Properties

Label 912.2.bo.f.529.1
Level $912$
Weight $2$
Character 912.529
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 529.1
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 912.529
Dual form 912.2.bo.f.481.1

$q$-expansion

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

Character values

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

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\) \(1\)

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 −0.767599 0.640930i \(-0.778549\pi\)
0.940518 0.339743i \(-0.110340\pi\)
\(6\) 0 0
\(7\) −0.326352 0.565258i −0.123349 0.213647i 0.797737 0.603005i \(-0.206030\pi\)
−0.921087 + 0.389358i \(0.872697\pi\)
\(8\) 0 0
\(9\) 0.766044 0.642788i 0.255348 0.214263i
\(10\) 0 0
\(11\) −0.766044 + 1.32683i −0.230971 + 0.400054i −0.958094 0.286453i \(-0.907524\pi\)
0.727123 + 0.686507i \(0.240857\pi\)
\(12\) 0 0
\(13\) 0.439693 + 0.160035i 0.121949 + 0.0443857i 0.402274 0.915519i \(-0.368220\pi\)
−0.280325 + 0.959905i \(0.590442\pi\)
\(14\) 0 0
\(15\) 0.386659 + 2.19285i 0.0998350 + 0.566192i
\(16\) 0 0
\(17\) −1.61334 1.35375i −0.391293 0.328333i 0.425824 0.904806i \(-0.359984\pi\)
−0.817116 + 0.576473i \(0.804429\pi\)
\(18\) 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 −0.883168 0.469058i \(-0.844594\pi\)
0.669479 0.742831i \(-0.266517\pi\)
\(24\) 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 −0.185412 + 0.982661i \(0.559362\pi\)
−0.999928 + 0.0119582i \(0.996193\pi\)
\(30\) 0 0
\(31\) −4.31908 7.48086i −0.775729 1.34360i −0.934384 0.356268i \(-0.884049\pi\)
0.158654 0.987334i \(-0.449284\pi\)
\(32\) 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 −0.584218 0.811597i \(-0.698599\pi\)
0.0741475 + 0.997247i \(0.476376\pi\)
\(42\) 0 0
\(43\) −1.78699 + 10.1345i −0.272513 + 1.54550i 0.474238 + 0.880396i \(0.342723\pi\)
−0.746752 + 0.665103i \(0.768388\pi\)
\(44\) 0 0
\(45\) −1.11334 1.92836i −0.165967 0.287463i
\(46\) 0 0
\(47\) 3.55303 2.98135i 0.518263 0.434874i −0.345763 0.938322i \(-0.612380\pi\)
0.864026 + 0.503448i \(0.167935\pi\)
\(48\) 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 −0.705045 0.709163i \(-0.749073\pi\)
0.419977 0.907535i \(-0.362038\pi\)
\(54\) 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 −0.951551 0.307492i \(-0.900510\pi\)
−0.468055 0.883699i \(-0.655045\pi\)
\(60\) 0 0
\(61\) −1.58378 8.98205i −0.202782 1.15003i −0.900892 0.434043i \(-0.857086\pi\)
0.698110 0.715991i \(-0.254025\pi\)
\(62\) 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 −0.654363 0.756180i \(-0.727063\pi\)
0.631063 + 0.775732i \(0.282619\pi\)
\(68\) 0 0
\(69\) 2.95084 + 5.11100i 0.355239 + 0.615292i
\(70\) 0 0
\(71\) 0.772441 4.38073i 0.0916719 0.519897i −0.904045 0.427438i \(-0.859416\pi\)
0.995716 0.0924590i \(-0.0294727\pi\)
\(72\) 0 0
\(73\) 8.54323 3.10948i 0.999910 0.363937i 0.210360 0.977624i \(-0.432536\pi\)
0.789550 + 0.613687i \(0.210314\pi\)
\(74\) 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 0.386057 0.922475i \(-0.373837\pi\)
0.888692 + 0.458504i \(0.151615\pi\)
\(80\) 0 0
\(81\) 0.173648 0.984808i 0.0192942 0.109423i
\(82\) 0 0
\(83\) 1.85457 + 3.21221i 0.203566 + 0.352586i 0.949675 0.313238i \(-0.101414\pi\)
−0.746109 + 0.665824i \(0.768080\pi\)
\(84\) 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 −0.678169 0.734906i \(-0.737226\pi\)
−0.991896 + 0.127051i \(0.959449\pi\)
\(90\) 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 0.733700 0.679474i \(-0.237792\pi\)
−0.541746 + 0.840543i \(0.682236\pi\)
\(98\) 0 0
\(99\) 0.266044 + 1.50881i 0.0267385 + 0.151641i
\(100\) 0 0
\(101\) 5.39306 + 1.96291i 0.536629 + 0.195317i 0.596096 0.802913i \(-0.296718\pi\)
−0.0594668 + 0.998230i \(0.518940\pi\)
\(102\) 0 0
\(103\) −6.90420 + 11.9584i −0.680291 + 1.17830i 0.294601 + 0.955620i \(0.404813\pi\)
−0.974892 + 0.222678i \(0.928520\pi\)
\(104\) 0 0
\(105\) 1.11334 0.934204i 0.108651 0.0911690i
\(106\) 0 0
\(107\) 0.956767 + 1.65717i 0.0924941 + 0.160205i 0.908560 0.417754i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(108\) 0 0
\(109\) −2.05169 + 11.6357i −0.196516 + 1.11450i 0.713727 + 0.700424i \(0.247006\pi\)
−0.910243 + 0.414074i \(0.864105\pi\)
\(110\) 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 0.712277 0.701898i \(-0.247664\pi\)
0.0944646 + 0.995528i \(0.469886\pi\)
\(128\) 0 0
\(129\) −1.78699 10.1345i −0.157336 0.892295i
\(130\) 0 0
\(131\) 1.45677 + 1.22237i 0.127278 + 0.106799i 0.704205 0.709997i \(-0.251304\pi\)
−0.576927 + 0.816796i \(0.695748\pi\)
\(132\) 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 0.968770 0.247960i \(-0.0797603\pi\)
−0.995154 + 0.0983323i \(0.968649\pi\)
\(138\) 0 0
\(139\) −0.705737 0.256867i −0.0598598 0.0217872i 0.311917 0.950109i \(-0.399029\pi\)
−0.371777 + 0.928322i \(0.621251\pi\)
\(140\) 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 −0.101519 0.994834i \(-0.532370\pi\)
0.561699 + 0.827342i \(0.310148\pi\)
\(150\) 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 0.618447 + 0.785826i \(0.287762\pi\)
−0.849919 + 0.526914i \(0.823349\pi\)
\(158\) 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 0.368286 + 0.929713i \(0.379945\pi\)
−0.989298 + 0.145911i \(0.953389\pi\)
\(164\) 0 0
\(165\) −3.20574 1.16679i −0.249566 0.0908347i
\(166\) 0 0
\(167\) 0.393056 + 2.22913i 0.0304156 + 0.172495i 0.996232 0.0867333i \(-0.0276428\pi\)
−0.965816 + 0.259229i \(0.916532\pi\)
\(168\) 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 0.873192 0.487376i \(-0.162046\pi\)
−0.328343 + 0.944559i \(0.606490\pi\)
\(174\) 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 0.404611 + 0.914489i \(0.367407\pi\)
−0.994276 + 0.106841i \(0.965926\pi\)
\(180\) 0 0
\(181\) 5.36437 4.50124i 0.398731 0.334575i −0.421272 0.906934i \(-0.638416\pi\)
0.820003 + 0.572360i \(0.193972\pi\)
\(182\) 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 −0.501022 0.865434i \(-0.667042\pi\)
0.172485 + 0.985012i \(0.444820\pi\)
\(194\) 0 0
\(195\) −0.180922 + 1.02606i −0.0129561 + 0.0734777i
\(196\) 0 0
\(197\) −10.1420 17.5665i −0.722589 1.25156i −0.959959 0.280142i \(-0.909618\pi\)
0.237369 0.971420i \(-0.423715\pi\)
\(198\) 0 0
\(199\) 17.2062 14.4377i 1.21972 1.02346i 0.220876 0.975302i \(-0.429108\pi\)
0.998840 0.0481609i \(-0.0153360\pi\)
\(200\) 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 0.866425 0.499307i \(-0.166412\pi\)
−0.341268 + 0.939966i \(0.610856\pi\)
\(212\) 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 −0.993939 0.109937i \(-0.964935\pi\)
0.971597 + 0.236640i \(0.0760463\pi\)
\(224\) 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 0.729345 + 0.684146i \(0.239825\pi\)
−0.919352 + 0.393437i \(0.871286\pi\)
\(234\) 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 −0.656359 0.754448i \(-0.727905\pi\)
0.981551 + 0.191200i \(0.0612378\pi\)
\(240\) 0 0
\(241\) 21.7062 + 7.90041i 1.39822 + 0.508910i 0.927649 0.373452i \(-0.121826\pi\)
0.470570 + 0.882363i \(0.344048\pi\)
\(242\) 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 −0.976023 0.217667i \(-0.930155\pi\)
0.842715 0.538360i \(-0.180956\pi\)
\(252\) 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 −0.732185 0.681106i \(-0.761499\pi\)
0.543615 + 0.839334i \(0.317055\pi\)
\(258\) 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 −0.0656242 0.997844i \(-0.520904\pi\)
0.591131 + 0.806576i \(0.298682\pi\)
\(264\) 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 0.624531 0.781000i \(-0.285290\pi\)
0.980436 + 0.196840i \(0.0630678\pi\)
\(270\) 0 0
\(271\) 2.92350 16.5800i 0.177590 1.00716i −0.757522 0.652809i \(-0.773590\pi\)
0.935112 0.354352i \(-0.115299\pi\)
\(272\) 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 −0.420681 0.907209i \(-0.638209\pi\)
0.996006 0.0892840i \(-0.0284579\pi\)
\(278\) 0 0
\(279\) −8.11721 2.95442i −0.485965 0.176877i
\(280\) 0 0
\(281\) −0.687319 3.89798i −0.0410020 0.232534i 0.957419 0.288701i \(-0.0932232\pi\)
−0.998421 + 0.0561668i \(0.982112\pi\)
\(282\) 0 0
\(283\) 5.03802 + 4.22740i 0.299479 + 0.251293i 0.780127 0.625621i \(-0.215154\pi\)
−0.480648 + 0.876913i \(0.659599\pi\)
\(284\) 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 0.353049 + 0.935605i \(0.385145\pi\)
−0.986782 + 0.162053i \(0.948188\pi\)
\(294\) 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 0.182727 0.983164i \(-0.441508\pi\)
0.771942 + 0.635693i \(0.219285\pi\)
\(308\) 0 0
\(309\) 2.39780 13.5986i 0.136406 0.773598i
\(310\) 0 0
\(311\) −0.812681 1.40761i −0.0460829 0.0798180i 0.842064 0.539378i \(-0.181341\pi\)
−0.888147 + 0.459560i \(0.848007\pi\)
\(312\) 0 0
\(313\) 23.0371 19.3305i 1.30214 1.09262i 0.312364 0.949962i \(-0.398879\pi\)
0.989772 0.142660i \(-0.0455654\pi\)
\(314\) 0 0
\(315\) −0.726682 + 1.25865i −0.0409439 + 0.0709169i
\(316\) 0 0
\(317\) 10.6493 + 3.87603i 0.598124 + 0.217699i 0.623299 0.781984i \(-0.285792\pi\)
−0.0251747 + 0.999683i \(0.508014\pi\)
\(318\) 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 −0.0347000 + 0.999398i \(0.511048\pi\)
−0.848154 + 0.529750i \(0.822286\pi\)
\(332\) 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 −0.411365 0.911471i \(-0.634948\pi\)
0.698298 0.715807i \(-0.253941\pi\)
\(338\) 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 −0.998277 0.0586772i \(-0.981312\pi\)
0.958142 + 0.286292i \(0.0924228\pi\)
\(348\) 0 0
\(349\) 1.33022 + 2.30401i 0.0712052 + 0.123331i 0.899430 0.437065i \(-0.143982\pi\)
−0.828225 + 0.560396i \(0.810649\pi\)
\(350\) 0 0
\(351\) −0.358441 + 0.300767i −0.0191321 + 0.0160538i
\(352\) 0 0
\(353\) −18.0963 + 31.3437i −0.963167 + 1.66825i −0.248706 + 0.968579i \(0.580005\pi\)
−0.714461 + 0.699675i \(0.753328\pi\)
\(354\) 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 0.604168 0.796857i \(-0.293506\pi\)
−0.679839 + 0.733362i \(0.737950\pi\)
\(360\) 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 0.427374 0.904075i \(-0.359439\pi\)
−0.253740 + 0.967272i \(0.581661\pi\)
\(368\) 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 0.569016 0.822326i \(-0.307324\pi\)
−0.996664 + 0.0816196i \(0.973991\pi\)
\(374\) 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 −0.615005 0.788523i \(-0.710846\pi\)
0.0357313 + 0.999361i \(0.488624\pi\)
\(384\) 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 −0.197309 0.980341i \(-0.563220\pi\)
0.931185 + 0.364546i \(0.118776\pi\)
\(390\) 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 0.922157 0.386815i \(-0.126425\pi\)
−0.220807 + 0.975318i \(0.570869\pi\)
\(398\) 0 0
\(399\) 2.68732 0.934204i 0.134534 0.0467687i
\(400\) 0 0
\(401\) 25.9577 + 21.7811i 1.29627 + 1.08770i 0.990777 + 0.135500i \(0.0432642\pi\)
0.305488 + 0.952196i \(0.401180\pi\)
\(402\) 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 −0.646057 0.763289i \(-0.723583\pi\)
0.639507 + 0.768786i \(0.279139\pi\)
\(410\) 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 −0.994403 0.105652i \(-0.966307\pi\)
−0.693845 + 0.720124i \(0.744085\pi\)
\(422\) 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 −0.123667 0.992324i \(-0.539465\pi\)
−0.732588 + 0.680673i \(0.761688\pi\)
\(432\) 0 0
\(433\) 3.86659 + 21.9285i 0.185817 + 1.05382i 0.924902 + 0.380206i \(0.124147\pi\)
−0.739085 + 0.673612i \(0.764742\pi\)
\(434\) 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 −0.998686 0.0512387i \(-0.983683\pi\)
−0.223880 0.974617i \(-0.571872\pi\)
\(440\) 0 0
\(441\) −1.14156 6.47410i −0.0543600 0.308291i
\(442\) 0 0
\(443\) 32.7904 + 11.9347i 1.55792 + 0.567037i 0.970259 0.242069i \(-0.0778262\pi\)
0.587662 + 0.809106i \(0.300048\pi\)
\(444\) 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 0.946273 0.323369i \(-0.104815\pi\)
−0.753182 + 0.657812i \(0.771482\pi\)
\(450\) 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 −0.997778 0.0666248i \(-0.978777\pi\)
0.960392 + 0.278653i \(0.0898880\pi\)
\(462\) 0 0
\(463\) 2.75624 + 4.77396i 0.128094 + 0.221865i 0.922938 0.384949i \(-0.125781\pi\)
−0.794844 + 0.606813i \(0.792448\pi\)
\(464\) 0 0
\(465\) 14.7344 12.3636i 0.683292 0.573350i
\(466\) 0 0
\(467\) 5.58466 9.67291i 0.258427 0.447609i −0.707394 0.706820i \(-0.750129\pi\)
0.965821 + 0.259211i \(0.0834625\pi\)
\(468\) 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 −0.999694 0.0247276i \(-0.992128\pi\)
0.930948 0.365152i \(-0.118983\pi\)
\(480\) 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 0.864956 0.501847i \(-0.167346\pi\)
−0.867091 + 0.498150i \(0.834013\pi\)
\(488\) 0 0
\(489\) 2.75356 15.6162i 0.124520 0.706189i
\(490\) 0 0
\(491\) −26.3075 + 9.57516i −1.18724 + 0.432121i −0.858754 0.512388i \(-0.828761\pi\)
−0.328488 + 0.944508i \(0.606539\pi\)
\(492\) 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 −0.408890 0.912584i \(-0.634084\pi\)
0.696353 0.717700i \(-0.254805\pi\)
\(500\) 0 0
\(501\) −1.13176 1.96026i −0.0505633 0.0875781i
\(502\) 0 0
\(503\) 17.3084 14.5235i 0.771743 0.647570i −0.169411 0.985545i \(-0.554187\pi\)
0.941155 + 0.337976i \(0.109742\pi\)
\(504\) 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 −0.340377 0.940289i \(-0.610555\pi\)
−0.00174780 0.999998i \(-0.500556\pi\)
\(510\) 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 −0.467801 0.883834i \(-0.654953\pi\)
0.999323 0.0367899i \(-0.0117132\pi\)
\(522\) 0 0
\(523\) 18.5462 15.5621i 0.810970 0.680485i −0.139869 0.990170i \(-0.544668\pi\)
0.950839 + 0.309685i \(0.100224\pi\)
\(524\) 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 0.128416 0.991720i \(-0.459011\pi\)
0.998953 + 0.0457455i \(0.0145663\pi\)
\(542\) 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 −0.922310 0.386451i \(-0.873701\pi\)
0.734514 0.678593i \(-0.237410\pi\)
\(548\) 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 0.549663 0.835386i \(-0.314756\pi\)
−0.115910 + 0.993260i \(0.536978\pi\)
\(558\) 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 0.988659 0.150175i \(-0.0479836\pi\)
−0.624385 + 0.781117i \(0.714650\pi\)
\(564\) 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 0.960267 0.279082i \(-0.0900302\pi\)
−0.721826 + 0.692075i \(0.756697\pi\)
\(578\) 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 −0.978479 0.206348i \(-0.933842\pi\)
−0.373124 0.927781i \(-0.621714\pi\)
\(588\) 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 0.846190 + 0.532881i \(0.178891\pi\)
−0.612903 + 0.790158i \(0.709998\pi\)
\(594\) 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 −0.775506 0.631341i \(-0.782505\pi\)
0.487084 + 0.873355i \(0.338061\pi\)
\(600\) 0 0
\(601\) −4.83884 8.38112i −0.197380 0.341873i 0.750298 0.661100i \(-0.229910\pi\)
−0.947678 + 0.319227i \(0.896577\pi\)
\(602\) 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 0.915981 + 0.401222i \(0.131414\pi\)
−0.997966 + 0.0637414i \(0.979697\pi\)
\(614\) 0 0
\(615\) −3.86959 6.70232i −0.156037 0.270264i
\(616\) 0 0
\(617\) 13.6459 11.4503i 0.549363 0.460970i −0.325362 0.945589i \(-0.605486\pi\)
0.874725 + 0.484619i \(0.161042\pi\)
\(618\) 0 0
\(619\) 13.9932 24.2369i 0.562434 0.974164i −0.434849 0.900503i \(-0.643198\pi\)
0.997283 0.0736609i \(-0.0234683\pi\)
\(620\) 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 0.995045 0.0994276i \(-0.0317012\pi\)
−0.969042 + 0.246894i \(0.920590\pi\)
\(632\) 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 −0.871649 0.490131i \(-0.836949\pi\)
0.986717 0.162451i \(-0.0519400\pi\)
\(642\) 0 0
\(643\) −20.8396 + 7.58500i −0.821834 + 0.299123i −0.718503 0.695524i \(-0.755172\pi\)
−0.103331 + 0.994647i \(0.532950\pi\)
\(644\) 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 0.999593 + 0.0285398i \(0.00908575\pi\)
−0.475080 + 0.879943i \(0.657581\pi\)
\(654\) 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 −0.00244038 0.999997i \(-0.500777\pi\)
−0.644655 + 0.764474i \(0.722999\pi\)
\(660\) 0 0
\(661\) 1.50593 + 8.54055i 0.0585739 + 0.332189i 0.999987 0.00506615i \(-0.00161261\pi\)
−0.941413 + 0.337255i \(0.890502\pi\)
\(662\) 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 −0.886134 0.463430i \(-0.846619\pi\)
0.844409 + 0.535699i \(0.179952\pi\)
\(674\) 0 0
\(675\) −0.0320889 + 0.0269258i −0.00123510 + 0.00103637i
\(676\) 0 0
\(677\) −6.37686 11.0450i −0.245083 0.424496i 0.717072 0.696999i \(-0.245482\pi\)
−0.962155 + 0.272503i \(0.912148\pi\)
\(678\) 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 0.974033 0.226407i \(-0.0726980\pi\)
−0.683091 + 0.730333i \(0.739365\pi\)
\(692\) 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 0.999793 0.0203518i \(-0.00647861\pi\)
0.153570 + 0.988138i \(0.450923\pi\)
\(702\) 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 −0.115562 0.993300i \(-0.536867\pi\)
−0.727006 + 0.686631i \(0.759089\pi\)
\(710\) 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 −0.890221 0.455530i \(-0.849450\pi\)
−0.389140 + 0.921179i \(0.627228\pi\)
\(720\) 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 0.685861 + 0.727733i \(0.259426\pi\)
−0.893398 + 0.449267i \(0.851685\pi\)
\(728\) 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 −0.794400 0.607396i \(-0.792214\pi\)
0.923220 + 0.384272i \(0.125548\pi\)
\(734\) 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 0.231241 0.972896i \(-0.425721\pi\)
−0.917961 + 0.396670i \(0.870166\pi\)
\(740\) 0 0
\(741\) −1.04529 + 1.75135i −0.0383998 + 0.0643376i
\(742\) 0 0
\(743\) 29.1536 + 24.4628i 1.06954 + 0.897453i 0.995011 0.0997653i \(-0.0318092\pi\)
0.0745322 + 0.997219i \(0.476254\pi\)
\(744\) 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 −0.600832 0.799376i \(-0.705164\pi\)
0.682898 + 0.730514i \(0.260719\pi\)
\(752\) 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 −0.528732 0.848789i \(-0.677332\pi\)
0.140559 + 0.990072i \(0.455110\pi\)
\(758\) 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 −0.529568 0.848268i \(-0.677646\pi\)
0.743422 + 0.668823i \(0.233201\pi\)
\(770\) 0 0
\(771\) 1.97313 3.41755i 0.0710604 0.123080i
\(772\) 0 0
\(773\) 5.78224 + 2.10456i 0.207973 + 0.0756959i 0.443906 0.896073i \(-0.353592\pi\)
−0.235933 + 0.971769i \(0.575815\pi\)
\(774\) 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 −0.928817 0.370540i \(-0.879173\pi\)
0.785305 + 0.619109i \(0.212506\pi\)
\(788\) 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 0.149246i