Properties

Label 1512.2.c.e.757.1
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 757.1
Root \(-1.37874 - 0.314750i\)
Character \(\chi\) = 1512.757
Dual form 1512.2.c.e.757.2

$q$-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 \(-0.991843\pi\)
0.999672 0.0256234i \(-0.00815707\pi\)
\(6\) 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 \(-0.980171\pi\)
0.998060 0.0622555i \(-0.0198294\pi\)
\(12\) 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 \(-0.598354\pi\)
−0.304094 + 0.952642i \(0.598354\pi\)
\(18\) 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 \(-0.652528\pi\)
−0.461053 + 0.887373i \(0.652528\pi\)
\(24\) 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 \(-0.944884\pi\)
0.985047 0.172287i \(-0.0551158\pi\)
\(30\) 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 \(-0.440015\pi\)
0.187336 + 0.982296i \(0.440015\pi\)
\(42\) 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 \(-0.323185\pi\)
0.527353 + 0.849646i \(0.323185\pi\)
\(48\) 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 \(0.280182\pi\)
−0.636983 + 0.770877i \(0.719818\pi\)
\(54\) 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 \(0.0894188\pi\)
−0.960801 + 0.277237i \(0.910581\pi\)
\(60\) 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 \(-0.488508\pi\)
0.0360946 + 0.999348i \(0.488508\pi\)
\(72\) 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 \(0.0863091\pi\)
−0.963464 + 0.267838i \(0.913691\pi\)
\(84\) 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 \(-0.313732\pi\)
0.552347 + 0.833614i \(0.313732\pi\)
\(90\) 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 \(0.00322920\pi\)
−0.999949 + 0.0101446i \(0.996771\pi\)
\(102\) 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 \(0.117548\pi\)
−0.932585 + 0.360951i \(0.882452\pi\)
\(108\) 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 \(-0.571411\pi\)
−0.222467 + 0.974940i \(0.571411\pi\)
\(114\) 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 \(0.299744\pi\)
−0.588435 + 0.808544i \(0.700256\pi\)
\(132\) 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 \(-0.382760\pi\)
0.360048 + 0.932934i \(0.382760\pi\)
\(138\) 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 \(0.358361\pi\)
−0.430432 + 0.902623i \(0.641639\pi\)
\(150\) 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 \(-0.411050\pi\)
0.275821 + 0.961209i \(0.411050\pi\)
\(168\) 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 \(0.290712\pi\)
−0.611138 + 0.791524i \(0.709288\pi\)
\(174\) 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 \(0.0905890\pi\)
−0.959776 + 0.280767i \(0.909411\pi\)
\(180\) 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 \(-0.148862\pi\)
0.892624 + 0.450802i \(0.148862\pi\)
\(192\) 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 \(-0.842770\pi\)
0.880465 0.474111i \(-0.157230\pi\)
\(198\) 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 \(-0.725921\pi\)
0.651646 0.758523i \(-0.274079\pi\)
\(228\) 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 \(-0.277068\pi\)
0.644494 + 0.764609i \(0.277068\pi\)
\(234\) 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 \(-0.781030\pi\)
−0.772573 + 0.634926i \(0.781030\pi\)
\(240\) 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 \(0.0854476\pi\)
−0.964185 + 0.265229i \(0.914552\pi\)
\(252\) 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 \(-0.533115\pi\)
−0.103846 + 0.994593i \(0.533115\pi\)
\(258\) 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 \(-0.333105\pi\)
0.500622 + 0.865666i \(0.333105\pi\)
\(264\) 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 \(-0.943940\pi\)
0.984531 0.175210i \(-0.0560605\pi\)
\(270\) 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 \(-0.703002\pi\)
−0.595389 + 0.803438i \(0.703002\pi\)
\(282\) 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 \(0.0671604\pi\)
−0.977824 + 0.209429i \(0.932840\pi\)
\(294\) 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 \(-0.695701\pi\)
−0.576806 + 0.816881i \(0.695701\pi\)
\(312\) 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 \(-0.833373\pi\)
0.866088 0.499891i \(-0.166627\pi\)
\(318\) 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 \(0.354647\pi\)
−0.440935 + 0.897539i \(0.645353\pi\)
\(348\) 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 \(-0.663247\pi\)
−0.490668 + 0.871347i \(0.663247\pi\)
\(354\) 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 \(-0.566067\pi\)
−0.206070 + 0.978537i \(0.566067\pi\)
\(360\) 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 \(-0.429507\pi\)
0.219653 + 0.975578i \(0.429507\pi\)
\(384\) 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 \(0.0318103\pi\)
−0.995011 + 0.0997688i \(0.968190\pi\)
\(390\) 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 \(-0.448117\pi\)
0.162276 + 0.986745i \(0.448117\pi\)
\(402\) 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 \(-0.550509\pi\)
0.158014 0.987437i \(-0.449491\pi\)
\(420\) 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 \(-0.670938\pi\)
−0.511575 + 0.859238i \(0.670938\pi\)
\(432\) 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 \(0.168899\pi\)
−0.862497 + 0.506062i \(0.831101\pi\)
\(444\) 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 \(-0.361296\pi\)
0.422093 + 0.906553i \(0.361296\pi\)
\(450\) 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 \(-0.829863\pi\)
0.860523 0.509412i \(-0.170137\pi\)
\(462\) 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 \(-0.911814\pi\)
0.961868 0.273514i \(-0.0881860\pi\)
\(468\) 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 \(-0.268643\pi\)
0.664504 + 0.747284i \(0.268643\pi\)
\(480\) 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 \(-0.849309\pi\)
0.890019 0.455923i \(-0.150691\pi\)
\(492\) 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 \(-0.735283\pi\)
−0.673669 + 0.739033i \(0.735283\pi\)
\(504\) 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 \(-0.987430\pi\)
0.999220 0.0394796i \(-0.0125700\pi\)
\(510\) 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 \(-0.540003\pi\)
−0.125342 + 0.992114i \(0.540003\pi\)
\(522\) 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 \(0.182174\pi\)
−0.840649 + 0.541581i \(0.817826\pi\)
\(558\) 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 \(-0.871646\pi\)
0.919796 0.392396i \(-0.128354\pi\)
\(564\) 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 \(-0.827025\pi\)
−0.855946 + 0.517065i \(0.827025\pi\)
\(570\) 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 \(-0.798206\pi\)
0.805692 0.592334i \(-0.201794\pi\)
\(588\) 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 \(-0.165727\pi\)
0.867498 + 0.497440i \(0.165727\pi\)
\(594\) 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 \(-0.279049\pi\)
0.639723 + 0.768605i \(0.279049\pi\)
\(600\) 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 \(-0.641461\pi\)
−0.429928 + 0.902863i \(0.641461\pi\)
\(618\) 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 \(-0.530516\pi\)
−0.0957210 + 0.995408i \(0.530516\pi\)
\(642\) 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 \(-0.854051\pi\)
−0.896712 + 0.442615i \(0.854051\pi\)
\(648\) 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 \(-0.960377\pi\)
0.992263 0.124158i \(-0.0396229\pi\)
\(654\) 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 \(-0.920552\pi\)
0.969013 0.247011i \(-0.0794484\pi\)
\(660\) 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 \(0.112855\pi\)
−0.937805 + 0.347163i \(0.887145\pi\)
\(678\) 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 \(0.290192\pi\)
−0.612429 + 0.790526i \(0.709808\pi\)
\(684\) 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 \(-0.785125\pi\)
0.780676 0.624936i \(-0.214875\pi\)
\(702\) 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 \(-0.467637\pi\)
0.101497 + 0.994836i \(0.467637\pi\)
\(720\) 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 \(-0.226125\pi\)
0.758106 + 0.652131i \(0.226125\pi\)
\(744\) 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 \(-0.343087\pi\)
0.473234 + 0.880937i \(0.343087\pi\)
\(762\) 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 \(-0.908667\pi\)
0.959117 0.283010i \(-0.0913329\pi\)
\(774\) 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