Properties

Label 690.3.k.b.277.4
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.4
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(3.38334 + 3.68144i) q^{5} +2.44949 q^{6} +(-2.06971 - 2.06971i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(3.38334 + 3.68144i) q^{5} +2.44949 q^{6} +(-2.06971 - 2.06971i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(0.298094 - 7.06478i) q^{10} +0.900062 q^{11} +(-2.44949 - 2.44949i) q^{12} +(6.37460 - 6.37460i) q^{13} +4.13941i q^{14} +(-8.65256 - 0.365089i) q^{15} -4.00000 q^{16} +(-18.4729 - 18.4729i) q^{17} +(-3.00000 + 3.00000i) q^{18} -9.86457i q^{19} +(-7.36288 + 6.76669i) q^{20} +5.06972 q^{21} +(-0.900062 - 0.900062i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-2.10597 + 24.9111i) q^{25} -12.7492 q^{26} +(3.67423 + 3.67423i) q^{27} +(4.13941 - 4.13941i) q^{28} -7.79905i q^{29} +(8.28747 + 9.01764i) q^{30} +18.5068 q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.10235 + 1.10235i) q^{33} +36.9457i q^{34} +(0.616966 - 14.6220i) q^{35} +6.00000 q^{36} +(-22.8521 - 22.8521i) q^{37} +(-9.86457 + 9.86457i) q^{38} +15.6145i q^{39} +(14.1296 + 0.596187i) q^{40} +36.6804 q^{41} +(-5.06972 - 5.06972i) q^{42} +(14.6911 - 14.6911i) q^{43} +1.80012i q^{44} +(11.0443 - 10.1500i) q^{45} -6.78233 q^{46} +(27.0328 + 27.0328i) q^{47} +(4.89898 - 4.89898i) q^{48} -40.4326i q^{49} +(27.0171 - 22.8052i) q^{50} +45.2491 q^{51} +(12.7492 + 12.7492i) q^{52} +(51.0631 - 51.0631i) q^{53} -7.34847i q^{54} +(3.04522 + 3.31352i) q^{55} -8.27882 q^{56} +(12.0816 + 12.0816i) q^{57} +(-7.79905 + 7.79905i) q^{58} +91.7327i q^{59} +(0.730177 - 17.3051i) q^{60} -44.5012 q^{61} +(-18.5068 - 18.5068i) q^{62} +(-6.20912 + 6.20912i) q^{63} -8.00000i q^{64} +(45.0351 + 1.90023i) q^{65} +2.20469 q^{66} +(-21.6784 - 21.6784i) q^{67} +(36.9457 - 36.9457i) q^{68} +8.30662i q^{69} +(-15.2390 + 14.0051i) q^{70} +84.1101 q^{71} +(-6.00000 - 6.00000i) q^{72} +(77.0736 - 77.0736i) q^{73} +45.7041i q^{74} +(-27.9305 - 33.0891i) q^{75} +19.7291 q^{76} +(-1.86286 - 1.86286i) q^{77} +(15.6145 - 15.6145i) q^{78} -31.3293i q^{79} +(-13.5334 - 14.7258i) q^{80} -9.00000 q^{81} +(-36.6804 - 36.6804i) q^{82} +(8.70034 - 8.70034i) q^{83} +10.1394i q^{84} +(5.50664 - 130.507i) q^{85} -29.3822 q^{86} +(9.55185 + 9.55185i) q^{87} +(1.80012 - 1.80012i) q^{88} -32.1361i q^{89} +(-21.1943 - 0.894281i) q^{90} -26.3871 q^{91} +(6.78233 + 6.78233i) q^{92} +(-22.6662 + 22.6662i) q^{93} -54.0656i q^{94} +(36.3158 - 33.3752i) q^{95} -9.79796 q^{96} +(-104.238 - 104.238i) q^{97} +(-40.4326 + 40.4326i) q^{98} -2.70019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 3.38334 + 3.68144i 0.676669 + 0.736288i
\(6\) 2.44949 0.408248
\(7\) −2.06971 2.06971i −0.295672 0.295672i 0.543644 0.839316i \(-0.317044\pi\)
−0.839316 + 0.543644i \(0.817044\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 0.298094 7.06478i 0.0298094 0.706478i
\(11\) 0.900062 0.0818238 0.0409119 0.999163i \(-0.486974\pi\)
0.0409119 + 0.999163i \(0.486974\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 6.37460 6.37460i 0.490354 0.490354i −0.418064 0.908418i \(-0.637291\pi\)
0.908418 + 0.418064i \(0.137291\pi\)
\(14\) 4.13941i 0.295672i
\(15\) −8.65256 0.365089i −0.576837 0.0243392i
\(16\) −4.00000 −0.250000
\(17\) −18.4729 18.4729i −1.08664 1.08664i −0.995872 0.0907667i \(-0.971068\pi\)
−0.0907667 0.995872i \(-0.528932\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 9.86457i 0.519188i −0.965718 0.259594i \(-0.916411\pi\)
0.965718 0.259594i \(-0.0835888\pi\)
\(20\) −7.36288 + 6.76669i −0.368144 + 0.338334i
\(21\) 5.06972 0.241415
\(22\) −0.900062 0.900062i −0.0409119 0.0409119i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −2.10597 + 24.9111i −0.0842387 + 0.996446i
\(26\) −12.7492 −0.490354
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 4.13941 4.13941i 0.147836 0.147836i
\(29\) 7.79905i 0.268933i −0.990918 0.134466i \(-0.957068\pi\)
0.990918 0.134466i \(-0.0429320\pi\)
\(30\) 8.28747 + 9.01764i 0.276249 + 0.300588i
\(31\) 18.5068 0.596995 0.298497 0.954410i \(-0.403515\pi\)
0.298497 + 0.954410i \(0.403515\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −1.10235 + 1.10235i −0.0334044 + 0.0334044i
\(34\) 36.9457i 1.08664i
\(35\) 0.616966 14.6220i 0.0176276 0.417772i
\(36\) 6.00000 0.166667
\(37\) −22.8521 22.8521i −0.617623 0.617623i 0.327298 0.944921i \(-0.393862\pi\)
−0.944921 + 0.327298i \(0.893862\pi\)
\(38\) −9.86457 + 9.86457i −0.259594 + 0.259594i
\(39\) 15.6145i 0.400372i
\(40\) 14.1296 + 0.596187i 0.353239 + 0.0149047i
\(41\) 36.6804 0.894643 0.447322 0.894373i \(-0.352378\pi\)
0.447322 + 0.894373i \(0.352378\pi\)
\(42\) −5.06972 5.06972i −0.120708 0.120708i
\(43\) 14.6911 14.6911i 0.341654 0.341654i −0.515335 0.856989i \(-0.672333\pi\)
0.856989 + 0.515335i \(0.172333\pi\)
\(44\) 1.80012i 0.0409119i
\(45\) 11.0443 10.1500i 0.245429 0.225556i
\(46\) −6.78233 −0.147442
\(47\) 27.0328 + 27.0328i 0.575166 + 0.575166i 0.933568 0.358401i \(-0.116678\pi\)
−0.358401 + 0.933568i \(0.616678\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 40.4326i 0.825156i
\(50\) 27.0171 22.8052i 0.540342 0.456103i
\(51\) 45.2491 0.887237
\(52\) 12.7492 + 12.7492i 0.245177 + 0.245177i
\(53\) 51.0631 51.0631i 0.963455 0.963455i −0.0359002 0.999355i \(-0.511430\pi\)
0.999355 + 0.0359002i \(0.0114298\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 3.04522 + 3.31352i 0.0553676 + 0.0602459i
\(56\) −8.27882 −0.147836
\(57\) 12.0816 + 12.0816i 0.211958 + 0.211958i
\(58\) −7.79905 + 7.79905i −0.134466 + 0.134466i
\(59\) 91.7327i 1.55479i 0.629012 + 0.777396i \(0.283460\pi\)
−0.629012 + 0.777396i \(0.716540\pi\)
\(60\) 0.730177 17.3051i 0.0121696 0.288419i
\(61\) −44.5012 −0.729528 −0.364764 0.931100i \(-0.618850\pi\)
−0.364764 + 0.931100i \(0.618850\pi\)
\(62\) −18.5068 18.5068i −0.298497 0.298497i
\(63\) −6.20912 + 6.20912i −0.0985574 + 0.0985574i
\(64\) 8.00000i 0.125000i
\(65\) 45.0351 + 1.90023i 0.692848 + 0.0292343i
\(66\) 2.20469 0.0334044
\(67\) −21.6784 21.6784i −0.323557 0.323557i 0.526573 0.850130i \(-0.323477\pi\)
−0.850130 + 0.526573i \(0.823477\pi\)
\(68\) 36.9457 36.9457i 0.543319 0.543319i
\(69\) 8.30662i 0.120386i
\(70\) −15.2390 + 14.0051i −0.217700 + 0.200072i
\(71\) 84.1101 1.18465 0.592325 0.805699i \(-0.298210\pi\)
0.592325 + 0.805699i \(0.298210\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 77.0736 77.0736i 1.05580 1.05580i 0.0574543 0.998348i \(-0.481702\pi\)
0.998348 0.0574543i \(-0.0182984\pi\)
\(74\) 45.7041i 0.617623i
\(75\) −27.9305 33.0891i −0.372407 0.441188i
\(76\) 19.7291 0.259594
\(77\) −1.86286 1.86286i −0.0241930 0.0241930i
\(78\) 15.6145 15.6145i 0.200186 0.200186i
\(79\) 31.3293i 0.396574i −0.980144 0.198287i \(-0.936462\pi\)
0.980144 0.198287i \(-0.0635378\pi\)
\(80\) −13.5334 14.7258i −0.169167 0.184072i
\(81\) −9.00000 −0.111111
\(82\) −36.6804 36.6804i −0.447322 0.447322i
\(83\) 8.70034 8.70034i 0.104823 0.104823i −0.652750 0.757573i \(-0.726385\pi\)
0.757573 + 0.652750i \(0.226385\pi\)
\(84\) 10.1394i 0.120708i
\(85\) 5.50664 130.507i 0.0647840 1.53537i
\(86\) −29.3822 −0.341654
\(87\) 9.55185 + 9.55185i 0.109791 + 0.109791i
\(88\) 1.80012 1.80012i 0.0204560 0.0204560i
\(89\) 32.1361i 0.361079i −0.983568 0.180540i \(-0.942216\pi\)
0.983568 0.180540i \(-0.0577844\pi\)
\(90\) −21.1943 0.894281i −0.235493 0.00993646i
\(91\) −26.3871 −0.289968
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −22.6662 + 22.6662i −0.243722 + 0.243722i
\(94\) 54.0656i 0.575166i
\(95\) 36.3158 33.3752i 0.382272 0.351318i
\(96\) −9.79796 −0.102062
\(97\) −104.238 104.238i −1.07461 1.07461i −0.996982 0.0776323i \(-0.975264\pi\)
−0.0776323 0.996982i \(-0.524736\pi\)
\(98\) −40.4326 + 40.4326i −0.412578 + 0.412578i
\(99\) 2.70019i 0.0272746i
\(100\) −49.8223 4.21193i −0.498223 0.0421193i
\(101\) 62.2349 0.616187 0.308094 0.951356i \(-0.400309\pi\)
0.308094 + 0.951356i \(0.400309\pi\)
\(102\) −45.2491 45.2491i −0.443618 0.443618i
\(103\) 118.903 118.903i 1.15440 1.15440i 0.168738 0.985661i \(-0.446031\pi\)
0.985661 0.168738i \(-0.0539692\pi\)
\(104\) 25.4984i 0.245177i
\(105\) 17.1526 + 18.6639i 0.163358 + 0.177751i
\(106\) −102.126 −0.963455
\(107\) −18.5364 18.5364i −0.173237 0.173237i 0.615163 0.788400i \(-0.289090\pi\)
−0.788400 + 0.615163i \(0.789090\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 73.8874i 0.677866i −0.940811 0.338933i \(-0.889934\pi\)
0.940811 0.338933i \(-0.110066\pi\)
\(110\) 0.268303 6.35874i 0.00243912 0.0578067i
\(111\) 55.9759 0.504287
\(112\) 8.27882 + 8.27882i 0.0739181 + 0.0739181i
\(113\) 80.0463 80.0463i 0.708374 0.708374i −0.257819 0.966193i \(-0.583004\pi\)
0.966193 + 0.257819i \(0.0830038\pi\)
\(114\) 24.1632i 0.211958i
\(115\) 23.9578 + 1.01088i 0.208329 + 0.00879030i
\(116\) 15.5981 0.134466
\(117\) −19.1238 19.1238i −0.163451 0.163451i
\(118\) 91.7327 91.7327i 0.777396 0.777396i
\(119\) 76.4668i 0.642578i
\(120\) −18.0353 + 16.5749i −0.150294 + 0.138124i
\(121\) −120.190 −0.993305
\(122\) 44.5012 + 44.5012i 0.364764 + 0.364764i
\(123\) −44.9241 + 44.9241i −0.365237 + 0.365237i
\(124\) 37.0137i 0.298497i
\(125\) −98.8340 + 76.5300i −0.790672 + 0.612240i
\(126\) 12.4182 0.0985574
\(127\) −27.4253 27.4253i −0.215947 0.215947i 0.590841 0.806788i \(-0.298796\pi\)
−0.806788 + 0.590841i \(0.798796\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 35.9857i 0.278959i
\(130\) −43.1349 46.9354i −0.331807 0.361041i
\(131\) 80.5645 0.614996 0.307498 0.951549i \(-0.400508\pi\)
0.307498 + 0.951549i \(0.400508\pi\)
\(132\) −2.20469 2.20469i −0.0167022 0.0167022i
\(133\) −20.4168 + 20.4168i −0.153510 + 0.153510i
\(134\) 43.3567i 0.323557i
\(135\) −1.09527 + 25.9577i −0.00811308 + 0.192279i
\(136\) −73.8914 −0.543319
\(137\) 54.9704 + 54.9704i 0.401244 + 0.401244i 0.878671 0.477427i \(-0.158431\pi\)
−0.477427 + 0.878671i \(0.658431\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 133.632i 0.961379i 0.876891 + 0.480690i \(0.159614\pi\)
−0.876891 + 0.480690i \(0.840386\pi\)
\(140\) 29.2440 + 1.23393i 0.208886 + 0.00881380i
\(141\) −66.2166 −0.469621
\(142\) −84.1101 84.1101i −0.592325 0.592325i
\(143\) 5.73753 5.73753i 0.0401226 0.0401226i
\(144\) 12.0000i 0.0833333i
\(145\) 28.7117 26.3869i 0.198012 0.181979i
\(146\) −154.147 −1.05580
\(147\) 49.5197 + 49.5197i 0.336868 + 0.336868i
\(148\) 45.7041 45.7041i 0.308812 0.308812i
\(149\) 193.876i 1.30118i 0.759428 + 0.650591i \(0.225479\pi\)
−0.759428 + 0.650591i \(0.774521\pi\)
\(150\) −5.15854 + 61.0196i −0.0343903 + 0.406797i
\(151\) 211.812 1.40273 0.701364 0.712803i \(-0.252575\pi\)
0.701364 + 0.712803i \(0.252575\pi\)
\(152\) −19.7291 19.7291i −0.129797 0.129797i
\(153\) −55.4186 + 55.4186i −0.362213 + 0.362213i
\(154\) 3.72573i 0.0241930i
\(155\) 62.6150 + 68.1318i 0.403968 + 0.439560i
\(156\) −31.2290 −0.200186
\(157\) −134.833 134.833i −0.858809 0.858809i 0.132389 0.991198i \(-0.457735\pi\)
−0.991198 + 0.132389i \(0.957735\pi\)
\(158\) −31.3293 + 31.3293i −0.198287 + 0.198287i
\(159\) 125.079i 0.786658i
\(160\) −1.19237 + 28.2591i −0.00745234 + 0.176620i
\(161\) −14.0374 −0.0871890
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −142.999 + 142.999i −0.877293 + 0.877293i −0.993254 0.115961i \(-0.963005\pi\)
0.115961 + 0.993254i \(0.463005\pi\)
\(164\) 73.3608i 0.447322i
\(165\) −7.78784 0.328602i −0.0471990 0.00199153i
\(166\) −17.4007 −0.104823
\(167\) −142.222 142.222i −0.851630 0.851630i 0.138704 0.990334i \(-0.455706\pi\)
−0.990334 + 0.138704i \(0.955706\pi\)
\(168\) 10.1394 10.1394i 0.0603539 0.0603539i
\(169\) 87.7290i 0.519107i
\(170\) −136.013 + 125.000i −0.800079 + 0.735295i
\(171\) −29.5937 −0.173063
\(172\) 29.3822 + 29.3822i 0.170827 + 0.170827i
\(173\) 147.140 147.140i 0.850518 0.850518i −0.139679 0.990197i \(-0.544607\pi\)
0.990197 + 0.139679i \(0.0446071\pi\)
\(174\) 19.1037i 0.109791i
\(175\) 55.9175 47.2000i 0.319528 0.269714i
\(176\) −3.60025 −0.0204560
\(177\) −112.349 112.349i −0.634741 0.634741i
\(178\) −32.1361 + 32.1361i −0.180540 + 0.180540i
\(179\) 119.989i 0.670327i 0.942160 + 0.335164i \(0.108792\pi\)
−0.942160 + 0.335164i \(0.891208\pi\)
\(180\) 20.3001 + 22.0886i 0.112778 + 0.122715i
\(181\) 142.935 0.789695 0.394847 0.918747i \(-0.370797\pi\)
0.394847 + 0.918747i \(0.370797\pi\)
\(182\) 26.3871 + 26.3871i 0.144984 + 0.144984i
\(183\) 54.5026 54.5026i 0.297828 0.297828i
\(184\) 13.5647i 0.0737210i
\(185\) 6.81206 161.445i 0.0368219 0.872675i
\(186\) 45.3323 0.243722
\(187\) −16.6267 16.6267i −0.0889129 0.0889129i
\(188\) −54.0656 + 54.0656i −0.287583 + 0.287583i
\(189\) 15.2092i 0.0804718i
\(190\) −69.6911 2.94057i −0.366795 0.0154767i
\(191\) 71.7202 0.375499 0.187749 0.982217i \(-0.439881\pi\)
0.187749 + 0.982217i \(0.439881\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 15.6998 15.6998i 0.0813462 0.0813462i −0.665263 0.746609i \(-0.731681\pi\)
0.746609 + 0.665263i \(0.231681\pi\)
\(194\) 208.475i 1.07461i
\(195\) −57.4838 + 52.8293i −0.294789 + 0.270919i
\(196\) 80.8653 0.412578
\(197\) 258.375 + 258.375i 1.31155 + 1.31155i 0.920274 + 0.391274i \(0.127965\pi\)
0.391274 + 0.920274i \(0.372035\pi\)
\(198\) −2.70019 + 2.70019i −0.0136373 + 0.0136373i
\(199\) 17.1356i 0.0861087i 0.999073 + 0.0430544i \(0.0137089\pi\)
−0.999073 + 0.0430544i \(0.986291\pi\)
\(200\) 45.6103 + 54.0342i 0.228052 + 0.270171i
\(201\) 53.1009 0.264184
\(202\) −62.2349 62.2349i −0.308094 0.308094i
\(203\) −16.1417 + 16.1417i −0.0795160 + 0.0795160i
\(204\) 90.4982i 0.443618i
\(205\) 124.102 + 135.037i 0.605377 + 0.658715i
\(206\) −237.806 −1.15440
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −25.4984 + 25.4984i −0.122588 + 0.122588i
\(209\) 8.87873i 0.0424819i
\(210\) 1.51125 35.8165i 0.00719644 0.170555i
\(211\) −87.8965 −0.416571 −0.208286 0.978068i \(-0.566788\pi\)
−0.208286 + 0.978068i \(0.566788\pi\)
\(212\) 102.126 + 102.126i 0.481728 + 0.481728i
\(213\) −103.013 + 103.013i −0.483631 + 0.483631i
\(214\) 37.0728i 0.173237i
\(215\) 103.789 + 4.37933i 0.482742 + 0.0203690i
\(216\) 14.6969 0.0680414
\(217\) −38.3037 38.3037i −0.176515 0.176515i
\(218\) −73.8874 + 73.8874i −0.338933 + 0.338933i
\(219\) 188.791i 0.862059i
\(220\) −6.62704 + 6.09044i −0.0301229 + 0.0276838i
\(221\) −235.514 −1.06567
\(222\) −55.9759 55.9759i −0.252144 0.252144i
\(223\) −158.653 + 158.653i −0.711447 + 0.711447i −0.966838 0.255391i \(-0.917796\pi\)
0.255391 + 0.966838i \(0.417796\pi\)
\(224\) 16.5576i 0.0739181i
\(225\) 74.7334 + 6.31790i 0.332149 + 0.0280796i
\(226\) −160.093 −0.708374
\(227\) 176.500 + 176.500i 0.777531 + 0.777531i 0.979410 0.201879i \(-0.0647048\pi\)
−0.201879 + 0.979410i \(0.564705\pi\)
\(228\) −24.1632 + 24.1632i −0.105979 + 0.105979i
\(229\) 140.584i 0.613902i −0.951725 0.306951i \(-0.900691\pi\)
0.951725 0.306951i \(-0.0993088\pi\)
\(230\) −22.9470 24.9687i −0.0997694 0.108560i
\(231\) 4.56306 0.0197535
\(232\) −15.5981 15.5981i −0.0672332 0.0672332i
\(233\) 23.4052 23.4052i 0.100451 0.100451i −0.655095 0.755546i \(-0.727371\pi\)
0.755546 + 0.655095i \(0.227371\pi\)
\(234\) 38.2476i 0.163451i
\(235\) −8.05831 + 190.981i −0.0342907 + 0.812685i
\(236\) −183.465 −0.777396
\(237\) 38.3704 + 38.3704i 0.161901 + 0.161901i
\(238\) 76.4668 76.4668i 0.321289 0.321289i
\(239\) 158.063i 0.661349i −0.943745 0.330675i \(-0.892724\pi\)
0.943745 0.330675i \(-0.107276\pi\)
\(240\) 34.6102 + 1.46035i 0.144209 + 0.00608481i
\(241\) 148.164 0.614786 0.307393 0.951583i \(-0.400543\pi\)
0.307393 + 0.951583i \(0.400543\pi\)
\(242\) 120.190 + 120.190i 0.496652 + 0.496652i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 89.0024i 0.364764i
\(245\) 148.850 136.798i 0.607552 0.558357i
\(246\) 89.8482 0.365237
\(247\) −62.8827 62.8827i −0.254586 0.254586i
\(248\) 37.0137 37.0137i 0.149249 0.149249i
\(249\) 21.3114i 0.0855879i
\(250\) 175.364 + 22.3040i 0.701456 + 0.0892162i
\(251\) −222.580 −0.886771 −0.443386 0.896331i \(-0.646223\pi\)
−0.443386 + 0.896331i \(0.646223\pi\)
\(252\) −12.4182 12.4182i −0.0492787 0.0492787i
\(253\) 3.05226 3.05226i 0.0120643 0.0120643i
\(254\) 54.8505i 0.215947i
\(255\) 153.093 + 166.582i 0.600366 + 0.653262i
\(256\) 16.0000 0.0625000
\(257\) −281.297 281.297i −1.09454 1.09454i −0.995037 0.0995018i \(-0.968275\pi\)
−0.0995018 0.995037i \(-0.531725\pi\)
\(258\) 35.9857 35.9857i 0.139480 0.139480i
\(259\) 94.5941i 0.365228i
\(260\) −3.80045 + 90.0703i −0.0146171 + 0.346424i
\(261\) −23.3972 −0.0896443
\(262\) −80.5645 80.5645i −0.307498 0.307498i
\(263\) −177.629 + 177.629i −0.675394 + 0.675394i −0.958954 0.283560i \(-0.908484\pi\)
0.283560 + 0.958954i \(0.408484\pi\)
\(264\) 4.40938i 0.0167022i
\(265\) 360.750 + 15.2216i 1.36132 + 0.0574400i
\(266\) 40.8335 0.153510
\(267\) 39.3585 + 39.3585i 0.147410 + 0.147410i
\(268\) 43.3567 43.3567i 0.161779 0.161779i
\(269\) 93.2801i 0.346766i 0.984854 + 0.173383i \(0.0554699\pi\)
−0.984854 + 0.173383i \(0.944530\pi\)
\(270\) 27.0529 24.8624i 0.100196 0.0920830i
\(271\) −351.552 −1.29724 −0.648620 0.761113i \(-0.724653\pi\)
−0.648620 + 0.761113i \(0.724653\pi\)
\(272\) 73.8914 + 73.8914i 0.271660 + 0.271660i
\(273\) 32.3174 32.3174i 0.118379 0.118379i
\(274\) 109.941i 0.401244i
\(275\) −1.89550 + 22.4216i −0.00689273 + 0.0815330i
\(276\) −16.6132 −0.0601929
\(277\) −211.987 211.987i −0.765297 0.765297i 0.211977 0.977275i \(-0.432010\pi\)
−0.977275 + 0.211977i \(0.932010\pi\)
\(278\) 133.632 133.632i 0.480690 0.480690i
\(279\) 55.5205i 0.198998i
\(280\) −28.0101 30.4780i −0.100036 0.108850i
\(281\) −135.367 −0.481732 −0.240866 0.970558i \(-0.577431\pi\)
−0.240866 + 0.970558i \(0.577431\pi\)
\(282\) 66.2166 + 66.2166i 0.234811 + 0.234811i
\(283\) 107.157 107.157i 0.378648 0.378648i −0.491966 0.870614i \(-0.663722\pi\)
0.870614 + 0.491966i \(0.163722\pi\)
\(284\) 168.220i 0.592325i
\(285\) −3.60144 + 85.3538i −0.0126366 + 0.299487i
\(286\) −11.4751 −0.0401226
\(287\) −75.9176 75.9176i −0.264521 0.264521i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 393.493i 1.36157i
\(290\) −55.0986 2.32485i −0.189995 0.00801672i
\(291\) 255.329 0.877419
\(292\) 154.147 + 154.147i 0.527901 + 0.527901i
\(293\) −130.004 + 130.004i −0.443700 + 0.443700i −0.893253 0.449553i \(-0.851583\pi\)
0.449553 + 0.893253i \(0.351583\pi\)
\(294\) 99.0393i 0.336868i
\(295\) −337.708 + 310.363i −1.14477 + 1.05208i
\(296\) −91.4083 −0.308812
\(297\) 3.30704 + 3.30704i 0.0111348 + 0.0111348i
\(298\) 193.876 193.876i 0.650591 0.650591i
\(299\) 43.2346i 0.144597i
\(300\) 66.1781 55.8610i 0.220594 0.186203i
\(301\) −60.8126 −0.202035
\(302\) −211.812 211.812i −0.701364 0.701364i
\(303\) −76.2219 + 76.2219i −0.251557 + 0.251557i
\(304\) 39.4583i 0.129797i
\(305\) −150.563 163.828i −0.493649 0.537142i
\(306\) 110.837 0.362213
\(307\) 6.52034 + 6.52034i 0.0212389 + 0.0212389i 0.717646 0.696408i \(-0.245219\pi\)
−0.696408 + 0.717646i \(0.745219\pi\)
\(308\) 3.72573 3.72573i 0.0120965 0.0120965i
\(309\) 291.252i 0.942563i
\(310\) 5.51677 130.747i 0.0177960 0.421764i
\(311\) 21.8579 0.0702825 0.0351412 0.999382i \(-0.488812\pi\)
0.0351412 + 0.999382i \(0.488812\pi\)
\(312\) 31.2290 + 31.2290i 0.100093 + 0.100093i
\(313\) 329.807 329.807i 1.05369 1.05369i 0.0552208 0.998474i \(-0.482414\pi\)
0.998474 0.0552208i \(-0.0175863\pi\)
\(314\) 269.666i 0.858809i
\(315\) −43.8661 1.85090i −0.139257 0.00587587i
\(316\) 62.6586 0.198287
\(317\) −187.213 187.213i −0.590579 0.590579i 0.347209 0.937788i \(-0.387129\pi\)
−0.937788 + 0.347209i \(0.887129\pi\)
\(318\) 125.079 125.079i 0.393329 0.393329i
\(319\) 7.01963i 0.0220051i
\(320\) 29.4515 27.0668i 0.0920359 0.0845836i
\(321\) 45.4047 0.141448
\(322\) 14.0374 + 14.0374i 0.0435945 + 0.0435945i
\(323\) −182.227 + 182.227i −0.564170 + 0.564170i
\(324\) 18.0000i 0.0555556i
\(325\) 145.374 + 172.223i 0.447304 + 0.529917i
\(326\) 285.998 0.877293
\(327\) 90.4932 + 90.4932i 0.276738 + 0.276738i
\(328\) 73.3608 73.3608i 0.223661 0.223661i
\(329\) 111.900i 0.340122i
\(330\) 7.45923 + 8.11644i 0.0226037 + 0.0245953i
\(331\) −514.692 −1.55496 −0.777480 0.628908i \(-0.783502\pi\)
−0.777480 + 0.628908i \(0.783502\pi\)
\(332\) 17.4007 + 17.4007i 0.0524117 + 0.0524117i
\(333\) −68.5562 + 68.5562i −0.205874 + 0.205874i
\(334\) 284.444i 0.851630i
\(335\) 6.46218 153.153i 0.0192901 0.457173i
\(336\) −20.2789 −0.0603539
\(337\) −131.193 131.193i −0.389296 0.389296i 0.485140 0.874436i \(-0.338769\pi\)
−0.874436 + 0.485140i \(0.838769\pi\)
\(338\) 87.7290 87.7290i 0.259553 0.259553i
\(339\) 196.073i 0.578385i
\(340\) 261.013 + 11.0133i 0.767687 + 0.0323920i
\(341\) 16.6573 0.0488484
\(342\) 29.5937 + 29.5937i 0.0865313 + 0.0865313i
\(343\) −185.099 + 185.099i −0.539648 + 0.539648i
\(344\) 58.7644i 0.170827i
\(345\) −30.5803 + 28.1042i −0.0886386 + 0.0814614i
\(346\) −294.279 −0.850518
\(347\) 8.51905 + 8.51905i 0.0245506 + 0.0245506i 0.719276 0.694725i \(-0.244474\pi\)
−0.694725 + 0.719276i \(0.744474\pi\)
\(348\) −19.1037 + 19.1037i −0.0548957 + 0.0548957i
\(349\) 141.333i 0.404965i −0.979286 0.202482i \(-0.935099\pi\)
0.979286 0.202482i \(-0.0649009\pi\)
\(350\) −103.117 8.71746i −0.294621 0.0249070i
\(351\) 46.8435 0.133457
\(352\) 3.60025 + 3.60025i 0.0102280 + 0.0102280i
\(353\) −358.841 + 358.841i −1.01655 + 1.01655i −0.0166867 + 0.999861i \(0.505312\pi\)
−0.999861 + 0.0166867i \(0.994688\pi\)
\(354\) 224.698i 0.634741i
\(355\) 284.574 + 309.646i 0.801616 + 0.872243i
\(356\) 64.2721 0.180540
\(357\) −93.6523 93.6523i −0.262331 0.262331i
\(358\) 119.989 119.989i 0.335164 0.335164i
\(359\) 233.537i 0.650520i −0.945625 0.325260i \(-0.894548\pi\)
0.945625 0.325260i \(-0.105452\pi\)
\(360\) 1.78856 42.3887i 0.00496823 0.117746i
\(361\) 263.690 0.730444
\(362\) −142.935 142.935i −0.394847 0.394847i
\(363\) 147.202 147.202i 0.405515 0.405515i
\(364\) 52.7742i 0.144984i
\(365\) 544.508 + 22.9751i 1.49180 + 0.0629456i
\(366\) −109.005 −0.297828
\(367\) −41.8520 41.8520i −0.114038 0.114038i 0.647785 0.761823i \(-0.275696\pi\)
−0.761823 + 0.647785i \(0.775696\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 110.041i 0.298214i
\(370\) −168.257 + 154.633i −0.454748 + 0.417926i
\(371\) −211.371 −0.569734
\(372\) −45.3323 45.3323i −0.121861 0.121861i
\(373\) 238.065 238.065i 0.638243 0.638243i −0.311879 0.950122i \(-0.600958\pi\)
0.950122 + 0.311879i \(0.100958\pi\)
\(374\) 33.2534i 0.0889129i
\(375\) 27.3168 214.776i 0.0728447 0.572736i
\(376\) 108.131 0.287583
\(377\) −49.7158 49.7158i −0.131872 0.131872i
\(378\) −15.2092 + 15.2092i −0.0402359 + 0.0402359i
\(379\) 253.908i 0.669941i 0.942229 + 0.334970i \(0.108726\pi\)
−0.942229 + 0.334970i \(0.891274\pi\)
\(380\) 66.7505 + 72.6316i 0.175659 + 0.191136i
\(381\) 67.1779 0.176320
\(382\) −71.7202 71.7202i −0.187749 0.187749i
\(383\) −68.9077 + 68.9077i −0.179916 + 0.179916i −0.791319 0.611403i \(-0.790605\pi\)
0.611403 + 0.791319i \(0.290605\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0.555308 13.1607i 0.00144236 0.0341837i
\(386\) −31.3996 −0.0813462
\(387\) −44.0733 44.0733i −0.113885 0.113885i
\(388\) 208.475 208.475i 0.537307 0.537307i
\(389\) 34.7594i 0.0893557i 0.999001 + 0.0446778i \(0.0142261\pi\)
−0.999001 + 0.0446778i \(0.985774\pi\)
\(390\) 110.313 + 4.65459i 0.282854 + 0.0119348i
\(391\) −125.289 −0.320432
\(392\) −80.8653 80.8653i −0.206289 0.206289i
\(393\) −98.6709 + 98.6709i −0.251071 + 0.251071i
\(394\) 516.750i 1.31155i
\(395\) 115.337 105.998i 0.291992 0.268349i
\(396\) 5.40037 0.0136373
\(397\) −490.772 490.772i −1.23620 1.23620i −0.961542 0.274659i \(-0.911435\pi\)
−0.274659 0.961542i \(-0.588565\pi\)
\(398\) 17.1356 17.1356i 0.0430544 0.0430544i
\(399\) 50.0107i 0.125340i
\(400\) 8.42387 99.6446i 0.0210597 0.249111i
\(401\) −473.229 −1.18012 −0.590061 0.807358i \(-0.700896\pi\)
−0.590061 + 0.807358i \(0.700896\pi\)
\(402\) −53.1009 53.1009i −0.132092 0.132092i
\(403\) 117.974 117.974i 0.292739 0.292739i
\(404\) 124.470i 0.308094i
\(405\) −30.4501 33.1329i −0.0751854 0.0818097i
\(406\) 32.2835 0.0795160
\(407\) −20.5683 20.5683i −0.0505363 0.0505363i
\(408\) 90.4982 90.4982i 0.221809 0.221809i
\(409\) 285.348i 0.697671i −0.937184 0.348836i \(-0.886577\pi\)
0.937184 0.348836i \(-0.113423\pi\)
\(410\) 10.9342 259.139i 0.0266688 0.632046i
\(411\) −134.650 −0.327614
\(412\) 237.806 + 237.806i 0.577200 + 0.577200i
\(413\) 189.860 189.860i 0.459709 0.459709i
\(414\) 20.3470i 0.0491473i
\(415\) 61.4660 + 2.59352i 0.148111 + 0.00624944i
\(416\) 50.9968 0.122588
\(417\) −163.665 163.665i −0.392481 0.392481i
\(418\) −8.87873 + 8.87873i −0.0212410 + 0.0212410i
\(419\) 290.087i 0.692331i −0.938173 0.346165i \(-0.887484\pi\)
0.938173 0.346165i \(-0.112516\pi\)
\(420\) −37.3277 + 34.3052i −0.0888756 + 0.0816791i
\(421\) −442.922 −1.05207 −0.526035 0.850463i \(-0.676322\pi\)
−0.526035 + 0.850463i \(0.676322\pi\)
\(422\) 87.8965 + 87.8965i 0.208286 + 0.208286i
\(423\) 81.0985 81.0985i 0.191722 0.191722i
\(424\) 204.252i 0.481728i
\(425\) 499.083 421.277i 1.17431 0.991240i
\(426\) 206.027 0.483631
\(427\) 92.1044 + 92.1044i 0.215701 + 0.215701i
\(428\) 37.0728 37.0728i 0.0866187 0.0866187i
\(429\) 14.0540i 0.0327600i
\(430\) −99.4102 108.169i −0.231186 0.251555i
\(431\) 377.479 0.875821 0.437910 0.899019i \(-0.355719\pi\)
0.437910 + 0.899019i \(0.355719\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −567.756 + 567.756i −1.31121 + 1.31121i −0.390695 + 0.920520i \(0.627765\pi\)
−0.920520 + 0.390695i \(0.872235\pi\)
\(434\) 76.6074i 0.176515i
\(435\) −2.84735 + 67.4818i −0.00654562 + 0.155130i
\(436\) 147.775 0.338933
\(437\) −33.4524 33.4524i −0.0765501 0.0765501i
\(438\) 188.791 188.791i 0.431030 0.431030i
\(439\) 295.256i 0.672564i 0.941761 + 0.336282i \(0.109170\pi\)
−0.941761 + 0.336282i \(0.890830\pi\)
\(440\) 12.7175 + 0.536606i 0.0289034 + 0.00121956i
\(441\) −121.298 −0.275052
\(442\) 235.514 + 235.514i 0.532837 + 0.532837i
\(443\) 419.157 419.157i 0.946179 0.946179i −0.0524451 0.998624i \(-0.516701\pi\)
0.998624 + 0.0524451i \(0.0167014\pi\)
\(444\) 111.952i 0.252144i
\(445\) 118.307 108.727i 0.265858 0.244331i
\(446\) 317.306 0.711447
\(447\) −237.449 237.449i −0.531206 0.531206i
\(448\) −16.5576 + 16.5576i −0.0369590 + 0.0369590i
\(449\) 646.254i 1.43932i −0.694328 0.719659i \(-0.744298\pi\)
0.694328 0.719659i \(-0.255702\pi\)
\(450\) −68.4155 81.0513i −0.152034 0.180114i
\(451\) 33.0146 0.0732031
\(452\) 160.093 + 160.093i 0.354187 + 0.354187i
\(453\) −259.416 + 259.416i −0.572661 + 0.572661i
\(454\) 352.999i 0.777531i
\(455\) −89.2766 97.1424i −0.196212 0.213500i
\(456\) 48.3263 0.105979
\(457\) 117.758 + 117.758i 0.257677 + 0.257677i 0.824109 0.566432i \(-0.191677\pi\)
−0.566432 + 0.824109i \(0.691677\pi\)
\(458\) −140.584 + 140.584i −0.306951 + 0.306951i
\(459\) 135.747i 0.295746i
\(460\) −2.02177 + 47.9157i −0.00439515 + 0.104165i
\(461\) 638.280 1.38456 0.692278 0.721631i \(-0.256607\pi\)
0.692278 + 0.721631i \(0.256607\pi\)
\(462\) −4.56306 4.56306i −0.00987676 0.00987676i
\(463\) 243.006 243.006i 0.524851 0.524851i −0.394182 0.919033i \(-0.628972\pi\)
0.919033 + 0.394182i \(0.128972\pi\)
\(464\) 31.1962i 0.0672332i
\(465\) −160.131 6.75664i −0.344369 0.0145304i
\(466\) −46.8103 −0.100451
\(467\) −180.259 180.259i −0.385994 0.385994i 0.487262 0.873256i \(-0.337996\pi\)
−0.873256 + 0.487262i \(0.837996\pi\)
\(468\) 38.2476 38.2476i 0.0817256 0.0817256i
\(469\) 89.7356i 0.191334i
\(470\) 199.039 182.923i 0.423488 0.389197i
\(471\) 330.272 0.701214
\(472\) 183.465 + 183.465i 0.388698 + 0.388698i
\(473\) 13.2229 13.2229i 0.0279554 0.0279554i
\(474\) 76.7409i 0.161901i
\(475\) 245.738 + 20.7745i 0.517343 + 0.0437357i
\(476\) −152.934 −0.321289
\(477\) −153.189 153.189i −0.321152 0.321152i
\(478\) −158.063 + 158.063i −0.330675 + 0.330675i
\(479\) 521.944i 1.08965i 0.838549 + 0.544827i \(0.183405\pi\)
−0.838549 + 0.544827i \(0.816595\pi\)
\(480\) −33.1499 36.0706i −0.0690622 0.0751470i
\(481\) −291.345 −0.605708
\(482\) −148.164 148.164i −0.307393 0.307393i
\(483\) 17.1923 17.1923i 0.0355948 0.0355948i
\(484\) 240.380i 0.496652i
\(485\) 31.0726 736.416i 0.0640672 1.51838i
\(486\) −22.0454 −0.0453609
\(487\) −173.549 173.549i −0.356364 0.356364i 0.506107 0.862471i \(-0.331084\pi\)
−0.862471 + 0.506107i \(0.831084\pi\)
\(488\) −89.0024 + 89.0024i −0.182382 + 0.182382i
\(489\) 350.274i 0.716307i
\(490\) −285.648 12.0527i −0.582955 0.0245974i
\(491\) −261.292 −0.532164 −0.266082 0.963950i \(-0.585729\pi\)
−0.266082 + 0.963950i \(0.585729\pi\)
\(492\) −89.8482 89.8482i −0.182618 0.182618i
\(493\) −144.071 + 144.071i −0.292233 + 0.292233i
\(494\) 125.765i 0.254586i
\(495\) 9.94057 9.13566i 0.0200820 0.0184559i
\(496\) −74.0274 −0.149249
\(497\) −174.083 174.083i −0.350268 0.350268i
\(498\) 21.3114 21.3114i 0.0427940 0.0427940i
\(499\) 391.452i 0.784473i −0.919864 0.392237i \(-0.871701\pi\)
0.919864 0.392237i \(-0.128299\pi\)
\(500\) −153.060 197.668i −0.306120 0.395336i
\(501\) 348.372 0.695353
\(502\) 222.580 + 222.580i 0.443386 + 0.443386i
\(503\) −451.156 + 451.156i −0.896930 + 0.896930i −0.995163 0.0982331i \(-0.968681\pi\)
0.0982331 + 0.995163i \(0.468681\pi\)
\(504\) 24.8365i 0.0492787i
\(505\) 210.562 + 229.114i 0.416955 + 0.453691i
\(506\) −6.10452 −0.0120643
\(507\) −107.446 107.446i −0.211924 0.211924i
\(508\) 54.8505 54.8505i 0.107973 0.107973i
\(509\) 15.5183i 0.0304878i −0.999884 0.0152439i \(-0.995148\pi\)
0.999884 0.0152439i \(-0.00485247\pi\)
\(510\) 13.4885 319.675i 0.0264480 0.626814i
\(511\) −319.039 −0.624343
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 36.2448 36.2448i 0.0706526 0.0706526i
\(514\) 562.593i 1.09454i
\(515\) 840.024 + 35.4443i 1.63112 + 0.0688238i
\(516\) −71.9714 −0.139480
\(517\) 24.3312 + 24.3312i 0.0470623 + 0.0470623i
\(518\) 94.5941 94.5941i 0.182614 0.182614i
\(519\) 360.417i 0.694445i
\(520\) 93.8707 86.2698i 0.180521 0.165904i
\(521\) −573.680 −1.10111 −0.550556 0.834798i \(-0.685584\pi\)
−0.550556 + 0.834798i \(0.685584\pi\)
\(522\) 23.3972 + 23.3972i 0.0448222 + 0.0448222i
\(523\) 159.178 159.178i 0.304356 0.304356i −0.538359 0.842715i \(-0.680956\pi\)
0.842715 + 0.538359i \(0.180956\pi\)
\(524\) 161.129i 0.307498i
\(525\) −10.6767 + 126.293i −0.0203365 + 0.240557i
\(526\) 355.257 0.675394
\(527\) −341.874 341.874i −0.648718 0.648718i
\(528\) 4.40938 4.40938i 0.00835111 0.00835111i
\(529\) 23.0000i 0.0434783i
\(530\) −345.528 375.971i −0.651940 0.709380i
\(531\) 275.198 0.518264
\(532\) −40.8335 40.8335i −0.0767548 0.0767548i
\(533\) 233.823 233.823i 0.438692 0.438692i
\(534\) 78.7170i 0.147410i
\(535\) 5.52559 130.956i 0.0103282 0.244777i
\(536\) −86.7134 −0.161779
\(537\) −146.955 146.955i −0.273660 0.273660i
\(538\) 93.2801 93.2801i 0.173383 0.173383i
\(539\) 36.3919i 0.0675174i
\(540\) −51.9153 2.19053i −0.0961395 0.00405654i
\(541\) 19.0291 0.0351740 0.0175870 0.999845i \(-0.494402\pi\)
0.0175870 + 0.999845i \(0.494402\pi\)
\(542\) 351.552 + 351.552i 0.648620 + 0.648620i
\(543\) −175.059 + 175.059i −0.322392 + 0.322392i
\(544\) 147.783i 0.271660i
\(545\) 272.012 249.986i 0.499104 0.458691i
\(546\) −64.6349 −0.118379
\(547\) −18.2605 18.2605i −0.0333830 0.0333830i 0.690218 0.723601i \(-0.257515\pi\)
−0.723601 + 0.690218i \(0.757515\pi\)
\(548\) −109.941 + 109.941i −0.200622 + 0.200622i
\(549\) 133.504i 0.243176i
\(550\) 24.3171 20.5261i 0.0442129 0.0373201i
\(551\) −76.9344 −0.139627
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) −64.8425 + 64.8425i −0.117256 + 0.117256i
\(554\) 423.975i 0.765297i
\(555\) 189.386 + 206.072i 0.341236 + 0.371301i
\(556\) −267.263 −0.480690
\(557\) 602.059 + 602.059i 1.08090 + 1.08090i 0.996426 + 0.0844703i \(0.0269198\pi\)
0.0844703 + 0.996426i \(0.473080\pi\)
\(558\) −55.5205 + 55.5205i −0.0994991 + 0.0994991i
\(559\) 187.300i 0.335062i
\(560\) −2.46787 + 58.4881i −0.00440690 + 0.104443i
\(561\) 40.7270 0.0725971
\(562\) 135.367 + 135.367i 0.240866 + 0.240866i
\(563\) −208.664 + 208.664i −0.370628 + 0.370628i −0.867706 0.497078i \(-0.834406\pi\)
0.497078 + 0.867706i \(0.334406\pi\)
\(564\) 132.433i 0.234811i
\(565\) 565.510 + 23.8613i 1.00090 + 0.0422324i
\(566\) −214.315 −0.378648
\(567\) 18.6274 + 18.6274i 0.0328525 + 0.0328525i
\(568\) 168.220 168.220i 0.296162 0.296162i
\(569\) 375.263i 0.659513i −0.944066 0.329756i \(-0.893033\pi\)
0.944066 0.329756i \(-0.106967\pi\)
\(570\) 88.9552 81.7523i 0.156062 0.143425i
\(571\) 999.501 1.75044 0.875219 0.483726i \(-0.160717\pi\)
0.875219 + 0.483726i \(0.160717\pi\)
\(572\) 11.4751 + 11.4751i 0.0200613 + 0.0200613i
\(573\) −87.8390 + 87.8390i −0.153297 + 0.153297i
\(574\) 151.835i 0.264521i
\(575\) 77.3361 + 91.6195i 0.134498 + 0.159338i
\(576\) −24.0000 −0.0416667
\(577\) 503.643 + 503.643i 0.872866 + 0.872866i 0.992784 0.119918i \(-0.0382632\pi\)
−0.119918 + 0.992784i \(0.538263\pi\)
\(578\) 393.493 393.493i 0.680784 0.680784i
\(579\) 38.4566i 0.0664189i
\(580\) 52.7738 + 57.4235i 0.0909893 + 0.0990060i
\(581\) −36.0143 −0.0619867
\(582\) −255.329 255.329i −0.438709 0.438709i
\(583\) 45.9600 45.9600i 0.0788336 0.0788336i
\(584\) 308.294i 0.527901i
\(585\) 5.70068 135.105i 0.00974475 0.230949i
\(586\) 260.008 0.443700
\(587\) 422.350 + 422.350i 0.719506 + 0.719506i 0.968504 0.248998i \(-0.0801013\pi\)
−0.248998 + 0.968504i \(0.580101\pi\)
\(588\) −99.0393 + 99.0393i −0.168434 + 0.168434i
\(589\) 182.562i 0.309953i
\(590\) 648.071 + 27.3449i 1.09843 + 0.0463473i
\(591\) −632.887 −1.07087
\(592\) 91.4083 + 91.4083i 0.154406 + 0.154406i
\(593\) −228.691 + 228.691i −0.385651 + 0.385651i −0.873133 0.487482i \(-0.837916\pi\)
0.487482 + 0.873133i \(0.337916\pi\)
\(594\) 6.61408i 0.0111348i
\(595\) −281.508 + 258.713i −0.473122 + 0.434812i
\(596\) −387.752 −0.650591
\(597\) −20.9868 20.9868i −0.0351537 0.0351537i
\(598\) −43.2346 + 43.2346i −0.0722987 + 0.0722987i
\(599\) 277.402i 0.463108i −0.972822 0.231554i \(-0.925619\pi\)
0.972822 0.231554i \(-0.0743811\pi\)
\(600\) −122.039 10.3171i −0.203399 0.0171951i
\(601\) −535.528 −0.891062 −0.445531 0.895266i \(-0.646985\pi\)
−0.445531 + 0.895266i \(0.646985\pi\)
\(602\) 60.8126 + 60.8126i 0.101018 + 0.101018i
\(603\) −65.0351 + 65.0351i −0.107852 + 0.107852i
\(604\) 423.624i 0.701364i
\(605\) −406.644 442.472i −0.672138 0.731358i
\(606\) 152.444 0.251557
\(607\) 689.127 + 689.127i 1.13530 + 1.13530i 0.989282 + 0.146018i \(0.0466458\pi\)
0.146018 + 0.989282i \(0.453354\pi\)
\(608\) 39.4583 39.4583i 0.0648985 0.0648985i
\(609\) 39.5391i 0.0649245i
\(610\) −13.2655 + 314.391i −0.0217468 + 0.515395i
\(611\) 344.647 0.564070
\(612\) −110.837 110.837i −0.181106 0.181106i
\(613\) 212.580 212.580i 0.346787 0.346787i −0.512124 0.858911i \(-0.671141\pi\)
0.858911 + 0.512124i \(0.171141\pi\)
\(614\) 13.0407i 0.0212389i
\(615\) −317.379 13.3916i −0.516063 0.0217749i
\(616\) −7.45145 −0.0120965
\(617\) 743.093 + 743.093i 1.20437 + 1.20437i 0.972825 + 0.231540i \(0.0743763\pi\)
0.231540 + 0.972825i \(0.425624\pi\)
\(618\) 291.252 291.252i 0.471281 0.471281i
\(619\) 837.046i 1.35225i 0.736785 + 0.676127i \(0.236343\pi\)
−0.736785 + 0.676127i \(0.763657\pi\)
\(620\) −136.264 + 125.230i −0.219780 + 0.201984i
\(621\) 24.9199 0.0401286
\(622\) −21.8579 21.8579i −0.0351412 0.0351412i
\(623\) −66.5122 + 66.5122i −0.106761 + 0.106761i
\(624\) 62.4580i 0.100093i
\(625\) −616.130 104.924i −0.985808 0.167879i
\(626\) −659.613 −1.05369
\(627\) 10.8742 + 10.8742i 0.0173432 + 0.0173432i
\(628\) 269.666 269.666i 0.429404 0.429404i
\(629\) 844.286i 1.34227i
\(630\) 42.0152 + 45.7170i 0.0666907 + 0.0725666i
\(631\) 455.081 0.721206 0.360603 0.932719i \(-0.382571\pi\)
0.360603 + 0.932719i \(0.382571\pi\)
\(632\) −62.6586 62.6586i −0.0991434 0.0991434i
\(633\) 107.651 107.651i 0.170064 0.170064i
\(634\) 374.427i 0.590579i
\(635\) 8.17530 193.754i 0.0128745 0.305124i
\(636\) −250.157 −0.393329
\(637\) −257.742 257.742i −0.404618 0.404618i
\(638\) −7.01963 + 7.01963i −0.0110026 + 0.0110026i
\(639\) 252.330i 0.394883i
\(640\) −56.5183 2.38475i −0.0883098 0.00372617i
\(641\) 295.317 0.460713 0.230357 0.973106i \(-0.426011\pi\)
0.230357 + 0.973106i \(0.426011\pi\)
\(642\) −45.4047 45.4047i −0.0707239 0.0707239i
\(643\) 5.55950 5.55950i 0.00864619 0.00864619i −0.702770 0.711417i \(-0.748054\pi\)
0.711417 + 0.702770i \(0.248054\pi\)
\(644\) 28.0749i 0.0435945i
\(645\) −132.479 + 121.752i −0.205394 + 0.188763i
\(646\) 364.454 0.564170
\(647\) 220.812 + 220.812i 0.341286 + 0.341286i 0.856851 0.515565i \(-0.172418\pi\)
−0.515565 + 0.856851i \(0.672418\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 82.5651i 0.127219i
\(650\) 26.8494 317.597i 0.0413067 0.488611i
\(651\) 93.8246 0.144124
\(652\) −285.998 285.998i −0.438647 0.438647i
\(653\) −643.901 + 643.901i −0.986065 + 0.986065i −0.999904 0.0138390i \(-0.995595\pi\)
0.0138390 + 0.999904i \(0.495595\pi\)
\(654\) 180.986i 0.276738i
\(655\) 272.577 + 296.593i 0.416149 + 0.452814i
\(656\) −146.722 −0.223661
\(657\) −231.221 231.221i −0.351934 0.351934i
\(658\) −111.900 + 111.900i −0.170061 + 0.170061i
\(659\) 576.226i 0.874395i −0.899366 0.437198i \(-0.855971\pi\)
0.899366 0.437198i \(-0.144029\pi\)
\(660\) 0.657205 15.5757i 0.000995765 0.0235995i
\(661\) −82.0390 −0.124113 −0.0620567 0.998073i \(-0.519766\pi\)
−0.0620567 + 0.998073i \(0.519766\pi\)
\(662\) 514.692 + 514.692i 0.777480 + 0.777480i
\(663\) 288.445 288.445i 0.435060 0.435060i
\(664\) 34.8014i 0.0524117i
\(665\) −144.240 6.08611i −0.216902 0.00915204i
\(666\) 137.112 0.205874
\(667\) −26.4479 26.4479i −0.0396520 0.0396520i
\(668\) 284.444 284.444i 0.425815 0.425815i
\(669\) 388.618i 0.580894i
\(670\) −159.615 + 146.691i −0.238231 + 0.218941i
\(671\) −40.0538 −0.0596927
\(672\) 20.2789 + 20.2789i 0.0301769 + 0.0301769i
\(673\) −187.726 + 187.726i −0.278939 + 0.278939i −0.832685 0.553747i \(-0.813198\pi\)
0.553747 + 0.832685i \(0.313198\pi\)
\(674\) 262.385i 0.389296i
\(675\) −99.2672 + 83.7916i −0.147063 + 0.124136i
\(676\) −175.458 −0.259553
\(677\) −155.129 155.129i −0.229142 0.229142i 0.583192 0.812334i \(-0.301803\pi\)
−0.812334 + 0.583192i \(0.801803\pi\)
\(678\) 196.073 196.073i 0.289193 0.289193i
\(679\) 431.482i 0.635467i
\(680\) −250.000 272.027i −0.367647 0.400039i
\(681\) −432.334 −0.634852
\(682\) −16.6573 16.6573i −0.0244242 0.0244242i
\(683\) −574.764 + 574.764i −0.841529 + 0.841529i −0.989058 0.147529i \(-0.952868\pi\)
0.147529 + 0.989058i \(0.452868\pi\)
\(684\) 59.1874i 0.0865313i
\(685\) −16.3863 + 388.354i −0.0239217 + 0.566940i
\(686\) 370.199 0.539648
\(687\) 172.179 + 172.179i 0.250625 + 0.250625i
\(688\) −58.7644 + 58.7644i −0.0854134 + 0.0854134i
\(689\) 651.014i 0.944868i
\(690\) 58.6845 + 2.47615i 0.0850500 + 0.00358863i
\(691\) −806.478 −1.16712 −0.583559 0.812071i \(-0.698340\pi\)
−0.583559 + 0.812071i \(0.698340\pi\)
\(692\) 294.279 + 294.279i 0.425259 + 0.425259i
\(693\) −5.58859 + 5.58859i −0.00806434 + 0.00806434i
\(694\) 17.0381i 0.0245506i
\(695\) −491.957 + 452.122i −0.707851 + 0.650535i
\(696\) 38.2074 0.0548957
\(697\) −677.592 677.592i −0.972154 0.972154i
\(698\) −141.333 + 141.333i −0.202482 + 0.202482i
\(699\) 57.3307i 0.0820182i
\(700\) 94.4000 + 111.835i 0.134857 + 0.159764i
\(701\) 909.201 1.29701 0.648503 0.761212i \(-0.275395\pi\)
0.648503 + 0.761212i \(0.275395\pi\)
\(702\) −46.8435 46.8435i −0.0667287 0.0667287i
\(703\) −225.426 + 225.426i −0.320663 + 0.320663i
\(704\) 7.20050i 0.0102280i
\(705\) −224.034 243.772i −0.317778 0.345776i
\(706\) 717.683 1.01655
\(707\) −128.808 128.808i −0.182189 0.182189i
\(708\) 224.698 224.698i 0.317370 0.317370i
\(709\) 425.987i 0.600827i 0.953809 + 0.300414i \(0.0971248\pi\)
−0.953809 + 0.300414i \(0.902875\pi\)
\(710\) 25.0727 594.220i 0.0353137 0.836929i
\(711\) −93.9880 −0.132191
\(712\) −64.2721 64.2721i −0.0902699 0.0902699i
\(713\) 62.7598 62.7598i 0.0880221 0.0880221i
\(714\) 187.305i 0.262331i
\(715\) 40.5344 + 1.71032i 0.0566915 + 0.00239206i
\(716\) −239.977 −0.335164
\(717\) 193.586 + 193.586i 0.269995 + 0.269995i
\(718\) −233.537 + 233.537i −0.325260 + 0.325260i
\(719\) 1319.34i 1.83497i −0.397776 0.917483i \(-0.630218\pi\)
0.397776 0.917483i \(-0.369782\pi\)
\(720\) −44.1773 + 40.6001i −0.0613573 + 0.0563891i
\(721\) −492.189 −0.682648
\(722\) −263.690 263.690i −0.365222 0.365222i
\(723\) −181.463 + 181.463i −0.250985 + 0.250985i
\(724\) 285.870i 0.394847i
\(725\) 194.283 + 16.4246i 0.267977 + 0.0226546i
\(726\) −294.404 −0.405515
\(727\) 951.508 + 951.508i 1.30881 + 1.30881i 0.922271 + 0.386544i \(0.126331\pi\)
0.386544 + 0.922271i \(0.373669\pi\)
\(728\) −52.7742 + 52.7742i −0.0724920 + 0.0724920i
\(729\) 27.0000i 0.0370370i
\(730\) −521.533 567.483i −0.714429 0.777374i
\(731\) −542.774 −0.742508
\(732\) 109.005 + 109.005i 0.148914 + 0.148914i
\(733\) 191.910 191.910i 0.261814 0.261814i −0.563977 0.825791i \(-0.690729\pi\)
0.825791 + 0.563977i \(0.190729\pi\)
\(734\) 83.7040i 0.114038i
\(735\) −14.7615 + 349.846i −0.0200837 + 0.475980i
\(736\) 27.1293 0.0368605
\(737\) −19.5119 19.5119i −0.0264747 0.0264747i
\(738\) −110.041 + 110.041i −0.149107 + 0.149107i
\(739\) 673.498i 0.911363i 0.890143 + 0.455682i \(0.150604\pi\)
−0.890143 + 0.455682i \(0.849396\pi\)
\(740\) 322.890 + 13.6241i 0.436337 + 0.0184110i
\(741\) 154.030 0.207868
\(742\) 211.371 + 211.371i 0.284867 + 0.284867i
\(743\) 122.642 122.642i 0.165063 0.165063i −0.619743 0.784805i \(-0.712763\pi\)
0.784805 + 0.619743i \(0.212763\pi\)
\(744\) 90.6646i 0.121861i
\(745\) −713.743 + 655.950i −0.958044 + 0.880470i
\(746\) −476.129 −0.638243
\(747\) −26.1010 26.1010i −0.0349411 0.0349411i
\(748\) 33.2534 33.2534i 0.0444565 0.0444565i
\(749\) 76.7298i 0.102443i
\(750\) −242.093 + 187.459i −0.322791 + 0.249946i
\(751\) 532.663 0.709272 0.354636 0.935005i \(-0.384605\pi\)
0.354636 + 0.935005i \(0.384605\pi\)
\(752\) −108.131 108.131i −0.143792 0.143792i
\(753\) 272.603 272.603i 0.362023 0.362023i
\(754\) 99.4317i 0.131872i
\(755\) 716.633 + 779.773i 0.949182 + 1.03281i
\(756\) 30.4183 0.0402359
\(757\) −786.166 786.166i −1.03853 1.03853i −0.999227 0.0393009i \(-0.987487\pi\)
−0.0393009 0.999227i \(-0.512513\pi\)
\(758\) 253.908 253.908i 0.334970 0.334970i
\(759\) 7.47648i 0.00985043i
\(760\) 5.88113 139.382i 0.00773833 0.183398i
\(761\) 54.7150 0.0718989 0.0359494 0.999354i \(-0.488554\pi\)
0.0359494 + 0.999354i \(0.488554\pi\)
\(762\) −67.1779 67.1779i −0.0881600 0.0881600i
\(763\) −152.925 + 152.925i −0.200426 + 0.200426i
\(764\) 143.440i 0.187749i
\(765\) −391.520 16.5199i −0.511791 0.0215947i
\(766\) 137.815 0.179916
\(767\) 584.759 + 584.759i 0.762397 + 0.762397i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 4.86567i 0.00632727i 0.999995 + 0.00316363i \(0.00100702\pi\)
−0.999995 + 0.00316363i \(0.998993\pi\)
\(770\) −13.7160 + 12.6054i −0.0178130 + 0.0163707i
\(771\) 689.033 0.893688
\(772\) 31.3996 + 31.3996i 0.0406731 + 0.0406731i
\(773\) −764.339 + 764.339i −0.988795 + 0.988795i −0.999938 0.0111426i \(-0.996453\pi\)
0.0111426 + 0.999938i \(0.496453\pi\)
\(774\) 88.1467i 0.113885i
\(775\) −38.9748 + 461.027i −0.0502901 + 0.594873i
\(776\) −416.950 −0.537307
\(777\) −115.854 115.854i −0.149104 0.149104i
\(778\) 34.7594 34.7594i 0.0446778 0.0446778i