Properties

Label 210.3.k.b.83.9
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.9
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(0.199427 - 2.99336i) q^{3} +2.00000i q^{4} +(4.37611 + 2.41861i) q^{5} +(3.19279 - 2.79394i) q^{6} +(4.76671 + 5.12625i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(0.199427 - 2.99336i) q^{3} +2.00000i q^{4} +(4.37611 + 2.41861i) q^{5} +(3.19279 - 2.79394i) q^{6} +(4.76671 + 5.12625i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +(1.95750 + 6.79472i) q^{10} +6.70149i q^{11} +(5.98673 + 0.398853i) q^{12} +(16.0066 - 16.0066i) q^{13} +(-0.359544 + 9.89296i) q^{14} +(8.11250 - 12.6169i) q^{15} -4.00000 q^{16} +(-7.21482 + 7.21482i) q^{17} +(-7.72655 - 10.1144i) q^{18} +8.06294 q^{19} +(-4.83722 + 8.75222i) q^{20} +(16.2954 - 13.2462i) q^{21} +(-6.70149 + 6.70149i) q^{22} +(11.7195 - 11.7195i) q^{23} +(5.58788 + 6.38558i) q^{24} +(13.3006 + 21.1682i) q^{25} +32.0132 q^{26} +(-5.35279 + 26.4641i) q^{27} +(-10.2525 + 9.53342i) q^{28} +6.17789 q^{29} +(20.7294 - 4.50445i) q^{30} -41.4735i q^{31} +(-4.00000 - 4.00000i) q^{32} +(20.0600 + 1.33645i) q^{33} -14.4296 q^{34} +(8.46122 + 33.9619i) q^{35} +(2.38782 - 17.8409i) q^{36} +(-37.8620 + 37.8620i) q^{37} +(8.06294 + 8.06294i) q^{38} +(-44.7214 - 51.1057i) q^{39} +(-13.5894 + 3.91499i) q^{40} -74.2121 q^{41} +(29.5415 + 3.04917i) q^{42} +(-42.3069 - 42.3069i) q^{43} -13.4030 q^{44} +(-36.1493 - 26.7998i) q^{45} +23.4390 q^{46} +(39.4156 - 39.4156i) q^{47} +(-0.797706 + 11.9735i) q^{48} +(-3.55696 + 48.8707i) q^{49} +(-7.86757 + 34.4688i) q^{50} +(20.1578 + 23.0354i) q^{51} +(32.0132 + 32.0132i) q^{52} +(-44.4204 + 44.4204i) q^{53} +(-31.8169 + 21.1113i) q^{54} +(-16.2083 + 29.3264i) q^{55} +(-19.7859 - 0.719089i) q^{56} +(1.60796 - 24.1353i) q^{57} +(6.17789 + 6.17789i) q^{58} -51.9749i q^{59} +(25.2339 + 16.2250i) q^{60} +15.0083i q^{61} +(41.4735 - 41.4735i) q^{62} +(-36.4009 - 51.4196i) q^{63} -8.00000i q^{64} +(108.760 - 31.3328i) q^{65} +(18.7235 + 21.3964i) q^{66} +(-38.7098 + 38.7098i) q^{67} +(-14.4296 - 14.4296i) q^{68} +(-32.7435 - 37.4179i) q^{69} +(-25.5006 + 42.4231i) q^{70} -128.871i q^{71} +(20.2287 - 15.4531i) q^{72} +(-54.2081 + 54.2081i) q^{73} -75.7239 q^{74} +(66.0167 - 35.5921i) q^{75} +16.1259i q^{76} +(-34.3535 + 31.9440i) q^{77} +(6.38427 - 95.8271i) q^{78} +25.7821i q^{79} +(-17.5044 - 9.67445i) q^{80} +(78.1491 + 21.3005i) q^{81} +(-74.2121 - 74.2121i) q^{82} +(27.7179 + 27.7179i) q^{83} +(26.4924 + 32.5907i) q^{84} +(-49.0227 + 14.1230i) q^{85} -84.6139i q^{86} +(1.23203 - 18.4927i) q^{87} +(-13.4030 - 13.4030i) q^{88} -32.5020i q^{89} +(-9.34946 - 62.9491i) q^{90} +(158.353 + 5.75508i) q^{91} +(23.4390 + 23.4390i) q^{92} +(-124.145 - 8.27091i) q^{93} +78.8312 q^{94} +(35.2843 + 19.5011i) q^{95} +(-12.7712 + 11.1758i) q^{96} +(-56.7224 - 56.7224i) q^{97} +(-52.4277 + 45.3138i) q^{98} +(8.00099 - 59.7803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 0.199427 2.99336i 0.0664755 0.997788i
\(4\) 2.00000i 0.500000i
\(5\) 4.37611 + 2.41861i 0.875222 + 0.483722i
\(6\) 3.19279 2.79394i 0.532132 0.465656i
\(7\) 4.76671 + 5.12625i 0.680959 + 0.732322i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −8.92046 1.19391i −0.991162 0.132657i
\(10\) 1.95750 + 6.79472i 0.195750 + 0.679472i
\(11\) 6.70149i 0.609226i 0.952476 + 0.304613i \(0.0985271\pi\)
−0.952476 + 0.304613i \(0.901473\pi\)
\(12\) 5.98673 + 0.398853i 0.498894 + 0.0332378i
\(13\) 16.0066 16.0066i 1.23128 1.23128i 0.267802 0.963474i \(-0.413703\pi\)
0.963474 0.267802i \(-0.0862972\pi\)
\(14\) −0.359544 + 9.89296i −0.0256817 + 0.706640i
\(15\) 8.11250 12.6169i 0.540833 0.841130i
\(16\) −4.00000 −0.250000
\(17\) −7.21482 + 7.21482i −0.424401 + 0.424401i −0.886716 0.462315i \(-0.847019\pi\)
0.462315 + 0.886716i \(0.347019\pi\)
\(18\) −7.72655 10.1144i −0.429253 0.561909i
\(19\) 8.06294 0.424365 0.212183 0.977230i \(-0.431943\pi\)
0.212183 + 0.977230i \(0.431943\pi\)
\(20\) −4.83722 + 8.75222i −0.241861 + 0.437611i
\(21\) 16.2954 13.2462i 0.775969 0.630771i
\(22\) −6.70149 + 6.70149i −0.304613 + 0.304613i
\(23\) 11.7195 11.7195i 0.509543 0.509543i −0.404843 0.914386i \(-0.632674\pi\)
0.914386 + 0.404843i \(0.132674\pi\)
\(24\) 5.58788 + 6.38558i 0.232828 + 0.266066i
\(25\) 13.3006 + 21.1682i 0.532025 + 0.846728i
\(26\) 32.0132 1.23128
\(27\) −5.35279 + 26.4641i −0.198252 + 0.980151i
\(28\) −10.2525 + 9.53342i −0.366161 + 0.340479i
\(29\) 6.17789 0.213031 0.106515 0.994311i \(-0.466031\pi\)
0.106515 + 0.994311i \(0.466031\pi\)
\(30\) 20.7294 4.50445i 0.690982 0.150148i
\(31\) 41.4735i 1.33785i −0.743328 0.668927i \(-0.766754\pi\)
0.743328 0.668927i \(-0.233246\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 20.0600 + 1.33645i 0.607879 + 0.0404986i
\(34\) −14.4296 −0.424401
\(35\) 8.46122 + 33.9619i 0.241749 + 0.970339i
\(36\) 2.38782 17.8409i 0.0663285 0.495581i
\(37\) −37.8620 + 37.8620i −1.02330 + 1.02330i −0.0235744 + 0.999722i \(0.507505\pi\)
−0.999722 + 0.0235744i \(0.992495\pi\)
\(38\) 8.06294 + 8.06294i 0.212183 + 0.212183i
\(39\) −44.7214 51.1057i −1.14670 1.31040i
\(40\) −13.5894 + 3.91499i −0.339736 + 0.0978748i
\(41\) −74.2121 −1.81005 −0.905025 0.425358i \(-0.860148\pi\)
−0.905025 + 0.425358i \(0.860148\pi\)
\(42\) 29.5415 + 3.04917i 0.703370 + 0.0725992i
\(43\) −42.3069 42.3069i −0.983882 0.983882i 0.0159899 0.999872i \(-0.494910\pi\)
−0.999872 + 0.0159899i \(0.994910\pi\)
\(44\) −13.4030 −0.304613
\(45\) −36.1493 26.7998i −0.803317 0.595551i
\(46\) 23.4390 0.509543
\(47\) 39.4156 39.4156i 0.838630 0.838630i −0.150049 0.988679i \(-0.547943\pi\)
0.988679 + 0.150049i \(0.0479431\pi\)
\(48\) −0.797706 + 11.9735i −0.0166189 + 0.249447i
\(49\) −3.55696 + 48.8707i −0.0725910 + 0.997362i
\(50\) −7.86757 + 34.4688i −0.157351 + 0.689377i
\(51\) 20.1578 + 23.0354i 0.395250 + 0.451675i
\(52\) 32.0132 + 32.0132i 0.615638 + 0.615638i
\(53\) −44.4204 + 44.4204i −0.838121 + 0.838121i −0.988611 0.150491i \(-0.951915\pi\)
0.150491 + 0.988611i \(0.451915\pi\)
\(54\) −31.8169 + 21.1113i −0.589201 + 0.390950i
\(55\) −16.2083 + 29.3264i −0.294696 + 0.533208i
\(56\) −19.7859 0.719089i −0.353320 0.0128409i
\(57\) 1.60796 24.1353i 0.0282099 0.423427i
\(58\) 6.17789 + 6.17789i 0.106515 + 0.106515i
\(59\) 51.9749i 0.880931i −0.897769 0.440466i \(-0.854813\pi\)
0.897769 0.440466i \(-0.145187\pi\)
\(60\) 25.2339 + 16.2250i 0.420565 + 0.270417i
\(61\) 15.0083i 0.246038i 0.992404 + 0.123019i \(0.0392576\pi\)
−0.992404 + 0.123019i \(0.960742\pi\)
\(62\) 41.4735 41.4735i 0.668927 0.668927i
\(63\) −36.4009 51.4196i −0.577793 0.816184i
\(64\) 8.00000i 0.125000i
\(65\) 108.760 31.3328i 1.67323 0.482043i
\(66\) 18.7235 + 21.3964i 0.283690 + 0.324189i
\(67\) −38.7098 + 38.7098i −0.577758 + 0.577758i −0.934285 0.356527i \(-0.883961\pi\)
0.356527 + 0.934285i \(0.383961\pi\)
\(68\) −14.4296 14.4296i −0.212201 0.212201i
\(69\) −32.7435 37.4179i −0.474544 0.542288i
\(70\) −25.5006 + 42.4231i −0.364295 + 0.606044i
\(71\) 128.871i 1.81508i −0.419962 0.907542i \(-0.637957\pi\)
0.419962 0.907542i \(-0.362043\pi\)
\(72\) 20.2287 15.4531i 0.280955 0.214626i
\(73\) −54.2081 + 54.2081i −0.742576 + 0.742576i −0.973073 0.230497i \(-0.925965\pi\)
0.230497 + 0.973073i \(0.425965\pi\)
\(74\) −75.7239 −1.02330
\(75\) 66.0167 35.5921i 0.880222 0.474562i
\(76\) 16.1259i 0.212183i
\(77\) −34.3535 + 31.9440i −0.446150 + 0.414858i
\(78\) 6.38427 95.8271i 0.0818497 1.22855i
\(79\) 25.7821i 0.326355i 0.986597 + 0.163178i \(0.0521743\pi\)
−0.986597 + 0.163178i \(0.947826\pi\)
\(80\) −17.5044 9.67445i −0.218805 0.120931i
\(81\) 78.1491 + 21.3005i 0.964804 + 0.262969i
\(82\) −74.2121 74.2121i −0.905025 0.905025i
\(83\) 27.7179 + 27.7179i 0.333950 + 0.333950i 0.854084 0.520134i \(-0.174118\pi\)
−0.520134 + 0.854084i \(0.674118\pi\)
\(84\) 26.4924 + 32.5907i 0.315385 + 0.387985i
\(85\) −49.0227 + 14.1230i −0.576737 + 0.166153i
\(86\) 84.6139i 0.983882i
\(87\) 1.23203 18.4927i 0.0141613 0.212559i
\(88\) −13.4030 13.4030i −0.152307 0.152307i
\(89\) 32.5020i 0.365191i −0.983188 0.182595i \(-0.941550\pi\)
0.983188 0.182595i \(-0.0584498\pi\)
\(90\) −9.34946 62.9491i −0.103883 0.699434i
\(91\) 158.353 + 5.75508i 1.74014 + 0.0632426i
\(92\) 23.4390 + 23.4390i 0.254772 + 0.254772i
\(93\) −124.145 8.27091i −1.33489 0.0889345i
\(94\) 78.8312 0.838630
\(95\) 35.2843 + 19.5011i 0.371414 + 0.205275i
\(96\) −12.7712 + 11.1758i −0.133033 + 0.116414i
\(97\) −56.7224 56.7224i −0.584767 0.584767i 0.351442 0.936210i \(-0.385691\pi\)
−0.936210 + 0.351442i \(0.885691\pi\)
\(98\) −52.4277 + 45.3138i −0.534976 + 0.462385i
\(99\) 8.00099 59.7803i 0.0808181 0.603842i
\(100\) −42.3364 + 26.6013i −0.423364 + 0.266013i
\(101\) 63.3063 0.626795 0.313398 0.949622i \(-0.398533\pi\)
0.313398 + 0.949622i \(0.398533\pi\)
\(102\) −2.87765 + 43.1932i −0.0282123 + 0.423463i
\(103\) −41.4114 + 41.4114i −0.402052 + 0.402052i −0.878956 0.476904i \(-0.841759\pi\)
0.476904 + 0.878956i \(0.341759\pi\)
\(104\) 64.0263i 0.615638i
\(105\) 103.348 18.5546i 0.984263 0.176711i
\(106\) −88.8408 −0.838121
\(107\) −3.96732 3.96732i −0.0370777 0.0370777i 0.688325 0.725403i \(-0.258346\pi\)
−0.725403 + 0.688325i \(0.758346\pi\)
\(108\) −52.9282 10.7056i −0.490076 0.0991258i
\(109\) 108.319i 0.993756i −0.867820 0.496878i \(-0.834480\pi\)
0.867820 0.496878i \(-0.165520\pi\)
\(110\) −45.5347 + 13.1181i −0.413952 + 0.119256i
\(111\) 105.784 + 120.885i 0.953009 + 1.08906i
\(112\) −19.0668 20.5050i −0.170240 0.183080i
\(113\) 17.5503 17.5503i 0.155312 0.155312i −0.625174 0.780486i \(-0.714972\pi\)
0.780486 + 0.625174i \(0.214972\pi\)
\(114\) 25.7433 22.5274i 0.225818 0.197608i
\(115\) 79.6307 22.9409i 0.692441 0.199486i
\(116\) 12.3558i 0.106515i
\(117\) −161.897 + 123.676i −1.38373 + 1.05706i
\(118\) 51.9749 51.9749i 0.440466 0.440466i
\(119\) −71.3760 2.59405i −0.599798 0.0217987i
\(120\) 9.00890 + 41.4589i 0.0750742 + 0.345491i
\(121\) 76.0901 0.628844
\(122\) −15.0083 + 15.0083i −0.123019 + 0.123019i
\(123\) −14.7999 + 222.144i −0.120324 + 1.80605i
\(124\) 82.9469 0.668927
\(125\) 7.00734 + 124.803i 0.0560587 + 0.998427i
\(126\) 15.0186 87.8205i 0.119195 0.696988i
\(127\) −95.1373 + 95.1373i −0.749113 + 0.749113i −0.974313 0.225200i \(-0.927696\pi\)
0.225200 + 0.974313i \(0.427696\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) −135.077 + 118.203i −1.04711 + 0.916302i
\(130\) 140.093 + 77.4274i 1.07764 + 0.595596i
\(131\) −70.4896 −0.538088 −0.269044 0.963128i \(-0.586708\pi\)
−0.269044 + 0.963128i \(0.586708\pi\)
\(132\) −2.67291 + 40.1200i −0.0202493 + 0.303939i
\(133\) 38.4337 + 41.3327i 0.288975 + 0.310772i
\(134\) −77.4196 −0.577758
\(135\) −87.4307 + 102.863i −0.647635 + 0.761951i
\(136\) 28.8593i 0.212201i
\(137\) 33.6211 + 33.6211i 0.245409 + 0.245409i 0.819084 0.573674i \(-0.194482\pi\)
−0.573674 + 0.819084i \(0.694482\pi\)
\(138\) 4.67436 70.1614i 0.0338722 0.508416i
\(139\) 116.378 0.837250 0.418625 0.908159i \(-0.362512\pi\)
0.418625 + 0.908159i \(0.362512\pi\)
\(140\) −67.9237 + 16.9224i −0.485169 + 0.120875i
\(141\) −110.125 125.846i −0.781026 0.892523i
\(142\) 128.871 128.871i 0.907542 0.907542i
\(143\) 107.268 + 107.268i 0.750125 + 0.750125i
\(144\) 35.6818 + 4.77565i 0.247791 + 0.0331642i
\(145\) 27.0351 + 14.9419i 0.186449 + 0.103048i
\(146\) −108.416 −0.742576
\(147\) 145.579 + 20.3934i 0.990330 + 0.138731i
\(148\) −75.7239 75.7239i −0.511648 0.511648i
\(149\) 129.115 0.866546 0.433273 0.901263i \(-0.357359\pi\)
0.433273 + 0.901263i \(0.357359\pi\)
\(150\) 101.609 + 30.4245i 0.677392 + 0.202830i
\(151\) −51.7299 −0.342582 −0.171291 0.985220i \(-0.554794\pi\)
−0.171291 + 0.985220i \(0.554794\pi\)
\(152\) −16.1259 + 16.1259i −0.106091 + 0.106091i
\(153\) 72.9734 55.7456i 0.476950 0.364351i
\(154\) −66.2976 2.40948i −0.430504 0.0156460i
\(155\) 100.308 181.492i 0.647150 1.17092i
\(156\) 102.211 89.4428i 0.655201 0.573351i
\(157\) 38.1320 + 38.1320i 0.242879 + 0.242879i 0.818040 0.575161i \(-0.195061\pi\)
−0.575161 + 0.818040i \(0.695061\pi\)
\(158\) −25.7821 + 25.7821i −0.163178 + 0.163178i
\(159\) 124.108 + 141.825i 0.780552 + 0.891981i
\(160\) −7.82998 27.1789i −0.0489374 0.169868i
\(161\) 115.941 + 4.21368i 0.720128 + 0.0261719i
\(162\) 56.8487 + 99.4496i 0.350918 + 0.613887i
\(163\) −61.7109 61.7109i −0.378594 0.378594i 0.492001 0.870595i \(-0.336266\pi\)
−0.870595 + 0.492001i \(0.836266\pi\)
\(164\) 148.424i 0.905025i
\(165\) 84.5523 + 54.3658i 0.512438 + 0.329490i
\(166\) 55.4357i 0.333950i
\(167\) 162.253 162.253i 0.971575 0.971575i −0.0280316 0.999607i \(-0.508924\pi\)
0.999607 + 0.0280316i \(0.00892391\pi\)
\(168\) −6.09833 + 59.0831i −0.0362996 + 0.351685i
\(169\) 343.421i 2.03208i
\(170\) −63.1457 34.8997i −0.371445 0.205292i
\(171\) −71.9251 9.62645i −0.420615 0.0562950i
\(172\) 84.6139 84.6139i 0.491941 0.491941i
\(173\) 90.7208 + 90.7208i 0.524398 + 0.524398i 0.918896 0.394499i \(-0.129082\pi\)
−0.394499 + 0.918896i \(0.629082\pi\)
\(174\) 19.7247 17.2606i 0.113360 0.0991991i
\(175\) −45.1133 + 169.085i −0.257791 + 0.966201i
\(176\) 26.8060i 0.152307i
\(177\) −155.580 10.3652i −0.878983 0.0585604i
\(178\) 32.5020 32.5020i 0.182595 0.182595i
\(179\) −23.3548 −0.130474 −0.0652369 0.997870i \(-0.520780\pi\)
−0.0652369 + 0.997870i \(0.520780\pi\)
\(180\) 53.5996 72.2985i 0.297776 0.401659i
\(181\) 132.268i 0.730762i −0.930858 0.365381i \(-0.880939\pi\)
0.930858 0.365381i \(-0.119061\pi\)
\(182\) 152.597 + 164.108i 0.838448 + 0.901690i
\(183\) 44.9254 + 2.99306i 0.245494 + 0.0163555i
\(184\) 46.8780i 0.254772i
\(185\) −257.261 + 74.1147i −1.39060 + 0.400620i
\(186\) −115.874 132.416i −0.622980 0.711915i
\(187\) −48.3500 48.3500i −0.258556 0.258556i
\(188\) 78.8312 + 78.8312i 0.419315 + 0.419315i
\(189\) −161.177 + 98.7068i −0.852787 + 0.522258i
\(190\) 15.7832 + 54.7854i 0.0830693 + 0.288344i
\(191\) 137.668i 0.720774i 0.932803 + 0.360387i \(0.117355\pi\)
−0.932803 + 0.360387i \(0.882645\pi\)
\(192\) −23.9469 1.59541i −0.124724 0.00830944i
\(193\) 188.004 + 188.004i 0.974116 + 0.974116i 0.999673 0.0255577i \(-0.00813615\pi\)
−0.0255577 + 0.999673i \(0.508136\pi\)
\(194\) 113.445i 0.584767i
\(195\) −72.1009 331.808i −0.369748 1.70158i
\(196\) −97.7415 7.11392i −0.498681 0.0362955i
\(197\) 2.30427 + 2.30427i 0.0116968 + 0.0116968i 0.712931 0.701234i \(-0.247367\pi\)
−0.701234 + 0.712931i \(0.747367\pi\)
\(198\) 67.7813 51.7793i 0.342330 0.261512i
\(199\) 266.282 1.33810 0.669051 0.743217i \(-0.266701\pi\)
0.669051 + 0.743217i \(0.266701\pi\)
\(200\) −68.9377 15.7351i −0.344688 0.0786757i
\(201\) 108.153 + 123.592i 0.538073 + 0.614887i
\(202\) 63.3063 + 63.3063i 0.313398 + 0.313398i
\(203\) 29.4482 + 31.6694i 0.145065 + 0.156007i
\(204\) −46.0708 + 40.3155i −0.225837 + 0.197625i
\(205\) −324.760 179.490i −1.58419 0.875562i
\(206\) −82.8227 −0.402052
\(207\) −118.535 + 90.5512i −0.572634 + 0.437446i
\(208\) −64.0263 + 64.0263i −0.307819 + 0.307819i
\(209\) 54.0337i 0.258534i
\(210\) 121.902 + 84.7930i 0.580487 + 0.403776i
\(211\) 104.157 0.493637 0.246819 0.969062i \(-0.420615\pi\)
0.246819 + 0.969062i \(0.420615\pi\)
\(212\) −88.8408 88.8408i −0.419060 0.419060i
\(213\) −385.758 25.7003i −1.81107 0.120659i
\(214\) 7.93464i 0.0370777i
\(215\) −82.8157 287.464i −0.385189 1.33704i
\(216\) −42.2226 63.6337i −0.195475 0.294601i
\(217\) 212.604 197.692i 0.979740 0.911023i
\(218\) 108.319 108.319i 0.496878 0.496878i
\(219\) 151.454 + 173.075i 0.691570 + 0.790297i
\(220\) −58.6529 32.4166i −0.266604 0.147348i
\(221\) 230.969i 1.04511i
\(222\) −15.1014 + 226.669i −0.0680242 + 1.02103i
\(223\) 2.59750 2.59750i 0.0116480 0.0116480i −0.701259 0.712907i \(-0.747378\pi\)
0.712907 + 0.701259i \(0.247378\pi\)
\(224\) 1.43818 39.5719i 0.00642044 0.176660i
\(225\) −93.3748 204.710i −0.414999 0.909822i
\(226\) 35.1005 0.155312
\(227\) 60.1162 60.1162i 0.264829 0.264829i −0.562183 0.827013i \(-0.690039\pi\)
0.827013 + 0.562183i \(0.190039\pi\)
\(228\) 48.2706 + 3.21593i 0.211713 + 0.0141050i
\(229\) −345.368 −1.50816 −0.754078 0.656785i \(-0.771916\pi\)
−0.754078 + 0.656785i \(0.771916\pi\)
\(230\) 102.572 + 56.6898i 0.445963 + 0.246477i
\(231\) 88.7692 + 109.203i 0.384282 + 0.472741i
\(232\) −12.3558 + 12.3558i −0.0532577 + 0.0532577i
\(233\) −258.641 + 258.641i −1.11005 + 1.11005i −0.116904 + 0.993143i \(0.537297\pi\)
−0.993143 + 0.116904i \(0.962703\pi\)
\(234\) −285.572 38.2209i −1.22039 0.163337i
\(235\) 267.818 77.1559i 1.13965 0.328323i
\(236\) 103.950 0.440466
\(237\) 77.1751 + 5.14163i 0.325633 + 0.0216946i
\(238\) −68.7819 73.9700i −0.289000 0.310798i
\(239\) 209.847 0.878022 0.439011 0.898482i \(-0.355329\pi\)
0.439011 + 0.898482i \(0.355329\pi\)
\(240\) −32.4500 + 50.4678i −0.135208 + 0.210282i
\(241\) 174.145i 0.722592i −0.932451 0.361296i \(-0.882334\pi\)
0.932451 0.361296i \(-0.117666\pi\)
\(242\) 76.0901 + 76.0901i 0.314422 + 0.314422i
\(243\) 79.3451 229.681i 0.326523 0.945189i
\(244\) −30.0166 −0.123019
\(245\) −133.765 + 205.261i −0.545979 + 0.837799i
\(246\) −236.944 + 207.344i −0.963185 + 0.842861i
\(247\) 129.060 129.060i 0.522511 0.522511i
\(248\) 82.9469 + 82.9469i 0.334464 + 0.334464i
\(249\) 88.4973 77.4420i 0.355411 0.311012i
\(250\) −117.796 + 131.811i −0.471184 + 0.527243i
\(251\) −425.295 −1.69440 −0.847202 0.531271i \(-0.821715\pi\)
−0.847202 + 0.531271i \(0.821715\pi\)
\(252\) 102.839 72.8019i 0.408092 0.288896i
\(253\) 78.5381 + 78.5381i 0.310427 + 0.310427i
\(254\) −190.275 −0.749113
\(255\) 32.4988 + 149.559i 0.127446 + 0.586507i
\(256\) 16.0000 0.0625000
\(257\) −24.8379 + 24.8379i −0.0966454 + 0.0966454i −0.753776 0.657131i \(-0.771770\pi\)
0.657131 + 0.753776i \(0.271770\pi\)
\(258\) −253.280 16.8743i −0.981706 0.0654041i
\(259\) −374.567 13.6131i −1.44620 0.0525601i
\(260\) 62.6656 + 217.520i 0.241022 + 0.836617i
\(261\) −55.1096 7.37586i −0.211148 0.0282600i
\(262\) −70.4896 70.4896i −0.269044 0.269044i
\(263\) 220.211 220.211i 0.837302 0.837302i −0.151201 0.988503i \(-0.548314\pi\)
0.988503 + 0.151201i \(0.0483140\pi\)
\(264\) −42.7929 + 37.4471i −0.162094 + 0.141845i
\(265\) −301.824 + 86.9527i −1.13896 + 0.328124i
\(266\) −2.89899 + 79.7664i −0.0108984 + 0.299874i
\(267\) −97.2902 6.48175i −0.364383 0.0242762i
\(268\) −77.4196 77.4196i −0.288879 0.288879i
\(269\) 251.260i 0.934053i −0.884243 0.467026i \(-0.845325\pi\)
0.884243 0.467026i \(-0.154675\pi\)
\(270\) −190.294 + 15.4326i −0.704793 + 0.0571579i
\(271\) 101.261i 0.373657i 0.982393 + 0.186829i \(0.0598209\pi\)
−0.982393 + 0.186829i \(0.940179\pi\)
\(272\) 28.8593 28.8593i 0.106100 0.106100i
\(273\) 48.8067 472.859i 0.178779 1.73208i
\(274\) 67.2421i 0.245409i
\(275\) −141.858 + 89.1340i −0.515849 + 0.324124i
\(276\) 74.8358 65.4871i 0.271144 0.237272i
\(277\) −298.311 + 298.311i −1.07693 + 1.07693i −0.0801518 + 0.996783i \(0.525541\pi\)
−0.996783 + 0.0801518i \(0.974459\pi\)
\(278\) 116.378 + 116.378i 0.418625 + 0.418625i
\(279\) −49.5157 + 369.962i −0.177476 + 1.32603i
\(280\) −84.8461 51.0013i −0.303022 0.182147i
\(281\) 105.319i 0.374801i −0.982284 0.187400i \(-0.939994\pi\)
0.982284 0.187400i \(-0.0600062\pi\)
\(282\) 15.7210 235.970i 0.0557483 0.836775i
\(283\) 205.970 205.970i 0.727811 0.727811i −0.242372 0.970183i \(-0.577926\pi\)
0.970183 + 0.242372i \(0.0779256\pi\)
\(284\) 257.742 0.907542
\(285\) 65.4106 101.730i 0.229511 0.356946i
\(286\) 214.536i 0.750125i
\(287\) −353.747 380.430i −1.23257 1.32554i
\(288\) 30.9062 + 40.4575i 0.107313 + 0.140477i
\(289\) 184.893i 0.639767i
\(290\) 12.0932 + 41.9770i 0.0417007 + 0.144748i
\(291\) −181.103 + 158.479i −0.622346 + 0.544601i
\(292\) −108.416 108.416i −0.371288 0.371288i
\(293\) −123.123 123.123i −0.420216 0.420216i 0.465062 0.885278i \(-0.346032\pi\)
−0.885278 + 0.465062i \(0.846032\pi\)
\(294\) 125.185 + 165.972i 0.425800 + 0.564530i
\(295\) 125.707 227.448i 0.426126 0.771010i
\(296\) 151.448i 0.511648i
\(297\) −177.349 35.8717i −0.597134 0.120780i
\(298\) 129.115 + 129.115i 0.433273 + 0.433273i
\(299\) 375.178i 1.25478i
\(300\) 71.1843 + 132.033i 0.237281 + 0.440111i
\(301\) 15.2112 418.541i 0.0505356 1.39050i
\(302\) −51.7299 51.7299i −0.171291 0.171291i
\(303\) 12.6250 189.499i 0.0416665 0.625409i
\(304\) −32.2518 −0.106091
\(305\) −36.2993 + 65.6780i −0.119014 + 0.215338i
\(306\) 128.719 + 17.2277i 0.420650 + 0.0562998i
\(307\) 234.650 + 234.650i 0.764331 + 0.764331i 0.977102 0.212771i \(-0.0682488\pi\)
−0.212771 + 0.977102i \(0.568249\pi\)
\(308\) −63.8881 68.7071i −0.207429 0.223075i
\(309\) 115.701 + 132.218i 0.374436 + 0.427889i
\(310\) 281.801 81.1842i 0.909034 0.261884i
\(311\) 312.785 1.00574 0.502870 0.864362i \(-0.332277\pi\)
0.502870 + 0.864362i \(0.332277\pi\)
\(312\) 191.654 + 12.7685i 0.614276 + 0.0409248i
\(313\) −240.526 + 240.526i −0.768452 + 0.768452i −0.977834 0.209382i \(-0.932855\pi\)
0.209382 + 0.977834i \(0.432855\pi\)
\(314\) 76.2640i 0.242879i
\(315\) −34.9304 313.057i −0.110890 0.993833i
\(316\) −51.5641 −0.163178
\(317\) 170.827 + 170.827i 0.538887 + 0.538887i 0.923202 0.384315i \(-0.125562\pi\)
−0.384315 + 0.923202i \(0.625562\pi\)
\(318\) −17.7172 + 265.933i −0.0557145 + 0.836267i
\(319\) 41.4010i 0.129784i
\(320\) 19.3489 35.0089i 0.0604653 0.109403i
\(321\) −12.6668 + 11.0844i −0.0394605 + 0.0345310i
\(322\) 111.727 + 120.154i 0.346978 + 0.373150i
\(323\) −58.1727 + 58.1727i −0.180101 + 0.180101i
\(324\) −42.6010 + 156.298i −0.131485 + 0.482402i
\(325\) 551.728 + 125.933i 1.69763 + 0.387486i
\(326\) 123.422i 0.378594i
\(327\) −324.240 21.6018i −0.991558 0.0660605i
\(328\) 148.424 148.424i 0.452513 0.452513i
\(329\) 389.937 + 14.1717i 1.18522 + 0.0430749i
\(330\) 30.1865 + 138.918i 0.0914743 + 0.420964i
\(331\) −421.233 −1.27261 −0.636303 0.771439i \(-0.719537\pi\)
−0.636303 + 0.771439i \(0.719537\pi\)
\(332\) −55.4357 + 55.4357i −0.166975 + 0.166975i
\(333\) 382.950 292.542i 1.15000 0.878505i
\(334\) 324.506 0.971575
\(335\) −263.022 + 75.7743i −0.785141 + 0.226192i
\(336\) −65.1814 + 52.9847i −0.193992 + 0.157693i
\(337\) 159.190 159.190i 0.472375 0.472375i −0.430307 0.902682i \(-0.641595\pi\)
0.902682 + 0.430307i \(0.141595\pi\)
\(338\) 343.421 343.421i 1.01604 1.01604i
\(339\) −49.0343 56.0343i −0.144644 0.165293i
\(340\) −28.2460 98.0454i −0.0830764 0.288369i
\(341\) 277.934 0.815056
\(342\) −62.2987 81.5516i −0.182160 0.238455i
\(343\) −267.479 + 214.719i −0.779821 + 0.626002i
\(344\) 169.228 0.491941
\(345\) −52.7899 242.939i −0.153014 0.704170i
\(346\) 181.442i 0.524398i
\(347\) −280.509 280.509i −0.808384 0.808384i 0.176005 0.984389i \(-0.443682\pi\)
−0.984389 + 0.176005i \(0.943682\pi\)
\(348\) 36.9853 + 2.46407i 0.106280 + 0.00708066i
\(349\) 504.442 1.44539 0.722697 0.691165i \(-0.242902\pi\)
0.722697 + 0.691165i \(0.242902\pi\)
\(350\) −214.198 + 123.972i −0.611996 + 0.354205i
\(351\) 337.920 + 509.279i 0.962734 + 1.45094i
\(352\) 26.8060 26.8060i 0.0761533 0.0761533i
\(353\) 205.433 + 205.433i 0.581964 + 0.581964i 0.935443 0.353479i \(-0.115001\pi\)
−0.353479 + 0.935443i \(0.615001\pi\)
\(354\) −145.215 165.945i −0.410211 0.468772i
\(355\) 311.689 563.953i 0.877996 1.58860i
\(356\) 65.0039 0.182595
\(357\) −21.9992 + 213.137i −0.0616224 + 0.597022i
\(358\) −23.3548 23.3548i −0.0652369 0.0652369i
\(359\) −428.176 −1.19269 −0.596346 0.802727i \(-0.703381\pi\)
−0.596346 + 0.802727i \(0.703381\pi\)
\(360\) 125.898 18.6989i 0.349717 0.0519415i
\(361\) −295.989 −0.819914
\(362\) 132.268 132.268i 0.365381 0.365381i
\(363\) 15.1744 227.765i 0.0418027 0.627453i
\(364\) −11.5102 + 316.705i −0.0316213 + 0.870069i
\(365\) −368.329 + 106.112i −1.00912 + 0.290718i
\(366\) 41.9323 + 47.9184i 0.114569 + 0.130925i
\(367\) 152.654 + 152.654i 0.415952 + 0.415952i 0.883806 0.467854i \(-0.154973\pi\)
−0.467854 + 0.883806i \(0.654973\pi\)
\(368\) −46.8780 + 46.8780i −0.127386 + 0.127386i
\(369\) 662.006 + 88.6027i 1.79405 + 0.240116i
\(370\) −331.376 183.147i −0.895611 0.494991i
\(371\) −439.449 15.9711i −1.18450 0.0430488i
\(372\) 16.5418 248.290i 0.0444673 0.667447i
\(373\) 382.613 + 382.613i 1.02577 + 1.02577i 0.999659 + 0.0261145i \(0.00831345\pi\)
0.0261145 + 0.999659i \(0.491687\pi\)
\(374\) 96.7001i 0.258556i
\(375\) 374.980 + 3.91361i 0.999946 + 0.0104363i
\(376\) 157.662i 0.419315i
\(377\) 98.8869 98.8869i 0.262299 0.262299i
\(378\) −259.884 62.4700i −0.687523 0.165264i
\(379\) 726.851i 1.91781i 0.283721 + 0.958907i \(0.408431\pi\)
−0.283721 + 0.958907i \(0.591569\pi\)
\(380\) −39.0022 + 70.5686i −0.102637 + 0.185707i
\(381\) 265.808 + 303.753i 0.697658 + 0.797253i
\(382\) −137.668 + 137.668i −0.360387 + 0.360387i
\(383\) 465.105 + 465.105i 1.21437 + 1.21437i 0.969573 + 0.244801i \(0.0787225\pi\)
0.244801 + 0.969573i \(0.421277\pi\)
\(384\) −22.3515 25.5423i −0.0582070 0.0665165i
\(385\) −227.595 + 56.7027i −0.591156 + 0.147280i
\(386\) 376.009i 0.974116i
\(387\) 326.886 + 427.908i 0.844668 + 1.10571i
\(388\) 113.445 113.445i 0.292384 0.292384i
\(389\) −120.366 −0.309424 −0.154712 0.987960i \(-0.549445\pi\)
−0.154712 + 0.987960i \(0.549445\pi\)
\(390\) 259.707 403.908i 0.665915 1.03566i
\(391\) 169.108i 0.432502i
\(392\) −90.6275 104.855i −0.231193 0.267488i
\(393\) −14.0575 + 211.001i −0.0357697 + 0.536898i
\(394\) 4.60854i 0.0116968i
\(395\) −62.3568 + 112.825i −0.157865 + 0.285633i
\(396\) 119.561 + 16.0020i 0.301921 + 0.0404090i
\(397\) −312.868 312.868i −0.788080 0.788080i 0.193100 0.981179i \(-0.438146\pi\)
−0.981179 + 0.193100i \(0.938146\pi\)
\(398\) 266.282 + 266.282i 0.669051 + 0.669051i
\(399\) 131.388 106.803i 0.329294 0.267677i
\(400\) −53.2025 84.6728i −0.133006 0.211682i
\(401\) 641.900i 1.60075i 0.599501 + 0.800374i \(0.295366\pi\)
−0.599501 + 0.800374i \(0.704634\pi\)
\(402\) −15.4395 + 231.745i −0.0384068 + 0.576480i
\(403\) −663.849 663.849i −1.64727 1.64727i
\(404\) 126.613i 0.313398i
\(405\) 290.471 + 282.226i 0.717213 + 0.696854i
\(406\) −2.22122 + 61.1176i −0.00547100 + 0.150536i
\(407\) −253.732 253.732i −0.623419 0.623419i
\(408\) −86.3864 5.75531i −0.211731 0.0141061i
\(409\) 134.590 0.329071 0.164535 0.986371i \(-0.447388\pi\)
0.164535 + 0.986371i \(0.447388\pi\)
\(410\) −145.270 504.250i −0.354317 1.22988i
\(411\) 107.345 93.9351i 0.261180 0.228553i
\(412\) −82.8227 82.8227i −0.201026 0.201026i
\(413\) 266.437 247.749i 0.645125 0.599878i
\(414\) −209.087 27.9841i −0.505040 0.0675945i
\(415\) 54.2576 + 188.335i 0.130741 + 0.453819i
\(416\) −128.053 −0.307819
\(417\) 23.2088 348.361i 0.0556566 0.835398i
\(418\) −54.0337 + 54.0337i −0.129267 + 0.129267i
\(419\) 268.374i 0.640510i 0.947331 + 0.320255i \(0.103769\pi\)
−0.947331 + 0.320255i \(0.896231\pi\)
\(420\) 37.1092 + 206.695i 0.0883553 + 0.492131i
\(421\) −28.9266 −0.0687092 −0.0343546 0.999410i \(-0.510938\pi\)
−0.0343546 + 0.999410i \(0.510938\pi\)
\(422\) 104.157 + 104.157i 0.246819 + 0.246819i
\(423\) −398.664 + 304.546i −0.942468 + 0.719968i
\(424\) 177.682i 0.419060i
\(425\) −248.687 56.7631i −0.585145 0.133560i
\(426\) −360.057 411.458i −0.845205 0.965864i
\(427\) −76.9365 + 71.5403i −0.180179 + 0.167542i
\(428\) 7.93464 7.93464i 0.0185389 0.0185389i
\(429\) 342.484 299.700i 0.798331 0.698601i
\(430\) 204.648 370.279i 0.475926 0.861115i
\(431\) 276.630i 0.641833i 0.947107 + 0.320917i \(0.103991\pi\)
−0.947107 + 0.320917i \(0.896009\pi\)
\(432\) 21.4112 105.856i 0.0495629 0.245038i
\(433\) 249.817 249.817i 0.576945 0.576945i −0.357116 0.934060i \(-0.616240\pi\)
0.934060 + 0.357116i \(0.116240\pi\)
\(434\) 410.296 + 14.9116i 0.945381 + 0.0343584i
\(435\) 50.1181 77.9461i 0.115214 0.179186i
\(436\) 216.639 0.496878
\(437\) 94.4936 94.4936i 0.216233 0.216233i
\(438\) −21.6210 + 324.529i −0.0493631 + 0.740934i
\(439\) −519.817 −1.18409 −0.592047 0.805903i \(-0.701680\pi\)
−0.592047 + 0.805903i \(0.701680\pi\)
\(440\) −26.2363 91.0695i −0.0596279 0.206976i
\(441\) 90.0771 431.703i 0.204256 0.978917i
\(442\) −230.969 + 230.969i −0.522555 + 0.522555i
\(443\) 388.588 388.588i 0.877173 0.877173i −0.116068 0.993241i \(-0.537029\pi\)
0.993241 + 0.116068i \(0.0370290\pi\)
\(444\) −241.771 + 211.568i −0.544529 + 0.476504i
\(445\) 78.6096 142.232i 0.176651 0.319623i
\(446\) 5.19500 0.0116480
\(447\) 25.7490 386.489i 0.0576041 0.864629i
\(448\) 41.0100 38.1337i 0.0915402 0.0851198i
\(449\) −283.968 −0.632445 −0.316223 0.948685i \(-0.602415\pi\)
−0.316223 + 0.948685i \(0.602415\pi\)
\(450\) 111.335 298.085i 0.247411 0.662410i
\(451\) 497.331i 1.10273i
\(452\) 35.1005 + 35.1005i 0.0776560 + 0.0776560i
\(453\) −10.3163 + 154.846i −0.0227733 + 0.341824i
\(454\) 120.232 0.264829
\(455\) 679.048 + 408.178i 1.49241 + 0.897095i
\(456\) 45.0547 + 51.4866i 0.0988042 + 0.112909i
\(457\) −201.368 + 201.368i −0.440630 + 0.440630i −0.892224 0.451594i \(-0.850856\pi\)
0.451594 + 0.892224i \(0.350856\pi\)
\(458\) −345.368 345.368i −0.754078 0.754078i
\(459\) −152.314 229.553i −0.331839 0.500116i
\(460\) 45.8817 + 159.261i 0.0997429 + 0.346220i
\(461\) −553.509 −1.20067 −0.600335 0.799749i \(-0.704966\pi\)
−0.600335 + 0.799749i \(0.704966\pi\)
\(462\) −20.4340 + 197.972i −0.0442293 + 0.428511i
\(463\) 574.866 + 574.866i 1.24161 + 1.24161i 0.959333 + 0.282278i \(0.0910902\pi\)
0.282278 + 0.959333i \(0.408910\pi\)
\(464\) −24.7116 −0.0532577
\(465\) −523.269 336.453i −1.12531 0.723556i
\(466\) −517.282 −1.11005
\(467\) −628.925 + 628.925i −1.34673 + 1.34673i −0.457549 + 0.889184i \(0.651273\pi\)
−0.889184 + 0.457549i \(0.848727\pi\)
\(468\) −247.351 323.793i −0.528528 0.691865i
\(469\) −382.955 13.9179i −0.816534 0.0296757i
\(470\) 344.974 + 190.662i 0.733987 + 0.405664i
\(471\) 121.748 106.538i 0.258487 0.226196i
\(472\) 103.950 + 103.950i 0.220233 + 0.220233i
\(473\) 283.519 283.519i 0.599407 0.599407i
\(474\) 72.0335 + 82.3167i 0.151969 + 0.173664i
\(475\) 107.242 + 170.678i 0.225773 + 0.359322i
\(476\) 5.18810 142.752i 0.0108994 0.299899i
\(477\) 449.284 343.216i 0.941896 0.719531i
\(478\) 209.847 + 209.847i 0.439011 + 0.439011i
\(479\) 229.796i 0.479742i 0.970805 + 0.239871i \(0.0771051\pi\)
−0.970805 + 0.239871i \(0.922895\pi\)
\(480\) −82.9178 + 18.0178i −0.172745 + 0.0375371i
\(481\) 1212.08i 2.51992i
\(482\) 174.145 174.145i 0.361296 0.361296i
\(483\) 35.7347 346.212i 0.0739849 0.716795i
\(484\) 152.180i 0.314422i
\(485\) −111.034 385.413i −0.228936 0.794666i
\(486\) 309.026 150.336i 0.635856 0.309333i
\(487\) 58.0212 58.0212i 0.119140 0.119140i −0.645023 0.764163i \(-0.723152\pi\)
0.764163 + 0.645023i \(0.223152\pi\)
\(488\) −30.0166 30.0166i −0.0615095 0.0615095i
\(489\) −197.030 + 172.416i −0.402924 + 0.352590i
\(490\) −339.026 + 71.4957i −0.691889 + 0.145910i
\(491\) 105.182i 0.214221i −0.994247 0.107110i \(-0.965840\pi\)
0.994247 0.107110i \(-0.0341598\pi\)
\(492\) −444.287 29.5997i −0.903023 0.0601620i
\(493\) −44.5724 + 44.5724i −0.0904105 + 0.0904105i
\(494\) 258.120 0.522511
\(495\) 179.599 242.254i 0.362825 0.489402i
\(496\) 165.894i 0.334464i
\(497\) 660.625 614.290i 1.32923 1.23600i
\(498\) 165.939 + 11.0554i 0.333211 + 0.0221995i
\(499\) 29.9809i 0.0600819i −0.999549 0.0300409i \(-0.990436\pi\)
0.999549 0.0300409i \(-0.00956377\pi\)
\(500\) −249.607 + 14.0147i −0.499214 + 0.0280293i
\(501\) −453.325 518.040i −0.904840 1.03401i
\(502\) −425.295 425.295i −0.847202 0.847202i
\(503\) 159.113 + 159.113i 0.316328 + 0.316328i 0.847355 0.531027i \(-0.178194\pi\)
−0.531027 + 0.847355i \(0.678194\pi\)
\(504\) 175.641 + 30.0373i 0.348494 + 0.0595977i
\(505\) 277.035 + 153.113i 0.548585 + 0.303195i
\(506\) 157.076i 0.310427i
\(507\) −1027.99 68.4873i −2.02758 0.135084i
\(508\) −190.275 190.275i −0.374556 0.374556i
\(509\) 782.408i 1.53715i −0.639761 0.768574i \(-0.720967\pi\)
0.639761 0.768574i \(-0.279033\pi\)
\(510\) −117.060 + 182.058i −0.229530 + 0.356977i
\(511\) −536.278 19.4902i −1.04947 0.0381413i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −43.1592 + 213.378i −0.0841311 + 0.415942i
\(514\) −49.6757 −0.0966454
\(515\) −281.379 + 81.0626i −0.546366 + 0.157403i
\(516\) −236.406 270.154i −0.458151 0.523555i
\(517\) 264.143 + 264.143i 0.510915 + 0.510915i
\(518\) −360.954 388.180i −0.696822 0.749383i
\(519\) 289.653 253.468i 0.558097 0.488378i
\(520\) −154.855 + 280.186i −0.297798 + 0.538819i
\(521\) 224.244 0.430411 0.215205 0.976569i \(-0.430958\pi\)
0.215205 + 0.976569i \(0.430958\pi\)
\(522\) −47.7337 62.4855i −0.0914439 0.119704i
\(523\) −278.114 + 278.114i −0.531767 + 0.531767i −0.921098 0.389331i \(-0.872706\pi\)
0.389331 + 0.921098i \(0.372706\pi\)
\(524\) 140.979i 0.269044i
\(525\) 497.137 + 168.761i 0.946927 + 0.321449i
\(526\) 440.421 0.837302
\(527\) 299.224 + 299.224i 0.567787 + 0.567787i
\(528\) −80.2400 5.34582i −0.151970 0.0101247i
\(529\) 254.307i 0.480731i
\(530\) −388.777 214.871i −0.733541 0.405418i
\(531\) −62.0535 + 463.640i −0.116862 + 0.873146i
\(532\) −82.6654 + 76.8674i −0.155386 + 0.144488i
\(533\) −1187.88 + 1187.88i −2.22867 + 2.22867i
\(534\) −90.8084 103.772i −0.170053 0.194329i
\(535\) −7.76601 26.9568i −0.0145159 0.0503866i
\(536\) 154.839i 0.288879i
\(537\) −4.65757 + 69.9095i −0.00867331 + 0.130185i
\(538\) 251.260 251.260i 0.467026 0.467026i
\(539\) −327.507 23.8369i −0.607619 0.0442243i
\(540\) −205.727 174.861i −0.380975 0.323817i
\(541\) 135.498 0.250458 0.125229 0.992128i \(-0.460033\pi\)
0.125229 + 0.992128i \(0.460033\pi\)
\(542\) −101.261 + 101.261i −0.186829 + 0.186829i
\(543\) −395.926 26.3777i −0.729146 0.0485778i
\(544\) 57.7186 0.106100
\(545\) 261.983 474.018i 0.480702 0.869757i
\(546\) 521.666 424.052i 0.955432 0.776653i
\(547\) −15.9985 + 15.9985i −0.0292477 + 0.0292477i −0.721579 0.692332i \(-0.756584\pi\)
0.692332 + 0.721579i \(0.256584\pi\)
\(548\) −67.2421 + 67.2421i −0.122705 + 0.122705i
\(549\) 17.9186 133.881i 0.0326387 0.243864i
\(550\) −230.993 52.7244i −0.419986 0.0958626i
\(551\) 49.8120 0.0904028
\(552\) 140.323 + 9.34871i 0.254208 + 0.0169361i
\(553\) −132.165 + 122.896i −0.238997 + 0.222234i
\(554\) −596.622 −1.07693
\(555\) 170.547 + 784.858i 0.307293 + 1.41416i
\(556\) 232.756i 0.418625i
\(557\) 502.514 + 502.514i 0.902180 + 0.902180i 0.995625 0.0934442i \(-0.0297877\pi\)
−0.0934442 + 0.995625i \(0.529788\pi\)
\(558\) −419.478 + 320.447i −0.751753 + 0.574277i
\(559\) −1354.38 −2.42286
\(560\) −33.8449 135.847i −0.0604373 0.242585i
\(561\) −154.372 + 135.087i −0.275172 + 0.240797i
\(562\) 105.319 105.319i 0.187400 0.187400i
\(563\) −502.281 502.281i −0.892150 0.892150i 0.102575 0.994725i \(-0.467292\pi\)
−0.994725 + 0.102575i \(0.967292\pi\)
\(564\) 251.691 220.249i 0.446261 0.390513i
\(565\) 119.249 34.3546i 0.211060 0.0608046i
\(566\) 411.941 0.727811
\(567\) 263.323 + 502.146i 0.464414 + 0.885618i
\(568\) 257.742 + 257.742i 0.453771 + 0.453771i
\(569\) 359.729 0.632212 0.316106 0.948724i \(-0.397624\pi\)
0.316106 + 0.948724i \(0.397624\pi\)
\(570\) 167.140 36.3191i 0.293229 0.0637178i
\(571\) 583.678 1.02220 0.511102 0.859520i \(-0.329238\pi\)
0.511102 + 0.859520i \(0.329238\pi\)
\(572\) −214.536 + 214.536i −0.375063 + 0.375063i
\(573\) 412.090 + 27.4546i 0.719180 + 0.0479138i
\(574\) 26.6825 734.177i 0.0464852 1.27905i
\(575\) 403.958 + 92.2040i 0.702535 + 0.160355i
\(576\) −9.55130 + 71.3637i −0.0165821 + 0.123895i
\(577\) 194.662 + 194.662i 0.337369 + 0.337369i 0.855376 0.518007i \(-0.173326\pi\)
−0.518007 + 0.855376i \(0.673326\pi\)
\(578\) −184.893 + 184.893i −0.319884 + 0.319884i
\(579\) 600.258 525.272i 1.03672 0.907206i
\(580\) −29.8838 + 54.0702i −0.0515238 + 0.0932245i
\(581\) −9.96580 + 274.212i −0.0171528 + 0.471965i
\(582\) −339.582 22.6239i −0.583474 0.0388727i
\(583\) −297.683 297.683i −0.510605 0.510605i
\(584\) 216.832i 0.371288i
\(585\) −1007.60 + 149.653i −1.72239 + 0.255817i
\(586\) 246.246i 0.420216i
\(587\) 505.473 505.473i 0.861113 0.861113i −0.130355 0.991467i \(-0.541612\pi\)
0.991467 + 0.130355i \(0.0416115\pi\)
\(588\) −40.7868 + 291.157i −0.0693653 + 0.495165i
\(589\) 334.398i 0.567739i
\(590\) 353.155 101.741i 0.598568 0.172442i
\(591\) 7.35705 6.43798i 0.0124485 0.0108934i
\(592\) 151.448 151.448i 0.255824 0.255824i
\(593\) 78.0986 + 78.0986i 0.131701 + 0.131701i 0.769884 0.638183i \(-0.220314\pi\)
−0.638183 + 0.769884i \(0.720314\pi\)
\(594\) −141.477 213.220i −0.238177 0.358957i
\(595\) −306.075 183.983i −0.514412 0.309214i
\(596\) 258.231i 0.433273i
\(597\) 53.1037 797.080i 0.0889510 1.33514i
\(598\) 375.178 375.178i 0.627388 0.627388i
\(599\) −516.399 −0.862102 −0.431051 0.902328i \(-0.641857\pi\)
−0.431051 + 0.902328i \(0.641857\pi\)
\(600\) −60.8490 + 203.218i −0.101415 + 0.338696i
\(601\) 894.037i 1.48758i −0.668412 0.743791i \(-0.733026\pi\)
0.668412 0.743791i \(-0.266974\pi\)
\(602\) 433.752 403.330i 0.720519 0.669983i
\(603\) 391.525 299.093i 0.649296 0.496008i
\(604\) 103.460i 0.171291i
\(605\) 332.978 + 184.032i 0.550377 + 0.304186i
\(606\) 202.124 176.874i 0.333538 0.291871i
\(607\) −71.3484 71.3484i −0.117543 0.117543i 0.645889 0.763431i \(-0.276487\pi\)
−0.763431 + 0.645889i \(0.776487\pi\)
\(608\) −32.2518 32.2518i −0.0530457 0.0530457i
\(609\) 100.671 81.8335i 0.165305 0.134374i
\(610\) −101.977 + 29.3787i −0.167176 + 0.0481618i
\(611\) 1261.82i 2.06517i
\(612\) 111.491 + 145.947i 0.182175 + 0.238475i
\(613\) −32.1532 32.1532i −0.0524522 0.0524522i 0.680394 0.732846i \(-0.261809\pi\)
−0.732846 + 0.680394i \(0.761809\pi\)
\(614\) 469.299i 0.764331i
\(615\) −602.045 + 936.330i −0.978935 + 1.52249i
\(616\) 4.81896 132.595i 0.00782299 0.215252i
\(617\) 771.937 + 771.937i 1.25111 + 1.25111i 0.955221 + 0.295892i \(0.0956170\pi\)
0.295892 + 0.955221i \(0.404383\pi\)
\(618\) −16.5170 + 247.919i −0.0267266 + 0.401163i
\(619\) 245.518 0.396636 0.198318 0.980138i \(-0.436452\pi\)
0.198318 + 0.980138i \(0.436452\pi\)
\(620\) 362.985 + 200.616i 0.585459 + 0.323575i
\(621\) 247.414 + 372.878i 0.398412 + 0.600447i
\(622\) 312.785 + 312.785i 0.502870 + 0.502870i
\(623\) 166.613 154.927i 0.267437 0.248680i
\(624\) 178.886 + 204.423i 0.286676 + 0.327600i
\(625\) −271.186 + 563.101i −0.433898 + 0.900962i
\(626\) −481.051 −0.768452
\(627\) 161.743 + 10.7758i 0.257963 + 0.0171862i
\(628\) −76.2640 + 76.2640i −0.121440 + 0.121440i
\(629\) 546.335i 0.868577i
\(630\) 278.127 347.988i 0.441471 0.552361i
\(631\) 405.528 0.642675 0.321337 0.946965i \(-0.395868\pi\)
0.321337 + 0.946965i \(0.395868\pi\)
\(632\) −51.5641 51.5641i −0.0815888 0.0815888i
\(633\) 20.7718 311.781i 0.0328148 0.492545i
\(634\) 341.654i 0.538887i
\(635\) −646.431 + 186.231i −1.01800 + 0.293277i
\(636\) −283.650 + 248.216i −0.445991 + 0.390276i
\(637\) 725.319 + 839.188i 1.13865 + 1.31741i
\(638\) −41.4010 + 41.4010i −0.0648919 + 0.0648919i
\(639\) −153.861 + 1149.59i −0.240783 + 1.79904i
\(640\) 54.3578 15.6600i 0.0849340 0.0244687i
\(641\) 891.470i 1.39075i −0.718648 0.695374i \(-0.755239\pi\)
0.718648 0.695374i \(-0.244761\pi\)
\(642\) −23.7513 1.58238i −0.0369957 0.00246476i
\(643\) 319.764 319.764i 0.497300 0.497300i −0.413297 0.910596i \(-0.635623\pi\)
0.910596 + 0.413297i \(0.135623\pi\)
\(644\) −8.42736 + 231.881i −0.0130860 + 0.360064i
\(645\) −876.999 + 190.570i −1.35969 + 0.295457i
\(646\) −116.345 −0.180101
\(647\) −185.628 + 185.628i −0.286906 + 0.286906i −0.835855 0.548950i \(-0.815028\pi\)
0.548950 + 0.835855i \(0.315028\pi\)
\(648\) −198.899 + 113.697i −0.306943 + 0.175459i
\(649\) 348.309 0.536686
\(650\) 425.795 + 677.661i 0.655070 + 1.04256i
\(651\) −549.365 675.825i −0.843879 1.03813i
\(652\) 123.422 123.422i 0.189297 0.189297i
\(653\) −528.502 + 528.502i −0.809345 + 0.809345i −0.984535 0.175190i \(-0.943946\pi\)
0.175190 + 0.984535i \(0.443946\pi\)
\(654\) −302.638 345.841i −0.462749 0.528809i
\(655\) −308.470 170.487i −0.470947 0.260285i
\(656\) 296.848 0.452513
\(657\) 548.280 418.841i 0.834521 0.637505i
\(658\) 375.765 + 404.109i 0.571072 + 0.614147i
\(659\) 101.666 0.154274 0.0771369 0.997021i \(-0.475422\pi\)
0.0771369 + 0.997021i \(0.475422\pi\)
\(660\) −108.732 + 169.105i −0.164745 + 0.256219i
\(661\) 563.886i 0.853080i −0.904469 0.426540i \(-0.859732\pi\)
0.904469 0.426540i \(-0.140268\pi\)
\(662\) −421.233 421.233i −0.636303 0.636303i
\(663\) 691.375 + 46.0614i 1.04280 + 0.0694742i
\(664\) −110.871 −0.166975
\(665\) 68.2223 + 273.832i 0.102590 + 0.411778i
\(666\) 675.492 + 90.4078i 1.01425 + 0.135747i
\(667\) 72.4017 72.4017i 0.108548 0.108548i
\(668\) 324.506 + 324.506i 0.485788 + 0.485788i
\(669\) −7.25725 8.29327i −0.0108479 0.0123965i
\(670\) −338.796 187.248i −0.505666 0.279475i
\(671\) −100.578 −0.149893
\(672\) −118.166 12.1967i −0.175842 0.0181498i
\(673\) −835.168 835.168i −1.24096 1.24096i −0.959602 0.281361i \(-0.909214\pi\)
−0.281361 0.959602i \(-0.590786\pi\)
\(674\) 318.381 0.472375
\(675\) −631.393 + 238.680i −0.935397 + 0.353600i
\(676\) 686.843 1.01604
\(677\) −710.321 + 710.321i −1.04922 + 1.04922i −0.0504936 + 0.998724i \(0.516079\pi\)
−0.998724 + 0.0504936i \(0.983921\pi\)
\(678\) 6.99998 105.069i 0.0103245 0.154969i
\(679\) 20.3942 561.153i 0.0300357 0.826440i
\(680\) 69.7994 126.291i 0.102646 0.185723i
\(681\) −167.961 191.938i −0.246639 0.281848i
\(682\) 277.934 + 277.934i 0.407528 + 0.407528i
\(683\) 228.514 228.514i 0.334573 0.334573i −0.519747 0.854320i \(-0.673974\pi\)
0.854320 + 0.519747i \(0.173974\pi\)
\(684\) 19.2529 143.850i 0.0281475 0.210307i
\(685\) 65.8131 + 228.446i 0.0960775 + 0.333497i
\(686\) −482.197 52.7601i −0.702912 0.0769097i
\(687\) −68.8755 + 1033.81i −0.100255 + 1.50482i
\(688\) 169.228 + 169.228i 0.245971 + 0.245971i
\(689\) 1422.04i 2.06391i
\(690\) 190.149 295.729i 0.275578 0.428592i
\(691\) 334.468i 0.484034i −0.970272 0.242017i \(-0.922191\pi\)
0.970272 0.242017i \(-0.0778090\pi\)
\(692\) −181.442 + 181.442i −0.262199 + 0.262199i
\(693\) 344.588 243.940i 0.497240 0.352006i
\(694\) 561.019i 0.808384i
\(695\) 509.282 + 281.473i 0.732780 + 0.404997i
\(696\) 34.5213 + 39.4494i 0.0495995 + 0.0566802i
\(697\) 535.427 535.427i 0.768188 0.768188i
\(698\) 504.442 + 504.442i 0.722697 + 0.722697i
\(699\) 722.627 + 825.787i 1.03380 + 1.18138i
\(700\) −338.170 90.2267i −0.483100 0.128895i
\(701\) 786.818i 1.12242i −0.827673 0.561211i \(-0.810336\pi\)
0.827673 0.561211i \(-0.189664\pi\)
\(702\) −171.360 + 847.199i −0.244102 + 1.20684i
\(703\) −305.279 + 305.279i −0.434252 + 0.434252i
\(704\) 53.6119 0.0761533
\(705\) −177.546 817.063i −0.251838 1.15896i
\(706\) 410.867i 0.581964i
\(707\) 301.763 + 324.524i 0.426821 + 0.459016i
\(708\) 20.7304 311.160i 0.0292802 0.439491i
\(709\) 1314.72i 1.85434i −0.374647 0.927168i \(-0.622236\pi\)
0.374647 0.927168i \(-0.377764\pi\)
\(710\) 875.642 252.264i 1.23330 0.355302i
\(711\) 30.7815 229.988i 0.0432933 0.323471i
\(712\) 65.0039 + 65.0039i 0.0912976 + 0.0912976i
\(713\) −486.048 486.048i −0.681695 0.681695i
\(714\) −235.136 + 191.138i −0.329322 + 0.267700i
\(715\) 209.977 + 728.855i 0.293673 + 1.01938i
\(716\) 46.7096i 0.0652369i
\(717\) 41.8491 628.149i 0.0583670 0.876080i
\(718\) −428.176 428.176i −0.596346 0.596346i
\(719\) 678.749i 0.944018i 0.881594 + 0.472009i \(0.156471\pi\)
−0.881594 + 0.472009i \(0.843529\pi\)
\(720\) 144.597 + 107.199i 0.200829 + 0.148888i
\(721\) −409.681 14.8892i −0.568212 0.0206508i
\(722\) −295.989 295.989i −0.409957 0.409957i
\(723\) −521.279 34.7291i −0.720994 0.0480347i
\(724\) 264.536 0.365381
\(725\) 82.1698 + 130.775i 0.113338 + 0.180379i
\(726\) 242.940 212.591i 0.334628 0.292825i
\(727\) 167.875 + 167.875i 0.230915 + 0.230915i 0.813074 0.582160i \(-0.197792\pi\)
−0.582160 + 0.813074i \(0.697792\pi\)
\(728\) −328.215 + 305.195i −0.450845 + 0.419224i
\(729\) −671.695 283.313i −0.921393 0.388633i
\(730\) −474.441 262.216i −0.649919 0.359201i
\(731\) 610.474 0.835122
\(732\) −5.98611 + 89.8507i −0.00817775 + 0.122747i
\(733\) −138.636 + 138.636i −0.189135 + 0.189135i −0.795322 0.606187i \(-0.792698\pi\)
0.606187 + 0.795322i \(0.292698\pi\)
\(734\) 305.309i 0.415952i
\(735\) 587.744 + 441.342i 0.799651 + 0.600465i
\(736\) −93.7560 −0.127386
\(737\) −259.413 259.413i −0.351985 0.351985i
\(738\) 573.403 + 750.608i 0.776969 + 1.01708i
\(739\) 467.931i 0.633195i 0.948560 + 0.316598i \(0.102540\pi\)
−0.948560 + 0.316598i \(0.897460\pi\)
\(740\) −148.229 514.523i −0.200310 0.695301i
\(741\) −360.586 412.062i −0.486621 0.556089i
\(742\) −423.478 455.420i −0.570725 0.613774i
\(743\) 164.867 164.867i 0.221893 0.221893i −0.587402 0.809295i \(-0.699849\pi\)
0.809295 + 0.587402i \(0.199849\pi\)
\(744\) 264.832 231.749i 0.355957 0.311490i
\(745\) 565.023 + 312.280i 0.758419 + 0.419168i
\(746\) 765.227i 1.02577i
\(747\) −214.163 280.349i −0.286698 0.375299i
\(748\) 96.7001 96.7001i 0.129278 0.129278i
\(749\) 1.42643 39.2485i 0.00190444 0.0524013i
\(750\) 371.066 + 378.893i 0.494755 + 0.505191i
\(751\) 661.864 0.881310 0.440655 0.897677i \(-0.354746\pi\)
0.440655 + 0.897677i \(0.354746\pi\)
\(752\) −157.662 + 157.662i −0.209657 + 0.209657i
\(753\) −84.8152 + 1273.06i −0.112636 + 1.69066i
\(754\) 197.774 0.262299
\(755\) −226.376 125.114i −0.299835 0.165715i
\(756\) −197.414 322.354i −0.261129 0.426394i
\(757\) 846.245 846.245i 1.11789 1.11789i 0.125843 0.992050i \(-0.459837\pi\)
0.992050 0.125843i \(-0.0401635\pi\)
\(758\) −726.851 + 726.851i −0.958907 + 0.958907i
\(759\) 250.756 219.430i 0.330376 0.289105i
\(760\) −109.571 + 31.5664i −0.144172 + 0.0415347i
\(761\) −29.8430 −0.0392155 −0.0196078 0.999808i \(-0.506242\pi\)
−0.0196078 + 0.999808i \(0.506242\pi\)
\(762\) −37.9458 + 569.561i −0.0497976 + 0.747456i
\(763\) 555.273 516.327i 0.727750 0.676707i
\(764\) −275.336 −0.360387
\(765\) 454.166 67.4547i 0.593682 0.0881761i
\(766\) 930.211i 1.21437i
\(767\) −831.941 831.941i −1.08467 1.08467i
\(768\) 3.19082