Properties

Label 600.2.k.d.301.1
Level 600
Weight 2
Character 600.301
Analytic conductor 4.791
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.214798336.3
Defining polynomial: \(x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 301.1
Root \(1.41216 - 0.0762223i\) of defining polynomial
Character \(\chi\) \(=\) 600.301
Dual form 600.2.k.d.301.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29150 - 0.576222i) q^{2} +1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} -1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-1.29150 - 0.576222i) q^{2} +1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} -1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} -1.00000 q^{9} -1.43055i q^{11} +(-1.48838 + 1.33594i) q^{12} +0.241319i q^{13} +(2.55298 + 1.13905i) q^{14} +(-0.430552 + 3.97676i) q^{16} -7.38407 q^{17} +(1.29150 + 0.576222i) q^{18} +3.04033i q^{19} -1.97676i q^{21} +(-0.824316 + 1.84756i) q^{22} +0.874337 q^{23} +(2.69204 - 0.867721i) q^{24} +(0.139054 - 0.311664i) q^{26} -1.00000i q^{27} +(-2.64082 - 2.94217i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(2.84756 - 4.88789i) q^{32} +1.43055 q^{33} +(9.53652 + 4.25487i) q^{34} +(-1.33594 - 1.48838i) q^{36} -8.81463i q^{37} +(1.75191 - 3.92658i) q^{38} -0.241319 q^{39} -1.91319 q^{41} +(-1.13905 + 2.55298i) q^{42} +11.2452i q^{43} +(2.12921 - 1.91113i) q^{44} +(-1.12921 - 0.503813i) q^{46} -3.34374 q^{47} +(-3.97676 - 0.430552i) q^{48} -3.09242 q^{49} -7.38407i q^{51} +(-0.359175 + 0.322387i) q^{52} -9.20632i q^{53} +(-0.576222 + 1.29150i) q^{54} +(1.71528 + 5.32151i) q^{56} -3.04033 q^{57} +(-5.23163 + 11.7258i) q^{58} -6.43616i q^{59} +4.57331i q^{61} +(9.61862 + 4.29150i) q^{62} +1.97676 q^{63} +(-6.49412 + 4.67187i) q^{64} +(-1.84756 - 0.824316i) q^{66} -4.86671i q^{67} +(-9.86465 - 10.9903i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(0.867721 + 2.69204i) q^{72} -4.12714 q^{73} +(-5.07918 + 11.3841i) q^{74} +(-4.52517 + 4.06169i) q^{76} +2.82786i q^{77} +(0.311664 + 0.139054i) q^{78} -13.6757 q^{79} +1.00000 q^{81} +(2.47088 + 1.10242i) q^{82} +12.3320i q^{83} +(2.94217 - 2.64082i) q^{84} +(6.47972 - 14.5231i) q^{86} +9.07918 q^{87} +(-3.85110 + 1.24132i) q^{88} -8.08066 q^{89} -0.477031i q^{91} +(1.16806 + 1.30135i) q^{92} -7.44764i q^{93} +(4.31844 + 1.92674i) q^{94} +(4.88789 + 2.84756i) q^{96} +10.6757 q^{97} +(3.99385 + 1.78192i) q^{98} +1.43055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} + 4q^{4} + 2q^{6} + 8q^{7} + 4q^{8} - 8q^{9} + O(q^{10}) \) \( 8q - 2q^{2} + 4q^{4} + 2q^{6} + 8q^{7} + 4q^{8} - 8q^{9} - 6q^{14} + 8q^{16} + 2q^{18} + 12q^{22} + 8q^{23} - 8q^{24} - 2q^{26} - 4q^{28} + 8q^{31} + 28q^{32} + 12q^{34} - 4q^{36} + 30q^{38} - 6q^{42} - 12q^{44} + 20q^{46} - 8q^{48} - 20q^{52} - 2q^{54} + 8q^{56} + 8q^{57} + 12q^{58} + 30q^{62} - 8q^{63} - 32q^{64} - 20q^{66} - 28q^{68} - 40q^{71} - 4q^{72} - 16q^{73} + 8q^{74} - 20q^{76} - 22q^{78} - 16q^{79} + 8q^{81} - 24q^{82} + 24q^{84} - 18q^{86} + 24q^{87} - 8q^{88} - 36q^{92} - 4q^{94} + 12q^{96} - 8q^{97} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29150 0.576222i −0.913227 0.407451i
\(3\) 1.00000i 0.577350i
\(4\) 1.33594 + 1.48838i 0.667968 + 0.744190i
\(5\) 0 0
\(6\) 0.576222 1.29150i 0.235242 0.527252i
\(7\) −1.97676 −0.747145 −0.373573 0.927601i \(-0.621867\pi\)
−0.373573 + 0.927601i \(0.621867\pi\)
\(8\) −0.867721 2.69204i −0.306786 0.951779i
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 1.43055i 0.431328i −0.976468 0.215664i \(-0.930808\pi\)
0.976468 0.215664i \(-0.0691915\pi\)
\(12\) −1.48838 + 1.33594i −0.429658 + 0.385651i
\(13\) 0.241319i 0.0669300i 0.999440 + 0.0334650i \(0.0106542\pi\)
−0.999440 + 0.0334650i \(0.989346\pi\)
\(14\) 2.55298 + 1.13905i 0.682313 + 0.304425i
\(15\) 0 0
\(16\) −0.430552 + 3.97676i −0.107638 + 0.994190i
\(17\) −7.38407 −1.79090 −0.895450 0.445161i \(-0.853146\pi\)
−0.895450 + 0.445161i \(0.853146\pi\)
\(18\) 1.29150 + 0.576222i 0.304409 + 0.135817i
\(19\) 3.04033i 0.697500i 0.937216 + 0.348750i \(0.113394\pi\)
−0.937216 + 0.348750i \(0.886606\pi\)
\(20\) 0 0
\(21\) 1.97676i 0.431365i
\(22\) −0.824316 + 1.84756i −0.175745 + 0.393900i
\(23\) 0.874337 0.182312 0.0911560 0.995837i \(-0.470944\pi\)
0.0911560 + 0.995837i \(0.470944\pi\)
\(24\) 2.69204 0.867721i 0.549510 0.177123i
\(25\) 0 0
\(26\) 0.139054 0.311664i 0.0272707 0.0611223i
\(27\) 1.00000i 0.192450i
\(28\) −2.64082 2.94217i −0.499069 0.556018i
\(29\) 9.07918i 1.68596i −0.537943 0.842981i \(-0.680799\pi\)
0.537943 0.842981i \(-0.319201\pi\)
\(30\) 0 0
\(31\) −7.44764 −1.33764 −0.668818 0.743426i \(-0.733200\pi\)
−0.668818 + 0.743426i \(0.733200\pi\)
\(32\) 2.84756 4.88789i 0.503381 0.864064i
\(33\) 1.43055 0.249027
\(34\) 9.53652 + 4.25487i 1.63550 + 0.729704i
\(35\) 0 0
\(36\) −1.33594 1.48838i −0.222656 0.248063i
\(37\) 8.81463i 1.44912i −0.689214 0.724558i \(-0.742044\pi\)
0.689214 0.724558i \(-0.257956\pi\)
\(38\) 1.75191 3.92658i 0.284197 0.636976i
\(39\) −0.241319 −0.0386420
\(40\) 0 0
\(41\) −1.91319 −0.298790 −0.149395 0.988778i \(-0.547733\pi\)
−0.149395 + 0.988778i \(0.547733\pi\)
\(42\) −1.13905 + 2.55298i −0.175760 + 0.393934i
\(43\) 11.2452i 1.71487i 0.514589 + 0.857437i \(0.327944\pi\)
−0.514589 + 0.857437i \(0.672056\pi\)
\(44\) 2.12921 1.91113i 0.320990 0.288113i
\(45\) 0 0
\(46\) −1.12921 0.503813i −0.166492 0.0742831i
\(47\) −3.34374 −0.487735 −0.243867 0.969809i \(-0.578416\pi\)
−0.243867 + 0.969809i \(0.578416\pi\)
\(48\) −3.97676 0.430552i −0.573996 0.0621448i
\(49\) −3.09242 −0.441774
\(50\) 0 0
\(51\) 7.38407i 1.03398i
\(52\) −0.359175 + 0.322387i −0.0498086 + 0.0447071i
\(53\) 9.20632i 1.26459i −0.774729 0.632293i \(-0.782114\pi\)
0.774729 0.632293i \(-0.217886\pi\)
\(54\) −0.576222 + 1.29150i −0.0784139 + 0.175751i
\(55\) 0 0
\(56\) 1.71528 + 5.32151i 0.229213 + 0.711117i
\(57\) −3.04033 −0.402702
\(58\) −5.23163 + 11.7258i −0.686946 + 1.53967i
\(59\) 6.43616i 0.837917i −0.908005 0.418958i \(-0.862395\pi\)
0.908005 0.418958i \(-0.137605\pi\)
\(60\) 0 0
\(61\) 4.57331i 0.585552i 0.956181 + 0.292776i \(0.0945790\pi\)
−0.956181 + 0.292776i \(0.905421\pi\)
\(62\) 9.61862 + 4.29150i 1.22157 + 0.545021i
\(63\) 1.97676 0.249048
\(64\) −6.49412 + 4.67187i −0.811765 + 0.583984i
\(65\) 0 0
\(66\) −1.84756 0.824316i −0.227418 0.101466i
\(67\) 4.86671i 0.594563i −0.954790 0.297282i \(-0.903920\pi\)
0.954790 0.297282i \(-0.0960801\pi\)
\(68\) −9.86465 10.9903i −1.19626 1.33277i
\(69\) 0.874337i 0.105258i
\(70\) 0 0
\(71\) −8.21808 −0.975307 −0.487653 0.873037i \(-0.662147\pi\)
−0.487653 + 0.873037i \(0.662147\pi\)
\(72\) 0.867721 + 2.69204i 0.102262 + 0.317260i
\(73\) −4.12714 −0.483045 −0.241523 0.970395i \(-0.577647\pi\)
−0.241523 + 0.970395i \(0.577647\pi\)
\(74\) −5.07918 + 11.3841i −0.590443 + 1.32337i
\(75\) 0 0
\(76\) −4.52517 + 4.06169i −0.519072 + 0.465907i
\(77\) 2.82786i 0.322264i
\(78\) 0.311664 + 0.139054i 0.0352890 + 0.0157447i
\(79\) −13.6757 −1.53864 −0.769320 0.638864i \(-0.779405\pi\)
−0.769320 + 0.638864i \(0.779405\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.47088 + 1.10242i 0.272863 + 0.121742i
\(83\) 12.3320i 1.35361i 0.736162 + 0.676806i \(0.236636\pi\)
−0.736162 + 0.676806i \(0.763364\pi\)
\(84\) 2.94217 2.64082i 0.321017 0.288138i
\(85\) 0 0
\(86\) 6.47972 14.5231i 0.698726 1.56607i
\(87\) 9.07918 0.973391
\(88\) −3.85110 + 1.24132i −0.410528 + 0.132325i
\(89\) −8.08066 −0.856548 −0.428274 0.903649i \(-0.640878\pi\)
−0.428274 + 0.903649i \(0.640878\pi\)
\(90\) 0 0
\(91\) 0.477031i 0.0500064i
\(92\) 1.16806 + 1.30135i 0.121779 + 0.135675i
\(93\) 7.44764i 0.772285i
\(94\) 4.31844 + 1.92674i 0.445413 + 0.198728i
\(95\) 0 0
\(96\) 4.88789 + 2.84756i 0.498868 + 0.290627i
\(97\) 10.6757 1.08396 0.541978 0.840393i \(-0.317676\pi\)
0.541978 + 0.840393i \(0.317676\pi\)
\(98\) 3.99385 + 1.78192i 0.403440 + 0.180001i
\(99\) 1.43055i 0.143776i
\(100\) 0 0
\(101\) 13.2063i 1.31408i 0.753856 + 0.657039i \(0.228191\pi\)
−0.753856 + 0.657039i \(0.771809\pi\)
\(102\) −4.25487 + 9.53652i −0.421295 + 0.944256i
\(103\) 19.4244 1.91394 0.956972 0.290181i \(-0.0937156\pi\)
0.956972 + 0.290181i \(0.0937156\pi\)
\(104\) 0.649641 0.209398i 0.0637025 0.0205331i
\(105\) 0 0
\(106\) −5.30489 + 11.8900i −0.515256 + 1.15485i
\(107\) 14.8085i 1.43159i 0.698311 + 0.715795i \(0.253935\pi\)
−0.698311 + 0.715795i \(0.746065\pi\)
\(108\) 1.48838 1.33594i 0.143219 0.128550i
\(109\) 15.2296i 1.45873i −0.684126 0.729364i \(-0.739816\pi\)
0.684126 0.729364i \(-0.260184\pi\)
\(110\) 0 0
\(111\) 8.81463 0.836647
\(112\) 0.851098 7.86110i 0.0804212 0.742804i
\(113\) −1.13890 −0.107138 −0.0535692 0.998564i \(-0.517060\pi\)
−0.0535692 + 0.998564i \(0.517060\pi\)
\(114\) 3.92658 + 1.75191i 0.367758 + 0.164081i
\(115\) 0 0
\(116\) 13.5133 12.1292i 1.25468 1.12617i
\(117\) 0.241319i 0.0223100i
\(118\) −3.70866 + 8.31229i −0.341410 + 0.765208i
\(119\) 14.5965 1.33806
\(120\) 0 0
\(121\) 8.95352 0.813956
\(122\) 2.63524 5.90642i 0.238583 0.534742i
\(123\) 1.91319i 0.172507i
\(124\) −9.94957 11.0849i −0.893498 0.995456i
\(125\) 0 0
\(126\) −2.55298 1.13905i −0.227438 0.101475i
\(127\) 2.43616 0.216174 0.108087 0.994141i \(-0.465527\pi\)
0.108087 + 0.994141i \(0.465527\pi\)
\(128\) 11.0792 2.29166i 0.979271 0.202556i
\(129\) −11.2452 −0.990083
\(130\) 0 0
\(131\) 6.90143i 0.602981i −0.953469 0.301491i \(-0.902516\pi\)
0.953469 0.301491i \(-0.0974842\pi\)
\(132\) 1.91113 + 2.12921i 0.166342 + 0.185324i
\(133\) 6.01001i 0.521134i
\(134\) −2.80431 + 6.28535i −0.242255 + 0.542972i
\(135\) 0 0
\(136\) 6.40731 + 19.8782i 0.549423 + 1.70454i
\(137\) −5.39022 −0.460518 −0.230259 0.973129i \(-0.573957\pi\)
−0.230259 + 0.973129i \(0.573957\pi\)
\(138\) 0.503813 1.12921i 0.0428874 0.0961243i
\(139\) 17.4244i 1.47792i 0.673750 + 0.738959i \(0.264682\pi\)
−0.673750 + 0.738959i \(0.735318\pi\)
\(140\) 0 0
\(141\) 3.34374i 0.281594i
\(142\) 10.6136 + 4.73544i 0.890677 + 0.397389i
\(143\) 0.345220 0.0288687
\(144\) 0.430552 3.97676i 0.0358793 0.331397i
\(145\) 0 0
\(146\) 5.33019 + 2.37815i 0.441130 + 0.196817i
\(147\) 3.09242i 0.255058i
\(148\) 13.1195 11.7758i 1.07842 0.967962i
\(149\) 2.28551i 0.187236i −0.995608 0.0936180i \(-0.970157\pi\)
0.995608 0.0936180i \(-0.0298432\pi\)
\(150\) 0 0
\(151\) 6.66425 0.542329 0.271164 0.962533i \(-0.412591\pi\)
0.271164 + 0.962533i \(0.412591\pi\)
\(152\) 8.18468 2.63816i 0.663865 0.213983i
\(153\) 7.38407 0.596967
\(154\) 1.62948 3.65217i 0.131307 0.294301i
\(155\) 0 0
\(156\) −0.322387 0.359175i −0.0258116 0.0287570i
\(157\) 17.4144i 1.38982i −0.719097 0.694910i \(-0.755444\pi\)
0.719097 0.694910i \(-0.244556\pi\)
\(158\) 17.6622 + 7.88026i 1.40513 + 0.626920i
\(159\) 9.20632 0.730109
\(160\) 0 0
\(161\) −1.72836 −0.136214
\(162\) −1.29150 0.576222i −0.101470 0.0452723i
\(163\) 4.66187i 0.365145i −0.983192 0.182573i \(-0.941557\pi\)
0.983192 0.182573i \(-0.0584425\pi\)
\(164\) −2.55590 2.84756i −0.199582 0.222357i
\(165\) 0 0
\(166\) 7.10597 15.9267i 0.551530 1.23615i
\(167\) −0.137419 −0.0106338 −0.00531690 0.999986i \(-0.501692\pi\)
−0.00531690 + 0.999986i \(0.501692\pi\)
\(168\) −5.32151 + 1.71528i −0.410564 + 0.132336i
\(169\) 12.9418 0.995520
\(170\) 0 0
\(171\) 3.04033i 0.232500i
\(172\) −16.7371 + 15.0228i −1.27619 + 1.14548i
\(173\) 3.96675i 0.301587i 0.988565 + 0.150793i \(0.0481828\pi\)
−0.988565 + 0.150793i \(0.951817\pi\)
\(174\) −11.7258 5.23163i −0.888927 0.396609i
\(175\) 0 0
\(176\) 5.68896 + 0.615927i 0.428822 + 0.0464272i
\(177\) 6.43616 0.483771
\(178\) 10.4362 + 4.65626i 0.782223 + 0.349001i
\(179\) 4.68749i 0.350359i 0.984537 + 0.175180i \(0.0560506\pi\)
−0.984537 + 0.175180i \(0.943949\pi\)
\(180\) 0 0
\(181\) 9.10242i 0.676578i 0.941042 + 0.338289i \(0.109848\pi\)
−0.941042 + 0.338289i \(0.890152\pi\)
\(182\) −0.274876 + 0.616084i −0.0203751 + 0.0456672i
\(183\) −4.57331 −0.338068
\(184\) −0.758681 2.35375i −0.0559307 0.173521i
\(185\) 0 0
\(186\) −4.29150 + 9.61862i −0.314668 + 0.705271i
\(187\) 10.5633i 0.772465i
\(188\) −4.46702 4.97676i −0.325791 0.362968i
\(189\) 1.97676i 0.143788i
\(190\) 0 0
\(191\) 15.2063 1.10029 0.550145 0.835069i \(-0.314572\pi\)
0.550145 + 0.835069i \(0.314572\pi\)
\(192\) −4.67187 6.49412i −0.337163 0.468673i
\(193\) −20.7564 −1.49408 −0.747039 0.664780i \(-0.768525\pi\)
−0.747039 + 0.664780i \(0.768525\pi\)
\(194\) −13.7877 6.15159i −0.989898 0.441659i
\(195\) 0 0
\(196\) −4.13127 4.60269i −0.295091 0.328764i
\(197\) 23.2508i 1.65655i 0.560322 + 0.828275i \(0.310677\pi\)
−0.560322 + 0.828275i \(0.689323\pi\)
\(198\) 0.824316 1.84756i 0.0585816 0.131300i
\(199\) −7.21633 −0.511552 −0.255776 0.966736i \(-0.582331\pi\)
−0.255776 + 0.966736i \(0.582331\pi\)
\(200\) 0 0
\(201\) 4.86671 0.343271
\(202\) 7.60978 17.0559i 0.535422 1.20005i
\(203\) 17.9474i 1.25966i
\(204\) 10.9903 9.86465i 0.769476 0.690663i
\(205\) 0 0
\(206\) −25.0866 11.1928i −1.74787 0.779838i
\(207\) −0.874337 −0.0607707
\(208\) −0.959669 0.103901i −0.0665411 0.00720420i
\(209\) 4.34935 0.300851
\(210\) 0 0
\(211\) 4.38407i 0.301812i −0.988548 0.150906i \(-0.951781\pi\)
0.988548 0.150906i \(-0.0482191\pi\)
\(212\) 13.7025 12.2991i 0.941092 0.844703i
\(213\) 8.21808i 0.563094i
\(214\) 8.53298 19.1251i 0.583302 1.30737i
\(215\) 0 0
\(216\) −2.69204 + 0.867721i −0.183170 + 0.0590409i
\(217\) 14.7222 0.999409
\(218\) −8.77561 + 19.6690i −0.594360 + 1.33215i
\(219\) 4.12714i 0.278886i
\(220\) 0 0
\(221\) 1.78192i 0.119865i
\(222\) −11.3841 5.07918i −0.764049 0.340892i
\(223\) −4.98852 −0.334056 −0.167028 0.985952i \(-0.553417\pi\)
−0.167028 + 0.985952i \(0.553417\pi\)
\(224\) −5.62894 + 9.66218i −0.376099 + 0.645582i
\(225\) 0 0
\(226\) 1.47088 + 0.656257i 0.0978416 + 0.0436536i
\(227\) 11.2569i 0.747149i 0.927600 + 0.373574i \(0.121868\pi\)
−0.927600 + 0.373574i \(0.878132\pi\)
\(228\) −4.06169 4.52517i −0.268992 0.299687i
\(229\) 15.8364i 1.04650i 0.852180 + 0.523249i \(0.175280\pi\)
−0.852180 + 0.523249i \(0.824720\pi\)
\(230\) 0 0
\(231\) −2.82786 −0.186059
\(232\) −24.4415 + 7.87820i −1.60466 + 0.517229i
\(233\) −10.9591 −0.717956 −0.358978 0.933346i \(-0.616875\pi\)
−0.358978 + 0.933346i \(0.616875\pi\)
\(234\) −0.139054 + 0.311664i −0.00909022 + 0.0203741i
\(235\) 0 0
\(236\) 9.57945 8.59830i 0.623569 0.559701i
\(237\) 13.6757i 0.888334i
\(238\) −18.8514 8.41086i −1.22196 0.545195i
\(239\) 17.3182 1.12022 0.560111 0.828418i \(-0.310758\pi\)
0.560111 + 0.828418i \(0.310758\pi\)
\(240\) 0 0
\(241\) 4.76869 0.307178 0.153589 0.988135i \(-0.450917\pi\)
0.153589 + 0.988135i \(0.450917\pi\)
\(242\) −11.5635 5.15922i −0.743327 0.331647i
\(243\) 1.00000i 0.0641500i
\(244\) −6.80682 + 6.10964i −0.435762 + 0.391130i
\(245\) 0 0
\(246\) −1.10242 + 2.47088i −0.0702879 + 0.157538i
\(247\) −0.733691 −0.0466836
\(248\) 6.46247 + 20.0493i 0.410367 + 1.27313i
\(249\) −12.3320 −0.781508
\(250\) 0 0
\(251\) 6.15837i 0.388713i 0.980931 + 0.194356i \(0.0622618\pi\)
−0.980931 + 0.194356i \(0.937738\pi\)
\(252\) 2.64082 + 2.94217i 0.166356 + 0.185339i
\(253\) 1.25079i 0.0786362i
\(254\) −3.14630 1.40377i −0.197416 0.0880804i
\(255\) 0 0
\(256\) −15.6293 3.42440i −0.976828 0.214025i
\(257\) −14.1584 −0.883175 −0.441587 0.897218i \(-0.645584\pi\)
−0.441587 + 0.897218i \(0.645584\pi\)
\(258\) 14.5231 + 6.47972i 0.904170 + 0.403410i
\(259\) 17.4244i 1.08270i
\(260\) 0 0
\(261\) 9.07918i 0.561987i
\(262\) −3.97676 + 8.91319i −0.245685 + 0.550659i
\(263\) −15.5960 −0.961691 −0.480845 0.876805i \(-0.659670\pi\)
−0.480845 + 0.876805i \(0.659670\pi\)
\(264\) −1.24132 3.85110i −0.0763979 0.237019i
\(265\) 0 0
\(266\) −3.46310 + 7.76191i −0.212336 + 0.475913i
\(267\) 8.08066i 0.494528i
\(268\) 7.24352 6.50161i 0.442468 0.397149i
\(269\) 11.3182i 0.690084i 0.938587 + 0.345042i \(0.112135\pi\)
−0.938587 + 0.345042i \(0.887865\pi\)
\(270\) 0 0
\(271\) −6.20485 −0.376918 −0.188459 0.982081i \(-0.560349\pi\)
−0.188459 + 0.982081i \(0.560349\pi\)
\(272\) 3.17923 29.3647i 0.192769 1.78050i
\(273\) 0.477031 0.0288712
\(274\) 6.96146 + 3.10597i 0.420557 + 0.187638i
\(275\) 0 0
\(276\) −1.30135 + 1.16806i −0.0783319 + 0.0703089i
\(277\) 18.9288i 1.13732i 0.822572 + 0.568661i \(0.192538\pi\)
−0.822572 + 0.568661i \(0.807462\pi\)
\(278\) 10.0403 22.5036i 0.602179 1.34968i
\(279\) 7.44764 0.445879
\(280\) 0 0
\(281\) −21.6231 −1.28993 −0.644963 0.764214i \(-0.723127\pi\)
−0.644963 + 0.764214i \(0.723127\pi\)
\(282\) −1.92674 + 4.31844i −0.114736 + 0.257159i
\(283\) 29.1522i 1.73292i −0.499247 0.866460i \(-0.666390\pi\)
0.499247 0.866460i \(-0.333610\pi\)
\(284\) −10.9788 12.2316i −0.651473 0.725814i
\(285\) 0 0
\(286\) −0.445851 0.198923i −0.0263637 0.0117626i
\(287\) 3.78192 0.223240
\(288\) −2.84756 + 4.88789i −0.167794 + 0.288021i
\(289\) 37.5245 2.20733
\(290\) 0 0
\(291\) 10.6757i 0.625822i
\(292\) −5.51359 6.14275i −0.322659 0.359477i
\(293\) 2.32427i 0.135785i −0.997693 0.0678927i \(-0.978372\pi\)
0.997693 0.0678927i \(-0.0216275\pi\)
\(294\) −1.78192 + 3.99385i −0.103924 + 0.232926i
\(295\) 0 0
\(296\) −23.7293 + 7.64863i −1.37924 + 0.444568i
\(297\) −1.43055 −0.0830090
\(298\) −1.31696 + 2.95173i −0.0762895 + 0.170989i
\(299\) 0.210995i 0.0122021i
\(300\) 0 0
\(301\) 22.2290i 1.28126i
\(302\) −8.60686 3.84009i −0.495269 0.220972i
\(303\) −13.2063 −0.758683
\(304\) −12.0907 1.30902i −0.693447 0.0750775i
\(305\) 0 0
\(306\) −9.53652 4.25487i −0.545166 0.243235i
\(307\) 3.52297i 0.201066i 0.994934 + 0.100533i \(0.0320549\pi\)
−0.994934 + 0.100533i \(0.967945\pi\)
\(308\) −4.20893 + 3.77784i −0.239826 + 0.215262i
\(309\) 19.4244i 1.10502i
\(310\) 0 0
\(311\) −21.6757 −1.22912 −0.614559 0.788871i \(-0.710666\pi\)
−0.614559 + 0.788871i \(0.710666\pi\)
\(312\) 0.209398 + 0.649641i 0.0118548 + 0.0367787i
\(313\) −12.5486 −0.709288 −0.354644 0.935001i \(-0.615398\pi\)
−0.354644 + 0.935001i \(0.615398\pi\)
\(314\) −10.0346 + 22.4907i −0.566283 + 1.26922i
\(315\) 0 0
\(316\) −18.2699 20.3547i −1.02776 1.14504i
\(317\) 10.8611i 0.610020i −0.952349 0.305010i \(-0.901340\pi\)
0.952349 0.305010i \(-0.0986599\pi\)
\(318\) −11.8900 5.30489i −0.666755 0.297483i
\(319\) −12.9882 −0.727202
\(320\) 0 0
\(321\) −14.8085 −0.826529
\(322\) 2.23217 + 0.995917i 0.124394 + 0.0555003i
\(323\) 22.4500i 1.24915i
\(324\) 1.33594 + 1.48838i 0.0742186 + 0.0826878i
\(325\) 0 0
\(326\) −2.68627 + 6.02079i −0.148779 + 0.333461i
\(327\) 15.2296 0.842197
\(328\) 1.66011 + 5.15038i 0.0916645 + 0.284382i
\(329\) 6.60978 0.364409
\(330\) 0 0
\(331\) 1.23185i 0.0677088i 0.999427 + 0.0338544i \(0.0107783\pi\)
−0.999427 + 0.0338544i \(0.989222\pi\)
\(332\) −18.3547 + 16.4747i −1.00734 + 0.904169i
\(333\) 8.81463i 0.483038i
\(334\) 0.177476 + 0.0791838i 0.00971107 + 0.00433275i
\(335\) 0 0
\(336\) 7.86110 + 0.851098i 0.428858 + 0.0464312i
\(337\) 4.13890 0.225460 0.112730 0.993626i \(-0.464040\pi\)
0.112730 + 0.993626i \(0.464040\pi\)
\(338\) −16.7143 7.45733i −0.909136 0.405625i
\(339\) 1.13890i 0.0618564i
\(340\) 0 0
\(341\) 10.6542i 0.576959i
\(342\) −1.75191 + 3.92658i −0.0947322 + 0.212325i
\(343\) 19.9503 1.07721
\(344\) 30.2724 9.75767i 1.63218 0.526098i
\(345\) 0 0
\(346\) 2.28573 5.12306i 0.122882 0.275417i
\(347\) 17.4586i 0.937226i −0.883404 0.468613i \(-0.844754\pi\)
0.883404 0.468613i \(-0.155246\pi\)
\(348\) 12.1292 + 13.5133i 0.650194 + 0.724388i
\(349\) 21.2196i 1.13586i −0.823078 0.567928i \(-0.807745\pi\)
0.823078 0.567928i \(-0.192255\pi\)
\(350\) 0 0
\(351\) 0.241319 0.0128807
\(352\) −6.99237 4.07358i −0.372695 0.217122i
\(353\) 21.0398 1.11984 0.559918 0.828548i \(-0.310833\pi\)
0.559918 + 0.828548i \(0.310833\pi\)
\(354\) −8.31229 3.70866i −0.441793 0.197113i
\(355\) 0 0
\(356\) −10.7952 12.0271i −0.572147 0.637435i
\(357\) 14.5965i 0.772531i
\(358\) 2.70103 6.05388i 0.142754 0.319957i
\(359\) 23.5153 1.24109 0.620546 0.784170i \(-0.286911\pi\)
0.620546 + 0.784170i \(0.286911\pi\)
\(360\) 0 0
\(361\) 9.75639 0.513494
\(362\) 5.24502 11.7558i 0.275672 0.617869i
\(363\) 8.95352i 0.469938i
\(364\) 0.710003 0.637282i 0.0372143 0.0334027i
\(365\) 0 0
\(366\) 5.90642 + 2.63524i 0.308733 + 0.137746i
\(367\) −25.4012 −1.32593 −0.662965 0.748650i \(-0.730702\pi\)
−0.662965 + 0.748650i \(0.730702\pi\)
\(368\) −0.376448 + 3.47703i −0.0196237 + 0.181253i
\(369\) 1.91319 0.0995967
\(370\) 0 0
\(371\) 18.1987i 0.944829i
\(372\) 11.0849 9.94957i 0.574727 0.515861i
\(373\) 10.0677i 0.521286i −0.965435 0.260643i \(-0.916065\pi\)
0.965435 0.260643i \(-0.0839345\pi\)
\(374\) 6.08681 13.6425i 0.314741 0.705436i
\(375\) 0 0
\(376\) 2.90143 + 9.00148i 0.149630 + 0.464216i
\(377\) 2.19098 0.112841
\(378\) 1.13905 2.55298i 0.0585866 0.131311i
\(379\) 18.9674i 0.974289i −0.873321 0.487145i \(-0.838038\pi\)
0.873321 0.487145i \(-0.161962\pi\)
\(380\) 0 0
\(381\) 2.43616i 0.124808i
\(382\) −19.6389 8.76222i −1.00482 0.448314i
\(383\) −28.7446 −1.46878 −0.734391 0.678727i \(-0.762532\pi\)
−0.734391 + 0.678727i \(0.762532\pi\)
\(384\) 2.29166 + 11.0792i 0.116946 + 0.565382i
\(385\) 0 0
\(386\) 26.8068 + 11.9603i 1.36443 + 0.608763i
\(387\) 11.2452i 0.571624i
\(388\) 14.2621 + 15.8895i 0.724048 + 0.806669i
\(389\) 29.8161i 1.51174i 0.654724 + 0.755868i \(0.272785\pi\)
−0.654724 + 0.755868i \(0.727215\pi\)
\(390\) 0 0
\(391\) −6.45617 −0.326503
\(392\) 2.68335 + 8.32490i 0.135530 + 0.420471i
\(393\) 6.90143 0.348131
\(394\) 13.3976 30.0283i 0.674962 1.51281i
\(395\) 0 0
\(396\) −2.12921 + 1.91113i −0.106997 + 0.0960377i
\(397\) 2.73167i 0.137099i 0.997648 + 0.0685494i \(0.0218371\pi\)
−0.997648 + 0.0685494i \(0.978163\pi\)
\(398\) 9.31988 + 4.15821i 0.467163 + 0.208432i
\(399\) 6.01001 0.300877
\(400\) 0 0
\(401\) 25.8744 1.29211 0.646054 0.763292i \(-0.276418\pi\)
0.646054 + 0.763292i \(0.276418\pi\)
\(402\) −6.28535 2.80431i −0.313485 0.139866i
\(403\) 1.79726i 0.0895279i
\(404\) −19.6560 + 17.6428i −0.977924 + 0.877762i
\(405\) 0 0
\(406\) 10.3417 23.1790i 0.513249 1.15035i
\(407\) −12.6098 −0.625044
\(408\) −19.8782 + 6.40731i −0.984117 + 0.317209i
\(409\) 22.4786 1.11150 0.555748 0.831351i \(-0.312432\pi\)
0.555748 + 0.831351i \(0.312432\pi\)
\(410\) 0 0
\(411\) 5.39022i 0.265880i
\(412\) 25.9498 + 28.9109i 1.27845 + 1.42434i
\(413\) 12.7227i 0.626045i
\(414\) 1.12921 + 0.503813i 0.0554974 + 0.0247610i
\(415\) 0 0
\(416\) 1.17954 + 0.687170i 0.0578318 + 0.0336913i
\(417\) −17.4244 −0.853277
\(418\) −5.61718 2.50619i −0.274745 0.122582i
\(419\) 24.5307i 1.19840i −0.800598 0.599201i \(-0.795485\pi\)
0.800598 0.599201i \(-0.204515\pi\)
\(420\) 0 0
\(421\) 33.3856i 1.62712i −0.581483 0.813558i \(-0.697527\pi\)
0.581483 0.813558i \(-0.302473\pi\)
\(422\) −2.52620 + 5.66202i −0.122974 + 0.275623i
\(423\) 3.34374 0.162578
\(424\) −24.7838 + 7.98852i −1.20361 + 0.387957i
\(425\) 0 0
\(426\) −4.73544 + 10.6136i −0.229433 + 0.514232i
\(427\) 9.04033i 0.437492i
\(428\) −22.0406 + 19.7832i −1.06537 + 0.956256i
\(429\) 0.345220i 0.0166674i
\(430\) 0 0
\(431\) 11.6548 0.561391 0.280696 0.959797i \(-0.409435\pi\)
0.280696 + 0.959797i \(0.409435\pi\)
\(432\) 3.97676 + 0.430552i 0.191332 + 0.0207149i
\(433\) 19.7681 0.949996 0.474998 0.879987i \(-0.342449\pi\)
0.474998 + 0.879987i \(0.342449\pi\)
\(434\) −19.0137 8.48326i −0.912687 0.407210i
\(435\) 0 0
\(436\) 22.6674 20.3457i 1.08557 0.974383i
\(437\) 2.65827i 0.127163i
\(438\) −2.37815 + 5.33019i −0.113632 + 0.254687i
\(439\) −25.1699 −1.20129 −0.600646 0.799515i \(-0.705090\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(440\) 0 0
\(441\) 3.09242 0.147258
\(442\) −1.02678 + 2.30135i −0.0488390 + 0.109464i
\(443\) 19.5515i 0.928922i −0.885594 0.464461i \(-0.846248\pi\)
0.885594 0.464461i \(-0.153752\pi\)
\(444\) 11.7758 + 13.1195i 0.558853 + 0.622625i
\(445\) 0 0
\(446\) 6.44266 + 2.87449i 0.305069 + 0.136111i
\(447\) 2.28551 0.108101
\(448\) 12.8373 9.23517i 0.606507 0.436321i
\(449\) −19.9612 −0.942029 −0.471014 0.882125i \(-0.656112\pi\)
−0.471014 + 0.882125i \(0.656112\pi\)
\(450\) 0 0
\(451\) 2.73692i 0.128876i
\(452\) −1.52149 1.69511i −0.0715650 0.0797313i
\(453\) 6.66425i 0.313114i
\(454\) 6.48650 14.5383i 0.304426 0.682317i
\(455\) 0 0
\(456\) 2.63816 + 8.18468i 0.123543 + 0.383283i
\(457\) −5.01176 −0.234440 −0.117220 0.993106i \(-0.537398\pi\)
−0.117220 + 0.993106i \(0.537398\pi\)
\(458\) 9.12528 20.4527i 0.426396 0.955690i
\(459\) 7.38407i 0.344659i
\(460\) 0 0
\(461\) 5.12566i 0.238726i −0.992851 0.119363i \(-0.961915\pi\)
0.992851 0.119363i \(-0.0380852\pi\)
\(462\) 3.65217 + 1.62948i 0.169915 + 0.0758101i
\(463\) −5.79515 −0.269324 −0.134662 0.990892i \(-0.542995\pi\)
−0.134662 + 0.990892i \(0.542995\pi\)
\(464\) 36.1057 + 3.90906i 1.67617 + 0.181474i
\(465\) 0 0
\(466\) 14.1537 + 6.31490i 0.655657 + 0.292532i
\(467\) 16.8208i 0.778373i −0.921159 0.389186i \(-0.872756\pi\)
0.921159 0.389186i \(-0.127244\pi\)
\(468\) 0.359175 0.322387i 0.0166029 0.0149024i
\(469\) 9.62032i 0.444225i
\(470\) 0 0
\(471\) 17.4144 0.802413
\(472\) −17.3264 + 5.58479i −0.797511 + 0.257061i
\(473\) 16.0868 0.739672
\(474\) −7.88026 + 17.6622i −0.361952 + 0.811251i
\(475\) 0 0
\(476\) 19.5000 + 21.7252i 0.893783 + 0.995773i
\(477\) 9.20632i 0.421529i
\(478\) −22.3664 9.97914i −1.02302 0.456435i
\(479\) −36.9065 −1.68630 −0.843151 0.537678i \(-0.819302\pi\)
−0.843151 + 0.537678i \(0.819302\pi\)
\(480\) 0 0
\(481\) 2.12714 0.0969892
\(482\) −6.15875 2.74782i −0.280523 0.125160i
\(483\) 1.72836i 0.0786429i
\(484\) 11.9613 + 13.3262i 0.543697 + 0.605738i
\(485\) 0 0
\(486\) 0.576222 1.29150i 0.0261380 0.0585836i
\(487\) −5.14984 −0.233361 −0.116681 0.993169i \(-0.537225\pi\)
−0.116681 + 0.993169i \(0.537225\pi\)
\(488\) 12.3115 3.96835i 0.557316 0.179639i
\(489\) 4.66187 0.210817
\(490\) 0 0
\(491\) 23.1154i 1.04318i 0.853195 + 0.521591i \(0.174661\pi\)
−0.853195 + 0.521591i \(0.825339\pi\)
\(492\) 2.84756 2.55590i 0.128378 0.115229i
\(493\) 67.0414i 3.01939i
\(494\) 0.947560 + 0.422769i 0.0426328 + 0.0190213i
\(495\) 0 0
\(496\) 3.20660 29.6175i 0.143980 1.32986i
\(497\) 16.2452 0.728696
\(498\) 15.9267 + 7.10597i 0.713694 + 0.318426i
\(499\) 14.3111i 0.640654i −0.947307 0.320327i \(-0.896207\pi\)
0.947307 0.320327i \(-0.103793\pi\)
\(500\) 0 0
\(501\) 0.137419i 0.00613942i
\(502\) 3.54859 7.95352i 0.158381 0.354983i
\(503\) 15.4224 0.687650 0.343825 0.939034i \(-0.388277\pi\)
0.343825 + 0.939034i \(0.388277\pi\)
\(504\) −1.71528 5.32151i −0.0764045 0.237039i
\(505\) 0 0
\(506\) −0.720730 + 1.61539i −0.0320404 + 0.0718127i
\(507\) 12.9418i 0.574764i
\(508\) 3.25455 + 3.62593i 0.144397 + 0.160875i
\(509\) 43.1578i 1.91294i −0.291835 0.956469i \(-0.594266\pi\)
0.291835 0.956469i \(-0.405734\pi\)
\(510\) 0 0
\(511\) 8.15837 0.360905
\(512\) 18.2119 + 13.4285i 0.804861 + 0.593463i
\(513\) 3.04033 0.134234
\(514\) 18.2855 + 8.15837i 0.806539 + 0.359850i
\(515\) 0 0
\(516\) −15.0228 16.7371i −0.661343 0.736810i
\(517\) 4.78340i 0.210374i
\(518\) 10.0403 22.5036i 0.441147 0.988751i
\(519\) −3.96675 −0.174121
\(520\) 0 0
\(521\) −17.8232 −0.780848 −0.390424 0.920635i \(-0.627672\pi\)
−0.390424 + 0.920635i \(0.627672\pi\)
\(522\) 5.23163 11.7258i 0.228982 0.513222i
\(523\) 24.7502i 1.08225i −0.840941 0.541126i \(-0.817998\pi\)
0.840941 0.541126i \(-0.182002\pi\)
\(524\) 10.2720 9.21987i 0.448733 0.402772i
\(525\) 0 0
\(526\) 20.1422 + 8.98677i 0.878242 + 0.391842i
\(527\) 54.9939 2.39557
\(528\) −0.615927 + 5.68896i −0.0268048 + 0.247580i
\(529\) −22.2355 −0.966762
\(530\) 0 0
\(531\) 6.43616i 0.279306i
\(532\) 8.94517 8.02898i 0.387822 0.348100i
\(533\) 0.461690i 0.0199980i
\(534\) −4.65626 + 10.4362i −0.201496 + 0.451617i
\(535\) 0 0
\(536\) −13.1014 + 4.22295i −0.565893 + 0.182403i
\(537\) −4.68749 −0.202280
\(538\) 6.52181 14.6175i 0.281175 0.630203i
\(539\) 4.42386i 0.190549i
\(540\) 0 0
\(541\) 16.9982i 0.730812i −0.930848 0.365406i \(-0.880930\pi\)
0.930848 0.365406i \(-0.119070\pi\)
\(542\) 8.01355 + 3.57537i 0.344211 + 0.153575i
\(543\) −9.10242 −0.390622
\(544\) −21.0266 + 36.0925i −0.901506 + 1.54745i
\(545\) 0 0
\(546\) −0.616084 0.274876i −0.0263660 0.0117636i
\(547\) 37.2385i 1.59220i 0.605163 + 0.796101i \(0.293108\pi\)
−0.605163 + 0.796101i \(0.706892\pi\)
\(548\) −7.20099 8.02270i −0.307611 0.342713i
\(549\) 4.57331i 0.195184i
\(550\) 0 0
\(551\) 27.6037 1.17596
\(552\) 2.35375 0.758681i 0.100182 0.0322916i
\(553\) 27.0336 1.14959
\(554\) 10.9072 24.4465i 0.463403 1.03863i
\(555\) 0 0
\(556\) −25.9341 + 23.2779i −1.09985 + 0.987202i
\(557\) 14.7604i 0.625420i −0.949849 0.312710i \(-0.898763\pi\)
0.949849 0.312710i \(-0.101237\pi\)
\(558\) −9.61862 4.29150i −0.407189 0.181674i
\(559\) −2.71368 −0.114776
\(560\) 0 0
\(561\) −10.5633 −0.445983
\(562\) 27.9262 + 12.4597i 1.17800 + 0.525581i
\(563\) 3.00561i 0.126671i 0.997992 + 0.0633356i \(0.0201739\pi\)
−0.997992 + 0.0633356i \(0.979826\pi\)
\(564\) 4.97676 4.46702i 0.209559 0.188096i
\(565\) 0 0
\(566\) −16.7982 + 37.6500i −0.706079 + 1.58255i
\(567\) −1.97676 −0.0830161
\(568\) 7.13100 + 22.1234i 0.299210 + 0.928276i
\(569\) −23.1840 −0.971923 −0.485962 0.873980i \(-0.661531\pi\)
−0.485962 + 0.873980i \(0.661531\pi\)
\(570\) 0 0
\(571\) 0.202739i 0.00848438i −0.999991 0.00424219i \(-0.998650\pi\)
0.999991 0.00424219i \(-0.00135033\pi\)
\(572\) 0.461192 + 0.513819i 0.0192834 + 0.0214838i
\(573\) 15.2063i 0.635253i
\(574\) −4.88434 2.17923i −0.203869 0.0909592i
\(575\) 0 0
\(576\) 6.49412 4.67187i 0.270588 0.194661i
\(577\) 21.8023 0.907643 0.453821 0.891093i \(-0.350060\pi\)
0.453821 + 0.891093i \(0.350060\pi\)
\(578\) −48.4629 21.6225i −2.01579 0.899376i
\(579\) 20.7564i 0.862606i
\(580\) 0 0
\(581\) 24.3774i 1.01134i
\(582\) 6.15159 13.7877i 0.254992 0.571518i
\(583\) −13.1701 −0.545451
\(584\) 3.58120 + 11.1104i 0.148191 + 0.459752i
\(585\) 0 0
\(586\) −1.33930 + 3.00179i −0.0553258 + 0.124003i
\(587\) 36.7126i 1.51529i −0.652667 0.757645i \(-0.726350\pi\)
0.652667 0.757645i \(-0.273650\pi\)
\(588\) 4.60269 4.13127i 0.189812 0.170371i
\(589\) 22.6433i 0.933001i
\(590\) 0 0
\(591\) −23.2508 −0.956409
\(592\) 35.0537 + 3.79515i 1.44070 + 0.155980i
\(593\) 10.6036 0.435439 0.217719 0.976011i \(-0.430138\pi\)
0.217719 + 0.976011i \(0.430138\pi\)
\(594\) 1.84756 + 0.824316i 0.0758061 + 0.0338221i
\(595\) 0 0
\(596\) 3.40170 3.05329i 0.139339 0.125068i
\(597\) 7.21633i 0.295345i
\(598\) 0.121580 0.272499i 0.00497177 0.0111433i
\(599\) −25.7988 −1.05411 −0.527056 0.849831i \(-0.676704\pi\)
−0.527056 + 0.849831i \(0.676704\pi\)
\(600\) 0 0
\(601\) 18.5021 0.754717 0.377358 0.926067i \(-0.376832\pi\)
0.377358 + 0.926067i \(0.376832\pi\)
\(602\) −12.8089 + 28.7087i −0.522050 + 1.17008i
\(603\) 4.86671i 0.198188i
\(604\) 8.90300 + 9.91893i 0.362258 + 0.403596i
\(605\) 0 0
\(606\) 17.0559 + 7.60978i 0.692850 + 0.309126i
\(607\) −37.5828 −1.52544 −0.762719 0.646730i \(-0.776136\pi\)
−0.762719 + 0.646730i \(0.776136\pi\)
\(608\) 14.8608 + 8.65751i 0.602685 + 0.351108i
\(609\) −17.9474 −0.727264
\(610\) 0 0
\(611\) 0.806910i 0.0326441i
\(612\) 9.86465 + 10.9903i 0.398755 + 0.444257i
\(613\) 4.93405i 0.199284i −0.995023 0.0996422i \(-0.968230\pi\)
0.995023 0.0996422i \(-0.0317698\pi\)
\(614\) 2.03001 4.54991i 0.0819247 0.183619i
\(615\) 0 0
\(616\) 7.61270 2.45379i 0.306724 0.0988661i
\(617\) −6.26043 −0.252035 −0.126018 0.992028i \(-0.540220\pi\)
−0.126018 + 0.992028i \(0.540220\pi\)
\(618\) 11.1928 25.0866i 0.450239 1.00913i
\(619\) 8.02562i 0.322577i −0.986907 0.161288i \(-0.948435\pi\)
0.986907 0.161288i \(-0.0515649\pi\)
\(620\) 0 0
\(621\) 0.874337i 0.0350860i
\(622\) 27.9942 + 12.4900i 1.12246 + 0.500805i
\(623\) 15.9735 0.639966
\(624\) 0.103901 0.959669i 0.00415935 0.0384175i
\(625\) 0 0
\(626\) 16.2065 + 7.23078i 0.647741 + 0.289000i
\(627\) 4.34935i 0.173696i
\(628\) 25.9192 23.2645i 1.03429 0.928355i
\(629\) 65.0878i 2.59522i
\(630\) 0 0
\(631\) −26.5248 −1.05594 −0.527968 0.849264i \(-0.677046\pi\)
−0.527968 + 0.849264i \(0.677046\pi\)
\(632\) 11.8667 + 36.8156i 0.472032 + 1.46444i
\(633\) 4.38407 0.174251
\(634\) −6.25841 + 14.0271i −0.248553 + 0.557087i
\(635\) 0 0
\(636\) 12.2991 + 13.7025i 0.487689 + 0.543340i
\(637\) 0.746260i 0.0295679i
\(638\) 16.7743 + 7.48412i 0.664101 + 0.296299i
\(639\) 8.21808 0.325102
\(640\) 0 0
\(641\) −26.5863 −1.05009 −0.525047 0.851073i \(-0.675952\pi\)
−0.525047 + 0.851073i \(0.675952\pi\)
\(642\) 19.1251 + 8.53298i 0.754808 + 0.336770i
\(643\) 2.89233i 0.114062i 0.998372 + 0.0570312i \(0.0181635\pi\)
−0.998372 + 0.0570312i \(0.981837\pi\)
\(644\) −2.30897 2.57245i −0.0909862 0.101369i
\(645\) 0 0
\(646\) −12.9362 + 28.9942i −0.508968 + 1.14076i
\(647\) −12.3472 −0.485420 −0.242710 0.970099i \(-0.578036\pi\)
−0.242710 + 0.970099i \(0.578036\pi\)
\(648\) −0.867721 2.69204i −0.0340873 0.105753i
\(649\) −9.20726 −0.361417
\(650\) 0 0
\(651\) 14.7222i 0.577009i
\(652\) 6.93863 6.22795i 0.271738 0.243905i
\(653\) 39.0507i 1.52817i 0.645114 + 0.764086i \(0.276810\pi\)
−0.645114 + 0.764086i \(0.723190\pi\)
\(654\) −19.6690 8.77561i −0.769117 0.343154i
\(655\) 0 0
\(656\) 0.823728 7.60830i 0.0321612 0.297054i
\(657\) 4.12714 0.161015
\(658\) −8.53652 3.80870i −0.332788 0.148479i
\(659\) 23.7738i 0.926094i −0.886334 0.463047i \(-0.846756\pi\)
0.886334 0.463047i \(-0.153244\pi\)
\(660\) 0 0
\(661\) 21.5051i 0.836450i 0.908343 + 0.418225i \(0.137348\pi\)
−0.908343 + 0.418225i \(0.862652\pi\)
\(662\) 0.709822 1.59094i 0.0275880 0.0618335i
\(663\) 1.78192 0.0692040
\(664\) 33.1982 10.7007i 1.28834 0.415268i
\(665\) 0 0
\(666\) 5.07918 11.3841i 0.196814 0.441124i
\(667\) 7.93827i 0.307371i
\(668\) −0.183583 0.204532i −0.00710303 0.00791356i
\(669\) 4.98852i 0.192867i
\(670\) 0 0
\(671\) 6.54235 0.252565
\(672\) −9.66218 5.62894i −0.372727 0.217141i
\(673\) −36.1896 −1.39501 −0.697503 0.716582i \(-0.745706\pi\)
−0.697503 + 0.716582i \(0.745706\pi\)
\(674\) −5.34538 2.38492i −0.205896 0.0918639i
\(675\) 0 0
\(676\) 17.2894 + 19.2623i 0.664976 + 0.740856i
\(677\) 9.17214i 0.352514i 0.984344 + 0.176257i \(0.0563990\pi\)
−0.984344 + 0.176257i \(0.943601\pi\)
\(678\) −0.656257 + 1.47088i −0.0252034 + 0.0564889i
\(679\) −21.1034 −0.809873
\(680\) 0 0
\(681\) −11.2569 −0.431367
\(682\) 6.13921 13.7599i 0.235083 0.526895i
\(683\) 16.3974i 0.627429i −0.949517 0.313714i \(-0.898427\pi\)
0.949517 0.313714i \(-0.101573\pi\)
\(684\) 4.52517 4.06169i 0.173024 0.155302i
\(685\) 0 0
\(686\) −25.7658 11.4958i −0.983742 0.438912i
\(687\) −15.8364 −0.604196
\(688\) −44.7194 4.84163i −1.70491 0.184586i
\(689\) 2.22166 0.0846387
\(690\) 0 0
\(691\) 24.4904i 0.931657i 0.884875 + 0.465828i \(0.154244\pi\)
−0.884875 + 0.465828i \(0.845756\pi\)
\(692\) −5.90404 + 5.29933i −0.224438 + 0.201450i
\(693\) 2.82786i 0.107421i
\(694\) −10.0600 + 22.5477i −0.381873 + 0.855900i
\(695\) 0 0
\(696\) −7.87820 24.4415i −0.298622 0.926452i
\(697\) 14.1271 0.535104
\(698\) −12.2272 + 27.4050i −0.462806 + 1.03730i
\(699\) 10.9591i 0.414512i
\(700\) 0 0
\(701\) 12.3887i 0.467916i −0.972247 0.233958i \(-0.924832\pi\)
0.972247 0.233958i \(-0.0751679\pi\)
\(702\) −0.311664 0.139054i −0.0117630 0.00524824i
\(703\) 26.7994 1.01076
\(704\) 6.68335 + 9.29018i 0.251888 + 0.350137i
\(705\) 0 0
\(706\) −27.1729 12.1236i −1.02266 0.456278i
\(707\) 26.1057i 0.981807i
\(708\) 8.59830 + 9.57945i 0.323144 + 0.360018i
\(709\) 33.4144i 1.25490i 0.778655 + 0.627452i \(0.215902\pi\)
−0.778655 + 0.627452i \(0.784098\pi\)
\(710\) 0 0
\(711\) 13.6757 0.512880
\(712\) 7.01176 + 21.7534i 0.262777 + 0.815244i
\(713\) −6.51175 −0.243867
\(714\) 8.41086 18.8514i 0.314768 0.705496i
\(715\) 0 0
\(716\) −6.97676 + 6.26218i −0.260734 + 0.234029i
\(717\) 17.3182i 0.646761i
\(718\) −30.3700 13.5501i −1.13340 0.505684i
\(719\) −33.8938 −1.26403 −0.632013 0.774958i \(-0.717771\pi\)
−0.632013 + 0.774958i \(0.717771\pi\)
\(720\) 0 0
\(721\) −38.3974 −1.42999
\(722\) −12.6004 5.62185i −0.468937 0.209224i
\(723\) 4.76869i 0.177349i
\(724\) −13.5479 + 12.1603i −0.503503 + 0.451932i
\(725\) 0 0
\(726\) 5.15922 11.5635i 0.191477 0.429160i
\(727\) 14.1846 0.526076 0.263038 0.964785i \(-0.415275\pi\)
0.263038 + 0.964785i \(0.415275\pi\)
\(728\) −1.28418 + 0.413929i −0.0475950 + 0.0153412i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 83.0352i 3.07117i
\(732\) −6.10964 6.80682i −0.225819 0.251587i
\(733\) 8.09296i 0.298920i 0.988768 + 0.149460i \(0.0477536\pi\)
−0.988768 + 0.149460i \(0.952246\pi\)
\(734\) 32.8056 + 14.6367i 1.21088 + 0.540251i
\(735\) 0 0
\(736\) 2.48972 4.27366i 0.0917725 0.157529i
\(737\) −6.96208 −0.256452
\(738\) −2.47088 1.10242i −0.0909544 0.0405808i
\(739\) 22.0919i 0.812663i −0.913726 0.406331i \(-0.866808\pi\)
0.913726 0.406331i \(-0.133192\pi\)
\(740\) 0 0
\(741\) 0.733691i 0.0269528i
\(742\) 10.4865 23.5036i 0.384971 0.862844i
\(743\) −8.78340 −0.322232 −0.161116 0.986936i \(-0.551509\pi\)
−0.161116 + 0.986936i \(0.551509\pi\)
\(744\) −20.0493 + 6.46247i −0.735044 + 0.236926i
\(745\) 0 0
\(746\) −5.80123 + 13.0024i −0.212398 + 0.476052i
\(747\) 12.3320i 0.451204i
\(748\) −15.7222 + 14.1119i −0.574861 + 0.515982i
\(749\) 29.2728i 1.06961i
\(750\) 0 0
\(751\) 13.3779 0.488167 0.244084 0.969754i \(-0.421513\pi\)
0.244084 + 0.969754i \(0.421513\pi\)
\(752\) 1.43965 13.2973i 0.0524988 0.484901i
\(753\) −6.15837 −0.224423
\(754\) −2.82965 1.26249i −0.103050 0.0459773i
\(755\) 0 0
\(756\) −2.94217 + 2.64082i −0.107006 + 0.0960459i
\(757\) 9.72450i 0.353443i 0.984261 + 0.176721i \(0.0565492\pi\)
−0.984261 + 0.176721i \(0.943451\pi\)
\(758\) −10.9294 + 24.4963i −0.396975 + 0.889747i
\(759\) 1.25079 0.0454006
\(760\) 0 0
\(761\) 33.8835 1.22828 0.614138 0.789198i \(-0.289504\pi\)
0.614138 + 0.789198i \(0.289504\pi\)
\(762\) 1.40377 3.14630i 0.0508532 0.113978i
\(763\) 30.1052i 1.08988i
\(764\) 20.3147 + 22.6328i 0.734959 + 0.818826i
\(765\) 0 0
\(766\) 37.1236 + 16.5633i 1.34133 + 0.598456i
\(767\) 1.55317 0.0560817
\(768\) 3.42440 15.6293i 0.123568 0.563972i
\(769\) 18.7334 0.675545 0.337772 0.941228i \(-0.390327\pi\)
0.337772 + 0.941228i \(0.390327\pi\)
\(770\) 0 0
\(771\) 14.1584i 0.509901i
\(772\) −27.7292 30.8934i −0.997996 1.11188i
\(773\) 22.5006i 0.809292i −0.914474 0.404646i \(-0.867395\pi\)
0.914474 0.404646i \(-0.132605\pi\)
\(774\) −6.47972 + 14.5231i −0.232909 + 0.522023i
\(775\) 0 0
\(776\) −9.26355 28.7395i −0.332542 1.03169i
\(777\) −17.4244 −0.625097
\(778\) 17.1807 38.5074i 0.615958 1.38056i
\(779\) 5.81673i 0.208406i
\(780\) 0 0
\(781\) 11.7564i 0.420677i
\(782\) 8.33813 + 3.72019i 0.298171 + 0.133034i
\(783\) −9.07918 −0.324464
\(784\) 1.33145 12.2978i 0.0475517 0.439207i
\(785\) 0 0
\(786\) −8.91319 3.97676i −0.317923 0.141846i
\(787\) 28.1063i 1.00188i −0.865482 0.500940i \(-0.832988\pi\)
0.865482 0.500940i \(-0.167012\pi\)
\(788\) −34.6060 + 31.0616i −1.23279 + 1.10652i
\(789\) 15.5960i 0.555232i