Properties

Label 690.3.k.a.277.1
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.1
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.85719 - 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 + 8.99906i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.85719 - 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 + 8.99906i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.67074 - 6.04365i) q^{10} +15.1040 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-3.57114 + 3.57114i) q^{13} +17.9981i q^{14} +(7.40193 - 4.49572i) q^{15} -4.00000 q^{16} +(7.84507 + 7.84507i) q^{17} +(3.00000 - 3.00000i) q^{18} +2.57794i q^{19} +(2.37291 - 9.71439i) q^{20} -22.0431 q^{21} +(15.1040 + 15.1040i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(22.1846 + 11.5257i) q^{25} -7.14227 q^{26} +(3.67423 + 3.67423i) q^{27} +(-17.9981 + 17.9981i) q^{28} +7.64648i q^{29} +(11.8976 + 2.90621i) q^{30} -55.4912 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-18.4986 + 18.4986i) q^{33} +15.6901i q^{34} +(-33.0332 - 54.3872i) q^{35} +6.00000 q^{36} +(24.3469 + 24.3469i) q^{37} +(-2.57794 + 2.57794i) q^{38} -8.74746i q^{39} +(12.0873 - 7.34147i) q^{40} -8.82642 q^{41} +(-22.0431 - 22.0431i) q^{42} +(-6.92644 + 6.92644i) q^{43} +30.2081i q^{44} +(-3.55937 + 14.5716i) q^{45} -6.78233 q^{46} +(-45.3582 - 45.3582i) q^{47} +(4.89898 - 4.89898i) q^{48} +112.966i q^{49} +(10.6590 + 33.7103i) q^{50} -19.2164 q^{51} +(-7.14227 - 7.14227i) q^{52} +(-39.7281 + 39.7281i) q^{53} +7.34847i q^{54} +(-73.3632 - 17.9203i) q^{55} -35.9962 q^{56} +(-3.15731 - 3.15731i) q^{57} +(-7.64648 + 7.64648i) q^{58} -80.7399i q^{59} +(8.99143 + 14.8039i) q^{60} -74.8025 q^{61} +(-55.4912 - 55.4912i) q^{62} +(26.9972 - 26.9972i) q^{63} -8.00000i q^{64} +(21.5827 - 13.1087i) q^{65} -36.9972 q^{66} +(92.9564 + 92.9564i) q^{67} +(-15.6901 + 15.6901i) q^{68} -8.30662i q^{69} +(21.3540 - 87.4203i) q^{70} -0.195500 q^{71} +(6.00000 + 6.00000i) q^{72} +(-49.4310 + 49.4310i) q^{73} +48.6938i q^{74} +(-41.2866 + 13.0545i) q^{75} -5.15587 q^{76} +(135.922 + 135.922i) q^{77} +(8.74746 - 8.74746i) q^{78} +41.8460i q^{79} +(19.4288 + 4.74582i) q^{80} -9.00000 q^{81} +(-8.82642 - 8.82642i) q^{82} +(26.4027 - 26.4027i) q^{83} -44.0862i q^{84} +(-28.7972 - 47.4128i) q^{85} -13.8529 q^{86} +(-9.36499 - 9.36499i) q^{87} +(-30.2081 + 30.2081i) q^{88} +16.8125i q^{89} +(-18.1309 + 11.0122i) q^{90} -64.2738 q^{91} +(-6.78233 - 6.78233i) q^{92} +(67.9625 - 67.9625i) q^{93} -90.7164i q^{94} +(3.05861 - 12.5215i) q^{95} +9.79796 q^{96} +(-10.2900 - 10.2900i) q^{97} +(-112.966 + 112.966i) q^{98} -45.3121i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.85719 1.18646i −0.971439 0.237291i
\(6\) −2.44949 −0.408248
\(7\) 8.99906 + 8.99906i 1.28558 + 1.28558i 0.937444 + 0.348136i \(0.113185\pi\)
0.348136 + 0.937444i \(0.386815\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −3.67074 6.04365i −0.367074 0.604365i
\(11\) 15.1040 1.37309 0.686547 0.727085i \(-0.259126\pi\)
0.686547 + 0.727085i \(0.259126\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −3.57114 + 3.57114i −0.274703 + 0.274703i −0.830990 0.556287i \(-0.812225\pi\)
0.556287 + 0.830990i \(0.312225\pi\)
\(14\) 17.9981i 1.28558i
\(15\) 7.40193 4.49572i 0.493462 0.299714i
\(16\) −4.00000 −0.250000
\(17\) 7.84507 + 7.84507i 0.461475 + 0.461475i 0.899139 0.437664i \(-0.144194\pi\)
−0.437664 + 0.899139i \(0.644194\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 2.57794i 0.135681i 0.997696 + 0.0678404i \(0.0216109\pi\)
−0.997696 + 0.0678404i \(0.978389\pi\)
\(20\) 2.37291 9.71439i 0.118646 0.485719i
\(21\) −22.0431 −1.04967
\(22\) 15.1040 + 15.1040i 0.686547 + 0.686547i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 22.1846 + 11.5257i 0.887386 + 0.461028i
\(26\) −7.14227 −0.274703
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −17.9981 + 17.9981i −0.642790 + 0.642790i
\(29\) 7.64648i 0.263672i 0.991272 + 0.131836i \(0.0420872\pi\)
−0.991272 + 0.131836i \(0.957913\pi\)
\(30\) 11.8976 + 2.90621i 0.396588 + 0.0968737i
\(31\) −55.4912 −1.79004 −0.895019 0.446028i \(-0.852838\pi\)
−0.895019 + 0.446028i \(0.852838\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −18.4986 + 18.4986i −0.560563 + 0.560563i
\(34\) 15.6901i 0.461475i
\(35\) −33.0332 54.3872i −0.943805 1.55392i
\(36\) 6.00000 0.166667
\(37\) 24.3469 + 24.3469i 0.658024 + 0.658024i 0.954912 0.296888i \(-0.0959488\pi\)
−0.296888 + 0.954912i \(0.595949\pi\)
\(38\) −2.57794 + 2.57794i −0.0678404 + 0.0678404i
\(39\) 8.74746i 0.224294i
\(40\) 12.0873 7.34147i 0.302182 0.183537i
\(41\) −8.82642 −0.215279 −0.107639 0.994190i \(-0.534329\pi\)
−0.107639 + 0.994190i \(0.534329\pi\)
\(42\) −22.0431 22.0431i −0.524836 0.524836i
\(43\) −6.92644 + 6.92644i −0.161080 + 0.161080i −0.783045 0.621965i \(-0.786335\pi\)
0.621965 + 0.783045i \(0.286335\pi\)
\(44\) 30.2081i 0.686547i
\(45\) −3.55937 + 14.5716i −0.0790971 + 0.323813i
\(46\) −6.78233 −0.147442
\(47\) −45.3582 45.3582i −0.965068 0.965068i 0.0343419 0.999410i \(-0.489066\pi\)
−0.999410 + 0.0343419i \(0.989066\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 112.966i 2.30543i
\(50\) 10.6590 + 33.7103i 0.213179 + 0.674207i
\(51\) −19.2164 −0.376792
\(52\) −7.14227 7.14227i −0.137351 0.137351i
\(53\) −39.7281 + 39.7281i −0.749586 + 0.749586i −0.974401 0.224815i \(-0.927822\pi\)
0.224815 + 0.974401i \(0.427822\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −73.3632 17.9203i −1.33388 0.325823i
\(56\) −35.9962 −0.642790
\(57\) −3.15731 3.15731i −0.0553915 0.0553915i
\(58\) −7.64648 + 7.64648i −0.131836 + 0.131836i
\(59\) 80.7399i 1.36847i −0.729260 0.684236i \(-0.760136\pi\)
0.729260 0.684236i \(-0.239864\pi\)
\(60\) 8.99143 + 14.8039i 0.149857 + 0.246731i
\(61\) −74.8025 −1.22627 −0.613135 0.789978i \(-0.710092\pi\)
−0.613135 + 0.789978i \(0.710092\pi\)
\(62\) −55.4912 55.4912i −0.895019 0.895019i
\(63\) 26.9972 26.9972i 0.428527 0.428527i
\(64\) 8.00000i 0.125000i
\(65\) 21.5827 13.1087i 0.332042 0.201672i
\(66\) −36.9972 −0.560563
\(67\) 92.9564 + 92.9564i 1.38741 + 1.38741i 0.830724 + 0.556684i \(0.187927\pi\)
0.556684 + 0.830724i \(0.312073\pi\)
\(68\) −15.6901 + 15.6901i −0.230737 + 0.230737i
\(69\) 8.30662i 0.120386i
\(70\) 21.3540 87.4203i 0.305057 1.24886i
\(71\) −0.195500 −0.00275352 −0.00137676 0.999999i \(-0.500438\pi\)
−0.00137676 + 0.999999i \(0.500438\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −49.4310 + 49.4310i −0.677137 + 0.677137i −0.959351 0.282214i \(-0.908931\pi\)
0.282214 + 0.959351i \(0.408931\pi\)
\(74\) 48.6938i 0.658024i
\(75\) −41.2866 + 13.0545i −0.550487 + 0.174060i
\(76\) −5.15587 −0.0678404
\(77\) 135.922 + 135.922i 1.76522 + 1.76522i
\(78\) 8.74746 8.74746i 0.112147 0.112147i
\(79\) 41.8460i 0.529696i 0.964290 + 0.264848i \(0.0853218\pi\)
−0.964290 + 0.264848i \(0.914678\pi\)
\(80\) 19.4288 + 4.74582i 0.242860 + 0.0593228i
\(81\) −9.00000 −0.111111
\(82\) −8.82642 8.82642i −0.107639 0.107639i
\(83\) 26.4027 26.4027i 0.318105 0.318105i −0.529934 0.848039i \(-0.677783\pi\)
0.848039 + 0.529934i \(0.177783\pi\)
\(84\) 44.0862i 0.524836i
\(85\) −28.7972 47.4128i −0.338790 0.557798i
\(86\) −13.8529 −0.161080
\(87\) −9.36499 9.36499i −0.107644 0.107644i
\(88\) −30.2081 + 30.2081i −0.343274 + 0.343274i
\(89\) 16.8125i 0.188904i 0.995529 + 0.0944521i \(0.0301099\pi\)
−0.995529 + 0.0944521i \(0.969890\pi\)
\(90\) −18.1309 + 11.0122i −0.201455 + 0.122358i
\(91\) −64.2738 −0.706305
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 67.9625 67.9625i 0.730780 0.730780i
\(94\) 90.7164i 0.965068i
\(95\) 3.05861 12.5215i 0.0321959 0.131806i
\(96\) 9.79796 0.102062
\(97\) −10.2900 10.2900i −0.106083 0.106083i 0.652073 0.758156i \(-0.273899\pi\)
−0.758156 + 0.652073i \(0.773899\pi\)
\(98\) −112.966 + 112.966i −1.15272 + 1.15272i
\(99\) 45.3121i 0.457698i
\(100\) −23.0514 + 44.3693i −0.230514 + 0.443693i
\(101\) 95.5471 0.946010 0.473005 0.881060i \(-0.343169\pi\)
0.473005 + 0.881060i \(0.343169\pi\)
\(102\) −19.2164 19.2164i −0.188396 0.188396i
\(103\) 26.9441 26.9441i 0.261593 0.261593i −0.564108 0.825701i \(-0.690780\pi\)
0.825701 + 0.564108i \(0.190780\pi\)
\(104\) 14.2845i 0.137351i
\(105\) 107.068 + 26.1532i 1.01969 + 0.249078i
\(106\) −79.4562 −0.749586
\(107\) 111.163 + 111.163i 1.03891 + 1.03891i 0.999212 + 0.0396962i \(0.0126390\pi\)
0.0396962 + 0.999212i \(0.487361\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 202.618i 1.85888i −0.368969 0.929442i \(-0.620289\pi\)
0.368969 0.929442i \(-0.379711\pi\)
\(110\) −55.4429 91.2835i −0.504027 0.829850i
\(111\) −59.6375 −0.537275
\(112\) −35.9962 35.9962i −0.321395 0.321395i
\(113\) 91.9703 91.9703i 0.813896 0.813896i −0.171319 0.985216i \(-0.554803\pi\)
0.985216 + 0.171319i \(0.0548029\pi\)
\(114\) 6.31463i 0.0553915i
\(115\) 20.4950 12.4481i 0.178217 0.108244i
\(116\) −15.2930 −0.131836
\(117\) 10.7134 + 10.7134i 0.0915676 + 0.0915676i
\(118\) 80.7399 80.7399i 0.684236 0.684236i
\(119\) 141.196i 1.18653i
\(120\) −5.81242 + 23.7953i −0.0484369 + 0.198294i
\(121\) 107.132 0.885388
\(122\) −74.8025 74.8025i −0.613135 0.613135i
\(123\) 10.8101 10.8101i 0.0878871 0.0878871i
\(124\) 110.982i 0.895019i
\(125\) −94.0804 82.3036i −0.752643 0.658429i
\(126\) 53.9944 0.428527
\(127\) −160.129 160.129i −1.26086 1.26086i −0.950676 0.310186i \(-0.899609\pi\)
−0.310186 0.950676i \(-0.600391\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 16.9662i 0.131521i
\(130\) 34.6914 + 8.47399i 0.266857 + 0.0651846i
\(131\) 198.335 1.51400 0.757002 0.653413i \(-0.226663\pi\)
0.757002 + 0.653413i \(0.226663\pi\)
\(132\) −36.9972 36.9972i −0.280282 0.280282i
\(133\) −23.1990 + 23.1990i −0.174429 + 0.174429i
\(134\) 185.913i 1.38741i
\(135\) −13.4871 22.2058i −0.0999048 0.164487i
\(136\) −31.3803 −0.230737
\(137\) 1.71018 + 1.71018i 0.0124831 + 0.0124831i 0.713321 0.700838i \(-0.247190\pi\)
−0.700838 + 0.713321i \(0.747190\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 123.424i 0.887941i 0.896041 + 0.443971i \(0.146431\pi\)
−0.896041 + 0.443971i \(0.853569\pi\)
\(140\) 108.774 66.0664i 0.776959 0.471903i
\(141\) 111.104 0.787975
\(142\) −0.195500 0.195500i −0.00137676 0.00137676i
\(143\) −53.9386 + 53.9386i −0.377193 + 0.377193i
\(144\) 12.0000i 0.0833333i
\(145\) 9.07221 37.1404i 0.0625670 0.256141i
\(146\) −98.8620 −0.677137
\(147\) −138.355 138.355i −0.941189 0.941189i
\(148\) −48.6938 + 48.6938i −0.329012 + 0.329012i
\(149\) 153.773i 1.03203i 0.856579 + 0.516015i \(0.172585\pi\)
−0.856579 + 0.516015i \(0.827415\pi\)
\(150\) −54.3411 28.2321i −0.362274 0.188214i
\(151\) −91.8615 −0.608354 −0.304177 0.952615i \(-0.598381\pi\)
−0.304177 + 0.952615i \(0.598381\pi\)
\(152\) −5.15587 5.15587i −0.0339202 0.0339202i
\(153\) 23.5352 23.5352i 0.153825 0.153825i
\(154\) 271.844i 1.76522i
\(155\) 269.531 + 65.8378i 1.73891 + 0.424760i
\(156\) 17.4949 0.112147
\(157\) 157.053 + 157.053i 1.00034 + 1.00034i 1.00000 0.000337781i \(0.000107519\pi\)
0.000337781 1.00000i \(0.499892\pi\)
\(158\) −41.8460 + 41.8460i −0.264848 + 0.264848i
\(159\) 97.3135i 0.612035i
\(160\) 14.6829 + 24.1746i 0.0917684 + 0.151091i
\(161\) −61.0346 −0.379097
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −138.558 + 138.558i −0.850052 + 0.850052i −0.990139 0.140087i \(-0.955262\pi\)
0.140087 + 0.990139i \(0.455262\pi\)
\(164\) 17.6528i 0.107639i
\(165\) 111.799 67.9035i 0.677570 0.411536i
\(166\) 52.8055 0.318105
\(167\) 9.08055 + 9.08055i 0.0543746 + 0.0543746i 0.733771 0.679397i \(-0.237758\pi\)
−0.679397 + 0.733771i \(0.737758\pi\)
\(168\) 44.0862 44.0862i 0.262418 0.262418i
\(169\) 143.494i 0.849077i
\(170\) 18.6157 76.2100i 0.109504 0.448294i
\(171\) 7.73381 0.0452270
\(172\) −13.8529 13.8529i −0.0805400 0.0805400i
\(173\) 235.387 235.387i 1.36062 1.36062i 0.487495 0.873126i \(-0.337911\pi\)
0.873126 0.487495i \(-0.162089\pi\)
\(174\) 18.7300i 0.107644i
\(175\) 95.9206 + 303.361i 0.548118 + 1.73349i
\(176\) −60.4161 −0.343274
\(177\) 98.8857 + 98.8857i 0.558677 + 0.558677i
\(178\) −16.8125 + 16.8125i −0.0944521 + 0.0944521i
\(179\) 46.2441i 0.258347i 0.991622 + 0.129174i \(0.0412324\pi\)
−0.991622 + 0.129174i \(0.958768\pi\)
\(180\) −29.1432 7.11874i −0.161906 0.0395485i
\(181\) 99.6130 0.550348 0.275174 0.961394i \(-0.411265\pi\)
0.275174 + 0.961394i \(0.411265\pi\)
\(182\) −64.2738 64.2738i −0.353153 0.353153i
\(183\) 91.6140 91.6140i 0.500623 0.500623i
\(184\) 13.5647i 0.0737210i
\(185\) −89.3711 147.144i −0.483087 0.795374i
\(186\) 135.925 0.730780
\(187\) 118.492 + 118.492i 0.633648 + 0.633648i
\(188\) 90.7164 90.7164i 0.482534 0.482534i
\(189\) 66.1293i 0.349891i
\(190\) 15.5801 9.46293i 0.0820008 0.0498049i
\(191\) 9.51368 0.0498099 0.0249049 0.999690i \(-0.492072\pi\)
0.0249049 + 0.999690i \(0.492072\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 52.7826 52.7826i 0.273485 0.273485i −0.557016 0.830501i \(-0.688054\pi\)
0.830501 + 0.557016i \(0.188054\pi\)
\(194\) 20.5800i 0.106083i
\(195\) −10.3785 + 42.4881i −0.0532230 + 0.217888i
\(196\) −225.932 −1.15272
\(197\) −117.478 117.478i −0.596335 0.596335i 0.343000 0.939335i \(-0.388557\pi\)
−0.939335 + 0.343000i \(0.888557\pi\)
\(198\) 45.3121 45.3121i 0.228849 0.228849i
\(199\) 336.042i 1.68866i 0.535827 + 0.844328i \(0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(200\) −67.4207 + 21.3179i −0.337103 + 0.106590i
\(201\) −227.696 −1.13281
\(202\) 95.5471 + 95.5471i 0.473005 + 0.473005i
\(203\) −68.8111 + 68.8111i −0.338971 + 0.338971i
\(204\) 38.4328i 0.188396i
\(205\) 42.8716 + 10.4722i 0.209130 + 0.0510837i
\(206\) 53.8882 0.261593
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 14.2845 14.2845i 0.0686757 0.0686757i
\(209\) 38.9372i 0.186303i
\(210\) 80.9144 + 133.221i 0.385307 + 0.634385i
\(211\) 23.3753 0.110783 0.0553917 0.998465i \(-0.482359\pi\)
0.0553917 + 0.998465i \(0.482359\pi\)
\(212\) −79.4562 79.4562i −0.374793 0.374793i
\(213\) 0.239438 0.239438i 0.00112412 0.00112412i
\(214\) 222.326i 1.03891i
\(215\) 41.8610 25.4251i 0.194702 0.118256i
\(216\) −14.6969 −0.0680414
\(217\) −499.369 499.369i −2.30124 2.30124i
\(218\) 202.618 202.618i 0.929442 0.929442i
\(219\) 121.081i 0.552880i
\(220\) 35.8405 146.726i 0.162912 0.666938i
\(221\) −56.0316 −0.253537
\(222\) −59.6375 59.6375i −0.268637 0.268637i
\(223\) 247.932 247.932i 1.11180 1.11180i 0.118897 0.992907i \(-0.462064\pi\)
0.992907 0.118897i \(-0.0379359\pi\)
\(224\) 71.9925i 0.321395i
\(225\) 34.5771 66.5539i 0.153676 0.295795i
\(226\) 183.941 0.813896
\(227\) −52.1924 52.1924i −0.229922 0.229922i 0.582738 0.812660i \(-0.301981\pi\)
−0.812660 + 0.582738i \(0.801981\pi\)
\(228\) 6.31463 6.31463i 0.0276957 0.0276957i
\(229\) 46.6243i 0.203600i 0.994805 + 0.101800i \(0.0324601\pi\)
−0.994805 + 0.101800i \(0.967540\pi\)
\(230\) 32.9431 + 8.04694i 0.143231 + 0.0349867i
\(231\) −332.940 −1.44130
\(232\) −15.2930 15.2930i −0.0659179 0.0659179i
\(233\) 76.6909 76.6909i 0.329146 0.329146i −0.523116 0.852262i \(-0.675231\pi\)
0.852262 + 0.523116i \(0.175231\pi\)
\(234\) 21.4268i 0.0915676i
\(235\) 166.498 + 274.129i 0.708502 + 1.16651i
\(236\) 161.480 0.684236
\(237\) −51.2507 51.2507i −0.216248 0.216248i
\(238\) −141.196 + 141.196i −0.593263 + 0.593263i
\(239\) 23.8390i 0.0997449i −0.998756 0.0498725i \(-0.984119\pi\)
0.998756 0.0498725i \(-0.0158815\pi\)
\(240\) −29.6077 + 17.9829i −0.123365 + 0.0749286i
\(241\) 179.664 0.745495 0.372748 0.927933i \(-0.378416\pi\)
0.372748 + 0.927933i \(0.378416\pi\)
\(242\) 107.132 + 107.132i 0.442694 + 0.442694i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 149.605i 0.613135i
\(245\) 134.029 548.699i 0.547059 2.23959i
\(246\) 21.6202 0.0878871
\(247\) −9.20616 9.20616i −0.0372719 0.0372719i
\(248\) 110.982 110.982i 0.447510 0.447510i
\(249\) 64.6732i 0.259732i
\(250\) −11.7768 176.384i −0.0471070 0.705536i
\(251\) −189.607 −0.755405 −0.377702 0.925927i \(-0.623286\pi\)
−0.377702 + 0.925927i \(0.623286\pi\)
\(252\) 53.9944 + 53.9944i 0.214263 + 0.214263i
\(253\) −51.2203 + 51.2203i −0.202452 + 0.202452i
\(254\) 320.259i 1.26086i
\(255\) 93.3378 + 22.7994i 0.366031 + 0.0894095i
\(256\) 16.0000 0.0625000
\(257\) 149.850 + 149.850i 0.583072 + 0.583072i 0.935746 0.352674i \(-0.114727\pi\)
−0.352674 + 0.935746i \(0.614727\pi\)
\(258\) 16.9662 16.9662i 0.0657606 0.0657606i
\(259\) 438.198i 1.69189i
\(260\) 26.2174 + 43.1654i 0.100836 + 0.166021i
\(261\) 22.9394 0.0878906
\(262\) 198.335 + 198.335i 0.757002 + 0.757002i
\(263\) 234.599 234.599i 0.892010 0.892010i −0.102702 0.994712i \(-0.532749\pi\)
0.994712 + 0.102702i \(0.0327487\pi\)
\(264\) 73.9944i 0.280282i
\(265\) 240.103 145.831i 0.906047 0.550307i
\(266\) −46.3980 −0.174429
\(267\) −20.5910 20.5910i −0.0771198 0.0771198i
\(268\) −185.913 + 185.913i −0.693704 + 0.693704i
\(269\) 139.224i 0.517563i −0.965936 0.258782i \(-0.916679\pi\)
0.965936 0.258782i \(-0.0833210\pi\)
\(270\) 8.71864 35.6929i 0.0322912 0.132196i
\(271\) −229.539 −0.847008 −0.423504 0.905894i \(-0.639200\pi\)
−0.423504 + 0.905894i \(0.639200\pi\)
\(272\) −31.3803 31.3803i −0.115369 0.115369i
\(273\) 78.7190 78.7190i 0.288348 0.288348i
\(274\) 3.42037i 0.0124831i
\(275\) 335.078 + 174.084i 1.21846 + 0.633034i
\(276\) 16.6132 0.0601929
\(277\) 12.8688 + 12.8688i 0.0464578 + 0.0464578i 0.729954 0.683496i \(-0.239541\pi\)
−0.683496 + 0.729954i \(0.739541\pi\)
\(278\) −123.424 + 123.424i −0.443971 + 0.443971i
\(279\) 166.474i 0.596679i
\(280\) 174.841 + 42.7080i 0.624431 + 0.152528i
\(281\) −363.206 −1.29255 −0.646274 0.763106i \(-0.723674\pi\)
−0.646274 + 0.763106i \(0.723674\pi\)
\(282\) 111.104 + 111.104i 0.393987 + 0.393987i
\(283\) 369.525 369.525i 1.30574 1.30574i 0.381282 0.924459i \(-0.375483\pi\)
0.924459 0.381282i \(-0.124517\pi\)
\(284\) 0.391000i 0.00137676i
\(285\) 11.5897 + 19.0817i 0.0406655 + 0.0669533i
\(286\) −107.877 −0.377193
\(287\) −79.4295 79.4295i −0.276758 0.276758i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 165.910i 0.574082i
\(290\) 46.2126 28.0682i 0.159354 0.0967869i
\(291\) 25.2053 0.0866161
\(292\) −98.8620 98.8620i −0.338569 0.338569i
\(293\) 140.958 140.958i 0.481085 0.481085i −0.424393 0.905478i \(-0.639512\pi\)
0.905478 + 0.424393i \(0.139512\pi\)
\(294\) 276.710i 0.941189i
\(295\) −95.7943 + 392.169i −0.324726 + 1.32939i
\(296\) −97.3876 −0.329012
\(297\) 55.4958 + 55.4958i 0.186854 + 0.186854i
\(298\) −153.773 + 153.773i −0.516015 + 0.516015i
\(299\) 24.2206i 0.0810055i
\(300\) −26.1090 82.5731i −0.0870300 0.275244i
\(301\) −124.663 −0.414162
\(302\) −91.8615 91.8615i −0.304177 0.304177i
\(303\) −117.021 + 117.021i −0.386207 + 0.386207i
\(304\) 10.3117i 0.0339202i
\(305\) 363.330 + 88.7499i 1.19125 + 0.290983i
\(306\) 47.0704 0.153825
\(307\) 173.192 + 173.192i 0.564145 + 0.564145i 0.930482 0.366337i \(-0.119388\pi\)
−0.366337 + 0.930482i \(0.619388\pi\)
\(308\) −271.844 + 271.844i −0.882611 + 0.882611i
\(309\) 65.9993i 0.213590i
\(310\) 203.694 + 335.369i 0.657076 + 1.08184i
\(311\) −46.2731 −0.148788 −0.0743941 0.997229i \(-0.523702\pi\)
−0.0743941 + 0.997229i \(0.523702\pi\)
\(312\) 17.4949 + 17.4949i 0.0560735 + 0.0560735i
\(313\) −205.897 + 205.897i −0.657817 + 0.657817i −0.954863 0.297046i \(-0.903999\pi\)
0.297046 + 0.954863i \(0.403999\pi\)
\(314\) 314.106i 1.00034i
\(315\) −163.161 + 99.0995i −0.517973 + 0.314602i
\(316\) −83.6920 −0.264848
\(317\) 276.139 + 276.139i 0.871100 + 0.871100i 0.992592 0.121492i \(-0.0387680\pi\)
−0.121492 + 0.992592i \(0.538768\pi\)
\(318\) 97.3135 97.3135i 0.306017 0.306017i
\(319\) 115.493i 0.362046i
\(320\) −9.49165 + 38.8575i −0.0296614 + 0.121430i
\(321\) −272.293 −0.848265
\(322\) −61.0346 61.0346i −0.189548 0.189548i
\(323\) −20.2241 + 20.2241i −0.0626133 + 0.0626133i
\(324\) 18.0000i 0.0555556i
\(325\) −120.384 + 38.0646i −0.370413 + 0.117122i
\(326\) −277.117 −0.850052
\(327\) 248.156 + 248.156i 0.758886 + 0.758886i
\(328\) 17.6528 17.6528i 0.0538197 0.0538197i
\(329\) 816.363i 2.48135i
\(330\) 179.702 + 43.8955i 0.544553 + 0.133017i
\(331\) 6.88214 0.0207920 0.0103960 0.999946i \(-0.496691\pi\)
0.0103960 + 0.999946i \(0.496691\pi\)
\(332\) 52.8055 + 52.8055i 0.159053 + 0.159053i
\(333\) 73.0407 73.0407i 0.219341 0.219341i
\(334\) 18.1611i 0.0543746i
\(335\) −341.218 561.796i −1.01856 1.67700i
\(336\) 88.1724 0.262418
\(337\) −128.298 128.298i −0.380706 0.380706i 0.490650 0.871356i \(-0.336759\pi\)
−0.871356 + 0.490650i \(0.836759\pi\)
\(338\) −143.494 + 143.494i −0.424538 + 0.424538i
\(339\) 225.280i 0.664544i
\(340\) 94.8257 57.5944i 0.278899 0.169395i
\(341\) −838.141 −2.45789
\(342\) 7.73381 + 7.73381i 0.0226135 + 0.0226135i
\(343\) −575.636 + 575.636i −1.67824 + 1.67824i
\(344\) 27.7057i 0.0805400i
\(345\) −9.85544 + 40.3469i −0.0285665 + 0.116947i
\(346\) 470.775 1.36062
\(347\) 348.345 + 348.345i 1.00388 + 1.00388i 0.999992 + 0.00388312i \(0.00123604\pi\)
0.00388312 + 0.999992i \(0.498764\pi\)
\(348\) 18.7300 18.7300i 0.0538218 0.0538218i
\(349\) 143.961i 0.412497i −0.978500 0.206248i \(-0.933875\pi\)
0.978500 0.206248i \(-0.0661255\pi\)
\(350\) −207.441 + 399.282i −0.592688 + 1.14081i
\(351\) −26.2424 −0.0747646
\(352\) −60.4161 60.4161i −0.171637 0.171637i
\(353\) −468.876 + 468.876i −1.32826 + 1.32826i −0.421375 + 0.906886i \(0.638453\pi\)
−0.906886 + 0.421375i \(0.861547\pi\)
\(354\) 197.771i 0.558677i
\(355\) 0.949582 + 0.231952i 0.00267488 + 0.000653387i
\(356\) −33.6249 −0.0944521
\(357\) −172.930 172.930i −0.484397 0.484397i
\(358\) −46.2441 + 46.2441i −0.129174 + 0.129174i
\(359\) 120.098i 0.334536i 0.985911 + 0.167268i \(0.0534945\pi\)
−0.985911 + 0.167268i \(0.946505\pi\)
\(360\) −22.0244 36.2619i −0.0611789 0.100727i
\(361\) 354.354 0.981591
\(362\) 99.6130 + 99.6130i 0.275174 + 0.275174i
\(363\) −131.209 + 131.209i −0.361458 + 0.361458i
\(364\) 128.548i 0.353153i
\(365\) 298.744 181.448i 0.818476 0.497118i
\(366\) 183.228 0.500623
\(367\) −167.307 167.307i −0.455876 0.455876i 0.441423 0.897299i \(-0.354474\pi\)
−0.897299 + 0.441423i \(0.854474\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 26.4793i 0.0717595i
\(370\) 57.7730 236.515i 0.156143 0.639230i
\(371\) −715.031 −1.92731
\(372\) 135.925 + 135.925i 0.365390 + 0.365390i
\(373\) 426.569 426.569i 1.14362 1.14362i 0.155834 0.987783i \(-0.450193\pi\)
0.987783 0.155834i \(-0.0498066\pi\)
\(374\) 236.984i 0.633648i
\(375\) 216.025 14.4235i 0.576068 0.0384627i
\(376\) 181.433 0.482534
\(377\) −27.3066 27.3066i −0.0724314 0.0724314i
\(378\) −66.1293 + 66.1293i −0.174945 + 0.174945i
\(379\) 218.341i 0.576097i −0.957616 0.288049i \(-0.906994\pi\)
0.957616 0.288049i \(-0.0930065\pi\)
\(380\) 25.0431 + 6.11722i 0.0659028 + 0.0160979i
\(381\) 392.235 1.02949
\(382\) 9.51368 + 9.51368i 0.0249049 + 0.0249049i
\(383\) 455.658 455.658i 1.18971 1.18971i 0.212559 0.977148i \(-0.431820\pi\)
0.977148 0.212559i \(-0.0681797\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −498.934 821.466i −1.29593 2.13368i
\(386\) 105.565 0.273485
\(387\) 20.7793 + 20.7793i 0.0536933 + 0.0536933i
\(388\) 20.5800 20.5800i 0.0530413 0.0530413i
\(389\) 300.379i 0.772183i 0.922460 + 0.386092i \(0.126175\pi\)
−0.922460 + 0.386092i \(0.873825\pi\)
\(390\) −52.8666 + 32.1096i −0.135555 + 0.0823324i
\(391\) −53.2078 −0.136081
\(392\) −225.932 225.932i −0.576358 0.576358i
\(393\) −242.909 + 242.909i −0.618090 + 0.618090i
\(394\) 234.956i 0.596335i
\(395\) 49.6484 203.254i 0.125692 0.514567i
\(396\) 90.6242 0.228849
\(397\) −397.353 397.353i −1.00089 1.00089i −1.00000 0.000889374i \(-0.999717\pi\)
−0.000889374 1.00000i \(-0.500283\pi\)
\(398\) −336.042 + 336.042i −0.844328 + 0.844328i
\(399\) 56.8257i 0.142420i
\(400\) −88.7386 46.1028i −0.221846 0.115257i
\(401\) 328.148 0.818325 0.409163 0.912461i \(-0.365821\pi\)
0.409163 + 0.912461i \(0.365821\pi\)
\(402\) −227.696 227.696i −0.566407 0.566407i
\(403\) 198.167 198.167i 0.491729 0.491729i
\(404\) 191.094i 0.473005i
\(405\) 43.7147 + 10.6781i 0.107938 + 0.0263657i
\(406\) −137.622 −0.338971
\(407\) 367.736 + 367.736i 0.903529 + 0.903529i
\(408\) 38.4328 38.4328i 0.0941981 0.0941981i
\(409\) 526.651i 1.28766i 0.765171 + 0.643828i \(0.222655\pi\)
−0.765171 + 0.643828i \(0.777345\pi\)
\(410\) 32.3995 + 53.3438i 0.0790231 + 0.130107i
\(411\) −4.18908 −0.0101924
\(412\) 53.8882 + 53.8882i 0.130797 + 0.130797i
\(413\) 726.583 726.583i 1.75928 1.75928i
\(414\) 20.3470i 0.0491473i
\(415\) −159.569 + 96.9175i −0.384503 + 0.233536i
\(416\) 28.5691 0.0686757
\(417\) −151.163 151.163i −0.362501 0.362501i
\(418\) −38.9372 + 38.9372i −0.0931513 + 0.0931513i
\(419\) 17.1539i 0.0409400i −0.999790 0.0204700i \(-0.993484\pi\)
0.999790 0.0204700i \(-0.00651626\pi\)
\(420\) −52.3064 + 214.135i −0.124539 + 0.509846i
\(421\) 769.518 1.82783 0.913917 0.405900i \(-0.133042\pi\)
0.913917 + 0.405900i \(0.133042\pi\)
\(422\) 23.3753 + 23.3753i 0.0553917 + 0.0553917i
\(423\) −136.075 + 136.075i −0.321689 + 0.321689i
\(424\) 158.912i 0.374793i
\(425\) 83.6202 + 264.460i 0.196753 + 0.622259i
\(426\) 0.478876 0.00112412
\(427\) −673.152 673.152i −1.57647 1.57647i
\(428\) −222.326 + 222.326i −0.519454 + 0.519454i
\(429\) 132.122i 0.307977i
\(430\) 67.2861 + 16.4358i 0.156479 + 0.0382228i
\(431\) −292.091 −0.677706 −0.338853 0.940839i \(-0.610039\pi\)
−0.338853 + 0.940839i \(0.610039\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −170.944 + 170.944i −0.394790 + 0.394790i −0.876391 0.481601i \(-0.840056\pi\)
0.481601 + 0.876391i \(0.340056\pi\)
\(434\) 998.737i 2.30124i
\(435\) 34.3764 + 56.5987i 0.0790262 + 0.130112i
\(436\) 405.237 0.929442
\(437\) −8.74221 8.74221i −0.0200051 0.0200051i
\(438\) 121.081 121.081i 0.276440 0.276440i
\(439\) 382.734i 0.871832i 0.899987 + 0.435916i \(0.143575\pi\)
−0.899987 + 0.435916i \(0.856425\pi\)
\(440\) 182.567 110.886i 0.414925 0.252013i
\(441\) 338.899 0.768477
\(442\) −56.0316 56.0316i −0.126768 0.126768i
\(443\) 58.5707 58.5707i 0.132214 0.132214i −0.637903 0.770117i \(-0.720198\pi\)
0.770117 + 0.637903i \(0.220198\pi\)
\(444\) 119.275i 0.268637i
\(445\) 19.9473 81.6614i 0.0448253 0.183509i
\(446\) 495.864 1.11180
\(447\) −188.332 188.332i −0.421325 0.421325i
\(448\) 71.9925 71.9925i 0.160698 0.160698i
\(449\) 268.969i 0.599040i −0.954090 0.299520i \(-0.903174\pi\)
0.954090 0.299520i \(-0.0968265\pi\)
\(450\) 101.131 31.9769i 0.224736 0.0710597i
\(451\) −133.315 −0.295598
\(452\) 183.941 + 183.941i 0.406948 + 0.406948i
\(453\) 112.507 112.507i 0.248360 0.248360i
\(454\) 104.385i 0.229922i
\(455\) 312.190 + 76.2580i 0.686132 + 0.167600i
\(456\) 12.6293 0.0276957
\(457\) −249.660 249.660i −0.546301 0.546301i 0.379068 0.925369i \(-0.376245\pi\)
−0.925369 + 0.379068i \(0.876245\pi\)
\(458\) −46.6243 + 46.6243i −0.101800 + 0.101800i
\(459\) 57.6492i 0.125597i
\(460\) 24.8961 + 40.9900i 0.0541221 + 0.0891087i
\(461\) −319.741 −0.693582 −0.346791 0.937942i \(-0.612729\pi\)
−0.346791 + 0.937942i \(0.612729\pi\)
\(462\) −332.940 332.940i −0.720649 0.720649i
\(463\) 147.161 147.161i 0.317842 0.317842i −0.530096 0.847938i \(-0.677844\pi\)
0.847938 + 0.530096i \(0.177844\pi\)
\(464\) 30.5859i 0.0659179i
\(465\) −410.742 + 249.473i −0.883316 + 0.536500i
\(466\) 153.382 0.329146
\(467\) −604.325 604.325i −1.29406 1.29406i −0.932254 0.361805i \(-0.882161\pi\)
−0.361805 0.932254i \(-0.617839\pi\)
\(468\) −21.4268 + 21.4268i −0.0457838 + 0.0457838i
\(469\) 1673.04i 3.56725i
\(470\) −107.631 + 440.627i −0.229002 + 0.937505i
\(471\) −384.700 −0.816772
\(472\) 161.480 + 161.480i 0.342118 + 0.342118i
\(473\) −104.617 + 104.617i −0.221178 + 0.221178i
\(474\) 102.501i 0.216248i
\(475\) −29.7125 + 57.1906i −0.0625526 + 0.120401i
\(476\) −282.393 −0.593263
\(477\) 119.184 + 119.184i 0.249862 + 0.249862i
\(478\) 23.8390 23.8390i 0.0498725 0.0498725i
\(479\) 838.912i 1.75138i −0.482872 0.875691i \(-0.660406\pi\)
0.482872 0.875691i \(-0.339594\pi\)
\(480\) −47.5906 11.6248i −0.0991470 0.0242184i
\(481\) −173.892 −0.361522
\(482\) 179.664 + 179.664i 0.372748 + 0.372748i
\(483\) 74.7518 74.7518i 0.154766 0.154766i
\(484\) 214.264i 0.442694i
\(485\) 37.7720 + 62.1893i 0.0778803 + 0.128225i
\(486\) 22.0454 0.0453609
\(487\) 416.968 + 416.968i 0.856197 + 0.856197i 0.990888 0.134690i \(-0.0430040\pi\)
−0.134690 + 0.990888i \(0.543004\pi\)
\(488\) 149.605 149.605i 0.306568 0.306568i
\(489\) 339.398i 0.694064i
\(490\) 682.728 414.669i 1.39332 0.846264i
\(491\) −677.675 −1.38019 −0.690096 0.723718i \(-0.742432\pi\)
−0.690096 + 0.723718i \(0.742432\pi\)
\(492\) 21.6202 + 21.6202i 0.0439436 + 0.0439436i
\(493\) −59.9871 + 59.9871i −0.121678 + 0.121678i
\(494\) 18.4123i 0.0372719i
\(495\) −53.7608 + 220.090i −0.108608 + 0.444626i
\(496\) 221.965 0.447510
\(497\) −1.75932 1.75932i −0.00353988 0.00353988i
\(498\) −64.6732 + 64.6732i −0.129866 + 0.129866i
\(499\) 649.807i 1.30222i 0.758984 + 0.651110i \(0.225696\pi\)
−0.758984 + 0.651110i \(0.774304\pi\)
\(500\) 164.607 188.161i 0.329214 0.376321i
\(501\) −22.2427 −0.0443966
\(502\) −189.607 189.607i −0.377702 0.377702i
\(503\) −114.648 + 114.648i −0.227928 + 0.227928i −0.811827 0.583899i \(-0.801527\pi\)
0.583899 + 0.811827i \(0.301527\pi\)
\(504\) 107.989i 0.214263i
\(505\) −464.090 113.362i −0.918991 0.224480i
\(506\) −102.441 −0.202452
\(507\) −175.743 175.743i −0.346634 0.346634i
\(508\) 320.259 320.259i 0.630431 0.630431i
\(509\) 291.723i 0.573129i 0.958061 + 0.286564i \(0.0925133\pi\)
−0.958061 + 0.286564i \(0.907487\pi\)
\(510\) 70.5384 + 116.137i 0.138311 + 0.227720i
\(511\) −889.665 −1.74103
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −9.47194 + 9.47194i −0.0184638 + 0.0184638i
\(514\) 299.699i 0.583072i
\(515\) −162.841 + 98.9046i −0.316195 + 0.192048i
\(516\) 33.9325 0.0657606
\(517\) −685.092 685.092i −1.32513 1.32513i
\(518\) −438.198 + 438.198i −0.845943 + 0.845943i
\(519\) 576.579i 1.11094i
\(520\) −16.9480 + 69.3828i −0.0325923 + 0.133428i
\(521\) 30.7577 0.0590358 0.0295179 0.999564i \(-0.490603\pi\)
0.0295179 + 0.999564i \(0.490603\pi\)
\(522\) 22.9394 + 22.9394i 0.0439453 + 0.0439453i
\(523\) −151.008 + 151.008i −0.288734 + 0.288734i −0.836580 0.547845i \(-0.815448\pi\)
0.547845 + 0.836580i \(0.315448\pi\)
\(524\) 396.669i 0.757002i
\(525\) −489.018 254.062i −0.931464 0.483928i
\(526\) 469.197 0.892010
\(527\) −435.332 435.332i −0.826057 0.826057i
\(528\) 73.9944 73.9944i 0.140141 0.140141i
\(529\) 23.0000i 0.0434783i
\(530\) 385.934 + 94.2712i 0.728177 + 0.177870i
\(531\) −242.220 −0.456157
\(532\) −46.3980 46.3980i −0.0872143 0.0872143i
\(533\) 31.5204 31.5204i 0.0591376 0.0591376i
\(534\) 41.1820i 0.0771198i
\(535\) −408.051 671.831i −0.762712 1.25576i
\(536\) −371.825 −0.693704
\(537\) −56.6373 56.6373i −0.105470 0.105470i
\(538\) 139.224 139.224i 0.258782 0.258782i
\(539\) 1706.25i 3.16558i
\(540\) 44.4116 26.9743i 0.0822436 0.0499524i
\(541\) 29.6112 0.0547342 0.0273671 0.999625i \(-0.491288\pi\)
0.0273671 + 0.999625i \(0.491288\pi\)
\(542\) −229.539 229.539i −0.423504 0.423504i
\(543\) −122.000 + 122.000i −0.224679 + 0.224679i
\(544\) 62.7605i 0.115369i
\(545\) −240.398 + 984.156i −0.441097 + 1.80579i
\(546\) 157.438 0.288348
\(547\) 479.020 + 479.020i 0.875722 + 0.875722i 0.993089 0.117367i \(-0.0374452\pi\)
−0.117367 + 0.993089i \(0.537445\pi\)
\(548\) −3.42037 + 3.42037i −0.00624155 + 0.00624155i
\(549\) 224.408i 0.408757i
\(550\) 160.993 + 509.162i 0.292715 + 0.925749i
\(551\) −19.7121 −0.0357752
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) −376.575 + 376.575i −0.680967 + 0.680967i
\(554\) 25.7376i 0.0464578i
\(555\) 289.671 + 70.7572i 0.521929 + 0.127491i
\(556\) −246.848 −0.443971
\(557\) 96.8915 + 96.8915i 0.173953 + 0.173953i 0.788713 0.614761i \(-0.210748\pi\)
−0.614761 + 0.788713i \(0.710748\pi\)
\(558\) −166.474 + 166.474i −0.298340 + 0.298340i
\(559\) 49.4705i 0.0884982i
\(560\) 132.133 + 217.549i 0.235951 + 0.388480i
\(561\) −290.245 −0.517371
\(562\) −363.206 363.206i −0.646274 0.646274i
\(563\) −767.945 + 767.945i −1.36402 + 1.36402i −0.495303 + 0.868720i \(0.664943\pi\)
−0.868720 + 0.495303i \(0.835057\pi\)
\(564\) 222.209i 0.393987i
\(565\) −555.836 + 337.599i −0.983781 + 0.597520i
\(566\) 739.049 1.30574
\(567\) −80.9915 80.9915i −0.142842 0.142842i
\(568\) 0.391000 0.391000i 0.000688381 0.000688381i
\(569\) 303.801i 0.533921i 0.963707 + 0.266961i \(0.0860194\pi\)
−0.963707 + 0.266961i \(0.913981\pi\)
\(570\) −7.49203 + 30.6714i −0.0131439 + 0.0538094i
\(571\) 368.780 0.645850 0.322925 0.946425i \(-0.395334\pi\)
0.322925 + 0.946425i \(0.395334\pi\)
\(572\) −107.877 107.877i −0.188596 0.188596i
\(573\) −11.6518 + 11.6518i −0.0203348 + 0.0203348i
\(574\) 158.859i 0.276758i
\(575\) −114.317 + 36.1463i −0.198813 + 0.0628631i
\(576\) −24.0000 −0.0416667
\(577\) −490.739 490.739i −0.850501 0.850501i 0.139694 0.990195i \(-0.455388\pi\)
−0.990195 + 0.139694i \(0.955388\pi\)
\(578\) 165.910 165.910i 0.287041 0.287041i
\(579\) 129.290i 0.223300i
\(580\) 74.2808 + 18.1444i 0.128070 + 0.0312835i
\(581\) 475.200 0.817900
\(582\) 25.2053 + 25.2053i 0.0433081 + 0.0433081i
\(583\) −600.054 + 600.054i −1.02925 + 1.02925i
\(584\) 197.724i 0.338569i
\(585\) −39.3261 64.7481i −0.0672241 0.110681i
\(586\) 281.916 0.481085
\(587\) 374.363 + 374.363i 0.637757 + 0.637757i 0.950002 0.312245i \(-0.101081\pi\)
−0.312245 + 0.950002i \(0.601081\pi\)
\(588\) 276.710 276.710i 0.470594 0.470594i
\(589\) 143.053i 0.242874i
\(590\) −487.963 + 296.375i −0.827057 + 0.502330i
\(591\) 287.761 0.486905
\(592\) −97.3876 97.3876i −0.164506 0.164506i
\(593\) 593.763 593.763i 1.00129 1.00129i 0.00128752 0.999999i \(-0.499590\pi\)
0.999999 0.00128752i \(-0.000409830\pi\)
\(594\) 110.992i 0.186854i
\(595\) 167.523 685.819i 0.281552 1.15264i
\(596\) −307.545 −0.516015
\(597\) −411.566 411.566i −0.689391 0.689391i
\(598\) 24.2206 24.2206i 0.0405027 0.0405027i
\(599\) 24.8982i 0.0415663i −0.999784 0.0207831i \(-0.993384\pi\)
0.999784 0.0207831i \(-0.00661595\pi\)
\(600\) 56.4641 108.682i 0.0941069 0.181137i
\(601\) 1067.99 1.77702 0.888511 0.458855i \(-0.151740\pi\)
0.888511 + 0.458855i \(0.151740\pi\)
\(602\) −124.663 124.663i −0.207081 0.207081i
\(603\) 278.869 278.869i 0.462469 0.462469i
\(604\) 183.723i 0.304177i
\(605\) −520.360 127.107i −0.860100 0.210095i
\(606\) −234.042 −0.386207
\(607\) 690.397 + 690.397i 1.13739 + 1.13739i 0.988916 + 0.148477i \(0.0474371\pi\)
0.148477 + 0.988916i \(0.452563\pi\)
\(608\) 10.3117 10.3117i 0.0169601 0.0169601i
\(609\) 168.552i 0.276769i
\(610\) 274.580 + 452.080i 0.450132 + 0.741115i
\(611\) 323.961 0.530214
\(612\) 47.0704 + 47.0704i 0.0769124 + 0.0769124i
\(613\) 726.595 726.595i 1.18531 1.18531i 0.206962 0.978349i \(-0.433642\pi\)
0.978349 0.206962i \(-0.0663575\pi\)
\(614\) 346.385i 0.564145i
\(615\) −65.3325 + 39.6811i −0.106232 + 0.0645221i
\(616\) −543.689 −0.882611
\(617\) −175.696 175.696i −0.284759 0.284759i 0.550244 0.835004i \(-0.314535\pi\)
−0.835004 + 0.550244i \(0.814535\pi\)
\(618\) −65.9993 + 65.9993i −0.106795 + 0.106795i
\(619\) 296.780i 0.479451i −0.970841 0.239725i \(-0.922943\pi\)
0.970841 0.239725i \(-0.0770574\pi\)
\(620\) −131.676 + 539.063i −0.212380 + 0.869456i
\(621\) −24.9199 −0.0401286
\(622\) −46.2731 46.2731i −0.0743941 0.0743941i
\(623\) −151.296 + 151.296i −0.242851 + 0.242851i
\(624\) 34.9899i 0.0560735i
\(625\) 359.317 + 511.387i 0.574907 + 0.818219i
\(626\) −411.794 −0.657817
\(627\) −47.6882 47.6882i −0.0760577 0.0760577i
\(628\) −314.106 + 314.106i −0.500169 + 0.500169i
\(629\) 382.006i 0.607323i
\(630\) −262.261 64.0619i −0.416287 0.101686i
\(631\) −348.114 −0.551686 −0.275843 0.961203i \(-0.588957\pi\)
−0.275843 + 0.961203i \(0.588957\pi\)
\(632\) −83.6920 83.6920i −0.132424 0.132424i
\(633\) −28.6288 + 28.6288i −0.0452271 + 0.0452271i
\(634\) 552.277i 0.871100i
\(635\) 587.793 + 967.766i 0.925658 + 1.52404i
\(636\) 194.627 0.306017
\(637\) −403.418 403.418i −0.633309 0.633309i
\(638\) −115.493 + 115.493i −0.181023 + 0.181023i
\(639\) 0.586501i 0.000917841i
\(640\) −48.3492 + 29.3659i −0.0755456 + 0.0458842i
\(641\) −104.423 −0.162907 −0.0814534 0.996677i \(-0.525956\pi\)
−0.0814534 + 0.996677i \(0.525956\pi\)
\(642\) −272.293 272.293i −0.424132 0.424132i
\(643\) 786.591 786.591i 1.22331 1.22331i 0.256868 0.966447i \(-0.417310\pi\)
0.966447 0.256868i \(-0.0826905\pi\)
\(644\) 122.069i 0.189548i
\(645\) −20.1297 + 82.4083i −0.0312088 + 0.127765i
\(646\) −40.4482 −0.0626133
\(647\) −601.105 601.105i −0.929065 0.929065i 0.0685808 0.997646i \(-0.478153\pi\)
−0.997646 + 0.0685808i \(0.978153\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1219.50i 1.87904i
\(650\) −158.449 82.3196i −0.243767 0.126646i
\(651\) 1223.20 1.87895
\(652\) −277.117 277.117i −0.425026 0.425026i
\(653\) −191.262 + 191.262i −0.292897 + 0.292897i −0.838224 0.545327i \(-0.816406\pi\)
0.545327 + 0.838224i \(0.316406\pi\)
\(654\) 496.311i 0.758886i
\(655\) −963.349 235.315i −1.47076 0.359260i
\(656\) 35.3057 0.0538197
\(657\) 148.293 + 148.293i 0.225712 + 0.225712i
\(658\) 816.363 816.363i 1.24067 1.24067i
\(659\) 1018.97i 1.54624i −0.634260 0.773120i \(-0.718695\pi\)
0.634260 0.773120i \(-0.281305\pi\)
\(660\) 135.807 + 223.598i 0.205768 + 0.338785i
\(661\) 210.000 0.317700 0.158850 0.987303i \(-0.449221\pi\)
0.158850 + 0.987303i \(0.449221\pi\)
\(662\) 6.88214 + 6.88214i 0.0103960 + 0.0103960i
\(663\) 68.6244 68.6244i 0.103506 0.103506i
\(664\) 105.611i 0.159053i
\(665\) 140.207 85.1574i 0.210837 0.128056i
\(666\) 146.081 0.219341
\(667\) −25.9305 25.9305i −0.0388763 0.0388763i
\(668\) −18.1611 + 18.1611i −0.0271873 + 0.0271873i
\(669\) 607.307i 0.907784i
\(670\) 220.577 903.014i 0.329220 1.34778i
\(671\) −1129.82 −1.68379
\(672\) 88.1724 + 88.1724i 0.131209 + 0.131209i
\(673\) 11.3881 11.3881i 0.0169214 0.0169214i −0.698595 0.715517i \(-0.746191\pi\)
0.715517 + 0.698595i \(0.246191\pi\)
\(674\) 256.596i 0.380706i
\(675\) 39.1635 + 123.860i 0.0580200 + 0.183496i
\(676\) −286.988 −0.424538
\(677\) 929.286 + 929.286i 1.37265 + 1.37265i 0.856491 + 0.516163i \(0.172640\pi\)
0.516163 + 0.856491i \(0.327360\pi\)
\(678\) −225.280 + 225.280i −0.332272 + 0.332272i
\(679\) 185.201i 0.272756i
\(680\) 152.420 + 37.2313i 0.224147 + 0.0547519i
\(681\) 127.845 0.187731
\(682\) −838.141 838.141i −1.22895 1.22895i
\(683\) 584.472 584.472i 0.855742 0.855742i −0.135091 0.990833i \(-0.543133\pi\)
0.990833 + 0.135091i \(0.0431327\pi\)
\(684\) 15.4676i 0.0226135i
\(685\) −6.27764 10.3358i −0.00916444 0.0150887i
\(686\) −1151.27 −1.67824
\(687\) −57.1029 57.1029i −0.0831192 0.0831192i
\(688\) 27.7057 27.7057i 0.0402700 0.0402700i
\(689\) 283.749i 0.411827i
\(690\) −50.2023 + 30.4914i −0.0727570 + 0.0441905i
\(691\) 842.687 1.21952 0.609759 0.792587i \(-0.291266\pi\)
0.609759 + 0.792587i \(0.291266\pi\)
\(692\) 470.775 + 470.775i 0.680310 + 0.680310i
\(693\) 407.766 407.766i 0.588408 0.588408i
\(694\) 696.690i 1.00388i
\(695\) 146.437 599.493i 0.210701 0.862580i
\(696\) 37.4599 0.0538218
\(697\) −69.2439 69.2439i −0.0993456 0.0993456i
\(698\) 143.961 143.961i 0.206248 0.206248i
\(699\) 187.854i 0.268746i
\(700\) −606.723 + 191.841i −0.866747 + 0.274059i
\(701\) 841.413 1.20030 0.600152 0.799886i \(-0.295107\pi\)
0.600152 + 0.799886i \(0.295107\pi\)
\(702\) −26.2424 26.2424i −0.0373823 0.0373823i
\(703\) −62.7648 + 62.7648i −0.0892813 + 0.0892813i
\(704\) 120.832i 0.171637i
\(705\) −539.656 131.821i −0.765469 0.186980i
\(706\) −937.753 −1.32826
\(707\) 859.834 + 859.834i 1.21617 + 1.21617i
\(708\) −197.771 + 197.771i −0.279338 + 0.279338i
\(709\) 249.971i 0.352569i −0.984339 0.176284i \(-0.943592\pi\)
0.984339 0.176284i \(-0.0564078\pi\)
\(710\) 0.717630 + 1.18153i 0.00101075 + 0.00166413i
\(711\) 125.538 0.176565
\(712\) −33.6249 33.6249i −0.0472260 0.0472260i
\(713\) 188.180 188.180i 0.263927 0.263927i
\(714\) 345.859i 0.484397i
\(715\) 325.986 197.994i 0.455924 0.276915i
\(716\) −92.4883 −0.129174
\(717\) 29.1967 + 29.1967i 0.0407207 + 0.0407207i
\(718\) −120.098 + 120.098i −0.167268 + 0.167268i
\(719\) 50.7687i 0.0706102i 0.999377 + 0.0353051i \(0.0112403\pi\)
−0.999377 + 0.0353051i \(0.988760\pi\)
\(720\) 14.2375 58.2863i 0.0197743 0.0809532i
\(721\) 484.943 0.672598
\(722\) 354.354 + 354.354i 0.490795 + 0.490795i
\(723\) −220.043 + 220.043i −0.304347 + 0.304347i
\(724\) 199.226i 0.275174i
\(725\) −88.1310 + 169.634i −0.121560 + 0.233979i
\(726\) −262.419 −0.361458
\(727\) 97.6824 + 97.6824i 0.134364 + 0.134364i 0.771090 0.636726i \(-0.219712\pi\)
−0.636726 + 0.771090i \(0.719712\pi\)
\(728\) 128.548 128.548i 0.176576 0.176576i
\(729\) 27.0000i 0.0370370i
\(730\) 480.192 + 117.295i 0.657797 + 0.160679i
\(731\) −108.677 −0.148669
\(732\) 183.228 + 183.228i 0.250311 + 0.250311i
\(733\) −391.414 + 391.414i −0.533990 + 0.533990i −0.921757 0.387768i \(-0.873246\pi\)
0.387768 + 0.921757i \(0.373246\pi\)
\(734\) 334.613i 0.455876i
\(735\) 507.864 + 836.168i 0.690971 + 1.13764i
\(736\) 27.1293 0.0368605
\(737\) 1404.02 + 1404.02i 1.90504 + 1.90504i
\(738\) −26.4793 + 26.4793i −0.0358798 + 0.0358798i
\(739\) 1224.73i 1.65728i −0.559785 0.828638i \(-0.689116\pi\)
0.559785 0.828638i \(-0.310884\pi\)
\(740\) 294.288 178.742i 0.397687 0.241543i
\(741\) 22.5504 0.0304324
\(742\) −715.031 715.031i −0.963653 0.963653i
\(743\) −876.956 + 876.956i −1.18029 + 1.18029i −0.200623 + 0.979669i \(0.564297\pi\)
−0.979669 + 0.200623i \(0.935703\pi\)
\(744\) 271.850i 0.365390i
\(745\) 182.444 746.903i 0.244892 1.00255i
\(746\) 853.139 1.14362
\(747\) −79.2082 79.2082i −0.106035 0.106035i
\(748\) −236.984 + 236.984i −0.316824 + 0.316824i
\(749\) 2000.73i 2.67120i
\(750\) 230.449 + 201.602i 0.307265 + 0.268802i
\(751\) −456.098 −0.607321 −0.303660 0.952780i \(-0.598209\pi\)
−0.303660 + 0.952780i \(0.598209\pi\)
\(752\) 181.433 + 181.433i 0.241267 + 0.241267i
\(753\) 232.220 232.220i 0.308393 0.308393i
\(754\) 54.6132i 0.0724314i
\(755\) 446.189 + 108.990i 0.590979 + 0.144357i
\(756\) −132.259 −0.174945
\(757\) 520.228 + 520.228i 0.687223 + 0.687223i 0.961617 0.274394i \(-0.0884773\pi\)
−0.274394 + 0.961617i \(0.588477\pi\)
\(758\) 218.341 218.341i 0.288049 0.288049i
\(759\) 125.464i 0.165301i
\(760\) 18.9259 + 31.1603i 0.0249024 + 0.0410004i
\(761\) 369.811 0.485954 0.242977 0.970032i \(-0.421876\pi\)
0.242977 + 0.970032i \(0.421876\pi\)
\(762\) 392.235 + 392.235i 0.514745 + 0.514745i
\(763\) 1823.37 1823.37i 2.38974 2.38974i
\(764\) 19.0274i 0.0249049i
\(765\) −142.239 + 86.3915i −0.185933 + 0.112930i
\(766\) 911.316 1.18971
\(767\) 288.333 + 288.333i 0.375923 + 0.375923i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 601.554i 0.782255i −0.920336 0.391128i \(-0.872085\pi\)
0.920336 0.391128i \(-0.127915\pi\)
\(770\) 322.531 1320.40i 0.418872 1.71481i
\(771\) −367.055 −0.476077
\(772\) 105.565 + 105.565i 0.136742 + 0.136742i
\(773\) 426.317 426.317i 0.551510 0.551510i −0.375367 0.926876i \(-0.622483\pi\)
0.926876 + 0.375367i \(0.122483\pi\)
\(774\) 41.5586i 0.0536933i
\(775\) −1231.05 639.574i −1.58845 0.825257i
\(776\) 41.1601 0.0530413
\(777\) −536.681 536.681i −0.690710 0.690710i
\(778\) −300.379 + 300.379i −0.386092 + 0.386092i
\(779\) 22.7540i