Properties

Label 324.3.o.a.5.11
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 5.11
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.897733 + 2.86253i) q^{3} +(-1.94378 + 1.44709i) q^{5} +(9.49800 - 6.24693i) q^{7} +(-7.38815 + 5.13957i) q^{9} +O(q^{10})\) \(q+(0.897733 + 2.86253i) q^{3} +(-1.94378 + 1.44709i) q^{5} +(9.49800 - 6.24693i) q^{7} +(-7.38815 + 5.13957i) q^{9} +(-2.00071 + 17.1171i) q^{11} +(2.68685 + 8.97472i) q^{13} +(-5.88732 - 4.26502i) q^{15} +(25.0778 + 4.42190i) q^{17} +(-5.00224 - 28.3691i) q^{19} +(26.4087 + 21.5802i) q^{21} +(-15.6168 + 23.7441i) q^{23} +(-5.48588 + 18.3241i) q^{25} +(-21.3448 - 16.5348i) q^{27} +(-16.6029 + 15.6641i) q^{29} +(-1.00203 + 17.2041i) q^{31} +(-50.7944 + 9.63953i) q^{33} +(-9.42213 + 25.8871i) q^{35} +(-40.0015 + 14.5594i) q^{37} +(-23.2783 + 15.7481i) q^{39} +(13.8323 - 58.3631i) q^{41} +(20.8820 + 48.4098i) q^{43} +(6.92350 - 20.6815i) q^{45} +(60.7845 - 3.54029i) q^{47} +(31.7799 - 73.6741i) q^{49} +(9.85538 + 75.7557i) q^{51} +(19.8891 + 11.4830i) q^{53} +(-20.8811 - 36.1671i) q^{55} +(76.7167 - 39.7869i) q^{57} +(0.566813 + 4.84939i) q^{59} +(-36.6054 - 18.3839i) q^{61} +(-38.0661 + 94.9689i) q^{63} +(-18.2098 - 13.5567i) q^{65} +(49.3145 - 52.2704i) q^{67} +(-81.9880 - 23.3876i) q^{69} +(10.8606 - 12.9431i) q^{71} +(106.603 - 89.4502i) q^{73} +(-57.3781 + 0.746666i) q^{75} +(87.9269 + 175.077i) q^{77} +(-41.3713 + 9.80519i) q^{79} +(28.1696 - 75.9439i) q^{81} +(19.1145 + 80.6503i) q^{83} +(-55.1446 + 27.6946i) q^{85} +(-59.7439 - 33.4643i) q^{87} +(-80.2312 - 95.6158i) q^{89} +(81.5842 + 68.4572i) q^{91} +(-50.1469 + 12.5764i) q^{93} +(50.7758 + 47.9045i) q^{95} +(71.9647 - 96.6654i) q^{97} +(-73.1933 - 136.747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

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
\(3\) 0.897733 + 2.86253i 0.299244 + 0.954177i
\(4\) 0 0
\(5\) −1.94378 + 1.44709i −0.388755 + 0.289418i −0.773737 0.633506i \(-0.781615\pi\)
0.384982 + 0.922924i \(0.374208\pi\)
\(6\) 0 0
\(7\) 9.49800 6.24693i 1.35686 0.892419i 0.357715 0.933831i \(-0.383556\pi\)
0.999142 + 0.0414120i \(0.0131856\pi\)
\(8\) 0 0
\(9\) −7.38815 + 5.13957i −0.820906 + 0.571064i
\(10\) 0 0
\(11\) −2.00071 + 17.1171i −0.181882 + 1.55610i 0.526439 + 0.850213i \(0.323527\pi\)
−0.708321 + 0.705890i \(0.750547\pi\)
\(12\) 0 0
\(13\) 2.68685 + 8.97472i 0.206681 + 0.690363i 0.996981 + 0.0776429i \(0.0247394\pi\)
−0.790300 + 0.612720i \(0.790075\pi\)
\(14\) 0 0
\(15\) −5.88732 4.26502i −0.392488 0.284335i
\(16\) 0 0
\(17\) 25.0778 + 4.42190i 1.47517 + 0.260112i 0.852645 0.522491i \(-0.174997\pi\)
0.622522 + 0.782603i \(0.286108\pi\)
\(18\) 0 0
\(19\) −5.00224 28.3691i −0.263276 1.49311i −0.773900 0.633307i \(-0.781697\pi\)
0.510625 0.859804i \(-0.329414\pi\)
\(20\) 0 0
\(21\) 26.4087 + 21.5802i 1.25756 + 1.02763i
\(22\) 0 0
\(23\) −15.6168 + 23.7441i −0.678990 + 1.03235i 0.317468 + 0.948269i \(0.397167\pi\)
−0.996459 + 0.0840855i \(0.973203\pi\)
\(24\) 0 0
\(25\) −5.48588 + 18.3241i −0.219435 + 0.732964i
\(26\) 0 0
\(27\) −21.3448 16.5348i −0.790547 0.612401i
\(28\) 0 0
\(29\) −16.6029 + 15.6641i −0.572515 + 0.540140i −0.917122 0.398607i \(-0.869494\pi\)
0.344607 + 0.938747i \(0.388012\pi\)
\(30\) 0 0
\(31\) −1.00203 + 17.2041i −0.0323235 + 0.554972i 0.942807 + 0.333340i \(0.108176\pi\)
−0.975130 + 0.221633i \(0.928861\pi\)
\(32\) 0 0
\(33\) −50.7944 + 9.63953i −1.53922 + 0.292107i
\(34\) 0 0
\(35\) −9.42213 + 25.8871i −0.269204 + 0.739631i
\(36\) 0 0
\(37\) −40.0015 + 14.5594i −1.08112 + 0.393496i −0.820325 0.571898i \(-0.806207\pi\)
−0.260797 + 0.965394i \(0.583985\pi\)
\(38\) 0 0
\(39\) −23.2783 + 15.7481i −0.596880 + 0.403797i
\(40\) 0 0
\(41\) 13.8323 58.3631i 0.337373 1.42349i −0.494816 0.868998i \(-0.664764\pi\)
0.832189 0.554492i \(-0.187087\pi\)
\(42\) 0 0
\(43\) 20.8820 + 48.4098i 0.485627 + 1.12581i 0.968250 + 0.249982i \(0.0804247\pi\)
−0.482623 + 0.875828i \(0.660316\pi\)
\(44\) 0 0
\(45\) 6.92350 20.6815i 0.153856 0.459589i
\(46\) 0 0
\(47\) 60.7845 3.54029i 1.29329 0.0753254i 0.602345 0.798236i \(-0.294233\pi\)
0.690942 + 0.722910i \(0.257196\pi\)
\(48\) 0 0
\(49\) 31.7799 73.6741i 0.648570 1.50355i
\(50\) 0 0
\(51\) 9.85538 + 75.7557i 0.193243 + 1.48541i
\(52\) 0 0
\(53\) 19.8891 + 11.4830i 0.375266 + 0.216660i 0.675757 0.737125i \(-0.263817\pi\)
−0.300491 + 0.953785i \(0.597150\pi\)
\(54\) 0 0
\(55\) −20.8811 36.1671i −0.379656 0.657583i
\(56\) 0 0
\(57\) 76.7167 39.7869i 1.34591 0.698017i
\(58\) 0 0
\(59\) 0.566813 + 4.84939i 0.00960700 + 0.0821931i 0.997191 0.0748969i \(-0.0238628\pi\)
−0.987584 + 0.157090i \(0.949789\pi\)
\(60\) 0 0
\(61\) −36.6054 18.3839i −0.600088 0.301376i 0.122702 0.992444i \(-0.460844\pi\)
−0.722790 + 0.691068i \(0.757141\pi\)
\(62\) 0 0
\(63\) −38.0661 + 94.9689i −0.604224 + 1.50744i
\(64\) 0 0
\(65\) −18.2098 13.5567i −0.280151 0.208565i
\(66\) 0 0
\(67\) 49.3145 52.2704i 0.736038 0.780155i −0.245913 0.969292i \(-0.579088\pi\)
0.981951 + 0.189137i \(0.0605691\pi\)
\(68\) 0 0
\(69\) −81.9880 23.3876i −1.18823 0.338950i
\(70\) 0 0
\(71\) 10.8606 12.9431i 0.152966 0.182297i −0.684120 0.729370i \(-0.739813\pi\)
0.837085 + 0.547072i \(0.184258\pi\)
\(72\) 0 0
\(73\) 106.603 89.4502i 1.46031 1.22535i 0.535712 0.844401i \(-0.320043\pi\)
0.924598 0.380944i \(-0.124401\pi\)
\(74\) 0 0
\(75\) −57.3781 + 0.746666i −0.765042 + 0.00995555i
\(76\) 0 0
\(77\) 87.9269 + 175.077i 1.14191 + 2.27372i
\(78\) 0 0
\(79\) −41.3713 + 9.80519i −0.523688 + 0.124116i −0.483953 0.875094i \(-0.660799\pi\)
−0.0397347 + 0.999210i \(0.512651\pi\)
\(80\) 0 0
\(81\) 28.1696 75.9439i 0.347772 0.937579i
\(82\) 0 0
\(83\) 19.1145 + 80.6503i 0.230295 + 0.971690i 0.958220 + 0.286033i \(0.0923367\pi\)
−0.727925 + 0.685657i \(0.759515\pi\)
\(84\) 0 0
\(85\) −55.1446 + 27.6946i −0.648760 + 0.325819i
\(86\) 0 0
\(87\) −59.7439 33.4643i −0.686711 0.384647i
\(88\) 0 0
\(89\) −80.2312 95.6158i −0.901474 1.07433i −0.996883 0.0788963i \(-0.974860\pi\)
0.0954092 0.995438i \(-0.469584\pi\)
\(90\) 0 0
\(91\) 81.5842 + 68.4572i 0.896529 + 0.752277i
\(92\) 0 0
\(93\) −50.1469 + 12.5764i −0.539214 + 0.135230i
\(94\) 0 0
\(95\) 50.7758 + 47.9045i 0.534483 + 0.504258i
\(96\) 0 0
\(97\) 71.9647 96.6654i 0.741904 0.996550i −0.257636 0.966242i \(-0.582944\pi\)
0.999541 0.0303084i \(-0.00964895\pi\)
\(98\) 0 0
\(99\) −73.1933 136.747i −0.739326 1.38128i
\(100\) 0 0
\(101\) −7.90639 + 15.7429i −0.0782811 + 0.155870i −0.929368 0.369154i \(-0.879648\pi\)
0.851087 + 0.525024i \(0.175944\pi\)
\(102\) 0 0
\(103\) 111.355 13.0155i 1.08112 0.126364i 0.443164 0.896440i \(-0.353856\pi\)
0.637952 + 0.770076i \(0.279782\pi\)
\(104\) 0 0
\(105\) −82.5611 3.73143i −0.786296 0.0355375i
\(106\) 0 0
\(107\) −6.66597 + 3.84860i −0.0622987 + 0.0359682i −0.530826 0.847481i \(-0.678118\pi\)
0.468527 + 0.883449i \(0.344785\pi\)
\(108\) 0 0
\(109\) 98.6717 170.904i 0.905245 1.56793i 0.0846573 0.996410i \(-0.473020\pi\)
0.820588 0.571520i \(-0.193646\pi\)
\(110\) 0 0
\(111\) −77.5873 101.435i −0.698984 0.913830i
\(112\) 0 0
\(113\) 141.662 + 61.1071i 1.25365 + 0.540771i 0.916256 0.400594i \(-0.131196\pi\)
0.337392 + 0.941364i \(0.390455\pi\)
\(114\) 0 0
\(115\) −4.00436 68.7522i −0.0348205 0.597845i
\(116\) 0 0
\(117\) −65.9771 52.4973i −0.563907 0.448695i
\(118\) 0 0
\(119\) 265.812 114.660i 2.23372 0.963532i
\(120\) 0 0
\(121\) −171.255 40.5882i −1.41533 0.335439i
\(122\) 0 0
\(123\) 179.484 12.7991i 1.45922 0.104058i
\(124\) 0 0
\(125\) −36.5736 100.485i −0.292589 0.803882i
\(126\) 0 0
\(127\) −111.468 40.5711i −0.877702 0.319458i −0.136420 0.990651i \(-0.543560\pi\)
−0.741282 + 0.671194i \(0.765782\pi\)
\(128\) 0 0
\(129\) −119.828 + 103.234i −0.928900 + 0.800266i
\(130\) 0 0
\(131\) −105.246 6.12988i −0.803404 0.0467930i −0.348472 0.937319i \(-0.613299\pi\)
−0.454932 + 0.890526i \(0.650336\pi\)
\(132\) 0 0
\(133\) −224.731 238.201i −1.68971 1.79099i
\(134\) 0 0
\(135\) 65.4168 + 1.25227i 0.484569 + 0.00927608i
\(136\) 0 0
\(137\) −97.8994 29.3092i −0.714594 0.213935i −0.0911881 0.995834i \(-0.529066\pi\)
−0.623406 + 0.781898i \(0.714252\pi\)
\(138\) 0 0
\(139\) 111.430 + 73.2885i 0.801653 + 0.527255i 0.882968 0.469433i \(-0.155542\pi\)
−0.0813154 + 0.996688i \(0.525912\pi\)
\(140\) 0 0
\(141\) 64.7025 + 170.819i 0.458883 + 1.21148i
\(142\) 0 0
\(143\) −158.997 + 28.0355i −1.11187 + 0.196052i
\(144\) 0 0
\(145\) 9.60512 54.4734i 0.0662422 0.375678i
\(146\) 0 0
\(147\) 239.424 + 24.8313i 1.62874 + 0.168920i
\(148\) 0 0
\(149\) −41.8444 + 12.5274i −0.280835 + 0.0840765i −0.424123 0.905605i \(-0.639418\pi\)
0.143288 + 0.989681i \(0.454232\pi\)
\(150\) 0 0
\(151\) −76.1921 8.90557i −0.504583 0.0589773i −0.140006 0.990151i \(-0.544712\pi\)
−0.364577 + 0.931173i \(0.618786\pi\)
\(152\) 0 0
\(153\) −208.005 + 96.2197i −1.35951 + 0.628887i
\(154\) 0 0
\(155\) −22.9482 34.8910i −0.148053 0.225103i
\(156\) 0 0
\(157\) 153.921 + 206.751i 0.980386 + 1.31689i 0.948291 + 0.317402i \(0.102811\pi\)
0.0320951 + 0.999485i \(0.489782\pi\)
\(158\) 0 0
\(159\) −15.0153 + 67.2418i −0.0944356 + 0.422904i
\(160\) 0 0
\(161\) 323.079i 2.00670i
\(162\) 0 0
\(163\) −24.1259 −0.148011 −0.0740057 0.997258i \(-0.523578\pi\)
−0.0740057 + 0.997258i \(0.523578\pi\)
\(164\) 0 0
\(165\) 84.7837 92.2411i 0.513841 0.559037i
\(166\) 0 0
\(167\) −122.999 + 91.5696i −0.736523 + 0.548321i −0.898765 0.438430i \(-0.855535\pi\)
0.162242 + 0.986751i \(0.448127\pi\)
\(168\) 0 0
\(169\) 67.8711 44.6395i 0.401604 0.264139i
\(170\) 0 0
\(171\) 182.762 + 183.886i 1.06879 + 1.07536i
\(172\) 0 0
\(173\) 33.6971 288.297i 0.194781 1.66646i −0.443214 0.896416i \(-0.646162\pi\)
0.637995 0.770040i \(-0.279764\pi\)
\(174\) 0 0
\(175\) 62.3646 + 208.312i 0.356369 + 1.19036i
\(176\) 0 0
\(177\) −13.3727 + 5.97598i −0.0755519 + 0.0337626i
\(178\) 0 0
\(179\) −62.9620 11.1019i −0.351743 0.0620218i −0.00501485 0.999987i \(-0.501596\pi\)
−0.346728 + 0.937966i \(0.612707\pi\)
\(180\) 0 0
\(181\) −21.4979 121.921i −0.118773 0.673595i −0.984813 0.173620i \(-0.944454\pi\)
0.866040 0.499975i \(-0.166658\pi\)
\(182\) 0 0
\(183\) 19.7626 121.288i 0.107993 0.662775i
\(184\) 0 0
\(185\) 56.6853 86.1858i 0.306407 0.465869i
\(186\) 0 0
\(187\) −125.864 + 420.414i −0.673067 + 2.24820i
\(188\) 0 0
\(189\) −306.025 23.7085i −1.61918 0.125442i
\(190\) 0 0
\(191\) 137.208 129.449i 0.718365 0.677743i −0.237553 0.971375i \(-0.576345\pi\)
0.955919 + 0.293632i \(0.0948640\pi\)
\(192\) 0 0
\(193\) 3.28408 56.3855i 0.0170160 0.292153i −0.979055 0.203595i \(-0.934737\pi\)
0.996071 0.0885574i \(-0.0282257\pi\)
\(194\) 0 0
\(195\) 22.4590 64.2965i 0.115174 0.329726i
\(196\) 0 0
\(197\) 20.2973 55.7663i 0.103032 0.283078i −0.877456 0.479657i \(-0.840761\pi\)
0.980488 + 0.196579i \(0.0629833\pi\)
\(198\) 0 0
\(199\) 151.646 55.1945i 0.762038 0.277359i 0.0683760 0.997660i \(-0.478218\pi\)
0.693662 + 0.720300i \(0.255996\pi\)
\(200\) 0 0
\(201\) 193.897 + 94.2395i 0.964660 + 0.468853i
\(202\) 0 0
\(203\) −59.8424 + 252.495i −0.294790 + 1.24382i
\(204\) 0 0
\(205\) 57.5696 + 133.461i 0.280827 + 0.651031i
\(206\) 0 0
\(207\) −6.65573 255.689i −0.0321533 1.23521i
\(208\) 0 0
\(209\) 495.606 28.8658i 2.37132 0.138114i
\(210\) 0 0
\(211\) −56.7781 + 131.626i −0.269090 + 0.623822i −0.998161 0.0606168i \(-0.980693\pi\)
0.729071 + 0.684438i \(0.239952\pi\)
\(212\) 0 0
\(213\) 46.7999 + 19.4692i 0.219718 + 0.0914048i
\(214\) 0 0
\(215\) −110.643 63.8799i −0.514619 0.297116i
\(216\) 0 0
\(217\) 97.9558 + 169.664i 0.451409 + 0.781864i
\(218\) 0 0
\(219\) 351.755 + 224.851i 1.60619 + 1.02672i
\(220\) 0 0
\(221\) 27.6952 + 236.947i 0.125318 + 1.07216i
\(222\) 0 0
\(223\) −85.7173 43.0489i −0.384383 0.193044i 0.246106 0.969243i \(-0.420849\pi\)
−0.630488 + 0.776199i \(0.717145\pi\)
\(224\) 0 0
\(225\) −53.6476 163.576i −0.238434 0.727006i
\(226\) 0 0
\(227\) −136.664 101.742i −0.602043 0.448204i 0.252492 0.967599i \(-0.418750\pi\)
−0.854534 + 0.519395i \(0.826157\pi\)
\(228\) 0 0
\(229\) −63.0448 + 66.8236i −0.275305 + 0.291806i −0.850243 0.526391i \(-0.823545\pi\)
0.574938 + 0.818197i \(0.305026\pi\)
\(230\) 0 0
\(231\) −422.228 + 408.865i −1.82783 + 1.76998i
\(232\) 0 0
\(233\) −63.5116 + 75.6902i −0.272582 + 0.324851i −0.884918 0.465747i \(-0.845786\pi\)
0.612336 + 0.790598i \(0.290230\pi\)
\(234\) 0 0
\(235\) −113.028 + 94.8421i −0.480972 + 0.403583i
\(236\) 0 0
\(237\) −65.2080 109.624i −0.275139 0.462549i
\(238\) 0 0
\(239\) −63.0115 125.466i −0.263647 0.524964i 0.722391 0.691484i \(-0.243043\pi\)
−0.986038 + 0.166521i \(0.946747\pi\)
\(240\) 0 0
\(241\) −2.35460 + 0.558049i −0.00977011 + 0.00231556i −0.235498 0.971875i \(-0.575672\pi\)
0.225728 + 0.974190i \(0.427524\pi\)
\(242\) 0 0
\(243\) 242.680 + 12.4589i 0.998685 + 0.0512711i
\(244\) 0 0
\(245\) 44.8399 + 189.194i 0.183020 + 0.772222i
\(246\) 0 0
\(247\) 241.164 121.117i 0.976374 0.490353i
\(248\) 0 0
\(249\) −213.704 + 127.118i −0.858249 + 0.510514i
\(250\) 0 0
\(251\) 13.3323 + 15.8888i 0.0531166 + 0.0633018i 0.791949 0.610588i \(-0.209067\pi\)
−0.738832 + 0.673890i \(0.764622\pi\)
\(252\) 0 0
\(253\) −375.187 314.819i −1.48295 1.24435i
\(254\) 0 0
\(255\) −128.782 132.991i −0.505027 0.521532i
\(256\) 0 0
\(257\) 107.530 + 101.450i 0.418406 + 0.394745i 0.866448 0.499267i \(-0.166397\pi\)
−0.448043 + 0.894012i \(0.647879\pi\)
\(258\) 0 0
\(259\) −288.983 + 388.171i −1.11576 + 1.49873i
\(260\) 0 0
\(261\) 42.1584 201.061i 0.161526 0.770347i
\(262\) 0 0
\(263\) −211.387 + 420.906i −0.803753 + 1.60040i −0.00406289 + 0.999992i \(0.501293\pi\)
−0.799690 + 0.600413i \(0.795003\pi\)
\(264\) 0 0
\(265\) −55.2768 + 6.46094i −0.208592 + 0.0243809i
\(266\) 0 0
\(267\) 201.677 315.501i 0.755344 1.18165i
\(268\) 0 0
\(269\) −75.1666 + 43.3974i −0.279430 + 0.161329i −0.633165 0.774017i \(-0.718245\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(270\) 0 0
\(271\) −100.669 + 174.364i −0.371473 + 0.643409i −0.989792 0.142517i \(-0.954480\pi\)
0.618320 + 0.785927i \(0.287814\pi\)
\(272\) 0 0
\(273\) −122.720 + 294.993i −0.449524 + 1.08056i
\(274\) 0 0
\(275\) −302.681 130.564i −1.10066 0.474777i
\(276\) 0 0
\(277\) 3.36070 + 57.7010i 0.0121325 + 0.208307i 0.998926 + 0.0463259i \(0.0147513\pi\)
−0.986794 + 0.161981i \(0.948212\pi\)
\(278\) 0 0
\(279\) −81.0188 132.257i −0.290390 0.474039i
\(280\) 0 0
\(281\) −42.1834 + 18.1962i −0.150119 + 0.0647550i −0.469814 0.882766i \(-0.655679\pi\)
0.319695 + 0.947521i \(0.396420\pi\)
\(282\) 0 0
\(283\) 246.202 + 58.3509i 0.869971 + 0.206187i 0.641275 0.767311i \(-0.278406\pi\)
0.228696 + 0.973498i \(0.426554\pi\)
\(284\) 0 0
\(285\) −91.5450 + 188.353i −0.321211 + 0.660887i
\(286\) 0 0
\(287\) −233.211 640.742i −0.812582 2.23255i
\(288\) 0 0
\(289\) 337.773 + 122.939i 1.16877 + 0.425396i
\(290\) 0 0
\(291\) 341.313 + 119.221i 1.17290 + 0.409696i
\(292\) 0 0
\(293\) −136.726 7.96340i −0.466642 0.0271788i −0.176787 0.984249i \(-0.556570\pi\)
−0.289856 + 0.957070i \(0.593607\pi\)
\(294\) 0 0
\(295\) −8.11926 8.60591i −0.0275229 0.0291726i
\(296\) 0 0
\(297\) 325.734 332.280i 1.09675 1.11879i
\(298\) 0 0
\(299\) −255.057 76.3590i −0.853033 0.255381i
\(300\) 0 0
\(301\) 500.750 + 329.348i 1.66362 + 1.09418i
\(302\) 0 0
\(303\) −52.1624 8.49934i −0.172153 0.0280506i
\(304\) 0 0
\(305\) 97.7558 17.2370i 0.320511 0.0565147i
\(306\) 0 0
\(307\) 34.3440 194.774i 0.111870 0.634444i −0.876383 0.481615i \(-0.840050\pi\)
0.988253 0.152829i \(-0.0488384\pi\)
\(308\) 0 0
\(309\) 137.224 + 307.073i 0.444092 + 0.993762i
\(310\) 0 0
\(311\) −49.3948 + 14.7878i −0.158826 + 0.0475493i −0.365229 0.930918i \(-0.619009\pi\)
0.206403 + 0.978467i \(0.433824\pi\)
\(312\) 0 0
\(313\) −401.918 46.9775i −1.28408 0.150088i −0.553465 0.832873i \(-0.686695\pi\)
−0.730620 + 0.682785i \(0.760769\pi\)
\(314\) 0 0
\(315\) −63.4365 239.683i −0.201386 0.760900i
\(316\) 0 0
\(317\) −272.816 414.796i −0.860617 1.30851i −0.949918 0.312500i \(-0.898833\pi\)
0.0893003 0.996005i \(-0.471537\pi\)
\(318\) 0 0
\(319\) −234.906 315.534i −0.736383 0.989135i
\(320\) 0 0
\(321\) −17.0010 15.6265i −0.0529626 0.0486807i
\(322\) 0 0
\(323\) 733.555i 2.27107i
\(324\) 0 0
\(325\) −179.193 −0.551364
\(326\) 0 0
\(327\) 577.800 + 129.024i 1.76697 + 0.394569i
\(328\) 0 0
\(329\) 555.215 413.342i 1.68758 1.25636i
\(330\) 0 0
\(331\) 158.817 104.455i 0.479809 0.315575i −0.286463 0.958091i \(-0.592480\pi\)
0.766272 + 0.642516i \(0.222109\pi\)
\(332\) 0 0
\(333\) 220.708 313.157i 0.662788 0.940413i
\(334\) 0 0
\(335\) −20.2166 + 172.964i −0.0603482 + 0.516312i
\(336\) 0 0
\(337\) 61.0407 + 203.890i 0.181130 + 0.605015i 0.999538 + 0.0303785i \(0.00967127\pi\)
−0.818409 + 0.574636i \(0.805144\pi\)
\(338\) 0 0
\(339\) −47.7461 + 460.370i −0.140844 + 1.35802i
\(340\) 0 0
\(341\) −292.481 51.5723i −0.857715 0.151238i
\(342\) 0 0
\(343\) −61.6623 349.704i −0.179773 1.01955i
\(344\) 0 0
\(345\) 193.210 73.1837i 0.560030 0.212127i
\(346\) 0 0
\(347\) −75.0383 + 114.090i −0.216249 + 0.328790i −0.927279 0.374371i \(-0.877859\pi\)
0.711030 + 0.703162i \(0.248229\pi\)
\(348\) 0 0
\(349\) −175.437 + 586.000i −0.502684 + 1.67908i 0.210084 + 0.977683i \(0.432626\pi\)
−0.712768 + 0.701400i \(0.752559\pi\)
\(350\) 0 0
\(351\) 91.0452 235.990i 0.259388 0.672336i
\(352\) 0 0
\(353\) 366.717 345.979i 1.03886 0.980112i 0.0390407 0.999238i \(-0.487570\pi\)
0.999817 + 0.0191259i \(0.00608832\pi\)
\(354\) 0 0
\(355\) −2.38068 + 40.8747i −0.00670615 + 0.115140i
\(356\) 0 0
\(357\) 566.847 + 657.962i 1.58781 + 1.84303i
\(358\) 0 0
\(359\) −137.503 + 377.786i −0.383016 + 1.05233i 0.587063 + 0.809541i \(0.300284\pi\)
−0.970080 + 0.242787i \(0.921938\pi\)
\(360\) 0 0
\(361\) −440.555 + 160.349i −1.22037 + 0.444180i
\(362\) 0 0
\(363\) −37.5564 526.660i −0.103461 1.45085i
\(364\) 0 0
\(365\) −77.7693 + 328.135i −0.213067 + 0.898999i
\(366\) 0 0
\(367\) 92.0158 + 213.317i 0.250724 + 0.581244i 0.996373 0.0850954i \(-0.0271195\pi\)
−0.745649 + 0.666339i \(0.767860\pi\)
\(368\) 0 0
\(369\) 197.766 + 502.288i 0.535952 + 1.36121i
\(370\) 0 0
\(371\) 260.640 15.1805i 0.702534 0.0409179i
\(372\) 0 0
\(373\) 46.7469 108.372i 0.125327 0.290540i −0.843988 0.536362i \(-0.819798\pi\)
0.969315 + 0.245821i \(0.0790576\pi\)
\(374\) 0 0
\(375\) 254.809 194.902i 0.679489 0.519738i
\(376\) 0 0
\(377\) −185.190 106.920i −0.491221 0.283606i
\(378\) 0 0
\(379\) 91.6055 + 158.665i 0.241703 + 0.418642i 0.961200 0.275854i \(-0.0889607\pi\)
−0.719496 + 0.694496i \(0.755627\pi\)
\(380\) 0 0
\(381\) 16.0673 355.503i 0.0421715 0.933079i
\(382\) 0 0
\(383\) 9.72594 + 83.2108i 0.0253941 + 0.217260i 0.999977 0.00676626i \(-0.00215378\pi\)
−0.974583 + 0.224027i \(0.928080\pi\)
\(384\) 0 0
\(385\) −424.262 213.072i −1.10198 0.553434i
\(386\) 0 0
\(387\) −403.085 250.335i −1.04156 0.646860i
\(388\) 0 0
\(389\) −39.4038 29.3350i −0.101295 0.0754114i 0.545319 0.838228i \(-0.316408\pi\)
−0.646615 + 0.762817i \(0.723816\pi\)
\(390\) 0 0
\(391\) −496.629 + 526.396i −1.27015 + 1.34628i
\(392\) 0 0
\(393\) −76.9358 306.773i −0.195765 0.780592i
\(394\) 0 0
\(395\) 66.2277 78.9271i 0.167665 0.199815i
\(396\) 0 0
\(397\) 522.591 438.506i 1.31635 1.10455i 0.329284 0.944231i \(-0.393193\pi\)
0.987066 0.160317i \(-0.0512518\pi\)
\(398\) 0 0
\(399\) 480.109 857.141i 1.20328 2.14822i
\(400\) 0 0
\(401\) −253.522 504.803i −0.632223 1.25886i −0.950459 0.310849i \(-0.899387\pi\)
0.318236 0.948012i \(-0.396910\pi\)
\(402\) 0 0
\(403\) −157.095 + 37.2321i −0.389813 + 0.0923873i
\(404\) 0 0
\(405\) 55.1422 + 188.382i 0.136154 + 0.465140i
\(406\) 0 0
\(407\) −169.183 713.840i −0.415684 1.75391i
\(408\) 0 0
\(409\) 367.542 184.586i 0.898635 0.451311i 0.0613738 0.998115i \(-0.480452\pi\)
0.837261 + 0.546803i \(0.184156\pi\)
\(410\) 0 0
\(411\) −3.98918 306.552i −0.00970604 0.745868i
\(412\) 0 0
\(413\) 35.6774 + 42.5187i 0.0863860 + 0.102951i
\(414\) 0 0
\(415\) −153.862 129.106i −0.370752 0.311098i
\(416\) 0 0
\(417\) −109.756 + 384.764i −0.263205 + 0.922696i
\(418\) 0 0
\(419\) 176.964 + 166.957i 0.422349 + 0.398466i 0.867859 0.496811i \(-0.165496\pi\)
−0.445509 + 0.895277i \(0.646977\pi\)
\(420\) 0 0
\(421\) 258.380 347.064i 0.613728 0.824380i −0.381250 0.924472i \(-0.624506\pi\)
0.994978 + 0.100092i \(0.0319136\pi\)
\(422\) 0 0
\(423\) −430.890 + 338.563i −1.01865 + 0.800385i
\(424\) 0 0
\(425\) −218.601 + 435.271i −0.514356 + 1.02417i
\(426\) 0 0
\(427\) −462.521 + 54.0609i −1.08319 + 0.126606i
\(428\) 0 0
\(429\) −222.989 429.965i −0.519788 1.00225i
\(430\) 0 0
\(431\) 172.873 99.8080i 0.401096 0.231573i −0.285861 0.958271i \(-0.592279\pi\)
0.686957 + 0.726698i \(0.258946\pi\)
\(432\) 0 0
\(433\) −3.08649 + 5.34596i −0.00712815 + 0.0123463i −0.869567 0.493814i \(-0.835602\pi\)
0.862439 + 0.506160i \(0.168936\pi\)
\(434\) 0 0
\(435\) 164.554 21.4076i 0.378286 0.0492128i
\(436\) 0 0
\(437\) 751.719 + 324.260i 1.72018 + 0.742014i
\(438\) 0 0
\(439\) 14.9041 + 255.894i 0.0339502 + 0.582902i 0.971792 + 0.235839i \(0.0757838\pi\)
−0.937842 + 0.347063i \(0.887179\pi\)
\(440\) 0 0
\(441\) 143.859 + 707.651i 0.326210 + 1.60465i
\(442\) 0 0
\(443\) 657.070 283.432i 1.48323 0.639802i 0.508071 0.861315i \(-0.330359\pi\)
0.975157 + 0.221513i \(0.0710996\pi\)
\(444\) 0 0
\(445\) 294.316 + 69.7541i 0.661384 + 0.156751i
\(446\) 0 0
\(447\) −73.4251 108.535i −0.164262 0.242807i
\(448\) 0 0
\(449\) 42.0679 + 115.581i 0.0936924 + 0.257418i 0.977683 0.210088i \(-0.0673750\pi\)
−0.883990 + 0.467506i \(0.845153\pi\)
\(450\) 0 0
\(451\) 971.334 + 353.537i 2.15373 + 0.783895i
\(452\) 0 0
\(453\) −42.9076 226.097i −0.0947189 0.499110i
\(454\) 0 0
\(455\) −257.645 15.0061i −0.566253 0.0329805i
\(456\) 0 0
\(457\) −73.9143 78.3445i −0.161738 0.171432i 0.641436 0.767176i \(-0.278339\pi\)
−0.803174 + 0.595744i \(0.796857\pi\)
\(458\) 0 0
\(459\) −462.165 509.042i −1.00690 1.10902i
\(460\) 0 0
\(461\) −25.4979 7.63356i −0.0553099 0.0165587i 0.259029 0.965870i \(-0.416598\pi\)
−0.314339 + 0.949311i \(0.601783\pi\)
\(462\) 0 0
\(463\) −271.756 178.737i −0.586946 0.386041i 0.221020 0.975269i \(-0.429061\pi\)
−0.807966 + 0.589229i \(0.799432\pi\)
\(464\) 0 0
\(465\) 79.2753 97.0127i 0.170484 0.208629i
\(466\) 0 0
\(467\) −686.646 + 121.074i −1.47033 + 0.259260i −0.850708 0.525638i \(-0.823827\pi\)
−0.619625 + 0.784898i \(0.712715\pi\)
\(468\) 0 0
\(469\) 141.860 804.528i 0.302474 1.71541i
\(470\) 0 0
\(471\) −453.652 + 626.210i −0.963168 + 1.32953i
\(472\) 0 0
\(473\) −870.416 + 260.585i −1.84020 + 0.550921i
\(474\) 0 0
\(475\) 547.280 + 63.9679i 1.15217 + 0.134669i
\(476\) 0 0
\(477\) −205.961 + 17.3835i −0.431785 + 0.0364434i
\(478\) 0 0
\(479\) −118.398 180.015i −0.247177 0.375814i 0.690495 0.723338i \(-0.257393\pi\)
−0.937671 + 0.347524i \(0.887023\pi\)
\(480\) 0 0
\(481\) −238.144 319.883i −0.495102 0.665038i
\(482\) 0 0
\(483\) −924.823 + 290.038i −1.91475 + 0.600494i
\(484\) 0 0
\(485\) 292.035i 0.602134i
\(486\) 0 0
\(487\) −99.8495 −0.205030 −0.102515 0.994731i \(-0.532689\pi\)
−0.102515 + 0.994731i \(0.532689\pi\)
\(488\) 0 0
\(489\) −21.6586 69.0610i −0.0442916 0.141229i
\(490\) 0 0
\(491\) 570.062 424.395i 1.16102 0.864349i 0.168414 0.985716i \(-0.446135\pi\)
0.992608 + 0.121367i \(0.0387279\pi\)
\(492\) 0 0
\(493\) −485.631 + 319.404i −0.985052 + 0.647879i
\(494\) 0 0
\(495\) 340.156 + 159.888i 0.687184 + 0.323006i
\(496\) 0 0
\(497\) 22.2989 190.779i 0.0448669 0.383861i
\(498\) 0 0
\(499\) 65.6719 + 219.360i 0.131607 + 0.439598i 0.998237 0.0593531i \(-0.0189038\pi\)
−0.866630 + 0.498951i \(0.833719\pi\)
\(500\) 0 0
\(501\) −372.541 269.884i −0.743595 0.538691i
\(502\) 0 0
\(503\) −666.492 117.521i −1.32503 0.233639i −0.534038 0.845460i \(-0.679326\pi\)
−0.790996 + 0.611821i \(0.790437\pi\)
\(504\) 0 0
\(505\) −7.41313 42.0419i −0.0146795 0.0832514i
\(506\) 0 0
\(507\) 188.712 + 154.209i 0.372213 + 0.304159i
\(508\) 0 0
\(509\) −286.352 + 435.378i −0.562578 + 0.855359i −0.999015 0.0443764i \(-0.985870\pi\)
0.436437 + 0.899735i \(0.356240\pi\)
\(510\) 0 0
\(511\) 453.722 1515.54i 0.887910 2.96583i
\(512\) 0 0
\(513\) −362.307 + 688.243i −0.706251 + 1.34160i
\(514\) 0 0
\(515\) −197.615 + 186.440i −0.383718 + 0.362019i
\(516\) 0 0
\(517\) −61.0122 + 1047.54i −0.118012 + 2.02619i
\(518\) 0 0
\(519\) 855.509 162.355i 1.64838 0.312822i
\(520\) 0 0
\(521\) −97.5297 + 267.961i −0.187197 + 0.514320i −0.997419 0.0718036i \(-0.977125\pi\)
0.810222 + 0.586124i \(0.199347\pi\)
\(522\) 0 0
\(523\) −72.7892 + 26.4931i −0.139176 + 0.0506560i −0.410669 0.911784i \(-0.634705\pi\)
0.271493 + 0.962440i \(0.412483\pi\)
\(524\) 0 0
\(525\) −540.313 + 365.529i −1.02917 + 0.696246i
\(526\) 0 0
\(527\) −101.204 + 427.012i −0.192037 + 0.810269i
\(528\) 0 0
\(529\) −110.375 255.878i −0.208648 0.483701i
\(530\) 0 0
\(531\) −29.1115 32.9149i −0.0548239 0.0619866i
\(532\) 0 0
\(533\) 560.958 32.6721i 1.05245 0.0612984i
\(534\) 0 0
\(535\) 7.38789 17.1271i 0.0138091 0.0320132i
\(536\) 0 0
\(537\) −24.7435 190.197i −0.0460774 0.354185i
\(538\) 0 0
\(539\) 1197.51 + 691.381i 2.22172 + 1.28271i
\(540\) 0 0
\(541\) 168.110 + 291.174i 0.310739 + 0.538215i 0.978522 0.206140i \(-0.0660903\pi\)
−0.667784 + 0.744355i \(0.732757\pi\)
\(542\) 0 0
\(543\) 329.702 170.991i 0.607187 0.314900i
\(544\) 0 0
\(545\) 55.5180 + 474.987i 0.101868 + 0.871535i
\(546\) 0 0
\(547\) 609.769 + 306.238i 1.11475 + 0.559849i 0.908179 0.418582i \(-0.137473\pi\)
0.206573 + 0.978431i \(0.433769\pi\)
\(548\) 0 0
\(549\) 364.932 52.3129i 0.664721 0.0952877i
\(550\) 0 0
\(551\) 527.428 + 392.655i 0.957219 + 0.712623i
\(552\) 0 0
\(553\) −331.693 + 351.574i −0.599806 + 0.635757i
\(554\) 0 0
\(555\) 297.598 + 84.8915i 0.536212 + 0.152958i
\(556\) 0 0
\(557\) 185.064 220.550i 0.332251 0.395961i −0.573894 0.818930i \(-0.694568\pi\)
0.906144 + 0.422969i \(0.139012\pi\)
\(558\) 0 0
\(559\) −378.358 + 317.480i −0.676847 + 0.567942i
\(560\) 0 0
\(561\) −1316.44 + 17.1309i −2.34659 + 0.0305364i
\(562\) 0 0
\(563\) −150.825 300.316i −0.267894 0.533422i 0.718956 0.695055i \(-0.244620\pi\)
−0.986851 + 0.161633i \(0.948324\pi\)
\(564\) 0 0
\(565\) −363.787 + 86.2191i −0.643871 + 0.152600i
\(566\) 0 0
\(567\) −206.862 897.288i −0.364836 1.58252i
\(568\) 0 0
\(569\) 98.2115 + 414.387i 0.172604 + 0.728272i 0.988644 + 0.150277i \(0.0480166\pi\)
−0.816040 + 0.577995i \(0.803835\pi\)
\(570\) 0 0
\(571\) 339.515 170.511i 0.594597 0.298618i −0.125936 0.992038i \(-0.540193\pi\)
0.720533 + 0.693420i \(0.243897\pi\)
\(572\) 0 0
\(573\) 493.727 + 276.551i 0.861653 + 0.482637i
\(574\) 0 0
\(575\) −349.419 416.421i −0.607685 0.724210i
\(576\) 0 0
\(577\) −34.8869 29.2736i −0.0604625 0.0507341i 0.612056 0.790815i \(-0.290343\pi\)
−0.672518 + 0.740081i \(0.734787\pi\)
\(578\) 0 0
\(579\) 164.353 41.2183i 0.283857 0.0711888i
\(580\) 0 0
\(581\) 685.366 + 646.609i 1.17963 + 1.11292i
\(582\) 0 0
\(583\) −236.348 + 317.470i −0.405399 + 0.544546i
\(584\) 0 0
\(585\) 204.213 + 6.56831i 0.349082 + 0.0112279i
\(586\) 0 0
\(587\) −20.5606 + 40.9395i −0.0350266 + 0.0697436i −0.910465 0.413586i \(-0.864276\pi\)
0.875439 + 0.483329i \(0.160573\pi\)
\(588\) 0 0
\(589\) 493.079 57.6326i 0.837145 0.0978482i
\(590\) 0 0
\(591\) 177.854 + 8.03831i 0.300938 + 0.0136012i
\(592\) 0 0
\(593\) 873.326 504.215i 1.47273 0.850278i 0.473196 0.880957i \(-0.343100\pi\)
0.999529 + 0.0306787i \(0.00976687\pi\)
\(594\) 0 0
\(595\) −350.757 + 607.528i −0.589507 + 1.02106i
\(596\) 0 0
\(597\) 294.133 + 384.540i 0.492685 + 0.644121i
\(598\) 0 0
\(599\) −511.569 220.669i −0.854039 0.368396i −0.0763767 0.997079i \(-0.524335\pi\)
−0.777662 + 0.628683i \(0.783594\pi\)
\(600\) 0 0
\(601\) −39.7856 683.092i −0.0661989 1.13659i −0.853867 0.520492i \(-0.825749\pi\)
0.787668 0.616100i \(-0.211288\pi\)
\(602\) 0 0
\(603\) −95.6959 + 639.637i −0.158700 + 1.06076i
\(604\) 0 0
\(605\) 391.616 168.927i 0.647299 0.279218i
\(606\) 0 0
\(607\) 143.441 + 33.9962i 0.236312 + 0.0560069i 0.347065 0.937841i \(-0.387178\pi\)
−0.110753 + 0.993848i \(0.535326\pi\)
\(608\) 0 0
\(609\) −776.496 + 55.3723i −1.27503 + 0.0909234i
\(610\) 0 0
\(611\) 195.092 + 536.011i 0.319300 + 0.877269i
\(612\) 0 0
\(613\) −457.443 166.496i −0.746237 0.271608i −0.0592158 0.998245i \(-0.518860\pi\)
−0.687022 + 0.726637i \(0.741082\pi\)
\(614\) 0 0
\(615\) −330.355 + 284.607i −0.537163 + 0.462776i
\(616\) 0 0
\(617\) 586.399 + 34.1538i 0.950403 + 0.0553547i 0.526336 0.850276i \(-0.323565\pi\)
0.424066 + 0.905631i \(0.360602\pi\)
\(618\) 0 0
\(619\) −155.656 164.986i −0.251464 0.266536i 0.589329 0.807893i \(-0.299392\pi\)
−0.840793 + 0.541357i \(0.817911\pi\)
\(620\) 0 0
\(621\) 725.942 248.593i 1.16899 0.400310i
\(622\) 0 0
\(623\) −1359.34 406.960i −2.18193 0.653226i
\(624\) 0 0
\(625\) −183.021 120.375i −0.292834 0.192600i
\(626\) 0 0
\(627\) 527.551 + 1392.77i 0.841389 + 2.22133i
\(628\) 0 0
\(629\) −1067.53 + 188.235i −1.69719 + 0.299260i
\(630\) 0 0
\(631\) −130.972 + 742.777i −0.207562 + 1.17714i 0.685795 + 0.727795i \(0.259455\pi\)
−0.893357 + 0.449347i \(0.851657\pi\)
\(632\) 0 0
\(633\) −427.756 44.3636i −0.675760 0.0700847i
\(634\) 0 0
\(635\) 275.379 82.4431i 0.433668 0.129832i
\(636\) 0 0
\(637\) 746.592 + 87.2641i 1.17204 + 0.136992i
\(638\) 0 0
\(639\) −13.7174 + 151.444i −0.0214670 + 0.237002i
\(640\) 0 0
\(641\) 419.263 + 637.459i 0.654077 + 0.994475i 0.998451 + 0.0556428i \(0.0177208\pi\)
−0.344374 + 0.938833i \(0.611909\pi\)
\(642\) 0 0
\(643\) −440.716 591.985i −0.685406 0.920660i 0.314182 0.949363i \(-0.398270\pi\)
−0.999588 + 0.0287026i \(0.990862\pi\)
\(644\) 0 0
\(645\) 83.5300 374.066i 0.129504 0.579948i
\(646\) 0 0
\(647\) 250.378i 0.386982i 0.981102 + 0.193491i \(0.0619811\pi\)
−0.981102 + 0.193491i \(0.938019\pi\)
\(648\) 0 0
\(649\) −84.1417 −0.129648
\(650\) 0 0
\(651\) −397.731 + 432.715i −0.610955 + 0.664693i
\(652\) 0 0
\(653\) 672.712 500.816i 1.03019 0.766946i 0.0573307 0.998355i \(-0.481741\pi\)
0.972856 + 0.231409i \(0.0743336\pi\)
\(654\) 0 0
\(655\) 213.445 140.385i 0.325870 0.214328i
\(656\) 0 0
\(657\) −327.860 + 1208.76i −0.499026 + 1.83982i
\(658\) 0 0
\(659\) −40.5416 + 346.855i −0.0615198 + 0.526336i 0.926980 + 0.375111i \(0.122396\pi\)
−0.988500 + 0.151224i \(0.951679\pi\)
\(660\) 0 0
\(661\) −179.794 600.554i −0.272003 0.908553i −0.979433 0.201770i \(-0.935331\pi\)
0.707430 0.706783i \(-0.249854\pi\)
\(662\) 0 0
\(663\) −653.406 + 291.994i −0.985529 + 0.440413i
\(664\) 0 0
\(665\) 781.525 + 137.804i 1.17523 + 0.207224i
\(666\) 0 0
\(667\) −112.646 638.845i −0.168884 0.957788i
\(668\) 0 0
\(669\) 46.2774 284.015i 0.0691740 0.424536i
\(670\) 0 0
\(671\) 387.917 589.798i 0.578117 0.878984i
\(672\) 0 0
\(673\) −127.420 + 425.614i −0.189332 + 0.632413i 0.809634 + 0.586936i \(0.199666\pi\)
−0.998965 + 0.0454768i \(0.985519\pi\)
\(674\) 0 0
\(675\) 420.081 300.416i 0.622342 0.445060i
\(676\) 0 0
\(677\) −874.762 + 825.296i −1.29212 + 1.21905i −0.330767 + 0.943712i \(0.607308\pi\)
−0.961348 + 0.275336i \(0.911211\pi\)
\(678\) 0 0
\(679\) 79.6587 1367.69i 0.117318 2.01427i
\(680\) 0 0
\(681\) 168.553 482.541i 0.247508 0.708578i
\(682\) 0 0
\(683\) −161.018 + 442.393i −0.235751 + 0.647720i 0.764245 + 0.644926i \(0.223112\pi\)
−0.999996 + 0.00279413i \(0.999111\pi\)
\(684\) 0 0
\(685\) 232.708 84.6986i 0.339719 0.123648i
\(686\) 0 0
\(687\) −247.882 120.478i −0.360818 0.175368i
\(688\) 0 0
\(689\) −49.6173 + 209.352i −0.0720136 + 0.303849i
\(690\) 0 0
\(691\) 513.568 + 1190.59i 0.743225 + 1.72299i 0.689336 + 0.724442i \(0.257902\pi\)
0.0538885 + 0.998547i \(0.482838\pi\)
\(692\) 0 0
\(693\) −1549.44 841.587i −2.23584 1.21441i
\(694\) 0 0
\(695\) −322.649 + 18.7922i −0.464244 + 0.0270391i
\(696\) 0 0
\(697\) 604.960 1402.45i 0.867948 2.01213i
\(698\) 0 0
\(699\) −273.682 113.854i −0.391534 0.162882i
\(700\) 0 0
\(701\) −84.4585 48.7621i −0.120483 0.0695608i 0.438547 0.898708i \(-0.355493\pi\)
−0.559030 + 0.829147i \(0.688826\pi\)
\(702\) 0 0
\(703\) 613.133 + 1061.98i 0.872167 + 1.51064i
\(704\) 0 0
\(705\) −372.958 238.404i −0.529018 0.338162i
\(706\) 0 0
\(707\) 23.2500 + 198.917i 0.0328855 + 0.281353i
\(708\) 0 0
\(709\) −197.598 99.2375i −0.278700 0.139968i 0.303959 0.952685i \(-0.401691\pi\)
−0.582659 + 0.812717i \(0.697988\pi\)
\(710\) 0 0
\(711\) 255.263 285.073i 0.359020 0.400947i
\(712\) 0 0
\(713\) −392.849 292.465i −0.550981 0.410190i
\(714\) 0 0
\(715\) 268.485 284.577i 0.375503 0.398010i
\(716\) 0 0
\(717\) 302.583 293.008i 0.422013 0.408658i
\(718\) 0 0
\(719\) 460.320 548.589i 0.640223 0.762988i −0.344182 0.938903i \(-0.611844\pi\)
0.984405 + 0.175915i \(0.0562883\pi\)
\(720\) 0 0
\(721\) 976.343 819.249i 1.35415 1.13627i
\(722\) 0 0
\(723\) −3.71123 6.23912i −0.00513310 0.00862949i
\(724\) 0 0
\(725\) −195.948 390.165i −0.270274 0.538159i
\(726\) 0 0
\(727\) −1172.89 + 277.981i −1.61333 + 0.382367i −0.935633 0.352974i \(-0.885171\pi\)
−0.677698 + 0.735340i \(0.737022\pi\)
\(728\) 0 0
\(729\) 182.198 + 705.865i 0.249929 + 0.968264i
\(730\) 0 0
\(731\) 309.611 + 1306.35i 0.423544 + 1.78707i
\(732\) 0 0
\(733\) 85.3175 42.8480i 0.116395 0.0584557i −0.389649 0.920963i \(-0.627404\pi\)
0.506044 + 0.862508i \(0.331107\pi\)
\(734\) 0 0
\(735\) −501.320 + 298.201i −0.682068 + 0.405716i
\(736\) 0 0
\(737\) 796.055 + 948.701i 1.08013 + 1.28725i
\(738\) 0 0
\(739\) −640.804 537.699i −0.867124 0.727603i 0.0963669 0.995346i \(-0.469278\pi\)
−0.963490 + 0.267743i \(0.913722\pi\)
\(740\) 0 0
\(741\) 563.203 + 581.609i 0.760058 + 0.784898i
\(742\) 0 0
\(743\) −464.350 438.092i −0.624966 0.589625i 0.307205 0.951643i \(-0.400606\pi\)
−0.932171 + 0.362018i \(0.882088\pi\)
\(744\) 0 0
\(745\) 63.2080 84.9030i 0.0848429 0.113964i
\(746\) 0 0
\(747\) −555.728 497.616i −0.743947 0.666153i
\(748\) 0 0
\(749\) −39.2714 + 78.1958i −0.0524318 + 0.104400i
\(750\) 0 0
\(751\) 300.724 35.1496i 0.400432 0.0468038i 0.0865062 0.996251i \(-0.472430\pi\)
0.313926 + 0.949448i \(0.398356\pi\)
\(752\) 0 0
\(753\) −33.5132 + 52.4278i −0.0445063 + 0.0696253i
\(754\) 0 0
\(755\) 160.987 92.9462i 0.213228 0.123108i
\(756\) 0 0
\(757\) 353.782 612.769i 0.467348 0.809470i −0.531956 0.846772i \(-0.678543\pi\)
0.999304 + 0.0373019i \(0.0118763\pi\)
\(758\) 0 0
\(759\) 564.362 1356.61i 0.743560 1.78736i
\(760\) 0 0
\(761\) −1031.17 444.802i −1.35502 0.584496i −0.410168 0.912010i \(-0.634530\pi\)
−0.944847 + 0.327513i \(0.893789\pi\)
\(762\) 0 0
\(763\) −130.445 2239.65i −0.170963 2.93532i
\(764\) 0 0
\(765\) 265.078 488.032i 0.346507 0.637950i
\(766\) 0 0
\(767\) −41.9990 + 18.1166i −0.0547575 + 0.0236201i
\(768\) 0 0
\(769\) −436.895 103.546i −0.568134 0.134650i −0.0634974 0.997982i \(-0.520225\pi\)
−0.504637 + 0.863332i \(0.668374\pi\)
\(770\) 0 0
\(771\) −193.869 + 398.883i −0.251451 + 0.517358i
\(772\) 0 0
\(773\) −18.9818 52.1520i −0.0245560 0.0674670i 0.926809 0.375533i \(-0.122540\pi\)
−0.951365 + 0.308066i \(0.900318\pi\)
\(774\) 0 0
\(775\) −309.753 112.741i −0.399682 0.145472i
\(776\) 0 0
\(777\) −1370.58 478.748i −1.76394 0.616149i
\(778\) 0 0
\(779\) −1724.90 100.464i −2.21425 0.128965i
\(780\) 0 0
\(781\) 199.820 + 211.797i 0.255852 + 0.271187i
\(782\) 0 0
\(783\) 613.389 59.8190i 0.783383 0.0763971i
\(784\) 0 0
\(785\) −598.375 179.142i −0.762261 0.228206i
\(786\) 0 0
\(787\) 734.950 + 483.384i 0.933862 + 0.614211i 0.922613 0.385726i \(-0.126049\pi\)
0.0112488 + 0.999937i \(0.496419\pi\)
\(788\) 0 0
\(789\) −1394.63 227.240i −1.76759 0.288011i
\(790\) 0 0
\(791\) 1727.24 304.559i 2.18361 0.385030i
\(792\) 0 0
\(793\) 66.6371 377.918i 0.0840316 0.476567i
\(794\) 0 0
\(795\) −68.1184 152.431i −0.0856836 0.191738i