Properties

Label 160.6.n.b.63.3
Level 160
Weight 6
Character 160.63
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 63.3
Root \(2.04998 + 2.04998i\) of defining polynomial
Character \(\chi\) \(=\) 160.63
Dual form 160.6.n.b.127.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.65790 + 5.65790i) q^{3} +(-54.5514 + 12.2124i) q^{5} +(23.8754 + 23.8754i) q^{7} +178.976i q^{9} +O(q^{10})\) \(q+(-5.65790 + 5.65790i) q^{3} +(-54.5514 + 12.2124i) q^{5} +(23.8754 + 23.8754i) q^{7} +178.976i q^{9} +218.294i q^{11} +(152.629 + 152.629i) q^{13} +(239.550 - 377.743i) q^{15} +(318.212 - 318.212i) q^{17} -2458.73 q^{19} -270.169 q^{21} +(-512.053 + 512.053i) q^{23} +(2826.71 - 1332.41i) q^{25} +(-2387.50 - 2387.50i) q^{27} -5946.31i q^{29} -3065.42i q^{31} +(-1235.09 - 1235.09i) q^{33} +(-1594.01 - 1010.86i) q^{35} +(1314.27 - 1314.27i) q^{37} -1727.12 q^{39} +6094.04 q^{41} +(-1906.24 + 1906.24i) q^{43} +(-2185.74 - 9763.41i) q^{45} +(-8043.61 - 8043.61i) q^{47} -15666.9i q^{49} +3600.83i q^{51} +(-8094.04 - 8094.04i) q^{53} +(-2665.90 - 11908.2i) q^{55} +(13911.3 - 13911.3i) q^{57} -41644.1 q^{59} +43094.2 q^{61} +(-4273.13 + 4273.13i) q^{63} +(-10190.1 - 6462.16i) q^{65} +(-41625.7 - 41625.7i) q^{67} -5794.29i q^{69} -23788.6i q^{71} +(9336.77 + 9336.77i) q^{73} +(-8454.62 + 23531.9i) q^{75} +(-5211.86 + 5211.86i) q^{77} +86090.7 q^{79} -16474.8 q^{81} +(-75841.2 + 75841.2i) q^{83} +(-13472.8 + 21245.1i) q^{85} +(33643.6 + 33643.6i) q^{87} -18677.4i q^{89} +7288.16i q^{91} +(17343.8 + 17343.8i) q^{93} +(134127. - 30027.1i) q^{95} +(-97740.2 + 97740.2i) q^{97} -39069.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −5.65790 + 5.65790i −0.362954 + 0.362954i −0.864900 0.501945i \(-0.832618\pi\)
0.501945 + 0.864900i \(0.332618\pi\)
\(4\) 0 0
\(5\) −54.5514 + 12.2124i −0.975845 + 0.218463i
\(6\) 0 0
\(7\) 23.8754 + 23.8754i 0.184164 + 0.184164i 0.793168 0.609003i \(-0.208430\pi\)
−0.609003 + 0.793168i \(0.708430\pi\)
\(8\) 0 0
\(9\) 178.976i 0.736528i
\(10\) 0 0
\(11\) 218.294i 0.543951i 0.962304 + 0.271976i \(0.0876770\pi\)
−0.962304 + 0.271976i \(0.912323\pi\)
\(12\) 0 0
\(13\) 152.629 + 152.629i 0.250483 + 0.250483i 0.821169 0.570685i \(-0.193322\pi\)
−0.570685 + 0.821169i \(0.693322\pi\)
\(14\) 0 0
\(15\) 239.550 377.743i 0.274895 0.433479i
\(16\) 0 0
\(17\) 318.212 318.212i 0.267051 0.267051i −0.560860 0.827911i \(-0.689529\pi\)
0.827911 + 0.560860i \(0.189529\pi\)
\(18\) 0 0
\(19\) −2458.73 −1.56253 −0.781264 0.624201i \(-0.785425\pi\)
−0.781264 + 0.624201i \(0.785425\pi\)
\(20\) 0 0
\(21\) −270.169 −0.133687
\(22\) 0 0
\(23\) −512.053 + 512.053i −0.201834 + 0.201834i −0.800786 0.598951i \(-0.795584\pi\)
0.598951 + 0.800786i \(0.295584\pi\)
\(24\) 0 0
\(25\) 2826.71 1332.41i 0.904548 0.426371i
\(26\) 0 0
\(27\) −2387.50 2387.50i −0.630281 0.630281i
\(28\) 0 0
\(29\) 5946.31i 1.31296i −0.754342 0.656482i \(-0.772044\pi\)
0.754342 0.656482i \(-0.227956\pi\)
\(30\) 0 0
\(31\) 3065.42i 0.572909i −0.958094 0.286454i \(-0.907523\pi\)
0.958094 0.286454i \(-0.0924767\pi\)
\(32\) 0 0
\(33\) −1235.09 1235.09i −0.197430 0.197430i
\(34\) 0 0
\(35\) −1594.01 1010.86i −0.219949 0.139483i
\(36\) 0 0
\(37\) 1314.27 1314.27i 0.157827 0.157827i −0.623776 0.781603i \(-0.714402\pi\)
0.781603 + 0.623776i \(0.214402\pi\)
\(38\) 0 0
\(39\) −1727.12 −0.181828
\(40\) 0 0
\(41\) 6094.04 0.566168 0.283084 0.959095i \(-0.408642\pi\)
0.283084 + 0.959095i \(0.408642\pi\)
\(42\) 0 0
\(43\) −1906.24 + 1906.24i −0.157220 + 0.157220i −0.781334 0.624114i \(-0.785460\pi\)
0.624114 + 0.781334i \(0.285460\pi\)
\(44\) 0 0
\(45\) −2185.74 9763.41i −0.160904 0.718737i
\(46\) 0 0
\(47\) −8043.61 8043.61i −0.531137 0.531137i 0.389774 0.920911i \(-0.372553\pi\)
−0.920911 + 0.389774i \(0.872553\pi\)
\(48\) 0 0
\(49\) 15666.9i 0.932167i
\(50\) 0 0
\(51\) 3600.83i 0.193855i
\(52\) 0 0
\(53\) −8094.04 8094.04i −0.395800 0.395800i 0.480949 0.876749i \(-0.340292\pi\)
−0.876749 + 0.480949i \(0.840292\pi\)
\(54\) 0 0
\(55\) −2665.90 11908.2i −0.118833 0.530812i
\(56\) 0 0
\(57\) 13911.3 13911.3i 0.567126 0.567126i
\(58\) 0 0
\(59\) −41644.1 −1.55748 −0.778742 0.627344i \(-0.784142\pi\)
−0.778742 + 0.627344i \(0.784142\pi\)
\(60\) 0 0
\(61\) 43094.2 1.48284 0.741420 0.671041i \(-0.234153\pi\)
0.741420 + 0.671041i \(0.234153\pi\)
\(62\) 0 0
\(63\) −4273.13 + 4273.13i −0.135642 + 0.135642i
\(64\) 0 0
\(65\) −10190.1 6462.16i −0.299154 0.189712i
\(66\) 0 0
\(67\) −41625.7 41625.7i −1.13285 1.13285i −0.989700 0.143154i \(-0.954276\pi\)
−0.143154 0.989700i \(1.45428\pi\)
\(68\) 0 0
\(69\) 5794.29i 0.146513i
\(70\) 0 0
\(71\) 23788.6i 0.560045i −0.959993 0.280023i \(-0.909658\pi\)
0.959993 0.280023i \(-0.0903419\pi\)
\(72\) 0 0
\(73\) 9336.77 + 9336.77i 0.205064 + 0.205064i 0.802166 0.597102i \(-0.203681\pi\)
−0.597102 + 0.802166i \(0.703681\pi\)
\(74\) 0 0
\(75\) −8454.62 + 23531.9i −0.173556 + 0.483063i
\(76\) 0 0
\(77\) −5211.86 + 5211.86i −0.100177 + 0.100177i
\(78\) 0 0
\(79\) 86090.7 1.55199 0.775994 0.630740i \(-0.217249\pi\)
0.775994 + 0.630740i \(0.217249\pi\)
\(80\) 0 0
\(81\) −16474.8 −0.279002
\(82\) 0 0
\(83\) −75841.2 + 75841.2i −1.20840 + 1.20840i −0.236852 + 0.971546i \(0.576116\pi\)
−0.971546 + 0.236852i \(0.923884\pi\)
\(84\) 0 0
\(85\) −13472.8 + 21245.1i −0.202260 + 0.318942i
\(86\) 0 0
\(87\) 33643.6 + 33643.6i 0.476546 + 0.476546i
\(88\) 0 0
\(89\) 18677.4i 0.249943i −0.992160 0.124971i \(-0.960116\pi\)
0.992160 0.124971i \(-0.0398839\pi\)
\(90\) 0 0
\(91\) 7288.16i 0.0922602i
\(92\) 0 0
\(93\) 17343.8 + 17343.8i 0.207940 + 0.207940i
\(94\) 0 0
\(95\) 134127. 30027.1i 1.52479 0.341354i
\(96\) 0 0
\(97\) −97740.2 + 97740.2i −1.05474 + 1.05474i −0.0563240 + 0.998413i \(0.517938\pi\)
−0.998413 + 0.0563240i \(0.982062\pi\)
\(98\) 0 0
\(99\) −39069.5 −0.400635
\(100\) 0 0
\(101\) −14938.3 −0.145713 −0.0728565 0.997342i \(-0.523211\pi\)
−0.0728565 + 0.997342i \(0.523211\pi\)
\(102\) 0 0
\(103\) 85212.1 85212.1i 0.791422 0.791422i −0.190303 0.981725i \(-0.560947\pi\)
0.981725 + 0.190303i \(0.0609472\pi\)
\(104\) 0 0
\(105\) 14738.1 3299.42i 0.130457 0.0292055i
\(106\) 0 0
\(107\) 78160.1 + 78160.1i 0.659972 + 0.659972i 0.955373 0.295401i \(-0.0954532\pi\)
−0.295401 + 0.955373i \(0.595453\pi\)
\(108\) 0 0
\(109\) 36099.2i 0.291026i 0.989356 + 0.145513i \(0.0464832\pi\)
−0.989356 + 0.145513i \(0.953517\pi\)
\(110\) 0 0
\(111\) 14872.0i 0.114568i
\(112\) 0 0
\(113\) −10180.6 10180.6i −0.0750028 0.0750028i 0.668610 0.743613i \(-0.266889\pi\)
−0.743613 + 0.668610i \(0.766889\pi\)
\(114\) 0 0
\(115\) 21679.8 34186.6i 0.152866 0.241052i
\(116\) 0 0
\(117\) −27317.0 + 27317.0i −0.184488 + 0.184488i
\(118\) 0 0
\(119\) 15194.9 0.0983627
\(120\) 0 0
\(121\) 113399. 0.704117
\(122\) 0 0
\(123\) −34479.5 + 34479.5i −0.205493 + 0.205493i
\(124\) 0 0
\(125\) −137929. + 107206.i −0.789553 + 0.613682i
\(126\) 0 0
\(127\) 88663.6 + 88663.6i 0.487794 + 0.487794i 0.907609 0.419816i \(-0.137905\pi\)
−0.419816 + 0.907609i \(0.637905\pi\)
\(128\) 0 0
\(129\) 21570.7i 0.114127i
\(130\) 0 0
\(131\) 4797.45i 0.0244249i 0.999925 + 0.0122124i \(0.00388744\pi\)
−0.999925 + 0.0122124i \(0.996113\pi\)
\(132\) 0 0
\(133\) −58703.3 58703.3i −0.287762 0.287762i
\(134\) 0 0
\(135\) 159399. + 101084.i 0.752749 + 0.477364i
\(136\) 0 0
\(137\) −149951. + 149951.i −0.682569 + 0.682569i −0.960578 0.278009i \(-0.910325\pi\)
0.278009 + 0.960578i \(0.410325\pi\)
\(138\) 0 0
\(139\) −22452.1 −0.0985642 −0.0492821 0.998785i \(-0.515693\pi\)
−0.0492821 + 0.998785i \(0.515693\pi\)
\(140\) 0 0
\(141\) 91019.9 0.385557
\(142\) 0 0
\(143\) −33318.0 + 33318.0i −0.136251 + 0.136251i
\(144\) 0 0
\(145\) 72618.9 + 324380.i 0.286833 + 1.28125i
\(146\) 0 0
\(147\) 88641.9 + 88641.9i 0.338334 + 0.338334i
\(148\) 0 0
\(149\) 107764.i 0.397656i 0.980034 + 0.198828i \(0.0637135\pi\)
−0.980034 + 0.198828i \(0.936286\pi\)
\(150\) 0 0
\(151\) 140313.i 0.500789i −0.968144 0.250394i \(-0.919440\pi\)
0.968144 0.250394i \(-0.0805603\pi\)
\(152\) 0 0
\(153\) 56952.5 + 56952.5i 0.196691 + 0.196691i
\(154\) 0 0
\(155\) 37436.2 + 167223.i 0.125159 + 0.559070i
\(156\) 0 0
\(157\) −151141. + 151141.i −0.489366 + 0.489366i −0.908106 0.418740i \(-0.862472\pi\)
0.418740 + 0.908106i \(0.362472\pi\)
\(158\) 0 0
\(159\) 91590.5 0.287315
\(160\) 0 0
\(161\) −24451.0 −0.0743415
\(162\) 0 0
\(163\) −126439. + 126439.i −0.372746 + 0.372746i −0.868476 0.495730i \(-0.834900\pi\)
0.495730 + 0.868476i \(0.334900\pi\)
\(164\) 0 0
\(165\) 82459.1 + 52292.3i 0.235792 + 0.149530i
\(166\) 0 0
\(167\) −125948. 125948.i −0.349463 0.349463i 0.510447 0.859909i \(-0.329480\pi\)
−0.859909 + 0.510447i \(0.829480\pi\)
\(168\) 0 0
\(169\) 324702.i 0.874516i
\(170\) 0 0
\(171\) 440055.i 1.15085i
\(172\) 0 0
\(173\) −399318. 399318.i −1.01439 1.01439i −0.999895 0.0144914i \(-0.995387\pi\)
−0.0144914 0.999895i \(-0.504613\pi\)
\(174\) 0 0
\(175\) 99300.8 + 35677.1i 0.245108 + 0.0880632i
\(176\) 0 0
\(177\) 235618. 235618.i 0.565296 0.565296i
\(178\) 0 0
\(179\) −457843. −1.06803 −0.534016 0.845474i \(-0.679318\pi\)
−0.534016 + 0.845474i \(0.679318\pi\)
\(180\) 0 0
\(181\) 625293. 1.41869 0.709344 0.704863i \(-0.248991\pi\)
0.709344 + 0.704863i \(0.248991\pi\)
\(182\) 0 0
\(183\) −243823. + 243823.i −0.538204 + 0.538204i
\(184\) 0 0
\(185\) −55644.8 + 87745.7i −0.119535 + 0.188494i
\(186\) 0 0
\(187\) 69463.9 + 69463.9i 0.145263 + 0.145263i
\(188\) 0 0
\(189\) 114005.i 0.232151i
\(190\) 0 0
\(191\) 426964.i 0.846853i −0.905930 0.423426i \(-0.860827\pi\)
0.905930 0.423426i \(-0.139173\pi\)
\(192\) 0 0
\(193\) −519101. 519101.i −1.00313 1.00313i −0.999995 0.00313800i \(-0.999001\pi\)
−0.00313800 0.999995i \(-0.500999\pi\)
\(194\) 0 0
\(195\) 94216.8 21092.3i 0.177436 0.0397226i
\(196\) 0 0
\(197\) 645637. 645637.i 1.18529 1.18529i 0.206930 0.978356i \(-0.433653\pi\)
0.978356 0.206930i \(-0.0663472\pi\)
\(198\) 0 0
\(199\) −824647. −1.47617 −0.738083 0.674710i \(-0.764269\pi\)
−0.738083 + 0.674710i \(0.764269\pi\)
\(200\) 0 0
\(201\) 471028. 0.822349
\(202\) 0 0
\(203\) 141971. 141971.i 0.241801 0.241801i
\(204\) 0 0
\(205\) −332438. + 74423.0i −0.552492 + 0.123687i
\(206\) 0 0
\(207\) −91645.4 91645.4i −0.148657 0.148657i
\(208\) 0 0
\(209\) 536727.i 0.849939i
\(210\) 0 0
\(211\) 1.27068e6i 1.96485i −0.186670 0.982423i \(-0.559769\pi\)
0.186670 0.982423i \(-0.440231\pi\)
\(212\) 0 0
\(213\) 134594. + 134594.i 0.203271 + 0.203271i
\(214\) 0 0
\(215\) 80708.4 127268.i 0.119076 0.187769i
\(216\) 0 0
\(217\) 73188.1 73188.1i 0.105509 0.105509i
\(218\) 0 0
\(219\) −105653. −0.148858
\(220\) 0 0
\(221\) 97136.9 0.133784
\(222\) 0 0
\(223\) −946335. + 946335.i −1.27433 + 1.27433i −0.330540 + 0.943792i \(0.607231\pi\)
−0.943792 + 0.330540i \(0.892769\pi\)
\(224\) 0 0
\(225\) 238470. + 505915.i 0.314034 + 0.666225i
\(226\) 0 0
\(227\) 751480. + 751480.i 0.967950 + 0.967950i 0.999502 0.0315523i \(-0.0100451\pi\)
−0.0315523 + 0.999502i \(0.510045\pi\)
\(228\) 0 0
\(229\) 792900.i 0.999147i −0.866271 0.499574i \(-0.833490\pi\)
0.866271 0.499574i \(-0.166510\pi\)
\(230\) 0 0
\(231\) 58976.4i 0.0727190i
\(232\) 0 0
\(233\) −310134. 310134.i −0.374248 0.374248i 0.494774 0.869022i \(-0.335251\pi\)
−0.869022 + 0.494774i \(0.835251\pi\)
\(234\) 0 0
\(235\) 537022. + 340558.i 0.634341 + 0.402274i
\(236\) 0 0
\(237\) −487092. + 487092.i −0.563301 + 0.563301i
\(238\) 0 0
\(239\) −1.36178e6 −1.54210 −0.771048 0.636777i \(-0.780267\pi\)
−0.771048 + 0.636777i \(0.780267\pi\)
\(240\) 0 0
\(241\) 77351.9 0.0857883 0.0428942 0.999080i \(-0.486342\pi\)
0.0428942 + 0.999080i \(0.486342\pi\)
\(242\) 0 0
\(243\) 673375. 673375.i 0.731546 0.731546i
\(244\) 0 0
\(245\) 191331. + 854653.i 0.203644 + 0.909651i
\(246\) 0 0
\(247\) −375274. 375274.i −0.391387 0.391387i
\(248\) 0 0
\(249\) 858204.i 0.877187i
\(250\) 0 0
\(251\) 312063.i 0.312649i −0.987706 0.156325i \(-0.950035\pi\)
0.987706 0.156325i \(-0.0499646\pi\)
\(252\) 0 0
\(253\) −111778. 111778.i −0.109788 0.109788i
\(254\) 0 0
\(255\) −43974.9 196430.i −0.0423501 0.189173i
\(256\) 0 0
\(257\) −981036. + 981036.i −0.926514 + 0.926514i −0.997479 0.0709649i \(-0.977392\pi\)
0.0709649 + 0.997479i \(0.477392\pi\)
\(258\) 0 0
\(259\) 62757.5 0.0581321
\(260\) 0 0
\(261\) 1.06425e6 0.967035
\(262\) 0 0
\(263\) −1.26719e6 + 1.26719e6i −1.12968 + 1.12968i −0.139446 + 0.990230i \(0.544532\pi\)
−0.990230 + 0.139446i \(0.955468\pi\)
\(264\) 0 0
\(265\) 540389. + 342693.i 0.472707 + 0.299772i
\(266\) 0 0
\(267\) 105675. + 105675.i 0.0907178 + 0.0907178i
\(268\) 0 0
\(269\) 396279.i 0.333903i −0.985965 0.166951i \(-0.946608\pi\)
0.985965 0.166951i \(-0.0533923\pi\)
\(270\) 0 0
\(271\) 490416.i 0.405640i −0.979216 0.202820i \(-0.934989\pi\)
0.979216 0.202820i \(-0.0650107\pi\)
\(272\) 0 0
\(273\) −41235.7 41235.7i −0.0334863 0.0334863i
\(274\) 0 0
\(275\) 290857. + 617055.i 0.231925 + 0.492030i
\(276\) 0 0
\(277\) 130834. 130834.i 0.102452 0.102452i −0.654023 0.756475i \(-0.726920\pi\)
0.756475 + 0.654023i \(0.226920\pi\)
\(278\) 0 0
\(279\) 548637. 0.421963
\(280\) 0 0
\(281\) 1.58558e6 1.19790 0.598952 0.800785i \(-0.295584\pi\)
0.598952 + 0.800785i \(0.295584\pi\)
\(282\) 0 0
\(283\) 269779. 269779.i 0.200236 0.200236i −0.599865 0.800101i \(-0.704779\pi\)
0.800101 + 0.599865i \(0.204779\pi\)
\(284\) 0 0
\(285\) −588989. + 928770.i −0.429532 + 0.677323i
\(286\) 0 0
\(287\) 145498. + 145498.i 0.104268 + 0.104268i
\(288\) 0 0
\(289\) 1.21734e6i 0.857367i
\(290\) 0 0
\(291\) 1.10601e6i 0.765643i
\(292\) 0 0
\(293\) −1.67347e6 1.67347e6i −1.13880 1.13880i −0.988665 0.150135i \(-0.952029\pi\)
−0.150135 0.988665i \(-0.547971\pi\)
\(294\) 0 0
\(295\) 2.27175e6 508576.i 1.51986 0.340252i
\(296\) 0 0
\(297\) 521177. 521177.i 0.342842 0.342842i
\(298\) 0 0
\(299\) −156308. −0.101112
\(300\) 0 0
\(301\) −91024.7 −0.0579086
\(302\) 0 0
\(303\) 84519.5 84519.5i 0.0528872 0.0528872i
\(304\) 0 0
\(305\) −2.35085e6 + 526285.i −1.44702 + 0.323945i
\(306\) 0 0
\(307\) 1.87184e6 + 1.87184e6i 1.13350 + 1.13350i 0.989590 + 0.143914i \(0.0459689\pi\)
0.143914 + 0.989590i \(0.454031\pi\)
\(308\) 0 0
\(309\) 964243.i 0.574500i
\(310\) 0 0
\(311\) 2.01273e6i 1.18001i 0.807400 + 0.590005i \(0.200874\pi\)
−0.807400 + 0.590005i \(0.799126\pi\)
\(312\) 0 0
\(313\) 1.09008e6 + 1.09008e6i 0.628921 + 0.628921i 0.947797 0.318876i \(-0.103305\pi\)
−0.318876 + 0.947797i \(0.603305\pi\)
\(314\) 0 0
\(315\) 180920. 285291.i 0.102733 0.161999i
\(316\) 0 0
\(317\) −2.18740e6 + 2.18740e6i −1.22259 + 1.22259i −0.255877 + 0.966709i \(0.582364\pi\)
−0.966709 + 0.255877i \(0.917636\pi\)
\(318\) 0 0
\(319\) 1.29804e6 0.714188
\(320\) 0 0
\(321\) −884444. −0.479080
\(322\) 0 0
\(323\) −782400. + 782400.i −0.417275 + 0.417275i
\(324\) 0 0
\(325\) 634803. + 228074.i 0.333373 + 0.119775i
\(326\) 0 0
\(327\) −204246. 204246.i −0.105629 0.105629i
\(328\) 0 0
\(329\) 384089.i 0.195633i
\(330\) 0 0
\(331\) 1.45657e6i 0.730738i −0.930863 0.365369i \(-0.880943\pi\)
0.930863 0.365369i \(-0.119057\pi\)
\(332\) 0 0
\(333\) 235223. + 235223.i 0.116244 + 0.116244i
\(334\) 0 0
\(335\) 2.77909e6 + 1.76239e6i 1.35298 + 0.858004i
\(336\) 0 0
\(337\) −1.63889e6 + 1.63889e6i −0.786096 + 0.786096i −0.980852 0.194756i \(-0.937609\pi\)
0.194756 + 0.980852i \(0.437609\pi\)
\(338\) 0 0
\(339\) 115202. 0.0544452
\(340\) 0 0
\(341\) 669162. 0.311634
\(342\) 0 0
\(343\) 775328. 775328.i 0.355836 0.355836i
\(344\) 0 0
\(345\) 70762.3 + 316087.i 0.0320077 + 0.142974i
\(346\) 0 0
\(347\) 1.26972e6 + 1.26972e6i 0.566087 + 0.566087i 0.931030 0.364943i \(-0.118912\pi\)
−0.364943 + 0.931030i \(0.618912\pi\)
\(348\) 0 0
\(349\) 26961.5i 0.0118490i −0.999982 0.00592449i \(-0.998114\pi\)
0.999982 0.00592449i \(-0.00188584\pi\)
\(350\) 0 0
\(351\) 728804.i 0.315750i
\(352\) 0 0
\(353\) −1.76514e6 1.76514e6i −0.753949 0.753949i 0.221265 0.975214i \(-0.428981\pi\)
−0.975214 + 0.221265i \(0.928981\pi\)
\(354\) 0 0
\(355\) 290516. + 1.29770e6i 0.122349 + 0.546517i
\(356\) 0 0
\(357\) −85971.3 + 85971.3i −0.0357012 + 0.0357012i
\(358\) 0 0
\(359\) 1.46738e6 0.600905 0.300453 0.953797i \(-0.402862\pi\)
0.300453 + 0.953797i \(0.402862\pi\)
\(360\) 0 0
\(361\) 3.56928e6 1.44149
\(362\) 0 0
\(363\) −641599. + 641599.i −0.255562 + 0.255562i
\(364\) 0 0
\(365\) −623359. 395310.i −0.244910 0.155312i
\(366\) 0 0
\(367\) −3.11806e6 3.11806e6i −1.20842 1.20842i −0.971537 0.236886i \(-0.923873\pi\)
−0.236886 0.971537i \(1.42387\pi\)
\(368\) 0 0
\(369\) 1.09069e6i 0.416999i
\(370\) 0 0
\(371\) 386497.i 0.145785i
\(372\) 0 0
\(373\) 2.88408e6 + 2.88408e6i 1.07333 + 1.07333i 0.997089 + 0.0762441i \(0.0242928\pi\)
0.0762441 + 0.997089i \(0.475707\pi\)
\(374\) 0 0
\(375\) 173830. 1.38695e6i 0.0638331 0.509311i
\(376\) 0 0
\(377\) 907580. 907580.i 0.328875 0.328875i
\(378\) 0 0
\(379\) −2.02320e6 −0.723505 −0.361753 0.932274i \(-0.617821\pi\)
−0.361753 + 0.932274i \(0.617821\pi\)
\(380\) 0 0
\(381\) −1.00330e6 −0.354094
\(382\) 0 0
\(383\) −2.69527e6 + 2.69527e6i −0.938871 + 0.938871i −0.998236 0.0593656i \(-0.981092\pi\)
0.0593656 + 0.998236i \(0.481092\pi\)
\(384\) 0 0
\(385\) 220665. 347964.i 0.0758720 0.119642i
\(386\) 0 0
\(387\) −341172. 341172.i −0.115797 0.115797i
\(388\) 0 0
\(389\) 4.00903e6i 1.34328i −0.740880 0.671638i \(-0.765591\pi\)
0.740880 0.671638i \(-0.234409\pi\)
\(390\) 0 0
\(391\) 325883.i 0.107800i
\(392\) 0 0
\(393\) −27143.5 27143.5i −0.00886512 0.00886512i
\(394\) 0 0
\(395\) −4.69637e6 + 1.05138e6i −1.51450 + 0.339051i
\(396\) 0 0
\(397\) 107569. 107569.i 0.0342541 0.0342541i −0.689772 0.724026i \(-0.742289\pi\)
0.724026 + 0.689772i \(0.242289\pi\)
\(398\) 0 0
\(399\) 664275. 0.208889
\(400\) 0 0
\(401\) −3.65913e6 −1.13636 −0.568182 0.822903i \(-0.692353\pi\)
−0.568182 + 0.822903i \(0.692353\pi\)
\(402\) 0 0
\(403\) 467872. 467872.i 0.143504 0.143504i
\(404\) 0 0
\(405\) 898722. 201197.i 0.272262 0.0609514i
\(406\) 0 0
\(407\) 286897. + 286897.i 0.0858500 + 0.0858500i
\(408\) 0 0
\(409\) 297521.i 0.0879445i −0.999033 0.0439723i \(-0.985999\pi\)
0.999033 0.0439723i \(-0.0140013\pi\)
\(410\) 0 0
\(411\) 1.69681e6i 0.495483i
\(412\) 0 0
\(413\) −994270. 994270.i −0.286833 0.286833i
\(414\) 0 0
\(415\) 3.21104e6 5.06345e6i 0.915220 1.44320i
\(416\) 0 0
\(417\) 127032. 127032.i 0.0357743 0.0357743i
\(418\) 0 0
\(419\) −6.52109e6 −1.81462 −0.907309 0.420464i \(-0.861867\pi\)
−0.907309 + 0.420464i \(0.861867\pi\)
\(420\) 0 0
\(421\) 4.57043e6 1.25676 0.628379 0.777907i \(-0.283719\pi\)
0.628379 + 0.777907i \(0.283719\pi\)
\(422\) 0 0
\(423\) 1.43962e6 1.43962e6i 0.391197 0.391197i
\(424\) 0 0
\(425\) 475506. 1.32348e6i 0.127698 0.355424i
\(426\) 0 0
\(427\) 1.02889e6 + 1.02889e6i 0.273087 + 0.273087i
\(428\) 0 0
\(429\) 377020.i 0.0989056i
\(430\) 0 0
\(431\) 4.64706e6i 1.20499i 0.798121 + 0.602497i \(0.205827\pi\)
−0.798121 + 0.602497i \(0.794173\pi\)
\(432\) 0 0
\(433\) −1.28765e6 1.28765e6i −0.330049 0.330049i 0.522556 0.852605i \(-0.324979\pi\)
−0.852605 + 0.522556i \(0.824979\pi\)
\(434\) 0 0
\(435\) −2.24618e6 1.42444e6i −0.569143 0.360928i
\(436\) 0 0
\(437\) 1.25900e6 1.25900e6i 0.315372 0.315372i
\(438\) 0 0
\(439\) 2.49221e6 0.617196 0.308598 0.951193i \(-0.400140\pi\)
0.308598 + 0.951193i \(0.400140\pi\)
\(440\) 0 0
\(441\) 2.80401e6 0.686567
\(442\) 0 0
\(443\) −108531. + 108531.i −0.0262751 + 0.0262751i −0.720122 0.693847i \(-0.755914\pi\)
0.693847 + 0.720122i \(0.255914\pi\)
\(444\) 0 0
\(445\) 228096. + 1.01888e6i 0.0546031 + 0.243905i
\(446\) 0 0
\(447\) −609717. 609717.i −0.144331 0.144331i
\(448\) 0 0
\(449\) 1.27740e6i 0.299029i −0.988760 0.149514i \(-0.952229\pi\)
0.988760 0.149514i \(-0.0477710\pi\)
\(450\) 0 0
\(451\) 1.33029e6i 0.307968i
\(452\) 0 0
\(453\) 793875. + 793875.i 0.181764 + 0.181764i
\(454\) 0 0
\(455\) −89006.2 397580.i −0.0201554 0.0900317i
\(456\) 0 0
\(457\) 4.12352e6 4.12352e6i 0.923586 0.923586i −0.0736949 0.997281i \(-0.523479\pi\)
0.997281 + 0.0736949i \(0.0234791\pi\)
\(458\) 0 0
\(459\) −1.51946e6 −0.336635
\(460\) 0 0
\(461\) −8.86506e6 −1.94280 −0.971402 0.237439i \(-0.923692\pi\)
−0.971402 + 0.237439i \(0.923692\pi\)
\(462\) 0 0
\(463\) 3.00796e6 3.00796e6i 0.652108 0.652108i −0.301392 0.953500i \(-0.597451\pi\)
0.953500 + 0.301392i \(0.0974513\pi\)
\(464\) 0 0
\(465\) −1.15794e6 734320.i −0.248344 0.157490i
\(466\) 0 0
\(467\) −2.19836e6 2.19836e6i −0.466452 0.466452i 0.434311 0.900763i \(-0.356992\pi\)
−0.900763 + 0.434311i \(0.856992\pi\)
\(468\) 0 0
\(469\) 1.98766e6i 0.417263i
\(470\) 0 0
\(471\) 1.71028e6i 0.355235i
\(472\) 0 0
\(473\) −416122. 416122.i −0.0855199 0.0855199i
\(474\) 0 0
\(475\) −6.95014e6 + 3.27604e6i −1.41338 + 0.666217i
\(476\) 0 0
\(477\) 1.44864e6 1.44864e6i 0.291518 0.291518i
\(478\) 0 0
\(479\) 3.12528e6 0.622372 0.311186 0.950349i \(-0.399274\pi\)
0.311186 + 0.950349i \(0.399274\pi\)
\(480\) 0 0
\(481\) 401191. 0.0790659
\(482\) 0 0
\(483\) 138341. 138341.i 0.0269826 0.0269826i
\(484\) 0 0
\(485\) 4.13822e6 6.52551e6i 0.798839 1.25968i
\(486\) 0 0
\(487\) −5.74900e6 5.74900e6i −1.09842 1.09842i −0.994595 0.103828i \(-0.966891\pi\)
−0.103828 0.994595i \(1.46689\pi\)
\(488\) 0 0
\(489\) 1.43076e6i 0.270580i
\(490\) 0 0
\(491\) 1.06215e6i 0.198830i −0.995046 0.0994149i \(-0.968303\pi\)
0.995046 0.0994149i \(-0.0316971\pi\)
\(492\) 0 0
\(493\) −1.89219e6 1.89219e6i −0.350629 0.350629i
\(494\) 0 0
\(495\) 2.13129e6 477133.i 0.390958 0.0875238i
\(496\) 0 0
\(497\) 567963. 567963.i 0.103140 0.103140i
\(498\) 0 0
\(499\) −1.96563e6 −0.353386 −0.176693 0.984266i \(-0.556540\pi\)
−0.176693 + 0.984266i \(0.556540\pi\)
\(500\) 0 0
\(501\) 1.42520e6 0.253678
\(502\) 0 0
\(503\) −4.00724e6 + 4.00724e6i −0.706196 + 0.706196i −0.965733 0.259537i \(-0.916430\pi\)
0.259537 + 0.965733i \(0.416430\pi\)
\(504\) 0 0
\(505\) 814906. 182433.i 0.142193 0.0318328i
\(506\) 0 0
\(507\) 1.83713e6 + 1.83713e6i 0.317410 + 0.317410i
\(508\) 0 0
\(509\) 4.63858e6i 0.793580i 0.917909 + 0.396790i \(0.129876\pi\)
−0.917909 + 0.396790i \(0.870124\pi\)
\(510\) 0 0
\(511\) 445839.i 0.0755310i
\(512\) 0 0
\(513\) 5.87023e6 + 5.87023e6i 0.984831 + 0.984831i
\(514\) 0 0
\(515\) −3.60779e6 + 5.68909e6i −0.599409 + 0.945201i
\(516\) 0 0
\(517\) 1.75587e6 1.75587e6i 0.288913 0.288913i
\(518\) 0 0
\(519\) 4.51860e6 0.736352
\(520\) 0 0
\(521\) −6.43145e6 −1.03804 −0.519021 0.854762i \(-0.673703\pi\)
−0.519021 + 0.854762i \(0.673703\pi\)
\(522\) 0 0
\(523\) 7.62526e6 7.62526e6i 1.21899 1.21899i 0.251006 0.967986i \(-0.419239\pi\)
0.967986 0.251006i \(-0.0807613\pi\)
\(524\) 0 0
\(525\) −763691. + 359976.i −0.120926 + 0.0570001i
\(526\) 0 0
\(527\) −975454. 975454.i −0.152996 0.152996i
\(528\) 0 0
\(529\) 5.91195e6i 0.918526i
\(530\) 0 0
\(531\) 7.45331e6i 1.14713i
\(532\) 0 0
\(533\) 930127. + 930127.i 0.141816 + 0.141816i
\(534\) 0 0
\(535\) −5.21827e6 3.30922e6i −0.788210 0.499852i
\(536\) 0 0
\(537\) 2.59043e6 2.59043e6i 0.387647 0.387647i
\(538\) 0 0
\(539\) 3.42000e6 0.507053
\(540\) 0 0
\(541\) −7.69592e6 −1.13049 −0.565246 0.824923i \(-0.691219\pi\)
−0.565246 + 0.824923i \(0.691219\pi\)
\(542\) 0 0
\(543\) −3.53784e6 + 3.53784e6i −0.514919 + 0.514919i
\(544\) 0 0
\(545\) −440859. 1.96926e6i −0.0635782 0.283996i
\(546\) 0 0
\(547\) 8.31090e6 + 8.31090e6i 1.18763 + 1.18763i 0.977722 + 0.209904i \(0.0673150\pi\)
0.209904 + 0.977722i \(0.432685\pi\)
\(548\) 0 0
\(549\) 7.71285e6i 1.09215i
\(550\) 0 0
\(551\) 1.46204e7i 2.05154i
\(552\) 0 0
\(553\) 2.05545e6 + 2.05545e6i 0.285821 + 0.285821i
\(554\) 0 0
\(555\) −181623. 811289.i −0.0250288 0.111800i
\(556\) 0 0
\(557\) −2.90207e6 + 2.90207e6i −0.396341 + 0.396341i −0.876940 0.480599i \(-0.840419\pi\)
0.480599 + 0.876940i \(0.340419\pi\)
\(558\) 0 0
\(559\) −581896. −0.0787619
\(560\) 0 0
\(561\) −786039. −0.105448
\(562\) 0 0
\(563\) 7.08912e6 7.08912e6i 0.942586 0.942586i −0.0558525 0.998439i \(-0.517788\pi\)
0.998439 + 0.0558525i \(0.0177877\pi\)
\(564\) 0 0
\(565\) 679697. + 431037.i 0.0895765 + 0.0568059i
\(566\) 0 0
\(567\) −393342. 393342.i −0.0513822 0.0513822i
\(568\) 0 0
\(569\) 1.02793e7i 1.33102i 0.746389 + 0.665509i \(0.231786\pi\)
−0.746389 + 0.665509i \(0.768214\pi\)
\(570\) 0 0
\(571\) 9.92423e6i 1.27382i 0.770940 + 0.636908i \(0.219787\pi\)
−0.770940 + 0.636908i \(0.780213\pi\)
\(572\) 0 0
\(573\) 2.41572e6 + 2.41572e6i 0.307369 + 0.307369i
\(574\) 0 0
\(575\) −765162. + 2.12969e6i −0.0965126 + 0.268625i
\(576\) 0 0
\(577\) −7.82091e6 + 7.82091e6i −0.977953 + 0.977953i −0.999762 0.0218096i \(-0.993057\pi\)
0.0218096 + 0.999762i \(0.493057\pi\)
\(578\) 0 0
\(579\) 5.87404e6 0.728183
\(580\) 0 0
\(581\) −3.62148e6 −0.445088
\(582\) 0 0
\(583\) 1.76688e6 1.76688e6i 0.215296 0.215296i
\(584\) 0 0
\(585\) 1.15657e6 1.82379e6i 0.139728 0.220335i
\(586\) 0 0
\(587\) 4.94337e6 + 4.94337e6i 0.592144 + 0.592144i 0.938210 0.346066i \(-0.112483\pi\)
−0.346066 + 0.938210i \(0.612483\pi\)
\(588\) 0 0
\(589\) 7.53705e6i 0.895185i
\(590\) 0 0
\(591\) 7.30590e6i 0.860409i
\(592\) 0 0
\(593\) −5.40438e6 5.40438e6i −0.631116 0.631116i 0.317232 0.948348i \(-0.397247\pi\)
−0.948348 + 0.317232i \(0.897247\pi\)
\(594\) 0 0
\(595\) −828904. + 185567.i −0.0959868 + 0.0214886i
\(596\) 0 0
\(597\) 4.66577e6 4.66577e6i 0.535781 0.535781i
\(598\) 0 0
\(599\) 3.02994e6 0.345039 0.172519 0.985006i \(-0.444809\pi\)
0.172519 + 0.985006i \(0.444809\pi\)
\(600\) 0 0
\(601\) −8.33982e6 −0.941825 −0.470913 0.882180i \(-0.656075\pi\)
−0.470913 + 0.882180i \(0.656075\pi\)
\(602\) 0 0
\(603\) 7.45001e6 7.45001e6i 0.834379 0.834379i
\(604\) 0 0
\(605\) −6.18606e6 + 1.38487e6i −0.687109 + 0.153823i
\(606\) 0 0
\(607\) −4.99673e6 4.99673e6i −0.550445 0.550445i 0.376124 0.926569i \(-0.377257\pi\)
−0.926569 + 0.376124i \(0.877257\pi\)
\(608\) 0 0
\(609\) 1.60651e6i 0.175526i
\(610\) 0 0
\(611\) 2.45538e6i 0.266082i
\(612\) 0 0
\(613\) 3.24993e6 + 3.24993e6i 0.349320 + 0.349320i 0.859856 0.510536i \(-0.170553\pi\)
−0.510536 + 0.859856i \(0.670553\pi\)
\(614\) 0 0
\(615\) 1.45982e6 2.30198e6i 0.155637 0.245422i
\(616\) 0 0
\(617\) 1.74236e6 1.74236e6i 0.184258 0.184258i −0.608951 0.793208i \(-0.708409\pi\)
0.793208 + 0.608951i \(0.208409\pi\)
\(618\) 0 0
\(619\) 1.08664e7 1.13988 0.569941 0.821686i \(-0.306966\pi\)
0.569941 + 0.821686i \(0.306966\pi\)
\(620\) 0 0
\(621\) 2.44505e6 0.254425
\(622\) 0 0
\(623\) 445929. 445929.i 0.0460305 0.0460305i
\(624\) 0 0
\(625\) 6.21499e6 7.53268e6i 0.636415 0.771347i
\(626\) 0 0
\(627\) 3.03675e6 + 3.03675e6i 0.308489 + 0.308489i
\(628\) 0 0
\(629\) 836434.i 0.0842956i
\(630\) 0 0
\(631\) 6.31541e6i 0.631434i 0.948853 + 0.315717i \(0.102245\pi\)
−0.948853 + 0.315717i \(0.897755\pi\)
\(632\) 0 0
\(633\) 7.18935e6 + 7.18935e6i 0.713149 + 0.713149i
\(634\) 0 0
\(635\) −5.91952e6 3.75393e6i −0.582576 0.369447i
\(636\) 0 0
\(637\) 2.39123e6 2.39123e6i 0.233492 0.233492i
\(638\) 0 0
\(639\) 4.25760e6 0.412489
\(640\) 0 0
\(641\) −1.01885e7 −0.979408 −0.489704 0.871889i \(-0.662895\pi\)
−0.489704 + 0.871889i \(0.662895\pi\)
\(642\) 0 0
\(643\) 1.11631e6 1.11631e6i 0.106478 0.106478i −0.651861 0.758339i \(-0.726011\pi\)
0.758339 + 0.651861i \(0.226011\pi\)
\(644\) 0 0
\(645\) 263430. + 1.17671e6i 0.0249325 + 0.111371i
\(646\) 0 0
\(647\) −1.08225e7 1.08225e7i −1.01640 1.01640i −0.999863 0.0165382i \(-0.994735\pi\)
−0.0165382 0.999863i \(1.49474\pi\)
\(648\) 0 0
\(649\) 9.09066e6i 0.847196i
\(650\) 0 0
\(651\) 828182.i 0.0765902i
\(652\) 0 0
\(653\) 5.19640e6 + 5.19640e6i 0.476892 + 0.476892i 0.904136 0.427244i \(-0.140516\pi\)
−0.427244 + 0.904136i \(0.640516\pi\)
\(654\) 0 0
\(655\) −58588.5 261708.i −0.00533592 0.0238349i
\(656\) 0 0
\(657\) −1.67106e6 + 1.67106e6i −0.151035 + 0.151035i
\(658\) 0 0
\(659\) 5.17149e6 0.463876 0.231938 0.972731i \(-0.425493\pi\)
0.231938 + 0.972731i \(0.425493\pi\)
\(660\) 0 0
\(661\) −8.28147e6 −0.737231 −0.368616 0.929582i \(-0.620168\pi\)
−0.368616 + 0.929582i \(0.620168\pi\)
\(662\) 0 0
\(663\) −549591. + 549591.i −0.0485574 + 0.0485574i
\(664\) 0 0
\(665\) 3.91926e6 + 2.48544e6i 0.343676 + 0.217946i
\(666\) 0 0
\(667\) 3.04483e6 + 3.04483e6i 0.265001 + 0.265001i
\(668\) 0 0
\(669\) 1.07085e7i 0.925049i
\(670\) 0 0
\(671\) 9.40721e6i 0.806593i
\(672\) 0 0
\(673\) 3.42754e6 + 3.42754e6i 0.291706 + 0.291706i 0.837754 0.546048i \(-0.183868\pi\)
−0.546048 + 0.837754i \(0.683868\pi\)
\(674\) 0 0
\(675\) −9.92991e6 3.56765e6i −0.838853 0.301386i
\(676\) 0 0
\(677\) −8.26736e6 + 8.26736e6i −0.693258 + 0.693258i −0.962947 0.269689i \(-0.913079\pi\)
0.269689 + 0.962947i \(0.413079\pi\)
\(678\) 0 0
\(679\) −4.66718e6 −0.388490
\(680\) 0 0
\(681\) −8.50360e6 −0.702643
\(682\) 0 0
\(683\) 3.18611e6 3.18611e6i 0.261342 0.261342i −0.564257 0.825599i \(-0.690837\pi\)
0.825599 + 0.564257i \(0.190837\pi\)
\(684\) 0 0
\(685\) 6.34876e6 1.00113e7i 0.516966 0.815198i
\(686\) 0 0
\(687\) 4.48615e6 + 4.48615e6i 0.362645 + 0.362645i
\(688\) 0 0
\(689\) 2.47077e6i 0.198283i
\(690\) 0 0
\(691\) 1.80913e6i 0.144137i −0.997400 0.0720685i \(-0.977040\pi\)
0.997400 0.0720685i \(-0.0229600\pi\)
\(692\) 0 0
\(693\) −932799. 932799.i −0.0737828 0.0737828i
\(694\) 0 0
\(695\) 1.22479e6 274194.i 0.0961834 0.0215326i
\(696\) 0 0
\(697\) 1.93920e6 1.93920e6i 0.151196 0.151196i
\(698\) 0 0
\(699\) 3.50941e6 0.271670
\(700\) 0 0
\(701\) 8.47023e6 0.651029 0.325514 0.945537i \(-0.394463\pi\)
0.325514 + 0.945537i \(0.394463\pi\)
\(702\) 0 0
\(703\) −3.23144e6 + 3.23144e6i −0.246608 + 0.246608i
\(704\) 0 0
\(705\) −4.96526e6 + 1.11157e6i −0.376244 + 0.0842297i
\(706\) 0 0
\(707\) −356658. 356658.i −0.0268351 0.0268351i
\(708\) 0 0
\(709\) 1.88589e7i 1.40896i 0.709722 + 0.704482i \(0.248821\pi\)
−0.709722 + 0.704482i \(0.751179\pi\)
\(710\) 0 0
\(711\) 1.54082e7i 1.14308i
\(712\) 0 0
\(713\) 1.56966e6 + 1.56966e6i 0.115633 + 0.115633i
\(714\) 0 0
\(715\) 1.41065e6 2.22444e6i 0.103194 0.162725i
\(716\) 0 0
\(717\) 7.70480e6 7.70480e6i 0.559711 0.559711i
\(718\) 0 0
\(719\) −1.02992e7 −0.742989 −0.371495 0.928435i \(-0.621155\pi\)
−0.371495 + 0.928435i \(0.621155\pi\)
\(720\) 0 0
\(721\) 4.06895e6 0.291504
\(722\) 0 0
\(723\) −437649. + 437649.i −0.0311373 + 0.0311373i
\(724\) 0 0
\(725\) −7.92293e6 1.68085e7i −0.559810 1.18764i
\(726\) 0 0
\(727\) −1.33721e7 1.33721e7i −0.938346 0.938346i 0.0598611 0.998207i \(-0.480934\pi\)
−0.998207 + 0.0598611i \(0.980934\pi\)
\(728\) 0 0
\(729\) 3.61641e6i 0.252034i
\(730\) 0 0
\(731\) 1.21318e6i 0.0839715i
\(732\) 0 0
\(733\) 1.34325e6 + 1.34325e6i 0.0923418 + 0.0923418i 0.751769 0.659427i \(-0.229201\pi\)
−0.659427 + 0.751769i \(0.729201\pi\)
\(734\) 0 0
\(735\) −5.91808e6 3.75301e6i −0.404075 0.256248i
\(736\) 0 0
\(737\) 9.08663e6 9.08663e6i 0.616218 0.616218i
\(738\) 0 0
\(739\) −3.77236e6 −0.254099 −0.127049 0.991896i \(-0.540551\pi\)
−0.127049 + 0.991896i \(0.540551\pi\)
\(740\) 0 0
\(741\) 4.24653e6 0.284111
\(742\) 0 0
\(743\) −4.63047e6 + 4.63047e6i −0.307718 + 0.307718i −0.844024 0.536306i \(-0.819819\pi\)
0.536306 + 0.844024i \(0.319819\pi\)
\(744\) 0 0
\(745\) −1.31606e6 5.87867e6i −0.0868729 0.388051i
\(746\) 0 0
\(747\) −1.35738e7 1.35738e7i −0.890019 0.890019i
\(748\) 0 0
\(749\) 3.73221e6i 0.243087i
\(750\) 0 0
\(751\) 2.08661e7i 1.35002i −0.737807 0.675012i \(-0.764138\pi\)
0.737807 0.675012i \(-0.235862\pi\)
\(752\) 0 0
\(753\) 1.76562e6 + 1.76562e6i 0.113477 + 0.113477i
\(754\) 0 0
\(755\) 1.71356e6 + 7.65426e6i 0.109404 + 0.488692i
\(756\) 0 0
\(757\) −964426. + 964426.i −0.0611687 + 0.0611687i −0.737029 0.675861i \(-0.763772\pi\)
0.675861 + 0.737029i \(0.263772\pi\)
\(758\) 0 0
\(759\) 1.26486e6 0.0796962
\(760\) 0 0
\(761\) 1.49933e7 0.938505 0.469252 0.883064i \(-0.344523\pi\)
0.469252 + 0.883064i \(0.344523\pi\)
\(762\) 0 0
\(763\) −861883. + 861883.i −0.0535966 + 0.0535966i
\(764\) 0 0
\(765\) −3.80237e6 2.41131e6i −0.234909 0.148970i
\(766\) 0 0
\(767\) −6.35610e6 6.35610e6i −0.390124 0.390124i
\(768\) 0 0
\(769\) 4.51581e6i 0.275372i −0.990476 0.137686i \(-0.956034\pi\)
0.990476 0.137686i \(-0.0439664\pi\)
\(770\) 0 0
\(771\) 1.11012e7i 0.672565i
\(772\) 0 0
\(773\) −1.29303e7 1.29303e7i −0.778320 0.778320i 0.201225 0.979545i \(-0.435508\pi\)
−0.979545 + 0.201225i \(0.935508\pi\)
\(774\) 0 0
\(775\) −4.08439e6 8.66505e6i −0.244272 0.518223i
\(776\) 0 0
\(777\) −355075. + 355075.i −0.0210993 + 0.0210993i
\(778\) 0 0
\(779\) −1.49836e7 −0.884653
\(780\) 0 0
\(781\) 5.19291e6 0.304637
\(782\) 0 0
\(783\) −1.41968e7 + 1.41968e7i −0.827536 + 0.827536i
\(784\) 0 0
\(785\) 6.39917e6 1.00908e7i 0.370637 0.584454i
\(786\) 0 0
\(787\) 3.11176e6 + 3.11176e6i 0.179089 + 0.179089i 0.790959 0.611869i \(-0.209582\pi\)
−0.611869 + 0.790959i \(0.709582\pi\)
\(788\) 0 0
\(789\) 1.43393e7i 0.820042i
\(790\) 0 0
\(791\) 486132.i 0.0276257i
\(792\) 0 0
\(793\) 6.57743e6 + 6.57743e6i 0.371427 + 0.371427i