Properties

Label 384.7.h.e.65.5
Level $384$
Weight $7$
Character 384.65
Analytic conductor $88.341$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 384.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(88.3407681100\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 172x^{6} + 13179x^{4} - 522628x^{2} + 8755681 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{26}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.5
Root \(7.10120 + 0.847848i\) of defining polynomial
Character \(\chi\) \(=\) 384.65
Dual form 384.7.h.e.65.7

$q$-expansion

\(f(q)\) \(=\) \(q+(4.41641 - 26.6364i) q^{3} -127.030 q^{5} +467.888 q^{7} +(-689.991 - 235.274i) q^{9} +O(q^{10})\) \(q+(4.41641 - 26.6364i) q^{3} -127.030 q^{5} +467.888 q^{7} +(-689.991 - 235.274i) q^{9} -554.827 q^{11} -357.218i q^{13} +(-561.017 + 3383.62i) q^{15} -4495.52i q^{17} -3243.70i q^{19} +(2066.38 - 12462.8i) q^{21} +17444.0i q^{23} +511.656 q^{25} +(-9314.12 + 17339.8i) q^{27} -17419.5 q^{29} +8039.04 q^{31} +(-2450.34 + 14778.6i) q^{33} -59435.8 q^{35} -79420.8i q^{37} +(-9514.99 - 1577.62i) q^{39} +61806.9i q^{41} +45444.9i q^{43} +(87649.6 + 29886.9i) q^{45} -159556. i q^{47} +101270. q^{49} +(-119744. - 19854.1i) q^{51} -190908. q^{53} +70479.7 q^{55} +(-86400.3 - 14325.5i) q^{57} -306549. q^{59} +251837. i q^{61} +(-322838. - 110082. i) q^{63} +45377.5i q^{65} +202398. i q^{67} +(464644. + 77039.7i) q^{69} +362276. i q^{71} -349729. q^{73} +(2259.68 - 13628.7i) q^{75} -259597. q^{77} +718180. q^{79} +(420733. + 324674. i) q^{81} +138716. q^{83} +571067. i q^{85} +(-76931.6 + 463992. i) q^{87} +1.22054e6i q^{89} -167138. i q^{91} +(35503.7 - 214131. i) q^{93} +412047. i q^{95} +1.15946e6 q^{97} +(382825. + 130536. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 72 q^{3} - 1656 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 72 q^{3} - 1656 q^{9} - 1648 q^{11} - 200 q^{25} - 21384 q^{27} - 22608 q^{33} - 136320 q^{35} + 105208 q^{49} - 275328 q^{51} - 391104 q^{57} - 836624 q^{59} - 1964944 q^{73} + 59400 q^{75} + 166536 q^{81} + 587024 q^{83} - 1477232 q^{97} + 1688976 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) 4.41641 26.6364i 0.163571 0.986532i
\(4\) 0 0
\(5\) −127.030 −1.01624 −0.508121 0.861286i \(-0.669660\pi\)
−0.508121 + 0.861286i \(0.669660\pi\)
\(6\) 0 0
\(7\) 467.888 1.36410 0.682052 0.731304i \(-0.261088\pi\)
0.682052 + 0.731304i \(0.261088\pi\)
\(8\) 0 0
\(9\) −689.991 235.274i −0.946489 0.322735i
\(10\) 0 0
\(11\) −554.827 −0.416849 −0.208425 0.978038i \(-0.566834\pi\)
−0.208425 + 0.978038i \(0.566834\pi\)
\(12\) 0 0
\(13\) 357.218i 0.162594i −0.996690 0.0812968i \(-0.974094\pi\)
0.996690 0.0812968i \(-0.0259062\pi\)
\(14\) 0 0
\(15\) −561.017 + 3383.62i −0.166227 + 1.00255i
\(16\) 0 0
\(17\) 4495.52i 0.915026i −0.889203 0.457513i \(-0.848740\pi\)
0.889203 0.457513i \(-0.151260\pi\)
\(18\) 0 0
\(19\) 3243.70i 0.472911i −0.971642 0.236456i \(-0.924014\pi\)
0.971642 0.236456i \(-0.0759858\pi\)
\(20\) 0 0
\(21\) 2066.38 12462.8i 0.223127 1.34573i
\(22\) 0 0
\(23\) 17444.0i 1.43371i 0.697221 + 0.716856i \(0.254419\pi\)
−0.697221 + 0.716856i \(0.745581\pi\)
\(24\) 0 0
\(25\) 511.656 0.0327460
\(26\) 0 0
\(27\) −9314.12 + 17339.8i −0.473206 + 0.880952i
\(28\) 0 0
\(29\) −17419.5 −0.714235 −0.357118 0.934059i \(-0.616241\pi\)
−0.357118 + 0.934059i \(0.616241\pi\)
\(30\) 0 0
\(31\) 8039.04 0.269848 0.134924 0.990856i \(-0.456921\pi\)
0.134924 + 0.990856i \(0.456921\pi\)
\(32\) 0 0
\(33\) −2450.34 + 14778.6i −0.0681843 + 0.411235i
\(34\) 0 0
\(35\) −59435.8 −1.38626
\(36\) 0 0
\(37\) 79420.8i 1.56794i −0.620800 0.783969i \(-0.713192\pi\)
0.620800 0.783969i \(-0.286808\pi\)
\(38\) 0 0
\(39\) −9514.99 1577.62i −0.160404 0.0265956i
\(40\) 0 0
\(41\) 61806.9i 0.896779i 0.893838 + 0.448389i \(0.148002\pi\)
−0.893838 + 0.448389i \(0.851998\pi\)
\(42\) 0 0
\(43\) 45444.9i 0.571584i 0.958292 + 0.285792i \(0.0922566\pi\)
−0.958292 + 0.285792i \(0.907743\pi\)
\(44\) 0 0
\(45\) 87649.6 + 29886.9i 0.961861 + 0.327977i
\(46\) 0 0
\(47\) 159556.i 1.53681i −0.639965 0.768404i \(-0.721051\pi\)
0.639965 0.768404i \(-0.278949\pi\)
\(48\) 0 0
\(49\) 101270. 0.860781
\(50\) 0 0
\(51\) −119744. 19854.1i −0.902702 0.149671i
\(52\) 0 0
\(53\) −190908. −1.28232 −0.641159 0.767408i \(-0.721546\pi\)
−0.641159 + 0.767408i \(0.721546\pi\)
\(54\) 0 0
\(55\) 70479.7 0.423620
\(56\) 0 0
\(57\) −86400.3 14325.5i −0.466542 0.0773544i
\(58\) 0 0
\(59\) −306549. −1.49260 −0.746300 0.665610i \(-0.768171\pi\)
−0.746300 + 0.665610i \(0.768171\pi\)
\(60\) 0 0
\(61\) 251837.i 1.10951i 0.832015 + 0.554753i \(0.187187\pi\)
−0.832015 + 0.554753i \(0.812813\pi\)
\(62\) 0 0
\(63\) −322838. 110082.i −1.29111 0.440245i
\(64\) 0 0
\(65\) 45377.5i 0.165234i
\(66\) 0 0
\(67\) 202398.i 0.672949i 0.941693 + 0.336475i \(0.109235\pi\)
−0.941693 + 0.336475i \(0.890765\pi\)
\(68\) 0 0
\(69\) 464644. + 77039.7i 1.41440 + 0.234513i
\(70\) 0 0
\(71\) 362276.i 1.01219i 0.862476 + 0.506097i \(0.168912\pi\)
−0.862476 + 0.506097i \(0.831088\pi\)
\(72\) 0 0
\(73\) −349729. −0.899008 −0.449504 0.893278i \(-0.648399\pi\)
−0.449504 + 0.893278i \(0.648399\pi\)
\(74\) 0 0
\(75\) 2259.68 13628.7i 0.00535629 0.0323050i
\(76\) 0 0
\(77\) −259597. −0.568626
\(78\) 0 0
\(79\) 718180. 1.45664 0.728320 0.685238i \(-0.240302\pi\)
0.728320 + 0.685238i \(0.240302\pi\)
\(80\) 0 0
\(81\) 420733. + 324674.i 0.791684 + 0.610931i
\(82\) 0 0
\(83\) 138716. 0.242601 0.121300 0.992616i \(-0.461294\pi\)
0.121300 + 0.992616i \(0.461294\pi\)
\(84\) 0 0
\(85\) 571067.i 0.929887i
\(86\) 0 0
\(87\) −76931.6 + 463992.i −0.116828 + 0.704616i
\(88\) 0 0
\(89\) 1.22054e6i 1.73134i 0.500618 + 0.865668i \(0.333106\pi\)
−0.500618 + 0.865668i \(0.666894\pi\)
\(90\) 0 0
\(91\) 167138.i 0.221795i
\(92\) 0 0
\(93\) 35503.7 214131.i 0.0441392 0.266214i
\(94\) 0 0
\(95\) 412047.i 0.480592i
\(96\) 0 0
\(97\) 1.15946e6 1.27040 0.635198 0.772350i \(-0.280919\pi\)
0.635198 + 0.772350i \(0.280919\pi\)
\(98\) 0 0
\(99\) 382825. + 130536.i 0.394544 + 0.134532i
\(100\) 0 0
\(101\) −533156. −0.517476 −0.258738 0.965948i \(-0.583307\pi\)
−0.258738 + 0.965948i \(0.583307\pi\)
\(102\) 0 0
\(103\) −1966.17 −0.00179933 −0.000899663 1.00000i \(-0.500286\pi\)
−0.000899663 1.00000i \(0.500286\pi\)
\(104\) 0 0
\(105\) −262493. + 1.58315e6i −0.226751 + 1.36759i
\(106\) 0 0
\(107\) 1.25359e6 1.02331 0.511653 0.859192i \(-0.329033\pi\)
0.511653 + 0.859192i \(0.329033\pi\)
\(108\) 0 0
\(109\) 2.18389e6i 1.68637i −0.537627 0.843183i \(-0.680679\pi\)
0.537627 0.843183i \(-0.319321\pi\)
\(110\) 0 0
\(111\) −2.11548e6 350755.i −1.54682 0.256469i
\(112\) 0 0
\(113\) 2.18039e6i 1.51112i 0.655082 + 0.755558i \(0.272634\pi\)
−0.655082 + 0.755558i \(0.727366\pi\)
\(114\) 0 0
\(115\) 2.21591e6i 1.45700i
\(116\) 0 0
\(117\) −84044.2 + 246477.i −0.0524747 + 0.153893i
\(118\) 0 0
\(119\) 2.10340e6i 1.24819i
\(120\) 0 0
\(121\) −1.46373e6 −0.826237
\(122\) 0 0
\(123\) 1.64631e6 + 272964.i 0.884701 + 0.146687i
\(124\) 0 0
\(125\) 1.91985e6 0.982963
\(126\) 0 0
\(127\) 2.67367e6 1.30526 0.652630 0.757677i \(-0.273666\pi\)
0.652630 + 0.757677i \(0.273666\pi\)
\(128\) 0 0
\(129\) 1.21049e6 + 200703.i 0.563885 + 0.0934943i
\(130\) 0 0
\(131\) 1.37296e6 0.610722 0.305361 0.952237i \(-0.401223\pi\)
0.305361 + 0.952237i \(0.401223\pi\)
\(132\) 0 0
\(133\) 1.51769e6i 0.645100i
\(134\) 0 0
\(135\) 1.18317e6 2.20267e6i 0.480892 0.895259i
\(136\) 0 0
\(137\) 3.93934e6i 1.53201i 0.642835 + 0.766005i \(0.277758\pi\)
−0.642835 + 0.766005i \(0.722242\pi\)
\(138\) 0 0
\(139\) 3.06914e6i 1.14281i 0.820670 + 0.571403i \(0.193601\pi\)
−0.820670 + 0.571403i \(0.806399\pi\)
\(140\) 0 0
\(141\) −4.24999e6 704664.i −1.51611 0.251377i
\(142\) 0 0
\(143\) 198194.i 0.0677771i
\(144\) 0 0
\(145\) 2.21280e6 0.725835
\(146\) 0 0
\(147\) 447249. 2.69746e6i 0.140798 0.849187i
\(148\) 0 0
\(149\) 1.04539e6 0.316024 0.158012 0.987437i \(-0.449492\pi\)
0.158012 + 0.987437i \(0.449492\pi\)
\(150\) 0 0
\(151\) −3.78383e6 −1.09901 −0.549504 0.835491i \(-0.685183\pi\)
−0.549504 + 0.835491i \(0.685183\pi\)
\(152\) 0 0
\(153\) −1.05768e6 + 3.10187e6i −0.295311 + 0.866062i
\(154\) 0 0
\(155\) −1.02120e6 −0.274231
\(156\) 0 0
\(157\) 7.20728e6i 1.86240i 0.364511 + 0.931199i \(0.381236\pi\)
−0.364511 + 0.931199i \(0.618764\pi\)
\(158\) 0 0
\(159\) −843126. + 5.08508e6i −0.209750 + 1.26505i
\(160\) 0 0
\(161\) 8.16182e6i 1.95573i
\(162\) 0 0
\(163\) 650337.i 0.150167i −0.997177 0.0750837i \(-0.976078\pi\)
0.997177 0.0750837i \(-0.0239224\pi\)
\(164\) 0 0
\(165\) 311267. 1.87732e6i 0.0692917 0.417914i
\(166\) 0 0
\(167\) 3.36276e6i 0.722015i 0.932563 + 0.361007i \(0.117567\pi\)
−0.932563 + 0.361007i \(0.882433\pi\)
\(168\) 0 0
\(169\) 4.69920e6 0.973563
\(170\) 0 0
\(171\) −763158. + 2.23812e6i −0.152625 + 0.447605i
\(172\) 0 0
\(173\) 7.62335e6 1.47234 0.736169 0.676797i \(-0.236633\pi\)
0.736169 + 0.676797i \(0.236633\pi\)
\(174\) 0 0
\(175\) 239398. 0.0446690
\(176\) 0 0
\(177\) −1.35384e6 + 8.16534e6i −0.244145 + 1.47250i
\(178\) 0 0
\(179\) −9.30814e6 −1.62295 −0.811473 0.584390i \(-0.801334\pi\)
−0.811473 + 0.584390i \(0.801334\pi\)
\(180\) 0 0
\(181\) 1.67832e6i 0.283035i 0.989936 + 0.141517i \(0.0451981\pi\)
−0.989936 + 0.141517i \(0.954802\pi\)
\(182\) 0 0
\(183\) 6.70801e6 + 1.11221e6i 1.09456 + 0.181483i
\(184\) 0 0
\(185\) 1.00888e7i 1.59340i
\(186\) 0 0
\(187\) 2.49424e6i 0.381428i
\(188\) 0 0
\(189\) −4.35796e6 + 8.11307e6i −0.645503 + 1.20171i
\(190\) 0 0
\(191\) 3.83352e6i 0.550171i 0.961420 + 0.275085i \(0.0887061\pi\)
−0.961420 + 0.275085i \(0.911294\pi\)
\(192\) 0 0
\(193\) −2.24738e6 −0.312612 −0.156306 0.987709i \(-0.549959\pi\)
−0.156306 + 0.987709i \(0.549959\pi\)
\(194\) 0 0
\(195\) 1.20869e6 + 200405.i 0.163009 + 0.0270275i
\(196\) 0 0
\(197\) −7.35513e6 −0.962036 −0.481018 0.876711i \(-0.659733\pi\)
−0.481018 + 0.876711i \(0.659733\pi\)
\(198\) 0 0
\(199\) −3.71907e6 −0.471927 −0.235964 0.971762i \(-0.575825\pi\)
−0.235964 + 0.971762i \(0.575825\pi\)
\(200\) 0 0
\(201\) 5.39115e6 + 893873.i 0.663885 + 0.110075i
\(202\) 0 0
\(203\) −8.15037e6 −0.974292
\(204\) 0 0
\(205\) 7.85134e6i 0.911343i
\(206\) 0 0
\(207\) 4.10411e6 1.20362e7i 0.462709 1.35699i
\(208\) 0 0
\(209\) 1.79969e6i 0.197133i
\(210\) 0 0
\(211\) 6.61991e6i 0.704701i −0.935868 0.352350i \(-0.885383\pi\)
0.935868 0.352350i \(-0.114617\pi\)
\(212\) 0 0
\(213\) 9.64970e6 + 1.59996e6i 0.998562 + 0.165565i
\(214\) 0 0
\(215\) 5.77287e6i 0.580867i
\(216\) 0 0
\(217\) 3.76137e6 0.368101
\(218\) 0 0
\(219\) −1.54455e6 + 9.31551e6i −0.147051 + 0.886900i
\(220\) 0 0
\(221\) −1.60588e6 −0.148777
\(222\) 0 0
\(223\) −1.10450e7 −0.995982 −0.497991 0.867182i \(-0.665929\pi\)
−0.497991 + 0.867182i \(0.665929\pi\)
\(224\) 0 0
\(225\) −353038. 120379.i −0.0309937 0.0105683i
\(226\) 0 0
\(227\) −1.13090e7 −0.966821 −0.483411 0.875394i \(-0.660602\pi\)
−0.483411 + 0.875394i \(0.660602\pi\)
\(228\) 0 0
\(229\) 2.64496e6i 0.220248i −0.993918 0.110124i \(-0.964875\pi\)
0.993918 0.110124i \(-0.0351248\pi\)
\(230\) 0 0
\(231\) −1.14648e6 + 6.91471e6i −0.0930105 + 0.560968i
\(232\) 0 0
\(233\) 2.97617e6i 0.235283i −0.993056 0.117641i \(-0.962467\pi\)
0.993056 0.117641i \(-0.0375333\pi\)
\(234\) 0 0
\(235\) 2.02684e7i 1.56177i
\(236\) 0 0
\(237\) 3.17178e6 1.91297e7i 0.238263 1.43702i
\(238\) 0 0
\(239\) 2.10038e7i 1.53852i −0.638935 0.769261i \(-0.720625\pi\)
0.638935 0.769261i \(-0.279375\pi\)
\(240\) 0 0
\(241\) −2.05051e7 −1.46491 −0.732455 0.680816i \(-0.761625\pi\)
−0.732455 + 0.680816i \(0.761625\pi\)
\(242\) 0 0
\(243\) 1.05063e7 9.77291e6i 0.732199 0.681091i
\(244\) 0 0
\(245\) −1.28643e7 −0.874761
\(246\) 0 0
\(247\) −1.15871e6 −0.0768923
\(248\) 0 0
\(249\) 612626. 3.69489e6i 0.0396824 0.239333i
\(250\) 0 0
\(251\) 1.33028e6 0.0841246 0.0420623 0.999115i \(-0.486607\pi\)
0.0420623 + 0.999115i \(0.486607\pi\)
\(252\) 0 0
\(253\) 9.67838e6i 0.597642i
\(254\) 0 0
\(255\) 1.52111e7 + 2.52206e6i 0.917363 + 0.152102i
\(256\) 0 0
\(257\) 7.94766e6i 0.468209i 0.972211 + 0.234104i \(0.0752158\pi\)
−0.972211 + 0.234104i \(0.924784\pi\)
\(258\) 0 0
\(259\) 3.71600e7i 2.13883i
\(260\) 0 0
\(261\) 1.20193e7 + 4.09835e6i 0.676016 + 0.230509i
\(262\) 0 0
\(263\) 1.89010e7i 1.03901i 0.854469 + 0.519503i \(0.173883\pi\)
−0.854469 + 0.519503i \(0.826117\pi\)
\(264\) 0 0
\(265\) 2.42510e7 1.30314
\(266\) 0 0
\(267\) 3.25107e7 + 5.39040e6i 1.70802 + 0.283196i
\(268\) 0 0
\(269\) −1.87304e7 −0.962255 −0.481127 0.876651i \(-0.659773\pi\)
−0.481127 + 0.876651i \(0.659773\pi\)
\(270\) 0 0
\(271\) −1.32087e7 −0.663668 −0.331834 0.943338i \(-0.607667\pi\)
−0.331834 + 0.943338i \(0.607667\pi\)
\(272\) 0 0
\(273\) −4.45195e6 738150.i −0.218807 0.0362791i
\(274\) 0 0
\(275\) −283881. −0.0136502
\(276\) 0 0
\(277\) 9.70493e6i 0.456618i 0.973589 + 0.228309i \(0.0733197\pi\)
−0.973589 + 0.228309i \(0.926680\pi\)
\(278\) 0 0
\(279\) −5.54686e6 1.89138e6i −0.255408 0.0870895i
\(280\) 0 0
\(281\) 1.56440e7i 0.705065i −0.935800 0.352533i \(-0.885321\pi\)
0.935800 0.352533i \(-0.114679\pi\)
\(282\) 0 0
\(283\) 3.52214e7i 1.55399i 0.629510 + 0.776993i \(0.283256\pi\)
−0.629510 + 0.776993i \(0.716744\pi\)
\(284\) 0 0
\(285\) 1.09754e7 + 1.81977e6i 0.474119 + 0.0786107i
\(286\) 0 0
\(287\) 2.89187e7i 1.22330i
\(288\) 0 0
\(289\) 3.92784e6 0.162727
\(290\) 0 0
\(291\) 5.12063e6 3.08837e7i 0.207799 1.25329i
\(292\) 0 0
\(293\) 7.23222e6 0.287520 0.143760 0.989613i \(-0.454081\pi\)
0.143760 + 0.989613i \(0.454081\pi\)
\(294\) 0 0
\(295\) 3.89409e7 1.51684
\(296\) 0 0
\(297\) 5.16772e6 9.62057e6i 0.197256 0.367224i
\(298\) 0 0
\(299\) 6.23131e6 0.233112
\(300\) 0 0
\(301\) 2.12631e7i 0.779700i
\(302\) 0 0
\(303\) −2.35463e6 + 1.42013e7i −0.0846438 + 0.510506i
\(304\) 0 0
\(305\) 3.19908e7i 1.12752i
\(306\) 0 0
\(307\) 2.78268e7i 0.961719i −0.876798 0.480859i \(-0.840325\pi\)
0.876798 0.480859i \(-0.159675\pi\)
\(308\) 0 0
\(309\) −8683.42 + 52371.7i −0.000294317 + 0.00177509i
\(310\) 0 0
\(311\) 4.86634e6i 0.161779i −0.996723 0.0808893i \(-0.974224\pi\)
0.996723 0.0808893i \(-0.0257760\pi\)
\(312\) 0 0
\(313\) −3.79223e7 −1.23669 −0.618346 0.785906i \(-0.712197\pi\)
−0.618346 + 0.785906i \(0.712197\pi\)
\(314\) 0 0
\(315\) 4.10102e7 + 1.39837e7i 1.31208 + 0.447395i
\(316\) 0 0
\(317\) 1.90057e7 0.596631 0.298316 0.954467i \(-0.403575\pi\)
0.298316 + 0.954467i \(0.403575\pi\)
\(318\) 0 0
\(319\) 9.66480e6 0.297729
\(320\) 0 0
\(321\) 5.53638e6 3.33912e7i 0.167383 1.00952i
\(322\) 0 0
\(323\) −1.45821e7 −0.432726
\(324\) 0 0
\(325\) 182773.i 0.00532429i
\(326\) 0 0
\(327\) −5.81709e7 9.64496e6i −1.66365 0.275840i
\(328\) 0 0
\(329\) 7.46543e7i 2.09637i
\(330\) 0 0
\(331\) 1.96231e7i 0.541107i 0.962705 + 0.270554i \(0.0872068\pi\)
−0.962705 + 0.270554i \(0.912793\pi\)
\(332\) 0 0
\(333\) −1.86856e7 + 5.47996e7i −0.506029 + 1.48404i
\(334\) 0 0
\(335\) 2.57107e7i 0.683878i
\(336\) 0 0
\(337\) −1.08566e7 −0.283665 −0.141833 0.989891i \(-0.545299\pi\)
−0.141833 + 0.989891i \(0.545299\pi\)
\(338\) 0 0
\(339\) 5.80775e7 + 9.62947e6i 1.49076 + 0.247174i
\(340\) 0 0
\(341\) −4.46027e6 −0.112486
\(342\) 0 0
\(343\) −7.66355e6 −0.189910
\(344\) 0 0
\(345\) −5.90238e7 9.78636e6i −1.43737 0.238322i
\(346\) 0 0
\(347\) −5.40929e7 −1.29465 −0.647325 0.762214i \(-0.724112\pi\)
−0.647325 + 0.762214i \(0.724112\pi\)
\(348\) 0 0
\(349\) 1.03836e7i 0.244272i 0.992513 + 0.122136i \(0.0389743\pi\)
−0.992513 + 0.122136i \(0.961026\pi\)
\(350\) 0 0
\(351\) 6.19408e6 + 3.32717e6i 0.143237 + 0.0769404i
\(352\) 0 0
\(353\) 7.61934e7i 1.73218i −0.499887 0.866091i \(-0.666625\pi\)
0.499887 0.866091i \(-0.333375\pi\)
\(354\) 0 0
\(355\) 4.60199e7i 1.02863i
\(356\) 0 0
\(357\) −5.60269e7 9.28947e6i −1.23138 0.204167i
\(358\) 0 0
\(359\) 6.26465e7i 1.35398i −0.735990 0.676992i \(-0.763283\pi\)
0.735990 0.676992i \(-0.236717\pi\)
\(360\) 0 0
\(361\) 3.65243e7 0.776355
\(362\) 0 0
\(363\) −6.46442e6 + 3.89884e7i −0.135148 + 0.815108i
\(364\) 0 0
\(365\) 4.44262e7 0.913609
\(366\) 0 0
\(367\) 1.47119e7 0.297627 0.148813 0.988865i \(-0.452455\pi\)
0.148813 + 0.988865i \(0.452455\pi\)
\(368\) 0 0
\(369\) 1.45416e7 4.26462e7i 0.289422 0.848792i
\(370\) 0 0
\(371\) −8.93233e7 −1.74921
\(372\) 0 0
\(373\) 4.99644e7i 0.962796i −0.876502 0.481398i \(-0.840129\pi\)
0.876502 0.481398i \(-0.159871\pi\)
\(374\) 0 0
\(375\) 8.47884e6 5.11378e7i 0.160784 0.969724i
\(376\) 0 0
\(377\) 6.22256e6i 0.116130i
\(378\) 0 0
\(379\) 2.82580e7i 0.519068i 0.965734 + 0.259534i \(0.0835690\pi\)
−0.965734 + 0.259534i \(0.916431\pi\)
\(380\) 0 0
\(381\) 1.18080e7 7.12169e7i 0.213502 1.28768i
\(382\) 0 0
\(383\) 3.93333e7i 0.700106i 0.936730 + 0.350053i \(0.113836\pi\)
−0.936730 + 0.350053i \(0.886164\pi\)
\(384\) 0 0
\(385\) 3.29766e7 0.577861
\(386\) 0 0
\(387\) 1.06920e7 3.13566e7i 0.184470 0.540998i
\(388\) 0 0
\(389\) 9.93800e7 1.68830 0.844151 0.536105i \(-0.180105\pi\)
0.844151 + 0.536105i \(0.180105\pi\)
\(390\) 0 0
\(391\) 7.84198e7 1.31188
\(392\) 0 0
\(393\) 6.06355e6 3.65706e7i 0.0998962 0.602497i
\(394\) 0 0
\(395\) −9.12305e7 −1.48030
\(396\) 0 0
\(397\) 1.72756e7i 0.276098i 0.990425 + 0.138049i \(0.0440831\pi\)
−0.990425 + 0.138049i \(0.955917\pi\)
\(398\) 0 0
\(399\) −4.04256e7 6.70272e6i −0.636412 0.105519i
\(400\) 0 0
\(401\) 2.51779e7i 0.390469i −0.980757 0.195235i \(-0.937453\pi\)
0.980757 0.195235i \(-0.0625468\pi\)
\(402\) 0 0
\(403\) 2.87169e6i 0.0438756i
\(404\) 0 0
\(405\) −5.34458e7 4.12434e7i −0.804542 0.620853i
\(406\) 0 0
\(407\) 4.40648e7i 0.653594i
\(408\) 0 0
\(409\) −1.22633e8 −1.79241 −0.896207 0.443637i \(-0.853688\pi\)
−0.896207 + 0.443637i \(0.853688\pi\)
\(410\) 0 0
\(411\) 1.04930e8 + 1.73977e7i 1.51138 + 0.250592i
\(412\) 0 0
\(413\) −1.43430e8 −2.03606
\(414\) 0 0
\(415\) −1.76211e7 −0.246541
\(416\) 0 0
\(417\) 8.17507e7 + 1.35546e7i 1.12741 + 0.186929i
\(418\) 0 0
\(419\) −1.16934e8 −1.58964 −0.794822 0.606843i \(-0.792436\pi\)
−0.794822 + 0.606843i \(0.792436\pi\)
\(420\) 0 0
\(421\) 2.29549e7i 0.307631i 0.988100 + 0.153815i \(0.0491561\pi\)
−0.988100 + 0.153815i \(0.950844\pi\)
\(422\) 0 0
\(423\) −3.75394e7 + 1.10092e8i −0.495982 + 1.45457i
\(424\) 0 0
\(425\) 2.30016e6i 0.0299635i
\(426\) 0 0
\(427\) 1.17831e8i 1.51348i
\(428\) 0 0
\(429\) 5.27917e6 + 875306.i 0.0668642 + 0.0110863i
\(430\) 0 0
\(431\) 7.18511e7i 0.897432i 0.893674 + 0.448716i \(0.148119\pi\)
−0.893674 + 0.448716i \(0.851881\pi\)
\(432\) 0 0
\(433\) −2.34813e7 −0.289240 −0.144620 0.989487i \(-0.546196\pi\)
−0.144620 + 0.989487i \(0.546196\pi\)
\(434\) 0 0
\(435\) 9.77263e6 5.89409e7i 0.118725 0.716060i
\(436\) 0 0
\(437\) 5.65830e7 0.678018
\(438\) 0 0
\(439\) −9.93662e7 −1.17448 −0.587239 0.809413i \(-0.699785\pi\)
−0.587239 + 0.809413i \(0.699785\pi\)
\(440\) 0 0
\(441\) −6.98753e7 2.38262e7i −0.814720 0.277804i
\(442\) 0 0
\(443\) −8.63633e7 −0.993386 −0.496693 0.867926i \(-0.665453\pi\)
−0.496693 + 0.867926i \(0.665453\pi\)
\(444\) 0 0
\(445\) 1.55045e8i 1.75946i
\(446\) 0 0
\(447\) 4.61687e6 2.78454e7i 0.0516922 0.311768i
\(448\) 0 0
\(449\) 1.10266e8i 1.21816i −0.793110 0.609079i \(-0.791539\pi\)
0.793110 0.609079i \(-0.208461\pi\)
\(450\) 0 0
\(451\) 3.42921e7i 0.373822i
\(452\) 0 0
\(453\) −1.67109e7 + 1.00787e8i −0.179765 + 1.08421i
\(454\) 0 0
\(455\) 2.12316e7i 0.225397i
\(456\) 0 0
\(457\) 8.86668e7 0.928993 0.464496 0.885575i \(-0.346235\pi\)
0.464496 + 0.885575i \(0.346235\pi\)
\(458\) 0 0
\(459\) 7.79513e7 + 4.18719e7i 0.806094 + 0.432996i
\(460\) 0 0
\(461\) 6.99786e7 0.714270 0.357135 0.934053i \(-0.383754\pi\)
0.357135 + 0.934053i \(0.383754\pi\)
\(462\) 0 0
\(463\) 1.27134e8 1.28091 0.640455 0.767996i \(-0.278746\pi\)
0.640455 + 0.767996i \(0.278746\pi\)
\(464\) 0 0
\(465\) −4.51004e6 + 2.72011e7i −0.0448561 + 0.270537i
\(466\) 0 0
\(467\) −9.45390e7 −0.928240 −0.464120 0.885772i \(-0.653629\pi\)
−0.464120 + 0.885772i \(0.653629\pi\)
\(468\) 0 0
\(469\) 9.46996e7i 0.917973i
\(470\) 0 0
\(471\) 1.91976e8 + 3.18303e7i 1.83731 + 0.304634i
\(472\) 0 0
\(473\) 2.52140e7i 0.238264i
\(474\) 0 0
\(475\) 1.65966e6i 0.0154860i
\(476\) 0 0
\(477\) 1.31724e8 + 4.49156e7i 1.21370 + 0.413849i
\(478\) 0 0
\(479\) 2.12756e8i 1.93586i −0.251217 0.967931i \(-0.580831\pi\)
0.251217 0.967931i \(-0.419169\pi\)
\(480\) 0 0
\(481\) −2.83706e7 −0.254937
\(482\) 0 0
\(483\) 2.17401e8 + 3.60459e7i 1.92939 + 0.319900i
\(484\) 0 0
\(485\) −1.47286e8 −1.29103
\(486\) 0 0
\(487\) −8.59613e7 −0.744246 −0.372123 0.928183i \(-0.621370\pi\)
−0.372123 + 0.928183i \(0.621370\pi\)
\(488\) 0 0
\(489\) −1.73226e7 2.87215e6i −0.148145 0.0245630i
\(490\) 0 0
\(491\) 3.52056e7 0.297418 0.148709 0.988881i \(-0.452488\pi\)
0.148709 + 0.988881i \(0.452488\pi\)
\(492\) 0 0
\(493\) 7.83097e7i 0.653544i
\(494\) 0 0
\(495\) −4.86303e7 1.65820e7i −0.400951 0.136717i
\(496\) 0 0
\(497\) 1.69504e8i 1.38074i
\(498\) 0 0
\(499\) 1.07651e8i 0.866398i −0.901298 0.433199i \(-0.857385\pi\)
0.901298 0.433199i \(-0.142615\pi\)
\(500\) 0 0
\(501\) 8.95716e7 + 1.48513e7i 0.712290 + 0.118100i
\(502\) 0 0
\(503\) 4.75253e7i 0.373440i 0.982413 + 0.186720i \(0.0597857\pi\)
−0.982413 + 0.186720i \(0.940214\pi\)
\(504\) 0 0
\(505\) 6.77268e7 0.525880
\(506\) 0 0
\(507\) 2.07536e7 1.25170e8i 0.159246 0.960451i
\(508\) 0 0
\(509\) −9.93663e7 −0.753504 −0.376752 0.926314i \(-0.622959\pi\)
−0.376752 + 0.926314i \(0.622959\pi\)
\(510\) 0 0
\(511\) −1.63634e8 −1.22634
\(512\) 0 0
\(513\) 5.62450e7 + 3.02122e7i 0.416612 + 0.223785i
\(514\) 0 0
\(515\) 249763. 0.00182855
\(516\) 0 0
\(517\) 8.85259e7i 0.640617i
\(518\) 0 0
\(519\) 3.36678e7 2.03058e8i 0.240831 1.45251i
\(520\) 0 0
\(521\) 1.28148e8i 0.906144i 0.891474 + 0.453072i \(0.149672\pi\)
−0.891474 + 0.453072i \(0.850328\pi\)
\(522\) 0 0
\(523\) 9.82990e7i 0.687138i −0.939127 0.343569i \(-0.888364\pi\)
0.939127 0.343569i \(-0.111636\pi\)
\(524\) 0 0
\(525\) 1.05728e6 6.37668e6i 0.00730653 0.0440673i
\(526\) 0 0
\(527\) 3.61397e7i 0.246918i
\(528\) 0 0
\(529\) −1.56256e8 −1.05553
\(530\) 0 0
\(531\) 2.11516e8 + 7.21229e7i 1.41273 + 0.481715i
\(532\) 0 0
\(533\) 2.20785e7 0.145811
\(534\) 0 0
\(535\) −1.59244e8 −1.03993
\(536\) 0 0
\(537\) −4.11086e7 + 2.47935e8i −0.265466 + 1.60109i
\(538\) 0 0
\(539\) −5.61873e7 −0.358816
\(540\) 0 0
\(541\) 1.70819e8i 1.07881i 0.842047 + 0.539404i \(0.181350\pi\)
−0.842047 + 0.539404i \(0.818650\pi\)
\(542\) 0 0
\(543\) 4.47044e7 + 7.41216e6i 0.279223 + 0.0462962i
\(544\) 0 0
\(545\) 2.77420e8i 1.71375i
\(546\) 0 0
\(547\) 1.63277e8i 0.997614i 0.866713 + 0.498807i \(0.166228\pi\)
−0.866713 + 0.498807i \(0.833772\pi\)
\(548\) 0 0
\(549\) 5.92506e7 1.73765e8i 0.358077 1.05013i
\(550\) 0 0
\(551\) 5.65036e7i 0.337770i
\(552\) 0 0
\(553\) 3.36028e8 1.98701
\(554\) 0 0
\(555\) 2.68730e8 + 4.45564e7i 1.57194 + 0.260634i
\(556\) 0 0
\(557\) −1.70053e8 −0.984056 −0.492028 0.870579i \(-0.663744\pi\)
−0.492028 + 0.870579i \(0.663744\pi\)
\(558\) 0 0
\(559\) 1.62338e7 0.0929359
\(560\) 0 0
\(561\) 6.64374e7 + 1.10156e7i 0.376291 + 0.0623905i
\(562\) 0 0
\(563\) −2.19497e7 −0.122999 −0.0614997 0.998107i \(-0.519588\pi\)
−0.0614997 + 0.998107i \(0.519588\pi\)
\(564\) 0 0
\(565\) 2.76975e8i 1.53566i
\(566\) 0 0
\(567\) 1.96856e8 + 1.51911e8i 1.07994 + 0.833373i
\(568\) 0 0
\(569\) 2.00451e8i 1.08811i 0.839051 + 0.544053i \(0.183111\pi\)
−0.839051 + 0.544053i \(0.816889\pi\)
\(570\) 0 0
\(571\) 3.51719e8i 1.88924i −0.328161 0.944622i \(-0.606429\pi\)
0.328161 0.944622i \(-0.393571\pi\)
\(572\) 0 0
\(573\) 1.02111e8 + 1.69304e7i 0.542761 + 0.0899918i
\(574\) 0 0
\(575\) 8.92532e6i 0.0469483i
\(576\) 0 0
\(577\) −9.02762e7 −0.469944 −0.234972 0.972002i \(-0.575500\pi\)
−0.234972 + 0.972002i \(0.575500\pi\)
\(578\) 0 0
\(579\) −9.92536e6 + 5.98621e7i −0.0511341 + 0.308401i
\(580\) 0 0
\(581\) 6.49035e7 0.330933
\(582\) 0 0
\(583\) 1.05921e8 0.534533
\(584\) 0 0
\(585\) 1.06761e7 3.13100e7i 0.0533270 0.156393i
\(586\) 0 0
\(587\) −1.80510e8 −0.892454 −0.446227 0.894920i \(-0.647233\pi\)
−0.446227 + 0.894920i \(0.647233\pi\)
\(588\) 0 0
\(589\) 2.60762e7i 0.127614i
\(590\) 0 0
\(591\) −3.24832e7 + 1.95914e8i −0.157361 + 0.949079i
\(592\) 0 0
\(593\) 2.01357e8i 0.965612i 0.875727 + 0.482806i \(0.160382\pi\)
−0.875727 + 0.482806i \(0.839618\pi\)
\(594\) 0 0
\(595\) 2.67195e8i 1.26846i
\(596\) 0 0
\(597\) −1.64249e7 + 9.90624e7i −0.0771934 + 0.465571i
\(598\) 0 0
\(599\) 7.43194e7i 0.345798i −0.984940 0.172899i \(-0.944687\pi\)
0.984940 0.172899i \(-0.0553134\pi\)
\(600\) 0 0
\(601\) 1.71387e8 0.789503 0.394751 0.918788i \(-0.370831\pi\)
0.394751 + 0.918788i \(0.370831\pi\)
\(602\) 0 0
\(603\) 4.76190e7 1.39653e8i 0.217184 0.636939i
\(604\) 0 0
\(605\) 1.85938e8 0.839656
\(606\) 0 0
\(607\) 2.37495e8 1.06191 0.530955 0.847400i \(-0.321833\pi\)
0.530955 + 0.847400i \(0.321833\pi\)
\(608\) 0 0
\(609\) −3.59953e7 + 2.17096e8i −0.159366 + 0.961169i
\(610\) 0 0
\(611\) −5.69963e7 −0.249875
\(612\) 0 0
\(613\) 3.27675e8i 1.42253i −0.702923 0.711266i \(-0.748122\pi\)
0.702923 0.711266i \(-0.251878\pi\)
\(614\) 0 0
\(615\) −2.09131e8 3.46747e7i −0.899069 0.149069i
\(616\) 0 0
\(617\) 1.80045e7i 0.0766525i 0.999265 + 0.0383262i \(0.0122026\pi\)
−0.999265 + 0.0383262i \(0.987797\pi\)
\(618\) 0 0
\(619\) 1.50189e8i 0.633236i 0.948553 + 0.316618i \(0.102547\pi\)
−0.948553 + 0.316618i \(0.897453\pi\)
\(620\) 0 0
\(621\) −3.02474e8 1.62475e8i −1.26303 0.678442i
\(622\) 0 0
\(623\) 5.71075e8i 2.36172i
\(624\) 0 0
\(625\) −2.51873e8 −1.03167
\(626\) 0 0
\(627\) 4.79372e7 + 7.94816e6i 0.194478 + 0.0322451i
\(628\) 0 0
\(629\) −3.57038e8 −1.43470
\(630\) 0 0
\(631\) −2.58819e8 −1.03017 −0.515085 0.857139i \(-0.672240\pi\)
−0.515085 + 0.857139i \(0.672240\pi\)
\(632\) 0 0
\(633\) −1.76330e8 2.92362e7i −0.695209 0.115268i
\(634\) 0 0
\(635\) −3.39637e8 −1.32646
\(636\) 0 0
\(637\) 3.61755e7i 0.139957i
\(638\) 0 0
\(639\) 8.52341e7 2.49967e8i 0.326671 0.958032i
\(640\) 0 0
\(641\) 1.39494e8i 0.529643i 0.964297 + 0.264821i \(0.0853130\pi\)
−0.964297 + 0.264821i \(0.914687\pi\)
\(642\) 0 0
\(643\) 1.32870e8i 0.499799i 0.968272 + 0.249900i \(0.0803976\pi\)
−0.968272 + 0.249900i \(0.919602\pi\)
\(644\) 0 0
\(645\) −1.53768e8 2.54954e7i −0.573044 0.0950128i
\(646\) 0 0
\(647\) 2.12047e8i 0.782923i −0.920195 0.391461i \(-0.871970\pi\)
0.920195 0.391461i \(-0.128030\pi\)
\(648\) 0 0
\(649\) 1.70081e8 0.622189
\(650\) 0 0
\(651\) 1.66117e7 1.00189e8i 0.0602105 0.363143i
\(652\) 0 0
\(653\) 5.44308e8 1.95481 0.977406 0.211371i \(-0.0677928\pi\)
0.977406 + 0.211371i \(0.0677928\pi\)
\(654\) 0 0
\(655\) −1.74407e8 −0.620641
\(656\) 0 0
\(657\) 2.41310e8 + 8.22822e7i 0.850901 + 0.290142i
\(658\) 0 0
\(659\) −2.74809e8 −0.960229 −0.480115 0.877206i \(-0.659405\pi\)
−0.480115 + 0.877206i \(0.659405\pi\)
\(660\) 0 0
\(661\) 4.26671e8i 1.47737i 0.674052 + 0.738684i \(0.264552\pi\)
−0.674052 + 0.738684i \(0.735448\pi\)
\(662\) 0 0
\(663\) −7.09223e6 + 4.27749e7i −0.0243356 + 0.146774i
\(664\) 0 0
\(665\) 1.92792e8i 0.655577i
\(666\) 0 0
\(667\) 3.03865e8i 1.02401i
\(668\) 0 0
\(669\) −4.87793e7 + 2.94199e8i −0.162913 + 0.982568i
\(670\) 0 0
\(671\) 1.39726e8i 0.462497i
\(672\) 0 0
\(673\) −2.68141e8 −0.879668 −0.439834 0.898079i \(-0.644963\pi\)
−0.439834 + 0.898079i \(0.644963\pi\)
\(674\) 0 0
\(675\) −4.76563e6 + 8.87200e6i −0.0154956 + 0.0288476i
\(676\) 0 0
\(677\) 4.37500e8 1.40998 0.704989 0.709218i \(-0.250952\pi\)
0.704989 + 0.709218i \(0.250952\pi\)
\(678\) 0 0
\(679\) 5.42495e8 1.73295
\(680\) 0 0
\(681\) −4.99451e7 + 3.01230e8i −0.158144 + 0.953800i
\(682\) 0 0
\(683\) −3.13239e8 −0.983136 −0.491568 0.870839i \(-0.663576\pi\)
−0.491568 + 0.870839i \(0.663576\pi\)
\(684\) 0 0
\(685\) 5.00415e8i 1.55689i
\(686\) 0 0
\(687\) −7.04520e7 1.16812e7i −0.217282 0.0360261i
\(688\) 0 0
\(689\) 6.81957e7i 0.208497i
\(690\) 0 0
\(691\) 4.18941e8i 1.26975i 0.772614 + 0.634876i \(0.218949\pi\)
−0.772614 + 0.634876i \(0.781051\pi\)
\(692\) 0 0
\(693\) 1.79119e8 + 6.10763e7i 0.538199 + 0.183516i
\(694\) 0 0
\(695\) 3.89873e8i 1.16137i
\(696\) 0 0
\(697\) 2.77854e8 0.820576
\(698\) 0 0
\(699\) −7.92743e7 1.31440e7i −0.232114 0.0384853i
\(700\) 0 0
\(701\) −3.49924e8 −1.01583 −0.507913 0.861408i \(-0.669583\pi\)
−0.507913 + 0.861408i \(0.669583\pi\)
\(702\) 0 0
\(703\) −2.57617e8 −0.741496
\(704\) 0 0
\(705\) 5.39877e8 + 8.95136e7i 1.54073 + 0.255459i
\(706\) 0 0
\(707\) −2.49457e8 −0.705891
\(708\) 0 0
\(709\) 5.25354e8i 1.47405i 0.675863 + 0.737027i \(0.263771\pi\)
−0.675863 + 0.737027i \(0.736229\pi\)
\(710\) 0 0
\(711\) −4.95538e8 1.68969e8i −1.37869 0.470109i
\(712\) 0 0
\(713\) 1.40233e8i 0.386884i
\(714\) 0 0
\(715\) 2.51766e7i 0.0688778i
\(716\) 0 0
\(717\) −5.59464e8 9.27612e7i −1.51780 0.251657i
\(718\) 0 0
\(719\) 5.20947e8i 1.40154i −0.713385 0.700772i \(-0.752839\pi\)
0.713385 0.700772i \(-0.247161\pi\)
\(720\) 0 0
\(721\) −919948. −0.00245447
\(722\) 0 0
\(723\) −9.05589e7 + 5.46181e8i −0.239616 + 1.44518i
\(724\) 0 0
\(725\) −8.91279e6 −0.0233884
\(726\) 0 0
\(727\) 3.30045e8 0.858954 0.429477 0.903078i \(-0.358698\pi\)
0.429477 + 0.903078i \(0.358698\pi\)
\(728\) 0 0
\(729\) −2.13915e8 3.23009e8i −0.552151 0.833744i
\(730\) 0 0
\(731\) 2.04299e8 0.523014
\(732\) 0 0
\(733\) 6.53999e8i 1.66060i 0.557316 + 0.830301i \(0.311831\pi\)
−0.557316 + 0.830301i \(0.688169\pi\)
\(734\) 0 0
\(735\) −5.68142e7 + 3.42659e8i −0.143085 + 0.862979i
\(736\) 0 0
\(737\) 1.12296e8i 0.280518i
\(738\) 0 0
\(739\) 4.59389e7i 0.113828i −0.998379 0.0569138i \(-0.981874\pi\)
0.998379 0.0569138i \(-0.0181260\pi\)
\(740\) 0 0
\(741\) −5.11733e6 + 3.08638e7i −0.0125773 + 0.0758567i
\(742\) 0 0
\(743\) 4.05609e8i 0.988873i 0.869214 + 0.494437i \(0.164626\pi\)
−0.869214 + 0.494437i \(0.835374\pi\)
\(744\) 0 0
\(745\) −1.32796e8 −0.321157
\(746\) 0 0
\(747\) −9.57127e7 3.26362e7i −0.229619 0.0782958i
\(748\) 0 0
\(749\) 5.86542e8 1.39590
\(750\) 0 0
\(751\) 6.97506e8 1.64675 0.823375 0.567497i \(-0.192088\pi\)
0.823375 + 0.567497i \(0.192088\pi\)
\(752\) 0 0
\(753\) 5.87507e6 3.54339e7i 0.0137603 0.0829915i
\(754\) 0 0
\(755\) 4.80661e8 1.11686
\(756\) 0 0
\(757\) 1.78773e8i 0.412111i 0.978540 + 0.206056i \(0.0660628\pi\)
−0.978540 + 0.206056i \(0.933937\pi\)
\(758\) 0 0
\(759\) −2.57797e8 4.27437e7i −0.589593 0.0977567i
\(760\) 0 0
\(761\) 6.37897e7i 0.144743i −0.997378 0.0723713i \(-0.976943\pi\)
0.997378 0.0723713i \(-0.0230567\pi\)
\(762\) 0 0
\(763\) 1.02182e9i 2.30038i
\(764\) 0 0
\(765\) 1.34357e8 3.94031e8i 0.300107 0.880128i
\(766\) 0 0
\(767\) 1.09505e8i 0.242687i
\(768\) 0 0
\(769\) −7.87883e7 −0.173254 −0.0866269 0.996241i \(-0.527609\pi\)
−0.0866269 + 0.996241i \(0.527609\pi\)
\(770\) 0 0
\(771\) 2.11697e8 + 3.51001e7i 0.461903 + 0.0765852i
\(772\) 0 0
\(773\) −3.67409e8 −0.795447 −0.397724 0.917505i \(-0.630200\pi\)
−0.397724 + 0.917505i \(0.630200\pi\)
\(774\) 0 0
\(775\) 4.11323e6 0.00883644
\(776\) 0 0
\(777\) −9.89807e8 1.64114e8i −2.11002 0.349850i
\(778\) 0 0
\(779\) 2.00483e8 0.424097
\(780\) 0 0
\(781\) 2.01000e8i 0.421933i
\(782\) 0 0
\(783\) 1.62247e8 3.02050e8i 0.337981 0.629207i
\(784\) 0 0
\(785\) 9.15542e8i 1.89265i
\(786\) 0 0
\(787\) 8.70858e8i 1.78658i 0.449478 + 0.893291i \(0.351610\pi\)
−0.449478 + 0.893291i \(0.648390\pi\)
\(788\) 0 0
\(789\) 5.03454e8 + 8.34746e7i 1.02501 + 0.169951i
\(790\)