Properties

Label 99.3.l.a.53.7
Level $99$
Weight $3$
Character 99.53
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 53.7
Character \(\chi\) \(=\) 99.53
Dual form 99.3.l.a.71.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.84833 + 0.925479i) q^{2} +(4.02041 + 2.92100i) q^{4} +(1.53284 - 0.498051i) q^{5} +(2.69388 + 1.95722i) q^{7} +(1.70668 + 2.34904i) q^{8} +O(q^{10})\) \(q+(2.84833 + 0.925479i) q^{2} +(4.02041 + 2.92100i) q^{4} +(1.53284 - 0.498051i) q^{5} +(2.69388 + 1.95722i) q^{7} +(1.70668 + 2.34904i) q^{8} +4.82698 q^{10} +(-9.45670 + 5.61879i) q^{11} +(2.33725 - 7.19331i) q^{13} +(5.86169 + 8.06793i) q^{14} +(-3.45544 - 10.6348i) q^{16} +(-26.9649 + 8.76142i) q^{17} +(21.0884 - 15.3216i) q^{19} +(7.61747 + 2.47507i) q^{20} +(-32.1359 + 7.25218i) q^{22} -19.5656i q^{23} +(-18.1239 + 13.1678i) q^{25} +(13.3145 - 18.3259i) q^{26} +(5.11347 + 15.7376i) q^{28} +(-1.26543 + 1.74171i) q^{29} +(-2.85173 + 8.77673i) q^{31} -45.1036i q^{32} -84.9135 q^{34} +(5.10409 + 1.65842i) q^{35} +(54.6363 + 39.6956i) q^{37} +(74.2465 - 24.1241i) q^{38} +(3.78602 + 2.75070i) q^{40} +(17.0809 + 23.5098i) q^{41} +0.719802 q^{43} +(-54.4323 - 5.03321i) q^{44} +(18.1076 - 55.7293i) q^{46} +(14.4154 + 19.8410i) q^{47} +(-11.7156 - 36.0568i) q^{49} +(-63.8093 + 20.7329i) q^{50} +(30.4084 - 22.0930i) q^{52} +(-5.50829 - 1.78975i) q^{53} +(-11.6972 + 13.3226i) q^{55} +9.66837i q^{56} +(-5.21628 + 3.78985i) q^{58} +(-43.4900 + 59.8589i) q^{59} +(22.3006 + 68.6343i) q^{61} +(-16.2454 + 22.3598i) q^{62} +(27.9206 - 85.9309i) q^{64} -12.1903i q^{65} -79.8310 q^{67} +(-134.002 - 43.5399i) q^{68} +(13.0033 + 9.44745i) q^{70} +(102.505 - 33.3059i) q^{71} +(73.1189 + 53.1240i) q^{73} +(118.885 + 163.631i) q^{74} +129.538 q^{76} +(-36.4724 - 3.37250i) q^{77} +(35.4758 - 109.183i) q^{79} +(-10.5933 - 14.5804i) q^{80} +(26.8942 + 82.7718i) q^{82} +(119.598 - 38.8596i) q^{83} +(-36.9693 + 26.8598i) q^{85} +(2.05023 + 0.666161i) q^{86} +(-29.3383 - 12.6247i) q^{88} +83.3041i q^{89} +(20.3751 - 14.8034i) q^{91} +(57.1511 - 78.6618i) q^{92} +(22.6973 + 69.8550i) q^{94} +(24.6942 - 33.9887i) q^{95} +(-24.1118 + 74.2085i) q^{97} -113.544i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7} + O(q^{10}) \) \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.84833 + 0.925479i 1.42417 + 0.462739i 0.916923 0.399064i \(-0.130665\pi\)
0.507243 + 0.861803i \(0.330665\pi\)
\(3\) 0 0
\(4\) 4.02041 + 2.92100i 1.00510 + 0.730250i
\(5\) 1.53284 0.498051i 0.306569 0.0996102i −0.151693 0.988428i \(-0.548472\pi\)
0.458261 + 0.888817i \(0.348472\pi\)
\(6\) 0 0
\(7\) 2.69388 + 1.95722i 0.384840 + 0.279602i 0.763338 0.646000i \(-0.223559\pi\)
−0.378498 + 0.925602i \(0.623559\pi\)
\(8\) 1.70668 + 2.34904i 0.213335 + 0.293630i
\(9\) 0 0
\(10\) 4.82698 0.482698
\(11\) −9.45670 + 5.61879i −0.859700 + 0.510799i
\(12\) 0 0
\(13\) 2.33725 7.19331i 0.179788 0.553332i −0.820031 0.572319i \(-0.806044\pi\)
0.999820 + 0.0189869i \(0.00604407\pi\)
\(14\) 5.86169 + 8.06793i 0.418692 + 0.576280i
\(15\) 0 0
\(16\) −3.45544 10.6348i −0.215965 0.664673i
\(17\) −26.9649 + 8.76142i −1.58617 + 0.515378i −0.963637 0.267215i \(-0.913896\pi\)
−0.622533 + 0.782593i \(0.713896\pi\)
\(18\) 0 0
\(19\) 21.0884 15.3216i 1.10991 0.806400i 0.127264 0.991869i \(-0.459380\pi\)
0.982650 + 0.185469i \(0.0593804\pi\)
\(20\) 7.61747 + 2.47507i 0.380874 + 0.123753i
\(21\) 0 0
\(22\) −32.1359 + 7.25218i −1.46072 + 0.329645i
\(23\) 19.5656i 0.850679i −0.905034 0.425339i \(-0.860155\pi\)
0.905034 0.425339i \(-0.139845\pi\)
\(24\) 0 0
\(25\) −18.1239 + 13.1678i −0.724955 + 0.526710i
\(26\) 13.3145 18.3259i 0.512097 0.704841i
\(27\) 0 0
\(28\) 5.11347 + 15.7376i 0.182624 + 0.562058i
\(29\) −1.26543 + 1.74171i −0.0436355 + 0.0600591i −0.830277 0.557351i \(-0.811818\pi\)
0.786642 + 0.617410i \(0.211818\pi\)
\(30\) 0 0
\(31\) −2.85173 + 8.77673i −0.0919914 + 0.283120i −0.986458 0.164015i \(-0.947556\pi\)
0.894467 + 0.447135i \(0.147556\pi\)
\(32\) 45.1036i 1.40949i
\(33\) 0 0
\(34\) −84.9135 −2.49745
\(35\) 5.10409 + 1.65842i 0.145831 + 0.0473834i
\(36\) 0 0
\(37\) 54.6363 + 39.6956i 1.47666 + 1.07285i 0.978615 + 0.205701i \(0.0659475\pi\)
0.498042 + 0.867153i \(0.334052\pi\)
\(38\) 74.2465 24.1241i 1.95385 0.634846i
\(39\) 0 0
\(40\) 3.78602 + 2.75070i 0.0946504 + 0.0687676i
\(41\) 17.0809 + 23.5098i 0.416607 + 0.573410i 0.964814 0.262932i \(-0.0846895\pi\)
−0.548207 + 0.836343i \(0.684690\pi\)
\(42\) 0 0
\(43\) 0.719802 0.0167396 0.00836979 0.999965i \(-0.497336\pi\)
0.00836979 + 0.999965i \(0.497336\pi\)
\(44\) −54.4323 5.03321i −1.23710 0.114391i
\(45\) 0 0
\(46\) 18.1076 55.7293i 0.393643 1.21151i
\(47\) 14.4154 + 19.8410i 0.306710 + 0.422150i 0.934352 0.356352i \(-0.115980\pi\)
−0.627642 + 0.778502i \(0.715980\pi\)
\(48\) 0 0
\(49\) −11.7156 36.0568i −0.239093 0.735853i
\(50\) −63.8093 + 20.7329i −1.27619 + 0.414658i
\(51\) 0 0
\(52\) 30.4084 22.0930i 0.584776 0.424865i
\(53\) −5.50829 1.78975i −0.103930 0.0337689i 0.256590 0.966520i \(-0.417401\pi\)
−0.360520 + 0.932751i \(0.617401\pi\)
\(54\) 0 0
\(55\) −11.6972 + 13.3226i −0.212676 + 0.242230i
\(56\) 9.66837i 0.172650i
\(57\) 0 0
\(58\) −5.21628 + 3.78985i −0.0899359 + 0.0653423i
\(59\) −43.4900 + 59.8589i −0.737119 + 1.01456i 0.261660 + 0.965160i \(0.415730\pi\)
−0.998779 + 0.0493973i \(0.984270\pi\)
\(60\) 0 0
\(61\) 22.3006 + 68.6343i 0.365584 + 1.12515i 0.949614 + 0.313421i \(0.101475\pi\)
−0.584030 + 0.811732i \(0.698525\pi\)
\(62\) −16.2454 + 22.3598i −0.262022 + 0.360642i
\(63\) 0 0
\(64\) 27.9206 85.9309i 0.436260 1.34267i
\(65\) 12.1903i 0.187543i
\(66\) 0 0
\(67\) −79.8310 −1.19151 −0.595754 0.803167i \(-0.703146\pi\)
−0.595754 + 0.803167i \(0.703146\pi\)
\(68\) −134.002 43.5399i −1.97062 0.640293i
\(69\) 0 0
\(70\) 13.0033 + 9.44745i 0.185761 + 0.134964i
\(71\) 102.505 33.3059i 1.44373 0.469097i 0.520674 0.853755i \(-0.325681\pi\)
0.923059 + 0.384658i \(0.125681\pi\)
\(72\) 0 0
\(73\) 73.1189 + 53.1240i 1.00163 + 0.727726i 0.962437 0.271506i \(-0.0875216\pi\)
0.0391919 + 0.999232i \(0.487522\pi\)
\(74\) 118.885 + 163.631i 1.60655 + 2.21123i
\(75\) 0 0
\(76\) 129.538 1.70445
\(77\) −36.4724 3.37250i −0.473667 0.0437987i
\(78\) 0 0
\(79\) 35.4758 109.183i 0.449060 1.38206i −0.428909 0.903348i \(-0.641102\pi\)
0.877969 0.478717i \(-0.158898\pi\)
\(80\) −10.5933 14.5804i −0.132416 0.182256i
\(81\) 0 0
\(82\) 26.8942 + 82.7718i 0.327978 + 1.00941i
\(83\) 119.598 38.8596i 1.44093 0.468188i 0.518746 0.854929i \(-0.326399\pi\)
0.922188 + 0.386741i \(0.126399\pi\)
\(84\) 0 0
\(85\) −36.9693 + 26.8598i −0.434933 + 0.315998i
\(86\) 2.05023 + 0.666161i 0.0238399 + 0.00774606i
\(87\) 0 0
\(88\) −29.3383 12.6247i −0.333390 0.143463i
\(89\) 83.3041i 0.936001i 0.883728 + 0.468000i \(0.155025\pi\)
−0.883728 + 0.468000i \(0.844975\pi\)
\(90\) 0 0
\(91\) 20.3751 14.8034i 0.223902 0.162675i
\(92\) 57.1511 78.6618i 0.621208 0.855020i
\(93\) 0 0
\(94\) 22.6973 + 69.8550i 0.241460 + 0.743138i
\(95\) 24.6942 33.9887i 0.259939 0.357776i
\(96\) 0 0
\(97\) −24.1118 + 74.2085i −0.248575 + 0.765036i 0.746452 + 0.665439i \(0.231756\pi\)
−0.995028 + 0.0995976i \(0.968244\pi\)
\(98\) 113.544i 1.15861i
\(99\) 0 0
\(100\) −111.328 −1.11328
\(101\) −37.0777 12.0473i −0.367106 0.119280i 0.119654 0.992816i \(-0.461821\pi\)
−0.486760 + 0.873536i \(0.661821\pi\)
\(102\) 0 0
\(103\) −24.3898 17.7202i −0.236794 0.172041i 0.463060 0.886327i \(-0.346752\pi\)
−0.699854 + 0.714286i \(0.746752\pi\)
\(104\) 20.8863 6.78638i 0.200830 0.0652537i
\(105\) 0 0
\(106\) −14.0331 10.1956i −0.132387 0.0961850i
\(107\) −29.2449 40.2522i −0.273317 0.376188i 0.650189 0.759772i \(-0.274690\pi\)
−0.923506 + 0.383584i \(0.874690\pi\)
\(108\) 0 0
\(109\) −149.823 −1.37453 −0.687263 0.726409i \(-0.741188\pi\)
−0.687263 + 0.726409i \(0.741188\pi\)
\(110\) −45.6473 + 27.1218i −0.414976 + 0.246562i
\(111\) 0 0
\(112\) 11.5060 35.4118i 0.102732 0.316177i
\(113\) −74.9246 103.125i −0.663050 0.912609i 0.336528 0.941673i \(-0.390747\pi\)
−0.999578 + 0.0290640i \(0.990747\pi\)
\(114\) 0 0
\(115\) −9.74467 29.9910i −0.0847363 0.260791i
\(116\) −10.1751 + 3.30609i −0.0877164 + 0.0285008i
\(117\) 0 0
\(118\) −179.272 + 130.249i −1.51926 + 1.10380i
\(119\) −89.7881 29.1739i −0.754522 0.245159i
\(120\) 0 0
\(121\) 57.8585 106.270i 0.478169 0.878268i
\(122\) 216.132i 1.77157i
\(123\) 0 0
\(124\) −37.1020 + 26.9562i −0.299210 + 0.217388i
\(125\) −44.9066 + 61.8086i −0.359253 + 0.494469i
\(126\) 0 0
\(127\) −73.5383 226.328i −0.579042 1.78211i −0.621983 0.783030i \(-0.713673\pi\)
0.0429415 0.999078i \(-0.486327\pi\)
\(128\) 53.0096 72.9614i 0.414137 0.570011i
\(129\) 0 0
\(130\) 11.2819 34.7220i 0.0867835 0.267092i
\(131\) 148.535i 1.13386i −0.823767 0.566929i \(-0.808131\pi\)
0.823767 0.566929i \(-0.191869\pi\)
\(132\) 0 0
\(133\) 86.7972 0.652610
\(134\) −227.385 73.8819i −1.69690 0.551357i
\(135\) 0 0
\(136\) −66.6014 48.3887i −0.489716 0.355800i
\(137\) 19.1720 6.22935i 0.139941 0.0454697i −0.238209 0.971214i \(-0.576560\pi\)
0.378150 + 0.925744i \(0.376560\pi\)
\(138\) 0 0
\(139\) −120.445 87.5083i −0.866509 0.629556i 0.0631388 0.998005i \(-0.479889\pi\)
−0.929648 + 0.368449i \(0.879889\pi\)
\(140\) 15.6763 + 21.5766i 0.111973 + 0.154118i
\(141\) 0 0
\(142\) 322.792 2.27319
\(143\) 18.3150 + 81.1575i 0.128077 + 0.567535i
\(144\) 0 0
\(145\) −1.07224 + 3.30003i −0.00739478 + 0.0227588i
\(146\) 159.102 + 218.985i 1.08974 + 1.49990i
\(147\) 0 0
\(148\) 103.710 + 319.185i 0.700741 + 2.15666i
\(149\) −42.7009 + 13.8744i −0.286583 + 0.0931166i −0.448781 0.893642i \(-0.648142\pi\)
0.162198 + 0.986758i \(0.448142\pi\)
\(150\) 0 0
\(151\) −37.6538 + 27.3571i −0.249363 + 0.181173i −0.705444 0.708765i \(-0.749253\pi\)
0.456081 + 0.889938i \(0.349253\pi\)
\(152\) 71.9822 + 23.3884i 0.473567 + 0.153871i
\(153\) 0 0
\(154\) −100.764 43.3604i −0.654313 0.281561i
\(155\) 14.8737i 0.0959591i
\(156\) 0 0
\(157\) −14.7026 + 10.6820i −0.0936468 + 0.0680384i −0.633623 0.773642i \(-0.718433\pi\)
0.539977 + 0.841680i \(0.318433\pi\)
\(158\) 202.093 278.158i 1.27907 1.76049i
\(159\) 0 0
\(160\) −22.4639 69.1367i −0.140399 0.432105i
\(161\) 38.2941 52.7073i 0.237852 0.327375i
\(162\) 0 0
\(163\) −43.0033 + 132.351i −0.263824 + 0.811967i 0.728138 + 0.685431i \(0.240386\pi\)
−0.991962 + 0.126536i \(0.959614\pi\)
\(164\) 144.412i 0.880564i
\(165\) 0 0
\(166\) 376.617 2.26878
\(167\) 138.107 + 44.8735i 0.826985 + 0.268704i 0.691775 0.722113i \(-0.256829\pi\)
0.135210 + 0.990817i \(0.456829\pi\)
\(168\) 0 0
\(169\) 90.4429 + 65.7106i 0.535165 + 0.388820i
\(170\) −130.159 + 42.2912i −0.765642 + 0.248772i
\(171\) 0 0
\(172\) 2.89390 + 2.10254i 0.0168250 + 0.0122241i
\(173\) −170.702 234.952i −0.986719 1.35810i −0.933130 0.359539i \(-0.882934\pi\)
−0.0535891 0.998563i \(-0.517066\pi\)
\(174\) 0 0
\(175\) −74.5956 −0.426261
\(176\) 92.4316 + 81.1544i 0.525179 + 0.461105i
\(177\) 0 0
\(178\) −77.0961 + 237.278i −0.433124 + 1.33302i
\(179\) 86.0584 + 118.449i 0.480773 + 0.661727i 0.978653 0.205519i \(-0.0658881\pi\)
−0.497880 + 0.867246i \(0.665888\pi\)
\(180\) 0 0
\(181\) 69.0532 + 212.524i 0.381509 + 1.17417i 0.938981 + 0.343969i \(0.111772\pi\)
−0.557471 + 0.830196i \(0.688228\pi\)
\(182\) 71.7353 23.3082i 0.394150 0.128067i
\(183\) 0 0
\(184\) 45.9605 33.3922i 0.249785 0.181479i
\(185\) 103.519 + 33.6355i 0.559564 + 0.181813i
\(186\) 0 0
\(187\) 205.770 234.364i 1.10038 1.25328i
\(188\) 121.876i 0.648279i
\(189\) 0 0
\(190\) 101.793 73.9571i 0.535754 0.389248i
\(191\) 13.6471 18.7836i 0.0714506 0.0983433i −0.771796 0.635870i \(-0.780641\pi\)
0.843247 + 0.537527i \(0.180641\pi\)
\(192\) 0 0
\(193\) −38.7623 119.298i −0.200841 0.618124i −0.999859 0.0168170i \(-0.994647\pi\)
0.799018 0.601307i \(-0.205353\pi\)
\(194\) −137.357 + 189.056i −0.708025 + 0.974513i
\(195\) 0 0
\(196\) 58.2205 179.184i 0.297043 0.914205i
\(197\) 12.3847i 0.0628665i 0.999506 + 0.0314333i \(0.0100072\pi\)
−0.999506 + 0.0314333i \(0.989993\pi\)
\(198\) 0 0
\(199\) 112.611 0.565885 0.282943 0.959137i \(-0.408689\pi\)
0.282943 + 0.959137i \(0.408689\pi\)
\(200\) −61.8633 20.1006i −0.309316 0.100503i
\(201\) 0 0
\(202\) −94.4601 68.6293i −0.467625 0.339749i
\(203\) −6.81782 + 2.21525i −0.0335853 + 0.0109125i
\(204\) 0 0
\(205\) 37.8914 + 27.5297i 0.184836 + 0.134291i
\(206\) −53.0705 73.0453i −0.257624 0.354589i
\(207\) 0 0
\(208\) −84.5754 −0.406613
\(209\) −113.338 + 263.383i −0.542286 + 1.26021i
\(210\) 0 0
\(211\) 47.5609 146.377i 0.225407 0.693732i −0.772843 0.634597i \(-0.781166\pi\)
0.998250 0.0591343i \(-0.0188340\pi\)
\(212\) −16.9177 23.2853i −0.0798006 0.109836i
\(213\) 0 0
\(214\) −46.0467 141.717i −0.215171 0.662229i
\(215\) 1.10334 0.358498i 0.00513183 0.00166743i
\(216\) 0 0
\(217\) −24.8602 + 18.0620i −0.114563 + 0.0832349i
\(218\) −426.746 138.658i −1.95755 0.636047i
\(219\) 0 0
\(220\) −85.9430 + 19.3950i −0.390650 + 0.0881589i
\(221\) 214.445i 0.970337i
\(222\) 0 0
\(223\) −228.453 + 165.981i −1.02445 + 0.744310i −0.967191 0.254049i \(-0.918237\pi\)
−0.0572631 + 0.998359i \(0.518237\pi\)
\(224\) 88.2774 121.503i 0.394096 0.542426i
\(225\) 0 0
\(226\) −117.970 363.075i −0.521992 1.60653i
\(227\) 119.241 164.121i 0.525290 0.723000i −0.461113 0.887341i \(-0.652550\pi\)
0.986404 + 0.164341i \(0.0525498\pi\)
\(228\) 0 0
\(229\) −129.515 + 398.606i −0.565568 + 1.74064i 0.100690 + 0.994918i \(0.467895\pi\)
−0.666258 + 0.745721i \(0.732105\pi\)
\(230\) 94.4428i 0.410621i
\(231\) 0 0
\(232\) −6.25105 −0.0269442
\(233\) 105.683 + 34.3384i 0.453574 + 0.147375i 0.526890 0.849934i \(-0.323358\pi\)
−0.0733156 + 0.997309i \(0.523358\pi\)
\(234\) 0 0
\(235\) 31.9783 + 23.2336i 0.136078 + 0.0988665i
\(236\) −349.696 + 113.623i −1.48176 + 0.481453i
\(237\) 0 0
\(238\) −228.746 166.194i −0.961119 0.698294i
\(239\) −184.598 254.077i −0.772375 1.06308i −0.996083 0.0884262i \(-0.971816\pi\)
0.223708 0.974656i \(-0.428184\pi\)
\(240\) 0 0
\(241\) −104.293 −0.432753 −0.216376 0.976310i \(-0.569424\pi\)
−0.216376 + 0.976310i \(0.569424\pi\)
\(242\) 263.151 249.146i 1.08740 1.02953i
\(243\) 0 0
\(244\) −110.823 + 341.079i −0.454193 + 1.39786i
\(245\) −35.9162 49.4345i −0.146597 0.201773i
\(246\) 0 0
\(247\) −60.9243 187.506i −0.246657 0.759132i
\(248\) −25.4839 + 8.28023i −0.102758 + 0.0333880i
\(249\) 0 0
\(250\) −185.111 + 134.491i −0.740446 + 0.537965i
\(251\) 317.213 + 103.069i 1.26380 + 0.410632i 0.862845 0.505468i \(-0.168680\pi\)
0.400950 + 0.916100i \(0.368680\pi\)
\(252\) 0 0
\(253\) 109.935 + 185.026i 0.434525 + 0.731329i
\(254\) 712.714i 2.80596i
\(255\) 0 0
\(256\) −73.8756 + 53.6738i −0.288577 + 0.209663i
\(257\) −180.443 + 248.359i −0.702114 + 0.966377i 0.297817 + 0.954623i \(0.403742\pi\)
−0.999931 + 0.0117541i \(0.996258\pi\)
\(258\) 0 0
\(259\) 69.4906 + 213.870i 0.268304 + 0.825753i
\(260\) 35.6079 49.0100i 0.136953 0.188500i
\(261\) 0 0
\(262\) 137.466 423.078i 0.524681 1.61480i
\(263\) 249.060i 0.946997i 0.880794 + 0.473499i \(0.157009\pi\)
−0.880794 + 0.473499i \(0.842991\pi\)
\(264\) 0 0
\(265\) −9.33473 −0.0352254
\(266\) 247.227 + 80.3289i 0.929425 + 0.301988i
\(267\) 0 0
\(268\) −320.953 233.186i −1.19759 0.870098i
\(269\) 187.289 60.8538i 0.696241 0.226222i 0.0605488 0.998165i \(-0.480715\pi\)
0.635692 + 0.771943i \(0.280715\pi\)
\(270\) 0 0
\(271\) 374.950 + 272.417i 1.38358 + 1.00523i 0.996536 + 0.0831675i \(0.0265037\pi\)
0.387043 + 0.922061i \(0.373496\pi\)
\(272\) 186.351 + 256.491i 0.685115 + 0.942980i
\(273\) 0 0
\(274\) 60.3733 0.220340
\(275\) 97.4053 226.358i 0.354201 0.823119i
\(276\) 0 0
\(277\) −7.24800 + 22.3070i −0.0261661 + 0.0805308i −0.963287 0.268475i \(-0.913480\pi\)
0.937121 + 0.349005i \(0.113480\pi\)
\(278\) −262.080 360.722i −0.942732 1.29756i
\(279\) 0 0
\(280\) 4.81534 + 14.8201i 0.0171977 + 0.0529289i
\(281\) 250.553 81.4096i 0.891647 0.289714i 0.172862 0.984946i \(-0.444698\pi\)
0.718785 + 0.695232i \(0.244698\pi\)
\(282\) 0 0
\(283\) 28.9820 21.0566i 0.102410 0.0744050i −0.535402 0.844597i \(-0.679840\pi\)
0.637812 + 0.770192i \(0.279840\pi\)
\(284\) 509.399 + 165.514i 1.79366 + 0.582795i
\(285\) 0 0
\(286\) −22.9424 + 248.114i −0.0802181 + 0.867530i
\(287\) 96.7636i 0.337155i
\(288\) 0 0
\(289\) 416.537 302.632i 1.44130 1.04717i
\(290\) −6.10821 + 8.40723i −0.0210628 + 0.0289904i
\(291\) 0 0
\(292\) 138.793 + 427.161i 0.475318 + 1.46288i
\(293\) −67.1224 + 92.3860i −0.229087 + 0.315311i −0.908050 0.418861i \(-0.862429\pi\)
0.678964 + 0.734172i \(0.262429\pi\)
\(294\) 0 0
\(295\) −36.8506 + 113.415i −0.124917 + 0.384456i
\(296\) 196.091i 0.662469i
\(297\) 0 0
\(298\) −134.467 −0.451231
\(299\) −140.742 45.7297i −0.470707 0.152942i
\(300\) 0 0
\(301\) 1.93906 + 1.40881i 0.00644205 + 0.00468042i
\(302\) −132.569 + 43.0743i −0.438970 + 0.142630i
\(303\) 0 0
\(304\) −235.811 171.327i −0.775695 0.563575i
\(305\) 68.3668 + 94.0988i 0.224153 + 0.308521i
\(306\) 0 0
\(307\) −224.438 −0.731070 −0.365535 0.930798i \(-0.619114\pi\)
−0.365535 + 0.930798i \(0.619114\pi\)
\(308\) −136.783 120.095i −0.444100 0.389918i
\(309\) 0 0
\(310\) −13.7653 + 42.3651i −0.0444041 + 0.136662i
\(311\) −100.614 138.483i −0.323518 0.445284i 0.616020 0.787731i \(-0.288744\pi\)
−0.939537 + 0.342447i \(0.888744\pi\)
\(312\) 0 0
\(313\) −84.7045 260.694i −0.270621 0.832887i −0.990345 0.138626i \(-0.955731\pi\)
0.719723 0.694261i \(-0.244269\pi\)
\(314\) −51.7637 + 16.8191i −0.164853 + 0.0535639i
\(315\) 0 0
\(316\) 461.551 335.337i 1.46060 1.06119i
\(317\) −588.275 191.142i −1.85576 0.602972i −0.995685 0.0927984i \(-0.970419\pi\)
−0.860072 0.510173i \(-0.829581\pi\)
\(318\) 0 0
\(319\) 2.18047 23.5811i 0.00683534 0.0739218i
\(320\) 145.625i 0.455077i
\(321\) 0 0
\(322\) 157.854 114.688i 0.490229 0.356172i
\(323\) −434.407 + 597.909i −1.34491 + 1.85111i
\(324\) 0 0
\(325\) 52.3598 + 161.147i 0.161107 + 0.495837i
\(326\) −244.975 + 337.180i −0.751459 + 1.03429i
\(327\) 0 0
\(328\) −26.0740 + 80.2475i −0.0794939 + 0.244657i
\(329\) 81.6633i 0.248217i
\(330\) 0 0
\(331\) −160.328 −0.484376 −0.242188 0.970229i \(-0.577865\pi\)
−0.242188 + 0.970229i \(0.577865\pi\)
\(332\) 594.340 + 193.113i 1.79018 + 0.581665i
\(333\) 0 0
\(334\) 351.844 + 255.629i 1.05342 + 0.765357i
\(335\) −122.368 + 39.7599i −0.365279 + 0.118686i
\(336\) 0 0
\(337\) 88.9953 + 64.6588i 0.264081 + 0.191866i 0.711944 0.702236i \(-0.247815\pi\)
−0.447863 + 0.894102i \(0.647815\pi\)
\(338\) 196.797 + 270.868i 0.582241 + 0.801386i
\(339\) 0 0
\(340\) −227.089 −0.667910
\(341\) −22.3466 99.0222i −0.0655325 0.290388i
\(342\) 0 0
\(343\) 89.4301 275.238i 0.260729 0.802442i
\(344\) 1.22847 + 1.69085i 0.00357114 + 0.00491525i
\(345\) 0 0
\(346\) −268.774 827.202i −0.776804 2.39076i
\(347\) −210.883 + 68.5202i −0.607733 + 0.197464i −0.596686 0.802475i \(-0.703516\pi\)
−0.0110468 + 0.999939i \(0.503516\pi\)
\(348\) 0 0
\(349\) 377.286 274.115i 1.08105 0.785429i 0.103184 0.994662i \(-0.467097\pi\)
0.977866 + 0.209234i \(0.0670969\pi\)
\(350\) −212.473 69.0367i −0.607066 0.197248i
\(351\) 0 0
\(352\) 253.427 + 426.531i 0.719964 + 1.21174i
\(353\) 494.404i 1.40058i −0.713860 0.700289i \(-0.753055\pi\)
0.713860 0.700289i \(-0.246945\pi\)
\(354\) 0 0
\(355\) 140.536 102.106i 0.395877 0.287621i
\(356\) −243.331 + 334.917i −0.683515 + 0.940777i
\(357\) 0 0
\(358\) 135.501 + 417.028i 0.378493 + 1.16488i
\(359\) 16.5578 22.7898i 0.0461219 0.0634814i −0.785333 0.619073i \(-0.787508\pi\)
0.831455 + 0.555592i \(0.187508\pi\)
\(360\) 0 0
\(361\) 98.4129 302.884i 0.272612 0.839013i
\(362\) 669.246i 1.84875i
\(363\) 0 0
\(364\) 125.157 0.343838
\(365\) 138.538 + 45.0138i 0.379557 + 0.123326i
\(366\) 0 0
\(367\) −24.1068 17.5146i −0.0656861 0.0477238i 0.554458 0.832212i \(-0.312926\pi\)
−0.620144 + 0.784488i \(0.712926\pi\)
\(368\) −208.076 + 67.6079i −0.565423 + 0.183717i
\(369\) 0 0
\(370\) 263.729 + 191.610i 0.712780 + 0.517865i
\(371\) −11.3357 15.6023i −0.0305545 0.0420547i
\(372\) 0 0
\(373\) −313.887 −0.841520 −0.420760 0.907172i \(-0.638237\pi\)
−0.420760 + 0.907172i \(0.638237\pi\)
\(374\) 803.001 477.110i 2.14706 1.27570i
\(375\) 0 0
\(376\) −22.0051 + 67.7246i −0.0585241 + 0.180119i
\(377\) 9.57107 + 13.1735i 0.0253875 + 0.0349428i
\(378\) 0 0
\(379\) −9.70792 29.8779i −0.0256146 0.0788335i 0.937432 0.348168i \(-0.113196\pi\)
−0.963047 + 0.269335i \(0.913196\pi\)
\(380\) 198.562 64.5167i 0.522532 0.169781i
\(381\) 0 0
\(382\) 56.2551 40.8718i 0.147265 0.106994i
\(383\) 451.654 + 146.751i 1.17925 + 0.383163i 0.832089 0.554642i \(-0.187145\pi\)
0.347164 + 0.937804i \(0.387145\pi\)
\(384\) 0 0
\(385\) −57.5861 + 12.9956i −0.149574 + 0.0337548i
\(386\) 375.674i 0.973249i
\(387\) 0 0
\(388\) −313.703 + 227.918i −0.808512 + 0.587418i
\(389\) −24.8910 + 34.2595i −0.0639871 + 0.0880706i −0.839811 0.542879i \(-0.817334\pi\)
0.775824 + 0.630949i \(0.217334\pi\)
\(390\) 0 0
\(391\) 171.423 + 527.584i 0.438421 + 1.34932i
\(392\) 64.7042 89.0577i 0.165062 0.227188i
\(393\) 0 0
\(394\) −11.4618 + 35.2757i −0.0290908 + 0.0895323i
\(395\) 185.029i 0.468429i
\(396\) 0 0
\(397\) −560.270 −1.41126 −0.705630 0.708580i \(-0.749336\pi\)
−0.705630 + 0.708580i \(0.749336\pi\)
\(398\) 320.754 + 104.219i 0.805915 + 0.261858i
\(399\) 0 0
\(400\) 202.662 + 147.243i 0.506655 + 0.368107i
\(401\) 537.622 174.684i 1.34070 0.435621i 0.451149 0.892449i \(-0.351014\pi\)
0.889555 + 0.456828i \(0.151014\pi\)
\(402\) 0 0
\(403\) 56.4686 + 41.0268i 0.140121 + 0.101804i
\(404\) −113.878 156.739i −0.281875 0.387968i
\(405\) 0 0
\(406\) −21.4696 −0.0528807
\(407\) −739.720 68.3999i −1.81750 0.168059i
\(408\) 0 0
\(409\) 53.8474 165.725i 0.131656 0.405196i −0.863399 0.504522i \(-0.831669\pi\)
0.995055 + 0.0993261i \(0.0316687\pi\)
\(410\) 82.4492 + 113.482i 0.201096 + 0.276784i
\(411\) 0 0
\(412\) −46.2962 142.485i −0.112370 0.345838i
\(413\) −234.314 + 76.1331i −0.567345 + 0.184342i
\(414\) 0 0
\(415\) 163.970 119.131i 0.395109 0.287063i
\(416\) −324.444 105.418i −0.779914 0.253409i
\(417\) 0 0
\(418\) −566.579 + 645.310i −1.35545 + 1.54380i
\(419\) 279.267i 0.666508i −0.942837 0.333254i \(-0.891853\pi\)
0.942837 0.333254i \(-0.108147\pi\)
\(420\) 0 0
\(421\) −313.096 + 227.478i −0.743696 + 0.540327i −0.893867 0.448333i \(-0.852018\pi\)
0.150170 + 0.988660i \(0.452018\pi\)
\(422\) 270.938 372.915i 0.642034 0.883684i
\(423\) 0 0
\(424\) −5.19668 15.9937i −0.0122563 0.0377211i
\(425\) 373.340 513.858i 0.878447 1.20908i
\(426\) 0 0
\(427\) −74.2570 + 228.540i −0.173904 + 0.535222i
\(428\) 247.255i 0.577698i
\(429\) 0 0
\(430\) 3.47447 0.00808017
\(431\) 304.315 + 98.8779i 0.706067 + 0.229415i 0.639972 0.768398i \(-0.278946\pi\)
0.0660949 + 0.997813i \(0.478946\pi\)
\(432\) 0 0
\(433\) −425.660 309.260i −0.983049 0.714227i −0.0246608 0.999696i \(-0.507851\pi\)
−0.958388 + 0.285469i \(0.907851\pi\)
\(434\) −87.5260 + 28.4389i −0.201673 + 0.0655275i
\(435\) 0 0
\(436\) −602.351 437.634i −1.38154 1.00375i
\(437\) −299.776 412.607i −0.685987 0.944180i
\(438\) 0 0
\(439\) 22.7817 0.0518946 0.0259473 0.999663i \(-0.491740\pi\)
0.0259473 + 0.999663i \(0.491740\pi\)
\(440\) −51.2588 4.73976i −0.116497 0.0107722i
\(441\) 0 0
\(442\) −198.464 + 610.809i −0.449013 + 1.38192i
\(443\) 35.2684 + 48.5428i 0.0796127 + 0.109577i 0.846966 0.531647i \(-0.178427\pi\)
−0.767353 + 0.641225i \(0.778427\pi\)
\(444\) 0 0
\(445\) 41.4897 + 127.692i 0.0932352 + 0.286949i
\(446\) −804.323 + 261.340i −1.80341 + 0.585965i
\(447\) 0 0
\(448\) 243.400 176.840i 0.543304 0.394733i
\(449\) 723.967 + 235.231i 1.61240 + 0.523900i 0.970131 0.242581i \(-0.0779939\pi\)
0.642267 + 0.766481i \(0.277994\pi\)
\(450\) 0 0
\(451\) −293.626 126.352i −0.651055 0.280159i
\(452\) 633.459i 1.40146i
\(453\) 0 0
\(454\) 491.528 357.116i 1.08266 0.786599i
\(455\) 23.8590 32.8391i 0.0524374 0.0721739i
\(456\) 0 0
\(457\) −243.795 750.325i −0.533469 1.64185i −0.746934 0.664898i \(-0.768475\pi\)
0.213465 0.976951i \(-0.431525\pi\)
\(458\) −737.804 + 1015.50i −1.61093 + 2.21725i
\(459\) 0 0
\(460\) 48.4262 149.040i 0.105274 0.324001i
\(461\) 726.842i 1.57666i 0.615250 + 0.788332i \(0.289055\pi\)
−0.615250 + 0.788332i \(0.710945\pi\)
\(462\) 0 0
\(463\) 301.548 0.651291 0.325646 0.945492i \(-0.394418\pi\)
0.325646 + 0.945492i \(0.394418\pi\)
\(464\) 22.8953 + 7.43915i 0.0493434 + 0.0160326i
\(465\) 0 0
\(466\) 269.240 + 195.614i 0.577769 + 0.419773i
\(467\) −278.170 + 90.3828i −0.595652 + 0.193539i −0.591300 0.806451i \(-0.701385\pi\)
−0.00435192 + 0.999991i \(0.501385\pi\)
\(468\) 0 0
\(469\) −215.055 156.246i −0.458539 0.333148i
\(470\) 69.5827 + 95.7724i 0.148048 + 0.203771i
\(471\) 0 0
\(472\) −214.835 −0.455158
\(473\) −6.80695 + 4.04441i −0.0143910 + 0.00855055i
\(474\) 0 0
\(475\) −180.452 + 555.373i −0.379898 + 1.16921i
\(476\) −275.768 379.562i −0.579345 0.797400i
\(477\) 0 0
\(478\) −290.652 894.536i −0.608059 1.87141i
\(479\) 472.561 153.544i 0.986557 0.320552i 0.229076 0.973409i \(-0.426430\pi\)
0.757481 + 0.652857i \(0.226430\pi\)
\(480\) 0 0
\(481\) 413.242 300.238i 0.859130 0.624194i
\(482\) −297.062 96.5214i −0.616312 0.200252i
\(483\) 0 0
\(484\) 543.031 258.246i 1.12196 0.533566i
\(485\) 125.759i 0.259297i
\(486\) 0 0
\(487\) −559.612 + 406.582i −1.14910 + 0.834870i −0.988361 0.152127i \(-0.951388\pi\)
−0.160739 + 0.986997i \(0.551388\pi\)
\(488\) −123.165 + 169.522i −0.252387 + 0.347381i
\(489\) 0 0
\(490\) −56.5508 174.045i −0.115410 0.355195i
\(491\) −174.127 + 239.665i −0.354638 + 0.488117i −0.948645 0.316343i \(-0.897545\pi\)
0.594007 + 0.804460i \(0.297545\pi\)
\(492\) 0 0
\(493\) 18.8623 58.0521i 0.0382602 0.117753i
\(494\) 590.462i 1.19527i
\(495\) 0 0
\(496\) 103.192 0.208049
\(497\) 341.323 + 110.903i 0.686766 + 0.223144i
\(498\) 0 0
\(499\) 108.411 + 78.7653i 0.217257 + 0.157846i 0.691091 0.722768i \(-0.257130\pi\)
−0.473834 + 0.880614i \(0.657130\pi\)
\(500\) −361.086 + 117.324i −0.722172 + 0.234648i
\(501\) 0 0
\(502\) 808.139 + 587.147i 1.60984 + 1.16962i
\(503\) −111.681 153.716i −0.222030 0.305598i 0.683442 0.730005i \(-0.260482\pi\)
−0.905471 + 0.424408i \(0.860482\pi\)
\(504\) 0 0
\(505\) −62.8345 −0.124425
\(506\) 141.893 + 628.758i 0.280422 + 1.24261i
\(507\) 0 0
\(508\) 365.449 1124.74i 0.719388 2.21405i
\(509\) −70.0055 96.3543i −0.137535 0.189301i 0.734693 0.678399i \(-0.237326\pi\)
−0.872229 + 0.489098i \(0.837326\pi\)
\(510\) 0 0
\(511\) 92.9982 + 286.219i 0.181992 + 0.560115i
\(512\) −603.181 + 195.985i −1.17809 + 0.382784i
\(513\) 0 0
\(514\) −743.813 + 540.412i −1.44711 + 1.05139i
\(515\) −46.2113 15.0150i −0.0897307 0.0291553i
\(516\) 0 0
\(517\) −247.804 106.634i −0.479312 0.206255i
\(518\) 673.485i 1.30016i
\(519\) 0 0
\(520\) 28.6355 20.8049i 0.0550683 0.0400095i
\(521\) 374.594 515.584i 0.718990 0.989605i −0.280567 0.959835i \(-0.590522\pi\)
0.999557 0.0297704i \(-0.00947761\pi\)
\(522\) 0 0
\(523\) 40.0788 + 123.350i 0.0766325 + 0.235851i 0.982033 0.188707i \(-0.0604297\pi\)
−0.905401 + 0.424558i \(0.860430\pi\)
\(524\) 433.872 597.173i 0.828000 1.13964i
\(525\) 0 0
\(526\) −230.500 + 709.406i −0.438213 + 1.34868i
\(527\) 261.649i 0.496487i
\(528\) 0 0
\(529\) 146.187 0.276346
\(530\) −26.5884 8.63910i −0.0501668 0.0163002i
\(531\) 0 0
\(532\) 348.960 + 253.535i 0.655940 + 0.476569i
\(533\) 209.036 67.9199i 0.392187 0.127429i
\(534\) 0 0
\(535\) −64.8755 47.1348i −0.121263 0.0881025i
\(536\) −136.246 187.526i −0.254190 0.349863i
\(537\) 0 0
\(538\) 589.779 1.09624
\(539\) 313.386 + 275.151i 0.581421 + 0.510484i
\(540\) 0 0
\(541\) −152.652 + 469.814i −0.282166 + 0.868417i 0.705068 + 0.709140i \(0.250916\pi\)
−0.987234 + 0.159278i \(0.949084\pi\)
\(542\) 815.865 + 1122.94i 1.50529 + 2.07185i
\(543\) 0 0
\(544\) 395.172 + 1216.21i 0.726418 + 2.23569i
\(545\) −229.656 + 74.6197i −0.421387 + 0.136917i
\(546\) 0 0
\(547\) 85.8592 62.3803i 0.156964 0.114041i −0.506531 0.862222i \(-0.669072\pi\)
0.663495 + 0.748181i \(0.269072\pi\)
\(548\) 95.2752 + 30.9568i 0.173860 + 0.0564905i
\(549\) 0 0
\(550\) 486.932 554.595i 0.885331 1.00836i
\(551\) 56.1183i 0.101848i
\(552\) 0 0
\(553\) 309.262 224.692i 0.559245 0.406315i
\(554\) −41.2894 + 56.8300i −0.0745296 + 0.102581i
\(555\) 0 0
\(556\) −228.626 703.639i −0.411198 1.26554i
\(557\) 486.473 669.572i 0.873380 1.20210i −0.104830 0.994490i \(-0.533430\pi\)
0.978211 0.207615i \(-0.0665700\pi\)
\(558\) 0 0
\(559\) 1.68236 5.17776i 0.00300958 0.00926254i
\(560\) 60.0113i 0.107163i
\(561\) 0 0
\(562\) 789.001 1.40392
\(563\) −447.869 145.521i −0.795504 0.258475i −0.117058 0.993125i \(-0.537346\pi\)
−0.678446 + 0.734650i \(0.737346\pi\)
\(564\) 0 0
\(565\) −166.209 120.758i −0.294176 0.213731i
\(566\) 102.038 33.1540i 0.180279 0.0585760i
\(567\) 0 0
\(568\) 253.180 + 183.946i 0.445740 + 0.323849i
\(569\) 117.601 + 161.863i 0.206679 + 0.284470i 0.899755 0.436395i \(-0.143745\pi\)
−0.693076 + 0.720865i \(0.743745\pi\)
\(570\) 0 0
\(571\) 658.692 1.15358 0.576788 0.816894i \(-0.304306\pi\)
0.576788 + 0.816894i \(0.304306\pi\)
\(572\) −163.427 + 379.785i −0.285712 + 0.663960i
\(573\) 0 0
\(574\) −89.5526 + 275.615i −0.156015 + 0.480165i
\(575\) 257.635 + 354.604i 0.448061 + 0.616703i
\(576\) 0 0
\(577\) −31.2037 96.0352i −0.0540792 0.166439i 0.920369 0.391051i \(-0.127888\pi\)
−0.974448 + 0.224612i \(0.927888\pi\)
\(578\) 1466.51 476.499i 2.53722 0.824394i
\(579\) 0 0
\(580\) −13.9502 + 10.1354i −0.0240521 + 0.0174749i
\(581\) 398.238 + 129.395i 0.685435 + 0.222711i
\(582\) 0 0
\(583\) 62.1465 14.0247i 0.106598 0.0240562i
\(584\) 262.425i 0.449358i
\(585\) 0 0
\(586\) −276.688 + 201.026i −0.472164 + 0.343047i
\(587\) 205.366 282.662i 0.349857 0.481537i −0.597431 0.801921i \(-0.703812\pi\)
0.947288 + 0.320383i \(0.103812\pi\)
\(588\) 0 0
\(589\) 74.3352 + 228.780i 0.126206 + 0.388421i
\(590\) −209.926 + 288.938i −0.355806 + 0.489725i
\(591\) 0 0
\(592\) 233.361 718.210i 0.394190 1.21319i
\(593\) 670.238i 1.13025i 0.825005 + 0.565125i \(0.191172\pi\)
−0.825005 + 0.565125i \(0.808828\pi\)
\(594\) 0 0
\(595\) −152.161 −0.255733
\(596\) −212.202 68.9488i −0.356044 0.115686i
\(597\) 0 0
\(598\) −358.557 260.507i −0.599593 0.435630i
\(599\) −733.577 + 238.354i −1.22467 + 0.397919i −0.848780 0.528746i \(-0.822662\pi\)
−0.375889 + 0.926665i \(0.622662\pi\)
\(600\) 0 0
\(601\) 150.252 + 109.165i 0.250004 + 0.181638i 0.705728 0.708482i \(-0.250620\pi\)
−0.455725 + 0.890121i \(0.650620\pi\)
\(602\) 4.21926 + 5.80731i 0.00700873 + 0.00964669i
\(603\) 0 0
\(604\) −231.294 −0.382937
\(605\) 35.7600 191.712i 0.0591074 0.316880i
\(606\) 0 0
\(607\) −150.857 + 464.292i −0.248530 + 0.764895i 0.746506 + 0.665378i \(0.231730\pi\)
−0.995036 + 0.0995170i \(0.968270\pi\)
\(608\) −691.059 951.161i −1.13661 1.56441i
\(609\) 0 0
\(610\) 107.645 + 331.297i 0.176467 + 0.543109i
\(611\) 176.415 57.3207i 0.288732 0.0938146i
\(612\) 0 0
\(613\) −412.972 + 300.041i −0.673689 + 0.489464i −0.871258 0.490825i \(-0.836695\pi\)
0.197569 + 0.980289i \(0.436695\pi\)
\(614\) −639.275 207.713i −1.04116 0.338295i
\(615\) 0 0
\(616\) −54.3245 91.4309i −0.0881891 0.148427i
\(617\) 1142.14i 1.85111i 0.378608 + 0.925557i \(0.376403\pi\)
−0.378608 + 0.925557i \(0.623597\pi\)
\(618\) 0 0
\(619\) 734.760 533.834i 1.18701 0.862414i 0.194066 0.980989i \(-0.437832\pi\)
0.992945 + 0.118575i \(0.0378325\pi\)
\(620\) −43.4460 + 59.7983i −0.0700742 + 0.0964488i
\(621\) 0 0
\(622\) −158.419 487.562i −0.254692 0.783862i
\(623\) −163.044 + 224.411i −0.261708 + 0.360210i
\(624\) 0 0
\(625\) 135.017 415.538i 0.216027 0.664862i
\(626\) 820.934i 1.31140i
\(627\) 0 0
\(628\) −90.3126 −0.143810
\(629\) −1821.05 591.696i −2.89515 0.940693i
\(630\) 0 0
\(631\) −764.038 555.106i −1.21084 0.879724i −0.215530 0.976497i \(-0.569148\pi\)
−0.995306 + 0.0967735i \(0.969148\pi\)
\(632\) 317.022 103.007i 0.501617 0.162985i
\(633\) 0 0
\(634\) −1498.70 1088.87i −2.36389 1.71746i
\(635\) −225.446 310.299i −0.355032 0.488660i
\(636\) 0 0
\(637\) −286.750 −0.450157
\(638\) 28.0345 65.1487i 0.0439412 0.102114i
\(639\) 0 0
\(640\) 44.9169 138.240i 0.0701826 0.216000i
\(641\) −211.062 290.502i −0.329270 0.453202i 0.611999 0.790859i \(-0.290366\pi\)
−0.941269 + 0.337657i \(0.890366\pi\)
\(642\) 0 0
\(643\) 286.813 + 882.719i 0.446054 + 1.37281i 0.881324 + 0.472513i \(0.156653\pi\)
−0.435269 + 0.900300i \(0.643347\pi\)
\(644\) 307.916 100.048i 0.478131 0.155354i
\(645\) 0 0
\(646\) −1790.69 + 1301.01i −2.77196 + 2.01395i
\(647\) −414.935 134.821i −0.641322 0.208378i −0.0297382 0.999558i \(-0.509467\pi\)
−0.611584 + 0.791180i \(0.709467\pi\)
\(648\) 0 0
\(649\) 74.9381 810.429i 0.115467 1.24873i
\(650\) 507.458i 0.780705i
\(651\) 0 0
\(652\) −559.487 + 406.491i −0.858110 + 0.623453i
\(653\) 143.077 196.928i 0.219107 0.301575i −0.685287 0.728273i \(-0.740323\pi\)
0.904394 + 0.426698i \(0.140323\pi\)
\(654\) 0 0
\(655\) −73.9782 227.682i −0.112944 0.347605i
\(656\) 190.999 262.888i 0.291158 0.400744i
\(657\) 0 0
\(658\) −75.5777 + 232.604i −0.114860 + 0.353502i
\(659\) 348.053i 0.528153i 0.964502 + 0.264076i \(0.0850671\pi\)
−0.964502 + 0.264076i \(0.914933\pi\)
\(660\) 0 0
\(661\) 601.901 0.910592 0.455296 0.890340i \(-0.349533\pi\)
0.455296 + 0.890340i \(0.349533\pi\)
\(662\) −456.669 148.381i −0.689832 0.224140i
\(663\) 0 0
\(664\) 295.398 + 214.619i 0.444876 + 0.323221i
\(665\) 133.046 43.2294i 0.200070 0.0650066i
\(666\) 0 0
\(667\) 34.0777 + 24.7589i 0.0510910 + 0.0371198i
\(668\) 424.170 + 583.819i 0.634984 + 0.873981i
\(669\) 0 0
\(670\) −385.343 −0.575138
\(671\) −596.532 523.752i −0.889020 0.780555i
\(672\) 0 0
\(673\) 228.328 702.722i 0.339269 1.04416i −0.625312 0.780375i \(-0.715028\pi\)
0.964581 0.263788i \(-0.0849719\pi\)
\(674\) 193.648 + 266.533i 0.287311 + 0.395450i
\(675\) 0 0
\(676\) 171.677 + 528.367i 0.253960 + 0.781608i
\(677\) 40.0554 13.0148i 0.0591661 0.0192242i −0.279284 0.960208i \(-0.590097\pi\)
0.338451 + 0.940984i \(0.390097\pi\)
\(678\) 0 0
\(679\) −210.196 + 152.717i −0.309568 + 0.224914i
\(680\) −126.190 41.0015i −0.185573 0.0602963i
\(681\) 0 0
\(682\) 27.9925 302.729i 0.0410448 0.443885i
\(683\) 543.110i 0.795183i 0.917562 + 0.397592i \(0.130154\pi\)
−0.917562 + 0.397592i \(0.869846\pi\)
\(684\) 0 0
\(685\) 26.2851 19.0972i 0.0383724 0.0278792i
\(686\) 509.453 701.202i 0.742643 1.02216i
\(687\) 0 0
\(688\) −2.48724 7.65492i −0.00361517 0.0111263i
\(689\) −25.7485 + 35.4398i −0.0373708 + 0.0514365i
\(690\) 0 0
\(691\) −132.313 + 407.217i −0.191480 + 0.589315i 0.808519 + 0.588469i \(0.200269\pi\)
−1.00000 0.000845986i \(0.999731\pi\)
\(692\) 1443.22i 2.08558i
\(693\) 0 0
\(694\) −664.080 −0.956887
\(695\) −228.207 74.1488i −0.328355 0.106689i
\(696\) 0 0
\(697\) −666.564 484.287i −0.956333 0.694816i
\(698\) 1328.32 431.599i 1.90304 0.618336i
\(699\) 0 0
\(700\) −299.905 217.894i −0.428436 0.311277i
\(701\) 1.63437 + 2.24952i 0.00233149 + 0.00320902i 0.810181 0.586180i \(-0.199369\pi\)
−0.807850 + 0.589389i \(0.799369\pi\)
\(702\) 0 0
\(703\) 1760.39 2.50411
\(704\) 218.790 + 969.503i 0.310781 + 1.37713i
\(705\) 0 0
\(706\) 457.560 1408.23i 0.648103 1.99465i
\(707\) −76.3037 105.023i −0.107926 0.148547i
\(708\) 0 0
\(709\) 332.968 + 1024.77i 0.469631 + 1.44537i 0.853064 + 0.521806i \(0.174742\pi\)
−0.383433 + 0.923568i \(0.625258\pi\)
\(710\) 494.790 160.767i 0.696888 0.226433i
\(711\) 0 0
\(712\) −195.685 + 142.173i −0.274838 + 0.199682i
\(713\) 171.722 + 55.7959i 0.240844 + 0.0782551i
\(714\) 0 0
\(715\) 68.4946 + 115.280i 0.0957967 + 0.161231i
\(716\) 727.591i 1.01619i
\(717\) 0 0
\(718\) 68.2535 49.5891i 0.0950606 0.0690656i
\(719\) −630.939 + 868.413i −0.877523 + 1.20781i 0.0995782 + 0.995030i \(0.468251\pi\)
−0.977101 + 0.212777i \(0.931749\pi\)
\(720\) 0 0
\(721\) −31.0208 95.4722i −0.0430247 0.132416i
\(722\) 560.625 771.634i 0.776489 1.06875i
\(723\) 0 0
\(724\) −343.160 + 1056.14i −0.473978 + 1.45875i
\(725\) 48.2295i 0.0665234i
\(726\) 0 0
\(727\) −212.371 −0.292119 −0.146060 0.989276i \(-0.546659\pi\)
−0.146060 + 0.989276i \(0.546659\pi\)
\(728\) 69.5476 + 22.5974i 0.0955325 + 0.0310404i
\(729\) 0 0
\(730\) 352.944 + 256.429i 0.483484 + 0.351272i
\(731\) −19.4094 + 6.30649i −0.0265518 + 0.00862721i
\(732\) 0 0
\(733\) 762.274 + 553.825i 1.03994 + 0.755559i 0.970273 0.242011i \(-0.0778072\pi\)
0.0696644 + 0.997570i \(0.477807\pi\)
\(734\) −52.4548 72.1978i −0.0714642 0.0983621i
\(735\) 0 0
\(736\) −882.479 −1.19902
\(737\) 754.938 448.553i 1.02434 0.608620i
\(738\) 0 0
\(739\) −222.759 + 685.580i −0.301432 + 0.927714i 0.679552 + 0.733627i \(0.262174\pi\)
−0.980984 + 0.194086i \(0.937826\pi\)
\(740\) 317.941 + 437.609i 0.429650 + 0.591363i
\(741\) 0 0
\(742\) −17.8483 54.9314i −0.0240543 0.0740316i
\(743\) 795.619 258.512i 1.07082 0.347931i 0.280013 0.959996i \(-0.409661\pi\)
0.790807 + 0.612066i \(0.209661\pi\)
\(744\) 0 0
\(745\) −58.5437 + 42.5345i −0.0785822 + 0.0570933i
\(746\) −894.054 290.496i −1.19846 0.389405i
\(747\) 0 0
\(748\) 1511.86 341.185i 2.02120 0.456130i
\(749\) 165.673i 0.221192i
\(750\) 0 0
\(751\) 28.5315 20.7293i 0.0379913 0.0276023i −0.568628 0.822595i \(-0.692525\pi\)
0.606619 + 0.794993i \(0.292525\pi\)
\(752\) 161.193 221.864i 0.214353 0.295031i
\(753\) 0 0
\(754\) 15.0698 + 46.3802i 0.0199865 + 0.0615122i
\(755\) −44.0922 + 60.6877i −0.0584002 + 0.0803810i
\(756\) 0 0
\(757\) 140.510 432.445i 0.185614 0.571262i −0.814344 0.580382i \(-0.802903\pi\)
0.999958 + 0.00912038i \(0.00290315\pi\)
\(758\) 94.0866i 0.124125i
\(759\) 0 0
\(760\) 121.986 0.160508
\(761\) 99.5654 + 32.3508i 0.130835 + 0.0425108i 0.373703 0.927549i \(-0.378088\pi\)
−0.242868 + 0.970059i \(0.578088\pi\)
\(762\) 0 0
\(763\) −403.605 293.237i −0.528972 0.384320i
\(764\) 109.734 35.6546i 0.143630 0.0466683i
\(765\) 0 0
\(766\) 1150.64 + 835.992i 1.50215 + 1.09137i
\(767\) 328.937 + 452.742i 0.428861 + 0.590277i
\(768\) 0 0
\(769\) −93.7806 −0.121951 −0.0609757 0.998139i \(-0.519421\pi\)
−0.0609757 + 0.998139i \(0.519421\pi\)
\(770\) −176.051 16.2790i −0.228638 0.0211415i
\(771\) 0 0
\(772\) 192.629 592.852i 0.249520 0.767943i
\(773\) −210.854 290.216i −0.272774 0.375441i 0.650550 0.759463i \(-0.274538\pi\)
−0.923324 + 0.384023i \(0.874538\pi\)
\(774\) 0 0
\(775\) −63.8855 196.619i −0.0824329 0.253702i
\(776\) −215.470 + 70.0105i −0.277668 + 0.0902197i
\(777\) 0 0
\(778\) −102.604 + 74.5463i −0.131882 + 0.0958178i
\(779\) 720.416 + 234.077i 0.924796 + 0.300485i
\(780\) 0 0
\(781\) −782.221 + 890.918i −1.00156 + 1.14074i
\(782\) 1661.38i 2.12453i
\(783\) 0 0
\(784\) −342.973 + 249.184i −0.437465 + 0.317837i
\(785\) −17.2165 + 23.6965i −0.0219319 + 0.0301866i
\(786\) 0 0
\(787\) 85.5717 + 263.363i 0.108732 + 0.334641i 0.990588 0.136876i \(-0.0437063\pi\)
−0.881857 + 0.471518i \(0.843706\pi\)