Properties

Label 210.3.k.a.83.10
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 83.10
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(0.282815 - 2.98664i) q^{3} +2.00000i q^{4} +(3.28357 - 3.77070i) q^{5} +(-3.26945 + 2.70382i) q^{6} +(-5.95686 + 3.67639i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-8.84003 - 1.68933i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(0.282815 - 2.98664i) 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} +(5.97328 + 0.565630i) q^{12} +(2.90656 - 2.90656i) q^{13} +(9.63325 + 2.28046i) q^{14} +(-10.3331 - 10.8733i) q^{15} -4.00000 q^{16} +(-16.3194 + 16.3194i) q^{17} +(7.15070 + 10.5294i) q^{18} +8.66094 q^{19} +(7.54139 + 6.56714i) q^{20} +(9.29537 + 18.8307i) 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} +(-7.54552 + 25.9242i) q^{27} +(-7.35279 - 11.9137i) q^{28} -31.3396 q^{29} +(-0.540189 + 21.2063i) q^{30} -39.4508i q^{31} +(4.00000 + 4.00000i) q^{32} +(-58.4116 - 5.53119i) 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} +(9.53535 - 28.1261i) q^{42} +(10.5096 + 10.5096i) q^{43} +39.1153 q^{44} +(-35.3968 + 27.7860i) q^{45} +13.4789 q^{46} +(29.2211 - 29.2211i) q^{47} +(-1.13126 + 11.9466i) 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} +(2.44944 - 25.8671i) q^{57} +(31.3396 + 31.3396i) q^{58} -42.5598i q^{59} +(21.7465 - 20.6661i) q^{60} +45.1131i q^{61} +(-39.4508 + 39.4508i) q^{62} +(58.8694 - 22.4363i) 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} +(-21.0587 + 14.3014i) q^{72} +(89.3562 - 89.3562i) q^{73} +50.3442 q^{74} +(-74.9291 + 3.25974i) q^{75} +17.3219i q^{76} +(71.9016 + 116.502i) q^{77} +(-1.64404 + 17.3617i) 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} +(-37.6614 + 18.5907i) q^{84} +(7.94959 + 115.122i) q^{85} -21.0192i q^{86} +(-8.86329 + 93.6000i) q^{87} +(-39.1153 - 39.1153i) q^{88} +4.80429i q^{89} +(63.1829 + 7.61081i) q^{90} +(-6.62831 + 27.9997i) q^{91} +(-13.4789 - 13.4789i) q^{92} +(-117.825 - 11.1573i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

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
\(3\) 0.282815 2.98664i 0.0942716 0.995547i
\(4\) 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 \(-0.651412\pi\)
0.457939 0.888984i \(-0.348588\pi\)
\(12\) 5.97328 + 0.565630i 0.497773 + 0.0471358i
\(13\) 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
\(15\) −10.3331 10.8733i −0.688871 0.724884i
\(16\) −4.00000 −0.250000
\(17\) −16.3194 + 16.3194i −0.959967 + 0.959967i −0.999229 0.0392622i \(-0.987499\pi\)
0.0392622 + 0.999229i \(0.487499\pi\)
\(18\) 7.15070 + 10.5294i 0.397261 + 0.584965i
\(19\) 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
\(21\) 9.29537 + 18.8307i 0.442637 + 0.896701i
\(22\) −19.5576 + 19.5576i −0.888984 + 0.888984i
\(23\) −6.73947 + 6.73947i −0.293021 + 0.293021i −0.838272 0.545252i \(-0.816434\pi\)
0.545252 + 0.838272i \(0.316434\pi\)
\(24\) −5.40765 6.53891i −0.225319 0.272455i
\(25\) −3.43630 24.7627i −0.137452 0.990508i
\(26\) −5.81313 −0.223582
\(27\) −7.54552 + 25.9242i −0.279464 + 0.960156i
\(28\) −7.35279 11.9137i −0.262600 0.425490i
\(29\) −31.3396 −1.08067 −0.540337 0.841449i \(-0.681703\pi\)
−0.540337 + 0.841449i \(0.681703\pi\)
\(30\) −0.540189 + 21.2063i −0.0180063 + 0.706877i
\(31\) 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
\(33\) −58.4116 5.53119i −1.77005 0.167612i
\(34\) 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 \(-0.244730\pi\)
0.718717 + 0.695303i \(0.244730\pi\)
\(42\) 9.53535 28.1261i 0.227032 0.669669i
\(43\) 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
\(45\) −35.3968 + 27.7860i −0.786597 + 0.617467i
\(46\) 13.4789 0.293021
\(47\) 29.2211 29.2211i 0.621725 0.621725i −0.324247 0.945972i \(-0.605111\pi\)
0.945972 + 0.324247i \(0.105111\pi\)
\(48\) −1.13126 + 11.9466i −0.0235679 + 0.248887i
\(49\) 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 −0.798019 0.602633i \(-0.794118\pi\)
0.602633 + 0.798019i \(0.294118\pi\)
\(54\) 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
\(57\) 2.44944 25.8671i 0.0429727 0.453809i
\(58\) 31.3396 + 31.3396i 0.540337 + 0.540337i
\(59\) 42.5598i 0.721353i −0.932691 0.360676i \(-0.882546\pi\)
0.932691 0.360676i \(-0.117454\pi\)
\(60\) 21.7465 20.6661i 0.362442 0.344436i
\(61\) 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
\(63\) 58.8694 22.4363i 0.934436 0.356132i
\(64\) 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 \(-0.891900\pi\)
0.942886 0.333117i \(-0.108100\pi\)
\(72\) −21.0587 + 14.3014i −0.292482 + 0.198631i
\(73\) 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
\(75\) −74.9291 + 3.25974i −0.999055 + 0.0434631i
\(76\) 17.3219i 0.227919i
\(77\) 71.9016 + 116.502i 0.933787 + 1.51301i
\(78\) −1.64404 + 17.3617i −0.0210774 + 0.222586i
\(79\) 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 0.382617 0.923907i \(-0.375023\pi\)
−0.923907 + 0.382617i \(0.875023\pi\)
\(84\) −37.6614 + 18.5907i −0.448350 + 0.221318i
\(85\) 7.94959 + 115.122i 0.0935246 + 1.35437i
\(86\) 21.0192i 0.244409i
\(87\) −8.86329 + 93.6000i −0.101877 + 1.07586i
\(88\) −39.1153 39.1153i −0.444492 0.444492i
\(89\) 4.80429i 0.0539807i 0.999636 + 0.0269904i \(0.00859234\pi\)
−0.999636 + 0.0269904i \(0.991408\pi\)
\(90\) 63.1829 + 7.61081i 0.702032 + 0.0845646i
\(91\) −6.62831 + 27.9997i −0.0728386 + 0.307689i
\(92\) −13.4789 13.4789i −0.146510 0.146510i
\(93\) −117.825 11.1573i −1.26694 0.119971i
\(94\) −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 \(-0.227509\pi\)
0.755262 + 0.655423i \(0.227509\pi\)
\(102\) 9.23076 97.4805i 0.0904976 0.955691i
\(103\) 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
\(105\) 101.527 + 26.7820i 0.966923 + 0.255067i
\(106\) 20.7109 0.195386
\(107\) −31.9911 31.9911i −0.298982 0.298982i 0.541633 0.840615i \(-0.317806\pi\)
−0.840615 + 0.541633i \(0.817806\pi\)
\(108\) −51.8484 15.0910i −0.480078 0.139732i
\(109\) 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 −0.919812 0.392360i \(-0.871659\pi\)
0.392360 + 0.919812i \(0.371659\pi\)
\(114\) −28.3165 + 23.4177i −0.248391 + 0.205418i
\(115\) 3.28296 + 47.5421i 0.0285475 + 0.413409i
\(116\) 62.6791i 0.540337i
\(117\) −30.6043 + 20.7840i −0.261575 + 0.177641i
\(118\) −42.5598 + 42.5598i −0.360676 + 0.360676i
\(119\) 37.2159 157.209i 0.312738 1.32109i
\(120\) −42.4126 1.08038i −0.353439 0.00900315i
\(121\) −261.501 −2.16117
\(122\) 45.1131 45.1131i 0.369779 0.369779i
\(123\) 16.6676 176.017i 0.135509 1.43103i
\(124\) 78.9016 0.636304
\(125\) −104.656 68.3529i −0.837248 0.546823i
\(126\) −81.3058 36.4331i −0.645284 0.289152i
\(127\) −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 \(-0.416446\pi\)
0.259489 + 0.965746i \(0.416446\pi\)
\(132\) 11.0624 116.823i 0.0838059 0.885025i
\(133\) −51.5920 + 31.8410i −0.387909 + 0.239406i
\(134\) −178.712 −1.33367
\(135\) 72.9761 + 113.576i 0.540564 + 0.841303i
\(136\) 65.2777i 0.479983i
\(137\) 43.2163 + 43.2163i 0.315448 + 0.315448i 0.847016 0.531568i \(-0.178397\pi\)
−0.531568 + 0.847016i \(0.678397\pi\)
\(138\) 3.81205 40.2568i 0.0276235 0.291716i
\(139\) 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
\(147\) −124.600 77.9984i −0.847621 0.530602i
\(148\) −50.3442 50.3442i −0.340163 0.340163i
\(149\) −63.8210 −0.428329 −0.214165 0.976798i \(-0.568703\pi\)
−0.214165 + 0.976798i \(0.568703\pi\)
\(150\) 78.1889 + 71.6694i 0.521259 + 0.477796i
\(151\) 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
\(153\) 171.833 116.695i 1.12309 0.762715i
\(154\) 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
\(162\) −45.4248 105.160i −0.280400 0.649135i
\(163\) 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
\(165\) −212.655 + 202.090i −1.28882 + 1.22479i
\(166\) 89.8542i 0.541290i
\(167\) −35.0842 + 35.0842i −0.210085 + 0.210085i −0.804304 0.594219i \(-0.797461\pi\)
0.594219 + 0.804304i \(0.297461\pi\)
\(168\) 56.2522 + 19.0707i 0.334834 + 0.113516i
\(169\) 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 \(0.120653\pi\)
0.370032 + 0.929019i \(0.379347\pi\)
\(174\) 102.463 84.7367i 0.588869 0.486992i
\(175\) 111.507 + 134.875i 0.637183 + 0.770713i
\(176\) 78.2306i 0.444492i
\(177\) −127.111 12.0366i −0.718140 0.0680031i
\(178\) 4.80429 4.80429i 0.0269904 0.0269904i
\(179\) 209.136 1.16836 0.584179 0.811625i \(-0.301417\pi\)
0.584179 + 0.811625i \(0.301417\pi\)
\(180\) −55.5721 70.7937i −0.308734 0.393298i
\(181\) 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
\(183\) 134.737 + 12.7587i 0.736265 + 0.0697194i
\(184\) 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
\(189\) −50.3601 182.167i −0.266455 0.963847i
\(190\) −61.0966 + 4.21895i −0.321561 + 0.0222050i
\(191\) 24.3448i 0.127460i −0.997967 0.0637298i \(-0.979700\pi\)
0.997967 0.0637298i \(-0.0202996\pi\)
\(192\) −23.8931 2.26252i −0.124443 0.0117840i
\(193\) −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
\(195\) −61.6376 1.57009i −0.316090 0.00805176i
\(196\) 87.5990 + 43.9365i 0.446934 + 0.224166i
\(197\) 24.0000 + 24.0000i 0.121827 + 0.121827i 0.765392 0.643565i \(-0.222545\pi\)
−0.643565 + 0.765392i \(0.722545\pi\)
\(198\) 205.930 139.851i 1.04005 0.706317i
\(199\) −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
\(207\) 70.9624 48.1919i 0.342813 0.232811i
\(208\) −11.6263 + 11.6263i −0.0558955 + 0.0558955i
\(209\) 169.388i 0.810467i
\(210\) −74.7450 128.309i −0.355928 0.610995i
\(211\) 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
\(213\) −141.276 13.3779i −0.663266 0.0628069i
\(214\) 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
\(222\) 14.2381 150.360i 0.0641355 0.677297i
\(223\) 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
\(225\) −11.4554 + 224.708i −0.0509130 + 0.998703i
\(226\) 119.204 0.527451
\(227\) −19.9546 + 19.9546i −0.0879055 + 0.0879055i −0.749692 0.661787i \(-0.769798\pi\)
0.661787 + 0.749692i \(0.269798\pi\)
\(228\) 51.7342 + 4.89888i 0.226904 + 0.0214863i
\(229\) −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
\(231\) 368.284 181.796i 1.59431 0.786994i
\(232\) −62.6791 + 62.6791i −0.270169 + 0.270169i
\(233\) −263.920 + 263.920i −1.13270 + 1.13270i −0.142978 + 0.989726i \(0.545668\pi\)
−0.989726 + 0.142978i \(0.954332\pi\)
\(234\) 51.3883 + 9.82031i 0.219608 + 0.0419671i
\(235\) −14.2343 206.133i −0.0605714 0.877163i
\(236\) 85.1196 0.360676
\(237\) −123.846 11.7274i −0.522558 0.0494828i
\(238\) −194.425 + 119.993i −0.816912 + 0.504174i
\(239\) 407.365 1.70446 0.852228 0.523171i \(-0.175251\pi\)
0.852228 + 0.523171i \(0.175251\pi\)
\(240\) 41.3323 + 43.4930i 0.172218 + 0.181221i
\(241\) 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
\(243\) 110.497 216.424i 0.454721 0.890634i
\(244\) −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 \(-0.558128\pi\)
−0.181600 + 0.983373i \(0.558128\pi\)
\(252\) 44.8726 + 117.739i 0.178066 + 0.467218i
\(253\) 131.808 + 131.808i 0.520981 + 0.520981i
\(254\) 232.715 0.916202
\(255\) 346.075 + 8.81557i 1.35716 + 0.0345709i
\(256\) 16.0000 0.0625000
\(257\) 221.675 221.675i 0.862547 0.862547i −0.129086 0.991633i \(-0.541204\pi\)
0.991633 + 0.129086i \(0.0412045\pi\)
\(258\) −62.7767 5.94453i −0.243320 0.0230408i
\(259\) 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 −0.999834 0.0182309i \(-0.994197\pi\)
0.0182309 + 0.999834i \(0.494197\pi\)
\(264\) −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
\(267\) 14.3487 + 1.35872i 0.0537403 + 0.00508885i
\(268\) 178.712 + 178.712i 0.666835 + 0.666835i
\(269\) 138.071i 0.513275i 0.966508 + 0.256637i \(0.0826146\pi\)
−0.966508 + 0.256637i \(0.917385\pi\)
\(270\) 40.5998 186.552i 0.150370 0.690933i
\(271\) 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
\(273\) 81.7503 + 27.7151i 0.299452 + 0.101521i
\(274\) 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 \(-0.861412\pi\)
0.906706 0.421762i \(-0.138588\pi\)
\(282\) −16.5283 + 174.546i −0.0586111 + 0.618956i
\(283\) −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
\(285\) −89.4941 94.1726i −0.314014 0.330430i
\(286\) 113.691i 0.397521i
\(287\) −351.066 + 216.667i −1.22323 + 0.754939i
\(288\) −28.6028 42.1175i −0.0993153 0.146241i
\(289\) 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 \(0.0750619\pi\)
0.233635 + 0.972324i \(0.424938\pi\)
\(294\) 46.6019 + 202.599i 0.158510 + 0.689111i
\(295\) −160.480 139.748i −0.544001 0.473723i
\(296\) 100.688i 0.340163i
\(297\) 507.017 + 147.573i 1.70713 + 0.496877i
\(298\) 63.8210 + 63.8210i 0.214165 + 0.214165i
\(299\) 39.1774i 0.131028i
\(300\) −6.51947 149.858i −0.0217316 0.499528i
\(301\) −101.241 23.9667i −0.336350 0.0796236i
\(302\) −100.225 100.225i −0.331869 0.331869i
\(303\) 43.1471 455.651i 0.142400 1.50380i
\(304\) −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 \(-0.548077\pi\)
−0.150464 + 0.988615i \(0.548077\pi\)
\(312\) −34.7234 3.28808i −0.111293 0.0105387i
\(313\) 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
\(315\) 108.702 295.650i 0.345084 0.938572i
\(316\) 82.9336 0.262448
\(317\) 183.110 + 183.110i 0.577633 + 0.577633i 0.934251 0.356617i \(-0.116070\pi\)
−0.356617 + 0.934251i \(0.616070\pi\)
\(318\) 5.85735 61.8560i 0.0184193 0.194516i
\(319\) 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
\(327\) −2.12156 0.200898i −0.00648796 0.000614367i
\(328\) 117.870 117.870i 0.359358 0.359358i
\(329\) −66.6376 + 281.494i −0.202546 + 0.855605i
\(330\) 414.746 + 10.5648i 1.25681 + 0.0320146i
\(331\) −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
\(333\) 265.046 179.998i 0.795934 0.540534i
\(334\) 70.1684 0.210085
\(335\) −43.5274 630.341i −0.129933 1.88161i
\(336\) −37.1815 75.3229i −0.110659 0.224175i
\(337\) 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
\(342\) 61.9318 + 91.1942i 0.181087 + 0.266650i
\(343\) 30.1624 + 341.671i 0.0879370 + 0.996126i
\(344\) 42.0383 0.122204
\(345\) 142.919 + 3.64059i 0.414259 + 0.0105524i
\(346\) 449.472i 1.29905i
\(347\) −373.074 373.074i −1.07514 1.07514i −0.996938 0.0782023i \(-0.975082\pi\)
−0.0782023 0.996938i \(-0.524918\pi\)
\(348\) −187.200 17.7266i −0.537931 0.0509385i
\(349\) 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 0.696372 0.717681i \(-0.254796\pi\)
−0.717681 + 0.696372i \(0.754796\pi\)
\(354\) 115.074 + 139.147i 0.325069 + 0.393072i
\(355\) −178.364 155.321i −0.502433 0.437525i
\(356\) −9.60857 −0.0269904
\(357\) −459.002 155.611i −1.28572 0.435886i
\(358\) −209.136 209.136i −0.584179 0.584179i
\(359\) 166.966 0.465085 0.232543 0.972586i \(-0.425295\pi\)
0.232543 + 0.972586i \(0.425295\pi\)
\(360\) −15.2216 + 126.366i −0.0422823 + 0.351016i
\(361\) −285.988 −0.792211
\(362\) 227.999 227.999i 0.629832 0.629832i
\(363\) −73.9565 + 781.010i −0.203737 + 2.15154i
\(364\) −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
\(372\) 22.3146 235.651i 0.0599854 0.633470i
\(373\) −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
\(375\) −233.744 + 293.239i −0.623317 + 0.781970i
\(376\) 116.884i 0.310863i
\(377\) −91.0905 + 91.0905i −0.241619 + 0.241619i
\(378\) −131.807 + 232.527i −0.348696 + 0.615151i
\(379\) 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 \(-0.920452\pi\)
−0.247315 0.968935i \(-0.579548\pi\)
\(384\) 21.6306 + 26.1556i 0.0563297 + 0.0681136i
\(385\) 675.388 + 111.424i 1.75425 + 0.289413i
\(386\) 238.354i 0.617497i
\(387\) −75.1509 110.659i −0.194188 0.285941i
\(388\) −4.02649 + 4.02649i −0.0103776 + 0.0103776i
\(389\) −341.962 −0.879079 −0.439540 0.898223i \(-0.644858\pi\)
−0.439540 + 0.898223i \(0.644858\pi\)
\(390\) 60.0675 + 63.2077i 0.154019 + 0.162071i
\(391\) 219.969i 0.562580i
\(392\) −43.6625 131.536i −0.111384 0.335550i
\(393\) 19.2275 203.050i 0.0489249 0.516667i
\(394\) 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
\(399\) 80.5067 + 163.092i 0.201771 + 0.408751i
\(400\) 13.7452 + 99.0508i 0.0343630 + 0.247627i
\(401\) 278.216i 0.693806i −0.937901 0.346903i \(-0.887233\pi\)
0.937901 0.346903i \(-0.112767\pi\)
\(402\) −50.5424 + 533.748i −0.125727 + 1.32773i
\(403\) −114.666 114.666i −0.284532 0.284532i
\(404\) 305.126i 0.755262i
\(405\) 359.849 185.832i 0.888516 0.458845i
\(406\) −301.902 71.4687i −0.743600 0.176031i
\(407\) 492.307 + 492.307i 1.20960 + 1.20960i
\(408\) 194.961 + 18.4615i 0.477846 + 0.0452488i
\(409\) −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
\(417\) 4.64201 49.0215i 0.0111319 0.117557i
\(418\) −169.388 + 169.388i −0.405233 + 0.405233i
\(419\) 12.3613i 0.0295020i −0.999891 0.0147510i \(-0.995304\pi\)
0.999891 0.0147510i \(-0.00469556\pi\)
\(420\) −53.5640 + 203.054i −0.127533 + 0.483462i
\(421\) 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
\(423\) −307.679 + 208.951i −0.727375 + 0.493974i
\(424\) 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 \(0.00284551\pi\)
−0.999960 + 0.00893932i \(0.997154\pi\)
\(432\) 30.1821 103.697i 0.0698659 0.240039i
\(433\) 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
\(435\) 323.834 + 340.763i 0.744445 + 0.783363i
\(436\) 1.42070 0.00325849
\(437\) −58.3702 + 58.3702i −0.133570 + 0.133570i
\(438\) −50.5425 + 533.749i −0.115394 + 1.21861i
\(439\) 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
\(441\) −268.192 + 350.077i −0.608145 + 0.793826i
\(442\) 94.8670 94.8670i 0.214631 0.214631i
\(443\) −163.039 + 163.039i −0.368035 + 0.368035i −0.866760 0.498725i \(-0.833802\pi\)
0.498725 + 0.866760i \(0.333802\pi\)
\(444\) −164.598 + 136.122i −0.370716 + 0.306581i
\(445\) 18.1155 + 15.7752i 0.0407090 + 0.0354499i
\(446\) −176.781 −0.396369
\(447\) −18.0495 + 190.610i −0.0403793 + 0.426422i
\(448\) 29.4111 + 47.6548i 0.0656499 + 0.106372i
\(449\) 681.871 1.51864 0.759322 0.650715i \(-0.225531\pi\)
0.759322 + 0.650715i \(0.225531\pi\)
\(450\) 236.164 213.253i 0.524808 0.473895i
\(451\) 1152.63i 2.55571i
\(452\) −119.204 119.204i −0.263726 0.263726i
\(453\) 28.3450 299.335i 0.0625717 0.660783i
\(454\) 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 \(-0.571583\pi\)
−0.222993 + 0.974820i \(0.571583\pi\)
\(462\) −550.080 186.489i −1.19065 0.403656i
\(463\) −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
\(465\) −428.959 + 407.648i −0.922492 + 0.876662i
\(466\) 527.840 1.13270
\(467\) 331.816 331.816i 0.710527 0.710527i −0.256118 0.966645i \(-0.582444\pi\)
0.966645 + 0.256118i \(0.0824436\pi\)
\(468\) −41.5679 61.2086i −0.0888204 0.130788i
\(469\) −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
\(477\) 109.036 74.0487i 0.228588 0.155238i
\(478\) −407.365 407.365i −0.852228 0.852228i
\(479\) 449.861i 0.939167i 0.882888 + 0.469584i \(0.155596\pi\)
−0.882888 + 0.469584i \(0.844404\pi\)
\(480\) 2.16076 84.8253i 0.00450157 0.176719i
\(481\) 146.329i 0.304217i
\(482\) −311.118 + 311.118i −0.645474 + 0.645474i
\(483\) −189.555 64.2632i −0.392454 0.133050i
\(484\) 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 \(0.366565\pi\)
−0.407029 + 0.913415i \(0.633435\pi\)
\(492\) 352.034 + 33.3353i 0.715516 + 0.0677546i
\(493\) 511.444 511.444i 1.03741 1.03741i
\(494\) −50.3472 −0.101917
\(495\) 543.429 + 692.279i 1.09784 + 1.39854i
\(496\) 157.803i 0.318152i
\(497\) 173.903 + 281.774i 0.349905 + 0.566951i
\(498\) 268.362 + 25.4121i 0.538880 + 0.0510283i
\(499\) 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 0.520970 0.853575i \(-0.325570\pi\)
−0.853575 + 0.520970i \(0.825570\pi\)
\(504\) 72.8662 162.612i 0.144576 0.322642i
\(505\) 500.952 575.269i 0.991983 1.13915i
\(506\) 263.616i 0.520981i
\(507\) 454.279 + 43.0172i 0.896014 + 0.0848466i
\(508\) −232.715 232.715i −0.458101 0.458101i
\(509\) 480.263i 0.943543i 0.881721 + 0.471771i \(0.156385\pi\)
−0.881721 + 0.471771i \(0.843615\pi\)
\(510\) −337.260 354.891i −0.661293 0.695864i
\(511\) −203.773 + 860.790i −0.398774 + 1.68452i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −65.3513 + 224.528i −0.127390 + 0.437676i
\(514\) −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 \(-0.448410\pi\)
0.161366 + 0.986895i \(0.448410\pi\)
\(522\) −224.100 329.986i −0.429310 0.632156i
\(523\) 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
\(525\) 434.358 294.887i 0.827348 0.561689i
\(526\) 516.323 0.981603
\(527\) 643.815 + 643.815i 1.22166 + 1.22166i
\(528\) 233.646 + 22.1248i 0.442512 + 0.0419030i
\(529\) 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
\(537\) 59.1468 624.614i 0.110143 1.16315i
\(538\) 138.071 138.071i 0.256637 0.256637i
\(539\) −856.615 429.647i −1.58927 0.797119i
\(540\) −227.152 + 145.952i −0.420652 + 0.270282i
\(541\) 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
\(543\) 680.952 + 64.4816i 1.25405 + 0.118751i
\(544\) −130.555 −0.239992
\(545\) −2.67852 2.33249i −0.00491471 0.00427980i
\(546\) −54.0352 109.465i −0.0989656 0.200486i
\(547\) 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
\(552\) 80.5135 + 7.62409i 0.145858 + 0.0138118i
\(553\) 152.448 + 247.012i 0.275675 + 0.446676i
\(554\) −211.024 −0.380910
\(555\) 533.807 + 13.5977i 0.961815 + 0.0245003i
\(556\) 32.8272i 0.0590417i
\(557\) 83.3059 + 83.3059i 0.149562 + 0.149562i 0.777922 0.628361i \(-0.216274\pi\)
−0.628361 + 0.777922i \(0.716274\pi\)
\(558\) 415.392 282.101i 0.744430 0.505557i
\(559\) 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 0.752445 0.658656i \(-0.228875\pi\)
−0.658656 + 0.752445i \(0.728875\pi\)
\(564\) 191.074 158.017i 0.338784 0.280173i
\(565\) 29.0336 + 420.448i 0.0513868 + 0.744157i
\(566\) 573.529 1.01330
\(567\) −558.310 + 98.8878i −0.984674 + 0.174405i
\(568\) −94.6051 94.6051i −0.166558 0.166558i
\(569\) 354.050 0.622233 0.311116 0.950372i \(-0.399297\pi\)
0.311116 + 0.950372i \(0.399297\pi\)
\(570\) −4.67854 + 183.667i −0.00820797 + 0.322222i
\(571\) 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
\(573\) −72.7090 6.88506i −0.126892 0.0120158i
\(574\) 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
\(582\) −12.0257 1.13875i −0.0206627 0.00195662i
\(583\) 202.528 + 202.528i 0.347390 + 0.347390i
\(584\) 357.425i 0.612029i
\(585\) −22.1213 + 183.645i −0.0378142 + 0.313923i
\(586\) 706.692i 1.20596i
\(587\) 130.869 130.869i 0.222946 0.222946i −0.586792 0.809738i \(-0.699609\pi\)
0.809738 + 0.586792i \(0.199609\pi\)
\(588\) 155.997 249.201i 0.265301 0.423811i
\(589\) 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 0.676611 0.736341i \(-0.263448\pi\)
−0.736341 + 0.676611i \(0.763448\pi\)
\(594\) −359.444 654.589i −0.605125 1.10200i
\(595\) −470.587 656.537i −0.790903 1.10342i
\(596\) 127.642i 0.214165i
\(597\) −41.5182 + 438.449i −0.0695448 + 0.734421i
\(598\) 39.1774 39.1774i 0.0655141 0.0655141i
\(599\) −442.029 −0.737946 −0.368973 0.929440i \(-0.620290\pi\)
−0.368973 + 0.929440i \(0.620290\pi\)
\(600\) −143.339 + 156.378i −0.238898 + 0.260630i
\(601\) 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
\(603\) −940.861 + 638.957i −1.56030 + 1.05963i
\(604\) 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
\(609\) −291.313 590.146i −0.478346 0.969042i
\(610\) −21.9757 318.240i −0.0360257 0.521705i
\(611\) 169.866i 0.278013i
\(612\) 233.391 + 343.667i 0.381357 + 0.561547i
\(613\) 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
\(615\) −608.977 640.813i −0.990207 1.04197i
\(616\) 376.807 + 89.2009i 0.611700 + 0.144807i
\(617\) −354.668 354.668i −0.574826 0.574826i 0.358647 0.933473i \(-0.383238\pi\)
−0.933473 + 0.358647i \(0.883238\pi\)
\(618\) −33.0596 + 349.122i −0.0534944 + 0.564923i
\(619\) 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
\(627\) −505.899 47.9053i −0.806857 0.0764040i
\(628\) 315.064 315.064i 0.501694 0.501694i
\(629\) 821.588i 1.30618i
\(630\) −404.352 + 186.949i −0.641828 + 0.296744i
\(631\) −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
\(633\) 34.8391 367.915i 0.0550381 0.581225i
\(634\) 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 \(-0.860790\pi\)
0.905881 0.423533i \(-0.139210\pi\)
\(642\) 191.092 + 18.0951i 0.297651 + 0.0281855i
\(643\) −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
\(645\) 5.67716 222.870i 0.00880180 0.345534i
\(646\) 282.683 0.437590
\(647\) 431.186 431.186i 0.666439 0.666439i −0.290451 0.956890i \(-0.593805\pi\)
0.956890 + 0.290451i \(0.0938052\pi\)
\(648\) 210.320 90.8496i 0.324567 0.140200i
\(649\) −832.370 −1.28254
\(650\) 19.9757 + 143.949i 0.0307318 + 0.221460i
\(651\) 742.887 366.710i 1.14115 0.563303i
\(652\) −261.601 + 261.601i −0.401229 + 0.401229i
\(653\) 698.488 698.488i 1.06966 1.06966i 0.0722752 0.997385i \(-0.476974\pi\)
0.997385 0.0722752i \(-0.0230260\pi\)
\(654\) 1.92067 + 2.32246i 0.00293680 + 0.00355116i
\(655\) 223.238 256.355i 0.340821 0.391382i
\(656\) −235.739 −0.359358
\(657\) −940.864 + 638.959i −1.43206 + 0.972541i
\(658\) 348.132 214.856i 0.529075 0.326530i
\(659\) −433.424 −0.657699 −0.328850 0.944382i \(-0.606661\pi\)
−0.328850 + 0.944382i \(0.606661\pi\)
\(660\) −404.181 425.311i −0.612395 0.644410i
\(661\) 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
\(663\) 283.334 + 26.8298i 0.427351 + 0.0404673i
\(664\) −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
\(672\) −38.1414 + 112.504i −0.0567580 + 0.167417i
\(673\) 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
\(675\) 667.883 + 97.7640i 0.989456 + 0.144836i
\(676\) −304.208 −0.450011
\(677\) 238.013 238.013i 0.351570 0.351570i −0.509123 0.860694i \(-0.670030\pi\)
0.860694 + 0.509123i \(0.170030\pi\)
\(678\) 33.7127 356.019i 0.0497237 0.525102i
\(679\) −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 −0.936245 0.351349i \(-0.885723\pi\)
0.351349 + 0.936245i \(0.385723\pi\)
\(684\) 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
\(687\) −82.5544 + 871.808i −0.120167 + 1.26901i
\(688\) −42.0383 42.0383i −0.0611022 0.0611022i
\(689\) 60.1976i 0.0873695i
\(690\) −139.279 146.560i −0.201853 0.212406i
\(691\) 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
\(693\) −438.802 1151.35i −0.633191 1.66140i
\(694\) 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 \(0.0585920\pi\)
−0.983106 + 0.183035i \(0.941408\pi\)
\(702\) 43.8631 150.701i 0.0624830 0.214674i
\(703\) −218.014 + 218.014i −0.310119 + 0.310119i
\(704\) −156.461 −0.222246
\(705\) −619.672 15.7849i −0.878967 0.0223899i
\(706\) 15.0443i 0.0213092i
\(707\) −908.796 + 560.882i −1.28543 + 0.793326i
\(708\) 24.0731 254.222i 0.0340016 0.359070i
\(709\) 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
\(714\) 303.390 + 614.613i 0.424917 + 0.860803i
\(715\) −401.004 + 27.6908i −0.560845 + 0.0387284i
\(716\) 418.272i 0.584179i
\(717\) 115.209 1216.65i 0.160682 1.69686i
\(718\) −166.966 166.966i −0.232543 0.232543i
\(719\) 648.915i 0.902524i −0.892391 0.451262i \(-0.850974\pi\)
0.892391 0.451262i \(-0.149026\pi\)
\(720\) 141.587 111.144i 0.196649 0.154367i
\(721\) −133.287 + 563.038i −0.184864 + 0.780912i
\(722\) 285.988 + 285.988i 0.396105 + 0.396105i
\(723\) −929.198 87.9889i −1.28520 0.121700i
\(724\) −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
\(732\) −25.5173 + 269.473i −0.0348597 + 0.368133i
\(733\) 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
\(735\) −703.243 + 213.717i −0.956793 + 0.290771i
\(736\) −53.9158 −0.0732551
\(737\) −1747.59 1747.59i −2.37122 2.37122i
\(738\) 421.425 + 620.546i 0.571036 + 0.840848i
\(739\) 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 −0.561695 0.827345i \(-0.689850\pi\)
0.827345 + 0.561695i \(0.189850\pi\)
\(744\) −257.965 + 213.336i −0.346728 + 0.286742i
\(745\) −209.561 + 240.650i −0.281290 + 0.323020i
\(746\) 129.751i 0.173928i
\(747\) 321.260 + 473.054i 0.430067 + 0.633271i
\(748\) −638.339 + 638.339i −0.853395 + 0.853395i
\(749\) 308.178 + 72.9545i 0.411453 + 0.0974026i
\(750\) 526.982 59.4948i 0.702643 0.0793264i
\(751\) 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
\(753\) −25.7823 + 272.271i −0.0342394 + 0.361582i
\(754\) 182.181 0.241619
\(755\) 329.095 377.916i 0.435887 0.500552i
\(756\) 364.334 100.720i 0.481924 0.133228i
\(757\) 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 \(-0.492708\pi\)
0.0229052 + 0.999738i \(0.492708\pi\)
\(762\) 65.8153 695.036i 0.0863718 0.912121i
\(763\) 2.61153 + 4.23146i 0.00342271 + 0.00554582i
\(764\) 48.6895 0.0637298
\(765\) 124.204 1031.11i 0.162358 1.34785i
\(766\) 931.648i 1.21625i
\(767\)