Properties

Label 684.3.g.b.343.12
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 343.12
Root \(-1.89728 - 0.632718i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.89728 + 0.632718i) q^{2} +(3.19934 + 2.40089i) q^{4} -5.79268 q^{5} -5.87536i q^{7} +(4.55095 + 6.57943i) q^{8} +O(q^{10})\) \(q+(1.89728 + 0.632718i) q^{2} +(3.19934 + 2.40089i) q^{4} -5.79268 q^{5} -5.87536i q^{7} +(4.55095 + 6.57943i) q^{8} +(-10.9903 - 3.66514i) q^{10} -8.07883i q^{11} -14.0396 q^{13} +(3.71745 - 11.1472i) q^{14} +(4.47149 + 15.3625i) q^{16} -29.9906 q^{17} -4.35890i q^{19} +(-18.5327 - 13.9076i) q^{20} +(5.11162 - 15.3278i) q^{22} -8.74865i q^{23} +8.55515 q^{25} +(-26.6370 - 8.88309i) q^{26} +(14.1061 - 18.7973i) q^{28} -13.4473 q^{29} -7.65793i q^{31} +(-1.23646 + 31.9761i) q^{32} +(-56.9006 - 18.9756i) q^{34} +34.0341i q^{35} +25.1221 q^{37} +(2.75796 - 8.27005i) q^{38} +(-26.3622 - 38.1125i) q^{40} -49.6861 q^{41} -47.2402i q^{43} +(19.3963 - 25.8469i) q^{44} +(5.53543 - 16.5986i) q^{46} -46.8391i q^{47} +14.4801 q^{49} +(16.2315 + 5.41300i) q^{50} +(-44.9173 - 33.7074i) q^{52} +14.1940 q^{53} +46.7981i q^{55} +(38.6565 - 26.7385i) q^{56} +(-25.5133 - 8.50835i) q^{58} -100.107i q^{59} -31.1928 q^{61} +(4.84532 - 14.5292i) q^{62} +(-22.5778 + 59.8853i) q^{64} +81.3267 q^{65} +34.5861i q^{67} +(-95.9501 - 72.0041i) q^{68} +(-21.5340 + 64.5722i) q^{70} +66.0243i q^{71} -27.5063 q^{73} +(47.6636 + 15.8952i) q^{74} +(10.4652 - 13.9456i) q^{76} -47.4661 q^{77} +40.9739i q^{79} +(-25.9019 - 88.9899i) q^{80} +(-94.2684 - 31.4373i) q^{82} +87.8564i q^{83} +173.726 q^{85} +(29.8898 - 89.6279i) q^{86} +(53.1541 - 36.7663i) q^{88} -28.6482 q^{89} +82.4875i q^{91} +(21.0045 - 27.9899i) q^{92} +(29.6360 - 88.8669i) q^{94} +25.2497i q^{95} +9.35629 q^{97} +(27.4728 + 9.16182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.89728 + 0.632718i 0.948639 + 0.316359i
\(3\) 0 0
\(4\) 3.19934 + 2.40089i 0.799834 + 0.600222i
\(5\) −5.79268 −1.15854 −0.579268 0.815137i \(-0.696662\pi\)
−0.579268 + 0.815137i \(0.696662\pi\)
\(6\) 0 0
\(7\) 5.87536i 0.839338i −0.907677 0.419669i \(-0.862146\pi\)
0.907677 0.419669i \(-0.137854\pi\)
\(8\) 4.55095 + 6.57943i 0.568868 + 0.822429i
\(9\) 0 0
\(10\) −10.9903 3.66514i −1.09903 0.366514i
\(11\) 8.07883i 0.734439i −0.930134 0.367219i \(-0.880310\pi\)
0.930134 0.367219i \(-0.119690\pi\)
\(12\) 0 0
\(13\) −14.0396 −1.07997 −0.539983 0.841676i \(-0.681569\pi\)
−0.539983 + 0.841676i \(0.681569\pi\)
\(14\) 3.71745 11.1472i 0.265532 0.796229i
\(15\) 0 0
\(16\) 4.47149 + 15.3625i 0.279468 + 0.960155i
\(17\) −29.9906 −1.76415 −0.882077 0.471104i \(-0.843855\pi\)
−0.882077 + 0.471104i \(0.843855\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) −18.5327 13.9076i −0.926636 0.695378i
\(21\) 0 0
\(22\) 5.11162 15.3278i 0.232346 0.696718i
\(23\) 8.74865i 0.380376i −0.981748 0.190188i \(-0.939090\pi\)
0.981748 0.190188i \(-0.0609098\pi\)
\(24\) 0 0
\(25\) 8.55515 0.342206
\(26\) −26.6370 8.88309i −1.02450 0.341657i
\(27\) 0 0
\(28\) 14.1061 18.7973i 0.503789 0.671331i
\(29\) −13.4473 −0.463700 −0.231850 0.972752i \(-0.574478\pi\)
−0.231850 + 0.972752i \(0.574478\pi\)
\(30\) 0 0
\(31\) 7.65793i 0.247030i −0.992343 0.123515i \(-0.960583\pi\)
0.992343 0.123515i \(-0.0394167\pi\)
\(32\) −1.23646 + 31.9761i −0.0386394 + 0.999253i
\(33\) 0 0
\(34\) −56.9006 18.9756i −1.67355 0.558107i
\(35\) 34.0341i 0.972403i
\(36\) 0 0
\(37\) 25.1221 0.678975 0.339488 0.940611i \(-0.389746\pi\)
0.339488 + 0.940611i \(0.389746\pi\)
\(38\) 2.75796 8.27005i 0.0725778 0.217633i
\(39\) 0 0
\(40\) −26.3622 38.1125i −0.659054 0.952813i
\(41\) −49.6861 −1.21186 −0.605928 0.795519i \(-0.707198\pi\)
−0.605928 + 0.795519i \(0.707198\pi\)
\(42\) 0 0
\(43\) 47.2402i 1.09861i −0.835622 0.549305i \(-0.814892\pi\)
0.835622 0.549305i \(-0.185108\pi\)
\(44\) 19.3963 25.8469i 0.440826 0.587429i
\(45\) 0 0
\(46\) 5.53543 16.5986i 0.120336 0.360840i
\(47\) 46.8391i 0.996577i −0.867011 0.498289i \(-0.833962\pi\)
0.867011 0.498289i \(-0.166038\pi\)
\(48\) 0 0
\(49\) 14.4801 0.295512
\(50\) 16.2315 + 5.41300i 0.324630 + 0.108260i
\(51\) 0 0
\(52\) −44.9173 33.7074i −0.863793 0.648219i
\(53\) 14.1940 0.267811 0.133906 0.990994i \(-0.457248\pi\)
0.133906 + 0.990994i \(0.457248\pi\)
\(54\) 0 0
\(55\) 46.7981i 0.850874i
\(56\) 38.6565 26.7385i 0.690295 0.477473i
\(57\) 0 0
\(58\) −25.5133 8.50835i −0.439884 0.146696i
\(59\) 100.107i 1.69673i −0.529415 0.848363i \(-0.677589\pi\)
0.529415 0.848363i \(-0.322411\pi\)
\(60\) 0 0
\(61\) −31.1928 −0.511357 −0.255678 0.966762i \(-0.582299\pi\)
−0.255678 + 0.966762i \(0.582299\pi\)
\(62\) 4.84532 14.5292i 0.0781503 0.234343i
\(63\) 0 0
\(64\) −22.5778 + 59.8853i −0.352778 + 0.935707i
\(65\) 81.3267 1.25118
\(66\) 0 0
\(67\) 34.5861i 0.516210i 0.966117 + 0.258105i \(0.0830981\pi\)
−0.966117 + 0.258105i \(0.916902\pi\)
\(68\) −95.9501 72.0041i −1.41103 1.05888i
\(69\) 0 0
\(70\) −21.5340 + 64.5722i −0.307629 + 0.922460i
\(71\) 66.0243i 0.929919i 0.885332 + 0.464960i \(0.153931\pi\)
−0.885332 + 0.464960i \(0.846069\pi\)
\(72\) 0 0
\(73\) −27.5063 −0.376798 −0.188399 0.982093i \(-0.560330\pi\)
−0.188399 + 0.982093i \(0.560330\pi\)
\(74\) 47.6636 + 15.8952i 0.644103 + 0.214800i
\(75\) 0 0
\(76\) 10.4652 13.9456i 0.137700 0.183494i
\(77\) −47.4661 −0.616442
\(78\) 0 0
\(79\) 40.9739i 0.518657i 0.965789 + 0.259329i \(0.0835013\pi\)
−0.965789 + 0.259329i \(0.916499\pi\)
\(80\) −25.9019 88.9899i −0.323774 1.11237i
\(81\) 0 0
\(82\) −94.2684 31.4373i −1.14961 0.383382i
\(83\) 87.8564i 1.05851i 0.848463 + 0.529255i \(0.177529\pi\)
−0.848463 + 0.529255i \(0.822471\pi\)
\(84\) 0 0
\(85\) 173.726 2.04384
\(86\) 29.8898 89.6279i 0.347555 1.04219i
\(87\) 0 0
\(88\) 53.1541 36.7663i 0.604024 0.417799i
\(89\) −28.6482 −0.321890 −0.160945 0.986963i \(-0.551454\pi\)
−0.160945 + 0.986963i \(0.551454\pi\)
\(90\) 0 0
\(91\) 82.4875i 0.906457i
\(92\) 21.0045 27.9899i 0.228310 0.304238i
\(93\) 0 0
\(94\) 29.6360 88.8669i 0.315276 0.945393i
\(95\) 25.2497i 0.265786i
\(96\) 0 0
\(97\) 9.35629 0.0964566 0.0482283 0.998836i \(-0.484642\pi\)
0.0482283 + 0.998836i \(0.484642\pi\)
\(98\) 27.4728 + 9.16182i 0.280334 + 0.0934879i
\(99\) 0 0
\(100\) 27.3708 + 20.5399i 0.273708 + 0.205399i
\(101\) 86.6846 0.858263 0.429132 0.903242i \(-0.358820\pi\)
0.429132 + 0.903242i \(0.358820\pi\)
\(102\) 0 0
\(103\) 139.602i 1.35536i 0.735358 + 0.677679i \(0.237014\pi\)
−0.735358 + 0.677679i \(0.762986\pi\)
\(104\) −63.8933 92.3723i −0.614359 0.888195i
\(105\) 0 0
\(106\) 26.9300 + 8.98081i 0.254057 + 0.0847246i
\(107\) 53.5627i 0.500586i 0.968170 + 0.250293i \(0.0805269\pi\)
−0.968170 + 0.250293i \(0.919473\pi\)
\(108\) 0 0
\(109\) −154.519 −1.41760 −0.708802 0.705408i \(-0.750764\pi\)
−0.708802 + 0.705408i \(0.750764\pi\)
\(110\) −29.6100 + 88.7890i −0.269182 + 0.807173i
\(111\) 0 0
\(112\) 90.2602 26.2716i 0.805894 0.234568i
\(113\) 66.0050 0.584115 0.292057 0.956401i \(-0.405660\pi\)
0.292057 + 0.956401i \(0.405660\pi\)
\(114\) 0 0
\(115\) 50.6782i 0.440680i
\(116\) −43.0224 32.2854i −0.370883 0.278323i
\(117\) 0 0
\(118\) 63.3394 189.931i 0.536775 1.60958i
\(119\) 176.206i 1.48072i
\(120\) 0 0
\(121\) 55.7325 0.460600
\(122\) −59.1814 19.7362i −0.485093 0.161772i
\(123\) 0 0
\(124\) 18.3858 24.5003i 0.148273 0.197583i
\(125\) 95.2598 0.762078
\(126\) 0 0
\(127\) 222.988i 1.75581i 0.478833 + 0.877906i \(0.341060\pi\)
−0.478833 + 0.877906i \(0.658940\pi\)
\(128\) −80.7268 + 99.3337i −0.630678 + 0.776044i
\(129\) 0 0
\(130\) 154.299 + 51.4569i 1.18692 + 0.395822i
\(131\) 199.333i 1.52163i −0.648971 0.760813i \(-0.724800\pi\)
0.648971 0.760813i \(-0.275200\pi\)
\(132\) 0 0
\(133\) −25.6101 −0.192557
\(134\) −21.8833 + 65.6195i −0.163308 + 0.489698i
\(135\) 0 0
\(136\) −136.486 197.321i −1.00357 1.45089i
\(137\) 6.01427 0.0438998 0.0219499 0.999759i \(-0.493013\pi\)
0.0219499 + 0.999759i \(0.493013\pi\)
\(138\) 0 0
\(139\) 77.3080i 0.556172i −0.960556 0.278086i \(-0.910300\pi\)
0.960556 0.278086i \(-0.0897001\pi\)
\(140\) −81.7120 + 108.887i −0.583657 + 0.777761i
\(141\) 0 0
\(142\) −41.7748 + 125.266i −0.294188 + 0.882158i
\(143\) 113.423i 0.793169i
\(144\) 0 0
\(145\) 77.8959 0.537213
\(146\) −52.1870 17.4037i −0.357445 0.119203i
\(147\) 0 0
\(148\) 80.3740 + 60.3153i 0.543067 + 0.407536i
\(149\) −250.996 −1.68454 −0.842270 0.539056i \(-0.818781\pi\)
−0.842270 + 0.539056i \(0.818781\pi\)
\(150\) 0 0
\(151\) 62.0159i 0.410701i −0.978688 0.205351i \(-0.934167\pi\)
0.978688 0.205351i \(-0.0658335\pi\)
\(152\) 28.6791 19.8371i 0.188678 0.130507i
\(153\) 0 0
\(154\) −90.0564 30.0326i −0.584782 0.195017i
\(155\) 44.3600i 0.286193i
\(156\) 0 0
\(157\) −100.150 −0.637898 −0.318949 0.947772i \(-0.603330\pi\)
−0.318949 + 0.947772i \(0.603330\pi\)
\(158\) −25.9250 + 77.7390i −0.164082 + 0.492019i
\(159\) 0 0
\(160\) 7.16242 185.227i 0.0447651 1.15767i
\(161\) −51.4015 −0.319264
\(162\) 0 0
\(163\) 187.915i 1.15285i −0.817150 0.576425i \(-0.804447\pi\)
0.817150 0.576425i \(-0.195553\pi\)
\(164\) −158.963 119.291i −0.969284 0.727382i
\(165\) 0 0
\(166\) −55.5883 + 166.688i −0.334869 + 1.00414i
\(167\) 24.2604i 0.145272i −0.997359 0.0726361i \(-0.976859\pi\)
0.997359 0.0726361i \(-0.0231412\pi\)
\(168\) 0 0
\(169\) 28.1093 0.166327
\(170\) 329.607 + 109.920i 1.93886 + 0.646587i
\(171\) 0 0
\(172\) 113.418 151.137i 0.659410 0.878706i
\(173\) 250.771 1.44954 0.724772 0.688989i \(-0.241945\pi\)
0.724772 + 0.688989i \(0.241945\pi\)
\(174\) 0 0
\(175\) 50.2646i 0.287226i
\(176\) 124.111 36.1244i 0.705175 0.205252i
\(177\) 0 0
\(178\) −54.3537 18.1263i −0.305358 0.101833i
\(179\) 62.4162i 0.348694i −0.984684 0.174347i \(-0.944219\pi\)
0.984684 0.174347i \(-0.0557815\pi\)
\(180\) 0 0
\(181\) −66.6789 −0.368392 −0.184196 0.982890i \(-0.558968\pi\)
−0.184196 + 0.982890i \(0.558968\pi\)
\(182\) −52.1914 + 156.502i −0.286766 + 0.859900i
\(183\) 0 0
\(184\) 57.5612 39.8147i 0.312832 0.216384i
\(185\) −145.524 −0.786617
\(186\) 0 0
\(187\) 242.289i 1.29566i
\(188\) 112.455 149.854i 0.598167 0.797096i
\(189\) 0 0
\(190\) −15.9760 + 47.9057i −0.0840840 + 0.252135i
\(191\) 218.487i 1.14391i −0.820285 0.571955i \(-0.806185\pi\)
0.820285 0.571955i \(-0.193815\pi\)
\(192\) 0 0
\(193\) 61.9485 0.320977 0.160488 0.987038i \(-0.448693\pi\)
0.160488 + 0.987038i \(0.448693\pi\)
\(194\) 17.7515 + 5.91990i 0.0915025 + 0.0305149i
\(195\) 0 0
\(196\) 46.3267 + 34.7651i 0.236361 + 0.177373i
\(197\) 355.348 1.80380 0.901898 0.431950i \(-0.142174\pi\)
0.901898 + 0.431950i \(0.142174\pi\)
\(198\) 0 0
\(199\) 208.471i 1.04759i 0.851843 + 0.523797i \(0.175485\pi\)
−0.851843 + 0.523797i \(0.824515\pi\)
\(200\) 38.9340 + 56.2880i 0.194670 + 0.281440i
\(201\) 0 0
\(202\) 164.465 + 54.8469i 0.814183 + 0.271519i
\(203\) 79.0078i 0.389201i
\(204\) 0 0
\(205\) 287.816 1.40398
\(206\) −88.3286 + 264.864i −0.428780 + 1.28575i
\(207\) 0 0
\(208\) −62.7777 215.682i −0.301816 1.03694i
\(209\) −35.2148 −0.168492
\(210\) 0 0
\(211\) 275.150i 1.30403i −0.758206 0.652015i \(-0.773924\pi\)
0.758206 0.652015i \(-0.226076\pi\)
\(212\) 45.4114 + 34.0782i 0.214205 + 0.160746i
\(213\) 0 0
\(214\) −33.8901 + 101.623i −0.158365 + 0.474876i
\(215\) 273.648i 1.27278i
\(216\) 0 0
\(217\) −44.9932 −0.207342
\(218\) −293.165 97.7669i −1.34479 0.448472i
\(219\) 0 0
\(220\) −112.357 + 149.723i −0.510713 + 0.680558i
\(221\) 421.055 1.90523
\(222\) 0 0
\(223\) 237.911i 1.06687i 0.845842 + 0.533434i \(0.179099\pi\)
−0.845842 + 0.533434i \(0.820901\pi\)
\(224\) 187.871 + 7.26466i 0.838711 + 0.0324315i
\(225\) 0 0
\(226\) 125.230 + 41.7626i 0.554114 + 0.184790i
\(227\) 157.067i 0.691924i 0.938249 + 0.345962i \(0.112447\pi\)
−0.938249 + 0.345962i \(0.887553\pi\)
\(228\) 0 0
\(229\) −177.569 −0.775412 −0.387706 0.921783i \(-0.626732\pi\)
−0.387706 + 0.921783i \(0.626732\pi\)
\(230\) −32.0650 + 96.1506i −0.139413 + 0.418046i
\(231\) 0 0
\(232\) −61.1979 88.4756i −0.263784 0.381360i
\(233\) −75.5890 −0.324416 −0.162208 0.986757i \(-0.551862\pi\)
−0.162208 + 0.986757i \(0.551862\pi\)
\(234\) 0 0
\(235\) 271.324i 1.15457i
\(236\) 240.345 320.275i 1.01841 1.35710i
\(237\) 0 0
\(238\) −111.489 + 334.312i −0.468440 + 1.40467i
\(239\) 1.99543i 0.00834909i 0.999991 + 0.00417454i \(0.00132880\pi\)
−0.999991 + 0.00417454i \(0.998671\pi\)
\(240\) 0 0
\(241\) −64.6551 −0.268278 −0.134139 0.990962i \(-0.542827\pi\)
−0.134139 + 0.990962i \(0.542827\pi\)
\(242\) 105.740 + 35.2630i 0.436943 + 0.145715i
\(243\) 0 0
\(244\) −99.7961 74.8903i −0.409000 0.306927i
\(245\) −83.8785 −0.342361
\(246\) 0 0
\(247\) 61.1970i 0.247761i
\(248\) 50.3848 34.8508i 0.203165 0.140528i
\(249\) 0 0
\(250\) 180.734 + 60.2726i 0.722937 + 0.241090i
\(251\) 245.790i 0.979245i −0.871935 0.489622i \(-0.837135\pi\)
0.871935 0.489622i \(-0.162865\pi\)
\(252\) 0 0
\(253\) −70.6789 −0.279363
\(254\) −141.089 + 423.071i −0.555467 + 1.66563i
\(255\) 0 0
\(256\) −216.012 + 137.386i −0.843795 + 0.536665i
\(257\) −276.853 −1.07725 −0.538625 0.842546i \(-0.681056\pi\)
−0.538625 + 0.842546i \(0.681056\pi\)
\(258\) 0 0
\(259\) 147.601i 0.569890i
\(260\) 260.191 + 195.256i 1.00074 + 0.750985i
\(261\) 0 0
\(262\) 126.122 378.190i 0.481380 1.44347i
\(263\) 95.4157i 0.362797i 0.983410 + 0.181399i \(0.0580624\pi\)
−0.983410 + 0.181399i \(0.941938\pi\)
\(264\) 0 0
\(265\) −82.2213 −0.310269
\(266\) −48.5895 16.2040i −0.182667 0.0609173i
\(267\) 0 0
\(268\) −83.0373 + 110.653i −0.309841 + 0.412882i
\(269\) 128.844 0.478974 0.239487 0.970900i \(-0.423021\pi\)
0.239487 + 0.970900i \(0.423021\pi\)
\(270\) 0 0
\(271\) 317.491i 1.17155i −0.810472 0.585777i \(-0.800789\pi\)
0.810472 0.585777i \(-0.199211\pi\)
\(272\) −134.103 460.730i −0.493025 1.69386i
\(273\) 0 0
\(274\) 11.4107 + 3.80534i 0.0416450 + 0.0138881i
\(275\) 69.1156i 0.251329i
\(276\) 0 0
\(277\) −29.1910 −0.105383 −0.0526913 0.998611i \(-0.516780\pi\)
−0.0526913 + 0.998611i \(0.516780\pi\)
\(278\) 48.9142 146.675i 0.175950 0.527607i
\(279\) 0 0
\(280\) −223.925 + 154.887i −0.799732 + 0.553169i
\(281\) −204.530 −0.727866 −0.363933 0.931425i \(-0.618566\pi\)
−0.363933 + 0.931425i \(0.618566\pi\)
\(282\) 0 0
\(283\) 502.549i 1.77579i −0.460044 0.887896i \(-0.652166\pi\)
0.460044 0.887896i \(-0.347834\pi\)
\(284\) −158.517 + 211.234i −0.558158 + 0.743781i
\(285\) 0 0
\(286\) −71.7649 + 215.195i −0.250926 + 0.752432i
\(287\) 291.924i 1.01716i
\(288\) 0 0
\(289\) 610.438 2.11224
\(290\) 147.790 + 49.2862i 0.509622 + 0.169952i
\(291\) 0 0
\(292\) −88.0017 66.0394i −0.301376 0.226162i
\(293\) −239.563 −0.817623 −0.408811 0.912619i \(-0.634057\pi\)
−0.408811 + 0.912619i \(0.634057\pi\)
\(294\) 0 0
\(295\) 579.887i 1.96572i
\(296\) 114.329 + 165.289i 0.386248 + 0.558409i
\(297\) 0 0
\(298\) −476.210 158.810i −1.59802 0.532919i
\(299\) 122.827i 0.410794i
\(300\) 0 0
\(301\) −277.554 −0.922105
\(302\) 39.2386 117.661i 0.129929 0.389608i
\(303\) 0 0
\(304\) 66.9635 19.4908i 0.220275 0.0641144i
\(305\) 180.690 0.592425
\(306\) 0 0
\(307\) 310.436i 1.01119i −0.862771 0.505595i \(-0.831273\pi\)
0.862771 0.505595i \(-0.168727\pi\)
\(308\) −151.860 113.961i −0.493051 0.370002i
\(309\) 0 0
\(310\) −28.0674 + 84.1632i −0.0905399 + 0.271494i
\(311\) 219.552i 0.705956i 0.935632 + 0.352978i \(0.114831\pi\)
−0.935632 + 0.352978i \(0.885169\pi\)
\(312\) 0 0
\(313\) 322.681 1.03093 0.515465 0.856911i \(-0.327619\pi\)
0.515465 + 0.856911i \(0.327619\pi\)
\(314\) −190.013 63.3668i −0.605136 0.201805i
\(315\) 0 0
\(316\) −98.3738 + 131.089i −0.311309 + 0.414840i
\(317\) 53.6396 0.169210 0.0846050 0.996415i \(-0.473037\pi\)
0.0846050 + 0.996415i \(0.473037\pi\)
\(318\) 0 0
\(319\) 108.638i 0.340559i
\(320\) 130.786 346.896i 0.408706 1.08405i
\(321\) 0 0
\(322\) −97.5231 32.5227i −0.302867 0.101002i
\(323\) 130.726i 0.404725i
\(324\) 0 0
\(325\) −120.111 −0.369571
\(326\) 118.897 356.526i 0.364715 1.09364i
\(327\) 0 0
\(328\) −226.119 326.906i −0.689387 0.996665i
\(329\) −275.197 −0.836465
\(330\) 0 0
\(331\) 165.098i 0.498786i 0.968402 + 0.249393i \(0.0802310\pi\)
−0.968402 + 0.249393i \(0.919769\pi\)
\(332\) −210.933 + 281.082i −0.635341 + 0.846632i
\(333\) 0 0
\(334\) 15.3500 46.0288i 0.0459582 0.137811i
\(335\) 200.346i 0.598048i
\(336\) 0 0
\(337\) −374.211 −1.11042 −0.555210 0.831710i \(-0.687362\pi\)
−0.555210 + 0.831710i \(0.687362\pi\)
\(338\) 53.3312 + 17.7853i 0.157785 + 0.0526191i
\(339\) 0 0
\(340\) 555.808 + 417.097i 1.63473 + 1.22676i
\(341\) −61.8671 −0.181429
\(342\) 0 0
\(343\) 372.969i 1.08737i
\(344\) 310.814 214.988i 0.903529 0.624965i
\(345\) 0 0
\(346\) 475.783 + 158.667i 1.37509 + 0.458577i
\(347\) 442.710i 1.27582i −0.770110 0.637911i \(-0.779799\pi\)
0.770110 0.637911i \(-0.220201\pi\)
\(348\) 0 0
\(349\) −163.363 −0.468090 −0.234045 0.972226i \(-0.575196\pi\)
−0.234045 + 0.972226i \(0.575196\pi\)
\(350\) 31.8033 95.3660i 0.0908667 0.272474i
\(351\) 0 0
\(352\) 258.329 + 9.98915i 0.733890 + 0.0283783i
\(353\) −410.271 −1.16224 −0.581120 0.813818i \(-0.697385\pi\)
−0.581120 + 0.813818i \(0.697385\pi\)
\(354\) 0 0
\(355\) 382.457i 1.07734i
\(356\) −91.6553 68.7812i −0.257459 0.193206i
\(357\) 0 0
\(358\) 39.4919 118.421i 0.110313 0.330785i
\(359\) 124.552i 0.346941i −0.984839 0.173470i \(-0.944502\pi\)
0.984839 0.173470i \(-0.0554981\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) −126.508 42.1890i −0.349471 0.116544i
\(363\) 0 0
\(364\) −198.043 + 263.905i −0.544075 + 0.725015i
\(365\) 159.335 0.436534
\(366\) 0 0
\(367\) 288.749i 0.786782i −0.919371 0.393391i \(-0.871302\pi\)
0.919371 0.393391i \(-0.128698\pi\)
\(368\) 134.401 39.1195i 0.365220 0.106303i
\(369\) 0 0
\(370\) −276.100 92.0758i −0.746216 0.248854i
\(371\) 83.3950i 0.224784i
\(372\) 0 0
\(373\) 380.740 1.02075 0.510376 0.859952i \(-0.329506\pi\)
0.510376 + 0.859952i \(0.329506\pi\)
\(374\) −153.301 + 459.690i −0.409895 + 1.22912i
\(375\) 0 0
\(376\) 308.175 213.162i 0.819614 0.566921i
\(377\) 188.794 0.500780
\(378\) 0 0
\(379\) 176.366i 0.465345i 0.972555 + 0.232673i \(0.0747471\pi\)
−0.972555 + 0.232673i \(0.925253\pi\)
\(380\) −60.6217 + 80.7823i −0.159531 + 0.212585i
\(381\) 0 0
\(382\) 138.241 414.530i 0.361886 1.08516i
\(383\) 389.993i 1.01826i 0.860690 + 0.509129i \(0.170032\pi\)
−0.860690 + 0.509129i \(0.829968\pi\)
\(384\) 0 0
\(385\) 274.956 0.714171
\(386\) 117.534 + 39.1960i 0.304491 + 0.101544i
\(387\) 0 0
\(388\) 29.9339 + 22.4634i 0.0771493 + 0.0578953i
\(389\) −5.08380 −0.0130689 −0.00653445 0.999979i \(-0.502080\pi\)
−0.00653445 + 0.999979i \(0.502080\pi\)
\(390\) 0 0
\(391\) 262.378i 0.671043i
\(392\) 65.8981 + 95.2707i 0.168107 + 0.243038i
\(393\) 0 0
\(394\) 674.194 + 224.835i 1.71115 + 0.570647i
\(395\) 237.349i 0.600883i
\(396\) 0 0
\(397\) 320.541 0.807409 0.403705 0.914889i \(-0.367722\pi\)
0.403705 + 0.914889i \(0.367722\pi\)
\(398\) −131.904 + 395.528i −0.331416 + 0.993789i
\(399\) 0 0
\(400\) 38.2543 + 131.428i 0.0956356 + 0.328571i
\(401\) 428.362 1.06823 0.534117 0.845410i \(-0.320644\pi\)
0.534117 + 0.845410i \(0.320644\pi\)
\(402\) 0 0
\(403\) 107.514i 0.266784i
\(404\) 277.333 + 208.120i 0.686468 + 0.515148i
\(405\) 0 0
\(406\) −49.9897 + 149.900i −0.123127 + 0.369211i
\(407\) 202.957i 0.498666i
\(408\) 0 0
\(409\) 109.550 0.267849 0.133925 0.990992i \(-0.457242\pi\)
0.133925 + 0.990992i \(0.457242\pi\)
\(410\) 546.067 + 182.106i 1.33187 + 0.444162i
\(411\) 0 0
\(412\) −335.168 + 446.633i −0.813515 + 1.08406i
\(413\) −588.164 −1.42413
\(414\) 0 0
\(415\) 508.924i 1.22632i
\(416\) 17.3594 448.930i 0.0417292 1.07916i
\(417\) 0 0
\(418\) −66.8123 22.2810i −0.159838 0.0533039i
\(419\) 305.115i 0.728199i −0.931360 0.364099i \(-0.881377\pi\)
0.931360 0.364099i \(-0.118623\pi\)
\(420\) 0 0
\(421\) −721.115 −1.71286 −0.856431 0.516261i \(-0.827323\pi\)
−0.856431 + 0.516261i \(0.827323\pi\)
\(422\) 174.093 522.037i 0.412542 1.23705i
\(423\) 0 0
\(424\) 64.5962 + 93.3885i 0.152349 + 0.220256i
\(425\) −256.574 −0.603704
\(426\) 0 0
\(427\) 183.269i 0.429201i
\(428\) −128.598 + 171.365i −0.300462 + 0.400386i
\(429\) 0 0
\(430\) −173.142 + 519.186i −0.402656 + 1.20741i
\(431\) 275.396i 0.638971i −0.947591 0.319485i \(-0.896490\pi\)
0.947591 0.319485i \(-0.103510\pi\)
\(432\) 0 0
\(433\) −445.559 −1.02900 −0.514502 0.857489i \(-0.672023\pi\)
−0.514502 + 0.857489i \(0.672023\pi\)
\(434\) −85.3646 28.4680i −0.196693 0.0655945i
\(435\) 0 0
\(436\) −494.357 370.982i −1.13385 0.850876i
\(437\) −38.1345 −0.0872643
\(438\) 0 0
\(439\) 501.542i 1.14246i −0.820788 0.571232i \(-0.806466\pi\)
0.820788 0.571232i \(-0.193534\pi\)
\(440\) −307.905 + 212.975i −0.699783 + 0.484035i
\(441\) 0 0
\(442\) 798.859 + 266.409i 1.80737 + 0.602736i
\(443\) 297.237i 0.670964i 0.942047 + 0.335482i \(0.108899\pi\)
−0.942047 + 0.335482i \(0.891101\pi\)
\(444\) 0 0
\(445\) 165.950 0.372922
\(446\) −150.531 + 451.384i −0.337513 + 1.01207i
\(447\) 0 0
\(448\) 351.848 + 132.653i 0.785374 + 0.296100i
\(449\) 286.813 0.638782 0.319391 0.947623i \(-0.396522\pi\)
0.319391 + 0.947623i \(0.396522\pi\)
\(450\) 0 0
\(451\) 401.405i 0.890034i
\(452\) 211.172 + 158.470i 0.467195 + 0.350598i
\(453\) 0 0
\(454\) −99.3789 + 297.999i −0.218896 + 0.656386i
\(455\) 477.824i 1.05016i
\(456\) 0 0
\(457\) 254.383 0.556637 0.278318 0.960489i \(-0.410223\pi\)
0.278318 + 0.960489i \(0.410223\pi\)
\(458\) −336.899 112.351i −0.735587 0.245309i
\(459\) 0 0
\(460\) −121.673 + 162.136i −0.264505 + 0.352470i
\(461\) 77.6648 0.168470 0.0842351 0.996446i \(-0.473155\pi\)
0.0842351 + 0.996446i \(0.473155\pi\)
\(462\) 0 0
\(463\) 543.071i 1.17294i −0.809971 0.586470i \(-0.800517\pi\)
0.809971 0.586470i \(-0.199483\pi\)
\(464\) −60.1295 206.584i −0.129589 0.445224i
\(465\) 0 0
\(466\) −143.413 47.8265i −0.307754 0.102632i
\(467\) 384.665i 0.823694i 0.911253 + 0.411847i \(0.135116\pi\)
−0.911253 + 0.411847i \(0.864884\pi\)
\(468\) 0 0
\(469\) 203.206 0.433275
\(470\) −171.672 + 514.778i −0.365259 + 1.09527i
\(471\) 0 0
\(472\) 658.646 455.581i 1.39544 0.965213i
\(473\) −381.646 −0.806862
\(474\) 0 0
\(475\) 37.2910i 0.0785074i
\(476\) −423.050 + 563.742i −0.888761 + 1.18433i
\(477\) 0 0
\(478\) −1.26255 + 3.78589i −0.00264131 + 0.00792027i
\(479\) 661.184i 1.38034i 0.723646 + 0.690171i \(0.242465\pi\)
−0.723646 + 0.690171i \(0.757535\pi\)
\(480\) 0 0
\(481\) −352.703 −0.733270
\(482\) −122.669 40.9085i −0.254500 0.0848724i
\(483\) 0 0
\(484\) 178.307 + 133.808i 0.368403 + 0.276462i
\(485\) −54.1980 −0.111748
\(486\) 0 0
\(487\) 626.822i 1.28711i −0.765401 0.643554i \(-0.777459\pi\)
0.765401 0.643554i \(-0.222541\pi\)
\(488\) −141.957 205.231i −0.290895 0.420555i
\(489\) 0 0
\(490\) −159.141 53.0715i −0.324778 0.108309i
\(491\) 973.335i 1.98235i −0.132555 0.991176i \(-0.542318\pi\)
0.132555 0.991176i \(-0.457682\pi\)
\(492\) 0 0
\(493\) 403.293 0.818039
\(494\) −38.7205 + 116.108i −0.0783815 + 0.235036i
\(495\) 0 0
\(496\) 117.645 34.2424i 0.237187 0.0690370i
\(497\) 387.917 0.780516
\(498\) 0 0
\(499\) 171.966i 0.344621i −0.985043 0.172311i \(-0.944877\pi\)
0.985043 0.172311i \(-0.0551233\pi\)
\(500\) 304.768 + 228.708i 0.609536 + 0.457416i
\(501\) 0 0
\(502\) 155.516 466.333i 0.309793 0.928950i
\(503\) 806.197i 1.60278i −0.598145 0.801388i \(-0.704095\pi\)
0.598145 0.801388i \(-0.295905\pi\)
\(504\) 0 0
\(505\) −502.136 −0.994329
\(506\) −134.098 44.7198i −0.265015 0.0883791i
\(507\) 0 0
\(508\) −535.369 + 713.414i −1.05388 + 1.40436i
\(509\) −944.065 −1.85475 −0.927373 0.374139i \(-0.877938\pi\)
−0.927373 + 0.374139i \(0.877938\pi\)
\(510\) 0 0
\(511\) 161.609i 0.316261i
\(512\) −496.761 + 123.986i −0.970236 + 0.242160i
\(513\) 0 0
\(514\) −525.268 175.170i −1.02192 0.340798i
\(515\) 808.669i 1.57023i
\(516\) 0 0
\(517\) −378.405 −0.731925
\(518\) 93.3901 280.041i 0.180290 0.540620i
\(519\) 0 0
\(520\) 370.113 + 535.083i 0.711757 + 1.02901i
\(521\) −168.936 −0.324253 −0.162126 0.986770i \(-0.551835\pi\)
−0.162126 + 0.986770i \(0.551835\pi\)
\(522\) 0 0
\(523\) 391.361i 0.748300i −0.927368 0.374150i \(-0.877935\pi\)
0.927368 0.374150i \(-0.122065\pi\)
\(524\) 478.576 637.733i 0.913313 1.21705i
\(525\) 0 0
\(526\) −60.3712 + 181.030i −0.114774 + 0.344164i
\(527\) 229.666i 0.435799i
\(528\) 0 0
\(529\) 452.461 0.855314
\(530\) −155.997 52.0230i −0.294334 0.0981565i
\(531\) 0 0
\(532\) −81.9354 61.4870i −0.154014 0.115577i
\(533\) 697.571 1.30876
\(534\) 0 0
\(535\) 310.272i 0.579947i
\(536\) −227.557 + 157.399i −0.424546 + 0.293656i
\(537\) 0 0
\(538\) 244.453 + 81.5220i 0.454374 + 0.151528i
\(539\) 116.982i 0.217036i
\(540\) 0 0
\(541\) −561.849 −1.03854 −0.519269 0.854611i \(-0.673796\pi\)
−0.519269 + 0.854611i \(0.673796\pi\)
\(542\) 200.883 602.370i 0.370632 1.11138i
\(543\) 0 0
\(544\) 37.0822 958.984i 0.0681659 1.76284i
\(545\) 895.078 1.64234
\(546\) 0 0
\(547\) 630.789i 1.15318i −0.817034 0.576590i \(-0.804383\pi\)
0.817034 0.576590i \(-0.195617\pi\)
\(548\) 19.2417 + 14.4396i 0.0351125 + 0.0263496i
\(549\) 0 0
\(550\) 43.7307 131.132i 0.0795103 0.238421i
\(551\) 58.6154i 0.106380i
\(552\) 0 0
\(553\) 240.737 0.435329
\(554\) −55.3834 18.4697i −0.0999700 0.0333387i
\(555\) 0 0
\(556\) 185.608 247.334i 0.333827 0.444845i
\(557\) −123.847 −0.222346 −0.111173 0.993801i \(-0.535461\pi\)
−0.111173 + 0.993801i \(0.535461\pi\)
\(558\) 0 0
\(559\) 663.232i 1.18646i
\(560\) −522.848 + 152.183i −0.933658 + 0.271756i
\(561\) 0 0
\(562\) −388.051 129.410i −0.690483 0.230267i
\(563\) 935.582i 1.66178i −0.556437 0.830890i \(-0.687832\pi\)
0.556437 0.830890i \(-0.312168\pi\)
\(564\) 0 0
\(565\) −382.346 −0.676718
\(566\) 317.972 953.476i 0.561788 1.68459i
\(567\) 0 0
\(568\) −434.402 + 300.473i −0.764792 + 0.529001i
\(569\) −373.028 −0.655586 −0.327793 0.944750i \(-0.606305\pi\)
−0.327793 + 0.944750i \(0.606305\pi\)
\(570\) 0 0
\(571\) 435.521i 0.762733i 0.924424 + 0.381367i \(0.124546\pi\)
−0.924424 + 0.381367i \(0.875454\pi\)
\(572\) −272.316 + 362.879i −0.476077 + 0.634404i
\(573\) 0 0
\(574\) −184.706 + 553.861i −0.321787 + 0.964915i
\(575\) 74.8460i 0.130167i
\(576\) 0 0
\(577\) −807.758 −1.39993 −0.699964 0.714178i \(-0.746801\pi\)
−0.699964 + 0.714178i \(0.746801\pi\)
\(578\) 1158.17 + 386.235i 2.00376 + 0.668227i
\(579\) 0 0
\(580\) 249.215 + 187.019i 0.429681 + 0.322447i
\(581\) 516.188 0.888448
\(582\) 0 0
\(583\) 114.671i 0.196691i
\(584\) −125.179 180.975i −0.214348 0.309889i
\(585\) 0 0
\(586\) −454.519 151.576i −0.775629 0.258662i
\(587\) 311.402i 0.530498i 0.964180 + 0.265249i \(0.0854542\pi\)
−0.964180 + 0.265249i \(0.914546\pi\)
\(588\) 0 0
\(589\) −33.3802 −0.0566726
\(590\) −366.905 + 1100.21i −0.621873 + 1.86476i
\(591\) 0 0
\(592\) 112.333 + 385.938i 0.189752 + 0.651922i
\(593\) 1048.73 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(594\) 0 0
\(595\) 1020.70i 1.71547i
\(596\) −803.021 602.614i −1.34735 1.01110i
\(597\) 0 0
\(598\) −77.7151 + 233.038i −0.129958 + 0.389695i
\(599\) 20.9544i 0.0349822i −0.999847 0.0174911i \(-0.994432\pi\)
0.999847 0.0174911i \(-0.00556788\pi\)
\(600\) 0 0
\(601\) 4.04669 0.00673326 0.00336663 0.999994i \(-0.498928\pi\)
0.00336663 + 0.999994i \(0.498928\pi\)
\(602\) −526.597 175.613i −0.874745 0.291716i
\(603\) 0 0
\(604\) 148.893 198.410i 0.246512 0.328493i
\(605\) −322.841 −0.533621
\(606\) 0 0
\(607\) 718.845i 1.18426i 0.805843 + 0.592129i \(0.201712\pi\)
−0.805843 + 0.592129i \(0.798288\pi\)
\(608\) 139.381 + 5.38961i 0.229244 + 0.00886449i
\(609\) 0 0
\(610\) 342.819 + 114.326i 0.561998 + 0.187419i
\(611\) 657.601i 1.07627i
\(612\) 0 0
\(613\) −568.157 −0.926847 −0.463424 0.886137i \(-0.653379\pi\)
−0.463424 + 0.886137i \(0.653379\pi\)
\(614\) 196.418 588.983i 0.319899 0.959255i
\(615\) 0 0
\(616\) −216.015 312.300i −0.350674 0.506980i
\(617\) −344.297 −0.558017 −0.279009 0.960289i \(-0.590006\pi\)
−0.279009 + 0.960289i \(0.590006\pi\)
\(618\) 0 0
\(619\) 269.442i 0.435286i −0.976028 0.217643i \(-0.930163\pi\)
0.976028 0.217643i \(-0.0698368\pi\)
\(620\) −106.503 + 141.922i −0.171779 + 0.228907i
\(621\) 0 0
\(622\) −138.915 + 416.552i −0.223336 + 0.669698i
\(623\) 168.319i 0.270175i
\(624\) 0 0
\(625\) −765.688 −1.22510
\(626\) 612.216 + 204.166i 0.977980 + 0.326144i
\(627\) 0 0
\(628\) −320.414 240.449i −0.510213 0.382880i
\(629\) −753.427 −1.19782
\(630\) 0 0
\(631\) 916.217i 1.45201i −0.687691 0.726004i \(-0.741375\pi\)
0.687691 0.726004i \(-0.258625\pi\)
\(632\) −269.585 + 186.470i −0.426559 + 0.295048i
\(633\) 0 0
\(634\) 101.769 + 33.9387i 0.160519 + 0.0535311i
\(635\) 1291.70i 2.03417i
\(636\) 0 0
\(637\) −203.294 −0.319143
\(638\) −68.7375 + 206.117i −0.107739 + 0.323068i
\(639\) 0 0
\(640\) 467.625 575.408i 0.730664 0.899075i
\(641\) −809.161 −1.26234 −0.631171 0.775644i \(-0.717425\pi\)
−0.631171 + 0.775644i \(0.717425\pi\)
\(642\) 0 0
\(643\) 611.403i 0.950859i 0.879754 + 0.475430i \(0.157707\pi\)
−0.879754 + 0.475430i \(0.842293\pi\)
\(644\) −164.451 123.409i −0.255358 0.191629i
\(645\) 0 0
\(646\) −82.7128 + 248.024i −0.128038 + 0.383938i
\(647\) 375.179i 0.579875i 0.957046 + 0.289938i \(0.0936345\pi\)
−0.957046 + 0.289938i \(0.906365\pi\)
\(648\) 0 0
\(649\) −808.746 −1.24614
\(650\) −227.883 75.9961i −0.350590 0.116917i
\(651\) 0 0
\(652\) 451.161 601.202i 0.691965 0.922088i
\(653\) −122.859 −0.188146 −0.0940729 0.995565i \(-0.529989\pi\)
−0.0940729 + 0.995565i \(0.529989\pi\)
\(654\) 0 0
\(655\) 1154.67i 1.76286i
\(656\) −222.171 763.302i −0.338675 1.16357i
\(657\) 0 0
\(658\) −522.125 174.122i −0.793504 0.264623i
\(659\) 104.791i 0.159015i 0.996834 + 0.0795074i \(0.0253347\pi\)
−0.996834 + 0.0795074i \(0.974665\pi\)
\(660\) 0 0
\(661\) −1185.52 −1.79352 −0.896762 0.442514i \(-0.854087\pi\)
−0.896762 + 0.442514i \(0.854087\pi\)
\(662\) −104.461 + 313.237i −0.157795 + 0.473168i
\(663\) 0 0
\(664\) −578.045 + 399.830i −0.870549 + 0.602153i
\(665\) 148.351 0.223085
\(666\) 0 0
\(667\) 117.646i 0.176381i
\(668\) 58.2466 77.6173i 0.0871955 0.116194i
\(669\) 0 0
\(670\) 126.763 380.113i 0.189198 0.567332i
\(671\) 252.001i 0.375560i
\(672\) 0 0
\(673\) 86.7624 0.128919 0.0644594 0.997920i \(-0.479468\pi\)
0.0644594 + 0.997920i \(0.479468\pi\)
\(674\) −709.983 236.770i −1.05339 0.351291i
\(675\) 0 0
\(676\) 89.9310 + 67.4872i 0.133034 + 0.0998332i
\(677\) 566.786 0.837202 0.418601 0.908170i \(-0.362521\pi\)
0.418601 + 0.908170i \(0.362521\pi\)
\(678\) 0 0
\(679\) 54.9716i 0.0809597i
\(680\) 790.618 + 1143.02i 1.16267 + 1.68091i
\(681\) 0 0
\(682\) −117.379 39.1445i −0.172110 0.0573966i
\(683\) 192.839i 0.282341i 0.989985 + 0.141170i \(0.0450865\pi\)
−0.989985 + 0.141170i \(0.954913\pi\)
\(684\) 0 0
\(685\) −34.8387 −0.0508595
\(686\) 235.984 707.626i 0.344000 1.03152i
\(687\) 0 0
\(688\) 725.727 211.234i 1.05484 0.307026i
\(689\) −199.278 −0.289227
\(690\) 0 0
\(691\) 639.216i 0.925059i 0.886604 + 0.462530i \(0.153058\pi\)
−0.886604 + 0.462530i \(0.846942\pi\)
\(692\) 802.301 + 602.073i 1.15939 + 0.870048i
\(693\) 0 0
\(694\) 280.111 839.945i 0.403618 1.21029i
\(695\) 447.820i 0.644346i
\(696\) 0 0
\(697\) 1490.12 2.13790
\(698\) −309.946 103.363i −0.444049 0.148085i
\(699\) 0 0
\(700\) 120.680 160.813i 0.172399 0.229733i
\(701\) −109.111 −0.155650 −0.0778250 0.996967i \(-0.524798\pi\)
−0.0778250 + 0.996967i \(0.524798\pi\)
\(702\) 0 0
\(703\) 109.505i 0.155768i
\(704\) 483.803 + 182.402i 0.687220 + 0.259094i
\(705\) 0 0
\(706\) −778.398 259.586i −1.10255 0.367685i
\(707\) 509.304i 0.720373i
\(708\) 0 0
\(709\) 1381.83 1.94898 0.974489 0.224434i \(-0.0720532\pi\)
0.974489 + 0.224434i \(0.0720532\pi\)
\(710\) 241.988 725.628i 0.340828 1.02201i
\(711\) 0 0
\(712\) −130.377 188.489i −0.183113 0.264732i
\(713\) −66.9966 −0.0939644
\(714\) 0 0
\(715\) 657.024i 0.918915i
\(716\) 149.854 199.690i 0.209294 0.278897i
\(717\) 0 0
\(718\) 78.8062 236.309i 0.109758 0.329122i
\(719\) 844.528i 1.17459i 0.809374 + 0.587293i \(0.199806\pi\)
−0.809374 + 0.587293i \(0.800194\pi\)
\(720\) 0 0
\(721\) 820.211 1.13760
\(722\) −36.0483 12.0216i −0.0499284 0.0166505i
\(723\) 0 0
\(724\) −213.328 160.088i −0.294652 0.221117i
\(725\) −115.044 −0.158681
\(726\) 0 0
\(727\) 926.186i 1.27398i 0.770871 + 0.636992i \(0.219821\pi\)
−0.770871 + 0.636992i \(0.780179\pi\)
\(728\) −542.721 + 375.396i −0.745496 + 0.515654i
\(729\) 0 0
\(730\) 302.303 + 100.814i 0.414113 + 0.138102i
\(731\) 1416.76i 1.93812i
\(732\) 0 0
\(733\) 108.418 0.147910 0.0739551 0.997262i \(-0.476438\pi\)
0.0739551 + 0.997262i \(0.476438\pi\)
\(734\) 182.697 547.837i 0.248906 0.746372i
\(735\) 0 0
\(736\) 279.748 + 10.8174i 0.380092 + 0.0146975i
\(737\) 279.415 0.379125
\(738\) 0 0
\(739\) 209.058i 0.282893i 0.989946 + 0.141447i \(0.0451753\pi\)
−0.989946 + 0.141447i \(0.954825\pi\)
\(740\) −465.581 349.387i −0.629163 0.472145i
\(741\) 0 0
\(742\) 52.7655 158.224i 0.0711126 0.213239i
\(743\) 862.421i 1.16073i 0.814357 + 0.580364i \(0.197090\pi\)
−0.814357 + 0.580364i \(0.802910\pi\)
\(744\) 0 0
\(745\) 1453.94 1.95160
\(746\) 722.371 + 240.901i 0.968325 + 0.322924i
\(747\) 0 0
\(748\) −581.709 + 775.164i −0.777685 + 1.03632i
\(749\) 314.700 0.420161
\(750\) 0 0
\(751\) 167.423i 0.222933i 0.993768 + 0.111467i \(0.0355548\pi\)
−0.993768 + 0.111467i \(0.964445\pi\)
\(752\) 719.565 209.441i 0.956869 0.278512i
\(753\) 0 0
\(754\) 358.195 + 119.454i 0.475060 + 0.158426i
\(755\) 359.238i 0.475812i
\(756\) 0 0
\(757\) 347.592 0.459171 0.229586 0.973288i \(-0.426263\pi\)
0.229586 + 0.973288i \(0.426263\pi\)
\(758\) −111.590 + 334.615i −0.147216 + 0.441445i
\(759\) 0 0
\(760\) −166.129 + 114.910i −0.218590 + 0.151197i
\(761\) −1395.24 −1.83343 −0.916714 0.399544i \(-0.869168\pi\)
−0.916714 + 0.399544i \(0.869168\pi\)
\(762\) 0 0
\(763\) 907.854i 1.18985i
\(764\) 524.562 699.012i 0.686599 0.914937i
\(765\) 0 0
\(766\) −246.756 + 739.925i −0.322135 + 0.965960i
\(767\) 1405.46i 1.83241i
\(768\) 0 0
\(769\) 1104.80 1.43667 0.718333 0.695700i \(-0.244906\pi\)
0.718333 + 0.695700i \(0.244906\pi\)
\(770\) 521.668 + 173.970i 0.677490 + 0.225934i
\(771\) 0 0
\(772\) 198.194 + 148.731i 0.256728 + 0.192657i
\(773\) 1508.32 1.95125 0.975627 0.219436i \(-0.0704217\pi\)
0.975627 + 0.219436i \(0.0704217\pi\)
\(774\) 0 0
\(775\) 65.5148i 0.0845352i
\(776\) 42.5800 + 61.5591i 0.0548711 + 0.0793287i
\(777\) 0 0
\(778\) −9.64539 3.21661i −0.0123977 0.00413447i
\(779\) 216.577i 0.278019i
\(780\) 0 0
\(781\) 533.399 0.682969
\(782\) −166.011 + 497.804i −0.212290 + 0.636578i
\(783\) 0 0
\(784\) 64.7476 + 222.450i 0.0825862 + 0.283737i
\(785\) 580.137 0.739028
\(786\) 0 0
\(787\) 964.500i 1.22554i 0.790261 + 0.612770i \(0.209945\pi\)
−0.790261 + 0.612770i \(0.790055\pi\)
\(788\) 1136.88 + 853.149i 1.44274 + 1.08268i
\(789\) 0 0
\(790\) 150.175 450.317i 0.190095 0.570022i
\(791\)