Properties

Label 230.3.f.b.93.1
Level $230$
Weight $3$
Character 230.93
Analytic conductor $6.267$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 93.1
Character \(\chi\) \(=\) 230.93
Dual form 230.3.f.b.47.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-3.78907 - 3.78907i) q^{3} -2.00000i q^{4} +(0.818077 + 4.93262i) q^{5} -7.57813 q^{6} +(-3.70466 + 3.70466i) q^{7} +(-2.00000 - 2.00000i) q^{8} +19.7140i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-3.78907 - 3.78907i) q^{3} -2.00000i q^{4} +(0.818077 + 4.93262i) q^{5} -7.57813 q^{6} +(-3.70466 + 3.70466i) q^{7} +(-2.00000 - 2.00000i) q^{8} +19.7140i q^{9} +(5.75070 + 4.11454i) q^{10} -13.1554 q^{11} +(-7.57813 + 7.57813i) q^{12} +(6.65224 + 6.65224i) q^{13} +7.40933i q^{14} +(15.5903 - 21.7898i) q^{15} -4.00000 q^{16} +(8.90104 - 8.90104i) q^{17} +(19.7140 + 19.7140i) q^{18} +10.0119i q^{19} +(9.86524 - 1.63615i) q^{20} +28.0744 q^{21} +(-13.1554 + 13.1554i) q^{22} +(3.39116 + 3.39116i) q^{23} +15.1563i q^{24} +(-23.6615 + 8.07053i) q^{25} +13.3045 q^{26} +(40.5962 - 40.5962i) q^{27} +(7.40933 + 7.40933i) q^{28} +40.4613i q^{29} +(-6.19950 - 37.3801i) q^{30} -59.9380 q^{31} +(-4.00000 + 4.00000i) q^{32} +(49.8468 + 49.8468i) q^{33} -17.8021i q^{34} +(-21.3044 - 15.2430i) q^{35} +39.4281 q^{36} +(11.4063 - 11.4063i) q^{37} +(10.0119 + 10.0119i) q^{38} -50.4115i q^{39} +(8.22909 - 11.5014i) q^{40} -2.32786 q^{41} +(28.0744 - 28.0744i) q^{42} +(12.0618 + 12.0618i) q^{43} +26.3109i q^{44} +(-97.2419 + 16.1276i) q^{45} +6.78233 q^{46} +(-38.4537 + 38.4537i) q^{47} +(15.1563 + 15.1563i) q^{48} +21.5509i q^{49} +(-15.5910 + 31.7320i) q^{50} -67.4532 q^{51} +(13.3045 - 13.3045i) q^{52} +(-49.3600 - 49.3600i) q^{53} -81.1924i q^{54} +(-10.7622 - 64.8908i) q^{55} +14.8187 q^{56} +(37.9359 - 37.9359i) q^{57} +(40.4613 + 40.4613i) q^{58} -23.6571i q^{59} +(-43.5795 - 31.1806i) q^{60} -97.8268 q^{61} +(-59.9380 + 59.9380i) q^{62} +(-73.0339 - 73.0339i) q^{63} +8.00000i q^{64} +(-27.3709 + 38.2550i) q^{65} +99.6937 q^{66} +(63.3064 - 63.3064i) q^{67} +(-17.8021 - 17.8021i) q^{68} -25.6987i q^{69} +(-36.5474 + 6.06140i) q^{70} -42.9229 q^{71} +(39.4281 - 39.4281i) q^{72} +(-9.09857 - 9.09857i) q^{73} -22.8127i q^{74} +(120.235 + 59.0752i) q^{75} +20.0239 q^{76} +(48.7365 - 48.7365i) q^{77} +(-50.4115 - 50.4115i) q^{78} +131.359i q^{79} +(-3.27231 - 19.7305i) q^{80} -130.217 q^{81} +(-2.32786 + 2.32786i) q^{82} +(76.9382 + 76.9382i) q^{83} -56.1489i q^{84} +(51.1872 + 36.6237i) q^{85} +24.1236 q^{86} +(153.311 - 153.311i) q^{87} +(26.3109 + 26.3109i) q^{88} +16.9832i q^{89} +(-81.1143 + 113.369i) q^{90} -49.2886 q^{91} +(6.78233 - 6.78233i) q^{92} +(227.109 + 227.109i) q^{93} +76.9073i q^{94} +(-49.3851 + 8.19053i) q^{95} +30.3125 q^{96} +(-41.5485 + 41.5485i) q^{97} +(21.5509 + 21.5509i) q^{98} -259.347i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −3.78907 3.78907i −1.26302 1.26302i −0.949621 0.313401i \(-0.898532\pi\)
−0.313401 0.949621i \(-0.601468\pi\)
\(4\) 2.00000i 0.500000i
\(5\) 0.818077 + 4.93262i 0.163615 + 0.986524i
\(6\) −7.57813 −1.26302
\(7\) −3.70466 + 3.70466i −0.529238 + 0.529238i −0.920345 0.391107i \(-0.872092\pi\)
0.391107 + 0.920345i \(0.372092\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 19.7140i 2.19045i
\(10\) 5.75070 + 4.11454i 0.575070 + 0.411454i
\(11\) −13.1554 −1.19595 −0.597975 0.801515i \(-0.704028\pi\)
−0.597975 + 0.801515i \(0.704028\pi\)
\(12\) −7.57813 + 7.57813i −0.631511 + 0.631511i
\(13\) 6.65224 + 6.65224i 0.511711 + 0.511711i 0.915050 0.403340i \(-0.132151\pi\)
−0.403340 + 0.915050i \(0.632151\pi\)
\(14\) 7.40933i 0.529238i
\(15\) 15.5903 21.7898i 1.03935 1.45265i
\(16\) −4.00000 −0.250000
\(17\) 8.90104 8.90104i 0.523591 0.523591i −0.395063 0.918654i \(-0.629277\pi\)
0.918654 + 0.395063i \(0.129277\pi\)
\(18\) 19.7140 + 19.7140i 1.09522 + 1.09522i
\(19\) 10.0119i 0.526944i 0.964667 + 0.263472i \(0.0848676\pi\)
−0.964667 + 0.263472i \(0.915132\pi\)
\(20\) 9.86524 1.63615i 0.493262 0.0818077i
\(21\) 28.0744 1.33688
\(22\) −13.1554 + 13.1554i −0.597975 + 0.597975i
\(23\) 3.39116 + 3.39116i 0.147442 + 0.147442i
\(24\) 15.1563i 0.631511i
\(25\) −23.6615 + 8.07053i −0.946460 + 0.322821i
\(26\) 13.3045 0.511711
\(27\) 40.5962 40.5962i 1.50356 1.50356i
\(28\) 7.40933 + 7.40933i 0.264619 + 0.264619i
\(29\) 40.4613i 1.39522i 0.716478 + 0.697609i \(0.245753\pi\)
−0.716478 + 0.697609i \(0.754247\pi\)
\(30\) −6.19950 37.3801i −0.206650 1.24600i
\(31\) −59.9380 −1.93348 −0.966742 0.255753i \(-0.917677\pi\)
−0.966742 + 0.255753i \(0.917677\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 49.8468 + 49.8468i 1.51051 + 1.51051i
\(34\) 17.8021i 0.523591i
\(35\) −21.3044 15.2430i −0.608697 0.435514i
\(36\) 39.4281 1.09522
\(37\) 11.4063 11.4063i 0.308280 0.308280i −0.535962 0.844242i \(-0.680051\pi\)
0.844242 + 0.535962i \(0.180051\pi\)
\(38\) 10.0119 + 10.0119i 0.263472 + 0.263472i
\(39\) 50.4115i 1.29260i
\(40\) 8.22909 11.5014i 0.205727 0.287535i
\(41\) −2.32786 −0.0567771 −0.0283885 0.999597i \(-0.509038\pi\)
−0.0283885 + 0.999597i \(0.509038\pi\)
\(42\) 28.0744 28.0744i 0.668439 0.668439i
\(43\) 12.0618 + 12.0618i 0.280507 + 0.280507i 0.833311 0.552804i \(-0.186442\pi\)
−0.552804 + 0.833311i \(0.686442\pi\)
\(44\) 26.3109i 0.597975i
\(45\) −97.2419 + 16.1276i −2.16093 + 0.358391i
\(46\) 6.78233 0.147442
\(47\) −38.4537 + 38.4537i −0.818163 + 0.818163i −0.985842 0.167679i \(-0.946373\pi\)
0.167679 + 0.985842i \(0.446373\pi\)
\(48\) 15.1563 + 15.1563i 0.315755 + 0.315755i
\(49\) 21.5509i 0.439815i
\(50\) −15.5910 + 31.7320i −0.311819 + 0.634641i
\(51\) −67.4532 −1.32261
\(52\) 13.3045 13.3045i 0.255855 0.255855i
\(53\) −49.3600 49.3600i −0.931320 0.931320i 0.0664687 0.997789i \(-0.478827\pi\)
−0.997789 + 0.0664687i \(0.978827\pi\)
\(54\) 81.1924i 1.50356i
\(55\) −10.7622 64.8908i −0.195676 1.17983i
\(56\) 14.8187 0.264619
\(57\) 37.9359 37.9359i 0.665541 0.665541i
\(58\) 40.4613 + 40.4613i 0.697609 + 0.697609i
\(59\) 23.6571i 0.400968i −0.979697 0.200484i \(-0.935748\pi\)
0.979697 0.200484i \(-0.0642515\pi\)
\(60\) −43.5795 31.1806i −0.726326 0.519676i
\(61\) −97.8268 −1.60372 −0.801859 0.597514i \(-0.796155\pi\)
−0.801859 + 0.597514i \(0.796155\pi\)
\(62\) −59.9380 + 59.9380i −0.966742 + 0.966742i
\(63\) −73.0339 73.0339i −1.15927 1.15927i
\(64\) 8.00000i 0.125000i
\(65\) −27.3709 + 38.2550i −0.421091 + 0.588539i
\(66\) 99.6937 1.51051
\(67\) 63.3064 63.3064i 0.944871 0.944871i −0.0536866 0.998558i \(-0.517097\pi\)
0.998558 + 0.0536866i \(0.0170972\pi\)
\(68\) −17.8021 17.8021i −0.261795 0.261795i
\(69\) 25.6987i 0.372445i
\(70\) −36.5474 + 6.06140i −0.522106 + 0.0865915i
\(71\) −42.9229 −0.604547 −0.302274 0.953221i \(-0.597746\pi\)
−0.302274 + 0.953221i \(0.597746\pi\)
\(72\) 39.4281 39.4281i 0.547612 0.547612i
\(73\) −9.09857 9.09857i −0.124638 0.124638i 0.642036 0.766674i \(-0.278090\pi\)
−0.766674 + 0.642036i \(0.778090\pi\)
\(74\) 22.8127i 0.308280i
\(75\) 120.235 + 59.0752i 1.60313 + 0.787670i
\(76\) 20.0239 0.263472
\(77\) 48.7365 48.7365i 0.632942 0.632942i
\(78\) −50.4115 50.4115i −0.646302 0.646302i
\(79\) 131.359i 1.66278i 0.555692 + 0.831388i \(0.312453\pi\)
−0.555692 + 0.831388i \(0.687547\pi\)
\(80\) −3.27231 19.7305i −0.0409039 0.246631i
\(81\) −130.217 −1.60762
\(82\) −2.32786 + 2.32786i −0.0283885 + 0.0283885i
\(83\) 76.9382 + 76.9382i 0.926967 + 0.926967i 0.997509 0.0705423i \(-0.0224730\pi\)
−0.0705423 + 0.997509i \(0.522473\pi\)
\(84\) 56.1489i 0.668439i
\(85\) 51.1872 + 36.6237i 0.602202 + 0.430867i
\(86\) 24.1236 0.280507
\(87\) 153.311 153.311i 1.76219 1.76219i
\(88\) 26.3109 + 26.3109i 0.298987 + 0.298987i
\(89\) 16.9832i 0.190822i 0.995438 + 0.0954111i \(0.0304166\pi\)
−0.995438 + 0.0954111i \(0.969583\pi\)
\(90\) −81.1143 + 113.369i −0.901270 + 1.25966i
\(91\) −49.2886 −0.541633
\(92\) 6.78233 6.78233i 0.0737210 0.0737210i
\(93\) 227.109 + 227.109i 2.44203 + 2.44203i
\(94\) 76.9073i 0.818163i
\(95\) −49.3851 + 8.19053i −0.519843 + 0.0862161i
\(96\) 30.3125 0.315755
\(97\) −41.5485 + 41.5485i −0.428335 + 0.428335i −0.888061 0.459726i \(-0.847948\pi\)
0.459726 + 0.888061i \(0.347948\pi\)
\(98\) 21.5509 + 21.5509i 0.219907 + 0.219907i
\(99\) 259.347i 2.61967i
\(100\) 16.1411 + 47.3230i 0.161411 + 0.473230i
\(101\) 172.994 1.71281 0.856406 0.516303i \(-0.172692\pi\)
0.856406 + 0.516303i \(0.172692\pi\)
\(102\) −67.4532 + 67.4532i −0.661306 + 0.661306i
\(103\) −107.544 107.544i −1.04412 1.04412i −0.998981 0.0451357i \(-0.985628\pi\)
−0.0451357 0.998981i \(-0.514372\pi\)
\(104\) 26.6089i 0.255855i
\(105\) 22.9671 + 138.481i 0.218734 + 1.31886i
\(106\) −98.7199 −0.931320
\(107\) 66.8707 66.8707i 0.624960 0.624960i −0.321836 0.946796i \(-0.604300\pi\)
0.946796 + 0.321836i \(0.104300\pi\)
\(108\) −81.1924 81.1924i −0.751782 0.751782i
\(109\) 95.4040i 0.875266i −0.899154 0.437633i \(-0.855817\pi\)
0.899154 0.437633i \(-0.144183\pi\)
\(110\) −75.6530 54.1286i −0.687754 0.492079i
\(111\) −86.4388 −0.778728
\(112\) 14.8187 14.8187i 0.132309 0.132309i
\(113\) −92.3049 92.3049i −0.816858 0.816858i 0.168794 0.985651i \(-0.446013\pi\)
−0.985651 + 0.168794i \(0.946013\pi\)
\(114\) 75.8717i 0.665541i
\(115\) −13.9531 + 19.5016i −0.121331 + 0.169579i
\(116\) 80.9227 0.697609
\(117\) −131.142 + 131.142i −1.12088 + 1.12088i
\(118\) −23.6571 23.6571i −0.200484 0.200484i
\(119\) 65.9507i 0.554208i
\(120\) −74.7601 + 12.3990i −0.623001 + 0.103325i
\(121\) 52.0656 0.430295
\(122\) −97.8268 + 97.8268i −0.801859 + 0.801859i
\(123\) 8.82042 + 8.82042i 0.0717107 + 0.0717107i
\(124\) 119.876i 0.966742i
\(125\) −59.1658 110.111i −0.473326 0.880887i
\(126\) −146.068 −1.15927
\(127\) −69.3611 + 69.3611i −0.546151 + 0.546151i −0.925325 0.379174i \(-0.876208\pi\)
0.379174 + 0.925325i \(0.376208\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 91.4060i 0.708574i
\(130\) 10.8841 + 65.6259i 0.0837237 + 0.504815i
\(131\) 219.399 1.67480 0.837401 0.546588i \(-0.184074\pi\)
0.837401 + 0.546588i \(0.184074\pi\)
\(132\) 99.6937 99.6937i 0.755255 0.755255i
\(133\) −37.0908 37.0908i −0.278879 0.278879i
\(134\) 126.613i 0.944871i
\(135\) 233.457 + 167.035i 1.72931 + 1.23730i
\(136\) −35.6042 −0.261795
\(137\) 77.1130 77.1130i 0.562869 0.562869i −0.367252 0.930121i \(-0.619701\pi\)
0.930121 + 0.367252i \(0.119701\pi\)
\(138\) −25.6987 25.6987i −0.186222 0.186222i
\(139\) 4.27993i 0.0307908i 0.999881 + 0.0153954i \(0.00490071\pi\)
−0.999881 + 0.0153954i \(0.995099\pi\)
\(140\) −30.4860 + 42.6088i −0.217757 + 0.304349i
\(141\) 291.407 2.06672
\(142\) −42.9229 + 42.9229i −0.302274 + 0.302274i
\(143\) −87.5131 87.5131i −0.611980 0.611980i
\(144\) 78.8562i 0.547612i
\(145\) −199.580 + 33.1005i −1.37642 + 0.228279i
\(146\) −18.1971 −0.124638
\(147\) 81.6579 81.6579i 0.555496 0.555496i
\(148\) −22.8127 22.8127i −0.154140 0.154140i
\(149\) 76.1990i 0.511402i −0.966756 0.255701i \(-0.917694\pi\)
0.966756 0.255701i \(-0.0823063\pi\)
\(150\) 179.310 61.1595i 1.19540 0.407730i
\(151\) 77.0391 0.510193 0.255096 0.966916i \(-0.417893\pi\)
0.255096 + 0.966916i \(0.417893\pi\)
\(152\) 20.0239 20.0239i 0.131736 0.131736i
\(153\) 175.475 + 175.475i 1.14690 + 1.14690i
\(154\) 97.4730i 0.632942i
\(155\) −49.0339 295.651i −0.316348 1.90743i
\(156\) −100.823 −0.646302
\(157\) −161.694 + 161.694i −1.02990 + 1.02990i −0.0303580 + 0.999539i \(0.509665\pi\)
−0.999539 + 0.0303580i \(0.990335\pi\)
\(158\) 131.359 + 131.359i 0.831388 + 0.831388i
\(159\) 374.056i 2.35255i
\(160\) −23.0028 16.4582i −0.143767 0.102864i
\(161\) −25.1263 −0.156064
\(162\) −130.217 + 130.217i −0.803809 + 0.803809i
\(163\) 226.296 + 226.296i 1.38832 + 1.38832i 0.828849 + 0.559473i \(0.188996\pi\)
0.559473 + 0.828849i \(0.311004\pi\)
\(164\) 4.65572i 0.0283885i
\(165\) −205.097 + 286.654i −1.24301 + 1.73730i
\(166\) 153.876 0.926967
\(167\) −129.180 + 129.180i −0.773531 + 0.773531i −0.978722 0.205191i \(-0.934218\pi\)
0.205191 + 0.978722i \(0.434218\pi\)
\(168\) −56.1489 56.1489i −0.334219 0.334219i
\(169\) 80.4955i 0.476305i
\(170\) 87.8109 14.5635i 0.516535 0.0856675i
\(171\) −197.376 −1.15424
\(172\) 24.1236 24.1236i 0.140254 0.140254i
\(173\) −102.806 102.806i −0.594254 0.594254i 0.344524 0.938778i \(-0.388040\pi\)
−0.938778 + 0.344524i \(0.888040\pi\)
\(174\) 306.621i 1.76219i
\(175\) 57.7593 117.557i 0.330053 0.671752i
\(176\) 52.6218 0.298987
\(177\) −89.6384 + 89.6384i −0.506432 + 0.506432i
\(178\) 16.9832 + 16.9832i 0.0954111 + 0.0954111i
\(179\) 278.400i 1.55530i −0.628694 0.777652i \(-0.716410\pi\)
0.628694 0.777652i \(-0.283590\pi\)
\(180\) 32.2552 + 194.484i 0.179196 + 1.08047i
\(181\) −267.758 −1.47933 −0.739663 0.672977i \(-0.765015\pi\)
−0.739663 + 0.672977i \(0.765015\pi\)
\(182\) −49.2886 + 49.2886i −0.270817 + 0.270817i
\(183\) 370.672 + 370.672i 2.02553 + 2.02553i
\(184\) 13.5647i 0.0737210i
\(185\) 65.5944 + 46.9319i 0.354565 + 0.253686i
\(186\) 454.218 2.44203
\(187\) −117.097 + 117.097i −0.626188 + 0.626188i
\(188\) 76.9073 + 76.9073i 0.409081 + 0.409081i
\(189\) 300.791i 1.59148i
\(190\) −41.1945 + 57.5756i −0.216813 + 0.303029i
\(191\) 227.882 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(192\) 30.3125 30.3125i 0.157878 0.157878i
\(193\) 216.098 + 216.098i 1.11968 + 1.11968i 0.991789 + 0.127888i \(0.0408197\pi\)
0.127888 + 0.991789i \(0.459180\pi\)
\(194\) 83.0970i 0.428335i
\(195\) 248.661 41.2405i 1.27518 0.211490i
\(196\) 43.1018 0.219907
\(197\) 120.946 120.946i 0.613939 0.613939i −0.330031 0.943970i \(-0.607059\pi\)
0.943970 + 0.330031i \(0.107059\pi\)
\(198\) −259.347 259.347i −1.30983 1.30983i
\(199\) 183.555i 0.922385i 0.887300 + 0.461193i \(0.152578\pi\)
−0.887300 + 0.461193i \(0.847422\pi\)
\(200\) 63.4641 + 31.1819i 0.317320 + 0.155910i
\(201\) −479.744 −2.38679
\(202\) 172.994 172.994i 0.856406 0.856406i
\(203\) −149.896 149.896i −0.738403 0.738403i
\(204\) 134.906i 0.661306i
\(205\) −1.90437 11.4825i −0.00928961 0.0560120i
\(206\) −215.088 −1.04412
\(207\) −66.8536 + 66.8536i −0.322964 + 0.322964i
\(208\) −26.6089 26.6089i −0.127928 0.127928i
\(209\) 131.711i 0.630198i
\(210\) 161.448 + 115.514i 0.768798 + 0.550064i
\(211\) 191.123 0.905794 0.452897 0.891563i \(-0.350390\pi\)
0.452897 + 0.891563i \(0.350390\pi\)
\(212\) −98.7199 + 98.7199i −0.465660 + 0.465660i
\(213\) 162.638 + 162.638i 0.763557 + 0.763557i
\(214\) 133.741i 0.624960i
\(215\) −49.6289 + 69.3639i −0.230832 + 0.322623i
\(216\) −162.385 −0.751782
\(217\) 222.050 222.050i 1.02327 1.02327i
\(218\) −95.4040 95.4040i −0.437633 0.437633i
\(219\) 68.9502i 0.314841i
\(220\) −129.782 + 21.5243i −0.589916 + 0.0978379i
\(221\) 118.424 0.535854
\(222\) −86.4388 + 86.4388i −0.389364 + 0.389364i
\(223\) −265.256 265.256i −1.18949 1.18949i −0.977209 0.212281i \(-0.931911\pi\)
−0.212281 0.977209i \(-0.568089\pi\)
\(224\) 29.6373i 0.132309i
\(225\) −159.103 466.464i −0.707123 2.07317i
\(226\) −184.610 −0.816858
\(227\) 2.98007 2.98007i 0.0131281 0.0131281i −0.700512 0.713640i \(-0.747045\pi\)
0.713640 + 0.700512i \(0.247045\pi\)
\(228\) −75.8717 75.8717i −0.332771 0.332771i
\(229\) 192.530i 0.840743i 0.907352 + 0.420372i \(0.138100\pi\)
−0.907352 + 0.420372i \(0.861900\pi\)
\(230\) 5.54847 + 33.4547i 0.0241238 + 0.145455i
\(231\) −369.332 −1.59884
\(232\) 80.9227 80.9227i 0.348805 0.348805i
\(233\) 9.84397 + 9.84397i 0.0422488 + 0.0422488i 0.727916 0.685667i \(-0.240489\pi\)
−0.685667 + 0.727916i \(0.740489\pi\)
\(234\) 262.285i 1.12088i
\(235\) −221.135 158.219i −0.941001 0.673273i
\(236\) −47.3143 −0.200484
\(237\) 497.729 497.729i 2.10012 2.10012i
\(238\) 65.9507 + 65.9507i 0.277104 + 0.277104i
\(239\) 290.916i 1.21722i 0.793468 + 0.608612i \(0.208273\pi\)
−0.793468 + 0.608612i \(0.791727\pi\)
\(240\) −62.3611 + 87.1591i −0.259838 + 0.363163i
\(241\) −50.2561 −0.208531 −0.104266 0.994549i \(-0.533249\pi\)
−0.104266 + 0.994549i \(0.533249\pi\)
\(242\) 52.0656 52.0656i 0.215147 0.215147i
\(243\) 128.035 + 128.035i 0.526893 + 0.526893i
\(244\) 195.654i 0.801859i
\(245\) −106.303 + 17.6303i −0.433888 + 0.0719605i
\(246\) 17.6408 0.0717107
\(247\) −66.6017 + 66.6017i −0.269643 + 0.269643i
\(248\) 119.876 + 119.876i 0.483371 + 0.483371i
\(249\) 583.048i 2.34156i
\(250\) −169.277 50.9451i −0.677107 0.203780i
\(251\) 205.930 0.820439 0.410220 0.911987i \(-0.365452\pi\)
0.410220 + 0.911987i \(0.365452\pi\)
\(252\) −146.068 + 146.068i −0.579634 + 0.579634i
\(253\) −44.6123 44.6123i −0.176333 0.176333i
\(254\) 138.722i 0.546151i
\(255\) −55.1820 332.721i −0.216400 1.30479i
\(256\) 16.0000 0.0625000
\(257\) 21.5059 21.5059i 0.0836807 0.0836807i −0.664027 0.747708i \(-0.731154\pi\)
0.747708 + 0.664027i \(0.231154\pi\)
\(258\) −91.4060 91.4060i −0.354287 0.354287i
\(259\) 84.5134i 0.326306i
\(260\) 76.5100 + 54.7418i 0.294269 + 0.210546i
\(261\) −797.657 −3.05616
\(262\) 219.399 219.399i 0.837401 0.837401i
\(263\) 180.933 + 180.933i 0.687958 + 0.687958i 0.961780 0.273822i \(-0.0882880\pi\)
−0.273822 + 0.961780i \(0.588288\pi\)
\(264\) 199.387i 0.755255i
\(265\) 203.094 283.854i 0.766391 1.07115i
\(266\) −74.1817 −0.278879
\(267\) 64.3504 64.3504i 0.241013 0.241013i
\(268\) −126.613 126.613i −0.472436 0.472436i
\(269\) 133.881i 0.497699i 0.968542 + 0.248849i \(0.0800524\pi\)
−0.968542 + 0.248849i \(0.919948\pi\)
\(270\) 400.491 66.4216i 1.48330 0.246006i
\(271\) −299.275 −1.10433 −0.552167 0.833734i \(-0.686199\pi\)
−0.552167 + 0.833734i \(0.686199\pi\)
\(272\) −35.6042 + 35.6042i −0.130898 + 0.130898i
\(273\) 186.758 + 186.758i 0.684095 + 0.684095i
\(274\) 154.226i 0.562869i
\(275\) 311.277 106.171i 1.13192 0.386078i
\(276\) −51.3974 −0.186222
\(277\) −221.291 + 221.291i −0.798885 + 0.798885i −0.982920 0.184035i \(-0.941084\pi\)
0.184035 + 0.982920i \(0.441084\pi\)
\(278\) 4.27993 + 4.27993i 0.0153954 + 0.0153954i
\(279\) 1181.62i 4.23520i
\(280\) 12.1228 + 73.0948i 0.0432957 + 0.261053i
\(281\) 86.9048 0.309270 0.154635 0.987972i \(-0.450580\pi\)
0.154635 + 0.987972i \(0.450580\pi\)
\(282\) 291.407 291.407i 1.03336 1.03336i
\(283\) 25.5811 + 25.5811i 0.0903927 + 0.0903927i 0.750857 0.660465i \(-0.229641\pi\)
−0.660465 + 0.750857i \(0.729641\pi\)
\(284\) 85.8457i 0.302274i
\(285\) 218.158 + 156.089i 0.765466 + 0.547680i
\(286\) −175.026 −0.611980
\(287\) 8.62394 8.62394i 0.0300486 0.0300486i
\(288\) −78.8562 78.8562i −0.273806 0.273806i
\(289\) 130.543i 0.451706i
\(290\) −166.480 + 232.681i −0.574069 + 0.802348i
\(291\) 314.860 1.08199
\(292\) −18.1971 + 18.1971i −0.0623190 + 0.0623190i
\(293\) −185.904 185.904i −0.634484 0.634484i 0.314705 0.949189i \(-0.398094\pi\)
−0.949189 + 0.314705i \(0.898094\pi\)
\(294\) 163.316i 0.555496i
\(295\) 116.692 19.3534i 0.395565 0.0656046i
\(296\) −45.6254 −0.154140
\(297\) −534.061 + 534.061i −1.79819 + 1.79819i
\(298\) −76.1990 76.1990i −0.255701 0.255701i
\(299\) 45.1177i 0.150895i
\(300\) 118.150 240.469i 0.393835 0.801565i
\(301\) −89.3700 −0.296910
\(302\) 77.0391 77.0391i 0.255096 0.255096i
\(303\) −655.485 655.485i −2.16332 2.16332i
\(304\) 40.0477i 0.131736i
\(305\) −80.0298 482.542i −0.262393 1.58211i
\(306\) 350.951 1.14690
\(307\) −165.430 + 165.430i −0.538859 + 0.538859i −0.923194 0.384335i \(-0.874431\pi\)
0.384335 + 0.923194i \(0.374431\pi\)
\(308\) −97.4730 97.4730i −0.316471 0.316471i
\(309\) 814.983i 2.63748i
\(310\) −344.685 246.618i −1.11189 0.795541i
\(311\) −192.859 −0.620124 −0.310062 0.950716i \(-0.600350\pi\)
−0.310062 + 0.950716i \(0.600350\pi\)
\(312\) −100.823 + 100.823i −0.323151 + 0.323151i
\(313\) 5.98024 + 5.98024i 0.0191062 + 0.0191062i 0.716595 0.697489i \(-0.245699\pi\)
−0.697489 + 0.716595i \(0.745699\pi\)
\(314\) 323.388i 1.02990i
\(315\) 300.501 419.996i 0.953972 1.33332i
\(316\) 262.719 0.831388
\(317\) 311.688 311.688i 0.983242 0.983242i −0.0166198 0.999862i \(-0.505291\pi\)
0.999862 + 0.0166198i \(0.00529050\pi\)
\(318\) 374.056 + 374.056i 1.17628 + 1.17628i
\(319\) 532.287i 1.66861i
\(320\) −39.4610 + 6.54462i −0.123316 + 0.0204519i
\(321\) −506.755 −1.57868
\(322\) −25.1263 + 25.1263i −0.0780319 + 0.0780319i
\(323\) 89.1166 + 89.1166i 0.275903 + 0.275903i
\(324\) 260.434i 0.803809i
\(325\) −211.089 103.715i −0.649505 0.319123i
\(326\) 452.593 1.38832
\(327\) −361.492 + 361.492i −1.10548 + 1.10548i
\(328\) 4.65572 + 4.65572i 0.0141943 + 0.0141943i
\(329\) 284.916i 0.866005i
\(330\) 81.5571 + 491.751i 0.247143 + 1.49015i
\(331\) −103.280 −0.312023 −0.156012 0.987755i \(-0.549864\pi\)
−0.156012 + 0.987755i \(0.549864\pi\)
\(332\) 153.876 153.876i 0.463483 0.463483i
\(333\) 224.865 + 224.865i 0.675271 + 0.675271i
\(334\) 258.359i 0.773531i
\(335\) 364.056 + 260.477i 1.08673 + 0.777543i
\(336\) −112.298 −0.334219
\(337\) −156.387 + 156.387i −0.464055 + 0.464055i −0.899982 0.435927i \(-0.856421\pi\)
0.435927 + 0.899982i \(0.356421\pi\)
\(338\) −80.4955 80.4955i −0.238152 0.238152i
\(339\) 699.499i 2.06342i
\(340\) 73.2474 102.374i 0.215434 0.301101i
\(341\) 788.511 2.31235
\(342\) −197.376 + 197.376i −0.577122 + 0.577122i
\(343\) −261.367 261.367i −0.762004 0.762004i
\(344\) 48.2473i 0.140254i
\(345\) 126.762 21.0235i 0.367426 0.0609377i
\(346\) −205.612 −0.594254
\(347\) −205.681 + 205.681i −0.592739 + 0.592739i −0.938370 0.345631i \(-0.887665\pi\)
0.345631 + 0.938370i \(0.387665\pi\)
\(348\) −306.621 306.621i −0.881096 0.881096i
\(349\) 436.934i 1.25196i 0.779839 + 0.625980i \(0.215301\pi\)
−0.779839 + 0.625980i \(0.784699\pi\)
\(350\) −59.7972 175.316i −0.170849 0.500902i
\(351\) 540.111 1.53878
\(352\) 52.6218 52.6218i 0.149494 0.149494i
\(353\) 287.500 + 287.500i 0.814447 + 0.814447i 0.985297 0.170850i \(-0.0546512\pi\)
−0.170850 + 0.985297i \(0.554651\pi\)
\(354\) 179.277i 0.506432i
\(355\) −35.1142 211.722i −0.0989133 0.596401i
\(356\) 33.9664 0.0954111
\(357\) 249.892 249.892i 0.699977 0.699977i
\(358\) −278.400 278.400i −0.777652 0.777652i
\(359\) 207.074i 0.576807i 0.957509 + 0.288403i \(0.0931244\pi\)
−0.957509 + 0.288403i \(0.906876\pi\)
\(360\) 226.739 + 162.229i 0.629831 + 0.450635i
\(361\) 260.761 0.722330
\(362\) −267.758 + 267.758i −0.739663 + 0.739663i
\(363\) −197.280 197.280i −0.543472 0.543472i
\(364\) 98.5772i 0.270817i
\(365\) 37.4365 52.3231i 0.102566 0.143351i
\(366\) 741.344 2.02553
\(367\) 69.0145 69.0145i 0.188051 0.188051i −0.606802 0.794853i \(-0.707548\pi\)
0.794853 + 0.606802i \(0.207548\pi\)
\(368\) −13.5647 13.5647i −0.0368605 0.0368605i
\(369\) 45.8915i 0.124367i
\(370\) 112.526 18.6625i 0.304125 0.0504393i
\(371\) 365.724 0.985779
\(372\) 454.218 454.218i 1.22102 1.22102i
\(373\) 257.438 + 257.438i 0.690181 + 0.690181i 0.962272 0.272091i \(-0.0877151\pi\)
−0.272091 + 0.962272i \(0.587715\pi\)
\(374\) 234.194i 0.626188i
\(375\) −193.034 + 641.401i −0.514758 + 1.71040i
\(376\) 153.815 0.409081
\(377\) −269.158 + 269.158i −0.713948 + 0.713948i
\(378\) 300.791 + 300.791i 0.795742 + 0.795742i
\(379\) 419.437i 1.10669i 0.832951 + 0.553346i \(0.186649\pi\)
−0.832951 + 0.553346i \(0.813351\pi\)
\(380\) 16.3811 + 98.7701i 0.0431081 + 0.259921i
\(381\) 525.628 1.37960
\(382\) 227.882 227.882i 0.596550 0.596550i
\(383\) −342.204 342.204i −0.893484 0.893484i 0.101365 0.994849i \(-0.467679\pi\)
−0.994849 + 0.101365i \(0.967679\pi\)
\(384\) 60.6251i 0.157878i
\(385\) 280.269 + 200.528i 0.727971 + 0.520853i
\(386\) 432.195 1.11968
\(387\) −237.787 + 237.787i −0.614437 + 0.614437i
\(388\) 83.0970 + 83.0970i 0.214168 + 0.214168i
\(389\) 2.95987i 0.00760892i −0.999993 0.00380446i \(-0.998789\pi\)
0.999993 0.00380446i \(-0.00121100\pi\)
\(390\) 207.420 289.901i 0.531847 0.743337i
\(391\) 60.3698 0.154398
\(392\) 43.1018 43.1018i 0.109954 0.109954i
\(393\) −831.318 831.318i −2.11531 2.11531i
\(394\) 241.892i 0.613939i
\(395\) −647.946 + 107.462i −1.64037 + 0.272056i
\(396\) −518.694 −1.30983
\(397\) 92.7715 92.7715i 0.233681 0.233681i −0.580546 0.814227i \(-0.697161\pi\)
0.814227 + 0.580546i \(0.197161\pi\)
\(398\) 183.555 + 183.555i 0.461193 + 0.461193i
\(399\) 281.079i 0.704459i
\(400\) 94.6460 32.2821i 0.236615 0.0807053i
\(401\) −23.9519 −0.0597303 −0.0298652 0.999554i \(-0.509508\pi\)
−0.0298652 + 0.999554i \(0.509508\pi\)
\(402\) −479.744 + 479.744i −1.19339 + 1.19339i
\(403\) −398.722 398.722i −0.989384 0.989384i
\(404\) 345.988i 0.856406i
\(405\) −106.528 642.311i −0.263031 1.58595i
\(406\) −299.791 −0.738403
\(407\) −150.055 + 150.055i −0.368687 + 0.368687i
\(408\) 134.906 + 134.906i 0.330653 + 0.330653i
\(409\) 659.636i 1.61280i 0.591370 + 0.806401i \(0.298587\pi\)
−0.591370 + 0.806401i \(0.701413\pi\)
\(410\) −13.3868 9.57808i −0.0326508 0.0233612i
\(411\) −584.373 −1.42183
\(412\) −215.088 + 215.088i −0.522058 + 0.522058i
\(413\) 87.6417 + 87.6417i 0.212208 + 0.212208i
\(414\) 133.707i 0.322964i
\(415\) −316.566 + 442.448i −0.762809 + 1.06614i
\(416\) −53.2179 −0.127928
\(417\) 16.2169 16.2169i 0.0388895 0.0388895i
\(418\) −131.711 131.711i −0.315099 0.315099i
\(419\) 221.284i 0.528124i 0.964506 + 0.264062i \(0.0850624\pi\)
−0.964506 + 0.264062i \(0.914938\pi\)
\(420\) 276.961 45.9341i 0.659431 0.109367i
\(421\) −105.381 −0.250311 −0.125155 0.992137i \(-0.539943\pi\)
−0.125155 + 0.992137i \(0.539943\pi\)
\(422\) 191.123 191.123i 0.452897 0.452897i
\(423\) −758.077 758.077i −1.79214 1.79214i
\(424\) 197.440i 0.465660i
\(425\) −138.776 + 282.448i −0.326531 + 0.664584i
\(426\) 325.275 0.763557
\(427\) 362.415 362.415i 0.848748 0.848748i
\(428\) −133.741 133.741i −0.312480 0.312480i
\(429\) 663.186i 1.54589i
\(430\) 19.7350 + 118.993i 0.0458953 + 0.276727i
\(431\) −224.659 −0.521251 −0.260626 0.965440i \(-0.583929\pi\)
−0.260626 + 0.965440i \(0.583929\pi\)
\(432\) −162.385 + 162.385i −0.375891 + 0.375891i
\(433\) 80.5022 + 80.5022i 0.185917 + 0.185917i 0.793928 0.608011i \(-0.208032\pi\)
−0.608011 + 0.793928i \(0.708032\pi\)
\(434\) 444.100i 1.02327i
\(435\) 881.644 + 630.804i 2.02677 + 1.45012i
\(436\) −190.808 −0.437633
\(437\) −33.9521 + 33.9521i −0.0776936 + 0.0776936i
\(438\) 68.9502 + 68.9502i 0.157420 + 0.157420i
\(439\) 191.215i 0.435569i 0.975997 + 0.217784i \(0.0698829\pi\)
−0.975997 + 0.217784i \(0.930117\pi\)
\(440\) −108.257 + 151.306i −0.246039 + 0.343877i
\(441\) −424.856 −0.963392
\(442\) 118.424 118.424i 0.267927 0.267927i
\(443\) 393.535 + 393.535i 0.888341 + 0.888341i 0.994364 0.106023i \(-0.0338116\pi\)
−0.106023 + 0.994364i \(0.533812\pi\)
\(444\) 172.878i 0.389364i
\(445\) −83.7716 + 13.8935i −0.188251 + 0.0312215i
\(446\) −530.512 −1.18949
\(447\) −288.723 + 288.723i −0.645912 + 0.645912i
\(448\) −29.6373 29.6373i −0.0661547 0.0661547i
\(449\) 6.06354i 0.0135045i 0.999977 + 0.00675227i \(0.00214933\pi\)
−0.999977 + 0.00675227i \(0.997851\pi\)
\(450\) −625.566 307.361i −1.39015 0.683025i
\(451\) 30.6240 0.0679025
\(452\) −184.610 + 184.610i −0.408429 + 0.408429i
\(453\) −291.906 291.906i −0.644384 0.644384i
\(454\) 5.96014i 0.0131281i
\(455\) −40.3219 243.122i −0.0886195 0.534334i
\(456\) −151.743 −0.332771
\(457\) 482.802 482.802i 1.05646 1.05646i 0.0581512 0.998308i \(-0.481479\pi\)
0.998308 0.0581512i \(-0.0185205\pi\)
\(458\) 192.530 + 192.530i 0.420372 + 0.420372i
\(459\) 722.697i 1.57450i
\(460\) 39.0031 + 27.9062i 0.0847894 + 0.0606656i
\(461\) 101.616 0.220426 0.110213 0.993908i \(-0.464847\pi\)
0.110213 + 0.993908i \(0.464847\pi\)
\(462\) −369.332 + 369.332i −0.799419 + 0.799419i
\(463\) −37.3060 37.3060i −0.0805745 0.0805745i 0.665671 0.746245i \(-0.268145\pi\)
−0.746245 + 0.665671i \(0.768145\pi\)
\(464\) 161.845i 0.348805i
\(465\) −934.450 + 1306.04i −2.00957 + 2.80868i
\(466\) 19.6879 0.0422488
\(467\) 155.236 155.236i 0.332412 0.332412i −0.521090 0.853502i \(-0.674474\pi\)
0.853502 + 0.521090i \(0.174474\pi\)
\(468\) 262.285 + 262.285i 0.560438 + 0.560438i
\(469\) 469.058i 1.00012i
\(470\) −379.355 + 62.9161i −0.807137 + 0.133864i
\(471\) 1225.34 2.60157
\(472\) −47.3143 + 47.3143i −0.100242 + 0.100242i
\(473\) −158.678 158.678i −0.335473 0.335473i
\(474\) 995.458i 2.10012i
\(475\) −80.8016 236.897i −0.170109 0.498731i
\(476\) 131.901 0.277104
\(477\) 973.084 973.084i 2.04001 2.04001i
\(478\) 290.916 + 290.916i 0.608612 + 0.608612i
\(479\) 166.864i 0.348358i 0.984714 + 0.174179i \(0.0557272\pi\)
−0.984714 + 0.174179i \(0.944273\pi\)
\(480\) 24.7980 + 149.520i 0.0516625 + 0.311500i
\(481\) 151.755 0.315500
\(482\) −50.2561 + 50.2561i −0.104266 + 0.104266i
\(483\) 95.2050 + 95.2050i 0.197112 + 0.197112i
\(484\) 104.131i 0.215147i
\(485\) −238.933 170.953i −0.492645 0.352481i
\(486\) 256.070 0.526893
\(487\) 434.139 434.139i 0.891456 0.891456i −0.103204 0.994660i \(-0.532910\pi\)
0.994660 + 0.103204i \(0.0329095\pi\)
\(488\) 195.654 + 195.654i 0.400929 + 0.400929i
\(489\) 1714.90i 3.50696i
\(490\) −88.6722 + 123.933i −0.180964 + 0.252924i
\(491\) 588.840 1.19927 0.599634 0.800275i \(-0.295313\pi\)
0.599634 + 0.800275i \(0.295313\pi\)
\(492\) 17.6408 17.6408i 0.0358554 0.0358554i
\(493\) 360.148 + 360.148i 0.730523 + 0.730523i
\(494\) 133.203i 0.269643i
\(495\) 1279.26 212.166i 2.58436 0.428618i
\(496\) 239.752 0.483371
\(497\) 159.015 159.015i 0.319949 0.319949i
\(498\) −583.048 583.048i −1.17078 1.17078i
\(499\) 280.896i 0.562918i −0.959573 0.281459i \(-0.909182\pi\)
0.959573 0.281459i \(-0.0908184\pi\)
\(500\) −220.222 + 118.332i −0.440444 + 0.236663i
\(501\) 978.941 1.95397
\(502\) 205.930 205.930i 0.410220 0.410220i
\(503\) −325.225 325.225i −0.646571 0.646571i 0.305592 0.952163i \(-0.401146\pi\)
−0.952163 + 0.305592i \(0.901146\pi\)
\(504\) 292.136i 0.579634i
\(505\) 141.522 + 853.314i 0.280242 + 1.68973i
\(506\) −89.2245 −0.176333
\(507\) −305.003 + 305.003i −0.601583 + 0.601583i
\(508\) 138.722 + 138.722i 0.273075 + 0.273075i
\(509\) 741.854i 1.45747i 0.684794 + 0.728737i \(0.259892\pi\)
−0.684794 + 0.728737i \(0.740108\pi\)
\(510\) −387.903 277.539i −0.760595 0.544195i
\(511\) 67.4143 0.131926
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 406.446 + 406.446i 0.792293 + 0.792293i
\(514\) 43.0119i 0.0836807i
\(515\) 442.495 618.453i 0.859213 1.20088i
\(516\) −182.812 −0.354287
\(517\) 505.875 505.875i 0.978481 0.978481i
\(518\) 84.5134 + 84.5134i 0.163153 + 0.163153i
\(519\) 779.077i 1.50111i
\(520\) 131.252 21.7682i 0.252407 0.0418619i
\(521\) −361.909 −0.694643 −0.347322 0.937746i \(-0.612909\pi\)
−0.347322 + 0.937746i \(0.612909\pi\)
\(522\) −797.657 + 797.657i −1.52808 + 1.52808i
\(523\) 160.404 + 160.404i 0.306700 + 0.306700i 0.843628 0.536928i \(-0.180415\pi\)
−0.536928 + 0.843628i \(0.680415\pi\)
\(524\) 438.798i 0.837401i
\(525\) −664.283 + 226.576i −1.26530 + 0.431572i
\(526\) 361.866 0.687958
\(527\) −533.511 + 533.511i −1.01235 + 1.01235i
\(528\) −199.387 199.387i −0.377628 0.377628i
\(529\) 23.0000i 0.0434783i
\(530\) −80.7605 486.948i −0.152378 0.918770i
\(531\) 466.378 0.878301
\(532\) −74.1817 + 74.1817i −0.139439 + 0.139439i
\(533\) −15.4855 15.4855i −0.0290534 0.0290534i
\(534\) 128.701i 0.241013i
\(535\) 384.553 + 275.143i 0.718791 + 0.514285i
\(536\) −253.225 −0.472436
\(537\) −1054.87 + 1054.87i −1.96438 + 1.96438i
\(538\) 133.881 + 133.881i 0.248849 + 0.248849i
\(539\) 283.512i 0.525996i
\(540\) 334.070 466.913i 0.618648 0.864654i
\(541\) 235.297 0.434930 0.217465 0.976068i \(-0.430221\pi\)
0.217465 + 0.976068i \(0.430221\pi\)
\(542\) −299.275 + 299.275i −0.552167 + 0.552167i
\(543\) 1014.55 + 1014.55i 1.86842 + 1.86842i
\(544\) 71.2083i 0.130898i
\(545\) 470.592 78.0478i 0.863471 0.143207i
\(546\) 373.516 0.684095
\(547\) −542.478 + 542.478i −0.991734 + 0.991734i −0.999966 0.00823214i \(-0.997380\pi\)
0.00823214 + 0.999966i \(0.497380\pi\)
\(548\) −154.226 154.226i −0.281434 0.281434i
\(549\) 1928.56i 3.51286i
\(550\) 205.106 417.449i 0.372920 0.758998i
\(551\) −405.096 −0.735202
\(552\) −51.3974 + 51.3974i −0.0931112 + 0.0931112i
\(553\) −486.642 486.642i −0.880004 0.880004i
\(554\) 442.582i 0.798885i
\(555\) −70.7136 426.370i −0.127412 0.768234i
\(556\) 8.55985 0.0153954
\(557\) 88.3077 88.3077i 0.158542 0.158542i −0.623379 0.781920i \(-0.714240\pi\)
0.781920 + 0.623379i \(0.214240\pi\)
\(558\) −1181.62 1181.62i −2.11760 2.11760i
\(559\) 160.476i 0.287077i
\(560\) 85.2176 + 60.9720i 0.152174 + 0.108879i
\(561\) 887.377 1.58178
\(562\) 86.9048 86.9048i 0.154635 0.154635i
\(563\) −210.944 210.944i −0.374678 0.374678i 0.494500 0.869178i \(-0.335351\pi\)
−0.869178 + 0.494500i \(0.835351\pi\)
\(564\) 582.814i 1.03336i
\(565\) 379.793 530.818i 0.672199 0.939500i
\(566\) 51.1623 0.0903927
\(567\) 482.410 482.410i 0.850812 0.850812i
\(568\) 85.8457 + 85.8457i 0.151137 + 0.151137i
\(569\) 310.506i 0.545705i 0.962056 + 0.272853i \(0.0879671\pi\)
−0.962056 + 0.272853i \(0.912033\pi\)
\(570\) 374.246 62.0689i 0.656573 0.108893i
\(571\) −842.633 −1.47571 −0.737857 0.674957i \(-0.764162\pi\)
−0.737857 + 0.674957i \(0.764162\pi\)
\(572\) −175.026 + 175.026i −0.305990 + 0.305990i
\(573\) −863.460 863.460i −1.50691 1.50691i
\(574\) 17.2479i 0.0300486i
\(575\) −107.609 52.8716i −0.187145 0.0919505i
\(576\) −157.712 −0.273806
\(577\) −140.531 + 140.531i −0.243554 + 0.243554i −0.818319 0.574765i \(-0.805094\pi\)
0.574765 + 0.818319i \(0.305094\pi\)
\(578\) 130.543 + 130.543i 0.225853 + 0.225853i
\(579\) 1637.62i 2.82835i
\(580\) 66.2010 + 399.161i 0.114140 + 0.688209i
\(581\) −570.061 −0.981171
\(582\) 314.860 314.860i 0.540997 0.540997i
\(583\) 649.352 + 649.352i 1.11381 + 1.11381i
\(584\) 36.3943i 0.0623190i
\(585\) −754.161 539.591i −1.28916 0.922379i
\(586\) −371.808 −0.634484
\(587\) −407.264 + 407.264i −0.693806 + 0.693806i −0.963067 0.269261i \(-0.913220\pi\)
0.269261 + 0.963067i \(0.413220\pi\)
\(588\) −163.316 163.316i −0.277748 0.277748i
\(589\) 600.095i 1.01884i
\(590\) 97.3383 136.045i 0.164980 0.230585i
\(591\) −916.544 −1.55084
\(592\) −45.6254 + 45.6254i −0.0770699 + 0.0770699i
\(593\) 67.3781 + 67.3781i 0.113623 + 0.113623i 0.761632 0.648010i \(-0.224398\pi\)
−0.648010 + 0.761632i \(0.724398\pi\)
\(594\) 1068.12i 1.79819i
\(595\) −325.310 + 53.9528i −0.546739 + 0.0906769i
\(596\) −152.398 −0.255701
\(597\) 695.501 695.501i 1.16499 1.16499i
\(598\) 45.1177 + 45.1177i 0.0754476 + 0.0754476i
\(599\) 401.280i 0.669916i −0.942233 0.334958i \(-0.891278\pi\)
0.942233 0.334958i \(-0.108722\pi\)
\(600\) −122.319 358.620i −0.203865 0.597700i
\(601\) −151.686 −0.252390 −0.126195 0.992005i \(-0.540276\pi\)
−0.126195 + 0.992005i \(0.540276\pi\)
\(602\) −89.3700 + 89.3700i −0.148455 + 0.148455i
\(603\) 1248.02 + 1248.02i 2.06969 + 2.06969i
\(604\) 154.078i 0.255096i
\(605\) 42.5937 + 256.820i 0.0704028 + 0.424496i
\(606\) −1310.97 −2.16332
\(607\) −16.0095 + 16.0095i −0.0263748 + 0.0263748i −0.720171 0.693796i \(-0.755937\pi\)
0.693796 + 0.720171i \(0.255937\pi\)
\(608\) −40.0477 40.0477i −0.0658680 0.0658680i
\(609\) 1135.93i 1.86524i
\(610\) −562.572 402.512i −0.922249 0.659857i
\(611\) −511.606 −0.837325
\(612\) 350.951 350.951i 0.573449 0.573449i
\(613\) 193.411 + 193.411i 0.315515 + 0.315515i 0.847042 0.531526i \(-0.178381\pi\)
−0.531526 + 0.847042i \(0.678381\pi\)
\(614\) 330.859i 0.538859i
\(615\) −36.2920 + 50.7236i −0.0590114 + 0.0824773i
\(616\) −194.946 −0.316471
\(617\) 616.656 616.656i 0.999443 0.999443i −0.000556768 1.00000i \(-0.500177\pi\)
1.00000 0.000556768i \(0.000177225\pi\)
\(618\) 814.983 + 814.983i 1.31874 + 1.31874i
\(619\) 889.291i 1.43666i 0.695703 + 0.718329i \(0.255093\pi\)
−0.695703 + 0.718329i \(0.744907\pi\)
\(620\) −591.303 + 98.0678i −0.953714 + 0.158174i
\(621\) 275.337 0.443377
\(622\) −192.859 + 192.859i −0.310062 + 0.310062i
\(623\) −62.9170 62.9170i −0.100990 0.100990i
\(624\) 201.646i 0.323151i
\(625\) 494.733 381.922i 0.791573 0.611075i
\(626\) 11.9605 0.0191062
\(627\) −499.063 + 499.063i −0.795954 + 0.795954i
\(628\) 323.388 + 323.388i 0.514949 + 0.514949i
\(629\) 203.057i 0.322825i
\(630\) −119.495 720.497i −0.189674 1.14365i
\(631\) −907.148 −1.43764 −0.718818 0.695199i \(-0.755316\pi\)
−0.718818 + 0.695199i \(0.755316\pi\)
\(632\) 262.719 262.719i 0.415694 0.415694i
\(633\) −724.176 724.176i −1.14404 1.14404i
\(634\) 623.375i 0.983242i
\(635\) −398.875 285.389i −0.628150 0.449432i
\(636\) 748.112 1.17628
\(637\) −143.362 + 143.362i −0.225058 + 0.225058i
\(638\) −532.287 532.287i −0.834305 0.834305i
\(639\) 846.183i 1.32423i
\(640\) −32.9164 + 46.0056i −0.0514318 + 0.0718837i
\(641\) −820.680 −1.28031 −0.640156 0.768245i \(-0.721130\pi\)
−0.640156 + 0.768245i \(0.721130\pi\)
\(642\) −506.755 + 506.755i −0.789338 + 0.789338i
\(643\) −224.861 224.861i −0.349707 0.349707i 0.510294 0.860000i \(-0.329537\pi\)
−0.860000 + 0.510294i \(0.829537\pi\)
\(644\) 50.2525i 0.0780319i
\(645\) 450.871 74.7772i 0.699025 0.115934i
\(646\) 178.233 0.275903
\(647\) −236.065 + 236.065i −0.364860 + 0.364860i −0.865599 0.500738i \(-0.833062\pi\)
0.500738 + 0.865599i \(0.333062\pi\)
\(648\) 260.434 + 260.434i 0.401904 + 0.401904i
\(649\) 311.220i 0.479538i
\(650\) −314.804 + 107.374i −0.484314 + 0.165191i
\(651\) −1682.73 −2.58483
\(652\) 452.593 452.593i 0.694161 0.694161i
\(653\) −574.018 574.018i −0.879048 0.879048i 0.114388 0.993436i \(-0.463509\pi\)
−0.993436 + 0.114388i \(0.963509\pi\)
\(654\) 722.984i 1.10548i
\(655\) 179.485 + 1082.21i 0.274024 + 1.65223i
\(656\) 9.31144 0.0141943
\(657\) 179.370 179.370i 0.273013 0.273013i
\(658\) −284.916 284.916i −0.433003 0.433003i
\(659\) 123.517i 0.187430i −0.995599 0.0937152i \(-0.970126\pi\)
0.995599 0.0937152i \(-0.0298743\pi\)
\(660\) 573.308 + 410.194i 0.868649 + 0.621506i
\(661\) 698.871 1.05729 0.528646 0.848842i \(-0.322700\pi\)
0.528646 + 0.848842i \(0.322700\pi\)
\(662\) −103.280 + 103.280i −0.156012 + 0.156012i
\(663\) −448.715 448.715i −0.676795 0.676795i
\(664\) 307.753i 0.463483i
\(665\) 152.612 213.298i 0.229492 0.320749i
\(666\) 449.730 0.675271
\(667\) −137.211 + 137.211i −0.205714 + 0.205714i
\(668\) 258.359 + 258.359i 0.386766 + 0.386766i
\(669\) 2010.15i 3.00470i
\(670\) 624.533 103.579i 0.932138 0.154595i
\(671\) 1286.95 1.91796
\(672\) −112.298 + 112.298i −0.167110 + 0.167110i
\(673\) −763.682 763.682i −1.13474 1.13474i −0.989378 0.145365i \(-0.953565\pi\)
−0.145365 0.989378i \(-0.546435\pi\)
\(674\) 312.773i 0.464055i
\(675\) −632.934 + 1288.20i −0.937680 + 1.90844i
\(676\) −160.991 −0.238152
\(677\) 18.4824 18.4824i 0.0273005 0.0273005i −0.693325 0.720625i \(-0.743855\pi\)
0.720625 + 0.693325i \(0.243855\pi\)
\(678\) 699.499 + 699.499i 1.03171 + 1.03171i
\(679\) 307.847i 0.453382i
\(680\) −29.1269 175.622i −0.0428337 0.258267i
\(681\) −22.5834 −0.0331620
\(682\) 788.511 788.511i 1.15617 1.15617i
\(683\) 416.193 + 416.193i 0.609360 + 0.609360i 0.942779 0.333419i \(-0.108202\pi\)
−0.333419 + 0.942779i \(0.608202\pi\)
\(684\) 394.751i 0.577122i
\(685\) 443.454 + 317.285i 0.647378 + 0.463190i
\(686\) −522.735 −0.762004
\(687\) 729.510 729.510i 1.06188 1.06188i
\(688\) −48.2473 48.2473i −0.0701268 0.0701268i
\(689\) 656.708i 0.953132i
\(690\) 105.738 147.785i 0.153244 0.214182i
\(691\) −187.344 −0.271120 −0.135560 0.990769i \(-0.543283\pi\)
−0.135560 + 0.990769i \(0.543283\pi\)
\(692\) −205.612 + 205.612i −0.297127 + 0.297127i
\(693\) 960.793 + 960.793i 1.38643 + 1.38643i
\(694\) 411.361i 0.592739i
\(695\) −21.1113 + 3.50131i −0.0303759 + 0.00503785i
\(696\) −613.243 −0.881096
\(697\) −20.7204 + 20.7204i −0.0297279 + 0.0297279i
\(698\) 436.934 + 436.934i 0.625980 + 0.625980i
\(699\) 74.5989i 0.106722i
\(700\) −235.113 115.519i −0.335876 0.165027i
\(701\) 533.465 0.761006 0.380503 0.924780i \(-0.375751\pi\)
0.380503 + 0.924780i \(0.375751\pi\)
\(702\) 540.111 540.111i 0.769389 0.769389i
\(703\) 114.200 + 114.200i 0.162446 + 0.162446i
\(704\) 105.244i 0.149494i
\(705\) 238.393 + 1437.40i 0.338146 + 2.03886i
\(706\) 575.000 0.814447
\(707\) −640.885 + 640.885i −0.906485 + 0.906485i
\(708\) 179.277 + 179.277i 0.253216 + 0.253216i
\(709\) 1343.63i 1.89510i −0.319600 0.947552i \(-0.603549\pi\)
0.319600 0.947552i \(-0.396451\pi\)
\(710\) −246.836 176.608i −0.347657 0.248744i
\(711\) −2589.62 −3.64223
\(712\) 33.9664 33.9664i 0.0477056 0.0477056i
\(713\) −203.260 203.260i −0.285077 0.285077i
\(714\) 499.783i 0.699977i
\(715\) 360.077 503.262i 0.503604 0.703862i
\(716\) −556.799 −0.777652
\(717\) 1102.30 1102.30i 1.53738 1.53738i
\(718\) 207.074 + 207.074i 0.288403 + 0.288403i
\(719\) 86.6051i 0.120452i 0.998185 + 0.0602261i \(0.0191822\pi\)
−0.998185 + 0.0602261i \(0.980818\pi\)
\(720\) 388.968 64.5104i 0.540233 0.0895978i
\(721\) 796.829 1.10517
\(722\) 260.761 260.761i 0.361165 0.361165i
\(723\) 190.423 + 190.423i 0.263380 + 0.263380i
\(724\) 535.516i 0.739663i
\(725\) −326.544 957.376i −0.450406 1.32052i
\(726\) −394.560 −0.543472
\(727\) 776.915 776.915i 1.06866 1.06866i 0.0711972 0.997462i \(-0.477318\pi\)
0.997462 0.0711972i \(-0.0226820\pi\)
\(728\) 98.5772 + 98.5772i 0.135408 + 0.135408i
\(729\) 201.687i 0.276662i
\(730\) −14.8867 89.7596i −0.0203927 0.122958i
\(731\) 214.725 0.293742
\(732\) 741.344 741.344i 1.01277 1.01277i
\(733\) 221.110 + 221.110i 0.301651 + 0.301651i 0.841660 0.540008i \(-0.181579\pi\)
−0.540008 + 0.841660i \(0.681579\pi\)
\(734\) 138.029i 0.188051i
\(735\) 469.590 + 335.985i 0.638898 + 0.457122i
\(736\) −27.1293 −0.0368605
\(737\) −832.823 + 832.823i −1.13002 + 1.13002i
\(738\) −45.8915 45.8915i −0.0621837 0.0621837i
\(739\) 793.629i 1.07392i 0.843607 + 0.536962i \(0.180428\pi\)
−0.843607 + 0.536962i \(0.819572\pi\)
\(740\) 93.8638 131.189i 0.126843 0.177282i
\(741\) 504.717 0.681129
\(742\) 365.724 365.724i 0.492890 0.492890i
\(743\) 821.820 + 821.820i 1.10608 + 1.10608i 0.993660 + 0.112423i \(0.0358613\pi\)
0.112423 + 0.993660i \(0.464139\pi\)
\(744\) 908.436i 1.22102i
\(745\) 375.861 62.3366i 0.504511 0.0836733i
\(746\) 514.875 0.690181
\(747\) −1516.76 + 1516.76i −2.03047 + 2.03047i
\(748\) 234.194 + 234.194i 0.313094 + 0.313094i
\(749\) 495.467i 0.661505i
\(750\) 448.366 + 834.435i 0.597822 + 1.11258i
\(751\) −1321.54 −1.75970 −0.879851 0.475250i \(-0.842358\pi\)
−0.879851 + 0.475250i \(0.842358\pi\)
\(752\) 153.815 153.815i 0.204541 0.204541i
\(753\) −780.283 780.283i −1.03623 1.03623i
\(754\) 538.317i 0.713948i
\(755\) 63.0239 + 380.005i 0.0834754 + 0.503317i
\(756\) 601.581 0.795742
\(757\) 874.570 874.570i 1.15531 1.15531i 0.169839 0.985472i \(-0.445675\pi\)
0.985472 0.169839i \(-0.0543247\pi\)
\(758\) 419.437 + 419.437i 0.553346 + 0.553346i
\(759\) 338.078i 0.445425i
\(760\) 115.151 + 82.3890i 0.151515 + 0.108407i
\(761\) 1233.20 1.62050 0.810252 0.586082i \(-0.199330\pi\)
0.810252 + 0.586082i \(0.199330\pi\)
\(762\) 525.628 525.628i 0.689800 0.689800i
\(763\) 353.440 + 353.440i 0.463224 + 0.463224i
\(764\) 455.764i 0.596550i
\(765\) −722.001 + 1009.11i −0.943793 + 1.31909i
\(766\) −684.409 −0.893484
\(767\) 157.373 157.373i 0.205180 0.205180i
\(768\) −60.6251 60.6251i −0.0789389 0.0789389i
\(769\) 691.258i 0.898905i −0.893304 0.449452i \(-0.851619\pi\)
0.893304 0.449452i \(-0.148381\pi\)
\(770\) 480.797 79.7404i 0.624412 0.103559i
\(771\) −162.975 −0.211381
\(772\) 432.195 432.195i 0.559838 0.559838i
\(773\) 311.187 + 311.187i 0.402571 + 0.402571i 0.879138 0.476567i \(-0.158119\pi\)
−0.476567 + 0.879138i \(0.658119\pi\)
\(774\) 475.574i 0.614437i
\(775\) 1418.22 483.731i 1.82997 0.624170i
\(776\) 166.194 0.214168
\(777\) 320.227 320.227i 0.412132