Properties

Label 804.2.s.b.5.7
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.7
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.02689 + 1.39481i) q^{3} +(-2.48625 + 0.730028i) q^{5} +(3.64531 + 3.15868i) q^{7} +(-0.891005 - 2.86463i) q^{9} +O(q^{10})\) \(q+(-1.02689 + 1.39481i) q^{3} +(-2.48625 + 0.730028i) q^{5} +(3.64531 + 3.15868i) q^{7} +(-0.891005 - 2.86463i) q^{9} +(6.01277 - 1.76551i) q^{11} +(2.22147 + 3.45668i) q^{13} +(1.53484 - 4.21751i) q^{15} +(-0.235591 - 0.0338728i) q^{17} +(-0.749547 - 0.865023i) q^{19} +(-8.14910 + 1.84092i) q^{21} +(-1.84028 + 0.840429i) q^{23} +(1.44221 - 0.926855i) q^{25} +(4.91059 + 1.69887i) q^{27} +0.303522i q^{29} +(-4.77999 + 7.43781i) q^{31} +(-3.71188 + 10.1997i) q^{33} +(-11.3691 - 5.19208i) q^{35} -2.20438 q^{37} +(-7.10262 - 0.451082i) q^{39} +(-0.648759 + 4.51222i) q^{41} +(3.70767 + 0.533082i) q^{43} +(4.30652 + 6.47172i) q^{45} +(-4.93924 + 2.25568i) q^{47} +(2.31483 + 16.1000i) q^{49} +(0.289171 - 0.293821i) q^{51} +(-1.07232 - 7.45815i) q^{53} +(-13.6603 + 8.77897i) q^{55} +(1.97625 - 0.157196i) q^{57} +(4.86335 - 7.56752i) q^{59} +(0.272313 - 0.927412i) q^{61} +(5.80047 - 13.2569i) q^{63} +(-8.04661 - 6.97242i) q^{65} +(6.65218 - 4.76954i) q^{67} +(0.717522 - 3.42988i) q^{69} +(-16.0736 + 2.31103i) q^{71} +(13.2311 + 3.88499i) q^{73} +(-0.188203 + 2.96340i) q^{75} +(27.4951 + 12.5566i) q^{77} +(-1.18099 - 1.83765i) q^{79} +(-7.41222 + 5.10480i) q^{81} +(1.09530 + 3.73026i) q^{83} +(0.610465 - 0.0877716i) q^{85} +(-0.423356 - 0.311683i) q^{87} +(-9.87966 - 4.51189i) q^{89} +(-2.82059 + 19.6176i) q^{91} +(-5.46584 - 14.3050i) q^{93} +(2.49505 + 1.60347i) q^{95} -2.79168i q^{97} +(-10.4149 - 15.6513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.02689 + 1.39481i −0.592874 + 0.805295i
\(4\) 0 0
\(5\) −2.48625 + 0.730028i −1.11188 + 0.326478i −0.785564 0.618781i \(-0.787627\pi\)
−0.326320 + 0.945259i \(0.605809\pi\)
\(6\) 0 0
\(7\) 3.64531 + 3.15868i 1.37780 + 1.19387i 0.958179 + 0.286170i \(0.0923821\pi\)
0.419620 + 0.907700i \(0.362163\pi\)
\(8\) 0 0
\(9\) −0.891005 2.86463i −0.297002 0.954877i
\(10\) 0 0
\(11\) 6.01277 1.76551i 1.81292 0.532320i 0.814090 0.580739i \(-0.197236\pi\)
0.998827 + 0.0484186i \(0.0154181\pi\)
\(12\) 0 0
\(13\) 2.22147 + 3.45668i 0.616126 + 0.958711i 0.999385 + 0.0350697i \(0.0111653\pi\)
−0.383259 + 0.923641i \(0.625198\pi\)
\(14\) 0 0
\(15\) 1.53484 4.21751i 0.396295 1.08896i
\(16\) 0 0
\(17\) −0.235591 0.0338728i −0.0571391 0.00821537i 0.113686 0.993517i \(-0.463734\pi\)
−0.170825 + 0.985301i \(0.554643\pi\)
\(18\) 0 0
\(19\) −0.749547 0.865023i −0.171958 0.198450i 0.663229 0.748417i \(-0.269186\pi\)
−0.835186 + 0.549967i \(0.814640\pi\)
\(20\) 0 0
\(21\) −8.14910 + 1.84092i −1.77828 + 0.401721i
\(22\) 0 0
\(23\) −1.84028 + 0.840429i −0.383725 + 0.175242i −0.597932 0.801547i \(-0.704011\pi\)
0.214207 + 0.976788i \(0.431283\pi\)
\(24\) 0 0
\(25\) 1.44221 0.926855i 0.288443 0.185371i
\(26\) 0 0
\(27\) 4.91059 + 1.69887i 0.945043 + 0.326947i
\(28\) 0 0
\(29\) 0.303522i 0.0563626i 0.999603 + 0.0281813i \(0.00897157\pi\)
−0.999603 + 0.0281813i \(0.991028\pi\)
\(30\) 0 0
\(31\) −4.77999 + 7.43781i −0.858511 + 1.33587i 0.0821840 + 0.996617i \(0.473810\pi\)
−0.940695 + 0.339253i \(0.889826\pi\)
\(32\) 0 0
\(33\) −3.71188 + 10.1997i −0.646155 + 1.77553i
\(34\) 0 0
\(35\) −11.3691 5.19208i −1.92172 0.877622i
\(36\) 0 0
\(37\) −2.20438 −0.362398 −0.181199 0.983446i \(-0.557998\pi\)
−0.181199 + 0.983446i \(0.557998\pi\)
\(38\) 0 0
\(39\) −7.10262 0.451082i −1.13733 0.0722309i
\(40\) 0 0
\(41\) −0.648759 + 4.51222i −0.101319 + 0.704690i 0.874327 + 0.485338i \(0.161303\pi\)
−0.975646 + 0.219352i \(0.929606\pi\)
\(42\) 0 0
\(43\) 3.70767 + 0.533082i 0.565414 + 0.0812942i 0.419093 0.907943i \(-0.362348\pi\)
0.146320 + 0.989237i \(0.453257\pi\)
\(44\) 0 0
\(45\) 4.30652 + 6.47172i 0.641978 + 0.964747i
\(46\) 0 0
\(47\) −4.93924 + 2.25568i −0.720463 + 0.329024i −0.741683 0.670751i \(-0.765972\pi\)
0.0212204 + 0.999775i \(0.493245\pi\)
\(48\) 0 0
\(49\) 2.31483 + 16.1000i 0.330691 + 2.30000i
\(50\) 0 0
\(51\) 0.289171 0.293821i 0.0404921 0.0411432i
\(52\) 0 0
\(53\) −1.07232 7.45815i −0.147294 1.02446i −0.920624 0.390451i \(-0.872319\pi\)
0.773329 0.634004i \(-0.218590\pi\)
\(54\) 0 0
\(55\) −13.6603 + 8.77897i −1.84196 + 1.18376i
\(56\) 0 0
\(57\) 1.97625 0.157196i 0.261760 0.0208211i
\(58\) 0 0
\(59\) 4.86335 7.56752i 0.633155 0.985208i −0.365368 0.930863i \(-0.619057\pi\)
0.998522 0.0543445i \(-0.0173069\pi\)
\(60\) 0 0
\(61\) 0.272313 0.927412i 0.0348661 0.118743i −0.940221 0.340564i \(-0.889382\pi\)
0.975087 + 0.221821i \(0.0712001\pi\)
\(62\) 0 0
\(63\) 5.80047 13.2569i 0.730790 1.67021i
\(64\) 0 0
\(65\) −8.04661 6.97242i −0.998059 0.864823i
\(66\) 0 0
\(67\) 6.65218 4.76954i 0.812693 0.582692i
\(68\) 0 0
\(69\) 0.717522 3.42988i 0.0863795 0.412908i
\(70\) 0 0
\(71\) −16.0736 + 2.31103i −1.90758 + 0.274269i −0.991839 0.127498i \(-0.959305\pi\)
−0.915742 + 0.401767i \(0.868396\pi\)
\(72\) 0 0
\(73\) 13.2311 + 3.88499i 1.54858 + 0.454704i 0.940676 0.339307i \(-0.110193\pi\)
0.607903 + 0.794011i \(0.292011\pi\)
\(74\) 0 0
\(75\) −0.188203 + 2.96340i −0.0217318 + 0.342183i
\(76\) 0 0
\(77\) 27.4951 + 12.5566i 3.13336 + 1.43096i
\(78\) 0 0
\(79\) −1.18099 1.83765i −0.132871 0.206752i 0.768442 0.639919i \(-0.221032\pi\)
−0.901313 + 0.433168i \(0.857396\pi\)
\(80\) 0 0
\(81\) −7.41222 + 5.10480i −0.823580 + 0.567200i
\(82\) 0 0
\(83\) 1.09530 + 3.73026i 0.120225 + 0.409449i 0.997510 0.0705203i \(-0.0224660\pi\)
−0.877285 + 0.479969i \(0.840648\pi\)
\(84\) 0 0
\(85\) 0.610465 0.0877716i 0.0662142 0.00952016i
\(86\) 0 0
\(87\) −0.423356 0.311683i −0.0453885 0.0334159i
\(88\) 0 0
\(89\) −9.87966 4.51189i −1.04724 0.478259i −0.183935 0.982938i \(-0.558884\pi\)
−0.863307 + 0.504679i \(0.831611\pi\)
\(90\) 0 0
\(91\) −2.82059 + 19.6176i −0.295678 + 2.05648i
\(92\) 0 0
\(93\) −5.46584 14.3050i −0.566781 1.48336i
\(94\) 0 0
\(95\) 2.49505 + 1.60347i 0.255987 + 0.164513i
\(96\) 0 0
\(97\) 2.79168i 0.283452i −0.989906 0.141726i \(-0.954735\pi\)
0.989906 0.141726i \(-0.0452652\pi\)
\(98\) 0 0
\(99\) −10.4149 15.6513i −1.04674 1.57301i
\(100\) 0 0
\(101\) 12.0577 + 13.9154i 1.19979 + 1.38463i 0.902973 + 0.429698i \(0.141380\pi\)
0.296818 + 0.954934i \(0.404074\pi\)
\(102\) 0 0
\(103\) −10.4201 6.69660i −1.02672 0.659836i −0.0850555 0.996376i \(-0.527107\pi\)
−0.941669 + 0.336540i \(0.890743\pi\)
\(104\) 0 0
\(105\) 18.9167 10.5260i 1.84608 1.02724i
\(106\) 0 0
\(107\) −0.143467 + 0.488605i −0.0138695 + 0.0472352i −0.966137 0.258030i \(-0.916927\pi\)
0.952268 + 0.305265i \(0.0987450\pi\)
\(108\) 0 0
\(109\) −8.72485 13.5761i −0.835689 1.30036i −0.951675 0.307107i \(-0.900639\pi\)
0.115986 0.993251i \(-0.462997\pi\)
\(110\) 0 0
\(111\) 2.26365 3.07470i 0.214856 0.291837i
\(112\) 0 0
\(113\) 6.52185 + 1.91499i 0.613524 + 0.180147i 0.573708 0.819060i \(-0.305505\pi\)
0.0398163 + 0.999207i \(0.487323\pi\)
\(114\) 0 0
\(115\) 3.96186 3.43297i 0.369445 0.320126i
\(116\) 0 0
\(117\) 7.92277 9.44362i 0.732460 0.873063i
\(118\) 0 0
\(119\) −0.751808 0.867633i −0.0689182 0.0795358i
\(120\) 0 0
\(121\) 23.7825 15.2841i 2.16205 1.38946i
\(122\) 0 0
\(123\) −5.62750 5.53844i −0.507414 0.499384i
\(124\) 0 0
\(125\) 5.57533 6.43428i 0.498673 0.575499i
\(126\) 0 0
\(127\) −4.09720 + 4.72842i −0.363568 + 0.419580i −0.907832 0.419334i \(-0.862264\pi\)
0.544264 + 0.838914i \(0.316809\pi\)
\(128\) 0 0
\(129\) −4.55090 + 4.62408i −0.400685 + 0.407128i
\(130\) 0 0
\(131\) −8.98874 + 4.10502i −0.785350 + 0.358657i −0.767389 0.641182i \(-0.778445\pi\)
−0.0179603 + 0.999839i \(0.505717\pi\)
\(132\) 0 0
\(133\) 5.52086i 0.478720i
\(134\) 0 0
\(135\) −13.4491 0.638942i −1.15752 0.0549914i
\(136\) 0 0
\(137\) 8.32825 + 18.2363i 0.711530 + 1.55803i 0.825407 + 0.564539i \(0.190946\pi\)
−0.113876 + 0.993495i \(0.536327\pi\)
\(138\) 0 0
\(139\) −1.43656 4.89247i −0.121847 0.414974i 0.875867 0.482553i \(-0.160291\pi\)
−0.997714 + 0.0675796i \(0.978472\pi\)
\(140\) 0 0
\(141\) 1.92580 9.20564i 0.162182 0.775255i
\(142\) 0 0
\(143\) 19.4600 + 16.8622i 1.62733 + 1.41009i
\(144\) 0 0
\(145\) −0.221579 0.754630i −0.0184012 0.0626686i
\(146\) 0 0
\(147\) −24.8336 13.3041i −2.04824 1.09731i
\(148\) 0 0
\(149\) −11.0450 + 9.57056i −0.904843 + 0.784051i −0.976977 0.213344i \(-0.931565\pi\)
0.0721340 + 0.997395i \(0.477019\pi\)
\(150\) 0 0
\(151\) −1.67622 + 11.6584i −0.136409 + 0.948743i 0.800541 + 0.599278i \(0.204546\pi\)
−0.936949 + 0.349465i \(0.886363\pi\)
\(152\) 0 0
\(153\) 0.112879 + 0.705061i 0.00912575 + 0.0570008i
\(154\) 0 0
\(155\) 6.45442 21.9818i 0.518432 1.76562i
\(156\) 0 0
\(157\) 2.48920 + 5.45059i 0.198660 + 0.435005i 0.982576 0.185863i \(-0.0595079\pi\)
−0.783916 + 0.620867i \(0.786781\pi\)
\(158\) 0 0
\(159\) 11.5039 + 6.16299i 0.912316 + 0.488757i
\(160\) 0 0
\(161\) −9.36305 2.74924i −0.737912 0.216671i
\(162\) 0 0
\(163\) 14.7249 1.15334 0.576672 0.816976i \(-0.304351\pi\)
0.576672 + 0.816976i \(0.304351\pi\)
\(164\) 0 0
\(165\) 1.78262 28.0686i 0.138776 2.18514i
\(166\) 0 0
\(167\) 13.1615 11.4045i 1.01847 0.882507i 0.0253561 0.999678i \(-0.491928\pi\)
0.993112 + 0.117171i \(0.0373826\pi\)
\(168\) 0 0
\(169\) −1.61330 + 3.53263i −0.124100 + 0.271741i
\(170\) 0 0
\(171\) −1.81012 + 2.91792i −0.138424 + 0.223139i
\(172\) 0 0
\(173\) −4.64811 + 7.23260i −0.353389 + 0.549885i −0.971751 0.236009i \(-0.924160\pi\)
0.618361 + 0.785894i \(0.287797\pi\)
\(174\) 0 0
\(175\) 8.18497 + 1.17682i 0.618725 + 0.0889593i
\(176\) 0 0
\(177\) 5.56116 + 14.5545i 0.418003 + 1.09398i
\(178\) 0 0
\(179\) 5.22231 11.4353i 0.390334 0.854712i −0.607826 0.794070i \(-0.707958\pi\)
0.998160 0.0606413i \(-0.0193146\pi\)
\(180\) 0 0
\(181\) 7.27604 + 15.9323i 0.540824 + 1.18424i 0.960937 + 0.276767i \(0.0892631\pi\)
−0.420113 + 0.907472i \(0.638010\pi\)
\(182\) 0 0
\(183\) 1.01393 + 1.33217i 0.0749520 + 0.0984771i
\(184\) 0 0
\(185\) 5.48063 1.60926i 0.402944 0.118315i
\(186\) 0 0
\(187\) −1.47635 + 0.212268i −0.107962 + 0.0155226i
\(188\) 0 0
\(189\) 12.5344 + 21.7039i 0.911746 + 1.57873i
\(190\) 0 0
\(191\) −3.15748 + 6.91391i −0.228467 + 0.500273i −0.988797 0.149264i \(-0.952310\pi\)
0.760331 + 0.649536i \(0.225037\pi\)
\(192\) 0 0
\(193\) −1.55588 0.999901i −0.111994 0.0719744i 0.483445 0.875375i \(-0.339385\pi\)
−0.595439 + 0.803401i \(0.703022\pi\)
\(194\) 0 0
\(195\) 17.9882 4.06361i 1.28816 0.291001i
\(196\) 0 0
\(197\) −1.04976 7.30122i −0.0747921 0.520190i −0.992434 0.122781i \(-0.960819\pi\)
0.917642 0.397409i \(-0.130091\pi\)
\(198\) 0 0
\(199\) 11.1805 12.9029i 0.792562 0.914665i −0.205387 0.978681i \(-0.565845\pi\)
0.997949 + 0.0640159i \(0.0203909\pi\)
\(200\) 0 0
\(201\) −0.178426 + 14.1763i −0.0125852 + 0.999921i
\(202\) 0 0
\(203\) −0.958729 + 1.10643i −0.0672896 + 0.0776563i
\(204\) 0 0
\(205\) −1.68107 11.6921i −0.117411 0.816612i
\(206\) 0 0
\(207\) 4.04722 + 4.52290i 0.281301 + 0.314364i
\(208\) 0 0
\(209\) −6.03406 3.87785i −0.417384 0.268237i
\(210\) 0 0
\(211\) 5.83106 12.7682i 0.401427 0.879002i −0.595697 0.803209i \(-0.703124\pi\)
0.997124 0.0757924i \(-0.0241486\pi\)
\(212\) 0 0
\(213\) 13.2823 24.7928i 0.910087 1.69877i
\(214\) 0 0
\(215\) −9.60734 + 1.38133i −0.655215 + 0.0942057i
\(216\) 0 0
\(217\) −40.9182 + 12.0147i −2.77771 + 0.815609i
\(218\) 0 0
\(219\) −19.0056 + 14.4654i −1.28428 + 0.977482i
\(220\) 0 0
\(221\) −0.406271 0.889609i −0.0273287 0.0598416i
\(222\) 0 0
\(223\) 9.47470 20.7467i 0.634473 1.38930i −0.270037 0.962850i \(-0.587036\pi\)
0.904510 0.426452i \(-0.140237\pi\)
\(224\) 0 0
\(225\) −3.94012 3.30558i −0.262675 0.220372i
\(226\) 0 0
\(227\) −8.02748 1.15418i −0.532802 0.0766054i −0.129338 0.991601i \(-0.541285\pi\)
−0.403465 + 0.914995i \(0.632194\pi\)
\(228\) 0 0
\(229\) −5.96495 + 9.28164i −0.394175 + 0.613348i −0.980451 0.196763i \(-0.936957\pi\)
0.586276 + 0.810111i \(0.300593\pi\)
\(230\) 0 0
\(231\) −45.7484 + 25.4563i −3.01003 + 1.67490i
\(232\) 0 0
\(233\) 6.11597 13.3921i 0.400671 0.877346i −0.596531 0.802590i \(-0.703455\pi\)
0.997202 0.0747565i \(-0.0238180\pi\)
\(234\) 0 0
\(235\) 10.6335 9.21395i 0.693651 0.601052i
\(236\) 0 0
\(237\) 3.77591 + 0.239805i 0.245272 + 0.0155770i
\(238\) 0 0
\(239\) 22.8427 1.47757 0.738784 0.673942i \(-0.235400\pi\)
0.738784 + 0.673942i \(0.235400\pi\)
\(240\) 0 0
\(241\) 11.3059 + 3.31970i 0.728275 + 0.213841i 0.624793 0.780791i \(-0.285183\pi\)
0.103482 + 0.994631i \(0.467002\pi\)
\(242\) 0 0
\(243\) 0.491277 15.5807i 0.0315154 0.999503i
\(244\) 0 0
\(245\) −17.5087 38.3387i −1.11859 2.44937i
\(246\) 0 0
\(247\) 1.32501 4.51257i 0.0843084 0.287128i
\(248\) 0 0
\(249\) −6.32776 2.30281i −0.401006 0.145935i
\(250\) 0 0
\(251\) −0.266123 + 1.85092i −0.0167975 + 0.116829i −0.996495 0.0836521i \(-0.973342\pi\)
0.979698 + 0.200481i \(0.0642506\pi\)
\(252\) 0 0
\(253\) −9.58140 + 8.30233i −0.602378 + 0.521963i
\(254\) 0 0
\(255\) −0.504454 + 0.941615i −0.0315901 + 0.0589662i
\(256\) 0 0
\(257\) −4.67380 15.9175i −0.291544 0.992907i −0.966845 0.255365i \(-0.917805\pi\)
0.675301 0.737542i \(-0.264014\pi\)
\(258\) 0 0
\(259\) −8.03565 6.96293i −0.499311 0.432655i
\(260\) 0 0
\(261\) 0.869478 0.270439i 0.0538193 0.0167398i
\(262\) 0 0
\(263\) −3.07107 10.4591i −0.189370 0.644935i −0.998367 0.0571226i \(-0.981807\pi\)
0.808997 0.587813i \(-0.200011\pi\)
\(264\) 0 0
\(265\) 8.11071 + 17.7600i 0.498237 + 1.09099i
\(266\) 0 0
\(267\) 16.4385 9.14707i 1.00602 0.559792i
\(268\) 0 0
\(269\) 12.6511i 0.771353i −0.922634 0.385676i \(-0.873968\pi\)
0.922634 0.385676i \(-0.126032\pi\)
\(270\) 0 0
\(271\) 16.8404 7.69077i 1.02298 0.467181i 0.167973 0.985792i \(-0.446278\pi\)
0.855011 + 0.518610i \(0.173550\pi\)
\(272\) 0 0
\(273\) −24.4665 24.0793i −1.48078 1.45734i
\(274\) 0 0
\(275\) 7.03533 8.11920i 0.424246 0.489606i
\(276\) 0 0
\(277\) −2.76721 + 3.19353i −0.166265 + 0.191880i −0.832768 0.553622i \(-0.813245\pi\)
0.666503 + 0.745503i \(0.267791\pi\)
\(278\) 0 0
\(279\) 25.5656 + 7.06578i 1.53057 + 0.423017i
\(280\) 0 0
\(281\) −1.13085 + 0.726751i −0.0674606 + 0.0433543i −0.573936 0.818900i \(-0.694584\pi\)
0.506476 + 0.862254i \(0.330948\pi\)
\(282\) 0 0
\(283\) −11.0999 12.8100i −0.659821 0.761474i 0.322927 0.946424i \(-0.395333\pi\)
−0.982748 + 0.184950i \(0.940788\pi\)
\(284\) 0 0
\(285\) −4.79868 + 1.83354i −0.284249 + 0.108610i
\(286\) 0 0
\(287\) −16.6176 + 14.3992i −0.980906 + 0.849960i
\(288\) 0 0
\(289\) −16.2570 4.77349i −0.956296 0.280794i
\(290\) 0 0
\(291\) 3.89387 + 2.86674i 0.228263 + 0.168051i
\(292\) 0 0
\(293\) 12.9485 + 20.1483i 0.756460 + 1.17708i 0.979338 + 0.202229i \(0.0648185\pi\)
−0.222878 + 0.974846i \(0.571545\pi\)
\(294\) 0 0
\(295\) −6.56699 + 22.3651i −0.382345 + 1.30215i
\(296\) 0 0
\(297\) 32.5256 + 1.54522i 1.88732 + 0.0896630i
\(298\) 0 0
\(299\) −6.99323 4.49428i −0.404429 0.259911i
\(300\) 0 0
\(301\) 11.8318 + 13.6546i 0.681972 + 0.787037i
\(302\) 0 0
\(303\) −31.7913 + 2.52877i −1.82636 + 0.145274i
\(304\) 0 0
\(305\) 2.50457i 0.143411i
\(306\) 0 0
\(307\) −17.6161 11.3212i −1.00541 0.646135i −0.0692060 0.997602i \(-0.522047\pi\)
−0.936200 + 0.351467i \(0.885683\pi\)
\(308\) 0 0
\(309\) 20.0408 7.65745i 1.14008 0.435617i
\(310\) 0 0
\(311\) −3.81967 + 26.5664i −0.216593 + 1.50644i 0.533892 + 0.845553i \(0.320729\pi\)
−0.750485 + 0.660887i \(0.770180\pi\)
\(312\) 0 0
\(313\) −7.13321 3.25763i −0.403193 0.184132i 0.203488 0.979077i \(-0.434772\pi\)
−0.606681 + 0.794945i \(0.707499\pi\)
\(314\) 0 0
\(315\) −4.74350 + 37.1944i −0.267266 + 2.09567i
\(316\) 0 0
\(317\) 27.3537 3.93286i 1.53633 0.220892i 0.678416 0.734678i \(-0.262667\pi\)
0.857918 + 0.513786i \(0.171757\pi\)
\(318\) 0 0
\(319\) 0.535870 + 1.82501i 0.0300030 + 0.102181i
\(320\) 0 0
\(321\) −0.534188 0.701852i −0.0298154 0.0391736i
\(322\) 0 0
\(323\) 0.147286 + 0.229181i 0.00819519 + 0.0127520i
\(324\) 0 0
\(325\) 6.40768 + 2.92629i 0.355434 + 0.162321i
\(326\) 0 0
\(327\) 27.8956 + 1.77163i 1.54263 + 0.0979712i
\(328\) 0 0
\(329\) −25.1301 7.37885i −1.38546 0.406809i
\(330\) 0 0
\(331\) −5.45068 + 0.783689i −0.299596 + 0.0430755i −0.290474 0.956883i \(-0.593813\pi\)
−0.00912255 + 0.999958i \(0.502904\pi\)
\(332\) 0 0
\(333\) 1.96411 + 6.31473i 0.107633 + 0.346045i
\(334\) 0 0
\(335\) −13.0571 + 16.7145i −0.713384 + 0.913212i
\(336\) 0 0
\(337\) 9.65316 + 8.36451i 0.525841 + 0.455644i 0.876875 0.480719i \(-0.159624\pi\)
−0.351033 + 0.936363i \(0.614170\pi\)
\(338\) 0 0
\(339\) −9.36825 + 7.13028i −0.508814 + 0.387264i
\(340\) 0 0
\(341\) −15.6094 + 53.1609i −0.845299 + 2.87882i
\(342\) 0 0
\(343\) −24.1623 + 37.5973i −1.30464 + 2.03006i
\(344\) 0 0
\(345\) 0.719968 + 9.05133i 0.0387618 + 0.487307i
\(346\) 0 0
\(347\) −1.27673 + 0.820506i −0.0685386 + 0.0440471i −0.574461 0.818532i \(-0.694788\pi\)
0.505923 + 0.862579i \(0.331152\pi\)
\(348\) 0 0
\(349\) −1.05529 7.33972i −0.0564885 0.392886i −0.998377 0.0569591i \(-0.981860\pi\)
0.941888 0.335927i \(-0.109050\pi\)
\(350\) 0 0
\(351\) 5.03629 + 20.7483i 0.268817 + 1.10746i
\(352\) 0 0
\(353\) 3.05627 + 21.2568i 0.162669 + 1.13139i 0.893577 + 0.448910i \(0.148188\pi\)
−0.730908 + 0.682476i \(0.760903\pi\)
\(354\) 0 0
\(355\) 38.2757 17.4799i 2.03146 0.927739i
\(356\) 0 0
\(357\) 1.98221 0.157670i 0.104910 0.00834480i
\(358\) 0 0
\(359\) 11.3677 + 1.63442i 0.599962 + 0.0862615i 0.435603 0.900139i \(-0.356535\pi\)
0.164359 + 0.986401i \(0.447444\pi\)
\(360\) 0 0
\(361\) 2.51754 17.5099i 0.132502 0.921571i
\(362\) 0 0
\(363\) −3.10352 + 48.8672i −0.162892 + 2.56487i
\(364\) 0 0
\(365\) −35.7318 −1.87029
\(366\) 0 0
\(367\) −17.9406 8.19319i −0.936491 0.427681i −0.112097 0.993697i \(-0.535757\pi\)
−0.824394 + 0.566016i \(0.808484\pi\)
\(368\) 0 0
\(369\) 13.5039 2.16195i 0.702984 0.112547i
\(370\) 0 0
\(371\) 19.6490 30.5744i 1.02012 1.58734i
\(372\) 0 0
\(373\) 4.59919i 0.238137i 0.992886 + 0.119069i \(0.0379908\pi\)
−0.992886 + 0.119069i \(0.962009\pi\)
\(374\) 0 0
\(375\) 3.24937 + 14.3838i 0.167797 + 0.742777i
\(376\) 0 0
\(377\) −1.04918 + 0.674266i −0.0540354 + 0.0347264i
\(378\) 0 0
\(379\) 21.4242 9.78412i 1.10049 0.502576i 0.219452 0.975623i \(-0.429573\pi\)
0.881037 + 0.473047i \(0.156846\pi\)
\(380\) 0 0
\(381\) −2.38790 10.5704i −0.122336 0.541537i
\(382\) 0 0
\(383\) 21.9247 + 25.3025i 1.12030 + 1.29290i 0.951638 + 0.307223i \(0.0993996\pi\)
0.168663 + 0.985674i \(0.446055\pi\)
\(384\) 0 0
\(385\) −77.5262 11.1466i −3.95110 0.568083i
\(386\) 0 0
\(387\) −1.77646 11.0961i −0.0903028 0.564045i
\(388\) 0 0
\(389\) 7.57002 + 11.7792i 0.383815 + 0.597228i 0.978379 0.206820i \(-0.0663116\pi\)
−0.594564 + 0.804049i \(0.702675\pi\)
\(390\) 0 0
\(391\) 0.462021 0.135662i 0.0233654 0.00686071i
\(392\) 0 0
\(393\) 3.50469 16.7530i 0.176788 0.845077i
\(394\) 0 0
\(395\) 4.27776 + 3.70670i 0.215237 + 0.186504i
\(396\) 0 0
\(397\) 15.7692 4.63025i 0.791433 0.232386i 0.139060 0.990284i \(-0.455592\pi\)
0.652373 + 0.757898i \(0.273774\pi\)
\(398\) 0 0
\(399\) 7.70057 + 5.66930i 0.385511 + 0.283820i
\(400\) 0 0
\(401\) −23.8879 −1.19290 −0.596452 0.802648i \(-0.703424\pi\)
−0.596452 + 0.802648i \(0.703424\pi\)
\(402\) 0 0
\(403\) −36.3287 −1.80966
\(404\) 0 0
\(405\) 14.7020 18.1029i 0.730547 0.899541i
\(406\) 0 0
\(407\) −13.2544 + 3.89185i −0.656997 + 0.192912i
\(408\) 0 0
\(409\) 3.01750 + 2.61468i 0.149206 + 0.129288i 0.726265 0.687415i \(-0.241254\pi\)
−0.577059 + 0.816702i \(0.695800\pi\)
\(410\) 0 0
\(411\) −33.9884 7.11030i −1.67653 0.350725i
\(412\) 0 0
\(413\) 41.6318 12.2242i 2.04857 0.601514i
\(414\) 0 0
\(415\) −5.44639 8.47474i −0.267353 0.416009i
\(416\) 0 0
\(417\) 8.29926 + 3.02028i 0.406417 + 0.147904i
\(418\) 0 0
\(419\) 4.20561 + 0.604675i 0.205457 + 0.0295403i 0.244275 0.969706i \(-0.421450\pi\)
−0.0388176 + 0.999246i \(0.512359\pi\)
\(420\) 0 0
\(421\) −3.22520 3.72208i −0.157187 0.181403i 0.671694 0.740829i \(-0.265567\pi\)
−0.828880 + 0.559426i \(0.811022\pi\)
\(422\) 0 0
\(423\) 10.8626 + 12.1393i 0.528156 + 0.590232i
\(424\) 0 0
\(425\) −0.371168 + 0.169507i −0.0180043 + 0.00822228i
\(426\) 0 0
\(427\) 3.92206 2.52056i 0.189802 0.121978i
\(428\) 0 0
\(429\) −43.5028 + 9.82749i −2.10034 + 0.474475i
\(430\) 0 0
\(431\) 36.6610i 1.76590i −0.469468 0.882949i \(-0.655554\pi\)
0.469468 0.882949i \(-0.344446\pi\)
\(432\) 0 0
\(433\) −3.85517 + 5.99876i −0.185268 + 0.288282i −0.921447 0.388505i \(-0.872992\pi\)
0.736179 + 0.676787i \(0.236628\pi\)
\(434\) 0 0
\(435\) 1.28010 + 0.465858i 0.0613763 + 0.0223362i
\(436\) 0 0
\(437\) 2.10637 + 0.961947i 0.100761 + 0.0460161i
\(438\) 0 0
\(439\) 16.9963 0.811187 0.405593 0.914054i \(-0.367065\pi\)
0.405593 + 0.914054i \(0.367065\pi\)
\(440\) 0 0
\(441\) 44.0581 20.9763i 2.09800 0.998873i
\(442\) 0 0
\(443\) −5.83435 + 40.5788i −0.277198 + 1.92796i 0.0861059 + 0.996286i \(0.472558\pi\)
−0.363304 + 0.931671i \(0.618351\pi\)
\(444\) 0 0
\(445\) 27.8571 + 4.00524i 1.32055 + 0.189867i
\(446\) 0 0
\(447\) −2.00715 25.2336i −0.0949351 1.19351i
\(448\) 0 0
\(449\) 14.1335 6.45457i 0.667003 0.304610i −0.0529862 0.998595i \(-0.516874\pi\)
0.719989 + 0.693985i \(0.244147\pi\)
\(450\) 0 0
\(451\) 4.06552 + 28.2763i 0.191438 + 1.33148i
\(452\) 0 0
\(453\) −14.5399 14.3098i −0.683146 0.672334i
\(454\) 0 0
\(455\) −7.30873 50.8333i −0.342639 2.38310i
\(456\) 0 0
\(457\) −14.0626 + 9.03746i −0.657819 + 0.422755i −0.826516 0.562913i \(-0.809680\pi\)
0.168697 + 0.985668i \(0.446044\pi\)
\(458\) 0 0
\(459\) −1.09934 0.566573i −0.0513129 0.0264454i
\(460\) 0 0
\(461\) 6.54290 10.1810i 0.304733 0.474175i −0.654787 0.755813i \(-0.727242\pi\)
0.959520 + 0.281639i \(0.0908780\pi\)
\(462\) 0 0
\(463\) 2.13123 7.25830i 0.0990466 0.337322i −0.895030 0.446007i \(-0.852846\pi\)
0.994076 + 0.108685i \(0.0346639\pi\)
\(464\) 0 0
\(465\) 24.0325 + 31.5755i 1.11448 + 1.46428i
\(466\) 0 0
\(467\) 7.55982 + 6.55062i 0.349827 + 0.303127i 0.811994 0.583666i \(-0.198382\pi\)
−0.462167 + 0.886793i \(0.652928\pi\)
\(468\) 0 0
\(469\) 39.3147 + 3.62566i 1.81539 + 0.167417i
\(470\) 0 0
\(471\) −10.1587 2.12517i −0.468088 0.0979228i
\(472\) 0 0
\(473\) 23.2345 3.34061i 1.06832 0.153602i
\(474\) 0 0
\(475\) −1.88276 0.552828i −0.0863869 0.0253655i
\(476\) 0 0
\(477\) −20.4094 + 9.71704i −0.934482 + 0.444913i
\(478\) 0 0
\(479\) −20.9351 9.56076i −0.956551 0.436842i −0.124917 0.992167i \(-0.539867\pi\)
−0.831633 + 0.555325i \(0.812594\pi\)
\(480\) 0 0
\(481\) −4.89697 7.61983i −0.223283 0.347434i
\(482\) 0 0
\(483\) 13.4495 10.2365i 0.611972 0.465779i
\(484\) 0 0
\(485\) 2.03800 + 6.94080i 0.0925409 + 0.315166i
\(486\) 0 0
\(487\) 25.6875 3.69331i 1.16401 0.167360i 0.466892 0.884314i \(-0.345374\pi\)
0.697120 + 0.716955i \(0.254465\pi\)
\(488\) 0 0
\(489\) −15.1208 + 20.5385i −0.683788 + 0.928783i
\(490\) 0 0
\(491\) −27.6162 12.6119i −1.24630 0.569166i −0.320525 0.947240i \(-0.603859\pi\)
−0.925775 + 0.378074i \(0.876586\pi\)
\(492\) 0 0
\(493\) 0.0102811 0.0715069i 0.000463039 0.00322051i
\(494\) 0 0
\(495\) 37.3200 + 31.3098i 1.67741 + 1.40727i
\(496\) 0 0
\(497\) −65.8930 42.3468i −2.95570 1.89952i
\(498\) 0 0
\(499\) 19.1108i 0.855517i −0.903893 0.427758i \(-0.859303\pi\)
0.903893 0.427758i \(-0.140697\pi\)
\(500\) 0 0
\(501\) 2.39177 + 30.0690i 0.106856 + 1.34338i
\(502\) 0 0
\(503\) −24.0623 27.7693i −1.07288 1.23817i −0.969903 0.243491i \(-0.921708\pi\)
−0.102981 0.994683i \(-0.532838\pi\)
\(504\) 0 0
\(505\) −40.1372 25.7946i −1.78608 1.14784i
\(506\) 0 0
\(507\) −3.27068 5.87787i −0.145256 0.261045i
\(508\) 0 0
\(509\) −0.587268 + 2.00005i −0.0260302 + 0.0886507i −0.971484 0.237106i \(-0.923801\pi\)
0.945453 + 0.325757i \(0.105619\pi\)
\(510\) 0 0
\(511\) 35.9599 + 55.9547i 1.59077 + 2.47529i
\(512\) 0 0
\(513\) −2.21115 5.52115i −0.0976248 0.243765i
\(514\) 0 0
\(515\) 30.7957 + 9.04243i 1.35702 + 0.398457i
\(516\) 0 0
\(517\) −25.7161 + 22.2831i −1.13099 + 0.980011i
\(518\) 0 0
\(519\) −5.31504 13.9103i −0.233304 0.610595i
\(520\) 0 0
\(521\) −4.40009 5.07797i −0.192771 0.222470i 0.651133 0.758964i \(-0.274294\pi\)
−0.843904 + 0.536494i \(0.819749\pi\)
\(522\) 0 0
\(523\) 34.4842 22.1616i 1.50789 0.969061i 0.514105 0.857727i \(-0.328124\pi\)
0.993783 0.111333i \(-0.0355121\pi\)
\(524\) 0 0
\(525\) −10.0465 + 10.2080i −0.438464 + 0.445515i
\(526\) 0 0
\(527\) 1.37806 1.59037i 0.0600293 0.0692775i
\(528\) 0 0
\(529\) −12.3815 + 14.2890i −0.538325 + 0.621260i
\(530\) 0 0
\(531\) −26.0114 7.18901i −1.12880 0.311976i
\(532\) 0 0
\(533\) −17.0385 + 7.78122i −0.738019 + 0.337042i
\(534\) 0 0
\(535\) 1.31953i 0.0570482i
\(536\) 0 0
\(537\) 10.5873 + 19.0269i 0.456877 + 0.821070i
\(538\) 0 0
\(539\) 42.3433 + 92.7188i 1.82385 + 3.99368i
\(540\) 0 0
\(541\) 6.48103 + 22.0724i 0.278641 + 0.948965i 0.973283 + 0.229609i \(0.0737447\pi\)
−0.694642 + 0.719356i \(0.744437\pi\)
\(542\) 0 0
\(543\) −29.6943 6.21197i −1.27430 0.266581i
\(544\) 0 0
\(545\) 31.6031 + 27.3842i 1.35373 + 1.17301i
\(546\) 0 0
\(547\) −11.8312 40.2932i −0.505864 1.72281i −0.675548 0.737316i \(-0.736093\pi\)
0.169684 0.985499i \(-0.445725\pi\)
\(548\) 0 0
\(549\) −2.89933 + 0.0462530i −0.123740 + 0.00197403i
\(550\) 0 0
\(551\) 0.262553 0.227504i 0.0111852 0.00969199i
\(552\) 0 0
\(553\) 1.49949 10.4292i 0.0637647 0.443493i
\(554\) 0 0
\(555\) −3.38338 + 9.29698i −0.143616 + 0.394635i
\(556\) 0 0
\(557\) 1.65371 5.63203i 0.0700701 0.238637i −0.917010 0.398864i \(-0.869405\pi\)
0.987080 + 0.160227i \(0.0512227\pi\)
\(558\) 0 0
\(559\) 6.39379 + 14.0004i 0.270428 + 0.592156i
\(560\) 0 0
\(561\) 1.21998 2.27721i 0.0515074 0.0961440i
\(562\) 0 0
\(563\) −20.3288 5.96908i −0.856757 0.251567i −0.176284 0.984339i \(-0.556408\pi\)
−0.680473 + 0.732773i \(0.738226\pi\)
\(564\) 0 0
\(565\) −17.6129 −0.740981
\(566\) 0 0
\(567\) −43.1443 4.80425i −1.81189 0.201760i
\(568\) 0 0
\(569\) 5.19009 4.49724i 0.217580 0.188534i −0.539250 0.842145i \(-0.681292\pi\)
0.756830 + 0.653611i \(0.226747\pi\)
\(570\) 0 0
\(571\) −8.43609 + 18.4725i −0.353040 + 0.773049i 0.646906 + 0.762570i \(0.276063\pi\)
−0.999945 + 0.0104787i \(0.996664\pi\)
\(572\) 0 0
\(573\) −6.40123 11.5039i −0.267415 0.480582i
\(574\) 0 0
\(575\) −1.87513 + 2.91775i −0.0781982 + 0.121679i
\(576\) 0 0
\(577\) 35.6420 + 5.12454i 1.48379 + 0.213337i 0.836106 0.548568i \(-0.184827\pi\)
0.647688 + 0.761906i \(0.275736\pi\)
\(578\) 0 0
\(579\) 2.99238 1.14337i 0.124359 0.0475168i
\(580\) 0 0
\(581\) −7.78998 + 17.0577i −0.323183 + 0.707672i
\(582\) 0 0
\(583\) −19.6150 42.9509i −0.812371 1.77884i
\(584\) 0 0
\(585\) −12.8039 + 29.2630i −0.529374 + 1.20988i
\(586\) 0 0
\(587\) −3.18875 + 0.936301i −0.131614 + 0.0386453i −0.346876 0.937911i \(-0.612758\pi\)
0.215262 + 0.976556i \(0.430939\pi\)
\(588\) 0 0
\(589\) 10.0167 1.44018i 0.412731 0.0593418i
\(590\) 0 0
\(591\) 11.2618 + 6.03332i 0.463249 + 0.248177i
\(592\) 0 0
\(593\) −3.67919 + 8.05629i −0.151086 + 0.330832i −0.970008 0.243072i \(-0.921845\pi\)
0.818922 + 0.573905i \(0.194572\pi\)
\(594\) 0 0
\(595\) 2.50258 + 1.60831i 0.102596 + 0.0659342i
\(596\) 0 0
\(597\) 6.51611 + 28.8445i 0.266687 + 1.18053i
\(598\) 0 0
\(599\) −2.55166 17.7472i −0.104258 0.725129i −0.973157 0.230141i \(-0.926081\pi\)
0.868900 0.494988i \(-0.164828\pi\)
\(600\) 0 0
\(601\) 4.28571 4.94597i 0.174818 0.201750i −0.661578 0.749876i \(-0.730113\pi\)
0.836396 + 0.548126i \(0.184658\pi\)
\(602\) 0 0
\(603\) −19.5901 14.8064i −0.797770 0.602962i
\(604\) 0 0
\(605\) −47.9714 + 55.3620i −1.95032 + 2.25079i
\(606\) 0 0
\(607\) −2.81396 19.5715i −0.114215 0.794384i −0.963741 0.266838i \(-0.914021\pi\)
0.849526 0.527546i \(-0.176888\pi\)
\(608\) 0 0
\(609\) −0.558759 2.47343i −0.0226421 0.100228i
\(610\) 0 0
\(611\) −18.7696 12.0625i −0.759335 0.487995i
\(612\) 0 0
\(613\) 7.55708 16.5477i 0.305228 0.668355i −0.693410 0.720544i \(-0.743892\pi\)
0.998637 + 0.0521884i \(0.0166196\pi\)
\(614\) 0 0
\(615\) 18.0346 + 9.66169i 0.727224 + 0.389597i
\(616\) 0 0
\(617\) 4.53596 0.652173i 0.182611 0.0262555i −0.0504026 0.998729i \(-0.516050\pi\)
0.233014 + 0.972473i \(0.425141\pi\)
\(618\) 0 0
\(619\) 11.7426 3.44793i 0.471973 0.138584i −0.0370918 0.999312i \(-0.511809\pi\)
0.509065 + 0.860728i \(0.329991\pi\)
\(620\) 0 0
\(621\) −10.4646 + 1.00060i −0.419932 + 0.0401527i
\(622\) 0 0
\(623\) −21.7628 47.6540i −0.871910 1.90922i
\(624\) 0 0
\(625\) −12.7253 + 27.8646i −0.509013 + 1.11458i
\(626\) 0 0
\(627\) 11.6052 4.43426i 0.463466 0.177087i
\(628\) 0 0
\(629\) 0.519331 + 0.0746685i 0.0207071 + 0.00297723i
\(630\) 0 0
\(631\) 1.62062 2.52174i 0.0645160 0.100389i −0.807497 0.589872i \(-0.799178\pi\)
0.872013 + 0.489483i \(0.162815\pi\)
\(632\) 0 0
\(633\) 11.8215 + 21.2448i 0.469861 + 0.844404i
\(634\) 0 0
\(635\) 6.73477 14.7471i 0.267261 0.585221i
\(636\) 0 0
\(637\) −50.5103 + 43.7674i −2.00129 + 1.73413i
\(638\) 0 0
\(639\) 20.9419 + 43.9857i 0.828447 + 1.74005i
\(640\) 0 0
\(641\) 40.6694 1.60634 0.803172 0.595747i \(-0.203144\pi\)
0.803172 + 0.595747i \(0.203144\pi\)
\(642\) 0 0
\(643\) −8.09347 2.37646i −0.319175 0.0937183i 0.118221 0.992987i \(-0.462281\pi\)
−0.437396 + 0.899269i \(0.644099\pi\)
\(644\) 0 0
\(645\) 7.93896 14.8189i 0.312596 0.583494i
\(646\) 0 0
\(647\) 12.7390 + 27.8944i 0.500820 + 1.09664i 0.976202 + 0.216864i \(0.0695827\pi\)
−0.475382 + 0.879780i \(0.657690\pi\)
\(648\) 0 0
\(649\) 15.8817 54.0880i 0.623410 2.12314i
\(650\) 0 0
\(651\) 25.2602 69.4110i 0.990025 2.72043i
\(652\) 0 0
\(653\) 5.75048 39.9955i 0.225034 1.56514i −0.493559 0.869712i \(-0.664304\pi\)
0.718593 0.695431i \(-0.244787\pi\)
\(654\) 0 0
\(655\) 19.3514 16.7681i 0.756123 0.655185i
\(656\) 0 0
\(657\) −0.659876 41.3637i −0.0257442 1.61375i
\(658\) 0 0
\(659\) 3.02418 + 10.2994i 0.117805 + 0.401208i 0.997191 0.0749021i \(-0.0238644\pi\)
−0.879385 + 0.476110i \(0.842046\pi\)
\(660\) 0 0
\(661\) −0.415841 0.360328i −0.0161743 0.0140151i 0.646736 0.762714i \(-0.276134\pi\)
−0.662910 + 0.748699i \(0.730679\pi\)
\(662\) 0 0
\(663\) 1.65803 + 0.346857i 0.0643927 + 0.0134708i
\(664\) 0 0
\(665\) 4.03038 + 13.7262i 0.156292 + 0.532280i
\(666\) 0 0
\(667\) −0.255088 0.558566i −0.00987707 0.0216278i
\(668\) 0 0
\(669\) 19.2083 + 34.5200i 0.742636 + 1.33462i
\(670\) 0 0
\(671\) 6.05708i 0.233831i
\(672\) 0 0
\(673\) −20.7848 + 9.49212i −0.801197 + 0.365894i −0.773560 0.633724i \(-0.781526\pi\)
−0.0276375 + 0.999618i \(0.508798\pi\)
\(674\) 0 0
\(675\) 8.65672 2.10127i 0.333197 0.0808778i
\(676\) 0 0
\(677\) 14.3718 16.5859i 0.552352 0.637449i −0.409077 0.912500i \(-0.634149\pi\)
0.961430 + 0.275051i \(0.0886948\pi\)
\(678\) 0 0
\(679\) 8.81802 10.1765i 0.338405 0.390540i
\(680\) 0 0
\(681\) 9.85318 10.0116i 0.377575 0.383646i
\(682\) 0 0
\(683\) 36.2668 23.3072i 1.38771 0.891827i 0.388152 0.921595i \(-0.373113\pi\)
0.999557 + 0.0297686i \(0.00947704\pi\)
\(684\) 0 0
\(685\) −34.0191 39.2601i −1.29980 1.50005i
\(686\) 0 0
\(687\) −6.82082 17.8512i −0.260230 0.681065i
\(688\) 0 0
\(689\) 23.3983 20.2747i 0.891404 0.772406i
\(690\) 0 0
\(691\) −18.4515 5.41786i −0.701929 0.206105i −0.0887557 0.996053i \(-0.528289\pi\)
−0.613173 + 0.789948i \(0.710107\pi\)
\(692\) 0 0
\(693\) 11.4717 89.9513i 0.435775 3.41697i
\(694\) 0 0
\(695\) 7.14328 + 11.1152i 0.270960 + 0.421622i
\(696\) 0 0
\(697\) 0.305683 1.04106i 0.0115786 0.0394330i
\(698\) 0 0
\(699\) 12.3991 + 22.2828i 0.468976 + 0.842814i
\(700\) 0 0
\(701\) −10.9597 7.04335i −0.413941 0.266023i 0.317053 0.948408i \(-0.397307\pi\)
−0.730994 + 0.682384i \(0.760943\pi\)
\(702\) 0 0
\(703\) 1.65229 + 1.90684i 0.0623171 + 0.0719178i
\(704\) 0 0
\(705\) 1.93236 + 24.2934i 0.0727771 + 0.914942i
\(706\) 0 0
\(707\) 88.8125i 3.34014i
\(708\) 0 0
\(709\) −21.3951 13.7498i −0.803511 0.516385i 0.0732489 0.997314i \(-0.476663\pi\)
−0.876760 + 0.480929i \(0.840300\pi\)
\(710\) 0 0
\(711\) −4.21192 + 5.02044i −0.157959 + 0.188281i
\(712\) 0 0
\(713\) 2.54558 17.7049i 0.0953328 0.663054i
\(714\) 0 0
\(715\) −60.6922 27.7172i −2.26976 1.03656i
\(716\) 0 0
\(717\) −23.4568 + 31.8612i −0.876012 + 1.18988i
\(718\) 0 0
\(719\) −49.2521 + 7.08138i −1.83679 + 0.264091i −0.971477 0.237134i \(-0.923792\pi\)
−0.865317 + 0.501225i \(0.832883\pi\)
\(720\) 0 0
\(721\) −16.8322 57.3250i −0.626862 2.13490i
\(722\) 0 0
\(723\) −16.2402 + 12.3606i −0.603980 + 0.459696i
\(724\) 0 0
\(725\) 0.281321 + 0.437744i 0.0104480 + 0.0162574i
\(726\) 0 0
\(727\) −29.3484 13.4030i −1.08847 0.497088i −0.211376 0.977405i \(-0.567795\pi\)
−0.877095 + 0.480317i \(0.840522\pi\)
\(728\) 0 0
\(729\) 21.2277 + 16.6849i 0.786211 + 0.617958i
\(730\) 0 0
\(731\) −0.855434 0.251178i −0.0316394 0.00929016i
\(732\) 0 0
\(733\) 6.92412 0.995538i 0.255748 0.0367710i −0.0132482 0.999912i \(-0.504217\pi\)
0.268996 + 0.963141i \(0.413308\pi\)
\(734\) 0 0
\(735\) 71.4548 + 14.9482i 2.63565 + 0.551372i
\(736\) 0 0
\(737\) 31.5773 40.4226i 1.16317 1.48899i
\(738\) 0 0
\(739\) 17.2341 + 14.9334i 0.633966 + 0.549335i 0.911458 0.411393i \(-0.134958\pi\)
−0.277492 + 0.960728i \(0.589503\pi\)
\(740\) 0 0
\(741\) 4.93356 + 6.48204i 0.181239 + 0.238124i
\(742\) 0 0
\(743\) 8.39865 28.6032i 0.308117 1.04935i −0.649274 0.760554i \(-0.724927\pi\)
0.957391 0.288795i \(-0.0932545\pi\)
\(744\) 0 0
\(745\) 20.4739 31.8580i 0.750104 1.16719i
\(746\) 0 0
\(747\) 9.70989 6.46132i 0.355266 0.236407i
\(748\) 0 0
\(749\) −2.06633 + 1.32795i −0.0755021 + 0.0485223i
\(750\) 0 0
\(751\) 4.00492 + 27.8548i 0.146142 + 1.01644i 0.922459 + 0.386095i \(0.126176\pi\)
−0.776318 + 0.630342i \(0.782915\pi\)
\(752\) 0 0
\(753\) −2.30841 2.27188i −0.0841233 0.0827920i
\(754\) 0 0
\(755\) −4.34343 30.2092i −0.158074 1.09943i
\(756\) 0 0
\(757\) 25.1592 11.4898i 0.914428 0.417605i 0.0980883 0.995178i \(-0.468727\pi\)
0.816339 + 0.577573i \(0.196000\pi\)
\(758\) 0 0
\(759\) −1.74118 21.8898i −0.0632008 0.794550i
\(760\) 0 0
\(761\) −37.7010 5.42058i −1.36666 0.196496i −0.580370 0.814353i \(-0.697092\pi\)
−0.786290 + 0.617857i \(0.788001\pi\)
\(762\) 0 0
\(763\) 11.0779 77.0483i 0.401046 2.78934i
\(764\) 0 0
\(765\) −0.795360 1.67055i −0.0287563 0.0603989i
\(766\) 0 0
\(767\) 36.9623 1.33463
\(768\) 0 0
\(769\) −24.3548 11.1224i −0.878255 0.401086i −0.0753250 0.997159i \(-0.523999\pi\)
−0.802930 + 0.596073i \(0.796727\pi\)
\(770\) 0 0
\(771\) 27.0014 + 9.82641i 0.972432 + 0.353889i
\(772\) 0 0
\(773\) 0.211784 0.329542i 0.00761734 0.0118528i −0.837424 0.546554i \(-0.815939\pi\)
0.845041 + 0.534701i \(0.179576\pi\)
\(774\) 0 0
\(775\) 15.1573i 0.544465i
\(776\) 0 0