Properties

Label 224.3.s.b.33.2
Level 224
Weight 3
Character 224.33
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 33.2
Root \(2.08703 + 2.02145i\) 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 \(\chi\) \(=\) 224.33
Dual form 224.3.s.b.129.2

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 \(-0.897913\pi\)
−0.201494 + 0.979490i \(0.564580\pi\)
\(4\) 0 0
\(5\) −7.80961 4.50888i −1.56192 0.901776i −0.997063 0.0765879i \(-0.975597\pi\)
−0.564859 0.825188i \(-0.691069\pi\)
\(6\) 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 0.946457 + 0.322830i \(0.104634\pi\)
−0.193650 + 0.981071i \(0.562033\pi\)
\(12\) 0 0
\(13\) 0.446263i 0.0343279i −0.999853 0.0171640i \(-0.994536\pi\)
0.999853 0.0171640i \(-0.00546373\pi\)
\(14\) 0 0
\(15\) 35.9399 2.39599
\(16\) 0 0
\(17\) 6.02041 3.47588i 0.354142 0.204464i −0.312366 0.949962i \(-0.601122\pi\)
0.666508 + 0.745498i \(0.267788\pi\)
\(18\) 0 0
\(19\) 11.0366 + 6.37198i 0.580873 + 0.335367i 0.761480 0.648188i \(-0.224473\pi\)
−0.180607 + 0.983555i \(0.557806\pi\)
\(20\) 0 0
\(21\) −10.6502 + 25.7854i −0.507151 + 1.22787i
\(22\) 0 0
\(23\) −13.2871 + 23.0140i −0.577701 + 1.00061i 0.418041 + 0.908428i \(0.362717\pi\)
−0.995742 + 0.0921795i \(0.970617\pi\)
\(24\) 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 \(-0.533824\pi\)
0.808110 + 0.589031i \(0.200491\pi\)
\(32\) 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 −0.0182908 0.999833i \(-0.505822\pi\)
0.875026 0.484076i \(-0.160844\pi\)
\(38\) 0 0
\(39\) 0.889283 + 1.54028i 0.0228021 + 0.0394944i
\(40\) 0 0
\(41\) 0.519795i 0.0126779i −0.999980 0.00633896i \(-0.997982\pi\)
0.999980 0.00633896i \(-0.00201777\pi\)
\(42\) 0 0
\(43\) 25.5364 0.593870 0.296935 0.954898i \(-0.404036\pi\)
0.296935 + 0.954898i \(0.404036\pi\)
\(44\) 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 \(-0.0727268\pi\)
0.290856 + 0.956767i \(0.406060\pi\)
\(48\) 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 0.897863 0.440274i \(-0.145119\pi\)
−0.830220 + 0.557435i \(0.811785\pi\)
\(54\) 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 \(-0.887395\pi\)
−0.169023 + 0.985612i \(0.554061\pi\)
\(60\) 0 0
\(61\) 39.8855 + 23.0279i 0.653861 + 0.377507i 0.789934 0.613192i \(-0.210115\pi\)
−0.136073 + 0.990699i \(0.543448\pi\)
\(62\) 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 \(-0.0631599\pi\)
−0.660903 + 0.750471i \(0.729827\pi\)
\(68\) 0 0
\(69\) 105.911i 1.53494i
\(70\) 0 0
\(71\) −60.0281 −0.845466 −0.422733 0.906254i \(-0.638929\pi\)
−0.422733 + 0.906254i \(0.638929\pi\)
\(72\) 0 0
\(73\) −40.5246 + 23.3969i −0.555132 + 0.320505i −0.751189 0.660087i \(-0.770519\pi\)
0.196058 + 0.980592i \(0.437186\pi\)
\(74\) 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 \(-0.945020\pi\)
0.641401 + 0.767206i \(0.278354\pi\)
\(80\) 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 0.768092 0.640339i \(-0.221206\pi\)
−0.170504 + 0.985357i \(0.554539\pi\)
\(90\) 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 \(-0.966537\pi\)
0.994479 0.104933i \(-0.0334629\pi\)
\(98\) 0 0
\(99\) 114.010 1.15161
\(100\) 0 0
\(101\) −155.237 + 89.6260i −1.53700 + 0.887386i −0.537985 + 0.842954i \(0.680814\pi\)
−0.999012 + 0.0444318i \(0.985852\pi\)
\(102\) 0 0
\(103\) 59.0242 + 34.0777i 0.573051 + 0.330851i 0.758367 0.651828i \(-0.225998\pi\)
−0.185316 + 0.982679i \(0.559331\pi\)
\(104\) 0 0
\(105\) 199.437 153.353i 1.89940 1.46051i
\(106\) 0 0
\(107\) 63.5657 110.099i 0.594072 1.02896i −0.399605 0.916688i \(-0.630853\pi\)
0.993677 0.112276i \(-0.0358141\pi\)
\(108\) 0 0
\(109\) 10.7852 + 18.6805i 0.0989468 + 0.171381i 0.911249 0.411856i \(-0.135119\pi\)
−0.812302 + 0.583237i \(0.801786\pi\)
\(110\) 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 \(-0.554090\pi\)
−0.169112 + 0.985597i \(0.554090\pi\)
\(128\) 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 \(-0.0700809\pi\)
0.298798 + 0.954316i \(0.403414\pi\)
\(132\) 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 −0.999223 0.0394252i \(-0.987447\pi\)
0.465468 0.885065i \(-0.345886\pi\)
\(138\) 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 −0.343839 0.939029i \(-0.611727\pi\)
0.985142 0.171741i \(-0.0549393\pi\)
\(150\) 0 0
\(151\) −14.3585 24.8696i −0.0950893 0.164700i 0.814557 0.580084i \(-0.196980\pi\)
−0.909646 + 0.415385i \(0.863647\pi\)
\(152\) 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 −0.110005 0.993931i \(-0.535087\pi\)
0.805767 + 0.592233i \(0.201753\pi\)
\(158\) 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 −0.152081 0.988368i \(-0.548597\pi\)
0.931992 0.362478i \(-0.118069\pi\)
\(164\) 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 0.730309 0.683117i \(-0.239376\pi\)
−0.226443 + 0.974025i \(0.572710\pi\)
\(174\) 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 0.986542 + 0.163506i \(0.0522804\pi\)
−0.351670 + 0.936124i \(0.614386\pi\)
\(180\) 0 0
\(181\) 27.1608i 0.150060i 0.997181 + 0.0750298i \(0.0239052\pi\)
−0.997181 + 0.0750298i \(0.976095\pi\)
\(182\) 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 \(-0.787081\pi\)
0.929297 + 0.369333i \(0.120414\pi\)
\(192\) 0 0
\(193\) 111.283 + 192.747i 0.576594 + 0.998689i 0.995866 + 0.0908292i \(0.0289517\pi\)
−0.419273 + 0.907860i \(0.637715\pi\)
\(194\) 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 \(-0.631173\pi\)
0.593263 + 0.805009i \(0.297840\pi\)
\(200\) 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 \(-0.393382\pi\)
0.328723 + 0.944426i \(0.393382\pi\)
\(212\) 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 −0.528930 + 0.848666i \(0.677406\pi\)
−0.999431 + 0.0337337i \(0.989260\pi\)
\(228\) 0 0
\(229\) −329.566 190.275i −1.43915 0.830895i −0.441361 0.897330i \(-0.645504\pi\)
−0.997791 + 0.0664348i \(0.978838\pi\)
\(230\) 0 0
\(231\) −458.030 + 60.7710i −1.98281 + 0.263078i
\(232\) 0 0
\(233\) 166.501 288.389i 0.714598 1.23772i −0.248516 0.968628i \(-0.579943\pi\)
0.963114 0.269093i \(-0.0867238\pi\)
\(234\) 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 \(-0.583378\pi\)
−0.258956 + 0.965889i \(0.583378\pi\)
\(240\) 0 0
\(241\) −72.1258 + 41.6418i −0.299277 + 0.172788i −0.642118 0.766606i \(-0.721944\pi\)
0.342841 + 0.939393i \(0.388611\pi\)
\(242\) 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 −0.00285088 0.999996i \(-0.500907\pi\)
−0.867447 + 0.497529i \(0.834241\pi\)
\(258\) 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 −0.948409 0.317050i \(-0.897308\pi\)
0.199631 0.979871i \(-0.436026\pi\)
\(264\) 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 −0.410829 0.911712i \(-0.634761\pi\)
0.584151 + 0.811645i \(0.301427\pi\)
\(270\) 0 0
\(271\) 41.1477 + 23.7567i 0.151837 + 0.0876629i 0.573993 0.818860i \(-0.305393\pi\)
−0.422157 + 0.906523i \(0.638727\pi\)
\(272\) 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 0.997710 0.0676314i \(-0.0215442\pi\)
−0.557426 + 0.830227i \(0.688211\pi\)
\(278\) 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 \(-0.637074\pi\)
0.578237 + 0.815869i \(0.303741\pi\)
\(284\) 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 \(-0.815433\pi\)
0.836554 0.547885i \(-0.184567\pi\)
\(294\) 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 \(-0.691357\pi\)
0.431390 + 0.902166i \(0.358023\pi\)
\(312\) 0 0
\(313\) 70.5536 + 40.7341i 0.225411 + 0.130141i 0.608453 0.793590i \(-0.291790\pi\)
−0.383042 + 0.923731i \(0.625124\pi\)
\(314\) 0 0
\(315\) −165.887 + 401.632i −0.526625 + 1.27502i
\(316\) 0 0
\(317\) −198.291 + 343.449i −0.625522 + 1.08344i 0.362917 + 0.931821i \(0.381781\pi\)
−0.988440 + 0.151615i \(0.951553\pi\)
\(318\) 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 0.246060 + 0.969255i \(0.420864\pi\)
−0.962429 + 0.271533i \(0.912469\pi\)
\(332\) 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 \(-0.0615742\pi\)
−0.657156 + 0.753754i \(0.728241\pi\)
\(348\) 0 0
\(349\) 414.621i 1.18802i 0.804456 + 0.594012i \(0.202457\pi\)
−0.804456 + 0.594012i \(0.797543\pi\)
\(350\) 0 0
\(351\) −3.76362 −0.0107226
\(352\) 0 0
\(353\) 173.723 100.299i 0.492134 0.284134i −0.233325 0.972399i \(-0.574961\pi\)
0.725459 + 0.688265i \(0.241627\pi\)
\(354\) 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 \(-0.900294\pi\)
0.742527 + 0.669817i \(0.233627\pi\)
\(360\) 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 \(-0.896916\pi\)
−0.198426 + 0.980116i \(0.563583\pi\)
\(368\) 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 −0.736736 0.676180i \(-0.763634\pi\)
0.953957 + 0.299942i \(0.0969674\pi\)
\(374\) 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 \(-0.671448\pi\)
−0.512951 + 0.858418i \(0.671448\pi\)
\(380\) 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 \(-0.321585\pi\)
−0.467702 + 0.883886i \(0.654918\pi\)
\(384\) 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 −0.932348 0.361562i \(-0.882244\pi\)
0.153052 0.988218i \(-0.451090\pi\)
\(390\) 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 0.985659 0.168750i \(-0.0539729\pi\)
0.346688 + 0.937980i \(0.387306\pi\)
\(398\) 0 0
\(399\) −281.846 + 216.720i −0.706380 + 0.543157i
\(400\) 0 0
\(401\) 107.055 185.424i 0.266969 0.462404i −0.701109 0.713054i \(-0.747311\pi\)
0.968078 + 0.250651i \(0.0806446\pi\)
\(402\) 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 −0.225778 0.974179i \(-0.572492\pi\)
0.730774 + 0.682619i \(0.239159\pi\)
\(410\) 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 −0.919931 0.392081i \(-0.871755\pi\)
0.120413 0.992724i \(-0.461578\pi\)
\(432\) 0 0
\(433\) 600.031i 1.38575i 0.721057 + 0.692876i \(0.243657\pi\)
−0.721057 + 0.692876i \(0.756343\pi\)
\(434\) 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 \(-0.273080\pi\)
−0.328116 + 0.944637i \(0.606414\pi\)
\(440\) 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 \(-0.907595\pi\)
0.726969 + 0.686670i \(0.240928\pi\)
\(444\) 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 −0.942147 0.335200i \(-0.891196\pi\)
0.761365 + 0.648323i \(0.224529\pi\)
\(458\) 0 0
\(459\) −29.3143 50.7738i −0.0638655 0.110618i
\(460\) 0 0
\(461\) 187.790i 0.407353i 0.979038 + 0.203677i \(0.0652891\pi\)
−0.979038 + 0.203677i \(0.934711\pi\)
\(462\) 0 0
\(463\) −678.682 −1.46584 −0.732918 0.680317i \(-0.761842\pi\)
−0.732918 + 0.680317i \(0.761842\pi\)
\(464\) 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 \(-0.327910\pi\)
−0.485174 + 0.874418i \(0.661244\pi\)
\(468\) 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 \(-0.470492\pi\)
0.908591 + 0.417686i \(0.137159\pi\)
\(480\) 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 \(-0.299070\pi\)
−0.994212 + 0.107435i \(0.965736\pi\)
\(488\) 0 0
\(489\) 1013.31i 2.07220i
\(490\) 0 0
\(491\) 96.8828 0.197317 0.0986586 0.995121i \(-0.468545\pi\)
0.0986586 + 0.995121i \(0.468545\pi\)
\(492\) 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 \(-0.882930\pi\)
0.777943 + 0.628335i \(0.216263\pi\)
\(500\) 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 0.425938 0.904752i \(-0.359944\pi\)
−0.570569 + 0.821249i \(0.693277\pi\)
\(510\) 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 −0.0441190 0.999026i \(-0.514048\pi\)
0.843123 + 0.537721i \(0.180715\pi\)
\(522\) 0 0
\(523\) −461.122 266.229i −0.881686 0.509042i −0.0104722 0.999945i \(-0.503333\pi\)
−0.871214 + 0.490903i \(0.836667\pi\)
\(524\) 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 −0.175593 0.984463i \(-0.556184\pi\)
0.940366 0.340164i \(-0.110483\pi\)
\(542\) 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 \(-0.708224\pi\)
−0.608489 + 0.793562i \(0.708224\pi\)
\(548\) 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 0.874360 0.485277i \(-0.161281\pi\)
−0.857443 + 0.514580i \(0.827948\pi\)
\(558\) 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 \(-0.516271\pi\)
0.839347 + 0.543596i \(0.182938\pi\)
\(564\) 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 −0.442725 0.896658i \(-0.645988\pi\)
0.997891 0.0649178i \(-0.0206785\pi\)
\(570\) 0 0
\(571\) 458.358 + 793.900i 0.802729 + 1.39037i 0.917813 + 0.397012i \(0.129953\pi\)
−0.115084 + 0.993356i \(0.536714\pi\)
\(572\) 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 −0.354889 0.934908i \(-0.615481\pi\)
0.632210 + 0.774797i \(0.282148\pi\)
\(578\) 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 0.853397 0.521261i \(-0.174538\pi\)
−0.0247264 + 0.999694i \(0.507871\pi\)
\(594\) 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 \(-0.0444079\pi\)
−0.615571 + 0.788081i \(0.711075\pi\)
\(600\) 0 0
\(601\) 939.633i 1.56345i −0.623623 0.781725i \(-0.714340\pi\)
0.623623 0.781725i \(-0.285660\pi\)
\(602\) 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 \(-0.275675\pi\)
−0.335804 + 0.941932i \(0.609008\pi\)
\(608\) 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 0.727093 0.686539i \(-0.240871\pi\)
−0.958107 + 0.286411i \(0.907538\pi\)
\(614\) 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 \(-0.506083\pi\)
0.856313 + 0.516457i \(0.172749\pi\)
\(620\) 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 \(-0.815767\pi\)
−0.837127 + 0.547008i \(0.815767\pi\)
\(632\) 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 0.532092 0.846686i \(-0.321406\pi\)
−0.999298 + 0.0374621i \(0.988073\pi\)
\(642\) 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 \(-0.789772\pi\)
0.136426 + 0.990650i \(0.456438\pi\)
\(648\) 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 −0.969523 0.245001i \(-0.921212\pi\)
0.696939 + 0.717131i \(0.254545\pi\)
\(654\) 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 \(-0.854322\pi\)
−0.897088 + 0.441852i \(0.854322\pi\)
\(660\) 0 0
\(661\) −76.0985 + 43.9355i −0.115126 + 0.0664682i −0.556457 0.830876i \(-0.687840\pi\)
0.441331 + 0.897344i \(0.354506\pi\)
\(662\) 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 0.553285 0.832992i \(-0.313374\pi\)
−0.444750 + 0.895655i \(0.646707\pi\)
\(678\) 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 \(-0.0954492\pi\)
−0.733503 + 0.679686i \(0.762116\pi\)
\(684\) 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 \(-0.392510\pi\)
−0.651461 + 0.758682i \(0.725844\pi\)
\(692\) 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 0.415244 + 0.909710i \(0.363696\pi\)
−0.995454 + 0.0952436i \(0.969637\pi\)
\(710\) 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 \(-0.00105202\pi\)
0.497135 + 0.867673i \(0.334385\pi\)
\(720\) 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 −0.0281317 0.999604i \(-0.508956\pi\)
−0.879749 + 0.475439i \(0.842289\pi\)
\(734\) 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 0.993445 + 0.114312i \(0.0364664\pi\)
−0.397725 + 0.917505i \(0.630200\pi\)
\(740\) 0 0
\(741\) 22.6660i 0.0305883i
\(742\) 0 0
\(743\) 984.949 1.32564 0.662819 0.748780i \(-0.269360\pi\)
0.662819 + 0.748780i \(0.269360\pi\)
\(744\) 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 \(-0.904706\pi\)
0.733172 + 0.680043i \(0.238039\pi\)
\(752\) 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 0.910675 0.413124i \(-0.135563\pi\)
0.0975611 + 0.995230i \(0.468896\pi\)
\(762\) 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 \(-0.912650\pi\)
0.962583 0.270988i \(-0.0873503\pi\)
\(770\) 0 0
\(771\) 1029.32 1.33504
\(772\) 0 0
\(773\) −57.9458 + 33.4550i −0.0749623 + 0.0432795i −0.537013 0.843574i \(-0.680447\pi\)
0.462050 + 0.886854i \(0.347114\pi\)
\(774\) 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 \(-0.950026\pi\)
−0.358443 + 0.933552i \(0.616692\pi\)
\(788\) 0 0
\(789\) 1359.40 + 784.851i 1.72294 + 0.994742i
\(790\) 0 0
\(791\)