Properties

Label 105.3.o.b.74.14
Level 105
Weight 3
Character 105.74
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 74.14
Character \(\chi\) \(=\) 105.74
Dual form 105.3.o.b.44.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.897800 + 1.55504i) q^{2} +(2.08367 + 2.15832i) q^{3} +(0.387909 - 0.671879i) q^{4} +(-4.89966 + 0.996641i) q^{5} +(-1.48554 + 5.17791i) q^{6} +(1.39571 + 6.85945i) q^{7} +8.57546 q^{8} +(-0.316668 + 8.99443i) q^{9} +O(q^{10})\) \(q+(0.897800 + 1.55504i) q^{2} +(2.08367 + 2.15832i) q^{3} +(0.387909 - 0.671879i) q^{4} +(-4.89966 + 0.996641i) q^{5} +(-1.48554 + 5.17791i) q^{6} +(1.39571 + 6.85945i) q^{7} +8.57546 q^{8} +(-0.316668 + 8.99443i) q^{9} +(-5.94873 - 6.72437i) q^{10} +(1.00783 + 0.581870i) q^{11} +(2.25840 - 0.562740i) q^{12} -12.4799i q^{13} +(-9.41362 + 8.32879i) q^{14} +(-12.3603 - 8.49836i) q^{15} +(6.14742 + 10.6476i) q^{16} +(9.31485 - 16.1338i) q^{17} +(-14.2710 + 7.58277i) q^{18} +(-15.2033 - 26.3329i) q^{19} +(-1.23100 + 3.67859i) q^{20} +(-11.8967 + 17.3052i) q^{21} +2.08961i q^{22} +(13.7201 + 23.7640i) q^{23} +(17.8684 + 18.5086i) q^{24} +(23.0134 - 9.76641i) q^{25} +(19.4067 - 11.2045i) q^{26} +(-20.0727 + 18.0579i) q^{27} +(5.15012 + 1.72310i) q^{28} -52.6691i q^{29} +(2.11815 - 26.8506i) q^{30} +(-17.2838 + 29.9364i) q^{31} +(6.11262 - 10.5874i) q^{32} +(0.844119 + 3.38764i) q^{33} +33.4515 q^{34} +(-13.6749 - 32.2180i) q^{35} +(5.92032 + 3.70178i) q^{36} +(-0.357210 + 0.206235i) q^{37} +(27.2991 - 47.2834i) q^{38} +(26.9356 - 26.0040i) q^{39} +(-42.0169 + 8.54666i) q^{40} -17.2132i q^{41} +(-37.5910 - 2.96317i) q^{42} +7.86972i q^{43} +(0.781892 - 0.451426i) q^{44} +(-7.41265 - 44.3853i) q^{45} +(-24.6359 + 42.6706i) q^{46} +(17.4089 + 30.1530i) q^{47} +(-10.1718 + 35.4542i) q^{48} +(-45.1040 + 19.1475i) q^{49} +(35.8486 + 27.0184i) q^{50} +(54.2309 - 13.5130i) q^{51} +(-8.38498 - 4.84107i) q^{52} +(-17.8667 + 30.9460i) q^{53} +(-46.1019 - 15.0013i) q^{54} +(-5.51794 - 1.84653i) q^{55} +(11.9688 + 58.8229i) q^{56} +(25.1561 - 87.6825i) q^{57} +(81.9023 - 47.2863i) q^{58} +(-32.3428 - 18.6731i) q^{59} +(-10.5046 + 5.00805i) q^{60} +(25.4414 + 44.0659i) q^{61} -62.0697 q^{62} +(-62.1388 + 10.3814i) q^{63} +71.1310 q^{64} +(12.4380 + 61.1474i) q^{65} +(-4.51005 + 4.35406i) q^{66} +(-24.9784 - 14.4213i) q^{67} +(-7.22664 - 12.5169i) q^{68} +(-22.7020 + 79.1285i) q^{69} +(37.8228 - 50.1902i) q^{70} +66.8477i q^{71} +(-2.71557 + 77.1314i) q^{72} +(-46.7701 - 27.0027i) q^{73} +(-0.641406 - 0.370316i) q^{74} +(69.0313 + 29.3203i) q^{75} -23.5900 q^{76} +(-2.58468 + 7.72527i) q^{77} +(64.6199 + 18.5395i) q^{78} +(-16.6402 - 28.8216i) q^{79} +(-40.7321 - 46.0431i) q^{80} +(-80.7994 - 5.69649i) q^{81} +(26.7672 - 15.4540i) q^{82} -72.0714 q^{83} +(7.01214 + 14.7060i) q^{84} +(-29.5601 + 88.3338i) q^{85} +(-12.2377 + 7.06544i) q^{86} +(113.677 - 109.745i) q^{87} +(8.64260 + 4.98981i) q^{88} +(-41.4850 + 23.9513i) q^{89} +(62.3656 - 51.3760i) q^{90} +(85.6053 - 17.4183i) q^{91} +21.2887 q^{92} +(-100.626 + 25.0736i) q^{93} +(-31.2594 + 54.1428i) q^{94} +(100.736 + 113.870i) q^{95} +(35.5876 - 8.86757i) q^{96} +66.7480i q^{97} +(-70.2695 - 52.9477i) q^{98} +(-5.55274 + 8.88059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.897800 + 1.55504i 0.448900 + 0.777518i 0.998315 0.0580320i \(-0.0184826\pi\)
−0.549415 + 0.835550i \(0.685149\pi\)
\(3\) 2.08367 + 2.15832i 0.694556 + 0.719439i
\(4\) 0.387909 0.671879i 0.0969773 0.167970i
\(5\) −4.89966 + 0.996641i −0.979933 + 0.199328i
\(6\) −1.48554 + 5.17791i −0.247591 + 0.862986i
\(7\) 1.39571 + 6.85945i 0.199386 + 0.979921i
\(8\) 8.57546 1.07193
\(9\) −0.316668 + 8.99443i −0.0351853 + 0.999381i
\(10\) −5.94873 6.72437i −0.594873 0.672437i
\(11\) 1.00783 + 0.581870i 0.0916208 + 0.0528973i 0.545110 0.838364i \(-0.316488\pi\)
−0.453490 + 0.891262i \(0.649821\pi\)
\(12\) 2.25840 0.562740i 0.188200 0.0468950i
\(13\) 12.4799i 0.959993i −0.877270 0.479996i \(-0.840638\pi\)
0.877270 0.479996i \(-0.159362\pi\)
\(14\) −9.41362 + 8.32879i −0.672401 + 0.594913i
\(15\) −12.3603 8.49836i −0.824022 0.566558i
\(16\) 6.14742 + 10.6476i 0.384213 + 0.665477i
\(17\) 9.31485 16.1338i 0.547933 0.949047i −0.450483 0.892785i \(-0.648748\pi\)
0.998416 0.0562623i \(-0.0179183\pi\)
\(18\) −14.2710 + 7.58277i −0.792831 + 0.421265i
\(19\) −15.2033 26.3329i −0.800174 1.38594i −0.919501 0.393087i \(-0.871407\pi\)
0.119327 0.992855i \(-0.461926\pi\)
\(20\) −1.23100 + 3.67859i −0.0615502 + 0.183929i
\(21\) −11.8967 + 17.3052i −0.566508 + 0.824056i
\(22\) 2.08961i 0.0949824i
\(23\) 13.7201 + 23.7640i 0.596527 + 1.03322i 0.993329 + 0.115311i \(0.0367865\pi\)
−0.396802 + 0.917904i \(0.629880\pi\)
\(24\) 17.8684 + 18.5086i 0.744517 + 0.771190i
\(25\) 23.0134 9.76641i 0.920537 0.390656i
\(26\) 19.4067 11.2045i 0.746412 0.430941i
\(27\) −20.0727 + 18.0579i −0.743432 + 0.668812i
\(28\) 5.15012 + 1.72310i 0.183933 + 0.0615392i
\(29\) 52.6691i 1.81617i −0.418781 0.908087i \(-0.637543\pi\)
0.418781 0.908087i \(-0.362457\pi\)
\(30\) 2.11815 26.8506i 0.0706049 0.895020i
\(31\) −17.2838 + 29.9364i −0.557542 + 0.965692i 0.440158 + 0.897920i \(0.354922\pi\)
−0.997701 + 0.0677718i \(0.978411\pi\)
\(32\) 6.11262 10.5874i 0.191019 0.330855i
\(33\) 0.844119 + 3.38764i 0.0255794 + 0.102656i
\(34\) 33.4515 0.983868
\(35\) −13.6749 32.2180i −0.390711 0.920513i
\(36\) 5.92032 + 3.70178i 0.164453 + 0.102827i
\(37\) −0.357210 + 0.206235i −0.00965431 + 0.00557392i −0.504819 0.863225i \(-0.668441\pi\)
0.495165 + 0.868799i \(0.335108\pi\)
\(38\) 27.2991 47.2834i 0.718396 1.24430i
\(39\) 26.9356 26.0040i 0.690656 0.666768i
\(40\) −42.0169 + 8.54666i −1.05042 + 0.213666i
\(41\) 17.2132i 0.419835i −0.977719 0.209918i \(-0.932680\pi\)
0.977719 0.209918i \(-0.0673195\pi\)
\(42\) −37.5910 2.96317i −0.895024 0.0705516i
\(43\) 7.86972i 0.183017i 0.995804 + 0.0915084i \(0.0291688\pi\)
−0.995804 + 0.0915084i \(0.970831\pi\)
\(44\) 0.781892 0.451426i 0.0177703 0.0102597i
\(45\) −7.41265 44.3853i −0.164726 0.986339i
\(46\) −24.6359 + 42.6706i −0.535562 + 0.927621i
\(47\) 17.4089 + 30.1530i 0.370401 + 0.641554i 0.989627 0.143659i \(-0.0458868\pi\)
−0.619226 + 0.785213i \(0.712553\pi\)
\(48\) −10.1718 + 35.4542i −0.211913 + 0.738629i
\(49\) −45.1040 + 19.1475i −0.920490 + 0.390766i
\(50\) 35.8486 + 27.0184i 0.716971 + 0.540368i
\(51\) 54.2309 13.5130i 1.06335 0.264962i
\(52\) −8.38498 4.84107i −0.161250 0.0930975i
\(53\) −17.8667 + 30.9460i −0.337107 + 0.583886i −0.983887 0.178790i \(-0.942782\pi\)
0.646780 + 0.762676i \(0.276115\pi\)
\(54\) −46.1019 15.0013i −0.853740 0.277802i
\(55\) −5.51794 1.84653i −0.100326 0.0335732i
\(56\) 11.9688 + 58.8229i 0.213729 + 1.05041i
\(57\) 25.1561 87.6825i 0.441336 1.53829i
\(58\) 81.9023 47.2863i 1.41211 0.815281i
\(59\) −32.3428 18.6731i −0.548184 0.316494i 0.200205 0.979754i \(-0.435839\pi\)
−0.748389 + 0.663260i \(0.769172\pi\)
\(60\) −10.5046 + 5.00805i −0.175076 + 0.0834675i
\(61\) 25.4414 + 44.0659i 0.417073 + 0.722391i 0.995644 0.0932408i \(-0.0297226\pi\)
−0.578571 + 0.815632i \(0.696389\pi\)
\(62\) −62.0697 −1.00112
\(63\) −62.1388 + 10.3814i −0.986330 + 0.164784i
\(64\) 71.1310 1.11142
\(65\) 12.4380 + 61.1474i 0.191354 + 0.940729i
\(66\) −4.51005 + 4.35406i −0.0683341 + 0.0659706i
\(67\) −24.9784 14.4213i −0.372812 0.215243i 0.301874 0.953348i \(-0.402388\pi\)
−0.674686 + 0.738105i \(0.735721\pi\)
\(68\) −7.22664 12.5169i −0.106274 0.184072i
\(69\) −22.7020 + 79.1285i −0.329014 + 1.14679i
\(70\) 37.8228 50.1902i 0.540325 0.717004i
\(71\) 66.8477i 0.941518i 0.882262 + 0.470759i \(0.156020\pi\)
−0.882262 + 0.470759i \(0.843980\pi\)
\(72\) −2.71557 + 77.1314i −0.0377163 + 1.07127i
\(73\) −46.7701 27.0027i −0.640686 0.369900i 0.144192 0.989550i \(-0.453942\pi\)
−0.784879 + 0.619649i \(0.787275\pi\)
\(74\) −0.641406 0.370316i −0.00866765 0.00500427i
\(75\) 69.0313 + 29.3203i 0.920417 + 0.390937i
\(76\) −23.5900 −0.310395
\(77\) −2.58468 + 7.72527i −0.0335672 + 0.100328i
\(78\) 64.6199 + 18.5395i 0.828460 + 0.237685i
\(79\) −16.6402 28.8216i −0.210635 0.364831i 0.741278 0.671198i \(-0.234220\pi\)
−0.951914 + 0.306367i \(0.900887\pi\)
\(80\) −40.7321 46.0431i −0.509152 0.575538i
\(81\) −80.7994 5.69649i −0.997524 0.0703270i
\(82\) 26.7672 15.4540i 0.326429 0.188464i
\(83\) −72.0714 −0.868330 −0.434165 0.900833i \(-0.642957\pi\)
−0.434165 + 0.900833i \(0.642957\pi\)
\(84\) 7.01214 + 14.7060i 0.0834779 + 0.175071i
\(85\) −29.5601 + 88.3338i −0.347765 + 1.03922i
\(86\) −12.2377 + 7.06544i −0.142299 + 0.0821562i
\(87\) 113.677 109.745i 1.30663 1.26143i
\(88\) 8.64260 + 4.98981i 0.0982114 + 0.0567024i
\(89\) −41.4850 + 23.9513i −0.466123 + 0.269116i −0.714615 0.699518i \(-0.753398\pi\)
0.248492 + 0.968634i \(0.420065\pi\)
\(90\) 62.3656 51.3760i 0.692951 0.570845i
\(91\) 85.6053 17.4183i 0.940717 0.191410i
\(92\) 21.2887 0.231398
\(93\) −100.626 + 25.0736i −1.08200 + 0.269609i
\(94\) −31.2594 + 54.1428i −0.332546 + 0.575987i
\(95\) 100.736 + 113.870i 1.06037 + 1.19863i
\(96\) 35.5876 8.86757i 0.370704 0.0923706i
\(97\) 66.7480i 0.688124i 0.938947 + 0.344062i \(0.111803\pi\)
−0.938947 + 0.344062i \(0.888197\pi\)
\(98\) −70.2695 52.9477i −0.717036 0.540283i
\(99\) −5.55274 + 8.88059i −0.0560883 + 0.0897029i
\(100\) 2.36527 19.2507i 0.0236527 0.192507i
\(101\) −19.3539 11.1740i −0.191623 0.110633i 0.401119 0.916026i \(-0.368621\pi\)
−0.592742 + 0.805392i \(0.701955\pi\)
\(102\) 69.7018 + 72.1990i 0.683351 + 0.707833i
\(103\) 12.8487 7.41823i 0.124745 0.0720216i −0.436329 0.899787i \(-0.643722\pi\)
0.561074 + 0.827766i \(0.310388\pi\)
\(104\) 107.021i 1.02905i
\(105\) 41.0427 96.6463i 0.390883 0.920441i
\(106\) −64.1628 −0.605309
\(107\) 16.9958 + 29.4376i 0.158840 + 0.275118i 0.934450 0.356093i \(-0.115891\pi\)
−0.775611 + 0.631211i \(0.782558\pi\)
\(108\) 4.34636 + 20.4912i 0.0402440 + 0.189734i
\(109\) 45.3155 78.4888i 0.415739 0.720081i −0.579767 0.814782i \(-0.696856\pi\)
0.995506 + 0.0947015i \(0.0301897\pi\)
\(110\) −2.08259 10.2384i −0.0189327 0.0930764i
\(111\) −1.18943 0.341247i −0.0107156 0.00307429i
\(112\) −64.4569 + 57.0288i −0.575508 + 0.509186i
\(113\) −76.2557 −0.674830 −0.337415 0.941356i \(-0.609552\pi\)
−0.337415 + 0.941356i \(0.609552\pi\)
\(114\) 158.935 39.6027i 1.39416 0.347392i
\(115\) −90.9081 102.761i −0.790505 0.893577i
\(116\) −35.3872 20.4308i −0.305062 0.176128i
\(117\) 112.250 + 3.95198i 0.959398 + 0.0337776i
\(118\) 67.0590i 0.568297i
\(119\) 123.670 + 41.3767i 1.03924 + 0.347703i
\(120\) −105.996 72.8774i −0.883296 0.607312i
\(121\) −59.8229 103.616i −0.494404 0.856332i
\(122\) −45.6827 + 79.1247i −0.374448 + 0.648563i
\(123\) 37.1516 35.8666i 0.302046 0.291599i
\(124\) 13.4091 + 23.2253i 0.108138 + 0.187300i
\(125\) −103.024 + 70.7882i −0.824195 + 0.566306i
\(126\) −71.9317 87.3076i −0.570886 0.692917i
\(127\) 0.573646i 0.00451690i −0.999997 0.00225845i \(-0.999281\pi\)
0.999997 0.00225845i \(-0.000718888\pi\)
\(128\) 39.4109 + 68.2617i 0.307898 + 0.533295i
\(129\) −16.9854 + 16.3979i −0.131669 + 0.127115i
\(130\) −83.9195 + 74.2396i −0.645535 + 0.571074i
\(131\) 199.680 115.285i 1.52427 0.880039i 0.524686 0.851296i \(-0.324183\pi\)
0.999587 0.0287429i \(-0.00915041\pi\)
\(132\) 2.60352 + 0.746951i 0.0197237 + 0.00565872i
\(133\) 159.410 141.039i 1.19857 1.06045i
\(134\) 51.7898i 0.386491i
\(135\) 80.3520 108.483i 0.595200 0.803577i
\(136\) 79.8792 138.355i 0.587347 1.01731i
\(137\) 13.9490 24.1603i 0.101817 0.176353i −0.810616 0.585578i \(-0.800868\pi\)
0.912433 + 0.409225i \(0.134201\pi\)
\(138\) −143.430 + 35.7392i −1.03934 + 0.258980i
\(139\) −130.478 −0.938693 −0.469346 0.883014i \(-0.655510\pi\)
−0.469346 + 0.883014i \(0.655510\pi\)
\(140\) −26.9512 3.30978i −0.192508 0.0236413i
\(141\) −28.8056 + 100.403i −0.204295 + 0.712076i
\(142\) −103.951 + 60.0159i −0.732047 + 0.422647i
\(143\) 7.26169 12.5776i 0.0507810 0.0879553i
\(144\) −97.7161 + 51.9207i −0.678584 + 0.360561i
\(145\) 52.4921 + 258.061i 0.362015 + 1.77973i
\(146\) 96.9723i 0.664194i
\(147\) −135.308 57.4517i −0.920464 0.390828i
\(148\) 0.320002i 0.00216218i
\(149\) −137.529 + 79.4024i −0.923013 + 0.532902i −0.884595 0.466360i \(-0.845565\pi\)
−0.0384179 + 0.999262i \(0.512232\pi\)
\(150\) 16.3822 + 133.670i 0.109215 + 0.891133i
\(151\) 24.0390 41.6367i 0.159198 0.275740i −0.775381 0.631493i \(-0.782442\pi\)
0.934580 + 0.355753i \(0.115776\pi\)
\(152\) −130.375 225.817i −0.857733 1.48564i
\(153\) 142.165 + 88.8908i 0.929180 + 0.580986i
\(154\) −14.3336 + 2.91649i −0.0930753 + 0.0189382i
\(155\) 54.8490 163.904i 0.353865 1.05745i
\(156\) −7.02294 28.1846i −0.0450188 0.180671i
\(157\) 112.848 + 65.1528i 0.718777 + 0.414986i 0.814302 0.580441i \(-0.197120\pi\)
−0.0955254 + 0.995427i \(0.530453\pi\)
\(158\) 29.8791 51.7522i 0.189108 0.327545i
\(159\) −104.019 + 25.9192i −0.654210 + 0.163014i
\(160\) −19.3980 + 57.9666i −0.121237 + 0.362292i
\(161\) −143.858 + 127.280i −0.893530 + 0.790559i
\(162\) −63.6835 130.760i −0.393108 0.807163i
\(163\) 121.121 69.9292i 0.743073 0.429013i −0.0801127 0.996786i \(-0.525528\pi\)
0.823185 + 0.567773i \(0.192195\pi\)
\(164\) −11.5652 6.67717i −0.0705195 0.0407145i
\(165\) −7.51216 15.7570i −0.0455282 0.0954970i
\(166\) −64.7057 112.074i −0.389794 0.675142i
\(167\) 224.419 1.34383 0.671915 0.740629i \(-0.265472\pi\)
0.671915 + 0.740629i \(0.265472\pi\)
\(168\) −102.020 + 148.400i −0.607259 + 0.883333i
\(169\) 13.2519 0.0784136
\(170\) −163.901 + 33.3391i −0.964125 + 0.196113i
\(171\) 241.664 128.406i 1.41324 0.750914i
\(172\) 5.28750 + 3.05274i 0.0307413 + 0.0177485i
\(173\) 146.827 + 254.312i 0.848711 + 1.47001i 0.882359 + 0.470577i \(0.155954\pi\)
−0.0336474 + 0.999434i \(0.510712\pi\)
\(174\) 272.716 + 78.2422i 1.56733 + 0.449668i
\(175\) 99.1121 + 144.228i 0.566355 + 0.824161i
\(176\) 14.3080i 0.0812954i
\(177\) −27.0891 108.715i −0.153046 0.614207i
\(178\) −74.4904 43.0071i −0.418485 0.241613i
\(179\) 211.424 + 122.066i 1.18114 + 0.681933i 0.956278 0.292458i \(-0.0944731\pi\)
0.224863 + 0.974390i \(0.427806\pi\)
\(180\) −32.6969 12.2371i −0.181650 0.0679837i
\(181\) 81.3669 0.449541 0.224771 0.974412i \(-0.427837\pi\)
0.224771 + 0.974412i \(0.427837\pi\)
\(182\) 103.942 + 117.481i 0.571112 + 0.645501i
\(183\) −42.0967 + 146.729i −0.230036 + 0.801799i
\(184\) 117.656 + 203.787i 0.639437 + 1.10754i
\(185\) 1.54466 1.36649i 0.00834954 0.00738644i
\(186\) −129.332 133.966i −0.695336 0.720248i
\(187\) 18.7756 10.8401i 0.100404 0.0579683i
\(188\) 27.0122 0.143682
\(189\) −151.883 112.484i −0.803613 0.595152i
\(190\) −86.6317 + 258.880i −0.455956 + 1.36253i
\(191\) −207.381 + 119.732i −1.08577 + 0.626867i −0.932446 0.361310i \(-0.882330\pi\)
−0.153319 + 0.988177i \(0.548996\pi\)
\(192\) 148.213 + 153.523i 0.771944 + 0.799600i
\(193\) 1.39114 + 0.803175i 0.00720798 + 0.00416153i 0.503600 0.863937i \(-0.332009\pi\)
−0.496392 + 0.868099i \(0.665342\pi\)
\(194\) −103.796 + 59.9264i −0.535029 + 0.308899i
\(195\) −106.059 + 154.256i −0.543891 + 0.791055i
\(196\) −4.63145 + 37.7319i −0.0236298 + 0.192510i
\(197\) −286.325 −1.45343 −0.726713 0.686941i \(-0.758953\pi\)
−0.726713 + 0.686941i \(0.758953\pi\)
\(198\) −18.7949 0.661713i −0.0949236 0.00334199i
\(199\) −44.6292 + 77.3000i −0.224267 + 0.388442i −0.956099 0.293043i \(-0.905332\pi\)
0.731832 + 0.681485i \(0.238665\pi\)
\(200\) 197.351 83.7515i 0.986753 0.418757i
\(201\) −20.9210 83.9605i −0.104084 0.417714i
\(202\) 40.1280i 0.198653i
\(203\) 361.281 73.5105i 1.77971 0.362121i
\(204\) 11.9575 41.6784i 0.0586154 0.204306i
\(205\) 17.1554 + 84.3391i 0.0836849 + 0.411410i
\(206\) 23.0712 + 13.3202i 0.111996 + 0.0646610i
\(207\) −218.088 + 115.879i −1.05356 + 0.559804i
\(208\) 132.882 76.7192i 0.638853 0.368842i
\(209\) 35.3854i 0.169308i
\(210\) 187.137 22.9462i 0.891126 0.109268i
\(211\) 174.205 0.825617 0.412808 0.910818i \(-0.364548\pi\)
0.412808 + 0.910818i \(0.364548\pi\)
\(212\) 13.8613 + 24.0085i 0.0653835 + 0.113247i
\(213\) −144.279 + 139.288i −0.677365 + 0.653936i
\(214\) −30.5177 + 52.8582i −0.142606 + 0.247001i
\(215\) −7.84328 38.5590i −0.0364804 0.179344i
\(216\) −172.132 + 154.855i −0.796909 + 0.716921i
\(217\) −229.471 76.7750i −1.05747 0.353802i
\(218\) 162.737 0.746501
\(219\) −39.1728 157.209i −0.178871 0.717851i
\(220\) −3.38110 + 2.99110i −0.0153686 + 0.0135959i
\(221\) −201.348 116.249i −0.911078 0.526011i
\(222\) −0.537217 2.15597i −0.00241989 0.00971158i
\(223\) 149.196i 0.669041i −0.942388 0.334521i \(-0.891426\pi\)
0.942388 0.334521i \(-0.108574\pi\)
\(224\) 81.1549 + 27.1523i 0.362299 + 0.121216i
\(225\) 80.5557 + 210.085i 0.358025 + 0.933712i
\(226\) −68.4624 118.580i −0.302931 0.524692i
\(227\) −46.1279 + 79.8959i −0.203207 + 0.351964i −0.949560 0.313586i \(-0.898470\pi\)
0.746353 + 0.665550i \(0.231803\pi\)
\(228\) −49.1537 50.9147i −0.215586 0.223310i
\(229\) −74.0138 128.196i −0.323205 0.559807i 0.657943 0.753068i \(-0.271427\pi\)
−0.981147 + 0.193261i \(0.938094\pi\)
\(230\) 78.1802 233.625i 0.339914 1.01576i
\(231\) −22.0592 + 10.5183i −0.0954943 + 0.0455339i
\(232\) 451.661i 1.94682i
\(233\) −201.616 349.210i −0.865306 1.49875i −0.866743 0.498755i \(-0.833791\pi\)
0.00143686 0.999999i \(-0.499543\pi\)
\(234\) 94.6323 + 178.100i 0.404411 + 0.761112i
\(235\) −115.349 130.389i −0.490848 0.554848i
\(236\) −25.0922 + 14.4870i −0.106323 + 0.0613855i
\(237\) 27.5337 95.9695i 0.116176 0.404935i
\(238\) 46.6885 + 229.459i 0.196170 + 0.964113i
\(239\) 42.1167i 0.176220i 0.996111 + 0.0881102i \(0.0280828\pi\)
−0.996111 + 0.0881102i \(0.971917\pi\)
\(240\) 14.5034 183.851i 0.0604307 0.766047i
\(241\) −133.166 + 230.650i −0.552554 + 0.957052i 0.445535 + 0.895265i \(0.353014\pi\)
−0.998089 + 0.0617877i \(0.980320\pi\)
\(242\) 107.418 186.053i 0.443876 0.768815i
\(243\) −156.064 186.260i −0.642240 0.766504i
\(244\) 39.4759 0.161786
\(245\) 201.911 138.769i 0.824128 0.566404i
\(246\) 89.1286 + 25.5710i 0.362312 + 0.103947i
\(247\) −328.632 + 189.736i −1.33049 + 0.768161i
\(248\) −148.217 + 256.719i −0.597648 + 1.03516i
\(249\) −150.173 155.553i −0.603104 0.624711i
\(250\) −202.574 96.6529i −0.810294 0.386612i
\(251\) 426.902i 1.70081i −0.526133 0.850403i \(-0.676358\pi\)
0.526133 0.850403i \(-0.323642\pi\)
\(252\) −17.1292 + 45.7767i −0.0679729 + 0.181654i
\(253\) 31.9333i 0.126219i
\(254\) 0.892041 0.515020i 0.00351197 0.00202764i
\(255\) −252.246 + 120.258i −0.989198 + 0.471601i
\(256\) 71.4957 123.834i 0.279280 0.483727i
\(257\) −8.35527 14.4718i −0.0325108 0.0563103i 0.849312 0.527891i \(-0.177017\pi\)
−0.881823 + 0.471581i \(0.843684\pi\)
\(258\) −40.7487 11.6908i −0.157941 0.0453132i
\(259\) −1.91322 2.16242i −0.00738694 0.00834910i
\(260\) 45.9084 + 15.3628i 0.176571 + 0.0590877i
\(261\) 473.728 + 16.6786i 1.81505 + 0.0639026i
\(262\) 358.545 + 207.006i 1.36849 + 0.790099i
\(263\) 0.756335 1.31001i 0.00287580 0.00498103i −0.864584 0.502488i \(-0.832418\pi\)
0.867460 + 0.497507i \(0.165751\pi\)
\(264\) 7.23871 + 29.0506i 0.0274194 + 0.110040i
\(265\) 56.6986 169.432i 0.213957 0.639364i
\(266\) 362.439 + 121.263i 1.36255 + 0.455875i
\(267\) −138.135 39.6311i −0.517361 0.148431i
\(268\) −19.3787 + 11.1883i −0.0723087 + 0.0417474i
\(269\) 10.5890 + 6.11353i 0.0393641 + 0.0227269i 0.519553 0.854438i \(-0.326099\pi\)
−0.480189 + 0.877165i \(0.659432\pi\)
\(270\) 240.835 + 27.5542i 0.891981 + 0.102053i
\(271\) −117.307 203.182i −0.432868 0.749749i 0.564251 0.825603i \(-0.309165\pi\)
−0.997119 + 0.0758540i \(0.975832\pi\)
\(272\) 229.049 0.842092
\(273\) 215.967 + 148.469i 0.791088 + 0.543844i
\(274\) 50.0935 0.182823
\(275\) 28.8764 + 3.54795i 0.105005 + 0.0129016i
\(276\) 44.3584 + 45.9477i 0.160719 + 0.166477i
\(277\) 427.929 + 247.065i 1.54487 + 0.891930i 0.998521 + 0.0543719i \(0.0173156\pi\)
0.546348 + 0.837558i \(0.316018\pi\)
\(278\) −117.143 202.898i −0.421379 0.729850i
\(279\) −263.788 164.938i −0.945477 0.591175i
\(280\) −117.269 276.284i −0.418816 0.986728i
\(281\) 67.0586i 0.238643i 0.992856 + 0.119321i \(0.0380719\pi\)
−0.992856 + 0.119321i \(0.961928\pi\)
\(282\) −181.991 + 45.3479i −0.645360 + 0.160808i
\(283\) 118.530 + 68.4334i 0.418834 + 0.241814i 0.694579 0.719417i \(-0.255591\pi\)
−0.275744 + 0.961231i \(0.588924\pi\)
\(284\) 44.9136 + 25.9309i 0.158146 + 0.0913058i
\(285\) −35.8686 + 454.687i −0.125855 + 1.59539i
\(286\) 26.0782 0.0911825
\(287\) 118.073 24.0246i 0.411405 0.0837094i
\(288\) 93.2917 + 58.3322i 0.323929 + 0.202542i
\(289\) −29.0330 50.2867i −0.100460 0.174002i
\(290\) −354.166 + 313.314i −1.22126 + 1.08039i
\(291\) −144.063 + 139.081i −0.495063 + 0.477940i
\(292\) −36.2851 + 20.9492i −0.124264 + 0.0717439i
\(293\) −98.9599 −0.337747 −0.168874 0.985638i \(-0.554013\pi\)
−0.168874 + 0.985638i \(0.554013\pi\)
\(294\) −32.1403 261.989i −0.109321 0.891120i
\(295\) 177.079 + 59.2579i 0.600269 + 0.200874i
\(296\) −3.06324 + 1.76856i −0.0103488 + 0.00597487i
\(297\) −30.7372 + 6.51961i −0.103492 + 0.0219515i
\(298\) −246.947 142.575i −0.828681 0.478439i
\(299\) 296.572 171.226i 0.991879 0.572662i
\(300\) 46.4776 35.0070i 0.154925 0.116690i
\(301\) −53.9819 + 10.9838i −0.179342 + 0.0364911i
\(302\) 86.3287 0.285857
\(303\) −16.2101 65.0547i −0.0534986 0.214702i
\(304\) 186.922 323.759i 0.614875 1.06500i
\(305\) −168.572 190.552i −0.552696 0.624761i
\(306\) −10.5930 + 300.877i −0.0346177 + 0.983259i
\(307\) 441.330i 1.43756i 0.695239 + 0.718778i \(0.255298\pi\)
−0.695239 + 0.718778i \(0.744702\pi\)
\(308\) 4.18782 + 4.73329i 0.0135968 + 0.0153678i
\(309\) 42.7834 + 12.2746i 0.138458 + 0.0397235i
\(310\) 304.120 61.8612i 0.981034 0.199552i
\(311\) 19.4380 + 11.2225i 0.0625015 + 0.0360853i 0.530925 0.847419i \(-0.321845\pi\)
−0.468424 + 0.883504i \(0.655178\pi\)
\(312\) 230.985 222.996i 0.740337 0.714731i
\(313\) −217.506 + 125.577i −0.694908 + 0.401206i −0.805448 0.592666i \(-0.798075\pi\)
0.110540 + 0.993872i \(0.464742\pi\)
\(314\) 233.977i 0.745149i
\(315\) 294.113 112.795i 0.933691 0.358081i
\(316\) −25.8195 −0.0817074
\(317\) 17.4496 + 30.2237i 0.0550462 + 0.0953428i 0.892235 0.451570i \(-0.149136\pi\)
−0.837189 + 0.546913i \(0.815803\pi\)
\(318\) −133.694 138.484i −0.420421 0.435483i
\(319\) 30.6466 53.0814i 0.0960707 0.166399i
\(320\) −348.518 + 70.8920i −1.08912 + 0.221538i
\(321\) −28.1221 + 98.0206i −0.0876079 + 0.305360i
\(322\) −327.081 109.433i −1.01578 0.339854i
\(323\) −566.466 −1.75377
\(324\) −35.1702 + 52.0777i −0.108550 + 0.160734i
\(325\) −121.884 287.205i −0.375027 0.883709i
\(326\) 217.485 + 125.565i 0.667131 + 0.385168i
\(327\) 263.826 65.7392i 0.806808 0.201037i
\(328\) 147.611i 0.450035i
\(329\) −182.535 + 161.500i −0.554819 + 0.490881i
\(330\) 17.7583 25.8283i 0.0538130 0.0782676i
\(331\) 136.010 + 235.577i 0.410908 + 0.711713i 0.994989 0.0999821i \(-0.0318786\pi\)
−0.584082 + 0.811695i \(0.698545\pi\)
\(332\) −27.9572 + 48.4232i −0.0842083 + 0.145853i
\(333\) −1.74185 3.27820i −0.00523078 0.00984446i
\(334\) 201.484 + 348.980i 0.603245 + 1.04485i
\(335\) 136.759 + 45.7650i 0.408235 + 0.136612i
\(336\) −257.393 20.2894i −0.766051 0.0603851i
\(337\) 600.523i 1.78197i −0.454036 0.890983i \(-0.650016\pi\)
0.454036 0.890983i \(-0.349984\pi\)
\(338\) 11.8976 + 20.6072i 0.0351999 + 0.0609680i
\(339\) −158.892 164.584i −0.468707 0.485499i
\(340\) 47.8829 + 54.1263i 0.140832 + 0.159195i
\(341\) −34.8383 + 20.1139i −0.102165 + 0.0589850i
\(342\) 416.642 + 260.513i 1.21825 + 0.761733i
\(343\) −194.293 282.664i −0.566453 0.824094i
\(344\) 67.4865i 0.196182i
\(345\) 32.3694 410.329i 0.0938243 1.18936i
\(346\) −263.643 + 456.643i −0.761973 + 1.31978i
\(347\) −77.0212 + 133.405i −0.221963 + 0.384451i −0.955404 0.295302i \(-0.904580\pi\)
0.733441 + 0.679753i \(0.237913\pi\)
\(348\) −29.6390 118.948i −0.0851694 0.341804i
\(349\) −20.2324 −0.0579726 −0.0289863 0.999580i \(-0.509228\pi\)
−0.0289863 + 0.999580i \(0.509228\pi\)
\(350\) −135.297 + 283.611i −0.386563 + 0.810317i
\(351\) 225.361 + 250.505i 0.642055 + 0.713689i
\(352\) 12.3210 7.11351i 0.0350027 0.0202088i
\(353\) 162.715 281.830i 0.460948 0.798386i −0.538060 0.842907i \(-0.680843\pi\)
0.999008 + 0.0445203i \(0.0141760\pi\)
\(354\) 144.735 139.729i 0.408855 0.394714i
\(355\) −66.6232 327.531i −0.187671 0.922624i
\(356\) 37.1638i 0.104393i
\(357\) 168.382 + 353.134i 0.471659 + 0.989170i
\(358\) 438.363i 1.22448i
\(359\) −499.939 + 288.640i −1.39259 + 0.804011i −0.993601 0.112945i \(-0.963972\pi\)
−0.398987 + 0.916957i \(0.630638\pi\)
\(360\) −63.5669 380.624i −0.176575 1.05729i
\(361\) −281.781 + 488.059i −0.780556 + 1.35196i
\(362\) 73.0513 + 126.528i 0.201799 + 0.349526i
\(363\) 98.9858 345.018i 0.272688 0.950464i
\(364\) 21.5041 64.2730i 0.0590772 0.176574i
\(365\) 256.070 + 85.6913i 0.701561 + 0.234771i
\(366\) −265.964 + 66.2718i −0.726677 + 0.181071i
\(367\) 435.739 + 251.574i 1.18730 + 0.685487i 0.957692 0.287796i \(-0.0929226\pi\)
0.229607 + 0.973283i \(0.426256\pi\)
\(368\) −168.687 + 292.174i −0.458388 + 0.793950i
\(369\) 154.823 + 5.45088i 0.419575 + 0.0147720i
\(370\) 3.51174 + 1.17517i 0.00949120 + 0.00317614i
\(371\) −237.209 79.3640i −0.639377 0.213919i
\(372\) −22.1874 + 77.3348i −0.0596434 + 0.207889i
\(373\) −185.731 + 107.232i −0.497938 + 0.287484i −0.727861 0.685724i \(-0.759486\pi\)
0.229924 + 0.973209i \(0.426152\pi\)
\(374\) 33.7134 + 19.4644i 0.0901428 + 0.0520440i
\(375\) −367.452 74.8603i −0.979872 0.199627i
\(376\) 149.289 + 258.576i 0.397045 + 0.687703i
\(377\) −657.305 −1.74351
\(378\) 38.5559 337.171i 0.102000 0.891987i
\(379\) −505.361 −1.33341 −0.666704 0.745323i \(-0.732295\pi\)
−0.666704 + 0.745323i \(0.732295\pi\)
\(380\) 115.583 23.5108i 0.304166 0.0618704i
\(381\) 1.23811 1.19529i 0.00324964 0.00313724i
\(382\) −372.374 214.990i −0.974800 0.562801i
\(383\) 202.429 + 350.617i 0.528535 + 0.915449i 0.999446 + 0.0332689i \(0.0105918\pi\)
−0.470912 + 0.882180i \(0.656075\pi\)
\(384\) −65.2112 + 227.296i −0.169821 + 0.591917i
\(385\) 4.96473 40.4272i 0.0128954 0.105006i
\(386\) 2.88436i 0.00747244i
\(387\) −70.7836 2.49209i −0.182903 0.00643950i
\(388\) 44.8466 + 25.8922i 0.115584 + 0.0667324i
\(389\) 168.810 + 97.4627i 0.433960 + 0.250547i 0.701032 0.713130i \(-0.252723\pi\)
−0.267072 + 0.963676i \(0.586056\pi\)
\(390\) −335.093 26.4343i −0.859213 0.0677802i
\(391\) 511.204 1.30743
\(392\) −386.788 + 164.199i −0.986703 + 0.418875i
\(393\) 664.888 + 190.756i 1.69183 + 0.485385i
\(394\) −257.063 445.245i −0.652443 1.13006i
\(395\) 110.256 + 124.632i 0.279129 + 0.315524i
\(396\) 3.81272 + 7.17563i 0.00962807 + 0.0181203i
\(397\) 500.171 288.774i 1.25988 0.727390i 0.286826 0.957983i \(-0.407400\pi\)
0.973050 + 0.230593i \(0.0740666\pi\)
\(398\) −160.272 −0.402694
\(399\) 636.564 + 50.1781i 1.59540 + 0.125760i
\(400\) 245.462 + 185.000i 0.613656 + 0.462501i
\(401\) 199.268 115.047i 0.496927 0.286901i −0.230517 0.973068i \(-0.574042\pi\)
0.727443 + 0.686168i \(0.240708\pi\)
\(402\) 111.779 107.913i 0.278057 0.268439i
\(403\) 373.604 + 215.700i 0.927057 + 0.535237i
\(404\) −15.0151 + 8.66897i −0.0371661 + 0.0214579i
\(405\) 401.567 52.6171i 0.991525 0.129919i
\(406\) 438.669 + 495.806i 1.08047 + 1.22120i
\(407\) −0.480008 −0.00117938
\(408\) 465.055 115.881i 1.13984 0.284021i
\(409\) 290.480 503.125i 0.710219 1.23014i −0.254556 0.967058i \(-0.581929\pi\)
0.964775 0.263077i \(-0.0847375\pi\)
\(410\) −115.748 + 102.397i −0.282313 + 0.249749i
\(411\) 81.2106 20.2357i 0.197593 0.0492354i
\(412\) 11.5104i 0.0279378i
\(413\) 82.9464 247.916i 0.200839 0.600281i
\(414\) −375.996 235.098i −0.908203 0.567869i
\(415\) 353.126 71.8293i 0.850905 0.173083i
\(416\) −132.129 76.2850i −0.317619 0.183377i
\(417\) −271.873 281.614i −0.651974 0.675332i
\(418\) 55.0256 31.7690i 0.131640 0.0760025i
\(419\) 220.813i 0.527000i −0.964659 0.263500i \(-0.915123\pi\)
0.964659 0.263500i \(-0.0848769\pi\)
\(420\) −49.0137 65.0657i −0.116699 0.154918i
\(421\) −747.852 −1.77637 −0.888185 0.459486i \(-0.848033\pi\)
−0.888185 + 0.459486i \(0.848033\pi\)
\(422\) 156.401 + 270.895i 0.370620 + 0.641932i
\(423\) −276.722 + 147.034i −0.654189 + 0.347599i
\(424\) −153.215 + 265.376i −0.361356 + 0.625887i
\(425\) 56.7973 462.267i 0.133641 1.08769i
\(426\) −346.132 99.3053i −0.812516 0.233111i
\(427\) −266.759 + 236.017i −0.624728 + 0.552734i
\(428\) 26.3714 0.0616153
\(429\) 42.2774 10.5345i 0.0985488 0.0245560i
\(430\) 52.9189 46.8149i 0.123067 0.108872i
\(431\) 310.115 + 179.045i 0.719523 + 0.415417i 0.814577 0.580055i \(-0.196969\pi\)
−0.0950539 + 0.995472i \(0.530302\pi\)
\(432\) −315.669 102.717i −0.730716 0.237770i
\(433\) 622.750i 1.43822i 0.694896 + 0.719110i \(0.255450\pi\)
−0.694896 + 0.719110i \(0.744550\pi\)
\(434\) −86.6310 425.764i −0.199611 0.981022i
\(435\) −447.601 + 651.007i −1.02897 + 1.49657i
\(436\) −35.1566 60.8931i −0.0806345 0.139663i
\(437\) 417.182 722.581i 0.954651 1.65350i
\(438\) 209.297 202.058i 0.477847 0.461319i
\(439\) 194.411 + 336.729i 0.442849 + 0.767036i 0.997900 0.0647799i \(-0.0206345\pi\)
−0.555051 + 0.831816i \(0.687301\pi\)
\(440\) −47.3189 15.8348i −0.107543 0.0359882i
\(441\) −157.938 411.748i −0.358136 0.933669i
\(442\) 417.472i 0.944506i
\(443\) 192.113 + 332.750i 0.433664 + 0.751128i 0.997186 0.0749733i \(-0.0238872\pi\)
−0.563522 + 0.826101i \(0.690554\pi\)
\(444\) −0.690666 + 0.666777i −0.00155555 + 0.00150175i
\(445\) 179.391 158.699i 0.403127 0.356627i
\(446\) 232.005 133.948i 0.520191 0.300333i
\(447\) −457.940 131.383i −1.02447 0.293922i
\(448\) 99.2779 + 487.919i 0.221602 + 1.08911i
\(449\) 33.9684i 0.0756535i −0.999284 0.0378267i \(-0.987957\pi\)
0.999284 0.0378267i \(-0.0120435\pi\)
\(450\) −254.367 + 313.881i −0.565260 + 0.697514i
\(451\) 10.0159 17.3480i 0.0222081 0.0384656i
\(452\) −29.5803 + 51.2346i −0.0654432 + 0.113351i
\(453\) 139.954 34.8733i 0.308950 0.0769830i
\(454\) −165.655 −0.364878
\(455\) −402.077 + 170.661i −0.883686 + 0.375080i
\(456\) 215.725 751.918i 0.473082 1.64894i
\(457\) −432.197 + 249.529i −0.945726 + 0.546015i −0.891751 0.452527i \(-0.850523\pi\)
−0.0539752 + 0.998542i \(0.517189\pi\)
\(458\) 132.899 230.188i 0.290173 0.502595i
\(459\) 104.369 + 492.055i 0.227383 + 1.07202i
\(460\) −104.307 + 21.2171i −0.226755 + 0.0461242i
\(461\) 816.492i 1.77113i 0.464513 + 0.885566i \(0.346229\pi\)
−0.464513 + 0.885566i \(0.653771\pi\)
\(462\) −36.1611 24.8595i −0.0782708 0.0538084i
\(463\) 353.851i 0.764258i −0.924109 0.382129i \(-0.875191\pi\)
0.924109 0.382129i \(-0.124809\pi\)
\(464\) 560.801 323.779i 1.20862 0.697799i
\(465\) 468.045 223.140i 1.00655 0.479872i
\(466\) 362.022 627.041i 0.776872 1.34558i
\(467\) −127.057 220.068i −0.272070 0.471238i 0.697322 0.716758i \(-0.254375\pi\)
−0.969392 + 0.245520i \(0.921041\pi\)
\(468\) 46.1979 73.8851i 0.0987135 0.157874i
\(469\) 64.0596 191.466i 0.136588 0.408243i
\(470\) 99.1994 296.436i 0.211063 0.630715i
\(471\) 94.5171 + 379.318i 0.200673 + 0.805347i
\(472\) −277.355 160.131i −0.587616 0.339260i
\(473\) −4.57916 + 7.93133i −0.00968109 + 0.0167681i
\(474\) 173.956 43.3456i 0.366995 0.0914464i
\(475\) −607.058 457.528i −1.27802 0.963217i
\(476\) 75.7728 67.0406i 0.159186 0.140842i
\(477\) −272.684 170.500i −0.571664 0.357442i
\(478\) −65.4930 + 37.8124i −0.137015 + 0.0791054i
\(479\) −220.662 127.400i −0.460673 0.265970i 0.251654 0.967817i \(-0.419025\pi\)
−0.712327 + 0.701847i \(0.752359\pi\)
\(480\) −165.529 + 78.9162i −0.344853 + 0.164409i
\(481\) 2.57379 + 4.45794i 0.00535092 + 0.00926807i
\(482\) −478.224 −0.992167
\(483\) −574.463 45.2829i −1.18936 0.0937535i
\(484\) −92.8234 −0.191784
\(485\) −66.5238 327.043i −0.137162 0.674315i
\(486\) 149.527 409.910i 0.307669 0.843437i
\(487\) 144.819 + 83.6115i 0.297370 + 0.171687i 0.641261 0.767323i \(-0.278412\pi\)
−0.343891 + 0.939010i \(0.611745\pi\)
\(488\) 218.172 + 377.885i 0.447074 + 0.774355i
\(489\) 403.305 + 115.708i 0.824754 + 0.236622i
\(490\) 397.067 + 189.392i 0.810340 + 0.386515i
\(491\) 663.001i 1.35031i −0.737677 0.675154i \(-0.764077\pi\)
0.737677 0.675154i \(-0.235923\pi\)
\(492\) −9.68657 38.8744i −0.0196881 0.0790130i
\(493\) −849.752 490.605i −1.72363 0.995141i
\(494\) −590.092 340.690i −1.19452 0.689655i
\(495\) 18.3558 49.0460i 0.0370824 0.0990828i
\(496\) −425.003 −0.856861
\(497\) −458.539 + 93.2998i −0.922613 + 0.187726i
\(498\) 107.065 373.180i 0.214991 0.749357i
\(499\) 213.627 + 370.012i 0.428109 + 0.741507i 0.996705 0.0811099i \(-0.0258465\pi\)
−0.568596 + 0.822617i \(0.692513\pi\)
\(500\) 7.59698 + 96.6793i 0.0151940 + 0.193359i
\(501\) 467.615 + 484.369i 0.933364 + 0.966803i
\(502\) 663.848 383.273i 1.32241 0.763492i
\(503\) 503.059 1.00012 0.500059 0.865991i \(-0.333312\pi\)
0.500059 + 0.865991i \(0.333312\pi\)
\(504\) −532.869 + 89.0254i −1.05728 + 0.176638i
\(505\) 105.964 + 35.4598i 0.209830 + 0.0702175i
\(506\) −49.6575 + 28.6698i −0.0981373 + 0.0566596i
\(507\) 27.6126 + 28.6018i 0.0544626 + 0.0564138i
\(508\) −0.385421 0.222523i −0.000758702 0.000438037i
\(509\) 481.244 277.846i 0.945469 0.545867i 0.0537984 0.998552i \(-0.482867\pi\)
0.891670 + 0.452685i \(0.149534\pi\)
\(510\) −413.472 284.283i −0.810729 0.557418i
\(511\) 119.947 358.505i 0.234729 0.701575i
\(512\) 572.043 1.11727
\(513\) 780.688 + 254.031i 1.52181 + 0.495188i
\(514\) 15.0027 25.9855i 0.0291882 0.0505554i
\(515\) −55.5612 + 49.1524i −0.107886 + 0.0954415i
\(516\) 4.42860 + 17.7730i 0.00858256 + 0.0344438i
\(517\) 40.5188i 0.0783729i
\(518\) 1.64495 4.91654i 0.00317557 0.00949139i
\(519\) −242.947 + 846.801i −0.468106 + 1.63160i
\(520\) 106.661 + 524.367i 0.205118 + 1.00840i
\(521\) 209.107 + 120.728i 0.401358 + 0.231724i 0.687070 0.726591i \(-0.258897\pi\)
−0.285712 + 0.958316i \(0.592230\pi\)
\(522\) 399.377 + 751.638i 0.765091 + 1.43992i
\(523\) −683.792 + 394.788i −1.30744 + 0.754852i −0.981669 0.190596i \(-0.938958\pi\)
−0.325773 + 0.945448i \(0.605625\pi\)
\(524\) 178.881i 0.341375i
\(525\) −104.774 + 514.439i −0.199569 + 0.979884i
\(526\) 2.71615 0.00516379
\(527\) 321.992 + 557.707i 0.610991 + 1.05827i
\(528\) −30.8812 + 29.8131i −0.0584871 + 0.0564642i
\(529\) −111.984 + 193.961i −0.211689 + 0.366656i
\(530\) 314.376 63.9473i 0.593163 0.120655i
\(531\) 178.196 284.992i 0.335586 0.536708i
\(532\) −32.9247 161.814i −0.0618885 0.304162i
\(533\) −214.820 −0.403039
\(534\) −62.3903 250.386i −0.116836 0.468888i
\(535\) −112.613 127.296i −0.210491 0.237936i
\(536\) −214.202 123.669i −0.399630 0.230726i
\(537\) 177.081 + 710.666i 0.329760 + 1.32340i
\(538\) 21.9549i 0.0408084i
\(539\) −56.5985 6.94725i −0.105007 0.0128891i
\(540\) −41.7181 96.0683i −0.0772557 0.177904i
\(541\) −394.171 682.723i −0.728596 1.26197i −0.957477 0.288511i \(-0.906840\pi\)
0.228880 0.973455i \(-0.426494\pi\)
\(542\) 210.637 364.834i 0.388629 0.673125i
\(543\) 169.542 + 175.616i 0.312231 + 0.323417i
\(544\) −113.876 197.240i −0.209332 0.362573i
\(545\) −143.806 + 429.732i −0.263864 + 0.788499i
\(546\) −36.9801 + 469.132i −0.0677291 + 0.859217i
\(547\) 2.30392i 0.00421191i −0.999998 0.00210596i \(-0.999330\pi\)
0.999998 0.00210596i \(-0.000670347\pi\)
\(548\) −10.8219 18.7440i −0.0197479 0.0342044i
\(549\) −404.404 + 214.877i −0.736619 + 0.391397i
\(550\) 20.4080 + 48.0891i 0.0371055 + 0.0874348i
\(551\) −1386.93 + 800.744i −2.51711 + 1.45326i
\(552\) −194.680 + 678.564i −0.352681 + 1.22928i
\(553\) 174.476 154.369i 0.315508 0.279148i
\(554\) 887.259i 1.60155i
\(555\) 6.16789 + 0.486563i 0.0111133 + 0.000876690i
\(556\) −50.6137 + 87.6656i −0.0910319 + 0.157672i
\(557\) 178.710 309.535i 0.320844 0.555718i −0.659819 0.751425i \(-0.729367\pi\)
0.980662 + 0.195707i \(0.0627003\pi\)
\(558\) 19.6555 558.281i 0.0352248 1.00050i
\(559\) 98.2134 0.175695
\(560\) 258.980 343.663i 0.462464 0.613683i
\(561\) 62.5183 + 17.9365i 0.111441 + 0.0319724i
\(562\) −104.279 + 60.2052i −0.185549 + 0.107127i
\(563\) 331.223 573.695i 0.588318 1.01900i −0.406135 0.913813i \(-0.633124\pi\)
0.994453 0.105183i \(-0.0335430\pi\)
\(564\) 56.2845 + 58.3010i 0.0997952 + 0.103371i
\(565\) 373.628 75.9996i 0.661288 0.134513i
\(566\) 245.758i 0.434202i
\(567\) −73.6975 562.190i −0.129978 0.991517i
\(568\) 573.250i 1.00924i
\(569\) 286.622 165.481i 0.503729 0.290828i −0.226523 0.974006i \(-0.572736\pi\)
0.730252 + 0.683178i \(0.239403\pi\)
\(570\) −739.257 + 352.441i −1.29694 + 0.618317i
\(571\) 420.825 728.890i 0.736996 1.27651i −0.216846 0.976206i \(-0.569577\pi\)
0.953842 0.300309i \(-0.0970897\pi\)
\(572\) −5.63375 9.75795i −0.00984922 0.0170593i
\(573\) −690.532 198.114i −1.20512 0.345748i
\(574\) 143.365 + 162.039i 0.249765 + 0.282298i
\(575\) 547.835 + 412.893i 0.952757 + 0.718075i
\(576\) −22.5249 + 639.782i −0.0391057 + 1.11073i
\(577\) 446.025 + 257.513i 0.773007 + 0.446296i 0.833946 0.551845i \(-0.186076\pi\)
−0.0609390 + 0.998141i \(0.519410\pi\)
\(578\) 52.1317 90.2948i 0.0901933 0.156219i
\(579\) 1.16516 + 4.67607i 0.00201237 + 0.00807611i
\(580\) 193.748 + 64.8358i 0.334048 + 0.111786i
\(581\) −100.590 494.370i −0.173133 0.850895i
\(582\) −345.615 99.1571i −0.593841 0.170373i
\(583\) −36.0131 + 20.7922i −0.0617720 + 0.0356641i
\(584\) −401.075 231.561i −0.686773 0.396508i
\(585\) −553.924 + 92.5092i −0.946879 + 0.158135i
\(586\) −88.8462 153.886i −0.151615 0.262604i
\(587\) 935.242 1.59326 0.796629 0.604469i \(-0.206615\pi\)
0.796629 + 0.604469i \(0.206615\pi\)
\(588\) −91.0879 + 68.6246i −0.154911 + 0.116709i
\(589\) 1051.08 1.78452
\(590\) 66.8338 + 328.567i 0.113278 + 0.556893i
\(591\) −596.605 617.980i −1.00948 1.04565i
\(592\) −4.39183 2.53563i −0.00741863 0.00428315i
\(593\) 244.872 + 424.131i 0.412938 + 0.715229i 0.995210 0.0977651i \(-0.0311694\pi\)
−0.582272 + 0.812994i \(0.697836\pi\)
\(594\) −37.7341 41.9441i −0.0635254 0.0706130i
\(595\) −647.178 79.4777i −1.08769 0.133576i
\(596\) 123.204i 0.206718i
\(597\) −259.830 + 64.7435i −0.435226 + 0.108448i
\(598\) 532.525 + 307.453i 0.890510 + 0.514136i
\(599\) −406.061 234.439i −0.677898 0.391384i 0.121165 0.992632i \(-0.461337\pi\)
−0.799063 + 0.601248i \(0.794670\pi\)
\(600\) 591.975 + 251.435i 0.986625 + 0.419059i
\(601\) 679.264 1.13022 0.565112 0.825014i \(-0.308833\pi\)
0.565112 + 0.825014i \(0.308833\pi\)
\(602\) −65.5452 74.0825i −0.108879 0.123061i
\(603\) 137.621 220.100i 0.228227 0.365008i
\(604\) −18.6499 32.3025i −0.0308773 0.0534810i
\(605\) 396.380 + 448.063i 0.655174 + 0.740600i
\(606\) 86.6089 83.6133i 0.142919 0.137976i
\(607\) −530.707 + 306.404i −0.874312 + 0.504784i −0.868779 0.495201i \(-0.835095\pi\)
−0.00553303 + 0.999985i \(0.501761\pi\)
\(608\) −371.728 −0.611395
\(609\) 911.447 + 626.587i 1.49663 + 1.02888i
\(610\) 144.971 433.214i 0.237657 0.710186i
\(611\) 376.307 217.261i 0.615887 0.355583i
\(612\) 114.871 61.0358i 0.187697 0.0997316i
\(613\) −173.001 99.8821i −0.282220 0.162940i 0.352208 0.935922i \(-0.385431\pi\)
−0.634428 + 0.772982i \(0.718764\pi\)
\(614\) −686.284 + 396.226i −1.11773 + 0.645319i
\(615\) −146.284 + 212.761i −0.237861 + 0.345953i
\(616\) −22.1648 + 66.2478i −0.0359818 + 0.107545i
\(617\) 530.227 0.859363 0.429682 0.902980i \(-0.358626\pi\)
0.429682 + 0.902980i \(0.358626\pi\)
\(618\) 19.3236 + 77.5498i 0.0312679 + 0.125485i
\(619\) −410.628 + 711.228i −0.663373 + 1.14900i 0.316351 + 0.948642i \(0.397542\pi\)
−0.979724 + 0.200353i \(0.935791\pi\)
\(620\) −88.8473 100.432i −0.143302 0.161987i
\(621\) −704.527 229.249i −1.13450 0.369161i
\(622\) 40.3023i 0.0647947i
\(623\) −222.194 251.135i −0.356651 0.403106i
\(624\) 442.465 + 126.943i 0.709079 + 0.203435i
\(625\) 434.234 449.517i 0.694775 0.719227i
\(626\) −390.555 225.487i −0.623889 0.360202i
\(627\) 76.3729 73.7314i 0.121807 0.117594i
\(628\) 87.5496 50.5468i 0.139410 0.0804885i
\(629\) 7.68420i 0.0122165i
\(630\) 439.455 + 356.088i 0.697548 + 0.565219i
\(631\) 314.044 0.497692 0.248846 0.968543i \(-0.419949\pi\)
0.248846 + 0.968543i \(0.419949\pi\)
\(632\) −142.697 247.159i −0.225787 0.391074i
\(633\) 362.986 + 375.990i 0.573437 + 0.593981i
\(634\) −31.3326 + 54.2697i −0.0494205 + 0.0855988i
\(635\) 0.571720 + 2.81068i 0.000900346 + 0.00442626i
\(636\) −22.9356 + 79.9427i −0.0360622 + 0.125696i
\(637\) 238.959 + 562.894i 0.375133 + 0.883664i
\(638\) 110.058 0.172505
\(639\) −601.257 21.1685i −0.940935 0.0331276i
\(640\) −261.133 295.181i −0.408020 0.461220i
\(641\) 633.511 + 365.758i 0.988317 + 0.570605i 0.904771 0.425899i \(-0.140042\pi\)
0.0835460 + 0.996504i \(0.473375\pi\)
\(642\) −177.674 + 44.2720i −0.276750 + 0.0689595i
\(643\) 326.029i 0.507044i 0.967330 + 0.253522i \(0.0815890\pi\)
−0.967330 + 0.253522i \(0.918411\pi\)
\(644\) 29.7127 + 146.028i 0.0461377 + 0.226752i
\(645\) 66.8797 97.2724i 0.103690 0.150810i
\(646\) −508.574 880.875i −0.787266 1.36358i
\(647\) −286.539 + 496.301i −0.442874 + 0.767080i −0.997901 0.0647521i \(-0.979374\pi\)
0.555028 + 0.831832i \(0.312708\pi\)
\(648\) −692.893 48.8500i −1.06928 0.0753859i
\(649\) −21.7307 37.6387i −0.0334834 0.0579949i
\(650\) 337.187 447.387i 0.518749 0.688287i
\(651\) −312.435 655.244i −0.479932 1.00652i
\(652\) 108.505i 0.166418i
\(653\) −451.271 781.625i −0.691074 1.19698i −0.971486 0.237096i \(-0.923804\pi\)
0.280412 0.959880i \(-0.409529\pi\)
\(654\) 339.090 + 351.239i 0.518486 + 0.537062i
\(655\) −863.465 + 763.867i −1.31827 + 1.16621i
\(656\) 183.280 105.817i 0.279391 0.161306i
\(657\) 257.685 412.119i 0.392214 0.627275i
\(658\) −415.019 138.855i −0.630727 0.211025i
\(659\) 1144.56i 1.73681i −0.495855 0.868405i \(-0.665145\pi\)
0.495855 0.868405i \(-0.334855\pi\)
\(660\) −13.5008 1.06503i −0.0204558 0.00161369i
\(661\) −374.330 + 648.358i −0.566308 + 0.980875i 0.430618 + 0.902534i \(0.358296\pi\)
−0.996927 + 0.0783407i \(0.975038\pi\)
\(662\) −244.220 + 423.002i −0.368913 + 0.638976i
\(663\) −168.642 676.797i −0.254361 1.02081i
\(664\) −618.046 −0.930792
\(665\) −640.489 + 849.919i −0.963141 + 1.27807i
\(666\) 3.53389 5.65181i 0.00530614 0.00848620i
\(667\) 1251.62 722.626i 1.87650 1.08340i
\(668\) 87.0544 150.783i 0.130321 0.225723i
\(669\) 322.013 310.875i 0.481334 0.464686i
\(670\) 51.6158 + 253.753i 0.0770385 + 0.378735i
\(671\) 59.2145i 0.0882481i
\(672\) 110.496 + 231.735i 0.164429 + 0.344843i
\(673\) 351.912i 0.522900i 0.965217 + 0.261450i \(0.0842007\pi\)
−0.965217 + 0.261450i \(0.915799\pi\)
\(674\) 933.834 539.149i 1.38551 0.799925i
\(675\) −285.579 + 611.612i −0.423081 + 0.906092i
\(676\) 5.14054 8.90367i 0.00760434 0.0131711i
\(677\) −284.770 493.237i −0.420636 0.728562i 0.575366 0.817896i \(-0.304860\pi\)
−0.996002 + 0.0893336i \(0.971526\pi\)
\(678\) 113.281 394.846i 0.167082 0.582368i
\(679\) −457.854 + 93.1606i −0.674307 + 0.137203i
\(680\) −253.491 + 757.503i −0.372781 + 1.11397i
\(681\) −268.556 + 66.9177i −0.394355 + 0.0982639i
\(682\) −62.5556 36.1165i −0.0917238 0.0529567i
\(683\) −390.284 + 675.992i −0.571426 + 0.989740i 0.424993 + 0.905196i \(0.360276\pi\)
−0.996420 + 0.0845432i \(0.973057\pi\)
\(684\) 7.47020 212.179i 0.0109213 0.310203i
\(685\) −44.2661 + 132.280i −0.0646220 + 0.193109i
\(686\) 265.116 555.909i 0.386467 0.810363i
\(687\) 122.467 426.863i 0.178263 0.621343i
\(688\) −83.7939 + 48.3784i −0.121793 + 0.0703175i
\(689\) 386.203 + 222.974i 0.560527 + 0.323620i
\(690\) 667.137 318.058i 0.966866 0.460953i
\(691\) −237.246 410.922i −0.343337 0.594678i 0.641713 0.766945i \(-0.278224\pi\)
−0.985050 + 0.172267i \(0.944891\pi\)
\(692\) 227.822 0.329223
\(693\) −68.6659 25.6940i −0.0990850 0.0370765i
\(694\) −276.599 −0.398557
\(695\) 639.300 130.040i 0.919856 0.187108i
\(696\) 974.829 941.112i 1.40062 1.35217i
\(697\) −277.715 160.339i −0.398443 0.230041i
\(698\) −18.1647 31.4621i −0.0260239 0.0450747i
\(699\) 333.604 1162.79i 0.477259 1.66350i
\(700\) 135.350 10.6438i 0.193358 0.0152055i
\(701\) 319.674i 0.456025i −0.973658 0.228013i \(-0.926777\pi\)
0.973658 0.228013i \(-0.0732227\pi\)
\(702\) −187.215 + 575.348i −0.266688 + 0.819584i
\(703\) 10.8615 + 6.27091i 0.0154503 + 0.00892021i
\(704\) 71.6879 + 41.3890i 0.101829 + 0.0587912i
\(705\) 41.0721 520.648i 0.0582583 0.738508i
\(706\) 584.342 0.827679
\(707\) 49.6349 148.353i 0.0702050 0.209834i
\(708\) −83.5512 23.9709i −0.118010 0.0338571i
\(709\) 679.847 + 1177.53i 0.958882 + 1.66083i 0.725225 + 0.688512i \(0.241736\pi\)
0.233657 + 0.972319i \(0.424931\pi\)
\(710\) 449.509 397.659i 0.633111 0.560084i
\(711\) 264.504 140.542i 0.372016 0.197668i
\(712\) −355.753 + 205.394i −0.499653 + 0.288475i
\(713\) −948.544 −1.33036
\(714\) −397.962 + 578.884i −0.557370 + 0.810762i
\(715\) −23.0445 + 68.8634i −0.0322300 + 0.0963124i
\(716\) 164.027 94.7010i 0.229088 0.132264i
\(717\) −90.9012 + 87.7571i −0.126780 + 0.122395i
\(718\) −897.691 518.282i −1.25027 0.721842i
\(719\) 10.4725 6.04630i 0.0145654 0.00840932i −0.492700 0.870199i \(-0.663990\pi\)
0.507265 + 0.861790i \(0.330657\pi\)
\(720\) 427.030 351.782i 0.593097 0.488586i
\(721\) 68.8180 + 77.7816i 0.0954480 + 0.107880i
\(722\) −1011.93 −1.40157
\(723\) −775.288 + 193.183i −1.07232 + 0.267197i
\(724\) 31.5630 54.6687i 0.0435953 0.0755092i
\(725\) −514.388 1212.09i −0.709500 1.67185i
\(726\) 625.385 155.831i 0.861412 0.214643i
\(727\) 806.023i 1.10870i −0.832284 0.554349i \(-0.812967\pi\)
0.832284 0.554349i \(-0.187033\pi\)
\(728\) 734.105 149.370i 1.00839 0.205178i
\(729\) 76.8232 724.941i 0.105382 0.994432i
\(730\) 96.6465 + 475.131i 0.132392 + 0.650865i
\(731\) 126.968 + 73.3053i 0.173692 + 0.100281i
\(732\) 82.2546 + 85.2015i 0.112370 + 0.116395i
\(733\) −229.808 + 132.680i −0.313517 + 0.181009i −0.648499 0.761215i \(-0.724603\pi\)
0.334982 + 0.942224i \(0.391270\pi\)
\(734\) 903.452i 1.23086i
\(735\) 720.223 + 146.640i 0.979896 + 0.199511i
\(736\) 335.464 0.455793
\(737\) −16.7827 29.0684i −0.0227716 0.0394415i
\(738\) 130.524 + 245.649i 0.176862 + 0.332858i
\(739\) 288.214 499.201i 0.390005 0.675509i −0.602444 0.798161i \(-0.705807\pi\)
0.992450 + 0.122652i \(0.0391398\pi\)
\(740\) −0.318927 1.56790i −0.000430982 0.00211879i
\(741\) −1094.27 313.946i −1.47675 0.423679i
\(742\) −89.5524 440.121i −0.120691 0.593155i
\(743\) −142.356 −0.191596 −0.0957979 0.995401i \(-0.530540\pi\)
−0.0957979 + 0.995401i \(0.530540\pi\)
\(744\) −862.915 + 215.018i −1.15983 + 0.289002i
\(745\) 594.710 526.112i 0.798268 0.706190i
\(746\) −333.498 192.545i −0.447049 0.258104i
\(747\) 22.8227 648.241i 0.0305525 0.867793i
\(748\) 16.8199i 0.0224864i
\(749\) −178.205 + 157.668i −0.237924 + 0.210505i
\(750\) −213.488 638.610i −0.284651 0.851481i
\(751\) −39.6817 68.7308i −0.0528385 0.0915190i 0.838396 0.545061i \(-0.183494\pi\)
−0.891235 + 0.453542i \(0.850160\pi\)
\(752\) −214.039 + 370.726i −0.284626 + 0.492987i
\(753\) 921.390 889.522i 1.22363 1.18130i
\(754\) −590.129 1022.13i −0.782664 1.35561i
\(755\) −76.2860 + 227.964i −0.101041 + 0.301939i
\(756\) −134.492 + 58.4133i −0.177900 + 0.0772663i
\(757\) 1310.05i 1.73058i 0.501268 + 0.865292i \(0.332867\pi\)
−0.501268 + 0.865292i \(0.667133\pi\)
\(758\) −453.714 785.855i −0.598567 1.03675i
\(759\) −68.9223 + 66.5384i −0.0908067 + 0.0876659i
\(760\) 863.854 + 976.489i 1.13665 + 1.28485i
\(761\) 363.973 210.140i 0.478283 0.276137i −0.241418 0.970421i \(-0.577612\pi\)
0.719701 + 0.694284i \(0.244279\pi\)
\(762\) 2.97029 + 0.852177i 0.00389802 + 0.00111834i
\(763\) 601.637 + 201.292i 0.788515 + 0.263817i
\(764\) 185.780i 0.243167i
\(765\)