Properties

Label 230.3.f.b.47.7
Level $230$
Weight $3$
Character 230.47
Analytic conductor $6.267$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.7
Character \(\chi\) \(=\) 230.47
Dual form 230.3.f.b.93.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(0.561611 - 0.561611i) q^{3} +2.00000i q^{4} +(-4.87730 - 1.10088i) q^{5} +1.12322 q^{6} +(-8.38816 - 8.38816i) q^{7} +(-2.00000 + 2.00000i) q^{8} +8.36919i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(0.561611 - 0.561611i) q^{3} +2.00000i q^{4} +(-4.87730 - 1.10088i) q^{5} +1.12322 q^{6} +(-8.38816 - 8.38816i) q^{7} +(-2.00000 + 2.00000i) q^{8} +8.36919i q^{9} +(-3.77642 - 5.97818i) q^{10} -11.2203 q^{11} +(1.12322 + 1.12322i) q^{12} +(-15.9498 + 15.9498i) q^{13} -16.7763i q^{14} +(-3.35741 + 2.12088i) q^{15} -4.00000 q^{16} +(14.2936 + 14.2936i) q^{17} +(-8.36919 + 8.36919i) q^{18} -35.4325i q^{19} +(2.20176 - 9.75460i) q^{20} -9.42176 q^{21} +(-11.2203 - 11.2203i) q^{22} +(-3.39116 + 3.39116i) q^{23} +2.24644i q^{24} +(22.5761 + 10.7386i) q^{25} -31.8996 q^{26} +(9.75472 + 9.75472i) q^{27} +(16.7763 - 16.7763i) q^{28} -26.2015i q^{29} +(-5.47829 - 1.23653i) q^{30} +19.1987 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-6.30145 + 6.30145i) q^{33} +28.5873i q^{34} +(31.6772 + 50.1459i) q^{35} -16.7384 q^{36} +(-26.7959 - 26.7959i) q^{37} +(35.4325 - 35.4325i) q^{38} +17.9152i q^{39} +(11.9564 - 7.55285i) q^{40} +19.3079 q^{41} +(-9.42176 - 9.42176i) q^{42} +(-44.0280 + 44.0280i) q^{43} -22.4406i q^{44} +(9.21345 - 40.8190i) q^{45} -6.78233 q^{46} +(-36.1558 - 36.1558i) q^{47} +(-2.24644 + 2.24644i) q^{48} +91.7225i q^{49} +(11.8375 + 33.3148i) q^{50} +16.0549 q^{51} +(-31.8996 - 31.8996i) q^{52} +(-0.502671 + 0.502671i) q^{53} +19.5094i q^{54} +(54.7249 + 12.3522i) q^{55} +33.5526 q^{56} +(-19.8993 - 19.8993i) q^{57} +(26.2015 - 26.2015i) q^{58} -5.81649i q^{59} +(-4.24176 - 6.71482i) q^{60} -0.344323 q^{61} +(19.1987 + 19.1987i) q^{62} +(70.2021 - 70.2021i) q^{63} -8.00000i q^{64} +(95.3508 - 60.2332i) q^{65} -12.6029 q^{66} +(-17.5051 - 17.5051i) q^{67} +(-28.5873 + 28.5873i) q^{68} +3.80903i q^{69} +(-18.4687 + 81.8232i) q^{70} -14.8564 q^{71} +(-16.7384 - 16.7384i) q^{72} +(-68.0071 + 68.0071i) q^{73} -53.5917i q^{74} +(18.7099 - 6.64807i) q^{75} +70.8650 q^{76} +(94.1179 + 94.1179i) q^{77} +(-17.9152 + 17.9152i) q^{78} +82.9910i q^{79} +(19.5092 + 4.40351i) q^{80} -64.3660 q^{81} +(19.3079 + 19.3079i) q^{82} +(-32.8277 + 32.8277i) q^{83} -18.8435i q^{84} +(-53.9788 - 85.4499i) q^{85} -88.0559 q^{86} +(-14.7150 - 14.7150i) q^{87} +(22.4406 - 22.4406i) q^{88} +59.4270i q^{89} +(50.0325 - 31.6056i) q^{90} +267.579 q^{91} +(-6.78233 - 6.78233i) q^{92} +(10.7822 - 10.7822i) q^{93} -72.3115i q^{94} +(-39.0068 + 172.815i) q^{95} -4.49289 q^{96} +(33.5713 + 33.5713i) q^{97} +(-91.7225 + 91.7225i) q^{98} -93.9050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 0.561611 0.561611i 0.187204 0.187204i −0.607282 0.794486i \(-0.707740\pi\)
0.794486 + 0.607282i \(0.207740\pi\)
\(4\) 2.00000i 0.500000i
\(5\) −4.87730 1.10088i −0.975460 0.220176i
\(6\) 1.12322 0.187204
\(7\) −8.38816 8.38816i −1.19831 1.19831i −0.974673 0.223636i \(-0.928207\pi\)
−0.223636 0.974673i \(-0.571793\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 8.36919i 0.929910i
\(10\) −3.77642 5.97818i −0.377642 0.597818i
\(11\) −11.2203 −1.02003 −0.510015 0.860166i \(-0.670360\pi\)
−0.510015 + 0.860166i \(0.670360\pi\)
\(12\) 1.12322 + 1.12322i 0.0936018 + 0.0936018i
\(13\) −15.9498 + 15.9498i −1.22691 + 1.22691i −0.261781 + 0.965127i \(0.584310\pi\)
−0.965127 + 0.261781i \(0.915690\pi\)
\(14\) 16.7763i 1.19831i
\(15\) −3.35741 + 2.12088i −0.223827 + 0.141392i
\(16\) −4.00000 −0.250000
\(17\) 14.2936 + 14.2936i 0.840802 + 0.840802i 0.988963 0.148161i \(-0.0473354\pi\)
−0.148161 + 0.988963i \(0.547335\pi\)
\(18\) −8.36919 + 8.36919i −0.464955 + 0.464955i
\(19\) 35.4325i 1.86487i −0.361340 0.932434i \(-0.617681\pi\)
0.361340 0.932434i \(-0.382319\pi\)
\(20\) 2.20176 9.75460i 0.110088 0.487730i
\(21\) −9.42176 −0.448655
\(22\) −11.2203 11.2203i −0.510015 0.510015i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 2.24644i 0.0936018i
\(25\) 22.5761 + 10.7386i 0.903045 + 0.429545i
\(26\) −31.8996 −1.22691
\(27\) 9.75472 + 9.75472i 0.361286 + 0.361286i
\(28\) 16.7763 16.7763i 0.599154 0.599154i
\(29\) 26.2015i 0.903499i −0.892145 0.451749i \(-0.850800\pi\)
0.892145 0.451749i \(-0.149200\pi\)
\(30\) −5.47829 1.23653i −0.182610 0.0412176i
\(31\) 19.1987 0.619312 0.309656 0.950849i \(-0.399786\pi\)
0.309656 + 0.950849i \(0.399786\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −6.30145 + 6.30145i −0.190953 + 0.190953i
\(34\) 28.5873i 0.840802i
\(35\) 31.6772 + 50.1459i 0.905064 + 1.43274i
\(36\) −16.7384 −0.464955
\(37\) −26.7959 26.7959i −0.724212 0.724212i 0.245248 0.969460i \(-0.421131\pi\)
−0.969460 + 0.245248i \(0.921131\pi\)
\(38\) 35.4325 35.4325i 0.932434 0.932434i
\(39\) 17.9152i 0.459363i
\(40\) 11.9564 7.55285i 0.298909 0.188821i
\(41\) 19.3079 0.470924 0.235462 0.971883i \(-0.424340\pi\)
0.235462 + 0.971883i \(0.424340\pi\)
\(42\) −9.42176 9.42176i −0.224328 0.224328i
\(43\) −44.0280 + 44.0280i −1.02391 + 1.02391i −0.0241987 + 0.999707i \(0.507703\pi\)
−0.999707 + 0.0241987i \(0.992297\pi\)
\(44\) 22.4406i 0.510015i
\(45\) 9.21345 40.8190i 0.204743 0.907090i
\(46\) −6.78233 −0.147442
\(47\) −36.1558 36.1558i −0.769272 0.769272i 0.208707 0.977978i \(-0.433075\pi\)
−0.977978 + 0.208707i \(0.933075\pi\)
\(48\) −2.24644 + 2.24644i −0.0468009 + 0.0468009i
\(49\) 91.7225i 1.87189i
\(50\) 11.8375 + 33.3148i 0.236750 + 0.666295i
\(51\) 16.0549 0.314802
\(52\) −31.8996 31.8996i −0.613454 0.613454i
\(53\) −0.502671 + 0.502671i −0.00948435 + 0.00948435i −0.711833 0.702349i \(-0.752135\pi\)
0.702349 + 0.711833i \(0.252135\pi\)
\(54\) 19.5094i 0.361286i
\(55\) 54.7249 + 12.3522i 0.994998 + 0.224586i
\(56\) 33.5526 0.599154
\(57\) −19.8993 19.8993i −0.349110 0.349110i
\(58\) 26.2015 26.2015i 0.451749 0.451749i
\(59\) 5.81649i 0.0985845i −0.998784 0.0492923i \(-0.984303\pi\)
0.998784 0.0492923i \(-0.0156966\pi\)
\(60\) −4.24176 6.71482i −0.0706960 0.111914i
\(61\) −0.344323 −0.00564464 −0.00282232 0.999996i \(-0.500898\pi\)
−0.00282232 + 0.999996i \(0.500898\pi\)
\(62\) 19.1987 + 19.1987i 0.309656 + 0.309656i
\(63\) 70.2021 70.2021i 1.11432 1.11432i
\(64\) 8.00000i 0.125000i
\(65\) 95.3508 60.2332i 1.46694 0.926665i
\(66\) −12.6029 −0.190953
\(67\) −17.5051 17.5051i −0.261270 0.261270i 0.564300 0.825570i \(-0.309146\pi\)
−0.825570 + 0.564300i \(0.809146\pi\)
\(68\) −28.5873 + 28.5873i −0.420401 + 0.420401i
\(69\) 3.80903i 0.0552033i
\(70\) −18.4687 + 81.8232i −0.263838 + 1.16890i
\(71\) −14.8564 −0.209245 −0.104623 0.994512i \(-0.533363\pi\)
−0.104623 + 0.994512i \(0.533363\pi\)
\(72\) −16.7384 16.7384i −0.232477 0.232477i
\(73\) −68.0071 + 68.0071i −0.931604 + 0.931604i −0.997806 0.0662018i \(-0.978912\pi\)
0.0662018 + 0.997806i \(0.478912\pi\)
\(74\) 53.5917i 0.724212i
\(75\) 18.7099 6.64807i 0.249466 0.0886410i
\(76\) 70.8650 0.932434
\(77\) 94.1179 + 94.1179i 1.22231 + 1.22231i
\(78\) −17.9152 + 17.9152i −0.229682 + 0.229682i
\(79\) 82.9910i 1.05052i 0.850942 + 0.525260i \(0.176032\pi\)
−0.850942 + 0.525260i \(0.823968\pi\)
\(80\) 19.5092 + 4.40351i 0.243865 + 0.0550439i
\(81\) −64.3660 −0.794642
\(82\) 19.3079 + 19.3079i 0.235462 + 0.235462i
\(83\) −32.8277 + 32.8277i −0.395514 + 0.395514i −0.876647 0.481133i \(-0.840225\pi\)
0.481133 + 0.876647i \(0.340225\pi\)
\(84\) 18.8435i 0.224328i
\(85\) −53.9788 85.4499i −0.635045 1.00529i
\(86\) −88.0559 −1.02391
\(87\) −14.7150 14.7150i −0.169138 0.169138i
\(88\) 22.4406 22.4406i 0.255007 0.255007i
\(89\) 59.4270i 0.667719i 0.942623 + 0.333859i \(0.108351\pi\)
−0.942623 + 0.333859i \(0.891649\pi\)
\(90\) 50.0325 31.6056i 0.555917 0.351173i
\(91\) 267.579 2.94043
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 10.7822 10.7822i 0.115937 0.115937i
\(94\) 72.3115i 0.769272i
\(95\) −39.0068 + 172.815i −0.410598 + 1.81910i
\(96\) −4.49289 −0.0468009
\(97\) 33.5713 + 33.5713i 0.346096 + 0.346096i 0.858653 0.512557i \(-0.171302\pi\)
−0.512557 + 0.858653i \(0.671302\pi\)
\(98\) −91.7225 + 91.7225i −0.935944 + 0.935944i
\(99\) 93.9050i 0.948535i
\(100\) −21.4772 + 45.1523i −0.214772 + 0.451523i
\(101\) −24.7403 −0.244953 −0.122477 0.992471i \(-0.539084\pi\)
−0.122477 + 0.992471i \(0.539084\pi\)
\(102\) 16.0549 + 16.0549i 0.157401 + 0.157401i
\(103\) −75.8899 + 75.8899i −0.736795 + 0.736795i −0.971956 0.235161i \(-0.924438\pi\)
0.235161 + 0.971956i \(0.424438\pi\)
\(104\) 63.7992i 0.613454i
\(105\) 45.9528 + 10.3722i 0.437645 + 0.0987829i
\(106\) −1.00534 −0.00948435
\(107\) 11.0949 + 11.0949i 0.103691 + 0.103691i 0.757049 0.653358i \(-0.226640\pi\)
−0.653358 + 0.757049i \(0.726640\pi\)
\(108\) −19.5094 + 19.5094i −0.180643 + 0.180643i
\(109\) 2.34795i 0.0215408i −0.999942 0.0107704i \(-0.996572\pi\)
0.999942 0.0107704i \(-0.00342839\pi\)
\(110\) 42.3727 + 67.0771i 0.385206 + 0.609792i
\(111\) −30.0977 −0.271150
\(112\) 33.5526 + 33.5526i 0.299577 + 0.299577i
\(113\) 62.0808 62.0808i 0.549387 0.549387i −0.376876 0.926264i \(-0.623002\pi\)
0.926264 + 0.376876i \(0.123002\pi\)
\(114\) 39.7985i 0.349110i
\(115\) 20.2730 12.8065i 0.176287 0.111361i
\(116\) 52.4029 0.451749
\(117\) −133.487 133.487i −1.14091 1.14091i
\(118\) 5.81649 5.81649i 0.0492923 0.0492923i
\(119\) 239.795i 2.01508i
\(120\) 2.47306 10.9566i 0.0206088 0.0913048i
\(121\) 4.89562 0.0404597
\(122\) −0.344323 0.344323i −0.00282232 0.00282232i
\(123\) 10.8435 10.8435i 0.0881587 0.0881587i
\(124\) 38.3973i 0.309656i
\(125\) −98.2887 77.2291i −0.786310 0.617833i
\(126\) 140.404 1.11432
\(127\) −119.724 119.724i −0.942709 0.942709i 0.0557367 0.998445i \(-0.482249\pi\)
−0.998445 + 0.0557367i \(0.982249\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 49.4531i 0.383358i
\(130\) 155.584 + 35.1176i 1.19680 + 0.270135i
\(131\) 210.891 1.60986 0.804929 0.593371i \(-0.202203\pi\)
0.804929 + 0.593371i \(0.202203\pi\)
\(132\) −12.6029 12.6029i −0.0954766 0.0954766i
\(133\) −297.213 + 297.213i −2.23469 + 2.23469i
\(134\) 35.0101i 0.261270i
\(135\) −36.8380 58.3155i −0.272874 0.431966i
\(136\) −57.1746 −0.420401
\(137\) −176.740 176.740i −1.29008 1.29008i −0.934738 0.355338i \(-0.884366\pi\)
−0.355338 0.934738i \(-0.615634\pi\)
\(138\) −3.80903 + 3.80903i −0.0276017 + 0.0276017i
\(139\) 117.576i 0.845872i −0.906160 0.422936i \(-0.860999\pi\)
0.906160 0.422936i \(-0.139001\pi\)
\(140\) −100.292 + 63.3545i −0.716370 + 0.452532i
\(141\) −40.6109 −0.288021
\(142\) −14.8564 14.8564i −0.104623 0.104623i
\(143\) 178.962 178.962i 1.25148 1.25148i
\(144\) 33.4767i 0.232477i
\(145\) −28.8446 + 127.792i −0.198928 + 0.881327i
\(146\) −136.014 −0.931604
\(147\) 51.5123 + 51.5123i 0.350424 + 0.350424i
\(148\) 53.5917 53.5917i 0.362106 0.362106i
\(149\) 60.9513i 0.409069i 0.978859 + 0.204535i \(0.0655681\pi\)
−0.978859 + 0.204535i \(0.934432\pi\)
\(150\) 25.3580 + 12.0619i 0.169053 + 0.0804124i
\(151\) −35.1827 −0.232998 −0.116499 0.993191i \(-0.537167\pi\)
−0.116499 + 0.993191i \(0.537167\pi\)
\(152\) 70.8650 + 70.8650i 0.466217 + 0.466217i
\(153\) −119.626 + 119.626i −0.781870 + 0.781870i
\(154\) 188.236i 1.22231i
\(155\) −93.6377 21.1354i −0.604114 0.136357i
\(156\) −35.8303 −0.229682
\(157\) 12.1894 + 12.1894i 0.0776393 + 0.0776393i 0.744860 0.667221i \(-0.232516\pi\)
−0.667221 + 0.744860i \(0.732516\pi\)
\(158\) −82.9910 + 82.9910i −0.525260 + 0.525260i
\(159\) 0.564610i 0.00355101i
\(160\) 15.1057 + 23.9127i 0.0944106 + 0.149454i
\(161\) 56.8913 0.353362
\(162\) −64.3660 64.3660i −0.397321 0.397321i
\(163\) 19.4474 19.4474i 0.119309 0.119309i −0.644931 0.764240i \(-0.723114\pi\)
0.764240 + 0.644931i \(0.223114\pi\)
\(164\) 38.6158i 0.235462i
\(165\) 37.6712 23.7970i 0.228310 0.144224i
\(166\) −65.6553 −0.395514
\(167\) 54.5586 + 54.5586i 0.326698 + 0.326698i 0.851330 0.524631i \(-0.175797\pi\)
−0.524631 + 0.851330i \(0.675797\pi\)
\(168\) 18.8435 18.8435i 0.112164 0.112164i
\(169\) 339.793i 2.01061i
\(170\) 31.4711 139.429i 0.185124 0.820169i
\(171\) 296.541 1.73416
\(172\) −88.0559 88.0559i −0.511953 0.511953i
\(173\) 87.6542 87.6542i 0.506672 0.506672i −0.406831 0.913503i \(-0.633366\pi\)
0.913503 + 0.406831i \(0.133366\pi\)
\(174\) 29.4300i 0.169138i
\(175\) −99.2950 279.450i −0.567400 1.59685i
\(176\) 44.8813 0.255007
\(177\) −3.26660 3.26660i −0.0184554 0.0184554i
\(178\) −59.4270 + 59.4270i −0.333859 + 0.333859i
\(179\) 94.3552i 0.527124i −0.964642 0.263562i \(-0.915103\pi\)
0.964642 0.263562i \(-0.0848974\pi\)
\(180\) 81.6381 + 18.4269i 0.453545 + 0.102372i
\(181\) −195.781 −1.08166 −0.540830 0.841132i \(-0.681890\pi\)
−0.540830 + 0.841132i \(0.681890\pi\)
\(182\) 267.579 + 267.579i 1.47021 + 1.47021i
\(183\) −0.193375 + 0.193375i −0.00105670 + 0.00105670i
\(184\) 13.5647i 0.0737210i
\(185\) 101.192 + 160.190i 0.546986 + 0.865894i
\(186\) 21.5644 0.115937
\(187\) −160.379 160.379i −0.857643 0.857643i
\(188\) 72.3115 72.3115i 0.384636 0.384636i
\(189\) 163.648i 0.865864i
\(190\) −211.822 + 133.808i −1.11485 + 0.704253i
\(191\) −149.478 −0.782605 −0.391302 0.920262i \(-0.627975\pi\)
−0.391302 + 0.920262i \(0.627975\pi\)
\(192\) −4.49289 4.49289i −0.0234004 0.0234004i
\(193\) −266.184 + 266.184i −1.37919 + 1.37919i −0.533200 + 0.845989i \(0.679011\pi\)
−0.845989 + 0.533200i \(0.820989\pi\)
\(194\) 67.1427i 0.346096i
\(195\) 19.7224 87.3776i 0.101141 0.448090i
\(196\) −183.445 −0.935944
\(197\) 142.425 + 142.425i 0.722967 + 0.722967i 0.969209 0.246241i \(-0.0791956\pi\)
−0.246241 + 0.969209i \(0.579196\pi\)
\(198\) 93.9050 93.9050i 0.474268 0.474268i
\(199\) 253.594i 1.27434i 0.770723 + 0.637170i \(0.219895\pi\)
−0.770723 + 0.637170i \(0.780105\pi\)
\(200\) −66.6295 + 23.6750i −0.333148 + 0.118375i
\(201\) −19.6621 −0.0978212
\(202\) −24.7403 24.7403i −0.122477 0.122477i
\(203\) −219.782 + 219.782i −1.08267 + 1.08267i
\(204\) 32.1098i 0.157401i
\(205\) −94.1705 21.2556i −0.459368 0.103686i
\(206\) −151.780 −0.736795
\(207\) −28.3813 28.3813i −0.137108 0.137108i
\(208\) 63.7992 63.7992i 0.306727 0.306727i
\(209\) 397.564i 1.90222i
\(210\) 35.5806 + 56.3250i 0.169431 + 0.268214i
\(211\) −51.9224 −0.246078 −0.123039 0.992402i \(-0.539264\pi\)
−0.123039 + 0.992402i \(0.539264\pi\)
\(212\) −1.00534 1.00534i −0.00474218 0.00474218i
\(213\) −8.34351 + 8.34351i −0.0391714 + 0.0391714i
\(214\) 22.1898i 0.103691i
\(215\) 263.207 166.268i 1.22422 0.773340i
\(216\) −39.0189 −0.180643
\(217\) −161.042 161.042i −0.742127 0.742127i
\(218\) 2.34795 2.34795i 0.0107704 0.0107704i
\(219\) 76.3871i 0.348799i
\(220\) −24.7044 + 109.450i −0.112293 + 0.497499i
\(221\) −455.962 −2.06317
\(222\) −30.0977 30.0977i −0.135575 0.135575i
\(223\) −30.5354 + 30.5354i −0.136930 + 0.136930i −0.772250 0.635319i \(-0.780868\pi\)
0.635319 + 0.772250i \(0.280868\pi\)
\(224\) 67.1053i 0.299577i
\(225\) −89.8736 + 188.944i −0.399438 + 0.839751i
\(226\) 124.162 0.549387
\(227\) −76.8906 76.8906i −0.338725 0.338725i 0.517162 0.855887i \(-0.326988\pi\)
−0.855887 + 0.517162i \(0.826988\pi\)
\(228\) 39.7985 39.7985i 0.174555 0.174555i
\(229\) 32.2750i 0.140939i −0.997514 0.0704693i \(-0.977550\pi\)
0.997514 0.0704693i \(-0.0224497\pi\)
\(230\) 33.0795 + 7.46652i 0.143824 + 0.0324631i
\(231\) 105.715 0.457642
\(232\) 52.4029 + 52.4029i 0.225875 + 0.225875i
\(233\) 266.708 266.708i 1.14467 1.14467i 0.157086 0.987585i \(-0.449790\pi\)
0.987585 0.157086i \(-0.0502101\pi\)
\(234\) 266.974i 1.14091i
\(235\) 136.540 + 216.146i 0.581019 + 0.919769i
\(236\) 11.6330 0.0492923
\(237\) 46.6086 + 46.6086i 0.196661 + 0.196661i
\(238\) 239.795 239.795i 1.00754 1.00754i
\(239\) 336.743i 1.40897i −0.709720 0.704484i \(-0.751179\pi\)
0.709720 0.704484i \(-0.248821\pi\)
\(240\) 13.4296 8.48352i 0.0559568 0.0353480i
\(241\) 196.781 0.816517 0.408258 0.912866i \(-0.366136\pi\)
0.408258 + 0.912866i \(0.366136\pi\)
\(242\) 4.89562 + 4.89562i 0.0202298 + 0.0202298i
\(243\) −123.941 + 123.941i −0.510046 + 0.510046i
\(244\) 0.688646i 0.00282232i
\(245\) 100.975 447.358i 0.412144 1.82595i
\(246\) 21.6870 0.0881587
\(247\) 565.141 + 565.141i 2.28802 + 2.28802i
\(248\) −38.3973 + 38.3973i −0.154828 + 0.154828i
\(249\) 36.8727i 0.148083i
\(250\) −21.0596 175.518i −0.0842385 0.702071i
\(251\) 156.618 0.623975 0.311988 0.950086i \(-0.399005\pi\)
0.311988 + 0.950086i \(0.399005\pi\)
\(252\) 140.404 + 140.404i 0.557159 + 0.557159i
\(253\) 38.0500 38.0500i 0.150395 0.150395i
\(254\) 239.448i 0.942709i
\(255\) −78.3047 17.6745i −0.307077 0.0693118i
\(256\) 16.0000 0.0625000
\(257\) 133.914 + 133.914i 0.521068 + 0.521068i 0.917894 0.396826i \(-0.129888\pi\)
−0.396826 + 0.917894i \(0.629888\pi\)
\(258\) −49.4531 + 49.4531i −0.191679 + 0.191679i
\(259\) 449.536i 1.73566i
\(260\) 120.466 + 190.702i 0.463332 + 0.733468i
\(261\) 219.285 0.840172
\(262\) 210.891 + 210.891i 0.804929 + 0.804929i
\(263\) 215.159 215.159i 0.818095 0.818095i −0.167737 0.985832i \(-0.553646\pi\)
0.985832 + 0.167737i \(0.0536459\pi\)
\(264\) 25.2058i 0.0954766i
\(265\) 3.00506 1.89830i 0.0113398 0.00716339i
\(266\) −594.427 −2.23469
\(267\) 33.3748 + 33.3748i 0.124999 + 0.124999i
\(268\) 35.0101 35.0101i 0.130635 0.130635i
\(269\) 247.520i 0.920149i −0.887880 0.460075i \(-0.847823\pi\)
0.887880 0.460075i \(-0.152177\pi\)
\(270\) 21.4775 95.1534i 0.0795463 0.352420i
\(271\) 428.867 1.58253 0.791267 0.611470i \(-0.209422\pi\)
0.791267 + 0.611470i \(0.209422\pi\)
\(272\) −57.1746 57.1746i −0.210201 0.210201i
\(273\) 150.275 150.275i 0.550459 0.550459i
\(274\) 353.481i 1.29008i
\(275\) −253.312 120.491i −0.921133 0.438148i
\(276\) −7.61806 −0.0276017
\(277\) 92.4879 + 92.4879i 0.333891 + 0.333891i 0.854062 0.520171i \(-0.174132\pi\)
−0.520171 + 0.854062i \(0.674132\pi\)
\(278\) 117.576 117.576i 0.422936 0.422936i
\(279\) 160.677i 0.575904i
\(280\) −163.646 36.9374i −0.584451 0.131919i
\(281\) 473.576 1.68532 0.842662 0.538442i \(-0.180987\pi\)
0.842662 + 0.538442i \(0.180987\pi\)
\(282\) −40.6109 40.6109i −0.144010 0.144010i
\(283\) −264.849 + 264.849i −0.935864 + 0.935864i −0.998064 0.0622000i \(-0.980188\pi\)
0.0622000 + 0.998064i \(0.480188\pi\)
\(284\) 29.7128i 0.104623i
\(285\) 75.1481 + 118.961i 0.263677 + 0.417408i
\(286\) 357.924 1.25148
\(287\) −161.958 161.958i −0.564313 0.564313i
\(288\) 33.4767 33.4767i 0.116239 0.116239i
\(289\) 119.616i 0.413897i
\(290\) −156.637 + 98.9478i −0.540128 + 0.341199i
\(291\) 37.7080 0.129581
\(292\) −136.014 136.014i −0.465802 0.465802i
\(293\) −128.536 + 128.536i −0.438689 + 0.438689i −0.891571 0.452882i \(-0.850396\pi\)
0.452882 + 0.891571i \(0.350396\pi\)
\(294\) 103.025i 0.350424i
\(295\) −6.40324 + 28.3688i −0.0217059 + 0.0961653i
\(296\) 107.183 0.362106
\(297\) −109.451 109.451i −0.368522 0.368522i
\(298\) −60.9513 + 60.9513i −0.204535 + 0.204535i
\(299\) 108.177i 0.361795i
\(300\) 13.2961 + 37.4199i 0.0443205 + 0.124733i
\(301\) 738.627 2.45391
\(302\) −35.1827 35.1827i −0.116499 0.116499i
\(303\) −13.8944 + 13.8944i −0.0458561 + 0.0458561i
\(304\) 141.730i 0.466217i
\(305\) 1.67937 + 0.379057i 0.00550612 + 0.00124281i
\(306\) −239.252 −0.781870
\(307\) 228.266 + 228.266i 0.743537 + 0.743537i 0.973257 0.229720i \(-0.0737809\pi\)
−0.229720 + 0.973257i \(0.573781\pi\)
\(308\) −188.236 + 188.236i −0.611155 + 0.611155i
\(309\) 85.2412i 0.275861i
\(310\) −72.5023 114.773i −0.233878 0.370236i
\(311\) −105.969 −0.340738 −0.170369 0.985380i \(-0.554496\pi\)
−0.170369 + 0.985380i \(0.554496\pi\)
\(312\) −35.8303 35.8303i −0.114841 0.114841i
\(313\) −51.0125 + 51.0125i −0.162979 + 0.162979i −0.783885 0.620906i \(-0.786765\pi\)
0.620906 + 0.783885i \(0.286765\pi\)
\(314\) 24.3787i 0.0776393i
\(315\) −419.681 + 265.113i −1.33232 + 0.841628i
\(316\) −165.982 −0.525260
\(317\) −345.566 345.566i −1.09011 1.09011i −0.995515 0.0945988i \(-0.969843\pi\)
−0.0945988 0.995515i \(-0.530157\pi\)
\(318\) −0.564610 + 0.564610i −0.00177550 + 0.00177550i
\(319\) 293.989i 0.921595i
\(320\) −8.80702 + 39.0184i −0.0275219 + 0.121933i
\(321\) 12.4620 0.0388226
\(322\) 56.8913 + 56.8913i 0.176681 + 0.176681i
\(323\) 506.459 506.459i 1.56799 1.56799i
\(324\) 128.732i 0.397321i
\(325\) −531.364 + 188.806i −1.63497 + 0.580942i
\(326\) 38.8948 0.119309
\(327\) −1.31863 1.31863i −0.00403251 0.00403251i
\(328\) −38.6158 + 38.6158i −0.117731 + 0.117731i
\(329\) 606.561i 1.84365i
\(330\) 61.4682 + 13.8743i 0.186267 + 0.0420432i
\(331\) −386.634 −1.16808 −0.584039 0.811726i \(-0.698528\pi\)
−0.584039 + 0.811726i \(0.698528\pi\)
\(332\) −65.6553 65.6553i −0.197757 0.197757i
\(333\) 224.260 224.260i 0.673452 0.673452i
\(334\) 109.117i 0.326698i
\(335\) 66.1065 + 104.648i 0.197333 + 0.312383i
\(336\) 37.6870 0.112164
\(337\) 122.880 + 122.880i 0.364629 + 0.364629i 0.865514 0.500885i \(-0.166992\pi\)
−0.500885 + 0.865514i \(0.666992\pi\)
\(338\) 339.793 339.793i 1.00530 1.00530i
\(339\) 69.7304i 0.205695i
\(340\) 170.900 107.958i 0.502647 0.317523i
\(341\) −215.415 −0.631716
\(342\) 296.541 + 296.541i 0.867080 + 0.867080i
\(343\) 358.363 358.363i 1.04479 1.04479i
\(344\) 176.112i 0.511953i
\(345\) 4.19328 18.5778i 0.0121544 0.0538486i
\(346\) 175.308 0.506672
\(347\) −71.2251 71.2251i −0.205260 0.205260i 0.596989 0.802249i \(-0.296363\pi\)
−0.802249 + 0.596989i \(0.796363\pi\)
\(348\) 29.4300 29.4300i 0.0845691 0.0845691i
\(349\) 53.6965i 0.153858i 0.997037 + 0.0769291i \(0.0245115\pi\)
−0.997037 + 0.0769291i \(0.975488\pi\)
\(350\) 180.155 378.745i 0.514728 1.08213i
\(351\) −311.172 −0.886529
\(352\) 44.8813 + 44.8813i 0.127504 + 0.127504i
\(353\) −242.586 + 242.586i −0.687214 + 0.687214i −0.961615 0.274402i \(-0.911520\pi\)
0.274402 + 0.961615i \(0.411520\pi\)
\(354\) 6.53320i 0.0184554i
\(355\) 72.4592 + 16.3551i 0.204110 + 0.0460707i
\(356\) −118.854 −0.333859
\(357\) −134.671 134.671i −0.377230 0.377230i
\(358\) 94.3552 94.3552i 0.263562 0.263562i
\(359\) 308.225i 0.858566i 0.903170 + 0.429283i \(0.141234\pi\)
−0.903170 + 0.429283i \(0.858766\pi\)
\(360\) 63.2112 + 100.065i 0.175587 + 0.277958i
\(361\) −894.462 −2.47773
\(362\) −195.781 195.781i −0.540830 0.540830i
\(363\) 2.74943 2.74943i 0.00757420 0.00757420i
\(364\) 535.158i 1.47021i
\(365\) 406.559 256.824i 1.11386 0.703627i
\(366\) −0.386751 −0.00105670
\(367\) 136.488 + 136.488i 0.371903 + 0.371903i 0.868170 0.496267i \(-0.165296\pi\)
−0.496267 + 0.868170i \(0.665296\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 161.591i 0.437917i
\(370\) −58.9979 + 261.383i −0.159454 + 0.706440i
\(371\) 8.43297 0.0227304
\(372\) 21.5644 + 21.5644i 0.0579687 + 0.0579687i
\(373\) 403.664 403.664i 1.08221 1.08221i 0.0859072 0.996303i \(-0.472621\pi\)
0.996303 0.0859072i \(-0.0273789\pi\)
\(374\) 320.758i 0.857643i
\(375\) −98.5727 + 11.8273i −0.262860 + 0.0315395i
\(376\) 144.623 0.384636
\(377\) 417.908 + 417.908i 1.10851 + 1.10851i
\(378\) 163.648 163.648i 0.432932 0.432932i
\(379\) 148.502i 0.391826i −0.980621 0.195913i \(-0.937233\pi\)
0.980621 0.195913i \(-0.0627670\pi\)
\(380\) −345.630 78.0137i −0.909552 0.205299i
\(381\) −134.477 −0.352957
\(382\) −149.478 149.478i −0.391302 0.391302i
\(383\) −6.49326 + 6.49326i −0.0169537 + 0.0169537i −0.715533 0.698579i \(-0.753816\pi\)
0.698579 + 0.715533i \(0.253816\pi\)
\(384\) 8.98577i 0.0234004i
\(385\) −355.429 562.653i −0.923192 1.46144i
\(386\) −532.367 −1.37919
\(387\) −368.478 368.478i −0.952140 0.952140i
\(388\) −67.1427 + 67.1427i −0.173048 + 0.173048i
\(389\) 275.558i 0.708376i 0.935174 + 0.354188i \(0.115243\pi\)
−0.935174 + 0.354188i \(0.884757\pi\)
\(390\) 107.100 67.6552i 0.274616 0.173475i
\(391\) −96.9442 −0.247939
\(392\) −183.445 183.445i −0.467972 0.467972i
\(393\) 118.439 118.439i 0.301371 0.301371i
\(394\) 284.849i 0.722967i
\(395\) 91.3630 404.772i 0.231299 1.02474i
\(396\) 187.810 0.474268
\(397\) −163.172 163.172i −0.411013 0.411013i 0.471078 0.882091i \(-0.343865\pi\)
−0.882091 + 0.471078i \(0.843865\pi\)
\(398\) −253.594 + 253.594i −0.637170 + 0.637170i
\(399\) 333.837i 0.836683i
\(400\) −90.3045 42.9545i −0.225761 0.107386i
\(401\) 13.1077 0.0326876 0.0163438 0.999866i \(-0.494797\pi\)
0.0163438 + 0.999866i \(0.494797\pi\)
\(402\) −19.6621 19.6621i −0.0489106 0.0489106i
\(403\) −306.215 + 306.215i −0.759839 + 0.759839i
\(404\) 49.4805i 0.122477i
\(405\) 313.932 + 70.8591i 0.775141 + 0.174961i
\(406\) −439.564 −1.08267
\(407\) 300.658 + 300.658i 0.738718 + 0.738718i
\(408\) −32.1098 + 32.1098i −0.0787006 + 0.0787006i
\(409\) 597.737i 1.46146i 0.682667 + 0.730730i \(0.260820\pi\)
−0.682667 + 0.730730i \(0.739180\pi\)
\(410\) −72.9148 115.426i −0.177841 0.281527i
\(411\) −198.519 −0.483014
\(412\) −151.780 151.780i −0.368398 0.368398i
\(413\) −48.7896 + 48.7896i −0.118135 + 0.118135i
\(414\) 56.7626i 0.137108i
\(415\) 196.250 123.971i 0.472891 0.298726i
\(416\) 127.598 0.306727
\(417\) −66.0321 66.0321i −0.158350 0.158350i
\(418\) −397.564 + 397.564i −0.951110 + 0.951110i
\(419\) 650.314i 1.55206i −0.630695 0.776031i \(-0.717230\pi\)
0.630695 0.776031i \(-0.282770\pi\)
\(420\) −20.7444 + 91.9055i −0.0493915 + 0.218823i
\(421\) −719.579 −1.70921 −0.854607 0.519276i \(-0.826202\pi\)
−0.854607 + 0.519276i \(0.826202\pi\)
\(422\) −51.9224 51.9224i −0.123039 0.123039i
\(423\) 302.594 302.594i 0.715353 0.715353i
\(424\) 2.01068i 0.00474218i
\(425\) 169.201 + 476.189i 0.398120 + 1.12045i
\(426\) −16.6870 −0.0391714
\(427\) 2.88824 + 2.88824i 0.00676402 + 0.00676402i
\(428\) −22.1898 + 22.1898i −0.0518454 + 0.0518454i
\(429\) 201.014i 0.468564i
\(430\) 429.475 + 96.9388i 0.998780 + 0.225439i
\(431\) −320.243 −0.743023 −0.371512 0.928428i \(-0.621160\pi\)
−0.371512 + 0.928428i \(0.621160\pi\)
\(432\) −39.0189 39.0189i −0.0903215 0.0903215i
\(433\) 475.562 475.562i 1.09830 1.09830i 0.103686 0.994610i \(-0.466936\pi\)
0.994610 0.103686i \(-0.0330638\pi\)
\(434\) 322.083i 0.742127i
\(435\) 55.5702 + 87.9691i 0.127748 + 0.202228i
\(436\) 4.69589 0.0107704
\(437\) 120.157 + 120.157i 0.274960 + 0.274960i
\(438\) −76.3871 + 76.3871i −0.174400 + 0.174400i
\(439\) 188.615i 0.429647i −0.976653 0.214823i \(-0.931082\pi\)
0.976653 0.214823i \(-0.0689176\pi\)
\(440\) −134.154 + 84.7454i −0.304896 + 0.192603i
\(441\) −767.643 −1.74069
\(442\) −455.962 455.962i −1.03159 1.03159i
\(443\) −479.576 + 479.576i −1.08256 + 1.08256i −0.0862935 + 0.996270i \(0.527502\pi\)
−0.996270 + 0.0862935i \(0.972498\pi\)
\(444\) 60.1953i 0.135575i
\(445\) 65.4218 289.843i 0.147015 0.651333i
\(446\) −61.0709 −0.136930
\(447\) 34.2309 + 34.2309i 0.0765793 + 0.0765793i
\(448\) −67.1053 + 67.1053i −0.149789 + 0.149789i
\(449\) 720.644i 1.60500i 0.596653 + 0.802499i \(0.296497\pi\)
−0.596653 + 0.802499i \(0.703503\pi\)
\(450\) −278.817 + 99.0703i −0.619594 + 0.220156i
\(451\) −216.641 −0.480357
\(452\) 124.162 + 124.162i 0.274694 + 0.274694i
\(453\) −19.7590 + 19.7590i −0.0436181 + 0.0436181i
\(454\) 153.781i 0.338725i
\(455\) −1305.06 294.572i −2.86827 0.647411i
\(456\) 79.5971 0.174555
\(457\) −549.320 549.320i −1.20201 1.20201i −0.973553 0.228461i \(-0.926631\pi\)
−0.228461 0.973553i \(-0.573369\pi\)
\(458\) 32.2750 32.2750i 0.0704693 0.0704693i
\(459\) 278.861i 0.607540i
\(460\) 25.6130 + 40.5460i 0.0556803 + 0.0881434i
\(461\) 236.518 0.513054 0.256527 0.966537i \(-0.417422\pi\)
0.256527 + 0.966537i \(0.417422\pi\)
\(462\) 105.715 + 105.715i 0.228821 + 0.228821i
\(463\) −271.311 + 271.311i −0.585985 + 0.585985i −0.936542 0.350556i \(-0.885993\pi\)
0.350556 + 0.936542i \(0.385993\pi\)
\(464\) 104.806i 0.225875i
\(465\) −64.4578 + 40.7181i −0.138619 + 0.0875658i
\(466\) 533.417 1.14467
\(467\) 162.650 + 162.650i 0.348287 + 0.348287i 0.859471 0.511184i \(-0.170793\pi\)
−0.511184 + 0.859471i \(0.670793\pi\)
\(468\) 266.974 266.974i 0.570457 0.570457i
\(469\) 293.671i 0.626163i
\(470\) −79.6062 + 352.685i −0.169375 + 0.750394i
\(471\) 13.6914 0.0290687
\(472\) 11.6330 + 11.6330i 0.0246461 + 0.0246461i
\(473\) 494.008 494.008i 1.04441 1.04441i
\(474\) 93.2173i 0.196661i
\(475\) 380.496 799.929i 0.801045 1.68406i
\(476\) 479.589 1.00754
\(477\) −4.20694 4.20694i −0.00881959 0.00881959i
\(478\) 336.743 336.743i 0.704484 0.704484i
\(479\) 632.742i 1.32096i −0.750842 0.660482i \(-0.770352\pi\)
0.750842 0.660482i \(-0.229648\pi\)
\(480\) 21.9132 + 4.94612i 0.0456524 + 0.0103044i
\(481\) 854.777 1.77708
\(482\) 196.781 + 196.781i 0.408258 + 0.408258i
\(483\) 31.9507 31.9507i 0.0661506 0.0661506i
\(484\) 9.79125i 0.0202298i
\(485\) −126.780 200.695i −0.261401 0.413805i
\(486\) −247.882 −0.510046
\(487\) 16.0549 + 16.0549i 0.0329669 + 0.0329669i 0.723398 0.690431i \(-0.242579\pi\)
−0.690431 + 0.723398i \(0.742579\pi\)
\(488\) 0.688646 0.688646i 0.00141116 0.00141116i
\(489\) 21.8437i 0.0446702i
\(490\) 548.334 346.383i 1.11905 0.706904i
\(491\) 524.300 1.06782 0.533910 0.845541i \(-0.320722\pi\)
0.533910 + 0.845541i \(0.320722\pi\)
\(492\) 21.6870 + 21.6870i 0.0440794 + 0.0440794i
\(493\) 374.514 374.514i 0.759664 0.759664i
\(494\) 1130.28i 2.28802i
\(495\) −103.378 + 458.003i −0.208844 + 0.925258i
\(496\) −76.7947 −0.154828
\(497\) 124.618 + 124.618i 0.250740 + 0.250740i
\(498\) −36.8727 + 36.8727i −0.0740416 + 0.0740416i
\(499\) 252.276i 0.505562i −0.967523 0.252781i \(-0.918655\pi\)
0.967523 0.252781i \(-0.0813453\pi\)
\(500\) 154.458 196.577i 0.308916 0.393155i
\(501\) 61.2814 0.122318
\(502\) 156.618 + 156.618i 0.311988 + 0.311988i
\(503\) −661.949 + 661.949i −1.31600 + 1.31600i −0.399089 + 0.916912i \(0.630674\pi\)
−0.916912 + 0.399089i \(0.869326\pi\)
\(504\) 280.808i 0.557159i
\(505\) 120.666 + 27.2360i 0.238942 + 0.0539327i
\(506\) 76.0999 0.150395
\(507\) −190.831 190.831i −0.376393 0.376393i
\(508\) 239.448 239.448i 0.471354 0.471354i
\(509\) 77.7088i 0.152670i 0.997082 + 0.0763348i \(0.0243218\pi\)
−0.997082 + 0.0763348i \(0.975678\pi\)
\(510\) −60.6302 95.9792i −0.118883 0.188195i
\(511\) 1140.91 2.23270
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 345.634 345.634i 0.673751 0.673751i
\(514\) 267.829i 0.521068i
\(515\) 453.684 286.593i 0.880939 0.556490i
\(516\) −98.9063 −0.191679
\(517\) 405.679 + 405.679i 0.784680 + 0.784680i
\(518\) −449.536 + 449.536i −0.867830 + 0.867830i
\(519\) 98.4551i 0.189702i
\(520\) −70.2351 + 311.168i −0.135068 + 0.598400i
\(521\) 184.322 0.353784 0.176892 0.984230i \(-0.443396\pi\)
0.176892 + 0.984230i \(0.443396\pi\)
\(522\) 219.285 + 219.285i 0.420086 + 0.420086i
\(523\) −606.795 + 606.795i −1.16022 + 1.16022i −0.175792 + 0.984427i \(0.556249\pi\)
−0.984427 + 0.175792i \(0.943751\pi\)
\(524\) 421.783i 0.804929i
\(525\) −212.707 101.177i −0.405156 0.192718i
\(526\) 430.318 0.818095
\(527\) 274.419 + 274.419i 0.520719 + 0.520719i
\(528\) 25.2058 25.2058i 0.0477383 0.0477383i
\(529\) 23.0000i 0.0434783i
\(530\) 4.90335 + 1.10676i 0.00925161 + 0.00208822i
\(531\) 48.6793 0.0916747
\(532\) −594.427 594.427i −1.11734 1.11734i
\(533\) −307.957 + 307.957i −0.577781 + 0.577781i
\(534\) 66.7496i 0.124999i
\(535\) −41.8991 66.3274i −0.0783161 0.123976i
\(536\) 70.0202 0.130635
\(537\) −52.9909 52.9909i −0.0986795 0.0986795i
\(538\) 247.520 247.520i 0.460075 0.460075i
\(539\) 1029.16i 1.90938i
\(540\) 116.631 73.6759i 0.215983 0.136437i
\(541\) −258.474 −0.477771 −0.238885 0.971048i \(-0.576782\pi\)
−0.238885 + 0.971048i \(0.576782\pi\)
\(542\) 428.867 + 428.867i 0.791267 + 0.791267i
\(543\) −109.952 + 109.952i −0.202491 + 0.202491i
\(544\) 114.349i 0.210201i
\(545\) −2.58480 + 11.4516i −0.00474276 + 0.0210122i
\(546\) 300.551 0.550459
\(547\) −185.276 185.276i −0.338713 0.338713i 0.517170 0.855883i \(-0.326985\pi\)
−0.855883 + 0.517170i \(0.826985\pi\)
\(548\) 353.481 353.481i 0.645038 0.645038i
\(549\) 2.88170i 0.00524900i
\(550\) −132.821 373.802i −0.241492 0.679641i
\(551\) −928.383 −1.68491
\(552\) −7.61806 7.61806i −0.0138008 0.0138008i
\(553\) 696.142 696.142i 1.25885 1.25885i
\(554\) 184.976i 0.333891i
\(555\) 146.795 + 33.1339i 0.264496 + 0.0597006i
\(556\) 235.152 0.422936
\(557\) 125.327 + 125.327i 0.225003 + 0.225003i 0.810601 0.585598i \(-0.199140\pi\)
−0.585598 + 0.810601i \(0.699140\pi\)
\(558\) −160.677 + 160.677i −0.287952 + 0.287952i
\(559\) 1404.47i 2.51248i
\(560\) −126.709 200.584i −0.226266 0.358185i
\(561\) −180.141 −0.321108
\(562\) 473.576 + 473.576i 0.842662 + 0.842662i
\(563\) −78.4316 + 78.4316i −0.139310 + 0.139310i −0.773323 0.634013i \(-0.781407\pi\)
0.634013 + 0.773323i \(0.281407\pi\)
\(564\) 81.2219i 0.144010i
\(565\) −371.130 + 234.443i −0.656867 + 0.414944i
\(566\) −529.699 −0.935864
\(567\) 539.912 + 539.912i 0.952226 + 0.952226i
\(568\) 29.7128 29.7128i 0.0523113 0.0523113i
\(569\) 530.486i 0.932313i −0.884702 0.466156i \(-0.845638\pi\)
0.884702 0.466156i \(-0.154362\pi\)
\(570\) −43.8133 + 194.109i −0.0768655 + 0.340543i
\(571\) −504.213 −0.883036 −0.441518 0.897252i \(-0.645560\pi\)
−0.441518 + 0.897252i \(0.645560\pi\)
\(572\) 357.924 + 357.924i 0.625741 + 0.625741i
\(573\) −83.9482 + 83.9482i −0.146506 + 0.146506i
\(574\) 323.916i 0.564313i
\(575\) −112.976 + 40.1430i −0.196480 + 0.0698138i
\(576\) 66.9535 0.116239
\(577\) −394.631 394.631i −0.683937 0.683937i 0.276948 0.960885i \(-0.410677\pi\)
−0.960885 + 0.276948i \(0.910677\pi\)
\(578\) −119.616 + 119.616i −0.206949 + 0.206949i
\(579\) 298.983i 0.516378i
\(580\) −255.585 57.6892i −0.440664 0.0994642i
\(581\) 550.727 0.947896
\(582\) 37.7080 + 37.7080i 0.0647904 + 0.0647904i
\(583\) 5.64013 5.64013i 0.00967432 0.00967432i
\(584\) 272.028i 0.465802i
\(585\) 504.103 + 798.009i 0.861715 + 1.36412i
\(586\) −257.072 −0.438689
\(587\) −133.142 133.142i −0.226817 0.226817i 0.584544 0.811362i \(-0.301273\pi\)
−0.811362 + 0.584544i \(0.801273\pi\)
\(588\) −103.025 + 103.025i −0.175212 + 0.175212i
\(589\) 680.257i 1.15494i
\(590\) −34.7720 + 21.9655i −0.0589356 + 0.0372297i
\(591\) 159.974 0.270684
\(592\) 107.183 + 107.183i 0.181053 + 0.181053i
\(593\) −529.877 + 529.877i −0.893553 + 0.893553i −0.994856 0.101303i \(-0.967699\pi\)
0.101303 + 0.994856i \(0.467699\pi\)
\(594\) 218.902i 0.368522i
\(595\) −263.985 + 1169.55i −0.443672 + 1.96563i
\(596\) −121.903 −0.204535
\(597\) 142.421 + 142.421i 0.238561 + 0.238561i
\(598\) 108.177 108.177i 0.180898 0.180898i
\(599\) 905.867i 1.51230i 0.654399 + 0.756150i \(0.272922\pi\)
−0.654399 + 0.756150i \(0.727078\pi\)
\(600\) −24.1237 + 50.7160i −0.0402062 + 0.0845267i
\(601\) 166.228 0.276586 0.138293 0.990391i \(-0.455838\pi\)
0.138293 + 0.990391i \(0.455838\pi\)
\(602\) 738.627 + 738.627i 1.22696 + 1.22696i
\(603\) 146.503 146.503i 0.242957 0.242957i
\(604\) 70.3654i 0.116499i
\(605\) −23.8774 5.38948i −0.0394668 0.00890824i
\(606\) −27.7888 −0.0458561
\(607\) 132.189 + 132.189i 0.217774 + 0.217774i 0.807560 0.589786i \(-0.200788\pi\)
−0.589786 + 0.807560i \(0.700788\pi\)
\(608\) −141.730 + 141.730i −0.233109 + 0.233109i
\(609\) 246.864i 0.405360i
\(610\) 1.30031 + 2.05842i 0.00213165 + 0.00337447i
\(611\) 1153.36 1.88765
\(612\) −239.252 239.252i −0.390935 0.390935i
\(613\) 404.008 404.008i 0.659066 0.659066i −0.296093 0.955159i \(-0.595684\pi\)
0.955159 + 0.296093i \(0.0956837\pi\)
\(614\) 456.532i 0.743537i
\(615\) −64.8245 + 40.9497i −0.105406 + 0.0665849i
\(616\) −376.471 −0.611155
\(617\) 717.669 + 717.669i 1.16316 + 1.16316i 0.983780 + 0.179379i \(0.0574089\pi\)
0.179379 + 0.983780i \(0.442591\pi\)
\(618\) −85.2412 + 85.2412i −0.137931 + 0.137931i
\(619\) 623.796i 1.00775i 0.863777 + 0.503874i \(0.168092\pi\)
−0.863777 + 0.503874i \(0.831908\pi\)
\(620\) 42.2708 187.275i 0.0681787 0.302057i
\(621\) −66.1597 −0.106537
\(622\) −105.969 105.969i −0.170369 0.170369i
\(623\) 498.483 498.483i 0.800133 0.800133i
\(624\) 71.6606i 0.114841i
\(625\) 394.364 + 484.873i 0.630982 + 0.775797i
\(626\) −102.025 −0.162979
\(627\) 223.276 + 223.276i 0.356102 + 0.356102i
\(628\) −24.3787 + 24.3787i −0.0388196 + 0.0388196i
\(629\) 766.021i 1.21784i
\(630\) −684.793 154.568i −1.08697 0.245346i
\(631\) −486.238 −0.770584 −0.385292 0.922795i \(-0.625899\pi\)
−0.385292 + 0.922795i \(0.625899\pi\)
\(632\) −165.982 165.982i −0.262630 0.262630i
\(633\) −29.1602 + 29.1602i −0.0460666 + 0.0460666i
\(634\) 691.132i 1.09011i
\(635\) 452.129 + 715.732i 0.712014 + 1.12714i
\(636\) −1.12922 −0.00177550
\(637\) −1462.96 1462.96i −2.29663 2.29663i
\(638\) −293.989 + 293.989i −0.460798 + 0.460798i
\(639\) 124.336i 0.194579i
\(640\) −47.8254 + 30.2114i −0.0747272 + 0.0472053i
\(641\) −679.444 −1.05998 −0.529988 0.848005i \(-0.677804\pi\)
−0.529988 + 0.848005i \(0.677804\pi\)
\(642\) 12.4620 + 12.4620i 0.0194113 + 0.0194113i
\(643\) −90.4151 + 90.4151i −0.140614 + 0.140614i −0.773910 0.633296i \(-0.781702\pi\)
0.633296 + 0.773910i \(0.281702\pi\)
\(644\) 113.783i 0.176681i
\(645\) 54.4419 241.198i 0.0844060 0.373950i
\(646\) 1012.92 1.56799
\(647\) 415.172 + 415.172i 0.641688 + 0.641688i 0.950970 0.309282i \(-0.100089\pi\)
−0.309282 + 0.950970i \(0.600089\pi\)
\(648\) 128.732 128.732i 0.198660 0.198660i
\(649\) 65.2629i 0.100559i
\(650\) −720.170 342.558i −1.10795 0.527012i
\(651\) −180.885 −0.277858
\(652\) 38.8948 + 38.8948i 0.0596546 + 0.0596546i
\(653\) 655.560 655.560i 1.00392 1.00392i 0.00392871 0.999992i \(-0.498749\pi\)
0.999992 0.00392871i \(-0.00125055\pi\)
\(654\) 2.63726i 0.00403251i
\(655\) −1028.58 232.166i −1.57035 0.354451i
\(656\) −77.2316 −0.117731
\(657\) −569.164 569.164i −0.866308 0.866308i
\(658\) −606.561 + 606.561i −0.921825 + 0.921825i
\(659\) 557.907i 0.846597i −0.905990 0.423298i \(-0.860872\pi\)
0.905990 0.423298i \(-0.139128\pi\)
\(660\) 47.5939 + 75.3424i 0.0721120 + 0.114155i
\(661\) 310.778 0.470163 0.235082 0.971976i \(-0.424464\pi\)
0.235082 + 0.971976i \(0.424464\pi\)
\(662\) −386.634 386.634i −0.584039 0.584039i
\(663\) −256.073 + 256.073i −0.386234 + 0.386234i
\(664\) 131.311i 0.197757i
\(665\) 1776.80 1122.40i 2.67187 1.68783i
\(666\) 448.519 0.673452
\(667\) 88.8535 + 88.8535i 0.133214 + 0.133214i
\(668\) −109.117 + 109.117i −0.163349 + 0.163349i
\(669\) 34.2981i 0.0512677i
\(670\) −38.5419 + 170.755i −0.0575252 + 0.254858i
\(671\) 3.86341 0.00575770
\(672\) 37.6870 + 37.6870i 0.0560819 + 0.0560819i
\(673\) 53.9294 53.9294i 0.0801328 0.0801328i −0.665904 0.746037i \(-0.731954\pi\)
0.746037 + 0.665904i \(0.231954\pi\)
\(674\) 245.760i 0.364629i
\(675\) 115.472 + 324.976i 0.171069 + 0.481446i
\(676\) 679.585 1.00530
\(677\) −132.335 132.335i −0.195472 0.195472i 0.602584 0.798056i \(-0.294138\pi\)
−0.798056 + 0.602584i \(0.794138\pi\)
\(678\) 69.7304 69.7304i 0.102847 0.102847i
\(679\) 563.204i 0.829460i
\(680\) 278.858 + 62.9422i 0.410085 + 0.0925621i
\(681\) −86.3652 −0.126821
\(682\) −215.415 215.415i −0.315858 0.315858i
\(683\) −633.830 + 633.830i −0.928009 + 0.928009i −0.997577 0.0695679i \(-0.977838\pi\)
0.0695679 + 0.997577i \(0.477838\pi\)
\(684\) 593.082i 0.867080i
\(685\) 667.447 + 1056.59i 0.974375 + 1.54246i
\(686\) 716.726 1.04479
\(687\) −18.1260 18.1260i −0.0263842 0.0263842i
\(688\) 176.112 176.112i 0.255976 0.255976i
\(689\) 16.0350i 0.0232729i
\(690\) 22.7711 14.3845i 0.0330015 0.0208471i
\(691\) 95.7685 0.138594 0.0692970 0.997596i \(-0.477924\pi\)
0.0692970 + 0.997596i \(0.477924\pi\)
\(692\) 175.308 + 175.308i 0.253336 + 0.253336i
\(693\) −787.690 + 787.690i −1.13664 + 1.13664i
\(694\) 142.450i 0.205260i
\(695\) −129.437 + 573.455i −0.186240 + 0.825115i
\(696\) 58.8601 0.0845691
\(697\) 275.980 + 275.980i 0.395954 + 0.395954i
\(698\) −53.6965 + 53.6965i −0.0769291 + 0.0769291i
\(699\) 299.573i 0.428573i
\(700\) 558.899 198.590i 0.798427 0.283700i
\(701\) −467.837 −0.667386 −0.333693 0.942682i \(-0.608295\pi\)
−0.333693 + 0.942682i \(0.608295\pi\)
\(702\) −311.172 311.172i −0.443265 0.443265i
\(703\) −949.444 + 949.444i −1.35056 + 1.35056i
\(704\) 89.7626i 0.127504i
\(705\) 198.072 + 44.7077i 0.280953 + 0.0634151i
\(706\) −485.173 −0.687214
\(707\) 207.525 + 207.525i 0.293530 + 0.293530i
\(708\) 6.53320 6.53320i 0.00922769 0.00922769i
\(709\) 744.912i 1.05065i 0.850901 + 0.525326i \(0.176057\pi\)
−0.850901 + 0.525326i \(0.823943\pi\)
\(710\) 56.1041 + 88.8142i 0.0790198 + 0.125090i
\(711\) −694.567 −0.976888
\(712\) −118.854 118.854i −0.166930 0.166930i
\(713\) −65.1059 + 65.1059i −0.0913126 + 0.0913126i
\(714\) 269.343i 0.377230i
\(715\) −1069.87 + 675.836i −1.49632 + 0.945225i
\(716\) 188.710 0.263562
\(717\) −189.119 189.119i −0.263764 0.263764i
\(718\) −308.225 + 308.225i −0.429283 + 0.429283i
\(719\) 611.347i 0.850274i 0.905129 + 0.425137i \(0.139774\pi\)
−0.905129 + 0.425137i \(0.860226\pi\)
\(720\) −36.8538 + 163.276i −0.0511858 + 0.226772i
\(721\) 1273.15 1.76582
\(722\) −894.462 894.462i −1.23887 1.23887i
\(723\) 110.514 110.514i 0.152855 0.152855i
\(724\) 391.561i 0.540830i
\(725\) 281.368 591.528i 0.388093 0.815901i
\(726\) 5.49887 0.00757420
\(727\) −917.283 917.283i −1.26174 1.26174i −0.950250 0.311488i \(-0.899173\pi\)
−0.311488 0.950250i \(-0.600827\pi\)
\(728\) −535.158 + 535.158i −0.735107 + 0.735107i
\(729\) 440.080i 0.603677i
\(730\) 663.382 + 149.735i 0.908743 + 0.205117i
\(731\) −1258.64 −1.72180
\(732\) −0.386751 0.386751i −0.000528348 0.000528348i
\(733\) 639.952 639.952i 0.873058 0.873058i −0.119746 0.992805i \(-0.538208\pi\)
0.992805 + 0.119746i \(0.0382081\pi\)
\(734\) 272.977i 0.371903i
\(735\) −194.532 307.950i −0.264670 0.418980i
\(736\) 27.1293 0.0368605
\(737\) 196.412 + 196.412i 0.266503 + 0.266503i
\(738\) −161.591 + 161.591i −0.218959 + 0.218959i
\(739\) 115.163i 0.155836i −0.996960 0.0779181i \(-0.975173\pi\)
0.996960 0.0779181i \(-0.0248273\pi\)
\(740\) −320.381 + 202.385i −0.432947 + 0.273493i
\(741\) 634.779 0.856652
\(742\) 8.43297 + 8.43297i 0.0113652 + 0.0113652i
\(743\) 204.199 204.199i 0.274831 0.274831i −0.556211 0.831041i \(-0.687745\pi\)
0.831041 + 0.556211i \(0.187745\pi\)
\(744\) 43.1287i 0.0579687i
\(745\) 67.1000 297.278i 0.0900671 0.399031i
\(746\) 807.329 1.08221
\(747\) −274.741 274.741i −0.367792 0.367792i
\(748\) 320.758 320.758i 0.428822 0.428822i
\(749\) 186.132i 0.248507i
\(750\) −110.400 86.7453i −0.147200 0.115660i
\(751\) 190.931 0.254236 0.127118 0.991888i \(-0.459427\pi\)
0.127118 + 0.991888i \(0.459427\pi\)
\(752\) 144.623 + 144.623i 0.192318 + 0.192318i
\(753\) 87.9582 87.9582i 0.116810 0.116810i
\(754\) 835.817i 1.10851i
\(755\) 171.597 + 38.7319i 0.227280 + 0.0513005i
\(756\) 327.297 0.432932
\(757\) −812.029 812.029i −1.07269 1.07269i −0.997142 0.0755517i \(-0.975928\pi\)
−0.0755517 0.997142i \(-0.524072\pi\)
\(758\) 148.502 148.502i 0.195913 0.195913i
\(759\) 42.7385i 0.0563090i
\(760\) −267.616 423.644i −0.352127 0.557426i
\(761\) −847.042 −1.11306 −0.556532 0.830826i \(-0.687869\pi\)
−0.556532 + 0.830826i \(0.687869\pi\)
\(762\) −134.477 134.477i −0.176478 0.176478i
\(763\) −19.6950 + 19.6950i −0.0258125 + 0.0258125i
\(764\) 298.955i 0.391302i
\(765\) 715.147 451.759i 0.934832 0.590535i
\(766\) −12.9865 −0.0169537
\(767\) 92.7719 + 92.7719i 0.120954 + 0.120954i
\(768\) 8.98577 8.98577i 0.0117002 0.0117002i
\(769\) 933.850i 1.21437i −0.794561 0.607185i \(-0.792299\pi\)
0.794561 0.607185i \(-0.207701\pi\)
\(770\) 207.225 918.082i 0.269123 1.19231i
\(771\) 150.416 0.195091
\(772\) −532.367 532.367i −0.689595 0.689595i
\(773\) −731.065 + 731.065i −0.945750 + 0.945750i −0.998602 0.0528523i \(-0.983169\pi\)
0.0528523 + 0.998602i \(0.483169\pi\)
\(774\) 736.956i 0.952140i
\(775\) 433.432 + 206.167i 0.559267 + 0.266022i
\(776\) −134.285 −0.173048