Properties

Label 99.3.l.a.53.2
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 53.2
Character \(\chi\) \(=\) 99.53
Dual form 99.3.l.a.71.2

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

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

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 −0.507243 0.861803i \(-0.669335\pi\)
−0.916923 + 0.399064i \(0.869335\pi\)
\(3\) 0 0
\(4\) 4.02041 + 2.92100i 1.00510 + 0.730250i
\(5\) −1.53284 + 0.498051i −0.306569 + 0.0996102i −0.458261 0.888817i \(-0.651528\pi\)
0.151693 + 0.988428i \(0.451528\pi\)
\(6\) 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 0.622533 0.782593i \(-0.286104\pi\)
0.963637 + 0.267215i \(0.0861035\pi\)
\(18\) 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 \(0.139845\pi\)
−0.905034 + 0.425339i \(0.860155\pi\)
\(24\) 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 −0.786642 0.617410i \(-0.788182\pi\)
0.830277 + 0.557351i \(0.188182\pi\)
\(30\) 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 0.548207 0.836343i \(-0.315310\pi\)
−0.964814 + 0.262932i \(0.915310\pi\)
\(42\) 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 0.627642 0.778502i \(-0.284020\pi\)
−0.934352 + 0.356352i \(0.884020\pi\)
\(48\) 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 0.360520 0.932751i \(-0.382599\pi\)
−0.256590 + 0.966520i \(0.582599\pi\)
\(54\) 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 \(-0.584270\pi\)
0.998779 0.0493973i \(-0.0157300\pi\)
\(60\) 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 −0.923059 0.384658i \(-0.874319\pi\)
−0.520674 + 0.853755i \(0.674319\pi\)
\(72\) 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 −0.922188 0.386741i \(-0.873601\pi\)
−0.518746 + 0.854929i \(0.673601\pi\)
\(84\) 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 \(-0.844975\pi\)
0.883728 0.468000i \(-0.155025\pi\)
\(90\) 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 0.486760 0.873536i \(-0.338179\pi\)
−0.119654 + 0.992816i \(0.538179\pi\)
\(102\) 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 0.923506 0.383584i \(-0.125310\pi\)
−0.650189 + 0.759772i \(0.725310\pi\)
\(108\) 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 0.999578 0.0290640i \(-0.00925266\pi\)
−0.336528 + 0.941673i \(0.609253\pi\)
\(114\) 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 \(0.191869\pi\)
−0.823767 + 0.566929i \(0.808131\pi\)
\(132\) 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 −0.378150 0.925744i \(-0.623440\pi\)
0.238209 + 0.971214i \(0.423440\pi\)
\(138\) 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 −0.162198 0.986758i \(-0.551858\pi\)
0.448781 + 0.893642i \(0.351858\pi\)
\(150\) 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 −0.135210 0.990817i \(-0.543171\pi\)
−0.691775 + 0.722113i \(0.743171\pi\)
\(168\) 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 \(0.117066\pi\)
0.0535891 + 0.998563i \(0.482934\pi\)
\(174\) 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 0.497880 0.867246i \(-0.334112\pi\)
−0.978653 + 0.205519i \(0.934112\pi\)
\(180\) 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 −0.843247 0.537527i \(-0.819359\pi\)
0.771796 + 0.635870i \(0.219359\pi\)
\(192\) 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 \(-0.989993\pi\)
0.999506 0.0314333i \(-0.0100072\pi\)
\(198\) 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 −0.986404 0.164341i \(-0.947450\pi\)
0.461113 + 0.887341i \(0.347450\pi\)
\(228\) 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 0.0733156 0.997309i \(-0.476642\pi\)
−0.526890 + 0.849934i \(0.676642\pi\)
\(234\) 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 \(0.0281837\pi\)
−0.223708 + 0.974656i \(0.571816\pi\)
\(240\) 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 −0.400950 0.916100i \(-0.631320\pi\)
−0.862845 + 0.505468i \(0.831320\pi\)
\(252\) 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 \(-0.596258\pi\)
0.999931 0.0117541i \(-0.00374153\pi\)
\(258\) 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 \(-0.842991\pi\)
0.880794 0.473499i \(-0.157009\pi\)
\(264\) 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 −0.635692 0.771943i \(-0.719285\pi\)
−0.0605488 + 0.998165i \(0.519285\pi\)
\(270\) 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 −0.718785 0.695232i \(-0.755302\pi\)
−0.172862 + 0.984946i \(0.555302\pi\)
\(282\) 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 −0.678964 0.734172i \(-0.737571\pi\)
0.908050 + 0.418861i \(0.137571\pi\)
\(294\) 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 0.939537 0.342447i \(-0.111256\pi\)
−0.616020 + 0.787731i \(0.711256\pi\)
\(312\) 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 \(0.0295812\pi\)
0.860072 + 0.510173i \(0.170419\pi\)
\(318\) 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 0.0110468 0.999939i \(-0.496484\pi\)
0.596686 + 0.802475i \(0.296484\pi\)
\(348\) 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 \(0.246945\pi\)
−0.713860 + 0.700289i \(0.753055\pi\)
\(354\) 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 −0.831455 0.555592i \(-0.812492\pi\)
0.785333 + 0.619073i \(0.212492\pi\)
\(360\) 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 −0.347164 0.937804i \(-0.612855\pi\)
−0.832089 + 0.554642i \(0.812855\pi\)
\(384\) 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 −0.775824 0.630949i \(-0.782666\pi\)
0.839811 + 0.542879i \(0.182666\pi\)
\(390\) 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 −0.889555 0.456828i \(-0.848986\pi\)
−0.451149 + 0.892449i \(0.648986\pi\)
\(402\) 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 \(0.108147\pi\)
−0.942837 + 0.333254i \(0.891853\pi\)
\(420\) 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 −0.0660949 0.997813i \(-0.521054\pi\)
−0.639972 + 0.768398i \(0.721054\pi\)
\(432\) 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 0.767353 0.641225i \(-0.221573\pi\)
−0.846966 + 0.531647i \(0.821573\pi\)
\(444\) 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 −0.642267 0.766481i \(-0.722006\pi\)
−0.970131 + 0.242581i \(0.922006\pi\)
\(450\) 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 \(-0.710945\pi\)
0.615250 0.788332i \(-0.289055\pi\)
\(462\) 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 0.00435192 0.999991i \(-0.498615\pi\)
0.591300 + 0.806451i \(0.298615\pi\)
\(468\) 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 −0.757481 0.652857i \(-0.773570\pi\)
−0.229076 + 0.973409i \(0.573570\pi\)
\(480\) 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 −0.594007 0.804460i \(-0.702455\pi\)
0.948645 + 0.316343i \(0.102455\pi\)
\(492\) 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 0.905471 0.424408i \(-0.139518\pi\)
−0.683442 + 0.730005i \(0.739518\pi\)
\(504\) 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 0.872229 0.489098i \(-0.162674\pi\)
−0.734693 + 0.678399i \(0.762674\pi\)
\(510\) 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 \(0.409478\pi\)
−0.999557 + 0.0297704i \(0.990522\pi\)
\(522\) 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 \(0.466570\pi\)
−0.978211 + 0.207615i \(0.933430\pi\)
\(558\) 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 0.678446 0.734650i \(-0.262654\pi\)
0.117058 + 0.993125i \(0.462654\pi\)
\(564\) 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 0.693076 0.720865i \(-0.256255\pi\)
−0.899755 + 0.436395i \(0.856255\pi\)
\(570\) 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 −0.947288 0.320383i \(-0.896188\pi\)
0.597431 + 0.801921i \(0.296188\pi\)
\(588\) 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 \(-0.808828\pi\)
0.825005 0.565125i \(-0.191172\pi\)
\(594\) 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 0.375889 0.926665i \(-0.377338\pi\)
0.848780 + 0.528746i \(0.177338\pi\)
\(600\) 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 \(-0.623597\pi\)
0.378608 0.925557i \(-0.376403\pi\)
\(618\) 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 0.941269 0.337657i \(-0.109634\pi\)
−0.611999 + 0.790859i \(0.709634\pi\)
\(642\) 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 0.611584 0.791180i \(-0.290533\pi\)
0.0297382 + 0.999558i \(0.490533\pi\)
\(648\) 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 −0.904394 0.426698i \(-0.859677\pi\)
0.685287 + 0.728273i \(0.259677\pi\)
\(654\) 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 \(-0.914933\pi\)
0.964502 0.264076i \(-0.0850671\pi\)
\(660\) 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 −0.338451 0.940984i \(-0.609903\pi\)
0.279284 + 0.960208i \(0.409903\pi\)
\(678\) 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 \(-0.869846\pi\)
0.917562 0.397592i \(-0.130154\pi\)
\(684\) 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 0.807850 0.589389i \(-0.200631\pi\)
−0.810181 + 0.586180i \(0.800631\pi\)
\(702\) 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 \(-0.531749\pi\)
0.977101 0.212777i \(-0.0682506\pi\)
\(720\) 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 −0.790807 0.612066i \(-0.790339\pi\)
−0.280013 + 0.959996i \(0.590339\pi\)
\(744\) 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 0.242868 0.970059i \(-0.421912\pi\)
−0.373703 + 0.927549i \(0.621912\pi\)
\(762\) 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 0.923324 0.384023i \(-0.125462\pi\)
−0.650550 + 0.759463i \(0.725462\pi\)
\(774\) 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 \(0.843706\pi\)