Properties

Label 1400.2.q.a.1201.1
Level $1400$
Weight $2$
Character 1400.1201
Analytic conductor $11.179$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1400.1201
Dual form 1400.2.q.a.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{3} +(-2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{3} +(-2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +3.00000 q^{13} +(-1.00000 + 1.73205i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-1.00000 - 5.19615i) q^{21} +(3.50000 + 6.06218i) q^{23} -4.00000 q^{27} -6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(1.00000 + 1.73205i) q^{33} +(-2.50000 - 4.33013i) q^{37} +(-3.00000 + 5.19615i) q^{39} -5.00000 q^{41} -6.00000 q^{43} +(-4.50000 - 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(5.50000 - 9.52628i) q^{53} -10.0000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(6.00000 + 10.3923i) q^{61} +(2.50000 + 0.866025i) q^{63} +(-2.00000 + 3.46410i) q^{67} -14.0000 q^{69} -4.00000 q^{71} +(6.00000 - 10.3923i) q^{73} +(0.500000 + 2.59808i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(5.50000 - 9.52628i) q^{81} +4.00000 q^{83} +(6.00000 - 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-6.00000 + 5.19615i) q^{91} +(-4.00000 - 6.92820i) q^{93} -6.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - 4q^{7} - q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 4q^{7} - q^{9} + q^{11} + 6q^{13} - 2q^{17} + 5q^{19} - 2q^{21} + 7q^{23} - 8q^{27} - 12q^{29} - 4q^{31} + 2q^{33} - 5q^{37} - 6q^{39} - 10q^{41} - 12q^{43} - 9q^{47} + 2q^{49} - 4q^{51} + 11q^{53} - 20q^{57} - 8q^{59} + 12q^{61} + 5q^{63} - 4q^{67} - 28q^{69} - 8q^{71} + 12q^{73} + q^{77} - 14q^{79} + 11q^{81} + 8q^{83} + 12q^{87} - 6q^{89} - 12q^{91} - 8q^{93} - 12q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 0 0
\(21\) −1.00000 5.19615i −0.218218 1.13389i
\(22\) 0 0
\(23\) 3.50000 + 6.06218i 0.729800 + 1.26405i 0.956967 + 0.290196i \(0.0937204\pi\)
−0.227167 + 0.973856i \(0.572946\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 1.00000 + 1.73205i 0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.50000 4.33013i −0.410997 0.711868i 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) 0 0
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i \(-0.560736\pi\)
0.945134 0.326683i \(-0.105931\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −10.0000 −1.32453
\(58\) 0 0
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0 0
\(61\) 6.00000 + 10.3923i 0.768221 + 1.33060i 0.938527 + 0.345207i \(0.112191\pi\)
−0.170305 + 0.985391i \(0.554475\pi\)
\(62\) 0 0
\(63\) 2.50000 + 0.866025i 0.314970 + 0.109109i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 0 0
\(69\) −14.0000 −1.68540
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 6.00000 10.3923i 0.702247 1.21633i −0.265429 0.964130i \(-0.585514\pi\)
0.967676 0.252197i \(-0.0811531\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.500000 + 2.59808i 0.0569803 + 0.296078i
\(78\) 0 0
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.00000 10.3923i 0.643268 1.11417i
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −6.00000 + 5.19615i −0.628971 + 0.544705i
\(92\) 0 0
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) 10.0000 + 17.3205i 0.985329 + 1.70664i 0.640464 + 0.767988i \(0.278742\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 0 0
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −20.0000 −1.88144 −0.940721 0.339182i \(-0.889850\pi\)
−0.940721 + 0.339182i \(0.889850\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.50000 2.59808i −0.138675 0.240192i
\(118\) 0 0
\(119\) −1.00000 5.19615i −0.0916698 0.476331i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −17.0000 −1.50851 −0.754253 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(128\) 0 0
\(129\) 6.00000 10.3923i 0.528271 0.914991i
\(130\) 0 0
\(131\) −3.50000 6.06218i −0.305796 0.529655i 0.671642 0.740876i \(-0.265589\pi\)
−0.977438 + 0.211221i \(0.932256\pi\)
\(132\) 0 0
\(133\) −12.5000 4.33013i −1.08389 0.375470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 18.0000 1.51587
\(142\) 0 0
\(143\) 1.50000 2.59808i 0.125436 0.217262i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 11.0000 + 8.66025i 0.907265 + 0.714286i
\(148\) 0 0
\(149\) −5.00000 8.66025i −0.409616 0.709476i 0.585231 0.810867i \(-0.301004\pi\)
−0.994847 + 0.101391i \(0.967671\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.50000 4.33013i 0.199522 0.345582i −0.748852 0.662738i \(-0.769394\pi\)
0.948373 + 0.317156i \(0.102728\pi\)
\(158\) 0 0
\(159\) 11.0000 + 19.0526i 0.872357 + 1.51097i
\(160\) 0 0
\(161\) −17.5000 6.06218i −1.37919 0.477767i
\(162\) 0 0
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.00000 −0.386912 −0.193456 0.981109i \(-0.561970\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 2.50000 4.33013i 0.191180 0.331133i
\(172\) 0 0
\(173\) 9.50000 + 16.4545i 0.722272 + 1.25101i 0.960087 + 0.279701i \(0.0902353\pi\)
−0.237816 + 0.971310i \(0.576431\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.00000 13.8564i −0.601317 1.04151i
\(178\) 0 0
\(179\) −4.50000 + 7.79423i −0.336346 + 0.582568i −0.983742 0.179585i \(-0.942524\pi\)
0.647397 + 0.762153i \(0.275858\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −24.0000 −1.77413
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 0 0
\(189\) 8.00000 6.92820i 0.581914 0.503953i
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) −10.0000 + 17.3205i −0.719816 + 1.24676i 0.241257 + 0.970461i \(0.422440\pi\)
−0.961073 + 0.276296i \(0.910893\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 27.0000 1.92367 0.961835 0.273629i \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) 0 0
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 0 0
\(201\) −4.00000 6.92820i −0.282138 0.488678i
\(202\) 0 0
\(203\) 12.0000 10.3923i 0.842235 0.729397i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.50000 6.06218i 0.243267 0.421350i
\(208\) 0 0
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 0 0
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.00000 10.3923i −0.135769 0.705476i
\(218\) 0 0
\(219\) 12.0000 + 20.7846i 0.810885 + 1.40449i
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.00000 + 6.92820i −0.265489 + 0.459841i −0.967692 0.252136i \(-0.918867\pi\)
0.702202 + 0.711977i \(0.252200\pi\)
\(228\) 0 0
\(229\) 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i \(0.209391\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(230\) 0 0
\(231\) −5.00000 1.73205i −0.328976 0.113961i
\(232\) 0 0
\(233\) 1.00000 + 1.73205i 0.0655122 + 0.113470i 0.896921 0.442191i \(-0.145799\pi\)
−0.831409 + 0.555661i \(0.812465\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 28.0000 1.81880
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −11.5000 + 19.9186i −0.740780 + 1.28307i 0.211360 + 0.977408i \(0.432211\pi\)
−0.952141 + 0.305661i \(0.901123\pi\)
\(242\) 0 0
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 7.50000 + 12.9904i 0.477214 + 0.826558i
\(248\) 0 0
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) 0 0
\(251\) 29.0000 1.83046 0.915232 0.402928i \(-0.132007\pi\)
0.915232 + 0.402928i \(0.132007\pi\)
\(252\) 0 0
\(253\) 7.00000 0.440086
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) 0 0
\(259\) 12.5000 + 4.33013i 0.776712 + 0.269061i
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 0 0
\(263\) 4.00000 6.92820i 0.246651 0.427211i −0.715944 0.698158i \(-0.754003\pi\)
0.962594 + 0.270947i \(0.0873367\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i \(-0.714120\pi\)
0.988908 + 0.148527i \(0.0474530\pi\)
\(270\) 0 0
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 0 0
\(273\) −3.00000 15.5885i −0.181568 0.943456i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 0 0
\(283\) −11.0000 + 19.0526i −0.653882 + 1.13256i 0.328291 + 0.944577i \(0.393527\pi\)
−0.982173 + 0.187980i \(0.939806\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.0000 8.66025i 0.590281 0.511199i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) 6.00000 10.3923i 0.351726 0.609208i
\(292\) 0 0
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.00000 + 3.46410i −0.116052 + 0.201008i
\(298\) 0 0
\(299\) 10.5000 + 18.1865i 0.607231 + 1.05175i
\(300\) 0 0
\(301\) 12.0000 10.3923i 0.691669 0.599002i
\(302\) 0 0
\(303\) −12.0000 20.7846i −0.689382 1.19404i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 6.00000 0.342438 0.171219 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) 0 0
\(309\) −40.0000 −2.27552
\(310\) 0 0
\(311\) 2.00000 3.46410i 0.113410 0.196431i −0.803733 0.594990i \(-0.797156\pi\)
0.917143 + 0.398559i \(0.130489\pi\)
\(312\) 0 0
\(313\) 8.00000 + 13.8564i 0.452187 + 0.783210i 0.998522 0.0543564i \(-0.0173107\pi\)
−0.546335 + 0.837567i \(0.683977\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 0 0
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) 0 0
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) −10.0000 −0.556415
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.00000 + 6.92820i 0.221201 + 0.383131i
\(328\) 0 0
\(329\) 22.5000 + 7.79423i 1.24047 + 0.429710i
\(330\) 0 0
\(331\) 13.5000 + 23.3827i 0.742027 + 1.28523i 0.951571 + 0.307429i \(0.0994688\pi\)
−0.209544 + 0.977799i \(0.567198\pi\)
\(332\) 0 0
\(333\) −2.50000 + 4.33013i −0.136999 + 0.237289i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 0 0
\(339\) 20.0000 34.6410i 1.08625 1.88144i
\(340\) 0 0
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.00000 6.92820i 0.214731 0.371925i −0.738458 0.674299i \(-0.764446\pi\)
0.953189 + 0.302374i \(0.0977791\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −12.0000 −0.640513
\(352\) 0 0
\(353\) 10.0000 17.3205i 0.532246 0.921878i −0.467045 0.884234i \(-0.654681\pi\)
0.999291 0.0376440i \(-0.0119853\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 10.0000 + 3.46410i 0.529256 + 0.183340i
\(358\) 0 0
\(359\) −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i \(-0.875879\pi\)
0.133263 0.991081i \(-0.457455\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) −20.0000 −1.04973
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) 0 0
\(369\) 2.50000 + 4.33013i 0.130145 + 0.225417i
\(370\) 0 0
\(371\) 5.50000 + 28.5788i 0.285546 + 1.48374i
\(372\) 0 0
\(373\) 7.00000 + 12.1244i 0.362446 + 0.627775i 0.988363 0.152115i \(-0.0486083\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −18.0000 −0.927047
\(378\) 0 0
\(379\) −21.0000 −1.07870 −0.539349 0.842082i \(-0.681330\pi\)
−0.539349 + 0.842082i \(0.681330\pi\)
\(380\) 0 0
\(381\) 17.0000 29.4449i 0.870936 1.50851i
\(382\) 0 0
\(383\) −10.5000 18.1865i −0.536525 0.929288i −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) 0 0
\(389\) 8.00000 13.8564i 0.405616 0.702548i −0.588777 0.808296i \(-0.700390\pi\)
0.994393 + 0.105748i \(0.0337237\pi\)
\(390\) 0 0
\(391\) −14.0000 −0.708010
\(392\) 0 0
\(393\) 14.0000 0.706207
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) 0 0
\(399\) 20.0000 17.3205i 1.00125 0.867110i
\(400\) 0 0
\(401\) −6.50000 11.2583i −0.324595 0.562214i 0.656836 0.754034i \(-0.271895\pi\)
−0.981430 + 0.191820i \(0.938561\pi\)
\(402\) 0 0
\(403\) −6.00000 + 10.3923i −0.298881 + 0.517678i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.00000 −0.247841
\(408\) 0 0
\(409\) 3.00000 5.19615i 0.148340 0.256933i −0.782274 0.622935i \(-0.785940\pi\)
0.930614 + 0.366002i \(0.119274\pi\)
\(410\) 0 0
\(411\) −12.0000 20.7846i −0.591916 1.02523i
\(412\) 0 0
\(413\) −4.00000 20.7846i −0.196827 1.02274i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.00000 + 6.92820i −0.195881 + 0.339276i
\(418\) 0 0
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 0 0
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −30.0000 10.3923i −1.45180 0.502919i
\(428\) 0 0
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 0 0
\(431\) 8.00000 13.8564i 0.385346 0.667440i −0.606471 0.795106i \(-0.707415\pi\)
0.991817 + 0.127666i \(0.0407486\pi\)
\(432\) 0 0
\(433\) −24.0000 −1.15337 −0.576683 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −17.5000 + 30.3109i −0.837139 + 1.44997i
\(438\) 0 0
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) 0 0
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) −16.0000 27.7128i −0.760183 1.31668i −0.942756 0.333483i \(-0.891776\pi\)
0.182573 0.983192i \(-0.441557\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 20.0000 0.945968
\(448\) 0 0
\(449\) 13.0000 0.613508 0.306754 0.951789i \(-0.400757\pi\)
0.306754 + 0.951789i \(0.400757\pi\)
\(450\) 0 0
\(451\) −2.50000 + 4.33013i −0.117720 + 0.203898i
\(452\) 0 0
\(453\) 10.0000 + 17.3205i 0.469841 + 0.813788i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 19.0526i −0.514558 0.891241i −0.999857 0.0168929i \(-0.994623\pi\)
0.485299 0.874348i \(-0.338711\pi\)
\(458\) 0 0
\(459\) 4.00000 6.92820i 0.186704 0.323381i
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.00000 8.66025i −0.231372 0.400749i 0.726840 0.686807i \(-0.240988\pi\)
−0.958212 + 0.286058i \(0.907655\pi\)
\(468\) 0 0
\(469\) −2.00000 10.3923i −0.0923514 0.479872i
\(470\) 0 0
\(471\) 5.00000 + 8.66025i 0.230388 + 0.399043i
\(472\) 0 0
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −11.0000 −0.503655
\(478\) 0 0
\(479\) 8.00000 13.8564i 0.365529 0.633115i −0.623332 0.781958i \(-0.714221\pi\)
0.988861 + 0.148842i \(0.0475547\pi\)
\(480\) 0 0
\(481\) −7.50000 12.9904i −0.341971 0.592310i
\(482\) 0 0
\(483\) 28.0000 24.2487i 1.27404 1.10335i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4.00000 + 6.92820i −0.181257 + 0.313947i −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) 0 0
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 6.00000 10.3923i 0.270226 0.468046i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.00000 6.92820i 0.358849 0.310772i
\(498\) 0 0
\(499\) −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i \(-0.951061\pi\)
0.361478 0.932381i \(-0.382272\pi\)
\(500\) 0 0
\(501\) 5.00000 8.66025i 0.223384 0.386912i
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.00000 6.92820i 0.177646 0.307692i
\(508\) 0 0
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 6.00000 + 31.1769i 0.265424 + 1.37919i
\(512\) 0 0
\(513\) −10.0000 17.3205i −0.441511 0.764719i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) −38.0000 −1.66801
\(520\) 0 0
\(521\) 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i \(-0.726763\pi\)
0.982231 + 0.187678i \(0.0600963\pi\)
\(522\) 0 0
\(523\) 14.0000 + 24.2487i 0.612177 + 1.06032i 0.990873 + 0.134801i \(0.0430394\pi\)
−0.378695 + 0.925521i \(0.623627\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.00000 6.92820i −0.174243 0.301797i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) −15.0000 −0.649722
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.00000 15.5885i −0.388379 0.672692i
\(538\) 0 0
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 0 0
\(541\) 20.0000 + 34.6410i 0.859867 + 1.48933i 0.872055 + 0.489408i \(0.162787\pi\)
−0.0121878 + 0.999926i \(0.503880\pi\)
\(542\) 0 0
\(543\) −2.00000 + 3.46410i −0.0858282 + 0.148659i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) 6.00000 10.3923i 0.256074 0.443533i
\(550\) 0 0
\(551\) −15.0000 25.9808i −0.639021 1.10682i
\(552\) 0 0
\(553\) 35.0000 + 12.1244i 1.48835 + 0.515580i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10.5000 18.1865i 0.444899 0.770588i −0.553146 0.833084i \(-0.686573\pi\)
0.998045 + 0.0624962i \(0.0199061\pi\)
\(558\) 0 0
\(559\) −18.0000 −0.761319
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) 3.00000 5.19615i 0.126435 0.218992i −0.795858 0.605483i \(-0.792980\pi\)
0.922293 + 0.386492i \(0.126313\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 5.50000 + 28.5788i 0.230978 + 1.20020i
\(568\) 0 0
\(569\) 5.50000 + 9.52628i 0.230572 + 0.399362i 0.957977 0.286846i \(-0.0926069\pi\)
−0.727405 + 0.686209i \(0.759274\pi\)
\(570\) 0 0
\(571\) −14.0000 + 24.2487i −0.585882 + 1.01478i 0.408883 + 0.912587i \(0.365918\pi\)
−0.994765 + 0.102190i \(0.967415\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2.00000 + 3.46410i −0.0832611 + 0.144212i −0.904649 0.426158i \(-0.859867\pi\)
0.821388 + 0.570370i \(0.193200\pi\)
\(578\) 0 0
\(579\) −20.0000 34.6410i −0.831172 1.43963i
\(580\) 0 0
\(581\) −8.00000 + 6.92820i −0.331896 + 0.287430i
\(582\) 0 0
\(583\) −5.50000 9.52628i −0.227787 0.394538i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −20.0000 −0.824086
\(590\) 0 0
\(591\) −27.0000 + 46.7654i −1.11063 + 1.92367i
\(592\) 0 0
\(593\) −6.00000 10.3923i −0.246390 0.426761i 0.716131 0.697966i \(-0.245911\pi\)
−0.962522 + 0.271205i \(0.912578\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.00000 + 6.92820i 0.163709 + 0.283552i
\(598\) 0 0
\(599\) −17.0000 + 29.4449i −0.694601 + 1.20308i 0.275714 + 0.961240i \(0.411086\pi\)
−0.970315 + 0.241845i \(0.922248\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 16.5000 + 28.5788i 0.669714 + 1.15998i 0.977984 + 0.208680i \(0.0669168\pi\)
−0.308270 + 0.951299i \(0.599750\pi\)
\(608\) 0 0
\(609\) 6.00000 + 31.1769i 0.243132 + 1.26335i
\(610\) 0 0
\(611\) −13.5000 23.3827i −0.546152 0.945962i
\(612\) 0 0
\(613\) −20.5000 + 35.5070i −0.827987 + 1.43412i 0.0716275 + 0.997431i \(0.477181\pi\)
−0.899615 + 0.436684i \(0.856153\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) 0 0
\(621\) −14.0000 24.2487i −0.561801 0.973067i
\(622\) 0 0
\(623\) 15.0000 + 5.19615i 0.600962 + 0.208179i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −5.00000 + 8.66025i −0.199681 + 0.345857i
\(628\) 0 0
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 13.0000 22.5167i 0.516704 0.894957i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 20.7846i 0.118864 0.823516i
\(638\) 0 0
\(639\) 2.00000 + 3.46410i 0.0791188 + 0.137038i
\(640\) 0 0
\(641\) −17.5000 + 30.3109i −0.691208 + 1.19721i 0.280234 + 0.959932i \(0.409588\pi\)
−0.971442 + 0.237276i \(0.923745\pi\)
\(642\) 0 0
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11.5000 19.9186i 0.452112 0.783080i −0.546405 0.837521i \(-0.684004\pi\)
0.998517 + 0.0544405i \(0.0173375\pi\)
\(648\) 0 0
\(649\) 4.00000 + 6.92820i 0.157014 + 0.271956i
\(650\) 0 0
\(651\) 20.0000 + 6.92820i 0.783862 + 0.271538i
\(652\) 0 0
\(653\) 22.5000 + 38.9711i 0.880493 + 1.52506i 0.850794 + 0.525500i \(0.176122\pi\)
0.0296993 + 0.999559i \(0.490545\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) −16.0000 −0.623272 −0.311636 0.950202i \(-0.600877\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(660\) 0 0
\(661\) 18.0000 31.1769i 0.700119 1.21264i −0.268306 0.963334i \(-0.586464\pi\)
0.968424 0.249308i \(-0.0802030\pi\)
\(662\) 0 0
\(663\) −6.00000 10.3923i −0.233021 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −21.0000 36.3731i −0.813123 1.40837i
\(668\) 0 0
\(669\) −16.0000 + 27.7128i −0.618596 + 1.07144i
\(670\) 0 0
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 42.0000 1.61898 0.809491 0.587133i \(-0.199743\pi\)
0.809491 + 0.587133i \(0.199743\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.5000 + 18.1865i 0.403548 + 0.698965i 0.994151 0.107997i \(-0.0344436\pi\)
−0.590603 + 0.806962i \(0.701110\pi\)
\(678\) 0 0
\(679\) 12.0000 10.3923i 0.460518 0.398820i
\(680\) 0 0
\(681\) −8.00000 13.8564i −0.306561 0.530979i
\(682\) 0 0
\(683\) −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i \(0.408507\pi\)
−0.972242 + 0.233977i \(0.924826\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −56.0000 −2.13653
\(688\) 0 0
\(689\) 16.5000 28.5788i 0.628600 1.08877i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 0 0
\(693\) 2.00000 1.73205i 0.0759737 0.0657952i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 5.00000 8.66025i 0.189389 0.328031i
\(698\) 0 0
\(699\) −4.00000 −0.151294
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) 12.5000 21.6506i 0.471446 0.816569i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.00000 31.1769i −0.225653 1.17253i
\(708\) 0 0
\(709\) 9.00000 + 15.5885i 0.338002 + 0.585437i 0.984057 0.177854i \(-0.0569156\pi\)
−0.646055 + 0.763291i \(0.723582\pi\)
\(710\) 0 0
\(711\) −7.00000 + 12.1244i −0.262521 + 0.454699i
\(712\) 0 0
\(713\) −28.0000 −1.04861
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 0 0
\(719\) 18.0000 + 31.1769i 0.671287 + 1.16270i 0.977539 + 0.210752i \(0.0675914\pi\)
−0.306253 + 0.951950i \(0.599075\pi\)
\(720\) 0 0
\(721\) −50.0000 17.3205i −1.86210 0.645049i
\(722\) 0 0
\(723\) −23.0000 39.8372i −0.855379 1.48156i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −41.0000 −1.52061 −0.760303 0.649569i \(-0.774949\pi\)
−0.760303 + 0.649569i \(0.774949\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 6.00000 10.3923i 0.221918 0.384373i
\(732\) 0 0
\(733\) 15.5000 + 26.8468i 0.572506 + 0.991609i 0.996308 + 0.0858539i \(0.0273618\pi\)
−0.423802 + 0.905755i \(0.639305\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.00000 + 3.46410i 0.0736709 + 0.127602i
\(738\) 0 0
\(739\) 20.5000 35.5070i 0.754105 1.30615i −0.191714 0.981451i \(-0.561404\pi\)
0.945818 0.324697i \(-0.105262\pi\)
\(740\) 0 0
\(741\) −30.0000 −1.10208
\(742\) 0 0
\(743\) 3.00000 0.110059 0.0550297 0.998485i \(-0.482475\pi\)
0.0550297 + 0.998485i \(0.482475\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.00000 3.46410i −0.0731762 0.126745i
\(748\) 0 0
\(749\) −30.0000 10.3923i −1.09618 0.379727i
\(750\) 0 0
\(751\) −9.00000 15.5885i −0.328415 0.568831i 0.653783 0.756682i \(-0.273181\pi\)
−0.982197 + 0.187851i \(0.939848\pi\)
\(752\) 0 0
\(753\) −29.0000 + 50.2295i −1.05682 + 1.83046i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) −7.00000 + 12.1244i −0.254084 + 0.440086i
\(760\) 0 0
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 0 0
\(763\) 2.00000 + 10.3923i 0.0724049 + 0.376227i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) 0 0
\(769\) −41.0000 −1.47850 −0.739249 0.673432i \(-0.764819\pi\)
−0.739249 + 0.673432i \(0.764819\pi\)
\(770\) 0 0
\(771\) −24.0000 −0.864339
\(772\) 0 0
\(773\) 7.50000 12.9904i 0.269756 0.467232i −0.699043 0.715080i \(-0.746390\pi\)
0.968799 + 0.247849i \(0.0797235\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −20.0000 + 17.3205i −0.717496 + 0.621370i
\(778\) 0 0
\(779\) −12.5000 21.6506i −0.447859 0.775715i
\(780\) 0 0
\(781\) −2.00000 + 3.46410i −0.0715656 + 0.123955i
\(782\) 0 0
\(783\) 24.0000 0.857690
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −9.00000 + 15.5885i −0.320815 + 0.555668i −0.980656 0.195737i \(-0.937290\pi\)
0.659841 + 0.751405i \(0.270624\pi\)
\(788\) 0 0
\(789\) 8.00000 + 13.8564i 0.284808 + 0.493301i
\(790\) 0 0
\(791\) 40.0000 34.6410i 1.42224 1.23169i
\(792\) 0 0
\(793\) 18.0000 + 31.1769i 0.639199 + 1.10712i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.00000 −0.0708436 −0.0354218 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794