Properties

Label 690.3.k.a.277.18
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
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: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.18
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.41665 - 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 + 0.381912i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.41665 - 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 + 0.381912i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(1.96054 - 6.79384i) q^{10} +6.70911 q^{11} +(2.44949 + 2.44949i) q^{12} +(3.27903 - 3.27903i) q^{13} +0.763823i q^{14} +(-8.32072 - 2.40116i) q^{15} -4.00000 q^{16} +(-12.9760 - 12.9760i) q^{17} +(3.00000 - 3.00000i) q^{18} -18.6900i q^{19} +(8.75438 - 4.83330i) q^{20} +0.935489 q^{21} +(6.70911 + 6.70911i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-13.3196 + 21.1563i) q^{25} +6.55805 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-0.763823 + 0.763823i) q^{28} -43.2683i q^{29} +(-5.91956 - 10.7219i) q^{30} +14.8962 q^{31} +(-4.00000 - 4.00000i) q^{32} +(8.21695 - 8.21695i) q^{33} -25.9520i q^{34} +(0.748754 - 2.59465i) q^{35} +6.00000 q^{36} +(-7.77957 - 7.77957i) q^{37} +(18.6900 - 18.6900i) q^{38} -8.03194i q^{39} +(13.5877 + 3.92108i) q^{40} -19.9186 q^{41} +(0.935489 + 0.935489i) q^{42} +(41.2213 - 41.2213i) q^{43} +13.4182i q^{44} +(-13.1316 + 7.24995i) q^{45} -6.78233 q^{46} +(-31.7502 - 31.7502i) q^{47} +(-4.89898 + 4.89898i) q^{48} -48.7083i q^{49} +(-34.4759 + 7.83666i) q^{50} -31.7846 q^{51} +(6.55805 + 6.55805i) q^{52} +(13.9434 - 13.9434i) q^{53} -7.34847i q^{54} +(-16.2136 - 29.3671i) q^{55} -1.52765 q^{56} +(-22.8905 - 22.8905i) q^{57} +(43.2683 - 43.2683i) q^{58} -2.31643i q^{59} +(4.80233 - 16.6414i) q^{60} +22.8724 q^{61} +(14.8962 + 14.8962i) q^{62} +(1.14574 - 1.14574i) q^{63} -8.00000i q^{64} +(-22.2772 - 6.42867i) q^{65} +16.4339 q^{66} +(59.1642 + 59.1642i) q^{67} +(25.9520 - 25.9520i) q^{68} +8.30662i q^{69} +(3.34340 - 1.84589i) q^{70} +29.7588 q^{71} +(6.00000 + 6.00000i) q^{72} +(-73.2037 + 73.2037i) q^{73} -15.5591i q^{74} +(9.59791 + 42.2242i) q^{75} +37.3801 q^{76} +(2.56229 + 2.56229i) q^{77} +(8.03194 - 8.03194i) q^{78} +12.0428i q^{79} +(9.66660 + 17.5088i) q^{80} -9.00000 q^{81} +(-19.9186 - 19.9186i) q^{82} +(-12.8507 + 12.8507i) q^{83} +1.87098i q^{84} +(-25.4400 + 88.1569i) q^{85} +82.4425 q^{86} +(-52.9926 - 52.9926i) q^{87} +(-13.4182 + 13.4182i) q^{88} -42.0148i q^{89} +(-20.3815 - 5.88163i) q^{90} +2.50460 q^{91} +(-6.78233 - 6.78233i) q^{92} +(18.2441 - 18.2441i) q^{93} -63.5004i q^{94} +(-81.8099 + 45.1673i) q^{95} -9.79796 q^{96} +(8.47487 + 8.47487i) q^{97} +(48.7083 - 48.7083i) q^{98} -20.1273i 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
\(5\) −2.41665 4.37719i −0.483330 0.875438i
\(6\) 2.44949 0.408248
\(7\) 0.381912 + 0.381912i 0.0545588 + 0.0545588i 0.733860 0.679301i \(-0.237717\pi\)
−0.679301 + 0.733860i \(0.737717\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 1.96054 6.79384i 0.196054 0.679384i
\(11\) 6.70911 0.609919 0.304960 0.952365i \(-0.401357\pi\)
0.304960 + 0.952365i \(0.401357\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 3.27903 3.27903i 0.252233 0.252233i −0.569653 0.821885i \(-0.692922\pi\)
0.821885 + 0.569653i \(0.192922\pi\)
\(14\) 0.763823i 0.0545588i
\(15\) −8.32072 2.40116i −0.554715 0.160078i
\(16\) −4.00000 −0.250000
\(17\) −12.9760 12.9760i −0.763294 0.763294i 0.213622 0.976916i \(-0.431474\pi\)
−0.976916 + 0.213622i \(0.931474\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 18.6900i 0.983686i −0.870684 0.491843i \(-0.836323\pi\)
0.870684 0.491843i \(-0.163677\pi\)
\(20\) 8.75438 4.83330i 0.437719 0.241665i
\(21\) 0.935489 0.0445471
\(22\) 6.70911 + 6.70911i 0.304960 + 0.304960i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −13.3196 + 21.1563i −0.532785 + 0.846251i
\(26\) 6.55805 0.252233
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −0.763823 + 0.763823i −0.0272794 + 0.0272794i
\(29\) 43.2683i 1.49201i −0.665941 0.746004i \(-0.731970\pi\)
0.665941 0.746004i \(-0.268030\pi\)
\(30\) −5.91956 10.7219i −0.197319 0.357396i
\(31\) 14.8962 0.480523 0.240262 0.970708i \(-0.422767\pi\)
0.240262 + 0.970708i \(0.422767\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 8.21695 8.21695i 0.248998 0.248998i
\(34\) 25.9520i 0.763294i
\(35\) 0.748754 2.59465i 0.0213930 0.0741328i
\(36\) 6.00000 0.166667
\(37\) −7.77957 7.77957i −0.210259 0.210259i 0.594119 0.804377i \(-0.297501\pi\)
−0.804377 + 0.594119i \(0.797501\pi\)
\(38\) 18.6900 18.6900i 0.491843 0.491843i
\(39\) 8.03194i 0.205947i
\(40\) 13.5877 + 3.92108i 0.339692 + 0.0980271i
\(41\) −19.9186 −0.485819 −0.242910 0.970049i \(-0.578102\pi\)
−0.242910 + 0.970049i \(0.578102\pi\)
\(42\) 0.935489 + 0.935489i 0.0222735 + 0.0222735i
\(43\) 41.2213 41.2213i 0.958634 0.958634i −0.0405438 0.999178i \(-0.512909\pi\)
0.999178 + 0.0405438i \(0.0129090\pi\)
\(44\) 13.4182i 0.304960i
\(45\) −13.1316 + 7.24995i −0.291813 + 0.161110i
\(46\) −6.78233 −0.147442
\(47\) −31.7502 31.7502i −0.675536 0.675536i 0.283450 0.958987i \(-0.408521\pi\)
−0.958987 + 0.283450i \(0.908521\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 48.7083i 0.994047i
\(50\) −34.4759 + 7.83666i −0.689518 + 0.156733i
\(51\) −31.7846 −0.623227
\(52\) 6.55805 + 6.55805i 0.126116 + 0.126116i
\(53\) 13.9434 13.9434i 0.263083 0.263083i −0.563223 0.826305i \(-0.690439\pi\)
0.826305 + 0.563223i \(0.190439\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −16.2136 29.3671i −0.294792 0.533947i
\(56\) −1.52765 −0.0272794
\(57\) −22.8905 22.8905i −0.401588 0.401588i
\(58\) 43.2683 43.2683i 0.746004 0.746004i
\(59\) 2.31643i 0.0392616i −0.999807 0.0196308i \(-0.993751\pi\)
0.999807 0.0196308i \(-0.00624908\pi\)
\(60\) 4.80233 16.6414i 0.0800388 0.277357i
\(61\) 22.8724 0.374957 0.187479 0.982269i \(-0.439968\pi\)
0.187479 + 0.982269i \(0.439968\pi\)
\(62\) 14.8962 + 14.8962i 0.240262 + 0.240262i
\(63\) 1.14574 1.14574i 0.0181863 0.0181863i
\(64\) 8.00000i 0.125000i
\(65\) −22.2772 6.42867i −0.342726 0.0989026i
\(66\) 16.4339 0.248998
\(67\) 59.1642 + 59.1642i 0.883047 + 0.883047i 0.993843 0.110796i \(-0.0353400\pi\)
−0.110796 + 0.993843i \(0.535340\pi\)
\(68\) 25.9520 25.9520i 0.381647 0.381647i
\(69\) 8.30662i 0.120386i
\(70\) 3.34340 1.84589i 0.0477629 0.0263699i
\(71\) 29.7588 0.419138 0.209569 0.977794i \(-0.432794\pi\)
0.209569 + 0.977794i \(0.432794\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −73.2037 + 73.2037i −1.00279 + 1.00279i −0.00279431 + 0.999996i \(0.500889\pi\)
−0.999996 + 0.00279431i \(0.999111\pi\)
\(74\) 15.5591i 0.210259i
\(75\) 9.59791 + 42.2242i 0.127972 + 0.562989i
\(76\) 37.3801 0.491843
\(77\) 2.56229 + 2.56229i 0.0332765 + 0.0332765i
\(78\) 8.03194 8.03194i 0.102974 0.102974i
\(79\) 12.0428i 0.152440i 0.997091 + 0.0762202i \(0.0242852\pi\)
−0.997091 + 0.0762202i \(0.975715\pi\)
\(80\) 9.66660 + 17.5088i 0.120832 + 0.218860i
\(81\) −9.00000 −0.111111
\(82\) −19.9186 19.9186i −0.242910 0.242910i
\(83\) −12.8507 + 12.8507i −0.154827 + 0.154827i −0.780270 0.625443i \(-0.784918\pi\)
0.625443 + 0.780270i \(0.284918\pi\)
\(84\) 1.87098i 0.0222735i
\(85\) −25.4400 + 88.1569i −0.299294 + 1.03714i
\(86\) 82.4425 0.958634
\(87\) −52.9926 52.9926i −0.609110 0.609110i
\(88\) −13.4182 + 13.4182i −0.152480 + 0.152480i
\(89\) 42.0148i 0.472076i −0.971744 0.236038i \(-0.924151\pi\)
0.971744 0.236038i \(-0.0758490\pi\)
\(90\) −20.3815 5.88163i −0.226461 0.0653514i
\(91\) 2.50460 0.0275230
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 18.2441 18.2441i 0.196173 0.196173i
\(94\) 63.5004i 0.675536i
\(95\) −81.8099 + 45.1673i −0.861157 + 0.475445i
\(96\) −9.79796 −0.102062
\(97\) 8.47487 + 8.47487i 0.0873698 + 0.0873698i 0.749441 0.662071i \(-0.230322\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(98\) 48.7083 48.7083i 0.497023 0.497023i
\(99\) 20.1273i 0.203306i
\(100\) −42.3125 26.6392i −0.423125 0.266392i
\(101\) −36.8005 −0.364361 −0.182180 0.983265i \(-0.558316\pi\)
−0.182180 + 0.983265i \(0.558316\pi\)
\(102\) −31.7846 31.7846i −0.311614 0.311614i
\(103\) 30.2577 30.2577i 0.293764 0.293764i −0.544801 0.838565i \(-0.683395\pi\)
0.838565 + 0.544801i \(0.183395\pi\)
\(104\) 13.1161i 0.126116i
\(105\) −2.26075 4.09481i −0.0215309 0.0389982i
\(106\) 27.8867 0.263083
\(107\) 58.5497 + 58.5497i 0.547193 + 0.547193i 0.925628 0.378435i \(-0.123538\pi\)
−0.378435 + 0.925628i \(0.623538\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 156.152i 1.43258i 0.697801 + 0.716291i \(0.254162\pi\)
−0.697801 + 0.716291i \(0.745838\pi\)
\(110\) 13.1535 45.5806i 0.119577 0.414369i
\(111\) −19.0560 −0.171675
\(112\) −1.52765 1.52765i −0.0136397 0.0136397i
\(113\) 79.0970 79.0970i 0.699973 0.699973i −0.264431 0.964405i \(-0.585184\pi\)
0.964405 + 0.264431i \(0.0851842\pi\)
\(114\) 45.7811i 0.401588i
\(115\) 23.0390 + 6.64852i 0.200339 + 0.0578132i
\(116\) 86.5365 0.746004
\(117\) −9.83708 9.83708i −0.0840776 0.0840776i
\(118\) 2.31643 2.31643i 0.0196308 0.0196308i
\(119\) 9.91138i 0.0832889i
\(120\) 21.4438 11.8391i 0.178698 0.0986593i
\(121\) −75.9878 −0.627999
\(122\) 22.8724 + 22.8724i 0.187479 + 0.187479i
\(123\) −24.3952 + 24.3952i −0.198335 + 0.198335i
\(124\) 29.7924i 0.240262i
\(125\) 124.794 + 7.17521i 0.998351 + 0.0574016i
\(126\) 2.29147 0.0181863
\(127\) 132.249 + 132.249i 1.04133 + 1.04133i 0.999108 + 0.0422197i \(0.0134429\pi\)
0.0422197 + 0.999108i \(0.486557\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 100.971i 0.782721i
\(130\) −15.8485 28.7059i −0.121912 0.220814i
\(131\) 45.0132 0.343612 0.171806 0.985131i \(-0.445040\pi\)
0.171806 + 0.985131i \(0.445040\pi\)
\(132\) 16.4339 + 16.4339i 0.124499 + 0.124499i
\(133\) 7.13794 7.13794i 0.0536688 0.0536688i
\(134\) 118.328i 0.883047i
\(135\) −7.20349 + 24.9622i −0.0533592 + 0.184905i
\(136\) 51.9040 0.381647
\(137\) 48.0021 + 48.0021i 0.350380 + 0.350380i 0.860251 0.509871i \(-0.170307\pi\)
−0.509871 + 0.860251i \(0.670307\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 64.5350i 0.464281i 0.972682 + 0.232140i \(0.0745729\pi\)
−0.972682 + 0.232140i \(0.925427\pi\)
\(140\) 5.18929 + 1.49751i 0.0370664 + 0.0106965i
\(141\) −77.7718 −0.551573
\(142\) 29.7588 + 29.7588i 0.209569 + 0.209569i
\(143\) 21.9994 21.9994i 0.153842 0.153842i
\(144\) 12.0000i 0.0833333i
\(145\) −189.393 + 104.564i −1.30616 + 0.721132i
\(146\) −146.407 −1.00279
\(147\) −59.6552 59.6552i −0.405818 0.405818i
\(148\) 15.5591 15.5591i 0.105129 0.105129i
\(149\) 68.2371i 0.457967i 0.973430 + 0.228984i \(0.0735402\pi\)
−0.973430 + 0.228984i \(0.926460\pi\)
\(150\) −32.6263 + 51.8221i −0.217508 + 0.345481i
\(151\) 24.9568 0.165277 0.0826386 0.996580i \(-0.473665\pi\)
0.0826386 + 0.996580i \(0.473665\pi\)
\(152\) 37.3801 + 37.3801i 0.245922 + 0.245922i
\(153\) −38.9280 + 38.9280i −0.254431 + 0.254431i
\(154\) 5.12458i 0.0332765i
\(155\) −35.9989 65.2036i −0.232251 0.420668i
\(156\) 16.0639 0.102974
\(157\) −74.5026 74.5026i −0.474539 0.474539i 0.428841 0.903380i \(-0.358922\pi\)
−0.903380 + 0.428841i \(0.858922\pi\)
\(158\) −12.0428 + 12.0428i −0.0762202 + 0.0762202i
\(159\) 34.1541i 0.214806i
\(160\) −7.84217 + 27.1754i −0.0490136 + 0.169846i
\(161\) −2.59025 −0.0160885
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −188.851 + 188.851i −1.15859 + 1.15859i −0.173816 + 0.984778i \(0.555610\pi\)
−0.984778 + 0.173816i \(0.944390\pi\)
\(164\) 39.8372i 0.242910i
\(165\) −55.8246 16.1097i −0.338331 0.0976344i
\(166\) −25.7014 −0.154827
\(167\) −48.1591 48.1591i −0.288378 0.288378i 0.548061 0.836439i \(-0.315366\pi\)
−0.836439 + 0.548061i \(0.815366\pi\)
\(168\) −1.87098 + 1.87098i −0.0111368 + 0.0111368i
\(169\) 147.496i 0.872757i
\(170\) −113.597 + 62.7169i −0.668217 + 0.368923i
\(171\) −56.0701 −0.327895
\(172\) 82.4425 + 82.4425i 0.479317 + 0.479317i
\(173\) 189.177 189.177i 1.09351 1.09351i 0.0983603 0.995151i \(-0.468640\pi\)
0.995151 0.0983603i \(-0.0313598\pi\)
\(174\) 105.985i 0.609110i
\(175\) −13.1667 + 2.99291i −0.0752385 + 0.0171024i
\(176\) −26.8364 −0.152480
\(177\) −2.83704 2.83704i −0.0160285 0.0160285i
\(178\) 42.0148 42.0148i 0.236038 0.236038i
\(179\) 229.026i 1.27947i −0.768594 0.639737i \(-0.779043\pi\)
0.768594 0.639737i \(-0.220957\pi\)
\(180\) −14.4999 26.2631i −0.0805550 0.145906i
\(181\) 200.947 1.11020 0.555102 0.831782i \(-0.312679\pi\)
0.555102 + 0.831782i \(0.312679\pi\)
\(182\) 2.50460 + 2.50460i 0.0137615 + 0.0137615i
\(183\) 28.0128 28.0128i 0.153076 0.153076i
\(184\) 13.5647i 0.0737210i
\(185\) −15.2522 + 52.8532i −0.0824442 + 0.285693i
\(186\) 36.4881 0.196173
\(187\) −87.0575 87.0575i −0.465548 0.465548i
\(188\) 63.5004 63.5004i 0.337768 0.337768i
\(189\) 2.80647i 0.0148490i
\(190\) −126.977 36.6426i −0.668301 0.192856i
\(191\) −57.4984 −0.301039 −0.150519 0.988607i \(-0.548095\pi\)
−0.150519 + 0.988607i \(0.548095\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −72.1304 + 72.1304i −0.373733 + 0.373733i −0.868835 0.495102i \(-0.835131\pi\)
0.495102 + 0.868835i \(0.335131\pi\)
\(194\) 16.9497i 0.0873698i
\(195\) −35.1573 + 19.4104i −0.180294 + 0.0995404i
\(196\) 97.4166 0.497023
\(197\) 167.259 + 167.259i 0.849032 + 0.849032i 0.990012 0.140980i \(-0.0450254\pi\)
−0.140980 + 0.990012i \(0.545025\pi\)
\(198\) 20.1273 20.1273i 0.101653 0.101653i
\(199\) 146.363i 0.735493i 0.929926 + 0.367747i \(0.119871\pi\)
−0.929926 + 0.367747i \(0.880129\pi\)
\(200\) −15.6733 68.9518i −0.0783666 0.344759i
\(201\) 144.922 0.721005
\(202\) −36.8005 36.8005i −0.182180 0.182180i
\(203\) 16.5247 16.5247i 0.0814022 0.0814022i
\(204\) 63.5692i 0.311614i
\(205\) 48.1362 + 87.1875i 0.234811 + 0.425305i
\(206\) 60.5153 0.293764
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −13.1161 + 13.1161i −0.0630582 + 0.0630582i
\(209\) 125.394i 0.599969i
\(210\) 1.83407 6.35556i 0.00873364 0.0302646i
\(211\) 237.399 1.12511 0.562556 0.826759i \(-0.309818\pi\)
0.562556 + 0.826759i \(0.309818\pi\)
\(212\) 27.8867 + 27.8867i 0.131541 + 0.131541i
\(213\) 36.4469 36.4469i 0.171112 0.171112i
\(214\) 117.099i 0.547193i
\(215\) −280.051 80.8160i −1.30256 0.375888i
\(216\) 14.6969 0.0680414
\(217\) 5.68904 + 5.68904i 0.0262168 + 0.0262168i
\(218\) −156.152 + 156.152i −0.716291 + 0.716291i
\(219\) 179.312i 0.818775i
\(220\) 58.7341 32.4271i 0.266973 0.147396i
\(221\) −85.0973 −0.385056
\(222\) −19.0560 19.0560i −0.0858377 0.0858377i
\(223\) −259.517 + 259.517i −1.16375 + 1.16375i −0.180104 + 0.983648i \(0.557644\pi\)
−0.983648 + 0.180104i \(0.942356\pi\)
\(224\) 3.05529i 0.0136397i
\(225\) 63.4688 + 39.9588i 0.282084 + 0.177595i
\(226\) 158.194 0.699973
\(227\) −5.33385 5.33385i −0.0234971 0.0234971i 0.695261 0.718758i \(-0.255289\pi\)
−0.718758 + 0.695261i \(0.755289\pi\)
\(228\) 45.7811 45.7811i 0.200794 0.200794i
\(229\) 129.029i 0.563447i −0.959496 0.281724i \(-0.909094\pi\)
0.959496 0.281724i \(-0.0909061\pi\)
\(230\) 16.3905 + 29.6876i 0.0712631 + 0.129076i
\(231\) 6.27630 0.0271701
\(232\) 86.5365 + 86.5365i 0.373002 + 0.373002i
\(233\) −228.635 + 228.635i −0.981267 + 0.981267i −0.999828 0.0185604i \(-0.994092\pi\)
0.0185604 + 0.999828i \(0.494092\pi\)
\(234\) 19.6742i 0.0840776i
\(235\) −62.2476 + 215.706i −0.264884 + 0.917897i
\(236\) 4.63287 0.0196308
\(237\) 14.7494 + 14.7494i 0.0622336 + 0.0622336i
\(238\) 9.91138 9.91138i 0.0416444 0.0416444i
\(239\) 354.637i 1.48384i −0.670489 0.741919i \(-0.733916\pi\)
0.670489 0.741919i \(-0.266084\pi\)
\(240\) 33.2829 + 9.60466i 0.138679 + 0.0400194i
\(241\) 338.822 1.40590 0.702951 0.711238i \(-0.251865\pi\)
0.702951 + 0.711238i \(0.251865\pi\)
\(242\) −75.9878 75.9878i −0.313999 0.313999i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 45.7448i 0.187479i
\(245\) −213.206 + 117.711i −0.870227 + 0.480452i
\(246\) −48.7904 −0.198335
\(247\) −61.2851 61.2851i −0.248118 0.248118i
\(248\) −29.7924 + 29.7924i −0.120131 + 0.120131i
\(249\) 31.4776i 0.126416i
\(250\) 117.619 + 131.969i 0.470475 + 0.527876i
\(251\) −288.350 −1.14880 −0.574402 0.818573i \(-0.694765\pi\)
−0.574402 + 0.818573i \(0.694765\pi\)
\(252\) 2.29147 + 2.29147i 0.00909314 + 0.00909314i
\(253\) −22.7517 + 22.7517i −0.0899277 + 0.0899277i
\(254\) 264.497i 1.04133i
\(255\) 76.8122 + 139.127i 0.301224 + 0.545597i
\(256\) 16.0000 0.0625000
\(257\) 31.1551 + 31.1551i 0.121226 + 0.121226i 0.765117 0.643891i \(-0.222681\pi\)
−0.643891 + 0.765117i \(0.722681\pi\)
\(258\) 100.971 100.971i 0.391361 0.391361i
\(259\) 5.94222i 0.0229429i
\(260\) 12.8573 44.5544i 0.0494513 0.171363i
\(261\) −129.805 −0.497336
\(262\) 45.0132 + 45.0132i 0.171806 + 0.171806i
\(263\) −147.593 + 147.593i −0.561190 + 0.561190i −0.929645 0.368455i \(-0.879887\pi\)
0.368455 + 0.929645i \(0.379887\pi\)
\(264\) 32.8678i 0.124499i
\(265\) −94.7291 27.3366i −0.357468 0.103157i
\(266\) 14.2759 0.0536688
\(267\) −51.4574 51.4574i −0.192724 0.192724i
\(268\) −118.328 + 118.328i −0.441524 + 0.441524i
\(269\) 172.598i 0.641627i −0.947142 0.320813i \(-0.896044\pi\)
0.947142 0.320813i \(-0.103956\pi\)
\(270\) −32.1657 + 17.7587i −0.119132 + 0.0657729i
\(271\) 381.051 1.40609 0.703046 0.711144i \(-0.251823\pi\)
0.703046 + 0.711144i \(0.251823\pi\)
\(272\) 51.9040 + 51.9040i 0.190824 + 0.190824i
\(273\) 3.06749 3.06749i 0.0112362 0.0112362i
\(274\) 96.0042i 0.350380i
\(275\) −89.3628 + 141.940i −0.324956 + 0.516145i
\(276\) −16.6132 −0.0601929
\(277\) 156.346 + 156.346i 0.564426 + 0.564426i 0.930561 0.366136i \(-0.119319\pi\)
−0.366136 + 0.930561i \(0.619319\pi\)
\(278\) −64.5350 + 64.5350i −0.232140 + 0.232140i
\(279\) 44.6886i 0.160174i
\(280\) 3.69179 + 6.68680i 0.0131850 + 0.0238814i
\(281\) −29.4130 −0.104673 −0.0523363 0.998630i \(-0.516667\pi\)
−0.0523363 + 0.998630i \(0.516667\pi\)
\(282\) −77.7718 77.7718i −0.275787 0.275787i
\(283\) 147.441 147.441i 0.520995 0.520995i −0.396877 0.917872i \(-0.629906\pi\)
0.917872 + 0.396877i \(0.129906\pi\)
\(284\) 59.5176i 0.209569i
\(285\) −44.8779 + 155.515i −0.157466 + 0.545665i
\(286\) 43.9987 0.153842
\(287\) −7.60714 7.60714i −0.0265057 0.0265057i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 47.7533i 0.165236i
\(290\) −293.958 84.8293i −1.01365 0.292515i
\(291\) 20.7591 0.0713371
\(292\) −146.407 146.407i −0.501395 0.501395i
\(293\) 7.83296 7.83296i 0.0267336 0.0267336i −0.693614 0.720347i \(-0.743982\pi\)
0.720347 + 0.693614i \(0.243982\pi\)
\(294\) 119.310i 0.405818i
\(295\) −10.1395 + 5.59801i −0.0343711 + 0.0189763i
\(296\) 31.1183 0.105129
\(297\) −24.6508 24.6508i −0.0829995 0.0829995i
\(298\) −68.2371 + 68.2371i −0.228984 + 0.228984i
\(299\) 22.2394i 0.0743794i
\(300\) −84.4483 + 19.1958i −0.281494 + 0.0639861i
\(301\) 31.4858 0.104604
\(302\) 24.9568 + 24.9568i 0.0826386 + 0.0826386i
\(303\) −45.0712 + 45.0712i −0.148750 + 0.148750i
\(304\) 74.7602i 0.245922i
\(305\) −55.2745 100.117i −0.181228 0.328252i
\(306\) −77.8560 −0.254431
\(307\) −336.989 336.989i −1.09768 1.09768i −0.994681 0.103002i \(-0.967155\pi\)
−0.103002 0.994681i \(-0.532845\pi\)
\(308\) −5.12458 + 5.12458i −0.0166382 + 0.0166382i
\(309\) 74.1158i 0.239857i
\(310\) 29.2047 101.203i 0.0942086 0.326460i
\(311\) 17.7007 0.0569155 0.0284578 0.999595i \(-0.490940\pi\)
0.0284578 + 0.999595i \(0.490940\pi\)
\(312\) 16.0639 + 16.0639i 0.0514868 + 0.0514868i
\(313\) −386.409 + 386.409i −1.23453 + 1.23453i −0.272331 + 0.962204i \(0.587794\pi\)
−0.962204 + 0.272331i \(0.912206\pi\)
\(314\) 149.005i 0.474539i
\(315\) −7.78394 2.24626i −0.0247109 0.00713099i
\(316\) −24.0856 −0.0762202
\(317\) 103.379 + 103.379i 0.326118 + 0.326118i 0.851108 0.524990i \(-0.175931\pi\)
−0.524990 + 0.851108i \(0.675931\pi\)
\(318\) 34.1541 34.1541i 0.107403 0.107403i
\(319\) 290.292i 0.910005i
\(320\) −35.0175 + 19.3332i −0.109430 + 0.0604162i
\(321\) 143.417 0.446781
\(322\) −2.59025 2.59025i −0.00804426 0.00804426i
\(323\) −242.522 + 242.522i −0.750842 + 0.750842i
\(324\) 18.0000i 0.0555556i
\(325\) 25.6966 + 113.047i 0.0790665 + 0.347838i
\(326\) −377.702 −1.15859
\(327\) 191.246 + 191.246i 0.584849 + 0.584849i
\(328\) 39.8372 39.8372i 0.121455 0.121455i
\(329\) 24.2516i 0.0737129i
\(330\) −39.7150 71.9343i −0.120348 0.217983i
\(331\) −148.156 −0.447602 −0.223801 0.974635i \(-0.571847\pi\)
−0.223801 + 0.974635i \(0.571847\pi\)
\(332\) −25.7014 25.7014i −0.0774137 0.0774137i
\(333\) −23.3387 + 23.3387i −0.0700862 + 0.0700862i
\(334\) 96.3182i 0.288378i
\(335\) 115.994 401.952i 0.346250 1.19986i
\(336\) −3.74196 −0.0111368
\(337\) 342.881 + 342.881i 1.01745 + 1.01745i 0.999845 + 0.0176066i \(0.00560466\pi\)
0.0176066 + 0.999845i \(0.494395\pi\)
\(338\) −147.496 + 147.496i −0.436379 + 0.436379i
\(339\) 193.747i 0.571526i
\(340\) −176.314 50.8800i −0.518570 0.149647i
\(341\) 99.9404 0.293080
\(342\) −56.0701 56.0701i −0.163948 0.163948i
\(343\) 37.3159 37.3159i 0.108793 0.108793i
\(344\) 164.885i 0.479317i
\(345\) 36.3597 20.0742i 0.105390 0.0581861i
\(346\) 378.355 1.09351
\(347\) −160.663 160.663i −0.463005 0.463005i 0.436634 0.899639i \(-0.356170\pi\)
−0.899639 + 0.436634i \(0.856170\pi\)
\(348\) 105.985 105.985i 0.304555 0.304555i
\(349\) 20.4812i 0.0586855i −0.999569 0.0293427i \(-0.990659\pi\)
0.999569 0.0293427i \(-0.00934142\pi\)
\(350\) −16.1597 10.1738i −0.0461704 0.0290681i
\(351\) −24.0958 −0.0686491
\(352\) −26.8364 26.8364i −0.0762399 0.0762399i
\(353\) −260.115 + 260.115i −0.736869 + 0.736869i −0.971971 0.235102i \(-0.924458\pi\)
0.235102 + 0.971971i \(0.424458\pi\)
\(354\) 5.67408i 0.0160285i
\(355\) −71.9166 130.260i −0.202582 0.366930i
\(356\) 84.0295 0.236038
\(357\) −12.1389 12.1389i −0.0340025 0.0340025i
\(358\) 229.026 229.026i 0.639737 0.639737i
\(359\) 549.920i 1.53181i −0.642953 0.765905i \(-0.722291\pi\)
0.642953 0.765905i \(-0.277709\pi\)
\(360\) 11.7633 40.7630i 0.0326757 0.113231i
\(361\) 11.6825 0.0323614
\(362\) 200.947 + 200.947i 0.555102 + 0.555102i
\(363\) −93.0657 + 93.0657i −0.256379 + 0.256379i
\(364\) 5.00919i 0.0137615i
\(365\) 497.334 + 143.519i 1.36256 + 0.393203i
\(366\) 56.0257 0.153076
\(367\) 73.6271 + 73.6271i 0.200619 + 0.200619i 0.800265 0.599646i \(-0.204692\pi\)
−0.599646 + 0.800265i \(0.704692\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 59.7558i 0.161940i
\(370\) −68.1053 + 37.6010i −0.184068 + 0.101624i
\(371\) 10.6503 0.0287069
\(372\) 36.4881 + 36.4881i 0.0980864 + 0.0980864i
\(373\) −151.835 + 151.835i −0.407063 + 0.407063i −0.880713 0.473650i \(-0.842936\pi\)
0.473650 + 0.880713i \(0.342936\pi\)
\(374\) 174.115i 0.465548i
\(375\) 161.628 144.053i 0.431009 0.384141i
\(376\) 127.001 0.337768
\(377\) −141.878 141.878i −0.376334 0.376334i
\(378\) 2.80647 2.80647i 0.00742451 0.00742451i
\(379\) 0.463933i 0.00122410i −1.00000 0.000612049i \(-0.999805\pi\)
1.00000 0.000612049i \(-0.000194821\pi\)
\(380\) −90.3345 163.620i −0.237722 0.430578i
\(381\) 323.942 0.850241
\(382\) −57.4984 57.4984i −0.150519 0.150519i
\(383\) 148.165 148.165i 0.386853 0.386853i −0.486710 0.873563i \(-0.661803\pi\)
0.873563 + 0.486710i \(0.161803\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 5.02347 17.4078i 0.0130480 0.0452150i
\(386\) −144.261 −0.373733
\(387\) −123.664 123.664i −0.319545 0.319545i
\(388\) −16.9497 + 16.9497i −0.0436849 + 0.0436849i
\(389\) 512.669i 1.31791i −0.752180 0.658957i \(-0.770998\pi\)
0.752180 0.658957i \(-0.229002\pi\)
\(390\) −54.5677 15.7470i −0.139917 0.0403768i
\(391\) 88.0075 0.225083
\(392\) 97.4166 + 97.4166i 0.248512 + 0.248512i
\(393\) 55.1296 55.1296i 0.140279 0.140279i
\(394\) 334.519i 0.849032i
\(395\) 52.7136 29.1032i 0.133452 0.0736790i
\(396\) 40.2547 0.101653
\(397\) 190.235 + 190.235i 0.479181 + 0.479181i 0.904870 0.425688i \(-0.139968\pi\)
−0.425688 + 0.904870i \(0.639968\pi\)
\(398\) −146.363 + 146.363i −0.367747 + 0.367747i
\(399\) 17.4843i 0.0438204i
\(400\) 53.2785 84.6251i 0.133196 0.211563i
\(401\) 351.265 0.875972 0.437986 0.898982i \(-0.355692\pi\)
0.437986 + 0.898982i \(0.355692\pi\)
\(402\) 144.922 + 144.922i 0.360503 + 0.360503i
\(403\) 48.8451 48.8451i 0.121204 0.121204i
\(404\) 73.6009i 0.182180i
\(405\) 21.7498 + 39.3947i 0.0537033 + 0.0972709i
\(406\) 33.0493 0.0814022
\(407\) −52.1940 52.1940i −0.128241 0.128241i
\(408\) 63.5692 63.5692i 0.155807 0.155807i
\(409\) 648.532i 1.58565i −0.609447 0.792827i \(-0.708608\pi\)
0.609447 0.792827i \(-0.291392\pi\)
\(410\) −39.0512 + 135.324i −0.0952469 + 0.330058i
\(411\) 117.581 0.286084
\(412\) 60.5153 + 60.5153i 0.146882 + 0.146882i
\(413\) 0.884673 0.884673i 0.00214207 0.00214207i
\(414\) 20.3470i 0.0491473i
\(415\) 87.3055 + 25.1943i 0.210375 + 0.0607092i
\(416\) −26.2322 −0.0630582
\(417\) 79.0390 + 79.0390i 0.189542 + 0.189542i
\(418\) 125.394 125.394i 0.299985 0.299985i
\(419\) 331.895i 0.792113i 0.918226 + 0.396056i \(0.129622\pi\)
−0.918226 + 0.396056i \(0.870378\pi\)
\(420\) 8.18963 4.52150i 0.0194991 0.0107655i
\(421\) 695.014 1.65086 0.825432 0.564501i \(-0.190931\pi\)
0.825432 + 0.564501i \(0.190931\pi\)
\(422\) 237.399 + 237.399i 0.562556 + 0.562556i
\(423\) −95.2506 + 95.2506i −0.225179 + 0.225179i
\(424\) 55.7735i 0.131541i
\(425\) 447.359 101.689i 1.05261 0.239267i
\(426\) 72.8939 0.171112
\(427\) 8.73523 + 8.73523i 0.0204572 + 0.0204572i
\(428\) −117.099 + 117.099i −0.273597 + 0.273597i
\(429\) 53.8872i 0.125611i
\(430\) −199.235 360.867i −0.463336 0.839225i
\(431\) 196.821 0.456660 0.228330 0.973584i \(-0.426673\pi\)
0.228330 + 0.973584i \(0.426673\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 314.673 314.673i 0.726727 0.726727i −0.243240 0.969966i \(-0.578210\pi\)
0.969966 + 0.243240i \(0.0782102\pi\)
\(434\) 11.3781i 0.0262168i
\(435\) −103.894 + 360.023i −0.238837 + 0.827639i
\(436\) −312.303 −0.716291
\(437\) 63.3810 + 63.3810i 0.145037 + 0.145037i
\(438\) −179.312 + 179.312i −0.409387 + 0.409387i
\(439\) 383.648i 0.873914i −0.899482 0.436957i \(-0.856056\pi\)
0.899482 0.436957i \(-0.143944\pi\)
\(440\) 91.1613 + 26.3070i 0.207185 + 0.0597886i
\(441\) −146.125 −0.331349
\(442\) −85.0973 85.0973i −0.192528 0.192528i
\(443\) −14.3200 + 14.3200i −0.0323251 + 0.0323251i −0.723085 0.690759i \(-0.757276\pi\)
0.690759 + 0.723085i \(0.257276\pi\)
\(444\) 38.1120i 0.0858377i
\(445\) −183.907 + 101.535i −0.413273 + 0.228168i
\(446\) −519.033 −1.16375
\(447\) 83.5731 + 83.5731i 0.186964 + 0.186964i
\(448\) 3.05529 3.05529i 0.00681985 0.00681985i
\(449\) 383.606i 0.854355i −0.904168 0.427178i \(-0.859508\pi\)
0.904168 0.427178i \(-0.140492\pi\)
\(450\) 23.5100 + 103.428i 0.0522444 + 0.229839i
\(451\) −133.636 −0.296310
\(452\) 158.194 + 158.194i 0.349987 + 0.349987i
\(453\) 30.5658 30.5658i 0.0674741 0.0674741i
\(454\) 10.6677i 0.0234971i
\(455\) −6.05273 10.9631i −0.0133027 0.0240947i
\(456\) 91.5621 0.200794
\(457\) 512.331 + 512.331i 1.12107 + 1.12107i 0.991580 + 0.129494i \(0.0413352\pi\)
0.129494 + 0.991580i \(0.458665\pi\)
\(458\) 129.029 129.029i 0.281724 0.281724i
\(459\) 95.3538i 0.207742i
\(460\) −13.2970 + 46.0781i −0.0289066 + 0.100170i
\(461\) 327.942 0.711370 0.355685 0.934606i \(-0.384248\pi\)
0.355685 + 0.934606i \(0.384248\pi\)
\(462\) 6.27630 + 6.27630i 0.0135851 + 0.0135851i
\(463\) 575.851 575.851i 1.24374 1.24374i 0.285300 0.958438i \(-0.407907\pi\)
0.958438 0.285300i \(-0.0920931\pi\)
\(464\) 173.073i 0.373002i
\(465\) −123.947 35.7683i −0.266553 0.0769210i
\(466\) −457.271 −0.981267
\(467\) 359.804 + 359.804i 0.770459 + 0.770459i 0.978187 0.207728i \(-0.0666068\pi\)
−0.207728 + 0.978187i \(0.566607\pi\)
\(468\) 19.6742 19.6742i 0.0420388 0.0420388i
\(469\) 45.1910i 0.0963560i
\(470\) −277.954 + 153.458i −0.591391 + 0.326507i
\(471\) −182.493 −0.387460
\(472\) 4.63287 + 4.63287i 0.00981540 + 0.00981540i
\(473\) 276.558 276.558i 0.584689 0.584689i
\(474\) 29.4987i 0.0622336i
\(475\) 395.412 + 248.944i 0.832445 + 0.524093i
\(476\) 19.8228 0.0416444
\(477\) −41.8301 41.8301i −0.0876942 0.0876942i
\(478\) 354.637 354.637i 0.741919 0.741919i
\(479\) 880.306i 1.83780i −0.394490 0.918900i \(-0.629079\pi\)
0.394490 0.918900i \(-0.370921\pi\)
\(480\) 23.6782 + 42.8875i 0.0493296 + 0.0893490i
\(481\) −51.0188 −0.106068
\(482\) 338.822 + 338.822i 0.702951 + 0.702951i
\(483\) −3.17240 + 3.17240i −0.00656811 + 0.00656811i
\(484\) 151.976i 0.313999i
\(485\) 16.6153 57.5769i 0.0342584 0.118715i
\(486\) −22.0454 −0.0453609
\(487\) −500.051 500.051i −1.02680 1.02680i −0.999631 0.0271685i \(-0.991351\pi\)
−0.0271685 0.999631i \(-0.508649\pi\)
\(488\) −45.7448 + 45.7448i −0.0937393 + 0.0937393i
\(489\) 462.588i 0.945988i
\(490\) −330.916 95.4947i −0.675339 0.194887i
\(491\) −224.036 −0.456286 −0.228143 0.973628i \(-0.573265\pi\)
−0.228143 + 0.973628i \(0.573265\pi\)
\(492\) −48.7904 48.7904i −0.0991674 0.0991674i
\(493\) −561.449 + 561.449i −1.13884 + 1.13884i
\(494\) 122.570i 0.248118i
\(495\) −88.1012 + 48.6407i −0.177982 + 0.0982641i
\(496\) −59.5849 −0.120131
\(497\) 11.3652 + 11.3652i 0.0228677 + 0.0228677i
\(498\) −31.4776 + 31.4776i −0.0632081 + 0.0632081i
\(499\) 74.3281i 0.148954i −0.997223 0.0744771i \(-0.976271\pi\)
0.997223 0.0744771i \(-0.0237288\pi\)
\(500\) −14.3504 + 249.588i −0.0287008 + 0.499176i
\(501\) −117.965 −0.235460
\(502\) −288.350 288.350i −0.574402 0.574402i
\(503\) 433.764 433.764i 0.862354 0.862354i −0.129257 0.991611i \(-0.541259\pi\)
0.991611 + 0.129257i \(0.0412592\pi\)
\(504\) 4.58294i 0.00909314i
\(505\) 88.9338 + 161.083i 0.176107 + 0.318976i
\(506\) −45.5034 −0.0899277
\(507\) 180.645 + 180.645i 0.356302 + 0.356302i
\(508\) −264.497 + 264.497i −0.520664 + 0.520664i
\(509\) 439.146i 0.862763i −0.902170 0.431381i \(-0.858026\pi\)
0.902170 0.431381i \(-0.141974\pi\)
\(510\) −62.3150 + 215.939i −0.122186 + 0.423411i
\(511\) −55.9147 −0.109422
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −68.6716 + 68.6716i −0.133863 + 0.133863i
\(514\) 62.3103i 0.121226i
\(515\) −205.566 59.3214i −0.399157 0.115187i
\(516\) 201.942 0.391361
\(517\) −213.016 213.016i −0.412023 0.412023i
\(518\) 5.94222 5.94222i 0.0114715 0.0114715i
\(519\) 463.388i 0.892848i
\(520\) 57.4117 31.6970i 0.110407 0.0609558i
\(521\) 564.612 1.08371 0.541855 0.840472i \(-0.317722\pi\)
0.541855 + 0.840472i \(0.317722\pi\)
\(522\) −129.805 129.805i −0.248668 0.248668i
\(523\) −178.399 + 178.399i −0.341107 + 0.341107i −0.856783 0.515676i \(-0.827541\pi\)
0.515676 + 0.856783i \(0.327541\pi\)
\(524\) 90.0263i 0.171806i
\(525\) −12.4603 + 19.7915i −0.0237340 + 0.0376980i
\(526\) −295.186 −0.561190
\(527\) −193.293 193.293i −0.366781 0.366781i
\(528\) −32.8678 + 32.8678i −0.0622496 + 0.0622496i
\(529\) 23.0000i 0.0434783i
\(530\) −67.3925 122.066i −0.127156 0.230313i
\(531\) −6.94930 −0.0130872
\(532\) 14.2759 + 14.2759i 0.0268344 + 0.0268344i
\(533\) −65.3136 + 65.3136i −0.122540 + 0.122540i
\(534\) 102.915i 0.192724i
\(535\) 114.789 397.777i 0.214559 0.743509i
\(536\) −236.657 −0.441524
\(537\) −280.498 280.498i −0.522343 0.522343i
\(538\) 172.598 172.598i 0.320813 0.320813i
\(539\) 326.789i 0.606288i
\(540\) −49.9243 14.4070i −0.0924525 0.0266796i
\(541\) 671.336 1.24092 0.620459 0.784239i \(-0.286946\pi\)
0.620459 + 0.784239i \(0.286946\pi\)
\(542\) 381.051 + 381.051i 0.703046 + 0.703046i
\(543\) 246.109 246.109i 0.453239 0.453239i
\(544\) 103.808i 0.190824i
\(545\) 683.505 377.363i 1.25414 0.692410i
\(546\) 6.13498 0.0112362
\(547\) −364.741 364.741i −0.666803 0.666803i 0.290172 0.956975i \(-0.406288\pi\)
−0.956975 + 0.290172i \(0.906288\pi\)
\(548\) −96.0042 + 96.0042i −0.175190 + 0.175190i
\(549\) 68.6172i 0.124986i
\(550\) −231.303 + 52.5770i −0.420550 + 0.0955946i
\(551\) −808.685 −1.46767
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −4.59929 + 4.59929i −0.00831697 + 0.00831697i
\(554\) 312.692i 0.564426i
\(555\) 46.0516 + 83.4117i 0.0829759 + 0.150291i
\(556\) −129.070 −0.232140
\(557\) 475.919 + 475.919i 0.854433 + 0.854433i 0.990675 0.136243i \(-0.0435028\pi\)
−0.136243 + 0.990675i \(0.543503\pi\)
\(558\) 44.6886 44.6886i 0.0800872 0.0800872i
\(559\) 270.331i 0.483598i
\(560\) −2.99502 + 10.3786i −0.00534824 + 0.0185332i
\(561\) −213.246 −0.380118
\(562\) −29.4130 29.4130i −0.0523363 0.0523363i
\(563\) 145.318 145.318i 0.258114 0.258114i −0.566172 0.824287i \(-0.691576\pi\)
0.824287 + 0.566172i \(0.191576\pi\)
\(564\) 155.544i 0.275787i
\(565\) −537.372 155.073i −0.951102 0.274466i
\(566\) 294.883 0.520995
\(567\) −3.43721 3.43721i −0.00606209 0.00606209i
\(568\) −59.5176 + 59.5176i −0.104785 + 0.104785i
\(569\) 265.620i 0.466820i 0.972378 + 0.233410i \(0.0749884\pi\)
−0.972378 + 0.233410i \(0.925012\pi\)
\(570\) −200.392 + 110.637i −0.351566 + 0.194100i
\(571\) 624.384 1.09349 0.546746 0.837298i \(-0.315866\pi\)
0.546746 + 0.837298i \(0.315866\pi\)
\(572\) 43.9987 + 43.9987i 0.0769208 + 0.0769208i
\(573\) −70.4209 + 70.4209i −0.122899 + 0.122899i
\(574\) 15.2143i 0.0265057i
\(575\) −26.5754 116.913i −0.0462181 0.203328i
\(576\) −24.0000 −0.0416667
\(577\) −281.919 281.919i −0.488595 0.488595i 0.419268 0.907863i \(-0.362287\pi\)
−0.907863 + 0.419268i \(0.862287\pi\)
\(578\) −47.7533 + 47.7533i −0.0826182 + 0.0826182i
\(579\) 176.683i 0.305151i
\(580\) −209.128 378.787i −0.360566 0.653081i
\(581\) −9.81565 −0.0168944
\(582\) 20.7591 + 20.7591i 0.0356686 + 0.0356686i
\(583\) 93.5476 93.5476i 0.160459 0.160459i
\(584\) 292.815i 0.501395i
\(585\) −19.2860 + 66.8315i −0.0329675 + 0.114242i
\(586\) 15.6659 0.0267336
\(587\) −5.58217 5.58217i −0.00950967 0.00950967i 0.702336 0.711846i \(-0.252140\pi\)
−0.711846 + 0.702336i \(0.752140\pi\)
\(588\) 119.310 119.310i 0.202909 0.202909i
\(589\) 278.411i 0.472684i
\(590\) −15.7375 4.54147i −0.0266737 0.00769740i
\(591\) 409.700 0.693232
\(592\) 31.1183 + 31.1183i 0.0525647 + 0.0525647i
\(593\) −494.483 + 494.483i −0.833866 + 0.833866i −0.988043 0.154177i \(-0.950727\pi\)
0.154177 + 0.988043i \(0.450727\pi\)
\(594\) 49.3017i 0.0829995i
\(595\) −43.3840 + 23.9523i −0.0729143 + 0.0402560i
\(596\) −136.474 −0.228984
\(597\) 179.258 + 179.258i 0.300264 + 0.300264i
\(598\) −22.2394 + 22.2394i −0.0371897 + 0.0371897i
\(599\) 79.8683i 0.133336i 0.997775 + 0.0666680i \(0.0212368\pi\)
−0.997775 + 0.0666680i \(0.978763\pi\)
\(600\) −103.644 65.2525i −0.172740 0.108754i
\(601\) −676.719 −1.12599 −0.562995 0.826461i \(-0.690351\pi\)
−0.562995 + 0.826461i \(0.690351\pi\)
\(602\) 31.4858 + 31.4858i 0.0523019 + 0.0523019i
\(603\) 177.493 177.493i 0.294349 0.294349i
\(604\) 49.9137i 0.0826386i
\(605\) 183.636 + 332.613i 0.303530 + 0.549774i
\(606\) −90.1423 −0.148750
\(607\) −641.010 641.010i −1.05603 1.05603i −0.998334 0.0576959i \(-0.981625\pi\)
−0.0576959 0.998334i \(-0.518375\pi\)
\(608\) −74.7602 + 74.7602i −0.122961 + 0.122961i
\(609\) 40.4770i 0.0664647i
\(610\) 44.8423 155.391i 0.0735119 0.254740i
\(611\) −208.220 −0.340785
\(612\) −77.8560 77.8560i −0.127216 0.127216i
\(613\) −781.053 + 781.053i −1.27415 + 1.27415i −0.330257 + 0.943891i \(0.607136\pi\)
−0.943891 + 0.330257i \(0.892864\pi\)
\(614\) 673.978i 1.09768i
\(615\) 165.737 + 47.8278i 0.269491 + 0.0777688i
\(616\) −10.2492 −0.0166382
\(617\) 181.860 + 181.860i 0.294749 + 0.294749i 0.838953 0.544204i \(-0.183168\pi\)
−0.544204 + 0.838953i \(0.683168\pi\)
\(618\) 74.1158 74.1158i 0.119928 0.119928i
\(619\) 907.156i 1.46552i −0.680488 0.732759i \(-0.738232\pi\)
0.680488 0.732759i \(-0.261768\pi\)
\(620\) 130.407 71.9979i 0.210334 0.116126i
\(621\) 24.9199 0.0401286
\(622\) 17.7007 + 17.7007i 0.0284578 + 0.0284578i
\(623\) 16.0459 16.0459i 0.0257559 0.0257559i
\(624\) 32.1278i 0.0514868i
\(625\) −270.176 563.587i −0.432281 0.901739i
\(626\) −772.819 −1.23453
\(627\) −153.575 153.575i −0.244936 0.244936i
\(628\) 149.005 149.005i 0.237270 0.237270i
\(629\) 201.895i 0.320978i
\(630\) −5.53768 10.0302i −0.00878997 0.0159210i
\(631\) −362.814 −0.574983 −0.287492 0.957783i \(-0.592821\pi\)
−0.287492 + 0.957783i \(0.592821\pi\)
\(632\) −24.0856 24.0856i −0.0381101 0.0381101i
\(633\) 290.753 290.753i 0.459325 0.459325i
\(634\) 206.759i 0.326118i
\(635\) 259.279 898.476i 0.408314 1.41492i
\(636\) 68.3083 0.107403
\(637\) −159.716 159.716i −0.250731 0.250731i
\(638\) 290.292 290.292i 0.455002 0.455002i
\(639\) 89.2764i 0.139713i
\(640\) −54.3507 15.6843i −0.0849230 0.0245068i
\(641\) −479.570 −0.748158 −0.374079 0.927397i \(-0.622041\pi\)
−0.374079 + 0.927397i \(0.622041\pi\)
\(642\) 143.417 + 143.417i 0.223391 + 0.223391i
\(643\) −131.420 + 131.420i −0.204386 + 0.204386i −0.801876 0.597490i \(-0.796165\pi\)
0.597490 + 0.801876i \(0.296165\pi\)
\(644\) 5.18050i 0.00804426i
\(645\) −441.970 + 244.012i −0.685224 + 0.378313i
\(646\) −485.044 −0.750842
\(647\) 508.219 + 508.219i 0.785500 + 0.785500i 0.980753 0.195253i \(-0.0625526\pi\)
−0.195253 + 0.980753i \(0.562553\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 15.5412i 0.0239464i
\(650\) −87.3507 + 138.744i −0.134386 + 0.213452i
\(651\) 13.9352 0.0214059
\(652\) −377.702 377.702i −0.579297 0.579297i
\(653\) −390.519 + 390.519i −0.598039 + 0.598039i −0.939790 0.341752i \(-0.888980\pi\)
0.341752 + 0.939790i \(0.388980\pi\)
\(654\) 382.492i 0.584849i
\(655\) −108.781 197.031i −0.166078 0.300811i
\(656\) 79.6743 0.121455
\(657\) 219.611 + 219.611i 0.334263 + 0.334263i
\(658\) 24.2516 24.2516i 0.0368565 0.0368565i
\(659\) 958.180i 1.45399i 0.686643 + 0.726995i \(0.259084\pi\)
−0.686643 + 0.726995i \(0.740916\pi\)
\(660\) 32.2194 111.649i 0.0488172 0.169166i
\(661\) 337.049 0.509908 0.254954 0.966953i \(-0.417940\pi\)
0.254954 + 0.966953i \(0.417940\pi\)
\(662\) −148.156 148.156i −0.223801 0.223801i
\(663\) −104.222 + 104.222i −0.157198 + 0.157198i
\(664\) 51.4027i 0.0774137i
\(665\) −48.4941 13.9942i −0.0729234 0.0210440i
\(666\) −46.6774 −0.0700862
\(667\) 146.730 + 146.730i 0.219985 + 0.219985i
\(668\) 96.3182 96.3182i 0.144189 0.144189i
\(669\) 635.683i 0.950199i
\(670\) 517.946 285.958i 0.773054 0.426803i
\(671\) 153.453 0.228694
\(672\) −3.74196 3.74196i −0.00556839 0.00556839i
\(673\) −268.654 + 268.654i −0.399188 + 0.399188i −0.877947 0.478758i \(-0.841087\pi\)
0.478758 + 0.877947i \(0.341087\pi\)
\(674\) 685.762i 1.01745i
\(675\) 126.672 28.7937i 0.187663 0.0426574i
\(676\) −294.992 −0.436379
\(677\) 252.012 + 252.012i 0.372248 + 0.372248i 0.868295 0.496048i \(-0.165216\pi\)
−0.496048 + 0.868295i \(0.665216\pi\)
\(678\) 193.747 193.747i 0.285763 0.285763i
\(679\) 6.47330i 0.00953358i
\(680\) −125.434 227.194i −0.184461 0.334109i
\(681\) −13.0652 −0.0191853
\(682\) 99.9404 + 99.9404i 0.146540 + 0.146540i
\(683\) −22.9869 + 22.9869i −0.0336558 + 0.0336558i −0.723734 0.690079i \(-0.757576\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(684\) 112.140i 0.163948i
\(685\) 94.1101 326.119i 0.137387 0.476085i
\(686\) 74.6319 0.108793
\(687\) −158.028 158.028i −0.230026 0.230026i
\(688\) −164.885 + 164.885i −0.239658 + 0.239658i
\(689\) 91.4414i 0.132716i
\(690\) 56.4339 + 16.2855i 0.0817882 + 0.0236022i
\(691\) −387.581 −0.560898 −0.280449 0.959869i \(-0.590483\pi\)
−0.280449 + 0.959869i \(0.590483\pi\)
\(692\) 378.355 + 378.355i 0.546756 + 0.546756i
\(693\) 7.68686 7.68686i 0.0110922 0.0110922i
\(694\) 321.326i 0.463005i
\(695\) 282.482 155.959i 0.406449 0.224401i
\(696\) 211.970 0.304555
\(697\) 258.464 + 258.464i 0.370823 + 0.370823i
\(698\) 20.4812 20.4812i 0.0293427 0.0293427i
\(699\) 560.040i 0.801201i
\(700\) −5.98582 26.3335i −0.00855118 0.0376193i
\(701\) −151.713 −0.216424 −0.108212 0.994128i \(-0.534513\pi\)
−0.108212 + 0.994128i \(0.534513\pi\)
\(702\) −24.0958 24.0958i −0.0343245 0.0343245i
\(703\) −145.400 + 145.400i −0.206829 + 0.206829i
\(704\) 53.6729i 0.0762399i
\(705\) 187.947 + 340.422i 0.266592 + 0.482868i
\(706\) −520.230 −0.736869
\(707\) −14.0545 14.0545i −0.0198791 0.0198791i
\(708\) 5.67408 5.67408i 0.00801424 0.00801424i
\(709\) 522.875i 0.737482i −0.929532 0.368741i \(-0.879789\pi\)
0.929532 0.368741i \(-0.120211\pi\)
\(710\) 58.3434 202.177i 0.0821738 0.284756i
\(711\) 36.1284 0.0508135
\(712\) 84.0295 + 84.0295i 0.118019 + 0.118019i
\(713\) −50.5155 + 50.5155i −0.0708493 + 0.0708493i
\(714\) 24.2778i 0.0340025i
\(715\) −149.460 43.1307i −0.209035 0.0603226i
\(716\) 458.052 0.639737
\(717\) −434.340 434.340i −0.605775 0.605775i
\(718\) 549.920 549.920i 0.765905 0.765905i
\(719\) 201.802i 0.280670i −0.990104 0.140335i \(-0.955182\pi\)
0.990104 0.140335i \(-0.0448180\pi\)
\(720\) 52.5263 28.9998i 0.0729532 0.0402775i
\(721\) 23.1115 0.0320548
\(722\) 11.6825 + 11.6825i 0.0161807 + 0.0161807i
\(723\) 414.971 414.971i 0.573957 0.573957i
\(724\) 401.894i 0.555102i
\(725\) 915.395 + 576.316i 1.26261 + 0.794919i
\(726\) −186.131 −0.256379
\(727\) 23.7355 + 23.7355i 0.0326486 + 0.0326486i 0.723243 0.690594i \(-0.242651\pi\)
−0.690594 + 0.723243i \(0.742651\pi\)
\(728\) −5.00919 + 5.00919i −0.00688076 + 0.00688076i
\(729\) 27.0000i 0.0370370i
\(730\) 353.815 + 640.853i 0.484679 + 0.877881i
\(731\) −1069.77 −1.46344
\(732\) 56.0257 + 56.0257i 0.0765378 + 0.0765378i
\(733\) −593.329 + 593.329i −0.809453 + 0.809453i −0.984551 0.175098i \(-0.943976\pi\)
0.175098 + 0.984551i \(0.443976\pi\)
\(734\) 147.254i 0.200619i
\(735\) −116.957 + 405.288i −0.159125 + 0.551412i
\(736\) 27.1293 0.0368605
\(737\) 396.939 + 396.939i 0.538588 + 0.538588i
\(738\) −59.7558 + 59.7558i −0.0809699 + 0.0809699i
\(739\) 1294.17i 1.75125i 0.482992 + 0.875625i \(0.339550\pi\)
−0.482992 + 0.875625i \(0.660450\pi\)
\(740\) −105.706 30.5044i −0.142846 0.0412221i
\(741\) −150.117 −0.202587
\(742\) 10.6503 + 10.6503i 0.0143535 + 0.0143535i
\(743\) −114.912 + 114.912i −0.154660 + 0.154660i −0.780196 0.625536i \(-0.784881\pi\)
0.625536 + 0.780196i \(0.284881\pi\)
\(744\) 72.9762i 0.0980864i
\(745\) 298.687 164.905i 0.400922 0.221349i
\(746\) −303.669 −0.407063
\(747\) 38.5520 + 38.5520i 0.0516092 + 0.0516092i
\(748\) 174.115 174.115i 0.232774 0.232774i
\(749\) 44.7216i 0.0597084i
\(750\) 305.681 + 17.5756i 0.407575 + 0.0234341i
\(751\) 1130.53 1.50537 0.752684 0.658382i \(-0.228759\pi\)
0.752684 + 0.658382i \(0.228759\pi\)
\(752\) 127.001 + 127.001i 0.168884 + 0.168884i
\(753\) −353.155 + 353.155i −0.468997 + 0.468997i
\(754\) 283.756i 0.376334i
\(755\) −60.3119 109.241i −0.0798834 0.144690i
\(756\) 5.61293 0.00742451
\(757\) 99.9974 + 99.9974i 0.132097 + 0.132097i 0.770064 0.637967i \(-0.220224\pi\)
−0.637967 + 0.770064i \(0.720224\pi\)
\(758\) 0.463933 0.463933i 0.000612049 0.000612049i
\(759\) 55.7301i 0.0734256i
\(760\) 73.2852 253.954i 0.0964279 0.334150i
\(761\) 29.0412 0.0381619 0.0190809 0.999818i \(-0.493926\pi\)
0.0190809 + 0.999818i \(0.493926\pi\)
\(762\) 323.942 + 323.942i 0.425120 + 0.425120i
\(763\) −59.6361 + 59.6361i −0.0781600 + 0.0781600i
\(764\) 114.997i 0.150519i
\(765\) 264.471 + 76.3200i 0.345713 + 0.0997647i
\(766\) 296.330 0.386853
\(767\) −7.59565 7.59565i −0.00990306 0.00990306i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 406.341i 0.528402i 0.964468 + 0.264201i \(0.0851082\pi\)
−0.964468 + 0.264201i \(0.914892\pi\)
\(770\) 22.4313 12.3843i 0.0291315 0.0160835i
\(771\) 76.3142 0.0989808
\(772\) −144.261 144.261i −0.186866 0.186866i
\(773\) 243.088 243.088i 0.314473 0.314473i −0.532166 0.846640i \(-0.678622\pi\)
0.846640 + 0.532166i \(0.178622\pi\)
\(774\) 247.328i 0.319545i
\(775\) −198.412 + 315.148i −0.256015 + 0.406643i
\(776\) −33.8995 −0.0436849
\(777\) −7.27770 7.27770i −0.00936641 0.00936641i
\(778\) 512.669 512.669i 0.658957 0.658957i
\(779\)