Properties

Label 690.3.k.a.277.5
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.5
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0159424 - 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 - 0.165312i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0159424 - 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 - 0.165312i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.01592 - 4.98403i) q^{10} +7.54349 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-15.1286 + 15.1286i) q^{13} -0.330624i q^{14} +(6.10417 + 6.14322i) q^{15} -4.00000 q^{16} +(-19.2185 - 19.2185i) q^{17} +(3.00000 - 3.00000i) q^{18} -11.4869i q^{19} +(9.99995 + 0.0318848i) q^{20} +0.404930 q^{21} +(7.54349 + 7.54349i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-24.9995 - 0.159423i) q^{25} -30.2572 q^{26} +(3.67423 + 3.67423i) q^{27} +(0.330624 - 0.330624i) q^{28} -10.0966i q^{29} +(-0.0390507 + 12.2474i) q^{30} -2.67257 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-9.23885 + 9.23885i) q^{33} -38.4370i q^{34} +(-0.829191 + 0.823920i) q^{35} +6.00000 q^{36} +(-34.3033 - 34.3033i) q^{37} +(11.4869 - 11.4869i) q^{38} -37.0573i q^{39} +(9.96806 + 10.0318i) q^{40} -29.0530 q^{41} +(0.404930 + 0.404930i) q^{42} +(-39.6178 + 39.6178i) q^{43} +15.0870i q^{44} +(-14.9999 - 0.0478272i) q^{45} +6.78233 q^{46} +(-18.2031 - 18.2031i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.9453i q^{49} +(-24.8401 - 25.1589i) q^{50} +47.0755 q^{51} +(-30.2572 - 30.2572i) q^{52} +(14.1802 - 14.1802i) q^{53} +7.34847i q^{54} +(0.120261 - 37.7172i) q^{55} +0.661248 q^{56} +(14.0685 + 14.0685i) q^{57} +(10.0966 - 10.0966i) q^{58} -95.0201i q^{59} +(-12.2864 + 12.2083i) q^{60} +21.1653 q^{61} +(-2.67257 - 2.67257i) q^{62} +(-0.495936 + 0.495936i) q^{63} -8.00000i q^{64} +(75.4013 + 75.8837i) q^{65} -18.4777 q^{66} +(-45.5947 - 45.5947i) q^{67} +(38.4370 - 38.4370i) q^{68} +8.30662i q^{69} +(-1.65311 - 0.00527094i) q^{70} +42.7065 q^{71} +(6.00000 + 6.00000i) q^{72} +(71.8554 - 71.8554i) q^{73} -68.6065i q^{74} +(30.8133 - 30.4227i) q^{75} +22.9738 q^{76} +(-1.24703 - 1.24703i) q^{77} +(37.0573 - 37.0573i) q^{78} +136.677i q^{79} +(-0.0637696 + 19.9999i) q^{80} -9.00000 q^{81} +(-29.0530 - 29.0530i) q^{82} +(-7.78717 + 7.78717i) q^{83} +0.809860i q^{84} +(-96.3984 + 95.7857i) q^{85} -79.2356 q^{86} +(12.3658 + 12.3658i) q^{87} +(-15.0870 + 15.0870i) q^{88} +154.201i q^{89} +(-14.9521 - 15.0478i) q^{90} +5.00187 q^{91} +(6.78233 + 6.78233i) q^{92} +(3.27322 - 3.27322i) q^{93} -36.4063i q^{94} +(-57.4341 - 0.183128i) q^{95} +9.79796 q^{96} +(35.7610 + 35.7610i) q^{97} +(48.9453 - 48.9453i) q^{98} -22.6305i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 0.0159424 4.99997i 0.00318848 0.999995i
\(6\) −2.44949 −0.408248
\(7\) −0.165312 0.165312i −0.0236160 0.0236160i 0.695200 0.718816i \(-0.255316\pi\)
−0.718816 + 0.695200i \(0.755316\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 5.01592 4.98403i 0.501592 0.498403i
\(11\) 7.54349 0.685771 0.342886 0.939377i \(-0.388596\pi\)
0.342886 + 0.939377i \(0.388596\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −15.1286 + 15.1286i −1.16374 + 1.16374i −0.180086 + 0.983651i \(0.557638\pi\)
−0.983651 + 0.180086i \(0.942362\pi\)
\(14\) 0.330624i 0.0236160i
\(15\) 6.10417 + 6.14322i 0.406945 + 0.409548i
\(16\) −4.00000 −0.250000
\(17\) −19.2185 19.2185i −1.13050 1.13050i −0.990094 0.140406i \(-0.955159\pi\)
−0.140406 0.990094i \(-0.544841\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 11.4869i 0.604573i −0.953217 0.302286i \(-0.902250\pi\)
0.953217 0.302286i \(-0.0977498\pi\)
\(20\) 9.99995 + 0.0318848i 0.499997 + 0.00159424i
\(21\) 0.404930 0.0192824
\(22\) 7.54349 + 7.54349i 0.342886 + 0.342886i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −24.9995 0.159423i −0.999980 0.00637693i
\(26\) −30.2572 −1.16374
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 0.330624 0.330624i 0.0118080 0.0118080i
\(29\) 10.0966i 0.348159i −0.984732 0.174080i \(-0.944305\pi\)
0.984732 0.174080i \(-0.0556950\pi\)
\(30\) −0.0390507 + 12.2474i −0.00130169 + 0.408246i
\(31\) −2.67257 −0.0862120 −0.0431060 0.999071i \(-0.513725\pi\)
−0.0431060 + 0.999071i \(0.513725\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −9.23885 + 9.23885i −0.279965 + 0.279965i
\(34\) 38.4370i 1.13050i
\(35\) −0.829191 + 0.823920i −0.0236912 + 0.0235406i
\(36\) 6.00000 0.166667
\(37\) −34.3033 34.3033i −0.927115 0.927115i 0.0704032 0.997519i \(-0.477571\pi\)
−0.997519 + 0.0704032i \(0.977571\pi\)
\(38\) 11.4869 11.4869i 0.302286 0.302286i
\(39\) 37.0573i 0.950187i
\(40\) 9.96806 + 10.0318i 0.249202 + 0.250796i
\(41\) −29.0530 −0.708609 −0.354305 0.935130i \(-0.615282\pi\)
−0.354305 + 0.935130i \(0.615282\pi\)
\(42\) 0.404930 + 0.404930i 0.00964119 + 0.00964119i
\(43\) −39.6178 + 39.6178i −0.921344 + 0.921344i −0.997125 0.0757805i \(-0.975855\pi\)
0.0757805 + 0.997125i \(0.475855\pi\)
\(44\) 15.0870i 0.342886i
\(45\) −14.9999 0.0478272i −0.333332 0.00106283i
\(46\) 6.78233 0.147442
\(47\) −18.2031 18.2031i −0.387301 0.387301i 0.486423 0.873724i \(-0.338302\pi\)
−0.873724 + 0.486423i \(0.838302\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 48.9453i 0.998885i
\(50\) −24.8401 25.1589i −0.496801 0.503178i
\(51\) 47.0755 0.923050
\(52\) −30.2572 30.2572i −0.581868 0.581868i
\(53\) 14.1802 14.1802i 0.267551 0.267551i −0.560562 0.828113i \(-0.689415\pi\)
0.828113 + 0.560562i \(0.189415\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0.120261 37.7172i 0.00218657 0.685768i
\(56\) 0.661248 0.0118080
\(57\) 14.0685 + 14.0685i 0.246816 + 0.246816i
\(58\) 10.0966 10.0966i 0.174080 0.174080i
\(59\) 95.0201i 1.61051i −0.592929 0.805255i \(-0.702028\pi\)
0.592929 0.805255i \(-0.297972\pi\)
\(60\) −12.2864 + 12.2083i −0.204774 + 0.203472i
\(61\) 21.1653 0.346971 0.173486 0.984836i \(-0.444497\pi\)
0.173486 + 0.984836i \(0.444497\pi\)
\(62\) −2.67257 2.67257i −0.0431060 0.0431060i
\(63\) −0.495936 + 0.495936i −0.00787200 + 0.00787200i
\(64\) 8.00000i 0.125000i
\(65\) 75.4013 + 75.8837i 1.16002 + 1.16744i
\(66\) −18.4777 −0.279965
\(67\) −45.5947 45.5947i −0.680518 0.680518i 0.279599 0.960117i \(-0.409798\pi\)
−0.960117 + 0.279599i \(0.909798\pi\)
\(68\) 38.4370 38.4370i 0.565250 0.565250i
\(69\) 8.30662i 0.120386i
\(70\) −1.65311 0.00527094i −0.0236159 7.52991e-5i
\(71\) 42.7065 0.601501 0.300750 0.953703i \(-0.402763\pi\)
0.300750 + 0.953703i \(0.402763\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 71.8554 71.8554i 0.984321 0.984321i −0.0155579 0.999879i \(-0.504952\pi\)
0.999879 + 0.0155579i \(0.00495242\pi\)
\(74\) 68.6065i 0.927115i
\(75\) 30.8133 30.4227i 0.410843 0.405637i
\(76\) 22.9738 0.302286
\(77\) −1.24703 1.24703i −0.0161952 0.0161952i
\(78\) 37.0573 37.0573i 0.475094 0.475094i
\(79\) 136.677i 1.73009i 0.501694 + 0.865045i \(0.332710\pi\)
−0.501694 + 0.865045i \(0.667290\pi\)
\(80\) −0.0637696 + 19.9999i −0.000797120 + 0.249999i
\(81\) −9.00000 −0.111111
\(82\) −29.0530 29.0530i −0.354305 0.354305i
\(83\) −7.78717 + 7.78717i −0.0938214 + 0.0938214i −0.752460 0.658638i \(-0.771133\pi\)
0.658638 + 0.752460i \(0.271133\pi\)
\(84\) 0.809860i 0.00964119i
\(85\) −96.3984 + 95.7857i −1.13410 + 1.12689i
\(86\) −79.2356 −0.921344
\(87\) 12.3658 + 12.3658i 0.142135 + 0.142135i
\(88\) −15.0870 + 15.0870i −0.171443 + 0.171443i
\(89\) 154.201i 1.73260i 0.499525 + 0.866300i \(0.333508\pi\)
−0.499525 + 0.866300i \(0.666492\pi\)
\(90\) −14.9521 15.0478i −0.166134 0.167197i
\(91\) 5.00187 0.0549656
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 3.27322 3.27322i 0.0351959 0.0351959i
\(94\) 36.4063i 0.387301i
\(95\) −57.4341 0.183128i −0.604569 0.00192767i
\(96\) 9.79796 0.102062
\(97\) 35.7610 + 35.7610i 0.368670 + 0.368670i 0.866992 0.498322i \(-0.166050\pi\)
−0.498322 + 0.866992i \(0.666050\pi\)
\(98\) 48.9453 48.9453i 0.499442 0.499442i
\(99\) 22.6305i 0.228590i
\(100\) 0.318846 49.9990i 0.00318846 0.499990i
\(101\) 106.463 1.05409 0.527044 0.849838i \(-0.323300\pi\)
0.527044 + 0.849838i \(0.323300\pi\)
\(102\) 47.0755 + 47.0755i 0.461525 + 0.461525i
\(103\) 72.3647 72.3647i 0.702569 0.702569i −0.262392 0.964961i \(-0.584511\pi\)
0.964961 + 0.262392i \(0.0845113\pi\)
\(104\) 60.5143i 0.581868i
\(105\) 0.00645555 2.02464i 6.14815e−5 0.0192823i
\(106\) 28.3604 0.267551
\(107\) −136.478 136.478i −1.27550 1.27550i −0.943160 0.332340i \(-0.892162\pi\)
−0.332340 0.943160i \(-0.607838\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 109.558i 1.00512i −0.864541 0.502562i \(-0.832391\pi\)
0.864541 0.502562i \(-0.167609\pi\)
\(110\) 37.8375 37.5970i 0.343977 0.341791i
\(111\) 84.0255 0.756987
\(112\) 0.661248 + 0.661248i 0.00590400 + 0.00590400i
\(113\) −117.597 + 117.597i −1.04068 + 1.04068i −0.0415426 + 0.999137i \(0.513227\pi\)
−0.999137 + 0.0415426i \(0.986773\pi\)
\(114\) 28.1370i 0.246816i
\(115\) −16.9017 17.0098i −0.146971 0.147911i
\(116\) 20.1932 0.174080
\(117\) 45.3857 + 45.3857i 0.387912 + 0.387912i
\(118\) 95.0201 95.0201i 0.805255 0.805255i
\(119\) 6.35410i 0.0533958i
\(120\) −24.4948 0.0781015i −0.204123 0.000650846i
\(121\) −64.0958 −0.529718
\(122\) 21.1653 + 21.1653i 0.173486 + 0.173486i
\(123\) 35.5825 35.5825i 0.289289 0.289289i
\(124\) 5.34514i 0.0431060i
\(125\) −1.19566 + 124.994i −0.00956531 + 0.999954i
\(126\) −0.991872 −0.00787200
\(127\) −71.2879 71.2879i −0.561322 0.561322i 0.368361 0.929683i \(-0.379919\pi\)
−0.929683 + 0.368361i \(0.879919\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 97.0434i 0.752274i
\(130\) −0.482372 + 151.285i −0.00371055 + 1.16373i
\(131\) −69.6458 −0.531647 −0.265824 0.964022i \(-0.585644\pi\)
−0.265824 + 0.964022i \(0.585644\pi\)
\(132\) −18.4777 18.4777i −0.139983 0.139983i
\(133\) −1.89892 + 1.89892i −0.0142776 + 0.0142776i
\(134\) 91.1894i 0.680518i
\(135\) 18.4297 18.3125i 0.136516 0.135648i
\(136\) 76.8740 0.565250
\(137\) 127.757 + 127.757i 0.932533 + 0.932533i 0.997864 0.0653303i \(-0.0208101\pi\)
−0.0653303 + 0.997864i \(0.520810\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 80.2923i 0.577642i −0.957383 0.288821i \(-0.906737\pi\)
0.957383 0.288821i \(-0.0932633\pi\)
\(140\) −1.64784 1.65838i −0.0117703 0.0118456i
\(141\) 44.5884 0.316230
\(142\) 42.7065 + 42.7065i 0.300750 + 0.300750i
\(143\) −114.122 + 114.122i −0.798057 + 0.798057i
\(144\) 12.0000i 0.0833333i
\(145\) −50.4829 0.160964i −0.348158 0.00111010i
\(146\) 143.711 0.984321
\(147\) 59.9456 + 59.9456i 0.407793 + 0.407793i
\(148\) 68.6065 68.6065i 0.463558 0.463558i
\(149\) 245.171i 1.64545i 0.568443 + 0.822723i \(0.307546\pi\)
−0.568443 + 0.822723i \(0.692454\pi\)
\(150\) 61.2360 + 0.390505i 0.408240 + 0.00260337i
\(151\) −266.303 −1.76360 −0.881800 0.471624i \(-0.843668\pi\)
−0.881800 + 0.471624i \(0.843668\pi\)
\(152\) 22.9738 + 22.9738i 0.151143 + 0.151143i
\(153\) −57.6555 + 57.6555i −0.376833 + 0.376833i
\(154\) 2.49406i 0.0161952i
\(155\) −0.0426072 + 13.3628i −0.000274885 + 0.0862116i
\(156\) 74.1146 0.475094
\(157\) 78.4391 + 78.4391i 0.499612 + 0.499612i 0.911317 0.411705i \(-0.135067\pi\)
−0.411705 + 0.911317i \(0.635067\pi\)
\(158\) −136.677 + 136.677i −0.865045 + 0.865045i
\(159\) 34.7343i 0.218455i
\(160\) −20.0637 + 19.9361i −0.125398 + 0.124601i
\(161\) −1.12120 −0.00696398
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −176.827 + 176.827i −1.08483 + 1.08483i −0.0887791 + 0.996051i \(0.528297\pi\)
−0.996051 + 0.0887791i \(0.971703\pi\)
\(164\) 58.1060i 0.354305i
\(165\) 46.0467 + 46.3413i 0.279071 + 0.280856i
\(166\) −15.5743 −0.0938214
\(167\) −5.89246 5.89246i −0.0352842 0.0352842i 0.689245 0.724529i \(-0.257943\pi\)
−0.724529 + 0.689245i \(0.757943\pi\)
\(168\) −0.809860 + 0.809860i −0.00482059 + 0.00482059i
\(169\) 288.748i 1.70857i
\(170\) −192.184 0.612778i −1.13049 0.00360458i
\(171\) −34.4606 −0.201524
\(172\) −79.2356 79.2356i −0.460672 0.460672i
\(173\) −152.579 + 152.579i −0.881959 + 0.881959i −0.993734 0.111774i \(-0.964347\pi\)
0.111774 + 0.993734i \(0.464347\pi\)
\(174\) 24.7316i 0.142135i
\(175\) 4.10636 + 4.15907i 0.0234649 + 0.0237661i
\(176\) −30.1739 −0.171443
\(177\) 116.375 + 116.375i 0.657488 + 0.657488i
\(178\) −154.201 + 154.201i −0.866300 + 0.866300i
\(179\) 166.077i 0.927806i 0.885886 + 0.463903i \(0.153551\pi\)
−0.885886 + 0.463903i \(0.846449\pi\)
\(180\) 0.0956544 29.9998i 0.000531413 0.166666i
\(181\) 61.0419 0.337248 0.168624 0.985680i \(-0.446068\pi\)
0.168624 + 0.985680i \(0.446068\pi\)
\(182\) 5.00187 + 5.00187i 0.0274828 + 0.0274828i
\(183\) −25.9220 + 25.9220i −0.141650 + 0.141650i
\(184\) 13.5647i 0.0737210i
\(185\) −172.062 + 170.969i −0.930067 + 0.924155i
\(186\) 6.54644 0.0351959
\(187\) −144.975 144.975i −0.775265 0.775265i
\(188\) 36.4063 36.4063i 0.193650 0.193650i
\(189\) 1.21479i 0.00642746i
\(190\) −57.2510 57.6172i −0.301321 0.303249i
\(191\) 255.678 1.33863 0.669315 0.742979i \(-0.266588\pi\)
0.669315 + 0.742979i \(0.266588\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −49.6596 + 49.6596i −0.257304 + 0.257304i −0.823957 0.566653i \(-0.808238\pi\)
0.566653 + 0.823957i \(0.308238\pi\)
\(194\) 71.5220i 0.368670i
\(195\) −185.286 0.590782i −0.950182 0.00302965i
\(196\) 97.8907 0.499442
\(197\) 37.9008 + 37.9008i 0.192390 + 0.192390i 0.796728 0.604338i \(-0.206562\pi\)
−0.604338 + 0.796728i \(0.706562\pi\)
\(198\) 22.6305 22.6305i 0.114295 0.114295i
\(199\) 194.128i 0.975519i −0.872978 0.487760i \(-0.837814\pi\)
0.872978 0.487760i \(-0.162186\pi\)
\(200\) 50.3178 49.6801i 0.251589 0.248401i
\(201\) 111.684 0.555641
\(202\) 106.463 + 106.463i 0.527044 + 0.527044i
\(203\) −1.66909 + 1.66909i −0.00822213 + 0.00822213i
\(204\) 94.1511i 0.461525i
\(205\) −0.463174 + 145.264i −0.00225939 + 0.708606i
\(206\) 144.729 0.702569
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 60.5143 60.5143i 0.290934 0.290934i
\(209\) 86.6511i 0.414599i
\(210\) 2.03109 2.01818i 0.00967188 0.00961040i
\(211\) 14.4359 0.0684165 0.0342083 0.999415i \(-0.489109\pi\)
0.0342083 + 0.999415i \(0.489109\pi\)
\(212\) 28.3604 + 28.3604i 0.133776 + 0.133776i
\(213\) −52.3046 + 52.3046i −0.245562 + 0.245562i
\(214\) 272.957i 1.27550i
\(215\) 197.456 + 198.720i 0.918402 + 0.924277i
\(216\) −14.6969 −0.0680414
\(217\) 0.441808 + 0.441808i 0.00203598 + 0.00203598i
\(218\) 109.558 109.558i 0.502562 0.502562i
\(219\) 176.009i 0.803695i
\(220\) 75.4345 + 0.240523i 0.342884 + 0.00109328i
\(221\) 581.497 2.63121
\(222\) 84.0255 + 84.0255i 0.378493 + 0.378493i
\(223\) 150.626 150.626i 0.675452 0.675452i −0.283516 0.958968i \(-0.591501\pi\)
0.958968 + 0.283516i \(0.0915009\pi\)
\(224\) 1.32250i 0.00590400i
\(225\) −0.478270 + 74.9985i −0.00212564 + 0.333327i
\(226\) −235.194 −1.04068
\(227\) −11.2773 11.2773i −0.0496799 0.0496799i 0.681830 0.731510i \(-0.261184\pi\)
−0.731510 + 0.681830i \(0.761184\pi\)
\(228\) −28.1370 + 28.1370i −0.123408 + 0.123408i
\(229\) 55.3008i 0.241488i 0.992684 + 0.120744i \(0.0385280\pi\)
−0.992684 + 0.120744i \(0.961472\pi\)
\(230\) 0.108127 33.9115i 0.000470116 0.147441i
\(231\) 3.05458 0.0132233
\(232\) 20.1932 + 20.1932i 0.0870399 + 0.0870399i
\(233\) −45.2074 + 45.2074i −0.194023 + 0.194023i −0.797432 0.603409i \(-0.793809\pi\)
0.603409 + 0.797432i \(0.293809\pi\)
\(234\) 90.7715i 0.387912i
\(235\) −91.3055 + 90.7251i −0.388534 + 0.386064i
\(236\) 190.040 0.805255
\(237\) −167.395 167.395i −0.706306 0.706306i
\(238\) −6.35410 + 6.35410i −0.0266979 + 0.0266979i
\(239\) 287.302i 1.20210i −0.799211 0.601050i \(-0.794749\pi\)
0.799211 0.601050i \(-0.205251\pi\)
\(240\) −24.4167 24.5729i −0.101736 0.102387i
\(241\) −298.409 −1.23821 −0.619106 0.785308i \(-0.712505\pi\)
−0.619106 + 0.785308i \(0.712505\pi\)
\(242\) −64.0958 64.0958i −0.264859 0.264859i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 42.3305i 0.173486i
\(245\) −244.725 0.780306i −0.998879 0.00318492i
\(246\) 71.1650 0.289289
\(247\) 173.780 + 173.780i 0.703563 + 0.703563i
\(248\) 5.34514 5.34514i 0.0215530 0.0215530i
\(249\) 19.0746i 0.0766048i
\(250\) −126.190 + 123.799i −0.504760 + 0.495194i
\(251\) 262.970 1.04769 0.523844 0.851814i \(-0.324497\pi\)
0.523844 + 0.851814i \(0.324497\pi\)
\(252\) −0.991872 0.991872i −0.00393600 0.00393600i
\(253\) 25.5812 25.5812i 0.101111 0.101111i
\(254\) 142.576i 0.561322i
\(255\) 0.750497 235.376i 0.00294313 0.923045i
\(256\) 16.0000 0.0625000
\(257\) 71.3647 + 71.3647i 0.277684 + 0.277684i 0.832184 0.554500i \(-0.187090\pi\)
−0.554500 + 0.832184i \(0.687090\pi\)
\(258\) 97.0434 97.0434i 0.376137 0.376137i
\(259\) 11.3415i 0.0437895i
\(260\) −151.767 + 150.803i −0.583721 + 0.580010i
\(261\) −30.2899 −0.116053
\(262\) −69.6458 69.6458i −0.265824 0.265824i
\(263\) 25.4045 25.4045i 0.0965951 0.0965951i −0.657158 0.753753i \(-0.728242\pi\)
0.753753 + 0.657158i \(0.228242\pi\)
\(264\) 36.9554i 0.139983i
\(265\) −70.6747 71.1268i −0.266697 0.268403i
\(266\) −3.79784 −0.0142776
\(267\) −188.857 188.857i −0.707331 0.707331i
\(268\) 91.1894 91.1894i 0.340259 0.340259i
\(269\) 443.315i 1.64801i −0.566582 0.824005i \(-0.691735\pi\)
0.566582 0.824005i \(-0.308265\pi\)
\(270\) 36.7422 + 0.117152i 0.136082 + 0.000433897i
\(271\) −30.4665 −0.112422 −0.0562112 0.998419i \(-0.517902\pi\)
−0.0562112 + 0.998419i \(0.517902\pi\)
\(272\) 76.8740 + 76.8740i 0.282625 + 0.282625i
\(273\) −6.12601 + 6.12601i −0.0224396 + 0.0224396i
\(274\) 255.514i 0.932533i
\(275\) −188.583 1.20261i −0.685757 0.00437311i
\(276\) −16.6132 −0.0601929
\(277\) 94.0269 + 94.0269i 0.339447 + 0.339447i 0.856159 0.516712i \(-0.172844\pi\)
−0.516712 + 0.856159i \(0.672844\pi\)
\(278\) 80.2923 80.2923i 0.288821 0.288821i
\(279\) 8.01772i 0.0287373i
\(280\) 0.0105419 3.30622i 3.76496e−5 0.0118079i
\(281\) 448.058 1.59451 0.797256 0.603642i \(-0.206284\pi\)
0.797256 + 0.603642i \(0.206284\pi\)
\(282\) 44.5884 + 44.5884i 0.158115 + 0.158115i
\(283\) −256.305 + 256.305i −0.905672 + 0.905672i −0.995919 0.0902473i \(-0.971234\pi\)
0.0902473 + 0.995919i \(0.471234\pi\)
\(284\) 85.4131i 0.300750i
\(285\) 70.5664 70.1178i 0.247601 0.246027i
\(286\) −228.244 −0.798057
\(287\) 4.80281 + 4.80281i 0.0167345 + 0.0167345i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 449.702i 1.55606i
\(290\) −50.3219 50.6438i −0.173524 0.174634i
\(291\) −87.5962 −0.301018
\(292\) 143.711 + 143.711i 0.492161 + 0.492161i
\(293\) −3.95685 + 3.95685i −0.0135046 + 0.0135046i −0.713827 0.700322i \(-0.753040\pi\)
0.700322 + 0.713827i \(0.253040\pi\)
\(294\) 119.891i 0.407793i
\(295\) −475.098 1.51485i −1.61050 0.00513508i
\(296\) 137.213 0.463558
\(297\) 27.7165 + 27.7165i 0.0933217 + 0.0933217i
\(298\) −245.171 + 245.171i −0.822723 + 0.822723i
\(299\) 102.607i 0.343167i
\(300\) 60.8455 + 61.6265i 0.202818 + 0.205422i
\(301\) 13.0986 0.0435169
\(302\) −266.303 266.303i −0.881800 0.881800i
\(303\) −130.390 + 130.390i −0.430330 + 0.430330i
\(304\) 45.9475i 0.151143i
\(305\) 0.337425 105.826i 0.00110631 0.346970i
\(306\) −115.311 −0.376833
\(307\) 265.253 + 265.253i 0.864015 + 0.864015i 0.991802 0.127786i \(-0.0407872\pi\)
−0.127786 + 0.991802i \(0.540787\pi\)
\(308\) 2.49406 2.49406i 0.00809759 0.00809759i
\(309\) 177.256i 0.573646i
\(310\) −13.4054 + 13.3202i −0.0432432 + 0.0429683i
\(311\) 81.5970 0.262370 0.131185 0.991358i \(-0.458122\pi\)
0.131185 + 0.991358i \(0.458122\pi\)
\(312\) 74.1146 + 74.1146i 0.237547 + 0.237547i
\(313\) 249.894 249.894i 0.798385 0.798385i −0.184456 0.982841i \(-0.559052\pi\)
0.982841 + 0.184456i \(0.0590523\pi\)
\(314\) 156.878i 0.499612i
\(315\) 2.47176 + 2.48757i 0.00784686 + 0.00789706i
\(316\) −273.354 −0.865045
\(317\) −79.4073 79.4073i −0.250496 0.250496i 0.570678 0.821174i \(-0.306681\pi\)
−0.821174 + 0.570678i \(0.806681\pi\)
\(318\) −34.7343 + 34.7343i −0.109227 + 0.109227i
\(319\) 76.1637i 0.238758i
\(320\) −39.9998 0.127539i −0.124999 0.000398560i
\(321\) 334.303 1.04144
\(322\) −1.12120 1.12120i −0.00348199 0.00348199i
\(323\) −220.761 + 220.761i −0.683469 + 0.683469i
\(324\) 18.0000i 0.0555556i
\(325\) 380.619 375.795i 1.17113 1.15629i
\(326\) −353.655 −1.08483
\(327\) 134.181 + 134.181i 0.410340 + 0.410340i
\(328\) 58.1060 58.1060i 0.177152 0.177152i
\(329\) 6.01839i 0.0182930i
\(330\) −0.294579 + 92.3880i −0.000892663 + 0.279964i
\(331\) 374.515 1.13146 0.565732 0.824589i \(-0.308594\pi\)
0.565732 + 0.824589i \(0.308594\pi\)
\(332\) −15.5743 15.5743i −0.0469107 0.0469107i
\(333\) −102.910 + 102.910i −0.309038 + 0.309038i
\(334\) 11.7849i 0.0352842i
\(335\) −228.699 + 227.245i −0.682684 + 0.678345i
\(336\) −1.61972 −0.00482059
\(337\) 51.5352 + 51.5352i 0.152923 + 0.152923i 0.779422 0.626499i \(-0.215513\pi\)
−0.626499 + 0.779422i \(0.715513\pi\)
\(338\) 288.748 288.748i 0.854283 0.854283i
\(339\) 288.052i 0.849711i
\(340\) −191.571 192.797i −0.563445 0.567050i
\(341\) −20.1605 −0.0591217
\(342\) −34.4606 34.4606i −0.100762 0.100762i
\(343\) −16.1915 + 16.1915i −0.0472056 + 0.0472056i
\(344\) 158.471i 0.460672i
\(345\) 41.5329 + 0.132428i 0.120385 + 0.000383848i
\(346\) −305.158 −0.881959
\(347\) 442.200 + 442.200i 1.27435 + 1.27435i 0.943782 + 0.330569i \(0.107241\pi\)
0.330569 + 0.943782i \(0.392759\pi\)
\(348\) −24.7316 + 24.7316i −0.0710677 + 0.0710677i
\(349\) 448.442i 1.28493i −0.766314 0.642467i \(-0.777911\pi\)
0.766314 0.642467i \(-0.222089\pi\)
\(350\) −0.0527091 + 8.26543i −0.000150597 + 0.0236155i
\(351\) −111.172 −0.316729
\(352\) −30.1739 30.1739i −0.0857214 0.0857214i
\(353\) 196.487 196.487i 0.556619 0.556619i −0.371724 0.928343i \(-0.621233\pi\)
0.928343 + 0.371724i \(0.121233\pi\)
\(354\) 232.751i 0.657488i
\(355\) 0.680845 213.532i 0.00191787 0.601498i
\(356\) −308.403 −0.866300
\(357\) −7.78215 7.78215i −0.0217987 0.0217987i
\(358\) −166.077 + 166.077i −0.463903 + 0.463903i
\(359\) 320.839i 0.893702i −0.894608 0.446851i \(-0.852545\pi\)
0.894608 0.446851i \(-0.147455\pi\)
\(360\) 30.0955 29.9042i 0.0835986 0.0830672i
\(361\) 229.052 0.634492
\(362\) 61.0419 + 61.0419i 0.168624 + 0.168624i
\(363\) 78.5010 78.5010i 0.216256 0.216256i
\(364\) 10.0037i 0.0274828i
\(365\) −358.130 360.421i −0.981178 0.987455i
\(366\) −51.8441 −0.141650
\(367\) −345.394 345.394i −0.941128 0.941128i 0.0572330 0.998361i \(-0.481772\pi\)
−0.998361 + 0.0572330i \(0.981772\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 87.1590i 0.236203i
\(370\) −343.031 1.09375i −0.927111 0.00295609i
\(371\) −4.68832 −0.0126370
\(372\) 6.54644 + 6.54644i 0.0175980 + 0.0175980i
\(373\) −472.984 + 472.984i −1.26805 + 1.26805i −0.320963 + 0.947092i \(0.604006\pi\)
−0.947092 + 0.320963i \(0.895994\pi\)
\(374\) 289.949i 0.775265i
\(375\) −151.622 154.550i −0.404325 0.412135i
\(376\) 72.8126 0.193650
\(377\) 152.748 + 152.748i 0.405166 + 0.405166i
\(378\) 1.21479 1.21479i 0.00321373 0.00321373i
\(379\) 160.661i 0.423908i −0.977280 0.211954i \(-0.932017\pi\)
0.977280 0.211954i \(-0.0679827\pi\)
\(380\) 0.366257 114.868i 0.000963834 0.302285i
\(381\) 174.619 0.458317
\(382\) 255.678 + 255.678i 0.669315 + 0.669315i
\(383\) 147.812 147.812i 0.385932 0.385932i −0.487301 0.873234i \(-0.662019\pi\)
0.873234 + 0.487301i \(0.162019\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −6.25499 + 6.21523i −0.0162467 + 0.0161435i
\(386\) −99.3192 −0.257304
\(387\) 118.853 + 118.853i 0.307115 + 0.307115i
\(388\) −71.5220 + 71.5220i −0.184335 + 0.184335i
\(389\) 496.097i 1.27531i 0.770320 + 0.637657i \(0.220096\pi\)
−0.770320 + 0.637657i \(0.779904\pi\)
\(390\) −184.695 185.876i −0.473576 0.476606i
\(391\) −130.346 −0.333366
\(392\) 97.8907 + 97.8907i 0.249721 + 0.249721i
\(393\) 85.2984 85.2984i 0.217044 0.217044i
\(394\) 75.8016i 0.192390i
\(395\) 683.382 + 2.17896i 1.73008 + 0.00551636i
\(396\) 45.2609 0.114295
\(397\) −62.1832 62.1832i −0.156633 0.156633i 0.624440 0.781073i \(-0.285327\pi\)
−0.781073 + 0.624440i \(0.785327\pi\)
\(398\) 194.128 194.128i 0.487760 0.487760i
\(399\) 4.65138i 0.0116576i
\(400\) 99.9980 + 0.637693i 0.249995 + 0.00159423i
\(401\) 498.128 1.24221 0.621107 0.783726i \(-0.286683\pi\)
0.621107 + 0.783726i \(0.286683\pi\)
\(402\) 111.684 + 111.684i 0.277820 + 0.277820i
\(403\) 40.4322 40.4322i 0.100328 0.100328i
\(404\) 212.926i 0.527044i
\(405\) −0.143482 + 44.9998i −0.000354276 + 0.111111i
\(406\) −3.33818 −0.00822213
\(407\) −258.766 258.766i −0.635789 0.635789i
\(408\) −94.1511 + 94.1511i −0.230762 + 0.230762i
\(409\) 603.860i 1.47643i −0.674565 0.738215i \(-0.735669\pi\)
0.674565 0.738215i \(-0.264331\pi\)
\(410\) −145.727 + 144.801i −0.355433 + 0.353173i
\(411\) −312.940 −0.761410
\(412\) 144.729 + 144.729i 0.351285 + 0.351285i
\(413\) −15.7080 + 15.7080i −0.0380338 + 0.0380338i
\(414\) 20.3470i 0.0491473i
\(415\) 38.8115 + 39.0598i 0.0935217 + 0.0941200i
\(416\) 121.029 0.290934
\(417\) 98.3375 + 98.3375i 0.235821 + 0.235821i
\(418\) 86.6511 86.6511i 0.207299 0.207299i
\(419\) 384.147i 0.916819i 0.888741 + 0.458409i \(0.151581\pi\)
−0.888741 + 0.458409i \(0.848419\pi\)
\(420\) 4.04928 + 0.0129111i 0.00964114 + 3.07407e-5i
\(421\) −495.820 −1.17772 −0.588860 0.808235i \(-0.700423\pi\)
−0.588860 + 0.808235i \(0.700423\pi\)
\(422\) 14.4359 + 14.4359i 0.0342083 + 0.0342083i
\(423\) −54.6094 + 54.6094i −0.129100 + 0.129100i
\(424\) 56.7209i 0.133776i
\(425\) 477.389 + 483.517i 1.12327 + 1.13769i
\(426\) −104.609 −0.245562
\(427\) −3.49887 3.49887i −0.00819407 0.00819407i
\(428\) 272.957 272.957i 0.637750 0.637750i
\(429\) 279.541i 0.651611i
\(430\) −1.26321 + 396.176i −0.00293769 + 0.921339i
\(431\) −226.640 −0.525846 −0.262923 0.964817i \(-0.584686\pi\)
−0.262923 + 0.964817i \(0.584686\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 253.188 253.188i 0.584730 0.584730i −0.351470 0.936199i \(-0.614318\pi\)
0.936199 + 0.351470i \(0.114318\pi\)
\(434\) 0.883616i 0.00203598i
\(435\) 62.0258 61.6315i 0.142588 0.141682i
\(436\) 219.117 0.502562
\(437\) −38.9539 38.9539i −0.0891394 0.0891394i
\(438\) −176.009 + 176.009i −0.401847 + 0.401847i
\(439\) 687.562i 1.56620i −0.621896 0.783100i \(-0.713637\pi\)
0.621896 0.783100i \(-0.286363\pi\)
\(440\) 75.1940 + 75.6750i 0.170895 + 0.171989i
\(441\) −146.836 −0.332962
\(442\) 581.497 + 581.497i 1.31560 + 1.31560i
\(443\) −204.555 + 204.555i −0.461750 + 0.461750i −0.899229 0.437479i \(-0.855872\pi\)
0.437479 + 0.899229i \(0.355872\pi\)
\(444\) 168.051i 0.378493i
\(445\) 771.003 + 2.45834i 1.73259 + 0.00552436i
\(446\) 301.251 0.675452
\(447\) −300.272 300.272i −0.671750 0.671750i
\(448\) −1.32250 + 1.32250i −0.00295200 + 0.00295200i
\(449\) 356.376i 0.793711i 0.917881 + 0.396855i \(0.129899\pi\)
−0.917881 + 0.396855i \(0.870101\pi\)
\(450\) −75.4767 + 74.5202i −0.167726 + 0.165600i
\(451\) −219.161 −0.485944
\(452\) −235.194 235.194i −0.520340 0.520340i
\(453\) 326.154 326.154i 0.719986 0.719986i
\(454\) 22.5547i 0.0496799i
\(455\) 0.0797418 25.0092i 0.000175257 0.0549653i
\(456\) −56.2740 −0.123408
\(457\) −48.4473 48.4473i −0.106012 0.106012i 0.652112 0.758123i \(-0.273883\pi\)
−0.758123 + 0.652112i \(0.773883\pi\)
\(458\) −55.3008 + 55.3008i −0.120744 + 0.120744i
\(459\) 141.227i 0.307683i
\(460\) 34.0196 33.8034i 0.0739557 0.0734855i
\(461\) 218.854 0.474737 0.237369 0.971420i \(-0.423715\pi\)
0.237369 + 0.971420i \(0.423715\pi\)
\(462\) 3.05458 + 3.05458i 0.00661165 + 0.00661165i
\(463\) −24.5288 + 24.5288i −0.0529779 + 0.0529779i −0.733099 0.680121i \(-0.761927\pi\)
0.680121 + 0.733099i \(0.261927\pi\)
\(464\) 40.3865i 0.0870399i
\(465\) −16.3138 16.4182i −0.0350835 0.0353079i
\(466\) −90.4148 −0.194023
\(467\) −127.774 127.774i −0.273606 0.273606i 0.556944 0.830550i \(-0.311974\pi\)
−0.830550 + 0.556944i \(0.811974\pi\)
\(468\) −90.7715 + 90.7715i −0.193956 + 0.193956i
\(469\) 15.0747i 0.0321422i
\(470\) −182.031 0.580404i −0.387299 0.00123490i
\(471\) −192.136 −0.407932
\(472\) 190.040 + 190.040i 0.402628 + 0.402628i
\(473\) −298.856 + 298.856i −0.631831 + 0.631831i
\(474\) 334.789i 0.706306i
\(475\) −1.83127 + 287.166i −0.00385531 + 0.604560i
\(476\) −12.7082 −0.0266979
\(477\) −42.5407 42.5407i −0.0891838 0.0891838i
\(478\) 287.302 287.302i 0.601050 0.601050i
\(479\) 425.945i 0.889239i −0.895720 0.444619i \(-0.853339\pi\)
0.895720 0.444619i \(-0.146661\pi\)
\(480\) 0.156203 48.9895i 0.000325423 0.102062i
\(481\) 1037.92 2.15784
\(482\) −298.409 298.409i −0.619106 0.619106i
\(483\) 1.37318 1.37318i 0.00284303 0.00284303i
\(484\) 128.192i 0.264859i
\(485\) 179.374 178.234i 0.369844 0.367493i
\(486\) 22.0454 0.0453609
\(487\) −433.520 433.520i −0.890185 0.890185i 0.104355 0.994540i \(-0.466722\pi\)
−0.994540 + 0.104355i \(0.966722\pi\)
\(488\) −42.3305 + 42.3305i −0.0867428 + 0.0867428i
\(489\) 433.137i 0.885760i
\(490\) −243.945 245.506i −0.497847 0.501032i
\(491\) −126.759 −0.258164 −0.129082 0.991634i \(-0.541203\pi\)
−0.129082 + 0.991634i \(0.541203\pi\)
\(492\) 71.1650 + 71.1650i 0.144644 + 0.144644i
\(493\) −194.042 + 194.042i −0.393594 + 0.393594i
\(494\) 347.560i 0.703563i
\(495\) −113.152 0.360784i −0.228589 0.000728856i
\(496\) 10.6903 0.0215530
\(497\) −7.05990 7.05990i −0.0142050 0.0142050i
\(498\) 19.0746 19.0746i 0.0383024 0.0383024i
\(499\) 40.4801i 0.0811225i 0.999177 + 0.0405612i \(0.0129146\pi\)
−0.999177 + 0.0405612i \(0.987085\pi\)
\(500\) −249.989 2.39133i −0.499977 0.00478266i
\(501\) 14.4335 0.0288094
\(502\) 262.970 + 262.970i 0.523844 + 0.523844i
\(503\) 221.151 221.151i 0.439664 0.439664i −0.452235 0.891899i \(-0.649373\pi\)
0.891899 + 0.452235i \(0.149373\pi\)
\(504\) 1.98374i 0.00393600i
\(505\) 1.69728 532.312i 0.00336094 1.05408i
\(506\) 51.1624 0.101111
\(507\) 353.642 + 353.642i 0.697519 + 0.697519i
\(508\) 142.576 142.576i 0.280661 0.280661i
\(509\) 628.639i 1.23505i −0.786552 0.617524i \(-0.788136\pi\)
0.786552 0.617524i \(-0.211864\pi\)
\(510\) 236.127 234.626i 0.462994 0.460051i
\(511\) −23.7571 −0.0464914
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 42.2055 42.2055i 0.0822719 0.0822719i
\(514\) 142.729i 0.277684i
\(515\) −360.668 362.975i −0.700326 0.704806i
\(516\) 194.087 0.376137
\(517\) −137.315 137.315i −0.265600 0.265600i
\(518\) −11.3415 + 11.3415i −0.0218947 + 0.0218947i
\(519\) 373.741i 0.720117i
\(520\) −302.570 0.964743i −0.581865 0.00185528i
\(521\) −845.308 −1.62247 −0.811236 0.584719i \(-0.801205\pi\)
−0.811236 + 0.584719i \(0.801205\pi\)
\(522\) −30.2899 30.2899i −0.0580266 0.0580266i
\(523\) 53.3810 53.3810i 0.102067 0.102067i −0.654229 0.756296i \(-0.727007\pi\)
0.756296 + 0.654229i \(0.227007\pi\)
\(524\) 139.292i 0.265824i
\(525\) −10.1230 0.0645552i −0.0192820 0.000122962i
\(526\) 50.8090 0.0965951
\(527\) 51.3628 + 51.3628i 0.0974627 + 0.0974627i
\(528\) 36.9554 36.9554i 0.0699913 0.0699913i
\(529\) 23.0000i 0.0434783i
\(530\) 0.452133 141.801i 0.000853082 0.267550i
\(531\) −285.060 −0.536837
\(532\) −3.79784 3.79784i −0.00713879 0.00713879i
\(533\) 439.530 439.530i 0.824635 0.824635i
\(534\) 377.715i 0.707331i
\(535\) −684.565 + 680.213i −1.27956 + 1.27143i
\(536\) 182.379 0.340259
\(537\) −203.402 203.402i −0.378775 0.378775i
\(538\) 443.315 443.315i 0.824005 0.824005i
\(539\) 369.219i 0.685007i
\(540\) 36.6250 + 36.8593i 0.0678241 + 0.0682580i
\(541\) −517.570 −0.956691 −0.478345 0.878172i \(-0.658763\pi\)
−0.478345 + 0.878172i \(0.658763\pi\)
\(542\) −30.4665 30.4665i −0.0562112 0.0562112i
\(543\) −74.7607 + 74.7607i −0.137681 + 0.137681i
\(544\) 153.748i 0.282625i
\(545\) −547.789 1.74662i −1.00512 0.00320482i
\(546\) −12.2520 −0.0224396
\(547\) 129.766 + 129.766i 0.237233 + 0.237233i 0.815703 0.578470i \(-0.196350\pi\)
−0.578470 + 0.815703i \(0.696350\pi\)
\(548\) −255.514 + 255.514i −0.466267 + 0.466267i
\(549\) 63.4958i 0.115657i
\(550\) −187.381 189.786i −0.340692 0.345065i
\(551\) −115.979 −0.210488
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 22.5944 22.5944i 0.0408578 0.0408578i
\(554\) 188.054i 0.339447i
\(555\) 1.33957 420.125i 0.00241364 0.756983i
\(556\) 160.585 0.288821
\(557\) −235.383 235.383i −0.422591 0.422591i 0.463504 0.886095i \(-0.346592\pi\)
−0.886095 + 0.463504i \(0.846592\pi\)
\(558\) −8.01772 + 8.01772i −0.0143687 + 0.0143687i
\(559\) 1198.72i 2.14440i
\(560\) 3.31676 3.29568i 0.00592279 0.00588514i
\(561\) 355.114 0.633001
\(562\) 448.058 + 448.058i 0.797256 + 0.797256i
\(563\) 65.1797 65.1797i 0.115772 0.115772i −0.646847 0.762620i \(-0.723913\pi\)
0.762620 + 0.646847i \(0.223913\pi\)
\(564\) 89.1768i 0.158115i
\(565\) 586.106 + 589.856i 1.03736 + 1.04399i
\(566\) −512.610 −0.905672
\(567\) 1.48781 + 1.48781i 0.00262400 + 0.00262400i
\(568\) −85.4131 + 85.4131i −0.150375 + 0.150375i
\(569\) 418.274i 0.735104i −0.930003 0.367552i \(-0.880196\pi\)
0.930003 0.367552i \(-0.119804\pi\)
\(570\) 140.684 + 0.448571i 0.246814 + 0.000786967i
\(571\) 906.028 1.58674 0.793369 0.608741i \(-0.208325\pi\)
0.793369 + 0.608741i \(0.208325\pi\)
\(572\) −228.244 228.244i −0.399029 0.399029i
\(573\) −313.141 + 313.141i −0.546493 + 0.546493i
\(574\) 9.60561i 0.0167345i
\(575\) −85.3180 + 84.2368i −0.148379 + 0.146499i
\(576\) −24.0000 −0.0416667
\(577\) 288.328 + 288.328i 0.499703 + 0.499703i 0.911345 0.411643i \(-0.135045\pi\)
−0.411643 + 0.911345i \(0.635045\pi\)
\(578\) −449.702 + 449.702i −0.778031 + 0.778031i
\(579\) 121.641i 0.210087i
\(580\) 0.321929 100.966i 0.000555050 0.174079i
\(581\) 2.57463 0.00443137
\(582\) −87.5962 87.5962i −0.150509 0.150509i
\(583\) 106.968 106.968i 0.183479 0.183479i
\(584\) 287.422i 0.492161i
\(585\) 227.651 226.204i 0.389147 0.386673i
\(586\) −7.91371 −0.0135046
\(587\) −563.086 563.086i −0.959261 0.959261i 0.0399411 0.999202i \(-0.487283\pi\)
−0.999202 + 0.0399411i \(0.987283\pi\)
\(588\) −119.891 + 119.891i −0.203896 + 0.203896i
\(589\) 30.6995i 0.0521214i
\(590\) −473.583 476.613i −0.802683 0.807819i
\(591\) −92.8376 −0.157086
\(592\) 137.213 + 137.213i 0.231779 + 0.231779i
\(593\) −357.448 + 357.448i −0.602780 + 0.602780i −0.941049 0.338270i \(-0.890158\pi\)
0.338270 + 0.941049i \(0.390158\pi\)
\(594\) 55.4331i 0.0933217i
\(595\) 31.7703 + 0.101300i 0.0533955 + 0.000170251i
\(596\) −490.343 −0.822723
\(597\) 237.758 + 237.758i 0.398254 + 0.398254i
\(598\) −102.607 + 102.607i −0.171584 + 0.171584i
\(599\) 717.906i 1.19851i −0.800559 0.599254i \(-0.795464\pi\)
0.800559 0.599254i \(-0.204536\pi\)
\(600\) −0.781011 + 122.472i −0.00130168 + 0.204120i
\(601\) −634.818 −1.05627 −0.528135 0.849160i \(-0.677108\pi\)
−0.528135 + 0.849160i \(0.677108\pi\)
\(602\) 13.0986 + 13.0986i 0.0217585 + 0.0217585i
\(603\) −136.784 + 136.784i −0.226839 + 0.226839i
\(604\) 532.607i 0.881800i
\(605\) −1.02184 + 320.477i −0.00168899 + 0.529715i
\(606\) −260.780 −0.430330
\(607\) 297.320 + 297.320i 0.489818 + 0.489818i 0.908249 0.418430i \(-0.137420\pi\)
−0.418430 + 0.908249i \(0.637420\pi\)
\(608\) −45.9475 + 45.9475i −0.0755716 + 0.0755716i
\(609\) 4.08842i 0.00671334i
\(610\) 106.163 105.488i 0.174038 0.172932i
\(611\) 550.775 0.901433
\(612\) −115.311 115.311i −0.188417 0.188417i
\(613\) −505.783 + 505.783i −0.825095 + 0.825095i −0.986834 0.161739i \(-0.948290\pi\)
0.161739 + 0.986834i \(0.448290\pi\)
\(614\) 530.505i 0.864015i
\(615\) −177.344 178.479i −0.288365 0.290210i
\(616\) 4.98811 0.00809759
\(617\) 367.182 + 367.182i 0.595109 + 0.595109i 0.939007 0.343898i \(-0.111747\pi\)
−0.343898 + 0.939007i \(0.611747\pi\)
\(618\) −177.256 + 177.256i −0.286823 + 0.286823i
\(619\) 475.667i 0.768444i 0.923241 + 0.384222i \(0.125530\pi\)
−0.923241 + 0.384222i \(0.874470\pi\)
\(620\) −26.7256 0.0852144i −0.0431058 0.000137443i
\(621\) 24.9199 0.0401286
\(622\) 81.5970 + 81.5970i 0.131185 + 0.131185i
\(623\) 25.4913 25.4913i 0.0409170 0.0409170i
\(624\) 148.229i 0.237547i
\(625\) 624.949 + 7.97100i 0.999919 + 0.0127536i
\(626\) 499.789 0.798385
\(627\) 106.125 + 106.125i 0.169259 + 0.169259i
\(628\) −156.878 + 156.878i −0.249806 + 0.249806i
\(629\) 1318.52i 2.09621i
\(630\) −0.0158128 + 4.95933i −2.50997e−5 + 0.00787196i
\(631\) −182.454 −0.289150 −0.144575 0.989494i \(-0.546182\pi\)
−0.144575 + 0.989494i \(0.546182\pi\)
\(632\) −273.354 273.354i −0.432523 0.432523i
\(633\) −17.6803 + 17.6803i −0.0279309 + 0.0279309i
\(634\) 158.815i 0.250496i
\(635\) −357.574 + 355.301i −0.563109 + 0.559529i
\(636\) −69.4686 −0.109227
\(637\) 740.473 + 740.473i 1.16244 + 1.16244i
\(638\) 76.1637 76.1637i 0.119379 0.119379i
\(639\) 128.120i 0.200500i
\(640\) −39.8723 40.1273i −0.0623004 0.0626990i
\(641\) −834.607 −1.30204 −0.651020 0.759061i \(-0.725658\pi\)
−0.651020 + 0.759061i \(0.725658\pi\)
\(642\) 334.303 + 334.303i 0.520721 + 0.520721i
\(643\) 458.258 458.258i 0.712687 0.712687i −0.254409 0.967097i \(-0.581881\pi\)
0.967097 + 0.254409i \(0.0818811\pi\)
\(644\) 2.24240i 0.00348199i
\(645\) −485.214 1.54710i −0.752270 0.00239861i
\(646\) −441.521 −0.683469
\(647\) −488.148 488.148i −0.754479 0.754479i 0.220832 0.975312i \(-0.429123\pi\)
−0.975312 + 0.220832i \(0.929123\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 716.783i 1.10444i
\(650\) 756.414 + 4.82369i 1.16371 + 0.00742106i
\(651\) −1.08220 −0.00166237
\(652\) −353.655 353.655i −0.542415 0.542415i
\(653\) 219.549 219.549i 0.336217 0.336217i −0.518725 0.854941i \(-0.673593\pi\)
0.854941 + 0.518725i \(0.173593\pi\)
\(654\) 268.362i 0.410340i
\(655\) −1.11032 + 348.227i −0.00169515 + 0.531645i
\(656\) 116.212 0.177152
\(657\) −215.566 215.566i −0.328107 0.328107i
\(658\) −6.01839 + 6.01839i −0.00914650 + 0.00914650i
\(659\) 177.268i 0.268995i −0.990914 0.134498i \(-0.957058\pi\)
0.990914 0.134498i \(-0.0429420\pi\)
\(660\) −92.6826 + 92.0934i −0.140428 + 0.139535i
\(661\) −670.999 −1.01513 −0.507564 0.861614i \(-0.669454\pi\)
−0.507564 + 0.861614i \(0.669454\pi\)
\(662\) 374.515 + 374.515i 0.565732 + 0.565732i
\(663\) −712.186 + 712.186i −1.07419 + 1.07419i
\(664\) 31.1487i 0.0469107i
\(665\) 9.46427 + 9.52481i 0.0142320 + 0.0143230i
\(666\) −205.820 −0.309038
\(667\) −34.2393 34.2393i −0.0513333 0.0513333i
\(668\) 11.7849 11.7849i 0.0176421 0.0176421i
\(669\) 368.956i 0.551504i
\(670\) −455.945 1.45378i −0.680514 0.00216982i
\(671\) 159.660 0.237943
\(672\) −1.61972 1.61972i −0.00241030 0.00241030i
\(673\) 831.221 831.221i 1.23510 1.23510i 0.273117 0.961981i \(-0.411945\pi\)
0.961981 0.273117i \(-0.0880547\pi\)
\(674\) 103.070i 0.152923i
\(675\) −91.2682 92.4398i −0.135212 0.136948i
\(676\) 577.496 0.854283
\(677\) −655.663 655.663i −0.968483 0.968483i 0.0310357 0.999518i \(-0.490119\pi\)
−0.999518 + 0.0310357i \(0.990119\pi\)
\(678\) 288.052 288.052i 0.424856 0.424856i
\(679\) 11.8234i 0.0174130i
\(680\) 1.22556 384.368i 0.00180229 0.565247i
\(681\) 27.6237 0.0405634
\(682\) −20.1605 20.1605i −0.0295609 0.0295609i
\(683\) −35.5313 + 35.5313i −0.0520224 + 0.0520224i −0.732639 0.680617i \(-0.761712\pi\)
0.680617 + 0.732639i \(0.261712\pi\)
\(684\) 68.9213i 0.100762i
\(685\) 640.819 636.745i 0.935502 0.929555i
\(686\) −32.3831 −0.0472056
\(687\) −67.7293 67.7293i −0.0985871 0.0985871i
\(688\) 158.471 158.471i 0.230336 0.230336i
\(689\) 429.053i 0.622718i
\(690\) 41.4005 + 41.6653i 0.0600007 + 0.0603845i
\(691\) −884.743 −1.28038 −0.640191 0.768216i \(-0.721145\pi\)
−0.640191 + 0.768216i \(0.721145\pi\)
\(692\) −305.158 305.158i −0.440980 0.440980i
\(693\) −3.74108 + 3.74108i −0.00539839 + 0.00539839i
\(694\) 884.400i 1.27435i
\(695\) −401.459 1.28005i −0.577639 0.00184180i
\(696\) −49.4631 −0.0710677
\(697\) 558.355 + 558.355i 0.801083 + 0.801083i
\(698\) 448.442 448.442i 0.642467 0.642467i
\(699\) 110.735i 0.158419i
\(700\) −8.31814 + 8.21272i −0.0118831 + 0.0117325i
\(701\) 52.6049 0.0750427 0.0375214 0.999296i \(-0.488054\pi\)
0.0375214 + 0.999296i \(0.488054\pi\)
\(702\) −111.172 111.172i −0.158365 0.158365i
\(703\) −394.037 + 394.037i −0.560508 + 0.560508i
\(704\) 60.3479i 0.0857214i
\(705\) 0.710846 222.941i 0.00100829 0.316228i
\(706\) 392.973 0.556619
\(707\) −17.5996 17.5996i −0.0248934 0.0248934i
\(708\) −232.751 + 232.751i −0.328744 + 0.328744i
\(709\) 835.312i 1.17816i −0.808076 0.589078i \(-0.799491\pi\)
0.808076 0.589078i \(-0.200509\pi\)
\(710\) 214.213 212.851i 0.301708 0.299790i
\(711\) 410.031 0.576697
\(712\) −308.403 308.403i −0.433150 0.433150i
\(713\) −9.06313 + 9.06313i −0.0127113 + 0.0127113i
\(714\) 15.5643i 0.0217987i
\(715\) 568.789 + 572.428i 0.795509 + 0.800598i
\(716\) −332.155 −0.463903
\(717\) 351.872 + 351.872i 0.490755 + 0.490755i
\(718\) 320.839 320.839i 0.446851 0.446851i
\(719\) 189.592i 0.263689i −0.991270 0.131845i \(-0.957910\pi\)
0.991270 0.131845i \(-0.0420900\pi\)
\(720\) 59.9997 + 0.191309i 0.0833329 + 0.000265707i
\(721\) −23.9255 −0.0331837
\(722\) 229.052 + 229.052i 0.317246 + 0.317246i
\(723\) 365.475 365.475i 0.505498 0.505498i
\(724\) 122.084i 0.168624i
\(725\) −1.60964 + 252.410i −0.00222019 + 0.348152i
\(726\) 157.002 0.216256
\(727\) 728.215 + 728.215i 1.00167 + 1.00167i 0.999999 + 0.00167235i \(0.000532324\pi\)
0.00167235 + 0.999999i \(0.499468\pi\)
\(728\) −10.0037 + 10.0037i −0.0137414 + 0.0137414i
\(729\) 27.0000i 0.0370370i
\(730\) 2.29110 718.551i 0.00313849 0.984316i
\(731\) 1522.79 2.08316
\(732\) −51.8441 51.8441i −0.0708252 0.0708252i
\(733\) −717.338 + 717.338i −0.978633 + 0.978633i −0.999776 0.0211431i \(-0.993269\pi\)
0.0211431 + 0.999776i \(0.493269\pi\)
\(734\) 690.788i 0.941128i
\(735\) 300.682 298.771i 0.409091 0.406491i
\(736\) −27.1293 −0.0368605
\(737\) −343.943 343.943i −0.466680 0.466680i
\(738\) −87.1590 + 87.1590i −0.118102 + 0.118102i
\(739\) 782.343i 1.05865i 0.848419 + 0.529325i \(0.177555\pi\)
−0.848419 + 0.529325i \(0.822445\pi\)
\(740\) −341.937 344.125i −0.462077 0.465033i
\(741\) −425.673 −0.574457
\(742\) −4.68832 4.68832i −0.00631849 0.00631849i
\(743\) −614.013 + 614.013i −0.826398 + 0.826398i −0.987017 0.160619i \(-0.948651\pi\)
0.160619 + 0.987017i \(0.448651\pi\)
\(744\) 13.0929i 0.0175980i
\(745\) 1225.85 + 3.90862i 1.64544 + 0.00524647i
\(746\) −945.969 −1.26805
\(747\) 23.3615 + 23.3615i 0.0312738 + 0.0312738i
\(748\) 289.949 289.949i 0.387632 0.387632i
\(749\) 45.1230i 0.0602444i
\(750\) 2.92877 306.172i 0.00390502 0.408230i
\(751\) −961.079 −1.27973 −0.639866 0.768486i \(-0.721010\pi\)
−0.639866 + 0.768486i \(0.721010\pi\)
\(752\) 72.8126 + 72.8126i 0.0968252 + 0.0968252i
\(753\) −322.071 + 322.071i −0.427717 + 0.427717i
\(754\) 305.495i 0.405166i
\(755\) −4.24552 + 1331.51i −0.00562320 + 1.76359i
\(756\) 2.42958 0.00321373
\(757\) 550.633 + 550.633i 0.727388 + 0.727388i 0.970099 0.242710i \(-0.0780365\pi\)
−0.242710 + 0.970099i \(0.578036\pi\)
\(758\) 160.661 160.661i 0.211954 0.211954i
\(759\) 62.6609i 0.0825572i
\(760\) 115.234 114.502i 0.151624 0.150660i
\(761\) −503.536 −0.661677 −0.330838 0.943687i \(-0.607332\pi\)
−0.330838 + 0.943687i \(0.607332\pi\)
\(762\) 174.619 + 174.619i 0.229159 + 0.229159i
\(763\) −18.1113 + 18.1113i −0.0237370 + 0.0237370i
\(764\) 511.357i 0.669315i
\(765\) 287.357 + 289.195i 0.375630 + 0.378033i
\(766\) 295.624 0.385932
\(767\) 1437.52 + 1437.52i 1.87421 + 1.87421i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 1471.34i 1.91331i 0.291221 + 0.956656i \(0.405939\pi\)
−0.291221 + 0.956656i \(0.594061\pi\)
\(770\) −12.4702 0.0397612i −0.0161951 5.16380e-5i
\(771\) −174.807 −0.226728
\(772\) −99.3192 99.3192i −0.128652 0.128652i
\(773\) 3.51558 3.51558i 0.00454797 0.00454797i −0.704829 0.709377i \(-0.748976\pi\)
0.709377 + 0.704829i \(0.248976\pi\)
\(774\) 237.707i 0.307115i
\(775\) 66.8129 + 0.426070i 0.0862103 + 0.000549768i
\(776\) −143.044 −0.184335
\(777\) −13.8904 13.8904i −0.0178770 0.0178770i
\(778\) −496.097 + 496.097i −0.637657 + 0.637657i