Properties

Label 912.2.ci.b.223.1
Level $912$
Weight $2$
Character 912.223
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.ci (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 223.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 912.223
Dual form 912.2.ci.b.319.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.173648 + 0.984808i) q^{3} +(-1.93969 - 1.62760i) q^{5} +(0.386659 - 0.223238i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\) \(q+(-0.173648 + 0.984808i) q^{3} +(-1.93969 - 1.62760i) q^{5} +(0.386659 - 0.223238i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(2.02094 + 1.16679i) q^{11} +(0.358441 - 0.0632028i) q^{13} +(1.93969 - 1.62760i) q^{15} +(-5.58512 + 2.03282i) q^{17} +(0.354570 - 4.34445i) q^{19} +(0.152704 + 0.419550i) q^{21} +(-2.14543 - 2.55682i) q^{23} +(0.245100 + 1.39003i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.449493 - 1.23497i) q^{29} +(-3.35117 - 5.80439i) q^{31} +(-1.50000 + 1.78763i) q^{33} +(-1.11334 - 0.196312i) q^{35} -7.52974i q^{37} +0.363970i q^{39} +(-11.2947 - 1.99157i) q^{41} +(4.52481 - 5.39246i) q^{43} +(1.26604 + 2.19285i) q^{45} +(2.66978 - 7.33515i) q^{47} +(-3.40033 + 5.88954i) q^{49} +(-1.03209 - 5.85327i) q^{51} +(-1.13176 - 1.34878i) q^{53} +(-2.02094 - 5.55250i) q^{55} +(4.21688 + 1.10359i) q^{57} +(-5.69119 + 2.07142i) q^{59} +(5.19459 - 4.35878i) q^{61} +(-0.439693 + 0.0775297i) q^{63} +(-0.798133 - 0.460802i) q^{65} +(8.71688 + 3.17269i) q^{67} +(2.89053 - 1.66885i) q^{69} +(4.11334 + 3.45150i) q^{71} +(-0.591052 + 3.35202i) q^{73} -1.41147 q^{75} +1.04189 q^{77} +(0.442219 - 2.50795i) q^{79} +(0.766044 + 0.642788i) q^{81} +(1.39053 - 0.802823i) q^{83} +(14.1420 + 5.14728i) q^{85} +(1.13816 + 0.657115i) q^{87} +(-6.14930 + 1.08429i) q^{89} +(0.124485 - 0.104455i) q^{91} +(6.29813 - 2.29233i) q^{93} +(-7.75877 + 7.84981i) q^{95} +(0.368241 + 1.01173i) q^{97} +(-1.50000 - 1.78763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{5} + 9 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 6 q^{13} + 6 q^{15} - 12 q^{17} + 18 q^{19} + 3 q^{21} + 3 q^{23} + 3 q^{27} + 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} + 39 q^{47} - 6 q^{49} + 3 q^{51} - 12 q^{53} - 9 q^{55} + 9 q^{57} + 12 q^{59} + 27 q^{61} + 3 q^{63} + 9 q^{65} + 36 q^{67} + 18 q^{71} - 9 q^{73} + 12 q^{75} - 18 q^{79} - 9 q^{83} + 27 q^{85} - 27 q^{87} + 3 q^{89} - 12 q^{91} + 24 q^{93} - 24 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.173648 + 0.984808i −0.100256 + 0.568579i
\(4\) 0 0
\(5\) −1.93969 1.62760i −0.867457 0.727883i 0.0961041 0.995371i \(-0.469362\pi\)
−0.963561 + 0.267489i \(0.913806\pi\)
\(6\) 0 0
\(7\) 0.386659 0.223238i 0.146143 0.0843760i −0.425145 0.905125i \(-0.639777\pi\)
0.571289 + 0.820749i \(0.306444\pi\)
\(8\) 0 0
\(9\) −0.939693 0.342020i −0.313231 0.114007i
\(10\) 0 0
\(11\) 2.02094 + 1.16679i 0.609338 + 0.351801i 0.772706 0.634764i \(-0.218903\pi\)
−0.163369 + 0.986565i \(0.552236\pi\)
\(12\) 0 0
\(13\) 0.358441 0.0632028i 0.0994136 0.0175293i −0.123720 0.992317i \(-0.539482\pi\)
0.223134 + 0.974788i \(0.428371\pi\)
\(14\) 0 0
\(15\) 1.93969 1.62760i 0.500826 0.420243i
\(16\) 0 0
\(17\) −5.58512 + 2.03282i −1.35459 + 0.493031i −0.914378 0.404862i \(-0.867319\pi\)
−0.440213 + 0.897893i \(0.645097\pi\)
\(18\) 0 0
\(19\) 0.354570 4.34445i 0.0813440 0.996686i
\(20\) 0 0
\(21\) 0.152704 + 0.419550i 0.0333227 + 0.0915533i
\(22\) 0 0
\(23\) −2.14543 2.55682i −0.447353 0.533135i 0.494492 0.869182i \(-0.335354\pi\)
−0.941845 + 0.336048i \(0.890910\pi\)
\(24\) 0 0
\(25\) 0.245100 + 1.39003i 0.0490200 + 0.278006i
\(26\) 0 0
\(27\) 0.500000 0.866025i 0.0962250 0.166667i
\(28\) 0 0
\(29\) 0.449493 1.23497i 0.0834687 0.229328i −0.890936 0.454129i \(-0.849951\pi\)
0.974405 + 0.224800i \(0.0721729\pi\)
\(30\) 0 0
\(31\) −3.35117 5.80439i −0.601887 1.04250i −0.992535 0.121959i \(-0.961082\pi\)
0.390648 0.920540i \(-0.372251\pi\)
\(32\) 0 0
\(33\) −1.50000 + 1.78763i −0.261116 + 0.311187i
\(34\) 0 0
\(35\) −1.11334 0.196312i −0.188189 0.0331828i
\(36\) 0 0
\(37\) 7.52974i 1.23788i −0.785438 0.618941i \(-0.787562\pi\)
0.785438 0.618941i \(-0.212438\pi\)
\(38\) 0 0
\(39\) 0.363970i 0.0582819i
\(40\) 0 0
\(41\) −11.2947 1.99157i −1.76394 0.311030i −0.804713 0.593664i \(-0.797681\pi\)
−0.959228 + 0.282634i \(0.908792\pi\)
\(42\) 0 0
\(43\) 4.52481 5.39246i 0.690028 0.822343i −0.301331 0.953520i \(-0.597431\pi\)
0.991359 + 0.131176i \(0.0418754\pi\)
\(44\) 0 0
\(45\) 1.26604 + 2.19285i 0.188731 + 0.326891i
\(46\) 0 0
\(47\) 2.66978 7.33515i 0.389427 1.06994i −0.577833 0.816155i \(-0.696101\pi\)
0.967260 0.253787i \(-0.0816763\pi\)
\(48\) 0 0
\(49\) −3.40033 + 5.88954i −0.485761 + 0.841363i
\(50\) 0 0
\(51\) −1.03209 5.85327i −0.144521 0.819621i
\(52\) 0 0
\(53\) −1.13176 1.34878i −0.155459 0.185269i 0.682693 0.730705i \(-0.260808\pi\)
−0.838152 + 0.545436i \(0.816364\pi\)
\(54\) 0 0
\(55\) −2.02094 5.55250i −0.272504 0.748699i
\(56\) 0 0
\(57\) 4.21688 + 1.10359i 0.558540 + 0.146174i
\(58\) 0 0
\(59\) −5.69119 + 2.07142i −0.740930 + 0.269676i −0.684784 0.728746i \(-0.740103\pi\)
−0.0561458 + 0.998423i \(0.517881\pi\)
\(60\) 0 0
\(61\) 5.19459 4.35878i 0.665099 0.558085i −0.246511 0.969140i \(-0.579284\pi\)
0.911610 + 0.411055i \(0.134840\pi\)
\(62\) 0 0
\(63\) −0.439693 + 0.0775297i −0.0553961 + 0.00976782i
\(64\) 0 0
\(65\) −0.798133 0.460802i −0.0989963 0.0571555i
\(66\) 0 0
\(67\) 8.71688 + 3.17269i 1.06494 + 0.387605i 0.814281 0.580471i \(-0.197132\pi\)
0.250656 + 0.968076i \(0.419354\pi\)
\(68\) 0 0
\(69\) 2.89053 1.66885i 0.347979 0.200906i
\(70\) 0 0
\(71\) 4.11334 + 3.45150i 0.488164 + 0.409618i 0.853368 0.521310i \(-0.174556\pi\)
−0.365204 + 0.930928i \(0.619001\pi\)
\(72\) 0 0
\(73\) −0.591052 + 3.35202i −0.0691774 + 0.392325i 0.930485 + 0.366331i \(0.119386\pi\)
−0.999662 + 0.0259938i \(0.991725\pi\)
\(74\) 0 0
\(75\) −1.41147 −0.162983
\(76\) 0 0
\(77\) 1.04189 0.118734
\(78\) 0 0
\(79\) 0.442219 2.50795i 0.0497535 0.282166i −0.949773 0.312940i \(-0.898686\pi\)
0.999526 + 0.0307739i \(0.00979720\pi\)
\(80\) 0 0
\(81\) 0.766044 + 0.642788i 0.0851160 + 0.0714208i
\(82\) 0 0
\(83\) 1.39053 0.802823i 0.152630 0.0881212i −0.421740 0.906717i \(-0.638580\pi\)
0.574370 + 0.818596i \(0.305247\pi\)
\(84\) 0 0
\(85\) 14.1420 + 5.14728i 1.53392 + 0.558301i
\(86\) 0 0
\(87\) 1.13816 + 0.657115i 0.122023 + 0.0704501i
\(88\) 0 0
\(89\) −6.14930 + 1.08429i −0.651825 + 0.114934i −0.489776 0.871848i \(-0.662921\pi\)
−0.162049 + 0.986783i \(0.551810\pi\)
\(90\) 0 0
\(91\) 0.124485 0.104455i 0.0130496 0.0109499i
\(92\) 0 0
\(93\) 6.29813 2.29233i 0.653086 0.237704i
\(94\) 0 0
\(95\) −7.75877 + 7.84981i −0.796033 + 0.805373i
\(96\) 0 0
\(97\) 0.368241 + 1.01173i 0.0373892 + 0.102726i 0.956982 0.290146i \(-0.0937038\pi\)
−0.919593 + 0.392872i \(0.871482\pi\)
\(98\) 0 0
\(99\) −1.50000 1.78763i −0.150756 0.179664i
\(100\) 0 0
\(101\) −2.84090 16.1115i −0.282680 1.60316i −0.713456 0.700700i \(-0.752871\pi\)
0.430776 0.902459i \(-0.358240\pi\)
\(102\) 0 0
\(103\) 0.794263 1.37570i 0.0782611 0.135552i −0.824239 0.566243i \(-0.808397\pi\)
0.902500 + 0.430690i \(0.141730\pi\)
\(104\) 0 0
\(105\) 0.386659 1.06234i 0.0377341 0.103674i
\(106\) 0 0
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 0 0
\(109\) −9.56418 + 11.3981i −0.916082 + 1.09174i 0.0794046 + 0.996842i \(0.474698\pi\)
−0.995487 + 0.0949016i \(0.969746\pi\)
\(110\) 0 0
\(111\) 7.41534 + 1.30753i 0.703833 + 0.124105i
\(112\) 0 0
\(113\) 8.51860i 0.801363i −0.916217 0.400681i \(-0.868773\pi\)
0.916217 0.400681i \(-0.131227\pi\)
\(114\) 0 0
\(115\) 8.45134i 0.788092i
\(116\) 0 0
\(117\) −0.358441 0.0632028i −0.0331379 0.00584310i
\(118\) 0 0
\(119\) −1.70574 + 2.03282i −0.156365 + 0.186348i
\(120\) 0 0
\(121\) −2.77719 4.81023i −0.252472 0.437294i
\(122\) 0 0
\(123\) 3.92262 10.7773i 0.353691 0.971757i
\(124\) 0 0
\(125\) −4.54323 + 7.86911i −0.406359 + 0.703835i
\(126\) 0 0
\(127\) 2.28359 + 12.9509i 0.202635 + 1.14920i 0.901117 + 0.433575i \(0.142748\pi\)
−0.698482 + 0.715628i \(0.746141\pi\)
\(128\) 0 0
\(129\) 4.52481 + 5.39246i 0.398388 + 0.474780i
\(130\) 0 0
\(131\) 1.52481 + 4.18939i 0.133224 + 0.366029i 0.988310 0.152456i \(-0.0487183\pi\)
−0.855087 + 0.518485i \(0.826496\pi\)
\(132\) 0 0
\(133\) −0.832748 1.75898i −0.0722084 0.152523i
\(134\) 0 0
\(135\) −2.37939 + 0.866025i −0.204785 + 0.0745356i
\(136\) 0 0
\(137\) 0.701867 0.588936i 0.0599645 0.0503162i −0.612313 0.790616i \(-0.709761\pi\)
0.672277 + 0.740299i \(0.265316\pi\)
\(138\) 0 0
\(139\) −12.0778 + 2.12965i −1.02443 + 0.180635i −0.660527 0.750802i \(-0.729667\pi\)
−0.363903 + 0.931437i \(0.618556\pi\)
\(140\) 0 0
\(141\) 6.76011 + 3.90295i 0.569304 + 0.328688i
\(142\) 0 0
\(143\) 0.798133 + 0.290497i 0.0667433 + 0.0242926i
\(144\) 0 0
\(145\) −2.88191 + 1.66387i −0.239330 + 0.138177i
\(146\) 0 0
\(147\) −5.20961 4.37138i −0.429681 0.360545i
\(148\) 0 0
\(149\) 0.187319 1.06234i 0.0153457 0.0870301i −0.976173 0.216994i \(-0.930375\pi\)
0.991519 + 0.129964i \(0.0414860\pi\)
\(150\) 0 0
\(151\) −11.0300 −0.897611 −0.448806 0.893629i \(-0.648150\pi\)
−0.448806 + 0.893629i \(0.648150\pi\)
\(152\) 0 0
\(153\) 5.94356 0.480509
\(154\) 0 0
\(155\) −2.94697 + 16.7131i −0.236706 + 1.34243i
\(156\) 0 0
\(157\) 4.06805 + 3.41350i 0.324666 + 0.272427i 0.790522 0.612433i \(-0.209809\pi\)
−0.465857 + 0.884860i \(0.654254\pi\)
\(158\) 0 0
\(159\) 1.52481 0.880352i 0.120926 0.0698165i
\(160\) 0 0
\(161\) −1.40033 0.509678i −0.110361 0.0401683i
\(162\) 0 0
\(163\) 11.5201 + 6.65111i 0.902321 + 0.520955i 0.877953 0.478748i \(-0.158909\pi\)
0.0243687 + 0.999703i \(0.492242\pi\)
\(164\) 0 0
\(165\) 5.81908 1.02606i 0.453015 0.0798787i
\(166\) 0 0
\(167\) −3.87939 + 3.25519i −0.300196 + 0.251894i −0.780426 0.625248i \(-0.784998\pi\)
0.480230 + 0.877143i \(0.340553\pi\)
\(168\) 0 0
\(169\) −12.0915 + 4.40095i −0.930117 + 0.338535i
\(170\) 0 0
\(171\) −1.81908 + 3.96118i −0.139108 + 0.302919i
\(172\) 0 0
\(173\) 4.58765 + 12.6045i 0.348792 + 0.958299i 0.982751 + 0.184933i \(0.0592067\pi\)
−0.633959 + 0.773367i \(0.718571\pi\)
\(174\) 0 0
\(175\) 0.405078 + 0.482753i 0.0306210 + 0.0364927i
\(176\) 0 0
\(177\) −1.05169 5.96443i −0.0790498 0.448314i
\(178\) 0 0
\(179\) −5.92855 + 10.2685i −0.443121 + 0.767507i −0.997919 0.0644774i \(-0.979462\pi\)
0.554799 + 0.831985i \(0.312795\pi\)
\(180\) 0 0
\(181\) 6.74170 18.5227i 0.501106 1.37678i −0.389089 0.921200i \(-0.627210\pi\)
0.890196 0.455578i \(-0.150568\pi\)
\(182\) 0 0
\(183\) 3.39053 + 5.87257i 0.250635 + 0.434113i
\(184\) 0 0
\(185\) −12.2554 + 14.6054i −0.901032 + 1.07381i
\(186\) 0 0
\(187\) −13.6591 2.40847i −0.998852 0.176125i
\(188\) 0 0
\(189\) 0.446476i 0.0324763i
\(190\) 0 0
\(191\) 9.45545i 0.684173i −0.939669 0.342086i \(-0.888866\pi\)
0.939669 0.342086i \(-0.111134\pi\)
\(192\) 0 0
\(193\) 4.93969 + 0.871001i 0.355567 + 0.0626960i 0.348579 0.937280i \(-0.386664\pi\)
0.00698825 + 0.999976i \(0.497776\pi\)
\(194\) 0 0
\(195\) 0.592396 0.705990i 0.0424224 0.0505570i
\(196\) 0 0
\(197\) −8.26651 14.3180i −0.588965 1.02012i −0.994368 0.105979i \(-0.966202\pi\)
0.405404 0.914138i \(-0.367131\pi\)
\(198\) 0 0
\(199\) 2.35638 6.47410i 0.167039 0.458937i −0.827725 0.561134i \(-0.810365\pi\)
0.994764 + 0.102197i \(0.0325873\pi\)
\(200\) 0 0
\(201\) −4.63816 + 8.03352i −0.327150 + 0.566641i
\(202\) 0 0
\(203\) −0.101892 0.577857i −0.00715140 0.0405576i
\(204\) 0 0
\(205\) 18.6668 + 22.2463i 1.30375 + 1.55375i
\(206\) 0 0
\(207\) 1.14156 + 3.13641i 0.0793439 + 0.217995i
\(208\) 0 0
\(209\) 5.78564 8.36619i 0.400201 0.578701i
\(210\) 0 0
\(211\) 20.7665 7.55839i 1.42963 0.520341i 0.492801 0.870142i \(-0.335973\pi\)
0.936824 + 0.349801i \(0.113751\pi\)
\(212\) 0 0
\(213\) −4.11334 + 3.45150i −0.281841 + 0.236493i
\(214\) 0 0
\(215\) −17.5535 + 3.09516i −1.19714 + 0.211088i
\(216\) 0 0
\(217\) −2.59152 1.49621i −0.175924 0.101570i
\(218\) 0 0
\(219\) −3.19846 1.16415i −0.216132 0.0786657i
\(220\) 0 0
\(221\) −1.87346 + 1.08164i −0.126022 + 0.0727590i
\(222\) 0 0
\(223\) 17.5797 + 14.7511i 1.17722 + 0.987806i 0.999993 + 0.00363588i \(0.00115734\pi\)
0.177228 + 0.984170i \(0.443287\pi\)
\(224\) 0 0
\(225\) 0.245100 1.39003i 0.0163400 0.0926687i
\(226\) 0 0
\(227\) −13.4338 −0.891630 −0.445815 0.895125i \(-0.647086\pi\)
−0.445815 + 0.895125i \(0.647086\pi\)
\(228\) 0 0
\(229\) 21.5526 1.42424 0.712119 0.702059i \(-0.247736\pi\)
0.712119 + 0.702059i \(0.247736\pi\)
\(230\) 0 0
\(231\) −0.180922 + 1.02606i −0.0119038 + 0.0675098i
\(232\) 0 0
\(233\) −14.5719 12.2273i −0.954638 0.801036i 0.0254344 0.999676i \(-0.491903\pi\)
−0.980073 + 0.198640i \(0.936348\pi\)
\(234\) 0 0
\(235\) −17.1172 + 9.88263i −1.11660 + 0.644671i
\(236\) 0 0
\(237\) 2.39306 + 0.871001i 0.155446 + 0.0565776i
\(238\) 0 0
\(239\) 14.3229 + 8.26936i 0.926475 + 0.534900i 0.885695 0.464268i \(-0.153682\pi\)
0.0407797 + 0.999168i \(0.487016\pi\)
\(240\) 0 0
\(241\) 16.1780 2.85262i 1.04212 0.183753i 0.373707 0.927547i \(-0.378087\pi\)
0.668409 + 0.743794i \(0.266976\pi\)
\(242\) 0 0
\(243\) −0.766044 + 0.642788i −0.0491418 + 0.0412348i
\(244\) 0 0
\(245\) 16.1814 5.88954i 1.03379 0.376269i
\(246\) 0 0
\(247\) −0.147489 1.57964i −0.00938451 0.100510i
\(248\) 0 0
\(249\) 0.549163 + 1.50881i 0.0348018 + 0.0956171i
\(250\) 0 0
\(251\) 14.0522 + 16.7467i 0.886964 + 1.05704i 0.997999 + 0.0632263i \(0.0201390\pi\)
−0.111035 + 0.993816i \(0.535417\pi\)
\(252\) 0 0
\(253\) −1.35251 7.67047i −0.0850316 0.482238i
\(254\) 0 0
\(255\) −7.52481 + 13.0334i −0.471222 + 0.816181i
\(256\) 0 0
\(257\) −0.637222 + 1.75075i −0.0397488 + 0.109209i −0.957979 0.286838i \(-0.907396\pi\)
0.918230 + 0.396047i \(0.129618\pi\)
\(258\) 0 0
\(259\) −1.68092 2.91144i −0.104447 0.180908i
\(260\) 0 0
\(261\) −0.844770 + 1.00676i −0.0522900 + 0.0623167i
\(262\) 0 0
\(263\) 11.4757 + 2.02347i 0.707619 + 0.124772i 0.515864 0.856670i \(-0.327471\pi\)
0.191755 + 0.981443i \(0.438582\pi\)
\(264\) 0 0
\(265\) 4.45826i 0.273869i
\(266\) 0 0
\(267\) 6.24416i 0.382137i
\(268\) 0 0
\(269\) −5.61856 0.990703i −0.342569 0.0604042i −0.000283157 1.00000i \(-0.500090\pi\)
−0.342286 + 0.939596i \(0.611201\pi\)
\(270\) 0 0
\(271\) −16.7306 + 19.9387i −1.01631 + 1.21119i −0.0390284 + 0.999238i \(0.512426\pi\)
−0.977280 + 0.211951i \(0.932018\pi\)
\(272\) 0 0
\(273\) 0.0812519 + 0.140732i 0.00491759 + 0.00851751i
\(274\) 0 0
\(275\) −1.12654 + 3.09516i −0.0679332 + 0.186645i
\(276\) 0 0
\(277\) 1.28833 2.23146i 0.0774084 0.134075i −0.824723 0.565537i \(-0.808669\pi\)
0.902131 + 0.431462i \(0.142002\pi\)
\(278\) 0 0
\(279\) 1.16385 + 6.60051i 0.0696778 + 0.395162i
\(280\) 0 0
\(281\) 21.4111 + 25.5167i 1.27728 + 1.52220i 0.725537 + 0.688183i \(0.241592\pi\)
0.551740 + 0.834016i \(0.313964\pi\)
\(282\) 0 0
\(283\) −6.91581 19.0010i −0.411102 1.12949i −0.956606 0.291386i \(-0.905884\pi\)
0.545503 0.838109i \(-0.316339\pi\)
\(284\) 0 0
\(285\) −6.38326 9.00400i −0.378111 0.533351i
\(286\) 0 0
\(287\) −4.81180 + 1.75135i −0.284032 + 0.103379i
\(288\) 0 0
\(289\) 14.0385 11.7797i 0.825793 0.692923i
\(290\) 0 0
\(291\) −1.06031 + 0.186961i −0.0621563 + 0.0109598i
\(292\) 0 0
\(293\) 11.6964 + 6.75292i 0.683311 + 0.394510i 0.801101 0.598529i \(-0.204248\pi\)
−0.117790 + 0.993038i \(0.537581\pi\)
\(294\) 0 0
\(295\) 14.4106 + 5.24503i 0.839017 + 0.305377i
\(296\) 0 0
\(297\) 2.02094 1.16679i 0.117267 0.0677042i
\(298\) 0 0
\(299\) −0.930608 0.780873i −0.0538184 0.0451590i
\(300\) 0 0
\(301\) 0.545759 3.09516i 0.0314571 0.178402i
\(302\) 0 0
\(303\) 16.3601 0.939863
\(304\) 0 0
\(305\) −17.1702 −0.983165
\(306\) 0 0
\(307\) 1.54576 8.76644i 0.0882212 0.500327i −0.908394 0.418116i \(-0.862691\pi\)
0.996615 0.0822113i \(-0.0261982\pi\)
\(308\) 0 0
\(309\) 1.21688 + 1.02108i 0.0692260 + 0.0580875i
\(310\) 0 0
\(311\) −1.62108 + 0.935932i −0.0919231 + 0.0530718i −0.545257 0.838269i \(-0.683568\pi\)
0.453334 + 0.891341i \(0.350235\pi\)
\(312\) 0 0
\(313\) 14.0881 + 5.12765i 0.796307 + 0.289832i 0.707955 0.706257i \(-0.249618\pi\)
0.0883520 + 0.996089i \(0.471840\pi\)
\(314\) 0 0
\(315\) 0.979055 + 0.565258i 0.0551635 + 0.0318487i
\(316\) 0 0
\(317\) 8.38460 1.47843i 0.470926 0.0830370i 0.0668513 0.997763i \(-0.478705\pi\)
0.404075 + 0.914726i \(0.367594\pi\)
\(318\) 0 0
\(319\) 2.34936 1.97134i 0.131539 0.110374i
\(320\) 0 0
\(321\) −5.63816 + 2.05212i −0.314691 + 0.114538i
\(322\) 0 0
\(323\) 6.85117 + 24.9851i 0.381209 + 1.39021i
\(324\) 0 0
\(325\) 0.175708 + 0.482753i 0.00974650 + 0.0267783i
\(326\) 0 0
\(327\) −9.56418 11.3981i −0.528900 0.630319i
\(328\) 0 0
\(329\) −0.605189 3.43220i −0.0333652 0.189223i
\(330\) 0 0
\(331\) 14.1630 24.5310i 0.778467 1.34834i −0.154358 0.988015i \(-0.549331\pi\)
0.932825 0.360330i \(-0.117336\pi\)
\(332\) 0 0
\(333\) −2.57532 + 7.07564i −0.141127 + 0.387743i
\(334\) 0 0
\(335\) −11.7442 20.3416i −0.641655 1.11138i
\(336\) 0 0
\(337\) −8.19506 + 9.76649i −0.446413 + 0.532015i −0.941583 0.336782i \(-0.890662\pi\)
0.495169 + 0.868796i \(0.335106\pi\)
\(338\) 0 0
\(339\) 8.38919 + 1.47924i 0.455638 + 0.0803413i
\(340\) 0 0
\(341\) 15.6405i 0.846979i
\(342\) 0 0
\(343\) 6.16166i 0.332698i
\(344\) 0 0
\(345\) −8.32295 1.46756i −0.448092 0.0790108i
\(346\) 0 0
\(347\) 18.1147 21.5882i 0.972447 1.15892i −0.0148269 0.999890i \(-0.504720\pi\)
0.987274 0.159027i \(-0.0508358\pi\)
\(348\) 0 0
\(349\) −12.9067 22.3551i −0.690881 1.19664i −0.971550 0.236837i \(-0.923889\pi\)
0.280668 0.959805i \(-0.409444\pi\)
\(350\) 0 0
\(351\) 0.124485 0.342020i 0.00664453 0.0182557i
\(352\) 0 0
\(353\) −10.8464 + 18.7865i −0.577297 + 0.999907i 0.418491 + 0.908221i \(0.362559\pi\)
−0.995788 + 0.0916863i \(0.970774\pi\)
\(354\) 0 0
\(355\) −2.36097 13.3897i −0.125307 0.710652i
\(356\) 0 0
\(357\) −1.70574 2.03282i −0.0902772 0.107588i
\(358\) 0 0
\(359\) −7.33527 20.1535i −0.387141 1.06366i −0.968282 0.249859i \(-0.919616\pi\)
0.581141 0.813803i \(-0.302606\pi\)
\(360\) 0 0
\(361\) −18.7486 3.08083i −0.986766 0.162149i
\(362\) 0 0
\(363\) 5.21941 1.89971i 0.273948 0.0997089i
\(364\) 0 0
\(365\) 6.60220 5.53990i 0.345575 0.289972i
\(366\) 0 0
\(367\) −13.4500 + 2.37159i −0.702082 + 0.123796i −0.513283 0.858220i \(-0.671571\pi\)
−0.188800 + 0.982016i \(0.560460\pi\)
\(368\) 0 0
\(369\) 9.93242 + 5.73448i 0.517061 + 0.298525i
\(370\) 0 0
\(371\) −0.738703 0.268866i −0.0383516 0.0139588i
\(372\) 0 0
\(373\) −7.90848 + 4.56596i −0.409486 + 0.236417i −0.690569 0.723267i \(-0.742640\pi\)
0.281083 + 0.959683i \(0.409306\pi\)
\(374\) 0 0
\(375\) −6.96064 5.84067i −0.359446 0.301611i
\(376\) 0 0
\(377\) 0.0830629 0.471073i 0.00427796 0.0242615i
\(378\) 0 0
\(379\) −35.9154 −1.84485 −0.922425 0.386176i \(-0.873796\pi\)
−0.922425 + 0.386176i \(0.873796\pi\)
\(380\) 0 0
\(381\) −13.1506 −0.673728
\(382\) 0 0
\(383\) 1.95512 11.0880i 0.0999019 0.566572i −0.893233 0.449595i \(-0.851568\pi\)
0.993135 0.116977i \(-0.0373204\pi\)
\(384\) 0 0
\(385\) −2.02094 1.69577i −0.102997 0.0864246i
\(386\) 0 0
\(387\) −6.09627 + 3.51968i −0.309891 + 0.178915i
\(388\) 0 0
\(389\) 18.3919 + 6.69409i 0.932505 + 0.339404i 0.763202 0.646160i \(-0.223626\pi\)
0.169303 + 0.985564i \(0.445848\pi\)
\(390\) 0 0
\(391\) 17.1800 + 9.91890i 0.868832 + 0.501621i
\(392\) 0 0
\(393\) −4.39053 + 0.774169i −0.221473 + 0.0390517i
\(394\) 0 0
\(395\) −4.93969 + 4.14489i −0.248543 + 0.208552i
\(396\) 0 0
\(397\) −8.54963 + 3.11181i −0.429094 + 0.156177i −0.547533 0.836784i \(-0.684433\pi\)
0.118440 + 0.992961i \(0.462211\pi\)
\(398\) 0 0
\(399\) 1.87686 0.514654i 0.0939605 0.0257649i
\(400\) 0 0
\(401\) 0.817734 + 2.24670i 0.0408357 + 0.112195i 0.958435 0.285313i \(-0.0920974\pi\)
−0.917599 + 0.397508i \(0.869875\pi\)
\(402\) 0 0
\(403\) −1.56805 1.86873i −0.0781100 0.0930879i
\(404\) 0 0
\(405\) −0.439693 2.49362i −0.0218485 0.123909i
\(406\) 0 0
\(407\) 8.78564 15.2172i 0.435488 0.754288i
\(408\) 0 0
\(409\) −9.90420 + 27.2116i −0.489731 + 1.34553i 0.411193 + 0.911548i \(0.365112\pi\)
−0.900924 + 0.433977i \(0.857110\pi\)
\(410\) 0 0
\(411\) 0.458111 + 0.793471i 0.0225969 + 0.0391391i
\(412\) 0 0
\(413\) −1.73813 + 2.07142i −0.0855278 + 0.101928i
\(414\) 0 0
\(415\) −4.00387 0.705990i −0.196542 0.0346557i
\(416\) 0 0
\(417\) 12.2642i 0.600579i
\(418\) 0 0
\(419\) 7.56185i 0.369420i −0.982793 0.184710i \(-0.940865\pi\)
0.982793 0.184710i \(-0.0591347\pi\)
\(420\) 0 0
\(421\) −36.6969 6.47065i −1.78850 0.315360i −0.821511 0.570193i \(-0.806868\pi\)
−0.966985 + 0.254833i \(0.917980\pi\)
\(422\) 0 0
\(423\) −5.01754 + 5.97967i −0.243961 + 0.290742i
\(424\) 0 0
\(425\) −4.19459 7.26525i −0.203468 0.352416i
\(426\) 0 0
\(427\) 1.03549 2.84499i 0.0501110 0.137679i
\(428\) 0 0
\(429\) −0.424678 + 0.735564i −0.0205036 + 0.0355133i
\(430\) 0 0
\(431\) −6.28581 35.6486i −0.302777 1.71713i −0.633790 0.773506i \(-0.718501\pi\)
0.331013 0.943626i \(-0.392610\pi\)
\(432\) 0 0
\(433\) −24.2335 28.8804i −1.16459 1.38790i −0.906725 0.421723i \(-0.861425\pi\)
−0.257865 0.966181i \(-0.583019\pi\)
\(434\) 0 0
\(435\) −1.13816 3.12706i −0.0545704 0.149931i
\(436\) 0 0
\(437\) −11.8687 + 8.41415i −0.567757 + 0.402503i
\(438\) 0 0
\(439\) −1.26130 + 0.459074i −0.0601984 + 0.0219104i −0.371944 0.928255i \(-0.621309\pi\)
0.311745 + 0.950166i \(0.399086\pi\)
\(440\) 0 0
\(441\) 5.20961 4.37138i 0.248077 0.208161i
\(442\) 0 0
\(443\) 31.7802 5.60370i 1.50992 0.266240i 0.643459 0.765481i \(-0.277499\pi\)
0.866463 + 0.499241i \(0.166388\pi\)
\(444\) 0 0
\(445\) 13.6925 + 7.90539i 0.649088 + 0.374751i
\(446\) 0 0
\(447\) 1.01367 + 0.368946i 0.0479450 + 0.0174505i
\(448\) 0 0
\(449\) −3.34302 + 1.93009i −0.157767 + 0.0910866i −0.576805 0.816882i \(-0.695701\pi\)
0.419038 + 0.907969i \(0.362367\pi\)
\(450\) 0 0
\(451\) −20.5023 17.2035i −0.965415 0.810079i
\(452\) 0 0
\(453\) 1.91534 10.8625i 0.0899907 0.510363i
\(454\) 0 0
\(455\) −0.411474 −0.0192902
\(456\) 0 0
\(457\) −5.79055 −0.270871 −0.135435 0.990786i \(-0.543243\pi\)
−0.135435 + 0.990786i \(0.543243\pi\)
\(458\) 0 0
\(459\) −1.03209 + 5.85327i −0.0481738 + 0.273207i
\(460\) 0 0
\(461\) −17.5517 14.7276i −0.817464 0.685933i 0.134913 0.990857i \(-0.456924\pi\)
−0.952377 + 0.304924i \(0.901369\pi\)
\(462\) 0 0
\(463\) 30.3840 17.5422i 1.41207 0.815256i 0.416483 0.909144i \(-0.363263\pi\)
0.995583 + 0.0938873i \(0.0299293\pi\)
\(464\) 0 0
\(465\) −15.9474 5.80439i −0.739545 0.269172i
\(466\) 0 0
\(467\) 11.6352 + 6.71756i 0.538411 + 0.310852i 0.744435 0.667695i \(-0.232719\pi\)
−0.206024 + 0.978547i \(0.566052\pi\)
\(468\) 0 0
\(469\) 4.07873 0.719189i 0.188338 0.0332091i
\(470\) 0 0
\(471\) −4.06805 + 3.41350i −0.187446 + 0.157286i
\(472\) 0 0
\(473\) 15.4363 5.61835i 0.709761 0.258332i
\(474\) 0 0
\(475\) 6.12583 0.571962i 0.281072 0.0262434i
\(476\) 0 0
\(477\) 0.602196 + 1.65452i 0.0275727 + 0.0757553i
\(478\) 0 0
\(479\) −26.1330 31.1441i −1.19405 1.42301i −0.880898 0.473306i \(-0.843061\pi\)
−0.313149 0.949704i \(-0.601384\pi\)
\(480\) 0 0
\(481\) −0.475900 2.69896i −0.0216992 0.123062i
\(482\) 0 0
\(483\) 0.745100 1.29055i 0.0339032 0.0587221i
\(484\) 0 0
\(485\) 0.932419 2.56180i 0.0423390 0.116325i
\(486\) 0 0
\(487\) 16.8935 + 29.2604i 0.765519 + 1.32592i 0.939972 + 0.341252i \(0.110851\pi\)
−0.174453 + 0.984665i \(0.555816\pi\)
\(488\) 0 0
\(489\) −8.55051 + 10.1901i −0.386667 + 0.460812i
\(490\) 0 0
\(491\) −1.48839 0.262443i −0.0671700 0.0118439i 0.139962 0.990157i \(-0.455302\pi\)
−0.207132 + 0.978313i \(0.566413\pi\)
\(492\) 0 0
\(493\) 7.81120i 0.351799i
\(494\) 0 0
\(495\) 5.90885i 0.265583i
\(496\) 0 0
\(497\) 2.36097 + 0.416302i 0.105904 + 0.0186737i
\(498\) 0 0
\(499\) −11.2827 + 13.4462i −0.505083 + 0.601935i −0.956987 0.290132i \(-0.906301\pi\)
0.451903 + 0.892067i \(0.350745\pi\)
\(500\) 0 0
\(501\) −2.53209 4.38571i −0.113125 0.195939i
\(502\) 0 0
\(503\) 8.82888 24.2571i 0.393660 1.08157i −0.571657 0.820493i \(-0.693699\pi\)
0.965317 0.261080i \(-0.0840786\pi\)
\(504\) 0 0
\(505\) −20.7126 + 35.8753i −0.921699 + 1.59643i
\(506\) 0 0
\(507\) −2.23442 12.6720i −0.0992342 0.562785i
\(508\) 0 0
\(509\) 4.24985 + 5.06477i 0.188371 + 0.224492i 0.851962 0.523604i \(-0.175413\pi\)
−0.663591 + 0.748096i \(0.730968\pi\)
\(510\) 0 0
\(511\) 0.519762 + 1.42804i 0.0229929 + 0.0631726i
\(512\) 0 0
\(513\) −3.58512 2.47929i −0.158287 0.109463i
\(514\) 0 0
\(515\) −3.77972 + 1.37570i −0.166554 + 0.0606208i
\(516\) 0 0
\(517\) 13.9541 11.7089i 0.613700 0.514955i
\(518\) 0 0
\(519\) −13.2096 + 2.32921i −0.579837 + 0.102241i
\(520\) 0 0
\(521\) 34.8252 + 20.1064i 1.52572 + 0.880875i 0.999535 + 0.0305060i \(0.00971187\pi\)
0.526186 + 0.850369i \(0.323621\pi\)
\(522\) 0 0
\(523\) 26.5292 + 9.65582i 1.16004 + 0.422220i 0.849111 0.528214i \(-0.177138\pi\)
0.310928 + 0.950434i \(0.399360\pi\)
\(524\) 0 0
\(525\) −0.545759 + 0.315094i −0.0238189 + 0.0137518i
\(526\) 0 0
\(527\) 30.5159 + 25.6059i 1.32930 + 1.11541i
\(528\) 0 0
\(529\) 2.05943 11.6796i 0.0895404 0.507809i
\(530\) 0 0
\(531\) 6.05644 0.262827
\(532\) 0 0
\(533\) −4.17436 −0.180812
\(534\) 0 0
\(535\) 2.63816 14.9617i 0.114057 0.646852i
\(536\) 0 0
\(537\) −9.08306 7.62159i −0.391963 0.328896i
\(538\) 0 0
\(539\) −13.7438 + 7.93496i −0.591985 + 0.341783i
\(540\) 0 0
\(541\) −33.2374 12.0974i −1.42899 0.520109i −0.492347 0.870399i \(-0.663861\pi\)
−0.936641 + 0.350290i \(0.886083\pi\)
\(542\) 0 0
\(543\) 17.0706 + 9.85570i 0.732568 + 0.422949i
\(544\) 0 0
\(545\) 37.1031 6.54228i 1.58932 0.280241i
\(546\) 0 0
\(547\) 15.7044 13.1776i 0.671471 0.563431i −0.242029 0.970269i \(-0.577813\pi\)
0.913500 + 0.406838i \(0.133369\pi\)
\(548\) 0 0
\(549\) −6.37211 + 2.31926i −0.271955 + 0.0989836i
\(550\) 0 0
\(551\) −5.20590 2.39068i −0.221779 0.101847i
\(552\) 0 0
\(553\) −0.388881 1.06844i −0.0165369 0.0454347i
\(554\) 0 0
\(555\) −12.2554 14.6054i −0.520211 0.619964i
\(556\) 0 0
\(557\) 6.71007 + 38.0547i 0.284315 + 1.61243i 0.707722 + 0.706491i \(0.249723\pi\)
−0.423407 + 0.905939i \(0.639166\pi\)
\(558\) 0 0
\(559\) 1.28106 2.21886i 0.0541830 0.0938478i
\(560\) 0 0
\(561\) 4.74376 13.0334i 0.200282 0.550269i
\(562\) 0 0
\(563\) −5.28833 9.15966i −0.222877 0.386034i 0.732804 0.680440i \(-0.238211\pi\)
−0.955680 + 0.294406i \(0.904878\pi\)
\(564\) 0 0
\(565\) −13.8648 + 16.5235i −0.583298 + 0.695148i
\(566\) 0 0
\(567\) 0.439693 + 0.0775297i 0.0184654 + 0.00325594i
\(568\) 0 0
\(569\) 6.06920i 0.254434i −0.991875 0.127217i \(-0.959396\pi\)
0.991875 0.127217i \(-0.0406045\pi\)
\(570\) 0 0
\(571\) 38.8698i 1.62665i 0.581809 + 0.813326i \(0.302345\pi\)
−0.581809 + 0.813326i \(0.697655\pi\)
\(572\) 0 0
\(573\) 9.31180 + 1.64192i 0.389006 + 0.0685923i
\(574\) 0 0
\(575\) 3.02822 3.60889i 0.126285 0.150501i
\(576\) 0 0
\(577\) −22.2319 38.5068i −0.925526 1.60306i −0.790713 0.612187i \(-0.790290\pi\)
−0.134813 0.990871i \(-0.543043\pi\)
\(578\) 0 0
\(579\) −1.71554 + 4.71340i −0.0712953 + 0.195882i
\(580\) 0 0
\(581\) 0.358441 0.620838i 0.0148706 0.0257567i
\(582\) 0 0
\(583\) −0.713478 4.04633i −0.0295492 0.167582i
\(584\) 0 0
\(585\) 0.592396 + 0.705990i 0.0244926 + 0.0291891i
\(586\) 0 0
\(587\) 9.10085 + 25.0044i 0.375632 + 1.03204i 0.973147 + 0.230184i \(0.0739327\pi\)
−0.597515 + 0.801858i \(0.703845\pi\)
\(588\) 0 0
\(589\) −26.4051 + 12.5009i −1.08800 + 0.515092i
\(590\) 0 0
\(591\) 15.5360 5.65463i 0.639064 0.232600i
\(592\) 0 0
\(593\) 36.3730 30.5206i 1.49366 1.25333i 0.603771 0.797158i \(-0.293664\pi\)
0.889891 0.456173i \(-0.150780\pi\)
\(594\) 0 0
\(595\) 6.61721 1.16679i 0.271279 0.0478338i
\(596\) 0 0
\(597\) 5.96657 + 3.44480i 0.244195 + 0.140986i
\(598\) 0 0
\(599\) −28.8050 10.4842i −1.17694 0.428371i −0.321820 0.946801i \(-0.604295\pi\)
−0.855120 + 0.518430i \(0.826517\pi\)
\(600\) 0 0
\(601\) 14.9153 8.61138i 0.608410 0.351265i −0.163933 0.986471i \(-0.552418\pi\)
0.772343 + 0.635206i \(0.219085\pi\)
\(602\) 0 0
\(603\) −7.10607 5.96270i −0.289381 0.242820i
\(604\) 0 0
\(605\) −2.44222 + 13.8505i −0.0992903 + 0.563103i
\(606\) 0 0
\(607\) −16.9659 −0.688623 −0.344311 0.938856i \(-0.611888\pi\)
−0.344311 + 0.938856i \(0.611888\pi\)
\(608\) 0 0
\(609\) 0.586771 0.0237772
\(610\) 0 0
\(611\) 0.493355 2.79796i 0.0199590 0.113193i
\(612\) 0 0
\(613\) −34.5069 28.9547i −1.39372 1.16947i −0.963808 0.266598i \(-0.914100\pi\)
−0.429911 0.902871i \(-0.641455\pi\)
\(614\) 0 0
\(615\) −25.1498 + 14.5202i −1.01414 + 0.585512i
\(616\) 0 0
\(617\) −1.12314 0.408790i −0.0452160 0.0164573i 0.319313 0.947649i \(-0.396548\pi\)
−0.364529 + 0.931192i \(0.618770\pi\)
\(618\) 0 0
\(619\) −23.5363 13.5887i −0.946002 0.546175i −0.0541655 0.998532i \(-0.517250\pi\)
−0.891837 + 0.452357i \(0.850583\pi\)
\(620\) 0 0
\(621\) −3.28699 + 0.579585i −0.131902 + 0.0232579i
\(622\) 0 0
\(623\) −2.13563 + 1.79201i −0.0855622 + 0.0717952i
\(624\) 0 0
\(625\) 28.2520 10.2829i 1.13008 0.411315i
\(626\) 0 0
\(627\) 7.23442 + 7.15052i 0.288915 + 0.285564i
\(628\) 0 0
\(629\) 15.3066 + 42.0545i 0.610314 + 1.67682i
\(630\) 0 0
\(631\) 10.1001 + 12.0369i 0.402080 + 0.479180i 0.928653 0.370950i \(-0.120968\pi\)
−0.526573 + 0.850130i \(0.676523\pi\)
\(632\) 0 0
\(633\) 3.83750 + 21.7635i 0.152527 + 0.865022i
\(634\) 0 0
\(635\) 16.6493 28.8374i 0.660707 1.14438i
\(636\) 0 0
\(637\) −0.846581 + 2.32596i −0.0335428 + 0.0921580i
\(638\) 0 0
\(639\) −2.68479 4.65020i −0.106209 0.183959i
\(640\) 0 0
\(641\) 22.1802 26.4333i 0.876066 1.04405i −0.122602 0.992456i \(-0.539124\pi\)
0.998668 0.0515983i \(-0.0164316\pi\)
\(642\) 0 0
\(643\) −7.89646 1.39236i −0.311406 0.0549093i 0.0157611 0.999876i \(-0.494983\pi\)
−0.327167 + 0.944967i \(0.606094\pi\)
\(644\) 0 0
\(645\) 17.8243i 0.701831i
\(646\) 0 0
\(647\) 47.3299i 1.86073i −0.366633 0.930366i \(-0.619490\pi\)
0.366633 0.930366i \(-0.380510\pi\)
\(648\) 0 0
\(649\) −13.9185 2.45421i −0.546349 0.0963361i
\(650\) 0 0
\(651\) 1.92350 2.29233i 0.0753877 0.0898436i
\(652\) 0 0
\(653\) −6.95723 12.0503i −0.272258 0.471564i 0.697182 0.716894i \(-0.254437\pi\)
−0.969440 + 0.245330i \(0.921104\pi\)
\(654\) 0 0
\(655\) 3.86097 10.6079i 0.150860 0.414486i
\(656\) 0 0
\(657\) 1.70187 2.94772i 0.0663961 0.115001i
\(658\) 0 0
\(659\) −6.23854 35.3805i −0.243019 1.37823i −0.825049 0.565062i \(-0.808852\pi\)
0.582029 0.813168i \(-0.302259\pi\)
\(660\) 0 0
\(661\) 7.82682 + 9.32764i 0.304428 + 0.362803i 0.896470 0.443104i \(-0.146123\pi\)
−0.592042 + 0.805907i \(0.701678\pi\)
\(662\) 0 0
\(663\) −0.739885 2.03282i −0.0287348 0.0789481i
\(664\) 0 0
\(665\) −1.24763 + 4.76725i −0.0483809 + 0.184866i
\(666\) 0 0
\(667\) −4.12196 + 1.50027i −0.159603 + 0.0580907i
\(668\) 0 0
\(669\) −17.5797 + 14.7511i −0.679669 + 0.570310i
\(670\) 0 0
\(671\) 15.5838 2.74784i 0.601605 0.106079i
\(672\) 0 0
\(673\) 18.4029 + 10.6249i 0.709378 + 0.409560i 0.810831 0.585281i \(-0.199016\pi\)
−0.101453 + 0.994840i \(0.532349\pi\)
\(674\) 0 0
\(675\) 1.32635 + 0.482753i 0.0510513 + 0.0185812i
\(676\) 0 0
\(677\) −9.71806 + 5.61073i −0.373496 + 0.215638i −0.674984 0.737832i \(-0.735850\pi\)
0.301489 + 0.953470i \(0.402516\pi\)
\(678\) 0 0
\(679\) 0.368241 + 0.308991i 0.0141318 + 0.0118580i
\(680\) 0 0
\(681\) 2.33275 13.2297i 0.0893911 0.506962i
\(682\) 0 0
\(683\) 36.4867 1.39612 0.698062 0.716037i \(-0.254046\pi\)
0.698062 + 0.716037i \(0.254046\pi\)
\(684\) 0 0
\(685\) −2.31996 −0.0886409
\(686\) 0 0
\(687\) −3.74257 + 21.2252i −0.142788 + 0.809792i
\(688\) 0 0
\(689\) −0.490915 0.411927i −0.0187024 0.0156932i
\(690\) 0 0
\(691\) −9.74990 + 5.62911i −0.370904 + 0.214141i −0.673853 0.738865i \(-0.735362\pi\)
0.302949 + 0.953007i \(0.402029\pi\)
\(692\) 0 0
\(693\) −0.979055 0.356347i −0.0371912 0.0135365i
\(694\) 0 0
\(695\) 26.8935 + 15.5270i 1.02013 + 0.588972i
\(696\) 0 0
\(697\) 67.1309 11.8370i 2.54277 0.448358i
\(698\) 0 0
\(699\) 14.5719 12.2273i 0.551161 0.462479i
\(700\) 0 0
\(701\) 0.0120217 0.00437554i 0.000454053 0.000165262i −0.341793 0.939775i \(-0.611034\pi\)
0.342247 + 0.939610i \(0.388812\pi\)
\(702\) 0 0
\(703\) −32.7126 2.66982i −1.23378 0.100694i
\(704\) 0 0
\(705\) −6.76011 18.5733i −0.254601 0.699510i
\(706\) 0 0
\(707\) −4.69517 5.59548i −0.176580 0.210440i
\(708\) 0 0
\(709\) 5.64694 + 32.0254i 0.212075 + 1.20274i 0.885910 + 0.463856i \(0.153535\pi\)
−0.673835 + 0.738882i \(0.735354\pi\)
\(710\) 0 0
\(711\) −1.27332 + 2.20545i −0.0477532 + 0.0827109i
\(712\) 0 0
\(713\) −7.65111 + 21.0213i −0.286536 + 0.787252i
\(714\) 0 0
\(715\) −1.07532 1.86251i −0.0402148 0.0696540i
\(716\) 0 0
\(717\) −10.6309 + 12.6694i −0.397018 + 0.473147i
\(718\) 0 0
\(719\) −50.9876 8.99048i −1.90152 0.335288i −0.905491 0.424366i \(-0.860497\pi\)
−0.996025 + 0.0890776i \(0.971608\pi\)
\(720\) 0 0
\(721\) 0.709238i 0.0264134i
\(722\) 0 0
\(723\) 16.4276i 0.610947i
\(724\) 0 0
\(725\) 1.82682 + 0.322117i 0.0678463 + 0.0119631i
\(726\) 0 0
\(727\) −17.8025 + 21.2162i −0.660257 + 0.786864i −0.987423 0.158103i \(-0.949462\pi\)
0.327165 + 0.944967i \(0.393907\pi\)
\(728\) 0 0
\(729\) −0.500000 0.866025i −0.0185185 0.0320750i
\(730\) 0 0
\(731\) −14.3097 + 39.3157i −0.529265 + 1.45414i
\(732\) 0 0
\(733\) −22.0608 + 38.2104i −0.814833 + 1.41133i 0.0946143 + 0.995514i \(0.469838\pi\)
−0.909448 + 0.415819i \(0.863495\pi\)
\(734\) 0 0
\(735\) 2.99020 + 16.9583i 0.110295 + 0.625515i
\(736\) 0 0
\(737\) 13.9145 + 16.5826i 0.512546 + 0.610829i
\(738\) 0 0
\(739\) 2.90436 + 7.97967i 0.106839 + 0.293537i 0.981579 0.191054i \(-0.0611906\pi\)
−0.874741 + 0.484591i \(0.838968\pi\)
\(740\) 0 0
\(741\) 1.58125 + 0.129053i 0.0580887 + 0.00474088i
\(742\) 0 0
\(743\) −1.31908 + 0.480105i −0.0483923 + 0.0176133i −0.366103 0.930574i \(-0.619308\pi\)
0.317711 + 0.948188i \(0.397086\pi\)
\(744\) 0 0
\(745\) −2.09240 + 1.75573i −0.0766595 + 0.0643249i
\(746\) 0 0
\(747\) −1.58125 + 0.278817i −0.0578550 + 0.0102014i
\(748\) 0 0
\(749\) 2.31996 + 1.33943i 0.0847693 + 0.0489416i
\(750\) 0 0
\(751\) −9.12196 3.32012i −0.332865 0.121153i 0.170180 0.985413i \(-0.445565\pi\)
−0.503045 + 0.864260i \(0.667787\pi\)
\(752\) 0 0
\(753\) −18.9324 + 10.9306i −0.689936 + 0.398335i
\(754\) 0 0
\(755\) 21.3949 + 17.9524i 0.778639 + 0.653356i
\(756\) 0 0
\(757\) 6.14858 34.8704i 0.223474 1.26738i −0.642107 0.766615i \(-0.721939\pi\)
0.865581 0.500769i \(-0.166950\pi\)
\(758\) 0 0
\(759\) 7.78880 0.282716
\(760\) 0 0
\(761\) 3.28817 0.119196 0.0595981 0.998222i \(-0.481018\pi\)
0.0595981 + 0.998222i \(0.481018\pi\)
\(762\) 0 0
\(763\) −1.15358 + 6.54228i −0.0417624 + 0.236847i
\(764\) 0 0
\(765\) −11.5287 9.67372i −0.416820 0.349754i
\(766\) 0 0
\(767\) −1.90903 + 1.10218i −0.0689312 + 0.0397975i
\(768\) 0 0
\(769\) 21.9443 + 7.98708i 0.791333 + 0.288022i 0.705890 0.708321i \(-0.250547\pi\)
0.0854429 + 0.996343i \(0.472769\pi\)
\(770\) 0 0
\(771\) −1.61350 0.931556i −0.0581089 0.0335492i
\(772\) 0 0
\(773\) 23.6550 4.17101i 0.850811 0.150021i 0.268794 0.963198i \(-0.413375\pi\)
0.582017 + 0.813177i \(0.302264\pi\)
\(774\) 0 0
\(775\) 7.24691 6.08088i 0.260317 0.218432i
\(776\) 0 0
\(777\) 3.15910 1.14982i 0.113332 0.0412495i
\(778\) 0 0
\(779\) −12.6570 + 48.3633i −0.453486 + 1.73279i
\(780\) 0 0
\(781\) 4.28564 + 11.7747i 0.153352 + 0.421332i
\(782\) 0 0
\(783\) −0.844770 1.00676i −0.0301896 0.0359786i
\(784\) 0 0
\(785\) −2.33497 13.2423i −0.0833387 0.472637i
\(786\) 0 0
\(787\) 9.58765 16.6063i 0.341763 0.591950i −0.642997 0.765868i \(-0.722309\pi\)
0.984760 + 0.173918i \(0.0556427\pi\)
\(788\) 0 0
\(789\) −3.98545 + 10.9499i −0.141886 + 0.389828i
\(790\) 0 0
\(791\) −1.90167 3.29380i −0.0676157