Properties

Label 324.3.o.a.5.5
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.61407 - 1.47195i) q^{3} +(7.35484 - 5.47548i) q^{5} +(2.16180 - 1.42184i) q^{7} +(4.66673 + 7.69556i) q^{9} +O(q^{10})\) \(q+(-2.61407 - 1.47195i) q^{3} +(7.35484 - 5.47548i) q^{5} +(2.16180 - 1.42184i) q^{7} +(4.66673 + 7.69556i) q^{9} +(1.90463 - 16.2951i) q^{11} +(5.51865 + 18.4336i) q^{13} +(-27.2857 + 3.48733i) q^{15} +(2.42175 + 0.427020i) q^{17} +(-0.578712 - 3.28204i) q^{19} +(-7.74398 + 0.534727i) q^{21} +(2.97065 - 4.51665i) q^{23} +(16.9428 - 56.5928i) q^{25} +(-0.871702 - 26.9859i) q^{27} +(-20.3292 + 19.1797i) q^{29} +(1.91430 - 32.8672i) q^{31} +(-28.9645 + 39.7932i) q^{33} +(8.11447 - 22.2943i) q^{35} +(-32.4429 + 11.8083i) q^{37} +(12.7071 - 56.3099i) q^{39} +(18.6748 - 78.7953i) q^{41} +(-11.9365 - 27.6720i) q^{43} +(76.4600 + 31.0470i) q^{45} +(64.6646 - 3.76628i) q^{47} +(-16.7561 + 38.8451i) q^{49} +(-5.70208 - 4.68095i) q^{51} +(-25.5689 - 14.7622i) q^{53} +(-75.2155 - 130.277i) q^{55} +(-3.31820 + 9.43132i) q^{57} +(8.73474 + 74.7305i) q^{59} +(17.6094 + 8.84378i) q^{61} +(21.0304 + 10.0009i) q^{63} +(141.522 + 105.359i) q^{65} +(-52.8216 + 55.9876i) q^{67} +(-14.4138 + 7.43420i) q^{69} +(-45.5910 + 54.3333i) q^{71} +(35.3645 - 29.6743i) q^{73} +(-127.591 + 122.999i) q^{75} +(-19.0517 - 37.9350i) q^{77} +(-110.642 + 26.2225i) q^{79} +(-37.4432 + 71.8262i) q^{81} +(21.6720 + 91.4413i) q^{83} +(20.1497 - 10.1196i) q^{85} +(81.3735 - 20.2134i) q^{87} +(60.8048 + 72.4644i) q^{89} +(38.1398 + 32.0031i) q^{91} +(-53.3830 + 83.0995i) q^{93} +(-22.2271 - 20.9702i) q^{95} +(84.6863 - 113.753i) q^{97} +(134.289 - 61.3879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) −2.61407 1.47195i −0.871357 0.490650i
\(4\) 0 0
\(5\) 7.35484 5.47548i 1.47097 1.09510i 0.497178 0.867648i \(-0.334369\pi\)
0.973790 0.227447i \(-0.0730380\pi\)
\(6\) 0 0
\(7\) 2.16180 1.42184i 0.308829 0.203120i −0.385628 0.922654i \(-0.626015\pi\)
0.694457 + 0.719534i \(0.255645\pi\)
\(8\) 0 0
\(9\) 4.66673 + 7.69556i 0.518526 + 0.855062i
\(10\) 0 0
\(11\) 1.90463 16.2951i 0.173148 1.48138i −0.575168 0.818035i \(-0.695063\pi\)
0.748316 0.663342i \(-0.230863\pi\)
\(12\) 0 0
\(13\) 5.51865 + 18.4336i 0.424512 + 1.41797i 0.856527 + 0.516102i \(0.172617\pi\)
−0.432015 + 0.901866i \(0.642197\pi\)
\(14\) 0 0
\(15\) −27.2857 + 3.48733i −1.81905 + 0.232489i
\(16\) 0 0
\(17\) 2.42175 + 0.427020i 0.142456 + 0.0251188i 0.244421 0.969669i \(-0.421402\pi\)
−0.101965 + 0.994788i \(0.532513\pi\)
\(18\) 0 0
\(19\) −0.578712 3.28204i −0.0304586 0.172739i 0.965784 0.259349i \(-0.0835078\pi\)
−0.996242 + 0.0866096i \(0.972397\pi\)
\(20\) 0 0
\(21\) −7.74398 + 0.534727i −0.368761 + 0.0254632i
\(22\) 0 0
\(23\) 2.97065 4.51665i 0.129158 0.196376i −0.765119 0.643889i \(-0.777320\pi\)
0.894277 + 0.447513i \(0.147690\pi\)
\(24\) 0 0
\(25\) 16.9428 56.5928i 0.677711 2.26371i
\(26\) 0 0
\(27\) −0.871702 26.9859i −0.0322853 0.999479i
\(28\) 0 0
\(29\) −20.3292 + 19.1797i −0.701008 + 0.661367i −0.951816 0.306670i \(-0.900785\pi\)
0.250808 + 0.968037i \(0.419304\pi\)
\(30\) 0 0
\(31\) 1.91430 32.8672i 0.0617515 1.06023i −0.815053 0.579386i \(-0.803292\pi\)
0.876805 0.480847i \(-0.159671\pi\)
\(32\) 0 0
\(33\) −28.9645 + 39.7932i −0.877711 + 1.20585i
\(34\) 0 0
\(35\) 8.11447 22.2943i 0.231842 0.636980i
\(36\) 0 0
\(37\) −32.4429 + 11.8083i −0.876835 + 0.319142i −0.740932 0.671580i \(-0.765616\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(38\) 0 0
\(39\) 12.7071 56.3099i 0.325824 1.44384i
\(40\) 0 0
\(41\) 18.6748 78.7953i 0.455483 1.92184i 0.0745983 0.997214i \(-0.476233\pi\)
0.380885 0.924622i \(-0.375619\pi\)
\(42\) 0 0
\(43\) −11.9365 27.6720i −0.277594 0.643536i 0.721195 0.692732i \(-0.243593\pi\)
−0.998789 + 0.0491965i \(0.984334\pi\)
\(44\) 0 0
\(45\) 76.4600 + 31.0470i 1.69911 + 0.689934i
\(46\) 0 0
\(47\) 64.6646 3.76628i 1.37584 0.0801336i 0.645784 0.763520i \(-0.276530\pi\)
0.730057 + 0.683386i \(0.239493\pi\)
\(48\) 0 0
\(49\) −16.7561 + 38.8451i −0.341962 + 0.792757i
\(50\) 0 0
\(51\) −5.70208 4.68095i −0.111805 0.0917834i
\(52\) 0 0
\(53\) −25.5689 14.7622i −0.482432 0.278532i 0.238998 0.971020i \(-0.423181\pi\)
−0.721429 + 0.692488i \(0.756515\pi\)
\(54\) 0 0
\(55\) −75.2155 130.277i −1.36755 2.36867i
\(56\) 0 0
\(57\) −3.31820 + 9.43132i −0.0582141 + 0.165462i
\(58\) 0 0
\(59\) 8.73474 + 74.7305i 0.148046 + 1.26662i 0.839165 + 0.543877i \(0.183044\pi\)
−0.691119 + 0.722741i \(0.742882\pi\)
\(60\) 0 0
\(61\) 17.6094 + 8.84378i 0.288679 + 0.144980i 0.587246 0.809409i \(-0.300212\pi\)
−0.298567 + 0.954389i \(0.596509\pi\)
\(62\) 0 0
\(63\) 21.0304 + 10.0009i 0.333816 + 0.158745i
\(64\) 0 0
\(65\) 141.522 + 105.359i 2.17725 + 1.62091i
\(66\) 0 0
\(67\) −52.8216 + 55.9876i −0.788382 + 0.835636i −0.989590 0.143913i \(-0.954032\pi\)
0.201209 + 0.979548i \(0.435513\pi\)
\(68\) 0 0
\(69\) −14.4138 + 7.43420i −0.208895 + 0.107742i
\(70\) 0 0
\(71\) −45.5910 + 54.3333i −0.642127 + 0.765257i −0.984705 0.174232i \(-0.944256\pi\)
0.342577 + 0.939490i \(0.388700\pi\)
\(72\) 0 0
\(73\) 35.3645 29.6743i 0.484445 0.406498i −0.367586 0.929990i \(-0.619815\pi\)
0.852031 + 0.523492i \(0.175371\pi\)
\(74\) 0 0
\(75\) −127.591 + 122.999i −1.70122 + 1.63998i
\(76\) 0 0
\(77\) −19.0517 37.9350i −0.247424 0.492662i
\(78\) 0 0
\(79\) −110.642 + 26.2225i −1.40053 + 0.331931i −0.860386 0.509643i \(-0.829777\pi\)
−0.540141 + 0.841574i \(0.681629\pi\)
\(80\) 0 0
\(81\) −37.4432 + 71.8262i −0.462262 + 0.886743i
\(82\) 0 0
\(83\) 21.6720 + 91.4413i 0.261108 + 1.10170i 0.932663 + 0.360748i \(0.117478\pi\)
−0.671555 + 0.740955i \(0.734373\pi\)
\(84\) 0 0
\(85\) 20.1497 10.1196i 0.237056 0.119054i
\(86\) 0 0
\(87\) 81.3735 20.2134i 0.935328 0.232337i
\(88\) 0 0
\(89\) 60.8048 + 72.4644i 0.683200 + 0.814206i 0.990515 0.137401i \(-0.0438750\pi\)
−0.307315 + 0.951608i \(0.599431\pi\)
\(90\) 0 0
\(91\) 38.1398 + 32.0031i 0.419119 + 0.351683i
\(92\) 0 0
\(93\) −53.3830 + 83.0995i −0.574010 + 0.893543i
\(94\) 0 0
\(95\) −22.2271 20.9702i −0.233969 0.220739i
\(96\) 0 0
\(97\) 84.6863 113.753i 0.873054 1.17272i −0.110818 0.993841i \(-0.535347\pi\)
0.983872 0.178875i \(-0.0572457\pi\)
\(98\) 0 0
\(99\) 134.289 61.3879i 1.35645 0.620080i
\(100\) 0 0
\(101\) 3.32962 6.62981i 0.0329665 0.0656417i −0.876546 0.481317i \(-0.840159\pi\)
0.909513 + 0.415676i \(0.136455\pi\)
\(102\) 0 0
\(103\) −45.0910 + 5.27038i −0.437777 + 0.0511688i −0.332127 0.943235i \(-0.607766\pi\)
−0.105650 + 0.994403i \(0.533692\pi\)
\(104\) 0 0
\(105\) −54.0279 + 46.3348i −0.514551 + 0.441284i
\(106\) 0 0
\(107\) 64.4406 37.2048i 0.602249 0.347708i −0.167677 0.985842i \(-0.553627\pi\)
0.769926 + 0.638134i \(0.220293\pi\)
\(108\) 0 0
\(109\) 28.5195 49.3972i 0.261646 0.453185i −0.705033 0.709174i \(-0.749068\pi\)
0.966680 + 0.255989i \(0.0824012\pi\)
\(110\) 0 0
\(111\) 102.189 + 16.8867i 0.920624 + 0.152132i
\(112\) 0 0
\(113\) 124.881 + 53.8682i 1.10514 + 0.476710i 0.868901 0.494986i \(-0.164827\pi\)
0.236236 + 0.971696i \(0.424086\pi\)
\(114\) 0 0
\(115\) −2.88217 49.4849i −0.0250623 0.430304i
\(116\) 0 0
\(117\) −116.103 + 128.494i −0.992330 + 1.09824i
\(118\) 0 0
\(119\) 5.84250 2.52021i 0.0490967 0.0211782i
\(120\) 0 0
\(121\) −144.166 34.1679i −1.19145 0.282380i
\(122\) 0 0
\(123\) −164.800 + 178.488i −1.33984 + 1.45112i
\(124\) 0 0
\(125\) −106.860 293.595i −0.854879 2.34876i
\(126\) 0 0
\(127\) 125.934 + 45.8361i 0.991604 + 0.360914i 0.786341 0.617792i \(-0.211973\pi\)
0.205263 + 0.978707i \(0.434195\pi\)
\(128\) 0 0
\(129\) −9.52883 + 89.9066i −0.0738669 + 0.696951i
\(130\) 0 0
\(131\) −208.470 12.1420i −1.59137 0.0926868i −0.760570 0.649256i \(-0.775080\pi\)
−0.830801 + 0.556570i \(0.812117\pi\)
\(132\) 0 0
\(133\) −5.91760 6.27229i −0.0444932 0.0471601i
\(134\) 0 0
\(135\) −154.172 193.704i −1.14202 1.43485i
\(136\) 0 0
\(137\) 164.825 + 49.3452i 1.20310 + 0.360184i 0.824760 0.565483i \(-0.191310\pi\)
0.378339 + 0.925667i \(0.376495\pi\)
\(138\) 0 0
\(139\) −26.7418 17.5884i −0.192387 0.126535i 0.449661 0.893199i \(-0.351545\pi\)
−0.642048 + 0.766664i \(0.721915\pi\)
\(140\) 0 0
\(141\) −174.581 85.3376i −1.23817 0.605231i
\(142\) 0 0
\(143\) 310.889 54.8181i 2.17405 0.383344i
\(144\) 0 0
\(145\) −44.5006 + 252.376i −0.306901 + 1.74052i
\(146\) 0 0
\(147\) 100.980 76.8797i 0.686937 0.522991i
\(148\) 0 0
\(149\) 94.4698 28.2824i 0.634025 0.189815i 0.0463677 0.998924i \(-0.485235\pi\)
0.587658 + 0.809110i \(0.300050\pi\)
\(150\) 0 0
\(151\) 1.12008 + 0.130919i 0.00741777 + 0.000867012i 0.119801 0.992798i \(-0.461774\pi\)
−0.112383 + 0.993665i \(0.535848\pi\)
\(152\) 0 0
\(153\) 8.01551 + 20.6295i 0.0523889 + 0.134833i
\(154\) 0 0
\(155\) −165.884 252.215i −1.07022 1.62719i
\(156\) 0 0
\(157\) 83.8996 + 112.697i 0.534392 + 0.717813i 0.984544 0.175139i \(-0.0560374\pi\)
−0.450152 + 0.892952i \(0.648630\pi\)
\(158\) 0 0
\(159\) 45.1097 + 76.2255i 0.283709 + 0.479406i
\(160\) 0 0
\(161\) 13.9879i 0.0868812i
\(162\) 0 0
\(163\) 211.418 1.29705 0.648523 0.761195i \(-0.275387\pi\)
0.648523 + 0.761195i \(0.275387\pi\)
\(164\) 0 0
\(165\) 4.85746 + 451.267i 0.0294391 + 2.73495i
\(166\) 0 0
\(167\) −187.010 + 139.224i −1.11982 + 0.833675i −0.987514 0.157534i \(-0.949646\pi\)
−0.132306 + 0.991209i \(0.542238\pi\)
\(168\) 0 0
\(169\) −168.144 + 110.590i −0.994936 + 0.654380i
\(170\) 0 0
\(171\) 22.5564 19.7699i 0.131909 0.115614i
\(172\) 0 0
\(173\) 2.63088 22.5086i 0.0152074 0.130107i −0.983502 0.180897i \(-0.942100\pi\)
0.998709 + 0.0507899i \(0.0161739\pi\)
\(174\) 0 0
\(175\) −43.8390 146.432i −0.250509 0.836757i
\(176\) 0 0
\(177\) 87.1662 208.208i 0.492464 1.17632i
\(178\) 0 0
\(179\) 286.613 + 50.5377i 1.60119 + 0.282333i 0.901718 0.432324i \(-0.142306\pi\)
0.699474 + 0.714658i \(0.253418\pi\)
\(180\) 0 0
\(181\) 39.5528 + 224.315i 0.218524 + 1.23931i 0.874686 + 0.484689i \(0.161067\pi\)
−0.656163 + 0.754619i \(0.727821\pi\)
\(182\) 0 0
\(183\) −33.0147 49.0384i −0.180408 0.267970i
\(184\) 0 0
\(185\) −173.957 + 264.488i −0.940307 + 1.42967i
\(186\) 0 0
\(187\) 11.5709 38.6495i 0.0618764 0.206682i
\(188\) 0 0
\(189\) −40.2541 57.0988i −0.212985 0.302110i
\(190\) 0 0
\(191\) −105.227 + 99.2761i −0.550924 + 0.519770i −0.910590 0.413311i \(-0.864372\pi\)
0.359666 + 0.933081i \(0.382891\pi\)
\(192\) 0 0
\(193\) 7.66984 131.686i 0.0397401 0.682311i −0.918337 0.395800i \(-0.870467\pi\)
0.958077 0.286511i \(-0.0924956\pi\)
\(194\) 0 0
\(195\) −214.864 483.728i −1.10187 2.48066i
\(196\) 0 0
\(197\) −0.663587 + 1.82319i −0.00336846 + 0.00925477i −0.941365 0.337389i \(-0.890456\pi\)
0.937997 + 0.346643i \(0.112679\pi\)
\(198\) 0 0
\(199\) 231.669 84.3205i 1.16416 0.423721i 0.313581 0.949561i \(-0.398471\pi\)
0.850583 + 0.525840i \(0.176249\pi\)
\(200\) 0 0
\(201\) 220.490 68.6049i 1.09697 0.341318i
\(202\) 0 0
\(203\) −16.6774 + 70.3675i −0.0821547 + 0.346638i
\(204\) 0 0
\(205\) −294.091 681.781i −1.43459 3.32576i
\(206\) 0 0
\(207\) 48.6213 + 1.78279i 0.234886 + 0.00861250i
\(208\) 0 0
\(209\) −54.5836 + 3.17913i −0.261165 + 0.0152112i
\(210\) 0 0
\(211\) −133.335 + 309.105i −0.631918 + 1.46495i 0.237757 + 0.971325i \(0.423588\pi\)
−0.869674 + 0.493626i \(0.835671\pi\)
\(212\) 0 0
\(213\) 199.154 74.9234i 0.934995 0.351753i
\(214\) 0 0
\(215\) −239.309 138.165i −1.11307 0.642629i
\(216\) 0 0
\(217\) −42.5936 73.7742i −0.196284 0.339973i
\(218\) 0 0
\(219\) −136.124 + 25.5161i −0.621572 + 0.116512i
\(220\) 0 0
\(221\) 5.49329 + 46.9981i 0.0248565 + 0.212661i
\(222\) 0 0
\(223\) 108.396 + 54.4385i 0.486080 + 0.244119i 0.674922 0.737889i \(-0.264177\pi\)
−0.188842 + 0.982007i \(0.560473\pi\)
\(224\) 0 0
\(225\) 514.581 133.720i 2.28703 0.594309i
\(226\) 0 0
\(227\) −117.879 87.7578i −0.519291 0.386598i 0.305362 0.952236i \(-0.401222\pi\)
−0.824653 + 0.565638i \(0.808630\pi\)
\(228\) 0 0
\(229\) 61.6777 65.3745i 0.269335 0.285478i −0.578563 0.815638i \(-0.696386\pi\)
0.847898 + 0.530159i \(0.177868\pi\)
\(230\) 0 0
\(231\) −6.03595 + 127.208i −0.0261297 + 0.550683i
\(232\) 0 0
\(233\) 223.982 266.932i 0.961298 1.14563i −0.0279834 0.999608i \(-0.508909\pi\)
0.989281 0.146022i \(-0.0466470\pi\)
\(234\) 0 0
\(235\) 454.976 381.770i 1.93607 1.62455i
\(236\) 0 0
\(237\) 327.823 + 94.3112i 1.38322 + 0.397938i
\(238\) 0 0
\(239\) 55.4982 + 110.506i 0.232210 + 0.462369i 0.979316 0.202337i \(-0.0648535\pi\)
−0.747106 + 0.664705i \(0.768557\pi\)
\(240\) 0 0
\(241\) −409.705 + 97.1020i −1.70002 + 0.402913i −0.962257 0.272144i \(-0.912267\pi\)
−0.737766 + 0.675057i \(0.764119\pi\)
\(242\) 0 0
\(243\) 203.604 132.644i 0.837875 0.545861i
\(244\) 0 0
\(245\) 89.4567 + 377.448i 0.365130 + 1.54060i
\(246\) 0 0
\(247\) 57.3061 28.7802i 0.232008 0.116519i
\(248\) 0 0
\(249\) 77.9448 270.934i 0.313031 1.08809i
\(250\) 0 0
\(251\) −87.4266 104.191i −0.348313 0.415103i 0.563235 0.826297i \(-0.309557\pi\)
−0.911548 + 0.411193i \(0.865112\pi\)
\(252\) 0 0
\(253\) −67.9415 57.0096i −0.268543 0.225335i
\(254\) 0 0
\(255\) −67.5684 3.20609i −0.264974 0.0125729i
\(256\) 0 0
\(257\) 33.1761 + 31.3000i 0.129090 + 0.121790i 0.748079 0.663609i \(-0.230976\pi\)
−0.618990 + 0.785399i \(0.712458\pi\)
\(258\) 0 0
\(259\) −53.3457 + 71.6557i −0.205968 + 0.276663i
\(260\) 0 0
\(261\) −242.469 66.9385i −0.929001 0.256470i
\(262\) 0 0
\(263\) 12.2130 24.3182i 0.0464374 0.0924645i −0.869217 0.494430i \(-0.835377\pi\)
0.915655 + 0.401966i \(0.131673\pi\)
\(264\) 0 0
\(265\) −268.885 + 31.4282i −1.01466 + 0.118597i
\(266\) 0 0
\(267\) −52.2843 278.929i −0.195821 1.04468i
\(268\) 0 0
\(269\) −125.773 + 72.6152i −0.467558 + 0.269945i −0.715217 0.698902i \(-0.753672\pi\)
0.247659 + 0.968847i \(0.420339\pi\)
\(270\) 0 0
\(271\) −217.713 + 377.090i −0.803370 + 1.39148i 0.114017 + 0.993479i \(0.463628\pi\)
−0.917386 + 0.397998i \(0.869705\pi\)
\(272\) 0 0
\(273\) −52.5933 139.798i −0.192649 0.512082i
\(274\) 0 0
\(275\) −889.919 383.874i −3.23607 1.39590i
\(276\) 0 0
\(277\) 2.73450 + 46.9495i 0.00987183 + 0.169493i 0.999641 + 0.0268115i \(0.00853538\pi\)
−0.989769 + 0.142681i \(0.954428\pi\)
\(278\) 0 0
\(279\) 261.865 138.651i 0.938584 0.496957i
\(280\) 0 0
\(281\) 176.050 75.9404i 0.626511 0.270250i −0.0590621 0.998254i \(-0.518811\pi\)
0.685573 + 0.728004i \(0.259552\pi\)
\(282\) 0 0
\(283\) 12.5946 + 2.98497i 0.0445037 + 0.0105476i 0.252807 0.967517i \(-0.418646\pi\)
−0.208304 + 0.978064i \(0.566794\pi\)
\(284\) 0 0
\(285\) 27.2362 + 87.5347i 0.0955655 + 0.307139i
\(286\) 0 0
\(287\) −71.6630 196.892i −0.249697 0.686036i
\(288\) 0 0
\(289\) −265.889 96.7755i −0.920030 0.334863i
\(290\) 0 0
\(291\) −388.815 + 172.706i −1.33613 + 0.593490i
\(292\) 0 0
\(293\) −282.337 16.4443i −0.963609 0.0561238i −0.430879 0.902410i \(-0.641797\pi\)
−0.532729 + 0.846286i \(0.678834\pi\)
\(294\) 0 0
\(295\) 473.428 + 501.804i 1.60484 + 1.70103i
\(296\) 0 0
\(297\) −441.400 37.1937i −1.48620 0.125231i
\(298\) 0 0
\(299\) 99.6520 + 29.8338i 0.333284 + 0.0997787i
\(300\) 0 0
\(301\) −65.1497 42.8496i −0.216444 0.142357i
\(302\) 0 0
\(303\) −18.4626 + 12.4298i −0.0609327 + 0.0410224i
\(304\) 0 0
\(305\) 177.938 31.3754i 0.583405 0.102870i
\(306\) 0 0
\(307\) −47.8807 + 271.545i −0.155963 + 0.884512i 0.801937 + 0.597409i \(0.203803\pi\)
−0.957900 + 0.287103i \(0.907308\pi\)
\(308\) 0 0
\(309\) 125.629 + 52.5945i 0.406566 + 0.170209i
\(310\) 0 0
\(311\) −96.2193 + 28.8062i −0.309387 + 0.0926243i −0.437733 0.899105i \(-0.644218\pi\)
0.128346 + 0.991729i \(0.459033\pi\)
\(312\) 0 0
\(313\) 232.509 + 27.1764i 0.742841 + 0.0868257i 0.479091 0.877765i \(-0.340966\pi\)
0.263750 + 0.964591i \(0.415041\pi\)
\(314\) 0 0
\(315\) 209.435 41.5963i 0.664874 0.132052i
\(316\) 0 0
\(317\) 186.925 + 284.206i 0.589669 + 0.896548i 0.999881 0.0154422i \(-0.00491559\pi\)
−0.410212 + 0.911990i \(0.634545\pi\)
\(318\) 0 0
\(319\) 273.816 + 367.798i 0.858356 + 1.15297i
\(320\) 0 0
\(321\) −223.216 + 2.40271i −0.695377 + 0.00748506i
\(322\) 0 0
\(323\) 8.19541i 0.0253728i
\(324\) 0 0
\(325\) 1136.71 3.49757
\(326\) 0 0
\(327\) −147.262 + 87.1485i −0.450343 + 0.266509i
\(328\) 0 0
\(329\) 134.437 100.085i 0.408623 0.304209i
\(330\) 0 0
\(331\) 91.5328 60.2020i 0.276534 0.181879i −0.403665 0.914907i \(-0.632264\pi\)
0.680199 + 0.733028i \(0.261893\pi\)
\(332\) 0 0
\(333\) −242.273 194.560i −0.727548 0.584265i
\(334\) 0 0
\(335\) −81.9355 + 701.003i −0.244584 + 2.09255i
\(336\) 0 0
\(337\) 108.367 + 361.973i 0.321565 + 1.07410i 0.954079 + 0.299554i \(0.0968378\pi\)
−0.632514 + 0.774549i \(0.717977\pi\)
\(338\) 0 0
\(339\) −247.155 324.633i −0.729072 0.957620i
\(340\) 0 0
\(341\) −531.930 93.7936i −1.55991 0.275055i
\(342\) 0 0
\(343\) 41.0242 + 232.660i 0.119604 + 0.678309i
\(344\) 0 0
\(345\) −65.3051 + 133.600i −0.189290 + 0.387245i
\(346\) 0 0
\(347\) 118.277 179.831i 0.340855 0.518245i −0.623862 0.781535i \(-0.714437\pi\)
0.964717 + 0.263290i \(0.0848075\pi\)
\(348\) 0 0
\(349\) 80.4521 268.729i 0.230522 0.769997i −0.761962 0.647622i \(-0.775764\pi\)
0.992484 0.122375i \(-0.0390511\pi\)
\(350\) 0 0
\(351\) 492.637 164.995i 1.40352 0.470070i
\(352\) 0 0
\(353\) 361.019 340.604i 1.02272 0.964883i 0.0233234 0.999728i \(-0.492575\pi\)
0.999393 + 0.0348451i \(0.0110938\pi\)
\(354\) 0 0
\(355\) −37.8142 + 649.246i −0.106519 + 1.82886i
\(356\) 0 0
\(357\) −18.9823 2.01186i −0.0531718 0.00563546i
\(358\) 0 0
\(359\) 7.97397 21.9083i 0.0222116 0.0610259i −0.928091 0.372353i \(-0.878551\pi\)
0.950303 + 0.311327i \(0.100773\pi\)
\(360\) 0 0
\(361\) 328.792 119.671i 0.910782 0.331497i
\(362\) 0 0
\(363\) 326.566 + 301.522i 0.899632 + 0.830640i
\(364\) 0 0
\(365\) 97.6191 411.888i 0.267450 1.12846i
\(366\) 0 0
\(367\) 56.6167 + 131.252i 0.154269 + 0.357636i 0.977770 0.209679i \(-0.0672417\pi\)
−0.823501 + 0.567314i \(0.807982\pi\)
\(368\) 0 0
\(369\) 693.524 224.003i 1.87947 0.607055i
\(370\) 0 0
\(371\) −76.2644 + 4.44189i −0.205564 + 0.0119728i
\(372\) 0 0
\(373\) −244.262 + 566.264i −0.654859 + 1.51813i 0.189231 + 0.981933i \(0.439400\pi\)
−0.844090 + 0.536201i \(0.819859\pi\)
\(374\) 0 0
\(375\) −152.818 + 924.771i −0.407514 + 2.46606i
\(376\) 0 0
\(377\) −465.740 268.895i −1.23538 0.713249i
\(378\) 0 0
\(379\) −338.338 586.019i −0.892713 1.54622i −0.836609 0.547800i \(-0.815466\pi\)
−0.0561038 0.998425i \(-0.517868\pi\)
\(380\) 0 0
\(381\) −261.731 305.187i −0.686959 0.801016i
\(382\) 0 0
\(383\) 1.60995 + 13.7740i 0.00420352 + 0.0359634i 0.995177 0.0980922i \(-0.0312740\pi\)
−0.990974 + 0.134056i \(0.957200\pi\)
\(384\) 0 0
\(385\) −347.834 174.689i −0.903465 0.453737i
\(386\) 0 0
\(387\) 157.247 220.996i 0.406323 0.571050i
\(388\) 0 0
\(389\) −417.802 311.042i −1.07404 0.799593i −0.0934427 0.995625i \(-0.529787\pi\)
−0.980598 + 0.196031i \(0.937195\pi\)
\(390\) 0 0
\(391\) 9.12286 9.66967i 0.0233321 0.0247306i
\(392\) 0 0
\(393\) 527.082 + 338.597i 1.34118 + 0.861569i
\(394\) 0 0
\(395\) −670.171 + 798.679i −1.69664 + 2.02197i
\(396\) 0 0
\(397\) −568.768 + 477.253i −1.43266 + 1.20215i −0.488548 + 0.872537i \(0.662473\pi\)
−0.944117 + 0.329611i \(0.893082\pi\)
\(398\) 0 0
\(399\) 6.23654 + 25.1066i 0.0156304 + 0.0629238i
\(400\) 0 0
\(401\) 87.1398 + 173.510i 0.217306 + 0.432692i 0.975702 0.219102i \(-0.0703128\pi\)
−0.758396 + 0.651794i \(0.774016\pi\)
\(402\) 0 0
\(403\) 616.425 146.095i 1.52959 0.362520i
\(404\) 0 0
\(405\) 117.894 + 733.290i 0.291096 + 1.81059i
\(406\) 0 0
\(407\) 130.626 + 551.152i 0.320947 + 1.35418i
\(408\) 0 0
\(409\) −611.565 + 307.140i −1.49527 + 0.750953i −0.993477 0.114035i \(-0.963622\pi\)
−0.501793 + 0.864988i \(0.667326\pi\)
\(410\) 0 0
\(411\) −358.229 371.605i −0.871605 0.904149i
\(412\) 0 0
\(413\) 125.138 + 149.133i 0.302996 + 0.361097i
\(414\) 0 0
\(415\) 660.079 + 553.872i 1.59055 + 1.33463i
\(416\) 0 0
\(417\) 44.0158 + 85.3399i 0.105554 + 0.204652i
\(418\) 0 0
\(419\) −28.9193 27.2839i −0.0690198 0.0651168i 0.650959 0.759113i \(-0.274367\pi\)
−0.719979 + 0.693996i \(0.755848\pi\)
\(420\) 0 0
\(421\) 254.401 341.720i 0.604278 0.811686i −0.389738 0.920926i \(-0.627434\pi\)
0.994015 + 0.109240i \(0.0348417\pi\)
\(422\) 0 0
\(423\) 330.756 + 480.054i 0.781929 + 1.13488i
\(424\) 0 0
\(425\) 65.1975 129.819i 0.153406 0.305456i
\(426\) 0 0
\(427\) 50.6425 5.91926i 0.118601 0.0138624i
\(428\) 0 0
\(429\) −893.375 314.314i −2.08246 0.732667i
\(430\) 0 0
\(431\) 452.147 261.047i 1.04907 0.605678i 0.126678 0.991944i \(-0.459569\pi\)
0.922388 + 0.386266i \(0.126235\pi\)
\(432\) 0 0
\(433\) −114.805 + 198.848i −0.265138 + 0.459232i −0.967600 0.252489i \(-0.918751\pi\)
0.702462 + 0.711721i \(0.252084\pi\)
\(434\) 0 0
\(435\) 487.812 594.225i 1.12141 1.36603i
\(436\) 0 0
\(437\) −16.5430 7.13594i −0.0378558 0.0163294i
\(438\) 0 0
\(439\) −12.7902 219.600i −0.0291349 0.500227i −0.981036 0.193823i \(-0.937911\pi\)
0.951902 0.306404i \(-0.0991259\pi\)
\(440\) 0 0
\(441\) −377.131 + 52.3319i −0.855173 + 0.118666i
\(442\) 0 0
\(443\) −209.963 + 90.5691i −0.473957 + 0.204445i −0.619640 0.784886i \(-0.712721\pi\)
0.145683 + 0.989331i \(0.453462\pi\)
\(444\) 0 0
\(445\) 843.987 + 200.029i 1.89660 + 0.449503i
\(446\) 0 0
\(447\) −288.581 65.1225i −0.645595 0.145688i
\(448\) 0 0
\(449\) 300.809 + 826.465i 0.669952 + 1.84068i 0.524707 + 0.851283i \(0.324175\pi\)
0.145245 + 0.989396i \(0.453603\pi\)
\(450\) 0 0
\(451\) −1248.41 454.385i −2.76810 1.00751i
\(452\) 0 0
\(453\) −2.73527 1.99094i −0.00603812 0.00439500i
\(454\) 0 0
\(455\) 455.745 + 26.5441i 1.00164 + 0.0583387i
\(456\) 0 0
\(457\) −445.066 471.742i −0.973886 1.03226i −0.999469 0.0325863i \(-0.989626\pi\)
0.0255828 0.999673i \(-0.491856\pi\)
\(458\) 0 0
\(459\) 9.41248 65.7254i 0.0205065 0.143193i
\(460\) 0 0
\(461\) −19.1993 5.74789i −0.0416471 0.0124683i 0.265912 0.963997i \(-0.414327\pi\)
−0.307559 + 0.951529i \(0.599512\pi\)
\(462\) 0 0
\(463\) −194.327 127.811i −0.419713 0.276049i 0.322036 0.946727i \(-0.395633\pi\)
−0.741749 + 0.670678i \(0.766003\pi\)
\(464\) 0 0
\(465\) 62.3860 + 903.481i 0.134163 + 1.94297i
\(466\) 0 0
\(467\) −129.981 + 22.9192i −0.278333 + 0.0490776i −0.311072 0.950386i \(-0.600688\pi\)
0.0327392 + 0.999464i \(0.489577\pi\)
\(468\) 0 0
\(469\) −34.5844 + 196.138i −0.0737407 + 0.418205i
\(470\) 0 0
\(471\) −53.4357 418.093i −0.113452 0.887671i
\(472\) 0 0
\(473\) −473.655 + 141.803i −1.00138 + 0.299795i
\(474\) 0 0
\(475\) −195.545 22.8559i −0.411674 0.0481178i
\(476\) 0 0
\(477\) −5.71977 265.658i −0.0119911 0.556935i
\(478\) 0 0
\(479\) 204.550 + 311.003i 0.427036 + 0.649277i 0.983356 0.181692i \(-0.0581573\pi\)
−0.556320 + 0.830968i \(0.687787\pi\)
\(480\) 0 0
\(481\) −396.710 532.874i −0.824760 1.10785i
\(482\) 0 0
\(483\) −20.5894 + 36.5653i −0.0426282 + 0.0757046i
\(484\) 0 0
\(485\) 1300.34i 2.68111i
\(486\) 0 0
\(487\) 545.569 1.12027 0.560133 0.828403i \(-0.310750\pi\)
0.560133 + 0.828403i \(0.310750\pi\)
\(488\) 0 0
\(489\) −552.663 311.197i −1.13019 0.636395i
\(490\) 0 0
\(491\) −154.242 + 114.829i −0.314139 + 0.233868i −0.742667 0.669661i \(-0.766440\pi\)
0.428528 + 0.903528i \(0.359032\pi\)
\(492\) 0 0
\(493\) −57.4225 + 37.7673i −0.116476 + 0.0766072i
\(494\) 0 0
\(495\) 651.544 1186.79i 1.31625 2.39756i
\(496\) 0 0
\(497\) −21.3056 + 182.281i −0.0428684 + 0.366763i
\(498\) 0 0
\(499\) 100.380 + 335.293i 0.201163 + 0.671930i 0.997728 + 0.0673768i \(0.0214630\pi\)
−0.796565 + 0.604553i \(0.793352\pi\)
\(500\) 0 0
\(501\) 693.787 88.6716i 1.38480 0.176989i
\(502\) 0 0
\(503\) −28.7858 5.07571i −0.0572281 0.0100909i 0.144961 0.989437i \(-0.453694\pi\)
−0.202189 + 0.979347i \(0.564806\pi\)
\(504\) 0 0
\(505\) −11.8126 66.9925i −0.0233913 0.132658i
\(506\) 0 0
\(507\) 602.324 41.5909i 1.18802 0.0820333i
\(508\) 0 0
\(509\) −382.853 + 582.099i −0.752166 + 1.14361i 0.233078 + 0.972458i \(0.425120\pi\)
−0.985244 + 0.171155i \(0.945250\pi\)
\(510\) 0 0
\(511\) 34.2589 114.433i 0.0670428 0.223939i
\(512\) 0 0
\(513\) −88.0645 + 18.4781i −0.171666 + 0.0360196i
\(514\) 0 0
\(515\) −302.780 + 285.658i −0.587921 + 0.554675i
\(516\) 0 0
\(517\) 61.7899 1060.89i 0.119516 2.05202i
\(518\) 0 0
\(519\) −40.0088 + 54.9665i −0.0770882 + 0.105908i
\(520\) 0 0
\(521\) 263.282 723.361i 0.505340 1.38841i −0.380656 0.924717i \(-0.624302\pi\)
0.885996 0.463693i \(-0.153476\pi\)
\(522\) 0 0
\(523\) −390.531 + 142.142i −0.746713 + 0.271781i −0.687222 0.726447i \(-0.741170\pi\)
−0.0594913 + 0.998229i \(0.518948\pi\)
\(524\) 0 0
\(525\) −100.943 + 447.314i −0.192272 + 0.852026i
\(526\) 0 0
\(527\) 18.6709 78.7788i 0.0354287 0.149485i
\(528\) 0 0
\(529\) 197.951 + 458.902i 0.374198 + 0.867489i
\(530\) 0 0
\(531\) −534.330 + 415.966i −1.00627 + 0.783363i
\(532\) 0 0
\(533\) 1555.54 90.5999i 2.91846 0.169981i
\(534\) 0 0
\(535\) 270.237 626.479i 0.505115 1.17099i
\(536\) 0 0
\(537\) −674.839 553.989i −1.25668 1.03164i
\(538\) 0 0
\(539\) 601.073 + 347.029i 1.11516 + 0.643839i
\(540\) 0 0
\(541\) −386.142 668.818i −0.713756 1.23626i −0.963437 0.267934i \(-0.913659\pi\)
0.249681 0.968328i \(-0.419674\pi\)
\(542\) 0 0
\(543\) 226.786 644.595i 0.417654 1.18710i
\(544\) 0 0
\(545\) −60.7169 519.466i −0.111407 0.953149i
\(546\) 0 0
\(547\) −828.761 416.220i −1.51510 0.760913i −0.519490 0.854477i \(-0.673878\pi\)
−0.995613 + 0.0935635i \(0.970174\pi\)
\(548\) 0 0
\(549\) 14.1206 + 176.786i 0.0257206 + 0.322014i
\(550\) 0 0
\(551\) 74.7132 + 55.6219i 0.135596 + 0.100947i
\(552\) 0 0
\(553\) −201.901 + 214.003i −0.365101 + 0.386985i
\(554\) 0 0
\(555\) 844.048 435.336i 1.52081 0.784389i
\(556\) 0 0
\(557\) 49.5814 59.0889i 0.0890152 0.106084i −0.719698 0.694287i \(-0.755720\pi\)
0.808713 + 0.588203i \(0.200164\pi\)
\(558\) 0 0
\(559\) 444.221 372.746i 0.794671 0.666808i
\(560\) 0 0
\(561\) −87.1372 + 84.0007i −0.155325 + 0.149734i
\(562\) 0 0
\(563\) 278.692 + 554.921i 0.495012 + 0.985650i 0.992961 + 0.118443i \(0.0377904\pi\)
−0.497949 + 0.867206i \(0.665913\pi\)
\(564\) 0 0
\(565\) 1213.43 287.588i 2.14767 0.509006i
\(566\) 0 0
\(567\) 21.1806 + 208.512i 0.0373555 + 0.367747i
\(568\) 0 0
\(569\) −193.097 814.738i −0.339361 1.43188i −0.828656 0.559759i \(-0.810894\pi\)
0.489294 0.872119i \(-0.337254\pi\)
\(570\) 0 0
\(571\) 50.7374 25.4813i 0.0888570 0.0446257i −0.403816 0.914840i \(-0.632316\pi\)
0.492673 + 0.870215i \(0.336020\pi\)
\(572\) 0 0
\(573\) 421.199 104.627i 0.735077 0.182595i
\(574\) 0 0
\(575\) −205.279 244.642i −0.357007 0.425464i
\(576\) 0 0
\(577\) −613.531 514.813i −1.06331 0.892224i −0.0688815 0.997625i \(-0.521943\pi\)
−0.994430 + 0.105401i \(0.966387\pi\)
\(578\) 0 0
\(579\) −213.885 + 332.947i −0.369404 + 0.575038i
\(580\) 0 0
\(581\) 176.865 + 166.864i 0.304416 + 0.287201i
\(582\) 0 0
\(583\) −289.252 + 388.532i −0.496143 + 0.666436i
\(584\) 0 0
\(585\) −150.352 + 1580.77i −0.257012 + 2.70217i
\(586\) 0 0
\(587\) 172.065 342.609i 0.293126 0.583661i −0.698076 0.716024i \(-0.745960\pi\)
0.991201 + 0.132363i \(0.0422564\pi\)
\(588\) 0 0
\(589\) −108.979 + 12.7379i −0.185024 + 0.0216263i
\(590\) 0 0
\(591\) 4.41831 3.78918i 0.00747598 0.00641147i
\(592\) 0 0
\(593\) 29.0302 16.7606i 0.0489549 0.0282641i −0.475323 0.879811i \(-0.657669\pi\)
0.524278 + 0.851547i \(0.324335\pi\)
\(594\) 0 0
\(595\) 29.1713 50.5262i 0.0490275 0.0849180i
\(596\) 0 0
\(597\) −729.714 120.585i −1.22230 0.201984i
\(598\) 0 0
\(599\) −824.965 355.855i −1.37724 0.594082i −0.426615 0.904433i \(-0.640294\pi\)
−0.950622 + 0.310351i \(0.899553\pi\)
\(600\) 0 0
\(601\) 8.23677 + 141.420i 0.0137051 + 0.235308i 0.998204 + 0.0599143i \(0.0190827\pi\)
−0.984498 + 0.175393i \(0.943880\pi\)
\(602\) 0 0
\(603\) −677.360 145.212i −1.12332 0.240816i
\(604\) 0 0
\(605\) −1247.40 + 538.077i −2.06182 + 0.889384i
\(606\) 0 0
\(607\) 816.212 + 193.446i 1.34467 + 0.318692i 0.839044 0.544063i \(-0.183115\pi\)
0.505622 + 0.862755i \(0.331263\pi\)
\(608\) 0 0
\(609\) 147.173 159.397i 0.241664 0.261736i
\(610\) 0 0
\(611\) 426.287 + 1171.21i 0.697688 + 1.91688i
\(612\) 0 0
\(613\) −42.2369 15.3730i −0.0689019 0.0250783i 0.307339 0.951600i \(-0.400561\pi\)
−0.376241 + 0.926522i \(0.622784\pi\)
\(614\) 0 0
\(615\) −234.770 + 2215.11i −0.381740 + 3.60181i
\(616\) 0 0
\(617\) 703.586 + 40.9792i 1.14033 + 0.0664169i 0.617896 0.786260i \(-0.287985\pi\)
0.522438 + 0.852677i \(0.325022\pi\)
\(618\) 0 0
\(619\) 306.113 + 324.461i 0.494529 + 0.524170i 0.925780 0.378062i \(-0.123409\pi\)
−0.431252 + 0.902232i \(0.641928\pi\)
\(620\) 0 0
\(621\) −124.475 76.2284i −0.200443 0.122751i
\(622\) 0 0
\(623\) 234.481 + 70.1989i 0.376374 + 0.112679i
\(624\) 0 0
\(625\) −1159.61 762.687i −1.85538 1.22030i
\(626\) 0 0
\(627\) 147.365 + 72.0338i 0.235032 + 0.114886i
\(628\) 0 0
\(629\) −83.6110 + 14.7429i −0.132927 + 0.0234386i
\(630\) 0 0
\(631\) −49.5577 + 281.055i −0.0785383 + 0.445413i 0.920027 + 0.391856i \(0.128167\pi\)
−0.998565 + 0.0535566i \(0.982944\pi\)
\(632\) 0 0
\(633\) 803.532 611.759i 1.26940 0.966444i
\(634\) 0 0
\(635\) 1177.20 352.430i 1.85386 0.555008i
\(636\) 0 0
\(637\) −808.526 94.5032i −1.26927 0.148357i
\(638\) 0 0
\(639\) −630.886 97.2895i −0.987302 0.152253i
\(640\) 0 0
\(641\) −557.286 847.312i −0.869401 1.32186i −0.945789 0.324782i \(-0.894709\pi\)
0.0763880 0.997078i \(-0.475661\pi\)
\(642\) 0 0
\(643\) −20.5039 27.5415i −0.0318879 0.0428329i 0.785893 0.618362i \(-0.212203\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(644\) 0 0
\(645\) 422.199 + 713.424i 0.654572 + 1.10608i
\(646\) 0 0
\(647\) 386.838i 0.597895i −0.954270 0.298948i \(-0.903364\pi\)
0.954270 0.298948i \(-0.0966356\pi\)
\(648\) 0 0
\(649\) 1234.38 1.90197
\(650\) 0 0
\(651\) 2.75072 + 255.547i 0.00422537 + 0.392545i
\(652\) 0 0
\(653\) 285.718 212.709i 0.437546 0.325741i −0.355746 0.934583i \(-0.615773\pi\)
0.793292 + 0.608842i \(0.208366\pi\)
\(654\) 0 0
\(655\) −1599.74 + 1052.17i −2.44236 + 1.60636i
\(656\) 0 0
\(657\) 393.397 + 133.667i 0.598778 + 0.203451i
\(658\) 0 0
\(659\) 132.851 1136.62i 0.201596 1.72476i −0.391973 0.919977i \(-0.628207\pi\)
0.593569 0.804783i \(-0.297719\pi\)
\(660\) 0 0
\(661\) −17.6345 58.9034i −0.0266785 0.0891125i 0.943614 0.331049i \(-0.107403\pi\)
−0.970292 + 0.241937i \(0.922217\pi\)
\(662\) 0 0
\(663\) 54.8190 130.942i 0.0826832 0.197500i
\(664\) 0 0
\(665\) −77.8668 13.7300i −0.117093 0.0206466i
\(666\) 0 0
\(667\) 26.2367 + 148.796i 0.0393354 + 0.223082i
\(668\) 0 0
\(669\) −203.224 301.859i −0.303773 0.451209i
\(670\) 0 0
\(671\) 177.650 270.104i 0.264754 0.402539i
\(672\) 0 0
\(673\) −97.4590 + 325.536i −0.144813 + 0.483708i −0.999364 0.0356587i \(-0.988647\pi\)
0.854551 + 0.519367i \(0.173832\pi\)
\(674\) 0 0
\(675\) −1541.98 407.885i −2.28441 0.604274i
\(676\) 0 0
\(677\) 790.504 745.802i 1.16766 1.10163i 0.174523 0.984653i \(-0.444162\pi\)
0.993135 0.116975i \(-0.0373197\pi\)
\(678\) 0 0
\(679\) 21.3359 366.323i 0.0314225 0.539503i
\(680\) 0 0
\(681\) 178.969 + 402.917i 0.262804 + 0.591655i
\(682\) 0 0
\(683\) 215.820 592.962i 0.315989 0.868172i −0.675427 0.737427i \(-0.736041\pi\)
0.991416 0.130745i \(-0.0417371\pi\)
\(684\) 0 0
\(685\) 1482.45 539.567i 2.16416 0.787689i
\(686\) 0 0
\(687\) −257.458 + 80.1073i −0.374757 + 0.116604i
\(688\) 0 0
\(689\) 131.015 552.794i 0.190152 0.802313i
\(690\) 0 0
\(691\) 13.0336 + 30.2153i 0.0188619 + 0.0437269i 0.927387 0.374104i \(-0.122050\pi\)
−0.908525 + 0.417831i \(0.862790\pi\)
\(692\) 0 0
\(693\) 203.022 323.646i 0.292961 0.467021i
\(694\) 0 0
\(695\) −292.987 + 17.0645i −0.421564 + 0.0245533i
\(696\) 0 0
\(697\) 78.8729 182.848i 0.113161 0.262336i
\(698\) 0 0
\(699\) −978.416 + 368.088i −1.39974 + 0.526592i
\(700\) 0 0
\(701\) 487.235 + 281.305i 0.695057 + 0.401291i 0.805504 0.592591i \(-0.201895\pi\)
−0.110447 + 0.993882i \(0.535228\pi\)
\(702\) 0 0
\(703\) 57.5303 + 99.6454i 0.0818354 + 0.141743i
\(704\) 0 0
\(705\) −1751.28 + 328.273i −2.48409 + 0.465635i
\(706\) 0 0
\(707\) −2.22856 19.0665i −0.00315213 0.0269682i
\(708\) 0 0
\(709\) 169.594 + 85.1731i 0.239201 + 0.120131i 0.564362 0.825527i \(-0.309122\pi\)
−0.325161 + 0.945659i \(0.605418\pi\)
\(710\) 0 0
\(711\) −718.132 729.075i −1.01003 1.02542i
\(712\) 0 0
\(713\) −142.763 106.283i −0.200228 0.149065i
\(714\) 0 0
\(715\) 1986.39 2105.45i 2.77816 2.94468i
\(716\) 0 0
\(717\) 17.5830 370.561i 0.0245230 0.516822i
\(718\) 0 0
\(719\) −63.7972 + 76.0306i −0.0887305 + 0.105745i −0.808583 0.588382i \(-0.799765\pi\)
0.719852 + 0.694127i \(0.244209\pi\)
\(720\) 0 0
\(721\) −89.9842 + 75.5057i −0.124805 + 0.104724i
\(722\) 0 0
\(723\) 1213.93 + 349.234i 1.67902 + 0.483035i
\(724\) 0 0
\(725\) 740.997 + 1475.45i 1.02206 + 2.03510i
\(726\) 0 0
\(727\) 370.614 87.8370i 0.509785 0.120821i 0.0323295 0.999477i \(-0.489707\pi\)
0.477455 + 0.878656i \(0.341559\pi\)
\(728\) 0 0
\(729\) −727.480 + 47.0474i −0.997915 + 0.0645369i
\(730\) 0 0
\(731\) −17.0908 72.1119i −0.0233801 0.0986483i
\(732\) 0 0
\(733\) −1036.27 + 520.435i −1.41374 + 0.710007i −0.981448 0.191727i \(-0.938591\pi\)
−0.432291 + 0.901734i \(0.642295\pi\)
\(734\) 0 0
\(735\) 321.737 1118.35i 0.437738 1.52157i
\(736\) 0 0
\(737\) 811.721 + 967.371i 1.10138 + 1.31258i
\(738\) 0 0
\(739\) −217.172 182.229i −0.293873 0.246589i 0.483916 0.875115i \(-0.339214\pi\)
−0.777789 + 0.628526i \(0.783659\pi\)
\(740\) 0 0
\(741\) −192.165 9.11815i −0.259332 0.0123052i
\(742\) 0 0
\(743\) 614.867 + 580.097i 0.827546 + 0.780750i 0.978162 0.207843i \(-0.0666442\pi\)
−0.150616 + 0.988592i \(0.548126\pi\)
\(744\) 0 0
\(745\) 539.951 725.280i 0.724766 0.973530i
\(746\) 0 0
\(747\) −602.554 + 593.510i −0.806632 + 0.794525i
\(748\) 0 0
\(749\) 86.4086 172.054i 0.115365 0.229711i
\(750\) 0 0
\(751\) −632.089 + 73.8806i −0.841663 + 0.0983763i −0.525989 0.850491i \(-0.676305\pi\)
−0.315674 + 0.948868i \(0.602231\pi\)
\(752\) 0 0
\(753\) 75.1755 + 401.050i 0.0998347 + 0.532603i
\(754\) 0 0
\(755\) 8.95488 5.17010i 0.0118608 0.00684781i
\(756\) 0 0
\(757\) −548.823 + 950.590i −0.724998 + 1.25573i 0.233977 + 0.972242i \(0.424826\pi\)
−0.958975 + 0.283491i \(0.908507\pi\)
\(758\) 0 0
\(759\) 93.6885 + 249.034i 0.123437 + 0.328108i
\(760\) 0 0
\(761\) −687.361 296.498i −0.903233 0.389617i −0.106756 0.994285i \(-0.534046\pi\)
−0.796477 + 0.604668i \(0.793306\pi\)
\(762\) 0 0
\(763\) −8.58140 147.337i −0.0112469 0.193102i
\(764\) 0 0
\(765\) 171.909 + 107.838i 0.224718 + 0.140965i
\(766\) 0 0
\(767\) −1329.35 + 573.424i −1.73318 + 0.747619i
\(768\) 0 0
\(769\) −121.445 28.7829i −0.157926 0.0374291i 0.150892 0.988550i \(-0.451785\pi\)
−0.308818 + 0.951121i \(0.599933\pi\)
\(770\) 0 0
\(771\) −40.6526 130.654i −0.0527271 0.169460i
\(772\) 0 0
\(773\) 285.093 + 783.286i 0.368813 + 1.01331i 0.975814 + 0.218604i \(0.0701504\pi\)
−0.607000 + 0.794702i \(0.707627\pi\)
\(774\) 0 0
\(775\) −1827.62 665.198i −2.35821 0.858320i
\(776\) 0 0
\(777\) 244.923 108.791i 0.315216 0.140014i
\(778\) 0 0
\(779\) −269.417 15.6917i −0.345849 0.0201434i
\(780\) 0 0
\(781\) 798.535 + 846.398i 1.02245 + 1.08374i
\(782\) 0 0
\(783\) 535.302 + 531.884i 0.683655 + 0.679290i
\(784\) 0 0
\(785\) 1234.14 + 369.476i 1.57215 + 0.470670i
\(786\) 0 0
\(787\) −181.521 119.388i −0.230649 0.151700i 0.428924 0.903340i \(-0.358893\pi\)
−0.659573 + 0.751640i \(0.729263\pi\)
\(788\) 0 0
\(789\) −67.7209 + 45.5924i −0.0858313 + 0.0577851i
\(790\) 0 0
\(791\) 346.559 61.1077i 0.438128 0.0772537i
\(792\) 0 0
\(793\) −65.8423 + 373.410i −0.0830294 + 0.470883i
\(794\) 0 0
\(795\) 749.146 + 313.630i 0.942322 + 0.394503i
\(796\)