Properties

Label 370.2.h.e.117.4
Level $370$
Weight $2$
Character 370.117
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 117.4
Root \(-0.794932 + 0.794932i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.e.253.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.794932 - 0.794932i) q^{3} +1.00000 q^{4} +(2.22550 + 0.217179i) q^{5} +(0.794932 + 0.794932i) q^{6} +(2.93770 + 2.93770i) q^{7} -1.00000 q^{8} -1.73617i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.794932 - 0.794932i) q^{3} +1.00000 q^{4} +(2.22550 + 0.217179i) q^{5} +(0.794932 + 0.794932i) q^{6} +(2.93770 + 2.93770i) q^{7} -1.00000 q^{8} -1.73617i q^{9} +(-2.22550 - 0.217179i) q^{10} +3.55539i q^{11} +(-0.794932 - 0.794932i) q^{12} -4.41538 q^{13} +(-2.93770 - 2.93770i) q^{14} +(-1.59648 - 1.94176i) q^{15} +1.00000 q^{16} +5.37801i q^{17} +1.73617i q^{18} +(1.98590 - 1.98590i) q^{19} +(2.22550 + 0.217179i) q^{20} -4.67054i q^{21} -3.55539i q^{22} +5.90774 q^{23} +(0.794932 + 0.794932i) q^{24} +(4.90567 + 0.966660i) q^{25} +4.41538 q^{26} +(-3.76493 + 3.76493i) q^{27} +(2.93770 + 2.93770i) q^{28} +(2.18437 + 2.18437i) q^{29} +(1.59648 + 1.94176i) q^{30} +(5.42197 - 5.42197i) q^{31} -1.00000 q^{32} +(2.82629 - 2.82629i) q^{33} -5.37801i q^{34} +(5.89983 + 7.17584i) q^{35} -1.73617i q^{36} +(-3.88900 - 4.67714i) q^{37} +(-1.98590 + 1.98590i) q^{38} +(3.50993 + 3.50993i) q^{39} +(-2.22550 - 0.217179i) q^{40} -6.34477i q^{41} +4.67054i q^{42} +1.78544 q^{43} +3.55539i q^{44} +(0.377058 - 3.86383i) q^{45} -5.90774 q^{46} +(1.82646 + 1.82646i) q^{47} +(-0.794932 - 0.794932i) q^{48} +10.2601i q^{49} +(-4.90567 - 0.966660i) q^{50} +(4.27515 - 4.27515i) q^{51} -4.41538 q^{52} +(-9.57437 + 9.57437i) q^{53} +(3.76493 - 3.76493i) q^{54} +(-0.772154 + 7.91250i) q^{55} +(-2.93770 - 2.93770i) q^{56} -3.15731 q^{57} +(-2.18437 - 2.18437i) q^{58} +(4.44588 - 4.44588i) q^{59} +(-1.59648 - 1.94176i) q^{60} +(1.44033 - 1.44033i) q^{61} +(-5.42197 + 5.42197i) q^{62} +(5.10033 - 5.10033i) q^{63} +1.00000 q^{64} +(-9.82642 - 0.958927i) q^{65} +(-2.82629 + 2.82629i) q^{66} +(7.88856 - 7.88856i) q^{67} +5.37801i q^{68} +(-4.69625 - 4.69625i) q^{69} +(-5.89983 - 7.17584i) q^{70} -11.2579 q^{71} +1.73617i q^{72} +(-4.02333 - 4.02333i) q^{73} +(3.88900 + 4.67714i) q^{74} +(-3.13124 - 4.66810i) q^{75} +(1.98590 - 1.98590i) q^{76} +(-10.4447 + 10.4447i) q^{77} +(-3.50993 - 3.50993i) q^{78} +(2.03059 - 2.03059i) q^{79} +(2.22550 + 0.217179i) q^{80} +0.777232 q^{81} +6.34477i q^{82} +(-4.51281 + 4.51281i) q^{83} -4.67054i q^{84} +(-1.16799 + 11.9687i) q^{85} -1.78544 q^{86} -3.47285i q^{87} -3.55539i q^{88} +(2.13937 + 2.13937i) q^{89} +(-0.377058 + 3.86383i) q^{90} +(-12.9711 - 12.9711i) q^{91} +5.90774 q^{92} -8.62020 q^{93} +(-1.82646 - 1.82646i) q^{94} +(4.85091 - 3.98832i) q^{95} +(0.794932 + 0.794932i) q^{96} -5.91995i q^{97} -10.2601i q^{98} +6.17274 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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.794932 0.794932i −0.458954 0.458954i 0.439358 0.898312i \(-0.355206\pi\)
−0.898312 + 0.439358i \(0.855206\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.22550 + 0.217179i 0.995272 + 0.0971252i
\(6\) 0.794932 + 0.794932i 0.324530 + 0.324530i
\(7\) 2.93770 + 2.93770i 1.11035 + 1.11035i 0.993103 + 0.117242i \(0.0374053\pi\)
0.117242 + 0.993103i \(0.462595\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.73617i 0.578722i
\(10\) −2.22550 0.217179i −0.703764 0.0686779i
\(11\) 3.55539i 1.07199i 0.844221 + 0.535995i \(0.180063\pi\)
−0.844221 + 0.535995i \(0.819937\pi\)
\(12\) −0.794932 0.794932i −0.229477 0.229477i
\(13\) −4.41538 −1.22461 −0.612303 0.790623i \(-0.709757\pi\)
−0.612303 + 0.790623i \(0.709757\pi\)
\(14\) −2.93770 2.93770i −0.785133 0.785133i
\(15\) −1.59648 1.94176i −0.412208 0.501360i
\(16\) 1.00000 0.250000
\(17\) 5.37801i 1.30436i 0.758065 + 0.652179i \(0.226145\pi\)
−0.758065 + 0.652179i \(0.773855\pi\)
\(18\) 1.73617i 0.409218i
\(19\) 1.98590 1.98590i 0.455597 0.455597i −0.441610 0.897207i \(-0.645592\pi\)
0.897207 + 0.441610i \(0.145592\pi\)
\(20\) 2.22550 + 0.217179i 0.497636 + 0.0485626i
\(21\) 4.67054i 1.01920i
\(22\) 3.55539i 0.758011i
\(23\) 5.90774 1.23185 0.615925 0.787805i \(-0.288783\pi\)
0.615925 + 0.787805i \(0.288783\pi\)
\(24\) 0.794932 + 0.794932i 0.162265 + 0.162265i
\(25\) 4.90567 + 0.966660i 0.981133 + 0.193332i
\(26\) 4.41538 0.865928
\(27\) −3.76493 + 3.76493i −0.724561 + 0.724561i
\(28\) 2.93770 + 2.93770i 0.555173 + 0.555173i
\(29\) 2.18437 + 2.18437i 0.405627 + 0.405627i 0.880210 0.474584i \(-0.157401\pi\)
−0.474584 + 0.880210i \(0.657401\pi\)
\(30\) 1.59648 + 1.94176i 0.291475 + 0.354515i
\(31\) 5.42197 5.42197i 0.973815 0.973815i −0.0258507 0.999666i \(-0.508229\pi\)
0.999666 + 0.0258507i \(0.00822946\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.82629 2.82629i 0.491994 0.491994i
\(34\) 5.37801i 0.922321i
\(35\) 5.89983 + 7.17584i 0.997253 + 1.21294i
\(36\) 1.73617i 0.289361i
\(37\) −3.88900 4.67714i −0.639348 0.768918i
\(38\) −1.98590 + 1.98590i −0.322156 + 0.322156i
\(39\) 3.50993 + 3.50993i 0.562039 + 0.562039i
\(40\) −2.22550 0.217179i −0.351882 0.0343389i
\(41\) 6.34477i 0.990886i −0.868640 0.495443i \(-0.835006\pi\)
0.868640 0.495443i \(-0.164994\pi\)
\(42\) 4.67054i 0.720680i
\(43\) 1.78544 0.272277 0.136139 0.990690i \(-0.456531\pi\)
0.136139 + 0.990690i \(0.456531\pi\)
\(44\) 3.55539i 0.535995i
\(45\) 0.377058 3.86383i 0.0562085 0.575986i
\(46\) −5.90774 −0.871049
\(47\) 1.82646 + 1.82646i 0.266417 + 0.266417i 0.827655 0.561238i \(-0.189675\pi\)
−0.561238 + 0.827655i \(0.689675\pi\)
\(48\) −0.794932 0.794932i −0.114739 0.114739i
\(49\) 10.2601i 1.46573i
\(50\) −4.90567 0.966660i −0.693766 0.136706i
\(51\) 4.27515 4.27515i 0.598641 0.598641i
\(52\) −4.41538 −0.612303
\(53\) −9.57437 + 9.57437i −1.31514 + 1.31514i −0.397567 + 0.917573i \(0.630145\pi\)
−0.917573 + 0.397567i \(0.869855\pi\)
\(54\) 3.76493 3.76493i 0.512342 0.512342i
\(55\) −0.772154 + 7.91250i −0.104117 + 1.06692i
\(56\) −2.93770 2.93770i −0.392566 0.392566i
\(57\) −3.15731 −0.418197
\(58\) −2.18437 2.18437i −0.286821 0.286821i
\(59\) 4.44588 4.44588i 0.578805 0.578805i −0.355769 0.934574i \(-0.615781\pi\)
0.934574 + 0.355769i \(0.115781\pi\)
\(60\) −1.59648 1.94176i −0.206104 0.250680i
\(61\) 1.44033 1.44033i 0.184416 0.184416i −0.608861 0.793277i \(-0.708373\pi\)
0.793277 + 0.608861i \(0.208373\pi\)
\(62\) −5.42197 + 5.42197i −0.688591 + 0.688591i
\(63\) 5.10033 5.10033i 0.642581 0.642581i
\(64\) 1.00000 0.125000
\(65\) −9.82642 0.958927i −1.21882 0.118940i
\(66\) −2.82629 + 2.82629i −0.347893 + 0.347893i
\(67\) 7.88856 7.88856i 0.963741 0.963741i −0.0356245 0.999365i \(-0.511342\pi\)
0.999365 + 0.0356245i \(0.0113420\pi\)
\(68\) 5.37801i 0.652179i
\(69\) −4.69625 4.69625i −0.565363 0.565363i
\(70\) −5.89983 7.17584i −0.705165 0.857677i
\(71\) −11.2579 −1.33606 −0.668032 0.744132i \(-0.732863\pi\)
−0.668032 + 0.744132i \(0.732863\pi\)
\(72\) 1.73617i 0.204609i
\(73\) −4.02333 4.02333i −0.470896 0.470896i 0.431309 0.902204i \(-0.358052\pi\)
−0.902204 + 0.431309i \(0.858052\pi\)
\(74\) 3.88900 + 4.67714i 0.452087 + 0.543707i
\(75\) −3.13124 4.66810i −0.361565 0.539026i
\(76\) 1.98590 1.98590i 0.227799 0.227799i
\(77\) −10.4447 + 10.4447i −1.19028 + 1.19028i
\(78\) −3.50993 3.50993i −0.397421 0.397421i
\(79\) 2.03059 2.03059i 0.228459 0.228459i −0.583590 0.812049i \(-0.698352\pi\)
0.812049 + 0.583590i \(0.198352\pi\)
\(80\) 2.22550 + 0.217179i 0.248818 + 0.0242813i
\(81\) 0.777232 0.0863591
\(82\) 6.34477i 0.700662i
\(83\) −4.51281 + 4.51281i −0.495345 + 0.495345i −0.909985 0.414640i \(-0.863907\pi\)
0.414640 + 0.909985i \(0.363907\pi\)
\(84\) 4.67054i 0.509598i
\(85\) −1.16799 + 11.9687i −0.126686 + 1.29819i
\(86\) −1.78544 −0.192529
\(87\) 3.47285i 0.372328i
\(88\) 3.55539i 0.379006i
\(89\) 2.13937 + 2.13937i 0.226773 + 0.226773i 0.811343 0.584570i \(-0.198737\pi\)
−0.584570 + 0.811343i \(0.698737\pi\)
\(90\) −0.377058 + 3.86383i −0.0397454 + 0.407283i
\(91\) −12.9711 12.9711i −1.35974 1.35974i
\(92\) 5.90774 0.615925
\(93\) −8.62020 −0.893873
\(94\) −1.82646 1.82646i −0.188385 0.188385i
\(95\) 4.85091 3.98832i 0.497693 0.409193i
\(96\) 0.794932 + 0.794932i 0.0811324 + 0.0811324i
\(97\) 5.91995i 0.601080i −0.953769 0.300540i \(-0.902833\pi\)
0.953769 0.300540i \(-0.0971669\pi\)
\(98\) 10.2601i 1.03643i
\(99\) 6.17274 0.620384
\(100\) 4.90567 + 0.966660i 0.490567 + 0.0966660i
\(101\) 9.23382i 0.918799i −0.888230 0.459399i \(-0.848065\pi\)
0.888230 0.459399i \(-0.151935\pi\)
\(102\) −4.27515 + 4.27515i −0.423303 + 0.423303i
\(103\) 8.03931i 0.792137i −0.918221 0.396068i \(-0.870374\pi\)
0.918221 0.396068i \(-0.129626\pi\)
\(104\) 4.41538 0.432964
\(105\) 1.01434 10.3943i 0.0989896 1.01438i
\(106\) 9.57437 9.57437i 0.929945 0.929945i
\(107\) 4.60753 + 4.60753i 0.445427 + 0.445427i 0.893831 0.448404i \(-0.148007\pi\)
−0.448404 + 0.893831i \(0.648007\pi\)
\(108\) −3.76493 + 3.76493i −0.362281 + 0.362281i
\(109\) −14.6123 + 14.6123i −1.39961 + 1.39961i −0.598443 + 0.801166i \(0.704214\pi\)
−0.801166 + 0.598443i \(0.795786\pi\)
\(110\) 0.772154 7.91250i 0.0736220 0.754428i
\(111\) −0.626522 + 6.80950i −0.0594668 + 0.646329i
\(112\) 2.93770 + 2.93770i 0.277586 + 0.277586i
\(113\) 8.61849i 0.810759i −0.914148 0.405380i \(-0.867139\pi\)
0.914148 0.405380i \(-0.132861\pi\)
\(114\) 3.15731 0.295710
\(115\) 13.1477 + 1.28304i 1.22603 + 0.119644i
\(116\) 2.18437 + 2.18437i 0.202813 + 0.202813i
\(117\) 7.66584i 0.708707i
\(118\) −4.44588 + 4.44588i −0.409277 + 0.409277i
\(119\) −15.7990 + 15.7990i −1.44829 + 1.44829i
\(120\) 1.59648 + 1.94176i 0.145738 + 0.177258i
\(121\) −1.64079 −0.149163
\(122\) −1.44033 + 1.44033i −0.130402 + 0.130402i
\(123\) −5.04366 + 5.04366i −0.454772 + 0.454772i
\(124\) 5.42197 5.42197i 0.486908 0.486908i
\(125\) 10.7076 + 3.21670i 0.957717 + 0.287711i
\(126\) −5.10033 + 5.10033i −0.454373 + 0.454373i
\(127\) −4.22966 4.22966i −0.375322 0.375322i 0.494089 0.869411i \(-0.335502\pi\)
−0.869411 + 0.494089i \(0.835502\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.41931 1.41931i −0.124963 0.124963i
\(130\) 9.82642 + 0.958927i 0.861834 + 0.0841034i
\(131\) −15.2680 + 15.2680i −1.33397 + 1.33397i −0.432188 + 0.901783i \(0.642258\pi\)
−0.901783 + 0.432188i \(0.857742\pi\)
\(132\) 2.82629 2.82629i 0.245997 0.245997i
\(133\) 11.6680 1.01174
\(134\) −7.88856 + 7.88856i −0.681468 + 0.681468i
\(135\) −9.19650 + 7.56118i −0.791509 + 0.650762i
\(136\) 5.37801i 0.461160i
\(137\) −14.4220 14.4220i −1.23215 1.23215i −0.963136 0.269015i \(-0.913302\pi\)
−0.269015 0.963136i \(-0.586698\pi\)
\(138\) 4.69625 + 4.69625i 0.399772 + 0.399772i
\(139\) 1.56244 0.132525 0.0662624 0.997802i \(-0.478893\pi\)
0.0662624 + 0.997802i \(0.478893\pi\)
\(140\) 5.89983 + 7.17584i 0.498627 + 0.606469i
\(141\) 2.90383i 0.244547i
\(142\) 11.2579 0.944740
\(143\) 15.6984i 1.31277i
\(144\) 1.73617i 0.144680i
\(145\) 4.38690 + 5.33570i 0.364312 + 0.443105i
\(146\) 4.02333 + 4.02333i 0.332973 + 0.332973i
\(147\) 8.15611 8.15611i 0.672705 0.672705i
\(148\) −3.88900 4.67714i −0.319674 0.384459i
\(149\) 8.42600i 0.690285i −0.938550 0.345142i \(-0.887831\pi\)
0.938550 0.345142i \(-0.112169\pi\)
\(150\) 3.13124 + 4.66810i 0.255665 + 0.381149i
\(151\) 9.65715i 0.785887i 0.919563 + 0.392944i \(0.128543\pi\)
−0.919563 + 0.392944i \(0.871457\pi\)
\(152\) −1.98590 + 1.98590i −0.161078 + 0.161078i
\(153\) 9.33711 0.754861
\(154\) 10.4447 10.4447i 0.841654 0.841654i
\(155\) 13.2441 10.8890i 1.06379 0.874629i
\(156\) 3.50993 + 3.50993i 0.281019 + 0.281019i
\(157\) −13.7789 13.7789i −1.09968 1.09968i −0.994448 0.105231i \(-0.966442\pi\)
−0.105231 0.994448i \(-0.533558\pi\)
\(158\) −2.03059 + 2.03059i −0.161545 + 0.161545i
\(159\) 15.2219 1.20718
\(160\) −2.22550 0.217179i −0.175941 0.0171695i
\(161\) 17.3552 + 17.3552i 1.36778 + 1.36778i
\(162\) −0.777232 −0.0610651
\(163\) 9.92434i 0.777334i −0.921378 0.388667i \(-0.872936\pi\)
0.921378 0.388667i \(-0.127064\pi\)
\(164\) 6.34477i 0.495443i
\(165\) 6.90371 5.67609i 0.537453 0.441883i
\(166\) 4.51281 4.51281i 0.350262 0.350262i
\(167\) 17.7622i 1.37448i 0.726431 + 0.687239i \(0.241178\pi\)
−0.726431 + 0.687239i \(0.758822\pi\)
\(168\) 4.67054i 0.360340i
\(169\) 6.49561 0.499662
\(170\) 1.16799 11.9687i 0.0895806 0.917960i
\(171\) −3.44786 3.44786i −0.263664 0.263664i
\(172\) 1.78544 0.136139
\(173\) −4.93605 4.93605i −0.375281 0.375281i 0.494116 0.869396i \(-0.335492\pi\)
−0.869396 + 0.494116i \(0.835492\pi\)
\(174\) 3.47285i 0.263276i
\(175\) 11.5716 + 17.2511i 0.874732 + 1.30406i
\(176\) 3.55539i 0.267998i
\(177\) −7.06835 −0.531290
\(178\) −2.13937 2.13937i −0.160353 0.160353i
\(179\) 3.68868 + 3.68868i 0.275705 + 0.275705i 0.831392 0.555687i \(-0.187545\pi\)
−0.555687 + 0.831392i \(0.687545\pi\)
\(180\) 0.377058 3.86383i 0.0281042 0.287993i
\(181\) −5.35458 −0.398002 −0.199001 0.979999i \(-0.563770\pi\)
−0.199001 + 0.979999i \(0.563770\pi\)
\(182\) 12.9711 + 12.9711i 0.961479 + 0.961479i
\(183\) −2.28994 −0.169277
\(184\) −5.90774 −0.435525
\(185\) −7.63918 11.2536i −0.561644 0.827379i
\(186\) 8.62020 0.632064
\(187\) −19.1209 −1.39826
\(188\) 1.82646 + 1.82646i 0.133209 + 0.133209i
\(189\) −22.1205 −1.60903
\(190\) −4.85091 + 3.98832i −0.351922 + 0.289343i
\(191\) 10.0773 + 10.0773i 0.729166 + 0.729166i 0.970454 0.241288i \(-0.0775698\pi\)
−0.241288 + 0.970454i \(0.577570\pi\)
\(192\) −0.794932 0.794932i −0.0573693 0.0573693i
\(193\) 24.7844 1.78402 0.892011 0.452014i \(-0.149294\pi\)
0.892011 + 0.452014i \(0.149294\pi\)
\(194\) 5.91995i 0.425028i
\(195\) 7.04905 + 8.57362i 0.504793 + 0.613970i
\(196\) 10.2601i 0.732867i
\(197\) 11.3006 + 11.3006i 0.805132 + 0.805132i 0.983893 0.178760i \(-0.0572087\pi\)
−0.178760 + 0.983893i \(0.557209\pi\)
\(198\) −6.17274 −0.438678
\(199\) −6.90680 6.90680i −0.489610 0.489610i 0.418573 0.908183i \(-0.362530\pi\)
−0.908183 + 0.418573i \(0.862530\pi\)
\(200\) −4.90567 0.966660i −0.346883 0.0683532i
\(201\) −12.5417 −0.884626
\(202\) 9.23382i 0.649689i
\(203\) 12.8340i 0.900771i
\(204\) 4.27515 4.27515i 0.299321 0.299321i
\(205\) 1.37795 14.1203i 0.0962400 0.986202i
\(206\) 8.03931i 0.560125i
\(207\) 10.2568i 0.712898i
\(208\) −4.41538 −0.306152
\(209\) 7.06065 + 7.06065i 0.488396 + 0.488396i
\(210\) −1.01434 + 10.3943i −0.0699962 + 0.717273i
\(211\) −22.7919 −1.56906 −0.784531 0.620090i \(-0.787096\pi\)
−0.784531 + 0.620090i \(0.787096\pi\)
\(212\) −9.57437 + 9.57437i −0.657570 + 0.657570i
\(213\) 8.94925 + 8.94925i 0.613193 + 0.613193i
\(214\) −4.60753 4.60753i −0.314964 0.314964i
\(215\) 3.97349 + 0.387760i 0.270990 + 0.0264450i
\(216\) 3.76493 3.76493i 0.256171 0.256171i
\(217\) 31.8562 2.16254
\(218\) 14.6123 14.6123i 0.989673 0.989673i
\(219\) 6.39655i 0.432239i
\(220\) −0.772154 + 7.91250i −0.0520586 + 0.533461i
\(221\) 23.7460i 1.59733i
\(222\) 0.626522 6.80950i 0.0420494 0.457024i
\(223\) −7.23324 + 7.23324i −0.484373 + 0.484373i −0.906525 0.422152i \(-0.861275\pi\)
0.422152 + 0.906525i \(0.361275\pi\)
\(224\) −2.93770 2.93770i −0.196283 0.196283i
\(225\) 1.67828 8.51705i 0.111885 0.567803i
\(226\) 8.61849i 0.573293i
\(227\) 3.53828i 0.234844i 0.993082 + 0.117422i \(0.0374630\pi\)
−0.993082 + 0.117422i \(0.962537\pi\)
\(228\) −3.15731 −0.209098
\(229\) 10.2694i 0.678622i −0.940674 0.339311i \(-0.889806\pi\)
0.940674 0.339311i \(-0.110194\pi\)
\(230\) −13.1477 1.28304i −0.866931 0.0846008i
\(231\) 16.6056 1.09257
\(232\) −2.18437 2.18437i −0.143411 0.143411i
\(233\) −0.731820 0.731820i −0.0479431 0.0479431i 0.682729 0.730672i \(-0.260793\pi\)
−0.730672 + 0.682729i \(0.760793\pi\)
\(234\) 7.66584i 0.501131i
\(235\) 3.66812 + 4.46146i 0.239282 + 0.291033i
\(236\) 4.44588 4.44588i 0.289402 0.289402i
\(237\) −3.22836 −0.209704
\(238\) 15.7990 15.7990i 1.02409 1.02409i
\(239\) 6.25677 6.25677i 0.404717 0.404717i −0.475175 0.879892i \(-0.657615\pi\)
0.879892 + 0.475175i \(0.157615\pi\)
\(240\) −1.59648 1.94176i −0.103052 0.125340i
\(241\) −6.31560 6.31560i −0.406823 0.406823i 0.473806 0.880629i \(-0.342880\pi\)
−0.880629 + 0.473806i \(0.842880\pi\)
\(242\) 1.64079 0.105474
\(243\) 10.6769 + 10.6769i 0.684926 + 0.684926i
\(244\) 1.44033 1.44033i 0.0922079 0.0922079i
\(245\) −2.22828 + 22.8339i −0.142360 + 1.45880i
\(246\) 5.04366 5.04366i 0.321572 0.321572i
\(247\) −8.76852 + 8.76852i −0.557927 + 0.557927i
\(248\) −5.42197 + 5.42197i −0.344296 + 0.344296i
\(249\) 7.17475 0.454681
\(250\) −10.7076 3.21670i −0.677208 0.203442i
\(251\) 3.90237 3.90237i 0.246315 0.246315i −0.573141 0.819457i \(-0.694275\pi\)
0.819457 + 0.573141i \(0.194275\pi\)
\(252\) 5.10033 5.10033i 0.321291 0.321291i
\(253\) 21.0043i 1.32053i
\(254\) 4.22966 + 4.22966i 0.265393 + 0.265393i
\(255\) 10.4428 8.58586i 0.653954 0.537668i
\(256\) 1.00000 0.0625000
\(257\) 2.21902i 0.138419i −0.997602 0.0692095i \(-0.977952\pi\)
0.997602 0.0692095i \(-0.0220477\pi\)
\(258\) 1.41931 + 1.41931i 0.0883621 + 0.0883621i
\(259\) 2.31533 25.1647i 0.143868 1.56366i
\(260\) −9.82642 0.958927i −0.609409 0.0594701i
\(261\) 3.79242 3.79242i 0.234745 0.234745i
\(262\) 15.2680 15.2680i 0.943260 0.943260i
\(263\) −11.1111 11.1111i −0.685141 0.685141i 0.276013 0.961154i \(-0.410987\pi\)
−0.961154 + 0.276013i \(0.910987\pi\)
\(264\) −2.82629 + 2.82629i −0.173946 + 0.173946i
\(265\) −23.3871 + 19.2284i −1.43666 + 1.18119i
\(266\) −11.6680 −0.715408
\(267\) 3.40131i 0.208157i
\(268\) 7.88856 7.88856i 0.481870 0.481870i
\(269\) 5.86174i 0.357396i −0.983904 0.178698i \(-0.942811\pi\)
0.983904 0.178698i \(-0.0571886\pi\)
\(270\) 9.19650 7.56118i 0.559681 0.460159i
\(271\) −4.91311 −0.298450 −0.149225 0.988803i \(-0.547678\pi\)
−0.149225 + 0.988803i \(0.547678\pi\)
\(272\) 5.37801i 0.326090i
\(273\) 20.6222i 1.24811i
\(274\) 14.4220 + 14.4220i 0.871262 + 0.871262i
\(275\) −3.43685 + 17.4416i −0.207250 + 1.05177i
\(276\) −4.69625 4.69625i −0.282681 0.282681i
\(277\) 8.21627 0.493668 0.246834 0.969058i \(-0.420610\pi\)
0.246834 + 0.969058i \(0.420610\pi\)
\(278\) −1.56244 −0.0937092
\(279\) −9.41344 9.41344i −0.563568 0.563568i
\(280\) −5.89983 7.17584i −0.352582 0.428838i
\(281\) −7.17894 7.17894i −0.428259 0.428259i 0.459776 0.888035i \(-0.347930\pi\)
−0.888035 + 0.459776i \(0.847930\pi\)
\(282\) 2.90383i 0.172921i
\(283\) 21.1149i 1.25515i −0.778557 0.627574i \(-0.784048\pi\)
0.778557 0.627574i \(-0.215952\pi\)
\(284\) −11.2579 −0.668032
\(285\) −7.02659 0.685701i −0.416219 0.0406174i
\(286\) 15.6984i 0.928266i
\(287\) 18.6390 18.6390i 1.10023 1.10023i
\(288\) 1.73617i 0.102305i
\(289\) −11.9230 −0.701352
\(290\) −4.38690 5.33570i −0.257608 0.313323i
\(291\) −4.70596 + 4.70596i −0.275868 + 0.275868i
\(292\) −4.02333 4.02333i −0.235448 0.235448i
\(293\) 8.03410 8.03410i 0.469357 0.469357i −0.432349 0.901706i \(-0.642315\pi\)
0.901706 + 0.432349i \(0.142315\pi\)
\(294\) −8.15611 + 8.15611i −0.475674 + 0.475674i
\(295\) 10.8598 8.92875i 0.632285 0.519852i
\(296\) 3.88900 + 4.67714i 0.226044 + 0.271854i
\(297\) −13.3858 13.3858i −0.776722 0.776722i
\(298\) 8.42600i 0.488105i
\(299\) −26.0849 −1.50853
\(300\) −3.13124 4.66810i −0.180782 0.269513i
\(301\) 5.24509 + 5.24509i 0.302322 + 0.302322i
\(302\) 9.65715i 0.555706i
\(303\) −7.34026 + 7.34026i −0.421687 + 0.421687i
\(304\) 1.98590 1.98590i 0.113899 0.113899i
\(305\) 3.51827 2.89265i 0.201455 0.165633i
\(306\) −9.33711 −0.533767
\(307\) 3.81755 3.81755i 0.217879 0.217879i −0.589725 0.807604i \(-0.700764\pi\)
0.807604 + 0.589725i \(0.200764\pi\)
\(308\) −10.4447 + 10.4447i −0.595140 + 0.595140i
\(309\) −6.39071 + 6.39071i −0.363555 + 0.363555i
\(310\) −13.2441 + 10.8890i −0.752215 + 0.618456i
\(311\) 8.92270 8.92270i 0.505960 0.505960i −0.407324 0.913284i \(-0.633538\pi\)
0.913284 + 0.407324i \(0.133538\pi\)
\(312\) −3.50993 3.50993i −0.198711 0.198711i
\(313\) −29.7794 −1.68323 −0.841616 0.540076i \(-0.818395\pi\)
−0.841616 + 0.540076i \(0.818395\pi\)
\(314\) 13.7789 + 13.7789i 0.777591 + 0.777591i
\(315\) 12.4584 10.2431i 0.701954 0.577132i
\(316\) 2.03059 2.03059i 0.114229 0.114229i
\(317\) −16.2699 + 16.2699i −0.913808 + 0.913808i −0.996569 0.0827610i \(-0.973626\pi\)
0.0827610 + 0.996569i \(0.473626\pi\)
\(318\) −15.2219 −0.853604
\(319\) −7.76627 + 7.76627i −0.434828 + 0.434828i
\(320\) 2.22550 + 0.217179i 0.124409 + 0.0121407i
\(321\) 7.32535i 0.408861i
\(322\) −17.3552 17.3552i −0.967165 0.967165i
\(323\) 10.6802 + 10.6802i 0.594262 + 0.594262i
\(324\) 0.777232 0.0431795
\(325\) −21.6604 4.26818i −1.20150 0.236756i
\(326\) 9.92434i 0.549658i
\(327\) 23.2316 1.28471
\(328\) 6.34477i 0.350331i
\(329\) 10.7312i 0.591630i
\(330\) −6.90371 + 5.67609i −0.380037 + 0.312459i
\(331\) 15.6327 + 15.6327i 0.859250 + 0.859250i 0.991250 0.132000i \(-0.0421399\pi\)
−0.132000 + 0.991250i \(0.542140\pi\)
\(332\) −4.51281 + 4.51281i −0.247672 + 0.247672i
\(333\) −8.12030 + 6.75195i −0.444990 + 0.370004i
\(334\) 17.7622i 0.971903i
\(335\) 19.2692 15.8427i 1.05279 0.865581i
\(336\) 4.67054i 0.254799i
\(337\) 22.0252 22.0252i 1.19979 1.19979i 0.225558 0.974230i \(-0.427580\pi\)
0.974230 0.225558i \(-0.0724204\pi\)
\(338\) −6.49561 −0.353315
\(339\) −6.85111 + 6.85111i −0.372101 + 0.372101i
\(340\) −1.16799 + 11.9687i −0.0633431 + 0.649096i
\(341\) 19.2772 + 19.2772i 1.04392 + 1.04392i
\(342\) 3.44786 + 3.44786i 0.186439 + 0.186439i
\(343\) −9.57729 + 9.57729i −0.517125 + 0.517125i
\(344\) −1.78544 −0.0962646
\(345\) −9.43157 11.4714i −0.507779 0.617601i
\(346\) 4.93605 + 4.93605i 0.265364 + 0.265364i
\(347\) −35.2079 −1.89006 −0.945029 0.326987i \(-0.893967\pi\)
−0.945029 + 0.326987i \(0.893967\pi\)
\(348\) 3.47285i 0.186164i
\(349\) 7.00272i 0.374847i 0.982279 + 0.187423i \(0.0600137\pi\)
−0.982279 + 0.187423i \(0.939986\pi\)
\(350\) −11.5716 17.2511i −0.618529 0.922111i
\(351\) 16.6236 16.6236i 0.887303 0.887303i
\(352\) 3.55539i 0.189503i
\(353\) 24.1991i 1.28799i −0.765030 0.643995i \(-0.777276\pi\)
0.765030 0.643995i \(-0.222724\pi\)
\(354\) 7.06835 0.375679
\(355\) −25.0544 2.44497i −1.32975 0.129766i
\(356\) 2.13937 + 2.13937i 0.113387 + 0.113387i
\(357\) 25.1182 1.32940
\(358\) −3.68868 3.68868i −0.194953 0.194953i
\(359\) 5.19872i 0.274378i 0.990545 + 0.137189i \(0.0438067\pi\)
−0.990545 + 0.137189i \(0.956193\pi\)
\(360\) −0.377058 + 3.86383i −0.0198727 + 0.203642i
\(361\) 11.1124i 0.584862i
\(362\) 5.35458 0.281430
\(363\) 1.30432 + 1.30432i 0.0684588 + 0.0684588i
\(364\) −12.9711 12.9711i −0.679868 0.679868i
\(365\) −8.08013 9.82769i −0.422933 0.514405i
\(366\) 2.28994 0.119697
\(367\) 22.4335 + 22.4335i 1.17102 + 1.17102i 0.981968 + 0.189049i \(0.0605405\pi\)
0.189049 + 0.981968i \(0.439460\pi\)
\(368\) 5.90774 0.307962
\(369\) −11.0156 −0.573448
\(370\) 7.63918 + 11.2536i 0.397142 + 0.585045i
\(371\) −56.2532 −2.92052
\(372\) −8.62020 −0.446937
\(373\) −10.4263 10.4263i −0.539852 0.539852i 0.383633 0.923486i \(-0.374673\pi\)
−0.923486 + 0.383633i \(0.874673\pi\)
\(374\) 19.1209 0.988719
\(375\) −5.95476 11.0689i −0.307502 0.571595i
\(376\) −1.82646 1.82646i −0.0941927 0.0941927i
\(377\) −9.64481 9.64481i −0.496733 0.496733i
\(378\) 22.1205 1.13775
\(379\) 15.9233i 0.817925i 0.912551 + 0.408963i \(0.134109\pi\)
−0.912551 + 0.408963i \(0.865891\pi\)
\(380\) 4.85091 3.98832i 0.248847 0.204597i
\(381\) 6.72459i 0.344511i
\(382\) −10.0773 10.0773i −0.515598 0.515598i
\(383\) 24.2531 1.23928 0.619638 0.784888i \(-0.287279\pi\)
0.619638 + 0.784888i \(0.287279\pi\)
\(384\) 0.794932 + 0.794932i 0.0405662 + 0.0405662i
\(385\) −25.5129 + 20.9762i −1.30026 + 1.06905i
\(386\) −24.7844 −1.26149
\(387\) 3.09982i 0.157573i
\(388\) 5.91995i 0.300540i
\(389\) 19.7499 19.7499i 1.00136 1.00136i 0.00136297 0.999999i \(-0.499566\pi\)
0.999999 0.00136297i \(-0.000433846\pi\)
\(390\) −7.04905 8.57362i −0.356943 0.434142i
\(391\) 31.7719i 1.60677i
\(392\) 10.2601i 0.518215i
\(393\) 24.2741 1.22446
\(394\) −11.3006 11.3006i −0.569314 0.569314i
\(395\) 4.96006 4.07806i 0.249568 0.205190i
\(396\) 6.17274 0.310192
\(397\) −1.71599 + 1.71599i −0.0861232 + 0.0861232i −0.748856 0.662733i \(-0.769397\pi\)
0.662733 + 0.748856i \(0.269397\pi\)
\(398\) 6.90680 + 6.90680i 0.346206 + 0.346206i
\(399\) −9.27524 9.27524i −0.464343 0.464343i
\(400\) 4.90567 + 0.966660i 0.245283 + 0.0483330i
\(401\) 9.29247 9.29247i 0.464044 0.464044i −0.435934 0.899978i \(-0.643582\pi\)
0.899978 + 0.435934i \(0.143582\pi\)
\(402\) 12.5417 0.625525
\(403\) −23.9401 + 23.9401i −1.19254 + 1.19254i
\(404\) 9.23382i 0.459399i
\(405\) 1.72973 + 0.168798i 0.0859508 + 0.00838764i
\(406\) 12.8340i 0.636941i
\(407\) 16.6291 13.8269i 0.824272 0.685374i
\(408\) −4.27515 + 4.27515i −0.211652 + 0.211652i
\(409\) 18.3866 + 18.3866i 0.909160 + 0.909160i 0.996204 0.0870446i \(-0.0277423\pi\)
−0.0870446 + 0.996204i \(0.527742\pi\)
\(410\) −1.37795 + 14.1203i −0.0680520 + 0.697350i
\(411\) 22.9290i 1.13100i
\(412\) 8.03931i 0.396068i
\(413\) 26.1213 1.28535
\(414\) 10.2568i 0.504095i
\(415\) −11.0233 + 9.06315i −0.541113 + 0.444892i
\(416\) 4.41538 0.216482
\(417\) −1.24204 1.24204i −0.0608228 0.0608228i
\(418\) −7.06065 7.06065i −0.345348 0.345348i
\(419\) 8.04256i 0.392905i −0.980513 0.196452i \(-0.937058\pi\)
0.980513 0.196452i \(-0.0629421\pi\)
\(420\) 1.01434 10.3943i 0.0494948 0.507188i
\(421\) 11.0268 11.0268i 0.537416 0.537416i −0.385353 0.922769i \(-0.625920\pi\)
0.922769 + 0.385353i \(0.125920\pi\)
\(422\) 22.7919 1.10949
\(423\) 3.17104 3.17104i 0.154181 0.154181i
\(424\) 9.57437 9.57437i 0.464972 0.464972i
\(425\) −5.19871 + 26.3827i −0.252174 + 1.27975i
\(426\) −8.94925 8.94925i −0.433593 0.433593i
\(427\) 8.46253 0.409530
\(428\) 4.60753 + 4.60753i 0.222713 + 0.222713i
\(429\) −12.4792 + 12.4792i −0.602500 + 0.602500i
\(430\) −3.97349 0.387760i −0.191619 0.0186994i
\(431\) 9.69563 9.69563i 0.467022 0.467022i −0.433926 0.900948i \(-0.642872\pi\)
0.900948 + 0.433926i \(0.142872\pi\)
\(432\) −3.76493 + 3.76493i −0.181140 + 0.181140i
\(433\) −7.39679 + 7.39679i −0.355467 + 0.355467i −0.862139 0.506672i \(-0.830876\pi\)
0.506672 + 0.862139i \(0.330876\pi\)
\(434\) −31.8562 −1.52915
\(435\) 0.754228 7.72880i 0.0361624 0.370568i
\(436\) −14.6123 + 14.6123i −0.699804 + 0.699804i
\(437\) 11.7322 11.7322i 0.561227 0.561227i
\(438\) 6.39655i 0.305639i
\(439\) 21.3840 + 21.3840i 1.02060 + 1.02060i 0.999783 + 0.0208186i \(0.00662725\pi\)
0.0208186 + 0.999783i \(0.493373\pi\)
\(440\) 0.772154 7.91250i 0.0368110 0.377214i
\(441\) 17.8133 0.848252
\(442\) 23.7460i 1.12948i
\(443\) −0.537851 0.537851i −0.0255541 0.0255541i 0.694214 0.719768i \(-0.255752\pi\)
−0.719768 + 0.694214i \(0.755752\pi\)
\(444\) −0.626522 + 6.80950i −0.0297334 + 0.323165i
\(445\) 4.29654 + 5.22579i 0.203676 + 0.247726i
\(446\) 7.23324 7.23324i 0.342504 0.342504i
\(447\) −6.69810 + 6.69810i −0.316809 + 0.316809i
\(448\) 2.93770 + 2.93770i 0.138793 + 0.138793i
\(449\) −17.9014 + 17.9014i −0.844820 + 0.844820i −0.989481 0.144661i \(-0.953791\pi\)
0.144661 + 0.989481i \(0.453791\pi\)
\(450\) −1.67828 + 8.51705i −0.0791150 + 0.401498i
\(451\) 22.5581 1.06222
\(452\) 8.61849i 0.405380i
\(453\) 7.67678 7.67678i 0.360686 0.360686i
\(454\) 3.53828i 0.166060i
\(455\) −26.0500 31.6841i −1.22124 1.48537i
\(456\) 3.15731 0.147855
\(457\) 10.3305i 0.483240i 0.970371 + 0.241620i \(0.0776787\pi\)
−0.970371 + 0.241620i \(0.922321\pi\)
\(458\) 10.2694i 0.479858i
\(459\) −20.2478 20.2478i −0.945088 0.945088i
\(460\) 13.1477 + 1.28304i 0.613013 + 0.0598218i
\(461\) −19.5325 19.5325i −0.909718 0.909718i 0.0865312 0.996249i \(-0.472422\pi\)
−0.996249 + 0.0865312i \(0.972422\pi\)
\(462\) −16.6056 −0.772562
\(463\) 13.2709 0.616752 0.308376 0.951265i \(-0.400214\pi\)
0.308376 + 0.951265i \(0.400214\pi\)
\(464\) 2.18437 + 2.18437i 0.101407 + 0.101407i
\(465\) −19.1842 1.87212i −0.889647 0.0868176i
\(466\) 0.731820 + 0.731820i 0.0339009 + 0.0339009i
\(467\) 40.7473i 1.88556i −0.333414 0.942780i \(-0.608201\pi\)
0.333414 0.942780i \(-0.391799\pi\)
\(468\) 7.66584i 0.354353i
\(469\) 46.3484 2.14017
\(470\) −3.66812 4.46146i −0.169198 0.205792i
\(471\) 21.9066i 1.00941i
\(472\) −4.44588 + 4.44588i −0.204638 + 0.204638i
\(473\) 6.34794i 0.291879i
\(474\) 3.22836 0.148283
\(475\) 11.6619 7.82248i 0.535083 0.358920i
\(476\) −15.7990 + 15.7990i −0.724144 + 0.724144i
\(477\) 16.6227 + 16.6227i 0.761100 + 0.761100i
\(478\) −6.25677 + 6.25677i −0.286178 + 0.286178i
\(479\) 8.91382 8.91382i 0.407283 0.407283i −0.473507 0.880790i \(-0.657012\pi\)
0.880790 + 0.473507i \(0.157012\pi\)
\(480\) 1.59648 + 1.94176i 0.0728688 + 0.0886288i
\(481\) 17.1714 + 20.6514i 0.782950 + 0.941622i
\(482\) 6.31560 + 6.31560i 0.287667 + 0.287667i
\(483\) 27.5924i 1.25550i
\(484\) −1.64079 −0.0745813
\(485\) 1.28569 13.1748i 0.0583800 0.598238i
\(486\) −10.6769 10.6769i −0.484316 0.484316i
\(487\) 27.7847i 1.25904i 0.776983 + 0.629522i \(0.216749\pi\)
−0.776983 + 0.629522i \(0.783251\pi\)
\(488\) −1.44033 + 1.44033i −0.0652008 + 0.0652008i
\(489\) −7.88918 + 7.88918i −0.356761 + 0.356761i
\(490\) 2.22828 22.8339i 0.100663 1.03153i
\(491\) −7.19820 −0.324850 −0.162425 0.986721i \(-0.551932\pi\)
−0.162425 + 0.986721i \(0.551932\pi\)
\(492\) −5.04366 + 5.04366i −0.227386 + 0.227386i
\(493\) −11.7475 + 11.7475i −0.529083 + 0.529083i
\(494\) 8.76852 8.76852i 0.394514 0.394514i
\(495\) 13.7374 + 1.34059i 0.617451 + 0.0602549i
\(496\) 5.42197 5.42197i 0.243454 0.243454i
\(497\) −33.0722 33.0722i −1.48349 1.48349i
\(498\) −7.17475 −0.321508
\(499\) −0.378337 0.378337i −0.0169367 0.0169367i 0.698588 0.715524i \(-0.253812\pi\)
−0.715524 + 0.698588i \(0.753812\pi\)
\(500\) 10.7076 + 3.21670i 0.478859 + 0.143855i
\(501\) 14.1197 14.1197i 0.630823 0.630823i
\(502\) −3.90237 + 3.90237i −0.174171 + 0.174171i
\(503\) 22.0885 0.984876 0.492438 0.870348i \(-0.336106\pi\)
0.492438 + 0.870348i \(0.336106\pi\)
\(504\) −5.10033 + 5.10033i −0.227187 + 0.227187i
\(505\) 2.00539 20.5498i 0.0892385 0.914455i
\(506\) 21.0043i 0.933756i
\(507\) −5.16357 5.16357i −0.229322 0.229322i
\(508\) −4.22966 4.22966i −0.187661 0.187661i
\(509\) 24.8176 1.10002 0.550011 0.835157i \(-0.314624\pi\)
0.550011 + 0.835157i \(0.314624\pi\)
\(510\) −10.4428 + 8.58586i −0.462415 + 0.380188i
\(511\) 23.6387i 1.04571i
\(512\) −1.00000 −0.0441942
\(513\) 14.9536i 0.660216i
\(514\) 2.21902i 0.0978769i
\(515\) 1.74597 17.8915i 0.0769364 0.788392i
\(516\) −1.41931 1.41931i −0.0624814 0.0624814i
\(517\) −6.49379 + 6.49379i −0.285597 + 0.285597i
\(518\) −2.31533 + 25.1647i −0.101730 + 1.10568i
\(519\) 7.84764i 0.344473i
\(520\) 9.82642 + 0.958927i 0.430917 + 0.0420517i
\(521\) 2.41522i 0.105813i 0.998599 + 0.0529064i \(0.0168485\pi\)
−0.998599 + 0.0529064i \(0.983151\pi\)
\(522\) −3.79242 + 3.79242i −0.165990 + 0.165990i
\(523\) 24.1447 1.05577 0.527887 0.849315i \(-0.322985\pi\)
0.527887 + 0.849315i \(0.322985\pi\)
\(524\) −15.2680 + 15.2680i −0.666986 + 0.666986i
\(525\) 4.51483 22.9121i 0.197043 0.999967i
\(526\) 11.1111 + 11.1111i 0.484468 + 0.484468i
\(527\) 29.1594 + 29.1594i 1.27020 + 1.27020i
\(528\) 2.82629 2.82629i 0.122999 0.122999i
\(529\) 11.9014 0.517453
\(530\) 23.3871 19.2284i 1.01587 0.835227i
\(531\) −7.71879 7.71879i −0.334967 0.334967i
\(532\) 11.6680 0.505870
\(533\) 28.0146i 1.21345i
\(534\) 3.40131i 0.147189i
\(535\) 9.25339 + 11.2547i 0.400059 + 0.486583i
\(536\) −7.88856 + 7.88856i −0.340734 + 0.340734i
\(537\) 5.86451i 0.253072i
\(538\) 5.86174i 0.252717i
\(539\) −36.4788 −1.57125
\(540\) −9.19650 + 7.56118i −0.395754 + 0.325381i
\(541\) 12.3532 + 12.3532i 0.531107 + 0.531107i 0.920902 0.389795i \(-0.127454\pi\)
−0.389795 + 0.920902i \(0.627454\pi\)
\(542\) 4.91311 0.211036
\(543\) 4.25652 + 4.25652i 0.182665 + 0.182665i
\(544\) 5.37801i 0.230580i
\(545\) −35.6932 + 29.3462i −1.52893 + 1.25705i
\(546\) 20.6222i 0.882550i
\(547\) −34.8143 −1.48855 −0.744277 0.667871i \(-0.767206\pi\)
−0.744277 + 0.667871i \(0.767206\pi\)
\(548\) −14.4220 14.4220i −0.616075 0.616075i
\(549\) −2.50066 2.50066i −0.106725 0.106725i
\(550\) 3.43685 17.4416i 0.146548 0.743710i
\(551\) 8.67587 0.369605
\(552\) 4.69625 + 4.69625i 0.199886 + 0.199886i
\(553\) 11.9305 0.507336
\(554\) −8.21627 −0.349076
\(555\) −2.87320 + 15.0185i −0.121961 + 0.637498i
\(556\) 1.56244 0.0662624
\(557\) 31.3271 1.32737 0.663685 0.748012i \(-0.268992\pi\)
0.663685 + 0.748012i \(0.268992\pi\)
\(558\) 9.41344 + 9.41344i 0.398503 + 0.398503i
\(559\) −7.88341 −0.333433
\(560\) 5.89983 + 7.17584i 0.249313 + 0.303235i
\(561\) 15.1998 + 15.1998i 0.641737 + 0.641737i
\(562\) 7.17894 + 7.17894i 0.302825 + 0.302825i
\(563\) 22.9644 0.967836 0.483918 0.875113i \(-0.339213\pi\)
0.483918 + 0.875113i \(0.339213\pi\)
\(564\) 2.90383i 0.122273i
\(565\) 1.87175 19.1804i 0.0787452 0.806926i
\(566\) 21.1149i 0.887524i
\(567\) 2.28327 + 2.28327i 0.0958884 + 0.0958884i
\(568\) 11.2579 0.472370
\(569\) 30.2581 + 30.2581i 1.26849 + 1.26849i 0.946870 + 0.321616i \(0.104226\pi\)
0.321616 + 0.946870i \(0.395774\pi\)
\(570\) 7.02659 + 0.685701i 0.294312 + 0.0287209i
\(571\) 25.3502 1.06087 0.530436 0.847725i \(-0.322028\pi\)
0.530436 + 0.847725i \(0.322028\pi\)
\(572\) 15.6984i 0.656383i
\(573\) 16.0215i 0.669307i
\(574\) −18.6390 + 18.6390i −0.777977 + 0.777977i
\(575\) 28.9814 + 5.71078i 1.20861 + 0.238156i
\(576\) 1.73617i 0.0723402i
\(577\) 29.6723i 1.23527i −0.786464 0.617637i \(-0.788090\pi\)
0.786464 0.617637i \(-0.211910\pi\)
\(578\) 11.9230 0.495931
\(579\) −19.7019 19.7019i −0.818784 0.818784i
\(580\) 4.38690 + 5.33570i 0.182156 + 0.221553i
\(581\) −26.5145 −1.10001
\(582\) 4.70596 4.70596i 0.195068 0.195068i
\(583\) −34.0406 34.0406i −1.40982 1.40982i
\(584\) 4.02333 + 4.02333i 0.166487 + 0.166487i
\(585\) −1.66486 + 17.0603i −0.0688333 + 0.705356i
\(586\) −8.03410 + 8.03410i −0.331886 + 0.331886i
\(587\) −16.9046 −0.697726 −0.348863 0.937174i \(-0.613432\pi\)
−0.348863 + 0.937174i \(0.613432\pi\)
\(588\) 8.15611 8.15611i 0.336352 0.336352i
\(589\) 21.5350i 0.887335i
\(590\) −10.8598 + 8.92875i −0.447093 + 0.367591i
\(591\) 17.9664i 0.739038i
\(592\) −3.88900 4.67714i −0.159837 0.192229i
\(593\) 13.2570 13.2570i 0.544398 0.544398i −0.380417 0.924815i \(-0.624220\pi\)
0.924815 + 0.380417i \(0.124220\pi\)
\(594\) 13.3858 + 13.3858i 0.549226 + 0.549226i
\(595\) −38.5917 + 31.7293i −1.58211 + 1.30078i
\(596\) 8.42600i 0.345142i
\(597\) 10.9809i 0.449417i
\(598\) 26.0849 1.06669
\(599\) 9.47521i 0.387147i −0.981086 0.193573i \(-0.937992\pi\)
0.981086 0.193573i \(-0.0620077\pi\)
\(600\) 3.13124 + 4.66810i 0.127832 + 0.190574i
\(601\) −0.0866615 −0.00353500 −0.00176750 0.999998i \(-0.500563\pi\)
−0.00176750 + 0.999998i \(0.500563\pi\)
\(602\) −5.24509 5.24509i −0.213774 0.213774i
\(603\) −13.6958 13.6958i −0.557738 0.557738i
\(604\) 9.65715i 0.392944i
\(605\) −3.65157 0.356344i −0.148457 0.0144875i
\(606\) 7.34026 7.34026i 0.298178 0.298178i
\(607\) −24.7793 −1.00576 −0.502880 0.864356i \(-0.667726\pi\)
−0.502880 + 0.864356i \(0.667726\pi\)
\(608\) −1.98590 + 1.98590i −0.0805390 + 0.0805390i
\(609\) 10.2022 10.2022i 0.413413 0.413413i
\(610\) −3.51827 + 2.89265i −0.142450 + 0.117120i
\(611\) −8.06454 8.06454i −0.326256 0.326256i
\(612\) 9.33711 0.377430
\(613\) −3.88165 3.88165i −0.156779 0.156779i 0.624359 0.781138i \(-0.285360\pi\)
−0.781138 + 0.624359i \(0.785360\pi\)
\(614\) −3.81755 + 3.81755i −0.154064 + 0.154064i
\(615\) −12.3200 + 10.1293i −0.496791 + 0.408452i
\(616\) 10.4447 10.4447i 0.420827 0.420827i
\(617\) −34.7871 + 34.7871i −1.40047 + 1.40047i −0.601911 + 0.798563i \(0.705594\pi\)
−0.798563 + 0.601911i \(0.794406\pi\)
\(618\) 6.39071 6.39071i 0.257072 0.257072i
\(619\) −14.8991 −0.598845 −0.299422 0.954121i \(-0.596794\pi\)
−0.299422 + 0.954121i \(0.596794\pi\)
\(620\) 13.2441 10.8890i 0.531897 0.437315i
\(621\) −22.2422 + 22.2422i −0.892550 + 0.892550i
\(622\) −8.92270 + 8.92270i −0.357768 + 0.357768i
\(623\) 12.5697i 0.503593i
\(624\) 3.50993 + 3.50993i 0.140510 + 0.140510i
\(625\) 23.1311 + 9.48423i 0.925245 + 0.379369i
\(626\) 29.7794 1.19022
\(627\) 11.2255i 0.448303i
\(628\) −13.7789 13.7789i −0.549840 0.549840i
\(629\) 25.1537 20.9151i 1.00294 0.833939i
\(630\) −12.4584 + 10.2431i −0.496356 + 0.408094i
\(631\) −26.9215 + 26.9215i −1.07173 + 1.07173i −0.0745080 + 0.997220i \(0.523739\pi\)
−0.997220 + 0.0745080i \(0.976261\pi\)
\(632\) −2.03059 + 2.03059i −0.0807724 + 0.0807724i
\(633\) 18.1180 + 18.1180i 0.720128 + 0.720128i
\(634\) 16.2699 16.2699i 0.646160 0.646160i
\(635\) −8.49450 10.3317i −0.337094 0.410000i
\(636\) 15.2219 0.603589
\(637\) 45.3024i 1.79495i
\(638\) 7.76627 7.76627i 0.307470 0.307470i
\(639\) 19.5455i 0.773210i
\(640\) −2.22550 0.217179i −0.0879705 0.00858474i
\(641\) −13.9581 −0.551314 −0.275657 0.961256i \(-0.588895\pi\)
−0.275657 + 0.961256i \(0.588895\pi\)
\(642\) 7.32535i 0.289109i
\(643\) 32.7954i 1.29332i −0.762777 0.646662i \(-0.776164\pi\)
0.762777 0.646662i \(-0.223836\pi\)
\(644\) 17.3552 + 17.3552i 0.683889 + 0.683889i
\(645\) −2.85042 3.46690i −0.112235 0.136509i
\(646\) −10.6802 10.6802i −0.420207 0.420207i
\(647\) 0.428355 0.0168404 0.00842020 0.999965i \(-0.497320\pi\)
0.00842020 + 0.999965i \(0.497320\pi\)
\(648\) −0.777232 −0.0305325
\(649\) 15.8068 + 15.8068i 0.620473 + 0.620473i
\(650\) 21.6604 + 4.26818i 0.849591 + 0.167412i
\(651\) −25.3235 25.3235i −0.992508 0.992508i
\(652\) 9.92434i 0.388667i
\(653\) 35.6290i 1.39427i 0.716939 + 0.697136i \(0.245543\pi\)
−0.716939 + 0.697136i \(0.754457\pi\)
\(654\) −23.2316 −0.908429
\(655\) −37.2948 + 30.6630i −1.45723 + 1.19810i
\(656\) 6.34477i 0.247722i
\(657\) −6.98517 + 6.98517i −0.272518 + 0.272518i
\(658\) 10.7312i 0.418346i
\(659\) −23.0667 −0.898552 −0.449276 0.893393i \(-0.648318\pi\)
−0.449276 + 0.893393i \(0.648318\pi\)
\(660\) 6.90371 5.67609i 0.268727 0.220942i
\(661\) 2.71363 2.71363i 0.105548 0.105548i −0.652361 0.757909i \(-0.726221\pi\)
0.757909 + 0.652361i \(0.226221\pi\)
\(662\) −15.6327 15.6327i −0.607581 0.607581i
\(663\) −18.8764 + 18.8764i −0.733100 + 0.733100i
\(664\) 4.51281 4.51281i 0.175131 0.175131i
\(665\) 25.9670 + 2.53403i 1.00696 + 0.0982655i
\(666\) 8.12030 6.75195i 0.314655 0.261633i
\(667\) 12.9047 + 12.9047i 0.499671 + 0.499671i
\(668\) 17.7622i 0.687239i
\(669\) 11.4999 0.444610
\(670\) −19.2692 + 15.8427i −0.744433 + 0.612058i
\(671\) 5.12095 + 5.12095i 0.197692 + 0.197692i
\(672\) 4.67054i 0.180170i
\(673\) −19.5626 + 19.5626i −0.754083 + 0.754083i −0.975238 0.221156i \(-0.929017\pi\)
0.221156 + 0.975238i \(0.429017\pi\)
\(674\) −22.0252 + 22.0252i −0.848378 + 0.848378i
\(675\) −22.1089 + 14.8301i −0.850972 + 0.570810i
\(676\) 6.49561 0.249831
\(677\) −23.4376 + 23.4376i −0.900781 + 0.900781i −0.995504 0.0947229i \(-0.969803\pi\)
0.0947229 + 0.995504i \(0.469803\pi\)
\(678\) 6.85111 6.85111i 0.263115 0.263115i
\(679\) 17.3910 17.3910i 0.667406 0.667406i
\(680\) 1.16799 11.9687i 0.0447903 0.458980i
\(681\) 2.81269 2.81269i 0.107783 0.107783i
\(682\) −19.2772 19.2772i −0.738163 0.738163i
\(683\) −15.8368 −0.605977 −0.302988 0.952994i \(-0.597984\pi\)
−0.302988 + 0.952994i \(0.597984\pi\)
\(684\) −3.44786 3.44786i −0.131832 0.131832i
\(685\) −28.9639 35.2281i −1.10665 1.34600i
\(686\) 9.57729 9.57729i 0.365663 0.365663i
\(687\) −8.16348 + 8.16348i −0.311456 + 0.311456i
\(688\) 1.78544 0.0680693
\(689\) 42.2745 42.2745i 1.61053 1.61053i
\(690\) 9.43157 + 11.4714i 0.359054 + 0.436710i
\(691\) 25.5077i 0.970358i 0.874415 + 0.485179i \(0.161246\pi\)
−0.874415 + 0.485179i \(0.838754\pi\)
\(692\) −4.93605 4.93605i −0.187640 0.187640i
\(693\) 18.1337 + 18.1337i 0.688841 + 0.688841i
\(694\) 35.2079 1.33647
\(695\) 3.47721 + 0.339330i 0.131898 + 0.0128715i
\(696\) 3.47285i 0.131638i
\(697\) 34.1222 1.29247
\(698\) 7.00272i 0.265057i
\(699\) 1.16349i 0.0440074i
\(700\) 11.5716 + 17.2511i 0.437366 + 0.652031i
\(701\) 6.69201 + 6.69201i 0.252754 + 0.252754i 0.822099 0.569345i \(-0.192803\pi\)
−0.569345 + 0.822099i \(0.692803\pi\)
\(702\) −16.6236 + 16.6236i −0.627418 + 0.627418i
\(703\) −17.0115 1.56518i −0.641602 0.0590318i
\(704\) 3.55539i 0.133999i
\(705\) 0.630650 6.46246i 0.0237516 0.243390i
\(706\) 24.1991i 0.910746i
\(707\) 27.1262 27.1262i 1.02018 1.02018i
\(708\) −7.06835 −0.265645
\(709\) −9.99501 + 9.99501i −0.375370 + 0.375370i −0.869429 0.494058i \(-0.835513\pi\)
0.494058 + 0.869429i \(0.335513\pi\)
\(710\) 25.0544 + 2.44497i 0.940274 + 0.0917581i
\(711\) −3.52544 3.52544i −0.132214 0.132214i
\(712\) −2.13937 2.13937i −0.0801764 0.0801764i
\(713\) 32.0316 32.0316i 1.19959 1.19959i
\(714\) −25.1182 −0.940025
\(715\) 3.40936 34.9367i 0.127503 1.30656i
\(716\) 3.68868 + 3.68868i 0.137853 + 0.137853i
\(717\) −9.94742 −0.371493
\(718\) 5.19872i 0.194014i
\(719\) 19.0225i 0.709421i −0.934976 0.354711i \(-0.884579\pi\)
0.934976 0.354711i \(-0.115421\pi\)
\(720\) 0.377058 3.86383i 0.0140521 0.143996i
\(721\) 23.6171 23.6171i 0.879545 0.879545i
\(722\) 11.1124i 0.413560i
\(723\) 10.0409i 0.373427i
\(724\) −5.35458 −0.199001
\(725\) 8.60423 + 12.8273i 0.319553 + 0.476394i
\(726\) −1.30432 1.30432i −0.0484077 0.0484077i
\(727\) 32.8141 1.21701 0.608504 0.793551i \(-0.291770\pi\)
0.608504 + 0.793551i \(0.291770\pi\)
\(728\) 12.9711 + 12.9711i 0.480739 + 0.480739i
\(729\) 19.3066i 0.715059i
\(730\) 8.08013 + 9.82769i 0.299059 + 0.363739i
\(731\) 9.60212i 0.355147i
\(732\) −2.28994 −0.0846384
\(733\) −30.2477 30.2477i −1.11722 1.11722i −0.992147 0.125077i \(-0.960082\pi\)
−0.125077 0.992147i \(-0.539918\pi\)
\(734\) −22.4335 22.4335i −0.828034 0.828034i
\(735\) 19.9227 16.3801i 0.734861 0.604188i
\(736\) −5.90774 −0.217762
\(737\) 28.0469 + 28.0469i 1.03312 + 1.03312i
\(738\) 11.0156 0.405489
\(739\) 27.9037 1.02646 0.513228 0.858253i \(-0.328450\pi\)
0.513228 + 0.858253i \(0.328450\pi\)
\(740\) −7.63918 11.2536i −0.280822 0.413690i
\(741\) 13.9408 0.512126
\(742\) 56.2532 2.06512
\(743\) −10.9502 10.9502i −0.401723 0.401723i 0.477117 0.878840i \(-0.341682\pi\)
−0.878840 + 0.477117i \(0.841682\pi\)
\(744\) 8.62020 0.316032
\(745\) 1.82995 18.7520i 0.0670440 0.687021i
\(746\) 10.4263 + 10.4263i 0.381733 + 0.381733i
\(747\) 7.83498 + 7.83498i 0.286667 + 0.286667i
\(748\) −19.1209 −0.699130
\(749\) 27.0711i 0.989155i
\(750\) 5.95476 + 11.0689i 0.217437 + 0.404178i
\(751\) 44.1738i 1.61193i 0.591966 + 0.805963i \(0.298352\pi\)
−0.591966 + 0.805963i \(0.701648\pi\)
\(752\) 1.82646 + 1.82646i 0.0666043 + 0.0666043i
\(753\) −6.20423 −0.226095
\(754\) 9.64481 + 9.64481i 0.351243 + 0.351243i
\(755\) −2.09733 + 21.4919i −0.0763295 + 0.782172i
\(756\) −22.1205 −0.804513
\(757\) 3.52885i 0.128258i −0.997942 0.0641291i \(-0.979573\pi\)
0.997942 0.0641291i \(-0.0204269\pi\)
\(758\) 15.9233i 0.578361i
\(759\) 16.6970 16.6970i 0.606063 0.606063i
\(760\) −4.85091 + 3.98832i −0.175961 + 0.144672i
\(761\) 15.9891i 0.579605i 0.957086 + 0.289803i \(0.0935896\pi\)
−0.957086 + 0.289803i \(0.906410\pi\)
\(762\) 6.72459i 0.243606i
\(763\) −85.8533 −3.10810
\(764\) 10.0773 + 10.0773i 0.364583 + 0.364583i
\(765\) 20.7797 + 2.02782i 0.751292 + 0.0733160i
\(766\) −24.2531 −0.876301
\(767\) −19.6303 + 19.6303i −0.708808 + 0.708808i
\(768\) −0.794932 0.794932i −0.0286846 0.0286846i
\(769\) −10.5741 10.5741i −0.381313 0.381313i 0.490262 0.871575i \(-0.336901\pi\)
−0.871575 + 0.490262i \(0.836901\pi\)
\(770\) 25.5129 20.9762i 0.919421 0.755929i
\(771\) −1.76397 + 1.76397i −0.0635280 + 0.0635280i
\(772\) 24.7844 0.892011
\(773\) −5.39429 + 5.39429i −0.194019 + 0.194019i −0.797430 0.603411i \(-0.793808\pi\)
0.603411 + 0.797430i \(0.293808\pi\)
\(774\) 3.09982i 0.111421i
\(775\) 31.8396 21.3572i 1.14371 0.767173i
\(776\) 5.91995i 0.212514i
\(777\) −21.8448 + 18.1637i −0.783678 + 0.651620i
\(778\) −19.7499 + 19.7499i