e9i) q^{9} -1.28375e10i q^{10} +7.30549e10i q^{11} +(1.22366e11 + 5.87718e11i) q^{12} -3.14236e11i q^{13} +(1.93645e12 - 8.36633e11i) q^{14} +(-9.48176e10 - 4.55406e11i) q^{15} +1.77450e13 q^{16} -1.38799e13 q^{17} +(1.17836e13 + 2.70715e13i) q^{18} +1.99201e13i q^{19} -2.66963e13 q^{20} +(6.25155e13 - 4.39818e13i) q^{21} +2.06201e14 q^{22} -2.36645e14i q^{23} +(1.06617e15 - 2.21981e14i) q^{24} -4.56151e14 q^{25} -8.86945e14 q^{26} +(6.17967e14 + 8.73315e14i) q^{27} +(-1.73982e15 - 4.02695e15i) q^{28} -4.13478e14i q^{29} +(-1.28541e15 + 2.67627e14i) q^{30} -4.96475e15i q^{31} -2.77556e16i q^{32} +(7.31489e15 - 1.52299e15i) q^{33} +3.91767e16i q^{34} +(1.34814e15 + 3.12037e15i) q^{35} +(5.62964e16 - 2.45046e16i) q^{36} +1.68899e16 q^{37} +5.62255e16 q^{38} +(-3.14640e16 + 6.55094e15i) q^{39} +4.84294e16i q^{40} +3.82916e16 q^{41} +(-1.24141e17 - 1.76453e17i) q^{42} +1.23817e17 q^{43} -4.28805e17i q^{44} +(-4.36225e16 + 1.89879e16i) q^{45} -6.67941e17 q^{46} +5.21576e17 q^{47} +(-3.69934e17 - 1.77678e18i) q^{48} +(-3.82827e17 + 4.06714e17i) q^{49} +1.28751e18i q^{50} +(2.89358e17 + 1.38978e18i) q^{51} +1.84445e18i q^{52} -4.78164e17i q^{53} +(2.46497e18 - 1.74424e18i) q^{54} +3.32269e17i q^{55} +(-7.30523e18 + 3.15618e18i) q^{56} +(1.99457e18 - 4.15279e17i) q^{57} -1.16706e18 q^{58} +4.67014e18 q^{59} +(5.56544e17 + 2.67307e18i) q^{60} +6.18188e18i q^{61} -1.40132e19 q^{62} +(-5.70711e18 - 5.34270e18i) q^{63} -4.11277e19 q^{64} -1.42921e18i q^{65} +(-4.29872e18 - 2.06466e19i) q^{66} -4.47340e18 q^{67} +8.14699e19 q^{68} +(-2.36949e19 + 4.93338e18i) q^{69} +(8.80740e18 - 3.80518e18i) q^{70} -1.47479e19i q^{71} +(-4.44534e19 - 1.02126e20i) q^{72} -3.45031e18i q^{73} -4.76725e19i q^{74} +(9.50948e18 + 4.56738e19i) q^{75} -1.16924e20i q^{76} +(-5.01205e19 + 2.16542e19i) q^{77} +(1.84903e19 + 8.88086e19i) q^{78} +9.44267e19 q^{79} +8.07080e19 q^{80} +(7.45609e19 - 8.00824e19i) q^{81} -1.08080e20i q^{82} +4.40648e19 q^{83} +(-3.66943e20 + 2.58157e20i) q^{84} -6.31288e19 q^{85} -3.49479e20i q^{86} +(-4.14009e19 + 8.61986e18i) q^{87} -7.77889e20 q^{88} -1.20740e20 q^{89} +(5.35943e19 + 1.23127e20i) q^{90} +(2.15586e20 - 9.31427e19i) q^{91} +1.38902e21i q^{92} +(-4.97113e20 + 1.03501e20i) q^{93} -1.47217e21i q^{94} +9.06009e19i q^{95} +(-2.77914e21 + 5.78628e20i) q^{96} +8.64106e20i q^{97} +(1.14797e21 + 1.08055e21i) q^{98} +(-3.04990e20 - 7.00680e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2822.55i 1.94907i −0.224245 0.974533i \(-0.571991\pi\)
0.224245 0.974533i \(-0.428009\pi\)
\(3\) −20847.2 100129.i −0.203833 0.979006i
\(4\) −5.86963e6 −2.79886
\(5\) 4.54821e6 0.208284 0.104142 0.994562i \(-0.466790\pi\)
0.104142 + 0.994562i \(0.466790\pi\)
\(6\) −2.82618e8 + 5.88423e7i −1.90815 + 0.397285i
\(7\) 2.96411e8 + 6.86066e8i 0.396611 + 0.917987i
\(8\) 1.06480e10i 3.50609i
\(9\) −9.59114e9 + 4.17481e9i −0.916904 + 0.399108i
\(10\) 1.28375e10i 0.405959i
\(11\) 7.30549e10i 0.849232i 0.905374 + 0.424616i \(0.139591\pi\)
−0.905374 + 0.424616i \(0.860409\pi\)
\(12\) 1.22366e11 + 5.87718e11i 0.570500 + 2.74010i
\(13\) 3.14236e11i 0.632194i −0.948727 0.316097i \(-0.897628\pi\)
0.948727 0.316097i \(-0.102372\pi\)
\(14\) 1.93645e12 8.36633e11i 1.78922 0.773020i
\(15\) −9.48176e10 4.55406e11i −0.0424552 0.203911i
\(16\) 1.77450e13 4.03475
\(17\) −1.38799e13 −1.66983 −0.834916 0.550377i \(-0.814484\pi\)
−0.834916 + 0.550377i \(0.814484\pi\)
\(18\) 1.17836e13 + 2.70715e13i 0.777888 + 1.78711i
\(19\) 1.99201e13i 0.745382i 0.927955 + 0.372691i \(0.121565\pi\)
−0.927955 + 0.372691i \(0.878435\pi\)
\(20\) −2.66963e13 −0.582957
\(21\) 6.25155e13 4.39818e13i 0.817872 0.575400i
\(22\) 2.06201e14 1.65521
\(23\) 2.36645e14i 1.19112i −0.803312 0.595558i \(-0.796931\pi\)
0.803312 0.595558i \(-0.203069\pi\)
\(24\) 1.06617e15 2.21981e14i 3.43248 0.714658i
\(25\) −4.56151e14 −0.956618
\(26\) −8.86945e14 −1.23219
\(27\) 6.17967e14 + 8.73315e14i 0.577624 + 0.816303i
\(28\) −1.73982e15 4.02695e15i −1.11006 2.56931i
\(29\) 4.13478e14i 0.182504i −0.995828 0.0912521i \(-0.970913\pi\)
0.995828 0.0912521i \(-0.0290869\pi\)
\(30\) −1.28541e15 + 2.67627e14i −0.397436 + 0.0827479i
\(31\) 4.96475e15i 1.08793i −0.839109 0.543963i \(-0.816923\pi\)
0.839109 0.543963i \(-0.183077\pi\)
\(32\) 2.77556e16i 4.35789i
\(33\) 7.31489e15 1.52299e15i 0.831403 0.173102i
\(34\) 3.91767e16i 3.25461i
\(35\) 1.34814e15 + 3.12037e15i 0.0826076 + 0.191202i
\(36\) 5.62964e16 2.45046e16i 2.56628 1.11705i
\(37\) 1.68899e16 0.577442 0.288721 0.957413i \(-0.406770\pi\)
0.288721 + 0.957413i \(0.406770\pi\)
\(38\) 5.62255e16 1.45280
\(39\) −3.14640e16 + 6.55094e15i −0.618921 + 0.128862i
\(40\) 4.84294e16i 0.730262i
\(41\) 3.82916e16 0.445526 0.222763 0.974873i \(-0.428492\pi\)
0.222763 + 0.974873i \(0.428492\pi\)
\(42\) −1.24141e17 1.76453e17i −1.12149 1.59409i
\(43\) 1.23817e17 0.873698 0.436849 0.899535i \(-0.356094\pi\)
0.436849 + 0.899535i \(0.356094\pi\)
\(44\) 4.28805e17i 2.37688i
\(45\) −4.36225e16 + 1.89879e16i −0.190976 + 0.0831277i
\(46\) −6.67941e17 −2.32157
\(47\) 5.21576e17 1.44641 0.723203 0.690635i \(-0.242669\pi\)
0.723203 + 0.690635i \(0.242669\pi\)
\(48\) −3.69934e17 1.77678e18i −0.822416 3.95004i
\(49\) −3.82827e17 + 4.06714e17i −0.685400 + 0.728167i
\(50\) 1.28751e18i 1.86451i
\(51\) 2.89358e17 + 1.38978e18i 0.340368 + 1.63478i
\(52\) 1.84445e18i 1.76942i
\(53\) 4.78164e17i 0.375561i −0.982211 0.187780i \(-0.939871\pi\)
0.982211 0.187780i \(-0.0601293\pi\)
\(54\) 2.46497e18 1.74424e18i 1.59103 1.12583i
\(55\) 3.32269e17i 0.176881i
\(56\) −7.30523e18 + 3.15618e18i −3.21855 + 1.39055i
\(57\) 1.99457e18 4.15279e17i 0.729733 0.151934i
\(58\) −1.16706e18 −0.355713
\(59\) 4.67014e18 1.18955 0.594777 0.803891i \(-0.297240\pi\)
0.594777 + 0.803891i \(0.297240\pi\)
\(60\) 5.56544e17 + 2.67307e18i 0.118826 + 0.570718i
\(61\) 6.18188e18i 1.10958i 0.831992 + 0.554788i \(0.187201\pi\)
−0.831992 + 0.554788i \(0.812799\pi\)
\(62\) −1.40132e19 −2.12044
\(63\) −5.70711e18 5.34270e18i −0.730030 0.683415i
\(64\) −4.11277e19 −4.45907
\(65\) 1.42921e18i 0.131676i
\(66\) −4.29872e18 2.06466e19i −0.337387 1.62046i
\(67\) −4.47340e18 −0.299814 −0.149907 0.988700i \(-0.547897\pi\)
−0.149907 + 0.988700i \(0.547897\pi\)
\(68\) 8.14699e19 4.67362
\(69\) −2.36949e19 + 4.93338e18i −1.16611 + 0.242789i
\(70\) 8.80740e18 3.80518e18i 0.372665 0.161008i
\(71\) 1.47479e19i 0.537674i −0.963186 0.268837i \(-0.913361\pi\)
0.963186 0.268837i \(-0.0866392\pi\)
\(72\) −4.44534e19 1.02126e20i −1.39931 3.21475i
\(73\) 3.45031e18i 0.0939653i −0.998896 0.0469827i \(-0.985039\pi\)
0.998896 0.0469827i \(-0.0149606\pi\)
\(74\) 4.76725e19i 1.12547i
\(75\) 9.50948e18 + 4.56738e19i 0.194991 + 0.936534i
\(76\) 1.16924e20i 2.08622i
\(77\) −5.01205e19 + 2.16542e19i −0.779584 + 0.336814i
\(78\) 1.84903e19 + 8.88086e19i 0.251161 + 1.20632i
\(79\) 9.44267e19 1.12204 0.561022 0.827801i \(-0.310408\pi\)
0.561022 + 0.827801i \(0.310408\pi\)
\(80\) 8.07080e19 0.840372
\(81\) 7.45609e19 8.00824e19i 0.681426 0.731887i
\(82\) 1.08080e20i 0.868359i
\(83\) 4.40648e19 0.311725 0.155863 0.987779i \(-0.450184\pi\)
0.155863 + 0.987779i \(0.450184\pi\)
\(84\) −3.66943e20 + 2.58157e20i −2.28911 + 1.61046i
\(85\) −6.31288e19 −0.347799
\(86\) 3.49479e20i 1.70289i
\(87\) −4.14009e19 + 8.61986e18i −0.178673 + 0.0372004i
\(88\) −7.77889e20 −2.97748
\(89\) −1.20740e20 −0.410447 −0.205224 0.978715i \(-0.565792\pi\)
−0.205224 + 0.978715i \(0.565792\pi\)
\(90\) 5.35943e19 + 1.23127e20i 0.162021 + 0.372225i
\(91\) 2.15586e20 9.31427e19i 0.580346 0.250735i
\(92\) 1.38902e21i 3.33377i
\(93\) −4.97113e20 + 1.03501e20i −1.06509 + 0.221756i
\(94\) 1.47217e21i 2.81914i
\(95\) 9.06009e19i 0.155251i
\(96\) −2.77914e21 + 5.78628e20i −4.26640 + 0.888284i
\(97\) 8.64106e20i 1.18977i 0.803810 + 0.594886i \(0.202803\pi\)
−0.803810 + 0.594886i \(0.797197\pi\)
\(98\) 1.14797e21 + 1.08055e21i 1.41924 + 1.33589i
\(99\) −3.04990e20 7.00680e20i −0.338935 0.778664i
\(100\) 2.67744e21 2.67744
\(101\) 1.20647e21 1.08678 0.543391 0.839480i \(-0.317140\pi\)
0.543391 + 0.839480i \(0.317140\pi\)
\(102\) 3.92271e21 8.16726e20i 3.18629 0.663399i
\(103\) 1.96297e21i 1.43920i 0.694386 + 0.719602i \(0.255676\pi\)
−0.694386 + 0.719602i \(0.744324\pi\)
\(104\) 3.34598e21 2.21653
\(105\) 2.84334e20 2.00038e20i 0.170349 0.119847i
\(106\) −1.34964e21 −0.731993
\(107\) 2.10165e20i 0.103284i −0.998666 0.0516418i \(-0.983555\pi\)
0.998666 0.0516418i \(-0.0164454\pi\)
\(108\) −3.62724e21 5.12603e21i −1.61669 2.28471i
\(109\) −2.61048e21 −1.05619 −0.528095 0.849186i \(-0.677093\pi\)
−0.528095 + 0.849186i \(0.677093\pi\)
\(110\) 9.37846e20 0.344753
\(111\) −3.52107e20 1.69116e21i −0.117702 0.565319i
\(112\) 5.25980e21 + 1.21742e22i 1.60022 + 3.70384i
\(113\) 2.84927e21i 0.789606i −0.918766 0.394803i \(-0.870813\pi\)
0.918766 0.394803i \(-0.129187\pi\)
\(114\) −1.17215e21 5.62978e21i −0.296129 1.42230i
\(115\) 1.07631e21i 0.248090i
\(116\) 2.42696e21i 0.510803i
\(117\) 1.31187e21 + 3.01388e21i 0.252313 + 0.579661i
\(118\) 1.31817e22i 2.31852i
\(119\) −4.11415e21 9.52254e21i −0.662273 1.53288i
\(120\) 4.84917e21 1.00962e21i 0.714931 0.148852i
\(121\) 2.06323e21 0.278806
\(122\) 1.74487e22 2.16264
\(123\) −7.98273e20 3.83408e21i −0.0908130 0.436172i
\(124\) 2.91412e22i 3.04495i
\(125\) −4.24343e21 −0.407532
\(126\) −1.50800e22 + 1.61086e22i −1.33202 + 1.42288i
\(127\) 1.93411e22 1.57232 0.786162 0.618021i \(-0.212065\pi\)
0.786162 + 0.618021i \(0.212065\pi\)
\(128\) 5.78771e22i 4.33314i
\(129\) −2.58124e21 1.23976e22i −0.178089 0.855355i
\(130\) −4.03401e21 −0.256645
\(131\) 2.69309e22 1.58089 0.790445 0.612533i \(-0.209849\pi\)
0.790445 + 0.612533i \(0.209849\pi\)
\(132\) −4.29357e22 + 8.93940e21i −2.32698 + 0.484487i
\(133\) −1.36665e22 + 5.90453e21i −0.684251 + 0.295626i
\(134\) 1.26264e22i 0.584357i
\(135\) 2.81064e21 + 3.97202e21i 0.120310 + 0.170023i
\(136\) 1.47793e23i 5.85459i
\(137\) 2.02386e22i 0.742361i −0.928561 0.371181i \(-0.878953\pi\)
0.928561 0.371181i \(-0.121047\pi\)
\(138\) 1.39247e22 + 6.68800e22i 0.473212 + 2.27283i
\(139\) 8.93099e21i 0.281348i −0.990056 0.140674i \(-0.955073\pi\)
0.990056 0.140674i \(-0.0449270\pi\)
\(140\) −7.91307e21 1.83154e22i −0.231207 0.535147i
\(141\) −1.08734e22 5.22247e22i −0.294826 1.41604i
\(142\) −4.16268e22 −1.04796
\(143\) 2.29564e22 0.536879
\(144\) −1.70195e23 + 7.40820e22i −3.69947 + 1.61030i
\(145\) 1.88058e21i 0.0380127i
\(146\) −9.73866e21 −0.183145
\(147\) 4.87047e22 + 2.98531e22i 0.852587 + 0.522586i
\(148\) −9.91373e22 −1.61618
\(149\) 6.95768e22i 1.05684i −0.848983 0.528419i \(-0.822785\pi\)
0.848983 0.528419i \(-0.177215\pi\)
\(150\) 1.28916e23 2.68410e22i 1.82537 0.380049i
\(151\) 9.93310e22 1.31168 0.655838 0.754901i \(-0.272315\pi\)
0.655838 + 0.754901i \(0.272315\pi\)
\(152\) −2.12109e23 −2.61338
\(153\) 1.33124e23 5.79460e22i 1.53108 0.666444i
\(154\) 6.11202e22 + 1.41468e23i 0.656473 + 1.51946i
\(155\) 2.25807e22i 0.226597i
\(156\) 1.84682e23 3.84516e22i 1.73227 0.360667i
\(157\) 8.43714e22i 0.740029i 0.929026 + 0.370014i \(0.120647\pi\)
−0.929026 + 0.370014i \(0.879353\pi\)
\(158\) 2.66524e23i 2.18694i
\(159\) −4.78779e22 + 9.96839e21i −0.367676 + 0.0765518i
\(160\) 1.26239e23i 0.907679i
\(161\) 1.62354e23 7.01440e22i 1.09343 0.472410i
\(162\) −2.26036e23 2.10452e23i −1.42650 1.32814i
\(163\) −4.43058e22 −0.262114 −0.131057 0.991375i \(-0.541837\pi\)
−0.131057 + 0.991375i \(0.541837\pi\)
\(164\) −2.24757e23 −1.24696
\(165\) 3.32697e22 6.92689e21i 0.173168 0.0360543i
\(166\) 1.24375e23i 0.607573i
\(167\) 7.95970e22 0.365068 0.182534 0.983200i \(-0.441570\pi\)
0.182534 + 0.983200i \(0.441570\pi\)
\(168\) 4.68318e23 + 6.65665e23i 2.01741 + 2.86753i
\(169\) 1.48321e23 0.600331
\(170\) 1.78184e23i 0.677883i
\(171\) −8.31627e22 1.91057e23i −0.297488 0.683444i
\(172\) −7.26760e23 −2.44536
\(173\) −3.57085e23 −1.13054 −0.565272 0.824905i \(-0.691229\pi\)
−0.565272 + 0.824905i \(0.691229\pi\)
\(174\) 2.43300e22 + 1.16856e23i 0.0725061 + 0.348245i
\(175\) −1.35208e23 3.12950e23i −0.379405 0.878163i
\(176\) 1.29636e24i 3.42643i
\(177\) −9.73595e22 4.67615e23i −0.242471 1.16458i
\(178\) 3.40796e23i 0.799989i
\(179\) 4.41100e23i 0.976294i −0.872761 0.488147i \(-0.837673\pi\)
0.872761 0.488147i \(-0.162327\pi\)
\(180\) 2.56048e23 1.11452e23i 0.534515 0.232663i
\(181\) 7.85797e23i 1.54769i 0.633372 + 0.773847i \(0.281670\pi\)
−0.633372 + 0.773847i \(0.718330\pi\)
\(182\) −2.62900e23 6.08503e23i −0.488698 1.13113i
\(183\) 6.18983e23 1.28875e23i 1.08628 0.226169i
\(184\) 2.51979e24 4.17616
\(185\) 7.68187e22 0.120272
\(186\) 2.92137e23 + 1.40313e24i 0.432216 + 2.07592i
\(187\) 1.01400e24i 1.41808i
\(188\) −3.06146e24 −4.04829
\(189\) −4.15980e23 + 6.82826e23i −0.520263 + 0.854006i
\(190\) 2.55725e23 0.302595
\(191\) 4.96369e22i 0.0555846i −0.999614 0.0277923i \(-0.991152\pi\)
0.999614 0.0277923i \(-0.00884770\pi\)
\(192\) 8.57399e23 + 4.11806e24i 0.908908 + 4.36546i
\(193\) −5.47484e23 −0.549565 −0.274783 0.961506i \(-0.588606\pi\)
−0.274783 + 0.961506i \(0.588606\pi\)
\(194\) 2.43898e24 2.31894
\(195\) −1.43105e23 + 2.97951e22i −0.128911 + 0.0268399i
\(196\) 2.24706e24 2.38726e24i 1.91834 2.03803i
\(197\) 1.48828e24i 1.20445i 0.798325 + 0.602226i \(0.205720\pi\)
−0.798325 + 0.602226i \(0.794280\pi\)
\(198\) −1.97770e24 + 8.60850e23i −1.51767 + 0.660607i
\(199\) 2.48286e24i 1.80715i 0.428430 + 0.903575i \(0.359067\pi\)
−0.428430 + 0.903575i \(0.640933\pi\)
\(200\) 4.85710e24i 3.35399i
\(201\) 9.32579e22 + 4.47915e23i 0.0611121 + 0.293520i
\(202\) 3.40532e24i 2.11821i
\(203\) 2.83673e23 1.22559e23i 0.167537 0.0723831i
\(204\) −1.69842e24 8.15747e24i −0.952640 4.57550i
\(205\) 1.74158e23 0.0927958
\(206\) 5.54058e24 2.80510
\(207\) 9.87946e23 + 2.26969e24i 0.475384 + 1.09214i
\(208\) 5.57611e24i 2.55074i
\(209\) −1.45526e24 −0.633002
\(210\) −5.64618e23 8.02546e23i −0.233589 0.332022i
\(211\) −2.81283e24 −1.10708 −0.553538 0.832824i \(-0.686723\pi\)
−0.553538 + 0.832824i \(0.686723\pi\)
\(212\) 2.80665e24i 1.05114i
\(213\) −1.47669e24 + 3.07454e23i −0.526386 + 0.109596i
\(214\) −5.93202e23 −0.201306
\(215\) 5.63146e23 0.181977
\(216\) −9.29906e24 + 6.58011e24i −2.86203 + 2.02520i
\(217\) 3.40614e24 1.47160e24i 0.998702 0.431483i
\(218\) 7.36820e24i 2.05858i
\(219\) −3.45475e23 + 7.19293e22i −0.0919926 + 0.0191533i
\(220\) 1.95030e24i 0.495065i
\(221\) 4.36156e24i 1.05566i
\(222\) −4.77338e24 + 9.93839e23i −1.10184 + 0.229409i
\(223\) 2.10755e24i 0.464063i 0.972708 + 0.232032i \(0.0745373\pi\)
−0.972708 + 0.232032i \(0.925463\pi\)
\(224\) 1.90422e25 8.22707e24i 4.00049 1.72839i
\(225\) 4.37501e24 1.90434e24i 0.877127 0.381794i
\(226\) −8.04222e24 −1.53899
\(227\) −4.72952e24 −0.864063 −0.432031 0.901859i \(-0.642203\pi\)
−0.432031 + 0.901859i \(0.642203\pi\)
\(228\) −1.17074e25 + 2.43753e24i −2.04242 + 0.425241i
\(229\) 1.23459e24i 0.205708i 0.994696 + 0.102854i \(0.0327974\pi\)
−0.994696 + 0.102854i \(0.967203\pi\)
\(230\) −3.03794e24 −0.483544
\(231\) 3.21308e24 + 4.56707e24i 0.488648 + 0.694563i
\(232\) 4.40271e24 0.639877
\(233\) 1.30483e25i 1.81266i 0.422571 + 0.906330i \(0.361128\pi\)
−0.422571 + 0.906330i \(0.638872\pi\)
\(234\) 8.50682e24 3.70283e24i 1.12980 0.491776i
\(235\) 2.37224e24 0.301263
\(236\) −2.74120e25 −3.32939
\(237\) −1.96853e24 9.45481e24i −0.228710 1.09849i
\(238\) −2.68778e25 + 1.16124e25i −2.98769 + 1.29081i
\(239\) 1.74054e24i 0.185142i −0.995706 0.0925711i \(-0.970491\pi\)
0.995706 0.0925711i \(-0.0295085\pi\)
\(240\) −1.68254e24 8.08118e24i −0.171296 0.822729i
\(241\) 1.57536e24i 0.153532i 0.997049 + 0.0767662i \(0.0244595\pi\)
−0.997049 + 0.0767662i \(0.975541\pi\)
\(242\) 5.82357e24i 0.543410i
\(243\) −9.57293e24 5.79619e24i −0.855419 0.517937i
\(244\) 3.62853e25i 3.10555i
\(245\) −1.74118e24 + 1.84982e24i −0.142758 + 0.151665i
\(246\) −1.08219e25 + 2.25317e24i −0.850128 + 0.177000i
\(247\) 6.25961e24 0.471226
\(248\) 5.28646e25 3.81437
\(249\) −9.18630e23 4.41215e24i −0.0635400 0.305181i
\(250\) 1.19773e25i 0.794306i
\(251\) −1.19217e25 −0.758167 −0.379083 0.925363i \(-0.623761\pi\)
−0.379083 + 0.925363i \(0.623761\pi\)
\(252\) 3.34986e25 + 3.13597e25i 2.04325 + 1.91278i
\(253\) 1.72880e25 1.01153
\(254\) 5.45912e25i 3.06456i
\(255\) 1.31606e24 + 6.32100e24i 0.0708931 + 0.340497i
\(256\) 7.71100e25 3.98649
\(257\) 2.64268e25 1.31144 0.655718 0.755006i \(-0.272366\pi\)
0.655718 + 0.755006i \(0.272366\pi\)
\(258\) −3.49929e25 + 7.28568e24i −1.66714 + 0.347107i
\(259\) 5.00634e24 + 1.15876e25i 0.229020 + 0.530084i
\(260\) 8.38893e24i 0.368542i
\(261\) 1.72619e24 + 3.96572e24i 0.0728389 + 0.167339i
\(262\) 7.60137e25i 3.08126i
\(263\) 1.97989e25i 0.771092i 0.922689 + 0.385546i \(0.125987\pi\)
−0.922689 + 0.385546i \(0.874013\pi\)
\(264\) 1.62168e25 + 7.78889e25i 0.606910 + 2.91497i
\(265\) 2.17479e24i 0.0782232i
\(266\) 1.66658e25 + 3.85744e25i 0.576195 + 1.33365i
\(267\) 2.51710e24 + 1.20896e25i 0.0836629 + 0.401830i
\(268\) 2.62572e25 0.839137
\(269\) 2.88993e25 0.888155 0.444077 0.895988i \(-0.353532\pi\)
0.444077 + 0.895988i \(0.353532\pi\)
\(270\) 1.12112e25 7.93318e24i 0.331385 0.234492i
\(271\) 2.99441e25i 0.851400i 0.904864 + 0.425700i \(0.139972\pi\)
−0.904864 + 0.425700i \(0.860028\pi\)
\(272\) −2.46299e26 −6.73735
\(273\) −1.38206e25 1.96446e25i −0.363764 0.517053i
\(274\) −5.71246e25 −1.44691
\(275\) 3.33241e25i 0.812390i
\(276\) 1.39080e26 2.89571e25i 3.26378 0.679533i
\(277\) −1.50940e25 −0.341010 −0.170505 0.985357i \(-0.554540\pi\)
−0.170505 + 0.985357i \(0.554540\pi\)
\(278\) −2.52082e25 −0.548366
\(279\) 2.07269e25 + 4.76176e25i 0.434200 + 0.997524i
\(280\) −3.32257e25 + 1.43550e25i −0.670371 + 0.289630i
\(281\) 9.89724e25i 1.92352i −0.273886 0.961762i \(-0.588309\pi\)
0.273886 0.961762i \(-0.411691\pi\)
\(282\) −1.47407e26 + 3.06908e25i −2.75996 + 0.574635i
\(283\) 2.13079e25i 0.384400i −0.981356 0.192200i \(-0.938438\pi\)
0.981356 0.192200i \(-0.0615623\pi\)
\(284\) 8.65650e25i 1.50487i
\(285\) 9.07174e24 1.88878e24i 0.151992 0.0316453i
\(286\) 6.47957e25i 1.04641i
\(287\) 1.13500e25 + 2.62706e25i 0.176700 + 0.408987i
\(288\) 1.15875e26 + 2.66208e26i 1.73927 + 3.99577i
\(289\) 1.23560e26 1.78834
\(290\) −5.30804e24 −0.0740892
\(291\) 8.65218e25 1.80142e25i 1.16479 0.242515i
\(292\) 2.02520e25i 0.262996i
\(293\) −1.82697e25 −0.228888 −0.114444 0.993430i \(-0.536509\pi\)
−0.114444 + 0.993430i \(0.536509\pi\)
\(294\) 8.42619e25 1.37471e26i 1.01855 1.66175i
\(295\) 2.12408e25 0.247765
\(296\) 1.79843e26i 2.02456i
\(297\) −6.37999e25 + 4.51455e25i −0.693230 + 0.490537i
\(298\) −1.96384e26 −2.05985
\(299\) −7.43622e25 −0.753017
\(300\) −5.58171e25 2.68088e26i −0.545751 2.62123i
\(301\) 3.67007e25 + 8.49466e25i 0.346518 + 0.802043i
\(302\) 2.80366e26i 2.55654i
\(303\) −2.51516e25 1.20802e26i −0.221522 1.06397i
\(304\) 3.53482e26i 3.00743i
\(305\) 2.81165e25i 0.231107i
\(306\) −1.63555e26 3.75749e26i −1.29894 2.98417i
\(307\) 1.29125e26i 0.990960i 0.868619 + 0.495480i \(0.165008\pi\)
−0.868619 + 0.495480i \(0.834992\pi\)
\(308\) 2.94189e26 1.27102e26i 2.18194 0.942695i
\(309\) 1.96549e26 4.09225e25i 1.40899 0.293358i
\(310\) −6.37352e25 −0.441653
\(311\) 1.10962e26 0.743345 0.371673 0.928364i \(-0.378784\pi\)
0.371673 + 0.928364i \(0.378784\pi\)
\(312\) −6.97544e25 3.35029e26i −0.451802 2.16999i
\(313\) 1.36190e26i 0.852959i −0.904497 0.426480i \(-0.859754\pi\)
0.904497 0.426480i \(-0.140246\pi\)
\(314\) 2.38142e26 1.44237
\(315\) −2.59571e25 2.42997e25i −0.152053 0.142344i
\(316\) −5.54250e26 −3.14044
\(317\) 3.98342e25i 0.218340i −0.994023 0.109170i \(-0.965181\pi\)
0.994023 0.109170i \(-0.0348194\pi\)
\(318\) 2.81363e25 + 1.35138e26i 0.149204 + 0.716625i
\(319\) 3.02066e25 0.154988
\(320\) −1.87057e26 −0.928753
\(321\) −2.10436e25 + 4.38136e24i −0.101115 + 0.0210526i
\(322\) −1.97985e26 4.58252e26i −0.920757 2.13117i
\(323\) 2.76489e26i 1.24466i
\(324\) −4.37645e26 + 4.70054e26i −1.90721 + 2.04845i
\(325\) 1.43339e26i 0.604768i
\(326\) 1.25055e26i 0.510878i
\(327\) 5.44212e25 + 2.61384e26i 0.215287 + 1.03402i
\(328\) 4.07729e26i 1.56205i
\(329\) 1.54601e26 + 3.57836e26i 0.573660 + 1.32778i
\(330\) −1.95515e25 9.39052e25i −0.0702722 0.337515i
\(331\) 3.34913e26 1.16611 0.583053 0.812434i \(-0.301858\pi\)
0.583053 + 0.812434i \(0.301858\pi\)
\(332\) −2.58644e26 −0.872475
\(333\) −1.61993e26 + 7.05120e25i −0.529459 + 0.230462i
\(334\) 2.24667e26i 0.711542i
\(335\) −2.03459e25 −0.0624464
\(336\) 1.10934e27 7.80456e26i 3.29991 2.32159i
\(337\) 2.58313e26 0.744787 0.372394 0.928075i \(-0.378537\pi\)
0.372394 + 0.928075i \(0.378537\pi\)
\(338\) 4.18642e26i 1.17008i
\(339\) −2.85294e26 + 5.93995e25i −0.773029 + 0.160948i
\(340\) 3.70542e26 0.973440
\(341\) 3.62699e26 0.923901
\(342\) −5.39267e26 + 2.34731e26i −1.33208 + 0.579824i
\(343\) −3.92507e26 1.42090e26i −0.940284 0.340390i
\(344\) 1.31840e27i 3.06327i
\(345\) −1.07769e26 + 2.24381e25i −0.242882 + 0.0505691i
\(346\) 1.00789e27i 2.20350i
\(347\) 6.04754e26i 1.28268i 0.767256 + 0.641341i \(0.221622\pi\)
−0.767256 + 0.641341i \(0.778378\pi\)
\(348\) 2.43008e26 5.05954e25i 0.500079 0.104119i
\(349\) 6.47340e26i 1.29260i −0.763082 0.646302i \(-0.776315\pi\)
0.763082 0.646302i \(-0.223685\pi\)
\(350\) −8.83316e26 + 3.81631e26i −1.71160 + 0.739485i
\(351\) 2.74427e26 1.94187e26i 0.516061 0.365171i
\(352\) 2.02769e27 3.70086
\(353\) 5.10240e26 0.903941 0.451971 0.892033i \(-0.350721\pi\)
0.451971 + 0.892033i \(0.350721\pi\)
\(354\) −1.31987e27 + 2.74802e26i −2.26984 + 0.472591i
\(355\) 6.70768e25i 0.111989i
\(356\) 7.08701e26 1.14878
\(357\) −8.67710e26 + 6.10463e26i −1.36571 + 0.960822i
\(358\) −1.24503e27 −1.90286
\(359\) 7.66525e26i 1.13772i 0.822435 + 0.568859i \(0.192615\pi\)
−0.822435 + 0.568859i \(0.807385\pi\)
\(360\) −2.02183e26 4.64493e26i −0.291453 0.669580i
\(361\) 3.17399e26 0.444405
\(362\) 2.21795e27 3.01656
\(363\) −4.30127e25 2.06589e26i −0.0568299 0.272952i
\(364\) −1.26541e27 + 5.46713e26i −1.62430 + 0.701771i
\(365\) 1.56927e25i 0.0195715i
\(366\) −3.63756e26 1.74711e27i −0.440818 2.11723i
\(367\) 1.93862e26i 0.228296i −0.993464 0.114148i \(-0.963586\pi\)
0.993464 0.114148i \(-0.0364138\pi\)
\(368\) 4.19926e27i 4.80585i
\(369\) −3.67260e26 + 1.59860e26i −0.408504 + 0.177813i
\(370\) 2.16825e26i 0.234418i
\(371\) 3.28052e26 1.41733e26i 0.344760 0.148951i
\(372\) 2.91787e27 6.07514e26i 2.98102 0.620662i
\(373\) 2.33075e26 0.231501 0.115750 0.993278i \(-0.463073\pi\)
0.115750 + 0.993278i \(0.463073\pi\)
\(374\) −2.86205e27 −2.76392
\(375\) 8.84637e25 + 4.24889e26i 0.0830686 + 0.398976i
\(376\) 5.55375e27i 5.07123i
\(377\) −1.29929e26 −0.115378
\(378\) 1.92731e27 + 1.17412e27i 1.66451 + 1.01403i
\(379\) −2.00863e26 −0.168728 −0.0843642 0.996435i \(-0.526886\pi\)
−0.0843642 + 0.996435i \(0.526886\pi\)
\(380\) 5.31794e26i 0.434526i
\(381\) −4.03208e26 1.93660e27i −0.320492 1.53931i
\(382\) −1.40103e26 −0.108338
\(383\) −1.83208e27 −1.37834 −0.689170 0.724600i \(-0.742025\pi\)
−0.689170 + 0.724600i \(0.742025\pi\)
\(384\) 5.79516e27 1.20658e27i 4.24216 0.883238i
\(385\) −2.27959e26 + 9.84881e25i −0.162375 + 0.0701530i
\(386\) 1.54530e27i 1.07114i
\(387\) −1.18755e27 + 5.16912e26i −0.801097 + 0.348700i
\(388\) 5.07198e27i 3.33000i
\(389\) 2.27075e27i 1.45110i 0.688167 + 0.725552i \(0.258416\pi\)
−0.688167 + 0.725552i \(0.741584\pi\)
\(390\) 8.40980e25 + 4.03920e26i 0.0523127 + 0.251257i
\(391\) 3.28461e27i 1.98897i
\(392\) −4.33070e27 4.07635e27i −2.55302 2.40308i
\(393\) −5.61434e26 2.69655e27i −0.322238 1.54770i
\(394\) 4.20075e27 2.34756
\(395\) 4.29472e26 0.233704
\(396\) 1.79018e27 + 4.11273e27i 0.948631 + 2.17937i
\(397\) 1.23637e27i 0.638042i −0.947748 0.319021i \(-0.896646\pi\)
0.947748 0.319021i \(-0.103354\pi\)
\(398\) 7.00798e27 3.52225
\(399\) 8.76122e26 + 1.24532e27i 0.428893 + 0.609627i
\(400\) −8.09440e27 −3.85971
\(401\) 8.93304e26i 0.414938i −0.978242 0.207469i \(-0.933477\pi\)
0.978242 0.207469i \(-0.0665226\pi\)
\(402\) 1.26426e27 2.63225e26i 0.572089 0.119111i
\(403\) −1.56010e27 −0.687780
\(404\) −7.08154e27 −3.04175
\(405\) 3.39119e26 3.64231e26i 0.141930 0.152440i
\(406\) −3.45929e26 8.00681e26i −0.141079 0.326540i
\(407\) 1.23389e27i 0.490382i
\(408\) −1.47983e28 + 3.08108e27i −5.73167 + 1.19336i
\(409\) 7.11975e26i 0.268764i −0.990930 0.134382i \(-0.957095\pi\)
0.990930 0.134382i \(-0.0429048\pi\)
\(410\) 4.91570e26i 0.180865i
\(411\) −2.02647e27 + 4.21920e26i −0.726776 + 0.151318i
\(412\) 1.15219e28i 4.02813i
\(413\) 1.38428e27 + 3.20403e27i 0.471789 + 1.09199i
\(414\) 6.40632e27 2.78853e27i 2.12865 0.926555i
\(415\) 2.00416e26 0.0649273
\(416\) −8.72181e27 −2.75503
\(417\) −8.94248e26 + 1.86186e26i −0.275442 + 0.0573482i
\(418\) 4.10755e27i 1.23376i
\(419\) 4.68503e27 1.37235 0.686175 0.727436i \(-0.259288\pi\)
0.686175 + 0.727436i \(0.259288\pi\)
\(420\) −1.66893e27 + 1.17415e27i −0.476784 + 0.335433i
\(421\) 1.27528e27 0.355339 0.177669 0.984090i \(-0.443144\pi\)
0.177669 + 0.984090i \(0.443144\pi\)
\(422\) 7.93935e27i 2.15776i
\(423\) −5.00251e27 + 2.17748e27i −1.32622 + 0.577272i
\(424\) 5.09149e27 1.31675
\(425\) 6.33133e27 1.59739
\(426\) 8.67803e26 + 4.16803e27i 0.213609 + 1.02596i
\(427\) −4.24118e27 + 1.83237e27i −1.01858 + 0.440070i
\(428\) 1.23359e27i 0.289076i
\(429\) −4.78578e26 2.29860e27i −0.109434 0.525607i
\(430\) 1.58951e27i 0.354685i
\(431\) 7.89964e27i 1.72027i −0.510068 0.860134i \(-0.670380\pi\)
0.510068 0.860134i \(-0.329620\pi\)
\(432\) 1.09658e28 + 1.54970e28i 2.33057 + 3.29357i
\(433\) 1.65572e27i 0.343450i −0.985145 0.171725i \(-0.945066\pi\)
0.985145 0.171725i \(-0.0549341\pi\)
\(434\) −4.15367e27 9.61401e27i −0.840989 1.94654i
\(435\) −1.88300e26 + 3.92049e25i −0.0372146 + 0.00774825i
\(436\) 1.53225e28 2.95612
\(437\) 4.71399e27 0.887837
\(438\) 2.03024e26 + 9.75119e26i 0.0373310 + 0.179300i
\(439\) 2.42738e27i 0.435774i −0.975974 0.217887i \(-0.930084\pi\)
0.975974 0.217887i \(-0.0699163\pi\)
\(440\) −3.53800e27 −0.620162
\(441\) 1.97380e27 5.49909e27i 0.337829 0.941207i
\(442\) 1.23107e28 2.05755
\(443\) 2.42490e27i 0.395780i −0.980224 0.197890i \(-0.936591\pi\)
0.980224 0.197890i \(-0.0634089\pi\)
\(444\) 2.06674e27 + 9.92648e27i 0.329431 + 1.58225i
\(445\) −5.49153e26 −0.0854896
\(446\) 5.94867e27 0.904490
\(447\) −6.96663e27 + 1.45048e27i −1.03465 + 0.215419i
\(448\) −1.21907e28 2.82163e28i −1.76852 4.09337i
\(449\) 9.06997e27i 1.28534i −0.766142 0.642672i \(-0.777826\pi\)
0.766142 0.642672i \(-0.222174\pi\)
\(450\) −5.37510e27 1.23487e28i −0.744141 1.70958i
\(451\) 2.79739e27i 0.378355i
\(452\) 1.67242e28i 2.21000i
\(453\) −2.07078e27 9.94588e27i −0.267363 1.28414i
\(454\) 1.33493e28i 1.68412i
\(455\) 9.80532e26 4.23633e26i 0.120877 0.0522240i
\(456\) 4.42189e27 + 2.12382e28i 0.532694 + 2.55851i
\(457\) −3.56460e27 −0.419653 −0.209826 0.977739i \(-0.567290\pi\)
−0.209826 + 0.977739i \(0.567290\pi\)
\(458\) 3.48469e27 0.400938
\(459\) −8.57732e27 1.21215e28i −0.964536 1.36309i
\(460\) 6.31754e27i 0.694370i
\(461\) −2.71423e27 −0.291600 −0.145800 0.989314i \(-0.546576\pi\)
−0.145800 + 0.989314i \(0.546576\pi\)
\(462\) 1.28908e28 9.06908e27i 1.35375 0.952407i
\(463\) −1.90778e28 −1.95852 −0.979261 0.202601i \(-0.935061\pi\)
−0.979261 + 0.202601i \(0.935061\pi\)
\(464\) 7.33716e27i 0.736358i
\(465\) −2.26098e27 + 4.70745e26i −0.221840 + 0.0461881i
\(466\) 3.68294e28 3.53299
\(467\) 1.87542e28 1.75902 0.879510 0.475881i \(-0.157871\pi\)
0.879510 + 0.475881i \(0.157871\pi\)
\(468\) −7.70021e27 1.76903e28i −0.706189 1.62239i
\(469\) −1.32596e27 3.06905e27i −0.118909 0.275225i
\(470\) 6.69576e27i 0.587182i
\(471\) 8.44799e27 1.75891e27i 0.724493 0.150843i
\(472\) 4.97277e28i 4.17068i
\(473\) 9.04544e27i 0.741972i
\(474\) −2.66867e28 + 5.55628e27i −2.14103 + 0.445771i
\(475\) 9.08658e27i 0.713046i
\(476\) 2.41486e28 + 5.58938e28i 1.85361 + 4.29033i
\(477\) 1.99624e27 + 4.58614e27i 0.149889 + 0.344353i
\(478\) −4.91275e27 −0.360854
\(479\) 5.46163e27 0.392463 0.196232 0.980558i \(-0.437130\pi\)
0.196232 + 0.980558i \(0.437130\pi\)
\(480\) −1.26401e28 + 2.63172e27i −0.888622 + 0.185015i
\(481\) 5.30740e27i 0.365055i
\(482\) 4.44652e27 0.299245
\(483\) −1.04080e28 1.47940e28i −0.685369 0.974181i
\(484\) −1.21104e28 −0.780337
\(485\) 3.93014e27i 0.247810i
\(486\) −1.63600e28 + 2.70201e28i −1.00949 + 1.66727i
\(487\) 1.36909e28 0.826754 0.413377 0.910560i \(-0.364349\pi\)
0.413377 + 0.910560i \(0.364349\pi\)
\(488\) −6.58247e28 −3.89028
\(489\) 9.23653e26 + 4.43628e27i 0.0534276 + 0.256611i
\(490\) 5.22122e27 + 4.91456e27i 0.295606 + 0.278244i
\(491\) 2.04125e28i 1.13120i 0.824679 + 0.565601i \(0.191356\pi\)
−0.824679 + 0.565601i \(0.808644\pi\)
\(492\) 4.68557e27 + 2.25047e28i 0.254173 + 1.22078i
\(493\) 5.73903e27i 0.304752i
\(494\) 1.76680e28i 0.918450i
\(495\) −1.38716e27 3.18684e27i −0.0705947 0.162183i
\(496\) 8.80994e28i 4.38950i
\(497\) 1.01181e28 4.37145e27i 0.493577 0.213247i
\(498\) −1.24535e28 + 2.59288e27i −0.594818 + 0.123844i
\(499\) −4.24208e26 −0.0198392 −0.00991958 0.999951i \(-0.503158\pi\)
−0.00991958 + 0.999951i \(0.503158\pi\)
\(500\) 2.49073e28 1.14062
\(501\) −1.65938e27 7.96994e27i −0.0744131 0.357404i
\(502\) 3.36496e28i 1.47772i
\(503\) 3.41707e27 0.146957 0.0734785 0.997297i \(-0.476590\pi\)
0.0734785 + 0.997297i \(0.476590\pi\)
\(504\) 5.68891e28 6.07693e28i 2.39612 2.55955i
\(505\) 5.48728e27 0.226359
\(506\) 4.87964e28i 1.97155i
\(507\) −3.09207e27 1.48511e28i −0.122367 0.587728i
\(508\) −1.13525e29 −4.40071
\(509\) −2.92017e27 −0.110884 −0.0554422 0.998462i \(-0.517657\pi\)
−0.0554422 + 0.998462i \(0.517657\pi\)
\(510\) 1.78413e28 3.71464e27i 0.663652 0.138175i
\(511\) 2.36714e27 1.02271e27i 0.0862590 0.0372676i
\(512\) 9.62696e28i 3.43680i
\(513\) −1.73965e28 + 1.23100e28i −0.608457 + 0.430551i
\(514\) 7.45910e28i 2.55608i
\(515\) 8.92800e27i 0.299763i
\(516\) 1.51509e28 + 7.27695e28i 0.498445 + 2.39402i
\(517\) 3.81037e28i 1.22833i
\(518\) 3.27065e28 1.41306e28i 1.03317 0.446374i
\(519\) 7.44423e27 + 3.57544e28i 0.230442 + 1.10681i
\(520\) 1.52182e28 0.461667
\(521\) 1.46429e28 0.435344 0.217672 0.976022i \(-0.430154\pi\)
0.217672 + 0.976022i \(0.430154\pi\)
\(522\) 1.11934e28 4.87226e27i 0.326154 0.141968i
\(523\) 2.32580e28i 0.664208i −0.943243 0.332104i \(-0.892241\pi\)
0.943243 0.332104i \(-0.107759\pi\)
\(524\) −1.58074e29 −4.42468
\(525\) −2.85165e28 + 2.00623e28i −0.782391 + 0.550438i
\(526\) 5.58834e28 1.50291
\(527\) 6.89103e28i 1.81665i
\(528\) 1.29803e29 2.70255e28i 3.35450 0.698421i
\(529\) −1.65291e28 −0.418759
\(530\) −6.13845e27 −0.152462
\(531\) −4.47920e28 + 1.94970e28i −1.09071 + 0.474760i
\(532\) 8.02174e28 3.46574e28i 1.91512 0.827416i
\(533\) 1.20326e28i 0.281659i
\(534\) 3.41234e28 7.10465e27i 0.783194 0.163064i
\(535\) 9.55876e26i 0.0215123i
\(536\) 4.76327e28i 1.05118i
\(537\) −4.41668e28 + 9.19572e27i −0.955797 + 0.199001i
\(538\) 8.15697e28i 1.73107i
\(539\) −2.97125e28 2.79674e28i −0.618382 0.582063i
\(540\) −1.64974e28 2.33143e28i −0.336730 0.475869i
\(541\) 3.43629e28 0.687889 0.343944 0.938990i \(-0.388237\pi\)
0.343944 + 0.938990i \(0.388237\pi\)
\(542\) 8.45186e28 1.65943
\(543\) 7.86808e28 1.63817e28i 1.51520 0.315472i
\(544\) 3.85246e29i 7.27695i
\(545\) −1.18730e28 −0.219987
\(546\) −5.54478e28 + 3.90094e28i −1.00777 + 0.709001i
\(547\) −6.34601e28 −1.13145 −0.565723 0.824595i \(-0.691403\pi\)
−0.565723 + 0.824595i \(0.691403\pi\)
\(548\) 1.18793e29i 2.07776i
\(549\) −2.58082e28 5.92913e28i −0.442841 1.01737i
\(550\) −9.40588e28 −1.58340
\(551\) 8.23652e27 0.136035
\(552\) −5.25307e28 2.52303e29i −0.851241 4.08849i
\(553\) 2.79891e28 + 6.47829e28i 0.445015 + 1.03002i
\(554\) 4.26036e28i 0.664652i
\(555\) −1.60146e27 7.69175e27i −0.0245154 0.117747i
\(556\) 5.24216e28i 0.787454i
\(557\) 1.18605e28i 0.174832i 0.996172 + 0.0874162i \(0.0278610\pi\)
−0.996172 + 0.0874162i \(0.972139\pi\)
\(558\) 1.34403e29 5.85026e28i 1.94424 0.846284i
\(559\) 3.89077e28i 0.552346i
\(560\) 2.39227e28 + 5.53710e28i 0.333300 + 0.771451i
\(561\) −1.01530e29 + 2.11390e28i −1.38830 + 0.289051i
\(562\) −2.79354e29 −3.74908
\(563\) −8.27726e28 −1.09031 −0.545153 0.838337i \(-0.683528\pi\)
−0.545153 + 0.838337i \(0.683528\pi\)
\(564\) 6.38230e28 + 3.06540e29i 0.825176 + 3.96329i
\(565\) 1.29591e28i 0.164462i
\(566\) −6.01426e28 −0.749221
\(567\) 7.70424e28 + 2.74165e28i 0.942124 + 0.335266i
\(568\) 1.57036e29 1.88513
\(569\) 4.84740e27i 0.0571255i 0.999592 + 0.0285628i \(0.00909304\pi\)
−0.999592 + 0.0285628i \(0.990907\pi\)
\(570\) −5.33117e27 2.56054e28i −0.0616788 0.296242i
\(571\) 5.95415e28 0.676302 0.338151 0.941092i \(-0.390199\pi\)
0.338151 + 0.941092i \(0.390199\pi\)
\(572\) −1.34746e29 −1.50265
\(573\) −4.97008e27 + 1.03479e27i −0.0544176 + 0.0113300i
\(574\) 7.41499e28 3.20360e28i 0.797142 0.344400i
\(575\) 1.07946e29i 1.13944i
\(576\) 3.94462e29 1.71700e29i 4.08854 1.77965i
\(577\) 4.08708e28i 0.415975i 0.978131 + 0.207988i \(0.0666914\pi\)
−0.978131 + 0.207988i \(0.933309\pi\)
\(578\) 3.48754e29i 3.48560i
\(579\) 1.14135e28 + 5.48188e28i 0.112020 + 0.538028i
\(580\) 1.10383e28i 0.106392i
\(581\) 1.30613e28 + 3.02314e28i 0.123634 + 0.286160i
\(582\) −5.08460e28 2.44212e29i −0.472678 2.27026i
\(583\) 3.49322e28 0.318938
\(584\) 3.67389e28 0.329451
\(585\) 5.96668e27 + 1.37077e28i 0.0525528 + 0.120734i
\(586\) 5.15672e28i 0.446117i
\(587\) 2.08509e29 1.77184 0.885919 0.463839i \(-0.153528\pi\)
0.885919 + 0.463839i \(0.153528\pi\)
\(588\) −2.85878e29 1.75227e29i −2.38627 1.46264i
\(589\) 9.88983e28 0.810921
\(590\) 5.99532e28i 0.482910i
\(591\) 1.49020e29 3.10266e28i 1.17917 0.245508i
\(592\) 2.99711e29 2.32983
\(593\) −8.48106e28 −0.647703 −0.323852 0.946108i \(-0.604978\pi\)
−0.323852 + 0.946108i \(0.604978\pi\)
\(594\) 1.27425e29 + 1.80078e29i 0.956089 + 1.35115i
\(595\) −1.87120e28 4.33105e28i −0.137941 0.319275i
\(596\) 4.08390e29i 2.95794i
\(597\) 2.48605e29 5.17607e28i 1.76921 0.368357i
\(598\) 2.09891e29i 1.46768i
\(599\) 1.25037e29i 0.859129i −0.903036 0.429565i \(-0.858667\pi\)
0.903036 0.429565i \(-0.141333\pi\)
\(600\) −4.86334e29 + 1.01257e29i −3.28357 + 0.683655i
\(601\) 9.97492e28i 0.661801i 0.943666 + 0.330900i \(0.107352\pi\)
−0.943666 + 0.330900i \(0.892648\pi\)
\(602\) 2.39766e29 1.03589e29i 1.56324 0.675386i
\(603\) 4.29050e28 1.86756e28i 0.274901 0.119658i
\(604\) −5.83036e29 −3.67120
\(605\) 9.38401e27 0.0580707
\(606\) −3.40970e29 + 7.09915e28i −2.07374 + 0.431762i
\(607\) 9.31313e28i 0.556691i −0.960481 0.278346i \(-0.910214\pi\)
0.960481 0.278346i \(-0.0897861\pi\)
\(608\) 5.52896e29 3.24830
\(609\) −1.81855e28 2.58488e28i −0.105013 0.149265i
\(610\) 7.93602e28 0.450442
\(611\) 1.63898e29i 0.914409i
\(612\) −7.81390e29 + 3.40121e29i −4.28526 + 1.86528i
\(613\) −7.95015e28 −0.428588 −0.214294 0.976769i \(-0.568745\pi\)
−0.214294 + 0.976769i \(0.568745\pi\)
\(614\) 3.64461e29 1.93145
\(615\) −3.63072e27 1.74382e28i −0.0189149 0.0908476i
\(616\) −2.30574e29 5.33683e29i −1.18090 2.73329i
\(617\) 1.87702e29i 0.945092i −0.881306 0.472546i \(-0.843335\pi\)
0.881306 0.472546i \(-0.156665\pi\)
\(618\) −1.15506e29 5.54770e29i −0.571774 2.74621i
\(619\) 5.03814e28i 0.245199i −0.992456 0.122599i \(-0.960877\pi\)
0.992456 0.122599i \(-0.0391230\pi\)
\(620\) 1.32540e29i 0.634214i
\(621\) 2.06665e29 1.46239e29i 0.972312 0.688018i
\(622\) 3.13196e29i 1.44883i
\(623\) −3.57887e28 8.28359e28i −0.162788 0.376785i
\(624\) −5.58328e29 + 1.16246e29i −2.49719 + 0.519926i
\(625\) 1.98210e29 0.871736
\(626\) −3.84402e29 −1.66247
\(627\) 3.03382e28 + 1.45713e29i 0.129027 + 0.619713i
\(628\) 4.95229e29i 2.07124i
\(629\) −2.34430e29 −0.964232
\(630\) −6.85871e28 + 7.32653e28i −0.277439 + 0.296362i
\(631\) 1.89931e29 0.755591 0.377795 0.925889i \(-0.376682\pi\)
0.377795 + 0.925889i \(0.376682\pi\)
\(632\) 1.00546e30i 3.93399i
\(633\) 5.86397e28 + 2.81645e29i 0.225659 + 1.08383i
\(634\) −1.12434e29 −0.425560
\(635\) 8.79674e28 0.327490
\(636\) 2.81026e29 5.85108e28i 1.02907 0.214258i
\(637\) 1.27804e29 + 1.20298e29i 0.460342 + 0.433306i
\(638\) 8.52595e28i 0.302083i
\(639\) 6.15699e28 + 1.41450e29i 0.214590 + 0.492995i
\(640\) 2.63237e29i 0.902522i
\(641\) 1.01567e29i 0.342565i −0.985222 0.171283i \(-0.945209\pi\)
0.985222 0.171283i \(-0.0547912\pi\)
\(642\) 1.23666e28 + 5.93965e28i 0.0410330 + 0.197080i
\(643\) 1.50938e29i 0.492701i 0.969181 + 0.246350i \(0.0792314\pi\)
−0.969181 + 0.246350i \(0.920769\pi\)
\(644\) −9.52957e29 + 4.11719e29i −3.06035 + 1.32221i
\(645\) −1.17400e28 5.63870e28i −0.0370930 0.178157i
\(646\) −7.80405e29 −2.42593
\(647\) −3.02033e29 −0.923761 −0.461880 0.886942i \(-0.652825\pi\)
−0.461880 + 0.886942i \(0.652825\pi\)
\(648\) 8.52717e29 + 7.93925e29i 2.56606 + 2.38914i
\(649\) 3.41177e29i 1.01021i
\(650\) 4.04581e29 1.17873
\(651\) −2.18358e29 3.10374e29i −0.625993 0.889784i
\(652\) 2.60059e29 0.733621
\(653\) 1.39825e29i 0.388147i 0.980987 + 0.194073i \(0.0621700\pi\)
−0.980987 + 0.194073i \(0.937830\pi\)
\(654\) 7.37768e29 1.53607e29i 2.01536 0.419608i
\(655\) 1.22487e29 0.329274
\(656\) 6.79484e29 1.79758
\(657\) 1.44044e28 + 3.30924e28i 0.0375023 + 0.0861572i
\(658\) 1.01001e30 4.36368e29i 2.58794 1.11810i
\(659\) 7.66724e29i 1.93349i −0.255738 0.966746i \(-0.582319\pi\)
0.255738 0.966746i \(-0.417681\pi\)
\(660\) −1.95281e29 + 4.06583e28i −0.484672 + 0.100911i
\(661\) 1.65340e28i 0.0403889i −0.999796 0.0201945i \(-0.993571\pi\)
0.999796 0.0201945i \(-0.00642853\pi\)
\(662\) 9.45308e29i 2.27282i
\(663\) 4.36717e29 9.09265e28i 1.03349 0.215178i
\(664\) 4.69202e29i 1.09294i
\(665\) −6.21582e28 + 2.68551e28i −0.142518 + 0.0615742i
\(666\) 1.99024e29 + 4.57234e29i 0.449185 + 1.03195i
\(667\) −9.78472e28 −0.217384
\(668\) −4.67205e29 −1.02177
\(669\) 2.11026e29 4.39366e28i 0.454320 0.0945915i
\(670\) 5.74274e28i 0.121712i
\(671\) −4.51617e29 −0.942287
\(672\) −1.22074e30 1.73516e30i −2.50753 3.56420i
\(673\) −6.92774e29 −1.40098 −0.700492 0.713660i \(-0.747036\pi\)
−0.700492 + 0.713660i \(0.747036\pi\)
\(674\) 7.29101e29i 1.45164i
\(675\) −2.81886e29 3.98363e29i −0.552566 0.780890i
\(676\) −8.70587e29 −1.68024
\(677\) 9.41956e28 0.178999 0.0894993 0.995987i \(-0.471473\pi\)
0.0894993 + 0.995987i \(0.471473\pi\)
\(678\) 1.67658e29 + 8.05256e29i 0.313698 + 1.50668i
\(679\) −5.92834e29 + 2.56130e29i −1.09220 + 0.471876i
\(680\) 6.72195e29i 1.21942i
\(681\) 9.85973e28 + 4.73560e29i 0.176125 + 0.845922i
\(682\) 1.02374e30i 1.80074i
\(683\) 1.09202e30i 1.89153i 0.324857 + 0.945763i \(0.394684\pi\)
−0.324857 + 0.945763i \(0.605316\pi\)
\(684\) 4.88134e29 + 1.12143e30i 0.832626 + 1.91286i
\(685\) 9.20496e28i 0.154622i
\(686\) −4.01057e29 + 1.10787e30i −0.663442 + 1.83268i
\(687\) 1.23618e29 2.57378e28i 0.201389 0.0419301i
\(688\) 2.19713e30 3.52515
\(689\) −1.50256e29 −0.237427
\(690\) 6.33326e28 + 3.04184e29i 0.0985625 + 0.473393i
\(691\) 4.19332e29i 0.642744i 0.946953 + 0.321372i \(0.104144\pi\)
−0.946953 + 0.321372i \(0.895856\pi\)
\(692\) 2.09596e30 3.16423
\(693\) 3.90310e29 4.16932e29i 0.580378 0.619964i
\(694\) 1.70695e30 2.50003
\(695\) 4.06200e28i 0.0586003i
\(696\) −9.17843e28 4.40837e29i −0.130428 0.626443i
\(697\) −5.31484e29 −0.743954
\(698\) −1.82715e30 −2.51937
\(699\) 1.30651e30 2.72021e29i 1.77460 0.369480i
\(700\) 7.93621e29 + 1.83690e30i 1.06190 + 2.45785i
\(701\) 2.35911e29i 0.310963i −0.987839 0.155482i \(-0.950307\pi\)
0.987839 0.155482i \(-0.0496929\pi\)
\(702\) −5.48103e29 7.74582e29i −0.711741 1.00584i
\(703\) 3.36448e29i 0.430415i
\(704\) 3.00458e30i 3.78679i
\(705\) −4.94546e28 2.37529e29i −0.0614075 0.294938i
\(706\) 1.44018e30i 1.76184i
\(707\) 3.57611e29 + 8.27719e29i 0.431029 + 0.997652i
\(708\) 5.71464e29 + 2.74473e30i 0.678641 + 3.25949i
\(709\) 4.53953e29 0.531160 0.265580 0.964089i \(-0.414436\pi\)
0.265580 + 0.964089i \(0.414436\pi\)
\(710\) −1.89327e29 −0.218273
\(711\) −9.05659e29 + 3.94213e29i −1.02881 + 0.447817i
\(712\) 1.28564e30i 1.43907i
\(713\) −1.17488e30 −1.29585
\(714\) 1.72306e30 + 2.44915e30i 1.87271 + 2.66186i
\(715\) 1.04411e29 0.111823
\(716\) 2.58910e30i 2.73251i
\(717\) −1.74278e29 + 3.62854e28i −0.181255 + 0.0377381i
\(718\) 2.16355e30 2.21749
\(719\) −1.00116e30 −1.01123 −0.505615 0.862759i \(-0.668734\pi\)
−0.505615 + 0.862759i \(0.668734\pi\)
\(720\) −7.74082e29 + 3.36940e29i −0.770541 + 0.335399i
\(721\) −1.34673e30 + 5.81845e29i −1.32117 + 0.570804i
\(722\) 8.95873e29i 0.866175i
\(723\) 1.57738e29 3.28418e28i 0.150309 0.0312950i
\(724\) 4.61234e30i 4.33178i
\(725\) 1.88608e29i 0.174587i
\(726\) −5.83106e29 + 1.21405e29i −0.532002 + 0.110765i
\(727\) 3.47338e29i 0.312349i −0.987729 0.156175i \(-0.950084\pi\)
0.987729 0.156175i \(-0.0499163\pi\)
\(728\) 9.91784e29 + 2.29556e30i 0.879099 + 2.03474i
\(729\) −3.80796e29 + 1.07936e30i −0.332700 + 0.943033i
\(730\) −4.42935e28 −0.0381461
\(731\) −1.71857e30 −1.45893
\(732\) −3.63320e30 + 7.56449e29i −3.04035 + 0.633014i
\(733\) 8.39113e29i 0.692195i −0.938198 0.346098i \(-0.887507\pi\)
0.938198 0.346098i \(-0.112493\pi\)
\(734\) −5.47184e29 −0.444964
\(735\) 2.21519e29 + 1.35778e29i 0.177580 + 0.108846i
\(736\) −6.56822e30 −5.19076
\(737\) 3.26803e29i 0.254612i
\(738\) 4.51213e29 + 1.03661e30i 0.346569 + 0.796202i
\(739\) 5.00868e29 0.379277 0.189639 0.981854i \(-0.439268\pi\)
0.189639 + 0.981854i \(0.439268\pi\)
\(740\) −4.50897e29 −0.336624
\(741\) −1.30495e29 6.26766e29i −0.0960515 0.461333i
\(742\) −4.00048e29 9.25943e29i −0.290316 0.671960i
\(743\) 6.56737e29i 0.469904i −0.972007 0.234952i \(-0.924507\pi\)
0.972007 0.234952i \(-0.0754932\pi\)
\(744\) −1.10208e30 5.29326e30i −0.777495 3.73429i
\(745\) 3.16450e29i 0.220122i
\(746\) 6.57865e29i 0.451210i
\(747\) −4.22632e29 + 1.83962e29i −0.285822 + 0.124412i
\(748\) 5.95178e30i 3.96899i
\(749\) 1.44187e29 6.22952e28i 0.0948129 0.0409633i
\(750\) 1.19927e30 2.49693e29i 0.777630 0.161906i
\(751\) 3.70180e28 0.0236697 0.0118349 0.999930i \(-0.496233\pi\)
0.0118349 + 0.999930i \(0.496233\pi\)
\(752\) 9.25537e30 5.83588
\(753\) 2.48535e29 + 1.19371e30i 0.154540 + 0.742249i
\(754\) 3.66732e29i 0.224879i
\(755\) 4.51778e29 0.273201
\(756\) 2.44165e30 4.00793e30i 1.45614 2.39024i
\(757\) −8.95308e29 −0.526581 −0.263291 0.964717i \(-0.584808\pi\)
−0.263291 + 0.964717i \(0.584808\pi\)
\(758\) 5.66946e29i 0.328863i
\(759\) −3.60408e29 1.73103e30i −0.206184 0.990298i
\(760\) −9.64718e29 −0.544324
\(761\) 2.77439e30 1.54393 0.771967 0.635662i \(-0.219273\pi\)
0.771967 + 0.635662i \(0.219273\pi\)
\(762\) −5.46614e30 + 1.13807e30i −3.00022 + 0.624660i
\(763\) −7.73773e29 1.79096e30i −0.418896 0.969568i
\(764\) 2.91350e29i 0.155573i
\(765\) 6.05477e29 2.63551e29i 0.318898 0.138809i
\(766\) 5.17112e30i 2.68647i
\(767\) 1.46752e30i 0.752028i
\(768\) −1.60753e30 7.72092e30i −0.812580 3.90280i
\(769\) 1.12666e30i 0.561779i −0.959740 0.280890i \(-0.909371\pi\)
0.959740 0.280890i \(-0.0906295\pi\)
\(770\) 2.77987e29 + 6.43424e29i 0.136733 + 0.316479i
\(771\) −5.50926e29 2.64608e30i −0.267314 1.28390i
\(772\) 3.21353e30 1.53816
\(773\) 3.15876e29 0.149153 0.0745766 0.997215i \(-0.476239\pi\)
0.0745766 + 0.997215i \(0.476239\pi\)
\(774\) 1.45901e30 + 3.35191e30i 0.679639 + 1.56139i
\(775\) 2.26467e30i 1.04073i
\(776\) −9.20100e30 −4.17145
\(777\) 1.05588e30 7.42847e29i 0.472274 0.332260i
\(778\) 6.40930e30 2.82830
\(779\) 7.62773e29i 0.332087i
\(780\) 8.39972e29 1.74886e29i 0.360804 0.0751210i
\(781\) 1.07741e30 0.456610
\(782\) 9.27096e30 3.87663
\(783\) 3.61096e29 2.55515e29i 0.148979 0.105419i
\(784\) −6.79327e30 + 7.21715e30i −2.76542 + 2.93797i
\(785\) 3.83739e29i 0.154136i
\(786\) −7.61114e30 + 1.58467e30i −3.01657 + 0.628063i
\(787\) 3.13600e30i 1.22643i 0.789918 + 0.613213i \(0.210123\pi\)
−0.789918 + 0.613213i \(0.789877\pi\)
\(788\) 8.73566e30i 3.37109i
\(789\) 1.98244e30 4.12753e29i 0.754904 0.157174i
\(790\) 1.21221e30i 0.455504i
\(791\) 1.95479e30 8.44555e29i 0.724848 0.313166i
\(792\) 7.46084e30 3.24754e30i 2.73007 1.18834i
\(793\) 1.94257e30 0.701467
\(794\) −3.48972e30 −1.24359
\(795\) −2.17759e29 + 4.53384e28i −0.0765810 + 0.0159445i
\(796\) 1.45734e31i 5.05795i
\(797\) −1.83033e30 −0.626926 −0.313463 0.949600i \(-0.601489\pi\)
−0.313463 + 0.949600i \(0.601489\pi\)
\(798\) 3.51497e30 2.47290e30i 1.18820 0.835941i
\(799\) −7.23943e30 −2.41526
\(800\) 1.26608e31i 4.16884i
\(801\) 1.15804e30 5.04068e29i 0.376341 0.163813i
\(802\) −2.52139e30 −0.808741
\(803\) 2.52062e29 0.0797983
\(804\) −5.47389e29 2.62910e30i −0.171044 0.821519i
\(805\) 7.38419e29 3.19030e29i 0.227744 0.0983953i
\(806\) 4.40346e30i 1.34053i
\(807\) −6.02471e29 2.89365e30i −0.181036 0.869509i
\(808\) 1.28465e31i 3.81036i
\(809\) 4.25626e30i 1.24615i −0.782164 0.623073i \(-0.785884\pi\)
0.782164 0.623073i \(-0.214116\pi\)
\(810\) −1.02806e30 9.57179e29i −0.297116 0.276631i
\(811\) 9.85036e29i 0.281017i 0.990079 + 0.140509i \(0.0448738\pi\)
−0.990079 + 0.140509i \(0.955126\pi\)
\(812\) −1.66505e30 + 7.19377e29i −0.468911 + 0.202590i
\(813\) 2.99826e30 6.24251e29i 0.833525 0.173544i
\(814\) 3.48271e30 0.955787
\(815\) −2.01512e29 −0.0545942
\(816\) 5.13465e30 + 2.46616e31i 1.37330 + 6.59590i
\(817\) 2.46645e30i 0.651239i
\(818\) −2.00959e30 −0.523838
\(819\) −1.67887e30 + 1.79338e30i −0.432051 + 0.461520i
\(820\) −1.02224e30 −0.259722
\(821\) 4.06072e30i 1.01859i 0.860592 + 0.509296i \(0.170094\pi\)
−0.860592 + 0.509296i \(0.829906\pi\)
\(822\) 1.19089e30 + 5.71980e30i 0.294929 + 1.41653i
\(823\) −2.66549e30 −0.651747 −0.325873 0.945413i \(-0.605658\pi\)
−0.325873 + 0.945413i \(0.605658\pi\)
\(824\) −2.09017e31 −5.04598
\(825\) −3.33669e30 + 6.94714e29i −0.795335 + 0.165592i
\(826\) 9.04352e30 3.90720e30i 2.12837 0.919549i
\(827\) 1.26604e30i 0.294197i 0.989122 + 0.147099i \(0.0469935\pi\)
−0.989122 + 0.147099i \(0.953007\pi\)
\(828\) −5.79888e30 1.33222e31i −1.33053 3.05674i
\(829\) 5.09586e30i 1.15450i −0.816567 0.577251i \(-0.804125\pi\)
0.816567 0.577251i \(-0.195875\pi\)
\(830\) 5.65684e29i 0.126548i
\(831\) 3.14669e29 + 1.51134e30i 0.0695093 + 0.333851i
\(832\) 1.29238e31i 2.81900i
\(833\) 5.31361e30 5.64516e30i 1.14450 1.21592i
\(834\) 5.25520e29 + 2.52406e30i 0.111775 + 0.536854i
\(835\) 3.62024e29 0.0760378
\(836\) 8.54185e30 1.77168
\(837\) 4.33579e30 3.06805e30i 0.888077 0.628413i
\(838\) 1.32237e31i 2.67480i
\(839\) 5.57443e30 1.11352 0.556762 0.830672i \(-0.312043\pi\)
0.556762 + 0.830672i \(0.312043\pi\)
\(840\) 2.13001e30 + 3.02759e30i 0.420193 + 0.597261i
\(841\) 4.96188e30 0.966692
\(842\) 3.59953e30i 0.692578i
\(843\) −9.90997e30 + 2.06330e30i −1.88314 + 0.392078i
\(844\) 1.65103e31 3.09855
\(845\) 6.74593e29 0.125039
\(846\) 6.14605e30 + 1.41198e31i 1.12514 + 2.58488i
\(847\) 6.11564e29 + 1.41551e30i 0.110577 + 0.255940i
\(848\) 8.48502e30i 1.51529i
\(849\) −2.13353e30 + 4.44211e29i −0.376330 + 0.0783535i
\(850\) 1.78705e31i 3.11342i
\(851\) 3.99690e30i 0.687801i
\(852\) 8.66763e30 1.80464e30i 1.47328 0.306743i
\(853\) 2.97889e30i 0.500138i 0.968228 + 0.250069i \(0.0804532\pi\)
−0.968228 + 0.250069i \(0.919547\pi\)
\(854\) 5.17197e30 + 1.19709e31i 0.857725 + 1.98527i
\(855\) −3.78241e29 8.68966e29i −0.0619619 0.142350i
\(856\) 2.23784e30 0.362122
\(857\) −8.11612e30 −1.29733 −0.648664 0.761075i \(-0.724672\pi\)
−0.648664 + 0.761075i \(0.724672\pi\)
\(858\) −6.48791e30 + 1.35081e30i −1.02444 + 0.213294i
\(859\) 1.03931e31i 1.62112i 0.585653 + 0.810562i \(0.300838\pi\)
−0.585653 + 0.810562i \(0.699162\pi\)
\(860\) −3.30546e30 −0.509328
\(861\) 2.39382e30 1.68413e30i 0.364383 0.256356i
\(862\) −2.22971e31 −3.35291
\(863\) 2.75035e30i 0.408577i 0.978911 + 0.204289i \(0.0654881\pi\)
−0.978911 + 0.204289i \(0.934512\pi\)
\(864\) 2.42394e31 1.71521e31i 3.55736 2.51723i
\(865\) −1.62410e30 −0.235474
\(866\) −4.67335e30 −0.669407
\(867\) −2.57588e30 1.23719e31i −0.364524 1.75080i
\(868\) −1.99928e31 + 8.63777e30i −2.79522 + 1.20766i
\(869\) 6.89833e30i 0.952876i
\(870\) 1.10658e29 + 5.31487e29i 0.0151018 + 0.0725338i
\(871\) 1.40570e30i 0.189541i
\(872\) 2.77964e31i 3.70310i
\(873\) −3.60748e30 8.28776e30i −0.474847 1.09091i
\(874\) 1.33055e31i 1.73045i
\(875\) −1.25780e30 2.91127e30i −0.161631 0.374109i
\(876\) 2.02781e30 4.22199e29i 0.257474 0.0536073i
\(877\) 4.33521e30 0.543894 0.271947 0.962312i \(-0.412333\pi\)
0.271947 + 0.962312i \(0.412333\pi\)
\(878\) −6.85141e30 −0.849351
\(879\) 3.80873e29 + 1.82932e30i 0.0466549 + 0.224082i
\(880\) 5.89611e30i 0.713671i
\(881\) 1.92140e30 0.229811 0.114906 0.993376i \(-0.463343\pi\)
0.114906 + 0.993376i \(0.463343\pi\)
\(882\) −1.55214e31 5.57113e30i −1.83448 0.658451i
\(883\) 4.99868e30 0.583805 0.291903 0.956448i \(-0.405712\pi\)
0.291903 + 0.956448i \(0.405712\pi\)
\(884\) 2.56008e31i 2.95464i
\(885\) −4.42812e29 2.12681e30i −0.0505027 0.242563i
\(886\) −6.84439e30 −0.771401
\(887\) 1.09139e31 1.21558 0.607788 0.794099i \(-0.292057\pi\)
0.607788 + 0.794099i \(0.292057\pi\)
\(888\) 1.80075e31 3.74924e30i 1.98206 0.412674i
\(889\) 5.73290e30 + 1.32693e31i 0.623600 + 1.44337i
\(890\) 1.55001e30i 0.166625i
\(891\) 5.85041e30 + 5.44704e30i 0.621542 + 0.578688i
\(892\) 1.23705e31i 1.29885i
\(893\) 1.03899e31i 1.07813i
\(894\) 4.09406e30 + 1.96637e31i 0.419866 + 2.01660i
\(895\) 2.00622e30i 0.203346i
\(896\) −3.97075e31 + 1.71554e31i −3.97776 + 1.71857i
\(897\) 1.55024e30 + 7.44578e30i 0.153490 + 0.737207i
\(898\) −2.56004e31 −2.50522
\(899\) −2.05281e30 −0.198551
\(900\) −2.56797e31 + 1.11778e31i −2.45495 + 1.06859i
\(901\) 6.63687e30i 0.627124i
\(902\) 7.89576e30 0.737438
\(903\) 7.74048e30 5.44569e30i 0.714573 0.502726i
\(904\) 3.03391e31 2.76843
\(905\) 3.57397e30i 0.322360i
\(906\) −2.80727e31 + 5.84486e30i −2.50287 + 0.521109i
\(907\) 5.96154e30 0.525390 0.262695 0.964879i \(-0.415389\pi\)
0.262695 + 0.964879i \(0.415389\pi\)
\(908\) 2.77605e31 2.41839
\(909\) −1.15714e31 + 5.03679e30i −0.996475 + 0.433743i
\(910\) −1.19572e30 2.76760e30i −0.101788 0.235596i
\(911\) 1.98630e31i 1.67148i 0.549122 + 0.835742i \(0.314962\pi\)
−0.549122 + 0.835742i \(0.685038\pi\)
\(912\) 3.53937e31 7.36913e30i 2.94429 0.613014i
\(913\) 3.21915e30i 0.264727i
\(914\) 1.00612e31i 0.817931i
\(915\) 2.81527e30 5.86151e29i 0.226255 0.0471073i
\(916\) 7.24659e30i 0.575746i
\(917\) 7.98259e30 + 1.84763e31i 0.626997 + 1.45124i
\(918\) −3.42136e31 + 2.42099e31i −2.65675 + 1.87994i
\(919\) −7.89000e30 −0.605709 −0.302855 0.953037i \(-0.597940\pi\)
−0.302855 + 0.953037i \(0.597940\pi\)
\(920\) 1.14605e31 0.869827
\(921\) 1.29291e31 2.69189e30i 0.970155 0.201991i
\(922\) 7.66106e30i 0.568348i
\(923\) −4.63433e30 −0.339914
\(924\) −1.88596e31 2.68070e31i −1.36766 1.94398i
\(925\) −7.70433e30 −0.552391
\(926\) 5.38481e31i 3.81729i
\(927\) −8.19502e30 1.88271e31i −0.574398 1.31961i
\(928\) −1.14763e31 −0.795334
\(929\) 2.45268e31 1.68065 0.840324 0.542084i \(-0.182365\pi\)
0.840324 + 0.542084i \(0.182365\pi\)
\(930\) 1.32870e30 + 6.38172e30i 0.0900236 + 0.432381i
\(931\) −8.10180e30 7.62597e30i −0.542762 0.510885i
\(932\) 7.65886e31i 5.07338i
\(933\) −2.31325e30 1.11105e31i −0.151518 0.727739i
\(934\) 5.29346e31i 3.42844i
\(935\) 4.61187e30i 0.295362i
\(936\) −3.20918e31 + 1.39688e31i −2.03234 + 0.884634i
\(937\) 2.02136e31i 1.26584i 0.774218 + 0.632919i \(0.218143\pi\)
−0.774218 + 0.632919i \(0.781857\pi\)
\(938\) −8.66253e30 + 3.74259e30i −0.536432 + 0.231762i
\(939\) −1.36365e31 + 2.83917e30i −0.835052 + 0.173861i
\(940\) −1.39242e31 −0.843193
\(941\) −2.54721e31 −1.52536 −0.762681 0.646775i \(-0.776117\pi\)
−0.762681 + 0.646775i \(0.776117\pi\)
\(942\) −4.96461e30 2.38449e31i −0.294002 1.41208i
\(943\) 9.06150e30i 0.530673i
\(944\) 8.28717e31 4.79955
\(945\) −1.89196e30 + 3.10564e30i −0.108362 + 0.177876i
\(946\) 2.55312e31 1.44615
\(947\) 4.04525e30i 0.226605i 0.993561 + 0.113303i \(0.0361430\pi\)
−0.993561 + 0.113303i \(0.963857\pi\)
\(948\) 1.15546e31 + 5.54963e31i 0.640127 + 3.07451i
\(949\) −1.08421e30 −0.0594043
\(950\) −2.56473e31 −1.38977
\(951\) −3.98855e30 + 8.30433e29i −0.213757 + 0.0445051i
\(952\) 1.01396e32 4.38075e31i 5.37443 2.32199i
\(953\) 1.55994e31i 0.817770i −0.912586 0.408885i \(-0.865918\pi\)
0.912586 0.408885i \(-0.134082\pi\)
\(954\) 1.29446e31 5.63450e30i 0.671167 0.292144i
\(955\) 2.25759e29i 0.0115774i
\(956\) 1.02163e31i 0.518187i
\(957\) −6.29723e29 3.02454e30i −0.0315918 0.151734i
\(958\) 1.54157e31i 0.764937i
\(959\) 1.38850e31 5.99895e30i 0.681478 0.294428i
\(960\) 3.89963e30 + 1.87298e31i 0.189311 + 0.909254i
\(961\) −3.82321e30 −0.183583
\(962\) −1.49804e31 −0.711517
\(963\) 8.77400e29 + 2.01572e30i 0.0412213 + 0.0947011i
\(964\) 9.24676e30i 0.429715i
\(965\) −2.49007e30 −0.114466
\(966\) −4.17567e31 + 2.93772e31i −1.89874 + 1.33583i
\(967\) 1.66736e31 0.749984 0.374992 0.927028i \(-0.377646\pi\)
0.374992 + 0.927028i \(0.377646\pi\)
\(968\) 2.19693e31i 0.977518i
\(969\) −2.76845e31 + 5.76404e30i −1.21853 + 0.253704i
\(970\) 1.10930e31 0.482998
\(971\) 2.26047e31 0.973635 0.486818 0.873504i \(-0.338158\pi\)
0.486818 + 0.873504i \(0.338158\pi\)
\(972\) 5.61895e31 + 3.40215e31i 2.39420 + 1.44963i
\(973\) 6.12725e30 2.64724e30i 0.258274 0.111586i
\(974\) 3.86431e31i 1.61140i
\(975\) 1.43523e31 2.98822e30i 0.592071 0.123272i
\(976\) 1.09697e32i 4.47686i
\(977\) 7.72016e30i 0.311698i 0.987781 + 0.155849i \(0.0498113\pi\)
−0.987781 + 0.155849i \(0.950189\pi\)
\(978\) 1.25216e31 2.60706e30i 0.500152 0.104134i
\(979\) 8.82068e30i 0.348565i
\(980\) 1.02201e31 1.08578e31i 0.399559 0.424490i
\(981\) 2.50375e31 1.08982e31i 0.968424 0.421534i
\(982\) 5.76153e31 2.20479
\(983\) −4.61990e31 −1.74912 −0.874562 0.484913i \(-0.838851\pi\)
−0.874562 + 0.484913i \(0.838851\pi\)
\(984\) 4.08253e31 8.50002e30i 1.52926 0.318399i
\(985\) 6.76902e30i 0.250868i
\(986\) 1.61987e31 0.593981
\(987\) 3.26066e31 2.29399e31i 1.18298 0.832263i
\(988\) −3.67416e31 −1.31889
\(989\) 2.93006e31i 1.04068i
\(990\) −8.99501e30 + 3.91533e30i −0.316105 + 0.137594i
\(991\) −3.83808e31 −1.33457 −0.667283 0.744804i \(-0.732543\pi\)
−0.667283 + 0.744804i \(0.732543\pi\)
\(992\) −1.37800e32 −4.74106
\(993\) −6.98201e30 3.35344e31i −0.237691 1.14162i
\(994\) −1.23386e31 2.85587e31i −0.415633 0.962015i
\(995\) 1.12925e31i 0.376400i
\(996\) 5.39201e30 + 2.58977e31i 0.177839 + 0.854158i
\(997\) 4.67974e31i 1.52729i 0.645634 + 0.763647i \(0.276593\pi\)
−0.645634 + 0.763647i \(0.723407\pi\)
\(998\) 1.19735e30i 0.0386678i
\(999\) 1.04374e31 + 1.47502e31i 0.333545 + 0.471367i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 21.22.c.b.20.27 yes 52
3.2 odd 2 inner 21.22.c.b.20.26 yes 52
7.6 odd 2 inner 21.22.c.b.20.25 52
21.20 even 2 inner 21.22.c.b.20.28 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.22.c.b.20.25 52 7.6 odd 2 inner
21.22.c.b.20.26 yes 52 3.2 odd 2 inner
21.22.c.b.20.27 yes 52 1.1 even 1 trivial
21.22.c.b.20.28 yes 52 21.20 even 2 inner