Properties

Label 690.3.b.a.599.2
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.2
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.99999 + 0.00596006i) q^{3} +2.00000 q^{4} +(1.21044 - 4.85127i) q^{5} +(4.24263 - 0.00842880i) q^{6} +6.90074i q^{7} -2.82843 q^{8} +(8.99993 - 0.0357603i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.99999 + 0.00596006i) q^{3} +2.00000 q^{4} +(1.21044 - 4.85127i) q^{5} +(4.24263 - 0.00842880i) q^{6} +6.90074i q^{7} -2.82843 q^{8} +(8.99993 - 0.0357603i) q^{9} +(-1.71182 + 6.86073i) q^{10} -1.93119i q^{11} +(-5.99999 + 0.0119201i) q^{12} +4.38117i q^{13} -9.75913i q^{14} +(-3.60241 + 14.5610i) q^{15} +4.00000 q^{16} +6.60993 q^{17} +(-12.7278 + 0.0505727i) q^{18} -16.9559 q^{19} +(2.42089 - 9.70254i) q^{20} +(-0.0411289 - 20.7022i) q^{21} +2.73112i q^{22} -4.79583 q^{23} +(8.48526 - 0.0168576i) q^{24} +(-22.0697 - 11.7444i) q^{25} -6.19592i q^{26} +(-26.9995 + 0.160921i) q^{27} +13.8015i q^{28} +5.45358i q^{29} +(5.09457 - 20.5924i) q^{30} +19.1195 q^{31} -5.65685 q^{32} +(0.0115100 + 5.79356i) q^{33} -9.34785 q^{34} +(33.4774 + 8.35296i) q^{35} +(17.9999 - 0.0715206i) q^{36} -4.29657i q^{37} +23.9793 q^{38} +(-0.0261121 - 13.1435i) q^{39} +(-3.42365 + 13.7215i) q^{40} -32.7285i q^{41} +(0.0581650 + 29.2773i) q^{42} +29.3732i q^{43} -3.86238i q^{44} +(10.7204 - 43.7044i) q^{45} +6.78233 q^{46} -23.8924 q^{47} +(-12.0000 + 0.0238402i) q^{48} +1.37973 q^{49} +(31.2112 + 16.6091i) q^{50} +(-19.8297 + 0.0393956i) q^{51} +8.76235i q^{52} -28.4218 q^{53} +(38.1831 - 0.227576i) q^{54} +(-9.36873 - 2.33760i) q^{55} -19.5183i q^{56} +(50.8677 - 0.101058i) q^{57} -7.71253i q^{58} +82.3938i q^{59} +(-7.20482 + 29.1220i) q^{60} +64.8349 q^{61} -27.0391 q^{62} +(0.246773 + 62.1062i) q^{63} +8.00000 q^{64} +(21.2543 + 5.30316i) q^{65} +(-0.0162776 - 8.19333i) q^{66} +62.3462i q^{67} +13.2199 q^{68} +(14.3875 - 0.0285834i) q^{69} +(-47.3442 - 11.8129i) q^{70} +130.312i q^{71} +(-25.4556 + 0.101145i) q^{72} +10.5750i q^{73} +6.07626i q^{74} +(66.2788 + 35.1015i) q^{75} -33.9119 q^{76} +13.3267 q^{77} +(0.0369280 + 18.5877i) q^{78} +72.0807 q^{79} +(4.84177 - 19.4051i) q^{80} +(80.9974 - 0.643680i) q^{81} +46.2851i q^{82} -93.0145 q^{83} +(-0.0822577 - 41.4044i) q^{84} +(8.00094 - 32.0665i) q^{85} -41.5400i q^{86} +(-0.0325037 - 16.3607i) q^{87} +5.46223i q^{88} +164.282i q^{89} +(-15.1610 + 61.8073i) q^{90} -30.2334 q^{91} -9.59166 q^{92} +(-57.3585 + 0.113954i) q^{93} +33.7889 q^{94} +(-20.5242 + 82.2578i) q^{95} +(16.9705 - 0.0337152i) q^{96} +69.5724i q^{97} -1.95123 q^{98} +(-0.0690599 - 17.3806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.99999 + 0.00596006i −0.999998 + 0.00198669i
\(4\) 2.00000 0.500000
\(5\) 1.21044 4.85127i 0.242089 0.970254i
\(6\) 4.24263 0.00842880i 0.707105 0.00140480i
\(7\) 6.90074i 0.985821i 0.870080 + 0.492910i \(0.164067\pi\)
−0.870080 + 0.492910i \(0.835933\pi\)
\(8\) −2.82843 −0.353553
\(9\) 8.99993 0.0357603i 0.999992 0.00397337i
\(10\) −1.71182 + 6.86073i −0.171182 + 0.686073i
\(11\) 1.93119i 0.175563i −0.996140 0.0877814i \(-0.972022\pi\)
0.996140 0.0877814i \(-0.0279777\pi\)
\(12\) −5.99999 + 0.0119201i −0.499999 + 0.000993343i
\(13\) 4.38117i 0.337013i 0.985701 + 0.168507i \(0.0538945\pi\)
−0.985701 + 0.168507i \(0.946106\pi\)
\(14\) 9.75913i 0.697080i
\(15\) −3.60241 + 14.5610i −0.240161 + 0.970733i
\(16\) 4.00000 0.250000
\(17\) 6.60993 0.388819 0.194410 0.980920i \(-0.437721\pi\)
0.194410 + 0.980920i \(0.437721\pi\)
\(18\) −12.7278 + 0.0505727i −0.707101 + 0.00280959i
\(19\) −16.9559 −0.892417 −0.446209 0.894929i \(-0.647226\pi\)
−0.446209 + 0.894929i \(0.647226\pi\)
\(20\) 2.42089 9.70254i 0.121044 0.485127i
\(21\) −0.0411289 20.7022i −0.00195852 0.985819i
\(22\) 2.73112i 0.124142i
\(23\) −4.79583 −0.208514
\(24\) 8.48526 0.0168576i 0.353553 0.000702400i
\(25\) −22.0697 11.7444i −0.882786 0.469775i
\(26\) 6.19592i 0.238304i
\(27\) −26.9995 + 0.160921i −0.999982 + 0.00596003i
\(28\) 13.8015i 0.492910i
\(29\) 5.45358i 0.188055i 0.995570 + 0.0940273i \(0.0299741\pi\)
−0.995570 + 0.0940273i \(0.970026\pi\)
\(30\) 5.09457 20.5924i 0.169819 0.686412i
\(31\) 19.1195 0.616759 0.308380 0.951263i \(-0.400213\pi\)
0.308380 + 0.951263i \(0.400213\pi\)
\(32\) −5.65685 −0.176777
\(33\) 0.0115100 + 5.79356i 0.000348788 + 0.175562i
\(34\) −9.34785 −0.274937
\(35\) 33.4774 + 8.35296i 0.956497 + 0.238656i
\(36\) 17.9999 0.0715206i 0.499996 0.00198668i
\(37\) 4.29657i 0.116123i −0.998313 0.0580617i \(-0.981508\pi\)
0.998313 0.0580617i \(-0.0184920\pi\)
\(38\) 23.9793 0.631034
\(39\) −0.0261121 13.1435i −0.000669540 0.337013i
\(40\) −3.42365 + 13.7215i −0.0855912 + 0.343037i
\(41\) 32.7285i 0.798256i −0.916895 0.399128i \(-0.869313\pi\)
0.916895 0.399128i \(-0.130687\pi\)
\(42\) 0.0581650 + 29.2773i 0.00138488 + 0.697079i
\(43\) 29.3732i 0.683098i 0.939864 + 0.341549i \(0.110951\pi\)
−0.939864 + 0.341549i \(0.889049\pi\)
\(44\) 3.86238i 0.0877814i
\(45\) 10.7204 43.7044i 0.238231 0.971208i
\(46\) 6.78233 0.147442
\(47\) −23.8924 −0.508348 −0.254174 0.967158i \(-0.581804\pi\)
−0.254174 + 0.967158i \(0.581804\pi\)
\(48\) −12.0000 + 0.0238402i −0.250000 + 0.000496672i
\(49\) 1.37973 0.0281577
\(50\) 31.2112 + 16.6091i 0.624224 + 0.332181i
\(51\) −19.8297 + 0.0393956i −0.388818 + 0.000772462i
\(52\) 8.76235i 0.168507i
\(53\) −28.4218 −0.536260 −0.268130 0.963383i \(-0.586406\pi\)
−0.268130 + 0.963383i \(0.586406\pi\)
\(54\) 38.1831 0.227576i 0.707094 0.00421438i
\(55\) −9.36873 2.33760i −0.170340 0.0425017i
\(56\) 19.5183i 0.348540i
\(57\) 50.8677 0.101058i 0.892416 0.00177295i
\(58\) 7.71253i 0.132975i
\(59\) 82.3938i 1.39650i 0.715852 + 0.698252i \(0.246039\pi\)
−0.715852 + 0.698252i \(0.753961\pi\)
\(60\) −7.20482 + 29.1220i −0.120080 + 0.485367i
\(61\) 64.8349 1.06287 0.531433 0.847100i \(-0.321654\pi\)
0.531433 + 0.847100i \(0.321654\pi\)
\(62\) −27.0391 −0.436115
\(63\) 0.246773 + 62.1062i 0.00391703 + 0.985813i
\(64\) 8.00000 0.125000
\(65\) 21.2543 + 5.30316i 0.326989 + 0.0815871i
\(66\) −0.0162776 8.19333i −0.000246631 0.124141i
\(67\) 62.3462i 0.930540i 0.885169 + 0.465270i \(0.154043\pi\)
−0.885169 + 0.465270i \(0.845957\pi\)
\(68\) 13.2199 0.194410
\(69\) 14.3875 0.0285834i 0.208514 0.000414253i
\(70\) −47.3442 11.8129i −0.676345 0.168755i
\(71\) 130.312i 1.83538i 0.397300 + 0.917689i \(0.369947\pi\)
−0.397300 + 0.917689i \(0.630053\pi\)
\(72\) −25.4556 + 0.101145i −0.353551 + 0.00140480i
\(73\) 10.5750i 0.144863i 0.997373 + 0.0724314i \(0.0230758\pi\)
−0.997373 + 0.0724314i \(0.976924\pi\)
\(74\) 6.07626i 0.0821117i
\(75\) 66.2788 + 35.1015i 0.883718 + 0.468020i
\(76\) −33.9119 −0.446209
\(77\) 13.3267 0.173073
\(78\) 0.0369280 + 18.5877i 0.000473436 + 0.238304i
\(79\) 72.0807 0.912414 0.456207 0.889874i \(-0.349208\pi\)
0.456207 + 0.889874i \(0.349208\pi\)
\(80\) 4.84177 19.4051i 0.0605221 0.242564i
\(81\) 80.9974 0.643680i 0.999968 0.00794667i
\(82\) 46.2851i 0.564452i
\(83\) −93.0145 −1.12066 −0.560328 0.828271i \(-0.689325\pi\)
−0.560328 + 0.828271i \(0.689325\pi\)
\(84\) −0.0822577 41.4044i −0.000979258 0.492909i
\(85\) 8.00094 32.0665i 0.0941287 0.377253i
\(86\) 41.5400i 0.483023i
\(87\) −0.0325037 16.3607i −0.000373606 0.188054i
\(88\) 5.46223i 0.0620708i
\(89\) 164.282i 1.84587i 0.384959 + 0.922934i \(0.374216\pi\)
−0.384959 + 0.922934i \(0.625784\pi\)
\(90\) −15.1610 + 61.8073i −0.168455 + 0.686748i
\(91\) −30.2334 −0.332235
\(92\) −9.59166 −0.104257
\(93\) −57.3585 + 0.113954i −0.616758 + 0.00122531i
\(94\) 33.7889 0.359456
\(95\) −20.5242 + 82.2578i −0.216044 + 0.865872i
\(96\) 16.9705 0.0337152i 0.176776 0.000351200i
\(97\) 69.5724i 0.717242i 0.933483 + 0.358621i \(0.116753\pi\)
−0.933483 + 0.358621i \(0.883247\pi\)
\(98\) −1.95123 −0.0199105
\(99\) −0.0690599 17.3806i −0.000697575 0.175561i
\(100\) −44.1393 23.4887i −0.441393 0.234887i
\(101\) 131.778i 1.30474i 0.757903 + 0.652368i \(0.226224\pi\)
−0.757903 + 0.652368i \(0.773776\pi\)
\(102\) 28.0435 0.0557137i 0.274936 0.000546213i
\(103\) 36.5773i 0.355120i 0.984110 + 0.177560i \(0.0568204\pi\)
−0.984110 + 0.177560i \(0.943180\pi\)
\(104\) 12.3918i 0.119152i
\(105\) −100.482 24.8593i −0.956969 0.236755i
\(106\) 40.1944 0.379193
\(107\) 79.1711 0.739917 0.369958 0.929048i \(-0.379372\pi\)
0.369958 + 0.929048i \(0.379372\pi\)
\(108\) −53.9990 + 0.321842i −0.499991 + 0.00298001i
\(109\) −87.8564 −0.806022 −0.403011 0.915195i \(-0.632036\pi\)
−0.403011 + 0.915195i \(0.632036\pi\)
\(110\) 13.2494 + 3.30586i 0.120449 + 0.0300533i
\(111\) 0.0256078 + 12.8897i 0.000230701 + 0.116123i
\(112\) 27.6030i 0.246455i
\(113\) 5.97436 0.0528704 0.0264352 0.999651i \(-0.491584\pi\)
0.0264352 + 0.999651i \(0.491584\pi\)
\(114\) −71.9378 + 0.142918i −0.631033 + 0.00125367i
\(115\) −5.80508 + 23.2659i −0.0504790 + 0.202312i
\(116\) 10.9072i 0.0940273i
\(117\) 0.156672 + 39.4303i 0.00133908 + 0.337011i
\(118\) 116.522i 0.987478i
\(119\) 45.6134i 0.383306i
\(120\) 10.1891 41.1847i 0.0849096 0.343206i
\(121\) 117.271 0.969178
\(122\) −91.6903 −0.751560
\(123\) 0.195064 + 98.1853i 0.00158589 + 0.798255i
\(124\) 38.2391 0.308380
\(125\) −83.6892 + 92.8500i −0.669514 + 0.742800i
\(126\) −0.348989 87.8314i −0.00276976 0.697075i
\(127\) 23.9163i 0.188317i 0.995557 + 0.0941586i \(0.0300161\pi\)
−0.995557 + 0.0941586i \(0.969984\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −0.175066 88.1194i −0.00135710 0.683096i
\(130\) −30.0581 7.49980i −0.231216 0.0576908i
\(131\) 4.82841i 0.0368581i −0.999830 0.0184291i \(-0.994134\pi\)
0.999830 0.0184291i \(-0.00586648\pi\)
\(132\) 0.0230200 + 11.5871i 0.000174394 + 0.0877812i
\(133\) 117.009i 0.879764i
\(134\) 88.1709i 0.657991i
\(135\) −31.9007 + 131.177i −0.236302 + 0.971680i
\(136\) −18.6957 −0.137468
\(137\) 260.934 1.90463 0.952314 0.305119i \(-0.0986964\pi\)
0.952314 + 0.305119i \(0.0986964\pi\)
\(138\) −20.3469 + 0.0404231i −0.147442 + 0.000292921i
\(139\) −10.8481 −0.0780440 −0.0390220 0.999238i \(-0.512424\pi\)
−0.0390220 + 0.999238i \(0.512424\pi\)
\(140\) 66.9548 + 16.7059i 0.478248 + 0.119328i
\(141\) 71.6769 0.142400i 0.508347 0.00100993i
\(142\) 184.289i 1.29781i
\(143\) 8.46088 0.0591670
\(144\) 35.9997 0.143041i 0.249998 0.000993342i
\(145\) 26.4568 + 6.60125i 0.182461 + 0.0455259i
\(146\) 14.9553i 0.102434i
\(147\) −4.13917 + 0.00822326i −0.0281576 + 5.59405e-5i
\(148\) 8.59314i 0.0580617i
\(149\) 88.4787i 0.593817i −0.954906 0.296908i \(-0.904044\pi\)
0.954906 0.296908i \(-0.0959556\pi\)
\(150\) −93.7324 49.6410i −0.624883 0.330940i
\(151\) −74.3683 −0.492505 −0.246253 0.969206i \(-0.579199\pi\)
−0.246253 + 0.969206i \(0.579199\pi\)
\(152\) 47.9586 0.315517
\(153\) 59.4889 0.236373i 0.388816 0.00154492i
\(154\) −18.8467 −0.122381
\(155\) 23.1431 92.7541i 0.149310 0.598413i
\(156\) −0.0522241 26.2870i −0.000334770 0.168506i
\(157\) 160.285i 1.02093i −0.859900 0.510463i \(-0.829474\pi\)
0.859900 0.510463i \(-0.170526\pi\)
\(158\) −101.937 −0.645174
\(159\) 85.2651 0.169395i 0.536259 0.00106538i
\(160\) −6.84730 + 27.4429i −0.0427956 + 0.171518i
\(161\) 33.0948i 0.205558i
\(162\) −114.548 + 0.910301i −0.707084 + 0.00561914i
\(163\) 147.791i 0.906694i 0.891334 + 0.453347i \(0.149770\pi\)
−0.891334 + 0.453347i \(0.850230\pi\)
\(164\) 65.4570i 0.399128i
\(165\) 28.1201 + 6.95693i 0.170425 + 0.0421632i
\(166\) 131.542 0.792424
\(167\) 253.815 1.51985 0.759926 0.650010i \(-0.225235\pi\)
0.759926 + 0.650010i \(0.225235\pi\)
\(168\) 0.116330 + 58.5546i 0.000692440 + 0.348540i
\(169\) 149.805 0.886422
\(170\) −11.3150 + 45.3489i −0.0665590 + 0.266758i
\(171\) −152.602 + 0.606349i −0.892410 + 0.00354590i
\(172\) 58.7464i 0.341549i
\(173\) −141.013 −0.815104 −0.407552 0.913182i \(-0.633617\pi\)
−0.407552 + 0.913182i \(0.633617\pi\)
\(174\) 0.0459672 + 23.1375i 0.000264179 + 0.132974i
\(175\) 81.0449 152.297i 0.463114 0.870269i
\(176\) 7.72476i 0.0438907i
\(177\) −0.491072 247.181i −0.00277442 1.39650i
\(178\) 232.330i 1.30523i
\(179\) 125.991i 0.703860i −0.936026 0.351930i \(-0.885525\pi\)
0.936026 0.351930i \(-0.114475\pi\)
\(180\) 21.4408 87.4088i 0.119116 0.485604i
\(181\) −226.332 −1.25045 −0.625227 0.780443i \(-0.714994\pi\)
−0.625227 + 0.780443i \(0.714994\pi\)
\(182\) 42.7564 0.234925
\(183\) −194.504 + 0.386420i −1.06286 + 0.00211158i
\(184\) 13.5647 0.0737210
\(185\) −20.8438 5.20075i −0.112669 0.0281122i
\(186\) 81.1172 0.161155i 0.436114 0.000866424i
\(187\) 12.7650i 0.0682622i
\(188\) −47.7847 −0.254174
\(189\) −1.11047 186.317i −0.00587552 0.985803i
\(190\) 29.0256 116.330i 0.152766 0.612264i
\(191\) 161.079i 0.843345i 0.906748 + 0.421673i \(0.138557\pi\)
−0.906748 + 0.421673i \(0.861443\pi\)
\(192\) −24.0000 + 0.0476805i −0.125000 + 0.000248336i
\(193\) 23.7745i 0.123184i −0.998101 0.0615921i \(-0.980382\pi\)
0.998101 0.0615921i \(-0.0196178\pi\)
\(194\) 98.3903i 0.507166i
\(195\) −63.7943 15.7828i −0.327150 0.0809373i
\(196\) 2.75945 0.0140788
\(197\) −132.922 −0.674730 −0.337365 0.941374i \(-0.609536\pi\)
−0.337365 + 0.941374i \(0.609536\pi\)
\(198\) 0.0976655 + 24.5798i 0.000493260 + 0.124141i
\(199\) 148.011 0.743775 0.371887 0.928278i \(-0.378711\pi\)
0.371887 + 0.928278i \(0.378711\pi\)
\(200\) 62.4224 + 33.2181i 0.312112 + 0.166091i
\(201\) −0.371587 187.038i −0.00184869 0.930539i
\(202\) 186.363i 0.922587i
\(203\) −37.6338 −0.185388
\(204\) −39.6595 + 0.0787911i −0.194409 + 0.000386231i
\(205\) −158.775 39.6160i −0.774512 0.193249i
\(206\) 51.7282i 0.251108i
\(207\) −43.1621 + 0.171500i −0.208513 + 0.000828504i
\(208\) 17.5247i 0.0842533i
\(209\) 32.7451i 0.156675i
\(210\) 142.103 + 35.1564i 0.676679 + 0.167411i
\(211\) −193.048 −0.914920 −0.457460 0.889230i \(-0.651241\pi\)
−0.457460 + 0.889230i \(0.651241\pi\)
\(212\) −56.8435 −0.268130
\(213\) −0.776666 390.935i −0.00364632 1.83537i
\(214\) −111.965 −0.523200
\(215\) 142.497 + 35.5546i 0.662778 + 0.165370i
\(216\) 76.3662 0.455153i 0.353547 0.00210719i
\(217\) 131.939i 0.608014i
\(218\) 124.248 0.569944
\(219\) −0.0630276 31.7249i −0.000287797 0.144863i
\(220\) −18.7375 4.67519i −0.0851702 0.0212509i
\(221\) 28.9592i 0.131037i
\(222\) −0.0362149 18.2288i −0.000163130 0.0821115i
\(223\) 44.5616i 0.199828i −0.994996 0.0999140i \(-0.968143\pi\)
0.994996 0.0999140i \(-0.0318568\pi\)
\(224\) 39.0365i 0.174270i
\(225\) −199.045 104.909i −0.884646 0.466264i
\(226\) −8.44901 −0.0373850
\(227\) 186.388 0.821094 0.410547 0.911839i \(-0.365338\pi\)
0.410547 + 0.911839i \(0.365338\pi\)
\(228\) 101.735 0.202117i 0.446208 0.000886477i
\(229\) 127.546 0.556970 0.278485 0.960441i \(-0.410168\pi\)
0.278485 + 0.960441i \(0.410168\pi\)
\(230\) 8.20962 32.9029i 0.0356940 0.143056i
\(231\) −39.9799 + 0.0794277i −0.173073 + 0.000343843i
\(232\) 15.4251i 0.0664873i
\(233\) −119.516 −0.512945 −0.256473 0.966551i \(-0.582560\pi\)
−0.256473 + 0.966551i \(0.582560\pi\)
\(234\) −0.221568 55.7628i −0.000946871 0.238303i
\(235\) −28.9203 + 115.908i −0.123065 + 0.493227i
\(236\) 164.788i 0.698252i
\(237\) −216.242 + 0.429605i −0.912412 + 0.00181268i
\(238\) 64.5071i 0.271038i
\(239\) 404.639i 1.69305i 0.532348 + 0.846526i \(0.321310\pi\)
−0.532348 + 0.846526i \(0.678690\pi\)
\(240\) −14.4096 + 58.2440i −0.0600401 + 0.242683i
\(241\) −156.085 −0.647654 −0.323827 0.946116i \(-0.604970\pi\)
−0.323827 + 0.946116i \(0.604970\pi\)
\(242\) −165.846 −0.685312
\(243\) −242.988 + 2.41379i −0.999951 + 0.00993328i
\(244\) 129.670 0.531433
\(245\) 1.67008 6.69343i 0.00681666 0.0273201i
\(246\) −0.275862 138.855i −0.00112139 0.564451i
\(247\) 74.2869i 0.300757i
\(248\) −54.0782 −0.218057
\(249\) 279.043 0.554372i 1.12065 0.00222639i
\(250\) 118.354 131.310i 0.473418 0.525239i
\(251\) 150.203i 0.598416i 0.954188 + 0.299208i \(0.0967225\pi\)
−0.954188 + 0.299208i \(0.903277\pi\)
\(252\) 0.493545 + 124.212i 0.00195851 + 0.492906i
\(253\) 9.26166i 0.0366074i
\(254\) 33.8227i 0.133160i
\(255\) −23.8117 + 96.2471i −0.0933790 + 0.377440i
\(256\) 16.0000 0.0625000
\(257\) −11.3432 −0.0441368 −0.0220684 0.999756i \(-0.507025\pi\)
−0.0220684 + 0.999756i \(0.507025\pi\)
\(258\) 0.247581 + 124.620i 0.000959616 + 0.483022i
\(259\) 29.6495 0.114477
\(260\) 42.5085 + 10.6063i 0.163494 + 0.0407935i
\(261\) 0.195022 + 49.0819i 0.000747210 + 0.188053i
\(262\) 6.82841i 0.0260626i
\(263\) −147.415 −0.560511 −0.280256 0.959925i \(-0.590419\pi\)
−0.280256 + 0.959925i \(0.590419\pi\)
\(264\) −0.0325552 16.3867i −0.000123315 0.0620707i
\(265\) −34.4029 + 137.882i −0.129822 + 0.520308i
\(266\) 165.475i 0.622087i
\(267\) −0.979132 492.846i −0.00366716 1.84586i
\(268\) 124.692i 0.465270i
\(269\) 205.779i 0.764976i 0.923960 + 0.382488i \(0.124933\pi\)
−0.923960 + 0.382488i \(0.875067\pi\)
\(270\) 45.1144 185.512i 0.167090 0.687081i
\(271\) −239.892 −0.885209 −0.442605 0.896717i \(-0.645945\pi\)
−0.442605 + 0.896717i \(0.645945\pi\)
\(272\) 26.4397 0.0972048
\(273\) 90.6999 0.180193i 0.332234 0.000660046i
\(274\) −369.016 −1.34678
\(275\) −22.6806 + 42.6207i −0.0824750 + 0.154984i
\(276\) 28.7749 0.0571669i 0.104257 0.000207126i
\(277\) 165.615i 0.597890i 0.954270 + 0.298945i \(0.0966347\pi\)
−0.954270 + 0.298945i \(0.903365\pi\)
\(278\) 15.3415 0.0551854
\(279\) 172.075 0.683721i 0.616755 0.00245061i
\(280\) −94.6883 23.6257i −0.338173 0.0843776i
\(281\) 215.556i 0.767104i −0.923519 0.383552i \(-0.874701\pi\)
0.923519 0.383552i \(-0.125299\pi\)
\(282\) −101.366 + 0.201384i −0.359456 + 0.000714127i
\(283\) 261.575i 0.924293i −0.886804 0.462147i \(-0.847079\pi\)
0.886804 0.462147i \(-0.152921\pi\)
\(284\) 260.624i 0.917689i
\(285\) 61.0822 246.895i 0.214323 0.866299i
\(286\) −11.9655 −0.0418374
\(287\) 225.851 0.786938
\(288\) −50.9113 + 0.202291i −0.176775 + 0.000702399i
\(289\) −245.309 −0.848820
\(290\) −37.4156 9.33558i −0.129019 0.0321917i
\(291\) −0.414656 208.717i −0.00142493 0.717240i
\(292\) 21.1500i 0.0724314i
\(293\) −529.882 −1.80847 −0.904235 0.427036i \(-0.859558\pi\)
−0.904235 + 0.427036i \(0.859558\pi\)
\(294\) 5.85367 0.0116294i 0.0199105 3.95559e-5i
\(295\) 399.715 + 99.7330i 1.35496 + 0.338078i
\(296\) 12.1525i 0.0410558i
\(297\) 0.310769 + 52.1412i 0.00104636 + 0.175560i
\(298\) 125.128i 0.419892i
\(299\) 21.0114i 0.0702721i
\(300\) 132.558 + 70.2030i 0.441859 + 0.234010i
\(301\) −202.697 −0.673412
\(302\) 105.173 0.348254
\(303\) −0.785407 395.334i −0.00259210 1.30473i
\(304\) −67.8237 −0.223104
\(305\) 78.4789 314.531i 0.257308 1.03125i
\(306\) −84.1300 + 0.334282i −0.274935 + 0.00109242i
\(307\) 122.092i 0.397693i 0.980031 + 0.198847i \(0.0637195\pi\)
−0.980031 + 0.198847i \(0.936280\pi\)
\(308\) 26.6533 0.0865367
\(309\) −0.218003 109.732i −0.000705512 0.355119i
\(310\) −32.7293 + 131.174i −0.105578 + 0.423142i
\(311\) 50.4037i 0.162070i 0.996711 + 0.0810348i \(0.0258225\pi\)
−0.996711 + 0.0810348i \(0.974178\pi\)
\(312\) 0.0738561 + 37.1754i 0.000236718 + 0.119152i
\(313\) 491.711i 1.57096i −0.618887 0.785480i \(-0.712416\pi\)
0.618887 0.785480i \(-0.287584\pi\)
\(314\) 226.678i 0.721904i
\(315\) 301.593 + 73.9789i 0.957437 + 0.234854i
\(316\) 144.161 0.456207
\(317\) 534.614 1.68648 0.843240 0.537538i \(-0.180645\pi\)
0.843240 + 0.537538i \(0.180645\pi\)
\(318\) −120.583 + 0.239561i −0.379192 + 0.000753337i
\(319\) 10.5319 0.0330154
\(320\) 9.68354 38.8102i 0.0302611 0.121282i
\(321\) −237.513 + 0.471865i −0.739915 + 0.00146998i
\(322\) 46.8031i 0.145351i
\(323\) −112.077 −0.346989
\(324\) 161.995 1.28736i 0.499984 0.00397333i
\(325\) 51.4541 96.6910i 0.158320 0.297511i
\(326\) 209.008i 0.641129i
\(327\) 263.569 0.523630i 0.806021 0.00160131i
\(328\) 92.5702i 0.282226i
\(329\) 164.875i 0.501140i
\(330\) −39.7678 9.83859i −0.120508 0.0298139i
\(331\) 360.609 1.08945 0.544727 0.838614i \(-0.316633\pi\)
0.544727 + 0.838614i \(0.316633\pi\)
\(332\) −186.029 −0.560328
\(333\) −0.153647 38.6688i −0.000461401 0.116123i
\(334\) −358.949 −1.07470
\(335\) 302.458 + 75.4665i 0.902861 + 0.225273i
\(336\) −0.164515 82.8088i −0.000489629 0.246455i
\(337\) 518.017i 1.53714i 0.639765 + 0.768571i \(0.279032\pi\)
−0.639765 + 0.768571i \(0.720968\pi\)
\(338\) −211.857 −0.626795
\(339\) −17.9230 + 0.0356075i −0.0528703 + 0.000105037i
\(340\) 16.0019 64.1331i 0.0470643 0.188627i
\(341\) 36.9235i 0.108280i
\(342\) 215.812 0.857507i 0.631029 0.00250733i
\(343\) 347.658i 1.01358i
\(344\) 83.0800i 0.241512i
\(345\) 17.2765 69.8321i 0.0500769 0.202412i
\(346\) 199.422 0.576365
\(347\) 341.360 0.983746 0.491873 0.870667i \(-0.336313\pi\)
0.491873 + 0.870667i \(0.336313\pi\)
\(348\) −0.0650074 32.7214i −0.000186803 0.0940271i
\(349\) −0.400677 −0.00114807 −0.000574036 1.00000i \(-0.500183\pi\)
−0.000574036 1.00000i \(0.500183\pi\)
\(350\) −114.615 + 215.381i −0.327471 + 0.615373i
\(351\) −0.705022 118.290i −0.00200861 0.337007i
\(352\) 10.9245i 0.0310354i
\(353\) −271.119 −0.768042 −0.384021 0.923324i \(-0.625461\pi\)
−0.384021 + 0.923324i \(0.625461\pi\)
\(354\) 0.694481 + 349.567i 0.00196181 + 0.987476i
\(355\) 632.178 + 157.735i 1.78078 + 0.444324i
\(356\) 328.564i 0.922934i
\(357\) −0.271859 136.840i −0.000761509 0.383305i
\(358\) 178.178i 0.497704i
\(359\) 348.233i 0.970008i 0.874512 + 0.485004i \(0.161182\pi\)
−0.874512 + 0.485004i \(0.838818\pi\)
\(360\) −30.3219 + 123.615i −0.0842276 + 0.343374i
\(361\) −73.4964 −0.203591
\(362\) 320.082 0.884205
\(363\) −351.811 + 0.698939i −0.969176 + 0.00192545i
\(364\) −60.4667 −0.166117
\(365\) 51.3021 + 12.8004i 0.140554 + 0.0350696i
\(366\) 275.070 0.546480i 0.751559 0.00149311i
\(367\) 546.201i 1.48828i −0.668021 0.744142i \(-0.732858\pi\)
0.668021 0.744142i \(-0.267142\pi\)
\(368\) −19.1833 −0.0521286
\(369\) −1.17038 294.554i −0.00317176 0.798250i
\(370\) 29.4776 + 7.35497i 0.0796692 + 0.0198783i
\(371\) 196.131i 0.528656i
\(372\) −114.717 + 0.227907i −0.308379 + 0.000612654i
\(373\) 561.225i 1.50463i 0.658806 + 0.752313i \(0.271062\pi\)
−0.658806 + 0.752313i \(0.728938\pi\)
\(374\) 18.0525i 0.0482686i
\(375\) 250.514 279.048i 0.668036 0.744129i
\(376\) 67.5778 0.179728
\(377\) −23.8931 −0.0633769
\(378\) 1.57045 + 263.492i 0.00415462 + 0.697068i
\(379\) −64.2274 −0.169465 −0.0847327 0.996404i \(-0.527004\pi\)
−0.0847327 + 0.996404i \(0.527004\pi\)
\(380\) −41.0484 + 164.516i −0.108022 + 0.432936i
\(381\) −0.142542 71.7487i −0.000374127 0.188317i
\(382\) 227.800i 0.596335i
\(383\) 54.9496 0.143471 0.0717357 0.997424i \(-0.477146\pi\)
0.0717357 + 0.997424i \(0.477146\pi\)
\(384\) 33.9411 0.0674304i 0.0883882 0.000175600i
\(385\) 16.1311 64.6512i 0.0418991 0.167925i
\(386\) 33.6223i 0.0871044i
\(387\) 1.05039 + 264.357i 0.00271420 + 0.683092i
\(388\) 139.145i 0.358621i
\(389\) 333.955i 0.858497i −0.903186 0.429248i \(-0.858778\pi\)
0.903186 0.429248i \(-0.141222\pi\)
\(390\) 90.2187 + 22.3202i 0.231330 + 0.0572313i
\(391\) −31.7001 −0.0810744
\(392\) −3.90246 −0.00995525
\(393\) 0.0287776 + 14.4852i 7.32255e−5 + 0.0368580i
\(394\) 187.980 0.477106
\(395\) 87.2495 349.683i 0.220885 0.885273i
\(396\) −0.138120 34.7612i −0.000348788 0.0877807i
\(397\) 188.644i 0.475175i −0.971366 0.237587i \(-0.923643\pi\)
0.971366 0.237587i \(-0.0763566\pi\)
\(398\) −209.319 −0.525928
\(399\) 0.697378 + 351.025i 0.00174781 + 0.879762i
\(400\) −88.2786 46.9775i −0.220697 0.117444i
\(401\) 200.819i 0.500796i 0.968143 + 0.250398i \(0.0805616\pi\)
−0.968143 + 0.250398i \(0.919438\pi\)
\(402\) 0.525504 + 264.512i 0.00130722 + 0.657990i
\(403\) 83.7660i 0.207856i
\(404\) 263.557i 0.652368i
\(405\) 94.9201 393.720i 0.234371 0.972147i
\(406\) 53.2222 0.131089
\(407\) −8.29749 −0.0203870
\(408\) 56.0870 0.111427i 0.137468 0.000273107i
\(409\) 324.047 0.792292 0.396146 0.918188i \(-0.370347\pi\)
0.396146 + 0.918188i \(0.370347\pi\)
\(410\) 224.542 + 56.0255i 0.547662 + 0.136647i
\(411\) −782.801 + 1.55518i −1.90462 + 0.00378390i
\(412\) 73.1547i 0.177560i
\(413\) −568.579 −1.37670
\(414\) 61.0405 0.242538i 0.147441 0.000585841i
\(415\) −112.589 + 451.238i −0.271298 + 1.08732i
\(416\) 24.7837i 0.0595761i
\(417\) 32.5443 0.0646554i 0.0780438 0.000155049i
\(418\) 46.3086i 0.110786i
\(419\) 51.6049i 0.123162i −0.998102 0.0615811i \(-0.980386\pi\)
0.998102 0.0615811i \(-0.0196143\pi\)
\(420\) −200.963 49.7186i −0.478484 0.118378i
\(421\) −444.406 −1.05560 −0.527798 0.849370i \(-0.676982\pi\)
−0.527798 + 0.849370i \(0.676982\pi\)
\(422\) 273.011 0.646946
\(423\) −215.030 + 0.854398i −0.508344 + 0.00201985i
\(424\) 80.3889 0.189596
\(425\) −145.879 77.6294i −0.343244 0.182658i
\(426\) 1.09837 + 552.865i 0.00257834 + 1.29781i
\(427\) 447.409i 1.04780i
\(428\) 158.342 0.369958
\(429\) −25.3826 + 0.0504274i −0.0591669 + 0.000117546i
\(430\) −201.522 50.2818i −0.468655 0.116934i
\(431\) 175.252i 0.406618i −0.979115 0.203309i \(-0.934830\pi\)
0.979115 0.203309i \(-0.0651695\pi\)
\(432\) −107.998 + 0.643683i −0.249996 + 0.00149001i
\(433\) 687.223i 1.58712i 0.608492 + 0.793560i \(0.291775\pi\)
−0.608492 + 0.793560i \(0.708225\pi\)
\(434\) 186.590i 0.429931i
\(435\) −79.4096 19.6460i −0.182551 0.0451633i
\(436\) −175.713 −0.403011
\(437\) 81.3178 0.186082
\(438\) 0.0891344 + 44.8658i 0.000203503 + 0.102433i
\(439\) 63.9919 0.145767 0.0728837 0.997340i \(-0.476780\pi\)
0.0728837 + 0.997340i \(0.476780\pi\)
\(440\) 26.4988 + 6.61172i 0.0602245 + 0.0150266i
\(441\) 12.4174 0.0493394i 0.0281575 0.000111881i
\(442\) 40.9545i 0.0926573i
\(443\) −619.458 −1.39833 −0.699163 0.714962i \(-0.746444\pi\)
−0.699163 + 0.714962i \(0.746444\pi\)
\(444\) 0.0512156 + 25.7794i 0.000115350 + 0.0580616i
\(445\) 796.977 + 198.854i 1.79096 + 0.446863i
\(446\) 63.0197i 0.141300i
\(447\) 0.527339 + 265.436i 0.00117973 + 0.593816i
\(448\) 55.2060i 0.123228i
\(449\) 321.746i 0.716583i −0.933610 0.358291i \(-0.883359\pi\)
0.933610 0.358291i \(-0.116641\pi\)
\(450\) 281.493 + 148.364i 0.625539 + 0.329698i
\(451\) −63.2050 −0.140144
\(452\) 11.9487 0.0264352
\(453\) 223.104 0.443239i 0.492504 0.000978453i
\(454\) −263.593 −0.580601
\(455\) −36.5958 + 146.670i −0.0804302 + 0.322352i
\(456\) −143.876 + 0.285836i −0.315517 + 0.000626834i
\(457\) 694.280i 1.51921i 0.650383 + 0.759607i \(0.274608\pi\)
−0.650383 + 0.759607i \(0.725392\pi\)
\(458\) −180.378 −0.393837
\(459\) −178.465 + 1.06367i −0.388812 + 0.00231737i
\(460\) −11.6102 + 46.5318i −0.0252395 + 0.101156i
\(461\) 878.547i 1.90574i −0.303376 0.952871i \(-0.598114\pi\)
0.303376 0.952871i \(-0.401886\pi\)
\(462\) 56.5401 0.112328i 0.122381 0.000243133i
\(463\) 266.191i 0.574926i −0.957792 0.287463i \(-0.907188\pi\)
0.957792 0.287463i \(-0.0928119\pi\)
\(464\) 21.8143i 0.0470136i
\(465\) −68.8764 + 278.400i −0.148121 + 0.598709i
\(466\) 169.022 0.362707
\(467\) 240.484 0.514956 0.257478 0.966284i \(-0.417109\pi\)
0.257478 + 0.966284i \(0.417109\pi\)
\(468\) 0.313344 + 78.8605i 0.000669539 + 0.168505i
\(469\) −430.235 −0.917346
\(470\) 40.8995 163.919i 0.0870203 0.348764i
\(471\) 0.955311 + 480.855i 0.00202826 + 1.02092i
\(472\) 233.045i 0.493739i
\(473\) 56.7252 0.119927
\(474\) 305.812 0.607554i 0.645173 0.00128176i
\(475\) 374.212 + 199.137i 0.787814 + 0.419235i
\(476\) 91.2268i 0.191653i
\(477\) −255.794 + 1.01637i −0.536255 + 0.00213076i
\(478\) 572.246i 1.19717i
\(479\) 477.380i 0.996617i 0.867000 + 0.498309i \(0.166045\pi\)
−0.867000 + 0.498309i \(0.833955\pi\)
\(480\) 20.3783 82.3694i 0.0424548 0.171603i
\(481\) 18.8240 0.0391352
\(482\) 220.737 0.457961
\(483\) 0.197247 + 99.2842i 0.000408379 + 0.205557i
\(484\) 234.541 0.484589
\(485\) 337.515 + 84.2135i 0.695907 + 0.173636i
\(486\) 343.637 3.41361i 0.707072 0.00702389i
\(487\) 521.050i 1.06992i −0.844878 0.534959i \(-0.820327\pi\)
0.844878 0.534959i \(-0.179673\pi\)
\(488\) −183.381 −0.375780
\(489\) −0.880844 443.372i −0.00180132 0.906692i
\(490\) −2.36185 + 9.46594i −0.00482010 + 0.0193182i
\(491\) 763.114i 1.55420i 0.629375 + 0.777102i \(0.283311\pi\)
−0.629375 + 0.777102i \(0.716689\pi\)
\(492\) 0.390128 + 196.371i 0.000792943 + 0.399127i
\(493\) 36.0478i 0.0731192i
\(494\) 105.058i 0.212667i
\(495\) −84.4015 20.7032i −0.170508 0.0418246i
\(496\) 76.4782 0.154190
\(497\) −899.249 −1.80935
\(498\) −394.626 + 0.784000i −0.792422 + 0.00157430i
\(499\) −605.819 −1.21407 −0.607033 0.794677i \(-0.707640\pi\)
−0.607033 + 0.794677i \(0.707640\pi\)
\(500\) −167.378 + 185.700i −0.334757 + 0.371400i
\(501\) −761.444 + 1.51275i −1.51985 + 0.00301947i
\(502\) 212.418i 0.423144i
\(503\) −325.402 −0.646923 −0.323462 0.946241i \(-0.604847\pi\)
−0.323462 + 0.946241i \(0.604847\pi\)
\(504\) −0.697978 175.663i −0.00138488 0.348537i
\(505\) 639.292 + 159.510i 1.26593 + 0.315862i
\(506\) 13.0980i 0.0258853i
\(507\) −449.415 + 0.892849i −0.886420 + 0.00176104i
\(508\) 47.8326i 0.0941586i
\(509\) 428.784i 0.842404i −0.906967 0.421202i \(-0.861608\pi\)
0.906967 0.421202i \(-0.138392\pi\)
\(510\) 33.6748 136.114i 0.0660289 0.266890i
\(511\) −72.9753 −0.142809
\(512\) −22.6274 −0.0441942
\(513\) 457.802 2.72856i 0.892402 0.00531883i
\(514\) 16.0416 0.0312094
\(515\) 177.447 + 44.2748i 0.344557 + 0.0859705i
\(516\) −0.350132 176.239i −0.000678551 0.341548i
\(517\) 46.1407i 0.0892470i
\(518\) −41.9307 −0.0809474
\(519\) 423.038 0.840446i 0.815102 0.00161936i
\(520\) −60.1161 14.9996i −0.115608 0.0288454i
\(521\) 700.778i 1.34506i −0.740069 0.672531i \(-0.765207\pi\)
0.740069 0.672531i \(-0.234793\pi\)
\(522\) −0.275802 69.4122i −0.000528357 0.132974i
\(523\) 411.838i 0.787454i 0.919228 + 0.393727i \(0.128814\pi\)
−0.919228 + 0.393727i \(0.871186\pi\)
\(524\) 9.65682i 0.0184291i
\(525\) −242.227 + 457.373i −0.461384 + 0.871187i
\(526\) 208.476 0.396341
\(527\) 126.379 0.239808
\(528\) 0.0460400 + 23.1742i 8.71971e−5 + 0.0438906i
\(529\) 23.0000 0.0434783
\(530\) 48.6531 194.994i 0.0917982 0.367913i
\(531\) 2.94643 + 741.538i 0.00554883 + 1.39649i
\(532\) 234.017i 0.439882i
\(533\) 143.389 0.269023
\(534\) 1.38470 + 696.989i 0.00259307 + 1.30522i
\(535\) 95.8321 384.080i 0.179125 0.717907i
\(536\) 176.342i 0.328996i
\(537\) 0.750914 + 377.972i 0.00139835 + 0.703859i
\(538\) 291.015i 0.540920i
\(539\) 2.66452i 0.00494344i
\(540\) −63.8014 + 262.354i −0.118151 + 0.485840i
\(541\) 598.358 1.10602 0.553011 0.833174i \(-0.313479\pi\)
0.553011 + 0.833174i \(0.313479\pi\)
\(542\) 339.258 0.625937
\(543\) 678.995 1.34895i 1.25045 0.00248426i
\(544\) −37.3914 −0.0687342
\(545\) −106.345 + 426.215i −0.195129 + 0.782047i
\(546\) −128.269 + 0.254831i −0.234925 + 0.000466723i
\(547\) 779.530i 1.42510i −0.701621 0.712550i \(-0.747540\pi\)
0.701621 0.712550i \(-0.252460\pi\)
\(548\) 521.868 0.952314
\(549\) 583.509 2.31851i 1.06286 0.00422316i
\(550\) 32.0752 60.2748i 0.0583186 0.109591i
\(551\) 92.4706i 0.167823i
\(552\) −40.6939 + 0.0808462i −0.0737208 + 0.000146461i
\(553\) 497.410i 0.899476i
\(554\) 234.216i 0.422772i
\(555\) 62.5623 + 15.4780i 0.112725 + 0.0278883i
\(556\) −21.6962 −0.0390220
\(557\) 185.855 0.333672 0.166836 0.985985i \(-0.446645\pi\)
0.166836 + 0.985985i \(0.446645\pi\)
\(558\) −243.350 + 0.966927i −0.436111 + 0.00173284i
\(559\) −128.689 −0.230213
\(560\) 133.910 + 33.4118i 0.239124 + 0.0596640i
\(561\) 0.0760803 + 38.2950i 0.000135616 + 0.0682620i
\(562\) 304.843i 0.542425i
\(563\) −252.783 −0.448994 −0.224497 0.974475i \(-0.572074\pi\)
−0.224497 + 0.974475i \(0.572074\pi\)
\(564\) 143.354 0.284800i 0.254174 0.000504964i
\(565\) 7.23162 28.9832i 0.0127993 0.0512977i
\(566\) 369.923i 0.653574i
\(567\) 4.44187 + 558.943i 0.00783399 + 0.985789i
\(568\) 368.577i 0.648904i
\(569\) 155.819i 0.273848i −0.990582 0.136924i \(-0.956278\pi\)
0.990582 0.136924i \(-0.0437216\pi\)
\(570\) −86.3832 + 349.163i −0.151550 + 0.612566i
\(571\) 217.567 0.381029 0.190514 0.981684i \(-0.438984\pi\)
0.190514 + 0.981684i \(0.438984\pi\)
\(572\) 16.9218 0.0295835
\(573\) −0.960040 483.236i −0.00167546 0.843344i
\(574\) −319.402 −0.556449
\(575\) 105.842 + 56.3240i 0.184074 + 0.0979548i
\(576\) 71.9994 0.286082i 0.124999 0.000496671i
\(577\) 824.725i 1.42933i 0.699466 + 0.714666i \(0.253421\pi\)
−0.699466 + 0.714666i \(0.746579\pi\)
\(578\) 346.919 0.600206
\(579\) 0.141698 + 71.3235i 0.000244728 + 0.123184i
\(580\) 52.9136 + 13.2025i 0.0912304 + 0.0227629i
\(581\) 641.869i 1.10477i
\(582\) 0.586412 + 295.170i 0.00100758 + 0.507165i
\(583\) 54.8878i 0.0941472i
\(584\) 29.9106i 0.0512168i
\(585\) 191.476 + 46.9680i 0.327310 + 0.0802872i
\(586\) 749.366 1.27878
\(587\) 455.443 0.775883 0.387942 0.921684i \(-0.373186\pi\)
0.387942 + 0.921684i \(0.373186\pi\)
\(588\) −8.27834 + 0.0164465i −0.0140788 + 2.79703e-5i
\(589\) −324.190 −0.550407
\(590\) −565.282 141.044i −0.958105 0.239057i
\(591\) 398.765 0.792223i 0.674729 0.00134048i
\(592\) 17.1863i 0.0290309i
\(593\) 264.393 0.445857 0.222928 0.974835i \(-0.428438\pi\)
0.222928 + 0.974835i \(0.428438\pi\)
\(594\) −0.439493 73.7388i −0.000739888 0.124139i
\(595\) 221.283 + 55.2124i 0.371904 + 0.0927940i
\(596\) 176.957i 0.296908i
\(597\) −444.033 + 0.882155i −0.743773 + 0.00147765i
\(598\) 29.7146i 0.0496899i
\(599\) 1090.92i 1.82124i −0.413249 0.910618i \(-0.635606\pi\)
0.413249 0.910618i \(-0.364394\pi\)
\(600\) −187.465 99.2821i −0.312441 0.165470i
\(601\) −73.3335 −0.122019 −0.0610096 0.998137i \(-0.519432\pi\)
−0.0610096 + 0.998137i \(0.519432\pi\)
\(602\) 286.657 0.476174
\(603\) 2.22952 + 561.111i 0.00369738 + 0.930533i
\(604\) −148.737 −0.246253
\(605\) 141.949 568.911i 0.234627 0.940349i
\(606\) 1.11073 + 559.087i 0.00183289 + 0.922585i
\(607\) 486.978i 0.802271i 0.916019 + 0.401135i \(0.131384\pi\)
−0.916019 + 0.401135i \(0.868616\pi\)
\(608\) 95.9172 0.157759
\(609\) 112.901 0.224300i 0.185388 0.000368308i
\(610\) −110.986 + 444.815i −0.181944 + 0.729204i
\(611\) 104.677i 0.171320i
\(612\) 118.978 0.472746i 0.194408 0.000772461i
\(613\) 977.971i 1.59538i 0.603065 + 0.797692i \(0.293946\pi\)
−0.603065 + 0.797692i \(0.706054\pi\)
\(614\) 172.664i 0.281211i
\(615\) 476.560 + 117.901i 0.774894 + 0.191710i
\(616\) −37.6935 −0.0611907
\(617\) 119.147 0.193107 0.0965534 0.995328i \(-0.469218\pi\)
0.0965534 + 0.995328i \(0.469218\pi\)
\(618\) 0.308303 + 155.184i 0.000498872 + 0.251107i
\(619\) −661.995 −1.06946 −0.534730 0.845023i \(-0.679587\pi\)
−0.534730 + 0.845023i \(0.679587\pi\)
\(620\) 46.2862 185.508i 0.0746552 0.299207i
\(621\) 129.485 0.771749i 0.208511 0.00124275i
\(622\) 71.2815i 0.114601i
\(623\) −1133.67 −1.81969
\(624\) −0.104448 52.5740i −0.000167385 0.0842532i
\(625\) 349.139 + 518.389i 0.558623 + 0.829422i
\(626\) 695.384i 1.11084i
\(627\) −0.195163 98.2352i −0.000311265 0.156675i
\(628\) 320.571i 0.510463i
\(629\) 28.4000i 0.0451510i
\(630\) −426.517 104.622i −0.677010 0.166067i
\(631\) −334.926 −0.530786 −0.265393 0.964140i \(-0.585502\pi\)
−0.265393 + 0.964140i \(0.585502\pi\)
\(632\) −203.875 −0.322587
\(633\) 579.143 1.15058i 0.914918 0.00181766i
\(634\) −756.058 −1.19252
\(635\) 116.024 + 28.9493i 0.182715 + 0.0455894i
\(636\) 170.530 0.338791i 0.268129 0.000532690i
\(637\) 6.04482i 0.00948952i
\(638\) −14.8944 −0.0233454
\(639\) 4.65999 + 1172.80i 0.00729263 + 1.83536i
\(640\) −13.6946 + 54.8859i −0.0213978 + 0.0857592i
\(641\) 21.9255i 0.0342052i 0.999854 + 0.0171026i \(0.00544419\pi\)
−0.999854 + 0.0171026i \(0.994556\pi\)
\(642\) 335.894 0.667317i 0.523199 0.00103943i
\(643\) 624.566i 0.971332i −0.874145 0.485666i \(-0.838577\pi\)
0.874145 0.485666i \(-0.161423\pi\)
\(644\) 66.1896i 0.102779i
\(645\) −427.703 105.814i −0.663106 0.164053i
\(646\) 158.501 0.245358
\(647\) −548.096 −0.847134 −0.423567 0.905865i \(-0.639222\pi\)
−0.423567 + 0.905865i \(0.639222\pi\)
\(648\) −229.095 + 1.82060i −0.353542 + 0.00280957i
\(649\) 159.118 0.245174
\(650\) −72.7671 + 136.742i −0.111949 + 0.210372i
\(651\) −0.786365 395.816i −0.00120793 0.608013i
\(652\) 295.582i 0.453347i
\(653\) 1074.01 1.64473 0.822366 0.568959i \(-0.192654\pi\)
0.822366 + 0.568959i \(0.192654\pi\)
\(654\) −372.743 + 0.740524i −0.569943 + 0.00113230i
\(655\) −23.4239 5.84452i −0.0357617 0.00892293i
\(656\) 130.914i 0.199564i
\(657\) 0.378165 + 95.1741i 0.000575593 + 0.144862i
\(658\) 233.169i 0.354359i
\(659\) 624.157i 0.947127i −0.880760 0.473564i \(-0.842967\pi\)
0.880760 0.473564i \(-0.157033\pi\)
\(660\) 56.2401 + 13.9139i 0.0852123 + 0.0210816i
\(661\) 497.027 0.751931 0.375966 0.926634i \(-0.377311\pi\)
0.375966 + 0.926634i \(0.377311\pi\)
\(662\) −509.978 −0.770360
\(663\) −0.172599 86.8775i −0.000260330 0.131037i
\(664\) 263.085 0.396212
\(665\) −567.640 141.632i −0.853594 0.212981i
\(666\) 0.217289 + 54.6859i 0.000326260 + 0.0821110i
\(667\) 26.1545i 0.0392121i
\(668\) 507.631 0.759926
\(669\) 0.265590 + 133.685i 0.000396996 + 0.199828i
\(670\) −427.741 106.726i −0.638419 0.159292i
\(671\) 125.208i 0.186600i
\(672\) 0.232660 + 117.109i 0.000346220 + 0.174270i
\(673\) 599.940i 0.891442i −0.895172 0.445721i \(-0.852947\pi\)
0.895172 0.445721i \(-0.147053\pi\)
\(674\) 732.586i 1.08692i
\(675\) 597.760 + 313.541i 0.885570 + 0.464505i
\(676\) 299.611 0.443211
\(677\) −302.950 −0.447488 −0.223744 0.974648i \(-0.571828\pi\)
−0.223744 + 0.974648i \(0.571828\pi\)
\(678\) 25.3470 0.0503566i 0.0373849 7.42723e-5i
\(679\) −480.102 −0.707072
\(680\) −22.6301 + 90.6979i −0.0332795 + 0.133379i
\(681\) −559.164 + 1.11089i −0.821093 + 0.00163126i
\(682\) 52.2177i 0.0765655i
\(683\) 287.077 0.420318 0.210159 0.977667i \(-0.432602\pi\)
0.210159 + 0.977667i \(0.432602\pi\)
\(684\) −305.204 + 1.21270i −0.446205 + 0.00177295i
\(685\) 315.846 1265.86i 0.461089 1.84797i
\(686\) 491.662i 0.716709i
\(687\) −382.638 + 0.760183i −0.556969 + 0.00110653i
\(688\) 117.493i 0.170774i
\(689\) 124.521i 0.180727i
\(690\) −24.4327 + 98.7575i −0.0354097 + 0.143127i
\(691\) −364.267 −0.527159 −0.263580 0.964638i \(-0.584903\pi\)
−0.263580 + 0.964638i \(0.584903\pi\)
\(692\) −282.026 −0.407552
\(693\) 119.939 0.476565i 0.173072 0.000687684i
\(694\) −482.756 −0.695613
\(695\) −13.1310 + 52.6271i −0.0188936 + 0.0757225i
\(696\) 0.0919343 + 46.2751i 0.000132090 + 0.0664872i
\(697\) 216.333i 0.310377i
\(698\) 0.566643 0.000811810
\(699\) 358.548 0.712324i 0.512944 0.00101906i
\(700\) 162.090 304.594i 0.231557 0.435134i
\(701\) 281.045i 0.400921i −0.979702 0.200460i \(-0.935756\pi\)
0.979702 0.200460i \(-0.0642438\pi\)
\(702\) 0.997052 + 167.287i 0.00142030 + 0.238300i
\(703\) 72.8523i 0.103631i
\(704\) 15.4495i 0.0219453i
\(705\) 86.0700 347.897i 0.122085 0.493470i
\(706\) 383.420 0.543087
\(707\) −909.368 −1.28624
\(708\) −0.982144 494.362i −0.00138721 0.698251i
\(709\) −734.625 −1.03614 −0.518071 0.855337i \(-0.673350\pi\)
−0.518071 + 0.855337i \(0.673350\pi\)
\(710\) −894.035 223.071i −1.25920 0.314185i
\(711\) 648.721 2.57763i 0.912407 0.00362535i
\(712\) 464.660i 0.652613i
\(713\) −91.6941 −0.128603
\(714\) 0.384466 + 193.521i 0.000538468 + 0.271038i
\(715\) 10.2414 41.0460i 0.0143237 0.0574070i
\(716\) 251.982i 0.351930i
\(717\) −2.41167 1213.92i −0.00336356 1.69305i
\(718\) 492.476i 0.685899i
\(719\) 976.727i 1.35845i −0.733929 0.679226i \(-0.762316\pi\)
0.733929 0.679226i \(-0.237684\pi\)
\(720\) 42.8817 174.818i 0.0595579 0.242802i
\(721\) −252.411 −0.350085
\(722\) 103.940 0.143961
\(723\) 468.253 0.930274i 0.647653 0.00128669i
\(724\) −452.664 −0.625227
\(725\) 64.0489 120.359i 0.0883433 0.166012i
\(726\) 497.536 0.988449i 0.685311 0.00136150i
\(727\) 1318.22i 1.81323i −0.421956 0.906616i \(-0.638656\pi\)
0.421956 0.906616i \(-0.361344\pi\)
\(728\) 85.5129 0.117463
\(729\) 728.948 8.68957i 0.999929 0.0119198i
\(730\) −72.5522 18.1025i −0.0993865 0.0247980i
\(731\) 194.155i 0.265602i
\(732\) −389.008 + 0.772839i −0.531432 + 0.00105579i
\(733\) 272.542i 0.371817i −0.982567 0.185908i \(-0.940477\pi\)
0.982567 0.185908i \(-0.0595228\pi\)
\(734\) 772.444i 1.05238i
\(735\) −4.97034 + 20.0902i −0.00676237 + 0.0273336i
\(736\) 27.1293 0.0368605
\(737\) 120.402 0.163368
\(738\) 1.65517 + 416.563i 0.00224278 + 0.564448i
\(739\) −1298.32 −1.75685 −0.878427 0.477876i \(-0.841407\pi\)
−0.878427 + 0.477876i \(0.841407\pi\)
\(740\) −41.6876 10.4015i −0.0563346 0.0140561i
\(741\) 0.442754 + 222.860i 0.000597509 + 0.300756i
\(742\) 277.372i 0.373816i
\(743\) 302.960 0.407753 0.203876 0.978997i \(-0.434646\pi\)
0.203876 + 0.978997i \(0.434646\pi\)
\(744\) 162.234 0.322310i 0.218057 0.000433212i
\(745\) −429.234 107.098i −0.576153 0.143756i
\(746\) 793.692i 1.06393i
\(747\) −837.124 + 3.32622i −1.12065 + 0.00445278i
\(748\) 25.5301i 0.0341311i
\(749\) 546.340i 0.729425i
\(750\) −354.280 + 394.634i −0.472373 + 0.526178i
\(751\) 708.772 0.943770 0.471885 0.881660i \(-0.343574\pi\)
0.471885 + 0.881660i \(0.343574\pi\)
\(752\) −95.5694 −0.127087
\(753\) −0.895216 450.607i −0.00118887 0.598415i
\(754\) 33.7899 0.0448142
\(755\) −90.0185 + 360.781i −0.119230 + 0.477855i
\(756\) −2.22095 372.634i −0.00293776 0.492902i
\(757\) 916.947i 1.21129i −0.795735 0.605645i \(-0.792915\pi\)
0.795735 0.605645i \(-0.207085\pi\)
\(758\) 90.8312 0.119830
\(759\) −0.0552001 27.7849i −7.27274e−5 0.0366073i
\(760\) 58.0512 232.660i 0.0763831 0.306132i
\(761\) 239.914i 0.315261i 0.987498 + 0.157631i \(0.0503855\pi\)
−0.987498 + 0.157631i \(0.949614\pi\)
\(762\) 0.201585 + 101.468i 0.000264548 + 0.133160i
\(763\) 606.275i 0.794593i
\(764\) 322.158i 0.421673i
\(765\) 70.8612 288.883i 0.0926290 0.377624i
\(766\) −77.7104 −0.101450
\(767\) −360.982 −0.470641
\(768\) −47.9999 + 0.0953610i −0.0624999 + 0.000124168i
\(769\) 391.054 0.508522 0.254261 0.967136i \(-0.418168\pi\)
0.254261 + 0.967136i \(0.418168\pi\)
\(770\) −22.8129 + 91.4306i −0.0296271 + 0.118741i
\(771\) 34.0294 0.0676059i 0.0441367 8.76860e-5i
\(772\) 47.5491i 0.0615921i
\(773\) 319.039 0.412729 0.206364 0.978475i \(-0.433837\pi\)
0.206364 + 0.978475i \(0.433837\pi\)
\(774\) −1.48548 373.857i −0.00191923 0.483019i
\(775\) −421.962 224.547i −0.544467 0.289738i
\(776\) 196.781i 0.253583i
\(777\) −88.9484 + 0.176713i −0.114477 + 0.000227430i
\(778\) 472.284i 0.607049i
\(779\) 554.942i 0.712378i
\(780\) −127.589 31.5655i −0.163575 0.0404687i
\(781\) 251.657 0.322224
\(782\) 44.8307 0.0573283