Properties

Label 105.3.o.b.44.7
Level 105
Weight 3
Character 105.44
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 44.7
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.897800 + 1.55504i) q^{2} +(-2.08367 + 2.15832i) q^{3} +(0.387909 + 0.671879i) q^{4} +(-3.31295 - 3.74491i) q^{5} +(-1.48554 - 5.17791i) q^{6} +(-1.39571 + 6.85945i) q^{7} -8.57546 q^{8} +(-0.316668 - 8.99443i) q^{9} +O(q^{10})\) \(q+(-0.897800 + 1.55504i) q^{2} +(-2.08367 + 2.15832i) q^{3} +(0.387909 + 0.671879i) q^{4} +(-3.31295 - 3.74491i) q^{5} +(-1.48554 - 5.17791i) q^{6} +(-1.39571 + 6.85945i) q^{7} -8.57546 q^{8} +(-0.316668 - 8.99443i) q^{9} +(8.79784 - 1.78957i) q^{10} +(1.00783 - 0.581870i) q^{11} +(-2.25840 - 0.562740i) q^{12} -12.4799i q^{13} +(-9.41362 - 8.32879i) q^{14} +(14.9858 + 0.652756i) 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} +(-3.04875 + 24.8134i) q^{25} +(19.4067 + 11.2045i) q^{26} +(20.0727 + 18.0579i) q^{27} +(-5.15012 + 1.72310i) q^{28} +52.6691i q^{29} +(-14.4693 + 22.7174i) q^{30} +(-17.2838 - 29.9364i) q^{31} +(-6.11262 - 10.5874i) q^{32} +(-0.844119 + 3.38764i) q^{33} +33.4515 q^{34} +(30.3119 - 17.4982i) 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} +(28.4101 + 32.1144i) q^{40} +17.2132i q^{41} +(37.5910 - 2.96317i) q^{42} +7.86972i q^{43} +(0.781892 + 0.451426i) q^{44} +(-32.6342 + 30.9840i) 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} +(5.37455 + 10.3218i) q^{60} +(25.4414 - 44.0659i) q^{61} +62.0697 q^{62} +(62.1388 + 10.3814i) q^{63} +71.1310 q^{64} +(-46.7362 + 41.3453i) 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} +(-0.00374100 + 62.8460i) q^{70} -66.8477i q^{71} +(2.71557 + 77.1314i) q^{72} +(46.7701 - 27.0027i) q^{73} +(-0.641406 + 0.370316i) q^{74} +(-47.2026 - 58.2830i) q^{75} -23.5900 q^{76} +(2.58468 + 7.72527i) q^{77} +(-64.6199 + 18.5395i) q^{78} +(-16.6402 + 28.8216i) q^{79} +(-60.2405 + 12.2535i) 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} +(-18.8821 - 78.5648i) q^{90} +(85.6053 + 17.4183i) q^{91} -21.2887 q^{92} +(100.626 + 25.0736i) q^{93} +(-31.2594 - 54.1428i) q^{94} +(148.982 - 30.3045i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 \(-0.981517\pi\)
0.549415 + 0.835550i \(0.314851\pi\)
\(3\) −2.08367 + 2.15832i −0.694556 + 0.719439i
\(4\) 0.387909 + 0.671879i 0.0969773 + 0.167970i
\(5\) −3.31295 3.74491i −0.662590 0.748983i
\(6\) −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
\(10\) 8.79784 1.78957i 0.879784 0.178957i
\(11\) 1.00783 0.581870i 0.0916208 0.0528973i −0.453490 0.891262i \(-0.649821\pi\)
0.545110 + 0.838364i \(0.316488\pi\)
\(12\) −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
\(15\) 14.9858 + 0.652756i 0.999053 + 0.0435171i
\(16\) 6.14742 10.6476i 0.384213 0.665477i
\(17\) −9.31485 16.1338i −0.547933 0.949047i −0.998416 0.0562623i \(-0.982082\pi\)
0.450483 0.892785i \(-0.351252\pi\)
\(18\) 14.2710 + 7.58277i 0.792831 + 0.421265i
\(19\) −15.2033 + 26.3329i −0.800174 + 1.38594i 0.119327 + 0.992855i \(0.461926\pi\)
−0.919501 + 0.393087i \(0.871407\pi\)
\(20\) 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 0.396802 + 0.917904i \(0.370120\pi\)
−0.993329 + 0.115311i \(0.963213\pi\)
\(24\) 17.8684 18.5086i 0.744517 0.771190i
\(25\) −3.04875 + 24.8134i −0.121950 + 0.992536i
\(26\) 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 \(0.362457\pi\)
−0.418781 + 0.908087i \(0.637543\pi\)
\(30\) −14.4693 + 22.7174i −0.482310 + 0.757246i
\(31\) −17.2838 29.9364i −0.557542 0.965692i −0.997701 0.0677718i \(-0.978411\pi\)
0.440158 0.897920i \(-0.354922\pi\)
\(32\) −6.11262 10.5874i −0.191019 0.330855i
\(33\) −0.844119 + 3.38764i −0.0255794 + 0.102656i
\(34\) 33.4515 0.983868
\(35\) 30.3119 17.4982i 0.866055 0.499948i
\(36\) 5.92032 3.70178i 0.164453 0.102827i
\(37\) 0.357210 + 0.206235i 0.00965431 + 0.00557392i 0.504819 0.863225i \(-0.331559\pi\)
−0.495165 + 0.868799i \(0.664892\pi\)
\(38\) −27.2991 47.2834i −0.718396 1.24430i
\(39\) 26.9356 + 26.0040i 0.690656 + 0.666768i
\(40\) 28.4101 + 32.1144i 0.710252 + 0.802859i
\(41\) 17.2132i 0.419835i 0.977719 + 0.209918i \(0.0673195\pi\)
−0.977719 + 0.209918i \(0.932680\pi\)
\(42\) 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
\(45\) −32.6342 + 30.9840i −0.725205 + 0.688533i
\(46\) −24.6359 42.6706i −0.535562 0.927621i
\(47\) −17.4089 + 30.1530i −0.370401 + 0.641554i −0.989627 0.143659i \(-0.954113\pi\)
0.619226 + 0.785213i \(0.287447\pi\)
\(48\) 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 \(-0.0572183\pi\)
−0.646780 + 0.762676i \(0.723885\pi\)
\(54\) −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 −0.748389 0.663260i \(-0.769172\pi\)
0.200205 + 0.979754i \(0.435839\pi\)
\(60\) 5.37455 + 10.3218i 0.0895759 + 0.172031i
\(61\) 25.4414 44.0659i 0.417073 0.722391i −0.578571 0.815632i \(-0.696389\pi\)
0.995644 + 0.0932408i \(0.0297226\pi\)
\(62\) 62.0697 1.00112
\(63\) 62.1388 + 10.3814i 0.986330 + 0.164784i
\(64\) 71.1310 1.11142
\(65\) −46.7362 + 41.3453i −0.719018 + 0.636081i
\(66\) −4.51005 4.35406i −0.0683341 0.0659706i
\(67\) 24.9784 14.4213i 0.372812 0.215243i −0.301874 0.953348i \(-0.597612\pi\)
0.674686 + 0.738105i \(0.264279\pi\)
\(68\) 7.22664 12.5169i 0.106274 0.184072i
\(69\) −22.7020 79.1285i −0.329014 1.14679i
\(70\) −0.00374100 + 62.8460i −5.34428e−5 + 0.897800i
\(71\) 66.8477i 0.941518i −0.882262 0.470759i \(-0.843980\pi\)
0.882262 0.470759i \(-0.156020\pi\)
\(72\) 2.71557 + 77.1314i 0.0377163 + 1.07127i
\(73\) 46.7701 27.0027i 0.640686 0.369900i −0.144192 0.989550i \(-0.546058\pi\)
0.784879 + 0.619649i \(0.212725\pi\)
\(74\) −0.641406 + 0.370316i −0.00866765 + 0.00500427i
\(75\) −47.2026 58.2830i −0.629368 0.777107i
\(76\) −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 −0.951914 0.306367i \(-0.900887\pi\)
0.741278 + 0.671198i \(0.234220\pi\)
\(80\) −60.2405 + 12.2535i −0.753007 + 0.153169i
\(81\) −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 \(-0.357043\pi\)
0.434165 + 0.900833i \(0.357043\pi\)
\(84\) 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 0.248492 0.968634i \(-0.420065\pi\)
−0.714615 + 0.699518i \(0.753398\pi\)
\(90\) −18.8821 78.5648i −0.209802 0.872943i
\(91\) 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
\(95\) 148.982 30.3045i 1.56823 0.318994i
\(96\) 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
\(100\) −17.8542 + 7.57696i −0.178542 + 0.0757696i
\(101\) −19.3539 + 11.1740i −0.191623 + 0.110633i −0.592742 0.805392i \(-0.701955\pi\)
0.401119 + 0.916026i \(0.368621\pi\)
\(102\) −69.7018 + 72.1990i −0.683351 + 0.707833i
\(103\) −12.8487 7.41823i −0.124745 0.0720216i 0.436329 0.899787i \(-0.356278\pi\)
−0.561074 + 0.827766i \(0.689612\pi\)
\(104\) 107.021i 1.02905i
\(105\) −25.3933 + 101.883i −0.241841 + 0.970316i
\(106\) −64.1628 −0.605309
\(107\) −16.9958 + 29.4376i −0.158840 + 0.275118i −0.934450 0.356093i \(-0.884109\pi\)
0.775611 + 0.631211i \(0.217442\pi\)
\(108\) −4.34636 + 20.4912i −0.0402440 + 0.189734i
\(109\) 45.3155 + 78.4888i 0.415739 + 0.720081i 0.995506 0.0947015i \(-0.0301897\pi\)
−0.579767 + 0.814782i \(0.696856\pi\)
\(110\) 7.82542 6.92278i 0.0711402 0.0629344i
\(111\) −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 \(-0.390448\pi\)
0.337415 + 0.941356i \(0.390448\pi\)
\(114\) 158.935 + 39.6027i 1.39416 + 0.347392i
\(115\) 134.448 27.3481i 1.16911 0.237809i
\(116\) −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
\(120\) −128.510 5.59769i −1.07092 0.0466474i
\(121\) −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
\(130\) −22.3337 109.796i −0.171797 0.844586i
\(131\) 199.680 + 115.285i 1.52427 + 0.880039i 0.999587 + 0.0287429i \(0.00915041\pi\)
0.524686 + 0.851296i \(0.324183\pi\)
\(132\) −2.60352 + 0.746951i −0.0197237 + 0.00565872i
\(133\) −159.410 141.039i −1.19857 1.06045i
\(134\) 51.7898i 0.386491i
\(135\) 1.12565 134.995i 0.00833815 0.999965i
\(136\) 79.8792 + 138.355i 0.587347 + 1.01731i
\(137\) −13.9490 24.1603i −0.101817 0.176353i 0.810616 0.585578i \(-0.199132\pi\)
−0.912433 + 0.409225i \(0.865799\pi\)
\(138\) 143.430 + 35.7392i 1.03934 + 0.258980i
\(139\) −130.478 −0.938693 −0.469346 0.883014i \(-0.655510\pi\)
−0.469346 + 0.883014i \(0.655510\pi\)
\(140\) 23.5149 + 13.5782i 0.167964 + 0.0969873i
\(141\) −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
\(145\) 197.241 174.490i 1.36028 1.20338i
\(146\) 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 −0.0384179 0.999262i \(-0.512232\pi\)
−0.884595 + 0.466360i \(0.845565\pi\)
\(150\) 133.011 21.0753i 0.886738 0.140502i
\(151\) 24.0390 + 41.6367i 0.159198 + 0.275740i 0.934580 0.355753i \(-0.115776\pi\)
−0.775381 + 0.631493i \(0.782442\pi\)
\(152\) 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 \(-0.802880\pi\)
0.0955254 + 0.995427i \(0.469547\pi\)
\(158\) −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 \(-0.474472\pi\)
−0.823185 + 0.567773i \(0.807805\pi\)
\(164\) −11.5652 + 6.67717i −0.0705195 + 0.0407145i
\(165\) 15.4829 8.06192i 0.0938360 0.0488601i
\(166\) −64.7057 + 112.074i −0.389794 + 0.675142i
\(167\) −224.419 −1.34383 −0.671915 0.740629i \(-0.734528\pi\)
−0.671915 + 0.740629i \(0.734528\pi\)
\(168\) 102.020 + 148.400i 0.607259 + 0.883333i
\(169\) 13.2519 0.0784136
\(170\) −110.823 125.273i −0.651901 0.736900i
\(171\) 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 0.0336474 + 0.999434i \(0.489288\pi\)
−0.882359 + 0.470577i \(0.844046\pi\)
\(174\) 272.716 78.2422i 1.56733 0.449668i
\(175\) −165.951 55.5449i −0.948292 0.317400i
\(176\) 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 0.224863 0.974390i \(-0.427806\pi\)
0.956278 + 0.292458i \(0.0944731\pi\)
\(180\) −33.4766 9.90728i −0.185981 0.0550405i
\(181\) 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
\(185\) −0.411085 2.02096i −0.00222208 0.0109241i
\(186\) −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 −0.153319 0.988177i \(-0.548996\pi\)
−0.932446 + 0.361310i \(0.882330\pi\)
\(192\) −148.213 + 153.523i −0.771944 + 0.799600i
\(193\) −1.39114 + 0.803175i −0.00720798 + 0.00416153i −0.503600 0.863937i \(-0.667991\pi\)
0.496392 + 0.868099i \(0.334658\pi\)
\(194\) −103.796 59.9264i −0.535029 0.308899i
\(195\) 8.14634 187.021i 0.0417761 0.959083i
\(196\) −4.63145 37.7319i −0.0236298 0.192510i
\(197\) 286.325 1.45343 0.726713 0.686941i \(-0.241047\pi\)
0.726713 + 0.686941i \(0.241047\pi\)
\(198\) 18.7949 0.661713i 0.0949236 0.00334199i
\(199\) −44.6292 77.3000i −0.224267 0.388442i 0.731832 0.681485i \(-0.238665\pi\)
−0.956099 + 0.293043i \(0.905332\pi\)
\(200\) 26.1444 212.786i 0.130722 1.06393i
\(201\) −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
\(205\) 64.4621 57.0266i 0.314449 0.278178i
\(206\) 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
\(210\) −135.634 130.958i −0.645876 0.623611i
\(211\) 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
\(215\) 29.4714 26.0720i 0.137076 0.121265i
\(216\) −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
\(220\) −0.899819 4.42367i −0.00409009 0.0201076i
\(221\) −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
\(225\) 224.148 + 19.5641i 0.996213 + 0.0869517i
\(226\) −68.4624 + 118.580i −0.302931 + 0.524692i
\(227\) 46.1279 + 79.8959i 0.203207 + 0.351964i 0.949560 0.313586i \(-0.101530\pi\)
−0.746353 + 0.665550i \(0.768197\pi\)
\(228\) 49.1537 50.9147i 0.215586 0.223310i
\(229\) −74.0138 + 128.196i −0.323205 + 0.559807i −0.981147 0.193261i \(-0.938094\pi\)
0.657943 + 0.753068i \(0.271427\pi\)
\(230\) −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 −0.00143686 0.999999i \(-0.500457\pi\)
0.866743 0.498755i \(-0.166209\pi\)
\(234\) 94.6323 178.100i 0.404411 0.761112i
\(235\) 170.595 34.7008i 0.725937 0.147663i
\(236\) −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 \(-0.971917\pi\)
0.996111 0.0881102i \(-0.0280828\pi\)
\(240\) 99.0742 155.550i 0.412809 0.648127i
\(241\) −133.166 230.650i −0.552554 0.957052i −0.998089 0.0617877i \(-0.980320\pi\)
0.445535 0.895265i \(-0.353014\pi\)
\(242\) −107.418 186.053i −0.443876 0.768815i
\(243\) 156.064 186.260i 0.642240 0.766504i
\(244\) 39.4759 0.161786
\(245\) 77.7214 + 232.345i 0.317230 + 0.948349i
\(246\) 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
\(250\) 17.5829 + 223.760i 0.0703316 + 0.895041i
\(251\) 426.902i 1.70081i 0.526133 + 0.850403i \(0.323642\pi\)
−0.526133 + 0.850403i \(0.676358\pi\)
\(252\) 17.1292 + 45.7767i 0.0679729 + 0.181654i
\(253\) 31.9333i 0.126219i
\(254\) 0.892041 + 0.515020i 0.00351197 + 0.00202764i
\(255\) −129.059 247.858i −0.506114 0.971993i
\(256\) 71.4957 + 123.834i 0.279280 + 0.483727i
\(257\) 8.35527 14.4718i 0.0325108 0.0563103i −0.849312 0.527891i \(-0.822983\pi\)
0.881823 + 0.471581i \(0.156316\pi\)
\(258\) 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 \(-0.167582\pi\)
−0.867460 + 0.497507i \(0.834249\pi\)
\(264\) 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 −0.480189 0.877165i \(-0.659432\pi\)
0.519553 + 0.854438i \(0.326099\pi\)
\(270\) 208.912 + 122.949i 0.773748 + 0.455368i
\(271\) −117.307 + 203.182i −0.432868 + 0.749749i −0.997119 0.0758540i \(-0.975832\pi\)
0.564251 + 0.825603i \(0.309165\pi\)
\(272\) −229.049 −0.842092
\(273\) −215.967 + 148.469i −0.791088 + 0.543844i
\(274\) 50.0935 0.182823
\(275\) 11.3656 + 26.7816i 0.0413293 + 0.0973878i
\(276\) 44.3584 45.9477i 0.160719 0.166477i
\(277\) −427.929 + 247.065i −1.54487 + 0.891930i −0.546348 + 0.837558i \(0.683982\pi\)
−0.998521 + 0.0543719i \(0.982684\pi\)
\(278\) 117.143 202.898i 0.421379 0.729850i
\(279\) −263.788 + 164.938i −0.945477 + 0.591175i
\(280\) −259.939 + 150.055i −0.928353 + 0.535911i
\(281\) 67.0586i 0.238643i −0.992856 0.119321i \(-0.961928\pi\)
0.992856 0.119321i \(-0.0380719\pi\)
\(282\) 181.991 + 45.3479i 0.645360 + 0.160808i
\(283\) −118.530 + 68.4334i −0.418834 + 0.241814i −0.694579 0.719417i \(-0.744409\pi\)
0.275744 + 0.961231i \(0.411076\pi\)
\(284\) 44.9136 25.9309i 0.158146 0.0913058i
\(285\) −245.022 + 384.695i −0.859728 + 1.34981i
\(286\) 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
\(290\) 94.2549 + 463.374i 0.325017 + 1.59784i
\(291\) −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 \(-0.445987\pi\)
0.168874 + 0.985638i \(0.445987\pi\)
\(294\) −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
\(300\) 20.8488 54.3230i 0.0694959 0.181077i
\(301\) −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
\(305\) −249.309 + 50.7120i −0.817407 + 0.166269i
\(306\) −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
\(310\) −205.634 232.445i −0.663334 0.749824i
\(311\) 19.4380 11.2225i 0.0625015 0.0360853i −0.468424 0.883504i \(-0.655178\pi\)
0.530925 + 0.847419i \(0.321845\pi\)
\(312\) −230.985 222.996i −0.740337 0.714731i
\(313\) 217.506 + 125.577i 0.694908 + 0.401206i 0.805448 0.592666i \(-0.201925\pi\)
−0.110540 + 0.993872i \(0.535258\pi\)
\(314\) 233.977i 0.745149i
\(315\) −166.985 267.097i −0.530111 0.847928i
\(316\) −25.8195 −0.0817074
\(317\) −17.4496 + 30.2237i −0.0550462 + 0.0953428i −0.892235 0.451570i \(-0.850864\pi\)
0.837189 + 0.546913i \(0.184197\pi\)
\(318\) 133.694 138.484i 0.420421 0.435483i
\(319\) 30.6466 + 53.0814i 0.0960707 + 0.166399i
\(320\) −235.653 266.379i −0.736416 0.832435i
\(321\) −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
\(325\) 309.669 + 38.0481i 0.952828 + 0.117071i
\(326\) 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
\(330\) −1.36401 + 31.3145i −0.00413336 + 0.0948925i
\(331\) 136.010 235.577i 0.410908 0.711713i −0.584082 0.811695i \(-0.698545\pi\)
0.994989 + 0.0999821i \(0.0318786\pi\)
\(332\) 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
\(340\) −70.8162 + 14.4047i −0.208283 + 0.0423668i
\(341\) −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
\(345\) −221.119 + 347.166i −0.640925 + 1.00628i
\(346\) −263.643 456.643i −0.761973 1.31978i
\(347\) 77.0212 + 133.405i 0.221963 + 0.384451i 0.955404 0.295302i \(-0.0954202\pi\)
−0.733441 + 0.679753i \(0.762087\pi\)
\(348\) 29.6390 118.948i 0.0851694 0.341804i
\(349\) −20.2324 −0.0579726 −0.0289863 0.999580i \(-0.509228\pi\)
−0.0289863 + 0.999580i \(0.509228\pi\)
\(350\) 235.365 208.192i 0.672472 0.594833i
\(351\) 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 \(-0.319157\pi\)
−0.999008 + 0.0445203i \(0.985824\pi\)
\(354\) 144.735 + 139.729i 0.408855 + 0.394714i
\(355\) −250.339 + 221.463i −0.705180 + 0.623840i
\(356\) 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 −0.398987 0.916957i \(-0.630638\pi\)
−0.993601 + 0.112945i \(0.963972\pi\)
\(360\) 279.854 265.702i 0.777371 0.738061i
\(361\) −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 \(-0.907077\pi\)
−0.229607 + 0.973283i \(0.573744\pi\)
\(368\) 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 \(-0.240514\pi\)
−0.229924 + 0.973209i \(0.573848\pi\)
\(374\) 33.7134 19.4644i 0.0901428 0.0520440i
\(375\) −61.8850 + 369.858i −0.165027 + 0.986289i
\(376\) 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 \(0.732295\pi\)
\(380\) 78.1525 + 88.3425i 0.205664 + 0.232480i
\(381\) 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 0.470912 + 0.882180i \(0.343925\pi\)
−0.999446 + 0.0332689i \(0.989408\pi\)
\(384\) −65.2112 227.296i −0.169821 0.591917i
\(385\) 20.3676 35.2728i 0.0529028 0.0916177i
\(386\) 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 −0.267072 0.963676i \(-0.586056\pi\)
0.701032 + 0.713130i \(0.252723\pi\)
\(390\) 283.511 + 180.576i 0.726951 + 0.463014i
\(391\) 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
\(395\) 163.063 33.1686i 0.412817 0.0839711i
\(396\) 3.81272 7.17563i 0.00962807 0.0181203i
\(397\) −500.171 288.774i −1.25988 0.727390i −0.286826 0.957983i \(-0.592600\pi\)
−0.973050 + 0.230593i \(0.925933\pi\)
\(398\) 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 0.727443 0.686168i \(-0.240708\pi\)
−0.230517 + 0.973068i \(0.574042\pi\)
\(402\) −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
\(405\) 289.017 + 283.715i 0.713623 + 0.700530i
\(406\) 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 0.964775 + 0.263077i \(0.0847375\pi\)
−0.254556 + 0.967058i \(0.581929\pi\)
\(410\) 30.8043 + 151.439i 0.0751324 + 0.369364i
\(411\) 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
\(415\) −238.769 269.901i −0.575347 0.650364i
\(416\) −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 \(0.0848769\pi\)
−0.964659 + 0.263500i \(0.915123\pi\)
\(420\) −78.3034 + 22.4602i −0.186437 + 0.0534767i
\(421\) −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
\(425\) 428.733 181.945i 1.00878 0.428107i
\(426\) −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
\(430\) 14.0834 + 69.2365i 0.0327521 + 0.161015i
\(431\) 310.115 179.045i 0.719523 0.415417i −0.0950539 0.995472i \(-0.530302\pi\)
0.814577 + 0.580055i \(0.196969\pi\)
\(432\) 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
\(435\) −34.3800 + 789.287i −0.0790346 + 1.81445i
\(436\) −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 −0.555051 0.831816i \(-0.687301\pi\)
0.997900 + 0.0647799i \(0.0206345\pi\)
\(440\) 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 \(-0.976113\pi\)
0.563522 + 0.826101i \(0.309446\pi\)
\(444\) −0.690666 0.666777i −0.00155555 0.00150175i
\(445\) 47.7418 + 234.707i 0.107285 + 0.527432i
\(446\) 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 \(0.0120435\pi\)
−0.999284 + 0.0378267i \(0.987957\pi\)
\(450\) −231.663 + 330.993i −0.514806 + 0.735540i
\(451\) 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
\(455\) −218.376 378.290i −0.479947 0.831407i
\(456\) 215.725 + 751.918i 0.473082 + 1.64894i
\(457\) 432.197 + 249.529i 0.945726 + 0.546015i 0.891751 0.452527i \(-0.149477\pi\)
0.0539752 + 0.998542i \(0.482811\pi\)
\(458\) −132.899 230.188i −0.290173 0.502595i
\(459\) 104.369 492.055i 0.227383 1.07202i
\(460\) 70.5282 + 79.7241i 0.153322 + 0.173313i
\(461\) 816.492i 1.77113i −0.464513 0.885566i \(-0.653771\pi\)
0.464513 0.885566i \(-0.346229\pi\)
\(462\) 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
\(465\) −239.470 459.903i −0.514990 0.989040i
\(466\) 362.022 + 627.041i 0.776872 + 1.34558i
\(467\) 127.057 220.068i 0.272070 0.471238i −0.697322 0.716758i \(-0.745625\pi\)
0.969392 + 0.245520i \(0.0789586\pi\)
\(468\) −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 −0.712327 0.701847i \(-0.752359\pi\)
0.251654 + 0.967817i \(0.419025\pi\)
\(480\) −84.6915 162.650i −0.176441 0.338855i
\(481\) 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
\(485\) 249.966 221.133i 0.515393 0.455944i
\(486\) 149.527 + 409.910i 0.307669 + 0.843437i
\(487\) −144.819 + 83.6115i −0.297370 + 0.171687i −0.641261 0.767323i \(-0.721588\pi\)
0.343891 + 0.939010i \(0.388255\pi\)
\(488\) −218.172 + 377.885i −0.447074 + 0.774355i
\(489\) 403.305 115.708i 0.824754 0.236622i
\(490\) −431.084 87.7402i −0.879763 0.179062i
\(491\) 663.001i 1.35031i 0.737677 + 0.675154i \(0.235923\pi\)
−0.737677 + 0.675154i \(0.764077\pi\)
\(492\) 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
\(495\) −14.8611 + 50.2154i −0.0300224 + 0.101445i
\(496\) −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 −0.568596 0.822617i \(-0.692513\pi\)
0.996705 + 0.0811099i \(0.0258465\pi\)
\(500\) 87.5252 + 41.7605i 0.175050 + 0.0835209i
\(501\) 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 \(-0.666688\pi\)
−0.500059 + 0.865991i \(0.666688\pi\)
\(504\) −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 0.891670 0.452685i \(-0.149534\pi\)
0.0537984 + 0.998552i \(0.482867\pi\)
\(510\) 501.297 + 21.8357i 0.982936 + 0.0428151i
\(511\) 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
\(515\) 14.7866 + 72.6936i 0.0287119 + 0.141153i
\(516\) 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
\(520\) 400.784 354.555i 0.770739 0.681836i
\(521\) 209.107 120.728i 0.401358 0.231724i −0.285712 0.958316i \(-0.592230\pi\)
0.687070 + 0.726591i \(0.258897\pi\)
\(522\) −399.377 + 751.638i −0.765091 + 1.43992i
\(523\) 683.792 + 394.788i 1.30744 + 0.754852i 0.981669 0.190596i \(-0.0610421\pi\)
0.325773 + 0.945448i \(0.394375\pi\)
\(524\) 178.881i 0.341375i
\(525\) 465.670 242.438i 0.886991 0.461787i
\(526\) 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
\(530\) 212.568 + 240.284i 0.401072 + 0.453366i
\(531\) 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
\(535\) 166.548 33.8775i 0.311304 0.0633224i
\(536\) −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
\(540\) 91.1371 51.6096i 0.168772 0.0955734i
\(541\) −394.171 + 682.723i −0.728596 + 1.26197i 0.228880 + 0.973455i \(0.426494\pi\)
−0.957477 + 0.288511i \(0.906840\pi\)
\(542\) −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
\(550\) −51.8504 6.37070i −0.0942735 0.0115831i
\(551\) −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
\(555\) 5.21845 + 3.32377i 0.00940261 + 0.00598877i
\(556\) −50.6137 87.6656i −0.0910319 0.157672i
\(557\) −178.710 309.535i −0.320844 0.555718i 0.659819 0.751425i \(-0.270633\pi\)
−0.980662 + 0.195707i \(0.937300\pi\)
\(558\) −19.6555 558.281i −0.0352248 1.00050i
\(559\) 98.2134 0.175695
\(560\) 0.0256154 430.319i 4.57417e−5 0.768427i
\(561\) 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 −0.994453 0.105183i \(-0.966457\pi\)
0.406135 0.913813i \(-0.366876\pi\)
\(564\) 56.2845 58.3010i 0.0997952 0.103371i
\(565\) −252.631 285.571i −0.447135 0.505436i
\(566\) 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 0.730252 0.683178i \(-0.239403\pi\)
−0.226523 + 0.974006i \(0.572736\pi\)
\(570\) −378.234 726.398i −0.663568 1.27438i
\(571\) 420.825 + 728.890i 0.736996 + 1.27651i 0.953842 + 0.300309i \(0.0970897\pi\)
−0.216846 + 0.976206i \(0.569577\pi\)
\(572\) 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 \(-0.813924\pi\)
0.0609390 + 0.998141i \(0.480590\pi\)
\(578\) −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
\(585\) 386.677 + 407.272i 0.660986 + 0.696192i
\(586\) −88.8462 + 153.886i −0.151615 + 0.262604i
\(587\) −935.242 −1.59326 −0.796629 0.604469i \(-0.793385\pi\)
−0.796629 + 0.604469i \(0.793385\pi\)
\(588\) 91.0879 + 68.6246i 0.154911 + 0.116709i
\(589\) 1051.08 1.78452
\(590\) −251.130 + 222.163i −0.425644 + 0.376548i
\(591\) −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 \(-0.968831\pi\)
0.582272 + 0.812994i \(0.302164\pi\)
\(594\) −37.7341 + 41.9441i −0.0635254 + 0.0706130i
\(595\) −564.664 326.054i −0.949015 0.547989i
\(596\) 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 −0.799063 0.601248i \(-0.794670\pi\)
0.121165 + 0.992632i \(0.461337\pi\)
\(600\) 404.784 + 499.804i 0.674641 + 0.833007i
\(601\) 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
\(605\) 586.224 119.244i 0.968965 0.197097i
\(606\) 86.6089 + 83.6133i 0.142919 + 0.137976i
\(607\) 530.707 + 306.404i 0.874312 + 0.504784i 0.868779 0.495201i \(-0.164905\pi\)
0.00553303 + 0.999985i \(0.498239\pi\)
\(608\) 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 \(-0.614569\pi\)
0.634428 + 0.772982i \(0.281236\pi\)
\(614\) −686.284 396.226i −1.11773 0.645319i
\(615\) −11.2360 + 257.954i −0.0182700 + 0.419437i
\(616\) −22.1648 66.2478i −0.0359818 0.107545i
\(617\) −530.227 −0.859363 −0.429682 0.902980i \(-0.641374\pi\)
−0.429682 + 0.902980i \(0.641374\pi\)
\(618\) −19.3236 + 77.5498i −0.0312679 + 0.125485i
\(619\) −410.628 711.228i −0.663373 1.14900i −0.979724 0.200353i \(-0.935791\pi\)
0.316351 0.948642i \(-0.397542\pi\)
\(620\) −131.400 + 26.7281i −0.211936 + 0.0431099i
\(621\) −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
\(625\) −606.410 151.300i −0.970256 0.242079i
\(626\) −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
\(630\) 565.265 19.8677i 0.897246 0.0315360i
\(631\) 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
\(635\) −2.14826 + 1.90046i −0.00338308 + 0.00299285i
\(636\) −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
\(640\) 386.201 78.5571i 0.603438 0.122745i
\(641\) 633.511 365.758i 0.988317 0.570605i 0.0835460 0.996504i \(-0.473375\pi\)
0.904771 + 0.425899i \(0.140042\pi\)
\(642\) 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
\(645\) −5.13701 + 117.934i −0.00796435 + 0.182843i
\(646\) −508.574 + 880.875i −0.787266 + 1.36358i
\(647\) 286.539 + 496.301i 0.442874 + 0.767080i 0.997901 0.0647521i \(-0.0206257\pi\)
−0.555028 + 0.831832i \(0.687292\pi\)
\(648\) 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 −0.280412 0.959880i \(-0.590471\pi\)
0.971486 0.237096i \(-0.0761956\pi\)
\(654\) 339.090 351.239i 0.518486 0.537062i
\(655\) −229.796 1129.72i −0.350833 1.72476i
\(656\) 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 \(0.334855\pi\)
−0.495855 + 0.868405i \(0.665145\pi\)
\(660\) 11.4226 + 7.27536i 0.0173070 + 0.0110233i
\(661\) −374.330 648.358i −0.566308 0.980875i −0.996927 0.0783407i \(-0.975038\pi\)
0.430618 0.902534i \(-0.358296\pi\)
\(662\) 244.220 + 423.002i 0.368913 + 0.638976i
\(663\) 168.642 676.797i 0.254361 1.02081i
\(664\) −618.046 −0.930792
\(665\) −0.0633499 + 1064.23i −9.52630e−5 + 1.60035i
\(666\) 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
\(670\) 193.948 171.577i 0.289475 0.256085i
\(671\) 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
\(675\) −509.275 + 443.017i −0.754481 + 0.656321i
\(676\) 5.14054 + 8.90367i 0.00760434 + 0.0131711i
\(677\) 284.770 493.237i 0.420636 0.728562i −0.575366 0.817896i \(-0.695140\pi\)
0.996002 + 0.0893336i \(0.0284737\pi\)
\(678\) −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 0.996420 + 0.0845432i \(0.0269431\pi\)
−0.424993 + 0.905196i \(0.639724\pi\)
\(684\) 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
\(690\) −341.334 655.533i −0.494688 0.950048i
\(691\) −237.246 + 410.922i −0.343337 + 0.594678i −0.985050 0.172267i \(-0.944891\pi\)
0.641713 + 0.766945i \(0.278224\pi\)
\(692\) −227.822 −0.329223
\(693\) 68.6659 25.6940i 0.0990850 0.0370765i
\(694\) −276.599 −0.398557
\(695\) 432.268 + 488.630i 0.621968 + 0.703065i
\(696\) 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
\(700\) −27.0545 133.045i −0.0386493 0.190065i
\(701\) 319.674i 0.456025i 0.973658 + 0.228013i \(0.0732227\pi\)
−0.973658 + 0.228013i \(0.926777\pi\)
\(702\) 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
\(705\) −280.568 + 440.503i −0.397969 + 0.624827i
\(706\) 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 0.233657 0.972319i \(-0.424931\pi\)
0.725225 0.688512i \(-0.241736\pi\)
\(710\) −119.629 588.116i −0.168491 0.828332i
\(711\) 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 0.507265 0.861790i \(-0.330657\pi\)
−0.492700 + 0.870199i \(0.663990\pi\)
\(720\) 129.290 + 537.949i 0.179569 + 0.747151i
\(721\) 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
\(725\) −1306.90 160.575i −1.80262 0.221482i
\(726\) 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
\(730\) 363.153 321.264i 0.497469 0.440088i
\(731\) 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 \(-0.275397\pi\)
−0.334982 + 0.942224i \(0.608730\pi\)
\(734\) 903.452i 1.23086i
\(735\) −663.421 316.383i −0.902613 0.430453i
\(736\) 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 0.992450 0.122652i \(-0.0391398\pi\)
−0.602444 + 0.798161i \(0.705807\pi\)
\(740\) 1.19838 1.06015i 0.00161943 0.00143263i
\(741\) −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 \(-0.469460\pi\)
0.0957979 + 0.995401i \(0.469460\pi\)
\(744\) −862.915 215.018i −1.15983 0.289002i
\(745\) 158.271 + 778.090i 0.212445 + 1.04442i
\(746\) −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
\(750\) −519.583 428.292i −0.692777 0.571056i
\(751\) −39.6817 + 68.7308i −0.0528385 + 0.0915190i −0.891235 0.453542i \(-0.850160\pi\)
0.838396 + 0.545061i \(0.183494\pi\)
\(752\) 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
\(760\) −1277.59 + 259.875i −1.68104 + 0.341941i
\(761\) 363.973 + 210.140i 0.478283 + 0.276137i 0.719701 0.694284i \(-0.244279\pi\)
−0.241418 + 0.970421i \(0.577612\pi\)
\(762\) −2.97029 + 0.852177i −0.00389802 + 0.00111834i
\(763\) −601.637 + 201.292i −0.788515 + 0.263817i