Properties

Label 210.3.k.a.83.1
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 83.1
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.1

$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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
\(7\) −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 \(-0.901473\pi\)
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 \(0.586297\pi\)
−0.963474 + 0.267802i \(0.913703\pi\)
\(14\) 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 −0.886716 0.462315i \(-0.847019\pi\)
0.462315 + 0.886716i \(0.347019\pi\)
\(18\) −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 −0.914386 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
\(28\) 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 \(0.233246\pi\)
−0.743328 + 0.668927i \(0.766754\pi\)
\(32\) 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 −0.0235744 + 0.999722i \(0.507505\pi\)
−0.999722 + 0.0235744i \(0.992495\pi\)
\(38\) 8.06294 + 8.06294i 0.212183 + 0.212183i
\(39\) 44.7214 51.1057i 1.14670 1.31040i
\(40\) 13.5894 3.91499i 0.339736 0.0978748i
\(41\) −74.2121 −1.81005 −0.905025 0.425358i \(-0.860148\pi\)
−0.905025 + 0.425358i \(0.860148\pi\)
\(42\) −3.04917 29.5415i −0.0725992 0.703370i
\(43\) −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 −0.150049 0.988679i \(-0.547943\pi\)
0.988679 + 0.150049i \(0.0479431\pi\)
\(48\) 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 \(-0.854813\pi\)
0.897769 0.440466i \(-0.145187\pi\)
\(60\) 12.7341 27.1632i 0.212236 0.452721i
\(61\) 15.0083i 0.246038i −0.992404 0.123019i \(-0.960742\pi\)
0.992404 0.123019i \(-0.0392576\pi\)
\(62\) 41.4735 41.4735i 0.668927 0.668927i
\(63\) −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 −0.934285 0.356527i \(-0.883961\pi\)
0.356527 + 0.934285i \(0.383961\pi\)
\(68\) −14.4296 14.4296i −0.212201 0.212201i
\(69\) 32.7435 37.4179i 0.474544 0.542288i
\(70\) −22.3538 + 44.1623i −0.319340 + 0.630890i
\(71\) 128.871i 1.81508i 0.419962 + 0.907542i \(0.362043\pi\)
−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 −0.230497 0.973073i \(-0.574035\pi\)
0.973073 + 0.230497i \(0.0740352\pi\)
\(74\) 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 \(0.0521743\pi\)
−0.986597 + 0.163178i \(0.947826\pi\)
\(80\) −17.5044 9.67445i −0.218805 0.120931i
\(81\) 78.1491 21.3005i 0.964804 0.262969i
\(82\) 74.2121 + 74.2121i 0.905025 + 0.905025i
\(83\) 27.7179 + 27.7179i 0.333950 + 0.333950i 0.854084 0.520134i \(-0.174118\pi\)
−0.520134 + 0.854084i \(0.674118\pi\)
\(84\) −26.4924 + 32.5907i −0.315385 + 0.387985i
\(85\) −49.0227 + 14.1230i −0.576737 + 0.166153i
\(86\) 84.6139i 0.983882i
\(87\) 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 \(-0.941550\pi\)
0.983188 0.182595i \(-0.0584498\pi\)
\(90\) −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 0.936210 0.351442i \(-0.114309\pi\)
−0.351442 + 0.936210i \(0.614309\pi\)
\(98\) 45.3138 52.4277i 0.462385 0.534976i
\(99\) −8.00099 59.7803i −0.0808181 0.603842i
\(100\) −42.3364 + 26.6013i −0.423364 + 0.266013i
\(101\) 63.3063 0.626795 0.313398 0.949622i \(-0.398533\pi\)
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 −0.476904 0.878956i \(-0.658241\pi\)
0.878956 + 0.476904i \(0.158241\pi\)
\(104\) 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 0.725403 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
\(112\) 20.5050 + 19.0668i 0.183080 + 0.170240i
\(113\) −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
\(126\) 15.0186 + 87.8205i 0.119195 + 0.696988i
\(127\) −95.1373 + 95.1373i −0.749113 + 0.749113i −0.974313 0.225200i \(-0.927696\pi\)
0.225200 + 0.974313i \(0.427696\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 135.077 + 118.203i 1.04711 + 0.916302i
\(130\) 140.093 + 77.4274i 1.07764 + 0.595596i
\(131\) −70.4896 −0.538088 −0.269044 0.963128i \(-0.586708\pi\)
−0.269044 + 0.963128i \(0.586708\pi\)
\(132\) −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 0.573674 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 \(-0.637488\pi\)
−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 0.575161 0.818040i \(-0.304939\pi\)
−0.818040 + 0.575161i \(0.804939\pi\)
\(158\) 25.7821 25.7821i 0.163178 0.163178i
\(159\) −124.108 + 141.825i −0.780552 + 0.891981i
\(160\) 7.82998 + 27.1789i 0.0489374 + 0.169868i
\(161\) 115.941 4.21368i 0.720128 0.0261719i
\(162\) −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 −0.0280316 0.999607i \(-0.508924\pi\)
0.999607 + 0.0280316i \(0.00892391\pi\)
\(168\) 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 0.918896 0.394499i \(-0.129082\pi\)
−0.394499 + 0.918896i \(0.629082\pi\)
\(174\) −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 \(0.119061\pi\)
−0.930858 + 0.365381i \(0.880939\pi\)
\(182\) −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 \(-0.882645\pi\)
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 \(-0.733299\pi\)
−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 −0.712907 0.701259i \(-0.752622\pi\)
0.701259 + 0.712907i \(0.252622\pi\)
\(224\) −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 −0.562183 0.827013i \(-0.690039\pi\)
0.827013 + 0.562183i \(0.190039\pi\)
\(228\) 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 0.116904 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
\(238\) −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 \(0.117666\pi\)
−0.932451 + 0.361296i \(0.882334\pi\)
\(242\) −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 −0.753776 0.657131i \(-0.771770\pi\)
0.657131 + 0.753776i \(0.271770\pi\)
\(258\) −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 \(-0.845325\pi\)
0.884243 0.467026i \(-0.154675\pi\)
\(270\) 88.1740 + 169.338i 0.326571 + 0.627178i
\(271\) 101.261i 0.373657i −0.982393 0.186829i \(-0.940179\pi\)
0.982393 0.186829i \(-0.0598209\pi\)
\(272\) 28.8593 28.8593i 0.106100 0.106100i
\(273\) −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 −0.0801518 + 0.996783i \(0.525541\pi\)
−0.996783 + 0.0801518i \(0.974459\pi\)
\(278\) 116.378 + 116.378i 0.418625 + 0.418625i
\(279\) 49.5157 + 369.962i 0.177476 + 1.32603i
\(280\) −88.3245 44.7077i −0.315445 0.159670i
\(281\) 105.319i 0.374801i 0.982284 + 0.187400i \(0.0600062\pi\)
−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 −0.970183 0.242372i \(-0.922074\pi\)
0.242372 + 0.970183i \(0.422074\pi\)
\(284\) −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 0.465062 0.885278i \(-0.346032\pi\)
−0.885278 + 0.465062i \(0.846032\pi\)
\(294\) −125.185 + 165.972i −0.425800 + 0.564530i
\(295\) 125.707 227.448i 0.426126 0.771010i
\(296\) 151.448i 0.511648i
\(297\) 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 0.212771 0.977102i \(-0.431751\pi\)
−0.977102 + 0.212771i \(0.931751\pi\)
\(308\) −68.7071 63.8881i −0.223075 0.207429i
\(309\) −115.701 + 132.218i −0.374436 + 0.427889i
\(310\) 281.801 81.1842i 0.909034 0.261884i
\(311\) 312.785 1.00574 0.502870 0.864362i \(-0.332277\pi\)
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 −0.209382 0.977834i \(-0.567145\pi\)
0.977834 + 0.209382i \(0.0671451\pi\)
\(314\) 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 0.384315 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
\(322\) −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 −0.430307 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
\(343\) 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 0.984389 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 \(-0.757098\pi\)
−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 0.935443 0.353479i \(-0.115001\pi\)
−0.353479 + 0.935443i \(0.615001\pi\)
\(354\) 145.215 165.945i 0.410211 0.468772i
\(355\) −311.689 + 563.953i −0.877996 + 1.58860i
\(356\) 65.0039 0.182595
\(357\) −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 0.467854 0.883806i \(-0.345027\pi\)
−0.883806 + 0.467854i \(0.845027\pi\)
\(368\) 46.8780 46.8780i 0.127386 0.127386i
\(369\) −662.006 + 88.6027i −1.79405 + 0.240116i
\(370\) 331.376 + 183.147i 0.895611 + 0.494991i
\(371\) −439.449 + 15.9711i −1.18450 + 0.0430488i
\(372\) 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
\(378\) −62.4700 259.884i −0.165264 0.687523i
\(379\) 726.851i 1.91781i 0.283721 + 0.958907i \(0.408431\pi\)
−0.283721 + 0.958907i \(0.591569\pi\)
\(380\) 39.0022 70.5686i 0.102637 0.185707i
\(381\) 265.808 303.753i 0.697658 0.797253i
\(382\) −137.668 + 137.668i −0.360387 + 0.360387i
\(383\) 465.105 + 465.105i 1.21437 + 1.21437i 0.969573 + 0.244801i \(0.0787225\pi\)
0.244801 + 0.969573i \(0.421277\pi\)
\(384\) 22.3515 25.5423i 0.0582070 0.0665165i
\(385\) −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 0.981179 0.193100i \(-0.0618541\pi\)
−0.193100 + 0.981179i \(0.561854\pi\)
\(398\) 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 \(-0.704634\pi\)
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 \(-0.552612\pi\)
−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 \(0.103769\pi\)
−0.947331 + 0.320255i \(0.896231\pi\)
\(420\) −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 \(-0.896009\pi\)
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 −0.934060 0.357116i \(-0.883760\pi\)
0.357116 + 0.934060i \(0.383760\pi\)
\(434\) −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 −0.993241 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
\(448\) −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 −0.892224 0.451594i \(-0.850856\pi\)
0.451594 + 0.892224i \(0.350856\pi\)
\(458\) −345.368 345.368i −0.754078 0.754078i
\(459\) 152.314 229.553i 0.331839 0.500116i
\(460\) −45.8817 159.261i −0.0997429 0.346220i
\(461\) −553.509 −1.20067 −0.600335 0.799749i \(-0.704966\pi\)
−0.600335 + 0.799749i \(0.704966\pi\)
\(462\) −197.972 + 20.4340i −0.428511 + 0.0442293i
\(463\) 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 \(0.651273\pi\)
−0.889184 + 0.457549i \(0.848727\pi\)
\(468\) −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 \(0.0771051\pi\)
−0.970805 + 0.239871i \(0.922895\pi\)
\(480\) −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 −0.645023 0.764163i \(-0.723152\pi\)
0.764163 + 0.645023i \(0.223152\pi\)
\(488\) −30.0166 30.0166i −0.0615095 0.0615095i
\(489\) 197.030 + 172.416i 0.402924 + 0.352590i
\(490\) 325.100 119.833i 0.663470 0.244557i
\(491\) 105.182i 0.214221i 0.994247 + 0.107110i \(0.0341598\pi\)
−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
\(497\) 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 \(-0.990436\pi\)
0.999549 0.0300409i \(-0.00956377\pi\)
\(500\) −249.607 + 14.0147i −0.499214 + 0.0280293i
\(501\) −453.325 + 518.040i −0.904840 + 1.03401i
\(502\) 425.295 + 425.295i 0.847202 + 0.847202i
\(503\) 159.113 + 159.113i 0.316328 + 0.316328i 0.847355 0.531027i \(-0.178194\pi\)
−0.531027 + 0.847355i \(0.678194\pi\)
\(504\) −175.641 + 30.0373i −0.348494 + 0.0595977i
\(505\) 277.035 + 153.113i 0.548585 + 0.303195i
\(506\) 157.076i 0.310427i
\(507\) 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 \(-0.720967\pi\)
0.639761 0.768574i \(-0.279033\pi\)
\(510\) −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 −0.389331 0.921098i \(-0.627294\pi\)
0.921098 + 0.389331i \(0.127294\pi\)
\(524\) 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 −0.721579 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
\(553\) 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 0.0934442 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
\(560\) 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 0.102575 0.994725i \(-0.467292\pi\)
−0.994725 + 0.102575i \(0.967292\pi\)
\(564\) −251.691 220.249i −0.446261 0.390513i
\(565\) −119.249 + 34.3546i −0.211060 + 0.0608046i
\(566\) 411.941 0.727811
\(567\) −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 0.518007 0.855376i \(-0.326674\pi\)
−0.855376 + 0.518007i \(0.826674\pi\)
\(578\) 184.893 184.893i 0.319884 0.319884i
\(579\) −600.258 525.272i −1.03672 0.907206i
\(580\) 29.8838 54.0702i 0.0515238 0.0932245i
\(581\) −9.96580 274.212i −0.0171528 0.471965i
\(582\) 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 −0.130355 0.991467i \(-0.541612\pi\)
0.991467 + 0.130355i \(0.0416115\pi\)
\(588\) 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 0.769884 0.638183i \(-0.220314\pi\)
−0.638183 + 0.769884i \(0.720314\pi\)
\(594\) 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 \(0.266974\pi\)
−0.668412 + 0.743791i \(0.733026\pi\)
\(602\) 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 0.763431 0.645889i \(-0.223513\pi\)
−0.645889 + 0.763431i \(0.723513\pi\)
\(608\) −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 0.680394 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 \(-0.563548\pi\)
−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 \(0.244761\pi\)
−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 −0.910596 0.413297i \(-0.864377\pi\)
0.413297 + 0.910596i \(0.364377\pi\)
\(644\) 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 −0.835855 0.548950i \(-0.815028\pi\)
0.548950 + 0.835855i \(0.315028\pi\)
\(648\) 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 −0.175190 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
\(658\) 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 \(0.140268\pi\)
−0.904469 + 0.426540i \(0.859732\pi\)
\(662\) 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 −0.959602 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 \(0.516079\pi\)
−0.998724 + 0.0504936i \(0.983921\pi\)
\(678\) −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 \(0.0778090\pi\)
−0.970272 + 0.242017i \(0.922191\pi\)
\(692\) −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 \(0.189664\pi\)
−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
\(707\) −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 \(-0.622236\pi\)
0.374647 0.927168i \(-0.377764\pi\)
\(710\) 875.642 252.264i 1.23330 0.355302i
\(711\) 30.7815 + 229.988i 0.0432933 + 0.323471i
\(712\) −65.0039 65.0039i −0.0912976 0.0912976i
\(713\) −486.048 486.048i −0.681695 0.681695i
\(714\) 235.136 + 191.138i 0.329322 + 0.267700i
\(715\) 209.977 + 728.855i 0.293673 + 1.01938i
\(716\) 46.7096i 0.0652369i
\(717\) 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 \(0.156471\pi\)
−0.881594 + 0.472009i \(0.843529\pi\)
\(720\) −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 0.582160 0.813074i \(-0.302208\pi\)
−0.813074 + 0.582160i \(0.802208\pi\)
\(728\) 305.195 328.215i 0.419224 0.450845i
\(729\) 671.695 283.313i 0.921393 0.388633i
\(730\) −474.441 262.216i −0.649919 0.359201i
\(731\) 610.474 0.835122
\(732\) −89.8507 + 5.98611i −0.122747 + 0.00817775i
\(733\) 138.636 138.636i 0.189135 0.189135i −0.606187 0.795322i \(-0.707302\pi\)
0.795322 + 0.606187i \(0.207302\pi\)
\(734\) 305.309i 0.415952i
\(735\) 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 \(0.102540\pi\)
−0.948560 + 0.316598i \(0.897460\pi\)
\(740\) −148.229 514.523i −0.200310 0.695301i
\(741\) −360.586 + 412.062i −0.486621 + 0.556089i
\(742\) 455.420 + 423.478i 0.613774 + 0.570725i
\(743\) −164.867 + 164.867i −0.221893 + 0.221893i −0.809295 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
\(756\) −197.414 + 322.354i −0.261129 + 0.426394i
\(757\) 846.245 846.245i 1.11789 1.11789i 0.125843 0.992050i \(-0.459837\pi\)
0.992050 0.125843i \(-0.0401635\pi\)
\(758\) 726.851 726.851i 0.958907 0.958907i
\(759\) −250.756 219.430i −0.330376 0.289105i
\(760\) −109.571 + 31.5664i −0.144172 + 0.0415347i
\(761\) −29.8430 −0.0392155 −0.0196078 0.999808i \(-0.506242\pi\)
−0.0196078 + 0.999808i \(0.506242\pi\)
\(762\) −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
\(767\)