Properties

Label 99.3.l.a.71.2
Level $99$
Weight $3$
Character 99.71
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 71.2
Character \(\chi\) \(=\) 99.71
Dual form 99.3.l.a.53.2

$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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 \(-0.869335\pi\)
−0.507243 + 0.861803i \(0.669335\pi\)
\(3\) 0 0
\(4\) 4.02041 2.92100i 1.00510 0.730250i
\(5\) −1.53284 0.498051i −0.306569 0.0996102i 0.151693 0.988428i \(-0.451528\pi\)
−0.458261 + 0.888817i \(0.651528\pi\)
\(6\) 0 0
\(7\) 2.69388 1.95722i 0.384840 0.279602i −0.378498 0.925602i \(-0.623559\pi\)
0.763338 + 0.646000i \(0.223559\pi\)
\(8\) −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 0.999820 0.0189869i \(-0.00604407\pi\)
−0.820031 + 0.572319i \(0.806044\pi\)
\(14\) −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 \(-0.0861035\pi\)
0.622533 + 0.782593i \(0.286104\pi\)
\(18\) 0 0
\(19\) 21.0884 + 15.3216i 1.10991 + 0.806400i 0.982650 0.185469i \(-0.0593804\pi\)
0.127264 + 0.991869i \(0.459380\pi\)
\(20\) −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 \(-0.188182\pi\)
−0.786642 + 0.617410i \(0.788182\pi\)
\(30\) 0 0
\(31\) −2.85173 8.77673i −0.0919914 0.283120i 0.894467 0.447135i \(-0.147556\pi\)
−0.986458 + 0.164015i \(0.947556\pi\)
\(32\) 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 0.498042 0.867153i \(-0.334052\pi\)
0.978615 0.205701i \(-0.0659475\pi\)
\(38\) −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 \(-0.915310\pi\)
0.548207 + 0.836343i \(0.315310\pi\)
\(42\) 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 \(-0.884020\pi\)
0.627642 + 0.778502i \(0.284020\pi\)
\(48\) 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 \(-0.582599\pi\)
0.360520 + 0.932751i \(0.382599\pi\)
\(54\) 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 0.998779 + 0.0493973i \(0.0157300\pi\)
−0.261660 + 0.965160i \(0.584270\pi\)
\(60\) 0 0
\(61\) 22.3006 68.6343i 0.365584 1.12515i −0.584030 0.811732i \(-0.698525\pi\)
0.949614 0.313421i \(-0.101475\pi\)
\(62\) 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 \(-0.674319\pi\)
−0.923059 + 0.384658i \(0.874319\pi\)
\(72\) 0 0
\(73\) 73.1189 53.1240i 1.00163 0.727726i 0.0391919 0.999232i \(-0.487522\pi\)
0.962437 + 0.271506i \(0.0875216\pi\)
\(74\) −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 0.877969 + 0.478717i \(0.158898\pi\)
−0.428909 + 0.903348i \(0.641102\pi\)
\(80\) 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 \(-0.673601\pi\)
−0.922188 + 0.386741i \(0.873601\pi\)
\(84\) 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 −0.995028 0.0995976i \(-0.968244\pi\)
0.746452 0.665439i \(-0.231756\pi\)
\(98\) 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 \(-0.538179\pi\)
0.486760 + 0.873536i \(0.338179\pi\)
\(102\) 0 0
\(103\) −24.3898 + 17.7202i −0.236794 + 0.172041i −0.699854 0.714286i \(-0.746752\pi\)
0.463060 + 0.886327i \(0.346752\pi\)
\(104\) −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 \(-0.725310\pi\)
0.923506 + 0.383584i \(0.125310\pi\)
\(108\) 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 \(-0.609253\pi\)
0.999578 + 0.0290640i \(0.00925266\pi\)
\(114\) 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 0.0429415 + 0.999078i \(0.486327\pi\)
−0.621983 + 0.783030i \(0.713673\pi\)
\(128\) −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 \(-0.423440\pi\)
−0.378150 + 0.925744i \(0.623440\pi\)
\(138\) 0 0
\(139\) −120.445 + 87.5083i −0.866509 + 0.629556i −0.929648 0.368449i \(-0.879889\pi\)
0.0631388 + 0.998005i \(0.479889\pi\)
\(140\) −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 \(-0.351858\pi\)
−0.162198 + 0.986758i \(0.551858\pi\)
\(150\) 0 0
\(151\) −37.6538 27.3571i −0.249363 0.181173i 0.456081 0.889938i \(-0.349253\pi\)
−0.705444 + 0.708765i \(0.749253\pi\)
\(152\) −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 0.539977 0.841680i \(-0.318433\pi\)
−0.633623 + 0.773642i \(0.718433\pi\)
\(158\) −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 −0.991962 0.126536i \(-0.959614\pi\)
0.728138 0.685431i \(-0.240386\pi\)
\(164\) 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 \(-0.743171\pi\)
−0.135210 + 0.990817i \(0.543171\pi\)
\(168\) 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 0.0535891 0.998563i \(-0.482934\pi\)
0.933130 0.359539i \(-0.117066\pi\)
\(174\) 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 \(-0.934112\pi\)
0.497880 + 0.867246i \(0.334112\pi\)
\(180\) 0 0
\(181\) 69.0532 212.524i 0.381509 1.17417i −0.557471 0.830196i \(-0.688228\pi\)
0.938981 0.343969i \(-0.111772\pi\)
\(182\) −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 \(-0.219359\pi\)
−0.843247 + 0.537527i \(0.819359\pi\)
\(192\) 0 0
\(193\) −38.7623 + 119.298i −0.200841 + 0.618124i 0.799018 + 0.601307i \(0.205353\pi\)
−0.999859 + 0.0168170i \(0.994647\pi\)
\(194\) 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 0.998250 + 0.0591343i \(0.0188340\pi\)
−0.772843 + 0.634597i \(0.781166\pi\)
\(212\) 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 −0.0572631 0.998359i \(-0.518237\pi\)
−0.967191 + 0.254049i \(0.918237\pi\)
\(224\) −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 \(-0.347450\pi\)
−0.986404 + 0.164341i \(0.947450\pi\)
\(228\) 0 0
\(229\) −129.515 398.606i −0.565568 1.74064i −0.666258 0.745721i \(-0.732105\pi\)
0.100690 0.994918i \(-0.467895\pi\)
\(230\) 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 \(-0.676642\pi\)
0.0733156 + 0.997309i \(0.476642\pi\)
\(234\) 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 −0.223708 0.974656i \(-0.571816\pi\)
0.996083 0.0884262i \(-0.0281837\pi\)
\(240\) 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 \(-0.831320\pi\)
−0.400950 + 0.916100i \(0.631320\pi\)
\(252\) 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 0.999931 + 0.0117541i \(0.00374153\pi\)
−0.297817 + 0.954623i \(0.596258\pi\)
\(258\) 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 \(-0.519285\pi\)
−0.635692 + 0.771943i \(0.719285\pi\)
\(270\) 0 0
\(271\) 374.950 272.417i 1.38358 1.00523i 0.387043 0.922061i \(-0.373496\pi\)
0.996536 0.0831675i \(-0.0265037\pi\)
\(272\) −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 0.937121 0.349005i \(-0.113480\pi\)
−0.963287 + 0.268475i \(0.913480\pi\)
\(278\) 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 \(-0.555302\pi\)
−0.718785 + 0.695232i \(0.755302\pi\)
\(282\) 0 0
\(283\) 28.9820 + 21.0566i 0.102410 + 0.0744050i 0.637812 0.770192i \(-0.279840\pi\)
−0.535402 + 0.844597i \(0.679840\pi\)
\(284\) −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 \(-0.137571\pi\)
−0.678964 + 0.734172i \(0.737571\pi\)
\(294\) 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 \(-0.711256\pi\)
0.939537 + 0.342447i \(0.111256\pi\)
\(312\) 0 0
\(313\) −84.7045 + 260.694i −0.270621 + 0.832887i 0.719723 + 0.694261i \(0.244269\pi\)
−0.990345 + 0.138626i \(0.955731\pi\)
\(314\) 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 0.860072 0.510173i \(-0.170419\pi\)
0.995685 0.0927984i \(-0.0295812\pi\)
\(318\) 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 −0.447863 0.894102i \(-0.647815\pi\)
0.711944 + 0.702236i \(0.247815\pi\)
\(338\) −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 \(-0.296484\pi\)
0.0110468 + 0.999939i \(0.496484\pi\)
\(348\) 0 0
\(349\) 377.286 + 274.115i 1.08105 + 0.785429i 0.977866 0.209234i \(-0.0670969\pi\)
0.103184 + 0.994662i \(0.467097\pi\)
\(350\) 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 \(-0.212492\pi\)
−0.831455 + 0.555592i \(0.812492\pi\)
\(360\) 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 −0.620144 0.784488i \(-0.712926\pi\)
0.554458 + 0.832212i \(0.312926\pi\)
\(368\) 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 −0.963047 0.269335i \(-0.913196\pi\)
0.937432 + 0.348168i \(0.113196\pi\)
\(380\) −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 \(-0.812855\pi\)
−0.347164 + 0.937804i \(0.612855\pi\)
\(384\) 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 \(-0.182666\pi\)
−0.775824 + 0.630949i \(0.782666\pi\)
\(390\) 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 \(-0.648986\pi\)
−0.889555 + 0.456828i \(0.848986\pi\)
\(402\) 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 0.995055 0.0993261i \(-0.0316687\pi\)
−0.863399 + 0.504522i \(0.831669\pi\)
\(410\) −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 0.150170 0.988660i \(-0.452018\pi\)
−0.893867 + 0.448333i \(0.852018\pi\)
\(422\) −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 \(-0.721054\pi\)
−0.0660949 + 0.997813i \(0.521054\pi\)
\(432\) 0 0
\(433\) −425.660 + 309.260i −0.983049 + 0.714227i −0.958388 0.285469i \(-0.907851\pi\)
−0.0246608 + 0.999696i \(0.507851\pi\)
\(434\) 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 \(-0.821573\pi\)
0.767353 + 0.641225i \(0.221573\pi\)
\(444\) 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 \(-0.922006\pi\)
−0.642267 + 0.766481i \(0.722006\pi\)
\(450\) 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 0.213465 + 0.976951i \(0.431525\pi\)
−0.746934 + 0.664898i \(0.768475\pi\)
\(458\) 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 \(-0.298615\pi\)
0.00435192 + 0.999991i \(0.498615\pi\)
\(468\) 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 \(-0.573570\pi\)
−0.757481 + 0.652857i \(0.773570\pi\)
\(480\) 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 −0.160739 0.986997i \(-0.551388\pi\)
−0.988361 + 0.152127i \(0.951388\pi\)
\(488\) 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 \(-0.102455\pi\)
−0.594007 + 0.804460i \(0.702455\pi\)
\(492\) 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 −0.473834 0.880614i \(-0.657130\pi\)
0.691091 + 0.722768i \(0.257130\pi\)
\(500\) 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 \(-0.739518\pi\)
0.905471 + 0.424408i \(0.139518\pi\)
\(504\) 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 \(-0.762674\pi\)
0.872229 + 0.489098i \(0.162674\pi\)
\(510\) 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 −0.999557 0.0297704i \(-0.990522\pi\)
0.280567 0.959835i \(-0.409478\pi\)
\(522\) 0 0
\(523\) 40.0788 123.350i 0.0766325 0.235851i −0.905401 0.424558i \(-0.860430\pi\)
0.982033 + 0.188707i \(0.0604297\pi\)
\(524\) −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 −0.987234 0.159278i \(-0.949084\pi\)
0.705068 0.709140i \(-0.250916\pi\)
\(542\) −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 0.663495 0.748181i \(-0.269072\pi\)
−0.506531 + 0.862222i \(0.669072\pi\)
\(548\) −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 −0.978211 0.207615i \(-0.933430\pi\)
0.104830 0.994490i \(-0.466570\pi\)
\(558\) 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 \(-0.462654\pi\)
0.678446 + 0.734650i \(0.262654\pi\)
\(564\) 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 \(-0.856255\pi\)
0.693076 + 0.720865i \(0.256255\pi\)
\(570\) 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 −0.974448 0.224612i \(-0.927888\pi\)
0.920369 + 0.391051i \(0.127888\pi\)
\(578\) −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 \(-0.296188\pi\)
−0.947288 + 0.320383i \(0.896188\pi\)
\(588\) 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 \(-0.177338\pi\)
0.375889 + 0.926665i \(0.377338\pi\)
\(600\) 0 0
\(601\) 150.252 109.165i 0.250004 0.181638i −0.455725 0.890121i \(-0.650620\pi\)
0.705728 + 0.708482i \(0.250620\pi\)
\(602\) −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 −0.995036 0.0995170i \(-0.968270\pi\)
0.746506 0.665378i \(-0.231730\pi\)
\(608\) 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 0.197569 0.980289i \(-0.436695\pi\)
−0.871258 + 0.490825i \(0.836695\pi\)
\(614\) 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 0.992945 0.118575i \(-0.0378325\pi\)
0.194066 + 0.980989i \(0.437832\pi\)
\(620\) 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 −0.995306 0.0967735i \(-0.969148\pi\)
−0.215530 + 0.976497i \(0.569148\pi\)
\(632\) −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 \(-0.709634\pi\)
0.941269 + 0.337657i \(0.109634\pi\)
\(642\) 0 0
\(643\) 286.813 882.719i 0.446054 1.37281i −0.435269 0.900300i \(-0.643347\pi\)
0.881324 0.472513i \(-0.156653\pi\)
\(644\) −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 \(-0.490533\pi\)
0.611584 + 0.791180i \(0.290533\pi\)
\(648\) 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 \(-0.259677\pi\)
−0.904394 + 0.426698i \(0.859677\pi\)
\(654\) 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 0.964581 + 0.263788i \(0.0849719\pi\)
−0.625312 + 0.780375i \(0.715028\pi\)
\(674\) −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 \(-0.409903\pi\)
−0.338451 + 0.940984i \(0.609903\pi\)
\(678\) 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 −1.00000 0.000845986i \(-0.999731\pi\)
0.808519 0.588469i \(-0.200269\pi\)
\(692\) 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 \(-0.800631\pi\)
0.807850 + 0.589389i \(0.200631\pi\)
\(702\) 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 −0.383433 0.923568i \(-0.625258\pi\)
0.853064 0.521806i \(-0.174742\pi\)
\(710\) −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 0.977101 + 0.212777i \(0.0682506\pi\)
−0.0995782 + 0.995030i \(0.531749\pi\)
\(720\) 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 0.0696644 0.997570i \(-0.477807\pi\)
0.970273 + 0.242011i \(0.0778072\pi\)
\(734\) 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 −0.980984 0.194086i \(-0.937826\pi\)
0.679552 0.733627i \(-0.262174\pi\)
\(740\) −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 \(-0.590339\pi\)
−0.790807 + 0.612066i \(0.790339\pi\)
\(744\) 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 0.606619 0.794993i \(-0.292525\pi\)
−0.568628 + 0.822595i \(0.692525\pi\)
\(752\) −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 0.999958 0.00912038i \(-0.00290315\pi\)
−0.814344 + 0.580382i \(0.802903\pi\)
\(758\) 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 \(-0.621912\pi\)
0.242868 + 0.970059i \(0.421912\pi\)
\(762\) 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 \(-0.725462\pi\)
0.923324 + 0.384023i \(0.125462\pi\)
\(774\) 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 −0.881857 0.471518i \(-0.843706\pi\)
0.990588 + 0.136876i