Properties

Label 546.2.g.a.209.2
Level $546$
Weight $2$
Character 546.209
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.2
Root \(1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 546.209
Dual form 546.2.g.a.209.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.618034 - 1.61803i) q^{3} -1.00000 q^{4} +3.23607 q^{5} +(-1.61803 - 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} +1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.618034 - 1.61803i) q^{3} -1.00000 q^{4} +3.23607 q^{5} +(-1.61803 - 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} +1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} -3.23607i q^{10} +(-0.618034 + 1.61803i) q^{12} +1.00000i q^{13} +(-0.381966 - 2.61803i) q^{14} +(2.00000 - 5.23607i) q^{15} +1.00000 q^{16} +2.47214 q^{17} +(-2.00000 + 2.23607i) q^{18} +6.00000i q^{19} -3.23607 q^{20} +(1.00000 - 4.47214i) q^{21} -3.23607i q^{23} +(1.61803 + 0.618034i) q^{24} +5.47214 q^{25} +1.00000 q^{26} +(-4.61803 + 2.38197i) q^{27} +(-2.61803 + 0.381966i) q^{28} -5.70820i q^{29} +(-5.23607 - 2.00000i) q^{30} +7.23607i q^{31} -1.00000i q^{32} -2.47214i q^{34} +(8.47214 - 1.23607i) q^{35} +(2.23607 + 2.00000i) q^{36} -9.23607 q^{37} +6.00000 q^{38} +(1.61803 + 0.618034i) q^{39} +3.23607i q^{40} -5.23607 q^{41} +(-4.47214 - 1.00000i) q^{42} -10.4721 q^{43} +(-7.23607 - 6.47214i) q^{45} -3.23607 q^{46} -6.47214 q^{47} +(0.618034 - 1.61803i) q^{48} +(6.70820 - 2.00000i) q^{49} -5.47214i q^{50} +(1.52786 - 4.00000i) q^{51} -1.00000i q^{52} -3.23607i q^{53} +(2.38197 + 4.61803i) q^{54} +(0.381966 + 2.61803i) q^{56} +(9.70820 + 3.70820i) q^{57} -5.70820 q^{58} -4.47214 q^{59} +(-2.00000 + 5.23607i) q^{60} +4.47214i q^{61} +7.23607 q^{62} +(-6.61803 - 4.38197i) q^{63} -1.00000 q^{64} +3.23607i q^{65} +6.94427 q^{67} -2.47214 q^{68} +(-5.23607 - 2.00000i) q^{69} +(-1.23607 - 8.47214i) q^{70} +14.4721i q^{71} +(2.00000 - 2.23607i) q^{72} -3.23607i q^{73} +9.23607i q^{74} +(3.38197 - 8.85410i) q^{75} -6.00000i q^{76} +(0.618034 - 1.61803i) q^{78} -8.94427 q^{79} +3.23607 q^{80} +(1.00000 + 8.94427i) q^{81} +5.23607i q^{82} +14.0000 q^{83} +(-1.00000 + 4.47214i) q^{84} +8.00000 q^{85} +10.4721i q^{86} +(-9.23607 - 3.52786i) q^{87} +6.18034 q^{89} +(-6.47214 + 7.23607i) q^{90} +(0.381966 + 2.61803i) q^{91} +3.23607i q^{92} +(11.7082 + 4.47214i) q^{93} +6.47214i q^{94} +19.4164i q^{95} +(-1.61803 - 0.618034i) q^{96} -0.763932i q^{97} +(-2.00000 - 6.70820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + 2q^{12} - 6q^{14} + 8q^{15} + 4q^{16} - 8q^{17} - 8q^{18} - 4q^{20} + 4q^{21} + 2q^{24} + 4q^{25} + 4q^{26} - 14q^{27} - 6q^{28} - 12q^{30} + 16q^{35} - 28q^{37} + 24q^{38} + 2q^{39} - 12q^{41} - 24q^{43} - 20q^{45} - 4q^{46} - 8q^{47} - 2q^{48} + 24q^{51} + 14q^{54} + 6q^{56} + 12q^{57} + 4q^{58} - 8q^{60} + 20q^{62} - 22q^{63} - 4q^{64} - 8q^{67} + 8q^{68} - 12q^{69} + 4q^{70} + 8q^{72} + 18q^{75} - 2q^{78} + 4q^{80} + 4q^{81} + 56q^{83} - 4q^{84} + 32q^{85} - 28q^{87} - 20q^{89} - 8q^{90} + 6q^{91} + 20q^{93} - 2q^{96} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.618034 1.61803i 0.356822 0.934172i
\(4\) −1.00000 −0.500000
\(5\) 3.23607 1.44721 0.723607 0.690212i \(-0.242483\pi\)
0.723607 + 0.690212i \(0.242483\pi\)
\(6\) −1.61803 0.618034i −0.660560 0.252311i
\(7\) 2.61803 0.381966i 0.989524 0.144370i
\(8\) 1.00000i 0.353553i
\(9\) −2.23607 2.00000i −0.745356 0.666667i
\(10\) 3.23607i 1.02333i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −0.618034 + 1.61803i −0.178411 + 0.467086i
\(13\) 1.00000i 0.277350i
\(14\) −0.381966 2.61803i −0.102085 0.699699i
\(15\) 2.00000 5.23607i 0.516398 1.35195i
\(16\) 1.00000 0.250000
\(17\) 2.47214 0.599581 0.299791 0.954005i \(-0.403083\pi\)
0.299791 + 0.954005i \(0.403083\pi\)
\(18\) −2.00000 + 2.23607i −0.471405 + 0.527046i
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) −3.23607 −0.723607
\(21\) 1.00000 4.47214i 0.218218 0.975900i
\(22\) 0 0
\(23\) 3.23607i 0.674767i −0.941367 0.337383i \(-0.890458\pi\)
0.941367 0.337383i \(-0.109542\pi\)
\(24\) 1.61803 + 0.618034i 0.330280 + 0.126156i
\(25\) 5.47214 1.09443
\(26\) 1.00000 0.196116
\(27\) −4.61803 + 2.38197i −0.888741 + 0.458410i
\(28\) −2.61803 + 0.381966i −0.494762 + 0.0721848i
\(29\) 5.70820i 1.05999i −0.848002 0.529993i \(-0.822194\pi\)
0.848002 0.529993i \(-0.177806\pi\)
\(30\) −5.23607 2.00000i −0.955971 0.365148i
\(31\) 7.23607i 1.29964i 0.760090 + 0.649818i \(0.225155\pi\)
−0.760090 + 0.649818i \(0.774845\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 2.47214i 0.423968i
\(35\) 8.47214 1.23607i 1.43205 0.208934i
\(36\) 2.23607 + 2.00000i 0.372678 + 0.333333i
\(37\) −9.23607 −1.51840 −0.759200 0.650857i \(-0.774410\pi\)
−0.759200 + 0.650857i \(0.774410\pi\)
\(38\) 6.00000 0.973329
\(39\) 1.61803 + 0.618034i 0.259093 + 0.0989646i
\(40\) 3.23607i 0.511667i
\(41\) −5.23607 −0.817736 −0.408868 0.912593i \(-0.634076\pi\)
−0.408868 + 0.912593i \(0.634076\pi\)
\(42\) −4.47214 1.00000i −0.690066 0.154303i
\(43\) −10.4721 −1.59699 −0.798493 0.602004i \(-0.794369\pi\)
−0.798493 + 0.602004i \(0.794369\pi\)
\(44\) 0 0
\(45\) −7.23607 6.47214i −1.07869 0.964809i
\(46\) −3.23607 −0.477132
\(47\) −6.47214 −0.944058 −0.472029 0.881583i \(-0.656478\pi\)
−0.472029 + 0.881583i \(0.656478\pi\)
\(48\) 0.618034 1.61803i 0.0892055 0.233543i
\(49\) 6.70820 2.00000i 0.958315 0.285714i
\(50\) 5.47214i 0.773877i
\(51\) 1.52786 4.00000i 0.213944 0.560112i
\(52\) 1.00000i 0.138675i
\(53\) 3.23607i 0.444508i −0.974989 0.222254i \(-0.928659\pi\)
0.974989 0.222254i \(-0.0713414\pi\)
\(54\) 2.38197 + 4.61803i 0.324145 + 0.628435i
\(55\) 0 0
\(56\) 0.381966 + 2.61803i 0.0510424 + 0.349850i
\(57\) 9.70820 + 3.70820i 1.28588 + 0.491164i
\(58\) −5.70820 −0.749524
\(59\) −4.47214 −0.582223 −0.291111 0.956689i \(-0.594025\pi\)
−0.291111 + 0.956689i \(0.594025\pi\)
\(60\) −2.00000 + 5.23607i −0.258199 + 0.675973i
\(61\) 4.47214i 0.572598i 0.958140 + 0.286299i \(0.0924251\pi\)
−0.958140 + 0.286299i \(0.907575\pi\)
\(62\) 7.23607 0.918982
\(63\) −6.61803 4.38197i −0.833794 0.552076i
\(64\) −1.00000 −0.125000
\(65\) 3.23607i 0.401385i
\(66\) 0 0
\(67\) 6.94427 0.848378 0.424189 0.905574i \(-0.360559\pi\)
0.424189 + 0.905574i \(0.360559\pi\)
\(68\) −2.47214 −0.299791
\(69\) −5.23607 2.00000i −0.630349 0.240772i
\(70\) −1.23607 8.47214i −0.147738 1.01261i
\(71\) 14.4721i 1.71753i 0.512373 + 0.858763i \(0.328767\pi\)
−0.512373 + 0.858763i \(0.671233\pi\)
\(72\) 2.00000 2.23607i 0.235702 0.263523i
\(73\) 3.23607i 0.378753i −0.981905 0.189377i \(-0.939353\pi\)
0.981905 0.189377i \(-0.0606467\pi\)
\(74\) 9.23607i 1.07367i
\(75\) 3.38197 8.85410i 0.390516 1.02238i
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) 0.618034 1.61803i 0.0699786 0.183206i
\(79\) −8.94427 −1.00631 −0.503155 0.864196i \(-0.667827\pi\)
−0.503155 + 0.864196i \(0.667827\pi\)
\(80\) 3.23607 0.361803
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 5.23607i 0.578227i
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) −1.00000 + 4.47214i −0.109109 + 0.487950i
\(85\) 8.00000 0.867722
\(86\) 10.4721i 1.12924i
\(87\) −9.23607 3.52786i −0.990210 0.378227i
\(88\) 0 0
\(89\) 6.18034 0.655115 0.327557 0.944831i \(-0.393775\pi\)
0.327557 + 0.944831i \(0.393775\pi\)
\(90\) −6.47214 + 7.23607i −0.682223 + 0.762749i
\(91\) 0.381966 + 2.61803i 0.0400409 + 0.274445i
\(92\) 3.23607i 0.337383i
\(93\) 11.7082 + 4.47214i 1.21408 + 0.463739i
\(94\) 6.47214i 0.667550i
\(95\) 19.4164i 1.99208i
\(96\) −1.61803 0.618034i −0.165140 0.0630778i
\(97\) 0.763932i 0.0775655i −0.999248 0.0387828i \(-0.987652\pi\)
0.999248 0.0387828i \(-0.0123480\pi\)
\(98\) −2.00000 6.70820i −0.202031 0.677631i
\(99\) 0 0
\(100\) −5.47214 −0.547214
\(101\) 18.1803 1.80901 0.904506 0.426461i \(-0.140240\pi\)
0.904506 + 0.426461i \(0.140240\pi\)
\(102\) −4.00000 1.52786i −0.396059 0.151281i
\(103\) 7.70820i 0.759512i −0.925087 0.379756i \(-0.876008\pi\)
0.925087 0.379756i \(-0.123992\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 3.23607 14.4721i 0.315808 1.41234i
\(106\) −3.23607 −0.314315
\(107\) 2.47214i 0.238990i −0.992835 0.119495i \(-0.961872\pi\)
0.992835 0.119495i \(-0.0381276\pi\)
\(108\) 4.61803 2.38197i 0.444371 0.229205i
\(109\) 6.18034 0.591969 0.295985 0.955193i \(-0.404352\pi\)
0.295985 + 0.955193i \(0.404352\pi\)
\(110\) 0 0
\(111\) −5.70820 + 14.9443i −0.541799 + 1.41845i
\(112\) 2.61803 0.381966i 0.247381 0.0360924i
\(113\) 16.0000i 1.50515i −0.658505 0.752577i \(-0.728811\pi\)
0.658505 0.752577i \(-0.271189\pi\)
\(114\) 3.70820 9.70820i 0.347305 0.909257i
\(115\) 10.4721i 0.976532i
\(116\) 5.70820i 0.529993i
\(117\) 2.00000 2.23607i 0.184900 0.206725i
\(118\) 4.47214i 0.411693i
\(119\) 6.47214 0.944272i 0.593300 0.0865613i
\(120\) 5.23607 + 2.00000i 0.477985 + 0.182574i
\(121\) 11.0000 1.00000
\(122\) 4.47214 0.404888
\(123\) −3.23607 + 8.47214i −0.291786 + 0.763907i
\(124\) 7.23607i 0.649818i
\(125\) 1.52786 0.136656
\(126\) −4.38197 + 6.61803i −0.390377 + 0.589581i
\(127\) −3.05573 −0.271152 −0.135576 0.990767i \(-0.543288\pi\)
−0.135576 + 0.990767i \(0.543288\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −6.47214 + 16.9443i −0.569840 + 1.49186i
\(130\) 3.23607 0.283822
\(131\) −5.23607 −0.457477 −0.228739 0.973488i \(-0.573460\pi\)
−0.228739 + 0.973488i \(0.573460\pi\)
\(132\) 0 0
\(133\) 2.29180 + 15.7082i 0.198724 + 1.36207i
\(134\) 6.94427i 0.599894i
\(135\) −14.9443 + 7.70820i −1.28620 + 0.663417i
\(136\) 2.47214i 0.211984i
\(137\) 7.52786i 0.643149i 0.946884 + 0.321574i \(0.104212\pi\)
−0.946884 + 0.321574i \(0.895788\pi\)
\(138\) −2.00000 + 5.23607i −0.170251 + 0.445724i
\(139\) 12.1803i 1.03312i 0.856250 + 0.516561i \(0.172788\pi\)
−0.856250 + 0.516561i \(0.827212\pi\)
\(140\) −8.47214 + 1.23607i −0.716026 + 0.104467i
\(141\) −4.00000 + 10.4721i −0.336861 + 0.881913i
\(142\) 14.4721 1.21447
\(143\) 0 0
\(144\) −2.23607 2.00000i −0.186339 0.166667i
\(145\) 18.4721i 1.53403i
\(146\) −3.23607 −0.267819
\(147\) 0.909830 12.0902i 0.0750415 0.997180i
\(148\) 9.23607 0.759200
\(149\) 17.4164i 1.42681i −0.700753 0.713404i \(-0.747153\pi\)
0.700753 0.713404i \(-0.252847\pi\)
\(150\) −8.85410 3.38197i −0.722934 0.276136i
\(151\) 3.70820 0.301769 0.150885 0.988551i \(-0.451788\pi\)
0.150885 + 0.988551i \(0.451788\pi\)
\(152\) −6.00000 −0.486664
\(153\) −5.52786 4.94427i −0.446901 0.399721i
\(154\) 0 0
\(155\) 23.4164i 1.88085i
\(156\) −1.61803 0.618034i −0.129546 0.0494823i
\(157\) 5.41641i 0.432276i 0.976363 + 0.216138i \(0.0693462\pi\)
−0.976363 + 0.216138i \(0.930654\pi\)
\(158\) 8.94427i 0.711568i
\(159\) −5.23607 2.00000i −0.415247 0.158610i
\(160\) 3.23607i 0.255834i
\(161\) −1.23607 8.47214i −0.0974158 0.667698i
\(162\) 8.94427 1.00000i 0.702728 0.0785674i
\(163\) −9.41641 −0.737550 −0.368775 0.929519i \(-0.620223\pi\)
−0.368775 + 0.929519i \(0.620223\pi\)
\(164\) 5.23607 0.408868
\(165\) 0 0
\(166\) 14.0000i 1.08661i
\(167\) 16.9443 1.31119 0.655594 0.755114i \(-0.272418\pi\)
0.655594 + 0.755114i \(0.272418\pi\)
\(168\) 4.47214 + 1.00000i 0.345033 + 0.0771517i
\(169\) −1.00000 −0.0769231
\(170\) 8.00000i 0.613572i
\(171\) 12.0000 13.4164i 0.917663 1.02598i
\(172\) 10.4721 0.798493
\(173\) −18.7639 −1.42660 −0.713298 0.700861i \(-0.752799\pi\)
−0.713298 + 0.700861i \(0.752799\pi\)
\(174\) −3.52786 + 9.23607i −0.267447 + 0.700185i
\(175\) 14.3262 2.09017i 1.08296 0.158002i
\(176\) 0 0
\(177\) −2.76393 + 7.23607i −0.207750 + 0.543896i
\(178\) 6.18034i 0.463236i
\(179\) 10.4721i 0.782724i 0.920237 + 0.391362i \(0.127996\pi\)
−0.920237 + 0.391362i \(0.872004\pi\)
\(180\) 7.23607 + 6.47214i 0.539345 + 0.482405i
\(181\) 4.47214i 0.332411i 0.986091 + 0.166206i \(0.0531515\pi\)
−0.986091 + 0.166206i \(0.946848\pi\)
\(182\) 2.61803 0.381966i 0.194062 0.0283132i
\(183\) 7.23607 + 2.76393i 0.534906 + 0.204316i
\(184\) 3.23607 0.238566
\(185\) −29.8885 −2.19745
\(186\) 4.47214 11.7082i 0.327913 0.858487i
\(187\) 0 0
\(188\) 6.47214 0.472029
\(189\) −11.1803 + 8.00000i −0.813250 + 0.581914i
\(190\) 19.4164 1.40861
\(191\) 21.7082i 1.57075i −0.619020 0.785375i \(-0.712470\pi\)
0.619020 0.785375i \(-0.287530\pi\)
\(192\) −0.618034 + 1.61803i −0.0446028 + 0.116772i
\(193\) 11.8885 0.855756 0.427878 0.903836i \(-0.359261\pi\)
0.427878 + 0.903836i \(0.359261\pi\)
\(194\) −0.763932 −0.0548471
\(195\) 5.23607 + 2.00000i 0.374963 + 0.143223i
\(196\) −6.70820 + 2.00000i −0.479157 + 0.142857i
\(197\) 25.4164i 1.81084i 0.424513 + 0.905422i \(0.360445\pi\)
−0.424513 + 0.905422i \(0.639555\pi\)
\(198\) 0 0
\(199\) 27.7082i 1.96418i 0.188406 + 0.982091i \(0.439668\pi\)
−0.188406 + 0.982091i \(0.560332\pi\)
\(200\) 5.47214i 0.386938i
\(201\) 4.29180 11.2361i 0.302720 0.792531i
\(202\) 18.1803i 1.27916i
\(203\) −2.18034 14.9443i −0.153030 1.04888i
\(204\) −1.52786 + 4.00000i −0.106972 + 0.280056i
\(205\) −16.9443 −1.18344
\(206\) −7.70820 −0.537056
\(207\) −6.47214 + 7.23607i −0.449845 + 0.502941i
\(208\) 1.00000i 0.0693375i
\(209\) 0 0
\(210\) −14.4721 3.23607i −0.998672 0.223310i
\(211\) −25.8885 −1.78224 −0.891120 0.453767i \(-0.850080\pi\)
−0.891120 + 0.453767i \(0.850080\pi\)
\(212\) 3.23607i 0.222254i
\(213\) 23.4164 + 8.94427i 1.60447 + 0.612851i
\(214\) −2.47214 −0.168992
\(215\) −33.8885 −2.31118
\(216\) −2.38197 4.61803i −0.162072 0.314217i
\(217\) 2.76393 + 18.9443i 0.187628 + 1.28602i
\(218\) 6.18034i 0.418585i
\(219\) −5.23607 2.00000i −0.353821 0.135147i
\(220\) 0 0
\(221\) 2.47214i 0.166294i
\(222\) 14.9443 + 5.70820i 1.00299 + 0.383110i
\(223\) 8.76393i 0.586876i −0.955978 0.293438i \(-0.905201\pi\)
0.955978 0.293438i \(-0.0947995\pi\)
\(224\) −0.381966 2.61803i −0.0255212 0.174925i
\(225\) −12.2361 10.9443i −0.815738 0.729618i
\(226\) −16.0000 −1.06430
\(227\) 3.52786 0.234153 0.117076 0.993123i \(-0.462648\pi\)
0.117076 + 0.993123i \(0.462648\pi\)
\(228\) −9.70820 3.70820i −0.642942 0.245582i
\(229\) 2.94427i 0.194563i −0.995257 0.0972815i \(-0.968985\pi\)
0.995257 0.0972815i \(-0.0310147\pi\)
\(230\) −10.4721 −0.690512
\(231\) 0 0
\(232\) 5.70820 0.374762
\(233\) 7.05573i 0.462236i −0.972926 0.231118i \(-0.925762\pi\)
0.972926 0.231118i \(-0.0742384\pi\)
\(234\) −2.23607 2.00000i −0.146176 0.130744i
\(235\) −20.9443 −1.36625
\(236\) 4.47214 0.291111
\(237\) −5.52786 + 14.4721i −0.359073 + 0.940066i
\(238\) −0.944272 6.47214i −0.0612081 0.419526i
\(239\) 0.583592i 0.0377494i −0.999822 0.0188747i \(-0.993992\pi\)
0.999822 0.0188747i \(-0.00600837\pi\)
\(240\) 2.00000 5.23607i 0.129099 0.337987i
\(241\) 10.6525i 0.686186i −0.939301 0.343093i \(-0.888525\pi\)
0.939301 0.343093i \(-0.111475\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 15.0902 + 3.90983i 0.968035 + 0.250816i
\(244\) 4.47214i 0.286299i
\(245\) 21.7082 6.47214i 1.38689 0.413490i
\(246\) 8.47214 + 3.23607i 0.540164 + 0.206324i
\(247\) −6.00000 −0.381771
\(248\) −7.23607 −0.459491
\(249\) 8.65248 22.6525i 0.548328 1.43554i
\(250\) 1.52786i 0.0966306i
\(251\) 14.7639 0.931891 0.465946 0.884813i \(-0.345714\pi\)
0.465946 + 0.884813i \(0.345714\pi\)
\(252\) 6.61803 + 4.38197i 0.416897 + 0.276038i
\(253\) 0 0
\(254\) 3.05573i 0.191733i
\(255\) 4.94427 12.9443i 0.309622 0.810602i
\(256\) 1.00000 0.0625000
\(257\) 2.47214 0.154208 0.0771038 0.997023i \(-0.475433\pi\)
0.0771038 + 0.997023i \(0.475433\pi\)
\(258\) 16.9443 + 6.47214i 1.05490 + 0.402938i
\(259\) −24.1803 + 3.52786i −1.50249 + 0.219211i
\(260\) 3.23607i 0.200692i
\(261\) −11.4164 + 12.7639i −0.706658 + 0.790068i
\(262\) 5.23607i 0.323485i
\(263\) 17.7082i 1.09193i −0.837806 0.545967i \(-0.816162\pi\)
0.837806 0.545967i \(-0.183838\pi\)
\(264\) 0 0
\(265\) 10.4721i 0.643298i
\(266\) 15.7082 2.29180i 0.963132 0.140519i
\(267\) 3.81966 10.0000i 0.233759 0.611990i
\(268\) −6.94427 −0.424189
\(269\) 8.29180 0.505560 0.252780 0.967524i \(-0.418655\pi\)
0.252780 + 0.967524i \(0.418655\pi\)
\(270\) 7.70820 + 14.9443i 0.469106 + 0.909479i
\(271\) 3.81966i 0.232028i 0.993248 + 0.116014i \(0.0370117\pi\)
−0.993248 + 0.116014i \(0.962988\pi\)
\(272\) 2.47214 0.149895
\(273\) 4.47214 + 1.00000i 0.270666 + 0.0605228i
\(274\) 7.52786 0.454775
\(275\) 0 0
\(276\) 5.23607 + 2.00000i 0.315174 + 0.120386i
\(277\) 32.4721 1.95106 0.975531 0.219863i \(-0.0705610\pi\)
0.975531 + 0.219863i \(0.0705610\pi\)
\(278\) 12.1803 0.730528
\(279\) 14.4721 16.1803i 0.866424 0.968692i
\(280\) 1.23607 + 8.47214i 0.0738692 + 0.506307i
\(281\) 4.47214i 0.266785i −0.991063 0.133393i \(-0.957413\pi\)
0.991063 0.133393i \(-0.0425871\pi\)
\(282\) 10.4721 + 4.00000i 0.623607 + 0.238197i
\(283\) 21.1246i 1.25573i −0.778323 0.627864i \(-0.783929\pi\)
0.778323 0.627864i \(-0.216071\pi\)
\(284\) 14.4721i 0.858763i
\(285\) 31.4164 + 12.0000i 1.86095 + 0.710819i
\(286\) 0 0
\(287\) −13.7082 + 2.00000i −0.809170 + 0.118056i
\(288\) −2.00000 + 2.23607i −0.117851 + 0.131762i
\(289\) −10.8885 −0.640503
\(290\) −18.4721 −1.08472
\(291\) −1.23607 0.472136i −0.0724596 0.0276771i
\(292\) 3.23607i 0.189377i
\(293\) −14.2918 −0.834936 −0.417468 0.908692i \(-0.637082\pi\)
−0.417468 + 0.908692i \(0.637082\pi\)
\(294\) −12.0902 0.909830i −0.705113 0.0530624i
\(295\) −14.4721 −0.842600
\(296\) 9.23607i 0.536836i
\(297\) 0 0
\(298\) −17.4164 −1.00891
\(299\) 3.23607 0.187147
\(300\) −3.38197 + 8.85410i −0.195258 + 0.511192i
\(301\) −27.4164 + 4.00000i −1.58026 + 0.230556i
\(302\) 3.70820i 0.213383i
\(303\) 11.2361 29.4164i 0.645495 1.68993i
\(304\) 6.00000i 0.344124i
\(305\) 14.4721i 0.828672i
\(306\) −4.94427 + 5.52786i −0.282645 + 0.316007i
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) 0 0
\(309\) −12.4721 4.76393i −0.709515 0.271011i
\(310\) 23.4164 1.32996
\(311\) −22.4721 −1.27428 −0.637139 0.770749i \(-0.719882\pi\)
−0.637139 + 0.770749i \(0.719882\pi\)
\(312\) −0.618034 + 1.61803i −0.0349893 + 0.0916031i
\(313\) 10.4721i 0.591920i −0.955200 0.295960i \(-0.904360\pi\)
0.955200 0.295960i \(-0.0956395\pi\)
\(314\) 5.41641 0.305666
\(315\) −21.4164 14.1803i −1.20668 0.798972i
\(316\) 8.94427 0.503155
\(317\) 6.94427i 0.390029i −0.980800 0.195015i \(-0.937525\pi\)
0.980800 0.195015i \(-0.0624754\pi\)
\(318\) −2.00000 + 5.23607i −0.112154 + 0.293624i
\(319\) 0 0
\(320\) −3.23607 −0.180902
\(321\) −4.00000 1.52786i −0.223258 0.0852771i
\(322\) −8.47214 + 1.23607i −0.472134 + 0.0688834i
\(323\) 14.8328i 0.825320i
\(324\) −1.00000 8.94427i −0.0555556 0.496904i
\(325\) 5.47214i 0.303539i
\(326\) 9.41641i 0.521527i
\(327\) 3.81966 10.0000i 0.211228 0.553001i
\(328\) 5.23607i 0.289113i
\(329\) −16.9443 + 2.47214i −0.934168 + 0.136293i
\(330\) 0 0
\(331\) 14.3607 0.789334 0.394667 0.918824i \(-0.370860\pi\)
0.394667 + 0.918824i \(0.370860\pi\)
\(332\) −14.0000 −0.768350
\(333\) 20.6525 + 18.4721i 1.13175 + 1.01227i
\(334\) 16.9443i 0.927149i
\(335\) 22.4721 1.22778
\(336\) 1.00000 4.47214i 0.0545545 0.243975i
\(337\) −19.8885 −1.08340 −0.541699 0.840573i \(-0.682219\pi\)
−0.541699 + 0.840573i \(0.682219\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) −25.8885 9.88854i −1.40607 0.537072i
\(340\) −8.00000 −0.433861
\(341\) 0 0
\(342\) −13.4164 12.0000i −0.725476 0.648886i
\(343\) 16.7984 7.79837i 0.907027 0.421073i
\(344\) 10.4721i 0.564620i
\(345\) −16.9443 6.47214i −0.912249 0.348448i
\(346\) 18.7639i 1.00876i
\(347\) 24.3607i 1.30775i 0.756603 + 0.653875i \(0.226858\pi\)
−0.756603 + 0.653875i \(0.773142\pi\)
\(348\) 9.23607 + 3.52786i 0.495105 + 0.189113i
\(349\) 35.3050i 1.88983i −0.327315 0.944915i \(-0.606144\pi\)
0.327315 0.944915i \(-0.393856\pi\)
\(350\) −2.09017 14.3262i −0.111724 0.765770i
\(351\) −2.38197 4.61803i −0.127140 0.246492i
\(352\) 0 0
\(353\) 19.1246 1.01790 0.508950 0.860796i \(-0.330034\pi\)
0.508950 + 0.860796i \(0.330034\pi\)
\(354\) 7.23607 + 2.76393i 0.384593 + 0.146901i
\(355\) 46.8328i 2.48563i
\(356\) −6.18034 −0.327557
\(357\) 2.47214 11.0557i 0.130839 0.585131i
\(358\) 10.4721 0.553470
\(359\) 21.8885i 1.15523i −0.816308 0.577617i \(-0.803983\pi\)
0.816308 0.577617i \(-0.196017\pi\)
\(360\) 6.47214 7.23607i 0.341112 0.381374i
\(361\) −17.0000 −0.894737
\(362\) 4.47214 0.235050
\(363\) 6.79837 17.7984i 0.356822 0.934172i
\(364\) −0.381966 2.61803i −0.0200205 0.137222i
\(365\) 10.4721i 0.548137i
\(366\) 2.76393 7.23607i 0.144473 0.378235i
\(367\) 12.6525i 0.660454i 0.943902 + 0.330227i \(0.107125\pi\)
−0.943902 + 0.330227i \(0.892875\pi\)
\(368\) 3.23607i 0.168692i
\(369\) 11.7082 + 10.4721i 0.609505 + 0.545158i
\(370\) 29.8885i 1.55383i
\(371\) −1.23607 8.47214i −0.0641735 0.439851i
\(372\) −11.7082 4.47214i −0.607042 0.231869i
\(373\) 17.4164 0.901787 0.450894 0.892578i \(-0.351105\pi\)
0.450894 + 0.892578i \(0.351105\pi\)
\(374\) 0 0
\(375\) 0.944272 2.47214i 0.0487620 0.127661i
\(376\) 6.47214i 0.333775i
\(377\) 5.70820 0.293987
\(378\) 8.00000 + 11.1803i 0.411476 + 0.575055i
\(379\) −30.0000 −1.54100 −0.770498 0.637442i \(-0.779993\pi\)
−0.770498 + 0.637442i \(0.779993\pi\)
\(380\) 19.4164i 0.996041i
\(381\) −1.88854 + 4.94427i −0.0967530 + 0.253303i
\(382\) −21.7082 −1.11069
\(383\) −30.4721 −1.55705 −0.778527 0.627611i \(-0.784033\pi\)
−0.778527 + 0.627611i \(0.784033\pi\)
\(384\) 1.61803 + 0.618034i 0.0825700 + 0.0315389i
\(385\) 0 0
\(386\) 11.8885i 0.605111i
\(387\) 23.4164 + 20.9443i 1.19032 + 1.06466i
\(388\) 0.763932i 0.0387828i
\(389\) 32.5410i 1.64990i −0.565209 0.824948i \(-0.691205\pi\)
0.565209 0.824948i \(-0.308795\pi\)
\(390\) 2.00000 5.23607i 0.101274 0.265139i
\(391\) 8.00000i 0.404577i
\(392\) 2.00000 + 6.70820i 0.101015 + 0.338815i
\(393\) −3.23607 + 8.47214i −0.163238 + 0.427363i
\(394\) 25.4164 1.28046
\(395\) −28.9443 −1.45634
\(396\) 0 0
\(397\) 28.8328i 1.44708i 0.690284 + 0.723539i \(0.257486\pi\)
−0.690284 + 0.723539i \(0.742514\pi\)
\(398\) 27.7082 1.38889
\(399\) 26.8328 + 6.00000i 1.34332 + 0.300376i
\(400\) 5.47214 0.273607
\(401\) 18.9443i 0.946032i 0.881054 + 0.473016i \(0.156835\pi\)
−0.881054 + 0.473016i \(0.843165\pi\)
\(402\) −11.2361 4.29180i −0.560404 0.214055i
\(403\) −7.23607 −0.360454
\(404\) −18.1803 −0.904506
\(405\) 3.23607 + 28.9443i 0.160802 + 1.43825i
\(406\) −14.9443 + 2.18034i −0.741672 + 0.108208i
\(407\) 0 0
\(408\) 4.00000 + 1.52786i 0.198030 + 0.0756405i
\(409\) 5.70820i 0.282253i −0.989992 0.141126i \(-0.954928\pi\)
0.989992 0.141126i \(-0.0450724\pi\)
\(410\) 16.9443i 0.836818i
\(411\) 12.1803 + 4.65248i 0.600812 + 0.229490i
\(412\) 7.70820i 0.379756i
\(413\) −11.7082 + 1.70820i −0.576123 + 0.0840552i
\(414\) 7.23607 + 6.47214i 0.355633 + 0.318088i
\(415\) 45.3050 2.22393
\(416\) 1.00000 0.0490290
\(417\) 19.7082 + 7.52786i 0.965115 + 0.368641i
\(418\) 0 0
\(419\) −11.7082 −0.571983 −0.285992 0.958232i \(-0.592323\pi\)
−0.285992 + 0.958232i \(0.592323\pi\)
\(420\) −3.23607 + 14.4721i −0.157904 + 0.706168i
\(421\) 14.7639 0.719550 0.359775 0.933039i \(-0.382853\pi\)
0.359775 + 0.933039i \(0.382853\pi\)
\(422\) 25.8885i 1.26023i
\(423\) 14.4721 + 12.9443i 0.703659 + 0.629372i
\(424\) 3.23607 0.157157
\(425\) 13.5279 0.656198
\(426\) 8.94427 23.4164i 0.433351 1.13453i
\(427\) 1.70820 + 11.7082i 0.0826658 + 0.566600i
\(428\) 2.47214i 0.119495i
\(429\) 0 0
\(430\) 33.8885i 1.63425i
\(431\) 20.0000i 0.963366i −0.876346 0.481683i \(-0.840026\pi\)
0.876346 0.481683i \(-0.159974\pi\)
\(432\) −4.61803 + 2.38197i −0.222185 + 0.114602i
\(433\) 19.4164i 0.933093i −0.884497 0.466547i \(-0.845498\pi\)
0.884497 0.466547i \(-0.154502\pi\)
\(434\) 18.9443 2.76393i 0.909354 0.132673i
\(435\) −29.8885 11.4164i −1.43305 0.547375i
\(436\) −6.18034 −0.295985
\(437\) 19.4164 0.928813
\(438\) −2.00000 + 5.23607i −0.0955637 + 0.250189i
\(439\) 34.5410i 1.64855i 0.566188 + 0.824276i \(0.308418\pi\)
−0.566188 + 0.824276i \(0.691582\pi\)
\(440\) 0 0
\(441\) −19.0000 8.94427i −0.904762 0.425918i
\(442\) 2.47214 0.117588
\(443\) 29.5279i 1.40291i 0.712713 + 0.701456i \(0.247466\pi\)
−0.712713 + 0.701456i \(0.752534\pi\)
\(444\) 5.70820 14.9443i 0.270899 0.709224i
\(445\) 20.0000 0.948091
\(446\) −8.76393 −0.414984
\(447\) −28.1803 10.7639i −1.33288 0.509117i
\(448\) −2.61803 + 0.381966i −0.123690 + 0.0180462i
\(449\) 18.3607i 0.866494i 0.901275 + 0.433247i \(0.142632\pi\)
−0.901275 + 0.433247i \(0.857368\pi\)
\(450\) −10.9443 + 12.2361i −0.515918 + 0.576814i
\(451\) 0 0
\(452\) 16.0000i 0.752577i
\(453\) 2.29180 6.00000i 0.107678 0.281905i
\(454\) 3.52786i 0.165571i
\(455\) 1.23607 + 8.47214i 0.0579478 + 0.397180i
\(456\) −3.70820 + 9.70820i −0.173653 + 0.454628i
\(457\) 26.9443 1.26040 0.630200 0.776433i \(-0.282973\pi\)
0.630200 + 0.776433i \(0.282973\pi\)
\(458\) −2.94427 −0.137577
\(459\) −11.4164 + 5.88854i −0.532872 + 0.274854i
\(460\) 10.4721i 0.488266i
\(461\) −20.7639 −0.967073 −0.483536 0.875324i \(-0.660648\pi\)
−0.483536 + 0.875324i \(0.660648\pi\)
\(462\) 0 0
\(463\) 15.7082 0.730022 0.365011 0.931003i \(-0.381065\pi\)
0.365011 + 0.931003i \(0.381065\pi\)
\(464\) 5.70820i 0.264997i
\(465\) 37.8885 + 14.4721i 1.75704 + 0.671129i
\(466\) −7.05573 −0.326850
\(467\) −18.1803 −0.841286 −0.420643 0.907226i \(-0.638195\pi\)
−0.420643 + 0.907226i \(0.638195\pi\)
\(468\) −2.00000 + 2.23607i −0.0924500 + 0.103362i
\(469\) 18.1803 2.65248i 0.839490 0.122480i
\(470\) 20.9443i 0.966087i
\(471\) 8.76393 + 3.34752i 0.403821 + 0.154246i
\(472\) 4.47214i 0.205847i
\(473\) 0 0
\(474\) 14.4721 + 5.52786i 0.664727 + 0.253903i
\(475\) 32.8328i 1.50647i
\(476\) −6.47214 + 0.944272i −0.296650 + 0.0432806i
\(477\) −6.47214 + 7.23607i −0.296339 + 0.331317i
\(478\) −0.583592 −0.0266929
\(479\) 14.4721 0.661249 0.330624 0.943762i \(-0.392741\pi\)
0.330624 + 0.943762i \(0.392741\pi\)
\(480\) −5.23607 2.00000i −0.238993 0.0912871i
\(481\) 9.23607i 0.421128i
\(482\) −10.6525 −0.485207
\(483\) −14.4721 3.23607i −0.658505 0.147246i
\(484\) −11.0000 −0.500000
\(485\) 2.47214i 0.112254i
\(486\) 3.90983 15.0902i 0.177353 0.684504i
\(487\) 10.7639 0.487760 0.243880 0.969805i \(-0.421580\pi\)
0.243880 + 0.969805i \(0.421580\pi\)
\(488\) −4.47214 −0.202444
\(489\) −5.81966 + 15.2361i −0.263174 + 0.688999i
\(490\) −6.47214 21.7082i −0.292381 0.980677i
\(491\) 3.41641i 0.154180i 0.997024 + 0.0770902i \(0.0245629\pi\)
−0.997024 + 0.0770902i \(0.975437\pi\)
\(492\) 3.23607 8.47214i 0.145893 0.381953i
\(493\) 14.1115i 0.635548i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 7.23607i 0.324909i
\(497\) 5.52786 + 37.8885i 0.247959 + 1.69953i
\(498\) −22.6525 8.65248i −1.01508 0.387727i
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) −1.52786 −0.0683282
\(501\) 10.4721 27.4164i 0.467861 1.22487i
\(502\) 14.7639i 0.658947i
\(503\) −4.94427 −0.220454 −0.110227 0.993906i \(-0.535158\pi\)
−0.110227 + 0.993906i \(0.535158\pi\)
\(504\) 4.38197 6.61803i 0.195188 0.294791i
\(505\) 58.8328 2.61803
\(506\) 0 0
\(507\) −0.618034 + 1.61803i −0.0274479 + 0.0718594i
\(508\) 3.05573 0.135576
\(509\) −7.23607 −0.320733 −0.160367 0.987058i \(-0.551268\pi\)
−0.160367 + 0.987058i \(0.551268\pi\)
\(510\) −12.9443 4.94427i −0.573182 0.218936i
\(511\) −1.23607 8.47214i −0.0546804 0.374785i
\(512\) 1.00000i 0.0441942i
\(513\) −14.2918 27.7082i −0.630998 1.22335i
\(514\) 2.47214i 0.109041i
\(515\) 24.9443i 1.09918i
\(516\) 6.47214 16.9443i 0.284920 0.745930i
\(517\) 0 0
\(518\) 3.52786 + 24.1803i 0.155005 + 1.06242i
\(519\) −11.5967 + 30.3607i −0.509041 + 1.33269i
\(520\) −3.23607 −0.141911
\(521\) −34.8328 −1.52605 −0.763027 0.646367i \(-0.776288\pi\)
−0.763027 + 0.646367i \(0.776288\pi\)
\(522\) 12.7639 + 11.4164i 0.558662 + 0.499683i
\(523\) 2.29180i 0.100213i 0.998744 + 0.0501066i \(0.0159561\pi\)
−0.998744 + 0.0501066i \(0.984044\pi\)
\(524\) 5.23607 0.228739
\(525\) 5.47214 24.4721i 0.238824 1.06805i
\(526\) −17.7082 −0.772114
\(527\) 17.8885i 0.779237i
\(528\) 0 0
\(529\) 12.5279 0.544690
\(530\) −10.4721 −0.454881
\(531\) 10.0000 + 8.94427i 0.433963 + 0.388148i
\(532\) −2.29180 15.7082i −0.0993620 0.681037i
\(533\) 5.23607i 0.226799i
\(534\) −10.0000 3.81966i −0.432742 0.165293i
\(535\) 8.00000i 0.345870i
\(536\) 6.94427i 0.299947i
\(537\) 16.9443 + 6.47214i 0.731199 + 0.279293i
\(538\) 8.29180i 0.357485i
\(539\) 0 0
\(540\) 14.9443 7.70820i 0.643099 0.331708i
\(541\) −28.6525 −1.23187 −0.615933 0.787798i \(-0.711221\pi\)
−0.615933 + 0.787798i \(0.711221\pi\)
\(542\) 3.81966 0.164068
\(543\) 7.23607 + 2.76393i 0.310529 + 0.118612i
\(544\) 2.47214i 0.105992i
\(545\) 20.0000 0.856706
\(546\) 1.00000 4.47214i 0.0427960 0.191390i
\(547\) 22.4721 0.960839 0.480420 0.877039i \(-0.340484\pi\)
0.480420 + 0.877039i \(0.340484\pi\)
\(548\) 7.52786i 0.321574i
\(549\) 8.94427 10.0000i 0.381732 0.426790i
\(550\) 0 0
\(551\) 34.2492 1.45907
\(552\) 2.00000 5.23607i 0.0851257 0.222862i
\(553\) −23.4164 + 3.41641i −0.995767 + 0.145280i
\(554\) 32.4721i 1.37961i
\(555\) −18.4721 + 48.3607i −0.784099 + 2.05280i
\(556\) 12.1803i 0.516561i
\(557\) 22.0000i 0.932170i 0.884740 + 0.466085i \(0.154336\pi\)
−0.884740 + 0.466085i \(0.845664\pi\)
\(558\) −16.1803 14.4721i −0.684968 0.612654i
\(559\) 10.4721i 0.442924i
\(560\) 8.47214 1.23607i 0.358013 0.0522334i
\(561\) 0 0
\(562\) −4.47214 −0.188646
\(563\) −9.81966 −0.413849 −0.206925 0.978357i \(-0.566346\pi\)
−0.206925 + 0.978357i \(0.566346\pi\)
\(564\) 4.00000 10.4721i 0.168430 0.440956i
\(565\) 51.7771i 2.17828i
\(566\) −21.1246 −0.887934
\(567\) 6.03444 + 23.0344i 0.253423 + 0.967356i
\(568\) −14.4721 −0.607237
\(569\) 8.36068i 0.350498i 0.984524 + 0.175249i \(0.0560730\pi\)
−0.984524 + 0.175249i \(0.943927\pi\)
\(570\) 12.0000 31.4164i 0.502625 1.31589i
\(571\) −22.4721 −0.940430 −0.470215 0.882552i \(-0.655824\pi\)
−0.470215 + 0.882552i \(0.655824\pi\)
\(572\) 0 0
\(573\) −35.1246 13.4164i −1.46735 0.560478i
\(574\) 2.00000 + 13.7082i 0.0834784 + 0.572169i
\(575\) 17.7082i 0.738483i
\(576\) 2.23607 + 2.00000i 0.0931695 + 0.0833333i
\(577\) 2.87539i 0.119704i −0.998207 0.0598520i \(-0.980937\pi\)
0.998207 0.0598520i \(-0.0190629\pi\)
\(578\) 10.8885i 0.452904i
\(579\) 7.34752 19.2361i 0.305353 0.799424i
\(580\) 18.4721i 0.767014i
\(581\) 36.6525 5.34752i 1.52060 0.221853i
\(582\) −0.472136 + 1.23607i −0.0195707 + 0.0512367i
\(583\) 0 0
\(584\) 3.23607 0.133909
\(585\) 6.47214 7.23607i 0.267590 0.299175i
\(586\) 14.2918i 0.590389i
\(587\) −5.41641 −0.223559 −0.111780 0.993733i \(-0.535655\pi\)
−0.111780 + 0.993733i \(0.535655\pi\)
\(588\) −0.909830 + 12.0902i −0.0375208 + 0.498590i
\(589\) −43.4164 −1.78894
\(590\) 14.4721i 0.595808i
\(591\) 41.1246 + 15.7082i 1.69164 + 0.646149i
\(592\) −9.23607 −0.379600
\(593\) −40.0689 −1.64543 −0.822716 0.568453i \(-0.807542\pi\)
−0.822716 + 0.568453i \(0.807542\pi\)
\(594\) 0 0
\(595\) 20.9443 3.05573i 0.858631 0.125273i
\(596\) 17.4164i 0.713404i
\(597\) 44.8328 + 17.1246i 1.83488 + 0.700864i
\(598\) 3.23607i 0.132333i
\(599\) 32.5410i 1.32959i −0.747026 0.664795i \(-0.768519\pi\)
0.747026 0.664795i \(-0.231481\pi\)
\(600\) 8.85410 + 3.38197i 0.361467 + 0.138068i
\(601\) 3.41641i 0.139358i −0.997569 0.0696791i \(-0.977802\pi\)
0.997569 0.0696791i \(-0.0221975\pi\)
\(602\) 4.00000 + 27.4164i 0.163028 + 1.11741i
\(603\) −15.5279 13.8885i −0.632344 0.565585i
\(604\) −3.70820 −0.150885
\(605\) 35.5967 1.44721
\(606\) −29.4164 11.2361i −1.19496 0.456434i
\(607\) 23.1246i 0.938599i −0.883039 0.469300i \(-0.844506\pi\)
0.883039 0.469300i \(-0.155494\pi\)
\(608\) 6.00000 0.243332
\(609\) −25.5279 5.70820i −1.03444 0.231308i
\(610\) 14.4721 0.585960
\(611\) 6.47214i 0.261835i
\(612\) 5.52786 + 4.94427i 0.223451 + 0.199860i
\(613\) 15.7082 0.634448 0.317224 0.948351i \(-0.397249\pi\)
0.317224 + 0.948351i \(0.397249\pi\)
\(614\) −18.0000 −0.726421
\(615\) −10.4721 + 27.4164i −0.422277 + 1.10554i
\(616\) 0 0
\(617\) 33.7771i 1.35981i −0.733298 0.679907i \(-0.762020\pi\)
0.733298 0.679907i \(-0.237980\pi\)
\(618\) −4.76393 + 12.4721i −0.191633 + 0.501703i
\(619\) 8.47214i 0.340524i −0.985399 0.170262i \(-0.945539\pi\)
0.985399 0.170262i \(-0.0544614\pi\)
\(620\) 23.4164i 0.940426i
\(621\) 7.70820 + 14.9443i 0.309320 + 0.599693i
\(622\) 22.4721i 0.901051i
\(623\) 16.1803 2.36068i 0.648252 0.0945786i
\(624\) 1.61803 + 0.618034i 0.0647732 + 0.0247412i
\(625\) −22.4164 −0.896656
\(626\) −10.4721 −0.418551
\(627\) 0 0
\(628\) 5.41641i 0.216138i
\(629\) −22.8328 −0.910404
\(630\) −14.1803 + 21.4164i −0.564958 + 0.853250i
\(631\) 25.8197 1.02786 0.513932 0.857831i \(-0.328188\pi\)
0.513932 + 0.857831i \(0.328188\pi\)
\(632\) 8.94427i 0.355784i
\(633\) −16.0000 + 41.8885i −0.635943 + 1.66492i
\(634\) −6.94427 −0.275792
\(635\) −9.88854 −0.392415
\(636\) 5.23607 + 2.00000i 0.207624 + 0.0793052i
\(637\) 2.00000 + 6.70820i 0.0792429 + 0.265789i
\(638\) 0 0
\(639\) 28.9443 32.3607i 1.14502 1.28017i
\(640\) 3.23607i 0.127917i
\(641\) 34.4721i 1.36157i 0.732484 + 0.680784i \(0.238361\pi\)
−0.732484 + 0.680784i \(0.761639\pi\)
\(642\) −1.52786 + 4.00000i −0.0603000 + 0.157867i
\(643\) 31.8885i 1.25756i 0.777583 + 0.628781i \(0.216446\pi\)
−0.777583 + 0.628781i \(0.783554\pi\)
\(644\) 1.23607 + 8.47214i 0.0487079 + 0.333849i
\(645\) −20.9443 + 54.8328i −0.824680 + 2.15904i
\(646\) 14.8328 0.583589
\(647\) 20.3607 0.800461 0.400230 0.916415i \(-0.368930\pi\)
0.400230 + 0.916415i \(0.368930\pi\)
\(648\) −8.94427 + 1.00000i −0.351364 + 0.0392837i
\(649\) 0 0
\(650\) 5.47214 0.214635
\(651\) 32.3607 + 7.23607i 1.26832 + 0.283604i
\(652\) 9.41641 0.368775
\(653\) 5.34752i 0.209265i −0.994511 0.104632i \(-0.966633\pi\)
0.994511 0.104632i \(-0.0333666\pi\)
\(654\) −10.0000 3.81966i −0.391031 0.149361i
\(655\) −16.9443 −0.662067
\(656\) −5.23607 −0.204434
\(657\) −6.47214 + 7.23607i −0.252502 + 0.282306i
\(658\) 2.47214 + 16.9443i 0.0963739 + 0.660556i
\(659\) 1.88854i 0.0735672i −0.999323 0.0367836i \(-0.988289\pi\)
0.999323 0.0367836i \(-0.0117112\pi\)
\(660\) 0 0
\(661\) 33.4164i 1.29975i 0.760042 + 0.649874i \(0.225178\pi\)
−0.760042 + 0.649874i \(0.774822\pi\)
\(662\) 14.3607i 0.558144i
\(663\) 4.00000 + 1.52786i 0.155347 + 0.0593373i
\(664\) 14.0000i 0.543305i
\(665\) 7.41641 + 50.8328i 0.287596 + 1.97121i
\(666\) 18.4721 20.6525i 0.715781 0.800267i
\(667\) −18.4721 −0.715244
\(668\) −16.9443 −0.655594
\(669\) −14.1803 5.41641i −0.548244 0.209410i
\(670\) 22.4721i 0.868174i
\(671\) 0 0
\(672\) −4.47214 1.00000i −0.172516 0.0385758i
\(673\) −12.8328 −0.494669 −0.247334 0.968930i \(-0.579555\pi\)
−0.247334 + 0.968930i \(0.579555\pi\)
\(674\) 19.8885i 0.766078i
\(675\) −25.2705 + 13.0344i −0.972662 + 0.501696i
\(676\) 1.00000 0.0384615
\(677\) 8.65248 0.332542 0.166271 0.986080i \(-0.446827\pi\)
0.166271 + 0.986080i \(0.446827\pi\)
\(678\) −9.88854 + 25.8885i −0.379767 + 0.994244i
\(679\) −0.291796 2.00000i −0.0111981 0.0767530i
\(680\) 8.00000i 0.306786i
\(681\) 2.18034 5.70820i 0.0835508 0.218739i
\(682\) 0 0
\(683\) 42.8328i 1.63895i −0.573113 0.819476i \(-0.694265\pi\)
0.573113 0.819476i \(-0.305735\pi\)
\(684\) −12.0000 + 13.4164i −0.458831 + 0.512989i
\(685\) 24.3607i 0.930774i
\(686\) −7.79837 16.7984i −0.297743 0.641365i
\(687\) −4.76393 1.81966i −0.181755 0.0694244i
\(688\) −10.4721 −0.399246
\(689\) 3.23607 0.123284
\(690\) −6.47214 + 16.9443i −0.246390 + 0.645057i
\(691\) 10.0000i 0.380418i 0.981744 + 0.190209i \(0.0609166\pi\)
−0.981744 + 0.190209i \(0.939083\pi\)
\(692\) 18.7639 0.713298
\(693\) 0 0
\(694\) 24.3607 0.924719
\(695\) 39.4164i 1.49515i
\(696\) 3.52786 9.23607i 0.133723 0.350092i
\(697\) −12.9443 −0.490299
\(698\) −35.3050 −1.33631
\(699\) −11.4164 4.36068i −0.431808 0.164936i
\(700\) −14.3262 + 2.09017i −0.541481 + 0.0790010i
\(701\) 12.7639i 0.482087i −0.970514 0.241044i \(-0.922510\pi\)
0.970514 0.241044i \(-0.0774897\pi\)
\(702\) −4.61803 + 2.38197i −0.174296 + 0.0899015i
\(703\) 55.4164i 2.09007i
\(704\) 0 0
\(705\) −12.9443 + 33.8885i −0.487509 + 1.27632i
\(706\) 19.1246i 0.719764i
\(707\) 47.5967 6.94427i 1.79006 0.261166i
\(708\) 2.76393 7.23607i 0.103875 0.271948i
\(709\) 2.76393 0.103802 0.0519008 0.998652i \(-0.483472\pi\)
0.0519008 + 0.998652i \(0.483472\pi\)
\(710\) 46.8328 1.75760
\(711\) 20.0000 + 17.8885i 0.750059 + 0.670873i
\(712\) 6.18034i 0.231618i
\(713\) 23.4164 0.876951
\(714\) −11.0557 2.47214i −0.413750 0.0925174i
\(715\) 0 0
\(716\) 10.4721i 0.391362i
\(717\) −0.944272 0.360680i −0.0352645 0.0134698i
\(718\) −21.8885 −0.816873
\(719\) 44.7214 1.66783 0.833913 0.551896i \(-0.186096\pi\)
0.833913 + 0.551896i \(0.186096\pi\)
\(720\) −7.23607 6.47214i −0.269672 0.241202i
\(721\) −2.94427 20.1803i −0.109650 0.751555i
\(722\) 17.0000i 0.632674i
\(723\) −17.2361 6.58359i −0.641016 0.244846i
\(724\) 4.47214i 0.166206i
\(725\) 31.2361i 1.16008i
\(726\) −17.7984 6.79837i −0.660560 0.252311i
\(727\) 38.1803i 1.41603i 0.706197 + 0.708015i \(0.250409\pi\)
−0.706197 + 0.708015i \(0.749591\pi\)
\(728\) −2.61803 + 0.381966i −0.0970308 + 0.0141566i
\(729\) 15.6525 22.0000i 0.579721 0.814815i
\(730\) −10.4721 −0.387591
\(731\) −25.8885 −0.957522
\(732\) −7.23607 2.76393i −0.267453 0.102158i
\(733\) 14.0000i 0.517102i 0.965998 + 0.258551i \(0.0832450\pi\)
−0.965998 + 0.258551i \(0.916755\pi\)
\(734\) 12.6525 0.467011
\(735\) 2.94427 39.1246i 0.108601 1.44313i
\(736\) −3.23607 −0.119283
\(737\) 0 0
\(738\) 10.4721 11.7082i 0.385485 0.430985i
\(739\) −16.8328 −0.619205 −0.309603 0.950866i \(-0.600196\pi\)
−0.309603 + 0.950866i \(0.600196\pi\)
\(740\) 29.8885 1.09872
\(741\) −3.70820 + 9.70820i −0.136224 + 0.356640i
\(742\) −8.47214 + 1.23607i −0.311022 + 0.0453775i
\(743\) 17.3050i 0.634857i −0.948282 0.317429i \(-0.897181\pi\)
0.948282 0.317429i \(-0.102819\pi\)
\(744\) −4.47214 + 11.7082i −0.163956 + 0.429244i
\(745\) 56.3607i 2.06490i
\(746\) 17.4164i 0.637660i
\(747\) −31.3050 28.0000i −1.14539 1.02447i
\(748\) 0 0
\(749\) −0.944272 6.47214i −0.0345029 0.236487i
\(750\) −2.47214 0.944272i −0.0902696 0.0344799i
\(751\) 33.3050 1.21531 0.607657 0.794199i \(-0.292109\pi\)
0.607657 + 0.794199i \(0.292109\pi\)
\(752\) −6.47214 −0.236015
\(753\) 9.12461 23.8885i 0.332519 0.870547i
\(754\) 5.70820i 0.207881i
\(755\) 12.0000 0.436725
\(756\) 11.1803 8.00000i 0.406625 0.290957i
\(757\) 10.3607 0.376565 0.188283 0.982115i \(-0.439708\pi\)
0.188283 + 0.982115i \(0.439708\pi\)
\(758\) 30.0000i 1.08965i
\(759\) 0 0
\(760\) −19.4164 −0.704307
\(761\) −39.7082 −1.43942 −0.719711 0.694274i \(-0.755726\pi\)
−0.719711 + 0.694274i \(0.755726\pi\)
\(762\) 4.94427 + 1.88854i 0.179112 + 0.0684147i
\(763\) 16.1803 2.36068i 0.585768 0.0854623i
\(764\) 21.7082i 0.785375i
\(765\) −17.8885 16.0000i −0.646762 0.578481i
\(766\) 30.4721i 1.10100i
\(767\) 4.47214i 0.161479i
\(768\) 0.618034 1.61803i 0.0223014 0.0583858i
\(769\) 52.5410i 1.89468i −0.320233 0.947339i \(-0.603761\pi\)
0.320233 0.947339i \(-0.396239\pi\)
\(770\) 0 0
\(771\) 1.52786 4.00000i 0.0550247 0.144056i
\(772\) −11.8885 −0.427878
\(773\) −14.2918 −0.514040 −0.257020 0.966406i \(-0.582741\pi\)
−0.257020 + 0.966406i \(0.582741\pi\)
\(774\) 20.9443 23.4164i 0.752826 0.841685i
\(775\) 39.5967i 1.42236i
\(776\) 0.763932 0.0274236
\(777\) −9.23607 + 41.3050i −0.331342 + 1.48181i
\(778\) −32.5410 −1.16665
\(779\) 31.4164i 1.12561i
\(780\) −5.23607 2.00000i −0.187481 0.0716115i
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) 13.5967 + 26.3607i 0.485908 + 0.942054i
\(784\) 6.70820 2.00000i 0.239579 0.0714286i
\(785\) 17.5279i