Properties

Label 210.3.k.a.83.16
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 83.16
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.99336 - 0.199427i) q^{3} +2.00000i q^{4} +(-4.37611 - 2.41861i) q^{5} +(-3.19279 - 2.79394i) q^{6} +(4.76671 + 5.12625i) q^{7} +(2.00000 - 2.00000i) q^{8} +(8.92046 - 1.19391i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.99336 - 0.199427i) 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} +(0.398853 + 5.98673i) q^{12} +(16.0066 - 16.0066i) q^{13} +(0.359544 - 9.89296i) q^{14} +(-13.5816 - 6.36707i) q^{15} -4.00000 q^{16} +(7.21482 - 7.21482i) q^{17} +(-10.1144 - 7.72655i) 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} +(26.4641 - 5.35279i) q^{27} +(-10.2525 + 9.53342i) q^{28} -6.17789 q^{29} +(7.21455 + 19.9487i) q^{30} -41.4735i q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.33645 - 20.0600i) 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} +(-0.896672 - 29.6849i) q^{42} +(-42.3069 - 42.3069i) q^{43} +13.4030 q^{44} +(-41.9245 - 16.3504i) q^{45} +23.4390 q^{46} +(-39.4156 + 39.4156i) q^{47} +(-11.9735 + 0.797706i) 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} +(24.1353 - 1.60796i) q^{57} +(6.17789 + 6.17789i) q^{58} +51.9749i q^{59} +(12.7341 - 27.1632i) q^{60} +15.0083i q^{61} +(-41.4735 + 41.4735i) q^{62} +(48.6415 + 40.0375i) 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} +(15.4531 - 20.2287i) q^{72} +(-54.2081 + 54.2081i) q^{73} +75.7239 q^{74} +(44.0351 + 60.7117i) q^{75} +16.1259i q^{76} +(34.3535 - 31.9440i) q^{77} +(-95.8271 + 6.38427i) 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} +(-18.4927 + 1.23203i) q^{87} +(-13.4030 - 13.4030i) q^{88} +32.5020i q^{89} +(25.5741 + 58.2749i) q^{90} +(158.353 + 5.75508i) q^{91} +(-23.4390 - 23.4390i) q^{92} +(-8.27091 - 124.145i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

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
\(3\) 2.99336 0.199427i 0.997788 0.0664755i
\(4\) 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 \(-0.901473\pi\)
0.952476 0.304613i \(-0.0985271\pi\)
\(12\) 0.398853 + 5.98673i 0.0332378 + 0.498894i
\(13\) 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
\(15\) −13.5816 6.36707i −0.905441 0.424472i
\(16\) −4.00000 −0.250000
\(17\) 7.21482 7.21482i 0.424401 0.424401i −0.462315 0.886716i \(-0.652981\pi\)
0.886716 + 0.462315i \(0.152981\pi\)
\(18\) −10.1144 7.72655i −0.561909 0.429253i
\(19\) 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
\(21\) 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 −0.914386 0.404843i \(-0.867326\pi\)
0.404843 + 0.914386i \(0.367326\pi\)
\(24\) 5.58788 6.38558i 0.232828 0.266066i
\(25\) 13.3006 + 21.1682i 0.532025 + 0.846728i
\(26\) −32.0132 −1.23128
\(27\) 26.4641 5.35279i 0.980151 0.198252i
\(28\) −10.2525 + 9.53342i −0.366161 + 0.340479i
\(29\) −6.17789 −0.213031 −0.106515 0.994311i \(-0.533969\pi\)
−0.106515 + 0.994311i \(0.533969\pi\)
\(30\) 7.21455 + 19.9487i 0.240485 + 0.664956i
\(31\) 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
\(33\) −1.33645 20.0600i −0.0404986 0.607879i
\(34\) −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 \(-0.139852\pi\)
0.905025 + 0.425358i \(0.139852\pi\)
\(42\) −0.896672 29.6849i −0.0213493 0.706784i
\(43\) −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
\(45\) −41.9245 16.3504i −0.931655 0.363343i
\(46\) 23.4390 0.509543
\(47\) −39.4156 + 39.4156i −0.838630 + 0.838630i −0.988679 0.150049i \(-0.952057\pi\)
0.150049 + 0.988679i \(0.452057\pi\)
\(48\) −11.9735 + 0.797706i −0.249447 + 0.0166189i
\(49\) −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 −0.150491 0.988611i \(-0.548085\pi\)
0.988611 + 0.150491i \(0.0480854\pi\)
\(54\) −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
\(57\) 24.1353 1.60796i 0.423427 0.0282099i
\(58\) 6.17789 + 6.17789i 0.106515 + 0.106515i
\(59\) 51.9749i 0.880931i 0.897769 + 0.440466i \(0.145187\pi\)
−0.897769 + 0.440466i \(0.854813\pi\)
\(60\) 12.7341 27.1632i 0.212236 0.452721i
\(61\) 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
\(63\) 48.6415 + 40.0375i 0.772088 + 0.635516i
\(64\) 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 \(0.362043\pi\)
−0.419962 + 0.907542i \(0.637957\pi\)
\(72\) 15.4531 20.2287i 0.214626 0.280955i
\(73\) −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
\(75\) 44.0351 + 60.7117i 0.587135 + 0.809489i
\(76\) 16.1259i 0.212183i
\(77\) 34.3535 31.9440i 0.446150 0.414858i
\(78\) −95.8271 + 6.38427i −1.22855 + 0.0818497i
\(79\) 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
\(87\) −18.4927 + 1.23203i −0.212559 + 0.0141613i
\(88\) −13.4030 13.4030i −0.152307 0.152307i
\(89\) 32.5020i 0.365191i 0.983188 + 0.182595i \(0.0584498\pi\)
−0.983188 + 0.182595i \(0.941550\pi\)
\(90\) 25.5741 + 58.2749i 0.284156 + 0.647499i
\(91\) 158.353 + 5.75508i 1.74014 + 0.0632426i
\(92\) −23.4390 23.4390i −0.254772 0.254772i
\(93\) −8.27091 124.145i −0.0889345 1.33489i
\(94\) 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 \(-0.601467\pi\)
−0.313398 + 0.949622i \(0.601467\pi\)
\(102\) −43.1932 + 2.87765i −0.423463 + 0.0282123i
\(103\) −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
\(105\) −32.1004 99.9728i −0.305718 0.952122i
\(106\) −88.8408 −0.838121
\(107\) 3.96732 + 3.96732i 0.0370777 + 0.0370777i 0.725403 0.688325i \(-0.241654\pi\)
−0.688325 + 0.725403i \(0.741654\pi\)
\(108\) 10.7056 + 52.9282i 0.0991258 + 0.490076i
\(109\) 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 −0.780486 0.625174i \(-0.785028\pi\)
0.625174 + 0.780486i \(0.285028\pi\)
\(114\) −25.7433 22.5274i −0.225818 0.197608i
\(115\) 79.6307 22.9409i 0.692441 0.199486i
\(116\) 12.3558i 0.106515i
\(117\) 123.676 161.897i 1.05706 1.38373i
\(118\) 51.9749 51.9749i 0.440466 0.440466i
\(119\) 71.3760 + 2.59405i 0.599798 + 0.0217987i
\(120\) −39.8974 + 14.4291i −0.332478 + 0.120242i
\(121\) 76.0901 0.628844
\(122\) 15.0083 15.0083i 0.123019 0.123019i
\(123\) 222.144 14.7999i 1.80605 0.120324i
\(124\) 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 \(0.413292\pi\)
\(132\) 40.1200 2.67291i 0.303939 0.0202493i
\(133\) 38.4337 + 41.3327i 0.288975 + 0.310772i
\(134\) 77.4196 0.577758
\(135\) −128.756 40.5819i −0.953748 0.300607i
\(136\) 28.8593i 0.212201i
\(137\) −33.6211 33.6211i −0.245409 0.245409i 0.573674 0.819084i \(-0.305518\pi\)
−0.819084 + 0.573674i \(0.805518\pi\)
\(138\) 70.1614 4.67436i 0.508416 0.0338722i
\(139\) 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
\(147\) −0.901155 + 146.997i −0.00613030 + 0.999981i
\(148\) −75.7239 75.7239i −0.511648 0.511648i
\(149\) −129.115 −0.866546 −0.433273 0.901263i \(-0.642641\pi\)
−0.433273 + 0.901263i \(0.642641\pi\)
\(150\) 16.6765 104.747i 0.111177 0.698312i
\(151\) −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
\(153\) 55.7456 72.9734i 0.364351 0.476950i
\(154\) −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
\(162\) −99.4496 56.8487i −0.613887 0.350918i
\(163\) −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
\(165\) −42.6689 + 91.0171i −0.258599 + 0.551618i
\(166\) 55.4357i 0.333950i
\(167\) −162.253 + 162.253i −0.971575 + 0.971575i −0.999607 0.0280316i \(-0.991076\pi\)
0.0280316 + 0.999607i \(0.491076\pi\)
\(168\) 59.3699 1.79334i 0.353392 0.0106747i
\(169\) 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
\(175\) −45.1133 + 169.085i −0.257791 + 0.966201i
\(176\) 26.8060i 0.152307i
\(177\) 10.3652 + 155.580i 0.0585604 + 0.878983i
\(178\) 32.5020 32.5020i 0.182595 0.182595i
\(179\) 23.3548 0.130474 0.0652369 0.997870i \(-0.479220\pi\)
0.0652369 + 0.997870i \(0.479220\pi\)
\(180\) 32.7009 83.8490i 0.181671 0.465828i
\(181\) 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
\(183\) 2.99306 + 44.9254i 0.0163555 + 0.245494i
\(184\) 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 \(-0.882645\pi\)
0.932803 0.360387i \(-0.117355\pi\)
\(192\) −1.59541 23.9469i −0.00830944 0.124724i
\(193\) 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
\(195\) −319.310 + 115.480i −1.63749 + 0.592206i
\(196\) −97.7415 7.11392i −0.498681 0.0362955i
\(197\) −2.30427 2.30427i −0.0116968 0.0116968i 0.701234 0.712931i \(-0.252633\pi\)
−0.712931 + 0.701234i \(0.752633\pi\)
\(198\) −51.7793 + 67.7813i −0.261512 + 0.342330i
\(199\) 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
\(207\) −90.5512 + 118.535i −0.437446 + 0.572634i
\(208\) −64.0263 + 64.0263i −0.307819 + 0.307819i
\(209\) 54.0337i 0.258534i
\(210\) −67.8724 + 132.073i −0.323202 + 0.628920i
\(211\) 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
\(213\) 25.7003 + 385.758i 0.120659 + 1.81107i
\(214\) 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
\(222\) 226.669 15.1014i 1.02103 0.0680242i
\(223\) 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
\(225\) 143.921 + 172.950i 0.639648 + 0.768668i
\(226\) 35.1005 0.155312
\(227\) −60.1162 + 60.1162i −0.264829 + 0.264829i −0.827013 0.562183i \(-0.809961\pi\)
0.562183 + 0.827013i \(0.309961\pi\)
\(228\) 3.21593 + 48.2706i 0.0141050 + 0.211713i
\(229\) −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
\(231\) 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 \(-0.462703\pi\)
0.993143 0.116904i \(-0.0372970\pi\)
\(234\) −285.572 + 38.2209i −1.22039 + 0.163337i
\(235\) 267.818 77.1559i 1.13965 0.328323i
\(236\) −103.950 −0.440466
\(237\) 5.14163 + 77.1751i 0.0216946 + 0.325633i
\(238\) −68.7819 73.9700i −0.289000 0.310798i
\(239\) −209.847 −0.878022 −0.439011 0.898482i \(-0.644671\pi\)
−0.439011 + 0.898482i \(0.644671\pi\)
\(240\) 54.3265 + 25.4683i 0.226360 + 0.106118i
\(241\) 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
\(243\) 229.681 79.3451i 0.945189 0.326523i
\(244\) −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 \(-0.178285\pi\)
0.847202 + 0.531271i \(0.178285\pi\)
\(252\) −80.0750 + 97.2831i −0.317758 + 0.386044i
\(253\) 78.5381 + 78.5381i 0.310427 + 0.310427i
\(254\) 190.275 0.749113
\(255\) −143.926 + 52.0517i −0.564417 + 0.204124i
\(256\) 16.0000 0.0625000
\(257\) 24.8379 24.8379i 0.0966454 0.0966454i −0.657131 0.753776i \(-0.728230\pi\)
0.753776 + 0.657131i \(0.228230\pi\)
\(258\) 16.8743 + 253.280i 0.0654041 + 0.981706i
\(259\) −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 −0.988503 0.151201i \(-0.951686\pi\)
0.151201 + 0.988503i \(0.451686\pi\)
\(264\) −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
\(267\) 6.48175 + 97.2902i 0.0242762 + 0.364383i
\(268\) −77.4196 77.4196i −0.288879 0.288879i
\(269\) 251.260i 0.934053i 0.884243 + 0.467026i \(0.154675\pi\)
−0.884243 + 0.467026i \(0.845325\pi\)
\(270\) 88.1740 + 169.338i 0.326571 + 0.627178i
\(271\) 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
\(273\) 475.155 14.3527i 1.74049 0.0525738i
\(274\) 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 \(0.0600062\pi\)
−0.982284 + 0.187400i \(0.939994\pi\)
\(282\) 235.970 15.7210i 0.836775 0.0557483i
\(283\) 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
\(285\) −109.508 51.3373i −0.384238 0.180131i
\(286\) 214.536i 0.750125i
\(287\) 353.747 + 380.430i 1.23257 + 1.32554i
\(288\) 40.4575 + 30.9062i 0.140477 + 0.107313i
\(289\) 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
\(297\) −35.8717 177.349i −0.120780 0.597134i
\(298\) 129.115 + 129.115i 0.433273 + 0.433273i
\(299\) 375.178i 1.25478i
\(300\) −121.423 + 88.0703i −0.404744 + 0.293568i
\(301\) 15.2112 418.541i 0.0505356 1.39050i
\(302\) 51.7299 + 51.7299i 0.171291 + 0.171291i
\(303\) −189.499 + 12.6250i −0.625409 + 0.0416665i
\(304\) −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 \(-0.667723\pi\)
−0.502870 + 0.864362i \(0.667723\pi\)
\(312\) −12.7685 191.654i −0.0409248 0.614276i
\(313\) −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
\(315\) −116.025 292.853i −0.368335 0.929693i
\(316\) −51.5641 −0.163178
\(317\) −170.827 170.827i −0.538887 0.538887i 0.384315 0.923202i \(-0.374438\pi\)
−0.923202 + 0.384315i \(0.874438\pi\)
\(318\) −265.933 + 17.7172i −0.836267 + 0.0557145i
\(319\) 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
\(327\) −21.6018 324.240i −0.0660605 0.991558i
\(328\) 148.424 148.424i 0.452513 0.452513i
\(329\) −389.937 14.1717i −1.18522 0.0430749i
\(330\) 133.686 48.3482i 0.405109 0.146510i
\(331\) −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
\(333\) −292.542 + 382.950i −0.878505 + 1.15000i
\(334\) 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
\(342\) −81.5516 62.2987i −0.238455 0.182160i
\(343\) −267.479 + 214.719i −0.779821 + 0.626002i
\(344\) −169.228 −0.491941
\(345\) 233.789 84.5508i 0.677648 0.245075i
\(346\) 181.442i 0.524398i
\(347\) 280.509 + 280.509i 0.808384 + 0.808384i 0.984389 0.176005i \(-0.0563175\pi\)
−0.176005 + 0.984389i \(0.556318\pi\)
\(348\) −2.46407 36.9853i −0.00708066 0.106280i
\(349\) 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 0.353479 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
\(357\) 214.172 6.46933i 0.599920 0.0181214i
\(358\) −23.3548 23.3548i −0.0652369 0.0652369i
\(359\) 428.176 1.19269 0.596346 0.802727i \(-0.296619\pi\)
0.596346 + 0.802727i \(0.296619\pi\)
\(360\) −116.550 + 51.1481i −0.323750 + 0.142078i
\(361\) −295.989 −0.819914
\(362\) −132.268 + 132.268i −0.365381 + 0.365381i
\(363\) 227.765 15.1744i 0.627453 0.0418027i
\(364\) −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
\(372\) 248.290 16.5418i 0.667447 0.0444673i
\(373\) 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
\(375\) −45.8646 372.185i −0.122306 0.992492i
\(376\) 157.662i 0.419315i
\(377\) −98.8869 + 98.8869i −0.262299 + 0.262299i
\(378\) −43.4400 263.733i −0.114921 0.697706i
\(379\) 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
\(385\) −227.595 + 56.7027i −0.591156 + 0.147280i
\(386\) 376.009i 0.974116i
\(387\) −427.908 326.886i −1.10571 0.844668i
\(388\) 113.445 113.445i 0.292384 0.292384i
\(389\) 120.366 0.309424 0.154712 0.987960i \(-0.450555\pi\)
0.154712 + 0.987960i \(0.450555\pi\)
\(390\) 434.791 + 203.830i 1.11485 + 0.522641i
\(391\) 169.108i 0.432502i
\(392\) 90.6275 + 104.855i 0.231193 + 0.267488i
\(393\) 211.001 14.0575i 0.536898 0.0357697i
\(394\) 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
\(399\) 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 \(-0.704634\pi\)
0.599501 0.800374i \(-0.295366\pi\)
\(402\) 231.745 15.4395i 0.576480 0.0384068i
\(403\) −663.849 663.849i −1.64727 1.64727i
\(404\) 126.613i 0.313398i
\(405\) −393.507 95.7992i −0.971621 0.236541i
\(406\) −2.22122 + 61.1176i −0.00547100 + 0.150536i
\(407\) 253.732 + 253.732i 0.623419 + 0.623419i
\(408\) −5.75531 86.3864i −0.0141061 0.211731i
\(409\) 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
\(417\) 348.361 23.2088i 0.835398 0.0556566i
\(418\) −54.0337 + 54.0337i −0.129267 + 0.129267i
\(419\) 268.374i 0.640510i −0.947331 0.320255i \(-0.896231\pi\)
0.947331 0.320255i \(-0.103769\pi\)
\(420\) 199.946 64.2008i 0.476061 0.152859i
\(421\) −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
\(423\) −304.546 + 398.664i −0.719968 + 0.942468i
\(424\) 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 \(-0.896009\pi\)
0.947107 0.320917i \(-0.103991\pi\)
\(432\) −105.856 + 21.4112i −0.245038 + 0.0495629i
\(433\) 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
\(435\) 83.9057 + 39.3351i 0.192887 + 0.0904254i
\(436\) 216.639 0.496878
\(437\) −94.4936 + 94.4936i −0.216233 + 0.216233i
\(438\) 324.529 21.6210i 0.740934 0.0493631i
\(439\) −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
\(441\) 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 −0.993241 0.116068i \(-0.962971\pi\)
0.116068 + 0.993241i \(0.462971\pi\)
\(444\) −241.771 211.568i −0.544529 0.476504i
\(445\) 78.6096 142.232i 0.176651 0.319623i
\(446\) −5.19500 −0.0116480
\(447\) −386.489 + 25.7490i −0.864629 + 0.0576041i
\(448\) 41.0100 38.1337i 0.0915402 0.0851198i
\(449\) 283.968 0.632445 0.316223 0.948685i \(-0.397585\pi\)
0.316223 + 0.948685i \(0.397585\pi\)
\(450\) 29.0296 316.871i 0.0645102 0.704158i
\(451\) 497.331i 1.10273i
\(452\) −35.1005 35.1005i −0.0776560 0.0776560i
\(453\) −154.846 + 10.3163i −0.341824 + 0.0227733i
\(454\) 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 \(-0.295034\pi\)
0.600335 + 0.799749i \(0.295034\pi\)
\(462\) −198.933 + 6.00904i −0.430592 + 0.0130066i
\(463\) 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
\(465\) −264.065 + 563.277i −0.567881 + 1.21135i
\(466\) −517.282 −1.11005
\(467\) 628.925 628.925i 1.34673 1.34673i 0.457549 0.889184i \(-0.348727\pi\)
0.889184 0.457549i \(-0.151273\pi\)
\(468\) 323.793 + 247.351i 0.691865 + 0.528528i
\(469\) −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
\(477\) 343.216 449.284i 0.719531 0.941896i
\(478\) 209.847 + 209.847i 0.439011 + 0.439011i
\(479\) 229.796i 0.479742i −0.970805 0.239871i \(-0.922895\pi\)
0.970805 0.239871i \(-0.0771051\pi\)
\(480\) −28.8582 79.7948i −0.0601212 0.166239i
\(481\) 1212.08i 2.51992i
\(482\) −174.145 + 174.145i −0.361296 + 0.361296i
\(483\) −347.893 + 10.5085i −0.720275 + 0.0217568i
\(484\) 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 \(0.0341598\pi\)
−0.994247 + 0.107110i \(0.965840\pi\)
\(492\) 29.5997 + 444.287i 0.0601620 + 0.903023i
\(493\) −44.5724 + 44.5724i −0.0904105 + 0.0904105i
\(494\) −258.120 −0.522511
\(495\) −109.572 + 280.956i −0.221358 + 0.567589i
\(496\) 165.894i 0.334464i
\(497\) −660.625 + 614.290i −1.32923 + 1.23600i
\(498\) 11.0554 + 165.939i 0.0221995 + 0.333211i
\(499\) 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
\(507\) −68.4873 1027.99i −0.135084 2.02758i
\(508\) −190.275 190.275i −0.374556 0.374556i
\(509\) 782.408i 1.53715i 0.639761 + 0.768574i \(0.279033\pi\)
−0.639761 + 0.768574i \(0.720967\pi\)
\(510\) 195.978 + 91.8746i 0.384270 + 0.180146i
\(511\) −536.278 19.4902i −1.04947 0.0381413i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 213.378 43.1592i 0.415942 0.0841311i
\(514\) −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 \(-0.569042\pi\)
−0.215205 + 0.976569i \(0.569042\pi\)
\(522\) 62.4855 + 47.7337i 0.119704 + 0.0914439i
\(523\) −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
\(525\) −101.321 + 515.130i −0.192992 + 0.981200i
\(526\) 440.421 0.837302
\(527\) −299.224 299.224i −0.567787 0.567787i
\(528\) 5.34582 + 80.2400i 0.0101247 + 0.151970i
\(529\) 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
\(537\) 69.9095 4.65757i 0.130185 0.00867331i
\(538\) 251.260 251.260i 0.467026 0.467026i
\(539\) 327.507 + 23.8369i 0.607619 + 0.0442243i
\(540\) 81.1639 257.512i 0.150304 0.476874i
\(541\) 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
\(543\) −26.3777 395.926i −0.0485778 0.729146i
\(544\) 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
\(552\) 9.34871 + 140.323i 0.0169361 + 0.254208i
\(553\) −132.165 + 122.896i −0.238997 + 0.222234i
\(554\) 596.622 1.07693
\(555\) 755.297 273.157i 1.36090 0.492175i
\(556\) 232.756i 0.418625i
\(557\) −502.514 502.514i −0.902180 0.902180i 0.0934442 0.995625i \(-0.470212\pi\)
−0.995625 + 0.0934442i \(0.970212\pi\)
\(558\) −320.447 + 419.478i −0.574277 + 0.751753i
\(559\) −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 0.994725 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
\(567\) 481.706 + 299.079i 0.849570 + 0.527476i
\(568\) 257.742 + 257.742i 0.453771 + 0.453771i
\(569\) −359.729 −0.632212 −0.316106 0.948724i \(-0.602376\pi\)
−0.316106 + 0.948724i \(0.602376\pi\)
\(570\) 58.1705 + 160.845i 0.102053 + 0.282184i
\(571\) 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
\(573\) −27.4546 412.090i −0.0479138 0.719180i
\(574\) 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
\(582\) 22.6239 + 339.582i 0.0388727 + 0.583474i
\(583\) −297.683 297.683i −0.510605 0.510605i
\(584\) 216.832i 0.371288i
\(585\) −932.783 + 409.353i −1.59450 + 0.699749i
\(586\) 246.246i 0.420216i
\(587\) −505.473 + 505.473i −0.861113 + 0.861113i −0.991467 0.130355i \(-0.958388\pi\)
0.130355 + 0.991467i \(0.458388\pi\)
\(588\) −293.994 1.80231i −0.499991 0.00306515i
\(589\) 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
\(595\) −306.075 183.983i −0.514412 0.309214i
\(596\) 258.231i 0.433273i
\(597\) 797.080 53.1037i 1.33514 0.0889510i
\(598\) 375.178 375.178i 0.627388 0.627388i
\(599\) 516.399 0.862102 0.431051 0.902328i \(-0.358143\pi\)
0.431051 + 0.902328i \(0.358143\pi\)
\(600\) 209.494 + 33.3530i 0.349156 + 0.0555884i
\(601\) 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
\(603\) −299.093 + 391.525i −0.496008 + 0.649296i
\(604\) 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
\(609\) −94.4649 88.9254i −0.155115 0.146019i
\(610\) −101.977 + 29.3787i −0.167176 + 0.0481618i
\(611\) 1261.82i 2.06517i
\(612\) 145.947 + 111.491i 0.238475 + 0.182175i
\(613\) −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
\(615\) −1007.92 472.514i −1.63889 0.768315i
\(616\) 4.81896 132.595i 0.00782299 0.215252i
\(617\) −771.937 771.937i −1.25111 1.25111i −0.955221 0.295892i \(-0.904383\pi\)
−0.295892 0.955221i \(-0.595617\pi\)
\(618\) 247.919 16.5170i 0.401163 0.0267266i
\(619\) 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
\(627\) −10.7758 161.743i −0.0171862 0.257963i
\(628\) −76.2640 + 76.2640i −0.121440 + 0.121440i
\(629\) 546.335i 0.868577i
\(630\) −176.828 + 408.879i −0.280679 + 0.649014i
\(631\) 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
\(633\) 311.781 20.7718i 0.492545 0.0328148i
\(634\) 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 \(0.244761\pi\)
−0.718648 + 0.695374i \(0.755239\pi\)
\(642\) −1.58238 23.7513i −0.00246476 0.0369957i
\(643\) 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
\(645\) 305.225 + 843.968i 0.473218 + 1.30848i
\(646\) −116.345 −0.180101
\(647\) 185.628 185.628i 0.286906 0.286906i −0.548950 0.835855i \(-0.684972\pi\)
0.835855 + 0.548950i \(0.184972\pi\)
\(648\) 113.697 198.899i 0.175459 0.306943i
\(649\) 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 −0.175190 0.984535i \(-0.556054\pi\)
0.984535 + 0.175190i \(0.0560540\pi\)
\(654\) −302.638 + 345.841i −0.462749 + 0.528809i
\(655\) −308.470 170.487i −0.470947 0.260285i
\(656\) −296.848 −0.452513
\(657\) −418.841 + 548.280i −0.637505 + 0.834521i
\(658\) 375.765 + 404.109i 0.571072 + 0.614147i
\(659\) −101.666 −0.154274 −0.0771369 0.997021i \(-0.524578\pi\)
−0.0771369 + 0.997021i \(0.524578\pi\)
\(660\) −182.034 85.3377i −0.275809 0.129300i
\(661\) 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
\(663\) −46.0614 691.375i −0.0694742 1.04280i
\(664\) −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
\(672\) 3.58669 + 118.740i 0.00533733 + 0.176696i
\(673\) −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
\(675\) 465.298 + 489.002i 0.689331 + 0.724447i
\(676\) 686.843 1.01604
\(677\) 710.321 710.321i 1.04922 1.04922i 0.0504936 0.998724i \(-0.483921\pi\)
0.998724 0.0504936i \(-0.0160794\pi\)
\(678\) 105.069 6.99998i 0.154969 0.0103245i
\(679\) 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 −0.854320 0.519747i \(-0.826026\pi\)
0.519747 + 0.854320i \(0.326026\pi\)
\(684\) 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
\(687\) −1033.81 + 68.8755i −1.50482 + 0.100255i
\(688\) 169.228 + 169.228i 0.245971 + 0.245971i
\(689\) 1422.04i 2.06391i
\(690\) −318.339 149.238i −0.461362 0.216287i
\(691\) 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
\(693\) 268.311 325.971i 0.387173 0.470376i
\(694\) 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 \(0.189664\pi\)
−0.827673 + 0.561211i \(0.810336\pi\)
\(702\) −847.199 + 171.360i −1.20684 + 0.244102i
\(703\) −305.279 + 305.279i −0.434252 + 0.434252i
\(704\) −53.6119 −0.0761533
\(705\) 786.290 284.366i 1.11530 0.403355i
\(706\) 410.867i 0.581964i
\(707\) −301.763 324.524i −0.426821 0.459016i
\(708\) −311.160 + 20.7304i −0.439491 + 0.0292802i
\(709\) 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
\(717\) −628.149 + 41.8491i −0.876080 + 0.0583670i
\(718\) −428.176 428.176i −0.596346 0.596346i
\(719\) 678.749i 0.944018i −0.881594 0.472009i \(-0.843529\pi\)
0.881594 0.472009i \(-0.156471\pi\)
\(720\) 167.698 + 65.4017i 0.232914 + 0.0908357i
\(721\) −409.681 14.8892i −0.568212 0.0206508i
\(722\) 295.989 + 295.989i 0.409957 + 0.409957i
\(723\) −34.7291 521.279i −0.0480347 0.720994i
\(724\) 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
\(732\) −89.8507 + 5.98611i −0.122747 + 0.00817775i
\(733\) −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
\(735\) 359.473 641.096i 0.489079 0.872240i
\(736\) −93.7560 −0.127386
\(737\) 259.413 + 259.413i 0.351985 + 0.351985i
\(738\) −750.608 573.403i −1.01708 0.776969i
\(739\) 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 −0.809295 0.587402i \(-0.800151\pi\)
0.587402 + 0.809295i \(0.300151\pi\)
\(744\) −264.832 231.749i −0.355957 0.311490i
\(745\) 565.023 + 312.280i 0.758419 + 0.419168i
\(746\) 765.227i 1.02577i
\(747\) −280.349 214.163i −0.375299 0.286698i
\(748\) 96.7001 96.7001i 0.129278 0.129278i
\(749\) −1.42643 + 39.2485i −0.00190444 + 0.0524013i
\(750\) −326.320 + 418.049i −0.435093 + 0.557399i
\(751\) 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
\(753\) 1273.06 84.8152i 1.69066 0.112636i
\(754\) 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 \(0.493758\pi\)
\(762\) 569.561 37.9458i 0.747456 0.0497976i
\(763\) 555.273 516.327i 0.727750 0.676707i
\(764\) 275.336 0.360387
\(765\) −420.443 + 184.512i −0.549599 + 0.241193i
\(766\) 930.211i 1.21437i