Properties

Label 624.2.cn.f.305.2
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.2
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.55432 - 0.764251i) q^{3} +(-0.504580 - 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.83184 + 2.37579i) q^{9} +O(q^{10})\) \(q+(-1.55432 - 0.764251i) q^{3} +(-0.504580 - 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.83184 + 2.37579i) q^{9} +(-0.296516 - 1.10661i) q^{11} +(3.23695 + 1.58812i) q^{13} +(0.398654 + 1.16991i) q^{15} +(-1.51919 - 2.63131i) q^{17} +(-4.59867 - 1.23221i) q^{19} +(-3.68744 + 4.21464i) q^{21} +(-2.43079 + 4.21025i) q^{23} -4.49080i q^{25} +(-1.03158 - 5.09273i) q^{27} +(-8.98018 - 5.18471i) q^{29} +(1.93142 - 1.93142i) q^{31} +(-0.384848 + 1.94665i) q^{33} +(-1.99805 + 1.15357i) q^{35} +(-7.49362 + 2.00791i) q^{37} +(-3.81755 - 4.94230i) q^{39} +(6.55081 - 1.75528i) q^{41} +(-1.98070 + 1.14356i) q^{43} +(0.274463 - 2.12308i) q^{45} +(1.27830 - 1.27830i) q^{47} +(-2.99079 - 1.72673i) q^{49} +(0.350327 + 5.25094i) q^{51} -2.42966i q^{53} +(-0.408758 + 0.707990i) q^{55} +(6.20611 + 5.42979i) q^{57} +(-5.61424 - 1.50433i) q^{59} +(-5.23702 - 9.07078i) q^{61} +(8.95251 - 3.73279i) q^{63} +(-0.831967 - 2.43463i) q^{65} +(1.57758 + 5.88762i) q^{67} +(6.99591 - 4.68635i) q^{69} +(1.02693 - 3.83254i) q^{71} +(-4.06395 - 4.06395i) q^{73} +(-3.43210 + 6.98015i) q^{75} -3.70409 q^{77} -6.77768 q^{79} +(-2.28872 + 8.70412i) q^{81} +(11.9425 + 11.9425i) q^{83} +(-0.561154 + 2.09426i) q^{85} +(9.99568 + 14.9218i) q^{87} +(2.07215 + 7.73338i) q^{89} +(7.66844 - 8.78010i) q^{91} +(-4.47815 + 1.52597i) q^{93} +(1.69865 + 2.94215i) q^{95} +(-0.989115 - 0.265032i) q^{97} +(2.08590 - 2.73160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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
\(3\) −1.55432 0.764251i −0.897389 0.441240i
\(4\) 0 0
\(5\) −0.504580 0.504580i −0.225655 0.225655i 0.585220 0.810875i \(-0.301008\pi\)
−0.810875 + 0.585220i \(0.801008\pi\)
\(6\) 0 0
\(7\) 0.836809 3.12301i 0.316284 1.18039i −0.606504 0.795080i \(-0.707429\pi\)
0.922788 0.385308i \(-0.125905\pi\)
\(8\) 0 0
\(9\) 1.83184 + 2.37579i 0.610614 + 0.791929i
\(10\) 0 0
\(11\) −0.296516 1.10661i −0.0894029 0.333656i 0.906709 0.421758i \(-0.138587\pi\)
−0.996112 + 0.0881015i \(0.971920\pi\)
\(12\) 0 0
\(13\) 3.23695 + 1.58812i 0.897769 + 0.440466i
\(14\) 0 0
\(15\) 0.398654 + 1.16991i 0.102932 + 0.302068i
\(16\) 0 0
\(17\) −1.51919 2.63131i −0.368457 0.638186i 0.620868 0.783916i \(-0.286780\pi\)
−0.989325 + 0.145729i \(0.953447\pi\)
\(18\) 0 0
\(19\) −4.59867 1.23221i −1.05501 0.282689i −0.310688 0.950512i \(-0.600560\pi\)
−0.744320 + 0.667823i \(0.767226\pi\)
\(20\) 0 0
\(21\) −3.68744 + 4.21464i −0.804665 + 0.919710i
\(22\) 0 0
\(23\) −2.43079 + 4.21025i −0.506854 + 0.877897i 0.493114 + 0.869964i \(0.335858\pi\)
−0.999969 + 0.00793257i \(0.997475\pi\)
\(24\) 0 0
\(25\) 4.49080i 0.898160i
\(26\) 0 0
\(27\) −1.03158 5.09273i −0.198527 0.980095i
\(28\) 0 0
\(29\) −8.98018 5.18471i −1.66758 0.962776i −0.968939 0.247301i \(-0.920456\pi\)
−0.698638 0.715475i \(-0.746210\pi\)
\(30\) 0 0
\(31\) 1.93142 1.93142i 0.346894 0.346894i −0.512057 0.858951i \(-0.671116\pi\)
0.858951 + 0.512057i \(0.171116\pi\)
\(32\) 0 0
\(33\) −0.384848 + 1.94665i −0.0669934 + 0.338867i
\(34\) 0 0
\(35\) −1.99805 + 1.15357i −0.337731 + 0.194989i
\(36\) 0 0
\(37\) −7.49362 + 2.00791i −1.23194 + 0.330098i −0.815336 0.578988i \(-0.803448\pi\)
−0.416608 + 0.909086i \(0.636781\pi\)
\(38\) 0 0
\(39\) −3.81755 4.94230i −0.611297 0.791401i
\(40\) 0 0
\(41\) 6.55081 1.75528i 1.02306 0.274129i 0.291986 0.956423i \(-0.405684\pi\)
0.731079 + 0.682293i \(0.239017\pi\)
\(42\) 0 0
\(43\) −1.98070 + 1.14356i −0.302054 + 0.174391i −0.643365 0.765559i \(-0.722462\pi\)
0.341311 + 0.939950i \(0.389129\pi\)
\(44\) 0 0
\(45\) 0.274463 2.12308i 0.0409146 0.316491i
\(46\) 0 0
\(47\) 1.27830 1.27830i 0.186459 0.186459i −0.607704 0.794163i \(-0.707909\pi\)
0.794163 + 0.607704i \(0.207909\pi\)
\(48\) 0 0
\(49\) −2.99079 1.72673i −0.427256 0.246676i
\(50\) 0 0
\(51\) 0.350327 + 5.25094i 0.0490556 + 0.735279i
\(52\) 0 0
\(53\) 2.42966i 0.333740i −0.985979 0.166870i \(-0.946634\pi\)
0.985979 0.166870i \(-0.0533660\pi\)
\(54\) 0 0
\(55\) −0.408758 + 0.707990i −0.0551169 + 0.0954653i
\(56\) 0 0
\(57\) 6.20611 + 5.42979i 0.822019 + 0.719194i
\(58\) 0 0
\(59\) −5.61424 1.50433i −0.730911 0.195847i −0.125876 0.992046i \(-0.540174\pi\)
−0.605035 + 0.796199i \(0.706841\pi\)
\(60\) 0 0
\(61\) −5.23702 9.07078i −0.670531 1.16139i −0.977754 0.209756i \(-0.932733\pi\)
0.307223 0.951638i \(-0.400600\pi\)
\(62\) 0 0
\(63\) 8.95251 3.73279i 1.12791 0.470287i
\(64\) 0 0
\(65\) −0.831967 2.43463i −0.103193 0.301979i
\(66\) 0 0
\(67\) 1.57758 + 5.88762i 0.192732 + 0.719287i 0.992842 + 0.119433i \(0.0381078\pi\)
−0.800110 + 0.599853i \(0.795226\pi\)
\(68\) 0 0
\(69\) 6.99591 4.68635i 0.842209 0.564171i
\(70\) 0 0
\(71\) 1.02693 3.83254i 0.121874 0.454839i −0.877835 0.478963i \(-0.841013\pi\)
0.999709 + 0.0241235i \(0.00767950\pi\)
\(72\) 0 0
\(73\) −4.06395 4.06395i −0.475650 0.475650i 0.428088 0.903737i \(-0.359187\pi\)
−0.903737 + 0.428088i \(0.859187\pi\)
\(74\) 0 0
\(75\) −3.43210 + 6.98015i −0.396304 + 0.805999i
\(76\) 0 0
\(77\) −3.70409 −0.422121
\(78\) 0 0
\(79\) −6.77768 −0.762549 −0.381274 0.924462i \(-0.624515\pi\)
−0.381274 + 0.924462i \(0.624515\pi\)
\(80\) 0 0
\(81\) −2.28872 + 8.70412i −0.254302 + 0.967125i
\(82\) 0 0
\(83\) 11.9425 + 11.9425i 1.31086 + 1.31086i 0.920783 + 0.390075i \(0.127551\pi\)
0.390075 + 0.920783i \(0.372449\pi\)
\(84\) 0 0
\(85\) −0.561154 + 2.09426i −0.0608657 + 0.227154i
\(86\) 0 0
\(87\) 9.99568 + 14.9218i 1.07165 + 1.59979i
\(88\) 0 0
\(89\) 2.07215 + 7.73338i 0.219648 + 0.819737i 0.984478 + 0.175505i \(0.0561559\pi\)
−0.764831 + 0.644231i \(0.777177\pi\)
\(90\) 0 0
\(91\) 7.66844 8.78010i 0.803871 0.920404i
\(92\) 0 0
\(93\) −4.47815 + 1.52597i −0.464363 + 0.158235i
\(94\) 0 0
\(95\) 1.69865 + 2.94215i 0.174278 + 0.301858i
\(96\) 0 0
\(97\) −0.989115 0.265032i −0.100429 0.0269100i 0.208254 0.978075i \(-0.433222\pi\)
−0.308684 + 0.951165i \(0.599888\pi\)
\(98\) 0 0
\(99\) 2.08590 2.73160i 0.209641 0.274536i
\(100\) 0 0
\(101\) −3.77328 + 6.53550i −0.375455 + 0.650307i −0.990395 0.138267i \(-0.955847\pi\)
0.614940 + 0.788574i \(0.289180\pi\)
\(102\) 0 0
\(103\) 6.31264i 0.622003i −0.950409 0.311001i \(-0.899336\pi\)
0.950409 0.311001i \(-0.100664\pi\)
\(104\) 0 0
\(105\) 3.98723 0.266016i 0.389114 0.0259605i
\(106\) 0 0
\(107\) 7.26480 + 4.19434i 0.702315 + 0.405482i 0.808209 0.588896i \(-0.200437\pi\)
−0.105894 + 0.994377i \(0.533770\pi\)
\(108\) 0 0
\(109\) 10.3472 10.3472i 0.991084 0.991084i −0.00887687 0.999961i \(-0.502826\pi\)
0.999961 + 0.00887687i \(0.00282563\pi\)
\(110\) 0 0
\(111\) 13.1821 + 2.60607i 1.25119 + 0.247357i
\(112\) 0 0
\(113\) 13.0474 7.53294i 1.22740 0.708639i 0.260914 0.965362i \(-0.415976\pi\)
0.966485 + 0.256723i \(0.0826428\pi\)
\(114\) 0 0
\(115\) 3.35093 0.897879i 0.312476 0.0837277i
\(116\) 0 0
\(117\) 2.15655 + 10.5995i 0.199373 + 0.979924i
\(118\) 0 0
\(119\) −9.48889 + 2.54254i −0.869845 + 0.233074i
\(120\) 0 0
\(121\) 8.38961 4.84374i 0.762692 0.440340i
\(122\) 0 0
\(123\) −11.5236 2.27818i −1.03904 0.205417i
\(124\) 0 0
\(125\) −4.78886 + 4.78886i −0.428329 + 0.428329i
\(126\) 0 0
\(127\) −7.12606 4.11423i −0.632336 0.365079i 0.149320 0.988789i \(-0.452291\pi\)
−0.781656 + 0.623710i \(0.785625\pi\)
\(128\) 0 0
\(129\) 3.95261 0.263706i 0.348008 0.0232181i
\(130\) 0 0
\(131\) 13.4099i 1.17163i −0.810446 0.585814i \(-0.800775\pi\)
0.810446 0.585814i \(-0.199225\pi\)
\(132\) 0 0
\(133\) −7.69642 + 13.3306i −0.667365 + 1.15591i
\(134\) 0 0
\(135\) −2.04917 + 3.09020i −0.176365 + 0.265962i
\(136\) 0 0
\(137\) 13.2257 + 3.54382i 1.12995 + 0.302769i 0.774904 0.632079i \(-0.217798\pi\)
0.355047 + 0.934849i \(0.384465\pi\)
\(138\) 0 0
\(139\) 9.49420 + 16.4444i 0.805288 + 1.39480i 0.916097 + 0.400957i \(0.131322\pi\)
−0.110809 + 0.993842i \(0.535344\pi\)
\(140\) 0 0
\(141\) −2.96383 + 1.00995i −0.249599 + 0.0850529i
\(142\) 0 0
\(143\) 0.797626 4.05296i 0.0667009 0.338925i
\(144\) 0 0
\(145\) 1.91512 + 7.14731i 0.159042 + 0.593552i
\(146\) 0 0
\(147\) 3.32900 + 4.96962i 0.274571 + 0.409887i
\(148\) 0 0
\(149\) 1.55037 5.78607i 0.127012 0.474014i −0.872892 0.487914i \(-0.837758\pi\)
0.999903 + 0.0139002i \(0.00442471\pi\)
\(150\) 0 0
\(151\) −10.9825 10.9825i −0.893741 0.893741i 0.101132 0.994873i \(-0.467753\pi\)
−0.994873 + 0.101132i \(0.967753\pi\)
\(152\) 0 0
\(153\) 3.46852 8.42940i 0.280413 0.681477i
\(154\) 0 0
\(155\) −1.94912 −0.156557
\(156\) 0 0
\(157\) 10.2214 0.815760 0.407880 0.913036i \(-0.366268\pi\)
0.407880 + 0.913036i \(0.366268\pi\)
\(158\) 0 0
\(159\) −1.85687 + 3.77648i −0.147260 + 0.299495i
\(160\) 0 0
\(161\) 11.1146 + 11.1146i 0.875950 + 0.875950i
\(162\) 0 0
\(163\) 5.56650 20.7745i 0.436002 1.62718i −0.302655 0.953100i \(-0.597873\pi\)
0.738657 0.674082i \(-0.235460\pi\)
\(164\) 0 0
\(165\) 1.17642 0.788051i 0.0915845 0.0613497i
\(166\) 0 0
\(167\) 2.83710 + 10.5882i 0.219542 + 0.819341i 0.984518 + 0.175283i \(0.0560839\pi\)
−0.764976 + 0.644058i \(0.777249\pi\)
\(168\) 0 0
\(169\) 7.95574 + 10.2814i 0.611980 + 0.790873i
\(170\) 0 0
\(171\) −5.49657 13.1827i −0.420333 1.00810i
\(172\) 0 0
\(173\) 10.1274 + 17.5412i 0.769975 + 1.33364i 0.937576 + 0.347781i \(0.113065\pi\)
−0.167601 + 0.985855i \(0.553602\pi\)
\(174\) 0 0
\(175\) −14.0248 3.75794i −1.06018 0.284074i
\(176\) 0 0
\(177\) 7.57665 + 6.62890i 0.569496 + 0.498259i
\(178\) 0 0
\(179\) 10.5903 18.3430i 0.791557 1.37102i −0.133445 0.991056i \(-0.542604\pi\)
0.925003 0.379961i \(-0.124063\pi\)
\(180\) 0 0
\(181\) 14.0377i 1.04342i −0.853124 0.521709i \(-0.825295\pi\)
0.853124 0.521709i \(-0.174705\pi\)
\(182\) 0 0
\(183\) 1.20767 + 18.1013i 0.0892732 + 1.33809i
\(184\) 0 0
\(185\) 4.79428 + 2.76798i 0.352483 + 0.203506i
\(186\) 0 0
\(187\) −2.46138 + 2.46138i −0.179994 + 0.179994i
\(188\) 0 0
\(189\) −16.7679 1.04001i −1.21968 0.0756496i
\(190\) 0 0
\(191\) 18.7332 10.8156i 1.35549 0.782592i 0.366477 0.930427i \(-0.380564\pi\)
0.989012 + 0.147835i \(0.0472305\pi\)
\(192\) 0 0
\(193\) −20.6023 + 5.52036i −1.48298 + 0.397364i −0.907361 0.420352i \(-0.861907\pi\)
−0.575622 + 0.817716i \(0.695240\pi\)
\(194\) 0 0
\(195\) −0.567526 + 4.42004i −0.0406414 + 0.316526i
\(196\) 0 0
\(197\) −24.7548 + 6.63302i −1.76371 + 0.472583i −0.987463 0.157851i \(-0.949543\pi\)
−0.776242 + 0.630435i \(0.782877\pi\)
\(198\) 0 0
\(199\) −13.6540 + 7.88312i −0.967904 + 0.558820i −0.898597 0.438776i \(-0.855412\pi\)
−0.0693073 + 0.997595i \(0.522079\pi\)
\(200\) 0 0
\(201\) 2.04754 10.3569i 0.144423 0.730521i
\(202\) 0 0
\(203\) −23.7066 + 23.7066i −1.66388 + 1.66388i
\(204\) 0 0
\(205\) −4.19109 2.41973i −0.292718 0.169001i
\(206\) 0 0
\(207\) −14.4555 + 1.93747i −1.00472 + 0.134664i
\(208\) 0 0
\(209\) 5.45432i 0.377283i
\(210\) 0 0
\(211\) 5.20303 9.01192i 0.358192 0.620406i −0.629467 0.777027i \(-0.716727\pi\)
0.987659 + 0.156621i \(0.0500601\pi\)
\(212\) 0 0
\(213\) −4.52520 + 5.17218i −0.310062 + 0.354392i
\(214\) 0 0
\(215\) 1.57644 + 0.422405i 0.107512 + 0.0288078i
\(216\) 0 0
\(217\) −4.41563 7.64810i −0.299753 0.519187i
\(218\) 0 0
\(219\) 3.21082 + 9.42258i 0.216967 + 0.636719i
\(220\) 0 0
\(221\) −0.738700 10.9301i −0.0496903 0.735237i
\(222\) 0 0
\(223\) 5.88651 + 21.9688i 0.394190 + 1.47114i 0.823156 + 0.567816i \(0.192211\pi\)
−0.428966 + 0.903321i \(0.641122\pi\)
\(224\) 0 0
\(225\) 10.6692 8.22643i 0.711278 0.548429i
\(226\) 0 0
\(227\) 5.14469 19.2003i 0.341465 1.27437i −0.555222 0.831702i \(-0.687367\pi\)
0.896688 0.442664i \(-0.145967\pi\)
\(228\) 0 0
\(229\) 1.16288 + 1.16288i 0.0768456 + 0.0768456i 0.744485 0.667639i \(-0.232695\pi\)
−0.667639 + 0.744485i \(0.732695\pi\)
\(230\) 0 0
\(231\) 5.75736 + 2.83086i 0.378806 + 0.186257i
\(232\) 0 0
\(233\) −23.8148 −1.56016 −0.780080 0.625680i \(-0.784822\pi\)
−0.780080 + 0.625680i \(0.784822\pi\)
\(234\) 0 0
\(235\) −1.29001 −0.0841507
\(236\) 0 0
\(237\) 10.5347 + 5.17985i 0.684303 + 0.336467i
\(238\) 0 0
\(239\) 3.10170 + 3.10170i 0.200632 + 0.200632i 0.800271 0.599639i \(-0.204689\pi\)
−0.599639 + 0.800271i \(0.704689\pi\)
\(240\) 0 0
\(241\) −2.25233 + 8.40583i −0.145086 + 0.541467i 0.854666 + 0.519178i \(0.173762\pi\)
−0.999752 + 0.0222886i \(0.992905\pi\)
\(242\) 0 0
\(243\) 10.2095 11.7799i 0.654942 0.755679i
\(244\) 0 0
\(245\) 0.637817 + 2.38037i 0.0407487 + 0.152076i
\(246\) 0 0
\(247\) −12.9288 11.2919i −0.822640 0.718484i
\(248\) 0 0
\(249\) −9.43543 27.6895i −0.597946 1.75475i
\(250\) 0 0
\(251\) −4.34184 7.52029i −0.274055 0.474677i 0.695842 0.718195i \(-0.255032\pi\)
−0.969896 + 0.243519i \(0.921698\pi\)
\(252\) 0 0
\(253\) 5.37988 + 1.44153i 0.338230 + 0.0906284i
\(254\) 0 0
\(255\) 2.47275 2.82629i 0.154850 0.176989i
\(256\) 0 0
\(257\) 2.99467 5.18692i 0.186802 0.323551i −0.757380 0.652974i \(-0.773521\pi\)
0.944182 + 0.329423i \(0.106854\pi\)
\(258\) 0 0
\(259\) 25.0829i 1.55858i
\(260\) 0 0
\(261\) −4.13250 30.8325i −0.255796 1.90849i
\(262\) 0 0
\(263\) −16.5914 9.57907i −1.02307 0.590670i −0.108079 0.994142i \(-0.534470\pi\)
−0.914992 + 0.403472i \(0.867803\pi\)
\(264\) 0 0
\(265\) −1.22596 + 1.22596i −0.0753101 + 0.0753101i
\(266\) 0 0
\(267\) 2.68945 13.6038i 0.164591 0.832540i
\(268\) 0 0
\(269\) 22.0370 12.7231i 1.34362 0.775741i 0.356285 0.934377i \(-0.384043\pi\)
0.987337 + 0.158637i \(0.0507098\pi\)
\(270\) 0 0
\(271\) 22.0299 5.90289i 1.33822 0.358575i 0.482447 0.875925i \(-0.339748\pi\)
0.855774 + 0.517350i \(0.173081\pi\)
\(272\) 0 0
\(273\) −18.6294 + 7.78650i −1.12750 + 0.471260i
\(274\) 0 0
\(275\) −4.96957 + 1.33159i −0.299677 + 0.0802981i
\(276\) 0 0
\(277\) −11.4444 + 6.60744i −0.687628 + 0.397002i −0.802723 0.596352i \(-0.796616\pi\)
0.115095 + 0.993355i \(0.463283\pi\)
\(278\) 0 0
\(279\) 8.12671 + 1.05059i 0.486534 + 0.0628971i
\(280\) 0 0
\(281\) 1.24623 1.24623i 0.0743436 0.0743436i −0.668957 0.743301i \(-0.733259\pi\)
0.743301 + 0.668957i \(0.233259\pi\)
\(282\) 0 0
\(283\) 20.1262 + 11.6199i 1.19638 + 0.690728i 0.959745 0.280871i \(-0.0906233\pi\)
0.236631 + 0.971600i \(0.423957\pi\)
\(284\) 0 0
\(285\) −0.391711 5.87124i −0.0232030 0.347782i
\(286\) 0 0
\(287\) 21.9271i 1.29432i
\(288\) 0 0
\(289\) 3.88414 6.72753i 0.228479 0.395737i
\(290\) 0 0
\(291\) 1.33485 + 1.16788i 0.0782504 + 0.0684622i
\(292\) 0 0
\(293\) 2.69061 + 0.720947i 0.157187 + 0.0421182i 0.336555 0.941664i \(-0.390738\pi\)
−0.179367 + 0.983782i \(0.557405\pi\)
\(294\) 0 0
\(295\) 2.07378 + 3.59188i 0.120740 + 0.209128i
\(296\) 0 0
\(297\) −5.32979 + 2.65163i −0.309266 + 0.153863i
\(298\) 0 0
\(299\) −14.5547 + 9.76799i −0.841722 + 0.564897i
\(300\) 0 0
\(301\) 1.91388 + 7.14269i 0.110314 + 0.411698i
\(302\) 0 0
\(303\) 10.8597 7.27456i 0.623871 0.417912i
\(304\) 0 0
\(305\) −1.93444 + 7.21942i −0.110766 + 0.413383i
\(306\) 0 0
\(307\) 15.5744 + 15.5744i 0.888881 + 0.888881i 0.994416 0.105535i \(-0.0336555\pi\)
−0.105535 + 0.994416i \(0.533656\pi\)
\(308\) 0 0
\(309\) −4.82444 + 9.81188i −0.274453 + 0.558179i
\(310\) 0 0
\(311\) −16.8640 −0.956272 −0.478136 0.878286i \(-0.658687\pi\)
−0.478136 + 0.878286i \(0.658687\pi\)
\(312\) 0 0
\(313\) 14.7731 0.835026 0.417513 0.908671i \(-0.362902\pi\)
0.417513 + 0.908671i \(0.362902\pi\)
\(314\) 0 0
\(315\) −6.40074 2.63377i −0.360641 0.148396i
\(316\) 0 0
\(317\) −3.02944 3.02944i −0.170150 0.170150i 0.616895 0.787045i \(-0.288390\pi\)
−0.787045 + 0.616895i \(0.788390\pi\)
\(318\) 0 0
\(319\) −3.07470 + 11.4749i −0.172150 + 0.642472i
\(320\) 0 0
\(321\) −8.08633 12.0715i −0.451335 0.673765i
\(322\) 0 0
\(323\) 3.74392 + 13.9725i 0.208317 + 0.777450i
\(324\) 0 0
\(325\) 7.13193 14.5365i 0.395609 0.806340i
\(326\) 0 0
\(327\) −23.9908 + 8.17505i −1.32669 + 0.452081i
\(328\) 0 0
\(329\) −2.92245 5.06183i −0.161120 0.279068i
\(330\) 0 0
\(331\) 0.735585 + 0.197099i 0.0404314 + 0.0108336i 0.278978 0.960297i \(-0.410004\pi\)
−0.238547 + 0.971131i \(0.576671\pi\)
\(332\) 0 0
\(333\) −18.4975 14.1251i −1.01366 0.774049i
\(334\) 0 0
\(335\) 2.17476 3.76679i 0.118820 0.205802i
\(336\) 0 0
\(337\) 6.15955i 0.335532i 0.985827 + 0.167766i \(0.0536554\pi\)
−0.985827 + 0.167766i \(0.946345\pi\)
\(338\) 0 0
\(339\) −26.0370 + 1.73711i −1.41413 + 0.0943468i
\(340\) 0 0
\(341\) −2.71004 1.56464i −0.146757 0.0847300i
\(342\) 0 0
\(343\) 8.10810 8.10810i 0.437796 0.437796i
\(344\) 0 0
\(345\) −5.89463 1.16536i −0.317356 0.0627407i
\(346\) 0 0
\(347\) 5.68995 3.28509i 0.305452 0.176353i −0.339437 0.940629i \(-0.610237\pi\)
0.644890 + 0.764276i \(0.276903\pi\)
\(348\) 0 0
\(349\) 1.81261 0.485688i 0.0970270 0.0259983i −0.209979 0.977706i \(-0.567340\pi\)
0.307006 + 0.951708i \(0.400673\pi\)
\(350\) 0 0
\(351\) 4.74870 18.1232i 0.253467 0.967344i
\(352\) 0 0
\(353\) −26.6737 + 7.14721i −1.41970 + 0.380407i −0.885377 0.464873i \(-0.846100\pi\)
−0.534323 + 0.845281i \(0.679433\pi\)
\(354\) 0 0
\(355\) −2.45199 + 1.41566i −0.130138 + 0.0751353i
\(356\) 0 0
\(357\) 16.6919 + 3.29996i 0.883431 + 0.174652i
\(358\) 0 0
\(359\) −10.1971 + 10.1971i −0.538182 + 0.538182i −0.922995 0.384813i \(-0.874266\pi\)
0.384813 + 0.922995i \(0.374266\pi\)
\(360\) 0 0
\(361\) 3.17498 + 1.83307i 0.167104 + 0.0964775i
\(362\) 0 0
\(363\) −16.7420 + 1.11698i −0.878727 + 0.0586260i
\(364\) 0 0
\(365\) 4.10118i 0.214665i
\(366\) 0 0
\(367\) 2.25960 3.91375i 0.117950 0.204296i −0.801005 0.598658i \(-0.795701\pi\)
0.918955 + 0.394362i \(0.129034\pi\)
\(368\) 0 0
\(369\) 16.1702 + 12.3479i 0.841788 + 0.642807i
\(370\) 0 0
\(371\) −7.58788 2.03316i −0.393943 0.105557i
\(372\) 0 0
\(373\) 2.40745 + 4.16983i 0.124653 + 0.215905i 0.921597 0.388147i \(-0.126885\pi\)
−0.796944 + 0.604053i \(0.793552\pi\)
\(374\) 0 0
\(375\) 11.1033 3.78355i 0.573374 0.195382i
\(376\) 0 0
\(377\) −20.8345 31.0443i −1.07303 1.59886i
\(378\) 0 0
\(379\) 0.736874 + 2.75005i 0.0378507 + 0.141261i 0.982265 0.187496i \(-0.0600371\pi\)
−0.944415 + 0.328757i \(0.893370\pi\)
\(380\) 0 0
\(381\) 7.93190 + 11.8409i 0.406363 + 0.606630i
\(382\) 0 0
\(383\) −1.67036 + 6.23387i −0.0853514 + 0.318536i −0.995381 0.0960085i \(-0.969392\pi\)
0.910029 + 0.414544i \(0.136059\pi\)
\(384\) 0 0
\(385\) 1.86901 + 1.86901i 0.0952536 + 0.0952536i
\(386\) 0 0
\(387\) −6.34518 2.61090i −0.322543 0.132720i
\(388\) 0 0
\(389\) −5.45516 −0.276588 −0.138294 0.990391i \(-0.544162\pi\)
−0.138294 + 0.990391i \(0.544162\pi\)
\(390\) 0 0
\(391\) 14.7713 0.747016
\(392\) 0 0
\(393\) −10.2485 + 20.8433i −0.516970 + 1.05141i
\(394\) 0 0
\(395\) 3.41988 + 3.41988i 0.172073 + 0.172073i
\(396\) 0 0
\(397\) −0.437429 + 1.63251i −0.0219539 + 0.0819331i −0.976034 0.217620i \(-0.930171\pi\)
0.954080 + 0.299553i \(0.0968374\pi\)
\(398\) 0 0
\(399\) 22.1507 14.8381i 1.10892 0.742832i
\(400\) 0 0
\(401\) −5.16790 19.2869i −0.258073 0.963141i −0.966355 0.257212i \(-0.917196\pi\)
0.708282 0.705929i \(-0.249470\pi\)
\(402\) 0 0
\(403\) 9.31927 3.18460i 0.464226 0.158636i
\(404\) 0 0
\(405\) 5.54676 3.23708i 0.275621 0.160852i
\(406\) 0 0
\(407\) 4.44396 + 7.69716i 0.220279 + 0.381534i
\(408\) 0 0
\(409\) 8.48733 + 2.27417i 0.419671 + 0.112451i 0.462474 0.886633i \(-0.346962\pi\)
−0.0428024 + 0.999084i \(0.513629\pi\)
\(410\) 0 0
\(411\) −17.8487 15.6160i −0.880411 0.770281i
\(412\) 0 0
\(413\) −9.39609 + 16.2745i −0.462351 + 0.800816i
\(414\) 0 0
\(415\) 12.0519i 0.591603i
\(416\) 0 0
\(417\) −2.18938 32.8159i −0.107214 1.60700i
\(418\) 0 0
\(419\) 7.34045 + 4.23801i 0.358604 + 0.207040i 0.668468 0.743741i \(-0.266950\pi\)
−0.309864 + 0.950781i \(0.600284\pi\)
\(420\) 0 0
\(421\) −15.5203 + 15.5203i −0.756412 + 0.756412i −0.975667 0.219255i \(-0.929637\pi\)
0.219255 + 0.975667i \(0.429637\pi\)
\(422\) 0 0
\(423\) 5.37860 + 0.695323i 0.261517 + 0.0338078i
\(424\) 0 0
\(425\) −11.8167 + 6.82236i −0.573193 + 0.330933i
\(426\) 0 0
\(427\) −32.7105 + 8.76477i −1.58297 + 0.424157i
\(428\) 0 0
\(429\) −4.33724 + 5.69002i −0.209404 + 0.274717i
\(430\) 0 0
\(431\) 26.3726 7.06652i 1.27032 0.340382i 0.440169 0.897915i \(-0.354919\pi\)
0.830155 + 0.557533i \(0.188252\pi\)
\(432\) 0 0
\(433\) 9.03766 5.21790i 0.434322 0.250756i −0.266864 0.963734i \(-0.585987\pi\)
0.701186 + 0.712978i \(0.252654\pi\)
\(434\) 0 0
\(435\) 2.48563 12.5729i 0.119177 0.602823i
\(436\) 0 0
\(437\) 16.3663 16.3663i 0.782907 0.782907i
\(438\) 0 0
\(439\) −22.1085 12.7643i −1.05518 0.609208i −0.131084 0.991371i \(-0.541846\pi\)
−0.924095 + 0.382163i \(0.875179\pi\)
\(440\) 0 0
\(441\) −1.37630 10.2686i −0.0655383 0.488980i
\(442\) 0 0
\(443\) 27.6082i 1.31170i −0.754889 0.655852i \(-0.772309\pi\)
0.754889 0.655852i \(-0.227691\pi\)
\(444\) 0 0
\(445\) 2.85654 4.94767i 0.135413 0.234542i
\(446\) 0 0
\(447\) −6.83179 + 7.80855i −0.323133 + 0.369332i
\(448\) 0 0
\(449\) 26.6058 + 7.12899i 1.25560 + 0.336438i 0.824499 0.565864i \(-0.191457\pi\)
0.431105 + 0.902302i \(0.358124\pi\)
\(450\) 0 0
\(451\) −3.88484 6.72874i −0.182930 0.316844i
\(452\) 0 0
\(453\) 8.67694 + 25.4637i 0.407678 + 1.19639i
\(454\) 0 0
\(455\) −8.29960 + 0.560921i −0.389091 + 0.0262964i
\(456\) 0 0
\(457\) 5.68707 + 21.2244i 0.266030 + 0.992838i 0.961617 + 0.274396i \(0.0884778\pi\)
−0.695587 + 0.718442i \(0.744856\pi\)
\(458\) 0 0
\(459\) −11.8334 + 10.4512i −0.552335 + 0.487820i
\(460\) 0 0
\(461\) 5.98430 22.3337i 0.278717 1.04019i −0.674593 0.738190i \(-0.735681\pi\)
0.953310 0.301995i \(-0.0976526\pi\)
\(462\) 0 0
\(463\) −8.48586 8.48586i −0.394371 0.394371i 0.481871 0.876242i \(-0.339957\pi\)
−0.876242 + 0.481871i \(0.839957\pi\)
\(464\) 0 0
\(465\) 3.02955 + 1.48961i 0.140492 + 0.0690791i
\(466\) 0 0
\(467\) 26.9837 1.24866 0.624329 0.781162i \(-0.285373\pi\)
0.624329 + 0.781162i \(0.285373\pi\)
\(468\) 0 0
\(469\) 19.7072 0.909996
\(470\) 0 0
\(471\) −15.8874 7.81175i −0.732054 0.359946i
\(472\) 0 0
\(473\) 1.85278 + 1.85278i 0.0851911 + 0.0851911i
\(474\) 0 0
\(475\) −5.53361 + 20.6517i −0.253900 + 0.947566i
\(476\) 0 0
\(477\) 5.77236 4.45076i 0.264298 0.203786i
\(478\) 0 0
\(479\) 5.46091 + 20.3804i 0.249515 + 0.931203i 0.971060 + 0.238836i \(0.0767657\pi\)
−0.721545 + 0.692368i \(0.756568\pi\)
\(480\) 0 0
\(481\) −27.4453 5.40127i −1.25140 0.246277i
\(482\) 0 0
\(483\) −8.78130 25.7699i −0.399563 1.17257i
\(484\) 0 0
\(485\) 0.365357 + 0.632817i 0.0165900 + 0.0287347i
\(486\) 0 0
\(487\) 15.7355 + 4.21633i 0.713046 + 0.191060i 0.597067 0.802192i \(-0.296333\pi\)
0.115979 + 0.993252i \(0.462999\pi\)
\(488\) 0 0
\(489\) −24.5290 + 28.0360i −1.10924 + 1.26783i
\(490\) 0 0
\(491\) −16.2519 + 28.1492i −0.733440 + 1.27036i 0.221965 + 0.975055i \(0.428753\pi\)
−0.955404 + 0.295300i \(0.904580\pi\)
\(492\) 0 0
\(493\) 31.5062i 1.41897i
\(494\) 0 0
\(495\) −2.43081 + 0.325803i −0.109257 + 0.0146438i
\(496\) 0 0
\(497\) −11.1097 6.41422i −0.498340 0.287717i
\(498\) 0 0
\(499\) −10.3481 + 10.3481i −0.463245 + 0.463245i −0.899718 0.436472i \(-0.856228\pi\)
0.436472 + 0.899718i \(0.356228\pi\)
\(500\) 0 0
\(501\) 3.68228 18.6258i 0.164512 0.832138i
\(502\) 0 0
\(503\) −19.4725 + 11.2424i −0.868235 + 0.501276i −0.866761 0.498723i \(-0.833803\pi\)
−0.00147394 + 0.999999i \(0.500469\pi\)
\(504\) 0 0
\(505\) 5.20160 1.39376i 0.231468 0.0620217i
\(506\) 0 0
\(507\) −4.50826 22.0607i −0.200219 0.979751i
\(508\) 0 0
\(509\) 27.6271 7.40267i 1.22455 0.328117i 0.412095 0.911141i \(-0.364797\pi\)
0.812455 + 0.583023i \(0.198130\pi\)
\(510\) 0 0
\(511\) −16.0925 + 9.29103i −0.711892 + 0.411011i
\(512\) 0 0
\(513\) −1.53143 + 24.6909i −0.0676141 + 1.09013i
\(514\) 0 0
\(515\) −3.18523 + 3.18523i −0.140358 + 0.140358i
\(516\) 0 0
\(517\) −1.79362 1.03554i −0.0788831 0.0455432i
\(518\) 0 0
\(519\) −2.33541 35.0047i −0.102513 1.53653i
\(520\) 0 0
\(521\) 7.17424i 0.314309i 0.987574 + 0.157155i \(0.0502321\pi\)
−0.987574 + 0.157155i \(0.949768\pi\)
\(522\) 0 0
\(523\) 11.5992 20.0904i 0.507199 0.878494i −0.492767 0.870161i \(-0.664014\pi\)
0.999965 0.00833218i \(-0.00265225\pi\)
\(524\) 0 0
\(525\) 18.9271 + 16.5595i 0.826047 + 0.722718i
\(526\) 0 0
\(527\) −8.01637 2.14798i −0.349199 0.0935675i
\(528\) 0 0
\(529\) −0.317449 0.549837i −0.0138021 0.0239060i
\(530\) 0 0
\(531\) −6.71042 16.0939i −0.291208 0.698417i
\(532\) 0 0
\(533\) 23.9923 + 4.72171i 1.03922 + 0.204520i
\(534\) 0 0
\(535\) −1.54930 5.78205i −0.0669819 0.249980i
\(536\) 0 0
\(537\) −30.4794 + 20.4172i −1.31528 + 0.881069i
\(538\) 0 0
\(539\) −1.02401 + 3.82165i −0.0441071 + 0.164610i
\(540\) 0 0
\(541\) 30.2641 + 30.2641i 1.30115 + 1.30115i 0.927615 + 0.373539i \(0.121856\pi\)
0.373539 + 0.927615i \(0.378144\pi\)
\(542\) 0 0
\(543\) −10.7284 + 21.8192i −0.460398 + 0.936351i
\(544\) 0 0
\(545\) −10.4420 −0.447286
\(546\) 0 0
\(547\) 29.5412 1.26309 0.631545 0.775339i \(-0.282421\pi\)
0.631545 + 0.775339i \(0.282421\pi\)
\(548\) 0 0
\(549\) 11.9568 29.0582i 0.510306 1.24018i
\(550\) 0 0
\(551\) 34.9083 + 34.9083i 1.48714 + 1.48714i
\(552\) 0 0
\(553\) −5.67163 + 21.1668i −0.241182 + 0.900104i
\(554\) 0 0
\(555\) −5.33643 7.96637i −0.226519 0.338153i
\(556\) 0 0
\(557\) 6.70422 + 25.0205i 0.284067 + 1.06015i 0.949518 + 0.313712i \(0.101572\pi\)
−0.665451 + 0.746441i \(0.731761\pi\)
\(558\) 0 0
\(559\) −8.22754 + 0.556051i −0.347988 + 0.0235185i
\(560\) 0 0
\(561\) 5.70688 1.94466i 0.240945 0.0821038i
\(562\) 0 0
\(563\) 2.40232 + 4.16095i 0.101246 + 0.175363i 0.912198 0.409749i \(-0.134384\pi\)
−0.810952 + 0.585112i \(0.801050\pi\)
\(564\) 0 0
\(565\) −10.3844 2.78250i −0.436876 0.117061i
\(566\) 0 0
\(567\) 25.2679 + 14.4314i 1.06115 + 0.606061i
\(568\) 0 0
\(569\) 1.00204 1.73559i 0.0420078 0.0727597i −0.844257 0.535938i \(-0.819958\pi\)
0.886265 + 0.463179i \(0.153291\pi\)
\(570\) 0 0
\(571\) 16.7105i 0.699311i 0.936878 + 0.349656i \(0.113701\pi\)
−0.936878 + 0.349656i \(0.886299\pi\)
\(572\) 0 0
\(573\) −37.3834 + 2.49411i −1.56171 + 0.104193i
\(574\) 0 0
\(575\) 18.9074 + 10.9162i 0.788492 + 0.455236i
\(576\) 0 0
\(577\) 14.2655 14.2655i 0.593883 0.593883i −0.344795 0.938678i \(-0.612052\pi\)
0.938678 + 0.344795i \(0.112052\pi\)
\(578\) 0 0
\(579\) 36.2415 + 7.16487i 1.50615 + 0.297762i
\(580\) 0 0
\(581\) 47.2901 27.3030i 1.96193 1.13272i
\(582\) 0 0
\(583\) −2.68870 + 0.720434i −0.111354 + 0.0298373i
\(584\) 0 0
\(585\) 4.26014 6.43644i 0.176135 0.266114i
\(586\) 0 0
\(587\) −1.79654 + 0.481380i −0.0741509 + 0.0198687i −0.295704 0.955280i \(-0.595554\pi\)
0.221553 + 0.975148i \(0.428887\pi\)
\(588\) 0 0
\(589\) −11.2619 + 6.50207i −0.464039 + 0.267913i
\(590\) 0 0
\(591\) 43.5462 + 8.60900i 1.79125 + 0.354127i
\(592\) 0 0
\(593\) −32.1956 + 32.1956i −1.32212 + 1.32212i −0.410057 + 0.912060i \(0.634491\pi\)
−0.912060 + 0.410057i \(0.865509\pi\)
\(594\) 0 0
\(595\) 6.07081 + 3.50499i 0.248879 + 0.143690i
\(596\) 0 0
\(597\) 27.2474 1.81786i 1.11516 0.0744001i
\(598\) 0 0
\(599\) 14.7278i 0.601762i −0.953662 0.300881i \(-0.902719\pi\)
0.953662 0.300881i \(-0.0972807\pi\)
\(600\) 0 0
\(601\) 23.2965 40.3507i 0.950282 1.64594i 0.205470 0.978663i \(-0.434128\pi\)
0.744812 0.667274i \(-0.232539\pi\)
\(602\) 0 0
\(603\) −11.0978 + 14.5332i −0.451939 + 0.591837i
\(604\) 0 0
\(605\) −6.67728 1.78917i −0.271470 0.0727402i
\(606\) 0 0
\(607\) −5.31772 9.21056i −0.215840 0.373845i 0.737692 0.675137i \(-0.235915\pi\)
−0.953532 + 0.301292i \(0.902582\pi\)
\(608\) 0 0
\(609\) 54.9655 18.7299i 2.22732 0.758975i
\(610\) 0 0
\(611\) 6.16788 2.10770i 0.249526 0.0852684i
\(612\) 0 0
\(613\) −4.55636 17.0046i −0.184030 0.686808i −0.994836 0.101494i \(-0.967638\pi\)
0.810806 0.585314i \(-0.199029\pi\)
\(614\) 0 0
\(615\) 4.66503 + 6.96408i 0.188112 + 0.280819i
\(616\) 0 0
\(617\) −1.61026 + 6.00956i −0.0648265 + 0.241936i −0.990734 0.135813i \(-0.956635\pi\)
0.925908 + 0.377749i \(0.123302\pi\)
\(618\) 0 0
\(619\) 20.3122 + 20.3122i 0.816415 + 0.816415i 0.985587 0.169172i \(-0.0541093\pi\)
−0.169172 + 0.985587i \(0.554109\pi\)
\(620\) 0 0
\(621\) 23.9492 + 8.03614i 0.961047 + 0.322479i
\(622\) 0 0
\(623\) 25.8854 1.03708
\(624\) 0 0
\(625\) −17.6213 −0.704851
\(626\) 0 0
\(627\) 4.16847 8.47777i 0.166473 0.338570i
\(628\) 0 0
\(629\) 16.6676 + 16.6676i 0.664583 + 0.664583i
\(630\) 0 0
\(631\) −7.88943 + 29.4438i −0.314073 + 1.17214i 0.610776 + 0.791804i \(0.290858\pi\)
−0.924849 + 0.380334i \(0.875809\pi\)
\(632\) 0 0
\(633\) −14.9746 + 10.0310i −0.595186 + 0.398697i
\(634\) 0 0
\(635\) 1.51971 + 5.67162i 0.0603077 + 0.225072i
\(636\) 0 0
\(637\) −6.93879 10.3391i −0.274925 0.409650i
\(638\) 0 0
\(639\) 10.9865 4.58085i 0.434618 0.181216i
\(640\) 0 0
\(641\) −15.6856 27.1682i −0.619543 1.07308i −0.989569 0.144058i \(-0.953985\pi\)
0.370026 0.929021i \(-0.379349\pi\)
\(642\) 0 0
\(643\) 4.97838 + 1.33395i 0.196328 + 0.0526060i 0.355643 0.934622i \(-0.384262\pi\)
−0.159315 + 0.987228i \(0.550929\pi\)
\(644\) 0 0
\(645\) −2.12747 1.86135i −0.0837690 0.0732905i
\(646\) 0 0
\(647\) 4.80729 8.32648i 0.188994 0.327348i −0.755921 0.654663i \(-0.772811\pi\)
0.944915 + 0.327315i \(0.106144\pi\)
\(648\) 0 0
\(649\) 6.65884i 0.261382i
\(650\) 0 0
\(651\) 1.01825 + 15.2623i 0.0399085 + 0.598176i
\(652\) 0 0
\(653\) −16.4158 9.47768i −0.642401 0.370890i 0.143138 0.989703i \(-0.454281\pi\)
−0.785539 + 0.618813i \(0.787614\pi\)
\(654\) 0 0
\(655\) −6.76636 + 6.76636i −0.264384 + 0.264384i
\(656\) 0 0
\(657\) 2.21057 17.0996i 0.0862424 0.667119i
\(658\) 0 0
\(659\) 23.6778 13.6704i 0.922357 0.532523i 0.0379709 0.999279i \(-0.487911\pi\)
0.884386 + 0.466756i \(0.154577\pi\)
\(660\) 0 0
\(661\) −9.46548 + 2.53627i −0.368165 + 0.0986494i −0.438158 0.898898i \(-0.644369\pi\)
0.0699932 + 0.997547i \(0.477702\pi\)
\(662\) 0 0
\(663\) −7.20515 + 17.5534i −0.279825 + 0.681719i
\(664\) 0 0
\(665\) 10.6098 2.84289i 0.411431 0.110243i
\(666\) 0 0
\(667\) 43.6578 25.2058i 1.69044 0.975974i
\(668\) 0 0
\(669\) 7.64010 38.6453i 0.295383 1.49411i
\(670\) 0 0
\(671\) −8.48497 + 8.48497i −0.327559 + 0.327559i
\(672\) 0 0
\(673\) −6.65548 3.84254i −0.256550 0.148119i 0.366210 0.930532i \(-0.380655\pi\)
−0.622760 + 0.782413i \(0.713989\pi\)
\(674\) 0 0
\(675\) −22.8704 + 4.63260i −0.880282 + 0.178309i
\(676\) 0 0
\(677\) 11.5419i 0.443593i 0.975093 + 0.221797i \(0.0711921\pi\)
−0.975093 + 0.221797i \(0.928808\pi\)
\(678\) 0 0
\(679\) −1.65540 + 2.86724i −0.0635284 + 0.110034i
\(680\) 0 0
\(681\) −22.6703 + 25.9116i −0.868729 + 0.992933i
\(682\) 0 0
\(683\) −19.8376 5.31546i −0.759063 0.203390i −0.141529 0.989934i \(-0.545202\pi\)
−0.617535 + 0.786544i \(0.711868\pi\)
\(684\) 0 0
\(685\) −4.88529 8.46157i −0.186657 0.323300i
\(686\) 0 0
\(687\) −0.918763 2.69623i −0.0350530 0.102868i
\(688\) 0 0
\(689\) 3.85860 7.86471i 0.147001 0.299622i
\(690\) 0 0
\(691\) −0.529217 1.97507i −0.0201324 0.0751350i 0.955129 0.296191i \(-0.0957164\pi\)
−0.975261 + 0.221056i \(0.929050\pi\)
\(692\) 0 0
\(693\) −6.78531 8.80013i −0.257753 0.334289i
\(694\) 0 0
\(695\) 3.50695 13.0881i 0.133026 0.496460i
\(696\) 0 0
\(697\) −14.5706 14.5706i −0.551901 0.551901i
\(698\) 0 0
\(699\) 37.0159 + 18.2005i 1.40007 + 0.688406i
\(700\) 0 0
\(701\) −13.4888 −0.509464 −0.254732 0.967012i \(-0.581987\pi\)
−0.254732 + 0.967012i \(0.581987\pi\)
\(702\) 0 0
\(703\) 36.9349 1.39303
\(704\) 0 0
\(705\) 2.00509 + 0.985888i 0.0755159 + 0.0371307i
\(706\) 0 0
\(707\) 17.2530 + 17.2530i 0.648864 + 0.648864i
\(708\) 0 0
\(709\) −3.48407 + 13.0027i −0.130847 + 0.488328i −0.999980 0.00624974i \(-0.998011\pi\)
0.869133 + 0.494578i \(0.164677\pi\)
\(710\) 0 0
\(711\) −12.4156 16.1023i −0.465623 0.603884i
\(712\) 0 0
\(713\) 3.43689 + 12.8267i 0.128713 + 0.480362i
\(714\) 0 0
\(715\) −2.44751 + 1.64257i −0.0915315 + 0.0614287i
\(716\) 0 0
\(717\) −2.45057 7.19152i −0.0915181 0.268572i
\(718\) 0 0
\(719\) −9.18916 15.9161i −0.342698 0.593570i 0.642235 0.766508i \(-0.278007\pi\)
−0.984933 + 0.172938i \(0.944674\pi\)
\(720\) 0 0
\(721\) −19.7145 5.28248i −0.734205 0.196730i
\(722\) 0 0
\(723\) 9.92502 11.3440i 0.369115 0.421889i
\(724\) 0 0
\(725\) −23.2835 + 40.3282i −0.864727 + 1.49775i
\(726\) 0 0
\(727\) 14.3838i 0.533466i 0.963770 + 0.266733i \(0.0859442\pi\)
−0.963770 + 0.266733i \(0.914056\pi\)
\(728\) 0 0
\(729\) −24.8717 + 10.5071i −0.921174 + 0.389151i
\(730\) 0 0
\(731\) 6.01811 + 3.47456i 0.222588 + 0.128511i
\(732\) 0 0
\(733\) 3.75917 3.75917i 0.138848 0.138848i −0.634266 0.773114i \(-0.718698\pi\)
0.773114 + 0.634266i \(0.218698\pi\)
\(734\) 0 0
\(735\) 0.827823 4.18731i 0.0305347 0.154451i
\(736\) 0 0
\(737\) 6.04753 3.49154i 0.222764 0.128613i
\(738\) 0 0
\(739\) −37.0517 + 9.92797i −1.36297 + 0.365206i −0.864905 0.501935i \(-0.832622\pi\)
−0.498063 + 0.867141i \(0.665955\pi\)
\(740\) 0 0
\(741\) 11.4657 + 27.4320i 0.421203 + 1.00774i
\(742\) 0 0
\(743\) −32.0441 + 8.58618i −1.17558 + 0.314996i −0.793173 0.608996i \(-0.791572\pi\)
−0.382410 + 0.923993i \(0.624906\pi\)
\(744\) 0 0
\(745\) −3.70182 + 2.13725i −0.135624 + 0.0783027i
\(746\) 0 0
\(747\) −6.49605 + 50.2495i −0.237678 + 1.83853i
\(748\) 0 0
\(749\) 19.1782 19.1782i 0.700757 0.700757i
\(750\) 0 0
\(751\) −19.2045 11.0877i −0.700782 0.404597i 0.106857 0.994274i \(-0.465921\pi\)
−0.807639 + 0.589678i \(0.799255\pi\)
\(752\) 0 0
\(753\) 1.00124 + 15.0072i 0.0364871 + 0.546893i
\(754\) 0 0
\(755\) 11.0831i 0.403354i
\(756\) 0 0
\(757\) 10.5455 18.2654i 0.383284 0.663868i −0.608245 0.793749i \(-0.708126\pi\)
0.991530 + 0.129881i \(0.0414597\pi\)
\(758\) 0 0
\(759\) −7.26037 6.35218i −0.263535 0.230570i
\(760\) 0 0
\(761\) 31.8738 + 8.54057i 1.15543 + 0.309595i 0.785137 0.619322i \(-0.212592\pi\)
0.370288 + 0.928917i \(0.379259\pi\)
\(762\) 0 0
\(763\) −23.6559 40.9732i −0.856400 1.48333i
\(764\) 0 0
\(765\) −6.00345 + 2.50316i −0.217055 + 0.0905020i
\(766\) 0 0
\(767\) −15.7840 13.7855i −0.569926 0.497767i
\(768\) 0 0
\(769\) −1.87152 6.98462i −0.0674889 0.251872i 0.923937 0.382546i \(-0.124953\pi\)
−0.991425 + 0.130674i \(0.958286\pi\)
\(770\) 0 0
\(771\) −8.61880 + 5.77347i −0.310398 + 0.207927i
\(772\) 0 0
\(773\) 2.16927 8.09584i 0.0780234 0.291187i −0.915878 0.401456i \(-0.868504\pi\)
0.993902 + 0.110268i \(0.0351710\pi\)
\(774\) 0 0
\(775\) −8.67364 8.67364i −0.311566 0.311566i
\(776\) 0 0
\(777\) 19.1697 38.9870i 0.687707 1.39865i
\(778\) 0 0
\(779\) −32.2879 −1.15684
\(780\) 0 0
\(781\) −4.54564 −0.162656
\(782\) 0 0
\(783\) −17.1405 + 51.0820i −0.612553 + 1.82552i
\(784\) 0 0
\(785\) −5.15753 5.15753i −0.184080 0.184080i
\(786\) 0 0
\(787\) −8.20017 + 30.6035i −0.292305 + 1.09090i 0.651030 + 0.759052i \(0.274337\pi\)
−0.943335 + 0.331843i \(0.892329\pi\)
\(788\) 0 0
\(789\) 18.4676 + 27.5690i 0.657465 + 0.981482i
\(790\) 0 0
\(791\) −12.6073 47.0509i −0.448263 1.67294i
\(792\) 0 0
\(793\) −2.54648 37.6787i −0.0904282 1.33801i
\(794\) 0 0
\(795\) 2.84248 0.968596i 0.100812 0.0343526i
\(796\) 0 0
\(797\) 19.0468