Properties

Label 210.3.o.b.31.3
Level 210
Weight 3
Character 210.31
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(1.92573 + 3.33546i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.31
Dual form 210.3.o.b.61.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(-2.67372 + 6.46925i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(-2.67372 + 6.46925i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-0.578394 + 1.00181i) q^{11} +(3.00000 - 1.73205i) q^{12} +14.8176i q^{13} +(9.81379 - 1.29982i) q^{14} -3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(10.9271 + 6.30878i) q^{17} +(2.12132 - 3.67423i) q^{18} +(16.7162 - 9.65108i) q^{19} +4.47214i q^{20} +(9.61312 - 7.38837i) q^{21} +1.63595 q^{22} +(12.1504 + 21.0450i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(18.1477 - 10.4776i) q^{26} -5.19615i q^{27} +(-8.53135 - 11.1003i) q^{28} +49.0382 q^{29} +(2.73861 + 4.74342i) q^{30} +(-24.9581 - 14.4096i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(1.73518 - 1.00181i) q^{33} -17.8439i q^{34} +(2.05520 + 15.5170i) q^{35} -6.00000 q^{36} +(26.6579 + 46.1728i) q^{37} +(-23.6402 - 13.6487i) q^{38} +(12.8324 - 22.2264i) q^{39} +(5.47723 - 3.16228i) q^{40} +38.0398i q^{41} +(-15.8464 - 6.54925i) q^{42} -63.5774 q^{43} +(-1.15679 - 2.00362i) q^{44} +(5.80948 + 3.35410i) q^{45} +(17.1832 - 29.7622i) q^{46} +(21.8175 - 12.5964i) q^{47} +6.92820i q^{48} +(-34.7024 - 34.5940i) q^{49} -7.07107 q^{50} +(-10.9271 - 18.9263i) q^{51} +(-25.6648 - 14.8176i) q^{52} +(-10.4160 + 18.0411i) q^{53} +(-6.36396 + 3.67423i) q^{54} +2.58666i q^{55} +(-7.56243 + 18.2978i) q^{56} -33.4323 q^{57} +(-34.6752 - 60.0593i) q^{58} +(21.1419 + 12.2063i) q^{59} +(3.87298 - 6.70820i) q^{60} +(5.53376 - 3.19492i) q^{61} +40.7564i q^{62} +(-20.8182 + 2.75734i) q^{63} +8.00000 q^{64} +(16.5665 + 28.6941i) q^{65} +(-2.45392 - 1.41677i) q^{66} +(-62.2451 + 107.812i) q^{67} +(-21.8543 + 12.6176i) q^{68} -42.0901i q^{69} +(17.5511 - 13.4892i) q^{70} -118.973 q^{71} +(4.24264 + 7.34847i) q^{72} +(-34.2336 - 19.7648i) q^{73} +(37.7000 - 65.2983i) q^{74} +(-7.50000 + 4.33013i) q^{75} +38.6043i q^{76} +(-4.93448 - 6.42033i) q^{77} -36.2955 q^{78} +(46.4356 + 80.4288i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(46.5891 - 26.8982i) q^{82} +5.79665i q^{83} +(3.18391 + 24.0388i) q^{84} +28.2137 q^{85} +(44.9560 + 77.8661i) q^{86} +(-73.5573 - 42.4683i) q^{87} +(-1.63595 + 2.83354i) q^{88} +(131.622 - 75.9919i) q^{89} -9.48683i q^{90} +(-95.8586 - 39.6181i) q^{91} -48.6014 q^{92} +(24.9581 + 43.2287i) q^{93} +(-30.8546 - 17.8139i) q^{94} +(21.5805 - 37.3785i) q^{95} +(8.48528 - 4.89898i) q^{96} -144.310i q^{97} +(-17.8305 + 66.9632i) q^{98} -3.47036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) −2.67372 + 6.46925i −0.381960 + 0.924179i
\(8\) 2.82843 0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −2.73861 1.58114i −0.273861 0.158114i
\(11\) −0.578394 + 1.00181i −0.0525813 + 0.0910735i −0.891118 0.453772i \(-0.850078\pi\)
0.838537 + 0.544845i \(0.183412\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 14.8176i 1.13981i 0.821710 + 0.569906i \(0.193021\pi\)
−0.821710 + 0.569906i \(0.806979\pi\)
\(14\) 9.81379 1.29982i 0.700985 0.0928446i
\(15\) −3.87298 −0.258199
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 10.9271 + 6.30878i 0.642772 + 0.371105i 0.785682 0.618631i \(-0.212312\pi\)
−0.142909 + 0.989736i \(0.545646\pi\)
\(18\) 2.12132 3.67423i 0.117851 0.204124i
\(19\) 16.7162 9.65108i 0.879798 0.507951i 0.00920603 0.999958i \(-0.497070\pi\)
0.870592 + 0.492006i \(0.163736\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 9.61312 7.38837i 0.457768 0.351827i
\(22\) 1.63595 0.0743612
\(23\) 12.1504 + 21.0450i 0.528277 + 0.915002i 0.999457 + 0.0329648i \(0.0104949\pi\)
−0.471180 + 0.882037i \(0.656172\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 18.1477 10.4776i 0.697990 0.402985i
\(27\) 5.19615i 0.192450i
\(28\) −8.53135 11.1003i −0.304691 0.396438i
\(29\) 49.0382 1.69097 0.845486 0.533998i \(-0.179311\pi\)
0.845486 + 0.533998i \(0.179311\pi\)
\(30\) 2.73861 + 4.74342i 0.0912871 + 0.158114i
\(31\) −24.9581 14.4096i −0.805100 0.464825i 0.0401515 0.999194i \(-0.487216\pi\)
−0.845251 + 0.534369i \(0.820549\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) 1.73518 1.00181i 0.0525813 0.0303578i
\(34\) 17.8439i 0.524822i
\(35\) 2.05520 + 15.5170i 0.0587201 + 0.443342i
\(36\) −6.00000 −0.166667
\(37\) 26.6579 + 46.1728i 0.720484 + 1.24791i 0.960806 + 0.277221i \(0.0894136\pi\)
−0.240322 + 0.970693i \(0.577253\pi\)
\(38\) −23.6402 13.6487i −0.622111 0.359176i
\(39\) 12.8324 22.2264i 0.329036 0.569906i
\(40\) 5.47723 3.16228i 0.136931 0.0790569i
\(41\) 38.0398i 0.927800i 0.885888 + 0.463900i \(0.153550\pi\)
−0.885888 + 0.463900i \(0.846450\pi\)
\(42\) −15.8464 6.54925i −0.377294 0.155935i
\(43\) −63.5774 −1.47854 −0.739272 0.673407i \(-0.764830\pi\)
−0.739272 + 0.673407i \(0.764830\pi\)
\(44\) −1.15679 2.00362i −0.0262906 0.0455367i
\(45\) 5.80948 + 3.35410i 0.129099 + 0.0745356i
\(46\) 17.1832 29.7622i 0.373548 0.647004i
\(47\) 21.8175 12.5964i 0.464203 0.268008i −0.249607 0.968347i \(-0.580301\pi\)
0.713810 + 0.700340i \(0.246968\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −34.7024 34.5940i −0.708213 0.705999i
\(50\) −7.07107 −0.141421
\(51\) −10.9271 18.9263i −0.214257 0.371105i
\(52\) −25.6648 14.8176i −0.493553 0.284953i
\(53\) −10.4160 + 18.0411i −0.196529 + 0.340397i −0.947401 0.320050i \(-0.896300\pi\)
0.750872 + 0.660448i \(0.229634\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 2.58666i 0.0470301i
\(56\) −7.56243 + 18.2978i −0.135043 + 0.326747i
\(57\) −33.4323 −0.586532
\(58\) −34.6752 60.0593i −0.597849 1.03550i
\(59\) 21.1419 + 12.2063i 0.358337 + 0.206886i 0.668351 0.743846i \(-0.267000\pi\)
−0.310014 + 0.950732i \(0.600334\pi\)
\(60\) 3.87298 6.70820i 0.0645497 0.111803i
\(61\) 5.53376 3.19492i 0.0907174 0.0523757i −0.453955 0.891025i \(-0.649987\pi\)
0.544672 + 0.838649i \(0.316654\pi\)
\(62\) 40.7564i 0.657361i
\(63\) −20.8182 + 2.75734i −0.330447 + 0.0437674i
\(64\) 8.00000 0.125000
\(65\) 16.5665 + 28.6941i 0.254870 + 0.441448i
\(66\) −2.45392 1.41677i −0.0371806 0.0214662i
\(67\) −62.2451 + 107.812i −0.929031 + 1.60913i −0.144085 + 0.989565i \(0.546024\pi\)
−0.784946 + 0.619564i \(0.787310\pi\)
\(68\) −21.8543 + 12.6176i −0.321386 + 0.185552i
\(69\) 42.0901i 0.610001i
\(70\) 17.5511 13.4892i 0.250730 0.192704i
\(71\) −118.973 −1.67567 −0.837835 0.545924i \(-0.816179\pi\)
−0.837835 + 0.545924i \(0.816179\pi\)
\(72\) 4.24264 + 7.34847i 0.0589256 + 0.102062i
\(73\) −34.2336 19.7648i −0.468953 0.270750i 0.246848 0.969054i \(-0.420605\pi\)
−0.715801 + 0.698304i \(0.753938\pi\)
\(74\) 37.7000 65.2983i 0.509459 0.882409i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 38.6043i 0.507951i
\(77\) −4.93448 6.42033i −0.0640842 0.0833809i
\(78\) −36.2955 −0.465327
\(79\) 46.4356 + 80.4288i 0.587792 + 1.01809i 0.994521 + 0.104537i \(0.0333360\pi\)
−0.406729 + 0.913549i \(0.633331\pi\)
\(80\) −7.74597 4.47214i −0.0968246 0.0559017i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 46.5891 26.8982i 0.568159 0.328027i
\(83\) 5.79665i 0.0698392i 0.999390 + 0.0349196i \(0.0111175\pi\)
−0.999390 + 0.0349196i \(0.988882\pi\)
\(84\) 3.18391 + 24.0388i 0.0379037 + 0.286176i
\(85\) 28.2137 0.331926
\(86\) 44.9560 + 77.8661i 0.522744 + 0.905420i
\(87\) −73.5573 42.4683i −0.845486 0.488142i
\(88\) −1.63595 + 2.83354i −0.0185903 + 0.0321993i
\(89\) 131.622 75.9919i 1.47890 0.853842i 0.479182 0.877715i \(-0.340933\pi\)
0.999715 + 0.0238738i \(0.00759998\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −95.8586 39.6181i −1.05339 0.435363i
\(92\) −48.6014 −0.528277
\(93\) 24.9581 + 43.2287i 0.268367 + 0.464825i
\(94\) −30.8546 17.8139i −0.328241 0.189510i
\(95\) 21.5805 37.3785i 0.227163 0.393458i
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 144.310i 1.48773i −0.668331 0.743864i \(-0.732991\pi\)
0.668331 0.743864i \(-0.267009\pi\)
\(98\) −17.8305 + 66.9632i −0.181943 + 0.683298i
\(99\) −3.47036 −0.0350542
\(100\) 5.00000 + 8.66025i 0.0500000 + 0.0866025i
\(101\) −33.8480 19.5422i −0.335129 0.193487i 0.322987 0.946403i \(-0.395313\pi\)
−0.658116 + 0.752917i \(0.728646\pi\)
\(102\) −15.4533 + 26.7659i −0.151503 + 0.262411i
\(103\) 32.7730 18.9215i 0.318185 0.183704i −0.332398 0.943139i \(-0.607858\pi\)
0.650583 + 0.759435i \(0.274525\pi\)
\(104\) 41.9104i 0.402985i
\(105\) 10.3553 25.0553i 0.0986217 0.238622i
\(106\) 29.4609 0.277933
\(107\) −41.5160 71.9079i −0.388000 0.672036i 0.604180 0.796848i \(-0.293501\pi\)
−0.992180 + 0.124811i \(0.960167\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) 23.8962 41.3894i 0.219231 0.379719i −0.735342 0.677696i \(-0.762978\pi\)
0.954573 + 0.297977i \(0.0963118\pi\)
\(110\) 3.16800 1.82904i 0.0288000 0.0166277i
\(111\) 92.3457i 0.831943i
\(112\) 27.7576 3.67646i 0.247836 0.0328255i
\(113\) −16.2283 −0.143613 −0.0718064 0.997419i \(-0.522876\pi\)
−0.0718064 + 0.997419i \(0.522876\pi\)
\(114\) 23.6402 + 40.9461i 0.207370 + 0.359176i
\(115\) 47.0582 + 27.1690i 0.409201 + 0.236252i
\(116\) −49.0382 + 84.9366i −0.422743 + 0.732212i
\(117\) −38.4972 + 22.2264i −0.329036 + 0.189969i
\(118\) 34.5246i 0.292581i
\(119\) −70.0292 + 53.8224i −0.588481 + 0.452289i
\(120\) −10.9545 −0.0912871
\(121\) 59.8309 + 103.630i 0.494470 + 0.856448i
\(122\) −7.82592 4.51830i −0.0641469 0.0370352i
\(123\) 32.9434 57.0597i 0.267833 0.463900i
\(124\) 49.9162 28.8191i 0.402550 0.232412i
\(125\) 11.1803i 0.0894427i
\(126\) 18.0977 + 23.5472i 0.143633 + 0.186883i
\(127\) 80.5643 0.634365 0.317182 0.948365i \(-0.397263\pi\)
0.317182 + 0.948365i \(0.397263\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) 95.3661 + 55.0597i 0.739272 + 0.426819i
\(130\) 23.4286 40.5796i 0.180220 0.312151i
\(131\) 107.981 62.3429i 0.824283 0.475900i −0.0276082 0.999619i \(-0.508789\pi\)
0.851891 + 0.523719i \(0.175456\pi\)
\(132\) 4.00723i 0.0303578i
\(133\) 17.7409 + 133.945i 0.133390 + 1.00711i
\(134\) 176.056 1.31385
\(135\) −5.80948 10.0623i −0.0430331 0.0745356i
\(136\) 30.9066 + 17.8439i 0.227254 + 0.131205i
\(137\) 38.0330 65.8750i 0.277613 0.480840i −0.693178 0.720766i \(-0.743790\pi\)
0.970791 + 0.239927i \(0.0771234\pi\)
\(138\) −51.5496 + 29.7622i −0.373548 + 0.215668i
\(139\) 91.7680i 0.660201i −0.943946 0.330101i \(-0.892917\pi\)
0.943946 0.330101i \(-0.107083\pi\)
\(140\) −28.9314 11.9572i −0.206653 0.0854089i
\(141\) −43.6350 −0.309468
\(142\) 84.1263 + 145.711i 0.592439 + 1.02613i
\(143\) −14.8444 8.57039i −0.103807 0.0599328i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 94.9620 54.8264i 0.654911 0.378113i
\(146\) 55.9032i 0.382898i
\(147\) 22.0944 + 81.9441i 0.150302 + 0.557443i
\(148\) −106.632 −0.720484
\(149\) 49.4579 + 85.6637i 0.331933 + 0.574924i 0.982891 0.184190i \(-0.0589660\pi\)
−0.650958 + 0.759114i \(0.725633\pi\)
\(150\) 10.6066 + 6.12372i 0.0707107 + 0.0408248i
\(151\) −48.8950 + 84.6886i −0.323808 + 0.560852i −0.981270 0.192635i \(-0.938297\pi\)
0.657462 + 0.753487i \(0.271630\pi\)
\(152\) 47.2804 27.2974i 0.311055 0.179588i
\(153\) 37.8527i 0.247403i
\(154\) −4.37406 + 10.5833i −0.0284030 + 0.0687230i
\(155\) −64.4415 −0.415752
\(156\) 25.6648 + 44.4527i 0.164518 + 0.284953i
\(157\) 115.530 + 66.7013i 0.735860 + 0.424849i 0.820562 0.571557i \(-0.193661\pi\)
−0.0847022 + 0.996406i \(0.526994\pi\)
\(158\) 65.6698 113.743i 0.415632 0.719895i
\(159\) 31.2480 18.0411i 0.196529 0.113466i
\(160\) 12.6491i 0.0790569i
\(161\) −168.632 + 22.3352i −1.04741 + 0.138728i
\(162\) 12.7279 0.0785674
\(163\) 16.3746 + 28.3616i 0.100458 + 0.173998i 0.911873 0.410472i \(-0.134636\pi\)
−0.811416 + 0.584469i \(0.801303\pi\)
\(164\) −65.8869 38.0398i −0.401749 0.231950i
\(165\) 2.24011 3.87999i 0.0135764 0.0235151i
\(166\) 7.09942 4.09885i 0.0427676 0.0246919i
\(167\) 171.659i 1.02790i −0.857821 0.513948i \(-0.828182\pi\)
0.857821 0.513948i \(-0.171818\pi\)
\(168\) 27.1900 20.8975i 0.161845 0.124390i
\(169\) −50.5603 −0.299173
\(170\) −19.9501 34.5546i −0.117354 0.203262i
\(171\) 50.1485 + 28.9532i 0.293266 + 0.169317i
\(172\) 63.5774 110.119i 0.369636 0.640229i
\(173\) 175.336 101.230i 1.01350 0.585145i 0.101287 0.994857i \(-0.467704\pi\)
0.912215 + 0.409712i \(0.134371\pi\)
\(174\) 120.119i 0.690336i
\(175\) 21.3284 + 27.7507i 0.121876 + 0.158575i
\(176\) 4.62715 0.0262906
\(177\) −21.1419 36.6188i −0.119446 0.206886i
\(178\) −186.141 107.469i −1.04574 0.603757i
\(179\) 39.3459 68.1491i 0.219810 0.380721i −0.734940 0.678132i \(-0.762790\pi\)
0.954750 + 0.297411i \(0.0961230\pi\)
\(180\) −11.6190 + 6.70820i −0.0645497 + 0.0372678i
\(181\) 58.1509i 0.321276i −0.987013 0.160638i \(-0.948645\pi\)
0.987013 0.160638i \(-0.0513551\pi\)
\(182\) 19.2602 + 145.416i 0.105825 + 0.798992i
\(183\) −11.0675 −0.0604783
\(184\) 34.3664 + 59.5244i 0.186774 + 0.323502i
\(185\) 103.246 + 59.6089i 0.558084 + 0.322210i
\(186\) 35.2961 61.1346i 0.189764 0.328681i
\(187\) −12.6404 + 7.29793i −0.0675956 + 0.0390263i
\(188\) 50.3854i 0.268008i
\(189\) 33.6152 + 13.8931i 0.177858 + 0.0735083i
\(190\) −61.0388 −0.321257
\(191\) −184.204 319.051i −0.964419 1.67042i −0.711168 0.703022i \(-0.751834\pi\)
−0.253251 0.967401i \(-0.581500\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) −140.409 + 243.196i −0.727510 + 1.26008i 0.230422 + 0.973091i \(0.425989\pi\)
−0.957932 + 0.286994i \(0.907344\pi\)
\(194\) −176.742 + 102.042i −0.911044 + 0.525991i
\(195\) 57.3882i 0.294298i
\(196\) 94.6209 25.5124i 0.482760 0.130165i
\(197\) 7.61779 0.0386690 0.0193345 0.999813i \(-0.493845\pi\)
0.0193345 + 0.999813i \(0.493845\pi\)
\(198\) 2.45392 + 4.25031i 0.0123935 + 0.0214662i
\(199\) −174.795 100.918i −0.878366 0.507125i −0.00824641 0.999966i \(-0.502625\pi\)
−0.870119 + 0.492841i \(0.835958\pi\)
\(200\) 7.07107 12.2474i 0.0353553 0.0612372i
\(201\) 186.735 107.812i 0.929031 0.536376i
\(202\) 55.2736i 0.273632i
\(203\) −131.114 + 317.240i −0.645884 + 1.56276i
\(204\) 43.7085 0.214257
\(205\) 42.5298 + 73.6638i 0.207462 + 0.359335i
\(206\) −46.3481 26.7591i −0.224991 0.129898i
\(207\) −36.4511 + 63.1351i −0.176092 + 0.305001i
\(208\) 51.3296 29.6351i 0.246777 0.142477i
\(209\) 22.3285i 0.106835i
\(210\) −38.0086 + 5.03420i −0.180994 + 0.0239724i
\(211\) 30.3818 0.143989 0.0719947 0.997405i \(-0.477064\pi\)
0.0719947 + 0.997405i \(0.477064\pi\)
\(212\) −20.8320 36.0821i −0.0982643 0.170199i
\(213\) 178.459 + 103.033i 0.837835 + 0.483724i
\(214\) −58.7126 + 101.693i −0.274358 + 0.475202i
\(215\) −123.117 + 71.0817i −0.572638 + 0.330613i
\(216\) 14.6969i 0.0680414i
\(217\) 159.950 122.933i 0.737097 0.566512i
\(218\) −67.5886 −0.310039
\(219\) 34.2336 + 59.2943i 0.156318 + 0.270750i
\(220\) −4.48022 2.58666i −0.0203646 0.0117575i
\(221\) −93.4808 + 161.914i −0.422990 + 0.732640i
\(222\) −113.100 + 65.2983i −0.509459 + 0.294136i
\(223\) 16.7377i 0.0750569i 0.999296 + 0.0375284i \(0.0119485\pi\)
−0.999296 + 0.0375284i \(0.988052\pi\)
\(224\) −24.1303 31.3963i −0.107725 0.140162i
\(225\) 15.0000 0.0666667
\(226\) 11.4751 + 19.8755i 0.0507748 + 0.0879446i
\(227\) −366.738 211.736i −1.61558 0.932758i −0.988044 0.154175i \(-0.950728\pi\)
−0.627541 0.778583i \(-0.715939\pi\)
\(228\) 33.4323 57.9065i 0.146633 0.253976i
\(229\) −350.596 + 202.417i −1.53099 + 0.883916i −0.531672 + 0.846951i \(0.678436\pi\)
−0.999317 + 0.0369660i \(0.988231\pi\)
\(230\) 76.8456i 0.334111i
\(231\) 1.84155 + 13.9039i 0.00797209 + 0.0601900i
\(232\) 138.701 0.597849
\(233\) −138.649 240.147i −0.595061 1.03068i −0.993538 0.113497i \(-0.963795\pi\)
0.398478 0.917178i \(-0.369539\pi\)
\(234\) 54.4432 + 31.4328i 0.232663 + 0.134328i
\(235\) 28.1663 48.7855i 0.119857 0.207598i
\(236\) −42.2838 + 24.4125i −0.179169 + 0.103443i
\(237\) 160.858i 0.678724i
\(238\) 115.437 + 47.7097i 0.485029 + 0.200461i
\(239\) 290.247 1.21442 0.607211 0.794541i \(-0.292288\pi\)
0.607211 + 0.794541i \(0.292288\pi\)
\(240\) 7.74597 + 13.4164i 0.0322749 + 0.0559017i
\(241\) −350.574 202.404i −1.45466 0.839850i −0.455922 0.890020i \(-0.650690\pi\)
−0.998741 + 0.0501703i \(0.984024\pi\)
\(242\) 84.6137 146.555i 0.349643 0.605600i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 12.7797i 0.0523757i
\(245\) −105.878 28.1924i −0.432156 0.115071i
\(246\) −93.1781 −0.378773
\(247\) 143.005 + 247.693i 0.578970 + 1.00280i
\(248\) −70.5922 40.7564i −0.284646 0.164340i
\(249\) 5.02005 8.69498i 0.0201608 0.0349196i
\(250\) −13.6931 + 7.90569i −0.0547723 + 0.0316228i
\(251\) 155.805i 0.620739i 0.950616 + 0.310369i \(0.100453\pi\)
−0.950616 + 0.310369i \(0.899547\pi\)
\(252\) 16.0423 38.8155i 0.0636600 0.154030i
\(253\) −28.1108 −0.111110
\(254\) −56.9676 98.6707i −0.224282 0.388467i
\(255\) −42.3206 24.4338i −0.165963 0.0958189i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −22.4315 + 12.9508i −0.0872821 + 0.0503923i −0.543006 0.839729i \(-0.682714\pi\)
0.455724 + 0.890121i \(0.349381\pi\)
\(258\) 155.732i 0.603613i
\(259\) −369.980 + 49.0033i −1.42849 + 0.189202i
\(260\) −66.2662 −0.254870
\(261\) 73.5573 + 127.405i 0.281829 + 0.488142i
\(262\) −152.708 88.1662i −0.582856 0.336512i
\(263\) 157.902 273.495i 0.600389 1.03990i −0.392373 0.919806i \(-0.628346\pi\)
0.992762 0.120098i \(-0.0383209\pi\)
\(264\) 4.90784 2.83354i 0.0185903 0.0107331i
\(265\) 46.5818i 0.175781i
\(266\) 151.504 116.442i 0.569564 0.437751i
\(267\) −263.244 −0.985931
\(268\) −124.490 215.623i −0.464516 0.804565i
\(269\) −41.4157 23.9114i −0.153962 0.0888899i 0.421040 0.907042i \(-0.361665\pi\)
−0.575002 + 0.818152i \(0.694999\pi\)
\(270\) −8.21584 + 14.2302i −0.0304290 + 0.0527046i
\(271\) 294.580 170.076i 1.08701 0.627587i 0.154233 0.988035i \(-0.450709\pi\)
0.932779 + 0.360448i \(0.117376\pi\)
\(272\) 50.4703i 0.185552i
\(273\) 109.478 + 142.443i 0.401017 + 0.521769i
\(274\) −107.573 −0.392604
\(275\) 2.89197 + 5.00904i 0.0105163 + 0.0182147i
\(276\) 72.9022 + 42.0901i 0.264138 + 0.152500i
\(277\) −105.293 + 182.374i −0.380121 + 0.658388i −0.991079 0.133274i \(-0.957451\pi\)
0.610959 + 0.791663i \(0.290784\pi\)
\(278\) −112.392 + 64.8898i −0.404289 + 0.233416i
\(279\) 86.4574i 0.309883i
\(280\) 5.81299 + 43.8886i 0.0207607 + 0.156745i
\(281\) 471.785 1.67895 0.839476 0.543397i \(-0.182862\pi\)
0.839476 + 0.543397i \(0.182862\pi\)
\(282\) 30.8546 + 53.4418i 0.109414 + 0.189510i
\(283\) 405.534 + 234.135i 1.43298 + 0.827333i 0.997347 0.0727901i \(-0.0231903\pi\)
0.435636 + 0.900123i \(0.356524\pi\)
\(284\) 118.973 206.067i 0.418917 0.725586i
\(285\) −64.7414 + 37.3785i −0.227163 + 0.131153i
\(286\) 24.2407i 0.0847578i
\(287\) −246.089 101.708i −0.857453 0.354383i
\(288\) −16.9706 −0.0589256
\(289\) −64.8985 112.408i −0.224562 0.388953i
\(290\) −134.297 77.5362i −0.463092 0.267366i
\(291\) −124.976 + 216.464i −0.429470 + 0.743864i
\(292\) 68.4671 39.5295i 0.234476 0.135375i
\(293\) 63.5067i 0.216746i −0.994110 0.108373i \(-0.965436\pi\)
0.994110 0.108373i \(-0.0345642\pi\)
\(294\) 84.7375 85.0032i 0.288223 0.289127i
\(295\) 54.5881 0.185044
\(296\) 75.3999 + 130.597i 0.254730 + 0.441204i
\(297\) 5.20555 + 3.00542i 0.0175271 + 0.0101193i
\(298\) 69.9441 121.147i 0.234712 0.406533i
\(299\) −311.836 + 180.039i −1.04293 + 0.602136i
\(300\) 17.3205i 0.0577350i
\(301\) 169.988 411.298i 0.564745 1.36644i
\(302\) 138.296 0.457934
\(303\) 33.8480 + 58.6265i 0.111710 + 0.193487i
\(304\) −66.8646 38.6043i −0.219949 0.126988i
\(305\) 7.14406 12.3739i 0.0234231 0.0405701i
\(306\) 46.3599 26.7659i 0.151503 0.0874703i
\(307\) 211.610i 0.689283i −0.938734 0.344642i \(-0.888000\pi\)
0.938734 0.344642i \(-0.112000\pi\)
\(308\) 16.0548 2.12644i 0.0521261 0.00690403i
\(309\) −65.5460 −0.212123
\(310\) 45.5670 + 78.9244i 0.146990 + 0.254595i
\(311\) 58.3090 + 33.6647i 0.187489 + 0.108247i 0.590806 0.806813i \(-0.298810\pi\)
−0.403318 + 0.915060i \(0.632143\pi\)
\(312\) 36.2955 62.8656i 0.116332 0.201492i
\(313\) −119.714 + 69.1168i −0.382472 + 0.220821i −0.678893 0.734237i \(-0.737540\pi\)
0.296421 + 0.955057i \(0.404207\pi\)
\(314\) 188.660i 0.600827i
\(315\) −37.2314 + 28.6150i −0.118195 + 0.0908413i
\(316\) −185.742 −0.587792
\(317\) −9.91216 17.1684i −0.0312686 0.0541589i 0.849968 0.526835i \(-0.176621\pi\)
−0.881236 + 0.472676i \(0.843288\pi\)
\(318\) −44.1914 25.5139i −0.138967 0.0802325i
\(319\) −28.3634 + 49.1268i −0.0889135 + 0.154003i
\(320\) 15.4919 8.94427i 0.0484123 0.0279508i
\(321\) 143.816i 0.448024i
\(322\) 146.596 + 190.738i 0.455267 + 0.592355i
\(323\) 243.546 0.754013
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 64.1619 + 37.0439i 0.197421 + 0.113981i
\(326\) 23.1572 40.1094i 0.0710342 0.123035i
\(327\) −71.6885 + 41.3894i −0.219231 + 0.126573i
\(328\) 107.593i 0.328027i
\(329\) 23.1550 + 174.822i 0.0703799 + 0.531374i
\(330\) −6.33599 −0.0192000
\(331\) 131.139 + 227.139i 0.396189 + 0.686220i 0.993252 0.115974i \(-0.0369991\pi\)
−0.597063 + 0.802194i \(0.703666\pi\)
\(332\) −10.0401 5.79665i −0.0302412 0.0174598i
\(333\) −79.9737 + 138.519i −0.240161 + 0.415972i
\(334\) −210.238 + 121.381i −0.629455 + 0.363416i
\(335\) 278.368i 0.830951i
\(336\) −44.8203 18.5241i −0.133394 0.0551312i
\(337\) 578.125 1.71550 0.857752 0.514063i \(-0.171860\pi\)
0.857752 + 0.514063i \(0.171860\pi\)
\(338\) 35.7515 + 61.9235i 0.105774 + 0.183206i
\(339\) 24.3424 + 14.0541i 0.0718064 + 0.0414575i
\(340\) −28.2137 + 48.8676i −0.0829816 + 0.143728i
\(341\) 28.8712 16.6688i 0.0846664 0.0488822i
\(342\) 81.8921i 0.239451i
\(343\) 316.582 132.004i 0.922978 0.384852i
\(344\) −179.824 −0.522744
\(345\) −47.0582 81.5071i −0.136400 0.236252i
\(346\) −247.962 143.161i −0.716654 0.413760i
\(347\) −229.861 + 398.131i −0.662423 + 1.14735i 0.317554 + 0.948240i \(0.397139\pi\)
−0.979977 + 0.199110i \(0.936195\pi\)
\(348\) 147.115 84.9366i 0.422743 0.244071i
\(349\) 389.147i 1.11504i −0.830165 0.557518i \(-0.811754\pi\)
0.830165 0.557518i \(-0.188246\pi\)
\(350\) 18.9061 45.7445i 0.0540173 0.130699i
\(351\) 76.9943 0.219357
\(352\) −3.27189 5.66708i −0.00929515 0.0160997i
\(353\) 559.415 + 322.978i 1.58475 + 0.914953i 0.994153 + 0.107983i \(0.0344393\pi\)
0.590593 + 0.806970i \(0.298894\pi\)
\(354\) −29.8991 + 51.7868i −0.0844608 + 0.146290i
\(355\) −230.389 + 133.015i −0.648984 + 0.374691i
\(356\) 303.968i 0.853842i
\(357\) 151.655 20.0866i 0.424805 0.0562649i
\(358\) −111.287 −0.310858
\(359\) 33.0206 + 57.1934i 0.0919794 + 0.159313i 0.908344 0.418224i \(-0.137347\pi\)
−0.816365 + 0.577537i \(0.804014\pi\)
\(360\) 16.4317 + 9.48683i 0.0456435 + 0.0263523i
\(361\) 5.78661 10.0227i 0.0160294 0.0277637i
\(362\) −71.2200 + 41.1189i −0.196740 + 0.113588i
\(363\) 207.260i 0.570965i
\(364\) 164.479 126.414i 0.451866 0.347291i
\(365\) −88.3907 −0.242166
\(366\) 7.82592 + 13.5549i 0.0213823 + 0.0370352i
\(367\) 519.556 + 299.966i 1.41568 + 0.817346i 0.995916 0.0902858i \(-0.0287781\pi\)
0.419768 + 0.907631i \(0.362111\pi\)
\(368\) 48.6014 84.1802i 0.132069 0.228750i
\(369\) −98.8303 + 57.0597i −0.267833 + 0.154633i
\(370\) 168.599i 0.455674i
\(371\) −88.8627 115.621i −0.239522 0.311646i
\(372\) −99.8324 −0.268367
\(373\) −202.376 350.526i −0.542564 0.939748i −0.998756 0.0498667i \(-0.984120\pi\)
0.456192 0.889881i \(-0.349213\pi\)
\(374\) 17.8762 + 10.3208i 0.0477973 + 0.0275958i
\(375\) −9.68246 + 16.7705i −0.0258199 + 0.0447214i
\(376\) 61.7093 35.6279i 0.164120 0.0947550i
\(377\) 726.627i 1.92739i
\(378\) −6.75409 50.9939i −0.0178680 0.134905i
\(379\) −239.675 −0.632388 −0.316194 0.948695i \(-0.602405\pi\)
−0.316194 + 0.948695i \(0.602405\pi\)
\(380\) 43.1609 + 74.7569i 0.113581 + 0.196729i
\(381\) −120.846 69.7707i −0.317182 0.183125i
\(382\) −260.504 + 451.206i −0.681947 + 1.18117i
\(383\) 553.486 319.555i 1.44513 0.834347i 0.446947 0.894561i \(-0.352511\pi\)
0.998186 + 0.0602133i \(0.0191781\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −16.7337 6.91600i −0.0434642 0.0179636i
\(386\) 397.138 1.02885
\(387\) −95.3661 165.179i −0.246424 0.426819i
\(388\) 249.952 + 144.310i 0.644205 + 0.371932i
\(389\) −260.797 + 451.714i −0.670429 + 1.16122i 0.307353 + 0.951596i \(0.400557\pi\)
−0.977782 + 0.209622i \(0.932777\pi\)
\(390\) −70.2859 + 40.5796i −0.180220 + 0.104050i
\(391\) 306.616i 0.784184i
\(392\) −98.1533 97.8465i −0.250391 0.249608i
\(393\) −215.962 −0.549522
\(394\) −5.38659 9.32985i −0.0136716 0.0236798i
\(395\) 179.844 + 103.833i 0.455302 + 0.262869i
\(396\) 3.47036 6.01085i 0.00876355 0.0151789i
\(397\) 125.712 72.5800i 0.316656 0.182821i −0.333245 0.942840i \(-0.608144\pi\)
0.649901 + 0.760019i \(0.274810\pi\)
\(398\) 285.439i 0.717182i
\(399\) 89.3887 216.282i 0.224032 0.542060i
\(400\) −20.0000 −0.0500000
\(401\) −107.021 185.366i −0.266886 0.462260i 0.701170 0.712994i \(-0.252661\pi\)
−0.968056 + 0.250734i \(0.919328\pi\)
\(402\) −264.084 152.469i −0.656924 0.379275i
\(403\) 213.515 369.818i 0.529813 0.917663i
\(404\) 67.6960 39.0843i 0.167564 0.0967434i
\(405\) 20.1246i 0.0496904i
\(406\) 481.250 63.7410i 1.18535 0.156998i
\(407\) −61.6751 −0.151536
\(408\) −30.9066 53.5318i −0.0757515 0.131205i
\(409\) −479.754 276.986i −1.17299 0.677228i −0.218610 0.975812i \(-0.570152\pi\)
−0.954383 + 0.298585i \(0.903486\pi\)
\(410\) 60.1462 104.176i 0.146698 0.254089i
\(411\) −114.099 + 65.8750i −0.277613 + 0.160280i
\(412\) 75.6861i 0.183704i
\(413\) −135.493 + 104.136i −0.328070 + 0.252145i
\(414\) 103.099 0.249032
\(415\) 6.48085 + 11.2252i 0.0156165 + 0.0270486i
\(416\) −72.5910 41.9104i −0.174497 0.100746i
\(417\) −79.4734 + 137.652i −0.190584 + 0.330101i
\(418\) 27.3467 15.7886i 0.0654228 0.0377719i
\(419\) 268.003i 0.639626i 0.947481 + 0.319813i \(0.103620\pi\)
−0.947481 + 0.319813i \(0.896380\pi\)
\(420\) 33.0418 + 42.9912i 0.0786709 + 0.102360i
\(421\) −9.12915 −0.0216844 −0.0108422 0.999941i \(-0.503451\pi\)
−0.0108422 + 0.999941i \(0.503451\pi\)
\(422\) −21.4831 37.2099i −0.0509079 0.0881751i
\(423\) 65.4526 + 37.7891i 0.154734 + 0.0893358i
\(424\) −29.4609 + 51.0278i −0.0694833 + 0.120349i
\(425\) 54.6357 31.5439i 0.128554 0.0742210i
\(426\) 291.422i 0.684089i
\(427\) 5.87299 + 44.3416i 0.0137541 + 0.103845i
\(428\) 166.064 0.388000
\(429\) 14.8444 + 25.7112i 0.0346022 + 0.0599328i
\(430\) 174.114 + 100.525i 0.404916 + 0.233778i
\(431\) 134.221 232.478i 0.311419 0.539393i −0.667251 0.744833i \(-0.732529\pi\)
0.978670 + 0.205440i \(0.0658626\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 472.254i 1.09066i −0.838223 0.545328i \(-0.816405\pi\)
0.838223 0.545328i \(-0.183595\pi\)
\(434\) −263.663 108.971i −0.607519 0.251086i
\(435\) −189.924 −0.436607
\(436\) 47.7924 + 82.7788i 0.109616 + 0.189860i
\(437\) 406.215 + 234.528i 0.929553 + 0.536678i
\(438\) 48.4136 83.8548i 0.110533 0.191449i
\(439\) 475.788 274.696i 1.08380 0.625731i 0.151880 0.988399i \(-0.451467\pi\)
0.931919 + 0.362667i \(0.118134\pi\)
\(440\) 7.31617i 0.0166277i
\(441\) 37.8241 142.050i 0.0857689 0.322110i
\(442\) 264.404 0.598198
\(443\) −235.405 407.734i −0.531388 0.920392i −0.999329 0.0366317i \(-0.988337\pi\)
0.467940 0.883760i \(-0.344996\pi\)
\(444\) 159.947 + 92.3457i 0.360242 + 0.207986i
\(445\) 169.923 294.315i 0.381850 0.661383i
\(446\) 20.4994 11.8353i 0.0459628 0.0265366i
\(447\) 171.327i 0.383283i
\(448\) −21.3898 + 51.7540i −0.0477450 + 0.115522i
\(449\) 559.525 1.24616 0.623079 0.782159i \(-0.285882\pi\)
0.623079 + 0.782159i \(0.285882\pi\)
\(450\) −10.6066 18.3712i −0.0235702 0.0408248i
\(451\) −38.1086 22.0020i −0.0844980 0.0487849i
\(452\) 16.2283 28.1082i 0.0359032 0.0621862i
\(453\) 146.685 84.6886i 0.323808 0.186951i
\(454\) 598.880i 1.31912i
\(455\) −229.924 + 30.4531i −0.505327 + 0.0669299i
\(456\) −94.5609 −0.207370
\(457\) −313.689 543.325i −0.686409 1.18890i −0.972992 0.230840i \(-0.925853\pi\)
0.286583 0.958055i \(-0.407481\pi\)
\(458\) 495.818 + 286.261i 1.08257 + 0.625023i
\(459\) 32.7814 56.7790i 0.0714192 0.123702i
\(460\) −94.1163 + 54.3381i −0.204601 + 0.118126i
\(461\) 223.659i 0.485160i 0.970131 + 0.242580i \(0.0779936\pi\)
−0.970131 + 0.242580i \(0.922006\pi\)
\(462\) 15.7265 12.0870i 0.0340401 0.0261623i
\(463\) −397.204 −0.857893 −0.428946 0.903330i \(-0.641115\pi\)
−0.428946 + 0.903330i \(0.641115\pi\)
\(464\) −98.0764 169.873i −0.211371 0.366106i
\(465\) 96.6623 + 55.8080i 0.207876 + 0.120017i
\(466\) −196.079 + 339.620i −0.420771 + 0.728797i
\(467\) −289.014 + 166.862i −0.618874 + 0.357307i −0.776430 0.630203i \(-0.782972\pi\)
0.157557 + 0.987510i \(0.449638\pi\)
\(468\) 88.9054i 0.189969i
\(469\) −531.035 690.937i −1.13227 1.47321i
\(470\) −79.6663 −0.169503
\(471\) −115.530 200.104i −0.245287 0.424849i
\(472\) 59.7983 + 34.5246i 0.126691 + 0.0731452i
\(473\) 36.7728 63.6924i 0.0777438 0.134656i
\(474\) −197.009 + 113.743i −0.415632 + 0.239965i
\(475\) 96.5108i 0.203181i
\(476\) −23.1940 175.117i −0.0487268 0.367892i
\(477\) −62.4961 −0.131019
\(478\) −205.235 355.478i −0.429363 0.743678i
\(479\) 527.265 + 304.417i 1.10076 + 0.635526i 0.936421 0.350878i \(-0.114117\pi\)
0.164341 + 0.986404i \(0.447450\pi\)
\(480\) 10.9545 18.9737i 0.0228218 0.0395285i
\(481\) −684.169 + 395.005i −1.42239 + 0.821217i
\(482\) 572.484i 1.18773i
\(483\) 272.291 + 112.537i 0.563750 + 0.232996i
\(484\) −239.324 −0.494470
\(485\) −161.343 279.454i −0.332666 0.576195i
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 159.238 275.809i 0.326978 0.566343i −0.654932 0.755687i \(-0.727303\pi\)
0.981911 + 0.189344i \(0.0606363\pi\)
\(488\) 15.6518 9.03659i 0.0320734 0.0185176i
\(489\) 56.7232i 0.115998i
\(490\) 40.3387 + 149.609i 0.0823238 + 0.305324i
\(491\) 523.303 1.06579 0.532895 0.846181i \(-0.321104\pi\)
0.532895 + 0.846181i \(0.321104\pi\)
\(492\) 65.8869 + 114.119i 0.133916 + 0.231950i
\(493\) 535.847 + 309.371i 1.08691 + 0.627528i
\(494\) 202.240 350.290i 0.409393 0.709090i
\(495\) −6.72033 + 3.87999i −0.0135764 + 0.00783836i
\(496\) 115.277i 0.232412i
\(497\) 318.100 769.663i 0.640039 1.54862i
\(498\) −14.1988 −0.0285117
\(499\) 391.909 + 678.806i 0.785388 + 1.36033i 0.928767 + 0.370664i \(0.120870\pi\)
−0.143379 + 0.989668i \(0.545797\pi\)
\(500\) 19.3649 + 11.1803i 0.0387298 + 0.0223607i
\(501\) −148.661 + 257.488i −0.296728 + 0.513948i
\(502\) 190.822 110.171i 0.380123 0.219464i
\(503\) 58.0772i 0.115462i −0.998332 0.0577308i \(-0.981613\pi\)
0.998332 0.0577308i \(-0.0183865\pi\)
\(504\) −58.8827 + 7.79895i −0.116831 + 0.0154741i
\(505\) −87.3952 −0.173060
\(506\) 19.8773 + 34.4286i 0.0392833 + 0.0680406i
\(507\) 75.8404 + 43.7865i 0.149587 + 0.0863639i
\(508\) −80.5643 + 139.541i −0.158591 + 0.274688i
\(509\) −811.110 + 468.295i −1.59354 + 0.920029i −0.600843 + 0.799367i \(0.705168\pi\)
−0.992694 + 0.120662i \(0.961498\pi\)
\(510\) 69.1092i 0.135508i
\(511\) 219.394 168.620i 0.429343 0.329981i
\(512\) 22.6274 0.0441942
\(513\) −50.1485 86.8597i −0.0977553 0.169317i
\(514\) 31.7229 + 18.3152i 0.0617178 + 0.0356328i
\(515\) 42.3098 73.2827i 0.0821549 0.142297i
\(516\) −190.732 + 110.119i −0.369636 + 0.213410i
\(517\) 29.1426i 0.0563687i
\(518\) 321.632 + 418.480i 0.620910 + 0.807876i
\(519\) −350.672 −0.675668
\(520\) 46.8573 + 81.1592i 0.0901101 + 0.156075i
\(521\) −607.133 350.528i −1.16532 0.672799i −0.212749 0.977107i \(-0.568242\pi\)
−0.952574 + 0.304308i \(0.901575\pi\)
\(522\) 104.026 180.178i 0.199283 0.345168i
\(523\) −594.464 + 343.214i −1.13664 + 0.656241i −0.945597 0.325340i \(-0.894521\pi\)
−0.191046 + 0.981581i \(0.561188\pi\)
\(524\) 249.372i 0.475900i
\(525\) −7.95977 60.0969i −0.0151615 0.114470i
\(526\) −446.615 −0.849078
\(527\) −181.814 314.910i −0.344997 0.597553i
\(528\) −6.94073 4.00723i −0.0131453 0.00758945i
\(529\) −30.7626 + 53.2824i −0.0581524 + 0.100723i
\(530\) 57.0509 32.9383i 0.107643 0.0621478i
\(531\) 73.2376i 0.137924i
\(532\) −249.741 103.217i −0.469438 0.194017i
\(533\) −563.657 −1.05752
\(534\) 186.141 + 322.406i 0.348579 + 0.603757i
\(535\) −160.791 92.8327i −0.300544 0.173519i
\(536\) −176.056 + 304.937i −0.328462 + 0.568913i
\(537\) −118.038 + 68.1491i −0.219810 + 0.126907i
\(538\) 67.6316i 0.125709i
\(539\) 54.7282 14.7562i 0.101537 0.0273770i
\(540\) 23.2379 0.0430331
\(541\) −398.250 689.789i −0.736136 1.27503i −0.954223 0.299096i \(-0.903315\pi\)
0.218087 0.975929i \(-0.430018\pi\)
\(542\) −416.599 240.524i −0.768634 0.443771i
\(543\) −50.3602 + 87.2263i −0.0927443 + 0.160638i
\(544\) −61.8132 + 35.6879i −0.113627 + 0.0656027i
\(545\) 106.867i 0.196086i
\(546\) 97.0440 234.805i 0.177736 0.430045i
\(547\) −395.055 −0.722221 −0.361111 0.932523i \(-0.617602\pi\)
−0.361111 + 0.932523i \(0.617602\pi\)
\(548\) 76.0659 + 131.750i 0.138806 + 0.240420i
\(549\) 16.6013 + 9.58476i 0.0302391 + 0.0174586i
\(550\) 4.08986 7.08385i 0.00743612 0.0128797i
\(551\) 819.730 473.271i 1.48771 0.858932i
\(552\) 119.049i 0.215668i
\(553\) −644.470 + 85.3592i −1.16541 + 0.154357i
\(554\) 297.815 0.537572
\(555\) −103.246 178.827i −0.186028 0.322210i
\(556\) 158.947 + 91.7680i 0.285876 + 0.165050i
\(557\) 20.8443 36.1034i 0.0374224 0.0648175i −0.846708 0.532059i \(-0.821419\pi\)
0.884130 + 0.467241i \(0.154752\pi\)
\(558\) −105.888 + 61.1346i −0.189764 + 0.109560i
\(559\) 942.063i 1.68526i
\(560\) 49.6419 38.1534i 0.0886463 0.0681310i
\(561\) 25.2808 0.0450637
\(562\) −333.603 577.817i −0.593599 1.02814i
\(563\) −640.642 369.875i −1.13791 0.656972i −0.191996 0.981396i \(-0.561496\pi\)
−0.945912 + 0.324424i \(0.894830\pi\)
\(564\) 43.6350 75.5781i 0.0773671 0.134004i
\(565\) −31.4259 + 18.1437i −0.0556210 + 0.0321128i
\(566\) 662.234i 1.17003i
\(567\) −38.3911 49.9512i −0.0677091 0.0880974i
\(568\) −336.505 −0.592439
\(569\) −2.38030 4.12281i −0.00418331 0.00724570i 0.863926 0.503618i \(-0.167998\pi\)
−0.868109 + 0.496373i \(0.834665\pi\)
\(570\) 91.5582 + 52.8611i 0.160628 + 0.0927388i
\(571\) −399.848 + 692.557i −0.700260 + 1.21289i 0.268116 + 0.963387i \(0.413599\pi\)
−0.968375 + 0.249498i \(0.919734\pi\)
\(572\) 29.6887 17.1408i 0.0519033 0.0299664i
\(573\) 638.101i 1.11362i
\(574\) 49.4451 + 373.315i 0.0861412 + 0.650374i
\(575\) 121.504 0.211311
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −148.871 85.9510i −0.258009 0.148962i 0.365417 0.930844i \(-0.380926\pi\)
−0.623426 + 0.781882i \(0.714260\pi\)
\(578\) −91.7804 + 158.968i −0.158790 + 0.275032i
\(579\) 421.228 243.196i 0.727510 0.420028i
\(580\) 219.305i 0.378113i
\(581\) −37.5000 15.4986i −0.0645439 0.0266758i
\(582\) 353.485 0.607362
\(583\) −12.0491 20.8697i −0.0206675 0.0357971i
\(584\) −96.8271 55.9032i −0.165800 0.0957246i
\(585\) −49.6996 + 86.0823i −0.0849566 + 0.147149i
\(586\) −77.7795 + 44.9060i −0.132730 + 0.0766314i
\(587\) 724.352i 1.23399i 0.786967 + 0.616994i \(0.211650\pi\)
−0.786967 + 0.616994i \(0.788350\pi\)
\(588\) −164.026 43.6755i −0.278955 0.0742781i
\(589\) −556.271 −0.944433
\(590\) −38.5996 66.8565i −0.0654231 0.113316i
\(591\) −11.4267 6.59720i −0.0193345 0.0111628i
\(592\) 106.632 184.691i 0.180121 0.311979i
\(593\) −894.293 + 516.320i −1.50808 + 0.870692i −0.508127 + 0.861282i \(0.669662\pi\)
−0.999956 + 0.00940925i \(0.997005\pi\)
\(594\) 8.50062i 0.0143108i
\(595\) −75.4357 + 182.522i −0.126783 + 0.306759i
\(596\) −197.832 −0.331933
\(597\) 174.795 + 302.753i 0.292789 + 0.507125i
\(598\) 441.003 + 254.613i 0.737464 + 0.425775i
\(599\) 212.436 367.949i 0.354650 0.614272i −0.632408 0.774636i \(-0.717933\pi\)
0.987058 + 0.160363i \(0.0512666\pi\)
\(600\) −21.2132 + 12.2474i −0.0353553 + 0.0204124i
\(601\) 749.418i 1.24695i 0.781843 + 0.623476i \(0.214280\pi\)
−0.781843 + 0.623476i \(0.785720\pi\)
\(602\) −623.935 + 82.6395i −1.03644 + 0.137275i
\(603\) −373.471 −0.619354
\(604\) −97.7900 169.377i −0.161904 0.280426i
\(605\) 231.724 + 133.786i 0.383015 + 0.221134i
\(606\) 47.8683 82.9104i 0.0789906 0.136816i
\(607\) −205.133 + 118.434i −0.337945 + 0.195113i −0.659363 0.751825i \(-0.729174\pi\)
0.321418 + 0.946938i \(0.395841\pi\)
\(608\) 109.189i 0.179588i
\(609\) 471.410 362.312i 0.774072 0.594929i
\(610\) −20.2064 −0.0331253
\(611\) 186.647 + 323.283i 0.305478 + 0.529104i
\(612\) −65.5628 37.8527i −0.107129 0.0618508i
\(613\) 469.189 812.659i 0.765398 1.32571i −0.174638 0.984633i \(-0.555876\pi\)
0.940036 0.341075i \(-0.110791\pi\)
\(614\) −259.168 + 149.631i −0.422098 + 0.243698i
\(615\) 147.328i 0.239557i
\(616\) −13.9568 18.1594i −0.0226572 0.0294796i
\(617\) 225.176 0.364952 0.182476 0.983210i \(-0.441589\pi\)
0.182476 + 0.983210i \(0.441589\pi\)
\(618\) 46.3481 + 80.2772i 0.0749969 + 0.129898i
\(619\) 916.115 + 528.919i 1.47999 + 0.854473i 0.999743 0.0226591i \(-0.00721323\pi\)
0.480248 + 0.877133i \(0.340547\pi\)
\(620\) 64.4415 111.616i 0.103938 0.180026i
\(621\) 109.353 63.1351i 0.176092 0.101667i
\(622\) 95.2182i 0.153084i
\(623\) 139.691 + 1054.68i 0.224222 + 1.69290i
\(624\) −102.659 −0.164518
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 169.301 + 97.7460i 0.270449 + 0.156144i
\(627\) 19.3371 33.4928i 0.0308406 0.0534175i
\(628\) −231.060 + 133.403i −0.367930 + 0.212424i
\(629\) 672.716i 1.06950i
\(630\) 61.3727 + 25.3652i 0.0974170 + 0.0402621i
\(631\) 877.283 1.39031 0.695153 0.718862i \(-0.255336\pi\)
0.695153 + 0.718862i \(0.255336\pi\)
\(632\) 131.340 + 227.487i 0.207816 + 0.359948i
\(633\) −45.5726 26.3114i −0.0719947 0.0415662i
\(634\) −14.0179 + 24.2797i −0.0221103 + 0.0382961i
\(635\) 156.012 90.0736i 0.245688 0.141848i
\(636\) 72.1643i 0.113466i
\(637\) 512.598 514.205i 0.804707 0.807230i
\(638\) 80.2238 0.125743
\(639\) −178.459 309.100i −0.279278 0.483724i
\(640\) −21.9089 12.6491i −0.0342327 0.0197642i
\(641\) −26.8684 + 46.5374i −0.0419163 + 0.0726012i −0.886222 0.463260i \(-0.846680\pi\)
0.844306 + 0.535861i \(0.180013\pi\)
\(642\) 176.138 101.693i 0.274358 0.158401i
\(643\) 99.7799i 0.155179i 0.996985 + 0.0775893i \(0.0247223\pi\)
−0.996985 + 0.0775893i \(0.975278\pi\)
\(644\) 129.947 314.415i 0.201781 0.488222i
\(645\) 246.234 0.381759
\(646\) −172.213 298.282i −0.266584 0.461737i
\(647\) −657.905 379.842i −1.01685 0.587081i −0.103663 0.994612i \(-0.533056\pi\)
−0.913191 + 0.407531i \(0.866390\pi\)
\(648\) −12.7279 + 22.0454i −0.0196419 + 0.0340207i
\(649\) −24.4567 + 14.1201i −0.0376836 + 0.0217567i
\(650\) 104.776i 0.161194i
\(651\) −346.388 + 45.8787i −0.532086 + 0.0704742i
\(652\) −65.4983 −0.100458
\(653\) −574.896 995.749i −0.880392 1.52488i −0.850906 0.525318i \(-0.823946\pi\)
−0.0294854 0.999565i \(-0.509387\pi\)
\(654\) 101.383 + 58.5334i 0.155020 + 0.0895007i
\(655\) 139.403 241.453i 0.212829 0.368631i
\(656\) 131.774 76.0796i 0.200875 0.115975i
\(657\) 118.589i 0.180500i
\(658\) 197.740 151.977i 0.300516 0.230968i
\(659\) 213.700 0.324280 0.162140 0.986768i \(-0.448160\pi\)
0.162140 + 0.986768i \(0.448160\pi\)
\(660\) 4.48022 + 7.75997i 0.00678821 + 0.0117575i
\(661\) 665.936 + 384.479i 1.00747 + 0.581662i 0.910449 0.413621i \(-0.135736\pi\)
0.0970187 + 0.995283i \(0.469069\pi\)
\(662\) 185.458 321.223i 0.280148 0.485231i
\(663\) 280.442 161.914i 0.422990 0.244213i
\(664\) 16.3954i 0.0246919i
\(665\) 184.111 + 239.549i 0.276858 + 0.360224i
\(666\) 226.200 0.339639
\(667\) 595.832 + 1032.01i 0.893301 + 1.54724i
\(668\) 297.322 + 171.659i 0.445092 + 0.256974i
\(669\) 14.4953 25.1065i 0.0216671 0.0375284i
\(670\) 340.930 196.836i 0.508851 0.293785i
\(671\) 7.39169i 0.0110159i
\(672\) 9.00545 + 67.9919i 0.0134010 + 0.101178i
\(673\) −1299.78 −1.93133 −0.965664 0.259796i \(-0.916345\pi\)
−0.965664 + 0.259796i \(0.916345\pi\)
\(674\) −408.796 708.056i −0.606523 1.05053i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) 50.5603 87.5730i 0.0747933 0.129546i
\(677\) 1073.60 619.840i 1.58581 0.915569i 0.591826 0.806066i \(-0.298407\pi\)
0.993986 0.109504i \(-0.0349261\pi\)
\(678\) 39.7509i 0.0586297i
\(679\) 933.575 + 385.844i 1.37493 + 0.568253i
\(680\) 79.8005 0.117354
\(681\) 366.738 + 635.208i 0.538528 + 0.932758i
\(682\) −40.8301 23.5733i −0.0598682 0.0345649i
\(683\) 233.043 403.643i 0.341205 0.590985i −0.643452 0.765487i \(-0.722498\pi\)
0.984657 + 0.174502i \(0.0558316\pi\)
\(684\) −100.297 + 57.9065i −0.146633 + 0.0846586i
\(685\) 170.089i 0.248304i
\(686\) −385.528 294.391i −0.561995 0.429141i
\(687\) 701.193 1.02066
\(688\) 127.155 + 220.239i 0.184818 + 0.320114i
\(689\) −267.325 154.340i −0.387989 0.224006i
\(690\) −66.5503 + 115.268i −0.0964497 + 0.167056i
\(691\) −93.9272 + 54.2289i −0.135929 + 0.0784788i −0.566423 0.824115i \(-0.691673\pi\)
0.430493 + 0.902594i \(0.358340\pi\)
\(692\) 404.921i 0.585145i
\(693\) 9.27879 22.4507i 0.0133893 0.0323963i
\(694\) 650.145 0.936808
\(695\) −102.600 177.708i −0.147626 0.255695i
\(696\) −208.051 120.119i −0.298924 0.172584i
\(697\) −239.985 + 415.666i −0.344311 + 0.596364i
\(698\) −476.606 + 275.169i −0.682817 + 0.394224i
\(699\) 480.295i 0.687117i
\(700\) −69.3940 + 9.19115i −0.0991342 + 0.0131302i
\(701\) 528.400 0.753780 0.376890 0.926258i \(-0.376993\pi\)
0.376890 + 0.926258i \(0.376993\pi\)
\(702\) −54.4432 94.2984i −0.0775544 0.134328i
\(703\) 891.235 + 514.555i 1.26776 + 0.731942i
\(704\) −4.62715 + 8.01446i −0.00657266 + 0.0113842i
\(705\) −84.4989 + 48.7855i −0.119857 + 0.0691992i
\(706\) 913.521i 1.29394i
\(707\) 216.923 166.721i 0.306822 0.235815i
\(708\) 84.5675 0.119446
\(709\) 466.779 + 808.484i 0.658362 + 1.14032i 0.981040 + 0.193808i \(0.0620837\pi\)
−0.322678 + 0.946509i \(0.604583\pi\)
\(710\) 325.820 + 188.112i 0.458901 + 0.264947i
\(711\) −139.307 + 241.286i −0.195931 + 0.339362i
\(712\) 372.283 214.938i 0.522869 0.301879i
\(713\) 700.326i 0.982224i
\(714\) −131.837 171.536i −0.184646 0.240246i
\(715\) −38.3280 −0.0536055
\(716\) 78.6918 + 136.298i 0.109905 + 0.190361i
\(717\) −435.370 251.361i −0.607211 0.350573i
\(718\) 46.6982 80.8836i 0.0650392 0.112651i
\(719\) 557.452 321.845i 0.775316 0.447629i −0.0594517 0.998231i \(-0.518935\pi\)
0.834768 + 0.550602i \(0.185602\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 34.7821 + 262.608i 0.0482414 + 0.364227i
\(722\) −16.3670 −0.0226690
\(723\) 350.574 + 607.211i 0.484887 + 0.839850i
\(724\) 100.720 + 58.1509i 0.139116 + 0.0803189i
\(725\) 122.595 212.342i 0.169097 0.292885i
\(726\) −253.841 + 146.555i −0.349643 + 0.201867i
\(727\) 317.353i 0.436524i −0.975890 0.218262i \(-0.929961\pi\)
0.975890 0.218262i \(-0.0700388\pi\)
\(728\) −271.129 112.057i −0.372430 0.153924i
\(729\) −27.0000 −0.0370370
\(730\) 62.5016 + 108.256i 0.0856187 + 0.148296i
\(731\) −694.719 401.096i −0.950368 0.548695i
\(732\) 11.0675 19.1695i 0.0151196 0.0261879i
\(733\) −727.023 + 419.747i −0.991846 + 0.572643i −0.905826 0.423651i \(-0.860748\pi\)
−0.0860205 + 0.996293i \(0.527415\pi\)
\(734\) 848.431i 1.15590i
\(735\) 134.402 + 133.982i 0.182860 + 0.182288i
\(736\) −137.466 −0.186774
\(737\) −72.0044 124.715i −0.0976993 0.169220i
\(738\) 139.767 + 80.6946i 0.189386 + 0.109342i
\(739\) 459.403 795.709i 0.621654 1.07674i −0.367523 0.930014i \(-0.619794\pi\)
0.989178 0.146723i \(-0.0468725\pi\)
\(740\) −206.491 + 119.218i −0.279042 + 0.161105i
\(741\) 495.386i 0.668537i
\(742\) −78.7703 + 190.590i −0.106160 + 0.256860i
\(743\) −1034.18 −1.39190 −0.695952 0.718088i \(-0.745017\pi\)
−0.695952 + 0.718088i \(0.745017\pi\)
\(744\) 70.5922 + 122.269i 0.0948819 + 0.164340i
\(745\) 191.550 + 110.591i 0.257114 + 0.148445i
\(746\) −286.203 + 495.719i −0.383651 + 0.664502i
\(747\) −15.0601 + 8.69498i −0.0201608 + 0.0116399i
\(748\) 29.1917i 0.0390263i
\(749\) 576.193 76.3160i 0.769283 0.101891i
\(750\) 27.3861 0.0365148
\(751\) 340.948 + 590.540i 0.453992 + 0.786338i 0.998630 0.0523339i \(-0.0166660\pi\)
−0.544637 + 0.838672i \(0.683333\pi\)
\(752\) −87.2701 50.3854i −0.116051 0.0670019i
\(753\) 134.931 233.708i 0.179192 0.310369i
\(754\) 889.932 513.803i 1.18028 0.681436i
\(755\) 218.665i 0.289623i
\(756\) −57.6787 + 44.3302i −0.0762946 + 0.0586378i
\(757\) 183.172 0.241971 0.120985 0.992654i \(-0.461395\pi\)
0.120985 + 0.992654i \(0.461395\pi\)
\(758\) 169.476 + 293.541i 0.223583 + 0.387257i
\(759\) 42.1662 + 24.3447i 0.0555549 + 0.0320747i
\(760\) 61.0388 105.722i 0.0803142 0.139108i
\(761\) −673.743 + 388.985i −0.885338 + 0.511150i −0.872415 0.488766i \(-0.837447\pi\)
−0.0129235 + 0.999916i \(0.504114\pi\)
\(762\) 197.341i 0.258978i
\(763\) 203.867 + 265.254i 0.267191 + 0.347646i
\(764\) 736.816 0.964419
\(765\) 42.3206 + 73.3014i 0.0553210 + 0.0958189i
\(766\) −782.747 451.919i −1.02186 0.589973i
\(767\) −180.867 + 313.271i −0.235811 + 0.408437i
\(768\) 24.0000 13.8564i 0.0312500 0.0180422i
\(769\) 302.546i 0.393428i 0.980461 + 0.196714i \(0.0630271\pi\)
−0.980461 + 0.196714i \(0.936973\pi\)
\(770\) 3.36220 + 25.3849i 0.00436649 + 0.0329674i