Properties

Label 370.2.h.e.253.7
Level $370$
Weight $2$
Character 370.253
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.7
Root \(1.28931 + 1.28931i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.28931 - 1.28931i) q^{3} +1.00000 q^{4} +(1.69364 - 1.45999i) q^{5} +(-1.28931 + 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000 q^{8} -0.324646i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.28931 - 1.28931i) q^{3} +1.00000 q^{4} +(1.69364 - 1.45999i) q^{5} +(-1.28931 + 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000 q^{8} -0.324646i q^{9} +(-1.69364 + 1.45999i) q^{10} -3.64633i q^{11} +(1.28931 - 1.28931i) q^{12} +3.10704 q^{13} +(-0.579841 + 0.579841i) q^{14} +(0.301249 - 4.06602i) q^{15} +1.00000 q^{16} +8.09027i q^{17} +0.324646i q^{18} +(-3.05234 - 3.05234i) q^{19} +(1.69364 - 1.45999i) q^{20} -1.49519i q^{21} +3.64633i q^{22} -7.79067 q^{23} +(-1.28931 + 1.28931i) q^{24} +(0.736849 - 4.94541i) q^{25} -3.10704 q^{26} +(3.44936 + 3.44936i) q^{27} +(0.579841 - 0.579841i) q^{28} +(1.37472 - 1.37472i) q^{29} +(-0.301249 + 4.06602i) q^{30} +(3.23904 + 3.23904i) q^{31} -1.00000 q^{32} +(-4.70126 - 4.70126i) q^{33} -8.09027i q^{34} +(0.135480 - 1.82861i) q^{35} -0.324646i q^{36} +(-4.87870 - 3.63294i) q^{37} +(3.05234 + 3.05234i) q^{38} +(4.00594 - 4.00594i) q^{39} +(-1.69364 + 1.45999i) q^{40} -9.31106i q^{41} +1.49519i q^{42} +10.9160 q^{43} -3.64633i q^{44} +(-0.473980 - 0.549834i) q^{45} +7.79067 q^{46} +(-4.11794 + 4.11794i) q^{47} +(1.28931 - 1.28931i) q^{48} +6.32757i q^{49} +(-0.736849 + 4.94541i) q^{50} +(10.4309 + 10.4309i) q^{51} +3.10704 q^{52} +(0.446555 + 0.446555i) q^{53} +(-3.44936 - 3.44936i) q^{54} +(-5.32361 - 6.17558i) q^{55} +(-0.579841 + 0.579841i) q^{56} -7.87084 q^{57} +(-1.37472 + 1.37472i) q^{58} +(-6.16388 - 6.16388i) q^{59} +(0.301249 - 4.06602i) q^{60} +(8.71382 + 8.71382i) q^{61} +(-3.23904 - 3.23904i) q^{62} +(-0.188243 - 0.188243i) q^{63} +1.00000 q^{64} +(5.26221 - 4.53625i) q^{65} +(4.70126 + 4.70126i) q^{66} +(-2.01024 - 2.01024i) q^{67} +8.09027i q^{68} +(-10.0446 + 10.0446i) q^{69} +(-0.135480 + 1.82861i) q^{70} +0.00151598 q^{71} +0.324646i q^{72} +(-9.32759 + 9.32759i) q^{73} +(4.87870 + 3.63294i) q^{74} +(-5.42614 - 7.32620i) q^{75} +(-3.05234 - 3.05234i) q^{76} +(-2.11429 - 2.11429i) q^{77} +(-4.00594 + 4.00594i) q^{78} +(0.760897 + 0.760897i) q^{79} +(1.69364 - 1.45999i) q^{80} +9.86854 q^{81} +9.31106i q^{82} +(3.16981 + 3.16981i) q^{83} -1.49519i q^{84} +(11.8117 + 13.7020i) q^{85} -10.9160 q^{86} -3.54488i q^{87} +3.64633i q^{88} +(-5.80016 + 5.80016i) q^{89} +(0.473980 + 0.549834i) q^{90} +(1.80159 - 1.80159i) q^{91} -7.79067 q^{92} +8.35226 q^{93} +(4.11794 - 4.11794i) q^{94} +(-9.62597 - 0.713182i) q^{95} +(-1.28931 + 1.28931i) q^{96} +14.6206i q^{97} -6.32757i q^{98} -1.18377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.28931 1.28931i 0.744384 0.744384i −0.229034 0.973418i \(-0.573557\pi\)
0.973418 + 0.229034i \(0.0735568\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.69364 1.45999i 0.757420 0.652928i
\(6\) −1.28931 + 1.28931i −0.526359 + 0.526359i
\(7\) 0.579841 0.579841i 0.219159 0.219159i −0.588985 0.808144i \(-0.700472\pi\)
0.808144 + 0.588985i \(0.200472\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.324646i 0.108215i
\(10\) −1.69364 + 1.45999i −0.535577 + 0.461690i
\(11\) 3.64633i 1.09941i −0.835359 0.549705i \(-0.814740\pi\)
0.835359 0.549705i \(-0.185260\pi\)
\(12\) 1.28931 1.28931i 0.372192 0.372192i
\(13\) 3.10704 0.861737 0.430868 0.902415i \(-0.358207\pi\)
0.430868 + 0.902415i \(0.358207\pi\)
\(14\) −0.579841 + 0.579841i −0.154969 + 0.154969i
\(15\) 0.301249 4.06602i 0.0777820 1.04984i
\(16\) 1.00000 0.250000
\(17\) 8.09027i 1.96218i 0.193558 + 0.981089i \(0.437997\pi\)
−0.193558 + 0.981089i \(0.562003\pi\)
\(18\) 0.324646i 0.0765198i
\(19\) −3.05234 3.05234i −0.700255 0.700255i 0.264210 0.964465i \(-0.414889\pi\)
−0.964465 + 0.264210i \(0.914889\pi\)
\(20\) 1.69364 1.45999i 0.378710 0.326464i
\(21\) 1.49519i 0.326278i
\(22\) 3.64633i 0.777401i
\(23\) −7.79067 −1.62447 −0.812233 0.583333i \(-0.801748\pi\)
−0.812233 + 0.583333i \(0.801748\pi\)
\(24\) −1.28931 + 1.28931i −0.263180 + 0.263180i
\(25\) 0.736849 4.94541i 0.147370 0.989081i
\(26\) −3.10704 −0.609340
\(27\) 3.44936 + 3.44936i 0.663830 + 0.663830i
\(28\) 0.579841 0.579841i 0.109580 0.109580i
\(29\) 1.37472 1.37472i 0.255279 0.255279i −0.567852 0.823131i \(-0.692225\pi\)
0.823131 + 0.567852i \(0.192225\pi\)
\(30\) −0.301249 + 4.06602i −0.0550002 + 0.742349i
\(31\) 3.23904 + 3.23904i 0.581749 + 0.581749i 0.935384 0.353635i \(-0.115054\pi\)
−0.353635 + 0.935384i \(0.615054\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.70126 4.70126i −0.818384 0.818384i
\(34\) 8.09027i 1.38747i
\(35\) 0.135480 1.82861i 0.0229004 0.309091i
\(36\) 0.324646i 0.0541076i
\(37\) −4.87870 3.63294i −0.802054 0.597252i
\(38\) 3.05234 + 3.05234i 0.495155 + 0.495155i
\(39\) 4.00594 4.00594i 0.641463 0.641463i
\(40\) −1.69364 + 1.45999i −0.267788 + 0.230845i
\(41\) 9.31106i 1.45414i −0.686562 0.727072i \(-0.740881\pi\)
0.686562 0.727072i \(-0.259119\pi\)
\(42\) 1.49519i 0.230713i
\(43\) 10.9160 1.66467 0.832334 0.554275i \(-0.187004\pi\)
0.832334 + 0.554275i \(0.187004\pi\)
\(44\) 3.64633i 0.549705i
\(45\) −0.473980 0.549834i −0.0706568 0.0819644i
\(46\) 7.79067 1.14867
\(47\) −4.11794 + 4.11794i −0.600663 + 0.600663i −0.940489 0.339825i \(-0.889632\pi\)
0.339825 + 0.940489i \(0.389632\pi\)
\(48\) 1.28931 1.28931i 0.186096 0.186096i
\(49\) 6.32757i 0.903938i
\(50\) −0.736849 + 4.94541i −0.104206 + 0.699386i
\(51\) 10.4309 + 10.4309i 1.46061 + 1.46061i
\(52\) 3.10704 0.430868
\(53\) 0.446555 + 0.446555i 0.0613390 + 0.0613390i 0.737111 0.675772i \(-0.236190\pi\)
−0.675772 + 0.737111i \(0.736190\pi\)
\(54\) −3.44936 3.44936i −0.469399 0.469399i
\(55\) −5.32361 6.17558i −0.717836 0.832715i
\(56\) −0.579841 + 0.579841i −0.0774846 + 0.0774846i
\(57\) −7.87084 −1.04252
\(58\) −1.37472 + 1.37472i −0.180509 + 0.180509i
\(59\) −6.16388 6.16388i −0.802468 0.802468i 0.181012 0.983481i \(-0.442063\pi\)
−0.983481 + 0.181012i \(0.942063\pi\)
\(60\) 0.301249 4.06602i 0.0388910 0.524920i
\(61\) 8.71382 + 8.71382i 1.11569 + 1.11569i 0.992366 + 0.123324i \(0.0393555\pi\)
0.123324 + 0.992366i \(0.460644\pi\)
\(62\) −3.23904 3.23904i −0.411359 0.411359i
\(63\) −0.188243 0.188243i −0.0237164 0.0237164i
\(64\) 1.00000 0.125000
\(65\) 5.26221 4.53625i 0.652697 0.562652i
\(66\) 4.70126 + 4.70126i 0.578685 + 0.578685i
\(67\) −2.01024 2.01024i −0.245590 0.245590i 0.573568 0.819158i \(-0.305559\pi\)
−0.819158 + 0.573568i \(0.805559\pi\)
\(68\) 8.09027i 0.981089i
\(69\) −10.0446 + 10.0446i −1.20923 + 1.20923i
\(70\) −0.135480 + 1.82861i −0.0161930 + 0.218560i
\(71\) 0.00151598 0.000179913 8.99567e−5 1.00000i \(-0.499971\pi\)
8.99567e−5 1.00000i \(0.499971\pi\)
\(72\) 0.324646i 0.0382599i
\(73\) −9.32759 + 9.32759i −1.09171 + 1.09171i −0.0963663 + 0.995346i \(0.530722\pi\)
−0.995346 + 0.0963663i \(0.969278\pi\)
\(74\) 4.87870 + 3.63294i 0.567138 + 0.422321i
\(75\) −5.42614 7.32620i −0.626557 0.845956i
\(76\) −3.05234 3.05234i −0.350128 0.350128i
\(77\) −2.11429 2.11429i −0.240946 0.240946i
\(78\) −4.00594 + 4.00594i −0.453583 + 0.453583i
\(79\) 0.760897 + 0.760897i 0.0856076 + 0.0856076i 0.748614 0.663006i \(-0.230720\pi\)
−0.663006 + 0.748614i \(0.730720\pi\)
\(80\) 1.69364 1.45999i 0.189355 0.163232i
\(81\) 9.86854 1.09650
\(82\) 9.31106i 1.02823i
\(83\) 3.16981 + 3.16981i 0.347932 + 0.347932i 0.859339 0.511407i \(-0.170875\pi\)
−0.511407 + 0.859339i \(0.670875\pi\)
\(84\) 1.49519i 0.163139i
\(85\) 11.8117 + 13.7020i 1.28116 + 1.48619i
\(86\) −10.9160 −1.17710
\(87\) 3.54488i 0.380051i
\(88\) 3.64633i 0.388700i
\(89\) −5.80016 + 5.80016i −0.614816 + 0.614816i −0.944197 0.329381i \(-0.893160\pi\)
0.329381 + 0.944197i \(0.393160\pi\)
\(90\) 0.473980 + 0.549834i 0.0499619 + 0.0579576i
\(91\) 1.80159 1.80159i 0.188858 0.188858i
\(92\) −7.79067 −0.812233
\(93\) 8.35226 0.866089
\(94\) 4.11794 4.11794i 0.424733 0.424733i
\(95\) −9.62597 0.713182i −0.987604 0.0731710i
\(96\) −1.28931 + 1.28931i −0.131590 + 0.131590i
\(97\) 14.6206i 1.48449i 0.670127 + 0.742246i \(0.266240\pi\)
−0.670127 + 0.742246i \(0.733760\pi\)
\(98\) 6.32757i 0.639181i
\(99\) −1.18377 −0.118973
\(100\) 0.736849 4.94541i 0.0736849 0.494541i
\(101\) 3.68870i 0.367039i −0.983016 0.183520i \(-0.941251\pi\)
0.983016 0.183520i \(-0.0587491\pi\)
\(102\) −10.4309 10.4309i −1.03281 1.03281i
\(103\) 11.1543i 1.09907i 0.835471 + 0.549535i \(0.185195\pi\)
−0.835471 + 0.549535i \(0.814805\pi\)
\(104\) −3.10704 −0.304670
\(105\) −2.18297 2.53232i −0.213036 0.247129i
\(106\) −0.446555 0.446555i −0.0433732 0.0433732i
\(107\) −3.88311 + 3.88311i −0.375394 + 0.375394i −0.869437 0.494043i \(-0.835519\pi\)
0.494043 + 0.869437i \(0.335519\pi\)
\(108\) 3.44936 + 3.44936i 0.331915 + 0.331915i
\(109\) 2.01583 + 2.01583i 0.193081 + 0.193081i 0.797026 0.603945i \(-0.206405\pi\)
−0.603945 + 0.797026i \(0.706405\pi\)
\(110\) 5.32361 + 6.17558i 0.507587 + 0.588819i
\(111\) −10.9742 + 1.60617i −1.04162 + 0.152451i
\(112\) 0.579841 0.579841i 0.0547899 0.0547899i
\(113\) 11.8892i 1.11844i 0.829019 + 0.559220i \(0.188899\pi\)
−0.829019 + 0.559220i \(0.811101\pi\)
\(114\) 7.87084 0.737171
\(115\) −13.1946 + 11.3743i −1.23040 + 1.06066i
\(116\) 1.37472 1.37472i 0.127639 0.127639i
\(117\) 1.00869i 0.0932531i
\(118\) 6.16388 + 6.16388i 0.567431 + 0.567431i
\(119\) 4.69107 + 4.69107i 0.430030 + 0.430030i
\(120\) −0.301249 + 4.06602i −0.0275001 + 0.371175i
\(121\) −2.29574 −0.208704
\(122\) −8.71382 8.71382i −0.788912 0.788912i
\(123\) −12.0049 12.0049i −1.08244 1.08244i
\(124\) 3.23904 + 3.23904i 0.290875 + 0.290875i
\(125\) −5.97229 9.45154i −0.534178 0.845372i
\(126\) 0.188243 + 0.188243i 0.0167700 + 0.0167700i
\(127\) 13.9019 13.9019i 1.23359 1.23359i 0.271015 0.962575i \(-0.412641\pi\)
0.962575 0.271015i \(-0.0873593\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 14.0741 14.0741i 1.23915 1.23915i
\(130\) −5.26221 + 4.53625i −0.461526 + 0.397855i
\(131\) 2.71250 + 2.71250i 0.236992 + 0.236992i 0.815603 0.578611i \(-0.196405\pi\)
−0.578611 + 0.815603i \(0.696405\pi\)
\(132\) −4.70126 4.70126i −0.409192 0.409192i
\(133\) −3.53975 −0.306935
\(134\) 2.01024 + 2.01024i 0.173658 + 0.173658i
\(135\) 10.8780 + 0.805947i 0.936232 + 0.0693648i
\(136\) 8.09027i 0.693735i
\(137\) −11.4519 + 11.4519i −0.978406 + 0.978406i −0.999772 0.0213660i \(-0.993198\pi\)
0.0213660 + 0.999772i \(0.493198\pi\)
\(138\) 10.0446 10.0446i 0.855053 0.855053i
\(139\) −2.41427 −0.204775 −0.102388 0.994745i \(-0.532648\pi\)
−0.102388 + 0.994745i \(0.532648\pi\)
\(140\) 0.135480 1.82861i 0.0114502 0.154546i
\(141\) 10.6186i 0.894248i
\(142\) −0.00151598 −0.000127218
\(143\) 11.3293i 0.947403i
\(144\) 0.324646i 0.0270538i
\(145\) 0.321204 4.33536i 0.0266746 0.360032i
\(146\) 9.32759 9.32759i 0.771957 0.771957i
\(147\) 8.15820 + 8.15820i 0.672877 + 0.672877i
\(148\) −4.87870 3.63294i −0.401027 0.298626i
\(149\) 4.02923i 0.330088i −0.986286 0.165044i \(-0.947223\pi\)
0.986286 0.165044i \(-0.0527765\pi\)
\(150\) 5.42614 + 7.32620i 0.443043 + 0.598181i
\(151\) 8.86568i 0.721479i −0.932667 0.360739i \(-0.882524\pi\)
0.932667 0.360739i \(-0.117476\pi\)
\(152\) 3.05234 + 3.05234i 0.247578 + 0.247578i
\(153\) 2.62647 0.212338
\(154\) 2.11429 + 2.11429i 0.170375 + 0.170375i
\(155\) 10.2148 + 0.756805i 0.820469 + 0.0607880i
\(156\) 4.00594 4.00594i 0.320732 0.320732i
\(157\) 6.87897 6.87897i 0.549001 0.549001i −0.377151 0.926152i \(-0.623096\pi\)
0.926152 + 0.377151i \(0.123096\pi\)
\(158\) −0.760897 0.760897i −0.0605337 0.0605337i
\(159\) 1.15150 0.0913196
\(160\) −1.69364 + 1.45999i −0.133894 + 0.115422i
\(161\) −4.51735 + 4.51735i −0.356017 + 0.356017i
\(162\) −9.86854 −0.775346
\(163\) 10.6733i 0.835995i −0.908448 0.417997i \(-0.862732\pi\)
0.908448 0.417997i \(-0.137268\pi\)
\(164\) 9.31106i 0.727072i
\(165\) −14.8260 1.09845i −1.15421 0.0855144i
\(166\) −3.16981 3.16981i −0.246025 0.246025i
\(167\) 0.864796i 0.0669199i 0.999440 + 0.0334600i \(0.0106526\pi\)
−0.999440 + 0.0334600i \(0.989347\pi\)
\(168\) 1.49519i 0.115357i
\(169\) −3.34633 −0.257410
\(170\) −11.8117 13.7020i −0.905918 1.05090i
\(171\) −0.990930 + 0.990930i −0.0757783 + 0.0757783i
\(172\) 10.9160 0.832334
\(173\) −2.14973 + 2.14973i −0.163441 + 0.163441i −0.784089 0.620648i \(-0.786870\pi\)
0.620648 + 0.784089i \(0.286870\pi\)
\(174\) 3.54488i 0.268737i
\(175\) −2.44030 3.29481i −0.184469 0.249064i
\(176\) 3.64633i 0.274853i
\(177\) −15.8943 −1.19469
\(178\) 5.80016 5.80016i 0.434741 0.434741i
\(179\) −0.313292 + 0.313292i −0.0234165 + 0.0234165i −0.718718 0.695302i \(-0.755271\pi\)
0.695302 + 0.718718i \(0.255271\pi\)
\(180\) −0.473980 0.549834i −0.0353284 0.0409822i
\(181\) 16.2161 1.20533 0.602667 0.797993i \(-0.294105\pi\)
0.602667 + 0.797993i \(0.294105\pi\)
\(182\) −1.80159 + 1.80159i −0.133543 + 0.133543i
\(183\) 22.4697 1.66100
\(184\) 7.79067 0.574336
\(185\) −13.5668 + 0.969960i −0.997454 + 0.0713129i
\(186\) −8.35226 −0.612418
\(187\) 29.4998 2.15724
\(188\) −4.11794 + 4.11794i −0.300332 + 0.300332i
\(189\) 4.00017 0.290969
\(190\) 9.62597 + 0.713182i 0.698341 + 0.0517397i
\(191\) 0.276686 0.276686i 0.0200203 0.0200203i −0.697026 0.717046i \(-0.745494\pi\)
0.717046 + 0.697026i \(0.245494\pi\)
\(192\) 1.28931 1.28931i 0.0930480 0.0930480i
\(193\) 8.78779 0.632559 0.316279 0.948666i \(-0.397566\pi\)
0.316279 + 0.948666i \(0.397566\pi\)
\(194\) 14.6206i 1.04969i
\(195\) 0.935990 12.6333i 0.0670276 0.904686i
\(196\) 6.32757i 0.451969i
\(197\) 8.41487 8.41487i 0.599535 0.599535i −0.340654 0.940189i \(-0.610649\pi\)
0.940189 + 0.340654i \(0.110649\pi\)
\(198\) 1.18377 0.0841266
\(199\) 4.20114 4.20114i 0.297811 0.297811i −0.542345 0.840156i \(-0.682463\pi\)
0.840156 + 0.542345i \(0.182463\pi\)
\(200\) −0.736849 + 4.94541i −0.0521031 + 0.349693i
\(201\) −5.18365 −0.365627
\(202\) 3.68870i 0.259536i
\(203\) 1.59424i 0.111894i
\(204\) 10.4309 + 10.4309i 0.730307 + 0.730307i
\(205\) −13.5941 15.7696i −0.949451 1.10140i
\(206\) 11.1543i 0.777160i
\(207\) 2.52921i 0.175792i
\(208\) 3.10704 0.215434
\(209\) −11.1299 + 11.1299i −0.769868 + 0.769868i
\(210\) 2.18297 + 2.53232i 0.150639 + 0.174747i
\(211\) −27.4901 −1.89250 −0.946248 0.323442i \(-0.895160\pi\)
−0.946248 + 0.323442i \(0.895160\pi\)
\(212\) 0.446555 + 0.446555i 0.0306695 + 0.0306695i
\(213\) 0.00195457 0.00195457i 0.000133925 0.000133925i
\(214\) 3.88311 3.88311i 0.265444 0.265444i
\(215\) 18.4877 15.9372i 1.26085 1.08691i
\(216\) −3.44936 3.44936i −0.234699 0.234699i
\(217\) 3.75626 0.254992
\(218\) −2.01583 2.01583i −0.136529 0.136529i
\(219\) 24.0523i 1.62531i
\(220\) −5.32361 6.17558i −0.358918 0.416358i
\(221\) 25.1367i 1.69088i
\(222\) 10.9742 1.60617i 0.736537 0.107799i
\(223\) −9.42660 9.42660i −0.631252 0.631252i 0.317130 0.948382i \(-0.397281\pi\)
−0.948382 + 0.317130i \(0.897281\pi\)
\(224\) −0.579841 + 0.579841i −0.0387423 + 0.0387423i
\(225\) −1.60551 0.239215i −0.107034 0.0159477i
\(226\) 11.8892i 0.790856i
\(227\) 17.9587i 1.19196i −0.802999 0.595981i \(-0.796763\pi\)
0.802999 0.595981i \(-0.203237\pi\)
\(228\) −7.87084 −0.521259
\(229\) 18.1673i 1.20053i −0.799802 0.600264i \(-0.795062\pi\)
0.799802 0.600264i \(-0.204938\pi\)
\(230\) 13.1946 11.3743i 0.870027 0.750000i
\(231\) −5.45197 −0.358713
\(232\) −1.37472 + 1.37472i −0.0902547 + 0.0902547i
\(233\) 2.23686 2.23686i 0.146541 0.146541i −0.630030 0.776571i \(-0.716957\pi\)
0.776571 + 0.630030i \(0.216957\pi\)
\(234\) 1.00869i 0.0659399i
\(235\) −0.962160 + 12.9865i −0.0627644 + 0.847144i
\(236\) −6.16388 6.16388i −0.401234 0.401234i
\(237\) 1.96207 0.127450
\(238\) −4.69107 4.69107i −0.304077 0.304077i
\(239\) 4.53542 + 4.53542i 0.293372 + 0.293372i 0.838411 0.545039i \(-0.183485\pi\)
−0.545039 + 0.838411i \(0.683485\pi\)
\(240\) 0.301249 4.06602i 0.0194455 0.262460i
\(241\) 2.95256 2.95256i 0.190191 0.190191i −0.605587 0.795779i \(-0.707062\pi\)
0.795779 + 0.605587i \(0.207062\pi\)
\(242\) 2.29574 0.147576
\(243\) 2.37553 2.37553i 0.152390 0.152390i
\(244\) 8.71382 + 8.71382i 0.557845 + 0.557845i
\(245\) 9.23820 + 10.7166i 0.590207 + 0.684661i
\(246\) 12.0049 + 12.0049i 0.765402 + 0.765402i
\(247\) −9.48374 9.48374i −0.603436 0.603436i
\(248\) −3.23904 3.23904i −0.205679 0.205679i
\(249\) 8.17374 0.517990
\(250\) 5.97229 + 9.45154i 0.377721 + 0.597768i
\(251\) −9.93109 9.93109i −0.626845 0.626845i 0.320428 0.947273i \(-0.396173\pi\)
−0.947273 + 0.320428i \(0.896173\pi\)
\(252\) −0.188243 0.188243i −0.0118582 0.0118582i
\(253\) 28.4074i 1.78596i
\(254\) −13.9019 + 13.9019i −0.872280 + 0.872280i
\(255\) 32.8951 + 2.43718i 2.05997 + 0.152622i
\(256\) 1.00000 0.0625000
\(257\) 15.1135i 0.942757i 0.881931 + 0.471378i \(0.156243\pi\)
−0.881931 + 0.471378i \(0.843757\pi\)
\(258\) −14.0741 + 14.0741i −0.876213 + 0.876213i
\(259\) −4.93540 + 0.722344i −0.306671 + 0.0448842i
\(260\) 5.26221 4.53625i 0.326348 0.281326i
\(261\) −0.446297 0.446297i −0.0276251 0.0276251i
\(262\) −2.71250 2.71250i −0.167579 0.167579i
\(263\) 9.74250 9.74250i 0.600749 0.600749i −0.339763 0.940511i \(-0.610347\pi\)
0.940511 + 0.339763i \(0.110347\pi\)
\(264\) 4.70126 + 4.70126i 0.289342 + 0.289342i
\(265\) 1.40827 + 0.104338i 0.0865094 + 0.00640942i
\(266\) 3.53975 0.217036
\(267\) 14.9564i 0.915319i
\(268\) −2.01024 2.01024i −0.122795 0.122795i
\(269\) 6.43418i 0.392299i −0.980574 0.196150i \(-0.937156\pi\)
0.980574 0.196150i \(-0.0628438\pi\)
\(270\) −10.8780 0.805947i −0.662016 0.0490483i
\(271\) −25.6662 −1.55911 −0.779556 0.626332i \(-0.784555\pi\)
−0.779556 + 0.626332i \(0.784555\pi\)
\(272\) 8.09027i 0.490544i
\(273\) 4.64561i 0.281165i
\(274\) 11.4519 11.4519i 0.691837 0.691837i
\(275\) −18.0326 2.68680i −1.08741 0.162020i
\(276\) −10.0446 + 10.0446i −0.604614 + 0.604614i
\(277\) −17.2625 −1.03720 −0.518602 0.855016i \(-0.673548\pi\)
−0.518602 + 0.855016i \(0.673548\pi\)
\(278\) 2.41427 0.144798
\(279\) 1.05154 1.05154i 0.0629541 0.0629541i
\(280\) −0.135480 + 1.82861i −0.00809650 + 0.109280i
\(281\) −3.84098 + 3.84098i −0.229134 + 0.229134i −0.812331 0.583197i \(-0.801802\pi\)
0.583197 + 0.812331i \(0.301802\pi\)
\(282\) 10.6186i 0.632329i
\(283\) 20.5564i 1.22195i 0.791650 + 0.610975i \(0.209222\pi\)
−0.791650 + 0.610975i \(0.790778\pi\)
\(284\) 0.00151598 8.99567e−5
\(285\) −13.3304 + 11.4914i −0.789624 + 0.680689i
\(286\) 11.3293i 0.669915i
\(287\) −5.39894 5.39894i −0.318689 0.318689i
\(288\) 0.324646i 0.0191299i
\(289\) −48.4524 −2.85014
\(290\) −0.321204 + 4.33536i −0.0188618 + 0.254581i
\(291\) 18.8504 + 18.8504i 1.10503 + 1.10503i
\(292\) −9.32759 + 9.32759i −0.545856 + 0.545856i
\(293\) −11.2671 11.2671i −0.658232 0.658232i 0.296729 0.954962i \(-0.404104\pi\)
−0.954962 + 0.296729i \(0.904104\pi\)
\(294\) −8.15820 8.15820i −0.475796 0.475796i
\(295\) −19.4386 1.44019i −1.13176 0.0838514i
\(296\) 4.87870 + 3.63294i 0.283569 + 0.211160i
\(297\) 12.5775 12.5775i 0.729822 0.729822i
\(298\) 4.02923i 0.233407i
\(299\) −24.2059 −1.39986
\(300\) −5.42614 7.32620i −0.313278 0.422978i
\(301\) 6.32952 6.32952i 0.364828 0.364828i
\(302\) 8.86568i 0.510163i
\(303\) −4.75588 4.75588i −0.273218 0.273218i
\(304\) −3.05234 3.05234i −0.175064 0.175064i
\(305\) 27.4802 + 2.03599i 1.57351 + 0.116581i
\(306\) −2.62647 −0.150145
\(307\) 9.43686 + 9.43686i 0.538590 + 0.538590i 0.923115 0.384525i \(-0.125635\pi\)
−0.384525 + 0.923115i \(0.625635\pi\)
\(308\) −2.11429 2.11429i −0.120473 0.120473i
\(309\) 14.3814 + 14.3814i 0.818131 + 0.818131i
\(310\) −10.2148 0.756805i −0.580159 0.0429836i
\(311\) 6.70368 + 6.70368i 0.380131 + 0.380131i 0.871149 0.491019i \(-0.163375\pi\)
−0.491019 + 0.871149i \(0.663375\pi\)
\(312\) −4.00594 + 4.00594i −0.226791 + 0.226791i
\(313\) −23.2157 −1.31223 −0.656114 0.754662i \(-0.727801\pi\)
−0.656114 + 0.754662i \(0.727801\pi\)
\(314\) −6.87897 + 6.87897i −0.388203 + 0.388203i
\(315\) −0.593650 0.0439832i −0.0334484 0.00247817i
\(316\) 0.760897 + 0.760897i 0.0428038 + 0.0428038i
\(317\) −15.3696 15.3696i −0.863245 0.863245i 0.128469 0.991714i \(-0.458994\pi\)
−0.991714 + 0.128469i \(0.958994\pi\)
\(318\) −1.15150 −0.0645727
\(319\) −5.01268 5.01268i −0.280656 0.280656i
\(320\) 1.69364 1.45999i 0.0946775 0.0816160i
\(321\) 10.0131i 0.558875i
\(322\) 4.51735 4.51735i 0.251742 0.251742i
\(323\) 24.6943 24.6943i 1.37403 1.37403i
\(324\) 9.86854 0.548252
\(325\) 2.28942 15.3656i 0.126994 0.852328i
\(326\) 10.6733i 0.591137i
\(327\) 5.19806 0.287454
\(328\) 9.31106i 0.514117i
\(329\) 4.77550i 0.263282i
\(330\) 14.8260 + 1.09845i 0.816147 + 0.0604678i
\(331\) −5.72839 + 5.72839i −0.314861 + 0.314861i −0.846789 0.531929i \(-0.821467\pi\)
0.531929 + 0.846789i \(0.321467\pi\)
\(332\) 3.16981 + 3.16981i 0.173966 + 0.173966i
\(333\) −1.17942 + 1.58385i −0.0646318 + 0.0867945i
\(334\) 0.864796i 0.0473195i
\(335\) −6.33957 0.469695i −0.346368 0.0256622i
\(336\) 1.49519i 0.0815694i
\(337\) 5.31333 + 5.31333i 0.289436 + 0.289436i 0.836857 0.547421i \(-0.184391\pi\)
−0.547421 + 0.836857i \(0.684391\pi\)
\(338\) 3.34633 0.182016
\(339\) 15.3288 + 15.3288i 0.832549 + 0.832549i
\(340\) 11.8117 + 13.7020i 0.640580 + 0.743096i
\(341\) 11.8106 11.8106i 0.639581 0.639581i
\(342\) 0.990930 0.990930i 0.0535834 0.0535834i
\(343\) 7.72788 + 7.72788i 0.417266 + 0.417266i
\(344\) −10.9160 −0.588549
\(345\) −2.34693 + 31.6770i −0.126354 + 1.70543i
\(346\) 2.14973 2.14973i 0.115570 0.115570i
\(347\) 32.7620 1.75876 0.879379 0.476123i \(-0.157958\pi\)
0.879379 + 0.476123i \(0.157958\pi\)
\(348\) 3.54488i 0.190026i
\(349\) 14.0604i 0.752637i 0.926490 + 0.376318i \(0.122810\pi\)
−0.926490 + 0.376318i \(0.877190\pi\)
\(350\) 2.44030 + 3.29481i 0.130439 + 0.176115i
\(351\) 10.7173 + 10.7173i 0.572047 + 0.572047i
\(352\) 3.64633i 0.194350i
\(353\) 6.79098i 0.361447i 0.983534 + 0.180724i \(0.0578440\pi\)
−0.983534 + 0.180724i \(0.942156\pi\)
\(354\) 15.8943 0.844773
\(355\) 0.00256752 0.00221331i 0.000136270 0.000117471i
\(356\) −5.80016 + 5.80016i −0.307408 + 0.307408i
\(357\) 12.0965 0.640215
\(358\) 0.313292 0.313292i 0.0165580 0.0165580i
\(359\) 4.91904i 0.259617i −0.991539 0.129808i \(-0.958564\pi\)
0.991539 0.129808i \(-0.0414362\pi\)
\(360\) 0.473980 + 0.549834i 0.0249810 + 0.0289788i
\(361\) 0.366413i 0.0192849i
\(362\) −16.2161 −0.852300
\(363\) −2.95992 + 2.95992i −0.155356 + 0.155356i
\(364\) 1.80159 1.80159i 0.0944289 0.0944289i
\(365\) −2.17940 + 29.4158i −0.114075 + 1.53969i
\(366\) −22.4697 −1.17451
\(367\) 21.4924 21.4924i 1.12189 1.12189i 0.130436 0.991457i \(-0.458362\pi\)
0.991457 0.130436i \(-0.0416378\pi\)
\(368\) −7.79067 −0.406117
\(369\) −3.02280 −0.157361
\(370\) 13.5668 0.969960i 0.705306 0.0504258i
\(371\) 0.517862 0.0268860
\(372\) 8.35226 0.433045
\(373\) 19.5734 19.5734i 1.01347 1.01347i 0.0135632 0.999908i \(-0.495683\pi\)
0.999908 0.0135632i \(-0.00431743\pi\)
\(374\) −29.4998 −1.52540
\(375\) −19.8861 4.48584i −1.02692 0.231648i
\(376\) 4.11794 4.11794i 0.212367 0.212367i
\(377\) 4.27130 4.27130i 0.219983 0.219983i
\(378\) −4.00017 −0.205746
\(379\) 1.90775i 0.0979943i −0.998799 0.0489972i \(-0.984397\pi\)
0.998799 0.0489972i \(-0.0156025\pi\)
\(380\) −9.62597 0.713182i −0.493802 0.0365855i
\(381\) 35.8476i 1.83653i
\(382\) −0.276686 + 0.276686i −0.0141565 + 0.0141565i
\(383\) 12.0669 0.616591 0.308295 0.951291i \(-0.400241\pi\)
0.308295 + 0.951291i \(0.400241\pi\)
\(384\) −1.28931 + 1.28931i −0.0657949 + 0.0657949i
\(385\) −6.66771 0.494007i −0.339818 0.0251769i
\(386\) −8.78779 −0.447287
\(387\) 3.54382i 0.180142i
\(388\) 14.6206i 0.742246i
\(389\) −16.8015 16.8015i −0.851868 0.851868i 0.138495 0.990363i \(-0.455773\pi\)
−0.990363 + 0.138495i \(0.955773\pi\)
\(390\) −0.935990 + 12.6333i −0.0473957 + 0.639710i
\(391\) 63.0286i 3.18749i
\(392\) 6.32757i 0.319590i
\(393\) 6.99450 0.352826
\(394\) −8.41487 + 8.41487i −0.423935 + 0.423935i
\(395\) 2.39959 + 0.177784i 0.120737 + 0.00894529i
\(396\) −1.18377 −0.0594865
\(397\) −6.99419 6.99419i −0.351028 0.351028i 0.509464 0.860492i \(-0.329844\pi\)
−0.860492 + 0.509464i \(0.829844\pi\)
\(398\) −4.20114 + 4.20114i −0.210584 + 0.210584i
\(399\) −4.56384 + 4.56384i −0.228478 + 0.228478i
\(400\) 0.736849 4.94541i 0.0368425 0.247270i
\(401\) 0.759591 + 0.759591i 0.0379322 + 0.0379322i 0.725818 0.687886i \(-0.241461\pi\)
−0.687886 + 0.725818i \(0.741461\pi\)
\(402\) 5.18365 0.258537
\(403\) 10.0638 + 10.0638i 0.501315 + 0.501315i
\(404\) 3.68870i 0.183520i
\(405\) 16.7138 14.4080i 0.830515 0.715939i
\(406\) 1.59424i 0.0791207i
\(407\) −13.2469 + 17.7894i −0.656625 + 0.881786i
\(408\) −10.4309 10.4309i −0.516405 0.516405i
\(409\) 22.0320 22.0320i 1.08941 1.08941i 0.0938237 0.995589i \(-0.470091\pi\)
0.995589 0.0938237i \(-0.0299090\pi\)
\(410\) 13.5941 + 15.7696i 0.671363 + 0.778805i
\(411\) 29.5302i 1.45662i
\(412\) 11.1543i 0.549535i
\(413\) −7.14814 −0.351737
\(414\) 2.52921i 0.124304i
\(415\) 9.99642 + 0.740629i 0.490705 + 0.0363560i
\(416\) −3.10704 −0.152335
\(417\) −3.11274 + 3.11274i −0.152432 + 0.152432i
\(418\) 11.1299 11.1299i 0.544379 0.544379i
\(419\) 13.7527i 0.671863i −0.941886 0.335931i \(-0.890949\pi\)
0.941886 0.335931i \(-0.109051\pi\)
\(420\) −2.18297 2.53232i −0.106518 0.123565i
\(421\) 4.62725 + 4.62725i 0.225519 + 0.225519i 0.810818 0.585299i \(-0.199023\pi\)
−0.585299 + 0.810818i \(0.699023\pi\)
\(422\) 27.4901 1.33820
\(423\) 1.33687 + 1.33687i 0.0650010 + 0.0650010i
\(424\) −0.446555 0.446555i −0.0216866 0.0216866i
\(425\) 40.0097 + 5.96131i 1.94075 + 0.289166i
\(426\) −0.00195457 + 0.00195457i −9.46990e−5 + 9.46990e-5i
\(427\) 10.1053 0.489028
\(428\) −3.88311 + 3.88311i −0.187697 + 0.187697i
\(429\) −14.6070 14.6070i −0.705231 0.705231i
\(430\) −18.4877 + 15.9372i −0.891557 + 0.768560i
\(431\) 2.01292 + 2.01292i 0.0969591 + 0.0969591i 0.753922 0.656963i \(-0.228159\pi\)
−0.656963 + 0.753922i \(0.728159\pi\)
\(432\) 3.44936 + 3.44936i 0.165958 + 0.165958i
\(433\) −23.2986 23.2986i −1.11966 1.11966i −0.991791 0.127870i \(-0.959186\pi\)
−0.127870 0.991791i \(-0.540814\pi\)
\(434\) −3.75626 −0.180306
\(435\) −5.17549 6.00376i −0.248146 0.287858i
\(436\) 2.01583 + 2.01583i 0.0965407 + 0.0965407i
\(437\) 23.7798 + 23.7798i 1.13754 + 1.13754i
\(438\) 24.0523i 1.14927i
\(439\) −6.59762 + 6.59762i −0.314887 + 0.314887i −0.846800 0.531912i \(-0.821474\pi\)
0.531912 + 0.846800i \(0.321474\pi\)
\(440\) 5.32361 + 6.17558i 0.253793 + 0.294409i
\(441\) 2.05422 0.0978199
\(442\) 25.1367i 1.19563i
\(443\) −28.2758 + 28.2758i −1.34343 + 1.34343i −0.450801 + 0.892625i \(0.648862\pi\)
−0.892625 + 0.450801i \(0.851138\pi\)
\(444\) −10.9742 + 1.60617i −0.520810 + 0.0762256i
\(445\) −1.35521 + 18.2916i −0.0642432 + 0.867105i
\(446\) 9.42660 + 9.42660i 0.446363 + 0.446363i
\(447\) −5.19493 5.19493i −0.245712 0.245712i
\(448\) 0.579841 0.579841i 0.0273949 0.0273949i
\(449\) 11.7576 + 11.7576i 0.554876 + 0.554876i 0.927844 0.372968i \(-0.121660\pi\)
−0.372968 + 0.927844i \(0.621660\pi\)
\(450\) 1.60551 + 0.239215i 0.0756843 + 0.0112767i
\(451\) −33.9512 −1.59870
\(452\) 11.8892i 0.559220i
\(453\) −11.4306 11.4306i −0.537057 0.537057i
\(454\) 17.9587i 0.842844i
\(455\) 0.420942 5.68155i 0.0197341 0.266355i
\(456\) 7.87084 0.368586
\(457\) 31.9954i 1.49668i −0.663314 0.748341i \(-0.730851\pi\)
0.663314 0.748341i \(-0.269149\pi\)
\(458\) 18.1673i 0.848901i
\(459\) −27.9063 + 27.9063i −1.30255 + 1.30255i
\(460\) −13.1946 + 11.3743i −0.615202 + 0.530330i
\(461\) −17.2203 + 17.2203i −0.802031 + 0.802031i −0.983413 0.181382i \(-0.941943\pi\)
0.181382 + 0.983413i \(0.441943\pi\)
\(462\) 5.45197 0.253648
\(463\) −13.3316 −0.619570 −0.309785 0.950807i \(-0.600257\pi\)
−0.309785 + 0.950807i \(0.600257\pi\)
\(464\) 1.37472 1.37472i 0.0638197 0.0638197i
\(465\) 14.1457 12.1942i 0.655993 0.565494i
\(466\) −2.23686 + 2.23686i −0.103620 + 0.103620i
\(467\) 32.1997i 1.49003i −0.667050 0.745013i \(-0.732443\pi\)
0.667050 0.745013i \(-0.267557\pi\)
\(468\) 1.00869i 0.0466265i
\(469\) −2.33124 −0.107647
\(470\) 0.962160 12.9865i 0.0443811 0.599022i
\(471\) 17.7383i 0.817336i
\(472\) 6.16388 + 6.16388i 0.283715 + 0.283715i
\(473\) 39.8032i 1.83015i
\(474\) −1.96207 −0.0901207
\(475\) −17.3442 + 12.8460i −0.795806 + 0.589413i
\(476\) 4.69107 + 4.69107i 0.215015 + 0.215015i
\(477\) 0.144972 0.144972i 0.00663782 0.00663782i
\(478\) −4.53542 4.53542i −0.207445 0.207445i
\(479\) 10.6512 + 10.6512i 0.486664 + 0.486664i 0.907252 0.420588i \(-0.138176\pi\)
−0.420588 + 0.907252i \(0.638176\pi\)
\(480\) −0.301249 + 4.06602i −0.0137501 + 0.185587i
\(481\) −15.1583 11.2877i −0.691159 0.514674i
\(482\) −2.95256 + 2.95256i −0.134486 + 0.134486i
\(483\) 11.6485i 0.530027i
\(484\) −2.29574 −0.104352
\(485\) 21.3459 + 24.7620i 0.969267 + 1.12438i
\(486\) −2.37553 + 2.37553i −0.107756 + 0.107756i
\(487\) 17.1695i 0.778022i −0.921233 0.389011i \(-0.872817\pi\)
0.921233 0.389011i \(-0.127183\pi\)
\(488\) −8.71382 8.71382i −0.394456 0.394456i
\(489\) −13.7612 13.7612i −0.622301 0.622301i
\(490\) −9.23820 10.7166i −0.417339 0.484128i
\(491\) −9.04897 −0.408374 −0.204187 0.978932i \(-0.565455\pi\)
−0.204187 + 0.978932i \(0.565455\pi\)
\(492\) −12.0049 12.0049i −0.541221 0.541221i
\(493\) 11.1218 + 11.1218i 0.500902 + 0.500902i
\(494\) 9.48374 + 9.48374i 0.426694 + 0.426694i
\(495\) −2.00488 + 1.72829i −0.0901125 + 0.0776808i
\(496\) 3.23904 + 3.23904i 0.145437 + 0.145437i
\(497\) 0.000879026 0 0.000879026i 3.94297e−5 0 3.94297e-5i
\(498\) −8.17374 −0.366274
\(499\) −8.81194 + 8.81194i −0.394477 + 0.394477i −0.876280 0.481803i \(-0.839982\pi\)
0.481803 + 0.876280i \(0.339982\pi\)
\(500\) −5.97229 9.45154i −0.267089 0.422686i
\(501\) 1.11499 + 1.11499i 0.0498141 + 0.0498141i
\(502\) 9.93109 + 9.93109i 0.443246 + 0.443246i
\(503\) 13.2027 0.588678 0.294339 0.955701i \(-0.404900\pi\)
0.294339 + 0.955701i \(0.404900\pi\)
\(504\) 0.188243 + 0.188243i 0.00838501 + 0.00838501i
\(505\) −5.38547 6.24734i −0.239650 0.278003i
\(506\) 28.4074i 1.26286i
\(507\) −4.31446 + 4.31446i −0.191612 + 0.191612i
\(508\) 13.9019 13.9019i 0.616795 0.616795i
\(509\) 25.2057 1.11722 0.558612 0.829429i \(-0.311334\pi\)
0.558612 + 0.829429i \(0.311334\pi\)
\(510\) −32.8951 2.43718i −1.45662 0.107920i
\(511\) 10.8170i 0.478518i
\(512\) −1.00000 −0.0441942
\(513\) 21.0573i 0.929701i
\(514\) 15.1135i 0.666630i
\(515\) 16.2853 + 18.8915i 0.717614 + 0.832458i
\(516\) 14.0741 14.0741i 0.619576 0.619576i
\(517\) 15.0154 + 15.0154i 0.660376 + 0.660376i
\(518\) 4.93540 0.722344i 0.216849 0.0317380i
\(519\) 5.54335i 0.243326i
\(520\) −5.26221 + 4.53625i −0.230763 + 0.198928i
\(521\) 8.65279i 0.379086i 0.981872 + 0.189543i \(0.0607006\pi\)
−0.981872 + 0.189543i \(0.939299\pi\)
\(522\) 0.446297 + 0.446297i 0.0195339 + 0.0195339i
\(523\) −28.4569 −1.24433 −0.622167 0.782884i \(-0.713748\pi\)
−0.622167 + 0.782884i \(0.713748\pi\)
\(524\) 2.71250 + 2.71250i 0.118496 + 0.118496i
\(525\) −7.39433 1.10173i −0.322715 0.0480835i
\(526\) −9.74250 + 9.74250i −0.424793 + 0.424793i
\(527\) −26.2047 + 26.2047i −1.14149 + 1.14149i
\(528\) −4.70126 4.70126i −0.204596 0.204596i
\(529\) 37.6945 1.63889
\(530\) −1.40827 0.104338i −0.0611713 0.00453215i
\(531\) −2.00108 + 2.00108i −0.0868393 + 0.0868393i
\(532\) −3.53975 −0.153468
\(533\) 28.9298i 1.25309i
\(534\) 14.9564i 0.647228i
\(535\) −0.907292 + 12.2459i −0.0392256 + 0.529437i
\(536\) 2.01024 + 2.01024i 0.0868292 + 0.0868292i
\(537\) 0.807861i 0.0348618i
\(538\) 6.43418i 0.277397i
\(539\) 23.0724 0.993799
\(540\) 10.8780 + 0.805947i 0.468116 + 0.0346824i
\(541\) 22.0757 22.0757i 0.949106 0.949106i −0.0496598 0.998766i \(-0.515814\pi\)
0.998766 + 0.0496598i \(0.0158137\pi\)
\(542\) 25.6662 1.10246
\(543\) 20.9076 20.9076i 0.897231 0.897231i
\(544\) 8.09027i 0.346867i
\(545\) 6.35719 + 0.471000i 0.272312 + 0.0201754i
\(546\) 4.64561i 0.198814i
\(547\) −24.7795 −1.05949 −0.529747 0.848155i \(-0.677713\pi\)
−0.529747 + 0.848155i \(0.677713\pi\)
\(548\) −11.4519 + 11.4519i −0.489203 + 0.489203i
\(549\) 2.82891 2.82891i 0.120735 0.120735i
\(550\) 18.0326 + 2.68680i 0.768913 + 0.114565i
\(551\) −8.39222 −0.357521
\(552\) 10.0446 10.0446i 0.427526 0.427526i
\(553\) 0.882399 0.0375234
\(554\) 17.2625 0.733415
\(555\) −16.2413 + 18.7425i −0.689405 + 0.795573i
\(556\) −2.41427 −0.102388
\(557\) −28.3582 −1.20157 −0.600787 0.799409i \(-0.705146\pi\)
−0.600787 + 0.799409i \(0.705146\pi\)
\(558\) −1.05154 + 1.05154i −0.0445153 + 0.0445153i
\(559\) 33.9163 1.43451
\(560\) 0.135480 1.82861i 0.00572509 0.0772728i
\(561\) 38.0344 38.0344i 1.60581 1.60581i
\(562\) 3.84098 3.84098i 0.162022 0.162022i
\(563\) −16.8486 −0.710085 −0.355043 0.934850i \(-0.615534\pi\)
−0.355043 + 0.934850i \(0.615534\pi\)
\(564\) 10.6186i 0.447124i
\(565\) 17.3581 + 20.1360i 0.730261 + 0.847128i
\(566\) 20.5564i 0.864049i
\(567\) 5.72219 5.72219i 0.240309 0.240309i
\(568\) −0.00151598 −6.36090e−5
\(569\) 4.89447 4.89447i 0.205187 0.205187i −0.597031 0.802218i \(-0.703653\pi\)
0.802218 + 0.597031i \(0.203653\pi\)
\(570\) 13.3304 11.4914i 0.558348 0.481320i
\(571\) −38.8520 −1.62590 −0.812952 0.582330i \(-0.802141\pi\)
−0.812952 + 0.582330i \(0.802141\pi\)
\(572\) 11.3293i 0.473701i
\(573\) 0.713470i 0.0298056i
\(574\) 5.39894 + 5.39894i 0.225347 + 0.225347i
\(575\) −5.74055 + 38.5280i −0.239397 + 1.60673i
\(576\) 0.324646i 0.0135269i
\(577\) 18.6556i 0.776642i 0.921524 + 0.388321i \(0.126945\pi\)
−0.921524 + 0.388321i \(0.873055\pi\)
\(578\) 48.4524 2.01535
\(579\) 11.3302 11.3302i 0.470867 0.470867i
\(580\) 0.321204 4.33536i 0.0133373 0.180016i
\(581\) 3.67597 0.152505
\(582\) −18.8504 18.8504i −0.781376 0.781376i
\(583\) 1.62829 1.62829i 0.0674368 0.0674368i
\(584\) 9.32759 9.32759i 0.385979 0.385979i
\(585\) −1.47267 1.70835i −0.0608876 0.0706317i
\(586\) 11.2671 + 11.2671i 0.465441 + 0.465441i
\(587\) −5.75904 −0.237701 −0.118851 0.992912i \(-0.537921\pi\)
−0.118851 + 0.992912i \(0.537921\pi\)
\(588\) 8.15820 + 8.15820i 0.336439 + 0.336439i
\(589\) 19.7733i 0.814746i
\(590\) 19.4386 + 1.44019i 0.800275 + 0.0592919i
\(591\) 21.6988i 0.892568i
\(592\) −4.87870 3.63294i −0.200513 0.149313i
\(593\) −16.3572 16.3572i −0.671709 0.671709i 0.286401 0.958110i \(-0.407541\pi\)
−0.958110 + 0.286401i \(0.907541\pi\)
\(594\) −12.5775 + 12.5775i −0.516062 + 0.516062i
\(595\) 14.7939 + 1.09607i 0.606492 + 0.0449346i
\(596\) 4.02923i 0.165044i
\(597\) 10.8332i 0.443372i
\(598\) 24.2059 0.989852
\(599\) 23.6157i 0.964910i 0.875921 + 0.482455i \(0.160255\pi\)
−0.875921 + 0.482455i \(0.839745\pi\)
\(600\) 5.42614 + 7.32620i 0.221521 + 0.299091i
\(601\) 30.4617 1.24256 0.621279 0.783589i \(-0.286613\pi\)
0.621279 + 0.783589i \(0.286613\pi\)
\(602\) −6.32952 + 6.32952i −0.257972 + 0.257972i
\(603\) −0.652617 + 0.652617i −0.0265766 + 0.0265766i
\(604\) 8.86568i 0.360739i
\(605\) −3.88816 + 3.35176i −0.158076 + 0.136268i
\(606\) 4.75588 + 4.75588i 0.193195 + 0.193195i
\(607\) −17.6781 −0.717530 −0.358765 0.933428i \(-0.616802\pi\)
−0.358765 + 0.933428i \(0.616802\pi\)
\(608\) 3.05234 + 3.05234i 0.123789 + 0.123789i
\(609\) −2.05547 2.05547i −0.0832918 0.0832918i
\(610\) −27.4802 2.03599i −1.11264 0.0824349i
\(611\) −12.7946 + 12.7946i −0.517614 + 0.517614i
\(612\) 2.62647 0.106169
\(613\) −24.9613 + 24.9613i −1.00818 + 1.00818i −0.00821132 + 0.999966i \(0.502614\pi\)
−0.999966 + 0.00821132i \(0.997386\pi\)
\(614\) −9.43686 9.43686i −0.380841 0.380841i
\(615\) −37.8589 2.80494i −1.52662 0.113106i
\(616\) 2.11429 + 2.11429i 0.0851873 + 0.0851873i
\(617\) −6.37297 6.37297i −0.256566 0.256566i 0.567090 0.823656i \(-0.308069\pi\)
−0.823656 + 0.567090i \(0.808069\pi\)
\(618\) −14.3814 14.3814i −0.578506 0.578506i
\(619\) −2.43520 −0.0978789 −0.0489394 0.998802i \(-0.515584\pi\)
−0.0489394 + 0.998802i \(0.515584\pi\)
\(620\) 10.2148 + 0.756805i 0.410234 + 0.0303940i
\(621\) −26.8729 26.8729i −1.07837 1.07837i
\(622\) −6.70368 6.70368i −0.268793 0.268793i
\(623\) 6.72635i 0.269485i
\(624\) 4.00594 4.00594i 0.160366 0.160366i
\(625\) −23.9141 7.28804i −0.956564 0.291522i
\(626\) 23.2157 0.927885
\(627\) 28.6997i 1.14616i
\(628\) 6.87897 6.87897i 0.274501 0.274501i
\(629\) 29.3915 39.4700i 1.17191 1.57377i
\(630\) 0.593650 + 0.0439832i 0.0236516 + 0.00175233i
\(631\) 8.01035 + 8.01035i 0.318887 + 0.318887i 0.848340 0.529453i \(-0.177603\pi\)
−0.529453 + 0.848340i \(0.677603\pi\)
\(632\) −0.760897 0.760897i −0.0302669 0.0302669i
\(633\) −35.4433 + 35.4433i −1.40874 + 1.40874i
\(634\) 15.3696 + 15.3696i 0.610406 + 0.610406i
\(635\) 3.24818 43.8414i 0.128900 1.73979i
\(636\) 1.15150 0.0456598
\(637\) 19.6600i 0.778957i
\(638\) 5.01268 + 5.01268i 0.198454 + 0.198454i
\(639\) 0 0.000492156i 0 1.94694e-5i
\(640\) −1.69364 + 1.45999i −0.0669471 + 0.0577112i
\(641\) 20.0552 0.792134 0.396067 0.918222i \(-0.370375\pi\)
0.396067 + 0.918222i \(0.370375\pi\)
\(642\) 10.0131i 0.395184i
\(643\) 2.02458i 0.0798417i −0.999203 0.0399208i \(-0.987289\pi\)
0.999203 0.0399208i \(-0.0127106\pi\)
\(644\) −4.51735 + 4.51735i −0.178009 + 0.178009i
\(645\) 3.28842 44.3844i 0.129481 1.74764i
\(646\) −24.6943 + 24.6943i −0.971583 + 0.971583i
\(647\) 37.8245 1.48703 0.743517 0.668717i \(-0.233156\pi\)
0.743517 + 0.668717i \(0.233156\pi\)
\(648\) −9.86854 −0.387673
\(649\) −22.4755 + 22.4755i −0.882242 + 0.882242i
\(650\) −2.28942 + 15.3656i −0.0897983 + 0.602687i
\(651\) 4.84299 4.84299i 0.189812 0.189812i
\(652\) 10.6733i 0.417997i
\(653\) 24.2252i 0.948006i 0.880523 + 0.474003i \(0.157192\pi\)
−0.880523 + 0.474003i \(0.842808\pi\)
\(654\) −5.19806 −0.203260
\(655\) 8.55422 + 0.633777i 0.334241 + 0.0247637i
\(656\) 9.31106i 0.363536i
\(657\) 3.02816 + 3.02816i 0.118140 + 0.118140i
\(658\) 4.77550i 0.186169i
\(659\) 16.7841 0.653814 0.326907 0.945056i \(-0.393994\pi\)
0.326907 + 0.945056i \(0.393994\pi\)
\(660\) −14.8260 1.09845i −0.577103 0.0427572i
\(661\) 2.96671 + 2.96671i 0.115392 + 0.115392i 0.762445 0.647053i \(-0.223999\pi\)
−0.647053 + 0.762445i \(0.723999\pi\)
\(662\) 5.72839 5.72839i 0.222640 0.222640i
\(663\) 32.4091 + 32.4091i 1.25866 + 1.25866i
\(664\) −3.16981 3.16981i −0.123012 0.123012i
\(665\) −5.99507 + 5.16800i −0.232479 + 0.200407i
\(666\) 1.17942 1.58385i 0.0457016 0.0613730i
\(667\) −10.7100 + 10.7100i −0.414692 + 0.414692i
\(668\) 0.864796i 0.0334600i
\(669\) −24.3077 −0.939788
\(670\) 6.33957 + 0.469695i 0.244919 + 0.0181459i
\(671\) 31.7735 31.7735i 1.22660 1.22660i
\(672\) 1.49519i 0.0576783i
\(673\) 23.2071 + 23.2071i 0.894567 + 0.894567i 0.994949 0.100382i \(-0.0320066\pi\)
−0.100382 + 0.994949i \(0.532007\pi\)
\(674\) −5.31333 5.31333i −0.204662 0.204662i
\(675\) 19.6002 14.5168i 0.754411 0.558754i
\(676\) −3.34633 −0.128705
\(677\) 4.70869 + 4.70869i 0.180970 + 0.180970i 0.791778 0.610809i \(-0.209156\pi\)
−0.610809 + 0.791778i \(0.709156\pi\)
\(678\) −15.3288 15.3288i −0.588701 0.588701i
\(679\) 8.47761 + 8.47761i 0.325341 + 0.325341i
\(680\) −11.8117 13.7020i −0.452959 0.525448i
\(681\) −23.1544 23.1544i −0.887277 0.887277i
\(682\) −11.8106 + 11.8106i −0.452252 + 0.452252i
\(683\) −46.0160 −1.76075 −0.880376 0.474277i \(-0.842710\pi\)
−0.880376 + 0.474277i \(0.842710\pi\)
\(684\) −0.990930 + 0.990930i −0.0378892 + 0.0378892i
\(685\) −2.67576 + 36.1152i −0.102235 + 1.37989i
\(686\) −7.72788 7.72788i −0.295052 0.295052i
\(687\) −23.4233 23.4233i −0.893653 0.893653i
\(688\) 10.9160 0.416167
\(689\) 1.38746 + 1.38746i 0.0528581 + 0.0528581i
\(690\) 2.34693 31.6770i 0.0893460 1.20592i
\(691\) 37.9434i 1.44344i 0.692187 + 0.721718i \(0.256647\pi\)
−0.692187 + 0.721718i \(0.743353\pi\)
\(692\) −2.14973 + 2.14973i −0.0817206 + 0.0817206i
\(693\) −0.686397 + 0.686397i −0.0260741 + 0.0260741i
\(694\) −32.7620 −1.24363
\(695\) −4.08890 + 3.52481i −0.155101 + 0.133704i
\(696\) 3.54488i 0.134368i
\(697\) 75.3290 2.85329
\(698\) 14.0604i 0.532194i
\(699\) 5.76801i 0.218166i
\(700\) −2.44030 3.29481i −0.0922345 0.124532i
\(701\) 11.9143 11.9143i 0.449995 0.449995i −0.445358 0.895353i \(-0.646923\pi\)
0.895353 + 0.445358i \(0.146923\pi\)
\(702\) −10.7173 10.7173i −0.404498 0.404498i
\(703\) 3.80249 + 25.9805i 0.143414 + 0.979871i
\(704\) 3.64633i 0.137426i
\(705\) 15.5031 + 17.9841i 0.583880 + 0.677322i
\(706\) 6.79098i 0.255582i
\(707\) −2.13886 2.13886i −0.0804402 0.0804402i
\(708\) −15.8943 −0.597345
\(709\) −13.4491 13.4491i −0.505093 0.505093i 0.407923 0.913016i \(-0.366253\pi\)
−0.913016 + 0.407923i \(0.866253\pi\)
\(710\) −0.00256752 + 0.00221331i −9.63574e−5 + 8.30642e-5i
\(711\) 0.247022 0.247022i 0.00926405 0.00926405i
\(712\) 5.80016 5.80016i 0.217370 0.217370i
\(713\) −25.2343 25.2343i −0.945032 0.945032i
\(714\) −12.0965 −0.452700
\(715\) −16.5407 19.1878i −0.618586 0.717582i
\(716\) −0.313292 + 0.313292i −0.0117083 + 0.0117083i
\(717\) 11.6951 0.436763
\(718\) 4.91904i 0.183577i
\(719\) 15.0482i 0.561204i −0.959824 0.280602i \(-0.909466\pi\)
0.959824 0.280602i \(-0.0905342\pi\)
\(720\) −0.473980 0.549834i −0.0176642 0.0204911i
\(721\) 6.46775 + 6.46775i 0.240872 + 0.240872i
\(722\) 0.366413i 0.0136365i
\(723\) 7.61354i 0.283151i
\(724\) 16.2161 0.602667
\(725\) −5.78558 7.81150i −0.214871 0.290112i
\(726\) 2.95992 2.95992i 0.109853 0.109853i
\(727\) −48.0498 −1.78207 −0.891033 0.453938i \(-0.850019\pi\)
−0.891033 + 0.453938i \(0.850019\pi\)
\(728\) −1.80159 + 1.80159i −0.0667713 + 0.0667713i
\(729\) 23.4800i 0.869631i
\(730\) 2.17940 29.4158i 0.0806632 1.08873i
\(731\) 88.3130i 3.26637i
\(732\) 22.4697 0.830502
\(733\) 17.9391 17.9391i 0.662596 0.662596i −0.293395 0.955991i \(-0.594785\pi\)
0.955991 + 0.293395i \(0.0947851\pi\)
\(734\) −21.4924 + 21.4924i −0.793298 + 0.793298i
\(735\) 25.7280 + 1.90617i 0.948991 + 0.0703102i
\(736\) 7.79067 0.287168
\(737\) −7.33001 + 7.33001i −0.270004 + 0.270004i
\(738\) 3.02280 0.111271
\(739\) 27.0049 0.993391 0.496696 0.867925i \(-0.334547\pi\)
0.496696 + 0.867925i \(0.334547\pi\)
\(740\) −13.5668 + 0.969960i −0.498727 + 0.0356564i
\(741\) −24.4550 −0.898376
\(742\) −0.517862 −0.0190113
\(743\) 21.8683 21.8683i 0.802270 0.802270i −0.181180 0.983450i \(-0.557992\pi\)
0.983450 + 0.181180i \(0.0579917\pi\)
\(744\) −8.35226 −0.306209
\(745\) −5.88265 6.82408i −0.215523 0.250015i
\(746\) −19.5734 + 19.5734i −0.716632 + 0.716632i
\(747\) 1.02907 1.02907i 0.0376515 0.0376515i
\(748\) 29.4998 1.07862
\(749\) 4.50318i 0.164542i
\(750\) 19.8861 + 4.48584i 0.726139 + 0.163800i
\(751\) 17.0169i 0.620957i −0.950580 0.310479i \(-0.899511\pi\)
0.950580 0.310479i \(-0.100489\pi\)
\(752\) −4.11794 + 4.11794i −0.150166 + 0.150166i
\(753\) −25.6085 −0.933227
\(754\) −4.27130 + 4.27130i −0.155552 + 0.155552i
\(755\) −12.9438 15.0153i −0.471074 0.546462i
\(756\) 4.00017 0.145485
\(757\) 31.0722i 1.12934i −0.825317 0.564669i \(-0.809004\pi\)
0.825317 0.564669i \(-0.190996\pi\)
\(758\) 1.90775i 0.0692925i
\(759\) 36.6259 + 36.6259i 1.32944 + 1.32944i
\(760\) 9.62597 + 0.713182i 0.349171 + 0.0258698i
\(761\) 14.8739i 0.539180i 0.962975 + 0.269590i \(0.0868882\pi\)
−0.962975 + 0.269590i \(0.913112\pi\)
\(762\) 35.8476i 1.29862i
\(763\) 2.33772 0.0846312
\(764\) 0.276686 0.276686i 0.0100102 0.0100102i
\(765\) 4.44830 3.83463i 0.160829 0.138641i
\(766\) −12.0669 −0.435996
\(767\) −19.1514 19.1514i −0.691516 0.691516i
\(768\) 1.28931 1.28931i 0.0465240 0.0465240i
\(769\) 21.6211 21.6211i 0.779677 0.779677i −0.200099 0.979776i \(-0.564126\pi\)
0.979776 + 0.200099i \(0.0641264\pi\)
\(770\) 6.66771 + 0.494007i 0.240288 + 0.0178028i
\(771\) 19.4861 + 19.4861i 0.701773 + 0.701773i
\(772\) 8.78779 0.316279
\(773\) 8.11195 + 8.11195i 0.291766 + 0.291766i 0.837778 0.546011i \(-0.183854\pi\)
−0.546011 + 0.837778i \(0.683854\pi\)
\(774\) 3.54382i 0.127380i
\(775\) 18.4051 13.6317i 0.661129 0.489665i
\(776\) 14.6206i 0.524847i
\(777\) −5.43194 + 7.29460i −0.194870 + 0.261692i