Properties

Label 1512.2.c.e.757.20
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.20
Root \(1.37874 + 0.314750i\)
Character \(\chi\) = 1512.757
Dual form 1512.2.c.e.757.19

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37874 + 0.314750i) q^{2} +(1.80186 + 0.867919i) q^{4} +0.114591i q^{5} -1.00000 q^{7} +(2.21113 + 1.76377i) q^{8} +O(q^{10})\) \(q+(1.37874 + 0.314750i) q^{2} +(1.80186 + 0.867919i) q^{4} +0.114591i q^{5} -1.00000 q^{7} +(2.21113 + 1.76377i) q^{8} +(-0.0360676 + 0.157992i) q^{10} +0.412956i q^{11} -1.73584i q^{13} +(-1.37874 - 0.314750i) q^{14} +(2.49343 + 3.12774i) q^{16} +2.50762 q^{17} +6.85261i q^{19} +(-0.0994559 + 0.206478i) q^{20} +(-0.129978 + 0.569360i) q^{22} +4.42226 q^{23} +4.98687 q^{25} +(0.546355 - 2.39327i) q^{26} +(-1.80186 - 0.867919i) q^{28} +1.85559i q^{29} +5.60373 q^{31} +(2.45335 + 5.09716i) q^{32} +(3.45737 + 0.789274i) q^{34} -0.114591i q^{35} +4.39099i q^{37} +(-2.15686 + 9.44798i) q^{38} +(-0.202113 + 0.253376i) q^{40} -2.39907 q^{41} +4.35614i q^{43} +(-0.358412 + 0.744091i) q^{44} +(6.09716 + 1.39191i) q^{46} -7.23070 q^{47} +1.00000 q^{49} +(6.87561 + 1.56962i) q^{50} +(1.50657 - 3.12774i) q^{52} -11.2241i q^{53} -0.0473212 q^{55} +(-2.21113 - 1.76377i) q^{56} +(-0.584047 + 2.55838i) q^{58} -4.25900i q^{59} -7.35936i q^{61} +(7.72610 + 1.76377i) q^{62} +(1.77820 + 7.79987i) q^{64} +0.198912 q^{65} +6.25549i q^{67} +(4.51840 + 2.17641i) q^{68} +(0.0360676 - 0.157992i) q^{70} -0.608276 q^{71} -14.1550 q^{73} +(-1.38207 + 6.05405i) q^{74} +(-5.94750 + 12.3475i) q^{76} -0.412956i q^{77} +8.19950 q^{79} +(-0.358412 + 0.285726i) q^{80} +(-3.30771 - 0.755108i) q^{82} -4.88023i q^{83} +0.287352i q^{85} +(-1.37110 + 6.00600i) q^{86} +(-0.728361 + 0.913100i) q^{88} -10.4217 q^{89} +1.73584i q^{91} +(7.96832 + 3.83816i) q^{92} +(-9.96928 - 2.27586i) q^{94} -0.785249 q^{95} -3.42009 q^{97} +(1.37874 + 0.314750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{4} - 20q^{7} + O(q^{10}) \) \( 20q - 2q^{4} - 20q^{7} - 12q^{10} - 14q^{16} + 8q^{22} - 28q^{25} + 2q^{28} + 36q^{31} - 6q^{34} - 16q^{40} - 18q^{46} + 20q^{49} + 94q^{52} + 48q^{55} + 66q^{58} + 22q^{64} + 12q^{70} + 12q^{76} + 64q^{79} - 92q^{88} - 24q^{94} + 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37874 + 0.314750i 0.974919 + 0.222562i
\(3\) 0 0
\(4\) 1.80186 + 0.867919i 0.900932 + 0.433959i
\(5\) 0.114591i 0.0512468i 0.999672 + 0.0256234i \(0.00815707\pi\)
−0.999672 + 0.0256234i \(0.991843\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.21113 + 1.76377i 0.781753 + 0.623588i
\(9\) 0 0
\(10\) −0.0360676 + 0.157992i −0.0114056 + 0.0499615i
\(11\) 0.412956i 0.124511i 0.998060 + 0.0622555i \(0.0198294\pi\)
−0.998060 + 0.0622555i \(0.980171\pi\)
\(12\) 0 0
\(13\) 1.73584i 0.481435i −0.970595 0.240717i \(-0.922617\pi\)
0.970595 0.240717i \(-0.0773827\pi\)
\(14\) −1.37874 0.314750i −0.368485 0.0841205i
\(15\) 0 0
\(16\) 2.49343 + 3.12774i 0.623359 + 0.781936i
\(17\) 2.50762 0.608188 0.304094 0.952642i \(-0.401646\pi\)
0.304094 + 0.952642i \(0.401646\pi\)
\(18\) 0 0
\(19\) 6.85261i 1.57210i 0.618166 + 0.786048i \(0.287876\pi\)
−0.618166 + 0.786048i \(0.712124\pi\)
\(20\) −0.0994559 + 0.206478i −0.0222390 + 0.0461699i
\(21\) 0 0
\(22\) −0.129978 + 0.569360i −0.0277114 + 0.121388i
\(23\) 4.42226 0.922106 0.461053 0.887373i \(-0.347472\pi\)
0.461053 + 0.887373i \(0.347472\pi\)
\(24\) 0 0
\(25\) 4.98687 0.997374
\(26\) 0.546355 2.39327i 0.107149 0.469360i
\(27\) 0 0
\(28\) −1.80186 0.867919i −0.340520 0.164021i
\(29\) 1.85559i 0.344575i 0.985047 + 0.172287i \(0.0551158\pi\)
−0.985047 + 0.172287i \(0.944884\pi\)
\(30\) 0 0
\(31\) 5.60373 1.00646 0.503230 0.864153i \(-0.332145\pi\)
0.503230 + 0.864153i \(0.332145\pi\)
\(32\) 2.45335 + 5.09716i 0.433695 + 0.901060i
\(33\) 0 0
\(34\) 3.45737 + 0.789274i 0.592934 + 0.135359i
\(35\) 0.114591i 0.0193695i
\(36\) 0 0
\(37\) 4.39099i 0.721875i 0.932590 + 0.360938i \(0.117543\pi\)
−0.932590 + 0.360938i \(0.882457\pi\)
\(38\) −2.15686 + 9.44798i −0.349888 + 1.53267i
\(39\) 0 0
\(40\) −0.202113 + 0.253376i −0.0319569 + 0.0400623i
\(41\) −2.39907 −0.374672 −0.187336 0.982296i \(-0.559985\pi\)
−0.187336 + 0.982296i \(0.559985\pi\)
\(42\) 0 0
\(43\) 4.35614i 0.664306i 0.943226 + 0.332153i \(0.107775\pi\)
−0.943226 + 0.332153i \(0.892225\pi\)
\(44\) −0.358412 + 0.744091i −0.0540327 + 0.112176i
\(45\) 0 0
\(46\) 6.09716 + 1.39191i 0.898978 + 0.205225i
\(47\) −7.23070 −1.05471 −0.527353 0.849646i \(-0.676815\pi\)
−0.527353 + 0.849646i \(0.676815\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 6.87561 + 1.56962i 0.972358 + 0.221977i
\(51\) 0 0
\(52\) 1.50657 3.12774i 0.208923 0.433740i
\(53\) 11.2241i 1.54175i −0.636983 0.770877i \(-0.719818\pi\)
0.636983 0.770877i \(-0.280182\pi\)
\(54\) 0 0
\(55\) −0.0473212 −0.00638079
\(56\) −2.21113 1.76377i −0.295475 0.235694i
\(57\) 0 0
\(58\) −0.584047 + 2.55838i −0.0766892 + 0.335932i
\(59\) 4.25900i 0.554475i −0.960801 0.277237i \(-0.910581\pi\)
0.960801 0.277237i \(-0.0894188\pi\)
\(60\) 0 0
\(61\) 7.35936i 0.942269i −0.882061 0.471135i \(-0.843845\pi\)
0.882061 0.471135i \(-0.156155\pi\)
\(62\) 7.72610 + 1.76377i 0.981216 + 0.223999i
\(63\) 0 0
\(64\) 1.77820 + 7.79987i 0.222276 + 0.974984i
\(65\) 0.198912 0.0246720
\(66\) 0 0
\(67\) 6.25549i 0.764230i 0.924115 + 0.382115i \(0.124804\pi\)
−0.924115 + 0.382115i \(0.875196\pi\)
\(68\) 4.51840 + 2.17641i 0.547936 + 0.263929i
\(69\) 0 0
\(70\) 0.0360676 0.157992i 0.00431090 0.0188837i
\(71\) −0.608276 −0.0721891 −0.0360946 0.999348i \(-0.511492\pi\)
−0.0360946 + 0.999348i \(0.511492\pi\)
\(72\) 0 0
\(73\) −14.1550 −1.65671 −0.828357 0.560201i \(-0.810724\pi\)
−0.828357 + 0.560201i \(0.810724\pi\)
\(74\) −1.38207 + 6.05405i −0.160662 + 0.703769i
\(75\) 0 0
\(76\) −5.94750 + 12.3475i −0.682225 + 1.41635i
\(77\) 0.412956i 0.0470607i
\(78\) 0 0
\(79\) 8.19950 0.922516 0.461258 0.887266i \(-0.347398\pi\)
0.461258 + 0.887266i \(0.347398\pi\)
\(80\) −0.358412 + 0.285726i −0.0400717 + 0.0319451i
\(81\) 0 0
\(82\) −3.30771 0.755108i −0.365275 0.0833878i
\(83\) 4.88023i 0.535675i −0.963464 0.267838i \(-0.913691\pi\)
0.963464 0.267838i \(-0.0863091\pi\)
\(84\) 0 0
\(85\) 0.287352i 0.0311677i
\(86\) −1.37110 + 6.00600i −0.147849 + 0.647644i
\(87\) 0 0
\(88\) −0.728361 + 0.913100i −0.0776436 + 0.0973368i
\(89\) −10.4217 −1.10469 −0.552347 0.833614i \(-0.686268\pi\)
−0.552347 + 0.833614i \(0.686268\pi\)
\(90\) 0 0
\(91\) 1.73584i 0.181965i
\(92\) 7.96832 + 3.83816i 0.830755 + 0.400156i
\(93\) 0 0
\(94\) −9.96928 2.27586i −1.02825 0.234737i
\(95\) −0.785249 −0.0805649
\(96\) 0 0
\(97\) −3.42009 −0.347258 −0.173629 0.984811i \(-0.555549\pi\)
−0.173629 + 0.984811i \(0.555549\pi\)
\(98\) 1.37874 + 0.314750i 0.139274 + 0.0317945i
\(99\) 0 0
\(100\) 8.98566 + 4.32820i 0.898566 + 0.432820i
\(101\) 0.203905i 0.0202893i −0.999949 0.0101446i \(-0.996771\pi\)
0.999949 0.0101446i \(-0.00322920\pi\)
\(102\) 0 0
\(103\) 7.16809 0.706293 0.353147 0.935568i \(-0.385112\pi\)
0.353147 + 0.935568i \(0.385112\pi\)
\(104\) 3.06162 3.83816i 0.300217 0.376363i
\(105\) 0 0
\(106\) 3.53280 15.4752i 0.343136 1.50309i
\(107\) 7.46742i 0.721902i −0.932585 0.360951i \(-0.882452\pi\)
0.932585 0.360951i \(-0.117548\pi\)
\(108\) 0 0
\(109\) 2.11355i 0.202442i −0.994864 0.101221i \(-0.967725\pi\)
0.994864 0.101221i \(-0.0322749\pi\)
\(110\) −0.0652438 0.0148943i −0.00622075 0.00142012i
\(111\) 0 0
\(112\) −2.49343 3.12774i −0.235607 0.295544i
\(113\) 4.72972 0.444935 0.222467 0.974940i \(-0.428589\pi\)
0.222467 + 0.974940i \(0.428589\pi\)
\(114\) 0 0
\(115\) 0.506753i 0.0472550i
\(116\) −1.61050 + 3.34353i −0.149531 + 0.310439i
\(117\) 0 0
\(118\) 1.34052 5.87207i 0.123405 0.540568i
\(119\) −2.50762 −0.229873
\(120\) 0 0
\(121\) 10.8295 0.984497
\(122\) 2.31636 10.1467i 0.209713 0.918636i
\(123\) 0 0
\(124\) 10.0972 + 4.86358i 0.906752 + 0.436763i
\(125\) 1.14441i 0.102359i
\(126\) 0 0
\(127\) −9.55123 −0.847535 −0.423767 0.905771i \(-0.639293\pi\)
−0.423767 + 0.905771i \(0.639293\pi\)
\(128\) −0.00332222 + 11.3137i −0.000293646 + 1.00000i
\(129\) 0 0
\(130\) 0.274248 + 0.0626075i 0.0240532 + 0.00549104i
\(131\) 18.5084i 1.61709i −0.588435 0.808544i \(-0.700256\pi\)
0.588435 0.808544i \(-0.299744\pi\)
\(132\) 0 0
\(133\) 6.85261i 0.594196i
\(134\) −1.96891 + 8.62471i −0.170088 + 0.745062i
\(135\) 0 0
\(136\) 5.54468 + 4.42288i 0.475453 + 0.379259i
\(137\) −8.42852 −0.720097 −0.360048 0.932934i \(-0.617240\pi\)
−0.360048 + 0.932934i \(0.617240\pi\)
\(138\) 0 0
\(139\) 13.8639i 1.17592i 0.808890 + 0.587961i \(0.200069\pi\)
−0.808890 + 0.587961i \(0.799931\pi\)
\(140\) 0.0994559 0.206478i 0.00840556 0.0174506i
\(141\) 0 0
\(142\) −0.838657 0.191455i −0.0703785 0.0160665i
\(143\) 0.716825 0.0599439
\(144\) 0 0
\(145\) −0.212635 −0.0176583
\(146\) −19.5161 4.45527i −1.61516 0.368721i
\(147\) 0 0
\(148\) −3.81103 + 7.91198i −0.313264 + 0.650361i
\(149\) 22.0358i 1.80525i −0.430432 0.902623i \(-0.641639\pi\)
0.430432 0.902623i \(-0.358361\pi\)
\(150\) 0 0
\(151\) 5.40696 0.440012 0.220006 0.975498i \(-0.429392\pi\)
0.220006 + 0.975498i \(0.429392\pi\)
\(152\) −12.0864 + 15.1520i −0.980340 + 1.22899i
\(153\) 0 0
\(154\) 0.129978 0.569360i 0.0104739 0.0458804i
\(155\) 0.642139i 0.0515778i
\(156\) 0 0
\(157\) 13.1081i 1.04614i −0.852290 0.523070i \(-0.824787\pi\)
0.852290 0.523070i \(-0.175213\pi\)
\(158\) 11.3050 + 2.58079i 0.899378 + 0.205317i
\(159\) 0 0
\(160\) −0.584091 + 0.281132i −0.0461764 + 0.0222255i
\(161\) −4.42226 −0.348523
\(162\) 0 0
\(163\) 23.1785i 1.81548i 0.419533 + 0.907740i \(0.362194\pi\)
−0.419533 + 0.907740i \(0.637806\pi\)
\(164\) −4.32281 2.08220i −0.337555 0.162593i
\(165\) 0 0
\(166\) 1.53605 6.72859i 0.119221 0.522240i
\(167\) −7.12880 −0.551643 −0.275821 0.961209i \(-0.588950\pi\)
−0.275821 + 0.961209i \(0.588950\pi\)
\(168\) 0 0
\(169\) 9.98687 0.768221
\(170\) −0.0904440 + 0.396184i −0.00693673 + 0.0303859i
\(171\) 0 0
\(172\) −3.78078 + 7.84918i −0.288282 + 0.598494i
\(173\) 20.8217i 1.58305i −0.611138 0.791524i \(-0.709288\pi\)
0.611138 0.791524i \(-0.290712\pi\)
\(174\) 0 0
\(175\) −4.98687 −0.376972
\(176\) −1.29162 + 1.02968i −0.0973596 + 0.0776150i
\(177\) 0 0
\(178\) −14.3688 3.28022i −1.07699 0.245863i
\(179\) 7.51282i 0.561535i −0.959776 0.280767i \(-0.909411\pi\)
0.959776 0.280767i \(-0.0905890\pi\)
\(180\) 0 0
\(181\) 4.48480i 0.333353i −0.986012 0.166676i \(-0.946697\pi\)
0.986012 0.166676i \(-0.0533035\pi\)
\(182\) −0.546355 + 2.39327i −0.0404985 + 0.177401i
\(183\) 0 0
\(184\) 9.77820 + 7.79987i 0.720859 + 0.575014i
\(185\) −0.503170 −0.0369938
\(186\) 0 0
\(187\) 1.03554i 0.0757260i
\(188\) −13.0287 6.27566i −0.950219 0.457700i
\(189\) 0 0
\(190\) −1.08266 0.247157i −0.0785442 0.0179307i
\(191\) −24.6726 −1.78525 −0.892624 0.450802i \(-0.851138\pi\)
−0.892624 + 0.450802i \(0.851138\pi\)
\(192\) 0 0
\(193\) −0.335818 −0.0241727 −0.0120863 0.999927i \(-0.503847\pi\)
−0.0120863 + 0.999927i \(0.503847\pi\)
\(194\) −4.71543 1.07647i −0.338548 0.0772864i
\(195\) 0 0
\(196\) 1.80186 + 0.867919i 0.128705 + 0.0619942i
\(197\) 13.3089i 0.948221i 0.880465 + 0.474111i \(0.157230\pi\)
−0.880465 + 0.474111i \(0.842770\pi\)
\(198\) 0 0
\(199\) −9.24682 −0.655490 −0.327745 0.944766i \(-0.606289\pi\)
−0.327745 + 0.944766i \(0.606289\pi\)
\(200\) 11.0266 + 8.79571i 0.779700 + 0.621951i
\(201\) 0 0
\(202\) 0.0641790 0.281132i 0.00451562 0.0197804i
\(203\) 1.85559i 0.130237i
\(204\) 0 0
\(205\) 0.274913i 0.0192008i
\(206\) 9.88296 + 2.25616i 0.688579 + 0.157194i
\(207\) 0 0
\(208\) 5.42926 4.32820i 0.376451 0.300106i
\(209\) −2.82983 −0.195743
\(210\) 0 0
\(211\) 4.73424i 0.325918i −0.986633 0.162959i \(-0.947896\pi\)
0.986633 0.162959i \(-0.0521039\pi\)
\(212\) 9.74165 20.2244i 0.669059 1.38902i
\(213\) 0 0
\(214\) 2.35037 10.2956i 0.160668 0.703796i
\(215\) −0.499176 −0.0340435
\(216\) 0 0
\(217\) −5.60373 −0.380406
\(218\) 0.665241 2.91405i 0.0450558 0.197364i
\(219\) 0 0
\(220\) −0.0852664 0.0410709i −0.00574866 0.00276900i
\(221\) 4.35282i 0.292803i
\(222\) 0 0
\(223\) 9.68005 0.648224 0.324112 0.946019i \(-0.394935\pi\)
0.324112 + 0.946019i \(0.394935\pi\)
\(224\) −2.45335 5.09716i −0.163921 0.340569i
\(225\) 0 0
\(226\) 6.52107 + 1.48868i 0.433775 + 0.0990255i
\(227\) 22.8566i 1.51705i 0.651646 + 0.758523i \(0.274079\pi\)
−0.651646 + 0.758523i \(0.725921\pi\)
\(228\) 0 0
\(229\) 16.7944i 1.10980i −0.831916 0.554901i \(-0.812756\pi\)
0.831916 0.554901i \(-0.187244\pi\)
\(230\) −0.159500 + 0.698682i −0.0105171 + 0.0460697i
\(231\) 0 0
\(232\) −3.27284 + 4.10296i −0.214873 + 0.269372i
\(233\) −19.6756 −1.28899 −0.644494 0.764609i \(-0.722932\pi\)
−0.644494 + 0.764609i \(0.722932\pi\)
\(234\) 0 0
\(235\) 0.828576i 0.0540503i
\(236\) 3.69647 7.67414i 0.240619 0.499544i
\(237\) 0 0
\(238\) −3.45737 0.789274i −0.224108 0.0511610i
\(239\) 23.8874 1.54515 0.772573 0.634926i \(-0.218970\pi\)
0.772573 + 0.634926i \(0.218970\pi\)
\(240\) 0 0
\(241\) −4.03141 −0.259686 −0.129843 0.991535i \(-0.541447\pi\)
−0.129843 + 0.991535i \(0.541447\pi\)
\(242\) 14.9311 + 3.40857i 0.959804 + 0.219111i
\(243\) 0 0
\(244\) 6.38732 13.2606i 0.408907 0.848921i
\(245\) 0.114591i 0.00732097i
\(246\) 0 0
\(247\) 11.8950 0.756861
\(248\) 12.3906 + 9.88371i 0.786803 + 0.627616i
\(249\) 0 0
\(250\) −0.360203 + 1.57785i −0.0227812 + 0.0997917i
\(251\) 8.40404i 0.530459i −0.964185 0.265229i \(-0.914552\pi\)
0.964185 0.265229i \(-0.0854476\pi\)
\(252\) 0 0
\(253\) 1.82620i 0.114812i
\(254\) −13.1687 3.00625i −0.826278 0.188629i
\(255\) 0 0
\(256\) −3.56557 + 15.5977i −0.222848 + 0.974853i
\(257\) 3.32955 0.207692 0.103846 0.994593i \(-0.466885\pi\)
0.103846 + 0.994593i \(0.466885\pi\)
\(258\) 0 0
\(259\) 4.39099i 0.272843i
\(260\) 0.358412 + 0.172639i 0.0222278 + 0.0107066i
\(261\) 0 0
\(262\) 5.82553 25.5184i 0.359902 1.57653i
\(263\) −16.2375 −1.00124 −0.500622 0.865666i \(-0.666895\pi\)
−0.500622 + 0.865666i \(0.666895\pi\)
\(264\) 0 0
\(265\) 1.28619 0.0790100
\(266\) 2.15686 9.44798i 0.132245 0.579293i
\(267\) 0 0
\(268\) −5.42926 + 11.2715i −0.331645 + 0.688519i
\(269\) 5.74732i 0.350420i 0.984531 + 0.175210i \(0.0560605\pi\)
−0.984531 + 0.175210i \(0.943940\pi\)
\(270\) 0 0
\(271\) −11.6089 −0.705189 −0.352595 0.935776i \(-0.614700\pi\)
−0.352595 + 0.935776i \(0.614700\pi\)
\(272\) 6.25259 + 7.84320i 0.379119 + 0.475564i
\(273\) 0 0
\(274\) −11.6208 2.65288i −0.702036 0.160266i
\(275\) 2.05936i 0.124184i
\(276\) 0 0
\(277\) 19.1097i 1.14819i −0.818788 0.574096i \(-0.805354\pi\)
0.818788 0.574096i \(-0.194646\pi\)
\(278\) −4.36366 + 19.1148i −0.261715 + 1.14643i
\(279\) 0 0
\(280\) 0.202113 0.253376i 0.0120786 0.0151421i
\(281\) 19.9611 1.19078 0.595389 0.803438i \(-0.296998\pi\)
0.595389 + 0.803438i \(0.296998\pi\)
\(282\) 0 0
\(283\) 16.1413i 0.959503i −0.877404 0.479752i \(-0.840727\pi\)
0.877404 0.479752i \(-0.159273\pi\)
\(284\) −1.09603 0.527934i −0.0650375 0.0313271i
\(285\) 0 0
\(286\) 0.988317 + 0.225621i 0.0584404 + 0.0133412i
\(287\) 2.39907 0.141613
\(288\) 0 0
\(289\) −10.7118 −0.630108
\(290\) −0.293169 0.0669268i −0.0172155 0.00393007i
\(291\) 0 0
\(292\) −25.5053 12.2854i −1.49259 0.718946i
\(293\) 7.16969i 0.418858i −0.977824 0.209429i \(-0.932840\pi\)
0.977824 0.209429i \(-0.0671604\pi\)
\(294\) 0 0
\(295\) 0.488044 0.0284150
\(296\) −7.74472 + 9.70907i −0.450153 + 0.564328i
\(297\) 0 0
\(298\) 6.93578 30.3818i 0.401779 1.75997i
\(299\) 7.67633i 0.443934i
\(300\) 0 0
\(301\) 4.35614i 0.251084i
\(302\) 7.45481 + 1.70184i 0.428976 + 0.0979300i
\(303\) 0 0
\(304\) −21.4332 + 17.0865i −1.22928 + 0.979979i
\(305\) 0.843319 0.0482883
\(306\) 0 0
\(307\) 15.4062i 0.879278i 0.898175 + 0.439639i \(0.144894\pi\)
−0.898175 + 0.439639i \(0.855106\pi\)
\(308\) 0.358412 0.744091i 0.0204224 0.0423985i
\(309\) 0 0
\(310\) −0.202113 + 0.885344i −0.0114793 + 0.0502842i
\(311\) 20.3442 1.15361 0.576806 0.816881i \(-0.304299\pi\)
0.576806 + 0.816881i \(0.304299\pi\)
\(312\) 0 0
\(313\) −26.5540 −1.50092 −0.750460 0.660916i \(-0.770168\pi\)
−0.750460 + 0.660916i \(0.770168\pi\)
\(314\) 4.12577 18.0727i 0.232831 1.01990i
\(315\) 0 0
\(316\) 14.7744 + 7.11650i 0.831125 + 0.400335i
\(317\) 17.8006i 0.999782i 0.866088 + 0.499891i \(0.166627\pi\)
−0.866088 + 0.499891i \(0.833373\pi\)
\(318\) 0 0
\(319\) −0.766278 −0.0429033
\(320\) −0.893798 + 0.203767i −0.0499648 + 0.0113909i
\(321\) 0 0
\(322\) −6.09716 1.39191i −0.339782 0.0775679i
\(323\) 17.1837i 0.956129i
\(324\) 0 0
\(325\) 8.65639i 0.480170i
\(326\) −7.29543 + 31.9572i −0.404057 + 1.76995i
\(327\) 0 0
\(328\) −5.30467 4.23142i −0.292901 0.233641i
\(329\) 7.23070 0.398641
\(330\) 0 0
\(331\) 27.1007i 1.48959i 0.667295 + 0.744793i \(0.267452\pi\)
−0.667295 + 0.744793i \(0.732548\pi\)
\(332\) 4.23565 8.79352i 0.232461 0.482607i
\(333\) 0 0
\(334\) −9.82878 2.24379i −0.537807 0.122775i
\(335\) −0.716825 −0.0391643
\(336\) 0 0
\(337\) −9.19674 −0.500978 −0.250489 0.968119i \(-0.580591\pi\)
−0.250489 + 0.968119i \(0.580591\pi\)
\(338\) 13.7693 + 3.14337i 0.748953 + 0.170977i
\(339\) 0 0
\(340\) −0.249398 + 0.517769i −0.0135255 + 0.0280800i
\(341\) 2.31409i 0.125315i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −7.68325 + 9.63200i −0.414253 + 0.519323i
\(345\) 0 0
\(346\) 6.55364 28.7078i 0.352326 1.54334i
\(347\) 33.4386i 1.79508i −0.440935 0.897539i \(-0.645353\pi\)
0.440935 0.897539i \(-0.354647\pi\)
\(348\) 0 0
\(349\) 17.5598i 0.939954i −0.882679 0.469977i \(-0.844262\pi\)
0.882679 0.469977i \(-0.155738\pi\)
\(350\) −6.87561 1.56962i −0.367517 0.0838995i
\(351\) 0 0
\(352\) −2.10491 + 1.01313i −0.112192 + 0.0539998i
\(353\) 18.4376 0.981335 0.490668 0.871347i \(-0.336753\pi\)
0.490668 + 0.871347i \(0.336753\pi\)
\(354\) 0 0
\(355\) 0.0697032i 0.00369946i
\(356\) −18.7784 9.04516i −0.995255 0.479393i
\(357\) 0 0
\(358\) 2.36466 10.3583i 0.124976 0.547451i
\(359\) 7.80894 0.412140 0.206070 0.978537i \(-0.433933\pi\)
0.206070 + 0.978537i \(0.433933\pi\)
\(360\) 0 0
\(361\) −27.9582 −1.47148
\(362\) 1.41159 6.18339i 0.0741916 0.324992i
\(363\) 0 0
\(364\) −1.50657 + 3.12774i −0.0789655 + 0.163938i
\(365\) 1.62204i 0.0849012i
\(366\) 0 0
\(367\) −18.2964 −0.955066 −0.477533 0.878614i \(-0.658469\pi\)
−0.477533 + 0.878614i \(0.658469\pi\)
\(368\) 11.0266 + 13.8317i 0.574802 + 0.721028i
\(369\) 0 0
\(370\) −0.693742 0.158373i −0.0360659 0.00823340i
\(371\) 11.2241i 0.582729i
\(372\) 0 0
\(373\) 29.4005i 1.52230i −0.648575 0.761150i \(-0.724635\pi\)
0.648575 0.761150i \(-0.275365\pi\)
\(374\) −0.325936 + 1.42774i −0.0168537 + 0.0738267i
\(375\) 0 0
\(376\) −15.9880 12.7533i −0.824520 0.657702i
\(377\) 3.22100 0.165890
\(378\) 0 0
\(379\) 2.46161i 0.126444i −0.997999 0.0632222i \(-0.979862\pi\)
0.997999 0.0632222i \(-0.0201377\pi\)
\(380\) −1.41491 0.681532i −0.0725835 0.0349619i
\(381\) 0 0
\(382\) −34.0172 7.76571i −1.74047 0.397328i
\(383\) −8.59739 −0.439306 −0.219653 0.975578i \(-0.570493\pi\)
−0.219653 + 0.975578i \(0.570493\pi\)
\(384\) 0 0
\(385\) 0.0473212 0.00241171
\(386\) −0.463006 0.105699i −0.0235664 0.00537992i
\(387\) 0 0
\(388\) −6.16255 2.96836i −0.312856 0.150696i
\(389\) 3.93550i 0.199538i −0.995011 0.0997688i \(-0.968190\pi\)
0.995011 0.0997688i \(-0.0318103\pi\)
\(390\) 0 0
\(391\) 11.0894 0.560813
\(392\) 2.21113 + 1.76377i 0.111679 + 0.0890840i
\(393\) 0 0
\(394\) −4.18898 + 18.3496i −0.211038 + 0.924439i
\(395\) 0.939592i 0.0472760i
\(396\) 0 0
\(397\) 27.3549i 1.37290i −0.727175 0.686452i \(-0.759167\pi\)
0.727175 0.686452i \(-0.240833\pi\)
\(398\) −12.7490 2.91044i −0.639049 0.145887i
\(399\) 0 0
\(400\) 12.4344 + 15.5977i 0.621722 + 0.779883i
\(401\) −6.49913 −0.324551 −0.162276 0.986745i \(-0.551883\pi\)
−0.162276 + 0.986745i \(0.551883\pi\)
\(402\) 0 0
\(403\) 9.72716i 0.484545i
\(404\) 0.176973 0.367409i 0.00880473 0.0182793i
\(405\) 0 0
\(406\) 0.584047 2.55838i 0.0289858 0.126970i
\(407\) −1.81329 −0.0898814
\(408\) 0 0
\(409\) 17.9897 0.889531 0.444765 0.895647i \(-0.353287\pi\)
0.444765 + 0.895647i \(0.353287\pi\)
\(410\) 0.0865289 0.379034i 0.00427336 0.0187192i
\(411\) 0 0
\(412\) 12.9159 + 6.22132i 0.636323 + 0.306503i
\(413\) 4.25900i 0.209572i
\(414\) 0 0
\(415\) 0.559232 0.0274516
\(416\) 8.84785 4.25861i 0.433801 0.208796i
\(417\) 0 0
\(418\) −3.90160 0.890687i −0.190834 0.0435649i
\(419\) 40.4247i 1.97487i 0.158014 + 0.987437i \(0.449491\pi\)
−0.158014 + 0.987437i \(0.550509\pi\)
\(420\) 0 0
\(421\) 11.3043i 0.550938i 0.961310 + 0.275469i \(0.0888332\pi\)
−0.961310 + 0.275469i \(0.911167\pi\)
\(422\) 1.49010 6.52730i 0.0725370 0.317744i
\(423\) 0 0
\(424\) 19.7969 24.8181i 0.961420 1.20527i
\(425\) 12.5052 0.606590
\(426\) 0 0
\(427\) 7.35936i 0.356144i
\(428\) 6.48111 13.4553i 0.313276 0.650385i
\(429\) 0 0
\(430\) −0.688236 0.157116i −0.0331897 0.00757679i
\(431\) 21.2412 1.02315 0.511575 0.859238i \(-0.329062\pi\)
0.511575 + 0.859238i \(0.329062\pi\)
\(432\) 0 0
\(433\) −5.34136 −0.256690 −0.128345 0.991730i \(-0.540966\pi\)
−0.128345 + 0.991730i \(0.540966\pi\)
\(434\) −7.72610 1.76377i −0.370865 0.0846638i
\(435\) 0 0
\(436\) 1.83439 3.80834i 0.0878514 0.182386i
\(437\) 30.3040i 1.44964i
\(438\) 0 0
\(439\) −20.0290 −0.955933 −0.477966 0.878378i \(-0.658626\pi\)
−0.477966 + 0.878378i \(0.658626\pi\)
\(440\) −0.104633 0.0834639i −0.00498820 0.00397898i
\(441\) 0 0
\(442\) 1.37005 6.00143i 0.0651667 0.285459i
\(443\) 21.3027i 1.01212i −0.862497 0.506062i \(-0.831101\pi\)
0.862497 0.506062i \(-0.168899\pi\)
\(444\) 0 0
\(445\) 1.19423i 0.0566121i
\(446\) 13.3463 + 3.04680i 0.631966 + 0.144270i
\(447\) 0 0
\(448\) −1.77820 7.79987i −0.0840123 0.368509i
\(449\) −17.8880 −0.844185 −0.422093 0.906553i \(-0.638704\pi\)
−0.422093 + 0.906553i \(0.638704\pi\)
\(450\) 0 0
\(451\) 0.990712i 0.0466508i
\(452\) 8.52232 + 4.10502i 0.400856 + 0.193084i
\(453\) 0 0
\(454\) −7.19411 + 31.5134i −0.337636 + 1.47900i
\(455\) −0.198912 −0.00932513
\(456\) 0 0
\(457\) 19.3625 0.905740 0.452870 0.891577i \(-0.350400\pi\)
0.452870 + 0.891577i \(0.350400\pi\)
\(458\) 5.28602 23.1551i 0.247000 1.08197i
\(459\) 0 0
\(460\) −0.439820 + 0.913100i −0.0205067 + 0.0425735i
\(461\) 21.8751i 1.01882i 0.860523 + 0.509412i \(0.170137\pi\)
−0.860523 + 0.509412i \(0.829863\pi\)
\(462\) 0 0
\(463\) 26.0449 1.21041 0.605204 0.796070i \(-0.293091\pi\)
0.605204 + 0.796070i \(0.293091\pi\)
\(464\) −5.80382 + 4.62680i −0.269435 + 0.214794i
\(465\) 0 0
\(466\) −27.1275 6.19288i −1.25666 0.286880i
\(467\) 11.8214i 0.547028i 0.961868 + 0.273514i \(0.0881860\pi\)
−0.961868 + 0.273514i \(0.911814\pi\)
\(468\) 0 0
\(469\) 6.25549i 0.288852i
\(470\) 0.260794 1.14239i 0.0120295 0.0526947i
\(471\) 0 0
\(472\) 7.51191 9.41721i 0.345764 0.433462i
\(473\) −1.79890 −0.0827133
\(474\) 0 0
\(475\) 34.1730i 1.56797i
\(476\) −4.51840 2.17641i −0.207100 0.0997557i
\(477\) 0 0
\(478\) 32.9345 + 7.51855i 1.50639 + 0.343890i
\(479\) −29.0868 −1.32901 −0.664504 0.747284i \(-0.731357\pi\)
−0.664504 + 0.747284i \(0.731357\pi\)
\(480\) 0 0
\(481\) 7.62205 0.347536
\(482\) −5.55828 1.26889i −0.253173 0.0577962i
\(483\) 0 0
\(484\) 19.5132 + 9.39910i 0.886965 + 0.427232i
\(485\) 0.391913i 0.0177959i
\(486\) 0 0
\(487\) −21.3338 −0.966728 −0.483364 0.875419i \(-0.660585\pi\)
−0.483364 + 0.875419i \(0.660585\pi\)
\(488\) 12.9802 16.2725i 0.587588 0.736622i
\(489\) 0 0
\(490\) −0.0360676 + 0.157992i −0.00162937 + 0.00713735i
\(491\) 20.2052i 0.911846i 0.890019 + 0.455923i \(0.150691\pi\)
−0.890019 + 0.455923i \(0.849309\pi\)
\(492\) 0 0
\(493\) 4.65312i 0.209566i
\(494\) 16.4002 + 3.74395i 0.737878 + 0.168448i
\(495\) 0 0
\(496\) 13.9725 + 17.5270i 0.627385 + 0.786987i
\(497\) 0.608276 0.0272849
\(498\) 0 0
\(499\) 25.2662i 1.13107i 0.824724 + 0.565535i \(0.191330\pi\)
−0.824724 + 0.565535i \(0.808670\pi\)
\(500\) −0.993254 + 2.06207i −0.0444196 + 0.0922186i
\(501\) 0 0
\(502\) 2.64517 11.5870i 0.118060 0.517154i
\(503\) 30.2176 1.34734 0.673669 0.739033i \(-0.264717\pi\)
0.673669 + 0.739033i \(0.264717\pi\)
\(504\) 0 0
\(505\) 0.0233657 0.00103976
\(506\) −0.574797 + 2.51786i −0.0255528 + 0.111933i
\(507\) 0 0
\(508\) −17.2100 8.28969i −0.763572 0.367796i
\(509\) 1.78140i 0.0789592i 0.999220 + 0.0394796i \(0.0125700\pi\)
−0.999220 + 0.0394796i \(0.987430\pi\)
\(510\) 0 0
\(511\) 14.1550 0.626179
\(512\) −9.82536 + 20.3829i −0.434224 + 0.900805i
\(513\) 0 0
\(514\) 4.59060 + 1.04798i 0.202483 + 0.0462243i
\(515\) 0.821401i 0.0361953i
\(516\) 0 0
\(517\) 2.98596i 0.131322i
\(518\) 1.38207 6.05405i 0.0607245 0.266000i
\(519\) 0 0
\(520\) 0.439820 + 0.350836i 0.0192874 + 0.0153852i
\(521\) 5.72198 0.250685 0.125342 0.992114i \(-0.459997\pi\)
0.125342 + 0.992114i \(0.459997\pi\)
\(522\) 0 0
\(523\) 0.348058i 0.0152195i 0.999971 + 0.00760976i \(0.00242229\pi\)
−0.999971 + 0.00760976i \(0.997578\pi\)
\(524\) 16.0638 33.3497i 0.701751 1.45689i
\(525\) 0 0
\(526\) −22.3873 5.11074i −0.976132 0.222839i
\(527\) 14.0520 0.612116
\(528\) 0 0
\(529\) −3.44359 −0.149721
\(530\) 1.77333 + 0.404828i 0.0770283 + 0.0175846i
\(531\) 0 0
\(532\) 5.94750 12.3475i 0.257857 0.535331i
\(533\) 4.16440i 0.180380i
\(534\) 0 0
\(535\) 0.855701 0.0369952
\(536\) −11.0333 + 13.8317i −0.476565 + 0.597439i
\(537\) 0 0
\(538\) −1.80897 + 7.92408i −0.0779902 + 0.341631i
\(539\) 0.412956i 0.0177873i
\(540\) 0 0
\(541\) 8.49464i 0.365213i 0.983186 + 0.182606i \(0.0584534\pi\)
−0.983186 + 0.182606i \(0.941547\pi\)
\(542\) −16.0057 3.65389i −0.687502 0.156948i
\(543\) 0 0
\(544\) 6.15207 + 12.7818i 0.263768 + 0.548014i
\(545\) 0.242195 0.0103745
\(546\) 0 0
\(547\) 31.5175i 1.34759i −0.738918 0.673796i \(-0.764663\pi\)
0.738918 0.673796i \(-0.235337\pi\)
\(548\) −15.1870 7.31527i −0.648759 0.312493i
\(549\) 0 0
\(550\) −0.648183 + 2.83933i −0.0276386 + 0.121069i
\(551\) −12.7156 −0.541704
\(552\) 0 0
\(553\) −8.19950 −0.348678
\(554\) 6.01478 26.3474i 0.255544 1.11939i
\(555\) 0 0
\(556\) −12.0327 + 24.9809i −0.510302 + 1.05943i
\(557\) 25.5635i 1.08316i −0.840649 0.541581i \(-0.817826\pi\)
0.840649 0.541581i \(-0.182174\pi\)
\(558\) 0 0
\(559\) 7.56156 0.319820
\(560\) 0.358412 0.285726i 0.0151457 0.0120741i
\(561\) 0 0
\(562\) 27.5212 + 6.28275i 1.16091 + 0.265022i
\(563\) 18.6212i 0.784791i 0.919796 + 0.392396i \(0.128354\pi\)
−0.919796 + 0.392396i \(0.871646\pi\)
\(564\) 0 0
\(565\) 0.541985i 0.0228015i
\(566\) 5.08049 22.2548i 0.213549 0.935438i
\(567\) 0 0
\(568\) −1.34498 1.07286i −0.0564341 0.0450163i
\(569\) 40.8350 1.71189 0.855946 0.517065i \(-0.172975\pi\)
0.855946 + 0.517065i \(0.172975\pi\)
\(570\) 0 0
\(571\) 20.7134i 0.866831i −0.901194 0.433415i \(-0.857308\pi\)
0.901194 0.433415i \(-0.142692\pi\)
\(572\) 1.29162 + 0.622146i 0.0540054 + 0.0260132i
\(573\) 0 0
\(574\) 3.30771 + 0.755108i 0.138061 + 0.0315176i
\(575\) 22.0532 0.919684
\(576\) 0 0
\(577\) 8.58023 0.357200 0.178600 0.983922i \(-0.442843\pi\)
0.178600 + 0.983922i \(0.442843\pi\)
\(578\) −14.7689 3.37155i −0.614304 0.140238i
\(579\) 0 0
\(580\) −0.383139 0.184550i −0.0159090 0.00766301i
\(581\) 4.88023i 0.202466i
\(582\) 0 0
\(583\) 4.63508 0.191965
\(584\) −31.2985 24.9662i −1.29514 1.03311i
\(585\) 0 0
\(586\) 2.25666 9.88516i 0.0932217 0.408352i
\(587\) 28.7023i 1.18467i 0.805692 + 0.592334i \(0.201794\pi\)
−0.805692 + 0.592334i \(0.798206\pi\)
\(588\) 0 0
\(589\) 38.4001i 1.58225i
\(590\) 0.672888 + 0.153612i 0.0277024 + 0.00632410i
\(591\) 0 0
\(592\) −13.7339 + 10.9487i −0.564460 + 0.449987i
\(593\) −42.2499 −1.73500 −0.867498 0.497440i \(-0.834273\pi\)
−0.867498 + 0.497440i \(0.834273\pi\)
\(594\) 0 0
\(595\) 0.287352i 0.0117803i
\(596\) 19.1253 39.7056i 0.783403 1.62640i
\(597\) 0 0
\(598\) 2.41612 10.5837i 0.0988027 0.432799i
\(599\) −31.3138 −1.27945 −0.639723 0.768605i \(-0.720951\pi\)
−0.639723 + 0.768605i \(0.720951\pi\)
\(600\) 0 0
\(601\) 9.40650 0.383699 0.191850 0.981424i \(-0.438551\pi\)
0.191850 + 0.981424i \(0.438551\pi\)
\(602\) 1.37110 6.00600i 0.0558817 0.244786i
\(603\) 0 0
\(604\) 9.74262 + 4.69280i 0.396421 + 0.190947i
\(605\) 1.24096i 0.0504523i
\(606\) 0 0
\(607\) 4.95314 0.201042 0.100521 0.994935i \(-0.467949\pi\)
0.100521 + 0.994935i \(0.467949\pi\)
\(608\) −34.9289 + 16.8118i −1.41655 + 0.681810i
\(609\) 0 0
\(610\) 1.16272 + 0.265434i 0.0470771 + 0.0107471i
\(611\) 12.5513i 0.507772i
\(612\) 0 0
\(613\) 6.61633i 0.267231i 0.991033 + 0.133616i \(0.0426587\pi\)
−0.991033 + 0.133616i \(0.957341\pi\)
\(614\) −4.84910 + 21.2412i −0.195694 + 0.857225i
\(615\) 0 0
\(616\) 0.728361 0.913100i 0.0293465 0.0367899i
\(617\) 21.3584 0.859855 0.429928 0.902863i \(-0.358539\pi\)
0.429928 + 0.902863i \(0.358539\pi\)
\(618\) 0 0
\(619\) 0.0210409i 0.000845707i −1.00000 0.000422854i \(-0.999865\pi\)
1.00000 0.000422854i \(-0.000134598\pi\)
\(620\) −0.557324 + 1.15705i −0.0223827 + 0.0464681i
\(621\) 0 0
\(622\) 28.0494 + 6.40332i 1.12468 + 0.256750i
\(623\) 10.4217 0.417535
\(624\) 0 0
\(625\) 24.8032 0.992128
\(626\) −36.6111 8.35786i −1.46327 0.334047i
\(627\) 0 0
\(628\) 11.3768 23.6190i 0.453982 0.942501i
\(629\) 11.0110i 0.439036i
\(630\) 0 0
\(631\) 19.6037 0.780411 0.390206 0.920728i \(-0.372404\pi\)
0.390206 + 0.920728i \(0.372404\pi\)
\(632\) 18.1302 + 14.4621i 0.721180 + 0.575270i
\(633\) 0 0
\(634\) −5.60274 + 24.5425i −0.222513 + 0.974706i
\(635\) 1.09449i 0.0434335i
\(636\) 0 0
\(637\) 1.73584i 0.0687764i
\(638\) −1.05650 0.241186i −0.0418273 0.00954864i
\(639\) 0 0
\(640\) −1.29645 0.000380698i −0.0512468 1.50484e-5i
\(641\) 4.84692 0.191442 0.0957210 0.995408i \(-0.469484\pi\)
0.0957210 + 0.995408i \(0.469484\pi\)
\(642\) 0 0
\(643\) 3.72899i 0.147057i 0.997293 + 0.0735285i \(0.0234260\pi\)
−0.997293 + 0.0735285i \(0.976574\pi\)
\(644\) −7.96832 3.83816i −0.313996 0.151245i
\(645\) 0 0
\(646\) −5.40858 + 23.6920i −0.212798 + 0.932148i
\(647\) 45.6179 1.79342 0.896712 0.442615i \(-0.145949\pi\)
0.896712 + 0.442615i \(0.145949\pi\)
\(648\) 0 0
\(649\) 1.75878 0.0690382
\(650\) 2.72460 11.9349i 0.106868 0.468127i
\(651\) 0 0
\(652\) −20.1171 + 41.7645i −0.787845 + 1.63563i
\(653\) 6.34542i 0.248315i 0.992263 + 0.124158i \(0.0396229\pi\)
−0.992263 + 0.124158i \(0.960377\pi\)
\(654\) 0 0
\(655\) 2.12090 0.0828706
\(656\) −5.98193 7.50369i −0.233555 0.292970i
\(657\) 0 0
\(658\) 9.96928 + 2.27586i 0.388643 + 0.0887224i
\(659\) 12.6820i 0.494022i 0.969013 + 0.247011i \(0.0794484\pi\)
−0.969013 + 0.247011i \(0.920552\pi\)
\(660\) 0 0
\(661\) 7.30385i 0.284087i −0.989860 0.142043i \(-0.954633\pi\)
0.989860 0.142043i \(-0.0453672\pi\)
\(662\) −8.52993 + 37.3648i −0.331525 + 1.45223i
\(663\) 0 0
\(664\) 8.60763 10.7908i 0.334041 0.418766i
\(665\) 0.785249 0.0304507
\(666\) 0 0
\(667\) 8.20591i 0.317734i
\(668\) −12.8451 6.18722i −0.496993 0.239391i
\(669\) 0 0
\(670\) −0.988317 0.225621i −0.0381820 0.00871648i
\(671\) 3.03909 0.117323
\(672\) 0 0
\(673\) −4.21222 −0.162369 −0.0811846 0.996699i \(-0.525870\pi\)
−0.0811846 + 0.996699i \(0.525870\pi\)
\(674\) −12.6799 2.89467i −0.488413 0.111499i
\(675\) 0 0
\(676\) 17.9950 + 8.66779i 0.692115 + 0.333377i
\(677\) 18.0658i 0.694326i −0.937805 0.347163i \(-0.887145\pi\)
0.937805 0.347163i \(-0.112855\pi\)
\(678\) 0 0
\(679\) 3.42009 0.131251
\(680\) −0.506823 + 0.635372i −0.0194358 + 0.0243654i
\(681\) 0 0
\(682\) −0.728361 + 3.19054i −0.0278904 + 0.122172i
\(683\) 41.3196i 1.58105i −0.612429 0.790526i \(-0.709808\pi\)
0.612429 0.790526i \(-0.290192\pi\)
\(684\) 0 0
\(685\) 0.965835i 0.0369027i
\(686\) −1.37874 0.314750i −0.0526407 0.0120172i
\(687\) 0 0
\(688\) −13.6249 + 10.8618i −0.519444 + 0.414101i
\(689\) −19.4833 −0.742254
\(690\) 0 0
\(691\) 44.2400i 1.68297i 0.540281 + 0.841485i \(0.318318\pi\)
−0.540281 + 0.841485i \(0.681682\pi\)
\(692\) 18.0716 37.5180i 0.686978 1.42622i
\(693\) 0 0
\(694\) 10.5248 46.1032i 0.399516 1.75006i
\(695\) −1.58868 −0.0602622
\(696\) 0 0
\(697\) −6.01597 −0.227871
\(698\) 5.52694 24.2104i 0.209198 0.916379i
\(699\) 0 0
\(700\) −8.98566 4.32820i −0.339626 0.163590i
\(701\) 33.0921i 1.24987i 0.780676 + 0.624936i \(0.214875\pi\)
−0.780676 + 0.624936i \(0.785125\pi\)
\(702\) 0 0
\(703\) −30.0898 −1.13486
\(704\) −3.22100 + 0.734320i −0.121396 + 0.0276757i
\(705\) 0 0
\(706\) 25.4207 + 5.80324i 0.956722 + 0.218408i
\(707\) 0.203905i 0.00766863i
\(708\) 0 0
\(709\) 28.0152i 1.05213i 0.850444 + 0.526066i \(0.176333\pi\)
−0.850444 + 0.526066i \(0.823667\pi\)
\(710\) 0.0219391 0.0961028i 0.000823359 0.00360667i
\(711\) 0 0
\(712\) −23.0437 18.3815i −0.863598 0.688875i
\(713\) 24.7812 0.928062
\(714\) 0 0
\(715\) 0.0821419i 0.00307193i
\(716\) 6.52052 13.5371i 0.243683 0.505905i
\(717\) 0 0
\(718\) 10.7665 + 2.45786i 0.401803 + 0.0917266i
\(719\) −5.44311 −0.202994 −0.101497 0.994836i \(-0.532363\pi\)
−0.101497 + 0.994836i \(0.532363\pi\)
\(720\) 0 0
\(721\) −7.16809 −0.266954
\(722\) −38.5472 8.79984i −1.43458 0.327496i
\(723\) 0 0
\(724\) 3.89244 8.08100i 0.144661 0.300328i
\(725\) 9.25359i 0.343670i
\(726\) 0 0
\(727\) 14.7480 0.546972 0.273486 0.961876i \(-0.411823\pi\)
0.273486 + 0.961876i \(0.411823\pi\)
\(728\) −3.06162 + 3.83816i −0.113471 + 0.142252i
\(729\) 0 0
\(730\) 0.510536 2.23637i 0.0188958 0.0827718i
\(731\) 10.9236i 0.404022i
\(732\) 0 0
\(733\) 45.4197i 1.67762i −0.544428 0.838808i \(-0.683253\pi\)
0.544428 0.838808i \(-0.316747\pi\)
\(734\) −25.2261 5.75880i −0.931111 0.212561i
\(735\) 0 0
\(736\) 10.8493 + 22.5410i 0.399912 + 0.830872i
\(737\) −2.58324 −0.0951550
\(738\) 0 0
\(739\) 3.03287i 0.111566i 0.998443 + 0.0557830i \(0.0177655\pi\)
−0.998443 + 0.0557830i \(0.982234\pi\)
\(740\) −0.906644 0.436711i −0.0333289 0.0160538i
\(741\) 0 0
\(742\) −3.53280 + 15.4752i −0.129693 + 0.568113i
\(743\) −41.3290 −1.51621 −0.758106 0.652131i \(-0.773875\pi\)
−0.758106 + 0.652131i \(0.773875\pi\)
\(744\) 0 0
\(745\) 2.52512 0.0925131
\(746\) 9.25381 40.5358i 0.338806 1.48412i
\(747\) 0 0
\(748\) −0.898763 + 1.86590i −0.0328620 + 0.0682241i
\(749\) 7.46742i 0.272853i
\(750\) 0 0
\(751\) 18.6220 0.679527 0.339763 0.940511i \(-0.389653\pi\)
0.339763 + 0.940511i \(0.389653\pi\)
\(752\) −18.0293 22.6158i −0.657460 0.824713i
\(753\) 0 0
\(754\) 4.44094 + 1.01381i 0.161729 + 0.0369208i
\(755\) 0.619591i 0.0225492i
\(756\) 0 0
\(757\) 48.7279i 1.77104i 0.464597 + 0.885522i \(0.346199\pi\)
−0.464597 + 0.885522i \(0.653801\pi\)
\(758\) 0.774792 3.39393i 0.0281417 0.123273i
\(759\) 0 0
\(760\) −1.73629 1.38500i −0.0629818 0.0502393i
\(761\) −26.1095 −0.946468 −0.473234 0.880937i \(-0.656913\pi\)
−0.473234 + 0.880937i \(0.656913\pi\)
\(762\) 0 0
\(763\) 2.11355i 0.0765157i
\(764\) −44.4567 21.4138i −1.60839 0.774725i
\(765\) 0 0
\(766\) −11.8536 2.70603i −0.428288 0.0977728i
\(767\) −7.39293 −0.266943
\(768\) 0 0
\(769\) 24.6590 0.889225 0.444612 0.895723i \(-0.353341\pi\)
0.444612 + 0.895723i \(0.353341\pi\)
\(770\) 0.0652438 + 0.0148943i 0.00235122 + 0.000536755i
\(771\) 0 0
\(772\) −0.605098 0.291463i −0.0217780 0.0104900i
\(773\) 15.7370i 0.566019i 0.959117 + 0.283010i \(0.0913329\pi\)
−0.959117 + 0.283010i \(0.908667\pi\)
\(774\) 0 0
\(775\) 27.9451 1.00382
\(776\) −7.56228 6.03227i −0.271470 0.216546i
\(777\) 0 0
\(778\) 1.23870 5.42604i 0.0444094 0.194533i
\(779\) 16.4399i 0.589021i
\(780\) 0 0
\(781\) 0.251191i 0.00898834i
\(782\) 15.2894 + 3.49038i 0.546747 + 0.124816i
\(783\) 0 0
\(784\) 2.49343 + 3.12774i 0.0890512 + 0.111705i
\(785\) 1.50207 0.0536113
\(786\) 0 0