Properties

Label 80.6.n.d.47.7
Level $80$
Weight $6$
Character 80.47
Analytic conductor $12.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + 14779507781220031 x^{6} + 824105698447750789 x^{4} + 12044868290803250652 x^{2} + 579398322543528055824\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{65}\cdot 3^{4}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.7
Root \(-5.50401 - 11.9953i\) of defining polynomial
Character \(\chi\) \(=\) 80.47
Dual form 80.6.n.d.63.7

$q$-expansion

\(f(q)\) \(=\) \(q+(7.48311 + 7.48311i) q^{3} +(34.7301 - 43.8043i) q^{5} +(19.2260 - 19.2260i) q^{7} -131.006i q^{9} +O(q^{10})\) \(q+(7.48311 + 7.48311i) q^{3} +(34.7301 - 43.8043i) q^{5} +(19.2260 - 19.2260i) q^{7} -131.006i q^{9} -180.642i q^{11} +(44.2050 - 44.2050i) q^{13} +(587.682 - 67.9032i) q^{15} +(-621.037 - 621.037i) q^{17} +2674.30 q^{19} +287.741 q^{21} +(2233.28 + 2233.28i) q^{23} +(-712.637 - 3042.66i) q^{25} +(2798.73 - 2798.73i) q^{27} -705.810i q^{29} -2761.15i q^{31} +(1351.77 - 1351.77i) q^{33} +(-174.460 - 1509.90i) q^{35} +(-3542.51 - 3542.51i) q^{37} +661.582 q^{39} +10907.4 q^{41} +(5349.56 + 5349.56i) q^{43} +(-5738.63 - 4549.86i) q^{45} +(-13279.7 + 13279.7i) q^{47} +16067.7i q^{49} -9294.57i q^{51} +(-15680.4 + 15680.4i) q^{53} +(-7912.91 - 6273.73i) q^{55} +(20012.1 + 20012.1i) q^{57} -45931.3 q^{59} -17547.9 q^{61} +(-2518.72 - 2518.72i) q^{63} +(-401.125 - 3471.62i) q^{65} +(-31089.0 + 31089.0i) q^{67} +33423.8i q^{69} -10610.1i q^{71} +(50962.5 - 50962.5i) q^{73} +(17435.8 - 28101.3i) q^{75} +(-3473.03 - 3473.03i) q^{77} -24770.6 q^{79} +10051.9 q^{81} +(48930.7 + 48930.7i) q^{83} +(-48772.8 + 5635.40i) q^{85} +(5281.66 - 5281.66i) q^{87} -26108.1i q^{89} -1699.77i q^{91} +(20662.0 - 20662.0i) q^{93} +(92878.7 - 117146. i) q^{95} +(39967.8 + 39967.8i) q^{97} -23665.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 44q^{5} + O(q^{10}) \) \( 20q - 44q^{5} + 804q^{13} - 2236q^{17} - 4520q^{21} + 948q^{25} - 11096q^{33} + 44260q^{37} - 6760q^{41} - 92816q^{45} + 182452q^{53} - 34288q^{57} - 41080q^{61} - 155772q^{65} + 264372q^{73} + 399304q^{77} - 520220q^{81} - 344796q^{85} + 713496q^{93} + 374772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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
\(3\) 7.48311 + 7.48311i 0.480042 + 0.480042i 0.905145 0.425103i \(-0.139762\pi\)
−0.425103 + 0.905145i \(0.639762\pi\)
\(4\) 0 0
\(5\) 34.7301 43.8043i 0.621271 0.783595i
\(6\) 0 0
\(7\) 19.2260 19.2260i 0.148301 0.148301i −0.629058 0.777359i \(-0.716559\pi\)
0.777359 + 0.629058i \(0.216559\pi\)
\(8\) 0 0
\(9\) 131.006i 0.539120i
\(10\) 0 0
\(11\) 180.642i 0.450130i −0.974344 0.225065i \(-0.927741\pi\)
0.974344 0.225065i \(-0.0722594\pi\)
\(12\) 0 0
\(13\) 44.2050 44.2050i 0.0725459 0.0725459i −0.669903 0.742449i \(-0.733664\pi\)
0.742449 + 0.669903i \(0.233664\pi\)
\(14\) 0 0
\(15\) 587.682 67.9032i 0.674395 0.0779224i
\(16\) 0 0
\(17\) −621.037 621.037i −0.521189 0.521189i 0.396742 0.917930i \(-0.370141\pi\)
−0.917930 + 0.396742i \(0.870141\pi\)
\(18\) 0 0
\(19\) 2674.30 1.69952 0.849759 0.527172i \(-0.176747\pi\)
0.849759 + 0.527172i \(0.176747\pi\)
\(20\) 0 0
\(21\) 287.741 0.142381
\(22\) 0 0
\(23\) 2233.28 + 2233.28i 0.880285 + 0.880285i 0.993563 0.113278i \(-0.0361351\pi\)
−0.113278 + 0.993563i \(0.536135\pi\)
\(24\) 0 0
\(25\) −712.637 3042.66i −0.228044 0.973651i
\(26\) 0 0
\(27\) 2798.73 2798.73i 0.738842 0.738842i
\(28\) 0 0
\(29\) 705.810i 0.155845i −0.996959 0.0779225i \(-0.975171\pi\)
0.996959 0.0779225i \(-0.0248287\pi\)
\(30\) 0 0
\(31\) 2761.15i 0.516043i −0.966139 0.258021i \(-0.916930\pi\)
0.966139 0.258021i \(-0.0830705\pi\)
\(32\) 0 0
\(33\) 1351.77 1351.77i 0.216081 0.216081i
\(34\) 0 0
\(35\) −174.460 1509.90i −0.0240728 0.208343i
\(36\) 0 0
\(37\) −3542.51 3542.51i −0.425409 0.425409i 0.461652 0.887061i \(-0.347257\pi\)
−0.887061 + 0.461652i \(0.847257\pi\)
\(38\) 0 0
\(39\) 661.582 0.0696502
\(40\) 0 0
\(41\) 10907.4 1.01336 0.506679 0.862135i \(-0.330873\pi\)
0.506679 + 0.862135i \(0.330873\pi\)
\(42\) 0 0
\(43\) 5349.56 + 5349.56i 0.441212 + 0.441212i 0.892419 0.451207i \(-0.149007\pi\)
−0.451207 + 0.892419i \(0.649007\pi\)
\(44\) 0 0
\(45\) −5738.63 4549.86i −0.422452 0.334940i
\(46\) 0 0
\(47\) −13279.7 + 13279.7i −0.876884 + 0.876884i −0.993211 0.116327i \(-0.962888\pi\)
0.116327 + 0.993211i \(0.462888\pi\)
\(48\) 0 0
\(49\) 16067.7i 0.956014i
\(50\) 0 0
\(51\) 9294.57i 0.500385i
\(52\) 0 0
\(53\) −15680.4 + 15680.4i −0.766774 + 0.766774i −0.977537 0.210763i \(-0.932405\pi\)
0.210763 + 0.977537i \(0.432405\pi\)
\(54\) 0 0
\(55\) −7912.91 6273.73i −0.352719 0.279653i
\(56\) 0 0
\(57\) 20012.1 + 20012.1i 0.815840 + 0.815840i
\(58\) 0 0
\(59\) −45931.3 −1.71783 −0.858913 0.512122i \(-0.828860\pi\)
−0.858913 + 0.512122i \(0.828860\pi\)
\(60\) 0 0
\(61\) −17547.9 −0.603809 −0.301904 0.953338i \(-0.597622\pi\)
−0.301904 + 0.953338i \(0.597622\pi\)
\(62\) 0 0
\(63\) −2518.72 2518.72i −0.0799519 0.0799519i
\(64\) 0 0
\(65\) −401.125 3471.62i −0.0117760 0.101917i
\(66\) 0 0
\(67\) −31089.0 + 31089.0i −0.846097 + 0.846097i −0.989644 0.143547i \(-0.954149\pi\)
0.143547 + 0.989644i \(0.454149\pi\)
\(68\) 0 0
\(69\) 33423.8i 0.845148i
\(70\) 0 0
\(71\) 10610.1i 0.249788i −0.992170 0.124894i \(-0.960141\pi\)
0.992170 0.124894i \(-0.0398592\pi\)
\(72\) 0 0
\(73\) 50962.5 50962.5i 1.11929 1.11929i 0.127447 0.991845i \(-0.459322\pi\)
0.991845 0.127447i \(-0.0406783\pi\)
\(74\) 0 0
\(75\) 17435.8 28101.3i 0.357923 0.576864i
\(76\) 0 0
\(77\) −3473.03 3473.03i −0.0667546 0.0667546i
\(78\) 0 0
\(79\) −24770.6 −0.446548 −0.223274 0.974756i \(-0.571674\pi\)
−0.223274 + 0.974756i \(0.571674\pi\)
\(80\) 0 0
\(81\) 10051.9 0.170231
\(82\) 0 0
\(83\) 48930.7 + 48930.7i 0.779626 + 0.779626i 0.979767 0.200141i \(-0.0641401\pi\)
−0.200141 + 0.979767i \(0.564140\pi\)
\(84\) 0 0
\(85\) −48772.8 + 5635.40i −0.732200 + 0.0846014i
\(86\) 0 0
\(87\) 5281.66 5281.66i 0.0748122 0.0748122i
\(88\) 0 0
\(89\) 26108.1i 0.349382i −0.984623 0.174691i \(-0.944107\pi\)
0.984623 0.174691i \(-0.0558926\pi\)
\(90\) 0 0
\(91\) 1699.77i 0.0215173i
\(92\) 0 0
\(93\) 20662.0 20662.0i 0.247722 0.247722i
\(94\) 0 0
\(95\) 92878.7 117146.i 1.05586 1.33173i
\(96\) 0 0
\(97\) 39967.8 + 39967.8i 0.431301 + 0.431301i 0.889071 0.457770i \(-0.151352\pi\)
−0.457770 + 0.889071i \(0.651352\pi\)
\(98\) 0 0
\(99\) −23665.2 −0.242674
\(100\) 0 0
\(101\) −196040. −1.91223 −0.956115 0.292991i \(-0.905350\pi\)
−0.956115 + 0.292991i \(0.905350\pi\)
\(102\) 0 0
\(103\) 148017. + 148017.i 1.37473 + 1.37473i 0.853282 + 0.521450i \(0.174609\pi\)
0.521450 + 0.853282i \(0.325391\pi\)
\(104\) 0 0
\(105\) 9993.27 12604.3i 0.0884575 0.111569i
\(106\) 0 0
\(107\) 40600.5 40600.5i 0.342824 0.342824i −0.514604 0.857428i \(-0.672061\pi\)
0.857428 + 0.514604i \(0.172061\pi\)
\(108\) 0 0
\(109\) 50412.1i 0.406414i −0.979136 0.203207i \(-0.934864\pi\)
0.979136 0.203207i \(-0.0651364\pi\)
\(110\) 0 0
\(111\) 53018.0i 0.408428i
\(112\) 0 0
\(113\) 152938. 152938.i 1.12673 1.12673i 0.136024 0.990706i \(-0.456568\pi\)
0.990706 0.136024i \(-0.0434323\pi\)
\(114\) 0 0
\(115\) 175389. 20265.2i 1.23668 0.142891i
\(116\) 0 0
\(117\) −5791.12 5791.12i −0.0391109 0.0391109i
\(118\) 0 0
\(119\) −23880.1 −0.154586
\(120\) 0 0
\(121\) 128419. 0.797383
\(122\) 0 0
\(123\) 81621.6 + 81621.6i 0.486455 + 0.486455i
\(124\) 0 0
\(125\) −158032. 74455.4i −0.904625 0.426207i
\(126\) 0 0
\(127\) −190114. + 190114.i −1.04593 + 1.04593i −0.0470414 + 0.998893i \(0.514979\pi\)
−0.998893 + 0.0470414i \(0.985021\pi\)
\(128\) 0 0
\(129\) 80062.7i 0.423600i
\(130\) 0 0
\(131\) 225175.i 1.14641i −0.819411 0.573207i \(-0.805699\pi\)
0.819411 0.573207i \(-0.194301\pi\)
\(132\) 0 0
\(133\) 51416.1 51416.1i 0.252040 0.252040i
\(134\) 0 0
\(135\) −25396.2 219797.i −0.119932 1.03797i
\(136\) 0 0
\(137\) 120197. + 120197.i 0.547133 + 0.547133i 0.925611 0.378477i \(-0.123552\pi\)
−0.378477 + 0.925611i \(0.623552\pi\)
\(138\) 0 0
\(139\) −336335. −1.47651 −0.738253 0.674524i \(-0.764349\pi\)
−0.738253 + 0.674524i \(0.764349\pi\)
\(140\) 0 0
\(141\) −198746. −0.841882
\(142\) 0 0
\(143\) −7985.29 7985.29i −0.0326551 0.0326551i
\(144\) 0 0
\(145\) −30917.5 24512.9i −0.122119 0.0968221i
\(146\) 0 0
\(147\) −120237. + 120237.i −0.458927 + 0.458927i
\(148\) 0 0
\(149\) 339978.i 1.25454i 0.778802 + 0.627270i \(0.215828\pi\)
−0.778802 + 0.627270i \(0.784172\pi\)
\(150\) 0 0
\(151\) 224030.i 0.799582i 0.916606 + 0.399791i \(0.130917\pi\)
−0.916606 + 0.399791i \(0.869083\pi\)
\(152\) 0 0
\(153\) −81359.5 + 81359.5i −0.280983 + 0.280983i
\(154\) 0 0
\(155\) −120950. 95895.0i −0.404369 0.320602i
\(156\) 0 0
\(157\) 168847. + 168847.i 0.546694 + 0.546694i 0.925483 0.378789i \(-0.123660\pi\)
−0.378789 + 0.925483i \(0.623660\pi\)
\(158\) 0 0
\(159\) −234676. −0.736168
\(160\) 0 0
\(161\) 85874.1 0.261094
\(162\) 0 0
\(163\) 343693. + 343693.i 1.01322 + 1.01322i 0.999912 + 0.0133036i \(0.00423478\pi\)
0.0133036 + 0.999912i \(0.495765\pi\)
\(164\) 0 0
\(165\) −12266.2 106160.i −0.0350752 0.303565i
\(166\) 0 0
\(167\) −220038. + 220038.i −0.610529 + 0.610529i −0.943084 0.332555i \(-0.892089\pi\)
0.332555 + 0.943084i \(0.392089\pi\)
\(168\) 0 0
\(169\) 367385.i 0.989474i
\(170\) 0 0
\(171\) 350349.i 0.916243i
\(172\) 0 0
\(173\) −103453. + 103453.i −0.262802 + 0.262802i −0.826192 0.563389i \(-0.809497\pi\)
0.563389 + 0.826192i \(0.309497\pi\)
\(174\) 0 0
\(175\) −72199.3 44797.0i −0.178212 0.110574i
\(176\) 0 0
\(177\) −343709. 343709.i −0.824628 0.824628i
\(178\) 0 0
\(179\) −377900. −0.881544 −0.440772 0.897619i \(-0.645295\pi\)
−0.440772 + 0.897619i \(0.645295\pi\)
\(180\) 0 0
\(181\) 583576. 1.32404 0.662020 0.749486i \(-0.269699\pi\)
0.662020 + 0.749486i \(0.269699\pi\)
\(182\) 0 0
\(183\) −131313. 131313.i −0.289854 0.289854i
\(184\) 0 0
\(185\) −278209. + 32145.4i −0.597643 + 0.0690541i
\(186\) 0 0
\(187\) −112185. + 112185.i −0.234602 + 0.234602i
\(188\) 0 0
\(189\) 107617.i 0.219142i
\(190\) 0 0
\(191\) 368495.i 0.730884i −0.930834 0.365442i \(-0.880918\pi\)
0.930834 0.365442i \(-0.119082\pi\)
\(192\) 0 0
\(193\) 169450. 169450.i 0.327453 0.327453i −0.524164 0.851617i \(-0.675622\pi\)
0.851617 + 0.524164i \(0.175622\pi\)
\(194\) 0 0
\(195\) 22976.8 28980.2i 0.0432717 0.0545776i
\(196\) 0 0
\(197\) 219866. + 219866.i 0.403638 + 0.403638i 0.879513 0.475875i \(-0.157868\pi\)
−0.475875 + 0.879513i \(0.657868\pi\)
\(198\) 0 0
\(199\) 672141. 1.20317 0.601586 0.798808i \(-0.294536\pi\)
0.601586 + 0.798808i \(0.294536\pi\)
\(200\) 0 0
\(201\) −465285. −0.812324
\(202\) 0 0
\(203\) −13569.9 13569.9i −0.0231120 0.0231120i
\(204\) 0 0
\(205\) 378817. 477793.i 0.629571 0.794063i
\(206\) 0 0
\(207\) 292573. 292573.i 0.474579 0.474579i
\(208\) 0 0
\(209\) 483091.i 0.765003i
\(210\) 0 0
\(211\) 594402.i 0.919124i 0.888146 + 0.459562i \(0.151994\pi\)
−0.888146 + 0.459562i \(0.848006\pi\)
\(212\) 0 0
\(213\) 79396.4 79396.4i 0.119909 0.119909i
\(214\) 0 0
\(215\) 420125. 48542.9i 0.619844 0.0716193i
\(216\) 0 0
\(217\) −53085.9 53085.9i −0.0765296 0.0765296i
\(218\) 0 0
\(219\) 762716. 1.07461
\(220\) 0 0
\(221\) −54905.8 −0.0756202
\(222\) 0 0
\(223\) 422559. + 422559.i 0.569017 + 0.569017i 0.931853 0.362836i \(-0.118191\pi\)
−0.362836 + 0.931853i \(0.618191\pi\)
\(224\) 0 0
\(225\) −398607. + 93359.7i −0.524914 + 0.122943i
\(226\) 0 0
\(227\) 747586. 747586.i 0.962934 0.962934i −0.0364031 0.999337i \(-0.511590\pi\)
0.999337 + 0.0364031i \(0.0115900\pi\)
\(228\) 0 0
\(229\) 740343.i 0.932920i −0.884542 0.466460i \(-0.845529\pi\)
0.884542 0.466460i \(-0.154471\pi\)
\(230\) 0 0
\(231\) 51978.1i 0.0640901i
\(232\) 0 0
\(233\) −427262. + 427262.i −0.515590 + 0.515590i −0.916234 0.400644i \(-0.868786\pi\)
0.400644 + 0.916234i \(0.368786\pi\)
\(234\) 0 0
\(235\) 120502. + 1.04291e6i 0.142339 + 1.23190i
\(236\) 0 0
\(237\) −185361. 185361.i −0.214362 0.214362i
\(238\) 0 0
\(239\) 508899. 0.576284 0.288142 0.957588i \(-0.406962\pi\)
0.288142 + 0.957588i \(0.406962\pi\)
\(240\) 0 0
\(241\) 5494.45 0.00609370 0.00304685 0.999995i \(-0.499030\pi\)
0.00304685 + 0.999995i \(0.499030\pi\)
\(242\) 0 0
\(243\) −604871. 604871.i −0.657124 0.657124i
\(244\) 0 0
\(245\) 703836. + 558034.i 0.749128 + 0.593944i
\(246\) 0 0
\(247\) 118217. 118217.i 0.123293 0.123293i
\(248\) 0 0
\(249\) 732308.i 0.748506i
\(250\) 0 0
\(251\) 150381.i 0.150664i −0.997159 0.0753321i \(-0.975998\pi\)
0.997159 0.0753321i \(-0.0240017\pi\)
\(252\) 0 0
\(253\) 403424. 403424.i 0.396242 0.396242i
\(254\) 0 0
\(255\) −407142. 322802.i −0.392099 0.310875i
\(256\) 0 0
\(257\) −1.07319e6 1.07319e6i −1.01355 1.01355i −0.999907 0.0136415i \(-0.995658\pi\)
−0.0136415 0.999907i \(-0.504342\pi\)
\(258\) 0 0
\(259\) −136217. −0.126177
\(260\) 0 0
\(261\) −92465.4 −0.0840191
\(262\) 0 0
\(263\) −1.13111e6 1.13111e6i −1.00836 1.00836i −0.999965 0.00839852i \(-0.997327\pi\)
−0.00839852 0.999965i \(1.49733\pi\)
\(264\) 0 0
\(265\) 142287. + 1.23145e6i 0.124466 + 1.07722i
\(266\) 0 0
\(267\) 195370. 195370.i 0.167718 0.167718i
\(268\) 0 0
\(269\) 1.59558e6i 1.34443i −0.740356 0.672216i \(-0.765343\pi\)
0.740356 0.672216i \(-0.234657\pi\)
\(270\) 0 0
\(271\) 2.05748e6i 1.70182i 0.525312 + 0.850910i \(0.323949\pi\)
−0.525312 + 0.850910i \(0.676051\pi\)
\(272\) 0 0
\(273\) 12719.6 12719.6i 0.0103292 0.0103292i
\(274\) 0 0
\(275\) −549633. + 128732.i −0.438269 + 0.102649i
\(276\) 0 0
\(277\) 1.50847e6 + 1.50847e6i 1.18123 + 1.18123i 0.979425 + 0.201809i \(0.0646820\pi\)
0.201809 + 0.979425i \(0.435318\pi\)
\(278\) 0 0
\(279\) −361727. −0.278209
\(280\) 0 0
\(281\) −113566. −0.0857993 −0.0428997 0.999079i \(-0.513660\pi\)
−0.0428997 + 0.999079i \(0.513660\pi\)
\(282\) 0 0
\(283\) −693960. 693960.i −0.515072 0.515072i 0.401004 0.916076i \(-0.368661\pi\)
−0.916076 + 0.401004i \(0.868661\pi\)
\(284\) 0 0
\(285\) 1.57164e6 181593.i 1.14615 0.132430i
\(286\) 0 0
\(287\) 209706. 209706.i 0.150282 0.150282i
\(288\) 0 0
\(289\) 648484.i 0.456725i
\(290\) 0 0
\(291\) 598167.i 0.414085i
\(292\) 0 0
\(293\) −1.44248e6 + 1.44248e6i −0.981616 + 0.981616i −0.999834 0.0182181i \(-0.994201\pi\)
0.0182181 + 0.999834i \(0.494201\pi\)
\(294\) 0 0
\(295\) −1.59520e6 + 2.01199e6i −1.06724 + 1.34608i
\(296\) 0 0
\(297\) −505569. 505569.i −0.332575 0.332575i
\(298\) 0 0
\(299\) 197444. 0.127722
\(300\) 0 0
\(301\) 205701. 0.130864
\(302\) 0 0
\(303\) −1.46699e6 1.46699e6i −0.917951 0.917951i
\(304\) 0 0
\(305\) −609439. + 768672.i −0.375129 + 0.473142i
\(306\) 0 0
\(307\) −415774. + 415774.i −0.251774 + 0.251774i −0.821698 0.569924i \(-0.806973\pi\)
0.569924 + 0.821698i \(0.306973\pi\)
\(308\) 0 0
\(309\) 2.21525e6i 1.31986i
\(310\) 0 0
\(311\) 722906.i 0.423819i −0.977289 0.211910i \(-0.932032\pi\)
0.977289 0.211910i \(-0.0679683\pi\)
\(312\) 0 0
\(313\) −768778. + 768778.i −0.443547 + 0.443547i −0.893202 0.449655i \(-0.851547\pi\)
0.449655 + 0.893202i \(0.351547\pi\)
\(314\) 0 0
\(315\) −197807. + 22855.4i −0.112322 + 0.0129781i
\(316\) 0 0
\(317\) 342207. + 342207.i 0.191267 + 0.191267i 0.796244 0.604976i \(-0.206817\pi\)
−0.604976 + 0.796244i \(0.706817\pi\)
\(318\) 0 0
\(319\) −127499. −0.0701505
\(320\) 0 0
\(321\) 607636. 0.329140
\(322\) 0 0
\(323\) −1.66084e6 1.66084e6i −0.885769 0.885769i
\(324\) 0 0
\(325\) −166003. 102999.i −0.0871781 0.0540908i
\(326\) 0 0
\(327\) 377239. 377239.i 0.195096 0.195096i
\(328\) 0 0
\(329\) 510629.i 0.260085i
\(330\) 0 0
\(331\) 595925.i 0.298966i 0.988764 + 0.149483i \(0.0477609\pi\)
−0.988764 + 0.149483i \(0.952239\pi\)
\(332\) 0 0
\(333\) −464090. + 464090.i −0.229346 + 0.229346i
\(334\) 0 0
\(335\) 282108. + 2.44156e6i 0.137342 + 1.18865i
\(336\) 0 0
\(337\) −1.54112e6 1.54112e6i −0.739199 0.739199i 0.233224 0.972423i \(-0.425072\pi\)
−0.972423 + 0.233224i \(0.925072\pi\)
\(338\) 0 0
\(339\) 2.28891e6 1.08175
\(340\) 0 0
\(341\) −498780. −0.232286
\(342\) 0 0
\(343\) 632050. + 632050.i 0.290079 + 0.290079i
\(344\) 0 0
\(345\) 1.46410e6 + 1.16081e6i 0.662254 + 0.525066i
\(346\) 0 0
\(347\) 334328. 334328.i 0.149056 0.149056i −0.628640 0.777696i \(-0.716388\pi\)
0.777696 + 0.628640i \(0.216388\pi\)
\(348\) 0 0
\(349\) 3.55159e6i 1.56084i −0.625254 0.780422i \(-0.715005\pi\)
0.625254 0.780422i \(-0.284995\pi\)
\(350\) 0 0
\(351\) 247436.i 0.107200i
\(352\) 0 0
\(353\) 942189. 942189.i 0.402440 0.402440i −0.476652 0.879092i \(-0.658150\pi\)
0.879092 + 0.476652i \(0.158150\pi\)
\(354\) 0 0
\(355\) −464767. 368489.i −0.195733 0.155186i
\(356\) 0 0
\(357\) −178698. 178698.i −0.0742075 0.0742075i
\(358\) 0 0
\(359\) 1.75716e6 0.719575 0.359787 0.933034i \(-0.382849\pi\)
0.359787 + 0.933034i \(0.382849\pi\)
\(360\) 0 0
\(361\) 4.67577e6 1.88836
\(362\) 0 0
\(363\) 960977. + 960977.i 0.382777 + 0.382777i
\(364\) 0 0
\(365\) −462444. 4.00231e6i −0.181688 1.57246i
\(366\) 0 0
\(367\) 2.33482e6 2.33482e6i 0.904876 0.904876i −0.0909771 0.995853i \(-0.528999\pi\)
0.995853 + 0.0909771i \(0.0289990\pi\)
\(368\) 0 0
\(369\) 1.42894e6i 0.546321i
\(370\) 0 0
\(371\) 602943.i 0.227427i
\(372\) 0 0
\(373\) −2.44665e6 + 2.44665e6i −0.910542 + 0.910542i −0.996315 0.0857724i \(-0.972664\pi\)
0.0857724 + 0.996315i \(0.472664\pi\)
\(374\) 0 0
\(375\) −625410. 1.73973e6i −0.229661 0.638856i
\(376\) 0 0
\(377\) −31200.4 31200.4i −0.0113059 0.0113059i
\(378\) 0 0
\(379\) 2.21109e6 0.790694 0.395347 0.918532i \(-0.370624\pi\)
0.395347 + 0.918532i \(0.370624\pi\)
\(380\) 0 0
\(381\) −2.84529e6 −1.00418
\(382\) 0 0
\(383\) 1.12909e6 + 1.12909e6i 0.393307 + 0.393307i 0.875865 0.482557i \(-0.160292\pi\)
−0.482557 + 0.875865i \(0.660292\pi\)
\(384\) 0 0
\(385\) −272752. + 31514.9i −0.0937814 + 0.0108359i
\(386\) 0 0
\(387\) 700825. 700825.i 0.237866 0.237866i
\(388\) 0 0
\(389\) 501579.i 0.168060i 0.996463 + 0.0840302i \(0.0267792\pi\)
−0.996463 + 0.0840302i \(0.973221\pi\)
\(390\) 0 0
\(391\) 2.77390e6i 0.917589i
\(392\) 0 0
\(393\) 1.68501e6 1.68501e6i 0.550327 0.550327i
\(394\) 0 0
\(395\) −860284. + 1.08506e6i −0.277427 + 0.349913i
\(396\) 0 0
\(397\) −2.04060e6 2.04060e6i −0.649802 0.649802i 0.303143 0.952945i \(-0.401964\pi\)
−0.952945 + 0.303143i \(0.901964\pi\)
\(398\) 0 0
\(399\) 769504. 0.241980
\(400\) 0 0
\(401\) 3.62084e6 1.12447 0.562236 0.826977i \(-0.309941\pi\)
0.562236 + 0.826977i \(0.309941\pi\)
\(402\) 0 0
\(403\) −122057. 122057.i −0.0374368 0.0374368i
\(404\) 0 0
\(405\) 349105. 440319.i 0.105759 0.133392i
\(406\) 0 0
\(407\) −639926. + 639926.i −0.191489 + 0.191489i
\(408\) 0 0
\(409\) 4.16692e6i 1.23171i 0.787861 + 0.615853i \(0.211189\pi\)
−0.787861 + 0.615853i \(0.788811\pi\)
\(410\) 0 0
\(411\) 1.79890e6i 0.525294i
\(412\) 0 0
\(413\) −883076. + 883076.i −0.254755 + 0.254755i
\(414\) 0 0
\(415\) 3.84275e6 444007.i 1.09527 0.126552i
\(416\) 0 0
\(417\) −2.51683e6 2.51683e6i −0.708784 0.708784i
\(418\) 0 0
\(419\) 256351. 0.0713346 0.0356673 0.999364i \(-0.488644\pi\)
0.0356673 + 0.999364i \(0.488644\pi\)
\(420\) 0 0
\(421\) −5.13509e6 −1.41203 −0.706013 0.708199i \(-0.749508\pi\)
−0.706013 + 0.708199i \(0.749508\pi\)
\(422\) 0 0
\(423\) 1.73971e6 + 1.73971e6i 0.472745 + 0.472745i
\(424\) 0 0
\(425\) −1.44703e6 + 2.33218e6i −0.388602 + 0.626309i
\(426\) 0 0
\(427\) −337375. + 337375.i −0.0895455 + 0.0895455i
\(428\) 0 0
\(429\) 119510.i 0.0313516i
\(430\) 0 0
\(431\) 541018.i 0.140287i −0.997537 0.0701437i \(-0.977654\pi\)
0.997537 0.0701437i \(-0.0223458\pi\)
\(432\) 0 0
\(433\) 3.73118e6 3.73118e6i 0.956372 0.956372i −0.0427150 0.999087i \(-0.513601\pi\)
0.999087 + 0.0427150i \(0.0136007\pi\)
\(434\) 0 0
\(435\) −47926.8 414792.i −0.0121438 0.105101i
\(436\) 0 0
\(437\) 5.97245e6 + 5.97245e6i 1.49606 + 1.49606i
\(438\) 0 0
\(439\) −4.37825e6 −1.08427 −0.542137 0.840290i \(-0.682385\pi\)
−0.542137 + 0.840290i \(0.682385\pi\)
\(440\) 0 0
\(441\) 2.10497e6 0.515406
\(442\) 0 0
\(443\) 880315. + 880315.i 0.213122 + 0.213122i 0.805592 0.592470i \(-0.201847\pi\)
−0.592470 + 0.805592i \(0.701847\pi\)
\(444\) 0 0
\(445\) −1.14365e6 906738.i −0.273774 0.217061i
\(446\) 0 0
\(447\) −2.54409e6 + 2.54409e6i −0.602232 + 0.602232i
\(448\) 0 0
\(449\) 1.14012e6i 0.266892i −0.991056 0.133446i \(-0.957396\pi\)
0.991056 0.133446i \(-0.0426042\pi\)
\(450\) 0 0
\(451\) 1.97034e6i 0.456143i
\(452\) 0 0
\(453\) −1.67644e6 + 1.67644e6i −0.383833 + 0.383833i
\(454\) 0 0
\(455\) −74457.3 59033.3i −0.0168608 0.0133681i
\(456\) 0 0
\(457\) 1.88319e6 + 1.88319e6i 0.421796 + 0.421796i 0.885822 0.464025i \(-0.153595\pi\)
−0.464025 + 0.885822i \(0.653595\pi\)
\(458\) 0 0
\(459\) −3.47623e6 −0.770152
\(460\) 0 0
\(461\) −3.75143e6 −0.822138 −0.411069 0.911604i \(-0.634845\pi\)
−0.411069 + 0.911604i \(0.634845\pi\)
\(462\) 0 0
\(463\) −3.38649e6 3.38649e6i −0.734171 0.734171i 0.237273 0.971443i \(-0.423747\pi\)
−0.971443 + 0.237273i \(0.923747\pi\)
\(464\) 0 0
\(465\) −187491. 1.62268e6i −0.0402113 0.348016i
\(466\) 0 0
\(467\) −5.16438e6 + 5.16438e6i −1.09579 + 1.09579i −0.100888 + 0.994898i \(0.532168\pi\)
−0.994898 + 0.100888i \(0.967832\pi\)
\(468\) 0 0
\(469\) 1.19544e6i 0.250954i
\(470\) 0 0
\(471\) 2.52700e6i 0.524872i
\(472\) 0 0
\(473\) 966356. 966356.i 0.198602 0.198602i
\(474\) 0 0
\(475\) −1.90580e6 8.13698e6i −0.387564 1.65474i
\(476\) 0 0
\(477\) 2.05423e6 + 2.05423e6i 0.413383 + 0.413383i
\(478\) 0 0
\(479\) −7.72951e6 −1.53926 −0.769632 0.638488i \(-0.779560\pi\)
−0.769632 + 0.638488i \(0.779560\pi\)
\(480\) 0 0
\(481\) −313193. −0.0617234
\(482\) 0 0
\(483\) 642605. + 642605.i 0.125336 + 0.125336i
\(484\) 0 0
\(485\) 3.13885e6 362675.i 0.605921 0.0700106i
\(486\) 0 0
\(487\) 237457. 237457.i 0.0453694 0.0453694i −0.684058 0.729428i \(-0.739787\pi\)
0.729428 + 0.684058i \(0.239787\pi\)
\(488\) 0 0
\(489\) 5.14379e6i 0.972771i
\(490\) 0 0
\(491\) 3.99956e6i 0.748701i −0.927287 0.374350i \(-0.877866\pi\)
0.927287 0.374350i \(-0.122134\pi\)
\(492\) 0 0
\(493\) −438334. + 438334.i −0.0812247 + 0.0812247i
\(494\) 0 0
\(495\) −821896. + 1.03664e6i −0.150766 + 0.190158i
\(496\) 0 0
\(497\) −203989. 203989.i −0.0370439 0.0370439i
\(498\) 0 0
\(499\) −6.58102e6 −1.18316 −0.591578 0.806248i \(-0.701495\pi\)
−0.591578 + 0.806248i \(0.701495\pi\)
\(500\) 0 0
\(501\) −3.29314e6 −0.586159
\(502\) 0 0
\(503\) 4.79249e6 + 4.79249e6i 0.844582 + 0.844582i 0.989451 0.144869i \(-0.0462761\pi\)
−0.144869 + 0.989451i \(0.546276\pi\)
\(504\) 0 0
\(505\) −6.80848e6 + 8.58738e6i −1.18801 + 1.49842i
\(506\) 0 0
\(507\) −2.74918e6 + 2.74918e6i −0.474989 + 0.474989i
\(508\) 0 0
\(509\) 4.21148e6i 0.720511i −0.932854 0.360255i \(-0.882690\pi\)
0.932854 0.360255i \(-0.117310\pi\)
\(510\) 0 0
\(511\) 1.95961e6i 0.331984i
\(512\) 0 0
\(513\) 7.48464e6 7.48464e6i 1.25567 1.25567i
\(514\) 0 0
\(515\) 1.16244e7 1.34313e6i 1.93132 0.223152i
\(516\) 0 0
\(517\) 2.39887e6 + 2.39887e6i 0.394711 + 0.394711i
\(518\) 0 0
\(519\) −1.54831e6 −0.252312
\(520\) 0 0
\(521\) 884172. 0.142706 0.0713531 0.997451i \(-0.477268\pi\)
0.0713531 + 0.997451i \(0.477268\pi\)
\(522\) 0 0
\(523\) 3.86026e6 + 3.86026e6i 0.617109 + 0.617109i 0.944789 0.327680i \(-0.106267\pi\)
−0.327680 + 0.944789i \(0.606267\pi\)
\(524\) 0 0
\(525\) −205055. 875497.i −0.0324692 0.138630i
\(526\) 0 0
\(527\) −1.71477e6 + 1.71477e6i −0.268955 + 0.268955i
\(528\) 0 0
\(529\) 3.53873e6i 0.549804i
\(530\) 0 0
\(531\) 6.01728e6i 0.926114i
\(532\) 0 0
\(533\) 482163. 482163.i 0.0735150 0.0735150i
\(534\) 0 0
\(535\) −368416. 3.18854e6i −0.0556486 0.481623i
\(536\) 0 0
\(537\) −2.82787e6 2.82787e6i −0.423178 0.423178i
\(538\) 0 0
\(539\) 2.90251e6 0.430330
\(540\) 0 0
\(541\) −4.20713e6 −0.618007 −0.309003 0.951061i \(-0.599995\pi\)
−0.309003 + 0.951061i \(0.599995\pi\)
\(542\) 0 0
\(543\) 4.36697e6 + 4.36697e6i 0.635595 + 0.635595i
\(544\) 0 0
\(545\) −2.20827e6 1.75082e6i −0.318464 0.252493i
\(546\) 0 0
\(547\) 6.13449e6 6.13449e6i 0.876617 0.876617i −0.116566 0.993183i \(-0.537189\pi\)
0.993183 + 0.116566i \(0.0371885\pi\)
\(548\) 0 0
\(549\) 2.29888e6i 0.325525i
\(550\) 0 0
\(551\) 1.88755e6i 0.264861i
\(552\) 0 0
\(553\) −476239. + 476239.i −0.0662235 + 0.0662235i
\(554\) 0 0
\(555\) −2.32242e6 1.84132e6i −0.320042 0.253745i
\(556\) 0 0
\(557\) 3.02695e6 + 3.02695e6i 0.413397 + 0.413397i 0.882920 0.469523i \(-0.155574\pi\)
−0.469523 + 0.882920i \(0.655574\pi\)
\(558\) 0 0
\(559\) 472955. 0.0640162
\(560\) 0 0
\(561\) −1.67899e6 −0.225238
\(562\) 0 0
\(563\) 1.91311e6 + 1.91311e6i 0.254372 + 0.254372i 0.822760 0.568388i \(-0.192433\pi\)
−0.568388 + 0.822760i \(0.692433\pi\)
\(564\) 0 0
\(565\) −1.38779e6 1.20109e7i −0.182895 1.58290i
\(566\) 0 0
\(567\) 193259. 193259.i 0.0252454 0.0252454i
\(568\) 0 0
\(569\) 399515.i 0.0517311i 0.999665 + 0.0258656i \(0.00823418\pi\)
−0.999665 + 0.0258656i \(0.991766\pi\)
\(570\) 0 0
\(571\) 1.17755e7i 1.51143i −0.654900 0.755716i \(-0.727289\pi\)
0.654900 0.755716i \(-0.272711\pi\)
\(572\) 0 0
\(573\) 2.75749e6 2.75749e6i 0.350855 0.350855i
\(574\) 0 0
\(575\) 5.20359e6 8.38662e6i 0.656347 1.05783i
\(576\) 0 0
\(577\) −3.88705e6 3.88705e6i −0.486050 0.486050i 0.421007 0.907057i \(-0.361677\pi\)
−0.907057 + 0.421007i \(0.861677\pi\)
\(578\) 0 0
\(579\) 2.53603e6 0.314383
\(580\) 0 0
\(581\) 1.88148e6 0.231239
\(582\) 0 0
\(583\) 2.83254e6 + 2.83254e6i 0.345148 + 0.345148i
\(584\) 0 0
\(585\) −454803. + 52549.8i −0.0549456 + 0.00634865i
\(586\) 0 0
\(587\) −4.87317e6 + 4.87317e6i −0.583735 + 0.583735i −0.935928 0.352192i \(-0.885436\pi\)
0.352192 + 0.935928i \(0.385436\pi\)
\(588\) 0 0
\(589\) 7.38413e6i 0.877023i
\(590\) 0 0
\(591\) 3.29056e6i 0.387527i
\(592\) 0 0
\(593\) 2.28474e6 2.28474e6i 0.266808 0.266808i −0.561004 0.827813i \(-0.689585\pi\)
0.827813 + 0.561004i \(0.189585\pi\)
\(594\) 0 0
\(595\) −829359. + 1.04605e6i −0.0960396 + 0.121133i
\(596\) 0 0
\(597\) 5.02971e6 + 5.02971e6i 0.577573 + 0.577573i
\(598\) 0 0
\(599\) 1.01689e7 1.15799 0.578997 0.815330i \(-0.303444\pi\)
0.578997 + 0.815330i \(0.303444\pi\)
\(600\) 0 0
\(601\) −1.61358e6 −0.182223 −0.0911117 0.995841i \(-0.529042\pi\)
−0.0911117 + 0.995841i \(0.529042\pi\)
\(602\) 0 0
\(603\) 4.07285e6 + 4.07285e6i 0.456147 + 0.456147i
\(604\) 0 0
\(605\) 4.46002e6 5.62532e6i 0.495391 0.624826i
\(606\) 0 0
\(607\) 1.14202e6 1.14202e6i 0.125806 0.125806i −0.641400 0.767206i \(-0.721646\pi\)
0.767206 + 0.641400i \(0.221646\pi\)
\(608\) 0 0
\(609\) 203090.i 0.0221894i
\(610\) 0 0
\(611\) 1.17405e6i 0.127229i
\(612\) 0 0
\(613\) 3.44148e6 3.44148e6i 0.369908 0.369908i −0.497536 0.867444i \(-0.665762\pi\)
0.867444 + 0.497536i \(0.165762\pi\)
\(614\) 0 0
\(615\) 6.41011e6 740650.i 0.683404 0.0789633i
\(616\) 0 0
\(617\) −7.50497e6 7.50497e6i −0.793663 0.793663i 0.188425 0.982088i \(-0.439662\pi\)
−0.982088 + 0.188425i \(0.939662\pi\)
\(618\) 0 0
\(619\) −2.89736e6 −0.303931 −0.151966 0.988386i \(-0.548560\pi\)
−0.151966 + 0.988386i \(0.548560\pi\)
\(620\) 0 0
\(621\) 1.25007e7 1.30078
\(622\) 0 0
\(623\) −501955. 501955.i −0.0518137 0.0518137i
\(624\) 0 0
\(625\) −8.74992e6 + 4.33662e6i −0.895992 + 0.444070i
\(626\) 0 0
\(627\) 3.61502e6 3.61502e6i 0.367234 0.367234i
\(628\) 0 0
\(629\) 4.40005e6i 0.443436i
\(630\) 0 0
\(631\) 1.03301e7i 1.03284i −0.856336 0.516420i \(-0.827264\pi\)
0.856336 0.516420i \(-0.172736\pi\)
\(632\) 0 0
\(633\) −4.44798e6 + 4.44798e6i −0.441218 + 0.441218i
\(634\) 0 0
\(635\) 1.72513e6 + 1.49305e7i 0.169780 + 1.46940i
\(636\) 0 0
\(637\) 710274. + 710274.i 0.0693549 + 0.0693549i
\(638\) 0 0
\(639\) −1.38998e6 −0.134666
\(640\) 0 0
\(641\) −3.35436e6 −0.322452 −0.161226 0.986918i \(-0.551545\pi\)
−0.161226 + 0.986918i \(0.551545\pi\)
\(642\) 0 0
\(643\) 126819. + 126819.i 0.0120964 + 0.0120964i 0.713129 0.701033i \(-0.247277\pi\)
−0.701033 + 0.713129i \(0.747277\pi\)
\(644\) 0 0
\(645\) 3.50709e6 + 2.78059e6i 0.331931 + 0.263171i
\(646\) 0 0
\(647\) −1.07986e7 + 1.07986e7i −1.01416 + 1.01416i −0.0142641 + 0.999898i \(0.504541\pi\)
−0.999898 + 0.0142641i \(0.995459\pi\)
\(648\) 0 0
\(649\) 8.29714e6i 0.773244i
\(650\) 0 0
\(651\) 794495.i 0.0734748i
\(652\) 0 0
\(653\) −5.57502e6 + 5.57502e6i −0.511639 + 0.511639i −0.915028 0.403390i \(-0.867832\pi\)
0.403390 + 0.915028i \(0.367832\pi\)
\(654\) 0 0
\(655\) −9.86362e6 7.82034e6i −0.898324 0.712234i
\(656\) 0 0
\(657\) −6.67640e6 6.67640e6i −0.603432 0.603432i
\(658\) 0 0
\(659\) −9.37611e6 −0.841026 −0.420513 0.907287i \(-0.638150\pi\)
−0.420513 + 0.907287i \(0.638150\pi\)
\(660\) 0 0
\(661\) −1.43499e6 −0.127746 −0.0638729 0.997958i \(-0.520345\pi\)
−0.0638729 + 0.997958i \(0.520345\pi\)
\(662\) 0 0
\(663\) −410867. 410867.i −0.0363009 0.0363009i
\(664\) 0 0
\(665\) −466559. 4.03793e6i −0.0409122 0.354083i
\(666\) 0 0
\(667\) 1.57627e6 1.57627e6i 0.137188 0.137188i
\(668\) 0 0
\(669\) 6.32411e6i 0.546304i
\(670\) 0 0
\(671\) 3.16988e6i 0.271792i
\(672\) 0 0
\(673\) −1.49219e7 + 1.49219e7i −1.26995 + 1.26995i −0.323834 + 0.946114i \(0.604972\pi\)
−0.946114 + 0.323834i \(0.895028\pi\)
\(674\) 0 0
\(675\) −1.05101e7 6.52110e6i −0.887862 0.550886i
\(676\) 0 0
\(677\) 1.54101e7 + 1.54101e7i 1.29221 + 1.29221i 0.933418 + 0.358791i \(0.116811\pi\)
0.358791 + 0.933418i \(0.383189\pi\)
\(678\) 0 0
\(679\) 1.53684e6 0.127925
\(680\) 0 0
\(681\) 1.11885e7 0.924497
\(682\) 0 0
\(683\) −9.68836e6 9.68836e6i −0.794691 0.794691i 0.187562 0.982253i \(-0.439942\pi\)
−0.982253 + 0.187562i \(0.939942\pi\)
\(684\) 0 0
\(685\) 9.43962e6 1.09069e6i 0.768649 0.0888129i
\(686\) 0 0
\(687\) 5.54007e6 5.54007e6i 0.447841 0.447841i
\(688\) 0 0
\(689\) 1.38630e6i 0.111253i
\(690\) 0 0
\(691\) 1.49923e7i 1.19447i 0.802068 + 0.597233i \(0.203733\pi\)
−0.802068 + 0.597233i \(0.796267\pi\)
\(692\) 0 0
\(693\) −454988. + 454988.i −0.0359887 + 0.0359887i
\(694\) 0 0
\(695\) −1.16810e7 + 1.47329e7i −0.917310 + 1.15698i
\(696\) 0 0
\(697\) −6.77392e6 6.77392e6i −0.528151 0.528151i
\(698\) 0 0
\(699\) −6.39450e6 −0.495010
\(700\) 0 0
\(701\) −4.06612e6 −0.312525 −0.156263 0.987716i \(-0.549945\pi\)
−0.156263 + 0.987716i \(0.549945\pi\)
\(702\) 0 0
\(703\) −9.47372e6 9.47372e6i −0.722990 0.722990i
\(704\) 0 0
\(705\) −6.90248e6 + 8.70594e6i −0.523037 + 0.659695i
\(706\) 0 0
\(707\) −3.76906e6 + 3.76906e6i −0.283586 + 0.283586i
\(708\) 0 0
\(709\) 1.00306e7i 0.749395i −0.927147 0.374698i \(-0.877746\pi\)
0.927147 0.374698i \(-0.122254\pi\)
\(710\) 0 0
\(711\) 3.24509e6i 0.240743i
\(712\) 0 0
\(713\) 6.16641e6 6.16641e6i 0.454265 0.454265i
\(714\) 0 0
\(715\) −627120. + 72460.0i −0.0458760 + 0.00530070i
\(716\) 0 0
\(717\) 3.80815e6 + 3.80815e6i 0.276640 + 0.276640i
\(718\) 0 0
\(719\) 4.83635e6 0.348895 0.174448 0.984666i \(-0.444186\pi\)
0.174448 + 0.984666i \(0.444186\pi\)
\(720\) 0 0
\(721\) 5.69154e6 0.407748
\(722\) 0 0
\(723\) 41115.6 + 41115.6i 0.00292523 + 0.00292523i
\(724\) 0 0
\(725\) −2.14754e6 + 502986.i −0.151739 + 0.0355395i
\(726\) 0 0
\(727\) 2.30692e6 2.30692e6i 0.161881 0.161881i −0.621519 0.783399i \(-0.713484\pi\)
0.783399 + 0.621519i \(0.213484\pi\)
\(728\) 0 0
\(729\) 1.14953e7i 0.801125i
\(730\) 0 0
\(731\) 6.64454e6i 0.459909i
\(732\) 0 0
\(733\) 5.94419e6 5.94419e6i 0.408632 0.408632i −0.472629 0.881261i \(-0.656695\pi\)
0.881261 + 0.472629i \(0.156695\pi\)
\(734\) 0 0
\(735\) 1.09105e6 + 9.44271e6i 0.0744948 + 0.644731i
\(736\) 0 0
\(737\) 5.61599e6 + 5.61599e6i 0.380853 + 0.380853i
\(738\) 0 0
\(739\) −1.19188e6 −0.0802829 −0.0401415 0.999194i \(-0.512781\pi\)
−0.0401415 + 0.999194i \(0.512781\pi\)
\(740\) 0 0
\(741\) 1.76927e6 0.118372
\(742\) 0 0
\(743\) −1.87097e7 1.87097e7i −1.24336 1.24336i −0.958600 0.284758i \(-0.908087\pi\)
−0.284758 0.958600i \(1.40809\pi\)
\(744\) 0 0
\(745\) 1.48925e7 + 1.18075e7i 0.983052 + 0.779410i
\(746\) 0 0
\(747\) 6.41022e6 6.41022e6i 0.420312 0.420312i
\(748\) 0 0
\(749\) 1.56117e6i 0.101682i
\(750\) 0 0
\(751\) 2.35884e7i 1.52615i 0.646308 + 0.763076i \(0.276312\pi\)
−0.646308 + 0.763076i \(0.723688\pi\)
\(752\) 0 0
\(753\) 1.12532e6 1.12532e6i 0.0723251 0.0723251i
\(754\) 0 0
\(755\) 9.81346e6 + 7.78058e6i 0.626549 + 0.496757i
\(756\) 0 0
\(757\) −2.08571e7 2.08571e7i −1.32286 1.32286i −0.911447 0.411417i \(-0.865034\pi\)
−0.411417 0.911447i \(-0.634966\pi\)
\(758\) 0 0
\(759\) 6.03774e6 0.380426
\(760\) 0 0
\(761\) −1.14245e7 −0.715114 −0.357557 0.933891i \(-0.616390\pi\)
−0.357557 + 0.933891i \(0.616390\pi\)
\(762\) 0 0
\(763\) −969223. 969223.i −0.0602716 0.0602716i
\(764\) 0 0
\(765\) 738272. + 6.38953e6i 0.0456103 + 0.394744i
\(766\) 0 0
\(767\) −2.03040e6 + 2.03040e6i −0.124621 + 0.124621i
\(768\) 0 0
\(769\) 1.61255e7i 0.983325i 0.870786 + 0.491663i \(0.163611\pi\)
−0.870786 + 0.491663i \(0.836389\pi\)
\(770\) 0 0
\(771\) 1.60616e7i 0.973092i
\(772\) 0 0
\(773\) −1.32344e7 + 1.32344e7i −0.796630 + 0.796630i −0.982563 0.185933i \(-0.940469\pi\)
0.185933 + 0.982563i \(0.440469\pi\)
\(774\) 0 0
\(775\) −8.40123e6 + 1.96770e6i −0.502445 + 0.117680i
\(776\) 0 0
\(777\) −1.01932e6 1.01932e6i −0.0605703 0.0605703i
\(778\) 0 0
\(779\) 2.91697e7 1.72222
\(780\) 0 0
\(781\) −1.91663e6 −0.112437
\(782\) 0 0
\(783\) −1.97537e6 1.97537e6i −0.115145 0.115145i
\(784\) 0 0
\(785\) 1.32603e7 1.53215e6i 0.768032 0.0887415i
\(786\) 0 0
\(787\) 1.61771e7 1.61771e7i 0.931032 0.931032i −0.0667386 0.997770i \(-0.521259\pi\)
0.997770 + 0.0667386i \(0.0212594\pi\)
\(788\) 0 0
\(789\) 1.69285e7i 0.968113i
\(790\)