Properties

Label 576.2.bb.e.49.17
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.17
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68781 + 0.388965i) q^{3} +(-0.846545 + 0.226831i) q^{5} +(0.567074 - 0.327400i) q^{7} +(2.69741 + 1.31300i) q^{9} +O(q^{10})\) \(q+(1.68781 + 0.388965i) q^{3} +(-0.846545 + 0.226831i) q^{5} +(0.567074 - 0.327400i) q^{7} +(2.69741 + 1.31300i) q^{9} +(1.54155 - 5.75313i) q^{11} +(1.19068 + 4.44367i) q^{13} +(-1.51704 + 0.0535712i) q^{15} +2.75816 q^{17} +(1.73499 - 1.73499i) q^{19} +(1.08446 - 0.332018i) q^{21} +(3.50762 + 2.02512i) q^{23} +(-3.66494 + 2.11595i) q^{25} +(4.04201 + 3.26530i) q^{27} +(2.47312 + 0.662669i) q^{29} +(-2.08801 + 3.61654i) q^{31} +(4.83961 - 9.11059i) q^{33} +(-0.405789 + 0.405789i) q^{35} +(-4.30563 - 4.30563i) q^{37} +(0.281205 + 7.96320i) q^{39} +(6.15806 + 3.55536i) q^{41} +(-0.225483 + 0.841515i) q^{43} +(-2.58131 - 0.499657i) q^{45} +(-4.65521 - 8.06305i) q^{47} +(-3.28562 + 5.69086i) q^{49} +(4.65526 + 1.07283i) q^{51} +(-7.64584 - 7.64584i) q^{53} +5.21996i q^{55} +(3.60318 - 2.25348i) q^{57} +(-6.83351 + 1.83103i) q^{59} +(-3.77755 - 1.01219i) q^{61} +(1.95951 - 0.138565i) q^{63} +(-2.01592 - 3.49168i) q^{65} +(-3.11705 - 11.6330i) q^{67} +(5.13249 + 4.78237i) q^{69} -4.34835i q^{71} -0.656583i q^{73} +(-7.00876 + 2.14580i) q^{75} +(-1.00941 - 3.76715i) q^{77} +(8.16172 + 14.1365i) q^{79} +(5.55206 + 7.08340i) q^{81} +(-5.36845 - 1.43847i) q^{83} +(-2.33491 + 0.625638i) q^{85} +(3.91640 + 2.08042i) q^{87} +5.11081i q^{89} +(2.13006 + 2.13006i) q^{91} +(-4.93087 + 5.29187i) q^{93} +(-1.07520 + 1.86230i) q^{95} +(3.05669 + 5.29434i) q^{97} +(11.7120 - 13.4945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.68781 + 0.388965i 0.974458 + 0.224569i
\(4\) 0 0
\(5\) −0.846545 + 0.226831i −0.378587 + 0.101442i −0.443094 0.896475i \(-0.646119\pi\)
0.0645072 + 0.997917i \(0.479452\pi\)
\(6\) 0 0
\(7\) 0.567074 0.327400i 0.214334 0.123746i −0.388990 0.921242i \(-0.627176\pi\)
0.603324 + 0.797496i \(0.293843\pi\)
\(8\) 0 0
\(9\) 2.69741 + 1.31300i 0.899137 + 0.437667i
\(10\) 0 0
\(11\) 1.54155 5.75313i 0.464794 1.73463i −0.192778 0.981242i \(-0.561750\pi\)
0.657572 0.753392i \(-0.271584\pi\)
\(12\) 0 0
\(13\) 1.19068 + 4.44367i 0.330234 + 1.23245i 0.908944 + 0.416918i \(0.136890\pi\)
−0.578710 + 0.815534i \(0.696444\pi\)
\(14\) 0 0
\(15\) −1.51704 + 0.0535712i −0.391698 + 0.0138320i
\(16\) 0 0
\(17\) 2.75816 0.668953 0.334477 0.942404i \(-0.391441\pi\)
0.334477 + 0.942404i \(0.391441\pi\)
\(18\) 0 0
\(19\) 1.73499 1.73499i 0.398034 0.398034i −0.479505 0.877539i \(-0.659184\pi\)
0.877539 + 0.479505i \(0.159184\pi\)
\(20\) 0 0
\(21\) 1.08446 0.332018i 0.236649 0.0724522i
\(22\) 0 0
\(23\) 3.50762 + 2.02512i 0.731389 + 0.422268i 0.818930 0.573893i \(-0.194568\pi\)
−0.0875410 + 0.996161i \(0.527901\pi\)
\(24\) 0 0
\(25\) −3.66494 + 2.11595i −0.732988 + 0.423191i
\(26\) 0 0
\(27\) 4.04201 + 3.26530i 0.777885 + 0.628407i
\(28\) 0 0
\(29\) 2.47312 + 0.662669i 0.459246 + 0.123055i 0.481022 0.876708i \(-0.340266\pi\)
−0.0217764 + 0.999763i \(0.506932\pi\)
\(30\) 0 0
\(31\) −2.08801 + 3.61654i −0.375018 + 0.649550i −0.990330 0.138734i \(-0.955697\pi\)
0.615312 + 0.788284i \(0.289030\pi\)
\(32\) 0 0
\(33\) 4.83961 9.11059i 0.842468 1.58595i
\(34\) 0 0
\(35\) −0.405789 + 0.405789i −0.0685909 + 0.0685909i
\(36\) 0 0
\(37\) −4.30563 4.30563i −0.707841 0.707841i 0.258240 0.966081i \(-0.416858\pi\)
−0.966081 + 0.258240i \(0.916858\pi\)
\(38\) 0 0
\(39\) 0.281205 + 7.96320i 0.0450288 + 1.27513i
\(40\) 0 0
\(41\) 6.15806 + 3.55536i 0.961728 + 0.555254i 0.896704 0.442630i \(-0.145954\pi\)
0.0650233 + 0.997884i \(0.479288\pi\)
\(42\) 0 0
\(43\) −0.225483 + 0.841515i −0.0343859 + 0.128330i −0.980985 0.194082i \(-0.937827\pi\)
0.946599 + 0.322412i \(0.104494\pi\)
\(44\) 0 0
\(45\) −2.58131 0.499657i −0.384799 0.0744845i
\(46\) 0 0
\(47\) −4.65521 8.06305i −0.679032 1.17612i −0.975273 0.221004i \(-0.929067\pi\)
0.296241 0.955113i \(-0.404267\pi\)
\(48\) 0 0
\(49\) −3.28562 + 5.69086i −0.469374 + 0.812980i
\(50\) 0 0
\(51\) 4.65526 + 1.07283i 0.651867 + 0.150226i
\(52\) 0 0
\(53\) −7.64584 7.64584i −1.05024 1.05024i −0.998669 0.0515677i \(-0.983578\pi\)
−0.0515677 0.998669i \(-0.516422\pi\)
\(54\) 0 0
\(55\) 5.21996i 0.703859i
\(56\) 0 0
\(57\) 3.60318 2.25348i 0.477253 0.298481i
\(58\) 0 0
\(59\) −6.83351 + 1.83103i −0.889647 + 0.238380i −0.674565 0.738216i \(-0.735669\pi\)
−0.215082 + 0.976596i \(0.569002\pi\)
\(60\) 0 0
\(61\) −3.77755 1.01219i −0.483666 0.129598i 0.00874306 0.999962i \(-0.497217\pi\)
−0.492409 + 0.870364i \(0.663884\pi\)
\(62\) 0 0
\(63\) 1.95951 0.138565i 0.246875 0.0174576i
\(64\) 0 0
\(65\) −2.01592 3.49168i −0.250045 0.433090i
\(66\) 0 0
\(67\) −3.11705 11.6330i −0.380809 1.42120i −0.844669 0.535289i \(-0.820203\pi\)
0.463860 0.885908i \(-0.346464\pi\)
\(68\) 0 0
\(69\) 5.13249 + 4.78237i 0.617880 + 0.575730i
\(70\) 0 0
\(71\) 4.34835i 0.516054i −0.966138 0.258027i \(-0.916928\pi\)
0.966138 0.258027i \(-0.0830723\pi\)
\(72\) 0 0
\(73\) 0.656583i 0.0768472i −0.999262 0.0384236i \(-0.987766\pi\)
0.999262 0.0384236i \(-0.0122336\pi\)
\(74\) 0 0
\(75\) −7.00876 + 2.14580i −0.809302 + 0.247775i
\(76\) 0 0
\(77\) −1.00941 3.76715i −0.115032 0.429307i
\(78\) 0 0
\(79\) 8.16172 + 14.1365i 0.918266 + 1.59048i 0.802048 + 0.597259i \(0.203744\pi\)
0.116217 + 0.993224i \(0.462923\pi\)
\(80\) 0 0
\(81\) 5.55206 + 7.08340i 0.616896 + 0.787045i
\(82\) 0 0
\(83\) −5.36845 1.43847i −0.589264 0.157893i −0.0481470 0.998840i \(-0.515332\pi\)
−0.541117 + 0.840948i \(0.681998\pi\)
\(84\) 0 0
\(85\) −2.33491 + 0.625638i −0.253257 + 0.0678599i
\(86\) 0 0
\(87\) 3.91640 + 2.08042i 0.419882 + 0.223044i
\(88\) 0 0
\(89\) 5.11081i 0.541744i 0.962615 + 0.270872i \(0.0873121\pi\)
−0.962615 + 0.270872i \(0.912688\pi\)
\(90\) 0 0
\(91\) 2.13006 + 2.13006i 0.223291 + 0.223291i
\(92\) 0 0
\(93\) −4.93087 + 5.29187i −0.511308 + 0.548741i
\(94\) 0 0
\(95\) −1.07520 + 1.86230i −0.110313 + 0.191068i
\(96\) 0 0
\(97\) 3.05669 + 5.29434i 0.310360 + 0.537559i 0.978440 0.206530i \(-0.0662171\pi\)
−0.668080 + 0.744089i \(0.732884\pi\)
\(98\) 0 0
\(99\) 11.7120 13.4945i 1.17711 1.35625i
\(100\) 0 0
\(101\) 3.30688 12.3415i 0.329047 1.22802i −0.581133 0.813809i \(-0.697390\pi\)
0.910180 0.414213i \(-0.135943\pi\)
\(102\) 0 0
\(103\) −1.82866 1.05577i −0.180183 0.104029i 0.407196 0.913341i \(-0.366507\pi\)
−0.587379 + 0.809312i \(0.699840\pi\)
\(104\) 0 0
\(105\) −0.842733 + 0.527057i −0.0822423 + 0.0514355i
\(106\) 0 0
\(107\) −7.26738 7.26738i −0.702564 0.702564i 0.262396 0.964960i \(-0.415487\pi\)
−0.964960 + 0.262396i \(0.915487\pi\)
\(108\) 0 0
\(109\) 5.73169 5.73169i 0.548996 0.548996i −0.377154 0.926150i \(-0.623097\pi\)
0.926150 + 0.377154i \(0.123097\pi\)
\(110\) 0 0
\(111\) −5.59235 8.94183i −0.530802 0.848721i
\(112\) 0 0
\(113\) 0.907975 1.57266i 0.0854151 0.147943i −0.820153 0.572144i \(-0.806112\pi\)
0.905568 + 0.424201i \(0.139445\pi\)
\(114\) 0 0
\(115\) −3.42872 0.918723i −0.319730 0.0856713i
\(116\) 0 0
\(117\) −2.62279 + 13.5498i −0.242477 + 1.25268i
\(118\) 0 0
\(119\) 1.56408 0.903023i 0.143379 0.0827800i
\(120\) 0 0
\(121\) −21.1959 12.2374i −1.92690 1.11249i
\(122\) 0 0
\(123\) 9.01073 + 8.39605i 0.812470 + 0.757046i
\(124\) 0 0
\(125\) 5.72115 5.72115i 0.511715 0.511715i
\(126\) 0 0
\(127\) −19.2026 −1.70395 −0.851976 0.523581i \(-0.824596\pi\)
−0.851976 + 0.523581i \(0.824596\pi\)
\(128\) 0 0
\(129\) −0.707893 + 1.33261i −0.0623265 + 0.117330i
\(130\) 0 0
\(131\) 3.12885 + 11.6770i 0.273369 + 1.02023i 0.956927 + 0.290330i \(0.0937650\pi\)
−0.683558 + 0.729896i \(0.739568\pi\)
\(132\) 0 0
\(133\) 0.415831 1.55190i 0.0360571 0.134567i
\(134\) 0 0
\(135\) −4.16242 1.84737i −0.358244 0.158996i
\(136\) 0 0
\(137\) −2.88080 + 1.66323i −0.246123 + 0.142099i −0.617988 0.786188i \(-0.712052\pi\)
0.371865 + 0.928287i \(0.378719\pi\)
\(138\) 0 0
\(139\) −10.4536 + 2.80104i −0.886666 + 0.237582i −0.673281 0.739387i \(-0.735116\pi\)
−0.213385 + 0.976968i \(0.568449\pi\)
\(140\) 0 0
\(141\) −4.72086 15.4196i −0.397568 1.29857i
\(142\) 0 0
\(143\) 27.4005 2.29134
\(144\) 0 0
\(145\) −2.24392 −0.186347
\(146\) 0 0
\(147\) −7.75905 + 8.32710i −0.639956 + 0.686808i
\(148\) 0 0
\(149\) −19.1223 + 5.12380i −1.56656 + 0.419758i −0.934733 0.355351i \(-0.884361\pi\)
−0.631827 + 0.775110i \(0.717695\pi\)
\(150\) 0 0
\(151\) −5.09441 + 2.94126i −0.414577 + 0.239356i −0.692754 0.721174i \(-0.743603\pi\)
0.278177 + 0.960530i \(0.410270\pi\)
\(152\) 0 0
\(153\) 7.43990 + 3.62147i 0.601481 + 0.292779i
\(154\) 0 0
\(155\) 0.947251 3.53519i 0.0760851 0.283953i
\(156\) 0 0
\(157\) 5.09096 + 18.9997i 0.406303 + 1.51634i 0.801640 + 0.597808i \(0.203961\pi\)
−0.395336 + 0.918536i \(0.629372\pi\)
\(158\) 0 0
\(159\) −9.93077 15.8787i −0.787561 1.25926i
\(160\) 0 0
\(161\) 2.65210 0.209015
\(162\) 0 0
\(163\) −5.00716 + 5.00716i −0.392191 + 0.392191i −0.875468 0.483277i \(-0.839446\pi\)
0.483277 + 0.875468i \(0.339446\pi\)
\(164\) 0 0
\(165\) −2.03038 + 8.81030i −0.158065 + 0.685881i
\(166\) 0 0
\(167\) −14.5023 8.37292i −1.12222 0.647916i −0.180255 0.983620i \(-0.557692\pi\)
−0.941967 + 0.335704i \(0.891026\pi\)
\(168\) 0 0
\(169\) −7.07014 + 4.08195i −0.543857 + 0.313996i
\(170\) 0 0
\(171\) 6.95802 2.40194i 0.532093 0.183681i
\(172\) 0 0
\(173\) −16.2848 4.36351i −1.23811 0.331751i −0.420379 0.907349i \(-0.638103\pi\)
−0.817733 + 0.575597i \(0.804770\pi\)
\(174\) 0 0
\(175\) −1.38553 + 2.39980i −0.104736 + 0.181408i
\(176\) 0 0
\(177\) −12.2459 + 0.432439i −0.920456 + 0.0325041i
\(178\) 0 0
\(179\) −6.56566 + 6.56566i −0.490740 + 0.490740i −0.908539 0.417799i \(-0.862802\pi\)
0.417799 + 0.908539i \(0.362802\pi\)
\(180\) 0 0
\(181\) 15.4877 + 15.4877i 1.15119 + 1.15119i 0.986315 + 0.164875i \(0.0527219\pi\)
0.164875 + 0.986315i \(0.447278\pi\)
\(182\) 0 0
\(183\) −5.98209 3.17773i −0.442209 0.234904i
\(184\) 0 0
\(185\) 4.62156 + 2.66826i 0.339784 + 0.196174i
\(186\) 0 0
\(187\) 4.25184 15.8681i 0.310925 1.16039i
\(188\) 0 0
\(189\) 3.36118 + 0.528309i 0.244490 + 0.0384288i
\(190\) 0 0
\(191\) 1.73038 + 2.99710i 0.125206 + 0.216863i 0.921813 0.387634i \(-0.126708\pi\)
−0.796608 + 0.604497i \(0.793374\pi\)
\(192\) 0 0
\(193\) 4.93395 8.54585i 0.355153 0.615144i −0.631991 0.774976i \(-0.717762\pi\)
0.987144 + 0.159832i \(0.0510953\pi\)
\(194\) 0 0
\(195\) −2.04436 6.67743i −0.146399 0.478181i
\(196\) 0 0
\(197\) 4.95292 + 4.95292i 0.352881 + 0.352881i 0.861180 0.508299i \(-0.169726\pi\)
−0.508299 + 0.861180i \(0.669726\pi\)
\(198\) 0 0
\(199\) 19.3983i 1.37511i −0.726132 0.687556i \(-0.758684\pi\)
0.726132 0.687556i \(-0.241316\pi\)
\(200\) 0 0
\(201\) −0.736162 20.8467i −0.0519248 1.47042i
\(202\) 0 0
\(203\) 1.61940 0.433916i 0.113659 0.0304549i
\(204\) 0 0
\(205\) −6.01954 1.61293i −0.420423 0.112652i
\(206\) 0 0
\(207\) 6.80250 + 10.0681i 0.472807 + 0.699781i
\(208\) 0 0
\(209\) −7.30705 12.6562i −0.505439 0.875446i
\(210\) 0 0
\(211\) 0.499784 + 1.86522i 0.0344066 + 0.128407i 0.980993 0.194043i \(-0.0621602\pi\)
−0.946586 + 0.322450i \(0.895494\pi\)
\(212\) 0 0
\(213\) 1.69136 7.33919i 0.115890 0.502873i
\(214\) 0 0
\(215\) 0.763527i 0.0520721i
\(216\) 0 0
\(217\) 2.73446i 0.185627i
\(218\) 0 0
\(219\) 0.255388 1.10819i 0.0172575 0.0748844i
\(220\) 0 0
\(221\) 3.28408 + 12.2564i 0.220911 + 0.824452i
\(222\) 0 0
\(223\) 6.56173 + 11.3653i 0.439406 + 0.761074i 0.997644 0.0686072i \(-0.0218555\pi\)
−0.558237 + 0.829681i \(0.688522\pi\)
\(224\) 0 0
\(225\) −12.6641 + 0.895533i −0.844273 + 0.0597022i
\(226\) 0 0
\(227\) −4.02317 1.07800i −0.267027 0.0715497i 0.122821 0.992429i \(-0.460806\pi\)
−0.389848 + 0.920879i \(0.627473\pi\)
\(228\) 0 0
\(229\) 26.9787 7.22892i 1.78280 0.477701i 0.791713 0.610894i \(-0.209190\pi\)
0.991090 + 0.133193i \(0.0425231\pi\)
\(230\) 0 0
\(231\) −0.238393 6.75086i −0.0156851 0.444174i
\(232\) 0 0
\(233\) 6.78106i 0.444242i 0.975019 + 0.222121i \(0.0712980\pi\)
−0.975019 + 0.222121i \(0.928702\pi\)
\(234\) 0 0
\(235\) 5.76980 + 5.76980i 0.376380 + 0.376380i
\(236\) 0 0
\(237\) 8.27683 + 27.0344i 0.537638 + 1.75607i
\(238\) 0 0
\(239\) 4.09048 7.08492i 0.264591 0.458286i −0.702865 0.711323i \(-0.748096\pi\)
0.967456 + 0.253038i \(0.0814296\pi\)
\(240\) 0 0
\(241\) −0.259428 0.449343i −0.0167112 0.0289447i 0.857549 0.514403i \(-0.171986\pi\)
−0.874260 + 0.485458i \(0.838653\pi\)
\(242\) 0 0
\(243\) 6.61563 + 14.1150i 0.424393 + 0.905478i
\(244\) 0 0
\(245\) 1.49056 5.56285i 0.0952285 0.355397i
\(246\) 0 0
\(247\) 9.77552 + 5.64390i 0.622002 + 0.359113i
\(248\) 0 0
\(249\) −8.50141 4.51601i −0.538755 0.286190i
\(250\) 0 0
\(251\) 13.9609 + 13.9609i 0.881207 + 0.881207i 0.993657 0.112450i \(-0.0358699\pi\)
−0.112450 + 0.993657i \(0.535870\pi\)
\(252\) 0 0
\(253\) 17.0580 17.0580i 1.07243 1.07243i
\(254\) 0 0
\(255\) −4.18424 + 0.147758i −0.262027 + 0.00925298i
\(256\) 0 0
\(257\) −8.72443 + 15.1112i −0.544215 + 0.942609i 0.454441 + 0.890777i \(0.349839\pi\)
−0.998656 + 0.0518315i \(0.983494\pi\)
\(258\) 0 0
\(259\) −3.85127 1.03195i −0.239307 0.0641220i
\(260\) 0 0
\(261\) 5.80093 + 5.03469i 0.359068 + 0.311640i
\(262\) 0 0
\(263\) 9.06417 5.23320i 0.558921 0.322693i −0.193791 0.981043i \(-0.562079\pi\)
0.752712 + 0.658350i \(0.228745\pi\)
\(264\) 0 0
\(265\) 8.20687 + 4.73824i 0.504144 + 0.291068i
\(266\) 0 0
\(267\) −1.98793 + 8.62607i −0.121659 + 0.527907i
\(268\) 0 0
\(269\) 14.8881 14.8881i 0.907746 0.907746i −0.0883440 0.996090i \(-0.528157\pi\)
0.996090 + 0.0883440i \(0.0281575\pi\)
\(270\) 0 0
\(271\) 1.64797 0.100107 0.0500534 0.998747i \(-0.484061\pi\)
0.0500534 + 0.998747i \(0.484061\pi\)
\(272\) 0 0
\(273\) 2.76662 + 4.42366i 0.167443 + 0.267732i
\(274\) 0 0
\(275\) 6.52368 + 24.3467i 0.393393 + 1.46816i
\(276\) 0 0
\(277\) 3.13780 11.7104i 0.188532 0.703612i −0.805315 0.592848i \(-0.798004\pi\)
0.993847 0.110764i \(-0.0353298\pi\)
\(278\) 0 0
\(279\) −10.3807 + 7.01374i −0.621479 + 0.419901i
\(280\) 0 0
\(281\) 2.28116 1.31703i 0.136083 0.0785674i −0.430413 0.902632i \(-0.641632\pi\)
0.566496 + 0.824065i \(0.308299\pi\)
\(282\) 0 0
\(283\) 10.3823 2.78192i 0.617162 0.165368i 0.0633245 0.997993i \(-0.479830\pi\)
0.553837 + 0.832625i \(0.313163\pi\)
\(284\) 0 0
\(285\) −2.53910 + 2.72499i −0.150403 + 0.161414i
\(286\) 0 0
\(287\) 4.65610 0.274841
\(288\) 0 0
\(289\) −9.39253 −0.552502
\(290\) 0 0
\(291\) 3.09980 + 10.1248i 0.181713 + 0.593526i
\(292\) 0 0
\(293\) 3.95963 1.06098i 0.231324 0.0619831i −0.141295 0.989968i \(-0.545127\pi\)
0.372619 + 0.927984i \(0.378460\pi\)
\(294\) 0 0
\(295\) 5.36954 3.10010i 0.312627 0.180495i
\(296\) 0 0
\(297\) 25.0166 18.2206i 1.45161 1.05727i
\(298\) 0 0
\(299\) −4.82254 + 17.9980i −0.278895 + 1.04085i
\(300\) 0 0
\(301\) 0.147646 + 0.551024i 0.00851020 + 0.0317605i
\(302\) 0 0
\(303\) 10.3818 19.5438i 0.596419 1.12276i
\(304\) 0 0
\(305\) 3.42747 0.196256
\(306\) 0 0
\(307\) −5.40346 + 5.40346i −0.308392 + 0.308392i −0.844286 0.535894i \(-0.819975\pi\)
0.535894 + 0.844286i \(0.319975\pi\)
\(308\) 0 0
\(309\) −2.67576 2.49323i −0.152219 0.141835i
\(310\) 0 0
\(311\) 13.4939 + 7.79068i 0.765167 + 0.441769i 0.831148 0.556052i \(-0.187684\pi\)
−0.0659811 + 0.997821i \(0.521018\pi\)
\(312\) 0 0
\(313\) 25.4594 14.6990i 1.43905 0.830835i 0.441265 0.897377i \(-0.354530\pi\)
0.997784 + 0.0665417i \(0.0211965\pi\)
\(314\) 0 0
\(315\) −1.62738 + 0.561779i −0.0916926 + 0.0316527i
\(316\) 0 0
\(317\) 5.27629 + 1.41378i 0.296346 + 0.0794057i 0.403929 0.914790i \(-0.367644\pi\)
−0.107583 + 0.994196i \(0.534311\pi\)
\(318\) 0 0
\(319\) 7.62485 13.2066i 0.426909 0.739429i
\(320\) 0 0
\(321\) −9.43920 15.0927i −0.526845 0.842393i
\(322\) 0 0
\(323\) 4.78538 4.78538i 0.266266 0.266266i
\(324\) 0 0
\(325\) −13.7664 13.7664i −0.763620 0.763620i
\(326\) 0 0
\(327\) 11.9034 7.44458i 0.658261 0.411686i
\(328\) 0 0
\(329\) −5.27969 3.04823i −0.291079 0.168054i
\(330\) 0 0
\(331\) 6.68483 24.9481i 0.367432 1.37127i −0.496663 0.867944i \(-0.665441\pi\)
0.864094 0.503330i \(-0.167892\pi\)
\(332\) 0 0
\(333\) −5.96076 17.2674i −0.326648 0.946245i
\(334\) 0 0
\(335\) 5.27746 + 9.14082i 0.288338 + 0.499416i
\(336\) 0 0
\(337\) −1.97680 + 3.42392i −0.107683 + 0.186513i −0.914831 0.403836i \(-0.867677\pi\)
0.807148 + 0.590349i \(0.201010\pi\)
\(338\) 0 0
\(339\) 2.14420 2.30118i 0.116457 0.124983i
\(340\) 0 0
\(341\) 17.5877 + 17.5877i 0.952425 + 0.952425i
\(342\) 0 0
\(343\) 8.88645i 0.479823i
\(344\) 0 0
\(345\) −5.42968 2.88428i −0.292324 0.155285i
\(346\) 0 0
\(347\) −4.56059 + 1.22201i −0.244825 + 0.0656008i −0.379145 0.925337i \(-0.623782\pi\)
0.134320 + 0.990938i \(0.457115\pi\)
\(348\) 0 0
\(349\) −7.74559 2.07543i −0.414612 0.111095i 0.0454819 0.998965i \(-0.485518\pi\)
−0.460094 + 0.887870i \(0.652184\pi\)
\(350\) 0 0
\(351\) −9.69716 + 21.8493i −0.517596 + 1.16623i
\(352\) 0 0
\(353\) 6.95793 + 12.0515i 0.370333 + 0.641436i 0.989617 0.143731i \(-0.0459101\pi\)
−0.619283 + 0.785168i \(0.712577\pi\)
\(354\) 0 0
\(355\) 0.986340 + 3.68107i 0.0523495 + 0.195371i
\(356\) 0 0
\(357\) 2.99112 0.915759i 0.158307 0.0484671i
\(358\) 0 0
\(359\) 0.491573i 0.0259443i −0.999916 0.0129721i \(-0.995871\pi\)
0.999916 0.0129721i \(-0.00412927\pi\)
\(360\) 0 0
\(361\) 12.9796i 0.683138i
\(362\) 0 0
\(363\) −31.0147 28.8989i −1.62785 1.51680i
\(364\) 0 0
\(365\) 0.148933 + 0.555827i 0.00779553 + 0.0290933i
\(366\) 0 0
\(367\) −3.97080 6.87763i −0.207274 0.359010i 0.743581 0.668646i \(-0.233126\pi\)
−0.950855 + 0.309637i \(0.899793\pi\)
\(368\) 0 0
\(369\) 11.9426 + 17.6758i 0.621709 + 0.920166i
\(370\) 0 0
\(371\) −6.83901 1.83251i −0.355064 0.0951390i
\(372\) 0 0
\(373\) 21.8895 5.86527i 1.13340 0.303692i 0.357103 0.934065i \(-0.383765\pi\)
0.776293 + 0.630373i \(0.217098\pi\)
\(374\) 0 0
\(375\) 11.8815 7.43088i 0.613560 0.383729i
\(376\) 0 0
\(377\) 11.7787i 0.606635i
\(378\) 0 0
\(379\) 24.5680 + 24.5680i 1.26197 + 1.26197i 0.950135 + 0.311839i \(0.100945\pi\)
0.311839 + 0.950135i \(0.399055\pi\)
\(380\) 0 0
\(381\) −32.4103 7.46914i −1.66043 0.382655i
\(382\) 0 0
\(383\) −3.67713 + 6.36897i −0.187892 + 0.325439i −0.944547 0.328375i \(-0.893499\pi\)
0.756655 + 0.653814i \(0.226832\pi\)
\(384\) 0 0
\(385\) 1.70901 + 2.96010i 0.0870995 + 0.150861i
\(386\) 0 0
\(387\) −1.71313 + 1.97385i −0.0870833 + 0.100337i
\(388\) 0 0
\(389\) −4.98406 + 18.6007i −0.252702 + 0.943095i 0.716653 + 0.697430i \(0.245673\pi\)
−0.969355 + 0.245665i \(0.920994\pi\)
\(390\) 0 0
\(391\) 9.67459 + 5.58563i 0.489265 + 0.282477i
\(392\) 0 0
\(393\) 0.738947 + 20.9256i 0.0372750 + 1.05556i
\(394\) 0 0
\(395\) −10.1159 10.1159i −0.508985 0.508985i
\(396\) 0 0
\(397\) −23.3235 + 23.3235i −1.17057 + 1.17057i −0.188500 + 0.982073i \(0.560362\pi\)
−0.982073 + 0.188500i \(0.939638\pi\)
\(398\) 0 0
\(399\) 1.30548 2.45757i 0.0653558 0.123033i
\(400\) 0 0
\(401\) −4.61036 + 7.98538i −0.230231 + 0.398771i −0.957876 0.287183i \(-0.907281\pi\)
0.727645 + 0.685954i \(0.240615\pi\)
\(402\) 0 0
\(403\) −18.5568 4.97229i −0.924382 0.247687i
\(404\) 0 0
\(405\) −6.30681 4.73704i −0.313388 0.235386i
\(406\) 0 0
\(407\) −31.4082 + 18.1335i −1.55685 + 0.898845i
\(408\) 0 0
\(409\) −17.2773 9.97503i −0.854306 0.493234i 0.00779552 0.999970i \(-0.497519\pi\)
−0.862101 + 0.506736i \(0.830852\pi\)
\(410\) 0 0
\(411\) −5.50919 + 1.68669i −0.271748 + 0.0831982i
\(412\) 0 0
\(413\) −3.27562 + 3.27562i −0.161183 + 0.161183i
\(414\) 0 0
\(415\) 4.87092 0.239104
\(416\) 0 0
\(417\) −18.7333 + 0.661529i −0.917373 + 0.0323952i
\(418\) 0 0
\(419\) −7.85913 29.3307i −0.383943 1.43290i −0.839826 0.542856i \(-0.817343\pi\)
0.455882 0.890040i \(-0.349324\pi\)
\(420\) 0 0
\(421\) −2.70420 + 10.0922i −0.131795 + 0.491864i −0.999991 0.00435733i \(-0.998613\pi\)
0.868196 + 0.496222i \(0.165280\pi\)
\(422\) 0 0
\(423\) −1.97022 27.8617i −0.0957952 1.35468i
\(424\) 0 0
\(425\) −10.1085 + 5.83615i −0.490335 + 0.283095i
\(426\) 0 0
\(427\) −2.47354 + 0.662784i −0.119703 + 0.0320744i
\(428\) 0 0
\(429\) 46.2468 + 10.6578i 2.23282 + 0.514565i
\(430\) 0 0
\(431\) −11.3639 −0.547382 −0.273691 0.961818i \(-0.588244\pi\)
−0.273691 + 0.961818i \(0.588244\pi\)
\(432\) 0 0
\(433\) −9.65126 −0.463810 −0.231905 0.972738i \(-0.574496\pi\)
−0.231905 + 0.972738i \(0.574496\pi\)
\(434\) 0 0
\(435\) −3.78731 0.872807i −0.181588 0.0418479i
\(436\) 0 0
\(437\) 9.59925 2.57211i 0.459194 0.123041i
\(438\) 0 0
\(439\) 13.6132 7.85957i 0.649722 0.375117i −0.138628 0.990345i \(-0.544269\pi\)
0.788350 + 0.615228i \(0.210936\pi\)
\(440\) 0 0
\(441\) −16.3348 + 11.0366i −0.777846 + 0.525551i
\(442\) 0 0
\(443\) 4.97116 18.5526i 0.236187 0.881461i −0.741424 0.671037i \(-0.765849\pi\)
0.977610 0.210424i \(-0.0674843\pi\)
\(444\) 0 0
\(445\) −1.15929 4.32653i −0.0549556 0.205097i
\(446\) 0 0
\(447\) −34.2678 + 1.21010i −1.62081 + 0.0572358i
\(448\) 0 0
\(449\) 35.3101 1.66639 0.833194 0.552982i \(-0.186510\pi\)
0.833194 + 0.552982i \(0.186510\pi\)
\(450\) 0 0
\(451\) 29.9474 29.9474i 1.41017 1.41017i
\(452\) 0 0
\(453\) −9.74244 + 2.98274i −0.457740 + 0.140141i
\(454\) 0 0
\(455\) −2.28636 1.32003i −0.107186 0.0618839i
\(456\) 0 0
\(457\) 0.565406 0.326437i 0.0264486 0.0152701i −0.486717 0.873559i \(-0.661806\pi\)
0.513166 + 0.858289i \(0.328473\pi\)
\(458\) 0 0
\(459\) 11.1485 + 9.00622i 0.520369 + 0.420374i
\(460\) 0 0
\(461\) −3.91317 1.04853i −0.182255 0.0488350i 0.166537 0.986035i \(-0.446741\pi\)
−0.348792 + 0.937200i \(0.613408\pi\)
\(462\) 0 0
\(463\) 21.0971 36.5413i 0.980466 1.69822i 0.319894 0.947453i \(-0.396353\pi\)
0.660571 0.750763i \(-0.270314\pi\)
\(464\) 0 0
\(465\) 2.97385 5.59828i 0.137909 0.259614i
\(466\) 0 0
\(467\) 0.180878 0.180878i 0.00837005 0.00837005i −0.702909 0.711279i \(-0.748116\pi\)
0.711279 + 0.702909i \(0.248116\pi\)
\(468\) 0 0
\(469\) −5.57625 5.57625i −0.257487 0.257487i
\(470\) 0 0
\(471\) 1.20234 + 34.0482i 0.0554011 + 1.56886i
\(472\) 0 0
\(473\) 4.49375 + 2.59447i 0.206623 + 0.119294i
\(474\) 0 0
\(475\) −2.68747 + 10.0298i −0.123310 + 0.460198i
\(476\) 0 0
\(477\) −10.5850 30.6630i −0.484654 1.40396i
\(478\) 0 0
\(479\) −6.98122 12.0918i −0.318980 0.552490i 0.661295 0.750126i \(-0.270007\pi\)
−0.980276 + 0.197636i \(0.936674\pi\)
\(480\) 0 0
\(481\) 14.0062 24.2594i 0.638627 1.10613i
\(482\) 0 0
\(483\) 4.47625 + 1.03158i 0.203677 + 0.0469384i
\(484\) 0 0
\(485\) −3.78855 3.78855i −0.172029 0.172029i
\(486\) 0 0
\(487\) 2.93338i 0.132924i −0.997789 0.0664621i \(-0.978829\pi\)
0.997789 0.0664621i \(-0.0211712\pi\)
\(488\) 0 0
\(489\) −10.3987 + 6.50352i −0.470247 + 0.294099i
\(490\) 0 0
\(491\) −17.7814 + 4.76452i −0.802465 + 0.215020i −0.636666 0.771140i \(-0.719687\pi\)
−0.165799 + 0.986160i \(0.553020\pi\)
\(492\) 0 0
\(493\) 6.82126 + 1.82775i 0.307214 + 0.0823178i
\(494\) 0 0
\(495\) −6.85380 + 14.0804i −0.308056 + 0.632866i
\(496\) 0 0
\(497\) −1.42365 2.46583i −0.0638594 0.110608i
\(498\) 0 0
\(499\) 4.74054 + 17.6919i 0.212216 + 0.791999i 0.987128 + 0.159931i \(0.0511271\pi\)
−0.774913 + 0.632068i \(0.782206\pi\)
\(500\) 0 0
\(501\) −21.2204 19.7728i −0.948057 0.883383i
\(502\) 0 0
\(503\) 7.01136i 0.312621i 0.987708 + 0.156311i \(0.0499601\pi\)
−0.987708 + 0.156311i \(0.950040\pi\)
\(504\) 0 0
\(505\) 11.1977i 0.498292i
\(506\) 0 0
\(507\) −13.5208 + 4.13952i −0.600480 + 0.183842i
\(508\) 0 0
\(509\) 1.25064 + 4.66745i 0.0554336 + 0.206881i 0.988088 0.153890i \(-0.0491802\pi\)
−0.932654 + 0.360771i \(0.882514\pi\)
\(510\) 0 0
\(511\) −0.214965 0.372331i −0.00950950 0.0164709i
\(512\) 0 0
\(513\) 12.6781 1.34759i 0.559751 0.0594975i
\(514\) 0 0
\(515\) 1.78752 + 0.478965i 0.0787676 + 0.0211057i
\(516\) 0 0
\(517\) −53.5640 + 14.3524i −2.35574 + 0.631219i
\(518\) 0 0
\(519\) −25.7885 13.6990i −1.13199 0.601320i
\(520\) 0 0
\(521\) 28.0687i 1.22971i −0.788640 0.614855i \(-0.789215\pi\)
0.788640 0.614855i \(-0.210785\pi\)
\(522\) 0 0
\(523\) −14.5264 14.5264i −0.635193 0.635193i 0.314173 0.949366i \(-0.398273\pi\)
−0.949366 + 0.314173i \(0.898273\pi\)
\(524\) 0 0
\(525\) −3.27195 + 3.51149i −0.142800 + 0.153254i
\(526\) 0 0
\(527\) −5.75907 + 9.97501i −0.250869 + 0.434518i
\(528\) 0 0
\(529\) −3.29774 5.71185i −0.143380 0.248341i
\(530\) 0 0
\(531\) −20.8369 4.03335i −0.904246 0.175032i
\(532\) 0 0
\(533\) −8.46657 + 31.5977i −0.366728 + 1.36865i
\(534\) 0 0
\(535\) 7.80063 + 4.50370i 0.337251 + 0.194712i
\(536\) 0 0
\(537\) −13.6354 + 8.52777i −0.588411 + 0.368001i
\(538\) 0 0
\(539\) 27.6753 + 27.6753i 1.19206 + 1.19206i
\(540\) 0 0
\(541\) 18.4081 18.4081i 0.791427 0.791427i −0.190299 0.981726i \(-0.560946\pi\)
0.981726 + 0.190299i \(0.0609458\pi\)
\(542\) 0 0
\(543\) 20.1161 + 32.1644i 0.863264 + 1.38031i
\(544\) 0 0
\(545\) −3.55201 + 6.15226i −0.152151 + 0.263534i
\(546\) 0 0
\(547\) 15.9583 + 4.27602i 0.682328 + 0.182829i 0.583302 0.812256i \(-0.301761\pi\)
0.0990263 + 0.995085i \(0.468427\pi\)
\(548\) 0 0
\(549\) −8.86061 7.69023i −0.378162 0.328211i
\(550\) 0 0
\(551\) 5.44055 3.14110i 0.231775 0.133816i
\(552\) 0 0
\(553\) 9.25660 + 5.34430i 0.393631 + 0.227263i
\(554\) 0 0
\(555\) 6.76246 + 6.30115i 0.287051 + 0.267469i
\(556\) 0 0
\(557\) −15.4219 + 15.4219i −0.653447 + 0.653447i −0.953821 0.300375i \(-0.902888\pi\)
0.300375 + 0.953821i \(0.402888\pi\)
\(558\) 0 0
\(559\) −4.00789 −0.169516
\(560\) 0 0
\(561\) 13.3484 25.1285i 0.563571 1.06093i
\(562\) 0 0
\(563\) −1.67165 6.23868i −0.0704516 0.262929i 0.921712 0.387875i \(-0.126791\pi\)
−0.992164 + 0.124946i \(0.960124\pi\)
\(564\) 0 0
\(565\) −0.411914 + 1.53728i −0.0173293 + 0.0646740i
\(566\) 0 0
\(567\) 5.46754 + 2.19907i 0.229615 + 0.0923521i
\(568\) 0 0
\(569\) 7.90864 4.56605i 0.331547 0.191419i −0.324981 0.945721i \(-0.605358\pi\)
0.656528 + 0.754302i \(0.272024\pi\)
\(570\) 0 0
\(571\) −27.5804 + 7.39016i −1.15421 + 0.309268i −0.784649 0.619940i \(-0.787157\pi\)
−0.369556 + 0.929208i \(0.620490\pi\)
\(572\) 0 0
\(573\) 1.75478 + 5.73160i 0.0733071 + 0.239441i
\(574\) 0 0
\(575\) −17.1403 −0.714799
\(576\) 0 0
\(577\) 0.350515 0.0145921 0.00729607 0.999973i \(-0.497678\pi\)
0.00729607 + 0.999973i \(0.497678\pi\)
\(578\) 0 0
\(579\) 11.6516 12.5046i 0.484224 0.519675i
\(580\) 0 0
\(581\) −3.51526 + 0.941911i −0.145838 + 0.0390771i
\(582\) 0 0
\(583\) −55.7739 + 32.2011i −2.30992 + 1.33363i
\(584\) 0 0
\(585\) −0.853197 12.0654i −0.0352754 0.498844i
\(586\) 0 0
\(587\) −0.259943 + 0.970122i −0.0107290 + 0.0400412i −0.971083 0.238743i \(-0.923265\pi\)
0.960354 + 0.278784i \(0.0899314\pi\)
\(588\) 0 0
\(589\) 2.65198 + 9.89733i 0.109273 + 0.407812i
\(590\) 0 0
\(591\) 6.43308 + 10.2861i 0.264621 + 0.423114i
\(592\) 0 0
\(593\) 7.12791 0.292708 0.146354 0.989232i \(-0.453246\pi\)
0.146354 + 0.989232i \(0.453246\pi\)
\(594\) 0 0
\(595\) −1.11923 + 1.11923i −0.0458841 + 0.0458841i
\(596\) 0 0
\(597\) 7.54528 32.7407i 0.308808 1.33999i
\(598\) 0 0
\(599\) 1.83973 + 1.06217i 0.0751695 + 0.0433991i 0.537114 0.843510i \(-0.319515\pi\)
−0.461944 + 0.886909i \(0.652848\pi\)
\(600\) 0 0
\(601\) 32.6223 18.8345i 1.33069 0.768275i 0.345286 0.938497i \(-0.387782\pi\)
0.985406 + 0.170222i \(0.0544485\pi\)
\(602\) 0 0
\(603\) 6.86616 35.4717i 0.279612 1.44452i
\(604\) 0 0
\(605\) 20.7191 + 5.55166i 0.842351 + 0.225707i
\(606\) 0 0
\(607\) −10.2096 + 17.6835i −0.414393 + 0.717750i −0.995365 0.0961740i \(-0.969339\pi\)
0.580971 + 0.813924i \(0.302673\pi\)
\(608\) 0 0
\(609\) 2.90201 0.102479i 0.117596 0.00415266i
\(610\) 0 0
\(611\) 30.2867 30.2867i 1.22527 1.22527i
\(612\) 0 0
\(613\) −10.2801 10.2801i −0.415208 0.415208i 0.468340 0.883548i \(-0.344852\pi\)
−0.883548 + 0.468340i \(0.844852\pi\)
\(614\) 0 0
\(615\) −9.53248 5.06372i −0.384387 0.204189i
\(616\) 0 0
\(617\) −41.2817 23.8340i −1.66194 0.959521i −0.971788 0.235856i \(-0.924210\pi\)
−0.690152 0.723665i \(-0.742456\pi\)
\(618\) 0 0
\(619\) 1.41291 5.27305i 0.0567896 0.211942i −0.931700 0.363228i \(-0.881675\pi\)
0.988490 + 0.151286i \(0.0483414\pi\)
\(620\) 0 0
\(621\) 7.56520 + 19.6390i 0.303581 + 0.788085i
\(622\) 0 0
\(623\) 1.67328 + 2.89820i 0.0670385 + 0.116114i
\(624\) 0 0
\(625\) 7.03430 12.1838i 0.281372 0.487350i
\(626\) 0 0
\(627\) −7.41010 24.2034i −0.295931 0.966592i
\(628\) 0 0
\(629\) −11.8756 11.8756i −0.473513 0.473513i
\(630\) 0 0
\(631\) 20.7362i 0.825496i −0.910845 0.412748i \(-0.864569\pi\)
0.910845 0.412748i \(-0.135431\pi\)
\(632\) 0 0
\(633\) 0.118035 + 3.34254i 0.00469148 + 0.132854i
\(634\) 0 0
\(635\) 16.2558 4.35574i 0.645094 0.172852i
\(636\) 0 0
\(637\) −29.2004 7.82422i −1.15696 0.310007i
\(638\) 0 0
\(639\) 5.70938 11.7293i 0.225860 0.464003i
\(640\) 0 0
\(641\) 3.67059 + 6.35766i 0.144980 + 0.251112i 0.929365 0.369161i \(-0.120355\pi\)
−0.784386 + 0.620273i \(0.787022\pi\)
\(642\) 0 0
\(643\) 2.23207 + 8.33019i 0.0880241 + 0.328511i 0.995870 0.0907942i \(-0.0289405\pi\)
−0.907846 + 0.419305i \(0.862274\pi\)
\(644\) 0 0
\(645\) 0.296986 1.28869i 0.0116938 0.0507421i
\(646\) 0 0
\(647\) 11.6387i 0.457566i 0.973477 + 0.228783i \(0.0734746\pi\)
−0.973477 + 0.228783i \(0.926525\pi\)
\(648\) 0 0
\(649\) 42.1367i 1.65401i
\(650\) 0 0
\(651\) −1.06361 + 4.61525i −0.0416862 + 0.180886i
\(652\) 0 0
\(653\) −5.20569 19.4279i −0.203715 0.760273i −0.989838 0.142203i \(-0.954581\pi\)
0.786123 0.618070i \(-0.212085\pi\)
\(654\) 0 0
\(655\) −5.29742 9.17541i −0.206988 0.358513i
\(656\) 0 0
\(657\) 0.862093 1.77107i 0.0336335 0.0690962i
\(658\) 0 0
\(659\) 14.5489 + 3.89836i 0.566744 + 0.151859i 0.530803 0.847495i \(-0.321890\pi\)
0.0359413 + 0.999354i \(0.488557\pi\)
\(660\) 0 0
\(661\) −9.83468 + 2.63519i −0.382525 + 0.102497i −0.444957 0.895552i \(-0.646781\pi\)
0.0624321 + 0.998049i \(0.480114\pi\)
\(662\) 0 0
\(663\) 0.775609 + 21.9638i 0.0301222 + 0.853004i
\(664\) 0 0
\(665\) 1.40808i 0.0546030i
\(666\) 0 0
\(667\) 7.33276 + 7.33276i 0.283926 + 0.283926i
\(668\) 0 0
\(669\) 6.65428 + 21.7347i 0.257269 + 0.840312i
\(670\) 0 0
\(671\) −11.6465 + 20.1724i −0.449610 + 0.778747i
\(672\) 0 0
\(673\) 16.1240 + 27.9276i 0.621534 + 1.07653i 0.989200 + 0.146571i \(0.0468236\pi\)
−0.367666 + 0.929958i \(0.619843\pi\)
\(674\) 0 0
\(675\) −21.7229 3.41441i −0.836116 0.131421i
\(676\) 0 0
\(677\) 9.43821 35.2239i 0.362740 1.35376i −0.507719 0.861523i \(-0.669511\pi\)
0.870459 0.492241i \(-0.163822\pi\)
\(678\) 0 0
\(679\) 3.46674 + 2.00152i 0.133041 + 0.0768113i
\(680\) 0 0
\(681\) −6.37104 3.38434i −0.244139 0.129688i
\(682\) 0 0
\(683\) 1.95185 + 1.95185i 0.0746855 + 0.0746855i 0.743463 0.668777i \(-0.233182\pi\)
−0.668777 + 0.743463i \(0.733182\pi\)
\(684\) 0 0
\(685\) 2.06146 2.06146i 0.0787642 0.0787642i
\(686\) 0 0
\(687\) 48.3467 1.70727i 1.84454 0.0651364i
\(688\) 0 0
\(689\) 24.8719 43.0793i 0.947542 1.64119i
\(690\) 0 0
\(691\) −1.50428 0.403069i −0.0572253 0.0153335i 0.230093 0.973169i \(-0.426097\pi\)
−0.287318 + 0.957835i \(0.592764\pi\)
\(692\) 0 0
\(693\) 2.22349 11.4869i 0.0844634 0.436352i
\(694\) 0 0
\(695\) 8.21412 4.74242i 0.311579 0.179890i
\(696\) 0 0
\(697\) 16.9849 + 9.80626i 0.643351 + 0.371439i
\(698\) 0 0
\(699\) −2.63760 + 11.4451i −0.0997631 + 0.432895i
\(700\) 0 0
\(701\) −21.5819 + 21.5819i −0.815136 + 0.815136i −0.985399 0.170263i \(-0.945538\pi\)
0.170263 + 0.985399i \(0.445538\pi\)
\(702\) 0 0
\(703\) −14.9404 −0.563489
\(704\) 0 0
\(705\) 7.49407 + 11.9826i 0.282243 + 0.451290i
\(706\) 0 0
\(707\) −2.16535 8.08119i −0.0814363 0.303925i
\(708\) 0 0
\(709\) −5.51773 + 20.5925i −0.207223 + 0.773366i 0.781538 + 0.623858i \(0.214436\pi\)
−0.988760 + 0.149508i \(0.952231\pi\)
\(710\) 0 0
\(711\) 3.45428 + 48.8484i 0.129545 + 1.83196i
\(712\) 0 0
\(713\) −14.6479 + 8.45696i −0.548568 + 0.316716i
\(714\) 0 0
\(715\) −23.1958 + 6.21528i −0.867472 + 0.232438i
\(716\) 0 0
\(717\) 9.65975 10.3670i 0.360750 0.387161i
\(718\) 0 0
\(719\) −28.4354 −1.06046 −0.530230 0.847854i \(-0.677894\pi\)
−0.530230 + 0.847854i \(0.677894\pi\)
\(720\) 0 0
\(721\) −1.38264 −0.0514923
\(722\) 0 0
\(723\) −0.263087 0.859315i −0.00978431 0.0319583i
\(724\) 0 0
\(725\) −10.4660 + 2.80436i −0.388697 + 0.104151i
\(726\) 0 0
\(727\) −23.2100 + 13.4003i −0.860812 + 0.496990i −0.864284 0.503004i \(-0.832228\pi\)
0.00347239 + 0.999994i \(0.498895\pi\)
\(728\) 0 0
\(729\) 5.67568 + 26.3967i 0.210210 + 0.977656i
\(730\) 0 0
\(731\) −0.621920 + 2.32104i −0.0230025 + 0.0858466i
\(732\) 0 0
\(733\) −6.44950 24.0699i −0.238218 0.889041i −0.976672 0.214737i \(-0.931110\pi\)
0.738454 0.674304i \(-0.235556\pi\)
\(734\) 0 0
\(735\) 4.67954 8.80926i 0.172607 0.324935i
\(736\) 0 0
\(737\) −71.7313 −2.64226
\(738\) 0 0
\(739\) 9.91976 9.91976i 0.364904 0.364904i −0.500711 0.865615i \(-0.666928\pi\)
0.865615 + 0.500711i \(0.166928\pi\)
\(740\) 0 0
\(741\) 14.3040 + 13.3282i 0.525469 + 0.489623i
\(742\) 0 0
\(743\) 15.1283 + 8.73432i 0.555003 + 0.320431i 0.751137 0.660146i \(-0.229506\pi\)
−0.196134 + 0.980577i \(0.562839\pi\)
\(744\) 0 0
\(745\) 15.0257 8.67507i 0.550497 0.317830i
\(746\) 0 0
\(747\) −12.5922 10.9289i −0.460725 0.399868i
\(748\) 0 0
\(749\) −6.50048 1.74180i −0.237522 0.0636439i
\(750\) 0 0
\(751\) 1.95134 3.37983i 0.0712056 0.123332i −0.828224 0.560397i \(-0.810649\pi\)
0.899430 + 0.437065i \(0.143982\pi\)
\(752\) 0 0
\(753\) 18.1331 + 28.9938i 0.660807 + 1.05659i
\(754\) 0 0
\(755\) 3.64548 3.64548i 0.132673 0.132673i
\(756\) 0 0
\(757\) 16.8568 + 16.8568i 0.612670 + 0.612670i 0.943641 0.330971i \(-0.107376\pi\)
−0.330971 + 0.943641i \(0.607376\pi\)
\(758\) 0 0
\(759\) 35.4256 22.1557i 1.28587 0.804200i
\(760\) 0 0
\(761\) 34.1207 + 19.6996i 1.23688 + 0.714111i 0.968454 0.249191i \(-0.0801647\pi\)
0.268422 + 0.963302i \(0.413498\pi\)
\(762\) 0 0
\(763\) 1.37373 5.12685i 0.0497325 0.185604i
\(764\) 0 0
\(765\) −7.11968 1.37814i −0.257413 0.0498266i
\(766\) 0 0
\(767\) −16.2730 28.1857i −0.587584 1.01773i
\(768\) 0 0
\(769\) 10.1180 17.5249i 0.364866 0.631966i −0.623889 0.781513i \(-0.714448\pi\)
0.988755 + 0.149547i \(0.0477816\pi\)
\(770\) 0 0
\(771\) −20.6029 + 22.1113i −0.741996 + 0.796318i
\(772\) 0 0
\(773\) −2.34590 2.34590i −0.0843761 0.0843761i 0.663659 0.748035i \(-0.269003\pi\)
−0.748035 + 0.663659i \(0.769003\pi\)
\(774\) 0 0
\(775\) 17.6725i 0.634816i
\(776\) 0 0
\(777\) −6.09883 3.23974i −0.218794 0.116225i
\(778\) 0 0
\(779\) 16.8527 4.51566i 0.603810 0.161790i
\(780\) 0 0
\(781\) −25.0166 6.70318i −0.895164 0.239859i
\(782\) 0 0
\(783\) 7.83255 + 10.7540i 0.279912 + 0.384316i
\(784\) 0 0
\(785\) −8.61946 14.9293i −0.307642 0.532851i
\(786\) 0 0
\(787\) 8.00353 + 29.8696i 0.285295 + 1.06474i 0.948623 + 0.316407i \(0.102477\pi\)
−0.663328 + 0.748328i \(0.730857\pi\)
\(788\) 0 0
\(789\) 17.3341 5.30701i 0.617112 0.188934i
\(790\) 0 0
\(791\) 1.18908i 0.0422790i
\(792\) 0 0
\(793\) 17.9914i 0.638893i
\(794\) 0 0
\(795\) 12.0086 + 11.1894i 0.425902 + 0.396848i
\(796\) 0 0
\(797\) 5.59514 +