Properties

Label 370.2.g.b.327.1
Level $370$
Weight $2$
Character 370.327
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 327.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 370.327
Dual form 370.2.g.b.43.1

$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) −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 0.219650 0.975579i \(-0.429509\pi\)
−0.975579 + 0.219650i \(0.929509\pi\)
\(8\) 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 \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 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 0.898272 0.439440i \(-0.144823\pi\)
−0.439440 + 0.898272i \(0.644823\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 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 −0.371391 + 0.928477i \(0.621119\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) −4.00000 4.00000i −0.718421 0.718421i 0.249861 0.968282i \(-0.419615\pi\)
−0.968282 + 0.249861i \(0.919615\pi\)
\(32\) 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 \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 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 0.546033 0.837763i \(-0.316137\pi\)
−0.837763 + 0.546033i \(0.816137\pi\)
\(48\) 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 −0.772444 0.635083i \(-0.780966\pi\)
0.635083 + 0.772444i \(0.280966\pi\)
\(54\) 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 0.825208 0.564830i \(-0.191058\pi\)
−0.564830 + 0.825208i \(0.691058\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.00000i 0.128037 + 0.128037i 0.768221 0.640184i \(-0.221142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 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 0.351123 0.936329i \(-0.385800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 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 0.885537 + 0.464568i \(0.153790\pi\)
0.464568 + 0.885537i \(0.346210\pi\)
\(80\) −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 −0.452638 0.891695i \(-0.649517\pi\)
0.891695 + 0.452638i \(0.149517\pi\)
\(84\) 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 −0.972962 0.230964i \(-0.925812\pi\)
0.230964 + 0.972962i \(0.425812\pi\)
\(90\) −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 \(-0.834245\pi\)
0.867453 0.497519i \(-0.165755\pi\)
\(102\) 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 0.978697 0.205308i \(-0.0658197\pi\)
−0.205308 + 0.978697i \(0.565820\pi\)
\(108\) 0 0
\(109\) −3.00000 3.00000i −0.287348 0.287348i 0.548683 0.836031i \(-0.315129\pi\)
−0.836031 + 0.548683i \(0.815129\pi\)
\(110\) 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 0.612781 0.790253i \(-0.290051\pi\)
−0.790253 + 0.612781i \(0.790051\pi\)
\(128\) 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 0.918844 0.394621i \(-0.129124\pi\)
−0.394621 + 0.918844i \(0.629124\pi\)
\(132\) 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 0.341743 0.939793i \(-0.388983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 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 \(-0.920959\pi\)
0.969328 0.245770i \(-0.0790407\pi\)
\(150\) 0 0
\(151\) 20.0000i 1.62758i −0.581161 0.813788i \(-0.697401\pi\)
0.581161 0.813788i \(-0.302599\pi\)
\(152\) 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 0.370265 0.928926i \(-0.379267\pi\)
−0.928926 + 0.370265i \(0.879267\pi\)
\(158\) −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 0.871154 0.491011i \(-0.163372\pi\)
−0.491011 + 0.871154i \(0.663372\pi\)
\(174\) 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 −0.777889 0.628402i \(-0.783709\pi\)
0.628402 + 0.777889i \(0.283709\pi\)
\(180\) −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 0.172754 0.984965i \(-0.444733\pi\)
0.984965 0.172754i \(-0.0552667\pi\)
\(192\) 0 0
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 12.0000i 0.861550i
\(195\) 0 0
\(196\) 1.00000i 0.0714286i
\(197\) 3.00000 + 3.00000i 0.213741 + 0.213741i 0.805855 0.592113i \(-0.201706\pi\)
−0.592113 + 0.805855i \(0.701706\pi\)
\(198\) 0 0
\(199\) 8.00000 8.00000i 0.567105 0.567105i −0.364211 0.931316i \(-0.618661\pi\)
0.931316 + 0.364211i \(0.118661\pi\)
\(200\) −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 −0.878863 0.477074i \(-0.841698\pi\)
0.477074 + 0.878863i \(0.341698\pi\)
\(224\) 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 \(-0.822697\pi\)
0.848837 0.528655i \(-0.177303\pi\)
\(230\) −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 0.524097 0.851658i \(-0.324403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 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 0.399330 0.916807i \(-0.369243\pi\)
−0.916807 + 0.399330i \(0.869243\pi\)
\(240\) 0 0
\(241\) −19.0000 + 19.0000i −1.22390 + 1.22390i −0.257663 + 0.966235i \(0.582952\pi\)
−0.966235 + 0.257663i \(0.917048\pi\)
\(242\) 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 0.110234 0.993906i \(-0.464840\pi\)
−0.993906 + 0.110234i \(0.964840\pi\)
\(252\) 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 0.328038 0.944664i \(-0.393613\pi\)
−0.944664 + 0.328038i \(0.893613\pi\)
\(264\) 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 \(0.140358\pi\)
−0.904347 + 0.426798i \(0.859642\pi\)
\(270\) 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 \(-0.882604\pi\)
0.932757 0.360505i \(-0.117396\pi\)
\(278\) 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 −0.676650 0.736305i \(-0.736569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(282\) 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 −0.393527 0.919313i \(-0.628745\pi\)
0.919313 + 0.393527i \(0.128745\pi\)
\(294\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.00000 + 12.0000i −0.227185 + 0.681554i
\(311\) −4.00000 4.00000i −0.226819 0.226819i 0.584543 0.811363i \(-0.301274\pi\)
−0.811363 + 0.584543i \(0.801274\pi\)
\(312\) 0 0
\(313\) 26.0000i 1.46961i 0.678280 + 0.734803i \(0.262726\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(314\) 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 −0.833439 0.552611i \(-0.813631\pi\)
0.552611 + 0.833439i \(0.313631\pi\)
\(318\) 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 −0.522717 0.852506i \(-0.675081\pi\)
0.852506 + 0.522717i \(0.175081\pi\)
\(332\) −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 −0.168585 0.985687i \(-0.553920\pi\)
0.985687 + 0.168585i \(0.0539198\pi\)
\(338\) 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 \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 0 0
\(349\) 14.0000i 0.749403i 0.927146 + 0.374701i \(0.122255\pi\)
−0.927146 + 0.374701i \(0.877745\pi\)
\(350\) −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 \(0.218315\pi\)
−0.773877 + 0.633336i \(0.781685\pi\)
\(360\) 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 0.998277 0.0586842i \(-0.0186905\pi\)
−0.0586842 + 0.998277i \(0.518691\pi\)
\(368\) 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 −0.932005 0.362446i \(-0.881942\pi\)
−0.362446 0.932005i \(-0.618058\pi\)
\(374\) 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 \(0.0327588\pi\)
−0.994709 + 0.102733i \(0.967241\pi\)
\(380\) 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 \(0.371614\pi\)
−0.392488 + 0.919757i \(0.628386\pi\)
\(384\) 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 0.991563 0.129628i \(-0.0413785\pi\)
−0.129628 + 0.991563i \(0.541378\pi\)
\(390\) 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 0.301131 0.953583i \(-0.402636\pi\)
0.953583 0.301131i \(-0.0973643\pi\)
\(398\) 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 0.731635 0.681697i \(-0.238758\pi\)
−0.681697 + 0.731635i \(0.738758\pi\)
\(402\) 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 −0.308436 0.951245i \(-0.599806\pi\)
0.951245 + 0.308436i \(0.0998057\pi\)
\(410\) 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 \(-0.657972\pi\)
0.476162 0.879358i \(-0.342028\pi\)
\(420\) 0 0
\(421\) 11.0000 + 11.0000i 0.536107 + 0.536107i 0.922383 0.386276i \(-0.126239\pi\)
−0.386276 + 0.922383i \(0.626239\pi\)
\(422\) 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 0.604177 0.796850i \(-0.293502\pi\)
−0.796850 + 0.604177i \(0.793502\pi\)
\(432\) 0 0
\(433\) −21.0000 + 21.0000i −1.00920 + 1.00920i −0.00923827 + 0.999957i \(0.502941\pi\)
−0.999957 + 0.00923827i \(0.997059\pi\)
\(434\) −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 −0.489938 0.871757i \(-0.662981\pi\)
0.871757 + 0.489938i \(0.162981\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −8.00000 −0.380521
\(443\) 20.0000 + 20.0000i 0.950229 + 0.950229i 0.998819 0.0485901i \(-0.0154728\pi\)
−0.0485901 + 0.998819i \(0.515473\pi\)
\(444\) 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 −0.995992 0.0894454i \(-0.971491\pi\)
−0.0894454 0.995992i \(-0.528509\pi\)
\(450\) 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 −0.994030 0.109111i \(-0.965200\pi\)
0.109111 + 0.994030i \(0.465200\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) −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 −0.941030 0.338322i \(-0.890141\pi\)
−0.338322 0.941030i \(-0.609859\pi\)
\(480\) 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 −0.750454 0.660922i \(-0.770165\pi\)
0.660922 + 0.750454i \(0.270165\pi\)
\(500\) 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 \(0.116099\pi\)
−0.934218 + 0.356702i \(0.883901\pi\)
\(504\) 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 \(0.0702971\pi\)
−0.975713 + 0.219054i \(0.929703\pi\)
\(522\) −21.0000 + 21.0000i −0.919145 + 0.919145i
\(523\) 24.0000i 1.04945i −0.851273 0.524723i \(-0.824169\pi\)
0.851273 0.524723i \(-0.175831\pi\)
\(524\) −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 −0.429934 0.902861i \(-0.641463\pi\)
0.902861 + 0.429934i \(0.141463\pi\)
\(542\) 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 \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) 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 \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) −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 \(-0.831220\pi\)
0.862686 0.505740i \(-0.168780\pi\)
\(564\) 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 −0.641422 0.767188i \(-0.721655\pi\)
0.767188 + 0.641422i \(0.221655\pi\)
\(570\) 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 \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) 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 −0.727341 0.686276i \(-0.759244\pi\)
0.686276 + 0.727341i \(0.259244\pi\)
\(594\) 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 \(-0.736966\pi\)
0.677568 0.735460i \(-0.263034\pi\)
\(600\) 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 \(-0.921694\pi\)
0.969893 0.243532i \(-0.0783062\pi\)
\(608\) −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 0.598886 0.800834i \(-0.295610\pi\)
−0.800834 + 0.598886i \(0.795610\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0000 15.0000i 0.603877 0.603877i −0.337462 0.941339i \(-0.609568\pi\)
0.941339 + 0.337462i \(0.109568\pi\)
\(618\) 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 0.949802 0.312852i \(-0.101284\pi\)
−0.312852 + 0.949802i \(0.601284\pi\)
\(632\) 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 \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 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 0.985644 0.168838i \(-0.0540016\pi\)
−0.168838 + 0.985644i \(0.554002\pi\)
\(662\) 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 −0.512038 0.858963i \(-0.671109\pi\)
0.858963 + 0.512038i \(0.171109\pi\)
\(674\) 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 −0.999261 0.0384331i \(-0.987763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 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 \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) −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 \(-0.875780\pi\)
0.924815 0.380418i \(-0.124220\pi\)
\(692\) −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 0.188847 0.982006i \(-0.439525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) 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 0.999901 + 0.0141058i \(0.00449016\pi\)
0.0141058 + 0.999901i \(0.495510\pi\)
\(710\) −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 \(0.0237640\pi\)
−0.997214 + 0.0745874i \(0.976236\pi\)
\(720\) 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 \(0.173782\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(728\) 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 0.927604 0.373566i \(-0.121865\pi\)
−0.373566 + 0.927604i \(0.621865\pi\)
\(734\) −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 0.866332 0.499468i \(-0.166471\pi\)
−0.499468 + 0.866332i \(0.666471\pi\)
\(744\) 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 \(-0.739608\pi\)
0.683650 0.729810i \(-0.260392\pi\)
\(752\) −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 −0.650943 0.759126i \(-0.725627\pi\)
0.759126 + 0.650943i \(0.225627\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 14.0000i 0.503871i
\(773\) −21.0000 + 21.0000i −0.755318 + 0.755318i −0.975466 0.220149i \(-0.929346\pi\)
0.220149 + 0.975466i \(0.429346\pi\)
\(774\) 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 0.460109 0.887863i \(-0.347810\pi\)
−0.887863 + 0.460109i \(0.847810\pi\)
\(788\) −3.00000 3.00000i −0.106871 0.106871i
\(789\) 0 0
\(790\) 12.0000 36.0000i 0.426941 1.28082i