Properties

Label 1805.2.b.i.1084.15
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1084.15
Root \(2.31447i\) of defining polynomial
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.i.1084.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.31447i q^{2} +2.90369i q^{3} -3.35679 q^{4} +(1.84346 + 1.26556i) q^{5} -6.72051 q^{6} +2.34671i q^{7} -3.14026i q^{8} -5.43140 q^{9} +O(q^{10})\) \(q+2.31447i q^{2} +2.90369i q^{3} -3.35679 q^{4} +(1.84346 + 1.26556i) q^{5} -6.72051 q^{6} +2.34671i q^{7} -3.14026i q^{8} -5.43140 q^{9} +(-2.92911 + 4.26665i) q^{10} -3.45040 q^{11} -9.74707i q^{12} -3.29131i q^{13} -5.43140 q^{14} +(-3.67479 + 5.35284i) q^{15} +0.554464 q^{16} +1.38276i q^{17} -12.5708i q^{18} +(-6.18812 - 4.24822i) q^{20} -6.81412 q^{21} -7.98585i q^{22} +8.90479i q^{23} +9.11833 q^{24} +(1.79671 + 4.66603i) q^{25} +7.61765 q^{26} -7.06003i q^{27} -7.87742i q^{28} +6.28677 q^{29} +(-12.3890 - 8.50521i) q^{30} +7.39730 q^{31} -4.99722i q^{32} -10.0189i q^{33} -3.20036 q^{34} +(-2.96990 + 4.32608i) q^{35} +18.2321 q^{36} +0.650489i q^{37} +9.55694 q^{39} +(3.97419 - 5.78895i) q^{40} -2.01205 q^{41} -15.7711i q^{42} +1.72022i q^{43} +11.5823 q^{44} +(-10.0126 - 6.87377i) q^{45} -20.6099 q^{46} -6.32206i q^{47} +1.60999i q^{48} +1.49295 q^{49} +(-10.7994 + 4.15845i) q^{50} -4.01510 q^{51} +11.0482i q^{52} +2.12219i q^{53} +16.3403 q^{54} +(-6.36068 - 4.36669i) q^{55} +7.36928 q^{56} +14.5506i q^{58} -6.06907 q^{59} +(12.3355 - 17.9684i) q^{60} +2.96638 q^{61} +17.1209i q^{62} -12.7459i q^{63} +12.6749 q^{64} +(4.16535 - 6.06741i) q^{65} +23.1884 q^{66} -2.46462i q^{67} -4.64164i q^{68} -25.8567 q^{69} +(-10.0126 - 6.87377i) q^{70} +5.69927 q^{71} +17.0560i q^{72} -6.88086i q^{73} -1.50554 q^{74} +(-13.5487 + 5.21709i) q^{75} -8.09708i q^{77} +22.1193i q^{78} +13.8708 q^{79} +(1.02213 + 0.701708i) q^{80} +4.20592 q^{81} -4.65683i q^{82} +1.84546i q^{83} +22.8736 q^{84} +(-1.74997 + 2.54907i) q^{85} -3.98141 q^{86} +18.2548i q^{87} +10.8351i q^{88} +6.47352 q^{89} +(15.9092 - 23.1739i) q^{90} +7.72375 q^{91} -29.8915i q^{92} +21.4795i q^{93} +14.6322 q^{94} +14.5104 q^{96} -7.61563i q^{97} +3.45539i q^{98} +18.7405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} - 16 q^{10} - 22 q^{11} - 6 q^{14} + 10 q^{15} + 8 q^{16} - 14 q^{20} - 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} - 2 q^{29} - 12 q^{30} + 16 q^{31} + 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} + 38 q^{40} + 26 q^{41} + 64 q^{44} - 2 q^{45} + 2 q^{46} + 20 q^{49} - 48 q^{50} - 38 q^{51} + 12 q^{54} - 10 q^{55} + 6 q^{56} - 10 q^{59} - 10 q^{60} - 30 q^{61} + 16 q^{64} - 36 q^{65} + 4 q^{66} - 68 q^{69} - 2 q^{70} - 20 q^{71} + 40 q^{74} - 32 q^{75} - 12 q^{79} + 40 q^{80} - 48 q^{81} + 2 q^{84} - 2 q^{85} - 20 q^{86} + 30 q^{90} - 86 q^{91} + 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.31447i 1.63658i 0.574805 + 0.818290i \(0.305078\pi\)
−0.574805 + 0.818290i \(0.694922\pi\)
\(3\) 2.90369i 1.67644i 0.545328 + 0.838222i \(0.316405\pi\)
−0.545328 + 0.838222i \(0.683595\pi\)
\(4\) −3.35679 −1.67840
\(5\) 1.84346 + 1.26556i 0.824422 + 0.565976i
\(6\) −6.72051 −2.74364
\(7\) 2.34671i 0.886973i 0.896281 + 0.443487i \(0.146259\pi\)
−0.896281 + 0.443487i \(0.853741\pi\)
\(8\) 3.14026i 1.11025i
\(9\) −5.43140 −1.81047
\(10\) −2.92911 + 4.26665i −0.926265 + 1.34923i
\(11\) −3.45040 −1.04033 −0.520167 0.854065i \(-0.674130\pi\)
−0.520167 + 0.854065i \(0.674130\pi\)
\(12\) 9.74707i 2.81374i
\(13\) 3.29131i 0.912845i −0.889763 0.456423i \(-0.849131\pi\)
0.889763 0.456423i \(-0.150869\pi\)
\(14\) −5.43140 −1.45160
\(15\) −3.67479 + 5.35284i −0.948827 + 1.38210i
\(16\) 0.554464 0.138616
\(17\) 1.38276i 0.335369i 0.985841 + 0.167684i \(0.0536289\pi\)
−0.985841 + 0.167684i \(0.946371\pi\)
\(18\) 12.5708i 2.96298i
\(19\) 0 0
\(20\) −6.18812 4.24822i −1.38371 0.949931i
\(21\) −6.81412 −1.48696
\(22\) 7.98585i 1.70259i
\(23\) 8.90479i 1.85678i 0.371610 + 0.928389i \(0.378806\pi\)
−0.371610 + 0.928389i \(0.621194\pi\)
\(24\) 9.11833 1.86127
\(25\) 1.79671 + 4.66603i 0.359343 + 0.933206i
\(26\) 7.61765 1.49394
\(27\) 7.06003i 1.35870i
\(28\) 7.87742i 1.48869i
\(29\) 6.28677 1.16742 0.583712 0.811961i \(-0.301600\pi\)
0.583712 + 0.811961i \(0.301600\pi\)
\(30\) −12.3890 8.50521i −2.26191 1.55283i
\(31\) 7.39730 1.32859 0.664297 0.747468i \(-0.268731\pi\)
0.664297 + 0.747468i \(0.268731\pi\)
\(32\) 4.99722i 0.883393i
\(33\) 10.0189i 1.74406i
\(34\) −3.20036 −0.548858
\(35\) −2.96990 + 4.32608i −0.502006 + 0.731240i
\(36\) 18.2321 3.03868
\(37\) 0.650489i 0.106940i 0.998569 + 0.0534698i \(0.0170281\pi\)
−0.998569 + 0.0534698i \(0.982972\pi\)
\(38\) 0 0
\(39\) 9.55694 1.53033
\(40\) 3.97419 5.78895i 0.628374 0.915313i
\(41\) −2.01205 −0.314229 −0.157115 0.987580i \(-0.550219\pi\)
−0.157115 + 0.987580i \(0.550219\pi\)
\(42\) 15.7711i 2.43353i
\(43\) 1.72022i 0.262332i 0.991360 + 0.131166i \(0.0418720\pi\)
−0.991360 + 0.131166i \(0.958128\pi\)
\(44\) 11.5823 1.74609
\(45\) −10.0126 6.87377i −1.49259 1.02468i
\(46\) −20.6099 −3.03877
\(47\) 6.32206i 0.922167i −0.887357 0.461083i \(-0.847461\pi\)
0.887357 0.461083i \(-0.152539\pi\)
\(48\) 1.60999i 0.232382i
\(49\) 1.49295 0.213278
\(50\) −10.7994 + 4.15845i −1.52727 + 0.588093i
\(51\) −4.01510 −0.562227
\(52\) 11.0482i 1.53212i
\(53\) 2.12219i 0.291505i 0.989321 + 0.145752i \(0.0465603\pi\)
−0.989321 + 0.145752i \(0.953440\pi\)
\(54\) 16.3403 2.22363
\(55\) −6.36068 4.36669i −0.857674 0.588804i
\(56\) 7.36928 0.984761
\(57\) 0 0
\(58\) 14.5506i 1.91058i
\(59\) −6.06907 −0.790126 −0.395063 0.918654i \(-0.629277\pi\)
−0.395063 + 0.918654i \(0.629277\pi\)
\(60\) 12.3355 17.9684i 1.59251 2.31971i
\(61\) 2.96638 0.379805 0.189903 0.981803i \(-0.439183\pi\)
0.189903 + 0.981803i \(0.439183\pi\)
\(62\) 17.1209i 2.17435i
\(63\) 12.7459i 1.60584i
\(64\) 12.6749 1.58436
\(65\) 4.16535 6.06741i 0.516648 0.752569i
\(66\) 23.1884 2.85430
\(67\) 2.46462i 0.301101i −0.988602 0.150551i \(-0.951895\pi\)
0.988602 0.150551i \(-0.0481046\pi\)
\(68\) 4.64164i 0.562881i
\(69\) −25.8567 −3.11279
\(70\) −10.0126 6.87377i −1.19673 0.821572i
\(71\) 5.69927 0.676379 0.338189 0.941078i \(-0.390186\pi\)
0.338189 + 0.941078i \(0.390186\pi\)
\(72\) 17.0560i 2.01007i
\(73\) 6.88086i 0.805344i −0.915344 0.402672i \(-0.868081\pi\)
0.915344 0.402672i \(-0.131919\pi\)
\(74\) −1.50554 −0.175015
\(75\) −13.5487 + 5.21709i −1.56447 + 0.602418i
\(76\) 0 0
\(77\) 8.09708i 0.922748i
\(78\) 22.1193i 2.50452i
\(79\) 13.8708 1.56058 0.780292 0.625415i \(-0.215070\pi\)
0.780292 + 0.625415i \(0.215070\pi\)
\(80\) 1.02213 + 0.701708i 0.114278 + 0.0784533i
\(81\) 4.20592 0.467325
\(82\) 4.65683i 0.514261i
\(83\) 1.84546i 0.202566i 0.994858 + 0.101283i \(0.0322947\pi\)
−0.994858 + 0.101283i \(0.967705\pi\)
\(84\) 22.8736 2.49571
\(85\) −1.74997 + 2.54907i −0.189811 + 0.276485i
\(86\) −3.98141 −0.429327
\(87\) 18.2548i 1.95712i
\(88\) 10.8351i 1.15503i
\(89\) 6.47352 0.686192 0.343096 0.939300i \(-0.388524\pi\)
0.343096 + 0.939300i \(0.388524\pi\)
\(90\) 15.9092 23.1739i 1.67697 2.44274i
\(91\) 7.72375 0.809669
\(92\) 29.8915i 3.11641i
\(93\) 21.4795i 2.22732i
\(94\) 14.6322 1.50920
\(95\) 0 0
\(96\) 14.5104 1.48096
\(97\) 7.61563i 0.773251i −0.922237 0.386625i \(-0.873641\pi\)
0.922237 0.386625i \(-0.126359\pi\)
\(98\) 3.45539i 0.349047i
\(99\) 18.7405 1.88349
\(100\) −6.03119 15.6629i −0.603119 1.56629i
\(101\) −16.5949 −1.65125 −0.825627 0.564216i \(-0.809179\pi\)
−0.825627 + 0.564216i \(0.809179\pi\)
\(102\) 9.29286i 0.920130i
\(103\) 8.09429i 0.797555i 0.917048 + 0.398777i \(0.130565\pi\)
−0.917048 + 0.398777i \(0.869435\pi\)
\(104\) −10.3356 −1.01349
\(105\) −12.5616 8.62368i −1.22588 0.841585i
\(106\) −4.91175 −0.477071
\(107\) 4.57981i 0.442747i 0.975189 + 0.221373i \(0.0710540\pi\)
−0.975189 + 0.221373i \(0.928946\pi\)
\(108\) 23.6991i 2.28044i
\(109\) −10.0829 −0.965762 −0.482881 0.875686i \(-0.660410\pi\)
−0.482881 + 0.875686i \(0.660410\pi\)
\(110\) 10.1066 14.7216i 0.963625 1.40365i
\(111\) −1.88882 −0.179278
\(112\) 1.30117i 0.122949i
\(113\) 15.1432i 1.42455i −0.701900 0.712276i \(-0.747665\pi\)
0.701900 0.712276i \(-0.252335\pi\)
\(114\) 0 0
\(115\) −11.2696 + 16.4157i −1.05089 + 1.53077i
\(116\) −21.1034 −1.95940
\(117\) 17.8764i 1.65268i
\(118\) 14.0467i 1.29310i
\(119\) −3.24494 −0.297463
\(120\) 16.8093 + 11.5398i 1.53447 + 1.05343i
\(121\) 0.905235 0.0822941
\(122\) 6.86560i 0.621582i
\(123\) 5.84236i 0.526788i
\(124\) −24.8312 −2.22991
\(125\) −2.59297 + 10.8755i −0.231922 + 0.972734i
\(126\) 29.5001 2.62808
\(127\) 1.24195i 0.110205i 0.998481 + 0.0551027i \(0.0175486\pi\)
−0.998481 + 0.0551027i \(0.982451\pi\)
\(128\) 19.3412i 1.70954i
\(129\) −4.99499 −0.439784
\(130\) 14.0429 + 9.64060i 1.23164 + 0.845537i
\(131\) −11.7603 −1.02750 −0.513751 0.857939i \(-0.671744\pi\)
−0.513751 + 0.857939i \(0.671744\pi\)
\(132\) 33.6313i 2.92723i
\(133\) 0 0
\(134\) 5.70430 0.492776
\(135\) 8.93490 13.0149i 0.768994 1.12015i
\(136\) 4.34222 0.372343
\(137\) 17.4117i 1.48758i 0.668412 + 0.743792i \(0.266975\pi\)
−0.668412 + 0.743792i \(0.733025\pi\)
\(138\) 59.8448i 5.09432i
\(139\) 10.5771 0.897137 0.448568 0.893748i \(-0.351934\pi\)
0.448568 + 0.893748i \(0.351934\pi\)
\(140\) 9.96935 14.5217i 0.842564 1.22731i
\(141\) 18.3573 1.54596
\(142\) 13.1908i 1.10695i
\(143\) 11.3563i 0.949663i
\(144\) −3.01152 −0.250960
\(145\) 11.5894 + 7.95629i 0.962450 + 0.660734i
\(146\) 15.9256 1.31801
\(147\) 4.33505i 0.357549i
\(148\) 2.18355i 0.179487i
\(149\) −3.63524 −0.297810 −0.148905 0.988852i \(-0.547575\pi\)
−0.148905 + 0.988852i \(0.547575\pi\)
\(150\) −12.0748 31.3581i −0.985905 2.56038i
\(151\) 8.01277 0.652070 0.326035 0.945358i \(-0.394287\pi\)
0.326035 + 0.945358i \(0.394287\pi\)
\(152\) 0 0
\(153\) 7.51033i 0.607174i
\(154\) 18.7405 1.51015
\(155\) 13.6367 + 9.36174i 1.09532 + 0.751953i
\(156\) −32.0806 −2.56851
\(157\) 2.19221i 0.174958i 0.996166 + 0.0874789i \(0.0278810\pi\)
−0.996166 + 0.0874789i \(0.972119\pi\)
\(158\) 32.1036i 2.55402i
\(159\) −6.16217 −0.488692
\(160\) 6.32429 9.21220i 0.499979 0.728288i
\(161\) −20.8970 −1.64691
\(162\) 9.73450i 0.764814i
\(163\) 1.75826i 0.137718i −0.997626 0.0688588i \(-0.978064\pi\)
0.997626 0.0688588i \(-0.0219358\pi\)
\(164\) 6.75402 0.527401
\(165\) 12.6795 18.4694i 0.987097 1.43784i
\(166\) −4.27128 −0.331515
\(167\) 3.62416i 0.280446i 0.990120 + 0.140223i \(0.0447819\pi\)
−0.990120 + 0.140223i \(0.955218\pi\)
\(168\) 21.3981i 1.65090i
\(169\) 2.16728 0.166714
\(170\) −5.89975 4.05025i −0.452490 0.310640i
\(171\) 0 0
\(172\) 5.77443i 0.440296i
\(173\) 1.49717i 0.113828i −0.998379 0.0569140i \(-0.981874\pi\)
0.998379 0.0569140i \(-0.0181261\pi\)
\(174\) −42.2503 −3.20299
\(175\) −10.9498 + 4.21637i −0.827729 + 0.318727i
\(176\) −1.91312 −0.144207
\(177\) 17.6227i 1.32460i
\(178\) 14.9828i 1.12301i
\(179\) −12.9371 −0.966963 −0.483481 0.875355i \(-0.660628\pi\)
−0.483481 + 0.875355i \(0.660628\pi\)
\(180\) 33.6102 + 23.0738i 2.50515 + 1.71982i
\(181\) −10.0013 −0.743390 −0.371695 0.928355i \(-0.621223\pi\)
−0.371695 + 0.928355i \(0.621223\pi\)
\(182\) 17.8764i 1.32509i
\(183\) 8.61343i 0.636723i
\(184\) 27.9633 2.06149
\(185\) −0.823233 + 1.19915i −0.0605253 + 0.0881634i
\(186\) −49.7137 −3.64518
\(187\) 4.77107i 0.348895i
\(188\) 21.2218i 1.54776i
\(189\) 16.5679 1.20513
\(190\) 0 0
\(191\) −24.3534 −1.76215 −0.881077 0.472973i \(-0.843181\pi\)
−0.881077 + 0.472973i \(0.843181\pi\)
\(192\) 36.8039i 2.65609i
\(193\) 6.49316i 0.467388i −0.972310 0.233694i \(-0.924919\pi\)
0.972310 0.233694i \(-0.0750813\pi\)
\(194\) 17.6262 1.26549
\(195\) 17.6179 + 12.0949i 1.26164 + 0.866132i
\(196\) −5.01151 −0.357965
\(197\) 2.13662i 0.152228i −0.997099 0.0761138i \(-0.975749\pi\)
0.997099 0.0761138i \(-0.0242512\pi\)
\(198\) 43.3744i 3.08248i
\(199\) 17.6660 1.25231 0.626156 0.779697i \(-0.284627\pi\)
0.626156 + 0.779697i \(0.284627\pi\)
\(200\) 14.6525 5.64214i 1.03609 0.398960i
\(201\) 7.15648 0.504779
\(202\) 38.4085i 2.70241i
\(203\) 14.7532i 1.03547i
\(204\) 13.4779 0.943639
\(205\) −3.70914 2.54637i −0.259057 0.177846i
\(206\) −18.7340 −1.30526
\(207\) 48.3655i 3.36164i
\(208\) 1.82491i 0.126535i
\(209\) 0 0
\(210\) 19.9593 29.0734i 1.37732 2.00626i
\(211\) 18.9939 1.30759 0.653796 0.756671i \(-0.273175\pi\)
0.653796 + 0.756671i \(0.273175\pi\)
\(212\) 7.12374i 0.489261i
\(213\) 16.5489i 1.13391i
\(214\) −10.5999 −0.724591
\(215\) −2.17705 + 3.17117i −0.148473 + 0.216272i
\(216\) −22.1703 −1.50850
\(217\) 17.3593i 1.17843i
\(218\) 23.3365i 1.58055i
\(219\) 19.9799 1.35012
\(220\) 21.3515 + 14.6581i 1.43952 + 0.988246i
\(221\) 4.55109 0.306140
\(222\) 4.37161i 0.293404i
\(223\) 20.2503i 1.35606i 0.735035 + 0.678029i \(0.237166\pi\)
−0.735035 + 0.678029i \(0.762834\pi\)
\(224\) 11.7270 0.783546
\(225\) −9.75867 25.3431i −0.650578 1.68954i
\(226\) 35.0485 2.33139
\(227\) 15.8466i 1.05177i 0.850554 + 0.525887i \(0.176266\pi\)
−0.850554 + 0.525887i \(0.823734\pi\)
\(228\) 0 0
\(229\) −9.87340 −0.652453 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(230\) −37.9936 26.0831i −2.50522 1.71987i
\(231\) 23.5114 1.54694
\(232\) 19.7421i 1.29613i
\(233\) 3.74263i 0.245188i 0.992457 + 0.122594i \(0.0391213\pi\)
−0.992457 + 0.122594i \(0.960879\pi\)
\(234\) −41.3745 −2.70474
\(235\) 8.00095 11.6545i 0.521924 0.760254i
\(236\) 20.3726 1.32614
\(237\) 40.2764i 2.61623i
\(238\) 7.51033i 0.486822i
\(239\) 21.2541 1.37482 0.687408 0.726272i \(-0.258749\pi\)
0.687408 + 0.726272i \(0.258749\pi\)
\(240\) −2.03754 + 2.96796i −0.131523 + 0.191581i
\(241\) −27.7142 −1.78523 −0.892613 0.450824i \(-0.851130\pi\)
−0.892613 + 0.450824i \(0.851130\pi\)
\(242\) 2.09514i 0.134681i
\(243\) 8.96741i 0.575260i
\(244\) −9.95750 −0.637464
\(245\) 2.75219 + 1.88942i 0.175831 + 0.120710i
\(246\) 13.5220 0.862130
\(247\) 0 0
\(248\) 23.2294i 1.47507i
\(249\) −5.35865 −0.339591
\(250\) −25.1711 6.00136i −1.59196 0.379559i
\(251\) −17.0524 −1.07634 −0.538168 0.842838i \(-0.680883\pi\)
−0.538168 + 0.842838i \(0.680883\pi\)
\(252\) 42.7854i 2.69523i
\(253\) 30.7251i 1.93167i
\(254\) −2.87446 −0.180360
\(255\) −7.40170 5.08136i −0.463512 0.318207i
\(256\) −19.4150 −1.21344
\(257\) 8.87646i 0.553699i −0.960913 0.276849i \(-0.910710\pi\)
0.960913 0.276849i \(-0.0892903\pi\)
\(258\) 11.5608i 0.719743i
\(259\) −1.52651 −0.0948526
\(260\) −13.9822 + 20.3670i −0.867140 + 1.26311i
\(261\) −34.1460 −2.11358
\(262\) 27.2189i 1.68159i
\(263\) 28.6398i 1.76600i 0.469370 + 0.883002i \(0.344481\pi\)
−0.469370 + 0.883002i \(0.655519\pi\)
\(264\) −31.4618 −1.93634
\(265\) −2.68576 + 3.91218i −0.164985 + 0.240323i
\(266\) 0 0
\(267\) 18.7971i 1.15036i
\(268\) 8.27321i 0.505367i
\(269\) 29.2060 1.78072 0.890362 0.455254i \(-0.150451\pi\)
0.890362 + 0.455254i \(0.150451\pi\)
\(270\) 30.1227 + 20.6796i 1.83321 + 1.25852i
\(271\) −13.1166 −0.796779 −0.398390 0.917216i \(-0.630431\pi\)
−0.398390 + 0.917216i \(0.630431\pi\)
\(272\) 0.766691i 0.0464875i
\(273\) 22.4274i 1.35737i
\(274\) −40.2990 −2.43455
\(275\) −6.19937 16.0996i −0.373836 0.970845i
\(276\) 86.7957 5.22449
\(277\) 6.23517i 0.374635i 0.982299 + 0.187317i \(0.0599793\pi\)
−0.982299 + 0.187317i \(0.940021\pi\)
\(278\) 24.4804i 1.46824i
\(279\) −40.1777 −2.40538
\(280\) 13.5850 + 9.32627i 0.811859 + 0.557351i
\(281\) −16.8127 −1.00296 −0.501480 0.865169i \(-0.667211\pi\)
−0.501480 + 0.865169i \(0.667211\pi\)
\(282\) 42.4875i 2.53009i
\(283\) 15.7304i 0.935076i −0.883973 0.467538i \(-0.845141\pi\)
0.883973 0.467538i \(-0.154859\pi\)
\(284\) −19.1312 −1.13523
\(285\) 0 0
\(286\) −26.2839 −1.55420
\(287\) 4.72169i 0.278713i
\(288\) 27.1419i 1.59935i
\(289\) 15.0880 0.887528
\(290\) −18.4146 + 26.8234i −1.08134 + 1.57513i
\(291\) 22.1134 1.29631
\(292\) 23.0976i 1.35169i
\(293\) 18.3605i 1.07263i −0.844016 0.536317i \(-0.819815\pi\)
0.844016 0.536317i \(-0.180185\pi\)
\(294\) −10.0334 −0.585158
\(295\) −11.1881 7.68078i −0.651397 0.447192i
\(296\) 2.04270 0.118730
\(297\) 24.3599i 1.41351i
\(298\) 8.41366i 0.487390i
\(299\) 29.3084 1.69495
\(300\) 45.4801 17.5127i 2.62580 1.01110i
\(301\) −4.03687 −0.232681
\(302\) 18.5454i 1.06717i
\(303\) 48.1864i 2.76824i
\(304\) 0 0
\(305\) 5.46840 + 3.75413i 0.313120 + 0.214961i
\(306\) 17.3825 0.993689
\(307\) 21.4942i 1.22674i −0.789796 0.613370i \(-0.789814\pi\)
0.789796 0.613370i \(-0.210186\pi\)
\(308\) 27.1802i 1.54874i
\(309\) −23.5033 −1.33706
\(310\) −21.6675 + 31.5617i −1.23063 + 1.79258i
\(311\) −31.3890 −1.77990 −0.889952 0.456054i \(-0.849262\pi\)
−0.889952 + 0.456054i \(0.849262\pi\)
\(312\) 30.0112i 1.69905i
\(313\) 21.6308i 1.22264i −0.791382 0.611321i \(-0.790638\pi\)
0.791382 0.611321i \(-0.209362\pi\)
\(314\) −5.07382 −0.286332
\(315\) 16.1307 23.4967i 0.908865 1.32389i
\(316\) −46.5613 −2.61928
\(317\) 26.0643i 1.46392i 0.681348 + 0.731959i \(0.261394\pi\)
−0.681348 + 0.731959i \(0.738606\pi\)
\(318\) 14.2622i 0.799784i
\(319\) −21.6918 −1.21451
\(320\) 23.3657 + 16.0408i 1.30618 + 0.896709i
\(321\) −13.2983 −0.742241
\(322\) 48.3655i 2.69530i
\(323\) 0 0
\(324\) −14.1184 −0.784356
\(325\) 15.3573 5.91354i 0.851872 0.328024i
\(326\) 4.06945 0.225386
\(327\) 29.2775i 1.61905i
\(328\) 6.31835i 0.348872i
\(329\) 14.8360 0.817937
\(330\) 42.7470 + 29.3464i 2.35315 + 1.61546i
\(331\) 1.38704 0.0762389 0.0381194 0.999273i \(-0.487863\pi\)
0.0381194 + 0.999273i \(0.487863\pi\)
\(332\) 6.19484i 0.339986i
\(333\) 3.53306i 0.193611i
\(334\) −8.38802 −0.458972
\(335\) 3.11912 4.54343i 0.170416 0.248234i
\(336\) −3.77818 −0.206117
\(337\) 18.9728i 1.03352i −0.856131 0.516758i \(-0.827139\pi\)
0.856131 0.516758i \(-0.172861\pi\)
\(338\) 5.01611i 0.272840i
\(339\) 43.9711 2.38818
\(340\) 5.87427 8.55669i 0.318577 0.464052i
\(341\) −25.5236 −1.38218
\(342\) 0 0
\(343\) 19.9305i 1.07615i
\(344\) 5.40195 0.291253
\(345\) −47.6659 32.7233i −2.56625 1.76176i
\(346\) 3.46517 0.186289
\(347\) 26.6474i 1.43051i −0.698865 0.715254i \(-0.746311\pi\)
0.698865 0.715254i \(-0.253689\pi\)
\(348\) 61.2776i 3.28482i
\(349\) 10.7692 0.576460 0.288230 0.957561i \(-0.406933\pi\)
0.288230 + 0.957561i \(0.406933\pi\)
\(350\) −9.75867 25.3431i −0.521623 1.35464i
\(351\) −23.2368 −1.24029
\(352\) 17.2424i 0.919023i
\(353\) 3.45433i 0.183856i −0.995766 0.0919278i \(-0.970697\pi\)
0.995766 0.0919278i \(-0.0293029\pi\)
\(354\) 40.7873 2.16782
\(355\) 10.5064 + 7.21277i 0.557621 + 0.382814i
\(356\) −21.7302 −1.15170
\(357\) 9.42229i 0.498680i
\(358\) 29.9425i 1.58251i
\(359\) 28.0316 1.47945 0.739725 0.672909i \(-0.234956\pi\)
0.739725 + 0.672909i \(0.234956\pi\)
\(360\) −21.5854 + 31.4421i −1.13765 + 1.65714i
\(361\) 0 0
\(362\) 23.1477i 1.21662i
\(363\) 2.62852i 0.137961i
\(364\) −25.9270 −1.35895
\(365\) 8.70815 12.6846i 0.455805 0.663943i
\(366\) −19.9356 −1.04205
\(367\) 0.122068i 0.00637192i −0.999995 0.00318596i \(-0.998986\pi\)
0.999995 0.00318596i \(-0.00101412\pi\)
\(368\) 4.93739i 0.257379i
\(369\) 10.9282 0.568901
\(370\) −2.77541 1.90535i −0.144286 0.0990545i
\(371\) −4.98016 −0.258557
\(372\) 72.1021i 3.73832i
\(373\) 32.4779i 1.68164i −0.541315 0.840820i \(-0.682073\pi\)
0.541315 0.840820i \(-0.317927\pi\)
\(374\) 11.0425 0.570995
\(375\) −31.5791 7.52917i −1.63074 0.388805i
\(376\) −19.8529 −1.02383
\(377\) 20.6917i 1.06568i
\(378\) 38.3459i 1.97230i
\(379\) −32.8185 −1.68578 −0.842888 0.538090i \(-0.819146\pi\)
−0.842888 + 0.538090i \(0.819146\pi\)
\(380\) 0 0
\(381\) −3.60624 −0.184753
\(382\) 56.3654i 2.88391i
\(383\) 23.5078i 1.20119i 0.799553 + 0.600596i \(0.205070\pi\)
−0.799553 + 0.600596i \(0.794930\pi\)
\(384\) −56.1609 −2.86595
\(385\) 10.2473 14.9267i 0.522253 0.760734i
\(386\) 15.0282 0.764918
\(387\) 9.34322i 0.474943i
\(388\) 25.5641i 1.29782i
\(389\) 32.8332 1.66471 0.832354 0.554244i \(-0.186993\pi\)
0.832354 + 0.554244i \(0.186993\pi\)
\(390\) −27.9933 + 40.7761i −1.41750 + 2.06478i
\(391\) −12.3132 −0.622705
\(392\) 4.68824i 0.236792i
\(393\) 34.1482i 1.72255i
\(394\) 4.94515 0.249133
\(395\) 25.5703 + 17.5543i 1.28658 + 0.883253i
\(396\) −62.9079 −3.16124
\(397\) 35.3737i 1.77535i 0.460467 + 0.887677i \(0.347682\pi\)
−0.460467 + 0.887677i \(0.652318\pi\)
\(398\) 40.8876i 2.04951i
\(399\) 0 0
\(400\) 0.996213 + 2.58715i 0.0498106 + 0.129357i
\(401\) 3.00886 0.150255 0.0751276 0.997174i \(-0.476064\pi\)
0.0751276 + 0.997174i \(0.476064\pi\)
\(402\) 16.5635i 0.826112i
\(403\) 24.3468i 1.21280i
\(404\) 55.7056 2.77146
\(405\) 7.75346 + 5.32285i 0.385273 + 0.264494i
\(406\) −34.1460 −1.69464
\(407\) 2.24444i 0.111253i
\(408\) 12.6085i 0.624212i
\(409\) −12.0147 −0.594087 −0.297043 0.954864i \(-0.596001\pi\)
−0.297043 + 0.954864i \(0.596001\pi\)
\(410\) 5.89350 8.58470i 0.291059 0.423968i
\(411\) −50.5582 −2.49385
\(412\) 27.1709i 1.33861i
\(413\) 14.2424i 0.700821i
\(414\) 111.941 5.50159
\(415\) −2.33555 + 3.40204i −0.114647 + 0.167000i
\(416\) −16.4474 −0.806401
\(417\) 30.7126i 1.50400i
\(418\) 0 0
\(419\) 10.0485 0.490900 0.245450 0.969409i \(-0.421064\pi\)
0.245450 + 0.969409i \(0.421064\pi\)
\(420\) 42.1666 + 28.9479i 2.05752 + 1.41251i
\(421\) −24.4034 −1.18935 −0.594675 0.803966i \(-0.702719\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(422\) 43.9608i 2.13998i
\(423\) 34.3376i 1.66955i
\(424\) 6.66422 0.323643
\(425\) −6.45200 + 2.48442i −0.312968 + 0.120512i
\(426\) −38.3020 −1.85574
\(427\) 6.96123i 0.336877i
\(428\) 15.3735i 0.743104i
\(429\) −32.9752 −1.59206
\(430\) −7.33959 5.03872i −0.353946 0.242989i
\(431\) 7.90872 0.380950 0.190475 0.981692i \(-0.438997\pi\)
0.190475 + 0.981692i \(0.438997\pi\)
\(432\) 3.91453i 0.188338i
\(433\) 1.34464i 0.0646191i −0.999478 0.0323095i \(-0.989714\pi\)
0.999478 0.0323095i \(-0.0102862\pi\)
\(434\) −40.1777 −1.92859
\(435\) −23.1026 + 33.6521i −1.10768 + 1.61349i
\(436\) 33.8460 1.62093
\(437\) 0 0
\(438\) 46.2429i 2.20957i
\(439\) 11.3408 0.541268 0.270634 0.962682i \(-0.412767\pi\)
0.270634 + 0.962682i \(0.412767\pi\)
\(440\) −13.7125 + 19.9742i −0.653719 + 0.952231i
\(441\) −8.10880 −0.386133
\(442\) 10.5334i 0.501022i
\(443\) 14.0383i 0.666978i −0.942754 0.333489i \(-0.891774\pi\)
0.942754 0.333489i \(-0.108226\pi\)
\(444\) 6.34036 0.300900
\(445\) 11.9337 + 8.19263i 0.565711 + 0.388368i
\(446\) −46.8687 −2.21930
\(447\) 10.5556i 0.499262i
\(448\) 29.7443i 1.40528i
\(449\) 3.88724 0.183450 0.0917252 0.995784i \(-0.470762\pi\)
0.0917252 + 0.995784i \(0.470762\pi\)
\(450\) 58.6559 22.5862i 2.76507 1.06472i
\(451\) 6.94236 0.326903
\(452\) 50.8325i 2.39096i
\(453\) 23.2666i 1.09316i
\(454\) −36.6765 −1.72131
\(455\) 14.2385 + 9.77488i 0.667509 + 0.458253i
\(456\) 0 0
\(457\) 31.0487i 1.45240i −0.687486 0.726198i \(-0.741286\pi\)
0.687486 0.726198i \(-0.258714\pi\)
\(458\) 22.8517i 1.06779i
\(459\) 9.76233 0.455667
\(460\) 37.8295 55.1039i 1.76381 2.56923i
\(461\) 31.2148 1.45382 0.726909 0.686734i \(-0.240956\pi\)
0.726909 + 0.686734i \(0.240956\pi\)
\(462\) 54.4165i 2.53169i
\(463\) 29.2480i 1.35927i 0.733551 + 0.679634i \(0.237861\pi\)
−0.733551 + 0.679634i \(0.762139\pi\)
\(464\) 3.48579 0.161824
\(465\) −27.1836 + 39.5966i −1.26061 + 1.83625i
\(466\) −8.66223 −0.401270
\(467\) 12.5589i 0.581155i 0.956851 + 0.290578i \(0.0938474\pi\)
−0.956851 + 0.290578i \(0.906153\pi\)
\(468\) 60.0074i 2.77384i
\(469\) 5.78375 0.267069
\(470\) 26.9740 + 18.5180i 1.24422 + 0.854171i
\(471\) −6.36551 −0.293307
\(472\) 19.0585i 0.877237i
\(473\) 5.93545i 0.272912i
\(474\) −93.2187 −4.28168
\(475\) 0 0
\(476\) 10.8926 0.499261
\(477\) 11.5265i 0.527760i
\(478\) 49.1921i 2.25000i
\(479\) −8.84075 −0.403944 −0.201972 0.979391i \(-0.564735\pi\)
−0.201972 + 0.979391i \(0.564735\pi\)
\(480\) 26.7493 + 18.3638i 1.22093 + 0.838187i
\(481\) 2.14096 0.0976193
\(482\) 64.1437i 2.92167i
\(483\) 60.6783i 2.76096i
\(484\) −3.03868 −0.138122
\(485\) 9.63805 14.0391i 0.437641 0.637485i
\(486\) 20.7548 0.941459
\(487\) 7.47254i 0.338613i 0.985563 + 0.169307i \(0.0541528\pi\)
−0.985563 + 0.169307i \(0.945847\pi\)
\(488\) 9.31518i 0.421679i
\(489\) 5.10544 0.230876
\(490\) −4.37300 + 6.36988i −0.197552 + 0.287762i
\(491\) 22.1507 0.999647 0.499823 0.866127i \(-0.333398\pi\)
0.499823 + 0.866127i \(0.333398\pi\)
\(492\) 19.6116i 0.884158i
\(493\) 8.69310i 0.391517i
\(494\) 0 0
\(495\) 34.5474 + 23.7172i 1.55279 + 1.06601i
\(496\) 4.10154 0.184165
\(497\) 13.3745i 0.599930i
\(498\) 12.4025i 0.555767i
\(499\) 3.30154 0.147797 0.0738985 0.997266i \(-0.476456\pi\)
0.0738985 + 0.997266i \(0.476456\pi\)
\(500\) 8.70405 36.5068i 0.389257 1.63263i
\(501\) −10.5234 −0.470152
\(502\) 39.4673i 1.76151i
\(503\) 21.3453i 0.951739i −0.879516 0.475870i \(-0.842133\pi\)
0.879516 0.475870i \(-0.157867\pi\)
\(504\) −40.0255 −1.78288
\(505\) −30.5921 21.0019i −1.36133 0.934570i
\(506\) 71.1124 3.16133
\(507\) 6.29310i 0.279486i
\(508\) 4.16897i 0.184968i
\(509\) 9.88579 0.438180 0.219090 0.975705i \(-0.429691\pi\)
0.219090 + 0.975705i \(0.429691\pi\)
\(510\) 11.7607 17.1310i 0.520771 0.758575i
\(511\) 16.1474 0.714319
\(512\) 6.25310i 0.276351i
\(513\) 0 0
\(514\) 20.5443 0.906172
\(515\) −10.2438 + 14.9215i −0.451397 + 0.657521i
\(516\) 16.7671 0.738132
\(517\) 21.8136i 0.959361i
\(518\) 3.53306i 0.155234i
\(519\) 4.34732 0.190826
\(520\) −19.0532 13.0803i −0.835539 0.573608i
\(521\) 26.6149 1.16602 0.583009 0.812465i \(-0.301875\pi\)
0.583009 + 0.812465i \(0.301875\pi\)
\(522\) 79.0300i 3.45905i
\(523\) 11.4971i 0.502732i 0.967892 + 0.251366i \(0.0808797\pi\)
−0.967892 + 0.251366i \(0.919120\pi\)
\(524\) 39.4769 1.72455
\(525\) −12.2430 31.7949i −0.534329 1.38764i
\(526\) −66.2860 −2.89021
\(527\) 10.2287i 0.445569i
\(528\) 5.55511i 0.241755i
\(529\) −56.2953 −2.44762
\(530\) −9.05463 6.21612i −0.393308 0.270011i
\(531\) 32.9636 1.43050
\(532\) 0 0
\(533\) 6.62227i 0.286842i
\(534\) −43.5053 −1.88266
\(535\) −5.79603 + 8.44271i −0.250584 + 0.365010i
\(536\) −7.73954 −0.334297
\(537\) 37.5652i 1.62106i
\(538\) 67.5966i 2.91430i
\(539\) −5.15126 −0.221881
\(540\) −29.9926 + 43.6883i −1.29068 + 1.88005i
\(541\) 11.5115 0.494919 0.247460 0.968898i \(-0.420404\pi\)
0.247460 + 0.968898i \(0.420404\pi\)
\(542\) 30.3581i 1.30399i
\(543\) 29.0406i 1.24625i
\(544\) 6.90996 0.296262
\(545\) −18.5874 12.7605i −0.796195 0.546598i
\(546\) −51.9076 −2.22144
\(547\) 37.0866i 1.58571i −0.609412 0.792854i \(-0.708594\pi\)
0.609412 0.792854i \(-0.291406\pi\)
\(548\) 58.4475i 2.49675i
\(549\) −16.1116 −0.687625
\(550\) 37.2622 14.3483i 1.58887 0.611813i
\(551\) 0 0
\(552\) 81.1968i 3.45597i
\(553\) 32.5507i 1.38420i
\(554\) −14.4311 −0.613120
\(555\) −3.48196 2.39041i −0.147801 0.101467i
\(556\) −35.5051 −1.50575
\(557\) 32.6114i 1.38179i 0.722955 + 0.690895i \(0.242783\pi\)
−0.722955 + 0.690895i \(0.757217\pi\)
\(558\) 92.9903i 3.93659i
\(559\) 5.66179 0.239468
\(560\) −1.64671 + 2.39865i −0.0695860 + 0.101362i
\(561\) 13.8537 0.584904
\(562\) 38.9125i 1.64143i
\(563\) 39.3465i 1.65826i 0.559059 + 0.829128i \(0.311162\pi\)
−0.559059 + 0.829128i \(0.688838\pi\)
\(564\) −61.6216 −2.59474
\(565\) 19.1646 27.9159i 0.806262 1.17443i
\(566\) 36.4076 1.53033
\(567\) 9.87008i 0.414505i
\(568\) 17.8972i 0.750949i
\(569\) −2.56181 −0.107397 −0.0536983 0.998557i \(-0.517101\pi\)
−0.0536983 + 0.998557i \(0.517101\pi\)
\(570\) 0 0
\(571\) 39.2894 1.64421 0.822105 0.569337i \(-0.192800\pi\)
0.822105 + 0.569337i \(0.192800\pi\)
\(572\) 38.1208i 1.59391i
\(573\) 70.7148i 2.95415i
\(574\) 10.9282 0.456136
\(575\) −41.5500 + 15.9994i −1.73276 + 0.667219i
\(576\) −68.8423 −2.86843
\(577\) 41.0561i 1.70919i 0.519297 + 0.854594i \(0.326194\pi\)
−0.519297 + 0.854594i \(0.673806\pi\)
\(578\) 34.9207i 1.45251i
\(579\) 18.8541 0.783550
\(580\) −38.9033 26.7076i −1.61537 1.10897i
\(581\) −4.33077 −0.179671
\(582\) 51.1809i 2.12152i
\(583\) 7.32239i 0.303262i
\(584\) −21.6077 −0.894133
\(585\) −22.6237 + 32.9545i −0.935375 + 1.36250i
\(586\) 42.4950 1.75545
\(587\) 10.7634i 0.444252i −0.975018 0.222126i \(-0.928700\pi\)
0.975018 0.222126i \(-0.0712997\pi\)
\(588\) 14.5519i 0.600109i
\(589\) 0 0
\(590\) 17.7770 25.8946i 0.731866 1.06606i
\(591\) 6.20407 0.255201
\(592\) 0.360673i 0.0148235i
\(593\) 7.83424i 0.321714i −0.986978 0.160857i \(-0.948574\pi\)
0.986978 0.160857i \(-0.0514257\pi\)
\(594\) −56.3804 −2.31332
\(595\) −5.98193 4.10667i −0.245235 0.168357i
\(596\) 12.2027 0.499843
\(597\) 51.2967i 2.09943i
\(598\) 67.8336i 2.77392i
\(599\) 29.7590 1.21592 0.607960 0.793968i \(-0.291988\pi\)
0.607960 + 0.793968i \(0.291988\pi\)
\(600\) 16.3830 + 42.5464i 0.668834 + 1.73695i
\(601\) 5.85799 0.238952 0.119476 0.992837i \(-0.461878\pi\)
0.119476 + 0.992837i \(0.461878\pi\)
\(602\) 9.34322i 0.380801i
\(603\) 13.3863i 0.545134i
\(604\) −26.8972 −1.09443
\(605\) 1.66877 + 1.14563i 0.0678450 + 0.0465765i
\(606\) 111.526 4.53044
\(607\) 4.74137i 0.192446i −0.995360 0.0962231i \(-0.969324\pi\)
0.995360 0.0962231i \(-0.0306762\pi\)
\(608\) 0 0
\(609\) −42.8388 −1.73591
\(610\) −8.68883 + 12.6565i −0.351801 + 0.512446i
\(611\) −20.8079 −0.841796
\(612\) 25.2106i 1.01908i
\(613\) 0.275200i 0.0111152i 0.999985 + 0.00555761i \(0.00176905\pi\)
−0.999985 + 0.00555761i \(0.998231\pi\)
\(614\) 49.7478 2.00766
\(615\) 7.39386 10.7702i 0.298149 0.434295i
\(616\) −25.4269 −1.02448
\(617\) 14.4721i 0.582626i −0.956628 0.291313i \(-0.905908\pi\)
0.956628 0.291313i \(-0.0940922\pi\)
\(618\) 54.3978i 2.18820i
\(619\) −22.3695 −0.899108 −0.449554 0.893253i \(-0.648417\pi\)
−0.449554 + 0.893253i \(0.648417\pi\)
\(620\) −45.7754 31.4254i −1.83838 1.26207i
\(621\) 62.8681 2.52281
\(622\) 72.6489i 2.91296i
\(623\) 15.1915i 0.608634i
\(624\) 5.29898 0.212129
\(625\) −18.5436 + 16.7670i −0.741746 + 0.670681i
\(626\) 50.0638 2.00095
\(627\) 0 0
\(628\) 7.35881i 0.293648i
\(629\) −0.899470 −0.0358642
\(630\) 54.3824 + 37.3342i 2.16665 + 1.48743i
\(631\) −0.112343 −0.00447232 −0.00223616 0.999997i \(-0.500712\pi\)
−0.00223616 + 0.999997i \(0.500712\pi\)
\(632\) 43.5578i 1.73264i
\(633\) 55.1523i 2.19211i
\(634\) −60.3252 −2.39582
\(635\) −1.57176 + 2.28949i −0.0623736 + 0.0908557i
\(636\) 20.6851 0.820218
\(637\) 4.91375i 0.194690i
\(638\) 50.2052i 1.98764i
\(639\) −30.9550 −1.22456
\(640\) −24.4775 + 35.6548i −0.967558 + 1.40938i
\(641\) 26.8374 1.06001 0.530006 0.847994i \(-0.322190\pi\)
0.530006 + 0.847994i \(0.322190\pi\)
\(642\) 30.7787i 1.21474i
\(643\) 3.66175i 0.144405i −0.997390 0.0722027i \(-0.976997\pi\)
0.997390 0.0722027i \(-0.0230028\pi\)
\(644\) 70.1468 2.76417
\(645\) −9.20808 6.32146i −0.362568 0.248907i
\(646\) 0 0
\(647\) 29.3983i 1.15577i 0.816120 + 0.577883i \(0.196121\pi\)
−0.816120 + 0.577883i \(0.803879\pi\)
\(648\) 13.2077i 0.518847i
\(649\) 20.9407 0.821995
\(650\) 13.6867 + 35.5442i 0.536838 + 1.39416i
\(651\) −50.4061 −1.97557
\(652\) 5.90211i 0.231144i
\(653\) 20.3618i 0.796819i 0.917208 + 0.398409i \(0.130438\pi\)
−0.917208 + 0.398409i \(0.869562\pi\)
\(654\) 67.7619 2.64970
\(655\) −21.6797 14.8834i −0.847095 0.581541i
\(656\) −1.11561 −0.0435572
\(657\) 37.3727i 1.45805i
\(658\) 34.3376i 1.33862i
\(659\) −25.7612 −1.00352 −0.501758 0.865008i \(-0.667313\pi\)
−0.501758 + 0.865008i \(0.667313\pi\)
\(660\) −42.5624 + 61.9980i −1.65674 + 2.41327i
\(661\) −9.09527 −0.353765 −0.176883 0.984232i \(-0.556601\pi\)
−0.176883 + 0.984232i \(0.556601\pi\)
\(662\) 3.21028i 0.124771i
\(663\) 13.2150i 0.513226i
\(664\) 5.79523 0.224899
\(665\) 0 0
\(666\) 8.17719 0.316860
\(667\) 55.9824i 2.16765i
\(668\) 12.1655i 0.470699i
\(669\) −58.8004 −2.27336
\(670\) 10.5157 + 7.21913i 0.406255 + 0.278899i
\(671\) −10.2352 −0.395124
\(672\) 34.0517i 1.31357i
\(673\) 8.00415i 0.308537i 0.988029 + 0.154269i \(0.0493021\pi\)
−0.988029 + 0.154269i \(0.950698\pi\)
\(674\) 43.9121 1.69143
\(675\) 32.9423 12.6848i 1.26795 0.488240i
\(676\) −7.27510 −0.279812
\(677\) 1.04002i 0.0399712i −0.999800 0.0199856i \(-0.993638\pi\)
0.999800 0.0199856i \(-0.00636204\pi\)
\(678\) 101.770i 3.90845i
\(679\) 17.8717 0.685853
\(680\) 8.00473 + 5.49535i 0.306967 + 0.210737i
\(681\) −46.0135 −1.76324
\(682\) 59.0738i 2.26205i
\(683\) 31.1559i 1.19215i 0.802930 + 0.596073i \(0.203273\pi\)
−0.802930 + 0.596073i \(0.796727\pi\)
\(684\) 0 0
\(685\) −22.0356 + 32.0979i −0.841936 + 1.22640i
\(686\) −46.1286 −1.76120
\(687\) 28.6693i 1.09380i
\(688\) 0.953802i 0.0363634i
\(689\) 6.98478 0.266099
\(690\) 75.7372 110.322i 2.88326 4.19987i
\(691\) 23.1659 0.881272 0.440636 0.897686i \(-0.354753\pi\)
0.440636 + 0.897686i \(0.354753\pi\)
\(692\) 5.02570i 0.191048i
\(693\) 43.9785i 1.67061i
\(694\) 61.6747 2.34114
\(695\) 19.4985 + 13.3859i 0.739619 + 0.507758i
\(696\) 57.3248 2.17289
\(697\) 2.78218i 0.105383i
\(698\) 24.9250i 0.943423i
\(699\) −10.8674 −0.411044
\(700\) 36.7563 14.1535i 1.38926 0.534950i
\(701\) 10.2358 0.386601 0.193300 0.981140i \(-0.438081\pi\)
0.193300 + 0.981140i \(0.438081\pi\)
\(702\) 53.7809i 2.02983i
\(703\) 0 0
\(704\) −43.7333 −1.64826
\(705\) 33.8410 + 23.2323i 1.27452 + 0.874977i
\(706\) 7.99497 0.300895
\(707\) 38.9434i 1.46462i
\(708\) 59.1557i 2.22321i
\(709\) −24.3417 −0.914171 −0.457085 0.889423i \(-0.651107\pi\)
−0.457085 + 0.889423i \(0.651107\pi\)
\(710\) −16.6938 + 24.3168i −0.626506 + 0.912592i
\(711\) −75.3378 −2.82539
\(712\) 20.3285i 0.761843i
\(713\) 65.8715i 2.46691i
\(714\) 21.8076 0.816131
\(715\) −14.3721 + 20.9350i −0.537487 + 0.782923i
\(716\) 43.4271 1.62295
\(717\) 61.7154i 2.30480i
\(718\) 64.8784i 2.42124i
\(719\) 22.3900 0.835007 0.417504 0.908675i \(-0.362905\pi\)
0.417504 + 0.908675i \(0.362905\pi\)
\(720\) −5.55162 3.81126i −0.206897 0.142037i
\(721\) −18.9950 −0.707410
\(722\) 0 0
\(723\) 80.4732i 2.99283i
\(724\) 33.5723 1.24770
\(725\) 11.2955 + 29.3342i 0.419505 + 1.08945i
\(726\) −6.08364 −0.225785
\(727\) 6.53528i 0.242380i −0.992629 0.121190i \(-0.961329\pi\)
0.992629 0.121190i \(-0.0386710\pi\)
\(728\) 24.2546i 0.898934i
\(729\) 38.6563 1.43172
\(730\) 29.3582 + 20.1548i 1.08660 + 0.745962i
\(731\) −2.37866 −0.0879778
\(732\) 28.9135i 1.06867i
\(733\) 10.5576i 0.389954i 0.980808 + 0.194977i \(0.0624632\pi\)
−0.980808 + 0.194977i \(0.937537\pi\)
\(734\) 0.282524 0.0104282
\(735\) −5.48627 + 7.99151i −0.202364 + 0.294771i
\(736\) 44.4992 1.64026
\(737\) 8.50391i 0.313246i
\(738\) 25.2931i 0.931053i
\(739\) −9.05935 −0.333254 −0.166627 0.986020i \(-0.553288\pi\)
−0.166627 + 0.986020i \(0.553288\pi\)
\(740\) 2.76342 4.02530i 0.101585 0.147973i
\(741\) 0 0
\(742\) 11.5265i 0.423150i
\(743\) 10.6892i 0.392147i −0.980589 0.196074i \(-0.937181\pi\)
0.980589 0.196074i \(-0.0628192\pi\)
\(744\) 67.4510 2.47288
\(745\) −6.70142 4.60061i −0.245521 0.168553i
\(746\) 75.1692 2.75214
\(747\) 10.0235i 0.366739i
\(748\) 16.0155i 0.585584i
\(749\) −10.7475 −0.392705
\(750\) 17.4261 73.0889i 0.636310 2.66883i
\(751\) 50.9596 1.85954 0.929772 0.368136i \(-0.120004\pi\)
0.929772 + 0.368136i \(0.120004\pi\)
\(752\) 3.50535i 0.127827i
\(753\) 49.5147i 1.80442i
\(754\) 47.8904 1.74407
\(755\) 14.7713 + 10.1406i 0.537581 + 0.369056i
\(756\) −55.6148 −2.02269
\(757\) 48.7783i 1.77288i 0.462847 + 0.886438i \(0.346828\pi\)
−0.462847 + 0.886438i \(0.653172\pi\)
\(758\) 75.9577i 2.75891i
\(759\) 89.2160 3.23834
\(760\) 0 0
\(761\) 30.3424 1.09991 0.549956 0.835193i \(-0.314644\pi\)
0.549956 + 0.835193i \(0.314644\pi\)
\(762\) 8.34654i 0.302363i
\(763\) 23.6615i 0.856605i
\(764\) 81.7494 2.95759
\(765\) 9.50478 13.8450i 0.343646 0.500567i
\(766\) −54.4082 −1.96585
\(767\) 19.9752i 0.721263i
\(768\) 56.3751i 2.03426i
\(769\) −13.4786 −0.486052 −0.243026 0.970020i \(-0.578140\pi\)
−0.243026 + 0.970020i \(0.578140\pi\)
\(770\) 34.5474 + 23.7172i 1.24500 + 0.854709i
\(771\) 25.7745 0.928245
\(772\) 21.7962i 0.784461i
\(773\) 16.3898i 0.589500i 0.955574 + 0.294750i \(0.0952364\pi\)
−0.955574 + 0.294750i \(0.904764\pi\)
\(774\) 21.6247 0.777282
\(775\) 13.2908 + 34.5160i 0.477421 + 1.23985i
\(776\) −23.9151 −0.858501
\(777\) 4.43250i 0.159015i
\(778\) 75.9915i 2.72443i
\(779\) 0 0
\(780\) −59.1395 40.6000i −2.11753 1.45371i
\(781\) −19.6647 −0.703659
\(782\) 28.4986i 1.01911i
\(783\) 44.3848i 1.58618i
\(784\) 0.827786 0.0295638
\(785\) −2.77438 + 4.04127i −0.0990219 + 0.144239i
\(786\) 79.0352 2.81909
\(787\) 13.6646i 0.487090i 0.969890 + 0.243545i \(0.0783103\pi\)
−0.969890 + 0.243545i \(0.921690\pi\)