Properties

Label 804.2.ba.b.41.1
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
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.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.1
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70276 + 0.317213i) q^{3} +(0.152781 - 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(2.79875 - 1.08027i) q^{9} +O(q^{10})\) \(q+(-1.70276 + 0.317213i) q^{3} +(0.152781 - 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(2.79875 - 1.08027i) q^{9} +(-1.16153 + 0.465006i) q^{11} +(-1.83241 - 1.92178i) q^{13} +(0.0769269 + 1.85784i) q^{15} +(-3.09077 + 1.06973i) q^{17} +(6.96190 + 0.664781i) q^{19} +(-1.63025 - 5.68258i) q^{21} +(-6.97890 + 0.332446i) q^{23} +(3.69165 + 1.08397i) q^{25} +(-4.42291 + 2.72724i) q^{27} +(-0.870238 + 0.502432i) q^{29} +(-4.01310 + 4.20882i) q^{31} +(1.83029 - 1.16024i) q^{33} +(3.66006 + 0.174350i) q^{35} +(-3.99087 + 6.91239i) q^{37} +(3.72976 + 2.69105i) q^{39} +(-3.54601 - 0.683437i) q^{41} +(1.94811 + 1.68805i) q^{43} +(-0.720320 - 3.13905i) q^{45} +(-5.36003 + 10.3970i) q^{47} +(-4.56579 + 0.879983i) q^{49} +(4.92350 - 2.80192i) q^{51} +(-4.61898 - 5.33059i) q^{53} +(0.316664 + 1.30531i) q^{55} +(-12.0653 + 1.07645i) q^{57} +(3.82125 + 13.0140i) q^{59} +(-3.61460 + 9.02884i) q^{61} +(4.57851 + 9.15891i) q^{63} +(-2.32208 + 1.65354i) q^{65} +(-7.45395 - 3.38209i) q^{67} +(11.7779 - 2.77987i) q^{69} +(10.5155 + 3.63946i) q^{71} +(-5.63753 - 2.25693i) q^{73} +(-6.62982 - 0.674690i) q^{75} +(-1.95681 - 3.79569i) q^{77} +(-9.16491 + 2.22338i) q^{79} +(6.66602 - 6.04683i) q^{81} +(8.90868 - 11.3283i) q^{83} +(0.664499 + 3.44775i) q^{85} +(1.32242 - 1.13157i) q^{87} +(-7.82886 + 12.1820i) q^{89} +(5.93517 - 6.84955i) q^{91} +(5.49823 - 8.43959i) q^{93} +(1.77006 - 7.29627i) q^{95} +(4.98536 + 2.87830i) q^{97} +(-2.74850 + 2.55620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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
\(3\) −1.70276 + 0.317213i −0.983086 + 0.183143i
\(4\) 0 0
\(5\) 0.152781 1.06262i 0.0683259 0.475217i −0.926716 0.375762i \(-0.877381\pi\)
0.995042 0.0994551i \(-0.0317100\pi\)
\(6\) 0 0
\(7\) 0.324444 + 3.39773i 0.122628 + 1.28422i 0.822010 + 0.569472i \(0.192852\pi\)
−0.699382 + 0.714748i \(0.746541\pi\)
\(8\) 0 0
\(9\) 2.79875 1.08027i 0.932917 0.360091i
\(10\) 0 0
\(11\) −1.16153 + 0.465006i −0.350214 + 0.140204i −0.540098 0.841602i \(-0.681613\pi\)
0.189884 + 0.981806i \(0.439189\pi\)
\(12\) 0 0
\(13\) −1.83241 1.92178i −0.508220 0.533006i 0.418770 0.908092i \(-0.362461\pi\)
−0.926990 + 0.375087i \(0.877613\pi\)
\(14\) 0 0
\(15\) 0.0769269 + 1.85784i 0.0198624 + 0.479693i
\(16\) 0 0
\(17\) −3.09077 + 1.06973i −0.749623 + 0.259447i −0.675053 0.737769i \(-0.735879\pi\)
−0.0745693 + 0.997216i \(0.523758\pi\)
\(18\) 0 0
\(19\) 6.96190 + 0.664781i 1.59717 + 0.152511i 0.855336 0.518074i \(-0.173351\pi\)
0.741833 + 0.670585i \(0.233957\pi\)
\(20\) 0 0
\(21\) −1.63025 5.68258i −0.355750 1.24004i
\(22\) 0 0
\(23\) −6.97890 + 0.332446i −1.45520 + 0.0693197i −0.760200 0.649689i \(-0.774899\pi\)
−0.695001 + 0.719009i \(0.744596\pi\)
\(24\) 0 0
\(25\) 3.69165 + 1.08397i 0.738330 + 0.216793i
\(26\) 0 0
\(27\) −4.42291 + 2.72724i −0.851190 + 0.524858i
\(28\) 0 0
\(29\) −0.870238 + 0.502432i −0.161599 + 0.0932993i −0.578619 0.815598i \(-0.696408\pi\)
0.417019 + 0.908898i \(0.363075\pi\)
\(30\) 0 0
\(31\) −4.01310 + 4.20882i −0.720774 + 0.755926i −0.977586 0.210536i \(-0.932479\pi\)
0.256813 + 0.966461i \(0.417328\pi\)
\(32\) 0 0
\(33\) 1.83029 1.16024i 0.318613 0.201972i
\(34\) 0 0
\(35\) 3.66006 + 0.174350i 0.618662 + 0.0294705i
\(36\) 0 0
\(37\) −3.99087 + 6.91239i −0.656095 + 1.13639i 0.325523 + 0.945534i \(0.394460\pi\)
−0.981618 + 0.190856i \(0.938874\pi\)
\(38\) 0 0
\(39\) 3.72976 + 2.69105i 0.597240 + 0.430914i
\(40\) 0 0
\(41\) −3.54601 0.683437i −0.553793 0.106735i −0.0953258 0.995446i \(-0.530389\pi\)
−0.458467 + 0.888711i \(0.651601\pi\)
\(42\) 0 0
\(43\) 1.94811 + 1.68805i 0.297084 + 0.257424i 0.790629 0.612296i \(-0.209754\pi\)
−0.493545 + 0.869720i \(0.664299\pi\)
\(44\) 0 0
\(45\) −0.720320 3.13905i −0.107379 0.467942i
\(46\) 0 0
\(47\) −5.36003 + 10.3970i −0.781841 + 1.51656i 0.0728031 + 0.997346i \(0.476806\pi\)
−0.854644 + 0.519214i \(0.826225\pi\)
\(48\) 0 0
\(49\) −4.56579 + 0.879983i −0.652255 + 0.125712i
\(50\) 0 0
\(51\) 4.92350 2.80192i 0.689428 0.392347i
\(52\) 0 0
\(53\) −4.61898 5.33059i −0.634466 0.732213i 0.343920 0.938999i \(-0.388245\pi\)
−0.978386 + 0.206786i \(0.933700\pi\)
\(54\) 0 0
\(55\) 0.316664 + 1.30531i 0.0426989 + 0.176007i
\(56\) 0 0
\(57\) −12.0653 + 1.07645i −1.59809 + 0.142579i
\(58\) 0 0
\(59\) 3.82125 + 13.0140i 0.497484 + 1.69428i 0.699280 + 0.714848i \(0.253504\pi\)
−0.201796 + 0.979428i \(0.564678\pi\)
\(60\) 0 0
\(61\) −3.61460 + 9.02884i −0.462803 + 1.15603i 0.495075 + 0.868850i \(0.335140\pi\)
−0.957878 + 0.287175i \(0.907284\pi\)
\(62\) 0 0
\(63\) 4.57851 + 9.15891i 0.576838 + 1.15391i
\(64\) 0 0
\(65\) −2.32208 + 1.65354i −0.288018 + 0.205097i
\(66\) 0 0
\(67\) −7.45395 3.38209i −0.910646 0.413188i
\(68\) 0 0
\(69\) 11.7779 2.77987i 1.41789 0.334657i
\(70\) 0 0
\(71\) 10.5155 + 3.63946i 1.24796 + 0.431925i 0.869611 0.493737i \(-0.164369\pi\)
0.378353 + 0.925661i \(0.376491\pi\)
\(72\) 0 0
\(73\) −5.63753 2.25693i −0.659823 0.264153i 0.0174913 0.999847i \(-0.494432\pi\)
−0.677314 + 0.735694i \(0.736856\pi\)
\(74\) 0 0
\(75\) −6.62982 0.674690i −0.765546 0.0779065i
\(76\) 0 0
\(77\) −1.95681 3.79569i −0.223000 0.432559i
\(78\) 0 0
\(79\) −9.16491 + 2.22338i −1.03113 + 0.250150i −0.715413 0.698702i \(-0.753761\pi\)
−0.315720 + 0.948852i \(0.602246\pi\)
\(80\) 0 0
\(81\) 6.66602 6.04683i 0.740669 0.671870i
\(82\) 0 0
\(83\) 8.90868 11.3283i 0.977855 1.24344i 0.00794744 0.999968i \(-0.497470\pi\)
0.969907 0.243475i \(-0.0782874\pi\)
\(84\) 0 0
\(85\) 0.664499 + 3.44775i 0.0720750 + 0.373961i
\(86\) 0 0
\(87\) 1.32242 1.13157i 0.141779 0.121317i
\(88\) 0 0
\(89\) −7.82886 + 12.1820i −0.829858 + 1.29128i 0.124380 + 0.992235i \(0.460306\pi\)
−0.954238 + 0.299050i \(0.903330\pi\)
\(90\) 0 0
\(91\) 5.93517 6.84955i 0.622174 0.718028i
\(92\) 0 0
\(93\) 5.49823 8.43959i 0.570140 0.875145i
\(94\) 0 0
\(95\) 1.77006 7.29627i 0.181604 0.748582i
\(96\) 0 0
\(97\) 4.98536 + 2.87830i 0.506186 + 0.292247i 0.731265 0.682094i \(-0.238930\pi\)
−0.225078 + 0.974341i \(0.572264\pi\)
\(98\) 0 0
\(99\) −2.74850 + 2.55620i −0.276234 + 0.256908i
\(100\) 0 0
\(101\) 6.06907 8.52281i 0.603895 0.848052i −0.393564 0.919297i \(-0.628758\pi\)
0.997459 + 0.0712456i \(0.0226974\pi\)
\(102\) 0 0
\(103\) −9.39509 8.95820i −0.925726 0.882678i 0.0676357 0.997710i \(-0.478454\pi\)
−0.993362 + 0.115032i \(0.963303\pi\)
\(104\) 0 0
\(105\) −6.28749 + 0.864142i −0.613596 + 0.0843316i
\(106\) 0 0
\(107\) 0.0851448 0.0122420i 0.00823125 0.00118348i −0.138198 0.990405i \(-0.544131\pi\)
0.146429 + 0.989221i \(0.453222\pi\)
\(108\) 0 0
\(109\) 3.46042 11.7851i 0.331448 1.12881i −0.610211 0.792239i \(-0.708915\pi\)
0.941659 0.336569i \(-0.109267\pi\)
\(110\) 0 0
\(111\) 4.60278 13.0361i 0.436876 1.23733i
\(112\) 0 0
\(113\) −9.11844 + 7.17082i −0.857790 + 0.674574i −0.946928 0.321446i \(-0.895831\pi\)
0.0891377 + 0.996019i \(0.471589\pi\)
\(114\) 0 0
\(115\) −0.712983 + 7.46669i −0.0664860 + 0.696273i
\(116\) 0 0
\(117\) −7.20451 3.39908i −0.666057 0.314245i
\(118\) 0 0
\(119\) −4.63742 10.1545i −0.425112 0.930865i
\(120\) 0 0
\(121\) −6.82816 + 6.51064i −0.620742 + 0.591876i
\(122\) 0 0
\(123\) 6.25478 + 0.0388863i 0.563974 + 0.00350626i
\(124\) 0 0
\(125\) 3.94569 8.63986i 0.352913 0.772773i
\(126\) 0 0
\(127\) 9.48549 0.905754i 0.841701 0.0803727i 0.334707 0.942322i \(-0.391363\pi\)
0.506994 + 0.861950i \(0.330757\pi\)
\(128\) 0 0
\(129\) −3.85262 2.25636i −0.339204 0.198662i
\(130\) 0 0
\(131\) 2.19930 + 3.42218i 0.192154 + 0.298997i 0.923940 0.382537i \(-0.124949\pi\)
−0.731786 + 0.681534i \(0.761313\pi\)
\(132\) 0 0
\(133\) 23.8703i 2.06982i
\(134\) 0 0
\(135\) 2.22228 + 5.11654i 0.191263 + 0.440362i
\(136\) 0 0
\(137\) 13.1710 8.46452i 1.12528 0.723173i 0.160709 0.987002i \(-0.448622\pi\)
0.964569 + 0.263829i \(0.0849855\pi\)
\(138\) 0 0
\(139\) 9.29511 + 1.33643i 0.788401 + 0.113355i 0.524742 0.851261i \(-0.324162\pi\)
0.263658 + 0.964616i \(0.415071\pi\)
\(140\) 0 0
\(141\) 5.82876 19.4038i 0.490870 1.63410i
\(142\) 0 0
\(143\) 3.02204 + 1.38012i 0.252715 + 0.115411i
\(144\) 0 0
\(145\) 0.400937 + 1.00149i 0.0332960 + 0.0831695i
\(146\) 0 0
\(147\) 7.49528 2.94672i 0.618200 0.243042i
\(148\) 0 0
\(149\) 13.8950 6.34561i 1.13832 0.519853i 0.245111 0.969495i \(-0.421176\pi\)
0.893209 + 0.449642i \(0.148448\pi\)
\(150\) 0 0
\(151\) −0.869270 2.51159i −0.0707402 0.204390i 0.904089 0.427345i \(-0.140551\pi\)
−0.974829 + 0.222955i \(0.928430\pi\)
\(152\) 0 0
\(153\) −7.49471 + 6.33278i −0.605911 + 0.511975i
\(154\) 0 0
\(155\) 3.85924 + 4.90742i 0.309981 + 0.394173i
\(156\) 0 0
\(157\) 0.361765 + 7.59438i 0.0288720 + 0.606098i 0.966222 + 0.257710i \(0.0829678\pi\)
−0.937350 + 0.348388i \(0.886729\pi\)
\(158\) 0 0
\(159\) 9.55593 + 7.61149i 0.757834 + 0.603630i
\(160\) 0 0
\(161\) −3.39382 23.6045i −0.267470 1.86030i
\(162\) 0 0
\(163\) −3.22544 5.58663i −0.252636 0.437579i 0.711615 0.702570i \(-0.247964\pi\)
−0.964251 + 0.264991i \(0.914631\pi\)
\(164\) 0 0
\(165\) −0.953260 2.12217i −0.0742112 0.165210i
\(166\) 0 0
\(167\) 9.05990 + 6.45152i 0.701076 + 0.499234i 0.874138 0.485677i \(-0.161427\pi\)
−0.173062 + 0.984911i \(0.555366\pi\)
\(168\) 0 0
\(169\) 0.283066 5.94229i 0.0217743 0.457099i
\(170\) 0 0
\(171\) 20.2028 5.66019i 1.54494 0.432845i
\(172\) 0 0
\(173\) 6.05483 + 1.46889i 0.460341 + 0.111677i 0.459221 0.888322i \(-0.348129\pi\)
0.00111938 + 0.999999i \(0.499644\pi\)
\(174\) 0 0
\(175\) −2.48529 + 12.8949i −0.187870 + 0.974763i
\(176\) 0 0
\(177\) −10.6349 20.9475i −0.799364 1.57451i
\(178\) 0 0
\(179\) 6.62139 + 4.25531i 0.494906 + 0.318057i 0.764176 0.645008i \(-0.223146\pi\)
−0.269270 + 0.963065i \(0.586782\pi\)
\(180\) 0 0
\(181\) 5.80714 + 2.99379i 0.431641 + 0.222526i 0.660334 0.750972i \(-0.270415\pi\)
−0.228693 + 0.973499i \(0.573445\pi\)
\(182\) 0 0
\(183\) 3.29072 16.5205i 0.243257 1.22123i
\(184\) 0 0
\(185\) 6.73550 + 5.29686i 0.495204 + 0.389433i
\(186\) 0 0
\(187\) 3.09259 2.67974i 0.226153 0.195962i
\(188\) 0 0
\(189\) −10.7014 14.1430i −0.778413 1.02875i
\(190\) 0 0
\(191\) −13.6843 + 7.05474i −0.990160 + 0.510463i −0.875643 0.482958i \(-0.839562\pi\)
−0.114517 + 0.993421i \(0.536532\pi\)
\(192\) 0 0
\(193\) 10.8125 3.17484i 0.778301 0.228530i 0.131630 0.991299i \(-0.457979\pi\)
0.646671 + 0.762769i \(0.276161\pi\)
\(194\) 0 0
\(195\) 3.42940 3.55217i 0.245585 0.254376i
\(196\) 0 0
\(197\) 4.30693 12.4440i 0.306856 0.886602i −0.681144 0.732149i \(-0.738517\pi\)
0.988000 0.154453i \(-0.0493614\pi\)
\(198\) 0 0
\(199\) 0.573623 + 0.805541i 0.0406631 + 0.0571033i 0.834407 0.551149i \(-0.185810\pi\)
−0.793744 + 0.608252i \(0.791871\pi\)
\(200\) 0 0
\(201\) 13.7651 + 3.39439i 0.970916 + 0.239422i
\(202\) 0 0
\(203\) −1.98947 2.79382i −0.139633 0.196088i
\(204\) 0 0
\(205\) −1.26800 + 3.66364i −0.0885607 + 0.255879i
\(206\) 0 0
\(207\) −19.1731 + 8.46954i −1.33262 + 0.588674i
\(208\) 0 0
\(209\) −8.39556 + 2.46516i −0.580733 + 0.170519i
\(210\) 0 0
\(211\) −6.01206 + 3.09943i −0.413888 + 0.213374i −0.652578 0.757722i \(-0.726312\pi\)
0.238690 + 0.971096i \(0.423282\pi\)
\(212\) 0 0
\(213\) −19.0599 2.86145i −1.30596 0.196063i
\(214\) 0 0
\(215\) 2.09138 1.81219i 0.142631 0.123591i
\(216\) 0 0
\(217\) −15.6024 12.2699i −1.05916 0.832934i
\(218\) 0 0
\(219\) 10.3153 + 2.05470i 0.697041 + 0.138844i
\(220\) 0 0
\(221\) 7.71935 + 3.97960i 0.519260 + 0.267697i
\(222\) 0 0
\(223\) −3.72053 2.39104i −0.249145 0.160116i 0.410108 0.912037i \(-0.365491\pi\)
−0.659253 + 0.751921i \(0.729127\pi\)
\(224\) 0 0
\(225\) 11.5030 0.954234i 0.766866 0.0636156i
\(226\) 0 0
\(227\) −2.92214 + 15.1615i −0.193949 + 1.00630i 0.746247 + 0.665669i \(0.231854\pi\)
−0.940196 + 0.340634i \(0.889358\pi\)
\(228\) 0 0
\(229\) −1.16775 0.283294i −0.0771672 0.0187206i 0.196989 0.980406i \(-0.436884\pi\)
−0.274157 + 0.961685i \(0.588399\pi\)
\(230\) 0 0
\(231\) 4.53601 + 5.84240i 0.298448 + 0.384402i
\(232\) 0 0
\(233\) −0.0185739 + 0.389913i −0.00121681 + 0.0255441i −0.999394 0.0348060i \(-0.988919\pi\)
0.998177 + 0.0603501i \(0.0192217\pi\)
\(234\) 0 0
\(235\) 10.2291 + 7.28414i 0.667276 + 0.475165i
\(236\) 0 0
\(237\) 14.9003 6.69311i 0.967879 0.434764i
\(238\) 0 0
\(239\) −2.07881 3.60060i −0.134467 0.232903i 0.790927 0.611911i \(-0.209599\pi\)
−0.925394 + 0.379007i \(0.876266\pi\)
\(240\) 0 0
\(241\) 1.04541 + 7.27101i 0.0673410 + 0.468367i 0.995390 + 0.0959090i \(0.0305758\pi\)
−0.928049 + 0.372458i \(0.878515\pi\)
\(242\) 0 0
\(243\) −9.43248 + 12.4108i −0.605094 + 0.796154i
\(244\) 0 0
\(245\) 0.237519 + 4.98613i 0.0151745 + 0.318552i
\(246\) 0 0
\(247\) −11.4795 14.5974i −0.730423 0.928809i
\(248\) 0 0
\(249\) −11.5758 + 22.1153i −0.733588 + 1.40150i
\(250\) 0 0
\(251\) −7.51263 21.7063i −0.474193 1.37009i −0.888049 0.459749i \(-0.847939\pi\)
0.413856 0.910343i \(-0.364182\pi\)
\(252\) 0 0
\(253\) 7.95159 3.63137i 0.499912 0.228302i
\(254\) 0 0
\(255\) −2.22515 5.65988i −0.139344 0.354436i
\(256\) 0 0
\(257\) −0.867445 2.16677i −0.0541098 0.135160i 0.898850 0.438256i \(-0.144404\pi\)
−0.952960 + 0.303097i \(0.901980\pi\)
\(258\) 0 0
\(259\) −24.7812 11.3172i −1.53983 0.703218i
\(260\) 0 0
\(261\) −1.89282 + 2.34628i −0.117162 + 0.145231i
\(262\) 0 0
\(263\) −15.9922 2.29933i −0.986119 0.141783i −0.369658 0.929168i \(-0.620525\pi\)
−0.616461 + 0.787385i \(0.711434\pi\)
\(264\) 0 0
\(265\) −6.37008 + 4.09380i −0.391311 + 0.251480i
\(266\) 0 0
\(267\) 9.46637 23.2263i 0.579332 1.42143i
\(268\) 0 0
\(269\) 22.0639i 1.34526i 0.739978 + 0.672631i \(0.234836\pi\)
−0.739978 + 0.672631i \(0.765164\pi\)
\(270\) 0 0
\(271\) −10.4091 16.1968i −0.632305 0.983886i −0.998574 0.0533769i \(-0.983002\pi\)
0.366269 0.930509i \(-0.380635\pi\)
\(272\) 0 0
\(273\) −7.93337 + 13.5458i −0.480149 + 0.819830i
\(274\) 0 0
\(275\) −4.79200 + 0.457581i −0.288969 + 0.0275932i
\(276\) 0 0
\(277\) −2.65963 + 5.82378i −0.159802 + 0.349917i −0.972549 0.232700i \(-0.925244\pi\)
0.812747 + 0.582617i \(0.197971\pi\)
\(278\) 0 0
\(279\) −6.68500 + 16.1147i −0.400220 + 0.964760i
\(280\) 0 0
\(281\) 12.9657 12.3628i 0.773468 0.737501i −0.196560 0.980492i \(-0.562977\pi\)
0.970028 + 0.242991i \(0.0781286\pi\)
\(282\) 0 0
\(283\) −5.54205 12.1354i −0.329441 0.721375i 0.670345 0.742049i \(-0.266146\pi\)
−0.999786 + 0.0206743i \(0.993419\pi\)
\(284\) 0 0
\(285\) −0.699501 + 12.9853i −0.0414349 + 0.769180i
\(286\) 0 0
\(287\) 1.17165 12.2701i 0.0691605 0.724281i
\(288\) 0 0
\(289\) −4.95434 + 3.89614i −0.291432 + 0.229184i
\(290\) 0 0
\(291\) −9.40188 3.31962i −0.551148 0.194599i
\(292\) 0 0
\(293\) −0.725462 + 2.47070i −0.0423819 + 0.144340i −0.977966 0.208765i \(-0.933056\pi\)
0.935584 + 0.353104i \(0.114874\pi\)
\(294\) 0 0
\(295\) 14.4127 2.07223i 0.839140 0.120650i
\(296\) 0 0
\(297\) 3.86916 5.22444i 0.224511 0.303153i
\(298\) 0 0
\(299\) 13.4271 + 12.8027i 0.776509 + 0.740400i
\(300\) 0 0
\(301\) −5.10347 + 7.16682i −0.294159 + 0.413088i
\(302\) 0 0
\(303\) −7.63059 + 16.4375i −0.438366 + 0.944307i
\(304\) 0 0
\(305\) 9.04197 + 5.22038i 0.517742 + 0.298918i
\(306\) 0 0
\(307\) −5.08377 + 20.9556i −0.290146 + 1.19600i 0.620966 + 0.783838i \(0.286741\pi\)
−0.911111 + 0.412160i \(0.864774\pi\)
\(308\) 0 0
\(309\) 18.8392 + 12.2734i 1.07172 + 0.698208i
\(310\) 0 0
\(311\) −7.70833 + 8.89589i −0.437099 + 0.504440i −0.930970 0.365096i \(-0.881036\pi\)
0.493871 + 0.869535i \(0.335582\pi\)
\(312\) 0 0
\(313\) 4.49750 6.99824i 0.254214 0.395564i −0.690567 0.723269i \(-0.742639\pi\)
0.944780 + 0.327705i \(0.106275\pi\)
\(314\) 0 0
\(315\) 10.4319 3.46589i 0.587773 0.195281i
\(316\) 0 0
\(317\) 1.16133 + 6.02556i 0.0652268 + 0.338429i 0.999852 0.0172055i \(-0.00547695\pi\)
−0.934625 + 0.355634i \(0.884265\pi\)
\(318\) 0 0
\(319\) 0.777172 0.988255i 0.0435133 0.0553316i
\(320\) 0 0
\(321\) −0.141097 + 0.0478541i −0.00787529 + 0.00267096i
\(322\) 0 0
\(323\) −22.2288 + 5.39264i −1.23684 + 0.300055i
\(324\) 0 0
\(325\) −4.68148 9.08081i −0.259682 0.503713i
\(326\) 0 0
\(327\) −2.15386 + 21.1648i −0.119109 + 1.17042i
\(328\) 0 0
\(329\) −37.0652 14.8387i −2.04347 0.818083i
\(330\) 0 0
\(331\) 4.35721 + 1.50804i 0.239494 + 0.0828896i 0.444178 0.895938i \(-0.353496\pi\)
−0.204685 + 0.978828i \(0.565617\pi\)
\(332\) 0 0
\(333\) −3.70219 + 23.6573i −0.202879 + 1.29641i
\(334\) 0 0
\(335\) −4.73270 + 7.40399i −0.258575 + 0.404523i
\(336\) 0 0
\(337\) 26.3193 18.7419i 1.43370 1.02094i 0.441374 0.897323i \(-0.354491\pi\)
0.992330 0.123613i \(-0.0394482\pi\)
\(338\) 0 0
\(339\) 13.2518 15.1026i 0.719738 0.820263i
\(340\) 0 0
\(341\) 2.70420 6.75477i 0.146441 0.365791i
\(342\) 0 0
\(343\) 2.25995 + 7.69668i 0.122026 + 0.415581i
\(344\) 0 0
\(345\) −1.15450 12.9401i −0.0621560 0.696673i
\(346\) 0 0
\(347\) 1.90552 + 7.85464i 0.102293 + 0.421659i 0.999813 0.0193145i \(-0.00614837\pi\)
−0.897520 + 0.440974i \(0.854633\pi\)
\(348\) 0 0
\(349\) −4.97083 5.73664i −0.266082 0.307075i 0.606948 0.794742i \(-0.292394\pi\)
−0.873030 + 0.487666i \(0.837848\pi\)
\(350\) 0 0
\(351\) 13.3458 + 3.50243i 0.712344 + 0.186946i
\(352\) 0 0
\(353\) 6.62243 1.27637i 0.352476 0.0679343i −0.00993986 0.999951i \(-0.503164\pi\)
0.362416 + 0.932016i \(0.381952\pi\)
\(354\) 0 0
\(355\) 5.47394 10.6180i 0.290526 0.563543i
\(356\) 0 0
\(357\) 11.1175 + 15.8196i 0.588403 + 0.837264i
\(358\) 0 0
\(359\) 28.2755 + 24.5009i 1.49232 + 1.29311i 0.850141 + 0.526555i \(0.176517\pi\)
0.642183 + 0.766551i \(0.278029\pi\)
\(360\) 0 0
\(361\) 29.3694 + 5.66049i 1.54576 + 0.297921i
\(362\) 0 0
\(363\) 9.56142 13.2520i 0.501845 0.695550i
\(364\) 0 0
\(365\) −3.25956 + 5.64573i −0.170613 + 0.295511i
\(366\) 0 0
\(367\) 26.1307 + 1.24476i 1.36401 + 0.0649760i 0.716771 0.697308i \(-0.245619\pi\)
0.647242 + 0.762284i \(0.275922\pi\)
\(368\) 0 0
\(369\) −10.6627 + 1.91788i −0.555078 + 0.0998410i
\(370\) 0 0
\(371\) 16.6133 17.4235i 0.862519 0.904584i
\(372\) 0 0
\(373\) 10.3411 5.97047i 0.535444 0.309139i −0.207786 0.978174i \(-0.566626\pi\)
0.743231 + 0.669035i \(0.233293\pi\)
\(374\) 0 0
\(375\) −3.97787 + 15.9632i −0.205416 + 0.824336i
\(376\) 0 0
\(377\) 2.56020 + 0.751742i 0.131857 + 0.0387167i
\(378\) 0 0
\(379\) −33.2501 + 1.58390i −1.70794 + 0.0813592i −0.878653 0.477462i \(-0.841557\pi\)
−0.829288 + 0.558821i \(0.811254\pi\)
\(380\) 0 0
\(381\) −15.8641 + 4.55120i −0.812745 + 0.233165i
\(382\) 0 0
\(383\) −18.4651 1.76320i −0.943522 0.0900955i −0.388057 0.921635i \(-0.626854\pi\)
−0.555465 + 0.831540i \(0.687460\pi\)
\(384\) 0 0
\(385\) −4.33233 + 1.49943i −0.220796 + 0.0764183i
\(386\) 0 0
\(387\) 7.27582 + 2.61993i 0.369851 + 0.133179i
\(388\) 0 0
\(389\) −12.6712 13.2892i −0.642455 0.673787i 0.319314 0.947649i \(-0.396547\pi\)
−0.961769 + 0.273862i \(0.911699\pi\)
\(390\) 0 0
\(391\) 21.2146 8.49303i 1.07287 0.429511i
\(392\) 0 0
\(393\) −4.83043 5.12949i −0.243663 0.258749i
\(394\) 0 0
\(395\) 0.962379 + 10.0785i 0.0484226 + 0.507104i
\(396\) 0 0
\(397\) −1.34766 + 9.37317i −0.0676370 + 0.470426i 0.927650 + 0.373451i \(0.121826\pi\)
−0.995287 + 0.0969747i \(0.969083\pi\)
\(398\) 0 0
\(399\) −7.57197 40.6453i −0.379073 2.03481i
\(400\) 0 0
\(401\) 28.6827 1.43235 0.716174 0.697922i \(-0.245892\pi\)
0.716174 + 0.697922i \(0.245892\pi\)
\(402\) 0 0
\(403\) 15.4421 0.769224
\(404\) 0 0
\(405\) −5.40702 8.00728i −0.268677 0.397885i
\(406\) 0 0
\(407\) 1.42121 9.88472i 0.0704467 0.489967i
\(408\) 0 0
\(409\) 1.22216 + 12.7991i 0.0604320 + 0.632872i 0.974055 + 0.226310i \(0.0726664\pi\)
−0.913623 + 0.406562i \(0.866728\pi\)
\(410\) 0 0
\(411\) −19.7420 + 18.5910i −0.973802 + 0.917028i
\(412\) 0 0
\(413\) −42.9782 + 17.2059i −2.11482 + 0.846645i
\(414\) 0 0
\(415\) −10.6766 11.1973i −0.524093 0.549653i
\(416\) 0 0
\(417\) −16.2512 + 0.672907i −0.795826 + 0.0329524i
\(418\) 0 0
\(419\) −1.30845 + 0.452859i −0.0639220 + 0.0221236i −0.358842 0.933398i \(-0.616828\pi\)
0.294920 + 0.955522i \(0.404707\pi\)
\(420\) 0 0
\(421\) 32.1300 + 3.06804i 1.56592 + 0.149527i 0.841663 0.540003i \(-0.181577\pi\)
0.724257 + 0.689530i \(0.242183\pi\)
\(422\) 0 0
\(423\) −3.76980 + 34.8890i −0.183294 + 1.69636i
\(424\) 0 0
\(425\) −12.5696 + 0.598764i −0.609715 + 0.0290443i
\(426\) 0 0
\(427\) −31.8503 9.35209i −1.54134 0.452579i
\(428\) 0 0
\(429\) −5.58358 1.39137i −0.269578 0.0671762i
\(430\) 0 0
\(431\) −11.4511 + 6.61130i −0.551580 + 0.318455i −0.749759 0.661711i \(-0.769831\pi\)
0.198179 + 0.980166i \(0.436497\pi\)
\(432\) 0 0
\(433\) −11.3091 + 11.8607i −0.543482 + 0.569988i −0.937000 0.349329i \(-0.886409\pi\)
0.393518 + 0.919317i \(0.371258\pi\)
\(434\) 0 0
\(435\) −1.00038 1.57812i −0.0479648 0.0756648i
\(436\) 0 0
\(437\) −48.8074 2.32498i −2.33477 0.111219i
\(438\) 0 0
\(439\) −20.0048 + 34.6493i −0.954777 + 1.65372i −0.219899 + 0.975523i \(0.570573\pi\)
−0.734878 + 0.678200i \(0.762760\pi\)
\(440\) 0 0
\(441\) −11.8279 + 7.39515i −0.563233 + 0.352150i
\(442\) 0 0
\(443\) 13.9459 + 2.68786i 0.662591 + 0.127704i 0.509450 0.860500i \(-0.329849\pi\)
0.153141 + 0.988204i \(0.451061\pi\)
\(444\) 0 0
\(445\) 11.7487 + 10.1803i 0.556940 + 0.482591i
\(446\) 0 0
\(447\) −21.6468 + 15.2127i −1.02386 + 0.719536i
\(448\) 0 0
\(449\) 9.31873 18.0758i 0.439778 0.853051i −0.559921 0.828546i \(-0.689169\pi\)
0.999700 0.0245051i \(-0.00780099\pi\)
\(450\) 0 0
\(451\) 4.43659 0.855082i 0.208911 0.0402643i
\(452\) 0 0
\(453\) 2.27686 + 4.00088i 0.106976 + 0.187978i
\(454\) 0 0
\(455\) −6.37167 7.35330i −0.298709 0.344728i
\(456\) 0 0
\(457\) 2.03728 + 8.39776i 0.0952997 + 0.392831i 0.999405 0.0344780i \(-0.0109769\pi\)
−0.904106 + 0.427309i \(0.859462\pi\)
\(458\) 0 0
\(459\) 10.7528 13.1606i 0.501899 0.614284i
\(460\) 0 0
\(461\) 5.51343 + 18.7770i 0.256786 + 0.874533i 0.982457 + 0.186491i \(0.0597115\pi\)
−0.725671 + 0.688042i \(0.758470\pi\)
\(462\) 0 0
\(463\) 4.70448 11.7512i 0.218636 0.546125i −0.777984 0.628284i \(-0.783757\pi\)
0.996619 + 0.0821593i \(0.0261816\pi\)
\(464\) 0 0
\(465\) −8.12803 7.13193i −0.376929 0.330736i
\(466\) 0 0
\(467\) 14.8938 10.6058i 0.689203 0.490779i −0.180993 0.983484i \(-0.557931\pi\)
0.870196 + 0.492705i \(0.163992\pi\)
\(468\) 0 0
\(469\) 9.07304 26.4238i 0.418954 1.22014i
\(470\) 0 0
\(471\) −3.02503 12.8166i −0.139386 0.590559i
\(472\) 0 0
\(473\) −3.04773 1.05483i −0.140135 0.0485012i
\(474\) 0 0
\(475\) 24.9803 + 10.0006i 1.14617 + 0.458859i
\(476\) 0 0
\(477\) −18.6859 9.92924i −0.855567 0.454629i
\(478\) 0 0
\(479\) −15.6875 30.4295i −0.716780 1.39036i −0.912243 0.409648i \(-0.865651\pi\)
0.195463 0.980711i \(-0.437379\pi\)
\(480\) 0 0
\(481\) 20.5970 4.99678i 0.939143 0.227834i
\(482\) 0 0
\(483\) 13.2665 + 39.1162i 0.603647 + 1.77985i
\(484\) 0 0
\(485\) 3.82020 4.85778i 0.173466 0.220580i
\(486\) 0 0
\(487\) −3.77448 19.5839i −0.171038 0.887430i −0.961476 0.274888i \(-0.911359\pi\)
0.790438 0.612542i \(-0.209853\pi\)
\(488\) 0 0
\(489\) 7.26429 + 8.48951i 0.328503 + 0.383909i
\(490\) 0 0
\(491\) 15.4080 23.9753i 0.695352 1.08199i −0.296554 0.955016i \(-0.595838\pi\)
0.991906 0.126973i \(-0.0405260\pi\)
\(492\) 0 0
\(493\) 2.15224 2.48382i 0.0969321 0.111866i
\(494\) 0 0
\(495\) 2.29635 + 3.31114i 0.103213 + 0.148825i
\(496\) 0 0
\(497\) −8.95420 + 36.9097i −0.401651 + 1.65563i
\(498\) 0 0
\(499\) −29.8604 17.2399i −1.33674 0.771765i −0.350414 0.936595i \(-0.613959\pi\)
−0.986322 + 0.164830i \(0.947292\pi\)
\(500\) 0 0
\(501\) −17.4733 8.11145i −0.780649 0.362393i
\(502\) 0 0
\(503\) −24.5267 + 34.4430i −1.09359 + 1.53574i −0.274929 + 0.961464i \(0.588654\pi\)
−0.818664 + 0.574272i \(0.805285\pi\)
\(504\) 0 0
\(505\) −8.12926 7.75123i −0.361747 0.344925i
\(506\) 0 0
\(507\) 1.40298 + 10.2081i 0.0623085 + 0.453356i
\(508\) 0 0
\(509\) 25.5162 3.66868i 1.13099 0.162611i 0.448690 0.893687i \(-0.351891\pi\)
0.682296 + 0.731076i \(0.260982\pi\)
\(510\) 0 0
\(511\) 5.83936 19.8870i 0.258318 0.879751i
\(512\) 0 0
\(513\) −32.6049 + 16.0465i −1.43954 + 0.708470i
\(514\) 0 0
\(515\) −10.9545 + 8.61475i −0.482715 + 0.379611i
\(516\) 0 0
\(517\) 1.39116 14.5689i 0.0611831 0.640738i
\(518\) 0 0
\(519\) −10.7759 0.580483i −0.473007 0.0254804i
\(520\) 0 0
\(521\) 5.35842 + 11.7333i 0.234756 + 0.514045i 0.989943 0.141465i \(-0.0451811\pi\)
−0.755187 + 0.655510i \(0.772454\pi\)
\(522\) 0 0
\(523\) 8.37239 7.98306i 0.366099 0.349075i −0.484592 0.874740i \(-0.661032\pi\)
0.850691 + 0.525665i \(0.176184\pi\)
\(524\) 0 0
\(525\) 0.141408 22.7452i 0.00617157 0.992683i
\(526\) 0 0
\(527\) 7.90129 17.3014i 0.344186 0.753661i
\(528\) 0 0
\(529\) 25.6986 2.45392i 1.11733 0.106692i
\(530\) 0 0
\(531\) 24.7534 + 32.2949i 1.07420 + 1.40148i
\(532\) 0 0
\(533\) 5.18433 + 8.06698i 0.224558 + 0.349420i
\(534\) 0 0
\(535\) 0.0923467i 0.00399250i
\(536\) 0 0
\(537\) −12.6245 5.14536i −0.544785 0.222039i
\(538\) 0 0
\(539\) 4.89409 3.14524i 0.210803 0.135475i
\(540\) 0 0
\(541\) 18.6189 + 2.67700i 0.800490 + 0.115093i 0.530406 0.847744i \(-0.322039\pi\)
0.270084 + 0.962837i \(0.412949\pi\)
\(542\) 0 0
\(543\) −10.8378 3.25559i −0.465095 0.139711i
\(544\) 0 0
\(545\) −11.9944 5.47765i −0.513783 0.234637i
\(546\) 0 0
\(547\) 11.5509 + 28.8527i 0.493879 + 1.23365i 0.940765 + 0.339059i \(0.110109\pi\)
−0.446886 + 0.894591i \(0.647467\pi\)
\(548\) 0 0
\(549\) −0.362770 + 29.1743i −0.0154826 + 1.24513i
\(550\) 0 0
\(551\) −6.39251 + 2.91936i −0.272330 + 0.124369i
\(552\) 0 0
\(553\) −10.5279 30.4185i −0.447694 1.29353i
\(554\) 0 0
\(555\) −13.1491 6.88267i −0.558150 0.292153i
\(556\) 0 0
\(557\) 21.7296 + 27.6314i 0.920712 + 1.17078i 0.984949 + 0.172846i \(0.0552962\pi\)
−0.0642371 + 0.997935i \(0.520461\pi\)
\(558\) 0 0
\(559\) −0.325688 6.83703i −0.0137751 0.289175i
\(560\) 0 0
\(561\) −4.41588 + 5.54396i −0.186438 + 0.234066i
\(562\) 0 0
\(563\) 5.63565 + 39.1968i 0.237515 + 1.65195i 0.664204 + 0.747552i \(0.268771\pi\)
−0.426689 + 0.904398i \(0.640320\pi\)
\(564\) 0 0
\(565\) 6.22671 + 10.7850i 0.261960 + 0.453728i
\(566\) 0 0
\(567\) 22.7082 + 20.6875i 0.953656 + 0.868792i
\(568\) 0 0
\(569\) −1.61100 1.14719i −0.0675368 0.0480927i 0.545790 0.837922i \(-0.316230\pi\)
−0.613327 + 0.789829i \(0.710169\pi\)
\(570\) 0 0
\(571\) 2.04251 42.8776i 0.0854765 1.79437i −0.396344 0.918102i \(-0.629721\pi\)
0.481821 0.876270i \(-0.339976\pi\)
\(572\) 0 0
\(573\) 21.0631 16.3533i 0.879925 0.683170i
\(574\) 0 0
\(575\) −26.1240 6.33761i −1.08945 0.264297i
\(576\) 0 0
\(577\) −1.44529 + 7.49887i −0.0601682 + 0.312182i −0.999527 0.0307538i \(-0.990209\pi\)
0.939359 + 0.342936i \(0.111421\pi\)
\(578\) 0 0
\(579\) −17.4039 + 8.83583i −0.723283 + 0.367205i
\(580\) 0 0
\(581\) 41.3809 + 26.5939i 1.71677 + 1.10330i
\(582\) 0 0
\(583\) 7.84383 + 4.04378i 0.324858 + 0.167476i
\(584\) 0 0
\(585\) −4.71264 + 7.13633i −0.194844 + 0.295051i
\(586\) 0 0
\(587\) 26.2994 + 20.6821i 1.08549 + 0.853641i 0.989898 0.141779i \(-0.0452824\pi\)
0.0955945 + 0.995420i \(0.469525\pi\)
\(588\) 0 0
\(589\) −30.7367 + 26.6335i −1.26648 + 1.09741i
\(590\) 0 0
\(591\) −3.38623 + 22.5554i −0.139291 + 0.927805i
\(592\) 0 0
\(593\) −32.6745 + 16.8449i −1.34178 + 0.691736i −0.971468 0.237172i \(-0.923780\pi\)
−0.370312 + 0.928907i \(0.620749\pi\)
\(594\) 0 0
\(595\) −11.4989 + 3.37638i −0.471409 + 0.138418i
\(596\) 0 0
\(597\) −1.23227 1.18968i −0.0504334 0.0486903i
\(598\) 0 0
\(599\) 3.14596 9.08965i 0.128540 0.371393i −0.862306 0.506388i \(-0.830981\pi\)
0.990846 + 0.134995i \(0.0431017\pi\)
\(600\) 0 0
\(601\) −4.55869 6.40178i −0.185953 0.261134i 0.711067 0.703124i \(-0.248212\pi\)
−0.897020 + 0.441990i \(0.854273\pi\)
\(602\) 0 0
\(603\) −24.5154 1.41334i −0.998342 0.0575556i
\(604\) 0 0
\(605\) 5.87510 + 8.25043i 0.238857 + 0.335428i
\(606\) 0 0
\(607\) 2.62671 7.58939i 0.106615 0.308044i −0.879057 0.476716i \(-0.841827\pi\)
0.985672 + 0.168673i \(0.0539481\pi\)
\(608\) 0 0
\(609\) 4.27382 + 4.12611i 0.173184 + 0.167198i
\(610\) 0 0
\(611\) 29.8026 8.75082i 1.20568 0.354020i
\(612\) 0 0
\(613\) −15.3235 + 7.89982i −0.618911 + 0.319071i −0.739013 0.673691i \(-0.764708\pi\)
0.120102 + 0.992762i \(0.461678\pi\)
\(614\) 0 0
\(615\) 0.996935 6.64050i 0.0402003 0.267771i
\(616\) 0 0
\(617\) 7.70303 6.67472i 0.310112 0.268714i −0.485873 0.874029i \(-0.661498\pi\)
0.795986 + 0.605315i \(0.206953\pi\)
\(618\) 0 0
\(619\) 29.4092 + 23.1276i 1.18205 + 0.929578i 0.998571 0.0534445i \(-0.0170200\pi\)
0.183484 + 0.983023i \(0.441262\pi\)
\(620\) 0 0
\(621\) 29.9604 20.5035i 1.20227 0.822777i
\(622\) 0 0
\(623\) −43.9310 22.6480i −1.76006 0.907373i
\(624\) 0 0
\(625\) 7.60557 + 4.88780i 0.304223 + 0.195512i
\(626\) 0 0
\(627\) 13.5136 6.86075i 0.539682 0.273992i
\(628\) 0 0
\(629\) 4.94051 25.6338i 0.196991 1.02209i
\(630\) 0 0
\(631\) −36.1058 8.75918i −1.43735 0.348698i −0.559978 0.828507i \(-0.689190\pi\)
−0.877373 + 0.479810i \(0.840706\pi\)
\(632\) 0 0
\(633\) 9.25389 7.18468i 0.367809 0.285566i
\(634\) 0 0
\(635\) 0.486735 10.2178i 0.0193155 0.405482i
\(636\) 0 0
\(637\) 10.0575 + 7.16194i 0.398494 + 0.283766i
\(638\) 0 0
\(639\) 33.3620 1.17369i 1.31978 0.0464304i
\(640\) 0 0
\(641\) −4.70490 8.14913i −0.185833 0.321871i 0.758024 0.652226i \(-0.226165\pi\)
−0.943857 + 0.330355i \(0.892832\pi\)
\(642\) 0 0
\(643\) −4.78557 33.2844i −0.188724 1.31261i −0.835316 0.549771i \(-0.814715\pi\)
0.646591 0.762837i \(-0.276194\pi\)
\(644\) 0 0
\(645\) −2.98626 + 3.74913i −0.117584 + 0.147622i
\(646\) 0 0
\(647\) −0.466056 9.78372i −0.0183226 0.384638i −0.989340 0.145627i \(-0.953480\pi\)
0.971017 0.239011i \(-0.0768230\pi\)
\(648\) 0 0
\(649\) −10.4901 13.3392i −0.411771 0.523609i
\(650\) 0 0
\(651\) 30.4593 + 15.9433i 1.19379 + 0.624868i
\(652\) 0 0
\(653\) −7.31137 21.1248i −0.286116 0.826678i −0.992868 0.119217i \(-0.961962\pi\)
0.706752 0.707461i \(-0.250159\pi\)
\(654\) 0 0
\(655\) 3.97248 1.81417i 0.155218 0.0708856i
\(656\) 0 0
\(657\) −18.2161 0.226510i −0.710679 0.00883701i
\(658\) 0 0
\(659\) −16.3965 40.9565i −0.638718 1.59544i −0.794238 0.607607i \(-0.792130\pi\)
0.155520 0.987833i \(-0.450295\pi\)
\(660\) 0 0
\(661\) −43.2103 19.7335i −1.68069 0.767544i −0.999368 0.0355573i \(-0.988679\pi\)
−0.681319 0.731987i \(-0.738593\pi\)
\(662\) 0 0
\(663\) −14.4065 4.32761i −0.559504 0.168070i
\(664\) 0 0
\(665\) 25.3650 + 3.64694i 0.983614 + 0.141422i
\(666\) 0 0
\(667\) 5.90627 3.79573i 0.228692 0.146971i
\(668\) 0 0
\(669\) 7.09363 + 2.89116i 0.274255 + 0.111779i
\(670\) 0 0
\(671\) 12.1681i 0.469743i
\(672\) 0 0
\(673\) 23.9329 + 37.2404i 0.922547 + 1.43551i 0.900061 + 0.435763i \(0.143522\pi\)
0.0224854 + 0.999747i \(0.492842\pi\)
\(674\) 0 0
\(675\) −19.2841 + 5.27373i −0.742245 + 0.202986i
\(676\) 0 0
\(677\) −19.4425 + 1.85653i −0.747236 + 0.0713524i −0.461725 0.887023i \(-0.652769\pi\)
−0.285511 + 0.958375i \(0.592163\pi\)
\(678\) 0 0
\(679\) −8.16220 + 17.8727i −0.313237 + 0.685892i
\(680\) 0 0
\(681\) 0.166264 26.7432i 0.00637126 1.02480i
\(682\) 0 0
\(683\) 26.8772 25.6273i 1.02843 0.980603i 0.0286069 0.999591i \(-0.490893\pi\)
0.999820 + 0.0189880i \(0.00604442\pi\)
\(684\) 0 0
\(685\) −6.98226 15.2890i −0.266778 0.584163i
\(686\) 0 0
\(687\) 2.07826 + 0.111954i 0.0792906 + 0.00427130i
\(688\) 0 0
\(689\) −1.78033 + 18.6445i −0.0678253 + 0.710299i
\(690\) 0 0
\(691\) 8.55640 6.72883i 0.325501 0.255977i −0.442014 0.897008i \(-0.645736\pi\)
0.767514 + 0.641032i \(0.221493\pi\)
\(692\) 0 0
\(693\) −9.57701 8.50930i −0.363800 0.323241i
\(694\) 0 0
\(695\) 2.84024 9.67297i 0.107736 0.366917i
\(696\) 0 0
\(697\) 11.6910 1.68091i 0.442828 0.0636690i
\(698\) 0 0
\(699\) −0.0920588 0.669819i −0.00348198 0.0253349i
\(700\) 0 0
\(701\) 16.5837 + 15.8125i 0.626358 + 0.597231i 0.935303 0.353849i \(-0.115127\pi\)
−0.308945 + 0.951080i \(0.599976\pi\)
\(702\) 0 0
\(703\) −32.3793 + 45.4703i −1.22121 + 1.71495i
\(704\) 0 0
\(705\) −19.7284 9.15829i −0.743013 0.344921i
\(706\) 0 0
\(707\) 30.9273 + 17.8559i 1.16314 + 0.671539i
\(708\) 0 0
\(709\) 5.35357 22.0677i 0.201058 0.828771i −0.778506 0.627637i \(-0.784022\pi\)
0.979564 0.201134i \(-0.0644626\pi\)
\(710\) 0 0
\(711\) −23.2485 + 16.1233i −0.871885 + 0.604671i
\(712\) 0 0
\(713\) 26.6078 30.7070i 0.996470 1.14999i
\(714\) 0 0
\(715\) 1.92825 3.00041i 0.0721124 0.112209i
\(716\) 0 0
\(717\) 4.68186 + 5.47152i 0.174847 + 0.204338i
\(718\) 0 0
\(719\) −2.01198 10.4392i −0.0750343 0.389315i −0.999958 0.00916223i \(-0.997084\pi\)
0.924924 0.380153i \(-0.124129\pi\)
\(720\) 0 0
\(721\) 27.3894 34.8284i 1.02003 1.29708i
\(722\) 0 0
\(723\) −4.08654 12.0491i −0.151980 0.448112i
\(724\) 0 0
\(725\) −3.75723 + 0.911495i −0.139540 + 0.0338521i
\(726\) 0 0
\(727\) −5.86785 11.3820i −0.217627 0.422137i 0.754598 0.656188i \(-0.227832\pi\)
−0.972224 + 0.234051i \(0.924802\pi\)
\(728\) 0 0
\(729\) 12.1243 24.1247i 0.449049 0.893507i
\(730\) 0 0
\(731\) −7.82691 3.13342i −0.289489 0.115894i
\(732\) 0 0
\(733\) −16.0598 5.55836i −0.593183 0.205303i 0.0139503 0.999903i \(-0.495559\pi\)
−0.607133 + 0.794600i \(0.707681\pi\)
\(734\) 0 0
\(735\) −1.98610 8.41482i −0.0732585 0.310385i
\(736\) 0 0
\(737\) 10.2307 + 0.462265i 0.376852 + 0.0170277i
\(738\) 0 0
\(739\) −36.7435 + 26.1649i −1.35163 + 0.962491i −0.351981 + 0.936007i \(0.614492\pi\)
−0.999649 + 0.0264840i \(0.991569\pi\)
\(740\) 0 0
\(741\) 24.1773 + 21.2143i 0.888174 + 0.779327i
\(742\) 0 0
\(743\) −12.6837 + 31.6823i −0.465319 + 1.16231i 0.491305 + 0.870987i \(0.336520\pi\)
−0.956625 + 0.291324i \(0.905904\pi\)
\(744\) 0 0
\(745\) −4.62007 15.7345i −0.169266 0.576469i
\(746\) 0 0
\(747\) 12.6955 41.3289i 0.464505 1.51215i
\(748\) 0 0
\(749\) 0.0692195 + 0.285327i 0.00252923 + 0.0104256i
\(750\) 0 0
\(751\) −12.4611 14.3809i −0.454713 0.524767i 0.481383 0.876510i \(-0.340135\pi\)
−0.936097 + 0.351743i \(0.885589\pi\)
\(752\) 0 0
\(753\) 19.6777 + 34.5775i 0.717096 + 1.26007i
\(754\) 0 0
\(755\) −2.80167 + 0.539977i −0.101963 + 0.0196518i
\(756\) 0 0
\(757\) 9.08557 17.6236i 0.330221 0.640539i −0.664019 0.747716i \(-0.731151\pi\)
0.994240 + 0.107177i \(0.0341810\pi\)
\(758\) 0 0
\(759\) −12.3877 + 8.70569i −0.449645 + 0.315996i
\(760\) 0 0
\(761\) 11.7391 + 10.1720i 0.425542 + 0.368734i 0.841143 0.540813i \(-0.181883\pi\)
−0.415601 + 0.909547i \(0.636429\pi\)
\(762\) 0 0
\(763\) 41.1653 + 7.93396i 1.49028 + 0.287228i
\(764\) 0 0
\(765\) 5.58427 + 8.93155i 0.201900 + 0.322921i
\(766\) 0 0
\(767\) 18.0079 31.1906i 0.650227 1.12623i
\(768\) 0 0
\(769\) 33.5752 + 1.59938i 1.21075 + 0.0576752i 0.643223 0.765679i \(-0.277597\pi\)
0.567528 + 0.823354i \(0.307900\pi\)
\(770\) 0 0
\(771\) 2.16438 + 3.41432i 0.0779481 + 0.122964i
\(772\) 0 0
\(773\) 6.40397 6.71629i 0.230335 0.241568i −0.598417 0.801185i \(-0.704203\pi\)
0.828751 + 0.559617i \(0.189052\pi\)
\(774\)