Properties

Label 804.2.y.b.121.1
Level 804
Weight 2
Character 804.121
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 121.1
Character \(\chi\) = 804.121
Dual form 804.2.y.b.505.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(-2.40809 + 1.54759i) q^{5} +(-2.21597 - 0.887140i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(-2.40809 + 1.54759i) q^{5} +(-2.21597 - 0.887140i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.0929229 + 1.95069i) q^{11} +(6.57525 - 0.627860i) q^{13} +(-0.407377 + 2.83337i) q^{15} +(-0.498266 - 2.05388i) q^{17} +(6.01505 - 2.40806i) q^{19} +(-2.12161 + 1.09376i) q^{21} +(5.97032 + 1.15068i) q^{23} +(1.32681 - 2.90531i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(3.14109 - 5.44053i) q^{29} +(6.99582 + 0.668020i) q^{31} +(1.53509 + 1.20720i) q^{33} +(6.70919 - 1.29309i) q^{35} +(0.506614 + 0.877481i) q^{37} +(3.83137 - 5.38040i) q^{39} +(-2.25239 + 2.14765i) q^{41} +(-4.07902 - 1.19771i) q^{43} +(1.87454 + 2.16334i) q^{45} +(2.70871 + 7.82632i) q^{47} +(-0.942638 - 0.898803i) q^{49} +(-1.87852 - 0.968442i) q^{51} +(-5.19321 + 1.52486i) q^{53} +(-3.24263 - 4.55364i) q^{55} +(2.11913 - 6.12282i) q^{57} +(-0.533864 - 1.16900i) q^{59} +(-0.212043 + 4.45133i) q^{61} +(-0.562745 + 2.31967i) q^{63} +(-14.8621 + 11.6877i) q^{65} +(2.37673 - 7.83270i) q^{67} +(4.77936 - 3.75853i) q^{69} +(-1.57953 + 6.51090i) q^{71} +(-0.0356447 + 0.748274i) q^{73} +(-1.32681 - 2.90531i) q^{75} +(1.52462 - 4.40511i) q^{77} +(-3.92414 - 5.51069i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(9.09130 + 4.68689i) q^{83} +(4.37843 + 4.17483i) q^{85} +(-2.05470 - 5.93667i) q^{87} +(-9.03106 - 10.4224i) q^{89} +(-15.1275 - 4.44185i) q^{91} +(5.08615 - 4.84963i) q^{93} +(-10.7581 + 15.1077i) q^{95} +(-5.11159 - 8.85353i) q^{97} +(1.91761 - 0.369589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{26}{33}\right)\) \(1\)

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
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) −2.40809 + 1.54759i −1.07693 + 0.692102i −0.953847 0.300294i \(-0.902915\pi\)
−0.123085 + 0.992396i \(0.539279\pi\)
\(6\) 0 0
\(7\) −2.21597 0.887140i −0.837557 0.335307i −0.0870783 0.996201i \(-0.527753\pi\)
−0.750479 + 0.660894i \(0.770177\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) 0.0929229 + 1.95069i 0.0280173 + 0.588155i 0.968605 + 0.248605i \(0.0799720\pi\)
−0.940588 + 0.339551i \(0.889725\pi\)
\(12\) 0 0
\(13\) 6.57525 0.627860i 1.82365 0.174137i 0.873682 0.486498i \(-0.161726\pi\)
0.949963 + 0.312361i \(0.101120\pi\)
\(14\) 0 0
\(15\) −0.407377 + 2.83337i −0.105184 + 0.731573i
\(16\) 0 0
\(17\) −0.498266 2.05388i −0.120847 0.498140i −0.999776 0.0211855i \(-0.993256\pi\)
0.878928 0.476954i \(-0.158259\pi\)
\(18\) 0 0
\(19\) 6.01505 2.40806i 1.37995 0.552448i 0.441310 0.897354i \(-0.354514\pi\)
0.938637 + 0.344907i \(0.112090\pi\)
\(20\) 0 0
\(21\) −2.12161 + 1.09376i −0.462973 + 0.238679i
\(22\) 0 0
\(23\) 5.97032 + 1.15068i 1.24490 + 0.239934i 0.768818 0.639468i \(-0.220845\pi\)
0.476080 + 0.879402i \(0.342057\pi\)
\(24\) 0 0
\(25\) 1.32681 2.90531i 0.265362 0.581062i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) 3.14109 5.44053i 0.583286 1.01028i −0.411800 0.911274i \(-0.635100\pi\)
0.995087 0.0990074i \(-0.0315667\pi\)
\(30\) 0 0
\(31\) 6.99582 + 0.668020i 1.25649 + 0.119980i 0.701978 0.712198i \(-0.252300\pi\)
0.554508 + 0.832178i \(0.312906\pi\)
\(32\) 0 0
\(33\) 1.53509 + 1.20720i 0.267224 + 0.210147i
\(34\) 0 0
\(35\) 6.70919 1.29309i 1.13406 0.218572i
\(36\) 0 0
\(37\) 0.506614 + 0.877481i 0.0832868 + 0.144257i 0.904660 0.426134i \(-0.140125\pi\)
−0.821373 + 0.570391i \(0.806792\pi\)
\(38\) 0 0
\(39\) 3.83137 5.38040i 0.613509 0.861553i
\(40\) 0 0
\(41\) −2.25239 + 2.14765i −0.351764 + 0.335407i −0.845273 0.534334i \(-0.820562\pi\)
0.493509 + 0.869741i \(0.335714\pi\)
\(42\) 0 0
\(43\) −4.07902 1.19771i −0.622044 0.182649i −0.0445017 0.999009i \(-0.514170\pi\)
−0.577542 + 0.816361i \(0.695988\pi\)
\(44\) 0 0
\(45\) 1.87454 + 2.16334i 0.279440 + 0.322491i
\(46\) 0 0
\(47\) 2.70871 + 7.82632i 0.395107 + 1.14159i 0.950695 + 0.310128i \(0.100372\pi\)
−0.555588 + 0.831458i \(0.687507\pi\)
\(48\) 0 0
\(49\) −0.942638 0.898803i −0.134663 0.128400i
\(50\) 0 0
\(51\) −1.87852 0.968442i −0.263045 0.135609i
\(52\) 0 0
\(53\) −5.19321 + 1.52486i −0.713343 + 0.209456i −0.618215 0.786009i \(-0.712144\pi\)
−0.0951274 + 0.995465i \(0.530326\pi\)
\(54\) 0 0
\(55\) −3.24263 4.55364i −0.437236 0.614013i
\(56\) 0 0
\(57\) 2.11913 6.12282i 0.280685 0.810987i
\(58\) 0 0
\(59\) −0.533864 1.16900i −0.0695031 0.152191i 0.871692 0.490054i \(-0.163023\pi\)
−0.941195 + 0.337864i \(0.890296\pi\)
\(60\) 0 0
\(61\) −0.212043 + 4.45133i −0.0271493 + 0.569934i 0.943781 + 0.330572i \(0.107241\pi\)
−0.970930 + 0.239363i \(0.923062\pi\)
\(62\) 0 0
\(63\) −0.562745 + 2.31967i −0.0708992 + 0.292251i
\(64\) 0 0
\(65\) −14.8621 + 11.6877i −1.84342 + 1.44968i
\(66\) 0 0
\(67\) 2.37673 7.83270i 0.290363 0.956916i
\(68\) 0 0
\(69\) 4.77936 3.75853i 0.575367 0.452474i
\(70\) 0 0
\(71\) −1.57953 + 6.51090i −0.187455 + 0.772702i 0.797984 + 0.602678i \(0.205900\pi\)
−0.985440 + 0.170024i \(0.945615\pi\)
\(72\) 0 0
\(73\) −0.0356447 + 0.748274i −0.00417189 + 0.0875788i −0.999993 0.00374676i \(-0.998807\pi\)
0.995821 + 0.0913256i \(0.0291104\pi\)
\(74\) 0 0
\(75\) −1.32681 2.90531i −0.153207 0.335476i
\(76\) 0 0
\(77\) 1.52462 4.40511i 0.173747 0.502008i
\(78\) 0 0
\(79\) −3.92414 5.51069i −0.441501 0.620001i 0.532532 0.846410i \(-0.321241\pi\)
−0.974032 + 0.226409i \(0.927301\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) 9.09130 + 4.68689i 0.997900 + 0.514453i 0.878168 0.478353i \(-0.158766\pi\)
0.119733 + 0.992806i \(0.461796\pi\)
\(84\) 0 0
\(85\) 4.37843 + 4.17483i 0.474908 + 0.452824i
\(86\) 0 0
\(87\) −2.05470 5.93667i −0.220287 0.636478i
\(88\) 0 0
\(89\) −9.03106 10.4224i −0.957290 1.10477i −0.994423 0.105461i \(-0.966368\pi\)
0.0371333 0.999310i \(-0.488177\pi\)
\(90\) 0 0
\(91\) −15.1275 4.44185i −1.58580 0.465632i
\(92\) 0 0
\(93\) 5.08615 4.84963i 0.527409 0.502883i
\(94\) 0 0
\(95\) −10.7581 + 15.1077i −1.10376 + 1.55001i
\(96\) 0 0
\(97\) −5.11159 8.85353i −0.519003 0.898940i −0.999756 0.0220839i \(-0.992970\pi\)
0.480753 0.876856i \(-0.340363\pi\)
\(98\) 0 0
\(99\) 1.91761 0.369589i 0.192727 0.0371451i
\(100\) 0 0
\(101\) 8.97811 + 7.06046i 0.893355 + 0.702542i 0.955332 0.295535i \(-0.0954980\pi\)
−0.0619765 + 0.998078i \(0.519740\pi\)
\(102\) 0 0
\(103\) 16.6613 + 1.59096i 1.64168 + 0.156762i 0.874620 0.484808i \(-0.161111\pi\)
0.767064 + 0.641570i \(0.221717\pi\)
\(104\) 0 0
\(105\) 3.41633 5.91726i 0.333400 0.577465i
\(106\) 0 0
\(107\) 4.50997 + 2.89838i 0.435996 + 0.280197i 0.740171 0.672419i \(-0.234745\pi\)
−0.304175 + 0.952616i \(0.598381\pi\)
\(108\) 0 0
\(109\) 3.15774 6.91448i 0.302457 0.662287i −0.695987 0.718054i \(-0.745033\pi\)
0.998444 + 0.0557667i \(0.0177603\pi\)
\(110\) 0 0
\(111\) 0.994917 + 0.191755i 0.0944334 + 0.0182005i
\(112\) 0 0
\(113\) −3.26500 + 1.68323i −0.307146 + 0.158345i −0.604908 0.796296i \(-0.706790\pi\)
0.297762 + 0.954640i \(0.403760\pi\)
\(114\) 0 0
\(115\) −16.1579 + 6.46864i −1.50673 + 0.603204i
\(116\) 0 0
\(117\) −1.55722 6.41897i −0.143965 0.593434i
\(118\) 0 0
\(119\) −0.717938 + 4.99337i −0.0658133 + 0.457742i
\(120\) 0 0
\(121\) 7.15363 0.683089i 0.650330 0.0620990i
\(122\) 0 0
\(123\) 0.148083 + 3.10865i 0.0133522 + 0.280298i
\(124\) 0 0
\(125\) −0.735747 5.11723i −0.0658072 0.457699i
\(126\) 0 0
\(127\) 12.0322 + 4.81697i 1.06769 + 0.427437i 0.837911 0.545807i \(-0.183777\pi\)
0.229775 + 0.973244i \(0.426201\pi\)
\(128\) 0 0
\(129\) −3.57635 + 2.29838i −0.314880 + 0.202361i
\(130\) 0 0
\(131\) −6.78088 + 7.82555i −0.592448 + 0.683721i −0.970233 0.242172i \(-0.922140\pi\)
0.377785 + 0.925893i \(0.376686\pi\)
\(132\) 0 0
\(133\) −15.4655 −1.34103
\(134\) 0 0
\(135\) 2.86251 0.246365
\(136\) 0 0
\(137\) 10.4044 12.0073i 0.888908 1.02585i −0.110580 0.993867i \(-0.535271\pi\)
0.999488 0.0319875i \(-0.0101837\pi\)
\(138\) 0 0
\(139\) −12.6415 + 8.12420i −1.07224 + 0.689085i −0.952752 0.303750i \(-0.901761\pi\)
−0.119486 + 0.992836i \(0.538125\pi\)
\(140\) 0 0
\(141\) 7.68857 + 3.07804i 0.647494 + 0.259218i
\(142\) 0 0
\(143\) 1.83575 + 12.7679i 0.153513 + 1.06771i
\(144\) 0 0
\(145\) 0.855656 + 17.9624i 0.0710583 + 1.49170i
\(146\) 0 0
\(147\) −1.29657 + 0.123807i −0.106939 + 0.0102114i
\(148\) 0 0
\(149\) 0.444328 3.09037i 0.0364008 0.253173i −0.963493 0.267733i \(-0.913726\pi\)
0.999894 + 0.0145597i \(0.00463466\pi\)
\(150\) 0 0
\(151\) 3.04315 + 12.5440i 0.247648 + 1.02082i 0.950807 + 0.309785i \(0.100257\pi\)
−0.703159 + 0.711033i \(0.748228\pi\)
\(152\) 0 0
\(153\) −1.96207 + 0.785493i −0.158624 + 0.0635033i
\(154\) 0 0
\(155\) −17.8804 + 9.21799i −1.43619 + 0.740407i
\(156\) 0 0
\(157\) −5.69161 1.09697i −0.454240 0.0875475i −0.0430006 0.999075i \(-0.513692\pi\)
−0.411239 + 0.911528i \(0.634904\pi\)
\(158\) 0 0
\(159\) −2.24842 + 4.92334i −0.178311 + 0.390446i
\(160\) 0 0
\(161\) −12.2092 7.84639i −0.962222 0.618382i
\(162\) 0 0
\(163\) −3.07027 + 5.31786i −0.240482 + 0.416527i −0.960852 0.277064i \(-0.910639\pi\)
0.720370 + 0.693590i \(0.243972\pi\)
\(164\) 0 0
\(165\) −5.56488 0.531382i −0.433226 0.0413680i
\(166\) 0 0
\(167\) 8.39815 + 6.60438i 0.649868 + 0.511062i 0.887806 0.460218i \(-0.152229\pi\)
−0.237937 + 0.971280i \(0.576471\pi\)
\(168\) 0 0
\(169\) 30.0746 5.79640i 2.31343 0.445877i
\(170\) 0 0
\(171\) −3.23958 5.61112i −0.247737 0.429093i
\(172\) 0 0
\(173\) 10.4968 14.7407i 0.798059 1.12072i −0.192184 0.981359i \(-0.561557\pi\)
0.990242 0.139357i \(-0.0445037\pi\)
\(174\) 0 0
\(175\) −5.51759 + 5.26101i −0.417091 + 0.397695i
\(176\) 0 0
\(177\) −1.23308 0.362064i −0.0926837 0.0272144i
\(178\) 0 0
\(179\) −10.8678 12.5421i −0.812298 0.937442i 0.186690 0.982419i \(-0.440224\pi\)
−0.998988 + 0.0449766i \(0.985679\pi\)
\(180\) 0 0
\(181\) −7.12164 20.5766i −0.529347 1.52945i −0.819852 0.572575i \(-0.805944\pi\)
0.290505 0.956874i \(-0.406177\pi\)
\(182\) 0 0
\(183\) 3.22523 + 3.07525i 0.238416 + 0.227329i
\(184\) 0 0
\(185\) −2.57795 1.32903i −0.189535 0.0977120i
\(186\) 0 0
\(187\) 3.96019 1.16282i 0.289598 0.0850336i
\(188\) 0 0
\(189\) 1.38457 + 1.94435i 0.100712 + 0.141431i
\(190\) 0 0
\(191\) 2.24376 6.48292i 0.162353 0.469088i −0.834256 0.551378i \(-0.814102\pi\)
0.996608 + 0.0822903i \(0.0262235\pi\)
\(192\) 0 0
\(193\) −0.948658 2.07727i −0.0682859 0.149525i 0.872411 0.488772i \(-0.162555\pi\)
−0.940697 + 0.339247i \(0.889828\pi\)
\(194\) 0 0
\(195\) −0.899645 + 18.8859i −0.0644249 + 1.35245i
\(196\) 0 0
\(197\) −5.74338 + 23.6746i −0.409199 + 1.68674i 0.278249 + 0.960509i \(0.410246\pi\)
−0.687448 + 0.726233i \(0.741269\pi\)
\(198\) 0 0
\(199\) −15.4771 + 12.1713i −1.09714 + 0.862804i −0.991306 0.131580i \(-0.957995\pi\)
−0.105838 + 0.994383i \(0.533753\pi\)
\(200\) 0 0
\(201\) −4.36313 6.92554i −0.307752 0.488490i
\(202\) 0 0
\(203\) −11.7871 + 9.26946i −0.827291 + 0.650589i
\(204\) 0 0
\(205\) 2.10029 8.65751i 0.146691 0.604667i
\(206\) 0 0
\(207\) 0.289307 6.07331i 0.0201083 0.422124i
\(208\) 0 0
\(209\) 5.25632 + 11.5097i 0.363587 + 0.796145i
\(210\) 0 0
\(211\) 4.64631 13.4246i 0.319865 0.924190i −0.664382 0.747393i \(-0.731305\pi\)
0.984247 0.176797i \(-0.0565735\pi\)
\(212\) 0 0
\(213\) 3.88624 + 5.45746i 0.266281 + 0.373939i
\(214\) 0 0
\(215\) 11.6762 3.42844i 0.796311 0.233818i
\(216\) 0 0
\(217\) −14.9099 7.68659i −1.01215 0.521799i
\(218\) 0 0
\(219\) 0.542165 + 0.516954i 0.0366361 + 0.0349325i
\(220\) 0 0
\(221\) −4.56577 13.1919i −0.307127 0.887386i
\(222\) 0 0
\(223\) −2.96708 3.42419i −0.198690 0.229301i 0.647657 0.761932i \(-0.275749\pi\)
−0.846348 + 0.532631i \(0.821203\pi\)
\(224\) 0 0
\(225\) −3.06456 0.899837i −0.204304 0.0599892i
\(226\) 0 0
\(227\) −9.77092 + 9.31655i −0.648518 + 0.618361i −0.941200 0.337849i \(-0.890301\pi\)
0.292682 + 0.956210i \(0.405452\pi\)
\(228\) 0 0
\(229\) −15.5608 + 21.8520i −1.02828 + 1.44402i −0.137003 + 0.990571i \(0.543747\pi\)
−0.891281 + 0.453452i \(0.850193\pi\)
\(230\) 0 0
\(231\) −2.33074 4.03696i −0.153352 0.265613i
\(232\) 0 0
\(233\) −24.9584 + 4.81034i −1.63508 + 0.315136i −0.922366 0.386318i \(-0.873747\pi\)
−0.712715 + 0.701454i \(0.752535\pi\)
\(234\) 0 0
\(235\) −18.6348 14.6545i −1.21560 0.955956i
\(236\) 0 0
\(237\) −6.73447 0.643064i −0.437451 0.0417715i
\(238\) 0 0
\(239\) −0.911474 + 1.57872i −0.0589584 + 0.102119i −0.893998 0.448071i \(-0.852111\pi\)
0.835040 + 0.550190i \(0.185445\pi\)
\(240\) 0 0
\(241\) −10.2632 6.59576i −0.661111 0.424870i 0.166600 0.986025i \(-0.446721\pi\)
−0.827711 + 0.561154i \(0.810357\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) 3.66094 + 0.705588i 0.233889 + 0.0450784i
\(246\) 0 0
\(247\) 38.0385 19.6102i 2.42033 1.24777i
\(248\) 0 0
\(249\) 9.49566 3.80149i 0.601763 0.240909i
\(250\) 0 0
\(251\) −4.02486 16.5907i −0.254047 1.04720i −0.945719 0.324985i \(-0.894641\pi\)
0.691672 0.722212i \(-0.256874\pi\)
\(252\) 0 0
\(253\) −1.68985 + 11.7532i −0.106240 + 0.738916i
\(254\) 0 0
\(255\) 6.02239 0.575069i 0.377137 0.0360122i
\(256\) 0 0
\(257\) 0.105536 + 2.21548i 0.00658318 + 0.138198i 0.999766 + 0.0216311i \(0.00688592\pi\)
−0.993183 + 0.116567i \(0.962811\pi\)
\(258\) 0 0
\(259\) −0.344192 2.39391i −0.0213870 0.148750i
\(260\) 0 0
\(261\) −5.83218 2.33485i −0.361003 0.144524i
\(262\) 0 0
\(263\) −18.8984 + 12.1453i −1.16533 + 0.748909i −0.972632 0.232350i \(-0.925359\pi\)
−0.192693 + 0.981259i \(0.561722\pi\)
\(264\) 0 0
\(265\) 10.1459 11.7090i 0.623256 0.719276i
\(266\) 0 0
\(267\) −13.7908 −0.843984
\(268\) 0 0
\(269\) −27.7856 −1.69412 −0.847058 0.531500i \(-0.821629\pi\)
−0.847058 + 0.531500i \(0.821629\pi\)
\(270\) 0 0
\(271\) 7.59717 8.76760i 0.461495 0.532594i −0.476531 0.879157i \(-0.658106\pi\)
0.938026 + 0.346564i \(0.112652\pi\)
\(272\) 0 0
\(273\) −13.2634 + 8.52384i −0.802735 + 0.515886i
\(274\) 0 0
\(275\) 5.79066 + 2.31823i 0.349190 + 0.139794i
\(276\) 0 0
\(277\) −1.11722 7.77043i −0.0671272 0.466880i −0.995464 0.0951394i \(-0.969670\pi\)
0.928337 0.371740i \(-0.121239\pi\)
\(278\) 0 0
\(279\) −0.334389 7.01968i −0.0200193 0.420257i
\(280\) 0 0
\(281\) 11.4831 1.09651i 0.685026 0.0654120i 0.253261 0.967398i \(-0.418497\pi\)
0.431765 + 0.901986i \(0.357891\pi\)
\(282\) 0 0
\(283\) −1.37935 + 9.59356i −0.0819936 + 0.570278i 0.906865 + 0.421421i \(0.138469\pi\)
−0.988859 + 0.148857i \(0.952441\pi\)
\(284\) 0 0
\(285\) 4.37254 + 18.0239i 0.259007 + 1.06764i
\(286\) 0 0
\(287\) 6.89649 2.76094i 0.407087 0.162973i
\(288\) 0 0
\(289\) 11.1400 5.74309i 0.655296 0.337829i
\(290\) 0 0
\(291\) −10.0384 1.93475i −0.588463 0.113417i
\(292\) 0 0
\(293\) 2.44506 5.35394i 0.142842 0.312780i −0.824666 0.565620i \(-0.808637\pi\)
0.967508 + 0.252839i \(0.0813643\pi\)
\(294\) 0 0
\(295\) 3.09472 + 1.98886i 0.180182 + 0.115796i
\(296\) 0 0
\(297\) 0.976451 1.69126i 0.0566595 0.0981371i
\(298\) 0 0
\(299\) 39.9788 + 3.81751i 2.31203 + 0.220772i
\(300\) 0 0
\(301\) 7.97644 + 6.27274i 0.459754 + 0.361555i
\(302\) 0 0
\(303\) 11.2154 2.16158i 0.644305 0.124180i
\(304\) 0 0
\(305\) −6.37820 11.0474i −0.365215 0.632570i
\(306\) 0 0
\(307\) −8.92660 + 12.5357i −0.509468 + 0.715448i −0.986559 0.163406i \(-0.947752\pi\)
0.477091 + 0.878854i \(0.341691\pi\)
\(308\) 0 0
\(309\) 12.1132 11.5499i 0.689095 0.657051i
\(310\) 0 0
\(311\) 1.21115 + 0.355625i 0.0686779 + 0.0201657i 0.315891 0.948795i \(-0.397697\pi\)
−0.247213 + 0.968961i \(0.579515\pi\)
\(312\) 0 0
\(313\) 14.0570 + 16.2227i 0.794551 + 0.916961i 0.998069 0.0621101i \(-0.0197830\pi\)
−0.203518 + 0.979071i \(0.565238\pi\)
\(314\) 0 0
\(315\) −2.23474 6.45687i −0.125914 0.363803i
\(316\) 0 0
\(317\) 21.4339 + 20.4372i 1.20385 + 1.14787i 0.985082 + 0.172088i \(0.0550514\pi\)
0.218765 + 0.975777i \(0.429797\pi\)
\(318\) 0 0
\(319\) 10.9047 + 5.62175i 0.610545 + 0.314758i
\(320\) 0 0
\(321\) 5.14386 1.51037i 0.287102 0.0843008i
\(322\) 0 0
\(323\) −7.94298 11.1543i −0.441959 0.620645i
\(324\) 0 0
\(325\) 6.89998 19.9362i 0.382742 1.10586i
\(326\) 0 0
\(327\) −3.15774 6.91448i −0.174623 0.382372i
\(328\) 0 0
\(329\) 0.940612 19.7459i 0.0518576 1.08863i
\(330\) 0 0
\(331\) −7.47518 + 30.8131i −0.410873 + 1.69364i 0.271335 + 0.962485i \(0.412535\pi\)
−0.682208 + 0.731158i \(0.738980\pi\)
\(332\) 0 0
\(333\) 0.796451 0.626336i 0.0436452 0.0343230i
\(334\) 0 0
\(335\) 6.39841 + 22.5401i 0.349582 + 1.23150i
\(336\) 0 0
\(337\) 6.36798 5.00784i 0.346886 0.272794i −0.429480 0.903076i \(-0.641303\pi\)
0.776366 + 0.630282i \(0.217061\pi\)
\(338\) 0 0
\(339\) −0.866025 + 3.56980i −0.0470360 + 0.193885i
\(340\) 0 0
\(341\) −0.653029 + 13.7088i −0.0353635 + 0.742371i
\(342\) 0 0
\(343\) 8.23252 + 18.0267i 0.444514 + 0.973350i
\(344\) 0 0
\(345\) −5.69249 + 16.4474i −0.306473 + 0.885496i
\(346\) 0 0
\(347\) −13.0088 18.2682i −0.698347 0.980691i −0.999631 0.0271563i \(-0.991355\pi\)
0.301285 0.953534i \(-0.402585\pi\)
\(348\) 0 0
\(349\) 15.9919 4.69564i 0.856025 0.251352i 0.175864 0.984414i \(-0.443728\pi\)
0.680161 + 0.733063i \(0.261910\pi\)
\(350\) 0 0
\(351\) −5.87090 3.02666i −0.313365 0.161551i
\(352\) 0 0
\(353\) −7.55064 7.19952i −0.401880 0.383192i 0.462008 0.886876i \(-0.347129\pi\)
−0.863888 + 0.503684i \(0.831978\pi\)
\(354\) 0 0
\(355\) −6.27254 18.1233i −0.332912 0.961886i
\(356\) 0 0
\(357\) 3.30359 + 3.81254i 0.174844 + 0.201781i
\(358\) 0 0
\(359\) 31.8007 + 9.33751i 1.67837 + 0.492815i 0.975776 0.218772i \(-0.0702050\pi\)
0.702598 + 0.711587i \(0.252023\pi\)
\(360\) 0 0
\(361\) 16.6311 15.8577i 0.875322 0.834618i
\(362\) 0 0
\(363\) 4.16839 5.85368i 0.218784 0.307239i
\(364\) 0 0
\(365\) −1.07218 1.85708i −0.0561207 0.0972038i
\(366\) 0 0
\(367\) −1.82089 + 0.350947i −0.0950495 + 0.0183193i −0.236554 0.971618i \(-0.576018\pi\)
0.141505 + 0.989938i \(0.454806\pi\)
\(368\) 0 0
\(369\) 2.44634 + 1.92382i 0.127351 + 0.100150i
\(370\) 0 0
\(371\) 12.8608 + 1.22805i 0.667698 + 0.0637574i
\(372\) 0 0
\(373\) −10.1961 + 17.6601i −0.527932 + 0.914404i 0.471538 + 0.881846i \(0.343699\pi\)
−0.999470 + 0.0325588i \(0.989634\pi\)
\(374\) 0 0
\(375\) −4.34916 2.79503i −0.224590 0.144335i
\(376\) 0 0
\(377\) 17.2376 37.7450i 0.887780 1.94397i
\(378\) 0 0
\(379\) −9.89327 1.90677i −0.508183 0.0979443i −0.0712863 0.997456i \(-0.522710\pi\)
−0.436897 + 0.899512i \(0.643923\pi\)
\(380\) 0 0
\(381\) 11.5198 5.93889i 0.590179 0.304259i
\(382\) 0 0
\(383\) 5.80952 2.32578i 0.296852 0.118842i −0.218455 0.975847i \(-0.570102\pi\)
0.515308 + 0.857005i \(0.327678\pi\)
\(384\) 0 0
\(385\) 3.14586 + 12.9674i 0.160328 + 0.660880i
\(386\) 0 0
\(387\) −0.605012 + 4.20795i −0.0307545 + 0.213902i
\(388\) 0 0
\(389\) −28.7904 + 2.74915i −1.45973 + 0.139388i −0.794507 0.607255i \(-0.792271\pi\)
−0.665226 + 0.746642i \(0.731665\pi\)
\(390\) 0 0
\(391\) −0.611439 12.8357i −0.0309218 0.649128i
\(392\) 0 0
\(393\) 1.47363 + 10.2493i 0.0743346 + 0.517008i
\(394\) 0 0
\(395\) 17.9780 + 7.19729i 0.904570 + 0.362135i
\(396\) 0 0
\(397\) −23.7386 + 15.2559i −1.19141 + 0.765671i −0.977449 0.211172i \(-0.932272\pi\)
−0.213958 + 0.976843i \(0.568636\pi\)
\(398\) 0 0
\(399\) −10.1277 + 11.6880i −0.507020 + 0.585132i
\(400\) 0 0
\(401\) 28.3871 1.41758 0.708792 0.705418i \(-0.249241\pi\)
0.708792 + 0.705418i \(0.249241\pi\)
\(402\) 0 0
\(403\) 46.4187 2.31228
\(404\) 0 0
\(405\) 1.87454 2.16334i 0.0931468 0.107497i
\(406\) 0 0
\(407\) −1.66462 + 1.06979i −0.0825121 + 0.0530273i
\(408\) 0 0
\(409\) −23.7005 9.48825i −1.17191 0.469164i −0.297679 0.954666i \(-0.596212\pi\)
−0.874235 + 0.485502i \(0.838637\pi\)
\(410\) 0 0
\(411\) −2.26109 15.7262i −0.111531 0.775719i
\(412\) 0 0
\(413\) 0.145960 + 3.06408i 0.00718222 + 0.150773i
\(414\) 0 0
\(415\) −29.1461 + 2.78311i −1.43073 + 0.136618i
\(416\) 0 0
\(417\) −2.13856 + 14.8740i −0.104726 + 0.728384i
\(418\) 0 0
\(419\) −5.02151 20.6990i −0.245317 1.01121i −0.952587 0.304267i \(-0.901589\pi\)
0.707270 0.706944i \(-0.249927\pi\)
\(420\) 0 0
\(421\) −8.87376 + 3.55252i −0.432481 + 0.173139i −0.577680 0.816263i \(-0.696042\pi\)
0.145199 + 0.989402i \(0.453618\pi\)
\(422\) 0 0
\(423\) 7.36117 3.79495i 0.357912 0.184517i
\(424\) 0 0
\(425\) −6.62827 1.27749i −0.321518 0.0619676i
\(426\) 0 0
\(427\) 4.41883 9.67589i 0.213842 0.468249i
\(428\) 0 0
\(429\) 10.8515 + 6.97385i 0.523916 + 0.336701i
\(430\) 0 0
\(431\) 14.0446 24.3260i 0.676506 1.17174i −0.299520 0.954090i \(-0.596827\pi\)
0.976026 0.217653i \(-0.0698402\pi\)
\(432\) 0 0
\(433\) −13.0116 1.24245i −0.625296 0.0597086i −0.222402 0.974955i \(-0.571390\pi\)
−0.402894 + 0.915246i \(0.631996\pi\)
\(434\) 0 0
\(435\) 14.1354 + 11.1162i 0.677742 + 0.532982i
\(436\) 0 0
\(437\) 38.6827 7.45548i 1.85044 0.356644i
\(438\) 0 0
\(439\) −3.87835 6.71750i −0.185103 0.320609i 0.758508 0.651664i \(-0.225929\pi\)
−0.943611 + 0.331055i \(0.892595\pi\)
\(440\) 0 0
\(441\) −0.755504 + 1.06096i −0.0359764 + 0.0505217i
\(442\) 0 0
\(443\) 19.1488 18.2584i 0.909788 0.867481i −0.0818355 0.996646i \(-0.526078\pi\)
0.991623 + 0.129165i \(0.0412297\pi\)
\(444\) 0 0
\(445\) 37.8772 + 11.1217i 1.79555 + 0.527221i
\(446\) 0 0
\(447\) −2.04457 2.35956i −0.0967050 0.111604i
\(448\) 0 0
\(449\) 5.05216 + 14.5973i 0.238426 + 0.688888i 0.999205 + 0.0398758i \(0.0126962\pi\)
−0.760778 + 0.649012i \(0.775183\pi\)
\(450\) 0 0
\(451\) −4.39870 4.19415i −0.207127 0.197495i
\(452\) 0 0
\(453\) 11.4730 + 5.91473i 0.539047 + 0.277898i
\(454\) 0 0
\(455\) 43.3027 12.7148i 2.03006 0.596080i
\(456\) 0 0
\(457\) 22.5687 + 31.6933i 1.05572 + 1.48255i 0.865565 + 0.500797i \(0.166960\pi\)
0.190156 + 0.981754i \(0.439101\pi\)
\(458\) 0 0
\(459\) −0.691244 + 1.99722i −0.0322645 + 0.0932222i
\(460\) 0 0
\(461\) −12.7244 27.8626i −0.592635 1.29769i −0.933837 0.357699i \(-0.883561\pi\)
0.341202 0.939990i \(-0.389166\pi\)
\(462\) 0 0
\(463\) −0.865967 + 18.1789i −0.0402449 + 0.844845i 0.885027 + 0.465540i \(0.154140\pi\)
−0.925272 + 0.379305i \(0.876163\pi\)
\(464\) 0 0
\(465\) −4.74269 + 19.5496i −0.219937 + 0.906592i
\(466\) 0 0
\(467\) −4.12624 + 3.24491i −0.190940 + 0.150156i −0.709053 0.705156i \(-0.750877\pi\)
0.518113 + 0.855312i \(0.326635\pi\)
\(468\) 0 0
\(469\) −12.2155 + 15.2485i −0.564057 + 0.704112i
\(470\) 0 0
\(471\) −4.55624 + 3.58307i −0.209941 + 0.165099i
\(472\) 0 0
\(473\) 1.95732 8.06819i 0.0899978 0.370976i
\(474\) 0 0
\(475\) 0.984664 20.6706i 0.0451795 0.948434i
\(476\) 0 0
\(477\) 2.24842 + 4.92334i 0.102948 + 0.225424i
\(478\) 0 0
\(479\) 14.1475 40.8764i 0.646414 1.86769i 0.178438 0.983951i \(-0.442896\pi\)
0.467977 0.883741i \(-0.344983\pi\)
\(480\) 0 0
\(481\) 3.88205 + 5.45157i 0.177006 + 0.248570i
\(482\) 0 0
\(483\) −13.9252 + 4.08882i −0.633621 + 0.186048i
\(484\) 0 0
\(485\) 26.0108 + 13.4095i 1.18109 + 0.608894i
\(486\) 0 0
\(487\) −18.6220 17.7561i −0.843844 0.804604i 0.138758 0.990326i \(-0.455689\pi\)
−0.982602 + 0.185723i \(0.940537\pi\)
\(488\) 0 0
\(489\) 2.00837 + 5.80281i 0.0908217 + 0.262412i
\(490\) 0 0
\(491\) −4.62424 5.33666i −0.208689 0.240840i 0.641750 0.766914i \(-0.278209\pi\)
−0.850439 + 0.526074i \(0.823663\pi\)
\(492\) 0 0
\(493\) −12.7393 3.74060i −0.573750 0.168468i
\(494\) 0 0
\(495\) −4.04582 + 3.85768i −0.181846 + 0.173390i
\(496\) 0 0
\(497\) 9.27627 13.0267i 0.416098 0.584327i
\(498\) 0 0
\(499\) 21.1000 + 36.5463i 0.944567 + 1.63604i 0.756617 + 0.653859i \(0.226851\pi\)
0.187950 + 0.982179i \(0.439816\pi\)
\(500\) 0 0
\(501\) 10.4909 2.02195i 0.468698 0.0903341i
\(502\) 0 0
\(503\) −16.4388 12.9276i −0.732970 0.576414i 0.180376 0.983598i \(-0.442269\pi\)
−0.913346 + 0.407183i \(0.866511\pi\)
\(504\) 0 0
\(505\) −32.5468 3.10784i −1.44831 0.138297i
\(506\) 0 0
\(507\) 15.3140 26.5247i 0.680120 1.17800i
\(508\) 0 0
\(509\) −33.8115 21.7293i −1.49867 0.963136i −0.995068 0.0991989i \(-0.968372\pi\)
−0.503601 0.863937i \(-0.667992\pi\)
\(510\) 0 0
\(511\) 0.742811 1.62653i 0.0328600 0.0719534i
\(512\) 0 0
\(513\) −6.36208 1.22619i −0.280893 0.0541376i
\(514\) 0 0
\(515\) −42.5841 + 21.9536i −1.87648 + 0.967392i
\(516\) 0 0
\(517\) −15.0150 + 6.01111i −0.660360 + 0.264368i
\(518\) 0 0
\(519\) −4.26634 17.5861i −0.187271 0.771944i
\(520\) 0 0
\(521\) −1.22689 + 8.53320i −0.0537510 + 0.373846i 0.945136 + 0.326677i \(0.105929\pi\)
−0.998887 + 0.0471690i \(0.984980\pi\)
\(522\) 0 0
\(523\) −8.40422 + 0.802505i −0.367491 + 0.0350911i −0.277168 0.960821i \(-0.589396\pi\)
−0.0903226 + 0.995913i \(0.528790\pi\)
\(524\) 0 0
\(525\) 0.362754 + 7.61515i 0.0158319 + 0.332352i
\(526\) 0 0
\(527\) −2.11375 14.7014i −0.0920763 0.640405i
\(528\) 0 0
\(529\) 12.9682 + 5.19168i 0.563834 + 0.225725i
\(530\) 0 0
\(531\) −1.08112 + 0.694796i −0.0469167 + 0.0301516i
\(532\) 0 0
\(533\) −13.4616 + 15.5355i −0.583086 + 0.672918i
\(534\) 0 0
\(535\) −15.3459 −0.663463
\(536\) 0 0
\(537\) −16.5956 −0.716153
\(538\) 0 0
\(539\) 1.66570 1.92231i 0.0717466 0.0828000i
\(540\) 0 0
\(541\) −9.92851 + 6.38067i −0.426860 + 0.274326i −0.736382 0.676566i \(-0.763467\pi\)
0.309522 + 0.950892i \(0.399831\pi\)
\(542\) 0 0
\(543\) −20.2145 8.09265i −0.867486 0.347289i
\(544\) 0 0
\(545\) 3.09664 + 21.5376i 0.132645 + 0.922569i
\(546\) 0 0
\(547\) 0.654749 + 13.7449i 0.0279950 + 0.587688i 0.968666 + 0.248368i \(0.0798941\pi\)
−0.940671 + 0.339320i \(0.889803\pi\)
\(548\) 0 0
\(549\) 4.43620 0.423605i 0.189332 0.0180790i
\(550\) 0 0
\(551\) 5.79269 40.2890i 0.246777 1.71637i
\(552\) 0 0
\(553\) 3.80703 + 15.6928i 0.161891 + 0.667325i
\(554\) 0 0
\(555\) −2.69261 + 1.07796i −0.114295 + 0.0457568i
\(556\) 0 0
\(557\) −5.98962 + 3.08786i −0.253788 + 0.130837i −0.580427 0.814312i \(-0.697114\pi\)
0.326639 + 0.945149i \(0.394084\pi\)
\(558\) 0 0
\(559\) −27.5725 5.31417i −1.16619 0.224765i
\(560\) 0 0
\(561\) 1.71457 3.75439i 0.0723894 0.158511i
\(562\) 0 0
\(563\) 16.2055 + 10.4147i 0.682982 + 0.438926i 0.835585 0.549362i \(-0.185129\pi\)
−0.152603 + 0.988288i \(0.548765\pi\)
\(564\) 0 0
\(565\) 5.25749 9.10624i 0.221184 0.383103i
\(566\) 0 0
\(567\) 2.37614 + 0.226894i 0.0997886 + 0.00952866i
\(568\) 0 0
\(569\) −25.3526 19.9375i −1.06284 0.835824i −0.0759291 0.997113i \(-0.524192\pi\)
−0.986907 + 0.161290i \(0.948435\pi\)
\(570\) 0 0
\(571\) −24.5983 + 4.74094i −1.02941 + 0.198402i −0.675872 0.737019i \(-0.736233\pi\)
−0.353536 + 0.935421i \(0.615021\pi\)
\(572\) 0 0
\(573\) −3.43011 5.94113i −0.143295 0.248194i
\(574\) 0 0
\(575\) 11.2646 15.8189i 0.469766 0.659694i
\(576\) 0 0
\(577\) 3.80338 3.62652i 0.158337 0.150974i −0.606769 0.794878i \(-0.707535\pi\)
0.765106 + 0.643904i \(0.222686\pi\)
\(578\) 0 0
\(579\) −2.19114 0.643376i −0.0910605 0.0267378i
\(580\) 0 0
\(581\) −15.9881 18.4513i −0.663299 0.765488i
\(582\) 0 0
\(583\) −3.45711 9.98866i −0.143179 0.413688i
\(584\) 0 0
\(585\) 13.6839 + 13.0475i 0.565758 + 0.539449i
\(586\) 0 0
\(587\) 15.4859 + 7.98356i 0.639173 + 0.329517i 0.747168 0.664635i \(-0.231413\pi\)
−0.107995 + 0.994151i \(0.534443\pi\)
\(588\) 0 0
\(589\) 43.6889 12.8282i 1.80017 0.528577i
\(590\) 0 0
\(591\) 14.1309 + 19.8441i 0.581268 + 0.816277i
\(592\) 0 0
\(593\) 11.2522 32.5111i 0.462072 1.33507i −0.437861 0.899043i \(-0.644264\pi\)
0.899933 0.436027i \(-0.143615\pi\)
\(594\) 0 0
\(595\) −5.99882 13.1356i −0.245928 0.538506i
\(596\) 0 0
\(597\) −0.936872 + 19.6674i −0.0383436 + 0.804932i
\(598\) 0 0
\(599\) −7.49485 + 30.8942i −0.306231 + 1.26230i 0.585847 + 0.810422i \(0.300762\pi\)
−0.892078 + 0.451881i \(0.850753\pi\)
\(600\) 0 0
\(601\) 3.47810 2.73521i 0.141875 0.111571i −0.544699 0.838631i \(-0.683356\pi\)
0.686574 + 0.727060i \(0.259114\pi\)
\(602\) 0 0
\(603\) −8.09122 1.23783i −0.329500 0.0504082i
\(604\) 0 0
\(605\) −16.1695 + 12.7158i −0.657382 + 0.516971i
\(606\) 0 0
\(607\) −2.80429 + 11.5594i −0.113823 + 0.469183i 0.886161 + 0.463378i \(0.153363\pi\)
−0.999983 + 0.00580484i \(0.998152\pi\)
\(608\) 0 0
\(609\) −0.713504 + 14.9783i −0.0289126 + 0.606951i
\(610\) 0 0
\(611\) 22.7243 + 49.7593i 0.919327 + 2.01304i
\(612\) 0 0
\(613\) 14.0522 40.6011i 0.567562 1.63986i −0.186048 0.982541i \(-0.559568\pi\)
0.753610 0.657322i \(-0.228311\pi\)
\(614\) 0 0
\(615\) −5.16751 7.25676i −0.208374 0.292621i
\(616\) 0 0
\(617\) 20.7253 6.08549i 0.834369 0.244993i 0.163476 0.986547i \(-0.447729\pi\)
0.670893 + 0.741555i \(0.265911\pi\)
\(618\) 0 0
\(619\) 41.8553 + 21.5779i 1.68231 + 0.867289i 0.989221 + 0.146434i \(0.0467795\pi\)
0.693085 + 0.720855i \(0.256251\pi\)
\(620\) 0 0
\(621\) −4.40045 4.19582i −0.176584 0.168372i
\(622\) 0 0
\(623\) 10.7664 + 31.1075i 0.431347 + 1.24630i
\(624\) 0 0
\(625\) 20.1490 + 23.2532i 0.805962 + 0.930130i
\(626\) 0 0
\(627\) 12.1406 + 3.56481i 0.484851 + 0.142365i
\(628\) 0 0
\(629\) 1.54981 1.47774i 0.0617951 0.0589215i
\(630\) 0 0
\(631\) −3.05237 + 4.28645i −0.121513 + 0.170641i −0.870852 0.491546i \(-0.836432\pi\)
0.749339 + 0.662187i \(0.230371\pi\)
\(632\) 0 0
\(633\) −7.10297 12.3027i −0.282318 0.488989i
\(634\) 0 0
\(635\) −36.4294 + 7.02118i −1.44565 + 0.278627i
\(636\) 0 0
\(637\) −6.76240 5.31801i −0.267936 0.210707i
\(638\) 0 0
\(639\) 6.66942 + 0.636853i 0.263838 + 0.0251935i
\(640\) 0 0
\(641\) −12.1023 + 20.9617i −0.478010 + 0.827938i −0.999682 0.0252079i \(-0.991975\pi\)
0.521672 + 0.853146i \(0.325309\pi\)
\(642\) 0 0
\(643\) −7.55952 4.85821i −0.298118 0.191589i 0.383027 0.923737i \(-0.374882\pi\)
−0.681146 + 0.732148i \(0.738518\pi\)
\(644\) 0 0
\(645\) 5.05524 11.0694i 0.199050 0.435859i
\(646\) 0 0
\(647\) −10.5459 2.03256i −0.414603 0.0799081i −0.0223157 0.999751i \(-0.507104\pi\)
−0.392287 + 0.919843i \(0.628316\pi\)
\(648\) 0 0
\(649\) 2.23075 1.15003i 0.0875645 0.0451426i
\(650\) 0 0
\(651\) −15.5730 + 6.23450i −0.610356 + 0.244350i
\(652\) 0 0
\(653\) 9.24076 + 38.0909i 0.361619 + 1.49061i 0.804457 + 0.594011i \(0.202456\pi\)
−0.442838 + 0.896602i \(0.646028\pi\)
\(654\) 0 0
\(655\) 4.21826 29.3387i 0.164821 1.14636i
\(656\) 0 0
\(657\) 0.745730 0.0712086i 0.0290937 0.00277811i
\(658\) 0 0
\(659\) −2.02839 42.5811i −0.0790148 1.65872i −0.596189 0.802844i \(-0.703319\pi\)
0.517174 0.855880i \(-0.326984\pi\)
\(660\) 0 0
\(661\) −1.30506 9.07690i −0.0507610 0.353051i −0.999334 0.0364920i \(-0.988382\pi\)
0.948573 0.316559i \(-0.102527\pi\)
\(662\) 0 0
\(663\) −12.9597 5.18830i −0.503315 0.201497i
\(664\) 0 0
\(665\) 37.2423 23.9341i 1.44419 0.928126i
\(666\) 0 0
\(667\) 25.0137 28.8673i 0.968533 1.11775i
\(668\) 0 0
\(669\) −4.53085 −0.175173
\(670\) 0 0
\(671\) −8.70287 −0.335971
\(672\) 0 0
\(673\) −32.5600 + 37.5763i −1.25510 + 1.44846i −0.411563 + 0.911381i \(0.635017\pi\)
−0.843533 + 0.537077i \(0.819528\pi\)
\(674\) 0 0
\(675\) −2.68691 + 1.72678i −0.103419 + 0.0664636i
\(676\) 0 0
\(677\) −41.5445 16.6319i −1.59669 0.639216i −0.608649 0.793440i \(-0.708288\pi\)
−0.988036 + 0.154223i \(0.950712\pi\)
\(678\) 0 0
\(679\) 3.47280 + 24.1538i 0.133274 + 0.926940i
\(680\) 0 0
\(681\) 0.642389 + 13.4854i 0.0246164 + 0.516762i
\(682\) 0 0
\(683\) −1.10169 + 0.105199i −0.0421551 + 0.00402533i −0.116112 0.993236i \(-0.537043\pi\)
0.0739572 + 0.997261i \(0.476437\pi\)
\(684\) 0 0
\(685\) −6.47239 + 45.0165i −0.247297 + 1.71999i
\(686\) 0 0
\(687\) 6.32453 + 26.0701i 0.241296 + 0.994635i
\(688\) 0 0
\(689\) −33.1892 + 13.2870i −1.26441 + 0.506193i
\(690\) 0 0
\(691\) 12.4814 6.43462i 0.474816 0.244785i −0.204171 0.978935i \(-0.565450\pi\)
0.678987 + 0.734151i \(0.262419\pi\)
\(692\) 0 0
\(693\) −4.57724 0.882192i −0.173875 0.0335117i
\(694\) 0 0
\(695\) 17.8690 39.1277i 0.677810 1.48420i
\(696\) 0 0
\(697\) 5.53331 + 3.55604i 0.209589 + 0.134695i
\(698\) 0 0
\(699\) −12.7089 + 22.0124i −0.480694 + 0.832586i
\(700\) 0 0
\(701\) −7.66802 0.732208i −0.289617 0.0276551i −0.0507637 0.998711i \(-0.516166\pi\)
−0.238854 + 0.971056i \(0.576772\pi\)
\(702\) 0 0
\(703\) 5.16034 + 4.05813i 0.194626 + 0.153055i
\(704\) 0 0
\(705\) −23.2783 + 4.48653i −0.876712 + 0.168972i
\(706\) 0 0
\(707\) −13.6316 23.6106i −0.512669 0.887968i
\(708\) 0 0
\(709\) 11.3239 15.9022i 0.425277 0.597218i −0.545231 0.838286i \(-0.683558\pi\)
0.970508 + 0.241068i \(0.0774975\pi\)
\(710\) 0 0
\(711\) −4.89613 + 4.66845i −0.183619 + 0.175081i
\(712\) 0 0
\(713\) 40.9986 + 12.0383i 1.53541 + 0.450837i
\(714\) 0 0
\(715\) −24.1802 27.9054i −0.904286 1.04360i
\(716\) 0 0
\(717\) 0.596228 + 1.72269i 0.0222665 + 0.0643349i
\(718\) 0 0
\(719\) 12.0022 + 11.4441i 0.447608 + 0.426793i 0.880059 0.474864i \(-0.157503\pi\)
−0.432451 + 0.901657i \(0.642351\pi\)
\(720\) 0 0
\(721\) −35.5095 18.3064i −1.32244 0.681766i
\(722\) 0 0
\(723\) −11.7057 + 3.43711i −0.435340 + 0.127827i
\(724\) 0 0
\(725\) −11.6388 16.3444i −0.432254 0.607016i
\(726\) 0 0
\(727\) −4.87250 + 14.0782i −0.180711 + 0.522130i −0.998580 0.0532744i \(-0.983034\pi\)
0.817869 + 0.575405i \(0.195155\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) −0.427513 + 8.97459i −0.0158121 + 0.331937i
\(732\) 0 0
\(733\) −2.09207 + 8.62362i −0.0772723 + 0.318521i −0.997309 0.0733112i \(-0.976643\pi\)
0.920037 + 0.391832i \(0.128159\pi\)
\(734\) 0 0
\(735\) 2.93065 2.30469i 0.108099 0.0850098i
\(736\) 0 0
\(737\) 15.5000 + 3.90842i 0.570951 + 0.143969i
\(738\) 0 0
\(739\) −31.5348 + 24.7993i −1.16003 + 0.912256i −0.997228 0.0744034i \(-0.976295\pi\)
−0.162799 + 0.986659i \(0.552052\pi\)
\(740\) 0 0
\(741\) 10.0895 41.5896i 0.370648 1.52783i
\(742\) 0 0
\(743\) −1.45325 + 30.5075i −0.0533147 + 1.11921i 0.800734 + 0.599020i \(0.204443\pi\)
−0.854049 + 0.520193i \(0.825860\pi\)
\(744\) 0 0
\(745\) 3.71264 + 8.12954i 0.136020 + 0.297843i
\(746\) 0 0
\(747\) 3.34536 9.66578i 0.122400 0.353652i
\(748\) 0 0
\(749\) −7.42269 10.4237i −0.271219 0.380874i
\(750\) 0 0
\(751\) 9.34219 2.74311i 0.340901 0.100098i −0.106801 0.994280i \(-0.534061\pi\)
0.447702 + 0.894183i \(0.352243\pi\)
\(752\) 0 0
\(753\) −15.1742 7.82282i −0.552977 0.285079i
\(754\) 0 0
\(755\) −26.7411 25.4976i −0.973210 0.927954i
\(756\) 0 0
\(757\) −5.78932 16.7271i −0.210416 0.607958i 0.789567 0.613664i \(-0.210305\pi\)
−0.999984 + 0.00570587i \(0.998184\pi\)
\(758\) 0 0
\(759\) 7.77584 + 8.97380i 0.282245 + 0.325728i
\(760\) 0 0
\(761\) 12.5219 + 3.67675i 0.453918 + 0.133282i 0.500696 0.865623i \(-0.333077\pi\)
−0.0467786 + 0.998905i \(0.514896\pi\)
\(762\) 0 0
\(763\) −13.1316 + 12.5209i −0.475395 + 0.453288i
\(764\) 0 0
\(765\) 3.50922 4.92801i 0.126876 0.178173i
\(766\) 0 0
\(767\) −4.24425 7.35126i −0.153251 0.265439i
\(768\) 0 0
\(769\) −3.69433 + 0.712024i −0.133221 + 0.0256762i −0.255426 0.966829i \(-0.582216\pi\)
0.122205 + 0.992505i \(0.461004\pi\)
\(770\) 0 0
\(771\) 1.74346 + 1.37107i 0.0627892 + 0.0493780i
\(772\) 0 0
\(773\) −46.3869 4.42941i −1.66842 0.159315i −0.782342 0.622849i \(-0.785975\pi\)
−0.886079 + 0.463534i \(0.846581\pi\)
\(774\) 0 0
\(775\) 11.2229 19.4387i 0.403140 0.698259i
\(776\) 0 0
\(777\) −2.03459 1.30755i −0.0729906 0.0469082i
\(778\)