Properties

Label 210.3.k.a.167.1
Level 210
Weight 3
Character 210.167
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 167.1
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.a.83.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.99336 - 0.199427i) q^{3} -2.00000i q^{4} +(4.37611 - 2.41861i) q^{5} +(3.19279 - 2.79394i) q^{6} +(-5.12625 + 4.76671i) q^{7} +(2.00000 + 2.00000i) q^{8} +(8.92046 + 1.19391i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.99336 - 0.199427i) 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} +(-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} +(16.2954 - 13.2462i) q^{21} +(-6.70149 - 6.70149i) q^{22} +(-11.7195 - 11.7195i) q^{23} +(-5.58788 - 6.38558i) q^{24} +(13.3006 - 21.1682i) q^{25} +32.0132 q^{26} +(-26.4641 - 5.35279i) q^{27} +(9.53342 + 10.2525i) 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} +(-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} +(-3.04917 + 29.5415i) 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} +(-51.4196 + 36.4009i) 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} +(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} +(-31.9440 - 34.3535i) 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} +(-26.4924 - 32.5907i) 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} +(45.3138 + 52.4277i) q^{98} +(-8.00099 + 59.7803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

Character values

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

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

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
\(7\) −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 \(0.901473\pi\)
\(12\) −0.398853 + 5.98673i −0.0332378 + 0.498894i
\(13\) −16.0066 16.0066i −1.23128 1.23128i −0.963474 0.267802i \(-0.913703\pi\)
−0.267802 0.963474i \(-0.586297\pi\)
\(14\) 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 \(-0.347019\pi\)
−0.886716 + 0.462315i \(0.847019\pi\)
\(18\) −10.1144 + 7.72655i −0.561909 + 0.429253i
\(19\) −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
\(21\) 16.2954 13.2462i 0.775969 0.630771i
\(22\) −6.70149 6.70149i −0.304613 0.304613i
\(23\) −11.7195 11.7195i −0.509543 0.509543i 0.404843 0.914386i \(-0.367326\pi\)
−0.914386 + 0.404843i \(0.867326\pi\)
\(24\) −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
\(28\) 9.53342 + 10.2525i 0.340479 + 0.366161i
\(29\) −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
\(35\) −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 −0.999722 0.0235744i \(-0.992495\pi\)
−0.0235744 0.999722i \(-0.507505\pi\)
\(38\) 8.06294 8.06294i 0.212183 0.212183i
\(39\) 44.7214 + 51.1057i 1.14670 + 1.31040i
\(40\) 13.5894 + 3.91499i 0.339736 + 0.0978748i
\(41\) −74.2121 −1.81005 −0.905025 0.425358i \(-0.860148\pi\)
−0.905025 + 0.425358i \(0.860148\pi\)
\(42\) −3.04917 + 29.5415i −0.0725992 + 0.703370i
\(43\) −42.3069 + 42.3069i −0.983882 + 0.983882i −0.999872 0.0159899i \(-0.994910\pi\)
0.0159899 + 0.999872i \(0.494910\pi\)
\(44\) 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 \(-0.0479431\pi\)
−0.150049 + 0.988679i \(0.547943\pi\)
\(48\) 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 0.988611 0.150491i \(-0.0480854\pi\)
−0.150491 + 0.988611i \(0.548085\pi\)
\(54\) 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
\(63\) −51.4196 + 36.4009i −0.816184 + 0.577793i
\(64\) 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 0.356527 0.934285i \(-0.383961\pi\)
−0.934285 + 0.356527i \(0.883961\pi\)
\(68\) −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 \(-0.362043\pi\)
\(72\) 15.4531 + 20.2287i 0.214626 + 0.280955i
\(73\) 54.2081 + 54.2081i 0.742576 + 0.742576i 0.973073 0.230497i \(-0.0740352\pi\)
−0.230497 + 0.973073i \(0.574035\pi\)
\(74\) 75.7239 1.02330
\(75\) −44.0351 + 60.7117i −0.587135 + 0.809489i
\(76\) 16.1259i 0.212183i
\(77\) −31.9440 34.3535i −0.414858 0.446150i
\(78\) −95.8271 6.38427i −1.22855 0.0818497i
\(79\) 25.7821i 0.326355i −0.986597 0.163178i \(-0.947826\pi\)
0.986597 0.163178i \(-0.0521743\pi\)
\(80\) −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 \(-0.674118\pi\)
0.854084 + 0.520134i \(0.174118\pi\)
\(84\) −26.4924 32.5907i −0.315385 0.387985i
\(85\) −49.0227 14.1230i −0.576737 0.166153i
\(86\) 84.6139i 0.983882i
\(87\) 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 \(-0.614309\pi\)
0.936210 + 0.351442i \(0.114309\pi\)
\(98\) 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 \(-0.398533\pi\)
0.313398 + 0.949622i \(0.398533\pi\)
\(102\) −43.1932 2.87765i −0.423463 0.0282123i
\(103\) 41.4114 + 41.4114i 0.402052 + 0.402052i 0.878956 0.476904i \(-0.158241\pi\)
−0.476904 + 0.878956i \(0.658241\pi\)
\(104\) 64.0263i 0.615638i
\(105\) 39.2728 97.3789i 0.374027 0.927418i
\(106\) −88.8408 −0.838121
\(107\) 3.96732 3.96732i 0.0370777 0.0370777i −0.688325 0.725403i \(-0.741654\pi\)
0.725403 + 0.688325i \(0.241654\pi\)
\(108\) −10.7056 + 52.9282i −0.0991258 + 0.490076i
\(109\) 108.319i 0.993756i 0.867820 + 0.496878i \(0.165520\pi\)
−0.867820 + 0.496878i \(0.834480\pi\)
\(110\) −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 \(-0.285028\pi\)
−0.780486 + 0.625174i \(0.785028\pi\)
\(114\) −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
\(126\) 15.0186 87.8205i 0.119195 0.696988i
\(127\) −95.1373 95.1373i −0.749113 0.749113i 0.225200 0.974313i \(-0.427696\pi\)
−0.974313 + 0.225200i \(0.927696\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 135.077 118.203i 1.04711 0.916302i
\(130\) 140.093 77.4274i 1.07764 0.595596i
\(131\) −70.4896 −0.538088 −0.269044 0.963128i \(-0.586708\pi\)
−0.269044 + 0.963128i \(0.586708\pi\)
\(132\) −40.1200 2.67291i −0.303939 0.0202493i
\(133\) 41.3327 38.4337i 0.310772 0.288975i
\(134\) 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 −0.819084 0.573674i \(-0.805518\pi\)
0.573674 + 0.819084i \(0.305518\pi\)
\(138\) −70.1614 4.67436i −0.508416 0.0338722i
\(139\) −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
\(147\) −20.3934 + 145.579i −0.138731 + 0.990330i
\(148\) −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 \(-0.804939\pi\)
0.575161 + 0.818040i \(0.304939\pi\)
\(158\) 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 −0.870595 0.492001i \(-0.836266\pi\)
0.492001 + 0.870595i \(0.336266\pi\)
\(164\) 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 \(-0.00892391\pi\)
−0.0280316 + 0.999607i \(0.508924\pi\)
\(168\) 59.0831 + 6.09833i 0.351685 + 0.0362996i
\(169\) 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 \(-0.629082\pi\)
0.918896 + 0.394499i \(0.129082\pi\)
\(174\) −19.7247 + 17.2606i −0.113360 + 0.0991991i
\(175\) 32.7203 + 171.914i 0.186973 + 0.982365i
\(176\) 26.8060i 0.152307i
\(177\) 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 \(-0.119061\pi\)
\(182\) −164.108 + 152.597i −0.901690 + 0.838448i
\(183\) 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
\(189\) 161.177 98.7068i 0.852787 0.522258i
\(190\) 15.7832 54.7854i 0.0830693 0.288344i
\(191\) 137.668i 0.720774i 0.932803 + 0.360387i \(0.117355\pi\)
−0.932803 + 0.360387i \(0.882645\pi\)
\(192\) 1.59541 23.9469i 0.00830944 0.124724i
\(193\) 188.004 188.004i 0.974116 0.974116i −0.0255577 0.999673i \(-0.508136\pi\)
0.999673 + 0.0255577i \(0.00813615\pi\)
\(194\) 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 −0.712931 0.701234i \(-0.752633\pi\)
0.701234 + 0.712931i \(0.252633\pi\)
\(198\) −51.7793 67.7813i −0.261512 0.342330i
\(199\) −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
\(207\) −90.5512 118.535i −0.437446 0.572634i
\(208\) 64.0263 + 64.0263i 0.307819 + 0.307819i
\(209\) 54.0337i 0.258534i
\(210\) 58.1060 + 136.652i 0.276695 + 0.650722i
\(211\) 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
\(217\) 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
\(222\) −226.669 15.1014i −1.02103 0.0680242i
\(223\) −2.59750 2.59750i −0.0116480 0.0116480i 0.701259 0.712907i \(-0.252622\pi\)
−0.712907 + 0.701259i \(0.752622\pi\)
\(224\) −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 \(-0.190039\pi\)
−0.562183 + 0.827013i \(0.690039\pi\)
\(228\) 3.21593 48.2706i 0.0141050 0.211713i
\(229\) 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
\(231\) 88.7692 + 109.203i 0.384282 + 0.472741i
\(232\) −12.3558 12.3558i −0.0532577 0.0532577i
\(233\) 258.641 + 258.641i 1.11005 + 1.11005i 0.993143 + 0.116904i \(0.0372970\pi\)
0.116904 + 0.993143i \(0.462703\pi\)
\(234\) 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
\(238\) −73.9700 + 68.7819i −0.310798 + 0.289000i
\(239\) −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
\(245\) −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 \(-0.821715\pi\)
−0.847202 + 0.531271i \(0.821715\pi\)
\(252\) 72.8019 + 102.839i 0.288896 + 0.408092i
\(253\) 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 \(-0.271770\pi\)
−0.753776 + 0.657131i \(0.771770\pi\)
\(258\) −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 0.151201 0.988503i \(-0.451686\pi\)
−0.988503 + 0.151201i \(0.951686\pi\)
\(264\) 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
\(273\) −472.859 48.8067i −1.73208 0.178779i
\(274\) 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 −0.996783 0.0801518i \(-0.974459\pi\)
−0.0801518 0.996783i \(-0.525541\pi\)
\(278\) 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 \(-0.0600062\pi\)
\(282\) 235.970 + 15.7210i 0.836775 + 0.0557483i
\(283\) −205.970 205.970i −0.727811 0.727811i 0.242372 0.970183i \(-0.422074\pi\)
−0.970183 + 0.242372i \(0.922074\pi\)
\(284\) −257.742 −0.907542
\(285\) 109.508 51.3373i 0.384238 0.180131i
\(286\) 214.536i 0.750125i
\(287\) 380.430 353.747i 1.32554 1.23257i
\(288\) 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 \(-0.846032\pi\)
0.465062 + 0.885278i \(0.346032\pi\)
\(294\) −125.185 165.972i −0.425800 0.564530i
\(295\) 125.707 + 227.448i 0.426126 + 0.771010i
\(296\) 151.448i 0.511648i
\(297\) 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 \(-0.931751\pi\)
0.212771 + 0.977102i \(0.431751\pi\)
\(308\) −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 \(-0.332277\pi\)
0.502870 + 0.864362i \(0.332277\pi\)
\(312\) −12.7685 + 191.654i −0.0409248 + 0.614276i
\(313\) 240.526 + 240.526i 0.768452 + 0.768452i 0.977834 0.209382i \(-0.0671451\pi\)
−0.209382 + 0.977834i \(0.567145\pi\)
\(314\) 76.2640i 0.242879i
\(315\) −136.978 + 283.658i −0.434850 + 0.900503i
\(316\) −51.5641 −0.163178
\(317\) −170.827 + 170.827i −0.538887 + 0.538887i −0.923202 0.384315i \(-0.874438\pi\)
0.384315 + 0.923202i \(0.374438\pi\)
\(318\) 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
\(322\) −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
\(327\) 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
\(336\) −65.1814 + 52.9847i −0.193992 + 0.157693i
\(337\) 159.190 + 159.190i 0.472375 + 0.472375i 0.902682 0.430307i \(-0.141595\pi\)
−0.430307 + 0.902682i \(0.641595\pi\)
\(338\) −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
\(343\) 214.719 + 267.479i 0.626002 + 0.779821i
\(344\) −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 −0.176005 0.984389i \(-0.556318\pi\)
0.984389 + 0.176005i \(0.0563175\pi\)
\(348\) 2.46407 36.9853i 0.00708066 0.106280i
\(349\) −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 \(-0.615001\pi\)
0.935443 + 0.353479i \(0.115001\pi\)
\(354\) 145.215 + 165.945i 0.410211 + 0.468772i
\(355\) −311.689 563.953i −0.877996 1.58860i
\(356\) 65.0039 0.182595
\(357\) −213.137 21.9992i −0.597022 0.0616224i
\(358\) −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 \(-0.845027\pi\)
0.467854 + 0.883806i \(0.345027\pi\)
\(368\) 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 0.0261145 0.999659i \(-0.491687\pi\)
0.999659 0.0261145i \(-0.00831345\pi\)
\(374\) 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
\(378\) −62.4700 + 259.884i −0.165264 + 0.687523i
\(379\) 726.851i 1.91781i −0.283721 0.958907i \(-0.591569\pi\)
0.283721 0.958907i \(-0.408431\pi\)
\(380\) 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 0.244801 0.969573i \(-0.421277\pi\)
0.969573 0.244801i \(-0.0787225\pi\)
\(384\) 22.3515 + 25.5423i 0.0582070 + 0.0665165i
\(385\) −222.878 73.0745i −0.578905 0.189804i
\(386\) 376.009i 0.974116i
\(387\) −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
\(392\) 104.855 90.6275i 0.267488 0.231193i
\(393\) 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 \(-0.561854\pi\)
0.981179 + 0.193100i \(0.0618541\pi\)
\(398\) 266.282 266.282i 0.669051 0.669051i
\(399\) −131.388 + 106.803i −0.329294 + 0.267677i
\(400\) −53.2025 + 84.6728i −0.133006 + 0.211682i
\(401\) 641.900i 1.60075i 0.599501 + 0.800374i \(0.295366\pi\)
−0.599501 + 0.800374i \(0.704634\pi\)
\(402\) −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 \(-0.552612\pi\)
−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
\(417\) 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 \(-0.103769\pi\)
\(420\) −194.758 78.5457i −0.463709 0.187014i
\(421\) −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
\(427\) −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 \(0.896009\pi\)
\(432\) 105.856 + 21.4112i 0.245038 + 0.0495629i
\(433\) −249.817 249.817i −0.576945 0.576945i 0.357116 0.934060i \(-0.383760\pi\)
−0.934060 + 0.357116i \(0.883760\pi\)
\(434\) −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 \(-0.298320\pi\)
0.592047 + 0.805903i \(0.298320\pi\)
\(440\) −26.2363 + 91.0695i −0.0596279 + 0.206976i
\(441\) 90.0771 431.703i 0.204256 0.978917i
\(442\) −230.969 230.969i −0.522555 0.522555i
\(443\) −388.588 388.588i −0.877173 0.877173i 0.116068 0.993241i \(-0.462971\pi\)
−0.993241 + 0.116068i \(0.962971\pi\)
\(444\) 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
\(448\) −38.1337 41.0100i −0.0851198 0.0915402i
\(449\) 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
\(455\) 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 0.451594 0.892224i \(-0.350856\pi\)
−0.892224 + 0.451594i \(0.850856\pi\)
\(458\) −345.368 + 345.368i −0.754078 + 0.754078i
\(459\) 152.314 + 229.553i 0.331839 + 0.500116i
\(460\) −45.8817 + 159.261i −0.0997429 + 0.346220i
\(461\) −553.509 −1.20067 −0.600335 0.799749i \(-0.704966\pi\)
−0.600335 + 0.799749i \(0.704966\pi\)
\(462\) −197.972 20.4340i −0.428511 0.0442293i
\(463\) 574.866 574.866i 1.24161 1.24161i 0.282278 0.959333i \(-0.408910\pi\)
0.959333 0.282278i \(-0.0910902\pi\)
\(464\) 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 −0.889184 0.457549i \(-0.848727\pi\)
−0.457549 0.889184i \(-0.651273\pi\)
\(468\) −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
\(483\) −346.212 35.7347i −0.716795 0.0739849i
\(484\) 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 0.764163 0.645023i \(-0.223152\pi\)
−0.645023 + 0.764163i \(0.723152\pi\)
\(488\) −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 \(-0.0341598\pi\)
\(492\) 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
\(497\) 614.290 + 660.625i 1.23600 + 1.32923i
\(498\) 11.0554 165.939i 0.0221995 0.333211i
\(499\) 29.9809i 0.0600819i 0.999549 + 0.0300409i \(0.00956377\pi\)
−0.999549 + 0.0300409i \(0.990436\pi\)
\(500\) −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 \(-0.678194\pi\)
0.847355 + 0.531027i \(0.178194\pi\)
\(504\) −175.641 30.0373i −0.348494 0.0595977i
\(505\) 277.035 153.113i 0.548585 0.303195i
\(506\) 157.076i 0.310427i
\(507\) 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
\(518\) −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 \(-0.430958\pi\)
0.215205 + 0.976569i \(0.430958\pi\)
\(522\) 62.4855 47.7337i 0.119704 0.0914439i
\(523\) 278.114 + 278.114i 0.531767 + 0.531767i 0.921098 0.389331i \(-0.127294\pi\)
−0.389331 + 0.921098i \(0.627294\pi\)
\(524\) 140.979i 0.269044i
\(525\) −63.6595 521.126i −0.121256 0.992621i
\(526\) 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
\(532\) −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
\(537\) −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
\(546\) 521.666 424.052i 0.955432 0.776653i
\(547\) −15.9985 15.9985i −0.0292477 0.0292477i 0.692332 0.721579i \(-0.256584\pi\)
−0.721579 + 0.692332i \(0.756584\pi\)
\(548\) 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
\(553\) 122.896 + 132.165i 0.222234 + 0.238997i
\(554\) 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 −0.995625 0.0934442i \(-0.970212\pi\)
0.0934442 + 0.995625i \(0.470212\pi\)
\(558\) 320.447 + 419.478i 0.574277 + 0.751753i
\(559\) 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 \(-0.967292\pi\)
0.102575 + 0.994725i \(0.467292\pi\)
\(564\) −251.691 + 220.249i −0.446261 + 0.390513i
\(565\) −119.249 34.3546i −0.211060 0.0608046i
\(566\) 411.941 0.727811
\(567\) −502.146 + 263.323i −0.885618 + 0.464414i
\(568\) 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 \(-0.826674\pi\)
0.518007 + 0.855376i \(0.326674\pi\)
\(578\) 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 \(-0.0416115\pi\)
−0.130355 + 0.991467i \(0.541612\pi\)
\(588\) 291.157 + 40.7868i 0.495165 + 0.0693653i
\(589\) 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 \(-0.720314\pi\)
0.769884 + 0.638183i \(0.220314\pi\)
\(594\) 141.477 + 213.220i 0.238177 + 0.358957i
\(595\) 318.623 161.279i 0.535501 0.271057i
\(596\) 258.231i 0.433273i
\(597\) 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 \(-0.266974\pi\)
\(602\) 403.330 + 433.752i 0.669983 + 0.720519i
\(603\) −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 \(-0.723513\pi\)
0.763431 + 0.645889i \(0.223513\pi\)
\(608\) −32.2518 + 32.2518i −0.0530457 + 0.0530457i
\(609\) −100.671 + 81.8335i −0.165305 + 0.134374i
\(610\) −101.977 29.3787i −0.167176 0.0481618i
\(611\) 1261.82i 2.06517i
\(612\) −145.947 + 111.491i −0.238475 + 0.182175i
\(613\) −32.1532 + 32.1532i −0.0524522 + 0.0524522i −0.732846 0.680394i \(-0.761809\pi\)
0.680394 + 0.732846i \(0.261809\pi\)
\(614\) 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 −0.295892 + 0.955221i \(0.595617\pi\)
−0.955221 + 0.295892i \(0.904383\pi\)
\(618\) 247.919 + 16.5170i 0.401163 + 0.0267266i
\(619\) −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
\(627\) −10.7758 + 161.743i −0.0171862 + 0.257963i
\(628\) 76.2640 + 76.2640i 0.121440 + 0.121440i
\(629\) 546.335i 0.868577i
\(630\) −146.681 420.636i −0.232826 0.667677i
\(631\) 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
\(637\) −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 \(-0.244761\pi\)
\(642\) 1.58238 23.7513i 0.00246476 0.0369957i
\(643\) −319.764 319.764i −0.497300 0.497300i 0.413297 0.910596i \(-0.364377\pi\)
−0.910596 + 0.413297i \(0.864377\pi\)
\(644\) 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 \(-0.315028\pi\)
−0.835855 + 0.548950i \(0.815028\pi\)
\(648\) 113.697 + 198.899i 0.175459 + 0.306943i
\(649\) −348.309 −0.536686
\(650\) 425.795 677.661i 0.655070 1.04256i
\(651\) −549.365 675.825i −0.843879 1.03813i
\(652\) 123.422 + 123.422i 0.189297 + 0.189297i
\(653\) 528.502 + 528.502i 0.809345 + 0.809345i 0.984535 0.175190i \(-0.0560540\pi\)
−0.175190 + 0.984535i \(0.556054\pi\)
\(654\) 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
\(658\) 404.109 375.765i 0.614147 0.571072i
\(659\) −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
\(665\) 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
\(672\) 12.1967 118.166i 0.0181498 0.175842i
\(673\) −835.168 + 835.168i −1.24096 + 1.24096i −0.281361 + 0.959602i \(0.590786\pi\)
−0.959602 + 0.281361i \(0.909214\pi\)
\(674\) −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 −0.998724 0.0504936i \(-0.983921\pi\)
−0.0504936 0.998724i \(-0.516079\pi\)
\(678\) −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 0.519747 0.854320i \(-0.326026\pi\)
−0.854320 + 0.519747i \(0.826026\pi\)
\(684\) −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
\(693\) −243.940 344.588i −0.352006 0.497240i
\(694\) 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 \(-0.189664\pi\)
\(702\) −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
\(707\) −324.524 + 301.763i −0.459016 + 0.426821i
\(708\) −311.160 20.7304i −0.439491 0.0292802i
\(709\) 1314.72i 1.85434i 0.374647 + 0.927168i \(0.377764\pi\)
−0.374647 + 0.927168i \(0.622236\pi\)
\(710\) 875.642 + 252.264i 1.23330 + 0.355302i
\(711\) 30.7815 229.988i 0.0432933 0.323471i
\(712\) −65.0039 + 65.0039i −0.0912976 + 0.0912976i
\(713\) −486.048 + 486.048i −0.681695 + 0.681695i
\(714\) 235.136 191.138i 0.329322 0.267700i
\(715\) 209.977 728.855i 0.293673 1.01938i
\(716\) 46.7096i 0.0652369i
\(717\) 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 \(-0.802208\pi\)
0.582160 + 0.813074i \(0.302208\pi\)
\(728\) 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
\(732\) −89.8507 5.98611i −0.122747 0.00817775i
\(733\) 138.636 + 138.636i 0.189135 + 0.189135i 0.795322 0.606187i \(-0.207302\pi\)
−0.606187 + 0.795322i \(0.707302\pi\)
\(734\) 305.309i 0.415952i
\(735\) 262.854 + 686.391i 0.357625 + 0.933865i
\(736\) −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 \(-0.897460\pi\)
0.948560 0.316598i \(-0.102540\pi\)
\(740\) −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 \(-0.300151\pi\)
−0.809295 + 0.587402i \(0.800151\pi\)
\(744\) −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
\(756\) −197.414 322.354i −0.261129 0.426394i
\(757\) 846.245 + 846.245i 1.11789 + 1.11789i 0.992050 + 0.125843i \(0.0401635\pi\)
0.125843 + 0.992050i \(0.459837\pi\)
\(758\) 726.851 + 726.851i 0.958907 + 0.958907i
\(759\) −250.756 + 219.430i −0.330376 + 0.289105i
\(760\) −109.571 31.5664i −0.144172 0.0415347i
\(761\) −29.8430 −0.0392155 −0.0196078 0.999808i \(-0.506242\pi\)
−0.0196078 + 0.999808i \(0.506242\pi\)
\(762\) −569.561 37.9458i −0.747456 0.0497976i
\(763\) −516.327 555.273i −0.676707 0.727750i
\(764\) 275.336 0.360387
\(765\) −420.443 184.512i −0.549599 0.241193i
\(766\) 930.211i 1.21437i
\(767\) 831.941 831.941i 1.08467 1.08467i
\(768\) −47.8938