Properties

Label 210.3.l.a.43.3
Level 210
Weight 3
Character 210.43
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.12745506816.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.3
Root \(0.323042 - 0.323042i\) of \(x^{8} + 23 x^{4} + 1\)
Character \(\chi\) \(=\) 210.43
Dual form 210.3.l.a.127.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(0.578661 + 4.96640i) q^{5} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(0.578661 + 4.96640i) q^{5} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(5.54506 + 4.38774i) q^{10} +19.5717 q^{11} +(2.44949 - 2.44949i) q^{12} +(8.03207 + 8.03207i) q^{13} +3.74166i q^{14} +(-5.37386 + 6.79129i) q^{15} -4.00000 q^{16} +(-2.19659 + 2.19659i) q^{17} +(3.00000 + 3.00000i) q^{18} +8.25097i q^{19} +(9.93280 - 1.15732i) q^{20} -4.58258 q^{21} +(19.5717 - 19.5717i) q^{22} +(-17.9068 - 17.9068i) q^{23} -4.89898i q^{24} +(-24.3303 + 5.74773i) q^{25} +16.0641 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} -19.7495i q^{29} +(1.41742 + 12.1652i) q^{30} +30.0043 q^{31} +(-4.00000 + 4.00000i) q^{32} +(23.9703 + 23.9703i) q^{33} +4.39319i q^{34} +(-10.3739 - 8.20871i) q^{35} +6.00000 q^{36} +(37.2346 - 37.2346i) q^{37} +(8.25097 + 8.25097i) q^{38} +19.6745i q^{39} +(8.77548 - 11.0901i) q^{40} -80.8620 q^{41} +(-4.58258 + 4.58258i) q^{42} +(-13.6780 - 13.6780i) q^{43} -39.1434i q^{44} +(-14.8992 + 1.73598i) q^{45} -35.8136 q^{46} +(-8.17549 + 8.17549i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +(-18.5826 + 30.0780i) q^{50} -5.38053 q^{51} +(16.0641 - 16.0641i) q^{52} +(-38.8560 - 38.8560i) q^{53} +7.34847i q^{54} +(11.3254 + 97.2008i) q^{55} +7.48331 q^{56} +(-10.1053 + 10.1053i) q^{57} +(-19.7495 - 19.7495i) q^{58} -74.3773i q^{59} +(13.5826 + 10.7477i) q^{60} +97.8414 q^{61} +(30.0043 - 30.0043i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +(-35.2426 + 44.5383i) q^{65} +47.9406 q^{66} +(-67.1712 + 67.1712i) q^{67} +(4.39319 + 4.39319i) q^{68} -43.8625i q^{69} +(-18.5826 + 2.16515i) q^{70} -13.3793 q^{71} +(6.00000 - 6.00000i) q^{72} +(-48.2738 - 48.2738i) q^{73} -74.4691i q^{74} +(-36.8379 - 22.7589i) q^{75} +16.5019 q^{76} +(-36.6153 + 36.6153i) q^{77} +(19.6745 + 19.6745i) q^{78} +40.2089i q^{79} +(-2.31464 - 19.8656i) q^{80} -9.00000 q^{81} +(-80.8620 + 80.8620i) q^{82} +(34.4137 + 34.4137i) q^{83} +9.16515i q^{84} +(-12.1803 - 9.63809i) q^{85} -27.3560 q^{86} +(24.1881 - 24.1881i) q^{87} +(-39.1434 - 39.1434i) q^{88} -157.941i q^{89} +(-13.1632 + 16.6352i) q^{90} -30.0532 q^{91} +(-35.8136 + 35.8136i) q^{92} +(36.7476 + 36.7476i) q^{93} +16.3510i q^{94} +(-40.9776 + 4.77451i) q^{95} -9.79796 q^{96} +(-73.2856 + 73.2856i) q^{97} +(-7.00000 - 7.00000i) q^{98} +58.7150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 16q^{8} + O(q^{10}) \) \( 8q + 8q^{2} - 16q^{8} - 8q^{11} + 8q^{13} + 12q^{15} - 32q^{16} - 32q^{17} + 24q^{18} - 8q^{22} - 40q^{23} - 48q^{25} + 16q^{26} + 48q^{30} + 144q^{31} - 32q^{32} + 120q^{33} - 28q^{35} + 48q^{36} + 160q^{37} - 320q^{41} - 32q^{43} - 80q^{46} - 144q^{47} - 112q^{50} + 72q^{51} + 16q^{52} - 200q^{53} + 184q^{55} - 24q^{57} - 64q^{58} + 72q^{60} + 288q^{61} + 144q^{62} + 24q^{65} + 240q^{66} + 80q^{67} + 64q^{68} - 112q^{70} - 280q^{71} + 48q^{72} + 312q^{73} - 56q^{77} + 48q^{78} - 72q^{81} - 320q^{82} - 320q^{83} + 80q^{85} - 64q^{86} - 48q^{87} + 16q^{88} - 80q^{92} + 48q^{93} - 472q^{95} - 24q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(5\) 0.578661 + 4.96640i 0.115732 + 0.993280i
\(6\) 2.44949 0.408248
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 5.54506 + 4.38774i 0.554506 + 0.438774i
\(11\) 19.5717 1.77924 0.889622 0.456698i \(-0.150968\pi\)
0.889622 + 0.456698i \(0.150968\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) 8.03207 + 8.03207i 0.617851 + 0.617851i 0.944980 0.327129i \(-0.106081\pi\)
−0.327129 + 0.944980i \(0.606081\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −5.37386 + 6.79129i −0.358258 + 0.452753i
\(16\) −4.00000 −0.250000
\(17\) −2.19659 + 2.19659i −0.129211 + 0.129211i −0.768755 0.639543i \(-0.779123\pi\)
0.639543 + 0.768755i \(0.279123\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 8.25097i 0.434261i 0.976143 + 0.217131i \(0.0696698\pi\)
−0.976143 + 0.217131i \(0.930330\pi\)
\(20\) 9.93280 1.15732i 0.496640 0.0578661i
\(21\) −4.58258 −0.218218
\(22\) 19.5717 19.5717i 0.889622 0.889622i
\(23\) −17.9068 17.9068i −0.778557 0.778557i 0.201028 0.979585i \(-0.435572\pi\)
−0.979585 + 0.201028i \(0.935572\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −24.3303 + 5.74773i −0.973212 + 0.229909i
\(26\) 16.0641 0.617851
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 3.74166 + 3.74166i 0.133631 + 0.133631i
\(29\) 19.7495i 0.681017i −0.940241 0.340508i \(-0.889401\pi\)
0.940241 0.340508i \(-0.110599\pi\)
\(30\) 1.41742 + 12.1652i 0.0472475 + 0.405505i
\(31\) 30.0043 0.967881 0.483940 0.875101i \(-0.339205\pi\)
0.483940 + 0.875101i \(0.339205\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 23.9703 + 23.9703i 0.726373 + 0.726373i
\(34\) 4.39319i 0.129211i
\(35\) −10.3739 8.20871i −0.296396 0.234535i
\(36\) 6.00000 0.166667
\(37\) 37.2346 37.2346i 1.00634 1.00634i 0.00635971 0.999980i \(-0.497976\pi\)
0.999980 0.00635971i \(-0.00202437\pi\)
\(38\) 8.25097 + 8.25097i 0.217131 + 0.217131i
\(39\) 19.6745i 0.504473i
\(40\) 8.77548 11.0901i 0.219387 0.277253i
\(41\) −80.8620 −1.97224 −0.986122 0.166023i \(-0.946907\pi\)
−0.986122 + 0.166023i \(0.946907\pi\)
\(42\) −4.58258 + 4.58258i −0.109109 + 0.109109i
\(43\) −13.6780 13.6780i −0.318093 0.318093i 0.529942 0.848034i \(-0.322214\pi\)
−0.848034 + 0.529942i \(0.822214\pi\)
\(44\) 39.1434i 0.889622i
\(45\) −14.8992 + 1.73598i −0.331093 + 0.0385774i
\(46\) −35.8136 −0.778557
\(47\) −8.17549 + 8.17549i −0.173947 + 0.173947i −0.788711 0.614764i \(-0.789251\pi\)
0.614764 + 0.788711i \(0.289251\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −18.5826 + 30.0780i −0.371652 + 0.601561i
\(51\) −5.38053 −0.105501
\(52\) 16.0641 16.0641i 0.308926 0.308926i
\(53\) −38.8560 38.8560i −0.733132 0.733132i 0.238107 0.971239i \(-0.423473\pi\)
−0.971239 + 0.238107i \(0.923473\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 11.3254 + 97.2008i 0.205916 + 1.76729i
\(56\) 7.48331 0.133631
\(57\) −10.1053 + 10.1053i −0.177287 + 0.177287i
\(58\) −19.7495 19.7495i −0.340508 0.340508i
\(59\) 74.3773i 1.26063i −0.776339 0.630316i \(-0.782925\pi\)
0.776339 0.630316i \(-0.217075\pi\)
\(60\) 13.5826 + 10.7477i 0.226376 + 0.179129i
\(61\) 97.8414 1.60396 0.801979 0.597352i \(-0.203781\pi\)
0.801979 + 0.597352i \(0.203781\pi\)
\(62\) 30.0043 30.0043i 0.483940 0.483940i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −35.2426 + 44.5383i −0.542194 + 0.685205i
\(66\) 47.9406 0.726373
\(67\) −67.1712 + 67.1712i −1.00255 + 1.00255i −0.00255792 + 0.999997i \(0.500814\pi\)
−0.999997 + 0.00255792i \(0.999186\pi\)
\(68\) 4.39319 + 4.39319i 0.0646057 + 0.0646057i
\(69\) 43.8625i 0.635689i
\(70\) −18.5826 + 2.16515i −0.265465 + 0.0309307i
\(71\) −13.3793 −0.188441 −0.0942203 0.995551i \(-0.530036\pi\)
−0.0942203 + 0.995551i \(0.530036\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) −48.2738 48.2738i −0.661285 0.661285i 0.294398 0.955683i \(-0.404881\pi\)
−0.955683 + 0.294398i \(0.904881\pi\)
\(74\) 74.4691i 1.00634i
\(75\) −36.8379 22.7589i −0.491172 0.303452i
\(76\) 16.5019 0.217131
\(77\) −36.6153 + 36.6153i −0.475523 + 0.475523i
\(78\) 19.6745 + 19.6745i 0.252237 + 0.252237i
\(79\) 40.2089i 0.508973i 0.967076 + 0.254487i \(0.0819065\pi\)
−0.967076 + 0.254487i \(0.918094\pi\)
\(80\) −2.31464 19.8656i −0.0289331 0.248320i
\(81\) −9.00000 −0.111111
\(82\) −80.8620 + 80.8620i −0.986122 + 0.986122i
\(83\) 34.4137 + 34.4137i 0.414623 + 0.414623i 0.883346 0.468722i \(-0.155285\pi\)
−0.468722 + 0.883346i \(0.655285\pi\)
\(84\) 9.16515i 0.109109i
\(85\) −12.1803 9.63809i −0.143297 0.113389i
\(86\) −27.3560 −0.318093
\(87\) 24.1881 24.1881i 0.278024 0.278024i
\(88\) −39.1434 39.1434i −0.444811 0.444811i
\(89\) 157.941i 1.77462i −0.461176 0.887309i \(-0.652572\pi\)
0.461176 0.887309i \(-0.347428\pi\)
\(90\) −13.1632 + 16.6352i −0.146258 + 0.184835i
\(91\) −30.0532 −0.330255
\(92\) −35.8136 + 35.8136i −0.389278 + 0.389278i
\(93\) 36.7476 + 36.7476i 0.395136 + 0.395136i
\(94\) 16.3510i 0.173947i
\(95\) −40.9776 + 4.77451i −0.431343 + 0.0502580i
\(96\) −9.79796 −0.102062
\(97\) −73.2856 + 73.2856i −0.755522 + 0.755522i −0.975504 0.219982i \(-0.929400\pi\)
0.219982 + 0.975504i \(0.429400\pi\)
\(98\) −7.00000 7.00000i −0.0714286 0.0714286i
\(99\) 58.7150i 0.593081i
\(100\) 11.4955 + 48.6606i 0.114955 + 0.486606i
\(101\) 121.236 1.20035 0.600176 0.799868i \(-0.295097\pi\)
0.600176 + 0.799868i \(0.295097\pi\)
\(102\) −5.38053 + 5.38053i −0.0527503 + 0.0527503i
\(103\) 23.5614 + 23.5614i 0.228751 + 0.228751i 0.812171 0.583419i \(-0.198286\pi\)
−0.583419 + 0.812171i \(0.698286\pi\)
\(104\) 32.1283i 0.308926i
\(105\) −2.65176 22.7589i −0.0252548 0.216752i
\(106\) −77.7120 −0.733132
\(107\) −14.4314 + 14.4314i −0.134873 + 0.134873i −0.771320 0.636447i \(-0.780403\pi\)
0.636447 + 0.771320i \(0.280403\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 34.6374i 0.317775i 0.987297 + 0.158887i \(0.0507907\pi\)
−0.987297 + 0.158887i \(0.949209\pi\)
\(110\) 108.526 + 85.8755i 0.986602 + 0.780686i
\(111\) 91.2057 0.821673
\(112\) 7.48331 7.48331i 0.0668153 0.0668153i
\(113\) −19.9430 19.9430i −0.176486 0.176486i 0.613336 0.789822i \(-0.289827\pi\)
−0.789822 + 0.613336i \(0.789827\pi\)
\(114\) 20.2107i 0.177287i
\(115\) 78.5704 99.2944i 0.683221 0.863429i
\(116\) −39.4990 −0.340508
\(117\) −24.0962 + 24.0962i −0.205950 + 0.205950i
\(118\) −74.3773 74.3773i −0.630316 0.630316i
\(119\) 8.21890i 0.0690664i
\(120\) 24.3303 2.83485i 0.202753 0.0236237i
\(121\) 262.051 2.16571
\(122\) 97.8414 97.8414i 0.801979 0.801979i
\(123\) −99.0353 99.0353i −0.805165 0.805165i
\(124\) 60.0086i 0.483940i
\(125\) −42.6245 117.508i −0.340996 0.940065i
\(126\) −11.2250 −0.0890871
\(127\) 13.8950 13.8950i 0.109410 0.109410i −0.650283 0.759692i \(-0.725350\pi\)
0.759692 + 0.650283i \(0.225350\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 33.5041i 0.259722i
\(130\) 9.29569 + 79.7809i 0.0715053 + 0.613700i
\(131\) 161.799 1.23511 0.617554 0.786528i \(-0.288124\pi\)
0.617554 + 0.786528i \(0.288124\pi\)
\(132\) 47.9406 47.9406i 0.363187 0.363187i
\(133\) −15.4361 15.4361i −0.116061 0.116061i
\(134\) 134.342i 1.00255i
\(135\) −20.3739 16.1216i −0.150918 0.119419i
\(136\) 8.78638 0.0646057
\(137\) −35.8023 + 35.8023i −0.261331 + 0.261331i −0.825595 0.564264i \(-0.809160\pi\)
0.564264 + 0.825595i \(0.309160\pi\)
\(138\) −43.8625 43.8625i −0.317845 0.317845i
\(139\) 89.7460i 0.645654i 0.946458 + 0.322827i \(0.104633\pi\)
−0.946458 + 0.322827i \(0.895367\pi\)
\(140\) −16.4174 + 20.7477i −0.117267 + 0.148198i
\(141\) −20.0258 −0.142027
\(142\) −13.3793 + 13.3793i −0.0942203 + 0.0942203i
\(143\) 157.201 + 157.201i 1.09931 + 1.09931i
\(144\) 12.0000i 0.0833333i
\(145\) 98.0839 11.4283i 0.676441 0.0788156i
\(146\) −96.5477 −0.661285
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) −74.4691 74.4691i −0.503170 0.503170i
\(149\) 293.641i 1.97075i −0.170408 0.985374i \(-0.554509\pi\)
0.170408 0.985374i \(-0.445491\pi\)
\(150\) −59.5968 + 14.0790i −0.397312 + 0.0938600i
\(151\) 231.725 1.53461 0.767303 0.641285i \(-0.221598\pi\)
0.767303 + 0.641285i \(0.221598\pi\)
\(152\) 16.5019 16.5019i 0.108565 0.108565i
\(153\) −6.58978 6.58978i −0.0430705 0.0430705i
\(154\) 73.2305i 0.475523i
\(155\) 17.3623 + 149.013i 0.112015 + 0.961377i
\(156\) 39.3489 0.252237
\(157\) 62.8204 62.8204i 0.400130 0.400130i −0.478149 0.878279i \(-0.658692\pi\)
0.878279 + 0.478149i \(0.158692\pi\)
\(158\) 40.2089 + 40.2089i 0.254487 + 0.254487i
\(159\) 95.1774i 0.598600i
\(160\) −22.1803 17.5510i −0.138627 0.109694i
\(161\) 67.0011 0.416156
\(162\) −9.00000 + 9.00000i −0.0555556 + 0.0555556i
\(163\) 97.0117 + 97.0117i 0.595164 + 0.595164i 0.939022 0.343858i \(-0.111734\pi\)
−0.343858 + 0.939022i \(0.611734\pi\)
\(164\) 161.724i 0.986122i
\(165\) −105.176 + 132.917i −0.637428 + 0.805557i
\(166\) 68.8275 0.414623
\(167\) −135.497 + 135.497i −0.811362 + 0.811362i −0.984838 0.173476i \(-0.944500\pi\)
0.173476 + 0.984838i \(0.444500\pi\)
\(168\) 9.16515 + 9.16515i 0.0545545 + 0.0545545i
\(169\) 39.9718i 0.236520i
\(170\) −21.8183 + 2.54217i −0.128343 + 0.0149539i
\(171\) −24.7529 −0.144754
\(172\) −27.3560 + 27.3560i −0.159046 + 0.159046i
\(173\) −66.1772 66.1772i −0.382527 0.382527i 0.489485 0.872012i \(-0.337185\pi\)
−0.872012 + 0.489485i \(0.837185\pi\)
\(174\) 48.3762i 0.278024i
\(175\) 34.7648 56.2708i 0.198656 0.321548i
\(176\) −78.2867 −0.444811
\(177\) 91.0932 91.0932i 0.514651 0.514651i
\(178\) −157.941 157.941i −0.887309 0.887309i
\(179\) 274.045i 1.53098i 0.643450 + 0.765488i \(0.277503\pi\)
−0.643450 + 0.765488i \(0.722497\pi\)
\(180\) 3.47197 + 29.7984i 0.0192887 + 0.165547i
\(181\) −36.0493 −0.199167 −0.0995836 0.995029i \(-0.531751\pi\)
−0.0995836 + 0.995029i \(0.531751\pi\)
\(182\) −30.0532 + 30.0532i −0.165128 + 0.165128i
\(183\) 119.831 + 119.831i 0.654813 + 0.654813i
\(184\) 71.6272i 0.389278i
\(185\) 206.468 + 163.376i 1.11604 + 0.883111i
\(186\) 73.4952 0.395136
\(187\) −42.9910 + 42.9910i −0.229899 + 0.229899i
\(188\) 16.3510 + 16.3510i 0.0869733 + 0.0869733i
\(189\) 13.7477i 0.0727393i
\(190\) −36.2031 + 45.7521i −0.190543 + 0.240801i
\(191\) 133.194 0.697352 0.348676 0.937243i \(-0.386631\pi\)
0.348676 + 0.937243i \(0.386631\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) −236.565 236.565i −1.22573 1.22573i −0.965566 0.260160i \(-0.916225\pi\)
−0.260160 0.965566i \(-0.583775\pi\)
\(194\) 146.571i 0.755522i
\(195\) −97.7113 + 11.3848i −0.501084 + 0.0583838i
\(196\) −14.0000 −0.0714286
\(197\) −203.011 + 203.011i −1.03051 + 1.03051i −0.0309909 + 0.999520i \(0.509866\pi\)
−0.999520 + 0.0309909i \(0.990134\pi\)
\(198\) 58.7150 + 58.7150i 0.296541 + 0.296541i
\(199\) 102.932i 0.517244i 0.965979 + 0.258622i \(0.0832684\pi\)
−0.965979 + 0.258622i \(0.916732\pi\)
\(200\) 60.1561 + 37.1652i 0.300780 + 0.185826i
\(201\) −164.535 −0.818582
\(202\) 121.236 121.236i 0.600176 0.600176i
\(203\) 36.9479 + 36.9479i 0.182009 + 0.182009i
\(204\) 10.7611i 0.0527503i
\(205\) −46.7917 401.593i −0.228252 1.95899i
\(206\) 47.1228 0.228751
\(207\) 53.7204 53.7204i 0.259519 0.259519i
\(208\) −32.1283 32.1283i −0.154463 0.154463i
\(209\) 161.485i 0.772657i
\(210\) −25.4107 20.1072i −0.121003 0.0957484i
\(211\) −216.191 −1.02460 −0.512301 0.858806i \(-0.671207\pi\)
−0.512301 + 0.858806i \(0.671207\pi\)
\(212\) −77.7120 + 77.7120i −0.366566 + 0.366566i
\(213\) −16.3862 16.3862i −0.0769306 0.0769306i
\(214\) 28.8629i 0.134873i
\(215\) 60.0154 75.8453i 0.279142 0.352769i
\(216\) 14.6969 0.0680414
\(217\) −56.1329 + 56.1329i −0.258677 + 0.258677i
\(218\) 34.6374 + 34.6374i 0.158887 + 0.158887i
\(219\) 118.246i 0.539937i
\(220\) 194.402 22.6507i 0.883644 0.102958i
\(221\) −35.2864 −0.159667
\(222\) 91.2057 91.2057i 0.410836 0.410836i
\(223\) 143.253 + 143.253i 0.642390 + 0.642390i 0.951142 0.308752i \(-0.0999114\pi\)
−0.308752 + 0.951142i \(0.599911\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −17.2432 72.9909i −0.0766364 0.324404i
\(226\) −39.8859 −0.176486
\(227\) 226.766 226.766i 0.998969 0.998969i −0.00103000 0.999999i \(-0.500328\pi\)
0.999999 + 0.00103000i \(0.000327858\pi\)
\(228\) 20.2107 + 20.2107i 0.0886433 + 0.0886433i
\(229\) 48.9068i 0.213567i −0.994282 0.106783i \(-0.965945\pi\)
0.994282 0.106783i \(-0.0340552\pi\)
\(230\) −20.7239 177.865i −0.0901041 0.773325i
\(231\) −89.6887 −0.388263
\(232\) −39.4990 + 39.4990i −0.170254 + 0.170254i
\(233\) −122.967 122.967i −0.527755 0.527755i 0.392147 0.919902i \(-0.371732\pi\)
−0.919902 + 0.392147i \(0.871732\pi\)
\(234\) 48.1924i 0.205950i
\(235\) −45.3336 35.8719i −0.192909 0.152647i
\(236\) −148.755 −0.630316
\(237\) −49.2456 + 49.2456i −0.207787 + 0.207787i
\(238\) −8.21890 8.21890i −0.0345332 0.0345332i
\(239\) 359.392i 1.50373i −0.659317 0.751865i \(-0.729154\pi\)
0.659317 0.751865i \(-0.270846\pi\)
\(240\) 21.4955 27.1652i 0.0895644 0.113188i
\(241\) −96.4510 −0.400212 −0.200106 0.979774i \(-0.564129\pi\)
−0.200106 + 0.979774i \(0.564129\pi\)
\(242\) 262.051 262.051i 1.08285 1.08285i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 195.683i 0.801979i
\(245\) 34.7648 4.05063i 0.141897 0.0165332i
\(246\) −198.071 −0.805165
\(247\) −66.2723 + 66.2723i −0.268309 + 0.268309i
\(248\) −60.0086 60.0086i −0.241970 0.241970i
\(249\) 84.2961i 0.338539i
\(250\) −160.133 74.8836i −0.640530 0.299534i
\(251\) −290.502 −1.15738 −0.578690 0.815548i \(-0.696436\pi\)
−0.578690 + 0.815548i \(0.696436\pi\)
\(252\) −11.2250 + 11.2250i −0.0445435 + 0.0445435i
\(253\) −350.466 350.466i −1.38524 1.38524i
\(254\) 27.7901i 0.109410i
\(255\) −3.11351 26.7219i −0.0122098 0.104792i
\(256\) 16.0000 0.0625000
\(257\) −225.583 + 225.583i −0.877755 + 0.877755i −0.993302 0.115547i \(-0.963138\pi\)
0.115547 + 0.993302i \(0.463138\pi\)
\(258\) −33.5041 33.5041i −0.129861 0.129861i
\(259\) 139.319i 0.537911i
\(260\) 89.0766 + 70.4852i 0.342602 + 0.271097i
\(261\) 59.2485 0.227006
\(262\) 161.799 161.799i 0.617554 0.617554i
\(263\) 245.931 + 245.931i 0.935097 + 0.935097i 0.998018 0.0629214i \(-0.0200417\pi\)
−0.0629214 + 0.998018i \(0.520042\pi\)
\(264\) 95.8813i 0.363187i
\(265\) 170.490 215.459i 0.643359 0.813053i
\(266\) −30.8723 −0.116061
\(267\) 193.437 193.437i 0.724485 0.724485i
\(268\) 134.342 + 134.342i 0.501277 + 0.501277i
\(269\) 306.198i 1.13828i 0.822240 + 0.569142i \(0.192724\pi\)
−0.822240 + 0.569142i \(0.807276\pi\)
\(270\) −36.4955 + 4.25227i −0.135168 + 0.0157492i
\(271\) −370.284 −1.36636 −0.683180 0.730250i \(-0.739404\pi\)
−0.683180 + 0.730250i \(0.739404\pi\)
\(272\) 8.78638 8.78638i 0.0323029 0.0323029i
\(273\) −36.8075 36.8075i −0.134826 0.134826i
\(274\) 71.6046i 0.261331i
\(275\) −476.185 + 112.493i −1.73158 + 0.409064i
\(276\) −87.7251 −0.317845
\(277\) −161.817 + 161.817i −0.584176 + 0.584176i −0.936048 0.351872i \(-0.885545\pi\)
0.351872 + 0.936048i \(0.385545\pi\)
\(278\) 89.7460 + 89.7460i 0.322827 + 0.322827i
\(279\) 90.0129i 0.322627i
\(280\) 4.33030 + 37.1652i 0.0154654 + 0.132733i
\(281\) −235.757 −0.838994 −0.419497 0.907757i \(-0.637793\pi\)
−0.419497 + 0.907757i \(0.637793\pi\)
\(282\) −20.0258 + 20.0258i −0.0710134 + 0.0710134i
\(283\) 2.26750 + 2.26750i 0.00801238 + 0.00801238i 0.711102 0.703089i \(-0.248197\pi\)
−0.703089 + 0.711102i \(0.748197\pi\)
\(284\) 26.7586i 0.0942203i
\(285\) −56.0347 44.3396i −0.196613 0.155577i
\(286\) 314.402 1.09931
\(287\) 151.279 151.279i 0.527104 0.527104i
\(288\) −12.0000 12.0000i −0.0416667 0.0416667i
\(289\) 279.350i 0.966609i
\(290\) 86.6556 109.512i 0.298813 0.377628i
\(291\) −179.512 −0.616881
\(292\) −96.5477 + 96.5477i −0.330643 + 0.330643i
\(293\) 199.403 + 199.403i 0.680556 + 0.680556i 0.960125 0.279570i \(-0.0901918\pi\)
−0.279570 + 0.960125i \(0.590192\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 369.387 43.0392i 1.25216 0.145896i
\(296\) −148.938 −0.503170
\(297\) −71.9110 + 71.9110i −0.242124 + 0.242124i
\(298\) −293.641 293.641i −0.985374 0.985374i
\(299\) 287.657i 0.962065i
\(300\) −45.5178 + 73.6758i −0.151726 + 0.245586i
\(301\) 51.1783 0.170028
\(302\) 231.725 231.725i 0.767303 0.767303i
\(303\) 148.483 + 148.483i 0.490042 + 0.490042i
\(304\) 33.0039i 0.108565i
\(305\) 56.6170 + 485.920i 0.185630 + 1.59318i
\(306\) −13.1796 −0.0430705
\(307\) −381.514 + 381.514i −1.24272 + 1.24272i −0.283847 + 0.958870i \(0.591611\pi\)
−0.958870 + 0.283847i \(0.908389\pi\)
\(308\) 73.2305 + 73.2305i 0.237761 + 0.237761i
\(309\) 57.7134i 0.186775i
\(310\) 166.376 + 131.651i 0.536696 + 0.424681i
\(311\) −388.702 −1.24985 −0.624923 0.780686i \(-0.714870\pi\)
−0.624923 + 0.780686i \(0.714870\pi\)
\(312\) 39.3489 39.3489i 0.126118 0.126118i
\(313\) −50.5806 50.5806i −0.161599 0.161599i 0.621675 0.783275i \(-0.286452\pi\)
−0.783275 + 0.621675i \(0.786452\pi\)
\(314\) 125.641i 0.400130i
\(315\) 24.6261 31.1216i 0.0781782 0.0987987i
\(316\) 80.4178 0.254487
\(317\) 54.9675 54.9675i 0.173399 0.173399i −0.615072 0.788471i \(-0.710873\pi\)
0.788471 + 0.615072i \(0.210873\pi\)
\(318\) −95.1774 95.1774i −0.299300 0.299300i
\(319\) 386.531i 1.21169i
\(320\) −39.7312 + 4.62929i −0.124160 + 0.0144665i
\(321\) −35.3497 −0.110124
\(322\) 67.0011 67.0011i 0.208078 0.208078i
\(323\) −18.1240 18.1240i −0.0561115 0.0561115i
\(324\) 18.0000i 0.0555556i
\(325\) −241.589 149.256i −0.743350 0.459251i
\(326\) 194.023 0.595164
\(327\) −42.4220 + 42.4220i −0.129731 + 0.129731i
\(328\) 161.724 + 161.724i 0.493061 + 0.493061i
\(329\) 30.5899i 0.0929783i
\(330\) 27.7414 + 238.092i 0.0840648 + 0.721492i
\(331\) 195.576 0.590865 0.295433 0.955364i \(-0.404536\pi\)
0.295433 + 0.955364i \(0.404536\pi\)
\(332\) 68.8275 68.8275i 0.207312 0.207312i
\(333\) 111.704 + 111.704i 0.335446 + 0.335446i
\(334\) 270.995i 0.811362i
\(335\) −372.468 294.730i −1.11185 0.879790i
\(336\) 18.3303 0.0545545
\(337\) 420.206 420.206i 1.24690 1.24690i 0.289822 0.957081i \(-0.406404\pi\)
0.957081 0.289822i \(-0.0935961\pi\)
\(338\) −39.9718 39.9718i −0.118260 0.118260i
\(339\) 48.8501i 0.144101i
\(340\) −19.2762 + 24.3605i −0.0566946 + 0.0716485i
\(341\) 587.235 1.72210
\(342\) −24.7529 + 24.7529i −0.0723769 + 0.0723769i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 54.7119i 0.159046i
\(345\) 217.839 25.3815i 0.631418 0.0735697i
\(346\) −132.354 −0.382527
\(347\) 21.4182 21.4182i 0.0617238 0.0617238i −0.675571 0.737295i \(-0.736103\pi\)
0.737295 + 0.675571i \(0.236103\pi\)
\(348\) −48.3762 48.3762i −0.139012 0.139012i
\(349\) 244.156i 0.699588i 0.936827 + 0.349794i \(0.113748\pi\)
−0.936827 + 0.349794i \(0.886252\pi\)
\(350\) −21.5060 91.0357i −0.0614458 0.260102i
\(351\) −59.0234 −0.168158
\(352\) −78.2867 + 78.2867i −0.222405 + 0.222405i
\(353\) 228.969 + 228.969i 0.648637 + 0.648637i 0.952664 0.304026i \(-0.0983311\pi\)
−0.304026 + 0.952664i \(0.598331\pi\)
\(354\) 182.186i 0.514651i
\(355\) −7.74207 66.4469i −0.0218087 0.187174i
\(356\) −315.882 −0.887309
\(357\) 10.0661 10.0661i 0.0281962 0.0281962i
\(358\) 274.045 + 274.045i 0.765488 + 0.765488i
\(359\) 165.483i 0.460956i −0.973078 0.230478i \(-0.925971\pi\)
0.973078 0.230478i \(-0.0740290\pi\)
\(360\) 33.2704 + 26.3264i 0.0924177 + 0.0731290i
\(361\) 292.922 0.811417
\(362\) −36.0493 + 36.0493i −0.0995836 + 0.0995836i
\(363\) 320.945 + 320.945i 0.884147 + 0.884147i
\(364\) 60.1065i 0.165128i
\(365\) 211.813 267.681i 0.580310 0.733374i
\(366\) 239.662 0.654813
\(367\) −225.601 + 225.601i −0.614715 + 0.614715i −0.944171 0.329456i \(-0.893135\pi\)
0.329456 + 0.944171i \(0.393135\pi\)
\(368\) 71.6272 + 71.6272i 0.194639 + 0.194639i
\(369\) 242.586i 0.657415i
\(370\) 369.844 43.0924i 0.999577 0.116466i
\(371\) 145.386 0.391876
\(372\) 73.4952 73.4952i 0.197568 0.197568i
\(373\) 279.406 + 279.406i 0.749078 + 0.749078i 0.974306 0.225228i \(-0.0723128\pi\)
−0.225228 + 0.974306i \(0.572313\pi\)
\(374\) 85.9821i 0.229899i
\(375\) 91.7133 196.122i 0.244569 0.522991i
\(376\) 32.7020 0.0869733
\(377\) 158.629 158.629i 0.420767 0.420767i
\(378\) −13.7477 13.7477i −0.0363696 0.0363696i
\(379\) 746.946i 1.97083i 0.170158 + 0.985417i \(0.445572\pi\)
−0.170158 + 0.985417i \(0.554428\pi\)
\(380\) 9.54903 + 81.9553i 0.0251290 + 0.215672i
\(381\) 34.0357 0.0893327
\(382\) 133.194 133.194i 0.348676 0.348676i
\(383\) 359.176 + 359.176i 0.937797 + 0.937797i 0.998176 0.0603788i \(-0.0192309\pi\)
−0.0603788 + 0.998176i \(0.519231\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −203.034 160.658i −0.527361 0.417294i
\(386\) −473.130 −1.22573
\(387\) 41.0339 41.0339i 0.106031 0.106031i
\(388\) 146.571 + 146.571i 0.377761 + 0.377761i
\(389\) 476.719i 1.22550i −0.790278 0.612749i \(-0.790064\pi\)
0.790278 0.612749i \(-0.209936\pi\)
\(390\) −86.3264 + 109.096i −0.221350 + 0.279734i
\(391\) 78.6680 0.201197
\(392\) −14.0000 + 14.0000i −0.0357143 + 0.0357143i
\(393\) 198.163 + 198.163i 0.504231 + 0.504231i
\(394\) 406.021i 1.03051i
\(395\) −199.693 + 23.2673i −0.505553 + 0.0589046i
\(396\) 117.430 0.296541
\(397\) −137.315 + 137.315i −0.345883 + 0.345883i −0.858573 0.512691i \(-0.828649\pi\)
0.512691 + 0.858573i \(0.328649\pi\)
\(398\) 102.932 + 102.932i 0.258622 + 0.258622i
\(399\) 37.8107i 0.0947636i
\(400\) 97.3212 22.9909i 0.243303 0.0574773i
\(401\) −691.294 −1.72392 −0.861962 0.506973i \(-0.830765\pi\)
−0.861962 + 0.506973i \(0.830765\pi\)
\(402\) −164.535 + 164.535i −0.409291 + 0.409291i
\(403\) 240.997 + 240.997i 0.598006 + 0.598006i
\(404\) 242.471i 0.600176i
\(405\) −5.20795 44.6976i −0.0128591 0.110364i
\(406\) 73.8958 0.182009
\(407\) 728.743 728.743i 1.79052 1.79052i
\(408\) 10.7611 + 10.7611i 0.0263752 + 0.0263752i
\(409\) 146.348i 0.357818i 0.983866 + 0.178909i \(0.0572568\pi\)
−0.983866 + 0.178909i \(0.942743\pi\)
\(410\) −448.385 354.801i −1.09362 0.865369i
\(411\) −87.6974 −0.213376
\(412\) 47.1228 47.1228i 0.114376 0.114376i
\(413\) 139.147 + 139.147i 0.336918 + 0.336918i
\(414\) 107.441i 0.259519i
\(415\) −150.999 + 190.826i −0.363852 + 0.459823i
\(416\) −64.2565 −0.154463
\(417\) −109.916 + 109.916i −0.263587 + 0.263587i
\(418\) 161.485 + 161.485i 0.386329 + 0.386329i
\(419\) 19.1814i 0.0457790i −0.999738 0.0228895i \(-0.992713\pi\)
0.999738 0.0228895i \(-0.00728659\pi\)
\(420\) −45.5178 + 5.30352i −0.108376 + 0.0126274i
\(421\) −343.060 −0.814870 −0.407435 0.913234i \(-0.633577\pi\)
−0.407435 + 0.913234i \(0.633577\pi\)
\(422\) −216.191 + 216.191i −0.512301 + 0.512301i
\(423\) −24.5265 24.5265i −0.0579822 0.0579822i
\(424\) 155.424i 0.366566i
\(425\) 40.8184 66.0692i 0.0960432 0.155457i
\(426\) −32.7724 −0.0769306
\(427\) −183.045 + 183.045i −0.428676 + 0.428676i
\(428\) 28.8629 + 28.8629i 0.0674366 + 0.0674366i
\(429\) 385.062i 0.897581i
\(430\) −15.8298 135.861i −0.0368136 0.315955i
\(431\) 251.794 0.584210 0.292105 0.956386i \(-0.405644\pi\)
0.292105 + 0.956386i \(0.405644\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) −125.195 125.195i −0.289133 0.289133i 0.547604 0.836737i \(-0.315540\pi\)
−0.836737 + 0.547604i \(0.815540\pi\)
\(434\) 112.266i 0.258677i
\(435\) 134.124 + 106.131i 0.308332 + 0.243979i
\(436\) 69.2749 0.158887
\(437\) 147.749 147.749i 0.338097 0.338097i
\(438\) −118.246 118.246i −0.269969 0.269969i
\(439\) 37.5609i 0.0855601i −0.999085 0.0427801i \(-0.986379\pi\)
0.999085 0.0427801i \(-0.0136215\pi\)
\(440\) 171.751 217.052i 0.390343 0.493301i
\(441\) 21.0000 0.0476190
\(442\) −35.2864 + 35.2864i −0.0798334 + 0.0798334i
\(443\) −583.967 583.967i −1.31821 1.31821i −0.915192 0.403019i \(-0.867961\pi\)
−0.403019 0.915192i \(-0.632039\pi\)
\(444\) 182.411i 0.410836i
\(445\) 784.398 91.3943i 1.76269 0.205380i
\(446\) 286.506 0.642390
\(447\) 359.636 359.636i 0.804554 0.804554i
\(448\) −14.9666 14.9666i −0.0334077 0.0334077i
\(449\) 595.556i 1.32640i 0.748440 + 0.663202i \(0.230803\pi\)
−0.748440 + 0.663202i \(0.769197\pi\)
\(450\) −90.2341 55.7477i −0.200520 0.123884i
\(451\) −1582.61 −3.50910
\(452\) −39.8859 + 39.8859i −0.0882432 + 0.0882432i
\(453\) 283.805 + 283.805i 0.626500 + 0.626500i
\(454\) 453.532i 0.998969i
\(455\) −17.3906 149.256i −0.0382212 0.328036i
\(456\) 40.4213 0.0886433
\(457\) 300.505 300.505i 0.657560 0.657560i −0.297242 0.954802i \(-0.596067\pi\)
0.954802 + 0.297242i \(0.0960668\pi\)
\(458\) −48.9068 48.9068i −0.106783 0.106783i
\(459\) 16.1416i 0.0351669i
\(460\) −198.589 157.141i −0.431715 0.341611i
\(461\) 565.424 1.22652 0.613258 0.789883i \(-0.289859\pi\)
0.613258 + 0.789883i \(0.289859\pi\)
\(462\) −89.6887 + 89.6887i −0.194131 + 0.194131i
\(463\) −247.619 247.619i −0.534815 0.534815i 0.387186 0.922001i \(-0.373447\pi\)
−0.922001 + 0.387186i \(0.873447\pi\)
\(464\) 78.9979i 0.170254i
\(465\) −161.239 + 203.768i −0.346751 + 0.438211i
\(466\) −245.934 −0.527755
\(467\) −310.936 + 310.936i −0.665816 + 0.665816i −0.956745 0.290929i \(-0.906036\pi\)
0.290929 + 0.956745i \(0.406036\pi\)
\(468\) 48.1924 + 48.1924i 0.102975 + 0.102975i
\(469\) 251.331i 0.535888i
\(470\) −81.2055 + 9.46167i −0.172778 + 0.0201312i
\(471\) 153.878 0.326705
\(472\) −148.755 + 148.755i −0.315158 + 0.315158i
\(473\) −267.701 267.701i −0.565964 0.565964i
\(474\) 98.4912i 0.207787i
\(475\) −47.4243 200.749i −0.0998407 0.422629i
\(476\) −16.4378 −0.0345332
\(477\) 116.568 116.568i 0.244377 0.244377i
\(478\) −359.392 359.392i −0.751865 0.751865i
\(479\) 337.547i 0.704692i −0.935870 0.352346i \(-0.885384\pi\)
0.935870 0.352346i \(-0.114616\pi\)
\(480\) −5.66970 48.6606i −0.0118119 0.101376i
\(481\) 598.141 1.24354
\(482\) −96.4510 + 96.4510i −0.200106 + 0.200106i
\(483\) 82.0593 + 82.0593i 0.169895 + 0.169895i
\(484\) 524.101i 1.08285i
\(485\) −406.373 321.558i −0.837883 0.663007i
\(486\) −22.0454 −0.0453609
\(487\) 153.784 153.784i 0.315778 0.315778i −0.531365 0.847143i \(-0.678321\pi\)
0.847143 + 0.531365i \(0.178321\pi\)
\(488\) −195.683 195.683i −0.400989 0.400989i
\(489\) 237.629i 0.485949i
\(490\) 30.7142 38.8154i 0.0626820 0.0792152i
\(491\) 320.910 0.653585 0.326792 0.945096i \(-0.394032\pi\)
0.326792 + 0.945096i \(0.394032\pi\)
\(492\) −198.071 + 198.071i −0.402583 + 0.402583i
\(493\) 43.3816 + 43.3816i 0.0879951 + 0.0879951i
\(494\) 132.545i 0.268309i
\(495\) −291.603 + 33.9761i −0.589096 + 0.0686386i
\(496\) −120.017 −0.241970
\(497\) 25.0304 25.0304i 0.0503629 0.0503629i
\(498\) 84.2961 + 84.2961i 0.169269 + 0.169269i
\(499\) 284.928i 0.570997i −0.958379 0.285499i \(-0.907841\pi\)
0.958379 0.285499i \(-0.0921592\pi\)
\(500\) −235.016 + 85.2490i −0.470032 + 0.170498i
\(501\) −331.900 −0.662474
\(502\) −290.502 + 290.502i −0.578690 + 0.578690i
\(503\) −548.564 548.564i −1.09058 1.09058i −0.995466 0.0951181i \(-0.969677\pi\)
−0.0951181 0.995466i \(-0.530323\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) 70.1543 + 602.105i 0.138919 + 1.19229i
\(506\) −700.933 −1.38524
\(507\) 48.9553 48.9553i 0.0965588 0.0965588i
\(508\) −27.7901 27.7901i −0.0547049 0.0547049i
\(509\) 558.480i 1.09721i 0.836081 + 0.548606i \(0.184841\pi\)
−0.836081 + 0.548606i \(0.815159\pi\)
\(510\) −29.8354 23.6084i −0.0585008 0.0462910i
\(511\) 180.624 0.353472
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) −30.3160 30.3160i −0.0590955 0.0590955i
\(514\) 451.166i 0.877755i
\(515\) −103.381 + 130.649i −0.200740 + 0.253688i
\(516\) −67.0081 −0.129861
\(517\) −160.008 + 160.008i −0.309493 + 0.309493i
\(518\) 139.319 + 139.319i 0.268956 + 0.268956i
\(519\) 162.100i 0.312332i
\(520\) 159.562 18.5914i 0.306850 0.0357526i
\(521\) 455.328 0.873949 0.436975 0.899474i \(-0.356050\pi\)
0.436975 + 0.899474i \(0.356050\pi\)
\(522\) 59.2485 59.2485i 0.113503 0.113503i
\(523\) 37.6920 + 37.6920i 0.0720687 + 0.0720687i 0.742222 0.670154i \(-0.233772\pi\)
−0.670154 + 0.742222i \(0.733772\pi\)
\(524\) 323.598i 0.617554i
\(525\) 111.495 26.3394i 0.212372 0.0501703i
\(526\) 491.861 0.935097
\(527\) −65.9073 + 65.9073i −0.125061 + 0.125061i
\(528\) −95.8813 95.8813i −0.181593 0.181593i
\(529\) 112.308i 0.212302i
\(530\) −44.9689 385.949i −0.0848470 0.728206i
\(531\) 223.132 0.420211
\(532\) −30.8723 + 30.8723i −0.0580306 + 0.0580306i
\(533\) −649.489 649.489i −1.21855 1.21855i
\(534\) 386.875i 0.724485i
\(535\) −80.0233 63.3214i −0.149576 0.118358i
\(536\) 268.685 0.501277
\(537\) −335.635 + 335.635i −0.625019 + 0.625019i
\(538\) 306.198 + 306.198i 0.569142 + 0.569142i
\(539\) 137.002i 0.254178i
\(540\) −32.2432 + 40.7477i −0.0597096 + 0.0754588i
\(541\) 122.456 0.226352 0.113176 0.993575i \(-0.463898\pi\)
0.113176 + 0.993575i \(0.463898\pi\)
\(542\) −370.284 + 370.284i −0.683180 + 0.683180i
\(543\) −44.1512 44.1512i −0.0813097 0.0813097i
\(544\) 17.5728i 0.0323029i
\(545\) −172.023 + 20.0433i −0.315639 + 0.0367768i
\(546\) −73.6151 −0.134826
\(547\) 630.975 630.975i 1.15352 1.15352i 0.167676 0.985842i \(-0.446374\pi\)
0.985842 0.167676i \(-0.0536264\pi\)
\(548\) 71.6046 + 71.6046i 0.130665 + 0.130665i
\(549\) 293.524i 0.534653i
\(550\) −363.692 + 588.678i −0.661259 + 1.07032i
\(551\) 162.952 0.295739
\(552\) −87.7251 + 87.7251i −0.158922 + 0.158922i
\(553\) −75.2239 75.2239i −0.136029 0.136029i
\(554\) 323.634i 0.584176i
\(555\) 52.7772 + 452.964i 0.0950940 + 0.816151i
\(556\) 179.492 0.322827
\(557\) 89.6207 89.6207i 0.160899 0.160899i −0.622066 0.782965i \(-0.713706\pi\)
0.782965 + 0.622066i \(0.213706\pi\)
\(558\) 90.0129 + 90.0129i 0.161313 + 0.161313i
\(559\) 219.725i 0.393068i
\(560\) 41.4955 + 32.8348i 0.0740990 + 0.0586337i
\(561\) −105.306 −0.187711
\(562\) −235.757 + 235.757i −0.419497 + 0.419497i
\(563\) −268.774 268.774i −0.477396 0.477396i 0.426902 0.904298i \(-0.359605\pi\)
−0.904298 + 0.426902i \(0.859605\pi\)
\(564\) 40.0516i 0.0710134i
\(565\) 87.5046 110.585i 0.154875 0.195726i
\(566\) 4.53501 0.00801238
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) 26.7586 + 26.7586i 0.0471102 + 0.0471102i
\(569\) 373.315i 0.656089i 0.944662 + 0.328045i \(0.106390\pi\)
−0.944662 + 0.328045i \(0.893610\pi\)
\(570\) −100.374 + 11.6951i −0.176095 + 0.0205178i
\(571\) 93.3963 0.163566 0.0817831 0.996650i \(-0.473939\pi\)
0.0817831 + 0.996650i \(0.473939\pi\)
\(572\) 314.402 314.402i 0.549654 0.549654i
\(573\) 163.129 + 163.129i 0.284693 + 0.284693i
\(574\) 302.558i 0.527104i
\(575\) 538.602 + 332.755i 0.936698 + 0.578704i
\(576\) −24.0000 −0.0416667
\(577\) −356.401 + 356.401i −0.617679 + 0.617679i −0.944936 0.327257i \(-0.893876\pi\)
0.327257 + 0.944936i \(0.393876\pi\)
\(578\) 279.350 + 279.350i 0.483304 + 0.483304i
\(579\) 579.464i 1.00080i
\(580\) −22.8565 196.168i −0.0394078 0.338220i
\(581\) −128.764 −0.221626
\(582\) −179.512 + 179.512i −0.308441 + 0.308441i
\(583\) −760.478 760.478i −1.30442 1.30442i
\(584\) 193.095i 0.330643i
\(585\) −133.615 105.728i −0.228402 0.180731i
\(586\) 398.806 0.680556
\(587\) −213.286 + 213.286i −0.363349 + 0.363349i −0.865044 0.501695i \(-0.832710\pi\)
0.501695 + 0.865044i \(0.332710\pi\)
\(588\) −17.1464 17.1464i −0.0291606 0.0291606i
\(589\) 247.565i 0.420313i
\(590\) 326.348 412.427i 0.553133 0.699028i
\(591\) −497.272 −0.841408
\(592\) −148.938 + 148.938i −0.251585 + 0.251585i
\(593\) 118.172 + 118.172i 0.199279 + 0.199279i 0.799691 0.600412i \(-0.204997\pi\)
−0.600412 + 0.799691i \(0.704997\pi\)
\(594\) 143.822i 0.242124i
\(595\) 40.8184 4.75596i 0.0686023 0.00799321i
\(596\) −587.283 −0.985374
\(597\) −126.065 + 126.065i −0.211164 + 0.211164i
\(598\) −287.657 287.657i −0.481032 0.481032i
\(599\) 210.890i 0.352071i −0.984384 0.176035i \(-0.943673\pi\)
0.984384 0.176035i \(-0.0563273\pi\)
\(600\) 28.1580 + 119.194i 0.0469300 + 0.198656i
\(601\) −238.143 −0.396244 −0.198122 0.980177i \(-0.563484\pi\)
−0.198122 + 0.980177i \(0.563484\pi\)
\(602\) 51.1783 51.1783i 0.0850138 0.0850138i
\(603\) −201.513 201.513i −0.334185 0.334185i
\(604\) 463.451i 0.767303i
\(605\) 151.639 + 1301.45i 0.250642 + 2.15116i
\(606\) 296.965 0.490042
\(607\) 617.412 617.412i 1.01715 1.01715i 0.0173035 0.999850i \(-0.494492\pi\)
0.999850 0.0173035i \(-0.00550814\pi\)
\(608\) −33.0039 33.0039i −0.0542827 0.0542827i
\(609\) 90.5035i 0.148610i
\(610\) 542.537 + 429.303i 0.889405 + 0.703775i
\(611\) −131.332 −0.214946
\(612\) −13.1796 + 13.1796i −0.0215352 + 0.0215352i
\(613\) −765.627 765.627i −1.24898 1.24898i −0.956169 0.292816i \(-0.905408\pi\)
−0.292816 0.956169i \(-0.594592\pi\)
\(614\) 763.028i 1.24272i
\(615\) 434.541 549.157i 0.706571 0.892938i
\(616\) 146.461 0.237761
\(617\) 42.0185 42.0185i 0.0681012 0.0681012i −0.672236 0.740337i \(-0.734666\pi\)
0.740337 + 0.672236i \(0.234666\pi\)
\(618\) 57.7134 + 57.7134i 0.0933874 + 0.0933874i
\(619\) 564.440i 0.911858i 0.890016 + 0.455929i \(0.150693\pi\)
−0.890016 + 0.455929i \(0.849307\pi\)
\(620\) 298.027 34.7247i 0.480689 0.0560075i
\(621\) 131.588 0.211896
\(622\) −388.702 + 388.702i −0.624923 + 0.624923i
\(623\) 295.480 + 295.480i 0.474287 + 0.474287i
\(624\) 78.6978i 0.126118i
\(625\) 558.927 279.688i 0.894284 0.447501i
\(626\) −101.161 −0.161599
\(627\) −197.778 + 197.778i −0.315436 + 0.315436i
\(628\) −125.641 125.641i −0.200065 0.200065i
\(629\) 163.578i 0.260061i
\(630\) −6.49545 55.7477i −0.0103102 0.0884885i
\(631\) 498.286 0.789676 0.394838 0.918751i \(-0.370801\pi\)
0.394838 + 0.918751i \(0.370801\pi\)
\(632\) 80.4178 80.4178i 0.127243 0.127243i
\(633\) −264.779 264.779i −0.418292 0.418292i
\(634\) 109.935i 0.173399i
\(635\) 77.0489 + 60.9678i 0.121337 + 0.0960123i
\(636\) −190.355 −0.299300
\(637\) 56.2245 56.2245i 0.0882645 0.0882645i
\(638\) −386.531 386.531i −0.605847 0.605847i
\(639\) 40.1379i 0.0628136i
\(640\) −35.1019 + 44.3605i −0.0548468 + 0.0693133i
\(641\) 145.183 0.226494 0.113247 0.993567i \(-0.463875\pi\)
0.113247 + 0.993567i \(0.463875\pi\)
\(642\) −35.3497 + 35.3497i −0.0550618 + 0.0550618i
\(643\) 646.724 + 646.724i 1.00579 + 1.00579i 0.999983 + 0.00580843i \(0.00184889\pi\)
0.00580843 + 0.999983i \(0.498151\pi\)
\(644\) 134.002i 0.208078i
\(645\) 166.395 19.3875i 0.257976 0.0300581i
\(646\) −36.2481 −0.0561115
\(647\) 190.030 190.030i 0.293710 0.293710i −0.544834 0.838544i \(-0.683407\pi\)
0.838544 + 0.544834i \(0.183407\pi\)
\(648\) 18.0000 + 18.0000i 0.0277778 + 0.0277778i
\(649\) 1455.69i 2.24297i
\(650\) −390.845 + 92.3322i −0.601300 + 0.142050i
\(651\) −137.497 −0.211209
\(652\) 194.023 194.023i 0.297582 0.297582i
\(653\) 416.099 + 416.099i 0.637212 + 0.637212i 0.949867 0.312655i \(-0.101218\pi\)
−0.312655 + 0.949867i \(0.601218\pi\)
\(654\) 84.8441i 0.129731i
\(655\) 93.6269 + 803.560i 0.142942 + 1.22681i
\(656\) 323.448 0.493061
\(657\) 144.822 144.822i 0.220428 0.220428i
\(658\) −30.5899 30.5899i −0.0464892 0.0464892i
\(659\) 615.296i 0.933682i 0.884341 + 0.466841i \(0.154608\pi\)
−0.884341 + 0.466841i \(0.845392\pi\)
\(660\) 265.834 + 210.351i 0.402779 + 0.318714i
\(661\) −455.425 −0.688994 −0.344497 0.938787i \(-0.611951\pi\)
−0.344497 + 0.938787i \(0.611951\pi\)
\(662\) 195.576 195.576i 0.295433 0.295433i
\(663\) −43.2168 43.2168i −0.0651837 0.0651837i
\(664\) 137.655i 0.207312i
\(665\) 67.7298 85.5944i 0.101849 0.128713i
\(666\) 223.407 0.335446
\(667\) −353.650 + 353.650i −0.530210 + 0.530210i
\(668\) 270.995 + 270.995i 0.405681 + 0.405681i
\(669\) 350.897i 0.524509i
\(670\) −667.198 + 77.7387i −0.995818 + 0.116028i
\(671\) 1914.92 2.85383
\(672\) 18.3303 18.3303i 0.0272772 0.0272772i
\(673\) 156.161 + 156.161i 0.232037 + 0.232037i 0.813543 0.581505i \(-0.197536\pi\)
−0.581505 + 0.813543i \(0.697536\pi\)
\(674\) 840.412i 1.24690i
\(675\) 68.2767 110.514i 0.101151 0.163724i
\(676\) −79.9437 −0.118260
\(677\) −567.709 + 567.709i −0.838566 + 0.838566i −0.988670 0.150104i \(-0.952039\pi\)
0.150104 + 0.988670i \(0.452039\pi\)
\(678\) −48.8501 48.8501i −0.0720503 0.0720503i
\(679\) 274.210i 0.403843i
\(680\) 5.08433 + 43.6367i 0.00747696 + 0.0641716i
\(681\) 555.461 0.815655
\(682\) 587.235 587.235i 0.861048 0.861048i
\(683\) −124.523 124.523i −0.182317 0.182317i 0.610047 0.792365i \(-0.291150\pi\)
−0.792365 + 0.610047i \(0.791150\pi\)
\(684\) 49.5058i 0.0723769i
\(685\) −198.526 157.091i −0.289819 0.229330i
\(686\) 26.1916 0.0381802
\(687\) 59.8984 59.8984i 0.0871883 0.0871883i
\(688\) 54.7119 + 54.7119i 0.0795231 + 0.0795231i
\(689\) 624.188i 0.905934i
\(690\) 192.457 243.221i 0.278924 0.352494i
\(691\) −1214.16 −1.75710 −0.878551 0.477648i \(-0.841489\pi\)
−0.878551 + 0.477648i \(0.841489\pi\)
\(692\) −132.354 + 132.354i −0.191263 + 0.191263i
\(693\) −109.846 109.846i −0.158508 0.158508i
\(694\) 42.8363i 0.0617238i
\(695\) −445.715 + 51.9325i −0.641316 + 0.0747230i
\(696\) −96.7523 −0.139012
\(697\) 177.621 177.621i 0.254836 0.254836i
\(698\) 244.156 + 244.156i 0.349794 + 0.349794i
\(699\) 301.206i 0.430910i
\(700\) −112.542 69.5296i −0.160774 0.0993280i
\(701\) −788.147 −1.12432 −0.562159 0.827029i \(-0.690029\pi\)
−0.562159 + 0.827029i \(0.690029\pi\)
\(702\) −59.0234 + 59.0234i −0.0840789 + 0.0840789i
\(703\) 307.221 + 307.221i 0.437014 + 0.437014i
\(704\) 156.573i 0.222405i
\(705\) −11.5881 99.4561i −0.0164371 0.141072i
\(706\) 457.938 0.648637
\(707\) −226.811 + 226.811i −0.320808 + 0.320808i
\(708\) −182.186 182.186i −0.257325 0.257325i
\(709\) 1230.75i 1.73589i 0.496660 + 0.867945i \(0.334560\pi\)
−0.496660 + 0.867945i \(0.665440\pi\)
\(710\) −74.1890 58.7049i −0.104492 0.0826829i
\(711\) −120.627 −0.169658
\(712\) −315.882 + 315.882i −0.443654 + 0.443654i
\(713\) −537.281 537.281i −0.753550 0.753550i
\(714\) 20.1321i 0.0281962i
\(715\) −689.757 + 871.690i −0.964696 + 1.21915i
\(716\) 548.090 0.765488
\(717\) 440.163 440.163i 0.613895 0.613895i
\(718\) −165.483 165.483i −0.230478 0.230478i
\(719\) 251.624i 0.349963i 0.984572 + 0.174982i \(0.0559866\pi\)
−0.984572 + 0.174982i \(0.944013\pi\)
\(720\) 59.5968 6.94393i 0.0827734 0.00964435i
\(721\) −88.1587 −0.122273
\(722\) 292.922 292.922i 0.405708 0.405708i
\(723\) −118.128 118.128i −0.163386 0.163386i
\(724\) 72.0985i 0.0995836i
\(725\) 113.515 + 480.511i 0.156572 + 0.662774i
\(726\) 641.891 0.884147
\(727\) 254.322 254.322i 0.349824 0.349824i −0.510220 0.860044i \(-0.670436\pi\)
0.860044 + 0.510220i \(0.170436\pi\)
\(728\) 60.1065 + 60.1065i 0.0825638 + 0.0825638i
\(729\) 27.0000i 0.0370370i
\(730\) −55.8684 479.495i −0.0765320 0.656842i
\(731\) 60.0899 0.0822024
\(732\) 239.662 239.662i 0.327406 0.327406i
\(733\) −27.6831 27.6831i −0.0377668 0.0377668i 0.687971 0.725738i \(-0.258502\pi\)
−0.725738 + 0.687971i \(0.758502\pi\)
\(734\) 451.201i 0.614715i
\(735\) 47.5390 + 37.6170i 0.0646789 + 0.0511797i
\(736\) 143.254 0.194639
\(737\) −1314.65 + 1314.65i −1.78379 + 1.78379i
\(738\) −242.586 242.586i −0.328707 0.328707i
\(739\) 434.621i 0.588121i −0.955787 0.294060i \(-0.904993\pi\)
0.955787 0.294060i \(-0.0950066\pi\)
\(740\) 326.751 412.936i 0.441556 0.558022i
\(741\) −162.333 −0.219073
\(742\) 145.386 145.386i 0.195938 0.195938i
\(743\) 126.704 + 126.704i 0.170530 + 0.170530i 0.787212 0.616682i \(-0.211524\pi\)
−0.616682 + 0.787212i \(0.711524\pi\)
\(744\) 146.990i 0.197568i
\(745\) 1458.34 169.919i 1.95750 0.228079i
\(746\) 558.812 0.749078
\(747\) −103.241 + 103.241i −0.138208 + 0.138208i
\(748\) 85.9821 + 85.9821i 0.114949 + 0.114949i
\(749\) 53.9975i 0.0720928i
\(750\) −104.408 287.835i −0.139211 0.383780i
\(751\) 735.755 0.979701 0.489851 0.871806i \(-0.337051\pi\)
0.489851 + 0.871806i \(0.337051\pi\)
\(752\) 32.7020 32.7020i 0.0434866 0.0434866i
\(753\) −355.791 355.791i −0.472498 0.472498i
\(754\) 317.258i 0.420767i
\(755\) 134.090 + 1150.84i 0.177603 + 1.52429i
\(756\) −27.4955 −0.0363696
\(757\) −255.322 + 255.322i −0.337281 + 0.337281i −0.855343 0.518062i \(-0.826654\pi\)
0.518062 + 0.855343i \(0.326654\pi\)
\(758\) 746.946 + 746.946i 0.985417 + 0.985417i
\(759\) 858.464i 1.13105i
\(760\) 91.5043 + 72.4062i 0.120400 + 0.0952713i
\(761\) 783.231 1.02921 0.514606 0.857427i \(-0.327938\pi\)
0.514606 + 0.857427i \(0.327938\pi\)
\(762\) 34.0357 34.0357i 0.0446663 0.0446663i
\(763\) −64.8007 64.8007i −0.0849289 0.0849289i
\(764\) 266.389i 0.348676i
\(765\) 28.9143 36.5408i 0.0377964 0.0477657i
\(766\) 718.352 0.937797
\(767\) 597.403 597.403i 0.778883 0.778883i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 186.068i 0.241961i 0.992655 + 0.120980i \(0.0386038\pi\)
−0.992655 + 0.120980i \(0.961396\pi\)
\(770\) −363.692 + 42.3757i −0.472328 + 0.0550333i
\(771\) −552.564 −0.716684
\(772\) −473.130 + 473.130i −0.612863 + 0.612863i
\(773\) −333.576 333.576i −0.431534 0.431534i 0.457616 0.889150i \(-0.348703\pi\)
−0.889150 + 0.457616i \(0.848703\pi\)
\(774\) 82.0679i 0.106031i
\(775\) −730.014 + 172.457i −0.941953 + 0.222525i
\(776\) 293.143 0.377761
\(777\) −170.630 + 170.630i −0.219601 + 0.219601i
\(778\) −476.719 476.719i −0.612749 0.612749i
\(779\) 667.190i 0.856469i
\(780\) 22.7697 + 195.423i 0.0291919 + 0.250542i
\(781\) −261.855