Properties

Label 804.2.s.b.5.2
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.58909 + 0.689041i) q^{3} +(3.06595 - 0.900243i) q^{5} +(0.591666 + 0.512682i) q^{7} +(2.05045 - 2.18990i) q^{9} +O(q^{10})\) \(q+(-1.58909 + 0.689041i) q^{3} +(3.06595 - 0.900243i) q^{5} +(0.591666 + 0.512682i) q^{7} +(2.05045 - 2.18990i) q^{9} +(4.86665 - 1.42898i) q^{11} +(-2.95958 - 4.60520i) q^{13} +(-4.25177 + 3.54313i) q^{15} +(-4.50325 - 0.647469i) q^{17} +(1.29471 + 1.49418i) q^{19} +(-1.29347 - 0.407017i) q^{21} +(-2.56007 + 1.16914i) q^{23} +(4.38332 - 2.81699i) q^{25} +(-1.74942 + 4.89280i) q^{27} -4.91969i q^{29} +(3.39701 - 5.28586i) q^{31} +(-6.74894 + 5.62410i) q^{33} +(2.27555 + 1.03921i) q^{35} +3.77494 q^{37} +(7.87622 + 5.27882i) q^{39} +(0.190364 - 1.32401i) q^{41} +(8.46946 + 1.21772i) q^{43} +(4.31511 - 8.56002i) q^{45} +(1.21808 - 0.556280i) q^{47} +(-0.908978 - 6.32208i) q^{49} +(7.60222 - 2.07403i) q^{51} +(1.69585 + 11.7949i) q^{53} +(13.6344 - 8.76233i) q^{55} +(-3.08697 - 1.48228i) q^{57} +(-4.76970 + 7.42180i) q^{59} +(3.83621 - 13.0649i) q^{61} +(2.33590 - 0.244466i) q^{63} +(-13.2197 - 11.4549i) q^{65} +(1.21150 + 8.09520i) q^{67} +(3.26261 - 3.62188i) q^{69} +(-4.49276 + 0.645961i) q^{71} +(2.01307 + 0.591090i) q^{73} +(-5.02449 + 7.49675i) q^{75} +(3.61204 + 1.64956i) q^{77} +(2.99859 + 4.66590i) q^{79} +(-0.591350 - 8.98055i) q^{81} +(-1.16155 - 3.95589i) q^{83} +(-14.3896 + 2.06891i) q^{85} +(3.38987 + 7.81785i) q^{87} +(14.3613 + 6.55861i) q^{89} +(0.609916 - 4.24206i) q^{91} +(-1.75601 + 10.7404i) q^{93} +(5.31463 + 3.41551i) q^{95} +3.09130i q^{97} +(6.84947 - 13.5875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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
\(3\) −1.58909 + 0.689041i −0.917464 + 0.397818i
\(4\) 0 0
\(5\) 3.06595 0.900243i 1.37113 0.402601i 0.488459 0.872587i \(-0.337559\pi\)
0.882674 + 0.469986i \(0.155741\pi\)
\(6\) 0 0
\(7\) 0.591666 + 0.512682i 0.223629 + 0.193775i 0.759468 0.650545i \(-0.225459\pi\)
−0.535839 + 0.844320i \(0.680005\pi\)
\(8\) 0 0
\(9\) 2.05045 2.18990i 0.683482 0.729968i
\(10\) 0 0
\(11\) 4.86665 1.42898i 1.46735 0.430852i 0.552112 0.833770i \(-0.313822\pi\)
0.915236 + 0.402917i \(0.132004\pi\)
\(12\) 0 0
\(13\) −2.95958 4.60520i −0.820840 1.27725i −0.958019 0.286705i \(-0.907440\pi\)
0.137179 0.990546i \(-0.456196\pi\)
\(14\) 0 0
\(15\) −4.25177 + 3.54313i −1.09780 + 0.914833i
\(16\) 0 0
\(17\) −4.50325 0.647469i −1.09220 0.157034i −0.427403 0.904061i \(-0.640572\pi\)
−0.664794 + 0.747027i \(0.731481\pi\)
\(18\) 0 0
\(19\) 1.29471 + 1.49418i 0.297027 + 0.342787i 0.884572 0.466404i \(-0.154451\pi\)
−0.587545 + 0.809192i \(0.699905\pi\)
\(20\) 0 0
\(21\) −1.29347 0.407017i −0.282259 0.0888185i
\(22\) 0 0
\(23\) −2.56007 + 1.16914i −0.533812 + 0.243784i −0.664036 0.747701i \(-0.731158\pi\)
0.130224 + 0.991485i \(0.458430\pi\)
\(24\) 0 0
\(25\) 4.38332 2.81699i 0.876664 0.563398i
\(26\) 0 0
\(27\) −1.74942 + 4.89280i −0.336676 + 0.941621i
\(28\) 0 0
\(29\) 4.91969i 0.913564i −0.889579 0.456782i \(-0.849002\pi\)
0.889579 0.456782i \(-0.150998\pi\)
\(30\) 0 0
\(31\) 3.39701 5.28586i 0.610122 0.949368i −0.389477 0.921036i \(-0.627344\pi\)
0.999599 0.0283318i \(-0.00901950\pi\)
\(32\) 0 0
\(33\) −6.74894 + 5.62410i −1.17484 + 0.979030i
\(34\) 0 0
\(35\) 2.27555 + 1.03921i 0.384639 + 0.175659i
\(36\) 0 0
\(37\) 3.77494 0.620596 0.310298 0.950639i \(-0.399571\pi\)
0.310298 + 0.950639i \(0.399571\pi\)
\(38\) 0 0
\(39\) 7.87622 + 5.27882i 1.26121 + 0.845288i
\(40\) 0 0
\(41\) 0.190364 1.32401i 0.0297299 0.206776i −0.969542 0.244924i \(-0.921237\pi\)
0.999272 + 0.0381483i \(0.0121459\pi\)
\(42\) 0 0
\(43\) 8.46946 + 1.21772i 1.29158 + 0.185701i 0.753643 0.657284i \(-0.228295\pi\)
0.537937 + 0.842985i \(0.319204\pi\)
\(44\) 0 0
\(45\) 4.31511 8.56002i 0.643258 1.27605i
\(46\) 0 0
\(47\) 1.21808 0.556280i 0.177676 0.0811417i −0.324591 0.945854i \(-0.605227\pi\)
0.502267 + 0.864713i \(0.332499\pi\)
\(48\) 0 0
\(49\) −0.908978 6.32208i −0.129854 0.903154i
\(50\) 0 0
\(51\) 7.60222 2.07403i 1.06452 0.290422i
\(52\) 0 0
\(53\) 1.69585 + 11.7949i 0.232943 + 1.62016i 0.685259 + 0.728299i \(0.259689\pi\)
−0.452316 + 0.891858i \(0.649402\pi\)
\(54\) 0 0
\(55\) 13.6344 8.76233i 1.83847 1.18151i
\(56\) 0 0
\(57\) −3.08697 1.48228i −0.408879 0.196333i
\(58\) 0 0
\(59\) −4.76970 + 7.42180i −0.620963 + 0.966237i 0.378216 + 0.925717i \(0.376538\pi\)
−0.999179 + 0.0405193i \(0.987099\pi\)
\(60\) 0 0
\(61\) 3.83621 13.0649i 0.491176 1.67279i −0.224590 0.974453i \(-0.572104\pi\)
0.715766 0.698340i \(-0.246078\pi\)
\(62\) 0 0
\(63\) 2.33590 0.244466i 0.294296 0.0307998i
\(64\) 0 0
\(65\) −13.2197 11.4549i −1.63970 1.42081i
\(66\) 0 0
\(67\) 1.21150 + 8.09520i 0.148008 + 0.988986i
\(68\) 0 0
\(69\) 3.26261 3.62188i 0.392772 0.436023i
\(70\) 0 0
\(71\) −4.49276 + 0.645961i −0.533192 + 0.0766614i −0.403652 0.914913i \(-0.632259\pi\)
−0.129540 + 0.991574i \(0.541350\pi\)
\(72\) 0 0
\(73\) 2.01307 + 0.591090i 0.235612 + 0.0691818i 0.397407 0.917643i \(-0.369910\pi\)
−0.161795 + 0.986824i \(0.551728\pi\)
\(74\) 0 0
\(75\) −5.02449 + 7.49675i −0.580178 + 0.865650i
\(76\) 0 0
\(77\) 3.61204 + 1.64956i 0.411630 + 0.187985i
\(78\) 0 0
\(79\) 2.99859 + 4.66590i 0.337368 + 0.524955i 0.967942 0.251175i \(-0.0808168\pi\)
−0.630574 + 0.776129i \(0.717180\pi\)
\(80\) 0 0
\(81\) −0.591350 8.98055i −0.0657056 0.997839i
\(82\) 0 0
\(83\) −1.16155 3.95589i −0.127497 0.434215i 0.870859 0.491533i \(-0.163563\pi\)
−0.998356 + 0.0573178i \(0.981745\pi\)
\(84\) 0 0
\(85\) −14.3896 + 2.06891i −1.56077 + 0.224405i
\(86\) 0 0
\(87\) 3.38987 + 7.81785i 0.363432 + 0.838162i
\(88\) 0 0
\(89\) 14.3613 + 6.55861i 1.52230 + 0.695211i 0.988614 0.150472i \(-0.0480795\pi\)
0.533685 + 0.845683i \(0.320807\pi\)
\(90\) 0 0
\(91\) 0.609916 4.24206i 0.0639366 0.444689i
\(92\) 0 0
\(93\) −1.75601 + 10.7404i −0.182089 + 1.11373i
\(94\) 0 0
\(95\) 5.31463 + 3.41551i 0.545270 + 0.350424i
\(96\) 0 0
\(97\) 3.09130i 0.313874i 0.987609 + 0.156937i \(0.0501619\pi\)
−0.987609 + 0.156937i \(0.949838\pi\)
\(98\) 0 0
\(99\) 6.84947 13.5875i 0.688398 1.36560i
\(100\) 0 0
\(101\) −2.16124 2.49420i −0.215051 0.248182i 0.637967 0.770064i \(-0.279776\pi\)
−0.853018 + 0.521882i \(0.825230\pi\)
\(102\) 0 0
\(103\) −4.11999 2.64776i −0.405955 0.260891i 0.321691 0.946845i \(-0.395749\pi\)
−0.727645 + 0.685954i \(0.759385\pi\)
\(104\) 0 0
\(105\) −4.33213 0.0834544i −0.422773 0.00814432i
\(106\) 0 0
\(107\) 3.05837 10.4159i 0.295664 1.00694i −0.668958 0.743300i \(-0.733259\pi\)
0.964622 0.263638i \(-0.0849225\pi\)
\(108\) 0 0
\(109\) 3.72176 + 5.79117i 0.356480 + 0.554693i 0.972460 0.233068i \(-0.0748765\pi\)
−0.615981 + 0.787761i \(0.711240\pi\)
\(110\) 0 0
\(111\) −5.99873 + 2.60109i −0.569375 + 0.246884i
\(112\) 0 0
\(113\) 13.7712 + 4.04358i 1.29548 + 0.380388i 0.855586 0.517661i \(-0.173197\pi\)
0.439896 + 0.898049i \(0.355015\pi\)
\(114\) 0 0
\(115\) −6.79652 + 5.88922i −0.633779 + 0.549173i
\(116\) 0 0
\(117\) −16.1534 2.96151i −1.49338 0.273792i
\(118\) 0 0
\(119\) −2.33247 2.69182i −0.213817 0.246758i
\(120\) 0 0
\(121\) 12.3885 7.96159i 1.12622 0.723781i
\(122\) 0 0
\(123\) 0.609792 + 2.23515i 0.0549831 + 0.201537i
\(124\) 0 0
\(125\) 0.440399 0.508248i 0.0393905 0.0454590i
\(126\) 0 0
\(127\) −9.03409 + 10.4259i −0.801646 + 0.925149i −0.998470 0.0552898i \(-0.982392\pi\)
0.196824 + 0.980439i \(0.436937\pi\)
\(128\) 0 0
\(129\) −14.2978 + 3.90072i −1.25885 + 0.343440i
\(130\) 0 0
\(131\) −14.8926 + 6.80123i −1.30117 + 0.594226i −0.940920 0.338628i \(-0.890037\pi\)
−0.360253 + 0.932854i \(0.617310\pi\)
\(132\) 0 0
\(133\) 1.54783i 0.134214i
\(134\) 0 0
\(135\) −0.958911 + 16.5760i −0.0825299 + 1.42663i
\(136\) 0 0
\(137\) 6.25736 + 13.7017i 0.534603 + 1.17062i 0.963609 + 0.267315i \(0.0861365\pi\)
−0.429006 + 0.903301i \(0.641136\pi\)
\(138\) 0 0
\(139\) −1.64168 5.59103i −0.139245 0.474225i 0.860111 0.510107i \(-0.170394\pi\)
−0.999356 + 0.0358817i \(0.988576\pi\)
\(140\) 0 0
\(141\) −1.55235 + 1.72329i −0.130731 + 0.145127i
\(142\) 0 0
\(143\) −20.9839 18.1827i −1.75477 1.52051i
\(144\) 0 0
\(145\) −4.42892 15.0835i −0.367801 1.25262i
\(146\) 0 0
\(147\) 5.80062 + 9.42006i 0.478427 + 0.776953i
\(148\) 0 0
\(149\) −15.6118 + 13.5277i −1.27897 + 1.10823i −0.290492 + 0.956877i \(0.593819\pi\)
−0.988479 + 0.151358i \(0.951635\pi\)
\(150\) 0 0
\(151\) −0.471751 + 3.28110i −0.0383906 + 0.267012i −0.999972 0.00750825i \(-0.997610\pi\)
0.961581 + 0.274521i \(0.0885191\pi\)
\(152\) 0 0
\(153\) −10.6516 + 8.53407i −0.861127 + 0.689939i
\(154\) 0 0
\(155\) 5.65651 19.2643i 0.454342 1.54735i
\(156\) 0 0
\(157\) −8.02015 17.5617i −0.640077 1.40157i −0.899977 0.435938i \(-0.856417\pi\)
0.259899 0.965636i \(-0.416311\pi\)
\(158\) 0 0
\(159\) −10.8221 17.5747i −0.858245 1.39377i
\(160\) 0 0
\(161\) −2.11411 0.620757i −0.166615 0.0489225i
\(162\) 0 0
\(163\) −18.4910 −1.44833 −0.724165 0.689627i \(-0.757775\pi\)
−0.724165 + 0.689627i \(0.757775\pi\)
\(164\) 0 0
\(165\) −15.6288 + 23.3189i −1.21670 + 1.81537i
\(166\) 0 0
\(167\) −4.74561 + 4.11209i −0.367226 + 0.318203i −0.818853 0.574004i \(-0.805389\pi\)
0.451627 + 0.892207i \(0.350844\pi\)
\(168\) 0 0
\(169\) −7.04833 + 15.4337i −0.542179 + 1.18721i
\(170\) 0 0
\(171\) 5.92683 + 0.228435i 0.453236 + 0.0174688i
\(172\) 0 0
\(173\) −11.1237 + 17.3088i −0.845718 + 1.31596i 0.101325 + 0.994853i \(0.467692\pi\)
−0.947042 + 0.321109i \(0.895944\pi\)
\(174\) 0 0
\(175\) 4.03768 + 0.580531i 0.305220 + 0.0438840i
\(176\) 0 0
\(177\) 2.46558 15.0805i 0.185325 1.13352i
\(178\) 0 0
\(179\) −9.19948 + 20.1440i −0.687601 + 1.50564i 0.166782 + 0.985994i \(0.446662\pi\)
−0.854384 + 0.519643i \(0.826065\pi\)
\(180\) 0 0
\(181\) 0.297134 + 0.650633i 0.0220858 + 0.0483612i 0.920353 0.391088i \(-0.127901\pi\)
−0.898268 + 0.439449i \(0.855174\pi\)
\(182\) 0 0
\(183\) 2.90617 + 23.4047i 0.214830 + 1.73013i
\(184\) 0 0
\(185\) 11.5738 3.39836i 0.850919 0.249853i
\(186\) 0 0
\(187\) −22.8409 + 3.28403i −1.67029 + 0.240152i
\(188\) 0 0
\(189\) −3.54352 + 1.99801i −0.257753 + 0.145334i
\(190\) 0 0
\(191\) 7.89553 17.2888i 0.571300 1.25097i −0.374802 0.927105i \(-0.622289\pi\)
0.946102 0.323868i \(-0.104984\pi\)
\(192\) 0 0
\(193\) 0.0158178 + 0.0101655i 0.00113859 + 0.000731725i 0.541210 0.840887i \(-0.317966\pi\)
−0.540071 + 0.841619i \(0.681603\pi\)
\(194\) 0 0
\(195\) 28.9003 + 9.09407i 2.06959 + 0.651240i
\(196\) 0 0
\(197\) −1.71963 11.9603i −0.122518 0.852135i −0.954687 0.297612i \(-0.903810\pi\)
0.832168 0.554523i \(-0.187099\pi\)
\(198\) 0 0
\(199\) 5.58649 6.44716i 0.396016 0.457027i −0.522366 0.852721i \(-0.674951\pi\)
0.918382 + 0.395694i \(0.129496\pi\)
\(200\) 0 0
\(201\) −7.50311 12.0293i −0.529228 0.848479i
\(202\) 0 0
\(203\) 2.52223 2.91081i 0.177026 0.204299i
\(204\) 0 0
\(205\) −0.608287 4.23073i −0.0424846 0.295487i
\(206\) 0 0
\(207\) −2.68897 + 8.00357i −0.186896 + 0.556287i
\(208\) 0 0
\(209\) 8.43604 + 5.42151i 0.583533 + 0.375014i
\(210\) 0 0
\(211\) 0.888906 1.94643i 0.0611948 0.133998i −0.876564 0.481286i \(-0.840170\pi\)
0.937759 + 0.347288i \(0.112897\pi\)
\(212\) 0 0
\(213\) 6.69432 4.12219i 0.458687 0.282448i
\(214\) 0 0
\(215\) 27.0631 3.89109i 1.84569 0.265370i
\(216\) 0 0
\(217\) 4.71986 1.38588i 0.320405 0.0940794i
\(218\) 0 0
\(219\) −3.60624 + 0.447788i −0.243687 + 0.0302587i
\(220\) 0 0
\(221\) 10.3460 + 22.6546i 0.695947 + 1.52391i
\(222\) 0 0
\(223\) −0.873755 + 1.91326i −0.0585110 + 0.128121i −0.936629 0.350323i \(-0.886072\pi\)
0.878118 + 0.478444i \(0.158799\pi\)
\(224\) 0 0
\(225\) 2.81882 15.3751i 0.187922 1.02501i
\(226\) 0 0
\(227\) 12.1107 + 1.74126i 0.803815 + 0.115571i 0.531963 0.846768i \(-0.321455\pi\)
0.271853 + 0.962339i \(0.412364\pi\)
\(228\) 0 0
\(229\) −2.95346 + 4.59567i −0.195170 + 0.303691i −0.925021 0.379916i \(-0.875953\pi\)
0.729851 + 0.683606i \(0.239589\pi\)
\(230\) 0 0
\(231\) −6.87649 0.132469i −0.452440 0.00871583i
\(232\) 0 0
\(233\) 11.4074 24.9786i 0.747320 1.63640i −0.0238023 0.999717i \(-0.507577\pi\)
0.771123 0.636687i \(-0.219696\pi\)
\(234\) 0 0
\(235\) 3.23379 2.80209i 0.210949 0.182788i
\(236\) 0 0
\(237\) −7.98004 5.34840i −0.518359 0.347416i
\(238\) 0 0
\(239\) −19.7308 −1.27628 −0.638139 0.769921i \(-0.720295\pi\)
−0.638139 + 0.769921i \(0.720295\pi\)
\(240\) 0 0
\(241\) 24.5144 + 7.19807i 1.57911 + 0.463668i 0.949636 0.313354i \(-0.101453\pi\)
0.629473 + 0.777023i \(0.283271\pi\)
\(242\) 0 0
\(243\) 7.12768 + 13.8635i 0.457241 + 0.889343i
\(244\) 0 0
\(245\) −8.47828 18.5648i −0.541658 1.18606i
\(246\) 0 0
\(247\) 3.04917 10.3845i 0.194014 0.660752i
\(248\) 0 0
\(249\) 4.57159 + 5.48593i 0.289713 + 0.347656i
\(250\) 0 0
\(251\) −1.52185 + 10.5847i −0.0960585 + 0.668102i 0.883720 + 0.468016i \(0.155031\pi\)
−0.979778 + 0.200086i \(0.935878\pi\)
\(252\) 0 0
\(253\) −10.7883 + 9.34809i −0.678253 + 0.587710i
\(254\) 0 0
\(255\) 21.4409 13.2027i 1.34268 0.826786i
\(256\) 0 0
\(257\) −1.85895 6.33100i −0.115958 0.394917i 0.880976 0.473161i \(-0.156887\pi\)
−0.996934 + 0.0782437i \(0.975069\pi\)
\(258\) 0 0
\(259\) 2.23350 + 1.93534i 0.138783 + 0.120256i
\(260\) 0 0
\(261\) −10.7736 10.0876i −0.666872 0.624404i
\(262\) 0 0
\(263\) 5.30404 + 18.0639i 0.327061 + 1.11387i 0.944845 + 0.327519i \(0.106213\pi\)
−0.617784 + 0.786348i \(0.711969\pi\)
\(264\) 0 0
\(265\) 15.8177 + 34.6359i 0.971673 + 2.12767i
\(266\) 0 0
\(267\) −27.3407 0.526693i −1.67322 0.0322331i
\(268\) 0 0
\(269\) 6.99643i 0.426580i 0.976989 + 0.213290i \(0.0684179\pi\)
−0.976989 + 0.213290i \(0.931582\pi\)
\(270\) 0 0
\(271\) 19.7238 9.00755i 1.19813 0.547170i 0.286464 0.958091i \(-0.407520\pi\)
0.911671 + 0.410921i \(0.134793\pi\)
\(272\) 0 0
\(273\) 1.95374 + 7.16129i 0.118246 + 0.433421i
\(274\) 0 0
\(275\) 17.3067 19.9729i 1.04363 1.20441i
\(276\) 0 0
\(277\) 2.37514 2.74106i 0.142708 0.164694i −0.679896 0.733309i \(-0.737975\pi\)
0.822604 + 0.568615i \(0.192520\pi\)
\(278\) 0 0
\(279\) −4.61012 18.2775i −0.276001 1.09424i
\(280\) 0 0
\(281\) −3.31710 + 2.13177i −0.197882 + 0.127171i −0.635829 0.771830i \(-0.719342\pi\)
0.437948 + 0.899000i \(0.355705\pi\)
\(282\) 0 0
\(283\) −7.98123 9.21083i −0.474435 0.547527i 0.467205 0.884149i \(-0.345261\pi\)
−0.941640 + 0.336622i \(0.890716\pi\)
\(284\) 0 0
\(285\) −10.7989 1.76557i −0.639671 0.104583i
\(286\) 0 0
\(287\) 0.791429 0.685777i 0.0467166 0.0404802i
\(288\) 0 0
\(289\) 3.54863 + 1.04197i 0.208743 + 0.0612924i
\(290\) 0 0
\(291\) −2.13003 4.91237i −0.124865 0.287968i
\(292\) 0 0
\(293\) 0.657398 + 1.02293i 0.0384056 + 0.0597603i 0.859926 0.510420i \(-0.170510\pi\)
−0.821520 + 0.570180i \(0.806874\pi\)
\(294\) 0 0
\(295\) −7.94223 + 27.0487i −0.462414 + 1.57484i
\(296\) 0 0
\(297\) −1.52210 + 26.3114i −0.0883213 + 1.52674i
\(298\) 0 0
\(299\) 12.9609 + 8.32945i 0.749547 + 0.481704i
\(300\) 0 0
\(301\) 4.38678 + 5.06262i 0.252850 + 0.291805i
\(302\) 0 0
\(303\) 5.15301 + 2.47434i 0.296033 + 0.142147i
\(304\) 0 0
\(305\) 43.5099i 2.49137i
\(306\) 0 0
\(307\) 12.7095 + 8.16791i 0.725370 + 0.466167i 0.850501 0.525973i \(-0.176299\pi\)
−0.125131 + 0.992140i \(0.539935\pi\)
\(308\) 0 0
\(309\) 8.37147 + 1.36870i 0.476236 + 0.0778624i
\(310\) 0 0
\(311\) −1.95696 + 13.6110i −0.110969 + 0.771807i 0.856011 + 0.516957i \(0.172935\pi\)
−0.966981 + 0.254850i \(0.917974\pi\)
\(312\) 0 0
\(313\) −8.14747 3.72083i −0.460522 0.210314i 0.171624 0.985163i \(-0.445099\pi\)
−0.632146 + 0.774849i \(0.717826\pi\)
\(314\) 0 0
\(315\) 6.94167 2.85240i 0.391119 0.160714i
\(316\) 0 0
\(317\) −19.4743 + 2.79998i −1.09379 + 0.157263i −0.665513 0.746387i \(-0.731787\pi\)
−0.428273 + 0.903649i \(0.640878\pi\)
\(318\) 0 0
\(319\) −7.03012 23.9424i −0.393611 1.34052i
\(320\) 0 0
\(321\) 2.31691 + 18.6591i 0.129317 + 1.04145i
\(322\) 0 0
\(323\) −4.86297 7.56692i −0.270583 0.421035i
\(324\) 0 0
\(325\) −25.9456 11.8489i −1.43920 0.657261i
\(326\) 0 0
\(327\) −9.90457 6.63827i −0.547724 0.367097i
\(328\) 0 0
\(329\) 1.00589 + 0.295357i 0.0554567 + 0.0162835i
\(330\) 0 0
\(331\) 25.6433 3.68695i 1.40948 0.202653i 0.604809 0.796371i \(-0.293249\pi\)
0.804673 + 0.593718i \(0.202340\pi\)
\(332\) 0 0
\(333\) 7.74030 8.26675i 0.424166 0.453015i
\(334\) 0 0
\(335\) 11.0020 + 23.7288i 0.601105 + 1.29644i
\(336\) 0 0
\(337\) 11.4752 + 9.94335i 0.625096 + 0.541649i 0.908784 0.417268i \(-0.137012\pi\)
−0.283687 + 0.958917i \(0.591558\pi\)
\(338\) 0 0
\(339\) −24.6699 + 3.06327i −1.33988 + 0.166374i
\(340\) 0 0
\(341\) 8.97870 30.5786i 0.486224 1.65593i
\(342\) 0 0
\(343\) 5.66622 8.81682i 0.305947 0.476063i
\(344\) 0 0
\(345\) 6.74241 14.0416i 0.362999 0.755975i
\(346\) 0 0
\(347\) −27.2097 + 17.4866i −1.46069 + 0.938731i −0.462041 + 0.886859i \(0.652883\pi\)
−0.998654 + 0.0518726i \(0.983481\pi\)
\(348\) 0 0
\(349\) 2.47093 + 17.1857i 0.132266 + 0.919931i 0.942591 + 0.333950i \(0.108382\pi\)
−0.810325 + 0.585981i \(0.800709\pi\)
\(350\) 0 0
\(351\) 27.7099 6.42423i 1.47904 0.342900i
\(352\) 0 0
\(353\) −3.94534 27.4404i −0.209989 1.46051i −0.773183 0.634183i \(-0.781337\pi\)
0.563194 0.826325i \(-0.309572\pi\)
\(354\) 0 0
\(355\) −13.1930 + 6.02505i −0.700213 + 0.319777i
\(356\) 0 0
\(357\) 5.56129 + 2.67038i 0.294335 + 0.141332i
\(358\) 0 0
\(359\) −1.35152 0.194319i −0.0713305 0.0102558i 0.106557 0.994307i \(-0.466017\pi\)
−0.177888 + 0.984051i \(0.556926\pi\)
\(360\) 0 0
\(361\) 2.14770 14.9376i 0.113037 0.786187i
\(362\) 0 0
\(363\) −14.2006 + 21.1879i −0.745338 + 1.11208i
\(364\) 0 0
\(365\) 6.70408 0.350908
\(366\) 0 0
\(367\) −28.9579 13.2246i −1.51159 0.690320i −0.524636 0.851327i \(-0.675798\pi\)
−0.986953 + 0.161007i \(0.948526\pi\)
\(368\) 0 0
\(369\) −2.50913 3.13170i −0.130620 0.163030i
\(370\) 0 0
\(371\) −5.04366 + 7.84809i −0.261854 + 0.407452i
\(372\) 0 0
\(373\) 8.07461i 0.418088i −0.977906 0.209044i \(-0.932965\pi\)
0.977906 0.209044i \(-0.0670351\pi\)
\(374\) 0 0
\(375\) −0.349632 + 1.11111i −0.0180549 + 0.0573773i
\(376\) 0 0
\(377\) −22.6561 + 14.5602i −1.16685 + 0.749889i
\(378\) 0 0
\(379\) −23.4477 + 10.7082i −1.20443 + 0.550044i −0.913554 0.406717i \(-0.866674\pi\)
−0.290875 + 0.956761i \(0.593946\pi\)
\(380\) 0 0
\(381\) 7.17216 22.7926i 0.367441 1.16770i
\(382\) 0 0
\(383\) 11.4000 + 13.1564i 0.582515 + 0.672259i 0.968144 0.250396i \(-0.0805607\pi\)
−0.385628 + 0.922654i \(0.626015\pi\)
\(384\) 0 0
\(385\) 12.5593 + 1.80576i 0.640082 + 0.0920299i
\(386\) 0 0
\(387\) 20.0329 16.0504i 1.01833 0.815888i
\(388\) 0 0
\(389\) 11.8584 + 18.4520i 0.601245 + 0.935555i 0.999830 + 0.0184238i \(0.00586481\pi\)
−0.398586 + 0.917131i \(0.630499\pi\)
\(390\) 0 0
\(391\) 12.2856 3.60738i 0.621310 0.182433i
\(392\) 0 0
\(393\) 18.9794 21.0694i 0.957387 1.06281i
\(394\) 0 0
\(395\) 13.3940 + 11.6059i 0.673923 + 0.583958i
\(396\) 0 0
\(397\) 21.6056 6.34398i 1.08436 0.318395i 0.309736 0.950823i \(-0.399759\pi\)
0.774620 + 0.632427i \(0.217941\pi\)
\(398\) 0 0
\(399\) −1.06652 2.45964i −0.0533926 0.123136i
\(400\) 0 0
\(401\) −23.7844 −1.18774 −0.593868 0.804563i \(-0.702400\pi\)
−0.593868 + 0.804563i \(0.702400\pi\)
\(402\) 0 0
\(403\) −34.3962 −1.71339
\(404\) 0 0
\(405\) −9.89773 27.0015i −0.491822 1.34172i
\(406\) 0 0
\(407\) 18.3713 5.39430i 0.910631 0.267385i
\(408\) 0 0
\(409\) −17.0685 14.7899i −0.843983 0.731316i 0.121273 0.992619i \(-0.461302\pi\)
−0.965257 + 0.261303i \(0.915848\pi\)
\(410\) 0 0
\(411\) −19.3846 17.4617i −0.956171 0.861325i
\(412\) 0 0
\(413\) −6.62709 + 1.94589i −0.326098 + 0.0957510i
\(414\) 0 0
\(415\) −7.12252 11.0829i −0.349631 0.544036i
\(416\) 0 0
\(417\) 6.46123 + 7.75350i 0.316408 + 0.379691i
\(418\) 0 0
\(419\) 3.62622 + 0.521372i 0.177153 + 0.0254707i 0.230320 0.973115i \(-0.426023\pi\)
−0.0531675 + 0.998586i \(0.516932\pi\)
\(420\) 0 0
\(421\) 5.73664 + 6.62044i 0.279587 + 0.322660i 0.878123 0.478436i \(-0.158796\pi\)
−0.598536 + 0.801096i \(0.704251\pi\)
\(422\) 0 0
\(423\) 1.27941 3.80810i 0.0622072 0.185156i
\(424\) 0 0
\(425\) −21.5631 + 9.84753i −1.04596 + 0.477675i
\(426\) 0 0
\(427\) 8.96791 5.76332i 0.433987 0.278907i
\(428\) 0 0
\(429\) 45.8741 + 14.4352i 2.21482 + 0.696939i
\(430\) 0 0
\(431\) 18.3086i 0.881892i −0.897534 0.440946i \(-0.854643\pi\)
0.897534 0.440946i \(-0.145357\pi\)
\(432\) 0 0
\(433\) −21.6063 + 33.6201i −1.03833 + 1.61568i −0.284424 + 0.958698i \(0.591802\pi\)
−0.753909 + 0.656979i \(0.771834\pi\)
\(434\) 0 0
\(435\) 17.4311 + 20.9174i 0.835758 + 1.00291i
\(436\) 0 0
\(437\) −5.06146 2.31149i −0.242122 0.110574i
\(438\) 0 0
\(439\) 31.7813 1.51684 0.758418 0.651768i \(-0.225972\pi\)
0.758418 + 0.651768i \(0.225972\pi\)
\(440\) 0 0
\(441\) −15.7085 10.9725i −0.748026 0.522500i
\(442\) 0 0
\(443\) −0.346201 + 2.40788i −0.0164485 + 0.114402i −0.996392 0.0848761i \(-0.972951\pi\)
0.979943 + 0.199278i \(0.0638597\pi\)
\(444\) 0 0
\(445\) 49.9354 + 7.17963i 2.36717 + 0.340347i
\(446\) 0 0
\(447\) 15.4875 32.2540i 0.732535 1.52556i
\(448\) 0 0
\(449\) −37.8266 + 17.2748i −1.78515 + 0.815250i −0.812504 + 0.582956i \(0.801896\pi\)
−0.972646 + 0.232294i \(0.925377\pi\)
\(450\) 0 0
\(451\) −0.965547 6.71553i −0.0454658 0.316222i
\(452\) 0 0
\(453\) −1.51116 5.53904i −0.0710003 0.260247i
\(454\) 0 0
\(455\) −1.94892 13.5550i −0.0913665 0.635468i
\(456\) 0 0
\(457\) 6.94117 4.46082i 0.324694 0.208668i −0.368131 0.929774i \(-0.620002\pi\)
0.692825 + 0.721106i \(0.256366\pi\)
\(458\) 0 0
\(459\) 11.0460 20.9008i 0.515583 0.975566i
\(460\) 0 0
\(461\) −17.1945 + 26.7552i −0.800828 + 1.24611i 0.164837 + 0.986321i \(0.447290\pi\)
−0.965665 + 0.259791i \(0.916346\pi\)
\(462\) 0 0
\(463\) −1.35839 + 4.62626i −0.0631298 + 0.215000i −0.985017 0.172458i \(-0.944829\pi\)
0.921887 + 0.387459i \(0.126647\pi\)
\(464\) 0 0
\(465\) 4.28516 + 34.5104i 0.198720 + 1.60038i
\(466\) 0 0
\(467\) 1.76214 + 1.52691i 0.0815423 + 0.0706568i 0.694678 0.719321i \(-0.255547\pi\)
−0.613136 + 0.789977i \(0.710092\pi\)
\(468\) 0 0
\(469\) −3.43346 + 5.41077i −0.158542 + 0.249846i
\(470\) 0 0
\(471\) 24.8455 + 22.3810i 1.14482 + 1.03126i
\(472\) 0 0
\(473\) 42.9579 6.17642i 1.97521 0.283992i
\(474\) 0 0
\(475\) 9.88421 + 2.90226i 0.453518 + 0.133165i
\(476\) 0 0
\(477\) 29.3070 + 20.4711i 1.34187 + 0.937306i
\(478\) 0 0
\(479\) −5.85237 2.67269i −0.267402 0.122118i 0.277202 0.960812i \(-0.410593\pi\)
−0.544604 + 0.838693i \(0.683320\pi\)
\(480\) 0 0
\(481\) −11.1722 17.3843i −0.509410 0.792657i
\(482\) 0 0
\(483\) 3.78724 0.470263i 0.172325 0.0213977i
\(484\) 0 0
\(485\) 2.78292 + 9.47776i 0.126366 + 0.430363i
\(486\) 0 0
\(487\) −14.0502 + 2.02011i −0.636675 + 0.0915400i −0.453091 0.891464i \(-0.649679\pi\)
−0.183583 + 0.983004i \(0.558770\pi\)
\(488\) 0 0
\(489\) 29.3840 12.7411i 1.32879 0.576172i
\(490\) 0 0
\(491\) 16.6419 + 7.60010i 0.751038 + 0.342988i 0.753883 0.657008i \(-0.228178\pi\)
−0.00284517 + 0.999996i \(0.500906\pi\)
\(492\) 0 0
\(493\) −3.18535 + 22.1546i −0.143461 + 0.997792i
\(494\) 0 0
\(495\) 8.76804 47.8248i 0.394094 2.14956i
\(496\) 0 0
\(497\) −2.98938 1.92116i −0.134092 0.0861758i
\(498\) 0 0
\(499\) 39.6955i 1.77702i 0.458862 + 0.888508i \(0.348257\pi\)
−0.458862 + 0.888508i \(0.651743\pi\)
\(500\) 0 0
\(501\) 4.70782 9.80442i 0.210330 0.438029i
\(502\) 0 0
\(503\) −0.907942 1.04782i −0.0404831 0.0467200i 0.735147 0.677908i \(-0.237113\pi\)
−0.775630 + 0.631188i \(0.782568\pi\)
\(504\) 0 0
\(505\) −8.87162 5.70144i −0.394782 0.253711i
\(506\) 0 0
\(507\) 0.566020 29.3822i 0.0251378 1.30491i
\(508\) 0 0
\(509\) 6.46433 22.0155i 0.286526 0.975819i −0.682915 0.730498i \(-0.739288\pi\)
0.969442 0.245322i \(-0.0788936\pi\)
\(510\) 0 0
\(511\) 0.888023 + 1.38179i 0.0392838 + 0.0611268i
\(512\) 0 0
\(513\) −9.57570 + 3.72083i −0.422777 + 0.164278i
\(514\) 0 0
\(515\) −15.0153 4.40889i −0.661653 0.194279i
\(516\) 0 0
\(517\) 5.13307 4.44783i 0.225752 0.195615i
\(518\) 0 0
\(519\) 5.75012 35.1700i 0.252402 1.54379i
\(520\) 0 0
\(521\) 24.3956 + 28.1540i 1.06879 + 1.23345i 0.971210 + 0.238224i \(0.0765652\pi\)
0.0975814 + 0.995228i \(0.468889\pi\)
\(522\) 0 0
\(523\) −13.5444 + 8.70448i −0.592257 + 0.380621i −0.802167 0.597100i \(-0.796319\pi\)
0.209909 + 0.977721i \(0.432683\pi\)
\(524\) 0 0
\(525\) −6.81627 + 1.85961i −0.297486 + 0.0811600i
\(526\) 0 0
\(527\) −18.7200 + 21.6041i −0.815457 + 0.941087i
\(528\) 0 0
\(529\) −9.87474 + 11.3961i −0.429336 + 0.495481i
\(530\) 0 0
\(531\) 6.47302 + 25.6632i 0.280905 + 1.11369i
\(532\) 0 0
\(533\) −6.66074 + 3.04186i −0.288509 + 0.131757i
\(534\) 0 0
\(535\) 34.6877i 1.49968i
\(536\) 0 0
\(537\) 0.738769 38.3496i 0.0318803 1.65491i
\(538\) 0 0
\(539\) −13.4578 29.4684i −0.579667 1.26929i
\(540\) 0 0
\(541\) −4.89120 16.6579i −0.210289 0.716179i −0.995312 0.0967127i \(-0.969167\pi\)
0.785023 0.619466i \(-0.212651\pi\)
\(542\) 0 0
\(543\) −0.920488 0.829181i −0.0395019 0.0355835i
\(544\) 0 0
\(545\) 16.6242 + 14.4049i 0.712101 + 0.617039i
\(546\) 0 0
\(547\) 9.47920 + 32.2832i 0.405301 + 1.38033i 0.869209 + 0.494446i \(0.164629\pi\)
−0.463907 + 0.885884i \(0.653553\pi\)
\(548\) 0 0
\(549\) −20.7450 35.1899i −0.885375 1.50187i
\(550\) 0 0
\(551\) 7.35088 6.36957i 0.313158 0.271353i
\(552\) 0 0
\(553\) −0.617956 + 4.29798i −0.0262781 + 0.182769i
\(554\) 0 0
\(555\) −16.0502 + 13.3751i −0.681292 + 0.567742i
\(556\) 0 0
\(557\) 11.2361 38.2666i 0.476088 1.62141i −0.275168 0.961396i \(-0.588733\pi\)
0.751256 0.660011i \(-0.229448\pi\)
\(558\) 0 0
\(559\) −19.4582 42.6075i −0.822993 1.80210i
\(560\) 0 0
\(561\) 34.0336 20.9570i 1.43690 0.884804i
\(562\) 0 0
\(563\) −28.2902 8.30676i −1.19229 0.350088i −0.375391 0.926867i \(-0.622491\pi\)
−0.816901 + 0.576778i \(0.804310\pi\)
\(564\) 0 0
\(565\) 45.8618 1.92942
\(566\) 0 0
\(567\) 4.25428 5.61666i 0.178663 0.235878i
\(568\) 0 0
\(569\) −4.57891 + 3.96765i −0.191958 + 0.166332i −0.745537 0.666464i \(-0.767807\pi\)
0.553579 + 0.832796i \(0.313262\pi\)
\(570\) 0 0
\(571\) −4.09520 + 8.96724i −0.171379 + 0.375267i −0.975759 0.218848i \(-0.929770\pi\)
0.804380 + 0.594115i \(0.202498\pi\)
\(572\) 0 0
\(573\) −0.634055 + 32.9139i −0.0264880 + 1.37500i
\(574\) 0 0
\(575\) −7.92814 + 12.3364i −0.330626 + 0.514464i
\(576\) 0 0
\(577\) 17.6365 + 2.53574i 0.734217 + 0.105564i 0.499273 0.866445i \(-0.333600\pi\)
0.234943 + 0.972009i \(0.424510\pi\)
\(578\) 0 0
\(579\) −0.0321403 0.00525479i −0.00133571 0.000218382i
\(580\) 0 0
\(581\) 1.34086 2.93607i 0.0556282 0.121809i
\(582\) 0 0
\(583\) 25.1078 + 54.9784i 1.03986 + 2.27697i
\(584\) 0 0
\(585\) −52.1915 + 5.46215i −2.15785 + 0.225832i
\(586\) 0 0
\(587\) 31.0273 9.11042i 1.28063 0.376027i 0.430497 0.902592i \(-0.358338\pi\)
0.850135 + 0.526565i \(0.176520\pi\)
\(588\) 0 0
\(589\) 12.2962 1.76792i 0.506654 0.0728459i
\(590\) 0 0
\(591\) 10.9738 + 17.8211i 0.451401 + 0.733063i
\(592\) 0 0
\(593\) −0.791302 + 1.73271i −0.0324949 + 0.0711538i −0.925183 0.379520i \(-0.876089\pi\)
0.892689 + 0.450674i \(0.148816\pi\)
\(594\) 0 0
\(595\) −9.57452 6.15317i −0.392517 0.252255i
\(596\) 0 0
\(597\) −4.43511 + 14.0945i −0.181517 + 0.576848i
\(598\) 0 0
\(599\) −1.67155 11.6259i −0.0682976 0.475021i −0.995052 0.0993532i \(-0.968323\pi\)
0.926755 0.375667i \(-0.122586\pi\)
\(600\) 0 0
\(601\) 2.88118 3.32506i 0.117526 0.135632i −0.693938 0.720035i \(-0.744126\pi\)
0.811464 + 0.584403i \(0.198671\pi\)
\(602\) 0 0
\(603\) 20.2118 + 13.9457i 0.823088 + 0.567913i
\(604\) 0 0
\(605\) 30.8150 35.5624i 1.25281 1.44582i
\(606\) 0 0
\(607\) −4.10078 28.5216i −0.166446 1.15766i −0.886158 0.463383i \(-0.846635\pi\)
0.719713 0.694272i \(-0.244274\pi\)
\(608\) 0 0
\(609\) −2.00240 + 6.36348i −0.0811413 + 0.257861i
\(610\) 0 0
\(611\) −6.16679 3.96316i −0.249482 0.160332i
\(612\) 0 0
\(613\) −2.51281 + 5.50228i −0.101491 + 0.222235i −0.953565 0.301186i \(-0.902617\pi\)
0.852074 + 0.523421i \(0.175345\pi\)
\(614\) 0 0
\(615\) 3.88177 + 6.30389i 0.156528 + 0.254197i
\(616\) 0 0
\(617\) −14.1110 + 2.02885i −0.568087 + 0.0816785i −0.420373 0.907352i \(-0.638101\pi\)
−0.147714 + 0.989030i \(0.547192\pi\)
\(618\) 0 0
\(619\) −29.7888 + 8.74678i −1.19731 + 0.351563i −0.818825 0.574044i \(-0.805374\pi\)
−0.378488 + 0.925606i \(0.623556\pi\)
\(620\) 0 0
\(621\) −1.24176 14.5712i −0.0498302 0.584724i
\(622\) 0 0
\(623\) 5.13464 + 11.2433i 0.205715 + 0.450453i
\(624\) 0 0
\(625\) −9.92983 + 21.7433i −0.397193 + 0.869732i
\(626\) 0 0
\(627\) −17.1413 2.80252i −0.684558 0.111922i
\(628\) 0 0
\(629\) −16.9995 2.44416i −0.677813 0.0974549i
\(630\) 0 0
\(631\) 7.97701 12.4125i 0.317560 0.494132i −0.645375 0.763865i \(-0.723299\pi\)
0.962935 + 0.269733i \(0.0869354\pi\)
\(632\) 0 0
\(633\) −0.0713841 + 3.70556i −0.00283726 + 0.147283i
\(634\) 0 0
\(635\) −18.3122 + 40.0981i −0.726697 + 1.59125i
\(636\) 0 0
\(637\) −26.4242 + 22.8967i −1.04697 + 0.907201i
\(638\) 0 0
\(639\) −7.79756 + 11.1632i −0.308467 + 0.441610i
\(640\) 0 0
\(641\) −22.0231 −0.869862 −0.434931 0.900464i \(-0.643227\pi\)
−0.434931 + 0.900464i \(0.643227\pi\)
\(642\) 0 0
\(643\) −0.988101 0.290133i −0.0389669 0.0114417i 0.262191 0.965016i \(-0.415555\pi\)
−0.301158 + 0.953574i \(0.597373\pi\)
\(644\) 0 0
\(645\) −40.3248 + 24.8309i −1.58779 + 0.977717i
\(646\) 0 0
\(647\) 18.3102 + 40.0937i 0.719847 + 1.57625i 0.814118 + 0.580699i \(0.197221\pi\)
−0.0942711 + 0.995547i \(0.530052\pi\)
\(648\) 0 0
\(649\) −12.6069 + 42.9351i −0.494863 + 1.68535i
\(650\) 0 0
\(651\) −6.54538 + 5.45447i −0.256534 + 0.213777i
\(652\) 0 0
\(653\) −3.35191 + 23.3131i −0.131171 + 0.912311i 0.812861 + 0.582457i \(0.197909\pi\)
−0.944032 + 0.329854i \(0.893000\pi\)
\(654\) 0 0
\(655\) −39.5372 + 34.2592i −1.54485 + 1.33862i
\(656\) 0 0
\(657\) 5.42211 3.19642i 0.211537 0.124704i
\(658\) 0 0
\(659\) 2.20150 + 7.49761i 0.0857582 + 0.292066i 0.991194 0.132418i \(-0.0422740\pi\)
−0.905436 + 0.424483i \(0.860456\pi\)
\(660\) 0 0
\(661\) −37.9559 32.8889i −1.47631 1.27923i −0.878634 0.477496i \(-0.841545\pi\)
−0.597678 0.801736i \(-0.703910\pi\)
\(662\) 0 0
\(663\) −32.0507 28.8714i −1.24475 1.12127i
\(664\) 0 0
\(665\) 1.39342 + 4.74555i 0.0540345 + 0.184025i
\(666\) 0 0
\(667\) 5.75183 + 12.5948i 0.222712 + 0.487671i
\(668\) 0 0
\(669\) 0.0701674 3.64240i 0.00271283 0.140823i
\(670\) 0 0
\(671\) 69.0642i 2.66620i
\(672\) 0 0
\(673\) 44.5977 20.3671i 1.71911 0.785093i 0.723626 0.690192i \(-0.242474\pi\)
0.995487 0.0949009i \(-0.0302534\pi\)
\(674\) 0 0
\(675\) 6.11471 + 26.3748i 0.235355 + 1.01517i
\(676\) 0 0
\(677\) −11.8582 + 13.6851i −0.455746 + 0.525959i −0.936392 0.350955i \(-0.885857\pi\)
0.480646 + 0.876915i \(0.340402\pi\)
\(678\) 0 0
\(679\) −1.58485 + 1.82902i −0.0608210 + 0.0701912i
\(680\) 0 0
\(681\) −20.4448 + 5.57775i −0.783448 + 0.213740i
\(682\) 0 0
\(683\) 3.07753 1.97781i 0.117759 0.0756788i −0.480436 0.877030i \(-0.659521\pi\)
0.598194 + 0.801351i \(0.295885\pi\)
\(684\) 0 0
\(685\) 31.5196 + 36.3756i 1.20430 + 1.38984i
\(686\) 0 0
\(687\) 1.52672 9.33801i 0.0582480 0.356267i
\(688\) 0 0
\(689\) 49.2989 42.7178i 1.87814 1.62742i
\(690\) 0 0
\(691\) −22.9206 6.73010i −0.871942 0.256025i −0.185001 0.982738i \(-0.559229\pi\)
−0.686941 + 0.726713i \(0.741047\pi\)
\(692\) 0 0
\(693\) 11.0187 4.52768i 0.418565 0.171992i
\(694\) 0 0
\(695\) −10.0666 15.6639i −0.381847 0.594166i
\(696\) 0 0
\(697\) −1.71451 + 5.83910i −0.0649419 + 0.221172i
\(698\) 0 0
\(699\) −0.916074 + 47.5535i −0.0346491 + 1.79864i
\(700\) 0 0
\(701\) 7.15827 + 4.60034i 0.270364 + 0.173752i 0.668797 0.743445i \(-0.266810\pi\)
−0.398433 + 0.917197i \(0.630446\pi\)
\(702\) 0 0
\(703\) 4.88745 + 5.64042i 0.184334 + 0.212732i
\(704\) 0 0
\(705\) −3.20804 + 6.68101i −0.120822 + 0.251621i
\(706\) 0 0
\(707\) 2.58376i 0.0971722i
\(708\) 0 0
\(709\) 3.78525 + 2.43263i 0.142158 + 0.0913595i 0.609787 0.792566i \(-0.291255\pi\)
−0.467629 + 0.883925i \(0.654891\pi\)
\(710\) 0 0
\(711\) 16.3663 + 3.00055i 0.613785 + 0.112529i
\(712\) 0 0
\(713\) −2.51666 + 17.5038i −0.0942497 + 0.655521i
\(714\) 0 0
\(715\) −80.7045 36.8565i −3.01818 1.37835i
\(716\) 0 0
\(717\) 31.3541 13.5953i 1.17094 0.507726i
\(718\) 0 0
\(719\) 43.8824 6.30933i 1.63654 0.235298i 0.738192 0.674591i \(-0.235680\pi\)
0.898344 + 0.439292i \(0.144771\pi\)
\(720\) 0 0
\(721\) −1.08020 3.67883i −0.0402288 0.137007i
\(722\) 0 0
\(723\) −43.9154 + 5.45299i −1.63323 + 0.202799i
\(724\) 0 0
\(725\) −13.8587 21.5646i −0.514700 0.800888i
\(726\) 0 0
\(727\) 10.1784 + 4.64832i 0.377496 + 0.172397i 0.595122 0.803636i \(-0.297104\pi\)
−0.217626 + 0.976032i \(0.569831\pi\)
\(728\) 0 0
\(729\) −20.8791 17.1191i −0.773299 0.634042i
\(730\) 0 0
\(731\) −37.3516 10.9674i −1.38150 0.405645i
\(732\) 0 0
\(733\) 0.719942 0.103512i 0.0265917 0.00382330i −0.129006 0.991644i \(-0.541179\pi\)
0.155598 + 0.987820i \(0.450270\pi\)
\(734\) 0 0
\(735\) 26.2647 + 23.6594i 0.968789 + 0.872691i
\(736\) 0 0
\(737\) 17.4638 + 37.6653i 0.643286 + 1.38742i
\(738\) 0 0
\(739\) −3.91386 3.39138i −0.143974 0.124754i 0.579896 0.814690i \(-0.303093\pi\)
−0.723870 + 0.689936i \(0.757639\pi\)
\(740\) 0 0
\(741\) 2.30994 + 18.6030i 0.0848578 + 0.683399i
\(742\) 0 0
\(743\) 9.27006 31.5709i 0.340085 1.15822i −0.594977 0.803742i \(-0.702839\pi\)
0.935063 0.354482i \(-0.115343\pi\)
\(744\) 0 0
\(745\) −35.6868 + 55.5297i −1.30746 + 2.03445i
\(746\) 0 0
\(747\) −11.0447 5.56764i −0.404105 0.203709i
\(748\) 0 0
\(749\) 7.14955 4.59474i 0.261239 0.167888i
\(750\) 0 0
\(751\) −4.72629 32.8721i −0.172465 1.19952i −0.873655 0.486546i \(-0.838257\pi\)
0.701190 0.712974i \(-0.252652\pi\)
\(752\) 0 0
\(753\) −4.87494 17.8687i −0.177653 0.651173i
\(754\) 0 0
\(755\) 1.50742 + 10.4844i 0.0548608 + 0.381565i
\(756\) 0 0
\(757\) 36.8168 16.8137i 1.33813 0.611103i 0.387626 0.921817i \(-0.373295\pi\)
0.950504 + 0.310713i \(0.100568\pi\)
\(758\) 0 0
\(759\) 10.7024 22.2886i 0.388471 0.809024i
\(760\) 0 0
\(761\) 38.6217 + 5.55295i 1.40003 + 0.201294i 0.800633 0.599155i \(-0.204497\pi\)
0.599401 + 0.800449i \(0.295406\pi\)
\(762\) 0 0
\(763\) −0.766987 + 5.33451i −0.0277668 + 0.193122i
\(764\) 0 0
\(765\) −24.9743 + 35.7540i −0.902949 + 1.29269i
\(766\) 0 0
\(767\) 48.2952 1.74384
\(768\) 0 0
\(769\) 4.79533 + 2.18995i 0.172924 + 0.0789717i 0.499996 0.866028i \(-0.333335\pi\)
−0.327072 + 0.944999i \(0.606062\pi\)
\(770\) 0 0
\(771\) 7.31636 + 8.77966i 0.263492 + 0.316192i
\(772\) 0 0
\(773\) −9.21678 + 14.3416i −0.331505 + 0.515831i −0.966494 0.256690i \(-0.917368\pi\)
0.634989 + 0.772521i \(0.281005\pi\)
\(774\) 0 0
\(775\) 32.7390i 1.17602i
\(776\) 0 0
\(777\)