Properties

Label 370.2.g.b.43.1
Level $370$
Weight $2$
Character 370.43
Analytic conductor $2.954$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 370.43
Dual form 370.2.g.b.327.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +1.00000i q^{8} +3.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +1.00000i q^{8} +3.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +4.00000i q^{13} +(2.00000 + 2.00000i) q^{14} +1.00000 q^{16} -2.00000 q^{17} +3.00000 q^{18} +(2.00000 - 2.00000i) q^{19} +(2.00000 + 1.00000i) q^{20} +4.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +(2.00000 - 2.00000i) q^{28} +(-7.00000 - 7.00000i) q^{29} +(-4.00000 + 4.00000i) q^{31} -1.00000i q^{32} +2.00000i q^{34} +(6.00000 - 2.00000i) q^{35} -3.00000i q^{36} +(-6.00000 + 1.00000i) q^{37} +(-2.00000 - 2.00000i) q^{38} +(1.00000 - 2.00000i) q^{40} +4.00000i q^{43} +(3.00000 - 6.00000i) q^{45} +4.00000 q^{46} +(-2.00000 + 2.00000i) q^{47} -1.00000i q^{49} +(4.00000 - 3.00000i) q^{50} -4.00000i q^{52} +(-1.00000 - 1.00000i) q^{53} +(-2.00000 - 2.00000i) q^{56} +(-7.00000 + 7.00000i) q^{58} +(2.00000 - 2.00000i) q^{59} +(1.00000 - 1.00000i) q^{61} +(4.00000 + 4.00000i) q^{62} +(-6.00000 - 6.00000i) q^{63} -1.00000 q^{64} +(4.00000 - 8.00000i) q^{65} +2.00000 q^{68} +(-2.00000 - 6.00000i) q^{70} +12.0000 q^{71} -3.00000 q^{72} +(-5.00000 + 5.00000i) q^{73} +(1.00000 + 6.00000i) q^{74} +(-2.00000 + 2.00000i) q^{76} +(12.0000 - 12.0000i) q^{79} +(-2.00000 - 1.00000i) q^{80} -9.00000 q^{81} +(4.00000 + 4.00000i) q^{83} +(4.00000 + 2.00000i) q^{85} +4.00000 q^{86} +(-7.00000 - 7.00000i) q^{89} +(-6.00000 - 3.00000i) q^{90} +(-8.00000 - 8.00000i) q^{91} -4.00000i q^{92} +(2.00000 + 2.00000i) q^{94} +(-6.00000 + 2.00000i) q^{95} -12.0000 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 4q^{5} - 4q^{7} + O(q^{10}) \) \( 2q - 2q^{4} - 4q^{5} - 4q^{7} - 2q^{10} + 4q^{14} + 2q^{16} - 4q^{17} + 6q^{18} + 4q^{19} + 4q^{20} + 6q^{25} + 8q^{26} + 4q^{28} - 14q^{29} - 8q^{31} + 12q^{35} - 12q^{37} - 4q^{38} + 2q^{40} + 6q^{45} + 8q^{46} - 4q^{47} + 8q^{50} - 2q^{53} - 4q^{56} - 14q^{58} + 4q^{59} + 2q^{61} + 8q^{62} - 12q^{63} - 2q^{64} + 8q^{65} + 4q^{68} - 4q^{70} + 24q^{71} - 6q^{72} - 10q^{73} + 2q^{74} - 4q^{76} + 24q^{79} - 4q^{80} - 18q^{81} + 8q^{83} + 8q^{85} + 8q^{86} - 14q^{89} - 12q^{90} - 16q^{91} + 4q^{94} - 12q^{95} - 24q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) −2.00000 + 2.00000i −0.755929 + 0.755929i −0.975579 0.219650i \(-0.929509\pi\)
0.219650 + 0.975579i \(0.429509\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 3.00000i 1.00000i
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000 + 2.00000i 0.534522 + 0.534522i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 3.00000 0.707107
\(19\) 2.00000 2.00000i 0.458831 0.458831i −0.439440 0.898272i \(-0.644823\pi\)
0.898272 + 0.439440i \(0.144823\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) 2.00000 2.00000i 0.377964 0.377964i
\(29\) −7.00000 7.00000i −1.29987 1.29987i −0.928477 0.371391i \(-0.878881\pi\)
−0.371391 0.928477i \(-0.621119\pi\)
\(30\) 0 0
\(31\) −4.00000 + 4.00000i −0.718421 + 0.718421i −0.968282 0.249861i \(-0.919615\pi\)
0.249861 + 0.968282i \(0.419615\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 2.00000i 0.342997i
\(35\) 6.00000 2.00000i 1.01419 0.338062i
\(36\) 3.00000i 0.500000i
\(37\) −6.00000 + 1.00000i −0.986394 + 0.164399i
\(38\) −2.00000 2.00000i −0.324443 0.324443i
\(39\) 0 0
\(40\) 1.00000 2.00000i 0.158114 0.316228i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 0 0
\(45\) 3.00000 6.00000i 0.447214 0.894427i
\(46\) 4.00000 0.589768
\(47\) −2.00000 + 2.00000i −0.291730 + 0.291730i −0.837763 0.546033i \(-0.816137\pi\)
0.546033 + 0.837763i \(0.316137\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) −1.00000 1.00000i −0.137361 0.137361i 0.635083 0.772444i \(-0.280966\pi\)
−0.772444 + 0.635083i \(0.780966\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.00000 2.00000i −0.267261 0.267261i
\(57\) 0 0
\(58\) −7.00000 + 7.00000i −0.919145 + 0.919145i
\(59\) 2.00000 2.00000i 0.260378 0.260378i −0.564830 0.825208i \(-0.691058\pi\)
0.825208 + 0.564830i \(0.191058\pi\)
\(60\) 0 0
\(61\) 1.00000 1.00000i 0.128037 0.128037i −0.640184 0.768221i \(-0.721142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 4.00000 + 4.00000i 0.508001 + 0.508001i
\(63\) −6.00000 6.00000i −0.755929 0.755929i
\(64\) −1.00000 −0.125000
\(65\) 4.00000 8.00000i 0.496139 0.992278i
\(66\) 0 0
\(67\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) −2.00000 6.00000i −0.239046 0.717137i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −3.00000 −0.353553
\(73\) −5.00000 + 5.00000i −0.585206 + 0.585206i −0.936329 0.351123i \(-0.885800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 1.00000 + 6.00000i 0.116248 + 0.697486i
\(75\) 0 0
\(76\) −2.00000 + 2.00000i −0.229416 + 0.229416i
\(77\) 0 0
\(78\) 0 0
\(79\) 12.0000 12.0000i 1.35011 1.35011i 0.464568 0.885537i \(-0.346210\pi\)
0.885537 0.464568i \(-0.153790\pi\)
\(80\) −2.00000 1.00000i −0.223607 0.111803i
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) 4.00000 + 4.00000i 0.439057 + 0.439057i 0.891695 0.452638i \(-0.149517\pi\)
−0.452638 + 0.891695i \(0.649517\pi\)
\(84\) 0 0
\(85\) 4.00000 + 2.00000i 0.433861 + 0.216930i
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 0 0
\(89\) −7.00000 7.00000i −0.741999 0.741999i 0.230964 0.972962i \(-0.425812\pi\)
−0.972962 + 0.230964i \(0.925812\pi\)
\(90\) −6.00000 3.00000i −0.632456 0.316228i
\(91\) −8.00000 8.00000i −0.838628 0.838628i
\(92\) 4.00000i 0.417029i
\(93\) 0 0
\(94\) 2.00000 + 2.00000i 0.206284 + 0.206284i
\(95\) −6.00000 + 2.00000i −0.615587 + 0.205196i
\(96\) 0 0
\(97\) −12.0000 −1.21842 −0.609208 0.793011i \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 10.0000i 0.995037i 0.867453 + 0.497519i \(0.165755\pi\)
−0.867453 + 0.497519i \(0.834245\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) −1.00000 + 1.00000i −0.0971286 + 0.0971286i
\(107\) 8.00000 8.00000i 0.773389 0.773389i −0.205308 0.978697i \(-0.565820\pi\)
0.978697 + 0.205308i \(0.0658197\pi\)
\(108\) 0 0
\(109\) −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i \(-0.815129\pi\)
0.548683 + 0.836031i \(0.315129\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.00000 + 2.00000i −0.188982 + 0.188982i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 4.00000 8.00000i 0.373002 0.746004i
\(116\) 7.00000 + 7.00000i 0.649934 + 0.649934i
\(117\) −12.0000 −1.10940
\(118\) −2.00000 2.00000i −0.184115 0.184115i
\(119\) 4.00000 4.00000i 0.366679 0.366679i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) −1.00000 1.00000i −0.0905357 0.0905357i
\(123\) 0 0
\(124\) 4.00000 4.00000i 0.359211 0.359211i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) −6.00000 + 6.00000i −0.534522 + 0.534522i
\(127\) −2.00000 + 2.00000i −0.177471 + 0.177471i −0.790253 0.612781i \(-0.790051\pi\)
0.612781 + 0.790253i \(0.290051\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −8.00000 4.00000i −0.701646 0.350823i
\(131\) 6.00000 6.00000i 0.524222 0.524222i −0.394621 0.918844i \(-0.629124\pi\)
0.918844 + 0.394621i \(0.129124\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) 0 0
\(135\) 0 0
\(136\) 2.00000i 0.171499i
\(137\) −7.00000 + 7.00000i −0.598050 + 0.598050i −0.939793 0.341743i \(-0.888983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −6.00000 + 2.00000i −0.507093 + 0.169031i
\(141\) 0 0
\(142\) 12.0000i 1.00702i
\(143\) 0 0
\(144\) 3.00000i 0.250000i
\(145\) 7.00000 + 21.0000i 0.581318 + 1.74396i
\(146\) 5.00000 + 5.00000i 0.413803 + 0.413803i
\(147\) 0 0
\(148\) 6.00000 1.00000i 0.493197 0.0821995i
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 0 0
\(151\) 20.0000i 1.62758i 0.581161 + 0.813788i \(0.302599\pi\)
−0.581161 + 0.813788i \(0.697401\pi\)
\(152\) 2.00000 + 2.00000i 0.162221 + 0.162221i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 12.0000 4.00000i 0.963863 0.321288i
\(156\) 0 0
\(157\) −7.00000 + 7.00000i −0.558661 + 0.558661i −0.928926 0.370265i \(-0.879267\pi\)
0.370265 + 0.928926i \(0.379267\pi\)
\(158\) −12.0000 12.0000i −0.954669 0.954669i
\(159\) 0 0
\(160\) −1.00000 + 2.00000i −0.0790569 + 0.158114i
\(161\) −8.00000 8.00000i −0.630488 0.630488i
\(162\) 9.00000i 0.707107i
\(163\) 24.0000 1.87983 0.939913 0.341415i \(-0.110906\pi\)
0.939913 + 0.341415i \(0.110906\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 4.00000 4.00000i 0.310460 0.310460i
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 2.00000 4.00000i 0.153393 0.306786i
\(171\) 6.00000 + 6.00000i 0.458831 + 0.458831i
\(172\) 4.00000i 0.304997i
\(173\) 5.00000 5.00000i 0.380143 0.380143i −0.491011 0.871154i \(-0.663372\pi\)
0.871154 + 0.491011i \(0.163372\pi\)
\(174\) 0 0
\(175\) −14.0000 2.00000i −1.05830 0.151186i
\(176\) 0 0
\(177\) 0 0
\(178\) −7.00000 + 7.00000i −0.524672 + 0.524672i
\(179\) −2.00000 2.00000i −0.149487 0.149487i 0.628402 0.777889i \(-0.283709\pi\)
−0.777889 + 0.628402i \(0.783709\pi\)
\(180\) −3.00000 + 6.00000i −0.223607 + 0.447214i
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) −8.00000 + 8.00000i −0.592999 + 0.592999i
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) 13.0000 + 4.00000i 0.955779 + 0.294086i
\(186\) 0 0
\(187\) 0 0
\(188\) 2.00000 2.00000i 0.145865 0.145865i
\(189\) 0 0
\(190\) 2.00000 + 6.00000i 0.145095 + 0.435286i
\(191\) 16.0000 + 16.0000i 1.15772 + 1.15772i 0.984965 + 0.172754i \(0.0552667\pi\)
0.172754 + 0.984965i \(0.444733\pi\)
\(192\) 0 0
\(193\) 14.0000i 1.00774i 0.863779 + 0.503871i \(0.168091\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 12.0000i 0.861550i
\(195\) 0 0
\(196\) 1.00000i 0.0714286i
\(197\) 3.00000 3.00000i 0.213741 0.213741i −0.592113 0.805855i \(-0.701706\pi\)
0.805855 + 0.592113i \(0.201706\pi\)
\(198\) 0 0
\(199\) 8.00000 + 8.00000i 0.567105 + 0.567105i 0.931316 0.364211i \(-0.118661\pi\)
−0.364211 + 0.931316i \(0.618661\pi\)
\(200\) −4.00000 + 3.00000i −0.282843 + 0.212132i
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 28.0000 1.96521
\(204\) 0 0
\(205\) 0 0
\(206\) 16.0000i 1.11477i
\(207\) −12.0000 −0.834058
\(208\) 4.00000i 0.277350i
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 1.00000 + 1.00000i 0.0686803 + 0.0686803i
\(213\) 0 0
\(214\) −8.00000 8.00000i −0.546869 0.546869i
\(215\) 4.00000 8.00000i 0.272798 0.545595i
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 3.00000 + 3.00000i 0.203186 + 0.203186i
\(219\) 0 0
\(220\) 0 0
\(221\) 8.00000i 0.538138i
\(222\) 0 0
\(223\) −6.00000 6.00000i −0.401790 0.401790i 0.477074 0.878863i \(-0.341698\pi\)
−0.878863 + 0.477074i \(0.841698\pi\)
\(224\) 2.00000 + 2.00000i 0.133631 + 0.133631i
\(225\) −12.0000 + 9.00000i −0.800000 + 0.600000i
\(226\) 14.0000i 0.931266i
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 0 0
\(229\) 16.0000i 1.05731i 0.848837 + 0.528655i \(0.177303\pi\)
−0.848837 + 0.528655i \(0.822697\pi\)
\(230\) −8.00000 4.00000i −0.527504 0.263752i
\(231\) 0 0
\(232\) 7.00000 7.00000i 0.459573 0.459573i
\(233\) −5.00000 + 5.00000i −0.327561 + 0.327561i −0.851658 0.524097i \(-0.824403\pi\)
0.524097 + 0.851658i \(0.324403\pi\)
\(234\) 12.0000i 0.784465i
\(235\) 6.00000 2.00000i 0.391397 0.130466i
\(236\) −2.00000 + 2.00000i −0.130189 + 0.130189i
\(237\) 0 0
\(238\) −4.00000 4.00000i −0.259281 0.259281i
\(239\) −8.00000 + 8.00000i −0.517477 + 0.517477i −0.916807 0.399330i \(-0.869243\pi\)
0.399330 + 0.916807i \(0.369243\pi\)
\(240\) 0 0
\(241\) −19.0000 19.0000i −1.22390 1.22390i −0.966235 0.257663i \(-0.917048\pi\)
−0.257663 0.966235i \(-0.582952\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 0 0
\(244\) −1.00000 + 1.00000i −0.0640184 + 0.0640184i
\(245\) −1.00000 + 2.00000i −0.0638877 + 0.127775i
\(246\) 0 0
\(247\) 8.00000 + 8.00000i 0.509028 + 0.509028i
\(248\) −4.00000 4.00000i −0.254000 0.254000i
\(249\) 0 0
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) −14.0000 + 14.0000i −0.883672 + 0.883672i −0.993906 0.110234i \(-0.964840\pi\)
0.110234 + 0.993906i \(0.464840\pi\)
\(252\) 6.00000 + 6.00000i 0.377964 + 0.377964i
\(253\) 0 0
\(254\) 2.00000 + 2.00000i 0.125491 + 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 10.0000 14.0000i 0.621370 0.869918i
\(260\) −4.00000 + 8.00000i −0.248069 + 0.496139i
\(261\) 21.0000 21.0000i 1.29987 1.29987i
\(262\) −6.00000 6.00000i −0.370681 0.370681i
\(263\) −10.0000 + 10.0000i −0.616626 + 0.616626i −0.944664 0.328038i \(-0.893613\pi\)
0.328038 + 0.944664i \(0.393613\pi\)
\(264\) 0 0
\(265\) 1.00000 + 3.00000i 0.0614295 + 0.184289i
\(266\) 8.00000 0.490511
\(267\) 0 0
\(268\) 0 0
\(269\) 14.0000i 0.853595i −0.904347 0.426798i \(-0.859642\pi\)
0.904347 0.426798i \(-0.140358\pi\)
\(270\) 0 0
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 7.00000 + 7.00000i 0.422885 + 0.422885i
\(275\) 0 0
\(276\) 0 0
\(277\) 12.0000i 0.721010i 0.932757 + 0.360505i \(0.117396\pi\)
−0.932757 + 0.360505i \(0.882604\pi\)
\(278\) 20.0000i 1.19952i
\(279\) −12.0000 12.0000i −0.718421 0.718421i
\(280\) 2.00000 + 6.00000i 0.119523 + 0.358569i
\(281\) 1.00000 + 1.00000i 0.0596550 + 0.0596550i 0.736305 0.676650i \(-0.236569\pi\)
−0.676650 + 0.736305i \(0.736569\pi\)
\(282\) 0 0
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) −13.0000 −0.764706
\(290\) 21.0000 7.00000i 1.23316 0.411054i
\(291\) 0 0
\(292\) 5.00000 5.00000i 0.292603 0.292603i
\(293\) 9.00000 + 9.00000i 0.525786 + 0.525786i 0.919313 0.393527i \(-0.128745\pi\)
−0.393527 + 0.919313i \(0.628745\pi\)
\(294\) 0 0
\(295\) −6.00000 + 2.00000i −0.349334 + 0.116445i
\(296\) −1.00000 6.00000i −0.0581238 0.348743i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −16.0000 −0.925304
\(300\) 0 0
\(301\) −8.00000 8.00000i −0.461112 0.461112i
\(302\) 20.0000 1.15087
\(303\) 0 0
\(304\) 2.00000 2.00000i 0.114708 0.114708i
\(305\) −3.00000 + 1.00000i −0.171780 + 0.0572598i
\(306\) −6.00000 −0.342997
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.00000 12.0000i −0.227185 0.681554i
\(311\) −4.00000 + 4.00000i −0.226819 + 0.226819i −0.811363 0.584543i \(-0.801274\pi\)
0.584543 + 0.811363i \(0.301274\pi\)
\(312\) 0 0
\(313\) 26.0000i 1.46961i −0.678280 0.734803i \(-0.737274\pi\)
0.678280 0.734803i \(-0.262726\pi\)
\(314\) 7.00000 + 7.00000i 0.395033 + 0.395033i
\(315\) 6.00000 + 18.0000i 0.338062 + 1.01419i
\(316\) −12.0000 + 12.0000i −0.675053 + 0.675053i
\(317\) −5.00000 5.00000i −0.280828 0.280828i 0.552611 0.833439i \(-0.313631\pi\)
−0.833439 + 0.552611i \(0.813631\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 2.00000 + 1.00000i 0.111803 + 0.0559017i
\(321\) 0 0
\(322\) −8.00000 + 8.00000i −0.445823 + 0.445823i
\(323\) −4.00000 + 4.00000i −0.222566 + 0.222566i
\(324\) 9.00000 0.500000
\(325\) −16.0000 + 12.0000i −0.887520 + 0.665640i
\(326\) 24.0000i 1.32924i
\(327\) 0 0
\(328\) 0 0
\(329\) 8.00000i 0.441054i
\(330\) 0 0
\(331\) 6.00000 + 6.00000i 0.329790 + 0.329790i 0.852506 0.522717i \(-0.175081\pi\)
−0.522717 + 0.852506i \(0.675081\pi\)
\(332\) −4.00000 4.00000i −0.219529 0.219529i
\(333\) −3.00000 18.0000i −0.164399 0.986394i
\(334\) 8.00000i 0.437741i
\(335\) 0 0
\(336\) 0 0
\(337\) 15.0000 + 15.0000i 0.817102 + 0.817102i 0.985687 0.168585i \(-0.0539198\pi\)
−0.168585 + 0.985687i \(0.553920\pi\)
\(338\) 3.00000i 0.163178i
\(339\) 0 0
\(340\) −4.00000 2.00000i −0.216930 0.108465i
\(341\) 0 0
\(342\) 6.00000 6.00000i 0.324443 0.324443i
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) −5.00000 5.00000i −0.268802 0.268802i
\(347\) 12.0000i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(348\) 0 0
\(349\) 14.0000i 0.749403i −0.927146 0.374701i \(-0.877745\pi\)
0.927146 0.374701i \(-0.122255\pi\)
\(350\) −2.00000 + 14.0000i −0.106904 + 0.748331i
\(351\) 0 0
\(352\) 0 0
\(353\) −36.0000 −1.91609 −0.958043 0.286623i \(-0.907467\pi\)
−0.958043 + 0.286623i \(0.907467\pi\)
\(354\) 0 0
\(355\) −24.0000 12.0000i −1.27379 0.636894i
\(356\) 7.00000 + 7.00000i 0.370999 + 0.370999i
\(357\) 0 0
\(358\) −2.00000 + 2.00000i −0.105703 + 0.105703i
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) 6.00000 + 3.00000i 0.316228 + 0.158114i
\(361\) 11.0000i 0.578947i
\(362\) 8.00000i 0.420471i
\(363\) 0 0
\(364\) 8.00000 + 8.00000i 0.419314 + 0.419314i
\(365\) 15.0000 5.00000i 0.785136 0.261712i
\(366\) 0 0
\(367\) 18.0000 18.0000i 0.939592 0.939592i −0.0586842 0.998277i \(-0.518691\pi\)
0.998277 + 0.0586842i \(0.0186905\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 0 0
\(370\) 4.00000 13.0000i 0.207950 0.675838i
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −25.0000 + 25.0000i −1.29445 + 1.29445i −0.362446 + 0.932005i \(0.618058\pi\)
−0.932005 + 0.362446i \(0.881942\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.00000 2.00000i −0.103142 0.103142i
\(377\) 28.0000 28.0000i 1.44207 1.44207i
\(378\) 0 0
\(379\) 4.00000i 0.205466i −0.994709 0.102733i \(-0.967241\pi\)
0.994709 0.102733i \(-0.0327588\pi\)
\(380\) 6.00000 2.00000i 0.307794 0.102598i
\(381\) 0 0
\(382\) 16.0000 16.0000i 0.818631 0.818631i
\(383\) 36.0000i 1.83951i −0.392488 0.919757i \(-0.628386\pi\)
0.392488 0.919757i \(-0.371614\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) −12.0000 −0.609994
\(388\) 12.0000 0.609208
\(389\) 17.0000 17.0000i 0.861934 0.861934i −0.129628 0.991563i \(-0.541378\pi\)
0.991563 + 0.129628i \(0.0413785\pi\)
\(390\) 0 0
\(391\) 8.00000i 0.404577i
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −3.00000 3.00000i −0.151138 0.151138i
\(395\) −36.0000 + 12.0000i −1.81136 + 0.603786i
\(396\) 0 0
\(397\) 25.0000 + 25.0000i 1.25471 + 1.25471i 0.953583 + 0.301131i \(0.0973643\pi\)
0.301131 + 0.953583i \(0.402636\pi\)
\(398\) 8.00000 8.00000i 0.401004 0.401004i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 1.00000 1.00000i 0.0499376 0.0499376i −0.681697 0.731635i \(-0.738758\pi\)
0.731635 + 0.681697i \(0.238758\pi\)
\(402\) 0 0
\(403\) −16.0000 16.0000i −0.797017 0.797017i
\(404\) 10.0000i 0.497519i
\(405\) 18.0000 + 9.00000i 0.894427 + 0.447214i
\(406\) 28.0000i 1.38962i
\(407\) 0 0
\(408\) 0 0
\(409\) 13.0000 + 13.0000i 0.642809 + 0.642809i 0.951245 0.308436i \(-0.0998057\pi\)
−0.308436 + 0.951245i \(0.599806\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 16.0000 0.788263
\(413\) 8.00000i 0.393654i
\(414\) 12.0000i 0.589768i
\(415\) −4.00000 12.0000i −0.196352 0.589057i
\(416\) 4.00000 0.196116
\(417\) 0 0
\(418\) 0 0
\(419\) 36.0000i 1.75872i 0.476162 + 0.879358i \(0.342028\pi\)
−0.476162 + 0.879358i \(0.657972\pi\)
\(420\) 0 0
\(421\) 11.0000 11.0000i 0.536107 0.536107i −0.386276 0.922383i \(-0.626239\pi\)
0.922383 + 0.386276i \(0.126239\pi\)
\(422\) 8.00000i 0.389434i
\(423\) −6.00000 6.00000i −0.291730 0.291730i
\(424\) 1.00000 1.00000i 0.0485643 0.0485643i
\(425\) −6.00000 8.00000i −0.291043 0.388057i
\(426\) 0 0
\(427\) 4.00000i 0.193574i
\(428\) −8.00000 + 8.00000i −0.386695 + 0.386695i
\(429\) 0 0
\(430\) −8.00000 4.00000i −0.385794 0.192897i
\(431\) −4.00000 + 4.00000i −0.192673 + 0.192673i −0.796850 0.604177i \(-0.793502\pi\)
0.604177 + 0.796850i \(0.293502\pi\)
\(432\) 0 0
\(433\) −21.0000 21.0000i −1.00920 1.00920i −0.999957 0.00923827i \(-0.997059\pi\)
−0.00923827 0.999957i \(-0.502941\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 3.00000 3.00000i 0.143674 0.143674i
\(437\) 8.00000 + 8.00000i 0.382692 + 0.382692i
\(438\) 0 0
\(439\) 8.00000 + 8.00000i 0.381819 + 0.381819i 0.871757 0.489938i \(-0.162981\pi\)
−0.489938 + 0.871757i \(0.662981\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −8.00000 −0.380521
\(443\) 20.0000 20.0000i 0.950229 0.950229i −0.0485901 0.998819i \(-0.515473\pi\)
0.998819 + 0.0485901i \(0.0154728\pi\)
\(444\) 0 0
\(445\) 7.00000 + 21.0000i 0.331832 + 0.995495i
\(446\) −6.00000 + 6.00000i −0.284108 + 0.284108i
\(447\) 0 0
\(448\) 2.00000 2.00000i 0.0944911 0.0944911i
\(449\) −23.0000 + 23.0000i −1.08544 + 1.08544i −0.0894454 + 0.995992i \(0.528509\pi\)
−0.995992 + 0.0894454i \(0.971491\pi\)
\(450\) 9.00000 + 12.0000i 0.424264 + 0.565685i
\(451\) 0 0
\(452\) −14.0000 −0.658505
\(453\) 0 0
\(454\) 12.0000i 0.563188i
\(455\) 8.00000 + 24.0000i 0.375046 + 1.12514i
\(456\) 0 0
\(457\) 28.0000 1.30978 0.654892 0.755722i \(-0.272714\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(458\) 16.0000 0.747631
\(459\) 0 0
\(460\) −4.00000 + 8.00000i −0.186501 + 0.373002i
\(461\) −19.0000 19.0000i −0.884918 0.884918i 0.109111 0.994030i \(-0.465200\pi\)
−0.994030 + 0.109111i \(0.965200\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i 0.995671 + 0.0929479i \(0.0296290\pi\)
−0.995671 + 0.0929479i \(0.970371\pi\)
\(464\) −7.00000 7.00000i −0.324967 0.324967i
\(465\) 0 0
\(466\) 5.00000 + 5.00000i 0.231621 + 0.231621i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 12.0000 0.554700
\(469\) 0 0
\(470\) −2.00000 6.00000i −0.0922531 0.276759i
\(471\) 0 0
\(472\) 2.00000 + 2.00000i 0.0920575 + 0.0920575i
\(473\) 0 0
\(474\) 0 0
\(475\) 14.0000 + 2.00000i 0.642364 + 0.0917663i
\(476\) −4.00000 + 4.00000i −0.183340 + 0.183340i
\(477\) 3.00000 3.00000i 0.137361 0.137361i
\(478\) 8.00000 + 8.00000i 0.365911 + 0.365911i
\(479\) −28.0000 + 28.0000i −1.27935 + 1.27935i −0.338322 + 0.941030i \(0.609859\pi\)
−0.941030 + 0.338322i \(0.890141\pi\)
\(480\) 0 0
\(481\) −4.00000 24.0000i −0.182384 1.09431i
\(482\) −19.0000 + 19.0000i −0.865426 + 0.865426i
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 24.0000 + 12.0000i 1.08978 + 0.544892i
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 1.00000 + 1.00000i 0.0452679 + 0.0452679i
\(489\) 0 0
\(490\) 2.00000 + 1.00000i 0.0903508 + 0.0451754i
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 0 0
\(493\) 14.0000 + 14.0000i 0.630528 + 0.630528i
\(494\) 8.00000 8.00000i 0.359937 0.359937i
\(495\) 0 0
\(496\) −4.00000 + 4.00000i −0.179605 + 0.179605i
\(497\) −24.0000 + 24.0000i −1.07655 + 1.07655i
\(498\) 0 0
\(499\) −2.00000 2.00000i −0.0895323 0.0895323i 0.660922 0.750454i \(-0.270165\pi\)
−0.750454 + 0.660922i \(0.770165\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 14.0000 + 14.0000i 0.624851 + 0.624851i
\(503\) 16.0000i 0.713405i −0.934218 0.356702i \(-0.883901\pi\)
0.934218 0.356702i \(-0.116099\pi\)
\(504\) 6.00000 6.00000i 0.267261 0.267261i
\(505\) 10.0000 20.0000i 0.444994 0.889988i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 2.00000i 0.0887357 0.0887357i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) 20.0000i 0.884748i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000i 0.793946i
\(515\) 32.0000 + 16.0000i 1.41009 + 0.705044i
\(516\) 0 0
\(517\) 0 0
\(518\) −14.0000 10.0000i −0.615125 0.439375i
\(519\) 0 0
\(520\) 8.00000 + 4.00000i 0.350823 + 0.175412i
\(521\) 10.0000i 0.438108i −0.975713 0.219054i \(-0.929703\pi\)
0.975713 0.219054i \(-0.0702971\pi\)
\(522\) −21.0000 21.0000i −0.919145 0.919145i
\(523\) 24.0000i 1.04945i 0.851273 + 0.524723i \(0.175831\pi\)
−0.851273 + 0.524723i \(0.824169\pi\)
\(524\) −6.00000 + 6.00000i −0.262111 + 0.262111i
\(525\) 0 0
\(526\) 10.0000 + 10.0000i 0.436021 + 0.436021i
\(527\) 8.00000 8.00000i 0.348485 0.348485i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 3.00000 1.00000i 0.130312 0.0434372i
\(531\) 6.00000 + 6.00000i 0.260378 + 0.260378i
\(532\) 8.00000i 0.346844i
\(533\) 0 0
\(534\) 0 0
\(535\) −24.0000 + 8.00000i −1.03761 + 0.345870i
\(536\) 0 0
\(537\) 0 0
\(538\) −14.0000 −0.603583
\(539\) 0 0
\(540\) 0 0
\(541\) 11.0000 + 11.0000i 0.472927 + 0.472927i 0.902861 0.429934i \(-0.141463\pi\)
−0.429934 + 0.902861i \(0.641463\pi\)
\(542\) 28.0000i 1.20270i
\(543\) 0 0
\(544\) 2.00000i 0.0857493i
\(545\) 9.00000 3.00000i 0.385518 0.128506i
\(546\) 0 0
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 7.00000 7.00000i 0.299025 0.299025i
\(549\) 3.00000 + 3.00000i 0.128037 + 0.128037i
\(550\) 0 0
\(551\) −28.0000 −1.19284
\(552\) 0 0
\(553\) 48.0000i 2.04117i
\(554\) 12.0000 0.509831
\(555\) 0 0
\(556\) −20.0000 −0.848189
\(557\) 12.0000i 0.508456i 0.967144 + 0.254228i \(0.0818214\pi\)
−0.967144 + 0.254228i \(0.918179\pi\)
\(558\) −12.0000 + 12.0000i −0.508001 + 0.508001i
\(559\) −16.0000 −0.676728
\(560\) 6.00000 2.00000i 0.253546 0.0845154i
\(561\) 0 0
\(562\) 1.00000 1.00000i 0.0421825 0.0421825i
\(563\) 24.0000i 1.01148i 0.862686 + 0.505740i \(0.168780\pi\)
−0.862686 + 0.505740i \(0.831220\pi\)
\(564\) 0 0
\(565\) −28.0000 14.0000i −1.17797 0.588984i
\(566\) 24.0000i 1.00880i
\(567\) 18.0000 18.0000i 0.755929 0.755929i
\(568\) 12.0000i 0.503509i
\(569\) 3.00000 + 3.00000i 0.125767 + 0.125767i 0.767188 0.641422i \(-0.221655\pi\)
−0.641422 + 0.767188i \(0.721655\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16.0000 + 12.0000i −0.667246 + 0.500435i
\(576\) 3.00000i 0.125000i
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 0 0
\(580\) −7.00000 21.0000i −0.290659 0.871978i
\(581\) −16.0000 −0.663792
\(582\) 0 0
\(583\) 0 0
\(584\) −5.00000 5.00000i −0.206901 0.206901i
\(585\) 24.0000 + 12.0000i 0.992278 + 0.496139i
\(586\) 9.00000 9.00000i 0.371787 0.371787i
\(587\) 28.0000i 1.15568i −0.816149 0.577842i \(-0.803895\pi\)
0.816149 0.577842i \(-0.196105\pi\)
\(588\) 0 0
\(589\) 16.0000i 0.659269i
\(590\) 2.00000 + 6.00000i 0.0823387 + 0.247016i
\(591\) 0 0
\(592\) −6.00000 + 1.00000i −0.246598 + 0.0410997i
\(593\) −1.00000 1.00000i −0.0410651 0.0410651i 0.686276 0.727341i \(-0.259244\pi\)
−0.727341 + 0.686276i \(0.759244\pi\)
\(594\) 0 0
\(595\) −12.0000 + 4.00000i −0.491952 + 0.163984i
\(596\) 6.00000i 0.245770i
\(597\) 0 0
\(598\) 16.0000i 0.654289i
\(599\) 36.0000i 1.47092i 0.677568 + 0.735460i \(0.263034\pi\)
−0.677568 + 0.735460i \(0.736966\pi\)
\(600\) 0 0
\(601\) 32.0000 1.30531 0.652654 0.757656i \(-0.273656\pi\)
0.652654 + 0.757656i \(0.273656\pi\)
\(602\) −8.00000 + 8.00000i −0.326056 + 0.326056i
\(603\) 0 0
\(604\) 20.0000i 0.813788i
\(605\) −22.0000 11.0000i −0.894427 0.447214i
\(606\) 0 0
\(607\) 12.0000i 0.487065i 0.969893 + 0.243532i \(0.0783062\pi\)
−0.969893 + 0.243532i \(0.921694\pi\)
\(608\) −2.00000 2.00000i −0.0811107 0.0811107i
\(609\) 0 0
\(610\) 1.00000 + 3.00000i 0.0404888 + 0.121466i
\(611\) −8.00000 8.00000i −0.323645 0.323645i
\(612\) 6.00000i 0.242536i
\(613\) −5.00000 + 5.00000i −0.201948 + 0.201948i −0.800834 0.598886i \(-0.795610\pi\)
0.598886 + 0.800834i \(0.295610\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0000 + 15.0000i 0.603877 + 0.603877i 0.941339 0.337462i \(-0.109568\pi\)
−0.337462 + 0.941339i \(0.609568\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) −12.0000 + 4.00000i −0.481932 + 0.160644i
\(621\) 0 0
\(622\) 4.00000 + 4.00000i 0.160385 + 0.160385i
\(623\) 28.0000 1.12180
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −26.0000 −1.03917
\(627\) 0 0
\(628\) 7.00000 7.00000i 0.279330 0.279330i
\(629\) 12.0000 2.00000i 0.478471 0.0797452i
\(630\) 18.0000 6.00000i 0.717137 0.239046i
\(631\) 16.0000 16.0000i 0.636950 0.636950i −0.312852 0.949802i \(-0.601284\pi\)
0.949802 + 0.312852i \(0.101284\pi\)
\(632\) 12.0000 + 12.0000i 0.477334 + 0.477334i
\(633\) 0 0
\(634\) −5.00000 + 5.00000i −0.198575 + 0.198575i
\(635\) 6.00000 2.00000i 0.238103 0.0793676i
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) 36.0000i 1.42414i
\(640\) 1.00000 2.00000i 0.0395285 0.0790569i
\(641\) −48.0000 −1.89589 −0.947943 0.318440i \(-0.896841\pi\)
−0.947943 + 0.318440i \(0.896841\pi\)
\(642\) 0 0
\(643\) 44.0000 1.73519 0.867595 0.497271i \(-0.165665\pi\)
0.867595 + 0.497271i \(0.165665\pi\)
\(644\) 8.00000 + 8.00000i 0.315244 + 0.315244i
\(645\) 0 0
\(646\) 4.00000 + 4.00000i 0.157378 + 0.157378i
\(647\) 32.0000i 1.25805i 0.777385 + 0.629025i \(0.216546\pi\)
−0.777385 + 0.629025i \(0.783454\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 0 0
\(650\) 12.0000 + 16.0000i 0.470679 + 0.627572i
\(651\) 0 0
\(652\) −24.0000 −0.939913
\(653\) 4.00000 0.156532 0.0782660 0.996933i \(-0.475062\pi\)
0.0782660 + 0.996933i \(0.475062\pi\)
\(654\) 0 0
\(655\) −18.0000 + 6.00000i −0.703318 + 0.234439i
\(656\) 0 0
\(657\) −15.0000 15.0000i −0.585206 0.585206i
\(658\) −8.00000 −0.311872
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) 21.0000 21.0000i 0.816805 0.816805i −0.168838 0.985644i \(-0.554002\pi\)
0.985644 + 0.168838i \(0.0540016\pi\)
\(662\) 6.00000 6.00000i 0.233197 0.233197i
\(663\) 0 0
\(664\) −4.00000 + 4.00000i −0.155230 + 0.155230i
\(665\) 8.00000 16.0000i 0.310227 0.620453i
\(666\) −18.0000 + 3.00000i −0.697486 + 0.116248i
\(667\) 28.0000 28.0000i 1.08416 1.08416i
\(668\) −8.00000 −0.309529
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 9.00000 + 9.00000i 0.346925 + 0.346925i 0.858963 0.512038i \(-0.171109\pi\)
−0.512038 + 0.858963i \(0.671109\pi\)
\(674\) 15.0000 15.0000i 0.577778 0.577778i
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −25.0000 25.0000i −0.960828 0.960828i 0.0384331 0.999261i \(-0.487763\pi\)
−0.999261 + 0.0384331i \(0.987763\pi\)
\(678\) 0 0
\(679\) 24.0000 24.0000i 0.921035 0.921035i
\(680\) −2.00000 + 4.00000i −0.0766965 + 0.153393i
\(681\) 0 0
\(682\) 0 0
\(683\) 36.0000i 1.37750i −0.724998 0.688751i \(-0.758159\pi\)
0.724998 0.688751i \(-0.241841\pi\)
\(684\) −6.00000 6.00000i −0.229416 0.229416i
\(685\) 21.0000 7.00000i 0.802369 0.267456i
\(686\) −12.0000 + 12.0000i −0.458162 + 0.458162i
\(687\) 0 0
\(688\) 4.00000i 0.152499i
\(689\) 4.00000 4.00000i 0.152388 0.152388i
\(690\) 0 0
\(691\) 20.0000i 0.760836i 0.924815 + 0.380418i \(0.124220\pi\)
−0.924815 + 0.380418i \(0.875780\pi\)
\(692\) −5.00000 + 5.00000i −0.190071 + 0.190071i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −40.0000 20.0000i −1.51729 0.758643i
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 −0.529908
\(699\) 0 0
\(700\) 14.0000 + 2.00000i 0.529150 + 0.0755929i
\(701\) 31.0000 + 31.0000i 1.17085 + 1.17085i 0.982006 + 0.188847i \(0.0604752\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) −10.0000 + 14.0000i −0.377157 + 0.528020i
\(704\) 0 0
\(705\) 0 0
\(706\) 36.0000i 1.35488i
\(707\) −20.0000 20.0000i −0.752177 0.752177i
\(708\) 0 0
\(709\) 27.0000 27.0000i 1.01401 1.01401i 0.0141058 0.999901i \(-0.495510\pi\)
0.999901 0.0141058i \(-0.00449016\pi\)
\(710\) −12.0000 + 24.0000i −0.450352 + 0.900704i
\(711\) 36.0000 + 36.0000i 1.35011 + 1.35011i
\(712\) 7.00000 7.00000i 0.262336 0.262336i
\(713\) −16.0000 16.0000i −0.599205 0.599205i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000 + 2.00000i 0.0747435 + 0.0747435i
\(717\) 0 0
\(718\) −24.0000 −0.895672
\(719\) 4.00000i 0.149175i −0.997214 0.0745874i \(-0.976236\pi\)
0.997214 0.0745874i \(-0.0237640\pi\)
\(720\) 3.00000 6.00000i 0.111803 0.223607i
\(721\) 32.0000 32.0000i 1.19174 1.19174i
\(722\) 11.0000 0.409378
\(723\) 0 0
\(724\) 8.00000 0.297318
\(725\) 7.00000 49.0000i 0.259973 1.81981i
\(726\) 0 0
\(727\) 28.0000i 1.03846i −0.854634 0.519231i \(-0.826218\pi\)
0.854634 0.519231i \(-0.173782\pi\)
\(728\) 8.00000 8.00000i 0.296500 0.296500i
\(729\) 27.0000i 1.00000i
\(730\) −5.00000 15.0000i −0.185058 0.555175i
\(731\) 8.00000i 0.295891i
\(732\) 0 0
\(733\) 15.0000 15.0000i 0.554038 0.554038i −0.373566 0.927604i \(-0.621865\pi\)
0.927604 + 0.373566i \(0.121865\pi\)
\(734\) −18.0000 18.0000i −0.664392 0.664392i
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 0 0
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −13.0000 4.00000i −0.477890 0.147043i
\(741\) 0 0
\(742\) 4.00000i 0.146845i
\(743\) 10.0000 10.0000i 0.366864 0.366864i −0.499468 0.866332i \(-0.666471\pi\)
0.866332 + 0.499468i \(0.166471\pi\)
\(744\) 0 0
\(745\) 6.00000 12.0000i 0.219823 0.439646i
\(746\) 25.0000 + 25.0000i 0.915315 + 0.915315i
\(747\) −12.0000 + 12.0000i −0.439057 + 0.439057i
\(748\) 0 0
\(749\) 32.0000i 1.16925i
\(750\) 0 0
\(751\) 40.0000i 1.45962i 0.683650 + 0.729810i \(0.260392\pi\)
−0.683650 + 0.729810i \(0.739608\pi\)
\(752\) −2.00000 + 2.00000i −0.0729325 + 0.0729325i
\(753\) 0 0
\(754\) −28.0000 28.0000i −1.01970 1.01970i
\(755\) 20.0000 40.0000i 0.727875 1.45575i
\(756\) 0 0
\(757\) 28.0000 1.01768 0.508839 0.860862i \(-0.330075\pi\)
0.508839 + 0.860862i \(0.330075\pi\)
\(758\) −4.00000 −0.145287
\(759\) 0 0
\(760\) −2.00000 6.00000i −0.0725476 0.217643i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 12.0000i 0.434429i
\(764\) −16.0000 16.0000i −0.578860 0.578860i
\(765\) −6.00000 + 12.0000i −0.216930 + 0.433861i
\(766\) −36.0000 −1.30073
\(767\) 8.00000 + 8.00000i 0.288863 + 0.288863i
\(768\) 0 0
\(769\) 3.00000 + 3.00000i 0.108183 + 0.108183i 0.759126 0.650943i \(-0.225627\pi\)
−0.650943 + 0.759126i \(0.725627\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 14.0000i 0.503871i
\(773\) −21.0000 21.0000i −0.755318 0.755318i 0.220149 0.975466i \(-0.429346\pi\)
−0.975466 + 0.220149i \(0.929346\pi\)
\(774\) 12.0000i 0.431331i
\(775\) −28.0000 4.00000i −1.00579 0.143684i
\(776\) 12.0000i 0.430775i
\(777\) 0 0
\(778\) −17.0000 17.0000i −0.609480 0.609480i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 21.0000 7.00000i 0.749522 0.249841i
\(786\) 0 0
\(787\) −12.0000 + 12.0000i −0.427754 + 0.427754i −0.887863 0.460109i \(-0.847810\pi\)
0.460109 + 0.887863i \(0.347810\pi\)
\(788\) −3.00000 + 3.00000i −0.106871 + 0.106871i
\(789\) 0 0
\(790\) 12.0000 + 36.0000i 0.426941 + 1.28082i