Properties

Label 624.2.cn.f.305.13
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 305.13
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.43902 + 0.963958i) q^{3} +(0.504580 + 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.14157 + 2.77431i) q^{9} +O(q^{10})\) \(q+(1.43902 + 0.963958i) q^{3} +(0.504580 + 0.504580i) q^{5} +(0.836809 - 3.12301i) q^{7} +(1.14157 + 2.77431i) q^{9} +(0.296516 + 1.10661i) q^{11} +(3.23695 + 1.58812i) q^{13} +(0.239708 + 1.21249i) q^{15} +(1.51919 + 2.63131i) q^{17} +(-4.59867 - 1.23221i) q^{19} +(4.21464 - 3.68744i) q^{21} +(2.43079 - 4.21025i) q^{23} -4.49080i q^{25} +(-1.03158 + 5.09273i) q^{27} +(8.98018 + 5.18471i) q^{29} +(1.93142 - 1.93142i) q^{31} +(-0.640035 + 1.87827i) q^{33} +(1.99805 - 1.15357i) q^{35} +(-7.49362 + 2.00791i) q^{37} +(3.12717 + 5.40563i) q^{39} +(-6.55081 + 1.75528i) q^{41} +(-1.98070 + 1.14356i) q^{43} +(-0.823849 + 1.97588i) q^{45} +(-1.27830 + 1.27830i) q^{47} +(-2.99079 - 1.72673i) q^{49} +(-0.350327 + 5.25094i) q^{51} +2.42966i q^{53} +(-0.408758 + 0.707990i) q^{55} +(-5.42979 - 6.20611i) q^{57} +(5.61424 + 1.50433i) q^{59} +(-5.23702 - 9.07078i) q^{61} +(9.61950 - 1.24357i) q^{63} +(0.831967 + 2.43463i) q^{65} +(1.57758 + 5.88762i) q^{67} +(7.55646 - 3.71546i) q^{69} +(-1.02693 + 3.83254i) q^{71} +(-4.06395 - 4.06395i) q^{73} +(4.32894 - 6.46236i) q^{75} +3.70409 q^{77} -6.77768 q^{79} +(-6.39363 + 6.33415i) q^{81} +(-11.9425 - 11.9425i) q^{83} +(-0.561154 + 2.09426i) q^{85} +(7.92484 + 16.1174i) q^{87} +(-2.07215 - 7.73338i) q^{89} +(7.66844 - 8.78010i) q^{91} +(4.64117 - 0.917551i) q^{93} +(-1.69865 - 2.94215i) q^{95} +(-0.989115 - 0.265032i) q^{97} +(-2.73160 + 2.08590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

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
\(3\) 1.43902 + 0.963958i 0.830820 + 0.556541i
\(4\) 0 0
\(5\) 0.504580 + 0.504580i 0.225655 + 0.225655i 0.810875 0.585220i \(-0.198992\pi\)
−0.585220 + 0.810875i \(0.698992\pi\)
\(6\) 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
\(9\) 1.14157 + 2.77431i 0.380523 + 0.924771i
\(10\) 0 0
\(11\) 0.296516 + 1.10661i 0.0894029 + 0.333656i 0.996112 0.0881015i \(-0.0280800\pi\)
−0.906709 + 0.421758i \(0.861413\pi\)
\(12\) 0 0
\(13\) 3.23695 + 1.58812i 0.897769 + 0.440466i
\(14\) 0 0
\(15\) 0.239708 + 1.21249i 0.0618923 + 0.313065i
\(16\) 0 0
\(17\) 1.51919 + 2.63131i 0.368457 + 0.638186i 0.989325 0.145729i \(-0.0465529\pi\)
−0.620868 + 0.783916i \(0.713220\pi\)
\(18\) 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
\(21\) 4.21464 3.68744i 0.919710 0.804665i
\(22\) 0 0
\(23\) 2.43079 4.21025i 0.506854 0.877897i −0.493114 0.869964i \(-0.664142\pi\)
0.999969 0.00793257i \(-0.00252504\pi\)
\(24\) 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 \(0.0795437\pi\)
0.698638 + 0.715475i \(0.253790\pi\)
\(30\) 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
\(33\) −0.640035 + 1.87827i −0.111416 + 0.326965i
\(34\) 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
\(39\) 3.12717 + 5.40563i 0.500747 + 0.865593i
\(40\) 0 0
\(41\) −6.55081 + 1.75528i −1.02306 + 0.274129i −0.731079 0.682293i \(-0.760983\pi\)
−0.291986 + 0.956423i \(0.594316\pi\)
\(42\) 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
\(45\) −0.823849 + 1.97588i −0.122812 + 0.294546i
\(46\) 0 0
\(47\) −1.27830 + 1.27830i −0.186459 + 0.186459i −0.794163 0.607704i \(-0.792091\pi\)
0.607704 + 0.794163i \(0.292091\pi\)
\(48\) 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 \(0.0533660\pi\)
−0.985979 + 0.166870i \(0.946634\pi\)
\(54\) 0 0
\(55\) −0.408758 + 0.707990i −0.0551169 + 0.0954653i
\(56\) 0 0
\(57\) −5.42979 6.20611i −0.719194 0.822019i
\(58\) 0 0
\(59\) 5.61424 + 1.50433i 0.730911 + 0.195847i 0.605035 0.796199i \(-0.293159\pi\)
0.125876 + 0.992046i \(0.459826\pi\)
\(60\) 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
\(63\) 9.61950 1.24357i 1.21194 0.156675i
\(64\) 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
\(69\) 7.55646 3.71546i 0.909690 0.447289i
\(70\) 0 0
\(71\) −1.02693 + 3.83254i −0.121874 + 0.454839i −0.999709 0.0241235i \(-0.992320\pi\)
0.877835 + 0.478963i \(0.158987\pi\)
\(72\) 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
\(75\) 4.32894 6.46236i 0.499863 0.746209i
\(76\) 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
\(81\) −6.39363 + 6.33415i −0.710404 + 0.703794i
\(82\) 0 0
\(83\) −11.9425 11.9425i −1.31086 1.31086i −0.920783 0.390075i \(-0.872449\pi\)
−0.390075 0.920783i \(-0.627551\pi\)
\(84\) 0 0
\(85\) −0.561154 + 2.09426i −0.0608657 + 0.227154i
\(86\) 0 0
\(87\) 7.92484 + 16.1174i 0.849632 + 1.72797i
\(88\) 0 0
\(89\) −2.07215 7.73338i −0.219648 0.819737i −0.984478 0.175505i \(-0.943844\pi\)
0.764831 0.644231i \(-0.222823\pi\)
\(90\) 0 0
\(91\) 7.66844 8.78010i 0.803871 0.920404i
\(92\) 0 0
\(93\) 4.64117 0.917551i 0.481267 0.0951456i
\(94\) 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
\(99\) −2.73160 + 2.08590i −0.274536 + 0.209641i
\(100\) 0 0
\(101\) 3.77328 6.53550i 0.375455 0.650307i −0.614940 0.788574i \(-0.710820\pi\)
0.990395 + 0.138267i \(0.0441532\pi\)
\(102\) 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 0.105894 0.994377i \(-0.466230\pi\)
−0.808209 + 0.588896i \(0.799563\pi\)
\(108\) 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
\(111\) −12.7190 4.33411i −1.20724 0.411375i
\(112\) 0 0
\(113\) −13.0474 + 7.53294i −1.22740 + 0.708639i −0.966485 0.256723i \(-0.917357\pi\)
−0.260914 + 0.965362i \(0.584024\pi\)
\(114\) 0 0
\(115\) 3.35093 0.897879i 0.312476 0.0837277i
\(116\) 0 0
\(117\) −0.710737 + 10.7933i −0.0657077 + 0.997839i
\(118\) 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
\(123\) −11.1188 3.78881i −1.00255 0.341626i
\(124\) 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 \(0.199225\pi\)
−0.810446 + 0.585814i \(0.800775\pi\)
\(132\) 0 0
\(133\) −7.69642 + 13.3306i −0.667365 + 1.15591i
\(134\) 0 0
\(135\) −3.09020 + 2.04917i −0.265962 + 0.176365i
\(136\) 0 0
\(137\) −13.2257 3.54382i −1.12995 0.302769i −0.355047 0.934849i \(-0.615535\pi\)
−0.774904 + 0.632079i \(0.782202\pi\)
\(138\) 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
\(141\) −3.07172 + 0.607274i −0.258686 + 0.0511417i
\(142\) 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
\(147\) −2.63932 5.36780i −0.217687 0.442729i
\(148\) 0 0
\(149\) −1.55037 + 5.78607i −0.127012 + 0.474014i −0.999903 0.0139002i \(-0.995575\pi\)
0.872892 + 0.487914i \(0.162242\pi\)
\(150\) 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
\(153\) −5.56582 + 7.21853i −0.449970 + 0.583583i
\(154\) 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
\(159\) −2.34209 + 3.49634i −0.185740 + 0.277278i
\(160\) 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
\(165\) −1.27068 + 0.624788i −0.0989227 + 0.0486396i
\(166\) 0 0
\(167\) −2.83710 10.5882i −0.219542 0.819341i −0.984518 0.175283i \(-0.943916\pi\)
0.764976 0.644058i \(-0.222751\pi\)
\(168\) 0 0
\(169\) 7.95574 + 10.2814i 0.611980 + 0.790873i
\(170\) 0 0
\(171\) −1.83117 14.1648i −0.140033 1.08321i
\(172\) 0 0
\(173\) −10.1274 17.5412i −0.769975 1.33364i −0.937576 0.347781i \(-0.886935\pi\)
0.167601 0.985855i \(-0.446398\pi\)
\(174\) 0 0
\(175\) −14.0248 3.75794i −1.06018 0.284074i
\(176\) 0 0
\(177\) 6.62890 + 7.57665i 0.498259 + 0.569496i
\(178\) 0 0
\(179\) −10.5903 + 18.3430i −0.791557 + 1.37102i 0.133445 + 0.991056i \(0.457396\pi\)
−0.925003 + 0.379961i \(0.875937\pi\)
\(180\) 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
\(189\) 15.0414 + 7.48327i 1.09410 + 0.544328i
\(190\) 0 0
\(191\) −18.7332 + 10.8156i −1.35549 + 0.782592i −0.989012 0.147835i \(-0.952769\pi\)
−0.366477 + 0.930427i \(0.619436\pi\)
\(192\) 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
\(195\) −1.14967 + 4.30548i −0.0823293 + 0.308321i
\(196\) 0 0
\(197\) 24.7548 6.63302i 1.76371 0.472583i 0.776242 0.630435i \(-0.217123\pi\)
0.987463 + 0.157851i \(0.0504567\pi\)
\(198\) 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
\(201\) −3.40524 + 9.99313i −0.240187 + 0.704861i
\(202\) 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
\(213\) −5.17218 + 4.52520i −0.354392 + 0.310062i
\(214\) 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
\(219\) −1.93064 9.76560i −0.130461 0.659898i
\(220\) 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
\(225\) 12.4589 5.12656i 0.830592 0.341771i
\(226\) 0 0
\(227\) −5.14469 + 19.2003i −0.341465 + 1.27437i 0.555222 + 0.831702i \(0.312633\pi\)
−0.896688 + 0.442664i \(0.854033\pi\)
\(228\) 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
\(231\) 5.33027 + 3.57059i 0.350706 + 0.234928i
\(232\) 0 0
\(233\) 23.8148 1.56016 0.780080 0.625680i \(-0.215178\pi\)
0.780080 + 0.625680i \(0.215178\pi\)
\(234\) 0 0
\(235\) −1.29001 −0.0841507
\(236\) 0 0
\(237\) −9.75323 6.53340i −0.633541 0.424390i
\(238\) 0 0
\(239\) −3.10170 3.10170i −0.200632 0.200632i 0.599639 0.800271i \(-0.295311\pi\)
−0.800271 + 0.599639i \(0.795311\pi\)
\(240\) 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
\(243\) −15.3064 + 2.95179i −0.981908 + 0.189357i
\(244\) 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
\(249\) −5.67345 28.6976i −0.359540 1.81863i
\(250\) 0 0
\(251\) 4.34184 + 7.52029i 0.274055 + 0.474677i 0.969896 0.243519i \(-0.0783018\pi\)
−0.695842 + 0.718195i \(0.744968\pi\)
\(252\) 0 0
\(253\) 5.37988 + 1.44153i 0.338230 + 0.0906284i
\(254\) 0 0
\(255\) −2.82629 + 2.47275i −0.176989 + 0.154850i
\(256\) 0 0
\(257\) −2.99467 + 5.18692i −0.186802 + 0.323551i −0.944182 0.329423i \(-0.893146\pi\)
0.757380 + 0.652974i \(0.226479\pi\)
\(258\) 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 0.914992 0.403472i \(-0.132197\pi\)
0.108079 + 0.994142i \(0.465530\pi\)
\(264\) 0 0
\(265\) −1.22596 + 1.22596i −0.0753101 + 0.0753101i
\(266\) 0 0
\(267\) 4.47278 13.1260i 0.273730 0.803297i
\(268\) 0 0
\(269\) −22.0370 + 12.7231i −1.34362 + 0.775741i −0.987337 0.158637i \(-0.949290\pi\)
−0.356285 + 0.934377i \(0.615957\pi\)
\(270\) 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
\(273\) 19.4987 5.24271i 1.18011 0.317303i
\(274\) 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
\(279\) 7.56323 + 3.15352i 0.452799 + 0.188796i
\(280\) 0 0
\(281\) −1.24623 + 1.24623i −0.0743436 + 0.0743436i −0.743301 0.668957i \(-0.766741\pi\)
0.668957 + 0.743301i \(0.266741\pi\)
\(282\) 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
\(291\) −1.16788 1.33485i −0.0684622 0.0782504i
\(292\) 0 0
\(293\) −2.69061 0.720947i −0.157187 0.0421182i 0.179367 0.983782i \(-0.442595\pi\)
−0.336555 + 0.941664i \(0.609262\pi\)
\(294\) 0 0
\(295\) 2.07378 + 3.59188i 0.120740 + 0.209128i
\(296\) 0 0
\(297\) −5.94155 + 0.368518i −0.344764 + 0.0213836i
\(298\) 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
\(303\) 11.7298 5.76746i 0.673858 0.331332i
\(304\) 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
\(309\) 6.08512 9.08403i 0.346170 0.516772i
\(310\) 0 0
\(311\) 16.8640 0.956272 0.478136 0.878286i \(-0.341313\pi\)
0.478136 + 0.878286i \(0.341313\pi\)
\(312\) 0 0
\(313\) 14.7731 0.835026 0.417513 0.908671i \(-0.362902\pi\)
0.417513 + 0.908671i \(0.362902\pi\)
\(314\) 0 0
\(315\) 5.48128 + 4.22632i 0.308835 + 0.238126i
\(316\) 0 0
\(317\) 3.02944 + 3.02944i 0.170150 + 0.170150i 0.787045 0.616895i \(-0.211610\pi\)
−0.616895 + 0.787045i \(0.711610\pi\)
\(318\) 0 0
\(319\) −3.07470 + 11.4749i −0.172150 + 0.642472i
\(320\) 0 0
\(321\) −6.41105 13.0387i −0.357830 0.727750i
\(322\) 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
\(327\) 24.8642 4.91559i 1.37499 0.271833i
\(328\) 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
\(333\) −14.1251 18.4975i −0.774049 1.01366i
\(334\) 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
\(345\) 5.68758 + 1.93809i 0.306209 + 0.104343i
\(346\) 0 0
\(347\) −5.68995 + 3.28509i −0.305452 + 0.176353i −0.644890 0.764276i \(-0.723097\pi\)
0.339437 + 0.940629i \(0.389763\pi\)
\(348\) 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
\(351\) −11.4270 + 14.8466i −0.609930 + 0.792455i
\(352\) 0 0
\(353\) 26.6737 7.14721i 1.41970 0.380407i 0.534323 0.845281i \(-0.320567\pi\)
0.885377 + 0.464873i \(0.153900\pi\)
\(354\) 0 0
\(355\) −2.45199 + 1.41566i −0.130138 + 0.0751353i
\(356\) 0 0
\(357\) 16.1056 + 5.48812i 0.852400 + 0.290462i
\(358\) 0 0
\(359\) 10.1971 10.1971i 0.538182 0.538182i −0.384813 0.922995i \(-0.625734\pi\)
0.922995 + 0.384813i \(0.125734\pi\)
\(360\) 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
\(369\) −12.3479 16.1702i −0.642807 0.841788i
\(370\) 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
\(375\) 11.5075 2.27502i 0.594247 0.117481i
\(376\) 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
\(381\) −6.28861 12.7897i −0.322175 0.655236i
\(382\) 0 0
\(383\) 1.67036 6.23387i 0.0853514 0.318536i −0.910029 0.414544i \(-0.863941\pi\)
0.995381 + 0.0960085i \(0.0306076\pi\)
\(384\) 0 0
\(385\) 1.86901 + 1.86901i 0.0952536 + 0.0952536i
\(386\) 0 0
\(387\) −5.43370 4.18963i −0.276210 0.212971i
\(388\) 0 0
\(389\) 5.45516 0.276588 0.138294 0.990391i \(-0.455838\pi\)
0.138294 + 0.990391i \(0.455838\pi\)
\(390\) 0 0
\(391\) 14.7713 0.747016
\(392\) 0 0
\(393\) −12.9266 + 19.2971i −0.652059 + 0.973412i
\(394\) 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
\(399\) −23.9255 + 11.7640i −1.19777 + 0.588937i
\(400\) 0 0
\(401\) 5.16790 + 19.2869i 0.258073 + 0.963141i 0.966355 + 0.257212i \(0.0828037\pi\)
−0.708282 + 0.705929i \(0.750530\pi\)
\(402\) 0 0
\(403\) 9.31927 3.18460i 0.464226 0.158636i
\(404\) 0 0
\(405\) −6.42218 0.0300156i −0.319121 0.00149149i
\(406\) 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
\(411\) −15.6160 17.8487i −0.770281 0.880411i
\(412\) 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 0.309864 0.950781i \(-0.399716\pi\)
−0.668468 + 0.743741i \(0.733050\pi\)
\(420\) 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
\(423\) −5.00567 2.08713i −0.243384 0.101480i
\(424\) 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
\(429\) −5.05468 + 5.06342i −0.244042 + 0.244464i
\(430\) 0 0
\(431\) −26.3726 + 7.06652i −1.27032 + 0.340382i −0.830155 0.557533i \(-0.811748\pi\)
−0.440169 + 0.897915i \(0.645081\pi\)
\(432\) 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
\(435\) −4.13381 + 12.1312i −0.198201 + 0.581648i
\(436\) 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 \(0.227691\pi\)
−0.754889 + 0.655852i \(0.772309\pi\)
\(444\) 0 0
\(445\) 2.85654 4.94767i 0.135413 0.234542i
\(446\) 0 0
\(447\) −7.80855 + 6.83179i −0.369332 + 0.323133i
\(448\) 0 0
\(449\) −26.6058 7.12899i −1.25560 0.336438i −0.431105 0.902302i \(-0.641876\pi\)
−0.824499 + 0.565864i \(0.808543\pi\)
\(450\) 0 0
\(451\) −3.88484 6.72874i −0.182930 0.316844i
\(452\) 0 0
\(453\) −5.21738 26.3907i −0.245134 1.23994i
\(454\) 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
\(459\) −14.9677 + 5.02240i −0.698632 + 0.234426i
\(460\) 0 0
\(461\) −5.98430 + 22.3337i −0.278717 + 1.04019i 0.674593 + 0.738190i \(0.264319\pi\)
−0.953310 + 0.301995i \(0.902347\pi\)
\(462\) 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
\(465\) 2.80482 + 1.87886i 0.130070 + 0.0871303i
\(466\) 0 0
\(467\) −26.9837 −1.24866 −0.624329 0.781162i \(-0.714627\pi\)
−0.624329 + 0.781162i \(0.714627\pi\)
\(468\) 0 0
\(469\) 19.7072 0.909996
\(470\) 0 0
\(471\) 14.7089 + 9.85304i 0.677750 + 0.454004i
\(472\) 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
\(477\) −6.74065 + 2.77363i −0.308633 + 0.126996i
\(478\) 0 0
\(479\) −5.46091 20.3804i −0.249515 0.931203i −0.971060 0.238836i \(-0.923234\pi\)
0.721545 0.692368i \(-0.243432\pi\)
\(480\) 0 0
\(481\) −27.4453 5.40127i −1.25140 0.246277i
\(482\) 0 0
\(483\) −5.28013 26.7081i −0.240254 1.21526i
\(484\) 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
\(489\) 28.0360 24.5290i 1.26783 1.10924i
\(490\) 0 0
\(491\) 16.2519 28.1492i 0.733440 1.27036i −0.221965 0.975055i \(-0.571247\pi\)
0.955404 0.295300i \(-0.0954197\pi\)
\(492\) 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
\(501\) 6.12394 17.9715i 0.273597 0.802909i
\(502\) 0 0
\(503\) 19.4725 11.2424i 0.868235 0.501276i 0.00147394 0.999999i \(-0.499531\pi\)
0.866761 + 0.498723i \(0.166197\pi\)
\(504\) 0 0
\(505\) 5.20160 1.39376i 0.231468 0.0620217i
\(506\) 0 0
\(507\) 1.53770 + 22.4641i 0.0682915 + 0.997665i
\(508\) 0 0
\(509\) −27.6271 + 7.40267i −1.22455 + 0.328117i −0.812455 0.583023i \(-0.801870\pi\)
−0.412095 + 0.911141i \(0.635203\pi\)
\(510\) 0 0
\(511\) −16.0925 + 9.29103i −0.711892 + 0.411011i
\(512\) 0 0
\(513\) 11.0192 22.1487i 0.486509 0.977887i
\(514\) 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 \(-0.949768\pi\)
0.987574 0.157155i \(-0.0502321\pi\)
\(522\) 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
\(525\) −16.5595 18.9271i −0.722718 0.826047i
\(526\) 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
\(531\) 2.23556 + 17.2930i 0.0970151 + 0.750450i
\(532\) 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
\(537\) −32.9215 + 16.1873i −1.42067 + 0.698534i
\(538\) 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
\(543\) 13.5318 20.2006i 0.580705 0.866892i
\(544\) 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
\(549\) 19.1868 24.8841i 0.818871 1.06203i
\(550\) 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
\(555\) −4.23086 8.60467i −0.179590 0.365248i
\(556\) 0 0
\(557\) −6.70422 25.0205i −0.284067 1.06015i −0.949518 0.313712i \(-0.898428\pi\)
0.665451 0.746441i \(-0.268239\pi\)
\(558\) 0 0
\(559\) −8.22754 + 0.556051i −0.347988 + 0.0235185i
\(560\) 0 0
\(561\) −5.91464 + 1.16931i −0.249716 + 0.0493684i
\(562\) 0 0
\(563\) −2.40232 4.16095i −0.101246 0.175363i 0.810952 0.585112i \(-0.198950\pi\)
−0.912198 + 0.409749i \(0.865616\pi\)
\(564\) 0 0
\(565\) −10.3844 2.78250i −0.436876 0.117061i
\(566\) 0 0
\(567\) 14.4314 + 25.2679i 0.606061 + 1.06115i
\(568\) 0 0
\(569\) −1.00204 + 1.73559i −0.0420078 + 0.0727597i −0.886265 0.463179i \(-0.846709\pi\)
0.844257 + 0.535938i \(0.180042\pi\)
\(570\) 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
\(579\) −34.9685 11.9158i −1.45324 0.495203i
\(580\) 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
\(585\) −5.80469 + 5.08745i −0.239994 + 0.210340i
\(586\) 0 0
\(587\) 1.79654 0.481380i 0.0741509 0.0198687i −0.221553 0.975148i \(-0.571113\pi\)
0.295704 + 0.955280i \(0.404446\pi\)
\(588\) 0 0
\(589\) −11.2619 + 6.50207i −0.464039 + 0.267913i
\(590\) 0 0
\(591\) 42.0166 + 14.3175i 1.72833 + 0.588943i
\(592\) 0 0
\(593\) 32.1956 32.1956i 1.32212 1.32212i 0.410057 0.912060i \(-0.365509\pi\)
0.912060 0.410057i \(-0.134491\pi\)
\(594\) 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 \(0.0972807\pi\)
−0.953662 + 0.300881i \(0.902719\pi\)
\(600\) 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
\(603\) −14.5332 + 11.0978i −0.591837 + 0.451939i
\(604\) 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
\(609\) 56.9665 11.2622i 2.30840 0.456366i
\(610\) 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
\(615\) −3.69855 7.52207i −0.149140 0.303319i
\(616\) 0 0
\(617\) 1.61026 6.00956i 0.0648265 0.241936i −0.925908 0.377749i \(-0.876698\pi\)
0.990734 + 0.135813i \(0.0433648\pi\)
\(618\) 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
\(621\) 18.9341 + 16.7225i 0.759799 + 0.671052i
\(622\) 0 0
\(623\) −25.8854 −1.03708
\(624\) 0 0
\(625\) −17.6213 −0.704851
\(626\) 0 0
\(627\) 5.25773 7.84889i 0.209974 0.313454i
\(628\) 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
\(633\) 16.1744 7.95285i 0.642875 0.316097i
\(634\) 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
\(639\) −11.8050 + 1.52610i −0.466998 + 0.0603716i
\(640\) 0 0
\(641\) 15.6856 + 27.1682i 0.619543 + 1.07308i 0.989569 + 0.144058i \(0.0460153\pi\)
−0.370026 + 0.929021i \(0.620651\pi\)
\(642\) 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
\(645\) −1.86135 2.12747i −0.0732905 0.0837690i
\(646\) 0 0
\(647\) −4.80729 + 8.32648i −0.188994 + 0.327348i −0.944915 0.327315i \(-0.893856\pi\)
0.755921 + 0.654663i \(0.227189\pi\)
\(648\) 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 0.785539 0.618813i \(-0.212386\pi\)
−0.143138 + 0.989703i \(0.545719\pi\)
\(654\) 0 0
\(655\) −6.76636 + 6.76636i −0.264384 + 0.264384i
\(656\) 0 0
\(657\) 6.63539 15.9140i 0.258871 0.620863i
\(658\) 0 0
\(659\) −23.6778 + 13.6704i −0.922357 + 0.532523i −0.884386 0.466756i \(-0.845423\pi\)
−0.0379709 + 0.999279i \(0.512089\pi\)
\(660\) 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
\(663\) −9.47313 + 16.4407i −0.367906 + 0.638504i
\(664\) 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
\(669\) −12.7061 + 37.2879i −0.491248 + 1.44163i
\(670\) 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 \(-0.928808\pi\)
0.975093 0.221797i \(-0.0711921\pi\)
\(678\) 0 0
\(679\) −1.65540 + 2.86724i −0.0635284 + 0.110034i
\(680\) 0 0
\(681\) −25.9116 + 22.6703i −0.992933 + 0.868729i
\(682\) 0 0
\(683\) 19.8376 + 5.31546i 0.759063 + 0.203390i 0.617535 0.786544i \(-0.288132\pi\)
0.141529 + 0.989934i \(0.454798\pi\)
\(684\) 0 0
\(685\) −4.88529 8.46157i −0.186657 0.323300i
\(686\) 0 0
\(687\) 0.552445 + 2.79439i 0.0210771 + 0.106613i
\(688\) 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
\(693\) 4.22848 + 10.2763i 0.160627 + 0.390365i
\(694\) 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
\(699\) 34.2700 + 22.9565i 1.29621 + 0.868294i
\(700\) 0 0
\(701\) 13.4888 0.509464 0.254732 0.967012i \(-0.418013\pi\)
0.254732 + 0.967012i \(0.418013\pi\)
\(702\) 0 0
\(703\) 36.9349 1.39303
\(704\) 0 0
\(705\) −1.85635 1.24351i −0.0699141 0.0468334i
\(706\) 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
\(711\) −7.73720 18.8034i −0.290168 0.705183i
\(712\) 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
\(717\) −1.47351 7.45333i −0.0550291 0.278350i
\(718\) 0 0
\(719\) 9.18916 + 15.9161i 0.342698 + 0.593570i 0.984933 0.172938i \(-0.0553260\pi\)
−0.642235 + 0.766508i \(0.721993\pi\)
\(720\) 0 0
\(721\) −19.7145 5.28248i −0.734205 0.196730i
\(722\) 0 0
\(723\) −11.3440 + 9.92502i −0.421889 + 0.369115i
\(724\) 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
\(735\) 1.37674 4.04023i 0.0507818 0.149026i
\(736\) 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
\(741\) −7.71994 28.7121i −0.283599 1.05476i
\(742\) 0 0
\(743\) 32.0441 8.58618i 1.17558 0.314996i 0.382410 0.923993i \(-0.375094\pi\)
0.793173 + 0.608996i \(0.208428\pi\)
\(744\) 0 0
\(745\) −3.70182 + 2.13725i −0.135624 + 0.0783027i
\(746\) 0 0
\(747\) 19.4990 46.7654i 0.713432 1.71106i
\(748\) 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
\(759\) 6.35218 + 7.26037i 0.230570 + 0.263535i
\(760\) 0 0
\(761\) −31.8738 8.54057i −1.15543 0.309595i −0.370288 0.928917i \(-0.620741\pi\)
−0.785137 + 0.619322i \(0.787408\pi\)
\(762\) 0 0
\(763\) −23.6559 40.9732i −0.856400 1.48333i
\(764\) 0 0
\(765\) −6.45072 + 0.833922i −0.233226 + 0.0301505i
\(766\) 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
\(771\) −9.30937 + 4.57736i −0.335269 + 0.164850i
\(772\) 0 0
\(773\) −2.16927 + 8.09584i −0.0780234 + 0.291187i −0.993902 0.110268i \(-0.964829\pi\)
0.915878 + 0.401456i \(0.131496\pi\)
\(774\) 0 0
\(775\) −8.67364 8.67364i −0.311566 0.311566i
\(776\) 0 0
\(777\) −24.1789 + 36.0949i −0.867413 + 1.29490i
\(778\) 0 0
\(779\) 32.2879 1.15684
\(780\) 0 0
\(781\) −4.54564 −0.162656
\(782\) 0 0
\(783\) −35.6680 + 40.3852i −1.27467 + 1.44325i
\(784\) 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
\(789\) 14.6416 + 29.7779i 0.521255 + 1.06012i
\(790\) 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
\(795\) −2.94596 + 0.582409i −0.104482 + 0.0206559i
\(796\) 0 0