Properties

Label 1148.2.k.b.337.2
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.2
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.32681 - 2.32681i) q^{3} -4.24622i q^{5} +(0.707107 + 0.707107i) q^{7} +7.82813i q^{9} +O(q^{10})\) \(q+(-2.32681 - 2.32681i) q^{3} -4.24622i q^{5} +(0.707107 + 0.707107i) q^{7} +7.82813i q^{9} +(-4.19464 - 4.19464i) q^{11} +(3.56747 + 3.56747i) q^{13} +(-9.88017 + 9.88017i) q^{15} +(-1.77688 + 1.77688i) q^{17} +(-2.53191 + 2.53191i) q^{19} -3.29061i q^{21} -2.95307 q^{23} -13.0304 q^{25} +(11.2341 - 11.2341i) q^{27} +(-1.24311 - 1.24311i) q^{29} -0.673818 q^{31} +19.5203i q^{33} +(3.00253 - 3.00253i) q^{35} +0.962447 q^{37} -16.6017i q^{39} +(0.364205 + 6.39276i) q^{41} +2.97093i q^{43} +33.2399 q^{45} +(5.82139 - 5.82139i) q^{47} +1.00000i q^{49} +8.26894 q^{51} +(-3.22446 - 3.22446i) q^{53} +(-17.8114 + 17.8114i) q^{55} +11.7826 q^{57} +1.27834 q^{59} -0.789980i q^{61} +(-5.53532 + 5.53532i) q^{63} +(15.1483 - 15.1483i) q^{65} +(-0.698946 + 0.698946i) q^{67} +(6.87125 + 6.87125i) q^{69} +(-4.91969 - 4.91969i) q^{71} +9.13102i q^{73} +(30.3193 + 30.3193i) q^{75} -5.93211i q^{77} +(7.06334 + 7.06334i) q^{79} -28.7952 q^{81} -13.7310 q^{83} +(7.54502 + 7.54502i) q^{85} +5.78496i q^{87} +(-5.05584 - 5.05584i) q^{89} +5.04517i q^{91} +(1.56785 + 1.56785i) q^{93} +(10.7511 + 10.7511i) q^{95} +(5.75578 - 5.75578i) q^{97} +(32.8361 - 32.8361i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.32681 2.32681i −1.34339 1.34339i −0.892664 0.450722i \(-0.851166\pi\)
−0.450722 0.892664i \(-0.648834\pi\)
\(4\) 0 0
\(5\) 4.24622i 1.89897i −0.313816 0.949484i \(-0.601607\pi\)
0.313816 0.949484i \(-0.398393\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 7.82813i 2.60938i
\(10\) 0 0
\(11\) −4.19464 4.19464i −1.26473 1.26473i −0.948774 0.315957i \(-0.897674\pi\)
−0.315957 0.948774i \(-0.602326\pi\)
\(12\) 0 0
\(13\) 3.56747 + 3.56747i 0.989438 + 0.989438i 0.999945 0.0105065i \(-0.00334437\pi\)
−0.0105065 + 0.999945i \(0.503344\pi\)
\(14\) 0 0
\(15\) −9.88017 + 9.88017i −2.55105 + 2.55105i
\(16\) 0 0
\(17\) −1.77688 + 1.77688i −0.430957 + 0.430957i −0.888954 0.457997i \(-0.848567\pi\)
0.457997 + 0.888954i \(0.348567\pi\)
\(18\) 0 0
\(19\) −2.53191 + 2.53191i −0.580861 + 0.580861i −0.935140 0.354279i \(-0.884726\pi\)
0.354279 + 0.935140i \(0.384726\pi\)
\(20\) 0 0
\(21\) 3.29061i 0.718070i
\(22\) 0 0
\(23\) −2.95307 −0.615758 −0.307879 0.951426i \(-0.599619\pi\)
−0.307879 + 0.951426i \(0.599619\pi\)
\(24\) 0 0
\(25\) −13.0304 −2.60608
\(26\) 0 0
\(27\) 11.2341 11.2341i 2.16201 2.16201i
\(28\) 0 0
\(29\) −1.24311 1.24311i −0.230839 0.230839i 0.582204 0.813043i \(-0.302191\pi\)
−0.813043 + 0.582204i \(0.802191\pi\)
\(30\) 0 0
\(31\) −0.673818 −0.121021 −0.0605106 0.998168i \(-0.519273\pi\)
−0.0605106 + 0.998168i \(0.519273\pi\)
\(32\) 0 0
\(33\) 19.5203i 3.39804i
\(34\) 0 0
\(35\) 3.00253 3.00253i 0.507520 0.507520i
\(36\) 0 0
\(37\) 0.962447 0.158225 0.0791126 0.996866i \(-0.474791\pi\)
0.0791126 + 0.996866i \(0.474791\pi\)
\(38\) 0 0
\(39\) 16.6017i 2.65840i
\(40\) 0 0
\(41\) 0.364205 + 6.39276i 0.0568793 + 0.998381i
\(42\) 0 0
\(43\) 2.97093i 0.453063i 0.974004 + 0.226532i \(0.0727386\pi\)
−0.974004 + 0.226532i \(0.927261\pi\)
\(44\) 0 0
\(45\) 33.2399 4.95512
\(46\) 0 0
\(47\) 5.82139 5.82139i 0.849137 0.849137i −0.140888 0.990026i \(-0.544996\pi\)
0.990026 + 0.140888i \(0.0449958\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 8.26894 1.15788
\(52\) 0 0
\(53\) −3.22446 3.22446i −0.442913 0.442913i 0.450077 0.892990i \(-0.351397\pi\)
−0.892990 + 0.450077i \(0.851397\pi\)
\(54\) 0 0
\(55\) −17.8114 + 17.8114i −2.40168 + 2.40168i
\(56\) 0 0
\(57\) 11.7826 1.56064
\(58\) 0 0
\(59\) 1.27834 0.166425 0.0832125 0.996532i \(-0.473482\pi\)
0.0832125 + 0.996532i \(0.473482\pi\)
\(60\) 0 0
\(61\) 0.789980i 0.101147i −0.998720 0.0505733i \(-0.983895\pi\)
0.998720 0.0505733i \(-0.0161048\pi\)
\(62\) 0 0
\(63\) −5.53532 + 5.53532i −0.697385 + 0.697385i
\(64\) 0 0
\(65\) 15.1483 15.1483i 1.87891 1.87891i
\(66\) 0 0
\(67\) −0.698946 + 0.698946i −0.0853899 + 0.0853899i −0.748512 0.663122i \(-0.769231\pi\)
0.663122 + 0.748512i \(0.269231\pi\)
\(68\) 0 0
\(69\) 6.87125 + 6.87125i 0.827201 + 0.827201i
\(70\) 0 0
\(71\) −4.91969 4.91969i −0.583859 0.583859i 0.352102 0.935962i \(-0.385467\pi\)
−0.935962 + 0.352102i \(0.885467\pi\)
\(72\) 0 0
\(73\) 9.13102i 1.06870i 0.845262 + 0.534352i \(0.179444\pi\)
−0.845262 + 0.534352i \(0.820556\pi\)
\(74\) 0 0
\(75\) 30.3193 + 30.3193i 3.50097 + 3.50097i
\(76\) 0 0
\(77\) 5.93211i 0.676027i
\(78\) 0 0
\(79\) 7.06334 + 7.06334i 0.794688 + 0.794688i 0.982252 0.187564i \(-0.0600593\pi\)
−0.187564 + 0.982252i \(0.560059\pi\)
\(80\) 0 0
\(81\) −28.7952 −3.19946
\(82\) 0 0
\(83\) −13.7310 −1.50717 −0.753584 0.657352i \(-0.771677\pi\)
−0.753584 + 0.657352i \(0.771677\pi\)
\(84\) 0 0
\(85\) 7.54502 + 7.54502i 0.818373 + 0.818373i
\(86\) 0 0
\(87\) 5.78496i 0.620212i
\(88\) 0 0
\(89\) −5.05584 5.05584i −0.535918 0.535918i 0.386410 0.922327i \(-0.373715\pi\)
−0.922327 + 0.386410i \(0.873715\pi\)
\(90\) 0 0
\(91\) 5.04517i 0.528877i
\(92\) 0 0
\(93\) 1.56785 + 1.56785i 0.162578 + 0.162578i
\(94\) 0 0
\(95\) 10.7511 + 10.7511i 1.10304 + 1.10304i
\(96\) 0 0
\(97\) 5.75578 5.75578i 0.584411 0.584411i −0.351701 0.936112i \(-0.614397\pi\)
0.936112 + 0.351701i \(0.114397\pi\)
\(98\) 0 0
\(99\) 32.8361 32.8361i 3.30016 3.30016i
\(100\) 0 0
\(101\) 8.05190 8.05190i 0.801194 0.801194i −0.182088 0.983282i \(-0.558286\pi\)
0.983282 + 0.182088i \(0.0582857\pi\)
\(102\) 0 0
\(103\) 10.3626i 1.02106i −0.859861 0.510528i \(-0.829450\pi\)
0.859861 0.510528i \(-0.170550\pi\)
\(104\) 0 0
\(105\) −13.9727 −1.36359
\(106\) 0 0
\(107\) −11.6638 −1.12758 −0.563792 0.825917i \(-0.690658\pi\)
−0.563792 + 0.825917i \(0.690658\pi\)
\(108\) 0 0
\(109\) 4.73917 4.73917i 0.453930 0.453930i −0.442726 0.896657i \(-0.645989\pi\)
0.896657 + 0.442726i \(0.145989\pi\)
\(110\) 0 0
\(111\) −2.23943 2.23943i −0.212558 0.212558i
\(112\) 0 0
\(113\) 9.20579 0.866008 0.433004 0.901392i \(-0.357454\pi\)
0.433004 + 0.901392i \(0.357454\pi\)
\(114\) 0 0
\(115\) 12.5394i 1.16930i
\(116\) 0 0
\(117\) −27.9266 + 27.9266i −2.58182 + 2.58182i
\(118\) 0 0
\(119\) −2.51289 −0.230356
\(120\) 0 0
\(121\) 24.1899i 2.19909i
\(122\) 0 0
\(123\) 14.0273 15.7222i 1.26480 1.41762i
\(124\) 0 0
\(125\) 34.0988i 3.04989i
\(126\) 0 0
\(127\) −8.39300 −0.744758 −0.372379 0.928081i \(-0.621458\pi\)
−0.372379 + 0.928081i \(0.621458\pi\)
\(128\) 0 0
\(129\) 6.91281 6.91281i 0.608639 0.608639i
\(130\) 0 0
\(131\) 19.8785i 1.73679i 0.495873 + 0.868395i \(0.334848\pi\)
−0.495873 + 0.868395i \(0.665152\pi\)
\(132\) 0 0
\(133\) −3.58067 −0.310483
\(134\) 0 0
\(135\) −47.7027 47.7027i −4.10559 4.10559i
\(136\) 0 0
\(137\) −13.0847 + 13.0847i −1.11790 + 1.11790i −0.125848 + 0.992050i \(0.540165\pi\)
−0.992050 + 0.125848i \(0.959835\pi\)
\(138\) 0 0
\(139\) 8.60496 0.729863 0.364931 0.931034i \(-0.381092\pi\)
0.364931 + 0.931034i \(0.381092\pi\)
\(140\) 0 0
\(141\) −27.0906 −2.28144
\(142\) 0 0
\(143\) 29.9285i 2.50275i
\(144\) 0 0
\(145\) −5.27851 + 5.27851i −0.438356 + 0.438356i
\(146\) 0 0
\(147\) 2.32681 2.32681i 0.191912 0.191912i
\(148\) 0 0
\(149\) −4.29787 + 4.29787i −0.352095 + 0.352095i −0.860889 0.508793i \(-0.830092\pi\)
0.508793 + 0.860889i \(0.330092\pi\)
\(150\) 0 0
\(151\) −10.2354 10.2354i −0.832942 0.832942i 0.154976 0.987918i \(-0.450470\pi\)
−0.987918 + 0.154976i \(0.950470\pi\)
\(152\) 0 0
\(153\) −13.9096 13.9096i −1.12453 1.12453i
\(154\) 0 0
\(155\) 2.86118i 0.229815i
\(156\) 0 0
\(157\) −12.9316 12.9316i −1.03206 1.03206i −0.999469 0.0325879i \(-0.989625\pi\)
−0.0325879 0.999469i \(-0.510375\pi\)
\(158\) 0 0
\(159\) 15.0054i 1.19001i
\(160\) 0 0
\(161\) −2.08814 2.08814i −0.164568 0.164568i
\(162\) 0 0
\(163\) −24.4625 −1.91605 −0.958024 0.286689i \(-0.907445\pi\)
−0.958024 + 0.286689i \(0.907445\pi\)
\(164\) 0 0
\(165\) 82.8874 6.45278
\(166\) 0 0
\(167\) 5.02460 + 5.02460i 0.388815 + 0.388815i 0.874265 0.485449i \(-0.161344\pi\)
−0.485449 + 0.874265i \(0.661344\pi\)
\(168\) 0 0
\(169\) 12.4537i 0.957976i
\(170\) 0 0
\(171\) −19.8201 19.8201i −1.51568 1.51568i
\(172\) 0 0
\(173\) 7.11453i 0.540908i 0.962733 + 0.270454i \(0.0871738\pi\)
−0.962733 + 0.270454i \(0.912826\pi\)
\(174\) 0 0
\(175\) −9.21388 9.21388i −0.696504 0.696504i
\(176\) 0 0
\(177\) −2.97445 2.97445i −0.223573 0.223573i
\(178\) 0 0
\(179\) 2.38569 2.38569i 0.178315 0.178315i −0.612306 0.790621i \(-0.709758\pi\)
0.790621 + 0.612306i \(0.209758\pi\)
\(180\) 0 0
\(181\) 11.5967 11.5967i 0.861974 0.861974i −0.129593 0.991567i \(-0.541367\pi\)
0.991567 + 0.129593i \(0.0413672\pi\)
\(182\) 0 0
\(183\) −1.83814 + 1.83814i −0.135879 + 0.135879i
\(184\) 0 0
\(185\) 4.08676i 0.300465i
\(186\) 0 0
\(187\) 14.9067 1.09009
\(188\) 0 0
\(189\) 15.8875 1.15564
\(190\) 0 0
\(191\) 0.597809 0.597809i 0.0432559 0.0432559i −0.685148 0.728404i \(-0.740262\pi\)
0.728404 + 0.685148i \(0.240262\pi\)
\(192\) 0 0
\(193\) −2.21881 2.21881i −0.159713 0.159713i 0.622726 0.782440i \(-0.286025\pi\)
−0.782440 + 0.622726i \(0.786025\pi\)
\(194\) 0 0
\(195\) −70.4944 −5.04821
\(196\) 0 0
\(197\) 10.5596i 0.752338i −0.926551 0.376169i \(-0.877241\pi\)
0.926551 0.376169i \(-0.122759\pi\)
\(198\) 0 0
\(199\) 13.3700 13.3700i 0.947774 0.947774i −0.0509280 0.998702i \(-0.516218\pi\)
0.998702 + 0.0509280i \(0.0162179\pi\)
\(200\) 0 0
\(201\) 3.25263 0.229423
\(202\) 0 0
\(203\) 1.75802i 0.123389i
\(204\) 0 0
\(205\) 27.1451 1.54650i 1.89589 0.108012i
\(206\) 0 0
\(207\) 23.1170i 1.60674i
\(208\) 0 0
\(209\) 21.2409 1.46927
\(210\) 0 0
\(211\) −3.28599 + 3.28599i −0.226217 + 0.226217i −0.811110 0.584893i \(-0.801136\pi\)
0.584893 + 0.811110i \(0.301136\pi\)
\(212\) 0 0
\(213\) 22.8944i 1.56870i
\(214\) 0 0
\(215\) 12.6152 0.860352
\(216\) 0 0
\(217\) −0.476461 0.476461i −0.0323443 0.0323443i
\(218\) 0 0
\(219\) 21.2462 21.2462i 1.43568 1.43568i
\(220\) 0 0
\(221\) −12.6779 −0.852810
\(222\) 0 0
\(223\) 4.96267 0.332325 0.166163 0.986098i \(-0.446862\pi\)
0.166163 + 0.986098i \(0.446862\pi\)
\(224\) 0 0
\(225\) 102.004i 6.80024i
\(226\) 0 0
\(227\) −14.0028 + 14.0028i −0.929399 + 0.929399i −0.997667 0.0682682i \(-0.978253\pi\)
0.0682682 + 0.997667i \(0.478253\pi\)
\(228\) 0 0
\(229\) −1.27538 + 1.27538i −0.0842794 + 0.0842794i −0.747990 0.663710i \(-0.768981\pi\)
0.663710 + 0.747990i \(0.268981\pi\)
\(230\) 0 0
\(231\) −13.8029 + 13.8029i −0.908165 + 0.908165i
\(232\) 0 0
\(233\) −11.0654 11.0654i −0.724917 0.724917i 0.244685 0.969603i \(-0.421315\pi\)
−0.969603 + 0.244685i \(0.921315\pi\)
\(234\) 0 0
\(235\) −24.7189 24.7189i −1.61248 1.61248i
\(236\) 0 0
\(237\) 32.8702i 2.13515i
\(238\) 0 0
\(239\) −6.38816 6.38816i −0.413216 0.413216i 0.469641 0.882857i \(-0.344383\pi\)
−0.882857 + 0.469641i \(0.844383\pi\)
\(240\) 0 0
\(241\) 13.9312i 0.897390i 0.893685 + 0.448695i \(0.148111\pi\)
−0.893685 + 0.448695i \(0.851889\pi\)
\(242\) 0 0
\(243\) 33.2986 + 33.2986i 2.13610 + 2.13610i
\(244\) 0 0
\(245\) 4.24622 0.271281
\(246\) 0 0
\(247\) −18.0651 −1.14945
\(248\) 0 0
\(249\) 31.9494 + 31.9494i 2.02471 + 2.02471i
\(250\) 0 0
\(251\) 11.5202i 0.727148i 0.931565 + 0.363574i \(0.118444\pi\)
−0.931565 + 0.363574i \(0.881556\pi\)
\(252\) 0 0
\(253\) 12.3871 + 12.3871i 0.778768 + 0.778768i
\(254\) 0 0
\(255\) 35.1117i 2.19878i
\(256\) 0 0
\(257\) −20.3499 20.3499i −1.26939 1.26939i −0.946401 0.322993i \(-0.895311\pi\)
−0.322993 0.946401i \(-0.604689\pi\)
\(258\) 0 0
\(259\) 0.680552 + 0.680552i 0.0422875 + 0.0422875i
\(260\) 0 0
\(261\) 9.73120 9.73120i 0.602346 0.602346i
\(262\) 0 0
\(263\) −19.7051 + 19.7051i −1.21507 + 1.21507i −0.245731 + 0.969338i \(0.579028\pi\)
−0.969338 + 0.245731i \(0.920972\pi\)
\(264\) 0 0
\(265\) −13.6918 + 13.6918i −0.841078 + 0.841078i
\(266\) 0 0
\(267\) 23.5280i 1.43989i
\(268\) 0 0
\(269\) 6.87162 0.418970 0.209485 0.977812i \(-0.432821\pi\)
0.209485 + 0.977812i \(0.432821\pi\)
\(270\) 0 0
\(271\) 19.6618 1.19437 0.597185 0.802104i \(-0.296286\pi\)
0.597185 + 0.802104i \(0.296286\pi\)
\(272\) 0 0
\(273\) 11.7392 11.7392i 0.710486 0.710486i
\(274\) 0 0
\(275\) 54.6578 + 54.6578i 3.29599 + 3.29599i
\(276\) 0 0
\(277\) −1.17740 −0.0707429 −0.0353714 0.999374i \(-0.511261\pi\)
−0.0353714 + 0.999374i \(0.511261\pi\)
\(278\) 0 0
\(279\) 5.27473i 0.315790i
\(280\) 0 0
\(281\) −15.8178 + 15.8178i −0.943612 + 0.943612i −0.998493 0.0548806i \(-0.982522\pi\)
0.0548806 + 0.998493i \(0.482522\pi\)
\(282\) 0 0
\(283\) −1.44959 −0.0861690 −0.0430845 0.999071i \(-0.513718\pi\)
−0.0430845 + 0.999071i \(0.513718\pi\)
\(284\) 0 0
\(285\) 50.0315i 2.96361i
\(286\) 0 0
\(287\) −4.26283 + 4.77789i −0.251627 + 0.282030i
\(288\) 0 0
\(289\) 10.6854i 0.628553i
\(290\) 0 0
\(291\) −26.7853 −1.57018
\(292\) 0 0
\(293\) −0.813256 + 0.813256i −0.0475109 + 0.0475109i −0.730463 0.682952i \(-0.760696\pi\)
0.682952 + 0.730463i \(0.260696\pi\)
\(294\) 0 0
\(295\) 5.42809i 0.316036i
\(296\) 0 0
\(297\) −94.2463 −5.46873
\(298\) 0 0
\(299\) −10.5350 10.5350i −0.609255 0.609255i
\(300\) 0 0
\(301\) −2.10077 + 2.10077i −0.121086 + 0.121086i
\(302\) 0 0
\(303\) −37.4705 −2.15263
\(304\) 0 0
\(305\) −3.35443 −0.192074
\(306\) 0 0
\(307\) 4.11500i 0.234855i 0.993081 + 0.117428i \(0.0374648\pi\)
−0.993081 + 0.117428i \(0.962535\pi\)
\(308\) 0 0
\(309\) −24.1118 + 24.1118i −1.37167 + 1.37167i
\(310\) 0 0
\(311\) −11.6645 + 11.6645i −0.661432 + 0.661432i −0.955718 0.294286i \(-0.904918\pi\)
0.294286 + 0.955718i \(0.404918\pi\)
\(312\) 0 0
\(313\) −5.86970 + 5.86970i −0.331775 + 0.331775i −0.853260 0.521485i \(-0.825378\pi\)
0.521485 + 0.853260i \(0.325378\pi\)
\(314\) 0 0
\(315\) 23.5042 + 23.5042i 1.32431 + 1.32431i
\(316\) 0 0
\(317\) −2.44834 2.44834i −0.137512 0.137512i 0.635000 0.772512i \(-0.281000\pi\)
−0.772512 + 0.635000i \(0.781000\pi\)
\(318\) 0 0
\(319\) 10.4288i 0.583899i
\(320\) 0 0
\(321\) 27.1395 + 27.1395i 1.51478 + 1.51478i
\(322\) 0 0
\(323\) 8.99781i 0.500652i
\(324\) 0 0
\(325\) −46.4855 46.4855i −2.57855 2.57855i
\(326\) 0 0
\(327\) −22.0543 −1.21961
\(328\) 0 0
\(329\) 8.23269 0.453883
\(330\) 0 0
\(331\) 7.04942 + 7.04942i 0.387471 + 0.387471i 0.873785 0.486313i \(-0.161659\pi\)
−0.486313 + 0.873785i \(0.661659\pi\)
\(332\) 0 0
\(333\) 7.53415i 0.412869i
\(334\) 0 0
\(335\) 2.96788 + 2.96788i 0.162153 + 0.162153i
\(336\) 0 0
\(337\) 28.6701i 1.56176i 0.624681 + 0.780880i \(0.285229\pi\)
−0.624681 + 0.780880i \(0.714771\pi\)
\(338\) 0 0
\(339\) −21.4202 21.4202i −1.16338 1.16338i
\(340\) 0 0
\(341\) 2.82642 + 2.82642i 0.153059 + 0.153059i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) 29.1768 29.1768i 1.57083 1.57083i
\(346\) 0 0
\(347\) 12.5714 12.5714i 0.674867 0.674867i −0.283967 0.958834i \(-0.591651\pi\)
0.958834 + 0.283967i \(0.0916507\pi\)
\(348\) 0 0
\(349\) 10.8944i 0.583165i −0.956546 0.291583i \(-0.905818\pi\)
0.956546 0.291583i \(-0.0941818\pi\)
\(350\) 0 0
\(351\) 80.1550 4.27836
\(352\) 0 0
\(353\) 32.5939 1.73480 0.867399 0.497614i \(-0.165790\pi\)
0.867399 + 0.497614i \(0.165790\pi\)
\(354\) 0 0
\(355\) −20.8901 + 20.8901i −1.10873 + 1.10873i
\(356\) 0 0
\(357\) 5.84702 + 5.84702i 0.309457 + 0.309457i
\(358\) 0 0
\(359\) 18.9230 0.998718 0.499359 0.866395i \(-0.333569\pi\)
0.499359 + 0.866395i \(0.333569\pi\)
\(360\) 0 0
\(361\) 6.17882i 0.325201i
\(362\) 0 0
\(363\) 56.2855 56.2855i 2.95422 2.95422i
\(364\) 0 0
\(365\) 38.7723 2.02944
\(366\) 0 0
\(367\) 7.25606i 0.378763i −0.981904 0.189381i \(-0.939352\pi\)
0.981904 0.189381i \(-0.0606483\pi\)
\(368\) 0 0
\(369\) −50.0433 + 2.85104i −2.60515 + 0.148419i
\(370\) 0 0
\(371\) 4.56007i 0.236747i
\(372\) 0 0
\(373\) −16.9241 −0.876299 −0.438149 0.898902i \(-0.644366\pi\)
−0.438149 + 0.898902i \(0.644366\pi\)
\(374\) 0 0
\(375\) 79.3416 79.3416i 4.09718 4.09718i
\(376\) 0 0
\(377\) 8.86949i 0.456802i
\(378\) 0 0
\(379\) −36.8055 −1.89057 −0.945287 0.326240i \(-0.894218\pi\)
−0.945287 + 0.326240i \(0.894218\pi\)
\(380\) 0 0
\(381\) 19.5289 + 19.5289i 1.00050 + 1.00050i
\(382\) 0 0
\(383\) −23.0952 + 23.0952i −1.18011 + 1.18011i −0.200393 + 0.979716i \(0.564222\pi\)
−0.979716 + 0.200393i \(0.935778\pi\)
\(384\) 0 0
\(385\) −25.1891 −1.28375
\(386\) 0 0
\(387\) −23.2568 −1.18221
\(388\) 0 0
\(389\) 20.9557i 1.06249i 0.847217 + 0.531247i \(0.178276\pi\)
−0.847217 + 0.531247i \(0.821724\pi\)
\(390\) 0 0
\(391\) 5.24725 5.24725i 0.265365 0.265365i
\(392\) 0 0
\(393\) 46.2535 46.2535i 2.33318 2.33318i
\(394\) 0 0
\(395\) 29.9925 29.9925i 1.50909 1.50909i
\(396\) 0 0
\(397\) −19.4766 19.4766i −0.977502 0.977502i 0.0222503 0.999752i \(-0.492917\pi\)
−0.999752 + 0.0222503i \(0.992917\pi\)
\(398\) 0 0
\(399\) 8.33155 + 8.33155i 0.417099 + 0.417099i
\(400\) 0 0
\(401\) 19.1947i 0.958537i −0.877668 0.479269i \(-0.840902\pi\)
0.877668 0.479269i \(-0.159098\pi\)
\(402\) 0 0
\(403\) −2.40383 2.40383i −0.119743 0.119743i
\(404\) 0 0
\(405\) 122.271i 6.07568i
\(406\) 0 0
\(407\) −4.03711 4.03711i −0.200112 0.200112i
\(408\) 0 0
\(409\) −0.263444 −0.0130265 −0.00651323 0.999979i \(-0.502073\pi\)
−0.00651323 + 0.999979i \(0.502073\pi\)
\(410\) 0 0
\(411\) 60.8911 3.00354
\(412\) 0 0
\(413\) 0.903919 + 0.903919i 0.0444790 + 0.0444790i
\(414\) 0 0
\(415\) 58.3047i 2.86206i
\(416\) 0 0
\(417\) −20.0221 20.0221i −0.980488 0.980488i
\(418\) 0 0
\(419\) 11.0853i 0.541553i 0.962642 + 0.270776i \(0.0872804\pi\)
−0.962642 + 0.270776i \(0.912720\pi\)
\(420\) 0 0
\(421\) 0.0941971 + 0.0941971i 0.00459089 + 0.00459089i 0.709398 0.704808i \(-0.248967\pi\)
−0.704808 + 0.709398i \(0.748967\pi\)
\(422\) 0 0
\(423\) 45.5706 + 45.5706i 2.21572 + 2.21572i
\(424\) 0 0
\(425\) 23.1534 23.1534i 1.12311 1.12311i
\(426\) 0 0
\(427\) 0.558600 0.558600i 0.0270325 0.0270325i
\(428\) 0 0
\(429\) −69.6380 + 69.6380i −3.36215 + 3.36215i
\(430\) 0 0
\(431\) 21.9320i 1.05643i 0.849111 + 0.528215i \(0.177138\pi\)
−0.849111 + 0.528215i \(0.822862\pi\)
\(432\) 0 0
\(433\) −37.5069 −1.80246 −0.901232 0.433336i \(-0.857336\pi\)
−0.901232 + 0.433336i \(0.857336\pi\)
\(434\) 0 0
\(435\) 24.5642 1.17776
\(436\) 0 0
\(437\) 7.47692 7.47692i 0.357670 0.357670i
\(438\) 0 0
\(439\) −7.42600 7.42600i −0.354424 0.354424i 0.507329 0.861752i \(-0.330633\pi\)
−0.861752 + 0.507329i \(0.830633\pi\)
\(440\) 0 0
\(441\) −7.82813 −0.372768
\(442\) 0 0
\(443\) 2.72125i 0.129290i −0.997908 0.0646452i \(-0.979408\pi\)
0.997908 0.0646452i \(-0.0205916\pi\)
\(444\) 0 0
\(445\) −21.4682 + 21.4682i −1.01769 + 1.01769i
\(446\) 0 0
\(447\) 20.0007 0.946000
\(448\) 0 0
\(449\) 14.7404i 0.695643i −0.937561 0.347821i \(-0.886922\pi\)
0.937561 0.347821i \(-0.113078\pi\)
\(450\) 0 0
\(451\) 25.2876 28.3430i 1.19075 1.33462i
\(452\) 0 0
\(453\) 47.6316i 2.23793i
\(454\) 0 0
\(455\) 21.4229 1.00432
\(456\) 0 0
\(457\) 11.5351 11.5351i 0.539591 0.539591i −0.383818 0.923409i \(-0.625391\pi\)
0.923409 + 0.383818i \(0.125391\pi\)
\(458\) 0 0
\(459\) 39.9235i 1.86347i
\(460\) 0 0
\(461\) −39.9279 −1.85963 −0.929814 0.368029i \(-0.880033\pi\)
−0.929814 + 0.368029i \(0.880033\pi\)
\(462\) 0 0
\(463\) 4.41264 + 4.41264i 0.205073 + 0.205073i 0.802169 0.597097i \(-0.203679\pi\)
−0.597097 + 0.802169i \(0.703679\pi\)
\(464\) 0 0
\(465\) 6.65743 6.65743i 0.308731 0.308731i
\(466\) 0 0
\(467\) −20.5955 −0.953046 −0.476523 0.879162i \(-0.658103\pi\)
−0.476523 + 0.879162i \(0.658103\pi\)
\(468\) 0 0
\(469\) −0.988459 −0.0456428
\(470\) 0 0
\(471\) 60.1790i 2.77290i
\(472\) 0 0
\(473\) 12.4620 12.4620i 0.573003 0.573003i
\(474\) 0 0
\(475\) 32.9918 32.9918i 1.51377 1.51377i
\(476\) 0 0
\(477\) 25.2415 25.2415i 1.15573 1.15573i
\(478\) 0 0
\(479\) 12.3753 + 12.3753i 0.565441 + 0.565441i 0.930848 0.365407i \(-0.119070\pi\)
−0.365407 + 0.930848i \(0.619070\pi\)
\(480\) 0 0
\(481\) 3.43350 + 3.43350i 0.156554 + 0.156554i
\(482\) 0 0
\(483\) 9.71741i 0.442158i
\(484\) 0 0
\(485\) −24.4403 24.4403i −1.10978 1.10978i
\(486\) 0 0
\(487\) 4.31210i 0.195400i −0.995216 0.0976998i \(-0.968851\pi\)
0.995216 0.0976998i \(-0.0311485\pi\)
\(488\) 0 0
\(489\) 56.9196 + 56.9196i 2.57399 + 2.57399i
\(490\) 0 0
\(491\) 15.7780 0.712052 0.356026 0.934476i \(-0.384132\pi\)
0.356026 + 0.934476i \(0.384132\pi\)
\(492\) 0 0
\(493\) 4.41770 0.198963
\(494\) 0 0
\(495\) −139.430 139.430i −6.26689 6.26689i
\(496\) 0 0
\(497\) 6.95749i 0.312086i
\(498\) 0 0
\(499\) −10.3963 10.3963i −0.465405 0.465405i 0.435017 0.900422i \(-0.356742\pi\)
−0.900422 + 0.435017i \(0.856742\pi\)
\(500\) 0 0
\(501\) 23.3826i 1.04466i
\(502\) 0 0
\(503\) 7.10039 + 7.10039i 0.316591 + 0.316591i 0.847456 0.530865i \(-0.178133\pi\)
−0.530865 + 0.847456i \(0.678133\pi\)
\(504\) 0 0
\(505\) −34.1901 34.1901i −1.52144 1.52144i
\(506\) 0 0
\(507\) 28.9774 28.9774i 1.28693 1.28693i
\(508\) 0 0
\(509\) 15.4522 15.4522i 0.684909 0.684909i −0.276193 0.961102i \(-0.589073\pi\)
0.961102 + 0.276193i \(0.0890730\pi\)
\(510\) 0 0
\(511\) −6.45660 + 6.45660i −0.285623 + 0.285623i
\(512\) 0 0
\(513\) 56.8878i 2.51166i
\(514\) 0 0
\(515\) −44.0018 −1.93895
\(516\) 0 0
\(517\) −48.8373 −2.14786
\(518\) 0 0
\(519\) 16.5542 16.5542i 0.726648 0.726648i
\(520\) 0 0
\(521\) 5.80627 + 5.80627i 0.254377 + 0.254377i 0.822763 0.568385i \(-0.192432\pi\)
−0.568385 + 0.822763i \(0.692432\pi\)
\(522\) 0 0
\(523\) 16.3083 0.713113 0.356556 0.934274i \(-0.383951\pi\)
0.356556 + 0.934274i \(0.383951\pi\)
\(524\) 0 0
\(525\) 42.8780i 1.87135i
\(526\) 0 0
\(527\) 1.19729 1.19729i 0.0521549 0.0521549i
\(528\) 0 0
\(529\) −14.2794 −0.620842
\(530\) 0 0
\(531\) 10.0070i 0.434265i
\(532\) 0 0
\(533\) −21.5067 + 24.1053i −0.931558 + 1.04412i
\(534\) 0 0
\(535\) 49.5271i 2.14124i
\(536\) 0 0
\(537\) −11.1021 −0.479092
\(538\) 0 0
\(539\) 4.19464 4.19464i 0.180676 0.180676i
\(540\) 0 0
\(541\) 6.45897i 0.277693i −0.990314 0.138846i \(-0.955661\pi\)
0.990314 0.138846i \(-0.0443394\pi\)
\(542\) 0 0
\(543\) −53.9666 −2.31593
\(544\) 0 0
\(545\) −20.1236 20.1236i −0.861999 0.861999i
\(546\) 0 0
\(547\) 23.6067 23.6067i 1.00935 1.00935i 0.00939353 0.999956i \(-0.497010\pi\)
0.999956 0.00939353i \(-0.00299010\pi\)
\(548\) 0 0
\(549\) 6.18406 0.263929
\(550\) 0 0
\(551\) 6.29488 0.268171
\(552\) 0 0
\(553\) 9.98907i 0.424779i
\(554\) 0 0
\(555\) −9.50913 + 9.50913i −0.403640 + 0.403640i
\(556\) 0 0
\(557\) −14.0015 + 14.0015i −0.593264 + 0.593264i −0.938512 0.345248i \(-0.887795\pi\)
0.345248 + 0.938512i \(0.387795\pi\)
\(558\) 0 0
\(559\) −10.5987 + 10.5987i −0.448278 + 0.448278i
\(560\) 0 0
\(561\) −34.6852 34.6852i −1.46441 1.46441i
\(562\) 0 0
\(563\) −7.83885 7.83885i −0.330368 0.330368i 0.522358 0.852726i \(-0.325052\pi\)
−0.852726 + 0.522358i \(0.825052\pi\)
\(564\) 0 0
\(565\) 39.0898i 1.64452i
\(566\) 0 0
\(567\) −20.3613 20.3613i −0.855093 0.855093i
\(568\) 0 0
\(569\) 19.7014i 0.825927i −0.910748 0.412964i \(-0.864494\pi\)
0.910748 0.412964i \(-0.135506\pi\)
\(570\) 0 0
\(571\) 6.75945 + 6.75945i 0.282874 + 0.282874i 0.834254 0.551380i \(-0.185899\pi\)
−0.551380 + 0.834254i \(0.685899\pi\)
\(572\) 0 0
\(573\) −2.78198 −0.116219
\(574\) 0 0
\(575\) 38.4797 1.60471
\(576\) 0 0
\(577\) −2.20792 2.20792i −0.0919167 0.0919167i 0.659653 0.751570i \(-0.270703\pi\)
−0.751570 + 0.659653i \(0.770703\pi\)
\(578\) 0 0
\(579\) 10.3255i 0.429113i
\(580\) 0 0
\(581\) −9.70925 9.70925i −0.402808 0.402808i
\(582\) 0 0
\(583\) 27.0509i 1.12033i
\(584\) 0 0
\(585\) 118.583 + 118.583i 4.90278 + 4.90278i
\(586\) 0 0
\(587\) 27.9128 + 27.9128i 1.15208 + 1.15208i 0.986134 + 0.165948i \(0.0530685\pi\)
0.165948 + 0.986134i \(0.446931\pi\)
\(588\) 0 0
\(589\) 1.70605 1.70605i 0.0702965 0.0702965i
\(590\) 0 0
\(591\) −24.5701 + 24.5701i −1.01068 + 1.01068i
\(592\) 0 0
\(593\) 14.3036 14.3036i 0.587378 0.587378i −0.349542 0.936921i \(-0.613663\pi\)
0.936921 + 0.349542i \(0.113663\pi\)
\(594\) 0 0
\(595\) 10.6703i 0.437439i
\(596\) 0 0
\(597\) −62.2190 −2.54645
\(598\) 0 0
\(599\) −6.71503 −0.274369 −0.137184 0.990546i \(-0.543805\pi\)
−0.137184 + 0.990546i \(0.543805\pi\)
\(600\) 0 0
\(601\) 32.9853 32.9853i 1.34550 1.34550i 0.455018 0.890482i \(-0.349633\pi\)
0.890482 0.455018i \(-0.150367\pi\)
\(602\) 0 0
\(603\) −5.47144 5.47144i −0.222814 0.222814i
\(604\) 0 0
\(605\) 102.716 4.17599
\(606\) 0 0
\(607\) 24.2536i 0.984424i 0.870475 + 0.492212i \(0.163812\pi\)
−0.870475 + 0.492212i \(0.836188\pi\)
\(608\) 0 0
\(609\) −4.09058 + 4.09058i −0.165759 + 0.165759i
\(610\) 0 0
\(611\) 41.5353 1.68034
\(612\) 0 0
\(613\) 1.38910i 0.0561052i −0.999606 0.0280526i \(-0.991069\pi\)
0.999606 0.0280526i \(-0.00893059\pi\)
\(614\) 0 0
\(615\) −66.7599 59.5631i −2.69202 2.40182i
\(616\) 0 0
\(617\) 44.3627i 1.78598i −0.450081 0.892988i \(-0.648605\pi\)
0.450081 0.892988i \(-0.351395\pi\)
\(618\) 0 0
\(619\) −19.6421 −0.789484 −0.394742 0.918792i \(-0.629166\pi\)
−0.394742 + 0.918792i \(0.629166\pi\)
\(620\) 0 0
\(621\) −33.1752 + 33.1752i −1.33128 + 1.33128i
\(622\) 0 0
\(623\) 7.15004i 0.286460i
\(624\) 0 0
\(625\) 79.6392 3.18557
\(626\) 0 0
\(627\) −49.4237 49.4237i −1.97379 1.97379i
\(628\) 0 0
\(629\) −1.71015 + 1.71015i −0.0681882 + 0.0681882i
\(630\) 0 0
\(631\) 18.3307 0.729734 0.364867 0.931060i \(-0.381114\pi\)
0.364867 + 0.931060i \(0.381114\pi\)
\(632\) 0 0
\(633\) 15.2918 0.607794
\(634\) 0 0
\(635\) 35.6385i 1.41427i
\(636\) 0 0
\(637\) −3.56747 + 3.56747i −0.141348 + 0.141348i
\(638\) 0 0
\(639\) 38.5119 38.5119i 1.52351 1.52351i
\(640\) 0 0
\(641\) −0.253891 + 0.253891i −0.0100281 + 0.0100281i −0.712103 0.702075i \(-0.752257\pi\)
0.702075 + 0.712103i \(0.252257\pi\)
\(642\) 0 0
\(643\) −28.2154 28.2154i −1.11270 1.11270i −0.992783 0.119922i \(-0.961736\pi\)
−0.119922 0.992783i \(-0.538264\pi\)
\(644\) 0 0
\(645\) −29.3533 29.3533i −1.15579 1.15579i
\(646\) 0 0
\(647\) 40.8997i 1.60793i 0.594675 + 0.803966i \(0.297281\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(648\) 0 0
\(649\) −5.36215 5.36215i −0.210483 0.210483i
\(650\) 0 0
\(651\) 2.21727i 0.0869018i
\(652\) 0 0
\(653\) −27.1887 27.1887i −1.06398 1.06398i −0.997808 0.0661686i \(-0.978922\pi\)
−0.0661686 0.997808i \(-0.521078\pi\)
\(654\) 0 0
\(655\) 84.4084 3.29811
\(656\) 0 0
\(657\) −71.4788 −2.78865
\(658\) 0 0
\(659\) 14.2022 + 14.2022i 0.553240 + 0.553240i 0.927375 0.374134i \(-0.122060\pi\)
−0.374134 + 0.927375i \(0.622060\pi\)
\(660\) 0 0
\(661\) 15.0450i 0.585182i −0.956238 0.292591i \(-0.905483\pi\)
0.956238 0.292591i \(-0.0945174\pi\)
\(662\) 0 0
\(663\) 29.4992 + 29.4992i 1.14565 + 1.14565i
\(664\) 0 0
\(665\) 15.2043i 0.589598i
\(666\) 0 0
\(667\) 3.67098 + 3.67098i 0.142141 + 0.142141i
\(668\) 0 0
\(669\) −11.5472 11.5472i −0.446441 0.446441i
\(670\) 0 0
\(671\) −3.31368 + 3.31368i −0.127923 + 0.127923i
\(672\) 0 0
\(673\) −1.78627 + 1.78627i −0.0688558 + 0.0688558i −0.740696 0.671840i \(-0.765504\pi\)
0.671840 + 0.740696i \(0.265504\pi\)
\(674\) 0 0
\(675\) −146.385 + 146.385i −5.63438 + 5.63438i
\(676\) 0 0
\(677\) 15.3842i 0.591263i −0.955302 0.295632i \(-0.904470\pi\)
0.955302 0.295632i \(-0.0955301\pi\)
\(678\) 0 0
\(679\) 8.13990 0.312381
\(680\) 0 0
\(681\) 65.1638 2.49708
\(682\) 0 0
\(683\) −12.9936 + 12.9936i −0.497188 + 0.497188i −0.910561 0.413374i \(-0.864350\pi\)
0.413374 + 0.910561i \(0.364350\pi\)
\(684\) 0 0
\(685\) 55.5603 + 55.5603i 2.12285 + 2.12285i
\(686\) 0 0
\(687\) 5.93514 0.226440
\(688\) 0 0
\(689\) 23.0063i 0.876471i
\(690\) 0 0
\(691\) −5.47679 + 5.47679i −0.208347 + 0.208347i −0.803565 0.595218i \(-0.797066\pi\)
0.595218 + 0.803565i \(0.297066\pi\)
\(692\) 0 0
\(693\) 46.4373 1.76401
\(694\) 0 0
\(695\) 36.5385i 1.38599i
\(696\) 0 0
\(697\) −12.0063 10.7120i −0.454771 0.405746i
\(698\) 0 0
\(699\) 51.4942i 1.94769i
\(700\) 0 0
\(701\) 32.2431 1.21780 0.608902 0.793246i \(-0.291610\pi\)
0.608902 + 0.793246i \(0.291610\pi\)
\(702\) 0 0
\(703\) −2.43683 + 2.43683i −0.0919069 + 0.0919069i
\(704\) 0 0
\(705\) 115.033i 4.33238i
\(706\) 0 0
\(707\) 11.3871 0.428256
\(708\) 0 0
\(709\) −1.52044 1.52044i −0.0571012 0.0571012i 0.677980 0.735081i \(-0.262856\pi\)
−0.735081 + 0.677980i \(0.762856\pi\)
\(710\) 0 0
\(711\) −55.2927 + 55.2927i −2.07364 + 2.07364i
\(712\) 0 0
\(713\) 1.98983 0.0745198
\(714\) 0 0
\(715\) −127.083 −4.75263
\(716\) 0 0
\(717\) 29.7281i 1.11022i
\(718\) 0 0
\(719\) −20.5352 + 20.5352i −0.765833 + 0.765833i −0.977370 0.211537i \(-0.932153\pi\)
0.211537 + 0.977370i \(0.432153\pi\)
\(720\) 0 0
\(721\) 7.32746 7.32746i 0.272889 0.272889i
\(722\) 0 0
\(723\) 32.4154 32.4154i 1.20554 1.20554i
\(724\) 0 0
\(725\) 16.1982 + 16.1982i 0.601585 + 0.601585i
\(726\) 0 0
\(727\) −22.6657 22.6657i −0.840625 0.840625i 0.148315 0.988940i \(-0.452615\pi\)
−0.988940 + 0.148315i \(0.952615\pi\)
\(728\) 0 0
\(729\) 68.5736i 2.53976i
\(730\) 0 0
\(731\) −5.27899 5.27899i −0.195251 0.195251i
\(732\) 0 0
\(733\) 35.9192i 1.32671i −0.748306 0.663353i \(-0.769133\pi\)
0.748306 0.663353i \(-0.230867\pi\)
\(734\) 0 0
\(735\) −9.88017 9.88017i −0.364435 0.364435i
\(736\) 0 0
\(737\) 5.86365 0.215990
\(738\) 0 0
\(739\) 11.4531 0.421309 0.210655 0.977561i \(-0.432440\pi\)
0.210655 + 0.977561i \(0.432440\pi\)
\(740\) 0 0
\(741\) 42.0340 + 42.0340i 1.54416 + 1.54416i
\(742\) 0 0
\(743\) 11.6759i 0.428348i −0.976796 0.214174i \(-0.931294\pi\)
0.976796 0.214174i \(-0.0687060\pi\)
\(744\) 0 0
\(745\) 18.2497 + 18.2497i 0.668617 + 0.668617i
\(746\) 0 0
\(747\) 107.488i 3.93277i
\(748\) 0 0
\(749\) −8.24756 8.24756i −0.301359 0.301359i
\(750\) 0 0
\(751\) −2.63679 2.63679i −0.0962178 0.0962178i 0.657359 0.753577i \(-0.271673\pi\)
−0.753577 + 0.657359i \(0.771673\pi\)
\(752\) 0 0
\(753\) 26.8053 26.8053i 0.976841 0.976841i
\(754\) 0 0
\(755\) −43.4616 + 43.4616i −1.58173 + 1.58173i
\(756\) 0 0
\(757\) −24.1160 + 24.1160i −0.876512 + 0.876512i −0.993172 0.116659i \(-0.962781\pi\)
0.116659 + 0.993172i \(0.462781\pi\)
\(758\) 0 0
\(759\) 57.6448i 2.09237i
\(760\) 0 0
\(761\) −21.8556 −0.792263 −0.396132 0.918194i \(-0.629648\pi\)
−0.396132 + 0.918194i \(0.629648\pi\)
\(762\) 0 0
\(763\) 6.70220 0.242636
\(764\) 0 0
\(765\) −59.0634 + 59.0634i −2.13544 + 2.13544i
\(766\) 0 0
\(767\) 4.56042 + 4.56042i 0.164667 + 0.164667i
\(768\) 0 0
\(769\) −3.19153 −0.115089 −0.0575447 0.998343i \(-0.518327\pi\)
−0.0575447 + 0.998343i \(0.518327\pi\)
\(770\) 0 0
\(771\) 94.7010i 3.41057i
\(772\) 0 0
\(773\) 12.0984 12.0984i 0.435147 0.435147i −0.455228 0.890375i \(-0.650442\pi\)
0.890375 + 0.455228i \(0.150442\pi\)
\(774\) 0 0
\(775\) 8.78011 0.315391
\(776\) 0 0
\(777\) 3.16704i 0.113617i
\(778\) 0 0
\(779\) −17.1081 15.2638i −0.612960 0.546882i
\(780\) 0 0
\(781\) 41.2726i 1.47685i
\(782\) 0 0
\(783\) −27.9305 −0.998154
\(784\) 0 0
\(785\) −54.9106 + 54.9106i −1.95984 + 1.95984i
\(786\) 0 0
\(787\) 51.3175i 1.82927i −0.404280 0.914635i \(-0.632478\pi\)
0.404280 0.914635i \(-0.367522\pi\)
\(788\) 0 0
\(789\) 91.7003 3.26462
\(790\) 0 0
\(791\) 6.50948 + 6.50948i 0.231450 + 0.231450i
\(792\) 0 0
\(793\) 2.81823 2.81823i 0.100078 0.100078i
\(794\) 0 0
\(795\) 63.7163 2.25979
\(796\) 0 0
\(797\) 14.1277 0.500429 0.250215 0.968190i \(-0.419499\pi\)
0.250215 + 0.968190i \(0.419499\pi\)
\(798\) 0 0
\(799\) 20.6878i 0.731883i
\(800\) 0 0
\(801\) 39.5777