Properties

Label 448.7.c.c.321.2
Level $448$
Weight $7$
Character 448.321
Analytic conductor $103.064$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [448,7,Mod(321,448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(448, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("448.321");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 448.c (of order \(2\), degree \(1\), not 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: \(103.064229462\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-510}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 510 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 321.2
Root \(22.5832i\) of defining polynomial
Character \(\chi\) \(=\) 448.321
Dual form 448.7.c.c.321.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+45.1664i q^{3} +45.1664i q^{5} +(-133.000 - 316.165i) q^{7} -1311.00 q^{9} +O(q^{10})\) \(q+45.1664i q^{3} +45.1664i q^{5} +(-133.000 - 316.165i) q^{7} -1311.00 q^{9} +874.000 q^{11} -2213.15i q^{13} -2040.00 q^{15} -5961.96i q^{17} +3116.48i q^{19} +(14280.0 - 6007.13i) q^{21} -4738.00 q^{23} +13585.0 q^{25} -26286.8i q^{27} -11146.0 q^{29} +27461.1i q^{31} +39475.4i q^{33} +(14280.0 - 6007.13i) q^{35} -3002.00 q^{37} +99960.0 q^{39} +57541.9i q^{41} +31418.0 q^{43} -59213.1i q^{45} +72446.8i q^{47} +(-82271.0 + 84099.8i) q^{49} +269280. q^{51} +76406.0 q^{53} +39475.4i q^{55} -140760. q^{57} +113232. i q^{59} +275108. i q^{61} +(174363. + 414492. i) q^{63} +99960.0 q^{65} +495242. q^{67} -213998. i q^{69} +184406. q^{71} -60974.6i q^{73} +613585. i q^{75} +(-116242. - 276328. i) q^{77} +534934. q^{79} +231561. q^{81} -714848. i q^{83} +269280. q^{85} -503424. i q^{87} -629529. i q^{89} +(-699720. + 294349. i) q^{91} -1.24032e6 q^{93} -140760. q^{95} +814440. i q^{97} -1.14581e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 266 q^{7} - 2622 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 266 q^{7} - 2622 q^{9} + 1748 q^{11} - 4080 q^{15} + 28560 q^{21} - 9476 q^{23} + 27170 q^{25} - 22292 q^{29} + 28560 q^{35} - 6004 q^{37} + 199920 q^{39} + 62836 q^{43} - 164542 q^{49} + 538560 q^{51} + 152812 q^{53} - 281520 q^{57} + 348726 q^{63} + 199920 q^{65} + 990484 q^{67} + 368812 q^{71} - 232484 q^{77} + 1069868 q^{79} + 463122 q^{81} + 538560 q^{85} - 1399440 q^{91} - 2480640 q^{93} - 281520 q^{95} - 2291628 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 45.1664i 1.67283i 0.548098 + 0.836414i \(0.315352\pi\)
−0.548098 + 0.836414i \(0.684648\pi\)
\(4\) 0 0
\(5\) 45.1664i 0.361331i 0.983545 + 0.180665i \(0.0578251\pi\)
−0.983545 + 0.180665i \(0.942175\pi\)
\(6\) 0 0
\(7\) −133.000 316.165i −0.387755 0.921762i
\(8\) 0 0
\(9\) −1311.00 −1.79835
\(10\) 0 0
\(11\) 874.000 0.656649 0.328325 0.944565i \(-0.393516\pi\)
0.328325 + 0.944565i \(0.393516\pi\)
\(12\) 0 0
\(13\) 2213.15i 1.00735i −0.863893 0.503676i \(-0.831981\pi\)
0.863893 0.503676i \(-0.168019\pi\)
\(14\) 0 0
\(15\) −2040.00 −0.604444
\(16\) 0 0
\(17\) 5961.96i 1.21351i −0.794890 0.606753i \(-0.792472\pi\)
0.794890 0.606753i \(-0.207528\pi\)
\(18\) 0 0
\(19\) 3116.48i 0.454363i 0.973852 + 0.227182i \(0.0729511\pi\)
−0.973852 + 0.227182i \(0.927049\pi\)
\(20\) 0 0
\(21\) 14280.0 6007.13i 1.54195 0.648648i
\(22\) 0 0
\(23\) −4738.00 −0.389414 −0.194707 0.980861i \(-0.562376\pi\)
−0.194707 + 0.980861i \(0.562376\pi\)
\(24\) 0 0
\(25\) 13585.0 0.869440
\(26\) 0 0
\(27\) 26286.8i 1.33551i
\(28\) 0 0
\(29\) −11146.0 −0.457009 −0.228505 0.973543i \(-0.573384\pi\)
−0.228505 + 0.973543i \(0.573384\pi\)
\(30\) 0 0
\(31\) 27461.1i 0.921793i 0.887454 + 0.460897i \(0.152472\pi\)
−0.887454 + 0.460897i \(0.847528\pi\)
\(32\) 0 0
\(33\) 39475.4i 1.09846i
\(34\) 0 0
\(35\) 14280.0 6007.13i 0.333061 0.140108i
\(36\) 0 0
\(37\) −3002.00 −0.0592660 −0.0296330 0.999561i \(-0.509434\pi\)
−0.0296330 + 0.999561i \(0.509434\pi\)
\(38\) 0 0
\(39\) 99960.0 1.68513
\(40\) 0 0
\(41\) 57541.9i 0.834897i 0.908701 + 0.417449i \(0.137076\pi\)
−0.908701 + 0.417449i \(0.862924\pi\)
\(42\) 0 0
\(43\) 31418.0 0.395160 0.197580 0.980287i \(-0.436692\pi\)
0.197580 + 0.980287i \(0.436692\pi\)
\(44\) 0 0
\(45\) 59213.1i 0.649801i
\(46\) 0 0
\(47\) 72446.8i 0.697792i 0.937161 + 0.348896i \(0.113443\pi\)
−0.937161 + 0.348896i \(0.886557\pi\)
\(48\) 0 0
\(49\) −82271.0 + 84099.8i −0.699292 + 0.714836i
\(50\) 0 0
\(51\) 269280. 2.02999
\(52\) 0 0
\(53\) 76406.0 0.513216 0.256608 0.966516i \(-0.417395\pi\)
0.256608 + 0.966516i \(0.417395\pi\)
\(54\) 0 0
\(55\) 39475.4i 0.237268i
\(56\) 0 0
\(57\) −140760. −0.760072
\(58\) 0 0
\(59\) 113232.i 0.551332i 0.961253 + 0.275666i \(0.0888984\pi\)
−0.961253 + 0.275666i \(0.911102\pi\)
\(60\) 0 0
\(61\) 275108.i 1.21203i 0.795452 + 0.606016i \(0.207233\pi\)
−0.795452 + 0.606016i \(0.792767\pi\)
\(62\) 0 0
\(63\) 174363. + 414492.i 0.697321 + 1.65766i
\(64\) 0 0
\(65\) 99960.0 0.363987
\(66\) 0 0
\(67\) 495242. 1.64662 0.823309 0.567593i \(-0.192125\pi\)
0.823309 + 0.567593i \(0.192125\pi\)
\(68\) 0 0
\(69\) 213998.i 0.651423i
\(70\) 0 0
\(71\) 184406. 0.515229 0.257614 0.966248i \(-0.417064\pi\)
0.257614 + 0.966248i \(0.417064\pi\)
\(72\) 0 0
\(73\) 60974.6i 0.156740i −0.996924 0.0783701i \(-0.975028\pi\)
0.996924 0.0783701i \(-0.0249716\pi\)
\(74\) 0 0
\(75\) 613585.i 1.45442i
\(76\) 0 0
\(77\) −116242. 276328.i −0.254619 0.605275i
\(78\) 0 0
\(79\) 534934. 1.08497 0.542486 0.840065i \(-0.317483\pi\)
0.542486 + 0.840065i \(0.317483\pi\)
\(80\) 0 0
\(81\) 231561. 0.435723
\(82\) 0 0
\(83\) 714848.i 1.25020i −0.780545 0.625100i \(-0.785058\pi\)
0.780545 0.625100i \(-0.214942\pi\)
\(84\) 0 0
\(85\) 269280. 0.438478
\(86\) 0 0
\(87\) 503424.i 0.764498i
\(88\) 0 0
\(89\) 629529.i 0.892988i −0.894787 0.446494i \(-0.852672\pi\)
0.894787 0.446494i \(-0.147328\pi\)
\(90\) 0 0
\(91\) −699720. + 294349.i −0.928539 + 0.390606i
\(92\) 0 0
\(93\) −1.24032e6 −1.54200
\(94\) 0 0
\(95\) −140760. −0.164176
\(96\) 0 0
\(97\) 814440.i 0.892368i 0.894941 + 0.446184i \(0.147217\pi\)
−0.894941 + 0.446184i \(0.852783\pi\)
\(98\) 0 0
\(99\) −1.14581e6 −1.18089
\(100\) 0 0
\(101\) 1.95195e6i 1.89455i 0.320425 + 0.947274i \(0.396174\pi\)
−0.320425 + 0.947274i \(0.603826\pi\)
\(102\) 0 0
\(103\) 1.69744e6i 1.55340i −0.629871 0.776700i \(-0.716892\pi\)
0.629871 0.776700i \(-0.283108\pi\)
\(104\) 0 0
\(105\) 271320. + 644976.i 0.234376 + 0.557154i
\(106\) 0 0
\(107\) 1.61603e6 1.31916 0.659579 0.751635i \(-0.270734\pi\)
0.659579 + 0.751635i \(0.270734\pi\)
\(108\) 0 0
\(109\) −199226. −0.153839 −0.0769195 0.997037i \(-0.524508\pi\)
−0.0769195 + 0.997037i \(0.524508\pi\)
\(110\) 0 0
\(111\) 135589.i 0.0991418i
\(112\) 0 0
\(113\) −1.80762e6 −1.25277 −0.626386 0.779513i \(-0.715467\pi\)
−0.626386 + 0.779513i \(0.715467\pi\)
\(114\) 0 0
\(115\) 213998.i 0.140707i
\(116\) 0 0
\(117\) 2.90144e6i 1.81157i
\(118\) 0 0
\(119\) −1.88496e6 + 792941.i −1.11857 + 0.470543i
\(120\) 0 0
\(121\) −1.00768e6 −0.568812
\(122\) 0 0
\(123\) −2.59896e6 −1.39664
\(124\) 0 0
\(125\) 1.31931e6i 0.675486i
\(126\) 0 0
\(127\) −3.32472e6 −1.62310 −0.811548 0.584286i \(-0.801375\pi\)
−0.811548 + 0.584286i \(0.801375\pi\)
\(128\) 0 0
\(129\) 1.41904e6i 0.661035i
\(130\) 0 0
\(131\) 3.13567e6i 1.39482i 0.716674 + 0.697408i \(0.245664\pi\)
−0.716674 + 0.697408i \(0.754336\pi\)
\(132\) 0 0
\(133\) 985320. 414492.i 0.418815 0.176182i
\(134\) 0 0
\(135\) 1.18728e6 0.482561
\(136\) 0 0
\(137\) 2.12927e6 0.828072 0.414036 0.910260i \(-0.364119\pi\)
0.414036 + 0.910260i \(0.364119\pi\)
\(138\) 0 0
\(139\) 1.68421e6i 0.627121i −0.949568 0.313561i \(-0.898478\pi\)
0.949568 0.313561i \(-0.101522\pi\)
\(140\) 0 0
\(141\) −3.27216e6 −1.16729
\(142\) 0 0
\(143\) 1.93429e6i 0.661477i
\(144\) 0 0
\(145\) 503424.i 0.165132i
\(146\) 0 0
\(147\) −3.79848e6 3.71588e6i −1.19580 1.16980i
\(148\) 0 0
\(149\) 2.59573e6 0.784696 0.392348 0.919817i \(-0.371663\pi\)
0.392348 + 0.919817i \(0.371663\pi\)
\(150\) 0 0
\(151\) 1.68557e6 0.489570 0.244785 0.969577i \(-0.421283\pi\)
0.244785 + 0.969577i \(0.421283\pi\)
\(152\) 0 0
\(153\) 7.81613e6i 2.18231i
\(154\) 0 0
\(155\) −1.24032e6 −0.333072
\(156\) 0 0
\(157\) 3.67641e6i 0.950002i −0.879985 0.475001i \(-0.842448\pi\)
0.879985 0.475001i \(-0.157552\pi\)
\(158\) 0 0
\(159\) 3.45098e6i 0.858521i
\(160\) 0 0
\(161\) 630154. + 1.49799e6i 0.150997 + 0.358947i
\(162\) 0 0
\(163\) 1.88191e6 0.434547 0.217274 0.976111i \(-0.430284\pi\)
0.217274 + 0.976111i \(0.430284\pi\)
\(164\) 0 0
\(165\) −1.78296e6 −0.396908
\(166\) 0 0
\(167\) 3.15595e6i 0.677612i 0.940856 + 0.338806i \(0.110023\pi\)
−0.940856 + 0.338806i \(0.889977\pi\)
\(168\) 0 0
\(169\) −71231.0 −0.0147574
\(170\) 0 0
\(171\) 4.08570e6i 0.817106i
\(172\) 0 0
\(173\) 2.29477e6i 0.443201i 0.975138 + 0.221600i \(0.0711280\pi\)
−0.975138 + 0.221600i \(0.928872\pi\)
\(174\) 0 0
\(175\) −1.80680e6 4.29509e6i −0.337130 0.801417i
\(176\) 0 0
\(177\) −5.11428e6 −0.922284
\(178\) 0 0
\(179\) 3.51846e6 0.613470 0.306735 0.951795i \(-0.400763\pi\)
0.306735 + 0.951795i \(0.400763\pi\)
\(180\) 0 0
\(181\) 7.48267e6i 1.26189i 0.775829 + 0.630944i \(0.217332\pi\)
−0.775829 + 0.630944i \(0.782668\pi\)
\(182\) 0 0
\(183\) −1.24256e7 −2.02752
\(184\) 0 0
\(185\) 135589.i 0.0214146i
\(186\) 0 0
\(187\) 5.21075e6i 0.796848i
\(188\) 0 0
\(189\) −8.31096e6 + 3.49615e6i −1.23102 + 0.517850i
\(190\) 0 0
\(191\) 7.20028e6 1.03335 0.516677 0.856180i \(-0.327169\pi\)
0.516677 + 0.856180i \(0.327169\pi\)
\(192\) 0 0
\(193\) −1.30889e7 −1.82067 −0.910335 0.413872i \(-0.864176\pi\)
−0.910335 + 0.413872i \(0.864176\pi\)
\(194\) 0 0
\(195\) 4.51483e6i 0.608888i
\(196\) 0 0
\(197\) 9.17476e6 1.20004 0.600020 0.799985i \(-0.295159\pi\)
0.600020 + 0.799985i \(0.295159\pi\)
\(198\) 0 0
\(199\) 6.78769e6i 0.861317i 0.902515 + 0.430658i \(0.141719\pi\)
−0.902515 + 0.430658i \(0.858281\pi\)
\(200\) 0 0
\(201\) 2.23683e7i 2.75451i
\(202\) 0 0
\(203\) 1.48242e6 + 3.52397e6i 0.177208 + 0.421254i
\(204\) 0 0
\(205\) −2.59896e6 −0.301674
\(206\) 0 0
\(207\) 6.21152e6 0.700304
\(208\) 0 0
\(209\) 2.72380e6i 0.298357i
\(210\) 0 0
\(211\) 8.40084e6 0.894284 0.447142 0.894463i \(-0.352442\pi\)
0.447142 + 0.894463i \(0.352442\pi\)
\(212\) 0 0
\(213\) 8.32895e6i 0.861889i
\(214\) 0 0
\(215\) 1.41904e6i 0.142784i
\(216\) 0 0
\(217\) 8.68224e6 3.65233e6i 0.849675 0.357430i
\(218\) 0 0
\(219\) 2.75400e6 0.262199
\(220\) 0 0
\(221\) −1.31947e7 −1.22243
\(222\) 0 0
\(223\) 4.90434e6i 0.442248i −0.975246 0.221124i \(-0.929027\pi\)
0.975246 0.221124i \(-0.0709726\pi\)
\(224\) 0 0
\(225\) −1.78099e7 −1.56356
\(226\) 0 0
\(227\) 1.32183e7i 1.13005i 0.825075 + 0.565023i \(0.191133\pi\)
−0.825075 + 0.565023i \(0.808867\pi\)
\(228\) 0 0
\(229\) 338974.i 0.0282266i 0.999900 + 0.0141133i \(0.00449256\pi\)
−0.999900 + 0.0141133i \(0.995507\pi\)
\(230\) 0 0
\(231\) 1.24807e7 5.25023e6i 1.01252 0.425934i
\(232\) 0 0
\(233\) 4.84146e6 0.382744 0.191372 0.981518i \(-0.438706\pi\)
0.191372 + 0.981518i \(0.438706\pi\)
\(234\) 0 0
\(235\) −3.27216e6 −0.252134
\(236\) 0 0
\(237\) 2.41610e7i 1.81497i
\(238\) 0 0
\(239\) 1.37297e7 1.00570 0.502850 0.864374i \(-0.332285\pi\)
0.502850 + 0.864374i \(0.332285\pi\)
\(240\) 0 0
\(241\) 3.66913e6i 0.262127i 0.991374 + 0.131064i \(0.0418392\pi\)
−0.991374 + 0.131064i \(0.958161\pi\)
\(242\) 0 0
\(243\) 8.70433e6i 0.606619i
\(244\) 0 0
\(245\) −3.79848e6 3.71588e6i −0.258292 0.252676i
\(246\) 0 0
\(247\) 6.89724e6 0.457704
\(248\) 0 0
\(249\) 3.22871e7 2.09137
\(250\) 0 0
\(251\) 1.57289e7i 0.994664i 0.867560 + 0.497332i \(0.165687\pi\)
−0.867560 + 0.497332i \(0.834313\pi\)
\(252\) 0 0
\(253\) −4.14101e6 −0.255708
\(254\) 0 0
\(255\) 1.21624e7i 0.733498i
\(256\) 0 0
\(257\) 7.54531e6i 0.444506i −0.974989 0.222253i \(-0.928659\pi\)
0.974989 0.222253i \(-0.0713411\pi\)
\(258\) 0 0
\(259\) 399266. + 949126.i 0.0229807 + 0.0546292i
\(260\) 0 0
\(261\) 1.46124e7 0.821864
\(262\) 0 0
\(263\) 1.32059e7 0.725942 0.362971 0.931800i \(-0.381762\pi\)
0.362971 + 0.931800i \(0.381762\pi\)
\(264\) 0 0
\(265\) 3.45098e6i 0.185441i
\(266\) 0 0
\(267\) 2.84335e7 1.49382
\(268\) 0 0
\(269\) 1.59600e7i 0.819930i −0.912101 0.409965i \(-0.865541\pi\)
0.912101 0.409965i \(-0.134459\pi\)
\(270\) 0 0
\(271\) 2.48446e7i 1.24831i 0.781299 + 0.624157i \(0.214557\pi\)
−0.781299 + 0.624157i \(0.785443\pi\)
\(272\) 0 0
\(273\) −1.32947e7 3.16038e7i −0.653416 1.55329i
\(274\) 0 0
\(275\) 1.18733e7 0.570917
\(276\) 0 0
\(277\) −1.60013e7 −0.752863 −0.376432 0.926444i \(-0.622849\pi\)
−0.376432 + 0.926444i \(0.622849\pi\)
\(278\) 0 0
\(279\) 3.60016e7i 1.65771i
\(280\) 0 0
\(281\) −603566. −0.0272023 −0.0136012 0.999908i \(-0.504330\pi\)
−0.0136012 + 0.999908i \(0.504330\pi\)
\(282\) 0 0
\(283\) 2.22195e7i 0.980334i 0.871629 + 0.490167i \(0.163064\pi\)
−0.871629 + 0.490167i \(0.836936\pi\)
\(284\) 0 0
\(285\) 6.35762e6i 0.274637i
\(286\) 0 0
\(287\) 1.81927e7 7.65308e6i 0.769577 0.323736i
\(288\) 0 0
\(289\) −1.14074e7 −0.472599
\(290\) 0 0
\(291\) −3.67853e7 −1.49278
\(292\) 0 0
\(293\) 4.28134e7i 1.70207i 0.525110 + 0.851034i \(0.324024\pi\)
−0.525110 + 0.851034i \(0.675976\pi\)
\(294\) 0 0
\(295\) −5.11428e6 −0.199213
\(296\) 0 0
\(297\) 2.29747e7i 0.876961i
\(298\) 0 0
\(299\) 1.04859e7i 0.392277i
\(300\) 0 0
\(301\) −4.17859e6 9.93326e6i −0.153225 0.364244i
\(302\) 0 0
\(303\) −8.81627e7 −3.16925
\(304\) 0 0
\(305\) −1.24256e7 −0.437945
\(306\) 0 0
\(307\) 4.02152e7i 1.38987i −0.719072 0.694936i \(-0.755433\pi\)
0.719072 0.694936i \(-0.244567\pi\)
\(308\) 0 0
\(309\) 7.66673e7 2.59857
\(310\) 0 0
\(311\) 1.47381e7i 0.489958i −0.969528 0.244979i \(-0.921219\pi\)
0.969528 0.244979i \(-0.0787811\pi\)
\(312\) 0 0
\(313\) 4.19490e7i 1.36801i 0.729479 + 0.684004i \(0.239763\pi\)
−0.729479 + 0.684004i \(0.760237\pi\)
\(314\) 0 0
\(315\) −1.87211e7 + 7.87534e6i −0.598962 + 0.251964i
\(316\) 0 0
\(317\) −4.30922e7 −1.35276 −0.676380 0.736553i \(-0.736452\pi\)
−0.676380 + 0.736553i \(0.736452\pi\)
\(318\) 0 0
\(319\) −9.74160e6 −0.300095
\(320\) 0 0
\(321\) 7.29900e7i 2.20673i
\(322\) 0 0
\(323\) 1.85803e7 0.551373
\(324\) 0 0
\(325\) 3.00657e7i 0.875832i
\(326\) 0 0
\(327\) 8.99831e6i 0.257346i
\(328\) 0 0
\(329\) 2.29051e7 9.63543e6i 0.643198 0.270572i
\(330\) 0 0
\(331\) −5.32204e7 −1.46755 −0.733777 0.679390i \(-0.762244\pi\)
−0.733777 + 0.679390i \(0.762244\pi\)
\(332\) 0 0
\(333\) 3.93562e6 0.106581
\(334\) 0 0
\(335\) 2.23683e7i 0.594974i
\(336\) 0 0
\(337\) 2.34579e6 0.0612913 0.0306456 0.999530i \(-0.490244\pi\)
0.0306456 + 0.999530i \(0.490244\pi\)
\(338\) 0 0
\(339\) 8.16437e7i 2.09567i
\(340\) 0 0
\(341\) 2.40010e7i 0.605295i
\(342\) 0 0
\(343\) 3.75314e7 + 1.48259e7i 0.930063 + 0.367400i
\(344\) 0 0
\(345\) 9.66552e6 0.235379
\(346\) 0 0
\(347\) −4.80596e7 −1.15025 −0.575124 0.818066i \(-0.695046\pi\)
−0.575124 + 0.818066i \(0.695046\pi\)
\(348\) 0 0
\(349\) 1.00499e7i 0.236421i −0.992989 0.118211i \(-0.962284\pi\)
0.992989 0.118211i \(-0.0377158\pi\)
\(350\) 0 0
\(351\) −5.81767e7 −1.34533
\(352\) 0 0
\(353\) 7.65216e7i 1.73964i −0.493368 0.869821i \(-0.664234\pi\)
0.493368 0.869821i \(-0.335766\pi\)
\(354\) 0 0
\(355\) 8.32895e6i 0.186168i
\(356\) 0 0
\(357\) −3.58142e7 8.51368e7i −0.787138 1.87117i
\(358\) 0 0
\(359\) −8.39735e6 −0.181493 −0.0907463 0.995874i \(-0.528925\pi\)
−0.0907463 + 0.995874i \(0.528925\pi\)
\(360\) 0 0
\(361\) 3.73334e7 0.793554
\(362\) 0 0
\(363\) 4.55135e7i 0.951525i
\(364\) 0 0
\(365\) 2.75400e6 0.0566351
\(366\) 0 0
\(367\) 3.82776e6i 0.0774366i 0.999250 + 0.0387183i \(0.0123275\pi\)
−0.999250 + 0.0387183i \(0.987672\pi\)
\(368\) 0 0
\(369\) 7.54375e7i 1.50144i
\(370\) 0 0
\(371\) −1.01620e7 2.41569e7i −0.199002 0.473063i
\(372\) 0 0
\(373\) 4.93836e7 0.951604 0.475802 0.879552i \(-0.342158\pi\)
0.475802 + 0.879552i \(0.342158\pi\)
\(374\) 0 0
\(375\) −5.95884e7 −1.12997
\(376\) 0 0
\(377\) 2.46678e7i 0.460369i
\(378\) 0 0
\(379\) 3.74561e7 0.688026 0.344013 0.938965i \(-0.388214\pi\)
0.344013 + 0.938965i \(0.388214\pi\)
\(380\) 0 0
\(381\) 1.50166e8i 2.71516i
\(382\) 0 0
\(383\) 5.01003e7i 0.891752i −0.895095 0.445876i \(-0.852892\pi\)
0.895095 0.445876i \(-0.147108\pi\)
\(384\) 0 0
\(385\) 1.24807e7 5.25023e6i 0.218704 0.0920017i
\(386\) 0 0
\(387\) −4.11890e7 −0.710638
\(388\) 0 0
\(389\) −224986. −0.00382214 −0.00191107 0.999998i \(-0.500608\pi\)
−0.00191107 + 0.999998i \(0.500608\pi\)
\(390\) 0 0
\(391\) 2.82478e7i 0.472557i
\(392\) 0 0
\(393\) −1.41627e8 −2.33329
\(394\) 0 0
\(395\) 2.41610e7i 0.392034i
\(396\) 0 0
\(397\) 871937.i 0.0139352i −0.999976 0.00696760i \(-0.997782\pi\)
0.999976 0.00696760i \(-0.00221787\pi\)
\(398\) 0 0
\(399\) 1.87211e7 + 4.45033e7i 0.294722 + 0.700606i
\(400\) 0 0
\(401\) 1.44909e7 0.224730 0.112365 0.993667i \(-0.464157\pi\)
0.112365 + 0.993667i \(0.464157\pi\)
\(402\) 0 0
\(403\) 6.07757e7 0.928570
\(404\) 0 0
\(405\) 1.04588e7i 0.157440i
\(406\) 0 0
\(407\) −2.62375e6 −0.0389170
\(408\) 0 0
\(409\) 1.04303e8i 1.52450i −0.647284 0.762249i \(-0.724095\pi\)
0.647284 0.762249i \(-0.275905\pi\)
\(410\) 0 0
\(411\) 9.61712e7i 1.38522i
\(412\) 0 0
\(413\) 3.58000e7 1.50599e7i 0.508197 0.213782i
\(414\) 0 0
\(415\) 3.22871e7 0.451736
\(416\) 0 0
\(417\) 7.60696e7 1.04907
\(418\) 0 0
\(419\) 8.22075e7i 1.11756i 0.829317 + 0.558778i \(0.188730\pi\)
−0.829317 + 0.558778i \(0.811270\pi\)
\(420\) 0 0
\(421\) 1.33780e7 0.179285 0.0896427 0.995974i \(-0.471427\pi\)
0.0896427 + 0.995974i \(0.471427\pi\)
\(422\) 0 0
\(423\) 9.49778e7i 1.25488i
\(424\) 0 0
\(425\) 8.09932e7i 1.05507i
\(426\) 0 0
\(427\) 8.69795e7 3.65894e7i 1.11721 0.469972i
\(428\) 0 0
\(429\) 8.73650e7 1.10654
\(430\) 0 0
\(431\) 1.34244e8 1.67673 0.838367 0.545106i \(-0.183510\pi\)
0.838367 + 0.545106i \(0.183510\pi\)
\(432\) 0 0
\(433\) 1.03230e8i 1.27158i 0.771863 + 0.635789i \(0.219325\pi\)
−0.771863 + 0.635789i \(0.780675\pi\)
\(434\) 0 0
\(435\) 2.27378e7 0.276237
\(436\) 0 0
\(437\) 1.47659e7i 0.176935i
\(438\) 0 0
\(439\) 2.65816e7i 0.314186i 0.987584 + 0.157093i \(0.0502123\pi\)
−0.987584 + 0.157093i \(0.949788\pi\)
\(440\) 0 0
\(441\) 1.07857e8 1.10255e8i 1.25757 1.28553i
\(442\) 0 0
\(443\) 1.31972e8 1.51799 0.758996 0.651096i \(-0.225690\pi\)
0.758996 + 0.651096i \(0.225690\pi\)
\(444\) 0 0
\(445\) 2.84335e7 0.322664
\(446\) 0 0
\(447\) 1.17240e8i 1.31266i
\(448\) 0 0
\(449\) 1.47766e8 1.63244 0.816218 0.577743i \(-0.196067\pi\)
0.816218 + 0.577743i \(0.196067\pi\)
\(450\) 0 0
\(451\) 5.02917e7i 0.548234i
\(452\) 0 0
\(453\) 7.61309e7i 0.818967i
\(454\) 0 0
\(455\) −1.32947e7 3.16038e7i −0.141138 0.335510i
\(456\) 0 0
\(457\) −8.22868e7 −0.862147 −0.431074 0.902317i \(-0.641865\pi\)
−0.431074 + 0.902317i \(0.641865\pi\)
\(458\) 0 0
\(459\) −1.56721e8 −1.62065
\(460\) 0 0
\(461\) 1.31884e8i 1.34614i 0.739580 + 0.673068i \(0.235024\pi\)
−0.739580 + 0.673068i \(0.764976\pi\)
\(462\) 0 0
\(463\) −1.39927e6 −0.0140981 −0.00704904 0.999975i \(-0.502244\pi\)
−0.00704904 + 0.999975i \(0.502244\pi\)
\(464\) 0 0
\(465\) 5.60207e7i 0.557173i
\(466\) 0 0
\(467\) 1.81321e7i 0.178032i −0.996030 0.0890158i \(-0.971628\pi\)
0.996030 0.0890158i \(-0.0283722\pi\)
\(468\) 0 0
\(469\) −6.58672e7 1.56578e8i −0.638485 1.51779i
\(470\) 0 0
\(471\) 1.66050e8 1.58919
\(472\) 0 0
\(473\) 2.74593e7 0.259482
\(474\) 0 0
\(475\) 4.23374e7i 0.395042i
\(476\) 0 0
\(477\) −1.00168e8 −0.922943
\(478\) 0 0
\(479\) 2.89375e7i 0.263303i 0.991296 + 0.131651i \(0.0420279\pi\)
−0.991296 + 0.131651i \(0.957972\pi\)
\(480\) 0 0
\(481\) 6.64388e6i 0.0597017i
\(482\) 0 0
\(483\) −6.76586e7 + 2.84618e7i −0.600457 + 0.252592i
\(484\) 0 0
\(485\) −3.67853e7 −0.322440
\(486\) 0 0
\(487\) 9.47515e7 0.820350 0.410175 0.912007i \(-0.365468\pi\)
0.410175 + 0.912007i \(0.365468\pi\)
\(488\) 0 0
\(489\) 8.49992e7i 0.726923i
\(490\) 0 0
\(491\) −2.58834e7 −0.218663 −0.109332 0.994005i \(-0.534871\pi\)
−0.109332 + 0.994005i \(0.534871\pi\)
\(492\) 0 0
\(493\) 6.64520e7i 0.554584i
\(494\) 0 0
\(495\) 5.17522e7i 0.426691i
\(496\) 0 0
\(497\) −2.45260e7 5.83026e7i −0.199783 0.474918i
\(498\) 0 0
\(499\) 1.56023e8 1.25571 0.627853 0.778332i \(-0.283934\pi\)
0.627853 + 0.778332i \(0.283934\pi\)
\(500\) 0 0
\(501\) −1.42543e8 −1.13353
\(502\) 0 0
\(503\) 1.11476e8i 0.875950i −0.898987 0.437975i \(-0.855696\pi\)
0.898987 0.437975i \(-0.144304\pi\)
\(504\) 0 0
\(505\) −8.81627e7 −0.684559
\(506\) 0 0
\(507\) 3.21724e6i 0.0246865i
\(508\) 0 0
\(509\) 7.45421e7i 0.565260i −0.959229 0.282630i \(-0.908793\pi\)
0.959229 0.282630i \(-0.0912068\pi\)
\(510\) 0 0
\(511\) −1.92780e7 + 8.10962e6i −0.144477 + 0.0607768i
\(512\) 0 0
\(513\) 8.19223e7 0.606806
\(514\) 0 0
\(515\) 7.66673e7 0.561291
\(516\) 0 0
\(517\) 6.33185e7i 0.458204i
\(518\) 0 0
\(519\) −1.03646e8 −0.741398
\(520\) 0 0
\(521\) 1.96232e8i 1.38758i −0.720179 0.693789i \(-0.755940\pi\)
0.720179 0.693789i \(-0.244060\pi\)
\(522\) 0 0
\(523\) 4.62080e7i 0.323007i 0.986872 + 0.161504i \(0.0516344\pi\)
−0.986872 + 0.161504i \(0.948366\pi\)
\(524\) 0 0
\(525\) 1.93994e8 8.16068e7i 1.34063 0.563960i
\(526\) 0 0
\(527\) 1.63722e8 1.11860
\(528\) 0 0
\(529\) −1.25587e8 −0.848357
\(530\) 0 0
\(531\) 1.48447e8i 0.991490i
\(532\) 0 0
\(533\) 1.27349e8 0.841035
\(534\) 0 0
\(535\) 7.29900e7i 0.476653i
\(536\) 0 0
\(537\) 1.58916e8i 1.02623i
\(538\) 0 0
\(539\) −7.19049e7 + 7.35032e7i −0.459189 + 0.469397i
\(540\) 0 0
\(541\) 7.52906e7 0.475498 0.237749 0.971327i \(-0.423590\pi\)
0.237749 + 0.971327i \(0.423590\pi\)
\(542\) 0 0
\(543\) −3.37965e8 −2.11092
\(544\) 0 0
\(545\) 8.99831e6i 0.0555868i
\(546\) 0 0
\(547\) 7.26760e7 0.444047 0.222023 0.975041i \(-0.428734\pi\)
0.222023 + 0.975041i \(0.428734\pi\)
\(548\) 0 0
\(549\) 3.60667e8i 2.17966i
\(550\) 0 0
\(551\) 3.47363e7i 0.207648i
\(552\) 0 0
\(553\) −7.11462e7 1.69127e8i −0.420704 1.00009i
\(554\) 0 0
\(555\) 6.12408e6 0.0358230
\(556\) 0 0
\(557\) 3.10741e8 1.79818 0.899090 0.437765i \(-0.144230\pi\)
0.899090 + 0.437765i \(0.144230\pi\)
\(558\) 0 0
\(559\) 6.95328e7i 0.398065i
\(560\) 0 0
\(561\) 2.35351e8 1.33299
\(562\) 0 0
\(563\) 5.66378e7i 0.317381i 0.987328 + 0.158690i \(0.0507272\pi\)
−0.987328 + 0.158690i \(0.949273\pi\)
\(564\) 0 0
\(565\) 8.16437e7i 0.452665i
\(566\) 0 0
\(567\) −3.07976e7 7.32114e7i −0.168954 0.401633i
\(568\) 0 0
\(569\) 5.17304e7 0.280808 0.140404 0.990094i \(-0.455160\pi\)
0.140404 + 0.990094i \(0.455160\pi\)
\(570\) 0 0
\(571\) 8.68765e7 0.466653 0.233326 0.972398i \(-0.425039\pi\)
0.233326 + 0.972398i \(0.425039\pi\)
\(572\) 0 0
\(573\) 3.25210e8i 1.72862i
\(574\) 0 0
\(575\) −6.43657e7 −0.338572
\(576\) 0 0
\(577\) 5.89865e7i 0.307062i 0.988144 + 0.153531i \(0.0490644\pi\)
−0.988144 + 0.153531i \(0.950936\pi\)
\(578\) 0 0
\(579\) 5.91178e8i 3.04567i
\(580\) 0 0
\(581\) −2.26010e8 + 9.50748e7i −1.15239 + 0.484771i
\(582\) 0 0
\(583\) 6.67788e7 0.337003
\(584\) 0 0
\(585\) −1.31048e8 −0.654578
\(586\) 0 0
\(587\) 3.10848e8i 1.53686i 0.639934 + 0.768430i \(0.278962\pi\)
−0.639934 + 0.768430i \(0.721038\pi\)
\(588\) 0 0
\(589\) −8.55821e7 −0.418829
\(590\) 0 0
\(591\) 4.14390e8i 2.00746i
\(592\) 0 0
\(593\) 3.46714e8i 1.66268i 0.555766 + 0.831339i \(0.312425\pi\)
−0.555766 + 0.831339i \(0.687575\pi\)
\(594\) 0 0
\(595\) −3.58142e7 8.51368e7i −0.170022 0.404172i
\(596\) 0 0
\(597\) −3.06575e8 −1.44083
\(598\) 0 0
\(599\) −9.47771e7 −0.440984 −0.220492 0.975389i \(-0.570766\pi\)
−0.220492 + 0.975389i \(0.570766\pi\)
\(600\) 0 0
\(601\) 2.04951e8i 0.944119i 0.881567 + 0.472060i \(0.156489\pi\)
−0.881567 + 0.472060i \(0.843511\pi\)
\(602\) 0 0
\(603\) −6.49262e8 −2.96120
\(604\) 0 0
\(605\) 4.55135e7i 0.205529i
\(606\) 0 0
\(607\) 3.28634e8i 1.46942i 0.678379 + 0.734712i \(0.262683\pi\)
−0.678379 + 0.734712i \(0.737317\pi\)
\(608\) 0 0
\(609\) −1.59165e8 + 6.69554e7i −0.704686 + 0.296438i
\(610\) 0 0
\(611\) 1.60336e8 0.702922
\(612\) 0 0
\(613\) −2.67967e8 −1.16332 −0.581660 0.813432i \(-0.697597\pi\)
−0.581660 + 0.813432i \(0.697597\pi\)
\(614\) 0 0
\(615\) 1.17386e8i 0.504649i
\(616\) 0 0
\(617\) −3.88909e8 −1.65574 −0.827870 0.560921i \(-0.810447\pi\)
−0.827870 + 0.560921i \(0.810447\pi\)
\(618\) 0 0
\(619\) 6.30894e7i 0.266002i 0.991116 + 0.133001i \(0.0424613\pi\)
−0.991116 + 0.133001i \(0.957539\pi\)
\(620\) 0 0
\(621\) 1.24547e8i 0.520066i
\(622\) 0 0
\(623\) −1.99035e8 + 8.37273e7i −0.823123 + 0.346261i
\(624\) 0 0
\(625\) 1.52677e8 0.625366
\(626\) 0 0
\(627\) −1.23024e8 −0.499101
\(628\) 0 0
\(629\) 1.78978e7i 0.0719197i
\(630\) 0 0
\(631\) 1.30827e8 0.520725 0.260363 0.965511i \(-0.416158\pi\)
0.260363 + 0.965511i \(0.416158\pi\)
\(632\) 0 0
\(633\) 3.79435e8i 1.49598i
\(634\) 0 0
\(635\) 1.50166e8i 0.586475i
\(636\) 0 0
\(637\) 1.86126e8 + 1.82078e8i 0.720091 + 0.704433i
\(638\) 0 0
\(639\) −2.41756e8 −0.926563
\(640\) 0 0
\(641\) −7.17536e7 −0.272439 −0.136220 0.990679i \(-0.543495\pi\)
−0.136220 + 0.990679i \(0.543495\pi\)
\(642\) 0 0
\(643\) 2.56068e8i 0.963214i −0.876387 0.481607i \(-0.840053\pi\)
0.876387 0.481607i \(-0.159947\pi\)
\(644\) 0 0
\(645\) −6.40927e7 −0.238852
\(646\) 0 0
\(647\) 4.93122e8i 1.82071i −0.413827 0.910356i \(-0.635808\pi\)
0.413827 0.910356i \(-0.364192\pi\)
\(648\) 0 0
\(649\) 9.89648e7i 0.362032i
\(650\) 0 0
\(651\) 1.64963e8 + 3.92145e8i 0.597919 + 1.42136i
\(652\) 0 0
\(653\) −1.55036e8 −0.556793 −0.278397 0.960466i \(-0.589803\pi\)
−0.278397 + 0.960466i \(0.589803\pi\)
\(654\) 0 0
\(655\) −1.41627e8 −0.503990
\(656\) 0 0
\(657\) 7.99377e7i 0.281874i
\(658\) 0 0
\(659\) −3.01683e8 −1.05413 −0.527065 0.849825i \(-0.676707\pi\)
−0.527065 + 0.849825i \(0.676707\pi\)
\(660\) 0 0
\(661\) 1.80227e8i 0.624044i 0.950075 + 0.312022i \(0.101006\pi\)
−0.950075 + 0.312022i \(0.898994\pi\)
\(662\) 0 0
\(663\) 5.95957e8i 2.04491i
\(664\) 0 0
\(665\) 1.87211e7 + 4.45033e7i 0.0636599 + 0.151331i
\(666\) 0 0
\(667\) 5.28097e7 0.177966
\(668\) 0 0
\(669\) 2.21511e8 0.739806
\(670\) 0 0
\(671\) 2.40445e8i 0.795880i
\(672\) 0 0
\(673\) 4.06265e8 1.33280 0.666399 0.745595i \(-0.267835\pi\)
0.666399 + 0.745595i \(0.267835\pi\)
\(674\) 0 0
\(675\) 3.57106e8i 1.16114i
\(676\) 0 0
\(677\) 1.77837e7i 0.0573133i 0.999589 + 0.0286566i \(0.00912294\pi\)
−0.999589 + 0.0286566i \(0.990877\pi\)
\(678\) 0 0
\(679\) 2.57497e8 1.08320e8i 0.822551 0.346020i
\(680\) 0 0
\(681\) −5.97020e8 −1.89037
\(682\) 0 0
\(683\) −2.66054e8 −0.835042 −0.417521 0.908667i \(-0.637101\pi\)
−0.417521 + 0.908667i \(0.637101\pi\)
\(684\) 0 0
\(685\) 9.61712e7i 0.299208i
\(686\) 0 0
\(687\) −1.53102e7 −0.0472183
\(688\) 0 0
\(689\) 1.69098e8i 0.516989i
\(690\) 0 0
\(691\) 2.44451e8i 0.740898i 0.928853 + 0.370449i \(0.120796\pi\)
−0.928853 + 0.370449i \(0.879204\pi\)
\(692\) 0 0
\(693\) 1.52393e8 + 3.62266e8i 0.457895 + 1.08850i
\(694\) 0 0
\(695\) 7.60696e7 0.226598
\(696\) 0 0
\(697\) 3.43063e8 1.01315
\(698\) 0 0
\(699\) 2.18671e8i 0.640265i
\(700\) 0 0
\(701\) −2.31727e8 −0.672702 −0.336351 0.941737i \(-0.609193\pi\)
−0.336351 + 0.941737i \(0.609193\pi\)
\(702\) 0 0
\(703\) 9.35567e6i 0.0269283i
\(704\) 0 0
\(705\) 1.47792e8i 0.421776i
\(706\) 0 0
\(707\) 6.17139e8 2.59610e8i 1.74632 0.734621i
\(708\) 0 0
\(709\) 3.09705e8 0.868979 0.434489 0.900677i \(-0.356929\pi\)
0.434489 + 0.900677i \(0.356929\pi\)
\(710\) 0 0
\(711\) −7.01298e8 −1.95117
\(712\) 0 0
\(713\) 1.30111e8i 0.358959i
\(714\) 0 0
\(715\) 8.73650e7 0.239012
\(716\) 0 0
\(717\) 6.20122e8i 1.68236i
\(718\) 0 0
\(719\) 3.85416e8i 1.03692i 0.855103 + 0.518458i \(0.173494\pi\)
−0.855103 + 0.518458i \(0.826506\pi\)
\(720\) 0 0
\(721\) −5.36671e8 + 2.25760e8i −1.43187 + 0.602339i
\(722\) 0 0
\(723\) −1.65721e8 −0.438494
\(724\) 0 0
\(725\) −1.51418e8 −0.397342
\(726\) 0 0
\(727\) 3.13918e8i 0.816983i −0.912762 0.408491i \(-0.866055\pi\)
0.912762 0.408491i \(-0.133945\pi\)
\(728\) 0 0
\(729\) 5.61951e8 1.45049
\(730\) 0 0
\(731\) 1.87313e8i 0.479530i
\(732\) 0 0
\(733\) 7.18118e7i 0.182341i 0.995835 + 0.0911704i \(0.0290608\pi\)
−0.995835 + 0.0911704i \(0.970939\pi\)
\(734\) 0 0
\(735\) 1.67833e8 1.71564e8i 0.422683 0.432079i
\(736\) 0 0
\(737\) 4.32842e8 1.08125
\(738\) 0 0
\(739\) 2.77815e7 0.0688370 0.0344185 0.999408i \(-0.489042\pi\)
0.0344185 + 0.999408i \(0.489042\pi\)
\(740\) 0 0
\(741\) 3.11523e8i 0.765660i
\(742\) 0 0
\(743\) 7.03366e8 1.71481 0.857403 0.514646i \(-0.172077\pi\)
0.857403 + 0.514646i \(0.172077\pi\)
\(744\) 0 0
\(745\) 1.17240e8i 0.283535i
\(746\) 0 0
\(747\) 9.37166e8i 2.24830i
\(748\) 0 0
\(749\) −2.14931e8 5.10930e8i −0.511510 1.21595i
\(750\) 0 0
\(751\) 3.00617e8 0.709731 0.354866 0.934917i \(-0.384527\pi\)
0.354866 + 0.934917i \(0.384527\pi\)
\(752\) 0 0
\(753\) −7.10416e8 −1.66390
\(754\) 0 0
\(755\) 7.61309e7i 0.176897i
\(756\) 0 0
\(757\) −1.17057e8 −0.269841 −0.134921 0.990856i \(-0.543078\pi\)
−0.134921 + 0.990856i \(0.543078\pi\)
\(758\) 0 0
\(759\) 1.87034e8i 0.427756i
\(760\) 0 0
\(761\) 2.63542e8i 0.597992i −0.954254 0.298996i \(-0.903348\pi\)
0.954254 0.298996i \(-0.0966518\pi\)
\(762\) 0 0
\(763\) 2.64971e7 + 6.29882e7i 0.0596519 + 0.141803i
\(764\) 0 0
\(765\) −3.53026e8 −0.788538
\(766\) 0 0
\(767\) 2.50600e8 0.555385
\(768\) 0 0
\(769\) 1.25689e8i 0.276388i −0.990405 0.138194i \(-0.955870\pi\)
0.990405 0.138194i \(-0.0441298\pi\)
\(770\) 0 0
\(771\) 3.40794e8 0.743582
\(772\) 0 0
\(773\) 1.58329e8i 0.342786i 0.985203 + 0.171393i \(0.0548268\pi\)
−0.985203 + 0.171393i \(0.945173\pi\)
\(774\) 0 0
\(775\) 3.73060e8i 0.801444i
\(776\) 0 0
\(777\) −4.28686e7 + 1.80334e7i −0.0913852 + 0.0384427i
\(778\) 0 0
\(779\) −1.79328e8 −0.379347
\(780\) 0 0
\(781\) 1.61171e8 0.338324
\(782\) 0 0
\(783\) 2.92993e8i 0.610340i
\(784\) 0 0
\(785\) 1.66050e8 0.343265
\(786\) 0 0
\(787\) 5.15726e8i 1.05802i 0.848615 + 0.529012i \(0.177437\pi\)