Properties

Label 1170.2.bs.h.361.4
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.4
Root \(-2.21837 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.h.901.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(3.84233 + 2.21837i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(3.84233 + 2.21837i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(2.84233 - 2.21837i) q^{13} +4.43674 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.842329 + 0.486319i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-0.379706 - 0.657671i) q^{23} -1.00000 q^{25} +(1.35234 - 3.34233i) q^{26} +(3.84233 - 2.21837i) q^{28} +(4.81645 + 8.34233i) q^{29} +6.16879i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.21837 + 3.84233i) q^{35} +(-1.50000 + 0.866025i) q^{37} +0.972638 q^{38} +1.00000 q^{40} +(5.19615 - 3.00000i) q^{41} +(1.34233 - 2.32498i) q^{43} +3.00000i q^{44} +(-0.657671 - 0.379706i) q^{46} -3.00000i q^{47} +(6.34233 + 10.9852i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-0.500000 - 3.57071i) q^{52} -4.43674 q^{53} +(-1.50000 - 2.59808i) q^{55} +(2.21837 - 3.84233i) q^{56} +(8.34233 + 4.81645i) q^{58} +(-4.05703 - 2.34233i) q^{59} +(5.68466 - 9.84612i) q^{61} +(3.08440 + 5.34233i) q^{62} -1.00000 q^{64} +(2.21837 + 2.84233i) q^{65} +(10.6847 - 6.16879i) q^{67} +4.43674i q^{70} +(-5.19615 - 3.00000i) q^{71} -6.92820i q^{73} +(-0.866025 + 1.50000i) q^{74} +(0.842329 - 0.486319i) q^{76} -13.3102 q^{77} -6.68466 q^{79} +(0.866025 - 0.500000i) q^{80} +(3.00000 - 5.19615i) q^{82} +9.36932i q^{83} -2.68466i q^{86} +(1.50000 + 2.59808i) q^{88} +(6.65511 - 3.84233i) q^{89} +(15.8423 - 2.21837i) q^{91} -0.759413 q^{92} +(-1.50000 - 2.59808i) q^{94} +(-0.486319 + 0.842329i) q^{95} +(4.68466 + 2.70469i) q^{97} +(10.9852 + 6.34233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 6 q^{7} + O(q^{10}) \) \( 8 q + 4 q^{4} + 6 q^{7} + 4 q^{10} - 2 q^{13} - 4 q^{16} - 18 q^{19} - 12 q^{22} - 8 q^{25} + 6 q^{28} - 12 q^{37} + 8 q^{40} - 14 q^{43} - 30 q^{46} + 26 q^{49} - 4 q^{52} - 12 q^{55} + 42 q^{58} - 4 q^{61} - 8 q^{64} + 36 q^{67} - 18 q^{76} - 4 q^{79} + 24 q^{82} + 12 q^{88} + 102 q^{91} - 12 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 3.84233 + 2.21837i 1.45226 + 0.838465i 0.998610 0.0527128i \(-0.0167868\pi\)
0.453654 + 0.891178i \(0.350120\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −2.59808 + 1.50000i −0.783349 + 0.452267i −0.837616 0.546259i \(-0.816051\pi\)
0.0542666 + 0.998526i \(0.482718\pi\)
\(12\) 0 0
\(13\) 2.84233 2.21837i 0.788320 0.615265i
\(14\) 4.43674 1.18577
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 0.842329 + 0.486319i 0.193244 + 0.111569i 0.593500 0.804834i \(-0.297746\pi\)
−0.400257 + 0.916403i \(0.631079\pi\)
\(20\) 0.866025 + 0.500000i 0.193649 + 0.111803i
\(21\) 0 0
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) −0.379706 0.657671i −0.0791743 0.137134i 0.823720 0.566997i \(-0.191895\pi\)
−0.902894 + 0.429863i \(0.858562\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 1.35234 3.34233i 0.265217 0.655485i
\(27\) 0 0
\(28\) 3.84233 2.21837i 0.726132 0.419232i
\(29\) 4.81645 + 8.34233i 0.894392 + 1.54913i 0.834556 + 0.550923i \(0.185724\pi\)
0.0598358 + 0.998208i \(0.480942\pi\)
\(30\) 0 0
\(31\) 6.16879i 1.10795i 0.832534 + 0.553974i \(0.186889\pi\)
−0.832534 + 0.553974i \(0.813111\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 0 0
\(35\) −2.21837 + 3.84233i −0.374973 + 0.649472i
\(36\) 0 0
\(37\) −1.50000 + 0.866025i −0.246598 + 0.142374i −0.618206 0.786016i \(-0.712140\pi\)
0.371607 + 0.928390i \(0.378807\pi\)
\(38\) 0.972638 0.157783
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 5.19615 3.00000i 0.811503 0.468521i −0.0359748 0.999353i \(-0.511454\pi\)
0.847477 + 0.530831i \(0.178120\pi\)
\(42\) 0 0
\(43\) 1.34233 2.32498i 0.204703 0.354556i −0.745335 0.666690i \(-0.767710\pi\)
0.950038 + 0.312134i \(0.101044\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 0 0
\(46\) −0.657671 0.379706i −0.0969683 0.0559847i
\(47\) 3.00000i 0.437595i −0.975770 0.218797i \(-0.929787\pi\)
0.975770 0.218797i \(-0.0702134\pi\)
\(48\) 0 0
\(49\) 6.34233 + 10.9852i 0.906047 + 1.56932i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 0 0
\(52\) −0.500000 3.57071i −0.0693375 0.495169i
\(53\) −4.43674 −0.609433 −0.304717 0.952443i \(-0.598562\pi\)
−0.304717 + 0.952443i \(0.598562\pi\)
\(54\) 0 0
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) 2.21837 3.84233i 0.296442 0.513453i
\(57\) 0 0
\(58\) 8.34233 + 4.81645i 1.09540 + 0.632430i
\(59\) −4.05703 2.34233i −0.528181 0.304945i 0.212095 0.977249i \(-0.431972\pi\)
−0.740275 + 0.672304i \(0.765305\pi\)
\(60\) 0 0
\(61\) 5.68466 9.84612i 0.727846 1.26067i −0.229946 0.973203i \(-0.573855\pi\)
0.957792 0.287463i \(-0.0928117\pi\)
\(62\) 3.08440 + 5.34233i 0.391719 + 0.678476i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.21837 + 2.84233i 0.275155 + 0.352548i
\(66\) 0 0
\(67\) 10.6847 6.16879i 1.30534 0.753638i 0.324024 0.946049i \(-0.394964\pi\)
0.981314 + 0.192411i \(0.0616307\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 4.43674i 0.530292i
\(71\) −5.19615 3.00000i −0.616670 0.356034i 0.158901 0.987294i \(-0.449205\pi\)
−0.775571 + 0.631260i \(0.782538\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) −0.866025 + 1.50000i −0.100673 + 0.174371i
\(75\) 0 0
\(76\) 0.842329 0.486319i 0.0966218 0.0557846i
\(77\) −13.3102 −1.51684
\(78\) 0 0
\(79\) −6.68466 −0.752083 −0.376041 0.926603i \(-0.622715\pi\)
−0.376041 + 0.926603i \(0.622715\pi\)
\(80\) 0.866025 0.500000i 0.0968246 0.0559017i
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 9.36932i 1.02842i 0.857665 + 0.514208i \(0.171914\pi\)
−0.857665 + 0.514208i \(0.828086\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.68466i 0.289494i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 6.65511 3.84233i 0.705440 0.407286i −0.103930 0.994585i \(-0.533142\pi\)
0.809370 + 0.587299i \(0.199809\pi\)
\(90\) 0 0
\(91\) 15.8423 2.21837i 1.66073 0.232548i
\(92\) −0.759413 −0.0791743
\(93\) 0 0
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −0.486319 + 0.842329i −0.0498953 + 0.0864212i
\(96\) 0 0
\(97\) 4.68466 + 2.70469i 0.475655 + 0.274620i 0.718604 0.695420i \(-0.244781\pi\)
−0.242949 + 0.970039i \(0.578115\pi\)
\(98\) 10.9852 + 6.34233i 1.10968 + 0.640672i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −8.87348 15.3693i −0.882944 1.52930i −0.848052 0.529913i \(-0.822225\pi\)
−0.0348922 0.999391i \(-0.511109\pi\)
\(102\) 0 0
\(103\) −2.31534 −0.228137 −0.114069 0.993473i \(-0.536388\pi\)
−0.114069 + 0.993473i \(0.536388\pi\)
\(104\) −2.21837 2.84233i −0.217529 0.278713i
\(105\) 0 0
\(106\) −3.84233 + 2.21837i −0.373200 + 0.215467i
\(107\) −4.43674 7.68466i −0.428916 0.742904i 0.567861 0.823124i \(-0.307771\pi\)
−0.996777 + 0.0802202i \(0.974438\pi\)
\(108\) 0 0
\(109\) 1.94528i 0.186324i 0.995651 + 0.0931618i \(0.0296974\pi\)
−0.995651 + 0.0931618i \(0.970303\pi\)
\(110\) −2.59808 1.50000i −0.247717 0.143019i
\(111\) 0 0
\(112\) 4.43674i 0.419232i
\(113\) −4.81645 + 8.34233i −0.453093 + 0.784780i −0.998576 0.0533414i \(-0.983013\pi\)
0.545483 + 0.838122i \(0.316346\pi\)
\(114\) 0 0
\(115\) 0.657671 0.379706i 0.0613281 0.0354078i
\(116\) 9.63289 0.894392
\(117\) 0 0
\(118\) −4.68466 −0.431258
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) 11.3693i 1.02933i
\(123\) 0 0
\(124\) 5.34233 + 3.08440i 0.479755 + 0.276987i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 4.84233 + 8.38716i 0.429687 + 0.744240i 0.996845 0.0793688i \(-0.0252905\pi\)
−0.567158 + 0.823609i \(0.691957\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 3.34233 + 1.35234i 0.293142 + 0.118608i
\(131\) 6.71498 0.586690 0.293345 0.956007i \(-0.405231\pi\)
0.293345 + 0.956007i \(0.405231\pi\)
\(132\) 0 0
\(133\) 2.15767 + 3.73720i 0.187094 + 0.324056i
\(134\) 6.16879 10.6847i 0.532902 0.923014i
\(135\) 0 0
\(136\) 0 0
\(137\) 6.33527 + 3.65767i 0.541259 + 0.312496i 0.745589 0.666406i \(-0.232168\pi\)
−0.204330 + 0.978902i \(0.565502\pi\)
\(138\) 0 0
\(139\) −10.8423 + 18.7795i −0.919634 + 1.59285i −0.119664 + 0.992814i \(0.538182\pi\)
−0.799971 + 0.600039i \(0.795152\pi\)
\(140\) 2.21837 + 3.84233i 0.187486 + 0.324736i
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) −4.05703 + 10.0270i −0.339266 + 0.838499i
\(144\) 0 0
\(145\) −8.34233 + 4.81645i −0.692793 + 0.399984i
\(146\) −3.46410 6.00000i −0.286691 0.496564i
\(147\) 0 0
\(148\) 1.73205i 0.142374i
\(149\) −19.6455 11.3423i −1.60942 0.929200i −0.989500 0.144536i \(-0.953831\pi\)
−0.619922 0.784664i \(-0.712836\pi\)
\(150\) 0 0
\(151\) 14.2829i 1.16232i −0.813788 0.581161i \(-0.802599\pi\)
0.813788 0.581161i \(-0.197401\pi\)
\(152\) 0.486319 0.842329i 0.0394457 0.0683219i
\(153\) 0 0
\(154\) −11.5270 + 6.65511i −0.928871 + 0.536284i
\(155\) −6.16879 −0.495489
\(156\) 0 0
\(157\) −16.3693 −1.30641 −0.653207 0.757180i \(-0.726577\pi\)
−0.653207 + 0.757180i \(0.726577\pi\)
\(158\) −5.78908 + 3.34233i −0.460555 + 0.265901i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 3.36932i 0.265539i
\(162\) 0 0
\(163\) −9.65767 5.57586i −0.756447 0.436735i 0.0715715 0.997435i \(-0.477199\pi\)
−0.828019 + 0.560701i \(0.810532\pi\)
\(164\) 6.00000i 0.468521i
\(165\) 0 0
\(166\) 4.68466 + 8.11407i 0.363600 + 0.629774i
\(167\) −15.9083 + 9.18466i −1.23102 + 0.710730i −0.967243 0.253853i \(-0.918302\pi\)
−0.263778 + 0.964583i \(0.584969\pi\)
\(168\) 0 0
\(169\) 3.15767 12.6107i 0.242898 0.970052i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.34233 2.32498i −0.102352 0.177278i
\(173\) −6.65511 + 11.5270i −0.505979 + 0.876381i 0.493997 + 0.869463i \(0.335535\pi\)
−0.999976 + 0.00691731i \(0.997798\pi\)
\(174\) 0 0
\(175\) −3.84233 2.21837i −0.290453 0.167693i
\(176\) 2.59808 + 1.50000i 0.195837 + 0.113067i
\(177\) 0 0
\(178\) 3.84233 6.65511i 0.287995 0.498822i
\(179\) −10.0126 17.3423i −0.748377 1.29623i −0.948600 0.316476i \(-0.897500\pi\)
0.200224 0.979750i \(-0.435833\pi\)
\(180\) 0 0
\(181\) −19.3693 −1.43971 −0.719855 0.694124i \(-0.755792\pi\)
−0.719855 + 0.694124i \(0.755792\pi\)
\(182\) 12.6107 9.84233i 0.934765 0.729562i
\(183\) 0 0
\(184\) −0.657671 + 0.379706i −0.0484841 + 0.0279923i
\(185\) −0.866025 1.50000i −0.0636715 0.110282i
\(186\) 0 0
\(187\) 0 0
\(188\) −2.59808 1.50000i −0.189484 0.109399i
\(189\) 0 0
\(190\) 0.972638i 0.0705626i
\(191\) 3.67733 6.36932i 0.266082 0.460868i −0.701765 0.712409i \(-0.747604\pi\)
0.967847 + 0.251541i \(0.0809375\pi\)
\(192\) 0 0
\(193\) 1.31534 0.759413i 0.0946804 0.0546637i −0.451912 0.892062i \(-0.649258\pi\)
0.546593 + 0.837399i \(0.315925\pi\)
\(194\) 5.40938 0.388371
\(195\) 0 0
\(196\) 12.6847 0.906047
\(197\) 14.7692 8.52699i 1.05226 0.607523i 0.128979 0.991647i \(-0.458830\pi\)
0.923281 + 0.384125i \(0.125497\pi\)
\(198\) 0 0
\(199\) −3.68466 + 6.38202i −0.261199 + 0.452409i −0.966561 0.256438i \(-0.917451\pi\)
0.705362 + 0.708847i \(0.250784\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) −15.3693 8.87348i −1.08138 0.624336i
\(203\) 42.7386i 2.99966i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) −2.00514 + 1.15767i −0.139705 + 0.0806587i
\(207\) 0 0
\(208\) −3.34233 1.35234i −0.231749 0.0937682i
\(209\) −2.91791 −0.201836
\(210\) 0 0
\(211\) −2.84233 4.92306i −0.195674 0.338917i 0.751447 0.659793i \(-0.229356\pi\)
−0.947121 + 0.320876i \(0.896023\pi\)
\(212\) −2.21837 + 3.84233i −0.152358 + 0.263892i
\(213\) 0 0
\(214\) −7.68466 4.43674i −0.525312 0.303289i
\(215\) 2.32498 + 1.34233i 0.158562 + 0.0915461i
\(216\) 0 0
\(217\) −13.6847 + 23.7025i −0.928975 + 1.60903i
\(218\) 0.972638 + 1.68466i 0.0658754 + 0.114099i
\(219\) 0 0
\(220\) −3.00000 −0.202260
\(221\) 0 0
\(222\) 0 0
\(223\) 12.8423 7.41452i 0.859986 0.496513i −0.00402162 0.999992i \(-0.501280\pi\)
0.864008 + 0.503479i \(0.167947\pi\)
\(224\) −2.21837 3.84233i −0.148221 0.256726i
\(225\) 0 0
\(226\) 9.63289i 0.640770i
\(227\) 18.5064 + 10.6847i 1.22831 + 0.709166i 0.966676 0.256001i \(-0.0824051\pi\)
0.261635 + 0.965167i \(0.415738\pi\)
\(228\) 0 0
\(229\) 11.9111i 0.787110i −0.919301 0.393555i \(-0.871245\pi\)
0.919301 0.393555i \(-0.128755\pi\)
\(230\) 0.379706 0.657671i 0.0250371 0.0433655i
\(231\) 0 0
\(232\) 8.34233 4.81645i 0.547701 0.316215i
\(233\) 20.0252 1.31189 0.655947 0.754807i \(-0.272269\pi\)
0.655947 + 0.754807i \(0.272269\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) −4.05703 + 2.34233i −0.264090 + 0.152473i
\(237\) 0 0
\(238\) 0 0
\(239\) 24.7386i 1.60021i 0.599861 + 0.800105i \(0.295223\pi\)
−0.599861 + 0.800105i \(0.704777\pi\)
\(240\) 0 0
\(241\) −18.1847 10.4989i −1.17138 0.676295i −0.217373 0.976089i \(-0.569749\pi\)
−0.954004 + 0.299794i \(0.903082\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) −5.68466 9.84612i −0.363923 0.630333i
\(245\) −10.9852 + 6.34233i −0.701821 + 0.405197i
\(246\) 0 0
\(247\) 3.47301 0.486319i 0.220982 0.0309437i
\(248\) 6.16879 0.391719
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −2.59808 + 4.50000i −0.163989 + 0.284037i −0.936296 0.351212i \(-0.885770\pi\)
0.772307 + 0.635250i \(0.219103\pi\)
\(252\) 0 0
\(253\) 1.97301 + 1.13912i 0.124042 + 0.0716158i
\(254\) 8.38716 + 4.84233i 0.526257 + 0.303835i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −15.2088 26.3423i −0.948696 1.64319i −0.748177 0.663500i \(-0.769070\pi\)
−0.200519 0.979690i \(-0.564263\pi\)
\(258\) 0 0
\(259\) −7.68466 −0.477501
\(260\) 3.57071 0.500000i 0.221446 0.0310087i
\(261\) 0 0
\(262\) 5.81534 3.35749i 0.359273 0.207426i
\(263\) 5.51599 + 9.55398i 0.340131 + 0.589123i 0.984457 0.175627i \(-0.0561954\pi\)
−0.644326 + 0.764751i \(0.722862\pi\)
\(264\) 0 0
\(265\) 4.43674i 0.272547i
\(266\) 3.73720 + 2.15767i 0.229142 + 0.132295i
\(267\) 0 0
\(268\) 12.3376i 0.753638i
\(269\) 8.87348 15.3693i 0.541026 0.937084i −0.457820 0.889045i \(-0.651370\pi\)
0.998845 0.0480388i \(-0.0152971\pi\)
\(270\) 0 0
\(271\) −7.02699 + 4.05703i −0.426859 + 0.246447i −0.698008 0.716090i \(-0.745930\pi\)
0.271149 + 0.962538i \(0.412597\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 7.31534 0.441936
\(275\) 2.59808 1.50000i 0.156670 0.0904534i
\(276\) 0 0
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 21.6847i 1.30056i
\(279\) 0 0
\(280\) 3.84233 + 2.21837i 0.229623 + 0.132573i
\(281\) 24.7386i 1.47578i −0.674919 0.737892i \(-0.735822\pi\)
0.674919 0.737892i \(-0.264178\pi\)
\(282\) 0 0
\(283\) −12.0270 20.8314i −0.714930 1.23830i −0.962986 0.269550i \(-0.913125\pi\)
0.248056 0.968746i \(-0.420208\pi\)
\(284\) −5.19615 + 3.00000i −0.308335 + 0.178017i
\(285\) 0 0
\(286\) 1.50000 + 10.7121i 0.0886969 + 0.633422i
\(287\) 26.6204 1.57135
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −4.81645 + 8.34233i −0.282831 + 0.489878i
\(291\) 0 0
\(292\) −6.00000 3.46410i −0.351123 0.202721i
\(293\) −8.93335 5.15767i −0.521892 0.301314i 0.215817 0.976434i \(-0.430759\pi\)
−0.737708 + 0.675120i \(0.764092\pi\)
\(294\) 0 0
\(295\) 2.34233 4.05703i 0.136376 0.236210i
\(296\) 0.866025 + 1.50000i 0.0503367 + 0.0871857i
\(297\) 0 0
\(298\) −22.6847 −1.31409
\(299\) −2.53821 1.02699i −0.146788 0.0593922i
\(300\) 0 0
\(301\) 10.3153 5.95557i 0.594566 0.343273i
\(302\) −7.14143 12.3693i −0.410943 0.711774i
\(303\) 0 0
\(304\) 0.972638i 0.0557846i
\(305\) 9.84612 + 5.68466i 0.563787 + 0.325503i
\(306\) 0 0
\(307\) 14.2829i 0.815166i 0.913168 + 0.407583i \(0.133628\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) −6.65511 + 11.5270i −0.379210 + 0.656811i
\(309\) 0 0
\(310\) −5.34233 + 3.08440i −0.303424 + 0.175182i
\(311\) 19.2658 1.09246 0.546231 0.837634i \(-0.316062\pi\)
0.546231 + 0.837634i \(0.316062\pi\)
\(312\) 0 0
\(313\) 19.3693 1.09482 0.547409 0.836865i \(-0.315614\pi\)
0.547409 + 0.836865i \(0.315614\pi\)
\(314\) −14.1762 + 8.18466i −0.800012 + 0.461887i
\(315\) 0 0
\(316\) −3.34233 + 5.78908i −0.188021 + 0.325661i
\(317\) 32.4233i 1.82107i −0.413428 0.910537i \(-0.635669\pi\)
0.413428 0.910537i \(-0.364331\pi\)
\(318\) 0 0
\(319\) −25.0270 14.4493i −1.40124 0.809008i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −1.68466 2.91791i −0.0938823 0.162609i
\(323\) 0 0
\(324\) 0 0
\(325\) −2.84233 + 2.21837i −0.157664 + 0.123053i
\(326\) −11.1517 −0.617637
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) 6.65511 11.5270i 0.366908 0.635503i
\(330\) 0 0
\(331\) −29.0540 16.7743i −1.59695 0.922000i −0.992070 0.125684i \(-0.959888\pi\)
−0.604881 0.796316i \(-0.706779\pi\)
\(332\) 8.11407 + 4.68466i 0.445317 + 0.257104i
\(333\) 0 0
\(334\) −9.18466 + 15.9083i −0.502562 + 0.870463i
\(335\) 6.16879 + 10.6847i 0.337037 + 0.583765i
\(336\) 0 0
\(337\) −4.63068 −0.252249 −0.126125 0.992014i \(-0.540254\pi\)
−0.126125 + 0.992014i \(0.540254\pi\)
\(338\) −3.57071 12.5000i −0.194221 0.679910i
\(339\) 0 0
\(340\) 0 0
\(341\) −9.25319 16.0270i −0.501088 0.867910i
\(342\) 0 0
\(343\) 25.2213i 1.36182i
\(344\) −2.32498 1.34233i −0.125355 0.0723735i
\(345\) 0 0
\(346\) 13.3102i 0.715562i
\(347\) −9.63289 + 16.6847i −0.517121 + 0.895679i 0.482682 + 0.875796i \(0.339663\pi\)
−0.999802 + 0.0198835i \(0.993670\pi\)
\(348\) 0 0
\(349\) 8.05398 4.64996i 0.431119 0.248907i −0.268704 0.963223i \(-0.586595\pi\)
0.699823 + 0.714316i \(0.253262\pi\)
\(350\) −4.43674 −0.237154
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) −8.11407 + 4.68466i −0.431868 + 0.249339i −0.700142 0.714003i \(-0.746880\pi\)
0.268274 + 0.963343i \(0.413547\pi\)
\(354\) 0 0
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) 7.68466i 0.407286i
\(357\) 0 0
\(358\) −17.3423 10.0126i −0.916571 0.529182i
\(359\) 27.3693i 1.44450i 0.691633 + 0.722249i \(0.256891\pi\)
−0.691633 + 0.722249i \(0.743109\pi\)
\(360\) 0 0
\(361\) −9.02699 15.6352i −0.475105 0.822905i
\(362\) −16.7743 + 9.68466i −0.881639 + 0.509014i
\(363\) 0 0
\(364\) 6.00000 14.8290i 0.314485 0.777253i
\(365\) 6.92820 0.362639
\(366\) 0 0
\(367\) 0.684658 + 1.18586i 0.0357389 + 0.0619016i 0.883342 0.468730i \(-0.155288\pi\)
−0.847603 + 0.530631i \(0.821955\pi\)
\(368\) −0.379706 + 0.657671i −0.0197936 + 0.0342835i
\(369\) 0 0
\(370\) −1.50000 0.866025i −0.0779813 0.0450225i
\(371\) −17.0474 9.84233i −0.885058 0.510988i
\(372\) 0 0
\(373\) −18.0270 + 31.2237i −0.933402 + 1.61670i −0.155943 + 0.987766i \(0.549842\pi\)
−0.777459 + 0.628934i \(0.783492\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) 32.1963 + 13.0270i 1.65819 + 0.670924i
\(378\) 0 0
\(379\) −31.2116 + 18.0201i −1.60323 + 0.925628i −0.612400 + 0.790548i \(0.709796\pi\)
−0.990835 + 0.135080i \(0.956871\pi\)
\(380\) 0.486319 + 0.842329i 0.0249476 + 0.0432106i
\(381\) 0 0
\(382\) 7.35465i 0.376297i
\(383\) 4.05703 + 2.34233i 0.207305 + 0.119687i 0.600058 0.799956i \(-0.295144\pi\)
−0.392753 + 0.919644i \(0.628477\pi\)
\(384\) 0 0
\(385\) 13.3102i 0.678352i
\(386\) 0.759413 1.31534i 0.0386531 0.0669491i
\(387\) 0 0
\(388\) 4.68466 2.70469i 0.237827 0.137310i
\(389\) 25.8610 1.31121 0.655603 0.755106i \(-0.272415\pi\)
0.655603 + 0.755106i \(0.272415\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 10.9852 6.34233i 0.554838 0.320336i
\(393\) 0 0
\(394\) 8.52699 14.7692i 0.429583 0.744060i
\(395\) 6.68466i 0.336342i
\(396\) 0 0
\(397\) −17.8153 10.2857i −0.894126 0.516224i −0.0188364 0.999823i \(-0.505996\pi\)
−0.875290 + 0.483598i \(0.839330\pi\)
\(398\) 7.36932i 0.369390i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 30.3576 17.5270i 1.51599 0.875256i 0.516164 0.856490i \(-0.327360\pi\)
0.999824 0.0187662i \(-0.00597382\pi\)
\(402\) 0 0
\(403\) 13.6847 + 17.5337i 0.681681 + 0.873417i
\(404\) −17.7470 −0.882944
\(405\) 0 0
\(406\) 21.3693 + 37.0127i 1.06054 + 1.83691i
\(407\) 2.59808 4.50000i 0.128782 0.223057i
\(408\) 0 0
\(409\) 19.2116 + 11.0918i 0.949955 + 0.548457i 0.893067 0.449924i \(-0.148549\pi\)
0.0568879 + 0.998381i \(0.481882\pi\)
\(410\) 5.19615 + 3.00000i 0.256620 + 0.148159i
\(411\) 0 0
\(412\) −1.15767 + 2.00514i −0.0570343 + 0.0987864i
\(413\) −10.3923 18.0000i −0.511372 0.885722i
\(414\) 0 0
\(415\) −9.36932 −0.459922
\(416\) −3.57071 + 0.500000i −0.175069 + 0.0245145i
\(417\) 0 0
\(418\) −2.52699 + 1.45896i −0.123599 + 0.0713599i
\(419\) 14.0696 + 24.3693i 0.687346 + 1.19052i 0.972693 + 0.232095i \(0.0745579\pi\)
−0.285347 + 0.958424i \(0.592109\pi\)
\(420\) 0 0
\(421\) 16.2281i 0.790911i −0.918485 0.395455i \(-0.870587\pi\)
0.918485 0.395455i \(-0.129413\pi\)
\(422\) −4.92306 2.84233i −0.239651 0.138362i
\(423\) 0 0
\(424\) 4.43674i 0.215467i
\(425\) 0 0
\(426\) 0 0
\(427\) 43.6847 25.2213i 2.11405 1.22055i
\(428\) −8.87348 −0.428916
\(429\) 0 0
\(430\) 2.68466 0.129466
\(431\) 18.5064 10.6847i 0.891421 0.514662i 0.0170137 0.999855i \(-0.494584\pi\)
0.874407 + 0.485193i \(0.161251\pi\)
\(432\) 0 0
\(433\) 5.31534 9.20644i 0.255439 0.442433i −0.709576 0.704629i \(-0.751113\pi\)
0.965015 + 0.262196i \(0.0844467\pi\)
\(434\) 27.3693i 1.31377i
\(435\) 0 0
\(436\) 1.68466 + 0.972638i 0.0806805 + 0.0465809i
\(437\) 0.738634i 0.0353336i
\(438\) 0 0
\(439\) 15.6847 + 27.1666i 0.748588 + 1.29659i 0.948500 + 0.316778i \(0.102601\pi\)
−0.199912 + 0.979814i \(0.564066\pi\)
\(440\) −2.59808 + 1.50000i −0.123858 + 0.0715097i
\(441\) 0 0
\(442\) 0 0
\(443\) −10.3923 −0.493753 −0.246877 0.969047i \(-0.579404\pi\)
−0.246877 + 0.969047i \(0.579404\pi\)
\(444\) 0 0
\(445\) 3.84233 + 6.65511i 0.182144 + 0.315482i
\(446\) 7.41452 12.8423i 0.351088 0.608102i
\(447\) 0 0
\(448\) −3.84233 2.21837i −0.181533 0.104808i
\(449\) 14.1295 + 8.15767i 0.666812 + 0.384984i 0.794868 0.606783i \(-0.207540\pi\)
−0.128055 + 0.991767i \(0.540874\pi\)
\(450\) 0 0
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) 4.81645 + 8.34233i 0.226547 + 0.392390i
\(453\) 0 0
\(454\) 21.3693 1.00291
\(455\) 2.21837 + 15.8423i 0.103999 + 0.742700i
\(456\) 0 0
\(457\) −3.00000 + 1.73205i −0.140334 + 0.0810219i −0.568523 0.822667i \(-0.692485\pi\)
0.428189 + 0.903689i \(0.359152\pi\)
\(458\) −5.95557 10.3153i −0.278285 0.482004i
\(459\) 0 0
\(460\) 0.759413i 0.0354078i
\(461\) −14.4493 8.34233i −0.672973 0.388541i 0.124229 0.992254i \(-0.460354\pi\)
−0.797202 + 0.603713i \(0.793687\pi\)
\(462\) 0 0
\(463\) 12.7640i 0.593195i 0.955003 + 0.296597i \(0.0958519\pi\)
−0.955003 + 0.296597i \(0.904148\pi\)
\(464\) 4.81645 8.34233i 0.223598 0.387283i
\(465\) 0 0
\(466\) 17.3423 10.0126i 0.803368 0.463825i
\(467\) −35.4939 −1.64246 −0.821231 0.570595i \(-0.806712\pi\)
−0.821231 + 0.570595i \(0.806712\pi\)
\(468\) 0 0
\(469\) 54.7386 2.52760
\(470\) 2.59808 1.50000i 0.119840 0.0691898i
\(471\) 0 0
\(472\) −2.34233 + 4.05703i −0.107814 + 0.186740i
\(473\) 8.05398i 0.370322i
\(474\) 0 0
\(475\) −0.842329 0.486319i −0.0386487 0.0223138i
\(476\) 0 0
\(477\) 0 0
\(478\) 12.3693 + 21.4243i 0.565759 + 0.979924i
\(479\) −2.27824 + 1.31534i −0.104095 + 0.0600995i −0.551144 0.834410i \(-0.685808\pi\)
0.447049 + 0.894510i \(0.352475\pi\)
\(480\) 0 0
\(481\) −2.34233 + 5.78908i −0.106801 + 0.263960i
\(482\) −20.9978 −0.956425
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) −2.70469 + 4.68466i −0.122814 + 0.212719i
\(486\) 0 0
\(487\) −11.1577 6.44188i −0.505602 0.291910i 0.225422 0.974261i \(-0.427624\pi\)
−0.731024 + 0.682352i \(0.760957\pi\)
\(488\) −9.84612 5.68466i −0.445713 0.257332i
\(489\) 0 0
\(490\) −6.34233 + 10.9852i −0.286517 + 0.496262i
\(491\) −2.97778 5.15767i −0.134385 0.232762i 0.790977 0.611846i \(-0.209573\pi\)
−0.925363 + 0.379083i \(0.876239\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.76456 2.15767i 0.124383 0.0970782i
\(495\) 0 0
\(496\) 5.34233 3.08440i 0.239878 0.138493i
\(497\) −13.3102 23.0540i −0.597045 1.03411i
\(498\) 0 0
\(499\) 25.1016i 1.12370i −0.827238 0.561851i \(-0.810089\pi\)
0.827238 0.561851i \(-0.189911\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) 0 0
\(502\) 5.19615i 0.231916i
\(503\) −17.8068 + 30.8423i −0.793967 + 1.37519i 0.129526 + 0.991576i \(0.458655\pi\)
−0.923493 + 0.383615i \(0.874679\pi\)
\(504\) 0 0
\(505\) 15.3693 8.87348i 0.683926 0.394865i
\(506\) 2.27824 0.101280
\(507\) 0 0
\(508\) 9.68466 0.429687
\(509\) −19.6455 + 11.3423i −0.870771 + 0.502740i −0.867604 0.497255i \(-0.834341\pi\)
−0.00316666 + 0.999995i \(0.501008\pi\)
\(510\) 0 0
\(511\) 15.3693 26.6204i 0.679899 1.17762i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −26.3423 15.2088i −1.16191 0.670829i
\(515\) 2.31534i 0.102026i
\(516\) 0 0
\(517\) 4.50000 + 7.79423i 0.197910 + 0.342790i
\(518\) −6.65511 + 3.84233i −0.292409 + 0.168822i
\(519\) 0 0
\(520\) 2.84233 2.21837i 0.124644 0.0972820i
\(521\) 5.95557 0.260918 0.130459 0.991454i \(-0.458355\pi\)
0.130459 + 0.991454i \(0.458355\pi\)
\(522\) 0 0
\(523\) 18.0270 + 31.2237i 0.788265 + 1.36532i 0.927029 + 0.374990i \(0.122354\pi\)
−0.138764 + 0.990326i \(0.544313\pi\)
\(524\) 3.35749 5.81534i 0.146673 0.254044i
\(525\) 0 0
\(526\) 9.55398 + 5.51599i 0.416573 + 0.240509i
\(527\) 0 0
\(528\) 0 0
\(529\) 11.2116 19.4191i 0.487463 0.844310i
\(530\) −2.21837 3.84233i −0.0963598 0.166900i
\(531\) 0 0
\(532\) 4.31534 0.187094
\(533\) 8.11407 20.0540i 0.351459 0.868634i
\(534\) 0 0
\(535\) 7.68466 4.43674i 0.332237 0.191817i
\(536\) −6.16879 10.6847i −0.266451 0.461507i
\(537\) 0 0
\(538\) 17.7470i 0.765126i
\(539\) −32.9557 19.0270i −1.41950 0.819550i
\(540\) 0 0
\(541\) 25.7675i 1.10783i −0.832572 0.553916i \(-0.813133\pi\)
0.832572 0.553916i \(-0.186867\pi\)
\(542\) −4.05703 + 7.02699i −0.174264 + 0.301835i
\(543\) 0 0
\(544\) 0 0
\(545\) −1.94528 −0.0833265
\(546\) 0 0
\(547\) 42.1080 1.80041 0.900203 0.435471i \(-0.143418\pi\)
0.900203 + 0.435471i \(0.143418\pi\)
\(548\) 6.33527 3.65767i 0.270629 0.156248i
\(549\) 0 0
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) 9.36932i 0.399146i
\(552\) 0 0
\(553\) −25.6847 14.8290i −1.09222 0.630595i
\(554\) 1.00000i 0.0424859i
\(555\) 0 0
\(556\) 10.8423 + 18.7795i 0.459817 + 0.796427i
\(557\) 11.8513 6.84233i 0.502154 0.289919i −0.227449 0.973790i \(-0.573038\pi\)
0.729603 + 0.683871i \(0.239705\pi\)
\(558\) 0 0
\(559\) −1.34233 9.58615i −0.0567745 0.405451i
\(560\) 4.43674 0.187486
\(561\) 0 0
\(562\) −12.3693 21.4243i −0.521768 0.903729i
\(563\) 20.0252 34.6847i 0.843961 1.46178i −0.0425587 0.999094i \(-0.513551\pi\)
0.886520 0.462690i \(-0.153116\pi\)
\(564\) 0 0
\(565\) −8.34233 4.81645i −0.350964 0.202629i
\(566\) −20.8314 12.0270i −0.875607 0.505532i
\(567\) 0 0
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) −10.3324 17.8963i −0.433158 0.750252i 0.563985 0.825785i \(-0.309268\pi\)
−0.997143 + 0.0755329i \(0.975934\pi\)
\(570\) 0 0
\(571\) −2.94602 −0.123287 −0.0616436 0.998098i \(-0.519634\pi\)
−0.0616436 + 0.998098i \(0.519634\pi\)
\(572\) 6.65511 + 8.52699i 0.278264 + 0.356531i
\(573\) 0 0
\(574\) 23.0540 13.3102i 0.962254 0.555558i
\(575\) 0.379706 + 0.657671i 0.0158349 + 0.0274268i
\(576\) 0 0
\(577\) 43.5145i 1.81153i 0.423778 + 0.905766i \(0.360704\pi\)
−0.423778 + 0.905766i \(0.639296\pi\)
\(578\) 14.7224 + 8.50000i 0.612372 + 0.353553i
\(579\) 0 0
\(580\) 9.63289i 0.399984i
\(581\) −20.7846 + 36.0000i −0.862291 + 1.49353i
\(582\) 0 0
\(583\) 11.5270 6.65511i 0.477399 0.275626i
\(584\) −6.92820 −0.286691
\(585\) 0 0
\(586\) −10.3153 −0.426123
\(587\) 13.3102 7.68466i 0.549372 0.317180i −0.199497 0.979898i \(-0.563931\pi\)
0.748868 + 0.662719i \(0.230597\pi\)
\(588\) 0 0
\(589\) −3.00000 + 5.19615i −0.123613 + 0.214104i
\(590\) 4.68466i 0.192864i
\(591\) 0 0
\(592\) 1.50000 + 0.866025i 0.0616496 + 0.0355934i
\(593\) 23.4233i 0.961879i −0.876754 0.480940i \(-0.840296\pi\)
0.876754 0.480940i \(-0.159704\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −19.6455 + 11.3423i −0.804711 + 0.464600i
\(597\) 0 0
\(598\) −2.71165 + 0.379706i −0.110887 + 0.0155273i
\(599\) 28.1393 1.14974 0.574870 0.818245i \(-0.305053\pi\)
0.574870 + 0.818245i \(0.305053\pi\)
\(600\) 0 0
\(601\) 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i \(0.0863789\pi\)
−0.249565 + 0.968358i \(0.580288\pi\)
\(602\) 5.95557 10.3153i 0.242731 0.420422i
\(603\) 0 0
\(604\) −12.3693 7.14143i −0.503300 0.290581i
\(605\) −1.73205 1.00000i −0.0704179 0.0406558i
\(606\) 0 0
\(607\) −21.5270 + 37.2858i −0.873753 + 1.51339i −0.0156688 + 0.999877i \(0.504988\pi\)
−0.858085 + 0.513508i \(0.828346\pi\)
\(608\) −0.486319 0.842329i −0.0197228 0.0341610i
\(609\) 0 0
\(610\) 11.3693 0.460330
\(611\) −6.65511 8.52699i −0.269237 0.344965i
\(612\) 0 0
\(613\) −10.5000 + 6.06218i −0.424091 + 0.244849i −0.696826 0.717240i \(-0.745405\pi\)
0.272735 + 0.962089i \(0.412072\pi\)
\(614\) 7.14143 + 12.3693i 0.288205 + 0.499185i
\(615\) 0 0
\(616\) 13.3102i 0.536284i
\(617\) −1.13912 0.657671i −0.0458592 0.0264768i 0.476895 0.878960i \(-0.341762\pi\)
−0.522754 + 0.852483i \(0.675095\pi\)
\(618\) 0 0
\(619\) 32.5760i 1.30934i −0.755915 0.654670i \(-0.772808\pi\)
0.755915 0.654670i \(-0.227192\pi\)
\(620\) −3.08440 + 5.34233i −0.123872 + 0.214553i
\(621\) 0 0
\(622\) 16.6847 9.63289i 0.668994 0.386244i
\(623\) 34.0948 1.36598
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 16.7743 9.68466i 0.670437 0.387077i
\(627\) 0 0
\(628\) −8.18466 + 14.1762i −0.326603 + 0.565694i
\(629\) 0 0
\(630\) 0 0
\(631\) −7.31534 4.22351i −0.291219 0.168135i 0.347272 0.937764i \(-0.387108\pi\)
−0.638492 + 0.769629i \(0.720441\pi\)
\(632\) 6.68466i 0.265901i
\(633\) 0 0
\(634\) −16.2116 28.0794i −0.643847 1.11518i
\(635\) −8.38716 + 4.84233i −0.332834 + 0.192162i
\(636\) 0 0
\(637\) 42.3963 + 17.1540i 1.67980 + 0.679667i
\(638\) −28.8987 −1.14411
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 5.13628 8.89630i 0.202871 0.351383i −0.746581 0.665294i \(-0.768306\pi\)
0.949452 + 0.313911i \(0.101639\pi\)
\(642\) 0 0
\(643\) 8.05398 + 4.64996i 0.317618 + 0.183377i 0.650330 0.759652i \(-0.274631\pi\)
−0.332712 + 0.943028i \(0.607964\pi\)
\(644\) −2.91791 1.68466i −0.114982 0.0663848i
\(645\) 0 0
\(646\) 0 0
\(647\) 14.7692 + 25.5810i 0.580636 + 1.00569i 0.995404 + 0.0957642i \(0.0305295\pi\)
−0.414768 + 0.909927i \(0.636137\pi\)
\(648\) 0 0
\(649\) 14.0540 0.551667
\(650\) −1.35234 + 3.34233i −0.0530433 + 0.131097i
\(651\) 0 0
\(652\) −9.65767 + 5.57586i −0.378224 + 0.218367i
\(653\) 22.2436 + 38.5270i 0.870458 + 1.50768i 0.861524 + 0.507717i \(0.169511\pi\)
0.00893438 + 0.999960i \(0.497156\pi\)
\(654\) 0 0
\(655\) 6.71498i 0.262376i
\(656\) −5.19615 3.00000i −0.202876 0.117130i
\(657\) 0 0
\(658\) 13.3102i 0.518886i
\(659\) 20.4049 35.3423i 0.794862 1.37674i −0.128064 0.991766i \(-0.540876\pi\)
0.922927 0.384976i \(-0.125790\pi\)
\(660\) 0 0
\(661\) 9.00000 5.19615i 0.350059 0.202107i −0.314652 0.949207i \(-0.601888\pi\)
0.664711 + 0.747100i \(0.268554\pi\)
\(662\) −33.5486 −1.30390
\(663\) 0 0
\(664\) 9.36932 0.363600
\(665\) −3.73720 + 2.15767i −0.144922 + 0.0836709i
\(666\) 0 0
\(667\) 3.65767 6.33527i 0.141626 0.245303i
\(668\) 18.3693i 0.710730i
\(669\) 0 0
\(670\) 10.6847 + 6.16879i 0.412784 + 0.238321i
\(671\) 34.1080i 1.31672i
\(672\) 0 0
\(673\) −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) −4.01029 + 2.31534i −0.154471 + 0.0891836i
\(675\) 0 0
\(676\) −9.34233 9.03996i −0.359320 0.347691i
\(677\) 22.3034 0.857191 0.428595 0.903497i \(-0.359009\pi\)
0.428595 + 0.903497i \(0.359009\pi\)
\(678\) 0 0
\(679\) 12.0000 + 20.7846i 0.460518 + 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) −16.0270 9.25319i −0.613705 0.354323i
\(683\) −23.7025 13.6847i −0.906952 0.523629i −0.0275027 0.999622i \(-0.508755\pi\)
−0.879449 + 0.475993i \(0.842089\pi\)
\(684\) 0 0
\(685\) −3.65767 + 6.33527i −0.139752 + 0.242058i
\(686\) 12.6107 + 21.8423i 0.481478 + 0.833944i
\(687\) 0 0
\(688\) −2.68466 −0.102352
\(689\) −12.6107 + 9.84233i −0.480428 + 0.374963i
\(690\) 0 0
\(691\) 14.5270 8.38716i 0.552633 0.319063i −0.197550 0.980293i \(-0.563299\pi\)
0.750183 + 0.661230i \(0.229965\pi\)
\(692\) 6.65511 + 11.5270i 0.252989 + 0.438190i
\(693\) 0 0
\(694\) 19.2658i 0.731319i
\(695\) −18.7795 10.8423i −0.712346 0.411273i
\(696\) 0 0
\(697\) 0 0
\(698\) 4.64996 8.05398i 0.176004 0.304847i
\(699\) 0 0
\(700\) −3.84233 + 2.21837i −0.145226 + 0.0838465i
\(701\) 30.4175 1.14885 0.574427 0.818556i \(-0.305225\pi\)
0.574427 + 0.818556i \(0.305225\pi\)
\(702\) 0 0
\(703\) −1.68466 −0.0635381
\(704\) 2.59808 1.50000i 0.0979187 0.0565334i
\(705\) 0 0
\(706\) −4.68466 + 8.11407i −0.176309 + 0.305377i
\(707\) 78.7386i 2.96127i
\(708\) 0 0
\(709\) −2.63068 1.51883i −0.0987974 0.0570407i 0.449787 0.893136i \(-0.351500\pi\)
−0.548585 + 0.836095i \(0.684833\pi\)
\(710\) 6.00000i 0.225176i
\(711\) 0 0
\(712\) −3.84233 6.65511i −0.143997 0.249411i
\(713\) 4.05703 2.34233i 0.151937 0.0877209i
\(714\) 0 0
\(715\) −10.0270 4.05703i −0.374988 0.151724i
\(716\) −20.0252 −0.748377
\(717\) 0 0
\(718\) 13.6847 + 23.7025i 0.510707 + 0.884570i
\(719\) 19.2658 33.3693i 0.718493 1.24447i −0.243104 0.970000i \(-0.578166\pi\)
0.961597 0.274465i \(-0.0885009\pi\)
\(720\) 0 0
\(721\) −8.89630 5.13628i −0.331316 0.191285i
\(722\) −15.6352 9.02699i −0.581882 0.335950i
\(723\) 0 0
\(724\) −9.68466 + 16.7743i −0.359927 + 0.623413i
\(725\) −4.81645 8.34233i −0.178878 0.309826i
\(726\) 0 0
\(727\) −24.3153 −0.901806 −0.450903 0.892573i \(-0.648898\pi\)
−0.450903 + 0.892573i \(0.648898\pi\)
\(728\) −2.21837 15.8423i −0.0822183 0.587156i
\(729\) 0 0
\(730\) 6.00000 3.46410i 0.222070 0.128212i
\(731\) 0 0
\(732\) 0 0
\(733\) 47.9512i 1.77112i 0.464526 + 0.885560i \(0.346225\pi\)
−0.464526 + 0.885560i \(0.653775\pi\)
\(734\) 1.18586 + 0.684658i 0.0437710 + 0.0252712i
\(735\) 0 0
\(736\) 0.759413i 0.0279923i
\(737\) −18.5064 + 32.0540i −0.681691 + 1.18072i
\(738\) 0 0
\(739\) 20.5270 11.8513i 0.755097 0.435956i −0.0724353 0.997373i \(-0.523077\pi\)
0.827533 + 0.561417i \(0.189744\pi\)
\(740\) −1.73205 −0.0636715
\(741\) 0 0
\(742\) −19.6847 −0.722647
\(743\) −6.33527 + 3.65767i −0.232419 + 0.134187i −0.611687 0.791100i \(-0.709509\pi\)
0.379269 + 0.925287i \(0.376176\pi\)
\(744\) 0 0
\(745\) 11.3423 19.6455i 0.415551 0.719755i
\(746\) 36.0540i 1.32003i
\(747\) 0 0
\(748\) 0 0
\(749\) 39.3693i 1.43852i
\(750\) 0 0
\(751\) 11.6577 + 20.1917i 0.425394 + 0.736805i 0.996457 0.0841016i \(-0.0268020\pi\)
−0.571063 + 0.820906i \(0.693469\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) 0 0
\(754\) 34.3963 4.81645i 1.25264 0.175405i
\(755\) 14.2829 0.519806
\(756\) 0 0
\(757\) 0.526988 + 0.912769i 0.0191537 + 0.0331752i 0.875443 0.483321i \(-0.160569\pi\)
−0.856290 + 0.516496i \(0.827236\pi\)
\(758\) −18.0201 + 31.2116i −0.654518 + 1.13366i
\(759\) 0 0
\(760\) 0.842329 + 0.486319i 0.0305545 + 0.0176406i
\(761\) 19.9653 + 11.5270i 0.723743 + 0.417853i 0.816129 0.577870i \(-0.196116\pi\)
−0.0923860 + 0.995723i \(0.529449\pi\)
\(762\) 0 0
\(763\) −4.31534 + 7.47439i −0.156226 + 0.270591i
\(764\) −3.67733 6.36932i −0.133041 0.230434i
\(765\) 0 0
\(766\) 4.68466 0.169264
\(767\) −16.7276 + 2.34233i −0.603998 + 0.0845766i
\(768\) 0 0
\(769\) 11.7116 6.76172i 0.422333 0.243834i −0.273742 0.961803i \(-0.588261\pi\)
0.696075 + 0.717969i \(0.254928\pi\)
\(770\) −6.65511 11.5270i −0.239833 0.415404i
\(771\) 0 0
\(772\) 1.51883i 0.0546637i
\(773\) 24.5218 + 14.1577i 0.881988 + 0.509216i 0.871313 0.490727i \(-0.163269\pi\)
0.0106746 + 0.999943i \(0.496602\pi\)
\(774\) 0 0
\(775\) 6.16879i 0.221589i
\(776\) 2.70469 4.68466i 0.0970927 0.168169i
\(777\) 0 0
\(778\) 22.3963 12.9305i 0.802946 0.463581i
\(779\) 5.83583 0.209090
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) 6.34233 10.9852i 0.226512 0.392330i
\(785\) 16.3693i 0.584246i
\(786\) 0 0
\(787\) −2.34233 1.35234i −0.0834950 0.0482059i 0.457671 0.889122i \(-0.348684\pi\)
−0.541166 + 0.840916i \(0.682017\pi\)
\(788\) 17.0540i 0.607523i
\(789\) 0 0
\(790\) −3.34233 5.78908i −0.118915 0.205966i
\(791\) −37.0127 + 21.3693i −1.31602