Properties

Label 684.3.m.a.353.11
Level $684$
Weight $3$
Character 684.353
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.11
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.79577 + 2.40317i) q^{3} -4.55087i q^{5} +(5.85150 - 10.1351i) q^{7} +(-2.55043 - 8.63107i) q^{9} +O(q^{10})\) \(q+(-1.79577 + 2.40317i) q^{3} -4.55087i q^{5} +(5.85150 - 10.1351i) q^{7} +(-2.55043 - 8.63107i) q^{9} +(14.0645 + 8.12016i) q^{11} +(-3.63225 + 6.29124i) q^{13} +(10.9365 + 8.17232i) q^{15} +(-19.6143 - 11.3243i) q^{17} +(-13.5931 - 13.2751i) q^{19} +(13.8484 + 32.2624i) q^{21} +(-33.4828 - 19.3313i) q^{23} +4.28954 q^{25} +(25.3219 + 9.37031i) q^{27} +25.8349i q^{29} +(14.0349 + 24.3091i) q^{31} +(-44.7708 + 19.2175i) q^{33} +(-46.1236 - 26.6295i) q^{35} -47.8191 q^{37} +(-8.59622 - 20.0265i) q^{39} -8.35430i q^{41} +(-39.1823 - 67.8657i) q^{43} +(-39.2789 + 11.6067i) q^{45} +16.4142i q^{47} +(-43.9802 - 76.1759i) q^{49} +(62.4370 - 26.8006i) q^{51} +(43.6381 - 25.1945i) q^{53} +(36.9538 - 64.0059i) q^{55} +(56.3123 - 8.82731i) q^{57} +74.9477i q^{59} +62.3287 q^{61} +(-102.401 - 24.6559i) q^{63} +(28.6306 + 16.5299i) q^{65} +(28.5642 - 49.4746i) q^{67} +(106.584 - 45.7502i) q^{69} +(-73.0839 - 42.1950i) q^{71} +(28.4345 - 49.2501i) q^{73} +(-7.70302 + 10.3085i) q^{75} +(164.597 - 95.0303i) q^{77} +(-59.5243 - 103.099i) q^{79} +(-67.9907 + 44.0258i) q^{81} +(-71.4114 - 41.2294i) q^{83} +(-51.5356 + 89.2622i) q^{85} +(-62.0856 - 46.3935i) q^{87} +(123.100 - 71.0719i) q^{89} +(42.5082 + 73.6264i) q^{91} +(-83.6224 - 9.92542i) q^{93} +(-60.4134 + 61.8603i) q^{95} +(-59.2528 - 102.629i) q^{97} +(34.2151 - 142.102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −1.79577 + 2.40317i −0.598590 + 0.801056i
\(4\) 0 0
\(5\) 4.55087i 0.910175i −0.890447 0.455087i \(-0.849608\pi\)
0.890447 0.455087i \(-0.150392\pi\)
\(6\) 0 0
\(7\) 5.85150 10.1351i 0.835929 1.44787i −0.0573428 0.998355i \(-0.518263\pi\)
0.893272 0.449517i \(-0.148404\pi\)
\(8\) 0 0
\(9\) −2.55043 8.63107i −0.283381 0.959008i
\(10\) 0 0
\(11\) 14.0645 + 8.12016i 1.27859 + 0.738197i 0.976590 0.215110i \(-0.0690110\pi\)
0.302004 + 0.953307i \(0.402344\pi\)
\(12\) 0 0
\(13\) −3.63225 + 6.29124i −0.279404 + 0.483941i −0.971237 0.238116i \(-0.923470\pi\)
0.691833 + 0.722058i \(0.256803\pi\)
\(14\) 0 0
\(15\) 10.9365 + 8.17232i 0.729101 + 0.544821i
\(16\) 0 0
\(17\) −19.6143 11.3243i −1.15378 0.666137i −0.203976 0.978976i \(-0.565387\pi\)
−0.949806 + 0.312839i \(0.898720\pi\)
\(18\) 0 0
\(19\) −13.5931 13.2751i −0.715424 0.698691i
\(20\) 0 0
\(21\) 13.8484 + 32.2624i 0.659447 + 1.53631i
\(22\) 0 0
\(23\) −33.4828 19.3313i −1.45577 0.840491i −0.456974 0.889480i \(-0.651067\pi\)
−0.998799 + 0.0489892i \(0.984400\pi\)
\(24\) 0 0
\(25\) 4.28954 0.171582
\(26\) 0 0
\(27\) 25.3219 + 9.37031i 0.937847 + 0.347048i
\(28\) 0 0
\(29\) 25.8349i 0.890858i 0.895317 + 0.445429i \(0.146949\pi\)
−0.895317 + 0.445429i \(0.853051\pi\)
\(30\) 0 0
\(31\) 14.0349 + 24.3091i 0.452738 + 0.784166i 0.998555 0.0537388i \(-0.0171138\pi\)
−0.545817 + 0.837905i \(0.683780\pi\)
\(32\) 0 0
\(33\) −44.7708 + 19.2175i −1.35669 + 0.582348i
\(34\) 0 0
\(35\) −46.1236 26.6295i −1.31782 0.760842i
\(36\) 0 0
\(37\) −47.8191 −1.29241 −0.646204 0.763164i \(-0.723645\pi\)
−0.646204 + 0.763164i \(0.723645\pi\)
\(38\) 0 0
\(39\) −8.59622 20.0265i −0.220416 0.513500i
\(40\) 0 0
\(41\) 8.35430i 0.203763i −0.994797 0.101882i \(-0.967514\pi\)
0.994797 0.101882i \(-0.0324863\pi\)
\(42\) 0 0
\(43\) −39.1823 67.8657i −0.911216 1.57827i −0.812349 0.583172i \(-0.801812\pi\)
−0.0988670 0.995101i \(-0.531522\pi\)
\(44\) 0 0
\(45\) −39.2789 + 11.6067i −0.872865 + 0.257926i
\(46\) 0 0
\(47\) 16.4142i 0.349239i 0.984636 + 0.174619i \(0.0558695\pi\)
−0.984636 + 0.174619i \(0.944131\pi\)
\(48\) 0 0
\(49\) −43.9802 76.1759i −0.897555 1.55461i
\(50\) 0 0
\(51\) 62.4370 26.8006i 1.22426 0.525502i
\(52\) 0 0
\(53\) 43.6381 25.1945i 0.823360 0.475367i −0.0282138 0.999602i \(-0.508982\pi\)
0.851574 + 0.524235i \(0.175649\pi\)
\(54\) 0 0
\(55\) 36.9538 64.0059i 0.671888 1.16374i
\(56\) 0 0
\(57\) 56.3123 8.82731i 0.987936 0.154865i
\(58\) 0 0
\(59\) 74.9477i 1.27030i 0.772389 + 0.635150i \(0.219062\pi\)
−0.772389 + 0.635150i \(0.780938\pi\)
\(60\) 0 0
\(61\) 62.3287 1.02178 0.510891 0.859645i \(-0.329315\pi\)
0.510891 + 0.859645i \(0.329315\pi\)
\(62\) 0 0
\(63\) −102.401 24.6559i −1.62541 0.391364i
\(64\) 0 0
\(65\) 28.6306 + 16.5299i 0.440471 + 0.254306i
\(66\) 0 0
\(67\) 28.5642 49.4746i 0.426331 0.738427i −0.570213 0.821497i \(-0.693139\pi\)
0.996544 + 0.0830700i \(0.0264725\pi\)
\(68\) 0 0
\(69\) 106.584 45.7502i 1.54469 0.663046i
\(70\) 0 0
\(71\) −73.0839 42.1950i −1.02935 0.594296i −0.112552 0.993646i \(-0.535902\pi\)
−0.916799 + 0.399350i \(0.869236\pi\)
\(72\) 0 0
\(73\) 28.4345 49.2501i 0.389514 0.674658i −0.602870 0.797839i \(-0.705976\pi\)
0.992384 + 0.123181i \(0.0393096\pi\)
\(74\) 0 0
\(75\) −7.70302 + 10.3085i −0.102707 + 0.137446i
\(76\) 0 0
\(77\) 164.597 95.0303i 2.13763 1.23416i
\(78\) 0 0
\(79\) −59.5243 103.099i −0.753472 1.30505i −0.946131 0.323785i \(-0.895044\pi\)
0.192659 0.981266i \(-0.438289\pi\)
\(80\) 0 0
\(81\) −67.9907 + 44.0258i −0.839391 + 0.543528i
\(82\) 0 0
\(83\) −71.4114 41.2294i −0.860379 0.496740i 0.00376048 0.999993i \(-0.498803\pi\)
−0.864139 + 0.503253i \(0.832136\pi\)
\(84\) 0 0
\(85\) −51.5356 + 89.2622i −0.606301 + 1.05014i
\(86\) 0 0
\(87\) −62.0856 46.3935i −0.713627 0.533259i
\(88\) 0 0
\(89\) 123.100 71.0719i 1.38315 0.798560i 0.390616 0.920554i \(-0.372262\pi\)
0.992531 + 0.121993i \(0.0389286\pi\)
\(90\) 0 0
\(91\) 42.5082 + 73.6264i 0.467123 + 0.809081i
\(92\) 0 0
\(93\) −83.6224 9.92542i −0.899165 0.106725i
\(94\) 0 0
\(95\) −60.4134 + 61.8603i −0.635931 + 0.651161i
\(96\) 0 0
\(97\) −59.2528 102.629i −0.610854 1.05803i −0.991097 0.133143i \(-0.957493\pi\)
0.380243 0.924887i \(-0.375840\pi\)
\(98\) 0 0
\(99\) 34.2151 142.102i 0.345607 1.43537i
\(100\) 0 0
\(101\) 90.1148i 0.892226i 0.894977 + 0.446113i \(0.147192\pi\)
−0.894977 + 0.446113i \(0.852808\pi\)
\(102\) 0 0
\(103\) −43.0937 74.6404i −0.418385 0.724664i 0.577392 0.816467i \(-0.304070\pi\)
−0.995777 + 0.0918028i \(0.970737\pi\)
\(104\) 0 0
\(105\) 146.822 63.0223i 1.39831 0.600212i
\(106\) 0 0
\(107\) 116.854i 1.09209i 0.837756 + 0.546045i \(0.183867\pi\)
−0.837756 + 0.546045i \(0.816133\pi\)
\(108\) 0 0
\(109\) −59.8897 + 103.732i −0.549447 + 0.951670i 0.448865 + 0.893599i \(0.351828\pi\)
−0.998312 + 0.0580708i \(0.981505\pi\)
\(110\) 0 0
\(111\) 85.8721 114.917i 0.773623 1.03529i
\(112\) 0 0
\(113\) −121.648 + 70.2335i −1.07653 + 0.621535i −0.929958 0.367665i \(-0.880157\pi\)
−0.146572 + 0.989200i \(0.546824\pi\)
\(114\) 0 0
\(115\) −87.9743 + 152.376i −0.764994 + 1.32501i
\(116\) 0 0
\(117\) 63.5639 + 15.3049i 0.543281 + 0.130811i
\(118\) 0 0
\(119\) −229.546 + 132.529i −1.92896 + 1.11369i
\(120\) 0 0
\(121\) 71.3740 + 123.623i 0.589868 + 1.02168i
\(122\) 0 0
\(123\) 20.0768 + 15.0024i 0.163226 + 0.121971i
\(124\) 0 0
\(125\) 133.293i 1.06634i
\(126\) 0 0
\(127\) −35.1261 60.8401i −0.276583 0.479056i 0.693950 0.720023i \(-0.255869\pi\)
−0.970533 + 0.240967i \(0.922535\pi\)
\(128\) 0 0
\(129\) 233.455 + 27.7096i 1.80973 + 0.214803i
\(130\) 0 0
\(131\) 2.59427i 0.0198036i −0.999951 0.00990178i \(-0.996848\pi\)
0.999951 0.00990178i \(-0.00315189\pi\)
\(132\) 0 0
\(133\) −214.085 + 60.0875i −1.60966 + 0.451786i
\(134\) 0 0
\(135\) 42.6431 115.237i 0.315875 0.853605i
\(136\) 0 0
\(137\) 148.184i 1.08164i 0.841139 + 0.540819i \(0.181886\pi\)
−0.841139 + 0.540819i \(0.818114\pi\)
\(138\) 0 0
\(139\) 66.7195 115.561i 0.479996 0.831378i −0.519741 0.854324i \(-0.673971\pi\)
0.999737 + 0.0229465i \(0.00730472\pi\)
\(140\) 0 0
\(141\) −39.4461 29.4761i −0.279760 0.209051i
\(142\) 0 0
\(143\) −102.172 + 58.9889i −0.714488 + 0.412510i
\(144\) 0 0
\(145\) 117.571 0.810837
\(146\) 0 0
\(147\) 262.042 + 31.1026i 1.78260 + 0.211582i
\(148\) 0 0
\(149\) 122.448i 0.821797i −0.911681 0.410899i \(-0.865215\pi\)
0.911681 0.410899i \(-0.134785\pi\)
\(150\) 0 0
\(151\) −36.8974 + 63.9082i −0.244354 + 0.423233i −0.961950 0.273226i \(-0.911909\pi\)
0.717596 + 0.696460i \(0.245243\pi\)
\(152\) 0 0
\(153\) −47.7162 + 198.174i −0.311871 + 1.29526i
\(154\) 0 0
\(155\) 110.628 63.8710i 0.713728 0.412071i
\(156\) 0 0
\(157\) 292.029 1.86005 0.930027 0.367491i \(-0.119783\pi\)
0.930027 + 0.367491i \(0.119783\pi\)
\(158\) 0 0
\(159\) −17.8174 + 150.113i −0.112059 + 0.944107i
\(160\) 0 0
\(161\) −391.849 + 226.234i −2.43385 + 1.40518i
\(162\) 0 0
\(163\) 39.5636 0.242722 0.121361 0.992608i \(-0.461274\pi\)
0.121361 + 0.992608i \(0.461274\pi\)
\(164\) 0 0
\(165\) 87.4564 + 203.746i 0.530039 + 1.23483i
\(166\) 0 0
\(167\) −2.36252 1.36400i −0.0141468 0.00816766i 0.492910 0.870080i \(-0.335933\pi\)
−0.507057 + 0.861913i \(0.669267\pi\)
\(168\) 0 0
\(169\) 58.1135 + 100.656i 0.343867 + 0.595595i
\(170\) 0 0
\(171\) −79.9105 + 151.180i −0.467313 + 0.884092i
\(172\) 0 0
\(173\) −103.541 + 59.7794i −0.598503 + 0.345546i −0.768452 0.639907i \(-0.778973\pi\)
0.169949 + 0.985453i \(0.445640\pi\)
\(174\) 0 0
\(175\) 25.1002 43.4749i 0.143430 0.248428i
\(176\) 0 0
\(177\) −180.112 134.589i −1.01758 0.760388i
\(178\) 0 0
\(179\) 16.1873i 0.0904318i −0.998977 0.0452159i \(-0.985602\pi\)
0.998977 0.0452159i \(-0.0143976\pi\)
\(180\) 0 0
\(181\) −171.692 297.380i −0.948576 1.64298i −0.748429 0.663215i \(-0.769191\pi\)
−0.200147 0.979766i \(-0.564142\pi\)
\(182\) 0 0
\(183\) −111.928 + 149.786i −0.611629 + 0.818505i
\(184\) 0 0
\(185\) 217.619i 1.17632i
\(186\) 0 0
\(187\) −183.911 318.543i −0.983480 1.70344i
\(188\) 0 0
\(189\) 243.140 201.809i 1.28646 1.06777i
\(190\) 0 0
\(191\) −10.9165 6.30263i −0.0571543 0.0329981i 0.471151 0.882053i \(-0.343839\pi\)
−0.528305 + 0.849055i \(0.677172\pi\)
\(192\) 0 0
\(193\) 137.420 0.712022 0.356011 0.934482i \(-0.384137\pi\)
0.356011 + 0.934482i \(0.384137\pi\)
\(194\) 0 0
\(195\) −91.1382 + 39.1203i −0.467375 + 0.200617i
\(196\) 0 0
\(197\) 191.963i 0.974429i 0.873282 + 0.487215i \(0.161987\pi\)
−0.873282 + 0.487215i \(0.838013\pi\)
\(198\) 0 0
\(199\) −64.5484 111.801i −0.324364 0.561815i 0.657019 0.753874i \(-0.271817\pi\)
−0.981383 + 0.192059i \(0.938484\pi\)
\(200\) 0 0
\(201\) 67.6011 + 157.490i 0.336324 + 0.783530i
\(202\) 0 0
\(203\) 261.839 + 151.173i 1.28985 + 0.744694i
\(204\) 0 0
\(205\) −38.0194 −0.185460
\(206\) 0 0
\(207\) −81.4544 + 338.295i −0.393499 + 1.63428i
\(208\) 0 0
\(209\) −83.3837 297.086i −0.398965 1.42147i
\(210\) 0 0
\(211\) 156.934 0.743765 0.371882 0.928280i \(-0.378712\pi\)
0.371882 + 0.928280i \(0.378712\pi\)
\(212\) 0 0
\(213\) 232.643 99.8603i 1.09222 0.468828i
\(214\) 0 0
\(215\) −308.848 + 178.314i −1.43650 + 0.829366i
\(216\) 0 0
\(217\) 328.501 1.51383
\(218\) 0 0
\(219\) 67.2943 + 156.775i 0.307280 + 0.715866i
\(220\) 0 0
\(221\) 142.488 82.2655i 0.644742 0.372242i
\(222\) 0 0
\(223\) −50.3370 87.1863i −0.225727 0.390970i 0.730811 0.682580i \(-0.239142\pi\)
−0.956537 + 0.291610i \(0.905809\pi\)
\(224\) 0 0
\(225\) −10.9401 37.0233i −0.0486229 0.164548i
\(226\) 0 0
\(227\) −27.5603 15.9119i −0.121411 0.0700967i 0.438065 0.898943i \(-0.355664\pi\)
−0.559476 + 0.828847i \(0.688997\pi\)
\(228\) 0 0
\(229\) −77.4200 134.095i −0.338078 0.585569i 0.645993 0.763344i \(-0.276444\pi\)
−0.984071 + 0.177774i \(0.943110\pi\)
\(230\) 0 0
\(231\) −67.2051 + 566.207i −0.290931 + 2.45111i
\(232\) 0 0
\(233\) 334.241 + 192.974i 1.43451 + 0.828215i 0.997460 0.0712220i \(-0.0226899\pi\)
0.437050 + 0.899437i \(0.356023\pi\)
\(234\) 0 0
\(235\) 74.6990 0.317868
\(236\) 0 0
\(237\) 354.656 + 42.0953i 1.49644 + 0.177617i
\(238\) 0 0
\(239\) 19.8128 11.4390i 0.0828990 0.0478617i −0.457978 0.888964i \(-0.651426\pi\)
0.540876 + 0.841102i \(0.318093\pi\)
\(240\) 0 0
\(241\) 206.571 0.857143 0.428571 0.903508i \(-0.359017\pi\)
0.428571 + 0.903508i \(0.359017\pi\)
\(242\) 0 0
\(243\) 16.2942 242.453i 0.0670544 0.997749i
\(244\) 0 0
\(245\) −346.667 + 200.148i −1.41497 + 0.816932i
\(246\) 0 0
\(247\) 132.890 37.2986i 0.538018 0.151006i
\(248\) 0 0
\(249\) 227.320 97.5751i 0.912930 0.391868i
\(250\) 0 0
\(251\) −170.812 + 98.6182i −0.680525 + 0.392901i −0.800053 0.599930i \(-0.795195\pi\)
0.119528 + 0.992831i \(0.461862\pi\)
\(252\) 0 0
\(253\) −313.946 543.771i −1.24089 2.14929i
\(254\) 0 0
\(255\) −121.966 284.143i −0.478298 1.11429i
\(256\) 0 0
\(257\) 175.563 + 101.361i 0.683125 + 0.394403i 0.801032 0.598622i \(-0.204285\pi\)
−0.117906 + 0.993025i \(0.537618\pi\)
\(258\) 0 0
\(259\) −279.814 + 484.652i −1.08036 + 1.87124i
\(260\) 0 0
\(261\) 222.983 65.8900i 0.854340 0.252452i
\(262\) 0 0
\(263\) 179.210 103.467i 0.681405 0.393409i −0.118979 0.992897i \(-0.537962\pi\)
0.800384 + 0.599487i \(0.204629\pi\)
\(264\) 0 0
\(265\) −114.657 198.591i −0.432667 0.749402i
\(266\) 0 0
\(267\) −50.2618 + 423.459i −0.188246 + 1.58599i
\(268\) 0 0
\(269\) 54.5399 + 31.4886i 0.202751 + 0.117058i 0.597938 0.801542i \(-0.295987\pi\)
−0.395187 + 0.918601i \(0.629320\pi\)
\(270\) 0 0
\(271\) −101.148 + 175.193i −0.373239 + 0.646469i −0.990062 0.140633i \(-0.955086\pi\)
0.616823 + 0.787102i \(0.288420\pi\)
\(272\) 0 0
\(273\) −253.272 30.0617i −0.927735 0.110116i
\(274\) 0 0
\(275\) 60.3303 + 34.8317i 0.219383 + 0.126661i
\(276\) 0 0
\(277\) −48.8226 + 84.5632i −0.176255 + 0.305282i −0.940595 0.339531i \(-0.889732\pi\)
0.764340 + 0.644813i \(0.223065\pi\)
\(278\) 0 0
\(279\) 174.019 183.135i 0.623724 0.656397i
\(280\) 0 0
\(281\) 228.082i 0.811679i 0.913944 + 0.405840i \(0.133021\pi\)
−0.913944 + 0.405840i \(0.866979\pi\)
\(282\) 0 0
\(283\) 206.080 0.728199 0.364099 0.931360i \(-0.381377\pi\)
0.364099 + 0.931360i \(0.381377\pi\)
\(284\) 0 0
\(285\) −40.1720 256.270i −0.140954 0.899194i
\(286\) 0 0
\(287\) −84.6716 48.8852i −0.295023 0.170332i
\(288\) 0 0
\(289\) 111.981 + 193.956i 0.387476 + 0.671128i
\(290\) 0 0
\(291\) 353.039 + 41.9034i 1.21319 + 0.143998i
\(292\) 0 0
\(293\) 218.824 126.338i 0.746840 0.431189i −0.0777107 0.996976i \(-0.524761\pi\)
0.824551 + 0.565787i \(0.191428\pi\)
\(294\) 0 0
\(295\) 341.078 1.15619
\(296\) 0 0
\(297\) 280.052 + 337.407i 0.942936 + 1.13605i
\(298\) 0 0
\(299\) 243.236 140.432i 0.813497 0.469673i
\(300\) 0 0
\(301\) −917.101 −3.04685
\(302\) 0 0
\(303\) −216.561 161.825i −0.714723 0.534077i
\(304\) 0 0
\(305\) 283.650i 0.930001i
\(306\) 0 0
\(307\) 261.675 453.234i 0.852361 1.47633i −0.0267099 0.999643i \(-0.508503\pi\)
0.879071 0.476690i \(-0.158164\pi\)
\(308\) 0 0
\(309\) 256.760 + 30.4757i 0.830937 + 0.0986268i
\(310\) 0 0
\(311\) 332.891 192.195i 1.07039 0.617989i 0.142101 0.989852i \(-0.454614\pi\)
0.928287 + 0.371863i \(0.121281\pi\)
\(312\) 0 0
\(313\) 220.518 0.704531 0.352265 0.935900i \(-0.385411\pi\)
0.352265 + 0.935900i \(0.385411\pi\)
\(314\) 0 0
\(315\) −112.206 + 466.012i −0.356209 + 1.47940i
\(316\) 0 0
\(317\) 192.289i 0.606590i −0.952897 0.303295i \(-0.901913\pi\)
0.952897 0.303295i \(-0.0980867\pi\)
\(318\) 0 0
\(319\) −209.784 + 363.356i −0.657629 + 1.13905i
\(320\) 0 0
\(321\) −280.819 209.842i −0.874825 0.653714i
\(322\) 0 0
\(323\) 116.286 + 414.314i 0.360020 + 1.28271i
\(324\) 0 0
\(325\) −15.5807 + 26.9865i −0.0479405 + 0.0830354i
\(326\) 0 0
\(327\) −141.737 330.204i −0.433447 1.00980i
\(328\) 0 0
\(329\) 166.360 + 96.0478i 0.505653 + 0.291939i
\(330\) 0 0
\(331\) 140.614 243.551i 0.424817 0.735804i −0.571586 0.820542i \(-0.693672\pi\)
0.996403 + 0.0847374i \(0.0270051\pi\)
\(332\) 0 0
\(333\) 121.959 + 412.730i 0.366244 + 1.23943i
\(334\) 0 0
\(335\) −225.153 129.992i −0.672098 0.388036i
\(336\) 0 0
\(337\) −498.307 −1.47866 −0.739328 0.673346i \(-0.764857\pi\)
−0.739328 + 0.673346i \(0.764857\pi\)
\(338\) 0 0
\(339\) 49.6689 418.464i 0.146516 1.23441i
\(340\) 0 0
\(341\) 455.862i 1.33684i
\(342\) 0 0
\(343\) −455.953 −1.32931
\(344\) 0 0
\(345\) −208.203 485.049i −0.603488 1.40594i
\(346\) 0 0
\(347\) 156.769i 0.451783i −0.974153 0.225891i \(-0.927471\pi\)
0.974153 0.225891i \(-0.0725294\pi\)
\(348\) 0 0
\(349\) −27.3145 + 47.3101i −0.0782651 + 0.135559i −0.902501 0.430687i \(-0.858271\pi\)
0.824236 + 0.566246i \(0.191605\pi\)
\(350\) 0 0
\(351\) −150.926 + 125.271i −0.429989 + 0.356897i
\(352\) 0 0
\(353\) 22.4457 + 12.9590i 0.0635854 + 0.0367111i 0.531456 0.847086i \(-0.321645\pi\)
−0.467870 + 0.883797i \(0.654979\pi\)
\(354\) 0 0
\(355\) −192.024 + 332.596i −0.540913 + 0.936889i
\(356\) 0 0
\(357\) 93.7238 789.629i 0.262532 2.21185i
\(358\) 0 0
\(359\) −551.226 318.250i −1.53545 0.886491i −0.999097 0.0424966i \(-0.986469\pi\)
−0.536351 0.843995i \(-0.680198\pi\)
\(360\) 0 0
\(361\) 8.54208 + 360.899i 0.0236623 + 0.999720i
\(362\) 0 0
\(363\) −425.259 50.4755i −1.17151 0.139051i
\(364\) 0 0
\(365\) −224.131 129.402i −0.614057 0.354526i
\(366\) 0 0
\(367\) 199.085 0.542466 0.271233 0.962514i \(-0.412569\pi\)
0.271233 + 0.962514i \(0.412569\pi\)
\(368\) 0 0
\(369\) −72.1065 + 21.3070i −0.195411 + 0.0577426i
\(370\) 0 0
\(371\) 589.702i 1.58949i
\(372\) 0 0
\(373\) 225.834 + 391.156i 0.605453 + 1.04867i 0.991980 + 0.126397i \(0.0403412\pi\)
−0.386527 + 0.922278i \(0.626325\pi\)
\(374\) 0 0
\(375\) 320.325 + 239.364i 0.854201 + 0.638303i
\(376\) 0 0
\(377\) −162.533 93.8388i −0.431123 0.248909i
\(378\) 0 0
\(379\) −98.6773 −0.260362 −0.130181 0.991490i \(-0.541556\pi\)
−0.130181 + 0.991490i \(0.541556\pi\)
\(380\) 0 0
\(381\) 209.287 + 24.8410i 0.549310 + 0.0651995i
\(382\) 0 0
\(383\) 395.105i 1.03161i 0.856707 + 0.515803i \(0.172506\pi\)
−0.856707 + 0.515803i \(0.827494\pi\)
\(384\) 0 0
\(385\) −432.471 749.062i −1.12330 1.94561i
\(386\) 0 0
\(387\) −485.822 + 511.271i −1.25535 + 1.32111i
\(388\) 0 0
\(389\) 251.142i 0.645610i −0.946466 0.322805i \(-0.895374\pi\)
0.946466 0.322805i \(-0.104626\pi\)
\(390\) 0 0
\(391\) 437.828 + 758.340i 1.11976 + 1.93949i
\(392\) 0 0
\(393\) 6.23446 + 4.65870i 0.0158638 + 0.0118542i
\(394\) 0 0
\(395\) −469.191 + 270.887i −1.18782 + 0.685791i
\(396\) 0 0
\(397\) 157.630 273.022i 0.397052 0.687714i −0.596309 0.802755i \(-0.703367\pi\)
0.993361 + 0.115041i \(0.0367000\pi\)
\(398\) 0 0
\(399\) 240.046 622.384i 0.601619 1.55986i
\(400\) 0 0
\(401\) 278.610i 0.694788i 0.937719 + 0.347394i \(0.112933\pi\)
−0.937719 + 0.347394i \(0.887067\pi\)
\(402\) 0 0
\(403\) −203.913 −0.505987
\(404\) 0 0
\(405\) 200.356 + 309.417i 0.494706 + 0.763993i
\(406\) 0 0
\(407\) −672.554 388.299i −1.65247 0.954052i
\(408\) 0 0
\(409\) 100.271 173.675i 0.245161 0.424632i −0.717016 0.697057i \(-0.754492\pi\)
0.962177 + 0.272425i \(0.0878257\pi\)
\(410\) 0 0
\(411\) −356.112 266.105i −0.866452 0.647457i
\(412\) 0 0
\(413\) 759.602 + 438.557i 1.83923 + 1.06188i
\(414\) 0 0
\(415\) −187.630 + 324.984i −0.452120 + 0.783095i
\(416\) 0 0
\(417\) 157.901 + 367.860i 0.378659 + 0.882158i
\(418\) 0 0
\(419\) 452.302 261.137i 1.07948 0.623238i 0.148723 0.988879i \(-0.452484\pi\)
0.930756 + 0.365641i \(0.119150\pi\)
\(420\) 0 0
\(421\) 129.320 + 223.990i 0.307174 + 0.532042i 0.977743 0.209806i \(-0.0672832\pi\)
−0.670569 + 0.741847i \(0.733950\pi\)
\(422\) 0 0
\(423\) 141.672 41.8632i 0.334922 0.0989674i
\(424\) 0 0
\(425\) −84.1363 48.5761i −0.197968 0.114297i
\(426\) 0 0
\(427\) 364.717 631.708i 0.854138 1.47941i
\(428\) 0 0
\(429\) 41.7167 351.466i 0.0972418 0.819269i
\(430\) 0 0
\(431\) 263.486 152.124i 0.611336 0.352955i −0.162152 0.986766i \(-0.551843\pi\)
0.773488 + 0.633811i \(0.218510\pi\)
\(432\) 0 0
\(433\) 398.394 + 690.039i 0.920079 + 1.59362i 0.799290 + 0.600945i \(0.205209\pi\)
0.120789 + 0.992678i \(0.461458\pi\)
\(434\) 0 0
\(435\) −211.131 + 282.544i −0.485359 + 0.649526i
\(436\) 0 0
\(437\) 198.508 + 707.259i 0.454251 + 1.61844i
\(438\) 0 0
\(439\) 251.837 + 436.195i 0.573662 + 0.993611i 0.996186 + 0.0872592i \(0.0278108\pi\)
−0.422524 + 0.906352i \(0.638856\pi\)
\(440\) 0 0
\(441\) −545.311 + 573.877i −1.23653 + 1.30131i
\(442\) 0 0
\(443\) 337.606i 0.762091i 0.924556 + 0.381045i \(0.124436\pi\)
−0.924556 + 0.381045i \(0.875564\pi\)
\(444\) 0 0
\(445\) −323.439 560.213i −0.726830 1.25891i
\(446\) 0 0
\(447\) 294.262 + 219.888i 0.658305 + 0.491919i
\(448\) 0 0
\(449\) 771.592i 1.71847i 0.511584 + 0.859233i \(0.329059\pi\)
−0.511584 + 0.859233i \(0.670941\pi\)
\(450\) 0 0
\(451\) 67.8382 117.499i 0.150417 0.260531i
\(452\) 0 0
\(453\) −87.3229 203.435i −0.192766 0.449084i
\(454\) 0 0
\(455\) 335.065 193.450i 0.736406 0.425164i
\(456\) 0 0
\(457\) 174.821 302.800i 0.382542 0.662581i −0.608883 0.793260i \(-0.708382\pi\)
0.991425 + 0.130678i \(0.0417155\pi\)
\(458\) 0 0
\(459\) −390.559 470.545i −0.850890 1.02515i
\(460\) 0 0
\(461\) 255.613 147.578i 0.554474 0.320126i −0.196450 0.980514i \(-0.562941\pi\)
0.750925 + 0.660388i \(0.229608\pi\)
\(462\) 0 0
\(463\) 78.9995 + 136.831i 0.170625 + 0.295532i 0.938639 0.344902i \(-0.112088\pi\)
−0.768013 + 0.640434i \(0.778755\pi\)
\(464\) 0 0
\(465\) −45.1694 + 380.555i −0.0971384 + 0.818398i
\(466\) 0 0
\(467\) 666.947i 1.42815i −0.700068 0.714076i \(-0.746847\pi\)
0.700068 0.714076i \(-0.253153\pi\)
\(468\) 0 0
\(469\) −334.287 579.002i −0.712765 1.23455i
\(470\) 0 0
\(471\) −524.416 + 701.793i −1.11341 + 1.49001i
\(472\) 0 0
\(473\) 1272.67i 2.69063i
\(474\) 0 0
\(475\) −58.3079 56.9442i −0.122753 0.119882i
\(476\) 0 0
\(477\) −328.751 312.387i −0.689205 0.654899i
\(478\) 0 0
\(479\) 193.176i 0.403290i −0.979459 0.201645i \(-0.935371\pi\)
0.979459 0.201645i \(-0.0646287\pi\)
\(480\) 0 0
\(481\) 173.691 300.842i 0.361104 0.625450i
\(482\) 0 0
\(483\) 159.992 1347.94i 0.331246 2.79077i
\(484\) 0 0
\(485\) −467.051 + 269.652i −0.962992 + 0.555984i
\(486\) 0 0
\(487\) −550.037 −1.12944 −0.564720 0.825282i \(-0.691016\pi\)
−0.564720 + 0.825282i \(0.691016\pi\)
\(488\) 0 0
\(489\) −71.0471 + 95.0780i −0.145291 + 0.194433i
\(490\) 0 0
\(491\) 255.091i 0.519534i 0.965671 + 0.259767i \(0.0836458\pi\)
−0.965671 + 0.259767i \(0.916354\pi\)
\(492\) 0 0
\(493\) 292.563 506.733i 0.593433 1.02786i
\(494\) 0 0
\(495\) −646.687 155.709i −1.30644 0.314563i
\(496\) 0 0
\(497\) −855.301 + 493.808i −1.72093 + 0.993578i
\(498\) 0 0
\(499\) 485.339 0.972622 0.486311 0.873786i \(-0.338342\pi\)
0.486311 + 0.873786i \(0.338342\pi\)
\(500\) 0 0
\(501\) 7.52046 3.22809i 0.0150109 0.00644330i
\(502\) 0 0
\(503\) −172.886 + 99.8159i −0.343710 + 0.198441i −0.661912 0.749582i \(-0.730255\pi\)
0.318201 + 0.948023i \(0.396921\pi\)
\(504\) 0 0
\(505\) 410.101 0.812082
\(506\) 0 0
\(507\) −346.251 41.0977i −0.682940 0.0810605i
\(508\) 0 0
\(509\) −178.301 102.942i −0.350298 0.202244i 0.314519 0.949251i \(-0.398157\pi\)
−0.664816 + 0.747007i \(0.731490\pi\)
\(510\) 0 0
\(511\) −332.770 576.374i −0.651212 1.12793i
\(512\) 0 0
\(513\) −219.809 463.522i −0.428479 0.903552i
\(514\) 0 0
\(515\) −339.679 + 196.114i −0.659571 + 0.380804i
\(516\) 0 0
\(517\) −133.286 + 230.858i −0.257807 + 0.446534i
\(518\) 0 0
\(519\) 42.2758 356.176i 0.0814563 0.686274i
\(520\) 0 0
\(521\) 570.510i 1.09503i −0.836796 0.547514i \(-0.815574\pi\)
0.836796 0.547514i \(-0.184426\pi\)
\(522\) 0 0
\(523\) −466.633 808.231i −0.892223 1.54538i −0.837205 0.546890i \(-0.815812\pi\)
−0.0550183 0.998485i \(-0.517522\pi\)
\(524\) 0 0
\(525\) 59.4032 + 138.391i 0.113149 + 0.263602i
\(526\) 0 0
\(527\) 635.742i 1.20634i
\(528\) 0 0
\(529\) 482.898 + 836.403i 0.912850 + 1.58110i
\(530\) 0 0
\(531\) 646.879 191.148i 1.21823 0.359978i
\(532\) 0 0
\(533\) 52.5589 + 30.3449i 0.0986095 + 0.0569322i
\(534\) 0 0
\(535\) 531.786 0.993993
\(536\) 0 0
\(537\) 38.9008 + 29.0686i 0.0724409 + 0.0541316i
\(538\) 0 0
\(539\) 1428.50i 2.65029i
\(540\) 0 0
\(541\) 77.8507 + 134.841i 0.143901 + 0.249245i 0.928963 0.370174i \(-0.120702\pi\)
−0.785061 + 0.619418i \(0.787368\pi\)
\(542\) 0 0
\(543\) 1022.97 + 121.420i 1.88393 + 0.223610i
\(544\) 0 0
\(545\) 472.072 + 272.551i 0.866186 + 0.500093i
\(546\) 0 0
\(547\) 34.1225 0.0623811 0.0311906 0.999513i \(-0.490070\pi\)
0.0311906 + 0.999513i \(0.490070\pi\)
\(548\) 0 0
\(549\) −158.965 537.963i −0.289553 0.979897i
\(550\) 0 0
\(551\) 342.961 351.175i 0.622435 0.637341i
\(552\) 0 0
\(553\) −1393.23 −2.51939
\(554\) 0 0
\(555\) −522.975 390.793i −0.942297 0.704132i
\(556\) 0 0
\(557\) 34.3037 19.8053i 0.0615865 0.0355570i −0.468891 0.883256i \(-0.655346\pi\)
0.530477 + 0.847699i \(0.322013\pi\)
\(558\) 0 0
\(559\) 569.279 1.01839
\(560\) 0 0
\(561\) 1095.77 + 130.061i 1.95325 + 0.231838i
\(562\) 0 0
\(563\) 31.8404 18.3831i 0.0565549 0.0326520i −0.471456 0.881890i \(-0.656271\pi\)
0.528011 + 0.849238i \(0.322938\pi\)
\(564\) 0 0
\(565\) 319.624 + 553.605i 0.565706 + 0.979831i
\(566\) 0 0
\(567\) 48.3582 + 946.709i 0.0852878 + 1.66968i
\(568\) 0 0
\(569\) −13.7340 7.92934i −0.0241371 0.0139356i 0.487883 0.872909i \(-0.337769\pi\)
−0.512020 + 0.858974i \(0.671103\pi\)
\(570\) 0 0
\(571\) 445.433 + 771.512i 0.780093 + 1.35116i 0.931887 + 0.362748i \(0.118161\pi\)
−0.151794 + 0.988412i \(0.548505\pi\)
\(572\) 0 0
\(573\) 34.7497 14.9160i 0.0606453 0.0260315i
\(574\) 0 0
\(575\) −143.626 82.9223i −0.249784 0.144213i
\(576\) 0 0
\(577\) 420.790 0.729272 0.364636 0.931150i \(-0.381193\pi\)
0.364636 + 0.931150i \(0.381193\pi\)
\(578\) 0 0
\(579\) −246.775 + 330.244i −0.426209 + 0.570370i
\(580\) 0 0
\(581\) −835.728 + 482.508i −1.43843 + 0.830478i
\(582\) 0 0
\(583\) 818.332 1.40366
\(584\) 0 0
\(585\) 69.6505 289.271i 0.119061 0.494481i
\(586\) 0 0
\(587\) 562.001 324.471i 0.957412 0.552762i 0.0620362 0.998074i \(-0.480241\pi\)
0.895375 + 0.445312i \(0.146907\pi\)
\(588\) 0 0
\(589\) 131.930 516.750i 0.223990 0.877335i
\(590\) 0 0
\(591\) −461.318 344.721i −0.780572 0.583283i
\(592\) 0 0
\(593\) 104.519 60.3443i 0.176255 0.101761i −0.409277 0.912410i \(-0.634219\pi\)
0.585532 + 0.810649i \(0.300886\pi\)
\(594\) 0 0
\(595\) 603.121 + 1044.64i 1.01365 + 1.75569i
\(596\) 0 0
\(597\) 384.591 + 45.6484i 0.644206 + 0.0764630i
\(598\) 0 0
\(599\) −417.863 241.253i −0.697601 0.402760i 0.108852 0.994058i \(-0.465282\pi\)
−0.806453 + 0.591298i \(0.798616\pi\)
\(600\) 0 0
\(601\) −191.870 + 332.329i −0.319251 + 0.552960i −0.980332 0.197355i \(-0.936765\pi\)
0.661081 + 0.750315i \(0.270098\pi\)
\(602\) 0 0
\(603\) −499.870 120.358i −0.828971 0.199599i
\(604\) 0 0
\(605\) 562.595 324.814i 0.929909 0.536883i
\(606\) 0 0
\(607\) −131.396 227.585i −0.216468 0.374934i 0.737258 0.675612i \(-0.236120\pi\)
−0.953726 + 0.300678i \(0.902787\pi\)
\(608\) 0 0
\(609\) −833.497 + 357.772i −1.36863 + 0.587474i
\(610\) 0 0
\(611\) −103.266 59.6205i −0.169011 0.0975786i
\(612\) 0 0
\(613\) −416.617 + 721.601i −0.679636 + 1.17716i 0.295455 + 0.955357i \(0.404529\pi\)
−0.975091 + 0.221807i \(0.928805\pi\)
\(614\) 0 0
\(615\) 68.2740 91.3669i 0.111015 0.148564i
\(616\) 0 0
\(617\) −1031.09 595.298i −1.67113 0.964826i −0.967008 0.254745i \(-0.918008\pi\)
−0.704120 0.710081i \(-0.748658\pi\)
\(618\) 0 0
\(619\) −515.688 + 893.198i −0.833099 + 1.44297i 0.0624707 + 0.998047i \(0.480102\pi\)
−0.895569 + 0.444922i \(0.853231\pi\)
\(620\) 0 0
\(621\) −666.707 803.249i −1.07360 1.29348i
\(622\) 0 0
\(623\) 1663.51i 2.67016i
\(624\) 0 0
\(625\) −499.361 −0.798978
\(626\) 0 0
\(627\) 863.686 + 333.113i 1.37749 + 0.531281i
\(628\) 0 0
\(629\) 937.939 + 541.519i 1.49116 + 0.860921i
\(630\) 0 0
\(631\) 121.585 + 210.592i 0.192686 + 0.333743i 0.946140 0.323759i \(-0.104947\pi\)
−0.753453 + 0.657502i \(0.771613\pi\)
\(632\) 0 0
\(633\) −281.818 + 377.140i −0.445210 + 0.595797i
\(634\) 0 0
\(635\) −276.876 + 159.854i −0.436025 + 0.251739i
\(636\) 0 0
\(637\) 638.988 1.00312
\(638\) 0 0
\(639\) −177.793 + 738.407i −0.278236 + 1.15557i
\(640\) 0 0
\(641\) 502.684 290.225i 0.784219 0.452769i −0.0537045 0.998557i \(-0.517103\pi\)
0.837923 + 0.545788i \(0.183770\pi\)
\(642\) 0 0
\(643\) −783.487 −1.21849 −0.609244 0.792983i \(-0.708527\pi\)
−0.609244 + 0.792983i \(0.708527\pi\)
\(644\) 0 0
\(645\) 126.103 1062.42i 0.195508 1.64717i
\(646\) 0 0
\(647\) 642.116i 0.992452i 0.868193 + 0.496226i \(0.165281\pi\)
−0.868193 + 0.496226i \(0.834719\pi\)
\(648\) 0 0
\(649\) −608.587 + 1054.10i −0.937731 + 1.62420i
\(650\) 0 0
\(651\) −589.912 + 789.442i −0.906162 + 1.21266i
\(652\) 0 0
\(653\) 546.629 315.597i 0.837104 0.483302i −0.0191745 0.999816i \(-0.506104\pi\)
0.856279 + 0.516514i \(0.172770\pi\)
\(654\) 0 0
\(655\) −11.8062 −0.0180247
\(656\) 0 0
\(657\) −497.601 119.812i −0.757383 0.182362i
\(658\) 0 0
\(659\) 170.496i 0.258720i 0.991598 + 0.129360i \(0.0412923\pi\)
−0.991598 + 0.129360i \(0.958708\pi\)
\(660\) 0 0
\(661\) 594.727 1030.10i 0.899738 1.55839i 0.0719098 0.997411i \(-0.477091\pi\)
0.827828 0.560981i \(-0.189576\pi\)
\(662\) 0 0
\(663\) −58.1779 + 490.153i −0.0877495 + 0.739295i
\(664\) 0 0
\(665\) 273.451 + 974.272i 0.411204 + 1.46507i
\(666\) 0 0
\(667\) 499.422 865.024i 0.748758 1.29689i
\(668\) 0 0
\(669\) 299.917 + 35.5982i 0.448306 + 0.0532110i
\(670\) 0 0
\(671\) 876.624 + 506.119i 1.30644 + 0.754276i
\(672\) 0 0
\(673\) −50.1653 + 86.8888i −0.0745398 + 0.129107i −0.900886 0.434056i \(-0.857082\pi\)
0.826346 + 0.563162i \(0.190415\pi\)
\(674\) 0 0
\(675\) 108.619 + 40.1943i 0.160917 + 0.0595471i
\(676\) 0 0
\(677\) 301.480 + 174.060i 0.445318 + 0.257105i 0.705851 0.708360i \(-0.250565\pi\)
−0.260533 + 0.965465i \(0.583898\pi\)
\(678\) 0 0
\(679\) −1386.87 −2.04252
\(680\) 0 0
\(681\) 87.7310 37.6578i 0.128827 0.0552978i
\(682\) 0 0
\(683\) 50.5434i 0.0740021i 0.999315 + 0.0370010i \(0.0117805\pi\)
−0.999315 + 0.0370010i \(0.988220\pi\)
\(684\) 0 0
\(685\) 674.368 0.984479
\(686\) 0 0
\(687\) 461.282 + 54.7511i 0.671444 + 0.0796960i
\(688\) 0 0
\(689\) 366.050i 0.531277i
\(690\) 0 0
\(691\) 203.726 352.863i 0.294827 0.510656i −0.680117 0.733103i \(-0.738071\pi\)
0.974945 + 0.222447i \(0.0714045\pi\)
\(692\) 0 0
\(693\) −1240.01 1178.28i −1.78933 1.70026i
\(694\) 0 0
\(695\) −525.906 303.632i −0.756699 0.436880i
\(696\) 0 0
\(697\) −94.6068 + 163.864i −0.135734 + 0.235099i
\(698\) 0 0
\(699\) −1063.97 + 456.700i −1.52213 + 0.653362i
\(700\) 0 0
\(701\) −106.817 61.6711i −0.152379 0.0879758i 0.421872 0.906655i \(-0.361373\pi\)
−0.574251 + 0.818680i \(0.694706\pi\)
\(702\) 0 0
\(703\) 650.008 + 634.805i 0.924620 + 0.902994i
\(704\) 0 0
\(705\) −134.142 + 179.514i −0.190273 + 0.254630i
\(706\) 0 0
\(707\) 913.323 + 527.307i 1.29183 + 0.745837i
\(708\) 0 0
\(709\) −230.842 −0.325588 −0.162794 0.986660i \(-0.552051\pi\)
−0.162794 + 0.986660i \(0.552051\pi\)
\(710\) 0 0
\(711\) −738.043 + 776.704i −1.03803 + 1.09241i
\(712\) 0 0
\(713\) 1085.25i 1.52209i
\(714\) 0 0
\(715\) 268.451 + 464.971i 0.375456 + 0.650309i
\(716\) 0 0
\(717\) −8.08959 + 68.1553i −0.0112826 + 0.0950562i
\(718\) 0 0
\(719\) 524.661 + 302.913i 0.729710 + 0.421298i 0.818316 0.574769i \(-0.194908\pi\)
−0.0886062 + 0.996067i \(0.528241\pi\)
\(720\) 0 0
\(721\) −1008.65 −1.39896
\(722\) 0 0
\(723\) −370.955 + 496.426i −0.513077 + 0.686619i
\(724\) 0 0
\(725\) 110.820i 0.152855i
\(726\) 0 0
\(727\) −277.882 481.306i −0.382231 0.662044i 0.609150 0.793055i \(-0.291511\pi\)
−0.991381 + 0.131012i \(0.958177\pi\)
\(728\) 0 0
\(729\) 553.395 + 474.548i 0.759115 + 0.650957i
\(730\) 0 0
\(731\) 1774.85i 2.42798i
\(732\) 0 0
\(733\) −42.5759 73.7436i −0.0580844 0.100605i 0.835521 0.549458i \(-0.185166\pi\)
−0.893605 + 0.448853i \(0.851833\pi\)
\(734\) 0 0
\(735\) 141.544 1192.52i 0.192577 1.62247i
\(736\) 0 0
\(737\) 803.484 463.892i 1.09021 0.629432i
\(738\) 0 0
\(739\) −294.756 + 510.533i −0.398859 + 0.690843i −0.993585 0.113085i \(-0.963927\pi\)
0.594727 + 0.803928i \(0.297260\pi\)
\(740\) 0 0
\(741\) −149.006 + 386.337i −0.201087 + 0.521373i
\(742\) 0 0
\(743\) 1406.01i 1.89234i −0.323672 0.946169i \(-0.604917\pi\)
0.323672 0.946169i \(-0.395083\pi\)
\(744\) 0 0
\(745\) −557.245 −0.747979
\(746\) 0 0
\(747\) −173.724 + 721.509i −0.232563 + 0.965876i
\(748\) 0 0
\(749\) 1184.32 + 683.770i 1.58121 + 0.912910i
\(750\) 0 0
\(751\) −4.98872 + 8.64072i −0.00664277 + 0.0115056i −0.869328 0.494236i \(-0.835448\pi\)
0.862685 + 0.505742i \(0.168781\pi\)
\(752\) 0 0
\(753\) 69.7425 587.585i 0.0926195 0.780325i
\(754\) 0 0
\(755\) 290.838 + 167.916i 0.385216 + 0.222405i
\(756\) 0 0
\(757\) −546.784 + 947.058i −0.722304 + 1.25107i 0.237770 + 0.971322i \(0.423584\pi\)
−0.960074 + 0.279746i \(0.909750\pi\)
\(758\) 0 0
\(759\) 1870.55 + 222.022i 2.46449 + 0.292519i
\(760\) 0 0
\(761\) 864.824 499.306i 1.13643 0.656118i 0.190886 0.981612i \(-0.438864\pi\)
0.945544 + 0.325494i \(0.105530\pi\)
\(762\) 0 0
\(763\) 700.890 + 1213.98i 0.918597 + 1.59106i
\(764\) 0 0
\(765\) 901.866 + 217.150i 1.17891 + 0.283857i
\(766\) 0 0
\(767\) −471.514 272.229i −0.614751 0.354926i
\(768\) 0 0
\(769\) −13.8515 + 23.9914i −0.0180123 + 0.0311982i −0.874891 0.484320i \(-0.839067\pi\)
0.856879 + 0.515518i \(0.172400\pi\)
\(770\) 0 0
\(771\) −558.860 + 239.886i −0.724850 + 0.311136i
\(772\) 0 0
\(773\) 258.082 149.004i 0.333870 0.192760i −0.323688 0.946164i \(-0.604923\pi\)
0.657558 + 0.753404i \(0.271589\pi\)
\(774\) 0 0
\(775\) 60.2032 + 104.275i 0.0776815 + 0.134548i
\(776\) 0 0
\(777\) −662.218 1542.76i −0.852275 1.98554i
\(778\) 0 0
\(779\) −110.904 + 113.560i −0.142368 + 0.145777i
\(780\) 0 0
\(781\) −685.260 1186.91i −0.877414 1.51973i
\(782\) 0 0
\(783\) −242.081 + 654.188i −0.309171 + 0.835489i
\(784\) 0 0
\(785\) 1328.99i 1.69297i
\(786\) 0 0
\(787\) 200.548 + 347.359i 0.254825 + 0.441370i 0.964848 0.262808i \(-0.0846487\pi\)
−0.710023 + 0.704179i \(0.751315\pi\)
\(788\) 0 0
\(789\) −73.1713 + 616.473i −0.0927392 + 0.781334i
\(790\) 0 0
\(791\) 1643.89i 2.07824i
\(792\) 0 0
\(793\) −226.393 + 392.125i −0.285490 + 0.494483i
\(794\) 0 0
\(795\) 683.146 + 81.0849i 0.859303 + 0.101994i
\(796\) 0 0
\(797\) −876.314 +