Properties

Label 108.3.k.a.41.3
Level 108
Weight 3
Character 108.41
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 41.3
Character \(\chi\) \(=\) 108.41
Dual form 108.3.k.a.29.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.776129 - 2.89787i) q^{3} +(2.68656 - 3.20172i) q^{5} +(-4.88621 - 1.77844i) q^{7} +(-7.79525 + 4.49824i) q^{9} +O(q^{10})\) \(q+(-0.776129 - 2.89787i) q^{3} +(2.68656 - 3.20172i) q^{5} +(-4.88621 - 1.77844i) q^{7} +(-7.79525 + 4.49824i) q^{9} +(-4.52170 - 5.38875i) q^{11} +(3.33062 - 18.8889i) q^{13} +(-11.3633 - 5.30034i) q^{15} +(20.3965 + 11.7759i) q^{17} +(-11.7859 - 20.4138i) q^{19} +(-1.36134 + 15.5399i) q^{21} +(8.16612 + 22.4362i) q^{23} +(1.30781 + 7.41698i) q^{25} +(19.0854 + 19.0984i) q^{27} +(21.2148 - 3.74075i) q^{29} +(24.0093 - 8.73866i) q^{31} +(-12.1065 + 17.2856i) q^{33} +(-18.8212 + 10.8664i) q^{35} +(-6.81584 + 11.8054i) q^{37} +(-57.3224 + 5.00853i) q^{39} +(50.7253 + 8.94424i) q^{41} +(3.55532 - 2.98327i) q^{43} +(-6.54032 + 37.0430i) q^{45} +(1.64224 - 4.51203i) q^{47} +(-16.8239 - 14.1170i) q^{49} +(18.2947 - 68.2459i) q^{51} +67.3308i q^{53} -29.4011 q^{55} +(-50.0089 + 49.9976i) q^{57} +(55.7367 - 66.4244i) q^{59} +(50.3038 + 18.3091i) q^{61} +(46.0891 - 8.11599i) q^{63} +(-51.5290 - 61.4098i) q^{65} +(3.49276 - 19.8084i) q^{67} +(58.6792 - 41.0777i) q^{69} +(-85.2808 - 49.2369i) q^{71} +(-69.6234 - 120.591i) q^{73} +(20.4784 - 9.54640i) q^{75} +(12.5104 + 34.3721i) q^{77} +(18.3268 + 103.937i) q^{79} +(40.5318 - 70.1297i) q^{81} +(-79.2540 + 13.9746i) q^{83} +(92.4995 - 33.6671i) q^{85} +(-27.3056 - 58.5744i) q^{87} +(-58.0744 + 33.5293i) q^{89} +(-49.8668 + 86.3718i) q^{91} +(-43.9577 - 62.7933i) q^{93} +(-97.0226 - 17.1077i) q^{95} +(-112.041 + 94.0132i) q^{97} +(59.4876 + 21.6670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.776129 2.89787i −0.258710 0.965955i
\(4\) 0 0
\(5\) 2.68656 3.20172i 0.537312 0.640344i −0.427271 0.904124i \(-0.640525\pi\)
0.964583 + 0.263780i \(0.0849693\pi\)
\(6\) 0 0
\(7\) −4.88621 1.77844i −0.698031 0.254062i −0.0314608 0.999505i \(-0.510016\pi\)
−0.666570 + 0.745443i \(0.732238\pi\)
\(8\) 0 0
\(9\) −7.79525 + 4.49824i −0.866139 + 0.499804i
\(10\) 0 0
\(11\) −4.52170 5.38875i −0.411064 0.489886i 0.520297 0.853986i \(-0.325821\pi\)
−0.931360 + 0.364099i \(0.881377\pi\)
\(12\) 0 0
\(13\) 3.33062 18.8889i 0.256202 1.45299i −0.536768 0.843730i \(-0.680355\pi\)
0.792970 0.609261i \(-0.208534\pi\)
\(14\) 0 0
\(15\) −11.3633 5.30034i −0.757551 0.353356i
\(16\) 0 0
\(17\) 20.3965 + 11.7759i 1.19979 + 0.692701i 0.960509 0.278249i \(-0.0897541\pi\)
0.239284 + 0.970950i \(0.423087\pi\)
\(18\) 0 0
\(19\) −11.7859 20.4138i −0.620310 1.07441i −0.989428 0.145026i \(-0.953674\pi\)
0.369118 0.929383i \(-0.379660\pi\)
\(20\) 0 0
\(21\) −1.36134 + 15.5399i −0.0648255 + 0.739995i
\(22\) 0 0
\(23\) 8.16612 + 22.4362i 0.355049 + 0.975489i 0.980723 + 0.195404i \(0.0626018\pi\)
−0.625674 + 0.780085i \(0.715176\pi\)
\(24\) 0 0
\(25\) 1.30781 + 7.41698i 0.0523125 + 0.296679i
\(26\) 0 0
\(27\) 19.0854 + 19.0984i 0.706867 + 0.707347i
\(28\) 0 0
\(29\) 21.2148 3.74075i 0.731546 0.128991i 0.204547 0.978857i \(-0.434428\pi\)
0.527000 + 0.849866i \(0.323317\pi\)
\(30\) 0 0
\(31\) 24.0093 8.73866i 0.774492 0.281892i 0.0756183 0.997137i \(-0.475907\pi\)
0.698874 + 0.715245i \(0.253685\pi\)
\(32\) 0 0
\(33\) −12.1065 + 17.2856i −0.366862 + 0.523807i
\(34\) 0 0
\(35\) −18.8212 + 10.8664i −0.537747 + 0.310469i
\(36\) 0 0
\(37\) −6.81584 + 11.8054i −0.184212 + 0.319064i −0.943311 0.331911i \(-0.892307\pi\)
0.759099 + 0.650975i \(0.225640\pi\)
\(38\) 0 0
\(39\) −57.3224 + 5.00853i −1.46981 + 0.128424i
\(40\) 0 0
\(41\) 50.7253 + 8.94424i 1.23720 + 0.218152i 0.753716 0.657200i \(-0.228259\pi\)
0.483486 + 0.875352i \(0.339370\pi\)
\(42\) 0 0
\(43\) 3.55532 2.98327i 0.0826818 0.0693783i −0.600510 0.799617i \(-0.705036\pi\)
0.683192 + 0.730239i \(0.260591\pi\)
\(44\) 0 0
\(45\) −6.54032 + 37.0430i −0.145340 + 0.823177i
\(46\) 0 0
\(47\) 1.64224 4.51203i 0.0349413 0.0960006i −0.920995 0.389574i \(-0.872622\pi\)
0.955937 + 0.293573i \(0.0948445\pi\)
\(48\) 0 0
\(49\) −16.8239 14.1170i −0.343346 0.288101i
\(50\) 0 0
\(51\) 18.2947 68.2459i 0.358720 1.33815i
\(52\) 0 0
\(53\) 67.3308i 1.27039i 0.772351 + 0.635196i \(0.219081\pi\)
−0.772351 + 0.635196i \(0.780919\pi\)
\(54\) 0 0
\(55\) −29.4011 −0.534565
\(56\) 0 0
\(57\) −50.0089 + 49.9976i −0.877350 + 0.877151i
\(58\) 0 0
\(59\) 55.7367 66.4244i 0.944690 1.12584i −0.0472185 0.998885i \(-0.515036\pi\)
0.991909 0.126953i \(-0.0405198\pi\)
\(60\) 0 0
\(61\) 50.3038 + 18.3091i 0.824653 + 0.300149i 0.719663 0.694324i \(-0.244297\pi\)
0.104991 + 0.994473i \(0.466519\pi\)
\(62\) 0 0
\(63\) 46.0891 8.11599i 0.731572 0.128825i
\(64\) 0 0
\(65\) −51.5290 61.4098i −0.792753 0.944767i
\(66\) 0 0
\(67\) 3.49276 19.8084i 0.0521307 0.295648i −0.947585 0.319505i \(-0.896483\pi\)
0.999715 + 0.0238568i \(0.00759458\pi\)
\(68\) 0 0
\(69\) 58.6792 41.0777i 0.850424 0.595330i
\(70\) 0 0
\(71\) −85.2808 49.2369i −1.20114 0.693477i −0.240329 0.970691i \(-0.577255\pi\)
−0.960808 + 0.277214i \(0.910589\pi\)
\(72\) 0 0
\(73\) −69.6234 120.591i −0.953745 1.65193i −0.737215 0.675659i \(-0.763859\pi\)
−0.216530 0.976276i \(-0.569474\pi\)
\(74\) 0 0
\(75\) 20.4784 9.54640i 0.273045 0.127285i
\(76\) 0 0
\(77\) 12.5104 + 34.3721i 0.162473 + 0.446391i
\(78\) 0 0
\(79\) 18.3268 + 103.937i 0.231985 + 1.31565i 0.848871 + 0.528600i \(0.177283\pi\)
−0.616886 + 0.787053i \(0.711606\pi\)
\(80\) 0 0
\(81\) 40.5318 70.1297i 0.500392 0.865799i
\(82\) 0 0
\(83\) −79.2540 + 13.9746i −0.954867 + 0.168369i −0.629311 0.777154i \(-0.716663\pi\)
−0.325557 + 0.945523i \(0.605552\pi\)
\(84\) 0 0
\(85\) 92.4995 33.6671i 1.08823 0.396083i
\(86\) 0 0
\(87\) −27.3056 58.5744i −0.313858 0.673269i
\(88\) 0 0
\(89\) −58.0744 + 33.5293i −0.652521 + 0.376733i −0.789421 0.613852i \(-0.789619\pi\)
0.136900 + 0.990585i \(0.456286\pi\)
\(90\) 0 0
\(91\) −49.8668 + 86.3718i −0.547987 + 0.949141i
\(92\) 0 0
\(93\) −43.9577 62.7933i −0.472664 0.675197i
\(94\) 0 0
\(95\) −97.0226 17.1077i −1.02129 0.180081i
\(96\) 0 0
\(97\) −112.041 + 94.0132i −1.15506 + 0.969208i −0.999826 0.0186698i \(-0.994057\pi\)
−0.155232 + 0.987878i \(0.549612\pi\)
\(98\) 0 0
\(99\) 59.4876 + 21.6670i 0.600885 + 0.218858i
\(100\) 0 0
\(101\) 33.7340 92.6834i 0.334000 0.917657i −0.653060 0.757306i \(-0.726515\pi\)
0.987060 0.160351i \(-0.0512626\pi\)
\(102\) 0 0
\(103\) 107.050 + 89.8257i 1.03932 + 0.872094i 0.991931 0.126783i \(-0.0404651\pi\)
0.0473903 + 0.998876i \(0.484910\pi\)
\(104\) 0 0
\(105\) 46.0970 + 46.1075i 0.439019 + 0.439119i
\(106\) 0 0
\(107\) 73.3054i 0.685098i 0.939500 + 0.342549i \(0.111290\pi\)
−0.939500 + 0.342549i \(0.888710\pi\)
\(108\) 0 0
\(109\) −82.6310 −0.758083 −0.379041 0.925380i \(-0.623746\pi\)
−0.379041 + 0.925380i \(0.623746\pi\)
\(110\) 0 0
\(111\) 39.5004 + 10.5889i 0.355859 + 0.0953953i
\(112\) 0 0
\(113\) 111.471 132.846i 0.986466 1.17562i 0.00200959 0.999998i \(-0.499360\pi\)
0.984457 0.175627i \(-0.0561952\pi\)
\(114\) 0 0
\(115\) 93.7733 + 34.1307i 0.815420 + 0.296789i
\(116\) 0 0
\(117\) 59.0036 + 162.225i 0.504305 + 1.38654i
\(118\) 0 0
\(119\) −78.7188 93.8134i −0.661503 0.788348i
\(120\) 0 0
\(121\) 12.4186 70.4291i 0.102633 0.582059i
\(122\) 0 0
\(123\) −13.4502 153.937i −0.109351 1.25152i
\(124\) 0 0
\(125\) 117.750 + 67.9832i 0.942003 + 0.543866i
\(126\) 0 0
\(127\) 111.534 + 193.183i 0.878223 + 1.52113i 0.853290 + 0.521437i \(0.174604\pi\)
0.0249327 + 0.999689i \(0.492063\pi\)
\(128\) 0 0
\(129\) −11.4045 7.98743i −0.0884069 0.0619181i
\(130\) 0 0
\(131\) 76.0508 + 208.948i 0.580540 + 1.59502i 0.787260 + 0.616621i \(0.211499\pi\)
−0.206719 + 0.978400i \(0.566279\pi\)
\(132\) 0 0
\(133\) 21.2838 + 120.706i 0.160029 + 0.907567i
\(134\) 0 0
\(135\) 112.422 9.79716i 0.832753 0.0725715i
\(136\) 0 0
\(137\) −159.835 + 28.1833i −1.16668 + 0.205717i −0.723247 0.690590i \(-0.757351\pi\)
−0.443434 + 0.896307i \(0.646240\pi\)
\(138\) 0 0
\(139\) −71.5107 + 26.0278i −0.514466 + 0.187250i −0.586189 0.810174i \(-0.699372\pi\)
0.0717232 + 0.997425i \(0.477150\pi\)
\(140\) 0 0
\(141\) −14.3498 1.25708i −0.101772 0.00891549i
\(142\) 0 0
\(143\) −116.848 + 67.4620i −0.817116 + 0.471762i
\(144\) 0 0
\(145\) 45.0181 77.9737i 0.310470 0.537749i
\(146\) 0 0
\(147\) −27.8515 + 59.7101i −0.189466 + 0.406191i
\(148\) 0 0
\(149\) −90.4646 15.9514i −0.607145 0.107056i −0.138380 0.990379i \(-0.544190\pi\)
−0.468765 + 0.883323i \(0.655301\pi\)
\(150\) 0 0
\(151\) 37.2582 31.2633i 0.246743 0.207042i −0.511025 0.859566i \(-0.670734\pi\)
0.757768 + 0.652524i \(0.226290\pi\)
\(152\) 0 0
\(153\) −211.966 0.0479806i −1.38540 0.000313599i
\(154\) 0 0
\(155\) 36.5236 100.348i 0.235636 0.647405i
\(156\) 0 0
\(157\) −78.3333 65.7295i −0.498938 0.418659i 0.358278 0.933615i \(-0.383364\pi\)
−0.857217 + 0.514956i \(0.827808\pi\)
\(158\) 0 0
\(159\) 195.116 52.2574i 1.22714 0.328663i
\(160\) 0 0
\(161\) 124.151i 0.771125i
\(162\) 0 0
\(163\) −42.0106 −0.257734 −0.128867 0.991662i \(-0.541134\pi\)
−0.128867 + 0.991662i \(0.541134\pi\)
\(164\) 0 0
\(165\) 22.8190 + 85.2004i 0.138297 + 0.516366i
\(166\) 0 0
\(167\) −7.62167 + 9.08316i −0.0456388 + 0.0543902i −0.788381 0.615187i \(-0.789080\pi\)
0.742742 + 0.669578i \(0.233525\pi\)
\(168\) 0 0
\(169\) −186.889 68.0220i −1.10585 0.402497i
\(170\) 0 0
\(171\) 183.700 + 106.115i 1.07427 + 0.620553i
\(172\) 0 0
\(173\) 119.692 + 142.643i 0.691860 + 0.824527i 0.991579 0.129500i \(-0.0413374\pi\)
−0.299719 + 0.954028i \(0.596893\pi\)
\(174\) 0 0
\(175\) 6.80037 38.5668i 0.0388592 0.220382i
\(176\) 0 0
\(177\) −235.748 109.964i −1.33191 0.621263i
\(178\) 0 0
\(179\) −82.0051 47.3456i −0.458129 0.264501i 0.253128 0.967433i \(-0.418541\pi\)
−0.711257 + 0.702932i \(0.751874\pi\)
\(180\) 0 0
\(181\) −56.7101 98.2247i −0.313315 0.542678i 0.665763 0.746164i \(-0.268106\pi\)
−0.979078 + 0.203486i \(0.934773\pi\)
\(182\) 0 0
\(183\) 14.0150 159.984i 0.0765849 0.874230i
\(184\) 0 0
\(185\) 19.4863 + 53.5383i 0.105332 + 0.289396i
\(186\) 0 0
\(187\) −28.7693 163.159i −0.153846 0.872506i
\(188\) 0 0
\(189\) −59.2901 127.261i −0.313704 0.673338i
\(190\) 0 0
\(191\) 305.366 53.8443i 1.59878 0.281907i 0.697970 0.716127i \(-0.254087\pi\)
0.900807 + 0.434220i \(0.142976\pi\)
\(192\) 0 0
\(193\) 207.986 75.7007i 1.07765 0.392232i 0.258616 0.965980i \(-0.416734\pi\)
0.819031 + 0.573749i \(0.194511\pi\)
\(194\) 0 0
\(195\) −137.964 + 196.986i −0.707509 + 1.01018i
\(196\) 0 0
\(197\) 129.101 74.5366i 0.655336 0.378359i −0.135161 0.990824i \(-0.543155\pi\)
0.790498 + 0.612465i \(0.209822\pi\)
\(198\) 0 0
\(199\) 84.5042 146.366i 0.424644 0.735506i −0.571743 0.820433i \(-0.693732\pi\)
0.996387 + 0.0849273i \(0.0270658\pi\)
\(200\) 0 0
\(201\) −60.1129 + 5.25235i −0.299069 + 0.0261311i
\(202\) 0 0
\(203\) −110.313 19.4511i −0.543413 0.0958184i
\(204\) 0 0
\(205\) 164.913 138.379i 0.804456 0.675019i
\(206\) 0 0
\(207\) −164.580 138.163i −0.795075 0.667454i
\(208\) 0 0
\(209\) −56.7124 + 155.816i −0.271351 + 0.745531i
\(210\) 0 0
\(211\) −163.282 137.010i −0.773849 0.649337i 0.167842 0.985814i \(-0.446320\pi\)
−0.941692 + 0.336477i \(0.890765\pi\)
\(212\) 0 0
\(213\) −76.4929 + 285.346i −0.359122 + 1.33965i
\(214\) 0 0
\(215\) 19.3978i 0.0902225i
\(216\) 0 0
\(217\) −132.856 −0.612238
\(218\) 0 0
\(219\) −295.420 + 295.354i −1.34895 + 1.34865i
\(220\) 0 0
\(221\) 290.367 346.046i 1.31388 1.56582i
\(222\) 0 0
\(223\) 51.1847 + 18.6297i 0.229528 + 0.0835412i 0.454224 0.890888i \(-0.349917\pi\)
−0.224696 + 0.974429i \(0.572139\pi\)
\(224\) 0 0
\(225\) −43.5580 51.9343i −0.193591 0.230819i
\(226\) 0 0
\(227\) 56.5301 + 67.3699i 0.249031 + 0.296784i 0.876050 0.482220i \(-0.160170\pi\)
−0.627019 + 0.779004i \(0.715725\pi\)
\(228\) 0 0
\(229\) −45.0976 + 255.761i −0.196933 + 1.11686i 0.712706 + 0.701462i \(0.247469\pi\)
−0.909639 + 0.415399i \(0.863642\pi\)
\(230\) 0 0
\(231\) 89.8961 62.9308i 0.389161 0.272428i
\(232\) 0 0
\(233\) 188.673 + 108.930i 0.809753 + 0.467511i 0.846870 0.531800i \(-0.178484\pi\)
−0.0371169 + 0.999311i \(0.511817\pi\)
\(234\) 0 0
\(235\) −10.0343 17.3798i −0.0426989 0.0739567i
\(236\) 0 0
\(237\) 286.970 133.777i 1.21085 0.564460i
\(238\) 0 0
\(239\) 103.904 + 285.473i 0.434744 + 1.19445i 0.942868 + 0.333165i \(0.108117\pi\)
−0.508125 + 0.861284i \(0.669661\pi\)
\(240\) 0 0
\(241\) −33.0793 187.602i −0.137259 0.778432i −0.973260 0.229705i \(-0.926224\pi\)
0.836002 0.548727i \(-0.184887\pi\)
\(242\) 0 0
\(243\) −234.684 63.0258i −0.965779 0.259366i
\(244\) 0 0
\(245\) −90.3970 + 15.9394i −0.368967 + 0.0650589i
\(246\) 0 0
\(247\) −424.847 + 154.632i −1.72003 + 0.626040i
\(248\) 0 0
\(249\) 102.008 + 218.821i 0.409670 + 0.878800i
\(250\) 0 0
\(251\) 244.229 141.006i 0.973023 0.561775i 0.0728668 0.997342i \(-0.476785\pi\)
0.900157 + 0.435566i \(0.143452\pi\)
\(252\) 0 0
\(253\) 83.9786 145.455i 0.331931 0.574921i
\(254\) 0 0
\(255\) −169.354 241.921i −0.664134 0.948710i
\(256\) 0 0
\(257\) −425.035 74.9451i −1.65383 0.291615i −0.732609 0.680649i \(-0.761698\pi\)
−0.921223 + 0.389034i \(0.872809\pi\)
\(258\) 0 0
\(259\) 54.2988 45.5621i 0.209648 0.175915i
\(260\) 0 0
\(261\) −148.548 + 124.589i −0.569150 + 0.477354i
\(262\) 0 0
\(263\) −111.156 + 305.400i −0.422648 + 1.16121i 0.527538 + 0.849531i \(0.323115\pi\)
−0.950186 + 0.311684i \(0.899107\pi\)
\(264\) 0 0
\(265\) 215.574 + 180.888i 0.813488 + 0.682597i
\(266\) 0 0
\(267\) 142.236 + 142.269i 0.532721 + 0.532841i
\(268\) 0 0
\(269\) 222.465i 0.827009i 0.910502 + 0.413504i \(0.135695\pi\)
−0.910502 + 0.413504i \(0.864305\pi\)
\(270\) 0 0
\(271\) 416.652 1.53746 0.768730 0.639574i \(-0.220889\pi\)
0.768730 + 0.639574i \(0.220889\pi\)
\(272\) 0 0
\(273\) 288.997 + 77.4716i 1.05860 + 0.283779i
\(274\) 0 0
\(275\) 34.0547 40.5848i 0.123835 0.147581i
\(276\) 0 0
\(277\) −55.3380 20.1414i −0.199776 0.0727126i 0.240194 0.970725i \(-0.422789\pi\)
−0.439971 + 0.898012i \(0.645011\pi\)
\(278\) 0 0
\(279\) −147.850 + 176.119i −0.529927 + 0.631252i
\(280\) 0 0
\(281\) 187.499 + 223.452i 0.667255 + 0.795204i 0.988408 0.151824i \(-0.0485146\pi\)
−0.321152 + 0.947028i \(0.604070\pi\)
\(282\) 0 0
\(283\) 15.3422 87.0101i 0.0542128 0.307456i −0.945629 0.325248i \(-0.894552\pi\)
0.999842 + 0.0177914i \(0.00566349\pi\)
\(284\) 0 0
\(285\) 25.7262 + 294.436i 0.0902675 + 1.03311i
\(286\) 0 0
\(287\) −231.948 133.915i −0.808181 0.466603i
\(288\) 0 0
\(289\) 132.844 + 230.093i 0.459668 + 0.796169i
\(290\) 0 0
\(291\) 359.396 + 251.712i 1.23504 + 0.864990i
\(292\) 0 0
\(293\) 105.430 + 289.667i 0.359830 + 0.988624i 0.979088 + 0.203437i \(0.0652111\pi\)
−0.619258 + 0.785187i \(0.712567\pi\)
\(294\) 0 0
\(295\) −62.9322 356.906i −0.213330 1.20985i
\(296\) 0 0
\(297\) 16.6179 189.204i 0.0559525 0.637049i
\(298\) 0 0
\(299\) 450.994 79.5224i 1.50834 0.265961i
\(300\) 0 0
\(301\) −22.6776 + 8.25397i −0.0753408 + 0.0274218i
\(302\) 0 0
\(303\) −294.766 25.8223i −0.972825 0.0852221i
\(304\) 0 0
\(305\) 193.765 111.870i 0.635295 0.366788i
\(306\) 0 0
\(307\) −93.8952 + 162.631i −0.305847 + 0.529743i −0.977450 0.211169i \(-0.932273\pi\)
0.671602 + 0.740912i \(0.265606\pi\)
\(308\) 0 0
\(309\) 177.218 379.933i 0.573521 1.22956i
\(310\) 0 0
\(311\) −551.764 97.2909i −1.77416 0.312833i −0.811664 0.584124i \(-0.801438\pi\)
−0.962497 + 0.271292i \(0.912549\pi\)
\(312\) 0 0
\(313\) −229.337 + 192.436i −0.732706 + 0.614813i −0.930868 0.365356i \(-0.880947\pi\)
0.198162 + 0.980169i \(0.436503\pi\)
\(314\) 0 0
\(315\) 97.8359 169.368i 0.310590 0.537677i
\(316\) 0 0
\(317\) −50.1956 + 137.911i −0.158346 + 0.435051i −0.993342 0.115205i \(-0.963248\pi\)
0.834996 + 0.550256i \(0.185470\pi\)
\(318\) 0 0
\(319\) −116.085 97.4069i −0.363903 0.305351i
\(320\) 0 0
\(321\) 212.429 56.8945i 0.661773 0.177241i
\(322\) 0 0
\(323\) 555.158i 1.71876i
\(324\) 0 0
\(325\) 144.454 0.444475
\(326\) 0 0
\(327\) 64.1323 + 239.454i 0.196123 + 0.732274i
\(328\) 0 0
\(329\) −16.0487 + 19.1261i −0.0487803 + 0.0581340i
\(330\) 0 0
\(331\) −203.791 74.1738i −0.615683 0.224090i 0.0153052 0.999883i \(-0.495128\pi\)
−0.630988 + 0.775793i \(0.717350\pi\)
\(332\) 0 0
\(333\) 0.0277709 122.685i 8.33962e−5 0.368424i
\(334\) 0 0
\(335\) −54.0374 64.3993i −0.161306 0.192237i
\(336\) 0 0
\(337\) −11.0619 + 62.7349i −0.0328245 + 0.186157i −0.996812 0.0797923i \(-0.974574\pi\)
0.963987 + 0.265949i \(0.0856854\pi\)
\(338\) 0 0
\(339\) −471.484 219.922i −1.39081 0.648737i
\(340\) 0 0
\(341\) −155.653 89.8664i −0.456461 0.263538i
\(342\) 0 0
\(343\) 184.494 + 319.554i 0.537884 + 0.931643i
\(344\) 0 0
\(345\) 26.1260 298.232i 0.0757274 0.864441i
\(346\) 0 0
\(347\) −31.7255 87.1651i −0.0914280 0.251196i 0.885547 0.464549i \(-0.153784\pi\)
−0.976975 + 0.213353i \(0.931561\pi\)
\(348\) 0 0
\(349\) 41.7475 + 236.762i 0.119620 + 0.678401i 0.984358 + 0.176178i \(0.0563733\pi\)
−0.864738 + 0.502223i \(0.832516\pi\)
\(350\) 0 0
\(351\) 424.313 296.892i 1.20887 0.845848i
\(352\) 0 0
\(353\) −326.982 + 57.6557i −0.926294 + 0.163331i −0.616393 0.787438i \(-0.711407\pi\)
−0.309900 + 0.950769i \(0.600296\pi\)
\(354\) 0 0
\(355\) −386.754 + 140.767i −1.08945 + 0.396527i
\(356\) 0 0
\(357\) −210.763 + 300.928i −0.590372 + 0.842935i
\(358\) 0 0
\(359\) 56.4254 32.5772i 0.157174 0.0907444i −0.419350 0.907825i \(-0.637742\pi\)
0.576524 + 0.817080i \(0.304409\pi\)
\(360\) 0 0
\(361\) −97.3142 + 168.553i −0.269569 + 0.466906i
\(362\) 0 0
\(363\) −213.733 + 18.6748i −0.588795 + 0.0514457i
\(364\) 0 0
\(365\) −573.146 101.061i −1.57026 0.276880i
\(366\) 0 0
\(367\) 305.024 255.946i 0.831129 0.697400i −0.124421 0.992229i \(-0.539707\pi\)
0.955550 + 0.294830i \(0.0952630\pi\)
\(368\) 0 0
\(369\) −435.649 + 158.452i −1.18062 + 0.429409i
\(370\) 0 0
\(371\) 119.744 328.993i 0.322759 0.886773i
\(372\) 0 0
\(373\) 106.450 + 89.3225i 0.285390 + 0.239471i 0.774232 0.632902i \(-0.218136\pi\)
−0.488842 + 0.872372i \(0.662581\pi\)
\(374\) 0 0
\(375\) 105.617 393.989i 0.281645 1.05064i
\(376\) 0 0
\(377\) 413.184i 1.09598i
\(378\) 0 0
\(379\) 447.841 1.18164 0.590819 0.806804i \(-0.298805\pi\)
0.590819 + 0.806804i \(0.298805\pi\)
\(380\) 0 0
\(381\) 473.253 473.146i 1.24213 1.24185i
\(382\) 0 0
\(383\) −318.172 + 379.182i −0.830735 + 0.990031i 0.169255 + 0.985572i \(0.445864\pi\)
−0.999990 + 0.00445916i \(0.998581\pi\)
\(384\) 0 0
\(385\) 143.660 + 52.2879i 0.373143 + 0.135813i
\(386\) 0 0
\(387\) −14.2951 + 39.2479i −0.0369384 + 0.101416i
\(388\) 0 0
\(389\) −297.166 354.149i −0.763924 0.910409i 0.234165 0.972197i \(-0.424764\pi\)
−0.998089 + 0.0617877i \(0.980320\pi\)
\(390\) 0 0
\(391\) −97.6470 + 553.784i −0.249737 + 1.41633i
\(392\) 0 0
\(393\) 546.477 382.555i 1.39053 0.973424i
\(394\) 0 0
\(395\) 382.012 + 220.555i 0.967119 + 0.558366i
\(396\) 0 0
\(397\) −36.0513 62.4427i −0.0908094 0.157286i 0.817043 0.576577i \(-0.195612\pi\)
−0.907852 + 0.419291i \(0.862279\pi\)
\(398\) 0 0
\(399\) 333.272 155.361i 0.835268 0.389377i
\(400\) 0 0
\(401\) −81.0353 222.643i −0.202083 0.555218i 0.796709 0.604364i \(-0.206573\pi\)
−0.998792 + 0.0491451i \(0.984350\pi\)
\(402\) 0 0
\(403\) −85.0978 482.613i −0.211161 1.19755i
\(404\) 0 0
\(405\) −115.645 318.179i −0.285542 0.785627i
\(406\) 0 0
\(407\) 94.4354 16.6515i 0.232028 0.0409128i
\(408\) 0 0
\(409\) 46.7510 17.0160i 0.114306 0.0416038i −0.284234 0.958755i \(-0.591739\pi\)
0.398540 + 0.917151i \(0.369517\pi\)
\(410\) 0 0
\(411\) 205.724 + 441.307i 0.500545 + 1.07374i
\(412\) 0 0
\(413\) −390.473 + 225.440i −0.945456 + 0.545859i
\(414\) 0 0
\(415\) −168.178 + 291.293i −0.405248 + 0.701910i
\(416\) 0 0
\(417\) 130.927 + 187.028i 0.313973 + 0.448507i
\(418\) 0 0
\(419\) 31.7034 + 5.59016i 0.0756643 + 0.0133417i 0.211352 0.977410i \(-0.432213\pi\)
−0.135688 + 0.990752i \(0.543324\pi\)
\(420\) 0 0
\(421\) −214.696 + 180.151i −0.509967 + 0.427913i −0.861117 0.508406i \(-0.830235\pi\)
0.351151 + 0.936319i \(0.385790\pi\)
\(422\) 0 0
\(423\) 7.49447 + 42.5596i 0.0177174 + 0.100614i
\(424\) 0 0
\(425\) −60.6669 + 166.681i −0.142746 + 0.392190i
\(426\) 0 0
\(427\) −213.234 178.924i −0.499377 0.419027i
\(428\) 0 0
\(429\) 286.184 + 286.249i 0.667097 + 0.667248i
\(430\) 0 0
\(431\) 109.024i 0.252955i −0.991969 0.126478i \(-0.959633\pi\)
0.991969 0.126478i \(-0.0403672\pi\)
\(432\) 0 0
\(433\) 364.275 0.841282 0.420641 0.907227i \(-0.361805\pi\)
0.420641 + 0.907227i \(0.361805\pi\)
\(434\) 0 0
\(435\) −260.897 69.9388i −0.599763 0.160779i
\(436\) 0 0
\(437\) 361.763 431.132i 0.827833 0.986573i
\(438\) 0 0
\(439\) −275.236 100.178i −0.626961 0.228195i 0.00894720 0.999960i \(-0.497152\pi\)
−0.635908 + 0.771765i \(0.719374\pi\)
\(440\) 0 0
\(441\) 194.648 + 34.3671i 0.441379 + 0.0779300i
\(442\) 0 0
\(443\) 424.424 + 505.809i 0.958068 + 1.14178i 0.989826 + 0.142285i \(0.0454450\pi\)
−0.0317580 + 0.999496i \(0.510111\pi\)
\(444\) 0 0
\(445\) −48.6691 + 276.016i −0.109369 + 0.620261i
\(446\) 0 0
\(447\) 23.9874 + 274.535i 0.0536630 + 0.614171i
\(448\) 0 0
\(449\) −73.8335 42.6278i −0.164440 0.0949394i 0.415522 0.909583i \(-0.363599\pi\)
−0.579961 + 0.814644i \(0.696932\pi\)
\(450\) 0 0
\(451\) −181.166 313.789i −0.401699 0.695763i
\(452\) 0 0
\(453\) −119.514 83.7048i −0.263828 0.184779i
\(454\) 0 0
\(455\) 142.568 + 391.703i 0.313336 + 0.860885i
\(456\) 0 0
\(457\) 92.6648 + 525.528i 0.202768 + 1.14995i 0.900914 + 0.433997i \(0.142897\pi\)
−0.698147 + 0.715955i \(0.745992\pi\)
\(458\) 0 0
\(459\) 164.374 + 614.287i 0.358114 + 1.33832i
\(460\) 0 0
\(461\) −657.017 + 115.850i −1.42520 + 0.251301i −0.832456 0.554091i \(-0.813066\pi\)
−0.592743 + 0.805392i \(0.701955\pi\)
\(462\) 0 0
\(463\) 417.085 151.807i 0.900831 0.327876i 0.150246 0.988649i \(-0.451994\pi\)
0.750586 + 0.660773i \(0.229771\pi\)
\(464\) 0 0
\(465\) −319.142 27.9577i −0.686326 0.0601240i
\(466\) 0 0
\(467\) −199.055 + 114.925i −0.426242 + 0.246091i −0.697745 0.716347i \(-0.745813\pi\)
0.271502 + 0.962438i \(0.412480\pi\)
\(468\) 0 0
\(469\) −52.2944 + 90.5765i −0.111502 + 0.193127i
\(470\) 0 0
\(471\) −129.678 + 278.014i −0.275326 + 0.590263i
\(472\) 0 0
\(473\) −32.1521 5.66929i −0.0679749 0.0119858i
\(474\) 0 0
\(475\) 135.995 114.113i 0.286304 0.240238i
\(476\) 0 0
\(477\) −302.870 524.860i −0.634947 1.10034i
\(478\) 0 0
\(479\) −143.940 + 395.471i −0.300501 + 0.825619i 0.693912 + 0.720060i \(0.255886\pi\)
−0.994413 + 0.105559i \(0.966337\pi\)
\(480\) 0 0
\(481\) 200.289 + 168.063i 0.416402 + 0.349403i
\(482\) 0 0
\(483\) −359.773 + 96.3574i −0.744873 + 0.199498i
\(484\) 0 0
\(485\) 611.294i 1.26040i
\(486\) 0 0
\(487\) −528.889 −1.08601 −0.543007 0.839728i \(-0.682714\pi\)
−0.543007 + 0.839728i \(0.682714\pi\)
\(488\) 0 0
\(489\) 32.6057 + 121.741i 0.0666782 + 0.248959i
\(490\) 0 0
\(491\) 388.337 462.802i 0.790911 0.942571i −0.208460 0.978031i \(-0.566845\pi\)
0.999371 + 0.0354597i \(0.0112895\pi\)
\(492\) 0 0
\(493\) 476.759 + 173.526i 0.967056 + 0.351980i
\(494\) 0 0
\(495\) 229.189 132.253i 0.463007 0.267178i
\(496\) 0 0
\(497\) 329.135 + 392.248i 0.662244 + 0.789232i
\(498\) 0 0
\(499\) 81.1625 460.295i 0.162650 0.922436i −0.788804 0.614645i \(-0.789299\pi\)
0.951454 0.307791i \(-0.0995897\pi\)
\(500\) 0 0
\(501\) 32.2372 + 15.0369i 0.0643456 + 0.0300137i
\(502\) 0 0
\(503\) −340.414 196.538i −0.676767 0.390732i 0.121869 0.992546i \(-0.461111\pi\)
−0.798636 + 0.601815i \(0.794445\pi\)
\(504\) 0 0
\(505\) −206.118 357.006i −0.408154 0.706943i
\(506\) 0 0
\(507\) −52.0686 + 594.372i −0.102699 + 1.17233i
\(508\) 0 0
\(509\) −88.2803 242.548i −0.173439 0.476519i 0.822266 0.569103i \(-0.192710\pi\)
−0.995705 + 0.0925841i \(0.970487\pi\)
\(510\) 0 0
\(511\) 125.731 + 713.055i 0.246049 + 1.39541i
\(512\) 0 0
\(513\) 164.931 614.696i 0.321503 1.19824i
\(514\) 0 0
\(515\) 575.193 101.422i 1.11688 0.196936i
\(516\) 0 0
\(517\) −31.7399 + 11.5524i −0.0613925 + 0.0223450i
\(518\) 0 0
\(519\) 320.464 457.560i 0.617465 0.881619i
\(520\) 0 0
\(521\) 610.780 352.634i 1.17232 0.676840i 0.218096 0.975927i \(-0.430015\pi\)
0.954226 + 0.299087i \(0.0966821\pi\)
\(522\) 0 0
\(523\) 157.023 271.972i 0.300235 0.520023i −0.675954 0.736944i \(-0.736268\pi\)
0.976189 + 0.216921i \(0.0696015\pi\)
\(524\) 0 0
\(525\) −117.039 + 10.2263i −0.222932 + 0.0194786i
\(526\) 0 0
\(527\) 592.610 + 104.493i 1.12450 + 0.198279i
\(528\) 0 0
\(529\) −31.4618 + 26.3996i −0.0594742 + 0.0499047i
\(530\) 0 0
\(531\) −135.689 + 768.512i −0.255534 + 1.44729i
\(532\) 0 0
\(533\) 337.893 928.354i 0.633946 1.74175i
\(534\) 0 0
\(535\) 234.703 + 196.939i 0.438698 + 0.368111i
\(536\) 0 0
\(537\) −73.5548 + 274.386i −0.136974 + 0.510961i
\(538\) 0 0
\(539\) 154.493i 0.286628i
\(540\) 0 0
\(541\) −430.803 −0.796309 −0.398155 0.917318i \(-0.630349\pi\)
−0.398155 + 0.917318i \(0.630349\pi\)
\(542\) 0 0
\(543\) −240.628 + 240.573i −0.443145 + 0.443045i
\(544\) 0 0
\(545\) −221.993 + 264.561i −0.407327 + 0.485433i
\(546\) 0 0
\(547\) −119.598 43.5300i −0.218643 0.0795796i 0.230376 0.973102i \(-0.426004\pi\)
−0.449019 + 0.893522i \(0.648227\pi\)
\(548\) 0 0
\(549\) −474.490 + 83.5546i −0.864280 + 0.152194i
\(550\) 0 0
\(551\) −326.398 388.986i −0.592375 0.705965i
\(552\) 0 0
\(553\) 95.2958 540.450i 0.172325 0.977305i
\(554\) 0 0
\(555\) 140.023 98.0214i 0.252293 0.176615i
\(556\) 0 0
\(557\) 205.962 + 118.912i 0.369770 + 0.213487i 0.673358 0.739316i \(-0.264851\pi\)
−0.303588 + 0.952803i \(0.598185\pi\)
\(558\) 0 0
\(559\) −44.5091 77.0921i −0.0796228 0.137911i
\(560\) 0 0
\(561\) −450.483 + 210.002i −0.803000 + 0.374334i
\(562\) 0 0
\(563\) 311.664 + 856.289i 0.553577 + 1.52094i 0.828792 + 0.559557i \(0.189029\pi\)
−0.275215 + 0.961383i \(0.588749\pi\)
\(564\) 0 0
\(565\) −125.861 713.795i −0.222764 1.26335i
\(566\) 0 0
\(567\) −322.768 + 270.586i −0.569256 + 0.477223i
\(568\) 0 0
\(569\) −346.766 + 61.1442i −0.609430 + 0.107459i −0.469842 0.882751i \(-0.655689\pi\)
−0.139588 + 0.990210i \(0.544578\pi\)
\(570\) 0 0
\(571\) −109.923 + 40.0089i −0.192510 + 0.0700681i −0.436476 0.899716i \(-0.643774\pi\)
0.243966 + 0.969784i \(0.421551\pi\)
\(572\) 0 0
\(573\) −393.037 843.120i −0.685929 1.47141i
\(574\) 0 0
\(575\) −155.729 + 89.9104i −0.270834 + 0.156366i
\(576\) 0 0
\(577\) 368.143 637.643i 0.638030 1.10510i −0.347834 0.937556i \(-0.613083\pi\)
0.985865 0.167544i \(-0.0535838\pi\)
\(578\) 0 0
\(579\) −380.794 543.962i −0.657676 0.939485i
\(580\) 0 0
\(581\) 412.105 + 72.6652i 0.709303 + 0.125069i
\(582\) 0 0
\(583\) 362.829 304.450i 0.622348 0.522212i
\(584\) 0 0
\(585\) 677.917 + 246.915i 1.15883 + 0.422078i
\(586\) 0 0
\(587\) 28.4590 78.1905i 0.0484821 0.133204i −0.913088 0.407762i \(-0.866309\pi\)
0.961570 + 0.274558i \(0.0885316\pi\)
\(588\) 0 0
\(589\) −461.359 387.126i −0.783293 0.657261i
\(590\) 0 0
\(591\) −316.196 316.268i −0.535019 0.535140i
\(592\) 0 0
\(593\) 775.560i 1.30786i 0.756556 + 0.653929i \(0.226880\pi\)
−0.756556 + 0.653929i \(0.773120\pi\)
\(594\) 0 0
\(595\) −511.847 −0.860247
\(596\) 0 0
\(597\) −489.734 131.283i −0.820325 0.219905i
\(598\) 0 0
\(599\) 302.130 360.064i 0.504390 0.601108i −0.452426 0.891802i \(-0.649441\pi\)
0.956816 + 0.290693i \(0.0938859\pi\)
\(600\) 0 0
\(601\) −481.410 175.219i −0.801015 0.291546i −0.0911082 0.995841i \(-0.529041\pi\)
−0.709907 + 0.704295i \(0.751263\pi\)
\(602\) 0 0
\(603\) 61.8760 + 170.123i 0.102614 + 0.282127i
\(604\) 0 0
\(605\) −192.131 228.973i −0.317572 0.378467i
\(606\) 0 0
\(607\) 84.9380 481.708i 0.139931 0.793587i −0.831368 0.555723i \(-0.812442\pi\)
0.971298 0.237864i \(-0.0764474\pi\)
\(608\) 0 0
\(609\) 29.2503 + 334.769i 0.0480300 + 0.549702i
\(610\) 0 0
\(611\) −79.7575 46.0480i −0.130536 0.0753650i
\(612\) 0 0
\(613\) −61.1107 105.847i −0.0996912 0.172670i 0.811866 0.583844i \(-0.198452\pi\)
−0.911557 + 0.411174i \(0.865119\pi\)
\(614\) 0 0
\(615\) −528.997 370.497i −0.860158 0.602434i
\(616\) 0 0
\(617\) −228.283 627.201i −0.369988 1.01653i −0.975365 0.220595i \(-0.929200\pi\)
0.605377 0.795939i \(-0.293022\pi\)
\(618\) 0 0
\(619\) −109.522 621.131i −0.176934 1.00344i −0.935888 0.352298i \(-0.885400\pi\)
0.758954 0.651144i \(-0.225711\pi\)
\(620\) 0 0
\(621\) −272.642 + 584.164i −0.439037 + 0.940683i
\(622\) 0 0
\(623\) 343.393 60.5495i 0.551193 0.0971902i
\(624\) 0 0
\(625\) 357.077 129.965i 0.571323 0.207945i
\(626\) 0 0
\(627\) 495.550 + 43.4115i 0.790351 + 0.0692369i
\(628\) 0 0
\(629\) −278.038 + 160.525i −0.442032 + 0.255207i
\(630\) 0 0
\(631\) 0.442857 0.767050i 0.000701833 0.00121561i −0.865674 0.500608i \(-0.833110\pi\)
0.866376 + 0.499392i \(0.166443\pi\)
\(632\) 0 0
\(633\) −270.309 + 579.507i −0.427028 + 0.915493i
\(634\) 0 0
\(635\) 918.161 + 161.897i 1.44592 + 0.254955i
\(636\) 0 0
\(637\) −322.688 + 270.767i −0.506574 + 0.425066i
\(638\) 0 0
\(639\) 886.264 + 0.200614i 1.38695 + 0.000313950i
\(640\) 0 0
\(641\) 100.064 274.923i 0.156106 0.428897i −0.836843 0.547443i \(-0.815601\pi\)
0.992949 + 0.118546i \(0.0378235\pi\)
\(642\) 0 0
\(643\) −368.253 309.001i −0.572710 0.480561i 0.309834 0.950791i \(-0.399727\pi\)
−0.882544 + 0.470230i \(0.844171\pi\)
\(644\) 0 0
\(645\) −56.2123 + 15.0552i −0.0871509 + 0.0233414i
\(646\) 0 0
\(647\) 283.657i 0.438419i 0.975678 + 0.219209i \(0.0703477\pi\)
−0.975678 + 0.219209i \(0.929652\pi\)
\(648\) 0 0
\(649\) −609.969 −0.939860
\(650\) 0 0
\(651\) 103.113 + 384.998i 0.158392 + 0.591394i
\(652\) 0 0
\(653\) −530.766 + 632.542i −0.812811 + 0.968670i −0.999907 0.0136713i \(-0.995648\pi\)
0.187096 + 0.982342i \(0.440093\pi\)
\(654\) 0 0
\(655\) 873.307 + 317.858i 1.33329 + 0.485279i
\(656\) 0 0
\(657\) 1085.18 + 626.856i 1.65172 + 0.954119i
\(658\) 0 0
\(659\) −760.069 905.814i −1.15337 1.37453i −0.915050 0.403341i \(-0.867849\pi\)
−0.238317 0.971187i \(-0.576596\pi\)
\(660\) 0 0
\(661\) 213.726 1212.10i 0.323338 1.83374i −0.197770 0.980248i \(-0.563370\pi\)
0.521108 0.853491i \(-0.325519\pi\)
\(662\) 0 0
\(663\) −1228.16 572.868i −1.85242 0.864054i
\(664\) 0 0
\(665\) 443.648 + 256.140i 0.667140 + 0.385173i
\(666\) 0 0
\(667\) 257.171 + 445.434i 0.385564 + 0.667817i
\(668\) 0 0
\(669\) 14.2604 162.785i 0.0213160 0.243326i
\(670\) 0 0
\(671\) −128.796 353.863i −0.191946 0.527367i
\(672\) 0 0
\(673\) 202.091 + 1146.11i 0.300284 + 1.70299i 0.644915 + 0.764255i \(0.276893\pi\)
−0.344631 + 0.938738i \(0.611996\pi\)
\(674\) 0 0
\(675\) −116.692 + 166.533i −0.172877 + 0.246716i
\(676\) 0 0
\(677\) −137.416 + 24.2302i −0.202978 + 0.0357905i −0.274213 0.961669i \(-0.588417\pi\)
0.0712346 + 0.997460i \(0.477306\pi\)
\(678\) 0 0
\(679\) 714.651 260.112i 1.05250 0.383080i
\(680\) 0 0
\(681\) 151.354 216.104i 0.222253 0.317334i
\(682\) 0 0
\(683\) −415.978 + 240.165i −0.609046 + 0.351633i −0.772592 0.634903i \(-0.781040\pi\)
0.163546 + 0.986536i \(0.447707\pi\)
\(684\) 0 0
\(685\) −339.172 + 587.463i −0.495142 + 0.857611i
\(686\) 0 0
\(687\) 776.163 67.8170i 1.12979 0.0987147i
\(688\) 0 0
\(689\) 1271.80 + 224.253i 1.84587 + 0.325476i
\(690\) 0 0
\(691\) −918.527 + 770.736i −1.32927 + 1.11539i −0.345025 + 0.938594i \(0.612129\pi\)
−0.984247 + 0.176798i \(0.943426\pi\)
\(692\) 0 0
\(693\) −252.136 211.664i −0.363832 0.305432i
\(694\) 0 0
\(695\) −108.784 + 298.882i −0.156524 + 0.430047i
\(696\) 0 0
\(697\) 929.291 + 779.767i 1.33327 + 1.11875i
\(698\) 0 0
\(699\) 169.231 631.291i 0.242104 0.903135i
\(700\) 0 0
\(701\) 105.488i 0.150482i −0.997165 0.0752410i \(-0.976027\pi\)
0.997165 0.0752410i \(-0.0239726\pi\)
\(702\) 0 0
\(703\) 321.323 0.457074
\(704\) 0 0
\(705\) −42.5765 + 42.5669i −0.0603922 + 0.0603786i
\(706\) 0 0
\(707\) −329.663 + 392.877i −0.466284 + 0.555696i
\(708\) 0 0
\(709\) 166.245 + 60.5082i 0.234478 + 0.0853431i 0.456587 0.889679i \(-0.349072\pi\)
−0.222109 + 0.975022i \(0.571294\pi\)
\(710\) 0 0
\(711\) −610.394 727.773i −0.858500 1.02359i
\(712\) 0 0
\(713\) 392.125 + 467.317i 0.549965 + 0.655423i
\(714\) 0 0
\(715\) −97.9238 + 555.353i −0.136956 + 0.776718i
\(716\) 0 0
\(717\) 746.620 522.663i 1.04131 0.728959i
\(718\) 0 0
\(719\) 276.181 + 159.453i 0.384119 + 0.221771i 0.679609 0.733575i \(-0.262150\pi\)
−0.295490 + 0.955346i \(0.595483\pi\)
\(720\) 0 0
\(721\) −363.320 629.289i −0.503911 0.872800i
\(722\) 0 0
\(723\) −517.972 + 241.463i −0.716421 + 0.333974i
\(724\) 0 0
\(725\) 55.4901 + 152.458i 0.0765381 + 0.210287i
\(726\) 0 0
\(727\) 133.363 + 756.339i 0.183443 + 1.04036i 0.927940 + 0.372730i \(0.121578\pi\)
−0.744497 + 0.667626i \(0.767311\pi\)
\(728\) 0 0
\(729\) −0.495048 + 729.000i −0.000679078 + 1.00000i
\(730\) 0 0
\(731\) 107.647 18.9810i 0.147259 0.0259658i
\(732\) 0 0
\(733\) 599.501 218.200i 0.817873 0.297681i 0.101001 0.994886i \(-0.467795\pi\)
0.716872 + 0.697205i \(0.245573\pi\)
\(734\) 0 0
\(735\) 116.350 + 249.587i 0.158299 + 0.339575i
\(736\) 0 0
\(737\) −122.536 + 70.7461i −0.166263 + 0.0959920i
\(738\) 0 0
\(739\) −47.0509 + 81.4946i −0.0636684 + 0.110277i −0.896103 0.443847i \(-0.853613\pi\)
0.832434 + 0.554124i \(0.186947\pi\)
\(740\) 0 0
\(741\) 777.838 + 1111.14i 1.04971 + 1.49951i
\(742\) 0 0
\(743\) −532.414 93.8789i −0.716573 0.126351i −0.196538 0.980496i \(-0.562970\pi\)
−0.520035 + 0.854145i \(0.674081\pi\)
\(744\) 0 0
\(745\) −294.110 + 246.788i −0.394779 + 0.331259i
\(746\) 0 0
\(747\) 554.943 465.439i 0.742896 0.623077i
\(748\) 0 0
\(749\) 130.369 358.186i 0.174057 0.478219i
\(750\) 0 0
\(751\) −212.859 178.610i −0.283434 0.237829i 0.489975 0.871736i \(-0.337006\pi\)
−0.773409 + 0.633907i \(0.781450\pi\)
\(752\) 0 0
\(753\) −598.168 598.304i −0.794380 0.794560i
\(754\) 0 0
\(755\) 203.281i 0.269246i
\(756\) 0 0
\(757\) −401.897 −0.530908 −0.265454 0.964124i \(-0.585522\pi\)
−0.265454 + 0.964124i \(0.585522\pi\)
\(758\) 0 0
\(759\) −486.688 130.467i −0.641222 0.171893i
\(760\) 0 0
\(761\) −31.3411 + 37.3509i −0.0411841 + 0.0490813i −0.786243 0.617917i \(-0.787977\pi\)
0.745059 + 0.666998i \(0.232421\pi\)
\(762\) 0 0
\(763\) 403.753 + 146.954i 0.529165 + 0.192600i
\(764\) 0 0
\(765\) −569.614 + 678.528i −0.744594 + 0.886964i
\(766\) 0 0
\(767\) −1069.05 1274.04i −1.39380 1.66107i
\(768\) 0 0
\(769\) −213.365 + 1210.05i −0.277457 + 1.57354i 0.453589 + 0.891211i \(0.350144\pi\)
−0.731046 + 0.682328i \(0.760968\pi\)
\(770\) 0 0
\(771\) 112.701 + 1289.86i 0.146175 + 1.67297i
\(772\) 0 0
\(773\) −334.794 193.294i −0.433110 0.250056i 0.267560 0.963541i \(-0.413782\pi\)
−0.700671 + 0.713485i \(0.747116\pi\)
\(774\) 0 0
\(775\) 96.2141 + 166.648i 0.124147 + 0.215029i
\(776\) 0 0
\(777\) −174.176 121.988i −0.224164 0.156999i
\(778\) 0 0
\(779\) −415.257 1140.91i −0.533064 1.46458i
\(780\) 0 0
\(781\) 120.289 + 682.191i 0.154019 + 0.873484i
\(782\) 0 0
\(783\) 476.336 + 333.775i 0.608347 + 0.426277i
\(784\)