Properties

Label 144.3.m.c.19.6
Level $144$
Weight $3$
Character 144.19
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.6
Root \(1.78012 + 0.911682i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.c.91.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.78012 - 0.911682i) q^{2} +(2.33767 - 3.24581i) q^{4} +(-1.00772 + 1.00772i) q^{5} +10.0236 q^{7} +(1.20220 - 7.90915i) q^{8} +O(q^{10})\) \(q+(1.78012 - 0.911682i) q^{2} +(2.33767 - 3.24581i) q^{4} +(-1.00772 + 1.00772i) q^{5} +10.0236 q^{7} +(1.20220 - 7.90915i) q^{8} +(-0.875146 + 2.71259i) q^{10} +(-2.26517 - 2.26517i) q^{11} +(-6.88229 - 6.88229i) q^{13} +(17.8432 - 9.13830i) q^{14} +(-5.07058 - 15.1753i) q^{16} +22.3801 q^{17} +(-16.8918 + 16.8918i) q^{19} +(0.915151 + 5.62660i) q^{20} +(-6.09740 - 1.96717i) q^{22} -33.2007 q^{23} +22.9690i q^{25} +(-18.5258 - 5.97686i) q^{26} +(23.4318 - 32.5346i) q^{28} +(24.6412 + 24.6412i) q^{29} +41.3761i q^{31} +(-22.8613 - 22.3911i) q^{32} +(39.8394 - 20.4036i) q^{34} +(-10.1010 + 10.1010i) q^{35} +(-6.60031 + 6.60031i) q^{37} +(-14.6695 + 45.4693i) q^{38} +(6.75875 + 9.18170i) q^{40} -47.1477i q^{41} +(-48.8218 - 48.8218i) q^{43} +(-12.6475 + 2.05709i) q^{44} +(-59.1013 + 30.2685i) q^{46} +45.6048i q^{47} +51.4717 q^{49} +(20.9404 + 40.8876i) q^{50} +(-38.4271 + 6.25007i) q^{52} +(-25.1401 + 25.1401i) q^{53} +4.56532 q^{55} +(12.0503 - 79.2779i) q^{56} +(66.3292 + 21.3994i) q^{58} +(-6.23974 - 6.23974i) q^{59} +(35.9513 + 35.9513i) q^{61} +(37.7219 + 73.6546i) q^{62} +(-61.1095 - 19.0167i) q^{64} +13.8709 q^{65} +(10.2045 - 10.2045i) q^{67} +(52.3174 - 72.6417i) q^{68} +(-8.77208 + 27.1898i) q^{70} -11.9529 q^{71} -111.332i q^{73} +(-5.73197 + 17.7667i) q^{74} +(15.3401 + 94.3149i) q^{76} +(-22.7051 - 22.7051i) q^{77} -4.46031i q^{79} +(20.4022 + 10.1827i) q^{80} +(-42.9837 - 83.9287i) q^{82} +(-10.1751 + 10.1751i) q^{83} +(-22.5530 + 22.5530i) q^{85} +(-131.419 - 42.3988i) q^{86} +(-20.6388 + 15.1924i) q^{88} -21.9364i q^{89} +(-68.9850 - 68.9850i) q^{91} +(-77.6124 + 107.763i) q^{92} +(41.5771 + 81.1821i) q^{94} -34.0444i q^{95} +107.309 q^{97} +(91.6260 - 46.9259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78012 0.911682i 0.890061 0.455841i
\(3\) 0 0
\(4\) 2.33767 3.24581i 0.584418 0.811453i
\(5\) −1.00772 + 1.00772i −0.201544 + 0.201544i −0.800661 0.599117i \(-0.795518\pi\)
0.599117 + 0.800661i \(0.295518\pi\)
\(6\) 0 0
\(7\) 10.0236 1.43194 0.715969 0.698133i \(-0.245985\pi\)
0.715969 + 0.698133i \(0.245985\pi\)
\(8\) 1.20220 7.90915i 0.150274 0.988644i
\(9\) 0 0
\(10\) −0.875146 + 2.71259i −0.0875146 + 0.271259i
\(11\) −2.26517 2.26517i −0.205925 0.205925i 0.596608 0.802533i \(-0.296515\pi\)
−0.802533 + 0.596608i \(0.796515\pi\)
\(12\) 0 0
\(13\) −6.88229 6.88229i −0.529407 0.529407i 0.390989 0.920395i \(-0.372133\pi\)
−0.920395 + 0.390989i \(0.872133\pi\)
\(14\) 17.8432 9.13830i 1.27451 0.652736i
\(15\) 0 0
\(16\) −5.07058 15.1753i −0.316911 0.948455i
\(17\) 22.3801 1.31648 0.658240 0.752809i \(-0.271301\pi\)
0.658240 + 0.752809i \(0.271301\pi\)
\(18\) 0 0
\(19\) −16.8918 + 16.8918i −0.889041 + 0.889041i −0.994431 0.105390i \(-0.966391\pi\)
0.105390 + 0.994431i \(0.466391\pi\)
\(20\) 0.915151 + 5.62660i 0.0457575 + 0.281330i
\(21\) 0 0
\(22\) −6.09740 1.96717i −0.277155 0.0894167i
\(23\) −33.2007 −1.44351 −0.721755 0.692149i \(-0.756664\pi\)
−0.721755 + 0.692149i \(0.756664\pi\)
\(24\) 0 0
\(25\) 22.9690i 0.918760i
\(26\) −18.5258 5.97686i −0.712530 0.229879i
\(27\) 0 0
\(28\) 23.4318 32.5346i 0.836850 1.16195i
\(29\) 24.6412 + 24.6412i 0.849696 + 0.849696i 0.990095 0.140399i \(-0.0448385\pi\)
−0.140399 + 0.990095i \(0.544839\pi\)
\(30\) 0 0
\(31\) 41.3761i 1.33471i 0.744738 + 0.667357i \(0.232574\pi\)
−0.744738 + 0.667357i \(0.767426\pi\)
\(32\) −22.8613 22.3911i −0.714415 0.699722i
\(33\) 0 0
\(34\) 39.8394 20.4036i 1.17175 0.600105i
\(35\) −10.1010 + 10.1010i −0.288599 + 0.288599i
\(36\) 0 0
\(37\) −6.60031 + 6.60031i −0.178387 + 0.178387i −0.790652 0.612266i \(-0.790258\pi\)
0.612266 + 0.790652i \(0.290258\pi\)
\(38\) −14.6695 + 45.4693i −0.386039 + 1.19656i
\(39\) 0 0
\(40\) 6.75875 + 9.18170i 0.168969 + 0.229543i
\(41\) 47.1477i 1.14994i −0.818173 0.574972i \(-0.805013\pi\)
0.818173 0.574972i \(-0.194987\pi\)
\(42\) 0 0
\(43\) −48.8218 48.8218i −1.13539 1.13539i −0.989266 0.146124i \(-0.953320\pi\)
−0.146124 0.989266i \(-0.546680\pi\)
\(44\) −12.6475 + 2.05709i −0.287444 + 0.0467521i
\(45\) 0 0
\(46\) −59.1013 + 30.2685i −1.28481 + 0.658011i
\(47\) 45.6048i 0.970315i 0.874427 + 0.485157i \(0.161238\pi\)
−0.874427 + 0.485157i \(0.838762\pi\)
\(48\) 0 0
\(49\) 51.4717 1.05044
\(50\) 20.9404 + 40.8876i 0.418808 + 0.817752i
\(51\) 0 0
\(52\) −38.4271 + 6.25007i −0.738983 + 0.120194i
\(53\) −25.1401 + 25.1401i −0.474341 + 0.474341i −0.903316 0.428975i \(-0.858875\pi\)
0.428975 + 0.903316i \(0.358875\pi\)
\(54\) 0 0
\(55\) 4.56532 0.0830059
\(56\) 12.0503 79.2779i 0.215184 1.41568i
\(57\) 0 0
\(58\) 66.3292 + 21.3994i 1.14361 + 0.368955i
\(59\) −6.23974 6.23974i −0.105758 0.105758i 0.652248 0.758006i \(-0.273826\pi\)
−0.758006 + 0.652248i \(0.773826\pi\)
\(60\) 0 0
\(61\) 35.9513 + 35.9513i 0.589366 + 0.589366i 0.937460 0.348093i \(-0.113171\pi\)
−0.348093 + 0.937460i \(0.613171\pi\)
\(62\) 37.7219 + 73.6546i 0.608417 + 1.18798i
\(63\) 0 0
\(64\) −61.1095 19.0167i −0.954835 0.297136i
\(65\) 13.8709 0.213398
\(66\) 0 0
\(67\) 10.2045 10.2045i 0.152307 0.152307i −0.626841 0.779147i \(-0.715652\pi\)
0.779147 + 0.626841i \(0.215652\pi\)
\(68\) 52.3174 72.6417i 0.769374 1.06826i
\(69\) 0 0
\(70\) −8.77208 + 27.1898i −0.125315 + 0.388426i
\(71\) −11.9529 −0.168350 −0.0841752 0.996451i \(-0.526826\pi\)
−0.0841752 + 0.996451i \(0.526826\pi\)
\(72\) 0 0
\(73\) 111.332i 1.52510i −0.646929 0.762550i \(-0.723947\pi\)
0.646929 0.762550i \(-0.276053\pi\)
\(74\) −5.73197 + 17.7667i −0.0774591 + 0.240091i
\(75\) 0 0
\(76\) 15.3401 + 94.3149i 0.201843 + 1.24099i
\(77\) −22.7051 22.7051i −0.294871 0.294871i
\(78\) 0 0
\(79\) 4.46031i 0.0564596i −0.999601 0.0282298i \(-0.991013\pi\)
0.999601 0.0282298i \(-0.00898702\pi\)
\(80\) 20.4022 + 10.1827i 0.255027 + 0.127284i
\(81\) 0 0
\(82\) −42.9837 83.9287i −0.524192 1.02352i
\(83\) −10.1751 + 10.1751i −0.122592 + 0.122592i −0.765741 0.643149i \(-0.777627\pi\)
0.643149 + 0.765741i \(0.277627\pi\)
\(84\) 0 0
\(85\) −22.5530 + 22.5530i −0.265329 + 0.265329i
\(86\) −131.419 42.3988i −1.52812 0.493010i
\(87\) 0 0
\(88\) −20.6388 + 15.1924i −0.234532 + 0.172641i
\(89\) 21.9364i 0.246476i −0.992377 0.123238i \(-0.960672\pi\)
0.992377 0.123238i \(-0.0393279\pi\)
\(90\) 0 0
\(91\) −68.9850 68.9850i −0.758077 0.758077i
\(92\) −77.6124 + 107.763i −0.843613 + 1.17134i
\(93\) 0 0
\(94\) 41.5771 + 81.1821i 0.442309 + 0.863640i
\(95\) 34.0444i 0.358362i
\(96\) 0 0
\(97\) 107.309 1.10628 0.553140 0.833088i \(-0.313429\pi\)
0.553140 + 0.833088i \(0.313429\pi\)
\(98\) 91.6260 46.9259i 0.934959 0.478835i
\(99\) 0 0
\(100\) 74.5530 + 53.6940i 0.745530 + 0.536940i
\(101\) 100.780 100.780i 0.997824 0.997824i −0.00217389 0.999998i \(-0.500692\pi\)
0.999998 + 0.00217389i \(0.000691973\pi\)
\(102\) 0 0
\(103\) 58.0562 0.563653 0.281826 0.959465i \(-0.409060\pi\)
0.281826 + 0.959465i \(0.409060\pi\)
\(104\) −62.7069 + 46.1592i −0.602951 + 0.443839i
\(105\) 0 0
\(106\) −21.8327 + 67.6722i −0.205968 + 0.638417i
\(107\) −112.747 112.747i −1.05371 1.05371i −0.998473 0.0552381i \(-0.982408\pi\)
−0.0552381 0.998473i \(-0.517592\pi\)
\(108\) 0 0
\(109\) −81.1384 81.1384i −0.744389 0.744389i 0.229030 0.973419i \(-0.426445\pi\)
−0.973419 + 0.229030i \(0.926445\pi\)
\(110\) 8.12684 4.16212i 0.0738803 0.0378375i
\(111\) 0 0
\(112\) −50.8252 152.110i −0.453797 1.35813i
\(113\) 171.844 1.52074 0.760371 0.649489i \(-0.225017\pi\)
0.760371 + 0.649489i \(0.225017\pi\)
\(114\) 0 0
\(115\) 33.4571 33.4571i 0.290931 0.290931i
\(116\) 137.584 22.3776i 1.18607 0.192910i
\(117\) 0 0
\(118\) −16.7962 5.41884i −0.142340 0.0459224i
\(119\) 224.329 1.88512
\(120\) 0 0
\(121\) 110.738i 0.915190i
\(122\) 96.7740 + 31.2216i 0.793230 + 0.255915i
\(123\) 0 0
\(124\) 134.299 + 96.7238i 1.08306 + 0.780031i
\(125\) −48.3394 48.3394i −0.386715 0.386715i
\(126\) 0 0
\(127\) 36.8333i 0.290026i 0.989430 + 0.145013i \(0.0463224\pi\)
−0.989430 + 0.145013i \(0.953678\pi\)
\(128\) −126.119 + 21.8603i −0.985309 + 0.170784i
\(129\) 0 0
\(130\) 24.6918 12.6458i 0.189937 0.0972754i
\(131\) 12.3686 12.3686i 0.0944170 0.0944170i −0.658321 0.752738i \(-0.728733\pi\)
0.752738 + 0.658321i \(0.228733\pi\)
\(132\) 0 0
\(133\) −169.316 + 169.316i −1.27305 + 1.27305i
\(134\) 8.86204 27.4686i 0.0661347 0.204990i
\(135\) 0 0
\(136\) 26.9053 177.008i 0.197833 1.30153i
\(137\) 145.679i 1.06335i 0.846949 + 0.531674i \(0.178437\pi\)
−0.846949 + 0.531674i \(0.821563\pi\)
\(138\) 0 0
\(139\) 82.5709 + 82.5709i 0.594035 + 0.594035i 0.938719 0.344684i \(-0.112014\pi\)
−0.344684 + 0.938719i \(0.612014\pi\)
\(140\) 9.17307 + 56.3985i 0.0655219 + 0.402847i
\(141\) 0 0
\(142\) −21.2776 + 10.8972i −0.149842 + 0.0767410i
\(143\) 31.1791i 0.218036i
\(144\) 0 0
\(145\) −49.6629 −0.342503
\(146\) −101.500 198.185i −0.695203 1.35743i
\(147\) 0 0
\(148\) 5.99399 + 36.8527i 0.0405000 + 0.249005i
\(149\) −196.248 + 196.248i −1.31710 + 1.31710i −0.401043 + 0.916059i \(0.631352\pi\)
−0.916059 + 0.401043i \(0.868648\pi\)
\(150\) 0 0
\(151\) 64.5007 0.427157 0.213578 0.976926i \(-0.431488\pi\)
0.213578 + 0.976926i \(0.431488\pi\)
\(152\) 113.292 + 153.907i 0.745345 + 1.01254i
\(153\) 0 0
\(154\) −61.1177 19.7180i −0.396868 0.128039i
\(155\) −41.6956 41.6956i −0.269004 0.269004i
\(156\) 0 0
\(157\) 54.4202 + 54.4202i 0.346625 + 0.346625i 0.858851 0.512226i \(-0.171179\pi\)
−0.512226 + 0.858851i \(0.671179\pi\)
\(158\) −4.06638 7.93990i −0.0257366 0.0502525i
\(159\) 0 0
\(160\) 45.6018 0.473799i 0.285011 0.00296124i
\(161\) −332.789 −2.06701
\(162\) 0 0
\(163\) 104.803 104.803i 0.642961 0.642961i −0.308321 0.951282i \(-0.599767\pi\)
0.951282 + 0.308321i \(0.0997671\pi\)
\(164\) −153.033 110.216i −0.933126 0.672048i
\(165\) 0 0
\(166\) −8.83647 + 27.3894i −0.0532317 + 0.164996i
\(167\) −53.3110 −0.319228 −0.159614 0.987180i \(-0.551025\pi\)
−0.159614 + 0.987180i \(0.551025\pi\)
\(168\) 0 0
\(169\) 74.2683i 0.439457i
\(170\) −19.5859 + 60.7081i −0.115211 + 0.357107i
\(171\) 0 0
\(172\) −272.596 + 44.3370i −1.58486 + 0.257773i
\(173\) 41.5780 + 41.5780i 0.240335 + 0.240335i 0.816989 0.576654i \(-0.195642\pi\)
−0.576654 + 0.816989i \(0.695642\pi\)
\(174\) 0 0
\(175\) 230.231i 1.31561i
\(176\) −22.8889 + 45.8604i −0.130051 + 0.260570i
\(177\) 0 0
\(178\) −19.9990 39.0495i −0.112354 0.219379i
\(179\) −53.0709 + 53.0709i −0.296486 + 0.296486i −0.839636 0.543150i \(-0.817231\pi\)
0.543150 + 0.839636i \(0.317231\pi\)
\(180\) 0 0
\(181\) −66.6042 + 66.6042i −0.367979 + 0.367979i −0.866740 0.498761i \(-0.833789\pi\)
0.498761 + 0.866740i \(0.333789\pi\)
\(182\) −185.694 59.9094i −1.02030 0.329172i
\(183\) 0 0
\(184\) −39.9138 + 262.590i −0.216923 + 1.42712i
\(185\) 13.3025i 0.0719056i
\(186\) 0 0
\(187\) −50.6949 50.6949i −0.271096 0.271096i
\(188\) 148.025 + 106.609i 0.787365 + 0.567070i
\(189\) 0 0
\(190\) −31.0377 60.6032i −0.163356 0.318964i
\(191\) 113.753i 0.595567i 0.954633 + 0.297784i \(0.0962474\pi\)
−0.954633 + 0.297784i \(0.903753\pi\)
\(192\) 0 0
\(193\) −26.5596 −0.137615 −0.0688073 0.997630i \(-0.521919\pi\)
−0.0688073 + 0.997630i \(0.521919\pi\)
\(194\) 191.023 97.8318i 0.984657 0.504288i
\(195\) 0 0
\(196\) 120.324 167.068i 0.613898 0.852386i
\(197\) −51.8935 + 51.8935i −0.263419 + 0.263419i −0.826442 0.563023i \(-0.809638\pi\)
0.563023 + 0.826442i \(0.309638\pi\)
\(198\) 0 0
\(199\) −136.741 −0.687140 −0.343570 0.939127i \(-0.611636\pi\)
−0.343570 + 0.939127i \(0.611636\pi\)
\(200\) 181.665 + 27.6132i 0.908327 + 0.138066i
\(201\) 0 0
\(202\) 87.5216 271.281i 0.433275 1.34297i
\(203\) 246.992 + 246.992i 1.21671 + 1.21671i
\(204\) 0 0
\(205\) 47.5118 + 47.5118i 0.231765 + 0.231765i
\(206\) 103.347 52.9288i 0.501686 0.256936i
\(207\) 0 0
\(208\) −69.5435 + 139.338i −0.334344 + 0.669893i
\(209\) 76.5255 0.366151
\(210\) 0 0
\(211\) −141.171 + 141.171i −0.669057 + 0.669057i −0.957498 0.288441i \(-0.906863\pi\)
0.288441 + 0.957498i \(0.406863\pi\)
\(212\) 22.8307 + 140.369i 0.107692 + 0.662119i
\(213\) 0 0
\(214\) −303.493 97.9142i −1.41819 0.457543i
\(215\) 98.3975 0.457663
\(216\) 0 0
\(217\) 414.736i 1.91123i
\(218\) −218.409 70.4639i −1.00188 0.323229i
\(219\) 0 0
\(220\) 10.6722 14.8182i 0.0485101 0.0673554i
\(221\) −154.027 154.027i −0.696953 0.696953i
\(222\) 0 0
\(223\) 122.607i 0.549806i −0.961472 0.274903i \(-0.911354\pi\)
0.961472 0.274903i \(-0.0886457\pi\)
\(224\) −229.151 224.439i −1.02300 1.00196i
\(225\) 0 0
\(226\) 305.903 156.667i 1.35355 0.693216i
\(227\) 295.844 295.844i 1.30328 1.30328i 0.377112 0.926168i \(-0.376917\pi\)
0.926168 0.377112i \(-0.123083\pi\)
\(228\) 0 0
\(229\) 73.3817 73.3817i 0.320444 0.320444i −0.528493 0.848937i \(-0.677243\pi\)
0.848937 + 0.528493i \(0.177243\pi\)
\(230\) 29.0555 90.0599i 0.126328 0.391565i
\(231\) 0 0
\(232\) 224.514 165.267i 0.967735 0.712359i
\(233\) 156.229i 0.670509i −0.942128 0.335255i \(-0.891178\pi\)
0.942128 0.335255i \(-0.108822\pi\)
\(234\) 0 0
\(235\) −45.9569 45.9569i −0.195561 0.195561i
\(236\) −34.8395 + 5.66655i −0.147625 + 0.0240108i
\(237\) 0 0
\(238\) 399.333 204.516i 1.67787 0.859313i
\(239\) 13.1716i 0.0551113i 0.999620 + 0.0275557i \(0.00877235\pi\)
−0.999620 + 0.0275557i \(0.991228\pi\)
\(240\) 0 0
\(241\) −189.519 −0.786386 −0.393193 0.919456i \(-0.628630\pi\)
−0.393193 + 0.919456i \(0.628630\pi\)
\(242\) −100.958 197.127i −0.417181 0.814575i
\(243\) 0 0
\(244\) 200.734 32.6488i 0.822679 0.133807i
\(245\) −51.8692 + 51.8692i −0.211711 + 0.211711i
\(246\) 0 0
\(247\) 232.508 0.941328
\(248\) 327.250 + 49.7422i 1.31956 + 0.200573i
\(249\) 0 0
\(250\) −130.120 41.9799i −0.520481 0.167920i
\(251\) 27.4434 + 27.4434i 0.109336 + 0.109336i 0.759658 0.650322i \(-0.225366\pi\)
−0.650322 + 0.759658i \(0.725366\pi\)
\(252\) 0 0
\(253\) 75.2053 + 75.2053i 0.297254 + 0.297254i
\(254\) 33.5802 + 65.5678i 0.132206 + 0.258141i
\(255\) 0 0
\(256\) −204.578 + 153.895i −0.799135 + 0.601152i
\(257\) −135.375 −0.526752 −0.263376 0.964693i \(-0.584836\pi\)
−0.263376 + 0.964693i \(0.584836\pi\)
\(258\) 0 0
\(259\) −66.1586 + 66.1586i −0.255438 + 0.255438i
\(260\) 32.4255 45.0222i 0.124714 0.173162i
\(261\) 0 0
\(262\) 10.7414 33.2939i 0.0409978 0.127076i
\(263\) −31.6123 −0.120199 −0.0600994 0.998192i \(-0.519142\pi\)
−0.0600994 + 0.998192i \(0.519142\pi\)
\(264\) 0 0
\(265\) 50.6684i 0.191201i
\(266\) −147.041 + 455.765i −0.552784 + 1.71340i
\(267\) 0 0
\(268\) −9.26715 56.9769i −0.0345789 0.212600i
\(269\) 194.213 + 194.213i 0.721981 + 0.721981i 0.969008 0.247028i \(-0.0794538\pi\)
−0.247028 + 0.969008i \(0.579454\pi\)
\(270\) 0 0
\(271\) 291.647i 1.07619i −0.842884 0.538095i \(-0.819144\pi\)
0.842884 0.538095i \(-0.180856\pi\)
\(272\) −113.480 339.625i −0.417207 1.24862i
\(273\) 0 0
\(274\) 132.813 + 259.326i 0.484717 + 0.946444i
\(275\) 52.0287 52.0287i 0.189195 0.189195i
\(276\) 0 0
\(277\) 305.166 305.166i 1.10168 1.10168i 0.107475 0.994208i \(-0.465723\pi\)
0.994208 0.107475i \(-0.0342765\pi\)
\(278\) 222.265 + 71.7079i 0.799513 + 0.257942i
\(279\) 0 0
\(280\) 67.7467 + 92.0333i 0.241952 + 0.328691i
\(281\) 211.861i 0.753955i −0.926222 0.376978i \(-0.876963\pi\)
0.926222 0.376978i \(-0.123037\pi\)
\(282\) 0 0
\(283\) 105.325 + 105.325i 0.372175 + 0.372175i 0.868269 0.496094i \(-0.165233\pi\)
−0.496094 + 0.868269i \(0.665233\pi\)
\(284\) −27.9419 + 38.7968i −0.0983870 + 0.136608i
\(285\) 0 0
\(286\) 28.4254 + 55.5027i 0.0993897 + 0.194065i
\(287\) 472.588i 1.64665i
\(288\) 0 0
\(289\) 211.871 0.733117
\(290\) −88.4060 + 45.2768i −0.304848 + 0.156127i
\(291\) 0 0
\(292\) −361.364 260.258i −1.23755 0.891296i
\(293\) 171.289 171.289i 0.584603 0.584603i −0.351562 0.936165i \(-0.614349\pi\)
0.936165 + 0.351562i \(0.114349\pi\)
\(294\) 0 0
\(295\) 12.5758 0.0426300
\(296\) 44.2680 + 60.1377i 0.149554 + 0.203168i
\(297\) 0 0
\(298\) −170.430 + 528.262i −0.571912 + 1.77269i
\(299\) 228.497 + 228.497i 0.764204 + 0.764204i
\(300\) 0 0
\(301\) −489.368 489.368i −1.62581 1.62581i
\(302\) 114.819 58.8041i 0.380196 0.194716i
\(303\) 0 0
\(304\) 341.988 + 170.686i 1.12496 + 0.561468i
\(305\) −72.4579 −0.237567
\(306\) 0 0
\(307\) −27.1124 + 27.1124i −0.0883140 + 0.0883140i −0.749884 0.661570i \(-0.769891\pi\)
0.661570 + 0.749884i \(0.269891\pi\)
\(308\) −126.773 + 20.6194i −0.411602 + 0.0669460i
\(309\) 0 0
\(310\) −112.236 36.2102i −0.362053 0.116807i
\(311\) −371.124 −1.19333 −0.596663 0.802492i \(-0.703507\pi\)
−0.596663 + 0.802492i \(0.703507\pi\)
\(312\) 0 0
\(313\) 374.501i 1.19649i 0.801313 + 0.598245i \(0.204135\pi\)
−0.801313 + 0.598245i \(0.795865\pi\)
\(314\) 146.488 + 47.2607i 0.466524 + 0.150512i
\(315\) 0 0
\(316\) −14.4773 10.4267i −0.0458143 0.0329960i
\(317\) 48.5840 + 48.5840i 0.153262 + 0.153262i 0.779573 0.626311i \(-0.215436\pi\)
−0.626311 + 0.779573i \(0.715436\pi\)
\(318\) 0 0
\(319\) 111.633i 0.349947i
\(320\) 80.7448 42.4178i 0.252328 0.132555i
\(321\) 0 0
\(322\) −592.406 + 303.398i −1.83977 + 0.942230i
\(323\) −378.040 + 378.040i −1.17040 + 1.17040i
\(324\) 0 0
\(325\) 158.079 158.079i 0.486398 0.486398i
\(326\) 91.0149 282.108i 0.279187 0.865363i
\(327\) 0 0
\(328\) −372.899 56.6808i −1.13689 0.172807i
\(329\) 457.122i 1.38943i
\(330\) 0 0
\(331\) −1.88883 1.88883i −0.00570644 0.00570644i 0.704248 0.709954i \(-0.251284\pi\)
−0.709954 + 0.704248i \(0.751284\pi\)
\(332\) 9.24040 + 56.8125i 0.0278325 + 0.171122i
\(333\) 0 0
\(334\) −94.9001 + 48.6027i −0.284132 + 0.145517i
\(335\) 20.5667i 0.0613931i
\(336\) 0 0
\(337\) −386.980 −1.14831 −0.574154 0.818747i \(-0.694669\pi\)
−0.574154 + 0.818747i \(0.694669\pi\)
\(338\) −67.7090 132.207i −0.200323 0.391144i
\(339\) 0 0
\(340\) 20.4812 + 125.924i 0.0602388 + 0.370365i
\(341\) 93.7240 93.7240i 0.274851 0.274851i
\(342\) 0 0
\(343\) 24.7757 0.0722325
\(344\) −444.832 + 327.446i −1.29312 + 0.951877i
\(345\) 0 0
\(346\) 111.920 + 36.1080i 0.323468 + 0.104358i
\(347\) −441.887 441.887i −1.27345 1.27345i −0.944266 0.329183i \(-0.893227\pi\)
−0.329183 0.944266i \(-0.606773\pi\)
\(348\) 0 0
\(349\) 119.382 + 119.382i 0.342068 + 0.342068i 0.857144 0.515076i \(-0.172236\pi\)
−0.515076 + 0.857144i \(0.672236\pi\)
\(350\) 209.898 + 409.840i 0.599707 + 1.17097i
\(351\) 0 0
\(352\) 1.06501 + 102.504i 0.00302560 + 0.291206i
\(353\) 515.642 1.46074 0.730371 0.683050i \(-0.239347\pi\)
0.730371 + 0.683050i \(0.239347\pi\)
\(354\) 0 0
\(355\) 12.0452 12.0452i 0.0339301 0.0339301i
\(356\) −71.2014 51.2801i −0.200004 0.144045i
\(357\) 0 0
\(358\) −46.0890 + 142.857i −0.128740 + 0.399041i
\(359\) −428.264 −1.19294 −0.596468 0.802637i \(-0.703430\pi\)
−0.596468 + 0.802637i \(0.703430\pi\)
\(360\) 0 0
\(361\) 209.664i 0.580786i
\(362\) −57.8418 + 179.286i −0.159784 + 0.495264i
\(363\) 0 0
\(364\) −385.177 + 62.6480i −1.05818 + 0.172110i
\(365\) 112.192 + 112.192i 0.307375 + 0.307375i
\(366\) 0 0
\(367\) 219.482i 0.598043i −0.954246 0.299021i \(-0.903340\pi\)
0.954246 0.299021i \(-0.0966602\pi\)
\(368\) 168.347 + 503.830i 0.457464 + 1.36910i
\(369\) 0 0
\(370\) −12.1277 23.6802i −0.0327775 0.0640004i
\(371\) −251.993 + 251.993i −0.679226 + 0.679226i
\(372\) 0 0
\(373\) 425.005 425.005i 1.13942 1.13942i 0.150870 0.988554i \(-0.451793\pi\)
0.988554 0.150870i \(-0.0482075\pi\)
\(374\) −136.461 44.0255i −0.364868 0.117715i
\(375\) 0 0
\(376\) 360.695 + 54.8259i 0.959296 + 0.145814i
\(377\) 339.175i 0.899669i
\(378\) 0 0
\(379\) 365.916 + 365.916i 0.965476 + 0.965476i 0.999424 0.0339473i \(-0.0108078\pi\)
−0.0339473 + 0.999424i \(0.510808\pi\)
\(380\) −110.502 79.5846i −0.290794 0.209433i
\(381\) 0 0
\(382\) 103.707 + 202.495i 0.271484 + 0.530091i
\(383\) 213.276i 0.556857i 0.960457 + 0.278428i \(0.0898135\pi\)
−0.960457 + 0.278428i \(0.910187\pi\)
\(384\) 0 0
\(385\) 45.7608 0.118859
\(386\) −47.2793 + 24.2139i −0.122485 + 0.0627303i
\(387\) 0 0
\(388\) 250.854 348.305i 0.646530 0.897694i
\(389\) 210.798 210.798i 0.541898 0.541898i −0.382187 0.924085i \(-0.624829\pi\)
0.924085 + 0.382187i \(0.124829\pi\)
\(390\) 0 0
\(391\) −743.037 −1.90035
\(392\) 61.8791 407.098i 0.157855 1.03852i
\(393\) 0 0
\(394\) −45.0665 + 139.687i −0.114382 + 0.354536i
\(395\) 4.49475 + 4.49475i 0.0113791 + 0.0113791i
\(396\) 0 0
\(397\) 392.907 + 392.907i 0.989690 + 0.989690i 0.999947 0.0102579i \(-0.00326524\pi\)
−0.0102579 + 0.999947i \(0.503265\pi\)
\(398\) −243.415 + 124.664i −0.611597 + 0.313226i
\(399\) 0 0
\(400\) 348.561 116.466i 0.871403 0.291165i
\(401\) −29.3290 −0.0731396 −0.0365698 0.999331i \(-0.511643\pi\)
−0.0365698 + 0.999331i \(0.511643\pi\)
\(402\) 0 0
\(403\) 284.762 284.762i 0.706606 0.706606i
\(404\) −91.5224 562.705i −0.226541 1.39283i
\(405\) 0 0
\(406\) 664.855 + 214.498i 1.63757 + 0.528321i
\(407\) 29.9017 0.0734684
\(408\) 0 0
\(409\) 601.115i 1.46972i −0.678219 0.734860i \(-0.737248\pi\)
0.678219 0.734860i \(-0.262752\pi\)
\(410\) 127.892 + 41.2612i 0.311933 + 0.100637i
\(411\) 0 0
\(412\) 135.716 188.440i 0.329409 0.457378i
\(413\) −62.5444 62.5444i −0.151439 0.151439i
\(414\) 0 0
\(415\) 20.5073i 0.0494153i
\(416\) 3.23584 + 311.440i 0.00777845 + 0.748654i
\(417\) 0 0
\(418\) 136.225 69.7669i 0.325897 0.166907i
\(419\) 518.885 518.885i 1.23839 1.23839i 0.277729 0.960659i \(-0.410418\pi\)
0.960659 0.277729i \(-0.0895819\pi\)
\(420\) 0 0
\(421\) −411.213 + 411.213i −0.976754 + 0.976754i −0.999736 0.0229817i \(-0.992684\pi\)
0.0229817 + 0.999736i \(0.492684\pi\)
\(422\) −122.599 + 380.005i −0.290518 + 0.900485i
\(423\) 0 0
\(424\) 168.613 + 229.060i 0.397673 + 0.540236i
\(425\) 514.049i 1.20953i
\(426\) 0 0
\(427\) 360.360 + 360.360i 0.843936 + 0.843936i
\(428\) −629.522 + 102.390i −1.47084 + 0.239229i
\(429\) 0 0
\(430\) 175.160 89.7072i 0.407348 0.208622i
\(431\) 41.1083i 0.0953789i 0.998862 + 0.0476895i \(0.0151858\pi\)
−0.998862 + 0.0476895i \(0.984814\pi\)
\(432\) 0 0
\(433\) −351.682 −0.812199 −0.406100 0.913829i \(-0.633111\pi\)
−0.406100 + 0.913829i \(0.633111\pi\)
\(434\) 378.107 + 738.281i 0.871215 + 1.70111i
\(435\) 0 0
\(436\) −453.035 + 73.6850i −1.03907 + 0.169002i
\(437\) 560.819 560.819i 1.28334 1.28334i
\(438\) 0 0
\(439\) −775.613 −1.76677 −0.883386 0.468646i \(-0.844742\pi\)
−0.883386 + 0.468646i \(0.844742\pi\)
\(440\) 5.48841 36.1079i 0.0124737 0.0820633i
\(441\) 0 0
\(442\) −414.609 133.763i −0.938030 0.302631i
\(443\) 241.372 + 241.372i 0.544858 + 0.544858i 0.924949 0.380091i \(-0.124107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(444\) 0 0
\(445\) 22.1058 + 22.1058i 0.0496759 + 0.0496759i
\(446\) −111.778 218.255i −0.250624 0.489361i
\(447\) 0 0
\(448\) −612.534 190.615i −1.36726 0.425480i
\(449\) −266.360 −0.593228 −0.296614 0.954997i \(-0.595858\pi\)
−0.296614 + 0.954997i \(0.595858\pi\)
\(450\) 0 0
\(451\) −106.798 + 106.798i −0.236802 + 0.236802i
\(452\) 401.714 557.772i 0.888749 1.23401i
\(453\) 0 0
\(454\) 256.923 796.355i 0.565910 1.75409i
\(455\) 139.035 0.305572
\(456\) 0 0
\(457\) 515.244i 1.12745i 0.825963 + 0.563725i \(0.190632\pi\)
−0.825963 + 0.563725i \(0.809368\pi\)
\(458\) 63.7277 197.529i 0.139143 0.431287i
\(459\) 0 0
\(460\) −30.3837 186.807i −0.0660514 0.406102i
\(461\) −5.67717 5.67717i −0.0123149 0.0123149i 0.700923 0.713237i \(-0.252772\pi\)
−0.713237 + 0.700923i \(0.752772\pi\)
\(462\) 0 0
\(463\) 464.510i 1.00326i 0.865082 + 0.501631i \(0.167267\pi\)
−0.865082 + 0.501631i \(0.832733\pi\)
\(464\) 248.992 498.882i 0.536621 1.07518i
\(465\) 0 0
\(466\) −142.431 278.106i −0.305646 0.596794i
\(467\) −495.985 + 495.985i −1.06207 + 1.06207i −0.0641248 + 0.997942i \(0.520426\pi\)
−0.997942 + 0.0641248i \(0.979574\pi\)
\(468\) 0 0
\(469\) 102.286 102.286i 0.218094 0.218094i
\(470\) −123.707 39.9109i −0.263207 0.0849167i
\(471\) 0 0
\(472\) −56.8525 + 41.8497i −0.120450 + 0.0886646i
\(473\) 221.180i 0.467610i
\(474\) 0 0
\(475\) −387.987 387.987i −0.816815 0.816815i
\(476\) 524.407 728.129i 1.10170 1.52968i
\(477\) 0 0
\(478\) 12.0083 + 23.4471i 0.0251220 + 0.0490525i
\(479\) 378.802i 0.790818i −0.918505 0.395409i \(-0.870603\pi\)
0.918505 0.395409i \(-0.129397\pi\)
\(480\) 0 0
\(481\) 90.8504 0.188878
\(482\) −337.367 + 172.781i −0.699932 + 0.358467i
\(483\) 0 0
\(484\) −359.435 258.869i −0.742633 0.534854i
\(485\) −108.138 + 108.138i −0.222964 + 0.222964i
\(486\) 0 0
\(487\) 147.446 0.302764 0.151382 0.988475i \(-0.451628\pi\)
0.151382 + 0.988475i \(0.451628\pi\)
\(488\) 327.565 241.124i 0.671240 0.494107i
\(489\) 0 0
\(490\) −45.0453 + 139.622i −0.0919292 + 0.284942i
\(491\) −109.547 109.547i −0.223110 0.223110i 0.586697 0.809807i \(-0.300428\pi\)
−0.809807 + 0.586697i \(0.800428\pi\)
\(492\) 0 0
\(493\) 551.473 + 551.473i 1.11861 + 1.11861i
\(494\) 413.893 211.973i 0.837840 0.429096i
\(495\) 0 0
\(496\) 627.894 209.801i 1.26592 0.422985i
\(497\) −119.810 −0.241067
\(498\) 0 0
\(499\) −360.523 + 360.523i −0.722491 + 0.722491i −0.969112 0.246621i \(-0.920680\pi\)
0.246621 + 0.969112i \(0.420680\pi\)
\(500\) −269.902 + 43.8989i −0.539804 + 0.0877977i
\(501\) 0 0
\(502\) 73.8722 + 23.8329i 0.147156 + 0.0474760i
\(503\) 927.420 1.84378 0.921889 0.387454i \(-0.126645\pi\)
0.921889 + 0.387454i \(0.126645\pi\)
\(504\) 0 0
\(505\) 203.117i 0.402211i
\(506\) 202.438 + 65.3114i 0.400075 + 0.129074i
\(507\) 0 0
\(508\) 119.554 + 86.1042i 0.235342 + 0.169496i
\(509\) −677.931 677.931i −1.33189 1.33189i −0.903680 0.428208i \(-0.859145\pi\)
−0.428208 0.903680i \(-0.640855\pi\)
\(510\) 0 0
\(511\) 1115.95i 2.18385i
\(512\) −223.872 + 460.462i −0.437249 + 0.899340i
\(513\) 0 0
\(514\) −240.984 + 123.419i −0.468841 + 0.240115i
\(515\) −58.5045 + 58.5045i −0.113601 + 0.113601i
\(516\) 0 0
\(517\) 103.303 103.303i 0.199812 0.199812i
\(518\) −57.4548 + 178.086i −0.110917 + 0.343795i
\(519\) 0 0
\(520\) 16.6755 109.707i 0.0320682 0.210974i
\(521\) 143.173i 0.274804i −0.990515 0.137402i \(-0.956125\pi\)
0.990515 0.137402i \(-0.0438753\pi\)
\(522\) 0 0
\(523\) 226.187 + 226.187i 0.432481 + 0.432481i 0.889471 0.456991i \(-0.151073\pi\)
−0.456991 + 0.889471i \(0.651073\pi\)
\(524\) −11.2324 69.0600i −0.0214359 0.131794i
\(525\) 0 0
\(526\) −56.2738 + 28.8204i −0.106984 + 0.0547916i
\(527\) 926.004i 1.75712i
\(528\) 0 0
\(529\) 573.288 1.08372
\(530\) −46.1934 90.1959i −0.0871574 0.170181i
\(531\) 0 0
\(532\) 153.762 + 945.371i 0.289027 + 1.77701i
\(533\) −324.484 + 324.484i −0.608788 + 0.608788i
\(534\) 0 0
\(535\) 227.235 0.424739
\(536\) −68.4415 92.9772i −0.127689 0.173465i
\(537\) 0 0
\(538\) 522.783 + 168.662i 0.971716 + 0.313499i
\(539\) −116.592 116.592i −0.216312 0.216312i
\(540\) 0 0
\(541\) −156.708 156.708i −0.289663 0.289663i 0.547284 0.836947i \(-0.315662\pi\)
−0.836947 + 0.547284i \(0.815662\pi\)
\(542\) −265.890 519.168i −0.490571 0.957875i
\(543\) 0 0
\(544\) −511.639 501.116i −0.940512 0.921170i
\(545\) 163.530 0.300055
\(546\) 0 0
\(547\) 247.357 247.357i 0.452207 0.452207i −0.443880 0.896086i \(-0.646398\pi\)
0.896086 + 0.443880i \(0.146398\pi\)
\(548\) 472.845 + 340.549i 0.862856 + 0.621440i
\(549\) 0 0
\(550\) 45.1839 140.051i 0.0821525 0.254638i
\(551\) −832.466 −1.51083
\(552\) 0 0
\(553\) 44.7082i 0.0808466i
\(554\) 265.019 821.447i 0.478373 1.48276i
\(555\) 0 0
\(556\) 461.033 74.9858i 0.829196 0.134867i
\(557\) 661.193 + 661.193i 1.18706 + 1.18706i 0.977876 + 0.209184i \(0.0670808\pi\)
0.209184 + 0.977876i \(0.432919\pi\)
\(558\) 0 0
\(559\) 672.011i 1.20217i
\(560\) 204.503 + 102.067i 0.365183 + 0.182263i
\(561\) 0 0
\(562\) −193.150 377.139i −0.343684 0.671066i
\(563\) −246.685 + 246.685i −0.438162 + 0.438162i −0.891393 0.453231i \(-0.850271\pi\)
0.453231 + 0.891393i \(0.350271\pi\)
\(564\) 0 0
\(565\) −173.171 + 173.171i −0.306497 + 0.306497i
\(566\) 283.516 + 91.4689i 0.500911 + 0.161606i
\(567\) 0 0
\(568\) −14.3697 + 94.5372i −0.0252988 + 0.166439i
\(569\) 243.567i 0.428061i −0.976827 0.214030i \(-0.931341\pi\)
0.976827 0.214030i \(-0.0686592\pi\)
\(570\) 0 0
\(571\) 59.9229 + 59.9229i 0.104944 + 0.104944i 0.757629 0.652685i \(-0.226358\pi\)
−0.652685 + 0.757629i \(0.726358\pi\)
\(572\) 101.202 + 72.8866i 0.176926 + 0.127424i
\(573\) 0 0
\(574\) −430.850 841.265i −0.750610 1.46562i
\(575\) 762.587i 1.32624i
\(576\) 0 0
\(577\) 136.609 0.236757 0.118378 0.992969i \(-0.462230\pi\)
0.118378 + 0.992969i \(0.462230\pi\)
\(578\) 377.156 193.159i 0.652519 0.334185i
\(579\) 0 0
\(580\) −116.096 + 161.196i −0.200165 + 0.277925i
\(581\) −101.991 + 101.991i −0.175543 + 0.175543i
\(582\) 0 0
\(583\) 113.893 0.195357
\(584\) −880.544 133.843i −1.50778 0.229184i
\(585\) 0 0
\(586\) 148.754 461.076i 0.253846 0.786818i
\(587\) 331.817 + 331.817i 0.565276 + 0.565276i 0.930801 0.365525i \(-0.119111\pi\)
−0.365525 + 0.930801i \(0.619111\pi\)
\(588\) 0 0
\(589\) −698.916 698.916i −1.18661 1.18661i
\(590\) 22.3865 11.4652i 0.0379433 0.0194325i
\(591\) 0 0
\(592\) 133.629 + 66.6942i 0.225724 + 0.112659i
\(593\) −131.285 −0.221391 −0.110695 0.993854i \(-0.535308\pi\)
−0.110695 + 0.993854i \(0.535308\pi\)
\(594\) 0 0
\(595\) −226.061 + 226.061i −0.379934 + 0.379934i
\(596\) 178.221 + 1095.75i 0.299028 + 1.83850i
\(597\) 0 0
\(598\) 615.069 + 198.436i 1.02854 + 0.331833i
\(599\) 136.119 0.227243 0.113621 0.993524i \(-0.463755\pi\)
0.113621 + 0.993524i \(0.463755\pi\)
\(600\) 0 0
\(601\) 498.566i 0.829561i 0.909922 + 0.414780i \(0.136142\pi\)
−0.909922 + 0.414780i \(0.863858\pi\)
\(602\) −1317.28 424.987i −2.18818 0.705959i
\(603\) 0 0
\(604\) 150.781 209.357i 0.249638 0.346617i
\(605\) 111.593 + 111.593i 0.184451 + 0.184451i
\(606\) 0 0
\(607\) 568.740i 0.936969i 0.883472 + 0.468484i \(0.155200\pi\)
−0.883472 + 0.468484i \(0.844800\pi\)
\(608\) 764.393 7.94198i 1.25723 0.0130625i
\(609\) 0 0
\(610\) −128.984 + 66.0585i −0.211449 + 0.108293i
\(611\) 313.865 313.865i 0.513691 0.513691i
\(612\) 0 0
\(613\) −168.441 + 168.441i −0.274782 + 0.274782i −0.831022 0.556240i \(-0.812244\pi\)
0.556240 + 0.831022i \(0.312244\pi\)
\(614\) −23.5455 + 72.9813i −0.0383478 + 0.118862i
\(615\) 0 0
\(616\) −206.874 + 152.282i −0.335834 + 0.247211i
\(617\) 599.157i 0.971081i 0.874214 + 0.485541i \(0.161377\pi\)
−0.874214 + 0.485541i \(0.838623\pi\)
\(618\) 0 0
\(619\) 126.719 + 126.719i 0.204715 + 0.204715i 0.802017 0.597301i \(-0.203760\pi\)
−0.597301 + 0.802017i \(0.703760\pi\)
\(620\) −232.807 + 37.8654i −0.375495 + 0.0610732i
\(621\) 0 0
\(622\) −660.647 + 338.347i −1.06213 + 0.543967i
\(623\) 219.881i 0.352939i
\(624\) 0 0
\(625\) −476.800 −0.762879
\(626\) 341.426 + 666.658i 0.545409 + 1.06495i
\(627\) 0 0
\(628\) 303.854 49.4210i 0.483844 0.0786959i
\(629\) −147.716 + 147.716i −0.234842 + 0.234842i
\(630\) 0 0
\(631\) 668.283 1.05909 0.529543 0.848283i \(-0.322363\pi\)
0.529543 + 0.848283i \(0.322363\pi\)
\(632\) −35.2773 5.36216i −0.0558185 0.00848444i
\(633\) 0 0
\(634\) 130.779 + 42.1923i 0.206275 + 0.0665494i
\(635\) −37.1177 37.1177i −0.0584531 0.0584531i
\(636\) 0 0
\(637\) −354.243 354.243i −0.556112 0.556112i
\(638\) −101.774 198.720i −0.159520 0.311474i
\(639\) 0 0
\(640\) 105.064 149.122i 0.164163 0.233004i
\(641\) −484.574 −0.755966 −0.377983 0.925813i \(-0.623382\pi\)
−0.377983 + 0.925813i \(0.623382\pi\)
\(642\) 0 0
\(643\) 75.2980 75.2980i 0.117104 0.117104i −0.646126 0.763230i \(-0.723612\pi\)
0.763230 + 0.646126i \(0.223612\pi\)
\(644\) −777.952 + 1080.17i −1.20800 + 1.67728i
\(645\) 0 0
\(646\) −328.306 + 1017.61i −0.508213 + 1.57525i
\(647\) 582.307 0.900011 0.450006 0.893026i \(-0.351422\pi\)
0.450006 + 0.893026i \(0.351422\pi\)
\(648\) 0 0
\(649\) 28.2682i 0.0435565i
\(650\) 137.282 425.518i 0.211204 0.654644i
\(651\) 0 0
\(652\) −95.1754 585.164i −0.145974 0.897491i
\(653\) −457.453 457.453i −0.700541 0.700541i 0.263986 0.964527i \(-0.414963\pi\)
−0.964527 + 0.263986i \(0.914963\pi\)
\(654\) 0 0
\(655\) 24.9283i 0.0380584i
\(656\) −715.480 + 239.066i −1.09067 + 0.364430i
\(657\) 0 0
\(658\) 416.750 + 813.734i 0.633359 + 1.23668i
\(659\) 430.079 430.079i 0.652623 0.652623i −0.301001 0.953624i \(-0.597321\pi\)
0.953624 + 0.301001i \(0.0973207\pi\)
\(660\) 0 0
\(661\) −513.622 + 513.622i −0.777038 + 0.777038i −0.979326 0.202288i \(-0.935162\pi\)
0.202288 + 0.979326i \(0.435162\pi\)
\(662\) −5.08436 1.64034i −0.00768031 0.00247785i
\(663\) 0 0
\(664\) 68.2440 + 92.7089i 0.102777 + 0.139622i
\(665\) 341.246i 0.513152i
\(666\) 0 0
\(667\) −818.105 818.105i −1.22654 1.22654i
\(668\) −124.624 + 173.037i −0.186562 + 0.259038i
\(669\) 0 0
\(670\) 18.7503 + 36.6112i 0.0279855 + 0.0546436i
\(671\) 162.872i 0.242730i
\(672\) 0 0
\(673\) −1112.68 −1.65332 −0.826659 0.562703i \(-0.809761\pi\)
−0.826659 + 0.562703i \(0.809761\pi\)
\(674\) −688.871 + 352.802i −1.02206 + 0.523446i
\(675\) 0 0
\(676\) −241.061 173.615i −0.356599 0.256827i
\(677\) −633.271 + 633.271i −0.935408 + 0.935408i −0.998037 0.0626291i \(-0.980051\pi\)
0.0626291 + 0.998037i \(0.480051\pi\)
\(678\) 0 0
\(679\) 1075.62 1.58412
\(680\) 151.262 + 205.488i 0.222444 + 0.302188i
\(681\) 0 0
\(682\) 81.3937 252.287i 0.119346 0.369922i
\(683\) 429.651 + 429.651i 0.629065 + 0.629065i 0.947833 0.318768i \(-0.103269\pi\)
−0.318768 + 0.947833i \(0.603269\pi\)
\(684\) 0 0
\(685\) −146.803 146.803i −0.214312 0.214312i
\(686\) 44.1038 22.5876i 0.0642913 0.0329265i
\(687\) 0 0
\(688\) −493.330 + 988.439i −0.717049 + 1.43668i
\(689\) 346.042 0.502239
\(690\) 0 0
\(691\) −151.617 + 151.617i −0.219417 + 0.219417i −0.808253 0.588836i \(-0.799586\pi\)
0.588836 + 0.808253i \(0.299586\pi\)
\(692\) 232.150 37.7586i 0.335477 0.0545644i
\(693\) 0 0
\(694\) −1189.47 383.753i −1.71394 0.552958i
\(695\) −166.417 −0.239449
\(696\) 0 0
\(697\) 1055.17i 1.51388i
\(698\) 321.353 + 103.676i 0.460391 + 0.148533i
\(699\) 0 0
\(700\) 747.287 + 538.205i 1.06755 + 0.768864i
\(701\) 920.704 + 920.704i 1.31341 + 1.31341i 0.918882 + 0.394533i \(0.129094\pi\)
0.394533 + 0.918882i \(0.370906\pi\)
\(702\) 0 0
\(703\) 222.982i 0.317186i
\(704\) 95.3473 + 181.500i 0.135437 + 0.257812i
\(705\) 0 0
\(706\) 917.906 470.102i 1.30015 0.665866i
\(707\) 1010.18 1010.18i 1.42882 1.42882i
\(708\) 0 0
\(709\) 405.348 405.348i 0.571718 0.571718i −0.360890 0.932608i \(-0.617527\pi\)
0.932608 + 0.360890i \(0.117527\pi\)
\(710\) 10.4605 32.4233i 0.0147331 0.0456666i
\(711\) 0 0
\(712\) −173.498 26.3718i −0.243677 0.0370391i
\(713\) 1373.72i 1.92667i
\(714\) 0 0
\(715\) −31.4199 31.4199i −0.0439439 0.0439439i
\(716\) 48.1958 + 296.321i 0.0673125 + 0.413856i
\(717\) 0 0
\(718\) −762.363 + 390.441i −1.06179 + 0.543789i
\(719\) 880.704i 1.22490i 0.790509 + 0.612450i \(0.209816\pi\)
−0.790509 + 0.612450i \(0.790184\pi\)
\(720\) 0 0
\(721\) 581.930 0.807115
\(722\) −191.147 373.227i −0.264746 0.516935i
\(723\) 0 0
\(724\) 60.4859 + 371.884i 0.0835440 + 0.513651i
\(725\) −565.983 + 565.983i −0.780667 + 0.780667i
\(726\) 0 0
\(727\) 1000.46 1.37615 0.688077 0.725637i \(-0.258455\pi\)
0.688077 + 0.725637i \(0.258455\pi\)
\(728\) −628.547 + 462.680i −0.863388 + 0.635549i
\(729\) 0 0
\(730\) 301.999 + 97.4320i 0.413697 + 0.133469i
\(731\) −1092.64 1092.64i −1.49472 1.49472i
\(732\) 0 0
\(733\) 540.306 + 540.306i 0.737116 + 0.737116i 0.972019 0.234903i \(-0.0754772\pi\)
−0.234903 + 0.972019i \(0.575477\pi\)
\(734\) −200.097 390.704i −0.272612 0.532295i
\(735\) 0 0
\(736\) 759.011 + 743.401i 1.03126 + 1.01006i
\(737\) −46.2301 −0.0627274
\(738\) 0 0
\(739\) 893.726 893.726i 1.20937 1.20937i 0.238142 0.971230i \(-0.423462\pi\)
0.971230 0.238142i \(-0.0765384\pi\)
\(740\) −43.1775 31.0970i −0.0583480 0.0420229i
\(741\) 0 0
\(742\) −218.841 + 678.316i −0.294934 + 0.914172i
\(743\) −1295.75 −1.74394 −0.871969 0.489561i \(-0.837157\pi\)
−0.871969 + 0.489561i \(0.837157\pi\)
\(744\) 0 0
\(745\) 395.527i 0.530909i
\(746\) 369.092 1144.03i 0.494761 1.53355i
\(747\) 0 0
\(748\) −283.054 + 46.0380i −0.378414 + 0.0615481i
\(749\) −1130.13 1130.13i −1.50885 1.50885i
\(750\) 0 0
\(751\) 229.818i 0.306016i 0.988225 + 0.153008i \(0.0488961\pi\)
−0.988225 + 0.153008i \(0.951104\pi\)
\(752\) 692.066 231.243i 0.920300 0.307504i
\(753\) 0 0
\(754\) −309.220 603.774i −0.410106 0.800761i
\(755\) −64.9987 + 64.9987i −0.0860910 + 0.0860910i
\(756\) 0 0
\(757\) −373.678 + 373.678i −0.493630 + 0.493630i −0.909448 0.415818i \(-0.863495\pi\)
0.415818 + 0.909448i \(0.363495\pi\)
\(758\) 984.973 + 317.776i 1.29944 + 0.419229i
\(759\) 0 0
\(760\) −269.262 40.9280i −0.354293 0.0538527i
\(761\) 384.012i 0.504615i 0.967647 + 0.252307i \(0.0811894\pi\)
−0.967647 + 0.252307i \(0.918811\pi\)
\(762\) 0 0
\(763\) −813.296 813.296i −1.06592 1.06592i
\(764\) 369.222 + 265.918i 0.483275 + 0.348060i
\(765\) 0 0
\(766\) 194.440 + 379.658i 0.253838 + 0.495637i
\(767\) 85.8874i 0.111978i
\(768\) 0 0
\(769\) 865.026 1.12487 0.562436 0.826841i \(-0.309864\pi\)
0.562436 + 0.826841i \(0.309864\pi\)
\(770\) 81.4598 41.7193i 0.105792 0.0541809i
\(771\) 0 0
\(772\) −62.0876 + 86.2074i −0.0804244 + 0.111668i
\(773\) 1.78859 1.78859i 0.00231383 0.00231383i −0.705949 0.708263i \(-0.749479\pi\)
0.708263 + 0.705949i \(0.249479\pi\)
\(774\) 0 0
\(775\) −950.368 −1.22628
\(776\) 129.007 848.725i 0.166246 1.09372i
\(777\) 0 0
\(778\) 183.066 567.428i 0.235303 0.729341i
\(779\) 796.409 + 796.409i 1.02235 + 1.02235i
\(780\) 0 0
\(781\) 27.0753 + 27.0753i 0.0346675 + 0.0346675i
\(782\) −1322.70 + 677.413i −1.69143 + 0.866257i
\(783\) 0 0
\(784\) −260.991 781.098i −0.332897 0.996299i
\(785\) −109.681