Properties

Label 1040.2.q.j.321.1
Level $1040$
Weight $2$
Character 1040.321
Analytic conductor $8.304$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 321.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1040.321
Dual form 1040.2.q.j.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(0.500000 - 0.866025i) q^{15} +(1.50000 + 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +4.00000 q^{31} +(-1.50000 - 2.59808i) q^{33} +(-0.500000 - 0.866025i) q^{35} +(3.50000 - 6.06218i) q^{37} +(-2.50000 - 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(5.50000 + 9.52628i) q^{43} +(1.00000 + 1.73205i) q^{45} +(3.00000 - 5.19615i) q^{49} +3.00000 q^{51} -6.00000 q^{53} +(1.50000 - 2.59808i) q^{55} -7.00000 q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(1.00000 - 1.73205i) q^{63} +(1.00000 - 3.46410i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-1.50000 - 2.59808i) q^{71} +2.00000 q^{73} +(0.500000 - 0.866025i) q^{75} -3.00000 q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +(1.50000 + 2.59808i) q^{85} +(1.50000 + 2.59808i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(2.00000 - 3.46410i) q^{93} +(-3.50000 - 6.06218i) q^{95} +(3.50000 + 6.06218i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + 2 q^{5} - q^{7} + 2 q^{9} + O(q^{10}) \) \( 2 q + q^{3} + 2 q^{5} - q^{7} + 2 q^{9} + 3 q^{11} + 2 q^{13} + q^{15} + 3 q^{17} - 7 q^{19} - 2 q^{21} - 3 q^{23} + 2 q^{25} + 10 q^{27} - 3 q^{29} + 8 q^{31} - 3 q^{33} - q^{35} + 7 q^{37} - 5 q^{39} + 9 q^{41} + 11 q^{43} + 2 q^{45} + 6 q^{49} + 6 q^{51} - 12 q^{53} + 3 q^{55} - 14 q^{57} - 3 q^{59} - 11 q^{61} + 2 q^{63} + 2 q^{65} - 7 q^{67} + 3 q^{69} - 3 q^{71} + 4 q^{73} + q^{75} - 6 q^{77} - 16 q^{79} - q^{81} + 24 q^{83} + 3 q^{85} + 3 q^{87} - 15 q^{89} - 7 q^{91} + 4 q^{93} - 7 q^{95} + 7 q^{97} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i 0.755929 0.654654i \(-0.227186\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 0 0
\(35\) −0.500000 0.866025i −0.0845154 0.146385i
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 0 0
\(39\) −2.50000 2.59808i −0.400320 0.416025i
\(40\) 0 0
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 5.50000 + 9.52628i 0.838742 + 1.45274i 0.890947 + 0.454108i \(0.150042\pi\)
−0.0522047 + 0.998636i \(0.516625\pi\)
\(44\) 0 0
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 1.50000 2.59808i 0.202260 0.350325i
\(56\) 0 0
\(57\) −7.00000 −0.927173
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) 0 0
\(63\) 1.00000 1.73205i 0.125988 0.218218i
\(64\) 0 0
\(65\) 1.00000 3.46410i 0.124035 0.429669i
\(66\) 0 0
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 0 0
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) −1.50000 2.59808i −0.178017 0.308335i 0.763184 0.646181i \(-0.223635\pi\)
−0.941201 + 0.337846i \(0.890302\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 0 0
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) 0 0
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) −3.50000 + 0.866025i −0.366900 + 0.0907841i
\(92\) 0 0
\(93\) 2.00000 3.46410i 0.207390 0.359211i
\(94\) 0 0
\(95\) −3.50000 6.06218i −0.359092 0.621966i
\(96\) 0 0
\(97\) 3.50000 + 6.06218i 0.355371 + 0.615521i 0.987181 0.159602i \(-0.0510211\pi\)
−0.631810 + 0.775123i \(0.717688\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) 0 0
\(107\) 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i \(-0.690071\pi\)
0.997298 + 0.0734594i \(0.0234039\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −3.50000 6.06218i −0.332205 0.575396i
\(112\) 0 0
\(113\) −4.50000 7.79423i −0.423324 0.733219i 0.572938 0.819599i \(-0.305804\pi\)
−0.996262 + 0.0863794i \(0.972470\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 0 0
\(117\) 7.00000 1.73205i 0.647150 0.160128i
\(118\) 0 0
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) −4.50000 7.79423i −0.405751 0.702782i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −9.50000 + 16.4545i −0.842989 + 1.46010i 0.0443678 + 0.999015i \(0.485873\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 11.0000 0.968496
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −3.50000 + 6.06218i −0.303488 + 0.525657i
\(134\) 0 0
\(135\) 5.00000 0.430331
\(136\) 0 0
\(137\) 7.50000 + 12.9904i 0.640768 + 1.10984i 0.985262 + 0.171054i \(0.0547174\pi\)
−0.344493 + 0.938789i \(0.611949\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.50000 7.79423i −0.627182 0.651786i
\(144\) 0 0
\(145\) −1.50000 + 2.59808i −0.124568 + 0.215758i
\(146\) 0 0
\(147\) −3.00000 5.19615i −0.247436 0.428571i
\(148\) 0 0
\(149\) 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i \(0.162991\pi\)
−0.0115483 + 0.999933i \(0.503676\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) −3.00000 + 5.19615i −0.242536 + 0.420084i
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 0 0
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) −0.500000 0.866025i −0.0391630 0.0678323i 0.845780 0.533533i \(-0.179136\pi\)
−0.884943 + 0.465700i \(0.845802\pi\)
\(164\) 0 0
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) 0 0
\(167\) −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) 7.00000 12.1244i 0.535303 0.927173i
\(172\) 0 0
\(173\) 1.50000 + 2.59808i 0.114043 + 0.197528i 0.917397 0.397974i \(-0.130287\pi\)
−0.803354 + 0.595502i \(0.796953\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.0377964 0.0654654i
\(176\) 0 0
\(177\) −3.00000 −0.225494
\(178\) 0 0
\(179\) −10.5000 + 18.1865i −0.784807 + 1.35933i 0.144308 + 0.989533i \(0.453905\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −11.0000 −0.813143
\(184\) 0 0
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 0 0
\(189\) −2.50000 4.33013i −0.181848 0.314970i
\(190\) 0 0
\(191\) −1.50000 2.59808i −0.108536 0.187990i 0.806641 0.591041i \(-0.201283\pi\)
−0.915177 + 0.403051i \(0.867950\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 0 0
\(195\) −2.50000 2.59808i −0.179029 0.186052i
\(196\) 0 0
\(197\) −10.5000 + 18.1865i −0.748094 + 1.29574i 0.200641 + 0.979665i \(0.435697\pi\)
−0.948735 + 0.316072i \(0.897636\pi\)
\(198\) 0 0
\(199\) 8.50000 + 14.7224i 0.602549 + 1.04365i 0.992434 + 0.122782i \(0.0391815\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 0 0
\(203\) 3.00000 0.210559
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 0 0
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) −21.0000 −1.45260
\(210\) 0 0
\(211\) 5.50000 9.52628i 0.378636 0.655816i −0.612228 0.790681i \(-0.709727\pi\)
0.990864 + 0.134865i \(0.0430600\pi\)
\(212\) 0 0
\(213\) −3.00000 −0.205557
\(214\) 0 0
\(215\) 5.50000 + 9.52628i 0.375097 + 0.649687i
\(216\) 0 0
\(217\) −2.00000 3.46410i −0.135769 0.235159i
\(218\) 0 0
\(219\) 1.00000 1.73205i 0.0675737 0.117041i
\(220\) 0 0
\(221\) 10.5000 2.59808i 0.706306 0.174766i
\(222\) 0 0
\(223\) −9.50000 + 16.4545i −0.636167 + 1.10187i 0.350100 + 0.936713i \(0.386148\pi\)
−0.986267 + 0.165161i \(0.947186\pi\)
\(224\) 0 0
\(225\) 1.00000 + 1.73205i 0.0666667 + 0.115470i
\(226\) 0 0
\(227\) 13.5000 + 23.3827i 0.896026 + 1.55196i 0.832529 + 0.553981i \(0.186892\pi\)
0.0634974 + 0.997982i \(0.479775\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) −1.50000 + 2.59808i −0.0986928 + 0.170941i
\(232\) 0 0
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4.00000 + 6.92820i −0.259828 + 0.450035i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 0 0
\(247\) −24.5000 + 6.06218i −1.55890 + 0.385727i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) 10.5000 + 18.1865i 0.662754 + 1.14792i 0.979889 + 0.199543i \(0.0639459\pi\)
−0.317135 + 0.948380i \(0.602721\pi\)
\(252\) 0 0
\(253\) 4.50000 + 7.79423i 0.282913 + 0.490019i
\(254\) 0 0
\(255\) 3.00000 0.187867
\(256\) 0 0
\(257\) −4.50000 + 7.79423i −0.280702 + 0.486191i −0.971558 0.236802i \(-0.923901\pi\)
0.690856 + 0.722993i \(0.257234\pi\)
\(258\) 0 0
\(259\) −7.00000 −0.434959
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 7.50000 + 12.9904i 0.458993 + 0.794998i
\(268\) 0 0
\(269\) −13.5000 23.3827i −0.823110 1.42567i −0.903356 0.428892i \(-0.858904\pi\)
0.0802460 0.996775i \(-0.474429\pi\)
\(270\) 0 0
\(271\) 11.5000 19.9186i 0.698575 1.20997i −0.270385 0.962752i \(-0.587151\pi\)
0.968960 0.247216i \(-0.0795156\pi\)
\(272\) 0 0
\(273\) −1.00000 + 3.46410i −0.0605228 + 0.209657i
\(274\) 0 0
\(275\) 1.50000 2.59808i 0.0904534 0.156670i
\(276\) 0 0
\(277\) 9.50000 + 16.4545i 0.570800 + 0.988654i 0.996484 + 0.0837823i \(0.0267000\pi\)
−0.425684 + 0.904872i \(0.639967\pi\)
\(278\) 0 0
\(279\) 4.00000 + 6.92820i 0.239474 + 0.414781i
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i \(-0.785854\pi\)
0.930714 + 0.365748i \(0.119187\pi\)
\(284\) 0 0
\(285\) −7.00000 −0.414644
\(286\) 0 0
\(287\) −9.00000 −0.531253
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 7.00000 0.410347
\(292\) 0 0
\(293\) 13.5000 + 23.3827i 0.788678 + 1.36603i 0.926777 + 0.375613i \(0.122568\pi\)
−0.138098 + 0.990419i \(0.544099\pi\)
\(294\) 0 0
\(295\) −1.50000 2.59808i −0.0873334 0.151266i
\(296\) 0 0
\(297\) 7.50000 12.9904i 0.435194 0.753778i
\(298\) 0 0
\(299\) 7.50000 + 7.79423i 0.433736 + 0.450752i
\(300\) 0 0
\(301\) 5.50000 9.52628i 0.317015 0.549086i
\(302\) 0 0
\(303\) −4.50000 7.79423i −0.258518 0.447767i
\(304\) 0 0
\(305\) −5.50000 9.52628i −0.314929 0.545473i
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 + 6.92820i −0.227552 + 0.394132i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 1.00000 1.73205i 0.0563436 0.0975900i
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) −4.50000 7.79423i −0.251166 0.435031i
\(322\) 0 0
\(323\) 10.5000 18.1865i 0.584236 1.01193i
\(324\) 0 0
\(325\) 1.00000 3.46410i 0.0554700 0.192154i
\(326\) 0 0
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −9.50000 16.4545i −0.522167 0.904420i −0.999667 0.0257885i \(-0.991790\pi\)
0.477500 0.878632i \(-0.341543\pi\)
\(332\) 0 0
\(333\) 14.0000 0.767195
\(334\) 0 0
\(335\) −3.50000 + 6.06218i −0.191225 + 0.331212i
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 0 0
\(339\) −9.00000 −0.488813
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 1.50000 + 2.59808i 0.0807573 + 0.139876i
\(346\) 0 0
\(347\) −16.5000 28.5788i −0.885766 1.53419i −0.844833 0.535031i \(-0.820300\pi\)
−0.0409337 0.999162i \(-0.513033\pi\)
\(348\) 0 0
\(349\) 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i \(-0.824813\pi\)
0.879097 + 0.476642i \(0.158146\pi\)
\(350\) 0 0
\(351\) 5.00000 17.3205i 0.266880 0.924500i
\(352\) 0 0
\(353\) −4.50000 + 7.79423i −0.239511 + 0.414845i −0.960574 0.278024i \(-0.910320\pi\)
0.721063 + 0.692869i \(0.243654\pi\)
\(354\) 0 0
\(355\) −1.50000 2.59808i −0.0796117 0.137892i
\(356\) 0 0
\(357\) −1.50000 2.59808i −0.0793884 0.137505i
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i \(-0.791675\pi\)
0.923869 + 0.382709i \(0.125009\pi\)
\(368\) 0 0
\(369\) 18.0000 0.937043
\(370\) 0 0
\(371\) 3.00000 + 5.19615i 0.155752 + 0.269771i
\(372\) 0 0
\(373\) 15.5000 + 26.8468i 0.802560 + 1.39007i 0.917926 + 0.396751i \(0.129862\pi\)
−0.115367 + 0.993323i \(0.536804\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) 7.50000 + 7.79423i 0.386270 + 0.401423i
\(378\) 0 0
\(379\) −0.500000 + 0.866025i −0.0256833 + 0.0444847i −0.878581 0.477593i \(-0.841509\pi\)
0.852898 + 0.522077i \(0.174843\pi\)
\(380\) 0 0
\(381\) 9.50000 + 16.4545i 0.486700 + 0.842989i
\(382\) 0 0
\(383\) −4.50000 7.79423i −0.229939 0.398266i 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(384\) 0 0
\(385\) −3.00000 −0.152894
\(386\) 0 0
\(387\) −11.0000 + 19.0526i −0.559161 + 0.968496i
\(388\) 0 0
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 6.00000 10.3923i 0.302660 0.524222i
\(394\) 0 0
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) −2.50000 4.33013i −0.125471 0.217323i 0.796446 0.604710i \(-0.206711\pi\)
−0.921917 + 0.387387i \(0.873378\pi\)
\(398\) 0 0
\(399\) 3.50000 + 6.06218i 0.175219 + 0.303488i
\(400\) 0 0
\(401\) 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i \(-0.525087\pi\)
0.902703 0.430263i \(-0.141579\pi\)
\(402\) 0 0
\(403\) 4.00000 13.8564i 0.199254 0.690237i
\(404\) 0 0
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) 0 0
\(407\) −10.5000 18.1865i −0.520466 0.901473i
\(408\) 0 0
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 0 0
\(411\) 15.0000 0.739895
\(412\) 0 0
\(413\) −1.50000 + 2.59808i −0.0738102 + 0.127843i
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 0 0
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.50000 + 2.59808i 0.0727607 + 0.126025i
\(426\) 0 0
\(427\) −5.50000 + 9.52628i −0.266164 + 0.461009i
\(428\) 0 0
\(429\) −10.5000 + 2.59808i −0.506945 + 0.125436i
\(430\) 0 0
\(431\) −4.50000 + 7.79423i −0.216757 + 0.375435i −0.953815 0.300395i \(-0.902881\pi\)
0.737057 + 0.675830i \(0.236215\pi\)
\(432\) 0 0
\(433\) −14.5000 25.1147i −0.696826 1.20694i −0.969561 0.244848i \(-0.921262\pi\)
0.272736 0.962089i \(-0.412071\pi\)
\(434\) 0 0
\(435\) 1.50000 + 2.59808i 0.0719195 + 0.124568i
\(436\) 0 0
\(437\) 21.0000 1.00457
\(438\) 0 0
\(439\) 5.50000 9.52628i 0.262501 0.454665i −0.704405 0.709798i \(-0.748786\pi\)
0.966906 + 0.255134i \(0.0821195\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) −7.50000 + 12.9904i −0.355534 + 0.615803i
\(446\) 0 0
\(447\) 21.0000 0.993266
\(448\) 0 0
\(449\) −1.50000 2.59808i −0.0707894 0.122611i 0.828458 0.560051i \(-0.189218\pi\)
−0.899247 + 0.437440i \(0.855885\pi\)
\(450\) 0 0
\(451\) −13.5000 23.3827i −0.635690 1.10105i
\(452\) 0 0
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 0 0
\(455\) −3.50000 + 0.866025i −0.164083 + 0.0405999i
\(456\) 0 0
\(457\) −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i \(-0.870643\pi\)
0.801611 + 0.597847i \(0.203977\pi\)
\(458\) 0 0
\(459\) 7.50000 + 12.9904i 0.350070 + 0.606339i
\(460\) 0 0
\(461\) −13.5000 23.3827i −0.628758 1.08904i −0.987801 0.155719i \(-0.950230\pi\)
0.359044 0.933321i \(-0.383103\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 0 0
\(465\) 2.00000 3.46410i 0.0927478 0.160644i
\(466\) 0 0
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) 7.00000 0.323230
\(470\) 0 0
\(471\) −5.00000 + 8.66025i −0.230388 + 0.399043i
\(472\) 0 0
\(473\) 33.0000 1.51734
\(474\) 0 0
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) −6.00000 10.3923i −0.274721 0.475831i
\(478\) 0 0
\(479\) 19.5000 33.7750i 0.890978 1.54322i 0.0522726 0.998633i \(-0.483354\pi\)
0.838705 0.544586i \(-0.183313\pi\)
\(480\) 0 0
\(481\) −17.5000 18.1865i −0.797931 0.829235i
\(482\) 0 0
\(483\) 1.50000 2.59808i 0.0682524 0.118217i
\(484\) 0 0
\(485\) 3.50000 + 6.06218i 0.158927 + 0.275269i
\(486\) 0 0
\(487\) 5.50000 + 9.52628i 0.249229 + 0.431677i 0.963312 0.268384i \(-0.0864896\pi\)
−0.714083 + 0.700061i \(0.753156\pi\)
\(488\) 0 0
\(489\) −1.00000 −0.0452216
\(490\) 0 0
\(491\) −4.50000 + 7.79423i −0.203082 + 0.351749i −0.949520 0.313707i \(-0.898429\pi\)
0.746438 + 0.665455i \(0.231763\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 0 0
\(497\) −1.50000 + 2.59808i −0.0672842 + 0.116540i
\(498\) 0 0
\(499\) −32.0000 −1.43252 −0.716258 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) 0 0
\(503\) 7.50000 + 12.9904i 0.334408 + 0.579212i 0.983371 0.181608i \(-0.0581302\pi\)
−0.648963 + 0.760820i \(0.724797\pi\)
\(504\) 0 0
\(505\) 4.50000 7.79423i 0.200247 0.346839i
\(506\) 0 0
\(507\) −11.5000 + 6.06218i −0.510733 + 0.269231i
\(508\) 0 0
\(509\) 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i \(-0.769415\pi\)
0.948353 + 0.317217i \(0.102748\pi\)
\(510\) 0 0
\(511\) −1.00000 1.73205i −0.0442374 0.0766214i
\(512\) 0 0
\(513\) −17.5000 30.3109i −0.772644 1.33826i
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 0.131685
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i \(-0.614728\pi\)
0.986718 0.162446i \(-0.0519382\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 3.00000 5.19615i 0.130189 0.225494i
\(532\) 0 0
\(533\) −22.5000 23.3827i −0.974583 1.01282i
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 0 0
\(537\) 10.5000 + 18.1865i 0.453108 + 0.784807i
\(538\) 0 0
\(539\) −9.00000 15.5885i −0.387657 0.671442i
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 0 0
\(543\) 1.00000 1.73205i 0.0429141 0.0743294i
\(544\) 0 0
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) 11.0000 19.0526i 0.469469 0.813143i
\(550\) 0 0
\(551\) 21.0000 0.894630
\(552\) 0 0
\(553\) 4.00000 + 6.92820i 0.170097 + 0.294617i
\(554\) 0 0
\(555\) −3.50000 6.06218i −0.148567 0.257325i
\(556\) 0 0
\(557\) 19.5000 33.7750i 0.826242 1.43109i −0.0747252 0.997204i \(-0.523808\pi\)
0.900967 0.433888i \(-0.142859\pi\)
\(558\) 0 0
\(559\) 38.5000 9.52628i 1.62838 0.402919i
\(560\) 0 0
\(561\) 4.50000 7.79423i 0.189990 0.329073i
\(562\) 0 0
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 0 0
\(565\) −4.50000 7.79423i −0.189316 0.327906i
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −13.5000 + 23.3827i −0.565949 + 0.980253i 0.431011 + 0.902347i \(0.358157\pi\)
−0.996961 + 0.0779066i \(0.975176\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) 0 0
\(575\) −1.50000 + 2.59808i −0.0625543 + 0.108347i
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 2.50000 + 4.33013i 0.103896 + 0.179954i
\(580\) 0 0
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) −9.00000 + 15.5885i −0.372742 + 0.645608i
\(584\) 0 0
\(585\) 7.00000 1.73205i 0.289414 0.0716115i
\(586\) 0 0
\(587\) 16.5000 28.5788i 0.681028 1.17957i −0.293640 0.955916i \(-0.594867\pi\)
0.974668 0.223659i \(-0.0718001\pi\)
\(588\) 0 0
\(589\) −14.0000 24.2487i −0.576860 0.999151i
\(590\) 0 0
\(591\) 10.5000 + 18.1865i 0.431912 + 0.748094i
\(592\) 0 0
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 1.50000 2.59808i 0.0614940 0.106511i
\(596\) 0 0
\(597\) 17.0000 0.695764
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 0 0
\(609\) 1.50000 2.59808i 0.0607831 0.105279i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 21.5000 37.2391i 0.868377 1.50407i 0.00472215 0.999989i \(-0.498497\pi\)
0.863655 0.504084i \(-0.168170\pi\)
\(614\) 0 0
\(615\) −4.50000 7.79423i −0.181458 0.314294i
\(616\) 0 0
\(617\) −16.5000 28.5788i −0.664265 1.15054i −0.979484 0.201522i \(-0.935411\pi\)
0.315219 0.949019i \(-0.397922\pi\)
\(618\) 0 0
\(619\) −44.0000 −1.76851 −0.884255 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) 0 0
\(621\) −7.50000 + 12.9904i −0.300965 + 0.521286i
\(622\) 0 0
\(623\) 15.0000 0.600962
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −10.5000 + 18.1865i −0.419330 + 0.726300i
\(628\) 0 0
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) 8.50000 + 14.7224i 0.338380 + 0.586091i 0.984128 0.177459i \(-0.0567879\pi\)
−0.645748 + 0.763550i \(0.723455\pi\)
\(632\) 0 0
\(633\) −5.50000 9.52628i −0.218605 0.378636i
\(634\) 0 0
\(635\) −9.50000 + 16.4545i −0.376996 + 0.652976i
\(636\) 0 0
\(637\) −15.0000 15.5885i −0.594322 0.617637i
\(638\) 0 0
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 0 0
\(641\) −13.5000 23.3827i −0.533218 0.923561i −0.999247 0.0387913i \(-0.987649\pi\)
0.466029 0.884769i \(-0.345684\pi\)
\(642\) 0 0
\(643\) 5.50000 + 9.52628i 0.216899 + 0.375680i 0.953858 0.300257i \(-0.0970725\pi\)
−0.736959 + 0.675937i \(0.763739\pi\)
\(644\) 0 0
\(645\) 11.0000 0.433125
\(646\) 0 0
\(647\) 22.5000 38.9711i 0.884566 1.53211i 0.0383563 0.999264i \(-0.487788\pi\)
0.846210 0.532850i \(-0.178879\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 0 0
\(653\) 19.5000 33.7750i 0.763094 1.32172i −0.178154 0.984003i \(-0.557013\pi\)
0.941248 0.337715i \(-0.109654\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) 2.00000 + 3.46410i 0.0780274 + 0.135147i
\(658\) 0 0
\(659\) −19.5000 33.7750i −0.759612 1.31569i −0.943049 0.332655i \(-0.892055\pi\)
0.183436 0.983032i \(-0.441278\pi\)
\(660\) 0 0
\(661\) 0.500000 0.866025i 0.0194477 0.0336845i −0.856138 0.516748i \(-0.827143\pi\)
0.875585 + 0.483063i \(0.160476\pi\)
\(662\) 0 0
\(663\) 3.00000 10.3923i 0.116510 0.403604i
\(664\) 0 0
\(665\) −3.50000 + 6.06218i −0.135724 + 0.235081i
\(666\) 0 0
\(667\) −4.50000 7.79423i −0.174241 0.301794i
\(668\) 0 0
\(669\) 9.50000 + 16.4545i 0.367291 + 0.636167i
\(670\) 0 0
\(671\) −33.0000 −1.27395
\(672\) 0 0
\(673\) −8.50000 + 14.7224i −0.327651 + 0.567508i −0.982045 0.188645i \(-0.939590\pi\)
0.654394 + 0.756153i \(0.272924\pi\)
\(674\) 0 0
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) 3.50000 6.06218i 0.134318 0.232645i
\(680\) 0 0
\(681\) 27.0000 1.03464
\(682\) 0 0
\(683\) 25.5000 + 44.1673i 0.975730 + 1.69001i 0.677503 + 0.735520i \(0.263062\pi\)
0.298227 + 0.954495i \(0.403605\pi\)
\(684\) 0 0
\(685\) 7.50000 + 12.9904i 0.286560 + 0.496337i
\(686\) 0 0
\(687\) −11.0000 + 19.0526i −0.419676 + 0.726900i
\(688\) 0 0
\(689\) −6.00000 + 20.7846i −0.228582 + 0.791831i
\(690\) 0 0
\(691\) 11.5000 19.9186i 0.437481 0.757739i −0.560014 0.828483i \(-0.689204\pi\)
0.997494 + 0.0707446i \(0.0225375\pi\)
\(692\) 0 0
\(693\) −3.00000 5.19615i −0.113961 0.197386i
\(694\) 0 0
\(695\) 2.50000 + 4.33013i 0.0948304 + 0.164251i
\(696\) 0 0
\(697\) 27.0000 1.02270
\(698\) 0 0
\(699\) 9.00000 15.5885i 0.340411 0.589610i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −49.0000 −1.84807
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.00000 −0.338480
\(708\) 0 0
\(709\) 18.5000 + 32.0429i 0.694782 + 1.20340i 0.970254 + 0.242089i \(0.0778325\pi\)
−0.275472 + 0.961309i \(0.588834\pi\)
\(710\) 0 0
\(711\) −8.00000 13.8564i −0.300023 0.519656i
\(712\) 0 0
\(713\) −6.00000 + 10.3923i −0.224702 + 0.389195i
\(714\) 0 0
\(715\) −7.50000 7.79423i −0.280484 0.291488i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.50000 + 7.79423i 0.167822 + 0.290676i 0.937654 0.347571i \(-0.112993\pi\)
−0.769832 + 0.638247i \(0.779660\pi\)
\(720\) 0 0
\(721\) 4.00000 + 6.92820i 0.148968 + 0.258020i
\(722\) 0 0
\(723\) 1.00000 0.0371904
\(724\) 0 0
\(725\) −1.50000 + 2.59808i −0.0557086 + 0.0964901i
\(726\) 0 0
\(727\) 52.0000 1.92857 0.964287 0.264861i \(-0.0853260\pi\)
0.964287 + 0.264861i \(0.0853260\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −16.5000 + 28.5788i −0.610275 + 1.05703i
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 0 0
\(735\) −3.00000 5.19615i −0.110657 0.191663i
\(736\) 0 0
\(737\) 10.5000 + 18.1865i 0.386772 + 0.669910i
\(738\) 0 0
\(739\) 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i \(-0.500993\pi\)
0.867581 0.497296i \(-0.165674\pi\)
\(740\) 0 0
\(741\) −7.00000 + 24.2487i −0.257151 + 0.890799i
\(742\) 0 0
\(743\) 10.5000 18.1865i 0.385208 0.667199i −0.606590 0.795015i \(-0.707463\pi\)
0.991798 + 0.127815i \(0.0407965\pi\)
\(744\) 0 0
\(745\) 10.5000 + 18.1865i 0.384690 + 0.666303i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 0 0
\(753\) 21.0000 0.765283
\(754\) 0 0
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −14.5000 + 25.1147i −0.527011 + 0.912811i 0.472493 + 0.881334i \(0.343354\pi\)
−0.999505 + 0.0314762i \(0.989979\pi\)
\(758\) 0 0
\(759\) 9.00000 0.326679
\(760\) 0 0
\(761\) −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i \(-0.183983\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(762\) 0 0
\(763\) −1.00000 1.73205i −0.0362024 0.0627044i
\(764\) 0 0
\(765\) −3.00000 + 5.19615i −0.108465 + 0.187867i
\(766\) 0 0
\(767\) −10.5000 + 2.59808i −0.379133 + 0.0938111i
\(768\) 0 0
\(769\) 6.50000 11.2583i 0.234396 0.405986i −0.724701 0.689063i \(-0.758022\pi\)
0.959097 + 0.283078i \(0.0913554\pi\)
\(770\) 0 0
\(771\) 4.50000 + 7.79423i 0.162064 + 0.280702i
\(772\) 0 0
\(773\) 13.5000 + 23.3827i 0.485561 + 0.841017i 0.999862 0.0165929i \(-0.00528194\pi\)
−0.514301 + 0.857610i \(0.671949\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) −3.50000 + 6.06218i −0.125562 + 0.217479i
\(778\) 0 0
\(779\) −63.0000 −2.25721
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) −7.50000 + 12.9904i −0.268028 + 0.464238i
\(784\) 0 0
\(785\) −10.0000 −0.356915
\(786\) 0 0
\(787\) −18.5000 32.0429i −0.659454 1.14221i −0.980757 0.195231i \(-0.937454\pi\)
0.321303 0.946976i \(-0.395879\pi\)
\(788\) 0 0
\(789\) 1.50000 + 2.59808i 0.0534014 + 0.0924940i
\(790\) 0 0
\(791\) −4.50000 + 7.79423i −0.160002 + 0.277131i
\(792\) 0 0
\(793\) −38.5000 + 9.52628i −1.36718 + 0.338288i
\(794\) 0 0
\(795\) −3.00000 + 5.19615i −0.106399 + 0.184289i
\(796\) 0 0
\(797\) 25.5000 + 44.1673i 0.903256 + 1.56449i 0.823241 + 0.567692i