Properties

Label 570.2.m.b.37.9
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.9
Root \(-0.922947 + 0.922947i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.b.493.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.42113 - 1.72638i) q^{5} -1.00000 q^{6} +(3.40461 + 3.40461i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.42113 - 1.72638i) q^{5} -1.00000 q^{6} +(3.40461 + 3.40461i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-0.215841 - 2.22563i) q^{10} +3.94163 q^{11} +(-0.707107 + 0.707107i) q^{12} +(4.03748 + 4.03748i) q^{13} +4.81484 q^{14} +(-2.22563 + 0.215841i) q^{15} -1.00000 q^{16} +(-3.90683 - 3.90683i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-3.49740 + 2.60158i) q^{19} +(-1.72638 - 1.42113i) q^{20} -4.81484i q^{21} +(2.78715 - 2.78715i) q^{22} +(0.537022 - 0.537022i) q^{23} +1.00000i q^{24} +(-0.960761 - 4.90683i) q^{25} +5.70985 q^{26} +(0.707107 - 0.707107i) q^{27} +(3.40461 - 3.40461i) q^{28} -6.28455 q^{29} +(-1.42113 + 1.72638i) q^{30} -7.00112i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.78715 - 2.78715i) q^{33} -5.52509 q^{34} +(10.7160 - 1.03924i) q^{35} +1.00000 q^{36} +(1.05593 - 1.05593i) q^{37} +(-0.633437 + 4.31263i) q^{38} -5.70985i q^{39} +(-2.22563 + 0.215841i) q^{40} +3.03704i q^{41} +(-3.40461 - 3.40461i) q^{42} +(-5.70094 + 5.70094i) q^{43} -3.94163i q^{44} +(1.72638 + 1.42113i) q^{45} -0.759463i q^{46} +(-2.04815 - 2.04815i) q^{47} +(0.707107 + 0.707107i) q^{48} +16.1827i q^{49} +(-4.14901 - 2.79029i) q^{50} +5.52509i q^{51} +(4.03748 - 4.03748i) q^{52} +(-4.39576 - 4.39576i) q^{53} -1.00000i q^{54} +(5.60158 - 6.80474i) q^{55} -4.81484i q^{56} +(4.31263 + 0.633437i) q^{57} +(-4.44385 + 4.44385i) q^{58} +2.32680 q^{59} +(0.215841 + 2.22563i) q^{60} -9.32341 q^{61} +(-4.95054 - 4.95054i) q^{62} +(-3.40461 + 3.40461i) q^{63} +1.00000i q^{64} +(12.7080 - 1.23242i) q^{65} -3.94163 q^{66} +(7.35838 - 7.35838i) q^{67} +(-3.90683 + 3.90683i) q^{68} -0.759463 q^{69} +(6.84253 - 8.31224i) q^{70} +9.62969i q^{71} +(0.707107 - 0.707107i) q^{72} +(4.47808 - 4.47808i) q^{73} -1.49331i q^{74} +(-2.79029 + 4.14901i) q^{75} +(2.60158 + 3.49740i) q^{76} +(13.4197 + 13.4197i) q^{77} +(-4.03748 - 4.03748i) q^{78} -0.991285 q^{79} +(-1.42113 + 1.72638i) q^{80} -1.00000 q^{81} +(2.14751 + 2.14751i) q^{82} +(6.64529 - 6.64529i) q^{83} -4.81484 q^{84} +(-12.2968 + 1.19254i) q^{85} +8.06235i q^{86} +(4.44385 + 4.44385i) q^{87} +(-2.78715 - 2.78715i) q^{88} -7.09242 q^{89} +(2.22563 - 0.215841i) q^{90} +27.4920i q^{91} +(-0.537022 - 0.537022i) q^{92} +(-4.95054 + 4.95054i) q^{93} -2.89652 q^{94} +(-0.478953 + 9.73502i) q^{95} +1.00000 q^{96} +(-7.11482 + 7.11482i) q^{97} +(11.4429 + 11.4429i) q^{98} +3.94163i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.42113 1.72638i 0.635550 0.772060i
\(6\) −1.00000 −0.408248
\(7\) 3.40461 + 3.40461i 1.28682 + 1.28682i 0.936707 + 0.350114i \(0.113857\pi\)
0.350114 + 0.936707i \(0.386143\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −0.215841 2.22563i −0.0682548 0.703805i
\(11\) 3.94163 1.18845 0.594223 0.804300i \(-0.297460\pi\)
0.594223 + 0.804300i \(0.297460\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 4.03748 + 4.03748i 1.11979 + 1.11979i 0.991771 + 0.128023i \(0.0408632\pi\)
0.128023 + 0.991771i \(0.459137\pi\)
\(14\) 4.81484 1.28682
\(15\) −2.22563 + 0.215841i −0.574654 + 0.0557298i
\(16\) −1.00000 −0.250000
\(17\) −3.90683 3.90683i −0.947544 0.947544i 0.0511467 0.998691i \(-0.483712\pi\)
−0.998691 + 0.0511467i \(0.983712\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) −3.49740 + 2.60158i −0.802358 + 0.596844i
\(20\) −1.72638 1.42113i −0.386030 0.317775i
\(21\) 4.81484i 1.05068i
\(22\) 2.78715 2.78715i 0.594223 0.594223i
\(23\) 0.537022 0.537022i 0.111977 0.111977i −0.648898 0.760875i \(-0.724770\pi\)
0.760875 + 0.648898i \(0.224770\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −0.960761 4.90683i −0.192152 0.981365i
\(26\) 5.70985 1.11979
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 3.40461 3.40461i 0.643411 0.643411i
\(29\) −6.28455 −1.16701 −0.583506 0.812109i \(-0.698319\pi\)
−0.583506 + 0.812109i \(0.698319\pi\)
\(30\) −1.42113 + 1.72638i −0.259462 + 0.315192i
\(31\) 7.00112i 1.25744i −0.777633 0.628719i \(-0.783580\pi\)
0.777633 0.628719i \(-0.216420\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −2.78715 2.78715i −0.485181 0.485181i
\(34\) −5.52509 −0.947544
\(35\) 10.7160 1.03924i 1.81134 0.175663i
\(36\) 1.00000 0.166667
\(37\) 1.05593 1.05593i 0.173594 0.173594i −0.614963 0.788556i \(-0.710829\pi\)
0.788556 + 0.614963i \(0.210829\pi\)
\(38\) −0.633437 + 4.31263i −0.102757 + 0.699601i
\(39\) 5.70985i 0.914308i
\(40\) −2.22563 + 0.215841i −0.351902 + 0.0341274i
\(41\) 3.03704i 0.474306i 0.971472 + 0.237153i \(0.0762142\pi\)
−0.971472 + 0.237153i \(0.923786\pi\)
\(42\) −3.40461 3.40461i −0.525342 0.525342i
\(43\) −5.70094 + 5.70094i −0.869386 + 0.869386i −0.992404 0.123018i \(-0.960743\pi\)
0.123018 + 0.992404i \(0.460743\pi\)
\(44\) 3.94163i 0.594223i
\(45\) 1.72638 + 1.42113i 0.257353 + 0.211850i
\(46\) 0.759463i 0.111977i
\(47\) −2.04815 2.04815i −0.298753 0.298753i 0.541772 0.840525i \(-0.317754\pi\)
−0.840525 + 0.541772i \(0.817754\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 16.1827i 2.31182i
\(50\) −4.14901 2.79029i −0.586759 0.394606i
\(51\) 5.52509i 0.773667i
\(52\) 4.03748 4.03748i 0.559897 0.559897i
\(53\) −4.39576 4.39576i −0.603804 0.603804i 0.337516 0.941320i \(-0.390413\pi\)
−0.941320 + 0.337516i \(0.890413\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 5.60158 6.80474i 0.755317 0.917551i
\(56\) 4.81484i 0.643411i
\(57\) 4.31263 + 0.633437i 0.571221 + 0.0839007i
\(58\) −4.44385 + 4.44385i −0.583506 + 0.583506i
\(59\) 2.32680 0.302923 0.151462 0.988463i \(-0.451602\pi\)
0.151462 + 0.988463i \(0.451602\pi\)
\(60\) 0.215841 + 2.22563i 0.0278649 + 0.287327i
\(61\) −9.32341 −1.19374 −0.596870 0.802338i \(-0.703589\pi\)
−0.596870 + 0.802338i \(0.703589\pi\)
\(62\) −4.95054 4.95054i −0.628719 0.628719i
\(63\) −3.40461 + 3.40461i −0.428940 + 0.428940i
\(64\) 1.00000i 0.125000i
\(65\) 12.7080 1.23242i 1.57623 0.152863i
\(66\) −3.94163 −0.485181
\(67\) 7.35838 7.35838i 0.898969 0.898969i −0.0963756 0.995345i \(-0.530725\pi\)
0.995345 + 0.0963756i \(0.0307250\pi\)
\(68\) −3.90683 + 3.90683i −0.473772 + 0.473772i
\(69\) −0.759463 −0.0914286
\(70\) 6.84253 8.31224i 0.817839 0.993503i
\(71\) 9.62969i 1.14283i 0.820660 + 0.571417i \(0.193606\pi\)
−0.820660 + 0.571417i \(0.806394\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) 4.47808 4.47808i 0.524119 0.524119i −0.394694 0.918813i \(-0.629149\pi\)
0.918813 + 0.394694i \(0.129149\pi\)
\(74\) 1.49331i 0.173594i
\(75\) −2.79029 + 4.14901i −0.322195 + 0.479086i
\(76\) 2.60158 + 3.49740i 0.298422 + 0.401179i
\(77\) 13.4197 + 13.4197i 1.52932 + 1.52932i
\(78\) −4.03748 4.03748i −0.457154 0.457154i
\(79\) −0.991285 −0.111528 −0.0557642 0.998444i \(-0.517759\pi\)
−0.0557642 + 0.998444i \(0.517759\pi\)
\(80\) −1.42113 + 1.72638i −0.158888 + 0.193015i
\(81\) −1.00000 −0.111111
\(82\) 2.14751 + 2.14751i 0.237153 + 0.237153i
\(83\) 6.64529 6.64529i 0.729416 0.729416i −0.241088 0.970503i \(-0.577504\pi\)
0.970503 + 0.241088i \(0.0775041\pi\)
\(84\) −4.81484 −0.525342
\(85\) −12.2968 + 1.19254i −1.33377 + 0.129349i
\(86\) 8.06235i 0.869386i
\(87\) 4.44385 + 4.44385i 0.476430 + 0.476430i
\(88\) −2.78715 2.78715i −0.297112 0.297112i
\(89\) −7.09242 −0.751795 −0.375897 0.926661i \(-0.622666\pi\)
−0.375897 + 0.926661i \(0.622666\pi\)
\(90\) 2.22563 0.215841i 0.234602 0.0227516i
\(91\) 27.4920i 2.88195i
\(92\) −0.537022 0.537022i −0.0559884 0.0559884i
\(93\) −4.95054 + 4.95054i −0.513347 + 0.513347i
\(94\) −2.89652 −0.298753
\(95\) −0.478953 + 9.73502i −0.0491396 + 0.998792i
\(96\) 1.00000 0.102062
\(97\) −7.11482 + 7.11482i −0.722401 + 0.722401i −0.969094 0.246693i \(-0.920656\pi\)
0.246693 + 0.969094i \(0.420656\pi\)
\(98\) 11.4429 + 11.4429i 1.15591 + 1.15591i
\(99\) 3.94163i 0.396149i
\(100\) −4.90683 + 0.960761i −0.490683 + 0.0960761i
\(101\) −8.97139 −0.892686 −0.446343 0.894862i \(-0.647274\pi\)
−0.446343 + 0.894862i \(0.647274\pi\)
\(102\) 3.90683 + 3.90683i 0.386833 + 0.386833i
\(103\) 0.231982 + 0.231982i 0.0228578 + 0.0228578i 0.718443 0.695585i \(-0.244855\pi\)
−0.695585 + 0.718443i \(0.744855\pi\)
\(104\) 5.70985i 0.559897i
\(105\) −8.31224 6.84253i −0.811191 0.667763i
\(106\) −6.21654 −0.603804
\(107\) 11.8222 11.8222i 1.14290 1.14290i 0.154981 0.987917i \(-0.450468\pi\)
0.987917 0.154981i \(-0.0495316\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −11.4774 −1.09934 −0.549670 0.835382i \(-0.685246\pi\)
−0.549670 + 0.835382i \(0.685246\pi\)
\(110\) −0.850764 8.77260i −0.0811172 0.836434i
\(111\) −1.49331 −0.141739
\(112\) −3.40461 3.40461i −0.321705 0.321705i
\(113\) 11.2993 + 11.2993i 1.06294 + 1.06294i 0.997881 + 0.0650630i \(0.0207248\pi\)
0.0650630 + 0.997881i \(0.479275\pi\)
\(114\) 3.49740 2.60158i 0.327561 0.243660i
\(115\) −0.163923 1.69028i −0.0152859 0.157620i
\(116\) 6.28455i 0.583506i
\(117\) −4.03748 + 4.03748i −0.373265 + 0.373265i
\(118\) 1.64529 1.64529i 0.151462 0.151462i
\(119\) 26.6024i 2.43864i
\(120\) 1.72638 + 1.42113i 0.157596 + 0.129731i
\(121\) 4.53645 0.412404
\(122\) −6.59265 + 6.59265i −0.596870 + 0.596870i
\(123\) 2.14751 2.14751i 0.193635 0.193635i
\(124\) −7.00112 −0.628719
\(125\) −9.83640 5.31462i −0.879795 0.475354i
\(126\) 4.81484i 0.428940i
\(127\) 2.01606 2.01606i 0.178896 0.178896i −0.611978 0.790875i \(-0.709626\pi\)
0.790875 + 0.611978i \(0.209626\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 8.06235 0.709851
\(130\) 8.11446 9.85736i 0.711685 0.864548i
\(131\) −10.6608 −0.931438 −0.465719 0.884933i \(-0.654204\pi\)
−0.465719 + 0.884933i \(0.654204\pi\)
\(132\) −2.78715 + 2.78715i −0.242591 + 0.242591i
\(133\) −20.7646 3.04990i −1.80052 0.264460i
\(134\) 10.4063i 0.898969i
\(135\) −0.215841 2.22563i −0.0185766 0.191551i
\(136\) 5.52509i 0.473772i
\(137\) 1.03924 + 1.03924i 0.0887882 + 0.0887882i 0.750106 0.661318i \(-0.230002\pi\)
−0.661318 + 0.750106i \(0.730002\pi\)
\(138\) −0.537022 + 0.537022i −0.0457143 + 0.0457143i
\(139\) 8.61936i 0.731084i 0.930795 + 0.365542i \(0.119116\pi\)
−0.930795 + 0.365542i \(0.880884\pi\)
\(140\) −1.03924 10.7160i −0.0878317 0.905671i
\(141\) 2.89652i 0.243931i
\(142\) 6.80922 + 6.80922i 0.571417 + 0.571417i
\(143\) 15.9142 + 15.9142i 1.33082 + 1.33082i
\(144\) 1.00000i 0.0833333i
\(145\) −8.93118 + 10.8495i −0.741694 + 0.901002i
\(146\) 6.33296i 0.524119i
\(147\) 11.4429 11.4429i 0.943795 0.943795i
\(148\) −1.05593 1.05593i −0.0867968 0.0867968i
\(149\) 4.87509i 0.399383i 0.979859 + 0.199691i \(0.0639940\pi\)
−0.979859 + 0.199691i \(0.936006\pi\)
\(150\) 0.960761 + 4.90683i 0.0784458 + 0.400641i
\(151\) 10.0048i 0.814177i 0.913389 + 0.407089i \(0.133456\pi\)
−0.913389 + 0.407089i \(0.866544\pi\)
\(152\) 4.31263 + 0.633437i 0.349800 + 0.0513785i
\(153\) 3.90683 3.90683i 0.315848 0.315848i
\(154\) 18.9783 1.52932
\(155\) −12.0866 9.94952i −0.970817 0.799165i
\(156\) −5.70985 −0.457154
\(157\) −7.71934 7.71934i −0.616070 0.616070i 0.328451 0.944521i \(-0.393473\pi\)
−0.944521 + 0.328451i \(0.893473\pi\)
\(158\) −0.700945 + 0.700945i −0.0557642 + 0.0557642i
\(159\) 6.21654i 0.493004i
\(160\) 0.215841 + 2.22563i 0.0170637 + 0.175951i
\(161\) 3.65670 0.288188
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −2.46610 + 2.46610i −0.193160 + 0.193160i −0.797060 0.603900i \(-0.793613\pi\)
0.603900 + 0.797060i \(0.293613\pi\)
\(164\) 3.03704 0.237153
\(165\) −8.77260 + 0.850764i −0.682946 + 0.0662319i
\(166\) 9.39786i 0.729416i
\(167\) 12.6049 12.6049i 0.975397 0.975397i −0.0243076 0.999705i \(-0.507738\pi\)
0.999705 + 0.0243076i \(0.00773810\pi\)
\(168\) −3.40461 + 3.40461i −0.262671 + 0.262671i
\(169\) 19.6024i 1.50788i
\(170\) −7.85188 + 9.53839i −0.602212 + 0.731561i
\(171\) −2.60158 3.49740i −0.198948 0.267453i
\(172\) 5.70094 + 5.70094i 0.434693 + 0.434693i
\(173\) 10.8629 + 10.8629i 0.825892 + 0.825892i 0.986946 0.161054i \(-0.0514893\pi\)
−0.161054 + 0.986946i \(0.551489\pi\)
\(174\) 6.28455 0.476430
\(175\) 13.4348 19.9768i 1.01558 1.51011i
\(176\) −3.94163 −0.297112
\(177\) −1.64529 1.64529i −0.123668 0.123668i
\(178\) −5.01510 + 5.01510i −0.375897 + 0.375897i
\(179\) 12.4563 0.931024 0.465512 0.885042i \(-0.345870\pi\)
0.465512 + 0.885042i \(0.345870\pi\)
\(180\) 1.42113 1.72638i 0.105925 0.128677i
\(181\) 11.5778i 0.860572i 0.902693 + 0.430286i \(0.141587\pi\)
−0.902693 + 0.430286i \(0.858413\pi\)
\(182\) 19.4398 + 19.4398i 1.44097 + 1.44097i
\(183\) 6.59265 + 6.59265i 0.487343 + 0.487343i
\(184\) −0.759463 −0.0559884
\(185\) −0.322317 3.32355i −0.0236972 0.244352i
\(186\) 7.00112i 0.513347i
\(187\) −15.3993 15.3993i −1.12611 1.12611i
\(188\) −2.04815 + 2.04815i −0.149377 + 0.149377i
\(189\) 4.81484 0.350228
\(190\) 6.54503 + 7.22237i 0.474826 + 0.523966i
\(191\) 7.59311 0.549418 0.274709 0.961527i \(-0.411418\pi\)
0.274709 + 0.961527i \(0.411418\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 9.61547 + 9.61547i 0.692137 + 0.692137i 0.962702 0.270565i \(-0.0872105\pi\)
−0.270565 + 0.962702i \(0.587211\pi\)
\(194\) 10.0619i 0.722401i
\(195\) −9.85736 8.11446i −0.705901 0.581089i
\(196\) 16.1827 1.15591
\(197\) −9.66171 9.66171i −0.688368 0.688368i 0.273503 0.961871i \(-0.411818\pi\)
−0.961871 + 0.273503i \(0.911818\pi\)
\(198\) 2.78715 + 2.78715i 0.198074 + 0.198074i
\(199\) 23.6158i 1.67408i −0.547142 0.837040i \(-0.684284\pi\)
0.547142 0.837040i \(-0.315716\pi\)
\(200\) −2.79029 + 4.14901i −0.197303 + 0.293379i
\(201\) −10.4063 −0.734005
\(202\) −6.34373 + 6.34373i −0.446343 + 0.446343i
\(203\) −21.3964 21.3964i −1.50173 1.50173i
\(204\) 5.52509 0.386833
\(205\) 5.24308 + 4.31604i 0.366192 + 0.301445i
\(206\) 0.328072 0.0228578
\(207\) 0.537022 + 0.537022i 0.0373256 + 0.0373256i
\(208\) −4.03748 4.03748i −0.279949 0.279949i
\(209\) −13.7854 + 10.2545i −0.953559 + 0.709316i
\(210\) −10.7160 + 1.03924i −0.739477 + 0.0717143i
\(211\) 16.4846i 1.13485i −0.823427 0.567423i \(-0.807941\pi\)
0.823427 0.567423i \(-0.192059\pi\)
\(212\) −4.39576 + 4.39576i −0.301902 + 0.301902i
\(213\) 6.80922 6.80922i 0.466560 0.466560i
\(214\) 16.7192i 1.14290i
\(215\) 1.74018 + 17.9438i 0.118680 + 1.22376i
\(216\) −1.00000 −0.0680414
\(217\) 23.8361 23.8361i 1.61810 1.61810i
\(218\) −8.11578 + 8.11578i −0.549670 + 0.549670i
\(219\) −6.33296 −0.427942
\(220\) −6.80474 5.60158i −0.458776 0.377659i
\(221\) 31.5474i 2.12211i
\(222\) −1.05593 + 1.05593i −0.0708693 + 0.0708693i
\(223\) 4.91506 + 4.91506i 0.329137 + 0.329137i 0.852258 0.523122i \(-0.175233\pi\)
−0.523122 + 0.852258i \(0.675233\pi\)
\(224\) −4.81484 −0.321705
\(225\) 4.90683 0.960761i 0.327122 0.0640507i
\(226\) 15.9796 1.06294
\(227\) −13.9125 + 13.9125i −0.923408 + 0.923408i −0.997269 0.0738603i \(-0.976468\pi\)
0.0738603 + 0.997269i \(0.476468\pi\)
\(228\) 0.633437 4.31263i 0.0419504 0.285611i
\(229\) 16.4303i 1.08574i −0.839816 0.542872i \(-0.817337\pi\)
0.839816 0.542872i \(-0.182663\pi\)
\(230\) −1.31112 1.07930i −0.0864527 0.0711668i
\(231\) 18.9783i 1.24868i
\(232\) 4.44385 + 4.44385i 0.291753 + 0.291753i
\(233\) 0.870707 0.870707i 0.0570419 0.0570419i −0.678010 0.735052i \(-0.737158\pi\)
0.735052 + 0.678010i \(0.237158\pi\)
\(234\) 5.70985i 0.373265i
\(235\) −6.44657 + 0.625186i −0.420528 + 0.0407827i
\(236\) 2.32680i 0.151462i
\(237\) 0.700945 + 0.700945i 0.0455312 + 0.0455312i
\(238\) −18.8108 18.8108i −1.21932 1.21932i
\(239\) 8.48625i 0.548930i 0.961597 + 0.274465i \(0.0885007\pi\)
−0.961597 + 0.274465i \(0.911499\pi\)
\(240\) 2.22563 0.215841i 0.143664 0.0139325i
\(241\) 2.53645i 0.163387i 0.996657 + 0.0816937i \(0.0260329\pi\)
−0.996657 + 0.0816937i \(0.973967\pi\)
\(242\) 3.20775 3.20775i 0.206202 0.206202i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 9.32341i 0.596870i
\(245\) 27.9375 + 22.9978i 1.78486 + 1.46928i
\(246\) 3.03704i 0.193635i
\(247\) −24.6245 3.61683i −1.56682 0.230133i
\(248\) −4.95054 + 4.95054i −0.314360 + 0.314360i
\(249\) −9.39786 −0.595565
\(250\) −10.7134 + 3.19739i −0.677574 + 0.202221i
\(251\) −15.7046 −0.991268 −0.495634 0.868531i \(-0.665064\pi\)
−0.495634 + 0.868531i \(0.665064\pi\)
\(252\) 3.40461 + 3.40461i 0.214470 + 0.214470i
\(253\) 2.11674 2.11674i 0.133078 0.133078i
\(254\) 2.85114i 0.178896i
\(255\) 9.53839 + 7.85188i 0.597317 + 0.491704i
\(256\) 1.00000 0.0625000
\(257\) −9.53833 + 9.53833i −0.594985 + 0.594985i −0.938974 0.343989i \(-0.888222\pi\)
0.343989 + 0.938974i \(0.388222\pi\)
\(258\) 5.70094 5.70094i 0.354925 0.354925i
\(259\) 7.19005 0.446768
\(260\) −1.23242 12.7080i −0.0764313 0.788117i
\(261\) 6.28455i 0.389004i
\(262\) −7.53832 + 7.53832i −0.465719 + 0.465719i
\(263\) −1.34136 + 1.34136i −0.0827120 + 0.0827120i −0.747252 0.664540i \(-0.768627\pi\)
0.664540 + 0.747252i \(0.268627\pi\)
\(264\) 3.94163i 0.242591i
\(265\) −13.8357 + 1.34178i −0.849921 + 0.0824251i
\(266\) −16.8394 + 12.5262i −1.03249 + 0.768031i
\(267\) 5.01510 + 5.01510i 0.306919 + 0.306919i
\(268\) −7.35838 7.35838i −0.449485 0.449485i
\(269\) 1.78351 0.108742 0.0543712 0.998521i \(-0.482685\pi\)
0.0543712 + 0.998521i \(0.482685\pi\)
\(270\) −1.72638 1.42113i −0.105064 0.0864874i
\(271\) 30.0221 1.82371 0.911857 0.410507i \(-0.134648\pi\)
0.911857 + 0.410507i \(0.134648\pi\)
\(272\) 3.90683 + 3.90683i 0.236886 + 0.236886i
\(273\) 19.4398 19.4398i 1.17655 1.17655i
\(274\) 1.46971 0.0887882
\(275\) −3.78697 19.3409i −0.228363 1.16630i
\(276\) 0.759463i 0.0457143i
\(277\) 14.5286 + 14.5286i 0.872936 + 0.872936i 0.992791 0.119855i \(-0.0382430\pi\)
−0.119855 + 0.992791i \(0.538243\pi\)
\(278\) 6.09481 + 6.09481i 0.365542 + 0.365542i
\(279\) 7.00112 0.419146
\(280\) −8.31224 6.84253i −0.496751 0.408920i
\(281\) 12.3316i 0.735640i −0.929897 0.367820i \(-0.880104\pi\)
0.929897 0.367820i \(-0.119896\pi\)
\(282\) 2.04815 + 2.04815i 0.121965 + 0.121965i
\(283\) −6.86004 + 6.86004i −0.407787 + 0.407787i −0.880966 0.473179i \(-0.843106\pi\)
0.473179 + 0.880966i \(0.343106\pi\)
\(284\) 9.62969 0.571417
\(285\) 7.22237 6.54503i 0.427816 0.387694i
\(286\) 22.5061 1.33082
\(287\) −10.3399 + 10.3399i −0.610347 + 0.610347i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 13.5266i 0.795681i
\(290\) 1.35646 + 13.9871i 0.0796541 + 0.821348i
\(291\) 10.0619 0.589838
\(292\) −4.47808 4.47808i −0.262060 0.262060i
\(293\) −18.7006 18.7006i −1.09250 1.09250i −0.995261 0.0972386i \(-0.968999\pi\)
−0.0972386 0.995261i \(-0.531001\pi\)
\(294\) 16.1827i 0.943795i
\(295\) 3.30669 4.01693i 0.192523 0.233875i
\(296\) −1.49331 −0.0867968
\(297\) 2.78715 2.78715i 0.161727 0.161727i
\(298\) 3.44721 + 3.44721i 0.199691 + 0.199691i
\(299\) 4.33642 0.250782
\(300\) 4.14901 + 2.79029i 0.239543 + 0.161097i
\(301\) −38.8190 −2.23749
\(302\) 7.07444 + 7.07444i 0.407089 + 0.407089i
\(303\) 6.34373 + 6.34373i 0.364438 + 0.364438i
\(304\) 3.49740 2.60158i 0.200589 0.149211i
\(305\) −13.2498 + 16.0957i −0.758682 + 0.921639i
\(306\) 5.52509i 0.315848i
\(307\) 12.1946 12.1946i 0.695981 0.695981i −0.267560 0.963541i \(-0.586217\pi\)
0.963541 + 0.267560i \(0.0862173\pi\)
\(308\) 13.4197 13.4197i 0.764659 0.764659i
\(309\) 0.328072i 0.0186633i
\(310\) −15.5819 + 1.51113i −0.884991 + 0.0858262i
\(311\) −3.15000 −0.178620 −0.0893102 0.996004i \(-0.528466\pi\)
−0.0893102 + 0.996004i \(0.528466\pi\)
\(312\) −4.03748 + 4.03748i −0.228577 + 0.228577i
\(313\) −0.351586 + 0.351586i −0.0198728 + 0.0198728i −0.716973 0.697101i \(-0.754473\pi\)
0.697101 + 0.716973i \(0.254473\pi\)
\(314\) −10.9168 −0.616070
\(315\) 1.03924 + 10.7160i 0.0585545 + 0.603781i
\(316\) 0.991285i 0.0557642i
\(317\) −6.49068 + 6.49068i −0.364553 + 0.364553i −0.865486 0.500933i \(-0.832990\pi\)
0.500933 + 0.865486i \(0.332990\pi\)
\(318\) 4.39576 + 4.39576i 0.246502 + 0.246502i
\(319\) −24.7714 −1.38693
\(320\) 1.72638 + 1.42113i 0.0965075 + 0.0794438i
\(321\) −16.7192 −0.933173
\(322\) 2.58567 2.58567i 0.144094 0.144094i
\(323\) 23.8276 + 3.49979i 1.32581 + 0.194734i
\(324\) 1.00000i 0.0555556i
\(325\) 15.9321 23.6902i 0.883756 1.31410i
\(326\) 3.48759i 0.193160i
\(327\) 8.11578 + 8.11578i 0.448803 + 0.448803i
\(328\) 2.14751 2.14751i 0.118576 0.118576i
\(329\) 13.9463i 0.768883i
\(330\) −5.60158 + 6.80474i −0.308357 + 0.374589i
\(331\) 27.0350i 1.48598i 0.669304 + 0.742988i \(0.266592\pi\)
−0.669304 + 0.742988i \(0.733408\pi\)
\(332\) −6.64529 6.64529i −0.364708 0.364708i
\(333\) 1.05593 + 1.05593i 0.0578645 + 0.0578645i
\(334\) 17.8260i 0.975397i
\(335\) −2.24611 23.1606i −0.122718 1.26540i
\(336\) 4.81484i 0.262671i
\(337\) 24.0565 24.0565i 1.31044 1.31044i 0.389349 0.921090i \(-0.372700\pi\)
0.921090 0.389349i \(-0.127300\pi\)
\(338\) 13.8610 + 13.8610i 0.753939 + 0.753939i
\(339\) 15.9796i 0.867890i
\(340\) 1.19254 + 12.2968i 0.0646745 + 0.666886i
\(341\) 27.5958i 1.49440i
\(342\) −4.31263 0.633437i −0.233200 0.0342523i
\(343\) −31.2636 + 31.2636i −1.68807 + 1.68807i
\(344\) 8.06235 0.434693
\(345\) −1.07930 + 1.31112i −0.0581075 + 0.0705883i
\(346\) 15.3625 0.825892
\(347\) 8.63756 + 8.63756i 0.463689 + 0.463689i 0.899862 0.436174i \(-0.143667\pi\)
−0.436174 + 0.899862i \(0.643667\pi\)
\(348\) 4.44385 4.44385i 0.238215 0.238215i
\(349\) 5.73255i 0.306856i −0.988160 0.153428i \(-0.950969\pi\)
0.988160 0.153428i \(-0.0490313\pi\)
\(350\) −4.62591 23.6256i −0.247266 1.26284i
\(351\) 5.70985 0.304769
\(352\) −2.78715 + 2.78715i −0.148556 + 0.148556i
\(353\) −1.17731 + 1.17731i −0.0626617 + 0.0626617i −0.737743 0.675082i \(-0.764108\pi\)
0.675082 + 0.737743i \(0.264108\pi\)
\(354\) −2.32680 −0.123668
\(355\) 16.6245 + 13.6851i 0.882336 + 0.726328i
\(356\) 7.09242i 0.375897i
\(357\) −18.8108 + 18.8108i −0.995571 + 0.995571i
\(358\) 8.80790 8.80790i 0.465512 0.465512i
\(359\) 30.2918i 1.59874i 0.600838 + 0.799371i \(0.294834\pi\)
−0.600838 + 0.799371i \(0.705166\pi\)
\(360\) −0.215841 2.22563i −0.0113758 0.117301i
\(361\) 5.46355 18.1975i 0.287555 0.957764i
\(362\) 8.18675 + 8.18675i 0.430286 + 0.430286i
\(363\) −3.20775 3.20775i −0.168363 0.168363i
\(364\) 27.4920 1.44097
\(365\) −1.36691 14.0948i −0.0715473 0.737755i
\(366\) 9.32341 0.487343
\(367\) 21.4259 + 21.4259i 1.11842 + 1.11842i 0.991973 + 0.126452i \(0.0403590\pi\)
0.126452 + 0.991973i \(0.459641\pi\)
\(368\) −0.537022 + 0.537022i −0.0279942 + 0.0279942i
\(369\) −3.03704 −0.158102
\(370\) −2.57802 2.12219i −0.134025 0.110327i
\(371\) 29.9317i 1.55398i
\(372\) 4.95054 + 4.95054i 0.256673 + 0.256673i
\(373\) −8.80310 8.80310i −0.455807 0.455807i 0.441469 0.897276i \(-0.354457\pi\)
−0.897276 + 0.441469i \(0.854457\pi\)
\(374\) −21.7778 −1.12611
\(375\) 3.19739 + 10.7134i 0.165112 + 0.553237i
\(376\) 2.89652i 0.149377i
\(377\) −25.3737 25.3737i −1.30681 1.30681i
\(378\) 3.40461 3.40461i 0.175114 0.175114i
\(379\) −25.6560 −1.31786 −0.658929 0.752205i \(-0.728990\pi\)
−0.658929 + 0.752205i \(0.728990\pi\)
\(380\) 9.73502 + 0.478953i 0.499396 + 0.0245698i
\(381\) −2.85114 −0.146068
\(382\) 5.36914 5.36914i 0.274709 0.274709i
\(383\) −8.22807 8.22807i −0.420435 0.420435i 0.464919 0.885353i \(-0.346084\pi\)
−0.885353 + 0.464919i \(0.846084\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 42.2387 4.09629i 2.15268 0.208767i
\(386\) 13.5983 0.692137
\(387\) −5.70094 5.70094i −0.289795 0.289795i
\(388\) 7.11482 + 7.11482i 0.361200 + 0.361200i
\(389\) 32.4669i 1.64614i −0.567940 0.823070i \(-0.692260\pi\)
0.567940 0.823070i \(-0.307740\pi\)
\(390\) −12.7080 + 1.23242i −0.643495 + 0.0624059i
\(391\) −4.19610 −0.212206
\(392\) 11.4429 11.4429i 0.577954 0.577954i
\(393\) 7.53832 + 7.53832i 0.380258 + 0.380258i
\(394\) −13.6637 −0.688368
\(395\) −1.40875 + 1.71133i −0.0708818 + 0.0861065i
\(396\) 3.94163 0.198074
\(397\) 19.6595 + 19.6595i 0.986681 + 0.986681i 0.999912 0.0132315i \(-0.00421184\pi\)
−0.0132315 + 0.999912i \(0.504212\pi\)
\(398\) −16.6989 16.6989i −0.837040 0.837040i
\(399\) 12.5262 + 16.8394i 0.627095 + 0.843025i
\(400\) 0.960761 + 4.90683i 0.0480381 + 0.245341i
\(401\) 7.83053i 0.391038i 0.980700 + 0.195519i \(0.0626391\pi\)
−0.980700 + 0.195519i \(0.937361\pi\)
\(402\) −7.35838 + 7.35838i −0.367003 + 0.367003i
\(403\) 28.2668 28.2668i 1.40807 1.40807i
\(404\) 8.97139i 0.446343i
\(405\) −1.42113 + 1.72638i −0.0706167 + 0.0857844i
\(406\) −30.2591 −1.50173
\(407\) 4.16208 4.16208i 0.206307 0.206307i
\(408\) 3.90683 3.90683i 0.193417 0.193417i
\(409\) 29.4446 1.45594 0.727970 0.685609i \(-0.240464\pi\)
0.727970 + 0.685609i \(0.240464\pi\)
\(410\) 6.75931 0.655516i 0.333819 0.0323736i
\(411\) 1.46971i 0.0724952i
\(412\) 0.231982 0.231982i 0.0114289 0.0114289i
\(413\) 7.92183 + 7.92183i 0.389808 + 0.389808i
\(414\) 0.759463 0.0373256
\(415\) −2.02844 20.9161i −0.0995723 1.02673i
\(416\) −5.70985 −0.279949
\(417\) 6.09481 6.09481i 0.298464 0.298464i
\(418\) −2.49677 + 16.9988i −0.122121 + 0.831438i
\(419\) 1.77581i 0.0867538i −0.999059 0.0433769i \(-0.986188\pi\)
0.999059 0.0433769i \(-0.0138116\pi\)
\(420\) −6.84253 + 8.31224i −0.333881 + 0.405596i
\(421\) 18.2662i 0.890238i 0.895471 + 0.445119i \(0.146839\pi\)
−0.895471 + 0.445119i \(0.853161\pi\)
\(422\) −11.6564 11.6564i −0.567423 0.567423i
\(423\) 2.04815 2.04815i 0.0995843 0.0995843i
\(424\) 6.21654i 0.301902i
\(425\) −15.4166 + 22.9236i −0.747814 + 1.11196i
\(426\) 9.62969i 0.466560i
\(427\) −31.7426 31.7426i −1.53613 1.53613i
\(428\) −11.8222 11.8222i −0.571449 0.571449i
\(429\) 22.5061i 1.08661i
\(430\) 13.9187 + 11.4577i 0.671218 + 0.552538i
\(431\) 23.1683i 1.11598i 0.829849 + 0.557988i \(0.188427\pi\)
−0.829849 + 0.557988i \(0.811573\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −17.1100 17.1100i −0.822256 0.822256i 0.164175 0.986431i \(-0.447504\pi\)
−0.986431 + 0.164175i \(0.947504\pi\)
\(434\) 33.7093i 1.61810i
\(435\) 13.9871 1.35646i 0.670628 0.0650373i
\(436\) 11.4774i 0.549670i
\(437\) −0.481072 + 3.27528i −0.0230128 + 0.156678i
\(438\) −4.47808 + 4.47808i −0.213971 + 0.213971i
\(439\) −13.6373 −0.650872 −0.325436 0.945564i \(-0.605511\pi\)
−0.325436 + 0.945564i \(0.605511\pi\)
\(440\) −8.77260 + 0.850764i −0.418217 + 0.0405586i
\(441\) −16.1827 −0.770606
\(442\) −22.3074 22.3074i −1.06105 1.06105i
\(443\) −0.0905461 + 0.0905461i −0.00430198 + 0.00430198i −0.709254 0.704953i \(-0.750968\pi\)
0.704953 + 0.709254i \(0.250968\pi\)
\(444\) 1.49331i 0.0708693i
\(445\) −10.0793 + 12.2442i −0.477803 + 0.580431i
\(446\) 6.95094 0.329137
\(447\) 3.44721 3.44721i 0.163047 0.163047i
\(448\) −3.40461 + 3.40461i −0.160853 + 0.160853i
\(449\) −1.35350 −0.0638754 −0.0319377 0.999490i \(-0.510168\pi\)
−0.0319377 + 0.999490i \(0.510168\pi\)
\(450\) 2.79029 4.14901i 0.131535 0.195586i
\(451\) 11.9709i 0.563687i
\(452\) 11.2993 11.2993i 0.531472 0.531472i
\(453\) 7.07444 7.07444i 0.332386 0.332386i
\(454\) 19.6753i 0.923408i
\(455\) 47.4617 + 39.0699i 2.22504 + 1.83162i
\(456\) −2.60158 3.49740i −0.121830 0.163781i
\(457\) 11.4431 + 11.4431i 0.535286 + 0.535286i 0.922141 0.386855i \(-0.126438\pi\)
−0.386855 + 0.922141i \(0.626438\pi\)
\(458\) −11.6180 11.6180i −0.542872 0.542872i
\(459\) −5.52509 −0.257889
\(460\) −1.69028 + 0.163923i −0.0788098 + 0.00764295i
\(461\) −32.5009 −1.51372 −0.756859 0.653578i \(-0.773267\pi\)
−0.756859 + 0.653578i \(0.773267\pi\)
\(462\) −13.4197 13.4197i −0.624341 0.624341i
\(463\) 10.2521 10.2521i 0.476455 0.476455i −0.427541 0.903996i \(-0.640620\pi\)
0.903996 + 0.427541i \(0.140620\pi\)
\(464\) 6.28455 0.291753
\(465\) 1.51113 + 15.5819i 0.0700768 + 0.722592i
\(466\) 1.23137i 0.0570419i
\(467\) −12.5702 12.5702i −0.581682 0.581682i 0.353684 0.935365i \(-0.384929\pi\)
−0.935365 + 0.353684i \(0.884929\pi\)
\(468\) 4.03748 + 4.03748i 0.186632 + 0.186632i
\(469\) 50.1048 2.31363
\(470\) −4.11634 + 5.00048i −0.189872 + 0.230655i
\(471\) 10.9168i 0.503019i
\(472\) −1.64529 1.64529i −0.0757308 0.0757308i
\(473\) −22.4710 + 22.4710i −1.03322 + 1.03322i
\(474\) 0.991285 0.0455312
\(475\) 16.1257 + 14.6616i 0.739896 + 0.672721i
\(476\) −26.6024 −1.21932
\(477\) 4.39576 4.39576i 0.201268 0.201268i
\(478\) 6.00068 + 6.00068i 0.274465 + 0.274465i
\(479\) 34.8202i 1.59098i 0.605969 + 0.795488i \(0.292786\pi\)
−0.605969 + 0.795488i \(0.707214\pi\)
\(480\) 1.42113 1.72638i 0.0648656 0.0787980i
\(481\) 8.52657 0.388778
\(482\) 1.79354 + 1.79354i 0.0816937 + 0.0816937i
\(483\) −2.58567 2.58567i −0.117652 0.117652i
\(484\) 4.53645i 0.206202i
\(485\) 2.17176 + 22.3940i 0.0986147 + 1.01686i
\(486\) 1.00000 0.0453609
\(487\) −19.1447 + 19.1447i −0.867529 + 0.867529i −0.992198 0.124669i \(-0.960213\pi\)
0.124669 + 0.992198i \(0.460213\pi\)
\(488\) 6.59265 + 6.59265i 0.298435 + 0.298435i
\(489\) 3.48759 0.157714
\(490\) 36.0167 3.49289i 1.62707 0.157793i
\(491\) −5.10573 −0.230418 −0.115209 0.993341i \(-0.536754\pi\)
−0.115209 + 0.993341i \(0.536754\pi\)
\(492\) −2.14751 2.14751i −0.0968173 0.0968173i
\(493\) 24.5526 + 24.5526i 1.10580 + 1.10580i
\(494\) −19.9696 + 14.8546i −0.898475 + 0.668342i
\(495\) 6.80474 + 5.60158i 0.305850 + 0.251772i
\(496\) 7.00112i 0.314360i
\(497\) −32.7853 + 32.7853i −1.47062 + 1.47062i
\(498\) −6.64529 + 6.64529i −0.297783 + 0.297783i
\(499\) 14.3736i 0.643450i −0.946833 0.321725i \(-0.895737\pi\)
0.946833 0.321725i \(-0.104263\pi\)
\(500\) −5.31462 + 9.83640i −0.237677 + 0.439897i
\(501\) −17.8260 −0.796408
\(502\) −11.1049 + 11.1049i −0.495634 + 0.495634i
\(503\) 5.66795 5.66795i 0.252721 0.252721i −0.569364 0.822085i \(-0.692811\pi\)
0.822085 + 0.569364i \(0.192811\pi\)
\(504\) 4.81484 0.214470
\(505\) −12.7495 + 15.4880i −0.567347 + 0.689207i
\(506\) 2.99352i 0.133078i
\(507\) 13.8610 13.8610i 0.615589 0.615589i
\(508\) −2.01606 2.01606i −0.0894481 0.0894481i
\(509\) −38.1688 −1.69180 −0.845900 0.533341i \(-0.820936\pi\)
−0.845900 + 0.533341i \(0.820936\pi\)
\(510\) 12.2968 1.19254i 0.544510 0.0528065i
\(511\) 30.4922 1.34890
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −0.633437 + 4.31263i −0.0279669 + 0.190407i
\(514\) 13.4892i 0.594985i
\(515\) 0.730165 0.0708112i 0.0321749 0.00312031i
\(516\) 8.06235i 0.354925i
\(517\) −8.07304 8.07304i −0.355052 0.355052i
\(518\) 5.08413 5.08413i 0.223384 0.223384i
\(519\) 15.3625i 0.674338i
\(520\) −9.85736 8.11446i −0.432274 0.355843i
\(521\) 18.9469i 0.830078i −0.909804 0.415039i \(-0.863768\pi\)
0.909804 0.415039i \(-0.136232\pi\)
\(522\) −4.44385 4.44385i −0.194502 0.194502i
\(523\) 2.96461 + 2.96461i 0.129633 + 0.129633i 0.768946 0.639313i \(-0.220781\pi\)
−0.639313 + 0.768946i \(0.720781\pi\)
\(524\) 10.6608i 0.465719i
\(525\) −23.6256 + 4.62591i −1.03111 + 0.201891i
\(526\) 1.89697i 0.0827120i
\(527\) −27.3522 + 27.3522i −1.19148 + 1.19148i
\(528\) 2.78715 + 2.78715i 0.121295 + 0.121295i
\(529\) 22.4232i 0.974922i
\(530\) −8.83454 + 10.7321i −0.383748 + 0.466173i
\(531\) 2.32680i 0.100974i
\(532\) −3.04990 + 20.7646i −0.132230 + 0.900261i
\(533\) −12.2620 + 12.2620i −0.531125 + 0.531125i
\(534\) 7.09242 0.306919
\(535\) −3.60867 37.2106i −0.156017 1.60875i
\(536\) −10.4063 −0.449485
\(537\) −8.80790 8.80790i −0.380089 0.380089i
\(538\) 1.26113 1.26113i 0.0543712 0.0543712i
\(539\) 63.7863i 2.74747i
\(540\) −2.22563 + 0.215841i −0.0957757 + 0.00928830i
\(541\) 32.1389 1.38176 0.690879 0.722970i \(-0.257224\pi\)
0.690879 + 0.722970i \(0.257224\pi\)
\(542\) 21.2289 21.2289i 0.911857 0.911857i
\(543\) 8.18675 8.18675i 0.351327 0.351327i
\(544\) 5.52509 0.236886
\(545\) −16.3110 + 19.8144i −0.698685 + 0.848756i
\(546\) 27.4920i 1.17655i
\(547\) −2.88206 + 2.88206i −0.123228 + 0.123228i −0.766031 0.642803i \(-0.777771\pi\)
0.642803 + 0.766031i \(0.277771\pi\)
\(548\) 1.03924 1.03924i 0.0443941 0.0443941i
\(549\) 9.32341i 0.397914i
\(550\) −16.3539 10.9983i −0.697331 0.468969i
\(551\) 21.9796 16.3498i 0.936361 0.696523i
\(552\) 0.537022 + 0.537022i 0.0228572 + 0.0228572i
\(553\) −3.37494 3.37494i −0.143517 0.143517i
\(554\) 20.5465 0.872936
\(555\) −2.12219 + 2.57802i −0.0900820 + 0.109431i
\(556\) 8.61936 0.365542
\(557\) 11.6948 + 11.6948i 0.495523 + 0.495523i 0.910041 0.414518i \(-0.136050\pi\)
−0.414518 + 0.910041i \(0.636050\pi\)
\(558\) 4.95054 4.95054i 0.209573 0.209573i
\(559\) −46.0349 −1.94707
\(560\) −10.7160 + 1.03924i −0.452835 + 0.0439159i
\(561\) 21.7778i 0.919461i
\(562\) −8.71974 8.71974i −0.367820 0.367820i
\(563\) 15.5373 + 15.5373i 0.654819 + 0.654819i 0.954149 0.299331i \(-0.0967634\pi\)
−0.299331 + 0.954149i \(0.596763\pi\)
\(564\) 2.89652 0.121965
\(565\) 35.5645 3.44904i 1.49621 0.145102i
\(566\) 9.70157i 0.407787i
\(567\) −3.40461 3.40461i −0.142980 0.142980i
\(568\) 6.80922 6.80922i 0.285708 0.285708i
\(569\) −13.6985 −0.574272 −0.287136 0.957890i \(-0.592703\pi\)
−0.287136 + 0.957890i \(0.592703\pi\)
\(570\) 0.478953 9.73502i 0.0200611 0.407755i
\(571\) 17.7058 0.740964 0.370482 0.928840i \(-0.379193\pi\)
0.370482 + 0.928840i \(0.379193\pi\)
\(572\) 15.9142 15.9142i 0.665408 0.665408i
\(573\) −5.36914 5.36914i −0.224299 0.224299i
\(574\) 14.6229i 0.610347i
\(575\) −3.15102 2.11912i −0.131407 0.0883735i
\(576\) −1.00000 −0.0416667
\(577\) −23.4215 23.4215i −0.975050 0.975050i 0.0246459 0.999696i \(-0.492154\pi\)
−0.999696 + 0.0246459i \(0.992154\pi\)
\(578\) 9.56473 + 9.56473i 0.397840 + 0.397840i
\(579\) 13.5983i 0.565127i
\(580\) 10.8495 + 8.93118i 0.450501 + 0.370847i
\(581\) 45.2492 1.87726
\(582\) 7.11482 7.11482i 0.294919 0.294919i
\(583\) −17.3265 17.3265i −0.717589 0.717589i
\(584\) −6.33296 −0.262060
\(585\) 1.23242 + 12.7080i 0.0509542 + 0.525411i
\(586\) −26.4466 −1.09250
\(587\) −19.2886 19.2886i −0.796126 0.796126i 0.186356 0.982482i \(-0.440332\pi\)
−0.982482 + 0.186356i \(0.940332\pi\)
\(588\) −11.4429 11.4429i −0.471898 0.471898i
\(589\) 18.2140 + 24.4857i 0.750494 + 1.00891i
\(590\) −0.502217 5.17858i −0.0206760 0.213199i
\(591\) 13.6637i 0.562050i
\(592\) −1.05593 + 1.05593i −0.0433984 + 0.0433984i
\(593\) 25.4634 25.4634i 1.04566 1.04566i 0.0467490 0.998907i \(-0.485114\pi\)
0.998907 0.0467490i \(-0.0148861\pi\)
\(594\) 3.94163i 0.161727i
\(595\) −45.9258 37.8056i −1.88278 1.54988i
\(596\) 4.87509 0.199691
\(597\) −16.6989 + 16.6989i −0.683440 + 0.683440i
\(598\) 3.06631 3.06631i 0.125391 0.125391i
\(599\) 44.5540 1.82043 0.910213 0.414140i \(-0.135918\pi\)
0.910213 + 0.414140i \(0.135918\pi\)
\(600\) 4.90683 0.960761i 0.200320 0.0392229i
\(601\) 21.3945i 0.872700i −0.899777 0.436350i \(-0.856271\pi\)
0.899777 0.436350i \(-0.143729\pi\)
\(602\) −27.4492 + 27.4492i −1.11874 + 1.11874i
\(603\) 7.35838 + 7.35838i 0.299656 + 0.299656i
\(604\) 10.0048 0.407089
\(605\) 6.44689 7.83162i 0.262104 0.318401i
\(606\) 8.97139 0.364438
\(607\) 3.46614 3.46614i 0.140686 0.140686i −0.633256 0.773942i \(-0.718282\pi\)
0.773942 + 0.633256i \(0.218282\pi\)
\(608\) 0.633437 4.31263i 0.0256893 0.174900i
\(609\) 30.2591i 1.22616i
\(610\) 2.01237 + 20.7504i 0.0814785 + 0.840160i
\(611\) 16.5387i 0.669084i
\(612\) −3.90683 3.90683i −0.157924 0.157924i
\(613\) 6.23977 6.23977i 0.252022 0.252022i −0.569777 0.821799i \(-0.692970\pi\)
0.821799 + 0.569777i \(0.192970\pi\)
\(614\) 17.2457i 0.695981i
\(615\) −0.655516 6.75931i −0.0264330 0.272562i
\(616\) 18.9783i 0.764659i
\(617\) −9.37481 9.37481i −0.377416 0.377416i 0.492753 0.870169i \(-0.335991\pi\)
−0.870169 + 0.492753i \(0.835991\pi\)
\(618\) −0.231982 0.231982i −0.00933167 0.00933167i
\(619\) 35.9982i 1.44689i 0.690383 + 0.723444i \(0.257442\pi\)
−0.690383 + 0.723444i \(0.742558\pi\)
\(620\) −9.94952 + 12.0866i −0.399582 + 0.485409i
\(621\) 0.759463i 0.0304762i
\(622\) −2.22739 + 2.22739i −0.0893102 + 0.0893102i
\(623\) −24.1469 24.1469i −0.967426 0.967426i
\(624\) 5.70985i 0.228577i
\(625\) −23.1539 + 9.42858i −0.926155 + 0.377143i
\(626\) 0.497217i 0.0198728i
\(627\) 16.9988 + 2.49677i 0.678866 + 0.0997115i
\(628\) −7.71934 + 7.71934i −0.308035 + 0.308035i
\(629\) −8.25066 −0.328975
\(630\) 8.31224 + 6.84253i 0.331168 + 0.272613i
\(631\) −4.26094 −0.169626 −0.0848128 0.996397i \(-0.527029\pi\)
−0.0848128 + 0.996397i \(0.527029\pi\)
\(632\) 0.700945 + 0.700945i 0.0278821 + 0.0278821i
\(633\) −11.6564 + 11.6564i −0.463299 + 0.463299i
\(634\) 9.17921i 0.364553i
\(635\) −0.615391 6.34556i −0.0244210 0.251816i
\(636\) 6.21654 0.246502
\(637\) −65.3373 + 65.3373i −2.58876 + 2.58876i
\(638\) −17.5160 + 17.5160i −0.693465 + 0.693465i
\(639\) −9.62969 −0.380945
\(640\) 2.22563 0.215841i 0.0879756 0.00853185i
\(641\) 23.3013i 0.920345i −0.887829 0.460173i \(-0.847787\pi\)
0.887829 0.460173i \(-0.152213\pi\)
\(642\) −11.8222 + 11.8222i −0.466586 + 0.466586i
\(643\) −25.8173 + 25.8173i −1.01814 + 1.01814i −0.0183043 + 0.999832i \(0.505827\pi\)
−0.999832 + 0.0183043i \(0.994173\pi\)
\(644\) 3.65670i 0.144094i
\(645\) 11.4577 13.9187i 0.451146 0.548047i
\(646\) 19.3234 14.3740i 0.760269 0.565536i
\(647\) 17.2171 + 17.2171i 0.676875 + 0.676875i 0.959292 0.282417i \(-0.0911362\pi\)
−0.282417 + 0.959292i \(0.591136\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) 9.17137 0.360008
\(650\) −5.48581 28.0173i −0.215171 1.09893i
\(651\) −33.7093 −1.32117
\(652\) 2.46610 + 2.46610i 0.0965799 + 0.0965799i
\(653\) 8.16718 8.16718i 0.319606 0.319606i −0.529010 0.848616i \(-0.677436\pi\)
0.848616 + 0.529010i \(0.177436\pi\)
\(654\) 11.4774 0.448803
\(655\) −15.1504 + 18.4046i −0.591975 + 0.719126i
\(656\) 3.03704i 0.118576i
\(657\) 4.47808 + 4.47808i 0.174706 + 0.174706i
\(658\) −9.86151 9.86151i −0.384442 0.384442i
\(659\) 49.4565 1.92655 0.963275 0.268517i \(-0.0865335\pi\)
0.963275 + 0.268517i \(0.0865335\pi\)
\(660\) 0.850764 + 8.77260i 0.0331159 + 0.341473i
\(661\) 42.8869i 1.66811i −0.551683 0.834054i \(-0.686014\pi\)
0.551683 0.834054i \(-0.313986\pi\)
\(662\) 19.1166 + 19.1166i 0.742988 + 0.742988i
\(663\) −22.3074 + 22.3074i −0.866348 + 0.866348i
\(664\) −9.39786 −0.364708
\(665\) −34.7746 + 31.5133i −1.34850 + 1.22203i
\(666\) 1.49331 0.0578645
\(667\) −3.37494 + 3.37494i −0.130678 + 0.130678i
\(668\) −12.6049 12.6049i −0.487698 0.487698i
\(669\) 6.95094i 0.268739i
\(670\) −17.9652 14.7888i −0.694058 0.571340i
\(671\) −36.7494 −1.41870
\(672\) 3.40461 + 3.40461i 0.131336 + 0.131336i
\(673\) 18.4285 + 18.4285i 0.710368 + 0.710368i 0.966612 0.256244i \(-0.0824852\pi\)
−0.256244 + 0.966612i \(0.582485\pi\)
\(674\) 34.0210i 1.31044i
\(675\) −4.14901 2.79029i −0.159695 0.107398i
\(676\) 19.6024 0.753939
\(677\) −16.5124 + 16.5124i −0.634623 + 0.634623i −0.949224 0.314601i \(-0.898129\pi\)
0.314601 + 0.949224i \(0.398129\pi\)
\(678\) −11.2993 11.2993i −0.433945 0.433945i
\(679\) −48.4464 −1.85920
\(680\) 9.53839 + 7.85188i 0.365780 + 0.301106i
\(681\) 19.6753 0.753960
\(682\) −19.5132 19.5132i −0.747199 0.747199i
\(683\) 0.431737 + 0.431737i 0.0165200 + 0.0165200i 0.715319 0.698799i \(-0.246282\pi\)
−0.698799 + 0.715319i \(0.746282\pi\)
\(684\) −3.49740 + 2.60158i −0.133726 + 0.0994739i
\(685\) 3.27102 0.317222i 0.124979 0.0121204i
\(686\) 44.2133i 1.68807i
\(687\) −11.6180 + 11.6180i −0.443253 + 0.443253i
\(688\) 5.70094 5.70094i 0.217346 0.217346i
\(689\) 35.4956i 1.35227i
\(690\) 0.163923 + 1.69028i 0.00624044 + 0.0643479i
\(691\) 9.51319 0.361899 0.180949 0.983492i \(-0.442083\pi\)
0.180949 + 0.983492i \(0.442083\pi\)
\(692\) 10.8629 10.8629i 0.412946 0.412946i
\(693\) −13.4197 + 13.4197i −0.509772 + 0.509772i
\(694\) 12.2154 0.463689
\(695\) 14.8803 + 12.2493i 0.564441 + 0.464641i
\(696\) 6.28455i 0.238215i
\(697\) 11.8652 11.8652i 0.449426 0.449426i
\(698\) −4.05352 4.05352i −0.153428 0.153428i
\(699\) −1.23137 −0.0465745
\(700\) −19.9768 13.4348i −0.755053 0.507788i
\(701\) 30.1150 1.13743 0.568715 0.822535i \(-0.307441\pi\)
0.568715 + 0.822535i \(0.307441\pi\)
\(702\) 4.03748 4.03748i 0.152385 0.152385i
\(703\) −0.945917 + 6.44008i −0.0356759 + 0.242892i
\(704\) 3.94163i 0.148556i
\(705\) 5.00048 + 4.11634i 0.188329 + 0.155030i
\(706\) 1.66496i 0.0626617i
\(707\) −30.5441 30.5441i −1.14873 1.14873i
\(708\) −1.64529 + 1.64529i −0.0618339 + 0.0618339i
\(709\) 15.3806i 0.577632i 0.957385 + 0.288816i \(0.0932616\pi\)
−0.957385 + 0.288816i \(0.906738\pi\)
\(710\) 21.4321 2.07848i 0.804332 0.0780039i
\(711\) 0.991285i 0.0371761i
\(712\) 5.01510 + 5.01510i 0.187949 + 0.187949i
\(713\) −3.75975 3.75975i −0.140804 0.140804i
\(714\) 26.6024i 0.995571i
\(715\) 50.0902 4.85774i 1.87327 0.181669i
\(716\) 12.4563i 0.465512i
\(717\) 6.00068 6.00068i 0.224100 0.224100i
\(718\) 21.4196 + 21.4196i 0.799371 + 0.799371i
\(719\) 8.69928i 0.324428i −0.986756 0.162214i \(-0.948136\pi\)
0.986756 0.162214i \(-0.0518636\pi\)
\(720\) −1.72638 1.42113i −0.0643383 0.0529625i
\(721\) 1.57961i 0.0588279i
\(722\) −9.00427 16.7309i −0.335104 0.622660i
\(723\) 1.79354 1.79354i 0.0667026 0.0667026i
\(724\) 11.5778 0.430286
\(725\) 6.03795 + 30.8372i 0.224244 + 1.14526i
\(726\) −4.53645 −0.168363
\(727\) −8.12640 8.12640i −0.301391 0.301391i 0.540167 0.841558i \(-0.318361\pi\)
−0.841558 + 0.540167i \(0.818361\pi\)
\(728\) 19.4398 19.4398i 0.720487 0.720487i
\(729\) 1.00000i 0.0370370i
\(730\) −10.9331 8.99997i −0.404651 0.333104i
\(731\) 44.5452 1.64756
\(732\) 6.59265 6.59265i 0.243671 0.243671i
\(733\) 3.98915 3.98915i 0.147343 0.147343i −0.629587 0.776930i \(-0.716776\pi\)
0.776930 + 0.629587i \(0.216776\pi\)
\(734\) 30.3008 1.11842
\(735\) −3.49289 36.0167i −0.128837 1.32850i
\(736\) 0.759463i 0.0279942i
\(737\) 29.0040 29.0040i 1.06838 1.06838i
\(738\) −2.14751 + 2.14751i −0.0790510 + 0.0790510i
\(739\) 10.1757i 0.374317i 0.982330 + 0.187159i \(0.0599279\pi\)
−0.982330 + 0.187159i \(0.940072\pi\)
\(740\) −3.32355 + 0.322317i −0.122176 + 0.0118486i
\(741\) 14.8546 + 19.9696i 0.545699 + 0.733602i
\(742\) −21.1649 21.1649i −0.776988 0.776988i
\(743\) −12.6705 12.6705i −0.464836 0.464836i 0.435401 0.900237i \(-0.356607\pi\)
−0.900237 + 0.435401i \(0.856607\pi\)
\(744\) 7.00112 0.256673
\(745\) 8.41625 + 6.92815i 0.308347 + 0.253828i
\(746\) −12.4495 −0.455807
\(747\) 6.64529 + 6.64529i 0.243139 + 0.243139i
\(748\) −15.3993 + 15.3993i −0.563053 + 0.563053i
\(749\) 80.5001 2.94141
\(750\) 9.83640 + 5.31462i 0.359175 + 0.194062i
\(751\) 23.7459i 0.866500i 0.901274 + 0.433250i \(0.142633\pi\)
−0.901274 + 0.433250i \(0.857367\pi\)
\(752\) 2.04815 + 2.04815i 0.0746883 + 0.0746883i
\(753\) 11.1049 + 11.1049i 0.404684 + 0.404684i
\(754\) −35.8839 −1.30681
\(755\) 17.2720 + 14.2181i 0.628593 + 0.517450i
\(756\) 4.81484i 0.175114i
\(757\) 33.7824 + 33.7824i 1.22784 + 1.22784i 0.964779 + 0.263062i \(0.0847322\pi\)
0.263062 + 0.964779i \(0.415268\pi\)
\(758\) −18.1415 + 18.1415i −0.658929 + 0.658929i
\(759\) −2.99352 −0.108658
\(760\) 7.22237 6.54503i 0.261983 0.237413i
\(761\) −20.8359 −0.755301 −0.377650 0.925948i \(-0.623268\pi\)
−0.377650 + 0.925948i \(0.623268\pi\)
\(762\) −2.01606 + 2.01606i −0.0730340 + 0.0730340i
\(763\) −39.0762 39.0762i −1.41465 1.41465i
\(764\) 7.59311i 0.274709i
\(765\) −1.19254 12.2968i −0.0431163 0.444591i
\(766\) −11.6363 −0.420435
\(767\) 9.39439 + 9.39439i 0.339212 + 0.339212i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 45.2621i 1.63219i −0.577916 0.816096i \(-0.696134\pi\)
0.577916 0.816096i \(-0.303866\pi\)
\(770\) 26.9707 32.7638i 0.971958 1.18072i
\(771\) 13.4892 0.485803
\(772\) 9.61547 9.61547i 0.346068 0.346068i
\(773\) 14.8984 + 14.8984i 0.535857 + 0.535857i 0.922309 0.386452i \(-0.126300\pi\)
−0.386452 + 0.922309i \(0.626300\pi\)
\(774\) −8.06235 −0.289795
\(775\) −34.3533 + 6.72640i −1.23401 + 0.241620i
\(776\) 10.0619 0.361200
\(777\) −5.08413 5.08413i −0.182392 0.182392i
\(778\) −22.9576 22.9576i −0.823070 0.823070i
\(779\)