Properties

Label 690.3.k.b.277.3
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 277.3
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-2.46815 + 4.34836i) q^{5} +2.44949 q^{6} +(-1.62328 - 1.62328i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-2.46815 + 4.34836i) q^{5} +2.44949 q^{6} +(-1.62328 - 1.62328i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.81651 - 1.88022i) q^{10} +0.00768588 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.99113 + 7.99113i) q^{13} +3.24656i q^{14} +(-2.30278 - 8.34848i) q^{15} -4.00000 q^{16} +(5.07503 + 5.07503i) q^{17} +(-3.00000 + 3.00000i) q^{18} +29.4268i q^{19} +(-8.69672 - 4.93629i) q^{20} +3.97621 q^{21} +(-0.00768588 - 0.00768588i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-12.8165 - 21.4648i) q^{25} +15.9823 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.24656 - 3.24656i) q^{28} +24.1950i q^{29} +(-6.04570 + 10.6513i) q^{30} -27.9270 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.00941325 + 0.00941325i) q^{33} -10.1501i q^{34} +(11.0651 - 3.05212i) q^{35} +6.00000 q^{36} +(-17.5169 - 17.5169i) q^{37} +(29.4268 - 29.4268i) q^{38} -19.5742i q^{39} +(3.76043 + 13.6330i) q^{40} +9.62845 q^{41} +(-3.97621 - 3.97621i) q^{42} +(33.5256 - 33.5256i) q^{43} +0.0153718i q^{44} +(13.0451 + 7.40444i) q^{45} -6.78233 q^{46} +(-48.5429 - 48.5429i) q^{47} +(4.89898 - 4.89898i) q^{48} -43.7299i q^{49} +(-8.64828 + 34.2813i) q^{50} -12.4312 q^{51} +(-15.9823 - 15.9823i) q^{52} +(41.9368 - 41.9368i) q^{53} -7.34847i q^{54} +(-0.0189699 + 0.0334210i) q^{55} -6.49313 q^{56} +(-36.0403 - 36.0403i) q^{57} +(24.1950 - 24.1950i) q^{58} -85.5954i q^{59} +(16.6970 - 4.60557i) q^{60} -10.2155 q^{61} +(27.9270 + 27.9270i) q^{62} +(-4.86985 + 4.86985i) q^{63} -8.00000i q^{64} +(-15.0251 - 54.4716i) q^{65} +0.0188265 q^{66} +(-80.3769 - 80.3769i) q^{67} +(-10.1501 + 10.1501i) q^{68} +8.30662i q^{69} +(-14.1172 - 8.01299i) q^{70} +49.4857 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-99.6326 + 99.6326i) q^{73} +35.0338i q^{74} +(41.9858 + 10.5919i) q^{75} -58.8536 q^{76} +(-0.0124764 - 0.0124764i) q^{77} +(-19.5742 + 19.5742i) q^{78} +114.819i q^{79} +(9.87259 - 17.3934i) q^{80} -9.00000 q^{81} +(-9.62845 - 9.62845i) q^{82} +(109.398 - 109.398i) q^{83} +7.95242i q^{84} +(-34.5940 + 9.54216i) q^{85} -67.0511 q^{86} +(-29.6328 - 29.6328i) q^{87} +(0.0153718 - 0.0153718i) q^{88} -16.9328i q^{89} +(-5.64065 - 20.4495i) q^{90} +25.9437 q^{91} +(6.78233 + 6.78233i) q^{92} +(34.2034 - 34.2034i) q^{93} +97.0859i q^{94} +(-127.958 - 72.6296i) q^{95} -9.79796 q^{96} +(-73.9763 - 73.9763i) q^{97} +(-43.7299 + 43.7299i) q^{98} -0.0230577i 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
\(5\) −2.46815 + 4.34836i −0.493629 + 0.869672i
\(6\) 2.44949 0.408248
\(7\) −1.62328 1.62328i −0.231897 0.231897i 0.581587 0.813484i \(-0.302432\pi\)
−0.813484 + 0.581587i \(0.802432\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.81651 1.88022i 0.681651 0.188022i
\(11\) 0.00768588 0.000698717 0.000349358 1.00000i \(-0.499889\pi\)
0.000349358 1.00000i \(0.499889\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −7.99113 + 7.99113i −0.614703 + 0.614703i −0.944168 0.329465i \(-0.893132\pi\)
0.329465 + 0.944168i \(0.393132\pi\)
\(14\) 3.24656i 0.231897i
\(15\) −2.30278 8.34848i −0.153519 0.556566i
\(16\) −4.00000 −0.250000
\(17\) 5.07503 + 5.07503i 0.298531 + 0.298531i 0.840438 0.541907i \(-0.182298\pi\)
−0.541907 + 0.840438i \(0.682298\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 29.4268i 1.54878i 0.632709 + 0.774389i \(0.281943\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(20\) −8.69672 4.93629i −0.434836 0.246815i
\(21\) 3.97621 0.189343
\(22\) −0.00768588 0.00768588i −0.000349358 0.000349358i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −12.8165 21.4648i −0.512660 0.858592i
\(26\) 15.9823 0.614703
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 3.24656 3.24656i 0.115949 0.115949i
\(29\) 24.1950i 0.834312i 0.908835 + 0.417156i \(0.136973\pi\)
−0.908835 + 0.417156i \(0.863027\pi\)
\(30\) −6.04570 + 10.6513i −0.201523 + 0.355042i
\(31\) −27.9270 −0.900870 −0.450435 0.892809i \(-0.648731\pi\)
−0.450435 + 0.892809i \(0.648731\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −0.00941325 + 0.00941325i −0.000285250 + 0.000285250i
\(34\) 10.1501i 0.298531i
\(35\) 11.0651 3.05212i 0.316146 0.0872034i
\(36\) 6.00000 0.166667
\(37\) −17.5169 17.5169i −0.473429 0.473429i 0.429593 0.903023i \(-0.358657\pi\)
−0.903023 + 0.429593i \(0.858657\pi\)
\(38\) 29.4268 29.4268i 0.774389 0.774389i
\(39\) 19.5742i 0.501903i
\(40\) 3.76043 + 13.6330i 0.0940108 + 0.340825i
\(41\) 9.62845 0.234840 0.117420 0.993082i \(-0.462538\pi\)
0.117420 + 0.993082i \(0.462538\pi\)
\(42\) −3.97621 3.97621i −0.0946717 0.0946717i
\(43\) 33.5256 33.5256i 0.779664 0.779664i −0.200109 0.979774i \(-0.564130\pi\)
0.979774 + 0.200109i \(0.0641297\pi\)
\(44\) 0.0153718i 0.000349358i
\(45\) 13.0451 + 7.40444i 0.289891 + 0.164543i
\(46\) −6.78233 −0.147442
\(47\) −48.5429 48.5429i −1.03283 1.03283i −0.999443 0.0333858i \(-0.989371\pi\)
−0.0333858 0.999443i \(-0.510629\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 43.7299i 0.892447i
\(50\) −8.64828 + 34.2813i −0.172966 + 0.685626i
\(51\) −12.4312 −0.243750
\(52\) −15.9823 15.9823i −0.307351 0.307351i
\(53\) 41.9368 41.9368i 0.791260 0.791260i −0.190439 0.981699i \(-0.560991\pi\)
0.981699 + 0.190439i \(0.0609911\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −0.0189699 + 0.0334210i −0.000344907 + 0.000607655i
\(56\) −6.49313 −0.115949
\(57\) −36.0403 36.0403i −0.632286 0.632286i
\(58\) 24.1950 24.1950i 0.417156 0.417156i
\(59\) 85.5954i 1.45077i −0.688344 0.725385i \(-0.741662\pi\)
0.688344 0.725385i \(-0.258338\pi\)
\(60\) 16.6970 4.60557i 0.278283 0.0767595i
\(61\) −10.2155 −0.167468 −0.0837338 0.996488i \(-0.526685\pi\)
−0.0837338 + 0.996488i \(0.526685\pi\)
\(62\) 27.9270 + 27.9270i 0.450435 + 0.450435i
\(63\) −4.86985 + 4.86985i −0.0772991 + 0.0772991i
\(64\) 8.00000i 0.125000i
\(65\) −15.0251 54.4716i −0.231155 0.838025i
\(66\) 0.0188265 0.000285250
\(67\) −80.3769 80.3769i −1.19965 1.19965i −0.974270 0.225385i \(-0.927636\pi\)
−0.225385 0.974270i \(-0.572364\pi\)
\(68\) −10.1501 + 10.1501i −0.149266 + 0.149266i
\(69\) 8.30662i 0.120386i
\(70\) −14.1172 8.01299i −0.201675 0.114471i
\(71\) 49.4857 0.696981 0.348491 0.937312i \(-0.386694\pi\)
0.348491 + 0.937312i \(0.386694\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −99.6326 + 99.6326i −1.36483 + 1.36483i −0.497185 + 0.867644i \(0.665633\pi\)
−0.867644 + 0.497185i \(0.834367\pi\)
\(74\) 35.0338i 0.473429i
\(75\) 41.9858 + 10.5919i 0.559811 + 0.141226i
\(76\) −58.8536 −0.774389
\(77\) −0.0124764 0.0124764i −0.000162031 0.000162031i
\(78\) −19.5742 + 19.5742i −0.250951 + 0.250951i
\(79\) 114.819i 1.45341i 0.686950 + 0.726705i \(0.258949\pi\)
−0.686950 + 0.726705i \(0.741051\pi\)
\(80\) 9.87259 17.3934i 0.123407 0.217418i
\(81\) −9.00000 −0.111111
\(82\) −9.62845 9.62845i −0.117420 0.117420i
\(83\) 109.398 109.398i 1.31805 1.31805i 0.402738 0.915315i \(-0.368058\pi\)
0.915315 0.402738i \(-0.131942\pi\)
\(84\) 7.95242i 0.0946717i
\(85\) −34.5940 + 9.54216i −0.406988 + 0.112261i
\(86\) −67.0511 −0.779664
\(87\) −29.6328 29.6328i −0.340606 0.340606i
\(88\) 0.0153718 0.0153718i 0.000174679 0.000174679i
\(89\) 16.9328i 0.190257i −0.995465 0.0951283i \(-0.969674\pi\)
0.995465 0.0951283i \(-0.0303261\pi\)
\(90\) −5.64065 20.4495i −0.0626739 0.227217i
\(91\) 25.9437 0.285096
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 34.2034 34.2034i 0.367779 0.367779i
\(94\) 97.0859i 1.03283i
\(95\) −127.958 72.6296i −1.34693 0.764522i
\(96\) −9.79796 −0.102062
\(97\) −73.9763 73.9763i −0.762642 0.762642i 0.214157 0.976799i \(-0.431299\pi\)
−0.976799 + 0.214157i \(0.931299\pi\)
\(98\) −43.7299 + 43.7299i −0.446224 + 0.446224i
\(99\) 0.0230577i 0.000232906i
\(100\) 42.9296 25.6330i 0.429296 0.256330i
\(101\) 26.3637 0.261027 0.130513 0.991447i \(-0.458337\pi\)
0.130513 + 0.991447i \(0.458337\pi\)
\(102\) 12.4312 + 12.4312i 0.121875 + 0.121875i
\(103\) −2.90947 + 2.90947i −0.0282473 + 0.0282473i −0.721089 0.692842i \(-0.756358\pi\)
0.692842 + 0.721089i \(0.256358\pi\)
\(104\) 31.9645i 0.307351i
\(105\) −9.81387 + 17.2900i −0.0934655 + 0.164667i
\(106\) −83.8736 −0.791260
\(107\) 17.4022 + 17.4022i 0.162637 + 0.162637i 0.783734 0.621097i \(-0.213313\pi\)
−0.621097 + 0.783734i \(0.713313\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 29.4112i 0.269827i 0.990857 + 0.134914i \(0.0430757\pi\)
−0.990857 + 0.134914i \(0.956924\pi\)
\(110\) 0.0523909 0.0144511i 0.000476281 0.000131374i
\(111\) 42.9074 0.386554
\(112\) 6.49313 + 6.49313i 0.0579744 + 0.0579744i
\(113\) −19.4842 + 19.4842i −0.172427 + 0.172427i −0.788045 0.615618i \(-0.788906\pi\)
0.615618 + 0.788045i \(0.288906\pi\)
\(114\) 72.0806i 0.632286i
\(115\) 6.37612 + 23.1159i 0.0554445 + 0.201008i
\(116\) −48.3901 −0.417156
\(117\) 23.9734 + 23.9734i 0.204901 + 0.204901i
\(118\) −85.5954 + 85.5954i −0.725385 + 0.725385i
\(119\) 16.4764i 0.138457i
\(120\) −21.3025 12.0914i −0.177521 0.100762i
\(121\) −121.000 −1.00000
\(122\) 10.2155 + 10.2155i 0.0837338 + 0.0837338i
\(123\) −11.7924 + 11.7924i −0.0958731 + 0.0958731i
\(124\) 55.8539i 0.450435i
\(125\) 124.970 2.75258i 0.999758 0.0220206i
\(126\) 9.73969 0.0772991
\(127\) −133.385 133.385i −1.05027 1.05027i −0.998668 0.0516046i \(-0.983566\pi\)
−0.0516046 0.998668i \(-0.516434\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 82.1205i 0.636593i
\(130\) −39.4466 + 69.4967i −0.303435 + 0.534590i
\(131\) −51.3311 −0.391841 −0.195920 0.980620i \(-0.562769\pi\)
−0.195920 + 0.980620i \(0.562769\pi\)
\(132\) −0.0188265 0.0188265i −0.000142625 0.000142625i
\(133\) 47.7680 47.7680i 0.359158 0.359158i
\(134\) 160.754i 1.19965i
\(135\) −25.0455 + 6.90835i −0.185522 + 0.0511730i
\(136\) 20.3001 0.149266
\(137\) −178.812 178.812i −1.30520 1.30520i −0.924839 0.380358i \(-0.875801\pi\)
−0.380358 0.924839i \(-0.624199\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 71.0797i 0.511364i 0.966761 + 0.255682i \(0.0823001\pi\)
−0.966761 + 0.255682i \(0.917700\pi\)
\(140\) 6.10424 + 22.1302i 0.0436017 + 0.158073i
\(141\) 118.905 0.843301
\(142\) −49.4857 49.4857i −0.348491 0.348491i
\(143\) −0.0614189 + 0.0614189i −0.000429503 + 0.000429503i
\(144\) 12.0000i 0.0833333i
\(145\) −105.209 59.7169i −0.725578 0.411841i
\(146\) 199.265 1.36483
\(147\) 53.5580 + 53.5580i 0.364340 + 0.364340i
\(148\) 35.0338 35.0338i 0.236715 0.236715i
\(149\) 112.421i 0.754500i −0.926111 0.377250i \(-0.876870\pi\)
0.926111 0.377250i \(-0.123130\pi\)
\(150\) −31.3939 52.5778i −0.209293 0.350519i
\(151\) 85.6195 0.567016 0.283508 0.958970i \(-0.408502\pi\)
0.283508 + 0.958970i \(0.408502\pi\)
\(152\) 58.8536 + 58.8536i 0.387195 + 0.387195i
\(153\) 15.2251 15.2251i 0.0995104 0.0995104i
\(154\) 0.0249527i 0.000162031i
\(155\) 68.9279 121.437i 0.444696 0.783462i
\(156\) 39.1484 0.250951
\(157\) 43.2587 + 43.2587i 0.275533 + 0.275533i 0.831323 0.555790i \(-0.187584\pi\)
−0.555790 + 0.831323i \(0.687584\pi\)
\(158\) 114.819 114.819i 0.726705 0.726705i
\(159\) 102.724i 0.646061i
\(160\) −27.2660 + 7.52086i −0.170413 + 0.0470054i
\(161\) −11.0096 −0.0683828
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 154.461 154.461i 0.947615 0.947615i −0.0510794 0.998695i \(-0.516266\pi\)
0.998695 + 0.0510794i \(0.0162661\pi\)
\(164\) 19.2569i 0.117420i
\(165\) −0.0176989 0.0641655i −0.000107266 0.000388882i
\(166\) −218.797 −1.31805
\(167\) 205.359 + 205.359i 1.22969 + 1.22969i 0.964080 + 0.265613i \(0.0855744\pi\)
0.265613 + 0.964080i \(0.414426\pi\)
\(168\) 7.95242 7.95242i 0.0473359 0.0473359i
\(169\) 41.2836i 0.244281i
\(170\) 44.1362 + 25.0518i 0.259624 + 0.147364i
\(171\) 88.2804 0.516259
\(172\) 67.0511 + 67.0511i 0.389832 + 0.389832i
\(173\) −22.0996 + 22.0996i −0.127744 + 0.127744i −0.768088 0.640344i \(-0.778792\pi\)
0.640344 + 0.768088i \(0.278792\pi\)
\(174\) 59.2655i 0.340606i
\(175\) −14.0386 + 55.6482i −0.0802206 + 0.317990i
\(176\) −0.0307435 −0.000174679
\(177\) 104.833 + 104.833i 0.592274 + 0.592274i
\(178\) −16.9328 + 16.9328i −0.0951283 + 0.0951283i
\(179\) 116.490i 0.650782i 0.945580 + 0.325391i \(0.105496\pi\)
−0.945580 + 0.325391i \(0.894504\pi\)
\(180\) −14.8089 + 26.0902i −0.0822715 + 0.144945i
\(181\) −179.408 −0.991205 −0.495602 0.868550i \(-0.665053\pi\)
−0.495602 + 0.868550i \(0.665053\pi\)
\(182\) −25.9437 25.9437i −0.142548 0.142548i
\(183\) 12.5114 12.5114i 0.0683684 0.0683684i
\(184\) 13.5647i 0.0737210i
\(185\) 119.404 32.9355i 0.645427 0.178030i
\(186\) −68.4068 −0.367779
\(187\) 0.0390061 + 0.0390061i 0.000208589 + 0.000208589i
\(188\) 97.0859 97.0859i 0.516414 0.516414i
\(189\) 11.9286i 0.0631145i
\(190\) 55.3287 + 200.588i 0.291204 + 1.05573i
\(191\) 48.4540 0.253686 0.126843 0.991923i \(-0.459516\pi\)
0.126843 + 0.991923i \(0.459516\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 3.48571 3.48571i 0.0180607 0.0180607i −0.698019 0.716079i \(-0.745935\pi\)
0.716079 + 0.698019i \(0.245935\pi\)
\(194\) 147.953i 0.762642i
\(195\) 85.1157 + 48.3120i 0.436491 + 0.247754i
\(196\) 87.4598 0.446224
\(197\) −189.488 189.488i −0.961868 0.961868i 0.0374314 0.999299i \(-0.488082\pi\)
−0.999299 + 0.0374314i \(0.988082\pi\)
\(198\) −0.0230577 + 0.0230577i −0.000116453 + 0.000116453i
\(199\) 320.034i 1.60821i 0.594486 + 0.804106i \(0.297355\pi\)
−0.594486 + 0.804106i \(0.702645\pi\)
\(200\) −68.5626 17.2966i −0.342813 0.0864828i
\(201\) 196.882 0.979514
\(202\) −26.3637 26.3637i −0.130513 0.130513i
\(203\) 39.2754 39.2754i 0.193475 0.193475i
\(204\) 24.8625i 0.121875i
\(205\) −23.7644 + 41.8680i −0.115924 + 0.204234i
\(206\) 5.81895 0.0282473
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 31.9645 31.9645i 0.153676 0.153676i
\(209\) 0.226171i 0.00108216i
\(210\) 27.1039 7.47614i 0.129066 0.0356007i
\(211\) −92.7388 −0.439520 −0.219760 0.975554i \(-0.570527\pi\)
−0.219760 + 0.975554i \(0.570527\pi\)
\(212\) 83.8736 + 83.8736i 0.395630 + 0.395630i
\(213\) −60.6073 + 60.6073i −0.284541 + 0.284541i
\(214\) 34.8043i 0.162637i
\(215\) 63.0353 + 228.527i 0.293187 + 1.06292i
\(216\) 14.6969 0.0680414
\(217\) 45.3333 + 45.3333i 0.208909 + 0.208909i
\(218\) 29.4112 29.4112i 0.134914 0.134914i
\(219\) 244.049i 1.11438i
\(220\) −0.0668420 0.0379398i −0.000303827 0.000172454i
\(221\) −81.1105 −0.367016
\(222\) −42.9074 42.9074i −0.193277 0.193277i
\(223\) 140.439 140.439i 0.629769 0.629769i −0.318241 0.948010i \(-0.603092\pi\)
0.948010 + 0.318241i \(0.103092\pi\)
\(224\) 12.9863i 0.0579744i
\(225\) −64.3944 + 38.4495i −0.286197 + 0.170887i
\(226\) 38.9684 0.172427
\(227\) 181.069 + 181.069i 0.797662 + 0.797662i 0.982726 0.185065i \(-0.0592495\pi\)
−0.185065 + 0.982726i \(0.559249\pi\)
\(228\) 72.0806 72.0806i 0.316143 0.316143i
\(229\) 215.841i 0.942537i −0.881990 0.471268i \(-0.843796\pi\)
0.881990 0.471268i \(-0.156204\pi\)
\(230\) 16.7398 29.4920i 0.0727817 0.128226i
\(231\) 0.0305607 0.000132297
\(232\) 48.3901 + 48.3901i 0.208578 + 0.208578i
\(233\) −71.0465 + 71.0465i −0.304921 + 0.304921i −0.842935 0.538015i \(-0.819174\pi\)
0.538015 + 0.842935i \(0.319174\pi\)
\(234\) 47.9468i 0.204901i
\(235\) 330.893 91.2712i 1.40806 0.388388i
\(236\) 171.191 0.725385
\(237\) −140.624 140.624i −0.593352 0.593352i
\(238\) −16.4764 + 16.4764i −0.0692286 + 0.0692286i
\(239\) 107.797i 0.451035i 0.974239 + 0.225518i \(0.0724073\pi\)
−0.974239 + 0.225518i \(0.927593\pi\)
\(240\) 9.21114 + 33.3939i 0.0383797 + 0.139141i
\(241\) 70.4171 0.292187 0.146094 0.989271i \(-0.453330\pi\)
0.146094 + 0.989271i \(0.453330\pi\)
\(242\) 121.000 + 121.000i 0.500000 + 0.500000i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 20.4311i 0.0837338i
\(245\) 190.153 + 107.932i 0.776137 + 0.440538i
\(246\) 23.5848 0.0958731
\(247\) −235.153 235.153i −0.952038 0.952038i
\(248\) −55.8539 + 55.8539i −0.225218 + 0.225218i
\(249\) 267.970i 1.07619i
\(250\) −127.722 122.217i −0.510889 0.488868i
\(251\) −145.088 −0.578041 −0.289020 0.957323i \(-0.593330\pi\)
−0.289020 + 0.957323i \(0.593330\pi\)
\(252\) −9.73969 9.73969i −0.0386496 0.0386496i
\(253\) 0.0260641 0.0260641i 0.000103020 0.000103020i
\(254\) 266.769i 1.05027i
\(255\) 30.6821 54.0555i 0.120322 0.211982i
\(256\) 16.0000 0.0625000
\(257\) −35.0507 35.0507i −0.136384 0.136384i 0.635619 0.772003i \(-0.280745\pi\)
−0.772003 + 0.635619i \(0.780745\pi\)
\(258\) 82.1205 82.1205i 0.318297 0.318297i
\(259\) 56.8697i 0.219574i
\(260\) 108.943 30.0501i 0.419013 0.115577i
\(261\) 72.5851 0.278104
\(262\) 51.3311 + 51.3311i 0.195920 + 0.195920i
\(263\) 115.541 115.541i 0.439319 0.439319i −0.452464 0.891783i \(-0.649455\pi\)
0.891783 + 0.452464i \(0.149455\pi\)
\(264\) 0.0376530i 0.000142625i
\(265\) 78.8502 + 285.862i 0.297548 + 1.07873i
\(266\) −95.5360 −0.359158
\(267\) 20.7384 + 20.7384i 0.0776719 + 0.0776719i
\(268\) 160.754 160.754i 0.599827 0.599827i
\(269\) 276.254i 1.02697i 0.858100 + 0.513483i \(0.171645\pi\)
−0.858100 + 0.513483i \(0.828355\pi\)
\(270\) 31.9538 + 18.1371i 0.118347 + 0.0671744i
\(271\) −157.430 −0.580921 −0.290461 0.956887i \(-0.593809\pi\)
−0.290461 + 0.956887i \(0.593809\pi\)
\(272\) −20.3001 20.3001i −0.0746328 0.0746328i
\(273\) −31.7744 + 31.7744i −0.116390 + 0.116390i
\(274\) 357.624i 1.30520i
\(275\) −0.0985062 0.164976i −0.000358204 0.000599912i
\(276\) −16.6132 −0.0601929
\(277\) −90.6970 90.6970i −0.327426 0.327426i 0.524181 0.851607i \(-0.324372\pi\)
−0.851607 + 0.524181i \(0.824372\pi\)
\(278\) 71.0797 71.0797i 0.255682 0.255682i
\(279\) 83.7809i 0.300290i
\(280\) 16.0260 28.2345i 0.0572357 0.100837i
\(281\) 102.396 0.364397 0.182199 0.983262i \(-0.441679\pi\)
0.182199 + 0.983262i \(0.441679\pi\)
\(282\) −118.905 118.905i −0.421650 0.421650i
\(283\) 37.0378 37.0378i 0.130875 0.130875i −0.638635 0.769510i \(-0.720500\pi\)
0.769510 + 0.638635i \(0.220500\pi\)
\(284\) 98.9714i 0.348491i
\(285\) 245.669 67.7636i 0.861997 0.237767i
\(286\) 0.122838 0.000429503
\(287\) −15.6297 15.6297i −0.0544588 0.0544588i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 237.488i 0.821758i
\(290\) 45.4919 + 164.926i 0.156869 + 0.568709i
\(291\) 181.204 0.622694
\(292\) −199.265 199.265i −0.682415 0.682415i
\(293\) −141.513 + 141.513i −0.482981 + 0.482981i −0.906082 0.423101i \(-0.860941\pi\)
0.423101 + 0.906082i \(0.360941\pi\)
\(294\) 107.116i 0.364340i
\(295\) 372.200 + 211.262i 1.26169 + 0.716142i
\(296\) −70.0676 −0.236715
\(297\) 0.0282397 + 0.0282397i 9.50833e−5 + 9.50833e-5i
\(298\) −112.421 + 112.421i −0.377250 + 0.377250i
\(299\) 54.1985i 0.181266i
\(300\) −21.1839 + 83.9717i −0.0706129 + 0.279906i
\(301\) −108.843 −0.361604
\(302\) −85.6195 85.6195i −0.283508 0.283508i
\(303\) −32.2888 + 32.2888i −0.106564 + 0.106564i
\(304\) 117.707i 0.387195i
\(305\) 25.2134 44.4208i 0.0826669 0.145642i
\(306\) −30.4502 −0.0995104
\(307\) 325.695 + 325.695i 1.06089 + 1.06089i 0.998022 + 0.0628732i \(0.0200264\pi\)
0.0628732 + 0.998022i \(0.479974\pi\)
\(308\) 0.0249527 0.0249527i 8.10153e−5 8.10153e-5i
\(309\) 7.12673i 0.0230638i
\(310\) −190.364 + 52.5087i −0.614079 + 0.169383i
\(311\) −23.8835 −0.0767959 −0.0383980 0.999263i \(-0.512225\pi\)
−0.0383980 + 0.999263i \(0.512225\pi\)
\(312\) −39.1484 39.1484i −0.125476 0.125476i
\(313\) −260.353 + 260.353i −0.831799 + 0.831799i −0.987763 0.155964i \(-0.950152\pi\)
0.155964 + 0.987763i \(0.450152\pi\)
\(314\) 86.5174i 0.275533i
\(315\) −9.15636 33.1953i −0.0290678 0.105382i
\(316\) −229.639 −0.726705
\(317\) −92.2203 92.2203i −0.290916 0.290916i 0.546526 0.837442i \(-0.315950\pi\)
−0.837442 + 0.546526i \(0.815950\pi\)
\(318\) 102.724 102.724i 0.323031 0.323031i
\(319\) 0.185960i 0.000582948i
\(320\) 34.7869 + 19.7452i 0.108709 + 0.0617037i
\(321\) −42.6264 −0.132793
\(322\) 11.0096 + 11.0096i 0.0341914 + 0.0341914i
\(323\) −149.342 + 149.342i −0.462359 + 0.462359i
\(324\) 18.0000i 0.0555556i
\(325\) 273.946 + 69.1096i 0.842912 + 0.212645i
\(326\) −308.923 −0.947615
\(327\) −36.0212 36.0212i −0.110157 0.110157i
\(328\) 19.2569 19.2569i 0.0587100 0.0587100i
\(329\) 157.598i 0.479020i
\(330\) −0.0464665 + 0.0818644i −0.000140808 + 0.000248074i
\(331\) 532.735 1.60947 0.804735 0.593634i \(-0.202307\pi\)
0.804735 + 0.593634i \(0.202307\pi\)
\(332\) 218.797 + 218.797i 0.659027 + 0.659027i
\(333\) −52.5507 + 52.5507i −0.157810 + 0.157810i
\(334\) 410.717i 1.22969i
\(335\) 547.890 151.126i 1.63549 0.451122i
\(336\) −15.9048 −0.0473359
\(337\) −399.875 399.875i −1.18657 1.18657i −0.978009 0.208563i \(-0.933122\pi\)
−0.208563 0.978009i \(-0.566878\pi\)
\(338\) 41.2836 41.2836i 0.122141 0.122141i
\(339\) 47.7264i 0.140786i
\(340\) −19.0843 69.1880i −0.0561303 0.203494i
\(341\) −0.214643 −0.000629453
\(342\) −88.2804 88.2804i −0.258130 0.258130i
\(343\) −150.527 + 150.527i −0.438854 + 0.438854i
\(344\) 134.102i 0.389832i
\(345\) −36.1202 20.5020i −0.104696 0.0594260i
\(346\) 44.1993 0.127744
\(347\) −105.898 105.898i −0.305182 0.305182i 0.537855 0.843037i \(-0.319235\pi\)
−0.843037 + 0.537855i \(0.819235\pi\)
\(348\) 59.2655 59.2655i 0.170303 0.170303i
\(349\) 171.397i 0.491109i 0.969383 + 0.245555i \(0.0789701\pi\)
−0.969383 + 0.245555i \(0.921030\pi\)
\(350\) 69.6868 41.6096i 0.199105 0.118885i
\(351\) −58.7226 −0.167301
\(352\) 0.0307435 + 0.0307435i 8.73396e−5 + 8.73396e-5i
\(353\) 234.785 234.785i 0.665113 0.665113i −0.291468 0.956581i \(-0.594144\pi\)
0.956581 + 0.291468i \(0.0941437\pi\)
\(354\) 209.665i 0.592274i
\(355\) −122.138 + 215.182i −0.344050 + 0.606146i
\(356\) 33.8657 0.0951283
\(357\) 20.1794 + 20.1794i 0.0565249 + 0.0565249i
\(358\) 116.490 116.490i 0.325391 0.325391i
\(359\) 219.996i 0.612801i 0.951903 + 0.306401i \(0.0991247\pi\)
−0.951903 + 0.306401i \(0.900875\pi\)
\(360\) 40.8991 11.2813i 0.113608 0.0313369i
\(361\) −504.936 −1.39871
\(362\) 179.408 + 179.408i 0.495602 + 0.495602i
\(363\) 148.194 148.194i 0.408248 0.408248i
\(364\) 51.8875i 0.142548i
\(365\) −187.331 679.146i −0.513235 1.86067i
\(366\) −25.0228 −0.0683684
\(367\) −198.319 198.319i −0.540380 0.540380i 0.383260 0.923640i \(-0.374801\pi\)
−0.923640 + 0.383260i \(0.874801\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 28.8853i 0.0782800i
\(370\) −152.340 86.4685i −0.411729 0.233699i
\(371\) −136.150 −0.366982
\(372\) 68.4068 + 68.4068i 0.183889 + 0.183889i
\(373\) −357.278 + 357.278i −0.957849 + 0.957849i −0.999147 0.0412982i \(-0.986851\pi\)
0.0412982 + 0.999147i \(0.486851\pi\)
\(374\) 0.0780122i 0.000208589i
\(375\) −149.685 + 156.427i −0.399159 + 0.417139i
\(376\) −194.172 −0.516414
\(377\) −193.346 193.346i −0.512854 0.512854i
\(378\) −11.9286 + 11.9286i −0.0315572 + 0.0315572i
\(379\) 632.919i 1.66997i −0.550271 0.834986i \(-0.685476\pi\)
0.550271 0.834986i \(-0.314524\pi\)
\(380\) 145.259 255.917i 0.382261 0.673465i
\(381\) 326.724 0.857544
\(382\) −48.4540 48.4540i −0.126843 0.126843i
\(383\) −456.210 + 456.210i −1.19115 + 1.19115i −0.214405 + 0.976745i \(0.568781\pi\)
−0.976745 + 0.214405i \(0.931219\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0.0850452 0.0234582i 0.000220897 6.09305e-5i
\(386\) −6.97142 −0.0180607
\(387\) −100.577 100.577i −0.259888 0.259888i
\(388\) 147.953 147.953i 0.381321 0.381321i
\(389\) 297.456i 0.764667i 0.924024 + 0.382334i \(0.124879\pi\)
−0.924024 + 0.382334i \(0.875121\pi\)
\(390\) −36.8037 133.428i −0.0943685 0.342122i
\(391\) 34.4205 0.0880321
\(392\) −87.4598 87.4598i −0.223112 0.223112i
\(393\) 62.8675 62.8675i 0.159968 0.159968i
\(394\) 378.976i 0.961868i
\(395\) −499.276 283.391i −1.26399 0.717446i
\(396\) 0.0461153 0.000116453
\(397\) −83.7492 83.7492i −0.210955 0.210955i 0.593718 0.804673i \(-0.297659\pi\)
−0.804673 + 0.593718i \(0.797659\pi\)
\(398\) 320.034 320.034i 0.804106 0.804106i
\(399\) 117.007i 0.293251i
\(400\) 51.2660 + 85.8592i 0.128165 + 0.214648i
\(401\) −365.707 −0.911988 −0.455994 0.889983i \(-0.650716\pi\)
−0.455994 + 0.889983i \(0.650716\pi\)
\(402\) −196.882 196.882i −0.489757 0.489757i
\(403\) 223.168 223.168i 0.553767 0.553767i
\(404\) 52.7274i 0.130513i
\(405\) 22.2133 39.1353i 0.0548477 0.0966303i
\(406\) −78.5507 −0.193475
\(407\) −0.134633 0.134633i −0.000330793 0.000330793i
\(408\) −24.8625 + 24.8625i −0.0609374 + 0.0609374i
\(409\) 432.702i 1.05795i 0.848637 + 0.528975i \(0.177423\pi\)
−0.848637 + 0.528975i \(0.822577\pi\)
\(410\) 65.6324 18.1036i 0.160079 0.0441550i
\(411\) 437.998 1.06569
\(412\) −5.81895 5.81895i −0.0141237 0.0141237i
\(413\) −138.945 + 138.945i −0.336430 + 0.336430i
\(414\) 20.3470i 0.0491473i
\(415\) 205.693 + 745.715i 0.495645 + 1.79690i
\(416\) −63.9291 −0.153676
\(417\) −87.0544 87.0544i −0.208764 0.208764i
\(418\) 0.226171 0.226171i 0.000541079 0.000541079i
\(419\) 275.957i 0.658610i 0.944224 + 0.329305i \(0.106814\pi\)
−0.944224 + 0.329305i \(0.893186\pi\)
\(420\) −34.5800 19.6277i −0.0823334 0.0467327i
\(421\) −754.476 −1.79211 −0.896053 0.443948i \(-0.853578\pi\)
−0.896053 + 0.443948i \(0.853578\pi\)
\(422\) 92.7388 + 92.7388i 0.219760 + 0.219760i
\(423\) −145.629 + 145.629i −0.344276 + 0.344276i
\(424\) 167.747i 0.395630i
\(425\) 43.8903 173.979i 0.103271 0.409362i
\(426\) 121.215 0.284541
\(427\) 16.5827 + 16.5827i 0.0388353 + 0.0388353i
\(428\) −34.8043 + 34.8043i −0.0813186 + 0.0813186i
\(429\) 0.150445i 0.000350688i
\(430\) 165.492 291.563i 0.384865 0.678053i
\(431\) −479.745 −1.11310 −0.556549 0.830815i \(-0.687875\pi\)
−0.556549 + 0.830815i \(0.687875\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 381.301 381.301i 0.880602 0.880602i −0.112994 0.993596i \(-0.536044\pi\)
0.993596 + 0.112994i \(0.0360440\pi\)
\(434\) 90.6667i 0.208909i
\(435\) 201.992 55.7160i 0.464349 0.128083i
\(436\) −58.8224 −0.134914
\(437\) 99.7911 + 99.7911i 0.228355 + 0.228355i
\(438\) −244.049 + 244.049i −0.557189 + 0.557189i
\(439\) 171.159i 0.389883i 0.980815 + 0.194942i \(0.0624518\pi\)
−0.980815 + 0.194942i \(0.937548\pi\)
\(440\) 0.0289022 + 0.104782i 6.56869e−5 + 0.000238140i
\(441\) −131.190 −0.297482
\(442\) 81.1105 + 81.1105i 0.183508 + 0.183508i
\(443\) −548.690 + 548.690i −1.23858 + 1.23858i −0.277995 + 0.960583i \(0.589670\pi\)
−0.960583 + 0.277995i \(0.910330\pi\)
\(444\) 85.8149i 0.193277i
\(445\) 73.6301 + 41.7927i 0.165461 + 0.0939162i
\(446\) −280.877 −0.629769
\(447\) 137.687 + 137.687i 0.308024 + 0.308024i
\(448\) −12.9863 + 12.9863i −0.0289872 + 0.0289872i
\(449\) 422.457i 0.940883i −0.882431 0.470442i \(-0.844095\pi\)
0.882431 0.470442i \(-0.155905\pi\)
\(450\) 102.844 + 25.9448i 0.228542 + 0.0576552i
\(451\) 0.0740031 0.000164087
\(452\) −38.9684 38.9684i −0.0862133 0.0862133i
\(453\) −104.862 + 104.862i −0.231483 + 0.231483i
\(454\) 362.138i 0.797662i
\(455\) −64.0329 + 112.813i −0.140732 + 0.247940i
\(456\) −144.161 −0.316143
\(457\) −245.799 245.799i −0.537854 0.537854i 0.385044 0.922898i \(-0.374186\pi\)
−0.922898 + 0.385044i \(0.874186\pi\)
\(458\) −215.841 + 215.841i −0.471268 + 0.471268i
\(459\) 37.2937i 0.0812499i
\(460\) −46.2318 + 12.7522i −0.100504 + 0.0277223i
\(461\) −751.846 −1.63090 −0.815451 0.578826i \(-0.803511\pi\)
−0.815451 + 0.578826i \(0.803511\pi\)
\(462\) −0.0305607 0.0305607i −6.61487e−5 6.61487e-5i
\(463\) 318.339 318.339i 0.687556 0.687556i −0.274135 0.961691i \(-0.588391\pi\)
0.961691 + 0.274135i \(0.0883915\pi\)
\(464\) 96.7802i 0.208578i
\(465\) 64.3098 + 233.148i 0.138301 + 0.501393i
\(466\) 142.093 0.304921
\(467\) −304.769 304.769i −0.652610 0.652610i 0.301010 0.953621i \(-0.402676\pi\)
−0.953621 + 0.301010i \(0.902676\pi\)
\(468\) −47.9468 + 47.9468i −0.102450 + 0.102450i
\(469\) 260.949i 0.556394i
\(470\) −422.165 239.622i −0.898222 0.509834i
\(471\) −105.962 −0.224972
\(472\) −171.191 171.191i −0.362692 0.362692i
\(473\) 0.257674 0.257674i 0.000544765 0.000544765i
\(474\) 281.249i 0.593352i
\(475\) 631.640 377.149i 1.32977 0.793997i
\(476\) 32.9528 0.0692286
\(477\) −125.810 125.810i −0.263753 0.263753i
\(478\) 107.797 107.797i 0.225518 0.225518i
\(479\) 511.063i 1.06694i −0.845820 0.533469i \(-0.820888\pi\)
0.845820 0.533469i \(-0.179112\pi\)
\(480\) 24.1828 42.6051i 0.0503808 0.0887606i
\(481\) 279.960 0.582037
\(482\) −70.4171 70.4171i −0.146094 0.146094i
\(483\) 13.4840 13.4840i 0.0279172 0.0279172i
\(484\) 242.000i 0.500000i
\(485\) 504.260 139.091i 1.03971 0.286786i
\(486\) −22.0454 −0.0453609
\(487\) 276.565 + 276.565i 0.567895 + 0.567895i 0.931538 0.363643i \(-0.118467\pi\)
−0.363643 + 0.931538i \(0.618467\pi\)
\(488\) −20.4311 + 20.4311i −0.0418669 + 0.0418669i
\(489\) 378.351i 0.773725i
\(490\) −82.2217 298.085i −0.167799 0.608337i
\(491\) 730.914 1.48862 0.744312 0.667832i \(-0.232778\pi\)
0.744312 + 0.667832i \(0.232778\pi\)
\(492\) −23.5848 23.5848i −0.0479365 0.0479365i
\(493\) −122.791 + 122.791i −0.249068 + 0.249068i
\(494\) 470.307i 0.952038i
\(495\) 0.100263 + 0.0569097i 0.000202552 + 0.000114969i
\(496\) 111.708 0.225218
\(497\) −80.3292 80.3292i −0.161628 0.161628i
\(498\) 267.970 267.970i 0.538093 0.538093i
\(499\) 318.628i 0.638533i 0.947665 + 0.319267i \(0.103437\pi\)
−0.947665 + 0.319267i \(0.896563\pi\)
\(500\) 5.50515 + 249.939i 0.0110103 + 0.499879i
\(501\) −503.024 −1.00404
\(502\) 145.088 + 145.088i 0.289020 + 0.289020i
\(503\) 123.220 123.220i 0.244970 0.244970i −0.573932 0.818903i \(-0.694583\pi\)
0.818903 + 0.573932i \(0.194583\pi\)
\(504\) 19.4794i 0.0386496i
\(505\) −65.0695 + 114.639i −0.128850 + 0.227008i
\(506\) −0.0521282 −0.000103020
\(507\) −50.5618 50.5618i −0.0997275 0.0997275i
\(508\) 266.769 266.769i 0.525136 0.525136i
\(509\) 785.649i 1.54352i −0.635917 0.771758i \(-0.719378\pi\)
0.635917 0.771758i \(-0.280622\pi\)
\(510\) −84.7376 + 23.3734i −0.166152 + 0.0458302i
\(511\) 323.463 0.633001
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −108.121 + 108.121i −0.210762 + 0.210762i
\(514\) 70.1014i 0.136384i
\(515\) −5.47044 19.8324i −0.0106222 0.0385096i
\(516\) −164.241 −0.318297
\(517\) −0.373095 0.373095i −0.000721654 0.000721654i
\(518\) 56.8697 56.8697i 0.109787 0.109787i
\(519\) 54.1328i 0.104302i
\(520\) −138.993 78.8932i −0.267295 0.151718i
\(521\) 12.4642 0.0239237 0.0119618 0.999928i \(-0.496192\pi\)
0.0119618 + 0.999928i \(0.496192\pi\)
\(522\) −72.5851 72.5851i −0.139052 0.139052i
\(523\) −529.257 + 529.257i −1.01196 + 1.01196i −0.0120361 + 0.999928i \(0.503831\pi\)
−0.999928 + 0.0120361i \(0.996169\pi\)
\(524\) 102.662i 0.195920i
\(525\) −50.9612 85.3486i −0.0970689 0.162569i
\(526\) −231.082 −0.439319
\(527\) −141.730 141.730i −0.268938 0.268938i
\(528\) 0.0376530 0.0376530i 7.13125e−5 7.13125e-5i
\(529\) 23.0000i 0.0434783i
\(530\) 207.012 364.713i 0.390589 0.688137i
\(531\) −256.786 −0.483590
\(532\) 95.5360 + 95.5360i 0.179579 + 0.179579i
\(533\) −76.9422 + 76.9422i −0.144357 + 0.144357i
\(534\) 41.4768i 0.0776719i
\(535\) −118.622 + 32.7198i −0.221723 + 0.0611586i
\(536\) −321.507 −0.599827
\(537\) −142.670 142.670i −0.265681 0.265681i
\(538\) 276.254 276.254i 0.513483 0.513483i
\(539\) 0.336103i 0.000623568i
\(540\) −13.8167 50.0909i −0.0255865 0.0927609i
\(541\) 146.788 0.271327 0.135663 0.990755i \(-0.456683\pi\)
0.135663 + 0.990755i \(0.456683\pi\)
\(542\) 157.430 + 157.430i 0.290461 + 0.290461i
\(543\) 219.729 219.729i 0.404658 0.404658i
\(544\) 40.6003i 0.0746328i
\(545\) −127.890 72.5911i −0.234661 0.133195i
\(546\) 63.5489 0.116390
\(547\) 186.682 + 186.682i 0.341283 + 0.341283i 0.856850 0.515567i \(-0.172418\pi\)
−0.515567 + 0.856850i \(0.672418\pi\)
\(548\) 357.624 357.624i 0.652599 0.652599i
\(549\) 30.6466i 0.0558226i
\(550\) −0.0664697 + 0.263482i −0.000120854 + 0.000479058i
\(551\) −711.982 −1.29216
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 186.384 186.384i 0.337042 0.337042i
\(554\) 181.394i 0.327426i
\(555\) −105.902 + 186.577i −0.190814 + 0.336175i
\(556\) −142.159 −0.255682
\(557\) 236.628 + 236.628i 0.424825 + 0.424825i 0.886861 0.462036i \(-0.152881\pi\)
−0.462036 + 0.886861i \(0.652881\pi\)
\(558\) 83.7809 83.7809i 0.150145 0.150145i
\(559\) 535.815i 0.958523i
\(560\) −44.2605 + 12.2085i −0.0790365 + 0.0218009i
\(561\) −0.0955451 −0.000170312
\(562\) −102.396 102.396i −0.182199 0.182199i
\(563\) 181.782 181.782i 0.322881 0.322881i −0.526990 0.849871i \(-0.676680\pi\)
0.849871 + 0.526990i \(0.176680\pi\)
\(564\) 237.811i 0.421650i
\(565\) −36.6345 132.814i −0.0648399 0.235070i
\(566\) −74.0755 −0.130875
\(567\) 14.6095 + 14.6095i 0.0257664 + 0.0257664i
\(568\) 98.9714 98.9714i 0.174245 0.174245i
\(569\) 33.5112i 0.0588949i −0.999566 0.0294475i \(-0.990625\pi\)
0.999566 0.0294475i \(-0.00937477\pi\)
\(570\) −313.433 177.906i −0.549882 0.312115i
\(571\) 661.886 1.15917 0.579585 0.814912i \(-0.303215\pi\)
0.579585 + 0.814912i \(0.303215\pi\)
\(572\) −0.122838 0.122838i −0.000214752 0.000214752i
\(573\) −59.3438 + 59.3438i −0.103567 + 0.103567i
\(574\) 31.2594i 0.0544588i
\(575\) −116.254 29.3277i −0.202180 0.0510048i
\(576\) −24.0000 −0.0416667
\(577\) 162.455 + 162.455i 0.281551 + 0.281551i 0.833727 0.552176i \(-0.186202\pi\)
−0.552176 + 0.833727i \(0.686202\pi\)
\(578\) −237.488 + 237.488i −0.410879 + 0.410879i
\(579\) 8.53821i 0.0147465i
\(580\) 119.434 210.418i 0.205920 0.362789i
\(581\) −355.169 −0.611306
\(582\) −181.204 181.204i −0.311347 0.311347i
\(583\) 0.322321 0.322321i 0.000552867 0.000552867i
\(584\) 398.530i 0.682415i
\(585\) −163.415 + 45.0752i −0.279342 + 0.0770516i
\(586\) 283.027 0.482981
\(587\) −500.855 500.855i −0.853245 0.853245i 0.137287 0.990531i \(-0.456162\pi\)
−0.990531 + 0.137287i \(0.956162\pi\)
\(588\) −107.116 + 107.116i −0.182170 + 0.182170i
\(589\) 821.801i 1.39525i
\(590\) −160.938 583.462i −0.272776 0.988918i
\(591\) 464.149 0.785362
\(592\) 70.0676 + 70.0676i 0.118357 + 0.118357i
\(593\) −758.069 + 758.069i −1.27836 + 1.27836i −0.336778 + 0.941584i \(0.609337\pi\)
−0.941584 + 0.336778i \(0.890663\pi\)
\(594\) 0.0564795i 9.50833e-5i
\(595\) 71.6454 + 40.6662i 0.120412 + 0.0683466i
\(596\) 224.841 0.377250
\(597\) −391.960 391.960i −0.656550 0.656550i
\(598\) 54.1985 54.1985i 0.0906330 0.0906330i
\(599\) 1117.30i 1.86527i −0.360816 0.932637i \(-0.617502\pi\)
0.360816 0.932637i \(-0.382498\pi\)
\(600\) 105.156 62.7878i 0.175259 0.104646i
\(601\) −340.477 −0.566518 −0.283259 0.959043i \(-0.591416\pi\)
−0.283259 + 0.959043i \(0.591416\pi\)
\(602\) 108.843 + 108.843i 0.180802 + 0.180802i
\(603\) −241.131 + 241.131i −0.399885 + 0.399885i
\(604\) 171.239i 0.283508i
\(605\) 298.646 526.152i 0.493629 0.869672i
\(606\) 64.5776 0.106564
\(607\) −59.2413 59.2413i −0.0975968 0.0975968i 0.656623 0.754219i \(-0.271984\pi\)
−0.754219 + 0.656623i \(0.771984\pi\)
\(608\) −117.707 + 117.707i −0.193597 + 0.193597i
\(609\) 96.2046i 0.157971i
\(610\) −69.6342 + 19.2074i −0.114154 + 0.0314875i
\(611\) 775.826 1.26976
\(612\) 30.4502 + 30.4502i 0.0497552 + 0.0497552i
\(613\) 106.898 106.898i 0.174385 0.174385i −0.614518 0.788903i \(-0.710649\pi\)
0.788903 + 0.614518i \(0.210649\pi\)
\(614\) 651.389i 1.06089i
\(615\) −22.1722 80.3829i −0.0360524 0.130704i
\(616\) −0.0499054 −8.10153e−5
\(617\) 579.410 + 579.410i 0.939076 + 0.939076i 0.998248 0.0591721i \(-0.0188461\pi\)
−0.0591721 + 0.998248i \(0.518846\pi\)
\(618\) −7.12673 + 7.12673i −0.0115319 + 0.0115319i
\(619\) 452.584i 0.731154i −0.930781 0.365577i \(-0.880872\pi\)
0.930781 0.365577i \(-0.119128\pi\)
\(620\) 242.873 + 137.856i 0.391731 + 0.222348i
\(621\) 24.9199 0.0401286
\(622\) 23.8835 + 23.8835i 0.0383980 + 0.0383980i
\(623\) −27.4868 + 27.4868i −0.0441200 + 0.0441200i
\(624\) 78.2968i 0.125476i
\(625\) −296.474 + 550.207i −0.474359 + 0.880332i
\(626\) 520.706 0.831799
\(627\) −0.277002 0.277002i −0.000441789 0.000441789i
\(628\) −86.5174 + 86.5174i −0.137767 + 0.137767i
\(629\) 177.798i 0.282667i
\(630\) −24.0390 + 42.3517i −0.0381571 + 0.0672249i
\(631\) 427.124 0.676900 0.338450 0.940984i \(-0.390097\pi\)
0.338450 + 0.940984i \(0.390097\pi\)
\(632\) 229.639 + 229.639i 0.363353 + 0.363353i
\(633\) 113.581 113.581i 0.179433 0.179433i
\(634\) 184.441i 0.290916i
\(635\) 909.217 250.792i 1.43184 0.394948i
\(636\) −205.447 −0.323031
\(637\) 349.452 + 349.452i 0.548590 + 0.548590i
\(638\) 0.185960 0.185960i 0.000291474 0.000291474i
\(639\) 148.457i 0.232327i
\(640\) −15.0417 54.5321i −0.0235027 0.0852064i
\(641\) 183.843 0.286806 0.143403 0.989664i \(-0.454195\pi\)
0.143403 + 0.989664i \(0.454195\pi\)
\(642\) 42.6264 + 42.6264i 0.0663963 + 0.0663963i
\(643\) 812.847 812.847i 1.26415 1.26415i 0.315085 0.949063i \(-0.397967\pi\)
0.949063 0.315085i \(-0.102033\pi\)
\(644\) 22.0193i 0.0341914i
\(645\) −357.090 202.686i −0.553628 0.314241i
\(646\) 298.684 0.462359
\(647\) 452.657 + 452.657i 0.699624 + 0.699624i 0.964329 0.264706i \(-0.0852747\pi\)
−0.264706 + 0.964329i \(0.585275\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 0.657876i 0.00101368i
\(650\) −204.837 343.056i −0.315134 0.527778i
\(651\) −111.044 −0.170574
\(652\) 308.923 + 308.923i 0.473808 + 0.473808i
\(653\) −486.664 + 486.664i −0.745275 + 0.745275i −0.973588 0.228313i \(-0.926679\pi\)
0.228313 + 0.973588i \(0.426679\pi\)
\(654\) 72.0424i 0.110157i
\(655\) 126.693 223.206i 0.193424 0.340773i
\(656\) −38.5138 −0.0587100
\(657\) 298.898 + 298.898i 0.454943 + 0.454943i
\(658\) 157.598 157.598i 0.239510 0.239510i
\(659\) 708.304i 1.07482i −0.843322 0.537408i \(-0.819404\pi\)
0.843322 0.537408i \(-0.180596\pi\)
\(660\) 0.128331 0.0353979i 0.000194441 5.36331e-5i
\(661\) −187.356 −0.283443 −0.141722 0.989907i \(-0.545264\pi\)
−0.141722 + 0.989907i \(0.545264\pi\)
\(662\) −532.735 532.735i −0.804735 0.804735i
\(663\) 99.3397 99.3397i 0.149834 0.149834i
\(664\) 437.594i 0.659027i
\(665\) 89.8141 + 325.611i 0.135059 + 0.489640i
\(666\) 105.101 0.157810
\(667\) 82.0494 + 82.0494i 0.123013 + 0.123013i
\(668\) −410.717 + 410.717i −0.614846 + 0.614846i
\(669\) 344.003i 0.514204i
\(670\) −699.015 396.764i −1.04331 0.592185i
\(671\) −0.0785154 −0.000117012
\(672\) 15.9048 + 15.9048i 0.0236679 + 0.0236679i
\(673\) −265.316 + 265.316i −0.394229 + 0.394229i −0.876192 0.481963i \(-0.839924\pi\)
0.481963 + 0.876192i \(0.339924\pi\)
\(674\) 799.749i 1.18657i
\(675\) 31.7758 125.958i 0.0470753 0.186604i
\(676\) −82.5671 −0.122141
\(677\) 670.523 + 670.523i 0.990433 + 0.990433i 0.999955 0.00952198i \(-0.00303099\pi\)
−0.00952198 + 0.999955i \(0.503031\pi\)
\(678\) −47.7264 + 47.7264i −0.0703929 + 0.0703929i
\(679\) 240.169i 0.353709i
\(680\) −50.1037 + 88.2723i −0.0736819 + 0.129812i
\(681\) −443.527 −0.651288
\(682\) 0.214643 + 0.214643i 0.000314726 + 0.000314726i
\(683\) −426.903 + 426.903i −0.625042 + 0.625042i −0.946816 0.321775i \(-0.895721\pi\)
0.321775 + 0.946816i \(0.395721\pi\)
\(684\) 176.561i 0.258130i
\(685\) 1218.87 336.205i 1.77938 0.490811i
\(686\) 301.054 0.438854
\(687\) 264.350 + 264.350i 0.384789 + 0.384789i
\(688\) −134.102 + 134.102i −0.194916 + 0.194916i
\(689\) 670.245i 0.972779i
\(690\) 15.6182 + 56.6222i 0.0226351 + 0.0820611i
\(691\) −121.817 −0.176291 −0.0881456 0.996108i \(-0.528094\pi\)
−0.0881456 + 0.996108i \(0.528094\pi\)
\(692\) −44.1993 44.1993i −0.0638718 0.0638718i
\(693\) −0.0374291 + 0.0374291i −5.40102e−5 + 5.40102e-5i
\(694\) 211.796i 0.305182i
\(695\) −309.080 175.435i −0.444720 0.252424i
\(696\) −118.531 −0.170303
\(697\) 48.8647 + 48.8647i 0.0701071 + 0.0701071i
\(698\) 171.397 171.397i 0.245555 0.245555i
\(699\) 174.028i 0.248967i
\(700\) −111.296 28.0772i −0.158995 0.0401103i
\(701\) 250.675 0.357596 0.178798 0.983886i \(-0.442779\pi\)
0.178798 + 0.983886i \(0.442779\pi\)
\(702\) 58.7226 + 58.7226i 0.0836504 + 0.0836504i
\(703\) 515.466 515.466i 0.733237 0.733237i
\(704\) 0.0614871i 8.73396e-5i
\(705\) −293.476 + 517.044i −0.416278 + 0.733395i
\(706\) −469.570 −0.665113
\(707\) −42.7957 42.7957i −0.0605314 0.0605314i
\(708\) −209.665 + 209.665i −0.296137 + 0.296137i
\(709\) 662.354i 0.934209i 0.884202 + 0.467105i \(0.154703\pi\)
−0.884202 + 0.467105i \(0.845297\pi\)
\(710\) 337.320 93.0438i 0.475098 0.131048i
\(711\) 344.458 0.484470
\(712\) −33.8657 33.8657i −0.0475642 0.0475642i
\(713\) −94.7050 + 94.7050i −0.132826 + 0.132826i
\(714\) 40.3588i 0.0565249i
\(715\) −0.115481 0.418663i −0.000161512 0.000585542i
\(716\) −232.980 −0.325391
\(717\) −132.024 132.024i −0.184134 0.184134i
\(718\) 219.996 219.996i 0.306401 0.306401i
\(719\) 702.256i 0.976712i −0.872645 0.488356i \(-0.837597\pi\)
0.872645 0.488356i \(-0.162403\pi\)
\(720\) −52.1803 29.6178i −0.0724727 0.0411358i
\(721\) 9.44579 0.0131010
\(722\) 504.936 + 504.936i 0.699357 + 0.699357i
\(723\) −86.2430 + 86.2430i −0.119285 + 0.119285i
\(724\) 358.816i 0.495602i
\(725\) 519.341 310.096i 0.716333 0.427719i
\(726\) −296.388 −0.408248
\(727\) −745.904 745.904i −1.02600 1.02600i −0.999653 0.0263497i \(-0.991612\pi\)
−0.0263497 0.999653i \(-0.508388\pi\)
\(728\) 51.8875 51.8875i 0.0712740 0.0712740i
\(729\) 27.0000i 0.0370370i
\(730\) −491.815 + 866.477i −0.673720 + 1.18695i
\(731\) 340.287 0.465508
\(732\) 25.0228 + 25.0228i 0.0341842 + 0.0341842i
\(733\) 20.0570 20.0570i 0.0273628 0.0273628i −0.693293 0.720656i \(-0.743841\pi\)
0.720656 + 0.693293i \(0.243841\pi\)
\(734\) 396.639i 0.540380i
\(735\) −365.078 + 100.701i −0.496705 + 0.137008i
\(736\) 27.1293 0.0368605
\(737\) −0.617767 0.617767i −0.000838219 0.000838219i
\(738\) −28.8853 + 28.8853i −0.0391400 + 0.0391400i
\(739\) 718.802i 0.972668i −0.873773 0.486334i \(-0.838334\pi\)
0.873773 0.486334i \(-0.161666\pi\)
\(740\) 65.8711 + 238.808i 0.0890150 + 0.322714i
\(741\) 576.006 0.777336
\(742\) 136.150 + 136.150i 0.183491 + 0.183491i
\(743\) −698.586 + 698.586i −0.940223 + 0.940223i −0.998311 0.0580882i \(-0.981500\pi\)
0.0580882 + 0.998311i \(0.481500\pi\)
\(744\) 136.814i 0.183889i
\(745\) 488.845 + 277.470i 0.656168 + 0.372443i
\(746\) 714.555 0.957849
\(747\) −328.195 328.195i −0.439351 0.439351i
\(748\) −0.0780122 + 0.0780122i −0.000104294 + 0.000104294i
\(749\) 56.4973i 0.0754303i
\(750\) 306.112 6.74241i 0.408149 0.00898987i
\(751\) −753.877 −1.00383 −0.501916 0.864917i \(-0.667371\pi\)
−0.501916 + 0.864917i \(0.667371\pi\)
\(752\) 194.172 + 194.172i 0.258207 + 0.258207i
\(753\) 177.696 177.696i 0.235984 0.235984i
\(754\) 386.692i 0.512854i
\(755\) −211.321 + 372.304i −0.279896 + 0.493118i
\(756\) 23.8573 0.0315572
\(757\) 812.375 + 812.375i 1.07315 + 1.07315i 0.997104 + 0.0760459i \(0.0242296\pi\)
0.0760459 + 0.997104i \(0.475770\pi\)
\(758\) −632.919 + 632.919i −0.834986 + 0.834986i
\(759\) 0.0638437i 8.41156e-5i
\(760\) −401.176 + 110.657i −0.527863 + 0.145602i
\(761\) −323.489 −0.425085 −0.212542 0.977152i \(-0.568174\pi\)
−0.212542 + 0.977152i \(0.568174\pi\)
\(762\) −326.724 326.724i −0.428772 0.428772i
\(763\) 47.7426 47.7426i 0.0625723 0.0625723i
\(764\) 96.9081i 0.126843i
\(765\) 28.6265 + 103.782i 0.0374202 + 0.135663i
\(766\) 912.421 1.19115
\(767\) 684.004 + 684.004i 0.891792 + 0.891792i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 35.2214i 0.0458016i 0.999738 + 0.0229008i \(0.00729019\pi\)
−0.999738 + 0.0229008i \(0.992710\pi\)
\(770\) −0.108503 0.0615869i −0.000140914 7.99830e-5i
\(771\) 85.8563 0.111357
\(772\) 6.97142 + 6.97142i 0.00903033 + 0.00903033i
\(773\) 77.8234 77.8234i 0.100677 0.100677i −0.654974 0.755651i \(-0.727321\pi\)
0.755651 + 0.654974i \(0.227321\pi\)
\(774\) 201.153i 0.259888i
\(775\) 357.926 + 599.447i 0.461840 + 0.773479i
\(776\) −295.905 −0.381321
\(777\) −69.6509 69.6509i −0.0896408 0.0896408i
\(778\) 297.456 297.456i