Properties

Label 690.3.k.b.277.19
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 277.19
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.19

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(0.815565 - 4.93304i) q^{5} -2.44949 q^{6} +(5.39766 + 5.39766i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(0.815565 - 4.93304i) q^{5} -2.44949 q^{6} +(5.39766 + 5.39766i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-5.74860 + 4.11747i) q^{10} -16.8789 q^{11} +(2.44949 + 2.44949i) q^{12} +(-15.3246 + 15.3246i) q^{13} -10.7953i q^{14} +(-5.04285 - 7.04057i) q^{15} -4.00000 q^{16} +(20.2469 + 20.2469i) q^{17} +(-3.00000 + 3.00000i) q^{18} +27.2666i q^{19} +(9.86607 + 1.63113i) q^{20} +13.2215 q^{21} +(16.8789 + 16.8789i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-23.6697 - 8.04642i) q^{25} +30.6493 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-10.7953 + 10.7953i) q^{28} -1.86234i q^{29} +(-1.99772 + 12.0834i) q^{30} -56.4076 q^{31} +(4.00000 + 4.00000i) q^{32} +(-20.6724 + 20.6724i) q^{33} -40.4937i q^{34} +(31.0290 - 22.2247i) q^{35} +6.00000 q^{36} +(14.7883 + 14.7883i) q^{37} +(27.2666 - 27.2666i) q^{38} +37.5375i q^{39} +(-8.23494 - 11.4972i) q^{40} -31.1689 q^{41} +(-13.2215 - 13.2215i) q^{42} +(3.71233 - 3.71233i) q^{43} -33.7579i q^{44} +(-14.7991 - 2.44669i) q^{45} +6.78233 q^{46} +(-52.2797 - 52.2797i) q^{47} +(-4.89898 + 4.89898i) q^{48} +9.26957i q^{49} +(15.6233 + 31.7161i) q^{50} +49.5945 q^{51} +(-30.6493 - 30.6493i) q^{52} +(-29.1368 + 29.1368i) q^{53} +7.34847i q^{54} +(-13.7659 + 83.2644i) q^{55} +21.5907 q^{56} +(33.3947 + 33.3947i) q^{57} +(-1.86234 + 1.86234i) q^{58} +44.5688i q^{59} +(14.0811 - 10.0857i) q^{60} +97.7394 q^{61} +(56.4076 + 56.4076i) q^{62} +(16.1930 - 16.1930i) q^{63} -8.00000i q^{64} +(63.0987 + 88.0952i) q^{65} +41.3448 q^{66} +(29.7413 + 29.7413i) q^{67} +(-40.4937 + 40.4937i) q^{68} +8.30662i q^{69} +(-53.2538 - 8.80429i) q^{70} +112.964 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-69.1242 + 69.1242i) q^{73} -29.5767i q^{74} +(-38.8442 + 19.1345i) q^{75} -54.5333 q^{76} +(-91.1068 - 91.1068i) q^{77} +(37.5375 - 37.5375i) q^{78} -17.0900i q^{79} +(-3.26226 + 19.7321i) q^{80} -9.00000 q^{81} +(31.1689 + 31.1689i) q^{82} +(70.4417 - 70.4417i) q^{83} +26.4430i q^{84} +(116.391 - 83.3659i) q^{85} -7.42467 q^{86} +(-2.28089 - 2.28089i) q^{87} +(-33.7579 + 33.7579i) q^{88} +103.307i q^{89} +(12.3524 + 17.2458i) q^{90} -165.434 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-69.0850 + 69.0850i) q^{93} +104.559i q^{94} +(134.507 + 22.2377i) q^{95} +9.79796 q^{96} +(-78.1167 - 78.1167i) q^{97} +(9.26957 - 9.26957i) q^{98} +50.6368i 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
\(5\) 0.815565 4.93304i 0.163113 0.986607i
\(6\) −2.44949 −0.408248
\(7\) 5.39766 + 5.39766i 0.771095 + 0.771095i 0.978298 0.207203i \(-0.0664361\pi\)
−0.207203 + 0.978298i \(0.566436\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −5.74860 + 4.11747i −0.574860 + 0.411747i
\(11\) −16.8789 −1.53445 −0.767224 0.641379i \(-0.778363\pi\)
−0.767224 + 0.641379i \(0.778363\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −15.3246 + 15.3246i −1.17882 + 1.17882i −0.198772 + 0.980046i \(0.563695\pi\)
−0.980046 + 0.198772i \(0.936305\pi\)
\(14\) 10.7953i 0.771095i
\(15\) −5.04285 7.04057i −0.336190 0.469371i
\(16\) −4.00000 −0.250000
\(17\) 20.2469 + 20.2469i 1.19099 + 1.19099i 0.976789 + 0.214203i \(0.0687153\pi\)
0.214203 + 0.976789i \(0.431285\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 27.2666i 1.43509i 0.696514 + 0.717543i \(0.254733\pi\)
−0.696514 + 0.717543i \(0.745267\pi\)
\(20\) 9.86607 + 1.63113i 0.493304 + 0.0815565i
\(21\) 13.2215 0.629596
\(22\) 16.8789 + 16.8789i 0.767224 + 0.767224i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −23.6697 8.04642i −0.946788 0.321857i
\(26\) 30.6493 1.17882
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −10.7953 + 10.7953i −0.385547 + 0.385547i
\(29\) 1.86234i 0.0642186i −0.999484 0.0321093i \(-0.989778\pi\)
0.999484 0.0321093i \(-0.0102225\pi\)
\(30\) −1.99772 + 12.0834i −0.0665906 + 0.402781i
\(31\) −56.4076 −1.81960 −0.909801 0.415046i \(-0.863766\pi\)
−0.909801 + 0.415046i \(0.863766\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −20.6724 + 20.6724i −0.626436 + 0.626436i
\(34\) 40.4937i 1.19099i
\(35\) 31.0290 22.2247i 0.886544 0.634992i
\(36\) 6.00000 0.166667
\(37\) 14.7883 + 14.7883i 0.399685 + 0.399685i 0.878122 0.478437i \(-0.158797\pi\)
−0.478437 + 0.878122i \(0.658797\pi\)
\(38\) 27.2666 27.2666i 0.717543 0.717543i
\(39\) 37.5375i 0.962501i
\(40\) −8.23494 11.4972i −0.205874 0.287430i
\(41\) −31.1689 −0.760216 −0.380108 0.924942i \(-0.624113\pi\)
−0.380108 + 0.924942i \(0.624113\pi\)
\(42\) −13.2215 13.2215i −0.314798 0.314798i
\(43\) 3.71233 3.71233i 0.0863334 0.0863334i −0.662621 0.748955i \(-0.730556\pi\)
0.748955 + 0.662621i \(0.230556\pi\)
\(44\) 33.7579i 0.767224i
\(45\) −14.7991 2.44669i −0.328869 0.0543710i
\(46\) 6.78233 0.147442
\(47\) −52.2797 52.2797i −1.11233 1.11233i −0.992834 0.119500i \(-0.961871\pi\)
−0.119500 0.992834i \(-0.538129\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 9.26957i 0.189175i
\(50\) 15.6233 + 31.7161i 0.312466 + 0.634323i
\(51\) 49.5945 0.972441
\(52\) −30.6493 30.6493i −0.589409 0.589409i
\(53\) −29.1368 + 29.1368i −0.549752 + 0.549752i −0.926369 0.376617i \(-0.877087\pi\)
0.376617 + 0.926369i \(0.377087\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −13.7659 + 83.2644i −0.250288 + 1.51390i
\(56\) 21.5907 0.385547
\(57\) 33.3947 + 33.3947i 0.585871 + 0.585871i
\(58\) −1.86234 + 1.86234i −0.0321093 + 0.0321093i
\(59\) 44.5688i 0.755404i 0.925927 + 0.377702i \(0.123286\pi\)
−0.925927 + 0.377702i \(0.876714\pi\)
\(60\) 14.0811 10.0857i 0.234686 0.168095i
\(61\) 97.7394 1.60228 0.801142 0.598474i \(-0.204226\pi\)
0.801142 + 0.598474i \(0.204226\pi\)
\(62\) 56.4076 + 56.4076i 0.909801 + 0.909801i
\(63\) 16.1930 16.1930i 0.257032 0.257032i
\(64\) 8.00000i 0.125000i
\(65\) 63.0987 + 88.0952i 0.970750 + 1.35531i
\(66\) 41.3448 0.626436
\(67\) 29.7413 + 29.7413i 0.443900 + 0.443900i 0.893321 0.449420i \(-0.148369\pi\)
−0.449420 + 0.893321i \(0.648369\pi\)
\(68\) −40.4937 + 40.4937i −0.595496 + 0.595496i
\(69\) 8.30662i 0.120386i
\(70\) −53.2538 8.80429i −0.760768 0.125776i
\(71\) 112.964 1.59104 0.795520 0.605928i \(-0.207198\pi\)
0.795520 + 0.605928i \(0.207198\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −69.1242 + 69.1242i −0.946907 + 0.946907i −0.998660 0.0517525i \(-0.983519\pi\)
0.0517525 + 0.998660i \(0.483519\pi\)
\(74\) 29.5767i 0.399685i
\(75\) −38.8442 + 19.1345i −0.517922 + 0.255127i
\(76\) −54.5333 −0.717543
\(77\) −91.1068 91.1068i −1.18321 1.18321i
\(78\) 37.5375 37.5375i 0.481250 0.481250i
\(79\) 17.0900i 0.216329i −0.994133 0.108164i \(-0.965503\pi\)
0.994133 0.108164i \(-0.0344973\pi\)
\(80\) −3.26226 + 19.7321i −0.0407782 + 0.246652i
\(81\) −9.00000 −0.111111
\(82\) 31.1689 + 31.1689i 0.380108 + 0.380108i
\(83\) 70.4417 70.4417i 0.848695 0.848695i −0.141275 0.989970i \(-0.545120\pi\)
0.989970 + 0.141275i \(0.0451203\pi\)
\(84\) 26.4430i 0.314798i
\(85\) 116.391 83.3659i 1.36931 0.980775i
\(86\) −7.42467 −0.0863334
\(87\) −2.28089 2.28089i −0.0262171 0.0262171i
\(88\) −33.7579 + 33.7579i −0.383612 + 0.383612i
\(89\) 103.307i 1.16075i 0.814349 + 0.580376i \(0.197094\pi\)
−0.814349 + 0.580376i \(0.802906\pi\)
\(90\) 12.3524 + 17.2458i 0.137249 + 0.191620i
\(91\) −165.434 −1.81796
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −69.0850 + 69.0850i −0.742849 + 0.742849i
\(94\) 104.559i 1.11233i
\(95\) 134.507 + 22.2377i 1.41587 + 0.234081i
\(96\) 9.79796 0.102062
\(97\) −78.1167 78.1167i −0.805326 0.805326i 0.178596 0.983922i \(-0.442844\pi\)
−0.983922 + 0.178596i \(0.942844\pi\)
\(98\) 9.26957 9.26957i 0.0945875 0.0945875i
\(99\) 50.6368i 0.511483i
\(100\) 16.0928 47.3394i 0.160928 0.473394i
\(101\) −35.5554 −0.352034 −0.176017 0.984387i \(-0.556321\pi\)
−0.176017 + 0.984387i \(0.556321\pi\)
\(102\) −49.5945 49.5945i −0.486220 0.486220i
\(103\) 93.4693 93.4693i 0.907469 0.907469i −0.0885985 0.996067i \(-0.528239\pi\)
0.996067 + 0.0885985i \(0.0282388\pi\)
\(104\) 61.2985i 0.589409i
\(105\) 10.7830 65.2223i 0.102695 0.621164i
\(106\) 58.2737 0.549752
\(107\) −72.7144 72.7144i −0.679574 0.679574i 0.280330 0.959904i \(-0.409556\pi\)
−0.959904 + 0.280330i \(0.909556\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 98.3783i 0.902553i 0.892384 + 0.451277i \(0.149031\pi\)
−0.892384 + 0.451277i \(0.850969\pi\)
\(110\) 97.0302 69.4985i 0.882093 0.631805i
\(111\) 36.2239 0.326341
\(112\) −21.5907 21.5907i −0.192774 0.192774i
\(113\) −3.23925 + 3.23925i −0.0286660 + 0.0286660i −0.721294 0.692629i \(-0.756453\pi\)
0.692629 + 0.721294i \(0.256453\pi\)
\(114\) 66.7893i 0.585871i
\(115\) 13.9630 + 19.4945i 0.121418 + 0.169517i
\(116\) 3.72468 0.0321093
\(117\) 45.9739 + 45.9739i 0.392939 + 0.392939i
\(118\) 44.5688 44.5688i 0.377702 0.377702i
\(119\) 218.572i 1.83674i
\(120\) −24.1668 3.99544i −0.201390 0.0332953i
\(121\) 163.898 1.35453
\(122\) −97.7394 97.7394i −0.801142 0.801142i
\(123\) −38.1739 + 38.1739i −0.310357 + 0.310357i
\(124\) 112.815i 0.909801i
\(125\) −58.9975 + 110.201i −0.471980 + 0.881609i
\(126\) −32.3860 −0.257032
\(127\) −21.7786 21.7786i −0.171485 0.171485i 0.616147 0.787632i \(-0.288693\pi\)
−0.787632 + 0.616147i \(0.788693\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 9.09333i 0.0704909i
\(130\) 24.9965 151.194i 0.192280 1.16303i
\(131\) 240.543 1.83620 0.918101 0.396346i \(-0.129722\pi\)
0.918101 + 0.396346i \(0.129722\pi\)
\(132\) −41.3448 41.3448i −0.313218 0.313218i
\(133\) −147.176 + 147.176i −1.10659 + 1.10659i
\(134\) 59.4827i 0.443900i
\(135\) −21.1217 + 15.1286i −0.156457 + 0.112063i
\(136\) 80.9875 0.595496
\(137\) 50.7479 + 50.7479i 0.370423 + 0.370423i 0.867631 0.497208i \(-0.165642\pi\)
−0.497208 + 0.867631i \(0.665642\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 76.8919i 0.553179i 0.960988 + 0.276589i \(0.0892042\pi\)
−0.960988 + 0.276589i \(0.910796\pi\)
\(140\) 44.4495 + 62.0581i 0.317496 + 0.443272i
\(141\) −128.059 −0.908217
\(142\) −112.964 112.964i −0.795520 0.795520i
\(143\) 258.663 258.663i 1.80883 1.80883i
\(144\) 12.0000i 0.0833333i
\(145\) −9.18699 1.51886i −0.0633585 0.0104749i
\(146\) 138.248 0.946907
\(147\) 11.3529 + 11.3529i 0.0772303 + 0.0772303i
\(148\) −29.5767 + 29.5767i −0.199842 + 0.199842i
\(149\) 211.594i 1.42009i 0.704155 + 0.710046i \(0.251326\pi\)
−0.704155 + 0.710046i \(0.748674\pi\)
\(150\) 57.9787 + 19.7096i 0.386525 + 0.131398i
\(151\) −264.463 −1.75141 −0.875705 0.482846i \(-0.839603\pi\)
−0.875705 + 0.482846i \(0.839603\pi\)
\(152\) 54.5333 + 54.5333i 0.358771 + 0.358771i
\(153\) 60.7406 60.7406i 0.396997 0.396997i
\(154\) 182.214i 1.18321i
\(155\) −46.0041 + 278.261i −0.296801 + 1.79523i
\(156\) −75.0750 −0.481250
\(157\) 66.1849 + 66.1849i 0.421560 + 0.421560i 0.885741 0.464181i \(-0.153651\pi\)
−0.464181 + 0.885741i \(0.653651\pi\)
\(158\) −17.0900 + 17.0900i −0.108164 + 0.108164i
\(159\) 71.3704i 0.448870i
\(160\) 22.9944 16.4699i 0.143715 0.102937i
\(161\) −36.6087 −0.227384
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −139.340 + 139.340i −0.854848 + 0.854848i −0.990726 0.135878i \(-0.956615\pi\)
0.135878 + 0.990726i \(0.456615\pi\)
\(164\) 62.3377i 0.380108i
\(165\) 85.1179 + 118.837i 0.515866 + 0.720226i
\(166\) −140.883 −0.848695
\(167\) −130.406 130.406i −0.780877 0.780877i 0.199102 0.979979i \(-0.436197\pi\)
−0.979979 + 0.199102i \(0.936197\pi\)
\(168\) 26.4430 26.4430i 0.157399 0.157399i
\(169\) 300.689i 1.77922i
\(170\) −199.757 33.0253i −1.17504 0.194266i
\(171\) 81.7999 0.478362
\(172\) 7.42467 + 7.42467i 0.0431667 + 0.0431667i
\(173\) 5.87862 5.87862i 0.0339805 0.0339805i −0.689912 0.723893i \(-0.742351\pi\)
0.723893 + 0.689912i \(0.242351\pi\)
\(174\) 4.56178i 0.0262171i
\(175\) −84.3293 171.193i −0.481881 0.978246i
\(176\) 67.5157 0.383612
\(177\) 54.5854 + 54.5854i 0.308392 + 0.308392i
\(178\) 103.307 103.307i 0.580376 0.580376i
\(179\) 149.359i 0.834409i −0.908813 0.417205i \(-0.863010\pi\)
0.908813 0.417205i \(-0.136990\pi\)
\(180\) 4.89339 29.5982i 0.0271855 0.164435i
\(181\) −43.4397 −0.239998 −0.119999 0.992774i \(-0.538289\pi\)
−0.119999 + 0.992774i \(0.538289\pi\)
\(182\) 165.434 + 165.434i 0.908980 + 0.908980i
\(183\) 119.706 119.706i 0.654130 0.654130i
\(184\) 13.5647i 0.0737210i
\(185\) 85.0123 60.8906i 0.459526 0.329138i
\(186\) 138.170 0.742849
\(187\) −341.745 341.745i −1.82752 1.82752i
\(188\) 104.559 104.559i 0.556167 0.556167i
\(189\) 39.6646i 0.209865i
\(190\) −112.270 156.745i −0.590892 0.824974i
\(191\) −157.052 −0.822261 −0.411131 0.911576i \(-0.634866\pi\)
−0.411131 + 0.911576i \(0.634866\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 30.1699 30.1699i 0.156320 0.156320i −0.624614 0.780934i \(-0.714743\pi\)
0.780934 + 0.624614i \(0.214743\pi\)
\(194\) 156.233i 0.805326i
\(195\) 185.174 + 30.6143i 0.949610 + 0.156996i
\(196\) −18.5391 −0.0945875
\(197\) 129.404 + 129.404i 0.656875 + 0.656875i 0.954639 0.297764i \(-0.0962409\pi\)
−0.297764 + 0.954639i \(0.596241\pi\)
\(198\) 50.6368 50.6368i 0.255741 0.255741i
\(199\) 38.6175i 0.194058i −0.995282 0.0970290i \(-0.969066\pi\)
0.995282 0.0970290i \(-0.0309339\pi\)
\(200\) −63.4323 + 31.2466i −0.317161 + 0.156233i
\(201\) 72.8511 0.362443
\(202\) 35.5554 + 35.5554i 0.176017 + 0.176017i
\(203\) 10.0523 10.0523i 0.0495186 0.0495186i
\(204\) 99.1890i 0.486220i
\(205\) −25.4202 + 153.757i −0.124001 + 0.750035i
\(206\) −186.939 −0.907469
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 61.2985 61.2985i 0.294704 0.294704i
\(209\) 460.231i 2.20206i
\(210\) −76.0053 + 54.4393i −0.361930 + 0.259235i
\(211\) 229.400 1.08721 0.543603 0.839343i \(-0.317060\pi\)
0.543603 + 0.839343i \(0.317060\pi\)
\(212\) −58.2737 58.2737i −0.274876 0.274876i
\(213\) 138.352 138.352i 0.649539 0.649539i
\(214\) 145.429i 0.679574i
\(215\) −15.2854 21.3407i −0.0710950 0.0992592i
\(216\) −14.6969 −0.0680414
\(217\) −304.469 304.469i −1.40309 1.40309i
\(218\) 98.3783 98.3783i 0.451277 0.451277i
\(219\) 169.319i 0.773147i
\(220\) −166.529 27.5317i −0.756949 0.125144i
\(221\) −620.551 −2.80792
\(222\) −36.2239 36.2239i −0.163171 0.163171i
\(223\) −118.733 + 118.733i −0.532433 + 0.532433i −0.921296 0.388863i \(-0.872868\pi\)
0.388863 + 0.921296i \(0.372868\pi\)
\(224\) 43.1813i 0.192774i
\(225\) −24.1393 + 71.0091i −0.107286 + 0.315596i
\(226\) 6.47851 0.0286660
\(227\) −140.299 140.299i −0.618059 0.618059i 0.326974 0.945033i \(-0.393971\pi\)
−0.945033 + 0.326974i \(0.893971\pi\)
\(228\) −66.7893 + 66.7893i −0.292936 + 0.292936i
\(229\) 208.203i 0.909183i −0.890700 0.454591i \(-0.849785\pi\)
0.890700 0.454591i \(-0.150215\pi\)
\(230\) 5.53143 33.4575i 0.0240497 0.145467i
\(231\) −223.165 −0.966083
\(232\) −3.72468 3.72468i −0.0160547 0.0160547i
\(233\) 237.245 237.245i 1.01822 1.01822i 0.0183890 0.999831i \(-0.494146\pi\)
0.999831 0.0183890i \(-0.00585372\pi\)
\(234\) 91.9478i 0.392939i
\(235\) −300.535 + 215.260i −1.27887 + 0.916001i
\(236\) −89.1376 −0.377702
\(237\) −20.9309 20.9309i −0.0883159 0.0883159i
\(238\) 218.572 218.572i 0.918368 0.918368i
\(239\) 101.498i 0.424678i 0.977196 + 0.212339i \(0.0681081\pi\)
−0.977196 + 0.212339i \(0.931892\pi\)
\(240\) 20.1714 + 28.1623i 0.0840475 + 0.117343i
\(241\) 78.4578 0.325551 0.162775 0.986663i \(-0.447955\pi\)
0.162775 + 0.986663i \(0.447955\pi\)
\(242\) −163.898 163.898i −0.677265 0.677265i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 195.479i 0.801142i
\(245\) 45.7271 + 7.55994i 0.186641 + 0.0308569i
\(246\) 76.3478 0.310357
\(247\) −417.851 417.851i −1.69170 1.69170i
\(248\) −112.815 + 112.815i −0.454900 + 0.454900i
\(249\) 172.546i 0.692957i
\(250\) 169.199 51.2037i 0.676795 0.204815i
\(251\) −480.688 −1.91509 −0.957545 0.288282i \(-0.906916\pi\)
−0.957545 + 0.288282i \(0.906916\pi\)
\(252\) 32.3860 + 32.3860i 0.128516 + 0.128516i
\(253\) 57.2392 57.2392i 0.226242 0.226242i
\(254\) 43.5572i 0.171485i
\(255\) 40.4475 244.651i 0.158618 0.959417i
\(256\) 16.0000 0.0625000
\(257\) −128.059 128.059i −0.498284 0.498284i 0.412619 0.910903i \(-0.364614\pi\)
−0.910903 + 0.412619i \(0.864614\pi\)
\(258\) −9.09333 + 9.09333i −0.0352454 + 0.0352454i
\(259\) 159.645i 0.616390i
\(260\) −176.190 + 126.197i −0.677655 + 0.485375i
\(261\) −5.58702 −0.0214062
\(262\) −240.543 240.543i −0.918101 0.918101i
\(263\) −109.271 + 109.271i −0.415480 + 0.415480i −0.883642 0.468163i \(-0.844916\pi\)
0.468163 + 0.883642i \(0.344916\pi\)
\(264\) 82.6895i 0.313218i
\(265\) 119.970 + 167.496i 0.452717 + 0.632061i
\(266\) 294.352 1.10659
\(267\) 126.525 + 126.525i 0.473875 + 0.473875i
\(268\) −59.4827 + 59.4827i −0.221950 + 0.221950i
\(269\) 262.095i 0.974330i −0.873310 0.487165i \(-0.838031\pi\)
0.873310 0.487165i \(-0.161969\pi\)
\(270\) 36.2503 + 5.99315i 0.134260 + 0.0221969i
\(271\) 6.42234 0.0236987 0.0118493 0.999930i \(-0.496228\pi\)
0.0118493 + 0.999930i \(0.496228\pi\)
\(272\) −80.9875 80.9875i −0.297748 0.297748i
\(273\) −202.615 + 202.615i −0.742179 + 0.742179i
\(274\) 101.496i 0.370423i
\(275\) 399.519 + 135.815i 1.45280 + 0.493873i
\(276\) −16.6132 −0.0601929
\(277\) 52.1441 + 52.1441i 0.188246 + 0.188246i 0.794937 0.606692i \(-0.207504\pi\)
−0.606692 + 0.794937i \(0.707504\pi\)
\(278\) 76.8919 76.8919i 0.276589 0.276589i
\(279\) 169.223i 0.606534i
\(280\) 17.6086 106.508i 0.0628878 0.380384i
\(281\) 295.578 1.05188 0.525939 0.850522i \(-0.323714\pi\)
0.525939 + 0.850522i \(0.323714\pi\)
\(282\) 128.059 + 128.059i 0.454109 + 0.454109i
\(283\) −264.543 + 264.543i −0.934782 + 0.934782i −0.998000 0.0632181i \(-0.979864\pi\)
0.0632181 + 0.998000i \(0.479864\pi\)
\(284\) 225.928i 0.795520i
\(285\) 191.973 137.502i 0.673588 0.482462i
\(286\) −517.327 −1.80883
\(287\) −168.239 168.239i −0.586199 0.586199i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 530.871i 1.83692i
\(290\) 7.66813 + 10.7058i 0.0264418 + 0.0369167i
\(291\) −191.346 −0.657546
\(292\) −138.248 138.248i −0.473454 0.473454i
\(293\) 167.891 167.891i 0.573007 0.573007i −0.359960 0.932968i \(-0.617210\pi\)
0.932968 + 0.359960i \(0.117210\pi\)
\(294\) 22.7057i 0.0772303i
\(295\) 219.860 + 36.3488i 0.745287 + 0.123216i
\(296\) 59.1533 0.199842
\(297\) 62.0171 + 62.0171i 0.208812 + 0.208812i
\(298\) 211.594 211.594i 0.710046 0.710046i
\(299\) 103.937i 0.347614i
\(300\) −38.2691 77.6883i −0.127564 0.258961i
\(301\) 40.0759 0.133142
\(302\) 264.463 + 264.463i 0.875705 + 0.875705i
\(303\) −43.5463 + 43.5463i −0.143717 + 0.143717i
\(304\) 109.067i 0.358771i
\(305\) 79.7128 482.152i 0.261353 1.58083i
\(306\) −121.481 −0.396997
\(307\) 61.9635 + 61.9635i 0.201835 + 0.201835i 0.800786 0.598951i \(-0.204415\pi\)
−0.598951 + 0.800786i \(0.704415\pi\)
\(308\) 182.214 182.214i 0.591603 0.591603i
\(309\) 228.952i 0.740945i
\(310\) 324.265 232.257i 1.04602 0.749216i
\(311\) −23.6111 −0.0759198 −0.0379599 0.999279i \(-0.512086\pi\)
−0.0379599 + 0.999279i \(0.512086\pi\)
\(312\) 75.0750 + 75.0750i 0.240625 + 0.240625i
\(313\) 5.59915 5.59915i 0.0178887 0.0178887i −0.698106 0.715995i \(-0.745974\pi\)
0.715995 + 0.698106i \(0.245974\pi\)
\(314\) 132.370i 0.421560i
\(315\) −66.6742 93.0871i −0.211664 0.295515i
\(316\) 34.1800 0.108164
\(317\) 191.306 + 191.306i 0.603490 + 0.603490i 0.941237 0.337747i \(-0.109665\pi\)
−0.337747 + 0.941237i \(0.609665\pi\)
\(318\) 71.3704 71.3704i 0.224435 0.224435i
\(319\) 31.4343i 0.0985401i
\(320\) −39.4643 6.52452i −0.123326 0.0203891i
\(321\) −178.113 −0.554870
\(322\) 36.6087 + 36.6087i 0.113692 + 0.113692i
\(323\) −552.064 + 552.064i −1.70918 + 1.70918i
\(324\) 18.0000i 0.0555556i
\(325\) 486.038 239.421i 1.49550 0.736680i
\(326\) 278.680 0.854848
\(327\) 120.488 + 120.488i 0.368466 + 0.368466i
\(328\) −62.3377 + 62.3377i −0.190054 + 0.190054i
\(329\) 564.377i 1.71543i
\(330\) 33.7193 203.955i 0.102180 0.618046i
\(331\) 141.318 0.426944 0.213472 0.976949i \(-0.431523\pi\)
0.213472 + 0.976949i \(0.431523\pi\)
\(332\) 140.883 + 140.883i 0.424348 + 0.424348i
\(333\) 44.3650 44.3650i 0.133228 0.133228i
\(334\) 260.813i 0.780877i
\(335\) 170.971 122.459i 0.510361 0.365549i
\(336\) −52.8861 −0.157399
\(337\) 68.1580 + 68.1580i 0.202249 + 0.202249i 0.800963 0.598714i \(-0.204321\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(338\) −300.689 + 300.689i −0.889611 + 0.889611i
\(339\) 7.93452i 0.0234057i
\(340\) 166.732 + 232.782i 0.490388 + 0.684654i
\(341\) 952.100 2.79208
\(342\) −81.7999 81.7999i −0.239181 0.239181i
\(343\) 214.452 214.452i 0.625223 0.625223i
\(344\) 14.8493i 0.0431667i
\(345\) 40.9769 + 6.77459i 0.118774 + 0.0196365i
\(346\) −11.7572 −0.0339805
\(347\) −331.456 331.456i −0.955204 0.955204i 0.0438349 0.999039i \(-0.486042\pi\)
−0.999039 + 0.0438349i \(0.986042\pi\)
\(348\) 4.56178 4.56178i 0.0131086 0.0131086i
\(349\) 341.273i 0.977859i 0.872323 + 0.488930i \(0.162612\pi\)
−0.872323 + 0.488930i \(0.837388\pi\)
\(350\) −86.8638 + 255.522i −0.248182 + 0.730064i
\(351\) 112.613 0.320834
\(352\) −67.5157 67.5157i −0.191806 0.191806i
\(353\) 173.856 173.856i 0.492509 0.492509i −0.416587 0.909096i \(-0.636774\pi\)
0.909096 + 0.416587i \(0.136774\pi\)
\(354\) 109.171i 0.308392i
\(355\) 92.1293 557.254i 0.259519 1.56973i
\(356\) −206.614 −0.580376
\(357\) 267.694 + 267.694i 0.749844 + 0.749844i
\(358\) −149.359 + 149.359i −0.417205 + 0.417205i
\(359\) 97.4524i 0.271455i 0.990746 + 0.135728i \(0.0433372\pi\)
−0.990746 + 0.135728i \(0.956663\pi\)
\(360\) −34.4916 + 24.7048i −0.0958100 + 0.0686245i
\(361\) −382.469 −1.05947
\(362\) 43.4397 + 43.4397i 0.119999 + 0.119999i
\(363\) 200.733 200.733i 0.552985 0.552985i
\(364\) 330.869i 0.908980i
\(365\) 284.617 + 397.368i 0.779773 + 1.08868i
\(366\) −239.412 −0.654130
\(367\) 323.497 + 323.497i 0.881462 + 0.881462i 0.993683 0.112221i \(-0.0357964\pi\)
−0.112221 + 0.993683i \(0.535796\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 93.5066i 0.253405i
\(370\) −145.903 24.1217i −0.394332 0.0651938i
\(371\) −314.542 −0.847821
\(372\) −138.170 138.170i −0.371425 0.371425i
\(373\) 70.3440 70.3440i 0.188590 0.188590i −0.606496 0.795086i \(-0.707426\pi\)
0.795086 + 0.606496i \(0.207426\pi\)
\(374\) 683.491i 1.82752i
\(375\) 62.7114 + 207.225i 0.167231 + 0.552600i
\(376\) −209.119 −0.556167
\(377\) 28.5397 + 28.5397i 0.0757020 + 0.0757020i
\(378\) −39.6646 + 39.6646i −0.104933 + 0.104933i
\(379\) 339.778i 0.896513i 0.893905 + 0.448256i \(0.147955\pi\)
−0.893905 + 0.448256i \(0.852045\pi\)
\(380\) −44.4754 + 269.015i −0.117041 + 0.707933i
\(381\) −53.3464 −0.140017
\(382\) 157.052 + 157.052i 0.411131 + 0.411131i
\(383\) −6.13355 + 6.13355i −0.0160145 + 0.0160145i −0.715069 0.699054i \(-0.753605\pi\)
0.699054 + 0.715069i \(0.253605\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −523.737 + 375.130i −1.36035 + 0.974363i
\(386\) −60.3397 −0.156320
\(387\) −11.1370 11.1370i −0.0287778 0.0287778i
\(388\) 156.233 156.233i 0.402663 0.402663i
\(389\) 316.963i 0.814814i 0.913247 + 0.407407i \(0.133567\pi\)
−0.913247 + 0.407407i \(0.866433\pi\)
\(390\) −154.560 215.788i −0.396307 0.553303i
\(391\) −137.321 −0.351204
\(392\) 18.5391 + 18.5391i 0.0472937 + 0.0472937i
\(393\) 294.603 294.603i 0.749627 0.749627i
\(394\) 258.809i 0.656875i
\(395\) −84.3056 13.9380i −0.213432 0.0352861i
\(396\) −101.274 −0.255741
\(397\) 73.1005 + 73.1005i 0.184132 + 0.184132i 0.793154 0.609021i \(-0.208438\pi\)
−0.609021 + 0.793154i \(0.708438\pi\)
\(398\) −38.6175 + 38.6175i −0.0970290 + 0.0970290i
\(399\) 360.506i 0.903525i
\(400\) 94.6788 + 32.1857i 0.236697 + 0.0804642i
\(401\) −313.533 −0.781878 −0.390939 0.920417i \(-0.627850\pi\)
−0.390939 + 0.920417i \(0.627850\pi\)
\(402\) −72.8511 72.8511i −0.181222 0.181222i
\(403\) 864.426 864.426i 2.14498 2.14498i
\(404\) 71.1108i 0.176017i
\(405\) −7.34008 + 44.3973i −0.0181237 + 0.109623i
\(406\) −20.1046 −0.0495186
\(407\) −249.611 249.611i −0.613295 0.613295i
\(408\) 99.1890 99.1890i 0.243110 0.243110i
\(409\) 543.161i 1.32802i 0.747723 + 0.664011i \(0.231147\pi\)
−0.747723 + 0.664011i \(0.768853\pi\)
\(410\) 179.177 128.337i 0.437018 0.313017i
\(411\) 124.306 0.302449
\(412\) 186.939 + 186.939i 0.453734 + 0.453734i
\(413\) −240.568 + 240.568i −0.582488 + 0.582488i
\(414\) 20.3470i 0.0491473i
\(415\) −290.042 404.941i −0.698896 0.975762i
\(416\) −122.597 −0.294704
\(417\) 94.1729 + 94.1729i 0.225834 + 0.225834i
\(418\) −460.231 + 460.231i −1.10103 + 1.10103i
\(419\) 42.3838i 0.101155i −0.998720 0.0505774i \(-0.983894\pi\)
0.998720 0.0505774i \(-0.0161061\pi\)
\(420\) 130.445 + 21.5660i 0.310582 + 0.0513477i
\(421\) 571.283 1.35697 0.678484 0.734616i \(-0.262637\pi\)
0.678484 + 0.734616i \(0.262637\pi\)
\(422\) −229.400 229.400i −0.543603 0.543603i
\(423\) −156.839 + 156.839i −0.370778 + 0.370778i
\(424\) 116.547i 0.274876i
\(425\) −316.323 642.152i −0.744288 1.51095i
\(426\) −276.704 −0.649539
\(427\) 527.564 + 527.564i 1.23551 + 1.23551i
\(428\) 145.429 145.429i 0.339787 0.339787i
\(429\) 633.593i 1.47691i
\(430\) −6.05530 + 36.6262i −0.0140821 + 0.0851771i
\(431\) −500.121 −1.16037 −0.580187 0.814483i \(-0.697020\pi\)
−0.580187 + 0.814483i \(0.697020\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −29.3072 + 29.3072i −0.0676841 + 0.0676841i −0.740139 0.672454i \(-0.765240\pi\)
0.672454 + 0.740139i \(0.265240\pi\)
\(434\) 608.939i 1.40309i
\(435\) −13.1119 + 9.39150i −0.0301424 + 0.0215897i
\(436\) −196.757 −0.451277
\(437\) −92.4656 92.4656i −0.211592 0.211592i
\(438\) 169.319 169.319i 0.386573 0.386573i
\(439\) 210.861i 0.480321i −0.970733 0.240160i \(-0.922800\pi\)
0.970733 0.240160i \(-0.0772000\pi\)
\(440\) 138.997 + 194.060i 0.315902 + 0.441047i
\(441\) 27.8087 0.0630583
\(442\) 620.551 + 620.551i 1.40396 + 1.40396i
\(443\) −235.554 + 235.554i −0.531725 + 0.531725i −0.921085 0.389361i \(-0.872696\pi\)
0.389361 + 0.921085i \(0.372696\pi\)
\(444\) 72.4478i 0.163171i
\(445\) 509.617 + 84.2534i 1.14521 + 0.189334i
\(446\) 237.465 0.532433
\(447\) 259.148 + 259.148i 0.579750 + 0.579750i
\(448\) 43.1813 43.1813i 0.0963869 0.0963869i
\(449\) 845.610i 1.88332i 0.336568 + 0.941659i \(0.390734\pi\)
−0.336568 + 0.941659i \(0.609266\pi\)
\(450\) 95.1484 46.8699i 0.211441 0.104155i
\(451\) 526.097 1.16651
\(452\) −6.47851 6.47851i −0.0143330 0.0143330i
\(453\) −323.900 + 323.900i −0.715010 + 0.715010i
\(454\) 280.599i 0.618059i
\(455\) −134.923 + 816.094i −0.296533 + 1.79361i
\(456\) 133.579 0.292936
\(457\) −358.568 358.568i −0.784612 0.784612i 0.195993 0.980605i \(-0.437207\pi\)
−0.980605 + 0.195993i \(0.937207\pi\)
\(458\) −208.203 + 208.203i −0.454591 + 0.454591i
\(459\) 148.783i 0.324147i
\(460\) −38.9889 + 27.9261i −0.0847585 + 0.0607088i
\(461\) −119.174 −0.258511 −0.129256 0.991611i \(-0.541259\pi\)
−0.129256 + 0.991611i \(0.541259\pi\)
\(462\) 223.165 + 223.165i 0.483041 + 0.483041i
\(463\) −385.179 + 385.179i −0.831921 + 0.831921i −0.987779 0.155859i \(-0.950186\pi\)
0.155859 + 0.987779i \(0.450186\pi\)
\(464\) 7.44936i 0.0160547i
\(465\) 284.455 + 397.142i 0.611732 + 0.854069i
\(466\) −474.490 −1.01822
\(467\) −61.8544 61.8544i −0.132451 0.132451i 0.637773 0.770224i \(-0.279856\pi\)
−0.770224 + 0.637773i \(0.779856\pi\)
\(468\) −91.9478 + 91.9478i −0.196470 + 0.196470i
\(469\) 321.067i 0.684579i
\(470\) 515.795 + 85.2750i 1.09744 + 0.181436i
\(471\) 162.119 0.344202
\(472\) 89.1376 + 89.1376i 0.188851 + 0.188851i
\(473\) −62.6602 + 62.6602i −0.132474 + 0.132474i
\(474\) 41.8618i 0.0883159i
\(475\) 219.399 645.393i 0.461892 1.35872i
\(476\) −437.143 −0.918368
\(477\) 87.4105 + 87.4105i 0.183251 + 0.183251i
\(478\) 101.498 101.498i 0.212339 0.212339i
\(479\) 161.028i 0.336175i −0.985772 0.168087i \(-0.946241\pi\)
0.985772 0.168087i \(-0.0537590\pi\)
\(480\) 7.99087 48.3337i 0.0166476 0.100695i
\(481\) −453.252 −0.942311
\(482\) −78.4578 78.4578i −0.162775 0.162775i
\(483\) −44.8364 + 44.8364i −0.0928289 + 0.0928289i
\(484\) 327.796i 0.677265i
\(485\) −449.062 + 321.643i −0.925900 + 0.663182i
\(486\) 22.0454 0.0453609
\(487\) −568.581 568.581i −1.16752 1.16752i −0.982790 0.184727i \(-0.940860\pi\)
−0.184727 0.982790i \(-0.559140\pi\)
\(488\) 195.479 195.479i 0.400571 0.400571i
\(489\) 341.312i 0.697980i
\(490\) −38.1672 53.2871i −0.0778922 0.108749i
\(491\) 417.266 0.849830 0.424915 0.905233i \(-0.360304\pi\)
0.424915 + 0.905233i \(0.360304\pi\)
\(492\) −76.3478 76.3478i −0.155178 0.155178i
\(493\) 37.7065 37.7065i 0.0764838 0.0764838i
\(494\) 835.702i 1.69170i
\(495\) 249.793 + 41.2976i 0.504633 + 0.0834295i
\(496\) 225.631 0.454900
\(497\) 609.741 + 609.741i 1.22684 + 1.22684i
\(498\) −172.546 + 172.546i −0.346478 + 0.346478i
\(499\) 569.095i 1.14047i −0.821481 0.570236i \(-0.806852\pi\)
0.821481 0.570236i \(-0.193148\pi\)
\(500\) −220.402 117.995i −0.440805 0.235990i
\(501\) −319.429 −0.637583
\(502\) 480.688 + 480.688i 0.957545 + 0.957545i
\(503\) 575.380 575.380i 1.14390 1.14390i 0.156167 0.987731i \(-0.450086\pi\)
0.987731 0.156167i \(-0.0499137\pi\)
\(504\) 64.7720i 0.128516i
\(505\) −28.9977 + 175.396i −0.0574212 + 0.347319i
\(506\) −114.478 −0.226242
\(507\) −368.267 368.267i −0.726364 0.726364i
\(508\) 43.5572 43.5572i 0.0857425 0.0857425i
\(509\) 108.397i 0.212960i −0.994315 0.106480i \(-0.966042\pi\)
0.994315 0.106480i \(-0.0339580\pi\)
\(510\) −285.099 + 204.204i −0.559018 + 0.400400i
\(511\) −746.219 −1.46031
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 100.184 100.184i 0.195290 0.195290i
\(514\) 256.118i 0.498284i
\(515\) −384.857 537.318i −0.747296 1.04334i
\(516\) 18.1867 0.0352454
\(517\) 882.425 + 882.425i 1.70682 + 1.70682i
\(518\) 159.645 159.645i 0.308195 0.308195i
\(519\) 14.3996i 0.0277449i
\(520\) 302.388 + 49.9929i 0.581515 + 0.0961402i
\(521\) 375.872 0.721443 0.360721 0.932674i \(-0.382531\pi\)
0.360721 + 0.932674i \(0.382531\pi\)
\(522\) 5.58702 + 5.58702i 0.0107031 + 0.0107031i
\(523\) −502.480 + 502.480i −0.960764 + 0.960764i −0.999259 0.0384946i \(-0.987744\pi\)
0.0384946 + 0.999259i \(0.487744\pi\)
\(524\) 481.085i 0.918101i
\(525\) −312.950 106.386i −0.596095 0.202640i
\(526\) 218.542 0.415480
\(527\) −1142.08 1142.08i −2.16713 2.16713i
\(528\) 82.6895 82.6895i 0.156609 0.156609i
\(529\) 23.0000i 0.0434783i
\(530\) 47.5260 287.466i 0.0896716 0.542389i
\(531\) 133.706 0.251801
\(532\) −294.352 294.352i −0.553294 0.553294i
\(533\) 477.651 477.651i 0.896156 0.896156i
\(534\) 253.049i 0.473875i
\(535\) −418.006 + 299.400i −0.781320 + 0.559625i
\(536\) 118.965 0.221950
\(537\) −182.927 182.927i −0.340646 0.340646i
\(538\) −262.095 + 262.095i −0.487165 + 0.487165i
\(539\) 156.460i 0.290279i
\(540\) −30.2571 42.2434i −0.0560317 0.0782286i
\(541\) 657.157 1.21471 0.607354 0.794431i \(-0.292231\pi\)
0.607354 + 0.794431i \(0.292231\pi\)
\(542\) −6.42234 6.42234i −0.0118493 0.0118493i
\(543\) −53.2026 + 53.2026i −0.0979789 + 0.0979789i
\(544\) 161.975i 0.297748i
\(545\) 485.304 + 80.2339i 0.890466 + 0.147218i
\(546\) 405.230 0.742179
\(547\) 426.043 + 426.043i 0.778872 + 0.778872i 0.979639 0.200767i \(-0.0643435\pi\)
−0.200767 + 0.979639i \(0.564344\pi\)
\(548\) −101.496 + 101.496i −0.185211 + 0.185211i
\(549\) 293.218i 0.534095i
\(550\) −263.704 535.334i −0.479462 0.973335i
\(551\) 50.7797 0.0921592
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 92.2460 92.2460i 0.166810 0.166810i
\(554\) 104.288i 0.188246i
\(555\) 29.5429 178.694i 0.0532305 0.321971i
\(556\) −153.784 −0.276589
\(557\) 161.428 + 161.428i 0.289816 + 0.289816i 0.837008 0.547191i \(-0.184303\pi\)
−0.547191 + 0.837008i \(0.684303\pi\)
\(558\) 169.223 169.223i 0.303267 0.303267i
\(559\) 113.780i 0.203543i
\(560\) −124.116 + 88.8989i −0.221636 + 0.158748i
\(561\) −837.102 −1.49216
\(562\) −295.578 295.578i −0.525939 0.525939i
\(563\) 3.66442 3.66442i 0.00650874 0.00650874i −0.703845 0.710354i \(-0.748535\pi\)
0.710354 + 0.703845i \(0.248535\pi\)
\(564\) 256.117i 0.454109i
\(565\) 13.3375 + 18.6212i 0.0236063 + 0.0329578i
\(566\) 529.086 0.934782
\(567\) −48.5790 48.5790i −0.0856772 0.0856772i
\(568\) 225.928 225.928i 0.397760 0.397760i
\(569\) 323.369i 0.568312i 0.958778 + 0.284156i \(0.0917133\pi\)
−0.958778 + 0.284156i \(0.908287\pi\)
\(570\) −329.474 54.4710i −0.578025 0.0955632i
\(571\) 634.022 1.11037 0.555185 0.831727i \(-0.312647\pi\)
0.555185 + 0.831727i \(0.312647\pi\)
\(572\) 517.327 + 517.327i 0.904417 + 0.904417i
\(573\) −192.349 + 192.349i −0.335687 + 0.335687i
\(574\) 336.478i 0.586199i
\(575\) 107.555 52.9811i 0.187052 0.0921411i
\(576\) −24.0000 −0.0416667
\(577\) 385.309 + 385.309i 0.667781 + 0.667781i 0.957202 0.289421i \(-0.0934629\pi\)
−0.289421 + 0.957202i \(0.593463\pi\)
\(578\) 530.871 530.871i 0.918462 0.918462i
\(579\) 73.9007i 0.127635i
\(580\) 3.03772 18.3740i 0.00523744 0.0316793i
\(581\) 760.441 1.30885
\(582\) 191.346 + 191.346i 0.328773 + 0.328773i
\(583\) 491.799 491.799i 0.843565 0.843565i
\(584\) 276.497i 0.473454i
\(585\) 264.286 189.296i 0.451770 0.323583i
\(586\) −335.782 −0.573007
\(587\) −151.774 151.774i −0.258558 0.258558i 0.565909 0.824467i \(-0.308525\pi\)
−0.824467 + 0.565909i \(0.808525\pi\)
\(588\) −22.7057 + 22.7057i −0.0386152 + 0.0386152i
\(589\) 1538.05i 2.61128i
\(590\) −183.511 256.208i −0.311035 0.434252i
\(591\) 316.975 0.536336
\(592\) −59.1533 59.1533i −0.0999212 0.0999212i
\(593\) −380.622 + 380.622i −0.641858 + 0.641858i −0.951012 0.309154i \(-0.899954\pi\)
0.309154 + 0.951012i \(0.399954\pi\)
\(594\) 124.034i 0.208812i
\(595\) 1078.22 + 178.259i 1.81214 + 0.299595i
\(596\) −423.188 −0.710046
\(597\) −47.2966 47.2966i −0.0792238 0.0792238i
\(598\) −103.937 + 103.937i −0.173807 + 0.173807i
\(599\) 267.371i 0.446362i −0.974777 0.223181i \(-0.928356\pi\)
0.974777 0.223181i \(-0.0716442\pi\)
\(600\) −39.4193 + 115.957i −0.0656988 + 0.193262i
\(601\) −733.969 −1.22125 −0.610623 0.791921i \(-0.709081\pi\)
−0.610623 + 0.791921i \(0.709081\pi\)
\(602\) −40.0759 40.0759i −0.0665712 0.0665712i
\(603\) 89.2240 89.2240i 0.147967 0.147967i
\(604\) 528.926i 0.875705i
\(605\) 133.670 808.516i 0.220941 1.33639i
\(606\) 87.0926 0.143717
\(607\) 472.725 + 472.725i 0.778789 + 0.778789i 0.979625 0.200836i \(-0.0643658\pi\)
−0.200836 + 0.979625i \(0.564366\pi\)
\(608\) −109.067 + 109.067i −0.179386 + 0.179386i
\(609\) 24.6230i 0.0404318i
\(610\) −561.865 + 402.439i −0.921090 + 0.659736i
\(611\) 1602.33 2.62248
\(612\) 121.481 + 121.481i 0.198499 + 0.198499i
\(613\) 57.4176 57.4176i 0.0936666 0.0936666i −0.658721 0.752387i \(-0.728902\pi\)
0.752387 + 0.658721i \(0.228902\pi\)
\(614\) 123.927i 0.201835i
\(615\) 157.180 + 219.447i 0.255577 + 0.356824i
\(616\) −364.427 −0.591603
\(617\) −316.532 316.532i −0.513018 0.513018i 0.402432 0.915450i \(-0.368165\pi\)
−0.915450 + 0.402432i \(0.868165\pi\)
\(618\) −228.952 + 228.952i −0.370473 + 0.370473i
\(619\) 621.040i 1.00330i 0.865072 + 0.501648i \(0.167273\pi\)
−0.865072 + 0.501648i \(0.832727\pi\)
\(620\) −556.522 92.0082i −0.897616 0.148400i
\(621\) 24.9199 0.0401286
\(622\) 23.6111 + 23.6111i 0.0379599 + 0.0379599i
\(623\) −557.616 + 557.616i −0.895049 + 0.895049i
\(624\) 150.150i 0.240625i
\(625\) 495.510 + 380.913i 0.792816 + 0.609461i
\(626\) −11.1983 −0.0178887
\(627\) −563.666 563.666i −0.898989 0.898989i
\(628\) −132.370 + 132.370i −0.210780 + 0.210780i
\(629\) 598.835i 0.952043i
\(630\) −26.4129 + 159.761i −0.0419252 + 0.253589i
\(631\) 903.819 1.43236 0.716180 0.697916i \(-0.245889\pi\)
0.716180 + 0.697916i \(0.245889\pi\)
\(632\) −34.1800 34.1800i −0.0540822 0.0540822i
\(633\) 280.957 280.957i 0.443850 0.443850i
\(634\) 382.613i 0.603490i
\(635\) −125.196 + 89.6728i −0.197160 + 0.141217i
\(636\) −142.741 −0.224435
\(637\) −142.053 142.053i −0.223003 0.223003i
\(638\) 31.4343 31.4343i 0.0492701 0.0492701i
\(639\) 338.891i 0.530346i
\(640\) 32.9398 + 45.9888i 0.0514684 + 0.0718575i
\(641\) 72.2655 0.112739 0.0563694 0.998410i \(-0.482048\pi\)
0.0563694 + 0.998410i \(0.482048\pi\)
\(642\) 178.113 + 178.113i 0.277435 + 0.277435i
\(643\) −824.283 + 824.283i −1.28193 + 1.28193i −0.342366 + 0.939567i \(0.611228\pi\)
−0.939567 + 0.342366i \(0.888772\pi\)
\(644\) 73.2175i 0.113692i
\(645\) −44.8577 7.41620i −0.0695468 0.0114980i
\(646\) 1104.13 1.70918
\(647\) −704.621 704.621i −1.08906 1.08906i −0.995626 0.0934333i \(-0.970216\pi\)
−0.0934333 0.995626i \(-0.529784\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 752.274i 1.15913i
\(650\) −725.459 246.617i −1.11609 0.379411i
\(651\) −745.795 −1.14561
\(652\) −278.680 278.680i −0.427424 0.427424i
\(653\) 304.501 304.501i 0.466311 0.466311i −0.434406 0.900717i \(-0.643042\pi\)
0.900717 + 0.434406i \(0.143042\pi\)
\(654\) 240.977i 0.368466i
\(655\) 196.178 1186.61i 0.299508 1.81161i
\(656\) 124.675 0.190054
\(657\) 207.373 + 207.373i 0.315636 + 0.315636i
\(658\) −564.377 + 564.377i −0.857715 + 0.857715i
\(659\) 138.577i 0.210284i 0.994457 + 0.105142i \(0.0335297\pi\)
−0.994457 + 0.105142i \(0.966470\pi\)
\(660\) −237.675 + 170.236i −0.360113 + 0.257933i
\(661\) 533.039 0.806413 0.403206 0.915109i \(-0.367896\pi\)
0.403206 + 0.915109i \(0.367896\pi\)
\(662\) −141.318 141.318i −0.213472 0.213472i
\(663\) −760.017 + 760.017i −1.14633 + 1.14633i
\(664\) 281.767i 0.424348i
\(665\) 605.994 + 846.057i 0.911268 + 1.27227i
\(666\) −88.7300 −0.133228
\(667\) 6.31550 + 6.31550i 0.00946852 + 0.00946852i
\(668\) 260.813 260.813i 0.390438 0.390438i
\(669\) 290.834i 0.434730i
\(670\) −293.430 48.5120i −0.437955 0.0724059i
\(671\) −1649.74 −2.45862
\(672\) 52.8861 + 52.8861i 0.0786996 + 0.0786996i
\(673\) −624.129 + 624.129i −0.927384 + 0.927384i −0.997536 0.0701527i \(-0.977651\pi\)
0.0701527 + 0.997536i \(0.477651\pi\)
\(674\) 136.316i 0.202249i
\(675\) 57.4036 + 116.533i 0.0850424 + 0.172641i
\(676\) 601.377 0.889611
\(677\) −40.6078 40.6078i −0.0599820 0.0599820i 0.676479 0.736461i \(-0.263505\pi\)
−0.736461 + 0.676479i \(0.763505\pi\)
\(678\) 7.93452 7.93452i 0.0117028 0.0117028i
\(679\) 843.295i 1.24197i
\(680\) 66.0505 399.514i 0.0971331 0.587521i
\(681\) −343.662 −0.504643
\(682\) −952.100 952.100i −1.39604 1.39604i
\(683\) −196.064 + 196.064i −0.287064 + 0.287064i −0.835918 0.548854i \(-0.815064\pi\)
0.548854 + 0.835918i \(0.315064\pi\)
\(684\) 163.600i 0.239181i
\(685\) 291.729 208.953i 0.425882 0.305041i
\(686\) −428.903 −0.625223
\(687\) −254.995 254.995i −0.371172 0.371172i
\(688\) −14.8493 + 14.8493i −0.0215833 + 0.0215833i
\(689\) 893.022i 1.29611i
\(690\) −34.2023 47.7515i −0.0495685 0.0692050i
\(691\) −153.130 −0.221606 −0.110803 0.993842i \(-0.535342\pi\)
−0.110803 + 0.993842i \(0.535342\pi\)
\(692\) 11.7572 + 11.7572i 0.0169902 + 0.0169902i
\(693\) −273.320 + 273.320i −0.394402 + 0.394402i
\(694\) 662.911i 0.955204i
\(695\) 379.310 + 62.7103i 0.545770 + 0.0902307i
\(696\) −9.12356 −0.0131086
\(697\) −631.072 631.072i −0.905411 0.905411i
\(698\) 341.273 341.273i 0.488930 0.488930i
\(699\) 581.130i 0.831373i
\(700\) 342.386 168.659i 0.489123 0.240941i
\(701\) −1249.93 −1.78307 −0.891534 0.452953i \(-0.850370\pi\)
−0.891534 + 0.452953i \(0.850370\pi\)
\(702\) −112.613 112.613i −0.160417 0.160417i
\(703\) −403.228 + 403.228i −0.573582 + 0.573582i
\(704\) 135.031i 0.191806i
\(705\) −104.440 + 631.718i −0.148142 + 0.896054i
\(706\) −347.711 −0.492509
\(707\) −191.916 191.916i −0.271451 0.271451i
\(708\) −109.171 + 109.171i −0.154196 + 0.154196i
\(709\) 499.790i 0.704923i 0.935826 + 0.352461i \(0.114655\pi\)
−0.935826 + 0.352461i \(0.885345\pi\)
\(710\) −649.384 + 465.125i −0.914625 + 0.655106i
\(711\) −51.2700 −0.0721097
\(712\) 206.614 + 206.614i 0.290188 + 0.290188i
\(713\) 191.288 191.288i 0.268286 0.268286i
\(714\) 535.389i 0.749844i
\(715\) −1065.04 1486.95i −1.48956 2.07965i
\(716\) 298.719 0.417205
\(717\) 124.309 + 124.309i 0.173374 + 0.173374i
\(718\) 97.4524 97.4524i 0.135728 0.135728i
\(719\) 1307.45i 1.81843i 0.416330 + 0.909213i \(0.363316\pi\)
−0.416330 + 0.909213i \(0.636684\pi\)
\(720\) 59.1964 + 9.78678i 0.0822173 + 0.0135927i
\(721\) 1009.03 1.39949
\(722\) 382.469 + 382.469i 0.529735 + 0.529735i
\(723\) 96.0907 96.0907i 0.132906 0.132906i
\(724\) 86.8794i 0.119999i
\(725\) −14.9852 + 44.0810i −0.0206692 + 0.0608014i
\(726\) −401.467 −0.552985
\(727\) 399.575 + 399.575i 0.549622 + 0.549622i 0.926332 0.376709i \(-0.122944\pi\)
−0.376709 + 0.926332i \(0.622944\pi\)
\(728\) −330.869 + 330.869i −0.454490 + 0.454490i
\(729\) 27.0000i 0.0370370i
\(730\) 112.751 681.985i 0.154453 0.934226i
\(731\) 150.326 0.205645
\(732\) 239.412 + 239.412i 0.327065 + 0.327065i
\(733\) 222.787 222.787i 0.303939 0.303939i −0.538614 0.842553i \(-0.681052\pi\)
0.842553 + 0.538614i \(0.181052\pi\)
\(734\) 646.993i 0.881462i
\(735\) 65.2631 46.7451i 0.0887933 0.0635987i
\(736\) −27.1293 −0.0368605
\(737\) −502.002 502.002i −0.681142 0.681142i
\(738\) 93.5066 93.5066i 0.126703 0.126703i
\(739\) 1354.80i 1.83329i 0.399703 + 0.916645i \(0.369113\pi\)
−0.399703 + 0.916645i \(0.630887\pi\)
\(740\) 121.781 + 170.025i 0.164569 + 0.229763i
\(741\) −1023.52 −1.38127
\(742\) 314.542 + 314.542i 0.423911 + 0.423911i
\(743\) 55.0211 55.0211i 0.0740526 0.0740526i −0.669110 0.743163i \(-0.733325\pi\)
0.743163 + 0.669110i \(0.233325\pi\)
\(744\) 276.340i 0.371425i
\(745\) 1043.80 + 172.568i 1.40107 + 0.231636i
\(746\) −140.688 −0.188590
\(747\) −211.325 211.325i −0.282898 0.282898i
\(748\) 683.491 683.491i 0.913758 0.913758i
\(749\) 784.976i 1.04803i
\(750\) 144.514 269.937i 0.192685 0.359915i
\(751\) 577.871 0.769469 0.384734 0.923027i \(-0.374293\pi\)
0.384734 + 0.923027i \(0.374293\pi\)
\(752\) 209.119 + 209.119i 0.278084 + 0.278084i
\(753\) −588.720 + 588.720i −0.781833 + 0.781833i
\(754\) 57.0793i 0.0757020i
\(755\) −215.687 + 1304.61i −0.285678 + 1.72795i
\(756\) 79.3291 0.104933
\(757\) 95.5246 + 95.5246i 0.126188 + 0.126188i 0.767380 0.641192i \(-0.221560\pi\)
−0.641192 + 0.767380i \(0.721560\pi\)
\(758\) 339.778 339.778i 0.448256 0.448256i
\(759\) 140.207i 0.184726i
\(760\) 313.490 224.539i 0.412487 0.295446i
\(761\) 953.861 1.25343 0.626715 0.779248i \(-0.284399\pi\)
0.626715 + 0.779248i \(0.284399\pi\)
\(762\) 53.3464 + 53.3464i 0.0700085 + 0.0700085i
\(763\) −531.013 + 531.013i −0.695954 + 0.695954i
\(764\) 314.104i 0.411131i
\(765\) −250.098 349.173i −0.326925 0.456436i
\(766\) 12.2671 0.0160145
\(767\) −683.001 683.001i −0.890483 0.890483i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 1519.77i 1.97630i 0.153492 + 0.988150i \(0.450948\pi\)
−0.153492 + 0.988150i \(0.549052\pi\)
\(770\) 898.866 + 148.607i 1.16736 + 0.192996i
\(771\) −313.679 −0.406847
\(772\) 60.3397 + 60.3397i 0.0781602 + 0.0781602i
\(773\) −19.2189 + 19.2189i −0.0248627 + 0.0248627i −0.719429 0.694566i \(-0.755596\pi\)
0.694566 + 0.719429i \(0.255596\pi\)
\(774\) 22.2740i 0.0287778i
\(775\) 1335.15 + 453.880i 1.72278 + 0.585651i
\(776\) −312.467 −0.402663
\(777\) 195.524 + 195.524i 0.251640 + 0.251640i
\(778\) 316.963 316.963i 0.407407 0.407407i
\(779\) 849.870i