Properties

Label 210.3.k.b.83.8
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 83.8
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-0.199427 + 2.99336i) q^{3} +2.00000i q^{4} +(-4.37611 - 2.41861i) q^{5} +(-3.19279 + 2.79394i) q^{6} +(-5.12625 - 4.76671i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +O(q^{10})\) \(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} +(-5.12625 - 4.76671i) 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} +(15.2908 - 14.3941i) 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} +(9.53342 - 10.2525i) 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} +(10.9042 + 33.2581i) 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} +(29.6849 + 0.896672i) 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} +(40.0375 + 48.6415i) 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} +(-22.3538 + 44.1623i) 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} +(31.9440 - 34.3535i) 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} +(28.7883 + 30.5816i) 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} +(-45.3138 + 52.4277i) 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
\(7\) −5.12625 4.76671i −0.732322 0.680959i
\(8\) −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 \(0.586297\pi\)
−0.963474 + 0.267802i \(0.913703\pi\)
\(14\) −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 −0.462315 0.886716i \(-0.652981\pi\)
0.886716 + 0.462315i \(0.152981\pi\)
\(18\) −7.72655 10.1144i −0.429253 0.561909i
\(19\) −8.06294 −0.424365 −0.212183 0.977230i \(-0.568057\pi\)
−0.212183 + 0.977230i \(0.568057\pi\)
\(20\) 4.83722 8.75222i 0.241861 0.437611i
\(21\) 15.2908 14.3941i 0.728134 0.685435i
\(22\) −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
\(28\) 9.53342 10.2525i 0.340479 0.366161i
\(29\) 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 \(0.233246\pi\)
−0.743328 + 0.668927i \(0.766754\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −20.0600 1.33645i −0.607879 0.0404986i
\(34\) 14.4296 0.424401
\(35\) 10.9042 + 33.2581i 0.311549 + 0.950230i
\(36\) 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 \(-0.139852\pi\)
0.905025 + 0.425358i \(0.139852\pi\)
\(42\) 29.6849 + 0.896672i 0.706784 + 0.0213493i
\(43\) −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 −0.988679 0.150049i \(-0.952057\pi\)
0.150049 + 0.988679i \(0.452057\pi\)
\(48\) 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 \(0.145187\pi\)
−0.897769 + 0.440466i \(0.854813\pi\)
\(60\) 25.2339 + 16.2250i 0.420565 + 0.270417i
\(61\) 15.0083i 0.246038i −0.992404 0.123019i \(-0.960742\pi\)
0.992404 0.123019i \(-0.0392576\pi\)
\(62\) −41.4735 + 41.4735i −0.668927 + 0.668927i
\(63\) 40.0375 + 48.6415i 0.635516 + 0.772088i
\(64\) 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
\(70\) −22.3538 + 44.1623i −0.319340 + 0.630890i
\(71\) 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 −0.230497 0.973073i \(-0.574035\pi\)
0.973073 + 0.230497i \(0.0740352\pi\)
\(74\) −75.7239 −1.02330
\(75\) −66.0167 + 35.5921i −0.880222 + 0.474562i
\(76\) 16.1259i 0.212183i
\(77\) 31.9440 34.3535i 0.414858 0.446150i
\(78\) 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 0.520134 0.854084i \(-0.325882\pi\)
−0.854084 + 0.520134i \(0.825882\pi\)
\(84\) 28.7883 + 30.5816i 0.342718 + 0.364067i
\(85\) −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 \(0.0584498\pi\)
−0.983188 + 0.182595i \(0.941550\pi\)
\(90\) 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 0.936210 0.351442i \(-0.114309\pi\)
−0.351442 + 0.936210i \(0.614309\pi\)
\(98\) −45.3138 + 52.4277i −0.462385 + 0.534976i
\(99\) 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 \(-0.601467\pi\)
−0.313398 + 0.949622i \(0.601467\pi\)
\(102\) −2.87765 + 43.1932i −0.0282123 + 0.423463i
\(103\) 41.4114 41.4114i 0.402052 0.402052i −0.476904 0.878956i \(-0.658241\pi\)
0.878956 + 0.476904i \(0.158241\pi\)
\(104\) 64.0263i 0.615638i
\(105\) −101.728 + 26.0078i −0.968839 + 0.247693i
\(106\) −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
\(112\) 20.5050 + 19.0668i 0.183080 + 0.170240i
\(113\) 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
\(126\) −8.60403 + 88.6790i −0.0682860 + 0.703802i
\(127\) −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 \(-0.413292\pi\)
0.269044 + 0.963128i \(0.413292\pi\)
\(132\) 2.67291 40.1200i 0.0202493 0.303939i
\(133\) 41.3327 + 38.4337i 0.310772 + 0.288975i
\(134\) −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 \(-0.637488\pi\)
−0.418625 + 0.908159i \(0.637488\pi\)
\(140\) −66.5161 + 21.8084i −0.475115 + 0.155775i
\(141\) −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
\(147\) −146.997 + 0.901155i −0.999981 + 0.00613030i
\(148\) −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 0.575161 0.818040i \(-0.304939\pi\)
−0.818040 + 0.575161i \(0.804939\pi\)
\(158\) −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 −0.999607 0.0280316i \(-0.991076\pi\)
0.0280316 + 0.999607i \(0.491076\pi\)
\(168\) −1.79334 + 59.3699i −0.0106747 + 0.353392i
\(169\) 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 0.394499 0.918896i \(-0.370918\pi\)
−0.918896 + 0.394499i \(0.870918\pi\)
\(174\) −19.7247 + 17.2606i −0.113360 + 0.0991991i
\(175\) 32.7203 171.914i 0.186973 0.982365i
\(176\) 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 \(0.119061\pi\)
−0.930858 + 0.365381i \(0.880939\pi\)
\(182\) 164.108 + 152.597i 0.901690 + 0.838448i
\(183\) 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
\(189\) −153.586 + 110.146i −0.812626 + 0.582785i
\(190\) 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 \(-0.733299\pi\)
−0.669051 + 0.743217i \(0.733299\pi\)
\(200\) −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
\(203\) −31.6694 29.4482i −0.156007 0.145065i
\(204\) −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
\(210\) −127.736 75.7203i −0.608266 0.360573i
\(211\) 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
\(217\) 197.692 212.604i 0.911023 0.979740i
\(218\) 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 −0.712907 0.701259i \(-0.752622\pi\)
0.701259 + 0.712907i \(0.252622\pi\)
\(224\) 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 −0.827013 0.562183i \(-0.809961\pi\)
0.562183 + 0.827013i \(0.309961\pi\)
\(228\) 48.2706 + 3.21593i 0.211713 + 0.0141050i
\(229\) 345.368 1.50816 0.754078 0.656785i \(-0.228084\pi\)
0.754078 + 0.656785i \(0.228084\pi\)
\(230\) −102.572 56.6898i −0.445963 0.246477i
\(231\) 96.4621 + 102.471i 0.417585 + 0.443598i
\(232\) −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
\(238\) −73.9700 68.7819i −0.310798 0.289000i
\(239\) 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 \(0.117666\pi\)
−0.932451 + 0.361296i \(0.882334\pi\)
\(242\) 76.0901 + 76.0901i 0.314422 + 0.314422i
\(243\) −79.3451 + 229.681i −0.326523 + 0.945189i
\(244\) 30.0166 0.123019
\(245\) 102.634 222.466i 0.418913 0.908026i
\(246\) −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 \(-0.178285\pi\)
0.847202 + 0.531271i \(0.178285\pi\)
\(252\) −97.2831 + 80.0750i −0.386044 + 0.317758i
\(253\) 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 −0.657131 0.753776i \(-0.728230\pi\)
0.753776 + 0.657131i \(0.228230\pi\)
\(258\) 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 \(0.154675\pi\)
−0.884243 + 0.467026i \(0.845325\pi\)
\(270\) −190.294 + 15.4326i −0.704793 + 0.0571579i
\(271\) 101.261i 0.373657i −0.982393 0.186829i \(-0.940179\pi\)
0.982393 0.186829i \(-0.0598209\pi\)
\(272\) −28.8593 + 28.8593i −0.106100 + 0.106100i
\(273\) −14.3527 + 475.155i −0.0525738 + 1.74049i
\(274\) 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
\(280\) −88.3245 44.7077i −0.315445 0.159670i
\(281\) 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 −0.970183 0.242372i \(-0.922074\pi\)
0.242372 + 0.970183i \(0.422074\pi\)
\(284\) 257.742 0.907542
\(285\) −65.4106 + 101.730i −0.229511 + 0.356946i
\(286\) 214.536i 0.750125i
\(287\) −380.430 353.747i −1.32554 1.23257i
\(288\) 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 0.885278 0.465062i \(-0.153968\pi\)
−0.465062 + 0.885278i \(0.653968\pi\)
\(294\) −147.898 146.096i −0.503056 0.496925i
\(295\) 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 0.212771 0.977102i \(-0.431751\pi\)
−0.977102 + 0.212771i \(0.931751\pi\)
\(308\) 68.7071 + 63.8881i 0.223075 + 0.207429i
\(309\) 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 \(-0.667723\pi\)
−0.502870 + 0.864362i \(0.667723\pi\)
\(312\) 191.654 + 12.7685i 0.614276 + 0.0409248i
\(313\) 240.526 240.526i 0.768452 0.768452i −0.209382 0.977834i \(-0.567145\pi\)
0.977834 + 0.209382i \(0.0671451\pi\)
\(314\) 76.2640i 0.242879i
\(315\) −57.5634 309.696i −0.182741 0.983161i
\(316\) −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
\(322\) −120.154 111.727i −0.373150 0.346978i
\(323\) −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
\(336\) −61.1632 + 57.5765i −0.182033 + 0.171359i
\(337\) 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
\(343\) 214.719 267.479i 0.626002 0.779821i
\(344\) 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 \(-0.757098\pi\)
−0.722697 + 0.691165i \(0.757098\pi\)
\(350\) 204.634 139.194i 0.584669 0.397696i
\(351\) 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 0.353479 0.935443i \(-0.384999\pi\)
−0.935443 + 0.353479i \(0.884999\pi\)
\(354\) −145.215 165.945i −0.410211 0.468772i
\(355\) −311.689 + 563.953i −0.877996 + 1.58860i
\(356\) −65.0039 −0.182595
\(357\) 6.46933 214.172i 0.0181214 0.599920i
\(358\) −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 0.467854 0.883806i \(-0.345027\pi\)
−0.883806 + 0.467854i \(0.845027\pi\)
\(368\) −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
\(378\) −263.733 43.4400i −0.697706 0.114921i
\(379\) 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 \(-0.921277\pi\)
−0.244801 0.969573i \(-0.578723\pi\)
\(384\) 22.3515 + 25.5423i 0.0582070 + 0.0665165i
\(385\) −222.878 + 73.0745i −0.578905 + 0.189804i
\(386\) 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
\(392\) −104.855 90.6275i −0.267488 0.231193i
\(393\) −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 0.981179 0.193100i \(-0.0618541\pi\)
−0.193100 + 0.981179i \(0.561854\pi\)
\(398\) −266.282 266.282i −0.669051 0.669051i
\(399\) −123.289 + 116.059i −0.308995 + 0.290875i
\(400\) −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 \(-0.552612\pi\)
−0.164535 + 0.986371i \(0.552612\pi\)
\(410\) −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
\(413\) 247.749 266.437i 0.599878 0.645125i
\(414\) −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 \(-0.896231\pi\)
0.947331 0.320255i \(-0.103769\pi\)
\(420\) −52.0155 203.456i −0.123846 0.484419i
\(421\) −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
\(427\) −71.5403 + 76.9365i −0.167542 + 0.180179i
\(428\) 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 −0.934060 0.357116i \(-0.883760\pi\)
0.357116 + 0.934060i \(0.383760\pi\)
\(434\) 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 \(-0.298320\pi\)
0.592047 + 0.805903i \(0.298320\pi\)
\(440\) 26.2363 + 91.0695i 0.0596279 + 0.206976i
\(441\) 26.6177 440.196i 0.0603575 0.998177i
\(442\) −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
\(448\) −38.1337 + 41.0100i −0.0851198 + 0.0915402i
\(449\) −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
\(455\) −706.887 357.808i −1.55360 0.786392i
\(456\) 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 \(-0.295034\pi\)
0.600335 + 0.799749i \(0.295034\pi\)
\(462\) −6.00904 + 198.933i −0.0130066 + 0.430592i
\(463\) 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 \(-0.348727\pi\)
0.889184 0.457549i \(-0.151273\pi\)
\(468\) 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 \(-0.922895\pi\)
0.970805 0.239871i \(-0.0771051\pi\)
\(480\) −82.9178 + 18.0178i −0.172745 + 0.0375371i
\(481\) 1212.08i 2.51992i
\(482\) −174.145 + 174.145i −0.361296 + 0.361296i
\(483\) 10.5085 347.893i 0.0217568 0.720275i
\(484\) 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
\(490\) 325.100 119.833i 0.663470 0.244557i
\(491\) 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
\(497\) −614.290 + 660.625i −1.23600 + 1.32923i
\(498\) 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 0.531027 0.847355i \(-0.321806\pi\)
−0.847355 + 0.531027i \(0.821806\pi\)
\(504\) −177.358 17.2081i −0.351901 0.0341430i
\(505\) 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 \(0.279033\pi\)
−0.639761 + 0.768574i \(0.720967\pi\)
\(510\) 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
\(518\) 388.180 + 360.954i 0.749383 + 0.696822i
\(519\) 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 \(-0.569042\pi\)
−0.215205 + 0.976569i \(0.569042\pi\)
\(522\) −47.7337 62.4855i −0.0914439 0.119704i
\(523\) 278.114 278.114i 0.531767 0.531767i −0.389331 0.921098i \(-0.627294\pi\)
0.921098 + 0.389331i \(0.127294\pi\)
\(524\) 140.979i 0.269044i
\(525\) 508.076 + 132.228i 0.967763 + 0.251863i
\(526\) 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
\(532\) −76.8674 + 82.6654i −0.144488 + 0.155386i
\(533\) −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
\(546\) −489.507 + 460.802i −0.896533 + 0.843960i
\(547\) −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
\(553\) 122.896 132.165i 0.222234 0.238997i
\(554\) −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
\(560\) −43.6169 133.032i −0.0778873 0.237558i
\(561\) −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 0.994725 0.102575i \(-0.0327081\pi\)
−0.102575 + 0.994725i \(0.532708\pi\)
\(564\) 251.691 220.249i 0.446261 0.390513i
\(565\) −119.249 + 34.3546i −0.211060 + 0.0608046i
\(566\) −411.941 −0.727811
\(567\) −299.079 481.706i −0.527476 0.849570i
\(568\) 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 0.518007 0.855376i \(-0.326674\pi\)
−0.855376 + 0.518007i \(0.826674\pi\)
\(578\) −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 −0.991467 0.130355i \(-0.958388\pi\)
0.130355 + 0.991467i \(0.458388\pi\)
\(588\) −1.80231 293.994i −0.00306515 0.499991i
\(589\) 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 0.638183 0.769884i \(-0.279686\pi\)
−0.769884 + 0.638183i \(0.779686\pi\)
\(594\) 141.477 + 213.220i 0.238177 + 0.358957i
\(595\) 318.623 + 161.279i 0.535501 + 0.271057i
\(596\) 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 \(0.266974\pi\)
−0.668412 + 0.743791i \(0.733026\pi\)
\(602\) −403.330 + 433.752i −0.669983 + 0.720519i
\(603\) 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 0.763431 0.645889i \(-0.223513\pi\)
−0.645889 + 0.763431i \(0.723513\pi\)
\(608\) 32.2518 + 32.2518i 0.0530457 + 0.0530457i
\(609\) 94.4649 88.9254i 0.155115 0.146019i
\(610\) −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 \(-0.563548\pi\)
−0.198318 + 0.980138i \(0.563548\pi\)
\(620\) 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
\(623\) 154.927 166.613i 0.248680 0.267437i
\(624\) 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
\(630\) 252.132 367.259i 0.400210 0.582951i
\(631\) 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
\(637\) −839.188 725.319i −1.31741 1.13865i
\(638\) −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 −0.910596 0.413297i \(-0.864377\pi\)
0.413297 + 0.910596i \(0.364377\pi\)
\(644\) −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 −0.548950 0.835855i \(-0.684972\pi\)
0.835855 + 0.548950i \(0.184972\pi\)
\(648\) −198.899 + 113.697i −0.306943 + 0.175459i
\(649\) −348.309 −0.536686
\(650\) −425.795 677.661i −0.655070 1.04256i
\(651\) 596.975 + 634.163i 0.917012 + 0.974137i
\(652\) 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
\(658\) 404.109 + 375.765i 0.614147 + 0.571072i
\(659\) 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 \(0.140268\pi\)
−0.904469 + 0.426540i \(0.859732\pi\)
\(662\) −421.233 421.233i −0.636303 0.636303i
\(663\) −691.375 46.0614i −1.04280 0.0694742i
\(664\) 110.871 0.166975
\(665\) −87.9201 268.158i −0.132211 0.403245i
\(666\) 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
\(672\) −118.740 3.58669i −0.176696 0.00533733i
\(673\) −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 \(-0.483921\pi\)
0.998724 0.0504936i \(-0.0160794\pi\)
\(678\) −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 \(0.0778090\pi\)
−0.970272 + 0.242017i \(0.922191\pi\)
\(692\) 181.442 181.442i 0.262199 0.262199i
\(693\) −325.971 + 268.311i −0.470376 + 0.387173i
\(694\) 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
\(700\) 343.828 + 65.4405i 0.491183 + 0.0934865i
\(701\) 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
\(707\) 324.524 + 301.763i 0.459016 + 0.426821i
\(708\) 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
\(714\) 220.641 207.702i 0.309021 0.290900i
\(715\) 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 \(-0.843529\pi\)
0.881594 0.472009i \(-0.156471\pi\)
\(720\) −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 0.582160 0.813074i \(-0.302208\pi\)
−0.813074 + 0.582160i \(0.802208\pi\)
\(728\) −305.195 + 328.215i −0.419224 + 0.450845i
\(729\) −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 −0.606187 0.795322i \(-0.707302\pi\)
0.795322 + 0.606187i \(0.207302\pi\)
\(734\) 305.309i 0.415952i
\(735\) 645.455 + 351.586i 0.878170 + 0.478348i
\(736\) −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
\(742\) 455.420 + 423.478i 0.613774 + 0.570725i
\(743\) 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
\(756\) −220.293 307.173i −0.291393 0.406313i
\(757\) 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 \(-0.493758\pi\)
0.0196078 + 0.999808i \(0.493758\pi\)
\(762\) 37.9458 569.561i 0.0497976 0.747456i
\(763\) −516.327 + 555.273i −0.676707 + 0.727750i
\(764\) −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