Properties

Label 912.2.bo.f.481.1
Level $912$
Weight $2$
Character 912.481
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.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 481.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 912.481
Dual form 912.2.bo.f.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.939693 - 0.342020i) q^{3} +(0.386659 + 2.19285i) q^{5} +(-0.326352 + 0.565258i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\) \(q+(-0.939693 - 0.342020i) q^{3} +(0.386659 + 2.19285i) q^{5} +(-0.326352 + 0.565258i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-0.766044 - 1.32683i) q^{11} +(0.439693 - 0.160035i) q^{13} +(0.386659 - 2.19285i) q^{15} +(-1.61334 + 1.35375i) q^{17} +(2.23396 + 3.74292i) q^{19} +(0.500000 - 0.419550i) q^{21} +(-1.02481 + 5.81201i) q^{23} +(0.0393628 - 0.0143269i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-6.38326 - 5.35619i) q^{29} +(-4.31908 + 7.48086i) q^{31} +(0.266044 + 1.50881i) q^{33} +(-1.36571 - 0.497079i) q^{35} -4.67499 q^{37} -0.467911 q^{39} +(-3.26604 - 1.18874i) q^{41} +(-1.78699 - 10.1345i) q^{43} +(-1.11334 + 1.92836i) q^{45} +(3.55303 + 2.98135i) q^{47} +(3.28699 + 5.69323i) q^{49} +(1.97906 - 0.720317i) q^{51} +(-2.07532 + 11.7697i) q^{53} +(2.61334 - 2.19285i) q^{55} +(-0.819078 - 4.28125i) q^{57} +(-10.9042 + 9.14971i) q^{59} +(-1.58378 + 8.98205i) q^{61} +(-0.613341 + 0.223238i) q^{63} +(0.520945 + 0.902302i) q^{65} +(-0.190722 - 0.160035i) q^{67} +(2.95084 - 5.11100i) q^{69} +(0.772441 + 4.38073i) q^{71} +(8.54323 + 3.10948i) q^{73} -0.0418891 q^{75} +1.00000 q^{77} +(11.3302 + 4.12386i) q^{79} +(0.173648 + 0.984808i) q^{81} +(1.85457 - 3.21221i) q^{83} +(-3.59240 - 3.01438i) q^{85} +(4.16637 + 7.21637i) q^{87} +(-15.7554 + 5.73448i) q^{89} +(-0.0530334 + 0.300767i) q^{91} +(6.61721 - 5.55250i) q^{93} +(-7.34389 + 6.34597i) q^{95} +(1.89053 - 1.58634i) q^{97} +(0.266044 - 1.50881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 9 q^{5} - 3 q^{7} + O(q^{10}) \) \( 6 q + 9 q^{5} - 3 q^{7} - 3 q^{13} + 9 q^{15} - 3 q^{17} + 18 q^{19} + 3 q^{21} + 21 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{29} - 9 q^{31} - 3 q^{33} - 18 q^{35} - 18 q^{37} - 12 q^{39} - 15 q^{41} - 3 q^{43} + 9 q^{47} + 12 q^{49} + 15 q^{51} + 12 q^{53} + 9 q^{55} + 12 q^{57} - 27 q^{59} + 3 q^{61} + 3 q^{63} - 21 q^{67} + 6 q^{69} - 39 q^{71} + 36 q^{73} + 6 q^{75} + 6 q^{77} + 45 q^{79} + 27 q^{83} - 18 q^{85} + 6 q^{87} - 30 q^{89} + 12 q^{91} + 9 q^{93} - 6 q^{97} - 3 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −0.939693 0.342020i −0.542532 0.197465i
\(4\) 0 0
\(5\) 0.386659 + 2.19285i 0.172919 + 0.980674i 0.940518 + 0.339743i \(0.110340\pi\)
−0.767599 + 0.640930i \(0.778549\pi\)
\(6\) 0 0
\(7\) −0.326352 + 0.565258i −0.123349 + 0.213647i −0.921087 0.389358i \(-0.872697\pi\)
0.797737 + 0.603005i \(0.206030\pi\)
\(8\) 0 0
\(9\) 0.766044 + 0.642788i 0.255348 + 0.214263i
\(10\) 0 0
\(11\) −0.766044 1.32683i −0.230971 0.400054i 0.727123 0.686507i \(-0.240857\pi\)
−0.958094 + 0.286453i \(0.907524\pi\)
\(12\) 0 0
\(13\) 0.439693 0.160035i 0.121949 0.0443857i −0.280325 0.959905i \(-0.590442\pi\)
0.402274 + 0.915519i \(0.368220\pi\)
\(14\) 0 0
\(15\) 0.386659 2.19285i 0.0998350 0.566192i
\(16\) 0 0
\(17\) −1.61334 + 1.35375i −0.391293 + 0.328333i −0.817116 0.576473i \(-0.804429\pi\)
0.425824 + 0.904806i \(0.359984\pi\)
\(18\) 0 0
\(19\) 2.23396 + 3.74292i 0.512505 + 0.858685i
\(20\) 0 0
\(21\) 0.500000 0.419550i 0.109109 0.0915533i
\(22\) 0 0
\(23\) −1.02481 + 5.81201i −0.213689 + 1.21189i 0.669479 + 0.742831i \(0.266517\pi\)
−0.883168 + 0.469058i \(0.844594\pi\)
\(24\) 0 0
\(25\) 0.0393628 0.0143269i 0.00787257 0.00286538i
\(26\) 0 0
\(27\) −0.500000 0.866025i −0.0962250 0.166667i
\(28\) 0 0
\(29\) −6.38326 5.35619i −1.18534 0.994619i −0.999928 0.0119582i \(-0.996193\pi\)
−0.185412 0.982661i \(-0.559362\pi\)
\(30\) 0 0
\(31\) −4.31908 + 7.48086i −0.775729 + 1.34360i 0.158654 + 0.987334i \(0.449284\pi\)
−0.934384 + 0.356268i \(0.884049\pi\)
\(32\) 0 0
\(33\) 0.266044 + 1.50881i 0.0463124 + 0.262651i
\(34\) 0 0
\(35\) −1.36571 0.497079i −0.230848 0.0840218i
\(36\) 0 0
\(37\) −4.67499 −0.768564 −0.384282 0.923216i \(-0.625551\pi\)
−0.384282 + 0.923216i \(0.625551\pi\)
\(38\) 0 0
\(39\) −0.467911 −0.0749257
\(40\) 0 0
\(41\) −3.26604 1.18874i −0.510070 0.185650i 0.0741475 0.997247i \(-0.476376\pi\)
−0.584218 + 0.811597i \(0.698599\pi\)
\(42\) 0 0
\(43\) −1.78699 10.1345i −0.272513 1.54550i −0.746752 0.665103i \(-0.768388\pi\)
0.474238 0.880396i \(-0.342723\pi\)
\(44\) 0 0
\(45\) −1.11334 + 1.92836i −0.165967 + 0.287463i
\(46\) 0 0
\(47\) 3.55303 + 2.98135i 0.518263 + 0.434874i 0.864026 0.503448i \(-0.167935\pi\)
−0.345763 + 0.938322i \(0.612380\pi\)
\(48\) 0 0
\(49\) 3.28699 + 5.69323i 0.469570 + 0.813319i
\(50\) 0 0
\(51\) 1.97906 0.720317i 0.277123 0.100865i
\(52\) 0 0
\(53\) −2.07532 + 11.7697i −0.285067 + 1.61670i 0.419977 + 0.907535i \(0.362038\pi\)
−0.705045 + 0.709163i \(0.749073\pi\)
\(54\) 0 0
\(55\) 2.61334 2.19285i 0.352383 0.295684i
\(56\) 0 0
\(57\) −0.819078 4.28125i −0.108490 0.567066i
\(58\) 0 0
\(59\) −10.9042 + 9.14971i −1.41961 + 1.19119i −0.468055 + 0.883699i \(0.655045\pi\)
−0.951551 + 0.307492i \(0.900510\pi\)
\(60\) 0 0
\(61\) −1.58378 + 8.98205i −0.202782 + 1.15003i 0.698110 + 0.715991i \(0.254025\pi\)
−0.900892 + 0.434043i \(0.857086\pi\)
\(62\) 0 0
\(63\) −0.613341 + 0.223238i −0.0772737 + 0.0281253i
\(64\) 0 0
\(65\) 0.520945 + 0.902302i 0.0646152 + 0.111917i
\(66\) 0 0
\(67\) −0.190722 0.160035i −0.0233004 0.0195514i 0.631063 0.775732i \(-0.282619\pi\)
−0.654363 + 0.756180i \(0.727063\pi\)
\(68\) 0 0
\(69\) 2.95084 5.11100i 0.355239 0.615292i
\(70\) 0 0
\(71\) 0.772441 + 4.38073i 0.0916719 + 0.519897i 0.995716 + 0.0924590i \(0.0294727\pi\)
−0.904045 + 0.427438i \(0.859416\pi\)
\(72\) 0 0
\(73\) 8.54323 + 3.10948i 0.999910 + 0.363937i 0.789550 0.613687i \(-0.210314\pi\)
0.210360 + 0.977624i \(0.432536\pi\)
\(74\) 0 0
\(75\) −0.0418891 −0.00483693
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 11.3302 + 4.12386i 1.27475 + 0.463971i 0.888692 0.458504i \(-0.151615\pi\)
0.386057 + 0.922475i \(0.373837\pi\)
\(80\) 0 0
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) 0 0
\(83\) 1.85457 3.21221i 0.203566 0.352586i −0.746109 0.665824i \(-0.768080\pi\)
0.949675 + 0.313238i \(0.101414\pi\)
\(84\) 0 0
\(85\) −3.59240 3.01438i −0.389650 0.326955i
\(86\) 0 0
\(87\) 4.16637 + 7.21637i 0.446682 + 0.773676i
\(88\) 0 0
\(89\) −15.7554 + 5.73448i −1.67007 + 0.607854i −0.991896 0.127051i \(-0.959449\pi\)
−0.678169 + 0.734906i \(0.737226\pi\)
\(90\) 0 0
\(91\) −0.0530334 + 0.300767i −0.00555941 + 0.0315290i
\(92\) 0 0
\(93\) 6.61721 5.55250i 0.686173 0.575767i
\(94\) 0 0
\(95\) −7.34389 + 6.34597i −0.753468 + 0.651083i
\(96\) 0 0
\(97\) 1.89053 1.58634i 0.191954 0.161069i −0.541746 0.840543i \(-0.682236\pi\)
0.733700 + 0.679474i \(0.237792\pi\)
\(98\) 0 0
\(99\) 0.266044 1.50881i 0.0267385 0.151641i
\(100\) 0 0
\(101\) 5.39306 1.96291i 0.536629 0.195317i −0.0594668 0.998230i \(-0.518940\pi\)
0.596096 + 0.802913i \(0.296718\pi\)
\(102\) 0 0
\(103\) −6.90420 11.9584i −0.680291 1.17830i −0.974892 0.222678i \(-0.928520\pi\)
0.294601 0.955620i \(-0.404813\pi\)
\(104\) 0 0
\(105\) 1.11334 + 0.934204i 0.108651 + 0.0911690i
\(106\) 0 0
\(107\) 0.956767 1.65717i 0.0924941 0.160205i −0.816066 0.577959i \(-0.803849\pi\)
0.908560 + 0.417754i \(0.137183\pi\)
\(108\) 0 0
\(109\) −2.05169 11.6357i −0.196516 1.11450i −0.910243 0.414074i \(-0.864105\pi\)
0.713727 0.700424i \(-0.247006\pi\)
\(110\) 0 0
\(111\) 4.39306 + 1.59894i 0.416970 + 0.151765i
\(112\) 0 0
\(113\) 5.39693 0.507700 0.253850 0.967244i \(-0.418303\pi\)
0.253850 + 0.967244i \(0.418303\pi\)
\(114\) 0 0
\(115\) −13.1411 −1.22542
\(116\) 0 0
\(117\) 0.439693 + 0.160035i 0.0406496 + 0.0147952i
\(118\) 0 0
\(119\) −0.238703 1.35375i −0.0218819 0.124098i
\(120\) 0 0
\(121\) 4.32635 7.49346i 0.393305 0.681224i
\(122\) 0 0
\(123\) 2.66250 + 2.23411i 0.240070 + 0.201443i
\(124\) 0 0
\(125\) 5.61334 + 9.72259i 0.502072 + 0.869615i
\(126\) 0 0
\(127\) 9.09152 3.30904i 0.806742 0.293630i 0.0944646 0.995528i \(-0.469886\pi\)
0.712277 + 0.701898i \(0.247664\pi\)
\(128\) 0 0
\(129\) −1.78699 + 10.1345i −0.157336 + 0.892295i
\(130\) 0 0
\(131\) 1.45677 1.22237i 0.127278 0.106799i −0.576927 0.816796i \(-0.695748\pi\)
0.704205 + 0.709997i \(0.251304\pi\)
\(132\) 0 0
\(133\) −2.84477 + 0.0412527i −0.246673 + 0.00357706i
\(134\) 0 0
\(135\) 1.70574 1.43128i 0.146806 0.123185i
\(136\) 0 0
\(137\) −0.308811 + 1.75135i −0.0263835 + 0.149628i −0.995154 0.0983323i \(-0.968649\pi\)
0.968770 + 0.247960i \(0.0797603\pi\)
\(138\) 0 0
\(139\) −0.705737 + 0.256867i −0.0598598 + 0.0217872i −0.371777 0.928322i \(-0.621251\pi\)
0.311917 + 0.950109i \(0.399029\pi\)
\(140\) 0 0
\(141\) −2.31908 4.01676i −0.195302 0.338272i
\(142\) 0 0
\(143\) −0.549163 0.460802i −0.0459233 0.0385342i
\(144\) 0 0
\(145\) 9.27719 16.0686i 0.770429 1.33442i
\(146\) 0 0
\(147\) −1.14156 6.47410i −0.0941542 0.533975i
\(148\) 0 0
\(149\) 5.61721 + 2.04450i 0.460180 + 0.167492i 0.561699 0.827342i \(-0.310148\pi\)
−0.101519 + 0.994834i \(0.532370\pi\)
\(150\) 0 0
\(151\) 16.5749 1.34885 0.674424 0.738345i \(-0.264392\pi\)
0.674424 + 0.738345i \(0.264392\pi\)
\(152\) 0 0
\(153\) −2.10607 −0.170265
\(154\) 0 0
\(155\) −18.0744 6.57856i −1.45177 0.528403i
\(156\) 0 0
\(157\) −2.90033 16.4486i −0.231472 1.31274i −0.849919 0.526914i \(-0.823349\pi\)
0.618447 0.785826i \(-0.287762\pi\)
\(158\) 0 0
\(159\) 5.97565 10.3501i 0.473900 0.820819i
\(160\) 0 0
\(161\) −2.95084 2.47605i −0.232559 0.195140i
\(162\) 0 0
\(163\) −7.92855 13.7326i −0.621012 1.07562i −0.989298 0.145911i \(-0.953389\pi\)
0.368286 0.929713i \(-0.379945\pi\)
\(164\) 0 0
\(165\) −3.20574 + 1.16679i −0.249566 + 0.0908347i
\(166\) 0 0
\(167\) 0.393056 2.22913i 0.0304156 0.172495i −0.965816 0.259229i \(-0.916532\pi\)
0.996232 + 0.0867333i \(0.0276428\pi\)
\(168\) 0 0
\(169\) −9.79086 + 8.21551i −0.753143 + 0.631962i
\(170\) 0 0
\(171\) −0.694593 + 4.30320i −0.0531168 + 0.329074i
\(172\) 0 0
\(173\) 7.16637 6.01330i 0.544849 0.457183i −0.328343 0.944559i \(-0.606490\pi\)
0.873192 + 0.487376i \(0.162046\pi\)
\(174\) 0 0
\(175\) −0.00474774 + 0.0269258i −0.000358895 + 0.00203540i
\(176\) 0 0
\(177\) 13.3760 4.86846i 1.00540 0.365936i
\(178\) 0 0
\(179\) −7.88919 13.6645i −0.589665 1.02133i −0.994276 0.106841i \(-0.965926\pi\)
0.404611 0.914489i \(-0.367407\pi\)
\(180\) 0 0
\(181\) 5.36437 + 4.50124i 0.398731 + 0.334575i 0.820003 0.572360i \(-0.193972\pi\)
−0.421272 + 0.906934i \(0.638416\pi\)
\(182\) 0 0
\(183\) 4.56031 7.89868i 0.337108 0.583888i
\(184\) 0 0
\(185\) −1.80763 10.2516i −0.132900 0.753711i
\(186\) 0 0
\(187\) 3.03209 + 1.10359i 0.221728 + 0.0807025i
\(188\) 0 0
\(189\) 0.652704 0.0474772
\(190\) 0 0
\(191\) −4.39187 −0.317785 −0.158892 0.987296i \(-0.550792\pi\)
−0.158892 + 0.987296i \(0.550792\pi\)
\(192\) 0 0
\(193\) −4.56418 1.66122i −0.328537 0.119578i 0.172485 0.985012i \(-0.444820\pi\)
−0.501022 + 0.865434i \(0.667042\pi\)
\(194\) 0 0
\(195\) −0.180922 1.02606i −0.0129561 0.0734777i
\(196\) 0 0
\(197\) −10.1420 + 17.5665i −0.722589 + 1.25156i 0.237369 + 0.971420i \(0.423715\pi\)
−0.959959 + 0.280142i \(0.909618\pi\)
\(198\) 0 0
\(199\) 17.2062 + 14.4377i 1.21972 + 1.02346i 0.998840 + 0.0481609i \(0.0153360\pi\)
0.220876 + 0.975302i \(0.429108\pi\)
\(200\) 0 0
\(201\) 0.124485 + 0.215615i 0.00878051 + 0.0152083i
\(202\) 0 0
\(203\) 5.11081 1.86018i 0.358709 0.130559i
\(204\) 0 0
\(205\) 1.34389 7.62159i 0.0938615 0.532315i
\(206\) 0 0
\(207\) −4.52094 + 3.79352i −0.314227 + 0.263668i
\(208\) 0 0
\(209\) 3.25490 5.83132i 0.225146 0.403361i
\(210\) 0 0
\(211\) 7.62836 6.40095i 0.525158 0.440660i −0.341268 0.939966i \(-0.610856\pi\)
0.866425 + 0.499307i \(0.166412\pi\)
\(212\) 0 0
\(213\) 0.772441 4.38073i 0.0529268 0.300163i
\(214\) 0 0
\(215\) 21.5326 7.83721i 1.46851 0.534493i
\(216\) 0 0
\(217\) −2.81908 4.88279i −0.191371 0.331465i
\(218\) 0 0
\(219\) −6.96451 5.84392i −0.470618 0.394895i
\(220\) 0 0
\(221\) −0.492726 + 0.853427i −0.0331443 + 0.0574077i
\(222\) 0 0
\(223\) −0.333626 1.89209i −0.0223412 0.126703i 0.971597 0.236640i \(-0.0760463\pi\)
−0.993939 + 0.109937i \(0.964935\pi\)
\(224\) 0 0
\(225\) 0.0393628 + 0.0143269i 0.00262419 + 0.000955127i
\(226\) 0 0
\(227\) −0.901674 −0.0598462 −0.0299231 0.999552i \(-0.509526\pi\)
−0.0299231 + 0.999552i \(0.509526\pi\)
\(228\) 0 0
\(229\) −0.354103 −0.0233998 −0.0116999 0.999932i \(-0.503724\pi\)
−0.0116999 + 0.999932i \(0.503724\pi\)
\(230\) 0 0
\(231\) −0.939693 0.342020i −0.0618272 0.0225033i
\(232\) 0 0
\(233\) −2.90033 16.4486i −0.190007 1.07758i −0.919352 0.393437i \(-0.871286\pi\)
0.729345 0.684146i \(-0.239825\pi\)
\(234\) 0 0
\(235\) −5.16385 + 8.94405i −0.336852 + 0.583445i
\(236\) 0 0
\(237\) −9.23648 7.75033i −0.599974 0.503438i
\(238\) 0 0
\(239\) 5.02734 + 8.70761i 0.325192 + 0.563248i 0.981551 0.191200i \(-0.0612378\pi\)
−0.656359 + 0.754448i \(0.727905\pi\)
\(240\) 0 0
\(241\) 21.7062 7.90041i 1.39822 0.508910i 0.470570 0.882363i \(-0.344048\pi\)
0.927649 + 0.373452i \(0.121826\pi\)
\(242\) 0 0
\(243\) 0.173648 0.984808i 0.0111395 0.0631754i
\(244\) 0 0
\(245\) −11.2135 + 9.40923i −0.716403 + 0.601133i
\(246\) 0 0
\(247\) 1.58125 + 1.28822i 0.100613 + 0.0819676i
\(248\) 0 0
\(249\) −2.84137 + 2.38419i −0.180064 + 0.151092i
\(250\) 0 0
\(251\) −2.11200 + 11.9777i −0.133308 + 0.756027i 0.842715 + 0.538360i \(0.180956\pi\)
−0.976023 + 0.217667i \(0.930155\pi\)
\(252\) 0 0
\(253\) 8.49660 3.09251i 0.534176 0.194424i
\(254\) 0 0
\(255\) 2.34477 + 4.06126i 0.146835 + 0.254326i
\(256\) 0 0
\(257\) −3.02300 2.53660i −0.188570 0.158229i 0.543615 0.839334i \(-0.317055\pi\)
−0.732185 + 0.681106i \(0.761499\pi\)
\(258\) 0 0
\(259\) 1.52569 2.64258i 0.0948019 0.164202i
\(260\) 0 0
\(261\) −1.44697 8.20616i −0.0895650 0.507948i
\(262\) 0 0
\(263\) 8.52229 + 3.10186i 0.525507 + 0.191269i 0.591131 0.806576i \(-0.298682\pi\)
−0.0656242 + 0.997844i \(0.520904\pi\)
\(264\) 0 0
\(265\) −26.6117 −1.63475
\(266\) 0 0
\(267\) 16.7665 1.02609
\(268\) 0 0
\(269\) 26.3234 + 9.58094i 1.60497 + 0.584160i 0.980436 0.196840i \(-0.0630678\pi\)
0.624531 + 0.781000i \(0.285290\pi\)
\(270\) 0 0
\(271\) 2.92350 + 16.5800i 0.177590 + 1.00716i 0.935112 + 0.354352i \(0.115299\pi\)
−0.757522 + 0.652809i \(0.773590\pi\)
\(272\) 0 0
\(273\) 0.152704 0.264490i 0.00924205 0.0160077i
\(274\) 0 0
\(275\) −0.0491630 0.0412527i −0.00296464 0.00248763i
\(276\) 0 0
\(277\) 9.57532 + 16.5849i 0.575325 + 0.996493i 0.996006 + 0.0892840i \(0.0284579\pi\)
−0.420681 + 0.907209i \(0.638209\pi\)
\(278\) 0 0
\(279\) −8.11721 + 2.95442i −0.485965 + 0.176877i
\(280\) 0 0
\(281\) −0.687319 + 3.89798i −0.0410020 + 0.232534i −0.998421 0.0561668i \(-0.982112\pi\)
0.957419 + 0.288701i \(0.0932232\pi\)
\(282\) 0 0
\(283\) 5.03802 4.22740i 0.299479 0.251293i −0.480648 0.876913i \(-0.659599\pi\)
0.780127 + 0.625621i \(0.215154\pi\)
\(284\) 0 0
\(285\) 9.07145 3.45150i 0.537346 0.204449i
\(286\) 0 0
\(287\) 1.73783 1.45821i 0.102581 0.0860754i
\(288\) 0 0
\(289\) −2.18180 + 12.3736i −0.128341 + 0.727859i
\(290\) 0 0
\(291\) −2.31908 + 0.844075i −0.135947 + 0.0494806i
\(292\) 0 0
\(293\) −10.8478 18.7889i −0.633733 1.09766i −0.986782 0.162053i \(-0.948188\pi\)
0.353049 0.935605i \(-0.385145\pi\)
\(294\) 0 0
\(295\) −24.2802 20.3735i −1.41365 1.18619i
\(296\) 0 0
\(297\) −0.766044 + 1.32683i −0.0444504 + 0.0769904i
\(298\) 0 0
\(299\) 0.479522 + 2.71951i 0.0277315 + 0.157273i
\(300\) 0 0
\(301\) 6.31180 + 2.29731i 0.363806 + 0.132415i
\(302\) 0 0
\(303\) −5.73917 −0.329707
\(304\) 0 0
\(305\) −20.3087 −1.16287
\(306\) 0 0
\(307\) 16.7271 + 6.08818i 0.954669 + 0.347471i 0.771942 0.635693i \(-0.219285\pi\)
0.182727 + 0.983164i \(0.441508\pi\)
\(308\) 0 0
\(309\) 2.39780 + 13.5986i 0.136406 + 0.773598i
\(310\) 0 0
\(311\) −0.812681 + 1.40761i −0.0460829 + 0.0798180i −0.888147 0.459560i \(-0.848007\pi\)
0.842064 + 0.539378i \(0.181341\pi\)
\(312\) 0 0
\(313\) 23.0371 + 19.3305i 1.30214 + 1.09262i 0.989772 + 0.142660i \(0.0455654\pi\)
0.312364 + 0.949962i \(0.398879\pi\)
\(314\) 0 0
\(315\) −0.726682 1.25865i −0.0409439 0.0709169i
\(316\) 0 0
\(317\) 10.6493 3.87603i 0.598124 0.217699i −0.0251747 0.999683i \(-0.508014\pi\)
0.623299 + 0.781984i \(0.285792\pi\)
\(318\) 0 0
\(319\) −2.21688 + 12.5726i −0.124122 + 0.703928i
\(320\) 0 0
\(321\) −1.46585 + 1.23000i −0.0818159 + 0.0686517i
\(322\) 0 0
\(323\) −8.67112 3.01438i −0.482474 0.167724i
\(324\) 0 0
\(325\) 0.0150147 0.0125989i 0.000832868 0.000698859i
\(326\) 0 0
\(327\) −2.05169 + 11.6357i −0.113459 + 0.643456i
\(328\) 0 0
\(329\) −2.84477 + 1.03541i −0.156837 + 0.0570841i
\(330\) 0 0
\(331\) −16.0621 27.8204i −0.882854 1.52915i −0.848154 0.529750i \(-0.822286\pi\)
−0.0347000 0.999398i \(-0.511048\pi\)
\(332\) 0 0
\(333\) −3.58125 3.00503i −0.196251 0.164674i
\(334\) 0 0
\(335\) 0.277189 0.480105i 0.0151444 0.0262309i
\(336\) 0 0
\(337\) 5.26739 + 29.8728i 0.286933 + 1.62728i 0.698298 + 0.715807i \(0.253941\pi\)
−0.411365 + 0.911471i \(0.634948\pi\)
\(338\) 0 0
\(339\) −5.07145 1.84586i −0.275443 0.100253i
\(340\) 0 0
\(341\) 13.2344 0.716684
\(342\) 0 0
\(343\) −8.85978 −0.478383
\(344\) 0 0
\(345\) 12.3486 + 4.49454i 0.664828 + 0.241978i
\(346\) 0 0
\(347\) −0.747626 4.24000i −0.0401347 0.227615i 0.958142 0.286292i \(-0.0924228\pi\)
−0.998277 + 0.0586772i \(0.981312\pi\)
\(348\) 0 0
\(349\) 1.33022 2.30401i 0.0712052 0.123331i −0.828225 0.560396i \(-0.810649\pi\)
0.899430 + 0.437065i \(0.143982\pi\)
\(350\) 0 0
\(351\) −0.358441 0.300767i −0.0191321 0.0160538i
\(352\) 0 0
\(353\) −18.0963 31.3437i −0.963167 1.66825i −0.714461 0.699675i \(-0.753328\pi\)
−0.248706 0.968579i \(-0.580005\pi\)
\(354\) 0 0
\(355\) −9.30763 + 3.38770i −0.493998 + 0.179800i
\(356\) 0 0
\(357\) −0.238703 + 1.35375i −0.0126335 + 0.0716482i
\(358\) 0 0
\(359\) −1.43376 + 1.20307i −0.0756711 + 0.0634956i −0.679839 0.733362i \(-0.737950\pi\)
0.604168 + 0.796857i \(0.293506\pi\)
\(360\) 0 0
\(361\) −9.01889 + 16.7230i −0.474678 + 0.880159i
\(362\) 0 0
\(363\) −6.62836 + 5.56185i −0.347898 + 0.291921i
\(364\) 0 0
\(365\) −3.51532 + 19.9364i −0.184000 + 1.04352i
\(366\) 0 0
\(367\) 3.32635 1.21069i 0.173634 0.0631977i −0.253740 0.967272i \(-0.581661\pi\)
0.427374 + 0.904075i \(0.359439\pi\)
\(368\) 0 0
\(369\) −1.73783 3.01000i −0.0904676 0.156694i
\(370\) 0 0
\(371\) −5.97565 5.01417i −0.310240 0.260323i
\(372\) 0 0
\(373\) −8.25924 + 14.3054i −0.427647 + 0.740707i −0.996664 0.0816196i \(-0.973991\pi\)
0.569016 + 0.822326i \(0.307324\pi\)
\(374\) 0 0
\(375\) −1.94949 11.0561i −0.100671 0.570936i
\(376\) 0 0
\(377\) −3.66385 1.33353i −0.188698 0.0686804i
\(378\) 0 0
\(379\) 3.56893 0.183323 0.0916617 0.995790i \(-0.470782\pi\)
0.0916617 + 0.995790i \(0.470782\pi\)
\(380\) 0 0
\(381\) −9.67499 −0.495665
\(382\) 0 0
\(383\) −11.3366 4.12619i −0.579274 0.210839i 0.0357313 0.999361i \(-0.488624\pi\)
−0.615005 + 0.788523i \(0.710846\pi\)
\(384\) 0 0
\(385\) 0.386659 + 2.19285i 0.0197060 + 0.111758i
\(386\) 0 0
\(387\) 5.14543 8.91215i 0.261557 0.453030i
\(388\) 0 0
\(389\) 14.4743 + 12.1454i 0.733877 + 0.615796i 0.931185 0.364546i \(-0.118776\pi\)
−0.197309 + 0.980341i \(0.563220\pi\)
\(390\) 0 0
\(391\) −6.21466 10.7641i −0.314289 0.544364i
\(392\) 0 0
\(393\) −1.78699 + 0.650411i −0.0901417 + 0.0328089i
\(394\) 0 0
\(395\) −4.66209 + 26.4400i −0.234575 + 1.33034i
\(396\) 0 0
\(397\) 13.9743 11.7258i 0.701350 0.588503i −0.220807 0.975318i \(-0.570869\pi\)
0.922157 + 0.386815i \(0.126425\pi\)
\(398\) 0 0
\(399\) 2.68732 + 0.934204i 0.134534 + 0.0467687i
\(400\) 0 0
\(401\) 25.9577 21.7811i 1.29627 1.08770i 0.305488 0.952196i \(-0.401180\pi\)
0.990777 0.135500i \(-0.0432642\pi\)
\(402\) 0 0
\(403\) −0.701867 + 3.98048i −0.0349625 + 0.198282i
\(404\) 0 0
\(405\) −2.09240 + 0.761570i −0.103972 + 0.0378427i
\(406\) 0 0
\(407\) 3.58125 + 6.20291i 0.177516 + 0.307467i
\(408\) 0 0
\(409\) −0.132474 0.111159i −0.00655043 0.00549647i 0.639507 0.768786i \(-0.279139\pi\)
−0.646057 + 0.763289i \(0.723583\pi\)
\(410\) 0 0
\(411\) 0.889185 1.54011i 0.0438603 0.0759682i
\(412\) 0 0
\(413\) −1.61334 9.14971i −0.0793873 0.450228i
\(414\) 0 0
\(415\) 7.76099 + 2.82477i 0.380972 + 0.138663i
\(416\) 0 0
\(417\) 0.751030 0.0367781
\(418\) 0 0
\(419\) 36.5800 1.78705 0.893524 0.449015i \(-0.148225\pi\)
0.893524 + 0.449015i \(0.148225\pi\)
\(420\) 0 0
\(421\) −34.6400 12.6079i −1.68825 0.614472i −0.693845 0.720124i \(-0.744085\pi\)
−0.994403 + 0.105652i \(0.966307\pi\)
\(422\) 0 0
\(423\) 0.805407 + 4.56769i 0.0391602 + 0.222089i
\(424\) 0 0
\(425\) −0.0441106 + 0.0764018i −0.00213968 + 0.00370603i
\(426\) 0 0
\(427\) −4.56031 3.82655i −0.220689 0.185180i
\(428\) 0 0
\(429\) 0.358441 + 0.620838i 0.0173057 + 0.0299743i
\(430\) 0 0
\(431\) −17.7763 + 6.47005i −0.856255 + 0.311651i −0.732588 0.680673i \(-0.761688\pi\)
−0.123667 + 0.992324i \(0.539465\pi\)
\(432\) 0 0
\(433\) 3.86659 21.9285i 0.185817 1.05382i −0.739085 0.673612i \(-0.764742\pi\)
0.924902 0.380206i \(-0.124147\pi\)
\(434\) 0 0
\(435\) −14.2135 + 11.9265i −0.681484 + 0.571833i
\(436\) 0 0
\(437\) −24.0433 + 9.14798i −1.15015 + 0.437607i
\(438\) 0 0
\(439\) −25.6156 + 21.4941i −1.22257 + 1.02586i −0.223880 + 0.974617i \(0.571872\pi\)
−0.998686 + 0.0512387i \(0.983683\pi\)
\(440\) 0 0
\(441\) −1.14156 + 6.47410i −0.0543600 + 0.308291i
\(442\) 0 0
\(443\) 32.7904 11.9347i 1.55792 0.567037i 0.587662 0.809106i \(-0.300048\pi\)
0.970259 + 0.242069i \(0.0778262\pi\)
\(444\) 0 0
\(445\) −18.6668 32.3319i −0.884893 1.53268i
\(446\) 0 0
\(447\) −4.57919 3.84240i −0.216588 0.181739i
\(448\) 0 0
\(449\) 4.09152 7.08672i 0.193091 0.334443i −0.753182 0.657812i \(-0.771482\pi\)
0.946273 + 0.323369i \(0.104815\pi\)
\(450\) 0 0
\(451\) 0.924678 + 5.24411i 0.0435414 + 0.246935i
\(452\) 0 0
\(453\) −15.5753 5.66895i −0.731792 0.266351i
\(454\) 0 0
\(455\) −0.680045 −0.0318810
\(456\) 0 0
\(457\) −41.0259 −1.91911 −0.959556 0.281519i \(-0.909162\pi\)
−0.959556 + 0.281519i \(0.909162\pi\)
\(458\) 0 0
\(459\) 1.97906 + 0.720317i 0.0923744 + 0.0336215i
\(460\) 0 0
\(461\) −0.802719 4.55245i −0.0373863 0.212029i 0.960392 0.278653i \(-0.0898880\pi\)
−0.997778 + 0.0666248i \(0.978777\pi\)
\(462\) 0 0
\(463\) 2.75624 4.77396i 0.128094 0.221865i −0.794844 0.606813i \(-0.792448\pi\)
0.922938 + 0.384949i \(0.125781\pi\)
\(464\) 0 0
\(465\) 14.7344 + 12.3636i 0.683292 + 0.573350i
\(466\) 0 0
\(467\) 5.58466 + 9.67291i 0.258427 + 0.447609i 0.965821 0.259211i \(-0.0834625\pi\)
−0.707394 + 0.706820i \(0.750129\pi\)
\(468\) 0 0
\(469\) 0.152704 0.0555796i 0.00705120 0.00256643i
\(470\) 0 0
\(471\) −2.90033 + 16.4486i −0.133640 + 0.757911i
\(472\) 0 0
\(473\) −12.0778 + 10.1345i −0.555340 + 0.465986i
\(474\) 0 0
\(475\) 0.141559 + 0.115326i 0.00649519 + 0.00529153i
\(476\) 0 0
\(477\) −9.15523 + 7.68215i −0.419189 + 0.351741i
\(478\) 0 0
\(479\) −1.50459 + 8.53293i −0.0687463 + 0.389879i 0.930948 + 0.365152i \(0.118983\pi\)
−0.999694 + 0.0247276i \(0.992128\pi\)
\(480\) 0 0
\(481\) −2.05556 + 0.748163i −0.0937255 + 0.0341133i
\(482\) 0 0
\(483\) 1.92602 + 3.33597i 0.0876370 + 0.151792i
\(484\) 0 0
\(485\) 4.20961 + 3.53228i 0.191148 + 0.160393i
\(486\) 0 0
\(487\) −0.0471036 + 0.0815859i −0.00213447 + 0.00369701i −0.867091 0.498150i \(-0.834013\pi\)
0.864956 + 0.501847i \(0.167346\pi\)
\(488\) 0 0
\(489\) 2.75356 + 15.6162i 0.124520 + 0.706189i
\(490\) 0 0
\(491\) −26.3075 9.57516i −1.18724 0.432121i −0.328488 0.944508i \(-0.606539\pi\)
−0.858754 + 0.512388i \(0.828761\pi\)
\(492\) 0 0
\(493\) 17.5493 0.790382
\(494\) 0 0
\(495\) 3.41147 0.153334
\(496\) 0 0
\(497\) −2.72833 0.993031i −0.122382 0.0445435i
\(498\) 0 0
\(499\) 6.42144 + 36.4178i 0.287463 + 1.63028i 0.696353 + 0.717700i \(0.254805\pi\)
−0.408890 + 0.912584i \(0.634084\pi\)
\(500\) 0 0
\(501\) −1.13176 + 1.96026i −0.0505633 + 0.0875781i
\(502\) 0 0
\(503\) 17.3084 + 14.5235i 0.771743 + 0.647570i 0.941155 0.337976i \(-0.109742\pi\)
−0.169411 + 0.985545i \(0.554187\pi\)
\(504\) 0 0
\(505\) 6.38965 + 11.0672i 0.284336 + 0.492484i
\(506\) 0 0
\(507\) 12.0103 4.37138i 0.533395 0.194140i
\(508\) 0 0
\(509\) −7.71869 + 43.7749i −0.342125 + 1.94029i −0.00174780 + 0.999998i \(0.500556\pi\)
−0.340377 + 0.940289i \(0.610555\pi\)
\(510\) 0 0
\(511\) −4.54576 + 3.81435i −0.201093 + 0.168737i
\(512\) 0 0
\(513\) 2.12449 3.80612i 0.0937983 0.168044i
\(514\) 0 0
\(515\) 23.5535 19.7637i 1.03789 0.870894i
\(516\) 0 0
\(517\) 1.23396 6.99811i 0.0542693 0.307777i
\(518\) 0 0
\(519\) −8.79086 + 3.19961i −0.385876 + 0.140447i
\(520\) 0 0
\(521\) 12.1322 + 21.0136i 0.531522 + 0.920624i 0.999323 + 0.0367899i \(0.0117132\pi\)
−0.467801 + 0.883834i \(0.654953\pi\)
\(522\) 0 0
\(523\) 18.5462 + 15.5621i 0.810970 + 0.680485i 0.950839 0.309685i \(-0.100224\pi\)
−0.139869 + 0.990170i \(0.544668\pi\)
\(524\) 0 0
\(525\) 0.0136706 0.0236781i 0.000596633 0.00103340i
\(526\) 0 0
\(527\) −3.15910 17.9161i −0.137613 0.780440i
\(528\) 0 0
\(529\) −11.1163 4.04601i −0.483319 0.175914i
\(530\) 0 0
\(531\) −14.2344 −0.617721
\(532\) 0 0
\(533\) −1.62630 −0.0704427
\(534\) 0 0
\(535\) 4.00387 + 1.45729i 0.173102 + 0.0630041i
\(536\) 0 0
\(537\) 2.73989 + 15.5387i 0.118235 + 0.670543i
\(538\) 0 0
\(539\) 5.03596 8.72254i 0.216914 0.375706i
\(540\) 0 0
\(541\) 26.2219 + 22.0028i 1.12737 + 0.945975i 0.998953 0.0457455i \(-0.0145663\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(542\) 0 0
\(543\) −3.50134 6.06451i −0.150257 0.260253i
\(544\) 0 0
\(545\) 24.7221 8.99811i 1.05898 0.385437i
\(546\) 0 0
\(547\) −4.39218 + 24.9093i −0.187796 + 1.06504i 0.734514 + 0.678593i \(0.237410\pi\)
−0.922310 + 0.386451i \(0.873701\pi\)
\(548\) 0 0
\(549\) −6.98680 + 5.86262i −0.298189 + 0.250210i
\(550\) 0 0
\(551\) 5.78787 35.8575i 0.246571 1.52758i
\(552\) 0 0
\(553\) −6.02869 + 5.05867i −0.256366 + 0.215116i
\(554\) 0 0
\(555\) −1.80763 + 10.2516i −0.0767296 + 0.435155i
\(556\) 0 0
\(557\) 10.2369 3.72594i 0.433753 0.157873i −0.115910 0.993260i \(-0.536978\pi\)
0.549663 + 0.835386i \(0.314756\pi\)
\(558\) 0 0
\(559\) −2.40760 4.17009i −0.101831 0.176376i
\(560\) 0 0
\(561\) −2.47178 2.07407i −0.104359 0.0875673i
\(562\) 0 0
\(563\) 8.64337 14.9708i 0.364275 0.630942i −0.624385 0.781117i \(-0.714650\pi\)
0.988659 + 0.150175i \(0.0479836\pi\)
\(564\) 0 0
\(565\) 2.08677 + 11.8347i 0.0877911 + 0.497888i
\(566\) 0 0
\(567\) −0.613341 0.223238i −0.0257579 0.00937511i
\(568\) 0 0
\(569\) 6.47834 0.271586 0.135793 0.990737i \(-0.456642\pi\)
0.135793 + 0.990737i \(0.456642\pi\)
\(570\) 0 0
\(571\) −38.5476 −1.61317 −0.806583 0.591121i \(-0.798686\pi\)
−0.806583 + 0.591121i \(0.798686\pi\)
\(572\) 0 0
\(573\) 4.12701 + 1.50211i 0.172408 + 0.0627515i
\(574\) 0 0
\(575\) 0.0429285 + 0.243460i 0.00179024 + 0.0101530i
\(576\) 0 0
\(577\) 5.72756 9.92042i 0.238441 0.412993i −0.721826 0.692075i \(-0.756697\pi\)
0.960267 + 0.279082i \(0.0900302\pi\)
\(578\) 0 0
\(579\) 3.72075 + 3.12208i 0.154629 + 0.129749i
\(580\) 0 0
\(581\) 1.21048 + 2.09662i 0.0502194 + 0.0869825i
\(582\) 0 0
\(583\) 17.2062 6.26255i 0.712608 0.259368i
\(584\) 0 0
\(585\) −0.180922 + 1.02606i −0.00748021 + 0.0424224i
\(586\) 0 0
\(587\) −32.7467 + 27.4778i −1.35160 + 1.13413i −0.373124 + 0.927781i \(0.621714\pi\)
−0.978479 + 0.206348i \(0.933842\pi\)
\(588\) 0 0
\(589\) −37.6489 + 0.545955i −1.55130 + 0.0224957i
\(590\) 0 0
\(591\) 15.5385 13.0383i 0.639168 0.536326i
\(592\) 0 0
\(593\) 5.68092 32.2181i 0.233288 1.32304i −0.612903 0.790158i \(-0.709998\pi\)
0.846190 0.532881i \(-0.178891\pi\)
\(594\) 0 0
\(595\) 2.87629 1.04688i 0.117916 0.0429180i
\(596\) 0 0
\(597\) −11.2306 19.4519i −0.459636 0.796113i
\(598\) 0 0
\(599\) −7.05896 5.92317i −0.288421 0.242014i 0.487084 0.873355i \(-0.338061\pi\)
−0.775506 + 0.631341i \(0.782505\pi\)
\(600\) 0 0
\(601\) −4.83884 + 8.38112i −0.197380 + 0.341873i −0.947678 0.319227i \(-0.896577\pi\)
0.750298 + 0.661100i \(0.229910\pi\)
\(602\) 0 0
\(603\) −0.0432332 0.245188i −0.00176059 0.00998482i
\(604\) 0 0
\(605\) 18.1049 + 6.58964i 0.736068 + 0.267907i
\(606\) 0 0
\(607\) −36.4766 −1.48054 −0.740269 0.672310i \(-0.765302\pi\)
−0.740269 + 0.672310i \(0.765302\pi\)
\(608\) 0 0
\(609\) −5.43882 −0.220392
\(610\) 0 0
\(611\) 2.03936 + 0.742267i 0.0825038 + 0.0300289i
\(612\) 0 0
\(613\) −2.02987 11.5119i −0.0819856 0.464963i −0.997966 0.0637414i \(-0.979697\pi\)
0.915981 0.401222i \(-0.131414\pi\)
\(614\) 0 0
\(615\) −3.86959 + 6.70232i −0.156037 + 0.270264i
\(616\) 0 0
\(617\) 13.6459 + 11.4503i 0.549363 + 0.460970i 0.874725 0.484619i \(-0.161042\pi\)
−0.325362 + 0.945589i \(0.605486\pi\)
\(618\) 0 0
\(619\) 13.9932 + 24.2369i 0.562434 + 0.974164i 0.997283 + 0.0736609i \(0.0234683\pi\)
−0.434849 + 0.900503i \(0.643198\pi\)
\(620\) 0 0
\(621\) 5.54576 2.01849i 0.222544 0.0809993i
\(622\) 0 0
\(623\) 1.90033 10.7773i 0.0761351 0.431784i
\(624\) 0 0
\(625\) −18.9893 + 15.9339i −0.759573 + 0.637357i
\(626\) 0 0
\(627\) −5.05303 + 4.36640i −0.201799 + 0.174377i
\(628\) 0 0
\(629\) 7.54236 6.32879i 0.300733 0.252345i
\(630\) 0 0
\(631\) 0.653170 3.70431i 0.0260023 0.147466i −0.969042 0.246894i \(-0.920590\pi\)
0.995045 + 0.0994276i \(0.0317012\pi\)
\(632\) 0 0
\(633\) −9.35756 + 3.40587i −0.371930 + 0.135371i
\(634\) 0 0
\(635\) 10.7716 + 18.6569i 0.427456 + 0.740376i
\(636\) 0 0
\(637\) 2.35638 + 1.97724i 0.0933632 + 0.0783410i
\(638\) 0 0
\(639\) −2.22416 + 3.85235i −0.0879862 + 0.152397i
\(640\) 0 0
\(641\) 2.91329 + 16.5221i 0.115068 + 0.652582i 0.986717 + 0.162451i \(0.0519400\pi\)
−0.871649 + 0.490131i \(0.836949\pi\)
\(642\) 0 0
\(643\) −20.8396 7.58500i −0.821834 0.299123i −0.103331 0.994647i \(-0.532950\pi\)
−0.718503 + 0.695524i \(0.755172\pi\)
\(644\) 0 0
\(645\) −22.9145 −0.902256
\(646\) 0 0
\(647\) −16.6759 −0.655598 −0.327799 0.944747i \(-0.606307\pi\)
−0.327799 + 0.944747i \(0.606307\pi\)
\(648\) 0 0
\(649\) 20.4932 + 7.45891i 0.804428 + 0.292788i
\(650\) 0 0
\(651\) 0.979055 + 5.55250i 0.0383722 + 0.217620i
\(652\) 0 0
\(653\) 13.4033 23.2152i 0.524513 0.908482i −0.475080 0.879943i \(-0.657581\pi\)
0.999593 0.0285398i \(-0.00908575\pi\)
\(654\) 0 0
\(655\) 3.24376 + 2.72183i 0.126744 + 0.106351i
\(656\) 0 0
\(657\) 4.54576 + 7.87349i 0.177347 + 0.307174i
\(658\) 0 0
\(659\) −16.6116 + 6.04612i −0.647096 + 0.235524i −0.644655 0.764474i \(-0.722999\pi\)
−0.00244038 + 0.999997i \(0.500777\pi\)
\(660\) 0 0
\(661\) 1.50593 8.54055i 0.0585739 0.332189i −0.941413 0.337255i \(-0.890502\pi\)
0.999987 + 0.00506615i \(0.00161261\pi\)
\(662\) 0 0
\(663\) 0.754900 0.633436i 0.0293179 0.0246006i
\(664\) 0 0
\(665\) −1.19042 6.22221i −0.0461624 0.241287i
\(666\) 0 0
\(667\) 37.6719 31.6105i 1.45866 1.22396i
\(668\) 0 0
\(669\) −0.333626 + 1.89209i −0.0128987 + 0.0731523i
\(670\) 0 0
\(671\) 13.1309 4.77925i 0.506912 0.184501i
\(672\) 0 0
\(673\) −1.08243 1.87483i −0.0417248 0.0722694i 0.844409 0.535699i \(-0.179952\pi\)
−0.886134 + 0.463430i \(0.846619\pi\)
\(674\) 0 0
\(675\) −0.0320889 0.0269258i −0.00123510 0.00103637i
\(676\) 0 0
\(677\) −6.37686 + 11.0450i −0.245083 + 0.424496i −0.962155 0.272503i \(-0.912148\pi\)
0.717072 + 0.696999i \(0.245482\pi\)
\(678\) 0 0
\(679\) 0.279715 + 1.58634i 0.0107345 + 0.0608782i
\(680\) 0 0
\(681\) 0.847296 + 0.308391i 0.0324685 + 0.0118176i
\(682\) 0 0
\(683\) 25.2608 0.966579 0.483289 0.875461i \(-0.339442\pi\)
0.483289 + 0.875461i \(0.339442\pi\)
\(684\) 0 0
\(685\) −3.95987 −0.151299
\(686\) 0 0
\(687\) 0.332748 + 0.121111i 0.0126951 + 0.00462065i
\(688\) 0 0
\(689\) 0.971066 + 5.50719i 0.0369947 + 0.209807i
\(690\) 0 0
\(691\) 7.64796 13.2466i 0.290942 0.503926i −0.683091 0.730333i \(-0.739365\pi\)
0.974033 + 0.226407i \(0.0726980\pi\)
\(692\) 0 0
\(693\) 0.766044 + 0.642788i 0.0290996 + 0.0244175i
\(694\) 0 0
\(695\) −0.836152 1.44826i −0.0317171 0.0549355i
\(696\) 0 0
\(697\) 6.87851 2.50357i 0.260542 0.0948296i
\(698\) 0 0
\(699\) −2.90033 + 16.4486i −0.109701 + 0.622143i
\(700\) 0 0
\(701\) 30.5369 25.6235i 1.15336 0.967786i 0.153570 0.988138i \(-0.450923\pi\)
0.999793 + 0.0203518i \(0.00647861\pi\)
\(702\) 0 0
\(703\) −10.4437 17.4981i −0.393893 0.659954i
\(704\) 0 0
\(705\) 7.91147 6.63852i 0.297963 0.250021i
\(706\) 0 0
\(707\) −0.650482 + 3.68907i −0.0244639 + 0.138742i
\(708\) 0 0
\(709\) −22.4351 + 8.16571i −0.842568 + 0.306670i −0.727006 0.686631i \(-0.759089\pi\)
−0.115562 + 0.993300i \(0.536867\pi\)
\(710\) 0 0
\(711\) 6.02869 + 10.4420i 0.226093 + 0.391605i
\(712\) 0 0
\(713\) −39.0526 32.7690i −1.46253 1.22721i
\(714\) 0 0
\(715\) 0.798133 1.38241i 0.0298485 0.0516991i
\(716\) 0 0
\(717\) −1.74598 9.90193i −0.0652047 0.369794i
\(718\) 0 0
\(719\) −34.3050 12.4860i −1.27936 0.465649i −0.389140 0.921179i \(-0.627228\pi\)
−0.890221 + 0.455530i \(0.849450\pi\)
\(720\) 0 0
\(721\) 9.01279 0.335654
\(722\) 0 0
\(723\) −23.0993 −0.859071
\(724\) 0 0
\(725\) −0.328001 0.119382i −0.0121816 0.00443375i
\(726\) 0 0
\(727\) −5.59580 31.7354i −0.207537 1.17700i −0.893398 0.449267i \(-0.851685\pi\)
0.685861 0.727733i \(-0.259426\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) 16.6027 + 13.9313i 0.614072 + 0.515267i
\(732\) 0 0
\(733\) 3.48767 + 6.04083i 0.128820 + 0.223123i 0.923220 0.384272i \(-0.125548\pi\)
−0.794400 + 0.607396i \(0.792214\pi\)
\(734\) 0 0
\(735\) 13.7554 5.00654i 0.507374 0.184669i
\(736\) 0 0
\(737\) −0.0662372 + 0.375650i −0.00243988 + 0.0138372i
\(738\) 0 0
\(739\) −18.6682 + 15.6645i −0.686720 + 0.576227i −0.917961 0.396670i \(-0.870166\pi\)
0.231241 + 0.972896i \(0.425721\pi\)
\(740\) 0 0
\(741\) −1.04529 1.75135i −0.0383998 0.0643376i
\(742\) 0 0
\(743\) 29.1536 24.4628i 1.06954 0.897453i 0.0745322 0.997219i \(-0.476254\pi\)
0.995011 + 0.0997653i \(0.0318092\pi\)
\(744\) 0 0
\(745\) −2.31134 + 13.1082i −0.0846808 + 0.480249i
\(746\) 0 0
\(747\) 3.48545 1.26860i 0.127526 0.0464157i
\(748\) 0 0
\(749\) 0.624485 + 1.08164i 0.0228182 + 0.0395223i
\(750\) 0 0
\(751\) 2.24897 + 1.88711i 0.0820661 + 0.0688616i 0.682898 0.730514i \(-0.260719\pi\)
−0.600832 + 0.799376i \(0.705164\pi\)
\(752\) 0 0
\(753\) 6.08125 10.5330i 0.221613 0.383845i
\(754\) 0 0
\(755\) 6.40884 + 36.3463i 0.233242 + 1.32278i
\(756\) 0 0
\(757\) −10.6800 3.88722i −0.388173 0.141283i 0.140559 0.990072i \(-0.455110\pi\)
−0.528732 + 0.848789i \(0.677332\pi\)
\(758\) 0 0
\(759\) −9.04189 −0.328200
\(760\) 0 0
\(761\) 10.4976 0.380538 0.190269 0.981732i \(-0.439064\pi\)
0.190269 + 0.981732i \(0.439064\pi\)
\(762\) 0 0
\(763\) 7.24675 + 2.63760i 0.262350 + 0.0954876i
\(764\) 0 0
\(765\) −0.814330 4.61830i −0.0294422 0.166975i
\(766\) 0 0
\(767\) −3.33022 + 5.76811i −0.120247 + 0.208275i
\(768\) 0 0
\(769\) 5.93036 + 4.97616i 0.213854 + 0.179445i 0.743422 0.668823i \(-0.233201\pi\)
−0.529568 + 0.848268i \(0.677646\pi\)
\(770\) 0 0
\(771\) 1.97313 + 3.41755i 0.0710604 + 0.123080i
\(772\) 0 0
\(773\) 5.78224 2.10456i 0.207973 0.0756959i −0.235933 0.971769i \(-0.575815\pi\)
0.443906 + 0.896073i \(0.353592\pi\)
\(774\) 0 0
\(775\) −0.0628336 + 0.356347i −0.00225705 + 0.0128004i
\(776\) 0 0
\(777\) −2.33750 + 1.96139i −0.0838572 + 0.0703646i
\(778\) 0 0
\(779\) −2.84683 14.8801i −0.101998 0.533136i
\(780\) 0 0
\(781\) 5.22075 4.38073i 0.186813 0.156755i
\(782\) 0 0
\(783\) −1.44697 + 8.20616i −0.0517104 + 0.293264i
\(784\) 0 0
\(785\) 34.9479 12.7200i 1.24734 0.453996i
\(786\) 0 0
\(787\) −4.02600 6.97323i −0.143511 0.248569i 0.785305 0.619109i \(-0.212506\pi\)
−0.928817 + 0.370540i \(0.879173\pi\)
\(788\) 0 0
\(789\) −6.94743 5.82959i −0.247335 0.207539i
\(790\) 0 0
\(791\) −1.76130 + 3.05066i −0.0626245 + 0.108469i
\(792\) 0 0
\(793\) 0.741067 + 4.20280i 0.0263161