Properties

Label 160.6.n.b.127.6
Level $160$
Weight $6$
Character 160.127
Analytic conductor $25.661$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.6614111701\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} - 97717112 x^{7} + 355171384 x^{6} - 910571904 x^{5} + 2428303248 x^{4} - 9166992192 x^{3} + 32237484304 x^{2} - 66916821408 x + 69451154208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{31}\cdot 5^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.6
Root \(-2.20370 + 2.20370i\) of defining polynomial
Character \(\chi\) \(=\) 160.127
Dual form 160.6.n.b.63.6

$q$-expansion

\(f(q)\) \(=\) \(q+(10.9598 + 10.9598i) q^{3} +(-14.9228 + 53.8731i) q^{5} +(-75.2427 + 75.2427i) q^{7} -2.76340i q^{9} +O(q^{10})\) \(q+(10.9598 + 10.9598i) q^{3} +(-14.9228 + 53.8731i) q^{5} +(-75.2427 + 75.2427i) q^{7} -2.76340i q^{9} +207.864i q^{11} +(-233.921 + 233.921i) q^{13} +(-753.993 + 426.889i) q^{15} +(-721.173 - 721.173i) q^{17} +114.040 q^{19} -1649.30 q^{21} +(-957.212 - 957.212i) q^{23} +(-2679.62 - 1607.88i) q^{25} +(2693.53 - 2693.53i) q^{27} +4187.54i q^{29} -2744.83i q^{31} +(-2278.16 + 2278.16i) q^{33} +(-2930.73 - 5176.39i) q^{35} +(6906.15 + 6906.15i) q^{37} -5127.48 q^{39} -8458.40 q^{41} +(-13397.2 - 13397.2i) q^{43} +(148.873 + 41.2377i) q^{45} +(6672.94 - 6672.94i) q^{47} +5484.06i q^{49} -15807.9i q^{51} +(-13054.5 + 13054.5i) q^{53} +(-11198.3 - 3101.92i) q^{55} +(1249.86 + 1249.86i) q^{57} -11302.5 q^{59} -56065.4 q^{61} +(207.926 + 207.926i) q^{63} +(-9111.29 - 16092.8i) q^{65} +(35802.8 - 35802.8i) q^{67} -20981.8i q^{69} +74255.2i q^{71} +(-58806.0 + 58806.0i) q^{73} +(-11746.1 - 46990.3i) q^{75} +(-15640.3 - 15640.3i) q^{77} -65319.6 q^{79} +58369.9 q^{81} +(35508.0 + 35508.0i) q^{83} +(49613.8 - 28089.9i) q^{85} +(-45894.8 + 45894.8i) q^{87} -11119.6i q^{89} -35201.7i q^{91} +(30083.0 - 30083.0i) q^{93} +(-1701.79 + 6143.67i) q^{95} +(86604.7 + 86604.7i) q^{97} +574.413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 10.9598 + 10.9598i 0.703075 + 0.703075i 0.965069 0.261995i \(-0.0843803\pi\)
−0.261995 + 0.965069i \(0.584380\pi\)
\(4\) 0 0
\(5\) −14.9228 + 53.8731i −0.266947 + 0.963711i
\(6\) 0 0
\(7\) −75.2427 + 75.2427i −0.580390 + 0.580390i −0.935010 0.354621i \(-0.884610\pi\)
0.354621 + 0.935010i \(0.384610\pi\)
\(8\) 0 0
\(9\) 2.76340i 0.0113720i
\(10\) 0 0
\(11\) 207.864i 0.517963i 0.965882 + 0.258981i \(0.0833868\pi\)
−0.965882 + 0.258981i \(0.916613\pi\)
\(12\) 0 0
\(13\) −233.921 + 233.921i −0.383894 + 0.383894i −0.872503 0.488609i \(-0.837504\pi\)
0.488609 + 0.872503i \(0.337504\pi\)
\(14\) 0 0
\(15\) −753.993 + 426.889i −0.865245 + 0.489877i
\(16\) 0 0
\(17\) −721.173 721.173i −0.605226 0.605226i 0.336469 0.941695i \(-0.390767\pi\)
−0.941695 + 0.336469i \(0.890767\pi\)
\(18\) 0 0
\(19\) 114.040 0.0724723 0.0362361 0.999343i \(-0.488463\pi\)
0.0362361 + 0.999343i \(0.488463\pi\)
\(20\) 0 0
\(21\) −1649.30 −0.816114
\(22\) 0 0
\(23\) −957.212 957.212i −0.377302 0.377302i 0.492826 0.870128i \(-0.335964\pi\)
−0.870128 + 0.492826i \(0.835964\pi\)
\(24\) 0 0
\(25\) −2679.62 1607.88i −0.857478 0.514520i
\(26\) 0 0
\(27\) 2693.53 2693.53i 0.711070 0.711070i
\(28\) 0 0
\(29\) 4187.54i 0.924622i 0.886718 + 0.462311i \(0.152980\pi\)
−0.886718 + 0.462311i \(0.847020\pi\)
\(30\) 0 0
\(31\) 2744.83i 0.512993i −0.966545 0.256497i \(-0.917432\pi\)
0.966545 0.256497i \(-0.0825683\pi\)
\(32\) 0 0
\(33\) −2278.16 + 2278.16i −0.364166 + 0.364166i
\(34\) 0 0
\(35\) −2930.73 5176.39i −0.404394 0.714261i
\(36\) 0 0
\(37\) 6906.15 + 6906.15i 0.829339 + 0.829339i 0.987425 0.158087i \(-0.0505325\pi\)
−0.158087 + 0.987425i \(0.550532\pi\)
\(38\) 0 0
\(39\) −5127.48 −0.539812
\(40\) 0 0
\(41\) −8458.40 −0.785830 −0.392915 0.919575i \(-0.628533\pi\)
−0.392915 + 0.919575i \(0.628533\pi\)
\(42\) 0 0
\(43\) −13397.2 13397.2i −1.10495 1.10495i −0.993804 0.111143i \(-0.964549\pi\)
−0.111143 0.993804i \(1.46455\pi\)
\(44\) 0 0
\(45\) 148.873 + 41.2377i 0.0109593 + 0.00303573i
\(46\) 0 0
\(47\) 6672.94 6672.94i 0.440629 0.440629i −0.451594 0.892223i \(-0.649145\pi\)
0.892223 + 0.451594i \(0.149145\pi\)
\(48\) 0 0
\(49\) 5484.06i 0.326296i
\(50\) 0 0
\(51\) 15807.9i 0.851038i
\(52\) 0 0
\(53\) −13054.5 + 13054.5i −0.638366 + 0.638366i −0.950152 0.311786i \(-0.899073\pi\)
0.311786 + 0.950152i \(0.399073\pi\)
\(54\) 0 0
\(55\) −11198.3 3101.92i −0.499166 0.138269i
\(56\) 0 0
\(57\) 1249.86 + 1249.86i 0.0509534 + 0.0509534i
\(58\) 0 0
\(59\) −11302.5 −0.422713 −0.211356 0.977409i \(-0.567788\pi\)
−0.211356 + 0.977409i \(0.567788\pi\)
\(60\) 0 0
\(61\) −56065.4 −1.92917 −0.964584 0.263774i \(-0.915033\pi\)
−0.964584 + 0.263774i \(0.915033\pi\)
\(62\) 0 0
\(63\) 207.926 + 207.926i 0.00660020 + 0.00660020i
\(64\) 0 0
\(65\) −9111.29 16092.8i −0.267483 0.472442i
\(66\) 0 0
\(67\) 35802.8 35802.8i 0.974384 0.974384i −0.0252960 0.999680i \(-0.508053\pi\)
0.999680 + 0.0252960i \(0.00805283\pi\)
\(68\) 0 0
\(69\) 20981.8i 0.530543i
\(70\) 0 0
\(71\) 74255.2i 1.74816i 0.485784 + 0.874079i \(0.338534\pi\)
−0.485784 + 0.874079i \(0.661466\pi\)
\(72\) 0 0
\(73\) −58806.0 + 58806.0i −1.29156 + 1.29156i −0.357737 + 0.933822i \(0.616452\pi\)
−0.933822 + 0.357737i \(0.883548\pi\)
\(74\) 0 0
\(75\) −11746.1 46990.3i −0.241125 0.964617i
\(76\) 0 0
\(77\) −15640.3 15640.3i −0.300620 0.300620i
\(78\) 0 0
\(79\) −65319.6 −1.17754 −0.588770 0.808301i \(-0.700388\pi\)
−0.588770 + 0.808301i \(0.700388\pi\)
\(80\) 0 0
\(81\) 58369.9 0.988499
\(82\) 0 0
\(83\) 35508.0 + 35508.0i 0.565758 + 0.565758i 0.930937 0.365180i \(-0.118992\pi\)
−0.365180 + 0.930937i \(0.618992\pi\)
\(84\) 0 0
\(85\) 49613.8 28089.9i 0.744826 0.421699i
\(86\) 0 0
\(87\) −45894.8 + 45894.8i −0.650078 + 0.650078i
\(88\) 0 0
\(89\) 11119.6i 0.148803i −0.997228 0.0744017i \(-0.976295\pi\)
0.997228 0.0744017i \(-0.0237047\pi\)
\(90\) 0 0
\(91\) 35201.7i 0.445616i
\(92\) 0 0
\(93\) 30083.0 30083.0i 0.360673 0.360673i
\(94\) 0 0
\(95\) −1701.79 + 6143.67i −0.0193463 + 0.0698423i
\(96\) 0 0
\(97\) 86604.7 + 86604.7i 0.934571 + 0.934571i 0.997987 0.0634164i \(-0.0201996\pi\)
−0.0634164 + 0.997987i \(0.520200\pi\)
\(98\) 0 0
\(99\) 574.413 0.00589028
\(100\) 0 0
\(101\) 60159.9 0.586818 0.293409 0.955987i \(-0.405210\pi\)
0.293409 + 0.955987i \(0.405210\pi\)
\(102\) 0 0
\(103\) 96594.3 + 96594.3i 0.897136 + 0.897136i 0.995182 0.0980456i \(-0.0312591\pi\)
−0.0980456 + 0.995182i \(0.531259\pi\)
\(104\) 0 0
\(105\) 24612.2 88852.8i 0.217860 0.786498i
\(106\) 0 0
\(107\) 140032. 140032.i 1.18241 1.18241i 0.203292 0.979118i \(-0.434836\pi\)
0.979118 0.203292i \(-0.0651641\pi\)
\(108\) 0 0
\(109\) 59153.9i 0.476889i 0.971156 + 0.238445i \(0.0766375\pi\)
−0.971156 + 0.238445i \(0.923362\pi\)
\(110\) 0 0
\(111\) 151381.i 1.16617i
\(112\) 0 0
\(113\) 22649.2 22649.2i 0.166862 0.166862i −0.618737 0.785598i \(-0.712355\pi\)
0.785598 + 0.618737i \(0.212355\pi\)
\(114\) 0 0
\(115\) 65852.3 37283.7i 0.464330 0.262890i
\(116\) 0 0
\(117\) 646.417 + 646.417i 0.00436564 + 0.00436564i
\(118\) 0 0
\(119\) 108526. 0.702533
\(120\) 0 0
\(121\) 117843. 0.731715
\(122\) 0 0
\(123\) −92702.8 92702.8i −0.552497 0.552497i
\(124\) 0 0
\(125\) 126609. 120365.i 0.724751 0.689011i
\(126\) 0 0
\(127\) −44108.6 + 44108.6i −0.242669 + 0.242669i −0.817953 0.575285i \(-0.804891\pi\)
0.575285 + 0.817953i \(0.304891\pi\)
\(128\) 0 0
\(129\) 293662.i 1.55372i
\(130\) 0 0
\(131\) 248718.i 1.26628i 0.774038 + 0.633139i \(0.218234\pi\)
−0.774038 + 0.633139i \(0.781766\pi\)
\(132\) 0 0
\(133\) −8580.66 + 8580.66i −0.0420621 + 0.0420621i
\(134\) 0 0
\(135\) 104914. + 185304.i 0.495448 + 0.875084i
\(136\) 0 0
\(137\) −22781.4 22781.4i −0.103700 0.103700i 0.653353 0.757053i \(-0.273362\pi\)
−0.757053 + 0.653353i \(0.773362\pi\)
\(138\) 0 0
\(139\) −67318.4 −0.295527 −0.147763 0.989023i \(-0.547207\pi\)
−0.147763 + 0.989023i \(0.547207\pi\)
\(140\) 0 0
\(141\) 146269. 0.619590
\(142\) 0 0
\(143\) −48623.9 48623.9i −0.198843 0.198843i
\(144\) 0 0
\(145\) −225596. 62489.9i −0.891069 0.246825i
\(146\) 0 0
\(147\) −60104.4 + 60104.4i −0.229410 + 0.229410i
\(148\) 0 0
\(149\) 465212.i 1.71666i 0.513096 + 0.858331i \(0.328499\pi\)
−0.513096 + 0.858331i \(0.671501\pi\)
\(150\) 0 0
\(151\) 389781.i 1.39116i 0.718447 + 0.695582i \(0.244853\pi\)
−0.718447 + 0.695582i \(0.755147\pi\)
\(152\) 0 0
\(153\) −1992.89 + 1992.89i −0.00688264 + 0.00688264i
\(154\) 0 0
\(155\) 147873. + 40960.6i 0.494377 + 0.136942i
\(156\) 0 0
\(157\) −134965. 134965.i −0.436991 0.436991i 0.454007 0.890998i \(-0.349994\pi\)
−0.890998 + 0.454007i \(0.849994\pi\)
\(158\) 0 0
\(159\) −286150. −0.897638
\(160\) 0 0
\(161\) 144047. 0.437964
\(162\) 0 0
\(163\) −38557.6 38557.6i −0.113669 0.113669i 0.647985 0.761653i \(-0.275612\pi\)
−0.761653 + 0.647985i \(0.775612\pi\)
\(164\) 0 0
\(165\) −88735.1 156728.i −0.253738 0.448165i
\(166\) 0 0
\(167\) 53486.3 53486.3i 0.148406 0.148406i −0.629000 0.777406i \(-0.716535\pi\)
0.777406 + 0.629000i \(0.216535\pi\)
\(168\) 0 0
\(169\) 261855.i 0.705251i
\(170\) 0 0
\(171\) 315.137i 0.000824156i
\(172\) 0 0
\(173\) 75193.4 75193.4i 0.191014 0.191014i −0.605120 0.796134i \(-0.706875\pi\)
0.796134 + 0.605120i \(0.206875\pi\)
\(174\) 0 0
\(175\) 322603. 80640.9i 0.796294 0.199049i
\(176\) 0 0
\(177\) −123874. 123874.i −0.297198 0.297198i
\(178\) 0 0
\(179\) 168957. 0.394133 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(180\) 0 0
\(181\) 130710. 0.296561 0.148280 0.988945i \(-0.452626\pi\)
0.148280 + 0.988945i \(0.452626\pi\)
\(182\) 0 0
\(183\) −614468. 614468.i −1.35635 1.35635i
\(184\) 0 0
\(185\) −475115. + 268997.i −1.02063 + 0.577853i
\(186\) 0 0
\(187\) 149906. 149906.i 0.313484 0.313484i
\(188\) 0 0
\(189\) 405337.i 0.825395i
\(190\) 0 0
\(191\) 931440.i 1.84744i −0.383063 0.923722i \(-0.625131\pi\)
0.383063 0.923722i \(-0.374869\pi\)
\(192\) 0 0
\(193\) −258847. + 258847.i −0.500207 + 0.500207i −0.911502 0.411295i \(-0.865077\pi\)
0.411295 + 0.911502i \(0.365077\pi\)
\(194\) 0 0
\(195\) 76516.4 276233.i 0.144101 0.520223i
\(196\) 0 0
\(197\) −650410. 650410.i −1.19405 1.19405i −0.975921 0.218126i \(-0.930005\pi\)
−0.218126 0.975921i \(-0.569995\pi\)
\(198\) 0 0
\(199\) −55293.9 −0.0989793 −0.0494897 0.998775i \(-0.515759\pi\)
−0.0494897 + 0.998775i \(0.515759\pi\)
\(200\) 0 0
\(201\) 784787. 1.37013
\(202\) 0 0
\(203\) −315082. 315082.i −0.536641 0.536641i
\(204\) 0 0
\(205\) 126223. 455680.i 0.209775 0.757313i
\(206\) 0 0
\(207\) −2645.16 + 2645.16i −0.00429068 + 0.00429068i
\(208\) 0 0
\(209\) 23704.8i 0.0375379i
\(210\) 0 0
\(211\) 447082.i 0.691322i 0.938359 + 0.345661i \(0.112345\pi\)
−0.938359 + 0.345661i \(0.887655\pi\)
\(212\) 0 0
\(213\) −813825. + 813825.i −1.22909 + 1.22909i
\(214\) 0 0
\(215\) 921670. 521823.i 1.35981 0.769887i
\(216\) 0 0
\(217\) 206529. + 206529.i 0.297736 + 0.297736i
\(218\) 0 0
\(219\) −1.28901e6 −1.81613
\(220\) 0 0
\(221\) 337395. 0.464685
\(222\) 0 0
\(223\) −562701. 562701.i −0.757732 0.757732i 0.218177 0.975909i \(-0.429989\pi\)
−0.975909 + 0.218177i \(0.929989\pi\)
\(224\) 0 0
\(225\) −4443.21 + 7404.86i −0.00585113 + 0.00975126i
\(226\) 0 0
\(227\) −290103. + 290103.i −0.373670 + 0.373670i −0.868812 0.495142i \(-0.835116\pi\)
0.495142 + 0.868812i \(0.335116\pi\)
\(228\) 0 0
\(229\) 887839.i 1.11878i 0.828904 + 0.559391i \(0.188965\pi\)
−0.828904 + 0.559391i \(0.811035\pi\)
\(230\) 0 0
\(231\) 342831.i 0.422717i
\(232\) 0 0
\(233\) −847028. + 847028.i −1.02213 + 1.02213i −0.0223850 + 0.999749i \(0.507126\pi\)
−0.999749 + 0.0223850i \(0.992874\pi\)
\(234\) 0 0
\(235\) 259913. + 459071.i 0.307014 + 0.542264i
\(236\) 0 0
\(237\) −715893. 715893.i −0.827899 0.827899i
\(238\) 0 0
\(239\) 386922. 0.438156 0.219078 0.975707i \(-0.429695\pi\)
0.219078 + 0.975707i \(0.429695\pi\)
\(240\) 0 0
\(241\) 523763. 0.580888 0.290444 0.956892i \(-0.406197\pi\)
0.290444 + 0.956892i \(0.406197\pi\)
\(242\) 0 0
\(243\) −14802.9 14802.9i −0.0160817 0.0160817i
\(244\) 0 0
\(245\) −295443. 81837.6i −0.314455 0.0871039i
\(246\) 0 0
\(247\) −26676.3 + 26676.3i −0.0278216 + 0.0278216i
\(248\) 0 0
\(249\) 778324.i 0.795540i
\(250\) 0 0
\(251\) 1.78268e6i 1.78604i 0.450022 + 0.893018i \(0.351416\pi\)
−0.450022 + 0.893018i \(0.648584\pi\)
\(252\) 0 0
\(253\) 198970. 198970.i 0.195428 0.195428i
\(254\) 0 0
\(255\) 851620. + 235898.i 0.820154 + 0.227182i
\(256\) 0 0
\(257\) −1.12252e6 1.12252e6i −1.06013 1.06013i −0.998072 0.0620619i \(-0.980232\pi\)
−0.0620619 0.998072i \(-0.519768\pi\)
\(258\) 0 0
\(259\) −1.03928e6 −0.962679
\(260\) 0 0
\(261\) 11571.9 0.0105148
\(262\) 0 0
\(263\) −829541. 829541.i −0.739517 0.739517i 0.232967 0.972485i \(-0.425156\pi\)
−0.972485 + 0.232967i \(0.925156\pi\)
\(264\) 0 0
\(265\) −508475. 898094.i −0.444790 0.785610i
\(266\) 0 0
\(267\) 121869. 121869.i 0.104620 0.104620i
\(268\) 0 0
\(269\) 1.20735e6i 1.01731i −0.860971 0.508655i \(-0.830143\pi\)
0.860971 0.508655i \(-0.169857\pi\)
\(270\) 0 0
\(271\) 334539.i 0.276709i 0.990383 + 0.138355i \(0.0441814\pi\)
−0.990383 + 0.138355i \(0.955819\pi\)
\(272\) 0 0
\(273\) 385806. 385806.i 0.313301 0.313301i
\(274\) 0 0
\(275\) 334220. 556998.i 0.266502 0.444142i
\(276\) 0 0
\(277\) 1.13650e6 + 1.13650e6i 0.889956 + 0.889956i 0.994518 0.104562i \(-0.0333442\pi\)
−0.104562 + 0.994518i \(0.533344\pi\)
\(278\) 0 0
\(279\) −7585.07 −0.00583377
\(280\) 0 0
\(281\) −57687.8 −0.0435831 −0.0217916 0.999763i \(-0.506937\pi\)
−0.0217916 + 0.999763i \(0.506937\pi\)
\(282\) 0 0
\(283\) 859732. + 859732.i 0.638112 + 0.638112i 0.950090 0.311977i \(-0.100991\pi\)
−0.311977 + 0.950090i \(0.600991\pi\)
\(284\) 0 0
\(285\) −85985.1 + 48682.3i −0.0627063 + 0.0355025i
\(286\) 0 0
\(287\) 636433. 636433.i 0.456087 0.456087i
\(288\) 0 0
\(289\) 379675.i 0.267404i
\(290\) 0 0
\(291\) 1.89835e6i 1.31415i
\(292\) 0 0
\(293\) 474947. 474947.i 0.323204 0.323204i −0.526791 0.849995i \(-0.676605\pi\)
0.849995 + 0.526791i \(0.176605\pi\)
\(294\) 0 0
\(295\) 168665. 608902.i 0.112842 0.407373i
\(296\) 0 0
\(297\) 559889. + 559889.i 0.368308 + 0.368308i
\(298\) 0 0
\(299\) 447824. 0.289687
\(300\) 0 0
\(301\) 2.01608e6 1.28260
\(302\) 0 0
\(303\) 659343. + 659343.i 0.412577 + 0.412577i
\(304\) 0 0
\(305\) 836653. 3.02042e6i 0.514987 1.85916i
\(306\) 0 0
\(307\) 1.52594e6 1.52594e6i 0.924043 0.924043i −0.0732691 0.997312i \(-0.523343\pi\)
0.997312 + 0.0732691i \(0.0233432\pi\)
\(308\) 0 0
\(309\) 2.11732e6i 1.26151i
\(310\) 0 0
\(311\) 816321.i 0.478586i 0.970947 + 0.239293i \(0.0769157\pi\)
−0.970947 + 0.239293i \(0.923084\pi\)
\(312\) 0 0
\(313\) −599168. + 599168.i −0.345691 + 0.345691i −0.858502 0.512811i \(-0.828604\pi\)
0.512811 + 0.858502i \(0.328604\pi\)
\(314\) 0 0
\(315\) −14304.4 + 8098.77i −0.00812259 + 0.00459878i
\(316\) 0 0
\(317\) 426253. + 426253.i 0.238242 + 0.238242i 0.816122 0.577880i \(-0.196120\pi\)
−0.577880 + 0.816122i \(0.696120\pi\)
\(318\) 0 0
\(319\) −870441. −0.478920
\(320\) 0 0
\(321\) 3.06946e6 1.66265
\(322\) 0 0
\(323\) −82242.4 82242.4i −0.0438621 0.0438621i
\(324\) 0 0
\(325\) 1.00294e6 250703.i 0.526701 0.131659i
\(326\) 0 0
\(327\) −648318. + 648318.i −0.335289 + 0.335289i
\(328\) 0 0
\(329\) 1.00418e6i 0.511473i
\(330\) 0 0
\(331\) 3.41024e6i 1.71086i 0.517915 + 0.855432i \(0.326708\pi\)
−0.517915 + 0.855432i \(0.673292\pi\)
\(332\) 0 0
\(333\) 19084.5 19084.5i 0.00943125 0.00943125i
\(334\) 0 0
\(335\) 1.39453e6 + 2.46309e6i 0.678915 + 1.19913i
\(336\) 0 0
\(337\) 461499. + 461499.i 0.221359 + 0.221359i 0.809070 0.587712i \(-0.199971\pi\)
−0.587712 + 0.809070i \(0.699971\pi\)
\(338\) 0 0
\(339\) 496464. 0.234633
\(340\) 0 0
\(341\) 570553. 0.265711
\(342\) 0 0
\(343\) −1.67724e6 1.67724e6i −0.769768 0.769768i
\(344\) 0 0
\(345\) 1.13035e6 + 313108.i 0.511290 + 0.141627i
\(346\) 0 0
\(347\) 2.76855e6 2.76855e6i 1.23432 1.23432i 0.272034 0.962288i \(-0.412304\pi\)
0.962288 0.272034i \(-0.0876965\pi\)
\(348\) 0 0
\(349\) 2.53035e6i 1.11203i −0.831172 0.556016i \(-0.812329\pi\)
0.831172 0.556016i \(-0.187671\pi\)
\(350\) 0 0
\(351\) 1.26015e6i 0.545951i
\(352\) 0 0
\(353\) 1.48632e6 1.48632e6i 0.634856 0.634856i −0.314426 0.949282i \(-0.601812\pi\)
0.949282 + 0.314426i \(0.101812\pi\)
\(354\) 0 0
\(355\) −4.00035e6 1.10810e6i −1.68472 0.466666i
\(356\) 0 0
\(357\) 1.18943e6 + 1.18943e6i 0.493933 + 0.493933i
\(358\) 0 0
\(359\) 1.53671e6 0.629296 0.314648 0.949208i \(-0.398114\pi\)
0.314648 + 0.949208i \(0.398114\pi\)
\(360\) 0 0
\(361\) −2.46309e6 −0.994748
\(362\) 0 0
\(363\) 1.29155e6 + 1.29155e6i 0.514450 + 0.514450i
\(364\) 0 0
\(365\) −2.29051e6 4.04561e6i −0.899912 1.58947i
\(366\) 0 0
\(367\) −1.81385e6 + 1.81385e6i −0.702970 + 0.702970i −0.965047 0.262077i \(-0.915593\pi\)
0.262077 + 0.965047i \(0.415593\pi\)
\(368\) 0 0
\(369\) 23373.9i 0.00893647i
\(370\) 0 0
\(371\) 1.96451e6i 0.741002i
\(372\) 0 0
\(373\) −2.79814e6 + 2.79814e6i −1.04135 + 1.04135i −0.0422450 + 0.999107i \(0.513451\pi\)
−0.999107 + 0.0422450i \(0.986549\pi\)
\(374\) 0 0
\(375\) 2.70680e6 + 68426.7i 0.993980 + 0.0251274i
\(376\) 0 0
\(377\) −979554. 979554.i −0.354957 0.354957i
\(378\) 0 0
\(379\) −3.26539e6 −1.16771 −0.583857 0.811856i \(-0.698457\pi\)
−0.583857 + 0.811856i \(0.698457\pi\)
\(380\) 0 0
\(381\) −966847. −0.341228
\(382\) 0 0
\(383\) 1.43914e6 + 1.43914e6i 0.501310 + 0.501310i 0.911845 0.410535i \(-0.134658\pi\)
−0.410535 + 0.911845i \(0.634658\pi\)
\(384\) 0 0
\(385\) 1.07599e6 609194.i 0.369961 0.209461i
\(386\) 0 0
\(387\) −37021.7 + 37021.7i −0.0125655 + 0.0125655i
\(388\) 0 0
\(389\) 3.84322e6i 1.28772i −0.765144 0.643859i \(-0.777332\pi\)
0.765144 0.643859i \(-0.222668\pi\)
\(390\) 0 0
\(391\) 1.38063e6i 0.456705i
\(392\) 0 0
\(393\) −2.72591e6 + 2.72591e6i −0.890288 + 0.890288i
\(394\) 0 0
\(395\) 974752. 3.51897e6i 0.314341 1.13481i
\(396\) 0 0
\(397\) −370411. 370411.i −0.117953 0.117953i 0.645667 0.763619i \(-0.276580\pi\)
−0.763619 + 0.645667i \(0.776580\pi\)
\(398\) 0 0
\(399\) −188085. −0.0591457
\(400\) 0 0
\(401\) −3.33019e6 −1.03421 −0.517105 0.855922i \(-0.672990\pi\)
−0.517105 + 0.855922i \(0.672990\pi\)
\(402\) 0 0
\(403\) 642074. + 642074.i 0.196935 + 0.196935i
\(404\) 0 0
\(405\) −871043. + 3.14456e6i −0.263877 + 0.952627i
\(406\) 0 0
\(407\) −1.43554e6 + 1.43554e6i −0.429567 + 0.429567i
\(408\) 0 0
\(409\) 6.13233e6i 1.81267i 0.422565 + 0.906333i \(0.361130\pi\)
−0.422565 + 0.906333i \(0.638870\pi\)
\(410\) 0 0
\(411\) 499362.i 0.145818i
\(412\) 0 0
\(413\) 850432. 850432.i 0.245338 0.245338i
\(414\) 0 0
\(415\) −2.44280e6 + 1.38304e6i −0.696254 + 0.394199i
\(416\) 0 0
\(417\) −737800. 737800.i −0.207777 0.207777i
\(418\) 0 0
\(419\) −217725. −0.0605861 −0.0302931 0.999541i \(-0.509644\pi\)
−0.0302931 + 0.999541i \(0.509644\pi\)
\(420\) 0 0
\(421\) −984530. −0.270722 −0.135361 0.990796i \(-0.543219\pi\)
−0.135361 + 0.990796i \(0.543219\pi\)
\(422\) 0 0
\(423\) −18440.0 18440.0i −0.00501084 0.00501084i
\(424\) 0 0
\(425\) 772912. + 3.09203e6i 0.207567 + 0.830369i
\(426\) 0 0
\(427\) 4.21851e6 4.21851e6i 1.11967 1.11967i
\(428\) 0 0
\(429\) 1.06582e6i 0.279602i
\(430\) 0 0
\(431\) 4.80717e6i 1.24651i −0.782018 0.623255i \(-0.785810\pi\)
0.782018 0.623255i \(-0.214190\pi\)
\(432\) 0 0
\(433\) 1.26993e6 1.26993e6i 0.325506 0.325506i −0.525369 0.850875i \(-0.676073\pi\)
0.850875 + 0.525369i \(0.176073\pi\)
\(434\) 0 0
\(435\) −1.78762e6 3.15738e6i −0.452951 0.800024i
\(436\) 0 0
\(437\) −109160. 109160.i −0.0273439 0.0273439i
\(438\) 0 0
\(439\) −4.26336e6 −1.05582 −0.527911 0.849300i \(-0.677024\pi\)
−0.527911 + 0.849300i \(0.677024\pi\)
\(440\) 0 0
\(441\) 15154.6 0.00371064
\(442\) 0 0
\(443\) −2.54712e6 2.54712e6i −0.616651 0.616651i 0.328019 0.944671i \(-0.393619\pi\)
−0.944671 + 0.328019i \(0.893619\pi\)
\(444\) 0 0
\(445\) 599045. + 165935.i 0.143403 + 0.0397227i
\(446\) 0 0
\(447\) −5.09865e6 + 5.09865e6i −1.20694 + 1.20694i
\(448\) 0 0
\(449\) 3.41756e6i 0.800020i −0.916511 0.400010i \(-0.869007\pi\)
0.916511 0.400010i \(-0.130993\pi\)
\(450\) 0 0
\(451\) 1.75820e6i 0.407031i
\(452\) 0 0
\(453\) −4.27194e6 + 4.27194e6i −0.978092 + 0.978092i
\(454\) 0 0
\(455\) 1.89643e6 + 525309.i 0.429445 + 0.118956i
\(456\) 0 0
\(457\) 1.39943e6 + 1.39943e6i 0.313445 + 0.313445i 0.846243 0.532798i \(-0.178859\pi\)
−0.532798 + 0.846243i \(0.678859\pi\)
\(458\) 0 0
\(459\) −3.88500e6 −0.860716
\(460\) 0 0
\(461\) 1.83239e6 0.401573 0.200787 0.979635i \(-0.435650\pi\)
0.200787 + 0.979635i \(0.435650\pi\)
\(462\) 0 0
\(463\) −4.50294e6 4.50294e6i −0.976212 0.976212i 0.0235115 0.999724i \(-0.492515\pi\)
−0.999724 + 0.0235115i \(0.992515\pi\)
\(464\) 0 0
\(465\) 1.17174e6 + 2.06958e6i 0.251304 + 0.443865i
\(466\) 0 0
\(467\) 6.07065e6 6.07065e6i 1.28808 1.28808i 0.352131 0.935951i \(-0.385457\pi\)
0.935951 0.352131i \(-0.114543\pi\)
\(468\) 0 0
\(469\) 5.38780e6i 1.13104i
\(470\) 0 0
\(471\) 2.95839e6i 0.614474i
\(472\) 0 0
\(473\) 2.78479e6 2.78479e6i 0.572322 0.572322i
\(474\) 0 0
\(475\) −305583. 183362.i −0.0621434 0.0372885i
\(476\) 0 0
\(477\) 36074.7 + 36074.7i 0.00725951 + 0.00725951i
\(478\) 0 0
\(479\) 9.07331e6 1.80687 0.903435 0.428725i \(-0.141037\pi\)
0.903435 + 0.428725i \(0.141037\pi\)
\(480\) 0 0
\(481\) −3.23099e6 −0.636756
\(482\) 0 0
\(483\) 1.57873e6 + 1.57873e6i 0.307921 + 0.307921i
\(484\) 0 0
\(485\) −5.95805e6 + 3.37328e6i −1.15014 + 0.651175i
\(486\) 0 0
\(487\) −4.28896e6 + 4.28896e6i −0.819464 + 0.819464i −0.986030 0.166566i \(-0.946732\pi\)
0.166566 + 0.986030i \(0.446732\pi\)
\(488\) 0 0
\(489\) 845171.i 0.159835i
\(490\) 0 0
\(491\) 4.97918e6i 0.932083i −0.884763 0.466041i \(-0.845680\pi\)
0.884763 0.466041i \(-0.154320\pi\)
\(492\) 0 0
\(493\) 3.01994e6 3.01994e6i 0.559605 0.559605i
\(494\) 0 0
\(495\) −8571.85 + 30945.4i −0.00157240 + 0.00567653i
\(496\) 0 0
\(497\) −5.58716e6 5.58716e6i −1.01461 1.01461i
\(498\) 0 0
\(499\) 8.06885e6 1.45064 0.725321 0.688411i \(-0.241692\pi\)
0.725321 + 0.688411i \(0.241692\pi\)
\(500\) 0 0
\(501\) 1.17240e6 0.208681
\(502\) 0 0
\(503\) −351210. 351210.i −0.0618938 0.0618938i 0.675482 0.737376i \(-0.263935\pi\)
−0.737376 + 0.675482i \(0.763935\pi\)
\(504\) 0 0
\(505\) −897755. + 3.24100e6i −0.156650 + 0.565523i
\(506\) 0 0
\(507\) −2.86989e6 + 2.86989e6i −0.495844 + 0.495844i
\(508\) 0 0
\(509\) 2.07197e6i 0.354477i −0.984168 0.177239i \(-0.943284\pi\)
0.984168 0.177239i \(-0.0567164\pi\)
\(510\) 0 0
\(511\) 8.84945e6i 1.49922i
\(512\) 0 0
\(513\) 307169. 307169.i 0.0515329 0.0515329i
\(514\) 0 0
\(515\) −6.64529e6 + 3.76237e6i −1.10407 + 0.625092i
\(516\) 0 0
\(517\) 1.38707e6 + 1.38707e6i 0.228229 + 0.228229i
\(518\) 0 0
\(519\) 1.64822e6 0.268594
\(520\) 0 0
\(521\) −8.07892e6 −1.30394 −0.651972 0.758243i \(-0.726058\pi\)
−0.651972 + 0.758243i \(0.726058\pi\)
\(522\) 0 0
\(523\) 2.55559e6 + 2.55559e6i 0.408543 + 0.408543i 0.881230 0.472687i \(-0.156716\pi\)
−0.472687 + 0.881230i \(0.656716\pi\)
\(524\) 0 0
\(525\) 4.41949e6 + 2.65187e6i 0.699800 + 0.419907i
\(526\) 0 0
\(527\) −1.97950e6 + 1.97950e6i −0.310477 + 0.310477i
\(528\) 0 0
\(529\) 4.60383e6i 0.715287i
\(530\) 0 0
\(531\) 31233.4i 0.00480709i
\(532\) 0 0
\(533\) 1.97860e6 1.97860e6i 0.301675 0.301675i
\(534\) 0 0
\(535\) 5.45429e6 + 9.63363e6i 0.823860 + 1.45514i
\(536\) 0 0
\(537\) 1.85174e6 + 1.85174e6i 0.277105 + 0.277105i
\(538\) 0 0
\(539\) −1.13994e6 −0.169009
\(540\) 0 0
\(541\) −821557. −0.120683 −0.0603413 0.998178i \(-0.519219\pi\)
−0.0603413 + 0.998178i \(0.519219\pi\)
\(542\) 0 0
\(543\) 1.43257e6 + 1.43257e6i 0.208504 + 0.208504i
\(544\) 0 0
\(545\) −3.18680e6 882743.i −0.459583 0.127304i
\(546\) 0 0
\(547\) −6.24214e6 + 6.24214e6i −0.892000 + 0.892000i −0.994711 0.102711i \(-0.967248\pi\)
0.102711 + 0.994711i \(0.467248\pi\)
\(548\) 0 0
\(549\) 154931.i 0.0219385i
\(550\) 0 0
\(551\) 477546.i 0.0670095i
\(552\) 0 0
\(553\) 4.91483e6 4.91483e6i 0.683432 0.683432i
\(554\) 0 0
\(555\) −8.15535e6 2.25903e6i −1.12385 0.311307i
\(556\) 0 0
\(557\) −883621. 883621.i −0.120678 0.120678i 0.644189 0.764867i \(-0.277195\pi\)
−0.764867 + 0.644189i \(0.777195\pi\)
\(558\) 0 0
\(559\) 6.26776e6 0.848365
\(560\) 0 0
\(561\) 3.28590e6 0.440806
\(562\) 0 0
\(563\) 9.36992e6 + 9.36992e6i 1.24585 + 1.24585i 0.957537 + 0.288310i \(0.0930934\pi\)
0.288310 + 0.957537i \(0.406907\pi\)
\(564\) 0 0
\(565\) 882193. + 1.55817e6i 0.116263 + 0.205350i
\(566\) 0 0
\(567\) −4.39191e6 + 4.39191e6i −0.573714 + 0.573714i
\(568\) 0 0
\(569\) 2.55469e6i 0.330794i 0.986227 + 0.165397i \(0.0528906\pi\)
−0.986227 + 0.165397i \(0.947109\pi\)
\(570\) 0 0
\(571\) 1.27093e7i 1.63129i 0.578549 + 0.815647i \(0.303619\pi\)
−0.578549 + 0.815647i \(0.696381\pi\)
\(572\) 0 0
\(573\) 1.02084e7 1.02084e7i 1.29889 1.29889i
\(574\) 0 0
\(575\) 1.02589e6 + 4.10404e6i 0.129399 + 0.517657i
\(576\) 0 0
\(577\) 5.55174e6 + 5.55174e6i 0.694208 + 0.694208i 0.963155 0.268947i \(-0.0866758\pi\)
−0.268947 + 0.963155i \(0.586676\pi\)
\(578\) 0 0
\(579\) −5.67385e6 −0.703366
\(580\) 0 0
\(581\) −5.34343e6 −0.656720
\(582\) 0 0
\(583\) −2.71356e6 2.71356e6i −0.330650 0.330650i
\(584\) 0 0
\(585\) −44470.9 + 25178.1i −0.00537262 + 0.00304182i
\(586\) 0 0
\(587\) 1.20230e6 1.20230e6i 0.144019 0.144019i −0.631421 0.775440i \(-0.717528\pi\)
0.775440 + 0.631421i \(0.217528\pi\)
\(588\) 0 0
\(589\) 313020.i 0.0371778i
\(590\) 0 0
\(591\) 1.42568e7i 1.67901i
\(592\) 0 0
\(593\) 5.12919e6 5.12919e6i 0.598980 0.598980i −0.341061 0.940041i \(-0.610786\pi\)
0.940041 + 0.341061i \(0.110786\pi\)
\(594\) 0 0
\(595\) −1.61952e6 + 5.84664e6i −0.187539 + 0.677039i
\(596\) 0 0
\(597\) −606013. 606013.i −0.0695898 0.0695898i
\(598\) 0 0
\(599\) 1.19407e7 1.35976 0.679881 0.733322i \(-0.262031\pi\)
0.679881 + 0.733322i \(0.262031\pi\)
\(600\) 0 0
\(601\) 9.12810e6 1.03085 0.515423 0.856936i \(-0.327635\pi\)
0.515423 + 0.856936i \(0.327635\pi\)
\(602\) 0 0
\(603\) −98937.5 98937.5i −0.0110807 0.0110807i
\(604\) 0 0
\(605\) −1.75855e6 + 6.34859e6i −0.195329 + 0.705161i
\(606\) 0 0
\(607\) −2.12288e6 + 2.12288e6i −0.233859 + 0.233859i −0.814301 0.580442i \(-0.802880\pi\)
0.580442 + 0.814301i \(0.302880\pi\)
\(608\) 0 0
\(609\) 6.90651e6i 0.754597i
\(610\) 0 0
\(611\) 3.12188e6i 0.338309i
\(612\) 0 0
\(613\) 6.53224e6 6.53224e6i 0.702119 0.702119i −0.262746 0.964865i \(-0.584628\pi\)
0.964865 + 0.262746i \(0.0846281\pi\)
\(614\) 0 0
\(615\) 6.37757e6 3.61080e6i 0.679935 0.384960i
\(616\) 0 0
\(617\) 3.08121e6 + 3.08121e6i 0.325843 + 0.325843i 0.851003 0.525160i \(-0.175995\pi\)
−0.525160 + 0.851003i \(0.675995\pi\)
\(618\) 0 0
\(619\) 1.26926e7 1.33145 0.665724 0.746198i \(-0.268123\pi\)
0.665724 + 0.746198i \(0.268123\pi\)
\(620\) 0 0
\(621\) −5.15656e6 −0.536576
\(622\) 0 0
\(623\) 836666. + 836666.i 0.0863639 + 0.0863639i
\(624\) 0 0
\(625\) 4.59509e6 + 8.61699e6i 0.470538 + 0.882380i
\(626\) 0 0
\(627\) −259801. + 259801.i −0.0263920 + 0.0263920i
\(628\) 0 0
\(629\) 9.96107e6i 1.00387i
\(630\) 0 0
\(631\) 8.30473e6i 0.830333i −0.909745 0.415166i \(-0.863723\pi\)
0.909745 0.415166i \(-0.136277\pi\)
\(632\) 0 0
\(633\) −4.89995e6 + 4.89995e6i −0.486051 + 0.486051i
\(634\) 0 0
\(635\) −1.71804e6 3.03449e6i −0.169083 0.298642i
\(636\) 0 0
\(637\) −1.28284e6 1.28284e6i −0.125263 0.125263i
\(638\) 0 0
\(639\) 205197. 0.0198801
\(640\) 0 0
\(641\) 6.99158e6 0.672095 0.336047 0.941845i \(-0.390910\pi\)
0.336047 + 0.941845i \(0.390910\pi\)
\(642\) 0 0
\(643\) 1.28978e7 + 1.28978e7i 1.23024 + 1.23024i 0.963873 + 0.266364i \(0.0858223\pi\)
0.266364 + 0.963873i \(0.414178\pi\)
\(644\) 0 0
\(645\) 1.58205e7 + 4.38226e6i 1.49734 + 0.414762i
\(646\) 0 0
\(647\) 9.64496e6 9.64496e6i 0.905816 0.905816i −0.0901155 0.995931i \(-0.528724\pi\)
0.995931 + 0.0901155i \(0.0287236\pi\)
\(648\) 0 0
\(649\) 2.34939e6i 0.218949i
\(650\) 0 0
\(651\) 4.52705e6i 0.418661i
\(652\) 0 0
\(653\) −1.31484e6 + 1.31484e6i −0.120667 + 0.120667i −0.764862 0.644194i \(-0.777193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(654\) 0 0
\(655\) −1.33992e7 3.71157e6i −1.22033 0.338030i
\(656\) 0 0
\(657\) 162504. + 162504.i 0.0146876 + 0.0146876i
\(658\) 0 0
\(659\) 533017. 0.0478109 0.0239055 0.999714i \(-0.492390\pi\)
0.0239055 + 0.999714i \(0.492390\pi\)
\(660\) 0 0
\(661\) −9.93132e6 −0.884104 −0.442052 0.896989i \(-0.645749\pi\)
−0.442052 + 0.896989i \(0.645749\pi\)
\(662\) 0 0
\(663\) 3.69780e6 + 3.69780e6i 0.326708 + 0.326708i
\(664\) 0 0
\(665\) −334219. 590314.i −0.0293074 0.0517641i
\(666\) 0 0
\(667\) 4.00837e6 4.00837e6i 0.348861 0.348861i
\(668\) 0 0
\(669\) 1.23342e7i 1.06548i
\(670\) 0 0
\(671\) 1.16540e7i 0.999238i
\(672\) 0 0
\(673\) −330472. + 330472.i −0.0281253 + 0.0281253i −0.721030 0.692904i \(-0.756331\pi\)
0.692904 + 0.721030i \(0.256331\pi\)
\(674\) 0 0
\(675\) −1.15485e7 + 2.88677e6i −0.975587 + 0.243867i
\(676\) 0 0
\(677\) 1.88339e6 + 1.88339e6i 0.157931 + 0.157931i 0.781649 0.623718i \(-0.214379\pi\)
−0.623718 + 0.781649i \(0.714379\pi\)
\(678\) 0 0
\(679\) −1.30328e7 −1.08483
\(680\) 0 0
\(681\) −6.35898e6 −0.525436
\(682\) 0 0
\(683\) 406485. + 406485.i 0.0333421 + 0.0333421i 0.723581 0.690239i \(-0.242495\pi\)
−0.690239 + 0.723581i \(0.742495\pi\)
\(684\) 0 0
\(685\) 1.56727e6 887342.i 0.127619 0.0722545i
\(686\) 0 0
\(687\) −9.73058e6 + 9.73058e6i −0.786587 + 0.786587i
\(688\) 0 0
\(689\) 6.10743e6i 0.490129i
\(690\) 0 0
\(691\) 8.41699e6i 0.670597i −0.942112 0.335299i \(-0.891163\pi\)
0.942112 0.335299i \(-0.108837\pi\)
\(692\) 0 0
\(693\) −43220.4 + 43220.4i −0.00341866 + 0.00341866i
\(694\) 0 0
\(695\) 1.00458e6 3.62665e6i 0.0788901 0.284802i
\(696\) 0 0
\(697\) 6.09997e6 + 6.09997e6i 0.475604 + 0.475604i
\(698\) 0 0
\(699\) −1.85666e7 −1.43727
\(700\) 0 0
\(701\) −1.79152e7 −1.37698 −0.688490 0.725246i \(-0.741726\pi\)
−0.688490 + 0.725246i \(0.741726\pi\)
\(702\) 0 0
\(703\) 787575. + 787575.i 0.0601041 + 0.0601041i
\(704\) 0 0
\(705\) −2.18274e6 + 7.87996e6i −0.165398 + 0.597106i
\(706\) 0 0
\(707\) −4.52660e6 + 4.52660e6i −0.340583 + 0.340583i
\(708\) 0 0
\(709\) 1.85631e7i 1.38686i 0.720522 + 0.693432i \(0.243902\pi\)
−0.720522 + 0.693432i \(0.756098\pi\)
\(710\) 0 0
\(711\) 180504.i 0.0133910i
\(712\) 0 0
\(713\) −2.62739e6 + 2.62739e6i −0.193553 + 0.193553i
\(714\) 0 0
\(715\) 3.34512e6 1.89391e6i 0.244707 0.138546i
\(716\) 0 0
\(717\) 4.24061e6 + 4.24061e6i 0.308057 + 0.308057i
\(718\) 0 0
\(719\) 1.73808e7 1.25386 0.626929 0.779077i \(-0.284312\pi\)
0.626929 + 0.779077i \(0.284312\pi\)
\(720\) 0 0
\(721\) −1.45360e7 −1.04138
\(722\) 0 0
\(723\) 5.74036e6 + 5.74036e6i 0.408407 + 0.408407i
\(724\) 0 0
\(725\) 6.73305e6 1.12210e7i 0.475737 0.792843i
\(726\) 0 0
\(727\) −882269. + 882269.i −0.0619106 + 0.0619106i −0.737384 0.675474i \(-0.763939\pi\)
0.675474 + 0.737384i \(0.263939\pi\)
\(728\) 0 0
\(729\) 1.45084e7i 1.01111i
\(730\) 0 0
\(731\) 1.93234e7i 1.33749i
\(732\) 0 0
\(733\) −6.82460e6 + 6.82460e6i −0.469156 + 0.469156i −0.901641 0.432485i \(-0.857637\pi\)
0.432485 + 0.901641i \(0.357637\pi\)
\(734\) 0 0
\(735\) −2.34108e6 4.13494e6i −0.159845 0.282326i
\(736\) 0 0
\(737\) 7.44213e6 + 7.44213e6i 0.504695 + 0.504695i
\(738\) 0 0
\(739\) −6.01199e6 −0.404955 −0.202478 0.979287i \(-0.564899\pi\)
−0.202478 + 0.979287i \(0.564899\pi\)
\(740\) 0 0
\(741\) −584736. −0.0391214
\(742\) 0 0
\(743\) −8.54128e6 8.54128e6i −0.567611 0.567611i 0.363847 0.931459i \(-0.381463\pi\)
−0.931459 + 0.363847i \(0.881463\pi\)
\(744\) 0 0
\(745\) −2.50624e7 6.94227e6i −1.65437 0.458259i
\(746\) 0 0
\(747\) 98122.7 98122.7i 0.00643381 0.00643381i
\(748\) 0 0
\(749\) 2.10728e7i 1.37252i
\(750\) 0 0
\(751\) 9.37871e6i 0.606797i −0.952864 0.303399i \(-0.901879\pi\)
0.952864 0.303399i \(-0.0981213\pi\)
\(752\) 0 0
\(753\) −1.95379e7 + 1.95379e7i −1.25572 + 1.25572i
\(754\) 0 0
\(755\) −2.09987e7 5.81663e6i −1.34068 0.371368i
\(756\) 0 0
\(757\) −6.77063e6 6.77063e6i −0.429427 0.429427i 0.459006 0.888433i \(-0.348206\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(758\) 0 0
\(759\) 4.36137e6 0.274801
\(760\) 0 0
\(761\) −9.79369e6 −0.613035 −0.306517 0.951865i \(-0.599164\pi\)
−0.306517 + 0.951865i \(0.599164\pi\)
\(762\) 0 0
\(763\) −4.45090e6 4.45090e6i −0.276781 0.276781i
\(764\) 0 0
\(765\) −77623.6 137103.i −0.00479557 0.00847018i
\(766\) 0 0
\(767\) 2.64390e6 2.64390e6i 0.162277 0.162277i
\(768\) 0 0
\(769\) 777622.i 0.0474191i −0.999719 0.0237095i \(-0.992452\pi\)
0.999719 0.0237095i \(-0.00754768\pi\)
\(770\) 0 0
\(771\) 2.46053e7i 1.49071i
\(772\) 0 0
\(773\) −7.92806e6 + 7.92806e6i −0.477220 + 0.477220i −0.904241 0.427022i \(-0.859563\pi\)
0.427022 + 0.904241i \(0.359563\pi\)
\(774\) 0 0
\(775\) −4.41335e6 + 7.35511e6i −0.263945 + 0.439880i
\(776\) 0 0
\(777\) −1.13903e7 1.13903e7i −0.676835 0.676835i
\(778\) 0 0
\(779\) −964593. −0.0569509
\(780\) 0 0
\(781\) −1.54350e7 −0.905481
\(782\) 0 0
\(783\) 1.12793e7 + 1.12793e7i 0.657471 + 0.657471i
\(784\) 0 0
\(785\) 9.28504e6 5.25693e6i 0.537786 0.304479i
\(786\) 0 0
\(787\) 1.94505e7 1.94505e7i 1.11942 1.11942i 0.127593 0.991827i \(-0.459275\pi\)
0.991827 0.127593i \(-0.0407251\pi\)
\(788\) 0 0
\(789\) 1.81833e7i 1.03987i
\(790\) 0 0
\(791\) 3.40838e6i 0.193690i
\(792\) 0 0