Properties

Label 1386.2.r.c.89.4
Level $1386$
Weight $2$
Character 1386.89
Analytic conductor $11.067$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.4
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.c.1277.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.25882 - 2.18034i) q^{5} +(1.48356 - 2.19067i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.25882 - 2.18034i) q^{5} +(1.48356 - 2.19067i) q^{7} +1.00000i q^{8} +(2.18034 - 1.25882i) q^{10} +(0.866025 - 0.500000i) q^{11} +2.44949i q^{13} +(2.38014 - 1.15539i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.64626 + 4.58346i) q^{17} +(-4.52761 - 2.61401i) q^{19} +2.51764 q^{20} +1.00000 q^{22} +(4.28376 + 2.47323i) q^{23} +(-0.669251 - 1.15918i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(2.63896 + 0.189469i) q^{28} -8.05986i q^{29} +(7.44414 - 4.29788i) q^{31} +(-0.866025 + 0.500000i) q^{32} +5.29253i q^{34} +(-2.90887 - 5.99233i) q^{35} +(5.91189 - 10.2397i) q^{37} +(-2.61401 - 4.52761i) q^{38} +(2.18034 + 1.25882i) q^{40} -1.92480 q^{41} -11.9841 q^{43} +(0.866025 + 0.500000i) q^{44} +(2.47323 + 4.28376i) q^{46} +(0.637756 - 1.10463i) q^{47} +(-2.59808 - 6.50000i) q^{49} -1.33850i q^{50} +(-2.12132 + 1.22474i) q^{52} +(0.414578 - 0.239357i) q^{53} -2.51764i q^{55} +(2.19067 + 1.48356i) q^{56} +(4.02993 - 6.98004i) q^{58} +(3.02494 + 5.23936i) q^{59} +(10.7536 + 6.20857i) q^{61} +8.59575 q^{62} -1.00000 q^{64} +(5.34072 + 3.08346i) q^{65} +(-6.11571 - 10.5927i) q^{67} +(-2.64626 + 4.58346i) q^{68} +(0.477014 - 6.64394i) q^{70} +14.7055i q^{71} +(-8.52432 + 4.92152i) q^{73} +(10.2397 - 5.91189i) q^{74} -5.22803i q^{76} +(0.189469 - 2.63896i) q^{77} +(3.52677 - 6.10854i) q^{79} +(1.25882 + 2.18034i) q^{80} +(-1.66693 - 0.962402i) q^{82} +9.35827 q^{83} +13.3247 q^{85} +(-10.3786 - 5.99207i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-7.92392 + 13.7246i) q^{89} +(5.36603 + 3.63397i) q^{91} +4.94646i q^{92} +(1.10463 - 0.637756i) q^{94} +(-11.3989 + 6.58114i) q^{95} +13.6556i q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + 8q^{5} + O(q^{10}) \) \( 8q + 4q^{4} + 8q^{5} - 4q^{16} - 4q^{17} + 24q^{19} + 16q^{20} + 8q^{22} + 24q^{23} - 4q^{25} + 12q^{31} + 16q^{35} + 12q^{37} - 8q^{38} + 16q^{41} - 32q^{43} + 8q^{46} + 48q^{53} - 4q^{58} + 16q^{59} + 24q^{62} - 8q^{64} - 12q^{65} - 24q^{67} + 4q^{68} - 20q^{70} - 24q^{73} - 12q^{74} + 40q^{79} + 8q^{80} + 12q^{82} + 72q^{83} - 32q^{85} - 24q^{86} + 4q^{88} - 16q^{89} + 36q^{91} + 24q^{95} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.25882 2.18034i 0.562961 0.975077i −0.434275 0.900780i \(-0.642995\pi\)
0.997236 0.0742968i \(-0.0236712\pi\)
\(6\) 0 0
\(7\) 1.48356 2.19067i 0.560734 0.827996i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.18034 1.25882i 0.689484 0.398074i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) 0 0
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) 2.38014 1.15539i 0.636119 0.308792i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.64626 + 4.58346i 0.641813 + 1.11165i 0.985028 + 0.172396i \(0.0551510\pi\)
−0.343214 + 0.939257i \(0.611516\pi\)
\(18\) 0 0
\(19\) −4.52761 2.61401i −1.03870 0.599696i −0.119238 0.992866i \(-0.538045\pi\)
−0.919466 + 0.393170i \(0.871379\pi\)
\(20\) 2.51764 0.562961
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 4.28376 + 2.47323i 0.893226 + 0.515704i 0.874996 0.484129i \(-0.160864\pi\)
0.0182299 + 0.999834i \(0.494197\pi\)
\(24\) 0 0
\(25\) −0.669251 1.15918i −0.133850 0.231835i
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) 2.63896 + 0.189469i 0.498716 + 0.0358062i
\(29\) 8.05986i 1.49668i −0.663317 0.748339i \(-0.730852\pi\)
0.663317 0.748339i \(-0.269148\pi\)
\(30\) 0 0
\(31\) 7.44414 4.29788i 1.33701 0.771922i 0.350645 0.936509i \(-0.385962\pi\)
0.986363 + 0.164587i \(0.0526291\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.29253i 0.907661i
\(35\) −2.90887 5.99233i −0.491688 1.01289i
\(36\) 0 0
\(37\) 5.91189 10.2397i 0.971909 1.68340i 0.282129 0.959376i \(-0.408959\pi\)
0.689780 0.724019i \(-0.257707\pi\)
\(38\) −2.61401 4.52761i −0.424049 0.734475i
\(39\) 0 0
\(40\) 2.18034 + 1.25882i 0.344742 + 0.199037i
\(41\) −1.92480 −0.300604 −0.150302 0.988640i \(-0.548025\pi\)
−0.150302 + 0.988640i \(0.548025\pi\)
\(42\) 0 0
\(43\) −11.9841 −1.82756 −0.913782 0.406204i \(-0.866852\pi\)
−0.913782 + 0.406204i \(0.866852\pi\)
\(44\) 0.866025 + 0.500000i 0.130558 + 0.0753778i
\(45\) 0 0
\(46\) 2.47323 + 4.28376i 0.364658 + 0.631606i
\(47\) 0.637756 1.10463i 0.0930263 0.161126i −0.815757 0.578395i \(-0.803679\pi\)
0.908783 + 0.417269i \(0.137013\pi\)
\(48\) 0 0
\(49\) −2.59808 6.50000i −0.371154 0.928571i
\(50\) 1.33850i 0.189293i
\(51\) 0 0
\(52\) −2.12132 + 1.22474i −0.294174 + 0.169842i
\(53\) 0.414578 0.239357i 0.0569467 0.0328782i −0.471256 0.881996i \(-0.656199\pi\)
0.528203 + 0.849118i \(0.322866\pi\)
\(54\) 0 0
\(55\) 2.51764i 0.339478i
\(56\) 2.19067 + 1.48356i 0.292741 + 0.198250i
\(57\) 0 0
\(58\) 4.02993 6.98004i 0.529155 0.916524i
\(59\) 3.02494 + 5.23936i 0.393814 + 0.682106i 0.992949 0.118542i \(-0.0378220\pi\)
−0.599135 + 0.800648i \(0.704489\pi\)
\(60\) 0 0
\(61\) 10.7536 + 6.20857i 1.37685 + 0.794925i 0.991779 0.127961i \(-0.0408432\pi\)
0.385072 + 0.922886i \(0.374177\pi\)
\(62\) 8.59575 1.09166
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.34072 + 3.08346i 0.662434 + 0.382457i
\(66\) 0 0
\(67\) −6.11571 10.5927i −0.747153 1.29411i −0.949182 0.314728i \(-0.898087\pi\)
0.202028 0.979380i \(-0.435247\pi\)
\(68\) −2.64626 + 4.58346i −0.320907 + 0.555827i
\(69\) 0 0
\(70\) 0.477014 6.64394i 0.0570140 0.794103i
\(71\) 14.7055i 1.74522i 0.488416 + 0.872611i \(0.337575\pi\)
−0.488416 + 0.872611i \(0.662425\pi\)
\(72\) 0 0
\(73\) −8.52432 + 4.92152i −0.997696 + 0.576020i −0.907566 0.419910i \(-0.862062\pi\)
−0.0901305 + 0.995930i \(0.528728\pi\)
\(74\) 10.2397 5.91189i 1.19034 0.687243i
\(75\) 0 0
\(76\) 5.22803i 0.599696i
\(77\) 0.189469 2.63896i 0.0215920 0.300737i
\(78\) 0 0
\(79\) 3.52677 6.10854i 0.396792 0.687265i −0.596536 0.802587i \(-0.703457\pi\)
0.993328 + 0.115322i \(0.0367899\pi\)
\(80\) 1.25882 + 2.18034i 0.140740 + 0.243769i
\(81\) 0 0
\(82\) −1.66693 0.962402i −0.184081 0.106279i
\(83\) 9.35827 1.02720 0.513602 0.858029i \(-0.328311\pi\)
0.513602 + 0.858029i \(0.328311\pi\)
\(84\) 0 0
\(85\) 13.3247 1.44526
\(86\) −10.3786 5.99207i −1.11915 0.646142i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −7.92392 + 13.7246i −0.839934 + 1.45481i 0.0500147 + 0.998748i \(0.484073\pi\)
−0.889949 + 0.456060i \(0.849260\pi\)
\(90\) 0 0
\(91\) 5.36603 + 3.63397i 0.562512 + 0.380944i
\(92\) 4.94646i 0.515704i
\(93\) 0 0
\(94\) 1.10463 0.637756i 0.113934 0.0657796i
\(95\) −11.3989 + 6.58114i −1.16950 + 0.675211i
\(96\) 0 0
\(97\) 13.6556i 1.38652i 0.720689 + 0.693259i \(0.243826\pi\)
−0.720689 + 0.693259i \(0.756174\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 0 0
\(100\) 0.669251 1.15918i 0.0669251 0.115918i
\(101\) −0.689211 1.19375i −0.0685791 0.118782i 0.829697 0.558214i \(-0.188513\pi\)
−0.898276 + 0.439432i \(0.855180\pi\)
\(102\) 0 0
\(103\) −9.08978 5.24799i −0.895643 0.517100i −0.0198589 0.999803i \(-0.506322\pi\)
−0.875784 + 0.482703i \(0.839655\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) 0.478713 0.0464968
\(107\) −2.50535 1.44646i −0.242201 0.139835i 0.373987 0.927434i \(-0.377991\pi\)
−0.616188 + 0.787599i \(0.711324\pi\)
\(108\) 0 0
\(109\) −6.76941 11.7250i −0.648392 1.12305i −0.983507 0.180870i \(-0.942109\pi\)
0.335115 0.942177i \(-0.391225\pi\)
\(110\) 1.25882 2.18034i 0.120024 0.207887i
\(111\) 0 0
\(112\) 1.15539 + 2.38014i 0.109175 + 0.224902i
\(113\) 14.5699i 1.37062i 0.728250 + 0.685312i \(0.240334\pi\)
−0.728250 + 0.685312i \(0.759666\pi\)
\(114\) 0 0
\(115\) 10.7850 6.22670i 1.00570 0.580643i
\(116\) 6.98004 4.02993i 0.648080 0.374169i
\(117\) 0 0
\(118\) 6.04989i 0.556937i
\(119\) 13.9668 + 1.00277i 1.28033 + 0.0919236i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 6.20857 + 10.7536i 0.562097 + 0.973581i
\(123\) 0 0
\(124\) 7.44414 + 4.29788i 0.668504 + 0.385961i
\(125\) 9.21833 0.824512
\(126\) 0 0
\(127\) −6.59675 −0.585367 −0.292683 0.956209i \(-0.594548\pi\)
−0.292683 + 0.956209i \(0.594548\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 3.08346 + 5.34072i 0.270438 + 0.468412i
\(131\) 0.757359 1.31178i 0.0661708 0.114611i −0.831042 0.556210i \(-0.812255\pi\)
0.897213 + 0.441599i \(0.145588\pi\)
\(132\) 0 0
\(133\) −12.4434 + 6.04044i −1.07898 + 0.523772i
\(134\) 12.2314i 1.05663i
\(135\) 0 0
\(136\) −4.58346 + 2.64626i −0.393029 + 0.226915i
\(137\) −12.0316 + 6.94646i −1.02793 + 0.593476i −0.916391 0.400284i \(-0.868912\pi\)
−0.111540 + 0.993760i \(0.535578\pi\)
\(138\) 0 0
\(139\) 13.5911i 1.15278i 0.817174 + 0.576391i \(0.195540\pi\)
−0.817174 + 0.576391i \(0.804460\pi\)
\(140\) 3.73508 5.51532i 0.315672 0.466129i
\(141\) 0 0
\(142\) −7.35275 + 12.7353i −0.617029 + 1.06873i
\(143\) 1.22474 + 2.12132i 0.102418 + 0.177394i
\(144\) 0 0
\(145\) −17.5732 10.1459i −1.45938 0.842571i
\(146\) −9.84304 −0.814616
\(147\) 0 0
\(148\) 11.8238 0.971909
\(149\) 5.76098 + 3.32611i 0.471958 + 0.272485i 0.717059 0.697012i \(-0.245488\pi\)
−0.245101 + 0.969498i \(0.578821\pi\)
\(150\) 0 0
\(151\) −4.00877 6.94339i −0.326229 0.565045i 0.655532 0.755168i \(-0.272445\pi\)
−0.981760 + 0.190123i \(0.939111\pi\)
\(152\) 2.61401 4.52761i 0.212025 0.367237i
\(153\) 0 0
\(154\) 1.48356 2.19067i 0.119549 0.176529i
\(155\) 21.6410i 1.73825i
\(156\) 0 0
\(157\) −19.0820 + 11.0170i −1.52291 + 0.879254i −0.523279 + 0.852161i \(0.675291\pi\)
−0.999633 + 0.0270921i \(0.991375\pi\)
\(158\) 6.10854 3.52677i 0.485969 0.280575i
\(159\) 0 0
\(160\) 2.51764i 0.199037i
\(161\) 11.7733 5.71512i 0.927864 0.450414i
\(162\) 0 0
\(163\) 5.03225 8.71611i 0.394156 0.682699i −0.598837 0.800871i \(-0.704370\pi\)
0.992993 + 0.118172i \(0.0377035\pi\)
\(164\) −0.962402 1.66693i −0.0751509 0.130165i
\(165\) 0 0
\(166\) 8.10450 + 4.67914i 0.629031 + 0.363171i
\(167\) −4.76268 −0.368547 −0.184274 0.982875i \(-0.558993\pi\)
−0.184274 + 0.982875i \(0.558993\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 11.5395 + 6.66234i 0.885040 + 0.510978i
\(171\) 0 0
\(172\) −5.99207 10.3786i −0.456891 0.791359i
\(173\) −7.36843 + 12.7625i −0.560211 + 0.970314i 0.437266 + 0.899332i \(0.355947\pi\)
−0.997478 + 0.0709824i \(0.977387\pi\)
\(174\) 0 0
\(175\) −3.53225 0.253604i −0.267013 0.0191707i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −13.7246 + 7.92392i −1.02871 + 0.593923i
\(179\) 2.03491 1.17486i 0.152096 0.0878129i −0.422020 0.906586i \(-0.638679\pi\)
0.574117 + 0.818773i \(0.305346\pi\)
\(180\) 0 0
\(181\) 11.9236i 0.886271i 0.896455 + 0.443136i \(0.146134\pi\)
−0.896455 + 0.443136i \(0.853866\pi\)
\(182\) 2.83013 + 5.83013i 0.209783 + 0.432158i
\(183\) 0 0
\(184\) −2.47323 + 4.28376i −0.182329 + 0.315803i
\(185\) −14.8840 25.7798i −1.09429 1.89537i
\(186\) 0 0
\(187\) 4.58346 + 2.64626i 0.335176 + 0.193514i
\(188\) 1.27551 0.0930263
\(189\) 0 0
\(190\) −13.1623 −0.954892
\(191\) 21.2839 + 12.2882i 1.54005 + 0.889146i 0.998835 + 0.0482604i \(0.0153677\pi\)
0.541212 + 0.840886i \(0.317966\pi\)
\(192\) 0 0
\(193\) 7.05657 + 12.2223i 0.507943 + 0.879783i 0.999958 + 0.00919638i \(0.00292734\pi\)
−0.492015 + 0.870587i \(0.663739\pi\)
\(194\) −6.82780 + 11.8261i −0.490208 + 0.849065i
\(195\) 0 0
\(196\) 4.33013 5.50000i 0.309295 0.392857i
\(197\) 0.579219i 0.0412676i −0.999787 0.0206338i \(-0.993432\pi\)
0.999787 0.0206338i \(-0.00656841\pi\)
\(198\) 0 0
\(199\) 2.08228 1.20220i 0.147609 0.0852220i −0.424377 0.905486i \(-0.639507\pi\)
0.571985 + 0.820264i \(0.306173\pi\)
\(200\) 1.15918 0.669251i 0.0819661 0.0473232i
\(201\) 0 0
\(202\) 1.37842i 0.0969854i
\(203\) −17.6565 11.9573i −1.23924 0.839239i
\(204\) 0 0
\(205\) −2.42298 + 4.19672i −0.169228 + 0.293112i
\(206\) −5.24799 9.08978i −0.365645 0.633315i
\(207\) 0 0
\(208\) −2.12132 1.22474i −0.147087 0.0849208i
\(209\) −5.22803 −0.361630
\(210\) 0 0
\(211\) −5.99343 −0.412605 −0.206302 0.978488i \(-0.566143\pi\)
−0.206302 + 0.978488i \(0.566143\pi\)
\(212\) 0.414578 + 0.239357i 0.0284733 + 0.0164391i
\(213\) 0 0
\(214\) −1.44646 2.50535i −0.0988782 0.171262i
\(215\) −15.0859 + 26.1295i −1.02885 + 1.78202i
\(216\) 0 0
\(217\) 1.62863 22.6838i 0.110558 1.53988i
\(218\) 13.5388i 0.916964i
\(219\) 0 0
\(220\) 2.18034 1.25882i 0.146998 0.0848696i
\(221\) −11.2271 + 6.48200i −0.755220 + 0.436026i
\(222\) 0 0
\(223\) 7.48993i 0.501563i −0.968044 0.250781i \(-0.919313\pi\)
0.968044 0.250781i \(-0.0806875\pi\)
\(224\) −0.189469 + 2.63896i −0.0126594 + 0.176323i
\(225\) 0 0
\(226\) −7.28497 + 12.6179i −0.484589 + 0.839332i
\(227\) −4.88304 8.45768i −0.324099 0.561356i 0.657231 0.753689i \(-0.271728\pi\)
−0.981330 + 0.192334i \(0.938394\pi\)
\(228\) 0 0
\(229\) 0.195181 + 0.112688i 0.0128980 + 0.00744664i 0.506435 0.862278i \(-0.330963\pi\)
−0.493537 + 0.869725i \(0.664296\pi\)
\(230\) 12.4534 0.821153
\(231\) 0 0
\(232\) 8.05986 0.529155
\(233\) −0.445759 0.257359i −0.0292027 0.0168602i 0.485328 0.874332i \(-0.338700\pi\)
−0.514530 + 0.857472i \(0.672034\pi\)
\(234\) 0 0
\(235\) −1.60564 2.78105i −0.104740 0.181416i
\(236\) −3.02494 + 5.23936i −0.196907 + 0.341053i
\(237\) 0 0
\(238\) 11.5942 + 7.85180i 0.751540 + 0.508957i
\(239\) 15.4899i 1.00196i −0.865459 0.500980i \(-0.832973\pi\)
0.865459 0.500980i \(-0.167027\pi\)
\(240\) 0 0
\(241\) −14.2882 + 8.24932i −0.920387 + 0.531386i −0.883759 0.467943i \(-0.844995\pi\)
−0.0366285 + 0.999329i \(0.511662\pi\)
\(242\) 0.866025 0.500000i 0.0556702 0.0321412i
\(243\) 0 0
\(244\) 12.4171i 0.794925i
\(245\) −17.4427 2.51764i −1.11437 0.160846i
\(246\) 0 0
\(247\) 6.40300 11.0903i 0.407413 0.705660i
\(248\) 4.29788 + 7.44414i 0.272915 + 0.472703i
\(249\) 0 0
\(250\) 7.98331 + 4.60916i 0.504909 + 0.291509i
\(251\) −18.6367 −1.17634 −0.588169 0.808738i \(-0.700151\pi\)
−0.588169 + 0.808738i \(0.700151\pi\)
\(252\) 0 0
\(253\) 4.94646 0.310981
\(254\) −5.71295 3.29837i −0.358463 0.206958i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.575454 0.996716i 0.0358959 0.0621734i −0.847519 0.530764i \(-0.821905\pi\)
0.883415 + 0.468591i \(0.155238\pi\)
\(258\) 0 0
\(259\) −13.6611 28.1423i −0.848862 1.74867i
\(260\) 6.16693i 0.382457i
\(261\) 0 0
\(262\) 1.31178 0.757359i 0.0810423 0.0467898i
\(263\) −6.18929 + 3.57339i −0.381648 + 0.220345i −0.678535 0.734568i \(-0.737385\pi\)
0.296887 + 0.954913i \(0.404052\pi\)
\(264\) 0 0
\(265\) 1.20523i 0.0740365i
\(266\) −13.7966 0.990548i −0.845921 0.0607344i
\(267\) 0 0
\(268\) 6.11571 10.5927i 0.373577 0.647054i
\(269\) −6.68968 11.5869i −0.407877 0.706464i 0.586774 0.809750i \(-0.300398\pi\)
−0.994652 + 0.103286i \(0.967064\pi\)
\(270\) 0 0
\(271\) 5.92100 + 3.41849i 0.359675 + 0.207659i 0.668938 0.743318i \(-0.266749\pi\)
−0.309263 + 0.950977i \(0.600082\pi\)
\(272\) −5.29253 −0.320907
\(273\) 0 0
\(274\) −13.8929 −0.839302
\(275\) −1.15918 0.669251i −0.0699010 0.0403573i
\(276\) 0 0
\(277\) 2.87404 + 4.97798i 0.172684 + 0.299098i 0.939357 0.342940i \(-0.111423\pi\)
−0.766673 + 0.642037i \(0.778089\pi\)
\(278\) −6.79555 + 11.7702i −0.407570 + 0.705932i
\(279\) 0 0
\(280\) 5.99233 2.90887i 0.358110 0.173838i
\(281\) 6.45821i 0.385265i 0.981271 + 0.192632i \(0.0617025\pi\)
−0.981271 + 0.192632i \(0.938298\pi\)
\(282\) 0 0
\(283\) 5.87843 3.39391i 0.349436 0.201747i −0.315001 0.949091i \(-0.602005\pi\)
0.664437 + 0.747344i \(0.268671\pi\)
\(284\) −12.7353 + 7.35275i −0.755703 + 0.436305i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) −2.85557 + 4.21661i −0.168559 + 0.248899i
\(288\) 0 0
\(289\) −5.50543 + 9.53568i −0.323849 + 0.560923i
\(290\) −10.1459 17.5732i −0.595788 1.03193i
\(291\) 0 0
\(292\) −8.52432 4.92152i −0.498848 0.288010i
\(293\) 3.15159 0.184118 0.0920589 0.995754i \(-0.470655\pi\)
0.0920589 + 0.995754i \(0.470655\pi\)
\(294\) 0 0
\(295\) 15.2314 0.886808
\(296\) 10.2397 + 5.91189i 0.595170 + 0.343622i
\(297\) 0 0
\(298\) 3.32611 + 5.76098i 0.192676 + 0.333725i
\(299\) −6.05816 + 10.4930i −0.350352 + 0.606828i
\(300\) 0 0
\(301\) −17.7792 + 26.2533i −1.02478 + 1.51322i
\(302\) 8.01753i 0.461357i
\(303\) 0 0
\(304\) 4.52761 2.61401i 0.259676 0.149924i
\(305\) 27.0736 15.6309i 1.55023 0.895024i
\(306\) 0 0
\(307\) 15.0711i 0.860151i 0.902793 + 0.430076i \(0.141513\pi\)
−0.902793 + 0.430076i \(0.858487\pi\)
\(308\) 2.38014 1.15539i 0.135621 0.0658347i
\(309\) 0 0
\(310\) 10.8205 18.7417i 0.614563 1.06445i
\(311\) −15.9573 27.6388i −0.904854 1.56725i −0.821113 0.570765i \(-0.806647\pi\)
−0.0837402 0.996488i \(-0.526687\pi\)
\(312\) 0 0
\(313\) 13.8126 + 7.97469i 0.780733 + 0.450756i 0.836690 0.547677i \(-0.184488\pi\)
−0.0559572 + 0.998433i \(0.517821\pi\)
\(314\) −22.0340 −1.24345
\(315\) 0 0
\(316\) 7.05354 0.396792
\(317\) 21.9318 + 12.6623i 1.23181 + 0.711188i 0.967408 0.253224i \(-0.0814910\pi\)
0.264405 + 0.964412i \(0.414824\pi\)
\(318\) 0 0
\(319\) −4.02993 6.98004i −0.225633 0.390807i
\(320\) −1.25882 + 2.18034i −0.0703701 + 0.121885i
\(321\) 0 0
\(322\) 13.0535 + 0.937200i 0.727444 + 0.0522281i
\(323\) 27.6695i 1.53957i
\(324\) 0 0
\(325\) 2.83939 1.63932i 0.157501 0.0909333i
\(326\) 8.71611 5.03225i 0.482741 0.278711i
\(327\) 0 0
\(328\) 1.92480i 0.106279i
\(329\) −1.47372 3.03590i −0.0812488 0.167374i
\(330\) 0 0
\(331\) −7.03882 + 12.1916i −0.386888 + 0.670110i −0.992029 0.126008i \(-0.959783\pi\)
0.605141 + 0.796118i \(0.293117\pi\)
\(332\) 4.67914 + 8.10450i 0.256801 + 0.444792i
\(333\) 0 0
\(334\) −4.12460 2.38134i −0.225688 0.130301i
\(335\) −30.7943 −1.68247
\(336\) 0 0
\(337\) −8.15142 −0.444036 −0.222018 0.975043i \(-0.571264\pi\)
−0.222018 + 0.975043i \(0.571264\pi\)
\(338\) 6.06218 + 3.50000i 0.329739 + 0.190375i
\(339\) 0 0
\(340\) 6.66234 + 11.5395i 0.361316 + 0.625817i
\(341\) 4.29788 7.44414i 0.232743 0.403123i
\(342\) 0 0
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 11.9841i 0.646142i
\(345\) 0 0
\(346\) −12.7625 + 7.36843i −0.686116 + 0.396129i
\(347\) −19.5502 + 11.2873i −1.04951 + 0.605933i −0.922511 0.385970i \(-0.873867\pi\)
−0.126996 + 0.991903i \(0.540534\pi\)
\(348\) 0 0
\(349\) 22.9498i 1.22848i 0.789121 + 0.614238i \(0.210536\pi\)
−0.789121 + 0.614238i \(0.789464\pi\)
\(350\) −2.93222 1.98575i −0.156734 0.106143i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 12.5990 + 21.8222i 0.670579 + 1.16148i 0.977740 + 0.209820i \(0.0672877\pi\)
−0.307161 + 0.951658i \(0.599379\pi\)
\(354\) 0 0
\(355\) 32.0630 + 18.5116i 1.70173 + 0.982492i
\(356\) −15.8478 −0.839934
\(357\) 0 0
\(358\) 2.34971 0.124186
\(359\) −17.0558 9.84714i −0.900168 0.519712i −0.0229134 0.999737i \(-0.507294\pi\)
−0.877255 + 0.480025i \(0.840628\pi\)
\(360\) 0 0
\(361\) 4.16614 + 7.21597i 0.219271 + 0.379788i
\(362\) −5.96178 + 10.3261i −0.313344 + 0.542728i
\(363\) 0 0
\(364\) −0.464102 + 6.46410i −0.0243255 + 0.338811i
\(365\) 24.7812i 1.29711i
\(366\) 0 0
\(367\) 2.81282 1.62398i 0.146828 0.0847712i −0.424786 0.905294i \(-0.639651\pi\)
0.571614 + 0.820523i \(0.306317\pi\)
\(368\) −4.28376 + 2.47323i −0.223307 + 0.128926i
\(369\) 0 0
\(370\) 29.7680i 1.54756i
\(371\) 0.0907012 1.26330i 0.00470897 0.0655875i
\(372\) 0 0
\(373\) −3.41177 + 5.90935i −0.176655 + 0.305975i −0.940733 0.339149i \(-0.889861\pi\)
0.764078 + 0.645124i \(0.223194\pi\)
\(374\) 2.64626 + 4.58346i 0.136835 + 0.237005i
\(375\) 0 0
\(376\) 1.10463 + 0.637756i 0.0569668 + 0.0328898i
\(377\) 19.7425 1.01679
\(378\) 0 0
\(379\) 18.8929 0.970464 0.485232 0.874385i \(-0.338735\pi\)
0.485232 + 0.874385i \(0.338735\pi\)
\(380\) −11.3989 6.58114i −0.584750 0.337605i
\(381\) 0 0
\(382\) 12.2882 + 21.2839i 0.628722 + 1.08898i
\(383\) 13.2165 22.8916i 0.675329 1.16970i −0.301043 0.953610i \(-0.597335\pi\)
0.976373 0.216094i \(-0.0693318\pi\)
\(384\) 0 0
\(385\) −5.51532 3.73508i −0.281087 0.190357i
\(386\) 14.1131i 0.718340i
\(387\) 0 0
\(388\) −11.8261 + 6.82780i −0.600380 + 0.346629i
\(389\) 10.1046 5.83391i 0.512325 0.295791i −0.221464 0.975169i \(-0.571083\pi\)
0.733789 + 0.679378i \(0.237750\pi\)
\(390\) 0 0
\(391\) 26.1793i 1.32394i
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 0 0
\(394\) 0.289609 0.501618i 0.0145903 0.0252711i
\(395\) −8.87913 15.3791i −0.446757 0.773806i
\(396\) 0 0
\(397\) −8.68678 5.01532i −0.435977 0.251711i 0.265913 0.963997i \(-0.414327\pi\)
−0.701890 + 0.712286i \(0.747660\pi\)
\(398\) 2.40441 0.120522
\(399\) 0 0
\(400\) 1.33850 0.0669251
\(401\) 4.52281 + 2.61125i 0.225858 + 0.130399i 0.608660 0.793431i \(-0.291707\pi\)
−0.382802 + 0.923831i \(0.625041\pi\)
\(402\) 0 0
\(403\) 10.5276 + 18.2343i 0.524417 + 0.908318i
\(404\) 0.689211 1.19375i 0.0342895 0.0593912i
\(405\) 0 0
\(406\) −9.31231 19.1836i −0.462162 0.952065i
\(407\) 11.8238i 0.586083i
\(408\) 0 0
\(409\) −16.6456 + 9.61037i −0.823074 + 0.475202i −0.851475 0.524395i \(-0.824292\pi\)
0.0284013 + 0.999597i \(0.490958\pi\)
\(410\) −4.19672 + 2.42298i −0.207261 + 0.119662i
\(411\) 0 0
\(412\) 10.4960i 0.517100i
\(413\) 15.9654 + 1.14626i 0.785606 + 0.0564040i
\(414\) 0 0
\(415\) 11.7804 20.4042i 0.578276 1.00160i
\(416\) −1.22474 2.12132i −0.0600481 0.104006i
\(417\) 0 0
\(418\) −4.52761 2.61401i −0.221452 0.127856i
\(419\) −17.4755 −0.853733 −0.426866 0.904315i \(-0.640383\pi\)
−0.426866 + 0.904315i \(0.640383\pi\)
\(420\) 0 0
\(421\) 27.8519 1.35742 0.678710 0.734406i \(-0.262539\pi\)
0.678710 + 0.734406i \(0.262539\pi\)
\(422\) −5.19046 2.99672i −0.252668 0.145878i
\(423\) 0 0
\(424\) 0.239357 + 0.414578i 0.0116242 + 0.0201337i
\(425\) 3.54203 6.13497i 0.171814 0.297590i
\(426\) 0 0
\(427\) 29.5545 14.3467i 1.43024 0.694285i
\(428\) 2.89293i 0.139835i
\(429\) 0 0
\(430\) −26.1295 + 15.0859i −1.26008 + 0.727505i
\(431\) −30.1846 + 17.4271i −1.45394 + 0.839434i −0.998702 0.0509348i \(-0.983780\pi\)
−0.455240 + 0.890369i \(0.650447\pi\)
\(432\) 0 0
\(433\) 27.2068i 1.30748i −0.756721 0.653738i \(-0.773200\pi\)
0.756721 0.653738i \(-0.226800\pi\)
\(434\) 12.7524 18.8305i 0.612132 0.903891i
\(435\) 0 0
\(436\) 6.76941 11.7250i 0.324196 0.561524i
\(437\) −12.9301 22.3956i −0.618532 1.07133i
\(438\) 0 0
\(439\) −20.0987 11.6040i −0.959260 0.553829i −0.0633147 0.997994i \(-0.520167\pi\)
−0.895945 + 0.444165i \(0.853501\pi\)
\(440\) 2.51764 0.120024
\(441\) 0 0
\(442\) −12.9640 −0.616634
\(443\) 15.7172 + 9.07435i 0.746749 + 0.431135i 0.824518 0.565836i \(-0.191446\pi\)
−0.0777693 + 0.996971i \(0.524780\pi\)
\(444\) 0 0
\(445\) 19.9496 + 34.5537i 0.945700 + 1.63800i
\(446\) 3.74496 6.48647i 0.177329 0.307143i
\(447\) 0 0
\(448\) −1.48356 + 2.19067i −0.0700918 + 0.103499i
\(449\) 31.9656i 1.50855i −0.656560 0.754274i \(-0.727989\pi\)
0.656560 0.754274i \(-0.272011\pi\)
\(450\) 0 0
\(451\) −1.66693 + 0.962402i −0.0784926 + 0.0453177i
\(452\) −12.6179 + 7.28497i −0.593497 + 0.342656i
\(453\) 0 0
\(454\) 9.76608i 0.458345i
\(455\) 14.6781 7.12524i 0.688122 0.334036i
\(456\) 0 0
\(457\) −12.9607 + 22.4486i −0.606276 + 1.05010i 0.385572 + 0.922678i \(0.374004\pi\)
−0.991848 + 0.127424i \(0.959329\pi\)
\(458\) 0.112688 + 0.195181i 0.00526557 + 0.00912023i
\(459\) 0 0
\(460\) 10.7850 + 6.22670i 0.502852 + 0.290322i
\(461\) 21.8282 1.01664 0.508321 0.861168i \(-0.330266\pi\)
0.508321 + 0.861168i \(0.330266\pi\)
\(462\) 0 0
\(463\) 4.92621 0.228940 0.114470 0.993427i \(-0.463483\pi\)
0.114470 + 0.993427i \(0.463483\pi\)
\(464\) 6.98004 + 4.02993i 0.324040 + 0.187085i
\(465\) 0 0
\(466\) −0.257359 0.445759i −0.0119219 0.0206494i
\(467\) 1.87404 3.24592i 0.0867200 0.150203i −0.819403 0.573218i \(-0.805695\pi\)
0.906123 + 0.423015i \(0.139028\pi\)
\(468\) 0 0
\(469\) −32.2782 2.31747i −1.49047 0.107011i
\(470\) 3.21128i 0.148125i
\(471\) 0 0
\(472\) −5.23936 + 3.02494i −0.241161 + 0.139234i
\(473\) −10.3786 + 5.99207i −0.477207 + 0.275516i
\(474\) 0 0
\(475\) 6.99772i 0.321078i
\(476\) 6.11496 + 12.5970i 0.280279 + 0.577381i
\(477\) 0 0
\(478\) 7.74496 13.4147i 0.354246 0.613573i
\(479\) −1.93134 3.34517i −0.0882450 0.152845i 0.818524 0.574472i \(-0.194793\pi\)
−0.906769 + 0.421627i \(0.861459\pi\)
\(480\) 0 0
\(481\) 25.0820 + 14.4811i 1.14364 + 0.660282i
\(482\) −16.4986 −0.751493
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 29.7739 + 17.1899i 1.35196 + 0.780555i
\(486\) 0 0
\(487\) −5.80946 10.0623i −0.263252 0.455966i 0.703852 0.710346i \(-0.251462\pi\)
−0.967104 + 0.254381i \(0.918128\pi\)
\(488\) −6.20857 + 10.7536i −0.281049 + 0.486790i
\(489\) 0 0
\(490\) −13.8470 10.9017i −0.625544 0.492488i
\(491\) 25.7345i 1.16138i −0.814124 0.580691i \(-0.802783\pi\)
0.814124 0.580691i \(-0.197217\pi\)
\(492\) 0 0
\(493\) 36.9421 21.3285i 1.66379 0.960588i
\(494\) 11.0903 6.40300i 0.498977 0.288085i
\(495\) 0 0
\(496\) 8.59575i 0.385961i
\(497\) 32.2149 + 21.8165i 1.44504 + 0.978606i
\(498\) 0 0
\(499\) −11.3984 + 19.7425i −0.510261 + 0.883797i 0.489669 + 0.871909i \(0.337118\pi\)
−0.999929 + 0.0118887i \(0.996216\pi\)
\(500\) 4.60916 + 7.98331i 0.206128 + 0.357024i
\(501\) 0 0
\(502\) −16.1399 9.31835i −0.720357 0.415898i
\(503\) 20.4955 0.913848 0.456924 0.889506i \(-0.348951\pi\)
0.456924 + 0.889506i \(0.348951\pi\)
\(504\) 0 0
\(505\) −3.47037 −0.154429
\(506\) 4.28376 + 2.47323i 0.190436 + 0.109949i
\(507\) 0 0
\(508\) −3.29837 5.71295i −0.146342 0.253471i
\(509\) −5.99259 + 10.3795i −0.265617 + 0.460062i −0.967725 0.252008i \(-0.918909\pi\)
0.702108 + 0.712070i \(0.252242\pi\)
\(510\) 0 0
\(511\) −1.86495 + 25.9754i −0.0825004 + 1.14908i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0.996716 0.575454i 0.0439633 0.0253822i
\(515\) −22.8848 + 13.2125i −1.00842 + 0.582214i
\(516\) 0 0
\(517\) 1.27551i 0.0560970i
\(518\) 2.24024 31.2025i 0.0984303 1.37096i
\(519\) 0 0
\(520\) −3.08346 + 5.34072i −0.135219 + 0.234206i
\(521\) −2.33369 4.04208i −0.102241 0.177087i 0.810367 0.585923i \(-0.199268\pi\)
−0.912608 + 0.408837i \(0.865935\pi\)
\(522\) 0 0
\(523\) −17.5494 10.1322i −0.767383 0.443049i 0.0645573 0.997914i \(-0.479436\pi\)
−0.831940 + 0.554865i \(0.812770\pi\)
\(524\) 1.51472 0.0661708
\(525\) 0 0
\(526\) −7.14678 −0.311614
\(527\) 39.3983 + 22.7466i 1.71622 + 0.990859i
\(528\) 0 0
\(529\) 0.733751 + 1.27089i 0.0319022 + 0.0552562i
\(530\) 0.602614 1.04376i 0.0261759 0.0453379i
\(531\) 0 0
\(532\) −11.4529 7.75611i −0.496546 0.336270i
\(533\) 4.71479i 0.204220i
\(534\) 0 0
\(535\) −6.30756 + 3.64167i −0.272700 + 0.157443i
\(536\) 10.5927 6.11571i 0.457536 0.264159i
\(537\) 0 0
\(538\) 13.3794i 0.576826i
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 0 0
\(541\) 6.53334 11.3161i 0.280890 0.486516i −0.690714 0.723128i \(-0.742704\pi\)
0.971604 + 0.236612i \(0.0760370\pi\)
\(542\) 3.41849 + 5.92100i 0.146837 + 0.254329i
\(543\) 0 0
\(544\) −4.58346 2.64626i −0.196514 0.113458i
\(545\) −34.0858 −1.46008
\(546\) 0 0
\(547\) 24.2492 1.03682 0.518411 0.855132i \(-0.326524\pi\)
0.518411 + 0.855132i \(0.326524\pi\)
\(548\) −12.0316 6.94646i −0.513966 0.296738i
\(549\) 0 0
\(550\) −0.669251 1.15918i −0.0285369 0.0494274i
\(551\) −21.0686 + 36.4918i −0.897552 + 1.55461i
\(552\) 0 0
\(553\) −8.14962 16.7884i −0.346557 0.713915i
\(554\) 5.74807i 0.244212i
\(555\) 0 0
\(556\) −11.7702 + 6.79555i −0.499170 + 0.288196i
\(557\) −20.6838 + 11.9418i −0.876402 + 0.505991i −0.869471 0.493985i \(-0.835540\pi\)
−0.00693183 + 0.999976i \(0.502206\pi\)
\(558\) 0 0
\(559\) 29.3550i 1.24159i
\(560\) 6.64394 + 0.477014i 0.280758 + 0.0201575i
\(561\) 0 0
\(562\) −3.22911 + 5.59298i −0.136212 + 0.235925i
\(563\) 1.15091 + 1.99343i 0.0485050 + 0.0840131i 0.889259 0.457405i \(-0.151221\pi\)
−0.840754 + 0.541418i \(0.817888\pi\)
\(564\) 0 0
\(565\) 31.7674 + 18.3409i 1.33646 + 0.771608i
\(566\) 6.78783 0.285314
\(567\) 0 0
\(568\) −14.7055 −0.617029
\(569\) −21.7718 12.5699i −0.912720 0.526959i −0.0314144 0.999506i \(-0.510001\pi\)
−0.881305 + 0.472548i \(0.843334\pi\)
\(570\) 0 0
\(571\) −17.9626 31.1122i −0.751713 1.30200i −0.946992 0.321257i \(-0.895895\pi\)
0.195279 0.980748i \(-0.437439\pi\)
\(572\) −1.22474 + 2.12132i −0.0512092 + 0.0886969i
\(573\) 0 0
\(574\) −4.58130 + 2.22391i −0.191220 + 0.0928241i
\(575\) 6.62085i 0.276108i
\(576\) 0 0
\(577\) −2.60396 + 1.50340i −0.108404 + 0.0625874i −0.553222 0.833034i \(-0.686602\pi\)
0.444818 + 0.895621i \(0.353269\pi\)
\(578\) −9.53568 + 5.50543i −0.396632 + 0.228996i
\(579\) 0 0
\(580\) 20.2918i 0.842571i
\(581\) 13.8836 20.5009i 0.575989 0.850520i
\(582\) 0 0
\(583\) 0.239357 0.414578i 0.00991314 0.0171701i
\(584\) −4.92152 8.52432i −0.203654 0.352739i
\(585\) 0 0
\(586\) 2.72936 + 1.57579i 0.112749 + 0.0650954i
\(587\) −30.2752 −1.24959 −0.624796 0.780788i \(-0.714818\pi\)
−0.624796 + 0.780788i \(0.714818\pi\)
\(588\) 0 0
\(589\) −44.9389 −1.85167
\(590\) 13.1908 + 7.61571i 0.543057 + 0.313534i
\(591\) 0 0
\(592\) 5.91189 + 10.2397i 0.242977 + 0.420849i
\(593\) −2.54071 + 4.40063i −0.104334 + 0.180712i −0.913466 0.406915i \(-0.866605\pi\)
0.809132 + 0.587627i \(0.199938\pi\)
\(594\) 0 0
\(595\) 19.7680 29.1900i 0.810409 1.19667i
\(596\) 6.65221i 0.272485i
\(597\) 0 0
\(598\) −10.4930 + 6.05816i −0.429092 + 0.247736i
\(599\) 34.0097 19.6355i 1.38960 0.802285i 0.396329 0.918108i \(-0.370284\pi\)
0.993270 + 0.115823i \(0.0369505\pi\)
\(600\) 0 0
\(601\) 8.04133i 0.328013i −0.986459 0.164006i \(-0.947558\pi\)
0.986459 0.164006i \(-0.0524417\pi\)
\(602\) −28.5239 + 13.8464i −1.16255 + 0.564338i
\(603\) 0 0
\(604\) 4.00877 6.94339i 0.163114 0.282522i
\(605\) −1.25882 2.18034i −0.0511783 0.0886434i
\(606\) 0 0
\(607\) 29.6848 + 17.1385i 1.20487 + 0.695632i 0.961634 0.274335i \(-0.0884578\pi\)
0.243236 + 0.969967i \(0.421791\pi\)
\(608\) 5.22803 0.212025
\(609\) 0 0
\(610\) 31.2618 1.26576
\(611\) 2.70577 + 1.56218i 0.109464 + 0.0631990i
\(612\) 0 0
\(613\) −18.8924 32.7226i −0.763057 1.32165i −0.941268 0.337661i \(-0.890364\pi\)
0.178211 0.983992i \(-0.442969\pi\)
\(614\) −7.53553 + 13.0519i −0.304109 + 0.526733i
\(615\) 0 0
\(616\) 2.63896 + 0.189469i 0.106327 + 0.00763391i
\(617\) 0.0377832i 0.00152109i −1.00000 0.000760547i \(-0.999758\pi\)
1.00000 0.000760547i \(-0.000242090\pi\)
\(618\) 0 0
\(619\) 5.61028 3.23910i 0.225496 0.130190i −0.382996 0.923750i \(-0.625108\pi\)
0.608493 + 0.793559i \(0.291774\pi\)
\(620\) 18.7417 10.8205i 0.752683 0.434562i
\(621\) 0 0
\(622\) 31.9145i 1.27966i
\(623\) 18.3105 + 37.7201i 0.733595 + 1.51122i
\(624\) 0 0
\(625\) 14.9505 25.8950i 0.598018 1.03580i
\(626\) 7.97469 + 13.8126i 0.318733 + 0.552061i
\(627\) 0 0
\(628\) −19.0820 11.0170i −0.761456 0.439627i
\(629\) 62.5777 2.49514
\(630\) 0 0
\(631\) −17.8145 −0.709184 −0.354592 0.935021i \(-0.615380\pi\)
−0.354592 + 0.935021i \(0.615380\pi\)
\(632\) 6.10854 + 3.52677i 0.242985 + 0.140287i
\(633\) 0 0
\(634\) 12.6623 + 21.9318i 0.502886 + 0.871023i
\(635\) −8.30411 + 14.3831i −0.329539 + 0.570778i
\(636\) 0 0
\(637\) 15.9217 6.36396i 0.630840 0.252149i
\(638\) 8.05986i 0.319093i
\(639\) 0 0
\(640\) −2.18034 + 1.25882i −0.0861854 + 0.0497592i
\(641\) 16.1473 9.32265i 0.637780 0.368222i −0.145979 0.989288i \(-0.546633\pi\)
0.783759 + 0.621065i \(0.213300\pi\)
\(642\) 0 0
\(643\) 7.04112i 0.277674i 0.990315 + 0.138837i \(0.0443365\pi\)
−0.990315 + 0.138837i \(0.955664\pi\)
\(644\) 10.8361 + 7.33839i 0.427001 + 0.289173i
\(645\) 0 0
\(646\) 13.8347 23.9625i 0.544321 0.942791i
\(647\) 25.0127 + 43.3232i 0.983350 + 1.70321i 0.649051 + 0.760745i \(0.275166\pi\)
0.334299 + 0.942467i \(0.391500\pi\)
\(648\) 0 0
\(649\) 5.23936 + 3.02494i 0.205663 + 0.118739i
\(650\) 3.27865 0.128599
\(651\) 0 0
\(652\) 10.0645 0.394156
\(653\) 2.68285 + 1.54894i 0.104988 + 0.0606149i 0.551575 0.834126i \(-0.314027\pi\)
−0.446587 + 0.894740i \(0.647361\pi\)
\(654\) 0 0
\(655\) −1.90676 3.30260i −0.0745031 0.129043i
\(656\) 0.962402 1.66693i 0.0375755 0.0650826i
\(657\) 0 0
\(658\) 0.241670 3.36603i 0.00942127 0.131221i
\(659\) 41.9739i 1.63507i 0.575878 + 0.817536i \(0.304660\pi\)
−0.575878 + 0.817536i \(0.695340\pi\)
\(660\) 0 0
\(661\) −22.8408 + 13.1872i −0.888405 + 0.512921i −0.873420 0.486967i \(-0.838103\pi\)
−0.0149846 + 0.999888i \(0.504770\pi\)
\(662\) −12.1916 + 7.03882i −0.473840 + 0.273571i
\(663\) 0 0
\(664\) 9.35827i 0.363171i
\(665\) −2.49384 + 34.7347i −0.0967070 + 1.34695i
\(666\) 0 0
\(667\) 19.9339 34.5265i 0.771843 1.33687i
\(668\) −2.38134 4.12460i −0.0921369 0.159586i
\(669\) 0 0
\(670\) −26.6687 15.3972i −1.03030 0.594844i
\(671\) 12.4171 0.479358
\(672\) 0 0
\(673\) −6.60164 −0.254475 −0.127237 0.991872i \(-0.540611\pi\)
−0.127237 + 0.991872i \(0.540611\pi\)
\(674\) −7.05934 4.07571i −0.271916 0.156991i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) 4.52228 7.83282i 0.173805 0.301040i −0.765942 0.642910i \(-0.777727\pi\)
0.939747 + 0.341870i \(0.111060\pi\)
\(678\) 0 0
\(679\) 29.9149 + 20.2590i 1.14803 + 0.777468i
\(680\) 13.3247i 0.510978i
\(681\) 0 0
\(682\) 7.44414 4.29788i 0.285051 0.164574i
\(683\) 27.2954 15.7590i 1.04443 0.603003i 0.123346 0.992364i \(-0.460637\pi\)
0.921085 + 0.389361i \(0.127304\pi\)
\(684\) 0 0
\(685\) 34.9774i 1.33642i
\(686\) −13.6938 12.4691i −0.522834 0.476073i
\(687\) 0 0
\(688\) 5.99207 10.3786i 0.228446 0.395679i
\(689\) 0.586302 + 1.01550i 0.0223363 + 0.0386876i
\(690\) 0 0
\(691\) 26.3742 + 15.2272i 1.00332 + 0.579268i 0.909230 0.416295i \(-0.136672\pi\)
0.0940927 + 0.995563i \(0.470005\pi\)
\(692\) −14.7369 −0.560211
\(693\) 0 0
\(694\) −22.5746 −0.856919
\(695\) 29.6332 + 17.1087i 1.12405 + 0.648972i
\(696\) 0 0
\(697\) −5.09354 8.82227i −0.192932 0.334167i
\(698\) −11.4749 + 19.8751i −0.434332 + 0.752284i
\(699\) 0 0
\(700\) −1.54650 3.18582i −0.0584521 0.120413i
\(701\) 26.3465i 0.995093i −0.867437 0.497547i \(-0.834234\pi\)
0.867437 0.497547i \(-0.165766\pi\)
\(702\) 0 0
\(703\) −53.5334 + 30.9075i −2.01905 + 1.16570i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 25.1981i 0.948342i
\(707\) −3.63760 0.261168i −0.136806 0.00982223i
\(708\) 0 0
\(709\) −5.35292 + 9.27154i −0.201033 + 0.348200i −0.948862 0.315692i \(-0.897763\pi\)
0.747828 + 0.663892i \(0.231097\pi\)
\(710\) 18.5116 + 32.0630i 0.694726 + 1.20330i
\(711\) 0 0
\(712\) −13.7246 7.92392i −0.514353 0.296962i
\(713\) 42.5186 1.59233
\(714\) 0 0
\(715\) 6.16693 0.230630
\(716\) 2.03491 + 1.17486i 0.0760482 + 0.0439065i
\(717\) 0 0
\(718\) −9.84714 17.0558i −0.367492 0.636515i
\(719\) 15.3059 26.5107i 0.570815 0.988681i −0.425667 0.904880i \(-0.639961\pi\)
0.996482 0.0838012i \(-0.0267061\pi\)
\(720\) 0 0
\(721\) −24.9819 + 12.1270i −0.930374 + 0.451633i
\(722\) 8.33229i 0.310096i
\(723\) 0 0
\(724\) −10.3261 + 5.96178i −0.383767 + 0.221568i
\(725\) −9.34279 + 5.39406i −0.346983 + 0.200331i
\(726\) 0 0
\(727\) 7.03188i 0.260798i 0.991462 + 0.130399i \(0.0416258\pi\)
−0.991462 + 0.130399i \(0.958374\pi\)
\(728\) −3.63397 + 5.36603i −0.134684 + 0.198878i
\(729\) 0 0
\(730\) −12.3906 + 21.4612i −0.458597 + 0.794313i
\(731\) −31.7132 54.9289i −1.17296 2.03162i
\(732\) 0 0
\(733\) 19.5539 + 11.2895i 0.722240 + 0.416985i 0.815577 0.578649i \(-0.196420\pi\)
−0.0933367 + 0.995635i \(0.529753\pi\)
\(734\) 3.24796 0.119885
\(735\) 0 0
\(736\) −4.94646 −0.182329
\(737\) −10.5927 6.11571i −0.390188 0.225275i
\(738\) 0 0
\(739\) −9.24921 16.0201i −0.340238 0.589309i 0.644239 0.764824i \(-0.277174\pi\)
−0.984477 + 0.175515i \(0.943841\pi\)
\(740\) 14.8840 25.7798i 0.547147 0.947686i
\(741\) 0 0
\(742\) 0.710202 1.04870i 0.0260723 0.0384991i
\(743\) 22.8029i 0.836558i −0.908319 0.418279i \(-0.862633\pi\)
0.908319 0.418279i \(-0.137367\pi\)
\(744\) 0 0
\(745\) 14.5041 8.37393i 0.531388 0.306797i
\(746\) −5.90935 + 3.41177i −0.216357 + 0.124914i
\(747\) 0 0
\(748\) 5.29253i 0.193514i
\(749\) −6.88557 + 3.34247i −0.251593 + 0.122131i
\(750\) 0 0
\(751\) 15.6992 27.1918i 0.572871 0.992242i −0.423398 0.905944i \(-0.639163\pi\)
0.996269 0.0862983i \(-0.0275038\pi\)
\(752\) 0.637756 + 1.10463i 0.0232566 + 0.0402816i
\(753\) 0 0
\(754\) 17.0975 + 9.87127i 0.622656 + 0.359490i
\(755\) −20.1852 −0.734616
\(756\) 0 0
\(757\) −15.6251 −0.567905 −0.283953 0.958838i \(-0.591646\pi\)
−0.283953 + 0.958838i \(0.591646\pi\)
\(758\) 16.3618 + 9.44646i 0.594286 + 0.343111i
\(759\) 0 0
\(760\) −6.58114 11.3989i −0.238723 0.413481i
\(761\) 20.4241 35.3755i 0.740372 1.28236i −0.211954 0.977280i \(-0.567983\pi\)
0.952326 0.305082i \(-0.0986840\pi\)
\(762\) 0 0
\(763\) −35.7284 2.56518i −1.29345 0.0928658i
\(764\) 24.5765i 0.889146i
\(765\) 0 0
\(766\) 22.8916 13.2165i 0.827106 0.477530i
\(767\) −12.8338 + 7.40957i −0.463400 + 0.267544i
\(768\) 0 0
\(769\) 1.71477i 0.0618361i 0.999522 + 0.0309181i \(0.00984309\pi\)
−0.999522 + 0.0309181i \(0.990157\pi\)
\(770\) −2.90887 5.99233i −0.104828 0.215949i
\(771\) 0 0
\(772\) −7.05657 + 12.2223i −0.253972 + 0.439892i
\(773\) −8.25433 14.2969i −0.296887 0.514224i 0.678535 0.734568i \(-0.262615\pi\)
−0.975422 + 0.220344i \(0.929282\pi\)
\(774\) 0 0
\(775\) −9.96399 5.75272i −0.357917 0.206644i
\(776\) −13.6556 −0.490208
\(777\) 0 0
\(778\) 11.6678 0.418312
\(779\) 8.71475 + 5.03146i 0.312238 + 0.180271i
\(780\) 0 0
\(781\) 7.35275 + 12.7353i 0.263102 + 0.455706i
\(782\) −13.0897 + 22.6719i −0.468085 + 0.810747i
\(783\) 0 0
\(784\) 6.92820 + 1.00000i 0.247436 + 0.0357143i
\(785\) 55.4737i 1.97994i
\(786\) 0 0
\(787\) 37.9077 21.8860i 1.35126 0.780153i 0.362838 0.931852i \(-0.381808\pi\)
0.988427 + 0.151699i \(0.0484744\pi\)
\(788\) 0.501618 0.289609i 0.0178694 0.0103169i
\(789\) 0 0