Properties

Label 224.3.s.b.33.7
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 33.7
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 \(\chi\) \(=\) 224.33
Dual form 224.3.s.b.129.7

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

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

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 0.201494 0.979490i \(-0.435420\pi\)
0.949010 + 0.315246i \(0.102087\pi\)
\(4\) 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 \(-0.895366\pi\)
0.193650 0.981071i \(-0.437967\pi\)
\(12\) 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 0.180607 0.983555i \(-0.442194\pi\)
−0.761480 + 0.648188i \(0.775527\pi\)
\(20\) 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 \(-0.637283\pi\)
0.995742 0.0921795i \(-0.0293833\pi\)
\(24\) 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 −0.808110 0.589031i \(-0.799509\pi\)
0.106061 + 0.994360i \(0.466176\pi\)
\(32\) 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 \(-0.595964\pi\)
−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 −0.290856 0.956767i \(-0.593940\pi\)
−0.974012 + 0.226495i \(0.927273\pi\)
\(48\) 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 0.169023 0.985612i \(-0.445939\pi\)
0.938077 + 0.346428i \(0.112605\pi\)
\(60\) 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 0.660903 0.750471i \(-0.270173\pi\)
−0.980379 + 0.197123i \(0.936840\pi\)
\(68\) 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 −0.751189 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 −0.641401 0.767206i \(-0.721646\pi\)
0.985120 + 0.171866i \(0.0549796\pi\)
\(80\) 0 0
\(81\) 47.7835 + 82.7635i 0.589920 + 1.02177i
\(82\) 0 0
\(83\) 11.4213i 0.137606i 0.997630 + 0.0688028i \(0.0219179\pi\)
−0.997630 + 0.0688028i \(0.978082\pi\)
\(84\) 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 0.185316 0.982679i \(-0.440669\pi\)
−0.758367 + 0.651828i \(0.774002\pi\)
\(104\) 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 \(0.369147\pi\)
−0.993677 + 0.112276i \(0.964186\pi\)
\(108\) 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 \(-0.445910\pi\)
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 −0.298798 0.954316i \(-0.596586\pi\)
−0.975861 + 0.218391i \(0.929919\pi\)
\(132\) 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 \(-0.881595\pi\)
0.931610 0.363460i \(-0.118405\pi\)
\(140\) 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 0.909646 0.415385i \(-0.136353\pi\)
−0.814557 + 0.580084i \(0.803020\pi\)
\(152\) 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 \(0.451403\pi\)
−0.931992 + 0.362478i \(0.881931\pi\)
\(164\) 0 0
\(165\) 297.614 + 515.483i 1.80372 + 3.12414i
\(166\) 0 0
\(167\) 1.71028i 0.0102412i −0.999987 0.00512059i \(-0.998370\pi\)
0.999987 0.00512059i \(-0.00162994\pi\)
\(168\) 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 \(-0.947720\pi\)
0.351670 0.936124i \(-0.385614\pi\)
\(180\) 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 −0.929297 0.369333i \(-0.879586\pi\)
0.784500 + 0.620128i \(0.212919\pi\)
\(192\) 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 −0.593263 0.805009i \(-0.702160\pi\)
0.400527 + 0.916285i \(0.368827\pi\)
\(200\) 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 \(-0.961972\pi\)
0.992872 0.119185i \(-0.0380281\pi\)
\(224\) 0 0
\(225\) 387.701 1.72312
\(226\) 0 0
\(227\) 346.938 200.305i 1.52836 0.882399i 0.528930 0.848666i \(-0.322594\pi\)
0.999431 0.0337337i \(-0.0107398\pi\)
\(228\) 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 \(-0.416622\pi\)
0.258956 + 0.965889i \(0.416622\pi\)
\(240\) 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 \(-0.702551\pi\)
0.594250 0.804281i \(-0.297449\pi\)
\(252\) 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 \(0.102692\pi\)
−0.199631 + 0.979871i \(0.563974\pi\)
\(264\) 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 0.422157 0.906523i \(-0.361273\pi\)
−0.573993 + 0.818860i \(0.694607\pi\)
\(272\) 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 −0.578237 0.815869i \(-0.696259\pi\)
0.417445 + 0.908702i \(0.362926\pi\)
\(284\) 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 \(0.376245\pi\)
−0.379066 + 0.925370i \(0.623755\pi\)
\(308\) 0 0
\(309\) −271.630 −0.879063
\(310\) 0 0
\(311\) 41.7405 24.0989i 0.134214 0.0774884i −0.431390 0.902166i \(-0.641977\pi\)
0.565604 + 0.824677i \(0.308643\pi\)
\(312\) 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 \(-0.579136\pi\)
0.962429 0.271533i \(-0.0875305\pi\)
\(332\) 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 0.657156 0.753754i \(-0.271759\pi\)
−0.981349 + 0.192237i \(0.938426\pi\)
\(348\) 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 −0.742527 0.669817i \(-0.766373\pi\)
0.951342 + 0.308139i \(0.0997060\pi\)
\(360\) 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 0.198426 0.980116i \(-0.436417\pi\)
0.948018 + 0.318216i \(0.103084\pi\)
\(368\) 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 \(-0.328552\pi\)
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 0.467702 0.883886i \(-0.345082\pi\)
−0.531617 + 0.846985i \(0.678415\pi\)
\(384\) 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 \(0.0482138\pi\)
−0.988551 + 0.150890i \(0.951786\pi\)
\(420\) 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 \(0.128245\pi\)
−0.120413 + 0.992724i \(0.538422\pi\)
\(432\) 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 0.328116 0.944637i \(-0.393586\pi\)
−0.654022 + 0.756475i \(0.726920\pi\)
\(440\) 0 0
\(441\) −238.996 238.033i −0.541941 0.539758i
\(442\) 0 0
\(443\) 102.417 177.391i 0.231189 0.400431i −0.726969 0.686670i \(-0.759072\pi\)
0.958158 + 0.286239i \(0.0924052\pi\)
\(444\) 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 \(-0.238158\pi\)
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 0.485174 0.874418i \(-0.338756\pi\)
−0.514681 + 0.857382i \(0.672090\pi\)
\(468\) 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 −0.908591 0.417686i \(-0.862841\pi\)
−0.0925686 + 0.995706i \(0.529508\pi\)
\(480\) 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 0.994212 0.107435i \(-0.0342638\pi\)
−0.590148 + 0.807295i \(0.700930\pi\)
\(488\) 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 −0.777943 0.628335i \(-0.783737\pi\)
0.933126 + 0.359551i \(0.117070\pi\)
\(500\) 0 0
\(501\) −3.40812 5.90304i −0.00680264 0.0117825i
\(502\) 0 0
\(503\) 710.432i 1.41239i 0.708018 + 0.706194i \(0.249590\pi\)
−0.708018 + 0.706194i \(0.750410\pi\)
\(504\) 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 0.871214 0.490903i \(-0.163333\pi\)
0.0104722 + 0.999945i \(0.496667\pi\)
\(524\) 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 \(-0.291776\pi\)
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 0.874360 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 −0.839347 0.543596i \(-0.817062\pi\)
0.0510945 + 0.998694i \(0.483729\pi\)
\(564\) 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 \(-0.870047\pi\)
0.115084 0.993356i \(-0.463286\pi\)
\(572\) 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 \(0.0385420\pi\)
−0.992678 + 0.120788i \(0.961458\pi\)
\(588\) 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 0.615571 0.788081i \(-0.288925\pi\)
−0.990284 + 0.139059i \(0.955592\pi\)
\(600\) 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 0.335804 0.941932i \(-0.390992\pi\)
−0.647835 + 0.761781i \(0.724325\pi\)
\(608\) 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 −0.856313 0.516457i \(-0.827251\pi\)
0.0191078 + 0.999817i \(0.493917\pi\)
\(620\) 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 0.532092 0.846686i \(-0.321406\pi\)
−0.999298 + 0.0374621i \(0.988073\pi\)
\(642\) 0 0
\(643\) 707.781i 1.10075i 0.834918 + 0.550374i \(0.185515\pi\)
−0.834918 + 0.550374i \(0.814485\pi\)
\(644\) 0 0
\(645\) 917.776 1.42291
\(646\) 0 0
\(647\) 422.678 244.033i 0.653289 0.377177i −0.136426 0.990650i \(-0.543562\pi\)
0.789715 + 0.613474i \(0.210228\pi\)
\(648\) 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 \(-0.145678\pi\)
0.897088 + 0.441852i \(0.145678\pi\)
\(660\) 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 0.733503 0.679686i \(-0.237884\pi\)
−0.955377 + 0.295389i \(0.904551\pi\)
\(684\) 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 0.651461 0.758682i \(-0.274156\pi\)
−0.331307 + 0.943523i \(0.607490\pi\)
\(692\) 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 −0.497135 0.867673i \(-0.665615\pi\)
−0.999995 + 0.00330501i \(0.998948\pi\)
\(720\) 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 \(-0.750924\pi\)
0.709156 0.705052i \(-0.249076\pi\)
\(728\) 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 \(-0.963534\pi\)
0.397725 0.917505i \(-0.369800\pi\)
\(740\) 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 −0.733172 0.680043i \(-0.761961\pi\)
0.955521 + 0.294924i \(0.0952943\pi\)
\(752\) 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 0.358443 0.933552i \(-0.383308\pi\)
0.987701 + 0.156355i \(0.0499745\pi\)
\(788\) 0 0
\(789\) 1359.40 + 784.851i 1.72294 + 0.994742i
\(790\) 0 0