Properties

Label 690.3.k.b.277.20
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.20
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.20

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.82966 - 1.29396i) q^{5} -2.44949 q^{6} +(5.84802 + 5.84802i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.82966 - 1.29396i) q^{5} -2.44949 q^{6} +(5.84802 + 5.84802i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(3.53570 + 6.12363i) q^{10} -1.76345 q^{11} +(2.44949 + 2.44949i) q^{12} +(5.00063 - 5.00063i) q^{13} -11.6960i q^{14} +(-7.49988 + 4.33033i) q^{15} -4.00000 q^{16} +(-8.50993 - 8.50993i) q^{17} +(-3.00000 + 3.00000i) q^{18} +22.3969i q^{19} +(2.58793 - 9.65933i) q^{20} +14.3247 q^{21} +(1.76345 + 1.76345i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(21.6513 + 12.4988i) q^{25} -10.0013 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-11.6960 + 11.6960i) q^{28} +38.8089i q^{29} +(11.8302 + 3.16955i) q^{30} +15.0913 q^{31} +(4.00000 + 4.00000i) q^{32} +(-2.15977 + 2.15977i) q^{33} +17.0199i q^{34} +(-20.6769 - 35.8111i) q^{35} +6.00000 q^{36} +(28.5900 + 28.5900i) q^{37} +(22.3969 - 22.3969i) q^{38} -12.2490i q^{39} +(-12.2473 + 7.07140i) q^{40} +63.9487 q^{41} +(-14.3247 - 14.3247i) q^{42} +(34.7533 - 34.7533i) q^{43} -3.52689i q^{44} +(-3.88189 + 14.4890i) q^{45} -6.78233 q^{46} +(2.22777 + 2.22777i) q^{47} +(-4.89898 + 4.89898i) q^{48} +19.3988i q^{49} +(-9.15250 - 34.1501i) q^{50} -20.8450 q^{51} +(10.0013 + 10.0013i) q^{52} +(67.8328 - 67.8328i) q^{53} +7.34847i q^{54} +(8.51686 + 2.28183i) q^{55} +23.3921 q^{56} +(27.4305 + 27.4305i) q^{57} +(38.8089 - 38.8089i) q^{58} -29.3548i q^{59} +(-8.66066 - 14.9998i) q^{60} +54.6267 q^{61} +(-15.0913 - 15.0913i) q^{62} +(17.5441 - 17.5441i) q^{63} -8.00000i q^{64} +(-30.6220 + 17.6807i) q^{65} +4.31954 q^{66} +(14.0005 + 14.0005i) q^{67} +(17.0199 - 17.0199i) q^{68} -8.30662i q^{69} +(-15.1343 + 56.4880i) q^{70} -36.0984 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-58.7921 + 58.7921i) q^{73} -57.1799i q^{74} +(41.8252 - 11.2095i) q^{75} -44.7938 q^{76} +(-10.3127 - 10.3127i) q^{77} +(-12.2490 + 12.2490i) q^{78} -128.176i q^{79} +(19.3187 + 5.17585i) q^{80} -9.00000 q^{81} +(-63.9487 - 63.9487i) q^{82} +(-68.9222 + 68.9222i) q^{83} +28.6494i q^{84} +(30.0886 + 52.1116i) q^{85} -69.5066 q^{86} +(47.5310 + 47.5310i) q^{87} +(-3.52689 + 3.52689i) q^{88} -19.7288i q^{89} +(18.3709 - 10.6071i) q^{90} +58.4876 q^{91} +(6.78233 + 6.78233i) q^{92} +(18.4829 - 18.4829i) q^{93} -4.45554i q^{94} +(28.9808 - 108.170i) q^{95} +9.79796 q^{96} +(85.9628 + 85.9628i) q^{97} +(19.3988 - 19.3988i) q^{98} +5.29034i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

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
\(5\) −4.82966 1.29396i −0.965933 0.258793i
\(6\) −2.44949 −0.408248
\(7\) 5.84802 + 5.84802i 0.835432 + 0.835432i 0.988254 0.152822i \(-0.0488360\pi\)
−0.152822 + 0.988254i \(0.548836\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 3.53570 + 6.12363i 0.353570 + 0.612363i
\(11\) −1.76345 −0.160313 −0.0801567 0.996782i \(-0.525542\pi\)
−0.0801567 + 0.996782i \(0.525542\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 5.00063 5.00063i 0.384664 0.384664i −0.488115 0.872779i \(-0.662315\pi\)
0.872779 + 0.488115i \(0.162315\pi\)
\(14\) 11.6960i 0.835432i
\(15\) −7.49988 + 4.33033i −0.499992 + 0.288689i
\(16\) −4.00000 −0.250000
\(17\) −8.50993 8.50993i −0.500584 0.500584i 0.411035 0.911619i \(-0.365167\pi\)
−0.911619 + 0.411035i \(0.865167\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 22.3969i 1.17879i 0.807847 + 0.589393i \(0.200633\pi\)
−0.807847 + 0.589393i \(0.799367\pi\)
\(20\) 2.58793 9.65933i 0.129396 0.482966i
\(21\) 14.3247 0.682127
\(22\) 1.76345 + 1.76345i 0.0801567 + 0.0801567i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 21.6513 + 12.4988i 0.866053 + 0.499953i
\(26\) −10.0013 −0.384664
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −11.6960 + 11.6960i −0.417716 + 0.417716i
\(29\) 38.8089i 1.33824i 0.743155 + 0.669120i \(0.233329\pi\)
−0.743155 + 0.669120i \(0.766671\pi\)
\(30\) 11.8302 + 3.16955i 0.394340 + 0.105652i
\(31\) 15.0913 0.486815 0.243407 0.969924i \(-0.421735\pi\)
0.243407 + 0.969924i \(0.421735\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −2.15977 + 2.15977i −0.0654476 + 0.0654476i
\(34\) 17.0199i 0.500584i
\(35\) −20.6769 35.8111i −0.590768 1.02318i
\(36\) 6.00000 0.166667
\(37\) 28.5900 + 28.5900i 0.772702 + 0.772702i 0.978578 0.205876i \(-0.0660044\pi\)
−0.205876 + 0.978578i \(0.566004\pi\)
\(38\) 22.3969 22.3969i 0.589393 0.589393i
\(39\) 12.2490i 0.314077i
\(40\) −12.2473 + 7.07140i −0.306181 + 0.176785i
\(41\) 63.9487 1.55972 0.779862 0.625951i \(-0.215289\pi\)
0.779862 + 0.625951i \(0.215289\pi\)
\(42\) −14.3247 14.3247i −0.341064 0.341064i
\(43\) 34.7533 34.7533i 0.808217 0.808217i −0.176147 0.984364i \(-0.556363\pi\)
0.984364 + 0.176147i \(0.0563634\pi\)
\(44\) 3.52689i 0.0801567i
\(45\) −3.88189 + 14.4890i −0.0862642 + 0.321978i
\(46\) −6.78233 −0.147442
\(47\) 2.22777 + 2.22777i 0.0473994 + 0.0473994i 0.730409 0.683010i \(-0.239329\pi\)
−0.683010 + 0.730409i \(0.739329\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 19.3988i 0.395894i
\(50\) −9.15250 34.1501i −0.183050 0.683003i
\(51\) −20.8450 −0.408725
\(52\) 10.0013 + 10.0013i 0.192332 + 0.192332i
\(53\) 67.8328 67.8328i 1.27986 1.27986i 0.339121 0.940743i \(-0.389871\pi\)
0.940743 0.339121i \(-0.110129\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 8.51686 + 2.28183i 0.154852 + 0.0414879i
\(56\) 23.3921 0.417716
\(57\) 27.4305 + 27.4305i 0.481237 + 0.481237i
\(58\) 38.8089 38.8089i 0.669120 0.669120i
\(59\) 29.3548i 0.497538i −0.968563 0.248769i \(-0.919974\pi\)
0.968563 0.248769i \(-0.0800260\pi\)
\(60\) −8.66066 14.9998i −0.144344 0.249996i
\(61\) 54.6267 0.895520 0.447760 0.894154i \(-0.352222\pi\)
0.447760 + 0.894154i \(0.352222\pi\)
\(62\) −15.0913 15.0913i −0.243407 0.243407i
\(63\) 17.5441 17.5441i 0.278477 0.278477i
\(64\) 8.00000i 0.125000i
\(65\) −30.6220 + 17.6807i −0.471108 + 0.272011i
\(66\) 4.31954 0.0654476
\(67\) 14.0005 + 14.0005i 0.208963 + 0.208963i 0.803826 0.594864i \(-0.202794\pi\)
−0.594864 + 0.803826i \(0.702794\pi\)
\(68\) 17.0199 17.0199i 0.250292 0.250292i
\(69\) 8.30662i 0.120386i
\(70\) −15.1343 + 56.4880i −0.216204 + 0.806971i
\(71\) −36.0984 −0.508428 −0.254214 0.967148i \(-0.581817\pi\)
−0.254214 + 0.967148i \(0.581817\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −58.7921 + 58.7921i −0.805371 + 0.805371i −0.983929 0.178558i \(-0.942857\pi\)
0.178558 + 0.983929i \(0.442857\pi\)
\(74\) 57.1799i 0.772702i
\(75\) 41.8252 11.2095i 0.557669 0.149460i
\(76\) −44.7938 −0.589393
\(77\) −10.3127 10.3127i −0.133931 0.133931i
\(78\) −12.2490 + 12.2490i −0.157038 + 0.157038i
\(79\) 128.176i 1.62248i −0.584713 0.811240i \(-0.698793\pi\)
0.584713 0.811240i \(-0.301207\pi\)
\(80\) 19.3187 + 5.17585i 0.241483 + 0.0646982i
\(81\) −9.00000 −0.111111
\(82\) −63.9487 63.9487i −0.779862 0.779862i
\(83\) −68.9222 + 68.9222i −0.830389 + 0.830389i −0.987570 0.157181i \(-0.949759\pi\)
0.157181 + 0.987570i \(0.449759\pi\)
\(84\) 28.6494i 0.341064i
\(85\) 30.0886 + 52.1116i 0.353983 + 0.613078i
\(86\) −69.5066 −0.808217
\(87\) 47.5310 + 47.5310i 0.546334 + 0.546334i
\(88\) −3.52689 + 3.52689i −0.0400783 + 0.0400783i
\(89\) 19.7288i 0.221672i −0.993839 0.110836i \(-0.964647\pi\)
0.993839 0.110836i \(-0.0353529\pi\)
\(90\) 18.3709 10.6071i 0.204121 0.117857i
\(91\) 58.4876 0.642721
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 18.4829 18.4829i 0.198741 0.198741i
\(94\) 4.45554i 0.0473994i
\(95\) 28.9808 108.170i 0.305061 1.13863i
\(96\) 9.79796 0.102062
\(97\) 85.9628 + 85.9628i 0.886215 + 0.886215i 0.994157 0.107942i \(-0.0344262\pi\)
−0.107942 + 0.994157i \(0.534426\pi\)
\(98\) 19.3988 19.3988i 0.197947 0.197947i
\(99\) 5.29034i 0.0534378i
\(100\) −24.9976 + 43.3026i −0.249976 + 0.433026i
\(101\) −9.56680 −0.0947207 −0.0473604 0.998878i \(-0.515081\pi\)
−0.0473604 + 0.998878i \(0.515081\pi\)
\(102\) 20.8450 + 20.8450i 0.204363 + 0.204363i
\(103\) 52.1473 52.1473i 0.506284 0.506284i −0.407100 0.913384i \(-0.633460\pi\)
0.913384 + 0.407100i \(0.133460\pi\)
\(104\) 20.0025i 0.192332i
\(105\) −69.1834 18.5356i −0.658889 0.176530i
\(106\) −135.666 −1.27986
\(107\) 125.340 + 125.340i 1.17140 + 1.17140i 0.981876 + 0.189525i \(0.0606947\pi\)
0.189525 + 0.981876i \(0.439305\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 65.7207i 0.602942i −0.953475 0.301471i \(-0.902522\pi\)
0.953475 0.301471i \(-0.0974777\pi\)
\(110\) −6.23502 10.7987i −0.0566820 0.0981699i
\(111\) 70.0308 0.630908
\(112\) −23.3921 23.3921i −0.208858 0.208858i
\(113\) 50.2423 50.2423i 0.444622 0.444622i −0.448940 0.893562i \(-0.648198\pi\)
0.893562 + 0.448940i \(0.148198\pi\)
\(114\) 54.8610i 0.481237i
\(115\) −20.7662 + 11.9901i −0.180576 + 0.104262i
\(116\) −77.6179 −0.669120
\(117\) −15.0019 15.0019i −0.128221 0.128221i
\(118\) −29.3548 + 29.3548i −0.248769 + 0.248769i
\(119\) 99.5325i 0.836408i
\(120\) −6.33910 + 23.6604i −0.0528258 + 0.197170i
\(121\) −117.890 −0.974300
\(122\) −54.6267 54.6267i −0.447760 0.447760i
\(123\) 78.3209 78.3209i 0.636755 0.636755i
\(124\) 30.1825i 0.243407i
\(125\) −88.3956 88.3811i −0.707165 0.707049i
\(126\) −35.0881 −0.278477
\(127\) 87.1032 + 87.1032i 0.685852 + 0.685852i 0.961312 0.275461i \(-0.0888304\pi\)
−0.275461 + 0.961312i \(0.588830\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 85.1279i 0.659906i
\(130\) 48.3027 + 12.9413i 0.371560 + 0.0995482i
\(131\) 151.951 1.15993 0.579966 0.814641i \(-0.303066\pi\)
0.579966 + 0.814641i \(0.303066\pi\)
\(132\) −4.31954 4.31954i −0.0327238 0.0327238i
\(133\) −130.978 + 130.978i −0.984795 + 0.984795i
\(134\) 28.0010i 0.208963i
\(135\) 12.9910 + 22.4996i 0.0962296 + 0.166664i
\(136\) −34.0397 −0.250292
\(137\) 67.2320 + 67.2320i 0.490745 + 0.490745i 0.908541 0.417796i \(-0.137197\pi\)
−0.417796 + 0.908541i \(0.637197\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 147.787i 1.06322i −0.846990 0.531610i \(-0.821587\pi\)
0.846990 0.531610i \(-0.178413\pi\)
\(140\) 71.6223 41.3537i 0.511588 0.295384i
\(141\) 5.45691 0.0387015
\(142\) 36.0984 + 36.0984i 0.254214 + 0.254214i
\(143\) −8.81835 + 8.81835i −0.0616668 + 0.0616668i
\(144\) 12.0000i 0.0833333i
\(145\) 50.2173 187.434i 0.346326 1.29265i
\(146\) 117.584 0.805371
\(147\) 23.7586 + 23.7586i 0.161623 + 0.161623i
\(148\) −57.1799 + 57.1799i −0.386351 + 0.386351i
\(149\) 34.3711i 0.230678i 0.993326 + 0.115339i \(0.0367955\pi\)
−0.993326 + 0.115339i \(0.963205\pi\)
\(150\) −53.0347 30.6157i −0.353565 0.204105i
\(151\) −187.555 −1.24208 −0.621042 0.783777i \(-0.713290\pi\)
−0.621042 + 0.783777i \(0.713290\pi\)
\(152\) 44.7938 + 44.7938i 0.294696 + 0.294696i
\(153\) −25.5298 + 25.5298i −0.166861 + 0.166861i
\(154\) 20.6254i 0.133931i
\(155\) −72.8857 19.5275i −0.470230 0.125984i
\(156\) 24.4980 0.157038
\(157\) 173.198 + 173.198i 1.10317 + 1.10317i 0.994026 + 0.109147i \(0.0348120\pi\)
0.109147 + 0.994026i \(0.465188\pi\)
\(158\) −128.176 + 128.176i −0.811240 + 0.811240i
\(159\) 166.156i 1.04500i
\(160\) −14.1428 24.4945i −0.0883925 0.153091i
\(161\) 39.6632 0.246355
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −12.3280 + 12.3280i −0.0756321 + 0.0756321i −0.743911 0.668279i \(-0.767031\pi\)
0.668279 + 0.743911i \(0.267031\pi\)
\(164\) 127.897i 0.779862i
\(165\) 13.2256 7.63631i 0.0801554 0.0462807i
\(166\) 137.844 0.830389
\(167\) 67.8791 + 67.8791i 0.406461 + 0.406461i 0.880503 0.474041i \(-0.157205\pi\)
−0.474041 + 0.880503i \(0.657205\pi\)
\(168\) 28.6494 28.6494i 0.170532 0.170532i
\(169\) 118.987i 0.704067i
\(170\) 22.0231 82.2002i 0.129547 0.483531i
\(171\) 67.1908 0.392928
\(172\) 69.5066 + 69.5066i 0.404108 + 0.404108i
\(173\) 36.4436 36.4436i 0.210656 0.210656i −0.593890 0.804546i \(-0.702409\pi\)
0.804546 + 0.593890i \(0.202409\pi\)
\(174\) 95.0621i 0.546334i
\(175\) 53.5241 + 199.711i 0.305852 + 1.14120i
\(176\) 7.05379 0.0400783
\(177\) −35.9521 35.9521i −0.203119 0.203119i
\(178\) −19.7288 + 19.7288i −0.110836 + 0.110836i
\(179\) 96.1704i 0.537265i −0.963243 0.268633i \(-0.913428\pi\)
0.963243 0.268633i \(-0.0865717\pi\)
\(180\) −28.9780 7.76378i −0.160989 0.0431321i
\(181\) 204.330 1.12889 0.564447 0.825469i \(-0.309089\pi\)
0.564447 + 0.825469i \(0.309089\pi\)
\(182\) −58.4876 58.4876i −0.321361 0.321361i
\(183\) 66.9038 66.9038i 0.365594 0.365594i
\(184\) 13.5647i 0.0737210i
\(185\) −101.086 175.074i −0.546409 0.946348i
\(186\) −36.9659 −0.198741
\(187\) 15.0068 + 15.0068i 0.0802503 + 0.0802503i
\(188\) −4.45554 + 4.45554i −0.0236997 + 0.0236997i
\(189\) 42.9740i 0.227376i
\(190\) −137.150 + 79.1888i −0.721844 + 0.416783i
\(191\) −103.300 −0.540835 −0.270418 0.962743i \(-0.587162\pi\)
−0.270418 + 0.962743i \(0.587162\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 21.4091 21.4091i 0.110928 0.110928i −0.649464 0.760392i \(-0.725007\pi\)
0.760392 + 0.649464i \(0.225007\pi\)
\(194\) 171.926i 0.886215i
\(195\) −15.8497 + 59.1585i −0.0812807 + 0.303377i
\(196\) −38.7976 −0.197947
\(197\) 5.19419 + 5.19419i 0.0263664 + 0.0263664i 0.720167 0.693801i \(-0.244065\pi\)
−0.693801 + 0.720167i \(0.744065\pi\)
\(198\) 5.29034 5.29034i 0.0267189 0.0267189i
\(199\) 343.482i 1.72604i 0.505168 + 0.863021i \(0.331430\pi\)
−0.505168 + 0.863021i \(0.668570\pi\)
\(200\) 68.3003 18.3050i 0.341501 0.0915250i
\(201\) 34.2941 0.170617
\(202\) 9.56680 + 9.56680i 0.0473604 + 0.0473604i
\(203\) −226.956 + 226.956i −1.11801 + 1.11801i
\(204\) 41.6900i 0.204363i
\(205\) −308.851 82.7473i −1.50659 0.403645i
\(206\) −104.295 −0.506284
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −20.0025 + 20.0025i −0.0961660 + 0.0961660i
\(209\) 39.4958i 0.188975i
\(210\) 50.6478 + 87.7190i 0.241180 + 0.417709i
\(211\) −203.788 −0.965819 −0.482910 0.875670i \(-0.660420\pi\)
−0.482910 + 0.875670i \(0.660420\pi\)
\(212\) 135.666 + 135.666i 0.639932 + 0.639932i
\(213\) −44.2113 + 44.2113i −0.207565 + 0.207565i
\(214\) 250.680i 1.17140i
\(215\) −212.816 + 122.877i −0.989844 + 0.571523i
\(216\) −14.6969 −0.0680414
\(217\) 88.2540 + 88.2540i 0.406701 + 0.406701i
\(218\) −65.7207 + 65.7207i −0.301471 + 0.301471i
\(219\) 144.011i 0.657583i
\(220\) −4.56367 + 17.0337i −0.0207440 + 0.0774260i
\(221\) −85.1100 −0.385113
\(222\) −70.0308 70.0308i −0.315454 0.315454i
\(223\) −232.124 + 232.124i −1.04091 + 1.04091i −0.0417883 + 0.999126i \(0.513306\pi\)
−0.999126 + 0.0417883i \(0.986694\pi\)
\(224\) 46.7842i 0.208858i
\(225\) 37.4964 64.9540i 0.166651 0.288684i
\(226\) −100.485 −0.444622
\(227\) −184.343 184.343i −0.812082 0.812082i 0.172863 0.984946i \(-0.444698\pi\)
−0.984946 + 0.172863i \(0.944698\pi\)
\(228\) −54.8610 + 54.8610i −0.240619 + 0.240619i
\(229\) 223.254i 0.974908i 0.873149 + 0.487454i \(0.162074\pi\)
−0.873149 + 0.487454i \(0.837926\pi\)
\(230\) 32.7564 + 8.77608i 0.142419 + 0.0381569i
\(231\) −25.2608 −0.109354
\(232\) 77.6179 + 77.6179i 0.334560 + 0.334560i
\(233\) −296.194 + 296.194i −1.27122 + 1.27122i −0.325769 + 0.945449i \(0.605623\pi\)
−0.945449 + 0.325769i \(0.894377\pi\)
\(234\) 30.0038i 0.128221i
\(235\) −7.87674 13.6420i −0.0335180 0.0580513i
\(236\) 58.7095 0.248769
\(237\) −156.983 156.983i −0.662375 0.662375i
\(238\) −99.5325 + 99.5325i −0.418204 + 0.418204i
\(239\) 2.15755i 0.00902741i −0.999990 0.00451370i \(-0.998563\pi\)
0.999990 0.00451370i \(-0.00143676\pi\)
\(240\) 29.9995 17.3213i 0.124998 0.0721722i
\(241\) −136.072 −0.564612 −0.282306 0.959324i \(-0.591099\pi\)
−0.282306 + 0.959324i \(0.591099\pi\)
\(242\) 117.890 + 117.890i 0.487150 + 0.487150i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 109.253i 0.447760i
\(245\) 25.1013 93.6896i 0.102454 0.382407i
\(246\) −156.642 −0.636755
\(247\) 111.999 + 111.999i 0.453436 + 0.453436i
\(248\) 30.1825 30.1825i 0.121704 0.121704i
\(249\) 168.824i 0.678009i
\(250\) 0.0145100 + 176.777i 5.80400e−5 + 0.707107i
\(251\) 191.977 0.764848 0.382424 0.923987i \(-0.375089\pi\)
0.382424 + 0.923987i \(0.375089\pi\)
\(252\) 35.0881 + 35.0881i 0.139239 + 0.139239i
\(253\) −5.98014 + 5.98014i −0.0236369 + 0.0236369i
\(254\) 174.206i 0.685852i
\(255\) 100.674 + 26.9726i 0.394801 + 0.105775i
\(256\) 16.0000 0.0625000
\(257\) 100.820 + 100.820i 0.392294 + 0.392294i 0.875504 0.483210i \(-0.160529\pi\)
−0.483210 + 0.875504i \(0.660529\pi\)
\(258\) −85.1279 + 85.1279i −0.329953 + 0.329953i
\(259\) 334.390i 1.29108i
\(260\) −35.3615 61.2440i −0.136006 0.235554i
\(261\) 116.427 0.446080
\(262\) −151.951 151.951i −0.579966 0.579966i
\(263\) −162.391 + 162.391i −0.617455 + 0.617455i −0.944878 0.327423i \(-0.893820\pi\)
0.327423 + 0.944878i \(0.393820\pi\)
\(264\) 8.63909i 0.0327238i
\(265\) −415.383 + 239.836i −1.56748 + 0.905043i
\(266\) 261.955 0.984795
\(267\) −24.1628 24.1628i −0.0904973 0.0904973i
\(268\) −28.0010 + 28.0010i −0.104481 + 0.104481i
\(269\) 166.072i 0.617366i −0.951165 0.308683i \(-0.900112\pi\)
0.951165 0.308683i \(-0.0998883\pi\)
\(270\) 9.50865 35.4906i 0.0352172 0.131447i
\(271\) −309.336 −1.14146 −0.570731 0.821137i \(-0.693340\pi\)
−0.570731 + 0.821137i \(0.693340\pi\)
\(272\) 34.0397 + 34.0397i 0.125146 + 0.125146i
\(273\) 71.6324 71.6324i 0.262390 0.262390i
\(274\) 134.464i 0.490745i
\(275\) −38.1809 22.0410i −0.138840 0.0801491i
\(276\) 16.6132 0.0601929
\(277\) −265.998 265.998i −0.960281 0.960281i 0.0389595 0.999241i \(-0.487596\pi\)
−0.999241 + 0.0389595i \(0.987596\pi\)
\(278\) −147.787 + 147.787i −0.531610 + 0.531610i
\(279\) 45.2738i 0.162272i
\(280\) −112.976 30.2685i −0.403486 0.108102i
\(281\) 57.9240 0.206135 0.103068 0.994674i \(-0.467134\pi\)
0.103068 + 0.994674i \(0.467134\pi\)
\(282\) −5.45691 5.45691i −0.0193507 0.0193507i
\(283\) −116.179 + 116.179i −0.410525 + 0.410525i −0.881922 0.471396i \(-0.843750\pi\)
0.471396 + 0.881922i \(0.343750\pi\)
\(284\) 72.1968i 0.254214i
\(285\) −96.9861 167.974i −0.340302 0.589383i
\(286\) 17.6367 0.0616668
\(287\) 373.974 + 373.974i 1.30304 + 1.30304i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 144.162i 0.498831i
\(290\) −237.651 + 137.217i −0.819488 + 0.473161i
\(291\) 210.565 0.723591
\(292\) −117.584 117.584i −0.402686 0.402686i
\(293\) 189.001 189.001i 0.645056 0.645056i −0.306738 0.951794i \(-0.599238\pi\)
0.951794 + 0.306738i \(0.0992376\pi\)
\(294\) 47.5171i 0.161623i
\(295\) −37.9840 + 141.774i −0.128759 + 0.480588i
\(296\) 114.360 0.386351
\(297\) 6.47932 + 6.47932i 0.0218159 + 0.0218159i
\(298\) 34.3711 34.3711i 0.115339 0.115339i
\(299\) 33.9159i 0.113431i
\(300\) 22.4190 + 83.6504i 0.0747299 + 0.278835i
\(301\) 406.477 1.35042
\(302\) 187.555 + 187.555i 0.621042 + 0.621042i
\(303\) −11.7169 + 11.7169i −0.0386696 + 0.0386696i
\(304\) 89.5877i 0.294696i
\(305\) −263.829 70.6849i −0.865012 0.231754i
\(306\) 51.0596 0.166861
\(307\) 307.822 + 307.822i 1.00268 + 1.00268i 0.999996 + 0.00268029i \(0.000853164\pi\)
0.00268029 + 0.999996i \(0.499147\pi\)
\(308\) 20.6254 20.6254i 0.0669655 0.0669655i
\(309\) 127.734i 0.413379i
\(310\) 53.3582 + 92.4132i 0.172123 + 0.298107i
\(311\) −529.789 −1.70350 −0.851750 0.523948i \(-0.824459\pi\)
−0.851750 + 0.523948i \(0.824459\pi\)
\(312\) −24.4980 24.4980i −0.0785192 0.0785192i
\(313\) 64.3377 64.3377i 0.205552 0.205552i −0.596822 0.802374i \(-0.703570\pi\)
0.802374 + 0.596822i \(0.203570\pi\)
\(314\) 346.396i 1.10317i
\(315\) −107.433 + 62.0306i −0.341058 + 0.196923i
\(316\) 256.352 0.811240
\(317\) −393.031 393.031i −1.23985 1.23985i −0.960064 0.279781i \(-0.909738\pi\)
−0.279781 0.960064i \(-0.590262\pi\)
\(318\) −166.156 + 166.156i −0.522502 + 0.522502i
\(319\) 68.4375i 0.214538i
\(320\) −10.3517 + 38.6373i −0.0323491 + 0.120742i
\(321\) 307.019 0.956445
\(322\) −39.6632 39.6632i −0.123178 0.123178i
\(323\) 190.596 190.596i 0.590081 0.590081i
\(324\) 18.0000i 0.0555556i
\(325\) 170.772 45.7683i 0.525453 0.140826i
\(326\) 24.6561 0.0756321
\(327\) −80.4911 80.4911i −0.246150 0.246150i
\(328\) 127.897 127.897i 0.389931 0.389931i
\(329\) 26.0561i 0.0791980i
\(330\) −20.8620 5.58933i −0.0632180 0.0169374i
\(331\) 179.754 0.543064 0.271532 0.962429i \(-0.412470\pi\)
0.271532 + 0.962429i \(0.412470\pi\)
\(332\) −137.844 137.844i −0.415194 0.415194i
\(333\) 85.7699 85.7699i 0.257567 0.257567i
\(334\) 135.758i 0.406461i
\(335\) −49.5016 85.7338i −0.147766 0.255922i
\(336\) −57.2987 −0.170532
\(337\) −118.371 118.371i −0.351251 0.351251i 0.509324 0.860575i \(-0.329895\pi\)
−0.860575 + 0.509324i \(0.829895\pi\)
\(338\) 118.987 118.987i 0.352034 0.352034i
\(339\) 123.068i 0.363033i
\(340\) −104.223 + 60.1771i −0.306539 + 0.176992i
\(341\) −26.6126 −0.0780429
\(342\) −67.1908 67.1908i −0.196464 0.196464i
\(343\) 173.109 173.109i 0.504690 0.504690i
\(344\) 139.013i 0.404108i
\(345\) −10.7485 + 40.1182i −0.0311550 + 0.116285i
\(346\) −72.8871 −0.210656
\(347\) 379.530 + 379.530i 1.09375 + 1.09375i 0.995125 + 0.0986223i \(0.0314436\pi\)
0.0986223 + 0.995125i \(0.468556\pi\)
\(348\) −95.0621 + 95.0621i −0.273167 + 0.273167i
\(349\) 540.641i 1.54912i −0.632503 0.774558i \(-0.717973\pi\)
0.632503 0.774558i \(-0.282027\pi\)
\(350\) 146.187 253.235i 0.417676 0.723528i
\(351\) −36.7470 −0.104692
\(352\) −7.05379 7.05379i −0.0200392 0.0200392i
\(353\) 51.2669 51.2669i 0.145232 0.145232i −0.630752 0.775984i \(-0.717254\pi\)
0.775984 + 0.630752i \(0.217254\pi\)
\(354\) 71.9042i 0.203119i
\(355\) 174.343 + 46.7100i 0.491107 + 0.131577i
\(356\) 39.4577 0.110836
\(357\) −121.902 121.902i −0.341462 0.341462i
\(358\) −96.1704 + 96.1704i −0.268633 + 0.268633i
\(359\) 217.517i 0.605898i 0.953007 + 0.302949i \(0.0979712\pi\)
−0.953007 + 0.302949i \(0.902029\pi\)
\(360\) 21.2142 + 36.7418i 0.0589284 + 0.102060i
\(361\) −140.622 −0.389534
\(362\) −204.330 204.330i −0.564447 0.564447i
\(363\) −144.385 + 144.385i −0.397756 + 0.397756i
\(364\) 116.975i 0.321361i
\(365\) 360.021 207.871i 0.986358 0.569510i
\(366\) −133.808 −0.365594
\(367\) −391.093 391.093i −1.06565 1.06565i −0.997688 0.0679602i \(-0.978351\pi\)
−0.0679602 0.997688i \(-0.521649\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 191.846i 0.519908i
\(370\) −73.9887 + 276.160i −0.199970 + 0.746378i
\(371\) 793.375 2.13848
\(372\) 36.9659 + 36.9659i 0.0993706 + 0.0993706i
\(373\) 281.397 281.397i 0.754414 0.754414i −0.220885 0.975300i \(-0.570895\pi\)
0.975300 + 0.220885i \(0.0708947\pi\)
\(374\) 30.0136i 0.0802503i
\(375\) −216.506 + 0.0177710i −0.577350 + 4.73894e-5i
\(376\) 8.91109 0.0236997
\(377\) 194.069 + 194.069i 0.514772 + 0.514772i
\(378\) −42.9740 + 42.9740i −0.113688 + 0.113688i
\(379\) 450.647i 1.18904i −0.804080 0.594521i \(-0.797342\pi\)
0.804080 0.594521i \(-0.202658\pi\)
\(380\) 216.339 + 57.9616i 0.569314 + 0.152530i
\(381\) 213.358 0.559996
\(382\) 103.300 + 103.300i 0.270418 + 0.270418i
\(383\) −120.781 + 120.781i −0.315354 + 0.315354i −0.846980 0.531625i \(-0.821581\pi\)
0.531625 + 0.846980i \(0.321581\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 36.4626 + 63.1510i 0.0947079 + 0.164029i
\(386\) −42.8181 −0.110928
\(387\) −104.260 104.260i −0.269406 0.269406i
\(388\) −171.926 + 171.926i −0.443107 + 0.443107i
\(389\) 136.553i 0.351035i 0.984476 + 0.175518i \(0.0561599\pi\)
−0.984476 + 0.175518i \(0.943840\pi\)
\(390\) 75.0083 43.3088i 0.192329 0.111048i
\(391\) −57.7171 −0.147614
\(392\) 38.7976 + 38.7976i 0.0989734 + 0.0989734i
\(393\) 186.101 186.101i 0.473540 0.473540i
\(394\) 10.3884i 0.0263664i
\(395\) −165.855 + 619.047i −0.419886 + 1.56721i
\(396\) −10.5807 −0.0267189
\(397\) −11.6153 11.6153i −0.0292576 0.0292576i 0.692327 0.721584i \(-0.256586\pi\)
−0.721584 + 0.692327i \(0.756586\pi\)
\(398\) 343.482 343.482i 0.863021 0.863021i
\(399\) 320.829i 0.804082i
\(400\) −86.6053 49.9953i −0.216513 0.124988i
\(401\) −325.917 −0.812760 −0.406380 0.913704i \(-0.633209\pi\)
−0.406380 + 0.913704i \(0.633209\pi\)
\(402\) −34.2941 34.2941i −0.0853086 0.0853086i
\(403\) 75.4658 75.4658i 0.187260 0.187260i
\(404\) 19.1336i 0.0473604i
\(405\) 43.4670 + 11.6457i 0.107326 + 0.0287547i
\(406\) 453.911 1.11801
\(407\) −50.4169 50.4169i −0.123874 0.123874i
\(408\) −41.6900 + 41.6900i −0.102181 + 0.102181i
\(409\) 447.168i 1.09332i −0.837354 0.546661i \(-0.815899\pi\)
0.837354 0.546661i \(-0.184101\pi\)
\(410\) 226.104 + 391.598i 0.551472 + 0.955117i
\(411\) 164.684 0.400691
\(412\) 104.295 + 104.295i 0.253142 + 0.253142i
\(413\) 171.667 171.667i 0.415659 0.415659i
\(414\) 20.3470i 0.0491473i
\(415\) 422.054 243.688i 1.01700 0.587201i
\(416\) 40.0050 0.0961660
\(417\) −181.002 181.002i −0.434057 0.434057i
\(418\) −39.4958 + 39.4958i −0.0944875 + 0.0944875i
\(419\) 356.216i 0.850157i 0.905157 + 0.425078i \(0.139753\pi\)
−0.905157 + 0.425078i \(0.860247\pi\)
\(420\) 37.0712 138.367i 0.0882648 0.329445i
\(421\) 415.752 0.987534 0.493767 0.869594i \(-0.335620\pi\)
0.493767 + 0.869594i \(0.335620\pi\)
\(422\) 203.788 + 203.788i 0.482910 + 0.482910i
\(423\) 6.68332 6.68332i 0.0157998 0.0157998i
\(424\) 271.331i 0.639932i
\(425\) −77.8872 290.615i −0.183264 0.683801i
\(426\) 88.4227 0.207565
\(427\) 319.458 + 319.458i 0.748146 + 0.748146i
\(428\) −250.680 + 250.680i −0.585700 + 0.585700i
\(429\) 21.6004i 0.0503507i
\(430\) 335.694 + 89.9390i 0.780683 + 0.209161i
\(431\) −456.460 −1.05907 −0.529536 0.848287i \(-0.677634\pi\)
−0.529536 + 0.848287i \(0.677634\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −56.6111 + 56.6111i −0.130741 + 0.130741i −0.769449 0.638708i \(-0.779469\pi\)
0.638708 + 0.769449i \(0.279469\pi\)
\(434\) 176.508i 0.406701i
\(435\) −168.056 291.062i −0.386335 0.669109i
\(436\) 131.441 0.301471
\(437\) 75.9516 + 75.9516i 0.173802 + 0.173802i
\(438\) 144.011 144.011i 0.328791 0.328791i
\(439\) 533.763i 1.21586i −0.793990 0.607931i \(-0.792000\pi\)
0.793990 0.607931i \(-0.208000\pi\)
\(440\) 21.5974 12.4700i 0.0490850 0.0283410i
\(441\) 58.1964 0.131965
\(442\) 85.1100 + 85.1100i 0.192557 + 0.192557i
\(443\) −308.316 + 308.316i −0.695973 + 0.695973i −0.963539 0.267567i \(-0.913780\pi\)
0.267567 + 0.963539i \(0.413780\pi\)
\(444\) 140.062i 0.315454i
\(445\) −25.5284 + 95.2836i −0.0573671 + 0.214121i
\(446\) 464.248 1.04091
\(447\) 42.0958 + 42.0958i 0.0941740 + 0.0941740i
\(448\) 46.7842 46.7842i 0.104429 0.104429i
\(449\) 479.262i 1.06740i 0.845674 + 0.533699i \(0.179199\pi\)
−0.845674 + 0.533699i \(0.820801\pi\)
\(450\) −102.450 + 27.4575i −0.227668 + 0.0610167i
\(451\) −112.770 −0.250045
\(452\) 100.485 + 100.485i 0.222311 + 0.222311i
\(453\) −229.707 + 229.707i −0.507079 + 0.507079i
\(454\) 368.685i 0.812082i
\(455\) −282.476 75.6808i −0.620825 0.166331i
\(456\) 109.722 0.240619
\(457\) 121.058 + 121.058i 0.264898 + 0.264898i 0.827040 0.562142i \(-0.190023\pi\)
−0.562142 + 0.827040i \(0.690023\pi\)
\(458\) 223.254 223.254i 0.487454 0.487454i
\(459\) 62.5350i 0.136242i
\(460\) −23.9803 41.5325i −0.0521311 0.0902880i
\(461\) −130.197 −0.282423 −0.141211 0.989979i \(-0.545100\pi\)
−0.141211 + 0.989979i \(0.545100\pi\)
\(462\) 25.2608 + 25.2608i 0.0546771 + 0.0546771i
\(463\) −84.8852 + 84.8852i −0.183337 + 0.183337i −0.792808 0.609471i \(-0.791382\pi\)
0.609471 + 0.792808i \(0.291382\pi\)
\(464\) 155.236i 0.334560i
\(465\) −113.183 + 65.3501i −0.243403 + 0.140538i
\(466\) 592.388 1.27122
\(467\) 93.2186 + 93.2186i 0.199612 + 0.199612i 0.799834 0.600222i \(-0.204921\pi\)
−0.600222 + 0.799834i \(0.704921\pi\)
\(468\) 30.0038 30.0038i 0.0641107 0.0641107i
\(469\) 163.751i 0.349148i
\(470\) −5.76531 + 21.5188i −0.0122666 + 0.0457846i
\(471\) 424.247 0.900737
\(472\) −58.7095 58.7095i −0.124385 0.124385i
\(473\) −61.2856 + 61.2856i −0.129568 + 0.129568i
\(474\) 313.966i 0.662375i
\(475\) −279.935 + 484.923i −0.589337 + 1.02089i
\(476\) 199.065 0.418204
\(477\) −203.498 203.498i −0.426621 0.426621i
\(478\) −2.15755 + 2.15755i −0.00451370 + 0.00451370i
\(479\) 376.346i 0.785690i 0.919605 + 0.392845i \(0.128509\pi\)
−0.919605 + 0.392845i \(0.871491\pi\)
\(480\) −47.3209 12.6782i −0.0985851 0.0264129i
\(481\) 285.936 0.594461
\(482\) 136.072 + 136.072i 0.282306 + 0.282306i
\(483\) 48.5773 48.5773i 0.100574 0.100574i
\(484\) 235.781i 0.487150i
\(485\) −303.939 526.404i −0.626678 1.08537i
\(486\) 22.0454 0.0453609
\(487\) −331.105 331.105i −0.679887 0.679887i 0.280088 0.959974i \(-0.409636\pi\)
−0.959974 + 0.280088i \(0.909636\pi\)
\(488\) 109.253 109.253i 0.223880 0.223880i
\(489\) 30.1974i 0.0617533i
\(490\) −118.791 + 68.5883i −0.242430 + 0.139976i
\(491\) 95.5294 0.194561 0.0972805 0.995257i \(-0.468986\pi\)
0.0972805 + 0.995257i \(0.468986\pi\)
\(492\) 156.642 + 156.642i 0.318377 + 0.318377i
\(493\) 330.261 330.261i 0.669901 0.669901i
\(494\) 223.997i 0.453436i
\(495\) 6.84550 25.5506i 0.0138293 0.0516173i
\(496\) −60.3650 −0.121704
\(497\) −211.104 211.104i −0.424757 0.424757i
\(498\) 168.824 168.824i 0.339005 0.339005i
\(499\) 134.022i 0.268581i −0.990942 0.134291i \(-0.957124\pi\)
0.990942 0.134291i \(-0.0428756\pi\)
\(500\) 176.762 176.791i 0.353524 0.353582i
\(501\) 166.269 0.331874
\(502\) −191.977 191.977i −0.382424 0.382424i
\(503\) −474.271 + 474.271i −0.942885 + 0.942885i −0.998455 0.0555696i \(-0.982303\pi\)
0.0555696 + 0.998455i \(0.482303\pi\)
\(504\) 70.1763i 0.139239i
\(505\) 46.2044 + 12.3791i 0.0914939 + 0.0245130i
\(506\) 11.9603 0.0236369
\(507\) 145.729 + 145.729i 0.287434 + 0.287434i
\(508\) −174.206 + 174.206i −0.342926 + 0.342926i
\(509\) 447.848i 0.879859i −0.898032 0.439930i \(-0.855003\pi\)
0.898032 0.439930i \(-0.144997\pi\)
\(510\) −73.7016 127.647i −0.144513 0.250288i
\(511\) −687.635 −1.34567
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 82.2915 82.2915i 0.160412 0.160412i
\(514\) 201.639i 0.392294i
\(515\) −319.330 + 184.377i −0.620059 + 0.358014i
\(516\) 170.256 0.329953
\(517\) −3.92856 3.92856i −0.00759876 0.00759876i
\(518\) 334.390 334.390i 0.645540 0.645540i
\(519\) 89.2681i 0.172000i
\(520\) −25.8825 + 96.6055i −0.0497741 + 0.185780i
\(521\) 348.685 0.669261 0.334631 0.942349i \(-0.391388\pi\)
0.334631 + 0.942349i \(0.391388\pi\)
\(522\) −116.427 116.427i −0.223040 0.223040i
\(523\) 550.982 550.982i 1.05350 1.05350i 0.0550166 0.998485i \(-0.482479\pi\)
0.998485 0.0550166i \(-0.0175212\pi\)
\(524\) 303.902i 0.579966i
\(525\) 310.148 + 179.041i 0.590758 + 0.341031i
\(526\) 324.781 0.617455
\(527\) −128.426 128.426i −0.243692 0.243692i
\(528\) 8.63909 8.63909i 0.0163619 0.0163619i
\(529\) 23.0000i 0.0434783i
\(530\) 655.219 + 175.546i 1.23626 + 0.331219i
\(531\) −88.0643 −0.165846
\(532\) −261.955 261.955i −0.492397 0.492397i
\(533\) 319.784 319.784i 0.599970 0.599970i
\(534\) 48.3256i 0.0904973i
\(535\) −443.164 767.535i −0.828345 1.43464i
\(536\) 56.0020 0.104481
\(537\) −117.784 117.784i −0.219338 0.219338i
\(538\) −166.072 + 166.072i −0.308683 + 0.308683i
\(539\) 34.2087i 0.0634670i
\(540\) −44.9993 + 25.9820i −0.0833320 + 0.0481148i
\(541\) 353.593 0.653591 0.326795 0.945095i \(-0.394031\pi\)
0.326795 + 0.945095i \(0.394031\pi\)
\(542\) 309.336 + 309.336i 0.570731 + 0.570731i
\(543\) 250.252 250.252i 0.460869 0.460869i
\(544\) 68.0794i 0.125146i
\(545\) −85.0401 + 317.409i −0.156037 + 0.582402i
\(546\) −143.265 −0.262390
\(547\) −39.6840 39.6840i −0.0725485 0.0725485i 0.669901 0.742450i \(-0.266336\pi\)
−0.742450 + 0.669901i \(0.766336\pi\)
\(548\) −134.464 + 134.464i −0.245372 + 0.245372i
\(549\) 163.880i 0.298507i
\(550\) 16.1400 + 60.2219i 0.0293454 + 0.109494i
\(551\) −869.201 −1.57750
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 749.576 749.576i 1.35547 1.35547i
\(554\) 531.996i 0.960281i
\(555\) −338.225 90.6173i −0.609415 0.163274i
\(556\) 295.575 0.531610
\(557\) −162.116 162.116i −0.291052 0.291052i 0.546444 0.837496i \(-0.315981\pi\)
−0.837496 + 0.546444i \(0.815981\pi\)
\(558\) −45.2738 + 45.2738i −0.0811358 + 0.0811358i
\(559\) 347.577i 0.621784i
\(560\) 82.7075 + 143.245i 0.147692 + 0.255794i
\(561\) 36.7590 0.0655241
\(562\) −57.9240 57.9240i −0.103068 0.103068i
\(563\) 99.3830 99.3830i 0.176524 0.176524i −0.613315 0.789839i \(-0.710164\pi\)
0.789839 + 0.613315i \(0.210164\pi\)
\(564\) 10.9138i 0.0193507i
\(565\) −307.665 + 177.642i −0.544540 + 0.314410i
\(566\) 232.357 0.410525
\(567\) −52.6322 52.6322i −0.0928258 0.0928258i
\(568\) −72.1968 + 72.1968i −0.127107 + 0.127107i
\(569\) 1021.63i 1.79548i −0.440530 0.897738i \(-0.645210\pi\)
0.440530 0.897738i \(-0.354790\pi\)
\(570\) −70.9881 + 264.960i −0.124541 + 0.464843i
\(571\) −454.037 −0.795161 −0.397580 0.917567i \(-0.630150\pi\)
−0.397580 + 0.917567i \(0.630150\pi\)
\(572\) −17.6367 17.6367i −0.0308334 0.0308334i
\(573\) −126.516 + 126.516i −0.220795 + 0.220795i
\(574\) 747.947i 1.30304i
\(575\) 115.809 31.0377i 0.201407 0.0539785i
\(576\) −24.0000 −0.0416667
\(577\) 112.620 + 112.620i 0.195182 + 0.195182i 0.797931 0.602749i \(-0.205928\pi\)
−0.602749 + 0.797931i \(0.705928\pi\)
\(578\) −144.162 + 144.162i −0.249416 + 0.249416i
\(579\) 52.4413i 0.0905721i
\(580\) 374.868 + 100.435i 0.646325 + 0.173163i
\(581\) −806.118 −1.38747
\(582\) −210.565 210.565i −0.361796 0.361796i
\(583\) −119.619 + 119.619i −0.205179 + 0.205179i
\(584\) 235.168i 0.402686i
\(585\) 53.0422 + 91.8660i 0.0906704 + 0.157036i
\(586\) −378.003 −0.645056
\(587\) 760.222 + 760.222i 1.29510 + 1.29510i 0.931592 + 0.363505i \(0.118420\pi\)
0.363505 + 0.931592i \(0.381580\pi\)
\(588\) −47.5171 + 47.5171i −0.0808114 + 0.0808114i
\(589\) 337.998i 0.573850i
\(590\) 179.758 103.790i 0.304674 0.175915i
\(591\) 12.7231 0.0215281
\(592\) −114.360 114.360i −0.193175 0.193175i
\(593\) −623.009 + 623.009i −1.05061 + 1.05061i −0.0519559 + 0.998649i \(0.516546\pi\)
−0.998649 + 0.0519559i \(0.983454\pi\)
\(594\) 12.9586i 0.0218159i
\(595\) −128.791 + 480.709i −0.216456 + 0.807914i
\(596\) −68.7421 −0.115339
\(597\) 420.678 + 420.678i 0.704653 + 0.704653i
\(598\) −33.9159 + 33.9159i −0.0567156 + 0.0567156i
\(599\) 320.986i 0.535870i −0.963437 0.267935i \(-0.913659\pi\)
0.963437 0.267935i \(-0.0863412\pi\)
\(600\) 61.2314 106.069i 0.102052 0.176782i
\(601\) −7.35941 −0.0122453 −0.00612264 0.999981i \(-0.501949\pi\)
−0.00612264 + 0.999981i \(0.501949\pi\)
\(602\) −406.477 406.477i −0.675210 0.675210i
\(603\) 42.0015 42.0015i 0.0696542 0.0696542i
\(604\) 375.109i 0.621042i
\(605\) 569.370 + 152.546i 0.941108 + 0.252142i
\(606\) 23.4338 0.0386696
\(607\) −360.752 360.752i −0.594319 0.594319i 0.344476 0.938795i \(-0.388057\pi\)
−0.938795 + 0.344476i \(0.888057\pi\)
\(608\) −89.5877 + 89.5877i −0.147348 + 0.147348i
\(609\) 555.925i 0.912850i
\(610\) 193.144 + 334.514i 0.316629 + 0.548383i
\(611\) 22.2805 0.0364657
\(612\) −51.0596 51.0596i −0.0834307 0.0834307i
\(613\) 649.344 649.344i 1.05929 1.05929i 0.0611606 0.998128i \(-0.480520\pi\)
0.998128 0.0611606i \(-0.0194802\pi\)
\(614\) 615.643i 1.00268i
\(615\) −479.608 + 276.919i −0.779850 + 0.450275i
\(616\) −41.2507 −0.0669655
\(617\) 686.962 + 686.962i 1.11339 + 1.11339i 0.992689 + 0.120701i \(0.0385143\pi\)
0.120701 + 0.992689i \(0.461486\pi\)
\(618\) −127.734 + 127.734i −0.206690 + 0.206690i
\(619\) 246.527i 0.398267i −0.979972 0.199133i \(-0.936187\pi\)
0.979972 0.199133i \(-0.0638127\pi\)
\(620\) 39.0551 145.771i 0.0629920 0.235115i
\(621\) −24.9199 −0.0401286
\(622\) 529.789 + 529.789i 0.851750 + 0.851750i
\(623\) 115.375 115.375i 0.185192 0.185192i
\(624\) 48.9960i 0.0785192i
\(625\) 312.559 + 541.232i 0.500095 + 0.865971i
\(626\) −128.675 −0.205552
\(627\) −48.3722 48.3722i −0.0771487 0.0771487i
\(628\) −346.396 + 346.396i −0.551586 + 0.551586i
\(629\) 486.597i 0.773605i
\(630\) 169.464 + 45.4028i 0.268990 + 0.0720679i
\(631\) 807.068 1.27903 0.639515 0.768778i \(-0.279135\pi\)
0.639515 + 0.768778i \(0.279135\pi\)
\(632\) −256.352 256.352i −0.405620 0.405620i
\(633\) −249.588 + 249.588i −0.394294 + 0.394294i
\(634\) 786.062i 1.23985i
\(635\) −307.971 533.387i −0.484993 0.839980i
\(636\) 332.311 0.522502
\(637\) 97.0062 + 97.0062i 0.152286 + 0.152286i
\(638\) −68.4375 + 68.4375i −0.107269 + 0.107269i
\(639\) 108.295i 0.169476i
\(640\) 48.9890 28.2856i 0.0765453 0.0441963i
\(641\) −926.142 −1.44484 −0.722420 0.691455i \(-0.756970\pi\)
−0.722420 + 0.691455i \(0.756970\pi\)
\(642\) −307.019 307.019i −0.478222 0.478222i
\(643\) 387.838 387.838i 0.603170 0.603170i −0.337982 0.941152i \(-0.609744\pi\)
0.941152 + 0.337982i \(0.109744\pi\)
\(644\) 79.3265i 0.123178i
\(645\) −110.152 + 411.139i −0.170779 + 0.637425i
\(646\) −381.192 −0.590081
\(647\) 873.903 + 873.903i 1.35070 + 1.35070i 0.884878 + 0.465822i \(0.154241\pi\)
0.465822 + 0.884878i \(0.345759\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 51.7655i 0.0797620i
\(650\) −216.541 125.004i −0.333139 0.192314i
\(651\) 216.177 0.332070
\(652\) −24.6561 24.6561i −0.0378160 0.0378160i
\(653\) −697.096 + 697.096i −1.06753 + 1.06753i −0.0699794 + 0.997548i \(0.522293\pi\)
−0.997548 + 0.0699794i \(0.977707\pi\)
\(654\) 160.982i 0.246150i
\(655\) −733.872 196.619i −1.12042 0.300182i
\(656\) −255.795 −0.389931
\(657\) 176.376 + 176.376i 0.268457 + 0.268457i
\(658\) 26.0561 26.0561i 0.0395990 0.0395990i
\(659\) 1089.85i 1.65380i −0.562352 0.826898i \(-0.690103\pi\)
0.562352 0.826898i \(-0.309897\pi\)
\(660\) 15.2726 + 26.4513i 0.0231403 + 0.0400777i
\(661\) −374.443 −0.566480 −0.283240 0.959049i \(-0.591409\pi\)
−0.283240 + 0.959049i \(0.591409\pi\)
\(662\) −179.754 179.754i −0.271532 0.271532i
\(663\) −104.238 + 104.238i −0.157222 + 0.157222i
\(664\) 275.689i 0.415194i
\(665\) 802.059 463.098i 1.20610 0.696388i
\(666\) −171.540 −0.257567
\(667\) 131.608 + 131.608i 0.197313 + 0.197313i
\(668\) −135.758 + 135.758i −0.203231 + 0.203231i
\(669\) 568.585i 0.849903i
\(670\) −36.2323 + 135.235i −0.0540780 + 0.201844i
\(671\) −96.3313 −0.143564
\(672\) 57.2987 + 57.2987i 0.0852659 + 0.0852659i
\(673\) 356.156 356.156i 0.529206 0.529206i −0.391130 0.920336i \(-0.627916\pi\)
0.920336 + 0.391130i \(0.127916\pi\)
\(674\) 236.743i 0.351251i
\(675\) −33.6284 125.476i −0.0498199 0.185890i
\(676\) −237.975 −0.352034
\(677\) −372.658 372.658i −0.550455 0.550455i 0.376117 0.926572i \(-0.377259\pi\)
−0.926572 + 0.376117i \(0.877259\pi\)
\(678\) −123.068 + 123.068i −0.181516 + 0.181516i
\(679\) 1005.43i 1.48074i
\(680\) 164.400 + 44.0461i 0.241765 + 0.0647737i
\(681\) −451.546 −0.663062
\(682\) 26.6126 + 26.6126i 0.0390214 + 0.0390214i
\(683\) 282.250 282.250i 0.413250 0.413250i −0.469619 0.882869i \(-0.655609\pi\)
0.882869 + 0.469619i \(0.155609\pi\)
\(684\) 134.382i 0.196464i
\(685\) −237.712 411.704i −0.347025 0.601028i
\(686\) −346.217 −0.504690
\(687\) 273.429 + 273.429i 0.398005 + 0.398005i
\(688\) −139.013 + 139.013i −0.202054 + 0.202054i
\(689\) 678.413i 0.984635i
\(690\) 50.8667 29.3697i 0.0737198 0.0425648i
\(691\) −560.128 −0.810605 −0.405303 0.914183i \(-0.632834\pi\)
−0.405303 + 0.914183i \(0.632834\pi\)
\(692\) 72.8871 + 72.8871i 0.105328 + 0.105328i
\(693\) −30.9380 + 30.9380i −0.0446436 + 0.0446436i
\(694\) 759.061i 1.09375i
\(695\) −191.232 + 713.764i −0.275153 + 1.02700i
\(696\) 190.124 0.273167
\(697\) −544.199 544.199i −0.780773 0.780773i
\(698\) −540.641 + 540.641i −0.774558 + 0.774558i
\(699\) 725.524i 1.03795i
\(700\) −399.422 + 107.048i −0.570602 + 0.152926i
\(701\) 149.533 0.213314 0.106657 0.994296i \(-0.465985\pi\)
0.106657 + 0.994296i \(0.465985\pi\)
\(702\) 36.7470 + 36.7470i 0.0523461 + 0.0523461i
\(703\) −640.327 + 640.327i −0.910850 + 0.910850i
\(704\) 14.1076i 0.0200392i
\(705\) −26.3550 7.06103i −0.0373830 0.0100157i
\(706\) −102.534 −0.145232
\(707\) −55.9469 55.9469i −0.0791328 0.0791328i
\(708\) 71.9042 71.9042i 0.101560 0.101560i
\(709\) 790.988i 1.11564i 0.829963 + 0.557819i \(0.188362\pi\)
−0.829963 + 0.557819i \(0.811638\pi\)
\(710\) −127.633 221.053i −0.179765 0.311342i
\(711\) −384.528 −0.540827
\(712\) −39.4577 39.4577i −0.0554181 0.0554181i
\(713\) 51.1769 51.1769i 0.0717769 0.0717769i
\(714\) 243.804i 0.341462i
\(715\) 54.0003 31.1790i 0.0755248 0.0436070i
\(716\) 192.341 0.268633
\(717\) −2.64245 2.64245i −0.00368542 0.00368542i
\(718\) 217.517 217.517i 0.302949 0.302949i
\(719\) 279.928i 0.389330i −0.980870 0.194665i \(-0.937638\pi\)
0.980870 0.194665i \(-0.0623620\pi\)
\(720\) 15.5276 57.9560i 0.0215661 0.0804944i
\(721\) 609.917 0.845932
\(722\) 140.622 + 140.622i 0.194767 + 0.194767i
\(723\) −166.653 + 166.653i −0.230502 + 0.230502i
\(724\) 408.660i 0.564447i
\(725\) −485.066 + 840.265i −0.669056 + 1.15899i
\(726\) 288.771 0.397756
\(727\) 738.912 + 738.912i 1.01639 + 1.01639i 0.999864 + 0.0165221i \(0.00525940\pi\)
0.0165221 + 0.999864i \(0.494741\pi\)
\(728\) 116.975 116.975i 0.160680 0.160680i
\(729\) 27.0000i 0.0370370i
\(730\) −567.892 152.150i −0.777934 0.208424i
\(731\) −591.497 −0.809161
\(732\) 133.808 + 133.808i 0.182797 + 0.182797i
\(733\) 709.411 709.411i 0.967819 0.967819i −0.0316790 0.999498i \(-0.510085\pi\)
0.999498 + 0.0316790i \(0.0100854\pi\)
\(734\) 782.186i 1.06565i
\(735\) −84.0032 145.489i −0.114290 0.197944i
\(736\) 27.1293 0.0368605
\(737\) −24.6891 24.6891i −0.0334995 0.0334995i
\(738\) −191.846 + 191.846i −0.259954 + 0.259954i
\(739\) 233.841i 0.316429i 0.987405 + 0.158214i \(0.0505737\pi\)
−0.987405 + 0.158214i \(0.949426\pi\)
\(740\) 350.149 202.171i 0.473174 0.273204i
\(741\) 274.340 0.370229
\(742\) −793.375 793.375i −1.06924 1.06924i
\(743\) −201.785 + 201.785i −0.271581 + 0.271581i −0.829736 0.558155i \(-0.811509\pi\)
0.558155 + 0.829736i \(0.311509\pi\)
\(744\) 73.9317i 0.0993706i
\(745\) 44.4749 166.001i 0.0596978 0.222820i
\(746\) −562.793 −0.754414
\(747\) 206.767 + 206.767i 0.276796 + 0.276796i
\(748\) −30.0136 + 30.0136i −0.0401251 + 0.0401251i
\(749\) 1465.98i 1.95725i
\(750\) 216.524 + 216.489i 0.288699 + 0.288651i
\(751\) 76.6521 0.102067 0.0510333 0.998697i \(-0.483749\pi\)
0.0510333 + 0.998697i \(0.483749\pi\)
\(752\) −8.91109 8.91109i −0.0118499 0.0118499i
\(753\) 235.123 235.123i 0.312248 0.312248i
\(754\) 388.138i 0.514772i
\(755\) 905.826 + 242.689i 1.19977 + 0.321442i
\(756\) 85.9481 0.113688
\(757\) −971.333 971.333i −1.28314 1.28314i −0.938874 0.344262i \(-0.888129\pi\)
−0.344262 0.938874i \(-0.611871\pi\)
\(758\) −450.647 + 450.647i −0.594521 + 0.594521i
\(759\) 14.6483i 0.0192995i
\(760\) −158.378 274.301i −0.208392 0.360922i
\(761\) 806.466 1.05975 0.529873 0.848077i \(-0.322240\pi\)
0.529873 + 0.848077i \(0.322240\pi\)
\(762\) −213.358 213.358i −0.279998 0.279998i
\(763\) 384.336 384.336i 0.503717 0.503717i
\(764\) 206.599i 0.270418i
\(765\) 156.335 90.2657i 0.204359 0.117994i
\(766\) 241.562 0.315354
\(767\) −146.792 146.792i −0.191385 0.191385i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 919.455i 1.19565i 0.801626 + 0.597825i \(0.203968\pi\)
−0.801626 + 0.597825i \(0.796032\pi\)
\(770\) 26.6885 99.6136i 0.0346603 0.129368i
\(771\) 246.956 0.320307
\(772\) 42.8181 + 42.8181i 0.0554639 + 0.0554639i
\(773\) 604.542 604.542i 0.782073 0.782073i −0.198107 0.980180i \(-0.563479\pi\)
0.980180 + 0.198107i \(0.0634794\pi\)
\(774\) 208.520i 0.269406i
\(775\) 326.746 + 188.623i 0.421607 + 0.243384i
\(776\) 343.851 0.443107
\(777\) 409.542 + 409.542i 0.527081 + 0.527081i
\(778\) 136.553 136.553i 0.175518 0.175518i
\(779\)