Properties

Label 690.2.e.a.551.14
Level $690$
Weight $2$
Character 690.551
Analytic conductor $5.510$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 551.14
Root \(1.37342 + 1.05533i\) of defining polynomial
Character \(\chi\) \(=\) 690.551
Dual form 690.2.e.a.551.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.05533 - 1.37342i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.37342 + 1.05533i) q^{6} -1.91110i q^{7} -1.00000i q^{8} +(-0.772562 - 2.89882i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.05533 - 1.37342i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.37342 + 1.05533i) q^{6} -1.91110i q^{7} -1.00000i q^{8} +(-0.772562 - 2.89882i) q^{9} -1.00000i q^{10} -2.07465 q^{11} +(-1.05533 + 1.37342i) q^{12} +1.28828 q^{13} +1.91110 q^{14} +(-1.05533 + 1.37342i) q^{15} +1.00000 q^{16} -4.04657 q^{17} +(2.89882 - 0.772562i) q^{18} -3.79764i q^{19} +1.00000 q^{20} +(-2.62474 - 2.01683i) q^{21} -2.07465i q^{22} +(-2.86177 - 3.84841i) q^{23} +(-1.37342 - 1.05533i) q^{24} +1.00000 q^{25} +1.28828i q^{26} +(-4.79660 - 1.99816i) q^{27} +1.91110i q^{28} -2.78403i q^{29} +(-1.37342 - 1.05533i) q^{30} +1.87654 q^{31} +1.00000i q^{32} +(-2.18944 + 2.84936i) q^{33} -4.04657i q^{34} +1.91110i q^{35} +(0.772562 + 2.89882i) q^{36} -2.18386i q^{37} +3.79764 q^{38} +(1.35956 - 1.76935i) q^{39} +1.00000i q^{40} +0.590353i q^{41} +(2.01683 - 2.62474i) q^{42} +0.332844i q^{43} +2.07465 q^{44} +(0.772562 + 2.89882i) q^{45} +(3.84841 - 2.86177i) q^{46} -4.11977i q^{47} +(1.05533 - 1.37342i) q^{48} +3.34771 q^{49} +1.00000i q^{50} +(-4.27046 + 5.55764i) q^{51} -1.28828 q^{52} +3.47550 q^{53} +(1.99816 - 4.79660i) q^{54} +2.07465 q^{55} -1.91110 q^{56} +(-5.21575 - 4.00776i) q^{57} +2.78403 q^{58} -2.07202i q^{59} +(1.05533 - 1.37342i) q^{60} +3.23836i q^{61} +1.87654i q^{62} +(-5.53992 + 1.47644i) q^{63} -1.00000 q^{64} -1.28828 q^{65} +(-2.84936 - 2.18944i) q^{66} -6.73067i q^{67} +4.04657 q^{68} +(-8.30559 - 0.130920i) q^{69} -1.91110 q^{70} +9.09793i q^{71} +(-2.89882 + 0.772562i) q^{72} -3.52030 q^{73} +2.18386 q^{74} +(1.05533 - 1.37342i) q^{75} +3.79764i q^{76} +3.96485i q^{77} +(1.76935 + 1.35956i) q^{78} -3.38420i q^{79} -1.00000 q^{80} +(-7.80630 + 4.47903i) q^{81} -0.590353 q^{82} +5.68044 q^{83} +(2.62474 + 2.01683i) q^{84} +4.04657 q^{85} -0.332844 q^{86} +(-3.82364 - 2.93807i) q^{87} +2.07465i q^{88} +10.9473 q^{89} +(-2.89882 + 0.772562i) q^{90} -2.46203i q^{91} +(2.86177 + 3.84841i) q^{92} +(1.98036 - 2.57727i) q^{93} +4.11977 q^{94} +3.79764i q^{95} +(1.37342 + 1.05533i) q^{96} +14.3560i q^{97} +3.34771i q^{98} +(1.60280 + 6.01403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} - 12q^{11} - 12q^{14} + 16q^{16} + 8q^{18} + 16q^{20} - 4q^{21} + 4q^{23} - 2q^{24} + 16q^{25} + 24q^{27} - 2q^{30} + 4q^{31} - 28q^{33} - 2q^{36} - 16q^{38} - 8q^{39} + 12q^{44} - 2q^{45} - 4q^{46} - 4q^{49} - 2q^{51} - 8q^{53} - 26q^{54} + 12q^{55} + 12q^{56} + 28q^{57} - 8q^{58} - 16q^{64} + 10q^{66} + 30q^{69} + 12q^{70} - 8q^{72} - 16q^{73} - 24q^{74} - 12q^{78} - 16q^{80} + 22q^{81} - 16q^{82} - 40q^{83} + 4q^{84} - 40q^{86} + 20q^{87} + 80q^{89} - 8q^{90} - 4q^{92} - 4q^{93} - 24q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.05533 1.37342i 0.609294 0.792944i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.37342 + 1.05533i 0.560696 + 0.430836i
\(7\) 1.91110i 0.722326i −0.932503 0.361163i \(-0.882380\pi\)
0.932503 0.361163i \(-0.117620\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.772562 2.89882i −0.257521 0.966273i
\(10\) 1.00000i 0.316228i
\(11\) −2.07465 −0.625530 −0.312765 0.949830i \(-0.601255\pi\)
−0.312765 + 0.949830i \(0.601255\pi\)
\(12\) −1.05533 + 1.37342i −0.304647 + 0.396472i
\(13\) 1.28828 0.357305 0.178652 0.983912i \(-0.442826\pi\)
0.178652 + 0.983912i \(0.442826\pi\)
\(14\) 1.91110 0.510762
\(15\) −1.05533 + 1.37342i −0.272485 + 0.354615i
\(16\) 1.00000 0.250000
\(17\) −4.04657 −0.981438 −0.490719 0.871318i \(-0.663266\pi\)
−0.490719 + 0.871318i \(0.663266\pi\)
\(18\) 2.89882 0.772562i 0.683258 0.182095i
\(19\) 3.79764i 0.871238i −0.900131 0.435619i \(-0.856530\pi\)
0.900131 0.435619i \(-0.143470\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.62474 2.01683i −0.572764 0.440109i
\(22\) 2.07465i 0.442317i
\(23\) −2.86177 3.84841i −0.596721 0.802449i
\(24\) −1.37342 1.05533i −0.280348 0.215418i
\(25\) 1.00000 0.200000
\(26\) 1.28828i 0.252652i
\(27\) −4.79660 1.99816i −0.923106 0.384545i
\(28\) 1.91110i 0.361163i
\(29\) 2.78403i 0.516981i −0.966014 0.258491i \(-0.916775\pi\)
0.966014 0.258491i \(-0.0832251\pi\)
\(30\) −1.37342 1.05533i −0.250751 0.192676i
\(31\) 1.87654 0.337036 0.168518 0.985699i \(-0.446102\pi\)
0.168518 + 0.985699i \(0.446102\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.18944 + 2.84936i −0.381132 + 0.496011i
\(34\) 4.04657i 0.693981i
\(35\) 1.91110i 0.323034i
\(36\) 0.772562 + 2.89882i 0.128760 + 0.483136i
\(37\) 2.18386i 0.359024i −0.983756 0.179512i \(-0.942548\pi\)
0.983756 0.179512i \(-0.0574519\pi\)
\(38\) 3.79764 0.616058
\(39\) 1.35956 1.76935i 0.217704 0.283323i
\(40\) 1.00000i 0.158114i
\(41\) 0.590353i 0.0921977i 0.998937 + 0.0460988i \(0.0146789\pi\)
−0.998937 + 0.0460988i \(0.985321\pi\)
\(42\) 2.01683 2.62474i 0.311204 0.405005i
\(43\) 0.332844i 0.0507583i 0.999678 + 0.0253791i \(0.00807929\pi\)
−0.999678 + 0.0253791i \(0.991921\pi\)
\(44\) 2.07465 0.312765
\(45\) 0.772562 + 2.89882i 0.115167 + 0.432130i
\(46\) 3.84841 2.86177i 0.567417 0.421946i
\(47\) 4.11977i 0.600931i −0.953793 0.300465i \(-0.902858\pi\)
0.953793 0.300465i \(-0.0971419\pi\)
\(48\) 1.05533 1.37342i 0.152324 0.198236i
\(49\) 3.34771 0.478245
\(50\) 1.00000i 0.141421i
\(51\) −4.27046 + 5.55764i −0.597985 + 0.778225i
\(52\) −1.28828 −0.178652
\(53\) 3.47550 0.477397 0.238698 0.971094i \(-0.423279\pi\)
0.238698 + 0.971094i \(0.423279\pi\)
\(54\) 1.99816 4.79660i 0.271914 0.652735i
\(55\) 2.07465 0.279746
\(56\) −1.91110 −0.255381
\(57\) −5.21575 4.00776i −0.690843 0.530840i
\(58\) 2.78403 0.365561
\(59\) 2.07202i 0.269753i −0.990862 0.134877i \(-0.956936\pi\)
0.990862 0.134877i \(-0.0430638\pi\)
\(60\) 1.05533 1.37342i 0.136242 0.177308i
\(61\) 3.23836i 0.414630i 0.978274 + 0.207315i \(0.0664725\pi\)
−0.978274 + 0.207315i \(0.933527\pi\)
\(62\) 1.87654i 0.238321i
\(63\) −5.53992 + 1.47644i −0.697964 + 0.186014i
\(64\) −1.00000 −0.125000
\(65\) −1.28828 −0.159791
\(66\) −2.84936 2.18944i −0.350733 0.269501i
\(67\) 6.73067i 0.822282i −0.911572 0.411141i \(-0.865130\pi\)
0.911572 0.411141i \(-0.134870\pi\)
\(68\) 4.04657 0.490719
\(69\) −8.30559 0.130920i −0.999876 0.0157609i
\(70\) −1.91110 −0.228420
\(71\) 9.09793i 1.07973i 0.841753 + 0.539863i \(0.181524\pi\)
−0.841753 + 0.539863i \(0.818476\pi\)
\(72\) −2.89882 + 0.772562i −0.341629 + 0.0910473i
\(73\) −3.52030 −0.412020 −0.206010 0.978550i \(-0.566048\pi\)
−0.206010 + 0.978550i \(0.566048\pi\)
\(74\) 2.18386 0.253868
\(75\) 1.05533 1.37342i 0.121859 0.158589i
\(76\) 3.79764i 0.435619i
\(77\) 3.96485i 0.451837i
\(78\) 1.76935 + 1.35956i 0.200339 + 0.153940i
\(79\) 3.38420i 0.380753i −0.981711 0.190376i \(-0.939029\pi\)
0.981711 0.190376i \(-0.0609708\pi\)
\(80\) −1.00000 −0.111803
\(81\) −7.80630 + 4.47903i −0.867366 + 0.497670i
\(82\) −0.590353 −0.0651936
\(83\) 5.68044 0.623509 0.311754 0.950163i \(-0.399083\pi\)
0.311754 + 0.950163i \(0.399083\pi\)
\(84\) 2.62474 + 2.01683i 0.286382 + 0.220055i
\(85\) 4.04657 0.438912
\(86\) −0.332844 −0.0358915
\(87\) −3.82364 2.93807i −0.409937 0.314994i
\(88\) 2.07465i 0.221158i
\(89\) 10.9473 1.16042 0.580208 0.814468i \(-0.302971\pi\)
0.580208 + 0.814468i \(0.302971\pi\)
\(90\) −2.89882 + 0.772562i −0.305562 + 0.0814352i
\(91\) 2.46203i 0.258090i
\(92\) 2.86177 + 3.84841i 0.298361 + 0.401224i
\(93\) 1.98036 2.57727i 0.205354 0.267251i
\(94\) 4.11977 0.424922
\(95\) 3.79764i 0.389629i
\(96\) 1.37342 + 1.05533i 0.140174 + 0.107709i
\(97\) 14.3560i 1.45763i 0.684712 + 0.728813i \(0.259928\pi\)
−0.684712 + 0.728813i \(0.740072\pi\)
\(98\) 3.34771i 0.338170i
\(99\) 1.60280 + 6.01403i 0.161087 + 0.604433i
\(100\) −1.00000 −0.100000
\(101\) 6.90670i 0.687243i 0.939108 + 0.343621i \(0.111654\pi\)
−0.939108 + 0.343621i \(0.888346\pi\)
\(102\) −5.55764 4.27046i −0.550289 0.422839i
\(103\) 15.1722i 1.49496i −0.664282 0.747482i \(-0.731262\pi\)
0.664282 0.747482i \(-0.268738\pi\)
\(104\) 1.28828i 0.126326i
\(105\) 2.62474 + 2.01683i 0.256148 + 0.196823i
\(106\) 3.47550i 0.337571i
\(107\) 15.9284 1.53986 0.769930 0.638129i \(-0.220291\pi\)
0.769930 + 0.638129i \(0.220291\pi\)
\(108\) 4.79660 + 1.99816i 0.461553 + 0.192273i
\(109\) 3.31710i 0.317721i 0.987301 + 0.158860i \(0.0507820\pi\)
−0.987301 + 0.158860i \(0.949218\pi\)
\(110\) 2.07465i 0.197810i
\(111\) −2.99935 2.30469i −0.284686 0.218751i
\(112\) 1.91110i 0.180582i
\(113\) 16.7721 1.57779 0.788893 0.614531i \(-0.210655\pi\)
0.788893 + 0.614531i \(0.210655\pi\)
\(114\) 4.00776 5.21575i 0.375361 0.488500i
\(115\) 2.86177 + 3.84841i 0.266862 + 0.358866i
\(116\) 2.78403i 0.258491i
\(117\) −0.995276 3.73449i −0.0920133 0.345254i
\(118\) 2.07202 0.190745
\(119\) 7.73339i 0.708918i
\(120\) 1.37342 + 1.05533i 0.125375 + 0.0963379i
\(121\) −6.69583 −0.608712
\(122\) −3.23836 −0.293188
\(123\) 0.810803 + 0.623017i 0.0731076 + 0.0561755i
\(124\) −1.87654 −0.168518
\(125\) −1.00000 −0.0894427
\(126\) −1.47644 5.53992i −0.131532 0.493535i
\(127\) −0.980016 −0.0869623 −0.0434812 0.999054i \(-0.513845\pi\)
−0.0434812 + 0.999054i \(0.513845\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.457135 + 0.351260i 0.0402485 + 0.0309267i
\(130\) 1.28828i 0.112990i
\(131\) 9.96859i 0.870960i 0.900198 + 0.435480i \(0.143421\pi\)
−0.900198 + 0.435480i \(0.856579\pi\)
\(132\) 2.18944 2.84936i 0.190566 0.248005i
\(133\) −7.25765 −0.629318
\(134\) 6.73067 0.581442
\(135\) 4.79660 + 1.99816i 0.412826 + 0.171974i
\(136\) 4.04657i 0.346991i
\(137\) 14.3513 1.22612 0.613058 0.790038i \(-0.289939\pi\)
0.613058 + 0.790038i \(0.289939\pi\)
\(138\) 0.130920 8.30559i 0.0111447 0.707019i
\(139\) −4.62609 −0.392380 −0.196190 0.980566i \(-0.562857\pi\)
−0.196190 + 0.980566i \(0.562857\pi\)
\(140\) 1.91110i 0.161517i
\(141\) −5.65817 4.34771i −0.476504 0.366144i
\(142\) −9.09793 −0.763482
\(143\) −2.67273 −0.223505
\(144\) −0.772562 2.89882i −0.0643802 0.241568i
\(145\) 2.78403i 0.231201i
\(146\) 3.52030i 0.291342i
\(147\) 3.53294 4.59782i 0.291392 0.379221i
\(148\) 2.18386i 0.179512i
\(149\) −21.2559 −1.74135 −0.870676 0.491856i \(-0.836319\pi\)
−0.870676 + 0.491856i \(0.836319\pi\)
\(150\) 1.37342 + 1.05533i 0.112139 + 0.0861672i
\(151\) 13.0135 1.05903 0.529514 0.848301i \(-0.322374\pi\)
0.529514 + 0.848301i \(0.322374\pi\)
\(152\) −3.79764 −0.308029
\(153\) 3.12623 + 11.7303i 0.252741 + 0.948337i
\(154\) −3.96485 −0.319497
\(155\) −1.87654 −0.150727
\(156\) −1.35956 + 1.76935i −0.108852 + 0.141661i
\(157\) 10.4319i 0.832557i 0.909237 + 0.416278i \(0.136666\pi\)
−0.909237 + 0.416278i \(0.863334\pi\)
\(158\) 3.38420 0.269233
\(159\) 3.66780 4.77332i 0.290875 0.378549i
\(160\) 1.00000i 0.0790569i
\(161\) −7.35468 + 5.46912i −0.579630 + 0.431027i
\(162\) −4.47903 7.80630i −0.351906 0.613321i
\(163\) −2.70739 −0.212059 −0.106030 0.994363i \(-0.533814\pi\)
−0.106030 + 0.994363i \(0.533814\pi\)
\(164\) 0.590353i 0.0460988i
\(165\) 2.18944 2.84936i 0.170448 0.221823i
\(166\) 5.68044i 0.440887i
\(167\) 16.7966i 1.29976i −0.760038 0.649879i \(-0.774819\pi\)
0.760038 0.649879i \(-0.225181\pi\)
\(168\) −2.01683 + 2.62474i −0.155602 + 0.202503i
\(169\) −11.3403 −0.872333
\(170\) 4.04657i 0.310358i
\(171\) −11.0087 + 2.93391i −0.841853 + 0.224362i
\(172\) 0.332844i 0.0253791i
\(173\) 18.5634i 1.41135i −0.708535 0.705676i \(-0.750644\pi\)
0.708535 0.705676i \(-0.249356\pi\)
\(174\) 2.93807 3.82364i 0.222734 0.289870i
\(175\) 1.91110i 0.144465i
\(176\) −2.07465 −0.156383
\(177\) −2.84575 2.18666i −0.213899 0.164359i
\(178\) 10.9473i 0.820538i
\(179\) 20.1835i 1.50859i 0.656538 + 0.754293i \(0.272020\pi\)
−0.656538 + 0.754293i \(0.727980\pi\)
\(180\) −0.772562 2.89882i −0.0575834 0.216065i
\(181\) 14.5787i 1.08362i 0.840500 + 0.541811i \(0.182261\pi\)
−0.840500 + 0.541811i \(0.817739\pi\)
\(182\) 2.46203 0.182498
\(183\) 4.44763 + 3.41754i 0.328778 + 0.252632i
\(184\) −3.84841 + 2.86177i −0.283708 + 0.210973i
\(185\) 2.18386i 0.160560i
\(186\) 2.57727 + 1.98036i 0.188975 + 0.145207i
\(187\) 8.39522 0.613919
\(188\) 4.11977i 0.300465i
\(189\) −3.81867 + 9.16676i −0.277767 + 0.666784i
\(190\) −3.79764 −0.275510
\(191\) −5.69209 −0.411865 −0.205932 0.978566i \(-0.566023\pi\)
−0.205932 + 0.978566i \(0.566023\pi\)
\(192\) −1.05533 + 1.37342i −0.0761618 + 0.0991180i
\(193\) −16.8306 −1.21149 −0.605746 0.795658i \(-0.707125\pi\)
−0.605746 + 0.795658i \(0.707125\pi\)
\(194\) −14.3560 −1.03070
\(195\) −1.35956 + 1.76935i −0.0973600 + 0.126706i
\(196\) −3.34771 −0.239122
\(197\) 6.99478i 0.498358i −0.968458 0.249179i \(-0.919839\pi\)
0.968458 0.249179i \(-0.0801607\pi\)
\(198\) −6.01403 + 1.60280i −0.427399 + 0.113906i
\(199\) 4.72003i 0.334594i 0.985907 + 0.167297i \(0.0535038\pi\)
−0.985907 + 0.167297i \(0.946496\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −9.24404 7.10307i −0.652024 0.501012i
\(202\) −6.90670 −0.485954
\(203\) −5.32055 −0.373429
\(204\) 4.27046 5.55764i 0.298992 0.389113i
\(205\) 0.590353i 0.0412321i
\(206\) 15.1722 1.05710
\(207\) −8.94494 + 11.2689i −0.621716 + 0.783243i
\(208\) 1.28828 0.0893261
\(209\) 7.87877i 0.544986i
\(210\) −2.01683 + 2.62474i −0.139175 + 0.181124i
\(211\) 22.6122 1.55669 0.778344 0.627838i \(-0.216060\pi\)
0.778344 + 0.627838i \(0.216060\pi\)
\(212\) −3.47550 −0.238698
\(213\) 12.4953 + 9.60131i 0.856162 + 0.657871i
\(214\) 15.9284i 1.08885i
\(215\) 0.332844i 0.0226998i
\(216\) −1.99816 + 4.79660i −0.135957 + 0.326367i
\(217\) 3.58624i 0.243450i
\(218\) −3.31710 −0.224662
\(219\) −3.71508 + 4.83485i −0.251042 + 0.326709i
\(220\) −2.07465 −0.139873
\(221\) −5.21312 −0.350672
\(222\) 2.30469 2.99935i 0.154680 0.201303i
\(223\) −23.3059 −1.56068 −0.780340 0.625355i \(-0.784954\pi\)
−0.780340 + 0.625355i \(0.784954\pi\)
\(224\) 1.91110 0.127690
\(225\) −0.772562 2.89882i −0.0515041 0.193255i
\(226\) 16.7721i 1.11566i
\(227\) 27.6254 1.83356 0.916780 0.399394i \(-0.130779\pi\)
0.916780 + 0.399394i \(0.130779\pi\)
\(228\) 5.21575 + 4.00776i 0.345421 + 0.265420i
\(229\) 24.2738i 1.60406i −0.597286 0.802028i \(-0.703754\pi\)
0.597286 0.802028i \(-0.296246\pi\)
\(230\) −3.84841 + 2.86177i −0.253757 + 0.188700i
\(231\) 5.44541 + 4.18422i 0.358282 + 0.275302i
\(232\) −2.78403 −0.182781
\(233\) 0.568005i 0.0372112i −0.999827 0.0186056i \(-0.994077\pi\)
0.999827 0.0186056i \(-0.00592269\pi\)
\(234\) 3.73449 0.995276i 0.244131 0.0650632i
\(235\) 4.11977i 0.268744i
\(236\) 2.07202i 0.134877i
\(237\) −4.64793 3.57145i −0.301916 0.231990i
\(238\) −7.73339 −0.501281
\(239\) 1.41185i 0.0913250i 0.998957 + 0.0456625i \(0.0145399\pi\)
−0.998957 + 0.0456625i \(0.985460\pi\)
\(240\) −1.05533 + 1.37342i −0.0681212 + 0.0886538i
\(241\) 0.433010i 0.0278926i 0.999903 + 0.0139463i \(0.00443939\pi\)
−0.999903 + 0.0139463i \(0.995561\pi\)
\(242\) 6.69583i 0.430424i
\(243\) −2.08662 + 15.4482i −0.133857 + 0.991001i
\(244\) 3.23836i 0.207315i
\(245\) −3.34771 −0.213878
\(246\) −0.623017 + 0.810803i −0.0397221 + 0.0516949i
\(247\) 4.89242i 0.311297i
\(248\) 1.87654i 0.119160i
\(249\) 5.99473 7.80162i 0.379900 0.494408i
\(250\) 1.00000i 0.0632456i
\(251\) 22.4064 1.41428 0.707140 0.707074i \(-0.249985\pi\)
0.707140 + 0.707074i \(0.249985\pi\)
\(252\) 5.53992 1.47644i 0.348982 0.0930070i
\(253\) 5.93718 + 7.98410i 0.373267 + 0.501956i
\(254\) 0.980016i 0.0614917i
\(255\) 4.27046 5.55764i 0.267427 0.348033i
\(256\) 1.00000 0.0625000
\(257\) 20.6632i 1.28894i −0.764632 0.644468i \(-0.777079\pi\)
0.764632 0.644468i \(-0.222921\pi\)
\(258\) −0.351260 + 0.457135i −0.0218685 + 0.0284600i
\(259\) −4.17356 −0.259332
\(260\) 1.28828 0.0798957
\(261\) −8.07040 + 2.15084i −0.499545 + 0.133133i
\(262\) −9.96859 −0.615862
\(263\) −2.57099 −0.158534 −0.0792669 0.996853i \(-0.525258\pi\)
−0.0792669 + 0.996853i \(0.525258\pi\)
\(264\) 2.84936 + 2.18944i 0.175366 + 0.134751i
\(265\) −3.47550 −0.213498
\(266\) 7.25765i 0.444995i
\(267\) 11.5530 15.0353i 0.707035 0.920145i
\(268\) 6.73067i 0.411141i
\(269\) 2.88848i 0.176113i 0.996115 + 0.0880567i \(0.0280657\pi\)
−0.996115 + 0.0880567i \(0.971934\pi\)
\(270\) −1.99816 + 4.79660i −0.121604 + 0.291912i
\(271\) 15.1639 0.921141 0.460571 0.887623i \(-0.347645\pi\)
0.460571 + 0.887623i \(0.347645\pi\)
\(272\) −4.04657 −0.245360
\(273\) −3.38139 2.59825i −0.204651 0.157253i
\(274\) 14.3513i 0.866994i
\(275\) −2.07465 −0.125106
\(276\) 8.30559 + 0.130920i 0.499938 + 0.00788047i
\(277\) 3.10829 0.186759 0.0933796 0.995631i \(-0.470233\pi\)
0.0933796 + 0.995631i \(0.470233\pi\)
\(278\) 4.62609i 0.277455i
\(279\) −1.44974 5.43974i −0.0867938 0.325669i
\(280\) 1.91110 0.114210
\(281\) −12.8651 −0.767468 −0.383734 0.923444i \(-0.625362\pi\)
−0.383734 + 0.923444i \(0.625362\pi\)
\(282\) 4.34771 5.65817i 0.258903 0.336939i
\(283\) 24.2159i 1.43948i −0.694242 0.719742i \(-0.744260\pi\)
0.694242 0.719742i \(-0.255740\pi\)
\(284\) 9.09793i 0.539863i
\(285\) 5.21575 + 4.00776i 0.308954 + 0.237399i
\(286\) 2.67273i 0.158042i
\(287\) 1.12822 0.0665968
\(288\) 2.89882 0.772562i 0.170815 0.0455237i
\(289\) −0.625250 −0.0367794
\(290\) −2.78403 −0.163484
\(291\) 19.7168 + 15.1503i 1.15582 + 0.888124i
\(292\) 3.52030 0.206010
\(293\) −27.3847 −1.59983 −0.799916 0.600112i \(-0.795123\pi\)
−0.799916 + 0.600112i \(0.795123\pi\)
\(294\) 4.59782 + 3.53294i 0.268150 + 0.206045i
\(295\) 2.07202i 0.120637i
\(296\) −2.18386 −0.126934
\(297\) 9.95127 + 4.14547i 0.577431 + 0.240545i
\(298\) 21.2559i 1.23132i
\(299\) −3.68677 4.95783i −0.213211 0.286719i
\(300\) −1.05533 + 1.37342i −0.0609294 + 0.0792944i
\(301\) 0.636097 0.0366640
\(302\) 13.0135i 0.748845i
\(303\) 9.48580 + 7.28884i 0.544945 + 0.418733i
\(304\) 3.79764i 0.217809i
\(305\) 3.23836i 0.185428i
\(306\) −11.7303 + 3.12623i −0.670575 + 0.178715i
\(307\) 27.5618 1.57304 0.786518 0.617567i \(-0.211882\pi\)
0.786518 + 0.617567i \(0.211882\pi\)
\(308\) 3.96485i 0.225919i
\(309\) −20.8378 16.0117i −1.18542 0.910874i
\(310\) 1.87654i 0.106580i
\(311\) 13.2819i 0.753148i 0.926387 + 0.376574i \(0.122898\pi\)
−0.926387 + 0.376574i \(0.877102\pi\)
\(312\) −1.76935 1.35956i −0.100170 0.0769699i
\(313\) 23.2441i 1.31383i −0.753963 0.656917i \(-0.771860\pi\)
0.753963 0.656917i \(-0.228140\pi\)
\(314\) −10.4319 −0.588706
\(315\) 5.53992 1.47644i 0.312139 0.0831879i
\(316\) 3.38420i 0.190376i
\(317\) 17.6217i 0.989733i −0.868969 0.494867i \(-0.835217\pi\)
0.868969 0.494867i \(-0.164783\pi\)
\(318\) 4.77332 + 3.66780i 0.267675 + 0.205680i
\(319\) 5.77589i 0.323388i
\(320\) 1.00000 0.0559017
\(321\) 16.8097 21.8764i 0.938228 1.22102i
\(322\) −5.46912 7.35468i −0.304782 0.409860i
\(323\) 15.3674i 0.855066i
\(324\) 7.80630 4.47903i 0.433683 0.248835i
\(325\) 1.28828 0.0714609
\(326\) 2.70739i 0.149948i
\(327\) 4.55577 + 3.50063i 0.251935 + 0.193585i
\(328\) 0.590353 0.0325968
\(329\) −7.87328 −0.434068
\(330\) 2.84936 + 2.18944i 0.156852 + 0.120525i
\(331\) 20.7361 1.13976 0.569879 0.821729i \(-0.306990\pi\)
0.569879 + 0.821729i \(0.306990\pi\)
\(332\) −5.68044 −0.311754
\(333\) −6.33060 + 1.68716i −0.346915 + 0.0924561i
\(334\) 16.7966 0.919068
\(335\) 6.73067i 0.367736i
\(336\) −2.62474 2.01683i −0.143191 0.110027i
\(337\) 9.08954i 0.495139i 0.968870 + 0.247569i \(0.0796318\pi\)
−0.968870 + 0.247569i \(0.920368\pi\)
\(338\) 11.3403i 0.616833i
\(339\) 17.7001 23.0351i 0.961336 1.25110i
\(340\) −4.04657 −0.219456
\(341\) −3.89316 −0.210826
\(342\) −2.93391 11.0087i −0.158648 0.595280i
\(343\) 19.7755i 1.06777i
\(344\) 0.332844 0.0179458
\(345\) 8.30559 + 0.130920i 0.447158 + 0.00704850i
\(346\) 18.5634 0.997976
\(347\) 28.2337i 1.51567i −0.652449 0.757833i \(-0.726258\pi\)
0.652449 0.757833i \(-0.273742\pi\)
\(348\) 3.82364 + 2.93807i 0.204969 + 0.157497i
\(349\) −9.07266 −0.485648 −0.242824 0.970070i \(-0.578074\pi\)
−0.242824 + 0.970070i \(0.578074\pi\)
\(350\) 1.91110 0.102152
\(351\) −6.17936 2.57418i −0.329830 0.137400i
\(352\) 2.07465i 0.110579i
\(353\) 1.12881i 0.0600806i −0.999549 0.0300403i \(-0.990436\pi\)
0.999549 0.0300403i \(-0.00956357\pi\)
\(354\) 2.18666 2.84575i 0.116220 0.151250i
\(355\) 9.09793i 0.482868i
\(356\) −10.9473 −0.580208
\(357\) 10.6212 + 8.16127i 0.562133 + 0.431940i
\(358\) −20.1835 −1.06673
\(359\) 14.4991 0.765233 0.382617 0.923907i \(-0.375023\pi\)
0.382617 + 0.923907i \(0.375023\pi\)
\(360\) 2.89882 0.772562i 0.152781 0.0407176i
\(361\) 4.57796 0.240945
\(362\) −14.5787 −0.766237
\(363\) −7.06630 + 9.19618i −0.370885 + 0.482674i
\(364\) 2.46203i 0.129045i
\(365\) 3.52030 0.184261
\(366\) −3.41754 + 4.44763i −0.178638 + 0.232481i
\(367\) 22.1178i 1.15454i −0.816553 0.577270i \(-0.804118\pi\)
0.816553 0.577270i \(-0.195882\pi\)
\(368\) −2.86177 3.84841i −0.149180 0.200612i
\(369\) 1.71133 0.456085i 0.0890881 0.0237428i
\(370\) −2.18386 −0.113533
\(371\) 6.64202i 0.344836i
\(372\) −1.98036 + 2.57727i −0.102677 + 0.133625i
\(373\) 19.6820i 1.01910i −0.860442 0.509548i \(-0.829813\pi\)
0.860442 0.509548i \(-0.170187\pi\)
\(374\) 8.39522i 0.434107i
\(375\) −1.05533 + 1.37342i −0.0544969 + 0.0709231i
\(376\) −4.11977 −0.212461
\(377\) 3.58661i 0.184720i
\(378\) −9.16676 3.81867i −0.471487 0.196411i
\(379\) 17.0269i 0.874613i −0.899312 0.437307i \(-0.855932\pi\)
0.899312 0.437307i \(-0.144068\pi\)
\(380\) 3.79764i 0.194815i
\(381\) −1.03424 + 1.34597i −0.0529857 + 0.0689563i
\(382\) 5.69209i 0.291232i
\(383\) 1.29893 0.0663722 0.0331861 0.999449i \(-0.489435\pi\)
0.0331861 + 0.999449i \(0.489435\pi\)
\(384\) −1.37342 1.05533i −0.0700870 0.0538545i
\(385\) 3.96485i 0.202068i
\(386\) 16.8306i 0.856654i
\(387\) 0.964855 0.257143i 0.0490463 0.0130713i
\(388\) 14.3560i 0.728813i
\(389\) 14.9186 0.756404 0.378202 0.925723i \(-0.376542\pi\)
0.378202 + 0.925723i \(0.376542\pi\)
\(390\) −1.76935 1.35956i −0.0895945 0.0688440i
\(391\) 11.5804 + 15.5729i 0.585645 + 0.787554i
\(392\) 3.34771i 0.169085i
\(393\) 13.6911 + 10.5201i 0.690622 + 0.530671i
\(394\) 6.99478 0.352392
\(395\) 3.38420i 0.170278i
\(396\) −1.60280 6.01403i −0.0805435 0.302217i
\(397\) 31.5845 1.58518 0.792591 0.609754i \(-0.208732\pi\)
0.792591 + 0.609754i \(0.208732\pi\)
\(398\) −4.72003 −0.236594
\(399\) −7.65920 + 9.96779i −0.383440 + 0.499014i
\(400\) 1.00000 0.0500000
\(401\) −29.5255 −1.47443 −0.737216 0.675657i \(-0.763860\pi\)
−0.737216 + 0.675657i \(0.763860\pi\)
\(402\) 7.10307 9.24404i 0.354269 0.461051i
\(403\) 2.41751 0.120425
\(404\) 6.90670i 0.343621i
\(405\) 7.80630 4.47903i 0.387898 0.222565i
\(406\) 5.32055i 0.264054i
\(407\) 4.53074i 0.224580i
\(408\) 5.55764 + 4.27046i 0.275144 + 0.211420i
\(409\) 32.5691 1.61044 0.805219 0.592978i \(-0.202048\pi\)
0.805219 + 0.592978i \(0.202048\pi\)
\(410\) 0.590353 0.0291555
\(411\) 15.1454 19.7104i 0.747065 0.972241i
\(412\) 15.1722i 0.747482i
\(413\) −3.95982 −0.194850
\(414\) −11.2689 8.94494i −0.553836 0.439620i
\(415\) −5.68044 −0.278842
\(416\) 1.28828i 0.0631631i
\(417\) −4.88205 + 6.35357i −0.239075 + 0.311136i
\(418\) −7.87877 −0.385363
\(419\) −1.54122 −0.0752934 −0.0376467 0.999291i \(-0.511986\pi\)
−0.0376467 + 0.999291i \(0.511986\pi\)
\(420\) −2.62474 2.01683i −0.128074 0.0984114i
\(421\) 7.43732i 0.362473i −0.983440 0.181236i \(-0.941990\pi\)
0.983440 0.181236i \(-0.0580099\pi\)
\(422\) 22.6122i 1.10075i
\(423\) −11.9425 + 3.18278i −0.580663 + 0.154752i
\(424\) 3.47550i 0.168785i
\(425\) −4.04657 −0.196288
\(426\) −9.60131 + 12.4953i −0.465185 + 0.605398i
\(427\) 6.18882 0.299498
\(428\) −15.9284 −0.769930
\(429\) −2.82061 + 3.67078i −0.136180 + 0.177227i
\(430\) 0.332844 0.0160512
\(431\) 1.28640 0.0619637 0.0309819 0.999520i \(-0.490137\pi\)
0.0309819 + 0.999520i \(0.490137\pi\)
\(432\) −4.79660 1.99816i −0.230777 0.0961363i
\(433\) 37.5477i 1.80443i 0.431291 + 0.902213i \(0.358058\pi\)
−0.431291 + 0.902213i \(0.641942\pi\)
\(434\) 3.58624 0.172145
\(435\) 3.82364 + 2.93807i 0.183330 + 0.140870i
\(436\) 3.31710i 0.158860i
\(437\) −14.6149 + 10.8680i −0.699123 + 0.519886i
\(438\) −4.83485 3.71508i −0.231018 0.177513i
\(439\) −14.9511 −0.713576 −0.356788 0.934185i \(-0.616128\pi\)
−0.356788 + 0.934185i \(0.616128\pi\)
\(440\) 2.07465i 0.0989051i
\(441\) −2.58632 9.70442i −0.123158 0.462115i
\(442\) 5.21312i 0.247963i
\(443\) 26.4573i 1.25702i 0.777800 + 0.628512i \(0.216336\pi\)
−0.777800 + 0.628512i \(0.783664\pi\)
\(444\) 2.99935 + 2.30469i 0.142343 + 0.109376i
\(445\) −10.9473 −0.518954
\(446\) 23.3059i 1.10357i
\(447\) −22.4320 + 29.1933i −1.06100 + 1.38080i
\(448\) 1.91110i 0.0902908i
\(449\) 5.06155i 0.238869i 0.992842 + 0.119435i \(0.0381082\pi\)
−0.992842 + 0.119435i \(0.961892\pi\)
\(450\) 2.89882 0.772562i 0.136652 0.0364189i
\(451\) 1.22478i 0.0576725i
\(452\) −16.7721 −0.788893
\(453\) 13.7336 17.8731i 0.645259 0.839749i
\(454\) 27.6254i 1.29652i
\(455\) 2.46203i 0.115422i
\(456\) −4.00776 + 5.21575i −0.187680 + 0.244250i
\(457\) 32.8030i 1.53446i 0.641373 + 0.767229i \(0.278365\pi\)
−0.641373 + 0.767229i \(0.721635\pi\)
\(458\) 24.2738 1.13424
\(459\) 19.4098 + 8.08568i 0.905972 + 0.377407i
\(460\) −2.86177 3.84841i −0.133431 0.179433i
\(461\) 0.398299i 0.0185506i 0.999957 + 0.00927532i \(0.00295247\pi\)
−0.999957 + 0.00927532i \(0.997048\pi\)
\(462\) −4.18422 + 5.44541i −0.194668 + 0.253343i
\(463\) −1.18031 −0.0548535 −0.0274267 0.999624i \(-0.508731\pi\)
−0.0274267 + 0.999624i \(0.508731\pi\)
\(464\) 2.78403i 0.129245i
\(465\) −1.98036 + 2.57727i −0.0918372 + 0.119518i
\(466\) 0.568005 0.0263123
\(467\) −3.01078 −0.139322 −0.0696610 0.997571i \(-0.522192\pi\)
−0.0696610 + 0.997571i \(0.522192\pi\)
\(468\) 0.995276 + 3.73449i 0.0460067 + 0.172627i
\(469\) −12.8630 −0.593956
\(470\) −4.11977 −0.190031
\(471\) 14.3274 + 11.0091i 0.660171 + 0.507272i
\(472\) −2.07202 −0.0953723
\(473\) 0.690535i 0.0317508i
\(474\) 3.57145 4.64793i 0.164042 0.213487i
\(475\) 3.79764i 0.174248i
\(476\) 7.73339i 0.354459i
\(477\) −2.68504 10.0748i −0.122940 0.461296i
\(478\) −1.41185 −0.0645765
\(479\) −42.0364 −1.92069 −0.960347 0.278807i \(-0.910061\pi\)
−0.960347 + 0.278807i \(0.910061\pi\)
\(480\) −1.37342 1.05533i −0.0626877 0.0481690i
\(481\) 2.81342i 0.128281i
\(482\) −0.433010 −0.0197231
\(483\) −0.250201 + 15.8728i −0.0113845 + 0.722236i
\(484\) 6.69583 0.304356
\(485\) 14.3560i 0.651870i
\(486\) −15.4482 2.08662i −0.700743 0.0946509i
\(487\) −19.4738 −0.882440 −0.441220 0.897399i \(-0.645454\pi\)
−0.441220 + 0.897399i \(0.645454\pi\)
\(488\) 3.23836 0.146594
\(489\) −2.85719 + 3.71838i −0.129206 + 0.168151i
\(490\) 3.34771i 0.151234i
\(491\) 32.6143i 1.47186i −0.677056 0.735931i \(-0.736745\pi\)
0.677056 0.735931i \(-0.263255\pi\)
\(492\) −0.810803 0.623017i −0.0365538 0.0280878i
\(493\) 11.2658i 0.507385i
\(494\) 4.89242 0.220120
\(495\) −1.60280 6.01403i −0.0720403 0.270311i
\(496\) 1.87654 0.0842591
\(497\) 17.3870 0.779914
\(498\) 7.80162 + 5.99473i 0.349599 + 0.268630i
\(499\) −6.60178 −0.295536 −0.147768 0.989022i \(-0.547209\pi\)
−0.147768 + 0.989022i \(0.547209\pi\)
\(500\) 1.00000 0.0447214
\(501\) −23.0687 17.7259i −1.03064 0.791935i
\(502\) 22.4064i 1.00005i
\(503\) 14.7686 0.658501 0.329251 0.944243i \(-0.393204\pi\)
0.329251 + 0.944243i \(0.393204\pi\)
\(504\) 1.47644 + 5.53992i 0.0657658 + 0.246768i
\(505\) 6.90670i 0.307344i
\(506\) −7.98410 + 5.93718i −0.354937 + 0.263940i
\(507\) −11.9678 + 15.5750i −0.531508 + 0.691712i
\(508\) 0.980016 0.0434812
\(509\) 29.6739i 1.31527i −0.753336 0.657636i \(-0.771557\pi\)
0.753336 0.657636i \(-0.228443\pi\)
\(510\) 5.55764 + 4.27046i 0.246097 + 0.189099i
\(511\) 6.72764i 0.297613i
\(512\) 1.00000i 0.0441942i
\(513\) −7.58827 + 18.2157i −0.335030 + 0.804245i
\(514\) 20.6632 0.911415
\(515\) 15.1722i 0.668569i
\(516\) −0.457135 0.351260i −0.0201242 0.0154634i
\(517\) 8.54708i 0.375900i
\(518\) 4.17356i 0.183376i
\(519\) −25.4954 19.5905i −1.11912 0.859928i
\(520\) 1.28828i 0.0564948i
\(521\) 20.0886 0.880099 0.440049 0.897974i \(-0.354961\pi\)
0.440049 + 0.897974i \(0.354961\pi\)
\(522\) −2.15084 8.07040i −0.0941395 0.353232i
\(523\) 31.7144i 1.38677i −0.720565 0.693387i \(-0.756117\pi\)
0.720565 0.693387i \(-0.243883\pi\)
\(524\) 9.96859i 0.435480i
\(525\) −2.62474 2.01683i −0.114553 0.0880219i
\(526\) 2.57099i 0.112100i
\(527\) −7.59355 −0.330780
\(528\) −2.18944 + 2.84936i −0.0952831 + 0.124003i
\(529\) −6.62050 + 22.0266i −0.287848 + 0.957676i
\(530\) 3.47550i 0.150966i
\(531\) −6.00640 + 1.60076i −0.260655 + 0.0694671i
\(532\) 7.25765 0.314659
\(533\) 0.760540i 0.0329427i
\(534\) 15.0353 + 11.5530i 0.650641 + 0.499949i
\(535\) −15.9284 −0.688646
\(536\) −6.73067 −0.290721
\(537\) 27.7204 + 21.3002i 1.19622 + 0.919173i
\(538\) −2.88848 −0.124531
\(539\) −6.94534 −0.299157
\(540\) −4.79660 1.99816i −0.206413 0.0859869i
\(541\) −26.2050 −1.12664 −0.563321 0.826238i \(-0.690476\pi\)
−0.563321 + 0.826238i \(0.690476\pi\)
\(542\) 15.1639i 0.651345i
\(543\) 20.0226 + 15.3853i 0.859252 + 0.660245i
\(544\) 4.04657i 0.173495i
\(545\) 3.31710i 0.142089i
\(546\) 2.59825 3.38139i 0.111195 0.144710i
\(547\) 16.0293 0.685363 0.342681 0.939452i \(-0.388665\pi\)
0.342681 + 0.939452i \(0.388665\pi\)
\(548\) −14.3513 −0.613058
\(549\) 9.38743 2.50184i 0.400646 0.106776i
\(550\) 2.07465i 0.0884634i
\(551\) −10.5727 −0.450414
\(552\) −0.130920 + 8.30559i −0.00557233 + 0.353509i
\(553\) −6.46754 −0.275028
\(554\) 3.10829i 0.132059i
\(555\) 2.99935 + 2.30469i 0.127315 + 0.0978285i
\(556\) 4.62609 0.196190
\(557\) −25.4592 −1.07874 −0.539370 0.842069i \(-0.681338\pi\)
−0.539370 + 0.842069i \(0.681338\pi\)
\(558\) 5.43974 1.44974i 0.230283 0.0613725i
\(559\) 0.428796i 0.0181362i
\(560\) 1.91110i 0.0807585i
\(561\) 8.85972 11.5302i 0.374058 0.486804i
\(562\) 12.8651i 0.542681i
\(563\) 14.8803 0.627130 0.313565 0.949567i \(-0.398477\pi\)
0.313565 + 0.949567i \(0.398477\pi\)
\(564\) 5.65817 + 4.34771i 0.238252 + 0.183072i
\(565\) −16.7721 −0.705607
\(566\) 24.2159 1.01787
\(567\) 8.55986 + 14.9186i 0.359480 + 0.626521i
\(568\) 9.09793 0.381741
\(569\) −2.00209 −0.0839320 −0.0419660 0.999119i \(-0.513362\pi\)
−0.0419660 + 0.999119i \(0.513362\pi\)
\(570\) −4.00776 + 5.21575i −0.167866 + 0.218464i
\(571\) 20.4145i 0.854319i 0.904176 + 0.427159i \(0.140486\pi\)
−0.904176 + 0.427159i \(0.859514\pi\)
\(572\) 2.67273 0.111752
\(573\) −6.00702 + 7.81762i −0.250947 + 0.326586i
\(574\) 1.12822i 0.0470911i
\(575\) −2.86177 3.84841i −0.119344 0.160490i
\(576\) 0.772562 + 2.89882i 0.0321901 + 0.120784i
\(577\) −16.5287 −0.688098 −0.344049 0.938952i \(-0.611799\pi\)
−0.344049 + 0.938952i \(0.611799\pi\)
\(578\) 0.625250i 0.0260070i
\(579\) −17.7618 + 23.1154i −0.738155 + 0.960645i
\(580\) 2.78403i 0.115601i
\(581\) 10.8559i 0.450377i
\(582\) −15.1503 + 19.7168i −0.627998 + 0.817286i
\(583\) −7.21045 −0.298626
\(584\) 3.52030i 0.145671i
\(585\) 0.995276 + 3.73449i 0.0411496 + 0.154402i
\(586\) 27.3847i 1.13125i
\(587\) 23.8478i 0.984305i 0.870509 + 0.492153i \(0.163790\pi\)
−0.870509 + 0.492153i \(0.836210\pi\)
\(588\) −3.53294 + 4.59782i −0.145696 + 0.189611i
\(589\) 7.12641i 0.293639i
\(590\) −2.07202 −0.0853035
\(591\) −9.60677 7.38179i −0.395170 0.303646i
\(592\) 2.18386i 0.0897560i
\(593\) 14.2410i 0.584810i 0.956295 + 0.292405i \(0.0944555\pi\)
−0.956295 + 0.292405i \(0.905545\pi\)
\(594\) −4.14547 + 9.95127i −0.170091 + 0.408305i
\(595\) 7.73339i 0.317038i
\(596\) 21.2559 0.870676
\(597\) 6.48258 + 4.98118i 0.265314 + 0.203866i
\(598\) 4.95783 3.68677i 0.202741 0.150763i
\(599\) 30.5083i 1.24653i −0.782009 0.623267i \(-0.785805\pi\)
0.782009 0.623267i \(-0.214195\pi\)
\(600\) −1.37342 1.05533i −0.0560696 0.0430836i
\(601\) −40.3133 −1.64441 −0.822207 0.569189i \(-0.807257\pi\)
−0.822207 + 0.569189i \(0.807257\pi\)
\(602\) 0.636097i 0.0259254i
\(603\) −19.5110 + 5.19986i −0.794549 + 0.211755i
\(604\) −13.0135 −0.529514
\(605\) 6.69583 0.272224
\(606\) −7.28884 + 9.48580i −0.296089 + 0.385334i
\(607\) 15.6385 0.634747 0.317373 0.948301i \(-0.397199\pi\)
0.317373 + 0.948301i \(0.397199\pi\)
\(608\) 3.79764 0.154015
\(609\) −5.61493 + 7.30734i −0.227528 + 0.296109i
\(610\) 3.23836 0.131118
\(611\) 5.30742i 0.214715i
\(612\) −3.12623 11.7303i −0.126370 0.474168i
\(613\) 19.8409i 0.801367i 0.916217 + 0.400684i \(0.131227\pi\)
−0.916217 + 0.400684i \(0.868773\pi\)
\(614\) 27.5618i 1.11230i
\(615\) −0.810803 0.623017i −0.0326947 0.0251225i
\(616\) 3.96485 0.159749
\(617\) −46.2270 −1.86103 −0.930515 0.366255i \(-0.880640\pi\)
−0.930515 + 0.366255i \(0.880640\pi\)
\(618\) 16.0117 20.8378i 0.644085 0.838221i
\(619\) 33.1341i 1.33177i −0.746053 0.665886i \(-0.768054\pi\)
0.746053 0.665886i \(-0.231946\pi\)
\(620\) 1.87654 0.0753636
\(621\) 6.03707 + 24.1775i 0.242259 + 0.970212i
\(622\) −13.2819 −0.532556
\(623\) 20.9214i 0.838199i
\(624\) 1.35956 1.76935i 0.0544259 0.0708306i
\(625\) 1.00000 0.0400000
\(626\) 23.2441 0.929021
\(627\) 10.8209 + 8.31469i 0.432143 + 0.332057i
\(628\) 10.4319i 0.416278i
\(629\) 8.83714i 0.352360i
\(630\) 1.47644 + 5.53992i 0.0588228 + 0.220716i
\(631\) 42.5630i 1.69440i 0.531271 + 0.847202i \(0.321715\pi\)
−0.531271 + 0.847202i \(0.678285\pi\)
\(632\) −3.38420 −0.134616
\(633\) 23.8633 31.0560i 0.948482 1.23437i
\(634\) 17.6217 0.699847
\(635\) 0.980016 0.0388907
\(636\) −3.66780 + 4.77332i −0.145438 + 0.189275i
\(637\) 4.31279 0.170879
\(638\) −5.77589 −0.228670
\(639\) 26.3733 7.02872i 1.04331 0.278052i
\(640\) 1.00000i 0.0395285i
\(641\) 15.4390 0.609803 0.304901 0.952384i \(-0.401376\pi\)
0.304901 + 0.952384i \(0.401376\pi\)
\(642\) 21.8764 + 16.8097i 0.863393 + 0.663427i
\(643\) 4.85712i 0.191546i −0.995403 0.0957730i \(-0.969468\pi\)
0.995403 0.0957730i \(-0.0305323\pi\)
\(644\) 7.35468 5.46912i 0.289815 0.215514i
\(645\) −0.457135 0.351260i −0.0179997 0.0138309i
\(646\) −15.3674 −0.604623
\(647\) 31.5461i 1.24021i 0.784521 + 0.620103i \(0.212909\pi\)
−0.784521 + 0.620103i \(0.787091\pi\)
\(648\) 4.47903 + 7.80630i 0.175953 + 0.306660i
\(649\) 4.29871i 0.168739i
\(650\) 1.28828i 0.0505305i
\(651\) −4.92542 3.78467i −0.193042 0.148333i
\(652\) 2.70739 0.106030
\(653\) 7.16896i 0.280543i −0.990113 0.140272i \(-0.955202\pi\)
0.990113 0.140272i \(-0.0447975\pi\)
\(654\) −3.50063 + 4.55577i −0.136886 + 0.178145i
\(655\) 9.96859i 0.389505i
\(656\) 0.590353i 0.0230494i
\(657\) 2.71965 + 10.2047i 0.106104 + 0.398124i
\(658\) 7.87328i 0.306932i
\(659\) 12.5890 0.490399 0.245199 0.969473i \(-0.421147\pi\)
0.245199 + 0.969473i \(0.421147\pi\)
\(660\) −2.18944 + 2.84936i −0.0852238 + 0.110911i
\(661\) 24.6283i 0.957931i −0.877834 0.478966i \(-0.841012\pi\)
0.877834 0.478966i \(-0.158988\pi\)
\(662\) 20.7361i 0.805930i
\(663\) −5.50155 + 7.15980i −0.213663 + 0.278064i
\(664\) 5.68044i 0.220444i
\(665\) 7.25765 0.281439
\(666\) −1.68716 6.33060i −0.0653763 0.245306i
\(667\) −10.7141 + 7.96727i −0.414851 + 0.308494i
\(668\) 16.7966i 0.649879i
\(669\) −24.5954 + 32.0088i −0.950914 + 1.23753i
\(670\) −6.73067 −0.260029
\(671\) 6.71847i 0.259364i
\(672\) 2.01683 2.62474i 0.0778011 0.101251i
\(673\) −6.41377 −0.247233 −0.123616 0.992330i \(-0.539449\pi\)
−0.123616 + 0.992330i \(0.539449\pi\)
\(674\) −9.08954 −0.350116
\(675\) −4.79660 1.99816i −0.184621 0.0769090i
\(676\) 11.3403 0.436167
\(677\) 8.85737 0.340416 0.170208 0.985408i \(-0.445556\pi\)
0.170208 + 0.985408i \(0.445556\pi\)
\(678\) 23.0351 + 17.7001i 0.884658 + 0.679767i
\(679\) 27.4356 1.05288
\(680\) 4.04657i 0.155179i
\(681\) 29.1538 37.9412i 1.11718 1.45391i
\(682\) 3.89316i 0.149077i
\(683\) 4.92339i 0.188388i −0.995554 0.0941941i \(-0.969973\pi\)
0.995554 0.0941941i \(-0.0300274\pi\)
\(684\) 11.0087 2.93391i 0.420927 0.112181i
\(685\) −14.3513 −0.548335
\(686\) 19.7755 0.755031
\(687\) −33.3381 25.6168i −1.27193 0.977342i
\(688\) 0.332844i 0.0126896i
\(689\) 4.47742 0.170576
\(690\) −0.130920 + 8.30559i −0.00498404 + 0.316188i
\(691\) 48.6905 1.85227 0.926137 0.377187i \(-0.123109\pi\)
0.926137 + 0.377187i \(0.123109\pi\)
\(692\) 18.5634i 0.705676i
\(693\) 11.4934 3.06310i 0.436598 0.116357i
\(694\) 28.2337 1.07174
\(695\) 4.62609 0.175478
\(696\) −2.93807 + 3.82364i −0.111367 + 0.144935i
\(697\) 2.38891i 0.0904863i
\(698\) 9.07266i 0.343405i
\(699\) −0.780109 0.599432i −0.0295064 0.0226726i
\(700\) 1.91110i 0.0722326i
\(701\) 5.73622 0.216654 0.108327 0.994115i \(-0.465451\pi\)
0.108327 + 0.994115i \(0.465451\pi\)
\(702\) 2.57418 6.17936i 0.0971563 0.233225i
\(703\) −8.29350 −0.312795
\(704\) 2.07465 0.0781913
\(705\) 5.65817 + 4.34771i 0.213099 + 0.163744i
\(706\) 1.12881 0.0424834
\(707\) 13.1994 0.496413
\(708\) 2.84575 + 2.18666i 0.106950 + 0.0821796i
\(709\) 28.6828i 1.07720i 0.842560 + 0.538602i \(0.181047\pi\)
−0.842560 + 0.538602i \(0.818953\pi\)
\(710\) 9.09793 0.341439
\(711\) −9.81019 + 2.61451i −0.367911 + 0.0980517i
\(712\) 10.9473i 0.410269i
\(713\) −5.37023 7.22169i −0.201117 0.270454i
\(714\) −8.16127 + 10.6212i −0.305428 + 0.397488i
\(715\) 2.67273 0.0999544
\(716\) 20.1835i 0.754293i
\(717\) 1.93906 + 1.48997i 0.0724156 + 0.0556438i
\(718\) 14.4991i 0.541102i
\(719\) 7.25724i 0.270650i 0.990801 + 0.135325i \(0.0432078\pi\)
−0.990801 + 0.135325i \(0.956792\pi\)
\(720\) 0.772562 + 2.89882i 0.0287917 + 0.108033i
\(721\) −28.9956 −1.07985
\(722\) 4.57796i 0.170374i
\(723\) 0.594704 + 0.456968i 0.0221173 + 0.0169948i
\(724\) 14.5787i 0.541811i
\(725\) 2.78403i 0.103396i
\(726\) −9.19618 7.06630i −0.341302 0.262255i
\(727\) 31.5613i 1.17054i 0.810837 + 0.585272i \(0.199012\pi\)
−0.810837 + 0.585272i \(0.800988\pi\)
\(728\) −2.46203 −0.0912488
\(729\) 19.0148 + 19.1687i 0.704250 + 0.709952i
\(730\) 3.52030i 0.130292i
\(731\) 1.34688i 0.0498161i
\(732\) −4.44763 3.41754i −0.164389 0.126316i
\(733\) 36.4315i 1.34563i 0.739811 + 0.672815i \(0.234915\pi\)
−0.739811 + 0.672815i \(0.765085\pi\)
\(734\) 22.1178 0.816383
\(735\) −3.53294 + 4.59782i −0.130314 + 0.169593i
\(736\) 3.84841 2.86177i 0.141854 0.105486i
\(737\) 13.9638i 0.514363i
\(738\) 0.456085 + 1.71133i 0.0167887 + 0.0629948i
\(739\) 7.94486 0.292257 0.146128 0.989266i \(-0.453319\pi\)
0.146128 + 0.989266i \(0.453319\pi\)
\(740\) 2.18386i 0.0802802i
\(741\) −6.71934 5.16311i −0.246841 0.189672i
\(742\) 6.64202 0.243836
\(743\) −53.0693 −1.94692 −0.973461 0.228851i \(-0.926503\pi\)
−0.973461 + 0.228851i \(0.926503\pi\)
\(744\) −2.57727 1.98036i −0.0944875 0.0726037i
\(745\) 21.2559 0.778757
\(746\) 19.6820 0.720609
\(747\) −4.38849 16.4666i −0.160566 0.602480i
\(748\) −8.39522 −0.306960
\(749\) 30.4408i 1.11228i
\(750\) −1.37342 1.05533i −0.0501502 0.0385352i
\(751\) 1.56981i 0.0572830i 0.999590 + 0.0286415i \(0.00911812\pi\)
−0.999590 + 0.0286415i \(0.990882\pi\)
\(752\) 4.11977i 0.150233i
\(753\) 23.6461 30.7734i 0.861713 1.12144i
\(754\) 3.58661 0.130617
\(755\) −13.0135 −0.473611
\(756\) 3.81867 9.16676i 0.138884 0.333392i
\(757\) 36.3159i 1.31992i −0.751299 0.659962i \(-0.770573\pi\)
0.751299 0.659962i \(-0.229427\pi\)
\(758\) 17.0269 0.618445
\(759\) 17.2312 + 0.271613i 0.625453 + 0.00985894i
\(760\) 3.79764 0.137755
\(761\) 38.7002i 1.40288i 0.712728 + 0.701440i \(0.247459\pi\)
−0.712728 + 0.701440i \(0.752541\pi\)
\(762\) −1.34597 1.03424i −0.0487594 0.0374665i
\(763\) 6.33930 0.229498
\(764\) 5.69209 0.205932
\(765\) −3.12623 11.7303i −0.113029 0.424109i
\(766\) 1.29893i 0.0469322i
\(767\) 2.66934i 0.0963842i
\(768\) 1.05533 1.37342i 0.0380809 0.0495590i
\(769\) 36.0369i 1.29952i 0.760137 + 0.649762i \(0.225132\pi\)
−0.760137 + 0.649762i \(0.774868\pi\)
\(770\) 3.96485 0.142883
\(771\) −28.3792 21.8065i −1.02205 0.785341i
\(772\) 16.8306 0.605746
\(773\) 52.6097 1.89224 0.946119 0.323819i \(-0.104967\pi\)
0.946119 + 0.323819i \(0.104967\pi\)
\(774\) 0.257143 + 0.964855i 0.00924280 + 0.0346810i
\(775\) 1.87654 0.0674072
\(776\) 14.3560 0.515349
\(777\) −4.40448 + 5.73205i −0.158010 + 0.205636i
\(778\) 14.9186i 0.534858i
\(779\) 2.24195 0.0803261
\(780\) 1.35956 1.76935i 0.0486800 0.0633529i
\(781\) 18.8750i 0.675401i
\(782\) −15.5729 + 11.5804i −0.556885 + 0.414113i
\(783\) −5.56292 + 13.3539i −0.198803 + 0.477229i
\(784\) 3.34771 0.119561