Properties

Label 315.3.ca.b.37.11
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.11
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.84280 - 0.493776i) q^{2} +(-0.312015 + 0.180142i) q^{4} +(1.82066 + 4.65674i) q^{5} +(-6.63712 - 2.22456i) q^{7} +(-5.88211 + 5.88211i) q^{8} +O(q^{10})\) \(q+(1.84280 - 0.493776i) q^{2} +(-0.312015 + 0.180142i) q^{4} +(1.82066 + 4.65674i) q^{5} +(-6.63712 - 2.22456i) q^{7} +(-5.88211 + 5.88211i) q^{8} +(5.65448 + 7.68243i) q^{10} +(5.24180 + 9.07906i) q^{11} +(1.40565 - 1.40565i) q^{13} +(-13.3293 - 0.822171i) q^{14} +(-7.21453 + 12.4959i) q^{16} +(-6.55621 + 24.4681i) q^{17} +(-9.07193 - 5.23768i) q^{19} +(-1.40694 - 1.12499i) q^{20} +(14.1426 + 14.1426i) q^{22} +(7.89111 + 29.4500i) q^{23} +(-18.3704 + 16.9566i) q^{25} +(1.89626 - 3.28441i) q^{26} +(2.47161 - 0.501525i) q^{28} -55.6217i q^{29} +(8.12663 + 14.0757i) q^{31} +(1.48729 - 5.55064i) q^{32} +48.3271i q^{34} +(-1.72469 - 34.9575i) q^{35} +(14.8150 - 3.96966i) q^{37} +(-19.3040 - 5.17248i) q^{38} +(-38.1008 - 16.6822i) q^{40} +28.7305 q^{41} +(3.17014 - 3.17014i) q^{43} +(-3.27104 - 1.88853i) q^{44} +(29.0834 + 50.3740i) q^{46} +(1.71038 - 0.458294i) q^{47} +(39.1026 + 29.5294i) q^{49} +(-25.4802 + 40.3185i) q^{50} +(-0.185367 + 0.691801i) q^{52} +(56.9591 + 15.2621i) q^{53} +(-32.7353 + 40.9395i) q^{55} +(52.1254 - 25.9551i) q^{56} +(-27.4647 - 102.499i) q^{58} +(-57.7727 + 33.3551i) q^{59} +(6.16473 - 10.6776i) q^{61} +(21.9260 + 21.9260i) q^{62} -68.6793i q^{64} +(9.10496 + 3.98655i) q^{65} +(28.5890 - 106.696i) q^{67} +(-2.36209 - 8.81545i) q^{68} +(-20.4394 - 63.5679i) q^{70} -29.9403 q^{71} +(115.286 + 30.8909i) q^{73} +(25.3408 - 14.6305i) q^{74} +3.77410 q^{76} +(-14.5935 - 71.9195i) q^{77} +(-99.9248 - 57.6916i) q^{79} +(-71.3255 - 10.8454i) q^{80} +(52.9444 - 14.1864i) q^{82} +(-24.2475 + 24.2475i) q^{83} +(-125.878 + 14.0174i) q^{85} +(4.27659 - 7.40727i) q^{86} +(-84.2370 - 22.5712i) q^{88} +(-18.3646 - 10.6028i) q^{89} +(-12.4564 + 6.20252i) q^{91} +(-7.76732 - 7.76732i) q^{92} +(2.92558 - 1.68909i) q^{94} +(7.87366 - 51.7816i) q^{95} +(56.7300 + 56.7300i) q^{97} +(86.6391 + 35.1087i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84280 0.493776i 0.921399 0.246888i 0.233216 0.972425i \(-0.425075\pi\)
0.688183 + 0.725537i \(0.258409\pi\)
\(3\) 0 0
\(4\) −0.312015 + 0.180142i −0.0780037 + 0.0450354i
\(5\) 1.82066 + 4.65674i 0.364131 + 0.931348i
\(6\) 0 0
\(7\) −6.63712 2.22456i −0.948160 0.317795i
\(8\) −5.88211 + 5.88211i −0.735264 + 0.735264i
\(9\) 0 0
\(10\) 5.65448 + 7.68243i 0.565448 + 0.768243i
\(11\) 5.24180 + 9.07906i 0.476527 + 0.825369i 0.999638 0.0268951i \(-0.00856202\pi\)
−0.523111 + 0.852265i \(0.675229\pi\)
\(12\) 0 0
\(13\) 1.40565 1.40565i 0.108127 0.108127i −0.650973 0.759101i \(-0.725639\pi\)
0.759101 + 0.650973i \(0.225639\pi\)
\(14\) −13.3293 0.822171i −0.952093 0.0587265i
\(15\) 0 0
\(16\) −7.21453 + 12.4959i −0.450908 + 0.780996i
\(17\) −6.55621 + 24.4681i −0.385659 + 1.43930i 0.451465 + 0.892289i \(0.350901\pi\)
−0.837125 + 0.547012i \(0.815765\pi\)
\(18\) 0 0
\(19\) −9.07193 5.23768i −0.477470 0.275667i 0.241892 0.970303i \(-0.422232\pi\)
−0.719362 + 0.694636i \(0.755566\pi\)
\(20\) −1.40694 1.12499i −0.0703472 0.0562497i
\(21\) 0 0
\(22\) 14.1426 + 14.1426i 0.642845 + 0.642845i
\(23\) 7.89111 + 29.4500i 0.343092 + 1.28044i 0.894826 + 0.446416i \(0.147300\pi\)
−0.551734 + 0.834020i \(0.686034\pi\)
\(24\) 0 0
\(25\) −18.3704 + 16.9566i −0.734817 + 0.678265i
\(26\) 1.89626 3.28441i 0.0729329 0.126323i
\(27\) 0 0
\(28\) 2.47161 0.501525i 0.0882719 0.0179116i
\(29\) 55.6217i 1.91799i −0.283425 0.958994i \(-0.591471\pi\)
0.283425 0.958994i \(-0.408529\pi\)
\(30\) 0 0
\(31\) 8.12663 + 14.0757i 0.262149 + 0.454056i 0.966813 0.255486i \(-0.0822354\pi\)
−0.704664 + 0.709542i \(0.748902\pi\)
\(32\) 1.48729 5.55064i 0.0464778 0.173457i
\(33\) 0 0
\(34\) 48.3271i 1.42138i
\(35\) −1.72469 34.9575i −0.0492768 0.998785i
\(36\) 0 0
\(37\) 14.8150 3.96966i 0.400404 0.107288i −0.0529966 0.998595i \(-0.516877\pi\)
0.453401 + 0.891307i \(0.350211\pi\)
\(38\) −19.3040 5.17248i −0.507999 0.136118i
\(39\) 0 0
\(40\) −38.1008 16.6822i −0.952519 0.417054i
\(41\) 28.7305 0.700743 0.350371 0.936611i \(-0.386055\pi\)
0.350371 + 0.936611i \(0.386055\pi\)
\(42\) 0 0
\(43\) 3.17014 3.17014i 0.0737243 0.0737243i −0.669283 0.743007i \(-0.733399\pi\)
0.743007 + 0.669283i \(0.233399\pi\)
\(44\) −3.27104 1.88853i −0.0743417 0.0429212i
\(45\) 0 0
\(46\) 29.0834 + 50.3740i 0.632249 + 1.09509i
\(47\) 1.71038 0.458294i 0.0363910 0.00975094i −0.240578 0.970630i \(-0.577337\pi\)
0.276969 + 0.960879i \(0.410670\pi\)
\(48\) 0 0
\(49\) 39.1026 + 29.5294i 0.798013 + 0.602640i
\(50\) −25.4802 + 40.3185i −0.509604 + 0.806370i
\(51\) 0 0
\(52\) −0.185367 + 0.691801i −0.00356476 + 0.0133039i
\(53\) 56.9591 + 15.2621i 1.07470 + 0.287965i 0.752423 0.658680i \(-0.228885\pi\)
0.322277 + 0.946645i \(0.395552\pi\)
\(54\) 0 0
\(55\) −32.7353 + 40.9395i −0.595188 + 0.744355i
\(56\) 52.1254 25.9551i 0.930811 0.463485i
\(57\) 0 0
\(58\) −27.4647 102.499i −0.473528 1.76723i
\(59\) −57.7727 + 33.3551i −0.979198 + 0.565340i −0.902028 0.431678i \(-0.857922\pi\)
−0.0771698 + 0.997018i \(0.524588\pi\)
\(60\) 0 0
\(61\) 6.16473 10.6776i 0.101061 0.175043i −0.811061 0.584962i \(-0.801110\pi\)
0.912122 + 0.409919i \(0.134443\pi\)
\(62\) 21.9260 + 21.9260i 0.353645 + 0.353645i
\(63\) 0 0
\(64\) 68.6793i 1.07311i
\(65\) 9.10496 + 3.98655i 0.140076 + 0.0613315i
\(66\) 0 0
\(67\) 28.5890 106.696i 0.426702 1.59247i −0.333476 0.942758i \(-0.608222\pi\)
0.760178 0.649715i \(-0.225112\pi\)
\(68\) −2.36209 8.81545i −0.0347367 0.129639i
\(69\) 0 0
\(70\) −20.4394 63.5679i −0.291992 0.908113i
\(71\) −29.9403 −0.421694 −0.210847 0.977519i \(-0.567622\pi\)
−0.210847 + 0.977519i \(0.567622\pi\)
\(72\) 0 0
\(73\) 115.286 + 30.8909i 1.57926 + 0.423162i 0.938698 0.344741i \(-0.112033\pi\)
0.640566 + 0.767903i \(0.278700\pi\)
\(74\) 25.3408 14.6305i 0.342444 0.197710i
\(75\) 0 0
\(76\) 3.77410 0.0496592
\(77\) −14.5935 71.9195i −0.189526 0.934020i
\(78\) 0 0
\(79\) −99.9248 57.6916i −1.26487 0.730274i −0.290858 0.956766i \(-0.593941\pi\)
−0.974013 + 0.226492i \(0.927274\pi\)
\(80\) −71.3255 10.8454i −0.891568 0.135567i
\(81\) 0 0
\(82\) 52.9444 14.1864i 0.645663 0.173005i
\(83\) −24.2475 + 24.2475i −0.292139 + 0.292139i −0.837925 0.545786i \(-0.816231\pi\)
0.545786 + 0.837925i \(0.316231\pi\)
\(84\) 0 0
\(85\) −125.878 + 14.0174i −1.48092 + 0.164911i
\(86\) 4.27659 7.40727i 0.0497278 0.0861311i
\(87\) 0 0
\(88\) −84.2370 22.5712i −0.957238 0.256491i
\(89\) −18.3646 10.6028i −0.206344 0.119133i 0.393267 0.919424i \(-0.371345\pi\)
−0.599611 + 0.800292i \(0.704678\pi\)
\(90\) 0 0
\(91\) −12.4564 + 6.20252i −0.136884 + 0.0681595i
\(92\) −7.76732 7.76732i −0.0844274 0.0844274i
\(93\) 0 0
\(94\) 2.92558 1.68909i 0.0311232 0.0179690i
\(95\) 7.87366 51.7816i 0.0828806 0.545070i
\(96\) 0 0
\(97\) 56.7300 + 56.7300i 0.584845 + 0.584845i 0.936231 0.351386i \(-0.114289\pi\)
−0.351386 + 0.936231i \(0.614289\pi\)
\(98\) 86.6391 + 35.1087i 0.884073 + 0.358252i
\(99\) 0 0
\(100\) 2.67725 8.60000i 0.0267725 0.0860000i
\(101\) 27.0096 + 46.7820i 0.267422 + 0.463188i 0.968195 0.250196i \(-0.0804950\pi\)
−0.700774 + 0.713384i \(0.747162\pi\)
\(102\) 0 0
\(103\) 40.5749 + 151.428i 0.393931 + 1.47017i 0.823593 + 0.567182i \(0.191966\pi\)
−0.429661 + 0.902990i \(0.641367\pi\)
\(104\) 16.5364i 0.159004i
\(105\) 0 0
\(106\) 112.500 1.06132
\(107\) 80.1432 21.4743i 0.749001 0.200694i 0.135926 0.990719i \(-0.456599\pi\)
0.613075 + 0.790025i \(0.289932\pi\)
\(108\) 0 0
\(109\) 145.762 84.1557i 1.33727 0.772070i 0.350864 0.936426i \(-0.385888\pi\)
0.986401 + 0.164356i \(0.0525546\pi\)
\(110\) −40.1096 + 91.6072i −0.364633 + 0.832793i
\(111\) 0 0
\(112\) 75.6817 66.8878i 0.675729 0.597212i
\(113\) −105.863 + 105.863i −0.936843 + 0.936843i −0.998121 0.0612774i \(-0.980483\pi\)
0.0612774 + 0.998121i \(0.480483\pi\)
\(114\) 0 0
\(115\) −122.774 + 90.3652i −1.06760 + 0.785784i
\(116\) 10.0198 + 17.3548i 0.0863775 + 0.149610i
\(117\) 0 0
\(118\) −89.9934 + 89.9934i −0.762656 + 0.762656i
\(119\) 97.9452 147.813i 0.823069 1.24213i
\(120\) 0 0
\(121\) 5.54707 9.60780i 0.0458435 0.0794033i
\(122\) 6.08799 22.7207i 0.0499016 0.186235i
\(123\) 0 0
\(124\) −5.07125 2.92789i −0.0408972 0.0236120i
\(125\) −112.409 54.6741i −0.899270 0.437393i
\(126\) 0 0
\(127\) −100.095 100.095i −0.788153 0.788153i 0.193038 0.981191i \(-0.438166\pi\)
−0.981191 + 0.193038i \(0.938166\pi\)
\(128\) −27.9631 104.360i −0.218461 0.815309i
\(129\) 0 0
\(130\) 18.7471 + 2.85059i 0.144208 + 0.0219276i
\(131\) −64.1225 + 111.063i −0.489485 + 0.847813i −0.999927 0.0120995i \(-0.996149\pi\)
0.510442 + 0.859912i \(0.329482\pi\)
\(132\) 0 0
\(133\) 48.5599 + 54.9442i 0.365112 + 0.413114i
\(134\) 210.735i 1.57265i
\(135\) 0 0
\(136\) −105.360 182.489i −0.774705 1.34183i
\(137\) −28.4034 + 106.003i −0.207324 + 0.773745i 0.781404 + 0.624025i \(0.214504\pi\)
−0.988729 + 0.149719i \(0.952163\pi\)
\(138\) 0 0
\(139\) 29.9231i 0.215274i −0.994190 0.107637i \(-0.965672\pi\)
0.994190 0.107637i \(-0.0343284\pi\)
\(140\) 6.83543 + 10.5966i 0.0488245 + 0.0756897i
\(141\) 0 0
\(142\) −55.1739 + 14.7838i −0.388549 + 0.104111i
\(143\) 20.1302 + 5.39386i 0.140770 + 0.0377193i
\(144\) 0 0
\(145\) 259.016 101.268i 1.78631 0.698399i
\(146\) 227.702 1.55960
\(147\) 0 0
\(148\) −3.90738 + 3.90738i −0.0264012 + 0.0264012i
\(149\) 20.3618 + 11.7559i 0.136657 + 0.0788987i 0.566770 0.823876i \(-0.308193\pi\)
−0.430113 + 0.902775i \(0.641526\pi\)
\(150\) 0 0
\(151\) 2.08556 + 3.61230i 0.0138117 + 0.0239225i 0.872849 0.487991i \(-0.162270\pi\)
−0.859037 + 0.511914i \(0.828937\pi\)
\(152\) 84.1708 22.5535i 0.553755 0.148378i
\(153\) 0 0
\(154\) −62.4050 125.327i −0.405227 0.813813i
\(155\) −50.7512 + 63.4706i −0.327427 + 0.409488i
\(156\) 0 0
\(157\) −71.2889 + 266.054i −0.454069 + 1.69461i 0.236741 + 0.971573i \(0.423921\pi\)
−0.690810 + 0.723036i \(0.742746\pi\)
\(158\) −212.628 56.9735i −1.34575 0.360592i
\(159\) 0 0
\(160\) 28.5557 3.17988i 0.178473 0.0198743i
\(161\) 13.1392 213.018i 0.0816102 1.32309i
\(162\) 0 0
\(163\) −10.2997 38.4390i −0.0631884 0.235822i 0.927108 0.374795i \(-0.122287\pi\)
−0.990296 + 0.138972i \(0.955620\pi\)
\(164\) −8.96432 + 5.17555i −0.0546605 + 0.0315583i
\(165\) 0 0
\(166\) −32.7104 + 56.6561i −0.197051 + 0.341302i
\(167\) 193.699 + 193.699i 1.15987 + 1.15987i 0.984503 + 0.175370i \(0.0561120\pi\)
0.175370 + 0.984503i \(0.443888\pi\)
\(168\) 0 0
\(169\) 165.048i 0.976617i
\(170\) −225.046 + 87.9869i −1.32380 + 0.517570i
\(171\) 0 0
\(172\) −0.418056 + 1.56021i −0.00243056 + 0.00907097i
\(173\) −49.1239 183.333i −0.283953 1.05973i −0.949601 0.313461i \(-0.898511\pi\)
0.665648 0.746266i \(-0.268155\pi\)
\(174\) 0 0
\(175\) 159.648 71.6769i 0.912273 0.409583i
\(176\) −151.269 −0.859480
\(177\) 0 0
\(178\) −39.0776 10.4708i −0.219537 0.0588248i
\(179\) 22.1740 12.8022i 0.123877 0.0715205i −0.436781 0.899568i \(-0.643882\pi\)
0.560658 + 0.828047i \(0.310548\pi\)
\(180\) 0 0
\(181\) 223.291 1.23365 0.616826 0.787100i \(-0.288418\pi\)
0.616826 + 0.787100i \(0.288418\pi\)
\(182\) −19.8920 + 17.5807i −0.109297 + 0.0965971i
\(183\) 0 0
\(184\) −219.645 126.812i −1.19372 0.689196i
\(185\) 45.4586 + 61.7620i 0.245722 + 0.333849i
\(186\) 0 0
\(187\) −256.514 + 68.7327i −1.37173 + 0.367554i
\(188\) −0.451105 + 0.451105i −0.00239949 + 0.00239949i
\(189\) 0 0
\(190\) −11.0590 99.3109i −0.0582051 0.522689i
\(191\) 79.1507 137.093i 0.414402 0.717765i −0.580964 0.813930i \(-0.697324\pi\)
0.995365 + 0.0961645i \(0.0306575\pi\)
\(192\) 0 0
\(193\) 34.5030 + 9.24505i 0.178772 + 0.0479018i 0.347095 0.937830i \(-0.387168\pi\)
−0.168322 + 0.985732i \(0.553835\pi\)
\(194\) 132.554 + 76.5300i 0.683267 + 0.394484i
\(195\) 0 0
\(196\) −17.5201 2.16958i −0.0893881 0.0110693i
\(197\) 233.837 + 233.837i 1.18699 + 1.18699i 0.977896 + 0.209092i \(0.0670509\pi\)
0.209092 + 0.977896i \(0.432949\pi\)
\(198\) 0 0
\(199\) −135.042 + 77.9668i −0.678605 + 0.391793i −0.799329 0.600893i \(-0.794812\pi\)
0.120724 + 0.992686i \(0.461478\pi\)
\(200\) 8.31614 207.798i 0.0415807 1.03899i
\(201\) 0 0
\(202\) 72.8730 + 72.8730i 0.360757 + 0.360757i
\(203\) −123.734 + 369.168i −0.609527 + 1.81856i
\(204\) 0 0
\(205\) 52.3082 + 133.790i 0.255162 + 0.652635i
\(206\) 149.543 + 259.016i 0.725936 + 1.25736i
\(207\) 0 0
\(208\) 7.42382 + 27.7061i 0.0356914 + 0.133202i
\(209\) 109.820i 0.525452i
\(210\) 0 0
\(211\) 71.3128 0.337975 0.168988 0.985618i \(-0.445950\pi\)
0.168988 + 0.985618i \(0.445950\pi\)
\(212\) −20.5214 + 5.49870i −0.0967991 + 0.0259372i
\(213\) 0 0
\(214\) 137.084 79.1455i 0.640580 0.369839i
\(215\) 20.5343 + 8.99079i 0.0955082 + 0.0418176i
\(216\) 0 0
\(217\) −22.6250 111.500i −0.104263 0.513827i
\(218\) 227.056 227.056i 1.04154 1.04154i
\(219\) 0 0
\(220\) 2.83898 18.6707i 0.0129044 0.0848670i
\(221\) 25.1779 + 43.6094i 0.113927 + 0.197328i
\(222\) 0 0
\(223\) −65.3363 + 65.3363i −0.292988 + 0.292988i −0.838259 0.545272i \(-0.816427\pi\)
0.545272 + 0.838259i \(0.316427\pi\)
\(224\) −22.2191 + 33.5317i −0.0991922 + 0.149695i
\(225\) 0 0
\(226\) −142.812 + 247.357i −0.631911 + 1.09450i
\(227\) −21.7660 + 81.2317i −0.0958853 + 0.357849i −0.997152 0.0754156i \(-0.975972\pi\)
0.901267 + 0.433264i \(0.142638\pi\)
\(228\) 0 0
\(229\) 148.580 + 85.7827i 0.648821 + 0.374597i 0.788004 0.615670i \(-0.211114\pi\)
−0.139183 + 0.990267i \(0.544448\pi\)
\(230\) −181.628 + 227.148i −0.789685 + 0.987598i
\(231\) 0 0
\(232\) 327.173 + 327.173i 1.41023 + 1.41023i
\(233\) −51.2177 191.147i −0.219818 0.820373i −0.984415 0.175863i \(-0.943728\pi\)
0.764596 0.644510i \(-0.222938\pi\)
\(234\) 0 0
\(235\) 5.24816 + 7.13038i 0.0223326 + 0.0303421i
\(236\) 12.0173 20.8145i 0.0509207 0.0881972i
\(237\) 0 0
\(238\) 107.507 320.752i 0.451708 1.34770i
\(239\) 88.3669i 0.369736i −0.982763 0.184868i \(-0.940814\pi\)
0.982763 0.184868i \(-0.0591857\pi\)
\(240\) 0 0
\(241\) −107.657 186.468i −0.446711 0.773727i 0.551458 0.834203i \(-0.314072\pi\)
−0.998170 + 0.0604755i \(0.980738\pi\)
\(242\) 5.47802 20.4442i 0.0226364 0.0844804i
\(243\) 0 0
\(244\) 4.44210i 0.0182053i
\(245\) −66.3182 + 235.854i −0.270686 + 0.962668i
\(246\) 0 0
\(247\) −20.1143 + 5.38962i −0.0814346 + 0.0218203i
\(248\) −130.597 34.9933i −0.526600 0.141102i
\(249\) 0 0
\(250\) −234.143 45.2485i −0.936574 0.180994i
\(251\) −202.957 −0.808594 −0.404297 0.914628i \(-0.632484\pi\)
−0.404297 + 0.914628i \(0.632484\pi\)
\(252\) 0 0
\(253\) −226.015 + 226.015i −0.893340 + 0.893340i
\(254\) −233.880 135.031i −0.920789 0.531618i
\(255\) 0 0
\(256\) 34.2982 + 59.4062i 0.133977 + 0.232055i
\(257\) −65.6771 + 17.5981i −0.255553 + 0.0684752i −0.384321 0.923200i \(-0.625564\pi\)
0.128768 + 0.991675i \(0.458898\pi\)
\(258\) 0 0
\(259\) −107.159 6.60975i −0.413743 0.0255203i
\(260\) −3.55903 + 0.396323i −0.0136886 + 0.00152432i
\(261\) 0 0
\(262\) −63.3243 + 236.330i −0.241696 + 0.902021i
\(263\) 445.592 + 119.396i 1.69427 + 0.453977i 0.971485 0.237099i \(-0.0761967\pi\)
0.722781 + 0.691077i \(0.242863\pi\)
\(264\) 0 0
\(265\) 32.6310 + 293.031i 0.123136 + 1.10578i
\(266\) 116.616 + 77.2733i 0.438407 + 0.290501i
\(267\) 0 0
\(268\) 10.3002 + 38.4407i 0.0384334 + 0.143435i
\(269\) 37.2279 21.4935i 0.138394 0.0799016i −0.429205 0.903207i \(-0.641206\pi\)
0.567598 + 0.823306i \(0.307873\pi\)
\(270\) 0 0
\(271\) 84.6401 146.601i 0.312325 0.540963i −0.666540 0.745469i \(-0.732226\pi\)
0.978865 + 0.204506i \(0.0655589\pi\)
\(272\) −258.452 258.452i −0.950191 0.950191i
\(273\) 0 0
\(274\) 209.367i 0.764113i
\(275\) −250.244 77.9030i −0.909980 0.283284i
\(276\) 0 0
\(277\) −59.9500 + 223.736i −0.216426 + 0.807712i 0.769234 + 0.638967i \(0.220638\pi\)
−0.985660 + 0.168745i \(0.946029\pi\)
\(278\) −14.7753 55.1422i −0.0531486 0.198353i
\(279\) 0 0
\(280\) 215.769 + 195.479i 0.770603 + 0.698140i
\(281\) 86.0504 0.306229 0.153115 0.988208i \(-0.451070\pi\)
0.153115 + 0.988208i \(0.451070\pi\)
\(282\) 0 0
\(283\) 65.1101 + 17.4462i 0.230071 + 0.0616474i 0.372013 0.928228i \(-0.378668\pi\)
−0.141941 + 0.989875i \(0.545334\pi\)
\(284\) 9.34181 5.39350i 0.0328937 0.0189912i
\(285\) 0 0
\(286\) 39.7592 0.139018
\(287\) −190.687 63.9127i −0.664416 0.222692i
\(288\) 0 0
\(289\) −305.423 176.336i −1.05683 0.610159i
\(290\) 427.310 314.512i 1.47348 1.08452i
\(291\) 0 0
\(292\) −41.5357 + 11.1295i −0.142246 + 0.0381146i
\(293\) −360.421 + 360.421i −1.23011 + 1.23011i −0.266183 + 0.963923i \(0.585762\pi\)
−0.963923 + 0.266183i \(0.914238\pi\)
\(294\) 0 0
\(295\) −260.510 208.304i −0.883084 0.706116i
\(296\) −63.7933 + 110.493i −0.215518 + 0.373288i
\(297\) 0 0
\(298\) 43.3275 + 11.6096i 0.145394 + 0.0389583i
\(299\) 52.4887 + 30.3043i 0.175547 + 0.101352i
\(300\) 0 0
\(301\) −28.0928 + 13.9884i −0.0933316 + 0.0464732i
\(302\) 5.62693 + 5.62693i 0.0186322 + 0.0186322i
\(303\) 0 0
\(304\) 130.899 75.5748i 0.430590 0.248601i
\(305\) 60.9467 + 9.26726i 0.199825 + 0.0303845i
\(306\) 0 0
\(307\) 22.4453 + 22.4453i 0.0731116 + 0.0731116i 0.742717 0.669605i \(-0.233537\pi\)
−0.669605 + 0.742717i \(0.733537\pi\)
\(308\) 17.5091 + 19.8110i 0.0568477 + 0.0643216i
\(309\) 0 0
\(310\) −62.1839 + 142.023i −0.200593 + 0.458140i
\(311\) −186.522 323.065i −0.599749 1.03880i −0.992858 0.119304i \(-0.961934\pi\)
0.393109 0.919492i \(-0.371400\pi\)
\(312\) 0 0
\(313\) −32.1578 120.014i −0.102741 0.383433i 0.895339 0.445386i \(-0.146934\pi\)
−0.998079 + 0.0619535i \(0.980267\pi\)
\(314\) 525.484i 1.67351i
\(315\) 0 0
\(316\) 41.5707 0.131553
\(317\) −325.028 + 87.0910i −1.02532 + 0.274735i −0.732019 0.681284i \(-0.761422\pi\)
−0.293306 + 0.956019i \(0.594755\pi\)
\(318\) 0 0
\(319\) 504.993 291.558i 1.58305 0.913974i
\(320\) 319.822 125.041i 0.999443 0.390754i
\(321\) 0 0
\(322\) −80.9700 399.036i −0.251460 1.23924i
\(323\) 187.634 187.634i 0.580909 0.580909i
\(324\) 0 0
\(325\) −1.98731 + 49.6576i −0.00611481 + 0.152793i
\(326\) −37.9606 65.7496i −0.116443 0.201686i
\(327\) 0 0
\(328\) −168.996 + 168.996i −0.515231 + 0.515231i
\(329\) −12.3715 0.763091i −0.0376033 0.00231942i
\(330\) 0 0
\(331\) 41.0476 71.0966i 0.124011 0.214793i −0.797335 0.603537i \(-0.793758\pi\)
0.921346 + 0.388744i \(0.127091\pi\)
\(332\) 3.19759 11.9336i 0.00963130 0.0359445i
\(333\) 0 0
\(334\) 452.591 + 261.304i 1.35506 + 0.782346i
\(335\) 548.905 61.1244i 1.63852 0.182461i
\(336\) 0 0
\(337\) 55.2295 + 55.2295i 0.163886 + 0.163886i 0.784286 0.620400i \(-0.213030\pi\)
−0.620400 + 0.784286i \(0.713030\pi\)
\(338\) 81.4969 + 304.151i 0.241115 + 0.899854i
\(339\) 0 0
\(340\) 36.7507 27.0496i 0.108090 0.0795575i
\(341\) −85.1963 + 147.564i −0.249843 + 0.432740i
\(342\) 0 0
\(343\) −193.839 282.976i −0.565128 0.825004i
\(344\) 37.2943i 0.108414i
\(345\) 0 0
\(346\) −181.051 313.589i −0.523268 0.906326i
\(347\) 24.0575 89.7837i 0.0693299 0.258743i −0.922558 0.385858i \(-0.873905\pi\)
0.991888 + 0.127116i \(0.0405720\pi\)
\(348\) 0 0
\(349\) 372.327i 1.06684i −0.845851 0.533419i \(-0.820907\pi\)
0.845851 0.533419i \(-0.179093\pi\)
\(350\) 258.806 210.916i 0.739446 0.602618i
\(351\) 0 0
\(352\) 58.1907 15.5921i 0.165314 0.0442959i
\(353\) 110.010 + 29.4770i 0.311642 + 0.0835042i 0.411250 0.911523i \(-0.365092\pi\)
−0.0996082 + 0.995027i \(0.531759\pi\)
\(354\) 0 0
\(355\) −54.5110 139.424i −0.153552 0.392744i
\(356\) 7.64003 0.0214608
\(357\) 0 0
\(358\) 34.5408 34.5408i 0.0964827 0.0964827i
\(359\) 85.1134 + 49.1402i 0.237085 + 0.136881i 0.613836 0.789434i \(-0.289626\pi\)
−0.376751 + 0.926314i \(0.622959\pi\)
\(360\) 0 0
\(361\) −125.633 217.603i −0.348015 0.602780i
\(362\) 411.480 110.256i 1.13669 0.304574i
\(363\) 0 0
\(364\) 2.76926 4.17920i 0.00760786 0.0114813i
\(365\) 66.0458 + 593.099i 0.180947 + 1.62493i
\(366\) 0 0
\(367\) 156.895 585.540i 0.427507 1.59548i −0.330881 0.943673i \(-0.607346\pi\)
0.758387 0.651804i \(-0.225988\pi\)
\(368\) −424.936 113.861i −1.15472 0.309406i
\(369\) 0 0
\(370\) 114.268 + 91.3685i 0.308831 + 0.246942i
\(371\) −344.093 228.006i −0.927473 0.614571i
\(372\) 0 0
\(373\) −131.534 490.890i −0.352637 1.31606i −0.883432 0.468560i \(-0.844773\pi\)
0.530795 0.847501i \(-0.321894\pi\)
\(374\) −438.764 + 253.321i −1.17317 + 0.677328i
\(375\) 0 0
\(376\) −7.36489 + 12.7564i −0.0195875 + 0.0339265i
\(377\) −78.1848 78.1848i −0.207387 0.207387i
\(378\) 0 0
\(379\) 329.156i 0.868486i −0.900796 0.434243i \(-0.857016\pi\)
0.900796 0.434243i \(-0.142984\pi\)
\(380\) 6.87133 + 17.5750i 0.0180825 + 0.0462500i
\(381\) 0 0
\(382\) 78.1655 291.718i 0.204622 0.763659i
\(383\) −16.9976 63.4359i −0.0443801 0.165629i 0.940179 0.340680i \(-0.110657\pi\)
−0.984559 + 0.175052i \(0.943991\pi\)
\(384\) 0 0
\(385\) 308.341 198.899i 0.800885 0.516620i
\(386\) 68.1470 0.176547
\(387\) 0 0
\(388\) −27.9200 7.48115i −0.0719588 0.0192813i
\(389\) 203.539 117.513i 0.523236 0.302091i −0.215021 0.976609i \(-0.568982\pi\)
0.738258 + 0.674519i \(0.235649\pi\)
\(390\) 0 0
\(391\) −772.322 −1.97525
\(392\) −403.701 + 56.3110i −1.02985 + 0.143651i
\(393\) 0 0
\(394\) 546.377 + 315.451i 1.38674 + 0.800636i
\(395\) 86.7262 570.360i 0.219560 1.44395i
\(396\) 0 0
\(397\) 167.401 44.8551i 0.421666 0.112985i −0.0417456 0.999128i \(-0.513292\pi\)
0.463411 + 0.886143i \(0.346625\pi\)
\(398\) −210.358 + 210.358i −0.528537 + 0.528537i
\(399\) 0 0
\(400\) −79.3549 351.890i −0.198387 0.879725i
\(401\) 255.698 442.881i 0.637650 1.10444i −0.348297 0.937384i \(-0.613240\pi\)
0.985947 0.167058i \(-0.0534267\pi\)
\(402\) 0 0
\(403\) 31.2088 + 8.36237i 0.0774412 + 0.0207503i
\(404\) −16.8548 9.73111i −0.0417197 0.0240869i
\(405\) 0 0
\(406\) −45.7305 + 741.398i −0.112637 + 1.82610i
\(407\) 113.698 + 113.698i 0.279356 + 0.279356i
\(408\) 0 0
\(409\) −603.075 + 348.185i −1.47451 + 0.851309i −0.999588 0.0287182i \(-0.990857\pi\)
−0.474923 + 0.880027i \(0.657524\pi\)
\(410\) 162.456 + 220.720i 0.396234 + 0.538341i
\(411\) 0 0
\(412\) −39.9384 39.9384i −0.0969379 0.0969379i
\(413\) 457.644 92.8625i 1.10810 0.224849i
\(414\) 0 0
\(415\) −157.061 68.7680i −0.378460 0.165706i
\(416\) −5.71166 9.89288i −0.0137299 0.0237810i
\(417\) 0 0
\(418\) −54.2262 202.375i −0.129728 0.484151i
\(419\) 751.985i 1.79471i −0.441305 0.897357i \(-0.645484\pi\)
0.441305 0.897357i \(-0.354516\pi\)
\(420\) 0 0
\(421\) 666.816 1.58389 0.791943 0.610596i \(-0.209070\pi\)
0.791943 + 0.610596i \(0.209070\pi\)
\(422\) 131.415 35.2125i 0.311410 0.0834420i
\(423\) 0 0
\(424\) −424.814 + 245.266i −1.00192 + 0.578458i
\(425\) −294.456 560.661i −0.692838 1.31920i
\(426\) 0 0
\(427\) −64.6691 + 57.1548i −0.151450 + 0.133852i
\(428\) −21.1374 + 21.1374i −0.0493865 + 0.0493865i
\(429\) 0 0
\(430\) 42.2799 + 6.42888i 0.0983254 + 0.0149509i
\(431\) −131.194 227.235i −0.304395 0.527228i 0.672731 0.739887i \(-0.265121\pi\)
−0.977127 + 0.212659i \(0.931788\pi\)
\(432\) 0 0
\(433\) 375.850 375.850i 0.868014 0.868014i −0.124239 0.992252i \(-0.539649\pi\)
0.992252 + 0.124239i \(0.0396488\pi\)
\(434\) −96.7496 194.301i −0.222925 0.447698i
\(435\) 0 0
\(436\) −30.3199 + 52.5156i −0.0695410 + 0.120449i
\(437\) 82.6623 308.500i 0.189158 0.705949i
\(438\) 0 0
\(439\) 597.304 + 344.854i 1.36060 + 0.785544i 0.989704 0.143129i \(-0.0457165\pi\)
0.370898 + 0.928673i \(0.379050\pi\)
\(440\) −48.2582 433.364i −0.109678 0.984918i
\(441\) 0 0
\(442\) 67.9311 + 67.9311i 0.153690 + 0.153690i
\(443\) −17.6494 65.8683i −0.0398405 0.148687i 0.943140 0.332395i \(-0.107857\pi\)
−0.982981 + 0.183708i \(0.941190\pi\)
\(444\) 0 0
\(445\) 15.9389 104.823i 0.0358177 0.235558i
\(446\) −88.1401 + 152.663i −0.197623 + 0.342294i
\(447\) 0 0
\(448\) −152.782 + 455.833i −0.341030 + 1.01748i
\(449\) 255.244i 0.568472i 0.958754 + 0.284236i \(0.0917398\pi\)
−0.958754 + 0.284236i \(0.908260\pi\)
\(450\) 0 0
\(451\) 150.599 + 260.846i 0.333923 + 0.578372i
\(452\) 13.9605 52.1013i 0.0308861 0.115268i
\(453\) 0 0
\(454\) 160.441i 0.353394i
\(455\) −51.5624 46.7138i −0.113324 0.102668i
\(456\) 0 0
\(457\) 8.92672 2.39191i 0.0195333 0.00523394i −0.249039 0.968493i \(-0.580115\pi\)
0.268572 + 0.963259i \(0.413448\pi\)
\(458\) 316.160 + 84.7149i 0.690306 + 0.184967i
\(459\) 0 0
\(460\) 22.0288 50.3120i 0.0478886 0.109374i
\(461\) 410.809 0.891127 0.445563 0.895250i \(-0.353003\pi\)
0.445563 + 0.895250i \(0.353003\pi\)
\(462\) 0 0
\(463\) −321.399 + 321.399i −0.694166 + 0.694166i −0.963146 0.268980i \(-0.913314\pi\)
0.268980 + 0.963146i \(0.413314\pi\)
\(464\) 695.045 + 401.284i 1.49794 + 0.864837i
\(465\) 0 0
\(466\) −188.768 326.955i −0.405081 0.701620i
\(467\) −465.574 + 124.750i −0.996946 + 0.267131i −0.720166 0.693802i \(-0.755934\pi\)
−0.276781 + 0.960933i \(0.589268\pi\)
\(468\) 0 0
\(469\) −427.100 + 644.554i −0.910661 + 1.37431i
\(470\) 13.1921 + 10.5484i 0.0280683 + 0.0224435i
\(471\) 0 0
\(472\) 143.627 536.024i 0.304295 1.13564i
\(473\) 45.3992 + 12.1647i 0.0959814 + 0.0257181i
\(474\) 0 0
\(475\) 255.469 57.6109i 0.537829 0.121286i
\(476\) −3.93305 + 63.7638i −0.00826270 + 0.133958i
\(477\) 0 0
\(478\) −43.6334 162.842i −0.0912833 0.340674i
\(479\) −679.727 + 392.441i −1.41905 + 0.819291i −0.996216 0.0869137i \(-0.972300\pi\)
−0.422838 + 0.906205i \(0.638966\pi\)
\(480\) 0 0
\(481\) 15.2447 26.4046i 0.0316938 0.0548953i
\(482\) −290.464 290.464i −0.602623 0.602623i
\(483\) 0 0
\(484\) 3.99703i 0.00825833i
\(485\) −160.891 + 367.462i −0.331734 + 0.757655i
\(486\) 0 0
\(487\) −93.7930 + 350.040i −0.192593 + 0.718769i 0.800283 + 0.599622i \(0.204682\pi\)
−0.992877 + 0.119146i \(0.961984\pi\)
\(488\) 26.5454 + 99.0686i 0.0543962 + 0.203009i
\(489\) 0 0
\(490\) −5.75213 + 467.377i −0.0117390 + 0.953830i
\(491\) −672.749 −1.37016 −0.685080 0.728468i \(-0.740233\pi\)
−0.685080 + 0.728468i \(0.740233\pi\)
\(492\) 0 0
\(493\) 1360.96 + 364.667i 2.76056 + 0.739690i
\(494\) −34.4054 + 19.8640i −0.0696465 + 0.0402104i
\(495\) 0 0
\(496\) −234.519 −0.472821
\(497\) 198.717 + 66.6041i 0.399834 + 0.134012i
\(498\) 0 0
\(499\) −266.252 153.721i −0.533571 0.308057i 0.208899 0.977937i \(-0.433012\pi\)
−0.742469 + 0.669880i \(0.766345\pi\)
\(500\) 44.9223 3.19039i 0.0898446 0.00638079i
\(501\) 0 0
\(502\) −374.009 + 100.215i −0.745037 + 0.199632i
\(503\) 573.532 573.532i 1.14022 1.14022i 0.151813 0.988409i \(-0.451489\pi\)
0.988409 0.151813i \(-0.0485112\pi\)
\(504\) 0 0
\(505\) −168.676 + 210.950i −0.334012 + 0.417724i
\(506\) −304.899 + 528.101i −0.602567 + 1.04368i
\(507\) 0 0
\(508\) 49.2626 + 13.1999i 0.0969736 + 0.0259840i
\(509\) 132.234 + 76.3454i 0.259792 + 0.149991i 0.624240 0.781233i \(-0.285409\pi\)
−0.364448 + 0.931224i \(0.618742\pi\)
\(510\) 0 0
\(511\) −696.450 461.488i −1.36291 0.903107i
\(512\) 398.124 + 398.124i 0.777586 + 0.777586i
\(513\) 0 0
\(514\) −112.340 + 64.8596i −0.218560 + 0.126186i
\(515\) −631.286 + 464.645i −1.22580 + 0.902222i
\(516\) 0 0
\(517\) 13.1263 + 13.1263i 0.0253894 + 0.0253894i
\(518\) −200.737 + 40.7323i −0.387523 + 0.0786338i
\(519\) 0 0
\(520\) −77.0058 + 30.1071i −0.148088 + 0.0578983i
\(521\) −145.704 252.366i −0.279662 0.484389i 0.691639 0.722244i \(-0.256889\pi\)
−0.971301 + 0.237855i \(0.923556\pi\)
\(522\) 0 0
\(523\) −149.003 556.086i −0.284900 1.06326i −0.948912 0.315540i \(-0.897814\pi\)
0.664012 0.747722i \(-0.268852\pi\)
\(524\) 46.2046i 0.0881766i
\(525\) 0 0
\(526\) 880.091 1.67318
\(527\) −397.686 + 106.560i −0.754623 + 0.202201i
\(528\) 0 0
\(529\) −346.907 + 200.287i −0.655779 + 0.378614i
\(530\) 204.824 + 523.884i 0.386460 + 0.988460i
\(531\) 0 0
\(532\) −25.0491 8.39573i −0.0470849 0.0157814i
\(533\) 40.3850 40.3850i 0.0757693 0.0757693i
\(534\) 0 0
\(535\) 245.913 + 334.108i 0.459651 + 0.624502i
\(536\) 459.432 + 795.760i 0.857150 + 1.48463i
\(537\) 0 0
\(538\) 57.9905 57.9905i 0.107789 0.107789i
\(539\) −63.1309 + 509.802i −0.117126 + 0.945830i
\(540\) 0 0
\(541\) −138.214 + 239.393i −0.255478 + 0.442501i −0.965025 0.262157i \(-0.915566\pi\)
0.709547 + 0.704658i \(0.248900\pi\)
\(542\) 83.5865 311.949i 0.154219 0.575552i
\(543\) 0 0
\(544\) 126.063 + 72.7823i 0.231733 + 0.133791i
\(545\) 657.273 + 525.557i 1.20601 + 0.964324i
\(546\) 0 0
\(547\) −582.880 582.880i −1.06559 1.06559i −0.997692 0.0679024i \(-0.978369\pi\)
−0.0679024 0.997692i \(-0.521631\pi\)
\(548\) −10.2333 38.1911i −0.0186739 0.0696918i
\(549\) 0 0
\(550\) −499.616 19.9948i −0.908394 0.0363542i
\(551\) −291.329 + 504.596i −0.528727 + 0.915782i
\(552\) 0 0
\(553\) 534.874 + 605.195i 0.967223 + 1.09439i
\(554\) 441.902i 0.797658i
\(555\) 0 0
\(556\) 5.39040 + 9.33644i 0.00969496 + 0.0167922i
\(557\) 188.562 703.723i 0.338532 1.26342i −0.561458 0.827505i \(-0.689759\pi\)
0.899989 0.435912i \(-0.143574\pi\)
\(558\) 0 0
\(559\) 8.91224i 0.0159432i
\(560\) 449.269 + 230.650i 0.802266 + 0.411875i
\(561\) 0 0
\(562\) 158.574 42.4896i 0.282159 0.0756043i
\(563\) 475.416 + 127.387i 0.844434 + 0.226265i 0.655001 0.755628i \(-0.272668\pi\)
0.189433 + 0.981894i \(0.439335\pi\)
\(564\) 0 0
\(565\) −685.718 300.237i −1.21366 0.531393i
\(566\) 128.599 0.227207
\(567\) 0 0
\(568\) 176.112 176.112i 0.310057 0.310057i
\(569\) 742.450 + 428.654i 1.30483 + 0.753346i 0.981229 0.192847i \(-0.0617719\pi\)
0.323604 + 0.946192i \(0.395105\pi\)
\(570\) 0 0
\(571\) 454.669 + 787.510i 0.796268 + 1.37918i 0.922031 + 0.387117i \(0.126529\pi\)
−0.125762 + 0.992060i \(0.540138\pi\)
\(572\) −7.25256 + 1.94332i −0.0126793 + 0.00339741i
\(573\) 0 0
\(574\) −382.957 23.6213i −0.667172 0.0411522i
\(575\) −644.336 407.203i −1.12058 0.708179i
\(576\) 0 0
\(577\) −68.1343 + 254.281i −0.118084 + 0.440695i −0.999499 0.0316475i \(-0.989925\pi\)
0.881415 + 0.472342i \(0.156591\pi\)
\(578\) −649.903 174.141i −1.12440 0.301282i
\(579\) 0 0
\(580\) −62.5741 + 78.2566i −0.107886 + 0.134925i
\(581\) 214.874 106.993i 0.369834 0.184154i
\(582\) 0 0
\(583\) 160.002 + 597.136i 0.274446 + 1.02425i
\(584\) −859.830 + 496.423i −1.47231 + 0.850040i
\(585\) 0 0
\(586\) −486.215 + 842.150i −0.829719 + 1.43712i
\(587\) −507.344 507.344i −0.864300 0.864300i 0.127534 0.991834i \(-0.459294\pi\)
−0.991834 + 0.127534i \(0.959294\pi\)
\(588\) 0 0
\(589\) 170.259i 0.289064i
\(590\) −582.922 255.229i −0.988004 0.432591i
\(591\) 0 0
\(592\) −57.2784 + 213.766i −0.0967541 + 0.361091i
\(593\) −47.3392 176.672i −0.0798301 0.297930i 0.914455 0.404688i \(-0.132620\pi\)
−0.994285 + 0.106758i \(0.965953\pi\)
\(594\) 0 0
\(595\) 866.651 + 186.989i 1.45656 + 0.314267i
\(596\) −8.47092 −0.0142129
\(597\) 0 0
\(598\) 111.690 + 29.9271i 0.186772 + 0.0500453i
\(599\) −218.188 + 125.971i −0.364254 + 0.210302i −0.670945 0.741507i \(-0.734111\pi\)
0.306691 + 0.951809i \(0.400778\pi\)
\(600\) 0 0
\(601\) 754.595 1.25557 0.627783 0.778388i \(-0.283963\pi\)
0.627783 + 0.778388i \(0.283963\pi\)
\(602\) −44.8622 + 39.6494i −0.0745219 + 0.0658628i
\(603\) 0 0
\(604\) −1.30145 0.751393i −0.00215472 0.00124403i
\(605\) 54.8403 + 8.33875i 0.0906452 + 0.0137831i
\(606\) 0 0
\(607\) −727.749 + 195.000i −1.19893 + 0.321251i −0.802408 0.596775i \(-0.796448\pi\)
−0.396518 + 0.918027i \(0.629782\pi\)
\(608\) −42.5651 + 42.5651i −0.0700083 + 0.0700083i
\(609\) 0 0
\(610\) 116.888 13.0164i 0.191620 0.0213383i
\(611\) 1.75999 3.04840i 0.00288051 0.00498919i
\(612\) 0 0
\(613\) −225.113 60.3190i −0.367232 0.0983996i 0.0704836 0.997513i \(-0.477546\pi\)
−0.437716 + 0.899113i \(0.644212\pi\)
\(614\) 52.4450 + 30.2792i 0.0854154 + 0.0493146i
\(615\) 0 0
\(616\) 508.879 + 337.198i 0.826103 + 0.547400i
\(617\) −383.218 383.218i −0.621098 0.621098i 0.324714 0.945812i \(-0.394732\pi\)
−0.945812 + 0.324714i \(0.894732\pi\)
\(618\) 0 0
\(619\) 262.181 151.370i 0.423556 0.244540i −0.273042 0.962002i \(-0.588030\pi\)
0.696597 + 0.717462i \(0.254696\pi\)
\(620\) 4.40141 28.9462i 0.00709905 0.0466874i
\(621\) 0 0
\(622\) −503.244 503.244i −0.809074 0.809074i
\(623\) 98.3013 + 111.225i 0.157787 + 0.178532i
\(624\) 0 0
\(625\) 49.9454 623.001i 0.0799126 0.996802i
\(626\) −118.521 205.284i −0.189330 0.327929i
\(627\) 0 0
\(628\) −25.6842 95.8547i −0.0408984 0.152635i
\(629\) 388.520i 0.617679i
\(630\) 0 0
\(631\) −616.232 −0.976596 −0.488298 0.872677i \(-0.662382\pi\)
−0.488298 + 0.872677i \(0.662382\pi\)
\(632\) 927.118 248.421i 1.46696 0.393071i
\(633\) 0 0
\(634\) −555.957 + 320.982i −0.876904 + 0.506281i
\(635\) 283.879 648.358i 0.447054 1.02104i
\(636\) 0 0
\(637\) 96.4728 13.4567i 0.151449 0.0211251i
\(638\) 786.635 786.635i 1.23297 1.23297i
\(639\) 0 0
\(640\) 435.064 320.219i 0.679788 0.500343i
\(641\) 315.011 + 545.614i 0.491436 + 0.851192i 0.999951 0.00986074i \(-0.00313882\pi\)
−0.508515 + 0.861053i \(0.669805\pi\)
\(642\) 0 0
\(643\) −129.985 + 129.985i −0.202154 + 0.202154i −0.800922 0.598768i \(-0.795657\pi\)
0.598768 + 0.800922i \(0.295657\pi\)
\(644\) 34.2737 + 68.8315i 0.0532200 + 0.106881i
\(645\) 0 0
\(646\) 253.122 438.420i 0.391829 0.678668i
\(647\) −243.586 + 909.075i −0.376485 + 1.40506i 0.474678 + 0.880160i \(0.342565\pi\)
−0.851163 + 0.524902i \(0.824102\pi\)
\(648\) 0 0
\(649\) −605.665 349.681i −0.933229 0.538800i
\(650\) 20.8575 + 92.4901i 0.0320885 + 0.142292i
\(651\) 0 0
\(652\) 10.1381 + 10.1381i 0.0155493 + 0.0155493i
\(653\) −79.6499 297.258i −0.121975 0.455218i 0.877738 0.479140i \(-0.159051\pi\)
−0.999714 + 0.0239217i \(0.992385\pi\)
\(654\) 0 0
\(655\) −633.939 96.3936i −0.967845 0.147166i
\(656\) −207.277 + 359.014i −0.315971 + 0.547277i
\(657\) 0 0
\(658\) −23.1749 + 4.70252i −0.0352202 + 0.00714668i
\(659\) 6.50016i 0.00986367i −0.999988 0.00493183i \(-0.998430\pi\)
0.999988 0.00493183i \(-0.00156986\pi\)
\(660\) 0 0
\(661\) −268.548 465.138i −0.406275 0.703688i 0.588194 0.808720i \(-0.299839\pi\)
−0.994469 + 0.105031i \(0.966506\pi\)
\(662\) 40.5367 151.285i 0.0612336 0.228527i
\(663\) 0 0
\(664\) 285.253i 0.429598i
\(665\) −167.450 + 326.165i −0.251804 + 0.490474i
\(666\) 0 0
\(667\) 1638.06 438.917i 2.45586 0.658046i
\(668\) −95.3300 25.5436i −0.142710 0.0382389i
\(669\) 0 0
\(670\) 981.338 383.676i 1.46468 0.572651i
\(671\) 129.257 0.192633
\(672\) 0 0
\(673\) −502.493 + 502.493i −0.746646 + 0.746646i −0.973848 0.227202i \(-0.927042\pi\)
0.227202 + 0.973848i \(0.427042\pi\)
\(674\) 129.048 + 74.5058i 0.191466 + 0.110543i
\(675\) 0 0
\(676\) −29.7321 51.4975i −0.0439824 0.0761797i
\(677\) 79.0768 21.1886i 0.116805 0.0312977i −0.199943 0.979807i \(-0.564076\pi\)
0.316748 + 0.948510i \(0.397409\pi\)
\(678\) 0 0
\(679\) −250.324 502.723i −0.368666 0.740387i
\(680\) 657.978 822.882i 0.967614 1.21012i
\(681\) 0 0
\(682\) −84.1358 + 313.999i −0.123366 + 0.460409i
\(683\) −670.938 179.777i −0.982340 0.263217i −0.268310 0.963333i \(-0.586465\pi\)
−0.714030 + 0.700115i \(0.753132\pi\)
\(684\) 0 0
\(685\) −545.341 + 60.7276i −0.796118 + 0.0886534i
\(686\) −496.932 425.755i −0.724391 0.620634i
\(687\) 0 0
\(688\) 16.7428 + 62.4850i 0.0243355 + 0.0908213i
\(689\) 101.518 58.6114i 0.147341 0.0850674i
\(690\) 0 0
\(691\) 57.5433 99.6680i 0.0832755 0.144237i −0.821380 0.570382i \(-0.806795\pi\)
0.904655 + 0.426145i \(0.140129\pi\)
\(692\) 48.3532 + 48.3532i 0.0698746 + 0.0698746i
\(693\) 0 0
\(694\) 177.332i 0.255522i
\(695\) 139.344 54.4796i 0.200495 0.0783879i
\(696\) 0 0
\(697\) −188.363 + 702.980i −0.270248 + 1.00858i
\(698\) −183.846 686.123i −0.263390 0.982984i
\(699\) 0 0
\(700\) −36.9004 + 51.1235i −0.0527149 + 0.0730335i
\(701\) −809.046 −1.15413 −0.577066 0.816698i \(-0.695802\pi\)
−0.577066 + 0.816698i \(0.695802\pi\)
\(702\) 0 0
\(703\) −155.192 41.5836i −0.220757 0.0591516i
\(704\) 623.544 360.003i 0.885716 0.511368i
\(705\) 0 0
\(706\) 217.280 0.307763
\(707\) −75.1963 370.582i −0.106360 0.524161i
\(708\) 0 0
\(709\) 1134.05 + 654.745i 1.59951 + 0.923477i 0.991582 + 0.129483i \(0.0413319\pi\)
0.607927 + 0.793993i \(0.292001\pi\)
\(710\) −169.297 230.014i −0.238446 0.323964i
\(711\) 0 0
\(712\) 170.390 45.6557i 0.239311 0.0641232i
\(713\) −350.403 + 350.403i −0.491448 + 0.491448i
\(714\) 0 0
\(715\) 11.5323 + 103.561i 0.0161291 + 0.144841i
\(716\) −4.61241 + 7.98893i −0.00644191 + 0.0111577i
\(717\) 0 0
\(718\) 181.111 + 48.5285i 0.252244 + 0.0675885i
\(719\) 968.813 + 559.345i 1.34745 + 0.777948i 0.987887 0.155174i \(-0.0495939\pi\)
0.359559 + 0.933123i \(0.382927\pi\)
\(720\) 0 0
\(721\) 67.5600 1095.30i 0.0937032 1.51915i
\(722\) −338.964 338.964i −0.469480 0.469480i
\(723\) 0 0
\(724\) −69.6700 + 40.2240i −0.0962293 + 0.0555580i
\(725\) 943.156 + 1021.79i 1.30091 + 1.40937i
\(726\) 0 0
\(727\) −28.5376 28.5376i −0.0392540 0.0392540i 0.687207 0.726461i \(-0.258836\pi\)
−0.726461 + 0.687207i \(0.758836\pi\)
\(728\) 36.7863 109.754i 0.0505307 0.150761i
\(729\) 0 0
\(730\) 414.567 + 1060.35i 0.567901 + 1.45253i
\(731\) 56.7833 + 98.3516i 0.0776789 + 0.134544i
\(732\) 0 0
\(733\) 167.588 + 625.448i 0.228633 + 0.853272i 0.980916 + 0.194431i \(0.0622861\pi\)
−0.752283 + 0.658841i \(0.771047\pi\)
\(734\) 1156.50i 1.57562i
\(735\) 0 0
\(736\) 175.203 0.238047
\(737\) 1118.55 299.716i 1.51771 0.406670i
\(738\) 0 0
\(739\) 838.233 483.954i 1.13428 0.654877i 0.189272 0.981925i \(-0.439387\pi\)
0.945008 + 0.327048i \(0.106054\pi\)
\(740\) −25.3097 11.0817i −0.0342022 0.0149752i
\(741\) 0 0
\(742\) −746.677 250.264i −1.00630 0.337283i
\(743\) 243.308 243.308i 0.327467 0.327467i −0.524155 0.851623i \(-0.675619\pi\)
0.851623 + 0.524155i \(0.175619\pi\)
\(744\) 0 0
\(745\) −17.6723 + 116.223i −0.0237212 + 0.156004i
\(746\) −484.780 839.663i −0.649839 1.12555i
\(747\) 0 0
\(748\) 67.6544 67.6544i 0.0904471 0.0904471i
\(749\) −579.690 35.7562i −0.773952 0.0477385i
\(750\) 0 0
\(751\) 75.0735 130.031i 0.0999647 0.173144i −0.811705 0.584067i \(-0.801460\pi\)
0.911670 + 0.410923i \(0.134794\pi\)
\(752\) −6.61275 + 24.6791i −0.00879356 + 0.0328180i
\(753\) 0 0
\(754\) −182.684 105.473i −0.242287 0.139884i
\(755\) −13.0244 + 16.2886i −0.0172509 + 0.0215744i
\(756\) 0 0
\(757\) 405.586 + 405.586i 0.535780 + 0.535780i 0.922287 0.386507i \(-0.126318\pi\)
−0.386507 + 0.922287i \(0.626318\pi\)
\(758\) −162.529 606.568i −0.214419 0.800222i
\(759\) 0 0
\(760\) 258.272 + 350.899i 0.339831 + 0.461709i
\(761\) 529.787 917.617i 0.696172 1.20580i −0.273612 0.961840i \(-0.588219\pi\)
0.969784 0.243965i \(-0.0784481\pi\)
\(762\) 0 0
\(763\) −1154.65 + 234.294i −1.51330 + 0.307070i
\(764\) 57.0334i 0.0746511i
\(765\) 0 0
\(766\) −62.6462 108.506i −0.0817836 0.141653i
\(767\) −34.3227 + 128.094i −0.0447492 + 0.167006i
\(768\) 0 0
\(769\) 370.215i 0.481424i −0.970597 0.240712i \(-0.922619\pi\)
0.970597 0.240712i \(-0.0773810\pi\)
\(770\) 469.998 518.781i 0.610387 0.673742i
\(771\) 0 0
\(772\) −12.4309 + 3.33084i −0.0161022 + 0.00431456i
\(773\) 1383.87 + 370.808i 1.79026 + 0.479700i 0.992391 0.123127i \(-0.0392923\pi\)
0.797872 + 0.602827i \(0.205959\pi\)
\(774\) 0 0
\(775\) −387.967 120.777i