Properties

Label 300.2.x.a.113.1
Level $300$
Weight $2$
Character 300.113
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 113.1
Character \(\chi\) \(=\) 300.113
Dual form 300.2.x.a.77.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73155 + 0.0417985i) q^{3} +(2.12124 - 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(2.99651 - 0.144752i) q^{9} +O(q^{10})\) \(q+(-1.73155 + 0.0417985i) q^{3} +(2.12124 - 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(2.99651 - 0.144752i) q^{9} +(1.16772 - 1.60723i) q^{11} +(1.08607 + 0.172017i) q^{13} +(-3.64347 + 1.31345i) q^{15} +(3.88627 - 1.98015i) q^{17} +(7.34866 + 2.38772i) q^{19} +(2.38038 - 2.49815i) q^{21} +(-0.596200 + 0.0944288i) q^{23} +(3.99936 - 3.00085i) q^{25} +(-5.18254 + 0.375894i) q^{27} +(1.20411 + 3.70588i) q^{29} +(2.08371 - 6.41301i) q^{31} +(-1.95478 + 2.83180i) q^{33} +(-1.99181 + 3.98468i) q^{35} +(-1.00762 + 6.36188i) q^{37} +(-1.88777 - 0.252459i) q^{39} +(-4.90769 - 6.75485i) q^{41} +(2.08869 + 2.08869i) q^{43} +(6.25393 - 2.42658i) q^{45} +(-1.27659 + 2.50545i) q^{47} +3.03101i q^{49} +(-6.64648 + 3.59117i) q^{51} +(-9.48136 - 4.83099i) q^{53} +(1.34017 - 4.23529i) q^{55} +(-12.8243 - 3.82729i) q^{57} +(-11.0153 + 8.00310i) q^{59} +(-7.73999 - 5.62344i) q^{61} +(-4.01733 + 4.42516i) q^{63} +(2.42549 - 0.403324i) q^{65} +(-5.76904 - 11.3224i) q^{67} +(1.02840 - 0.188428i) q^{69} +(2.90043 - 0.942408i) q^{71} +(1.52706 + 9.64150i) q^{73} +(-6.79964 + 5.36329i) q^{75} +(0.619145 + 3.90913i) q^{77} +(8.77277 - 2.85044i) q^{79} +(8.95809 - 0.867500i) q^{81} +(1.61164 + 3.16301i) q^{83} +(6.84310 - 6.94927i) q^{85} +(-2.23988 - 6.36657i) q^{87} +(2.65779 + 1.93100i) q^{89} +(-1.77229 + 1.28765i) q^{91} +(-3.33999 + 11.1915i) q^{93} +(17.2772 - 0.133005i) q^{95} +(1.19966 + 0.611256i) q^{97} +(3.26643 - 4.98510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\)

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
\(3\) −1.73155 + 0.0417985i −0.999709 + 0.0241324i
\(4\) 0 0
\(5\) 2.12124 0.707333i 0.948650 0.316329i
\(6\) 0 0
\(7\) −1.40872 + 1.40872i −0.532446 + 0.532446i −0.921300 0.388853i \(-0.872871\pi\)
0.388853 + 0.921300i \(0.372871\pi\)
\(8\) 0 0
\(9\) 2.99651 0.144752i 0.998835 0.0482507i
\(10\) 0 0
\(11\) 1.16772 1.60723i 0.352081 0.484597i −0.595840 0.803103i \(-0.703181\pi\)
0.947921 + 0.318506i \(0.103181\pi\)
\(12\) 0 0
\(13\) 1.08607 + 0.172017i 0.301222 + 0.0477088i 0.305216 0.952283i \(-0.401271\pi\)
−0.00399423 + 0.999992i \(0.501271\pi\)
\(14\) 0 0
\(15\) −3.64347 + 1.31345i −0.940739 + 0.339130i
\(16\) 0 0
\(17\) 3.88627 1.98015i 0.942558 0.480257i 0.0859928 0.996296i \(-0.472594\pi\)
0.856565 + 0.516038i \(0.172594\pi\)
\(18\) 0 0
\(19\) 7.34866 + 2.38772i 1.68590 + 0.547781i 0.986041 0.166502i \(-0.0532472\pi\)
0.699857 + 0.714283i \(0.253247\pi\)
\(20\) 0 0
\(21\) 2.38038 2.49815i 0.519442 0.545141i
\(22\) 0 0
\(23\) −0.596200 + 0.0944288i −0.124316 + 0.0196898i −0.218282 0.975886i \(-0.570045\pi\)
0.0939663 + 0.995575i \(0.470045\pi\)
\(24\) 0 0
\(25\) 3.99936 3.00085i 0.799872 0.600171i
\(26\) 0 0
\(27\) −5.18254 + 0.375894i −0.997380 + 0.0723409i
\(28\) 0 0
\(29\) 1.20411 + 3.70588i 0.223598 + 0.688164i 0.998431 + 0.0559981i \(0.0178341\pi\)
−0.774833 + 0.632166i \(0.782166\pi\)
\(30\) 0 0
\(31\) 2.08371 6.41301i 0.374246 1.15181i −0.569740 0.821825i \(-0.692956\pi\)
0.943986 0.329986i \(-0.107044\pi\)
\(32\) 0 0
\(33\) −1.95478 + 2.83180i −0.340284 + 0.492953i
\(34\) 0 0
\(35\) −1.99181 + 3.98468i −0.336677 + 0.673533i
\(36\) 0 0
\(37\) −1.00762 + 6.36188i −0.165652 + 1.04589i 0.755063 + 0.655652i \(0.227606\pi\)
−0.920715 + 0.390235i \(0.872394\pi\)
\(38\) 0 0
\(39\) −1.88777 0.252459i −0.302285 0.0404257i
\(40\) 0 0
\(41\) −4.90769 6.75485i −0.766452 1.05493i −0.996650 0.0817869i \(-0.973937\pi\)
0.230198 0.973144i \(-0.426063\pi\)
\(42\) 0 0
\(43\) 2.08869 + 2.08869i 0.318522 + 0.318522i 0.848199 0.529677i \(-0.177687\pi\)
−0.529677 + 0.848199i \(0.677687\pi\)
\(44\) 0 0
\(45\) 6.25393 2.42658i 0.932281 0.361734i
\(46\) 0 0
\(47\) −1.27659 + 2.50545i −0.186210 + 0.365458i −0.965173 0.261612i \(-0.915746\pi\)
0.778963 + 0.627070i \(0.215746\pi\)
\(48\) 0 0
\(49\) 3.03101i 0.433001i
\(50\) 0 0
\(51\) −6.64648 + 3.59117i −0.930694 + 0.502864i
\(52\) 0 0
\(53\) −9.48136 4.83099i −1.30236 0.663588i −0.341311 0.939950i \(-0.610871\pi\)
−0.961053 + 0.276362i \(0.910871\pi\)
\(54\) 0 0
\(55\) 1.34017 4.23529i 0.180709 0.571086i
\(56\) 0 0
\(57\) −12.8243 3.82729i −1.69863 0.506937i
\(58\) 0 0
\(59\) −11.0153 + 8.00310i −1.43407 + 1.04192i −0.444834 + 0.895613i \(0.646737\pi\)
−0.989240 + 0.146302i \(0.953263\pi\)
\(60\) 0 0
\(61\) −7.73999 5.62344i −0.991005 0.720007i −0.0308639 0.999524i \(-0.509826\pi\)
−0.960141 + 0.279516i \(0.909826\pi\)
\(62\) 0 0
\(63\) −4.01733 + 4.42516i −0.506135 + 0.557517i
\(64\) 0 0
\(65\) 2.42549 0.403324i 0.300845 0.0500262i
\(66\) 0 0
\(67\) −5.76904 11.3224i −0.704800 1.38325i −0.914137 0.405405i \(-0.867131\pi\)
0.209337 0.977844i \(-0.432869\pi\)
\(68\) 0 0
\(69\) 1.02840 0.188428i 0.123805 0.0226841i
\(70\) 0 0
\(71\) 2.90043 0.942408i 0.344218 0.111843i −0.131806 0.991276i \(-0.542078\pi\)
0.476024 + 0.879432i \(0.342078\pi\)
\(72\) 0 0
\(73\) 1.52706 + 9.64150i 0.178729 + 1.12845i 0.900029 + 0.435829i \(0.143545\pi\)
−0.721300 + 0.692623i \(0.756455\pi\)
\(74\) 0 0
\(75\) −6.79964 + 5.36329i −0.785155 + 0.619299i
\(76\) 0 0
\(77\) 0.619145 + 3.90913i 0.0705581 + 0.445486i
\(78\) 0 0
\(79\) 8.77277 2.85044i 0.987013 0.320700i 0.229349 0.973344i \(-0.426340\pi\)
0.757665 + 0.652644i \(0.226340\pi\)
\(80\) 0 0
\(81\) 8.95809 0.867500i 0.995344 0.0963889i
\(82\) 0 0
\(83\) 1.61164 + 3.16301i 0.176900 + 0.347186i 0.962383 0.271698i \(-0.0875852\pi\)
−0.785483 + 0.618884i \(0.787585\pi\)
\(84\) 0 0
\(85\) 6.84310 6.94927i 0.742238 0.753755i
\(86\) 0 0
\(87\) −2.23988 6.36657i −0.240140 0.682568i
\(88\) 0 0
\(89\) 2.65779 + 1.93100i 0.281725 + 0.204685i 0.719670 0.694317i \(-0.244293\pi\)
−0.437944 + 0.899002i \(0.644293\pi\)
\(90\) 0 0
\(91\) −1.77229 + 1.28765i −0.185787 + 0.134982i
\(92\) 0 0
\(93\) −3.33999 + 11.1915i −0.346341 + 1.16051i
\(94\) 0 0
\(95\) 17.2772 0.133005i 1.77261 0.0136460i
\(96\) 0 0
\(97\) 1.19966 + 0.611256i 0.121807 + 0.0620636i 0.513832 0.857891i \(-0.328225\pi\)
−0.392025 + 0.919954i \(0.628225\pi\)
\(98\) 0 0
\(99\) 3.26643 4.98510i 0.328288 0.501021i
\(100\) 0 0
\(101\) 16.1183i 1.60383i 0.597435 + 0.801917i \(0.296187\pi\)
−0.597435 + 0.801917i \(0.703813\pi\)
\(102\) 0 0
\(103\) −2.72904 + 5.35604i −0.268900 + 0.527746i −0.985487 0.169752i \(-0.945703\pi\)
0.716587 + 0.697498i \(0.245703\pi\)
\(104\) 0 0
\(105\) 3.28235 6.98291i 0.320325 0.681462i
\(106\) 0 0
\(107\) −5.18489 5.18489i −0.501242 0.501242i 0.410582 0.911824i \(-0.365326\pi\)
−0.911824 + 0.410582i \(0.865326\pi\)
\(108\) 0 0
\(109\) −2.24729 3.09313i −0.215251 0.296268i 0.687714 0.725982i \(-0.258614\pi\)
−0.902965 + 0.429714i \(0.858614\pi\)
\(110\) 0 0
\(111\) 1.47883 11.0580i 0.140364 1.04958i
\(112\) 0 0
\(113\) 2.96892 18.7450i 0.279292 1.76338i −0.305493 0.952194i \(-0.598821\pi\)
0.584786 0.811188i \(-0.301179\pi\)
\(114\) 0 0
\(115\) −1.19789 + 0.622019i −0.111704 + 0.0580035i
\(116\) 0 0
\(117\) 3.27931 + 0.358238i 0.303173 + 0.0331191i
\(118\) 0 0
\(119\) −2.68518 + 8.26415i −0.246150 + 0.757573i
\(120\) 0 0
\(121\) 2.17957 + 6.70804i 0.198143 + 0.609822i
\(122\) 0 0
\(123\) 8.78023 + 11.4912i 0.791687 + 1.03613i
\(124\) 0 0
\(125\) 6.36101 9.19443i 0.568946 0.822375i
\(126\) 0 0
\(127\) −1.51917 + 0.240614i −0.134805 + 0.0213510i −0.223472 0.974710i \(-0.571739\pi\)
0.0886673 + 0.996061i \(0.471739\pi\)
\(128\) 0 0
\(129\) −3.70397 3.52936i −0.326116 0.310743i
\(130\) 0 0
\(131\) −9.46918 3.07672i −0.827326 0.268814i −0.135407 0.990790i \(-0.543234\pi\)
−0.691918 + 0.721976i \(0.743234\pi\)
\(132\) 0 0
\(133\) −13.7158 + 6.98857i −1.18931 + 0.605986i
\(134\) 0 0
\(135\) −10.7276 + 4.46315i −0.923281 + 0.384126i
\(136\) 0 0
\(137\) 6.36073 + 1.00744i 0.543434 + 0.0860715i 0.422115 0.906542i \(-0.361288\pi\)
0.121319 + 0.992614i \(0.461288\pi\)
\(138\) 0 0
\(139\) 1.21863 1.67731i 0.103363 0.142267i −0.754202 0.656642i \(-0.771976\pi\)
0.857565 + 0.514375i \(0.171976\pi\)
\(140\) 0 0
\(141\) 2.10575 4.39167i 0.177336 0.369845i
\(142\) 0 0
\(143\) 1.54469 1.54469i 0.129174 0.129174i
\(144\) 0 0
\(145\) 5.17551 + 7.00937i 0.429803 + 0.582096i
\(146\) 0 0
\(147\) −0.126692 5.24834i −0.0104493 0.432875i
\(148\) 0 0
\(149\) −6.16481 −0.505041 −0.252520 0.967592i \(-0.581259\pi\)
−0.252520 + 0.967592i \(0.581259\pi\)
\(150\) 0 0
\(151\) −11.8069 −0.960833 −0.480417 0.877040i \(-0.659515\pi\)
−0.480417 + 0.877040i \(0.659515\pi\)
\(152\) 0 0
\(153\) 11.3586 6.49608i 0.918288 0.525177i
\(154\) 0 0
\(155\) −0.116070 15.0775i −0.00932298 1.21105i
\(156\) 0 0
\(157\) −8.22907 + 8.22907i −0.656751 + 0.656751i −0.954610 0.297859i \(-0.903728\pi\)
0.297859 + 0.954610i \(0.403728\pi\)
\(158\) 0 0
\(159\) 16.6193 + 7.96878i 1.31800 + 0.631966i
\(160\) 0 0
\(161\) 0.706855 0.972903i 0.0557080 0.0766755i
\(162\) 0 0
\(163\) 21.5564 + 3.41420i 1.68843 + 0.267421i 0.925413 0.378959i \(-0.123718\pi\)
0.763016 + 0.646380i \(0.223718\pi\)
\(164\) 0 0
\(165\) −2.14354 + 7.38962i −0.166875 + 0.575281i
\(166\) 0 0
\(167\) 12.8596 6.55227i 0.995102 0.507030i 0.120938 0.992660i \(-0.461410\pi\)
0.874164 + 0.485630i \(0.161410\pi\)
\(168\) 0 0
\(169\) −11.2138 3.64358i −0.862598 0.280275i
\(170\) 0 0
\(171\) 22.3659 + 6.09109i 1.71036 + 0.465798i
\(172\) 0 0
\(173\) 5.05212 0.800177i 0.384106 0.0608364i 0.0386042 0.999255i \(-0.487709\pi\)
0.345501 + 0.938418i \(0.387709\pi\)
\(174\) 0 0
\(175\) −1.40661 + 9.86135i −0.106330 + 0.745448i
\(176\) 0 0
\(177\) 18.7390 14.3182i 1.40851 1.07622i
\(178\) 0 0
\(179\) 2.20404 + 6.78334i 0.164738 + 0.507011i 0.999017 0.0443316i \(-0.0141158\pi\)
−0.834279 + 0.551342i \(0.814116\pi\)
\(180\) 0 0
\(181\) −0.142407 + 0.438283i −0.0105850 + 0.0325773i −0.956210 0.292683i \(-0.905452\pi\)
0.945625 + 0.325260i \(0.105452\pi\)
\(182\) 0 0
\(183\) 13.6372 + 9.41372i 1.00809 + 0.695882i
\(184\) 0 0
\(185\) 2.36256 + 14.2078i 0.173699 + 1.04458i
\(186\) 0 0
\(187\) 1.35551 8.55838i 0.0991250 0.625851i
\(188\) 0 0
\(189\) 6.77122 7.83028i 0.492534 0.569569i
\(190\) 0 0
\(191\) −15.1190 20.8095i −1.09397 1.50572i −0.843142 0.537691i \(-0.819297\pi\)
−0.250829 0.968031i \(-0.580703\pi\)
\(192\) 0 0
\(193\) −16.8215 16.8215i −1.21084 1.21084i −0.970751 0.240087i \(-0.922824\pi\)
−0.240087 0.970751i \(-0.577176\pi\)
\(194\) 0 0
\(195\) −4.18300 + 0.799756i −0.299551 + 0.0572717i
\(196\) 0 0
\(197\) −9.07122 + 17.8033i −0.646298 + 1.26843i 0.302681 + 0.953092i \(0.402118\pi\)
−0.948979 + 0.315339i \(0.897882\pi\)
\(198\) 0 0
\(199\) 14.9399i 1.05906i 0.848291 + 0.529530i \(0.177632\pi\)
−0.848291 + 0.529530i \(0.822368\pi\)
\(200\) 0 0
\(201\) 10.4626 + 19.3641i 0.737976 + 1.36584i
\(202\) 0 0
\(203\) −6.91681 3.52429i −0.485465 0.247357i
\(204\) 0 0
\(205\) −15.1883 10.8573i −1.06080 0.758308i
\(206\) 0 0
\(207\) −1.77285 + 0.369257i −0.123221 + 0.0256652i
\(208\) 0 0
\(209\) 12.4188 9.02277i 0.859025 0.624118i
\(210\) 0 0
\(211\) 0.810432 + 0.588813i 0.0557925 + 0.0405356i 0.615332 0.788268i \(-0.289022\pi\)
−0.559539 + 0.828804i \(0.689022\pi\)
\(212\) 0 0
\(213\) −4.98285 + 1.75306i −0.341419 + 0.120118i
\(214\) 0 0
\(215\) 5.90802 + 2.95322i 0.402924 + 0.201408i
\(216\) 0 0
\(217\) 6.09877 + 11.9695i 0.414012 + 0.812544i
\(218\) 0 0
\(219\) −3.04718 16.6309i −0.205909 1.12381i
\(220\) 0 0
\(221\) 4.56138 1.48208i 0.306831 0.0996956i
\(222\) 0 0
\(223\) −3.95868 24.9941i −0.265093 1.67373i −0.657127 0.753780i \(-0.728228\pi\)
0.392034 0.919951i \(-0.371772\pi\)
\(224\) 0 0
\(225\) 11.5497 9.57099i 0.769982 0.638066i
\(226\) 0 0
\(227\) 3.09802 + 19.5601i 0.205623 + 1.29825i 0.847233 + 0.531221i \(0.178267\pi\)
−0.641610 + 0.767031i \(0.721733\pi\)
\(228\) 0 0
\(229\) −18.2285 + 5.92281i −1.20458 + 0.391390i −0.841442 0.540347i \(-0.818293\pi\)
−0.363133 + 0.931737i \(0.618293\pi\)
\(230\) 0 0
\(231\) −1.23547 6.74295i −0.0812882 0.443654i
\(232\) 0 0
\(233\) −5.12583 10.0600i −0.335804 0.659053i 0.659929 0.751328i \(-0.270586\pi\)
−0.995734 + 0.0922745i \(0.970586\pi\)
\(234\) 0 0
\(235\) −0.935774 + 6.21765i −0.0610431 + 0.405595i
\(236\) 0 0
\(237\) −15.0713 + 5.30237i −0.978987 + 0.344426i
\(238\) 0 0
\(239\) −6.41867 4.66343i −0.415189 0.301652i 0.360510 0.932755i \(-0.382603\pi\)
−0.775699 + 0.631103i \(0.782603\pi\)
\(240\) 0 0
\(241\) 15.5433 11.2929i 1.00123 0.727439i 0.0388814 0.999244i \(-0.487621\pi\)
0.962352 + 0.271805i \(0.0876205\pi\)
\(242\) 0 0
\(243\) −15.4751 + 1.87655i −0.992728 + 0.120381i
\(244\) 0 0
\(245\) 2.14393 + 6.42952i 0.136971 + 0.410767i
\(246\) 0 0
\(247\) 7.57043 + 3.85733i 0.481695 + 0.245436i
\(248\) 0 0
\(249\) −2.92283 5.40954i −0.185227 0.342816i
\(250\) 0 0
\(251\) 16.7296i 1.05596i 0.849255 + 0.527982i \(0.177051\pi\)
−0.849255 + 0.527982i \(0.822949\pi\)
\(252\) 0 0
\(253\) −0.544425 + 1.06849i −0.0342277 + 0.0671757i
\(254\) 0 0
\(255\) −11.5587 + 12.3190i −0.723832 + 0.771447i
\(256\) 0 0
\(257\) 14.2215 + 14.2215i 0.887111 + 0.887111i 0.994245 0.107134i \(-0.0341673\pi\)
−0.107134 + 0.994245i \(0.534167\pi\)
\(258\) 0 0
\(259\) −7.54266 10.3816i −0.468678 0.645080i
\(260\) 0 0
\(261\) 4.14456 + 10.9304i 0.256542 + 0.676574i
\(262\) 0 0
\(263\) 2.01269 12.7077i 0.124108 0.783587i −0.844602 0.535394i \(-0.820163\pi\)
0.968710 0.248193i \(-0.0798369\pi\)
\(264\) 0 0
\(265\) −23.5294 3.54124i −1.44540 0.217537i
\(266\) 0 0
\(267\) −4.68280 3.23252i −0.286583 0.197827i
\(268\) 0 0
\(269\) −3.43765 + 10.5800i −0.209597 + 0.645074i 0.789896 + 0.613241i \(0.210135\pi\)
−0.999493 + 0.0318333i \(0.989865\pi\)
\(270\) 0 0
\(271\) 5.91811 + 18.2141i 0.359499 + 1.10643i 0.953354 + 0.301853i \(0.0976053\pi\)
−0.593855 + 0.804572i \(0.702395\pi\)
\(272\) 0 0
\(273\) 3.01499 2.30370i 0.182475 0.139426i
\(274\) 0 0
\(275\) −0.152928 9.93204i −0.00922190 0.598924i
\(276\) 0 0
\(277\) −6.94071 + 1.09930i −0.417027 + 0.0660505i −0.361422 0.932402i \(-0.617709\pi\)
−0.0556046 + 0.998453i \(0.517709\pi\)
\(278\) 0 0
\(279\) 5.31557 19.5183i 0.318235 1.16853i
\(280\) 0 0
\(281\) −29.8705 9.70552i −1.78193 0.578983i −0.782860 0.622197i \(-0.786240\pi\)
−0.999066 + 0.0432145i \(0.986240\pi\)
\(282\) 0 0
\(283\) 13.6669 6.96363i 0.812412 0.413945i 0.00213954 0.999998i \(-0.499319\pi\)
0.810273 + 0.586053i \(0.199319\pi\)
\(284\) 0 0
\(285\) −29.9107 + 0.952465i −1.77176 + 0.0564191i
\(286\) 0 0
\(287\) 16.4293 + 2.60214i 0.969789 + 0.153599i
\(288\) 0 0
\(289\) 1.18972 1.63751i 0.0699837 0.0963243i
\(290\) 0 0
\(291\) −2.10281 1.00827i −0.123269 0.0591060i
\(292\) 0 0
\(293\) −19.7002 + 19.7002i −1.15090 + 1.15090i −0.164528 + 0.986372i \(0.552610\pi\)
−0.986372 + 0.164528i \(0.947390\pi\)
\(294\) 0 0
\(295\) −17.7053 + 24.7681i −1.03085 + 1.44205i
\(296\) 0 0
\(297\) −5.44760 + 8.76846i −0.316102 + 0.508797i
\(298\) 0 0
\(299\) −0.663758 −0.0383861
\(300\) 0 0
\(301\) −5.88476 −0.339192
\(302\) 0 0
\(303\) −0.673722 27.9096i −0.0387043 1.60337i
\(304\) 0 0
\(305\) −20.3961 6.45393i −1.16788 0.369551i
\(306\) 0 0
\(307\) 16.0403 16.0403i 0.915468 0.915468i −0.0812272 0.996696i \(-0.525884\pi\)
0.996696 + 0.0812272i \(0.0258839\pi\)
\(308\) 0 0
\(309\) 4.50158 9.38830i 0.256086 0.534081i
\(310\) 0 0
\(311\) −15.0505 + 20.7152i −0.853433 + 1.17465i 0.129663 + 0.991558i \(0.458611\pi\)
−0.983096 + 0.183092i \(0.941389\pi\)
\(312\) 0 0
\(313\) −0.120497 0.0190849i −0.00681092 0.00107874i 0.153028 0.988222i \(-0.451098\pi\)
−0.159839 + 0.987143i \(0.551098\pi\)
\(314\) 0 0
\(315\) −5.39167 + 12.2284i −0.303786 + 0.688994i
\(316\) 0 0
\(317\) −13.7216 + 6.99151i −0.770682 + 0.392682i −0.794679 0.607030i \(-0.792361\pi\)
0.0239969 + 0.999712i \(0.492361\pi\)
\(318\) 0 0
\(319\) 7.36226 + 2.39214i 0.412207 + 0.133934i
\(320\) 0 0
\(321\) 9.19459 + 8.76115i 0.513192 + 0.489000i
\(322\) 0 0
\(323\) 33.2869 5.27213i 1.85213 0.293349i
\(324\) 0 0
\(325\) 4.85978 2.57118i 0.269572 0.142623i
\(326\) 0 0
\(327\) 4.02057 + 5.26196i 0.222338 + 0.290987i
\(328\) 0 0
\(329\) −1.73112 5.32784i −0.0954398 0.293734i
\(330\) 0 0
\(331\) 0.542755 1.67043i 0.0298325 0.0918151i −0.935032 0.354564i \(-0.884629\pi\)
0.964864 + 0.262749i \(0.0846292\pi\)
\(332\) 0 0
\(333\) −2.09845 + 19.2093i −0.114995 + 1.05266i
\(334\) 0 0
\(335\) −20.2462 19.9369i −1.10617 1.08927i
\(336\) 0 0
\(337\) 1.61810 10.2163i 0.0881434 0.556516i −0.903610 0.428356i \(-0.859093\pi\)
0.991754 0.128160i \(-0.0409070\pi\)
\(338\) 0 0
\(339\) −4.35731 + 32.5819i −0.236656 + 1.76961i
\(340\) 0 0
\(341\) −7.87398 10.8376i −0.426400 0.586889i
\(342\) 0 0
\(343\) −14.1309 14.1309i −0.762997 0.762997i
\(344\) 0 0
\(345\) 2.04821 1.12712i 0.110272 0.0606823i
\(346\) 0 0
\(347\) 14.2252 27.9185i 0.763647 1.49874i −0.100189 0.994968i \(-0.531945\pi\)
0.863836 0.503773i \(-0.168055\pi\)
\(348\) 0 0
\(349\) 16.4381i 0.879913i −0.898019 0.439956i \(-0.854994\pi\)
0.898019 0.439956i \(-0.145006\pi\)
\(350\) 0 0
\(351\) −5.69326 0.483235i −0.303884 0.0257932i
\(352\) 0 0
\(353\) 0.230966 + 0.117683i 0.0122931 + 0.00626364i 0.460126 0.887854i \(-0.347804\pi\)
−0.447833 + 0.894117i \(0.647804\pi\)
\(354\) 0 0
\(355\) 5.48593 4.05065i 0.291163 0.214986i
\(356\) 0 0
\(357\) 4.30409 14.4220i 0.227797 0.763293i
\(358\) 0 0
\(359\) −17.7312 + 12.8824i −0.935815 + 0.679909i −0.947410 0.320024i \(-0.896309\pi\)
0.0115948 + 0.999933i \(0.496309\pi\)
\(360\) 0 0
\(361\) 32.9302 + 23.9252i 1.73317 + 1.25922i
\(362\) 0 0
\(363\) −4.05442 11.5242i −0.212802 0.604863i
\(364\) 0 0
\(365\) 10.0590 + 19.3718i 0.526514 + 1.01397i
\(366\) 0 0
\(367\) 0.897351 + 1.76115i 0.0468413 + 0.0919313i 0.913241 0.407420i \(-0.133572\pi\)
−0.866399 + 0.499352i \(0.833572\pi\)
\(368\) 0 0
\(369\) −15.6837 19.5306i −0.816460 1.01672i
\(370\) 0 0
\(371\) 20.1621 6.55107i 1.04676 0.340114i
\(372\) 0 0
\(373\) 0.199978 + 1.26261i 0.0103545 + 0.0653755i 0.992325 0.123661i \(-0.0394635\pi\)
−0.981970 + 0.189037i \(0.939464\pi\)
\(374\) 0 0
\(375\) −10.6301 + 16.1865i −0.548935 + 0.835865i
\(376\) 0 0
\(377\) 0.670278 + 4.23197i 0.0345211 + 0.217958i
\(378\) 0 0
\(379\) −5.76610 + 1.87352i −0.296185 + 0.0962362i −0.453340 0.891338i \(-0.649768\pi\)
0.157155 + 0.987574i \(0.449768\pi\)
\(380\) 0 0
\(381\) 2.62046 0.480133i 0.134250 0.0245979i
\(382\) 0 0
\(383\) 14.1048 + 27.6823i 0.720723 + 1.41450i 0.902294 + 0.431121i \(0.141882\pi\)
−0.181571 + 0.983378i \(0.558118\pi\)
\(384\) 0 0
\(385\) 4.07841 + 7.85427i 0.207855 + 0.400291i
\(386\) 0 0
\(387\) 6.56111 + 5.95643i 0.333520 + 0.302782i
\(388\) 0 0
\(389\) 3.47117 + 2.52196i 0.175996 + 0.127868i 0.672296 0.740283i \(-0.265308\pi\)
−0.496300 + 0.868151i \(0.665308\pi\)
\(390\) 0 0
\(391\) −2.13001 + 1.54754i −0.107719 + 0.0782625i
\(392\) 0 0
\(393\) 16.5249 + 4.93169i 0.833572 + 0.248771i
\(394\) 0 0
\(395\) 16.5930 12.2518i 0.834883 0.616453i
\(396\) 0 0
\(397\) 13.0514 + 6.65001i 0.655030 + 0.333754i 0.749723 0.661752i \(-0.230187\pi\)
−0.0946927 + 0.995507i \(0.530187\pi\)
\(398\) 0 0
\(399\) 23.4575 12.6743i 1.17434 0.634511i
\(400\) 0 0
\(401\) 9.19743i 0.459297i 0.973274 + 0.229649i \(0.0737577\pi\)
−0.973274 + 0.229649i \(0.926242\pi\)
\(402\) 0 0
\(403\) 3.36620 6.60655i 0.167683 0.329096i
\(404\) 0 0
\(405\) 18.3887 8.17654i 0.913742 0.406295i
\(406\) 0 0
\(407\) 9.04837 + 9.04837i 0.448511 + 0.448511i
\(408\) 0 0
\(409\) −14.8606 20.4539i −0.734809 1.01138i −0.998901 0.0468802i \(-0.985072\pi\)
0.264091 0.964498i \(-0.414928\pi\)
\(410\) 0 0
\(411\) −11.0560 1.47856i −0.545353 0.0729321i
\(412\) 0 0
\(413\) 4.24338 26.7917i 0.208803 1.31833i
\(414\) 0 0
\(415\) 5.65598 + 5.56956i 0.277641 + 0.273399i
\(416\) 0 0
\(417\) −2.04001 + 2.95527i −0.0998999 + 0.144720i
\(418\) 0 0
\(419\) 1.79122 5.51280i 0.0875066 0.269318i −0.897722 0.440563i \(-0.854779\pi\)
0.985228 + 0.171245i \(0.0547789\pi\)
\(420\) 0 0
\(421\) 5.27994 + 16.2500i 0.257328 + 0.791975i 0.993362 + 0.115030i \(0.0366965\pi\)
−0.736034 + 0.676945i \(0.763304\pi\)
\(422\) 0 0
\(423\) −3.46265 + 7.69239i −0.168360 + 0.374017i
\(424\) 0 0
\(425\) 9.60043 19.5815i 0.465689 0.949840i
\(426\) 0 0
\(427\) 18.8253 2.98164i 0.911022 0.144292i
\(428\) 0 0
\(429\) −2.61014 + 2.73928i −0.126019 + 0.132253i
\(430\) 0 0
\(431\) −7.18994 2.33615i −0.346327 0.112528i 0.130688 0.991424i \(-0.458281\pi\)
−0.477015 + 0.878895i \(0.658281\pi\)
\(432\) 0 0
\(433\) −4.16519 + 2.12227i −0.200166 + 0.101990i −0.551200 0.834373i \(-0.685830\pi\)
0.351034 + 0.936363i \(0.385830\pi\)
\(434\) 0 0
\(435\) −9.25462 11.9207i −0.443725 0.571555i
\(436\) 0 0
\(437\) −4.60674 0.729636i −0.220370 0.0349032i
\(438\) 0 0
\(439\) −3.13091 + 4.30933i −0.149430 + 0.205673i −0.877170 0.480181i \(-0.840571\pi\)
0.727739 + 0.685854i \(0.240571\pi\)
\(440\) 0 0
\(441\) 0.438745 + 9.08244i 0.0208926 + 0.432497i
\(442\) 0 0
\(443\) 13.2529 13.2529i 0.629663 0.629663i −0.318320 0.947983i \(-0.603119\pi\)
0.947983 + 0.318320i \(0.103119\pi\)
\(444\) 0 0
\(445\) 7.00368 + 2.21618i 0.332006 + 0.105057i
\(446\) 0 0
\(447\) 10.6747 0.257680i 0.504894 0.0121878i
\(448\) 0 0
\(449\) −0.687206 −0.0324313 −0.0162156 0.999869i \(-0.505162\pi\)
−0.0162156 + 0.999869i \(0.505162\pi\)
\(450\) 0 0
\(451\) −16.5874 −0.781070
\(452\) 0 0
\(453\) 20.4442 0.493511i 0.960553 0.0231872i
\(454\) 0 0
\(455\) −2.84867 + 3.98501i −0.133548 + 0.186820i
\(456\) 0 0
\(457\) 20.4930 20.4930i 0.958623 0.958623i −0.0405546 0.999177i \(-0.512912\pi\)
0.999177 + 0.0405546i \(0.0129125\pi\)
\(458\) 0 0
\(459\) −19.3964 + 11.7230i −0.905347 + 0.547185i
\(460\) 0 0
\(461\) 2.51720 3.46463i 0.117238 0.161364i −0.746365 0.665537i \(-0.768203\pi\)
0.863603 + 0.504173i \(0.168203\pi\)
\(462\) 0 0
\(463\) 29.9000 + 4.73569i 1.38957 + 0.220086i 0.805971 0.591955i \(-0.201644\pi\)
0.583599 + 0.812042i \(0.301644\pi\)
\(464\) 0 0
\(465\) 0.831195 + 26.1025i 0.0385458 + 1.21047i
\(466\) 0 0
\(467\) −22.7856 + 11.6099i −1.05439 + 0.537241i −0.893190 0.449680i \(-0.851538\pi\)
−0.161205 + 0.986921i \(0.551538\pi\)
\(468\) 0 0
\(469\) 24.0770 + 7.82310i 1.11177 + 0.361237i
\(470\) 0 0
\(471\) 13.9050 14.5930i 0.640711 0.672409i
\(472\) 0 0
\(473\) 5.79600 0.917996i 0.266500 0.0422095i
\(474\) 0 0
\(475\) 36.5551 12.5029i 1.67726 0.573672i
\(476\) 0 0
\(477\) −29.1102 13.1037i −1.33287 0.599975i
\(478\) 0 0
\(479\) −2.06837 6.36579i −0.0945063 0.290860i 0.892618 0.450813i \(-0.148866\pi\)
−0.987125 + 0.159953i \(0.948866\pi\)
\(480\) 0 0
\(481\) −2.18870 + 6.73612i −0.0997960 + 0.307141i
\(482\) 0 0
\(483\) −1.18329 + 1.71417i −0.0538414 + 0.0779975i
\(484\) 0 0
\(485\) 2.97713 + 0.448066i 0.135184 + 0.0203456i
\(486\) 0 0
\(487\) −2.38639 + 15.0671i −0.108138 + 0.682755i 0.872748 + 0.488171i \(0.162336\pi\)
−0.980886 + 0.194584i \(0.937664\pi\)
\(488\) 0 0
\(489\) −37.4687 5.01082i −1.69439 0.226597i
\(490\) 0 0
\(491\) 0.878303 + 1.20888i 0.0396373 + 0.0545560i 0.828376 0.560173i \(-0.189265\pi\)
−0.788738 + 0.614729i \(0.789265\pi\)
\(492\) 0 0
\(493\) 12.0177 + 12.0177i 0.541250 + 0.541250i
\(494\) 0 0
\(495\) 3.40277 12.8851i 0.152943 0.579141i
\(496\) 0 0
\(497\) −2.75831 + 5.41349i −0.123727 + 0.242828i
\(498\) 0 0
\(499\) 11.6309i 0.520672i 0.965518 + 0.260336i \(0.0838333\pi\)
−0.965518 + 0.260336i \(0.916167\pi\)
\(500\) 0 0
\(501\) −21.9930 + 11.8831i −0.982576 + 0.530896i
\(502\) 0 0
\(503\) −18.6581 9.50679i −0.831925 0.423887i −0.0144808 0.999895i \(-0.504610\pi\)
−0.817444 + 0.576008i \(0.804610\pi\)
\(504\) 0 0
\(505\) 11.4010 + 34.1909i 0.507340 + 1.52148i
\(506\) 0 0
\(507\) 19.5695 + 5.84030i 0.869111 + 0.259377i
\(508\) 0 0
\(509\) 29.0463 21.1033i 1.28745 0.935389i 0.287702 0.957720i \(-0.407109\pi\)
0.999751 + 0.0223311i \(0.00710880\pi\)
\(510\) 0 0
\(511\) −15.7334 11.4310i −0.696004 0.505676i
\(512\) 0 0
\(513\) −38.9822 9.61215i −1.72111 0.424387i
\(514\) 0 0
\(515\) −2.00045 + 13.2918i −0.0881504 + 0.585707i
\(516\) 0 0
\(517\) 2.53613 + 4.97744i 0.111539 + 0.218907i
\(518\) 0 0
\(519\) −8.71453 + 1.59671i −0.382526 + 0.0700880i
\(520\) 0 0
\(521\) 39.1289 12.7138i 1.71427 0.557000i 0.723235 0.690602i \(-0.242655\pi\)
0.991035 + 0.133602i \(0.0426545\pi\)
\(522\) 0 0
\(523\) 0.431314 + 2.72321i 0.0188601 + 0.119078i 0.995322 0.0966111i \(-0.0308003\pi\)
−0.976462 + 0.215689i \(0.930800\pi\)
\(524\) 0 0
\(525\) 2.02343 17.1342i 0.0883097 0.747797i
\(526\) 0 0
\(527\) −4.60087 29.0488i −0.200417 1.26538i
\(528\) 0 0
\(529\) −21.5278 + 6.99479i −0.935990 + 0.304121i
\(530\) 0 0
\(531\) −31.8490 + 25.5758i −1.38213 + 1.10990i
\(532\) 0 0
\(533\) −4.16815 8.18045i −0.180542 0.354334i
\(534\) 0 0
\(535\) −14.6659 7.33097i −0.634060 0.316946i
\(536\) 0 0
\(537\) −4.09993 11.6535i −0.176925 0.502888i
\(538\) 0 0
\(539\) 4.87152 + 3.53937i 0.209831 + 0.152451i
\(540\) 0 0
\(541\) 17.6370 12.8140i 0.758273 0.550918i −0.140107 0.990136i \(-0.544745\pi\)
0.898380 + 0.439219i \(0.144745\pi\)
\(542\) 0 0
\(543\) 0.228265 0.764860i 0.00979577 0.0328233i
\(544\) 0 0
\(545\) −6.95492 4.97170i −0.297916 0.212964i
\(546\) 0 0
\(547\) −26.1267 13.3122i −1.11710 0.569189i −0.204834 0.978797i \(-0.565665\pi\)
−0.912262 + 0.409608i \(0.865665\pi\)
\(548\) 0 0
\(549\) −24.0069 15.7303i −1.02459 0.671352i
\(550\) 0 0
\(551\) 30.1083i 1.28266i
\(552\) 0 0
\(553\) −8.34290 + 16.3739i −0.354776 + 0.696287i
\(554\) 0 0
\(555\) −4.68474 24.5028i −0.198856 1.04008i
\(556\) 0 0
\(557\) 12.3449 + 12.3449i 0.523071 + 0.523071i 0.918498 0.395427i \(-0.129403\pi\)
−0.395427 + 0.918498i \(0.629403\pi\)
\(558\) 0 0
\(559\) 1.90917 + 2.62775i 0.0807494 + 0.111142i
\(560\) 0 0
\(561\) −1.98941 + 14.8759i −0.0839929 + 0.628060i
\(562\) 0 0
\(563\) −6.59138 + 41.6164i −0.277794 + 1.75392i 0.315491 + 0.948928i \(0.397831\pi\)
−0.593285 + 0.804992i \(0.702169\pi\)
\(564\) 0 0
\(565\) −6.96117 41.8628i −0.292859 1.76118i
\(566\) 0 0
\(567\) −11.3974 + 13.8415i −0.478645 + 0.581289i
\(568\) 0 0
\(569\) 2.68424 8.26124i 0.112529 0.346329i −0.878894 0.477016i \(-0.841718\pi\)
0.991424 + 0.130687i \(0.0417183\pi\)
\(570\) 0 0
\(571\) −3.08502 9.49470i −0.129104 0.397341i 0.865523 0.500870i \(-0.166987\pi\)
−0.994626 + 0.103529i \(0.966987\pi\)
\(572\) 0 0
\(573\) 27.0490 + 35.4007i 1.12999 + 1.47888i
\(574\) 0 0
\(575\) −2.10105 + 2.16676i −0.0876198 + 0.0903603i
\(576\) 0 0
\(577\) 10.6032 1.67937i 0.441415 0.0699133i 0.0682288 0.997670i \(-0.478265\pi\)
0.373186 + 0.927756i \(0.378265\pi\)
\(578\) 0 0
\(579\) 29.8303 + 28.4241i 1.23971 + 1.18127i
\(580\) 0 0
\(581\) −6.72615 2.18546i −0.279048 0.0906681i
\(582\) 0 0
\(583\) −18.8361 + 9.59746i −0.780110 + 0.397486i
\(584\) 0 0
\(585\) 7.20962 1.55966i 0.298081 0.0644839i
\(586\) 0 0
\(587\) −22.9124 3.62898i −0.945698 0.149784i −0.335507 0.942038i \(-0.608907\pi\)
−0.610191 + 0.792254i \(0.708907\pi\)
\(588\) 0 0
\(589\) 30.6250 42.1517i 1.26188 1.73683i
\(590\) 0 0
\(591\) 14.9631 31.2064i 0.615500 1.28366i
\(592\) 0 0
\(593\) −6.63871 + 6.63871i −0.272619 + 0.272619i −0.830154 0.557535i \(-0.811747\pi\)
0.557535 + 0.830154i \(0.311747\pi\)
\(594\) 0 0
\(595\) 0.149574 + 19.4296i 0.00613194 + 0.796536i
\(596\) 0 0
\(597\) −0.624464 25.8691i −0.0255576 1.05875i
\(598\) 0 0
\(599\) −3.40483 −0.139118 −0.0695588 0.997578i \(-0.522159\pi\)
−0.0695588 + 0.997578i \(0.522159\pi\)
\(600\) 0 0
\(601\) 2.96693 0.121024 0.0605118 0.998167i \(-0.480727\pi\)
0.0605118 + 0.998167i \(0.480727\pi\)
\(602\) 0 0
\(603\) −18.9259 33.0925i −0.770722 1.34763i
\(604\) 0 0
\(605\) 9.36823 + 12.6877i 0.380873 + 0.515829i
\(606\) 0 0
\(607\) −11.7030 + 11.7030i −0.475010 + 0.475010i −0.903532 0.428521i \(-0.859035\pi\)
0.428521 + 0.903532i \(0.359035\pi\)
\(608\) 0 0
\(609\) 12.1241 + 5.81336i 0.491293 + 0.235569i
\(610\) 0 0
\(611\) −1.81745 + 2.50150i −0.0735260 + 0.101200i
\(612\) 0 0
\(613\) 41.1420 + 6.51626i 1.66171 + 0.263189i 0.915440 0.402454i \(-0.131843\pi\)
0.746271 + 0.665643i \(0.231843\pi\)
\(614\) 0 0
\(615\) 26.7531 + 18.1651i 1.07879 + 0.732488i
\(616\) 0 0
\(617\) 8.90536 4.53751i 0.358516 0.182673i −0.265450 0.964125i \(-0.585520\pi\)
0.623966 + 0.781451i \(0.285520\pi\)
\(618\) 0 0
\(619\) −0.701573 0.227955i −0.0281986 0.00916228i 0.294884 0.955533i \(-0.404719\pi\)
−0.323082 + 0.946371i \(0.604719\pi\)
\(620\) 0 0
\(621\) 3.05433 0.713489i 0.122566 0.0286313i
\(622\) 0 0
\(623\) −6.46432 + 1.02385i −0.258988 + 0.0410196i
\(624\) 0 0
\(625\) 6.98974 24.0030i 0.279590 0.960120i
\(626\) 0 0
\(627\) −21.1266 + 16.1424i −0.843714 + 0.644667i
\(628\) 0 0
\(629\) 8.68160 + 26.7192i 0.346158 + 1.06537i
\(630\) 0 0
\(631\) 7.30043 22.4684i 0.290626 0.894454i −0.694030 0.719946i \(-0.744167\pi\)
0.984656 0.174508i \(-0.0558334\pi\)
\(632\) 0 0
\(633\) −1.42791 0.985683i −0.0567544 0.0391774i
\(634\) 0 0
\(635\) −3.05235 + 1.58496i −0.121129 + 0.0628973i
\(636\) 0 0
\(637\) −0.521384 + 3.29189i −0.0206580 + 0.130429i
\(638\) 0 0
\(639\) 8.55475 3.24378i 0.338421 0.128322i
\(640\) 0 0
\(641\) 10.1942 + 14.0312i 0.402648 + 0.554198i 0.961406 0.275133i \(-0.0887220\pi\)
−0.558758 + 0.829331i \(0.688722\pi\)
\(642\) 0 0
\(643\) −19.4481 19.4481i −0.766958 0.766958i 0.210612 0.977570i \(-0.432454\pi\)
−0.977570 + 0.210612i \(0.932454\pi\)
\(644\) 0 0
\(645\) −10.3535 4.86669i −0.407667 0.191626i
\(646\) 0 0
\(647\) −0.917006 + 1.79973i −0.0360512 + 0.0707546i −0.908330 0.418255i \(-0.862642\pi\)
0.872278 + 0.489010i \(0.162642\pi\)
\(648\) 0 0
\(649\) 27.0495i 1.06179i
\(650\) 0 0
\(651\) −11.0606 20.4709i −0.433500 0.802316i
\(652\) 0 0
\(653\) −17.2019 8.76480i −0.673162 0.342993i 0.0837716 0.996485i \(-0.473303\pi\)
−0.756934 + 0.653492i \(0.773303\pi\)
\(654\) 0 0
\(655\) −22.2627 + 0.171384i −0.869876 + 0.00669653i
\(656\) 0 0
\(657\) 5.97148 + 28.6698i 0.232970 + 1.11851i
\(658\) 0 0
\(659\) −31.9956 + 23.2462i −1.24637 + 0.905543i −0.998006 0.0631231i \(-0.979894\pi\)
−0.248367 + 0.968666i \(0.579894\pi\)
\(660\) 0 0
\(661\) −29.5919 21.4997i −1.15099 0.836243i −0.162378 0.986729i \(-0.551916\pi\)
−0.988612 + 0.150486i \(0.951916\pi\)
\(662\) 0 0
\(663\) −7.83629 + 2.75695i −0.304336 + 0.107071i
\(664\) 0 0
\(665\) −24.1514 + 24.5261i −0.936552 + 0.951083i
\(666\) 0 0
\(667\) −1.06783 2.09574i −0.0413467 0.0811474i
\(668\) 0 0
\(669\) 7.89936 + 43.1130i 0.305407 + 1.66685i
\(670\) 0 0
\(671\) −18.0763 + 5.87334i −0.697827 + 0.226738i
\(672\) 0 0
\(673\) −4.75453 30.0189i −0.183274 1.15714i −0.892126 0.451787i \(-0.850787\pi\)
0.708852 0.705357i \(-0.249213\pi\)
\(674\) 0 0
\(675\) −19.5988 + 17.0554i −0.754359 + 0.656462i
\(676\) 0 0
\(677\) −4.63953 29.2929i −0.178312 1.12582i −0.900736 0.434366i \(-0.856972\pi\)
0.722425 0.691450i \(-0.243028\pi\)
\(678\) 0 0
\(679\) −2.55107 + 0.828893i −0.0979011 + 0.0318100i
\(680\) 0 0
\(681\) −6.18195 33.7398i −0.236893 1.29291i
\(682\) 0 0
\(683\) 4.38498 + 8.60601i 0.167787 + 0.329300i 0.959555 0.281522i \(-0.0908392\pi\)
−0.791768 + 0.610822i \(0.790839\pi\)
\(684\) 0 0
\(685\) 14.2053 2.36213i 0.542755 0.0902523i
\(686\) 0 0
\(687\) 31.3160 11.0175i 1.19478 0.420346i
\(688\) 0 0
\(689\) −9.46640 6.87775i −0.360641 0.262021i
\(690\) 0 0
\(691\) −9.38046 + 6.81530i −0.356849 + 0.259266i −0.751737 0.659463i \(-0.770784\pi\)
0.394887 + 0.918730i \(0.370784\pi\)
\(692\) 0 0
\(693\) 2.42112 + 11.6241i 0.0919709 + 0.441563i
\(694\) 0 0
\(695\) 1.39861 4.41996i 0.0530522 0.167659i
\(696\) 0 0
\(697\) −32.4482 16.5332i −1.22906 0.626239i
\(698\) 0 0
\(699\) 9.29611 + 17.2051i 0.351611 + 0.650758i
\(700\) 0 0
\(701\) 47.4850i 1.79348i −0.442556 0.896741i \(-0.645928\pi\)
0.442556 0.896741i \(-0.354072\pi\)
\(702\) 0 0
\(703\) −22.5951 + 44.3454i −0.852190 + 1.67252i
\(704\) 0 0
\(705\) 1.36045 10.8053i 0.0512374 0.406950i
\(706\) 0 0
\(707\) −22.7062 22.7062i −0.853956 0.853956i
\(708\) 0 0
\(709\) 24.5873 + 33.8414i 0.923394 + 1.27094i 0.962381 + 0.271703i \(0.0875867\pi\)
−0.0389877 + 0.999240i \(0.512413\pi\)
\(710\) 0 0
\(711\) 25.8750 9.81125i 0.970390 0.367951i
\(712\) 0 0
\(713\) −0.636737 + 4.02020i −0.0238460 + 0.150558i
\(714\) 0 0
\(715\) 2.18406 4.36929i 0.0816792 0.163402i
\(716\) 0 0
\(717\) 11.3091 + 7.80666i 0.422348 + 0.291545i
\(718\) 0 0
\(719\) 3.07429 9.46170i 0.114652 0.352862i −0.877222 0.480084i \(-0.840606\pi\)
0.991874 + 0.127222i \(0.0406062\pi\)
\(720\) 0 0
\(721\) −3.70071 11.3896i −0.137822 0.424171i
\(722\) 0 0
\(723\) −26.4420 + 20.2038i −0.983387 + 0.751389i
\(724\) 0 0
\(725\) 15.9365 + 11.2078i 0.591866 + 0.416246i
\(726\) 0 0
\(727\) −34.3889 + 5.44666i −1.27541 + 0.202005i −0.757164 0.653225i \(-0.773416\pi\)
−0.518248 + 0.855230i \(0.673416\pi\)
\(728\) 0 0
\(729\) 26.7174 3.89617i 0.989534 0.144303i
\(730\) 0 0
\(731\) 12.2531 + 3.98128i 0.453198 + 0.147253i
\(732\) 0 0
\(733\) −11.5143 + 5.86682i −0.425290 + 0.216696i −0.653517 0.756912i \(-0.726707\pi\)
0.228227 + 0.973608i \(0.426707\pi\)
\(734\) 0 0
\(735\) −3.98107 11.0434i −0.146844 0.407342i
\(736\) 0 0
\(737\) −24.9343 3.94920i −0.918465 0.145471i
\(738\) 0 0
\(739\) 7.98551 10.9911i 0.293752 0.404315i −0.636476 0.771296i \(-0.719609\pi\)
0.930228 + 0.366981i \(0.119609\pi\)
\(740\) 0 0
\(741\) −13.2698 6.36271i −0.487477 0.233740i
\(742\) 0 0
\(743\) −17.0201 + 17.0201i −0.624409 + 0.624409i −0.946656 0.322247i \(-0.895562\pi\)
0.322247 + 0.946656i \(0.395562\pi\)
\(744\) 0 0
\(745\) −13.0771 + 4.36057i −0.479107 + 0.159759i
\(746\) 0 0
\(747\) 5.28713 + 9.24470i 0.193446 + 0.338246i
\(748\) 0 0
\(749\) 14.6081 0.533769
\(750\) 0 0
\(751\) 4.62541 0.168784 0.0843918 0.996433i \(-0.473105\pi\)
0.0843918 + 0.996433i \(0.473105\pi\)
\(752\) 0 0
\(753\) −0.699273 28.9681i −0.0254829 1.05566i
\(754\) 0 0
\(755\) −25.0454 + 8.35142i −0.911494 + 0.303939i
\(756\) 0 0
\(757\) −37.1450 + 37.1450i −1.35006 + 1.35006i −0.464471 + 0.885588i \(0.653756\pi\)
−0.885588 + 0.464471i \(0.846244\pi\)
\(758\) 0 0
\(759\) 0.898036 1.87290i 0.0325967 0.0679821i
\(760\) 0 0
\(761\) 2.00068 2.75371i 0.0725248 0.0998218i −0.771214 0.636577i \(-0.780350\pi\)
0.843738 + 0.536755i \(0.180350\pi\)
\(762\) 0 0
\(763\) 7.52316 + 1.19155i 0.272357 + 0.0431371i
\(764\) 0 0
\(765\) 19.4995 21.8141i 0.705004 0.788690i
\(766\) 0 0
\(767\) −13.3401 + 6.79711i −0.481682 + 0.245429i
\(768\) 0 0
\(769\) 25.5702 + 8.30827i 0.922086 + 0.299604i 0.731322 0.682032i \(-0.238904\pi\)
0.190764 + 0.981636i \(0.438904\pi\)
\(770\) 0 0
\(771\) −25.2196 24.0307i −0.908261 0.865444i
\(772\) 0 0
\(773\) −24.1237 + 3.82081i −0.867668 + 0.137425i −0.574370 0.818596i \(-0.694753\pi\)
−0.293298 + 0.956021i \(0.594753\pi\)
\(774\) 0 0
\(775\) −10.9110 31.9009i −0.391935 1.14591i
\(776\) 0 0
\(777\) 13.4944 + 17.6609i 0.484109 + 0.633582i
\(778\) 0 0
\(779\) −19.9362 61.3573i −0.714288 2.19835i
\(780\) 0 0
\(781\) 1.87223 5.76213i 0.0669936 0.206185i
\(782\) 0 0
\(783\) −7.63338 18.7532i −0.272795 0.670186i
\(784\) 0 0
\(785\) −11.6352 + 23.2766i −0.415277 + 0.830776i
\(786\) 0 0
\(787\) −4.41590 + 27.8809i −0.157410 + 0.993846i 0.774873 + 0.632117i \(0.217814\pi\)
−0.932283 + 0.361730i \(0.882186\pi\)
\(788\) 0 0
\(789\) −2.95391 + 22.0880i −0.105162 + 0.786354i
\(790\) 0 0
\(791\) 22.2241 + 30.5889i 0.790198 + 1.08761i
\(792\) 0 0
\(793\) −7.43885 7.43885i −0.264161 0.264161i
\(794\) 0 0
\(795\) 40.8903 + 5.14832i 1.45023 + 0.182592i
\(796\) 0 0