Properties

Label 1148.2.ba.a.113.19
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.19
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.90590i q^{3} +(-0.726535 - 2.23605i) q^{5} +(-0.587785 - 0.809017i) q^{7} -5.44428 q^{9} +O(q^{10})\) \(q+2.90590i q^{3} +(-0.726535 - 2.23605i) q^{5} +(-0.587785 - 0.809017i) q^{7} -5.44428 q^{9} +(-4.77283 - 1.55079i) q^{11} +(0.248079 - 0.341451i) q^{13} +(6.49774 - 2.11124i) q^{15} +(5.89651 + 1.91589i) q^{17} +(0.733357 + 1.00938i) q^{19} +(2.35093 - 1.70805i) q^{21} +(-2.51563 - 1.82771i) q^{23} +(-0.426963 + 0.310207i) q^{25} -7.10286i q^{27} +(7.39618 - 2.40316i) q^{29} +(1.65461 - 5.09237i) q^{31} +(4.50644 - 13.8694i) q^{33} +(-1.38195 + 1.90209i) q^{35} +(-3.61986 - 11.1408i) q^{37} +(0.992224 + 0.720893i) q^{39} +(3.63509 - 5.27126i) q^{41} +(3.80506 + 2.76454i) q^{43} +(3.95546 + 12.1737i) q^{45} +(4.46898 - 6.15102i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-5.56740 + 17.1347i) q^{51} +(8.91995 - 2.89827i) q^{53} +11.7990i q^{55} +(-2.93316 + 2.13107i) q^{57} +(-9.13002 - 6.63335i) q^{59} +(-4.00070 + 2.90668i) q^{61} +(3.20007 + 4.40452i) q^{63} +(-0.943738 - 0.306639i) q^{65} +(-8.17082 + 2.65486i) q^{67} +(5.31116 - 7.31018i) q^{69} +(-3.69294 - 1.19991i) q^{71} +0.525670 q^{73} +(-0.901431 - 1.24071i) q^{75} +(1.55079 + 4.77283i) q^{77} +12.5264i q^{79} +4.30737 q^{81} +1.32207 q^{83} -14.5768i q^{85} +(6.98337 + 21.4926i) q^{87} +(-5.80911 - 7.99555i) q^{89} -0.422057 q^{91} +(14.7980 + 4.80815i) q^{93} +(1.72421 - 2.37317i) q^{95} +(-7.11564 + 2.31201i) q^{97} +(25.9847 + 8.44293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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 0
\(3\) 2.90590i 1.67772i 0.544343 + 0.838862i \(0.316779\pi\)
−0.544343 + 0.838862i \(0.683221\pi\)
\(4\) 0 0
\(5\) −0.726535 2.23605i −0.324916 0.999990i −0.971478 0.237129i \(-0.923794\pi\)
0.646562 0.762862i \(-0.276206\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) −5.44428 −1.81476
\(10\) 0 0
\(11\) −4.77283 1.55079i −1.43906 0.467580i −0.517458 0.855708i \(-0.673122\pi\)
−0.921605 + 0.388128i \(0.873122\pi\)
\(12\) 0 0
\(13\) 0.248079 0.341451i 0.0688046 0.0947014i −0.773228 0.634128i \(-0.781359\pi\)
0.842032 + 0.539427i \(0.181359\pi\)
\(14\) 0 0
\(15\) 6.49774 2.11124i 1.67771 0.545121i
\(16\) 0 0
\(17\) 5.89651 + 1.91589i 1.43011 + 0.464672i 0.918801 0.394722i \(-0.129159\pi\)
0.511314 + 0.859394i \(0.329159\pi\)
\(18\) 0 0
\(19\) 0.733357 + 1.00938i 0.168244 + 0.231567i 0.884811 0.465951i \(-0.154288\pi\)
−0.716567 + 0.697518i \(0.754288\pi\)
\(20\) 0 0
\(21\) 2.35093 1.70805i 0.513014 0.372727i
\(22\) 0 0
\(23\) −2.51563 1.82771i −0.524545 0.381104i 0.293768 0.955877i \(-0.405091\pi\)
−0.818313 + 0.574772i \(0.805091\pi\)
\(24\) 0 0
\(25\) −0.426963 + 0.310207i −0.0853925 + 0.0620413i
\(26\) 0 0
\(27\) 7.10286i 1.36695i
\(28\) 0 0
\(29\) 7.39618 2.40316i 1.37344 0.446256i 0.472930 0.881100i \(-0.343196\pi\)
0.900506 + 0.434844i \(0.143196\pi\)
\(30\) 0 0
\(31\) 1.65461 5.09237i 0.297177 0.914617i −0.685304 0.728257i \(-0.740331\pi\)
0.982481 0.186360i \(-0.0596692\pi\)
\(32\) 0 0
\(33\) 4.50644 13.8694i 0.784471 2.41435i
\(34\) 0 0
\(35\) −1.38195 + 1.90209i −0.233593 + 0.321513i
\(36\) 0 0
\(37\) −3.61986 11.1408i −0.595102 1.83154i −0.554218 0.832372i \(-0.686982\pi\)
−0.0408844 0.999164i \(-0.513018\pi\)
\(38\) 0 0
\(39\) 0.992224 + 0.720893i 0.158883 + 0.115435i
\(40\) 0 0
\(41\) 3.63509 5.27126i 0.567705 0.823232i
\(42\) 0 0
\(43\) 3.80506 + 2.76454i 0.580266 + 0.421588i 0.838820 0.544409i \(-0.183246\pi\)
−0.258554 + 0.965997i \(0.583246\pi\)
\(44\) 0 0
\(45\) 3.95546 + 12.1737i 0.589646 + 1.81474i
\(46\) 0 0
\(47\) 4.46898 6.15102i 0.651868 0.897219i −0.347310 0.937750i \(-0.612905\pi\)
0.999178 + 0.0405311i \(0.0129050\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −5.56740 + 17.1347i −0.779592 + 2.39934i
\(52\) 0 0
\(53\) 8.91995 2.89827i 1.22525 0.398108i 0.376259 0.926515i \(-0.377210\pi\)
0.848991 + 0.528407i \(0.177210\pi\)
\(54\) 0 0
\(55\) 11.7990i 1.59097i
\(56\) 0 0
\(57\) −2.93316 + 2.13107i −0.388507 + 0.282267i
\(58\) 0 0
\(59\) −9.13002 6.63335i −1.18863 0.863589i −0.195509 0.980702i \(-0.562636\pi\)
−0.993119 + 0.117113i \(0.962636\pi\)
\(60\) 0 0
\(61\) −4.00070 + 2.90668i −0.512237 + 0.372162i −0.813672 0.581325i \(-0.802535\pi\)
0.301434 + 0.953487i \(0.402535\pi\)
\(62\) 0 0
\(63\) 3.20007 + 4.40452i 0.403171 + 0.554917i
\(64\) 0 0
\(65\) −0.943738 0.306639i −0.117056 0.0380339i
\(66\) 0 0
\(67\) −8.17082 + 2.65486i −0.998224 + 0.324343i −0.762156 0.647394i \(-0.775859\pi\)
−0.236068 + 0.971736i \(0.575859\pi\)
\(68\) 0 0
\(69\) 5.31116 7.31018i 0.639388 0.880043i
\(70\) 0 0
\(71\) −3.69294 1.19991i −0.438271 0.142403i 0.0815668 0.996668i \(-0.474008\pi\)
−0.519838 + 0.854265i \(0.674008\pi\)
\(72\) 0 0
\(73\) 0.525670 0.0615250 0.0307625 0.999527i \(-0.490206\pi\)
0.0307625 + 0.999527i \(0.490206\pi\)
\(74\) 0 0
\(75\) −0.901431 1.24071i −0.104088 0.143265i
\(76\) 0 0
\(77\) 1.55079 + 4.77283i 0.176729 + 0.543915i
\(78\) 0 0
\(79\) 12.5264i 1.40933i 0.709542 + 0.704663i \(0.248902\pi\)
−0.709542 + 0.704663i \(0.751098\pi\)
\(80\) 0 0
\(81\) 4.30737 0.478597
\(82\) 0 0
\(83\) 1.32207 0.145116 0.0725579 0.997364i \(-0.476884\pi\)
0.0725579 + 0.997364i \(0.476884\pi\)
\(84\) 0 0
\(85\) 14.5768i 1.58108i
\(86\) 0 0
\(87\) 6.98337 + 21.4926i 0.748695 + 2.30425i
\(88\) 0 0
\(89\) −5.80911 7.99555i −0.615764 0.847527i 0.381272 0.924463i \(-0.375486\pi\)
−0.997036 + 0.0769361i \(0.975486\pi\)
\(90\) 0 0
\(91\) −0.422057 −0.0442435
\(92\) 0 0
\(93\) 14.7980 + 4.80815i 1.53448 + 0.498582i
\(94\) 0 0
\(95\) 1.72421 2.37317i 0.176900 0.243482i
\(96\) 0 0
\(97\) −7.11564 + 2.31201i −0.722484 + 0.234749i −0.647100 0.762405i \(-0.724018\pi\)
−0.0753842 + 0.997155i \(0.524018\pi\)
\(98\) 0 0
\(99\) 25.9847 + 8.44293i 2.61156 + 0.848546i
\(100\) 0 0
\(101\) 0.102287 + 0.140786i 0.0101779 + 0.0140087i 0.814076 0.580759i \(-0.197244\pi\)
−0.803898 + 0.594768i \(0.797244\pi\)
\(102\) 0 0
\(103\) 6.73237 4.89135i 0.663360 0.481959i −0.204436 0.978880i \(-0.565536\pi\)
0.867796 + 0.496921i \(0.165536\pi\)
\(104\) 0 0
\(105\) −5.52731 4.01582i −0.539410 0.391904i
\(106\) 0 0
\(107\) −2.43783 + 1.77119i −0.235674 + 0.171227i −0.699354 0.714776i \(-0.746529\pi\)
0.463680 + 0.886003i \(0.346529\pi\)
\(108\) 0 0
\(109\) 6.16999i 0.590978i 0.955346 + 0.295489i \(0.0954825\pi\)
−0.955346 + 0.295489i \(0.904517\pi\)
\(110\) 0 0
\(111\) 32.3741 10.5190i 3.07281 0.998418i
\(112\) 0 0
\(113\) 5.59020 17.2049i 0.525881 1.61850i −0.236685 0.971587i \(-0.576061\pi\)
0.762566 0.646910i \(-0.223939\pi\)
\(114\) 0 0
\(115\) −2.25915 + 6.95296i −0.210667 + 0.648367i
\(116\) 0 0
\(117\) −1.35061 + 1.85896i −0.124864 + 0.171860i
\(118\) 0 0
\(119\) −1.91589 5.89651i −0.175630 0.540532i
\(120\) 0 0
\(121\) 11.4758 + 8.33767i 1.04326 + 0.757970i
\(122\) 0 0
\(123\) 15.3178 + 10.5632i 1.38116 + 0.952453i
\(124\) 0 0
\(125\) −8.50663 6.18043i −0.760856 0.552794i
\(126\) 0 0
\(127\) −5.82882 17.9393i −0.517224 1.59185i −0.779198 0.626777i \(-0.784373\pi\)
0.261974 0.965075i \(-0.415627\pi\)
\(128\) 0 0
\(129\) −8.03348 + 11.0571i −0.707308 + 0.973526i
\(130\) 0 0
\(131\) 1.79703 5.53070i 0.157008 0.483220i −0.841351 0.540489i \(-0.818239\pi\)
0.998359 + 0.0572692i \(0.0182393\pi\)
\(132\) 0 0
\(133\) 0.385549 1.18660i 0.0334313 0.102891i
\(134\) 0 0
\(135\) −15.8823 + 5.16048i −1.36693 + 0.444143i
\(136\) 0 0
\(137\) 15.8668i 1.35560i 0.735248 + 0.677798i \(0.237066\pi\)
−0.735248 + 0.677798i \(0.762934\pi\)
\(138\) 0 0
\(139\) −14.3953 + 10.4588i −1.22099 + 0.887101i −0.996182 0.0873019i \(-0.972176\pi\)
−0.224808 + 0.974403i \(0.572176\pi\)
\(140\) 0 0
\(141\) 17.8743 + 12.9864i 1.50529 + 1.09365i
\(142\) 0 0
\(143\) −1.71356 + 1.24497i −0.143295 + 0.104110i
\(144\) 0 0
\(145\) −10.7472 14.7922i −0.892504 1.22843i
\(146\) 0 0
\(147\) −2.76368 0.897974i −0.227944 0.0740636i
\(148\) 0 0
\(149\) 2.08749 0.678266i 0.171014 0.0555657i −0.222259 0.974988i \(-0.571343\pi\)
0.393272 + 0.919422i \(0.371343\pi\)
\(150\) 0 0
\(151\) −4.56570 + 6.28414i −0.371551 + 0.511396i −0.953322 0.301957i \(-0.902360\pi\)
0.581771 + 0.813353i \(0.302360\pi\)
\(152\) 0 0
\(153\) −32.1023 10.4307i −2.59532 0.843269i
\(154\) 0 0
\(155\) −12.5889 −1.01117
\(156\) 0 0
\(157\) −8.58928 11.8221i −0.685499 0.943509i 0.314484 0.949263i \(-0.398168\pi\)
−0.999983 + 0.00575395i \(0.998168\pi\)
\(158\) 0 0
\(159\) 8.42209 + 25.9205i 0.667915 + 2.05563i
\(160\) 0 0
\(161\) 3.10949i 0.245062i
\(162\) 0 0
\(163\) −10.3868 −0.813556 −0.406778 0.913527i \(-0.633348\pi\)
−0.406778 + 0.913527i \(0.633348\pi\)
\(164\) 0 0
\(165\) −34.2867 −2.66922
\(166\) 0 0
\(167\) 0.923298i 0.0714470i −0.999362 0.0357235i \(-0.988626\pi\)
0.999362 0.0357235i \(-0.0113736\pi\)
\(168\) 0 0
\(169\) 3.96218 + 12.1943i 0.304783 + 0.938025i
\(170\) 0 0
\(171\) −3.99260 5.49535i −0.305322 0.420240i
\(172\) 0 0
\(173\) −0.214787 −0.0163299 −0.00816496 0.999967i \(-0.502599\pi\)
−0.00816496 + 0.999967i \(0.502599\pi\)
\(174\) 0 0
\(175\) 0.501925 + 0.163085i 0.0379419 + 0.0123281i
\(176\) 0 0
\(177\) 19.2759 26.5310i 1.44886 1.99419i
\(178\) 0 0
\(179\) 22.9289 7.45005i 1.71379 0.556843i 0.722830 0.691026i \(-0.242841\pi\)
0.990957 + 0.134183i \(0.0428409\pi\)
\(180\) 0 0
\(181\) 1.62666 + 0.528533i 0.120908 + 0.0392855i 0.368846 0.929490i \(-0.379753\pi\)
−0.247938 + 0.968776i \(0.579753\pi\)
\(182\) 0 0
\(183\) −8.44653 11.6257i −0.624385 0.859393i
\(184\) 0 0
\(185\) −22.2814 + 16.1884i −1.63816 + 1.19019i
\(186\) 0 0
\(187\) −25.1719 18.2885i −1.84075 1.33739i
\(188\) 0 0
\(189\) −5.74633 + 4.17495i −0.417984 + 0.303683i
\(190\) 0 0
\(191\) 6.33542i 0.458415i 0.973378 + 0.229208i \(0.0736135\pi\)
−0.973378 + 0.229208i \(0.926387\pi\)
\(192\) 0 0
\(193\) 2.00704 0.652128i 0.144470 0.0469412i −0.235889 0.971780i \(-0.575800\pi\)
0.380359 + 0.924839i \(0.375800\pi\)
\(194\) 0 0
\(195\) 0.891064 2.74241i 0.0638104 0.196388i
\(196\) 0 0
\(197\) −2.43110 + 7.48217i −0.173209 + 0.533083i −0.999547 0.0300917i \(-0.990420\pi\)
0.826338 + 0.563174i \(0.190420\pi\)
\(198\) 0 0
\(199\) 13.2737 18.2697i 0.940947 1.29510i −0.0144862 0.999895i \(-0.504611\pi\)
0.955433 0.295207i \(-0.0953888\pi\)
\(200\) 0 0
\(201\) −7.71477 23.7436i −0.544158 1.67475i
\(202\) 0 0
\(203\) −6.29156 4.57109i −0.441581 0.320828i
\(204\) 0 0
\(205\) −14.4278 4.29846i −1.00768 0.300218i
\(206\) 0 0
\(207\) 13.6958 + 9.95058i 0.951924 + 0.691613i
\(208\) 0 0
\(209\) −1.93486 5.95488i −0.133837 0.411908i
\(210\) 0 0
\(211\) −4.66055 + 6.41469i −0.320845 + 0.441606i −0.938725 0.344667i \(-0.887992\pi\)
0.617880 + 0.786273i \(0.287992\pi\)
\(212\) 0 0
\(213\) 3.48682 10.7313i 0.238913 0.735298i
\(214\) 0 0
\(215\) 3.41712 10.5168i 0.233046 0.717241i
\(216\) 0 0
\(217\) −5.09237 + 1.65461i −0.345693 + 0.112322i
\(218\) 0 0
\(219\) 1.52755i 0.103222i
\(220\) 0 0
\(221\) 2.11698 1.53808i 0.142404 0.103462i
\(222\) 0 0
\(223\) 6.66151 + 4.83987i 0.446088 + 0.324102i 0.788049 0.615612i \(-0.211091\pi\)
−0.341961 + 0.939714i \(0.611091\pi\)
\(224\) 0 0
\(225\) 2.32451 1.68885i 0.154967 0.112590i
\(226\) 0 0
\(227\) −15.2206 20.9494i −1.01023 1.39046i −0.918834 0.394643i \(-0.870868\pi\)
−0.0913924 0.995815i \(-0.529132\pi\)
\(228\) 0 0
\(229\) 12.7491 + 4.14245i 0.842487 + 0.273741i 0.698296 0.715809i \(-0.253942\pi\)
0.144191 + 0.989550i \(0.453942\pi\)
\(230\) 0 0
\(231\) −13.8694 + 4.50644i −0.912540 + 0.296502i
\(232\) 0 0
\(233\) −0.887101 + 1.22099i −0.0581159 + 0.0799897i −0.837086 0.547072i \(-0.815742\pi\)
0.778970 + 0.627061i \(0.215742\pi\)
\(234\) 0 0
\(235\) −17.0008 5.52391i −1.10901 0.360340i
\(236\) 0 0
\(237\) −36.4004 −2.36446
\(238\) 0 0
\(239\) 17.7379 + 24.4141i 1.14737 + 1.57922i 0.749825 + 0.661637i \(0.230138\pi\)
0.397545 + 0.917583i \(0.369862\pi\)
\(240\) 0 0
\(241\) 4.87693 + 15.0097i 0.314151 + 0.966857i 0.976103 + 0.217311i \(0.0697284\pi\)
−0.661952 + 0.749547i \(0.730272\pi\)
\(242\) 0 0
\(243\) 8.79175i 0.563991i
\(244\) 0 0
\(245\) 2.35112 0.150207
\(246\) 0 0
\(247\) 0.526584 0.0335057
\(248\) 0 0
\(249\) 3.84181i 0.243465i
\(250\) 0 0
\(251\) −4.17207 12.8403i −0.263339 0.810473i −0.992072 0.125675i \(-0.959890\pi\)
0.728733 0.684798i \(-0.240110\pi\)
\(252\) 0 0
\(253\) 9.17229 + 12.6246i 0.576657 + 0.793700i
\(254\) 0 0
\(255\) 42.3589 2.65262
\(256\) 0 0
\(257\) −3.00094 0.975064i −0.187193 0.0608228i 0.213920 0.976851i \(-0.431377\pi\)
−0.401114 + 0.916028i \(0.631377\pi\)
\(258\) 0 0
\(259\) −6.88539 + 9.47693i −0.427837 + 0.588868i
\(260\) 0 0
\(261\) −40.2669 + 13.0835i −2.49246 + 0.809849i
\(262\) 0 0
\(263\) 9.81843 + 3.19020i 0.605430 + 0.196716i 0.595661 0.803236i \(-0.296890\pi\)
0.00976941 + 0.999952i \(0.496890\pi\)
\(264\) 0 0
\(265\) −12.9613 17.8397i −0.796208 1.09589i
\(266\) 0 0
\(267\) 23.2343 16.8807i 1.42192 1.03308i
\(268\) 0 0
\(269\) −17.1783 12.4808i −1.04738 0.760966i −0.0756673 0.997133i \(-0.524109\pi\)
−0.971712 + 0.236167i \(0.924109\pi\)
\(270\) 0 0
\(271\) 13.1341 9.54251i 0.797842 0.579666i −0.112438 0.993659i \(-0.535866\pi\)
0.910280 + 0.413993i \(0.135866\pi\)
\(272\) 0 0
\(273\) 1.22646i 0.0742285i
\(274\) 0 0
\(275\) 2.51889 0.818436i 0.151895 0.0493535i
\(276\) 0 0
\(277\) −7.48606 + 23.0397i −0.449794 + 1.38432i 0.427346 + 0.904088i \(0.359449\pi\)
−0.877140 + 0.480235i \(0.840551\pi\)
\(278\) 0 0
\(279\) −9.00818 + 27.7243i −0.539306 + 1.65981i
\(280\) 0 0
\(281\) 6.39227 8.79820i 0.381331 0.524857i −0.574606 0.818430i \(-0.694845\pi\)
0.955936 + 0.293574i \(0.0948446\pi\)
\(282\) 0 0
\(283\) 3.74286 + 11.5193i 0.222490 + 0.684754i 0.998537 + 0.0540784i \(0.0172221\pi\)
−0.776047 + 0.630676i \(0.782778\pi\)
\(284\) 0 0
\(285\) 6.89621 + 5.01039i 0.408496 + 0.296790i
\(286\) 0 0
\(287\) −6.40119 + 0.157521i −0.377850 + 0.00929815i
\(288\) 0 0
\(289\) 17.3449 + 12.6018i 1.02029 + 0.741284i
\(290\) 0 0
\(291\) −6.71849 20.6774i −0.393845 1.21213i
\(292\) 0 0
\(293\) 3.35516 4.61798i 0.196010 0.269785i −0.699687 0.714450i \(-0.746677\pi\)
0.895697 + 0.444665i \(0.146677\pi\)
\(294\) 0 0
\(295\) −8.19919 + 25.2345i −0.477375 + 1.46921i
\(296\) 0 0
\(297\) −11.0150 + 33.9008i −0.639156 + 1.96712i
\(298\) 0 0
\(299\) −1.24815 + 0.405548i −0.0721823 + 0.0234534i
\(300\) 0 0
\(301\) 4.70331i 0.271094i
\(302\) 0 0
\(303\) −0.409110 + 0.297236i −0.0235028 + 0.0170757i
\(304\) 0 0
\(305\) 9.40612 + 6.83394i 0.538593 + 0.391310i
\(306\) 0 0
\(307\) 18.5160 13.4527i 1.05676 0.767784i 0.0832770 0.996526i \(-0.473461\pi\)
0.973487 + 0.228742i \(0.0734614\pi\)
\(308\) 0 0
\(309\) 14.2138 + 19.5636i 0.808595 + 1.11294i
\(310\) 0 0
\(311\) −8.82919 2.86878i −0.500658 0.162674i 0.0477917 0.998857i \(-0.484782\pi\)
−0.548449 + 0.836184i \(0.684782\pi\)
\(312\) 0 0
\(313\) 0.217363 0.0706255i 0.0122861 0.00399199i −0.302868 0.953033i \(-0.597944\pi\)
0.315154 + 0.949041i \(0.397944\pi\)
\(314\) 0 0
\(315\) 7.52374 10.3555i 0.423915 0.583469i
\(316\) 0 0
\(317\) −28.2440 9.17702i −1.58634 0.515433i −0.622659 0.782493i \(-0.713948\pi\)
−0.963680 + 0.267061i \(0.913948\pi\)
\(318\) 0 0
\(319\) −39.0275 −2.18512
\(320\) 0 0
\(321\) −5.14691 7.08411i −0.287272 0.395397i
\(322\) 0 0
\(323\) 2.39039 + 7.35685i 0.133005 + 0.409346i
\(324\) 0 0
\(325\) 0.222742i 0.0123555i
\(326\) 0 0
\(327\) −17.9294 −0.991498
\(328\) 0 0
\(329\) −7.60308 −0.419172
\(330\) 0 0
\(331\) 17.3341i 0.952766i −0.879238 0.476383i \(-0.841948\pi\)
0.879238 0.476383i \(-0.158052\pi\)
\(332\) 0 0
\(333\) 19.7076 + 60.6537i 1.07997 + 3.32380i
\(334\) 0 0
\(335\) 11.8728 + 16.3415i 0.648679 + 0.892830i
\(336\) 0 0
\(337\) −13.4045 −0.730192 −0.365096 0.930970i \(-0.618964\pi\)
−0.365096 + 0.930970i \(0.618964\pi\)
\(338\) 0 0
\(339\) 49.9957 + 16.2446i 2.71539 + 0.882284i
\(340\) 0 0
\(341\) −15.7944 + 21.7391i −0.855314 + 1.17724i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) −20.2046 6.56489i −1.08778 0.353442i
\(346\) 0 0
\(347\) 15.4823 + 21.3096i 0.831135 + 1.14396i 0.987711 + 0.156293i \(0.0499543\pi\)
−0.156576 + 0.987666i \(0.550046\pi\)
\(348\) 0 0
\(349\) −19.3479 + 14.0571i −1.03567 + 0.752458i −0.969436 0.245346i \(-0.921099\pi\)
−0.0662344 + 0.997804i \(0.521099\pi\)
\(350\) 0 0
\(351\) −2.42528 1.76207i −0.129452 0.0940521i
\(352\) 0 0
\(353\) 26.7863 19.4614i 1.42569 1.03583i 0.434892 0.900482i \(-0.356786\pi\)
0.990799 0.135343i \(-0.0432136\pi\)
\(354\) 0 0
\(355\) 9.12935i 0.484536i
\(356\) 0 0
\(357\) 17.1347 5.56740i 0.906865 0.294658i
\(358\) 0 0
\(359\) 2.82170 8.68431i 0.148924 0.458340i −0.848571 0.529082i \(-0.822537\pi\)
0.997495 + 0.0707414i \(0.0225365\pi\)
\(360\) 0 0
\(361\) 5.39029 16.5896i 0.283699 0.873137i
\(362\) 0 0
\(363\) −24.2285 + 33.3476i −1.27167 + 1.75030i
\(364\) 0 0
\(365\) −0.381918 1.17542i −0.0199905 0.0615244i
\(366\) 0 0
\(367\) 2.83816 + 2.06204i 0.148151 + 0.107638i 0.659392 0.751800i \(-0.270814\pi\)
−0.511241 + 0.859437i \(0.670814\pi\)
\(368\) 0 0
\(369\) −19.7904 + 28.6982i −1.03025 + 1.49397i
\(370\) 0 0
\(371\) −7.58777 5.51283i −0.393937 0.286212i
\(372\) 0 0
\(373\) −0.127453 0.392260i −0.00659926 0.0203104i 0.947703 0.319155i \(-0.103399\pi\)
−0.954302 + 0.298844i \(0.903399\pi\)
\(374\) 0 0
\(375\) 17.9597 24.7195i 0.927437 1.27651i
\(376\) 0 0
\(377\) 1.01427 3.12160i 0.0522376 0.160771i
\(378\) 0 0
\(379\) −3.73524 + 11.4959i −0.191866 + 0.590504i 0.808132 + 0.589001i \(0.200479\pi\)
−0.999999 + 0.00150332i \(0.999521\pi\)
\(380\) 0 0
\(381\) 52.1298 16.9380i 2.67069 0.867760i
\(382\) 0 0
\(383\) 30.3337i 1.54998i 0.631973 + 0.774990i \(0.282245\pi\)
−0.631973 + 0.774990i \(0.717755\pi\)
\(384\) 0 0
\(385\) 9.54557 6.93527i 0.486488 0.353454i
\(386\) 0 0
\(387\) −20.7158 15.0509i −1.05304 0.765081i
\(388\) 0 0
\(389\) 13.3750 9.71751i 0.678140 0.492697i −0.194600 0.980883i \(-0.562341\pi\)
0.872740 + 0.488185i \(0.162341\pi\)
\(390\) 0 0
\(391\) −11.3317 15.5968i −0.573071 0.788764i
\(392\) 0 0
\(393\) 16.0717 + 5.22201i 0.810709 + 0.263415i
\(394\) 0 0
\(395\) 28.0095 9.10085i 1.40931 0.457913i
\(396\) 0 0
\(397\) −6.67368 + 9.18553i −0.334942 + 0.461008i −0.942956 0.332918i \(-0.891967\pi\)
0.608013 + 0.793927i \(0.291967\pi\)
\(398\) 0 0
\(399\) 3.44814 + 1.12037i 0.172623 + 0.0560885i
\(400\) 0 0
\(401\) 39.6870 1.98187 0.990937 0.134331i \(-0.0428885\pi\)
0.990937 + 0.134331i \(0.0428885\pi\)
\(402\) 0 0
\(403\) −1.32832 1.82828i −0.0661684 0.0910730i
\(404\) 0 0
\(405\) −3.12946 9.63148i −0.155504 0.478592i
\(406\) 0 0
\(407\) 58.7868i 2.91395i
\(408\) 0 0
\(409\) −4.81376 −0.238025 −0.119012 0.992893i \(-0.537973\pi\)
−0.119012 + 0.992893i \(0.537973\pi\)
\(410\) 0 0
\(411\) −46.1075 −2.27432
\(412\) 0 0
\(413\) 11.2853i 0.555315i
\(414\) 0 0
\(415\) −0.960529 2.95621i −0.0471505 0.145114i
\(416\) 0 0
\(417\) −30.3922 41.8313i −1.48831 2.04849i
\(418\) 0 0
\(419\) 2.06373 0.100820 0.0504099 0.998729i \(-0.483947\pi\)
0.0504099 + 0.998729i \(0.483947\pi\)
\(420\) 0 0
\(421\) 15.8001 + 5.13376i 0.770049 + 0.250204i 0.667586 0.744533i \(-0.267328\pi\)
0.102463 + 0.994737i \(0.467328\pi\)
\(422\) 0 0
\(423\) −24.3304 + 33.4879i −1.18298 + 1.62824i
\(424\) 0 0
\(425\) −3.11191 + 1.01112i −0.150950 + 0.0490466i
\(426\) 0 0
\(427\) 4.70310 + 1.52813i 0.227599 + 0.0739514i
\(428\) 0 0
\(429\) −3.61777 4.97943i −0.174667 0.240409i
\(430\) 0 0
\(431\) 30.3663 22.0624i 1.46269 1.06271i 0.480042 0.877245i \(-0.340621\pi\)
0.982651 0.185464i \(-0.0593787\pi\)
\(432\) 0 0
\(433\) 1.70515 + 1.23887i 0.0819444 + 0.0595361i 0.628003 0.778211i \(-0.283872\pi\)
−0.546059 + 0.837747i \(0.683872\pi\)
\(434\) 0 0
\(435\) 42.9848 31.2302i 2.06096 1.49738i
\(436\) 0 0
\(437\) 3.87959i 0.185586i
\(438\) 0 0
\(439\) 4.09799 1.33152i 0.195587 0.0635499i −0.209586 0.977790i \(-0.567212\pi\)
0.405172 + 0.914240i \(0.367212\pi\)
\(440\) 0 0
\(441\) 1.68238 5.17782i 0.0801131 0.246563i
\(442\) 0 0
\(443\) −6.99947 + 21.5422i −0.332555 + 1.02350i 0.635359 + 0.772217i \(0.280852\pi\)
−0.967914 + 0.251282i \(0.919148\pi\)
\(444\) 0 0
\(445\) −13.6579 + 18.7985i −0.647447 + 0.891134i
\(446\) 0 0
\(447\) 1.97098 + 6.06604i 0.0932240 + 0.286914i
\(448\) 0 0
\(449\) 8.57166 + 6.22767i 0.404521 + 0.293902i 0.771380 0.636375i \(-0.219567\pi\)
−0.366859 + 0.930277i \(0.619567\pi\)
\(450\) 0 0
\(451\) −25.5243 + 19.5216i −1.20189 + 0.919236i
\(452\) 0 0
\(453\) −18.2611 13.2675i −0.857982 0.623360i
\(454\) 0 0
\(455\) 0.306639 + 0.943738i 0.0143755 + 0.0442431i
\(456\) 0 0
\(457\) −0.120284 + 0.165557i −0.00562667 + 0.00774445i −0.811821 0.583906i \(-0.801524\pi\)
0.806194 + 0.591651i \(0.201524\pi\)
\(458\) 0 0
\(459\) 13.6083 41.8821i 0.635182 1.95489i
\(460\) 0 0
\(461\) −7.45306 + 22.9382i −0.347124 + 1.06834i 0.613313 + 0.789840i \(0.289836\pi\)
−0.960437 + 0.278497i \(0.910164\pi\)
\(462\) 0 0
\(463\) −10.7040 + 3.47793i −0.497455 + 0.161633i −0.546990 0.837139i \(-0.684226\pi\)
0.0495342 + 0.998772i \(0.484226\pi\)
\(464\) 0 0
\(465\) 36.5822i 1.69646i
\(466\) 0 0
\(467\) 26.9050 19.5476i 1.24501 0.904556i 0.247093 0.968992i \(-0.420525\pi\)
0.997922 + 0.0644357i \(0.0205247\pi\)
\(468\) 0 0
\(469\) 6.95051 + 5.04984i 0.320945 + 0.233180i
\(470\) 0 0
\(471\) 34.3540 24.9596i 1.58295 1.15008i
\(472\) 0 0
\(473\) −13.8737 19.0955i −0.637913 0.878012i
\(474\) 0 0
\(475\) −0.626232 0.203475i −0.0287335 0.00933608i
\(476\) 0 0
\(477\) −48.5628 + 15.7790i −2.22354 + 0.722471i
\(478\) 0 0
\(479\) 25.1855 34.6649i 1.15076 1.58388i 0.410030 0.912072i \(-0.365518\pi\)
0.740726 0.671808i \(-0.234482\pi\)
\(480\) 0 0
\(481\) −4.70205 1.52779i −0.214395 0.0696611i
\(482\) 0 0
\(483\) −9.03588 −0.411147
\(484\) 0 0
\(485\) 10.3395 + 14.2311i 0.469494 + 0.646203i
\(486\) 0 0
\(487\) 3.17612 + 9.77511i 0.143924 + 0.442952i 0.996871 0.0790450i \(-0.0251871\pi\)
−0.852947 + 0.521997i \(0.825187\pi\)
\(488\) 0 0
\(489\) 30.1830i 1.36492i
\(490\) 0 0
\(491\) −21.5980 −0.974703 −0.487352 0.873206i \(-0.662037\pi\)
−0.487352 + 0.873206i \(0.662037\pi\)
\(492\) 0 0
\(493\) 48.2159 2.17153
\(494\) 0 0
\(495\) 64.2370i 2.88724i
\(496\) 0 0
\(497\) 1.19991 + 3.69294i 0.0538232 + 0.165651i
\(498\) 0 0
\(499\) −18.7697 25.8342i −0.840246 1.15650i −0.985928 0.167168i \(-0.946538\pi\)
0.145682 0.989331i \(-0.453462\pi\)
\(500\) 0 0
\(501\) 2.68302 0.119868
\(502\) 0 0
\(503\) 31.6161 + 10.2727i 1.40969 + 0.458036i 0.912311 0.409497i \(-0.134296\pi\)
0.497379 + 0.867533i \(0.334296\pi\)
\(504\) 0 0
\(505\) 0.240488 0.331004i 0.0107016 0.0147295i
\(506\) 0 0
\(507\) −35.4355 + 11.5137i −1.57375 + 0.511342i
\(508\) 0 0
\(509\) −8.14726 2.64721i −0.361121 0.117335i 0.122836 0.992427i \(-0.460801\pi\)
−0.483957 + 0.875092i \(0.660801\pi\)
\(510\) 0 0
\(511\) −0.308981 0.425276i −0.0136685 0.0188131i
\(512\) 0 0
\(513\) 7.16948 5.20893i 0.316540 0.229980i
\(514\) 0 0
\(515\) −15.8286 11.5001i −0.697491 0.506757i
\(516\) 0 0
\(517\) −30.8686 + 22.4274i −1.35760 + 0.986355i
\(518\) 0 0
\(519\) 0.624150i 0.0273971i
\(520\) 0 0
\(521\) 7.98370 2.59406i 0.349772 0.113648i −0.128861 0.991663i \(-0.541132\pi\)
0.478634 + 0.878015i \(0.341132\pi\)
\(522\) 0 0
\(523\) −0.969993 + 2.98533i −0.0424149 + 0.130539i −0.970022 0.243019i \(-0.921862\pi\)
0.927607 + 0.373558i \(0.121862\pi\)
\(524\) 0 0
\(525\) −0.473910 + 1.45855i −0.0206831 + 0.0636561i
\(526\) 0 0
\(527\) 19.5129 26.8572i 0.849995 1.16992i
\(528\) 0 0
\(529\) −4.11953 12.6786i −0.179110 0.551244i
\(530\) 0 0
\(531\) 49.7064 + 36.1138i 2.15708 + 1.56721i
\(532\) 0 0
\(533\) −0.898088 2.54889i −0.0389005 0.110405i
\(534\) 0 0
\(535\) 5.73163 + 4.16428i 0.247800 + 0.180037i
\(536\) 0 0
\(537\) 21.6491 + 66.6292i 0.934230 + 2.87526i
\(538\) 0 0
\(539\) 2.94977 4.06002i 0.127056 0.174877i
\(540\) 0 0
\(541\) 12.6485 38.9280i 0.543800 1.67364i −0.180027 0.983662i \(-0.557619\pi\)
0.723827 0.689982i \(-0.242381\pi\)
\(542\) 0 0
\(543\) −1.53587 + 4.72691i −0.0659103 + 0.202851i
\(544\) 0 0
\(545\) 13.7964 4.48271i 0.590972 0.192018i
\(546\) 0 0
\(547\) 12.1156i 0.518024i 0.965874 + 0.259012i \(0.0833970\pi\)
−0.965874 + 0.259012i \(0.916603\pi\)
\(548\) 0 0
\(549\) 21.7809 15.8248i 0.929588 0.675385i
\(550\) 0 0
\(551\) 7.84974 + 5.70317i 0.334410 + 0.242963i
\(552\) 0 0
\(553\) 10.1340 7.36282i 0.430943 0.313099i
\(554\) 0 0
\(555\) −47.0419 64.7476i −1.99682 2.74838i
\(556\) 0 0
\(557\) −37.6203 12.2236i −1.59402 0.517930i −0.628405 0.777887i \(-0.716292\pi\)
−0.965620 + 0.259957i \(0.916292\pi\)
\(558\) 0 0
\(559\) 1.88791 0.613418i 0.0798499 0.0259448i
\(560\) 0 0
\(561\) 53.1446 73.1472i 2.24377 3.08828i
\(562\) 0 0
\(563\) 14.0115 + 4.55261i 0.590514 + 0.191869i 0.589005 0.808129i \(-0.299520\pi\)
0.00150854 + 0.999999i \(0.499520\pi\)
\(564\) 0 0
\(565\) −42.5323 −1.78935
\(566\) 0 0
\(567\) −2.53181 3.48474i −0.106326 0.146345i
\(568\) 0 0
\(569\) 11.1768 + 34.3988i 0.468557 + 1.44207i 0.854453 + 0.519528i \(0.173892\pi\)
−0.385896 + 0.922542i \(0.626108\pi\)
\(570\) 0 0
\(571\) 5.78334i 0.242025i 0.992651 + 0.121013i \(0.0386142\pi\)
−0.992651 + 0.121013i \(0.961386\pi\)
\(572\) 0 0
\(573\) −18.4101 −0.769095
\(574\) 0 0
\(575\) 1.64105 0.0684365
\(576\) 0 0
\(577\) 46.0210i 1.91588i −0.286968 0.957940i \(-0.592647\pi\)
0.286968 0.957940i \(-0.407353\pi\)
\(578\) 0 0
\(579\) 1.89502 + 5.83227i 0.0787544 + 0.242381i
\(580\) 0 0
\(581\) −0.777092 1.06958i −0.0322392 0.0443735i
\(582\) 0 0
\(583\) −47.0681 −1.94936
\(584\) 0 0
\(585\) 5.13798 + 1.66943i 0.212429 + 0.0690224i
\(586\) 0 0
\(587\) −9.85118 + 13.5590i −0.406602 + 0.559639i −0.962386 0.271687i \(-0.912418\pi\)
0.555784 + 0.831327i \(0.312418\pi\)
\(588\) 0 0
\(589\) 6.35356 2.06440i 0.261794 0.0850620i
\(590\) 0 0
\(591\) −21.7425 7.06456i −0.894366 0.290597i
\(592\) 0 0
\(593\) −11.4632 15.7777i −0.470737 0.647914i 0.505955 0.862560i \(-0.331140\pi\)
−0.976692 + 0.214646i \(0.931140\pi\)
\(594\) 0 0
\(595\) −11.7929 + 8.56805i −0.483462 + 0.351256i
\(596\) 0 0
\(597\) 53.0899 + 38.5721i 2.17283 + 1.57865i
\(598\) 0 0
\(599\) 4.56803 3.31887i 0.186645 0.135605i −0.490539 0.871419i \(-0.663200\pi\)
0.677184 + 0.735814i \(0.263200\pi\)
\(600\) 0 0
\(601\) 14.2231i 0.580172i −0.957001 0.290086i \(-0.906316\pi\)
0.957001 0.290086i \(-0.0936839\pi\)
\(602\) 0 0
\(603\) 44.4842 14.4538i 1.81154 0.588604i
\(604\) 0 0
\(605\) 10.3058 31.7181i 0.418991 1.28952i
\(606\) 0 0
\(607\) −3.11043 + 9.57292i −0.126248 + 0.388553i −0.994126 0.108225i \(-0.965483\pi\)
0.867878 + 0.496777i \(0.165483\pi\)
\(608\) 0 0
\(609\) 13.2831 18.2827i 0.538260 0.740852i
\(610\) 0 0
\(611\) −0.991614 3.05187i −0.0401164 0.123466i
\(612\) 0 0
\(613\) 33.8404 + 24.5865i 1.36680 + 0.993038i 0.997979 + 0.0635371i \(0.0202381\pi\)
0.368820 + 0.929501i \(0.379762\pi\)
\(614\) 0 0
\(615\) 12.4909 41.9258i 0.503683 1.69061i
\(616\) 0 0
\(617\) −18.3094 13.3025i −0.737107 0.535540i 0.154697 0.987962i \(-0.450560\pi\)
−0.891804 + 0.452422i \(0.850560\pi\)
\(618\) 0 0
\(619\) 10.8023 + 33.2459i 0.434180 + 1.33627i 0.893925 + 0.448217i \(0.147941\pi\)
−0.459745 + 0.888051i \(0.652059\pi\)
\(620\) 0 0
\(621\) −12.9820 + 17.8682i −0.520949 + 0.717025i
\(622\) 0 0
\(623\) −3.05403 + 9.39934i −0.122357 + 0.376576i
\(624\) 0 0
\(625\) −8.45478 + 26.0211i −0.338191 + 1.04085i
\(626\) 0 0
\(627\) 17.3043 5.62251i 0.691068 0.224542i
\(628\) 0 0
\(629\) 72.6271i 2.89583i
\(630\) 0 0
\(631\) −40.2156 + 29.2183i −1.60096 + 1.16316i −0.715306 + 0.698812i \(0.753713\pi\)
−0.885651 + 0.464351i \(0.846287\pi\)
\(632\) 0 0
\(633\) −18.6405 13.5431i −0.740893 0.538290i
\(634\) 0 0
\(635\) −35.8782 + 26.0670i −1.42378 + 1.03444i
\(636\) 0 0
\(637\) 0.248079 + 0.341451i 0.00982923 + 0.0135288i
\(638\) 0 0
\(639\) 20.1054 + 6.53264i 0.795357 + 0.258427i
\(640\) 0 0
\(641\) −14.2980 + 4.64570i −0.564737 + 0.183494i −0.577451 0.816425i \(-0.695953\pi\)
0.0127146 + 0.999919i \(0.495953\pi\)
\(642\) 0 0
\(643\) −20.4655 + 28.1684i −0.807081 + 1.11085i 0.184686 + 0.982798i \(0.440873\pi\)
−0.991767 + 0.128055i \(0.959127\pi\)
\(644\) 0 0
\(645\) 30.5609 + 9.92983i 1.20333 + 0.390987i
\(646\) 0 0
\(647\) −25.3856 −0.998012 −0.499006 0.866599i \(-0.666301\pi\)
−0.499006 + 0.866599i \(0.666301\pi\)
\(648\) 0 0
\(649\) 33.2892 + 45.8186i 1.30671 + 1.79854i
\(650\) 0 0
\(651\) −4.80815 14.7980i −0.188446 0.579978i
\(652\) 0 0
\(653\) 12.1027i 0.473615i −0.971557 0.236808i \(-0.923899\pi\)
0.971557 0.236808i \(-0.0761011\pi\)
\(654\) 0 0
\(655\) −13.6725 −0.534229
\(656\) 0 0
\(657\) −2.86189 −0.111653
\(658\) 0 0
\(659\) 4.99529i 0.194589i 0.995256 + 0.0972945i \(0.0310189\pi\)
−0.995256 + 0.0972945i \(0.968981\pi\)
\(660\) 0 0
\(661\) −7.93165 24.4111i −0.308505 0.949482i −0.978346 0.206977i \(-0.933637\pi\)
0.669840 0.742505i \(-0.266363\pi\)
\(662\) 0 0
\(663\) 4.46951 + 6.15175i 0.173581 + 0.238914i
\(664\) 0 0
\(665\) −2.93340 −0.113752
\(666\) 0 0
\(667\) −22.9983 7.47261i −0.890499 0.289341i
\(668\) 0 0
\(669\) −14.0642 + 19.3577i −0.543754 + 0.748413i
\(670\) 0 0
\(671\) 23.6023 7.66886i 0.911157 0.296053i
\(672\) 0 0
\(673\) −19.8851 6.46106i −0.766514 0.249056i −0.100442 0.994943i \(-0.532026\pi\)
−0.666072 + 0.745887i \(0.732026\pi\)
\(674\) 0 0
\(675\) 2.20335 + 3.03265i 0.0848071 + 0.116727i
\(676\) 0 0
\(677\) −10.9123 + 7.92828i −0.419395 + 0.304708i −0.777394 0.629013i \(-0.783459\pi\)
0.357999 + 0.933722i \(0.383459\pi\)
\(678\) 0 0
\(679\) 6.05293 + 4.39771i 0.232290 + 0.168769i
\(680\) 0 0
\(681\) 60.8769 44.2296i 2.33281 1.69488i
\(682\) 0 0
\(683\) 19.4682i 0.744930i −0.928046 0.372465i \(-0.878513\pi\)
0.928046 0.372465i \(-0.121487\pi\)
\(684\) 0 0
\(685\) 35.4790 11.5278i 1.35558 0.440455i
\(686\) 0 0
\(687\) −12.0376 + 37.0478i −0.459261 + 1.41346i
\(688\) 0 0
\(689\) 1.22323 3.76472i 0.0466015 0.143425i
\(690\) 0 0
\(691\) −14.8862 + 20.4891i −0.566297 + 0.779441i −0.992110 0.125370i \(-0.959988\pi\)
0.425813 + 0.904811i \(0.359988\pi\)
\(692\) 0 0
\(693\) −8.44293 25.9847i −0.320720 0.987076i
\(694\) 0 0
\(695\) 33.8450 + 24.5898i 1.28381 + 0.932744i
\(696\) 0 0
\(697\) 31.5335 24.1176i 1.19442 0.913519i
\(698\) 0 0
\(699\) −3.54808 2.57783i −0.134201 0.0975025i
\(700\) 0 0
\(701\) 5.50977 + 16.9573i 0.208101 + 0.640469i 0.999572 + 0.0292620i \(0.00931570\pi\)
−0.791471 + 0.611207i \(0.790684\pi\)
\(702\) 0 0
\(703\) 8.59064 11.8240i 0.324002 0.445951i
\(704\) 0 0
\(705\) 16.0520 49.4028i 0.604552 1.86062i
\(706\) 0 0
\(707\) 0.0537754 0.165504i 0.00202243 0.00622440i
\(708\) 0 0
\(709\) −19.5175 + 6.34162i −0.732995 + 0.238164i −0.651648 0.758521i \(-0.725922\pi\)
−0.0813467 + 0.996686i \(0.525922\pi\)
\(710\) 0 0
\(711\) 68.1971i 2.55759i
\(712\) 0 0
\(713\) −13.4698 + 9.78637i −0.504448 + 0.366503i
\(714\) 0 0
\(715\) 4.02877 + 2.92707i 0.150668 + 0.109466i
\(716\) 0 0
\(717\) −70.9452 + 51.5447i −2.64950 + 1.92497i
\(718\) 0 0
\(719\) 5.18710 + 7.13943i 0.193446 + 0.266256i 0.894711 0.446645i \(-0.147381\pi\)
−0.701265 + 0.712900i \(0.747381\pi\)
\(720\) 0 0
\(721\) −7.91437 2.57153i −0.294747 0.0957690i
\(722\) 0 0
\(723\) −43.6166 + 14.1719i −1.62212 + 0.527059i
\(724\) 0 0
\(725\) −2.41241 + 3.32040i −0.0895948 + 0.123317i
\(726\) 0 0
\(727\) 7.79091 + 2.53142i 0.288949 + 0.0938852i 0.449905 0.893076i \(-0.351458\pi\)
−0.160956 + 0.986962i \(0.551458\pi\)
\(728\) 0 0
\(729\) 38.4701 1.42482
\(730\) 0 0
\(731\) 17.1400 + 23.5912i 0.633946 + 0.872552i
\(732\) 0 0
\(733\) 5.73236 + 17.6424i 0.211729 + 0.651636i 0.999370 + 0.0355008i \(0.0113026\pi\)
−0.787640 + 0.616135i \(0.788697\pi\)
\(734\) 0 0
\(735\) 6.83212i 0.252007i
\(736\) 0 0
\(737\) 43.1151 1.58816
\(738\) 0 0
\(739\) 38.1266 1.40251 0.701256 0.712910i \(-0.252623\pi\)
0.701256 + 0.712910i \(0.252623\pi\)
\(740\) 0 0
\(741\) 1.53020i 0.0562134i
\(742\) 0 0
\(743\) 8.54675 + 26.3042i 0.313550 + 0.965007i 0.976347 + 0.216209i \(0.0693691\pi\)
−0.662797 + 0.748799i \(0.730631\pi\)
\(744\) 0 0
\(745\) −3.03327 4.17493i −0.111130 0.152958i
\(746\) 0 0
\(747\) −7.19772 −0.263351
\(748\) 0 0
\(749\) 2.86585 + 0.931170i 0.104716 + 0.0340242i
\(750\) 0 0
\(751\) 13.6308 18.7612i 0.497395 0.684606i −0.484335 0.874883i \(-0.660938\pi\)
0.981731 + 0.190276i \(0.0609384\pi\)
\(752\) 0 0
\(753\) 37.3127 12.1236i 1.35975 0.441810i
\(754\) 0 0
\(755\) 17.3688 + 5.64345i 0.632114 + 0.205386i
\(756\) 0 0
\(757\) 8.00729 + 11.0211i 0.291030 + 0.400568i 0.929348 0.369204i \(-0.120370\pi\)
−0.638318 + 0.769772i \(0.720370\pi\)
\(758\) 0 0
\(759\) −36.6858 + 26.6538i −1.33161 + 0.967472i
\(760\) 0 0
\(761\) 22.5410 + 16.3770i 0.817111 + 0.593666i 0.915884 0.401444i \(-0.131492\pi\)
−0.0987723 + 0.995110i \(0.531492\pi\)
\(762\) 0 0
\(763\) 4.99163 3.62663i 0.180709 0.131293i
\(764\) 0 0
\(765\) 79.3604i 2.86928i
\(766\) 0 0
\(767\) −4.52993 + 1.47186i −0.163566 + 0.0531459i
\(768\) 0 0
\(769\) −8.18457 + 25.1895i −0.295143 + 0.908357i 0.688030 + 0.725682i \(0.258476\pi\)
−0.983173 + 0.182675i \(0.941524\pi\)
\(770\) 0 0
\(771\) 2.83344 8.72044i 0.102044 0.314059i
\(772\) 0 0
\(773\) 5.59401 7.69950i 0.201203 0.276932i −0.696478 0.717578i \(-0.745251\pi\)
0.897681 + 0.440646i \(0.145251\pi\)
\(774\) 0 0
\(775\) 0.873230 + 2.68753i 0.0313673 + 0.0965388i
\(776\) 0 0
\(777\) −27.5391 20.0083i −0.987958 0.717793i
\(778\) 0 0
\(779\) 7.98651 0.196532i 0.286147 0.00704150i
\(780\) 0 0
\(781\) 15.7650 + 11.4539i 0.564115 + 0.409854i
\(782\) 0 0
\(783\) −17.0693 52.5340i −0.610008 1.87741i
\(784\) 0 0
\(785\) −20.1944 + 27.7952i −0.720769 + 0.992054i
\(786\) 0 0
\(787\) −8.83279 + 27.1845i −0.314855 + 0.969024i 0.660959 + 0.750422i \(0.270150\pi\)
−0.975814 + 0.218602i \(0.929850\pi\)
\(788\) 0 0
\(789\) −9.27042 + 28.5314i −0.330036 + 1.01575i
\(790\) 0 0
\(791\) −17.2049 + 5.59020i −0.611734 + 0.198765i
\(792\) 0 0
\(793\) 2.08713i 0.0741161i
\(794\) 0 0
\(795\) 51.8406 37.6644i 1.83860 1.33582i
\(796\) 0 0
\(797\) 30.7194 + 22.3190i 1.08814 + 0.790579i 0.979084