Properties

Label 138.6.d.a.137.15
Level $138$
Weight $6$
Character 138.137
Analytic conductor $22.133$
Analytic rank $0$
Dimension $40$
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] = [138,6,Mod(137,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.137");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 138.d (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: \(22.1329671342\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 137.15
Character \(\chi\) \(=\) 138.137
Dual form 138.6.d.a.137.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000i q^{2} +(15.5676 - 0.805444i) q^{3} -16.0000 q^{4} -10.2990 q^{5} +(3.22177 + 62.2705i) q^{6} -139.754i q^{7} -64.0000i q^{8} +(241.703 - 25.0777i) q^{9} +O(q^{10})\) \(q+4.00000i q^{2} +(15.5676 - 0.805444i) q^{3} -16.0000 q^{4} -10.2990 q^{5} +(3.22177 + 62.2705i) q^{6} -139.754i q^{7} -64.0000i q^{8} +(241.703 - 25.0777i) q^{9} -41.1960i q^{10} -570.013 q^{11} +(-249.082 + 12.8871i) q^{12} -754.278 q^{13} +559.016 q^{14} +(-160.331 + 8.29526i) q^{15} +256.000 q^{16} -143.694 q^{17} +(100.311 + 966.810i) q^{18} -2086.45i q^{19} +164.784 q^{20} +(-112.564 - 2175.64i) q^{21} -2280.05i q^{22} +(-2486.09 - 505.680i) q^{23} +(-51.5484 - 996.329i) q^{24} -3018.93 q^{25} -3017.11i q^{26} +(3742.54 - 585.078i) q^{27} +2236.06i q^{28} +5651.76i q^{29} +(-33.1810 - 641.324i) q^{30} +2627.23 q^{31} +1024.00i q^{32} +(-8873.76 + 459.113i) q^{33} -574.778i q^{34} +1439.33i q^{35} +(-3867.24 + 401.243i) q^{36} -7249.40i q^{37} +8345.81 q^{38} +(-11742.3 + 607.529i) q^{39} +659.136i q^{40} +965.744i q^{41} +(8702.56 - 450.256i) q^{42} -12064.3i q^{43} +9120.21 q^{44} +(-2489.29 + 258.275i) q^{45} +(2022.72 - 9944.35i) q^{46} -19373.9i q^{47} +(3985.31 - 206.194i) q^{48} -2724.18 q^{49} -12075.7i q^{50} +(-2236.98 + 115.738i) q^{51} +12068.4 q^{52} +28893.1 q^{53} +(2340.31 + 14970.2i) q^{54} +5870.56 q^{55} -8944.26 q^{56} +(-1680.52 - 32481.1i) q^{57} -22607.1 q^{58} +20760.7i q^{59} +(2565.30 - 132.724i) q^{60} +8371.14i q^{61} +10508.9i q^{62} +(-3504.71 - 33778.9i) q^{63} -4096.00 q^{64} +7768.30 q^{65} +(-1836.45 - 35495.0i) q^{66} -28343.6i q^{67} +2299.11 q^{68} +(-39109.8 - 5869.84i) q^{69} -5757.30 q^{70} -49123.7i q^{71} +(-1604.97 - 15469.0i) q^{72} +1894.77 q^{73} +28997.6 q^{74} +(-46997.6 + 2431.58i) q^{75} +33383.2i q^{76} +79661.6i q^{77} +(-2430.11 - 46969.3i) q^{78} +99145.8i q^{79} -2636.54 q^{80} +(57791.2 - 12122.7i) q^{81} -3862.98 q^{82} -86038.4 q^{83} +(1801.02 + 34810.2i) q^{84} +1479.91 q^{85} +48257.3 q^{86} +(4552.18 + 87984.6i) q^{87} +36480.8i q^{88} -17436.3 q^{89} +(-1033.10 - 9957.17i) q^{90} +105413. i q^{91} +(39777.4 + 8090.89i) q^{92} +(40899.7 - 2116.08i) q^{93} +77495.8 q^{94} +21488.4i q^{95} +(824.774 + 15941.3i) q^{96} +165173. i q^{97} -10896.7i q^{98} +(-137774. + 14294.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + 64 q^{12} - 1048 q^{13} + 10240 q^{16} + 1280 q^{18} - 1280 q^{24} + 30480 q^{25} + 1700 q^{27} - 22576 q^{31} - 8064 q^{36} + 55608 q^{39} + 1088 q^{46} - 1024 q^{48} - 23224 q^{49} + 16768 q^{52} + 25456 q^{54} + 210400 q^{55} - 83168 q^{58} - 163840 q^{64} + 99076 q^{69} + 167520 q^{70} - 20480 q^{72} + 241160 q^{73} - 255604 q^{75} - 233440 q^{78} + 78512 q^{81} - 8832 q^{82} - 460296 q^{85} - 4136 q^{87} + 500704 q^{93} - 138272 q^{94} + 20480 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 15.5676 0.805444i 0.998664 0.0516692i
\(4\) −16.0000 −0.500000
\(5\) −10.2990 −0.184234 −0.0921170 0.995748i \(-0.529363\pi\)
−0.0921170 + 0.995748i \(0.529363\pi\)
\(6\) 3.22177 + 62.2705i 0.0365357 + 0.706162i
\(7\) 139.754i 1.07800i −0.842305 0.539001i \(-0.818802\pi\)
0.842305 0.539001i \(-0.181198\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 241.703 25.0777i 0.994661 0.103200i
\(10\) 41.1960i 0.130273i
\(11\) −570.013 −1.42038 −0.710188 0.704012i \(-0.751390\pi\)
−0.710188 + 0.704012i \(0.751390\pi\)
\(12\) −249.082 + 12.8871i −0.499332 + 0.0258346i
\(13\) −754.278 −1.23786 −0.618932 0.785444i \(-0.712434\pi\)
−0.618932 + 0.785444i \(0.712434\pi\)
\(14\) 559.016 0.762262
\(15\) −160.331 + 8.29526i −0.183988 + 0.00951923i
\(16\) 256.000 0.250000
\(17\) −143.694 −0.120592 −0.0602959 0.998181i \(-0.519204\pi\)
−0.0602959 + 0.998181i \(0.519204\pi\)
\(18\) 100.311 + 966.810i 0.0729737 + 0.703331i
\(19\) 2086.45i 1.32594i −0.748645 0.662971i \(-0.769295\pi\)
0.748645 0.662971i \(-0.230705\pi\)
\(20\) 164.784 0.0921170
\(21\) −112.564 2175.64i −0.0556995 1.07656i
\(22\) 2280.05i 1.00436i
\(23\) −2486.09 505.680i −0.979934 0.199323i
\(24\) −51.5484 996.329i −0.0182678 0.353081i
\(25\) −3018.93 −0.966058
\(26\) 3017.11i 0.875302i
\(27\) 3742.54 585.078i 0.988000 0.154456i
\(28\) 2236.06i 0.539001i
\(29\) 5651.76i 1.24793i 0.781454 + 0.623963i \(0.214479\pi\)
−0.781454 + 0.623963i \(0.785521\pi\)
\(30\) −33.1810 641.324i −0.00673111 0.130099i
\(31\) 2627.23 0.491013 0.245507 0.969395i \(-0.421046\pi\)
0.245507 + 0.969395i \(0.421046\pi\)
\(32\) 1024.00i 0.176777i
\(33\) −8873.76 + 459.113i −1.41848 + 0.0733897i
\(34\) 574.778i 0.0852713i
\(35\) 1439.33i 0.198604i
\(36\) −3867.24 + 401.243i −0.497330 + 0.0516002i
\(37\) 7249.40i 0.870558i −0.900296 0.435279i \(-0.856650\pi\)
0.900296 0.435279i \(-0.143350\pi\)
\(38\) 8345.81 0.937582
\(39\) −11742.3 + 607.529i −1.23621 + 0.0639595i
\(40\) 659.136i 0.0651366i
\(41\) 965.744i 0.0897227i 0.998993 + 0.0448613i \(0.0142846\pi\)
−0.998993 + 0.0448613i \(0.985715\pi\)
\(42\) 8702.56 450.256i 0.761244 0.0393855i
\(43\) 12064.3i 0.995021i −0.867458 0.497510i \(-0.834248\pi\)
0.867458 0.497510i \(-0.165752\pi\)
\(44\) 9120.21 0.710188
\(45\) −2489.29 + 258.275i −0.183250 + 0.0190130i
\(46\) 2022.72 9944.35i 0.140942 0.692918i
\(47\) 19373.9i 1.27930i −0.768665 0.639651i \(-0.779079\pi\)
0.768665 0.639651i \(-0.220921\pi\)
\(48\) 3985.31 206.194i 0.249666 0.0129173i
\(49\) −2724.18 −0.162086
\(50\) 12075.7i 0.683106i
\(51\) −2236.98 + 115.738i −0.120431 + 0.00623089i
\(52\) 12068.4 0.618932
\(53\) 28893.1 1.41288 0.706438 0.707775i \(-0.250301\pi\)
0.706438 + 0.707775i \(0.250301\pi\)
\(54\) 2340.31 + 14970.2i 0.109217 + 0.698621i
\(55\) 5870.56 0.261681
\(56\) −8944.26 −0.381131
\(57\) −1680.52 32481.1i −0.0685104 1.32417i
\(58\) −22607.1 −0.882417
\(59\) 20760.7i 0.776447i 0.921565 + 0.388223i \(0.126911\pi\)
−0.921565 + 0.388223i \(0.873089\pi\)
\(60\) 2565.30 132.724i 0.0919939 0.00475961i
\(61\) 8371.14i 0.288045i 0.989574 + 0.144022i \(0.0460037\pi\)
−0.989574 + 0.144022i \(0.953996\pi\)
\(62\) 10508.9i 0.347199i
\(63\) −3504.71 33778.9i −0.111250 1.07225i
\(64\) −4096.00 −0.125000
\(65\) 7768.30 0.228057
\(66\) −1836.45 35495.0i −0.0518944 1.00302i
\(67\) 28343.6i 0.771380i −0.922628 0.385690i \(-0.873963\pi\)
0.922628 0.385690i \(-0.126037\pi\)
\(68\) 2299.11 0.0602959
\(69\) −39109.8 5869.84i −0.988924 0.148424i
\(70\) −5757.30 −0.140435
\(71\) 49123.7i 1.15650i −0.815860 0.578249i \(-0.803736\pi\)
0.815860 0.578249i \(-0.196264\pi\)
\(72\) −1604.97 15469.0i −0.0364869 0.351666i
\(73\) 1894.77 0.0416149 0.0208075 0.999784i \(-0.493376\pi\)
0.0208075 + 0.999784i \(0.493376\pi\)
\(74\) 28997.6 0.615577
\(75\) −46997.6 + 2431.58i −0.964767 + 0.0499155i
\(76\) 33383.2i 0.662971i
\(77\) 79661.6i 1.53117i
\(78\) −2430.11 46969.3i −0.0452262 0.874133i
\(79\) 99145.8i 1.78734i 0.448727 + 0.893669i \(0.351877\pi\)
−0.448727 + 0.893669i \(0.648123\pi\)
\(80\) −2636.54 −0.0460585
\(81\) 57791.2 12122.7i 0.978699 0.205299i
\(82\) −3862.98 −0.0634435
\(83\) −86038.4 −1.37087 −0.685436 0.728133i \(-0.740388\pi\)
−0.685436 + 0.728133i \(0.740388\pi\)
\(84\) 1801.02 + 34810.2i 0.0278497 + 0.538281i
\(85\) 1479.91 0.0222171
\(86\) 48257.3 0.703586
\(87\) 4552.18 + 87984.6i 0.0644794 + 1.24626i
\(88\) 36480.8i 0.502179i
\(89\) −17436.3 −0.233335 −0.116667 0.993171i \(-0.537221\pi\)
−0.116667 + 0.993171i \(0.537221\pi\)
\(90\) −1033.10 9957.17i −0.0134442 0.129578i
\(91\) 105413.i 1.33442i
\(92\) 39777.4 + 8090.89i 0.489967 + 0.0996613i
\(93\) 40899.7 2116.08i 0.490357 0.0253703i
\(94\) 77495.8 0.904604
\(95\) 21488.4i 0.244283i
\(96\) 824.774 + 15941.3i 0.00913392 + 0.176541i
\(97\) 165173.i 1.78242i 0.453595 + 0.891208i \(0.350141\pi\)
−0.453595 + 0.891208i \(0.649859\pi\)
\(98\) 10896.7i 0.114612i
\(99\) −137774. + 14294.6i −1.41279 + 0.146583i
\(100\) 48302.9 0.483029
\(101\) 176896.i 1.72550i −0.505632 0.862749i \(-0.668741\pi\)
0.505632 0.862749i \(-0.331259\pi\)
\(102\) −462.951 8947.93i −0.00440590 0.0851574i
\(103\) 1007.58i 0.00935811i −0.999989 0.00467906i \(-0.998511\pi\)
0.999989 0.00467906i \(-0.00148940\pi\)
\(104\) 48273.8i 0.437651i
\(105\) 1159.30 + 22406.9i 0.0102617 + 0.198339i
\(106\) 115572.i 0.999054i
\(107\) −219789. −1.85587 −0.927935 0.372743i \(-0.878417\pi\)
−0.927935 + 0.372743i \(0.878417\pi\)
\(108\) −59880.6 + 9361.25i −0.494000 + 0.0772280i
\(109\) 115327.i 0.929751i 0.885376 + 0.464875i \(0.153901\pi\)
−0.885376 + 0.464875i \(0.846099\pi\)
\(110\) 23482.2i 0.185037i
\(111\) −5838.98 112856.i −0.0449811 0.869395i
\(112\) 35777.0i 0.269500i
\(113\) 125019. 0.921041 0.460520 0.887649i \(-0.347663\pi\)
0.460520 + 0.887649i \(0.347663\pi\)
\(114\) 129924. 6722.08i 0.936330 0.0484442i
\(115\) 25604.2 + 5208.00i 0.180537 + 0.0367220i
\(116\) 90428.2i 0.623963i
\(117\) −182311. + 18915.6i −1.23125 + 0.127748i
\(118\) −83042.7 −0.549031
\(119\) 20081.9i 0.129998i
\(120\) 530.897 + 10261.2i 0.00336556 + 0.0650495i
\(121\) 163864. 1.01747
\(122\) −33484.6 −0.203678
\(123\) 777.852 + 15034.3i 0.00463590 + 0.0896028i
\(124\) −42035.6 −0.245507
\(125\) 63276.3 0.362215
\(126\) 135116. 14018.8i 0.758192 0.0786658i
\(127\) 86118.7 0.473792 0.236896 0.971535i \(-0.423870\pi\)
0.236896 + 0.971535i \(0.423870\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −9717.14 187813.i −0.0514120 0.993692i
\(130\) 31073.2i 0.161260i
\(131\) 235204.i 1.19747i 0.800946 + 0.598737i \(0.204330\pi\)
−0.800946 + 0.598737i \(0.795670\pi\)
\(132\) 141980. 7345.82i 0.709239 0.0366949i
\(133\) −291590. −1.42937
\(134\) 113374. 0.545448
\(135\) −38544.4 + 6025.72i −0.182023 + 0.0284560i
\(136\) 9196.45i 0.0426356i
\(137\) −134787. −0.613547 −0.306774 0.951783i \(-0.599249\pi\)
−0.306774 + 0.951783i \(0.599249\pi\)
\(138\) 23479.4 156439.i 0.104952 0.699275i
\(139\) 293765. 1.28962 0.644812 0.764341i \(-0.276936\pi\)
0.644812 + 0.764341i \(0.276936\pi\)
\(140\) 23029.2i 0.0993022i
\(141\) −15604.6 301606.i −0.0661006 1.27759i
\(142\) 196495. 0.817767
\(143\) 429948. 1.75823
\(144\) 61875.8 6419.89i 0.248665 0.0258001i
\(145\) 58207.5i 0.229910i
\(146\) 7579.07i 0.0294262i
\(147\) −42409.1 + 2194.18i −0.161870 + 0.00837487i
\(148\) 115990.i 0.435279i
\(149\) −90268.2 −0.333096 −0.166548 0.986033i \(-0.553262\pi\)
−0.166548 + 0.986033i \(0.553262\pi\)
\(150\) −9726.32 187990.i −0.0352956 0.682194i
\(151\) −21481.7 −0.0766703 −0.0383351 0.999265i \(-0.512205\pi\)
−0.0383351 + 0.999265i \(0.512205\pi\)
\(152\) −133533. −0.468791
\(153\) −34731.3 + 3603.53i −0.119948 + 0.0124451i
\(154\) −318646. −1.08270
\(155\) −27057.8 −0.0904613
\(156\) 187877. 9720.46i 0.618105 0.0319798i
\(157\) 54700.0i 0.177108i −0.996071 0.0885540i \(-0.971775\pi\)
0.996071 0.0885540i \(-0.0282246\pi\)
\(158\) −396583. −1.26384
\(159\) 449797. 23271.7i 1.41099 0.0730022i
\(160\) 10546.2i 0.0325683i
\(161\) −70670.9 + 347441.i −0.214870 + 1.05637i
\(162\) 48490.8 + 231165.i 0.145168 + 0.692045i
\(163\) −454850. −1.34091 −0.670454 0.741951i \(-0.733901\pi\)
−0.670454 + 0.741951i \(0.733901\pi\)
\(164\) 15451.9i 0.0448613i
\(165\) 91390.7 4728.41i 0.261332 0.0135209i
\(166\) 344153.i 0.969353i
\(167\) 296189.i 0.821822i −0.911675 0.410911i \(-0.865211\pi\)
0.911675 0.410911i \(-0.134789\pi\)
\(168\) −139241. + 7204.10i −0.380622 + 0.0196927i
\(169\) 197642. 0.532308
\(170\) 5919.63i 0.0157099i
\(171\) −52323.4 504301.i −0.136838 1.31886i
\(172\) 193029.i 0.497510i
\(173\) 170665.i 0.433541i 0.976223 + 0.216771i \(0.0695524\pi\)
−0.976223 + 0.216771i \(0.930448\pi\)
\(174\) −351938. + 18208.7i −0.881239 + 0.0455938i
\(175\) 421908.i 1.04141i
\(176\) −145923. −0.355094
\(177\) 16721.6 + 323195.i 0.0401184 + 0.775410i
\(178\) 69745.2i 0.164993i
\(179\) 690824.i 1.61152i −0.592244 0.805758i \(-0.701758\pi\)
0.592244 0.805758i \(-0.298242\pi\)
\(180\) 39828.7 4132.40i 0.0916251 0.00950651i
\(181\) 265516.i 0.602412i 0.953559 + 0.301206i \(0.0973892\pi\)
−0.953559 + 0.301206i \(0.902611\pi\)
\(182\) −421654. −0.943577
\(183\) 6742.48 + 130319.i 0.0148831 + 0.287660i
\(184\) −32363.5 + 159110.i −0.0704712 + 0.346459i
\(185\) 74661.5i 0.160386i
\(186\) 8464.33 + 163599.i 0.0179395 + 0.346735i
\(187\) 81907.7 0.171286
\(188\) 309983.i 0.639651i
\(189\) −81767.1 523035.i −0.166504 1.06506i
\(190\) −85953.4 −0.172735
\(191\) 614862. 1.21954 0.609768 0.792580i \(-0.291263\pi\)
0.609768 + 0.792580i \(0.291263\pi\)
\(192\) −63765.0 + 3299.10i −0.124833 + 0.00645865i
\(193\) 86677.4 0.167499 0.0837496 0.996487i \(-0.473310\pi\)
0.0837496 + 0.996487i \(0.473310\pi\)
\(194\) −660691. −1.26036
\(195\) 120934. 6256.93i 0.227752 0.0117835i
\(196\) 43586.9 0.0810431
\(197\) 735801.i 1.35081i −0.737446 0.675406i \(-0.763969\pi\)
0.737446 0.675406i \(-0.236031\pi\)
\(198\) −57178.5 551094.i −0.103650 0.998994i
\(199\) 1.01667e6i 1.81991i −0.414710 0.909954i \(-0.636117\pi\)
0.414710 0.909954i \(-0.363883\pi\)
\(200\) 193212.i 0.341553i
\(201\) −22829.2 441243.i −0.0398566 0.770350i
\(202\) 707584. 1.22011
\(203\) 789857. 1.34527
\(204\) 35791.7 1851.81i 0.0602154 0.00311544i
\(205\) 9946.19i 0.0165300i
\(206\) 4030.34 0.00661719
\(207\) −613575. 59878.8i −0.995272 0.0971287i
\(208\) −193095. −0.309466
\(209\) 1.18930e6i 1.88333i
\(210\) −89627.6 + 4637.18i −0.140247 + 0.00725615i
\(211\) −153148. −0.236813 −0.118406 0.992965i \(-0.537779\pi\)
−0.118406 + 0.992965i \(0.537779\pi\)
\(212\) −462289. −0.706438
\(213\) −39566.3 764739.i −0.0597554 1.15495i
\(214\) 879158.i 1.31230i
\(215\) 124250.i 0.183317i
\(216\) −37445.0 239522.i −0.0546084 0.349311i
\(217\) 367165.i 0.529313i
\(218\) −461310. −0.657433
\(219\) 29497.1 1526.13i 0.0415593 0.00215021i
\(220\) −93929.0 −0.130841
\(221\) 108386. 0.149276
\(222\) 451424. 23355.9i 0.614755 0.0318064i
\(223\) −532364. −0.716880 −0.358440 0.933553i \(-0.616691\pi\)
−0.358440 + 0.933553i \(0.616691\pi\)
\(224\) 143108. 0.190565
\(225\) −729683. + 75707.9i −0.960900 + 0.0996976i
\(226\) 500075.i 0.651274i
\(227\) 626086. 0.806435 0.403218 0.915104i \(-0.367892\pi\)
0.403218 + 0.915104i \(0.367892\pi\)
\(228\) 26888.3 + 519698.i 0.0342552 + 0.662085i
\(229\) 1.15320e6i 1.45317i −0.687078 0.726583i \(-0.741107\pi\)
0.687078 0.726583i \(-0.258893\pi\)
\(230\) −20832.0 + 102417.i −0.0259664 + 0.127659i
\(231\) 64162.9 + 1.24014e6i 0.0791142 + 1.52912i
\(232\) 361713. 0.441209
\(233\) 395664.i 0.477460i 0.971086 + 0.238730i \(0.0767311\pi\)
−0.971086 + 0.238730i \(0.923269\pi\)
\(234\) −75662.3 729244.i −0.0903316 0.870629i
\(235\) 199532.i 0.235691i
\(236\) 332171.i 0.388223i
\(237\) 79856.4 + 1.54347e6i 0.0923504 + 1.78495i
\(238\) −80327.5 −0.0919225
\(239\) 1.37069e6i 1.55218i −0.630619 0.776092i \(-0.717199\pi\)
0.630619 0.776092i \(-0.282801\pi\)
\(240\) −41044.7 + 2123.59i −0.0459970 + 0.00237981i
\(241\) 715572.i 0.793616i 0.917902 + 0.396808i \(0.129882\pi\)
−0.917902 + 0.396808i \(0.870118\pi\)
\(242\) 655456.i 0.719457i
\(243\) 889908. 235269.i 0.966784 0.255593i
\(244\) 133938.i 0.144022i
\(245\) 28056.3 0.0298618
\(246\) −60137.4 + 3111.41i −0.0633588 + 0.00327808i
\(247\) 1.57376e6i 1.64134i
\(248\) 168142.i 0.173599i
\(249\) −1.33941e6 + 69299.1i −1.36904 + 0.0708319i
\(250\) 253105.i 0.256124i
\(251\) 679196. 0.680473 0.340236 0.940340i \(-0.389493\pi\)
0.340236 + 0.940340i \(0.389493\pi\)
\(252\) 56075.4 + 540462.i 0.0556251 + 0.536123i
\(253\) 1.41710e6 + 288244.i 1.39187 + 0.283113i
\(254\) 344475.i 0.335022i
\(255\) 23038.7 1191.98i 0.0221874 0.00114794i
\(256\) 65536.0 0.0625000
\(257\) 1.38868e6i 1.31150i −0.754977 0.655751i \(-0.772352\pi\)
0.754977 0.655751i \(-0.227648\pi\)
\(258\) 751253. 38868.6i 0.702646 0.0363538i
\(259\) −1.01313e6 −0.938462
\(260\) −124293. −0.114028
\(261\) 141733. + 1.36605e6i 0.128787 + 1.24126i
\(262\) −940815. −0.846742
\(263\) 1.06490e6 0.949333 0.474666 0.880166i \(-0.342569\pi\)
0.474666 + 0.880166i \(0.342569\pi\)
\(264\) 29383.3 + 567920.i 0.0259472 + 0.501508i
\(265\) −297570. −0.260300
\(266\) 1.16636e6i 1.01071i
\(267\) −271442. + 14044.0i −0.233023 + 0.0120562i
\(268\) 453498.i 0.385690i
\(269\) 102901.i 0.0867041i 0.999060 + 0.0433520i \(0.0138037\pi\)
−0.999060 + 0.0433520i \(0.986196\pi\)
\(270\) −24102.9 154177.i −0.0201215 0.128710i
\(271\) 1.82316e6 1.50800 0.753999 0.656876i \(-0.228122\pi\)
0.753999 + 0.656876i \(0.228122\pi\)
\(272\) −36785.8 −0.0301480
\(273\) 84904.5 + 1.64104e6i 0.0689484 + 1.33264i
\(274\) 539150.i 0.433843i
\(275\) 1.72083e6 1.37216
\(276\) 625757. + 93917.5i 0.494462 + 0.0742119i
\(277\) 559043. 0.437769 0.218885 0.975751i \(-0.429758\pi\)
0.218885 + 0.975751i \(0.429758\pi\)
\(278\) 1.17506e6i 0.911901i
\(279\) 635007. 65884.8i 0.488391 0.0506728i
\(280\) 92116.8 0.0702173
\(281\) −1.09166e6 −0.824746 −0.412373 0.911015i \(-0.635300\pi\)
−0.412373 + 0.911015i \(0.635300\pi\)
\(282\) 1.20643e6 62418.5i 0.903395 0.0467402i
\(283\) 75110.5i 0.0557487i 0.999611 + 0.0278743i \(0.00887383\pi\)
−0.999611 + 0.0278743i \(0.991126\pi\)
\(284\) 785978.i 0.578249i
\(285\) 17307.7 + 334523.i 0.0126219 + 0.243957i
\(286\) 1.71979e6i 1.24326i
\(287\) 134967. 0.0967212
\(288\) 25679.6 + 247503.i 0.0182434 + 0.175833i
\(289\) −1.39921e6 −0.985458
\(290\) 232830. 0.162571
\(291\) 133037. + 2.57135e6i 0.0920961 + 1.78003i
\(292\) −30316.3 −0.0208075
\(293\) −1.69883e6 −1.15606 −0.578030 0.816015i \(-0.696178\pi\)
−0.578030 + 0.816015i \(0.696178\pi\)
\(294\) −8776.71 169636.i −0.00592193 0.114459i
\(295\) 213814.i 0.143048i
\(296\) −463961. −0.307789
\(297\) −2.13330e6 + 333502.i −1.40333 + 0.219385i
\(298\) 361073.i 0.235534i
\(299\) 1.87520e6 + 381424.i 1.21303 + 0.246734i
\(300\) 751962. 38905.3i 0.482384 0.0249577i
\(301\) −1.68604e6 −1.07263
\(302\) 85926.9i 0.0542141i
\(303\) −142480. 2.75385e6i −0.0891552 1.72319i
\(304\) 534132.i 0.331485i
\(305\) 86214.3i 0.0530677i
\(306\) −14414.1 138925.i −0.00880003 0.0848160i
\(307\) −1.38489e6 −0.838627 −0.419313 0.907842i \(-0.637729\pi\)
−0.419313 + 0.907842i \(0.637729\pi\)
\(308\) 1.27459e6i 0.765583i
\(309\) −811.553 15685.7i −0.000483527 0.00934561i
\(310\) 108231.i 0.0639658i
\(311\) 1.77927e6i 1.04314i 0.853210 + 0.521568i \(0.174653\pi\)
−0.853210 + 0.521568i \(0.825347\pi\)
\(312\) 38881.8 + 751509.i 0.0226131 + 0.437067i
\(313\) 95522.0i 0.0551116i −0.999620 0.0275558i \(-0.991228\pi\)
0.999620 0.0275558i \(-0.00877239\pi\)
\(314\) 218800. 0.125234
\(315\) 36095.0 + 347889.i 0.0204961 + 0.197544i
\(316\) 1.58633e6i 0.893669i
\(317\) 320032.i 0.178873i −0.995993 0.0894366i \(-0.971493\pi\)
0.995993 0.0894366i \(-0.0285066\pi\)
\(318\) 93087.0 + 1.79919e6i 0.0516204 + 0.997720i
\(319\) 3.22158e6i 1.77252i
\(320\) 42184.7 0.0230292
\(321\) −3.42160e6 + 177028.i −1.85339 + 0.0958913i
\(322\) −1.38976e6 282683.i −0.746966 0.151936i
\(323\) 299812.i 0.159898i
\(324\) −924659. + 193963.i −0.489350 + 0.102649i
\(325\) 2.27711e6 1.19585
\(326\) 1.81940e6i 0.948166i
\(327\) 92889.8 + 1.79538e6i 0.0480395 + 0.928509i
\(328\) 61807.6 0.0317218
\(329\) −2.70759e6 −1.37909
\(330\) 18913.6 + 365563.i 0.00956071 + 0.184790i
\(331\) 476574. 0.239089 0.119545 0.992829i \(-0.461857\pi\)
0.119545 + 0.992829i \(0.461857\pi\)
\(332\) 1.37661e6 0.685436
\(333\) −181798. 1.75220e6i −0.0898419 0.865909i
\(334\) 1.18476e6 0.581116
\(335\) 291911.i 0.142114i
\(336\) −28816.4 556964.i −0.0139249 0.269140i
\(337\) 3.64337e6i 1.74755i −0.486333 0.873774i \(-0.661666\pi\)
0.486333 0.873774i \(-0.338334\pi\)
\(338\) 790570.i 0.376399i
\(339\) 1.94624e6 100695.i 0.919810 0.0475895i
\(340\) −23678.5 −0.0111086
\(341\) −1.49755e6 −0.697423
\(342\) 2.01720e6 209294.i 0.932576 0.0967589i
\(343\) 1.96813e6i 0.903272i
\(344\) −772117. −0.351793
\(345\) 402792. + 60453.5i 0.182193 + 0.0273447i
\(346\) −682662. −0.306560
\(347\) 2.43354e6i 1.08496i 0.840067 + 0.542482i \(0.182515\pi\)
−0.840067 + 0.542482i \(0.817485\pi\)
\(348\) −72834.8 1.40775e6i −0.0322397 0.623130i
\(349\) 1.08698e6 0.477702 0.238851 0.971056i \(-0.423229\pi\)
0.238851 + 0.971056i \(0.423229\pi\)
\(350\) −1.68763e6 −0.736389
\(351\) −2.82291e6 + 441312.i −1.22301 + 0.191196i
\(352\) 583693.i 0.251089i
\(353\) 1.83446e6i 0.783559i 0.920059 + 0.391779i \(0.128140\pi\)
−0.920059 + 0.391779i \(0.871860\pi\)
\(354\) −1.29278e6 + 66886.3i −0.548297 + 0.0283680i
\(355\) 505924.i 0.213066i
\(356\) 278981. 0.116667
\(357\) 16174.8 + 312627.i 0.00671690 + 0.129824i
\(358\) 2.76330e6 1.13951
\(359\) 3.97038e6 1.62591 0.812953 0.582329i \(-0.197859\pi\)
0.812953 + 0.582329i \(0.197859\pi\)
\(360\) 16529.6 + 159315.i 0.00672212 + 0.0647888i
\(361\) −1.87718e6 −0.758121
\(362\) −1.06206e6 −0.425970
\(363\) 2.55097e6 131983.i 1.01611 0.0525717i
\(364\) 1.68661e6i 0.667210i
\(365\) −19514.2 −0.00766688
\(366\) −521276. + 26969.9i −0.203406 + 0.0105239i
\(367\) 2.68260e6i 1.03966i 0.854270 + 0.519830i \(0.174005\pi\)
−0.854270 + 0.519830i \(0.825995\pi\)
\(368\) −636438. 129454.i −0.244983 0.0498306i
\(369\) 24218.6 + 233423.i 0.00925942 + 0.0892436i
\(370\) −298646. −0.113410
\(371\) 4.03792e6i 1.52308i
\(372\) −654395. + 33857.3i −0.245179 + 0.0126851i
\(373\) 1.09025e6i 0.405747i 0.979205 + 0.202873i \(0.0650280\pi\)
−0.979205 + 0.202873i \(0.934972\pi\)
\(374\) 327631.i 0.121117i
\(375\) 985062. 50965.5i 0.361731 0.0187154i
\(376\) −1.23993e6 −0.452302
\(377\) 4.26300e6i 1.54476i
\(378\) 2.09214e6 327068.i 0.753114 0.117736i
\(379\) 3.15942e6i 1.12982i −0.825153 0.564909i \(-0.808911\pi\)
0.825153 0.564909i \(-0.191089\pi\)
\(380\) 343814.i 0.122142i
\(381\) 1.34066e6 69363.8i 0.473160 0.0244805i
\(382\) 2.45945e6i 0.862342i
\(383\) 177620. 0.0618721 0.0309361 0.999521i \(-0.490151\pi\)
0.0309361 + 0.999521i \(0.490151\pi\)
\(384\) −13196.4 255060.i −0.00456696 0.0882703i
\(385\) 820434.i 0.282093i
\(386\) 346710.i 0.118440i
\(387\) −302546. 2.91598e6i −0.102687 0.989708i
\(388\) 2.64276e6i 0.891208i
\(389\) −2.29354e6 −0.768480 −0.384240 0.923233i \(-0.625536\pi\)
−0.384240 + 0.923233i \(0.625536\pi\)
\(390\) 25027.7 + 483737.i 0.00833220 + 0.161045i
\(391\) 357237. + 72663.5i 0.118172 + 0.0240367i
\(392\) 174348.i 0.0573061i
\(393\) 189443. + 3.66157e6i 0.0618725 + 1.19587i
\(394\) 2.94320e6 0.955168
\(395\) 1.02110e6i 0.329288i
\(396\) 2.20438e6 228714.i 0.706396 0.0732917i
\(397\) −4.47721e6 −1.42571 −0.712856 0.701311i \(-0.752599\pi\)
−0.712856 + 0.701311i \(0.752599\pi\)
\(398\) 4.06670e6 1.28687
\(399\) −4.53937e6 + 234859.i −1.42746 + 0.0738543i
\(400\) −772846. −0.241514
\(401\) −3.59903e6 −1.11770 −0.558849 0.829269i \(-0.688757\pi\)
−0.558849 + 0.829269i \(0.688757\pi\)
\(402\) 1.76497e6 91316.8i 0.544719 0.0281829i
\(403\) −1.98166e6 −0.607808
\(404\) 2.83034e6i 0.862749i
\(405\) −595191. + 124852.i −0.180310 + 0.0378230i
\(406\) 3.15943e6i 0.951247i
\(407\) 4.13225e6i 1.23652i
\(408\) 7407.22 + 143167.i 0.00220295 + 0.0425787i
\(409\) 884663. 0.261499 0.130749 0.991415i \(-0.458262\pi\)
0.130749 + 0.991415i \(0.458262\pi\)
\(410\) 39784.8 0.0116885
\(411\) −2.09832e6 + 108564.i −0.612728 + 0.0317015i
\(412\) 16121.3i 0.00467906i
\(413\) 2.90139e6 0.837010
\(414\) 239515. 2.45430e6i 0.0686804 0.703763i
\(415\) 886108. 0.252561
\(416\) 772381.i 0.218826i
\(417\) 4.57322e6 236611.i 1.28790 0.0666339i
\(418\) −4.75722e6 −1.33172
\(419\) −3.89660e6 −1.08430 −0.542151 0.840281i \(-0.682390\pi\)
−0.542151 + 0.840281i \(0.682390\pi\)
\(420\) −18548.7 358510.i −0.00513087 0.0991696i
\(421\) 1.39428e6i 0.383393i −0.981454 0.191696i \(-0.938601\pi\)
0.981454 0.191696i \(-0.0613988\pi\)
\(422\) 612591.i 0.167452i
\(423\) −485854. 4.68273e6i −0.132025 1.27247i
\(424\) 1.84916e6i 0.499527i
\(425\) 433804. 0.116499
\(426\) 3.05896e6 158265.i 0.816675 0.0422534i
\(427\) 1.16990e6 0.310513
\(428\) 3.51663e6 0.927935
\(429\) 6.69328e6 346299.i 1.75588 0.0908465i
\(430\) −497002. −0.129624
\(431\) −3.67150e6 −0.952029 −0.476014 0.879437i \(-0.657919\pi\)
−0.476014 + 0.879437i \(0.657919\pi\)
\(432\) 958090. 149780.i 0.247000 0.0386140i
\(433\) 3.33060e6i 0.853695i −0.904324 0.426847i \(-0.859624\pi\)
0.904324 0.426847i \(-0.140376\pi\)
\(434\) 1.46866e6 0.374281
\(435\) −46882.8 906153.i −0.0118793 0.229603i
\(436\) 1.84524e6i 0.464875i
\(437\) −1.05508e6 + 5.18710e6i −0.264290 + 1.29934i
\(438\) 6104.52 + 117988.i 0.00152043 + 0.0293869i
\(439\) 6.64997e6 1.64687 0.823434 0.567413i \(-0.192056\pi\)
0.823434 + 0.567413i \(0.192056\pi\)
\(440\) 375716.i 0.0925183i
\(441\) −658442. + 68316.3i −0.161221 + 0.0167274i
\(442\) 433542.i 0.105554i
\(443\) 4.09635e6i 0.991717i −0.868403 0.495859i \(-0.834853\pi\)
0.868403 0.495859i \(-0.165147\pi\)
\(444\) 93423.7 + 1.80570e6i 0.0224905 + 0.434697i
\(445\) 179576. 0.0429882
\(446\) 2.12946e6i 0.506911i
\(447\) −1.40526e6 + 72705.9i −0.332651 + 0.0172108i
\(448\) 572432.i 0.134750i
\(449\) 3.04276e6i 0.712282i −0.934432 0.356141i \(-0.884092\pi\)
0.934432 0.356141i \(-0.115908\pi\)
\(450\) −302831. 2.91873e6i −0.0704968 0.679459i
\(451\) 550487.i 0.127440i
\(452\) −2.00030e6 −0.460520
\(453\) −334420. + 17302.3i −0.0765679 + 0.00396149i
\(454\) 2.50435e6i 0.570236i
\(455\) 1.08565e6i 0.245845i
\(456\) −2.07879e6 + 107553.i −0.468165 + 0.0242221i
\(457\) 3.83305e6i 0.858526i 0.903179 + 0.429263i \(0.141227\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(458\) 4.61280e6 1.02754
\(459\) −537782. + 84072.5i −0.119145 + 0.0186261i
\(460\) −409667. 83328.0i −0.0902686 0.0183610i
\(461\) 2.62615e6i 0.575530i 0.957701 + 0.287765i \(0.0929121\pi\)
−0.957701 + 0.287765i \(0.907088\pi\)
\(462\) −4.96057e6 + 256652.i −1.08125 + 0.0559422i
\(463\) −3.08478e6 −0.668762 −0.334381 0.942438i \(-0.608527\pi\)
−0.334381 + 0.942438i \(0.608527\pi\)
\(464\) 1.44685e6i 0.311982i
\(465\) −421226. + 21793.5i −0.0903405 + 0.00467407i
\(466\) −1.58266e6 −0.337615
\(467\) 1.08071e6 0.229307 0.114654 0.993406i \(-0.463424\pi\)
0.114654 + 0.993406i \(0.463424\pi\)
\(468\) 2.91697e6 302649.i 0.615627 0.0638741i
\(469\) −3.96113e6 −0.831548
\(470\) −798128. −0.166659
\(471\) −44057.8 851550.i −0.00915104 0.176871i
\(472\) 1.32868e6 0.274515
\(473\) 6.87683e6i 1.41330i
\(474\) −6.17386e6 + 319425.i −1.26215 + 0.0653016i
\(475\) 6.29885e6i 1.28094i
\(476\) 321310.i 0.0649990i
\(477\) 6.98353e6 724572.i 1.40533 0.145809i
\(478\) 5.48275e6 1.09756
\(479\) 4.99012e6 0.993738 0.496869 0.867826i \(-0.334483\pi\)
0.496869 + 0.867826i \(0.334483\pi\)
\(480\) −8494.35 164179.i −0.00168278 0.0325248i
\(481\) 5.46806e6i 1.07763i
\(482\) −2.86229e6 −0.561171
\(483\) −820334. + 5.46575e6i −0.160001 + 1.06606i
\(484\) −2.62182e6 −0.508733
\(485\) 1.70111e6i 0.328382i
\(486\) 941077. + 3.55963e6i 0.180732 + 0.683620i
\(487\) 7.59571e6 1.45126 0.725631 0.688084i \(-0.241548\pi\)
0.725631 + 0.688084i \(0.241548\pi\)
\(488\) 535753. 0.101839
\(489\) −7.08094e6 + 366356.i −1.33912 + 0.0692837i
\(490\) 112225.i 0.0211155i
\(491\) 1.51703e6i 0.283981i −0.989868 0.141990i \(-0.954650\pi\)
0.989868 0.141990i \(-0.0453502\pi\)
\(492\) −12445.6 240550.i −0.00231795 0.0448014i
\(493\) 812127.i 0.150490i
\(494\) −6.29506e6 −1.16060
\(495\) 1.41893e6 147220.i 0.260284 0.0270056i
\(496\) 672570. 0.122753
\(497\) −6.86523e6 −1.24671
\(498\) −277196. 5.35765e6i −0.0500857 0.968058i
\(499\) −7.32400e6 −1.31673 −0.658365 0.752698i \(-0.728752\pi\)
−0.658365 + 0.752698i \(0.728752\pi\)
\(500\) −1.01242e6 −0.181107
\(501\) −238564. 4.61096e6i −0.0424629 0.820725i
\(502\) 2.71678e6i 0.481167i
\(503\) 2.32651e6 0.410001 0.205000 0.978762i \(-0.434280\pi\)
0.205000 + 0.978762i \(0.434280\pi\)
\(504\) −2.16185e6 + 224301.i −0.379096 + 0.0393329i
\(505\) 1.82185e6i 0.317895i
\(506\) −1.15298e6 + 5.66841e6i −0.200191 + 0.984204i
\(507\) 3.07682e6 159190.i 0.531597 0.0275040i
\(508\) −1.37790e6 −0.236896
\(509\) 4.52964e6i 0.774943i −0.921882 0.387471i \(-0.873349\pi\)
0.921882 0.387471i \(-0.126651\pi\)
\(510\) 4767.93 + 92154.7i 0.000811717 + 0.0156889i
\(511\) 264802.i 0.0448609i
\(512\) 262144.i 0.0441942i
\(513\) −1.22074e6 7.80863e6i −0.204800 1.31003i
\(514\) 5.55472e6 0.927372
\(515\) 10377.1i 0.00172408i
\(516\) 155474. + 3.00501e6i 0.0257060 + 0.496846i
\(517\) 1.10434e7i 1.81709i
\(518\) 4.05253e6i 0.663593i
\(519\) 137461. + 2.65686e6i 0.0224007 + 0.432962i
\(520\) 497171.i 0.0806302i
\(521\) −7.46633e6 −1.20507 −0.602535 0.798092i \(-0.705843\pi\)
−0.602535 + 0.798092i \(0.705843\pi\)
\(522\) −5.46418e6 + 566933.i −0.877706 + 0.0910659i
\(523\) 672885.i 0.107569i 0.998553 + 0.0537844i \(0.0171284\pi\)
−0.998553 + 0.0537844i \(0.982872\pi\)
\(524\) 3.76326e6i 0.598737i
\(525\) 339823. + 6.56810e6i 0.0538089 + 1.04002i
\(526\) 4.25959e6i 0.671279i
\(527\) −377518. −0.0592122
\(528\) −2.27168e6 + 117533.i −0.354620 + 0.0183474i
\(529\) 5.92492e6 + 2.51433e6i 0.920541 + 0.390646i
\(530\) 1.19028e6i 0.184060i
\(531\) 520630. + 5.01791e6i 0.0801296 + 0.772301i
\(532\) 4.66544e6 0.714683
\(533\) 728439.i 0.111065i
\(534\) −56175.9 1.08577e6i −0.00852504 0.164772i
\(535\) 2.26361e6 0.341914
\(536\) −1.81399e6 −0.272724
\(537\) −556420. 1.07545e7i −0.0832659 1.60936i
\(538\) −411605. −0.0613091
\(539\) 1.55282e6 0.230223
\(540\) 616710. 96411.5i 0.0910116 0.0142280i
\(541\) 481127. 0.0706752 0.0353376 0.999375i \(-0.488749\pi\)
0.0353376 + 0.999375i \(0.488749\pi\)
\(542\) 7.29263e6i 1.06632i
\(543\) 213858. + 4.13345e6i 0.0311262 + 0.601608i
\(544\) 147143.i 0.0213178i
\(545\) 1.18776e6i 0.171292i
\(546\) −6.56415e6 + 339618.i −0.942316 + 0.0487539i
\(547\) 2.76810e6 0.395561 0.197780 0.980246i \(-0.436627\pi\)
0.197780 + 0.980246i \(0.436627\pi\)
\(548\) 2.15660e6 0.306774
\(549\) 209929. + 2.02333e6i 0.0297264 + 0.286507i
\(550\) 6.88332e6i 0.970267i
\(551\) 1.17921e7 1.65468
\(552\) −375670. + 2.50303e6i −0.0524758 + 0.349637i
\(553\) 1.38560e7 1.92675
\(554\) 2.23617e6i 0.309550i
\(555\) 60135.6 + 1.16230e6i 0.00828704 + 0.160172i
\(556\) −4.70024e6 −0.644812
\(557\) 1.35648e7 1.85258 0.926289 0.376815i \(-0.122981\pi\)
0.926289 + 0.376815i \(0.122981\pi\)
\(558\) 263539. + 2.54003e6i 0.0358311 + 0.345345i
\(559\) 9.09986e6i 1.23170i
\(560\) 368467.i 0.0496511i
\(561\) 1.27511e6 65972.1i 0.171057 0.00885020i
\(562\) 4.36663e6i 0.583184i
\(563\) −3.99287e6 −0.530902 −0.265451 0.964124i \(-0.585521\pi\)
−0.265451 + 0.964124i \(0.585521\pi\)
\(564\) 249674. + 4.82570e6i 0.0330503 + 0.638797i
\(565\) −1.28757e6 −0.169687
\(566\) −300442. −0.0394203
\(567\) −1.69419e6 8.07655e6i −0.221312 1.05504i
\(568\) −3.14391e6 −0.408884
\(569\) 5.99029e6 0.775653 0.387826 0.921732i \(-0.373226\pi\)
0.387826 + 0.921732i \(0.373226\pi\)
\(570\) −1.33809e6 + 69230.6i −0.172504 + 0.00892506i
\(571\) 1.11294e7i 1.42850i 0.699889 + 0.714251i \(0.253233\pi\)
−0.699889 + 0.714251i \(0.746767\pi\)
\(572\) −6.87917e6 −0.879116
\(573\) 9.57195e6 495237.i 1.21791 0.0630125i
\(574\) 539866.i 0.0683922i
\(575\) 7.50533e6 + 1.52661e6i 0.946673 + 0.192557i
\(576\) −990014. + 102718.i −0.124333 + 0.0129001i
\(577\) −9.78949e6 −1.22411 −0.612055 0.790815i \(-0.709657\pi\)
−0.612055 + 0.790815i \(0.709657\pi\)
\(578\) 5.59684e6i 0.696824i
\(579\) 1.34936e6 69813.8i 0.167276 0.00865456i
\(580\) 931320.i 0.114955i
\(581\) 1.20242e7i 1.47780i
\(582\) −1.02854e7 + 532149.i −1.25867 + 0.0651217i
\(583\) −1.64694e7 −2.00681
\(584\) 121265.i 0.0147131i
\(585\) 1.87762e6 194811.i 0.226839 0.0235356i
\(586\) 6.79531e6i 0.817458i
\(587\) 1.27469e7i 1.52690i −0.645869 0.763448i \(-0.723505\pi\)
0.645869 0.763448i \(-0.276495\pi\)
\(588\) 678546. 35106.8i 0.0809349 0.00418744i
\(589\) 5.48158e6i 0.651055i
\(590\) 855257. 0.101150
\(591\) −592646. 1.14547e7i −0.0697954 1.34901i
\(592\) 1.85585e6i 0.217639i
\(593\) 3.33570e6i 0.389538i −0.980849 0.194769i \(-0.937604\pi\)
0.980849 0.194769i \(-0.0623958\pi\)
\(594\) −1.33401e6 8.53318e6i −0.155129 0.992304i
\(595\) 206823.i 0.0239501i
\(596\) 1.44429e6 0.166548
\(597\) −818874. 1.58272e7i −0.0940332 1.81748i
\(598\) −1.52569e6 + 7.50080e6i −0.174468 + 0.857738i
\(599\) 2.57446e6i 0.293169i −0.989198 0.146585i \(-0.953172\pi\)
0.989198 0.146585i \(-0.0468281\pi\)
\(600\) 155621. + 3.00785e6i 0.0176478 + 0.341097i
\(601\) 6.52370e6 0.736729 0.368365 0.929681i \(-0.379918\pi\)
0.368365 + 0.929681i \(0.379918\pi\)
\(602\) 6.74416e6i 0.758467i
\(603\) −710793. 6.85072e6i −0.0796067 0.767261i
\(604\) 343708. 0.0383351
\(605\) −1.68763e6 −0.187452
\(606\) 1.10154e7 569919.i 1.21848 0.0630422i
\(607\) −8.25756e6 −0.909662 −0.454831 0.890578i \(-0.650300\pi\)
−0.454831 + 0.890578i \(0.650300\pi\)
\(608\) 2.13653e6 0.234396
\(609\) 1.22962e7 636185.i 1.34347 0.0695089i
\(610\) 344857. 0.0375245
\(611\) 1.46133e7i 1.58360i
\(612\) 555701. 57656.5i 0.0599740 0.00622256i
\(613\) 2.72531e6i 0.292930i 0.989216 + 0.146465i \(0.0467896\pi\)
−0.989216 + 0.146465i \(0.953210\pi\)
\(614\) 5.53955e6i 0.592999i
\(615\) −8011.10 154839.i −0.000854091 0.0165079i
\(616\) 5.09834e6 0.541349
\(617\) −167441. −0.0177072 −0.00885358 0.999961i \(-0.502818\pi\)
−0.00885358 + 0.999961i \(0.502818\pi\)
\(618\) 62742.8 3246.21i 0.00660835 0.000341905i
\(619\) 4.02548e6i 0.422271i −0.977457 0.211135i \(-0.932284\pi\)
0.977457 0.211135i \(-0.0677161\pi\)
\(620\) 432924. 0.0452306
\(621\) −9.60014e6 437972.i −0.998961 0.0455740i
\(622\) −7.11708e6 −0.737609
\(623\) 2.43679e6i 0.251535i
\(624\) −3.00604e6 + 155527.i −0.309053 + 0.0159899i
\(625\) 8.78248e6 0.899326
\(626\) 382088. 0.0389698
\(627\) 957918. + 1.85147e7i 0.0973105 + 1.88082i
\(628\) 875200.i 0.0885540i
\(629\) 1.04170e6i 0.104982i
\(630\) −1.39155e6 + 144380.i −0.139685 + 0.0144929i
\(631\) 5.31227e6i 0.531137i −0.964092 0.265569i \(-0.914440\pi\)
0.964092 0.265569i \(-0.0855597\pi\)
\(632\) 6.34533e6 0.631919
\(633\) −2.38415e6 + 123352.i −0.236496 + 0.0122359i
\(634\) 1.28013e6 0.126482
\(635\) −886936. −0.0872887
\(636\) −7.19675e6 + 372348.i −0.705494 + 0.0365011i
\(637\) 2.05479e6 0.200641
\(638\) 1.28863e7 1.25336
\(639\) −1.23191e6 1.18733e7i −0.119351 1.15032i
\(640\) 168739.i 0.0162841i
\(641\) −8.94382e6 −0.859761 −0.429881 0.902886i \(-0.641444\pi\)
−0.429881 + 0.902886i \(0.641444\pi\)
\(642\) −708112. 1.36864e7i −0.0678054 1.31054i
\(643\) 1.57124e6i 0.149870i −0.997188 0.0749350i \(-0.976125\pi\)
0.997188 0.0749350i \(-0.0238749\pi\)
\(644\) 1.13073e6 5.55905e6i 0.107435 0.528185i
\(645\) 100077. + 1.93429e6i 0.00947183 + 0.183072i
\(646\) −1.19925e6 −0.113065
\(647\) 1.02267e7i 0.960450i 0.877145 + 0.480225i \(0.159445\pi\)
−0.877145 + 0.480225i \(0.840555\pi\)
\(648\) −775852. 3.69864e6i −0.0725841 0.346022i
\(649\) 1.18339e7i 1.10285i
\(650\) 9.10845e6i 0.845593i
\(651\) −295731. 5.71589e6i −0.0273492 0.528606i
\(652\) 7.27760e6 0.670454
\(653\) 1.09647e7i 1.00627i −0.864209 0.503133i \(-0.832181\pi\)
0.864209 0.503133i \(-0.167819\pi\)
\(654\) −7.18151e6 + 371559.i −0.656555 + 0.0339691i
\(655\) 2.42236e6i 0.220615i
\(656\) 247230.i 0.0224307i
\(657\) 457970. 47516.5i 0.0413927 0.00429468i
\(658\) 1.08303e7i 0.975164i
\(659\) −1.26624e7 −1.13581 −0.567903 0.823096i \(-0.692245\pi\)
−0.567903 + 0.823096i \(0.692245\pi\)
\(660\) −1.46225e6 + 75654.5i −0.130666 + 0.00676044i
\(661\) 5.76883e6i 0.513552i −0.966471 0.256776i \(-0.917340\pi\)
0.966471 0.256776i \(-0.0826602\pi\)
\(662\) 1.90629e6i 0.169062i
\(663\) 1.68731e6 87298.5i 0.149077 0.00771299i
\(664\) 5.50645e6i 0.484676i
\(665\) 3.00308e6 0.263338
\(666\) 7.00879e6 727193.i 0.612290 0.0635278i
\(667\) 2.85799e6 1.40508e7i 0.248740 1.22289i
\(668\) 4.73903e6i 0.410911i
\(669\) −8.28765e6 + 428789.i −0.715922 + 0.0370406i
\(670\) −1.16764e6 −0.100490
\(671\) 4.77166e6i 0.409132i
\(672\) 2.22785e6 115266.i 0.190311 0.00984637i
\(673\) −2.25262e7 −1.91713 −0.958564 0.284878i \(-0.908047\pi\)
−0.958564 + 0.284878i \(0.908047\pi\)
\(674\) 1.45735e7 1.23570
\(675\) −1.12985e7 + 1.76631e6i −0.954465 + 0.149213i
\(676\) −3.16228e6 −0.266154
\(677\) −2.32505e6 −0.194967 −0.0974833 0.995237i \(-0.531079\pi\)
−0.0974833 + 0.995237i \(0.531079\pi\)
\(678\) 402782. + 7.78498e6i 0.0336508 + 0.650404i
\(679\) 2.30835e7 1.92145
\(680\) 94714.1i 0.00785493i
\(681\) 9.74668e6 504277.i 0.805358 0.0416679i
\(682\) 5.99021e6i 0.493152i
\(683\) 2.41065e7i 1.97735i −0.150077 0.988674i \(-0.547952\pi\)
0.150077 0.988674i \(-0.452048\pi\)
\(684\) 837175. + 8.06881e6i 0.0684189 + 0.659431i
\(685\) 1.38817e6 0.113036
\(686\) 7.87252e6 0.638710
\(687\) −928837. 1.79526e7i −0.0750840 1.45123i
\(688\) 3.08847e6i 0.248755i
\(689\) −2.17934e7 −1.74895
\(690\) −241814. + 1.61117e6i −0.0193356 + 0.128830i
\(691\) 1.69825e7 1.35302 0.676512 0.736431i \(-0.263491\pi\)
0.676512 + 0.736431i \(0.263491\pi\)
\(692\) 2.73065e6i 0.216771i
\(693\) 1.99773e6 + 1.92544e7i 0.158017 + 1.52299i
\(694\) −9.73417e6 −0.767185
\(695\) −3.02548e6 −0.237592
\(696\) 5.63101e6 291339.i 0.440619 0.0227969i
\(697\) 138772.i 0.0108198i
\(698\) 4.34791e6i 0.337787i
\(699\) 318685. + 6.15956e6i 0.0246700 + 0.476822i
\(700\) 6.75052e6i 0.520706i
\(701\) −3.19831e6 −0.245825 −0.122912 0.992418i \(-0.539223\pi\)
−0.122912 + 0.992418i \(0.539223\pi\)
\(702\) −1.76525e6 1.12917e7i −0.135196 0.864798i
\(703\) −1.51255e7 −1.15431
\(704\) 2.33477e6 0.177547
\(705\) 160712. + 3.10624e6i 0.0121780 + 0.235376i
\(706\) −7.33784e6 −0.554060
\(707\) −2.47219e7 −1.86009
\(708\) −267545. 5.17112e6i −0.0200592 0.387705i
\(709\) 331472.i 0.0247646i −0.999923 0.0123823i \(-0.996058\pi\)
0.999923 0.0123823i \(-0.00394151\pi\)
\(710\) −2.02370e6 −0.150661
\(711\) 2.48635e6 + 2.39638e7i 0.184454 + 1.77779i
\(712\) 1.11592e6i 0.0824963i
\(713\) −6.53151e6 1.32854e6i −0.481160 0.0978700i
\(714\) −1.25051e6 + 64699.3i −0.0917997 + 0.00474957i
\(715\) −4.42804e6 −0.323926
\(716\) 1.10532e7i 0.805758i
\(717\) −1.10401e6 2.13383e7i −0.0802002 1.55011i
\(718\) 1.58815e7i 1.14969i
\(719\) 2.48340e7i 1.79153i 0.444530 + 0.895764i \(0.353371\pi\)
−0.444530 + 0.895764i \(0.646629\pi\)
\(720\) −637259. + 66118.4i −0.0458126 + 0.00475326i
\(721\) −140814. −0.0100881
\(722\) 7.50873e6i 0.536072i
\(723\) 576353. + 1.11398e7i 0.0410055 + 0.792556i
\(724\) 4.24825e6i 0.301206i
\(725\) 1.70623e7i 1.20557i
\(726\) 527933. + 1.02039e7i 0.0371738 + 0.718496i
\(727\) 4.76809e6i 0.334586i −0.985907 0.167293i \(-0.946497\pi\)
0.985907 0.167293i \(-0.0535027\pi\)
\(728\) 6.74646e6 0.471788
\(729\) 1.36643e7 4.37936e6i 0.952287 0.305205i
\(730\) 78056.8i 0.00542130i
\(731\) 1.73358e6i 0.119991i
\(732\) −107880. 2.08510e6i −0.00744153 0.143830i
\(733\) 2.36493e6i 0.162577i −0.996691 0.0812883i \(-0.974097\pi\)
0.996691 0.0812883i \(-0.0259034\pi\)
\(734\) −1.07304e7 −0.735151
\(735\) 436771. 22597.8i 0.0298219 0.00154294i
\(736\) 517817. 2.54575e6i 0.0352356 0.173229i
\(737\) 1.61562e7i 1.09565i
\(738\) −933691. + 96874.6i −0.0631048 + 0.00654740i
\(739\) −1.64314e7 −1.10678 −0.553391 0.832921i \(-0.686667\pi\)
−0.553391 + 0.832921i \(0.686667\pi\)
\(740\) 1.19458e6i 0.0801932i
\(741\) 1.26758e6 + 2.44998e7i 0.0848066 + 1.63914i
\(742\) 1.61517e7 1.07698
\(743\) 880922. 0.0585417 0.0292708 0.999572i \(-0.490681\pi\)
0.0292708 + 0.999572i \(0.490681\pi\)
\(744\) −135429. 2.61758e6i −0.00896975 0.173367i
\(745\) 929671. 0.0613675
\(746\) −4.36101e6 −0.286906
\(747\) −2.07957e7 + 2.15764e6i −1.36355 + 0.141475i
\(748\) −1.31052e6 −0.0856428
\(749\) 3.07165e7i 2.00063i
\(750\) 203862. + 3.94025e6i 0.0132338 + 0.255782i
\(751\) 1.49362e7i 0.966360i 0.875521 + 0.483180i \(0.160518\pi\)
−0.875521 + 0.483180i \(0.839482\pi\)
\(752\) 4.95973e6i 0.319826i
\(753\) 1.05735e7 547054.i 0.679564 0.0351595i
\(754\) 1.70520e7 1.09231
\(755\) 221240. 0.0141253
\(756\) 1.30827e6 + 8.36856e6i 0.0832518 + 0.532532i
\(757\) 2.64695e7i 1.67883i −0.543495 0.839413i \(-0.682899\pi\)
0.543495 0.839413i \(-0.317101\pi\)
\(758\) 1.26377e7 0.798903
\(759\) 2.22931e7 + 3.34589e6i 1.40464 + 0.210818i
\(760\) 1.37525e6 0.0863673
\(761\) 5.98030e6i 0.374336i 0.982328 + 0.187168i \(0.0599308\pi\)
−0.982328 + 0.187168i \(0.940069\pi\)
\(762\) 277455. + 5.36266e6i 0.0173103 + 0.334574i
\(763\) 1.61175e7 1.00227
\(764\) −9.83780e6 −0.609768
\(765\) 357698. 37112.7i 0.0220985 0.00229282i
\(766\) 710480.i 0.0437502i
\(767\) 1.56593e7i 0.961136i
\(768\) 1.02024e6 52785.6i 0.0624165 0.00322933i
\(769\) 1.63013e7i 0.994046i 0.867737 + 0.497023i \(0.165573\pi\)
−0.867737 + 0.497023i \(0.834427\pi\)
\(770\) 3.28174e6 0.199470
\(771\) −1.11850e6 2.16185e7i −0.0677643 1.30975i
\(772\) −1.38684e6 −0.0837496
\(773\) −1.75987e7 −1.05933 −0.529667 0.848206i \(-0.677683\pi\)
−0.529667 + 0.848206i \(0.677683\pi\)
\(774\) 1.16639e7 1.21018e6i 0.699829 0.0726104i
\(775\) −7.93141e6 −0.474347
\(776\) 1.05711e7 0.630179
\(777\) −1.57721e7 + 816021.i −0.937209 + 0.0484896i
\(778\) 9.17416e6i 0.543397i
\(779\) 2.01498e6 0.118967
\(780\) −1.93495e6 + 100111.i −0.113876 + 0.00589176i
\(781\) 2.80011e7i 1.64266i
\(782\) −290654. + 1.42895e6i −0.0169965 + 0.0835602i
\(783\) 3.30672e6 + 2.11519e7i 0.192750 + 1.23295i
\(784\) −697391. −0.0405216
\(785\) 563355.i 0.0326293i
\(786\) −1.46463e7 + 757773.i −0.845611 + 0.0437505i
\(787\) 2.02421e7i 1.16498i −0.812838 0.582490i \(-0.802078\pi\)
0.812838 0.582490i \(-0.197922\pi\)
\(788\) 1.17728e7i 0.675406i
\(789\) 1.65779e7 857715.i 0.948064 0.0490513i
\(790\) 4.08441e6 0.232842
\(791\) 1.74719e7i 0.992883i
\(792\) 914856. + 8.81751e6i 0.0518250 + 0.499497i
\(793\) 6.31417e6i 0.356561i
\(794\) 1.79089e7i 1.00813i
\(795\) −4.63245e6 + 239676.i −0.259952 + 0.0134495i
\(796\) 1.62668e7i 0.909954i
\(797\) 3.03091e7 1.69016 0.845080 0.534640i \(-0.179553\pi\)
0.845080 + 0.534640i \(0.179553\pi\)
\(798\) −939437. 1.81575e7i −0.0522229 1.00936i
\(799\) 2.78393e6i 0.154273i
\(800\) 3.09139e6i 0.170777i
\(801\) −4.21440e6 + 437263.i −0.232089 + 0.0240803i
\(802\) 1.43961e7i 0.790332i
\(803\) −1.08004e6 −0.0591088
\(804\) 365267. + 7.05989e6i 0.0199283 + 0.385175i
\(805\) 727839. 3.57829e6i 0.0395863 0.194619i
\(806\) 7.92663e6i 0.429785i
\(807\) 82881.1 + 1.60193e6i 0.00447993 + 0.0865883i
\(808\) −1.13213e7 −0.610056
\(809\) 1.30668e7i 0.701938i 0.936387 + 0.350969i \(0.114148\pi\)
−0.936387 + 0.350969i \(0.885852\pi\)
\(810\) −499406. 2.38077e6i −0.0267449 0.127498i
\(811\) 1.74183e7 0.929935 0.464968 0.885328i \(-0.346066\pi\)
0.464968 + 0.885328i \(0.346066\pi\)
\(812\) −1.26377e7 −0.672633
\(813\) 2.83822e7 1.46845e6i 1.50598 0.0779171i
\(814\) −1.65290e7 −0.874351
\(815\) 4.68450e6 0.247041
\(816\) −572668. + 29628.9i −0.0301077 + 0.00155772i
\(817\) −2.51717e7 −1.31934
\(818\) 3.53865e6i 0.184907i
\(819\) 2.64353e6 + 2.54787e7i 0.137713 + 1.32729i
\(820\) 159139.i 0.00826498i
\(821\) 1.35544e7i 0.701816i −0.936410 0.350908i \(-0.885873\pi\)
0.936410 0.350908i \(-0.114127\pi\)
\(822\) −434255. 8.39329e6i −0.0224164 0.433264i
\(823\) −1.27411e7 −0.655705 −0.327852 0.944729i \(-0.606325\pi\)
−0.327852 + 0.944729i \(0.606325\pi\)
\(824\) −64485.4 −0.00330859
\(825\) 2.67893e7 1.38603e6i 1.37033 0.0708987i
\(826\) 1.16056e7i 0.591856i
\(827\) −6.73222e6 −0.342290 −0.171145 0.985246i \(-0.554747\pi\)
−0.171145 + 0.985246i \(0.554747\pi\)
\(828\) 9.81720e6 + 958061.i 0.497636 + 0.0485643i
\(829\) −8.06147e6 −0.407406 −0.203703 0.979033i \(-0.565298\pi\)
−0.203703 + 0.979033i \(0.565298\pi\)
\(830\) 3.54443e6i 0.178588i
\(831\) 8.70297e6 450277.i 0.437185 0.0226192i
\(832\) 3.08952e6 0.154733
\(833\) 391450. 0.0195463
\(834\) 946444. + 1.82929e7i 0.0471173 + 0.910683i
\(835\) 3.05045e6i 0.151408i
\(836\) 1.90289e7i 0.941667i
\(837\) 9.83249e6 1.53713e6i 0.485121 0.0758399i
\(838\) 1.55864e7i 0.766718i
\(839\) 5.25374e6 0.257670 0.128835 0.991666i \(-0.458876\pi\)
0.128835 + 0.991666i \(0.458876\pi\)
\(840\) 1.43404e6 74194.9i 0.0701235 0.00362807i
\(841\) −1.14313e7 −0.557321
\(842\) 5.57711e6 0.271099
\(843\) −1.69945e7 + 879268.i −0.823645 + 0.0426140i
\(844\) 2.45036e6 0.118406
\(845\) −2.03552e6 −0.0980693
\(846\) 1.87309e7 1.94342e6i 0.899774 0.0933555i
\(847\) 2.29006e7i 1.09683i
\(848\) 7.39663e6 0.353219
\(849\) 60497.3 + 1.16929e6i 0.00288049 + 0.0556742i
\(850\) 1.73521e6i 0.0823770i
\(851\) −3.66588e6 + 1.80226e7i −0.173522 + 0.853089i
\(852\) 633061. + 1.22358e7i 0.0298777 + 0.577476i
\(853\) 1.51042e7 0.710764 0.355382 0.934721i \(-0.384351\pi\)
0.355382 + 0.934721i \(0.384351\pi\)
\(854\) 4.67960e6i 0.219566i
\(855\) 538879. + 5.19379e6i 0.0252102 + 0.242979i
\(856\) 1.40665e7i 0.656149i
\(857\) 3.62300e7i 1.68506i 0.538648 + 0.842531i \(0.318935\pi\)
−0.538648 + 0.842531i \(0.681065\pi\)
\(858\) 1.38520e6 + 2.67731e7i 0.0642382 + 1.24160i
\(859\) −1.86346e7 −0.861660 −0.430830 0.902433i \(-0.641779\pi\)
−0.430830 + 0.902433i \(0.641779\pi\)
\(860\) 1.98801e6i 0.0916583i
\(861\) 2.10111e6 108708.i 0.0965920 0.00499751i
\(862\) 1.46860e7i 0.673186i
\(863\) 3.58311e7i 1.63770i −0.574011 0.818848i \(-0.694613\pi\)
0.574011 0.818848i \(-0.305387\pi\)
\(864\) 599120. + 3.83236e6i 0.0273042 + 0.174655i
\(865\) 1.75768e6i 0.0798730i
\(866\) 1.33224e7 0.603653
\(867\) −2.17824e7 + 1.12698e6i −0.984141 + 0.0509178i
\(868\) 5.87464e6i 0.264656i
\(869\) 5.65144e7i 2.53869i
\(870\) 3.62461e6 187531.i 0.162354 0.00839993i
\(871\) 2.13790e7i 0.954864i
\(872\) 7.38096e6 0.328717
\(873\) 4.14215e6 + 3.99227e7i 0.183946 + 1.77290i
\(874\) −2.07484e7 4.22031e6i −0.918769 0.186881i
\(875\) 8.84312e6i 0.390468i
\(876\) −471953. + 24418.1i −0.0207797 + 0.00107511i
\(877\) 2.02561e7 0.889317 0.444658 0.895700i \(-0.353325\pi\)
0.444658 + 0.895700i \(0.353325\pi\)
\(878\) 2.65999e7i 1.16451i
\(879\) −2.64467e7 + 1.36831e6i −1.15452 + 0.0597327i
\(880\) 1.50286e6 0.0654204
\(881\) −1.08688e7 −0.471782 −0.235891 0.971779i \(-0.575801\pi\)
−0.235891 + 0.971779i \(0.575801\pi\)
\(882\) −273265. 2.63377e6i −0.0118280 0.114000i
\(883\) 2.48720e7 1.07351 0.536757 0.843737i \(-0.319649\pi\)
0.536757 + 0.843737i \(0.319649\pi\)
\(884\) −1.73417e6 −0.0746382
\(885\) −172215. 3.32858e6i −0.00739118 0.142857i
\(886\) 1.63854e7 0.701250
\(887\) 3.71436e7i 1.58517i 0.609765 + 0.792583i \(0.291264\pi\)
−0.609765 + 0.792583i \(0.708736\pi\)
\(888\) −7.22278e6 + 373695.i −0.307378 + 0.0159032i
\(889\) 1.20354e7i 0.510749i
\(890\) 718306.i 0.0303972i
\(891\) −3.29418e7 + 6.91009e6i −1.39012 + 0.291601i
\(892\) 8.51782e6 0.358440
\(893\) −4.04228e7 −1.69628
\(894\) −290824. 5.62105e6i −0.0121699 0.235220i
\(895\) 7.11479e6i 0.296896i
\(896\) −2.28973e6 −0.0952827
\(897\) 2.94997e7 + 4.42749e6i 1.22415 + 0.183729i
\(898\) 1.21710e7 0.503659
\(899\) 1.48485e7i 0.612748i
\(900\) 1.16749e7 1.21133e6i 0.480450 0.0498488i
\(901\) −4.15178e6 −0.170381
\(902\) 2.20195e6 0.0901136
\(903\) −2.62476e7 + 1.35801e6i −1.07120 + 0.0554222i
\(904\) 8.00119e6i 0.325637i
\(905\) 2.73454e6i 0.110985i
\(906\) −69209.3 1.33768e6i −0.00280120 0.0541417i
\(907\) 1.30765e7i 0.527803i 0.964550 + 0.263902i \(0.0850094\pi\)
−0.964550 + 0.263902i \(0.914991\pi\)
\(908\) −1.00174e7 −0.403218
\(909\) −4.43615e6 4.27562e7i −0.178072 1.71629i
\(910\) 4.34261e6 0.173839
\(911\) 1.76520e7 0.704690 0.352345 0.935870i \(-0.385384\pi\)
0.352345 + 0.935870i \(0.385384\pi\)
\(912\) −430213. 8.31517e6i −0.0171276 0.331043i
\(913\) 4.90430e7 1.94715
\(914\) −1.53322e7 −0.607070
\(915\) −69440.8 1.34215e6i −0.00274197 0.0529968i
\(916\) 1.84512e7i 0.726583i
\(917\) 3.28707e7 1.29088
\(918\) −336290. 2.15113e6i −0.0131707 0.0842480i
\(919\) 2.87633e7i 1.12344i −0.827327 0.561721i \(-0.810140\pi\)
0.827327 0.561721i \(-0.189860\pi\)
\(920\) 333312. 1.63867e6i 0.0129832 0.0638295i
\(921\) −2.15594e7 + 1.11545e6i −0.837507 + 0.0433312i
\(922\) −1.05046e7 −0.406961
\(923\) 3.70529e7i 1.43159i
\(924\) −1.02661e6 1.98423e7i −0.0395571 0.764560i
\(925\) 2.18854e7i 0.841009i
\(926\) 1.23391e7i 0.472886i
\(927\) −25267.9 243536.i −0.000965762 0.00930815i
\(928\) −5.78741e6 −0.220604
\(929\) 3.89993e7i 1.48258i −0.671186 0.741289i \(-0.734215\pi\)
0.671186 0.741289i \(-0.265785\pi\)
\(930\) −87174.1 1.68490e6i −0.00330506 0.0638804i
\(931\) 5.68388e6i 0.214917i
\(932\) 6.33063e6i 0.238730i
\(933\) 1.43310e6 + 2.76990e7i 0.0538981 + 1.04174i
\(934\) 4.32285e6i 0.162145i
\(935\) −843567. −0.0315566
\(936\) 1.21060e6 + 1.16679e7i 0.0451658 + 0.435314i
\(937\) 1.09436e7i 0.407204i −0.979054 0.203602i \(-0.934735\pi\)
0.979054 0.203602i \(-0.0652648\pi\)
\(938\) 1.58445e7i 0.587993i
\(939\) −76937.6 1.48705e6i −0.00284757 0.0550380i
\(940\) 3.19251e6i 0.117846i
\(941\) −3.22825e7 −1.18848 −0.594242 0.804287i \(-0.702548\pi\)
−0.594242 + 0.804287i \(0.702548\pi\)
\(942\) 3.40620e6 176231.i 0.125067 0.00647076i
\(943\) 488358. 2.40092e6i 0.0178838 0.0879223i
\(944\) 5.31474e6i 0.194112i
\(945\) 842118. + 5.38673e6i 0.0306756 + 0.196221i
\(946\) −2.75073e7 −0.999356
\(947\) 1.93494e7i 0.701120i 0.936540 + 0.350560i \(0.114009\pi\)
−0.936540 + 0.350560i \(0.885991\pi\)
\(948\) −1.27770e6 2.46954e7i −0.0461752 0.892475i
\(949\) −1.42918e6 −0.0515136
\(950\) −2.51954e7 −0.905759
\(951\) −257768. 4.98214e6i −0.00924224 0.178634i
\(952\) 1.28524e6 0.0459613
\(953\) 4.27930e7 1.52630 0.763151 0.646221i \(-0.223651\pi\)
0.763151 + 0.646221i \(0.223651\pi\)
\(954\) 2.89829e6 + 2.79341e7i 0.103103 + 0.993720i
\(955\) −6.33246e6 −0.224680
\(956\) 2.19310e7i 0.776092i
\(957\) −2.59480e6 5.01524e7i −0.0915850 1.77016i
\(958\) 1.99605e7i 0.702679i
\(959\) 1.88371e7i 0.661404i
\(960\) 656716. 33977.4i 0.0229985 0.00118990i
\(961\) −2.17268e7 −0.758906
\(962\) −2.18722e7 −0.762001
\(963\) −5.31237e7 + 5.51181e6i −1.84596 + 0.191527i
\(964\) 1.14491e7i 0.396808i
\(965\) −892690. −0.0308591
\(966\) −2.18630e7 3.28134e6i −0.753819 0.113138i
\(967\) −5.40541e7 −1.85893 −0.929465 0.368911i \(-0.879731\pi\)
−0.929465 + 0.368911i \(0.879731\pi\)
\(968\) 1.04873e7i 0.359729i
\(969\) 241481. + 4.66736e6i 0.00826179 + 0.159684i
\(970\) 6.80445e6 0.232201
\(971\) −3.80597e6 −0.129544 −0.0647721 0.997900i \(-0.520632\pi\)
−0.0647721 + 0.997900i \(0.520632\pi\)
\(972\) −1.42385e7 + 3.76431e6i −0.483392 + 0.127797i
\(973\) 4.10548e7i 1.39022i
\(974\) 3.03828e7i 1.02620i
\(975\) 3.54493e7 1.83409e6i 1.19425 0.0617886i
\(976\) 2.14301e6i 0.0720112i
\(977\) 4.53725e7 1.52075 0.760373 0.649487i \(-0.225016\pi\)
0.760373 + 0.649487i \(0.225016\pi\)
\(978\) −1.46542e6 2.83238e7i −0.0489910 0.946899i
\(979\) 9.93892e6 0.331423
\(980\) −448902. −0.0149309
\(981\) 2.89215e6 + 2.78749e7i 0.0959507 + 0.924787i
\(982\) 6.06810e6 0.200805
\(983\) 4.31706e7 1.42497 0.712483 0.701690i \(-0.247571\pi\)
0.712483 + 0.701690i \(0.247571\pi\)
\(984\) 962198. 49782.5i 0.0316794 0.00163904i
\(985\) 7.57801e6i 0.248865i
\(986\) 3.24851e6 0.106412
\(987\) −4.21507e7 + 2.18081e6i −1.37725 + 0.0712565i
\(988\) 2.51802e7i 0.820668i
\(989\) −6.10070e6 + 2.99930e7i −0.198330 + 0.975055i
\(990\) 588881. + 5.67572e6i 0.0190959 + 0.184049i
\(991\) 6.02354e7 1.94835 0.974176 0.225790i \(-0.0724963\pi\)
0.974176 + 0.225790i \(0.0724963\pi\)
\(992\) 2.69028e6i 0.0867997i
\(993\) 7.41912e6 383853.i 0.238770 0.0123536i
\(994\) 2.74609e7i 0.881554i
\(995\) 1.04707e7i 0.335289i
\(996\) 2.14306e7 1.10878e6i 0.684520 0.0354160i
\(997\) −2.68093e7 −0.854176 −0.427088 0.904210i \(-0.640461\pi\)
−0.427088 + 0.904210i \(0.640461\pi\)
\(998\) 2.92960e7i 0.931069i
\(999\) −4.24147e6 2.71311e7i −0.134463 0.860111i
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 138.6.d.a.137.15 yes 40
3.2 odd 2 inner 138.6.d.a.137.14 yes 40
23.22 odd 2 inner 138.6.d.a.137.16 yes 40
69.68 even 2 inner 138.6.d.a.137.13 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.6.d.a.137.13 40 69.68 even 2 inner
138.6.d.a.137.14 yes 40 3.2 odd 2 inner
138.6.d.a.137.15 yes 40 1.1 even 1 trivial
138.6.d.a.137.16 yes 40 23.22 odd 2 inner