Properties

Label 684.3.g.b.343.8
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: \( x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384 \) Copy content Toggle raw display
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 343.8
Root \(0.645572 - 1.89294i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.645572 + 1.89294i) q^{2} +(-3.16647 - 2.44406i) q^{4} +2.38184 q^{5} -12.3764i q^{7} +(6.67066 - 4.41614i) q^{8} +O(q^{10})\) \(q+(-0.645572 + 1.89294i) q^{2} +(-3.16647 - 2.44406i) q^{4} +2.38184 q^{5} -12.3764i q^{7} +(6.67066 - 4.41614i) q^{8} +(-1.53765 + 4.50868i) q^{10} -9.15034i q^{11} +0.940214 q^{13} +(23.4279 + 7.98989i) q^{14} +(4.05310 + 15.4781i) q^{16} -27.1792 q^{17} +4.35890i q^{19} +(-7.54202 - 5.82136i) q^{20} +(17.3211 + 5.90721i) q^{22} +13.8004i q^{23} -19.3269 q^{25} +(-0.606976 + 1.77977i) q^{26} +(-30.2488 + 39.1897i) q^{28} -49.8488 q^{29} +24.6752i q^{31} +(-31.9158 - 2.31995i) q^{32} +(17.5461 - 51.4487i) q^{34} -29.4787i q^{35} -27.3757 q^{37} +(-8.25115 - 2.81398i) q^{38} +(15.8884 - 10.5185i) q^{40} +38.4024 q^{41} +41.2108i q^{43} +(-22.3640 + 28.9743i) q^{44} +(-26.1234 - 8.90917i) q^{46} +45.1842i q^{47} -104.176 q^{49} +(12.4769 - 36.5846i) q^{50} +(-2.97716 - 2.29794i) q^{52} +19.9964 q^{53} -21.7946i q^{55} +(-54.6561 - 82.5591i) q^{56} +(32.1810 - 94.3610i) q^{58} -34.7054i q^{59} +33.2008 q^{61} +(-46.7088 - 15.9296i) q^{62} +(24.9955 - 58.9171i) q^{64} +2.23944 q^{65} -3.48192i q^{67} +(86.0622 + 66.4277i) q^{68} +(55.8015 + 19.0306i) q^{70} -88.8887i q^{71} -19.8573 q^{73} +(17.6730 - 51.8206i) q^{74} +(10.6534 - 13.8023i) q^{76} -113.249 q^{77} +51.7431i q^{79} +(9.65383 + 36.8664i) q^{80} +(-24.7915 + 72.6936i) q^{82} -6.62943i q^{83} -64.7365 q^{85} +(-78.0097 - 26.6046i) q^{86} +(-40.4091 - 61.0388i) q^{88} -31.5105 q^{89} -11.6365i q^{91} +(33.7291 - 43.6987i) q^{92} +(-85.5312 - 29.1697i) q^{94} +10.3822i q^{95} +159.282 q^{97} +(67.2534 - 197.200i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.645572 + 1.89294i −0.322786 + 0.946472i
\(3\) 0 0
\(4\) −3.16647 2.44406i −0.791618 0.611016i
\(5\) 2.38184 0.476367 0.238184 0.971220i \(-0.423448\pi\)
0.238184 + 0.971220i \(0.423448\pi\)
\(6\) 0 0
\(7\) 12.3764i 1.76806i −0.467427 0.884032i \(-0.654819\pi\)
0.467427 0.884032i \(-0.345181\pi\)
\(8\) 6.67066 4.41614i 0.833833 0.552017i
\(9\) 0 0
\(10\) −1.53765 + 4.50868i −0.153765 + 0.450868i
\(11\) 9.15034i 0.831849i −0.909399 0.415925i \(-0.863458\pi\)
0.909399 0.415925i \(-0.136542\pi\)
\(12\) 0 0
\(13\) 0.940214 0.0723242 0.0361621 0.999346i \(-0.488487\pi\)
0.0361621 + 0.999346i \(0.488487\pi\)
\(14\) 23.4279 + 7.98989i 1.67342 + 0.570706i
\(15\) 0 0
\(16\) 4.05310 + 15.4781i 0.253319 + 0.967383i
\(17\) −27.1792 −1.59878 −0.799388 0.600814i \(-0.794843\pi\)
−0.799388 + 0.600814i \(0.794843\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) −7.54202 5.82136i −0.377101 0.291068i
\(21\) 0 0
\(22\) 17.3211 + 5.90721i 0.787322 + 0.268509i
\(23\) 13.8004i 0.600018i 0.953936 + 0.300009i \(0.0969898\pi\)
−0.953936 + 0.300009i \(0.903010\pi\)
\(24\) 0 0
\(25\) −19.3269 −0.773074
\(26\) −0.606976 + 1.77977i −0.0233452 + 0.0684528i
\(27\) 0 0
\(28\) −30.2488 + 39.1897i −1.08032 + 1.39963i
\(29\) −49.8488 −1.71892 −0.859462 0.511200i \(-0.829201\pi\)
−0.859462 + 0.511200i \(0.829201\pi\)
\(30\) 0 0
\(31\) 24.6752i 0.795974i 0.917391 + 0.397987i \(0.130291\pi\)
−0.917391 + 0.397987i \(0.869709\pi\)
\(32\) −31.9158 2.31995i −0.997369 0.0724986i
\(33\) 0 0
\(34\) 17.5461 51.4487i 0.516063 1.51320i
\(35\) 29.4787i 0.842248i
\(36\) 0 0
\(37\) −27.3757 −0.739883 −0.369942 0.929055i \(-0.620622\pi\)
−0.369942 + 0.929055i \(0.620622\pi\)
\(38\) −8.25115 2.81398i −0.217136 0.0740522i
\(39\) 0 0
\(40\) 15.8884 10.5185i 0.397211 0.262963i
\(41\) 38.4024 0.936644 0.468322 0.883558i \(-0.344859\pi\)
0.468322 + 0.883558i \(0.344859\pi\)
\(42\) 0 0
\(43\) 41.2108i 0.958391i 0.877708 + 0.479195i \(0.159071\pi\)
−0.877708 + 0.479195i \(0.840929\pi\)
\(44\) −22.3640 + 28.9743i −0.508273 + 0.658507i
\(45\) 0 0
\(46\) −26.1234 8.90917i −0.567901 0.193678i
\(47\) 45.1842i 0.961367i 0.876894 + 0.480683i \(0.159611\pi\)
−0.876894 + 0.480683i \(0.840389\pi\)
\(48\) 0 0
\(49\) −104.176 −2.12605
\(50\) 12.4769 36.5846i 0.249538 0.731693i
\(51\) 0 0
\(52\) −2.97716 2.29794i −0.0572531 0.0441912i
\(53\) 19.9964 0.377291 0.188646 0.982045i \(-0.439590\pi\)
0.188646 + 0.982045i \(0.439590\pi\)
\(54\) 0 0
\(55\) 21.7946i 0.396266i
\(56\) −54.6561 82.5591i −0.976001 1.47427i
\(57\) 0 0
\(58\) 32.1810 94.3610i 0.554845 1.62691i
\(59\) 34.7054i 0.588228i −0.955770 0.294114i \(-0.904976\pi\)
0.955770 0.294114i \(-0.0950245\pi\)
\(60\) 0 0
\(61\) 33.2008 0.544276 0.272138 0.962258i \(-0.412269\pi\)
0.272138 + 0.962258i \(0.412269\pi\)
\(62\) −46.7088 15.9296i −0.753367 0.256929i
\(63\) 0 0
\(64\) 24.9955 58.9171i 0.390555 0.920580i
\(65\) 2.23944 0.0344529
\(66\) 0 0
\(67\) 3.48192i 0.0519690i −0.999662 0.0259845i \(-0.991728\pi\)
0.999662 0.0259845i \(-0.00827205\pi\)
\(68\) 86.0622 + 66.4277i 1.26562 + 0.976878i
\(69\) 0 0
\(70\) 55.8015 + 19.0306i 0.797164 + 0.271866i
\(71\) 88.8887i 1.25195i −0.779842 0.625977i \(-0.784700\pi\)
0.779842 0.625977i \(-0.215300\pi\)
\(72\) 0 0
\(73\) −19.8573 −0.272018 −0.136009 0.990708i \(-0.543428\pi\)
−0.136009 + 0.990708i \(0.543428\pi\)
\(74\) 17.6730 51.8206i 0.238824 0.700279i
\(75\) 0 0
\(76\) 10.6534 13.8023i 0.140177 0.181610i
\(77\) −113.249 −1.47076
\(78\) 0 0
\(79\) 51.7431i 0.654976i 0.944855 + 0.327488i \(0.106202\pi\)
−0.944855 + 0.327488i \(0.893798\pi\)
\(80\) 9.65383 + 36.8664i 0.120673 + 0.460830i
\(81\) 0 0
\(82\) −24.7915 + 72.6936i −0.302336 + 0.886507i
\(83\) 6.62943i 0.0798727i −0.999202 0.0399363i \(-0.987284\pi\)
0.999202 0.0399363i \(-0.0127155\pi\)
\(84\) 0 0
\(85\) −64.7365 −0.761605
\(86\) −78.0097 26.6046i −0.907090 0.309355i
\(87\) 0 0
\(88\) −40.4091 61.0388i −0.459195 0.693623i
\(89\) −31.5105 −0.354051 −0.177025 0.984206i \(-0.556647\pi\)
−0.177025 + 0.984206i \(0.556647\pi\)
\(90\) 0 0
\(91\) 11.6365i 0.127874i
\(92\) 33.7291 43.6987i 0.366621 0.474986i
\(93\) 0 0
\(94\) −85.5312 29.1697i −0.909907 0.310316i
\(95\) 10.3822i 0.109286i
\(96\) 0 0
\(97\) 159.282 1.64208 0.821039 0.570873i \(-0.193395\pi\)
0.821039 + 0.570873i \(0.193395\pi\)
\(98\) 67.2534 197.200i 0.686259 2.01225i
\(99\) 0 0
\(100\) 61.1980 + 47.2361i 0.611980 + 0.472361i
\(101\) −35.1573 −0.348092 −0.174046 0.984738i \(-0.555684\pi\)
−0.174046 + 0.984738i \(0.555684\pi\)
\(102\) 0 0
\(103\) 117.214i 1.13800i −0.822339 0.568998i \(-0.807331\pi\)
0.822339 0.568998i \(-0.192669\pi\)
\(104\) 6.27185 4.15211i 0.0603063 0.0399242i
\(105\) 0 0
\(106\) −12.9092 + 37.8522i −0.121784 + 0.357096i
\(107\) 191.832i 1.79282i −0.443228 0.896409i \(-0.646167\pi\)
0.443228 0.896409i \(-0.353833\pi\)
\(108\) 0 0
\(109\) −183.807 −1.68630 −0.843152 0.537675i \(-0.819303\pi\)
−0.843152 + 0.537675i \(0.819303\pi\)
\(110\) 41.2560 + 14.0700i 0.375055 + 0.127909i
\(111\) 0 0
\(112\) 191.564 50.1630i 1.71039 0.447884i
\(113\) −72.9718 −0.645768 −0.322884 0.946439i \(-0.604652\pi\)
−0.322884 + 0.946439i \(0.604652\pi\)
\(114\) 0 0
\(115\) 32.8704i 0.285829i
\(116\) 157.845 + 121.834i 1.36073 + 1.05029i
\(117\) 0 0
\(118\) 65.6954 + 22.4049i 0.556741 + 0.189872i
\(119\) 336.382i 2.82674i
\(120\) 0 0
\(121\) 37.2713 0.308027
\(122\) −21.4335 + 62.8473i −0.175685 + 0.515142i
\(123\) 0 0
\(124\) 60.3078 78.1334i 0.486353 0.630108i
\(125\) −105.579 −0.844635
\(126\) 0 0
\(127\) 11.4215i 0.0899331i −0.998988 0.0449665i \(-0.985682\pi\)
0.998988 0.0449665i \(-0.0143181\pi\)
\(128\) 95.3904 + 85.3503i 0.745237 + 0.666799i
\(129\) 0 0
\(130\) −1.44572 + 4.23913i −0.0111209 + 0.0326087i
\(131\) 36.9512i 0.282070i 0.990005 + 0.141035i \(0.0450430\pi\)
−0.990005 + 0.141035i \(0.954957\pi\)
\(132\) 0 0
\(133\) 53.9477 0.405622
\(134\) 6.59108 + 2.24783i 0.0491872 + 0.0167749i
\(135\) 0 0
\(136\) −181.303 + 120.027i −1.33311 + 0.882552i
\(137\) 162.786 1.18822 0.594109 0.804385i \(-0.297505\pi\)
0.594109 + 0.804385i \(0.297505\pi\)
\(138\) 0 0
\(139\) 229.233i 1.64916i −0.565744 0.824581i \(-0.691411\pi\)
0.565744 0.824581i \(-0.308589\pi\)
\(140\) −72.0478 + 93.3434i −0.514627 + 0.666739i
\(141\) 0 0
\(142\) 168.261 + 57.3841i 1.18494 + 0.404113i
\(143\) 8.60328i 0.0601628i
\(144\) 0 0
\(145\) −118.732 −0.818839
\(146\) 12.8193 37.5887i 0.0878035 0.257457i
\(147\) 0 0
\(148\) 86.6844 + 66.9079i 0.585705 + 0.452081i
\(149\) 110.328 0.740459 0.370229 0.928940i \(-0.379279\pi\)
0.370229 + 0.928940i \(0.379279\pi\)
\(150\) 0 0
\(151\) 104.737i 0.693621i −0.937935 0.346810i \(-0.887265\pi\)
0.937935 0.346810i \(-0.112735\pi\)
\(152\) 19.2495 + 29.0767i 0.126641 + 0.191294i
\(153\) 0 0
\(154\) 73.1102 214.373i 0.474742 1.39204i
\(155\) 58.7723i 0.379176i
\(156\) 0 0
\(157\) −147.695 −0.940732 −0.470366 0.882471i \(-0.655878\pi\)
−0.470366 + 0.882471i \(0.655878\pi\)
\(158\) −97.9468 33.4039i −0.619917 0.211417i
\(159\) 0 0
\(160\) −76.0182 5.52575i −0.475114 0.0345360i
\(161\) 170.800 1.06087
\(162\) 0 0
\(163\) 183.104i 1.12334i 0.827363 + 0.561668i \(0.189840\pi\)
−0.827363 + 0.561668i \(0.810160\pi\)
\(164\) −121.600 93.8580i −0.741465 0.572305i
\(165\) 0 0
\(166\) 12.5491 + 4.27978i 0.0755973 + 0.0257818i
\(167\) 214.501i 1.28444i −0.766522 0.642218i \(-0.778014\pi\)
0.766522 0.642218i \(-0.221986\pi\)
\(168\) 0 0
\(169\) −168.116 −0.994769
\(170\) 41.7921 122.542i 0.245836 0.720838i
\(171\) 0 0
\(172\) 100.722 130.493i 0.585592 0.758680i
\(173\) −27.1849 −0.157138 −0.0785692 0.996909i \(-0.525035\pi\)
−0.0785692 + 0.996909i \(0.525035\pi\)
\(174\) 0 0
\(175\) 239.198i 1.36684i
\(176\) 141.630 37.0873i 0.804717 0.210723i
\(177\) 0 0
\(178\) 20.3423 59.6476i 0.114283 0.335099i
\(179\) 185.284i 1.03511i −0.855651 0.517553i \(-0.826843\pi\)
0.855651 0.517553i \(-0.173157\pi\)
\(180\) 0 0
\(181\) 17.0150 0.0940053 0.0470026 0.998895i \(-0.485033\pi\)
0.0470026 + 0.998895i \(0.485033\pi\)
\(182\) 22.0273 + 7.51221i 0.121029 + 0.0412759i
\(183\) 0 0
\(184\) 60.9445 + 92.0580i 0.331220 + 0.500315i
\(185\) −65.2044 −0.352456
\(186\) 0 0
\(187\) 248.699i 1.32994i
\(188\) 110.433 143.075i 0.587411 0.761036i
\(189\) 0 0
\(190\) −19.6529 6.70245i −0.103436 0.0352761i
\(191\) 2.41797i 0.0126595i 0.999980 + 0.00632976i \(0.00201484\pi\)
−0.999980 + 0.00632976i \(0.997985\pi\)
\(192\) 0 0
\(193\) −150.712 −0.780892 −0.390446 0.920626i \(-0.627679\pi\)
−0.390446 + 0.920626i \(0.627679\pi\)
\(194\) −102.828 + 301.511i −0.530040 + 1.55418i
\(195\) 0 0
\(196\) 329.872 + 254.614i 1.68302 + 1.29905i
\(197\) −268.203 −1.36144 −0.680718 0.732545i \(-0.738332\pi\)
−0.680718 + 0.732545i \(0.738332\pi\)
\(198\) 0 0
\(199\) 308.615i 1.55083i −0.631452 0.775415i \(-0.717541\pi\)
0.631452 0.775415i \(-0.282459\pi\)
\(200\) −128.923 + 85.3500i −0.644615 + 0.426750i
\(201\) 0 0
\(202\) 22.6966 66.5507i 0.112359 0.329459i
\(203\) 616.951i 3.03917i
\(204\) 0 0
\(205\) 91.4683 0.446187
\(206\) 221.879 + 75.6698i 1.07708 + 0.367329i
\(207\) 0 0
\(208\) 3.81078 + 14.5528i 0.0183211 + 0.0699652i
\(209\) 39.8854 0.190839
\(210\) 0 0
\(211\) 334.011i 1.58299i 0.611176 + 0.791495i \(0.290697\pi\)
−0.611176 + 0.791495i \(0.709303\pi\)
\(212\) −63.3182 48.8726i −0.298671 0.230531i
\(213\) 0 0
\(214\) 363.126 + 123.841i 1.69685 + 0.578697i
\(215\) 98.1574i 0.456546i
\(216\) 0 0
\(217\) 305.391 1.40733
\(218\) 118.661 347.937i 0.544316 1.59604i
\(219\) 0 0
\(220\) −53.2675 + 69.0121i −0.242125 + 0.313691i
\(221\) −25.5543 −0.115630
\(222\) 0 0
\(223\) 290.142i 1.30108i 0.759470 + 0.650542i \(0.225458\pi\)
−0.759470 + 0.650542i \(0.774542\pi\)
\(224\) −28.7128 + 395.004i −0.128182 + 1.76341i
\(225\) 0 0
\(226\) 47.1086 138.132i 0.208445 0.611202i
\(227\) 76.2561i 0.335930i −0.985793 0.167965i \(-0.946280\pi\)
0.985793 0.167965i \(-0.0537195\pi\)
\(228\) 0 0
\(229\) −212.780 −0.929169 −0.464585 0.885529i \(-0.653796\pi\)
−0.464585 + 0.885529i \(0.653796\pi\)
\(230\) −62.2218 21.2202i −0.270529 0.0922617i
\(231\) 0 0
\(232\) −332.525 + 220.139i −1.43330 + 0.948875i
\(233\) 108.504 0.465680 0.232840 0.972515i \(-0.425198\pi\)
0.232840 + 0.972515i \(0.425198\pi\)
\(234\) 0 0
\(235\) 107.622i 0.457964i
\(236\) −84.8223 + 109.894i −0.359416 + 0.465652i
\(237\) 0 0
\(238\) −636.752 217.159i −2.67543 0.912432i
\(239\) 14.5126i 0.0607222i −0.999539 0.0303611i \(-0.990334\pi\)
0.999539 0.0303611i \(-0.00966573\pi\)
\(240\) 0 0
\(241\) −278.238 −1.15451 −0.577257 0.816563i \(-0.695877\pi\)
−0.577257 + 0.816563i \(0.695877\pi\)
\(242\) −24.0613 + 70.5524i −0.0994268 + 0.291539i
\(243\) 0 0
\(244\) −105.130 81.1449i −0.430859 0.332561i
\(245\) −248.131 −1.01278
\(246\) 0 0
\(247\) 4.09830i 0.0165923i
\(248\) 108.969 + 164.600i 0.439391 + 0.663710i
\(249\) 0 0
\(250\) 68.1591 199.856i 0.272636 0.799423i
\(251\) 344.252i 1.37152i 0.727828 + 0.685760i \(0.240530\pi\)
−0.727828 + 0.685760i \(0.759470\pi\)
\(252\) 0 0
\(253\) 126.279 0.499125
\(254\) 21.6203 + 7.37340i 0.0851191 + 0.0290291i
\(255\) 0 0
\(256\) −223.145 + 125.469i −0.871659 + 0.490113i
\(257\) −50.0048 −0.194571 −0.0972856 0.995257i \(-0.531016\pi\)
−0.0972856 + 0.995257i \(0.531016\pi\)
\(258\) 0 0
\(259\) 338.814i 1.30816i
\(260\) −7.09112 5.47333i −0.0272735 0.0210513i
\(261\) 0 0
\(262\) −69.9465 23.8546i −0.266971 0.0910483i
\(263\) 155.273i 0.590391i 0.955437 + 0.295195i \(0.0953848\pi\)
−0.955437 + 0.295195i \(0.904615\pi\)
\(264\) 0 0
\(265\) 47.6283 0.179729
\(266\) −34.8271 + 102.120i −0.130929 + 0.383909i
\(267\) 0 0
\(268\) −8.51004 + 11.0254i −0.0317539 + 0.0411396i
\(269\) 457.281 1.69993 0.849964 0.526840i \(-0.176623\pi\)
0.849964 + 0.526840i \(0.176623\pi\)
\(270\) 0 0
\(271\) 349.279i 1.28885i −0.764666 0.644427i \(-0.777096\pi\)
0.764666 0.644427i \(-0.222904\pi\)
\(272\) −110.160 420.683i −0.405000 1.54663i
\(273\) 0 0
\(274\) −105.090 + 308.144i −0.383540 + 1.12461i
\(275\) 176.847i 0.643081i
\(276\) 0 0
\(277\) −108.548 −0.391870 −0.195935 0.980617i \(-0.562774\pi\)
−0.195935 + 0.980617i \(0.562774\pi\)
\(278\) 433.926 + 147.987i 1.56089 + 0.532326i
\(279\) 0 0
\(280\) −130.182 196.642i −0.464935 0.702294i
\(281\) −190.452 −0.677767 −0.338883 0.940828i \(-0.610049\pi\)
−0.338883 + 0.940828i \(0.610049\pi\)
\(282\) 0 0
\(283\) 289.950i 1.02456i −0.858819 0.512279i \(-0.828802\pi\)
0.858819 0.512279i \(-0.171198\pi\)
\(284\) −217.250 + 281.464i −0.764964 + 0.991069i
\(285\) 0 0
\(286\) 16.2855 + 5.55404i 0.0569424 + 0.0194197i
\(287\) 475.285i 1.65605i
\(288\) 0 0
\(289\) 449.709 1.55609
\(290\) 76.6499 224.752i 0.264310 0.775009i
\(291\) 0 0
\(292\) 62.8776 + 48.5325i 0.215334 + 0.166207i
\(293\) 177.881 0.607102 0.303551 0.952815i \(-0.401828\pi\)
0.303551 + 0.952815i \(0.401828\pi\)
\(294\) 0 0
\(295\) 82.6627i 0.280212i
\(296\) −182.614 + 120.895i −0.616939 + 0.408428i
\(297\) 0 0
\(298\) −71.2249 + 208.845i −0.239010 + 0.700823i
\(299\) 12.9754i 0.0433958i
\(300\) 0 0
\(301\) 510.043 1.69450
\(302\) 198.261 + 67.6151i 0.656492 + 0.223891i
\(303\) 0 0
\(304\) −67.4676 + 17.6671i −0.221933 + 0.0581153i
\(305\) 79.0790 0.259275
\(306\) 0 0
\(307\) 554.295i 1.80552i −0.430143 0.902761i \(-0.641537\pi\)
0.430143 0.902761i \(-0.358463\pi\)
\(308\) 358.599 + 276.787i 1.16428 + 0.898659i
\(309\) 0 0
\(310\) −111.253 37.9418i −0.358880 0.122393i
\(311\) 67.7563i 0.217866i −0.994049 0.108933i \(-0.965257\pi\)
0.994049 0.108933i \(-0.0347434\pi\)
\(312\) 0 0
\(313\) 447.248 1.42891 0.714454 0.699683i \(-0.246675\pi\)
0.714454 + 0.699683i \(0.246675\pi\)
\(314\) 95.3477 279.578i 0.303655 0.890376i
\(315\) 0 0
\(316\) 126.463 163.843i 0.400201 0.518491i
\(317\) −67.2154 −0.212036 −0.106018 0.994364i \(-0.533810\pi\)
−0.106018 + 0.994364i \(0.533810\pi\)
\(318\) 0 0
\(319\) 456.133i 1.42989i
\(320\) 59.5352 140.331i 0.186048 0.438534i
\(321\) 0 0
\(322\) −110.264 + 323.315i −0.342434 + 1.00408i
\(323\) 118.471i 0.366785i
\(324\) 0 0
\(325\) −18.1714 −0.0559119
\(326\) −346.605 118.207i −1.06321 0.362597i
\(327\) 0 0
\(328\) 256.170 169.590i 0.781005 0.517043i
\(329\) 559.220 1.69976
\(330\) 0 0
\(331\) 178.449i 0.539122i −0.962983 0.269561i \(-0.913121\pi\)
0.962983 0.269561i \(-0.0868785\pi\)
\(332\) −16.2028 + 20.9919i −0.0488035 + 0.0632287i
\(333\) 0 0
\(334\) 406.038 + 138.476i 1.21568 + 0.414598i
\(335\) 8.29337i 0.0247563i
\(336\) 0 0
\(337\) −280.146 −0.831292 −0.415646 0.909526i \(-0.636445\pi\)
−0.415646 + 0.909526i \(0.636445\pi\)
\(338\) 108.531 318.234i 0.321098 0.941521i
\(339\) 0 0
\(340\) 204.986 + 158.220i 0.602901 + 0.465353i
\(341\) 225.787 0.662131
\(342\) 0 0
\(343\) 682.888i 1.99093i
\(344\) 181.992 + 274.903i 0.529048 + 0.799138i
\(345\) 0 0
\(346\) 17.5498 51.4596i 0.0507221 0.148727i
\(347\) 89.6003i 0.258214i 0.991631 + 0.129107i \(0.0412111\pi\)
−0.991631 + 0.129107i \(0.958789\pi\)
\(348\) 0 0
\(349\) 5.38420 0.0154275 0.00771376 0.999970i \(-0.497545\pi\)
0.00771376 + 0.999970i \(0.497545\pi\)
\(350\) −452.788 154.419i −1.29368 0.441198i
\(351\) 0 0
\(352\) −21.2284 + 292.040i −0.0603079 + 0.829660i
\(353\) −357.844 −1.01372 −0.506861 0.862028i \(-0.669194\pi\)
−0.506861 + 0.862028i \(0.669194\pi\)
\(354\) 0 0
\(355\) 211.718i 0.596390i
\(356\) 99.7772 + 77.0137i 0.280273 + 0.216331i
\(357\) 0 0
\(358\) 350.732 + 119.614i 0.979699 + 0.334118i
\(359\) 415.792i 1.15820i −0.815258 0.579098i \(-0.803405\pi\)
0.815258 0.579098i \(-0.196595\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) −10.9844 + 32.2084i −0.0303436 + 0.0889734i
\(363\) 0 0
\(364\) −28.4404 + 36.8467i −0.0781329 + 0.101227i
\(365\) −47.2968 −0.129580
\(366\) 0 0
\(367\) 262.695i 0.715789i −0.933762 0.357894i \(-0.883495\pi\)
0.933762 0.357894i \(-0.116505\pi\)
\(368\) −213.605 + 55.9345i −0.580448 + 0.151996i
\(369\) 0 0
\(370\) 42.0942 123.428i 0.113768 0.333590i
\(371\) 247.485i 0.667075i
\(372\) 0 0
\(373\) 158.344 0.424516 0.212258 0.977214i \(-0.431918\pi\)
0.212258 + 0.977214i \(0.431918\pi\)
\(374\) −470.773 160.553i −1.25875 0.429287i
\(375\) 0 0
\(376\) 199.540 + 301.409i 0.530691 + 0.801619i
\(377\) −46.8685 −0.124320
\(378\) 0 0
\(379\) 539.136i 1.42252i −0.702928 0.711261i \(-0.748124\pi\)
0.702928 0.711261i \(-0.251876\pi\)
\(380\) 25.3747 32.8749i 0.0667756 0.0865129i
\(381\) 0 0
\(382\) −4.57708 1.56097i −0.0119819 0.00408631i
\(383\) 422.810i 1.10394i −0.833863 0.551971i \(-0.813876\pi\)
0.833863 0.551971i \(-0.186124\pi\)
\(384\) 0 0
\(385\) −269.740 −0.700623
\(386\) 97.2956 285.290i 0.252061 0.739092i
\(387\) 0 0
\(388\) −504.361 389.294i −1.29990 1.00334i
\(389\) 487.091 1.25216 0.626081 0.779758i \(-0.284658\pi\)
0.626081 + 0.779758i \(0.284658\pi\)
\(390\) 0 0
\(391\) 375.085i 0.959296i
\(392\) −694.926 + 460.057i −1.77277 + 1.17362i
\(393\) 0 0
\(394\) 173.144 507.693i 0.439453 1.28856i
\(395\) 123.244i 0.312009i
\(396\) 0 0
\(397\) −646.684 −1.62893 −0.814464 0.580215i \(-0.802969\pi\)
−0.814464 + 0.580215i \(0.802969\pi\)
\(398\) 584.191 + 199.233i 1.46782 + 0.500586i
\(399\) 0 0
\(400\) −78.3337 299.143i −0.195834 0.747859i
\(401\) 14.0555 0.0350512 0.0175256 0.999846i \(-0.494421\pi\)
0.0175256 + 0.999846i \(0.494421\pi\)
\(402\) 0 0
\(403\) 23.2000i 0.0575682i
\(404\) 111.325 + 85.9266i 0.275556 + 0.212690i
\(405\) 0 0
\(406\) −1167.85 398.286i −2.87649 0.981001i
\(407\) 250.497i 0.615471i
\(408\) 0 0
\(409\) 143.668 0.351266 0.175633 0.984456i \(-0.443803\pi\)
0.175633 + 0.984456i \(0.443803\pi\)
\(410\) −59.0494 + 173.144i −0.144023 + 0.422303i
\(411\) 0 0
\(412\) −286.477 + 371.153i −0.695333 + 0.900858i
\(413\) −429.530 −1.04002
\(414\) 0 0
\(415\) 15.7902i 0.0380488i
\(416\) −30.0077 2.18125i −0.0721338 0.00524340i
\(417\) 0 0
\(418\) −25.7489 + 75.5008i −0.0616003 + 0.180624i
\(419\) 572.449i 1.36623i −0.730312 0.683114i \(-0.760625\pi\)
0.730312 0.683114i \(-0.239375\pi\)
\(420\) 0 0
\(421\) 718.562 1.70680 0.853399 0.521258i \(-0.174537\pi\)
0.853399 + 0.521258i \(0.174537\pi\)
\(422\) −632.264 215.628i −1.49825 0.510967i
\(423\) 0 0
\(424\) 133.390 88.3070i 0.314598 0.208271i
\(425\) 525.289 1.23597
\(426\) 0 0
\(427\) 410.908i 0.962314i
\(428\) −468.849 + 607.429i −1.09544 + 1.41923i
\(429\) 0 0
\(430\) −185.807 63.3677i −0.432108 0.147367i
\(431\) 252.198i 0.585147i −0.956243 0.292573i \(-0.905488\pi\)
0.956243 0.292573i \(-0.0945116\pi\)
\(432\) 0 0
\(433\) 239.008 0.551982 0.275991 0.961160i \(-0.410994\pi\)
0.275991 + 0.961160i \(0.410994\pi\)
\(434\) −197.152 + 578.089i −0.454268 + 1.33200i
\(435\) 0 0
\(436\) 582.021 + 449.237i 1.33491 + 1.03036i
\(437\) −60.1547 −0.137654
\(438\) 0 0
\(439\) 17.2750i 0.0393508i −0.999806 0.0196754i \(-0.993737\pi\)
0.999806 0.0196754i \(-0.00626327\pi\)
\(440\) −96.2480 145.385i −0.218745 0.330420i
\(441\) 0 0
\(442\) 16.4971 48.3728i 0.0373238 0.109441i
\(443\) 161.249i 0.363993i 0.983299 + 0.181997i \(0.0582560\pi\)
−0.983299 + 0.181997i \(0.941744\pi\)
\(444\) 0 0
\(445\) −75.0529 −0.168658
\(446\) −549.222 187.307i −1.23144 0.419972i
\(447\) 0 0
\(448\) −729.184 309.355i −1.62764 0.690525i
\(449\) −561.952 −1.25156 −0.625782 0.779998i \(-0.715220\pi\)
−0.625782 + 0.779998i \(0.715220\pi\)
\(450\) 0 0
\(451\) 351.395i 0.779147i
\(452\) 231.063 + 178.348i 0.511202 + 0.394575i
\(453\) 0 0
\(454\) 144.349 + 49.2288i 0.317948 + 0.108434i
\(455\) 27.7163i 0.0609149i
\(456\) 0 0
\(457\) −107.375 −0.234957 −0.117479 0.993075i \(-0.537481\pi\)
−0.117479 + 0.993075i \(0.537481\pi\)
\(458\) 137.365 402.780i 0.299923 0.879433i
\(459\) 0 0
\(460\) 80.3373 104.083i 0.174646 0.226268i
\(461\) −666.303 −1.44534 −0.722672 0.691191i \(-0.757086\pi\)
−0.722672 + 0.691191i \(0.757086\pi\)
\(462\) 0 0
\(463\) 272.358i 0.588246i 0.955768 + 0.294123i \(0.0950276\pi\)
−0.955768 + 0.294123i \(0.904972\pi\)
\(464\) −202.042 771.566i −0.435436 1.66286i
\(465\) 0 0
\(466\) −70.0469 + 205.391i −0.150315 + 0.440753i
\(467\) 703.386i 1.50618i 0.657917 + 0.753090i \(0.271438\pi\)
−0.657917 + 0.753090i \(0.728562\pi\)
\(468\) 0 0
\(469\) −43.0938 −0.0918844
\(470\) −203.721 69.4775i −0.433450 0.147824i
\(471\) 0 0
\(472\) −153.264 231.508i −0.324712 0.490484i
\(473\) 377.093 0.797237
\(474\) 0 0
\(475\) 84.2438i 0.177355i
\(476\) 822.139 1065.14i 1.72718 2.23770i
\(477\) 0 0
\(478\) 27.4716 + 9.36894i 0.0574719 + 0.0196003i
\(479\) 451.971i 0.943572i −0.881713 0.471786i \(-0.843609\pi\)
0.881713 0.471786i \(-0.156391\pi\)
\(480\) 0 0
\(481\) −25.7390 −0.0535114
\(482\) 179.623 526.689i 0.372661 1.09272i
\(483\) 0 0
\(484\) −118.018 91.0934i −0.243840 0.188209i
\(485\) 379.383 0.782232
\(486\) 0 0
\(487\) 293.894i 0.603478i −0.953391 0.301739i \(-0.902433\pi\)
0.953391 0.301739i \(-0.0975671\pi\)
\(488\) 221.472 146.619i 0.453835 0.300449i
\(489\) 0 0
\(490\) 160.187 469.699i 0.326912 0.958568i
\(491\) 91.3499i 0.186049i −0.995664 0.0930243i \(-0.970347\pi\)
0.995664 0.0930243i \(-0.0296534\pi\)
\(492\) 0 0
\(493\) 1354.85 2.74818
\(494\) −7.75785 2.64575i −0.0157041 0.00535576i
\(495\) 0 0
\(496\) −381.926 + 100.011i −0.770012 + 0.201635i
\(497\) −1100.13 −2.21353
\(498\) 0 0
\(499\) 758.796i 1.52063i 0.649553 + 0.760316i \(0.274956\pi\)
−0.649553 + 0.760316i \(0.725044\pi\)
\(500\) 334.314 + 258.043i 0.668628 + 0.516085i
\(501\) 0 0
\(502\) −651.649 222.239i −1.29811 0.442708i
\(503\) 55.4556i 0.110250i −0.998479 0.0551248i \(-0.982444\pi\)
0.998479 0.0551248i \(-0.0175557\pi\)
\(504\) 0 0
\(505\) −83.7389 −0.165820
\(506\) −81.5220 + 239.038i −0.161111 + 0.472408i
\(507\) 0 0
\(508\) −27.9149 + 36.1659i −0.0549505 + 0.0711927i
\(509\) 479.828 0.942688 0.471344 0.881949i \(-0.343769\pi\)
0.471344 + 0.881949i \(0.343769\pi\)
\(510\) 0 0
\(511\) 245.763i 0.480945i
\(512\) −93.4494 503.400i −0.182518 0.983202i
\(513\) 0 0
\(514\) 32.2817 94.6563i 0.0628049 0.184156i
\(515\) 279.184i 0.542104i
\(516\) 0 0
\(517\) 413.451 0.799712
\(518\) −641.355 218.729i −1.23814 0.422256i
\(519\) 0 0
\(520\) 14.9385 9.88966i 0.0287279 0.0190186i
\(521\) −29.8875 −0.0573656 −0.0286828 0.999589i \(-0.509131\pi\)
−0.0286828 + 0.999589i \(0.509131\pi\)
\(522\) 0 0
\(523\) 324.051i 0.619600i 0.950802 + 0.309800i \(0.100262\pi\)
−0.950802 + 0.309800i \(0.899738\pi\)
\(524\) 90.3110 117.005i 0.172349 0.223292i
\(525\) 0 0
\(526\) −293.923 100.240i −0.558788 0.190570i
\(527\) 670.652i 1.27259i
\(528\) 0 0
\(529\) 338.548 0.639978
\(530\) −30.7475 + 90.1577i −0.0580141 + 0.170109i
\(531\) 0 0
\(532\) −170.824 131.852i −0.321097 0.247841i
\(533\) 36.1065 0.0677420
\(534\) 0 0
\(535\) 456.912i 0.854040i
\(536\) −15.3766 23.2267i −0.0286878 0.0433334i
\(537\) 0 0
\(538\) −295.208 + 865.607i −0.548713 + 1.60893i
\(539\) 953.250i 1.76855i
\(540\) 0 0
\(541\) −584.274 −1.07999 −0.539994 0.841669i \(-0.681574\pi\)
−0.539994 + 0.841669i \(0.681574\pi\)
\(542\) 661.166 + 225.485i 1.21986 + 0.416024i
\(543\) 0 0
\(544\) 867.446 + 63.0545i 1.59457 + 0.115909i
\(545\) −437.799 −0.803301
\(546\) 0 0
\(547\) 173.706i 0.317562i −0.987314 0.158781i \(-0.949244\pi\)
0.987314 0.158781i \(-0.0507564\pi\)
\(548\) −515.457 397.859i −0.940614 0.726020i
\(549\) 0 0
\(550\) −334.762 114.168i −0.608658 0.207578i
\(551\) 217.286i 0.394348i
\(552\) 0 0
\(553\) 640.396 1.15804
\(554\) 70.0755 205.475i 0.126490 0.370894i
\(555\) 0 0
\(556\) −560.261 + 725.862i −1.00766 + 1.30551i
\(557\) 590.355 1.05988 0.529942 0.848034i \(-0.322214\pi\)
0.529942 + 0.848034i \(0.322214\pi\)
\(558\) 0 0
\(559\) 38.7470i 0.0693148i
\(560\) 456.275 119.480i 0.814776 0.213357i
\(561\) 0 0
\(562\) 122.951 360.516i 0.218774 0.641487i
\(563\) 1015.03i 1.80290i 0.432882 + 0.901450i \(0.357497\pi\)
−0.432882 + 0.901450i \(0.642503\pi\)
\(564\) 0 0
\(565\) −173.807 −0.307623
\(566\) 548.859 + 187.183i 0.969715 + 0.330713i
\(567\) 0 0
\(568\) −392.545 592.947i −0.691100 1.04392i
\(569\) 98.2869 0.172736 0.0863681 0.996263i \(-0.472474\pi\)
0.0863681 + 0.996263i \(0.472474\pi\)
\(570\) 0 0
\(571\) 366.213i 0.641354i −0.947189 0.320677i \(-0.896090\pi\)
0.947189 0.320677i \(-0.103910\pi\)
\(572\) −21.0270 + 27.2421i −0.0367604 + 0.0476260i
\(573\) 0 0
\(574\) 899.689 + 306.831i 1.56740 + 0.534549i
\(575\) 266.719i 0.463859i
\(576\) 0 0
\(577\) −267.138 −0.462977 −0.231489 0.972838i \(-0.574360\pi\)
−0.231489 + 0.972838i \(0.574360\pi\)
\(578\) −290.320 + 851.275i −0.502284 + 1.47279i
\(579\) 0 0
\(580\) 375.961 + 290.188i 0.648208 + 0.500324i
\(581\) −82.0488 −0.141220
\(582\) 0 0
\(583\) 182.974i 0.313850i
\(584\) −132.461 + 87.6925i −0.226817 + 0.150158i
\(585\) 0 0
\(586\) −114.835 + 336.719i −0.195964 + 0.574605i
\(587\) 245.452i 0.418147i 0.977900 + 0.209074i \(0.0670448\pi\)
−0.977900 + 0.209074i \(0.932955\pi\)
\(588\) 0 0
\(589\) −107.557 −0.182609
\(590\) 156.476 + 53.3647i 0.265213 + 0.0904487i
\(591\) 0 0
\(592\) −110.956 423.724i −0.187426 0.715750i
\(593\) −33.3697 −0.0562726 −0.0281363 0.999604i \(-0.508957\pi\)
−0.0281363 + 0.999604i \(0.508957\pi\)
\(594\) 0 0
\(595\) 801.207i 1.34657i
\(596\) −349.352 269.649i −0.586160 0.452432i
\(597\) 0 0
\(598\) −24.5616 8.37653i −0.0410729 0.0140076i
\(599\) 427.260i 0.713288i −0.934240 0.356644i \(-0.883921\pi\)
0.934240 0.356644i \(-0.116079\pi\)
\(600\) 0 0
\(601\) −316.625 −0.526831 −0.263415 0.964683i \(-0.584849\pi\)
−0.263415 + 0.964683i \(0.584849\pi\)
\(602\) −329.270 + 965.483i −0.546960 + 1.60379i
\(603\) 0 0
\(604\) −255.983 + 331.646i −0.423813 + 0.549083i
\(605\) 88.7741 0.146734
\(606\) 0 0
\(607\) 467.840i 0.770741i 0.922762 + 0.385370i \(0.125926\pi\)
−0.922762 + 0.385370i \(0.874074\pi\)
\(608\) 10.1124 139.118i 0.0166323 0.228812i
\(609\) 0 0
\(610\) −51.0512 + 149.692i −0.0836905 + 0.245397i
\(611\) 42.4829i 0.0695300i
\(612\) 0 0
\(613\) −636.118 −1.03771 −0.518856 0.854861i \(-0.673642\pi\)
−0.518856 + 0.854861i \(0.673642\pi\)
\(614\) 1049.25 + 357.838i 1.70888 + 0.582797i
\(615\) 0 0
\(616\) −755.444 + 500.122i −1.22637 + 0.811886i
\(617\) −331.487 −0.537256 −0.268628 0.963244i \(-0.586570\pi\)
−0.268628 + 0.963244i \(0.586570\pi\)
\(618\) 0 0
\(619\) 479.724i 0.774999i 0.921870 + 0.387500i \(0.126661\pi\)
−0.921870 + 0.387500i \(0.873339\pi\)
\(620\) 143.643 186.101i 0.231683 0.300163i
\(621\) 0 0
\(622\) 128.259 + 43.7416i 0.206204 + 0.0703241i
\(623\) 389.988i 0.625984i
\(624\) 0 0
\(625\) 231.698 0.370718
\(626\) −288.731 + 846.615i −0.461231 + 1.35242i
\(627\) 0 0
\(628\) 467.672 + 360.976i 0.744700 + 0.574802i
\(629\) 744.049 1.18291
\(630\) 0 0
\(631\) 389.892i 0.617896i −0.951079 0.308948i \(-0.900023\pi\)
0.951079 0.308948i \(-0.0999768\pi\)
\(632\) 228.505 + 345.161i 0.361558 + 0.546141i
\(633\) 0 0
\(634\) 43.3924 127.235i 0.0684423 0.200686i
\(635\) 27.2042i 0.0428412i
\(636\) 0 0
\(637\) −97.9481 −0.153765
\(638\) −863.435 294.467i −1.35335 0.461547i
\(639\) 0 0
\(640\) 227.204 + 203.291i 0.355007 + 0.317642i
\(641\) 170.264 0.265623 0.132811 0.991141i \(-0.457600\pi\)
0.132811 + 0.991141i \(0.457600\pi\)
\(642\) 0 0
\(643\) 420.651i 0.654200i 0.944990 + 0.327100i \(0.106071\pi\)
−0.944990 + 0.327100i \(0.893929\pi\)
\(644\) −540.834 417.447i −0.839805 0.648209i
\(645\) 0 0
\(646\) 224.260 + 76.4819i 0.347151 + 0.118393i
\(647\) 178.658i 0.276133i 0.990423 + 0.138067i \(0.0440888\pi\)
−0.990423 + 0.138067i \(0.955911\pi\)
\(648\) 0 0
\(649\) −317.566 −0.489317
\(650\) 11.7309 34.3974i 0.0180476 0.0529191i
\(651\) 0 0
\(652\) 447.517 579.793i 0.686376 0.889253i
\(653\) 950.370 1.45539 0.727696 0.685900i \(-0.240591\pi\)
0.727696 + 0.685900i \(0.240591\pi\)
\(654\) 0 0
\(655\) 88.0117i 0.134369i
\(656\) 155.649 + 594.397i 0.237270 + 0.906094i
\(657\) 0 0
\(658\) −361.017 + 1058.57i −0.548658 + 1.60877i
\(659\) 327.948i 0.497645i −0.968549 0.248823i \(-0.919956\pi\)
0.968549 0.248823i \(-0.0800436\pi\)
\(660\) 0 0
\(661\) 256.403 0.387902 0.193951 0.981011i \(-0.437870\pi\)
0.193951 + 0.981011i \(0.437870\pi\)
\(662\) 337.794 + 115.202i 0.510264 + 0.174021i
\(663\) 0 0
\(664\) −29.2765 44.2227i −0.0440911 0.0666005i
\(665\) 128.495 0.193225
\(666\) 0 0
\(667\) 687.935i 1.03139i
\(668\) −524.254 + 679.211i −0.784811 + 1.01678i
\(669\) 0 0
\(670\) 15.6989 + 5.35397i 0.0234312 + 0.00799100i
\(671\) 303.799i 0.452755i
\(672\) 0 0
\(673\) −624.347 −0.927707 −0.463853 0.885912i \(-0.653534\pi\)
−0.463853 + 0.885912i \(0.653534\pi\)
\(674\) 180.854 530.300i 0.268330 0.786795i
\(675\) 0 0
\(676\) 532.335 + 410.886i 0.787477 + 0.607820i
\(677\) 135.259 0.199791 0.0998955 0.994998i \(-0.468149\pi\)
0.0998955 + 0.994998i \(0.468149\pi\)
\(678\) 0 0
\(679\) 1971.34i 2.90330i
\(680\) −431.835 + 285.885i −0.635052 + 0.420419i
\(681\) 0 0
\(682\) −145.762 + 427.401i −0.213727 + 0.626688i
\(683\) 84.9635i 0.124398i 0.998064 + 0.0621988i \(0.0198113\pi\)
−0.998064 + 0.0621988i \(0.980189\pi\)
\(684\) 0 0
\(685\) 387.729 0.566028
\(686\) −1292.67 440.853i −1.88436 0.642644i
\(687\) 0 0
\(688\) −637.866 + 167.032i −0.927131 + 0.242778i
\(689\) 18.8009 0.0272873
\(690\) 0 0
\(691\) 673.647i 0.974887i 0.873155 + 0.487443i \(0.162070\pi\)
−0.873155 + 0.487443i \(0.837930\pi\)
\(692\) 86.0804 + 66.4418i 0.124394 + 0.0960141i
\(693\) 0 0
\(694\) −169.608 57.8435i −0.244392 0.0833479i
\(695\) 545.997i 0.785607i
\(696\) 0 0
\(697\) −1043.75 −1.49749
\(698\) −3.47589 + 10.1920i −0.00497979 + 0.0146017i
\(699\) 0 0
\(700\) 584.615 757.413i 0.835164 1.08202i
\(701\) −406.227 −0.579496 −0.289748 0.957103i \(-0.593571\pi\)
−0.289748 + 0.957103i \(0.593571\pi\)
\(702\) 0 0
\(703\) 119.328i 0.169741i
\(704\) −539.112 228.717i −0.765784 0.324883i
\(705\) 0 0
\(706\) 231.014 677.378i 0.327215 0.959459i
\(707\) 435.122i 0.615448i
\(708\) 0 0
\(709\) 668.985 0.943561 0.471780 0.881716i \(-0.343611\pi\)
0.471780 + 0.881716i \(0.343611\pi\)
\(710\) 400.771 + 136.680i 0.564466 + 0.192506i
\(711\) 0 0
\(712\) −210.196 + 139.155i −0.295219 + 0.195442i
\(713\) −340.528 −0.477599
\(714\) 0 0
\(715\) 20.4916i 0.0286596i
\(716\) −452.846 + 586.697i −0.632467 + 0.819409i
\(717\) 0 0
\(718\) 787.072 + 268.424i 1.09620 + 0.373850i
\(719\) 357.444i 0.497140i −0.968614 0.248570i \(-0.920039\pi\)
0.968614 0.248570i \(-0.0799606\pi\)
\(720\) 0 0
\(721\) −1450.69 −2.01205
\(722\) 12.2659 35.9659i 0.0169887 0.0498143i
\(723\) 0 0
\(724\) −53.8774 41.5857i −0.0744163 0.0574387i
\(725\) 963.420 1.32886
\(726\) 0 0
\(727\) 931.519i 1.28132i 0.767825 + 0.640659i \(0.221339\pi\)
−0.767825 + 0.640659i \(0.778661\pi\)
\(728\) −51.3884 77.6232i −0.0705885 0.106625i
\(729\) 0 0
\(730\) 30.5335 89.5303i 0.0418267 0.122644i
\(731\) 1120.08i 1.53225i
\(732\) 0 0
\(733\) −342.315 −0.467006 −0.233503 0.972356i \(-0.575019\pi\)
−0.233503 + 0.972356i \(0.575019\pi\)
\(734\) 497.266 + 169.588i 0.677474 + 0.231047i
\(735\) 0 0
\(736\) 32.0164 440.451i 0.0435005 0.598440i
\(737\) −31.8608 −0.0432303
\(738\) 0 0
\(739\) 233.486i 0.315949i −0.987443 0.157975i \(-0.949504\pi\)
0.987443 0.157975i \(-0.0504964\pi\)
\(740\) 206.468 + 159.364i 0.279011 + 0.215356i
\(741\) 0 0
\(742\) 468.475 + 159.769i 0.631368 + 0.215323i
\(743\) 684.601i 0.921401i 0.887556 + 0.460701i \(0.152402\pi\)
−0.887556 + 0.460701i \(0.847598\pi\)
\(744\) 0 0
\(745\) 262.784 0.352730
\(746\) −102.223 + 299.737i −0.137028 + 0.401792i
\(747\) 0 0
\(748\) 607.836 787.499i 0.812615 1.05281i
\(749\) −2374.19 −3.16982
\(750\) 0 0
\(751\) 985.017i 1.31161i −0.754931 0.655804i \(-0.772330\pi\)
0.754931 0.655804i \(-0.227670\pi\)
\(752\) −699.367 + 183.136i −0.930010 + 0.243532i
\(753\) 0 0
\(754\) 30.2570 88.7195i 0.0401287 0.117665i
\(755\) 249.466i 0.330418i
\(756\) 0 0
\(757\) 1162.89 1.53619 0.768094 0.640338i \(-0.221206\pi\)
0.768094 + 0.640338i \(0.221206\pi\)
\(758\) 1020.55 + 348.051i 1.34638 + 0.459171i
\(759\) 0 0
\(760\) 45.8491 + 69.2561i 0.0603278 + 0.0911264i
\(761\) 460.254 0.604802 0.302401 0.953181i \(-0.402212\pi\)
0.302401 + 0.953181i \(0.402212\pi\)
\(762\) 0 0
\(763\) 2274.88i 2.98149i
\(764\) 5.90967 7.65643i 0.00773516 0.0100215i
\(765\) 0 0
\(766\) 800.356 + 272.954i 1.04485 + 0.356337i
\(767\) 32.6305i 0.0425431i
\(768\) 0 0
\(769\) 757.145 0.984584 0.492292 0.870430i \(-0.336159\pi\)
0.492292 + 0.870430i \(0.336159\pi\)
\(770\) 174.137 510.603i 0.226151 0.663120i
\(771\) 0 0
\(772\) 477.226 + 368.350i 0.618168 + 0.477138i
\(773\) −1071.48 −1.38614 −0.693068 0.720872i \(-0.743742\pi\)
−0.693068 + 0.720872i \(0.743742\pi\)
\(774\) 0 0
\(775\) 476.894i 0.615347i
\(776\) 1062.51 703.409i 1.36922 0.906455i
\(777\) 0 0
\(778\) −314.452 + 922.036i −0.404180 + 1.18514i
\(779\) 167.392i 0.214881i
\(780\) 0 0
\(781\) −813.362 −1.04144
\(782\) 710.014 + 242.144i 0.907946 + 0.309647i
\(783\) 0 0
\(784\) −422.238 1612.46i −0.538568 2.05670i
\(785\) −351.785 −0.448134
\(786\) 0 0
\(787\) 625.691i 0.795033i 0.917595 + 0.397517i \(0.130128\pi\)
−0.917595 + 0.397517i \(0.869872\pi\)
\(788\) 849.257 + 655.505i 1.07774