Properties

Label 363.3.b.m.122.3
Level $363$
Weight $3$
Character 363.122
Analytic conductor $9.891$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89103359628\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \( x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 122.3
Root \(-2.00420i\) of defining polynomial
Character \(\chi\) \(=\) 363.122
Dual form 363.3.b.m.122.6

$q$-expansion

\(f(q)\) \(=\) \(q-2.00420i q^{2} +(2.80061 + 1.07544i) q^{3} -0.0168066 q^{4} +5.48438i q^{5} +(2.15539 - 5.61298i) q^{6} +5.59084 q^{7} -7.98311i q^{8} +(6.68687 + 6.02376i) q^{9} +O(q^{10})\) \(q-2.00420i q^{2} +(2.80061 + 1.07544i) q^{3} -0.0168066 q^{4} +5.48438i q^{5} +(2.15539 - 5.61298i) q^{6} +5.59084 q^{7} -7.98311i q^{8} +(6.68687 + 6.02376i) q^{9} +10.9918 q^{10} +(-0.0470687 - 0.0180744i) q^{12} -9.71679 q^{13} -11.2051i q^{14} +(-5.89810 + 15.3596i) q^{15} -16.0669 q^{16} +17.8716i q^{17} +(12.0728 - 13.4018i) q^{18} +18.6589 q^{19} -0.0921737i q^{20} +(15.6578 + 6.01259i) q^{21} -12.3649i q^{23} +(8.58532 - 22.3576i) q^{24} -5.07844 q^{25} +19.4744i q^{26} +(12.2492 + 24.0615i) q^{27} -0.0939629 q^{28} +2.47732i q^{29} +(30.7837 + 11.8210i) q^{30} +49.2308 q^{31} +0.268903i q^{32} +35.8182 q^{34} +30.6623i q^{35} +(-0.112383 - 0.101239i) q^{36} -39.3307 q^{37} -37.3961i q^{38} +(-27.2130 - 10.4498i) q^{39} +43.7824 q^{40} -56.5236i q^{41} +(12.0504 - 31.3813i) q^{42} -43.9060 q^{43} +(-33.0366 + 36.6734i) q^{45} -24.7816 q^{46} +57.7840i q^{47} +(-44.9973 - 17.2790i) q^{48} -17.7425 q^{49} +10.1782i q^{50} +(-19.2197 + 50.0514i) q^{51} +0.163306 q^{52} -43.1158i q^{53} +(48.2241 - 24.5498i) q^{54} -44.6323i q^{56} +(52.2564 + 20.0665i) q^{57} +4.96505 q^{58} -90.0311i q^{59} +(0.0991269 - 0.258143i) q^{60} -30.8695 q^{61} -98.6683i q^{62} +(37.3852 + 33.6779i) q^{63} -63.7288 q^{64} -53.2906i q^{65} +34.0775 q^{67} -0.300360i q^{68} +(13.2976 - 34.6292i) q^{69} +61.4533 q^{70} -37.5962i q^{71} +(48.0883 - 53.3820i) q^{72} -12.1261 q^{73} +78.8265i q^{74} +(-14.2228 - 5.46154i) q^{75} -0.313592 q^{76} +(-20.9434 + 54.5402i) q^{78} -63.1447 q^{79} -88.1173i q^{80} +(8.42858 + 80.5603i) q^{81} -113.284 q^{82} -9.70147i q^{83} +(-0.263154 - 0.101051i) q^{84} -98.0146 q^{85} +87.9962i q^{86} +(-2.66420 + 6.93803i) q^{87} -34.1289i q^{89} +(73.5007 + 66.2119i) q^{90} -54.3250 q^{91} +0.207811i q^{92} +(137.877 + 52.9446i) q^{93} +115.811 q^{94} +102.333i q^{95} +(-0.289188 + 0.753095i) q^{96} -37.8227 q^{97} +35.5595i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9} - 6 q^{10} + 53 q^{12} + 44 q^{13} - 54 q^{15} - 14 q^{16} + q^{18} + 68 q^{19} - 6 q^{21} + 33 q^{24} + 42 q^{25} - 25 q^{27} - 118 q^{28} + 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} + 38 q^{39} + 58 q^{40} + 174 q^{42} - 78 q^{43} - 36 q^{45} - 286 q^{46} - 285 q^{48} - 140 q^{49} + 58 q^{51} - 102 q^{52} + 523 q^{54} - 22 q^{57} - 68 q^{58} + 262 q^{60} + 22 q^{61} + 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} + 489 q^{72} - 378 q^{73} - 33 q^{75} - 450 q^{76} - 246 q^{78} - 252 q^{79} + 11 q^{81} - 200 q^{82} + 450 q^{84} - 156 q^{85} + 66 q^{87} + 598 q^{90} - 148 q^{91} + 380 q^{93} - 460 q^{94} + 399 q^{96} - 324 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00420i 1.00210i −0.865419 0.501049i \(-0.832948\pi\)
0.865419 0.501049i \(-0.167052\pi\)
\(3\) 2.80061 + 1.07544i 0.933538 + 0.358479i
\(4\) −0.0168066 −0.00420164
\(5\) 5.48438i 1.09688i 0.836191 + 0.548438i \(0.184777\pi\)
−0.836191 + 0.548438i \(0.815223\pi\)
\(6\) 2.15539 5.61298i 0.359231 0.935497i
\(7\) 5.59084 0.798691 0.399346 0.916800i \(-0.369237\pi\)
0.399346 + 0.916800i \(0.369237\pi\)
\(8\) 7.98311i 0.997888i
\(9\) 6.68687 + 6.02376i 0.742986 + 0.669307i
\(10\) 10.9918 1.09918
\(11\) 0 0
\(12\) −0.0470687 0.0180744i −0.00392239 0.00150620i
\(13\) −9.71679 −0.747446 −0.373723 0.927540i \(-0.621919\pi\)
−0.373723 + 0.927540i \(0.621919\pi\)
\(14\) 11.2051i 0.800368i
\(15\) −5.89810 + 15.3596i −0.393207 + 1.02398i
\(16\) −16.0669 −1.00418
\(17\) 17.8716i 1.05127i 0.850710 + 0.525635i \(0.176172\pi\)
−0.850710 + 0.525635i \(0.823828\pi\)
\(18\) 12.0728 13.4018i 0.670712 0.744545i
\(19\) 18.6589 0.982047 0.491024 0.871146i \(-0.336623\pi\)
0.491024 + 0.871146i \(0.336623\pi\)
\(20\) 0.0921737i 0.00460868i
\(21\) 15.6578 + 6.01259i 0.745609 + 0.286314i
\(22\) 0 0
\(23\) 12.3649i 0.537603i −0.963196 0.268801i \(-0.913372\pi\)
0.963196 0.268801i \(-0.0866275\pi\)
\(24\) 8.58532 22.3576i 0.357722 0.931566i
\(25\) −5.07844 −0.203138
\(26\) 19.4744i 0.749014i
\(27\) 12.2492 + 24.0615i 0.453673 + 0.891168i
\(28\) −0.0939629 −0.00335582
\(29\) 2.47732i 0.0854250i 0.999087 + 0.0427125i \(0.0135999\pi\)
−0.999087 + 0.0427125i \(0.986400\pi\)
\(30\) 30.7837 + 11.8210i 1.02612 + 0.394032i
\(31\) 49.2308 1.58809 0.794046 0.607858i \(-0.207971\pi\)
0.794046 + 0.607858i \(0.207971\pi\)
\(32\) 0.268903i 0.00840323i
\(33\) 0 0
\(34\) 35.8182 1.05348
\(35\) 30.6623i 0.876066i
\(36\) −0.112383 0.101239i −0.00312176 0.00281219i
\(37\) −39.3307 −1.06299 −0.531496 0.847061i \(-0.678370\pi\)
−0.531496 + 0.847061i \(0.678370\pi\)
\(38\) 37.3961i 0.984108i
\(39\) −27.2130 10.4498i −0.697769 0.267943i
\(40\) 43.7824 1.09456
\(41\) 56.5236i 1.37862i −0.724465 0.689312i \(-0.757913\pi\)
0.724465 0.689312i \(-0.242087\pi\)
\(42\) 12.0504 31.3813i 0.286915 0.747174i
\(43\) −43.9060 −1.02107 −0.510534 0.859857i \(-0.670552\pi\)
−0.510534 + 0.859857i \(0.670552\pi\)
\(44\) 0 0
\(45\) −33.0366 + 36.6734i −0.734147 + 0.814964i
\(46\) −24.7816 −0.538731
\(47\) 57.7840i 1.22945i 0.788743 + 0.614723i \(0.210732\pi\)
−0.788743 + 0.614723i \(0.789268\pi\)
\(48\) −44.9973 17.2790i −0.937444 0.359979i
\(49\) −17.7425 −0.362092
\(50\) 10.1782i 0.203564i
\(51\) −19.2197 + 50.0514i −0.376858 + 0.981400i
\(52\) 0.163306 0.00314050
\(53\) 43.1158i 0.813506i −0.913538 0.406753i \(-0.866661\pi\)
0.913538 0.406753i \(-0.133339\pi\)
\(54\) 48.2241 24.5498i 0.893038 0.454625i
\(55\) 0 0
\(56\) 44.6323i 0.797005i
\(57\) 52.2564 + 20.0665i 0.916778 + 0.352043i
\(58\) 4.96505 0.0856042
\(59\) 90.0311i 1.52595i −0.646427 0.762976i \(-0.723738\pi\)
0.646427 0.762976i \(-0.276262\pi\)
\(60\) 0.0991269 0.258143i 0.00165211 0.00430238i
\(61\) −30.8695 −0.506058 −0.253029 0.967459i \(-0.581427\pi\)
−0.253029 + 0.967459i \(0.581427\pi\)
\(62\) 98.6683i 1.59142i
\(63\) 37.3852 + 33.6779i 0.593417 + 0.534570i
\(64\) −63.7288 −0.995763
\(65\) 53.2906i 0.819855i
\(66\) 0 0
\(67\) 34.0775 0.508620 0.254310 0.967123i \(-0.418152\pi\)
0.254310 + 0.967123i \(0.418152\pi\)
\(68\) 0.300360i 0.00441706i
\(69\) 13.2976 34.6292i 0.192719 0.501872i
\(70\) 61.4533 0.877904
\(71\) 37.5962i 0.529524i −0.964314 0.264762i \(-0.914707\pi\)
0.964314 0.264762i \(-0.0852934\pi\)
\(72\) 48.0883 53.3820i 0.667893 0.741417i
\(73\) −12.1261 −0.166111 −0.0830554 0.996545i \(-0.526468\pi\)
−0.0830554 + 0.996545i \(0.526468\pi\)
\(74\) 78.8265i 1.06522i
\(75\) −14.2228 5.46154i −0.189637 0.0728205i
\(76\) −0.313592 −0.00412621
\(77\) 0 0
\(78\) −20.9434 + 54.5402i −0.268506 + 0.699233i
\(79\) −63.1447 −0.799300 −0.399650 0.916668i \(-0.630868\pi\)
−0.399650 + 0.916668i \(0.630868\pi\)
\(80\) 88.1173i 1.10147i
\(81\) 8.42858 + 80.5603i 0.104056 + 0.994571i
\(82\) −113.284 −1.38152
\(83\) 9.70147i 0.116885i −0.998291 0.0584426i \(-0.981387\pi\)
0.998291 0.0584426i \(-0.0186135\pi\)
\(84\) −0.263154 0.101051i −0.00313278 0.00120299i
\(85\) −98.0146 −1.15311
\(86\) 87.9962i 1.02321i
\(87\) −2.66420 + 6.93803i −0.0306230 + 0.0797474i
\(88\) 0 0
\(89\) 34.1289i 0.383471i −0.981447 0.191735i \(-0.938588\pi\)
0.981447 0.191735i \(-0.0614115\pi\)
\(90\) 73.5007 + 66.2119i 0.816674 + 0.735688i
\(91\) −54.3250 −0.596978
\(92\) 0.207811i 0.00225881i
\(93\) 137.877 + 52.9446i 1.48254 + 0.569297i
\(94\) 115.811 1.23203
\(95\) 102.333i 1.07718i
\(96\) −0.289188 + 0.753095i −0.00301238 + 0.00784473i
\(97\) −37.8227 −0.389925 −0.194962 0.980811i \(-0.562458\pi\)
−0.194962 + 0.980811i \(0.562458\pi\)
\(98\) 35.5595i 0.362852i
\(99\) 0 0
\(100\) 0.0853512 0.000853512
\(101\) 46.9047i 0.464403i −0.972668 0.232202i \(-0.925407\pi\)
0.972668 0.232202i \(-0.0745929\pi\)
\(102\) 100.313 + 38.5202i 0.983460 + 0.377649i
\(103\) 104.797 1.01744 0.508722 0.860931i \(-0.330118\pi\)
0.508722 + 0.860931i \(0.330118\pi\)
\(104\) 77.5702i 0.745867i
\(105\) −32.9753 + 85.8733i −0.314051 + 0.817841i
\(106\) −86.4126 −0.815213
\(107\) 46.6302i 0.435796i −0.975972 0.217898i \(-0.930080\pi\)
0.975972 0.217898i \(-0.0699200\pi\)
\(108\) −0.205867 0.404392i −0.00190617 0.00374437i
\(109\) −168.413 −1.54507 −0.772537 0.634969i \(-0.781013\pi\)
−0.772537 + 0.634969i \(0.781013\pi\)
\(110\) 0 0
\(111\) −110.150 42.2977i −0.992344 0.381060i
\(112\) −89.8277 −0.802033
\(113\) 46.3202i 0.409913i 0.978771 + 0.204957i \(0.0657053\pi\)
−0.978771 + 0.204957i \(0.934295\pi\)
\(114\) 40.2171 104.732i 0.352782 0.918702i
\(115\) 67.8136 0.589684
\(116\) 0.0416353i 0.000358925i
\(117\) −64.9750 58.5317i −0.555342 0.500271i
\(118\) −180.440 −1.52915
\(119\) 99.9172i 0.839640i
\(120\) 122.618 + 47.0852i 1.02181 + 0.392376i
\(121\) 0 0
\(122\) 61.8686i 0.507120i
\(123\) 60.7875 158.301i 0.494207 1.28700i
\(124\) −0.827402 −0.00667260
\(125\) 109.257i 0.874059i
\(126\) 67.4971 74.9274i 0.535692 0.594662i
\(127\) −68.2888 −0.537707 −0.268854 0.963181i \(-0.586645\pi\)
−0.268854 + 0.963181i \(0.586645\pi\)
\(128\) 128.801i 1.00626i
\(129\) −122.964 47.2180i −0.953206 0.366031i
\(130\) −106.805 −0.821576
\(131\) 162.272i 1.23872i 0.785109 + 0.619358i \(0.212607\pi\)
−0.785109 + 0.619358i \(0.787393\pi\)
\(132\) 0 0
\(133\) 104.319 0.784353
\(134\) 68.2981i 0.509687i
\(135\) −131.963 + 67.1792i −0.977501 + 0.497624i
\(136\) 142.671 1.04905
\(137\) 52.8671i 0.385891i −0.981209 0.192946i \(-0.938196\pi\)
0.981209 0.192946i \(-0.0618041\pi\)
\(138\) −69.4037 26.6510i −0.502926 0.193124i
\(139\) −86.5357 −0.622559 −0.311279 0.950318i \(-0.600758\pi\)
−0.311279 + 0.950318i \(0.600758\pi\)
\(140\) 0.515328i 0.00368092i
\(141\) −62.1430 + 161.831i −0.440730 + 1.14773i
\(142\) −75.3502 −0.530635
\(143\) 0 0
\(144\) −107.438 96.7835i −0.746095 0.672107i
\(145\) −13.5866 −0.0937006
\(146\) 24.3031i 0.166459i
\(147\) −49.6899 19.0809i −0.338027 0.129802i
\(148\) 0.661015 0.00446631
\(149\) 64.4499i 0.432550i −0.976332 0.216275i \(-0.930609\pi\)
0.976332 0.216275i \(-0.0693908\pi\)
\(150\) −10.9460 + 28.5052i −0.0729734 + 0.190035i
\(151\) 44.6348 0.295595 0.147797 0.989018i \(-0.452782\pi\)
0.147797 + 0.989018i \(0.452782\pi\)
\(152\) 148.956i 0.979973i
\(153\) −107.654 + 119.505i −0.703622 + 0.781079i
\(154\) 0 0
\(155\) 270.001i 1.74194i
\(156\) 0.457357 + 0.175625i 0.00293178 + 0.00112580i
\(157\) −141.066 −0.898510 −0.449255 0.893404i \(-0.648311\pi\)
−0.449255 + 0.893404i \(0.648311\pi\)
\(158\) 126.554i 0.800978i
\(159\) 46.3683 120.751i 0.291625 0.759439i
\(160\) −1.47477 −0.00921731
\(161\) 69.1300i 0.429379i
\(162\) 161.459 16.8925i 0.996659 0.104275i
\(163\) 120.965 0.742114 0.371057 0.928610i \(-0.378995\pi\)
0.371057 + 0.928610i \(0.378995\pi\)
\(164\) 0.949967i 0.00579248i
\(165\) 0 0
\(166\) −19.4437 −0.117130
\(167\) 107.432i 0.643304i 0.946858 + 0.321652i \(0.104238\pi\)
−0.946858 + 0.321652i \(0.895762\pi\)
\(168\) 47.9992 124.998i 0.285709 0.744034i
\(169\) −74.5839 −0.441325
\(170\) 196.441i 1.15553i
\(171\) 124.770 + 112.397i 0.729647 + 0.657291i
\(172\) 0.737909 0.00429017
\(173\) 328.814i 1.90066i 0.311246 + 0.950329i \(0.399254\pi\)
−0.311246 + 0.950329i \(0.600746\pi\)
\(174\) 13.9052 + 5.33959i 0.0799148 + 0.0306873i
\(175\) −28.3928 −0.162244
\(176\) 0 0
\(177\) 96.8227 252.142i 0.547021 1.42453i
\(178\) −68.4011 −0.384276
\(179\) 48.2985i 0.269824i −0.990858 0.134912i \(-0.956925\pi\)
0.990858 0.134912i \(-0.0430752\pi\)
\(180\) 0.555232 0.616354i 0.00308462 0.00342419i
\(181\) 0.0665674 0.000367776 0.000183888 1.00000i \(-0.499941\pi\)
0.000183888 1.00000i \(0.499941\pi\)
\(182\) 108.878i 0.598231i
\(183\) −86.4536 33.1982i −0.472424 0.181411i
\(184\) −98.7100 −0.536467
\(185\) 215.705i 1.16597i
\(186\) 106.111 276.332i 0.570492 1.48566i
\(187\) 0 0
\(188\) 0.971151i 0.00516570i
\(189\) 68.4832 + 134.524i 0.362345 + 0.711768i
\(190\) 205.095 1.07944
\(191\) 197.414i 1.03358i −0.856112 0.516790i \(-0.827127\pi\)
0.856112 0.516790i \(-0.172873\pi\)
\(192\) −178.480 68.5363i −0.929583 0.356960i
\(193\) 1.52366 0.00789462 0.00394731 0.999992i \(-0.498744\pi\)
0.00394731 + 0.999992i \(0.498744\pi\)
\(194\) 75.8042i 0.390743i
\(195\) 57.3106 149.246i 0.293901 0.765366i
\(196\) 0.298191 0.00152138
\(197\) 215.460i 1.09370i −0.837229 0.546852i \(-0.815826\pi\)
0.837229 0.546852i \(-0.184174\pi\)
\(198\) 0 0
\(199\) −106.663 −0.535993 −0.267997 0.963420i \(-0.586362\pi\)
−0.267997 + 0.963420i \(0.586362\pi\)
\(200\) 40.5417i 0.202709i
\(201\) 95.4380 + 36.6482i 0.474816 + 0.182329i
\(202\) −94.0063 −0.465378
\(203\) 13.8503i 0.0682282i
\(204\) 0.323018 0.841193i 0.00158342 0.00412349i
\(205\) 309.997 1.51218
\(206\) 210.033i 1.01958i
\(207\) 74.4830 82.6823i 0.359821 0.399431i
\(208\) 156.119 0.750573
\(209\) 0 0
\(210\) 172.107 + 66.0891i 0.819557 + 0.314710i
\(211\) 214.825 1.01813 0.509065 0.860728i \(-0.329991\pi\)
0.509065 + 0.860728i \(0.329991\pi\)
\(212\) 0.724629i 0.00341806i
\(213\) 40.4323 105.292i 0.189823 0.494331i
\(214\) −93.4561 −0.436711
\(215\) 240.797i 1.11999i
\(216\) 192.086 97.7865i 0.889286 0.452715i
\(217\) 275.242 1.26840
\(218\) 337.533i 1.54832i
\(219\) −33.9605 13.0408i −0.155071 0.0595472i
\(220\) 0 0
\(221\) 173.654i 0.785767i
\(222\) −84.7729 + 220.763i −0.381860 + 0.994426i
\(223\) 44.7688 0.200757 0.100379 0.994949i \(-0.467995\pi\)
0.100379 + 0.994949i \(0.467995\pi\)
\(224\) 1.50340i 0.00671159i
\(225\) −33.9589 30.5913i −0.150928 0.135961i
\(226\) 92.8348 0.410773
\(227\) 224.504i 0.989004i −0.869177 0.494502i \(-0.835351\pi\)
0.869177 0.494502i \(-0.164649\pi\)
\(228\) −0.878250 0.337248i −0.00385197 0.00147916i
\(229\) −104.101 −0.454589 −0.227294 0.973826i \(-0.572988\pi\)
−0.227294 + 0.973826i \(0.572988\pi\)
\(230\) 135.912i 0.590921i
\(231\) 0 0
\(232\) 19.7767 0.0852446
\(233\) 61.5290i 0.264073i −0.991245 0.132036i \(-0.957848\pi\)
0.991245 0.132036i \(-0.0421516\pi\)
\(234\) −117.309 + 130.223i −0.501320 + 0.556507i
\(235\) −316.909 −1.34855
\(236\) 1.51311i 0.00641150i
\(237\) −176.844 67.9081i −0.746177 0.286532i
\(238\) 200.254 0.841402
\(239\) 149.260i 0.624520i 0.949997 + 0.312260i \(0.101086\pi\)
−0.949997 + 0.312260i \(0.898914\pi\)
\(240\) 94.7645 246.782i 0.394852 1.02826i
\(241\) 358.881 1.48913 0.744567 0.667548i \(-0.232656\pi\)
0.744567 + 0.667548i \(0.232656\pi\)
\(242\) 0 0
\(243\) −63.0323 + 234.683i −0.259392 + 0.965772i
\(244\) 0.518811 0.00212627
\(245\) 97.3067i 0.397170i
\(246\) −317.266 121.830i −1.28970 0.495244i
\(247\) −181.305 −0.734027
\(248\) 393.015i 1.58474i
\(249\) 10.4333 27.1701i 0.0419008 0.109117i
\(250\) 218.973 0.875894
\(251\) 357.022i 1.42240i −0.702990 0.711199i \(-0.748152\pi\)
0.702990 0.711199i \(-0.251848\pi\)
\(252\) −0.628318 0.566010i −0.00249332 0.00224607i
\(253\) 0 0
\(254\) 136.864i 0.538836i
\(255\) −274.501 105.408i −1.07647 0.413366i
\(256\) 3.22681 0.0126047
\(257\) 66.0935i 0.257173i 0.991698 + 0.128586i \(0.0410440\pi\)
−0.991698 + 0.128586i \(0.958956\pi\)
\(258\) −94.6343 + 246.443i −0.366800 + 0.955207i
\(259\) −219.892 −0.849003
\(260\) 0.895632i 0.00344474i
\(261\) −14.9228 + 16.5656i −0.0571755 + 0.0634696i
\(262\) 325.224 1.24131
\(263\) 85.4194i 0.324789i −0.986726 0.162394i \(-0.948078\pi\)
0.986726 0.162394i \(-0.0519216\pi\)
\(264\) 0 0
\(265\) 236.464 0.892315
\(266\) 209.076i 0.785999i
\(267\) 36.7035 95.5819i 0.137466 0.357985i
\(268\) −0.572726 −0.00213704
\(269\) 161.784i 0.601427i −0.953715 0.300713i \(-0.902775\pi\)
0.953715 0.300713i \(-0.0972248\pi\)
\(270\) 134.640 + 264.479i 0.498668 + 0.979553i
\(271\) −259.994 −0.959386 −0.479693 0.877436i \(-0.659252\pi\)
−0.479693 + 0.877436i \(0.659252\pi\)
\(272\) 287.142i 1.05567i
\(273\) −152.143 58.4231i −0.557302 0.214004i
\(274\) −105.956 −0.386701
\(275\) 0 0
\(276\) −0.223487 + 0.581998i −0.000809737 + 0.00210869i
\(277\) −86.7920 −0.313329 −0.156664 0.987652i \(-0.550074\pi\)
−0.156664 + 0.987652i \(0.550074\pi\)
\(278\) 173.435i 0.623865i
\(279\) 329.200 + 296.555i 1.17993 + 1.06292i
\(280\) 244.780 0.874216
\(281\) 484.715i 1.72496i 0.506087 + 0.862482i \(0.331091\pi\)
−0.506087 + 0.862482i \(0.668909\pi\)
\(282\) 324.340 + 124.547i 1.15014 + 0.441655i
\(283\) 432.072 1.52676 0.763379 0.645951i \(-0.223539\pi\)
0.763379 + 0.645951i \(0.223539\pi\)
\(284\) 0.631864i 0.00222487i
\(285\) −110.052 + 286.594i −0.386148 + 1.00559i
\(286\) 0 0
\(287\) 316.014i 1.10109i
\(288\) −1.61981 + 1.79812i −0.00562434 + 0.00624348i
\(289\) −30.3935 −0.105168
\(290\) 27.2302i 0.0938973i
\(291\) −105.927 40.6759i −0.364010 0.139780i
\(292\) 0.203798 0.000697939
\(293\) 5.52957i 0.0188723i −0.999955 0.00943613i \(-0.996996\pi\)
0.999955 0.00943613i \(-0.00300366\pi\)
\(294\) −38.2419 + 99.5884i −0.130075 + 0.338736i
\(295\) 493.765 1.67378
\(296\) 313.981i 1.06075i
\(297\) 0 0
\(298\) −129.170 −0.433458
\(299\) 120.147i 0.401829i
\(300\) 0.239036 + 0.0917898i 0.000796786 + 0.000305966i
\(301\) −245.471 −0.815519
\(302\) 89.4569i 0.296215i
\(303\) 50.4430 131.362i 0.166479 0.433538i
\(304\) −299.791 −0.986156
\(305\) 169.300i 0.555083i
\(306\) 239.512 + 215.760i 0.782718 + 0.705099i
\(307\) 219.257 0.714191 0.357095 0.934068i \(-0.383767\pi\)
0.357095 + 0.934068i \(0.383767\pi\)
\(308\) 0 0
\(309\) 293.495 + 112.702i 0.949823 + 0.364732i
\(310\) 541.135 1.74560
\(311\) 142.150i 0.457075i −0.973535 0.228537i \(-0.926606\pi\)
0.973535 0.228537i \(-0.0733943\pi\)
\(312\) −83.4218 + 217.244i −0.267377 + 0.696295i
\(313\) 94.2857 0.301232 0.150616 0.988592i \(-0.451874\pi\)
0.150616 + 0.988592i \(0.451874\pi\)
\(314\) 282.724i 0.900396i
\(315\) −184.702 + 205.035i −0.586357 + 0.650905i
\(316\) 1.06125 0.00335838
\(317\) 501.215i 1.58112i 0.612385 + 0.790560i \(0.290210\pi\)
−0.612385 + 0.790560i \(0.709790\pi\)
\(318\) −242.008 92.9312i −0.761032 0.292237i
\(319\) 0 0
\(320\) 349.513i 1.09223i
\(321\) 50.1478 130.593i 0.156224 0.406832i
\(322\) −138.550 −0.430280
\(323\) 333.464i 1.03240i
\(324\) −0.141655 1.35394i −0.000437208 0.00417883i
\(325\) 49.3462 0.151834
\(326\) 242.437i 0.743672i
\(327\) −471.660 181.118i −1.44239 0.553876i
\(328\) −451.234 −1.37571
\(329\) 323.061i 0.981948i
\(330\) 0 0
\(331\) −653.489 −1.97429 −0.987143 0.159839i \(-0.948903\pi\)
−0.987143 + 0.159839i \(0.948903\pi\)
\(332\) 0.163048i 0.000491110i
\(333\) −263.000 236.919i −0.789789 0.711468i
\(334\) 215.314 0.644654
\(335\) 186.894i 0.557893i
\(336\) −251.573 96.6040i −0.748728 0.287512i
\(337\) 659.365 1.95657 0.978287 0.207256i \(-0.0664532\pi\)
0.978287 + 0.207256i \(0.0664532\pi\)
\(338\) 149.481i 0.442251i
\(339\) −49.8144 + 129.725i −0.146945 + 0.382669i
\(340\) 1.64729 0.00484497
\(341\) 0 0
\(342\) 225.265 250.063i 0.658670 0.731179i
\(343\) −373.147 −1.08789
\(344\) 350.506i 1.01891i
\(345\) 189.920 + 72.9292i 0.550492 + 0.211389i
\(346\) 659.008 1.90465
\(347\) 277.880i 0.800806i 0.916339 + 0.400403i \(0.131130\pi\)
−0.916339 + 0.400403i \(0.868870\pi\)
\(348\) 0.0447761 0.116604i 0.000128667 0.000335070i
\(349\) −252.775 −0.724284 −0.362142 0.932123i \(-0.617954\pi\)
−0.362142 + 0.932123i \(0.617954\pi\)
\(350\) 56.9047i 0.162585i
\(351\) −119.023 233.801i −0.339096 0.666100i
\(352\) 0 0
\(353\) 560.803i 1.58868i 0.607476 + 0.794338i \(0.292182\pi\)
−0.607476 + 0.794338i \(0.707818\pi\)
\(354\) −505.343 194.052i −1.42752 0.548169i
\(355\) 206.192 0.580823
\(356\) 0.573590i 0.00161121i
\(357\) −107.455 + 279.829i −0.300993 + 0.783836i
\(358\) −96.7998 −0.270390
\(359\) 296.063i 0.824689i 0.911028 + 0.412345i \(0.135290\pi\)
−0.911028 + 0.412345i \(0.864710\pi\)
\(360\) 292.767 + 263.735i 0.813243 + 0.732597i
\(361\) −12.8456 −0.0355834
\(362\) 0.133414i 0.000368547i
\(363\) 0 0
\(364\) 0.913018 0.00250829
\(365\) 66.5041i 0.182203i
\(366\) −66.5357 + 173.270i −0.181792 + 0.473415i
\(367\) 84.8579 0.231220 0.115610 0.993295i \(-0.463118\pi\)
0.115610 + 0.993295i \(0.463118\pi\)
\(368\) 198.666i 0.539852i
\(369\) 340.485 377.966i 0.922722 1.02430i
\(370\) −432.315 −1.16842
\(371\) 241.054i 0.649740i
\(372\) −2.31723 0.889818i −0.00622912 0.00239198i
\(373\) 316.098 0.847447 0.423724 0.905792i \(-0.360723\pi\)
0.423724 + 0.905792i \(0.360723\pi\)
\(374\) 0 0
\(375\) −117.499 + 305.988i −0.313332 + 0.815968i
\(376\) 461.296 1.22685
\(377\) 24.0716i 0.0638505i
\(378\) 269.613 137.254i 0.713262 0.363105i
\(379\) −108.737 −0.286905 −0.143453 0.989657i \(-0.545820\pi\)
−0.143453 + 0.989657i \(0.545820\pi\)
\(380\) 1.71986i 0.00452594i
\(381\) −191.251 73.4403i −0.501970 0.192757i
\(382\) −395.656 −1.03575
\(383\) 442.014i 1.15408i −0.816715 0.577041i \(-0.804207\pi\)
0.816715 0.577041i \(-0.195793\pi\)
\(384\) −138.517 + 360.721i −0.360721 + 0.939378i
\(385\) 0 0
\(386\) 3.05372i 0.00791119i
\(387\) −293.594 264.479i −0.758640 0.683408i
\(388\) 0.635670 0.00163833
\(389\) 509.597i 1.31002i −0.755621 0.655009i \(-0.772665\pi\)
0.755621 0.655009i \(-0.227335\pi\)
\(390\) −299.119 114.862i −0.766972 0.294517i
\(391\) 220.980 0.565165
\(392\) 141.640i 0.361327i
\(393\) −174.513 + 454.460i −0.444053 + 1.15639i
\(394\) −431.824 −1.09600
\(395\) 346.310i 0.876734i
\(396\) 0 0
\(397\) 13.0481 0.0328668 0.0164334 0.999865i \(-0.494769\pi\)
0.0164334 + 0.999865i \(0.494769\pi\)
\(398\) 213.773i 0.537118i
\(399\) 292.157 + 112.188i 0.732223 + 0.281174i
\(400\) 81.5950 0.203988
\(401\) 549.606i 1.37059i −0.728267 0.685294i \(-0.759674\pi\)
0.728267 0.685294i \(-0.240326\pi\)
\(402\) 73.4502 191.277i 0.182712 0.475812i
\(403\) −478.366 −1.18701
\(404\) 0.788308i 0.00195126i
\(405\) −441.823 + 46.2255i −1.09092 + 0.114137i
\(406\) 27.7588 0.0683714
\(407\) 0 0
\(408\) 399.566 + 153.433i 0.979327 + 0.376062i
\(409\) 618.166 1.51141 0.755704 0.654913i \(-0.227295\pi\)
0.755704 + 0.654913i \(0.227295\pi\)
\(410\) 621.295i 1.51535i
\(411\) 56.8552 148.060i 0.138334 0.360244i
\(412\) −1.76128 −0.00427494
\(413\) 503.350i 1.21876i
\(414\) −165.712 149.279i −0.400270 0.360576i
\(415\) 53.2066 0.128209
\(416\) 2.61288i 0.00628096i
\(417\) −242.353 93.0636i −0.581182 0.223174i
\(418\) 0 0
\(419\) 440.342i 1.05094i −0.850814 0.525468i \(-0.823890\pi\)
0.850814 0.525468i \(-0.176110\pi\)
\(420\) 0.554203 1.44324i 0.00131953 0.00343627i
\(421\) 574.230 1.36397 0.681983 0.731368i \(-0.261118\pi\)
0.681983 + 0.731368i \(0.261118\pi\)
\(422\) 430.552i 1.02027i
\(423\) −348.077 + 386.394i −0.822877 + 0.913462i
\(424\) −344.198 −0.811788
\(425\) 90.7598i 0.213552i
\(426\) −211.027 81.0344i −0.495368 0.190222i
\(427\) −172.587 −0.404184
\(428\) 0.783693i 0.00183106i
\(429\) 0 0
\(430\) −482.605 −1.12234
\(431\) 661.481i 1.53476i 0.641193 + 0.767380i \(0.278440\pi\)
−0.641193 + 0.767380i \(0.721560\pi\)
\(432\) −196.807 386.595i −0.455572 0.894897i
\(433\) 212.781 0.491412 0.245706 0.969344i \(-0.420980\pi\)
0.245706 + 0.969344i \(0.420980\pi\)
\(434\) 551.639i 1.27106i
\(435\) −38.0508 14.6115i −0.0874731 0.0335897i
\(436\) 2.83045 0.00649185
\(437\) 230.715i 0.527951i
\(438\) −26.1364 + 68.0635i −0.0596722 + 0.155396i
\(439\) −103.815 −0.236482 −0.118241 0.992985i \(-0.537725\pi\)
−0.118241 + 0.992985i \(0.537725\pi\)
\(440\) 0 0
\(441\) −118.642 106.877i −0.269029 0.242351i
\(442\) −348.038 −0.787416
\(443\) 276.769i 0.624760i 0.949957 + 0.312380i \(0.101126\pi\)
−0.949957 + 0.312380i \(0.898874\pi\)
\(444\) 1.85125 + 0.710879i 0.00416947 + 0.00160108i
\(445\) 187.176 0.420620
\(446\) 89.7255i 0.201178i
\(447\) 69.3118 180.499i 0.155060 0.403802i
\(448\) −356.298 −0.795308
\(449\) 497.877i 1.10886i 0.832231 + 0.554428i \(0.187063\pi\)
−0.832231 + 0.554428i \(0.812937\pi\)
\(450\) −61.3111 + 68.0603i −0.136247 + 0.151245i
\(451\) 0 0
\(452\) 0.778483i 0.00172231i
\(453\) 125.005 + 48.0018i 0.275949 + 0.105964i
\(454\) −449.950 −0.991079
\(455\) 297.939i 0.654812i
\(456\) 160.193 417.168i 0.351300 0.914842i
\(457\) 811.116 1.77487 0.887435 0.460932i \(-0.152485\pi\)
0.887435 + 0.460932i \(0.152485\pi\)
\(458\) 208.638i 0.455543i
\(459\) −430.018 + 218.912i −0.936858 + 0.476933i
\(460\) −1.13971 −0.00247764
\(461\) 790.057i 1.71379i −0.515492 0.856894i \(-0.672391\pi\)
0.515492 0.856894i \(-0.327609\pi\)
\(462\) 0 0
\(463\) 540.381 1.16713 0.583565 0.812067i \(-0.301658\pi\)
0.583565 + 0.812067i \(0.301658\pi\)
\(464\) 39.8030i 0.0857824i
\(465\) −290.369 + 756.168i −0.624449 + 1.62617i
\(466\) −123.316 −0.264627
\(467\) 277.866i 0.595003i 0.954721 + 0.297501i \(0.0961533\pi\)
−0.954721 + 0.297501i \(0.903847\pi\)
\(468\) 1.09201 + 0.983716i 0.00233335 + 0.00210196i
\(469\) 190.522 0.406230
\(470\) 635.149i 1.35138i
\(471\) −395.072 151.708i −0.838793 0.322097i
\(472\) −718.728 −1.52273
\(473\) 0 0
\(474\) −136.101 + 354.430i −0.287133 + 0.747743i
\(475\) −94.7581 −0.199491
\(476\) 1.67927i 0.00352787i
\(477\) 259.719 288.310i 0.544485 0.604423i
\(478\) 299.147 0.625831
\(479\) 470.226i 0.981683i 0.871249 + 0.490841i \(0.163311\pi\)
−0.871249 + 0.490841i \(0.836689\pi\)
\(480\) −4.13026 1.58602i −0.00860470 0.00330421i
\(481\) 382.168 0.794529
\(482\) 719.269i 1.49226i
\(483\) 74.3449 193.606i 0.153923 0.400841i
\(484\) 0 0
\(485\) 207.434i 0.427699i
\(486\) 470.350 + 126.329i 0.967799 + 0.259936i
\(487\) 254.199 0.521969 0.260984 0.965343i \(-0.415953\pi\)
0.260984 + 0.965343i \(0.415953\pi\)
\(488\) 246.435i 0.504989i
\(489\) 338.775 + 130.090i 0.692792 + 0.266032i
\(490\) −195.022 −0.398004
\(491\) 123.123i 0.250760i 0.992109 + 0.125380i \(0.0400151\pi\)
−0.992109 + 0.125380i \(0.959985\pi\)
\(492\) −1.02163 + 2.66049i −0.00207648 + 0.00540750i
\(493\) −44.2737 −0.0898047
\(494\) 363.370i 0.735567i
\(495\) 0 0
\(496\) −790.989 −1.59474
\(497\) 210.194i 0.422926i
\(498\) −54.4542 20.9104i −0.109346 0.0419888i
\(499\) 65.3282 0.130918 0.0654591 0.997855i \(-0.479149\pi\)
0.0654591 + 0.997855i \(0.479149\pi\)
\(500\) 1.83624i 0.00367249i
\(501\) −115.536 + 300.875i −0.230611 + 0.600549i
\(502\) −715.543 −1.42538
\(503\) 425.899i 0.846718i 0.905962 + 0.423359i \(0.139149\pi\)
−0.905962 + 0.423359i \(0.860851\pi\)
\(504\) 268.854 298.450i 0.533441 0.592163i
\(505\) 257.243 0.509393
\(506\) 0 0
\(507\) −208.881 80.2103i −0.411994 0.158206i
\(508\) 1.14770 0.00225925
\(509\) 69.8611i 0.137252i −0.997642 0.0686258i \(-0.978139\pi\)
0.997642 0.0686258i \(-0.0218614\pi\)
\(510\) −211.259 + 550.154i −0.414234 + 1.07873i
\(511\) −67.7951 −0.132671
\(512\) 508.736i 0.993625i
\(513\) 228.556 + 448.962i 0.445529 + 0.875169i
\(514\) 132.464 0.257713
\(515\) 574.746i 1.11601i
\(516\) 2.06660 + 0.793574i 0.00400503 + 0.00153793i
\(517\) 0 0
\(518\) 440.706i 0.850785i
\(519\) −353.618 + 920.881i −0.681346 + 1.77434i
\(520\) −425.424 −0.818124
\(521\) 100.640i 0.193168i −0.995325 0.0965839i \(-0.969208\pi\)
0.995325 0.0965839i \(-0.0307916\pi\)
\(522\) 33.2006 + 29.9083i 0.0636028 + 0.0572955i
\(523\) −851.945 −1.62896 −0.814479 0.580193i \(-0.802977\pi\)
−0.814479 + 0.580193i \(0.802977\pi\)
\(524\) 2.72723i 0.00520464i
\(525\) −79.5171 30.5346i −0.151461 0.0581611i
\(526\) −171.197 −0.325470
\(527\) 879.833i 1.66951i
\(528\) 0 0
\(529\) 376.110 0.710983
\(530\) 473.920i 0.894188i
\(531\) 542.326 602.027i 1.02133 1.13376i
\(532\) −1.75324 −0.00329557
\(533\) 549.228i 1.03045i
\(534\) −191.565 73.5610i −0.358736 0.137755i
\(535\) 255.738 0.478014
\(536\) 272.044i 0.507546i
\(537\) 51.9420 135.265i 0.0967262 0.251891i
\(538\) −324.247 −0.602689
\(539\) 0 0
\(540\) 2.21784 1.12905i 0.00410711 0.00209084i
\(541\) 731.425 1.35199 0.675994 0.736907i \(-0.263715\pi\)
0.675994 + 0.736907i \(0.263715\pi\)
\(542\) 521.078i 0.961399i
\(543\) 0.186430 + 0.0715890i 0.000343332 + 0.000131840i
\(544\) −4.80573 −0.00883406
\(545\) 923.642i 1.69476i
\(546\) −117.091 + 304.925i −0.214453 + 0.558472i
\(547\) −123.279 −0.225373 −0.112686 0.993631i \(-0.535946\pi\)
−0.112686 + 0.993631i \(0.535946\pi\)
\(548\) 0.888514i 0.00162138i
\(549\) −206.421 185.951i −0.375994 0.338708i
\(550\) 0 0
\(551\) 46.2241i 0.0838913i
\(552\) −276.449 106.156i −0.500813 0.192312i
\(553\) −353.032 −0.638394
\(554\) 173.948i 0.313986i
\(555\) 231.977 604.105i 0.417976 1.08848i
\(556\) 1.45437 0.00261577
\(557\) 201.775i 0.362253i −0.983460 0.181127i \(-0.942026\pi\)
0.983460 0.181127i \(-0.0579744\pi\)
\(558\) 594.355 659.783i 1.06515 1.18241i
\(559\) 426.625 0.763193
\(560\) 492.649i 0.879731i
\(561\) 0 0
\(562\) 971.465 1.72858
\(563\) 484.108i 0.859871i −0.902860 0.429936i \(-0.858536\pi\)
0.902860 0.429936i \(-0.141464\pi\)
\(564\) 1.04441 2.71982i 0.00185179 0.00482237i
\(565\) −254.037 −0.449624
\(566\) 865.958i 1.52996i
\(567\) 47.1228 + 450.400i 0.0831090 + 0.794356i
\(568\) −300.135 −0.528406
\(569\) 467.419i 0.821474i −0.911754 0.410737i \(-0.865271\pi\)
0.911754 0.410737i \(-0.134729\pi\)
\(570\) 574.391 + 220.566i 1.00770 + 0.386958i
\(571\) 656.796 1.15026 0.575128 0.818064i \(-0.304952\pi\)
0.575128 + 0.818064i \(0.304952\pi\)
\(572\) 0 0
\(573\) 212.306 552.879i 0.370516 0.964885i
\(574\) −633.355 −1.10341
\(575\) 62.7942i 0.109207i
\(576\) −426.147 383.887i −0.739838 0.666471i
\(577\) −873.454 −1.51378 −0.756892 0.653540i \(-0.773283\pi\)
−0.756892 + 0.653540i \(0.773283\pi\)
\(578\) 60.9146i 0.105389i
\(579\) 4.26719 + 1.63860i 0.00736993 + 0.00283005i
\(580\) 0.228344 0.000393697
\(581\) 54.2394i 0.0933552i
\(582\) −81.5225 + 212.298i −0.140073 + 0.364774i
\(583\) 0 0
\(584\) 96.8039i 0.165760i
\(585\) 321.010 356.348i 0.548735 0.609141i
\(586\) −11.0824 −0.0189119
\(587\) 790.603i 1.34685i 0.739254 + 0.673427i \(0.235178\pi\)
−0.739254 + 0.673427i \(0.764822\pi\)
\(588\) 0.835117 + 0.320685i 0.00142027 + 0.000545383i
\(589\) 918.593 1.55958
\(590\) 989.603i 1.67729i
\(591\) 231.713 603.419i 0.392069 1.02101i
\(592\) 631.924 1.06744
\(593\) 928.634i 1.56599i 0.622026 + 0.782997i \(0.286310\pi\)
−0.622026 + 0.782997i \(0.713690\pi\)
\(594\) 0 0
\(595\) −547.984 −0.920981
\(596\) 1.08318i 0.00181742i
\(597\) −298.721 114.709i −0.500370 0.192142i
\(598\) 240.798 0.402672
\(599\) 917.368i 1.53150i 0.643139 + 0.765749i \(0.277632\pi\)
−0.643139 + 0.765749i \(0.722368\pi\)
\(600\) −43.6000 + 113.542i −0.0726667 + 0.189236i
\(601\) 955.662 1.59012 0.795060 0.606530i \(-0.207439\pi\)
0.795060 + 0.606530i \(0.207439\pi\)
\(602\) 491.973i 0.817230i
\(603\) 227.872 + 205.275i 0.377897 + 0.340423i
\(604\) −0.750158 −0.00124198
\(605\) 0 0
\(606\) −263.275 101.098i −0.434448 0.166828i
\(607\) −781.619 −1.28768 −0.643838 0.765162i \(-0.722659\pi\)
−0.643838 + 0.765162i \(0.722659\pi\)
\(608\) 5.01744i 0.00825237i
\(609\) −14.8951 + 38.7894i −0.0244584 + 0.0636936i
\(610\) −339.311 −0.556248
\(611\) 561.475i 0.918944i
\(612\) 1.80930 2.00847i 0.00295637 0.00328181i
\(613\) 85.9782 0.140258 0.0701290 0.997538i \(-0.477659\pi\)
0.0701290 + 0.997538i \(0.477659\pi\)
\(614\) 439.433i 0.715690i
\(615\) 868.181 + 333.382i 1.41168 + 0.542084i
\(616\) 0 0
\(617\) 7.47837i 0.0121205i −0.999982 0.00606027i \(-0.998071\pi\)
0.999982 0.00606027i \(-0.00192905\pi\)
\(618\) 225.878 588.223i 0.365498 0.951817i
\(619\) 325.144 0.525273 0.262636 0.964895i \(-0.415408\pi\)
0.262636 + 0.964895i \(0.415408\pi\)
\(620\) 4.53779i 0.00731901i
\(621\) 297.518 151.459i 0.479094 0.243896i
\(622\) −284.897 −0.458034
\(623\) 190.809i 0.306275i
\(624\) 437.229 + 167.896i 0.700688 + 0.269064i
\(625\) −726.170 −1.16187
\(626\) 188.967i 0.301864i
\(627\) 0 0
\(628\) 2.37084 0.00377522
\(629\) 702.902i 1.11749i
\(630\) 410.931 + 370.180i 0.652271 + 0.587587i
\(631\) −685.538 −1.08643 −0.543216 0.839593i \(-0.682793\pi\)
−0.543216 + 0.839593i \(0.682793\pi\)
\(632\) 504.091i 0.797612i
\(633\) 601.643 + 231.031i 0.950463 + 0.364978i
\(634\) 1004.53 1.58444
\(635\) 374.522i 0.589798i
\(636\) −0.779292 + 2.02941i −0.00122530 + 0.00319089i
\(637\) 172.400 0.270644
\(638\) 0 0
\(639\) 226.471 251.401i 0.354414 0.393429i
\(640\) −706.393 −1.10374
\(641\) 273.299i 0.426364i 0.977013 + 0.213182i \(0.0683826\pi\)
−0.977013 + 0.213182i \(0.931617\pi\)
\(642\) −261.734 100.506i −0.407686 0.156551i
\(643\) 184.624 0.287129 0.143564 0.989641i \(-0.454144\pi\)
0.143564 + 0.989641i \(0.454144\pi\)
\(644\) 1.16184i 0.00180410i
\(645\) 258.962 674.379i 0.401491 1.04555i
\(646\) 668.328 1.03456
\(647\) 360.098i 0.556565i 0.960499 + 0.278283i \(0.0897652\pi\)
−0.960499 + 0.278283i \(0.910235\pi\)
\(648\) 643.121 67.2862i 0.992471 0.103837i
\(649\) 0 0
\(650\) 98.8995i 0.152153i
\(651\) 770.846 + 296.005i 1.18410 + 0.454693i
\(652\) −2.03300 −0.00311810
\(653\) 1030.37i 1.57789i 0.614461 + 0.788947i \(0.289374\pi\)
−0.614461 + 0.788947i \(0.710626\pi\)
\(654\) −362.995 + 945.300i −0.555039 + 1.44541i
\(655\) −889.960 −1.35872
\(656\) 908.161i 1.38439i
\(657\) −81.0857 73.0447i −0.123418 0.111179i
\(658\) 647.478 0.984009
\(659\) 1071.63i 1.62614i −0.582166 0.813070i \(-0.697795\pi\)
0.582166 0.813070i \(-0.302205\pi\)
\(660\) 0 0
\(661\) 441.357 0.667712 0.333856 0.942624i \(-0.391650\pi\)
0.333856 + 0.942624i \(0.391650\pi\)
\(662\) 1309.72i 1.97843i
\(663\) 186.754 486.339i 0.281681 0.733543i
\(664\) −77.4479 −0.116638
\(665\) 572.125i 0.860338i
\(666\) −474.832 + 527.103i −0.712961 + 0.791446i
\(667\) 30.6318 0.0459247
\(668\) 1.80556i 0.00270293i
\(669\) 125.380 + 48.1460i 0.187414 + 0.0719671i
\(670\) 374.573 0.559064
\(671\) 0 0
\(672\) −1.61681 + 4.21043i −0.00240596 + 0.00626552i
\(673\) −370.702 −0.550820 −0.275410 0.961327i \(-0.588814\pi\)
−0.275410 + 0.961327i \(0.588814\pi\)
\(674\) 1321.50i 1.96068i
\(675\) −62.2068 122.195i −0.0921582 0.181030i
\(676\) 1.25350 0.00185429
\(677\) 75.2277i 0.111119i −0.998455 0.0555596i \(-0.982306\pi\)
0.998455 0.0555596i \(-0.0176943\pi\)
\(678\) 259.994 + 99.8379i 0.383472 + 0.147253i
\(679\) −211.461 −0.311430
\(680\) 782.461i 1.15068i
\(681\) 241.440 628.749i 0.354537 0.923272i
\(682\) 0 0
\(683\) 987.234i 1.44544i 0.691142 + 0.722719i \(0.257108\pi\)
−0.691142 + 0.722719i \(0.742892\pi\)
\(684\) −2.09695 1.88900i −0.00306572 0.00276170i
\(685\) 289.943 0.423275
\(686\) 747.860i 1.09017i
\(687\) −291.546 111.954i −0.424376 0.162960i
\(688\) 705.434 1.02534
\(689\) 418.947i 0.608051i
\(690\) 146.165 380.637i 0.211833 0.551647i
\(691\) 1026.80 1.48597 0.742983 0.669311i \(-0.233411\pi\)
0.742983 + 0.669311i \(0.233411\pi\)
\(692\) 5.52624i 0.00798589i
\(693\) 0 0
\(694\) 556.925 0.802486
\(695\) 474.595i 0.682870i
\(696\) 55.3870 + 21.2686i 0.0795790 + 0.0305584i
\(697\) 1010.17 1.44931
\(698\) 506.611i 0.725804i
\(699\) 66.1705 172.319i 0.0946645 0.246522i
\(700\) 0.477185 0.000681693
\(701\) 186.947i 0.266687i 0.991070 + 0.133343i \(0.0425713\pi\)
−0.991070 + 0.133343i \(0.957429\pi\)
\(702\) −468.583 + 238.545i −0.667498 + 0.339808i
\(703\) −733.868 −1.04391
\(704\) 0 0
\(705\) −887.541 340.816i −1.25892 0.483427i
\(706\) 1123.96 1.59201
\(707\) 262.237i 0.370915i
\(708\) −1.62726 + 4.23765i −0.00229839 + 0.00598538i
\(709\) −713.675 −1.00659 −0.503297 0.864114i \(-0.667880\pi\)
−0.503297 + 0.864114i \(0.667880\pi\)
\(710\) 413.249i 0.582042i
\(711\) −422.241 380.369i −0.593869 0.534977i
\(712\) −272.455 −0.382661
\(713\) 608.733i 0.853762i
\(714\) 560.833 + 215.360i 0.785481 + 0.301625i
\(715\) 0 0
\(716\) 0.811733i 0.00113370i
\(717\) −160.520 + 418.020i −0.223877 + 0.583013i
\(718\) 593.369 0.826420
\(719\) 498.723i 0.693634i −0.937933 0.346817i \(-0.887262\pi\)
0.937933 0.346817i \(-0.112738\pi\)
\(720\) 530.797 589.229i 0.737219 0.818374i
\(721\) 585.902 0.812624
\(722\) 25.7452i 0.0356581i
\(723\) 1005.09 + 385.954i 1.39016 + 0.533823i
\(724\) −0.00111877 −1.54526e−6
\(725\) 12.5809i 0.0173530i
\(726\) 0 0
\(727\) 427.838 0.588498 0.294249 0.955729i \(-0.404930\pi\)
0.294249 + 0.955729i \(0.404930\pi\)
\(728\) 433.683i 0.595718i
\(729\) −428.915 + 589.468i −0.588361 + 0.808598i
\(730\) −133.287 −0.182585
\(731\) 784.669i 1.07342i
\(732\) 1.45299 + 0.557948i 0.00198496 + 0.000762224i
\(733\) 957.424 1.30617 0.653086 0.757284i \(-0.273474\pi\)
0.653086 + 0.757284i \(0.273474\pi\)
\(734\) 170.072i 0.231706i
\(735\) 104.647 272.518i 0.142377 0.370773i
\(736\) 3.32495 0.00451760
\(737\) 0 0
\(738\) −757.518 682.398i −1.02645 0.924659i
\(739\) −1134.98 −1.53584 −0.767918 0.640549i \(-0.778707\pi\)
−0.767918 + 0.640549i \(0.778707\pi\)
\(740\) 3.62526i 0.00489900i
\(741\) −507.764 194.982i −0.685242 0.263133i
\(742\) −483.119 −0.651104
\(743\) 866.886i 1.16674i 0.812207 + 0.583369i \(0.198266\pi\)
−0.812207 + 0.583369i \(0.801734\pi\)
\(744\) 422.663 1100.68i 0.568095 1.47941i
\(745\) 353.468 0.474454
\(746\) 633.522i 0.849226i
\(747\) 58.4393 64.8725i 0.0782321 0.0868441i
\(748\) 0 0
\(749\) 260.702i 0.348067i
\(750\) 613.260 + 235.492i 0.817680 + 0.313989i
\(751\) −1157.47 −1.54124 −0.770618 0.637297i \(-0.780053\pi\)
−0.770618 + 0.637297i \(0.780053\pi\)
\(752\) 928.412i 1.23459i
\(753\) 383.954 999.881i 0.509900 1.32786i
\(754\) −48.2443 −0.0639845
\(755\) 244.794i 0.324231i
\(756\) −1.15097 2.26089i −0.00152244 0.00299060i
\(757\) −410.295 −0.542001 −0.271001 0.962579i \(-0.587355\pi\)
−0.271001 + 0.962579i \(0.587355\pi\)
\(758\) 217.931i 0.287508i
\(759\) 0 0
\(760\) 816.931 1.07491
\(761\) 253.490i 0.333101i −0.986033 0.166550i \(-0.946737\pi\)
0.986033 0.166550i \(-0.0532629\pi\)
\(762\) −147.189 + 383.304i −0.193161 + 0.503024i
\(763\) −941.571 −1.23404
\(764\) 3.31785i 0.00434273i
\(765\) −655.411 590.417i −0.856747 0.771786i
\(766\) −885.883 −1.15650
\(767\) 874.814i 1.14057i
\(768\) 9.03703 + 3.47022i 0.0117670 + 0.00451852i
\(769\) −788.887 −1.02586 −0.512931 0.858430i \(-0.671440\pi\)
−0.512931 + 0.858430i \(0.671440\pi\)
\(770\) 0 0
\(771\) −71.0793 + 185.102i −0.0921910 + 0.240081i
\(772\) −0.0256075 −3.31704e−5
\(773\) 343.352i 0.444182i 0.975026 + 0.222091i \(0.0712881\pi\)
−0.975026 + 0.222091i \(0.928712\pi\)
\(774\) −530.068 + 588.419i −0.684843 + 0.760232i
\(775\) −250.016 −0.322601
\(776\) 301.943i 0.389101i
\(777\) −615.832 236.480i −0.792576 0.304349i
\(778\) −1021.33 −1.31277
\(779\) 1054.67i 1.35387i
\(780\) −0.963195 + 2.50832i −0.00123487 + 0.00321580i
\(781\) 0 0
\(782\) 442.887i 0.566351i