Properties

Label 225.4.f.c.107.6
Level $225$
Weight $4$
Character 225.107
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.6
Root \(3.78139 - 0.0336790i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.4.f.c.143.6

$q$-expansion

\(f(q)\) \(=\) \(q+(3.74771 - 3.74771i) q^{2} -20.0907i q^{4} +(-1.80948 - 1.80948i) q^{7} +(-45.3126 - 45.3126i) q^{8} +O(q^{10})\) \(q+(3.74771 - 3.74771i) q^{2} -20.0907i q^{4} +(-1.80948 - 1.80948i) q^{7} +(-45.3126 - 45.3126i) q^{8} -46.0907i q^{11} +(-18.6099 + 18.6099i) q^{13} -13.5628 q^{14} -178.911 q^{16} +(-14.5793 + 14.5793i) q^{17} -74.4577i q^{19} +(-172.735 - 172.735i) q^{22} +(59.6003 + 59.6003i) q^{23} +139.489i q^{26} +(-36.3538 + 36.3538i) q^{28} +202.168 q^{29} -49.5423 q^{31} +(-308.008 + 308.008i) q^{32} +109.278i q^{34} +(45.0594 + 45.0594i) q^{37} +(-279.046 - 279.046i) q^{38} +306.253i q^{41} +(230.784 - 230.784i) q^{43} -925.996 q^{44} +446.730 q^{46} +(176.943 - 176.943i) q^{47} -336.452i q^{49} +(373.886 + 373.886i) q^{52} +(85.1290 + 85.1290i) q^{53} +163.985i q^{56} +(757.669 - 757.669i) q^{58} +330.873 q^{59} +678.639 q^{61} +(-185.670 + 185.670i) q^{62} +877.361i q^{64} +(-756.373 - 756.373i) q^{67} +(292.909 + 292.909i) q^{68} +100.264i q^{71} +(-586.919 + 586.919i) q^{73} +337.739 q^{74} -1495.91 q^{76} +(-83.4004 + 83.4004i) q^{77} +286.986i q^{79} +(1147.75 + 1147.75i) q^{82} +(947.796 + 947.796i) q^{83} -1729.83i q^{86} +(-2088.49 + 2088.49i) q^{88} +688.442 q^{89} +67.3485 q^{91} +(1197.41 - 1197.41i) q^{92} -1326.26i q^{94} +(-920.676 - 920.676i) q^{97} +(-1260.92 - 1260.92i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.74771 3.74771i 1.32502 1.32502i 0.415360 0.909657i \(-0.363656\pi\)
0.909657 0.415360i \(-0.136344\pi\)
\(3\) 0 0
\(4\) 20.0907i 2.51134i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.80948 1.80948i −0.0977029 0.0977029i 0.656566 0.754269i \(-0.272008\pi\)
−0.754269 + 0.656566i \(0.772008\pi\)
\(8\) −45.3126 45.3126i −2.00255 2.00255i
\(9\) 0 0
\(10\) 0 0
\(11\) 46.0907i 1.26335i −0.775232 0.631676i \(-0.782367\pi\)
0.775232 0.631676i \(-0.217633\pi\)
\(12\) 0 0
\(13\) −18.6099 + 18.6099i −0.397035 + 0.397035i −0.877186 0.480151i \(-0.840582\pi\)
0.480151 + 0.877186i \(0.340582\pi\)
\(14\) −13.5628 −0.258916
\(15\) 0 0
\(16\) −178.911 −2.79549
\(17\) −14.5793 + 14.5793i −0.208000 + 0.208000i −0.803417 0.595417i \(-0.796987\pi\)
0.595417 + 0.803417i \(0.296987\pi\)
\(18\) 0 0
\(19\) 74.4577i 0.899041i −0.893270 0.449520i \(-0.851595\pi\)
0.893270 0.449520i \(-0.148405\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −172.735 172.735i −1.67396 1.67396i
\(23\) 59.6003 + 59.6003i 0.540327 + 0.540327i 0.923625 0.383298i \(-0.125212\pi\)
−0.383298 + 0.923625i \(0.625212\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 139.489i 1.05216i
\(27\) 0 0
\(28\) −36.3538 + 36.3538i −0.245365 + 0.245365i
\(29\) 202.168 1.29454 0.647271 0.762260i \(-0.275910\pi\)
0.647271 + 0.762260i \(0.275910\pi\)
\(30\) 0 0
\(31\) −49.5423 −0.287034 −0.143517 0.989648i \(-0.545841\pi\)
−0.143517 + 0.989648i \(0.545841\pi\)
\(32\) −308.008 + 308.008i −1.70152 + 1.70152i
\(33\) 0 0
\(34\) 109.278i 0.551208i
\(35\) 0 0
\(36\) 0 0
\(37\) 45.0594 + 45.0594i 0.200209 + 0.200209i 0.800089 0.599881i \(-0.204785\pi\)
−0.599881 + 0.800089i \(0.704785\pi\)
\(38\) −279.046 279.046i −1.19124 1.19124i
\(39\) 0 0
\(40\) 0 0
\(41\) 306.253i 1.16655i 0.812274 + 0.583276i \(0.198229\pi\)
−0.812274 + 0.583276i \(0.801771\pi\)
\(42\) 0 0
\(43\) 230.784 230.784i 0.818472 0.818472i −0.167415 0.985887i \(-0.553542\pi\)
0.985887 + 0.167415i \(0.0535420\pi\)
\(44\) −925.996 −3.17271
\(45\) 0 0
\(46\) 446.730 1.43189
\(47\) 176.943 176.943i 0.549143 0.549143i −0.377050 0.926193i \(-0.623062\pi\)
0.926193 + 0.377050i \(0.123062\pi\)
\(48\) 0 0
\(49\) 336.452i 0.980908i
\(50\) 0 0
\(51\) 0 0
\(52\) 373.886 + 373.886i 0.997090 + 0.997090i
\(53\) 85.1290 + 85.1290i 0.220630 + 0.220630i 0.808764 0.588134i \(-0.200137\pi\)
−0.588134 + 0.808764i \(0.700137\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 163.985i 0.391310i
\(57\) 0 0
\(58\) 757.669 757.669i 1.71529 1.71529i
\(59\) 330.873 0.730103 0.365051 0.930987i \(-0.381051\pi\)
0.365051 + 0.930987i \(0.381051\pi\)
\(60\) 0 0
\(61\) 678.639 1.42444 0.712220 0.701956i \(-0.247690\pi\)
0.712220 + 0.701956i \(0.247690\pi\)
\(62\) −185.670 + 185.670i −0.380325 + 0.380325i
\(63\) 0 0
\(64\) 877.361i 1.71360i
\(65\) 0 0
\(66\) 0 0
\(67\) −756.373 756.373i −1.37919 1.37919i −0.845990 0.533199i \(-0.820990\pi\)
−0.533199 0.845990i \(-0.679010\pi\)
\(68\) 292.909 + 292.909i 0.522360 + 0.522360i
\(69\) 0 0
\(70\) 0 0
\(71\) 100.264i 0.167594i 0.996483 + 0.0837972i \(0.0267048\pi\)
−0.996483 + 0.0837972i \(0.973295\pi\)
\(72\) 0 0
\(73\) −586.919 + 586.919i −0.941010 + 0.941010i −0.998354 0.0573449i \(-0.981737\pi\)
0.0573449 + 0.998354i \(0.481737\pi\)
\(74\) 337.739 0.530560
\(75\) 0 0
\(76\) −1495.91 −2.25780
\(77\) −83.4004 + 83.4004i −0.123433 + 0.123433i
\(78\) 0 0
\(79\) 286.986i 0.408714i 0.978896 + 0.204357i \(0.0655103\pi\)
−0.978896 + 0.204357i \(0.934490\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 1147.75 + 1147.75i 1.54570 + 1.54570i
\(83\) 947.796 + 947.796i 1.25342 + 1.25342i 0.954175 + 0.299248i \(0.0967359\pi\)
0.299248 + 0.954175i \(0.403264\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1729.83i 2.16898i
\(87\) 0 0
\(88\) −2088.49 + 2088.49i −2.52993 + 2.52993i
\(89\) 688.442 0.819941 0.409970 0.912099i \(-0.365539\pi\)
0.409970 + 0.912099i \(0.365539\pi\)
\(90\) 0 0
\(91\) 67.3485 0.0775829
\(92\) 1197.41 1197.41i 1.35695 1.35695i
\(93\) 0 0
\(94\) 1326.26i 1.45525i
\(95\) 0 0
\(96\) 0 0
\(97\) −920.676 920.676i −0.963716 0.963716i 0.0356483 0.999364i \(-0.488650\pi\)
−0.999364 + 0.0356483i \(0.988650\pi\)
\(98\) −1260.92 1260.92i −1.29972 1.29972i
\(99\) 0 0
\(100\) 0 0
\(101\) 1018.42i 1.00333i 0.865061 + 0.501667i \(0.167280\pi\)
−0.865061 + 0.501667i \(0.832720\pi\)
\(102\) 0 0
\(103\) 381.856 381.856i 0.365295 0.365295i −0.500463 0.865758i \(-0.666837\pi\)
0.865758 + 0.500463i \(0.166837\pi\)
\(104\) 1686.52 1.59017
\(105\) 0 0
\(106\) 638.078 0.584676
\(107\) −11.6954 + 11.6954i −0.0105667 + 0.0105667i −0.712370 0.701804i \(-0.752378\pi\)
0.701804 + 0.712370i \(0.252378\pi\)
\(108\) 0 0
\(109\) 1346.99i 1.18366i −0.806064 0.591828i \(-0.798406\pi\)
0.806064 0.591828i \(-0.201594\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 323.737 + 323.737i 0.273127 + 0.273127i
\(113\) −677.607 677.607i −0.564105 0.564105i 0.366366 0.930471i \(-0.380602\pi\)
−0.930471 + 0.366366i \(0.880602\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4061.71i 3.25104i
\(117\) 0 0
\(118\) 1240.02 1240.02i 0.967398 0.967398i
\(119\) 52.7621 0.0406445
\(120\) 0 0
\(121\) −793.355 −0.596059
\(122\) 2543.35 2543.35i 1.88741 1.88741i
\(123\) 0 0
\(124\) 995.340i 0.720840i
\(125\) 0 0
\(126\) 0 0
\(127\) 1220.98 + 1220.98i 0.853107 + 0.853107i 0.990515 0.137408i \(-0.0438771\pi\)
−0.137408 + 0.990515i \(0.543877\pi\)
\(128\) 824.034 + 824.034i 0.569023 + 0.569023i
\(129\) 0 0
\(130\) 0 0
\(131\) 215.023i 0.143409i 0.997426 + 0.0717046i \(0.0228439\pi\)
−0.997426 + 0.0717046i \(0.977156\pi\)
\(132\) 0 0
\(133\) −134.730 + 134.730i −0.0878389 + 0.0878389i
\(134\) −5669.34 −3.65490
\(135\) 0 0
\(136\) 1321.25 0.833063
\(137\) −877.965 + 877.965i −0.547516 + 0.547516i −0.925721 0.378206i \(-0.876541\pi\)
0.378206 + 0.925721i \(0.376541\pi\)
\(138\) 0 0
\(139\) 2489.62i 1.51918i 0.650400 + 0.759592i \(0.274601\pi\)
−0.650400 + 0.759592i \(0.725399\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 375.762 + 375.762i 0.222065 + 0.222065i
\(143\) 857.743 + 857.743i 0.501595 + 0.501595i
\(144\) 0 0
\(145\) 0 0
\(146\) 4399.21i 2.49371i
\(147\) 0 0
\(148\) 905.276 905.276i 0.502792 0.502792i
\(149\) 1497.94 0.823596 0.411798 0.911275i \(-0.364901\pi\)
0.411798 + 0.911275i \(0.364901\pi\)
\(150\) 0 0
\(151\) −1614.69 −0.870209 −0.435104 0.900380i \(-0.643289\pi\)
−0.435104 + 0.900380i \(0.643289\pi\)
\(152\) −3373.87 + 3373.87i −1.80038 + 1.80038i
\(153\) 0 0
\(154\) 625.121i 0.327102i
\(155\) 0 0
\(156\) 0 0
\(157\) 456.938 + 456.938i 0.232278 + 0.232278i 0.813643 0.581365i \(-0.197481\pi\)
−0.581365 + 0.813643i \(0.697481\pi\)
\(158\) 1075.54 + 1075.54i 0.541553 + 0.541553i
\(159\) 0 0
\(160\) 0 0
\(161\) 215.691i 0.105583i
\(162\) 0 0
\(163\) −1434.13 + 1434.13i −0.689140 + 0.689140i −0.962042 0.272902i \(-0.912017\pi\)
0.272902 + 0.962042i \(0.412017\pi\)
\(164\) 6152.83 2.92961
\(165\) 0 0
\(166\) 7104.14 3.32162
\(167\) −1129.18 + 1129.18i −0.523226 + 0.523226i −0.918544 0.395318i \(-0.870634\pi\)
0.395318 + 0.918544i \(0.370634\pi\)
\(168\) 0 0
\(169\) 1504.34i 0.684726i
\(170\) 0 0
\(171\) 0 0
\(172\) −4636.62 4636.62i −2.05546 2.05546i
\(173\) 1656.73 + 1656.73i 0.728084 + 0.728084i 0.970238 0.242154i \(-0.0778538\pi\)
−0.242154 + 0.970238i \(0.577854\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 8246.15i 3.53169i
\(177\) 0 0
\(178\) 2580.08 2580.08i 1.08644 1.08644i
\(179\) −1449.32 −0.605180 −0.302590 0.953121i \(-0.597851\pi\)
−0.302590 + 0.953121i \(0.597851\pi\)
\(180\) 0 0
\(181\) −1120.24 −0.460037 −0.230019 0.973186i \(-0.573879\pi\)
−0.230019 + 0.973186i \(0.573879\pi\)
\(182\) 252.403 252.403i 0.102799 0.102799i
\(183\) 0 0
\(184\) 5401.29i 2.16407i
\(185\) 0 0
\(186\) 0 0
\(187\) 671.972 + 671.972i 0.262778 + 0.262778i
\(188\) −3554.90 3554.90i −1.37908 1.37908i
\(189\) 0 0
\(190\) 0 0
\(191\) 3827.59i 1.45002i −0.688737 0.725012i \(-0.741834\pi\)
0.688737 0.725012i \(-0.258166\pi\)
\(192\) 0 0
\(193\) −1792.85 + 1792.85i −0.668665 + 0.668665i −0.957407 0.288742i \(-0.906763\pi\)
0.288742 + 0.957407i \(0.406763\pi\)
\(194\) −6900.86 −2.55388
\(195\) 0 0
\(196\) −6759.55 −2.46339
\(197\) −2222.09 + 2222.09i −0.803640 + 0.803640i −0.983663 0.180022i \(-0.942383\pi\)
0.180022 + 0.983663i \(0.442383\pi\)
\(198\) 0 0
\(199\) 1421.45i 0.506352i 0.967420 + 0.253176i \(0.0814752\pi\)
−0.967420 + 0.253176i \(0.918525\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3816.75 + 3816.75i 1.32943 + 1.32943i
\(203\) −365.820 365.820i −0.126481 0.126481i
\(204\) 0 0
\(205\) 0 0
\(206\) 2862.17i 0.968043i
\(207\) 0 0
\(208\) 3329.52 3329.52i 1.10991 1.10991i
\(209\) −3431.81 −1.13580
\(210\) 0 0
\(211\) 1133.67 0.369883 0.184942 0.982749i \(-0.440790\pi\)
0.184942 + 0.982749i \(0.440790\pi\)
\(212\) 1710.30 1710.30i 0.554076 0.554076i
\(213\) 0 0
\(214\) 87.6623i 0.0280022i
\(215\) 0 0
\(216\) 0 0
\(217\) 89.6459 + 89.6459i 0.0280441 + 0.0280441i
\(218\) −5048.15 5048.15i −1.56837 1.56837i
\(219\) 0 0
\(220\) 0 0
\(221\) 542.639i 0.165167i
\(222\) 0 0
\(223\) −666.458 + 666.458i −0.200131 + 0.200131i −0.800056 0.599925i \(-0.795197\pi\)
0.599925 + 0.800056i \(0.295197\pi\)
\(224\) 1114.67 0.332487
\(225\) 0 0
\(226\) −5078.95 −1.49490
\(227\) 2292.99 2292.99i 0.670446 0.670446i −0.287373 0.957819i \(-0.592782\pi\)
0.957819 + 0.287373i \(0.0927819\pi\)
\(228\) 0 0
\(229\) 2535.40i 0.731634i 0.930687 + 0.365817i \(0.119210\pi\)
−0.930687 + 0.365817i \(0.880790\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −9160.77 9160.77i −2.59239 2.59239i
\(233\) −1699.70 1699.70i −0.477902 0.477902i 0.426558 0.904460i \(-0.359726\pi\)
−0.904460 + 0.426558i \(0.859726\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6647.49i 1.83354i
\(237\) 0 0
\(238\) 197.737 197.737i 0.0538546 0.0538546i
\(239\) 3948.41 1.06863 0.534313 0.845287i \(-0.320570\pi\)
0.534313 + 0.845287i \(0.320570\pi\)
\(240\) 0 0
\(241\) −2447.20 −0.654101 −0.327050 0.945007i \(-0.606055\pi\)
−0.327050 + 0.945007i \(0.606055\pi\)
\(242\) −2973.27 + 2973.27i −0.789788 + 0.789788i
\(243\) 0 0
\(244\) 13634.3i 3.57725i
\(245\) 0 0
\(246\) 0 0
\(247\) 1385.65 + 1385.65i 0.356951 + 0.356951i
\(248\) 2244.89 + 2244.89i 0.574801 + 0.574801i
\(249\) 0 0
\(250\) 0 0
\(251\) 4755.75i 1.19594i 0.801519 + 0.597969i \(0.204025\pi\)
−0.801519 + 0.597969i \(0.795975\pi\)
\(252\) 0 0
\(253\) 2747.02 2747.02i 0.682624 0.682624i
\(254\) 9151.78 2.26076
\(255\) 0 0
\(256\) −842.400 −0.205664
\(257\) 1127.34 1127.34i 0.273624 0.273624i −0.556933 0.830557i \(-0.688022\pi\)
0.830557 + 0.556933i \(0.188022\pi\)
\(258\) 0 0
\(259\) 163.068i 0.0391219i
\(260\) 0 0
\(261\) 0 0
\(262\) 805.843 + 805.843i 0.190020 + 0.190020i
\(263\) 358.621 + 358.621i 0.0840817 + 0.0840817i 0.747897 0.663815i \(-0.231064\pi\)
−0.663815 + 0.747897i \(0.731064\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1009.86i 0.232776i
\(267\) 0 0
\(268\) −15196.1 + 15196.1i −3.46361 + 3.46361i
\(269\) −3824.41 −0.866834 −0.433417 0.901193i \(-0.642692\pi\)
−0.433417 + 0.901193i \(0.642692\pi\)
\(270\) 0 0
\(271\) 535.546 0.120045 0.0600223 0.998197i \(-0.480883\pi\)
0.0600223 + 0.998197i \(0.480883\pi\)
\(272\) 2608.41 2608.41i 0.581463 0.581463i
\(273\) 0 0
\(274\) 6580.72i 1.45093i
\(275\) 0 0
\(276\) 0 0
\(277\) −1108.08 1108.08i −0.240354 0.240354i 0.576643 0.816996i \(-0.304362\pi\)
−0.816996 + 0.576643i \(0.804362\pi\)
\(278\) 9330.37 + 9330.37i 2.01294 + 2.01294i
\(279\) 0 0
\(280\) 0 0
\(281\) 3439.91i 0.730277i 0.930953 + 0.365139i \(0.118978\pi\)
−0.930953 + 0.365139i \(0.881022\pi\)
\(282\) 0 0
\(283\) −2726.08 + 2726.08i −0.572610 + 0.572610i −0.932857 0.360247i \(-0.882693\pi\)
0.360247 + 0.932857i \(0.382693\pi\)
\(284\) 2014.38 0.420886
\(285\) 0 0
\(286\) 6429.15 1.32924
\(287\) 554.159 554.159i 0.113975 0.113975i
\(288\) 0 0
\(289\) 4487.89i 0.913472i
\(290\) 0 0
\(291\) 0 0
\(292\) 11791.6 + 11791.6i 2.36320 + 2.36320i
\(293\) −4347.55 4347.55i −0.866849 0.866849i 0.125273 0.992122i \(-0.460019\pi\)
−0.992122 + 0.125273i \(0.960019\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4083.51i 0.801856i
\(297\) 0 0
\(298\) 5613.84 5613.84i 1.09128 1.09128i
\(299\) −2218.31 −0.429058
\(300\) 0 0
\(301\) −835.200 −0.159934
\(302\) −6051.39 + 6051.39i −1.15304 + 1.15304i
\(303\) 0 0
\(304\) 13321.3i 2.51326i
\(305\) 0 0
\(306\) 0 0
\(307\) −3137.18 3137.18i −0.583220 0.583220i 0.352567 0.935787i \(-0.385309\pi\)
−0.935787 + 0.352567i \(0.885309\pi\)
\(308\) 1675.57 + 1675.57i 0.309983 + 0.309983i
\(309\) 0 0
\(310\) 0 0
\(311\) 8268.00i 1.50751i −0.657157 0.753754i \(-0.728241\pi\)
0.657157 0.753754i \(-0.271759\pi\)
\(312\) 0 0
\(313\) 4673.46 4673.46i 0.843959 0.843959i −0.145412 0.989371i \(-0.546451\pi\)
0.989371 + 0.145412i \(0.0464507\pi\)
\(314\) 3424.95 0.615544
\(315\) 0 0
\(316\) 5765.75 1.02642
\(317\) −3271.78 + 3271.78i −0.579690 + 0.579690i −0.934818 0.355128i \(-0.884437\pi\)
0.355128 + 0.934818i \(0.384437\pi\)
\(318\) 0 0
\(319\) 9318.09i 1.63546i
\(320\) 0 0
\(321\) 0 0
\(322\) −808.350 808.350i −0.139899 0.139899i
\(323\) 1085.54 + 1085.54i 0.187001 + 0.187001i
\(324\) 0 0
\(325\) 0 0
\(326\) 10749.4i 1.82624i
\(327\) 0 0
\(328\) 13877.1 13877.1i 2.33608 2.33608i
\(329\) −640.349 −0.107306
\(330\) 0 0
\(331\) 9665.06 1.60495 0.802477 0.596684i \(-0.203515\pi\)
0.802477 + 0.596684i \(0.203515\pi\)
\(332\) 19041.9 19041.9i 3.14777 3.14777i
\(333\) 0 0
\(334\) 8463.70i 1.38657i
\(335\) 0 0
\(336\) 0 0
\(337\) −1911.95 1911.95i −0.309053 0.309053i 0.535489 0.844542i \(-0.320127\pi\)
−0.844542 + 0.535489i \(0.820127\pi\)
\(338\) 5637.85 + 5637.85i 0.907274 + 0.907274i
\(339\) 0 0
\(340\) 0 0
\(341\) 2283.44i 0.362625i
\(342\) 0 0
\(343\) −1229.46 + 1229.46i −0.193540 + 0.193540i
\(344\) −20914.9 −3.27806
\(345\) 0 0
\(346\) 12417.9 1.92945
\(347\) 7023.71 7023.71i 1.08661 1.08661i 0.0907318 0.995875i \(-0.471079\pi\)
0.995875 0.0907318i \(-0.0289206\pi\)
\(348\) 0 0
\(349\) 9259.70i 1.42023i −0.704085 0.710115i \(-0.748643\pi\)
0.704085 0.710115i \(-0.251357\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 14196.3 + 14196.3i 2.14962 + 2.14962i
\(353\) 4338.33 + 4338.33i 0.654125 + 0.654125i 0.953984 0.299859i \(-0.0969396\pi\)
−0.299859 + 0.953984i \(0.596940\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 13831.3i 2.05915i
\(357\) 0 0
\(358\) −5431.64 + 5431.64i −0.801874 + 0.801874i
\(359\) 5949.44 0.874650 0.437325 0.899304i \(-0.355926\pi\)
0.437325 + 0.899304i \(0.355926\pi\)
\(360\) 0 0
\(361\) 1315.05 0.191726
\(362\) −4198.34 + 4198.34i −0.609557 + 0.609557i
\(363\) 0 0
\(364\) 1353.08i 0.194837i
\(365\) 0 0
\(366\) 0 0
\(367\) 9153.79 + 9153.79i 1.30197 + 1.30197i 0.927061 + 0.374912i \(0.122327\pi\)
0.374912 + 0.927061i \(0.377673\pi\)
\(368\) −10663.2 10663.2i −1.51048 1.51048i
\(369\) 0 0
\(370\) 0 0
\(371\) 308.079i 0.0431123i
\(372\) 0 0
\(373\) 6473.68 6473.68i 0.898644 0.898644i −0.0966723 0.995316i \(-0.530820\pi\)
0.995316 + 0.0966723i \(0.0308199\pi\)
\(374\) 5036.72 0.696370
\(375\) 0 0
\(376\) −16035.4 −2.19937
\(377\) −3762.33 + 3762.33i −0.513979 + 0.513979i
\(378\) 0 0
\(379\) 245.031i 0.0332094i 0.999862 + 0.0166047i \(0.00528569\pi\)
−0.999862 + 0.0166047i \(0.994714\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −14344.7 14344.7i −1.92131 1.92131i
\(383\) −4476.48 4476.48i −0.597225 0.597225i 0.342348 0.939573i \(-0.388778\pi\)
−0.939573 + 0.342348i \(0.888778\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13438.2i 1.77199i
\(387\) 0 0
\(388\) −18497.0 + 18497.0i −2.42022 + 2.42022i
\(389\) −4429.26 −0.577307 −0.288654 0.957434i \(-0.593208\pi\)
−0.288654 + 0.957434i \(0.593208\pi\)
\(390\) 0 0
\(391\) −1737.87 −0.224777
\(392\) −15245.5 + 15245.5i −1.96432 + 1.96432i
\(393\) 0 0
\(394\) 16655.5i 2.12967i
\(395\) 0 0
\(396\) 0 0
\(397\) −4786.16 4786.16i −0.605065 0.605065i 0.336588 0.941652i \(-0.390727\pi\)
−0.941652 + 0.336588i \(0.890727\pi\)
\(398\) 5327.19 + 5327.19i 0.670925 + 0.670925i
\(399\) 0 0
\(400\) 0 0
\(401\) 4521.85i 0.563119i −0.959544 0.281559i \(-0.909148\pi\)
0.959544 0.281559i \(-0.0908516\pi\)
\(402\) 0 0
\(403\) 921.977 921.977i 0.113963 0.113963i
\(404\) 20460.8 2.51971
\(405\) 0 0
\(406\) −2741.98 −0.335178
\(407\) 2076.82 2076.82i 0.252934 0.252934i
\(408\) 0 0
\(409\) 10162.9i 1.22866i −0.789048 0.614331i \(-0.789426\pi\)
0.789048 0.614331i \(-0.210574\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7671.76 7671.76i −0.917379 0.917379i
\(413\) −598.710 598.710i −0.0713331 0.0713331i
\(414\) 0 0
\(415\) 0 0
\(416\) 11464.0i 1.35113i
\(417\) 0 0
\(418\) −12861.4 + 12861.4i −1.50496 + 1.50496i
\(419\) 13243.2 1.54409 0.772044 0.635569i \(-0.219234\pi\)
0.772044 + 0.635569i \(0.219234\pi\)
\(420\) 0 0
\(421\) −7488.37 −0.866891 −0.433445 0.901180i \(-0.642702\pi\)
−0.433445 + 0.901180i \(0.642702\pi\)
\(422\) 4248.69 4248.69i 0.490102 0.490102i
\(423\) 0 0
\(424\) 7714.83i 0.883644i
\(425\) 0 0
\(426\) 0 0
\(427\) −1227.99 1227.99i −0.139172 0.139172i
\(428\) 234.970 + 234.970i 0.0265367 + 0.0265367i
\(429\) 0 0
\(430\) 0 0
\(431\) 5842.63i 0.652969i 0.945202 + 0.326485i \(0.105864\pi\)
−0.945202 + 0.326485i \(0.894136\pi\)
\(432\) 0 0
\(433\) 5310.04 5310.04i 0.589340 0.589340i −0.348112 0.937453i \(-0.613177\pi\)
0.937453 + 0.348112i \(0.113177\pi\)
\(434\) 671.934 0.0743177
\(435\) 0 0
\(436\) −27062.1 −2.97257
\(437\) 4437.70 4437.70i 0.485776 0.485776i
\(438\) 0 0
\(439\) 10440.4i 1.13506i −0.823352 0.567530i \(-0.807899\pi\)
0.823352 0.567530i \(-0.192101\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −2033.66 2033.66i −0.218849 0.218849i
\(443\) −2729.46 2729.46i −0.292732 0.292732i 0.545426 0.838159i \(-0.316368\pi\)
−0.838159 + 0.545426i \(0.816368\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 4995.38i 0.530355i
\(447\) 0 0
\(448\) 1587.57 1587.57i 0.167423 0.167423i
\(449\) −2227.63 −0.234139 −0.117070 0.993124i \(-0.537350\pi\)
−0.117070 + 0.993124i \(0.537350\pi\)
\(450\) 0 0
\(451\) 14115.4 1.47377
\(452\) −13613.6 + 13613.6i −1.41666 + 1.41666i
\(453\) 0 0
\(454\) 17187.0i 1.77670i
\(455\) 0 0
\(456\) 0 0
\(457\) −4328.64 4328.64i −0.443075 0.443075i 0.449969 0.893044i \(-0.351435\pi\)
−0.893044 + 0.449969i \(0.851435\pi\)
\(458\) 9501.96 + 9501.96i 0.969427 + 0.969427i
\(459\) 0 0
\(460\) 0 0
\(461\) 8223.98i 0.830865i 0.909624 + 0.415433i \(0.136370\pi\)
−0.909624 + 0.415433i \(0.863630\pi\)
\(462\) 0 0
\(463\) 2611.01 2611.01i 0.262082 0.262082i −0.563817 0.825899i \(-0.690668\pi\)
0.825899 + 0.563817i \(0.190668\pi\)
\(464\) −36170.2 −3.61888
\(465\) 0 0
\(466\) −12740.0 −1.26646
\(467\) 12010.6 12010.6i 1.19012 1.19012i 0.213085 0.977034i \(-0.431649\pi\)
0.977034 0.213085i \(-0.0683511\pi\)
\(468\) 0 0
\(469\) 2737.29i 0.269501i
\(470\) 0 0
\(471\) 0 0
\(472\) −14992.7 14992.7i −1.46207 1.46207i
\(473\) −10637.0 10637.0i −1.03402 1.03402i
\(474\) 0 0
\(475\) 0 0
\(476\) 1060.03i 0.102072i
\(477\) 0 0
\(478\) 14797.5 14797.5i 1.41595 1.41595i
\(479\) −6186.30 −0.590103 −0.295051 0.955481i \(-0.595337\pi\)
−0.295051 + 0.955481i \(0.595337\pi\)
\(480\) 0 0
\(481\) −1677.10 −0.158980
\(482\) −9171.42 + 9171.42i −0.866694 + 0.866694i
\(483\) 0 0
\(484\) 15939.1i 1.49691i
\(485\) 0 0
\(486\) 0 0
\(487\) 12791.1 + 12791.1i 1.19019 + 1.19019i 0.977015 + 0.213173i \(0.0683797\pi\)
0.213173 + 0.977015i \(0.431620\pi\)
\(488\) −30750.9 30750.9i −2.85251 2.85251i
\(489\) 0 0
\(490\) 0 0
\(491\) 13622.3i 1.25207i −0.779796 0.626034i \(-0.784677\pi\)
0.779796 0.626034i \(-0.215323\pi\)
\(492\) 0 0
\(493\) −2947.48 + 2947.48i −0.269265 + 0.269265i
\(494\) 10386.0 0.945931
\(495\) 0 0
\(496\) 8863.68 0.802401
\(497\) 181.427 181.427i 0.0163744 0.0163744i
\(498\) 0 0
\(499\) 15358.5i 1.37784i 0.724837 + 0.688920i \(0.241915\pi\)
−0.724837 + 0.688920i \(0.758085\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 17823.2 + 17823.2i 1.58464 + 1.58464i
\(503\) 9784.44 + 9784.44i 0.867329 + 0.867329i 0.992176 0.124847i \(-0.0398440\pi\)
−0.124847 + 0.992176i \(0.539844\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 20590.1i 1.80898i
\(507\) 0 0
\(508\) 24530.4 24530.4i 2.14244 2.14244i
\(509\) −5300.61 −0.461583 −0.230791 0.973003i \(-0.574131\pi\)
−0.230791 + 0.973003i \(0.574131\pi\)
\(510\) 0 0
\(511\) 2124.04 0.183879
\(512\) −9749.34 + 9749.34i −0.841532 + 0.841532i
\(513\) 0 0
\(514\) 8449.89i 0.725114i
\(515\) 0 0
\(516\) 0 0
\(517\) −8155.41 8155.41i −0.693761 0.693761i
\(518\) −611.134 611.134i −0.0518372 0.0518372i
\(519\) 0 0
\(520\) 0 0
\(521\) 8512.67i 0.715829i 0.933754 + 0.357915i \(0.116512\pi\)
−0.933754 + 0.357915i \(0.883488\pi\)
\(522\) 0 0
\(523\) −7880.88 + 7880.88i −0.658904 + 0.658904i −0.955121 0.296217i \(-0.904275\pi\)
0.296217 + 0.955121i \(0.404275\pi\)
\(524\) 4319.96 0.360149
\(525\) 0 0
\(526\) 2688.02 0.222819
\(527\) 722.293 722.293i 0.0597032 0.0597032i
\(528\) 0 0
\(529\) 5062.61i 0.416093i
\(530\) 0 0
\(531\) 0 0
\(532\) 2706.82 + 2706.82i 0.220593 + 0.220593i
\(533\) −5699.33 5699.33i −0.463162 0.463162i
\(534\) 0 0
\(535\) 0 0
\(536\) 68546.4i 5.52379i
\(537\) 0 0
\(538\) −14332.8 + 14332.8i −1.14857 + 1.14857i
\(539\) −15507.3 −1.23923
\(540\) 0 0
\(541\) 8961.43 0.712166 0.356083 0.934454i \(-0.384112\pi\)
0.356083 + 0.934454i \(0.384112\pi\)
\(542\) 2007.07 2007.07i 0.159061 0.159061i
\(543\) 0 0
\(544\) 8981.10i 0.707833i
\(545\) 0 0
\(546\) 0 0
\(547\) −13458.8 13458.8i −1.05203 1.05203i −0.998570 0.0534553i \(-0.982977\pi\)
−0.0534553 0.998570i \(-0.517023\pi\)
\(548\) 17639.0 + 17639.0i 1.37500 + 1.37500i
\(549\) 0 0
\(550\) 0 0
\(551\) 15053.0i 1.16385i
\(552\) 0 0
\(553\) 519.296 519.296i 0.0399325 0.0399325i
\(554\) −8305.52 −0.636946
\(555\) 0 0
\(556\) 50018.2 3.81519
\(557\) −12265.3 + 12265.3i −0.933031 + 0.933031i −0.997894 0.0648635i \(-0.979339\pi\)
0.0648635 + 0.997894i \(0.479339\pi\)
\(558\) 0 0
\(559\) 8589.74i 0.649924i
\(560\) 0 0
\(561\) 0 0
\(562\) 12891.8 + 12891.8i 0.967630 + 0.967630i
\(563\) 10874.1 + 10874.1i 0.814011 + 0.814011i 0.985233 0.171222i \(-0.0547714\pi\)
−0.171222 + 0.985233i \(0.554771\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20433.2i 1.51744i
\(567\) 0 0
\(568\) 4543.24 4543.24i 0.335616 0.335616i
\(569\) 5162.54 0.380360 0.190180 0.981749i \(-0.439093\pi\)
0.190180 + 0.981749i \(0.439093\pi\)
\(570\) 0 0
\(571\) 6356.12 0.465842 0.232921 0.972496i \(-0.425172\pi\)
0.232921 + 0.972496i \(0.425172\pi\)
\(572\) 17232.7 17232.7i 1.25968 1.25968i
\(573\) 0 0
\(574\) 4153.66i 0.302039i
\(575\) 0 0
\(576\) 0 0
\(577\) 7183.63 + 7183.63i 0.518299 + 0.518299i 0.917056 0.398758i \(-0.130559\pi\)
−0.398758 + 0.917056i \(0.630559\pi\)
\(578\) 16819.3 + 16819.3i 1.21037 + 1.21037i
\(579\) 0 0
\(580\) 0 0
\(581\) 3430.04i 0.244926i
\(582\) 0 0
\(583\) 3923.66 3923.66i 0.278733 0.278733i
\(584\) 53189.6 3.76884
\(585\) 0 0
\(586\) −32586.8 −2.29718
\(587\) −6007.01 + 6007.01i −0.422378 + 0.422378i −0.886022 0.463644i \(-0.846542\pi\)
0.463644 + 0.886022i \(0.346542\pi\)
\(588\) 0 0
\(589\) 3688.81i 0.258055i
\(590\) 0 0
\(591\) 0 0
\(592\) −8061.64 8061.64i −0.559681 0.559681i
\(593\) −0.276387 0.276387i −1.91397e−5 1.91397e-5i 0.707097 0.707116i \(-0.250004\pi\)
−0.707116 + 0.707097i \(0.750004\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 30094.7i 2.06833i
\(597\) 0 0
\(598\) −8313.59 + 8313.59i −0.568509 + 0.568509i
\(599\) −792.766 −0.0540761 −0.0270380 0.999634i \(-0.508608\pi\)
−0.0270380 + 0.999634i \(0.508608\pi\)
\(600\) 0 0
\(601\) −6779.60 −0.460142 −0.230071 0.973174i \(-0.573896\pi\)
−0.230071 + 0.973174i \(0.573896\pi\)
\(602\) −3130.09 + 3130.09i −0.211915 + 0.211915i
\(603\) 0 0
\(604\) 32440.3i 2.18539i
\(605\) 0 0
\(606\) 0 0
\(607\) 14598.9 + 14598.9i 0.976194 + 0.976194i 0.999723 0.0235289i \(-0.00749016\pi\)
−0.0235289 + 0.999723i \(0.507490\pi\)
\(608\) 22933.6 + 22933.6i 1.52974 + 1.52974i
\(609\) 0 0
\(610\) 0 0
\(611\) 6585.76i 0.436058i
\(612\) 0 0
\(613\) −9862.97 + 9862.97i −0.649856 + 0.649856i −0.952958 0.303102i \(-0.901978\pi\)
0.303102 + 0.952958i \(0.401978\pi\)
\(614\) −23514.5 −1.54555
\(615\) 0 0
\(616\) 7558.17 0.494363
\(617\) −10135.5 + 10135.5i −0.661329 + 0.661329i −0.955693 0.294364i \(-0.904892\pi\)
0.294364 + 0.955693i \(0.404892\pi\)
\(618\) 0 0
\(619\) 27282.6i 1.77153i 0.464132 + 0.885766i \(0.346366\pi\)
−0.464132 + 0.885766i \(0.653634\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −30986.1 30986.1i −1.99747 1.99747i
\(623\) −1245.72 1245.72i −0.0801106 0.0801106i
\(624\) 0 0
\(625\) 0 0
\(626\) 35029.5i 2.23652i
\(627\) 0 0
\(628\) 9180.22 9180.22i 0.583329 0.583329i
\(629\) −1313.87 −0.0832869
\(630\) 0 0
\(631\) −28414.9 −1.79268 −0.896340 0.443368i \(-0.853783\pi\)
−0.896340 + 0.443368i \(0.853783\pi\)
\(632\) 13004.1 13004.1i 0.818471 0.818471i
\(633\) 0 0
\(634\) 24523.4i 1.53620i
\(635\) 0 0
\(636\) 0 0
\(637\) 6261.33 + 6261.33i 0.389455 + 0.389455i
\(638\) −34921.5 34921.5i −2.16702 2.16702i
\(639\) 0 0
\(640\) 0 0
\(641\) 26402.3i 1.62688i 0.581650 + 0.813439i \(0.302407\pi\)
−0.581650 + 0.813439i \(0.697593\pi\)
\(642\) 0 0
\(643\) 2361.97 2361.97i 0.144863 0.144863i −0.630956 0.775819i \(-0.717337\pi\)
0.775819 + 0.630956i \(0.217337\pi\)
\(644\) −4333.40 −0.265155
\(645\) 0 0
\(646\) 8136.61 0.495558
\(647\) 11204.5 11204.5i 0.680826 0.680826i −0.279360 0.960186i \(-0.590122\pi\)
0.960186 + 0.279360i \(0.0901224\pi\)
\(648\) 0 0
\(649\) 15250.2i 0.922377i
\(650\) 0 0
\(651\) 0 0
\(652\) 28812.7 + 28812.7i 1.73066 + 1.73066i
\(653\) −18407.7 18407.7i −1.10314 1.10314i −0.994030 0.109108i \(-0.965201\pi\)
−0.109108 0.994030i \(-0.534799\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 54792.0i 3.26108i
\(657\) 0 0
\(658\) −2399.84 + 2399.84i −0.142182 + 0.142182i
\(659\) 8165.28 0.482662 0.241331 0.970443i \(-0.422416\pi\)
0.241331 + 0.970443i \(0.422416\pi\)
\(660\) 0 0
\(661\) −16725.1 −0.984163 −0.492082 0.870549i \(-0.663764\pi\)
−0.492082 + 0.870549i \(0.663764\pi\)
\(662\) 36221.9 36221.9i 2.12659 2.12659i
\(663\) 0 0
\(664\) 85894.2i 5.02009i
\(665\) 0 0
\(666\) 0 0
\(667\) 12049.3 + 12049.3i 0.699476 + 0.699476i
\(668\) 22686.1 + 22686.1i 1.31400 + 1.31400i
\(669\) 0 0
\(670\) 0 0
\(671\) 31279.0i 1.79957i
\(672\) 0 0
\(673\) −321.610 + 321.610i −0.0184208 + 0.0184208i −0.716257 0.697836i \(-0.754146\pi\)
0.697836 + 0.716257i \(0.254146\pi\)
\(674\) −14330.9 −0.819000
\(675\) 0 0
\(676\) 30223.4 1.71958
\(677\) −4497.58 + 4497.58i −0.255326 + 0.255326i −0.823150 0.567824i \(-0.807785\pi\)
0.567824 + 0.823150i \(0.307785\pi\)
\(678\) 0 0
\(679\) 3331.89i 0.188316i
\(680\) 0 0
\(681\) 0 0
\(682\) 8557.68 + 8557.68i 0.480485 + 0.480485i
\(683\) 7479.00 + 7479.00i 0.418999 + 0.418999i 0.884859 0.465860i \(-0.154255\pi\)
−0.465860 + 0.884859i \(0.654255\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 9215.30i 0.512889i
\(687\) 0 0
\(688\) −41289.9 + 41289.9i −2.28803 + 2.28803i
\(689\) −3168.48 −0.175195
\(690\) 0 0
\(691\) −22650.6 −1.24699 −0.623496 0.781827i \(-0.714288\pi\)
−0.623496 + 0.781827i \(0.714288\pi\)
\(692\) 33284.8 33284.8i 1.82847 1.82847i
\(693\) 0 0
\(694\) 52645.7i 2.87955i
\(695\) 0 0
\(696\) 0 0
\(697\) −4464.96 4464.96i −0.242643 0.242643i
\(698\) −34702.7 34702.7i −1.88183 1.88183i
\(699\) 0 0
\(700\) 0 0
\(701\) 1858.50i 0.100135i −0.998746 0.0500676i \(-0.984056\pi\)
0.998746 0.0500676i \(-0.0159437\pi\)
\(702\) 0 0
\(703\) 3355.02 3355.02i 0.179996 0.179996i
\(704\) 40438.2 2.16487
\(705\) 0 0
\(706\) 32517.6 1.73345
\(707\) 1842.82 1842.82i 0.0980286 0.0980286i
\(708\) 0 0
\(709\) 14344.6i 0.759836i 0.925020 + 0.379918i \(0.124048\pi\)
−0.925020 + 0.379918i \(0.875952\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −31195.1 31195.1i −1.64197 1.64197i
\(713\) −2952.74 2952.74i −0.155092 0.155092i
\(714\) 0 0
\(715\) 0 0
\(716\) 29117.9i 1.51981i
\(717\) 0 0
\(718\) 22296.8 22296.8i 1.15893 1.15893i
\(719\) −10128.2 −0.525337 −0.262669 0.964886i \(-0.584603\pi\)
−0.262669 + 0.964886i \(0.584603\pi\)
\(720\) 0 0
\(721\) −1381.92 −0.0713807
\(722\) 4928.43 4928.43i 0.254040 0.254040i
\(723\) 0 0
\(724\) 22506.4i 1.15531i
\(725\) 0 0
\(726\) 0 0
\(727\) −15769.7 15769.7i −0.804490 0.804490i 0.179304 0.983794i \(-0.442615\pi\)
−0.983794 + 0.179304i \(0.942615\pi\)
\(728\) −3051.74 3051.74i −0.155364 0.155364i
\(729\) 0 0
\(730\) 0 0
\(731\) 6729.36i 0.340485i
\(732\) 0 0
\(733\) −22982.0 + 22982.0i −1.15806 + 1.15806i −0.173169 + 0.984892i \(0.555401\pi\)
−0.984892 + 0.173169i \(0.944599\pi\)
\(734\) 68611.5 3.45027
\(735\) 0 0
\(736\) −36714.7 −1.83875
\(737\) −34861.8 + 34861.8i −1.74240 + 1.74240i
\(738\) 0 0
\(739\) 1989.79i 0.0990467i −0.998773 0.0495234i \(-0.984230\pi\)
0.998773 0.0495234i \(-0.0157702\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1154.59 1154.59i −0.0571245 0.0571245i
\(743\) 4460.57 + 4460.57i 0.220246 + 0.220246i 0.808602 0.588356i \(-0.200225\pi\)
−0.588356 + 0.808602i \(0.700225\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 48523.0i 2.38144i
\(747\) 0 0
\(748\) 13500.4 13500.4i 0.659924 0.659924i
\(749\) 42.3254 0.00206480
\(750\) 0 0
\(751\) 7038.34 0.341988 0.170994 0.985272i \(-0.445302\pi\)
0.170994 + 0.985272i \(0.445302\pi\)
\(752\) −31657.0 + 31657.0i −1.53512 + 1.53512i
\(753\) 0 0
\(754\) 28200.3i 1.36206i
\(755\) 0 0
\(756\) 0 0
\(757\) 8036.02 + 8036.02i 0.385831 + 0.385831i 0.873198 0.487366i \(-0.162042\pi\)
−0.487366 + 0.873198i \(0.662042\pi\)
\(758\) 918.304 + 918.304i 0.0440031 + 0.0440031i
\(759\) 0 0
\(760\) 0 0
\(761\) 11486.5i 0.547154i −0.961850 0.273577i \(-0.911793\pi\)
0.961850 0.273577i \(-0.0882068\pi\)
\(762\) 0 0
\(763\) −2437.36 + 2437.36i −0.115647 + 0.115647i
\(764\) −76899.0 −3.64150
\(765\) 0 0
\(766\) −33553.1 −1.58267
\(767\) −6157.52 + 6157.52i −0.289876 + 0.289876i
\(768\) 0 0
\(769\) 11244.4i 0.527289i 0.964620 + 0.263644i \(0.0849245\pi\)
−0.964620 + 0.263644i \(0.915075\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 36019.7 + 36019.7i 1.67925 + 1.67925i
\(773\) 21176.6 + 21176.6i 0.985341 + 0.985341i 0.999894 0.0145529i \(-0.00463251\pi\)
−0.0145529 + 0.999894i \(0.504633\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 83436.4i 3.85978i
\(777\) 0 0
\(778\) −16599.6 + 16599.6i −0.764942 + 0.764942i
\(779\) 22802.9 1.04878
\(780\) 0 0
\(781\) 4621.26 0.211731
\(782\) −6513.02 + 6513.02i −0.297833 + 0.297833i
\(783\) 0 0
\(784\) 60195.0i 2.74212i
\(785\) 0 0
\(786\) 0 0
\(787\) 1608.25 + 1608.25i 0.0728437 + 0.0728437i 0.742590 0.669746i \(-0.233597\pi\)
−0.669746 + 0.742590i \(0.733597\pi\)
\(788\) 44643.3 + 44643.3i 2.01821 + 2.01821i
\(789\) 0 0
\(790\) 0 0
\(791\) 2452.24i 0.110229i
\(792\) 0 0