Properties

Label 690.3.k.b.553.8
Level $690$
Weight $3$
Character 690.553
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 553.8
Character \(\chi\) \(=\) 690.553
Dual form 690.3.k.b.277.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.55939 - 4.29529i) q^{5} +2.44949 q^{6} +(5.47277 - 5.47277i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.55939 - 4.29529i) q^{5} +2.44949 q^{6} +(5.47277 - 5.47277i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.85468 + 1.73590i) q^{10} +18.3249 q^{11} +(-2.44949 + 2.44949i) q^{12} +(7.21738 + 7.21738i) q^{13} +10.9455i q^{14} +(-2.12604 + 8.39523i) q^{15} -4.00000 q^{16} +(1.48954 - 1.48954i) q^{17} +(-3.00000 - 3.00000i) q^{18} +13.9116i q^{19} +(-8.59058 + 5.11878i) q^{20} -13.4055 q^{21} +(-18.3249 + 18.3249i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-11.8991 + 21.9866i) q^{25} -14.4348 q^{26} +(3.67423 - 3.67423i) q^{27} +(-10.9455 - 10.9455i) q^{28} -0.950775i q^{29} +(-6.26919 - 10.5213i) q^{30} +56.4791 q^{31} +(4.00000 - 4.00000i) q^{32} +(-22.4433 - 22.4433i) q^{33} +2.97907i q^{34} +(-37.5141 - 9.50020i) q^{35} +6.00000 q^{36} +(44.4969 - 44.4969i) q^{37} +(-13.9116 - 13.9116i) q^{38} -17.6789i q^{39} +(3.47181 - 13.7094i) q^{40} -44.8287 q^{41} +(13.4055 - 13.4055i) q^{42} +(31.1063 + 31.1063i) q^{43} -36.6498i q^{44} +(12.8859 - 7.67816i) q^{45} +6.78233 q^{46} +(25.7168 - 25.7168i) q^{47} +(4.89898 + 4.89898i) q^{48} -10.9024i q^{49} +(-10.0876 - 33.8857i) q^{50} -3.64860 q^{51} +(14.4348 - 14.4348i) q^{52} +(-17.7789 - 17.7789i) q^{53} +7.34847i q^{54} +(-46.9005 - 78.7108i) q^{55} +21.8911 q^{56} +(17.0382 - 17.0382i) q^{57} +(0.950775 + 0.950775i) q^{58} -0.459649i q^{59} +(16.7905 + 4.25208i) q^{60} +24.6543 q^{61} +(-56.4791 + 56.4791i) q^{62} +(16.4183 + 16.4183i) q^{63} +8.00000i q^{64} +(12.5287 - 49.4728i) q^{65} +44.8867 q^{66} +(-32.6237 + 32.6237i) q^{67} +(-2.97907 - 2.97907i) q^{68} +8.30662i q^{69} +(47.0143 - 28.0139i) q^{70} +46.7310 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-0.372008 - 0.372008i) q^{73} +88.9939i q^{74} +(41.5013 - 12.3547i) q^{75} +27.8232 q^{76} +(100.288 - 100.288i) q^{77} +(17.6789 + 17.6789i) q^{78} -65.5336i q^{79} +(10.2376 + 17.1812i) q^{80} -9.00000 q^{81} +(44.8287 - 44.8287i) q^{82} +(-85.4484 - 85.4484i) q^{83} +26.8110i q^{84} +(-10.2103 - 2.58569i) q^{85} -62.2125 q^{86} +(-1.16446 + 1.16446i) q^{87} +(36.6498 + 36.6498i) q^{88} +64.0437i q^{89} +(-5.20771 + 20.5640i) q^{90} +78.9980 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-69.1725 - 69.1725i) q^{93} +51.4335i q^{94} +(59.7544 - 35.6052i) q^{95} -9.79796 q^{96} +(49.4654 - 49.4654i) q^{97} +(10.9024 + 10.9024i) q^{98} +54.9747i 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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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
\(5\) −2.55939 4.29529i −0.511878 0.859058i
\(6\) 2.44949 0.408248
\(7\) 5.47277 5.47277i 0.781824 0.781824i −0.198315 0.980138i \(-0.563547\pi\)
0.980138 + 0.198315i \(0.0635468\pi\)
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.85468 + 1.73590i 0.685468 + 0.173590i
\(11\) 18.3249 1.66590 0.832950 0.553348i \(-0.186650\pi\)
0.832950 + 0.553348i \(0.186650\pi\)
\(12\) −2.44949 + 2.44949i −0.204124 + 0.204124i
\(13\) 7.21738 + 7.21738i 0.555183 + 0.555183i 0.927932 0.372749i \(-0.121585\pi\)
−0.372749 + 0.927932i \(0.621585\pi\)
\(14\) 10.9455i 0.781824i
\(15\) −2.12604 + 8.39523i −0.141736 + 0.559682i
\(16\) −4.00000 −0.250000
\(17\) 1.48954 1.48954i 0.0876198 0.0876198i −0.661938 0.749558i \(-0.730266\pi\)
0.749558 + 0.661938i \(0.230266\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 13.9116i 0.732190i 0.930578 + 0.366095i \(0.119305\pi\)
−0.930578 + 0.366095i \(0.880695\pi\)
\(20\) −8.59058 + 5.11878i −0.429529 + 0.255939i
\(21\) −13.4055 −0.638357
\(22\) −18.3249 + 18.3249i −0.832950 + 0.832950i
\(23\) −3.39116 3.39116i −0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −11.8991 + 21.9866i −0.475963 + 0.879465i
\(26\) −14.4348 −0.555183
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −10.9455 10.9455i −0.390912 0.390912i
\(29\) 0.950775i 0.0327854i −0.999866 0.0163927i \(-0.994782\pi\)
0.999866 0.0163927i \(-0.00521818\pi\)
\(30\) −6.26919 10.5213i −0.208973 0.350709i
\(31\) 56.4791 1.82191 0.910954 0.412508i \(-0.135347\pi\)
0.910954 + 0.412508i \(0.135347\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −22.4433 22.4433i −0.680101 0.680101i
\(34\) 2.97907i 0.0876198i
\(35\) −37.5141 9.50020i −1.07183 0.271434i
\(36\) 6.00000 0.166667
\(37\) 44.4969 44.4969i 1.20262 1.20262i 0.229254 0.973367i \(-0.426372\pi\)
0.973367 0.229254i \(-0.0736285\pi\)
\(38\) −13.9116 13.9116i −0.366095 0.366095i
\(39\) 17.6789i 0.453305i
\(40\) 3.47181 13.7094i 0.0867952 0.342734i
\(41\) −44.8287 −1.09338 −0.546692 0.837334i \(-0.684113\pi\)
−0.546692 + 0.837334i \(0.684113\pi\)
\(42\) 13.4055 13.4055i 0.319178 0.319178i
\(43\) 31.1063 + 31.1063i 0.723402 + 0.723402i 0.969296 0.245895i \(-0.0790818\pi\)
−0.245895 + 0.969296i \(0.579082\pi\)
\(44\) 36.6498i 0.832950i
\(45\) 12.8859 7.67816i 0.286353 0.170626i
\(46\) 6.78233 0.147442
\(47\) 25.7168 25.7168i 0.547165 0.547165i −0.378455 0.925620i \(-0.623544\pi\)
0.925620 + 0.378455i \(0.123544\pi\)
\(48\) 4.89898 + 4.89898i 0.102062 + 0.102062i
\(49\) 10.9024i 0.222497i
\(50\) −10.0876 33.8857i −0.201751 0.677714i
\(51\) −3.64860 −0.0715412
\(52\) 14.4348 14.4348i 0.277591 0.277591i
\(53\) −17.7789 17.7789i −0.335450 0.335450i 0.519202 0.854652i \(-0.326229\pi\)
−0.854652 + 0.519202i \(0.826229\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −46.9005 78.7108i −0.852737 1.43111i
\(56\) 21.8911 0.390912
\(57\) 17.0382 17.0382i 0.298915 0.298915i
\(58\) 0.950775 + 0.950775i 0.0163927 + 0.0163927i
\(59\) 0.459649i 0.00779066i −0.999992 0.00389533i \(-0.998760\pi\)
0.999992 0.00389533i \(-0.00123992\pi\)
\(60\) 16.7905 + 4.25208i 0.279841 + 0.0708680i
\(61\) 24.6543 0.404169 0.202084 0.979368i \(-0.435228\pi\)
0.202084 + 0.979368i \(0.435228\pi\)
\(62\) −56.4791 + 56.4791i −0.910954 + 0.910954i
\(63\) 16.4183 + 16.4183i 0.260608 + 0.260608i
\(64\) 8.00000i 0.125000i
\(65\) 12.5287 49.4728i 0.192749 0.761120i
\(66\) 44.8867 0.680101
\(67\) −32.6237 + 32.6237i −0.486920 + 0.486920i −0.907333 0.420413i \(-0.861885\pi\)
0.420413 + 0.907333i \(0.361885\pi\)
\(68\) −2.97907 2.97907i −0.0438099 0.0438099i
\(69\) 8.30662i 0.120386i
\(70\) 47.0143 28.0139i 0.671632 0.400198i
\(71\) 46.7310 0.658183 0.329092 0.944298i \(-0.393258\pi\)
0.329092 + 0.944298i \(0.393258\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) −0.372008 0.372008i −0.00509599 0.00509599i 0.704554 0.709650i \(-0.251147\pi\)
−0.709650 + 0.704554i \(0.751147\pi\)
\(74\) 88.9939i 1.20262i
\(75\) 41.5013 12.3547i 0.553351 0.164729i
\(76\) 27.8232 0.366095
\(77\) 100.288 100.288i 1.30244 1.30244i
\(78\) 17.6789 + 17.6789i 0.226652 + 0.226652i
\(79\) 65.5336i 0.829539i −0.909926 0.414770i \(-0.863862\pi\)
0.909926 0.414770i \(-0.136138\pi\)
\(80\) 10.2376 + 17.1812i 0.127969 + 0.214765i
\(81\) −9.00000 −0.111111
\(82\) 44.8287 44.8287i 0.546692 0.546692i
\(83\) −85.4484 85.4484i −1.02950 1.02950i −0.999551 0.0299470i \(-0.990466\pi\)
−0.0299470 0.999551i \(-0.509534\pi\)
\(84\) 26.8110i 0.319178i
\(85\) −10.2103 2.58569i −0.120121 0.0304199i
\(86\) −62.2125 −0.723402
\(87\) −1.16446 + 1.16446i −0.0133846 + 0.0133846i
\(88\) 36.6498 + 36.6498i 0.416475 + 0.416475i
\(89\) 64.0437i 0.719592i 0.933031 + 0.359796i \(0.117154\pi\)
−0.933031 + 0.359796i \(0.882846\pi\)
\(90\) −5.20771 + 20.5640i −0.0578635 + 0.228489i
\(91\) 78.9980 0.868110
\(92\) −6.78233 + 6.78233i −0.0737210 + 0.0737210i
\(93\) −69.1725 69.1725i −0.743791 0.743791i
\(94\) 51.4335i 0.547165i
\(95\) 59.7544 35.6052i 0.628994 0.374791i
\(96\) −9.79796 −0.102062
\(97\) 49.4654 49.4654i 0.509953 0.509953i −0.404559 0.914512i \(-0.632575\pi\)
0.914512 + 0.404559i \(0.132575\pi\)
\(98\) 10.9024 + 10.9024i 0.111249 + 0.111249i
\(99\) 54.9747i 0.555300i
\(100\) 43.9733 + 23.7981i 0.439733 + 0.237981i
\(101\) −122.832 −1.21616 −0.608078 0.793877i \(-0.708059\pi\)
−0.608078 + 0.793877i \(0.708059\pi\)
\(102\) 3.64860 3.64860i 0.0357706 0.0357706i
\(103\) 40.9149 + 40.9149i 0.397232 + 0.397232i 0.877256 0.480024i \(-0.159372\pi\)
−0.480024 + 0.877256i \(0.659372\pi\)
\(104\) 28.8695i 0.277591i
\(105\) 34.3098 + 57.5805i 0.326760 + 0.548386i
\(106\) 35.5577 0.335450
\(107\) 124.288 124.288i 1.16157 1.16157i 0.177442 0.984131i \(-0.443218\pi\)
0.984131 0.177442i \(-0.0567822\pi\)
\(108\) −7.34847 7.34847i −0.0680414 0.0680414i
\(109\) 28.6845i 0.263161i 0.991306 + 0.131580i \(0.0420051\pi\)
−0.991306 + 0.131580i \(0.957995\pi\)
\(110\) 125.611 + 31.8103i 1.14192 + 0.289184i
\(111\) −108.995 −0.981935
\(112\) −21.8911 + 21.8911i −0.195456 + 0.195456i
\(113\) −124.706 124.706i −1.10360 1.10360i −0.993973 0.109624i \(-0.965035\pi\)
−0.109624 0.993973i \(-0.534965\pi\)
\(114\) 34.0763i 0.298915i
\(115\) −5.88674 + 23.2454i −0.0511890 + 0.202133i
\(116\) −1.90155 −0.0163927
\(117\) −21.6521 + 21.6521i −0.185061 + 0.185061i
\(118\) 0.459649 + 0.459649i 0.00389533 + 0.00389533i
\(119\) 16.3038i 0.137006i
\(120\) −21.0425 + 12.5384i −0.175355 + 0.104487i
\(121\) 214.802 1.77522
\(122\) −24.6543 + 24.6543i −0.202084 + 0.202084i
\(123\) 54.9038 + 54.9038i 0.446372 + 0.446372i
\(124\) 112.958i 0.910954i
\(125\) 124.893 5.16236i 0.999147 0.0412989i
\(126\) −32.8366 −0.260608
\(127\) −18.1196 + 18.1196i −0.142674 + 0.142674i −0.774836 0.632162i \(-0.782168\pi\)
0.632162 + 0.774836i \(0.282168\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 76.1945i 0.590655i
\(130\) 36.9441 + 62.0015i 0.284186 + 0.476934i
\(131\) −88.8228 −0.678037 −0.339018 0.940780i \(-0.610095\pi\)
−0.339018 + 0.940780i \(0.610095\pi\)
\(132\) −44.8867 + 44.8867i −0.340050 + 0.340050i
\(133\) 76.1350 + 76.1350i 0.572443 + 0.572443i
\(134\) 65.2473i 0.486920i
\(135\) −25.1857 6.37812i −0.186561 0.0472453i
\(136\) 5.95814 0.0438099
\(137\) 84.4843 84.4843i 0.616674 0.616674i −0.328003 0.944677i \(-0.606376\pi\)
0.944677 + 0.328003i \(0.106376\pi\)
\(138\) −8.30662 8.30662i −0.0601929 0.0601929i
\(139\) 1.42790i 0.0102727i 0.999987 + 0.00513633i \(0.00163495\pi\)
−0.999987 + 0.00513633i \(0.998365\pi\)
\(140\) −19.0004 + 75.0281i −0.135717 + 0.535915i
\(141\) −62.9930 −0.446759
\(142\) −46.7310 + 46.7310i −0.329092 + 0.329092i
\(143\) 132.258 + 132.258i 0.924879 + 0.924879i
\(144\) 12.0000i 0.0833333i
\(145\) −4.08386 + 2.43340i −0.0281645 + 0.0167821i
\(146\) 0.744015 0.00509599
\(147\) −13.3526 + 13.3526i −0.0908341 + 0.0908341i
\(148\) −88.9939 88.9939i −0.601310 0.601310i
\(149\) 267.416i 1.79474i 0.441280 + 0.897369i \(0.354525\pi\)
−0.441280 + 0.897369i \(0.645475\pi\)
\(150\) −29.1466 + 53.8560i −0.194311 + 0.359040i
\(151\) −160.559 −1.06331 −0.531653 0.846962i \(-0.678429\pi\)
−0.531653 + 0.846962i \(0.678429\pi\)
\(152\) −27.8232 + 27.8232i −0.183047 + 0.183047i
\(153\) 4.46861 + 4.46861i 0.0292066 + 0.0292066i
\(154\) 200.576i 1.30244i
\(155\) −144.552 242.594i −0.932594 1.56513i
\(156\) −35.3578 −0.226652
\(157\) 93.2547 93.2547i 0.593979 0.593979i −0.344725 0.938704i \(-0.612028\pi\)
0.938704 + 0.344725i \(0.112028\pi\)
\(158\) 65.5336 + 65.5336i 0.414770 + 0.414770i
\(159\) 43.5491i 0.273894i
\(160\) −27.4187 6.94362i −0.171367 0.0433976i
\(161\) −37.1181 −0.230547
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) −213.296 213.296i −1.30857 1.30857i −0.922451 0.386115i \(-0.873817\pi\)
−0.386115 0.922451i \(-0.626183\pi\)
\(164\) 89.6575i 0.546692i
\(165\) −38.9595 + 153.842i −0.236118 + 0.932375i
\(166\) 170.897 1.02950
\(167\) −13.9577 + 13.9577i −0.0835792 + 0.0835792i −0.747660 0.664081i \(-0.768823\pi\)
0.664081 + 0.747660i \(0.268823\pi\)
\(168\) −26.8110 26.8110i −0.159589 0.159589i
\(169\) 64.8190i 0.383544i
\(170\) 12.7960 7.62460i 0.0752705 0.0448506i
\(171\) −41.7348 −0.244063
\(172\) 62.2125 62.2125i 0.361701 0.361701i
\(173\) −187.546 187.546i −1.08408 1.08408i −0.996124 0.0879593i \(-0.971965\pi\)
−0.0879593 0.996124i \(-0.528035\pi\)
\(174\) 2.32891i 0.0133846i
\(175\) 55.2069 + 185.449i 0.315468 + 1.05971i
\(176\) −73.2996 −0.416475
\(177\) −0.562953 + 0.562953i −0.00318052 + 0.00318052i
\(178\) −64.0437 64.0437i −0.359796 0.359796i
\(179\) 59.2046i 0.330752i 0.986231 + 0.165376i \(0.0528837\pi\)
−0.986231 + 0.165376i \(0.947116\pi\)
\(180\) −15.3563 25.7718i −0.0853129 0.143176i
\(181\) 218.953 1.20968 0.604842 0.796346i \(-0.293236\pi\)
0.604842 + 0.796346i \(0.293236\pi\)
\(182\) −78.9980 + 78.9980i −0.434055 + 0.434055i
\(183\) −30.1952 30.1952i −0.165001 0.165001i
\(184\) 13.5647i 0.0737210i
\(185\) −305.012 77.2424i −1.64872 0.417527i
\(186\) 138.345 0.743791
\(187\) 27.2956 27.2956i 0.145966 0.145966i
\(188\) −51.4335 51.4335i −0.273583 0.273583i
\(189\) 40.2165i 0.212786i
\(190\) −24.1492 + 95.3596i −0.127101 + 0.501893i
\(191\) −24.7100 −0.129371 −0.0646857 0.997906i \(-0.520604\pi\)
−0.0646857 + 0.997906i \(0.520604\pi\)
\(192\) 9.79796 9.79796i 0.0510310 0.0510310i
\(193\) 116.701 + 116.701i 0.604667 + 0.604667i 0.941548 0.336880i \(-0.109372\pi\)
−0.336880 + 0.941548i \(0.609372\pi\)
\(194\) 98.9308i 0.509953i
\(195\) −75.9360 + 45.2471i −0.389415 + 0.232037i
\(196\) −21.8047 −0.111249
\(197\) 124.625 124.625i 0.632612 0.632612i −0.316111 0.948722i \(-0.602377\pi\)
0.948722 + 0.316111i \(0.102377\pi\)
\(198\) −54.9747 54.9747i −0.277650 0.277650i
\(199\) 261.088i 1.31200i 0.754760 + 0.656001i \(0.227753\pi\)
−0.754760 + 0.656001i \(0.772247\pi\)
\(200\) −67.7714 + 20.1751i −0.338857 + 0.100876i
\(201\) 79.9113 0.397569
\(202\) 122.832 122.832i 0.608078 0.608078i
\(203\) −5.20337 5.20337i −0.0256324 0.0256324i
\(204\) 7.29721i 0.0357706i
\(205\) 114.734 + 192.552i 0.559679 + 0.939280i
\(206\) −81.8298 −0.397232
\(207\) 10.1735 10.1735i 0.0491473 0.0491473i
\(208\) −28.8695 28.8695i −0.138796 0.138796i
\(209\) 254.929i 1.21975i
\(210\) −91.8903 23.2706i −0.437573 0.110813i
\(211\) −164.286 −0.778605 −0.389303 0.921110i \(-0.627284\pi\)
−0.389303 + 0.921110i \(0.627284\pi\)
\(212\) −35.5577 + 35.5577i −0.167725 + 0.167725i
\(213\) −57.2335 57.2335i −0.268702 0.268702i
\(214\) 248.577i 1.16157i
\(215\) 53.9975 213.224i 0.251151 0.991737i
\(216\) 14.6969 0.0680414
\(217\) 309.097 309.097i 1.42441 1.42441i
\(218\) −28.6845 28.6845i −0.131580 0.131580i
\(219\) 0.911229i 0.00416086i
\(220\) −157.422 + 93.8011i −0.715553 + 0.426368i
\(221\) 21.5011 0.0972900
\(222\) 108.995 108.995i 0.490968 0.490968i
\(223\) −187.046 187.046i −0.838771 0.838771i 0.149926 0.988697i \(-0.452097\pi\)
−0.988697 + 0.149926i \(0.952097\pi\)
\(224\) 43.7821i 0.195456i
\(225\) −65.9599 35.6972i −0.293155 0.158654i
\(226\) 249.413 1.10360
\(227\) −218.115 + 218.115i −0.960860 + 0.960860i −0.999262 0.0384021i \(-0.987773\pi\)
0.0384021 + 0.999262i \(0.487773\pi\)
\(228\) −34.0763 34.0763i −0.149458 0.149458i
\(229\) 358.055i 1.56356i 0.623556 + 0.781779i \(0.285687\pi\)
−0.623556 + 0.781779i \(0.714313\pi\)
\(230\) −17.3586 29.1321i −0.0754722 0.126661i
\(231\) −245.654 −1.06344
\(232\) 1.90155 1.90155i 0.00819634 0.00819634i
\(233\) 40.1742 + 40.1742i 0.172422 + 0.172422i 0.788042 0.615621i \(-0.211095\pi\)
−0.615621 + 0.788042i \(0.711095\pi\)
\(234\) 43.3043i 0.185061i
\(235\) −176.280 44.6419i −0.750129 0.189965i
\(236\) −0.919298 −0.00389533
\(237\) −80.2619 + 80.2619i −0.338658 + 0.338658i
\(238\) 16.3038 + 16.3038i 0.0685032 + 0.0685032i
\(239\) 42.3559i 0.177221i 0.996066 + 0.0886106i \(0.0282427\pi\)
−0.996066 + 0.0886106i \(0.971757\pi\)
\(240\) 8.50416 33.5809i 0.0354340 0.139921i
\(241\) 138.250 0.573652 0.286826 0.957983i \(-0.407400\pi\)
0.286826 + 0.957983i \(0.407400\pi\)
\(242\) −214.802 + 214.802i −0.887612 + 0.887612i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 49.3086i 0.202084i
\(245\) −46.8288 + 27.9034i −0.191138 + 0.113891i
\(246\) −109.808 −0.446372
\(247\) −100.405 + 100.405i −0.406499 + 0.406499i
\(248\) 112.958 + 112.958i 0.455477 + 0.455477i
\(249\) 209.305i 0.840582i
\(250\) −119.731 + 130.056i −0.478924 + 0.520223i
\(251\) −167.580 −0.667649 −0.333824 0.942635i \(-0.608339\pi\)
−0.333824 + 0.942635i \(0.608339\pi\)
\(252\) 32.8366 32.8366i 0.130304 0.130304i
\(253\) −62.1428 62.1428i −0.245624 0.245624i
\(254\) 36.2391i 0.142674i
\(255\) 9.33819 + 15.6718i 0.0366204 + 0.0614581i
\(256\) 16.0000 0.0625000
\(257\) −137.640 + 137.640i −0.535565 + 0.535565i −0.922223 0.386658i \(-0.873629\pi\)
0.386658 + 0.922223i \(0.373629\pi\)
\(258\) 76.1945 + 76.1945i 0.295327 + 0.295327i
\(259\) 487.043i 1.88047i
\(260\) −98.9456 25.0573i −0.380560 0.0963744i
\(261\) 2.85233 0.0109285
\(262\) 88.8228 88.8228i 0.339018 0.339018i
\(263\) −147.620 147.620i −0.561293 0.561293i 0.368381 0.929675i \(-0.379912\pi\)
−0.929675 + 0.368381i \(0.879912\pi\)
\(264\) 89.7733i 0.340050i
\(265\) −30.8624 + 121.868i −0.116462 + 0.459881i
\(266\) −152.270 −0.572443
\(267\) 78.4372 78.4372i 0.293772 0.293772i
\(268\) 65.2473 + 65.2473i 0.243460 + 0.243460i
\(269\) 43.0679i 0.160104i −0.996791 0.0800518i \(-0.974491\pi\)
0.996791 0.0800518i \(-0.0255086\pi\)
\(270\) 31.5638 18.8076i 0.116903 0.0696577i
\(271\) −455.005 −1.67898 −0.839492 0.543372i \(-0.817147\pi\)
−0.839492 + 0.543372i \(0.817147\pi\)
\(272\) −5.95814 + 5.95814i −0.0219049 + 0.0219049i
\(273\) −96.7524 96.7524i −0.354405 0.354405i
\(274\) 168.969i 0.616674i
\(275\) −218.049 + 402.903i −0.792906 + 1.46510i
\(276\) 16.6132 0.0601929
\(277\) 75.2499 75.2499i 0.271660 0.271660i −0.558108 0.829768i \(-0.688472\pi\)
0.829768 + 0.558108i \(0.188472\pi\)
\(278\) −1.42790 1.42790i −0.00513633 0.00513633i
\(279\) 169.437i 0.607303i
\(280\) −56.0277 94.0285i −0.200099 0.335816i
\(281\) 34.5423 0.122926 0.0614632 0.998109i \(-0.480423\pi\)
0.0614632 + 0.998109i \(0.480423\pi\)
\(282\) 62.9930 62.9930i 0.223379 0.223379i
\(283\) 84.0695 + 84.0695i 0.297065 + 0.297065i 0.839863 0.542798i \(-0.182635\pi\)
−0.542798 + 0.839863i \(0.682635\pi\)
\(284\) 93.4620i 0.329092i
\(285\) −116.791 29.5766i −0.409794 0.103778i
\(286\) −264.515 −0.924879
\(287\) −245.337 + 245.337i −0.854833 + 0.854833i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 284.563i 0.984646i
\(290\) 1.65045 6.51726i 0.00569122 0.0224733i
\(291\) −121.165 −0.416375
\(292\) −0.744015 + 0.744015i −0.00254800 + 0.00254800i
\(293\) 358.395 + 358.395i 1.22319 + 1.22319i 0.966491 + 0.256700i \(0.0826354\pi\)
0.256700 + 0.966491i \(0.417365\pi\)
\(294\) 26.7052i 0.0908341i
\(295\) −1.97433 + 1.17642i −0.00669263 + 0.00398786i
\(296\) 177.988 0.601310
\(297\) 67.3300 67.3300i 0.226700 0.226700i
\(298\) −267.416 267.416i −0.897369 0.897369i
\(299\) 48.9506i 0.163714i
\(300\) −24.7094 83.0027i −0.0823647 0.276676i
\(301\) 340.475 1.13115
\(302\) 160.559 160.559i 0.531653 0.531653i
\(303\) 150.438 + 150.438i 0.496494 + 0.496494i
\(304\) 55.6464i 0.183047i
\(305\) −63.0999 105.897i −0.206885 0.347205i
\(306\) −8.93722 −0.0292066
\(307\) −43.1449 + 43.1449i −0.140537 + 0.140537i −0.773875 0.633338i \(-0.781684\pi\)
0.633338 + 0.773875i \(0.281684\pi\)
\(308\) −200.576 200.576i −0.651220 0.651220i
\(309\) 100.221i 0.324338i
\(310\) 387.146 + 98.0424i 1.24886 + 0.316266i
\(311\) 188.459 0.605976 0.302988 0.952994i \(-0.402016\pi\)
0.302988 + 0.952994i \(0.402016\pi\)
\(312\) 35.3578 35.3578i 0.113326 0.113326i
\(313\) −140.266 140.266i −0.448134 0.448134i 0.446600 0.894734i \(-0.352635\pi\)
−0.894734 + 0.446600i \(0.852635\pi\)
\(314\) 186.509i 0.593979i
\(315\) 28.5006 112.542i 0.0904781 0.357277i
\(316\) −131.067 −0.414770
\(317\) −127.294 + 127.294i −0.401557 + 0.401557i −0.878782 0.477224i \(-0.841643\pi\)
0.477224 + 0.878782i \(0.341643\pi\)
\(318\) −43.5491 43.5491i −0.136947 0.136947i
\(319\) 17.4229i 0.0546171i
\(320\) 34.3623 20.4751i 0.107382 0.0639847i
\(321\) −304.443 −0.948421
\(322\) 37.1181 37.1181i 0.115274 0.115274i
\(323\) 20.7218 + 20.7218i 0.0641543 + 0.0641543i
\(324\) 18.0000i 0.0555556i
\(325\) −244.566 + 72.8058i −0.752510 + 0.224018i
\(326\) 426.592 1.30857
\(327\) 35.1312 35.1312i 0.107435 0.107435i
\(328\) −89.6575 89.6575i −0.273346 0.273346i
\(329\) 281.484i 0.855574i
\(330\) −114.882 192.801i −0.348128 0.584246i
\(331\) 432.406 1.30636 0.653182 0.757201i \(-0.273434\pi\)
0.653182 + 0.757201i \(0.273434\pi\)
\(332\) −170.897 + 170.897i −0.514749 + 0.514749i
\(333\) 133.491 + 133.491i 0.400873 + 0.400873i
\(334\) 27.9154i 0.0835792i
\(335\) 223.625 + 56.6316i 0.667537 + 0.169049i
\(336\) 53.6219 0.159589
\(337\) 251.277 251.277i 0.745630 0.745630i −0.228025 0.973655i \(-0.573227\pi\)
0.973655 + 0.228025i \(0.0732269\pi\)
\(338\) 64.8190 + 64.8190i 0.191772 + 0.191772i
\(339\) 305.467i 0.901083i
\(340\) −5.17138 + 20.4206i −0.0152100 + 0.0600605i
\(341\) 1034.97 3.03512
\(342\) 41.7348 41.7348i 0.122032 0.122032i
\(343\) 208.500 + 208.500i 0.607870 + 0.607870i
\(344\) 124.425i 0.361701i
\(345\) 35.6794 21.2599i 0.103418 0.0616228i
\(346\) 375.093 1.08408
\(347\) 151.537 151.537i 0.436707 0.436707i −0.454195 0.890902i \(-0.650073\pi\)
0.890902 + 0.454195i \(0.150073\pi\)
\(348\) 2.32891 + 2.32891i 0.00669228 + 0.00669228i
\(349\) 642.693i 1.84153i −0.390120 0.920764i \(-0.627566\pi\)
0.390120 0.920764i \(-0.372434\pi\)
\(350\) −240.655 130.242i −0.687587 0.372119i
\(351\) 53.0367 0.151102
\(352\) 73.2996 73.2996i 0.208238 0.208238i
\(353\) 412.979 + 412.979i 1.16991 + 1.16991i 0.982230 + 0.187681i \(0.0600973\pi\)
0.187681 + 0.982230i \(0.439903\pi\)
\(354\) 1.12591i 0.00318052i
\(355\) −119.603 200.723i −0.336909 0.565418i
\(356\) 128.087 0.359796
\(357\) −19.9680 + 19.9680i −0.0559326 + 0.0559326i
\(358\) −59.2046 59.2046i −0.165376 0.165376i
\(359\) 149.819i 0.417324i 0.977988 + 0.208662i \(0.0669109\pi\)
−0.977988 + 0.208662i \(0.933089\pi\)
\(360\) 41.1281 + 10.4154i 0.114245 + 0.0289317i
\(361\) 167.467 0.463898
\(362\) −218.953 + 218.953i −0.604842 + 0.604842i
\(363\) −263.078 263.078i −0.724732 0.724732i
\(364\) 157.996i 0.434055i
\(365\) −0.645770 + 2.54999i −0.00176923 + 0.00698628i
\(366\) 60.3905 0.165001
\(367\) −257.690 + 257.690i −0.702152 + 0.702152i −0.964872 0.262720i \(-0.915380\pi\)
0.262720 + 0.964872i \(0.415380\pi\)
\(368\) 13.5647 + 13.5647i 0.0368605 + 0.0368605i
\(369\) 134.486i 0.364461i
\(370\) 382.255 227.770i 1.03312 0.615594i
\(371\) −194.599 −0.524526
\(372\) −138.345 + 138.345i −0.371895 + 0.371895i
\(373\) −274.503 274.503i −0.735934 0.735934i 0.235854 0.971788i \(-0.424211\pi\)
−0.971788 + 0.235854i \(0.924211\pi\)
\(374\) 54.5912i 0.145966i
\(375\) −159.285 146.640i −0.424760 0.391040i
\(376\) 102.867 0.273583
\(377\) 6.86210 6.86210i 0.0182019 0.0182019i
\(378\) 40.2165 + 40.2165i 0.106393 + 0.106393i
\(379\) 543.361i 1.43367i 0.697243 + 0.716834i \(0.254410\pi\)
−0.697243 + 0.716834i \(0.745590\pi\)
\(380\) −71.2104 119.509i −0.187396 0.314497i
\(381\) 44.3837 0.116493
\(382\) 24.7100 24.7100i 0.0646857 0.0646857i
\(383\) 322.889 + 322.889i 0.843053 + 0.843053i 0.989255 0.146202i \(-0.0467049\pi\)
−0.146202 + 0.989255i \(0.546705\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −687.442 174.090i −1.78556 0.452182i
\(386\) −233.402 −0.604667
\(387\) −93.3188 + 93.3188i −0.241134 + 0.241134i
\(388\) −98.9308 98.9308i −0.254976 0.254976i
\(389\) 720.417i 1.85197i −0.377557 0.925986i \(-0.623236\pi\)
0.377557 0.925986i \(-0.376764\pi\)
\(390\) 30.6889 121.183i 0.0786894 0.310726i
\(391\) −10.1025 −0.0258377
\(392\) 21.8047 21.8047i 0.0556243 0.0556243i
\(393\) 108.785 + 108.785i 0.276807 + 0.276807i
\(394\) 249.249i 0.632612i
\(395\) −281.486 + 167.726i −0.712623 + 0.424622i
\(396\) 109.949 0.277650
\(397\) 139.692 139.692i 0.351869 0.351869i −0.508936 0.860804i \(-0.669961\pi\)
0.860804 + 0.508936i \(0.169961\pi\)
\(398\) −261.088 261.088i −0.656001 0.656001i
\(399\) 186.492i 0.467398i
\(400\) 47.5963 87.9465i 0.118991 0.219866i
\(401\) 410.867 1.02461 0.512303 0.858805i \(-0.328793\pi\)
0.512303 + 0.858805i \(0.328793\pi\)
\(402\) −79.9113 + 79.9113i −0.198784 + 0.198784i
\(403\) 407.631 + 407.631i 1.01149 + 1.01149i
\(404\) 245.664i 0.608078i
\(405\) 23.0345 + 38.6576i 0.0568753 + 0.0954509i
\(406\) 10.4067 0.0256324
\(407\) 815.402 815.402i 2.00345 2.00345i
\(408\) −7.29721 7.29721i −0.0178853 0.0178853i
\(409\) 185.429i 0.453372i −0.973968 0.226686i \(-0.927211\pi\)
0.973968 0.226686i \(-0.0727891\pi\)
\(410\) −307.287 77.8184i −0.749480 0.189801i
\(411\) −206.943 −0.503512
\(412\) 81.8298 81.8298i 0.198616 0.198616i
\(413\) −2.51555 2.51555i −0.00609092 0.00609092i
\(414\) 20.3470i 0.0491473i
\(415\) −148.330 + 585.721i −0.357422 + 1.41138i
\(416\) 57.7390 0.138796
\(417\) 1.74881 1.74881i 0.00419379 0.00419379i
\(418\) −254.929 254.929i −0.609877 0.609877i
\(419\) 203.166i 0.484884i −0.970166 0.242442i \(-0.922052\pi\)
0.970166 0.242442i \(-0.0779484\pi\)
\(420\) 115.161 68.6197i 0.274193 0.163380i
\(421\) −622.636 −1.47895 −0.739473 0.673187i \(-0.764925\pi\)
−0.739473 + 0.673187i \(0.764925\pi\)
\(422\) 164.286 164.286i 0.389303 0.389303i
\(423\) 77.1503 + 77.1503i 0.182388 + 0.182388i
\(424\) 71.1154i 0.167725i
\(425\) 15.0258 + 50.4740i 0.0353548 + 0.118762i
\(426\) 114.467 0.268702
\(427\) 134.927 134.927i 0.315989 0.315989i
\(428\) −248.577 248.577i −0.580787 0.580787i
\(429\) 323.964i 0.755161i
\(430\) 159.226 + 267.221i 0.370293 + 0.621444i
\(431\) 645.267 1.49714 0.748570 0.663056i \(-0.230741\pi\)
0.748570 + 0.663056i \(0.230741\pi\)
\(432\) −14.6969 + 14.6969i −0.0340207 + 0.0340207i
\(433\) 332.543 + 332.543i 0.767998 + 0.767998i 0.977754 0.209756i \(-0.0672669\pi\)
−0.209756 + 0.977754i \(0.567267\pi\)
\(434\) 618.194i 1.42441i
\(435\) 7.98198 + 2.02139i 0.0183494 + 0.00464686i
\(436\) 57.3690 0.131580
\(437\) 47.1765 47.1765i 0.107955 0.107955i
\(438\) −0.911229 0.911229i −0.00208043 0.00208043i
\(439\) 42.1637i 0.0960448i 0.998846 + 0.0480224i \(0.0152919\pi\)
−0.998846 + 0.0480224i \(0.984708\pi\)
\(440\) 63.6205 251.223i 0.144592 0.570961i
\(441\) 32.7071 0.0741657
\(442\) −21.5011 + 21.5011i −0.0486450 + 0.0486450i
\(443\) −18.6195 18.6195i −0.0420305 0.0420305i 0.685779 0.727810i \(-0.259462\pi\)
−0.727810 + 0.685779i \(0.759462\pi\)
\(444\) 217.990i 0.490968i
\(445\) 275.086 163.913i 0.618172 0.368343i
\(446\) 374.092 0.838771
\(447\) 327.517 327.517i 0.732699 0.732699i
\(448\) 43.7821 + 43.7821i 0.0977280 + 0.0977280i
\(449\) 256.938i 0.572245i 0.958193 + 0.286123i \(0.0923665\pi\)
−0.958193 + 0.286123i \(0.907633\pi\)
\(450\) 101.657 30.2627i 0.225905 0.0672505i
\(451\) −821.482 −1.82147
\(452\) −249.413 + 249.413i −0.551798 + 0.551798i
\(453\) 196.644 + 196.644i 0.434093 + 0.434093i
\(454\) 436.231i 0.960860i
\(455\) −202.187 339.320i −0.444366 0.745757i
\(456\) 68.1527 0.149458
\(457\) −343.079 + 343.079i −0.750719 + 0.750719i −0.974613 0.223894i \(-0.928123\pi\)
0.223894 + 0.974613i \(0.428123\pi\)
\(458\) −358.055 358.055i −0.781779 0.781779i
\(459\) 10.9458i 0.0238471i
\(460\) 46.4907 + 11.7735i 0.101067 + 0.0255945i
\(461\) −518.066 −1.12379 −0.561893 0.827210i \(-0.689927\pi\)
−0.561893 + 0.827210i \(0.689927\pi\)
\(462\) 245.654 245.654i 0.531719 0.531719i
\(463\) 581.305 + 581.305i 1.25552 + 1.25552i 0.953211 + 0.302307i \(0.0977567\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(464\) 3.80310i 0.00819634i
\(465\) −120.077 + 474.156i −0.258230 + 1.01969i
\(466\) −80.3485 −0.172422
\(467\) −175.982 + 175.982i −0.376835 + 0.376835i −0.869959 0.493124i \(-0.835855\pi\)
0.493124 + 0.869959i \(0.335855\pi\)
\(468\) 43.3043 + 43.3043i 0.0925305 + 0.0925305i
\(469\) 357.084i 0.761372i
\(470\) 220.922 131.638i 0.470047 0.280082i
\(471\) −228.426 −0.484982
\(472\) 0.919298 0.919298i 0.00194766 0.00194766i
\(473\) 570.019 + 570.019i 1.20511 + 1.20511i
\(474\) 160.524i 0.338658i
\(475\) −305.869 165.535i −0.643936 0.348495i
\(476\) −32.6075 −0.0685032
\(477\) 53.3366 53.3366i 0.111817 0.111817i
\(478\) −42.3559 42.3559i −0.0886106 0.0886106i
\(479\) 92.7211i 0.193572i −0.995305 0.0967861i \(-0.969144\pi\)
0.995305 0.0967861i \(-0.0308563\pi\)
\(480\) 25.0768 + 42.0851i 0.0522433 + 0.0876773i
\(481\) 642.302 1.33535
\(482\) −138.250 + 138.250i −0.286826 + 0.286826i
\(483\) 45.4602 + 45.4602i 0.0941205 + 0.0941205i
\(484\) 429.604i 0.887612i
\(485\) −339.069 85.8672i −0.699112 0.177046i
\(486\) −22.0454 −0.0453609
\(487\) −359.308 + 359.308i −0.737800 + 0.737800i −0.972152 0.234352i \(-0.924703\pi\)
0.234352 + 0.972152i \(0.424703\pi\)
\(488\) 49.3086 + 49.3086i 0.101042 + 0.101042i
\(489\) 522.467i 1.06844i
\(490\) 18.9255 74.7322i 0.0386234 0.152515i
\(491\) 215.844 0.439601 0.219801 0.975545i \(-0.429459\pi\)
0.219801 + 0.975545i \(0.429459\pi\)
\(492\) 109.808 109.808i 0.223186 0.223186i
\(493\) −1.41621 1.41621i −0.00287264 0.00287264i
\(494\) 200.811i 0.406499i
\(495\) 236.132 140.702i 0.477035 0.284246i
\(496\) −225.917 −0.455477
\(497\) 255.748 255.748i 0.514583 0.514583i
\(498\) −209.305 209.305i −0.420291 0.420291i
\(499\) 236.340i 0.473626i 0.971555 + 0.236813i \(0.0761029\pi\)
−0.971555 + 0.236813i \(0.923897\pi\)
\(500\) −10.3247 249.787i −0.0206494 0.499573i
\(501\) 34.1893 0.0682421
\(502\) 167.580 167.580i 0.333824 0.333824i
\(503\) 158.114 + 158.114i 0.314342 + 0.314342i 0.846589 0.532247i \(-0.178652\pi\)
−0.532247 + 0.846589i \(0.678652\pi\)
\(504\) 65.6732i 0.130304i
\(505\) 314.374 + 527.599i 0.622523 + 1.04475i
\(506\) 124.286 0.245624
\(507\) −79.3867 + 79.3867i −0.156581 + 0.156581i
\(508\) 36.2391 + 36.2391i 0.0713368 + 0.0713368i
\(509\) 895.884i 1.76009i −0.474894 0.880043i \(-0.657514\pi\)
0.474894 0.880043i \(-0.342486\pi\)
\(510\) −25.0100 6.33363i −0.0490392 0.0124189i
\(511\) −4.07182 −0.00796834
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) 51.1145 + 51.1145i 0.0996384 + 0.0996384i
\(514\) 275.281i 0.535565i
\(515\) 71.0243 280.458i 0.137911 0.544579i
\(516\) −152.389 −0.295327
\(517\) 471.257 471.257i 0.911523 0.911523i
\(518\) 487.043 + 487.043i 0.940237 + 0.940237i
\(519\) 459.393i 0.885150i
\(520\) 124.003 73.8883i 0.238467 0.142093i
\(521\) 624.757 1.19915 0.599575 0.800319i \(-0.295336\pi\)
0.599575 + 0.800319i \(0.295336\pi\)
\(522\) −2.85233 + 2.85233i −0.00546423 + 0.00546423i
\(523\) −604.436 604.436i −1.15571 1.15571i −0.985389 0.170321i \(-0.945520\pi\)
−0.170321 0.985389i \(-0.554480\pi\)
\(524\) 177.646i 0.339018i
\(525\) 159.513 294.742i 0.303834 0.561413i
\(526\) 295.240 0.561293
\(527\) 84.1277 84.1277i 0.159635 0.159635i
\(528\) 89.7733 + 89.7733i 0.170025 + 0.170025i
\(529\) 23.0000i 0.0434783i
\(530\) −91.0060 152.731i −0.171709 0.288171i
\(531\) 1.37895 0.00259689
\(532\) 152.270 152.270i 0.286222 0.286222i
\(533\) −323.546 323.546i −0.607028 0.607028i
\(534\) 156.874i 0.293772i
\(535\) −851.957 215.753i −1.59244 0.403276i
\(536\) −130.495 −0.243460
\(537\) 72.5105 72.5105i 0.135029 0.135029i
\(538\) 43.0679 + 43.0679i 0.0800518 + 0.0800518i
\(539\) 199.785i 0.370658i
\(540\) −12.7562 + 50.3714i −0.0236227 + 0.0932804i
\(541\) 1001.87 1.85188 0.925938 0.377675i \(-0.123276\pi\)
0.925938 + 0.377675i \(0.123276\pi\)
\(542\) 455.005 455.005i 0.839492 0.839492i
\(543\) −268.161 268.161i −0.493851 0.493851i
\(544\) 11.9163i 0.0219049i
\(545\) 123.208 73.4148i 0.226070 0.134706i
\(546\) 193.505 0.354405
\(547\) 408.706 408.706i 0.747177 0.747177i −0.226771 0.973948i \(-0.572817\pi\)
0.973948 + 0.226771i \(0.0728170\pi\)
\(548\) −168.969 168.969i −0.308337 0.308337i
\(549\) 73.9629i 0.134723i
\(550\) −184.854 620.952i −0.336098 1.12900i
\(551\) 13.2268 0.0240051
\(552\) −16.6132 + 16.6132i −0.0300965 + 0.0300965i
\(553\) −358.650 358.650i −0.648554 0.648554i
\(554\) 150.500i 0.271660i
\(555\) 278.960 + 468.165i 0.502631 + 0.843540i
\(556\) 2.85580 0.00513633
\(557\) 749.003 749.003i 1.34471 1.34471i 0.453402 0.891306i \(-0.350210\pi\)
0.891306 0.453402i \(-0.149790\pi\)
\(558\) −169.437 169.437i −0.303651 0.303651i
\(559\) 449.011i 0.803240i
\(560\) 150.056 + 38.0008i 0.267958 + 0.0678586i
\(561\) −66.8603 −0.119181
\(562\) −34.5423 + 34.5423i −0.0614632 + 0.0614632i
\(563\) −428.420 428.420i −0.760959 0.760959i 0.215537 0.976496i \(-0.430850\pi\)
−0.976496 + 0.215537i \(0.930850\pi\)
\(564\) 125.986i 0.223379i
\(565\) −216.478 + 854.823i −0.383148 + 1.51296i
\(566\) −168.139 −0.297065
\(567\) −49.2549 + 49.2549i −0.0868693 + 0.0868693i
\(568\) 93.4620 + 93.4620i 0.164546 + 0.164546i
\(569\) 800.840i 1.40745i 0.710472 + 0.703725i \(0.248481\pi\)
−0.710472 + 0.703725i \(0.751519\pi\)
\(570\) 146.368 87.2145i 0.256786 0.153008i
\(571\) 675.867 1.18366 0.591828 0.806064i \(-0.298407\pi\)
0.591828 + 0.806064i \(0.298407\pi\)
\(572\) 264.515 264.515i 0.462440 0.462440i
\(573\) 30.2634 + 30.2634i 0.0528157 + 0.0528157i
\(574\) 490.674i 0.854833i
\(575\) 114.912 34.2086i 0.199847 0.0594932i
\(576\) −24.0000 −0.0416667
\(577\) −639.279 + 639.279i −1.10794 + 1.10794i −0.114515 + 0.993422i \(0.536531\pi\)
−0.993422 + 0.114515i \(0.963469\pi\)
\(578\) −284.563 284.563i −0.492323 0.492323i
\(579\) 285.857i 0.493709i
\(580\) 4.86681 + 8.16771i 0.00839104 + 0.0140823i
\(581\) −935.278 −1.60977
\(582\) 121.165 121.165i 0.208187 0.208187i
\(583\) −325.796 325.796i −0.558826 0.558826i
\(584\) 1.48803i 0.00254800i
\(585\) 148.418 + 37.5860i 0.253707 + 0.0642496i
\(586\) −716.790 −1.22319
\(587\) −578.249 + 578.249i −0.985092 + 0.985092i −0.999890 0.0147984i \(-0.995289\pi\)
0.0147984 + 0.999890i \(0.495289\pi\)
\(588\) 26.7052 + 26.7052i 0.0454170 + 0.0454170i
\(589\) 785.715i 1.33398i
\(590\) 0.797906 3.15075i 0.00135238 0.00534025i
\(591\) −305.267 −0.516525
\(592\) −177.988 + 177.988i −0.300655 + 0.300655i
\(593\) 118.071 + 118.071i 0.199109 + 0.199109i 0.799618 0.600509i \(-0.205035\pi\)
−0.600509 + 0.799618i \(0.705035\pi\)
\(594\) 134.660i 0.226700i
\(595\) −70.0294 + 41.7277i −0.117697 + 0.0701305i
\(596\) 534.832 0.897369
\(597\) 319.767 319.767i 0.535623 0.535623i
\(598\) 48.9506 + 48.9506i 0.0818572 + 0.0818572i
\(599\) 262.366i 0.438006i 0.975724 + 0.219003i \(0.0702805\pi\)
−0.975724 + 0.219003i \(0.929720\pi\)
\(600\) 107.712 + 58.2933i 0.179520 + 0.0971555i
\(601\) −409.994 −0.682186 −0.341093 0.940030i \(-0.610797\pi\)
−0.341093 + 0.940030i \(0.610797\pi\)
\(602\) −340.475 + 340.475i −0.565573 + 0.565573i
\(603\) −97.8710 97.8710i −0.162307 0.162307i
\(604\) 321.118i 0.531653i
\(605\) −549.762 922.637i −0.908697 1.52502i
\(606\) −300.875 −0.496494
\(607\) 590.141 590.141i 0.972226 0.972226i −0.0273990 0.999625i \(-0.508722\pi\)
0.999625 + 0.0273990i \(0.00872246\pi\)
\(608\) 55.6464 + 55.6464i 0.0915237 + 0.0915237i
\(609\) 12.7456i 0.0209287i
\(610\) 168.997 + 42.7975i 0.277045 + 0.0701598i
\(611\) 371.215 0.607554
\(612\) 8.93722 8.93722i 0.0146033 0.0146033i
\(613\) −29.4751 29.4751i −0.0480834 0.0480834i 0.682656 0.730740i \(-0.260825\pi\)
−0.730740 + 0.682656i \(0.760825\pi\)
\(614\) 86.2897i 0.140537i
\(615\) 95.3077 376.348i 0.154972 0.611947i
\(616\) 401.152 0.651220
\(617\) −97.0052 + 97.0052i −0.157221 + 0.157221i −0.781334 0.624113i \(-0.785460\pi\)
0.624113 + 0.781334i \(0.285460\pi\)
\(618\) 100.221 + 100.221i 0.162169 + 0.162169i
\(619\) 464.849i 0.750968i −0.926829 0.375484i \(-0.877476\pi\)
0.926829 0.375484i \(-0.122524\pi\)
\(620\) −485.189 + 289.104i −0.782563 + 0.466297i
\(621\) −24.9199 −0.0401286
\(622\) −188.459 + 188.459i −0.302988 + 0.302988i
\(623\) 350.496 + 350.496i 0.562594 + 0.562594i
\(624\) 70.7156i 0.113326i
\(625\) −341.824 523.241i −0.546919 0.837186i
\(626\) 280.532 0.448134
\(627\) 312.223 312.223i 0.497963 0.497963i
\(628\) −186.509 186.509i −0.296989 0.296989i
\(629\) 132.560i 0.210747i
\(630\) 84.0416 + 141.043i 0.133399 + 0.223877i
\(631\) −1003.19 −1.58984 −0.794920 0.606714i \(-0.792487\pi\)
−0.794920 + 0.606714i \(0.792487\pi\)
\(632\) 131.067 131.067i 0.207385 0.207385i
\(633\) 201.208 + 201.208i 0.317864 + 0.317864i
\(634\) 254.587i 0.401557i
\(635\) 124.204 + 31.4538i 0.195596 + 0.0495336i
\(636\) 87.0982 0.136947
\(637\) 78.6864 78.6864i 0.123527 0.123527i
\(638\) 17.4229 + 17.4229i 0.0273086 + 0.0273086i
\(639\) 140.193i 0.219394i
\(640\) −13.8872 + 54.8374i −0.0216988 + 0.0856835i
\(641\) −118.638 −0.185082 −0.0925410 0.995709i \(-0.529499\pi\)
−0.0925410 + 0.995709i \(0.529499\pi\)
\(642\) 304.443 304.443i 0.474210 0.474210i
\(643\) −790.836 790.836i −1.22992 1.22992i −0.963995 0.265920i \(-0.914324\pi\)
−0.265920 0.963995i \(-0.585676\pi\)
\(644\) 74.2362i 0.115274i
\(645\) −327.278 + 195.011i −0.507407 + 0.302343i
\(646\) −41.4437 −0.0641543
\(647\) −672.665 + 672.665i −1.03967 + 1.03967i −0.0404870 + 0.999180i \(0.512891\pi\)
−0.999180 + 0.0404870i \(0.987109\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 8.42302i 0.0129785i
\(650\) 171.760 317.372i 0.264246 0.488264i
\(651\) −757.130 −1.16303
\(652\) −426.592 + 426.592i −0.654283 + 0.654283i
\(653\) 702.904 + 702.904i 1.07642 + 1.07642i 0.996827 + 0.0795956i \(0.0253629\pi\)
0.0795956 + 0.996827i \(0.474637\pi\)
\(654\) 70.2624i 0.107435i
\(655\) 227.332 + 381.520i 0.347072 + 0.582473i
\(656\) 179.315 0.273346
\(657\) 1.11602 1.11602i 0.00169866 0.00169866i
\(658\) 281.484 + 281.484i 0.427787 + 0.427787i
\(659\) 1097.53i 1.66545i −0.553683 0.832727i \(-0.686778\pi\)
0.553683 0.832727i \(-0.313222\pi\)
\(660\) 307.684 + 77.9189i 0.466187 + 0.118059i
\(661\) −620.423 −0.938613 −0.469306 0.883035i \(-0.655496\pi\)
−0.469306 + 0.883035i \(0.655496\pi\)
\(662\) −432.406 + 432.406i −0.653182 + 0.653182i
\(663\) −26.3333 26.3333i −0.0397185 0.0397185i
\(664\) 341.793i 0.514749i
\(665\) 132.163 521.881i 0.198741 0.784783i
\(666\) −266.982 −0.400873
\(667\) −3.22424 + 3.22424i −0.00483394 + 0.00483394i
\(668\) 27.9154 + 27.9154i 0.0417896 + 0.0417896i
\(669\) 458.167i 0.684854i
\(670\) −280.256 + 166.993i −0.418293 + 0.249244i
\(671\) 451.788 0.673305
\(672\) −53.6219 + 53.6219i −0.0797946 + 0.0797946i
\(673\) −512.487 512.487i −0.761496 0.761496i 0.215097 0.976593i \(-0.430993\pi\)
−0.976593 + 0.215097i \(0.930993\pi\)
\(674\) 502.555i 0.745630i
\(675\) 37.0641 + 124.504i 0.0549098 + 0.184450i
\(676\) −129.638 −0.191772
\(677\) −141.059 + 141.059i −0.208359 + 0.208359i −0.803570 0.595211i \(-0.797069\pi\)
0.595211 + 0.803570i \(0.297069\pi\)
\(678\) −305.467 305.467i −0.450542 0.450542i
\(679\) 541.425i 0.797386i
\(680\) −15.2492 25.5920i −0.0224253 0.0376352i
\(681\) 534.271 0.784539
\(682\) −1034.97 + 1034.97i −1.51756 + 1.51756i
\(683\) −606.606 606.606i −0.888150 0.888150i 0.106196 0.994345i \(-0.466133\pi\)
−0.994345 + 0.106196i \(0.966133\pi\)
\(684\) 83.4696i 0.122032i
\(685\) −579.113 146.657i −0.845420 0.214097i
\(686\) −416.999 −0.607870
\(687\) 438.526 438.526i 0.638320 0.638320i
\(688\) −124.425 124.425i −0.180850 0.180850i
\(689\) 256.633i 0.372472i
\(690\) −14.4195 + 56.9392i −0.0208978 + 0.0825206i
\(691\) 646.171 0.935125 0.467563 0.883960i \(-0.345132\pi\)
0.467563 + 0.883960i \(0.345132\pi\)
\(692\) −375.093 + 375.093i −0.542042 + 0.542042i
\(693\) 300.864 + 300.864i 0.434147 + 0.434147i
\(694\) 303.075i 0.436707i
\(695\) 6.13324 3.65455i 0.00882481 0.00525834i
\(696\) −4.65783 −0.00669228
\(697\) −66.7740 + 66.7740i −0.0958020 + 0.0958020i
\(698\) 642.693 + 642.693i 0.920764 + 0.920764i
\(699\) 98.4064i 0.140782i
\(700\) 370.897 110.414i 0.529853 0.157734i
\(701\) −439.029 −0.626290 −0.313145 0.949705i \(-0.601383\pi\)
−0.313145 + 0.949705i \(0.601383\pi\)
\(702\) −53.0367 + 53.0367i −0.0755508 + 0.0755508i
\(703\) 619.024 + 619.024i 0.880546 + 0.880546i
\(704\) 146.599i 0.208238i
\(705\) 161.223 + 270.573i 0.228686 + 0.383792i
\(706\) −825.957 −1.16991
\(707\) −672.230 + 672.230i −0.950820 + 0.950820i
\(708\) 1.12591 + 1.12591i 0.00159026 + 0.00159026i
\(709\) 101.093i 0.142585i −0.997455 0.0712927i \(-0.977288\pi\)
0.997455 0.0712927i \(-0.0227124\pi\)
\(710\) 320.326 + 81.1205i 0.451163 + 0.114254i
\(711\) 196.601 0.276513
\(712\) −128.087 + 128.087i −0.179898 + 0.179898i
\(713\) −191.530 191.530i −0.268626 0.268626i
\(714\) 39.9359i 0.0559326i
\(715\) 229.587 906.584i 0.321100 1.26795i
\(716\) 118.409 0.165376
\(717\) 51.8751 51.8751i 0.0723502 0.0723502i
\(718\) −149.819 149.819i −0.208662 0.208662i
\(719\) 1336.70i 1.85911i 0.368680 + 0.929556i \(0.379810\pi\)
−0.368680 + 0.929556i \(0.620190\pi\)
\(720\) −51.5435 + 30.7127i −0.0715882 + 0.0426565i
\(721\) 447.835 0.621131
\(722\) −167.467 + 167.467i −0.231949 + 0.231949i
\(723\) −169.321 169.321i −0.234192 0.234192i
\(724\) 437.906i 0.604842i
\(725\) 20.9043 + 11.3133i 0.0288336 + 0.0156046i
\(726\) 526.155 0.724732
\(727\) −512.751 + 512.751i −0.705297 + 0.705297i −0.965542 0.260246i \(-0.916196\pi\)
0.260246 + 0.965542i \(0.416196\pi\)
\(728\) 157.996 + 157.996i 0.217028 + 0.217028i
\(729\) 27.0000i 0.0370370i
\(730\) −1.90422 3.19576i −0.00260852 0.00437776i
\(731\) 92.6678 0.126769
\(732\) −60.3905 + 60.3905i −0.0825006 + 0.0825006i
\(733\) 163.456 + 163.456i 0.222995 + 0.222995i 0.809759 0.586763i \(-0.199598\pi\)
−0.586763 + 0.809759i \(0.699598\pi\)
\(734\) 515.380i 0.702152i
\(735\) 91.5279 + 23.1789i 0.124528 + 0.0315359i
\(736\) −27.1293 −0.0368605
\(737\) −597.826 + 597.826i −0.811161 + 0.811161i
\(738\) 134.486 + 134.486i 0.182231 + 0.182231i
\(739\) 622.996i 0.843026i −0.906822 0.421513i \(-0.861499\pi\)
0.906822 0.421513i \(-0.138501\pi\)
\(740\) −154.485 + 610.025i −0.208763 + 0.824358i
\(741\) 245.942 0.331905
\(742\) 194.599 194.599i 0.262263 0.262263i
\(743\) 499.375 + 499.375i 0.672106 + 0.672106i 0.958201 0.286095i \(-0.0923572\pi\)
−0.286095 + 0.958201i \(0.592357\pi\)
\(744\) 276.690i 0.371895i
\(745\) 1148.63 684.422i 1.54179 0.918687i
\(746\) 549.007 0.735934
\(747\) 256.345 256.345i 0.343166 0.343166i
\(748\) −54.5912 54.5912i −0.0729829 0.0729829i
\(749\) 1360.40i 1.81629i
\(750\) 305.925 12.6451i 0.407900 0.0168602i
\(751\) −1496.23 −1.99231 −0.996157 0.0875833i \(-0.972086\pi\)
−0.996157 + 0.0875833i \(0.972086\pi\)
\(752\) −102.867 + 102.867i −0.136791 + 0.136791i
\(753\) 205.243 + 205.243i 0.272566 + 0.272566i
\(754\) 13.7242i 0.0182019i
\(755\) 410.933 + 689.648i 0.544282 + 0.913442i
\(756\) −80.4329 −0.106393
\(757\) −810.088 + 810.088i −1.07013 + 1.07013i −0.0727809 + 0.997348i \(0.523187\pi\)
−0.997348 + 0.0727809i \(0.976813\pi\)
\(758\) −543.361 543.361i −0.716834 0.716834i
\(759\) 152.218i 0.200551i
\(760\) 190.719 + 48.2984i 0.250946 + 0.0635506i
\(761\) 374.404 0.491989 0.245995 0.969271i \(-0.420885\pi\)
0.245995 + 0.969271i \(0.420885\pi\)
\(762\) −44.3837 + 44.3837i −0.0582463 + 0.0582463i
\(763\) 156.984 + 156.984i 0.205745 + 0.205745i
\(764\) 49.4199i 0.0646857i
\(765\) 7.75708 30.6309i 0.0101400 0.0400404i
\(766\) −645.779 −0.843053
\(767\) 3.31746 3.31746i 0.00432524 0.00432524i
\(768\) −19.5959 19.5959i −0.0255155 0.0255155i
\(769\) 1015.53i 1.32058i 0.751009 + 0.660291i \(0.229567\pi\)
−0.751009 + 0.660291i \(0.770433\pi\)
\(770\) 861.532 513.351i 1.11887 0.666690i
\(771\) 337.149 0.437287
\(772\) 233.402 233.402i 0.302334 0.302334i
\(773\) 477.540 + 477.540i 0.617774 + 0.617774i 0.944960 0.327186i \(-0.106100\pi\)
−0.327186 + 0.944960i \(0.606100\pi\)
\(774\) 186.638i 0.241134i
\(775\) −672.049 + 1241.79i −0.867160 + 1.60230i
\(776\) 197.862 0.254976
\(777\) −596.503 + 596.503i −0.767700 + 0.767700i
\(778\) 720.417 + 720.417i 0.925986 + 0.925986i