Properties

Label 76.8.d.a.75.1
Level $76$
Weight $8$
Character 76.75
Analytic conductor $23.741$
Analytic rank $0$
Dimension $68$
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] = [76,8,Mod(75,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.75");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 76.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: \(23.7412619368\)
Analytic rank: \(0\)
Dimension: \(68\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 75.1
Character \(\chi\) \(=\) 76.75
Dual form 76.8.d.a.75.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.3050 - 0.442790i) q^{2} +16.6522 q^{3} +(127.608 + 10.0115i) q^{4} +341.116 q^{5} +(-188.254 - 7.37345i) q^{6} -1382.96i q^{7} +(-1438.18 - 169.684i) q^{8} -1909.70 q^{9} +O(q^{10})\) \(q+(-11.3050 - 0.442790i) q^{2} +16.6522 q^{3} +(127.608 + 10.0115i) q^{4} +341.116 q^{5} +(-188.254 - 7.37345i) q^{6} -1382.96i q^{7} +(-1438.18 - 169.684i) q^{8} -1909.70 q^{9} +(-3856.33 - 151.043i) q^{10} -3929.55i q^{11} +(2124.96 + 166.714i) q^{12} -1276.78i q^{13} +(-612.359 + 15634.4i) q^{14} +5680.35 q^{15} +(16183.5 + 2555.10i) q^{16} -3972.88 q^{17} +(21589.3 + 845.598i) q^{18} +(-19789.9 + 22410.5i) q^{19} +(43529.1 + 3415.09i) q^{20} -23029.3i q^{21} +(-1739.97 + 44423.8i) q^{22} -61712.8i q^{23} +(-23948.9 - 2825.62i) q^{24} +38235.1 q^{25} +(-565.347 + 14434.1i) q^{26} -68219.3 q^{27} +(13845.5 - 176476. i) q^{28} +237876. i q^{29} +(-64216.6 - 2515.20i) q^{30} -176262. q^{31} +(-181824. - 36051.4i) q^{32} -65435.9i q^{33} +(44913.6 + 1759.15i) q^{34} -471748. i q^{35} +(-243693. - 19119.0i) q^{36} -49926.2i q^{37} +(233649. - 244589. i) q^{38} -21261.3i q^{39} +(-490586. - 57882.0i) q^{40} -696583. i q^{41} +(-10197.2 + 260347. i) q^{42} -231172. i q^{43} +(39340.8 - 501442. i) q^{44} -651430. q^{45} +(-27325.9 + 697666. i) q^{46} +728161. i q^{47} +(269492. + 42548.1i) q^{48} -1.08902e6 q^{49} +(-432250. - 16930.1i) q^{50} -66157.4 q^{51} +(12782.5 - 162928. i) q^{52} -1.67316e6i q^{53} +(771222. + 30206.9i) q^{54} -1.34043e6i q^{55} +(-234666. + 1.98894e6i) q^{56} +(-329547. + 373185. i) q^{57} +(105329. - 2.68920e6i) q^{58} -2.09273e6 q^{59} +(724857. + 56869.0i) q^{60} +488351. q^{61} +(1.99265e6 + 78047.2i) q^{62} +2.64103e6i q^{63} +(2.03957e6 + 488073. i) q^{64} -435531. i q^{65} +(-28974.4 + 739755. i) q^{66} +463413. q^{67} +(-506971. - 39774.6i) q^{68} -1.02766e6i q^{69} +(-208886. + 5.33313e6i) q^{70} +3.96707e6 q^{71} +(2.74649e6 + 324046. i) q^{72} -204855. q^{73} +(-22106.8 + 564417. i) q^{74} +636701. q^{75} +(-2.74971e6 + 2.66163e6i) q^{76} -5.43440e6 q^{77} +(-9414.30 + 240360. i) q^{78} +3.63759e6 q^{79} +(5.52046e6 + 871585. i) q^{80} +3.04051e6 q^{81} +(-308440. + 7.87490e6i) q^{82} -3.67550e6i q^{83} +(230559. - 2.93872e6i) q^{84} -1.35521e6 q^{85} +(-102361. + 2.61341e6i) q^{86} +3.96117e6i q^{87} +(-666783. + 5.65140e6i) q^{88} -9.78887e6i q^{89} +(7.36444e6 + 288447. i) q^{90} -1.76573e6 q^{91} +(617840. - 7.87504e6i) q^{92} -2.93516e6 q^{93} +(322423. - 8.23189e6i) q^{94} +(-6.75066e6 + 7.64458e6i) q^{95} +(-3.02778e6 - 600337. i) q^{96} -9.38988e6i q^{97} +(1.23114e7 + 482209. i) q^{98} +7.50428e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.3050 0.442790i −0.999234 0.0391375i
\(3\) 16.6522 0.356081 0.178040 0.984023i \(-0.443024\pi\)
0.178040 + 0.984023i \(0.443024\pi\)
\(4\) 127.608 + 10.0115i 0.996937 + 0.0782150i
\(5\) 341.116 1.22041 0.610207 0.792242i \(-0.291086\pi\)
0.610207 + 0.792242i \(0.291086\pi\)
\(6\) −188.254 7.37345i −0.355808 0.0139361i
\(7\) 1382.96i 1.52393i −0.647618 0.761965i \(-0.724235\pi\)
0.647618 0.761965i \(-0.275765\pi\)
\(8\) −1438.18 169.684i −0.993112 0.117173i
\(9\) −1909.70 −0.873207
\(10\) −3856.33 151.043i −1.21948 0.0477640i
\(11\) 3929.55i 0.890161i −0.895490 0.445081i \(-0.853175\pi\)
0.895490 0.445081i \(-0.146825\pi\)
\(12\) 2124.96 + 166.714i 0.354990 + 0.0278509i
\(13\) 1276.78i 0.161182i −0.996747 0.0805908i \(-0.974319\pi\)
0.996747 0.0805908i \(-0.0256807\pi\)
\(14\) −612.359 + 15634.4i −0.0596428 + 1.52276i
\(15\) 5680.35 0.434566
\(16\) 16183.5 + 2555.10i 0.987765 + 0.155951i
\(17\) −3972.88 −0.196126 −0.0980629 0.995180i \(-0.531265\pi\)
−0.0980629 + 0.995180i \(0.531265\pi\)
\(18\) 21589.3 + 845.598i 0.872537 + 0.0341751i
\(19\) −19789.9 + 22410.5i −0.661921 + 0.749573i
\(20\) 43529.1 + 3415.09i 1.21667 + 0.0954547i
\(21\) 23029.3i 0.542642i
\(22\) −1739.97 + 44423.8i −0.0348387 + 0.889479i
\(23\) 61712.8i 1.05762i −0.848741 0.528808i \(-0.822639\pi\)
0.848741 0.528808i \(-0.177361\pi\)
\(24\) −23948.9 2825.62i −0.353628 0.0417230i
\(25\) 38235.1 0.489410
\(26\) −565.347 + 14434.1i −0.00630825 + 0.161058i
\(27\) −68219.3 −0.667013
\(28\) 13845.5 176476.i 0.119194 1.51926i
\(29\) 237876.i 1.81116i 0.424170 + 0.905582i \(0.360566\pi\)
−0.424170 + 0.905582i \(0.639434\pi\)
\(30\) −64216.6 2515.20i −0.434233 0.0170078i
\(31\) −176262. −1.06266 −0.531329 0.847166i \(-0.678307\pi\)
−0.531329 + 0.847166i \(0.678307\pi\)
\(32\) −181824. 36051.4i −0.980904 0.194490i
\(33\) 65435.9i 0.316969i
\(34\) 44913.6 + 1759.15i 0.195975 + 0.00767587i
\(35\) 471748.i 1.85983i
\(36\) −243693. 19119.0i −0.870531 0.0682979i
\(37\) 49926.2i 0.162040i −0.996712 0.0810200i \(-0.974182\pi\)
0.996712 0.0810200i \(-0.0258178\pi\)
\(38\) 233649. 244589.i 0.690751 0.723093i
\(39\) 21261.3i 0.0573937i
\(40\) −490586. 57882.0i −1.21201 0.142999i
\(41\) 696583.i 1.57844i −0.614108 0.789222i \(-0.710484\pi\)
0.614108 0.789222i \(-0.289516\pi\)
\(42\) −10197.2 + 260347.i −0.0212377 + 0.542226i
\(43\) 231172.i 0.443401i −0.975115 0.221700i \(-0.928839\pi\)
0.975115 0.221700i \(-0.0711606\pi\)
\(44\) 39340.8 501442.i 0.0696240 0.887434i
\(45\) −651430. −1.06567
\(46\) −27325.9 + 697666.i −0.0413925 + 1.05681i
\(47\) 728161.i 1.02302i 0.859277 + 0.511511i \(0.170914\pi\)
−0.859277 + 0.511511i \(0.829086\pi\)
\(48\) 269492. + 42548.1i 0.351724 + 0.0555311i
\(49\) −1.08902e6 −1.32236
\(50\) −432250. 16930.1i −0.489035 0.0191543i
\(51\) −66157.4 −0.0698366
\(52\) 12782.5 162928.i 0.0126068 0.160688i
\(53\) 1.67316e6i 1.54373i −0.635785 0.771866i \(-0.719323\pi\)
0.635785 0.771866i \(-0.280677\pi\)
\(54\) 771222. + 30206.9i 0.666502 + 0.0261052i
\(55\) 1.34043e6i 1.08637i
\(56\) −234666. + 1.98894e6i −0.178563 + 1.51343i
\(57\) −329547. + 373185.i −0.235697 + 0.266909i
\(58\) 105329. 2.68920e6i 0.0708845 1.80978i
\(59\) −2.09273e6 −1.32657 −0.663285 0.748367i \(-0.730838\pi\)
−0.663285 + 0.748367i \(0.730838\pi\)
\(60\) 724857. + 56869.0i 0.433234 + 0.0339896i
\(61\) 488351. 0.275472 0.137736 0.990469i \(-0.456017\pi\)
0.137736 + 0.990469i \(0.456017\pi\)
\(62\) 1.99265e6 + 78047.2i 1.06184 + 0.0415898i
\(63\) 2.64103e6i 1.33071i
\(64\) 2.03957e6 + 488073.i 0.972541 + 0.232731i
\(65\) 435531.i 0.196708i
\(66\) −28974.4 + 739755.i −0.0124054 + 0.316726i
\(67\) 463413. 0.188238 0.0941189 0.995561i \(-0.469997\pi\)
0.0941189 + 0.995561i \(0.469997\pi\)
\(68\) −506971. 39774.6i −0.195525 0.0153400i
\(69\) 1.02766e6i 0.376597i
\(70\) −208886. + 5.33313e6i −0.0727889 + 1.85840i
\(71\) 3.96707e6 1.31542 0.657712 0.753269i \(-0.271524\pi\)
0.657712 + 0.753269i \(0.271524\pi\)
\(72\) 2.74649e6 + 324046.i 0.867191 + 0.102316i
\(73\) −204855. −0.0616336 −0.0308168 0.999525i \(-0.509811\pi\)
−0.0308168 + 0.999525i \(0.509811\pi\)
\(74\) −22106.8 + 564417.i −0.00634184 + 0.161916i
\(75\) 636701. 0.174269
\(76\) −2.74971e6 + 2.66163e6i −0.718521 + 0.695505i
\(77\) −5.43440e6 −1.35654
\(78\) −9414.30 + 240360.i −0.00224624 + 0.0573497i
\(79\) 3.63759e6 0.830078 0.415039 0.909804i \(-0.363768\pi\)
0.415039 + 0.909804i \(0.363768\pi\)
\(80\) 5.52046e6 + 871585.i 1.20548 + 0.190325i
\(81\) 3.04051e6 0.635696
\(82\) −308440. + 7.87490e6i −0.0617764 + 1.57724i
\(83\) 3.67550e6i 0.705575i −0.935703 0.352787i \(-0.885234\pi\)
0.935703 0.352787i \(-0.114766\pi\)
\(84\) 230559. 2.93872e6i 0.0424428 0.540980i
\(85\) −1.35521e6 −0.239355
\(86\) −102361. + 2.61341e6i −0.0173536 + 0.443061i
\(87\) 3.96117e6i 0.644921i
\(88\) −666783. + 5.65140e6i −0.104303 + 0.884029i
\(89\) 9.78887e6i 1.47186i −0.677055 0.735932i \(-0.736744\pi\)
0.677055 0.735932i \(-0.263256\pi\)
\(90\) 7.36444e6 + 288447.i 1.06486 + 0.0417078i
\(91\) −1.76573e6 −0.245629
\(92\) 617840. 7.87504e6i 0.0827215 1.05438i
\(93\) −2.93516e6 −0.378392
\(94\) 322423. 8.23189e6i 0.0400385 1.02224i
\(95\) −6.75066e6 + 7.64458e6i −0.807818 + 0.914789i
\(96\) −3.02778e6 600337.i −0.349281 0.0692542i
\(97\) 9.38988e6i 1.04462i −0.852755 0.522311i \(-0.825070\pi\)
0.852755 0.522311i \(-0.174930\pi\)
\(98\) 1.23114e7 + 482209.i 1.32135 + 0.0517540i
\(99\) 7.50428e6i 0.777295i
\(100\) 4.87910e6 + 382792.i 0.487910 + 0.0382792i
\(101\) −1.92683e7 −1.86088 −0.930439 0.366447i \(-0.880574\pi\)
−0.930439 + 0.366447i \(0.880574\pi\)
\(102\) 747913. + 29293.9i 0.0697831 + 0.00273323i
\(103\) 8.81693e6 0.795037 0.397518 0.917594i \(-0.369872\pi\)
0.397518 + 0.917594i \(0.369872\pi\)
\(104\) −216650. + 1.83624e6i −0.0188861 + 0.160071i
\(105\) 7.85567e6i 0.662248i
\(106\) −740859. + 1.89151e7i −0.0604178 + 1.54255i
\(107\) −8.47923e6 −0.669134 −0.334567 0.942372i \(-0.608590\pi\)
−0.334567 + 0.942372i \(0.608590\pi\)
\(108\) −8.70532e6 682979.i −0.664969 0.0521704i
\(109\) 1.22891e6i 0.0908926i −0.998967 0.0454463i \(-0.985529\pi\)
0.998967 0.0454463i \(-0.0144710\pi\)
\(110\) −593531. + 1.51537e7i −0.0425176 + 1.08553i
\(111\) 831383.i 0.0576993i
\(112\) 3.53359e6 2.23811e7i 0.237658 1.50528i
\(113\) 904238.i 0.0589533i 0.999565 + 0.0294767i \(0.00938407\pi\)
−0.999565 + 0.0294767i \(0.990616\pi\)
\(114\) 3.89078e6 4.07296e6i 0.245963 0.257479i
\(115\) 2.10512e7i 1.29073i
\(116\) −2.38150e6 + 3.03549e7i −0.141660 + 1.80562i
\(117\) 2.43828e6i 0.140745i
\(118\) 2.36584e7 + 926639.i 1.32555 + 0.0519187i
\(119\) 5.49432e6i 0.298882i
\(120\) −8.16936e6 963866.i −0.431572 0.0509193i
\(121\) 4.04579e6 0.207613
\(122\) −5.52083e6 216237.i −0.275261 0.0107813i
\(123\) 1.15997e7i 0.562054i
\(124\) −2.24925e7 1.76465e6i −1.05940 0.0831158i
\(125\) −1.36071e7 −0.623132
\(126\) 1.16942e6 2.98570e7i 0.0520805 1.32969i
\(127\) 1.67092e7 0.723841 0.361920 0.932209i \(-0.382121\pi\)
0.361920 + 0.932209i \(0.382121\pi\)
\(128\) −2.28413e7 6.42078e6i −0.962687 0.270616i
\(129\) 3.84954e6i 0.157886i
\(130\) −192849. + 4.92370e6i −0.00769867 + 0.196557i
\(131\) 2.17373e7i 0.844804i −0.906409 0.422402i \(-0.861187\pi\)
0.906409 0.422402i \(-0.138813\pi\)
\(132\) 655113. 8.35013e6i 0.0247918 0.315998i
\(133\) 3.09927e7 + 2.73686e7i 1.14230 + 1.00872i
\(134\) −5.23891e6 205195.i −0.188093 0.00736716i
\(135\) −2.32707e7 −0.814031
\(136\) 5.71372e6 + 674136.i 0.194775 + 0.0229806i
\(137\) 5.05332e7 1.67902 0.839508 0.543347i \(-0.182843\pi\)
0.839508 + 0.543347i \(0.182843\pi\)
\(138\) −455037. + 1.16177e7i −0.0147391 + 0.376308i
\(139\) 2.00717e7i 0.633917i 0.948439 + 0.316958i \(0.102662\pi\)
−0.948439 + 0.316958i \(0.897338\pi\)
\(140\) 4.72292e6 6.01988e7i 0.145466 1.85413i
\(141\) 1.21255e7i 0.364279i
\(142\) −4.48479e7 1.75658e6i −1.31442 0.0514824i
\(143\) −5.01719e6 −0.143478
\(144\) −3.09057e7 4.87948e6i −0.862523 0.136177i
\(145\) 8.11434e7i 2.21037i
\(146\) 2.31590e6 + 90708.0i 0.0615863 + 0.00241218i
\(147\) −1.81347e7 −0.470868
\(148\) 499837. 6.37097e6i 0.0126740 0.161544i
\(149\) −7.42164e6 −0.183801 −0.0919006 0.995768i \(-0.529294\pi\)
−0.0919006 + 0.995768i \(0.529294\pi\)
\(150\) −7.19793e6 281925.i −0.174136 0.00682047i
\(151\) 4.07360e7 0.962851 0.481426 0.876487i \(-0.340119\pi\)
0.481426 + 0.876487i \(0.340119\pi\)
\(152\) 3.22642e7 2.88723e7i 0.745191 0.666851i
\(153\) 7.58703e6 0.171258
\(154\) 6.14361e7 + 2.40630e6i 1.35550 + 0.0530917i
\(155\) −6.01259e7 −1.29688
\(156\) 212858. 2.71311e6i 0.00448905 0.0572178i
\(157\) 5.41329e7 1.11638 0.558190 0.829713i \(-0.311496\pi\)
0.558190 + 0.829713i \(0.311496\pi\)
\(158\) −4.11231e7 1.61069e6i −0.829442 0.0324872i
\(159\) 2.78619e7i 0.549693i
\(160\) −6.20231e7 1.22977e7i −1.19711 0.237358i
\(161\) −8.53461e7 −1.61173
\(162\) −3.43731e7 1.34631e6i −0.635209 0.0248796i
\(163\) 4.49136e7i 0.812310i 0.913804 + 0.406155i \(0.133131\pi\)
−0.913804 + 0.406155i \(0.866869\pi\)
\(164\) 6.97386e6 8.88895e7i 0.123458 1.57361i
\(165\) 2.23212e7i 0.386834i
\(166\) −1.62748e6 + 4.15517e7i −0.0276144 + 0.705034i
\(167\) −3.74649e7 −0.622468 −0.311234 0.950333i \(-0.600742\pi\)
−0.311234 + 0.950333i \(0.600742\pi\)
\(168\) −3.90771e6 + 3.31203e7i −0.0635829 + 0.538904i
\(169\) 6.11183e7 0.974020
\(170\) 1.53208e7 + 600076.i 0.239171 + 0.00936774i
\(171\) 3.77929e7 4.27974e7i 0.577994 0.654532i
\(172\) 2.31439e6 2.94994e7i 0.0346806 0.442042i
\(173\) 1.03878e8i 1.52532i −0.646799 0.762660i \(-0.723893\pi\)
0.646799 0.762660i \(-0.276107\pi\)
\(174\) 1.75397e6 4.47812e7i 0.0252406 0.644427i
\(175\) 5.28775e7i 0.745826i
\(176\) 1.00404e7 6.35941e7i 0.138821 0.879270i
\(177\) −3.48486e7 −0.472366
\(178\) −4.33442e6 + 1.10664e8i −0.0576051 + 1.47074i
\(179\) 5.04771e7 0.657823 0.328911 0.944361i \(-0.393318\pi\)
0.328911 + 0.944361i \(0.393318\pi\)
\(180\) −8.31276e7 6.52181e6i −1.06241 0.0833517i
\(181\) 7.05772e7i 0.884686i 0.896846 + 0.442343i \(0.145853\pi\)
−0.896846 + 0.442343i \(0.854147\pi\)
\(182\) 1.99617e7 + 781850.i 0.245441 + 0.00961333i
\(183\) 8.13214e6 0.0980903
\(184\) −1.04717e7 + 8.87541e7i −0.123924 + 1.05033i
\(185\) 1.70306e7i 0.197756i
\(186\) 3.31821e7 + 1.29966e6i 0.378102 + 0.0148093i
\(187\) 1.56117e7i 0.174584i
\(188\) −7.29001e6 + 9.29191e7i −0.0800157 + 1.01989i
\(189\) 9.43443e7i 1.01648i
\(190\) 7.97014e7 8.34332e7i 0.843002 0.882473i
\(191\) 9.92474e7i 1.03063i 0.857001 + 0.515314i \(0.172325\pi\)
−0.857001 + 0.515314i \(0.827675\pi\)
\(192\) 3.39634e7 + 8.12751e6i 0.346303 + 0.0828711i
\(193\) 1.52590e8i 1.52784i 0.645313 + 0.763918i \(0.276727\pi\)
−0.645313 + 0.763918i \(0.723273\pi\)
\(194\) −4.15775e6 + 1.06153e8i −0.0408839 + 1.04382i
\(195\) 7.25257e6i 0.0700440i
\(196\) −1.38968e8 1.09028e7i −1.31831 0.103429i
\(197\) 1.15293e8 1.07441 0.537207 0.843450i \(-0.319479\pi\)
0.537207 + 0.843450i \(0.319479\pi\)
\(198\) 3.32282e6 8.48362e7i 0.0304214 0.776699i
\(199\) 7.81895e7i 0.703336i 0.936125 + 0.351668i \(0.114385\pi\)
−0.936125 + 0.351668i \(0.885615\pi\)
\(200\) −5.49890e7 6.48790e6i −0.486038 0.0573455i
\(201\) 7.71687e6 0.0670278
\(202\) 2.17829e8 + 8.53180e6i 1.85945 + 0.0728301i
\(203\) 3.28972e8 2.76009
\(204\) −8.44221e6 662337.i −0.0696227 0.00546227i
\(205\) 2.37616e8i 1.92636i
\(206\) −9.96757e7 3.90405e6i −0.794427 0.0311158i
\(207\) 1.17853e8i 0.923517i
\(208\) 3.26231e6 2.06629e7i 0.0251364 0.159209i
\(209\) 8.80633e7 + 7.77655e7i 0.667241 + 0.589217i
\(210\) −3.47841e6 + 8.88086e7i −0.0259187 + 0.661741i
\(211\) −2.29615e8 −1.68272 −0.841359 0.540476i \(-0.818244\pi\)
−0.841359 + 0.540476i \(0.818244\pi\)
\(212\) 1.67509e7 2.13508e8i 0.120743 1.53900i
\(213\) 6.60607e7 0.468397
\(214\) 9.58581e7 + 3.75452e6i 0.668622 + 0.0261883i
\(215\) 7.88566e7i 0.541132i
\(216\) 9.81116e7 + 1.15757e7i 0.662418 + 0.0781557i
\(217\) 2.43763e8i 1.61942i
\(218\) −544151. + 1.38929e7i −0.00355731 + 0.0908230i
\(219\) −3.41130e6 −0.0219465
\(220\) 1.34198e7 1.71050e8i 0.0849701 1.08304i
\(221\) 5.07251e6i 0.0316119i
\(222\) −368128. + 9.39882e6i −0.00225821 + 0.0576551i
\(223\) 7.73459e7 0.467057 0.233529 0.972350i \(-0.424973\pi\)
0.233529 + 0.972350i \(0.424973\pi\)
\(224\) −4.98575e7 + 2.51455e8i −0.296389 + 1.49483i
\(225\) −7.30177e7 −0.427356
\(226\) 400388. 1.02224e7i 0.00230729 0.0589082i
\(227\) −1.80672e8 −1.02518 −0.512589 0.858634i \(-0.671314\pi\)
−0.512589 + 0.858634i \(0.671314\pi\)
\(228\) −4.57889e7 + 4.43221e7i −0.255852 + 0.247656i
\(229\) 1.03804e8 0.571204 0.285602 0.958348i \(-0.407806\pi\)
0.285602 + 0.958348i \(0.407806\pi\)
\(230\) −9.32129e6 + 2.37985e8i −0.0505159 + 1.28974i
\(231\) −9.04949e7 −0.483039
\(232\) 4.03638e7 3.42109e8i 0.212219 1.79869i
\(233\) −1.12943e8 −0.584942 −0.292471 0.956274i \(-0.594477\pi\)
−0.292471 + 0.956274i \(0.594477\pi\)
\(234\) 1.07965e6 2.75648e7i 0.00550840 0.140637i
\(235\) 2.48387e8i 1.24851i
\(236\) −2.67048e8 2.09514e7i −1.32251 0.103758i
\(237\) 6.05741e7 0.295575
\(238\) 2.43283e6 6.21135e7i 0.0116975 0.298653i
\(239\) 4.08044e8i 1.93337i −0.255971 0.966685i \(-0.582395\pi\)
0.255971 0.966685i \(-0.417605\pi\)
\(240\) 9.19281e7 + 1.45139e7i 0.429249 + 0.0677709i
\(241\) 2.81664e8i 1.29620i −0.761555 0.648100i \(-0.775564\pi\)
0.761555 0.648100i \(-0.224436\pi\)
\(242\) −4.57378e7 1.79144e6i −0.207454 0.00812545i
\(243\) 1.99827e8 0.893372
\(244\) 6.23174e7 + 4.88914e6i 0.274628 + 0.0215461i
\(245\) −3.71483e8 −1.61383
\(246\) −5.13622e6 + 1.31135e8i −0.0219974 + 0.561623i
\(247\) 2.86134e7 + 2.52674e7i 0.120817 + 0.106690i
\(248\) 2.53497e8 + 2.99089e7i 1.05534 + 0.124515i
\(249\) 6.12053e7i 0.251242i
\(250\) 1.53829e8 + 6.02508e6i 0.622654 + 0.0243878i
\(251\) 6.78510e7i 0.270831i 0.990789 + 0.135416i \(0.0432369\pi\)
−0.990789 + 0.135416i \(0.956763\pi\)
\(252\) −2.64408e7 + 3.37017e8i −0.104081 + 1.32663i
\(253\) −2.42504e8 −0.941449
\(254\) −1.88898e8 7.39868e6i −0.723286 0.0283293i
\(255\) −2.25674e7 −0.0852295
\(256\) 2.55378e8 + 8.27011e7i 0.951359 + 0.308086i
\(257\) 1.35735e7i 0.0498799i 0.999689 + 0.0249400i \(0.00793946\pi\)
−0.999689 + 0.0249400i \(0.992061\pi\)
\(258\) −1.70454e6 + 4.35192e7i −0.00617928 + 0.157765i
\(259\) −6.90457e7 −0.246938
\(260\) 4.36033e6 5.55772e7i 0.0153855 0.196106i
\(261\) 4.54273e8i 1.58152i
\(262\) −9.62506e6 + 2.45741e8i −0.0330635 + 0.844156i
\(263\) 4.95451e7i 0.167940i 0.996468 + 0.0839702i \(0.0267601\pi\)
−0.996468 + 0.0839702i \(0.973240\pi\)
\(264\) −1.11034e7 + 9.41085e7i −0.0371402 + 0.314786i
\(265\) 5.70742e8i 1.88399i
\(266\) −3.38256e8 3.23126e8i −1.10194 1.05266i
\(267\) 1.63007e8i 0.524102i
\(268\) 5.91352e7 + 4.63947e6i 0.187661 + 0.0147230i
\(269\) 3.42904e8i 1.07409i 0.843555 + 0.537043i \(0.180459\pi\)
−0.843555 + 0.537043i \(0.819541\pi\)
\(270\) 2.63076e8 + 1.03040e7i 0.813408 + 0.0318592i
\(271\) 3.03598e8i 0.926629i −0.886194 0.463314i \(-0.846660\pi\)
0.886194 0.463314i \(-0.153340\pi\)
\(272\) −6.42953e7 1.01511e7i −0.193726 0.0305860i
\(273\) −2.94034e7 −0.0874639
\(274\) −5.71280e8 2.23756e7i −1.67773 0.0657125i
\(275\) 1.50247e8i 0.435653i
\(276\) 1.02884e7 1.31137e8i 0.0294555 0.375443i
\(277\) −2.85659e8 −0.807547 −0.403774 0.914859i \(-0.632302\pi\)
−0.403774 + 0.914859i \(0.632302\pi\)
\(278\) 8.88755e6 2.26911e8i 0.0248099 0.633431i
\(279\) 3.36609e8 0.927920
\(280\) −8.00482e7 + 6.78458e8i −0.217921 + 1.84701i
\(281\) 2.23933e8i 0.602068i −0.953613 0.301034i \(-0.902668\pi\)
0.953613 0.301034i \(-0.0973318\pi\)
\(282\) 5.36907e6 1.37080e8i 0.0142570 0.363999i
\(283\) 2.12357e8i 0.556946i 0.960444 + 0.278473i \(0.0898283\pi\)
−0.960444 + 0.278473i \(0.910172\pi\)
\(284\) 5.06230e8 + 3.97165e7i 1.31139 + 0.102886i
\(285\) −1.12414e8 + 1.27299e8i −0.287648 + 0.325739i
\(286\) 5.67195e7 + 2.22156e6i 0.143368 + 0.00561536i
\(287\) −9.63343e8 −2.40544
\(288\) 3.47230e8 + 6.88475e7i 0.856532 + 0.169830i
\(289\) −3.94555e8 −0.961535
\(290\) 3.59295e7 9.17329e8i 0.0865084 2.20868i
\(291\) 1.56363e8i 0.371970i
\(292\) −2.61411e7 2.05091e6i −0.0614447 0.00482067i
\(293\) 5.27037e8i 1.22407i −0.790832 0.612033i \(-0.790352\pi\)
0.790832 0.612033i \(-0.209648\pi\)
\(294\) 2.05013e8 + 8.02986e6i 0.470507 + 0.0184286i
\(295\) −7.13862e8 −1.61896
\(296\) −8.47168e6 + 7.18028e7i −0.0189867 + 0.160924i
\(297\) 2.68071e8i 0.593749i
\(298\) 8.39020e7 + 3.28623e6i 0.183660 + 0.00719352i
\(299\) −7.87939e7 −0.170468
\(300\) 8.12480e7 + 6.37435e6i 0.173735 + 0.0136305i
\(301\) −3.19701e8 −0.675711
\(302\) −4.60522e8 1.80375e7i −0.962114 0.0376836i
\(303\) −3.20860e8 −0.662623
\(304\) −3.77532e8 + 3.12116e8i −0.770719 + 0.637175i
\(305\) 1.66584e8 0.336190
\(306\) −8.57716e7 3.35946e6i −0.171127 0.00670262i
\(307\) 4.84311e8 0.955300 0.477650 0.878550i \(-0.341489\pi\)
0.477650 + 0.878550i \(0.341489\pi\)
\(308\) −6.93472e8 5.44066e7i −1.35239 0.106102i
\(309\) 1.46822e8 0.283097
\(310\) 6.79725e8 + 2.66232e7i 1.29589 + 0.0507567i
\(311\) 5.70320e8i 1.07512i −0.843225 0.537561i \(-0.819346\pi\)
0.843225 0.537561i \(-0.180654\pi\)
\(312\) −3.60771e6 + 3.05776e7i −0.00672497 + 0.0569983i
\(313\) 6.70728e8 1.23635 0.618175 0.786041i \(-0.287872\pi\)
0.618175 + 0.786041i \(0.287872\pi\)
\(314\) −6.11974e8 2.39695e7i −1.11553 0.0436924i
\(315\) 9.00899e8i 1.62401i
\(316\) 4.64185e8 + 3.64178e7i 0.827536 + 0.0649246i
\(317\) 7.09547e8i 1.25105i 0.780205 + 0.625524i \(0.215115\pi\)
−0.780205 + 0.625524i \(0.784885\pi\)
\(318\) −1.23370e7 + 3.14980e8i −0.0215136 + 0.549272i
\(319\) 9.34747e8 1.61223
\(320\) 6.95729e8 + 1.66489e8i 1.18690 + 0.284028i
\(321\) −1.41198e8 −0.238266
\(322\) 9.64841e8 + 3.77904e7i 1.61050 + 0.0630792i
\(323\) 7.86230e7 8.90343e7i 0.129820 0.147011i
\(324\) 3.87994e8 + 3.04402e7i 0.633749 + 0.0497210i
\(325\) 4.88180e7i 0.0788838i
\(326\) 1.98873e7 5.07751e8i 0.0317918 0.811687i
\(327\) 2.04642e7i 0.0323651i
\(328\) −1.18199e8 + 1.00181e9i −0.184951 + 1.56757i
\(329\) 1.00701e9 1.55901
\(330\) −9.88362e6 + 2.52342e8i −0.0151397 + 0.386537i
\(331\) 9.88943e8 1.49890 0.749451 0.662060i \(-0.230317\pi\)
0.749451 + 0.662060i \(0.230317\pi\)
\(332\) 3.67974e7 4.69023e8i 0.0551866 0.703413i
\(333\) 9.53441e7i 0.141494i
\(334\) 4.23542e8 + 1.65891e7i 0.621991 + 0.0243619i
\(335\) 1.58078e8 0.229728
\(336\) 5.88422e7 3.72696e8i 0.0846255 0.536003i
\(337\) 1.89407e8i 0.269582i −0.990874 0.134791i \(-0.956964\pi\)
0.990874 0.134791i \(-0.0430363\pi\)
\(338\) −6.90945e8 2.70626e7i −0.973274 0.0381207i
\(339\) 1.50576e7i 0.0209921i
\(340\) −1.72936e8 1.35678e7i −0.238621 0.0187211i
\(341\) 6.92632e8i 0.945937i
\(342\) −4.46200e8 + 4.67092e8i −0.603168 + 0.631410i
\(343\) 3.67147e8i 0.491259i
\(344\) −3.92263e7 + 3.32467e8i −0.0519544 + 0.440346i
\(345\) 3.50550e8i 0.459604i
\(346\) −4.59961e7 + 1.17434e9i −0.0596973 + 1.52415i
\(347\) 1.24000e9i 1.59320i 0.604510 + 0.796598i \(0.293369\pi\)
−0.604510 + 0.796598i \(0.706631\pi\)
\(348\) −3.96574e7 + 5.05477e8i −0.0504425 + 0.642945i
\(349\) −8.25219e8 −1.03915 −0.519577 0.854423i \(-0.673911\pi\)
−0.519577 + 0.854423i \(0.673911\pi\)
\(350\) −2.34136e7 + 5.97782e8i −0.0291898 + 0.745255i
\(351\) 8.71013e7i 0.107510i
\(352\) −1.41666e8 + 7.14488e8i −0.173128 + 0.873163i
\(353\) 5.70208e7 0.0689957 0.0344979 0.999405i \(-0.489017\pi\)
0.0344979 + 0.999405i \(0.489017\pi\)
\(354\) 3.93965e8 + 1.54306e7i 0.472004 + 0.0184872i
\(355\) 1.35323e9 1.60536
\(356\) 9.80016e7 1.24914e9i 0.115122 1.46735i
\(357\) 9.14928e7i 0.106426i
\(358\) −5.70646e8 2.23508e7i −0.657319 0.0257456i
\(359\) 1.45777e9i 1.66287i −0.555624 0.831434i \(-0.687521\pi\)
0.555624 0.831434i \(-0.312479\pi\)
\(360\) 9.36873e8 + 1.10537e8i 1.05833 + 0.124868i
\(361\) −1.10590e8 8.87004e8i −0.123720 0.992317i
\(362\) 3.12509e7 7.97878e8i 0.0346244 0.884009i
\(363\) 6.73714e7 0.0739269
\(364\) −2.25322e8 1.76777e7i −0.244877 0.0192119i
\(365\) −6.98794e7 −0.0752184
\(366\) −9.19342e7 3.60083e6i −0.0980151 0.00383901i
\(367\) 1.02185e9i 1.07908i 0.841958 + 0.539542i \(0.181403\pi\)
−0.841958 + 0.539542i \(0.818597\pi\)
\(368\) 1.57682e8 9.98732e8i 0.164936 1.04468i
\(369\) 1.33027e9i 1.37831i
\(370\) −7.54099e6 + 1.92532e8i −0.00773967 + 0.197604i
\(371\) −2.31391e9 −2.35254
\(372\) −3.74550e8 2.93855e7i −0.377233 0.0295959i
\(373\) 8.51247e8i 0.849326i −0.905351 0.424663i \(-0.860393\pi\)
0.905351 0.424663i \(-0.139607\pi\)
\(374\) 6.91269e6 1.76490e8i 0.00683277 0.174450i
\(375\) −2.26588e8 −0.221885
\(376\) 1.23558e8 1.04723e9i 0.119870 1.01598i
\(377\) 3.03716e8 0.291926
\(378\) 4.17747e7 1.06657e9i 0.0397825 1.01570i
\(379\) −2.22179e8 −0.209636 −0.104818 0.994491i \(-0.533426\pi\)
−0.104818 + 0.994491i \(0.533426\pi\)
\(380\) −9.37971e8 + 9.07925e8i −0.876893 + 0.848804i
\(381\) 2.78246e8 0.257746
\(382\) 4.39458e7 1.12200e9i 0.0403362 1.02984i
\(383\) −7.90357e8 −0.718832 −0.359416 0.933177i \(-0.617024\pi\)
−0.359416 + 0.933177i \(0.617024\pi\)
\(384\) −3.80358e8 1.06920e8i −0.342794 0.0963610i
\(385\) −1.85376e9 −1.65554
\(386\) 6.75656e7 1.72504e9i 0.0597957 1.52667i
\(387\) 4.41470e8i 0.387180i
\(388\) 9.40070e7 1.19822e9i 0.0817051 1.04142i
\(389\) 1.68344e9 1.45002 0.725012 0.688736i \(-0.241834\pi\)
0.725012 + 0.688736i \(0.241834\pi\)
\(390\) −3.21137e6 + 8.19906e7i −0.00274135 + 0.0699903i
\(391\) 2.45178e8i 0.207426i
\(392\) 1.56621e9 + 1.84790e8i 1.31325 + 0.154945i
\(393\) 3.61975e8i 0.300818i
\(394\) −1.30339e9 5.10507e7i −1.07359 0.0420499i
\(395\) 1.24084e9 1.01304
\(396\) −7.51293e7 + 9.57605e8i −0.0607961 + 0.774913i
\(397\) 1.69708e9 1.36125 0.680623 0.732634i \(-0.261709\pi\)
0.680623 + 0.732634i \(0.261709\pi\)
\(398\) 3.46216e7 8.83936e8i 0.0275268 0.702797i
\(399\) 5.16099e8 + 4.55748e8i 0.406750 + 0.359186i
\(400\) 6.18780e8 + 9.76945e7i 0.483422 + 0.0763238i
\(401\) 1.20644e9i 0.934328i 0.884171 + 0.467164i \(0.154724\pi\)
−0.884171 + 0.467164i \(0.845276\pi\)
\(402\) −8.72396e7 3.41696e6i −0.0669765 0.00262330i
\(403\) 2.25049e8i 0.171281i
\(404\) −2.45878e9 1.92905e8i −1.85518 0.145549i
\(405\) 1.03717e9 0.775812
\(406\) −3.71904e9 1.45666e8i −2.75797 0.108023i
\(407\) −1.96187e8 −0.144242
\(408\) 9.51463e7 + 1.12259e7i 0.0693555 + 0.00818295i
\(409\) 8.49225e8i 0.613750i 0.951750 + 0.306875i \(0.0992833\pi\)
−0.951750 + 0.306875i \(0.900717\pi\)
\(410\) −1.05214e8 + 2.68625e9i −0.0753928 + 1.92488i
\(411\) 8.41491e8 0.597865
\(412\) 1.12511e9 + 8.82709e7i 0.792601 + 0.0621838i
\(413\) 2.89415e9i 2.02160i
\(414\) 5.21843e7 1.33233e9i 0.0361442 0.922810i
\(415\) 1.25377e9i 0.861093i
\(416\) −4.60298e7 + 2.32150e8i −0.0313482 + 0.158104i
\(417\) 3.34239e8i 0.225726i
\(418\) −9.61125e8 9.18136e8i −0.643669 0.614879i
\(419\) 2.09310e9i 1.39008i −0.718969 0.695042i \(-0.755386\pi\)
0.718969 0.695042i \(-0.244614\pi\)
\(420\) 7.86472e7 1.00245e9i 0.0517978 0.660219i
\(421\) 6.68196e8i 0.436432i −0.975900 0.218216i \(-0.929976\pi\)
0.975900 0.218216i \(-0.0700237\pi\)
\(422\) 2.59581e9 + 1.01671e8i 1.68143 + 0.0658574i
\(423\) 1.39057e9i 0.893310i
\(424\) −2.83909e8 + 2.40630e9i −0.180883 + 1.53310i
\(425\) −1.51904e8 −0.0959858
\(426\) −7.46819e8 2.92510e7i −0.468039 0.0183319i
\(427\) 6.75367e8i 0.419800i
\(428\) −1.08202e9 8.48901e7i −0.667085 0.0523364i
\(429\) −8.35474e7 −0.0510896
\(430\) −3.49169e7 + 8.91477e8i −0.0211786 + 0.540717i
\(431\) 9.56966e8 0.575740 0.287870 0.957670i \(-0.407053\pi\)
0.287870 + 0.957670i \(0.407053\pi\)
\(432\) −1.10403e9 1.74307e8i −0.658852 0.104021i
\(433\) 2.67539e9i 1.58372i 0.610700 + 0.791862i \(0.290888\pi\)
−0.610700 + 0.791862i \(0.709112\pi\)
\(434\) 1.07936e8 2.75575e9i 0.0633799 1.61818i
\(435\) 1.35122e9i 0.787070i
\(436\) 1.23033e7 1.56819e8i 0.00710917 0.0906142i
\(437\) 1.38302e9 + 1.22129e9i 0.792761 + 0.700059i
\(438\) 3.85649e7 + 1.51049e6i 0.0219297 + 0.000858932i
\(439\) −2.69019e9 −1.51760 −0.758801 0.651323i \(-0.774214\pi\)
−0.758801 + 0.651323i \(0.774214\pi\)
\(440\) −2.27450e8 + 1.92778e9i −0.127292 + 1.07888i
\(441\) 2.07971e9 1.15470
\(442\) 2.24606e6 5.73449e7i 0.00123721 0.0315876i
\(443\) 9.26357e8i 0.506251i −0.967433 0.253125i \(-0.918542\pi\)
0.967433 0.253125i \(-0.0814585\pi\)
\(444\) 8.32341e6 1.06091e8i 0.00451295 0.0575226i
\(445\) 3.33914e9i 1.79628i
\(446\) −8.74399e8 3.42480e7i −0.466700 0.0182795i
\(447\) −1.23587e8 −0.0654480
\(448\) 6.74983e8 2.82063e9i 0.354666 1.48208i
\(449\) 1.13367e9i 0.591048i −0.955335 0.295524i \(-0.904506\pi\)
0.955335 0.295524i \(-0.0954942\pi\)
\(450\) 8.25468e8 + 3.23315e7i 0.427028 + 0.0167256i
\(451\) −2.73726e9 −1.40507
\(452\) −9.05280e6 + 1.15388e8i −0.00461104 + 0.0587727i
\(453\) 6.78346e8 0.342853
\(454\) 2.04250e9 + 7.99997e7i 1.02439 + 0.0401229i
\(455\) −6.02320e8 −0.299770
\(456\) 5.37271e8 4.80788e8i 0.265348 0.237453i
\(457\) −2.33566e8 −0.114473 −0.0572365 0.998361i \(-0.518229\pi\)
−0.0572365 + 0.998361i \(0.518229\pi\)
\(458\) −1.17351e9 4.59636e7i −0.570766 0.0223555i
\(459\) 2.71027e8 0.130818
\(460\) 2.10755e8 2.68630e9i 0.100954 1.28678i
\(461\) −3.21670e9 −1.52918 −0.764588 0.644519i \(-0.777058\pi\)
−0.764588 + 0.644519i \(0.777058\pi\)
\(462\) 1.02305e9 + 4.00703e7i 0.482669 + 0.0189049i
\(463\) 7.50901e8i 0.351600i −0.984426 0.175800i \(-0.943749\pi\)
0.984426 0.175800i \(-0.0562513\pi\)
\(464\) −6.07797e8 + 3.84968e9i −0.282453 + 1.78900i
\(465\) −1.00123e9 −0.461795
\(466\) 1.27682e9 + 5.00099e7i 0.584493 + 0.0228932i
\(467\) 2.12548e9i 0.965712i −0.875700 0.482856i \(-0.839600\pi\)
0.875700 0.482856i \(-0.160400\pi\)
\(468\) −2.44109e7 + 3.11143e8i −0.0110084 + 0.140314i
\(469\) 6.40880e8i 0.286861i
\(470\) 1.09984e8 2.80803e9i 0.0488636 1.24755i
\(471\) 9.01434e8 0.397522
\(472\) 3.00972e9 + 3.55103e8i 1.31743 + 0.155438i
\(473\) −9.08404e8 −0.394698
\(474\) −6.84792e8 2.68216e7i −0.295348 0.0115681i
\(475\) −7.56670e8 + 8.56868e8i −0.323951 + 0.366848i
\(476\) −5.50065e7 + 7.01119e8i −0.0233771 + 0.297966i
\(477\) 3.19524e9i 1.34800i
\(478\) −1.80678e8 + 4.61296e9i −0.0756673 + 1.93189i
\(479\) 1.56967e8i 0.0652579i −0.999468 0.0326289i \(-0.989612\pi\)
0.999468 0.0326289i \(-0.0103880\pi\)
\(480\) −1.03282e9 2.04785e8i −0.426268 0.0845187i
\(481\) −6.37449e7 −0.0261179
\(482\) −1.24718e8 + 3.18422e9i −0.0507300 + 1.29521i
\(483\) −1.42120e9 −0.573907
\(484\) 5.16274e8 + 4.05045e7i 0.206977 + 0.0162384i
\(485\) 3.20304e9i 1.27487i
\(486\) −2.25905e9 8.84815e7i −0.892687 0.0349643i
\(487\) 2.15061e9 0.843744 0.421872 0.906655i \(-0.361373\pi\)
0.421872 + 0.906655i \(0.361373\pi\)
\(488\) −7.02336e8 8.28654e7i −0.273574 0.0322778i
\(489\) 7.47913e8i 0.289248i
\(490\) 4.19963e9 + 1.64489e8i 1.61259 + 0.0631613i
\(491\) 3.14545e9i 1.19922i 0.800293 + 0.599609i \(0.204677\pi\)
−0.800293 + 0.599609i \(0.795323\pi\)
\(492\) 1.16130e8 1.48021e9i 0.0439611 0.560332i
\(493\) 9.45055e8i 0.355216i
\(494\) −3.12287e8 2.98319e8i −0.116549 0.111336i
\(495\) 2.55983e9i 0.948621i
\(496\) −2.85255e9 4.50368e8i −1.04966 0.165722i
\(497\) 5.48629e9i 2.00462i
\(498\) −2.71011e7 + 6.91929e8i −0.00983297 + 0.251049i
\(499\) 1.35215e9i 0.487160i 0.969881 + 0.243580i \(0.0783219\pi\)
−0.969881 + 0.243580i \(0.921678\pi\)
\(500\) −1.73637e9 1.36228e8i −0.621223 0.0487383i
\(501\) −6.23875e8 −0.221649
\(502\) 3.00438e7 7.67059e8i 0.0105997 0.270624i
\(503\) 7.68337e8i 0.269193i 0.990900 + 0.134597i \(0.0429739\pi\)
−0.990900 + 0.134597i \(0.957026\pi\)
\(504\) 4.48142e8 3.79828e9i 0.155922 1.32154i
\(505\) −6.57271e9 −2.27104
\(506\) 2.74152e9 + 1.07378e8i 0.940728 + 0.0368460i
\(507\) 1.01776e9 0.346830
\(508\) 2.13223e9 + 1.67285e8i 0.721623 + 0.0566152i
\(509\) 6.08575e8i 0.204551i 0.994756 + 0.102276i \(0.0326123\pi\)
−0.994756 + 0.102276i \(0.967388\pi\)
\(510\) 2.55125e8 + 9.99261e6i 0.0851642 + 0.00333567i
\(511\) 2.83306e8i 0.0939252i
\(512\) −2.85044e9 1.04802e9i −0.938572 0.345083i
\(513\) 1.35005e9 1.52883e9i 0.441510 0.499975i
\(514\) 6.01021e6 1.53449e8i 0.00195218 0.0498417i
\(515\) 3.00760e9 0.970274
\(516\) 3.85398e7 4.91231e8i 0.0123491 0.157403i
\(517\) 2.86135e9 0.910655
\(518\) 7.80564e8 + 3.05728e7i 0.246748 + 0.00966452i
\(519\) 1.72980e9i 0.543137i
\(520\) −7.39028e7 + 6.26372e8i −0.0230488 + 0.195353i
\(521\) 1.19148e8i 0.0369108i 0.999830 + 0.0184554i \(0.00587487\pi\)
−0.999830 + 0.0184554i \(0.994125\pi\)
\(522\) −2.01148e8 + 5.13557e9i −0.0618968 + 1.58031i
\(523\) 3.57520e9 1.09281 0.546404 0.837522i \(-0.315996\pi\)
0.546404 + 0.837522i \(0.315996\pi\)
\(524\) 2.17623e8 2.77385e9i 0.0660764 0.842216i
\(525\) 8.80529e8i 0.265574i
\(526\) 2.19381e7 5.60109e8i 0.00657277 0.167812i
\(527\) 7.00270e8 0.208415
\(528\) 1.67195e8 1.05898e9i 0.0494316 0.313091i
\(529\) −4.03650e8 −0.118552
\(530\) −2.52719e8 + 6.45226e9i −0.0737348 + 1.88255i
\(531\) 3.99648e9 1.15837
\(532\) 3.68092e9 + 3.80273e9i 1.05990 + 1.09498i
\(533\) −8.89385e8 −0.254416
\(534\) −7.21778e7 + 1.84280e9i −0.0205121 + 0.523701i
\(535\) −2.89240e9 −0.816621
\(536\) −6.66471e8 7.86339e7i −0.186941 0.0220563i
\(537\) 8.40558e8 0.234238
\(538\) 1.51835e8 3.87654e9i 0.0420371 1.07326i
\(539\) 4.27937e9i 1.17712i
\(540\) −2.96952e9 2.32975e8i −0.811538 0.0636695i
\(541\) −5.19745e8 −0.141124 −0.0705618 0.997507i \(-0.522479\pi\)
−0.0705618 + 0.997507i \(0.522479\pi\)
\(542\) −1.34430e8 + 3.43218e9i −0.0362659 + 0.925919i
\(543\) 1.17527e9i 0.315020i
\(544\) 7.22366e8 + 1.43228e8i 0.192381 + 0.0381445i
\(545\) 4.19202e8i 0.110927i
\(546\) 3.32407e8 + 1.30196e7i 0.0873969 + 0.00342312i
\(547\) −2.69595e8 −0.0704297 −0.0352149 0.999380i \(-0.511212\pi\)
−0.0352149 + 0.999380i \(0.511212\pi\)
\(548\) 6.44844e9 + 5.05915e8i 1.67387 + 0.131324i
\(549\) −9.32605e8 −0.240544
\(550\) −6.65279e7 + 1.69855e9i −0.0170504 + 0.435320i
\(551\) −5.33093e9 4.70755e9i −1.35760 1.19885i
\(552\) −1.74377e8 + 1.47796e9i −0.0441269 + 0.374003i
\(553\) 5.03063e9i 1.26498i
\(554\) 3.22938e9 + 1.26487e8i 0.806929 + 0.0316054i
\(555\) 2.83598e8i 0.0704170i
\(556\) −2.00948e8 + 2.56131e9i −0.0495818 + 0.631975i
\(557\) −3.40830e9 −0.835688 −0.417844 0.908519i \(-0.637214\pi\)
−0.417844 + 0.908519i \(0.637214\pi\)
\(558\) −3.80537e9 1.49047e8i −0.927209 0.0363165i
\(559\) −2.95157e8 −0.0714680
\(560\) 1.20536e9 7.63456e9i 0.290041 1.83707i
\(561\) 2.59969e8i 0.0621658i
\(562\) −9.91553e7 + 2.53157e9i −0.0235635 + 0.601607i
\(563\) 4.67616e9 1.10436 0.552179 0.833726i \(-0.313797\pi\)
0.552179 + 0.833726i \(0.313797\pi\)
\(564\) −1.21395e8 + 1.54731e9i −0.0284921 + 0.363163i
\(565\) 3.08450e8i 0.0719474i
\(566\) 9.40294e7 2.40070e9i 0.0217975 0.556519i
\(567\) 4.20490e9i 0.968757i
\(568\) −5.70536e9 6.73150e8i −1.30636 0.154132i
\(569\) 2.38691e9i 0.543179i 0.962413 + 0.271590i \(0.0875493\pi\)
−0.962413 + 0.271590i \(0.912451\pi\)
\(570\) 1.32721e9 1.38935e9i 0.300177 0.314231i
\(571\) 5.45658e9i 1.22657i 0.789860 + 0.613287i \(0.210153\pi\)
−0.789860 + 0.613287i \(0.789847\pi\)
\(572\) −6.40232e8 5.02297e7i −0.143038 0.0112221i
\(573\) 1.65269e9i 0.366987i
\(574\) 1.08906e10 + 4.26559e8i 2.40360 + 0.0941429i
\(575\) 2.35960e9i 0.517608i
\(576\) −3.89497e9 9.32074e8i −0.849229 0.203222i
\(577\) −2.30793e9 −0.500159 −0.250079 0.968225i \(-0.580457\pi\)
−0.250079 + 0.968225i \(0.580457\pi\)
\(578\) 4.46046e9 + 1.74705e8i 0.960798 + 0.0376321i
\(579\) 2.54097e9i 0.544033i
\(580\) −8.12369e8 + 1.03545e10i −0.172884 + 2.20360i
\(581\) −5.08305e9 −1.07525
\(582\) −6.92358e7 + 1.76769e9i −0.0145580 + 0.371685i
\(583\) −6.57477e9 −1.37417
\(584\) 2.94619e8 + 3.47607e7i 0.0612090 + 0.00722177i
\(585\) 8.31735e8i 0.171767i
\(586\) −2.33367e8 + 5.95818e9i −0.0479069 + 1.22313i
\(587\) 2.65678e9i 0.542154i 0.962558 + 0.271077i \(0.0873799\pi\)
−0.962558 + 0.271077i \(0.912620\pi\)
\(588\) −2.31413e9 1.81556e8i −0.469426 0.0368290i
\(589\) 3.48822e9 3.95013e9i 0.703396 0.796540i
\(590\) 8.07024e9 + 3.16091e8i 1.61772 + 0.0633623i
\(591\) 1.91989e9 0.382578
\(592\) 1.27566e8 8.07982e8i 0.0252703 0.160057i
\(593\) 6.41729e9 1.26375 0.631874 0.775071i \(-0.282286\pi\)
0.631874 + 0.775071i \(0.282286\pi\)
\(594\) 1.18699e8 3.03056e9i 0.0232379 0.593294i
\(595\) 1.87420e9i 0.364760i
\(596\) −9.47060e8 7.43020e7i −0.183238 0.0143760i
\(597\) 1.30203e9i 0.250444i
\(598\) 8.90768e8 + 3.48892e7i 0.170338 + 0.00667170i
\(599\) −3.51493e9 −0.668226 −0.334113 0.942533i \(-0.608437\pi\)
−0.334113 + 0.942533i \(0.608437\pi\)
\(600\) −9.15690e8 1.08038e8i −0.173069 0.0204196i
\(601\) 3.72426e9i 0.699808i −0.936786 0.349904i \(-0.886214\pi\)
0.936786 0.349904i \(-0.113786\pi\)
\(602\) 3.61423e9 + 1.41561e8i 0.675194 + 0.0264457i
\(603\) −8.84982e8 −0.164370
\(604\) 5.19824e9 + 4.07830e8i 0.959902 + 0.0753095i
\(605\) 1.38008e9 0.253374
\(606\) 3.62733e9 + 1.42074e8i 0.662115 + 0.0259334i
\(607\) 8.69807e9 1.57856 0.789282 0.614031i \(-0.210453\pi\)
0.789282 + 0.614031i \(0.210453\pi\)
\(608\) 4.40622e9 3.36132e9i 0.795066 0.606523i
\(609\) 5.47813e9 0.982814
\(610\) −1.88324e9 7.37619e7i −0.335932 0.0131576i
\(611\) 9.29704e8 0.164892
\(612\) 9.68164e8 + 7.59577e7i 0.170734 + 0.0133950i
\(613\) −9.45776e9 −1.65835 −0.829176 0.558988i \(-0.811190\pi\)
−0.829176 + 0.558988i \(0.811190\pi\)
\(614\) −5.47515e9 2.14448e8i −0.954568 0.0373881i
\(615\) 3.95683e9i 0.685938i
\(616\) 7.81564e9 + 9.22131e8i 1.34720 + 0.158950i
\(617\) 7.94564e9 1.36185 0.680927 0.732351i \(-0.261577\pi\)
0.680927 + 0.732351i \(0.261577\pi\)
\(618\) −1.65983e9 6.50112e7i −0.282880 0.0110797i
\(619\) 7.11840e8i 0.120633i −0.998179 0.0603164i \(-0.980789\pi\)
0.998179 0.0603164i \(-0.0192110\pi\)
\(620\) −7.67254e9 6.01952e8i −1.29291 0.101436i
\(621\) 4.21001e9i 0.705444i
\(622\) −2.52532e8 + 6.44749e9i −0.0420776 + 1.07430i
\(623\) −1.35376e10 −2.24302
\(624\) 5.43247e7 3.44083e8i 0.00895059 0.0566914i
\(625\) −7.62871e9 −1.24989
\(626\) −7.58260e9 2.96992e8i −1.23540 0.0483876i
\(627\) 1.46645e9 + 1.29497e9i 0.237592 + 0.209809i
\(628\) 6.90778e9 + 5.41953e8i 1.11296 + 0.0873178i
\(629\) 1.98351e8i 0.0317802i
\(630\) 3.98909e8 1.01847e10i 0.0635598 1.62277i
\(631\) 1.07070e10i 1.69655i −0.529557 0.848274i \(-0.677642\pi\)
0.529557 0.848274i \(-0.322358\pi\)
\(632\) −5.23151e9 6.17242e8i −0.824361 0.0972626i
\(633\) −3.82361e9 −0.599184
\(634\) 3.14181e8 8.02146e9i 0.0489629 1.25009i
\(635\) 5.69978e9 0.883385
\(636\) 2.78940e8 3.55540e9i 0.0429943 0.548009i
\(637\) 1.39045e9i 0.213141i
\(638\) −1.05674e10 4.13897e8i −1.61099 0.0630986i
\(639\) −7.57593e9 −1.14864
\(640\) −7.79152e9 2.19023e9i −1.17488 0.330263i
\(641\) 5.39388e9i 0.808906i −0.914559 0.404453i \(-0.867462\pi\)
0.914559 0.404453i \(-0.132538\pi\)
\(642\) 1.59625e9 + 6.25213e7i 0.238083 + 0.00932513i
\(643\) 5.02019e9i 0.744701i 0.928092 + 0.372350i \(0.121448\pi\)
−0.928092 + 0.372350i \(0.878552\pi\)
\(644\) −1.08908e10 8.54445e8i −1.60680 0.126062i
\(645\) 1.31314e9i 0.192687i
\(646\) −9.28260e8 + 9.71723e8i −0.135474 + 0.141817i
\(647\) 1.12648e10i 1.63515i −0.575822 0.817575i \(-0.695318\pi\)
0.575822 0.817575i \(-0.304682\pi\)
\(648\) −4.37281e9 5.15927e8i −0.631317 0.0744863i
\(649\) 8.22348e9i 1.18086i
\(650\) −2.16161e7 + 5.51889e8i −0.00308732 + 0.0788234i
\(651\) 4.05920e9i 0.576643i
\(652\) −4.49654e8 + 5.73133e9i −0.0635349 + 0.809821i
\(653\) −1.68561e9 −0.236898 −0.118449 0.992960i \(-0.537792\pi\)
−0.118449 + 0.992960i \(0.537792\pi\)
\(654\) −9.06134e6 + 2.31348e8i −0.00126669 + 0.0323403i
\(655\) 7.41494e9i 1.03101i
\(656\) 1.77984e9 1.12732e10i 0.246160 1.55913i
\(657\) 3.91213e8 0.0538188
\(658\) −1.13843e10 4.45896e8i −1.55782 0.0610160i
\(659\) −2.26846e9 −0.308768 −0.154384 0.988011i \(-0.549339\pi\)
−0.154384 + 0.988011i \(0.549339\pi\)
\(660\) 2.23470e8 2.84836e9i 0.0302562 0.385649i
\(661\) 8.80186e9i 1.18541i −0.805419 0.592706i \(-0.798060\pi\)
0.805419 0.592706i \(-0.201940\pi\)
\(662\) −1.11800e10 4.37894e8i −1.49775 0.0586633i
\(663\) 8.44687e7i 0.0112564i
\(664\) −6.23675e8 + 5.28603e9i −0.0826742 + 0.700715i
\(665\) 1.05721e10 + 9.33586e9i 1.39408 + 1.23106i
\(666\) 4.22175e7 1.07787e9i 0.00553774 0.141386i
\(667\) 1.46800e10 1.91552
\(668\) −4.78082e9 3.75081e8i −0.620561 0.0486864i
\(669\) 1.28798e9 0.166310
\(670\) −1.78707e9 6.99953e7i −0.229552 0.00899098i
\(671\) 1.91900e9i 0.245215i
\(672\) −8.30239e8 + 4.18729e9i −0.105538 + 0.532280i
\(673\) 7.03798e8i 0.0890011i 0.999009 + 0.0445006i \(0.0141696\pi\)
−0.999009 + 0.0445006i \(0.985830\pi\)
\(674\) −8.38675e7 + 2.14125e9i −0.0105508 + 0.269375i
\(675\) −2.60837e9 −0.326442
\(676\) 7.79918e9 + 6.11888e8i 0.971037 + 0.0761831i
\(677\) 1.53717e10i 1.90398i 0.306126 + 0.951991i \(0.400967\pi\)
−0.306126 + 0.951991i \(0.599033\pi\)
\(678\) 6.66736e6 1.70227e8i 0.000821580 0.0209761i
\(679\) −1.29858e10 −1.59193
\(680\) 1.94904e9 + 2.29959e8i 0.237706 + 0.0280458i
\(681\) −3.00859e9 −0.365046
\(682\) 3.06691e8 7.83023e9i 0.0370216 0.945212i
\(683\) 6.42983e9 0.772195 0.386098 0.922458i \(-0.373823\pi\)
0.386098 + 0.922458i \(0.373823\pi\)
\(684\) 5.25113e9 5.08292e9i 0.627418 0.607319i
\(685\) 1.72377e10 2.04909
\(686\) 1.62569e8 4.15061e9i 0.0192267 0.490883i
\(687\) 1.72858e9 0.203395
\(688\) 5.90668e8 3.74119e9i 0.0691487 0.437975i
\(689\) −2.13626e9 −0.248821
\(690\) −1.55220e8 + 3.96299e9i −0.0179878 + 0.459252i
\(691\) 1.42377e9i 0.164160i −0.996626 0.0820801i \(-0.973844\pi\)
0.996626 0.0820801i \(-0.0261563\pi\)
\(692\) 1.03997e9 1.32556e10i 0.119303 1.52065i
\(693\) 1.03781e10 1.18454
\(694\) 5.49061e8 1.40183e10i 0.0623537 1.59197i
\(695\) 6.84678e9i 0.773641i
\(696\) 6.72149e8 5.69688e9i 0.0755671 0.640478i
\(697\) 2.76744e9i 0.309574i
\(698\) 9.32913e9 + 3.65399e8i 1.03836 + 0.0406699i
\(699\) −1.88075e9 −0.208286
\(700\) 5.29384e8 6.74758e9i 0.0583348 0.743541i
\(701\) −2.62220e9 −0.287510 −0.143755 0.989613i \(-0.545918\pi\)
−0.143755 + 0.989613i \(0.545918\pi\)
\(702\) 3.85676e7 9.84683e8i 0.00420768 0.107428i
\(703\) 1.11887e9 + 9.88035e8i 0.121461 + 0.107258i
\(704\) 1.91791e9 8.01458e9i 0.207168 0.865718i
\(705\) 4.13621e9i 0.444571i
\(706\) −6.44623e8 2.52483e7i −0.0689428 0.00270032i
\(707\) 2.66472e10i 2.83585i
\(708\) −4.44696e9 3.48888e8i −0.470919 0.0369461i
\(709\) −3.91774e8 −0.0412832 −0.0206416 0.999787i \(-0.506571\pi\)
−0.0206416 + 0.999787i \(0.506571\pi\)
\(710\) −1.52983e10 5.99198e8i −1.60413 0.0628299i
\(711\) −6.94672e9 −0.724830
\(712\) −1.66102e9 + 1.40782e10i −0.172462 + 1.46173i
\(713\) 1.08776e10i 1.12388i
\(714\) 4.05121e7 1.03433e9i 0.00416525 0.106345i
\(715\) −1.71144e9 −0.175102
\(716\) 6.44128e9 + 5.05353e8i 0.655808 + 0.0514517i
\(717\) 6.79486e9i 0.688435i
\(718\) −6.45485e8 + 1.64801e10i −0.0650805 + 1.66159i
\(719\) 1.00281e9i 0.100616i −0.998734 0.0503081i \(-0.983980\pi\)
0.998734 0.0503081i \(-0.0160203\pi\)
\(720\) −1.05424e10 1.66447e9i −1.05263 0.166193i
\(721\) 1.21934e10i 1.21158i
\(722\) 8.57468e8 + 1.00766e10i 0.0847886 + 0.996399i
\(723\) 4.69034e9i 0.461552i
\(724\) −7.06585e8 + 9.00620e9i −0.0691958 + 0.881976i
\(725\) 9.09523e9i 0.886401i
\(726\) −7.61637e8 2.98314e7i −0.0738703 0.00289332i
\(727\) 2.26549e8i 0.0218671i −0.999940 0.0109336i \(-0.996520\pi\)
0.999940 0.0109336i \(-0.00348033\pi\)
\(728\) 2.53944e9 + 2.99617e8i 0.243937 + 0.0287811i
\(729\) −3.32204e9 −0.317584
\(730\) 7.89990e8 + 3.09419e7i 0.0751608 + 0.00294386i
\(731\) 9.18421e8i 0.0869623i
\(732\) 1.03772e9 + 8.14151e7i 0.0977898 + 0.00767214i
\(733\) 1.63102e9 0.152966 0.0764831 0.997071i \(-0.475631\pi\)
0.0764831 + 0.997071i \(0.475631\pi\)
\(734\) 4.52465e8 1.15520e10i 0.0422327 1.07826i
\(735\) −6.18603e9 −0.574654
\(736\) −2.22484e9 + 1.12209e10i −0.205696 + 1.03742i
\(737\) 1.82101e9i 0.167562i
\(738\) 5.89029e8 1.50387e10i 0.0539436 1.37725i
\(739\) 1.46814e10i 1.33817i −0.743184 0.669087i \(-0.766685\pi\)
0.743184 0.669087i \(-0.233315\pi\)
\(740\) 1.70502e8 2.17324e9i 0.0154675 0.197150i
\(741\) 4.76477e8 + 4.20760e8i 0.0430207 + 0.0379901i
\(742\) 2.61588e10 + 1.02458e9i 2.35074 + 0.0920726i
\(743\) 2.11568e10 1.89229 0.946147 0.323738i \(-0.104940\pi\)
0.946147 + 0.323738i \(0.104940\pi\)
\(744\) 4.22129e9 + 4.98051e8i 0.375785 + 0.0443372i
\(745\) −2.53164e9 −0.224313
\(746\) −3.76924e8 + 9.62338e9i −0.0332405 + 0.848675i
\(747\) 7.01911e9i 0.616113i
\(748\) −1.56297e8 + 1.99217e9i −0.0136551 + 0.174049i
\(749\) 1.17264e10i 1.01971i
\(750\) 2.56159e9 + 1.00331e8i 0.221715 + 0.00868403i
\(751\) 6.87719e9 0.592477 0.296238 0.955114i \(-0.404268\pi\)
0.296238 + 0.955114i \(0.404268\pi\)
\(752\) −1.86052e9 + 1.17842e10i −0.159541 + 1.01051i
\(753\) 1.12987e9i 0.0964377i
\(754\) −3.43353e9 1.34483e8i −0.291703 0.0114253i
\(755\) 1.38957e10 1.17508
\(756\) −9.44530e8 + 1.20391e10i −0.0795041 + 1.01337i
\(757\) −1.31587e10 −1.10250 −0.551249 0.834341i \(-0.685849\pi\)
−0.551249 + 0.834341i \(0.685849\pi\)
\(758\) 2.51175e9 + 9.83788e7i 0.209476 + 0.00820464i
\(759\) −4.03823e9 −0.335232
\(760\) 1.10058e10 9.84880e9i 0.909442 0.813834i
\(761\) 2.03795e10 1.67628 0.838140 0.545455i \(-0.183643\pi\)
0.838140 + 0.545455i \(0.183643\pi\)
\(762\) −3.14558e9 1.23205e8i −0.257548 0.0100875i
\(763\) −1.69953e9 −0.138514
\(764\) −9.93618e8 + 1.26647e10i −0.0806107 + 1.02747i
\(765\) 2.58806e9 0.209006
\(766\) 8.93502e9 + 3.49962e8i 0.718281 + 0.0281333i
\(767\) 2.67196e9i 0.213819i
\(768\) 4.25262e9 + 1.37716e9i 0.338760 + 0.109703i
\(769\) −4.03215e9 −0.319738 −0.159869 0.987138i \(-0.551107\pi\)
−0.159869 + 0.987138i \(0.551107\pi\)
\(770\) 2.09568e10 + 8.20827e8i 1.65428 + 0.0647939i
\(771\) 2.26029e8i 0.0177613i
\(772\) −1.52766e9 + 1.94717e10i −0.119500 + 1.52316i
\(773\) 1.43109e10i 1.11440i −0.830380 0.557198i \(-0.811877\pi\)
0.830380 0.557198i \(-0.188123\pi\)
\(774\) 1.95479e8 4.99084e9i 0.0151533 0.386884i
\(775\) −6.73941e9 −0.520075
\(776\) −1.59331e9 + 1.35043e10i −0.122401 + 1.03743i
\(777\) −1.14977e9 −0.0879297
\(778\) −1.90314e10 7.45413e8i −1.44891 0.0567503i
\(779\) 1.56108e10 + 1.37853e10i 1.18316 + 1.04481i
\(780\) 7.26093e7 9.25485e8i 0.00547849 0.0698294i
\(781\) 1.55888e10i 1.17094i
\(782\) 1.08562e8 2.77175e9i 0.00811813 0.207267i
\(783\) 1.62277e10i 1.20807i
\(784\) −1.76242e10 2.78256e9i −1.30618 0.206224i
\(785\) 1.84656e10 1.36245
\(786\) −1.60279e8 + 4.09214e9i −0.0117733 + 0.300588i
\(787\) 2.06321e9 0.150880 0.0754399 0.997150i \(-0.475964\pi\)
0.0754399 + 0.997150i \(0.475964\pi\)
\(788\) 1.47123e10 + 1.15426e9i 1.07112 + 0.0840354i
\(789\) 8.25036e8i 0.0598003i
\(790\) −1.40278e10 5.49432e8i −1.01226 0.0396478i
\(791\) 1.25052e9 0.0898407
\(792\) 1.27336e9 1.07925e10i 0.0910777 0.771940i
\(793\) 6.23518e8i 0.0444010i
\(794\) −1.91856e10 7.51452e8i −1.36020 0.0532758i
\(795\) 9.50413e9i 0.670853i
\(796\) −7.82797e8 + 9.97760e9i −0.0550115 + 0.701181i
\(797\) 6.81836e9i 0.477063i 0.971135 + 0.238532i \(0.0766661\pi\)
−0.971135 + 0.238532i \(0.923334\pi\)
\(798\) −5.63272e9 5.38078e9i −0.392381 0.374830i
\(799\) 2.89290e9i 0.200641i
\(800\) −6.95207e9 1.37843e9i −0.480064 0.0951853i
\(801\) 1.86938e10i 1.28524i
\(802\) 5.34199e8 1.36388e10i 0.0365673 0.933612i
\(803\) 8.04990e8i 0.0548638i
\(804\) 9.84734e8 + 7.72577e7i 0.0668225 + 0.00524258i
\(805\) −2.91129e10 −1.96698
\(806\) 9.96494e7 2.54418e9i 0.00670351 0.171150i
\(807\) 5.71012e9i 0.382462i
\(808\) 2.77112e10 + 3.26952e9i 1.84806 + 0.218044i
\(809\) −2.06110e10 −1.36861 −0.684304 0.729196i \(-0.739894\pi\)
−0.684304 + 0.729196i \(0.739894\pi\)
\(810\) −1.17252e10 4.59248e8i −0.775218 0.0303634i
\(811\) −2.17656e10 −1.43284 −0.716419 0.697670i \(-0.754220\pi\)
−0.716419 + 0.697670i \(0.754220\pi\)
\(812\) 4.19794e10 + 3.29351e9i 2.75163 + 0.215880i
\(813\) 5.05558e9i 0.329955i
\(814\) 2.21791e9 + 8.68699e7i 0.144131 + 0.00564526i
\(815\) 1.53208e10i 0.991354i
\(816\) −1.07066e9 1.69039e8i −0.0689821 0.0108911i
\(817\) 5.18069e9 + 4.57488e9i 0.332361 + 0.293496i
\(818\) 3.76029e8 9.60053e9i 0.0240206 0.613280i
\(819\) 3.37203e9 0.214485
\(820\) 2.37889e9 3.03216e10i 0.150670 1.92045i
\(821\) 2.36908e10 1.49410 0.747048 0.664770i \(-0.231471\pi\)
0.747048 + 0.664770i \(0.231471\pi\)
\(822\) −9.51310e9 3.72604e8i −0.597407 0.0233990i
\(823\) 1.69861e10i 1.06217i 0.847318 + 0.531085i \(0.178216\pi\)
−0.847318 + 0.531085i \(0.821784\pi\)
\(824\) −1.26803e10 1.49609e9i −0.789560 0.0931566i
\(825\) 2.50195e9i 0.155128i
\(826\) 1.28150e9 3.27185e10i 0.0791204 2.02005i
\(827\) −4.08965e9 −0.251430 −0.125715 0.992066i \(-0.540122\pi\)
−0.125715 + 0.992066i \(0.540122\pi\)
\(828\) −1.17989e9 + 1.50390e10i −0.0722330 + 0.920688i
\(829\) 9.54054e9i 0.581610i −0.956782 0.290805i \(-0.906077\pi\)
0.956782 0.290805i \(-0.0939231\pi\)
\(830\) −5.55158e8 + 1.41739e10i −0.0337011 + 0.860434i
\(831\) −4.75686e9 −0.287552
\(832\) 6.23163e8 2.60408e9i 0.0375120 0.156756i
\(833\) 4.32656e9 0.259349
\(834\) 1.47998e8 3.77858e9i 0.00883433 0.225553i
\(835\) −1.27799e10 −0.759669
\(836\) 1.04590e10 + 1.08051e10i 0.619111 + 0.639600i
\(837\) 1.20245e10 0.708806
\(838\) −9.26805e8 + 2.36626e10i −0.0544044 + 1.38902i
\(839\) −8.77153e9 −0.512753 −0.256377 0.966577i \(-0.582529\pi\)
−0.256377 + 0.966577i \(0.582529\pi\)
\(840\) −1.33298e9 + 1.12979e10i −0.0775974 + 0.657686i
\(841\) −3.93352e10 −2.28032
\(842\) −2.95871e8 + 7.55398e9i −0.0170809 + 0.436098i
\(843\) 3.72899e9i 0.214385i
\(844\) −2.93007e10 2.29880e9i −1.67756 0.131614i
\(845\) 2.08484e10 1.18871
\(846\) −6.15732e8 + 1.57205e10i −0.0349619 + 0.892625i
\(847\) 5.59514e9i 0.316388i
\(848\) 4.27509e9 2.70777e10i 0.240746 1.52484i
\(849\) 3.53621e9i 0.198318i
\(850\) 1.71728e9 + 6.72615e7i 0.0959123 + 0.00375665i
\(851\) −3.08109e9 −0.171376
\(852\) 8.42986e9 + 6.61368e8i 0.466962 + 0.0366357i
\(853\) −1.64301e10 −0.906398 −0.453199 0.891409i \(-0.649717\pi\)
−0.453199 + 0.891409i \(0.649717\pi\)
\(854\) −2.99046e8 + 7.63506e9i −0.0164299 + 0.419478i
\(855\) 1.28917e10 1.45989e10i 0.705392 0.798800i
\(856\) 1.21947e10 + 1.43879e9i 0.664525 + 0.0784043i
\(857\) 1.62196e10i 0.880250i −0.897936 0.440125i \(-0.854934\pi\)
0.897936 0.440125i \(-0.145066\pi\)
\(858\) 9.44507e8 + 3.69940e7i 0.0510505 + 0.00199952i
\(859\) 1.31545e10i 0.708108i −0.935225 0.354054i \(-0.884803\pi\)
0.935225 0.354054i \(-0.115197\pi\)
\(860\) 7.89475e8 1.00627e10i 0.0423247 0.539474i
\(861\) −1.60418e10 −0.856531
\(862\) −1.08185e10 4.23736e8i −0.575299 0.0225330i
\(863\) 1.14711e9 0.0607529 0.0303764 0.999539i \(-0.490329\pi\)
0.0303764 + 0.999539i \(0.490329\pi\)
\(864\) 1.24039e10 + 2.45940e9i 0.654276 + 0.129727i
\(865\) 3.54344e10i 1.86152i
\(866\) 1.18464e9 3.02454e10i 0.0619830 1.58251i
\(867\) −6.57023e9 −0.342384
\(868\) −2.44044e9 + 3.11061e10i −0.126663 + 1.61446i
\(869\) 1.42941e10i 0.738904i
\(870\) 5.98307e8 1.52756e10i 0.0308040 0.786467i
\(871\) 5.91678e8i 0.0303405i
\(872\) −2.08527e8 + 1.76740e9i −0.0106501 + 0.0902665i
\(873\) 1.79319e10i 0.912170i
\(874\) −1.50943e10 1.44191e10i −0.764755 0.730549i
\(875\) 1.88180e10i 0.949609i
\(876\) −4.35309e8 3.41523e7i −0.0218793 0.00171655i
\(877\) 2.64207e10i 1.32265i −0.750098 0.661327i \(-0.769994\pi\)
0.750098 0.661327i \(-0.230006\pi\)
\(878\) 3.04127e10 + 1.19119e9i 1.51644 + 0.0593951i
\(879\) 8.77635e9i 0.435866i
\(880\) 3.42494e9 2.16930e10i 0.169420 1.07307i
\(881\) −2.65953e10 −1.31036 −0.655178 0.755474i \(-0.727406\pi\)
−0.655178 + 0.755474i \(0.727406\pi\)
\(882\) −2.35112e10 9.20876e8i −1.15381 0.0451919i
\(883\) 1.86252e10i 0.910413i 0.890386 + 0.455207i \(0.150435\pi\)
−0.890386 + 0.455207i \(0.849565\pi\)
\(884\) −5.07836e7 + 6.47292e8i −0.00247252 + 0.0315150i
\(885\) −1.18874e10 −0.576482
\(886\) −4.10182e8 + 1.04725e10i −0.0198134 + 0.505863i
\(887\) 1.57386e10 0.757239 0.378620 0.925552i \(-0.376399\pi\)
0.378620 + 0.925552i \(0.376399\pi\)
\(888\) −1.41073e8 + 1.19568e9i −0.00676079 + 0.0573019i
\(889\) 2.31081e10i 1.10308i
\(890\) −1.47854e9 + 3.77491e10i −0.0703020 + 1.79491i
\(891\) 1.19479e10i 0.565872i
\(892\) 9.86995e9 + 7.74351e8i 0.465627 + 0.0365309i
\(893\) −1.63185e10 1.44103e10i −0.766830 0.677160i
\(894\) 1.39716e9 + 5.47232e7i 0.0653979 + 0.00256147i
\(895\) 1.72186e10 0.802816
\(896\) −8.87966e9 + 3.15885e10i −0.412399 + 1.46707i
\(897\) −1.31210e9 −0.0607005
\(898\) −5.01976e8 + 1.28161e10i −0.0231321 + 0.590595i
\(899\) 4.19286e10i 1.92465i
\(900\) −9.31763e9 7.31019e8i −0.426046 0.0334256i
\(901\) 6.64727e9i 0.302766i
\(902\) 3.09448e10 + 1.21203e9i 1.40399 + 0.0549910i
\(903\) −5.32374e9 −0.240608
\(904\) 1.53435e8 1.30046e9i 0.00690772 0.0585472i
\(905\) 2.40750e10i 1.07968i
\(906\) −7.66873e9 3.00365e8i −0.342590 0.0134184i
\(907\) −1.00339e10 −0.446525 −0.223263 0.974758i \(-0.571671\pi\)
−0.223263 + 0.974758i \(0.571671\pi\)
\(908\) −2.30551e10 1.80880e9i −1.02204 0.0801844i
\(909\) 3.67967e10 1.62493
\(910\) 6.80925e9 + 2.66702e8i 0.299540 + 0.0117322i
\(911\) −1.58345e10 −0.693888 −0.346944 0.937886i \(-0.612781\pi\)
−0.346944 + 0.937886i \(0.612781\pi\)
\(912\) −6.28676e9 + 5.19743e9i −0.274438 + 0.226886i
\(913\) −1.44431e10 −0.628076
\(914\) 2.64048e9 + 1.03421e8i 0.114385 + 0.00448019i
\(915\) 2.77400e9 0.119711
\(916\) 1.32463e10 + 1.03924e9i 0.569454 + 0.0446768i
\(917\) −3.00617e10 −1.28742
\(918\) −3.06398e9 1.20008e8i −0.130718 0.00511991i
\(919\) 6.01772e9i 0.255757i 0.991790 + 0.127879i \(0.0408168\pi\)
−0.991790 + 0.127879i \(0.959183\pi\)
\(920\) −3.57206e9 + 3.02755e10i −0.151238 + 1.28184i
\(921\) 8.06487e9 0.340164
\(922\) 3.63649e10 + 1.42432e9i 1.52800 + 0.0598482i
\(923\) 5.06509e9i 0.212022i
\(924\) −1.15479e10 9.05992e8i −0.481559 0.0377809i
\(925\) 1.90893e9i 0.0793039i
\(926\) −3.32492e8 + 8.48897e9i −0.0137608 + 0.351331i
\(927\) −1.68377e10 −0.694231
\(928\) 8.57577e9 4.32516e10i 0.352254 1.77658i
\(929\) 4.56774e9 0.186916 0.0934579 0.995623i \(-0.470208\pi\)
0.0934579 + 0.995623i \(0.470208\pi\)
\(930\) 1.13190e10 + 4.43335e8i 0.461441 + 0.0180735i
\(931\) 2.15517e10 2.44056e10i 0.875300 0.991208i
\(932\) −1.44124e10 1.13073e9i −0.583150 0.0457512i
\(933\) 9.49712e9i 0.382830i
\(934\) −9.41141e8 + 2.40286e10i −0.0377955 + 0.964972i
\(935\) 5.32539e9i 0.213064i
\(936\) 4.13737e8 3.50668e9i 0.0164915 0.139775i
\(937\) 1.10333e10 0.438146 0.219073 0.975709i \(-0.429697\pi\)
0.219073 + 0.975709i \(0.429697\pi\)
\(938\) −2.83775e8 + 7.24517e9i −0.0112270 + 0.286641i
\(939\) 1.11691e10 0.440240
\(940\) −2.48674e9 + 3.16962e10i −0.0976523 + 1.24469i
\(941\) 2.95981e10i 1.15798i 0.815335 + 0.578990i \(0.196553\pi\)
−0.815335 + 0.578990i \(0.803447\pi\)
\(942\) −1.01907e10 3.99146e8i −0.397217 0.0155580i
\(943\) −4.29881e10 −1.66939
\(944\) −3.38677e10 5.34712e9i −1.31034 0.206880i
\(945\) 3.21823e10i 1.24053i
\(946\) 1.02695e10 + 4.02232e8i 0.394396 + 0.0154475i
\(947\) 2.38397e10i 0.912169i 0.889937 + 0.456084i \(0.150748\pi\)
−0.889937 + 0.456084i \(0.849252\pi\)
\(948\) 7.72973e9 + 6.06439e8i 0.294669 + 0.0231184i
\(949\) 2.61556e8i 0.00993419i
\(950\) 8.93360e9 9.35189e9i 0.338060 0.353889i
\(951\) 1.18156e10i 0.445474i
\(952\) 9.32300e8 7.90182e9i 0.0350208 0.296823i
\(953\) 3.29758e10i 1.23416i −0.786902 0.617078i \(-0.788316\pi\)
0.786902 0.617078i \(-0.211684\pi\)
\(954\) 1.41482e9 3.61223e10i 0.0527573 1.34696i
\(955\) 3.38549e10i 1.25779i
\(956\) 4.08515e9 5.20697e10i 0.151219 1.92745i
\(957\) 1.55656e10 0.574084
\(958\) −6.95033e7 + 1.77451e9i −0.00255403 + 0.0652079i
\(959\) 6.98852e10i 2.55870i
\(960\) 1.15854e10 + 2.77242e9i 0.422633 + 0.101137i
\(961\) 3.55577e9 0.129242
\(962\) 7.20639e8 + 2.82256e7i 0.0260978 + 0.00102219i
\(963\) 1.61928e10 0.584293
\(964\) 2.81989e9 3.59426e10i 0.101382 1.29223i
\(965\) 5.20510e10i 1.86459i
\(966\) 1.60668e10 + 6.29296e8i 0.573467 + 0.0224613i
\(967\) 3.06333e10i 1.08943i 0.838620 + 0.544717i \(0.183363\pi\)
−0.838620 + 0.544717i \(0.816637\pi\)
\(968\) −5.81857e9 6.86506e8i −0.206183 0.0243266i
\(969\) 1.30925e9 1.48262e9i 0.0462263 0.0523477i
\(970\) −1.41827e9 + 3.62105e10i −0.0498952 + 1.27389i
\(971\) 1.86762e10 0.654667 0.327334 0.944909i \(-0.393850\pi\)
0.327334 + 0.944909i \(0.393850\pi\)
\(972\) 2.54995e10 + 2.00057e9i 0.890635 + 0.0698751i
\(973\) 2.77583e10 0.966045
\(974\) −2.43128e10 9.52270e8i −0.843098 0.0330220i
\(975\) 8.12929e8i 0.0280890i
\(976\) 7.90324e9 + 1.24778e9i 0.272102 + 0.0429601i
\(977\) 4.63388e10i 1.58970i −0.606809 0.794848i \(-0.707551\pi\)
0.606809 0.794848i \(-0.292449\pi\)
\(978\) 3.31169e8 8.45519e9i 0.0113204 0.289026i
\(979\) −3.84659e10 −1.31020
\(980\) −4.74042e10 3.71911e9i −1.60889 0.126226i
\(981\) 2.34686e9i 0.0793680i
\(982\) 1.39278e9 3.55595e10i 0.0469344 1.19830i
\(983\) −1.38258e10 −0.464251 −0.232126 0.972686i \(-0.574568\pi\)
−0.232126 + 0.972686i \(0.574568\pi\)
\(984\) −1.96828e9 + 1.66824e10i −0.0658574 + 0.558182i
\(985\) 3.93284e10 1.31123
\(986\) −4.18461e8 + 1.06839e10i −0.0139023 + 0.354944i
\(987\) 1.67691e10 0.555135
\(988\) 3.39832e9 + 3.51079e9i 0.112103 + 0.115812i
\(989\) −1.42663e10 −0.468948
\(990\) 1.13347e9 2.89390e10i 0.0371267 0.947894i
\(991\) −4.33942e10 −1.41636 −0.708180 0.706032i \(-0.750483\pi\)
−0.708180 + 0.706032i \(0.750483\pi\)
\(992\) 3.20487e10 + 6.35450e9i 1.04237 + 0.206676i
\(993\) 1.64681e10 0.533730
\(994\) −2.42927e9 + 6.20227e10i −0.0784557 + 2.00308i
\(995\) 2.66717e10i 0.858361i
\(996\) 6.12759e8 7.81028e9i 0.0196509 0.250472i
\(997\) −3.34859e10 −1.07011 −0.535055 0.844817i \(-0.679709\pi\)
−0.535055 + 0.844817i \(0.679709\pi\)
\(998\) 5.98718e8 1.52861e10i 0.0190662 0.486787i
\(999\) 3.40593e9i 0.108083i
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 76.8.d.a.75.1 68
4.3 odd 2 inner 76.8.d.a.75.67 yes 68
19.18 odd 2 inner 76.8.d.a.75.68 yes 68
76.75 even 2 inner 76.8.d.a.75.2 yes 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.8.d.a.75.1 68 1.1 even 1 trivial
76.8.d.a.75.2 yes 68 76.75 even 2 inner
76.8.d.a.75.67 yes 68 4.3 odd 2 inner
76.8.d.a.75.68 yes 68 19.18 odd 2 inner