Properties

Label 504.2.c.f.253.5
Level 504
Weight 2
Character 504.253
Analytic conductor 4.024
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.386672896.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 253.5
Root \(0.621372 + 1.27039i\)
Character \(\chi\) = 504.253
Dual form 504.2.c.f.253.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.621372 - 1.27039i) q^{2} +(-1.22779 - 1.57877i) q^{4} -3.69833i q^{5} +1.00000 q^{7} +(-2.76858 + 0.578773i) q^{8} +O(q^{10})\) \(q+(0.621372 - 1.27039i) q^{2} +(-1.22779 - 1.57877i) q^{4} -3.69833i q^{5} +1.00000 q^{7} +(-2.76858 + 0.578773i) q^{8} +(-4.69833 - 2.29804i) q^{10} -3.21284i q^{11} +5.08157i q^{13} +(0.621372 - 1.27039i) q^{14} +(-0.985049 + 3.87681i) q^{16} -0.616762 q^{17} -4.48549i q^{19} +(-5.83882 + 4.54078i) q^{20} +(-4.08157 - 1.99637i) q^{22} -1.38324 q^{23} -8.67765 q^{25} +(6.45559 + 3.15755i) q^{26} +(-1.22779 - 1.57877i) q^{28} +5.67765i q^{29} +6.91117 q^{31} +(4.31299 + 3.66034i) q^{32} +(-0.383238 + 0.783529i) q^{34} -3.69833i q^{35} -6.91117i q^{37} +(-5.69833 - 2.78716i) q^{38} +(2.14049 + 10.2391i) q^{40} +0.616762 q^{41} -7.99274i q^{43} +(-5.07235 + 3.94470i) q^{44} +(-0.859506 + 1.75726i) q^{46} -4.97098 q^{47} +1.00000 q^{49} +(-5.39205 + 11.0240i) q^{50} +(8.02264 - 6.23912i) q^{52} -4.48549i q^{53} -11.8822 q^{55} +(-2.76858 + 0.578773i) q^{56} +(7.21284 + 3.52793i) q^{58} -4.00000i q^{59} +12.4782i q^{61} +(4.29441 - 8.77990i) q^{62} +(7.33004 - 3.20476i) q^{64} +18.7933 q^{65} -9.56706i q^{67} +(0.757255 + 0.973726i) q^{68} +(-4.69833 - 2.29804i) q^{70} +15.2056 q^{71} +15.5598 q^{73} +(-8.77990 - 4.29441i) q^{74} +(-7.08157 + 5.50725i) q^{76} -3.21284i q^{77} -5.23352 q^{79} +(14.3377 + 3.64304i) q^{80} +(0.383238 - 0.783529i) q^{82} +10.4257i q^{83} +2.28099i q^{85} +(-10.1539 - 4.96647i) q^{86} +(1.85951 + 8.89500i) q^{88} +14.1766 q^{89} +5.08157i q^{91} +(1.69833 + 2.18382i) q^{92} +(-3.08883 + 6.31509i) q^{94} -16.5888 q^{95} +9.73746 q^{97} +(0.621372 - 1.27039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} + O(q^{10}) \) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} - 4q^{10} - 6q^{16} - 4q^{17} - 24q^{20} - 12q^{23} - 24q^{25} + 28q^{26} + 2q^{28} + 8q^{31} + 30q^{32} - 4q^{34} - 12q^{38} + 28q^{40} + 4q^{41} - 16q^{44} + 4q^{46} + 8q^{49} + 20q^{50} - 12q^{52} - 8q^{55} + 6q^{56} + 44q^{58} - 12q^{62} + 26q^{64} + 16q^{65} + 16q^{68} - 4q^{70} + 28q^{71} - 8q^{73} - 4q^{74} - 24q^{76} - 40q^{79} + 4q^{80} + 4q^{82} - 24q^{86} + 4q^{88} - 20q^{89} - 20q^{92} - 72q^{94} - 40q^{95} + 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.621372 1.27039i 0.439377 0.898303i
\(3\) 0 0
\(4\) −1.22779 1.57877i −0.613897 0.789387i
\(5\) 3.69833i 1.65394i −0.562243 0.826972i \(-0.690062\pi\)
0.562243 0.826972i \(-0.309938\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.76858 + 0.578773i −0.978840 + 0.204627i
\(9\) 0 0
\(10\) −4.69833 2.29804i −1.48574 0.726704i
\(11\) 3.21284i 0.968708i −0.874872 0.484354i \(-0.839055\pi\)
0.874872 0.484354i \(-0.160945\pi\)
\(12\) 0 0
\(13\) 5.08157i 1.40937i 0.709518 + 0.704687i \(0.248912\pi\)
−0.709518 + 0.704687i \(0.751088\pi\)
\(14\) 0.621372 1.27039i 0.166069 0.339527i
\(15\) 0 0
\(16\) −0.985049 + 3.87681i −0.246262 + 0.969203i
\(17\) −0.616762 −0.149587 −0.0747933 0.997199i \(-0.523830\pi\)
−0.0747933 + 0.997199i \(0.523830\pi\)
\(18\) 0 0
\(19\) 4.48549i 1.02904i −0.857478 0.514521i \(-0.827970\pi\)
0.857478 0.514521i \(-0.172030\pi\)
\(20\) −5.83882 + 4.54078i −1.30560 + 1.01535i
\(21\) 0 0
\(22\) −4.08157 1.99637i −0.870193 0.425628i
\(23\) −1.38324 −0.288425 −0.144213 0.989547i \(-0.546065\pi\)
−0.144213 + 0.989547i \(0.546065\pi\)
\(24\) 0 0
\(25\) −8.67765 −1.73553
\(26\) 6.45559 + 3.15755i 1.26604 + 0.619246i
\(27\) 0 0
\(28\) −1.22779 1.57877i −0.232031 0.298360i
\(29\) 5.67765i 1.05431i 0.849768 + 0.527156i \(0.176742\pi\)
−0.849768 + 0.527156i \(0.823258\pi\)
\(30\) 0 0
\(31\) 6.91117 1.24128 0.620642 0.784094i \(-0.286872\pi\)
0.620642 + 0.784094i \(0.286872\pi\)
\(32\) 4.31299 + 3.66034i 0.762436 + 0.647063i
\(33\) 0 0
\(34\) −0.383238 + 0.783529i −0.0657249 + 0.134374i
\(35\) 3.69833i 0.625132i
\(36\) 0 0
\(37\) 6.91117i 1.13619i −0.822963 0.568095i \(-0.807681\pi\)
0.822963 0.568095i \(-0.192319\pi\)
\(38\) −5.69833 2.78716i −0.924391 0.452137i
\(39\) 0 0
\(40\) 2.14049 + 10.2391i 0.338442 + 1.61895i
\(41\) 0.616762 0.0963220 0.0481610 0.998840i \(-0.484664\pi\)
0.0481610 + 0.998840i \(0.484664\pi\)
\(42\) 0 0
\(43\) 7.99274i 1.21888i −0.792832 0.609441i \(-0.791394\pi\)
0.792832 0.609441i \(-0.208606\pi\)
\(44\) −5.07235 + 3.94470i −0.764685 + 0.594687i
\(45\) 0 0
\(46\) −0.859506 + 1.75726i −0.126727 + 0.259093i
\(47\) −4.97098 −0.725092 −0.362546 0.931966i \(-0.618092\pi\)
−0.362546 + 0.931966i \(0.618092\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −5.39205 + 11.0240i −0.762551 + 1.55903i
\(51\) 0 0
\(52\) 8.02264 6.23912i 1.11254 0.865210i
\(53\) 4.48549i 0.616129i −0.951365 0.308065i \(-0.900319\pi\)
0.951365 0.308065i \(-0.0996813\pi\)
\(54\) 0 0
\(55\) −11.8822 −1.60219
\(56\) −2.76858 + 0.578773i −0.369967 + 0.0773418i
\(57\) 0 0
\(58\) 7.21284 + 3.52793i 0.947092 + 0.463240i
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) 0 0
\(61\) 12.4782i 1.59767i 0.601548 + 0.798837i \(0.294551\pi\)
−0.601548 + 0.798837i \(0.705449\pi\)
\(62\) 4.29441 8.77990i 0.545391 1.11505i
\(63\) 0 0
\(64\) 7.33004 3.20476i 0.916255 0.400595i
\(65\) 18.7933 2.33102
\(66\) 0 0
\(67\) 9.56706i 1.16880i −0.811465 0.584401i \(-0.801329\pi\)
0.811465 0.584401i \(-0.198671\pi\)
\(68\) 0.757255 + 0.973726i 0.0918307 + 0.118082i
\(69\) 0 0
\(70\) −4.69833 2.29804i −0.561558 0.274668i
\(71\) 15.2056 1.80457 0.902285 0.431139i \(-0.141888\pi\)
0.902285 + 0.431139i \(0.141888\pi\)
\(72\) 0 0
\(73\) 15.5598 1.82114 0.910568 0.413358i \(-0.135644\pi\)
0.910568 + 0.413358i \(0.135644\pi\)
\(74\) −8.77990 4.29441i −1.02064 0.499215i
\(75\) 0 0
\(76\) −7.08157 + 5.50725i −0.812312 + 0.631725i
\(77\) 3.21284i 0.366137i
\(78\) 0 0
\(79\) −5.23352 −0.588817 −0.294409 0.955680i \(-0.595123\pi\)
−0.294409 + 0.955680i \(0.595123\pi\)
\(80\) 14.3377 + 3.64304i 1.60301 + 0.407304i
\(81\) 0 0
\(82\) 0.383238 0.783529i 0.0423216 0.0865263i
\(83\) 10.4257i 1.14437i 0.820125 + 0.572184i \(0.193904\pi\)
−0.820125 + 0.572184i \(0.806096\pi\)
\(84\) 0 0
\(85\) 2.28099i 0.247408i
\(86\) −10.1539 4.96647i −1.09492 0.535548i
\(87\) 0 0
\(88\) 1.85951 + 8.89500i 0.198224 + 0.948210i
\(89\) 14.1766 1.50271 0.751356 0.659897i \(-0.229400\pi\)
0.751356 + 0.659897i \(0.229400\pi\)
\(90\) 0 0
\(91\) 5.08157i 0.532693i
\(92\) 1.69833 + 2.18382i 0.177063 + 0.227679i
\(93\) 0 0
\(94\) −3.08883 + 6.31509i −0.318588 + 0.651352i
\(95\) −16.5888 −1.70198
\(96\) 0 0
\(97\) 9.73746 0.988689 0.494344 0.869266i \(-0.335408\pi\)
0.494344 + 0.869266i \(0.335408\pi\)
\(98\) 0.621372 1.27039i 0.0627681 0.128329i
\(99\) 0 0
\(100\) 10.6544 + 13.7000i 1.06544 + 1.37000i
\(101\) 5.27265i 0.524648i 0.964980 + 0.262324i \(0.0844889\pi\)
−0.964980 + 0.262324i \(0.915511\pi\)
\(102\) 0 0
\(103\) 1.94019 0.191173 0.0955865 0.995421i \(-0.469527\pi\)
0.0955865 + 0.995421i \(0.469527\pi\)
\(104\) −2.94108 14.0687i −0.288396 1.37955i
\(105\) 0 0
\(106\) −5.69833 2.78716i −0.553471 0.270713i
\(107\) 4.78716i 0.462792i −0.972860 0.231396i \(-0.925671\pi\)
0.972860 0.231396i \(-0.0743293\pi\)
\(108\) 0 0
\(109\) 0.970978i 0.0930028i 0.998918 + 0.0465014i \(0.0148072\pi\)
−0.998918 + 0.0465014i \(0.985193\pi\)
\(110\) −7.38324 + 15.0950i −0.703964 + 1.43925i
\(111\) 0 0
\(112\) −0.985049 + 3.87681i −0.0930783 + 0.366324i
\(113\) −15.5598 −1.46374 −0.731871 0.681443i \(-0.761353\pi\)
−0.731871 + 0.681443i \(0.761353\pi\)
\(114\) 0 0
\(115\) 5.11567i 0.477039i
\(116\) 8.96372 6.97098i 0.832260 0.647239i
\(117\) 0 0
\(118\) −5.08157 2.48549i −0.467796 0.228808i
\(119\) −0.616762 −0.0565384
\(120\) 0 0
\(121\) 0.677649 0.0616045
\(122\) 15.8522 + 7.75363i 1.43520 + 0.701980i
\(123\) 0 0
\(124\) −8.48549 10.9112i −0.762019 0.979852i
\(125\) 13.6012i 1.21652i
\(126\) 0 0
\(127\) −3.73746 −0.331646 −0.165823 0.986156i \(-0.553028\pi\)
−0.165823 + 0.986156i \(0.553028\pi\)
\(128\) 0.483388 11.3034i 0.0427259 0.999087i
\(129\) 0 0
\(130\) 11.6776 23.8749i 1.02420 2.09397i
\(131\) 3.39666i 0.296768i −0.988930 0.148384i \(-0.952593\pi\)
0.988930 0.148384i \(-0.0474071\pi\)
\(132\) 0 0
\(133\) 4.48549i 0.388941i
\(134\) −12.1539 5.94470i −1.04994 0.513544i
\(135\) 0 0
\(136\) 1.70755 0.356965i 0.146421 0.0306095i
\(137\) −13.0559 −1.11544 −0.557719 0.830030i \(-0.688323\pi\)
−0.557719 + 0.830030i \(0.688323\pi\)
\(138\) 0 0
\(139\) 2.80784i 0.238158i 0.992885 + 0.119079i \(0.0379942\pi\)
−0.992885 + 0.119079i \(0.962006\pi\)
\(140\) −5.83882 + 4.54078i −0.493471 + 0.383766i
\(141\) 0 0
\(142\) 9.44833 19.3171i 0.792886 1.62105i
\(143\) 16.3263 1.36527
\(144\) 0 0
\(145\) 20.9978 1.74377
\(146\) 9.66843 19.7670i 0.800165 1.63593i
\(147\) 0 0
\(148\) −10.9112 + 8.48549i −0.896893 + 0.697503i
\(149\) 12.4855i 1.02285i −0.859328 0.511426i \(-0.829118\pi\)
0.859328 0.511426i \(-0.170882\pi\)
\(150\) 0 0
\(151\) 8.97098 0.730048 0.365024 0.930998i \(-0.381061\pi\)
0.365024 + 0.930998i \(0.381061\pi\)
\(152\) 2.59608 + 12.4184i 0.210570 + 1.00727i
\(153\) 0 0
\(154\) −4.08157 1.99637i −0.328902 0.160872i
\(155\) 25.5598i 2.05301i
\(156\) 0 0
\(157\) 15.1665i 1.21042i 0.796068 + 0.605208i \(0.206910\pi\)
−0.796068 + 0.605208i \(0.793090\pi\)
\(158\) −3.25197 + 6.64863i −0.258713 + 0.528936i
\(159\) 0 0
\(160\) 13.5372 15.9509i 1.07021 1.26103i
\(161\) −1.38324 −0.109014
\(162\) 0 0
\(163\) 13.2263i 1.03596i −0.855392 0.517980i \(-0.826684\pi\)
0.855392 0.517980i \(-0.173316\pi\)
\(164\) −0.757255 0.973726i −0.0591317 0.0760353i
\(165\) 0 0
\(166\) 13.2447 + 6.47823i 1.02799 + 0.502808i
\(167\) −3.05587 −0.236470 −0.118235 0.992986i \(-0.537724\pi\)
−0.118235 + 0.992986i \(0.537724\pi\)
\(168\) 0 0
\(169\) −12.8223 −0.986334
\(170\) 2.89775 + 1.41734i 0.222247 + 0.108705i
\(171\) 0 0
\(172\) −12.6187 + 9.81343i −0.962169 + 0.748267i
\(173\) 13.8615i 1.05387i 0.849906 + 0.526934i \(0.176658\pi\)
−0.849906 + 0.526934i \(0.823342\pi\)
\(174\) 0 0
\(175\) −8.67765 −0.655969
\(176\) 12.4556 + 3.16480i 0.938875 + 0.238556i
\(177\) 0 0
\(178\) 8.80892 18.0098i 0.660257 1.34989i
\(179\) 18.3883i 1.37441i 0.726465 + 0.687204i \(0.241162\pi\)
−0.726465 + 0.687204i \(0.758838\pi\)
\(180\) 0 0
\(181\) 6.05255i 0.449882i −0.974372 0.224941i \(-0.927781\pi\)
0.974372 0.224941i \(-0.0722190\pi\)
\(182\) 6.45559 + 3.15755i 0.478520 + 0.234053i
\(183\) 0 0
\(184\) 3.82960 0.800581i 0.282322 0.0590196i
\(185\) −25.5598 −1.87919
\(186\) 0 0
\(187\) 1.98156i 0.144906i
\(188\) 6.10333 + 7.84805i 0.445131 + 0.572378i
\(189\) 0 0
\(190\) −10.3078 + 21.0743i −0.747809 + 1.52889i
\(191\) 15.2056 1.10024 0.550119 0.835086i \(-0.314582\pi\)
0.550119 + 0.835086i \(0.314582\pi\)
\(192\) 0 0
\(193\) −19.4419 −1.39946 −0.699731 0.714406i \(-0.746697\pi\)
−0.699731 + 0.714406i \(0.746697\pi\)
\(194\) 6.05058 12.3704i 0.434407 0.888142i
\(195\) 0 0
\(196\) −1.22779 1.57877i −0.0876995 0.112770i
\(197\) 15.2520i 1.08666i 0.839520 + 0.543329i \(0.182836\pi\)
−0.839520 + 0.543329i \(0.817164\pi\)
\(198\) 0 0
\(199\) −3.02902 −0.214722 −0.107361 0.994220i \(-0.534240\pi\)
−0.107361 + 0.994220i \(0.534240\pi\)
\(200\) 24.0247 5.02239i 1.69881 0.355137i
\(201\) 0 0
\(202\) 6.69833 + 3.27628i 0.471293 + 0.230518i
\(203\) 5.67765i 0.398493i
\(204\) 0 0
\(205\) 2.28099i 0.159311i
\(206\) 1.20558 2.46481i 0.0839969 0.171731i
\(207\) 0 0
\(208\) −19.7003 5.00559i −1.36597 0.347075i
\(209\) −14.4112 −0.996841
\(210\) 0 0
\(211\) 0.963719i 0.0663452i 0.999450 + 0.0331726i \(0.0105611\pi\)
−0.999450 + 0.0331726i \(0.989439\pi\)
\(212\) −7.08157 + 5.50725i −0.486364 + 0.378240i
\(213\) 0 0
\(214\) −6.08157 2.97461i −0.415728 0.203340i
\(215\) −29.5598 −2.01596
\(216\) 0 0
\(217\) 6.91117 0.469161
\(218\) 1.23352 + 0.603339i 0.0835447 + 0.0408633i
\(219\) 0 0
\(220\) 14.5888 + 18.7592i 0.983578 + 1.26475i
\(221\) 3.13412i 0.210823i
\(222\) 0 0
\(223\) −22.1486 −1.48318 −0.741591 0.670853i \(-0.765928\pi\)
−0.741591 + 0.670853i \(0.765928\pi\)
\(224\) 4.31299 + 3.66034i 0.288174 + 0.244567i
\(225\) 0 0
\(226\) −9.66843 + 19.7670i −0.643134 + 1.31488i
\(227\) 0.929615i 0.0617007i −0.999524 0.0308504i \(-0.990178\pi\)
0.999524 0.0308504i \(-0.00982153\pi\)
\(228\) 0 0
\(229\) 1.42236i 0.0939924i 0.998895 + 0.0469962i \(0.0149649\pi\)
−0.998895 + 0.0469962i \(0.985035\pi\)
\(230\) 6.49891 + 3.17874i 0.428526 + 0.209600i
\(231\) 0 0
\(232\) −3.28607 15.7190i −0.215741 1.03200i
\(233\) −10.9710 −0.718733 −0.359366 0.933197i \(-0.617007\pi\)
−0.359366 + 0.933197i \(0.617007\pi\)
\(234\) 0 0
\(235\) 18.3843i 1.19926i
\(236\) −6.31509 + 4.91117i −0.411077 + 0.319690i
\(237\) 0 0
\(238\) −0.383238 + 0.783529i −0.0248417 + 0.0507886i
\(239\) 4.82126 0.311862 0.155931 0.987768i \(-0.450162\pi\)
0.155931 + 0.987768i \(0.450162\pi\)
\(240\) 0 0
\(241\) −0.204501 −0.0131731 −0.00658654 0.999978i \(-0.502097\pi\)
−0.00658654 + 0.999978i \(0.502097\pi\)
\(242\) 0.421072 0.860880i 0.0270676 0.0553395i
\(243\) 0 0
\(244\) 19.7003 15.3207i 1.26118 0.980806i
\(245\) 3.69833i 0.236278i
\(246\) 0 0
\(247\) 22.7933 1.45030
\(248\) −19.1341 + 4.00000i −1.21502 + 0.254000i
\(249\) 0 0
\(250\) 17.2788 + 8.45138i 1.09281 + 0.534513i
\(251\) 3.10727i 0.196129i −0.995180 0.0980646i \(-0.968735\pi\)
0.995180 0.0980646i \(-0.0312652\pi\)
\(252\) 0 0
\(253\) 4.44413i 0.279400i
\(254\) −2.32235 + 4.74803i −0.145717 + 0.297918i
\(255\) 0 0
\(256\) −14.0594 7.63770i −0.878710 0.477356i
\(257\) 14.1497 0.882635 0.441318 0.897351i \(-0.354511\pi\)
0.441318 + 0.897351i \(0.354511\pi\)
\(258\) 0 0
\(259\) 6.91117i 0.429439i
\(260\) −23.0743 29.6704i −1.43101 1.84008i
\(261\) 0 0
\(262\) −4.31509 2.11059i −0.266587 0.130393i
\(263\) −2.94304 −0.181475 −0.0907377 0.995875i \(-0.528923\pi\)
−0.0907377 + 0.995875i \(0.528923\pi\)
\(264\) 0 0
\(265\) −16.5888 −1.01904
\(266\) −5.69833 2.78716i −0.349387 0.170892i
\(267\) 0 0
\(268\) −15.1042 + 11.7464i −0.922637 + 0.717524i
\(269\) 0.642463i 0.0391717i −0.999808 0.0195858i \(-0.993765\pi\)
0.999808 0.0195858i \(-0.00623476\pi\)
\(270\) 0 0
\(271\) −0.526852 −0.0320040 −0.0160020 0.999872i \(-0.505094\pi\)
−0.0160020 + 0.999872i \(0.505094\pi\)
\(272\) 0.607540 2.39107i 0.0368375 0.144980i
\(273\) 0 0
\(274\) −8.11255 + 16.5861i −0.490097 + 1.00200i
\(275\) 27.8799i 1.68122i
\(276\) 0 0
\(277\) 21.7190i 1.30497i 0.757802 + 0.652484i \(0.226273\pi\)
−0.757802 + 0.652484i \(0.773727\pi\)
\(278\) 3.56706 + 1.74471i 0.213938 + 0.104641i
\(279\) 0 0
\(280\) 2.14049 + 10.2391i 0.127919 + 0.611904i
\(281\) 4.79332 0.285946 0.142973 0.989727i \(-0.454334\pi\)
0.142973 + 0.989727i \(0.454334\pi\)
\(282\) 0 0
\(283\) 22.6486i 1.34632i 0.739496 + 0.673161i \(0.235064\pi\)
−0.739496 + 0.673161i \(0.764936\pi\)
\(284\) −18.6693 24.0062i −1.10782 1.42450i
\(285\) 0 0
\(286\) 10.1447 20.7408i 0.599868 1.22643i
\(287\) 0.616762 0.0364063
\(288\) 0 0
\(289\) −16.6196 −0.977624
\(290\) 13.0475 26.6755i 0.766174 1.56644i
\(291\) 0 0
\(292\) −19.1042 24.5654i −1.11799 1.43758i
\(293\) 24.3285i 1.42129i 0.703552 + 0.710644i \(0.251596\pi\)
−0.703552 + 0.710644i \(0.748404\pi\)
\(294\) 0 0
\(295\) −14.7933 −0.861301
\(296\) 4.00000 + 19.1341i 0.232495 + 1.11215i
\(297\) 0 0
\(298\) −15.8615 7.75814i −0.918830 0.449417i
\(299\) 7.02902i 0.406499i
\(300\) 0 0
\(301\) 7.99274i 0.460694i
\(302\) 5.57432 11.3967i 0.320766 0.655804i
\(303\) 0 0
\(304\) 17.3894 + 4.41842i 0.997351 + 0.253414i
\(305\) 46.1486 2.64246
\(306\) 0 0
\(307\) 3.51451i 0.200584i −0.994958 0.100292i \(-0.968022\pi\)
0.994958 0.100292i \(-0.0319777\pi\)
\(308\) −5.07235 + 3.94470i −0.289024 + 0.224770i
\(309\) 0 0
\(310\) −32.4710 15.8822i −1.84423 0.902046i
\(311\) 4.97098 0.281878 0.140939 0.990018i \(-0.454988\pi\)
0.140939 + 0.990018i \(0.454988\pi\)
\(312\) 0 0
\(313\) −25.6447 −1.44952 −0.724762 0.689000i \(-0.758050\pi\)
−0.724762 + 0.689000i \(0.758050\pi\)
\(314\) 19.2674 + 9.42402i 1.08732 + 0.531828i
\(315\) 0 0
\(316\) 6.42568 + 8.26254i 0.361473 + 0.464804i
\(317\) 3.51451i 0.197395i 0.995118 + 0.0986973i \(0.0314676\pi\)
−0.995118 + 0.0986973i \(0.968532\pi\)
\(318\) 0 0
\(319\) 18.2414 1.02132
\(320\) −11.8522 27.1089i −0.662561 1.51543i
\(321\) 0 0
\(322\) −0.859506 + 1.75726i −0.0478984 + 0.0979280i
\(323\) 2.76648i 0.153931i
\(324\) 0 0
\(325\) 44.0961i 2.44601i
\(326\) −16.8025 8.21843i −0.930607 0.455177i
\(327\) 0 0
\(328\) −1.70755 + 0.356965i −0.0942838 + 0.0197101i
\(329\) −4.97098 −0.274059
\(330\) 0 0
\(331\) 25.1849i 1.38429i 0.721760 + 0.692144i \(0.243334\pi\)
−0.721760 + 0.692144i \(0.756666\pi\)
\(332\) 16.4598 12.8006i 0.903348 0.702523i
\(333\) 0 0
\(334\) −1.89883 + 3.88215i −0.103899 + 0.212422i
\(335\) −35.3821 −1.93313
\(336\) 0 0
\(337\) 21.7643 1.18558 0.592788 0.805358i \(-0.298027\pi\)
0.592788 + 0.805358i \(0.298027\pi\)
\(338\) −7.96745 + 16.2894i −0.433372 + 0.886027i
\(339\) 0 0
\(340\) 3.60116 2.80058i 0.195300 0.151883i
\(341\) 22.2045i 1.20244i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 4.62598 + 22.1285i 0.249416 + 1.19309i
\(345\) 0 0
\(346\) 17.6095 + 8.61313i 0.946693 + 0.463045i
\(347\) 31.9068i 1.71284i 0.516276 + 0.856422i \(0.327318\pi\)
−0.516276 + 0.856422i \(0.672682\pi\)
\(348\) 0 0
\(349\) 1.04021i 0.0556810i −0.999612 0.0278405i \(-0.991137\pi\)
0.999612 0.0278405i \(-0.00886305\pi\)
\(350\) −5.39205 + 11.0240i −0.288217 + 0.589259i
\(351\) 0 0
\(352\) 11.7601 13.8570i 0.626815 0.738578i
\(353\) 13.8503 0.737176 0.368588 0.929593i \(-0.379841\pi\)
0.368588 + 0.929593i \(0.379841\pi\)
\(354\) 0 0
\(355\) 56.2353i 2.98466i
\(356\) −17.4059 22.3816i −0.922510 1.18622i
\(357\) 0 0
\(358\) 23.3604 + 11.4260i 1.23463 + 0.603882i
\(359\) −0.412260 −0.0217583 −0.0108791 0.999941i \(-0.503463\pi\)
−0.0108791 + 0.999941i \(0.503463\pi\)
\(360\) 0 0
\(361\) −1.11961 −0.0589269
\(362\) −7.68911 3.76088i −0.404131 0.197668i
\(363\) 0 0
\(364\) 8.02264 6.23912i 0.420501 0.327018i
\(365\) 57.5453i 3.01206i
\(366\) 0 0
\(367\) 4.97098 0.259483 0.129741 0.991548i \(-0.458585\pi\)
0.129741 + 0.991548i \(0.458585\pi\)
\(368\) 1.36256 5.36256i 0.0710282 0.279543i
\(369\) 0 0
\(370\) −15.8822 + 32.4710i −0.825674 + 1.68809i
\(371\) 4.48549i 0.232875i
\(372\) 0 0
\(373\) 2.16314i 0.112003i −0.998431 0.0560015i \(-0.982165\pi\)
0.998431 0.0560015i \(-0.0178352\pi\)
\(374\) 2.51735 + 1.23128i 0.130169 + 0.0636682i
\(375\) 0 0
\(376\) 13.7625 2.87707i 0.709749 0.148373i
\(377\) −28.8514 −1.48592
\(378\) 0 0
\(379\) 23.7570i 1.22032i −0.792279 0.610159i \(-0.791106\pi\)
0.792279 0.610159i \(-0.208894\pi\)
\(380\) 20.3676 + 26.1900i 1.04484 + 1.34352i
\(381\) 0 0
\(382\) 9.44833 19.3171i 0.483418 0.988347i
\(383\) 37.5598 1.91922 0.959608 0.281340i \(-0.0907790\pi\)
0.959608 + 0.281340i \(0.0907790\pi\)
\(384\) 0 0
\(385\) −11.8822 −0.605570
\(386\) −12.0807 + 24.6989i −0.614891 + 1.25714i
\(387\) 0 0
\(388\) −11.9556 15.3732i −0.606953 0.780458i
\(389\) 0.826283i 0.0418942i −0.999781 0.0209471i \(-0.993332\pi\)
0.999781 0.0209471i \(-0.00666816\pi\)
\(390\) 0 0
\(391\) 0.853128 0.0431446
\(392\) −2.76858 + 0.578773i −0.139834 + 0.0292325i
\(393\) 0 0
\(394\) 19.3760 + 9.47715i 0.976148 + 0.477452i
\(395\) 19.3553i 0.973871i
\(396\) 0 0
\(397\) 8.81902i 0.442614i 0.975204 + 0.221307i \(0.0710323\pi\)
−0.975204 + 0.221307i \(0.928968\pi\)
\(398\) −1.88215 + 3.84805i −0.0943437 + 0.192885i
\(399\) 0 0
\(400\) 8.54791 33.6416i 0.427395 1.68208i
\(401\) 8.64687 0.431804 0.215902 0.976415i \(-0.430731\pi\)
0.215902 + 0.976415i \(0.430731\pi\)
\(402\) 0 0
\(403\) 35.1196i 1.74943i
\(404\) 8.32431 6.47372i 0.414150 0.322080i
\(405\) 0 0
\(406\) 7.21284 + 3.52793i 0.357967 + 0.175088i
\(407\) −22.2045 −1.10064
\(408\) 0 0
\(409\) −18.7084 −0.925072 −0.462536 0.886600i \(-0.653060\pi\)
−0.462536 + 0.886600i \(0.653060\pi\)
\(410\) −2.89775 1.41734i −0.143110 0.0699976i
\(411\) 0 0
\(412\) −2.38216 3.06313i −0.117360 0.150909i
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) 38.5576 1.89272
\(416\) −18.6003 + 21.9168i −0.911954 + 1.07456i
\(417\) 0 0
\(418\) −8.95470 + 18.3078i −0.437989 + 0.895465i
\(419\) 12.9710i 0.633674i 0.948480 + 0.316837i \(0.102621\pi\)
−0.948480 + 0.316837i \(0.897379\pi\)
\(420\) 0 0
\(421\) 3.54136i 0.172595i 0.996269 + 0.0862976i \(0.0275036\pi\)
−0.996269 + 0.0862976i \(0.972496\pi\)
\(422\) 1.22430 + 0.598828i 0.0595981 + 0.0291505i
\(423\) 0 0
\(424\) 2.59608 + 12.4184i 0.126077 + 0.603092i
\(425\) 5.35204 0.259612
\(426\) 0 0
\(427\) 12.4782i 0.603864i
\(428\) −7.55784 + 5.87764i −0.365322 + 0.284106i
\(429\) 0 0
\(430\) −18.3676 + 37.5525i −0.885766 + 1.81094i
\(431\) −14.6168 −0.704065 −0.352032 0.935988i \(-0.614509\pi\)
−0.352032 + 0.935988i \(0.614509\pi\)
\(432\) 0 0
\(433\) −2.97098 −0.142776 −0.0713880 0.997449i \(-0.522743\pi\)
−0.0713880 + 0.997449i \(0.522743\pi\)
\(434\) 4.29441 8.77990i 0.206138 0.421449i
\(435\) 0 0
\(436\) 1.53295 1.19216i 0.0734152 0.0570941i
\(437\) 6.20450i 0.296802i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 32.8967 6.87707i 1.56829 0.327851i
\(441\) 0 0
\(442\) −3.98156 1.94745i −0.189383 0.0926309i
\(443\) 27.1983i 1.29223i −0.763239 0.646116i \(-0.776392\pi\)
0.763239 0.646116i \(-0.223608\pi\)
\(444\) 0 0
\(445\) 52.4296i 2.48540i
\(446\) −13.7625 + 28.1374i −0.651675 + 1.33235i
\(447\) 0 0
\(448\) 7.33004 3.20476i 0.346312 0.151410i
\(449\) 31.5598 1.48940 0.744700 0.667400i \(-0.232593\pi\)
0.744700 + 0.667400i \(0.232593\pi\)
\(450\) 0 0
\(451\) 1.98156i 0.0933079i
\(452\) 19.1042 + 24.5654i 0.898587 + 1.15546i
\(453\) 0 0
\(454\) −1.18098 0.577637i −0.0554259 0.0271099i
\(455\) 18.7933 0.881045
\(456\) 0 0
\(457\) 28.1117 1.31501 0.657506 0.753450i \(-0.271612\pi\)
0.657506 + 0.753450i \(0.271612\pi\)
\(458\) 1.80696 + 0.883817i 0.0844336 + 0.0412981i
\(459\) 0 0
\(460\) 8.07649 6.28099i 0.376568 0.292853i
\(461\) 5.19440i 0.241927i −0.992657 0.120964i \(-0.961402\pi\)
0.992657 0.120964i \(-0.0385984\pi\)
\(462\) 0 0
\(463\) −10.7665 −0.500361 −0.250180 0.968199i \(-0.580490\pi\)
−0.250180 + 0.968199i \(0.580490\pi\)
\(464\) −22.0112 5.59276i −1.02184 0.259637i
\(465\) 0 0
\(466\) −6.81706 + 13.9374i −0.315794 + 0.645640i
\(467\) 30.7520i 1.42303i −0.702670 0.711515i \(-0.748009\pi\)
0.702670 0.711515i \(-0.251991\pi\)
\(468\) 0 0
\(469\) 9.56706i 0.441766i
\(470\) 23.3553 + 11.4235i 1.07730 + 0.526927i
\(471\) 0 0
\(472\) 2.31509 + 11.0743i 0.106561 + 0.509736i
\(473\) −25.6794 −1.18074
\(474\) 0 0
\(475\) 38.9235i 1.78593i
\(476\) 0.757255 + 0.973726i 0.0347087 + 0.0446307i
\(477\) 0 0
\(478\) 2.99580 6.12489i 0.137025 0.280146i
\(479\) −16.3263 −0.745967 −0.372983 0.927838i \(-0.621665\pi\)
−0.372983 + 0.927838i \(0.621665\pi\)
\(480\) 0 0
\(481\) 35.1196 1.60132
\(482\) −0.127071 + 0.259797i −0.00578794 + 0.0118334i
\(483\) 0 0
\(484\) −0.832013 1.06985i −0.0378188 0.0486297i
\(485\) 36.0123i 1.63524i
\(486\) 0 0
\(487\) 14.7933 0.670349 0.335175 0.942156i \(-0.391205\pi\)
0.335175 + 0.942156i \(0.391205\pi\)
\(488\) −7.22206 34.5469i −0.326927 1.56387i
\(489\) 0 0
\(490\) −4.69833 2.29804i −0.212249 0.103815i
\(491\) 14.0475i 0.633956i −0.948433 0.316978i \(-0.897332\pi\)
0.948433 0.316978i \(-0.102668\pi\)
\(492\) 0 0
\(493\) 3.50176i 0.157711i
\(494\) 14.1631 28.9565i 0.637230 1.30281i
\(495\) 0 0
\(496\) −6.80784 + 26.7933i −0.305681 + 1.20306i
\(497\) 15.2056 0.682064
\(498\) 0 0
\(499\) 34.1414i 1.52838i 0.644993 + 0.764189i \(0.276860\pi\)
−0.644993 + 0.764189i \(0.723140\pi\)
\(500\) 21.4731 16.6994i 0.960308 0.746820i
\(501\) 0 0
\(502\) −3.94745 1.93077i −0.176183 0.0861746i
\(503\) 27.3821 1.22091 0.610455 0.792051i \(-0.290987\pi\)
0.610455 + 0.792051i \(0.290987\pi\)
\(504\) 0 0
\(505\) 19.5000 0.867738
\(506\) 5.64578 + 2.76146i 0.250986 + 0.122762i
\(507\) 0 0
\(508\) 4.58882 + 5.90059i 0.203596 + 0.261796i
\(509\) 2.49165i 0.110441i −0.998474 0.0552203i \(-0.982414\pi\)
0.998474 0.0552203i \(-0.0175861\pi\)
\(510\) 0 0
\(511\) 15.5598 0.688325
\(512\) −18.4390 + 13.1150i −0.814895 + 0.579609i
\(513\) 0 0
\(514\) 8.79224 17.9757i 0.387809 0.792874i
\(515\) 7.17548i 0.316189i
\(516\) 0 0
\(517\) 15.9710i 0.702402i
\(518\) −8.77990 4.29441i −0.385767 0.188686i
\(519\) 0 0
\(520\) −52.0308 + 10.8771i −2.28170 + 0.476991i
\(521\) 3.00108 0.131480 0.0657399 0.997837i \(-0.479059\pi\)
0.0657399 + 0.997837i \(0.479059\pi\)
\(522\) 0 0
\(523\) 16.8514i 0.736859i −0.929656 0.368429i \(-0.879896\pi\)
0.929656 0.368429i \(-0.120104\pi\)
\(524\) −5.36256 + 4.17040i −0.234264 + 0.182185i
\(525\) 0 0
\(526\) −1.82872 + 3.73881i −0.0797361 + 0.163020i
\(527\) −4.26254 −0.185679
\(528\) 0 0
\(529\) −21.0867 −0.916811
\(530\) −10.3078 + 21.0743i −0.447744 + 0.915410i
\(531\) 0 0
\(532\) −7.08157 + 5.50725i −0.307025 + 0.238770i
\(533\) 3.13412i 0.135754i
\(534\) 0 0
\(535\) −17.7045 −0.765432
\(536\) 5.53716 + 26.4871i 0.239169 + 1.14407i
\(537\) 0 0
\(538\) −0.816180 0.399209i −0.0351880 0.0172111i
\(539\) 3.21284i 0.138387i
\(540\) 0 0
\(541\) 24.6319i 1.05901i −0.848307 0.529505i \(-0.822378\pi\)
0.848307 0.529505i \(-0.177622\pi\)
\(542\) −0.327371 + 0.669309i −0.0140618 + 0.0287493i
\(543\) 0 0
\(544\) −2.66009 2.25756i −0.114050 0.0967920i
\(545\) 3.59100 0.153821
\(546\) 0 0
\(547\) 25.8564i 1.10554i 0.833333 + 0.552771i \(0.186430\pi\)
−0.833333 + 0.552771i \(0.813570\pi\)
\(548\) 16.0299 + 20.6123i 0.684764 + 0.880512i
\(549\) 0 0
\(550\) 35.4184 + 17.3238i 1.51025 + 0.738689i
\(551\) 25.4670 1.08493
\(552\) 0 0
\(553\) −5.23352 −0.222552
\(554\) 27.5917 + 13.4956i 1.17226 + 0.573373i
\(555\) 0 0
\(556\) 4.43294 3.44745i 0.187999 0.146204i
\(557\) 27.2788i 1.15584i 0.816093 + 0.577920i \(0.196136\pi\)
−0.816093 + 0.577920i \(0.803864\pi\)
\(558\) 0 0
\(559\) 40.6157 1.71786
\(560\) 14.3377 + 3.64304i 0.605880 + 0.153946i
\(561\) 0 0
\(562\) 2.97844 6.08940i 0.125638 0.256866i
\(563\) 13.1776i 0.555371i 0.960672 + 0.277686i \(0.0895674\pi\)
−0.960672 + 0.277686i \(0.910433\pi\)
\(564\) 0 0
\(565\) 57.5453i 2.42095i
\(566\) 28.7726 + 14.0732i 1.20940 + 0.591542i
\(567\) 0 0
\(568\) −42.0978 + 8.80058i −1.76639 + 0.369264i
\(569\) −17.4380 −0.731040 −0.365520 0.930803i \(-0.619109\pi\)
−0.365520 + 0.930803i \(0.619109\pi\)
\(570\) 0 0
\(571\) 4.71569i 0.197346i 0.995120 + 0.0986728i \(0.0314597\pi\)
−0.995120 + 0.0986728i \(0.968540\pi\)
\(572\) −20.0453 25.7755i −0.838136 1.07773i
\(573\) 0 0
\(574\) 0.383238 0.783529i 0.0159961 0.0327039i
\(575\) 12.0033 0.500570
\(576\) 0 0
\(577\) −11.8223 −0.492171 −0.246085 0.969248i \(-0.579144\pi\)
−0.246085 + 0.969248i \(0.579144\pi\)
\(578\) −10.3270 + 21.1134i −0.429545 + 0.878202i
\(579\) 0 0
\(580\) −25.7810 33.1508i −1.07050 1.37651i
\(581\) 10.4257i 0.432530i
\(582\) 0 0
\(583\) −14.4112 −0.596849
\(584\) −43.0785 + 9.00559i −1.78260 + 0.372654i
\(585\) 0 0
\(586\) 30.9068 + 15.1171i 1.27675 + 0.624480i
\(587\) 13.7810i 0.568802i −0.958705 0.284401i \(-0.908205\pi\)
0.958705 0.284401i \(-0.0917947\pi\)
\(588\) 0 0
\(589\) 31.0000i 1.27733i
\(590\) −9.19216 + 18.7933i −0.378435 + 0.773709i
\(591\) 0 0
\(592\) 26.7933 + 6.80784i 1.10120 + 0.279800i
\(593\) −36.8872 −1.51477 −0.757387 0.652966i \(-0.773524\pi\)
−0.757387 + 0.652966i \(0.773524\pi\)
\(594\) 0 0
\(595\) 2.28099i 0.0935114i
\(596\) −19.7118 + 15.3296i −0.807425 + 0.627925i
\(597\) 0 0
\(598\) −8.92962 4.36764i −0.365159 0.178606i
\(599\) 35.0895 1.43372 0.716859 0.697218i \(-0.245579\pi\)
0.716859 + 0.697218i \(0.245579\pi\)
\(600\) 0 0
\(601\) 18.3263 0.747544 0.373772 0.927521i \(-0.378064\pi\)
0.373772 + 0.927521i \(0.378064\pi\)
\(602\) −10.1539 4.96647i −0.413843 0.202418i
\(603\) 0 0
\(604\) −11.0145 14.1631i −0.448174 0.576290i
\(605\) 2.50617i 0.101890i
\(606\) 0 0
\(607\) −12.4459 −0.505163 −0.252582 0.967576i \(-0.581280\pi\)
−0.252582 + 0.967576i \(0.581280\pi\)
\(608\) 16.4184 19.3459i 0.665855 0.784579i
\(609\) 0 0
\(610\) 28.6755 58.6269i 1.16104 2.37373i
\(611\) 25.2604i 1.02193i
\(612\) 0 0
\(613\) 14.2682i 0.576288i −0.957587 0.288144i \(-0.906962\pi\)
0.957587 0.288144i \(-0.0930383\pi\)
\(614\) −4.46481 2.18382i −0.180185 0.0881318i
\(615\) 0 0
\(616\) 1.85951 + 8.89500i 0.0749216 + 0.358390i
\(617\) −2.94413 −0.118526 −0.0592632 0.998242i \(-0.518875\pi\)
−0.0592632 + 0.998242i \(0.518875\pi\)
\(618\) 0 0
\(619\) 13.2604i 0.532979i −0.963838 0.266490i \(-0.914136\pi\)
0.963838 0.266490i \(-0.0858638\pi\)
\(620\) −40.3531 + 31.3821i −1.62062 + 1.26034i
\(621\) 0 0
\(622\) 3.08883 6.31509i 0.123851 0.253212i
\(623\) 14.1766 0.567972
\(624\) 0 0
\(625\) 6.91335 0.276534
\(626\) −15.9349 + 32.5788i −0.636887 + 1.30211i
\(627\) 0 0
\(628\) 23.9444 18.6213i 0.955485 0.743070i
\(629\) 4.26254i 0.169959i
\(630\) 0 0
\(631\) 36.2335 1.44243 0.721217 0.692710i \(-0.243583\pi\)
0.721217 + 0.692710i \(0.243583\pi\)
\(632\) 14.4894 3.02902i 0.576358 0.120488i
\(633\) 0 0
\(634\) 4.46481 + 2.18382i 0.177320 + 0.0867306i
\(635\) 13.8223i 0.548523i
\(636\) 0 0
\(637\) 5.08157i 0.201339i
\(638\) 11.3347 23.1737i 0.448745 0.917456i
\(639\) 0 0
\(640\) −41.8036 1.78773i −1.65243 0.0706662i
\(641\) −25.9441 −1.02473 −0.512366 0.858767i \(-0.671231\pi\)
−0.512366 + 0.858767i \(0.671231\pi\)
\(642\) 0 0
\(643\) 27.2643i 1.07520i −0.843200 0.537599i \(-0.819331\pi\)
0.843200 0.537599i \(-0.180669\pi\)
\(644\) 1.69833 + 2.18382i 0.0669236 + 0.0860545i
\(645\) 0 0
\(646\) 3.51451 + 1.71901i 0.138277 + 0.0676336i
\(647\) 7.41118 0.291364 0.145682 0.989332i \(-0.453462\pi\)
0.145682 + 0.989332i \(0.453462\pi\)
\(648\) 0 0
\(649\) −12.8514 −0.504460
\(650\) −56.0193 27.4001i −2.19726 1.07472i
\(651\) 0 0
\(652\) −20.8813 + 16.2391i −0.817774 + 0.635973i
\(653\) 17.7045i 0.692830i −0.938081 0.346415i \(-0.887399\pi\)
0.938081 0.346415i \(-0.112601\pi\)
\(654\) 0 0
\(655\) −12.5620 −0.490837
\(656\) −0.607540 + 2.39107i −0.0237205 + 0.0933556i
\(657\) 0 0
\(658\) −3.08883 + 6.31509i −0.120415 + 0.246188i
\(659\) 39.2252i 1.52800i 0.645219 + 0.763998i \(0.276766\pi\)
−0.645219 + 0.763998i \(0.723234\pi\)
\(660\) 0 0
\(661\) 8.35862i 0.325113i −0.986699 0.162556i \(-0.948026\pi\)
0.986699 0.162556i \(-0.0519739\pi\)
\(662\) 31.9947 + 15.6492i 1.24351 + 0.608223i
\(663\) 0 0
\(664\) −6.03410 28.8643i −0.234169 1.12015i
\(665\) −16.5888 −0.643287
\(666\) 0 0
\(667\) 7.85354i 0.304090i
\(668\) 3.75197 + 4.82452i 0.145168 + 0.186666i
\(669\) 0 0
\(670\) −21.9855 + 44.9492i −0.849373 + 1.73654i
\(671\) 40.0906 1.54768
\(672\) 0 0
\(673\) 37.9090 1.46128 0.730642 0.682761i \(-0.239221\pi\)
0.730642 + 0.682761i \(0.239221\pi\)
\(674\) 13.5237 27.6492i 0.520915 1.06501i
\(675\) 0 0
\(676\) 15.7432 + 20.2436i 0.605507 + 0.778599i
\(677\) 41.5844i 1.59822i 0.601186 + 0.799109i \(0.294695\pi\)
−0.601186 + 0.799109i \(0.705305\pi\)
\(678\) 0 0
\(679\) 9.73746 0.373689
\(680\) −1.32017 6.31509i −0.0506264 0.242173i
\(681\) 0 0
\(682\) −28.2084 13.7973i −1.08016 0.528324i
\(683\) 1.49559i 0.0572272i −0.999591 0.0286136i \(-0.990891\pi\)
0.999591 0.0286136i \(-0.00910924\pi\)
\(684\) 0 0
\(685\) 48.2849i 1.84487i
\(686\) 0.621372 1.27039i 0.0237241 0.0485038i
\(687\) 0 0
\(688\) 30.9864 + 7.87324i 1.18134 + 0.300164i
\(689\) 22.7933 0.868356
\(690\) 0 0
\(691\) 19.9028i 0.757137i −0.925573 0.378568i \(-0.876417\pi\)
0.925573 0.378568i \(-0.123583\pi\)
\(692\) 21.8841 17.0190i 0.831909 0.646966i
\(693\) 0 0
\(694\) 40.5341 + 19.8260i 1.53865 + 0.752584i
\(695\) 10.3843 0.393900
\(696\) 0 0
\(697\) −0.380395 −0.0144085
\(698\) −1.32147 0.646355i −0.0500184 0.0244649i
\(699\) 0 0
\(700\) 10.6544 + 13.7000i 0.402697 + 0.517813i
\(701\) 44.5347i 1.68205i 0.540994 + 0.841026i \(0.318048\pi\)
−0.540994 + 0.841026i \(0.681952\pi\)
\(702\) 0 0
\(703\) −31.0000 −1.16919
\(704\) −10.2964 23.5503i −0.388059 0.887584i
\(705\) 0 0
\(706\) 8.60618 17.5953i 0.323898 0.662208i
\(707\) 5.27265i 0.198298i
\(708\) 0 0
\(709\) 35.3553i 1.32780i −0.747823 0.663898i \(-0.768901\pi\)
0.747823 0.663898i \(-0.231099\pi\)
\(710\) −71.4409 34.9430i −2.68113 1.31139i
\(711\) 0 0
\(712\) −39.2489 + 8.20501i −1.47092 + 0.307496i
\(713\) −9.55980 −0.358017
\(714\) 0 0
\(715\) 60.3800i 2.25808i
\(716\) 29.0310 22.5771i 1.08494 0.843744i
\(717\) 0 0
\(718\) −0.256167 + 0.523732i −0.00956007 + 0.0195455i
\(719\) −11.0928 −0.413690 −0.206845 0.978374i \(-0.566320\pi\)
−0.206845 + 0.978374i \(0.566320\pi\)
\(720\) 0 0
\(721\) 1.94019 0.0722566
\(722\) −0.695696 + 1.42235i −0.0258911 + 0.0529342i
\(723\) 0 0
\(724\) −9.55560 + 7.43128i −0.355131 + 0.276181i
\(725\) 49.2686i 1.82979i
\(726\) 0 0
\(727\) −38.1135 −1.41355 −0.706776 0.707438i \(-0.749851\pi\)
−0.706776 + 0.707438i \(0.749851\pi\)
\(728\) −2.94108 14.0687i −0.109003 0.521421i
\(729\) 0 0
\(730\) −73.1051 35.7570i −2.70574 1.32343i
\(731\) 4.92962i 0.182328i
\(732\) 0 0
\(733\) 27.9576i 1.03264i −0.856396 0.516319i \(-0.827302\pi\)
0.856396 0.516319i \(-0.172698\pi\)
\(734\) 3.08883 6.31509i 0.114011 0.233094i
\(735\) 0 0
\(736\) −5.96590 5.06313i −0.219906 0.186629i
\(737\) −30.7374 −1.13223
\(738\) 0 0
\(739\) 1.56706i 0.0576452i 0.999585 + 0.0288226i \(0.00917578\pi\)
−0.999585 + 0.0288226i \(0.990824\pi\)
\(740\) 31.3821 + 40.3531i 1.15363 + 1.48341i
\(741\) 0 0
\(742\) −5.69833 2.78716i −0.209192 0.102320i
\(743\) −44.0569 −1.61629 −0.808146 0.588982i \(-0.799529\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(744\) 0 0
\(745\) −46.1755 −1.69174
\(746\) −2.74803 1.34411i −0.100613 0.0492115i
\(747\) 0 0
\(748\) 3.12843 2.43294i 0.114387 0.0889572i
\(749\) 4.78716i 0.174919i
\(750\) 0 0
\(751\) −53.5039 −1.95239 −0.976193 0.216904i \(-0.930404\pi\)
−0.976193 + 0.216904i \(0.930404\pi\)
\(752\) 4.89665 19.2716i 0.178563 0.702761i
\(753\) 0 0
\(754\) −17.9274 + 36.6526i −0.652879 + 1.33481i
\(755\) 33.1776i 1.20746i
\(756\) 0 0
\(757\) 34.1486i 1.24115i 0.784146 + 0.620576i \(0.213101\pi\)
−0.784146 + 0.620576i \(0.786899\pi\)
\(758\) −30.1808 14.7620i −1.09621 0.536179i
\(759\) 0 0
\(760\) 45.9274 9.60116i 1.66596 0.348271i
\(761\) 8.23460 0.298504 0.149252 0.988799i \(-0.452313\pi\)
0.149252 + 0.988799i \(0.452313\pi\)
\(762\) 0 0
\(763\) 0.970978i 0.0351518i
\(764\) −18.6693 24.0062i −0.675432 0.868513i
\(765\) 0 0
\(766\) 23.3386 47.7157i 0.843259 1.72404i
\(767\) 20.3263 0.733939
\(768\) 0 0
\(769\) 17.4380 0.628831 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(770\) −7.38324 + 15.0950i −0.266073 + 0.543986i
\(771\) 0 0
\(772\) 23.8707 + 30.6944i 0.859125 + 1.10472i
\(773\) 13.8470i 0.498040i −0.968498 0.249020i \(-0.919891\pi\)
0.968498 0.249020i \(-0.0801085\pi\)
\(774\) 0 0
\(775\) −59.9727 −2.15428
\(776\) −26.9589 + 5.63578i −0.967768 + 0.202313i
\(777\) 0 0
\(778\) −1.04970 0.513429i −0.0376337 0.0184073i
\(779\) 2.76648i 0.0991193i
\(780\) 0 0
\(781\) 48.8531i 1.74810i
\(782\) 0.530110 1.08381i 0.0189567 0.0387569i
\(783\) 0 0
\(784\) −0.985049 + 3.87681i −0.0351803 + 0.138458i
\(785\) 56.0906 2.00196
\(786\) 0 0
\(787\) 48.8368i 1.74085i 0.492305 + 0.870423i \(0.336155\pi\)
−0.492305 + 0.870423i \(0.663845\pi\)
\(788\) 24.0794 18.7263i 0.857793 0.667095i
\(789\) 0 0
\(790\) 24.5888 + 12.0268i 0.874831 + 0.427896i
\(791\) −15.5598 −0.553243
\(792\) 0 0
\(793\) −63.4090 −2.25172
\(794\) 11.2036