Properties

Label 6.21.b.a.5.1
Level $6$
Weight $21$
Character 6.5
Analytic conductor $15.211$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6,21,Mod(5,6)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 21, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6.5");
 
S:= CuspForms(chi, 21);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 6.b (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: \(15.2108259062\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 3396x^{4} + 2813589x^{2} + 548136050 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{31}\cdot 3^{17} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(-29.2393i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.21.b.a.5.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-724.077i q^{2} +(-57693.2 + 12580.8i) q^{3} -524288. q^{4} +8.94833e6i q^{5} +(9.10944e6 + 4.17744e7i) q^{6} -3.40159e7 q^{7} +3.79625e8i q^{8} +(3.17023e9 - 1.45165e9i) q^{9} +O(q^{10})\) \(q-724.077i q^{2} +(-57693.2 + 12580.8i) q^{3} -524288. q^{4} +8.94833e6i q^{5} +(9.10944e6 + 4.17744e7i) q^{6} -3.40159e7 q^{7} +3.79625e8i q^{8} +(3.17023e9 - 1.45165e9i) q^{9} +6.47928e9 q^{10} -6.27231e9i q^{11} +(3.02479e10 - 6.59594e9i) q^{12} -1.12795e11 q^{13} +2.46301e10i q^{14} +(-1.12577e11 - 5.16258e11i) q^{15} +2.74878e11 q^{16} -3.26898e12i q^{17} +(-1.05111e12 - 2.29549e12i) q^{18} +8.13493e12 q^{19} -4.69150e12i q^{20} +(1.96249e12 - 4.27946e11i) q^{21} -4.54164e12 q^{22} -5.77587e13i q^{23} +(-4.77597e12 - 2.19018e13i) q^{24} +1.52949e13 q^{25} +8.16720e13i q^{26} +(-1.64638e14 + 1.23634e14i) q^{27} +1.78341e13 q^{28} +6.61014e14i q^{29} +(-3.73811e14 + 8.15143e13i) q^{30} +1.33200e15 q^{31} -1.99033e14i q^{32} +(7.89104e13 + 3.61870e14i) q^{33} -2.36699e15 q^{34} -3.04385e14i q^{35} +(-1.66212e15 + 7.61082e14i) q^{36} +1.65175e15 q^{37} -5.89032e15i q^{38} +(6.50748e15 - 1.41904e15i) q^{39} -3.39701e15 q^{40} -1.90964e16i q^{41} +(-3.09866e14 - 1.42099e15i) q^{42} +1.96411e16 q^{43} +3.28850e15i q^{44} +(1.29898e16 + 2.83683e16i) q^{45} -4.18218e16 q^{46} +2.59733e16i q^{47} +(-1.58586e16 + 3.45817e15i) q^{48} -7.86352e16 q^{49} -1.10747e16i q^{50} +(4.11262e16 + 1.88598e17i) q^{51} +5.91368e16 q^{52} -1.97975e17i q^{53} +(8.95208e16 + 1.19211e17i) q^{54} +5.61267e16 q^{55} -1.29133e16i q^{56} +(-4.69330e17 + 1.02344e17i) q^{57} +4.78626e17 q^{58} -7.73122e17i q^{59} +(5.90226e16 + 2.70668e17i) q^{60} -1.23592e17 q^{61} -9.64471e17i q^{62} +(-1.07838e17 + 4.93791e16i) q^{63} -1.44115e17 q^{64} -1.00932e18i q^{65} +(2.62022e17 - 5.71373e16i) q^{66} -3.35174e17 q^{67} +1.71389e18i q^{68} +(7.26649e17 + 3.33229e18i) q^{69} -2.20398e17 q^{70} +1.61150e18i q^{71} +(5.51083e17 + 1.20350e18i) q^{72} +3.68460e17 q^{73} -1.19599e18i q^{74} +(-8.82412e17 + 1.92421e17i) q^{75} -4.26505e18 q^{76} +2.13358e17i q^{77} +(-1.02750e18 - 4.71192e18i) q^{78} +2.03414e18 q^{79} +2.45970e18i q^{80} +(7.94309e18 - 9.20414e18i) q^{81} -1.38272e19 q^{82} +8.34509e18i q^{83} +(-1.02891e18 + 2.24367e17i) q^{84} +2.92519e19 q^{85} -1.42217e19i q^{86} +(-8.31607e18 - 3.81361e19i) q^{87} +2.38113e18 q^{88} +1.06627e19i q^{89} +(2.05408e19 - 9.40564e18i) q^{90} +3.83680e18 q^{91} +3.02822e19i q^{92} +(-7.68474e19 + 1.67576e19i) q^{93} +1.88066e19 q^{94} +7.27940e19i q^{95} +(2.50399e18 + 1.14828e19i) q^{96} -6.98216e19 q^{97} +5.69380e19i q^{98} +(-9.10520e18 - 1.98847e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + 5360984064 q^{10} - 9880731648 q^{12} - 49898545620 q^{13} + 487708151328 q^{15} + 1649267441664 q^{16} - 3239129751552 q^{18} + 15927597287292 q^{19} - 20677554127188 q^{21} + 21184189636608 q^{22} - 18380312543232 q^{24} + 337510512308454 q^{25} - 10\!\cdots\!62 q^{27}+ \cdots - 22\!\cdots\!32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 724.077i 0.707107i
\(3\) −57693.2 + 12580.8i −0.977040 + 0.213056i
\(4\) −524288. −0.500000
\(5\) 8.94833e6i 0.916309i 0.888873 + 0.458154i \(0.151489\pi\)
−0.888873 + 0.458154i \(0.848511\pi\)
\(6\) 9.10944e6 + 4.17744e7i 0.150654 + 0.690872i
\(7\) −3.40159e7 −0.120421 −0.0602103 0.998186i \(-0.519177\pi\)
−0.0602103 + 0.998186i \(0.519177\pi\)
\(8\) 3.79625e8i 0.353553i
\(9\) 3.17023e9 1.45165e9i 0.909214 0.416329i
\(10\) 6.47928e9 0.647928
\(11\) 6.27231e9i 0.241825i −0.992663 0.120912i \(-0.961418\pi\)
0.992663 0.120912i \(-0.0385820\pi\)
\(12\) 3.02479e10 6.59594e9i 0.488520 0.106528i
\(13\) −1.12795e11 −0.818191 −0.409095 0.912492i \(-0.634156\pi\)
−0.409095 + 0.912492i \(0.634156\pi\)
\(14\) 2.46301e10i 0.0851503i
\(15\) −1.12577e11 5.16258e11i −0.195225 0.895270i
\(16\) 2.74878e11 0.250000
\(17\) 3.26898e12i 1.62152i −0.585378 0.810761i \(-0.699054\pi\)
0.585378 0.810761i \(-0.300946\pi\)
\(18\) −1.05111e12 2.29549e12i −0.294389 0.642911i
\(19\) 8.13493e12 1.32684 0.663419 0.748248i \(-0.269105\pi\)
0.663419 + 0.748248i \(0.269105\pi\)
\(20\) 4.69150e12i 0.458154i
\(21\) 1.96249e12 4.27946e11i 0.117656 0.0256564i
\(22\) −4.54164e12 −0.170996
\(23\) 5.77587e13i 1.39425i −0.716952 0.697123i \(-0.754463\pi\)
0.716952 0.697123i \(-0.245537\pi\)
\(24\) −4.77597e12 2.19018e13i −0.0753268 0.345436i
\(25\) 1.52949e13 0.160379
\(26\) 8.16720e13i 0.578548i
\(27\) −1.64638e14 + 1.23634e14i −0.799637 + 0.600484i
\(28\) 1.78341e13 0.0602103
\(29\) 6.61014e14i 1.57120i 0.618736 + 0.785599i \(0.287645\pi\)
−0.618736 + 0.785599i \(0.712355\pi\)
\(30\) −3.73811e14 + 8.15143e13i −0.633052 + 0.138045i
\(31\) 1.33200e15 1.62513 0.812564 0.582873i \(-0.198071\pi\)
0.812564 + 0.582873i \(0.198071\pi\)
\(32\) 1.99033e14i 0.176777i
\(33\) 7.89104e13 + 3.61870e14i 0.0515223 + 0.236272i
\(34\) −2.36699e15 −1.14659
\(35\) 3.04385e14i 0.110343i
\(36\) −1.66212e15 + 7.61082e14i −0.454607 + 0.208165i
\(37\) 1.65175e15 0.343499 0.171750 0.985141i \(-0.445058\pi\)
0.171750 + 0.985141i \(0.445058\pi\)
\(38\) 5.89032e15i 0.938216i
\(39\) 6.50748e15 1.41904e15i 0.799405 0.174321i
\(40\) −3.39701e15 −0.323964
\(41\) 1.90964e16i 1.42270i −0.702840 0.711348i \(-0.748085\pi\)
0.702840 0.711348i \(-0.251915\pi\)
\(42\) −3.09866e14 1.42099e15i −0.0181418 0.0831952i
\(43\) 1.96411e16 0.908826 0.454413 0.890791i \(-0.349849\pi\)
0.454413 + 0.890791i \(0.349849\pi\)
\(44\) 3.28850e15i 0.120912i
\(45\) 1.29898e16 + 2.83683e16i 0.381486 + 0.833121i
\(46\) −4.18218e16 −0.985880
\(47\) 2.59733e16i 0.493796i 0.969041 + 0.246898i \(0.0794113\pi\)
−0.969041 + 0.246898i \(0.920589\pi\)
\(48\) −1.58586e16 + 3.45817e15i −0.244260 + 0.0532641i
\(49\) −7.86352e16 −0.985499
\(50\) 1.10747e16i 0.113405i
\(51\) 4.11262e16 + 1.88598e17i 0.345475 + 1.58429i
\(52\) 5.91368e16 0.409095
\(53\) 1.97975e17i 1.13201i −0.824400 0.566007i \(-0.808488\pi\)
0.824400 0.566007i \(-0.191512\pi\)
\(54\) 8.95208e16 + 1.19211e17i 0.424606 + 0.565429i
\(55\) 5.61267e16 0.221586
\(56\) 1.29133e16i 0.0425751i
\(57\) −4.69330e17 + 1.02344e17i −1.29637 + 0.282691i
\(58\) 4.78626e17 1.11100
\(59\) 7.73122e17i 1.51261i −0.654217 0.756307i \(-0.727002\pi\)
0.654217 0.756307i \(-0.272998\pi\)
\(60\) 5.90226e16 + 2.70668e17i 0.0976127 + 0.447635i
\(61\) −1.23592e17 −0.173258 −0.0866288 0.996241i \(-0.527609\pi\)
−0.0866288 + 0.996241i \(0.527609\pi\)
\(62\) 9.64471e17i 1.14914i
\(63\) −1.07838e17 + 4.93791e16i −0.109488 + 0.0501346i
\(64\) −1.44115e17 −0.125000
\(65\) 1.00932e18i 0.749715i
\(66\) 2.62022e17 5.71373e16i 0.167070 0.0364318i
\(67\) −3.35174e17 −0.183875 −0.0919373 0.995765i \(-0.529306\pi\)
−0.0919373 + 0.995765i \(0.529306\pi\)
\(68\) 1.71389e18i 0.810761i
\(69\) 7.26649e17 + 3.33229e18i 0.297053 + 1.36223i
\(70\) −2.20398e17 −0.0780239
\(71\) 1.61150e18i 0.495047i 0.968882 + 0.247524i \(0.0796167\pi\)
−0.968882 + 0.247524i \(0.920383\pi\)
\(72\) 5.51083e17 + 1.20350e18i 0.147195 + 0.321456i
\(73\) 3.68460e17 0.0857357 0.0428679 0.999081i \(-0.486351\pi\)
0.0428679 + 0.999081i \(0.486351\pi\)
\(74\) 1.19599e18i 0.242891i
\(75\) −8.82412e17 + 1.92421e17i −0.156696 + 0.0341697i
\(76\) −4.26505e18 −0.663419
\(77\) 2.13358e17i 0.0291207i
\(78\) −1.02750e18 4.71192e18i −0.123263 0.565265i
\(79\) 2.03414e18 0.214838 0.107419 0.994214i \(-0.465741\pi\)
0.107419 + 0.994214i \(0.465741\pi\)
\(80\) 2.45970e18i 0.229077i
\(81\) 7.94309e18 9.20414e18i 0.653340 0.757064i
\(82\) −1.38272e19 −1.00600
\(83\) 8.34509e18i 0.537836i 0.963163 + 0.268918i \(0.0866661\pi\)
−0.963163 + 0.268918i \(0.913334\pi\)
\(84\) −1.02891e18 + 2.24367e17i −0.0588279 + 0.0128282i
\(85\) 2.92519e19 1.48581
\(86\) 1.42217e19i 0.642637i
\(87\) −8.31607e18 3.81361e19i −0.334754 1.53512i
\(88\) 2.38113e18 0.0854979
\(89\) 1.06627e19i 0.341955i 0.985275 + 0.170977i \(0.0546925\pi\)
−0.985275 + 0.170977i \(0.945307\pi\)
\(90\) 2.05408e19 9.40564e18i 0.589105 0.269751i
\(91\) 3.83680e18 0.0985271
\(92\) 3.02822e19i 0.697123i
\(93\) −7.68474e19 + 1.67576e19i −1.58781 + 0.346244i
\(94\) 1.88066e19 0.349167
\(95\) 7.27940e19i 1.21579i
\(96\) 2.50399e18 + 1.14828e19i 0.0376634 + 0.172718i
\(97\) −6.98216e19 −0.946831 −0.473416 0.880839i \(-0.656979\pi\)
−0.473416 + 0.880839i \(0.656979\pi\)
\(98\) 5.69380e19i 0.696853i
\(99\) −9.10520e18 1.98847e19i −0.100679 0.219870i
\(100\) −8.01893e18 −0.0801893
\(101\) 2.06224e19i 0.186692i −0.995634 0.0933458i \(-0.970244\pi\)
0.995634 0.0933458i \(-0.0297562\pi\)
\(102\) 1.36559e20 2.97786e19i 1.12026 0.244288i
\(103\) 1.43042e20 1.06436 0.532182 0.846630i \(-0.321372\pi\)
0.532182 + 0.846630i \(0.321372\pi\)
\(104\) 4.28196e19i 0.289274i
\(105\) 3.82940e18 + 1.75610e19i 0.0235092 + 0.107809i
\(106\) −1.43349e20 −0.800455
\(107\) 5.16777e19i 0.262703i −0.991336 0.131352i \(-0.958068\pi\)
0.991336 0.131352i \(-0.0419317\pi\)
\(108\) 8.63178e19 6.48200e19i 0.399818 0.300242i
\(109\) −1.71463e20 −0.724280 −0.362140 0.932124i \(-0.617954\pi\)
−0.362140 + 0.932124i \(0.617954\pi\)
\(110\) 4.06401e19i 0.156685i
\(111\) −9.52945e19 + 2.07802e19i −0.335613 + 0.0731847i
\(112\) −9.35021e18 −0.0301052
\(113\) 5.90152e20i 1.73852i −0.494356 0.869260i \(-0.664596\pi\)
0.494356 0.869260i \(-0.335404\pi\)
\(114\) 7.41047e19 + 3.39831e20i 0.199893 + 0.916674i
\(115\) 5.16844e20 1.27756
\(116\) 3.46562e20i 0.785599i
\(117\) −3.57585e20 + 1.63738e20i −0.743911 + 0.340637i
\(118\) −5.59800e20 −1.06958
\(119\) 1.11197e20i 0.195265i
\(120\) 1.95984e20 4.27370e19i 0.316526 0.0690226i
\(121\) 6.33408e20 0.941521
\(122\) 8.94902e19i 0.122512i
\(123\) 2.40247e20 + 1.10173e21i 0.303114 + 1.39003i
\(124\) −6.98352e20 −0.812564
\(125\) 9.90243e20i 1.06326i
\(126\) 3.57543e19 + 7.80832e19i 0.0354505 + 0.0774198i
\(127\) 1.01666e21 0.931403 0.465701 0.884942i \(-0.345802\pi\)
0.465701 + 0.884942i \(0.345802\pi\)
\(128\) 1.04351e20i 0.0883883i
\(129\) −1.13316e21 + 2.47100e20i −0.887959 + 0.193631i
\(130\) −7.30828e20 −0.530129
\(131\) 1.29442e21i 0.869688i −0.900506 0.434844i \(-0.856804\pi\)
0.900506 0.434844i \(-0.143196\pi\)
\(132\) −4.13718e19 1.89724e20i −0.0257611 0.118136i
\(133\) −2.76717e20 −0.159779
\(134\) 2.42692e20i 0.130019i
\(135\) −1.10632e21 1.47324e21i −0.550229 0.732714i
\(136\) 1.24099e21 0.573294
\(137\) 1.30008e21i 0.558166i −0.960267 0.279083i \(-0.909970\pi\)
0.960267 0.279083i \(-0.0900304\pi\)
\(138\) 2.41283e21 5.26150e20i 0.963245 0.210048i
\(139\) 4.71307e20 0.175048 0.0875238 0.996162i \(-0.472105\pi\)
0.0875238 + 0.996162i \(0.472105\pi\)
\(140\) 1.59585e20i 0.0551713i
\(141\) −3.26763e20 1.49848e21i −0.105206 0.482459i
\(142\) 1.16685e21 0.350051
\(143\) 7.07483e20i 0.197859i
\(144\) 8.71427e20 3.99026e20i 0.227304 0.104082i
\(145\) −5.91497e21 −1.43970
\(146\) 2.66794e20i 0.0606243i
\(147\) 4.53672e21 9.89291e20i 0.962872 0.209967i
\(148\) −8.65990e20 −0.171750
\(149\) 5.11768e21i 0.948878i 0.880288 + 0.474439i \(0.157349\pi\)
−0.880288 + 0.474439i \(0.842651\pi\)
\(150\) 1.39328e20 + 6.38934e20i 0.0241616 + 0.110801i
\(151\) 4.26746e21 0.692469 0.346234 0.938148i \(-0.387460\pi\)
0.346234 + 0.938148i \(0.387460\pi\)
\(152\) 3.08822e21i 0.469108i
\(153\) −4.74541e21 1.03634e22i −0.675086 1.47431i
\(154\) 1.54488e20 0.0205914
\(155\) 1.19192e22i 1.48912i
\(156\) −3.41180e21 + 7.43987e20i −0.399703 + 0.0871604i
\(157\) −1.25544e22 −1.37975 −0.689874 0.723930i \(-0.742334\pi\)
−0.689874 + 0.723930i \(0.742334\pi\)
\(158\) 1.47288e21i 0.151913i
\(159\) 2.49068e21 + 1.14218e22i 0.241183 + 1.10602i
\(160\) 1.78101e21 0.161982
\(161\) 1.96471e21i 0.167896i
\(162\) −6.66451e21 5.75141e21i −0.535325 0.461981i
\(163\) 2.46622e22 1.86275 0.931376 0.364058i \(-0.118609\pi\)
0.931376 + 0.364058i \(0.118609\pi\)
\(164\) 1.00120e22i 0.711348i
\(165\) −3.23813e21 + 7.06116e20i −0.216498 + 0.0472103i
\(166\) 6.04249e21 0.380307
\(167\) 1.78096e22i 1.05558i −0.849376 0.527789i \(-0.823021\pi\)
0.849376 0.527789i \(-0.176979\pi\)
\(168\) 1.62459e20 + 7.45009e20i 0.00907090 + 0.0415976i
\(169\) −6.28235e21 −0.330564
\(170\) 2.11806e22i 1.05063i
\(171\) 2.57896e22 1.18091e22i 1.20638 0.552401i
\(172\) −1.02976e22 −0.454413
\(173\) 4.02033e22i 1.67417i −0.547069 0.837087i \(-0.684257\pi\)
0.547069 0.837087i \(-0.315743\pi\)
\(174\) −2.76135e22 + 6.02147e21i −1.08550 + 0.236707i
\(175\) −5.20269e20 −0.0193129
\(176\) 1.72412e21i 0.0604562i
\(177\) 9.72646e21 + 4.46039e22i 0.322272 + 1.47788i
\(178\) 7.72065e21 0.241799
\(179\) 1.83768e22i 0.544176i 0.962272 + 0.272088i \(0.0877141\pi\)
−0.962272 + 0.272088i \(0.912286\pi\)
\(180\) −6.81041e21 1.48731e22i −0.190743 0.416560i
\(181\) −3.72326e22 −0.986592 −0.493296 0.869862i \(-0.664208\pi\)
−0.493296 + 0.869862i \(0.664208\pi\)
\(182\) 2.77814e21i 0.0696692i
\(183\) 7.13043e21 1.55488e21i 0.169280 0.0369136i
\(184\) 2.19267e22 0.492940
\(185\) 1.47804e22i 0.314751i
\(186\) 1.21338e22 + 5.56435e22i 0.244831 + 1.12275i
\(187\) −2.05040e22 −0.392124
\(188\) 1.36175e22i 0.246898i
\(189\) 5.60031e21 4.20553e21i 0.0962928 0.0723107i
\(190\) 5.27085e22 0.859695
\(191\) 9.66181e21i 0.149529i −0.997201 0.0747644i \(-0.976180\pi\)
0.997201 0.0747644i \(-0.0238205\pi\)
\(192\) 8.31447e21 1.81308e21i 0.122130 0.0266320i
\(193\) −4.32416e22 −0.603016 −0.301508 0.953464i \(-0.597490\pi\)
−0.301508 + 0.953464i \(0.597490\pi\)
\(194\) 5.05563e22i 0.669511i
\(195\) 1.26980e22 + 5.82311e22i 0.159732 + 0.732502i
\(196\) 4.12275e22 0.492749
\(197\) 2.07513e22i 0.235713i −0.993031 0.117856i \(-0.962398\pi\)
0.993031 0.117856i \(-0.0376022\pi\)
\(198\) −1.43981e22 + 6.59287e21i −0.155472 + 0.0711906i
\(199\) −1.69741e23 −1.74283 −0.871415 0.490547i \(-0.836797\pi\)
−0.871415 + 0.490547i \(0.836797\pi\)
\(200\) 5.80632e21i 0.0567024i
\(201\) 1.93373e22 4.21674e21i 0.179653 0.0391757i
\(202\) −1.49322e22 −0.132011
\(203\) 2.24850e22i 0.189205i
\(204\) −2.15620e22 9.88796e22i −0.172738 0.792146i
\(205\) 1.70880e23 1.30363
\(206\) 1.03573e23i 0.752618i
\(207\) −8.38454e22 1.83109e23i −0.580465 1.26767i
\(208\) −3.10047e22 −0.204548
\(209\) 5.10248e22i 0.320862i
\(210\) 1.27155e22 2.77278e21i 0.0762325 0.0166235i
\(211\) 3.30449e23 1.88921 0.944605 0.328210i \(-0.106445\pi\)
0.944605 + 0.328210i \(0.106445\pi\)
\(212\) 1.03796e23i 0.566007i
\(213\) −2.02739e22 9.29726e22i −0.105473 0.483681i
\(214\) −3.74186e22 −0.185759
\(215\) 1.75755e23i 0.832765i
\(216\) −4.69347e22 6.25008e22i −0.212303 0.282714i
\(217\) −4.53091e22 −0.195699
\(218\) 1.24153e23i 0.512143i
\(219\) −2.12577e22 + 4.63551e21i −0.0837672 + 0.0182665i
\(220\) −2.94265e22 −0.110793
\(221\) 3.68723e23i 1.32671i
\(222\) 1.50465e22 + 6.90006e22i 0.0517494 + 0.237314i
\(223\) −2.13081e23 −0.700640 −0.350320 0.936630i \(-0.613927\pi\)
−0.350320 + 0.936630i \(0.613927\pi\)
\(224\) 6.77028e21i 0.0212876i
\(225\) 4.84884e22 2.22028e22i 0.145818 0.0667703i
\(226\) −4.27316e23 −1.22932
\(227\) 1.26750e23i 0.348889i 0.984667 + 0.174445i \(0.0558130\pi\)
−0.984667 + 0.174445i \(0.944187\pi\)
\(228\) 2.46064e23 5.36575e22i 0.648187 0.141346i
\(229\) 3.25585e23 0.820936 0.410468 0.911875i \(-0.365365\pi\)
0.410468 + 0.911875i \(0.365365\pi\)
\(230\) 3.74235e23i 0.903371i
\(231\) −2.68421e21 1.23093e22i −0.00620435 0.0284521i
\(232\) −2.50938e23 −0.555502
\(233\) 2.33845e23i 0.495872i 0.968776 + 0.247936i \(0.0797523\pi\)
−0.968776 + 0.247936i \(0.920248\pi\)
\(234\) 1.18559e23 + 2.58919e23i 0.240866 + 0.526024i
\(235\) −2.32417e23 −0.452470
\(236\) 4.05339e23i 0.756307i
\(237\) −1.17356e23 + 2.55911e22i −0.209905 + 0.0457725i
\(238\) 8.05153e22 0.138073
\(239\) 8.68378e23i 1.42801i −0.700143 0.714003i \(-0.746880\pi\)
0.700143 0.714003i \(-0.253120\pi\)
\(240\) −3.09449e22 1.41908e23i −0.0488063 0.223818i
\(241\) 1.05378e24 1.59433 0.797167 0.603759i \(-0.206331\pi\)
0.797167 + 0.603759i \(0.206331\pi\)
\(242\) 4.58636e23i 0.665756i
\(243\) −3.42468e23 + 6.30946e23i −0.477042 + 0.878880i
\(244\) 6.47978e22 0.0866288
\(245\) 7.03653e23i 0.903021i
\(246\) 7.97738e23 1.73957e23i 0.982900 0.214334i
\(247\) −9.17576e23 −1.08561
\(248\) 5.05661e23i 0.574569i
\(249\) −1.04988e23 4.81455e23i −0.114589 0.525487i
\(250\) 7.17012e23 0.751842
\(251\) 9.08149e23i 0.914998i −0.889210 0.457499i \(-0.848745\pi\)
0.889210 0.457499i \(-0.151255\pi\)
\(252\) 5.65383e22 2.58889e22i 0.0547441 0.0250673i
\(253\) −3.62281e23 −0.337163
\(254\) 7.36139e23i 0.658601i
\(255\) −1.68764e24 + 3.68011e23i −1.45170 + 0.316562i
\(256\) 7.55579e22 0.0625000
\(257\) 3.56336e23i 0.283484i −0.989904 0.141742i \(-0.954730\pi\)
0.989904 0.141742i \(-0.0452703\pi\)
\(258\) 1.78919e23 + 8.20494e23i 0.136918 + 0.627882i
\(259\) −5.61856e22 −0.0413644
\(260\) 5.29176e23i 0.374858i
\(261\) 9.59561e23 + 2.09557e24i 0.654135 + 1.42856i
\(262\) −9.37262e23 −0.614962
\(263\) 1.05160e24i 0.664188i 0.943246 + 0.332094i \(0.107755\pi\)
−0.943246 + 0.332094i \(0.892245\pi\)
\(264\) −1.37375e23 + 2.99564e22i −0.0835349 + 0.0182159i
\(265\) 1.77155e24 1.03727
\(266\) 2.00364e23i 0.112981i
\(267\) −1.34145e23 6.15168e23i −0.0728556 0.334104i
\(268\) 1.75728e23 0.0919373
\(269\) 1.96187e24i 0.988888i 0.869209 + 0.494444i \(0.164628\pi\)
−0.869209 + 0.494444i \(0.835372\pi\)
\(270\) −1.06674e24 + 8.01061e23i −0.518107 + 0.389070i
\(271\) 2.44812e22 0.0114588 0.00572940 0.999984i \(-0.498176\pi\)
0.00572940 + 0.999984i \(0.498176\pi\)
\(272\) 8.98570e23i 0.405380i
\(273\) −2.21358e23 + 4.82699e22i −0.0962649 + 0.0209918i
\(274\) −9.41356e23 −0.394683
\(275\) 9.59343e22i 0.0387835i
\(276\) −3.80973e23 1.74708e24i −0.148526 0.681117i
\(277\) 1.05647e24 0.397247 0.198623 0.980076i \(-0.436353\pi\)
0.198623 + 0.980076i \(0.436353\pi\)
\(278\) 3.41263e23i 0.123777i
\(279\) 4.22275e24 1.93360e24i 1.47759 0.676588i
\(280\) 1.15552e23 0.0390120
\(281\) 2.00543e23i 0.0653347i −0.999466 0.0326674i \(-0.989600\pi\)
0.999466 0.0326674i \(-0.0104002\pi\)
\(282\) −1.08502e24 + 2.36602e23i −0.341150 + 0.0743922i
\(283\) −2.42419e24 −0.735702 −0.367851 0.929885i \(-0.619906\pi\)
−0.367851 + 0.929885i \(0.619906\pi\)
\(284\) 8.44889e23i 0.247524i
\(285\) −9.15804e23 4.19972e24i −0.259032 1.18788i
\(286\) 5.12272e23 0.139907
\(287\) 6.49579e23i 0.171322i
\(288\) −2.88926e23 6.30981e23i −0.0735973 0.160728i
\(289\) −6.62198e24 −1.62933
\(290\) 4.28290e24i 1.01802i
\(291\) 4.02823e24 8.78409e23i 0.925092 0.201728i
\(292\) −1.93179e23 −0.0428679
\(293\) 2.70956e24i 0.581061i −0.956866 0.290531i \(-0.906168\pi\)
0.956866 0.290531i \(-0.0938319\pi\)
\(294\) −7.16323e23 3.28493e24i −0.148469 0.680853i
\(295\) 6.91815e24 1.38602
\(296\) 6.27044e23i 0.121445i
\(297\) 7.75473e23 + 1.03266e24i 0.145212 + 0.193372i
\(298\) 3.70559e24 0.670958
\(299\) 6.51487e24i 1.14076i
\(300\) 4.62638e23 1.00884e23i 0.0783481 0.0170848i
\(301\) −6.68108e23 −0.109441
\(302\) 3.08997e24i 0.489649i
\(303\) 2.59445e23 + 1.18977e24i 0.0397758 + 0.182405i
\(304\) 2.23611e24 0.331709
\(305\) 1.10594e24i 0.158757i
\(306\) −7.50392e24 + 3.43604e24i −1.04249 + 0.477358i
\(307\) −4.68021e24 −0.629334 −0.314667 0.949202i \(-0.601893\pi\)
−0.314667 + 0.949202i \(0.601893\pi\)
\(308\) 1.11861e23i 0.0145603i
\(309\) −8.25253e24 + 1.79957e24i −1.03993 + 0.226769i
\(310\) 8.63040e24 1.05297
\(311\) 1.01483e25i 1.19892i 0.800406 + 0.599458i \(0.204617\pi\)
−0.800406 + 0.599458i \(0.795383\pi\)
\(312\) 5.38704e23 + 2.47040e24i 0.0616317 + 0.282632i
\(313\) −1.15960e25 −1.28489 −0.642443 0.766334i \(-0.722079\pi\)
−0.642443 + 0.766334i \(0.722079\pi\)
\(314\) 9.09036e24i 0.975629i
\(315\) −4.41860e23 9.64972e23i −0.0459388 0.100325i
\(316\) −1.06648e24 −0.107419
\(317\) 1.95397e24i 0.190688i −0.995444 0.0953442i \(-0.969605\pi\)
0.995444 0.0953442i \(-0.0303952\pi\)
\(318\) 8.27028e24 1.80344e24i 0.782076 0.170542i
\(319\) 4.14609e24 0.379955
\(320\) 1.28959e24i 0.114539i
\(321\) 6.50145e23 + 2.98145e24i 0.0559706 + 0.256671i
\(322\) 1.42260e24 0.118720
\(323\) 2.65929e25i 2.15150i
\(324\) −4.16447e24 + 4.82562e24i −0.326670 + 0.378532i
\(325\) −1.72518e24 −0.131220
\(326\) 1.78573e25i 1.31717i
\(327\) 9.89227e24 2.15714e24i 0.707650 0.154312i
\(328\) 7.24946e24 0.502999
\(329\) 8.83503e23i 0.0594633i
\(330\) 5.11283e23 + 2.34466e24i 0.0333827 + 0.153088i
\(331\) 3.47626e23 0.0220207 0.0110104 0.999939i \(-0.496495\pi\)
0.0110104 + 0.999939i \(0.496495\pi\)
\(332\) 4.37523e24i 0.268918i
\(333\) 5.23642e24 2.39776e24i 0.312314 0.143009i
\(334\) −1.28955e25 −0.746406
\(335\) 2.99924e24i 0.168486i
\(336\) 5.39444e23 1.17633e23i 0.0294140 0.00641410i
\(337\) 2.00958e25 1.06367 0.531835 0.846848i \(-0.321503\pi\)
0.531835 + 0.846848i \(0.321503\pi\)
\(338\) 4.54891e24i 0.233744i
\(339\) 7.42456e24 + 3.40478e25i 0.370403 + 1.69860i
\(340\) −1.53364e25 −0.742907
\(341\) 8.35472e24i 0.392996i
\(342\) −8.55068e24 1.86737e25i −0.390607 0.853039i
\(343\) 5.38905e24 0.239095
\(344\) 7.45625e24i 0.321319i
\(345\) −2.98184e25 + 6.50229e24i −1.24823 + 0.272192i
\(346\) −2.91103e25 −1.18382
\(347\) 1.98604e25i 0.784682i −0.919820 0.392341i \(-0.871665\pi\)
0.919820 0.392341i \(-0.128335\pi\)
\(348\) 4.36001e24 + 1.99943e25i 0.167377 + 0.767562i
\(349\) 6.39167e24 0.238430 0.119215 0.992868i \(-0.461962\pi\)
0.119215 + 0.992868i \(0.461962\pi\)
\(350\) 3.76715e23i 0.0136563i
\(351\) 1.85703e25 1.39453e25i 0.654256 0.491310i
\(352\) −1.24840e24 −0.0427490
\(353\) 3.71258e25i 1.23574i 0.786279 + 0.617872i \(0.212005\pi\)
−0.786279 + 0.617872i \(0.787995\pi\)
\(354\) 3.22967e25 7.04271e24i 1.04502 0.227881i
\(355\) −1.44202e25 −0.453616
\(356\) 5.59035e24i 0.170977i
\(357\) −1.39894e24 6.41532e24i −0.0416024 0.190781i
\(358\) 1.33062e25 0.384790
\(359\) 5.59063e25i 1.57223i 0.618080 + 0.786115i \(0.287911\pi\)
−0.618080 + 0.786115i \(0.712089\pi\)
\(360\) −1.07693e25 + 4.93127e24i −0.294553 + 0.134876i
\(361\) 2.85871e25 0.760498
\(362\) 2.69593e25i 0.697626i
\(363\) −3.65434e25 + 7.96876e24i −0.919903 + 0.200597i
\(364\) −2.01159e24 −0.0492636
\(365\) 3.29710e24i 0.0785604i
\(366\) −1.12586e24 5.16298e24i −0.0261019 0.119699i
\(367\) 1.51052e24 0.0340774 0.0170387 0.999855i \(-0.494576\pi\)
0.0170387 + 0.999855i \(0.494576\pi\)
\(368\) 1.58766e25i 0.348561i
\(369\) −2.77212e25 6.05399e25i −0.592309 1.29353i
\(370\) 1.07021e25 0.222563
\(371\) 6.73429e24i 0.136318i
\(372\) 4.02902e25 8.78580e24i 0.793907 0.173122i
\(373\) 1.98247e25 0.380293 0.190146 0.981756i \(-0.439104\pi\)
0.190146 + 0.981756i \(0.439104\pi\)
\(374\) 1.48465e25i 0.277273i
\(375\) −1.24580e25 5.71303e25i −0.226535 1.03885i
\(376\) −9.86010e24 −0.174583
\(377\) 7.45588e25i 1.28554i
\(378\) −3.04513e24 4.05506e24i −0.0511314 0.0680893i
\(379\) 2.76776e25 0.452622 0.226311 0.974055i \(-0.427333\pi\)
0.226311 + 0.974055i \(0.427333\pi\)
\(380\) 3.81650e25i 0.607896i
\(381\) −5.86543e25 + 1.27903e25i −0.910018 + 0.198441i
\(382\) −6.99590e24 −0.105733
\(383\) 2.45606e25i 0.361620i −0.983518 0.180810i \(-0.942128\pi\)
0.983518 0.180810i \(-0.0578718\pi\)
\(384\) −1.31281e24 6.02032e24i −0.0188317 0.0863589i
\(385\) −1.90920e24 −0.0266835
\(386\) 3.13103e25i 0.426397i
\(387\) 6.22668e25 2.85120e25i 0.826317 0.378371i
\(388\) 3.66066e25 0.473416
\(389\) 1.14023e26i 1.43713i 0.695461 + 0.718564i \(0.255200\pi\)
−0.695461 + 0.718564i \(0.744800\pi\)
\(390\) 4.21638e25 9.19437e24i 0.517957 0.112947i
\(391\) −1.88812e26 −2.26080
\(392\) 2.98519e25i 0.348426i
\(393\) 1.62848e25 + 7.46794e25i 0.185292 + 0.849719i
\(394\) −1.50255e25 −0.166674
\(395\) 1.82022e25i 0.196858i
\(396\) 4.77375e24 + 1.04253e25i 0.0503393 + 0.109935i
\(397\) 1.65157e26 1.69822 0.849108 0.528219i \(-0.177140\pi\)
0.849108 + 0.528219i \(0.177140\pi\)
\(398\) 1.22905e26i 1.23237i
\(399\) 1.59647e25 3.48131e24i 0.156110 0.0340419i
\(400\) 4.20423e24 0.0400946
\(401\) 4.85521e25i 0.451611i −0.974172 0.225805i \(-0.927499\pi\)
0.974172 0.225805i \(-0.0725014\pi\)
\(402\) −3.05325e24 1.40017e25i −0.0277014 0.127034i
\(403\) −1.50242e26 −1.32966
\(404\) 1.08121e25i 0.0933458i
\(405\) 8.23616e25 + 7.10774e25i 0.693705 + 0.598661i
\(406\) −1.62809e25 −0.133788
\(407\) 1.03603e25i 0.0830666i
\(408\) −7.15965e25 + 1.56125e25i −0.560131 + 0.122144i
\(409\) 1.02044e26 0.779032 0.389516 0.921020i \(-0.372642\pi\)
0.389516 + 0.921020i \(0.372642\pi\)
\(410\) 1.23731e26i 0.921804i
\(411\) 1.63560e25 + 7.50056e25i 0.118921 + 0.545350i
\(412\) −7.49949e25 −0.532182
\(413\) 2.62984e25i 0.182150i
\(414\) −1.32585e26 + 6.07106e25i −0.896376 + 0.410451i
\(415\) −7.46745e25 −0.492824
\(416\) 2.24498e25i 0.144637i
\(417\) −2.71912e25 + 5.92941e24i −0.171029 + 0.0372950i
\(418\) −3.69459e25 −0.226884
\(419\) 1.36478e26i 0.818320i −0.912463 0.409160i \(-0.865822\pi\)
0.912463 0.409160i \(-0.134178\pi\)
\(420\) −2.00771e24 9.20700e24i −0.0117546 0.0539045i
\(421\) 2.27236e26 1.29914 0.649572 0.760300i \(-0.274948\pi\)
0.649572 + 0.760300i \(0.274948\pi\)
\(422\) 2.39271e26i 1.33587i
\(423\) 3.77041e25 + 8.23413e25i 0.205582 + 0.448966i
\(424\) 7.51563e25 0.400227
\(425\) 4.99987e25i 0.260057i
\(426\) −6.73193e25 + 1.46799e25i −0.342014 + 0.0745806i
\(427\) 4.20409e24 0.0208638
\(428\) 2.70940e25i 0.131352i
\(429\) −8.90067e24 4.08170e25i −0.0421551 0.193316i
\(430\) 1.27260e26 0.588854
\(431\) 1.13707e26i 0.514062i −0.966403 0.257031i \(-0.917256\pi\)
0.966403 0.257031i \(-0.0827443\pi\)
\(432\) −4.52554e25 + 3.39843e25i −0.199909 + 0.150121i
\(433\) 8.08804e24 0.0349112 0.0174556 0.999848i \(-0.494443\pi\)
0.0174556 + 0.999848i \(0.494443\pi\)
\(434\) 3.28073e25i 0.138380i
\(435\) 3.41254e26 7.44149e25i 1.40665 0.306738i
\(436\) 8.98962e25 0.362140
\(437\) 4.69863e26i 1.84994i
\(438\) 3.35647e24 + 1.53922e25i 0.0129164 + 0.0592324i
\(439\) −4.09891e26 −1.54178 −0.770892 0.636966i \(-0.780189\pi\)
−0.770892 + 0.636966i \(0.780189\pi\)
\(440\) 2.13071e25i 0.0783425i
\(441\) −2.49292e26 + 1.14151e26i −0.896029 + 0.410292i
\(442\) 2.66984e26 0.938129
\(443\) 4.13953e26i 1.42205i 0.703168 + 0.711024i \(0.251768\pi\)
−0.703168 + 0.711024i \(0.748232\pi\)
\(444\) 4.99618e25 1.08948e25i 0.167806 0.0365924i
\(445\) −9.54137e25 −0.313336
\(446\) 1.54287e26i 0.495427i
\(447\) −6.43843e25 2.95255e26i −0.202164 0.927091i
\(448\) 4.90220e24 0.0150526
\(449\) 4.87243e26i 1.46313i 0.681774 + 0.731563i \(0.261209\pi\)
−0.681774 + 0.731563i \(0.738791\pi\)
\(450\) −1.60766e25 3.51093e25i −0.0472137 0.103109i
\(451\) −1.19778e26 −0.344043
\(452\) 3.09410e26i 0.869260i
\(453\) −2.46204e26 + 5.36879e25i −0.676570 + 0.147535i
\(454\) 9.17765e25 0.246702
\(455\) 3.43330e25i 0.0902812i
\(456\) −3.88522e25 1.78170e26i −0.0999464 0.458337i
\(457\) −3.83152e26 −0.964293 −0.482146 0.876091i \(-0.660143\pi\)
−0.482146 + 0.876091i \(0.660143\pi\)
\(458\) 2.35749e26i 0.580490i
\(459\) 4.04158e26 + 5.38198e26i 0.973697 + 1.29663i
\(460\) −2.70975e26 −0.638780
\(461\) 6.01682e26i 1.38790i 0.720024 + 0.693949i \(0.244131\pi\)
−0.720024 + 0.693949i \(0.755869\pi\)
\(462\) −8.91290e24 + 1.94357e24i −0.0201187 + 0.00438714i
\(463\) 3.27432e26 0.723287 0.361644 0.932316i \(-0.382216\pi\)
0.361644 + 0.932316i \(0.382216\pi\)
\(464\) 1.81698e26i 0.392800i
\(465\) −1.49952e26 6.87656e26i −0.317266 1.45493i
\(466\) 1.69322e26 0.350635
\(467\) 7.17003e26i 1.45329i −0.687013 0.726645i \(-0.741078\pi\)
0.687013 0.726645i \(-0.258922\pi\)
\(468\) 1.87478e26 8.58460e25i 0.371955 0.170318i
\(469\) 1.14012e25 0.0221423
\(470\) 1.68288e26i 0.319944i
\(471\) 7.24304e26 1.57944e26i 1.34807 0.293964i
\(472\) 2.93497e26 0.534790
\(473\) 1.23195e26i 0.219777i
\(474\) 1.85299e25 + 8.49750e25i 0.0323661 + 0.148425i
\(475\) 1.24423e26 0.212796
\(476\) 5.82993e25i 0.0976324i
\(477\) −2.87390e26 6.27627e26i −0.471290 1.02924i
\(478\) −6.28773e26 −1.00975
\(479\) 9.67519e26i 1.52161i 0.648978 + 0.760807i \(0.275197\pi\)
−0.648978 + 0.760807i \(0.724803\pi\)
\(480\) −1.02752e26 + 2.24065e25i −0.158263 + 0.0345113i
\(481\) −1.86308e26 −0.281048
\(482\) 7.63018e26i 1.12736i
\(483\) −2.47176e25 1.13351e26i −0.0357713 0.164041i
\(484\) −3.32088e26 −0.470760
\(485\) 6.24787e26i 0.867590i
\(486\) 4.56854e26 + 2.47973e26i 0.621462 + 0.337320i
\(487\) 1.81474e26 0.241838 0.120919 0.992662i \(-0.461416\pi\)
0.120919 + 0.992662i \(0.461416\pi\)
\(488\) 4.69186e25i 0.0612558i
\(489\) −1.42284e27 + 3.10269e26i −1.81998 + 0.396871i
\(490\) −5.09499e26 −0.638532
\(491\) 2.54099e26i 0.312024i −0.987755 0.156012i \(-0.950136\pi\)
0.987755 0.156012i \(-0.0498639\pi\)
\(492\) −1.25958e26 5.77624e26i −0.151557 0.695015i
\(493\) 2.16084e27 2.54773
\(494\) 6.64396e26i 0.767640i
\(495\) 1.77935e26 8.14763e25i 0.201469 0.0922527i
\(496\) 3.66137e26 0.406282
\(497\) 5.48165e25i 0.0596139i
\(498\) −3.48611e26 + 7.60191e25i −0.371576 + 0.0810269i
\(499\) 1.56657e25 0.0163661 0.00818306 0.999967i \(-0.497395\pi\)
0.00818306 + 0.999967i \(0.497395\pi\)
\(500\) 5.19172e26i 0.531632i
\(501\) 2.24059e26 + 1.02749e27i 0.224897 + 1.03134i
\(502\) −6.57570e26 −0.647001
\(503\) 1.98270e25i 0.0191240i 0.999954 + 0.00956198i \(0.00304372\pi\)
−0.999954 + 0.00956198i \(0.996956\pi\)
\(504\) −1.87456e25 4.09381e25i −0.0177253 0.0387099i
\(505\) 1.84536e26 0.171067
\(506\) 2.62319e26i 0.238410i
\(507\) 3.62449e26 7.90367e25i 0.322974 0.0704287i
\(508\) −5.33021e26 −0.465701
\(509\) 5.01291e26i 0.429450i 0.976675 + 0.214725i \(0.0688855\pi\)
−0.976675 + 0.214725i \(0.931115\pi\)
\(510\) 2.66468e26 + 1.22198e27i 0.223843 + 1.02651i
\(511\) −1.25335e25 −0.0103244
\(512\) 5.47097e25i 0.0441942i
\(513\) −1.33932e27 + 1.00576e27i −1.06099 + 0.796745i
\(514\) −2.58014e26 −0.200453
\(515\) 1.27998e27i 0.975285i
\(516\) 5.94101e26 1.29551e26i 0.443980 0.0968156i
\(517\) 1.62912e26 0.119412
\(518\) 4.06827e25i 0.0292491i
\(519\) 5.05788e26 + 2.31946e27i 0.356693 + 1.63574i
\(520\) 3.83164e26 0.265064
\(521\) 2.48658e27i 1.68743i −0.536792 0.843714i \(-0.680364\pi\)
0.536792 0.843714i \(-0.319636\pi\)
\(522\) 1.51735e27 6.94797e26i 1.01014 0.462544i
\(523\) −2.14559e27 −1.40130 −0.700649 0.713506i \(-0.747106\pi\)
−0.700649 + 0.713506i \(0.747106\pi\)
\(524\) 6.78650e26i 0.434844i
\(525\) 3.00160e25 6.54538e24i 0.0188695 0.00411474i
\(526\) 7.61437e26 0.469652
\(527\) 4.35428e27i 2.63518i
\(528\) 2.16907e25 + 9.94700e25i 0.0128806 + 0.0590681i
\(529\) −1.61991e27 −0.943921
\(530\) 1.28274e27i 0.733464i
\(531\) −1.12230e27 2.45098e27i −0.629745 1.37529i
\(532\) 1.45079e26 0.0798894
\(533\) 2.15397e27i 1.16404i
\(534\) −4.45429e26 + 9.71316e25i −0.236247 + 0.0515167i
\(535\) 4.62429e26 0.240717
\(536\) 1.27240e26i 0.0650095i
\(537\) −2.31194e26 1.06022e27i −0.115940 0.531681i
\(538\) 1.42055e27 0.699250
\(539\) 4.93224e26i 0.238318i
\(540\) 5.80030e26 + 7.72400e26i 0.275114 + 0.366357i
\(541\) 1.38669e27 0.645666 0.322833 0.946456i \(-0.395365\pi\)
0.322833 + 0.946456i \(0.395365\pi\)
\(542\) 1.77263e25i 0.00810259i
\(543\) 2.14807e27 4.68414e26i 0.963940 0.210200i
\(544\) −6.50634e26 −0.286647
\(545\) 1.53431e27i 0.663664i
\(546\) 3.49512e25 + 1.60280e26i 0.0148435 + 0.0680696i
\(547\) 4.53095e26 0.188936 0.0944682 0.995528i \(-0.469885\pi\)
0.0944682 + 0.995528i \(0.469885\pi\)
\(548\) 6.81615e26i 0.279083i
\(549\) −3.91816e26 + 1.79412e26i −0.157528 + 0.0721322i
\(550\) −6.94639e25 −0.0274241
\(551\) 5.37731e27i 2.08472i
\(552\) −1.26502e27 + 2.75854e26i −0.481622 + 0.105024i
\(553\) −6.91931e25 −0.0258709
\(554\) 7.64967e26i 0.280896i
\(555\) −1.85948e26 8.52727e26i −0.0670598 0.307525i
\(556\) −2.47101e26 −0.0875238
\(557\) 6.94941e26i 0.241767i −0.992667 0.120883i \(-0.961427\pi\)
0.992667 0.120883i \(-0.0385727\pi\)
\(558\) −1.40007e27 3.05760e27i −0.478420 1.04481i
\(559\) −2.21541e27 −0.743593
\(560\) 8.36687e25i 0.0275856i
\(561\) 1.18294e27 2.57956e26i 0.383121 0.0835445i
\(562\) −1.45209e26 −0.0461986
\(563\) 1.02406e27i 0.320067i 0.987112 + 0.160033i \(0.0511602\pi\)
−0.987112 + 0.160033i \(0.948840\pi\)
\(564\) 1.71318e26 + 7.85636e26i 0.0526032 + 0.241229i
\(565\) 5.28087e27 1.59302
\(566\) 1.75530e27i 0.520220i
\(567\) −2.70191e26 + 3.13087e26i −0.0786757 + 0.0911662i
\(568\) −6.11765e26 −0.175026
\(569\) 5.02276e27i 1.41195i 0.708236 + 0.705975i \(0.249491\pi\)
−0.708236 + 0.705975i \(0.750509\pi\)
\(570\) −3.04092e27 + 6.63113e26i −0.839957 + 0.183163i
\(571\) −4.72620e27 −1.28278 −0.641388 0.767217i \(-0.721641\pi\)
−0.641388 + 0.767217i \(0.721641\pi\)
\(572\) 3.70925e26i 0.0989294i
\(573\) 1.21553e26 + 5.57421e26i 0.0318580 + 0.146096i
\(574\) 4.70345e26 0.121143
\(575\) 8.83414e26i 0.223607i
\(576\) −4.56879e26 + 2.09205e26i −0.113652 + 0.0520411i
\(577\) −1.59165e27 −0.389125 −0.194562 0.980890i \(-0.562329\pi\)
−0.194562 + 0.980890i \(0.562329\pi\)
\(578\) 4.79483e27i 1.15211i
\(579\) 2.49475e27 5.44013e26i 0.589171 0.128476i
\(580\) 3.10115e27 0.719851
\(581\) 2.83865e26i 0.0647666i
\(582\) −6.36036e26 2.91675e27i −0.142643 0.654139i
\(583\) −1.24176e27 −0.273749
\(584\) 1.39877e26i 0.0303122i
\(585\) −1.46518e27 3.19979e27i −0.312128 0.681652i
\(586\) −1.96193e27 −0.410873
\(587\) 5.36082e26i 0.110370i −0.998476 0.0551849i \(-0.982425\pi\)
0.998476 0.0551849i \(-0.0175748\pi\)
\(588\) −2.37855e27 + 5.18673e26i −0.481436 + 0.104983i
\(589\) 1.08357e28 2.15628
\(590\) 5.00927e27i 0.980065i
\(591\) 2.61067e26 + 1.19721e27i 0.0502201 + 0.230301i
\(592\) 4.54028e26 0.0858748
\(593\) 1.93679e26i 0.0360194i −0.999838 0.0180097i \(-0.994267\pi\)
0.999838 0.0180097i \(-0.00573298\pi\)
\(594\) 7.47727e26 5.61502e26i 0.136735 0.102680i
\(595\) −9.95028e26 −0.178923
\(596\) 2.68314e27i 0.474439i
\(597\) 9.79288e27 2.13547e27i 1.70281 0.371321i
\(598\) 4.71727e27 0.806638
\(599\) 1.09596e28i 1.84300i −0.388377 0.921501i \(-0.626964\pi\)
0.388377 0.921501i \(-0.373036\pi\)
\(600\) −7.30480e25 3.34986e26i −0.0120808 0.0554005i
\(601\) −1.07060e28 −1.74134 −0.870668 0.491871i \(-0.836313\pi\)
−0.870668 + 0.491871i \(0.836313\pi\)
\(602\) 4.83762e26i 0.0773868i
\(603\) −1.06258e27 + 4.86555e26i −0.167181 + 0.0765524i
\(604\) −2.23738e27 −0.346234
\(605\) 5.66794e27i 0.862724i
\(606\) 8.61486e26 1.87858e26i 0.128980 0.0281258i
\(607\) −7.53237e27 −1.10929 −0.554644 0.832088i \(-0.687146\pi\)
−0.554644 + 0.832088i \(0.687146\pi\)
\(608\) 1.61912e27i 0.234554i
\(609\) 2.82878e26 + 1.29723e27i 0.0403113 + 0.184861i
\(610\) −8.00788e26 −0.112258
\(611\) 2.92964e27i 0.404020i
\(612\) 2.48796e27 + 5.43342e27i 0.337543 + 0.737155i
\(613\) −9.64517e26 −0.128738 −0.0643688 0.997926i \(-0.520503\pi\)
−0.0643688 + 0.997926i \(0.520503\pi\)
\(614\) 3.38883e27i 0.445007i
\(615\) −9.85864e27 + 2.14981e27i −1.27370 + 0.277746i
\(616\) −8.09961e25 −0.0102957
\(617\) 1.68600e27i 0.210865i −0.994426 0.105433i \(-0.966377\pi\)
0.994426 0.105433i \(-0.0336228\pi\)
\(618\) 1.30303e27 + 5.97547e27i 0.160350 + 0.735338i
\(619\) −5.30171e26 −0.0641962 −0.0320981 0.999485i \(-0.510219\pi\)
−0.0320981 + 0.999485i \(0.510219\pi\)
\(620\) 6.24908e27i 0.744559i
\(621\) 7.14096e27 + 9.50929e27i 0.837222 + 1.11489i
\(622\) 7.34815e27 0.847762
\(623\) 3.62702e26i 0.0411784i
\(624\) 1.78876e27 3.90063e26i 0.199851 0.0435802i
\(625\) −7.40238e27 −0.813900
\(626\) 8.39639e27i 0.908551i
\(627\) 6.41931e26 + 2.94379e27i 0.0683617 + 0.313495i
\(628\) 6.58212e27 0.689874
\(629\) 5.39952e27i 0.556992i
\(630\) −6.98714e26 + 3.19941e26i −0.0709405 + 0.0324836i
\(631\) 9.11781e27 0.911165 0.455582 0.890194i \(-0.349431\pi\)
0.455582 + 0.890194i \(0.349431\pi\)
\(632\) 7.72212e26i 0.0759566i
\(633\) −1.90647e28 + 4.15730e27i −1.84583 + 0.402508i
\(634\) −1.41482e27 −0.134837
\(635\) 9.09738e27i 0.853452i
\(636\) −1.30583e27 5.98832e27i −0.120591 0.553011i
\(637\) 8.86962e27 0.806326
\(638\) 3.00209e27i 0.268668i
\(639\) 2.33933e27 + 5.10883e27i 0.206102 + 0.450104i
\(640\) −9.33763e26 −0.0809910
\(641\) 7.97553e27i 0.681051i −0.940235 0.340525i \(-0.889395\pi\)
0.940235 0.340525i \(-0.110605\pi\)
\(642\) 2.15880e27 4.70755e26i 0.181494 0.0395772i
\(643\) 1.57198e28 1.30118 0.650590 0.759430i \(-0.274522\pi\)
0.650590 + 0.759430i \(0.274522\pi\)
\(644\) 1.03008e27i 0.0839480i
\(645\) −2.21113e27 1.01399e28i −0.177426 0.813645i
\(646\) −1.92553e28 −1.52134
\(647\) 9.57693e27i 0.745047i 0.928023 + 0.372523i \(0.121507\pi\)
−0.928023 + 0.372523i \(0.878493\pi\)
\(648\) 3.49412e27 + 3.01540e27i 0.267663 + 0.230991i
\(649\) −4.84926e27 −0.365787
\(650\) 1.24916e27i 0.0927868i
\(651\) 2.61403e27 5.70024e26i 0.191206 0.0416949i
\(652\) −1.29301e28 −0.931376
\(653\) 1.11408e28i 0.790287i −0.918619 0.395144i \(-0.870695\pi\)
0.918619 0.395144i \(-0.129305\pi\)
\(654\) −1.56194e27 7.16277e27i −0.109115 0.500384i
\(655\) 1.15829e28 0.796902
\(656\) 5.24917e27i 0.355674i
\(657\) 1.16810e27 5.34875e26i 0.0779521 0.0356943i
\(658\) −6.39724e26 −0.0420469
\(659\) 1.35425e27i 0.0876687i −0.999039 0.0438343i \(-0.986043\pi\)
0.999039 0.0438343i \(-0.0139574\pi\)
\(660\) 1.69771e27 3.70208e26i 0.108249 0.0236052i
\(661\) −1.35330e28 −0.849923 −0.424962 0.905211i \(-0.639712\pi\)
−0.424962 + 0.905211i \(0.639712\pi\)
\(662\) 2.51708e26i 0.0155710i
\(663\) −4.63881e27 2.12728e28i −0.282665 1.29625i
\(664\) −3.16800e27 −0.190154
\(665\) 2.47615e27i 0.146407i
\(666\) −1.73616e27 3.79157e27i −0.101122 0.220840i
\(667\) 3.81794e28 2.19064
\(668\) 9.33737e27i 0.527789i
\(669\) 1.22933e28 2.68072e27i 0.684554 0.149276i
\(670\) −2.17168e27 −0.119138
\(671\) 7.75208e26i 0.0418980i
\(672\) −8.51752e25 3.90599e26i −0.00453545 0.0207988i
\(673\) −2.20466e28 −1.15662 −0.578310 0.815817i \(-0.696288\pi\)
−0.578310 + 0.815817i \(0.696288\pi\)
\(674\) 1.45509e28i 0.752128i
\(675\) −2.51812e27 + 1.89097e27i −0.128245 + 0.0963048i
\(676\) 3.29376e27 0.165282
\(677\) 2.69058e28i 1.33033i 0.746697 + 0.665165i \(0.231639\pi\)
−0.746697 + 0.665165i \(0.768361\pi\)
\(678\) 2.46532e28 5.37596e27i 1.20109 0.261914i
\(679\) 2.37504e27 0.114018
\(680\) 1.11047e28i 0.525315i
\(681\) −1.59461e27 7.31259e27i −0.0743331 0.340879i
\(682\) −6.04946e27 −0.277890
\(683\) 1.64443e28i 0.744405i 0.928152 + 0.372203i \(0.121397\pi\)
−0.928152 + 0.372203i \(0.878603\pi\)
\(684\) −1.35212e28 + 6.19135e27i −0.603190 + 0.276201i
\(685\) 1.16335e28 0.511452
\(686\) 3.90209e27i 0.169066i
\(687\) −1.87840e28 + 4.09611e27i −0.802088 + 0.174906i
\(688\) 5.39890e27 0.227207
\(689\) 2.23305e28i 0.926204i
\(690\) 4.70816e27 + 2.15908e28i 0.192469 + 0.882629i
\(691\) −2.42166e27 −0.0975736 −0.0487868 0.998809i \(-0.515535\pi\)
−0.0487868 + 0.998809i \(0.515535\pi\)
\(692\) 2.10781e28i 0.837087i
\(693\) 3.09721e26 + 6.76395e26i 0.0121238 + 0.0264769i
\(694\) −1.43805e28 −0.554854
\(695\) 4.21741e27i 0.160398i
\(696\) 1.44774e28 3.15699e27i 0.542748 0.118353i
\(697\) −6.24255e28 −2.30693
\(698\) 4.62807e27i 0.168595i
\(699\) −2.94195e27 1.34913e28i −0.105649 0.484487i
\(700\) 2.72771e26 0.00965645
\(701\) 2.52344e27i 0.0880670i 0.999030 + 0.0440335i \(0.0140208\pi\)
−0.999030 + 0.0440335i \(0.985979\pi\)
\(702\) −1.00975e28 1.34463e28i −0.347409 0.462629i
\(703\) 1.34368e28 0.455768
\(704\) 9.03935e26i 0.0302281i
\(705\) 1.34089e28 2.92398e27i 0.442081 0.0964015i
\(706\) 2.68819e28 0.873803
\(707\) 7.01488e26i 0.0224815i
\(708\) −5.09947e27 2.33853e28i −0.161136 0.738942i
\(709\) 1.94408e28 0.605692 0.302846 0.953039i \(-0.402063\pi\)
0.302846 + 0.953039i \(0.402063\pi\)
\(710\) 1.04414e28i 0.320755i
\(711\) 6.44871e27 2.95286e27i 0.195333 0.0894432i
\(712\) −4.04784e27 −0.120899
\(713\) 7.69346e28i 2.26583i
\(714\) −4.64519e27 + 1.01294e27i −0.134903 + 0.0294173i
\(715\) −6.33078e27 −0.181300
\(716\) 9.63473e27i 0.272088i
\(717\) 1.09249e28 + 5.00996e28i 0.304246 + 1.39522i
\(718\) 4.04805e28 1.11174
\(719\) 1.12460e28i 0.304585i −0.988335 0.152292i \(-0.951334\pi\)
0.988335 0.152292i \(-0.0486655\pi\)
\(720\) 3.57062e27 + 7.79781e27i 0.0953715 + 0.208280i
\(721\) −4.86568e27 −0.128171
\(722\) 2.06993e28i 0.537753i
\(723\) −6.07959e28 + 1.32573e28i −1.55773 + 0.339683i
\(724\) 1.95206e28 0.493296
\(725\) 1.01101e28i 0.251987i
\(726\) 5.77000e27 + 2.64602e28i 0.141843 + 0.650470i
\(727\) −9.91377e27 −0.240378 −0.120189 0.992751i \(-0.538350\pi\)
−0.120189 + 0.992751i \(0.538350\pi\)
\(728\) 1.45655e27i 0.0348346i
\(729\) 1.18203e28 4.07098e28i 0.278838 0.960338i
\(730\) 2.38736e27 0.0555506
\(731\) 6.42062e28i 1.47368i
\(732\) −3.73840e27 + 8.15206e26i −0.0846398 + 0.0184568i
\(733\) 3.83319e28 0.856092 0.428046 0.903757i \(-0.359202\pi\)
0.428046 + 0.903757i \(0.359202\pi\)
\(734\) 1.09373e27i 0.0240963i
\(735\) 8.85249e27 + 4.05960e28i 0.192394 + 0.882288i
\(736\) −1.14959e28 −0.246470
\(737\) 2.10231e27i 0.0444654i
\(738\) −4.38356e28 + 2.00723e28i −0.914667 + 0.418826i
\(739\) −7.41025e27 −0.152542 −0.0762708 0.997087i \(-0.524301\pi\)
−0.0762708 + 0.997087i \(0.524301\pi\)
\(740\) 7.74916e27i 0.157376i
\(741\) 5.29379e28 1.15438e28i 1.06068 0.231295i
\(742\) 4.87615e27 0.0963913
\(743\) 1.78527e28i 0.348189i −0.984729 0.174094i \(-0.944300\pi\)
0.984729 0.174094i \(-0.0556998\pi\)
\(744\) −6.36160e27 2.91732e28i −0.122416 0.561377i
\(745\) −4.57946e28 −0.869465
\(746\) 1.43546e28i 0.268908i
\(747\) 1.21141e28 + 2.64559e28i 0.223917 + 0.489008i
\(748\) 1.07500e28 0.196062
\(749\) 1.75786e27i 0.0316349i
\(750\) −4.13668e28 + 9.02056e27i −0.734579 + 0.160185i
\(751\) 2.22914e28 0.390605 0.195302 0.980743i \(-0.437431\pi\)
0.195302 + 0.980743i \(0.437431\pi\)
\(752\) 7.13947e27i 0.123449i
\(753\) 1.14252e28 + 5.23941e28i 0.194946 + 0.893989i
\(754\) −5.39864e28 −0.909014
\(755\) 3.81866e28i 0.634515i
\(756\) −2.93617e27 + 2.20491e27i −0.0481464 + 0.0361553i
\(757\) −6.75656e28 −1.09337 −0.546685 0.837339i \(-0.684110\pi\)
−0.546685 + 0.837339i \(0.684110\pi\)
\(758\) 2.00407e28i 0.320052i
\(759\) 2.09011e28 4.55777e27i 0.329422 0.0718347i
\(760\) −2.76344e28 −0.429848
\(761\) 1.26732e29i 1.94554i 0.231771 + 0.972770i \(0.425548\pi\)
−0.231771 + 0.972770i \(0.574452\pi\)
\(762\) 9.26119e27 + 4.24702e28i 0.140319 + 0.643480i
\(763\) 5.83247e27 0.0872182
\(764\) 5.06557e27i 0.0747644i
\(765\) 9.27353e28 4.24635e28i 1.35092 0.618587i
\(766\) −1.77838e28 −0.255704
\(767\) 8.72040e28i 1.23761i
\(768\) −4.35918e27 + 9.50575e26i −0.0610650 + 0.0133160i
\(769\) 4.01610e28 0.555317 0.277658 0.960680i \(-0.410442\pi\)
0.277658 + 0.960680i \(0.410442\pi\)
\(770\) 1.38241e27i 0.0188681i
\(771\) 4.48297e27 + 2.05581e28i 0.0603980 + 0.276975i
\(772\) 2.26711e28 0.301508
\(773\) 2.41271e28i 0.316746i −0.987379 0.158373i \(-0.949375\pi\)
0.987379 0.158373i \(-0.0506248\pi\)
\(774\) −2.06449e28 4.50860e28i −0.267548 0.584295i
\(775\) 2.03728e28 0.260636
\(776\) 2.65060e28i 0.334755i
\(777\) 3.24153e27 7.06857e26i 0.0404147 0.00881295i
\(778\) 8.25613e28 1.01620
\(779\) 1.55347e29i 1.88769i
\(780\) −6.65743e27 3.05299e28i −0.0798658 0.366251i
\(781\) 1.01078e28 0.119715
\(782\) 1.36714e29i 1.59863i
\(783\) −8.17241e28 1.08828e29i −0.943479 1.25639i
\(784\) −2.16151e28 −0.246375
\(785\) 1.12341e29i 1.26427i
\(786\) 5.40737e28 1.17915e28i 0.600842 0.131022i
\(787\) −1.14847e29 −1.26000 −0.630002 0.776594i \(-0.716946\pi\)
−0.630002 + 0.776594i \(0.716946\pi\)
\(788\) 1.08797e28i 0.117856i
\(789\) −1.32299e28 6.06700e28i −0.141510 0.648939i
\(790\) 1.31798e28 0.139199
\(791\) 2.00745e28i 0.209354i
\(792\) 7.54873e27 3.45656e27i 0.0777359 0.0355953i
\(793\) 1.39405e28 0.141758
\(794\) 1.19587e29i 1.20082i
\(795\) −1.02206e29 + 2.22874e28i −1.01346 + 0.220998i
\(796\) 8.89930e28 0.871415
\(797\) 1.24679e29i 1.20562i 0.797884 + 0.602810i \(0.205952\pi\)
−0.797884 + 0.602810i \(0.794048\pi\)
\(798\) −2.52074e27 1.15597e28i −0.0240712 0.110387i
\(799\) 8.49060e28 0.800701
\(800\) 3.04419e27i 0.0283512i
\(801\) 1.54786e28 + 3.38034e28i 0.142366 + 0.310910i
\(802\) −3.51555e28 −0.319337
\(803\) 2.31110e27i 0.0207330i
\(804\) −1.01383e28 + 2.21079e27i −0.0898264 + 0.0195878i
\(805\) −1.75809e28 −0.153845
\(806\) 1.08787e29i 0.940215i
\(807\) −2.46818e28 1.13187e29i −0.210689 0.966183i
\(808\) 7.82877e27 0.0660055
\(809\) 2.58748e28i 0.215473i 0.994179 + 0.107736i \(0.0343603\pi\)
−0.994179 + 0.107736i \(0.965640\pi\)
\(810\) 5.14655e28 5.96362e28i 0.423317 0.490523i
\(811\) −1.27235e29 −1.03371 −0.516856 0.856072i \(-0.672898\pi\)
−0.516856 + 0.856072i \(0.672898\pi\)
\(812\) 1.17886e28i 0.0946024i
\(813\) −1.41240e27 + 3.07992e26i −0.0111957 + 0.00244137i
\(814\) −7.50163e27 −0.0587370
\(815\) 2.20685e29i 1.70686i
\(816\) 1.13047e28 + 5.18414e28i 0.0863688 + 0.396073i
\(817\) 1.59779e29 1.20586
\(818\) 7.38879e28i 0.550859i
\(819\) 1.21636e28 5.56970e27i 0.0895822 0.0410197i
\(820\) −8.95906e28 −0.651814
\(821\) 2.27509e29i 1.63518i −0.575799 0.817591i \(-0.695309\pi\)
0.575799 0.817591i \(-0.304691\pi\)
\(822\) 5.43099e28 1.18430e28i 0.385621 0.0840897i
\(823\) −3.57076e28 −0.250474 −0.125237 0.992127i \(-0.539969\pi\)
−0.125237 + 0.992127i \(0.539969\pi\)
\(824\) 5.43021e28i 0.376309i
\(825\) 1.20693e27 + 5.53476e27i 0.00826307 + 0.0378930i
\(826\) 1.90421e28 0.128799
\(827\) 1.32016e29i 0.882210i 0.897455 + 0.441105i \(0.145413\pi\)
−0.897455 + 0.441105i \(0.854587\pi\)
\(828\) 4.39592e28 + 9.60017e28i 0.290232 + 0.633834i
\(829\) 1.43965e29 0.939097 0.469549 0.882907i \(-0.344417\pi\)
0.469549 + 0.882907i \(0.344417\pi\)
\(830\) 5.40701e28i 0.348479i
\(831\) −6.09513e28 + 1.32912e28i −0.388126 + 0.0846359i
\(832\) 1.62554e28 0.102274
\(833\) 2.57057e29i 1.59801i
\(834\) 4.29335e27 + 1.96886e28i 0.0263715 + 0.120935i
\(835\) 1.59366e29 0.967234
\(836\) 2.67517e28i 0.160431i
\(837\) −2.19298e29 + 1.64681e29i −1.29951 + 0.975863i
\(838\) −9.88209e28 −0.578640
\(839\) 2.06955e29i 1.19745i −0.800955 0.598724i \(-0.795675\pi\)
0.800955 0.598724i \(-0.204325\pi\)
\(840\) −6.66658e27 + 1.45373e27i −0.0381163 + 0.00831175i
\(841\) −2.59946e29 −1.46866
\(842\) 1.64537e29i 0.918633i
\(843\) 2.52298e27 + 1.15700e28i 0.0139200 + 0.0638346i
\(844\) −1.73251e29 −0.944605
\(845\) 5.62165e28i 0.302898i
\(846\) 5.96215e28 2.73007e28i 0.317467 0.145368i
\(847\) −2.15459e28 −0.113379
\(848\) 5.44190e28i 0.283003i
\(849\) 1.39859e29 3.04981e28i 0.718810 0.156746i
\(850\) −3.62029e28 −0.183888
\(851\) 9.54027e28i 0.478922i
\(852\) 1.06294e28 + 4.87444e28i 0.0527364 + 0.241840i
\(853\) −7.04114e28 −0.345265 −0.172632 0.984986i \(-0.555227\pi\)
−0.172632 + 0.984986i \(0.555227\pi\)
\(854\) 3.04409e27i 0.0147529i
\(855\) 1.05671e29 + 2.30774e29i 0.506170 + 1.10542i
\(856\) 1.96181e28 0.0928796
\(857\) 2.94528e29i 1.37822i −0.724658 0.689109i \(-0.758002\pi\)
0.724658 0.689109i \(-0.241998\pi\)
\(858\) −2.95546e28 + 6.44477e27i −0.136695 + 0.0298081i
\(859\) 2.41150e29 1.10244 0.551222 0.834359i \(-0.314162\pi\)
0.551222 + 0.834359i \(0.314162\pi\)
\(860\) 9.21461e28i 0.416383i
\(861\) −8.17220e27 3.74763e28i −0.0365012 0.167388i
\(862\) −8.23329e28 −0.363497
\(863\) 2.67410e29i 1.16700i −0.812115 0.583498i \(-0.801684\pi\)
0.812115 0.583498i \(-0.198316\pi\)
\(864\) 2.46073e28 + 3.27684e28i 0.106152 + 0.141357i
\(865\) 3.59752e29 1.53406
\(866\) 5.85637e27i 0.0246859i
\(867\) 3.82043e29 8.33096e28i 1.59192 0.347139i
\(868\) 2.37550e28 0.0978495
\(869\) 1.27588e28i 0.0519531i
\(870\) −5.38821e28 2.47094e29i −0.216896 0.994649i
\(871\) 3.78058e28 0.150445
\(872\) 6.50918e28i 0.256071i
\(873\) −2.21351e29 + 1.01357e29i −0.860872 + 0.394193i
\(874\) −3.40217e29 −1.30810
\(875\) 3.36840e28i 0.128039i
\(876\) 1.11451e28 2.43034e27i 0.0418836 0.00913327i
\(877\) −2.36384e29 −0.878258 −0.439129 0.898424i \(-0.644713\pi\)
−0.439129 + 0.898424i \(0.644713\pi\)
\(878\) 2.96793e29i 1.09021i
\(879\) 3.40883e28 + 1.56323e29i 0.123799 + 0.567720i
\(880\) 1.54280e28 0.0553965
\(881\) 1.19713e28i 0.0424994i 0.999774 + 0.0212497i \(0.00676450\pi\)
−0.999774 + 0.0212497i \(0.993236\pi\)
\(882\) 8.26540e28 + 1.80507e29i 0.290120 + 0.633588i
\(883\) 1.99349e29 0.691841 0.345921 0.938264i \(-0.387567\pi\)
0.345921 + 0.938264i \(0.387567\pi\)
\(884\) 1.93317e29i 0.663357i
\(885\) −3.99130e29 + 8.70356e28i −1.35420 + 0.295300i
\(886\) 2.99734e29 1.00554
\(887\) 1.42732e29i 0.473461i 0.971575 + 0.236730i \(0.0760758\pi\)
−0.971575 + 0.236730i \(0.923924\pi\)
\(888\) −7.88869e27 3.61762e28i −0.0258747 0.118657i
\(889\) −3.45825e28 −0.112160
\(890\) 6.90869e28i 0.221562i
\(891\) −5.77312e28 4.98215e28i −0.183077 0.157994i
\(892\) 1.11716e29 0.350320
\(893\) 2.11291e29i 0.655187i
\(894\) −2.13788e29 + 4.66192e28i −0.655553 + 0.142952i
\(895\) −1.64441e29 −0.498633
\(896\) 3.54957e27i 0.0106438i
\(897\) −8.19620e28 3.75864e29i −0.243046 1.11457i
\(898\) 3.52801e29 1.03459
\(899\) 8.80471e29i 2.55340i
\(900\) −2.54219e28 + 1.16407e28i −0.0729092 + 0.0333851i
\(901\) −6.47176e29 −1.83558
\(902\) 8.67287e28i 0.243275i
\(903\) 3.85453e28 8.40531e27i 0.106929 0.0233172i
\(904\) 2.24037e29 0.614659
\(905\) 3.33169e29i 0.904023i
\(906\) 3.88742e28 + 1.78270e29i 0.104323 + 0.478407i
\(907\) 2.67162e28 0.0709090 0.0354545 0.999371i \(-0.488712\pi\)
0.0354545 + 0.999371i \(0.488712\pi\)
\(908\) 6.64533e28i 0.174445i
\(909\) −2.99365e28 6.53777e28i −0.0777251 0.169743i
\(910\) 2.48597e28 0.0638385
\(911\) 3.11664e29i 0.791594i −0.918338 0.395797i \(-0.870468\pi\)
0.918338 0.395797i \(-0.129532\pi\)
\(912\) −1.29009e29 + 2.81320e28i −0.324093 + 0.0706728i
\(913\) 5.23430e28 0.130062
\(914\) 2.77432e29i 0.681858i
\(915\) 1.39136e28 + 6.38054e28i 0.0338243 + 0.155112i
\(916\) −1.70700e29 −0.410468
\(917\) 4.40309e28i 0.104728i
\(918\) 3.89697e29 2.92641e29i 0.916855 0.688508i
\(919\) −2.53137e28 −0.0589116 −0.0294558 0.999566i \(-0.509377\pi\)
−0.0294558 + 0.999566i \(0.509377\pi\)
\(920\) 1.96207e29i 0.451685i
\(921\) 2.70016e29 5.88806e28i 0.614885 0.134084i
\(922\) 4.35664e29 0.981392
\(923\) 1.81768e29i 0.405043i
\(924\) 1.40730e27 + 6.45363e27i 0.00310217 + 0.0142260i
\(925\) 2.52633e28 0.0550899
\(926\) 2.37086e29i 0.511441i
\(927\) 4.53475e29 2.07646e29i 0.967734 0.443125i
\(928\) 1.31564e29 0.277751
\(929\) 8.29659e29i 1.73278i 0.499370 + 0.866389i \(0.333565\pi\)
−0.499370 + 0.866389i \(0.666435\pi\)
\(930\) −4.97916e29 + 1.08577e29i −1.02879 + 0.224341i
\(931\) −6.39692e29 −1.30760
\(932\) 1.22602e29i 0.247936i
\(933\) −1.27673e29 5.85488e29i −0.255437 1.17139i
\(934\) −5.19166e29 −1.02763
\(935\) 1.83477e29i 0.359307i
\(936\) −6.21591e28 1.35748e29i −0.120433 0.263012i
\(937\) 9.65495e29 1.85078 0.925388 0.379020i \(-0.123739\pi\)
0.925388 + 0.379020i \(0.123739\pi\)
\(938\) 8.25537e27i 0.0156570i
\(939\) 6.69010e29 1.45886e29i 1.25538 0.273753i
\(940\) 1.21854e29 0.226235
\(941\) 2.29411e29i 0.421423i 0.977548 + 0.210711i \(0.0675780\pi\)
−0.977548 + 0.210711i \(0.932422\pi\)
\(942\) −1.14364e29 5.24452e29i −0.207864 0.953228i
\(943\) −1.10298e30 −1.98359
\(944\) 2.12514e29i 0.378153i
\(945\) 3.76324e28 + 5.01134e28i 0.0662589 + 0.0882339i
\(946\) −8.92027e28 −0.155406
\(947\) 7.09753e29i 1.22351i −0.791047 0.611755i \(-0.790464\pi\)
0.791047 0.611755i \(-0.209536\pi\)
\(948\) 6.15285e28 1.34171e28i 0.104953 0.0228863i
\(949\) −4.15603e28 −0.0701482
\(950\) 9.00918e28i 0.150470i
\(951\) 2.45824e28 + 1.12731e29i 0.0406274 + 0.186310i
\(952\) −4.22132e28 −0.0690365
\(953\) 1.87844e29i 0.303997i −0.988381 0.151998i \(-0.951429\pi\)
0.988381 0.151998i \(-0.0485708\pi\)
\(954\) −4.54451e29 + 2.08093e29i −0.727785 + 0.333253i
\(955\) 8.64570e28 0.137014
\(956\) 4.55280e29i 0.714003i
\(957\) −2.39201e29 + 5.21609e28i −0.371231 + 0.0809517i
\(958\) 7.00559e29 1.07594
\(959\) 4.42232e28i 0.0672147i
\(960\) 1.62240e28 + 7.44006e28i 0.0244032 + 0.111909i
\(961\) 1.10243e30 1.64104
\(962\) 1.34901e29i 0.198731i
\(963\) −7.50179e28 1.63830e29i −0.109371 0.238853i
\(964\) −5.52484e29 −0.797167
\(965\) 3.86940e29i 0.552549i
\(966\) −8.20746e28 + 1.78974e28i −0.115995 + 0.0252941i
\(967\) −4.74584e29 −0.663817 −0.331909 0.943312i \(-0.607693\pi\)
−0.331909 + 0.943312i \(0.607693\pi\)
\(968\) 2.40458e29i 0.332878i
\(969\) 3.34559e29 + 1.53423e30i 0.458390 + 2.10210i
\(970\) −4.52394e29 −0.613478
\(971\) 8.35211e29i 1.12100i 0.828156 + 0.560498i \(0.189390\pi\)
−0.828156 + 0.560498i \(0.810610\pi\)
\(972\) 1.79552e29 3.30798e29i 0.238521 0.439440i
\(973\) −1.60319e28 −0.0210794
\(974\) 1.31401e29i 0.171005i
\(975\) 9.95313e28 2.17041e28i 0.128207 0.0279573i
\(976\) −3.39727e28 −0.0433144
\(977\) 1.73023e29i 0.218352i 0.994022 + 0.109176i \(0.0348213\pi\)
−0.994022 + 0.109176i \(0.965179\pi\)
\(978\) 2.24659e29 + 1.03025e30i 0.280630 + 1.28692i
\(979\) 6.68800e28 0.0826931
\(980\) 3.68917e29i 0.451511i
\(981\) −5.43579e29 + 2.48905e29i −0.658525 + 0.301539i
\(982\) −1.83987e29 −0.220634
\(983\) 1.37945e30i 1.63746i 0.574181 + 0.818728i \(0.305320\pi\)
−0.574181 + 0.818728i \(0.694680\pi\)
\(984\) −4.18244e29 + 9.12037e28i −0.491450 + 0.107167i
\(985\) 1.85689e29 0.215986
\(986\) 1.56462e30i 1.80152i
\(987\) 1.11151e28 + 5.09721e28i 0.0126690 + 0.0580980i
\(988\) 4.81074e29 0.542803
\(989\) 1.13444e30i 1.26713i
\(990\) −5.89951e28 1.28838e29i −0.0652325 0.142460i
\(991\) 1.31180e30 1.43592 0.717959 0.696085i \(-0.245077\pi\)
0.717959 + 0.696085i \(0.245077\pi\)
\(992\) 2.65112e29i 0.287285i
\(993\) −2.00557e28 + 4.37340e27i −0.0215151 + 0.00469166i
\(994\) −3.96914e28 −0.0421534
\(995\) 1.51889e30i 1.59697i
\(996\) 5.50437e28 + 2.52421e29i 0.0572947 + 0.262744i
\(997\) −1.40329e29 −0.144609 −0.0723045 0.997383i \(-0.523035\pi\)
−0.0723045 + 0.997383i \(0.523035\pi\)
\(998\) 1.13432e28i 0.0115726i
\(999\) −2.71940e29 + 2.04212e29i −0.274675 + 0.206266i
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 6.21.b.a.5.1 6
3.2 odd 2 inner 6.21.b.a.5.4 yes 6
4.3 odd 2 48.21.e.b.17.5 6
12.11 even 2 48.21.e.b.17.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.21.b.a.5.1 6 1.1 even 1 trivial
6.21.b.a.5.4 yes 6 3.2 odd 2 inner
48.21.e.b.17.5 6 4.3 odd 2
48.21.e.b.17.6 6 12.11 even 2