Properties

Label 804.2.y.b.157.1
Level 804
Weight 2
Character 804.157
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 157.1
Character \(\chi\) = 804.157
Dual form 804.2.y.b.169.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.142315 - 0.989821i) q^{3} +(-1.67835 - 3.67507i) q^{5} +(2.54620 - 2.42780i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\) \(q+(0.142315 - 0.989821i) q^{3} +(-1.67835 - 3.67507i) q^{5} +(2.54620 - 2.42780i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(5.23241 + 0.499635i) q^{11} +(-2.29438 - 0.442205i) q^{13} +(-3.87652 + 1.13825i) q^{15} +(-1.39626 - 0.719822i) q^{17} +(-0.391195 - 0.373004i) q^{19} +(-2.04072 - 2.86579i) q^{21} +(7.68293 - 3.07578i) q^{23} +(-7.41501 + 8.55738i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-0.551633 + 0.955456i) q^{29} +(-7.91988 + 1.52643i) q^{31} +(1.23920 - 5.10805i) q^{33} +(-13.1957 - 5.28278i) q^{35} +(5.09972 + 8.83298i) q^{37} +(-0.764229 + 2.20809i) q^{39} +(-0.441935 - 9.27736i) q^{41} +(-7.98049 + 5.12875i) q^{43} +(0.574977 + 3.99905i) q^{45} +(-3.79700 - 2.98600i) q^{47} +(0.255863 - 5.37124i) q^{49} +(-0.911204 + 1.27961i) q^{51} +(-4.24648 - 2.72905i) q^{53} +(-6.94562 - 20.0681i) q^{55} +(-0.424880 + 0.334129i) q^{57} +(2.79526 + 3.22590i) q^{59} +(4.29709 - 0.410322i) q^{61} +(-3.12705 + 1.61211i) q^{63} +(2.22563 + 9.17419i) q^{65} +(4.22580 + 7.01018i) q^{67} +(-1.95108 - 8.04245i) q^{69} +(13.0777 - 6.74203i) q^{71} +(6.99211 - 0.667666i) q^{73} +(7.41501 + 8.55738i) q^{75} +(14.5358 - 11.4311i) q^{77} +(-2.12207 - 6.13133i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-9.30173 + 13.0624i) q^{83} +(-0.301986 + 6.33947i) q^{85} +(0.867226 + 0.681994i) q^{87} +(0.140072 + 0.974221i) q^{89} +(-6.91553 + 4.44434i) q^{91} +(0.383778 + 8.05650i) q^{93} +(-0.714254 + 2.06370i) q^{95} +(0.846818 + 1.46673i) q^{97} +(-4.87970 - 1.95354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{14}{33}\right)\) \(1\)

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
\(3\) 0.142315 0.989821i 0.0821655 0.571474i
\(4\) 0 0
\(5\) −1.67835 3.67507i −0.750581 1.64354i −0.765318 0.643652i \(-0.777418\pi\)
0.0147373 0.999891i \(-0.495309\pi\)
\(6\) 0 0
\(7\) 2.54620 2.42780i 0.962373 0.917621i −0.0342765 0.999412i \(-0.510913\pi\)
0.996649 + 0.0817916i \(0.0260642\pi\)
\(8\) 0 0
\(9\) −0.959493 0.281733i −0.319831 0.0939109i
\(10\) 0 0
\(11\) 5.23241 + 0.499635i 1.57763 + 0.150646i 0.846800 0.531912i \(-0.178526\pi\)
0.730832 + 0.682558i \(0.239132\pi\)
\(12\) 0 0
\(13\) −2.29438 0.442205i −0.636346 0.122646i −0.139133 0.990274i \(-0.544431\pi\)
−0.497214 + 0.867628i \(0.665644\pi\)
\(14\) 0 0
\(15\) −3.87652 + 1.13825i −1.00091 + 0.293895i
\(16\) 0 0
\(17\) −1.39626 0.719822i −0.338643 0.174582i 0.280514 0.959850i \(-0.409495\pi\)
−0.619157 + 0.785267i \(0.712525\pi\)
\(18\) 0 0
\(19\) −0.391195 0.373004i −0.0897463 0.0855729i 0.643878 0.765128i \(-0.277324\pi\)
−0.733624 + 0.679555i \(0.762173\pi\)
\(20\) 0 0
\(21\) −2.04072 2.86579i −0.445322 0.625368i
\(22\) 0 0
\(23\) 7.68293 3.07578i 1.60200 0.641344i 0.613111 0.789997i \(-0.289918\pi\)
0.988890 + 0.148652i \(0.0474935\pi\)
\(24\) 0 0
\(25\) −7.41501 + 8.55738i −1.48300 + 1.71148i
\(26\) 0 0
\(27\) −0.415415 + 0.909632i −0.0799467 + 0.175059i
\(28\) 0 0
\(29\) −0.551633 + 0.955456i −0.102436 + 0.177424i −0.912688 0.408658i \(-0.865997\pi\)
0.810252 + 0.586082i \(0.199330\pi\)
\(30\) 0 0
\(31\) −7.91988 + 1.52643i −1.42245 + 0.274155i −0.841709 0.539932i \(-0.818450\pi\)
−0.580743 + 0.814087i \(0.697238\pi\)
\(32\) 0 0
\(33\) 1.23920 5.10805i 0.215717 0.889197i
\(34\) 0 0
\(35\) −13.1957 5.28278i −2.23049 0.892953i
\(36\) 0 0
\(37\) 5.09972 + 8.83298i 0.838389 + 1.45213i 0.891241 + 0.453530i \(0.149836\pi\)
−0.0528518 + 0.998602i \(0.516831\pi\)
\(38\) 0 0
\(39\) −0.764229 + 2.20809i −0.122375 + 0.353578i
\(40\) 0 0
\(41\) −0.441935 9.27736i −0.0690187 1.44888i −0.722203 0.691681i \(-0.756870\pi\)
0.653184 0.757199i \(-0.273433\pi\)
\(42\) 0 0
\(43\) −7.98049 + 5.12875i −1.21701 + 0.782127i −0.981819 0.189822i \(-0.939209\pi\)
−0.235194 + 0.971948i \(0.575573\pi\)
\(44\) 0 0
\(45\) 0.574977 + 3.99905i 0.0857125 + 0.596144i
\(46\) 0 0
\(47\) −3.79700 2.98600i −0.553850 0.435552i 0.301602 0.953434i \(-0.402478\pi\)
−0.855452 + 0.517881i \(0.826721\pi\)
\(48\) 0 0
\(49\) 0.255863 5.37124i 0.0365519 0.767319i
\(50\) 0 0
\(51\) −0.911204 + 1.27961i −0.127594 + 0.179181i
\(52\) 0 0
\(53\) −4.24648 2.72905i −0.583299 0.374863i 0.215462 0.976512i \(-0.430874\pi\)
−0.798761 + 0.601649i \(0.794511\pi\)
\(54\) 0 0
\(55\) −6.94562 20.0681i −0.936548 2.70598i
\(56\) 0 0
\(57\) −0.424880 + 0.334129i −0.0562767 + 0.0442565i
\(58\) 0 0
\(59\) 2.79526 + 3.22590i 0.363911 + 0.419976i 0.907946 0.419086i \(-0.137650\pi\)
−0.544035 + 0.839063i \(0.683104\pi\)
\(60\) 0 0
\(61\) 4.29709 0.410322i 0.550186 0.0525364i 0.183738 0.982975i \(-0.441180\pi\)
0.366447 + 0.930439i \(0.380574\pi\)
\(62\) 0 0
\(63\) −3.12705 + 1.61211i −0.393971 + 0.203106i
\(64\) 0 0
\(65\) 2.22563 + 9.17419i 0.276056 + 1.13792i
\(66\) 0 0
\(67\) 4.22580 + 7.01018i 0.516263 + 0.856430i
\(68\) 0 0
\(69\) −1.95108 8.04245i −0.234882 0.968198i
\(70\) 0 0
\(71\) 13.0777 6.74203i 1.55204 0.800132i 0.552595 0.833450i \(-0.313638\pi\)
0.999445 + 0.0333182i \(0.0106075\pi\)
\(72\) 0 0
\(73\) 6.99211 0.667666i 0.818365 0.0781444i 0.322528 0.946560i \(-0.395467\pi\)
0.495837 + 0.868416i \(0.334861\pi\)
\(74\) 0 0
\(75\) 7.41501 + 8.55738i 0.856212 + 0.988121i
\(76\) 0 0
\(77\) 14.5358 11.4311i 1.65651 1.30269i
\(78\) 0 0
\(79\) −2.12207 6.13133i −0.238752 0.689829i −0.999183 0.0404102i \(-0.987134\pi\)
0.760431 0.649419i \(-0.224988\pi\)
\(80\) 0 0
\(81\) 0.841254 + 0.540641i 0.0934726 + 0.0600712i
\(82\) 0 0
\(83\) −9.30173 + 13.0624i −1.02100 + 1.43379i −0.123723 + 0.992317i \(0.539483\pi\)
−0.897274 + 0.441473i \(0.854456\pi\)
\(84\) 0 0
\(85\) −0.301986 + 6.33947i −0.0327550 + 0.687612i
\(86\) 0 0
\(87\) 0.867226 + 0.681994i 0.0929763 + 0.0731174i
\(88\) 0 0
\(89\) 0.140072 + 0.974221i 0.0148476 + 0.103267i 0.995898 0.0904874i \(-0.0288425\pi\)
−0.981050 + 0.193755i \(0.937933\pi\)
\(90\) 0 0
\(91\) −6.91553 + 4.44434i −0.724945 + 0.465894i
\(92\) 0 0
\(93\) 0.383778 + 8.05650i 0.0397959 + 0.835420i
\(94\) 0 0
\(95\) −0.714254 + 2.06370i −0.0732809 + 0.211731i
\(96\) 0 0
\(97\) 0.846818 + 1.46673i 0.0859814 + 0.148924i 0.905809 0.423686i \(-0.139264\pi\)
−0.819828 + 0.572610i \(0.805931\pi\)
\(98\) 0 0
\(99\) −4.87970 1.95354i −0.490428 0.196338i
\(100\) 0 0
\(101\) 2.16283 8.91531i 0.215210 0.887106i −0.757079 0.653323i \(-0.773374\pi\)
0.972289 0.233783i \(-0.0751105\pi\)
\(102\) 0 0
\(103\) 6.23895 1.20246i 0.614742 0.118482i 0.127631 0.991822i \(-0.459263\pi\)
0.487111 + 0.873340i \(0.338051\pi\)
\(104\) 0 0
\(105\) −7.10696 + 12.3096i −0.693568 + 1.20130i
\(106\) 0 0
\(107\) 4.52537 9.90918i 0.437484 0.957957i −0.554569 0.832138i \(-0.687117\pi\)
0.992053 0.125819i \(-0.0401558\pi\)
\(108\) 0 0
\(109\) 7.16502 8.26887i 0.686284 0.792014i −0.300547 0.953767i \(-0.597169\pi\)
0.986831 + 0.161753i \(0.0517148\pi\)
\(110\) 0 0
\(111\) 9.46884 3.79075i 0.898742 0.359802i
\(112\) 0 0
\(113\) 3.20300 + 4.49799i 0.301313 + 0.423135i 0.937278 0.348583i \(-0.113337\pi\)
−0.635965 + 0.771718i \(0.719398\pi\)
\(114\) 0 0
\(115\) −24.1984 23.0731i −2.25651 2.15158i
\(116\) 0 0
\(117\) 2.07686 + 1.07069i 0.192006 + 0.0989857i
\(118\) 0 0
\(119\) −5.30274 + 1.55702i −0.486101 + 0.142732i
\(120\) 0 0
\(121\) 16.3273 + 3.14682i 1.48430 + 0.286075i
\(122\) 0 0
\(123\) −9.24583 0.882869i −0.833668 0.0796056i
\(124\) 0 0
\(125\) 24.5114 + 7.19719i 2.19236 + 0.643736i
\(126\) 0 0
\(127\) −7.42001 + 7.07497i −0.658420 + 0.627802i −0.943763 0.330624i \(-0.892741\pi\)
0.285343 + 0.958425i \(0.407892\pi\)
\(128\) 0 0
\(129\) 3.94080 + 8.62915i 0.346968 + 0.759755i
\(130\) 0 0
\(131\) −2.62424 + 18.2520i −0.229281 + 1.59469i 0.471866 + 0.881670i \(0.343581\pi\)
−0.701147 + 0.713016i \(0.747328\pi\)
\(132\) 0 0
\(133\) −1.90164 −0.164893
\(134\) 0 0
\(135\) 4.04018 0.347723
\(136\) 0 0
\(137\) −0.663672 + 4.61594i −0.0567013 + 0.394366i 0.941631 + 0.336645i \(0.109292\pi\)
−0.998333 + 0.0577207i \(0.981617\pi\)
\(138\) 0 0
\(139\) −4.01197 8.78500i −0.340291 0.745134i 0.659688 0.751539i \(-0.270688\pi\)
−0.999979 + 0.00640560i \(0.997961\pi\)
\(140\) 0 0
\(141\) −3.49597 + 3.33340i −0.294414 + 0.280723i
\(142\) 0 0
\(143\) −11.7842 3.46015i −0.985444 0.289352i
\(144\) 0 0
\(145\) 4.43721 + 0.423702i 0.368490 + 0.0351865i
\(146\) 0 0
\(147\) −5.28015 1.01767i −0.435500 0.0839357i
\(148\) 0 0
\(149\) −9.87527 + 2.89964i −0.809014 + 0.237548i −0.659979 0.751284i \(-0.729435\pi\)
−0.149035 + 0.988832i \(0.547617\pi\)
\(150\) 0 0
\(151\) 15.7758 + 8.13301i 1.28382 + 0.661855i 0.958862 0.283873i \(-0.0916195\pi\)
0.324958 + 0.945728i \(0.394650\pi\)
\(152\) 0 0
\(153\) 1.13690 + 1.08404i 0.0919133 + 0.0876391i
\(154\) 0 0
\(155\) 18.9021 + 26.5442i 1.51825 + 2.13209i
\(156\) 0 0
\(157\) 9.48751 3.79822i 0.757186 0.303131i 0.0392392 0.999230i \(-0.487507\pi\)
0.717946 + 0.696098i \(0.245082\pi\)
\(158\) 0 0
\(159\) −3.30560 + 3.81487i −0.262151 + 0.302539i
\(160\) 0 0
\(161\) 12.0949 26.4841i 0.953211 2.08724i
\(162\) 0 0
\(163\) −4.18083 + 7.24141i −0.327468 + 0.567191i −0.982009 0.188836i \(-0.939529\pi\)
0.654541 + 0.756027i \(0.272862\pi\)
\(164\) 0 0
\(165\) −20.8523 + 4.01894i −1.62335 + 0.312874i
\(166\) 0 0
\(167\) 3.94678 16.2688i 0.305411 1.25892i −0.587698 0.809080i \(-0.699966\pi\)
0.893109 0.449840i \(-0.148519\pi\)
\(168\) 0 0
\(169\) −7.00015 2.80244i −0.538473 0.215572i
\(170\) 0 0
\(171\) 0.270262 + 0.468107i 0.0206674 + 0.0357970i
\(172\) 0 0
\(173\) −6.72267 + 19.4239i −0.511115 + 1.47677i 0.334201 + 0.942502i \(0.391534\pi\)
−0.845316 + 0.534267i \(0.820588\pi\)
\(174\) 0 0
\(175\) 1.89548 + 39.7909i 0.143284 + 3.00791i
\(176\) 0 0
\(177\) 3.59087 2.30771i 0.269906 0.173458i
\(178\) 0 0
\(179\) −2.11934 14.7403i −0.158407 1.10174i −0.901570 0.432633i \(-0.857585\pi\)
0.743163 0.669110i \(-0.233325\pi\)
\(180\) 0 0
\(181\) 11.1141 + 8.74019i 0.826102 + 0.649654i 0.938986 0.343955i \(-0.111767\pi\)
−0.112885 + 0.993608i \(0.536009\pi\)
\(182\) 0 0
\(183\) 0.205394 4.31174i 0.0151831 0.318733i
\(184\) 0 0
\(185\) 23.9027 33.5667i 1.75736 2.46787i
\(186\) 0 0
\(187\) −6.94616 4.46402i −0.507953 0.326442i
\(188\) 0 0
\(189\) 1.15067 + 3.32465i 0.0836990 + 0.241833i
\(190\) 0 0
\(191\) 10.2641 8.07177i 0.742684 0.584053i −0.173490 0.984836i \(-0.555504\pi\)
0.916173 + 0.400783i \(0.131262\pi\)
\(192\) 0 0
\(193\) −8.38577 9.67769i −0.603621 0.696615i 0.368890 0.929473i \(-0.379738\pi\)
−0.972511 + 0.232858i \(0.925192\pi\)
\(194\) 0 0
\(195\) 9.39755 0.897357i 0.672973 0.0642611i
\(196\) 0 0
\(197\) 7.62815 3.93259i 0.543483 0.280185i −0.164544 0.986370i \(-0.552615\pi\)
0.708028 + 0.706184i \(0.249585\pi\)
\(198\) 0 0
\(199\) −0.678186 2.79552i −0.0480753 0.198169i 0.942709 0.333615i \(-0.108269\pi\)
−0.990785 + 0.135446i \(0.956753\pi\)
\(200\) 0 0
\(201\) 7.54022 3.18513i 0.531846 0.224662i
\(202\) 0 0
\(203\) 0.915086 + 3.77203i 0.0642264 + 0.264745i
\(204\) 0 0
\(205\) −33.3533 + 17.1948i −2.32949 + 1.20094i
\(206\) 0 0
\(207\) −8.23826 + 0.786659i −0.572599 + 0.0546765i
\(208\) 0 0
\(209\) −1.86053 2.14716i −0.128695 0.148522i
\(210\) 0 0
\(211\) 12.0964 9.51273i 0.832752 0.654883i −0.107936 0.994158i \(-0.534424\pi\)
0.940687 + 0.339275i \(0.110182\pi\)
\(212\) 0 0
\(213\) −4.81225 13.9041i −0.329730 0.952693i
\(214\) 0 0
\(215\) 32.2426 + 20.7211i 2.19893 + 1.41316i
\(216\) 0 0
\(217\) −16.4597 + 23.1144i −1.11736 + 1.56911i
\(218\) 0 0
\(219\) 0.334211 7.01596i 0.0225839 0.474095i
\(220\) 0 0
\(221\) 2.88524 + 2.26898i 0.194082 + 0.152628i
\(222\) 0 0
\(223\) 0.617833 + 4.29713i 0.0413732 + 0.287757i 0.999995 + 0.00307510i \(0.000978837\pi\)
−0.958622 + 0.284682i \(0.908112\pi\)
\(224\) 0 0
\(225\) 9.52554 6.12169i 0.635036 0.408113i
\(226\) 0 0
\(227\) 0.396759 + 8.32899i 0.0263338 + 0.552815i 0.973029 + 0.230683i \(0.0740962\pi\)
−0.946695 + 0.322131i \(0.895601\pi\)
\(228\) 0 0
\(229\) −2.30699 + 6.66562i −0.152451 + 0.440477i −0.995204 0.0978231i \(-0.968812\pi\)
0.842753 + 0.538300i \(0.180933\pi\)
\(230\) 0 0
\(231\) −9.24605 16.0146i −0.608345 1.05369i
\(232\) 0 0
\(233\) 3.30554 + 1.32334i 0.216553 + 0.0866948i 0.477402 0.878685i \(-0.341578\pi\)
−0.260849 + 0.965379i \(0.584003\pi\)
\(234\) 0 0
\(235\) −4.60106 + 18.9658i −0.300140 + 1.23719i
\(236\) 0 0
\(237\) −6.37093 + 1.22790i −0.413836 + 0.0797604i
\(238\) 0 0
\(239\) −0.700503 + 1.21331i −0.0453118 + 0.0784823i −0.887792 0.460245i \(-0.847761\pi\)
0.842480 + 0.538728i \(0.181095\pi\)
\(240\) 0 0
\(241\) −2.71668 + 5.94869i −0.174997 + 0.383189i −0.976724 0.214501i \(-0.931187\pi\)
0.801727 + 0.597690i \(0.203915\pi\)
\(242\) 0 0
\(243\) 0.654861 0.755750i 0.0420093 0.0484814i
\(244\) 0 0
\(245\) −20.1691 + 8.07450i −1.28856 + 0.515861i
\(246\) 0 0
\(247\) 0.732606 + 1.02880i 0.0466146 + 0.0654610i
\(248\) 0 0
\(249\) 11.6057 + 11.0660i 0.735483 + 0.701281i
\(250\) 0 0
\(251\) −15.4514 7.96576i −0.975285 0.502794i −0.104535 0.994521i \(-0.533335\pi\)
−0.870749 + 0.491727i \(0.836366\pi\)
\(252\) 0 0
\(253\) 41.7370 12.2551i 2.62398 0.770471i
\(254\) 0 0
\(255\) 6.23197 + 1.20111i 0.390261 + 0.0752166i
\(256\) 0 0
\(257\) 28.9862 + 2.76785i 1.80811 + 0.172654i 0.943846 0.330385i \(-0.107179\pi\)
0.864264 + 0.503038i \(0.167785\pi\)
\(258\) 0 0
\(259\) 34.4296 + 10.1094i 2.13935 + 0.628170i
\(260\) 0 0
\(261\) 0.798471 0.761341i 0.0494241 0.0471258i
\(262\) 0 0
\(263\) −9.83483 21.5353i −0.606442 1.32792i −0.924981 0.380013i \(-0.875920\pi\)
0.318539 0.947910i \(-0.396808\pi\)
\(264\) 0 0
\(265\) −2.90237 + 20.1864i −0.178291 + 1.24004i
\(266\) 0 0
\(267\) 0.984240 0.0602345
\(268\) 0 0
\(269\) 3.13815 0.191336 0.0956681 0.995413i \(-0.469501\pi\)
0.0956681 + 0.995413i \(0.469501\pi\)
\(270\) 0 0
\(271\) 4.10986 28.5847i 0.249656 1.73640i −0.350544 0.936546i \(-0.614003\pi\)
0.600200 0.799850i \(-0.295088\pi\)
\(272\) 0 0
\(273\) 3.41492 + 7.47764i 0.206681 + 0.452567i
\(274\) 0 0
\(275\) −43.0739 + 41.0709i −2.59746 + 2.47667i
\(276\) 0 0
\(277\) 21.7647 + 6.39071i 1.30772 + 0.383980i 0.860045 0.510218i \(-0.170435\pi\)
0.447671 + 0.894198i \(0.352253\pi\)
\(278\) 0 0
\(279\) 8.02911 + 0.766687i 0.480690 + 0.0459004i
\(280\) 0 0
\(281\) 7.94088 + 1.53048i 0.473713 + 0.0913007i 0.420520 0.907283i \(-0.361848\pi\)
0.0531937 + 0.998584i \(0.483060\pi\)
\(282\) 0 0
\(283\) −4.11994 + 1.20972i −0.244905 + 0.0719106i −0.401881 0.915692i \(-0.631644\pi\)
0.156976 + 0.987602i \(0.449825\pi\)
\(284\) 0 0
\(285\) 1.94105 + 1.00068i 0.114978 + 0.0592751i
\(286\) 0 0
\(287\) −23.6488 22.5491i −1.39594 1.33103i
\(288\) 0 0
\(289\) −8.42957 11.8377i −0.495857 0.696334i
\(290\) 0 0
\(291\) 1.57232 0.629461i 0.0921709 0.0368997i
\(292\) 0 0
\(293\) 4.90890 5.66517i 0.286781 0.330963i −0.594020 0.804451i \(-0.702460\pi\)
0.880800 + 0.473488i \(0.157005\pi\)
\(294\) 0 0
\(295\) 7.16400 15.6870i 0.417104 0.913330i
\(296\) 0 0
\(297\) −2.62811 + 4.55201i −0.152498 + 0.264135i
\(298\) 0 0
\(299\) −18.9877 + 3.65957i −1.09809 + 0.211639i
\(300\) 0 0
\(301\) −7.86836 + 32.4338i −0.453525 + 1.86945i
\(302\) 0 0
\(303\) −8.51676 3.40960i −0.489275 0.195876i
\(304\) 0 0
\(305\) −8.71998 15.1035i −0.499305 0.864821i
\(306\) 0 0
\(307\) 4.92971 14.2435i 0.281353 0.812917i −0.712446 0.701727i \(-0.752413\pi\)
0.993799 0.111190i \(-0.0354662\pi\)
\(308\) 0 0
\(309\) −0.302325 6.34657i −0.0171986 0.361044i
\(310\) 0 0
\(311\) −10.3488 + 6.65074i −0.586824 + 0.377129i −0.800103 0.599862i \(-0.795222\pi\)
0.213279 + 0.976991i \(0.431586\pi\)
\(312\) 0 0
\(313\) 0.957129 + 6.65698i 0.0541001 + 0.376275i 0.998827 + 0.0484169i \(0.0154176\pi\)
−0.944727 + 0.327858i \(0.893673\pi\)
\(314\) 0 0
\(315\) 11.1729 + 8.78646i 0.629521 + 0.495061i
\(316\) 0 0
\(317\) −1.51000 + 31.6987i −0.0848099 + 1.78038i 0.410695 + 0.911773i \(0.365286\pi\)
−0.495505 + 0.868605i \(0.665017\pi\)
\(318\) 0 0
\(319\) −3.36375 + 4.72373i −0.188334 + 0.264478i
\(320\) 0 0
\(321\) −9.16429 5.88953i −0.511501 0.328722i
\(322\) 0 0
\(323\) 0.277714 + 0.802401i 0.0154524 + 0.0446468i
\(324\) 0 0
\(325\) 20.7970 16.3549i 1.15361 0.907207i
\(326\) 0 0
\(327\) −7.16502 8.26887i −0.396226 0.457269i
\(328\) 0 0
\(329\) −16.9173 + 1.61541i −0.932682 + 0.0890604i
\(330\) 0 0
\(331\) 8.11228 4.18217i 0.445891 0.229873i −0.220632 0.975357i \(-0.570812\pi\)
0.666523 + 0.745484i \(0.267782\pi\)
\(332\) 0 0
\(333\) −2.40461 9.91194i −0.131772 0.543171i
\(334\) 0 0
\(335\) 18.6706 27.2957i 1.02008 1.49132i
\(336\) 0 0
\(337\) −1.73051 7.13327i −0.0942670 0.388574i 0.905059 0.425286i \(-0.139827\pi\)
−0.999326 + 0.0367125i \(0.988311\pi\)
\(338\) 0 0
\(339\) 4.90804 2.53027i 0.266568 0.137425i
\(340\) 0 0
\(341\) −42.2027 + 4.02987i −2.28540 + 0.218230i
\(342\) 0 0
\(343\) 3.73847 + 4.31442i 0.201858 + 0.232957i
\(344\) 0 0
\(345\) −26.2820 + 20.6684i −1.41498 + 1.11275i
\(346\) 0 0
\(347\) −3.51360 10.1519i −0.188620 0.544982i 0.810552 0.585667i \(-0.199167\pi\)
−0.999172 + 0.0406848i \(0.987046\pi\)
\(348\) 0 0
\(349\) −23.9207 15.3729i −1.28045 0.822892i −0.289503 0.957177i \(-0.593490\pi\)
−0.990943 + 0.134285i \(0.957126\pi\)
\(350\) 0 0
\(351\) 1.35536 1.90334i 0.0723440 0.101593i
\(352\) 0 0
\(353\) 0.0931665 1.95581i 0.00495875 0.104097i −0.995031 0.0995658i \(-0.968255\pi\)
0.999990 0.00453124i \(-0.00144234\pi\)
\(354\) 0 0
\(355\) −46.7265 36.7461i −2.47998 1.95028i
\(356\) 0 0
\(357\) 0.786518 + 5.47035i 0.0416269 + 0.289522i
\(358\) 0 0
\(359\) −7.39494 + 4.75244i −0.390290 + 0.250824i −0.721039 0.692895i \(-0.756335\pi\)
0.330749 + 0.943719i \(0.392699\pi\)
\(360\) 0 0
\(361\) −0.890155 18.6866i −0.0468502 0.983508i
\(362\) 0 0
\(363\) 5.43841 15.7132i 0.285442 0.824732i
\(364\) 0 0
\(365\) −14.1889 24.5760i −0.742683 1.28636i
\(366\) 0 0
\(367\) 14.0056 + 5.60698i 0.731084 + 0.292682i 0.707181 0.707032i \(-0.249967\pi\)
0.0239028 + 0.999714i \(0.492391\pi\)
\(368\) 0 0
\(369\) −2.18970 + 9.02607i −0.113991 + 0.469879i
\(370\) 0 0
\(371\) −17.4379 + 3.36089i −0.905333 + 0.174489i
\(372\) 0 0
\(373\) −6.66882 + 11.5507i −0.345298 + 0.598074i −0.985408 0.170209i \(-0.945556\pi\)
0.640110 + 0.768284i \(0.278889\pi\)
\(374\) 0 0
\(375\) 10.6123 23.2376i 0.548015 1.19999i
\(376\) 0 0
\(377\) 1.68816 1.94824i 0.0869448 0.100340i
\(378\) 0 0
\(379\) 0.272717 0.109180i 0.0140086 0.00560818i −0.364648 0.931146i \(-0.618811\pi\)
0.378656 + 0.925537i \(0.376386\pi\)
\(380\) 0 0
\(381\) 5.94698 + 8.35136i 0.304673 + 0.427853i
\(382\) 0 0
\(383\) −10.9944 10.4832i −0.561790 0.535666i 0.355088 0.934833i \(-0.384451\pi\)
−0.916878 + 0.399167i \(0.869299\pi\)
\(384\) 0 0
\(385\) −66.4061 34.2347i −3.38437 1.74476i
\(386\) 0 0
\(387\) 9.10216 2.67263i 0.462689 0.135858i
\(388\) 0 0
\(389\) 28.4319 + 5.47981i 1.44156 + 0.277837i 0.849299 0.527912i \(-0.177025\pi\)
0.592257 + 0.805749i \(0.298237\pi\)
\(390\) 0 0
\(391\) −12.9414 1.23575i −0.654473 0.0624946i
\(392\) 0 0
\(393\) 17.6928 + 5.19507i 0.892482 + 0.262057i
\(394\) 0 0
\(395\) −18.9715 + 18.0893i −0.954561 + 0.910172i
\(396\) 0 0
\(397\) −9.01108 19.7315i −0.452253 0.990297i −0.989185 0.146671i \(-0.953144\pi\)
0.536932 0.843626i \(-0.319583\pi\)
\(398\) 0 0
\(399\) −0.270631 + 1.88228i −0.0135485 + 0.0942320i
\(400\) 0 0
\(401\) −13.0777 −0.653067 −0.326534 0.945186i \(-0.605881\pi\)
−0.326534 + 0.945186i \(0.605881\pi\)
\(402\) 0 0
\(403\) 18.8462 0.938796
\(404\) 0 0
\(405\) 0.574977 3.99905i 0.0285708 0.198715i
\(406\) 0 0
\(407\) 22.2706 + 48.7658i 1.10391 + 2.41723i
\(408\) 0 0
\(409\) 10.0109 9.54534i 0.495006 0.471987i −0.400969 0.916091i \(-0.631327\pi\)
0.895975 + 0.444105i \(0.146478\pi\)
\(410\) 0 0
\(411\) 4.47450 + 1.31383i 0.220711 + 0.0648066i
\(412\) 0 0
\(413\) 14.9491 + 1.42747i 0.735597 + 0.0702410i
\(414\) 0 0
\(415\) 63.6170 + 12.2612i 3.12284 + 0.601878i
\(416\) 0 0
\(417\) −9.26654 + 2.72090i −0.453784 + 0.133243i
\(418\) 0 0
\(419\) −12.0969 6.23638i −0.590972 0.304667i 0.136678 0.990615i \(-0.456357\pi\)
−0.727650 + 0.685948i \(0.759388\pi\)
\(420\) 0 0
\(421\) −6.67393 6.36358i −0.325267 0.310142i 0.509796 0.860295i \(-0.329721\pi\)
−0.835064 + 0.550153i \(0.814569\pi\)
\(422\) 0 0
\(423\) 2.80195 + 3.93478i 0.136235 + 0.191316i
\(424\) 0 0
\(425\) 16.5131 6.61083i 0.801001 0.320673i
\(426\) 0 0
\(427\) 9.94506 11.4772i 0.481275 0.555421i
\(428\) 0 0
\(429\) −5.10200 + 11.1718i −0.246327 + 0.539381i
\(430\) 0 0
\(431\) −3.40149 + 5.89155i −0.163844 + 0.283786i −0.936244 0.351350i \(-0.885723\pi\)
0.772400 + 0.635136i \(0.219056\pi\)
\(432\) 0 0
\(433\) −30.6733 + 5.91180i −1.47406 + 0.284103i −0.862082 0.506768i \(-0.830840\pi\)
−0.611983 + 0.790871i \(0.709628\pi\)
\(434\) 0 0
\(435\) 1.05087 4.33174i 0.0503853 0.207691i
\(436\) 0 0
\(437\) −4.15280 1.66253i −0.198655 0.0795296i
\(438\) 0 0
\(439\) 15.2854 + 26.4750i 0.729530 + 1.26358i 0.957082 + 0.289817i \(0.0935945\pi\)
−0.227552 + 0.973766i \(0.573072\pi\)
\(440\) 0 0
\(441\) −1.75875 + 5.08158i −0.0837501 + 0.241980i
\(442\) 0 0
\(443\) −0.429360 9.01338i −0.0203995 0.428238i −0.985848 0.167643i \(-0.946384\pi\)
0.965448 0.260595i \(-0.0839187\pi\)
\(444\) 0 0
\(445\) 3.34525 2.14986i 0.158580 0.101913i
\(446\) 0 0
\(447\) 1.46473 + 10.1874i 0.0692793 + 0.481848i
\(448\) 0 0
\(449\) 13.4050 + 10.5418i 0.632619 + 0.497497i 0.882211 0.470854i \(-0.156054\pi\)
−0.249592 + 0.968351i \(0.580297\pi\)
\(450\) 0 0
\(451\) 2.32291 48.7638i 0.109381 2.29620i
\(452\) 0 0
\(453\) 10.2954 14.4578i 0.483718 0.679288i
\(454\) 0 0
\(455\) 27.9400 + 17.9559i 1.30985 + 0.841787i
\(456\) 0 0
\(457\) 7.14609 + 20.6473i 0.334280 + 0.965839i 0.979430 + 0.201783i \(0.0646736\pi\)
−0.645150 + 0.764056i \(0.723205\pi\)
\(458\) 0 0
\(459\) 1.23480 0.971058i 0.0576355 0.0453251i
\(460\) 0 0
\(461\) −4.65104 5.36759i −0.216621 0.249993i 0.637031 0.770838i \(-0.280162\pi\)
−0.853651 + 0.520845i \(0.825617\pi\)
\(462\) 0 0
\(463\) −36.1727 + 3.45408i −1.68109 + 0.160525i −0.891472 0.453075i \(-0.850327\pi\)
−0.789617 + 0.613600i \(0.789721\pi\)
\(464\) 0 0
\(465\) 28.9641 14.9320i 1.34318 0.692457i
\(466\) 0 0
\(467\) −1.34648 5.55027i −0.0623077 0.256836i 0.932136 0.362109i \(-0.117943\pi\)
−0.994443 + 0.105274i \(0.966428\pi\)
\(468\) 0 0
\(469\) 27.7790 + 7.58994i 1.28272 + 0.350471i
\(470\) 0 0
\(471\) −2.40935 9.93148i −0.111017 0.457619i
\(472\) 0 0
\(473\) −44.3197 + 22.8484i −2.03782 + 1.05057i
\(474\) 0 0
\(475\) 6.09265 0.581778i 0.279550 0.0266938i
\(476\) 0 0
\(477\) 3.30560 + 3.81487i 0.151353 + 0.174671i
\(478\) 0 0
\(479\) 6.92510 5.44596i 0.316416 0.248832i −0.447301 0.894383i \(-0.647615\pi\)
0.763717 + 0.645551i \(0.223372\pi\)
\(480\) 0 0
\(481\) −7.79471 22.5213i −0.355408 1.02688i
\(482\) 0 0
\(483\) −24.4933 15.7409i −1.11448 0.716234i
\(484\) 0 0
\(485\) 3.96909 5.57381i 0.180227 0.253094i
\(486\) 0 0
\(487\) −0.268082 + 5.62774i −0.0121480 + 0.255017i 0.984621 + 0.174701i \(0.0558960\pi\)
−0.996769 + 0.0803159i \(0.974407\pi\)
\(488\) 0 0
\(489\) 6.57271 + 5.16884i 0.297228 + 0.233743i
\(490\) 0 0
\(491\) 1.69012 + 11.7550i 0.0762738 + 0.530496i 0.991756 + 0.128138i \(0.0409002\pi\)
−0.915482 + 0.402358i \(0.868191\pi\)
\(492\) 0 0
\(493\) 1.45798 0.936988i 0.0656642 0.0421998i
\(494\) 0 0
\(495\) 1.01045 + 21.2120i 0.0454164 + 0.953407i
\(496\) 0 0
\(497\) 16.9302 48.9166i 0.759423 2.19421i
\(498\) 0 0
\(499\) −4.45174 7.71064i −0.199287 0.345176i 0.749010 0.662558i \(-0.230529\pi\)
−0.948298 + 0.317383i \(0.897196\pi\)
\(500\) 0 0
\(501\) −15.5416 6.22190i −0.694345 0.277974i
\(502\) 0 0
\(503\) −0.818886 + 3.37550i −0.0365123 + 0.150506i −0.987150 0.159798i \(-0.948916\pi\)
0.950637 + 0.310304i \(0.100431\pi\)
\(504\) 0 0
\(505\) −36.3944 + 7.01445i −1.61953 + 0.312139i
\(506\) 0 0
\(507\) −3.77014 + 6.53007i −0.167438 + 0.290011i
\(508\) 0 0
\(509\) −4.51665 + 9.89009i −0.200197 + 0.438370i −0.982928 0.183990i \(-0.941099\pi\)
0.782731 + 0.622360i \(0.213826\pi\)
\(510\) 0 0
\(511\) 16.1824 18.6754i 0.715865 0.826153i
\(512\) 0 0
\(513\) 0.501805 0.200892i 0.0221552 0.00886961i
\(514\) 0 0
\(515\) −14.8903 20.9105i −0.656144 0.921425i
\(516\) 0 0
\(517\) −18.3756 17.5211i −0.808157 0.770576i
\(518\) 0 0
\(519\) 18.2694 + 9.41854i 0.801939 + 0.413428i
\(520\) 0 0
\(521\) 23.7070 6.96100i 1.03862 0.304967i 0.282410 0.959294i \(-0.408866\pi\)
0.756212 + 0.654327i \(0.227048\pi\)
\(522\) 0 0
\(523\) 2.33956 + 0.450914i 0.102302 + 0.0197171i 0.240145 0.970737i \(-0.422805\pi\)
−0.137843 + 0.990454i \(0.544017\pi\)
\(524\) 0 0
\(525\) 39.6557 + 3.78666i 1.73071 + 0.165263i
\(526\) 0 0
\(527\) 12.1570 + 3.56961i 0.529566 + 0.155494i
\(528\) 0 0
\(529\) 32.9211 31.3902i 1.43135 1.36479i
\(530\) 0 0
\(531\) −1.77319 3.88274i −0.0769498 0.168497i
\(532\) 0 0
\(533\) −3.08853 + 21.4812i −0.133779 + 0.930455i
\(534\) 0 0
\(535\) −44.0121 −1.90281
\(536\) 0 0
\(537\) −14.8919 −0.642633
\(538\) 0 0
\(539\) 4.02244 27.9767i 0.173259 1.20504i
\(540\) 0 0
\(541\) 13.2116 + 28.9294i 0.568013 + 1.24377i 0.947849 + 0.318720i \(0.103253\pi\)
−0.379836 + 0.925054i \(0.624020\pi\)
\(542\) 0 0
\(543\) 10.2329 9.75708i 0.439137 0.418716i
\(544\) 0 0
\(545\) −42.4141 12.4539i −1.81682 0.533467i
\(546\) 0 0
\(547\) 8.99779 + 0.859185i 0.384718 + 0.0367361i 0.285623 0.958342i \(-0.407799\pi\)
0.0990943 + 0.995078i \(0.468405\pi\)
\(548\) 0 0
\(549\) −4.23863 0.816928i −0.180900 0.0348656i
\(550\) 0 0
\(551\) 0.572185 0.168009i 0.0243759 0.00715741i
\(552\) 0 0
\(553\) −20.2889 10.4596i −0.862770 0.444789i
\(554\) 0 0
\(555\) −29.8233 28.4365i −1.26593 1.20706i
\(556\) 0 0
\(557\) 3.15958 + 4.43701i 0.133876 + 0.188002i 0.876072 0.482181i \(-0.160155\pi\)
−0.742196 + 0.670183i \(0.766216\pi\)
\(558\) 0 0
\(559\) 20.5782 8.23828i 0.870366 0.348442i
\(560\) 0 0
\(561\) −5.40713 + 6.24016i −0.228289 + 0.263460i
\(562\) 0 0
\(563\) −8.94352 + 19.5836i −0.376924 + 0.825349i 0.622173 + 0.782879i \(0.286250\pi\)
−0.999098 + 0.0424697i \(0.986477\pi\)
\(564\) 0 0
\(565\) 11.1547 19.3205i 0.469281 0.812819i
\(566\) 0 0
\(567\) 3.45457 0.665813i 0.145078 0.0279615i
\(568\) 0 0
\(569\) −2.04295 + 8.42116i −0.0856450 + 0.353034i −0.998469 0.0553205i \(-0.982382\pi\)
0.912824 + 0.408354i \(0.133897\pi\)
\(570\) 0 0
\(571\) −2.48396 0.994428i −0.103951 0.0416155i 0.319104 0.947720i \(-0.396618\pi\)
−0.423055 + 0.906104i \(0.639042\pi\)
\(572\) 0 0
\(573\) −6.52888 11.3083i −0.272748 0.472413i
\(574\) 0 0
\(575\) −30.6484 + 88.5526i −1.27813 + 3.69290i
\(576\) 0 0
\(577\) 0.932346 + 19.5723i 0.0388141 + 0.814808i 0.931415 + 0.363959i \(0.118575\pi\)
−0.892601 + 0.450848i \(0.851122\pi\)
\(578\) 0 0
\(579\) −10.7726 + 6.92313i −0.447694 + 0.287716i
\(580\) 0 0
\(581\) 8.02891 + 55.8423i 0.333095 + 2.31673i
\(582\) 0 0
\(583\) −20.8558 16.4012i −0.863759 0.679267i
\(584\) 0 0
\(585\) 0.449188 9.42961i 0.0185716 0.389866i
\(586\) 0 0
\(587\) −22.3482 + 31.3837i −0.922409 + 1.29534i 0.0328153 + 0.999461i \(0.489553\pi\)
−0.955225 + 0.295881i \(0.904387\pi\)
\(588\) 0 0
\(589\) 3.66758 + 2.35701i 0.151120 + 0.0971190i
\(590\) 0 0
\(591\) −2.80696 8.11017i −0.115463 0.333608i
\(592\) 0 0
\(593\) −19.3285 + 15.2001i −0.793727 + 0.624194i −0.930451 0.366415i \(-0.880585\pi\)
0.136725 + 0.990609i \(0.456342\pi\)
\(594\) 0 0
\(595\) 14.6220 + 16.8747i 0.599445 + 0.691796i
\(596\) 0 0
\(597\) −2.86358 + 0.273439i −0.117199 + 0.0111911i
\(598\) 0 0
\(599\) −2.31677 + 1.19438i −0.0946607 + 0.0488010i −0.504907 0.863174i \(-0.668473\pi\)
0.410246 + 0.911975i \(0.365443\pi\)
\(600\) 0 0
\(601\) 1.22099 + 5.03300i 0.0498054 + 0.205301i 0.991278 0.131790i \(-0.0420724\pi\)
−0.941472 + 0.337090i \(0.890557\pi\)
\(602\) 0 0
\(603\) −2.07963 7.91676i −0.0846890 0.322396i
\(604\) 0 0
\(605\) −15.8381 65.2854i −0.643909 2.65423i
\(606\) 0 0
\(607\) 8.29159 4.27461i 0.336545 0.173501i −0.281667 0.959512i \(-0.590887\pi\)
0.618212 + 0.786011i \(0.287857\pi\)
\(608\) 0 0
\(609\) 3.86387 0.368955i 0.156572 0.0149508i
\(610\) 0 0
\(611\) 7.39135 + 8.53007i 0.299022 + 0.345090i
\(612\) 0 0
\(613\) 25.2903 19.8885i 1.02146 0.803288i 0.0408356 0.999166i \(-0.486998\pi\)
0.980628 + 0.195878i \(0.0627556\pi\)
\(614\) 0 0
\(615\) 12.2731 + 35.4609i 0.494900 + 1.42992i
\(616\) 0 0
\(617\) −16.8964 10.8587i −0.680224 0.437153i 0.154375 0.988012i \(-0.450664\pi\)
−0.834598 + 0.550859i \(0.814300\pi\)
\(618\) 0 0
\(619\) −20.3543 + 28.5836i −0.818107 + 1.14887i 0.168491 + 0.985703i \(0.446111\pi\)
−0.986598 + 0.163168i \(0.947829\pi\)
\(620\) 0 0
\(621\) −0.393775 + 8.26636i −0.0158017 + 0.331718i
\(622\) 0 0
\(623\) 2.72186 + 2.14050i 0.109049 + 0.0857572i
\(624\) 0 0
\(625\) −6.63129 46.1216i −0.265252 1.84487i
\(626\) 0 0
\(627\) −2.39009 + 1.53602i −0.0954510 + 0.0613426i
\(628\) 0 0
\(629\) −0.762366 16.0040i −0.0303975 0.638122i
\(630\) 0 0
\(631\) −7.54574 + 21.8020i −0.300391 + 0.867923i 0.689271 + 0.724504i \(0.257931\pi\)
−0.989662 + 0.143419i \(0.954190\pi\)
\(632\) 0 0
\(633\) −7.69440 13.3271i −0.305825 0.529704i
\(634\) 0 0
\(635\) 38.4544 + 15.3948i 1.52602 + 0.610925i
\(636\) 0 0
\(637\) −2.96224 + 12.2105i −0.117368 + 0.483798i
\(638\) 0 0
\(639\) −14.4474 + 2.78451i −0.571531 + 0.110154i
\(640\) 0 0
\(641\) 4.58346 7.93878i 0.181036 0.313563i −0.761198 0.648520i \(-0.775388\pi\)
0.942233 + 0.334957i \(0.108722\pi\)
\(642\) 0 0
\(643\) −18.8277 + 41.2268i −0.742491 + 1.62583i 0.0369234 + 0.999318i \(0.488244\pi\)
−0.779414 + 0.626509i \(0.784483\pi\)
\(644\) 0 0
\(645\) 25.0987 28.9655i 0.988262 1.14051i
\(646\) 0 0
\(647\) −5.07457 + 2.03155i −0.199502 + 0.0798685i −0.469262 0.883059i \(-0.655480\pi\)
0.269760 + 0.962928i \(0.413056\pi\)
\(648\) 0 0
\(649\) 13.0142 + 18.2758i 0.510851 + 0.717389i
\(650\) 0 0
\(651\) 20.5367 + 19.5817i 0.804897 + 0.767468i
\(652\) 0 0
\(653\) −15.4472 7.96357i −0.604495 0.311639i 0.128672 0.991687i \(-0.458928\pi\)
−0.733167 + 0.680048i \(0.761959\pi\)
\(654\) 0 0
\(655\) 71.4820 20.9890i 2.79303 0.820108i
\(656\) 0 0
\(657\) −6.89699 1.32929i −0.269077 0.0518604i
\(658\) 0 0
\(659\) 22.0552 + 2.10602i 0.859149 + 0.0820388i 0.515325 0.856995i \(-0.327671\pi\)
0.343825 + 0.939034i \(0.388277\pi\)
\(660\) 0 0
\(661\) −17.7369 5.20802i −0.689885 0.202568i −0.0820456 0.996629i \(-0.526145\pi\)
−0.607839 + 0.794060i \(0.707963\pi\)
\(662\) 0 0
\(663\) 2.65650 2.53296i 0.103170 0.0983722i
\(664\) 0 0
\(665\) 3.19161 + 6.98866i 0.123766 + 0.271009i
\(666\) 0 0
\(667\) −1.29938 + 9.03740i −0.0503123 + 0.349930i
\(668\) 0 0
\(669\) 4.34131 0.167845
\(670\) 0 0
\(671\) 22.6891 0.875904
\(672\) 0 0
\(673\) −6.72494 + 46.7730i −0.259227 + 1.80297i 0.279135 + 0.960252i \(0.409952\pi\)
−0.538362 + 0.842714i \(0.680957\pi\)
\(674\) 0 0
\(675\) −4.70376 10.2998i −0.181048 0.396439i
\(676\) 0 0
\(677\) 27.5201 26.2403i 1.05768 1.00850i 0.0577331 0.998332i \(-0.481613\pi\)
0.999948 0.0101652i \(-0.00323574\pi\)
\(678\) 0 0
\(679\) 5.71710 + 1.67869i 0.219402 + 0.0644222i
\(680\) 0 0
\(681\) 8.30068 + 0.792619i 0.318083 + 0.0303732i
\(682\) 0 0
\(683\) −33.7875 6.51202i −1.29284 0.249175i −0.503965 0.863724i \(-0.668126\pi\)
−0.788879 + 0.614548i \(0.789338\pi\)
\(684\) 0 0
\(685\) 18.0778 5.30812i 0.690717 0.202813i
\(686\) 0 0
\(687\) 6.26946 + 3.23213i 0.239195 + 0.123313i
\(688\) 0 0
\(689\) 8.53623 + 8.13928i 0.325205 + 0.310082i
\(690\) 0 0
\(691\) 24.6692 + 34.6431i 0.938461 + 1.31788i 0.948114 + 0.317930i \(0.102988\pi\)
−0.00965323 + 0.999953i \(0.503073\pi\)
\(692\) 0 0
\(693\) −17.1675 + 6.87282i −0.652138 + 0.261077i
\(694\) 0 0
\(695\) −25.5520 + 29.4886i −0.969243 + 1.11857i
\(696\) 0 0
\(697\) −6.06099 + 13.2717i −0.229576 + 0.502702i
\(698\) 0 0
\(699\) 1.78030 3.08356i 0.0673370 0.116631i
\(700\) 0 0
\(701\) 12.0481 2.32208i 0.455049 0.0877036i 0.0434241 0.999057i \(-0.486173\pi\)
0.411625 + 0.911353i \(0.364961\pi\)
\(702\) 0 0
\(703\) 1.29975 5.35763i 0.0490209 0.202067i
\(704\) 0 0
\(705\) 18.1180 + 7.25335i 0.682363 + 0.273177i
\(706\) 0 0
\(707\) −16.1376 27.9511i −0.606915 1.05121i
\(708\) 0 0
\(709\) −16.3278 + 47.1760i −0.613203 + 1.77173i 0.0224389 + 0.999748i \(0.492857\pi\)
−0.635642 + 0.771984i \(0.719264\pi\)
\(710\) 0 0
\(711\) 0.308720 + 6.48083i 0.0115779 + 0.243050i
\(712\) 0 0
\(713\) −56.1529 + 36.0872i −2.10294 + 1.35148i
\(714\) 0 0
\(715\) 7.06169 + 49.1151i 0.264092 + 1.83680i
\(716\) 0 0
\(717\) 1.10127 + 0.866044i 0.0411275 + 0.0323430i
\(718\) 0 0
\(719\) −1.68414 + 35.3545i −0.0628078 + 1.31850i 0.719013 + 0.694996i \(0.244594\pi\)
−0.781821 + 0.623503i \(0.785709\pi\)
\(720\) 0 0
\(721\) 12.9663 18.2086i 0.482890 0.678124i
\(722\) 0 0
\(723\) 5.50152 + 3.53561i 0.204604 + 0.131491i
\(724\) 0 0
\(725\) −4.08584 11.8052i −0.151744 0.438436i
\(726\) 0 0
\(727\) −24.5160 + 19.2796i −0.909248 + 0.715041i −0.958906 0.283725i \(-0.908430\pi\)
0.0496572 + 0.998766i \(0.484187\pi\)
\(728\) 0 0
\(729\) −0.654861 0.755750i −0.0242541 0.0279907i
\(730\) 0 0
\(731\) 14.8346 1.41653i 0.548678 0.0523924i
\(732\) 0 0
\(733\) 34.5566 17.8152i 1.27638 0.658019i 0.319246 0.947672i \(-0.396570\pi\)
0.957132 + 0.289653i \(0.0935399\pi\)
\(734\) 0 0
\(735\) 5.12195 + 21.1129i 0.188926 + 0.778763i
\(736\) 0 0
\(737\) 18.6086 + 38.7915i 0.685456 + 1.42890i
\(738\) 0 0
\(739\) 5.59628 + 23.0682i 0.205863 + 0.848577i 0.977229 + 0.212186i \(0.0680584\pi\)
−0.771367 + 0.636391i \(0.780426\pi\)
\(740\) 0 0
\(741\) 1.12259 0.578735i 0.0412394 0.0212604i
\(742\) 0 0
\(743\) 0.100586 0.00960481i 0.00369015 0.000352366i −0.0932108 0.995646i \(-0.529713\pi\)
0.0969010 + 0.995294i \(0.469107\pi\)
\(744\) 0 0
\(745\) 27.2306 + 31.4257i 0.997651 + 1.15135i
\(746\) 0 0
\(747\) 12.6051 9.91273i 0.461195 0.362688i
\(748\) 0 0
\(749\) −12.5350 36.2174i −0.458018 1.32336i
\(750\) 0 0
\(751\) 33.9577 + 21.8233i 1.23913 + 0.796343i 0.985288 0.170902i \(-0.0546680\pi\)
0.253846 + 0.967245i \(0.418304\pi\)
\(752\) 0 0
\(753\) −10.0836 + 14.1605i −0.367468 + 0.516037i
\(754\) 0 0
\(755\) 3.41204 71.6274i 0.124177 2.60679i
\(756\) 0 0
\(757\) −13.4066 10.5431i −0.487271 0.383194i 0.344081 0.938940i \(-0.388190\pi\)
−0.831352 + 0.555745i \(0.812433\pi\)
\(758\) 0 0
\(759\) −6.19056 43.0563i −0.224703 1.56284i
\(760\) 0 0
\(761\) 31.8627 20.4769i 1.15502 0.742287i 0.184388 0.982854i \(-0.440970\pi\)
0.970633 + 0.240567i \(0.0773333\pi\)
\(762\) 0 0
\(763\) −1.83157 38.4494i −0.0663073 1.39196i
\(764\) 0 0
\(765\) 2.07579 5.99760i 0.0750503 0.216844i
\(766\) 0 0
\(767\) −4.98687 8.63751i −0.180065 0.311883i
\(768\) 0 0
\(769\) 26.9406 + 10.7854i 0.971502 + 0.388931i 0.802478 0.596681i \(-0.203514\pi\)
0.169023 + 0.985612i \(0.445939\pi\)
\(770\) 0 0
\(771\) 6.86484 28.2973i 0.247231 1.01910i
\(772\) 0 0
\(773\) −14.2944 + 2.75501i −0.514132 + 0.0990909i −0.439717 0.898136i \(-0.644921\pi\)
−0.0744154 + 0.997227i \(0.523709\pi\)
\(774\) 0 0
\(775\) 45.6637 79.0919i 1.64029 2.84106i
\(776\) 0 0
\(777\) 14.9064 32.6404i 0.534763 1.17097i
\(778\) 0 0