Properties

Label 224.3.s.b.129.7
Level 224
Weight 3
Character 224.129
Analytic conductor 6.104
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{20}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.7
Root \(-2.79414 + 0.796701i\) of \(x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} - 33728 x^{7} - 49760 x^{6} + 203528 x^{5} + 27401 x^{4} - 156928 x^{3} + 114964 x^{2} - 248608 x + 208849\)
Character \(\chi\) \(=\) 224.129
Dual form 224.3.s.b.33.7

$q$-expansion

\(f(q)\) \(=\) \(q+(3.45151 + 1.99273i) q^{3} +(-7.80961 + 4.50888i) q^{5} +(-5.54917 - 4.26693i) q^{7} +(3.44195 + 5.96164i) q^{9} +O(q^{10})\) \(q+(3.45151 + 1.99273i) q^{3} +(-7.80961 + 4.50888i) q^{5} +(-5.54917 - 4.26693i) q^{7} +(3.44195 + 5.96164i) q^{9} +(-8.28088 + 14.3429i) q^{11} +0.446263i q^{13} -35.9399 q^{15} +(6.02041 + 3.47588i) q^{17} +(-11.0366 + 6.37198i) q^{19} +(-10.6502 - 25.7854i) q^{21} +(13.2871 + 23.0140i) q^{23} +(28.1600 - 48.7745i) q^{25} -8.43362i q^{27} +26.4655 q^{29} +(-21.7635 - 12.5652i) q^{31} +(-57.1631 + 33.0031i) q^{33} +(62.5759 + 8.30251i) q^{35} +(31.6992 + 54.9046i) q^{37} +(-0.889283 + 1.54028i) q^{39} +0.519795i q^{41} -25.5364 q^{43} +(-53.7606 - 31.0387i) q^{45} +(-59.4488 + 34.3228i) q^{47} +(12.5866 + 47.3559i) q^{49} +(13.8530 + 23.9941i) q^{51} +(3.58507 - 6.20953i) q^{53} -149.350i q^{55} -50.7906 q^{57} +(65.3189 + 37.7119i) q^{59} +(39.8855 - 23.0279i) q^{61} +(6.33791 - 47.7687i) q^{63} +(-2.01215 - 3.48514i) q^{65} +(-21.4049 + 37.0743i) q^{67} +105.911i q^{69} +60.0281 q^{71} +(-40.5246 - 23.3969i) q^{73} +(194.389 - 112.230i) q^{75} +(107.152 - 44.2573i) q^{77} +(27.1539 + 47.0319i) q^{79} +(47.7835 - 82.7635i) q^{81} -11.4213i q^{83} -62.6894 q^{85} +(91.3459 + 52.7386i) q^{87} +(53.1854 - 30.7066i) q^{89} +(1.90417 - 2.47639i) q^{91} +(-50.0780 - 86.7377i) q^{93} +(57.4610 - 99.5253i) q^{95} +20.3570i q^{97} -114.010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 40q^{9} + O(q^{10}) \) \( 16q + 40q^{9} - 48q^{17} - 136q^{21} + 80q^{25} - 16q^{29} - 264q^{33} + 72q^{37} + 312q^{45} + 128q^{49} + 40q^{53} + 368q^{57} + 216q^{61} - 168q^{65} - 312q^{73} + 64q^{77} - 384q^{81} - 1072q^{85} + 24q^{89} - 168q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.45151 + 1.99273i 1.15050 + 0.664244i 0.949010 0.315246i \(-0.102087\pi\)
0.201494 + 0.979490i \(0.435420\pi\)
\(4\) 0 0
\(5\) −7.80961 + 4.50888i −1.56192 + 0.901776i −0.564859 + 0.825188i \(0.691069\pi\)
−0.997063 + 0.0765879i \(0.975597\pi\)
\(6\) 0 0
\(7\) −5.54917 4.26693i −0.792739 0.609562i
\(8\) 0 0
\(9\) 3.44195 + 5.96164i 0.382439 + 0.662404i
\(10\) 0 0
\(11\) −8.28088 + 14.3429i −0.752807 + 1.30390i 0.193650 + 0.981071i \(0.437967\pi\)
−0.946457 + 0.322830i \(0.895366\pi\)
\(12\) 0 0
\(13\) 0.446263i 0.0343279i 0.999853 + 0.0171640i \(0.00546373\pi\)
−0.999853 + 0.0171640i \(0.994536\pi\)
\(14\) 0 0
\(15\) −35.9399 −2.39599
\(16\) 0 0
\(17\) 6.02041 + 3.47588i 0.354142 + 0.204464i 0.666508 0.745498i \(-0.267788\pi\)
−0.312366 + 0.949962i \(0.601122\pi\)
\(18\) 0 0
\(19\) −11.0366 + 6.37198i −0.580873 + 0.335367i −0.761480 0.648188i \(-0.775527\pi\)
0.180607 + 0.983555i \(0.442194\pi\)
\(20\) 0 0
\(21\) −10.6502 25.7854i −0.507151 1.22787i
\(22\) 0 0
\(23\) 13.2871 + 23.0140i 0.577701 + 1.00061i 0.995742 + 0.0921795i \(0.0293833\pi\)
−0.418041 + 0.908428i \(0.637283\pi\)
\(24\) 0 0
\(25\) 28.1600 48.7745i 1.12640 1.95098i
\(26\) 0 0
\(27\) 8.43362i 0.312356i
\(28\) 0 0
\(29\) 26.4655 0.912603 0.456301 0.889825i \(-0.349174\pi\)
0.456301 + 0.889825i \(0.349174\pi\)
\(30\) 0 0
\(31\) −21.7635 12.5652i −0.702049 0.405328i 0.106061 0.994360i \(-0.466176\pi\)
−0.808110 + 0.589031i \(0.799509\pi\)
\(32\) 0 0
\(33\) −57.1631 + 33.0031i −1.73221 + 1.00009i
\(34\) 0 0
\(35\) 62.5759 + 8.30251i 1.78788 + 0.237215i
\(36\) 0 0
\(37\) 31.6992 + 54.9046i 0.856735 + 1.48391i 0.875026 + 0.484076i \(0.160844\pi\)
−0.0182908 + 0.999833i \(0.505822\pi\)
\(38\) 0 0
\(39\) −0.889283 + 1.54028i −0.0228021 + 0.0394944i
\(40\) 0 0
\(41\) 0.519795i 0.0126779i 0.999980 + 0.00633896i \(0.00201777\pi\)
−0.999980 + 0.00633896i \(0.997982\pi\)
\(42\) 0 0
\(43\) −25.5364 −0.593870 −0.296935 0.954898i \(-0.595964\pi\)
−0.296935 + 0.954898i \(0.595964\pi\)
\(44\) 0 0
\(45\) −53.7606 31.0387i −1.19468 0.689749i
\(46\) 0 0
\(47\) −59.4488 + 34.3228i −1.26487 + 0.730272i −0.974012 0.226495i \(-0.927273\pi\)
−0.290856 + 0.956767i \(0.593940\pi\)
\(48\) 0 0
\(49\) 12.5866 + 47.3559i 0.256869 + 0.966446i
\(50\) 0 0
\(51\) 13.8530 + 23.9941i 0.271627 + 0.470473i
\(52\) 0 0
\(53\) 3.58507 6.20953i 0.0676429 0.117161i −0.830220 0.557435i \(-0.811785\pi\)
0.897863 + 0.440274i \(0.145119\pi\)
\(54\) 0 0
\(55\) 149.350i 2.71545i
\(56\) 0 0
\(57\) −50.7906 −0.891062
\(58\) 0 0
\(59\) 65.3189 + 37.7119i 1.10710 + 0.639184i 0.938077 0.346428i \(-0.112605\pi\)
0.169023 + 0.985612i \(0.445939\pi\)
\(60\) 0 0
\(61\) 39.8855 23.0279i 0.653861 0.377507i −0.136073 0.990699i \(-0.543448\pi\)
0.789934 + 0.613192i \(0.210115\pi\)
\(62\) 0 0
\(63\) 6.33791 47.7687i 0.100602 0.758233i
\(64\) 0 0
\(65\) −2.01215 3.48514i −0.0309561 0.0536175i
\(66\) 0 0
\(67\) −21.4049 + 37.0743i −0.319476 + 0.553348i −0.980379 0.197123i \(-0.936840\pi\)
0.660903 + 0.750471i \(0.270173\pi\)
\(68\) 0 0
\(69\) 105.911i 1.53494i
\(70\) 0 0
\(71\) 60.0281 0.845466 0.422733 0.906254i \(-0.361071\pi\)
0.422733 + 0.906254i \(0.361071\pi\)
\(72\) 0 0
\(73\) −40.5246 23.3969i −0.555132 0.320505i 0.196058 0.980592i \(-0.437186\pi\)
−0.751189 + 0.660087i \(0.770519\pi\)
\(74\) 0 0
\(75\) 194.389 112.230i 2.59185 1.49641i
\(76\) 0 0
\(77\) 107.152 44.2573i 1.39159 0.574770i
\(78\) 0 0
\(79\) 27.1539 + 47.0319i 0.343720 + 0.595340i 0.985120 0.171866i \(-0.0549796\pi\)
−0.641401 + 0.767206i \(0.721646\pi\)
\(80\) 0 0
\(81\) 47.7835 82.7635i 0.589920 1.02177i
\(82\) 0 0
\(83\) 11.4213i 0.137606i −0.997630 0.0688028i \(-0.978082\pi\)
0.997630 0.0688028i \(-0.0219179\pi\)
\(84\) 0 0
\(85\) −62.6894 −0.737522
\(86\) 0 0
\(87\) 91.3459 + 52.7386i 1.04995 + 0.606190i
\(88\) 0 0
\(89\) 53.1854 30.7066i 0.597589 0.345018i −0.170504 0.985357i \(-0.554539\pi\)
0.768092 + 0.640339i \(0.221206\pi\)
\(90\) 0 0
\(91\) 1.90417 2.47639i 0.0209250 0.0272131i
\(92\) 0 0
\(93\) −50.0780 86.7377i −0.538473 0.932663i
\(94\) 0 0
\(95\) 57.4610 99.5253i 0.604852 1.04763i
\(96\) 0 0
\(97\) 20.3570i 0.209866i 0.994479 + 0.104933i \(0.0334629\pi\)
−0.994479 + 0.104933i \(0.966537\pi\)
\(98\) 0 0
\(99\) −114.010 −1.15161
\(100\) 0 0
\(101\) −155.237 89.6260i −1.53700 0.887386i −0.999012 0.0444318i \(-0.985852\pi\)
−0.537985 0.842954i \(-0.680814\pi\)
\(102\) 0 0
\(103\) −59.0242 + 34.0777i −0.573051 + 0.330851i −0.758367 0.651828i \(-0.774002\pi\)
0.185316 + 0.982679i \(0.440669\pi\)
\(104\) 0 0
\(105\) 199.437 + 153.353i 1.89940 + 1.46051i
\(106\) 0 0
\(107\) −63.5657 110.099i −0.594072 1.02896i −0.993677 0.112276i \(-0.964186\pi\)
0.399605 0.916688i \(-0.369147\pi\)
\(108\) 0 0
\(109\) 10.7852 18.6805i 0.0989468 0.171381i −0.812302 0.583237i \(-0.801786\pi\)
0.911249 + 0.411856i \(0.135119\pi\)
\(110\) 0 0
\(111\) 252.672i 2.27632i
\(112\) 0 0
\(113\) 82.1812 0.727267 0.363634 0.931542i \(-0.381536\pi\)
0.363634 + 0.931542i \(0.381536\pi\)
\(114\) 0 0
\(115\) −207.534 119.820i −1.80465 1.04191i
\(116\) 0 0
\(117\) −2.66046 + 1.53602i −0.0227390 + 0.0131283i
\(118\) 0 0
\(119\) −18.5769 44.9769i −0.156109 0.377957i
\(120\) 0 0
\(121\) −76.6459 132.755i −0.633437 1.09715i
\(122\) 0 0
\(123\) −1.03581 + 1.79408i −0.00842123 + 0.0145860i
\(124\) 0 0
\(125\) 282.436i 2.25949i
\(126\) 0 0
\(127\) 42.9545 0.338225 0.169112 0.985597i \(-0.445910\pi\)
0.169112 + 0.985597i \(0.445910\pi\)
\(128\) 0 0
\(129\) −88.1392 50.8872i −0.683249 0.394474i
\(130\) 0 0
\(131\) −166.980 + 96.4062i −1.27466 + 0.735925i −0.975861 0.218391i \(-0.929919\pi\)
−0.298798 + 0.954316i \(0.596586\pi\)
\(132\) 0 0
\(133\) 88.4327 + 11.7332i 0.664908 + 0.0882193i
\(134\) 0 0
\(135\) 38.0262 + 65.8633i 0.281675 + 0.487876i
\(136\) 0 0
\(137\) −73.1244 + 126.655i −0.533754 + 0.924490i 0.465468 + 0.885065i \(0.345886\pi\)
−0.999223 + 0.0394252i \(0.987447\pi\)
\(138\) 0 0
\(139\) 101.042i 0.726921i 0.931610 + 0.363460i \(0.118405\pi\)
−0.931610 + 0.363460i \(0.881595\pi\)
\(140\) 0 0
\(141\) −273.584 −1.94031
\(142\) 0 0
\(143\) −6.40071 3.69545i −0.0447602 0.0258423i
\(144\) 0 0
\(145\) −206.685 + 119.330i −1.42541 + 0.822963i
\(146\) 0 0
\(147\) −50.9247 + 188.531i −0.346426 + 1.28252i
\(148\) 0 0
\(149\) 95.5542 + 165.505i 0.641303 + 1.11077i 0.985142 + 0.171741i \(0.0549393\pi\)
−0.343839 + 0.939029i \(0.611727\pi\)
\(150\) 0 0
\(151\) 14.3585 24.8696i 0.0950893 0.164700i −0.814557 0.580084i \(-0.803020\pi\)
0.909646 + 0.415385i \(0.136353\pi\)
\(152\) 0 0
\(153\) 47.8553i 0.312780i
\(154\) 0 0
\(155\) 226.619 1.46206
\(156\) 0 0
\(157\) 109.235 + 63.0666i 0.695762 + 0.401698i 0.805767 0.592233i \(-0.201753\pi\)
−0.110005 + 0.993931i \(0.535087\pi\)
\(158\) 0 0
\(159\) 24.7478 14.2882i 0.155647 0.0898627i
\(160\) 0 0
\(161\) 24.4665 184.404i 0.151966 1.14536i
\(162\) 0 0
\(163\) −127.126 220.188i −0.779911 1.35085i −0.931992 0.362478i \(-0.881931\pi\)
0.152081 0.988368i \(-0.451403\pi\)
\(164\) 0 0
\(165\) 297.614 515.483i 1.80372 3.12414i
\(166\) 0 0
\(167\) 1.71028i 0.0102412i 0.999987 + 0.00512059i \(0.00162994\pi\)
−0.999987 + 0.00512059i \(0.998370\pi\)
\(168\) 0 0
\(169\) 168.801 0.998822
\(170\) 0 0
\(171\) −75.9748 43.8641i −0.444297 0.256515i
\(172\) 0 0
\(173\) 87.1688 50.3270i 0.503866 0.290907i −0.226443 0.974025i \(-0.572710\pi\)
0.730309 + 0.683117i \(0.239376\pi\)
\(174\) 0 0
\(175\) −364.382 + 150.501i −2.08218 + 0.860008i
\(176\) 0 0
\(177\) 150.299 + 260.326i 0.849148 + 1.47077i
\(178\) 0 0
\(179\) −113.642 + 196.834i −0.634872 + 1.09963i 0.351670 + 0.936124i \(0.385614\pi\)
−0.986542 + 0.163506i \(0.947720\pi\)
\(180\) 0 0
\(181\) 27.1608i 0.150060i −0.997181 0.0750298i \(-0.976095\pi\)
0.997181 0.0750298i \(-0.0239052\pi\)
\(182\) 0 0
\(183\) 183.554 1.00303
\(184\) 0 0
\(185\) −495.117 285.856i −2.67631 1.54517i
\(186\) 0 0
\(187\) −99.7085 + 57.5667i −0.533201 + 0.307844i
\(188\) 0 0
\(189\) −35.9857 + 46.7996i −0.190400 + 0.247617i
\(190\) 0 0
\(191\) −27.6562 47.9019i −0.144797 0.250795i 0.784500 0.620128i \(-0.212919\pi\)
−0.929297 + 0.369333i \(0.879586\pi\)
\(192\) 0 0
\(193\) 111.283 192.747i 0.576594 0.998689i −0.419273 0.907860i \(-0.637715\pi\)
0.995866 0.0908292i \(-0.0289517\pi\)
\(194\) 0 0
\(195\) 16.0387i 0.0822496i
\(196\) 0 0
\(197\) −15.2516 −0.0774191 −0.0387095 0.999251i \(-0.512325\pi\)
−0.0387095 + 0.999251i \(0.512325\pi\)
\(198\) 0 0
\(199\) −38.3544 22.1439i −0.192736 0.111276i 0.400527 0.916285i \(-0.368827\pi\)
−0.593263 + 0.805009i \(0.702160\pi\)
\(200\) 0 0
\(201\) −147.758 + 85.3083i −0.735116 + 0.424419i
\(202\) 0 0
\(203\) −146.861 112.926i −0.723455 0.556287i
\(204\) 0 0
\(205\) −2.34369 4.05939i −0.0114326 0.0198019i
\(206\) 0 0
\(207\) −91.4673 + 158.426i −0.441871 + 0.765343i
\(208\) 0 0
\(209\) 211.062i 1.00987i
\(210\) 0 0
\(211\) −138.721 −0.657446 −0.328723 0.944426i \(-0.606618\pi\)
−0.328723 + 0.944426i \(0.606618\pi\)
\(212\) 0 0
\(213\) 207.188 + 119.620i 0.972712 + 0.561596i
\(214\) 0 0
\(215\) 199.429 115.141i 0.927578 0.535537i
\(216\) 0 0
\(217\) 67.1548 + 162.590i 0.309469 + 0.749261i
\(218\) 0 0
\(219\) −93.2474 161.509i −0.425787 0.737485i
\(220\) 0 0
\(221\) −1.55116 + 2.68669i −0.00701882 + 0.0121570i
\(222\) 0 0
\(223\) 53.1564i 0.238370i 0.992872 + 0.119185i \(0.0380281\pi\)
−0.992872 + 0.119185i \(0.961972\pi\)
\(224\) 0 0
\(225\) 387.701 1.72312
\(226\) 0 0
\(227\) 346.938 + 200.305i 1.52836 + 0.882399i 0.999431 + 0.0337337i \(0.0107398\pi\)
0.528930 + 0.848666i \(0.322594\pi\)
\(228\) 0 0
\(229\) −329.566 + 190.275i −1.43915 + 0.830895i −0.997791 0.0664348i \(-0.978838\pi\)
−0.441361 + 0.897330i \(0.645504\pi\)
\(230\) 0 0
\(231\) 458.030 + 60.7710i 1.98281 + 0.263078i
\(232\) 0 0
\(233\) 166.501 + 288.389i 0.714598 + 1.23772i 0.963114 + 0.269093i \(0.0867238\pi\)
−0.248516 + 0.968628i \(0.579943\pi\)
\(234\) 0 0
\(235\) 309.514 536.095i 1.31708 2.28125i
\(236\) 0 0
\(237\) 216.441i 0.913255i
\(238\) 0 0
\(239\) 123.781 0.517912 0.258956 0.965889i \(-0.416622\pi\)
0.258956 + 0.965889i \(0.416622\pi\)
\(240\) 0 0
\(241\) −72.1258 41.6418i −0.299277 0.172788i 0.342841 0.939393i \(-0.388611\pi\)
−0.642118 + 0.766606i \(0.721944\pi\)
\(242\) 0 0
\(243\) 264.117 152.488i 1.08690 0.627523i
\(244\) 0 0
\(245\) −311.818 313.079i −1.27273 1.27787i
\(246\) 0 0
\(247\) −2.84358 4.92523i −0.0115125 0.0199402i
\(248\) 0 0
\(249\) 22.7595 39.4206i 0.0914036 0.158316i
\(250\) 0 0
\(251\) 403.749i 1.60856i 0.594250 + 0.804281i \(0.297449\pi\)
−0.594250 + 0.804281i \(0.702551\pi\)
\(252\) 0 0
\(253\) −440.116 −1.73959
\(254\) 0 0
\(255\) −216.373 124.923i −0.848521 0.489894i
\(256\) 0 0
\(257\) −223.667 + 129.134i −0.870298 + 0.502467i −0.867447 0.497529i \(-0.834241\pi\)
−0.00285088 + 0.999996i \(0.500907\pi\)
\(258\) 0 0
\(259\) 58.3699 439.933i 0.225367 1.69858i
\(260\) 0 0
\(261\) 91.0929 + 157.778i 0.349015 + 0.604512i
\(262\) 0 0
\(263\) 196.929 341.090i 0.748778 1.29692i −0.199631 0.979871i \(-0.563974\pi\)
0.948409 0.317050i \(-0.102692\pi\)
\(264\) 0 0
\(265\) 64.6586i 0.243995i
\(266\) 0 0
\(267\) 244.760 0.916704
\(268\) 0 0
\(269\) 46.6236 + 26.9181i 0.173322 + 0.100067i 0.584151 0.811645i \(-0.301427\pi\)
−0.410829 + 0.911712i \(0.634761\pi\)
\(270\) 0 0
\(271\) −41.1477 + 23.7567i −0.151837 + 0.0876629i −0.573993 0.818860i \(-0.694607\pi\)
0.422157 + 0.906523i \(0.361273\pi\)
\(272\) 0 0
\(273\) 11.5071 4.75278i 0.0421504 0.0174095i
\(274\) 0 0
\(275\) 466.379 + 807.791i 1.69592 + 2.93742i
\(276\) 0 0
\(277\) 121.959 211.239i 0.440285 0.762595i −0.557426 0.830227i \(-0.688211\pi\)
0.997710 + 0.0676314i \(0.0215442\pi\)
\(278\) 0 0
\(279\) 172.995i 0.620053i
\(280\) 0 0
\(281\) 173.857 0.618709 0.309355 0.950947i \(-0.399887\pi\)
0.309355 + 0.950947i \(0.399887\pi\)
\(282\) 0 0
\(283\) −45.5040 26.2717i −0.160792 0.0928330i 0.417445 0.908702i \(-0.362926\pi\)
−0.578237 + 0.815869i \(0.696259\pi\)
\(284\) 0 0
\(285\) 396.654 229.008i 1.39177 0.803539i
\(286\) 0 0
\(287\) 2.21793 2.88443i 0.00772797 0.0100503i
\(288\) 0 0
\(289\) −120.336 208.429i −0.416389 0.721207i
\(290\) 0 0
\(291\) −40.5661 + 70.2625i −0.139402 + 0.241452i
\(292\) 0 0
\(293\) 321.060i 1.09577i 0.836554 + 0.547885i \(0.184567\pi\)
−0.836554 + 0.547885i \(0.815433\pi\)
\(294\) 0 0
\(295\) −680.153 −2.30560
\(296\) 0 0
\(297\) 120.963 + 69.8378i 0.407282 + 0.235144i
\(298\) 0 0
\(299\) −10.2703 + 5.92955i −0.0343488 + 0.0198313i
\(300\) 0 0
\(301\) 141.706 + 108.962i 0.470784 + 0.362000i
\(302\) 0 0
\(303\) −357.201 618.690i −1.17888 2.04188i
\(304\) 0 0
\(305\) −207.660 + 359.678i −0.680853 + 1.17927i
\(306\) 0 0
\(307\) 568.177i 1.85074i −0.379066 0.925370i \(-0.623755\pi\)
0.379066 0.925370i \(-0.376245\pi\)
\(308\) 0 0
\(309\) −271.630 −0.879063
\(310\) 0 0
\(311\) 41.7405 + 24.0989i 0.134214 + 0.0774884i 0.565604 0.824677i \(-0.308643\pi\)
−0.431390 + 0.902166i \(0.641977\pi\)
\(312\) 0 0
\(313\) 70.5536 40.7341i 0.225411 0.130141i −0.383042 0.923731i \(-0.625124\pi\)
0.608453 + 0.793590i \(0.291790\pi\)
\(314\) 0 0
\(315\) 165.887 + 401.632i 0.526625 + 1.27502i
\(316\) 0 0
\(317\) −198.291 343.449i −0.625522 1.08344i −0.988440 0.151615i \(-0.951553\pi\)
0.362917 0.931821i \(-0.381781\pi\)
\(318\) 0 0
\(319\) −219.157 + 379.592i −0.687014 + 1.18994i
\(320\) 0 0
\(321\) 506.678i 1.57844i
\(322\) 0 0
\(323\) −88.5930 −0.274282
\(324\) 0 0
\(325\) 21.7663 + 12.5668i 0.0669731 + 0.0386670i
\(326\) 0 0
\(327\) 74.4505 42.9840i 0.227677 0.131450i
\(328\) 0 0
\(329\) 476.344 + 63.2009i 1.44786 + 0.192100i
\(330\) 0 0
\(331\) 237.118 + 410.701i 0.716369 + 1.24079i 0.962429 + 0.271533i \(0.0875305\pi\)
−0.246060 + 0.969255i \(0.579136\pi\)
\(332\) 0 0
\(333\) −218.214 + 377.958i −0.655298 + 1.13501i
\(334\) 0 0
\(335\) 386.048i 1.15238i
\(336\) 0 0
\(337\) 234.392 0.695526 0.347763 0.937583i \(-0.386941\pi\)
0.347763 + 0.937583i \(0.386941\pi\)
\(338\) 0 0
\(339\) 283.649 + 163.765i 0.836724 + 0.483083i
\(340\) 0 0
\(341\) 360.442 208.101i 1.05702 0.610268i
\(342\) 0 0
\(343\) 132.219 316.492i 0.385478 0.922717i
\(344\) 0 0
\(345\) −477.538 827.120i −1.38417 2.39745i
\(346\) 0 0
\(347\) −112.495 + 194.846i −0.324192 + 0.561517i −0.981349 0.192237i \(-0.938426\pi\)
0.657156 + 0.753754i \(0.271759\pi\)
\(348\) 0 0
\(349\) 414.621i 1.18802i −0.804456 0.594012i \(-0.797543\pi\)
0.804456 0.594012i \(-0.202457\pi\)
\(350\) 0 0
\(351\) 3.76362 0.0107226
\(352\) 0 0
\(353\) 173.723 + 100.299i 0.492134 + 0.284134i 0.725459 0.688265i \(-0.241627\pi\)
−0.233325 + 0.972399i \(0.574961\pi\)
\(354\) 0 0
\(355\) −468.796 + 270.659i −1.32055 + 0.762421i
\(356\) 0 0
\(357\) 25.5085 192.257i 0.0714524 0.538536i
\(358\) 0 0
\(359\) 74.9646 + 129.842i 0.208815 + 0.361678i 0.951342 0.308139i \(-0.0997060\pi\)
−0.742527 + 0.669817i \(0.766373\pi\)
\(360\) 0 0
\(361\) −99.2957 + 171.985i −0.275057 + 0.476413i
\(362\) 0 0
\(363\) 610.939i 1.68303i
\(364\) 0 0
\(365\) 421.975 1.15610
\(366\) 0 0
\(367\) 420.745 + 242.917i 1.14644 + 0.661900i 0.948018 0.318216i \(-0.103084\pi\)
0.198426 + 0.980116i \(0.436417\pi\)
\(368\) 0 0
\(369\) −3.09883 + 1.78911i −0.00839790 + 0.00484853i
\(370\) 0 0
\(371\) −46.3898 + 19.1605i −0.125040 + 0.0516455i
\(372\) 0 0
\(373\) 81.0234 + 140.337i 0.217221 + 0.376238i 0.953957 0.299942i \(-0.0969674\pi\)
−0.736736 + 0.676180i \(0.763634\pi\)
\(374\) 0 0
\(375\) −562.818 + 974.830i −1.50085 + 2.59955i
\(376\) 0 0
\(377\) 11.8106i 0.0313278i
\(378\) 0 0
\(379\) 388.817 1.02590 0.512951 0.858418i \(-0.328552\pi\)
0.512951 + 0.858418i \(0.328552\pi\)
\(380\) 0 0
\(381\) 148.258 + 85.5968i 0.389129 + 0.224664i
\(382\) 0 0
\(383\) −24.4796 + 14.1333i −0.0639153 + 0.0369015i −0.531617 0.846985i \(-0.678415\pi\)
0.467702 + 0.883886i \(0.345082\pi\)
\(384\) 0 0
\(385\) −637.266 + 828.768i −1.65524 + 2.15264i
\(386\) 0 0
\(387\) −87.8951 152.239i −0.227119 0.393382i
\(388\) 0 0
\(389\) −303.146 + 525.065i −0.779296 + 1.34978i 0.153052 + 0.988218i \(0.451090\pi\)
−0.932348 + 0.361562i \(0.882244\pi\)
\(390\) 0 0
\(391\) 184.738i 0.472476i
\(392\) 0 0
\(393\) −768.446 −1.95533
\(394\) 0 0
\(395\) −424.122 244.867i −1.07373 0.619916i
\(396\) 0 0
\(397\) 528.942 305.385i 1.33235 0.769231i 0.346688 0.937980i \(-0.387306\pi\)
0.985659 + 0.168750i \(0.0539729\pi\)
\(398\) 0 0
\(399\) 281.846 + 216.720i 0.706380 + 0.543157i
\(400\) 0 0
\(401\) 107.055 + 185.424i 0.266969 + 0.462404i 0.968078 0.250651i \(-0.0806446\pi\)
−0.701109 + 0.713054i \(0.747311\pi\)
\(402\) 0 0
\(403\) 5.60738 9.71226i 0.0139141 0.0240999i
\(404\) 0 0
\(405\) 861.800i 2.12790i
\(406\) 0 0
\(407\) −1049.99 −2.57983
\(408\) 0 0
\(409\) 206.544 + 119.248i 0.504996 + 0.291560i 0.730774 0.682619i \(-0.239159\pi\)
−0.225778 + 0.974179i \(0.572492\pi\)
\(410\) 0 0
\(411\) −504.779 + 291.434i −1.22817 + 0.709086i
\(412\) 0 0
\(413\) −201.552 487.981i −0.488019 1.18155i
\(414\) 0 0
\(415\) 51.4971 + 89.1955i 0.124089 + 0.214929i
\(416\) 0 0
\(417\) −201.349 + 348.748i −0.482852 + 0.836325i
\(418\) 0 0
\(419\) 126.446i 0.301779i −0.988551 0.150890i \(-0.951786\pi\)
0.988551 0.150890i \(-0.0482138\pi\)
\(420\) 0 0
\(421\) −113.097 −0.268639 −0.134319 0.990938i \(-0.542885\pi\)
−0.134319 + 0.990938i \(0.542885\pi\)
\(422\) 0 0
\(423\) −409.240 236.275i −0.967470 0.558569i
\(424\) 0 0
\(425\) 339.069 195.762i 0.797809 0.460615i
\(426\) 0 0
\(427\) −319.590 42.4029i −0.748455 0.0993043i
\(428\) 0 0
\(429\) −14.7281 25.5098i −0.0343312 0.0594634i
\(430\) 0 0
\(431\) 344.592 596.851i 0.799517 1.38480i −0.120413 0.992724i \(-0.538422\pi\)
0.919931 0.392081i \(-0.128245\pi\)
\(432\) 0 0
\(433\) 600.031i 1.38575i −0.721057 0.692876i \(-0.756343\pi\)
0.721057 0.692876i \(-0.243657\pi\)
\(434\) 0 0
\(435\) −951.167 −2.18659
\(436\) 0 0
\(437\) −293.289 169.331i −0.671142 0.387484i
\(438\) 0 0
\(439\) −143.073 + 82.6032i −0.325906 + 0.188162i −0.654022 0.756475i \(-0.726920\pi\)
0.328116 + 0.944637i \(0.393586\pi\)
\(440\) 0 0
\(441\) −238.996 + 238.033i −0.541941 + 0.539758i
\(442\) 0 0
\(443\) 102.417 + 177.391i 0.231189 + 0.400431i 0.958158 0.286239i \(-0.0924052\pi\)
−0.726969 + 0.686670i \(0.759072\pi\)
\(444\) 0 0
\(445\) −276.905 + 479.613i −0.622258 + 1.07778i
\(446\) 0 0
\(447\) 761.655i 1.70393i
\(448\) 0 0
\(449\) −112.007 −0.249458 −0.124729 0.992191i \(-0.539806\pi\)
−0.124729 + 0.992191i \(0.539806\pi\)
\(450\) 0 0
\(451\) −7.45536 4.30436i −0.0165307 0.00954403i
\(452\) 0 0
\(453\) 99.1169 57.2252i 0.218801 0.126325i
\(454\) 0 0
\(455\) −3.70511 + 27.9253i −0.00814309 + 0.0613744i
\(456\) 0 0
\(457\) −82.6173 143.097i −0.180782 0.313123i 0.761365 0.648323i \(-0.224529\pi\)
−0.942147 + 0.335200i \(0.891196\pi\)
\(458\) 0 0
\(459\) 29.3143 50.7738i 0.0638655 0.110618i
\(460\) 0 0
\(461\) 187.790i 0.407353i −0.979038 0.203677i \(-0.934711\pi\)
0.979038 0.203677i \(-0.0652891\pi\)
\(462\) 0 0
\(463\) 678.682 1.46584 0.732918 0.680317i \(-0.238158\pi\)
0.732918 + 0.680317i \(0.238158\pi\)
\(464\) 0 0
\(465\) 782.179 + 451.591i 1.68211 + 0.971164i
\(466\) 0 0
\(467\) −13.7799 + 7.95581i −0.0295072 + 0.0170360i −0.514681 0.857382i \(-0.672090\pi\)
0.485174 + 0.874418i \(0.338756\pi\)
\(468\) 0 0
\(469\) 276.973 114.399i 0.590560 0.243920i
\(470\) 0 0
\(471\) 251.350 + 435.350i 0.533651 + 0.924311i
\(472\) 0 0
\(473\) 211.464 366.266i 0.447069 0.774347i
\(474\) 0 0
\(475\) 717.739i 1.51103i
\(476\) 0 0
\(477\) 49.3586 0.103477
\(478\) 0 0
\(479\) −479.556 276.872i −1.00116 0.578020i −0.0925686 0.995706i \(-0.529508\pi\)
−0.908591 + 0.417686i \(0.862841\pi\)
\(480\) 0 0
\(481\) −24.5019 + 14.1462i −0.0509395 + 0.0294100i
\(482\) 0 0
\(483\) 451.913 587.716i 0.935638 1.21680i
\(484\) 0 0
\(485\) −91.7874 158.980i −0.189252 0.327795i
\(486\) 0 0
\(487\) 196.779 340.832i 0.404065 0.699860i −0.590148 0.807295i \(-0.700930\pi\)
0.994212 + 0.107435i \(0.0342638\pi\)
\(488\) 0 0
\(489\) 1013.31i 2.07220i
\(490\) 0 0
\(491\) −96.8828 −0.197317 −0.0986586 0.995121i \(-0.531455\pi\)
−0.0986586 + 0.995121i \(0.531455\pi\)
\(492\) 0 0
\(493\) 159.333 + 91.9909i 0.323191 + 0.186594i
\(494\) 0 0
\(495\) 890.370 514.055i 1.79873 1.03850i
\(496\) 0 0
\(497\) −333.106 256.136i −0.670234 0.515364i
\(498\) 0 0
\(499\) 77.4362 + 134.123i 0.155183 + 0.268784i 0.933126 0.359551i \(-0.117070\pi\)
−0.777943 + 0.628335i \(0.783737\pi\)
\(500\) 0 0
\(501\) −3.40812 + 5.90304i −0.00680264 + 0.0117825i
\(502\) 0 0
\(503\) 710.432i 1.41239i −0.708018 0.706194i \(-0.750410\pi\)
0.708018 0.706194i \(-0.249590\pi\)
\(504\) 0 0
\(505\) 1616.45 3.20089
\(506\) 0 0
\(507\) 582.618 + 336.375i 1.14915 + 0.663461i
\(508\) 0 0
\(509\) −73.6172 + 42.5029i −0.144631 + 0.0835027i −0.570569 0.821249i \(-0.693277\pi\)
0.425938 + 0.904752i \(0.359944\pi\)
\(510\) 0 0
\(511\) 125.045 + 302.749i 0.244707 + 0.592464i
\(512\) 0 0
\(513\) 53.7389 + 93.0784i 0.104754 + 0.181439i
\(514\) 0 0
\(515\) 307.304 532.266i 0.596707 1.03353i
\(516\) 0 0
\(517\) 1136.89i 2.19902i
\(518\) 0 0
\(519\) 401.152 0.772933
\(520\) 0 0
\(521\) 416.281 + 240.340i 0.799004 + 0.461305i 0.843123 0.537721i \(-0.180715\pi\)
−0.0441190 + 0.999026i \(0.514048\pi\)
\(522\) 0 0
\(523\) 461.122 266.229i 0.881686 0.509042i 0.0104722 0.999945i \(-0.496667\pi\)
0.871214 + 0.490903i \(0.163333\pi\)
\(524\) 0 0
\(525\) −1557.58 206.658i −2.96681 0.393634i
\(526\) 0 0
\(527\) −87.3502 151.295i −0.165750 0.287087i
\(528\) 0 0
\(529\) −88.5952 + 153.451i −0.167477 + 0.290078i
\(530\) 0 0
\(531\) 519.210i 0.977796i
\(532\) 0 0
\(533\) −0.231965 −0.000435207
\(534\) 0 0
\(535\) 992.847 + 573.220i 1.85579 + 1.07144i
\(536\) 0 0
\(537\) −784.474 + 452.916i −1.46084 + 0.843419i
\(538\) 0 0
\(539\) −783.449 211.620i −1.45352 0.392615i
\(540\) 0 0
\(541\) 413.743 + 716.623i 0.764774 + 1.32463i 0.940366 + 0.340164i \(0.110483\pi\)
−0.175593 + 0.984463i \(0.556184\pi\)
\(542\) 0 0
\(543\) 54.1241 93.7458i 0.0996761 0.172644i
\(544\) 0 0
\(545\) 194.517i 0.356911i
\(546\) 0 0
\(547\) 665.687 1.21698 0.608489 0.793562i \(-0.291776\pi\)
0.608489 + 0.793562i \(0.291776\pi\)
\(548\) 0 0
\(549\) 274.568 + 158.522i 0.500124 + 0.288747i
\(550\) 0 0
\(551\) −292.089 + 168.637i −0.530107 + 0.306057i
\(552\) 0 0
\(553\) 50.0003 376.852i 0.0904165 0.681467i
\(554\) 0 0
\(555\) −1139.27 1973.27i −2.05273 3.55544i
\(556\) 0 0
\(557\) 9.42314 16.3214i 0.0169177 0.0293023i −0.857443 0.514580i \(-0.827948\pi\)
0.874360 + 0.485277i \(0.161281\pi\)
\(558\) 0 0
\(559\) 11.3960i 0.0203863i
\(560\) 0 0
\(561\) −458.860 −0.817932
\(562\) 0 0
\(563\) −443.786 256.220i −0.788253 0.455098i 0.0510945 0.998694i \(-0.483729\pi\)
−0.839347 + 0.543596i \(0.817062\pi\)
\(564\) 0 0
\(565\) −641.803 + 370.545i −1.13593 + 0.655832i
\(566\) 0 0
\(567\) −618.305 + 255.380i −1.09048 + 0.450405i
\(568\) 0 0
\(569\) 315.889 + 547.136i 0.555166 + 0.961575i 0.997891 + 0.0649178i \(0.0206785\pi\)
−0.442725 + 0.896658i \(0.645988\pi\)
\(570\) 0 0
\(571\) −458.358 + 793.900i −0.802729 + 1.39037i 0.115084 + 0.993356i \(0.463286\pi\)
−0.917813 + 0.397012i \(0.870047\pi\)
\(572\) 0 0
\(573\) 220.445i 0.384721i
\(574\) 0 0
\(575\) 1496.66 2.60289
\(576\) 0 0
\(577\) 160.014 + 92.3843i 0.277321 + 0.160111i 0.632210 0.774797i \(-0.282148\pi\)
−0.354889 + 0.934908i \(0.615481\pi\)
\(578\) 0 0
\(579\) 768.186 443.512i 1.32675 0.765997i
\(580\) 0 0
\(581\) −48.7337 + 63.3785i −0.0838790 + 0.109085i
\(582\) 0 0
\(583\) 59.3751 + 102.841i 0.101844 + 0.176399i
\(584\) 0 0
\(585\) 13.8514 23.9914i 0.0236776 0.0410109i
\(586\) 0 0
\(587\) 141.805i 0.241575i −0.992678 0.120788i \(-0.961458\pi\)
0.992678 0.120788i \(-0.0385420\pi\)
\(588\) 0 0
\(589\) 320.260 0.543735
\(590\) 0 0
\(591\) −52.6409 30.3923i −0.0890710 0.0514251i
\(592\) 0 0
\(593\) 491.402 283.711i 0.828671 0.478433i −0.0247264 0.999694i \(-0.507871\pi\)
0.853397 + 0.521261i \(0.174538\pi\)
\(594\) 0 0
\(595\) 347.874 + 267.491i 0.584662 + 0.449565i
\(596\) 0 0
\(597\) −88.2538 152.860i −0.147829 0.256047i
\(598\) 0 0
\(599\) −224.453 + 388.764i −0.374713 + 0.649022i −0.990284 0.139059i \(-0.955592\pi\)
0.615571 + 0.788081i \(0.288925\pi\)
\(600\) 0 0
\(601\) 939.633i 1.56345i 0.623623 + 0.781725i \(0.285660\pi\)
−0.623623 + 0.781725i \(0.714340\pi\)
\(602\) 0 0
\(603\) −294.698 −0.488720
\(604\) 0 0
\(605\) 1197.15 + 691.174i 1.97876 + 1.14244i
\(606\) 0 0
\(607\) −189.403 + 109.352i −0.312031 + 0.180151i −0.647835 0.761781i \(-0.724325\pi\)
0.335804 + 0.941932i \(0.390992\pi\)
\(608\) 0 0
\(609\) −281.862 682.422i −0.462828 1.12056i
\(610\) 0 0
\(611\) −15.3170 26.5298i −0.0250687 0.0434203i
\(612\) 0 0
\(613\) −141.612 + 245.279i −0.231014 + 0.400128i −0.958107 0.286411i \(-0.907538\pi\)
0.727093 + 0.686539i \(0.240871\pi\)
\(614\) 0 0
\(615\) 18.6814i 0.0303762i
\(616\) 0 0
\(617\) −1099.79 −1.78247 −0.891236 0.453539i \(-0.850161\pi\)
−0.891236 + 0.453539i \(0.850161\pi\)
\(618\) 0 0
\(619\) −518.230 299.200i −0.837206 0.483361i 0.0191078 0.999817i \(-0.493917\pi\)
−0.856313 + 0.516457i \(0.827251\pi\)
\(620\) 0 0
\(621\) 194.091 112.059i 0.312546 0.180449i
\(622\) 0 0
\(623\) −426.158 56.5422i −0.684042 0.0907580i
\(624\) 0 0
\(625\) −569.469 986.349i −0.911150 1.57816i
\(626\) 0 0
\(627\) 420.590 728.484i 0.670798 1.16186i
\(628\) 0 0
\(629\) 440.731i 0.700685i
\(630\) 0 0
\(631\) 1056.45 1.67425 0.837127 0.547008i \(-0.184233\pi\)
0.837127 + 0.547008i \(0.184233\pi\)
\(632\) 0 0
\(633\) −478.797 276.434i −0.756394 0.436704i
\(634\) 0 0
\(635\) −335.458 + 193.677i −0.528280 + 0.305003i
\(636\) 0 0
\(637\) −21.1332 + 5.61694i −0.0331761 + 0.00881780i
\(638\) 0 0
\(639\) 206.614 + 357.866i 0.323339 + 0.560040i
\(640\) 0 0
\(641\) −299.479 + 518.713i −0.467206 + 0.809224i −0.999298 0.0374621i \(-0.988073\pi\)
0.532092 + 0.846686i \(0.321406\pi\)
\(642\) 0 0
\(643\) 707.781i 1.10075i −0.834918 0.550374i \(-0.814485\pi\)
0.834918 0.550374i \(-0.185515\pi\)
\(644\) 0 0
\(645\) 917.776 1.42291
\(646\) 0 0
\(647\) 422.678 + 244.033i 0.653289 + 0.377177i 0.789715 0.613474i \(-0.210228\pi\)
−0.136426 + 0.990650i \(0.543562\pi\)
\(648\) 0 0
\(649\) −1081.80 + 624.575i −1.66686 + 0.962365i
\(650\) 0 0
\(651\) −92.2121 + 695.002i −0.141647 + 1.06759i
\(652\) 0 0
\(653\) −177.997 308.300i −0.272584 0.472129i 0.696939 0.717131i \(-0.254545\pi\)
−0.969523 + 0.245001i \(0.921212\pi\)
\(654\) 0 0
\(655\) 869.368 1505.79i 1.32728 2.29891i
\(656\) 0 0
\(657\) 322.124i 0.490295i
\(658\) 0 0
\(659\) 1182.36 1.79418 0.897088 0.441852i \(-0.145678\pi\)
0.897088 + 0.441852i \(0.145678\pi\)
\(660\) 0 0
\(661\) −76.0985 43.9355i −0.115126 0.0664682i 0.441331 0.897344i \(-0.354506\pi\)
−0.556457 + 0.830876i \(0.687840\pi\)
\(662\) 0 0
\(663\) −10.7077 + 6.18209i −0.0161504 + 0.00932441i
\(664\) 0 0
\(665\) −743.528 + 307.101i −1.11809 + 0.461806i
\(666\) 0 0
\(667\) 351.650 + 609.076i 0.527211 + 0.913157i
\(668\) 0 0
\(669\) −105.926 + 183.470i −0.158336 + 0.274245i
\(670\) 0 0
\(671\) 762.766i 1.13676i
\(672\) 0 0
\(673\) 939.720 1.39631 0.698157 0.715944i \(-0.254004\pi\)
0.698157 + 0.715944i \(0.254004\pi\)
\(674\) 0 0
\(675\) −411.346 237.491i −0.609401 0.351838i
\(676\) 0 0
\(677\) 73.4780 42.4226i 0.108535 0.0626626i −0.444750 0.895655i \(-0.646707\pi\)
0.553285 + 0.832992i \(0.313374\pi\)
\(678\) 0 0
\(679\) 86.8621 112.965i 0.127926 0.166369i
\(680\) 0 0
\(681\) 798.306 + 1382.71i 1.17226 + 2.03041i
\(682\) 0 0
\(683\) −151.540 + 262.475i −0.221874 + 0.384297i −0.955377 0.295389i \(-0.904551\pi\)
0.733503 + 0.679686i \(0.237884\pi\)
\(684\) 0 0
\(685\) 1318.84i 1.92531i
\(686\) 0 0
\(687\) −1516.67 −2.20767
\(688\) 0 0
\(689\) 2.77108 + 1.59989i 0.00402189 + 0.00232204i
\(690\) 0 0
\(691\) 221.226 127.725i 0.320154 0.184841i −0.331307 0.943523i \(-0.607490\pi\)
0.651461 + 0.758682i \(0.274156\pi\)
\(692\) 0 0
\(693\) 632.658 + 486.471i 0.912927 + 0.701978i
\(694\) 0 0
\(695\) −455.586 789.098i −0.655519 1.13539i
\(696\) 0 0
\(697\) −1.80675 + 3.12938i −0.00259217 + 0.00448978i
\(698\) 0 0
\(699\) 1327.17i 1.89867i
\(700\) 0 0
\(701\) −560.333 −0.799333 −0.399667 0.916661i \(-0.630874\pi\)
−0.399667 + 0.916661i \(0.630874\pi\)
\(702\) 0 0
\(703\) −699.702 403.973i −0.995309 0.574642i
\(704\) 0 0
\(705\) 2136.58 1233.56i 3.03062 1.74973i
\(706\) 0 0
\(707\) 479.007 + 1159.73i 0.677521 + 1.64036i
\(708\) 0 0
\(709\) −411.369 712.512i −0.580210 1.00495i −0.995454 0.0952436i \(-0.969637\pi\)
0.415244 0.909710i \(-0.363696\pi\)
\(710\) 0 0
\(711\) −186.925 + 323.763i −0.262904 + 0.455363i
\(712\) 0 0
\(713\) 667.820i 0.936634i
\(714\) 0 0
\(715\) 66.6494 0.0932159
\(716\) 0 0
\(717\) 427.231 + 246.662i 0.595860 + 0.344020i
\(718\) 0 0
\(719\) −1076.44 + 621.481i −1.49713 + 0.864368i −0.999995 0.00330501i \(-0.998948\pi\)
−0.497135 + 0.867673i \(0.665615\pi\)
\(720\) 0 0
\(721\) 472.943 + 62.7496i 0.655954 + 0.0870313i
\(722\) 0 0
\(723\) −165.962 287.454i −0.229546 0.397586i
\(724\) 0 0
\(725\) 745.267 1290.84i 1.02795 1.78047i
\(726\) 0 0
\(727\) 1025.14i 1.41010i 0.709156 + 0.705052i \(0.249076\pi\)
−0.709156 + 0.705052i \(0.750924\pi\)
\(728\) 0 0
\(729\) 355.367 0.487472
\(730\) 0 0
\(731\) −153.740 88.7616i −0.210314 0.121425i
\(732\) 0 0
\(733\) −665.476 + 384.213i −0.907880 + 0.524165i −0.879749 0.475439i \(-0.842289\pi\)
−0.0281317 + 0.999604i \(0.508956\pi\)
\(734\) 0 0
\(735\) −452.362 1701.97i −0.615458 2.31560i
\(736\) 0 0
\(737\) −354.502 614.016i −0.481007 0.833129i
\(738\) 0 0
\(739\) −440.237 + 762.513i −0.595720 + 1.03182i 0.397725 + 0.917505i \(0.369800\pi\)
−0.993445 + 0.114312i \(0.963534\pi\)
\(740\) 0 0
\(741\) 22.6660i 0.0305883i
\(742\) 0 0
\(743\) −984.949 −1.32564 −0.662819 0.748780i \(-0.730640\pi\)
−0.662819 + 0.748780i \(0.730640\pi\)
\(744\) 0 0
\(745\) −1492.48 861.685i −2.00333 1.15662i
\(746\) 0 0
\(747\) 68.0894 39.3114i 0.0911504 0.0526257i
\(748\) 0 0
\(749\) −117.048 + 882.189i −0.156272 + 1.17782i
\(750\) 0 0
\(751\) 166.984 + 289.224i 0.222349 + 0.385119i 0.955521 0.294924i \(-0.0952943\pi\)
−0.733172 + 0.680043i \(0.761961\pi\)
\(752\) 0 0
\(753\) −804.563 + 1393.54i −1.06848 + 1.85066i
\(754\) 0 0
\(755\) 258.963i 0.342997i
\(756\) 0 0
\(757\) −964.869 −1.27460 −0.637298 0.770617i \(-0.719948\pi\)
−0.637298 + 0.770617i \(0.719948\pi\)
\(758\) 0 0
\(759\) −1519.07 877.033i −2.00140 1.15551i
\(760\) 0 0
\(761\) 767.267 442.982i 1.00824 0.582105i 0.0975611 0.995230i \(-0.468896\pi\)
0.910675 + 0.413124i \(0.135563\pi\)
\(762\) 0 0
\(763\) −139.557 + 57.6417i −0.182906 + 0.0755461i
\(764\) 0 0
\(765\) −215.774 373.731i −0.282057 0.488537i
\(766\) 0 0
\(767\) −16.8294 + 29.1494i −0.0219419 + 0.0380045i
\(768\) 0 0
\(769\) 416.779i 0.541976i 0.962583 + 0.270988i \(0.0873503\pi\)
−0.962583 + 0.270988i \(0.912650\pi\)
\(770\) 0 0
\(771\) −1029.32 −1.33504
\(772\) 0 0
\(773\) −57.9458 33.4550i −0.0749623 0.0432795i 0.462050 0.886854i \(-0.347114\pi\)
−0.537013 + 0.843574i \(0.680447\pi\)
\(774\) 0 0
\(775\) −1225.72 + 707.670i −1.58157 + 0.913122i
\(776\) 0 0
\(777\) 1078.13 1402.12i 1.38756 1.80453i
\(778\) 0 0
\(779\) −3.31212 5.73676i −0.00425176 0.00736426i
\(780\) 0 0
\(781\) −497.085 + 860.977i −0.636473 + 1.10240i
\(782\) 0 0
\(783\) 223.200i 0.285057i
\(784\) 0 0
\(785\) −1137.44 −1.44897
\(786\) 0 0
\(787\) 1059.42 + 611.654i 1.34614 + 0.777196i 0.987701 0.156355i \(-0.0499745\pi\)
0.358443 + 0.933552i \(0.383308\pi\)
\(788\) 0 0
\(789\) 1359.40 784.851i 1.72294 0.994742i
\(790\) 0 0