Properties

Label 210.3.k.b.83.15
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 83.15
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(2.98664 - 0.282815i) q^{3} +2.00000i q^{4} +(-3.28357 + 3.77070i) q^{5} +(3.26945 + 2.70382i) q^{6} +(-5.95686 + 3.67639i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.84003 - 1.68933i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(2.98664 - 0.282815i) q^{3} +2.00000i q^{4} +(-3.28357 + 3.77070i) q^{5} +(3.26945 + 2.70382i) q^{6} +(-5.95686 + 3.67639i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.84003 - 1.68933i) q^{9} +(-7.05427 + 0.487124i) q^{10} +19.5576i q^{11} +(0.565630 + 5.97328i) q^{12} +(2.90656 - 2.90656i) q^{13} +(-9.63325 - 2.28046i) q^{14} +(-8.74044 + 12.1904i) q^{15} -4.00000 q^{16} +(16.3194 - 16.3194i) q^{17} +(10.5294 + 7.15070i) q^{18} +8.66094 q^{19} +(-7.54139 - 6.56714i) q^{20} +(-16.7512 + 12.6647i) q^{21} +(-19.5576 + 19.5576i) q^{22} +(6.73947 - 6.73947i) q^{23} +(-5.40765 + 6.53891i) q^{24} +(-3.43630 - 24.7627i) q^{25} +5.81313 q^{26} +(25.9242 - 7.54552i) q^{27} +(-7.35279 - 11.9137i) q^{28} +31.3396 q^{29} +(-20.9308 + 3.44992i) q^{30} -39.4508i q^{31} +(-4.00000 - 4.00000i) q^{32} +(5.53119 + 58.4116i) q^{33} +32.6389 q^{34} +(5.69720 - 34.5332i) q^{35} +(3.37866 + 17.6801i) q^{36} +(-25.1721 + 25.1721i) q^{37} +(8.66094 + 8.66094i) q^{38} +(7.85884 - 9.50288i) q^{39} +(-0.974248 - 14.1085i) q^{40} -58.9348 q^{41} +(-29.4160 - 4.08649i) q^{42} +(10.5096 + 10.5096i) q^{43} -39.1153 q^{44} +(-22.6569 + 38.8801i) q^{45} +13.4789 q^{46} +(-29.2211 + 29.2211i) q^{47} +(-11.9466 + 1.13126i) q^{48} +(21.9683 - 43.7995i) q^{49} +(21.3264 - 28.1990i) q^{50} +(44.1249 - 53.3556i) q^{51} +(5.81313 + 5.81313i) q^{52} +(10.3554 - 10.3554i) q^{53} +(33.4697 + 18.3787i) q^{54} +(-73.7459 - 64.2189i) q^{55} +(4.56092 - 19.2665i) q^{56} +(25.8671 - 2.44944i) q^{57} +(31.3396 + 31.3396i) q^{58} +42.5598i q^{59} +(-24.3807 - 17.4809i) q^{60} +45.1131i q^{61} +(39.4508 - 39.4508i) q^{62} +(-46.4481 + 42.5625i) q^{63} -8.00000i q^{64} +(1.41586 + 20.5037i) q^{65} +(-52.8804 + 63.9428i) q^{66} +(89.3559 - 89.3559i) q^{67} +(32.6389 + 32.6389i) q^{68} +(18.2224 - 22.0344i) q^{69} +(40.2304 - 28.8360i) q^{70} +47.3026i q^{71} +(-14.3014 + 21.0587i) q^{72} +(89.3562 - 89.3562i) q^{73} -50.3442 q^{74} +(-17.2663 - 72.9855i) q^{75} +17.3219i q^{76} +(-71.9016 - 116.502i) q^{77} +(17.3617 - 1.64404i) q^{78} -41.4668i q^{79} +(13.1343 - 15.0828i) q^{80} +(75.2923 - 29.8675i) q^{81} +(-58.9348 - 58.9348i) q^{82} +(44.9271 + 44.9271i) q^{83} +(-25.3295 - 33.5025i) q^{84} +(7.94959 + 115.122i) q^{85} +21.0192i q^{86} +(93.6000 - 8.86329i) q^{87} +(-39.1153 - 39.1153i) q^{88} -4.80429i q^{89} +(-61.5370 + 16.2232i) q^{90} +(-6.62831 + 27.9997i) q^{91} +(13.4789 + 13.4789i) q^{92} +(-11.1573 - 117.825i) q^{93} -58.4422 q^{94} +(-28.4388 + 32.6578i) q^{95} +(-13.0778 - 10.8153i) q^{96} +(2.01325 + 2.01325i) q^{97} +(65.7678 - 21.8312i) q^{98} +(33.0394 + 172.890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 2.98664 0.282815i 0.995547 0.0942716i
\(4\) 2.00000i 0.500000i
\(5\) −3.28357 + 3.77070i −0.656714 + 0.754139i
\(6\) 3.26945 + 2.70382i 0.544909 + 0.450637i
\(7\) −5.95686 + 3.67639i −0.850979 + 0.525199i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 8.84003 1.68933i 0.982226 0.187704i
\(10\) −7.05427 + 0.487124i −0.705427 + 0.0487124i
\(11\) 19.5576i 1.77797i 0.457939 + 0.888984i \(0.348588\pi\)
−0.457939 + 0.888984i \(0.651412\pi\)
\(12\) 0.565630 + 5.97328i 0.0471358 + 0.497773i
\(13\) 2.90656 2.90656i 0.223582 0.223582i −0.586423 0.810005i \(-0.699464\pi\)
0.810005 + 0.586423i \(0.199464\pi\)
\(14\) −9.63325 2.28046i −0.688089 0.162890i
\(15\) −8.74044 + 12.1904i −0.582696 + 0.812690i
\(16\) −4.00000 −0.250000
\(17\) 16.3194 16.3194i 0.959967 0.959967i −0.0392622 0.999229i \(-0.512501\pi\)
0.999229 + 0.0392622i \(0.0125008\pi\)
\(18\) 10.5294 + 7.15070i 0.584965 + 0.397261i
\(19\) 8.66094 0.455839 0.227919 0.973680i \(-0.426808\pi\)
0.227919 + 0.973680i \(0.426808\pi\)
\(20\) −7.54139 6.56714i −0.377070 0.328357i
\(21\) −16.7512 + 12.6647i −0.797678 + 0.603083i
\(22\) −19.5576 + 19.5576i −0.888984 + 0.888984i
\(23\) 6.73947 6.73947i 0.293021 0.293021i −0.545252 0.838272i \(-0.683566\pi\)
0.838272 + 0.545252i \(0.183566\pi\)
\(24\) −5.40765 + 6.53891i −0.225319 + 0.272455i
\(25\) −3.43630 24.7627i −0.137452 0.990508i
\(26\) 5.81313 0.223582
\(27\) 25.9242 7.54552i 0.960156 0.279464i
\(28\) −7.35279 11.9137i −0.262600 0.425490i
\(29\) 31.3396 1.08067 0.540337 0.841449i \(-0.318297\pi\)
0.540337 + 0.841449i \(0.318297\pi\)
\(30\) −20.9308 + 3.44992i −0.697693 + 0.114997i
\(31\) 39.4508i 1.27261i −0.771439 0.636304i \(-0.780463\pi\)
0.771439 0.636304i \(-0.219537\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 5.53119 + 58.4116i 0.167612 + 1.77005i
\(34\) 32.6389 0.959967
\(35\) 5.69720 34.5332i 0.162777 0.986663i
\(36\) 3.37866 + 17.6801i 0.0938518 + 0.491113i
\(37\) −25.1721 + 25.1721i −0.680326 + 0.680326i −0.960074 0.279747i \(-0.909749\pi\)
0.279747 + 0.960074i \(0.409749\pi\)
\(38\) 8.66094 + 8.66094i 0.227919 + 0.227919i
\(39\) 7.85884 9.50288i 0.201509 0.243664i
\(40\) −0.974248 14.1085i −0.0243562 0.352713i
\(41\) −58.9348 −1.43743 −0.718717 0.695303i \(-0.755270\pi\)
−0.718717 + 0.695303i \(0.755270\pi\)
\(42\) −29.4160 4.08649i −0.700381 0.0972974i
\(43\) 10.5096 + 10.5096i 0.244409 + 0.244409i 0.818671 0.574262i \(-0.194711\pi\)
−0.574262 + 0.818671i \(0.694711\pi\)
\(44\) −39.1153 −0.888984
\(45\) −22.6569 + 38.8801i −0.503487 + 0.864003i
\(46\) 13.4789 0.293021
\(47\) −29.2211 + 29.2211i −0.621725 + 0.621725i −0.945972 0.324247i \(-0.894889\pi\)
0.324247 + 0.945972i \(0.394889\pi\)
\(48\) −11.9466 + 1.13126i −0.248887 + 0.0235679i
\(49\) 21.9683 43.7995i 0.448332 0.893867i
\(50\) 21.3264 28.1990i 0.426528 0.563980i
\(51\) 44.1249 53.3556i 0.865194 1.04619i
\(52\) 5.81313 + 5.81313i 0.111791 + 0.111791i
\(53\) 10.3554 10.3554i 0.195386 0.195386i −0.602633 0.798019i \(-0.705882\pi\)
0.798019 + 0.602633i \(0.205882\pi\)
\(54\) 33.4697 + 18.3787i 0.619810 + 0.340346i
\(55\) −73.7459 64.2189i −1.34084 1.16762i
\(56\) 4.56092 19.2665i 0.0814451 0.344045i
\(57\) 25.8671 2.44944i 0.453809 0.0429727i
\(58\) 31.3396 + 31.3396i 0.540337 + 0.540337i
\(59\) 42.5598i 0.721353i 0.932691 + 0.360676i \(0.117454\pi\)
−0.932691 + 0.360676i \(0.882546\pi\)
\(60\) −24.3807 17.4809i −0.406345 0.291348i
\(61\) 45.1131i 0.739559i 0.929120 + 0.369779i \(0.120567\pi\)
−0.929120 + 0.369779i \(0.879433\pi\)
\(62\) 39.4508 39.4508i 0.636304 0.636304i
\(63\) −46.4481 + 42.5625i −0.737272 + 0.675596i
\(64\) 8.00000i 0.125000i
\(65\) 1.41586 + 20.5037i 0.0217824 + 0.315441i
\(66\) −52.8804 + 63.9428i −0.801219 + 0.968831i
\(67\) 89.3559 89.3559i 1.33367 1.33367i 0.431611 0.902060i \(-0.357945\pi\)
0.902060 0.431611i \(-0.142055\pi\)
\(68\) 32.6389 + 32.6389i 0.479983 + 0.479983i
\(69\) 18.2224 22.0344i 0.264092 0.319339i
\(70\) 40.2304 28.8360i 0.574720 0.411943i
\(71\) 47.3026i 0.666233i 0.942886 + 0.333117i \(0.108100\pi\)
−0.942886 + 0.333117i \(0.891900\pi\)
\(72\) −14.3014 + 21.0587i −0.198631 + 0.292482i
\(73\) 89.3562 89.3562i 1.22406 1.22406i 0.257880 0.966177i \(-0.416976\pi\)
0.966177 0.257880i \(-0.0830240\pi\)
\(74\) −50.3442 −0.680326
\(75\) −17.2663 72.9855i −0.230217 0.973139i
\(76\) 17.3219i 0.227919i
\(77\) −71.9016 116.502i −0.933787 1.51301i
\(78\) 17.3617 1.64404i 0.222586 0.0210774i
\(79\) 41.4668i 0.524896i −0.964946 0.262448i \(-0.915470\pi\)
0.964946 0.262448i \(-0.0845298\pi\)
\(80\) 13.1343 15.0828i 0.164179 0.188535i
\(81\) 75.2923 29.8675i 0.929535 0.368735i
\(82\) −58.9348 58.9348i −0.718717 0.718717i
\(83\) 44.9271 + 44.9271i 0.541290 + 0.541290i 0.923907 0.382617i \(-0.124977\pi\)
−0.382617 + 0.923907i \(0.624977\pi\)
\(84\) −25.3295 33.5025i −0.301542 0.398839i
\(85\) 7.94959 + 115.122i 0.0935246 + 1.35437i
\(86\) 21.0192i 0.244409i
\(87\) 93.6000 8.86329i 1.07586 0.101877i
\(88\) −39.1153 39.1153i −0.444492 0.444492i
\(89\) 4.80429i 0.0539807i −0.999636 0.0269904i \(-0.991408\pi\)
0.999636 0.0269904i \(-0.00859234\pi\)
\(90\) −61.5370 + 16.2232i −0.683745 + 0.180258i
\(91\) −6.62831 + 27.9997i −0.0728386 + 0.307689i
\(92\) 13.4789 + 13.4789i 0.146510 + 0.146510i
\(93\) −11.1573 117.825i −0.119971 1.26694i
\(94\) −58.4422 −0.621725
\(95\) −28.4388 + 32.6578i −0.299356 + 0.343766i
\(96\) −13.0778 10.8153i −0.136227 0.112659i
\(97\) 2.01325 + 2.01325i 0.0207551 + 0.0207551i 0.717408 0.696653i \(-0.245328\pi\)
−0.696653 + 0.717408i \(0.745328\pi\)
\(98\) 65.7678 21.8312i 0.671100 0.222768i
\(99\) 33.0394 + 172.890i 0.333731 + 1.74637i
\(100\) 49.5254 6.87261i 0.495254 0.0687261i
\(101\) −152.563 −1.51052 −0.755262 0.655423i \(-0.772491\pi\)
−0.755262 + 0.655423i \(0.772491\pi\)
\(102\) 97.4805 9.23076i 0.955691 0.0904976i
\(103\) 58.4473 58.4473i 0.567450 0.567450i −0.363963 0.931413i \(-0.618577\pi\)
0.931413 + 0.363963i \(0.118577\pi\)
\(104\) 11.6263i 0.111791i
\(105\) 7.24899 104.749i 0.0690380 0.997614i
\(106\) 20.7109 0.195386
\(107\) 31.9911 + 31.9911i 0.298982 + 0.298982i 0.840615 0.541633i \(-0.182194\pi\)
−0.541633 + 0.840615i \(0.682194\pi\)
\(108\) 15.0910 + 51.8484i 0.139732 + 0.480078i
\(109\) 0.710351i 0.00651698i −0.999995 0.00325849i \(-0.998963\pi\)
0.999995 0.00325849i \(-0.00103721\pi\)
\(110\) −9.52700 137.965i −0.0866090 1.25423i
\(111\) −68.0609 + 82.2990i −0.613161 + 0.741432i
\(112\) 23.8274 14.7056i 0.212745 0.131300i
\(113\) 59.6020 59.6020i 0.527451 0.527451i −0.392360 0.919812i \(-0.628341\pi\)
0.919812 + 0.392360i \(0.128341\pi\)
\(114\) 28.3165 + 23.4177i 0.248391 + 0.205418i
\(115\) 3.28296 + 47.5421i 0.0285475 + 0.413409i
\(116\) 62.6791i 0.540337i
\(117\) 20.7840 30.6043i 0.177641 0.261575i
\(118\) −42.5598 + 42.5598i −0.360676 + 0.360676i
\(119\) −37.2159 + 157.209i −0.312738 + 1.32109i
\(120\) −6.89983 41.8616i −0.0574986 0.348847i
\(121\) −261.501 −2.16117
\(122\) −45.1131 + 45.1131i −0.369779 + 0.369779i
\(123\) −176.017 + 16.6676i −1.43103 + 0.135509i
\(124\) 78.9016 0.636304
\(125\) 104.656 + 68.3529i 0.837248 + 0.546823i
\(126\) −89.0107 3.88560i −0.706434 0.0308381i
\(127\) −116.358 + 116.358i −0.916202 + 0.916202i −0.996751 0.0805491i \(-0.974333\pi\)
0.0805491 + 0.996751i \(0.474333\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 34.3606 + 28.4161i 0.266361 + 0.220280i
\(130\) −19.0878 + 21.9195i −0.146829 + 0.168612i
\(131\) −67.9862 −0.518978 −0.259489 0.965746i \(-0.583554\pi\)
−0.259489 + 0.965746i \(0.583554\pi\)
\(132\) −116.823 + 11.0624i −0.885025 + 0.0838059i
\(133\) −51.5920 + 31.8410i −0.387909 + 0.239406i
\(134\) 178.712 1.33367
\(135\) −56.6722 + 122.529i −0.419794 + 0.907619i
\(136\) 65.2777i 0.479983i
\(137\) −43.2163 43.2163i −0.315448 0.315448i 0.531568 0.847016i \(-0.321603\pi\)
−0.847016 + 0.531568i \(0.821603\pi\)
\(138\) 40.2568 3.81205i 0.291716 0.0276235i
\(139\) 16.4136 0.118083 0.0590417 0.998256i \(-0.481196\pi\)
0.0590417 + 0.998256i \(0.481196\pi\)
\(140\) 69.0664 + 11.3944i 0.493331 + 0.0813886i
\(141\) −79.0087 + 95.5370i −0.560345 + 0.677567i
\(142\) −47.3026 + 47.3026i −0.333117 + 0.333117i
\(143\) 56.8456 + 56.8456i 0.397521 + 0.397521i
\(144\) −35.3601 + 6.75733i −0.245556 + 0.0469259i
\(145\) −102.906 + 118.172i −0.709695 + 0.814979i
\(146\) 178.712 1.22406
\(147\) 53.2241 137.026i 0.362069 0.932151i
\(148\) −50.3442 50.3442i −0.340163 0.340163i
\(149\) 63.8210 0.428329 0.214165 0.976798i \(-0.431297\pi\)
0.214165 + 0.976798i \(0.431297\pi\)
\(150\) 55.7192 90.2517i 0.371461 0.601678i
\(151\) 100.225 0.663739 0.331869 0.943325i \(-0.392321\pi\)
0.331869 + 0.943325i \(0.392321\pi\)
\(152\) −17.3219 + 17.3219i −0.113960 + 0.113960i
\(153\) 116.695 171.833i 0.762715 1.12309i
\(154\) 44.6005 188.404i 0.289613 1.22340i
\(155\) 148.757 + 129.540i 0.959723 + 0.835740i
\(156\) 19.0058 + 15.7177i 0.121832 + 0.100754i
\(157\) −157.532 157.532i −1.00339 1.00339i −0.999994 0.00339453i \(-0.998919\pi\)
−0.00339453 0.999994i \(-0.501081\pi\)
\(158\) 41.4668 41.4668i 0.262448 0.262448i
\(159\) 27.9993 33.8567i 0.176096 0.212935i
\(160\) 28.2171 1.94850i 0.176357 0.0121781i
\(161\) −15.3691 + 64.9230i −0.0954604 + 0.403249i
\(162\) 105.160 + 45.4248i 0.649135 + 0.280400i
\(163\) 130.800 + 130.800i 0.802457 + 0.802457i 0.983479 0.181022i \(-0.0579405\pi\)
−0.181022 + 0.983479i \(0.557941\pi\)
\(164\) 117.870i 0.718717i
\(165\) −238.415 170.942i −1.44494 1.03601i
\(166\) 89.8542i 0.541290i
\(167\) 35.0842 35.0842i 0.210085 0.210085i −0.594219 0.804304i \(-0.702539\pi\)
0.804304 + 0.594219i \(0.202539\pi\)
\(168\) 8.17299 58.8320i 0.0486487 0.350190i
\(169\) 152.104i 0.900022i
\(170\) −107.172 + 123.071i −0.630424 + 0.723949i
\(171\) 76.5630 14.6312i 0.447737 0.0855626i
\(172\) −21.0192 + 21.0192i −0.122204 + 0.122204i
\(173\) −224.736 224.736i −1.29905 1.29905i −0.929019 0.370032i \(-0.879347\pi\)
−0.370032 0.929019i \(-0.620653\pi\)
\(174\) 102.463 + 84.7367i 0.588869 + 0.486992i
\(175\) 111.507 + 134.875i 0.637183 + 0.770713i
\(176\) 78.2306i 0.444492i
\(177\) 12.0366 + 127.111i 0.0680031 + 0.718140i
\(178\) 4.80429 4.80429i 0.0269904 0.0269904i
\(179\) −209.136 −1.16836 −0.584179 0.811625i \(-0.698583\pi\)
−0.584179 + 0.811625i \(0.698583\pi\)
\(180\) −77.7602 45.3138i −0.432001 0.251744i
\(181\) 227.999i 1.25966i 0.776731 + 0.629832i \(0.216876\pi\)
−0.776731 + 0.629832i \(0.783124\pi\)
\(182\) −34.6280 + 21.3714i −0.190264 + 0.117425i
\(183\) 12.7587 + 134.737i 0.0697194 + 0.736265i
\(184\) 26.9579i 0.146510i
\(185\) −12.2619 177.571i −0.0662807 0.959841i
\(186\) 106.668 128.983i 0.573484 0.693455i
\(187\) 319.170 + 319.170i 1.70679 + 1.70679i
\(188\) −58.4422 58.4422i −0.310863 0.310863i
\(189\) −126.687 + 140.255i −0.670299 + 0.742091i
\(190\) −61.0966 + 4.21895i −0.321561 + 0.0222050i
\(191\) 24.3448i 0.127460i 0.997967 + 0.0637298i \(0.0202996\pi\)
−0.997967 + 0.0637298i \(0.979700\pi\)
\(192\) −2.26252 23.8931i −0.0117840 0.124443i
\(193\) −119.177 119.177i −0.617497 0.617497i 0.327392 0.944889i \(-0.393830\pi\)
−0.944889 + 0.327392i \(0.893830\pi\)
\(194\) 4.02649i 0.0207551i
\(195\) 10.0274 + 60.8367i 0.0514226 + 0.311983i
\(196\) 87.5990 + 43.9365i 0.446934 + 0.224166i
\(197\) −24.0000 24.0000i −0.121827 0.121827i 0.643565 0.765392i \(-0.277455\pi\)
−0.765392 + 0.643565i \(0.777455\pi\)
\(198\) −139.851 + 205.930i −0.706317 + 1.04005i
\(199\) −146.804 −0.737706 −0.368853 0.929488i \(-0.620249\pi\)
−0.368853 + 0.929488i \(0.620249\pi\)
\(200\) 56.3980 + 42.6528i 0.281990 + 0.213264i
\(201\) 241.603 292.145i 1.20200 1.45346i
\(202\) −152.563 152.563i −0.755262 0.755262i
\(203\) −186.685 + 115.217i −0.919632 + 0.567569i
\(204\) 106.711 + 88.2498i 0.523095 + 0.432597i
\(205\) 193.517 222.225i 0.943984 1.08403i
\(206\) 116.895 0.567450
\(207\) 48.1919 70.9624i 0.232811 0.342813i
\(208\) −11.6263 + 11.6263i −0.0558955 + 0.0558955i
\(209\) 169.388i 0.810467i
\(210\) 111.998 97.5005i 0.533326 0.464288i
\(211\) 123.187 0.583825 0.291912 0.956445i \(-0.405708\pi\)
0.291912 + 0.956445i \(0.405708\pi\)
\(212\) 20.7109 + 20.7109i 0.0976929 + 0.0976929i
\(213\) 13.3779 + 141.276i 0.0628069 + 0.663266i
\(214\) 63.9822i 0.298982i
\(215\) −74.1374 + 5.11947i −0.344825 + 0.0238115i
\(216\) −36.7574 + 66.9395i −0.170173 + 0.309905i
\(217\) 145.037 + 235.003i 0.668372 + 1.08296i
\(218\) 0.710351 0.710351i 0.00325849 0.00325849i
\(219\) 241.603 292.146i 1.10321 1.33400i
\(220\) 128.438 147.492i 0.583808 0.670418i
\(221\) 94.8670i 0.429262i
\(222\) −150.360 + 14.2381i −0.677297 + 0.0641355i
\(223\) 88.3904 88.3904i 0.396369 0.396369i −0.480581 0.876950i \(-0.659574\pi\)
0.876950 + 0.480581i \(0.159574\pi\)
\(224\) 38.5330 + 9.12185i 0.172022 + 0.0407225i
\(225\) −72.2095 213.098i −0.320931 0.947103i
\(226\) 119.204 0.527451
\(227\) 19.9546 19.9546i 0.0879055 0.0879055i −0.661787 0.749692i \(-0.730202\pi\)
0.749692 + 0.661787i \(0.230202\pi\)
\(228\) 4.89888 + 51.7342i 0.0214863 + 0.226904i
\(229\) −291.903 −1.27468 −0.637342 0.770581i \(-0.719966\pi\)
−0.637342 + 0.770581i \(0.719966\pi\)
\(230\) −44.2591 + 50.8250i −0.192431 + 0.220978i
\(231\) −247.693 327.615i −1.07226 1.41825i
\(232\) −62.6791 + 62.6791i −0.270169 + 0.270169i
\(233\) 263.920 263.920i 1.13270 1.13270i 0.142978 0.989726i \(-0.454332\pi\)
0.989726 0.142978i \(-0.0456679\pi\)
\(234\) 51.3883 9.82031i 0.219608 0.0419671i
\(235\) −14.2343 206.133i −0.0605714 0.877163i
\(236\) −85.1196 −0.360676
\(237\) −11.7274 123.846i −0.0494828 0.522558i
\(238\) −194.425 + 119.993i −0.816912 + 0.504174i
\(239\) −407.365 −1.70446 −0.852228 0.523171i \(-0.824749\pi\)
−0.852228 + 0.523171i \(0.824749\pi\)
\(240\) 34.9618 48.7614i 0.145674 0.203173i
\(241\) 311.118i 1.29095i −0.763783 0.645474i \(-0.776660\pi\)
0.763783 0.645474i \(-0.223340\pi\)
\(242\) −261.501 261.501i −1.08058 1.08058i
\(243\) 216.424 110.497i 0.890634 0.454721i
\(244\) −90.2262 −0.369779
\(245\) 93.0202 + 226.654i 0.379674 + 0.925120i
\(246\) −192.685 159.349i −0.783271 0.647761i
\(247\) 25.1736 25.1736i 0.101917 0.101917i
\(248\) 78.9016 + 78.9016i 0.318152 + 0.318152i
\(249\) 146.887 + 121.475i 0.589908 + 0.487851i
\(250\) 36.3031 + 173.009i 0.145212 + 0.692036i
\(251\) 91.1631 0.363200 0.181600 0.983373i \(-0.441872\pi\)
0.181600 + 0.983373i \(0.441872\pi\)
\(252\) −85.1251 92.8963i −0.337798 0.368636i
\(253\) 131.808 + 131.808i 0.520981 + 0.520981i
\(254\) −232.715 −0.916202
\(255\) 56.3007 + 341.579i 0.220787 + 1.33952i
\(256\) 16.0000 0.0625000
\(257\) −221.675 + 221.675i −0.862547 + 0.862547i −0.991633 0.129086i \(-0.958796\pi\)
0.129086 + 0.991633i \(0.458796\pi\)
\(258\) 5.94453 + 62.7767i 0.0230408 + 0.243320i
\(259\) 57.4040 242.489i 0.221637 0.936251i
\(260\) −41.0074 + 2.83171i −0.157721 + 0.0108912i
\(261\) 277.043 52.9429i 1.06147 0.202846i
\(262\) −67.9862 67.9862i −0.259489 0.259489i
\(263\) 258.162 258.162i 0.981603 0.981603i −0.0182309 0.999834i \(-0.505803\pi\)
0.999834 + 0.0182309i \(0.00580340\pi\)
\(264\) −127.886 105.761i −0.484415 0.400609i
\(265\) 5.04439 + 73.0501i 0.0190354 + 0.275661i
\(266\) −83.4330 19.7509i −0.313658 0.0742517i
\(267\) −1.35872 14.3487i −0.00508885 0.0537403i
\(268\) 178.712 + 178.712i 0.666835 + 0.666835i
\(269\) 138.071i 0.513275i −0.966508 0.256637i \(-0.917385\pi\)
0.966508 0.256637i \(-0.0826146\pi\)
\(270\) −179.201 + 65.8564i −0.663707 + 0.243913i
\(271\) 95.9122i 0.353920i −0.984218 0.176960i \(-0.943374\pi\)
0.984218 0.176960i \(-0.0566263\pi\)
\(272\) −65.2777 + 65.2777i −0.239992 + 0.239992i
\(273\) −11.8777 + 85.4995i −0.0435079 + 0.313185i
\(274\) 86.4327i 0.315448i
\(275\) 484.300 67.2060i 1.76109 0.244385i
\(276\) 44.0688 + 36.4447i 0.159670 + 0.132046i
\(277\) 105.512 105.512i 0.380910 0.380910i −0.490520 0.871430i \(-0.663193\pi\)
0.871430 + 0.490520i \(0.163193\pi\)
\(278\) 16.4136 + 16.4136i 0.0590417 + 0.0590417i
\(279\) −66.6456 348.747i −0.238873 1.24999i
\(280\) 57.6720 + 80.4608i 0.205971 + 0.287360i
\(281\) 237.031i 0.843525i 0.906706 + 0.421762i \(0.138588\pi\)
−0.906706 + 0.421762i \(0.861412\pi\)
\(282\) −174.546 + 16.5283i −0.618956 + 0.0586111i
\(283\) −286.765 + 286.765i −1.01330 + 1.01330i −0.0133925 + 0.999910i \(0.504263\pi\)
−0.999910 + 0.0133925i \(0.995737\pi\)
\(284\) −94.6051 −0.333117
\(285\) −75.7004 + 105.580i −0.265615 + 0.370456i
\(286\) 113.691i 0.397521i
\(287\) 351.066 216.667i 1.22323 0.754939i
\(288\) −42.1175 28.6028i −0.146241 0.0993153i
\(289\) 243.648i 0.843072i
\(290\) −221.078 + 15.2662i −0.762337 + 0.0526422i
\(291\) 6.58222 + 5.44346i 0.0226193 + 0.0187061i
\(292\) 178.712 + 178.712i 0.612029 + 0.612029i
\(293\) −353.346 353.346i −1.20596 1.20596i −0.972324 0.233635i \(-0.924938\pi\)
−0.233635 0.972324i \(-0.575062\pi\)
\(294\) 190.250 83.8021i 0.647110 0.285041i
\(295\) −160.480 139.748i −0.544001 0.473723i
\(296\) 100.688i 0.340163i
\(297\) 147.573 + 507.017i 0.496877 + 1.70713i
\(298\) 63.8210 + 63.8210i 0.214165 + 0.214165i
\(299\) 39.1774i 0.131028i
\(300\) 145.971 34.5325i 0.486570 0.115108i
\(301\) −101.241 23.9667i −0.336350 0.0796236i
\(302\) 100.225 + 100.225i 0.331869 + 0.331869i
\(303\) −455.651 + 43.1471i −1.50380 + 0.142400i
\(304\) −34.6437 −0.113960
\(305\) −170.108 148.132i −0.557730 0.485679i
\(306\) 288.529 55.1379i 0.942904 0.180189i
\(307\) −268.995 268.995i −0.876204 0.876204i 0.116935 0.993140i \(-0.462693\pi\)
−0.993140 + 0.116935i \(0.962693\pi\)
\(308\) 233.004 143.803i 0.756507 0.466893i
\(309\) 158.031 191.091i 0.511428 0.618417i
\(310\) 19.2174 + 278.297i 0.0619917 + 0.897731i
\(311\) 93.5888 0.300929 0.150464 0.988615i \(-0.451923\pi\)
0.150464 + 0.988615i \(0.451923\pi\)
\(312\) 3.28808 + 34.7234i 0.0105387 + 0.111293i
\(313\) 65.0697 65.0697i 0.207890 0.207890i −0.595480 0.803370i \(-0.703038\pi\)
0.803370 + 0.595480i \(0.203038\pi\)
\(314\) 315.064i 1.00339i
\(315\) −7.97459 314.899i −0.0253161 0.999679i
\(316\) 82.9336 0.262448
\(317\) −183.110 183.110i −0.577633 0.577633i 0.356617 0.934251i \(-0.383930\pi\)
−0.934251 + 0.356617i \(0.883930\pi\)
\(318\) 61.8560 5.85735i 0.194516 0.0184193i
\(319\) 612.928i 1.92140i
\(320\) 30.1656 + 26.2686i 0.0942674 + 0.0820893i
\(321\) 104.593 + 86.4983i 0.325836 + 0.269465i
\(322\) −80.2921 + 49.5539i −0.249354 + 0.153894i
\(323\) 141.342 141.342i 0.437590 0.437590i
\(324\) 59.7350 + 150.585i 0.184367 + 0.464767i
\(325\) −81.9623 61.9866i −0.252192 0.190728i
\(326\) 261.601i 0.802457i
\(327\) −0.200898 2.12156i −0.000614367 0.00648796i
\(328\) 117.870 117.870i 0.359358 0.359358i
\(329\) 66.6376 281.494i 0.202546 0.855605i
\(330\) −67.4722 409.357i −0.204461 1.24048i
\(331\) −389.930 −1.17804 −0.589018 0.808120i \(-0.700485\pi\)
−0.589018 + 0.808120i \(0.700485\pi\)
\(332\) −89.8542 + 89.8542i −0.270645 + 0.270645i
\(333\) −179.998 + 265.046i −0.540534 + 0.795934i
\(334\) 70.1684 0.210085
\(335\) 43.5274 + 630.341i 0.129933 + 1.88161i
\(336\) 67.0050 50.6590i 0.199420 0.150771i
\(337\) 201.311 201.311i 0.597362 0.597362i −0.342248 0.939610i \(-0.611188\pi\)
0.939610 + 0.342248i \(0.111188\pi\)
\(338\) −152.104 + 152.104i −0.450011 + 0.450011i
\(339\) 161.153 194.866i 0.475379 0.574826i
\(340\) −230.243 + 15.8992i −0.677186 + 0.0467623i
\(341\) 771.565 2.26265
\(342\) 91.1942 + 61.9318i 0.266650 + 0.181087i
\(343\) 30.1624 + 341.671i 0.0879370 + 0.996126i
\(344\) −42.0383 −0.122204
\(345\) 23.2506 + 141.063i 0.0673931 + 0.408877i
\(346\) 449.472i 1.29905i
\(347\) 373.074 + 373.074i 1.07514 + 1.07514i 0.996938 + 0.0782023i \(0.0249180\pi\)
0.0782023 + 0.996938i \(0.475082\pi\)
\(348\) 17.7266 + 187.200i 0.0509385 + 0.537931i
\(349\) 413.538 1.18492 0.592461 0.805599i \(-0.298157\pi\)
0.592461 + 0.805599i \(0.298157\pi\)
\(350\) −23.3677 + 246.382i −0.0667648 + 0.703948i
\(351\) 53.4189 97.2820i 0.152191 0.277157i
\(352\) 78.2306 78.2306i 0.222246 0.222246i
\(353\) 7.52215 + 7.52215i 0.0213092 + 0.0213092i 0.717681 0.696372i \(-0.245204\pi\)
−0.696372 + 0.717681i \(0.745204\pi\)
\(354\) −115.074 + 139.147i −0.325069 + 0.393072i
\(355\) −178.364 155.321i −0.502433 0.437525i
\(356\) 9.60857 0.0269904
\(357\) −66.6892 + 480.052i −0.186805 + 1.34468i
\(358\) −209.136 209.136i −0.584179 0.584179i
\(359\) −166.966 −0.465085 −0.232543 0.972586i \(-0.574705\pi\)
−0.232543 + 0.972586i \(0.574705\pi\)
\(360\) −32.4464 123.074i −0.0901289 0.341872i
\(361\) −285.988 −0.792211
\(362\) −227.999 + 227.999i −0.629832 + 0.629832i
\(363\) −781.010 + 73.9565i −2.15154 + 0.203737i
\(364\) −55.9993 13.2566i −0.153844 0.0364193i
\(365\) 43.5275 + 630.342i 0.119254 + 1.72697i
\(366\) −121.978 + 147.495i −0.333273 + 0.402992i
\(367\) 216.400 + 216.400i 0.589646 + 0.589646i 0.937535 0.347890i \(-0.113102\pi\)
−0.347890 + 0.937535i \(0.613102\pi\)
\(368\) −26.9579 + 26.9579i −0.0732551 + 0.0732551i
\(369\) −520.985 + 99.5604i −1.41188 + 0.269811i
\(370\) 165.309 189.833i 0.446780 0.513061i
\(371\) −23.6152 + 99.7566i −0.0636529 + 0.268886i
\(372\) 235.651 22.3146i 0.633470 0.0599854i
\(373\) −64.8753 64.8753i −0.173928 0.173928i 0.614775 0.788703i \(-0.289247\pi\)
−0.788703 + 0.614775i \(0.789247\pi\)
\(374\) 638.339i 1.70679i
\(375\) 331.901 + 174.547i 0.885069 + 0.465459i
\(376\) 116.884i 0.310863i
\(377\) 91.0905 91.0905i 0.241619 0.241619i
\(378\) −266.942 + 13.5687i −0.706195 + 0.0358959i
\(379\) 44.8235i 0.118268i 0.998250 + 0.0591339i \(0.0188339\pi\)
−0.998250 + 0.0591339i \(0.981166\pi\)
\(380\) −65.3155 56.8776i −0.171883 0.149678i
\(381\) −314.611 + 380.426i −0.825749 + 0.998493i
\(382\) −24.3448 + 24.3448i −0.0637298 + 0.0637298i
\(383\) 465.824 + 465.824i 1.21625 + 1.21625i 0.968935 + 0.247315i \(0.0795483\pi\)
0.247315 + 0.968935i \(0.420452\pi\)
\(384\) 21.6306 26.1556i 0.0563297 0.0681136i
\(385\) 675.388 + 111.424i 1.75425 + 0.289413i
\(386\) 238.354i 0.617497i
\(387\) 110.659 + 75.1509i 0.285941 + 0.194188i
\(388\) −4.02649 + 4.02649i −0.0103776 + 0.0103776i
\(389\) 341.962 0.879079 0.439540 0.898223i \(-0.355142\pi\)
0.439540 + 0.898223i \(0.355142\pi\)
\(390\) −50.8093 + 70.8641i −0.130280 + 0.181703i
\(391\) 219.969i 0.562580i
\(392\) 43.6625 + 131.536i 0.111384 + 0.335550i
\(393\) −203.050 + 19.2275i −0.516667 + 0.0489249i
\(394\) 48.0000i 0.121827i
\(395\) 156.359 + 136.159i 0.395845 + 0.344707i
\(396\) −345.780 + 66.0787i −0.873183 + 0.166865i
\(397\) 214.201 + 214.201i 0.539549 + 0.539549i 0.923397 0.383847i \(-0.125401\pi\)
−0.383847 + 0.923397i \(0.625401\pi\)
\(398\) −146.804 146.804i −0.368853 0.368853i
\(399\) −145.081 + 109.689i −0.363613 + 0.274909i
\(400\) 13.7452 + 99.0508i 0.0343630 + 0.247627i
\(401\) 278.216i 0.693806i 0.937901 + 0.346903i \(0.112767\pi\)
−0.937901 + 0.346903i \(0.887233\pi\)
\(402\) 533.748 50.5424i 1.32773 0.125727i
\(403\) −114.666 114.666i −0.284532 0.284532i
\(404\) 305.126i 0.755262i
\(405\) −134.606 + 381.977i −0.332362 + 0.943152i
\(406\) −301.902 71.4687i −0.743600 0.176031i
\(407\) −492.307 492.307i −1.20960 1.20960i
\(408\) 18.4615 + 194.961i 0.0452488 + 0.477846i
\(409\) −481.543 −1.17737 −0.588684 0.808364i \(-0.700354\pi\)
−0.588684 + 0.808364i \(0.700354\pi\)
\(410\) 415.742 28.7085i 1.01400 0.0700208i
\(411\) −141.294 116.849i −0.343781 0.284305i
\(412\) 116.895 + 116.895i 0.283725 + 0.283725i
\(413\) −156.467 253.523i −0.378854 0.613856i
\(414\) 119.154 22.7704i 0.287812 0.0550010i
\(415\) −316.928 + 21.8851i −0.763682 + 0.0527351i
\(416\) −23.2525 −0.0558955
\(417\) 49.0215 4.64201i 0.117557 0.0111319i
\(418\) −169.388 + 169.388i −0.405233 + 0.405233i
\(419\) 12.3613i 0.0295020i 0.999891 + 0.0147510i \(0.00469556\pi\)
−0.999891 + 0.0147510i \(0.995304\pi\)
\(420\) 209.499 + 14.4980i 0.498807 + 0.0345190i
\(421\) 10.9249 0.0259498 0.0129749 0.999916i \(-0.495870\pi\)
0.0129749 + 0.999916i \(0.495870\pi\)
\(422\) 123.187 + 123.187i 0.291912 + 0.291912i
\(423\) −208.951 + 307.679i −0.493974 + 0.727375i
\(424\) 41.4218i 0.0976929i
\(425\) −460.192 348.035i −1.08280 0.818906i
\(426\) −127.898 + 154.654i −0.300230 + 0.363036i
\(427\) −165.853 268.732i −0.388416 0.629349i
\(428\) −63.9822 + 63.9822i −0.149491 + 0.149491i
\(429\) 185.854 + 153.700i 0.433226 + 0.358276i
\(430\) −79.2569 69.0180i −0.184318 0.160507i
\(431\) 7.70570i 0.0178786i −0.999960 0.00893932i \(-0.997154\pi\)
0.999960 0.00893932i \(-0.00284551\pi\)
\(432\) −103.697 + 30.1821i −0.240039 + 0.0698659i
\(433\) 16.6929 16.6929i 0.0385516 0.0385516i −0.687568 0.726120i \(-0.741322\pi\)
0.726120 + 0.687568i \(0.241322\pi\)
\(434\) −89.9661 + 380.040i −0.207295 + 0.875667i
\(435\) −273.921 + 382.040i −0.629704 + 0.878254i
\(436\) 1.42070 0.00325849
\(437\) 58.3702 58.3702i 0.133570 0.133570i
\(438\) 533.749 50.5425i 1.21861 0.115394i
\(439\) 717.592 1.63461 0.817303 0.576208i \(-0.195468\pi\)
0.817303 + 0.576208i \(0.195468\pi\)
\(440\) 275.930 19.0540i 0.627113 0.0433045i
\(441\) 120.208 424.301i 0.272581 0.962133i
\(442\) 94.8670 94.8670i 0.214631 0.214631i
\(443\) 163.039 163.039i 0.368035 0.368035i −0.498725 0.866760i \(-0.666198\pi\)
0.866760 + 0.498725i \(0.166198\pi\)
\(444\) −164.598 136.122i −0.370716 0.306581i
\(445\) 18.1155 + 15.7752i 0.0407090 + 0.0354499i
\(446\) 176.781 0.396369
\(447\) 190.610 18.0495i 0.426422 0.0403793i
\(448\) 29.4111 + 47.6548i 0.0656499 + 0.106372i
\(449\) −681.871 −1.51864 −0.759322 0.650715i \(-0.774469\pi\)
−0.759322 + 0.650715i \(0.774469\pi\)
\(450\) 140.889 285.308i 0.313086 0.634017i
\(451\) 1152.63i 2.55571i
\(452\) 119.204 + 119.204i 0.263726 + 0.263726i
\(453\) 299.335 28.3450i 0.660783 0.0625717i
\(454\) 39.9091 0.0879055
\(455\) −83.8137 116.932i −0.184206 0.256994i
\(456\) −46.8353 + 56.6331i −0.102709 + 0.124195i
\(457\) 201.532 201.532i 0.440990 0.440990i −0.451355 0.892345i \(-0.649059\pi\)
0.892345 + 0.451355i \(0.149059\pi\)
\(458\) −291.903 291.903i −0.637342 0.637342i
\(459\) 299.930 546.207i 0.653442 1.18999i
\(460\) −95.0841 + 6.56592i −0.206705 + 0.0142737i
\(461\) 205.599 0.445985 0.222993 0.974820i \(-0.428417\pi\)
0.222993 + 0.974820i \(0.428417\pi\)
\(462\) 79.9222 575.307i 0.172992 1.24525i
\(463\) −172.047 172.047i −0.371592 0.371592i 0.496465 0.868057i \(-0.334631\pi\)
−0.868057 + 0.496465i \(0.834631\pi\)
\(464\) −125.358 −0.270169
\(465\) 480.920 + 344.817i 1.03424 + 0.741543i
\(466\) 527.840 1.13270
\(467\) −331.816 + 331.816i −0.710527 + 0.710527i −0.966645 0.256118i \(-0.917556\pi\)
0.256118 + 0.966645i \(0.417556\pi\)
\(468\) 61.2086 + 41.5679i 0.130788 + 0.0888204i
\(469\) −203.773 + 860.788i −0.434484 + 1.83537i
\(470\) 191.899 220.368i 0.408296 0.468867i
\(471\) −515.044 425.939i −1.09351 0.904329i
\(472\) −85.1196 85.1196i −0.180338 0.180338i
\(473\) −205.543 + 205.543i −0.434551 + 0.434551i
\(474\) 112.119 135.574i 0.236538 0.286021i
\(475\) −29.7616 214.468i −0.0626560 0.451512i
\(476\) −314.418 74.4317i −0.660543 0.156369i
\(477\) 74.0487 109.036i 0.155238 0.228588i
\(478\) −407.365 407.365i −0.852228 0.852228i
\(479\) 449.861i 0.939167i −0.882888 0.469584i \(-0.844404\pi\)
0.882888 0.469584i \(-0.155596\pi\)
\(480\) 83.7232 13.7997i 0.174423 0.0287493i
\(481\) 146.329i 0.304217i
\(482\) 311.118 311.118i 0.645474 0.645474i
\(483\) −27.5408 + 198.248i −0.0570203 + 0.410452i
\(484\) 523.003i 1.08058i
\(485\) −14.2020 + 0.980700i −0.0292824 + 0.00202206i
\(486\) 326.921 + 105.927i 0.672678 + 0.217956i
\(487\) −281.676 + 281.676i −0.578391 + 0.578391i −0.934460 0.356069i \(-0.884117\pi\)
0.356069 + 0.934460i \(0.384117\pi\)
\(488\) −90.2262 90.2262i −0.184890 0.184890i
\(489\) 427.646 + 353.662i 0.874532 + 0.723234i
\(490\) −133.634 + 319.675i −0.272723 + 0.652397i
\(491\) 896.974i 1.82683i −0.407029 0.913415i \(-0.633435\pi\)
0.407029 0.913415i \(-0.366565\pi\)
\(492\) −33.3353 352.034i −0.0677546 0.715516i
\(493\) 511.444 511.444i 1.03741 1.03741i
\(494\) 50.3472 0.101917
\(495\) −760.403 443.116i −1.53617 0.895184i
\(496\) 157.803i 0.318152i
\(497\) −173.903 281.774i −0.349905 0.566951i
\(498\) 25.4121 + 268.362i 0.0510283 + 0.538880i
\(499\) 0.286254i 0.000573655i 1.00000 0.000286827i \(9.13000e-5\pi\)
−1.00000 0.000286827i \(0.999909\pi\)
\(500\) −136.706 + 209.312i −0.273412 + 0.418624i
\(501\) 94.8615 114.706i 0.189344 0.228954i
\(502\) 91.1631 + 91.1631i 0.181600 + 0.181600i
\(503\) 167.300 + 167.300i 0.332605 + 0.332605i 0.853575 0.520970i \(-0.174430\pi\)
−0.520970 + 0.853575i \(0.674430\pi\)
\(504\) 7.77120 178.021i 0.0154190 0.353217i
\(505\) 500.952 575.269i 0.991983 1.13915i
\(506\) 263.616i 0.520981i
\(507\) 43.0172 + 454.279i 0.0848466 + 0.896014i
\(508\) −232.715 232.715i −0.458101 0.458101i
\(509\) 480.263i 0.943543i −0.881721 0.471771i \(-0.843615\pi\)
0.881721 0.471771i \(-0.156385\pi\)
\(510\) −285.278 + 397.879i −0.559369 + 0.780156i
\(511\) −203.773 + 860.790i −0.398774 + 1.68452i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 224.528 65.3513i 0.437676 0.127390i
\(514\) −443.349 −0.862547
\(515\) 28.4711 + 412.303i 0.0552837 + 0.800589i
\(516\) −56.8321 + 68.7212i −0.110140 + 0.133181i
\(517\) −571.496 571.496i −1.10541 1.10541i
\(518\) 299.893 185.085i 0.578944 0.357307i
\(519\) −734.764 607.646i −1.41573 1.17080i
\(520\) −43.8391 38.1757i −0.0843060 0.0734147i
\(521\) −168.144 −0.322733 −0.161366 0.986895i \(-0.551590\pi\)
−0.161366 + 0.986895i \(0.551590\pi\)
\(522\) 329.986 + 224.100i 0.632156 + 0.429310i
\(523\) 4.84540 4.84540i 0.00926463 0.00926463i −0.702459 0.711724i \(-0.747915\pi\)
0.711724 + 0.702459i \(0.247915\pi\)
\(524\) 135.972i 0.259489i
\(525\) 371.176 + 371.286i 0.707002 + 0.707212i
\(526\) 516.323 0.981603
\(527\) −643.815 643.815i −1.22166 1.22166i
\(528\) −22.1248 233.646i −0.0419030 0.442512i
\(529\) 438.159i 0.828278i
\(530\) −68.0057 + 78.0945i −0.128313 + 0.147348i
\(531\) 71.8977 + 376.230i 0.135401 + 0.708531i
\(532\) −63.6820 103.184i −0.119703 0.193955i
\(533\) −171.298 + 171.298i −0.321384 + 0.321384i
\(534\) 12.9899 15.7074i 0.0243257 0.0294146i
\(535\) −225.674 + 15.5836i −0.421820 + 0.0291283i
\(536\) 357.424i 0.666835i
\(537\) −624.614 + 59.1468i −1.16315 + 0.110143i
\(538\) 138.071 138.071i 0.256637 0.256637i
\(539\) 856.615 + 429.647i 1.58927 + 0.797119i
\(540\) −245.057 113.344i −0.453810 0.209897i
\(541\) 664.777 1.22879 0.614397 0.788997i \(-0.289400\pi\)
0.614397 + 0.788997i \(0.289400\pi\)
\(542\) 95.9122 95.9122i 0.176960 0.176960i
\(543\) 64.4816 + 680.952i 0.118751 + 1.25405i
\(544\) −130.555 −0.239992
\(545\) 2.67852 + 2.33249i 0.00491471 + 0.00427980i
\(546\) −97.3771 + 73.6218i −0.178346 + 0.134839i
\(547\) 367.452 367.452i 0.671758 0.671758i −0.286363 0.958121i \(-0.592446\pi\)
0.958121 + 0.286363i \(0.0924464\pi\)
\(548\) 86.4327 86.4327i 0.157724 0.157724i
\(549\) 76.2110 + 398.801i 0.138818 + 0.726414i
\(550\) 551.506 + 417.094i 1.00274 + 0.758353i
\(551\) 271.430 0.492613
\(552\) 7.62409 + 80.5135i 0.0138118 + 0.145858i
\(553\) 152.448 + 247.012i 0.275675 + 0.446676i
\(554\) 211.024 0.380910
\(555\) −86.8416 526.872i −0.156471 0.949318i
\(556\) 32.8272i 0.0590417i
\(557\) −83.3059 83.3059i −0.149562 0.149562i 0.628361 0.777922i \(-0.283726\pi\)
−0.777922 + 0.628361i \(0.783726\pi\)
\(558\) 282.101 415.392i 0.505557 0.744430i
\(559\) 61.0936 0.109291
\(560\) −22.7888 + 138.133i −0.0406943 + 0.246666i
\(561\) 1043.51 + 862.979i 1.86009 + 1.53829i
\(562\) −237.031 + 237.031i −0.421762 + 0.421762i
\(563\) −52.8031 52.8031i −0.0937889 0.0937889i 0.658656 0.752445i \(-0.271125\pi\)
−0.752445 + 0.658656i \(0.771125\pi\)
\(564\) −191.074 158.017i −0.338784 0.280173i
\(565\) 29.0336 + 420.448i 0.0513868 + 0.744157i
\(566\) −573.529 −1.01330
\(567\) −338.701 + 454.721i −0.597356 + 0.801976i
\(568\) −94.6051 94.6051i −0.166558 0.166558i
\(569\) −354.050 −0.622233 −0.311116 0.950372i \(-0.600703\pi\)
−0.311116 + 0.950372i \(0.600703\pi\)
\(570\) −181.280 + 29.8795i −0.318036 + 0.0524202i
\(571\) 490.557 0.859119 0.429559 0.903039i \(-0.358669\pi\)
0.429559 + 0.903039i \(0.358669\pi\)
\(572\) −113.691 + 113.691i −0.198761 + 0.198761i
\(573\) 6.88506 + 72.7090i 0.0120158 + 0.126892i
\(574\) 567.733 + 134.399i 0.989083 + 0.234144i
\(575\) −190.047 143.729i −0.330516 0.249963i
\(576\) −13.5147 70.7203i −0.0234629 0.122778i
\(577\) −677.908 677.908i −1.17488 1.17488i −0.981031 0.193852i \(-0.937902\pi\)
−0.193852 0.981031i \(-0.562098\pi\)
\(578\) 243.648 243.648i 0.421536 0.421536i
\(579\) −389.643 322.233i −0.672959 0.556534i
\(580\) −236.344 205.811i −0.407489 0.354847i
\(581\) −432.794 102.455i −0.744912 0.176342i
\(582\) 1.13875 + 12.0257i 0.00195662 + 0.0206627i
\(583\) 202.528 + 202.528i 0.347390 + 0.347390i
\(584\) 357.425i 0.612029i
\(585\) 47.1538 + 178.861i 0.0806047 + 0.305746i
\(586\) 706.692i 1.20596i
\(587\) −130.869 + 130.869i −0.222946 + 0.222946i −0.809738 0.586792i \(-0.800391\pi\)
0.586792 + 0.809738i \(0.300391\pi\)
\(588\) 274.052 + 106.448i 0.466076 + 0.181034i
\(589\) 341.681i 0.580104i
\(590\) −20.7319 300.228i −0.0351388 0.508862i
\(591\) −78.4668 64.8917i −0.132770 0.109800i
\(592\) 100.688 100.688i 0.170082 0.170082i
\(593\) 35.4197 + 35.4197i 0.0597296 + 0.0597296i 0.736341 0.676611i \(-0.236552\pi\)
−0.676611 + 0.736341i \(0.736552\pi\)
\(594\) −359.444 + 654.589i −0.605125 + 1.10200i
\(595\) −470.587 656.537i −0.790903 1.10342i
\(596\) 127.642i 0.214165i
\(597\) −438.449 + 41.5182i −0.734421 + 0.0695448i
\(598\) 39.1774 39.1774i 0.0655141 0.0655141i
\(599\) 442.029 0.737946 0.368973 0.929440i \(-0.379710\pi\)
0.368973 + 0.929440i \(0.379710\pi\)
\(600\) 180.503 + 111.438i 0.300839 + 0.185731i
\(601\) 468.548i 0.779614i 0.920897 + 0.389807i \(0.127458\pi\)
−0.920897 + 0.389807i \(0.872542\pi\)
\(602\) −77.2747 125.208i −0.128363 0.207987i
\(603\) 638.957 940.861i 1.05963 1.56030i
\(604\) 200.449i 0.331869i
\(605\) 858.659 986.042i 1.41927 1.62982i
\(606\) −498.798 412.504i −0.823099 0.680699i
\(607\) 622.632 + 622.632i 1.02575 + 1.02575i 0.999660 + 0.0260927i \(0.00830650\pi\)
0.0260927 + 0.999660i \(0.491694\pi\)
\(608\) −34.6437 34.6437i −0.0569798 0.0569798i
\(609\) −524.976 + 396.908i −0.862030 + 0.651737i
\(610\) −21.9757 318.240i −0.0360257 0.521705i
\(611\) 169.866i 0.278013i
\(612\) 343.667 + 233.391i 0.561547 + 0.381357i
\(613\) 140.330 + 140.330i 0.228923 + 0.228923i 0.812243 0.583319i \(-0.198246\pi\)
−0.583319 + 0.812243i \(0.698246\pi\)
\(614\) 537.990i 0.876204i
\(615\) 515.116 718.436i 0.837587 1.16819i
\(616\) 376.807 + 89.2009i 0.611700 + 0.144807i
\(617\) 354.668 + 354.668i 0.574826 + 0.574826i 0.933473 0.358647i \(-0.116762\pi\)
−0.358647 + 0.933473i \(0.616762\pi\)
\(618\) 349.122 33.0596i 0.564923 0.0534944i
\(619\) 802.714 1.29679 0.648396 0.761304i \(-0.275440\pi\)
0.648396 + 0.761304i \(0.275440\pi\)
\(620\) −259.079 + 297.514i −0.417870 + 0.479862i
\(621\) 123.863 225.568i 0.199457 0.363234i
\(622\) 93.5888 + 93.5888i 0.150464 + 0.150464i
\(623\) 17.6624 + 28.6184i 0.0283506 + 0.0459365i
\(624\) −31.4354 + 38.0115i −0.0503772 + 0.0609159i
\(625\) −601.384 + 170.184i −0.962214 + 0.272295i
\(626\) 130.139 0.207890
\(627\) 47.9053 + 505.899i 0.0764040 + 0.806857i
\(628\) 315.064 315.064i 0.501694 0.501694i
\(629\) 821.588i 1.30618i
\(630\) 306.924 322.874i 0.487182 0.512498i
\(631\) −1193.86 −1.89202 −0.946010 0.324137i \(-0.894926\pi\)
−0.946010 + 0.324137i \(0.894926\pi\)
\(632\) 82.9336 + 82.9336i 0.131224 + 0.131224i
\(633\) 367.915 34.8391i 0.581225 0.0550381i
\(634\) 366.220i 0.577633i
\(635\) −56.6806 820.818i −0.0892607 1.29263i
\(636\) 67.7133 + 55.9986i 0.106467 + 0.0880482i
\(637\) −63.4539 191.158i −0.0996136 0.300091i
\(638\) −612.928 + 612.928i −0.960702 + 0.960702i
\(639\) 79.9097 + 418.156i 0.125054 + 0.654391i
\(640\) 3.89699 + 56.4342i 0.00608905 + 0.0881784i
\(641\) 542.970i 0.847067i 0.905881 + 0.423533i \(0.139210\pi\)
−0.905881 + 0.423533i \(0.860790\pi\)
\(642\) 18.0951 + 191.092i 0.0281855 + 0.297651i
\(643\) −487.269 + 487.269i −0.757806 + 0.757806i −0.975923 0.218117i \(-0.930009\pi\)
0.218117 + 0.975923i \(0.430009\pi\)
\(644\) −129.846 30.7382i −0.201624 0.0477302i
\(645\) −219.974 + 36.2572i −0.341045 + 0.0562127i
\(646\) 282.683 0.437590
\(647\) −431.186 + 431.186i −0.666439 + 0.666439i −0.956890 0.290451i \(-0.906195\pi\)
0.290451 + 0.956890i \(0.406195\pi\)
\(648\) −90.8496 + 210.320i −0.140200 + 0.324567i
\(649\) −832.370 −1.28254
\(650\) −19.9757 143.949i −0.0307318 0.221460i
\(651\) 499.635 + 660.850i 0.767488 + 1.01513i
\(652\) −261.601 + 261.601i −0.401229 + 0.401229i
\(653\) −698.488 + 698.488i −1.06966 + 1.06966i −0.0722752 + 0.997385i \(0.523026\pi\)
−0.997385 + 0.0722752i \(0.976974\pi\)
\(654\) 1.92067 2.32246i 0.00293680 0.00355116i
\(655\) 223.238 256.355i 0.340821 0.391382i
\(656\) 235.739 0.359358
\(657\) 638.959 940.864i 0.972541 1.43206i
\(658\) 348.132 214.856i 0.529075 0.326530i
\(659\) 433.424 0.657699 0.328850 0.944382i \(-0.393339\pi\)
0.328850 + 0.944382i \(0.393339\pi\)
\(660\) 341.885 476.829i 0.518007 0.722468i
\(661\) 797.271i 1.20616i 0.797681 + 0.603079i \(0.206060\pi\)
−0.797681 + 0.603079i \(0.793940\pi\)
\(662\) −389.930 389.930i −0.589018 0.589018i
\(663\) −26.8298 283.334i −0.0404673 0.427351i
\(664\) −179.708 −0.270645
\(665\) 49.3431 299.090i 0.0742002 0.449759i
\(666\) −445.044 + 85.0480i −0.668234 + 0.127700i
\(667\) 211.212 211.212i 0.316660 0.316660i
\(668\) 70.1684 + 70.1684i 0.105043 + 0.105043i
\(669\) 238.992 288.988i 0.357238 0.431971i
\(670\) −586.813 + 673.868i −0.875841 + 1.00577i
\(671\) −882.305 −1.31491
\(672\) 117.664 + 16.3460i 0.175095 + 0.0243244i
\(673\) 369.528 + 369.528i 0.549076 + 0.549076i 0.926174 0.377098i \(-0.123078\pi\)
−0.377098 + 0.926174i \(0.623078\pi\)
\(674\) 402.622 0.597362
\(675\) −275.931 616.025i −0.408787 0.912630i
\(676\) −304.208 −0.450011
\(677\) −238.013 + 238.013i −0.351570 + 0.351570i −0.860694 0.509123i \(-0.829970\pi\)
0.509123 + 0.860694i \(0.329970\pi\)
\(678\) 356.019 33.7127i 0.525102 0.0497237i
\(679\) −19.3941 4.59113i −0.0285627 0.00676161i
\(680\) −246.143 214.344i −0.361974 0.315212i
\(681\) 53.9536 65.2405i 0.0792270 0.0958010i
\(682\) 771.565 + 771.565i 1.13133 + 1.13133i
\(683\) 399.484 399.484i 0.584896 0.584896i −0.351349 0.936245i \(-0.614277\pi\)
0.936245 + 0.351349i \(0.114277\pi\)
\(684\) 29.2624 + 153.126i 0.0427813 + 0.223868i
\(685\) 304.860 21.0517i 0.445051 0.0307324i
\(686\) −311.509 + 371.834i −0.454095 + 0.542032i
\(687\) −871.808 + 82.5544i −1.26901 + 0.120167i
\(688\) −42.0383 42.0383i −0.0611022 0.0611022i
\(689\) 60.1976i 0.0873695i
\(690\) −117.812 + 164.313i −0.170742 + 0.238135i
\(691\) 964.818i 1.39626i 0.715969 + 0.698132i \(0.245985\pi\)
−0.715969 + 0.698132i \(0.754015\pi\)
\(692\) 449.472 449.472i 0.649526 0.649526i
\(693\) −832.423 908.416i −1.20119 1.31085i
\(694\) 746.147i 1.07514i
\(695\) −53.8952 + 61.8907i −0.0775471 + 0.0890513i
\(696\) −169.473 + 204.927i −0.243496 + 0.294435i
\(697\) −961.782 + 961.782i −1.37989 + 1.37989i
\(698\) 413.538 + 413.538i 0.592461 + 0.592461i
\(699\) 713.594 862.875i 1.02088 1.23444i
\(700\) −269.749 + 223.014i −0.385356 + 0.318592i
\(701\) 256.614i 0.366069i −0.983106 0.183035i \(-0.941408\pi\)
0.983106 0.183035i \(-0.0585920\pi\)
\(702\) 150.701 43.8631i 0.214674 0.0624830i
\(703\) −218.014 + 218.014i −0.310119 + 0.310119i
\(704\) 156.461 0.222246
\(705\) −100.810 611.620i −0.142993 0.867547i
\(706\) 15.0443i 0.0213092i
\(707\) 908.796 560.882i 1.28543 0.793326i
\(708\) −254.222 + 24.0731i −0.359070 + 0.0340016i
\(709\) 271.653i 0.383149i −0.981478 0.191575i \(-0.938641\pi\)
0.981478 0.191575i \(-0.0613594\pi\)
\(710\) −23.0422 333.685i −0.0324538 0.469979i
\(711\) −70.0512 366.568i −0.0985249 0.515566i
\(712\) 9.60857 + 9.60857i 0.0134952 + 0.0134952i
\(713\) −265.878 265.878i −0.372900 0.372900i
\(714\) −546.742 + 413.363i −0.765745 + 0.578940i
\(715\) −401.004 + 27.6908i −0.560845 + 0.0387284i
\(716\) 418.272i 0.584179i
\(717\) −1216.65 + 115.209i −1.69686 + 0.160682i
\(718\) −166.966 166.966i −0.232543 0.232543i
\(719\) 648.915i 0.902524i 0.892391 + 0.451262i \(0.149026\pi\)
−0.892391 + 0.451262i \(0.850974\pi\)
\(720\) 90.6277 155.520i 0.125872 0.216001i
\(721\) −133.287 + 563.038i −0.184864 + 0.780912i
\(722\) −285.988 285.988i −0.396105 0.396105i
\(723\) −87.9889 929.198i −0.121700 1.28520i
\(724\) −455.999 −0.629832
\(725\) −107.692 776.052i −0.148541 1.07042i
\(726\) −854.967 707.054i −1.17764 0.973903i
\(727\) −165.102 165.102i −0.227100 0.227100i 0.584380 0.811480i \(-0.301338\pi\)
−0.811480 + 0.584380i \(0.801338\pi\)
\(728\) −42.7427 69.2560i −0.0587125 0.0951318i
\(729\) 615.130 391.223i 0.843800 0.536658i
\(730\) −586.815 + 673.870i −0.803856 + 0.923110i
\(731\) 343.021 0.469249
\(732\) −269.473 + 25.5173i −0.368133 + 0.0348597i
\(733\) 927.909 927.909i 1.26591 1.26591i 0.317721 0.948184i \(-0.397082\pi\)
0.948184 0.317721i \(-0.102918\pi\)
\(734\) 432.800i 0.589646i
\(735\) 341.919 + 650.628i 0.465196 + 0.885208i
\(736\) −53.9158 −0.0732551
\(737\) 1747.59 + 1747.59i 2.37122 + 2.37122i
\(738\) −620.546 421.425i −0.840848 0.571036i
\(739\) 960.261i 1.29941i −0.760188 0.649703i \(-0.774893\pi\)
0.760188 0.649703i \(-0.225107\pi\)
\(740\) 355.141 24.5238i 0.479921 0.0331403i
\(741\) 68.0649 82.3039i 0.0918555 0.111071i
\(742\) −123.372 + 76.1414i −0.166269 + 0.102616i
\(743\) −197.378 + 197.378i −0.265650 + 0.265650i −0.827345 0.561695i \(-0.810150\pi\)
0.561695 + 0.827345i \(0.310150\pi\)
\(744\) 257.965 + 213.336i 0.346728 + 0.286742i
\(745\) −209.561 + 240.650i −0.281290 + 0.323020i
\(746\) 129.751i 0.173928i
\(747\) 473.054 + 321.260i 0.633271 + 0.430067i
\(748\) −638.339 + 638.339i −0.853395 + 0.853395i
\(749\) −308.178 72.9545i −0.411453 0.0974026i
\(750\) 157.354 + 506.448i 0.209805 + 0.675264i
\(751\) 1038.60 1.38295 0.691477 0.722398i \(-0.256960\pi\)
0.691477 + 0.722398i \(0.256960\pi\)
\(752\) 116.884 116.884i 0.155431 0.155431i
\(753\) 272.271 25.7823i 0.361582 0.0342394i
\(754\) 182.181 0.241619
\(755\) −329.095 + 377.916i −0.435887 + 0.500552i
\(756\) −280.510 253.373i −0.371046 0.335150i
\(757\) 230.964 230.964i 0.305105 0.305105i −0.537902 0.843007i \(-0.680783\pi\)
0.843007 + 0.537902i \(0.180783\pi\)
\(758\) −44.8235 + 44.8235i −0.0591339 + 0.0591339i
\(759\) 430.941 + 356.386i 0.567775 + 0.469547i
\(760\) −8.43790 122.193i −0.0111025 0.160780i
\(761\) −34.8617 −0.0458103 −0.0229052 0.999738i \(-0.507292\pi\)
−0.0229052 + 0.999738i \(0.507292\pi\)
\(762\) −695.036 + 65.8153i −0.912121 + 0.0863718i
\(763\) 2.61153 + 4.23146i 0.00342271 + 0.00554582i
\(764\) −48.6895 −0.0637298
\(765\) 264.753 + 1004.25i 0.346083 + 1.31274i
\(766\) 931.648i 1.21625i
\(767\) 123.703 + 123.703i 0.161281 + 0.161281i
\(768\) 47.7862 4.52504i