Properties

Label 731.2.m.c.87.11
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.11
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.624813 - 0.624813i) q^{2} +(2.88236 - 1.19391i) q^{3} -1.21922i q^{4} +(-1.21824 - 2.94109i) q^{5} +(-2.54691 - 1.05496i) q^{6} +(0.920964 - 2.22340i) q^{7} +(-2.01141 + 2.01141i) q^{8} +(4.76125 - 4.76125i) q^{9} +O(q^{10})\) \(q+(-0.624813 - 0.624813i) q^{2} +(2.88236 - 1.19391i) q^{3} -1.21922i q^{4} +(-1.21824 - 2.94109i) q^{5} +(-2.54691 - 1.05496i) q^{6} +(0.920964 - 2.22340i) q^{7} +(-2.01141 + 2.01141i) q^{8} +(4.76125 - 4.76125i) q^{9} +(-1.07646 + 2.59880i) q^{10} +(0.310479 + 0.128605i) q^{11} +(-1.45564 - 3.51423i) q^{12} +5.45402i q^{13} +(-1.96464 + 0.813780i) q^{14} +(-7.02282 - 7.02282i) q^{15} +0.0750704 q^{16} +(3.54745 - 2.10134i) q^{17} -5.94978 q^{18} +(2.89789 + 2.89789i) q^{19} +(-3.58584 + 1.48530i) q^{20} -7.50820i q^{21} +(-0.113638 - 0.274345i) q^{22} +(6.21903 + 2.57601i) q^{23} +(-3.39616 + 8.19905i) q^{24} +(-3.63039 + 3.63039i) q^{25} +(3.40774 - 3.40774i) q^{26} +(4.45738 - 10.7611i) q^{27} +(-2.71081 - 1.12286i) q^{28} +(1.31012 + 3.16292i) q^{29} +8.77589i q^{30} +(-8.18548 + 3.39054i) q^{31} +(3.97591 + 3.97591i) q^{32} +1.04846 q^{33} +(-3.52943 - 0.903547i) q^{34} -7.66119 q^{35} +(-5.80500 - 5.80500i) q^{36} +(-8.11528 + 3.36146i) q^{37} -3.62128i q^{38} +(6.51162 + 15.7204i) q^{39} +(8.36612 + 3.46536i) q^{40} +(3.16704 - 7.64591i) q^{41} +(-4.69122 + 4.69122i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(0.156797 - 0.378542i) q^{44} +(-19.8036 - 8.20293i) q^{45} +(-2.27621 - 5.49525i) q^{46} -4.38757i q^{47} +(0.216380 - 0.0896274i) q^{48} +(0.854402 + 0.854402i) q^{49} +4.53662 q^{50} +(7.71620 - 10.2922i) q^{51} +6.64964 q^{52} +(6.74607 + 6.74607i) q^{53} +(-9.50868 + 3.93862i) q^{54} -1.06982i q^{55} +(2.61974 + 6.32460i) q^{56} +(11.8126 + 4.89293i) q^{57} +(1.15765 - 2.79481i) q^{58} +(-5.55757 + 5.55757i) q^{59} +(-8.56235 + 8.56235i) q^{60} +(-3.77139 + 9.10493i) q^{61} +(7.23284 + 2.99594i) q^{62} +(-6.20124 - 14.9711i) q^{63} -5.11854i q^{64} +(16.0408 - 6.64431i) q^{65} +(-0.655089 - 0.655089i) q^{66} -1.86246 q^{67} +(-2.56199 - 4.32511i) q^{68} +21.0010 q^{69} +(4.78681 + 4.78681i) q^{70} +(7.01102 - 2.90406i) q^{71} +19.1536i q^{72} +(-3.81569 - 9.21189i) q^{73} +(7.17081 + 2.97025i) q^{74} +(-6.12972 + 14.7984i) q^{75} +(3.53316 - 3.53316i) q^{76} +(0.571880 - 0.571880i) q^{77} +(5.75379 - 13.8909i) q^{78} +(-0.280713 - 0.116275i) q^{79} +(-0.0914538 - 0.220789i) q^{80} -16.1387i q^{81} +(-6.75606 + 2.79845i) q^{82} +(-7.70045 - 7.70045i) q^{83} -9.15413 q^{84} +(-10.5019 - 7.87344i) q^{85} +0.883619 q^{86} +(7.55249 + 7.55249i) q^{87} +(-0.883178 + 0.365824i) q^{88} +1.50936i q^{89} +(7.24826 + 17.4988i) q^{90} +(12.1265 + 5.02295i) q^{91} +(3.14072 - 7.58236i) q^{92} +(-19.5455 + 19.5455i) q^{93} +(-2.74141 + 2.74141i) q^{94} +(4.99264 - 12.0533i) q^{95} +(16.2069 + 6.71312i) q^{96} +(-3.59196 - 8.67175i) q^{97} -1.06768i q^{98} +(2.09059 - 0.865950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.624813 0.624813i −0.441809 0.441809i 0.450810 0.892620i \(-0.351135\pi\)
−0.892620 + 0.450810i \(0.851135\pi\)
\(3\) 2.88236 1.19391i 1.66413 0.689306i 0.665749 0.746175i \(-0.268112\pi\)
0.998382 + 0.0568699i \(0.0181120\pi\)
\(4\) 1.21922i 0.609609i
\(5\) −1.21824 2.94109i −0.544814 1.31530i −0.921292 0.388872i \(-0.872865\pi\)
0.376478 0.926426i \(-0.377135\pi\)
\(6\) −2.54691 1.05496i −1.03977 0.430687i
\(7\) 0.920964 2.22340i 0.348092 0.840367i −0.648754 0.760998i \(-0.724710\pi\)
0.996845 0.0793689i \(-0.0252905\pi\)
\(8\) −2.01141 + 2.01141i −0.711140 + 0.711140i
\(9\) 4.76125 4.76125i 1.58708 1.58708i
\(10\) −1.07646 + 2.59880i −0.340407 + 0.821814i
\(11\) 0.310479 + 0.128605i 0.0936131 + 0.0387758i 0.428999 0.903305i \(-0.358867\pi\)
−0.335385 + 0.942081i \(0.608867\pi\)
\(12\) −1.45564 3.51423i −0.420207 1.01447i
\(13\) 5.45402i 1.51267i 0.654183 + 0.756336i \(0.273013\pi\)
−0.654183 + 0.756336i \(0.726987\pi\)
\(14\) −1.96464 + 0.813780i −0.525072 + 0.217492i
\(15\) −7.02282 7.02282i −1.81328 1.81328i
\(16\) 0.0750704 0.0187676
\(17\) 3.54745 2.10134i 0.860382 0.509649i
\(18\) −5.94978 −1.40238
\(19\) 2.89789 + 2.89789i 0.664822 + 0.664822i 0.956513 0.291691i \(-0.0942179\pi\)
−0.291691 + 0.956513i \(0.594218\pi\)
\(20\) −3.58584 + 1.48530i −0.801817 + 0.332124i
\(21\) 7.50820i 1.63842i
\(22\) −0.113638 0.274345i −0.0242276 0.0584906i
\(23\) 6.21903 + 2.57601i 1.29676 + 0.537135i 0.920993 0.389580i \(-0.127380\pi\)
0.375765 + 0.926715i \(0.377380\pi\)
\(24\) −3.39616 + 8.19905i −0.693238 + 1.67362i
\(25\) −3.63039 + 3.63039i −0.726077 + 0.726077i
\(26\) 3.40774 3.40774i 0.668313 0.668313i
\(27\) 4.45738 10.7611i 0.857823 2.07097i
\(28\) −2.71081 1.12286i −0.512296 0.212200i
\(29\) 1.31012 + 3.16292i 0.243284 + 0.587339i 0.997605 0.0691665i \(-0.0220340\pi\)
−0.754321 + 0.656505i \(0.772034\pi\)
\(30\) 8.77589i 1.60225i
\(31\) −8.18548 + 3.39054i −1.47016 + 0.608958i −0.966895 0.255176i \(-0.917867\pi\)
−0.503261 + 0.864134i \(0.667867\pi\)
\(32\) 3.97591 + 3.97591i 0.702849 + 0.702849i
\(33\) 1.04846 0.182513
\(34\) −3.52943 0.903547i −0.605293 0.154957i
\(35\) −7.66119 −1.29498
\(36\) −5.80500 5.80500i −0.967500 0.967500i
\(37\) −8.11528 + 3.36146i −1.33414 + 0.552620i −0.931834 0.362884i \(-0.881792\pi\)
−0.402309 + 0.915504i \(0.631792\pi\)
\(38\) 3.62128i 0.587449i
\(39\) 6.51162 + 15.7204i 1.04269 + 2.51728i
\(40\) 8.36612 + 3.46536i 1.32280 + 0.547922i
\(41\) 3.16704 7.64591i 0.494608 1.19409i −0.457742 0.889085i \(-0.651342\pi\)
0.952351 0.305005i \(-0.0986582\pi\)
\(42\) −4.69122 + 4.69122i −0.723870 + 0.723870i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) 0.156797 0.378542i 0.0236381 0.0570674i
\(45\) −19.8036 8.20293i −2.95215 1.22282i
\(46\) −2.27621 5.49525i −0.335609 0.810231i
\(47\) 4.38757i 0.639993i −0.947419 0.319997i \(-0.896318\pi\)
0.947419 0.319997i \(-0.103682\pi\)
\(48\) 0.216380 0.0896274i 0.0312317 0.0129366i
\(49\) 0.854402 + 0.854402i 0.122057 + 0.122057i
\(50\) 4.53662 0.641575
\(51\) 7.71620 10.2922i 1.08048 1.44119i
\(52\) 6.64964 0.922139
\(53\) 6.74607 + 6.74607i 0.926644 + 0.926644i 0.997487 0.0708435i \(-0.0225691\pi\)
−0.0708435 + 0.997487i \(0.522569\pi\)
\(54\) −9.50868 + 3.93862i −1.29397 + 0.535979i
\(55\) 1.06982i 0.144255i
\(56\) 2.61974 + 6.32460i 0.350077 + 0.845161i
\(57\) 11.8126 + 4.89293i 1.56462 + 0.648085i
\(58\) 1.15765 2.79481i 0.152007 0.366977i
\(59\) −5.55757 + 5.55757i −0.723534 + 0.723534i −0.969323 0.245789i \(-0.920953\pi\)
0.245789 + 0.969323i \(0.420953\pi\)
\(60\) −8.56235 + 8.56235i −1.10539 + 1.10539i
\(61\) −3.77139 + 9.10493i −0.482876 + 1.16577i 0.475360 + 0.879791i \(0.342318\pi\)
−0.958237 + 0.285976i \(0.907682\pi\)
\(62\) 7.23284 + 2.99594i 0.918572 + 0.380485i
\(63\) −6.20124 14.9711i −0.781282 1.88618i
\(64\) 5.11854i 0.639818i
\(65\) 16.0408 6.64431i 1.98961 0.824125i
\(66\) −0.655089 0.655089i −0.0806358 0.0806358i
\(67\) −1.86246 −0.227536 −0.113768 0.993507i \(-0.536292\pi\)
−0.113768 + 0.993507i \(0.536292\pi\)
\(68\) −2.56199 4.32511i −0.310687 0.524497i
\(69\) 21.0010 2.52822
\(70\) 4.78681 + 4.78681i 0.572133 + 0.572133i
\(71\) 7.01102 2.90406i 0.832055 0.344648i 0.0743389 0.997233i \(-0.476315\pi\)
0.757716 + 0.652585i \(0.226315\pi\)
\(72\) 19.1536i 2.25728i
\(73\) −3.81569 9.21189i −0.446593 1.07817i −0.973590 0.228303i \(-0.926682\pi\)
0.526997 0.849867i \(-0.323318\pi\)
\(74\) 7.17081 + 2.97025i 0.833590 + 0.345284i
\(75\) −6.12972 + 14.7984i −0.707799 + 1.70878i
\(76\) 3.53316 3.53316i 0.405281 0.405281i
\(77\) 0.571880 0.571880i 0.0651718 0.0651718i
\(78\) 5.75379 13.8909i 0.651488 1.57283i
\(79\) −0.280713 0.116275i −0.0315827 0.0130820i 0.366836 0.930286i \(-0.380441\pi\)
−0.398419 + 0.917204i \(0.630441\pi\)
\(80\) −0.0914538 0.220789i −0.0102248 0.0246850i
\(81\) 16.1387i 1.79319i
\(82\) −6.75606 + 2.79845i −0.746083 + 0.309037i
\(83\) −7.70045 7.70045i −0.845235 0.845235i 0.144299 0.989534i \(-0.453907\pi\)
−0.989534 + 0.144299i \(0.953907\pi\)
\(84\) −9.15413 −0.998797
\(85\) −10.5019 7.87344i −1.13909 0.853994i
\(86\) 0.883619 0.0952830
\(87\) 7.55249 + 7.55249i 0.809712 + 0.809712i
\(88\) −0.883178 + 0.365824i −0.0941470 + 0.0389970i
\(89\) 1.50936i 0.159992i 0.996795 + 0.0799962i \(0.0254908\pi\)
−0.996795 + 0.0799962i \(0.974509\pi\)
\(90\) 7.24826 + 17.4988i 0.764034 + 1.84454i
\(91\) 12.1265 + 5.02295i 1.27120 + 0.526548i
\(92\) 3.14072 7.58236i 0.327442 0.790515i
\(93\) −19.5455 + 19.5455i −2.02677 + 2.02677i
\(94\) −2.74141 + 2.74141i −0.282755 + 0.282755i
\(95\) 4.99264 12.0533i 0.512234 1.23664i
\(96\) 16.2069 + 6.71312i 1.65411 + 0.685155i
\(97\) −3.59196 8.67175i −0.364708 0.880483i −0.994598 0.103799i \(-0.966900\pi\)
0.629891 0.776684i \(-0.283100\pi\)
\(98\) 1.06768i 0.107852i
\(99\) 2.09059 0.865950i 0.210112 0.0870313i
\(100\) 4.42623 + 4.42623i 0.442623 + 0.442623i
\(101\) −8.42993 −0.838810 −0.419405 0.907799i \(-0.637761\pi\)
−0.419405 + 0.907799i \(0.637761\pi\)
\(102\) −11.2518 + 1.60949i −1.11410 + 0.159363i
\(103\) −0.399566 −0.0393704 −0.0196852 0.999806i \(-0.506266\pi\)
−0.0196852 + 0.999806i \(0.506266\pi\)
\(104\) −10.9703 10.9703i −1.07572 1.07572i
\(105\) −22.0823 + 9.14679i −2.15501 + 0.892635i
\(106\) 8.43006i 0.818800i
\(107\) −3.19770 7.71993i −0.309133 0.746314i −0.999734 0.0230773i \(-0.992654\pi\)
0.690600 0.723237i \(-0.257346\pi\)
\(108\) −13.1201 5.43452i −1.26248 0.522937i
\(109\) 2.34114 5.65200i 0.224240 0.541364i −0.771217 0.636572i \(-0.780352\pi\)
0.995457 + 0.0952084i \(0.0303517\pi\)
\(110\) −0.668437 + 0.668437i −0.0637330 + 0.0637330i
\(111\) −19.3779 + 19.3779i −1.83927 + 1.83927i
\(112\) 0.0691371 0.166912i 0.00653284 0.0157717i
\(113\) 2.51351 + 1.04113i 0.236451 + 0.0979411i 0.497763 0.867313i \(-0.334155\pi\)
−0.261312 + 0.965254i \(0.584155\pi\)
\(114\) −4.32349 10.4378i −0.404932 0.977592i
\(115\) 21.4290i 1.99826i
\(116\) 3.85628 1.59733i 0.358047 0.148308i
\(117\) 25.9679 + 25.9679i 2.40074 + 2.40074i
\(118\) 6.94488 0.639328
\(119\) −1.40505 9.82266i −0.128801 0.900442i
\(120\) 28.2515 2.57900
\(121\) −7.69832 7.69832i −0.699847 0.699847i
\(122\) 8.04529 3.33247i 0.728386 0.301707i
\(123\) 25.8194i 2.32806i
\(124\) 4.13380 + 9.97989i 0.371227 + 0.896220i
\(125\) 0.394526 + 0.163418i 0.0352875 + 0.0146166i
\(126\) −5.47953 + 13.2287i −0.488155 + 1.17851i
\(127\) −6.78286 + 6.78286i −0.601881 + 0.601881i −0.940811 0.338930i \(-0.889935\pi\)
0.338930 + 0.940811i \(0.389935\pi\)
\(128\) 4.75369 4.75369i 0.420171 0.420171i
\(129\) −1.19391 + 2.88236i −0.105118 + 0.253778i
\(130\) −14.1739 5.87103i −1.24314 0.514924i
\(131\) 4.06901 + 9.82347i 0.355511 + 0.858280i 0.995920 + 0.0902455i \(0.0287652\pi\)
−0.640408 + 0.768035i \(0.721235\pi\)
\(132\) 1.27830i 0.111261i
\(133\) 9.11203 3.77433i 0.790113 0.327276i
\(134\) 1.16369 + 1.16369i 0.100528 + 0.100528i
\(135\) −37.0795 −3.19129
\(136\) −2.90872 + 11.3620i −0.249420 + 0.974285i
\(137\) −19.4855 −1.66476 −0.832378 0.554209i \(-0.813021\pi\)
−0.832378 + 0.554209i \(0.813021\pi\)
\(138\) −13.1217 13.1217i −1.11699 1.11699i
\(139\) 11.6492 4.82527i 0.988074 0.409274i 0.170664 0.985329i \(-0.445409\pi\)
0.817411 + 0.576056i \(0.195409\pi\)
\(140\) 9.34066i 0.789430i
\(141\) −5.23838 12.6466i −0.441151 1.06503i
\(142\) −6.19506 2.56608i −0.519878 0.215341i
\(143\) −0.701413 + 1.69336i −0.0586551 + 0.141606i
\(144\) 0.357429 0.357429i 0.0297857 0.0297857i
\(145\) 7.70639 7.70639i 0.639981 0.639981i
\(146\) −3.37161 + 8.13980i −0.279037 + 0.673654i
\(147\) 3.48277 + 1.44261i 0.287254 + 0.118985i
\(148\) 4.09835 + 9.89429i 0.336882 + 0.813306i
\(149\) 6.73779i 0.551982i 0.961160 + 0.275991i \(0.0890059\pi\)
−0.961160 + 0.275991i \(0.910994\pi\)
\(150\) 13.0762 5.41633i 1.06767 0.442242i
\(151\) 14.6666 + 14.6666i 1.19355 + 1.19355i 0.976063 + 0.217488i \(0.0697864\pi\)
0.217488 + 0.976063i \(0.430214\pi\)
\(152\) −11.6577 −0.945563
\(153\) 6.88528 26.8953i 0.556642 2.17435i
\(154\) −0.714636 −0.0575870
\(155\) 19.9438 + 19.9438i 1.60192 + 1.60192i
\(156\) 19.1666 7.93909i 1.53456 0.635636i
\(157\) 1.30295i 0.103987i 0.998647 + 0.0519934i \(0.0165575\pi\)
−0.998647 + 0.0519934i \(0.983443\pi\)
\(158\) 0.102743 + 0.248044i 0.00817379 + 0.0197333i
\(159\) 27.4988 + 11.3904i 2.18080 + 0.903316i
\(160\) 6.84991 16.5371i 0.541533 1.30738i
\(161\) 11.4550 11.4550i 0.902781 0.902781i
\(162\) −10.0837 + 10.0837i −0.792248 + 0.792248i
\(163\) −3.13736 + 7.57426i −0.245737 + 0.593262i −0.997833 0.0657915i \(-0.979043\pi\)
0.752096 + 0.659053i \(0.229043\pi\)
\(164\) −9.32203 3.86131i −0.727928 0.301518i
\(165\) −1.27727 3.08361i −0.0994355 0.240059i
\(166\) 9.62268i 0.746865i
\(167\) 14.0237 5.80881i 1.08519 0.449499i 0.232861 0.972510i \(-0.425191\pi\)
0.852326 + 0.523011i \(0.175191\pi\)
\(168\) 15.1020 + 15.1020i 1.16515 + 1.16515i
\(169\) −16.7463 −1.28818
\(170\) 1.64228 + 11.4811i 0.125957 + 0.880562i
\(171\) 27.5951 2.11025
\(172\) 0.862117 + 0.862117i 0.0657358 + 0.0657358i
\(173\) −0.478666 + 0.198270i −0.0363923 + 0.0150742i −0.400805 0.916163i \(-0.631270\pi\)
0.364413 + 0.931237i \(0.381270\pi\)
\(174\) 9.43778i 0.715476i
\(175\) 4.72836 + 11.4153i 0.357430 + 0.862913i
\(176\) 0.0233078 + 0.00965441i 0.00175689 + 0.000727728i
\(177\) −9.38367 + 22.6542i −0.705320 + 1.70279i
\(178\) 0.943070 0.943070i 0.0706861 0.0706861i
\(179\) −7.81595 + 7.81595i −0.584192 + 0.584192i −0.936052 0.351861i \(-0.885549\pi\)
0.351861 + 0.936052i \(0.385549\pi\)
\(180\) −10.0012 + 24.1449i −0.745443 + 1.79966i
\(181\) −13.7034 5.67614i −1.01857 0.421904i −0.189993 0.981785i \(-0.560847\pi\)
−0.828573 + 0.559882i \(0.810847\pi\)
\(182\) −4.43837 10.7152i −0.328994 0.794262i
\(183\) 30.7464i 2.27284i
\(184\) −17.6904 + 7.32761i −1.30415 + 0.540199i
\(185\) 19.7727 + 19.7727i 1.45372 + 1.45372i
\(186\) 24.4245 1.79089
\(187\) 1.37165 0.196204i 0.100305 0.0143478i
\(188\) −5.34941 −0.390146
\(189\) −19.8211 19.8211i −1.44177 1.44177i
\(190\) −10.6505 + 4.41159i −0.772670 + 0.320050i
\(191\) 16.2004i 1.17222i −0.810231 0.586111i \(-0.800658\pi\)
0.810231 0.586111i \(-0.199342\pi\)
\(192\) −6.11109 14.7535i −0.441030 1.06474i
\(193\) 14.5157 + 6.01261i 1.04486 + 0.432797i 0.838056 0.545585i \(-0.183692\pi\)
0.206808 + 0.978381i \(0.433692\pi\)
\(194\) −3.17392 + 7.66252i −0.227874 + 0.550137i
\(195\) 38.3026 38.3026i 2.74290 2.74290i
\(196\) 1.04170 1.04170i 0.0744073 0.0744073i
\(197\) 5.61106 13.5463i 0.399771 0.965134i −0.587948 0.808898i \(-0.700064\pi\)
0.987720 0.156235i \(-0.0499358\pi\)
\(198\) −1.84728 0.765170i −0.131281 0.0543782i
\(199\) 2.53066 + 6.10955i 0.179394 + 0.433095i 0.987840 0.155476i \(-0.0496910\pi\)
−0.808446 + 0.588570i \(0.799691\pi\)
\(200\) 14.6044i 1.03269i
\(201\) −5.36829 + 2.22362i −0.378650 + 0.156842i
\(202\) 5.26713 + 5.26713i 0.370594 + 0.370594i
\(203\) 8.23901 0.578265
\(204\) −12.5484 9.40774i −0.878562 0.658673i
\(205\) −26.3455 −1.84005
\(206\) 0.249654 + 0.249654i 0.0173942 + 0.0173942i
\(207\) 41.8754 17.3453i 2.91054 1.20558i
\(208\) 0.409435i 0.0283892i
\(209\) 0.527053 + 1.27242i 0.0364570 + 0.0880150i
\(210\) 19.5123 + 8.08227i 1.34648 + 0.557730i
\(211\) 1.38190 3.33621i 0.0951341 0.229674i −0.869148 0.494553i \(-0.835332\pi\)
0.964282 + 0.264879i \(0.0853319\pi\)
\(212\) 8.22493 8.22493i 0.564891 0.564891i
\(213\) 16.7411 16.7411i 1.14708 1.14708i
\(214\) −2.82555 + 6.82147i −0.193150 + 0.466306i
\(215\) 2.94109 + 1.21824i 0.200581 + 0.0830833i
\(216\) 12.6793 + 30.6105i 0.862716 + 2.08278i
\(217\) 21.3222i 1.44744i
\(218\) −4.99422 + 2.06867i −0.338251 + 0.140108i
\(219\) −21.9964 21.9964i −1.48638 1.48638i
\(220\) −1.30434 −0.0879389
\(221\) 11.4607 + 19.3478i 0.770932 + 1.30148i
\(222\) 24.2151 1.62521
\(223\) 20.2557 + 20.2557i 1.35642 + 1.35642i 0.878284 + 0.478139i \(0.158689\pi\)
0.478139 + 0.878284i \(0.341311\pi\)
\(224\) 12.5017 5.17838i 0.835306 0.345995i
\(225\) 34.5703i 2.30469i
\(226\) −0.919960 2.22098i −0.0611948 0.147737i
\(227\) −5.88537 2.43780i −0.390626 0.161803i 0.178721 0.983900i \(-0.442804\pi\)
−0.569347 + 0.822097i \(0.692804\pi\)
\(228\) 5.96555 14.4021i 0.395078 0.953804i
\(229\) −7.65871 + 7.65871i −0.506102 + 0.506102i −0.913328 0.407226i \(-0.866496\pi\)
0.407226 + 0.913328i \(0.366496\pi\)
\(230\) −13.3891 + 13.3891i −0.882850 + 0.882850i
\(231\) 0.965590 2.33114i 0.0635311 0.153378i
\(232\) −8.99711 3.72672i −0.590689 0.244671i
\(233\) −5.24792 12.6696i −0.343803 0.830013i −0.997324 0.0731051i \(-0.976709\pi\)
0.653522 0.756908i \(-0.273291\pi\)
\(234\) 32.4502i 2.12134i
\(235\) −12.9043 + 5.34512i −0.841781 + 0.348677i
\(236\) 6.77589 + 6.77589i 0.441073 + 0.441073i
\(237\) −0.947939 −0.0615753
\(238\) −5.25943 + 7.01522i −0.340918 + 0.454729i
\(239\) 21.8480 1.41323 0.706615 0.707598i \(-0.250221\pi\)
0.706615 + 0.707598i \(0.250221\pi\)
\(240\) −0.527205 0.527205i −0.0340310 0.0340310i
\(241\) 21.9606 9.09638i 1.41461 0.585949i 0.461107 0.887344i \(-0.347452\pi\)
0.953499 + 0.301395i \(0.0974524\pi\)
\(242\) 9.62001i 0.618398i
\(243\) −5.89606 14.2344i −0.378233 0.913134i
\(244\) 11.1009 + 4.59814i 0.710662 + 0.294366i
\(245\) 1.47201 3.55374i 0.0940432 0.227040i
\(246\) −16.1323 + 16.1323i −1.02856 + 1.02856i
\(247\) −15.8051 + 15.8051i −1.00566 + 1.00566i
\(248\) 9.64459 23.2841i 0.612432 1.47854i
\(249\) −31.3891 13.0018i −1.98921 0.823956i
\(250\) −0.144399 0.348611i −0.00913262 0.0220481i
\(251\) 19.7362i 1.24574i −0.782325 0.622870i \(-0.785967\pi\)
0.782325 0.622870i \(-0.214033\pi\)
\(252\) −18.2530 + 7.56066i −1.14983 + 0.476277i
\(253\) 1.59959 + 1.59959i 0.100566 + 0.100566i
\(254\) 8.47603 0.531833
\(255\) −39.6704 10.1558i −2.48426 0.635978i
\(256\) −16.1774 −1.01109
\(257\) 12.8291 + 12.8291i 0.800258 + 0.800258i 0.983136 0.182878i \(-0.0585413\pi\)
−0.182878 + 0.983136i \(0.558541\pi\)
\(258\) 2.54691 1.05496i 0.158563 0.0656791i
\(259\) 21.1393i 1.31353i
\(260\) −8.10086 19.5572i −0.502394 1.21289i
\(261\) 21.2972 + 8.82161i 1.31827 + 0.546044i
\(262\) 3.59546 8.68020i 0.222128 0.536264i
\(263\) −10.8680 + 10.8680i −0.670151 + 0.670151i −0.957751 0.287600i \(-0.907143\pi\)
0.287600 + 0.957751i \(0.407143\pi\)
\(264\) −2.10887 + 2.10887i −0.129792 + 0.129792i
\(265\) 11.6225 28.0592i 0.713964 1.72366i
\(266\) −8.05156 3.33506i −0.493673 0.204486i
\(267\) 1.80205 + 4.35053i 0.110284 + 0.266248i
\(268\) 2.27075i 0.138708i
\(269\) −17.1735 + 7.11348i −1.04708 + 0.433716i −0.838850 0.544363i \(-0.816772\pi\)
−0.208234 + 0.978079i \(0.566772\pi\)
\(270\) 23.1677 + 23.1677i 1.40994 + 1.40994i
\(271\) −8.60890 −0.522953 −0.261477 0.965210i \(-0.584209\pi\)
−0.261477 + 0.965210i \(0.584209\pi\)
\(272\) 0.266308 0.157748i 0.0161473 0.00956489i
\(273\) 40.9498 2.47840
\(274\) 12.1748 + 12.1748i 0.735505 + 0.735505i
\(275\) −1.59405 + 0.660275i −0.0961246 + 0.0398161i
\(276\) 25.6048i 1.54123i
\(277\) 2.52682 + 6.10029i 0.151822 + 0.366531i 0.981431 0.191813i \(-0.0614368\pi\)
−0.829609 + 0.558344i \(0.811437\pi\)
\(278\) −10.2935 4.26369i −0.617361 0.255719i
\(279\) −22.8299 + 55.1163i −1.36679 + 3.29973i
\(280\) 15.4098 15.4098i 0.920911 0.920911i
\(281\) −10.2182 + 10.2182i −0.609566 + 0.609566i −0.942833 0.333266i \(-0.891849\pi\)
0.333266 + 0.942833i \(0.391849\pi\)
\(282\) −4.62873 + 11.1747i −0.275637 + 0.665446i
\(283\) −7.41958 3.07329i −0.441048 0.182688i 0.151098 0.988519i \(-0.451719\pi\)
−0.592146 + 0.805831i \(0.701719\pi\)
\(284\) −3.54068 8.54796i −0.210101 0.507228i
\(285\) 40.7027i 2.41102i
\(286\) 1.49628 0.619781i 0.0884772 0.0366484i
\(287\) −14.0832 14.0832i −0.831305 0.831305i
\(288\) 37.8606 2.23096
\(289\) 8.16876 14.9088i 0.480515 0.876986i
\(290\) −9.63010 −0.565499
\(291\) −20.7066 20.7066i −1.21384 1.21384i
\(292\) −11.2313 + 4.65216i −0.657262 + 0.272247i
\(293\) 25.6835i 1.50045i 0.661184 + 0.750224i \(0.270054\pi\)
−0.661184 + 0.750224i \(0.729946\pi\)
\(294\) −1.27472 3.07744i −0.0743431 0.179480i
\(295\) 23.1158 + 9.57488i 1.34585 + 0.557471i
\(296\) 9.56187 23.0844i 0.555773 1.34175i
\(297\) 2.76785 2.76785i 0.160607 0.160607i
\(298\) 4.20986 4.20986i 0.243871 0.243871i
\(299\) −14.0496 + 33.9187i −0.812509 + 1.96157i
\(300\) 18.0425 + 7.47346i 1.04169 + 0.431481i
\(301\) 0.920964 + 2.22340i 0.0530835 + 0.128155i
\(302\) 18.3278i 1.05464i
\(303\) −24.2981 + 10.0646i −1.39589 + 0.578196i
\(304\) 0.217546 + 0.217546i 0.0124771 + 0.0124771i
\(305\) 31.3729 1.79641
\(306\) −21.1065 + 12.5025i −1.20658 + 0.714720i
\(307\) −27.6891 −1.58030 −0.790149 0.612915i \(-0.789997\pi\)
−0.790149 + 0.612915i \(0.789997\pi\)
\(308\) −0.697247 0.697247i −0.0397293 0.0397293i
\(309\) −1.15169 + 0.477047i −0.0655176 + 0.0271383i
\(310\) 24.9222i 1.41549i
\(311\) −0.566280 1.36712i −0.0321108 0.0775224i 0.907011 0.421108i \(-0.138359\pi\)
−0.939121 + 0.343585i \(0.888359\pi\)
\(312\) −44.7177 18.5227i −2.53164 1.04864i
\(313\) −9.27711 + 22.3969i −0.524373 + 1.26595i 0.410789 + 0.911730i \(0.365253\pi\)
−0.935163 + 0.354219i \(0.884747\pi\)
\(314\) 0.814100 0.814100i 0.0459423 0.0459423i
\(315\) −36.4768 + 36.4768i −2.05524 + 2.05524i
\(316\) −0.141765 + 0.342251i −0.00797490 + 0.0192531i
\(317\) 9.54907 + 3.95536i 0.536329 + 0.222155i 0.634373 0.773027i \(-0.281258\pi\)
−0.0980435 + 0.995182i \(0.531258\pi\)
\(318\) −10.0648 24.2985i −0.564403 1.36259i
\(319\) 1.15051i 0.0644161i
\(320\) −15.0541 + 6.23562i −0.841550 + 0.348582i
\(321\) −18.4338 18.4338i −1.02888 1.02888i
\(322\) −14.3145 −0.797714
\(323\) 16.3696 + 4.19066i 0.910827 + 0.233175i
\(324\) −19.6766 −1.09314
\(325\) −19.8002 19.8002i −1.09832 1.09832i
\(326\) 6.69275 2.77223i 0.370677 0.153540i
\(327\) 19.0862i 1.05547i
\(328\) 9.00883 + 21.7492i 0.497430 + 1.20090i
\(329\) −9.75534 4.04079i −0.537829 0.222776i
\(330\) −1.12862 + 2.72473i −0.0621286 + 0.149992i
\(331\) −13.7256 + 13.7256i −0.754427 + 0.754427i −0.975302 0.220875i \(-0.929109\pi\)
0.220875 + 0.975302i \(0.429109\pi\)
\(332\) −9.38853 + 9.38853i −0.515263 + 0.515263i
\(333\) −22.6341 + 54.6436i −1.24034 + 2.99445i
\(334\) −12.3916 5.13277i −0.678039 0.280853i
\(335\) 2.26893 + 5.47768i 0.123965 + 0.299278i
\(336\) 0.563643i 0.0307492i
\(337\) −5.48082 + 2.27023i −0.298559 + 0.123667i −0.526935 0.849906i \(-0.676659\pi\)
0.228375 + 0.973573i \(0.426659\pi\)
\(338\) 10.4633 + 10.4633i 0.569129 + 0.569129i
\(339\) 8.48784 0.460996
\(340\) −9.59944 + 12.8041i −0.520603 + 0.694399i
\(341\) −2.97746 −0.161239
\(342\) −17.2418 17.2418i −0.932330 0.932330i
\(343\) 18.2504 7.55955i 0.985427 0.408177i
\(344\) 2.84456i 0.153368i
\(345\) −25.5843 61.7659i −1.37741 3.32537i
\(346\) 0.422958 + 0.175195i 0.0227384 + 0.00941854i
\(347\) −3.75883 + 9.07461i −0.201784 + 0.487151i −0.992085 0.125569i \(-0.959924\pi\)
0.790300 + 0.612719i \(0.209924\pi\)
\(348\) 9.20813 9.20813i 0.493608 0.493608i
\(349\) 14.8671 14.8671i 0.795817 0.795817i −0.186616 0.982433i \(-0.559752\pi\)
0.982433 + 0.186616i \(0.0597520\pi\)
\(350\) 4.17807 10.0867i 0.223327 0.539159i
\(351\) 58.6910 + 24.3106i 3.13270 + 1.29761i
\(352\) 0.723117 + 1.74576i 0.0385423 + 0.0930493i
\(353\) 11.3683i 0.605072i 0.953138 + 0.302536i \(0.0978332\pi\)
−0.953138 + 0.302536i \(0.902167\pi\)
\(354\) 20.0176 8.29158i 1.06393 0.440693i
\(355\) −17.0822 17.0822i −0.906630 0.906630i
\(356\) 1.84025 0.0975328
\(357\) −15.7773 26.6349i −0.835021 1.40967i
\(358\) 9.76701 0.516203
\(359\) −19.3741 19.3741i −1.02253 1.02253i −0.999740 0.0227868i \(-0.992746\pi\)
−0.0227868 0.999740i \(-0.507254\pi\)
\(360\) 56.3326 23.3337i 2.96899 1.22980i
\(361\) 2.20447i 0.116025i
\(362\) 5.01554 + 12.1086i 0.263611 + 0.636413i
\(363\) −31.3804 12.9982i −1.64705 0.682229i
\(364\) 6.12407 14.7848i 0.320989 0.774935i
\(365\) −22.4446 + 22.4446i −1.17480 + 1.17480i
\(366\) 19.2107 19.2107i 1.00416 1.00416i
\(367\) 1.00100 2.41662i 0.0522517 0.126147i −0.895598 0.444864i \(-0.853252\pi\)
0.947850 + 0.318717i \(0.103252\pi\)
\(368\) 0.466865 + 0.193382i 0.0243370 + 0.0100807i
\(369\) −21.3250 51.4831i −1.11014 2.68010i
\(370\) 24.7085i 1.28453i
\(371\) 21.2121 8.78635i 1.10128 0.456164i
\(372\) 23.8302 + 23.8302i 1.23554 + 1.23554i
\(373\) 22.7759 1.17929 0.589645 0.807662i \(-0.299268\pi\)
0.589645 + 0.807662i \(0.299268\pi\)
\(374\) −0.979616 0.734435i −0.0506547 0.0379767i
\(375\) 1.33227 0.0687983
\(376\) 8.82520 + 8.82520i 0.455125 + 0.455125i
\(377\) −17.2506 + 7.14543i −0.888451 + 0.368008i
\(378\) 24.7689i 1.27398i
\(379\) −5.57565 13.4608i −0.286402 0.691436i 0.713556 0.700598i \(-0.247083\pi\)
−0.999958 + 0.00916236i \(0.997083\pi\)
\(380\) −14.6956 6.08712i −0.753868 0.312262i
\(381\) −11.4525 + 27.6488i −0.586729 + 1.41649i
\(382\) −10.1222 + 10.1222i −0.517899 + 0.517899i
\(383\) 8.45057 8.45057i 0.431804 0.431804i −0.457438 0.889242i \(-0.651233\pi\)
0.889242 + 0.457438i \(0.151233\pi\)
\(384\) 8.02636 19.3773i 0.409594 0.988846i
\(385\) −2.37864 0.985266i −0.121227 0.0502138i
\(386\) −5.31285 12.8264i −0.270417 0.652844i
\(387\) 6.73342i 0.342279i
\(388\) −10.5728 + 4.37938i −0.536750 + 0.222329i
\(389\) −7.11038 7.11038i −0.360511 0.360511i 0.503490 0.864001i \(-0.332049\pi\)
−0.864001 + 0.503490i \(0.832049\pi\)
\(390\) −47.8639 −2.42368
\(391\) 27.4747 3.93004i 1.38946 0.198751i
\(392\) −3.43710 −0.173600
\(393\) 23.4567 + 23.4567i 1.18323 + 1.18323i
\(394\) −11.9698 + 4.95804i −0.603028 + 0.249782i
\(395\) 0.967256i 0.0486679i
\(396\) −1.05578 2.54888i −0.0530551 0.128086i
\(397\) −23.8273 9.86958i −1.19586 0.495340i −0.306199 0.951968i \(-0.599057\pi\)
−0.889658 + 0.456628i \(0.849057\pi\)
\(398\) 2.23614 5.39851i 0.112087 0.270603i
\(399\) 21.7579 21.7579i 1.08926 1.08926i
\(400\) −0.272535 + 0.272535i −0.0136267 + 0.0136267i
\(401\) 5.36440 12.9508i 0.267886 0.646733i −0.731498 0.681844i \(-0.761178\pi\)
0.999383 + 0.0351108i \(0.0111784\pi\)
\(402\) 4.74352 + 1.96483i 0.236585 + 0.0979969i
\(403\) −18.4920 44.6438i −0.921155 2.22386i
\(404\) 10.2779i 0.511346i
\(405\) −47.4654 + 19.6608i −2.35858 + 0.976954i
\(406\) −5.14784 5.14784i −0.255483 0.255483i
\(407\) −2.95193 −0.146322
\(408\) 5.18128 + 36.2222i 0.256512 + 1.79326i
\(409\) −12.4896 −0.617570 −0.308785 0.951132i \(-0.599922\pi\)
−0.308785 + 0.951132i \(0.599922\pi\)
\(410\) 16.4610 + 16.4610i 0.812952 + 0.812952i
\(411\) −56.1641 + 23.2639i −2.77037 + 1.14753i
\(412\) 0.487159i 0.0240006i
\(413\) 7.23840 + 17.4750i 0.356178 + 0.859891i
\(414\) −37.0018 15.3267i −1.81854 0.753265i
\(415\) −13.2667 + 32.0288i −0.651239 + 1.57223i
\(416\) −21.6847 + 21.6847i −1.06318 + 1.06318i
\(417\) 27.8163 27.8163i 1.36217 1.36217i
\(418\) 0.465714 1.12433i 0.0227788 0.0549929i
\(419\) 4.10240 + 1.69927i 0.200415 + 0.0830147i 0.480633 0.876922i \(-0.340407\pi\)
−0.280218 + 0.959936i \(0.590407\pi\)
\(420\) 11.1519 + 26.9231i 0.544159 + 1.31372i
\(421\) 7.17673i 0.349773i 0.984589 + 0.174886i \(0.0559558\pi\)
−0.984589 + 0.174886i \(0.944044\pi\)
\(422\) −2.94793 + 1.22107i −0.143503 + 0.0594410i
\(423\) −20.8903 20.8903i −1.01572 1.01572i
\(424\) −27.1382 −1.31795
\(425\) −5.24993 + 20.5073i −0.254659 + 0.994749i
\(426\) −20.9201 −1.01358
\(427\) 16.7706 + 16.7706i 0.811587 + 0.811587i
\(428\) −9.41228 + 3.89869i −0.454960 + 0.188450i
\(429\) 5.71830i 0.276082i
\(430\) −1.07646 2.59880i −0.0519115 0.125326i
\(431\) −11.6378 4.82053i −0.560573 0.232197i 0.0843612 0.996435i \(-0.473115\pi\)
−0.644934 + 0.764238i \(0.723115\pi\)
\(432\) 0.334617 0.807837i 0.0160993 0.0388671i
\(433\) 15.8069 15.8069i 0.759632 0.759632i −0.216623 0.976255i \(-0.569504\pi\)
0.976255 + 0.216623i \(0.0695042\pi\)
\(434\) 13.3224 13.3224i 0.639494 0.639494i
\(435\) 13.0118 31.4133i 0.623869 1.50615i
\(436\) −6.89103 2.85436i −0.330020 0.136699i
\(437\) 10.5571 + 25.4871i 0.505014 + 1.21921i
\(438\) 27.4872i 1.31339i
\(439\) −27.9846 + 11.5916i −1.33563 + 0.553237i −0.932257 0.361797i \(-0.882163\pi\)
−0.403376 + 0.915034i \(0.632163\pi\)
\(440\) 2.15185 + 2.15185i 0.102585 + 0.102585i
\(441\) 8.13604 0.387430
\(442\) 4.92796 19.2496i 0.234399 0.915610i
\(443\) 25.3507 1.20445 0.602224 0.798327i \(-0.294281\pi\)
0.602224 + 0.798327i \(0.294281\pi\)
\(444\) 23.6258 + 23.6258i 1.12123 + 1.12123i
\(445\) 4.43918 1.83877i 0.210437 0.0871661i
\(446\) 25.3121i 1.19856i
\(447\) 8.04433 + 19.4207i 0.380484 + 0.918570i
\(448\) −11.3806 4.71399i −0.537682 0.222715i
\(449\) 1.80510 4.35791i 0.0851881 0.205662i −0.875545 0.483137i \(-0.839497\pi\)
0.960733 + 0.277474i \(0.0894974\pi\)
\(450\) 21.6000 21.6000i 1.01823 1.01823i
\(451\) 1.96660 1.96660i 0.0926036 0.0926036i
\(452\) 1.26936 3.06451i 0.0597058 0.144143i
\(453\) 59.7851 + 24.7638i 2.80895 + 1.16350i
\(454\) 2.15409 + 5.20042i 0.101096 + 0.244068i
\(455\) 41.7843i 1.95888i
\(456\) −33.6016 + 13.9182i −1.57354 + 0.651782i
\(457\) 17.9567 + 17.9567i 0.839980 + 0.839980i 0.988856 0.148875i \(-0.0475654\pi\)
−0.148875 + 0.988856i \(0.547565\pi\)
\(458\) 9.57052 0.447201
\(459\) −6.80032 47.5408i −0.317412 2.21901i
\(460\) −26.1266 −1.21816
\(461\) −25.1464 25.1464i −1.17118 1.17118i −0.981928 0.189256i \(-0.939392\pi\)
−0.189256 0.981928i \(-0.560608\pi\)
\(462\) −2.05984 + 0.853213i −0.0958324 + 0.0396951i
\(463\) 19.7152i 0.916244i 0.888889 + 0.458122i \(0.151478\pi\)
−0.888889 + 0.458122i \(0.848522\pi\)
\(464\) 0.0983514 + 0.237441i 0.00456585 + 0.0110229i
\(465\) 81.2962 + 33.6740i 3.77002 + 1.56159i
\(466\) −4.63716 + 11.1951i −0.214812 + 0.518603i
\(467\) 6.07948 6.07948i 0.281325 0.281325i −0.552312 0.833637i \(-0.686254\pi\)
0.833637 + 0.552312i \(0.186254\pi\)
\(468\) 31.6606 31.6606i 1.46351 1.46351i
\(469\) −1.71526 + 4.14101i −0.0792034 + 0.191214i
\(470\) 11.4024 + 4.72305i 0.525956 + 0.217858i
\(471\) 1.55561 + 3.75557i 0.0716786 + 0.173048i
\(472\) 22.3571i 1.02907i
\(473\) −0.310479 + 0.128605i −0.0142759 + 0.00591325i
\(474\) 0.592284 + 0.592284i 0.0272045 + 0.0272045i
\(475\) −21.0409 −0.965424
\(476\) −11.9760 + 1.71306i −0.548917 + 0.0785182i
\(477\) 64.2394 2.94132
\(478\) −13.6509 13.6509i −0.624378 0.624378i
\(479\) −2.12619 + 0.880695i −0.0971479 + 0.0402400i −0.430728 0.902482i \(-0.641743\pi\)
0.333580 + 0.942722i \(0.391743\pi\)
\(480\) 55.8442i 2.54893i
\(481\) −18.3335 44.2609i −0.835933 2.01812i
\(482\) −19.4048 8.03773i −0.883864 0.366108i
\(483\) 19.3412 46.6937i 0.880054 2.12464i
\(484\) −9.38593 + 9.38593i −0.426633 + 0.426633i
\(485\) −21.1286 + 21.1286i −0.959398 + 0.959398i
\(486\) −5.20987 + 12.5777i −0.236325 + 0.570538i
\(487\) −38.3269 15.8755i −1.73676 0.719389i −0.999018 0.0443052i \(-0.985893\pi\)
−0.737741 0.675084i \(-0.764107\pi\)
\(488\) −10.7279 25.8995i −0.485631 1.17242i
\(489\) 25.5775i 1.15665i
\(490\) −3.14015 + 1.30069i −0.141858 + 0.0587594i
\(491\) 7.60261 + 7.60261i 0.343101 + 0.343101i 0.857532 0.514431i \(-0.171997\pi\)
−0.514431 + 0.857532i \(0.671997\pi\)
\(492\) −31.4795 −1.41921
\(493\) 11.2939 + 8.46726i 0.508654 + 0.381346i
\(494\) 19.7505 0.888617
\(495\) −5.09368 5.09368i −0.228944 0.228944i
\(496\) −0.614487 + 0.254529i −0.0275913 + 0.0114287i
\(497\) 18.2628i 0.819201i
\(498\) 11.4886 + 27.7360i 0.514818 + 1.24288i
\(499\) 20.3602 + 8.43346i 0.911447 + 0.377534i 0.788610 0.614893i \(-0.210801\pi\)
0.122837 + 0.992427i \(0.460801\pi\)
\(500\) 0.199242 0.481014i 0.00891039 0.0215116i
\(501\) 33.4861 33.4861i 1.49605 1.49605i
\(502\) −12.3314 + 12.3314i −0.550379 + 0.550379i
\(503\) 0.550878 1.32994i 0.0245624 0.0592989i −0.911122 0.412136i \(-0.864783\pi\)
0.935685 + 0.352837i \(0.114783\pi\)
\(504\) 42.5862 + 17.6398i 1.89694 + 0.785739i
\(505\) 10.2697 + 24.7932i 0.456995 + 1.10328i
\(506\) 1.99889i 0.0888617i
\(507\) −48.2689 + 19.9936i −2.14370 + 0.887948i
\(508\) 8.26978 + 8.26978i 0.366912 + 0.366912i
\(509\) 16.3855 0.726274 0.363137 0.931736i \(-0.381706\pi\)
0.363137 + 0.931736i \(0.381706\pi\)
\(510\) 18.4411 + 31.1320i 0.816586 + 1.37855i
\(511\) −23.9959 −1.06151
\(512\) 0.600467 + 0.600467i 0.0265372 + 0.0265372i
\(513\) 44.1014 18.2674i 1.94712 0.806525i
\(514\) 16.0316i 0.707123i
\(515\) 0.486768 + 1.17516i 0.0214496 + 0.0517838i
\(516\) 3.51423 + 1.45564i 0.154705 + 0.0640810i
\(517\) 0.564263 1.36225i 0.0248162 0.0599117i
\(518\) 13.2081 13.2081i 0.580331 0.580331i
\(519\) −1.14297 + 1.14297i −0.0501708 + 0.0501708i
\(520\) −18.9001 + 45.6290i −0.828826 + 2.00096i
\(521\) 38.4312 + 15.9187i 1.68370 + 0.697412i 0.999492 0.0318725i \(-0.0101471\pi\)
0.684210 + 0.729285i \(0.260147\pi\)
\(522\) −7.79494 18.8186i −0.341175 0.823670i
\(523\) 24.2374i 1.05983i −0.848051 0.529915i \(-0.822224\pi\)
0.848051 0.529915i \(-0.177776\pi\)
\(524\) 11.9769 4.96101i 0.523215 0.216723i
\(525\) 27.2577 + 27.2577i 1.18962 + 1.18962i
\(526\) 13.5810 0.592158
\(527\) −21.9129 + 29.2282i −0.954541 + 1.27320i
\(528\) 0.0787080 0.00342533
\(529\) 15.7771 + 15.7771i 0.685960 + 0.685960i
\(530\) −24.7936 + 10.2698i −1.07696 + 0.446094i
\(531\) 52.9220i 2.29662i
\(532\) −4.60173 11.1096i −0.199510 0.481660i
\(533\) 41.7009 + 17.2731i 1.80627 + 0.748180i
\(534\) 1.59232 3.84421i 0.0689066 0.166355i
\(535\) −18.8095 + 18.8095i −0.813204 + 0.813204i
\(536\) 3.74618 3.74618i 0.161810 0.161810i
\(537\) −13.1968 + 31.8599i −0.569485 + 1.37486i
\(538\) 15.1748 + 6.28560i 0.654231 + 0.270991i
\(539\) 0.155394 + 0.375154i 0.00669329 + 0.0161590i
\(540\) 45.2079i 1.94544i
\(541\) 20.5470 8.51085i 0.883385 0.365910i 0.105576 0.994411i \(-0.466331\pi\)
0.777809 + 0.628501i \(0.216331\pi\)
\(542\) 5.37895 + 5.37895i 0.231046 + 0.231046i
\(543\) −46.2749 −1.98585
\(544\) 22.4591 + 5.74960i 0.962925 + 0.246512i
\(545\) −19.4751 −0.834223
\(546\) −25.5860 25.5860i −1.09498 1.09498i
\(547\) 11.6509 4.82595i 0.498156 0.206343i −0.119436 0.992842i \(-0.538109\pi\)
0.617591 + 0.786499i \(0.288109\pi\)
\(548\) 23.7570i 1.01485i
\(549\) 25.3943 + 61.3073i 1.08380 + 2.61653i
\(550\) 1.40853 + 0.583432i 0.0600598 + 0.0248776i
\(551\) −5.36919 + 12.9624i −0.228735 + 0.552216i
\(552\) −42.2416 + 42.2416i −1.79792 + 1.79792i
\(553\) −0.517054 + 0.517054i −0.0219874 + 0.0219874i
\(554\) 2.23275 5.39033i 0.0948604 0.229013i
\(555\) 80.5990 + 33.3852i 3.42124 + 1.41712i
\(556\) −5.88305 14.2029i −0.249497 0.602339i
\(557\) 21.8585i 0.926173i −0.886313 0.463086i \(-0.846742\pi\)
0.886313 0.463086i \(-0.153258\pi\)
\(558\) 48.7018 20.1729i 2.06171 0.853988i
\(559\) −3.85657 3.85657i −0.163116 0.163116i
\(560\) −0.575128 −0.0243036
\(561\) 3.71934 2.20316i 0.157031 0.0930175i
\(562\) 12.7689 0.538624
\(563\) −30.4159 30.4159i −1.28188 1.28188i −0.939597 0.342281i \(-0.888800\pi\)
−0.342281 0.939597i \(-0.611200\pi\)
\(564\) −15.4189 + 6.38672i −0.649253 + 0.268930i
\(565\) 8.66080i 0.364363i
\(566\) 2.71562 + 6.55608i 0.114146 + 0.275573i
\(567\) −35.8828 14.8632i −1.50694 0.624194i
\(568\) −8.26077 + 19.9433i −0.346614 + 0.836801i
\(569\) 14.5172 14.5172i 0.608594 0.608594i −0.333985 0.942578i \(-0.608393\pi\)
0.942578 + 0.333985i \(0.108393\pi\)
\(570\) −25.4316 + 25.4316i −1.06521 + 1.06521i
\(571\) 0.0919704 0.222036i 0.00384884 0.00929193i −0.921943 0.387325i \(-0.873399\pi\)
0.925792 + 0.378033i \(0.123399\pi\)
\(572\) 2.06458 + 0.855175i 0.0863242 + 0.0357567i
\(573\) −19.3419 46.6955i −0.808019 1.95073i
\(574\) 17.5987i 0.734557i
\(575\) −31.9294 + 13.2256i −1.33155 + 0.551545i
\(576\) −24.3706 24.3706i −1.01544 1.01544i
\(577\) −27.7861 −1.15675 −0.578376 0.815770i \(-0.696313\pi\)
−0.578376 + 0.815770i \(0.696313\pi\)
\(578\) −14.4191 + 4.21125i −0.599757 + 0.175165i
\(579\) 49.0180 2.03712
\(580\) −9.39577 9.39577i −0.390138 0.390138i
\(581\) −24.2130 + 10.0294i −1.00453 + 0.416088i
\(582\) 25.8755i 1.07257i
\(583\) 1.22694 + 2.96209i 0.0508146 + 0.122677i
\(584\) 26.2038 + 10.8540i 1.08432 + 0.449140i
\(585\) 44.7389 108.009i 1.84973 4.46564i
\(586\) 16.0474 16.0474i 0.662912 0.662912i
\(587\) 1.91046 1.91046i 0.0788530 0.0788530i −0.666580 0.745433i \(-0.732243\pi\)
0.745433 + 0.666580i \(0.232243\pi\)
\(588\) 1.75886 4.24626i 0.0725341 0.175113i
\(589\) −33.5460 13.8952i −1.38224 0.572542i
\(590\) −8.46054 20.4256i −0.348315 0.840907i
\(591\) 45.7444i 1.88167i
\(592\) −0.609217 + 0.252346i −0.0250387 + 0.0103714i
\(593\) 18.4755 + 18.4755i 0.758700 + 0.758700i 0.976086 0.217386i \(-0.0697531\pi\)
−0.217386 + 0.976086i \(0.569753\pi\)
\(594\) −3.45877 −0.141915
\(595\) −27.1777 + 16.0988i −1.11418 + 0.659984i
\(596\) 8.21484 0.336493
\(597\) 14.5885 + 14.5885i 0.597069 + 0.597069i
\(598\) 29.9712 12.4145i 1.22561 0.507666i
\(599\) 2.48091i 0.101367i −0.998715 0.0506837i \(-0.983860\pi\)
0.998715 0.0506837i \(-0.0161400\pi\)
\(600\) −17.4364 42.0951i −0.711836 1.71852i
\(601\) 18.8319 + 7.80044i 0.768170 + 0.318187i 0.732131 0.681164i \(-0.238526\pi\)
0.0360393 + 0.999350i \(0.488526\pi\)
\(602\) 0.813780 1.96464i 0.0331672 0.0800727i
\(603\) −8.86766 + 8.86766i −0.361119 + 0.361119i
\(604\) 17.8818 17.8818i 0.727600 0.727600i
\(605\) −13.2631 + 32.0199i −0.539220 + 1.30179i
\(606\) 21.4703 + 8.89327i 0.872169 + 0.361264i
\(607\) −4.09532 9.88698i −0.166224 0.401300i 0.818716 0.574199i \(-0.194687\pi\)
−0.984940 + 0.172899i \(0.944687\pi\)
\(608\) 23.0435i 0.934538i
\(609\) 23.7478 9.83666i 0.962309 0.398601i
\(610\) −19.6022 19.6022i −0.793670 0.793670i
\(611\) 23.9299 0.968100
\(612\) −32.7912 8.39466i −1.32551 0.339334i
\(613\) −21.8975 −0.884431 −0.442216 0.896909i \(-0.645807\pi\)
−0.442216 + 0.896909i \(0.645807\pi\)
\(614\) 17.3005 + 17.3005i 0.698190 + 0.698190i
\(615\) −75.9373 + 31.4543i −3.06209 + 1.26836i
\(616\) 2.30057i 0.0926926i
\(617\) −5.24036 12.6514i −0.210969 0.509324i 0.782604 0.622520i \(-0.213891\pi\)
−0.993573 + 0.113196i \(0.963891\pi\)
\(618\) 1.01766 + 0.421528i 0.0409362 + 0.0169563i
\(619\) 4.12163 9.95049i 0.165662 0.399944i −0.819147 0.573584i \(-0.805553\pi\)
0.984809 + 0.173640i \(0.0555528\pi\)
\(620\) 24.3158 24.3158i 0.976546 0.976546i
\(621\) 55.4412 55.4412i 2.22478 2.22478i
\(622\) −0.500376 + 1.20801i −0.0200632 + 0.0484370i
\(623\) 3.35593 + 1.39007i 0.134452 + 0.0556920i
\(624\) 0.488830 + 1.18014i 0.0195688 + 0.0472434i
\(625\) 24.3113i 0.972452i
\(626\) 19.7903 8.19743i 0.790981 0.327635i
\(627\) 3.03831 + 3.03831i 0.121338 + 0.121338i
\(628\) 1.58858 0.0633912
\(629\) −21.7250 + 28.9775i −0.866231 + 1.15541i
\(630\) 45.5824 1.81605
\(631\) −21.5640 21.5640i −0.858447 0.858447i 0.132708 0.991155i \(-0.457633\pi\)
−0.991155 + 0.132708i \(0.957633\pi\)
\(632\) 0.798506 0.330752i 0.0317629 0.0131566i
\(633\) 11.2660i 0.447784i
\(634\) −3.49503 8.43774i −0.138805 0.335105i
\(635\) 28.2122 + 11.6859i 1.11957 + 0.463739i
\(636\) 13.8874 33.5271i 0.550670 1.32943i
\(637\) −4.65992 + 4.65992i −0.184633 + 0.184633i
\(638\) 0.718852 0.718852i 0.0284596 0.0284596i
\(639\) 19.5542 47.2081i 0.773554 1.86752i
\(640\) −19.7722 8.18992i −0.781565 0.323735i
\(641\) 9.65860 + 23.3179i 0.381492 + 0.921003i 0.991678 + 0.128744i \(0.0410947\pi\)
−0.610186 + 0.792258i \(0.708905\pi\)
\(642\) 23.0354i 0.909134i
\(643\) −18.5426 + 7.68059i −0.731248 + 0.302893i −0.717065 0.697007i \(-0.754515\pi\)
−0.0141833 + 0.999899i \(0.504515\pi\)
\(644\) −13.9661 13.9661i −0.550343 0.550343i
\(645\) 9.93176 0.391063
\(646\) −7.60953 12.8463i −0.299393 0.505430i
\(647\) −41.8015 −1.64339 −0.821693 0.569930i \(-0.806970\pi\)
−0.821693 + 0.569930i \(0.806970\pi\)
\(648\) 32.4615 + 32.4615i 1.27521 + 1.27521i
\(649\) −2.44024 + 1.01078i −0.0957879 + 0.0396766i
\(650\) 24.7428i 0.970494i
\(651\) 25.4568 + 61.4582i 0.997731 + 2.40874i
\(652\) 9.23467 + 3.82513i 0.361658 + 0.149804i
\(653\) 7.08207 17.0976i 0.277143 0.669082i −0.722611 0.691254i \(-0.757058\pi\)
0.999754 + 0.0221728i \(0.00705839\pi\)
\(654\) −11.9253 + 11.9253i −0.466317 + 0.466317i
\(655\) 23.9347 23.9347i 0.935206 0.935206i
\(656\) 0.237751 0.573981i 0.00928261 0.0224102i
\(657\) −62.0275 25.6927i −2.41993 1.00237i
\(658\) 3.57052 + 8.62000i 0.139193 + 0.336043i
\(659\) 10.7730i 0.419658i 0.977738 + 0.209829i \(0.0672908\pi\)
−0.977738 + 0.209829i \(0.932709\pi\)
\(660\) −3.75959 + 1.55727i −0.146342 + 0.0606168i
\(661\) 4.11861 + 4.11861i 0.160195 + 0.160195i 0.782653 0.622458i \(-0.213866\pi\)
−0.622458 + 0.782653i \(0.713866\pi\)
\(662\) 17.1518 0.666625
\(663\) 56.1336 + 42.0843i 2.18005 + 1.63442i
\(664\) 30.9775 1.20216
\(665\) −22.2013 22.2013i −0.860929 0.860929i
\(666\) 48.2841 19.9999i 1.87097 0.774981i
\(667\) 23.0452i 0.892312i
\(668\) −7.08221 17.0980i −0.274019 0.661540i
\(669\) 82.5678 + 34.2007i 3.19226 + 1.32228i
\(670\) 2.00487 4.84018i 0.0774549 0.186993i
\(671\) −2.34188 + 2.34188i −0.0904071 + 0.0904071i
\(672\) 29.8519 29.8519i 1.15156 1.15156i
\(673\) −8.19181 + 19.7768i −0.315771 + 0.762339i 0.683698 + 0.729765i \(0.260370\pi\)
−0.999469 + 0.0325740i \(0.989630\pi\)
\(674\) 4.84295 + 2.00602i 0.186544 + 0.0772689i
\(675\) 22.8848 + 55.2488i 0.880837 + 2.12653i
\(676\) 20.4174i 0.785285i
\(677\) 7.07753 2.93161i 0.272012 0.112671i −0.242508 0.970149i \(-0.577970\pi\)
0.514520 + 0.857478i \(0.327970\pi\)
\(678\) −5.30331 5.30331i −0.203672 0.203672i
\(679\) −22.5888 −0.866880
\(680\) 36.9603 5.28686i 1.41736 0.202742i
\(681\) −19.8743 −0.761584
\(682\) 1.86036 + 1.86036i 0.0712367 + 0.0712367i
\(683\) −17.9875 + 7.45067i −0.688273 + 0.285092i −0.699281 0.714847i \(-0.746496\pi\)
0.0110074 + 0.999939i \(0.496496\pi\)
\(684\) 33.6445i 1.28643i
\(685\) 23.7380 + 57.3086i 0.906982 + 2.18965i
\(686\) −16.1264 6.67976i −0.615708 0.255034i
\(687\) −12.9313 + 31.2190i −0.493361 + 1.19108i
\(688\) −0.0530828 + 0.0530828i −0.00202376 + 0.00202376i
\(689\) −36.7932 + 36.7932i −1.40171 + 1.40171i
\(690\) −22.6068 + 54.5775i −0.860624 + 2.07773i
\(691\) 21.2962 + 8.82117i 0.810145 + 0.335573i 0.749012 0.662557i \(-0.230529\pi\)
0.0611332 + 0.998130i \(0.480529\pi\)
\(692\) 0.241734 + 0.583598i 0.00918936 + 0.0221851i
\(693\) 5.44573i 0.206866i
\(694\) 8.01850 3.32137i 0.304378 0.126077i
\(695\) −28.3831 28.3831i −1.07663 1.07663i
\(696\) −30.3823 −1.15164
\(697\) −4.83173 33.7785i −0.183015 1.27945i
\(698\) −18.5783 −0.703199
\(699\) −30.2528 30.2528i −1.14427 1.14427i
\(700\) 13.9177 5.76490i 0.526040 0.217893i
\(701\) 34.0976i 1.28785i −0.765089 0.643924i \(-0.777305\pi\)
0.765089 0.643924i \(-0.222695\pi\)
\(702\) −21.4813 51.8605i −0.810760 1.95735i
\(703\) −33.2583 13.7760i −1.25436 0.519573i
\(704\) 0.658269 1.58920i 0.0248094 0.0598953i
\(705\) −30.8131 + 30.8131i −1.16049 + 1.16049i
\(706\) 7.10303 7.10303i 0.267326 0.267326i
\(707\) −7.76366 + 18.7431i −0.291983 + 0.704908i
\(708\) 27.6204 + 11.4407i 1.03804 + 0.429969i
\(709\) −7.25734 17.5208i −0.272555 0.658006i 0.727036 0.686599i \(-0.240897\pi\)
−0.999591 + 0.0285932i \(0.990897\pi\)
\(710\) 21.3464i 0.801115i
\(711\) −1.89016 + 0.782931i −0.0708866 + 0.0293622i
\(712\) −3.03595 3.03595i −0.113777 0.113777i
\(713\) −59.6398 −2.23353
\(714\) −6.78401 + 26.4997i −0.253885 + 0.991725i
\(715\) 5.83482 0.218210
\(716\) 9.52935 + 9.52935i 0.356129 + 0.356129i
\(717\) 62.9738 26.0846i 2.35180 0.974147i
\(718\) 24.2104i 0.903524i
\(719\) −15.3426 37.0403i −0.572183 1.38137i −0.899693 0.436523i \(-0.856210\pi\)
0.327510 0.944848i \(-0.393790\pi\)
\(720\) −1.48667 0.615797i −0.0554047 0.0229494i
\(721\) −0.367986 + 0.888397i −0.0137045 + 0.0330856i
\(722\) −1.37738 + 1.37738i −0.0512607 + 0.0512607i
\(723\) 52.4381 52.4381i 1.95019 1.95019i
\(724\) −6.92045 + 16.7074i −0.257196 + 0.620927i
\(725\) −16.2389 6.72636i −0.603096 0.249811i
\(726\) 11.4854 + 27.7283i 0.426265 + 1.02909i
\(727\) 13.1530i 0.487819i −0.969798 0.243910i \(-0.921570\pi\)
0.969798 0.243910i \(-0.0784300\pi\)
\(728\) −34.4945 + 14.2881i −1.27845 + 0.529552i
\(729\) 0.246218 + 0.246218i 0.00911918 + 0.00911918i
\(730\) 28.0473 1.03808
\(731\) −1.02255 + 3.99429i −0.0378205 + 0.147734i
\(732\) 37.4866 1.38554
\(733\) 27.2575 + 27.2575i 1.00678 + 1.00678i 0.999977 + 0.00680041i \(0.00216465\pi\)
0.00680041 + 0.999977i \(0.497835\pi\)
\(734\) −2.13537 + 0.884500i −0.0788180 + 0.0326475i
\(735\) 12.0006i 0.442649i
\(736\) 14.4843 + 34.9683i 0.533900 + 1.28895i
\(737\) −0.578257 0.239522i −0.0213004 0.00882290i
\(738\) −18.8432 + 45.4914i −0.693627 + 1.67456i
\(739\) −7.83798 + 7.83798i −0.288325 + 0.288325i −0.836418 0.548093i \(-0.815354\pi\)
0.548093 + 0.836418i \(0.315354\pi\)
\(740\) 24.1073 24.1073i 0.886201 0.886201i
\(741\) −26.6861 + 64.4261i −0.980340 + 2.36675i
\(742\) −18.7434 7.76378i −0.688093 0.285017i
\(743\) −5.25184 12.6791i −0.192671 0.465150i 0.797791 0.602934i \(-0.206002\pi\)
−0.990462 + 0.137784i \(0.956002\pi\)
\(744\) 78.6279i 2.88264i
\(745\) 19.8165 8.20826i 0.726020 0.300727i
\(746\) −14.2307 14.2307i −0.521021 0.521021i
\(747\) −73.3275 −2.68291
\(748\) −0.239215 1.67234i −0.00874657 0.0611469i
\(749\) −20.1095 −0.734784
\(750\) −0.832422 0.832422i −0.0303957 0.0303957i
\(751\) 50.1528 20.7740i 1.83010 0.758053i 0.862274 0.506441i \(-0.169039\pi\)
0.967828 0.251612i \(-0.0809607\pi\)
\(752\) 0.329377i 0.0120111i
\(753\) −23.5633 56.8869i −0.858695 2.07307i
\(754\) 15.2429 + 6.31384i 0.555115 + 0.229936i
\(755\) 25.2684 61.0033i 0.919611 2.22014i
\(756\) −24.1662 + 24.1662i −0.878918 + 0.878918i
\(757\) −21.8212 + 21.8212i −0.793104 + 0.793104i −0.981998 0.188894i \(-0.939510\pi\)
0.188894 + 0.981998i \(0.439510\pi\)
\(758\) −4.92675 + 11.8942i −0.178948 + 0.432018i
\(759\) 6.52038 + 2.70083i 0.236675 + 0.0980339i
\(760\) 14.2019 + 34.2863i 0.515156 + 1.24370i
\(761\) 21.0626i