Properties

Label 684.3.g.b.343.10
Level $684$
Weight $3$
Character 684.343
Analytic conductor $18.638$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 343.10
Root \(-0.0607713 - 1.99908i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0607713 + 1.99908i) q^{2} +(-3.99261 + 0.242973i) q^{4} +5.82257 q^{5} +5.45132i q^{7} +(-0.728358 - 7.96677i) q^{8} +O(q^{10})\) \(q+(0.0607713 + 1.99908i) q^{2} +(-3.99261 + 0.242973i) q^{4} +5.82257 q^{5} +5.45132i q^{7} +(-0.728358 - 7.96677i) q^{8} +(0.353845 + 11.6398i) q^{10} -1.60915i q^{11} +23.5274 q^{13} +(-10.8976 + 0.331284i) q^{14} +(15.8819 - 1.94019i) q^{16} +5.92676 q^{17} -4.35890i q^{19} +(-23.2473 + 1.41473i) q^{20} +(3.21681 - 0.0977900i) q^{22} -26.6121i q^{23} +8.90234 q^{25} +(1.42979 + 47.0331i) q^{26} +(-1.32452 - 21.7650i) q^{28} +1.49241 q^{29} +31.3933i q^{31} +(4.84376 + 31.6313i) q^{32} +(0.360177 + 11.8480i) q^{34} +31.7407i q^{35} +26.8255 q^{37} +(8.71377 - 0.264896i) q^{38} +(-4.24092 - 46.3871i) q^{40} +44.0382 q^{41} +27.8586i q^{43} +(0.390980 + 6.42471i) q^{44} +(53.1996 - 1.61725i) q^{46} +32.5166i q^{47} +19.2831 q^{49} +(0.541007 + 17.7965i) q^{50} +(-93.9360 + 5.71653i) q^{52} -76.7637 q^{53} -9.36938i q^{55} +(43.4294 - 3.97051i) q^{56} +(0.0906959 + 2.98345i) q^{58} +33.8895i q^{59} +53.0162 q^{61} +(-62.7575 + 1.90781i) q^{62} +(-62.9390 + 11.6053i) q^{64} +136.990 q^{65} +76.1917i q^{67} +(-23.6632 + 1.44004i) q^{68} +(-63.4521 + 1.92892i) q^{70} -59.9326i q^{71} -49.8188 q^{73} +(1.63022 + 53.6263i) q^{74} +(1.05909 + 17.4034i) q^{76} +8.77198 q^{77} -23.3990i q^{79} +(92.4737 - 11.2969i) q^{80} +(2.67626 + 88.0358i) q^{82} +137.116i q^{83} +34.5090 q^{85} +(-55.6915 + 1.69300i) q^{86} +(-12.8197 + 1.17204i) q^{88} -116.608 q^{89} +128.256i q^{91} +(6.46602 + 106.252i) q^{92} +(-65.0032 + 1.97608i) q^{94} -25.3800i q^{95} -65.7341 q^{97} +(1.17186 + 38.5484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0607713 + 1.99908i 0.0303857 + 0.999538i
\(3\) 0 0
\(4\) −3.99261 + 0.242973i −0.998153 + 0.0607433i
\(5\) 5.82257 1.16451 0.582257 0.813005i \(-0.302170\pi\)
0.582257 + 0.813005i \(0.302170\pi\)
\(6\) 0 0
\(7\) 5.45132i 0.778760i 0.921077 + 0.389380i \(0.127311\pi\)
−0.921077 + 0.389380i \(0.872689\pi\)
\(8\) −0.728358 7.96677i −0.0910448 0.995847i
\(9\) 0 0
\(10\) 0.353845 + 11.6398i 0.0353845 + 1.16398i
\(11\) 1.60915i 0.146286i −0.997321 0.0731431i \(-0.976697\pi\)
0.997321 0.0731431i \(-0.0233030\pi\)
\(12\) 0 0
\(13\) 23.5274 1.80980 0.904901 0.425622i \(-0.139945\pi\)
0.904901 + 0.425622i \(0.139945\pi\)
\(14\) −10.8976 + 0.331284i −0.778401 + 0.0236631i
\(15\) 0 0
\(16\) 15.8819 1.94019i 0.992621 0.121262i
\(17\) 5.92676 0.348633 0.174316 0.984690i \(-0.444228\pi\)
0.174316 + 0.984690i \(0.444228\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) −23.2473 + 1.41473i −1.16236 + 0.0707364i
\(21\) 0 0
\(22\) 3.21681 0.0977900i 0.146219 0.00444500i
\(23\) 26.6121i 1.15705i −0.815665 0.578524i \(-0.803629\pi\)
0.815665 0.578524i \(-0.196371\pi\)
\(24\) 0 0
\(25\) 8.90234 0.356094
\(26\) 1.42979 + 47.0331i 0.0549920 + 1.80897i
\(27\) 0 0
\(28\) −1.32452 21.7650i −0.0473044 0.777322i
\(29\) 1.49241 0.0514625 0.0257313 0.999669i \(-0.491809\pi\)
0.0257313 + 0.999669i \(0.491809\pi\)
\(30\) 0 0
\(31\) 31.3933i 1.01269i 0.862332 + 0.506343i \(0.169003\pi\)
−0.862332 + 0.506343i \(0.830997\pi\)
\(32\) 4.84376 + 31.6313i 0.151368 + 0.988478i
\(33\) 0 0
\(34\) 0.360177 + 11.8480i 0.0105934 + 0.348472i
\(35\) 31.7407i 0.906877i
\(36\) 0 0
\(37\) 26.8255 0.725015 0.362507 0.931981i \(-0.381921\pi\)
0.362507 + 0.931981i \(0.381921\pi\)
\(38\) 8.71377 0.264896i 0.229310 0.00697095i
\(39\) 0 0
\(40\) −4.24092 46.3871i −0.106023 1.15968i
\(41\) 44.0382 1.07410 0.537051 0.843550i \(-0.319538\pi\)
0.537051 + 0.843550i \(0.319538\pi\)
\(42\) 0 0
\(43\) 27.8586i 0.647875i 0.946079 + 0.323937i \(0.105007\pi\)
−0.946079 + 0.323937i \(0.894993\pi\)
\(44\) 0.390980 + 6.42471i 0.00888590 + 0.146016i
\(45\) 0 0
\(46\) 53.1996 1.61725i 1.15651 0.0351577i
\(47\) 32.5166i 0.691843i 0.938264 + 0.345921i \(0.112434\pi\)
−0.938264 + 0.345921i \(0.887566\pi\)
\(48\) 0 0
\(49\) 19.2831 0.393533
\(50\) 0.541007 + 17.7965i 0.0108201 + 0.355929i
\(51\) 0 0
\(52\) −93.9360 + 5.71653i −1.80646 + 0.109933i
\(53\) −76.7637 −1.44837 −0.724186 0.689605i \(-0.757784\pi\)
−0.724186 + 0.689605i \(0.757784\pi\)
\(54\) 0 0
\(55\) 9.36938i 0.170352i
\(56\) 43.4294 3.97051i 0.775526 0.0709020i
\(57\) 0 0
\(58\) 0.0906959 + 2.98345i 0.00156372 + 0.0514388i
\(59\) 33.8895i 0.574398i 0.957871 + 0.287199i \(0.0927241\pi\)
−0.957871 + 0.287199i \(0.907276\pi\)
\(60\) 0 0
\(61\) 53.0162 0.869118 0.434559 0.900643i \(-0.356904\pi\)
0.434559 + 0.900643i \(0.356904\pi\)
\(62\) −62.7575 + 1.90781i −1.01222 + 0.0307711i
\(63\) 0 0
\(64\) −62.9390 + 11.6053i −0.983422 + 0.181333i
\(65\) 136.990 2.10754
\(66\) 0 0
\(67\) 76.1917i 1.13719i 0.822618 + 0.568594i \(0.192513\pi\)
−0.822618 + 0.568594i \(0.807487\pi\)
\(68\) −23.6632 + 1.44004i −0.347989 + 0.0211771i
\(69\) 0 0
\(70\) −63.4521 + 1.92892i −0.906459 + 0.0275561i
\(71\) 59.9326i 0.844121i −0.906568 0.422060i \(-0.861307\pi\)
0.906568 0.422060i \(-0.138693\pi\)
\(72\) 0 0
\(73\) −49.8188 −0.682450 −0.341225 0.939982i \(-0.610842\pi\)
−0.341225 + 0.939982i \(0.610842\pi\)
\(74\) 1.63022 + 53.6263i 0.0220301 + 0.724680i
\(75\) 0 0
\(76\) 1.05909 + 17.4034i 0.0139355 + 0.228992i
\(77\) 8.77198 0.113922
\(78\) 0 0
\(79\) 23.3990i 0.296190i −0.988973 0.148095i \(-0.952686\pi\)
0.988973 0.148095i \(-0.0473141\pi\)
\(80\) 92.4737 11.2969i 1.15592 0.141212i
\(81\) 0 0
\(82\) 2.67626 + 88.0358i 0.0326373 + 1.07361i
\(83\) 137.116i 1.65200i 0.563667 + 0.826002i \(0.309390\pi\)
−0.563667 + 0.826002i \(0.690610\pi\)
\(84\) 0 0
\(85\) 34.5090 0.405988
\(86\) −55.6915 + 1.69300i −0.647576 + 0.0196861i
\(87\) 0 0
\(88\) −12.8197 + 1.17204i −0.145679 + 0.0133186i
\(89\) −116.608 −1.31020 −0.655101 0.755541i \(-0.727374\pi\)
−0.655101 + 0.755541i \(0.727374\pi\)
\(90\) 0 0
\(91\) 128.256i 1.40940i
\(92\) 6.46602 + 106.252i 0.0702828 + 1.15491i
\(93\) 0 0
\(94\) −65.0032 + 1.97608i −0.691523 + 0.0210221i
\(95\) 25.3800i 0.267158i
\(96\) 0 0
\(97\) −65.7341 −0.677671 −0.338836 0.940846i \(-0.610033\pi\)
−0.338836 + 0.940846i \(0.610033\pi\)
\(98\) 1.17186 + 38.5484i 0.0119577 + 0.393351i
\(99\) 0 0
\(100\) −35.5436 + 2.16303i −0.355436 + 0.0216303i
\(101\) −1.81406 −0.0179609 −0.00898047 0.999960i \(-0.502859\pi\)
−0.00898047 + 0.999960i \(0.502859\pi\)
\(102\) 0 0
\(103\) 0.494673i 0.00480265i −0.999997 0.00240133i \(-0.999236\pi\)
0.999997 0.00240133i \(-0.000764367\pi\)
\(104\) −17.1364 187.438i −0.164773 1.80229i
\(105\) 0 0
\(106\) −4.66503 153.457i −0.0440097 1.44770i
\(107\) 11.7361i 0.109684i 0.998495 + 0.0548418i \(0.0174654\pi\)
−0.998495 + 0.0548418i \(0.982535\pi\)
\(108\) 0 0
\(109\) −28.9819 −0.265889 −0.132945 0.991123i \(-0.542443\pi\)
−0.132945 + 0.991123i \(0.542443\pi\)
\(110\) 18.7301 0.569390i 0.170274 0.00517627i
\(111\) 0 0
\(112\) 10.5766 + 86.5775i 0.0944341 + 0.773013i
\(113\) 140.725 1.24536 0.622678 0.782478i \(-0.286045\pi\)
0.622678 + 0.782478i \(0.286045\pi\)
\(114\) 0 0
\(115\) 154.951i 1.34740i
\(116\) −5.95863 + 0.362616i −0.0513675 + 0.00312600i
\(117\) 0 0
\(118\) −67.7477 + 2.05951i −0.574133 + 0.0174535i
\(119\) 32.3086i 0.271501i
\(120\) 0 0
\(121\) 118.411 0.978600
\(122\) 3.22186 + 105.983i 0.0264087 + 0.868716i
\(123\) 0 0
\(124\) −7.62772 125.341i −0.0615138 1.01082i
\(125\) −93.7298 −0.749838
\(126\) 0 0
\(127\) 50.4262i 0.397056i −0.980095 0.198528i \(-0.936384\pi\)
0.980095 0.198528i \(-0.0636161\pi\)
\(128\) −27.0248 125.115i −0.211131 0.977458i
\(129\) 0 0
\(130\) 8.32507 + 273.854i 0.0640390 + 2.10657i
\(131\) 124.954i 0.953847i −0.878945 0.476924i \(-0.841752\pi\)
0.878945 0.476924i \(-0.158248\pi\)
\(132\) 0 0
\(133\) 23.7618 0.178660
\(134\) −152.313 + 4.63027i −1.13666 + 0.0345542i
\(135\) 0 0
\(136\) −4.31680 47.2171i −0.0317412 0.347185i
\(137\) −137.151 −1.00110 −0.500551 0.865707i \(-0.666869\pi\)
−0.500551 + 0.865707i \(0.666869\pi\)
\(138\) 0 0
\(139\) 89.6885i 0.645241i −0.946528 0.322621i \(-0.895436\pi\)
0.946528 0.322621i \(-0.104564\pi\)
\(140\) −7.71214 126.728i −0.0550867 0.905203i
\(141\) 0 0
\(142\) 119.810 3.64218i 0.843731 0.0256492i
\(143\) 37.8591i 0.264749i
\(144\) 0 0
\(145\) 8.68969 0.0599289
\(146\) −3.02756 99.5917i −0.0207367 0.682135i
\(147\) 0 0
\(148\) −107.104 + 6.51788i −0.723676 + 0.0440398i
\(149\) −18.9194 −0.126976 −0.0634878 0.997983i \(-0.520222\pi\)
−0.0634878 + 0.997983i \(0.520222\pi\)
\(150\) 0 0
\(151\) 269.061i 1.78186i −0.454141 0.890930i \(-0.650054\pi\)
0.454141 0.890930i \(-0.349946\pi\)
\(152\) −34.7264 + 3.17484i −0.228463 + 0.0208871i
\(153\) 0 0
\(154\) 0.533085 + 17.5359i 0.00346159 + 0.113869i
\(155\) 182.790i 1.17929i
\(156\) 0 0
\(157\) 11.4972 0.0732305 0.0366153 0.999329i \(-0.488342\pi\)
0.0366153 + 0.999329i \(0.488342\pi\)
\(158\) 46.7764 1.42199i 0.296053 0.00899993i
\(159\) 0 0
\(160\) 28.2032 + 184.175i 0.176270 + 1.15110i
\(161\) 145.071 0.901063
\(162\) 0 0
\(163\) 126.564i 0.776465i −0.921562 0.388232i \(-0.873086\pi\)
0.921562 0.388232i \(-0.126914\pi\)
\(164\) −175.828 + 10.7001i −1.07212 + 0.0652445i
\(165\) 0 0
\(166\) −274.106 + 8.33274i −1.65124 + 0.0501972i
\(167\) 14.2424i 0.0852836i 0.999090 + 0.0426418i \(0.0135774\pi\)
−0.999090 + 0.0426418i \(0.986423\pi\)
\(168\) 0 0
\(169\) 384.540 2.27539
\(170\) 2.09715 + 68.9860i 0.0123362 + 0.405800i
\(171\) 0 0
\(172\) −6.76889 111.229i −0.0393540 0.646678i
\(173\) 217.817 1.25906 0.629528 0.776978i \(-0.283248\pi\)
0.629528 + 0.776978i \(0.283248\pi\)
\(174\) 0 0
\(175\) 48.5295i 0.277312i
\(176\) −3.12206 25.5564i −0.0177390 0.145207i
\(177\) 0 0
\(178\) −7.08642 233.108i −0.0398114 1.30960i
\(179\) 180.223i 1.00684i −0.864043 0.503418i \(-0.832076\pi\)
0.864043 0.503418i \(-0.167924\pi\)
\(180\) 0 0
\(181\) −95.0637 −0.525214 −0.262607 0.964903i \(-0.584582\pi\)
−0.262607 + 0.964903i \(0.584582\pi\)
\(182\) −256.393 + 7.79426i −1.40875 + 0.0428256i
\(183\) 0 0
\(184\) −212.013 + 19.3831i −1.15224 + 0.105343i
\(185\) 156.194 0.844290
\(186\) 0 0
\(187\) 9.53703i 0.0510001i
\(188\) −7.90066 129.826i −0.0420248 0.690565i
\(189\) 0 0
\(190\) 50.7366 1.54238i 0.267035 0.00811777i
\(191\) 25.4789i 0.133397i 0.997773 + 0.0666987i \(0.0212466\pi\)
−0.997773 + 0.0666987i \(0.978753\pi\)
\(192\) 0 0
\(193\) 339.566 1.75941 0.879705 0.475520i \(-0.157740\pi\)
0.879705 + 0.475520i \(0.157740\pi\)
\(194\) −3.99475 131.407i −0.0205915 0.677358i
\(195\) 0 0
\(196\) −76.9900 + 4.68527i −0.392806 + 0.0239045i
\(197\) −136.859 −0.694717 −0.347358 0.937732i \(-0.612921\pi\)
−0.347358 + 0.937732i \(0.612921\pi\)
\(198\) 0 0
\(199\) 199.411i 1.00207i 0.865428 + 0.501034i \(0.167047\pi\)
−0.865428 + 0.501034i \(0.832953\pi\)
\(200\) −6.48409 70.9230i −0.0324205 0.354615i
\(201\) 0 0
\(202\) −0.110243 3.62644i −0.000545755 0.0179527i
\(203\) 8.13563i 0.0400770i
\(204\) 0 0
\(205\) 256.416 1.25081
\(206\) 0.988890 0.0300619i 0.00480044 0.000145932i
\(207\) 0 0
\(208\) 373.661 45.6478i 1.79645 0.219461i
\(209\) −7.01411 −0.0335604
\(210\) 0 0
\(211\) 363.655i 1.72348i 0.507347 + 0.861742i \(0.330626\pi\)
−0.507347 + 0.861742i \(0.669374\pi\)
\(212\) 306.488 18.6515i 1.44570 0.0879788i
\(213\) 0 0
\(214\) −23.4614 + 0.713221i −0.109633 + 0.00333281i
\(215\) 162.209i 0.754460i
\(216\) 0 0
\(217\) −171.135 −0.788640
\(218\) −1.76127 57.9371i −0.00807922 0.265766i
\(219\) 0 0
\(220\) 2.27651 + 37.4083i 0.0103478 + 0.170038i
\(221\) 139.441 0.630956
\(222\) 0 0
\(223\) 268.968i 1.20614i −0.797690 0.603068i \(-0.793945\pi\)
0.797690 0.603068i \(-0.206055\pi\)
\(224\) −172.432 + 26.4049i −0.769787 + 0.117879i
\(225\) 0 0
\(226\) 8.55206 + 281.320i 0.0378410 + 1.24478i
\(227\) 79.9913i 0.352384i −0.984356 0.176192i \(-0.943622\pi\)
0.984356 0.176192i \(-0.0563780\pi\)
\(228\) 0 0
\(229\) 297.342 1.29843 0.649217 0.760603i \(-0.275097\pi\)
0.649217 + 0.760603i \(0.275097\pi\)
\(230\) 309.759 9.41657i 1.34678 0.0409416i
\(231\) 0 0
\(232\) −1.08701 11.8897i −0.00468539 0.0512488i
\(233\) 255.975 1.09860 0.549302 0.835624i \(-0.314894\pi\)
0.549302 + 0.835624i \(0.314894\pi\)
\(234\) 0 0
\(235\) 189.330i 0.805661i
\(236\) −8.23423 135.308i −0.0348908 0.573337i
\(237\) 0 0
\(238\) −64.5875 + 1.96344i −0.271376 + 0.00824974i
\(239\) 148.674i 0.622067i −0.950399 0.311034i \(-0.899325\pi\)
0.950399 0.311034i \(-0.100675\pi\)
\(240\) 0 0
\(241\) −330.295 −1.37052 −0.685259 0.728299i \(-0.740311\pi\)
−0.685259 + 0.728299i \(0.740311\pi\)
\(242\) 7.19597 + 236.712i 0.0297354 + 0.978148i
\(243\) 0 0
\(244\) −211.673 + 12.8815i −0.867513 + 0.0527930i
\(245\) 112.277 0.458274
\(246\) 0 0
\(247\) 102.554i 0.415197i
\(248\) 250.103 22.8655i 1.00848 0.0921997i
\(249\) 0 0
\(250\) −5.69608 187.373i −0.0227843 0.749492i
\(251\) 253.493i 1.00993i −0.863139 0.504966i \(-0.831505\pi\)
0.863139 0.504966i \(-0.168495\pi\)
\(252\) 0 0
\(253\) −42.8228 −0.169260
\(254\) 100.806 3.06446i 0.396873 0.0120648i
\(255\) 0 0
\(256\) 248.471 61.6281i 0.970591 0.240735i
\(257\) −254.160 −0.988950 −0.494475 0.869192i \(-0.664640\pi\)
−0.494475 + 0.869192i \(0.664640\pi\)
\(258\) 0 0
\(259\) 146.235i 0.564613i
\(260\) −546.949 + 33.2849i −2.10365 + 0.128019i
\(261\) 0 0
\(262\) 249.793 7.59362i 0.953407 0.0289833i
\(263\) 190.047i 0.722613i −0.932447 0.361306i \(-0.882331\pi\)
0.932447 0.361306i \(-0.117669\pi\)
\(264\) 0 0
\(265\) −446.962 −1.68665
\(266\) 1.44403 + 47.5016i 0.00542870 + 0.178577i
\(267\) 0 0
\(268\) −18.5125 304.204i −0.0690766 1.13509i
\(269\) −233.427 −0.867758 −0.433879 0.900971i \(-0.642855\pi\)
−0.433879 + 0.900971i \(0.642855\pi\)
\(270\) 0 0
\(271\) 2.73196i 0.0100810i −0.999987 0.00504051i \(-0.998396\pi\)
0.999987 0.00504051i \(-0.00160445\pi\)
\(272\) 94.1283 11.4991i 0.346060 0.0422760i
\(273\) 0 0
\(274\) −8.33485 274.175i −0.0304192 1.00064i
\(275\) 14.3252i 0.0520916i
\(276\) 0 0
\(277\) −20.4896 −0.0739697 −0.0369848 0.999316i \(-0.511775\pi\)
−0.0369848 + 0.999316i \(0.511775\pi\)
\(278\) 179.294 5.45049i 0.644943 0.0196061i
\(279\) 0 0
\(280\) 252.871 23.1186i 0.903111 0.0825664i
\(281\) 285.339 1.01544 0.507721 0.861522i \(-0.330488\pi\)
0.507721 + 0.861522i \(0.330488\pi\)
\(282\) 0 0
\(283\) 4.45505i 0.0157422i −0.999969 0.00787112i \(-0.997495\pi\)
0.999969 0.00787112i \(-0.00250548\pi\)
\(284\) 14.5620 + 239.288i 0.0512746 + 0.842562i
\(285\) 0 0
\(286\) 75.6833 2.30075i 0.264627 0.00804458i
\(287\) 240.066i 0.836468i
\(288\) 0 0
\(289\) −253.874 −0.878455
\(290\) 0.528084 + 17.3713i 0.00182098 + 0.0599012i
\(291\) 0 0
\(292\) 198.907 12.1046i 0.681190 0.0414542i
\(293\) −326.981 −1.11598 −0.557988 0.829849i \(-0.688426\pi\)
−0.557988 + 0.829849i \(0.688426\pi\)
\(294\) 0 0
\(295\) 197.324i 0.668895i
\(296\) −19.5386 213.713i −0.0660088 0.722004i
\(297\) 0 0
\(298\) −1.14975 37.8213i −0.00385824 0.126917i
\(299\) 626.114i 2.09403i
\(300\) 0 0
\(301\) −151.866 −0.504539
\(302\) 537.873 16.3512i 1.78104 0.0541430i
\(303\) 0 0
\(304\) −8.45711 69.2277i −0.0278195 0.227723i
\(305\) 308.690 1.01210
\(306\) 0 0
\(307\) 352.091i 1.14688i −0.819249 0.573438i \(-0.805609\pi\)
0.819249 0.573438i \(-0.194391\pi\)
\(308\) −35.0231 + 2.13136i −0.113711 + 0.00691998i
\(309\) 0 0
\(310\) −365.410 + 11.1084i −1.17874 + 0.0358334i
\(311\) 75.4387i 0.242568i 0.992618 + 0.121284i \(0.0387012\pi\)
−0.992618 + 0.121284i \(0.961299\pi\)
\(312\) 0 0
\(313\) −13.1951 −0.0421569 −0.0210784 0.999778i \(-0.506710\pi\)
−0.0210784 + 0.999778i \(0.506710\pi\)
\(314\) 0.698699 + 22.9838i 0.00222516 + 0.0731967i
\(315\) 0 0
\(316\) 5.68533 + 93.4232i 0.0179915 + 0.295643i
\(317\) −276.427 −0.872011 −0.436005 0.899944i \(-0.643607\pi\)
−0.436005 + 0.899944i \(0.643607\pi\)
\(318\) 0 0
\(319\) 2.40151i 0.00752826i
\(320\) −366.467 + 67.5729i −1.14521 + 0.211165i
\(321\) 0 0
\(322\) 8.81616 + 290.008i 0.0273794 + 0.900647i
\(323\) 25.8341i 0.0799818i
\(324\) 0 0
\(325\) 209.449 0.644459
\(326\) 253.011 7.69145i 0.776106 0.0235934i
\(327\) 0 0
\(328\) −32.0756 350.843i −0.0977914 1.06964i
\(329\) −177.258 −0.538779
\(330\) 0 0
\(331\) 550.110i 1.66196i −0.556301 0.830981i \(-0.687780\pi\)
0.556301 0.830981i \(-0.312220\pi\)
\(332\) −33.3156 547.453i −0.100348 1.64895i
\(333\) 0 0
\(334\) −28.4716 + 0.865527i −0.0852442 + 0.00259140i
\(335\) 443.631i 1.32427i
\(336\) 0 0
\(337\) −179.034 −0.531259 −0.265630 0.964075i \(-0.585580\pi\)
−0.265630 + 0.964075i \(0.585580\pi\)
\(338\) 23.3690 + 768.725i 0.0691391 + 2.27433i
\(339\) 0 0
\(340\) −137.781 + 8.38475i −0.405238 + 0.0246610i
\(341\) 50.5164 0.148142
\(342\) 0 0
\(343\) 372.233i 1.08523i
\(344\) 221.943 20.2910i 0.645184 0.0589856i
\(345\) 0 0
\(346\) 13.2370 + 435.432i 0.0382573 + 1.25848i
\(347\) 161.757i 0.466157i 0.972458 + 0.233079i \(0.0748800\pi\)
−0.972458 + 0.233079i \(0.925120\pi\)
\(348\) 0 0
\(349\) −472.810 −1.35476 −0.677378 0.735635i \(-0.736884\pi\)
−0.677378 + 0.735635i \(0.736884\pi\)
\(350\) −97.0142 + 2.94920i −0.277184 + 0.00842629i
\(351\) 0 0
\(352\) 50.8994 7.79433i 0.144601 0.0221430i
\(353\) −319.200 −0.904249 −0.452125 0.891955i \(-0.649334\pi\)
−0.452125 + 0.891955i \(0.649334\pi\)
\(354\) 0 0
\(355\) 348.962i 0.982991i
\(356\) 465.571 28.3326i 1.30778 0.0795860i
\(357\) 0 0
\(358\) 360.281 10.9524i 1.00637 0.0305933i
\(359\) 545.770i 1.52025i −0.649776 0.760126i \(-0.725137\pi\)
0.649776 0.760126i \(-0.274863\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) −5.77715 190.040i −0.0159590 0.524971i
\(363\) 0 0
\(364\) −31.1626 512.075i −0.0856117 1.40680i
\(365\) −290.074 −0.794723
\(366\) 0 0
\(367\) 90.4491i 0.246455i 0.992378 + 0.123228i \(0.0393246\pi\)
−0.992378 + 0.123228i \(0.960675\pi\)
\(368\) −51.6327 422.651i −0.140306 1.14851i
\(369\) 0 0
\(370\) 9.49210 + 312.243i 0.0256543 + 0.843900i
\(371\) 418.464i 1.12793i
\(372\) 0 0
\(373\) 468.975 1.25731 0.628653 0.777686i \(-0.283606\pi\)
0.628653 + 0.777686i \(0.283606\pi\)
\(374\) 19.0652 0.579578i 0.0509766 0.00154967i
\(375\) 0 0
\(376\) 259.052 23.6837i 0.688969 0.0629886i
\(377\) 35.1127 0.0931370
\(378\) 0 0
\(379\) 196.529i 0.518545i 0.965804 + 0.259273i \(0.0834828\pi\)
−0.965804 + 0.259273i \(0.916517\pi\)
\(380\) 6.16666 + 101.333i 0.0162280 + 0.266665i
\(381\) 0 0
\(382\) −50.9342 + 1.54839i −0.133336 + 0.00405337i
\(383\) 24.8045i 0.0647637i −0.999476 0.0323819i \(-0.989691\pi\)
0.999476 0.0323819i \(-0.0103093\pi\)
\(384\) 0 0
\(385\) 51.0755 0.132664
\(386\) 20.6359 + 678.819i 0.0534608 + 1.75860i
\(387\) 0 0
\(388\) 262.451 15.9716i 0.676420 0.0411639i
\(389\) 126.462 0.325095 0.162547 0.986701i \(-0.448029\pi\)
0.162547 + 0.986701i \(0.448029\pi\)
\(390\) 0 0
\(391\) 157.723i 0.403385i
\(392\) −14.0450 153.624i −0.0358291 0.391898i
\(393\) 0 0
\(394\) −8.31712 273.592i −0.0211094 0.694396i
\(395\) 136.242i 0.344917i
\(396\) 0 0
\(397\) 403.878 1.01732 0.508662 0.860966i \(-0.330140\pi\)
0.508662 + 0.860966i \(0.330140\pi\)
\(398\) −398.639 + 12.1185i −1.00160 + 0.0304485i
\(399\) 0 0
\(400\) 141.386 17.2723i 0.353466 0.0431807i
\(401\) −345.608 −0.861865 −0.430933 0.902384i \(-0.641815\pi\)
−0.430933 + 0.902384i \(0.641815\pi\)
\(402\) 0 0
\(403\) 738.603i 1.83276i
\(404\) 7.24282 0.440767i 0.0179278 0.00109101i
\(405\) 0 0
\(406\) −16.2637 + 0.494413i −0.0400585 + 0.00121777i
\(407\) 43.1663i 0.106060i
\(408\) 0 0
\(409\) −429.506 −1.05014 −0.525069 0.851060i \(-0.675960\pi\)
−0.525069 + 0.851060i \(0.675960\pi\)
\(410\) 15.5827 + 512.595i 0.0380066 + 1.25023i
\(411\) 0 0
\(412\) 0.120192 + 1.97504i 0.000291729 + 0.00479378i
\(413\) −184.742 −0.447318
\(414\) 0 0
\(415\) 798.370i 1.92378i
\(416\) 113.961 + 744.203i 0.273945 + 1.78895i
\(417\) 0 0
\(418\) −0.426257 14.0218i −0.00101975 0.0335449i
\(419\) 345.206i 0.823881i 0.911211 + 0.411940i \(0.135149\pi\)
−0.911211 + 0.411940i \(0.864851\pi\)
\(420\) 0 0
\(421\) −195.468 −0.464295 −0.232148 0.972681i \(-0.574575\pi\)
−0.232148 + 0.972681i \(0.574575\pi\)
\(422\) −726.974 + 22.0998i −1.72269 + 0.0523692i
\(423\) 0 0
\(424\) 55.9115 + 611.559i 0.131867 + 1.44236i
\(425\) 52.7620 0.124146
\(426\) 0 0
\(427\) 289.008i 0.676834i
\(428\) −2.85157 46.8579i −0.00666254 0.109481i
\(429\) 0 0
\(430\) −324.268 + 9.85764i −0.754111 + 0.0229247i
\(431\) 643.698i 1.49350i 0.665106 + 0.746749i \(0.268386\pi\)
−0.665106 + 0.746749i \(0.731614\pi\)
\(432\) 0 0
\(433\) −755.385 −1.74454 −0.872269 0.489026i \(-0.837352\pi\)
−0.872269 + 0.489026i \(0.837352\pi\)
\(434\) −10.4001 342.112i −0.0239633 0.788275i
\(435\) 0 0
\(436\) 115.714 7.04183i 0.265398 0.0161510i
\(437\) −115.999 −0.265445
\(438\) 0 0
\(439\) 522.862i 1.19103i −0.803345 0.595514i \(-0.796948\pi\)
0.803345 0.595514i \(-0.203052\pi\)
\(440\) −74.6437 + 6.82426i −0.169645 + 0.0155097i
\(441\) 0 0
\(442\) 8.47403 + 278.754i 0.0191720 + 0.630665i
\(443\) 5.86286i 0.0132345i 0.999978 + 0.00661723i \(0.00210634\pi\)
−0.999978 + 0.00661723i \(0.997894\pi\)
\(444\) 0 0
\(445\) −678.959 −1.52575
\(446\) 537.688 16.3455i 1.20558 0.0366492i
\(447\) 0 0
\(448\) −63.2644 343.101i −0.141215 0.765850i
\(449\) −626.982 −1.39640 −0.698199 0.715904i \(-0.746015\pi\)
−0.698199 + 0.715904i \(0.746015\pi\)
\(450\) 0 0
\(451\) 70.8640i 0.157126i
\(452\) −561.861 + 34.1924i −1.24306 + 0.0756470i
\(453\) 0 0
\(454\) 159.909 4.86117i 0.352222 0.0107074i
\(455\) 746.777i 1.64127i
\(456\) 0 0
\(457\) −451.537 −0.988046 −0.494023 0.869449i \(-0.664474\pi\)
−0.494023 + 0.869449i \(0.664474\pi\)
\(458\) 18.0698 + 594.408i 0.0394538 + 1.29784i
\(459\) 0 0
\(460\) 37.6489 + 618.659i 0.0818454 + 1.34491i
\(461\) −50.7723 −0.110135 −0.0550675 0.998483i \(-0.517537\pi\)
−0.0550675 + 0.998483i \(0.517537\pi\)
\(462\) 0 0
\(463\) 69.7862i 0.150726i −0.997156 0.0753631i \(-0.975988\pi\)
0.997156 0.0753631i \(-0.0240116\pi\)
\(464\) 23.7024 2.89557i 0.0510828 0.00624046i
\(465\) 0 0
\(466\) 15.5559 + 511.713i 0.0333818 + 1.09810i
\(467\) 461.829i 0.988927i 0.869198 + 0.494464i \(0.164635\pi\)
−0.869198 + 0.494464i \(0.835365\pi\)
\(468\) 0 0
\(469\) −415.345 −0.885597
\(470\) −378.486 + 11.5058i −0.805289 + 0.0244805i
\(471\) 0 0
\(472\) 269.990 24.6837i 0.572012 0.0522959i
\(473\) 44.8286 0.0947751
\(474\) 0 0
\(475\) 38.8044i 0.0816935i
\(476\) −7.85013 128.996i −0.0164919 0.271000i
\(477\) 0 0
\(478\) 297.211 9.03512i 0.621780 0.0189019i
\(479\) 814.201i 1.69979i 0.526949 + 0.849897i \(0.323336\pi\)
−0.526949 + 0.849897i \(0.676664\pi\)
\(480\) 0 0
\(481\) 631.136 1.31213
\(482\) −20.0725 660.285i −0.0416441 1.36989i
\(483\) 0 0
\(484\) −472.768 + 28.7706i −0.976793 + 0.0594434i
\(485\) −382.742 −0.789158
\(486\) 0 0
\(487\) 149.015i 0.305986i 0.988227 + 0.152993i \(0.0488912\pi\)
−0.988227 + 0.152993i \(0.951109\pi\)
\(488\) −38.6148 422.368i −0.0791286 0.865508i
\(489\) 0 0
\(490\) 6.82323 + 224.451i 0.0139250 + 0.458063i
\(491\) 367.294i 0.748053i 0.927418 + 0.374027i \(0.122023\pi\)
−0.927418 + 0.374027i \(0.877977\pi\)
\(492\) 0 0
\(493\) 8.84517 0.0179415
\(494\) 205.013 6.23232i 0.415005 0.0126160i
\(495\) 0 0
\(496\) 60.9091 + 498.586i 0.122801 + 1.00521i
\(497\) 326.712 0.657368
\(498\) 0 0
\(499\) 138.107i 0.276767i −0.990379 0.138384i \(-0.955809\pi\)
0.990379 0.138384i \(-0.0441907\pi\)
\(500\) 374.227 22.7738i 0.748454 0.0455476i
\(501\) 0 0
\(502\) 506.752 15.4051i 1.00947 0.0306875i
\(503\) 31.6936i 0.0630092i −0.999504 0.0315046i \(-0.989970\pi\)
0.999504 0.0315046i \(-0.0100299\pi\)
\(504\) 0 0
\(505\) −10.5625 −0.0209158
\(506\) −2.60240 85.6061i −0.00514308 0.169182i
\(507\) 0 0
\(508\) 12.2522 + 201.332i 0.0241185 + 0.396323i
\(509\) 564.839 1.10970 0.554852 0.831949i \(-0.312775\pi\)
0.554852 + 0.831949i \(0.312775\pi\)
\(510\) 0 0
\(511\) 271.578i 0.531465i
\(512\) 138.299 + 492.968i 0.270116 + 0.962828i
\(513\) 0 0
\(514\) −15.4457 508.086i −0.0300499 0.988494i
\(515\) 2.88027i 0.00559276i
\(516\) 0 0
\(517\) 52.3240 0.101207
\(518\) −292.334 + 8.88687i −0.564352 + 0.0171561i
\(519\) 0 0
\(520\) −99.7779 1091.37i −0.191881 2.09879i
\(521\) 304.845 0.585114 0.292557 0.956248i \(-0.405494\pi\)
0.292557 + 0.956248i \(0.405494\pi\)
\(522\) 0 0
\(523\) 812.948i 1.55439i −0.629257 0.777197i \(-0.716641\pi\)
0.629257 0.777197i \(-0.283359\pi\)
\(524\) 30.3604 + 498.893i 0.0579398 + 0.952086i
\(525\) 0 0
\(526\) 379.919 11.5494i 0.722279 0.0219571i
\(527\) 186.060i 0.353055i
\(528\) 0 0
\(529\) −179.204 −0.338759
\(530\) −27.1625 893.512i −0.0512500 1.68587i
\(531\) 0 0
\(532\) −94.8715 + 5.77347i −0.178330 + 0.0108524i
\(533\) 1036.11 1.94391
\(534\) 0 0
\(535\) 68.3345i 0.127728i
\(536\) 607.002 55.4948i 1.13247 0.103535i
\(537\) 0 0
\(538\) −14.1857 466.638i −0.0263674 0.867357i
\(539\) 31.0294i 0.0575684i
\(540\) 0 0
\(541\) −396.300 −0.732532 −0.366266 0.930510i \(-0.619364\pi\)
−0.366266 + 0.930510i \(0.619364\pi\)
\(542\) 5.46139 0.166025i 0.0100764 0.000306319i
\(543\) 0 0
\(544\) 28.7078 + 187.471i 0.0527717 + 0.344616i
\(545\) −168.749 −0.309632
\(546\) 0 0
\(547\) 526.396i 0.962333i −0.876629 0.481167i \(-0.840213\pi\)
0.876629 0.481167i \(-0.159787\pi\)
\(548\) 547.591 33.3240i 0.999254 0.0608102i
\(549\) 0 0
\(550\) 28.6371 0.870560i 0.0520675 0.00158284i
\(551\) 6.50528i 0.0118063i
\(552\) 0 0
\(553\) 127.555 0.230661
\(554\) −1.24518 40.9603i −0.00224762 0.0739355i
\(555\) 0 0
\(556\) 21.7919 + 358.092i 0.0391940 + 0.644050i
\(557\) −68.8105 −0.123538 −0.0617688 0.998090i \(-0.519674\pi\)
−0.0617688 + 0.998090i \(0.519674\pi\)
\(558\) 0 0
\(559\) 655.442i 1.17253i
\(560\) 61.5832 + 504.104i 0.109970 + 0.900185i
\(561\) 0 0
\(562\) 17.3404 + 570.415i 0.0308549 + 1.01497i
\(563\) 588.997i 1.04618i −0.852279 0.523088i \(-0.824780\pi\)
0.852279 0.523088i \(-0.175220\pi\)
\(564\) 0 0
\(565\) 819.383 1.45023
\(566\) 8.90599 0.270739i 0.0157350 0.000478338i
\(567\) 0 0
\(568\) −477.469 + 43.6524i −0.840615 + 0.0768528i
\(569\) 421.857 0.741401 0.370700 0.928752i \(-0.379118\pi\)
0.370700 + 0.928752i \(0.379118\pi\)
\(570\) 0 0
\(571\) 393.676i 0.689451i 0.938704 + 0.344725i \(0.112028\pi\)
−0.938704 + 0.344725i \(0.887972\pi\)
\(572\) 9.19875 + 151.157i 0.0160817 + 0.264260i
\(573\) 0 0
\(574\) −479.911 + 14.5892i −0.836082 + 0.0254166i
\(575\) 236.910i 0.412017i
\(576\) 0 0
\(577\) 703.416 1.21909 0.609546 0.792751i \(-0.291352\pi\)
0.609546 + 0.792751i \(0.291352\pi\)
\(578\) −15.4282 507.513i −0.0266924 0.878050i
\(579\) 0 0
\(580\) −34.6946 + 2.11136i −0.0598182 + 0.00364027i
\(581\) −747.465 −1.28651
\(582\) 0 0
\(583\) 123.524i 0.211877i
\(584\) 36.2860 + 396.895i 0.0621335 + 0.679615i
\(585\) 0 0
\(586\) −19.8711 653.660i −0.0339097 1.11546i
\(587\) 56.2392i 0.0958078i 0.998852 + 0.0479039i \(0.0152541\pi\)
−0.998852 + 0.0479039i \(0.984746\pi\)
\(588\) 0 0
\(589\) 136.840 0.232326
\(590\) −394.466 + 11.9916i −0.668586 + 0.0203248i
\(591\) 0 0
\(592\) 426.041 52.0468i 0.719665 0.0879169i
\(593\) −553.916 −0.934090 −0.467045 0.884233i \(-0.654681\pi\)
−0.467045 + 0.884233i \(0.654681\pi\)
\(594\) 0 0
\(595\) 188.119i 0.316167i
\(596\) 75.5377 4.59690i 0.126741 0.00771291i
\(597\) 0 0
\(598\) 1251.65 38.0498i 2.09306 0.0636284i
\(599\) 724.179i 1.20898i −0.796613 0.604490i \(-0.793377\pi\)
0.796613 0.604490i \(-0.206623\pi\)
\(600\) 0 0
\(601\) −393.734 −0.655132 −0.327566 0.944828i \(-0.606228\pi\)
−0.327566 + 0.944828i \(0.606228\pi\)
\(602\) −9.22911 303.592i −0.0153308 0.504306i
\(603\) 0 0
\(604\) 65.3745 + 1074.26i 0.108236 + 1.77857i
\(605\) 689.454 1.13959
\(606\) 0 0
\(607\) 860.362i 1.41740i −0.705510 0.708700i \(-0.749282\pi\)
0.705510 0.708700i \(-0.250718\pi\)
\(608\) 137.878 21.1135i 0.226772 0.0347261i
\(609\) 0 0
\(610\) 18.7595 + 617.096i 0.0307533 + 1.01163i
\(611\) 765.032i 1.25210i
\(612\) 0 0
\(613\) 563.747 0.919652 0.459826 0.888009i \(-0.347912\pi\)
0.459826 + 0.888009i \(0.347912\pi\)
\(614\) 703.856 21.3970i 1.14635 0.0348486i
\(615\) 0 0
\(616\) −6.38914 69.8844i −0.0103720 0.113449i
\(617\) 677.849 1.09862 0.549310 0.835619i \(-0.314891\pi\)
0.549310 + 0.835619i \(0.314891\pi\)
\(618\) 0 0
\(619\) 997.063i 1.61076i −0.592756 0.805382i \(-0.701960\pi\)
0.592756 0.805382i \(-0.298040\pi\)
\(620\) −44.4129 729.808i −0.0716338 1.17711i
\(621\) 0 0
\(622\) −150.808 + 4.58451i −0.242456 + 0.00737060i
\(623\) 635.668i 1.02033i
\(624\) 0 0
\(625\) −768.307 −1.22929
\(626\) −0.801884 26.3780i −0.00128096 0.0421374i
\(627\) 0 0
\(628\) −45.9038 + 2.79351i −0.0730953 + 0.00444826i
\(629\) 158.988 0.252764
\(630\) 0 0
\(631\) 1071.78i 1.69854i 0.527959 + 0.849270i \(0.322958\pi\)
−0.527959 + 0.849270i \(0.677042\pi\)
\(632\) −186.415 + 17.0429i −0.294960 + 0.0269665i
\(633\) 0 0
\(634\) −16.7989 552.599i −0.0264966 0.871608i
\(635\) 293.610i 0.462378i
\(636\) 0 0
\(637\) 453.682 0.712216
\(638\) 4.80081 0.145943i 0.00752478 0.000228751i
\(639\) 0 0
\(640\) −157.354 728.489i −0.245866 1.13826i
\(641\) 627.241 0.978536 0.489268 0.872134i \(-0.337264\pi\)
0.489268 + 0.872134i \(0.337264\pi\)
\(642\) 0 0
\(643\) 620.131i 0.964433i 0.876052 + 0.482217i \(0.160168\pi\)
−0.876052 + 0.482217i \(0.839832\pi\)
\(644\) −579.213 + 35.2484i −0.899399 + 0.0547335i
\(645\) 0 0
\(646\) 51.6444 1.56997i 0.0799449 0.00243030i
\(647\) 1270.23i 1.96327i 0.190778 + 0.981633i \(0.438899\pi\)
−0.190778 + 0.981633i \(0.561101\pi\)
\(648\) 0 0
\(649\) 54.5332 0.0840265
\(650\) 12.7285 + 418.705i 0.0195823 + 0.644162i
\(651\) 0 0
\(652\) 30.7516 + 505.320i 0.0471650 + 0.775031i
\(653\) −775.383 −1.18742 −0.593708 0.804681i \(-0.702337\pi\)
−0.593708 + 0.804681i \(0.702337\pi\)
\(654\) 0 0
\(655\) 727.554i 1.11077i
\(656\) 699.412 85.4427i 1.06618 0.130248i
\(657\) 0 0
\(658\) −10.7722 354.353i −0.0163712 0.538531i
\(659\) 516.735i 0.784119i −0.919940 0.392060i \(-0.871763\pi\)
0.919940 0.392060i \(-0.128237\pi\)
\(660\) 0 0
\(661\) −987.675 −1.49421 −0.747107 0.664704i \(-0.768558\pi\)
−0.747107 + 0.664704i \(0.768558\pi\)
\(662\) 1099.71 33.4309i 1.66119 0.0504998i
\(663\) 0 0
\(664\) 1092.37 99.8698i 1.64514 0.150406i
\(665\) 138.355 0.208052
\(666\) 0 0
\(667\) 39.7163i 0.0595446i
\(668\) −3.46051 56.8643i −0.00518041 0.0851261i
\(669\) 0 0
\(670\) −886.853 + 26.9601i −1.32366 + 0.0402389i
\(671\) 85.3109i 0.127140i
\(672\) 0 0
\(673\) −237.022 −0.352187 −0.176094 0.984373i \(-0.556346\pi\)
−0.176094 + 0.984373i \(0.556346\pi\)
\(674\) −10.8802 357.904i −0.0161427 0.531014i
\(675\) 0 0
\(676\) −1535.32 + 93.4329i −2.27118 + 0.138214i
\(677\) −894.692 −1.32155 −0.660777 0.750582i \(-0.729773\pi\)
−0.660777 + 0.750582i \(0.729773\pi\)
\(678\) 0 0
\(679\) 358.338i 0.527743i
\(680\) −25.1349 274.925i −0.0369631 0.404302i
\(681\) 0 0
\(682\) 3.06995 + 100.986i 0.00450139 + 0.148074i
\(683\) 1327.94i 1.94427i −0.234421 0.972135i \(-0.575320\pi\)
0.234421 0.972135i \(-0.424680\pi\)
\(684\) 0 0
\(685\) −798.572 −1.16580
\(686\) −744.122 + 22.6211i −1.08473 + 0.0329754i
\(687\) 0 0
\(688\) 54.0511 + 442.449i 0.0785627 + 0.643094i
\(689\) −1806.05 −2.62127
\(690\) 0 0
\(691\) 552.974i 0.800252i −0.916460 0.400126i \(-0.868966\pi\)
0.916460 0.400126i \(-0.131034\pi\)
\(692\) −869.658 + 52.9236i −1.25673 + 0.0764792i
\(693\) 0 0
\(694\) −323.364 + 9.83016i −0.465942 + 0.0141645i
\(695\) 522.218i 0.751393i
\(696\) 0 0
\(697\) 261.004 0.374467
\(698\) −28.7333 945.183i −0.0411652 1.35413i
\(699\) 0 0
\(700\) −11.7914 193.760i −0.0168448 0.276799i
\(701\) −815.608 −1.16349 −0.581746 0.813370i \(-0.697630\pi\)
−0.581746 + 0.813370i \(0.697630\pi\)
\(702\) 0 0
\(703\) 116.930i 0.166330i
\(704\) 18.6747 + 101.278i 0.0265266 + 0.143861i
\(705\) 0 0
\(706\) −19.3982 638.105i −0.0274762 0.903832i
\(707\) 9.88900i 0.0139873i
\(708\) 0 0
\(709\) 764.747 1.07863 0.539314 0.842105i \(-0.318684\pi\)
0.539314 + 0.842105i \(0.318684\pi\)
\(710\) 697.601 21.2069i 0.982537 0.0298688i
\(711\) 0 0
\(712\) 84.9324 + 928.990i 0.119287 + 1.30476i
\(713\) 835.441 1.17173
\(714\) 0 0
\(715\) 220.437i 0.308304i
\(716\) 43.7894 + 719.563i 0.0611584 + 1.00498i
\(717\) 0 0
\(718\) 1091.04 33.1672i 1.51955 0.0461938i
\(719\) 713.170i 0.991892i 0.868353 + 0.495946i \(0.165179\pi\)
−0.868353 + 0.495946i \(0.834821\pi\)
\(720\) 0 0
\(721\) 2.69662 0.00374011
\(722\) −1.15465 37.9825i −0.00159925 0.0526073i
\(723\) 0 0
\(724\) 379.553 23.0979i 0.524244 0.0319032i
\(725\) 13.2860 0.0183255
\(726\) 0 0
\(727\) 890.749i 1.22524i 0.790378 + 0.612619i \(0.209884\pi\)
−0.790378 + 0.612619i \(0.790116\pi\)
\(728\) 1021.78 93.4160i 1.40355 0.128319i
\(729\) 0 0
\(730\) −17.6282 579.880i −0.0241482 0.794356i
\(731\) 165.111i 0.225870i
\(732\) 0 0
\(733\) −221.785 −0.302572 −0.151286 0.988490i \(-0.548341\pi\)
−0.151286 + 0.988490i \(0.548341\pi\)
\(734\) −180.815 + 5.49671i −0.246342 + 0.00748871i
\(735\) 0 0
\(736\) 841.775 128.903i 1.14372 0.175140i
\(737\) 122.604 0.166355
\(738\) 0 0
\(739\) 635.372i 0.859772i 0.902883 + 0.429886i \(0.141446\pi\)
−0.902883 + 0.429886i \(0.858554\pi\)
\(740\) −623.621 + 37.9508i −0.842731 + 0.0512849i
\(741\) 0 0
\(742\) 836.541 25.4306i 1.12741 0.0342730i
\(743\) 795.274i 1.07036i 0.844740 + 0.535178i \(0.179755\pi\)
−0.844740 + 0.535178i \(0.820245\pi\)
\(744\) 0 0
\(745\) −110.159 −0.147865
\(746\) 28.5002 + 937.518i 0.0382041 + 1.25673i
\(747\) 0 0
\(748\) 2.31724 + 38.0777i 0.00309791 + 0.0509060i
\(749\) −63.9775 −0.0854172
\(750\) 0 0
\(751\) 84.7437i 0.112841i 0.998407 + 0.0564206i \(0.0179688\pi\)
−0.998407 + 0.0564206i \(0.982031\pi\)
\(752\) 63.0885 + 516.426i 0.0838943 + 0.686737i
\(753\) 0 0
\(754\) 2.13384 + 70.1929i 0.00283003 + 0.0930940i
\(755\) 1566.63i 2.07500i
\(756\) 0 0
\(757\) 1207.44 1.59503 0.797514 0.603301i \(-0.206148\pi\)
0.797514 + 0.603301i \(0.206148\pi\)
\(758\) −392.876 + 11.9433i −0.518306 + 0.0157563i
\(759\) 0 0
\(760\) −202.197 + 18.4857i −0.266048 + 0.0243233i
\(761\) −524.706 −0.689495 −0.344748 0.938695i \(-0.612035\pi\)
−0.344748 + 0.938695i \(0.612035\pi\)
\(762\) 0 0
\(763\) 157.990i 0.207064i
\(764\) −6.19068 101.727i −0.00810299 0.133151i
\(765\) 0 0
\(766\) 49.5861 1.50740i 0.0647338 0.00196789i
\(767\) 797.332i 1.03955i
\(768\) 0 0
\(769\) 531.656 0.691360 0.345680 0.938352i \(-0.387648\pi\)
0.345680 + 0.938352i \(0.387648\pi\)
\(770\) 3.10393 + 102.104i 0.00403107 + 0.132602i
\(771\) 0 0
\(772\) −1355.76 + 82.5054i −1.75616 + 0.106872i
\(773\) 249.261 0.322459 0.161229 0.986917i \(-0.448454\pi\)
0.161229 + 0.986917i \(0.448454\pi\)
\(774\) 0 0
\(775\) 279.474i 0.360611i
\(776\) 47.8780 + 523.689i 0.0616984 + 0.674857i
\(777\) 0 0
\(778\) 7.68525 + 252.807i 0.00987821 + 0.324944i
\(779\) 191.958i 0.246416i
\(780\) 0 0
\(781\) −96.4404 −0.123483
\(782\) 315.301 9.58506i 0.403198 0.0122571i
\(783\) 0 0
\(784\) 306.253 37.4130i 0.390629 0.0477206i
\(785\) 66.9432 0.0852780
\(786\) 0 0
\(787\) 226.270i 0.287509i 0.989613 + 0.143755i \(0.0459176\pi\)
−0.989613 + 0.143755i \(0.954082\pi\)
\(788\) 546.426 33.2531i 0.693434 0.0421994i
\(789\) 0 0
\(790\) 272.359 8.27963i 0.344758 0.0104805i