Properties

Label 210.3.k.b.167.2
Level 210
Weight 3
Character 210.167
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 167.2
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.b.83.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-2.98664 - 0.282815i) q^{3} -2.00000i q^{4} +(3.28357 + 3.77070i) q^{5} +(-3.26945 + 2.70382i) q^{6} +(-3.67639 - 5.95686i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(8.84003 + 1.68933i) q^{9} +O(q^{10})\) \(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} +(-3.67639 - 5.95686i) 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} +(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} +(-25.9242 - 7.54552i) q^{27} +(-11.9137 + 7.35279i) 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} +(10.3898 - 33.4223i) 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} +(28.1261 + 9.53535i) 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} +(-22.4363 - 58.8694i) 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} +(-23.0325 - 43.8121i) 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} +(-116.502 + 71.9016i) 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} +(37.6614 - 18.5907i) 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} +(21.8312 + 65.7678i) 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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) −2.98664 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
\(7\) −3.67639 5.95686i −0.525199 0.850979i
\(8\) −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 \(-0.348588\pi\)
\(12\) −0.565630 + 5.97328i −0.0471358 + 0.497773i
\(13\) −2.90656 2.90656i −0.223582 0.223582i 0.586423 0.810005i \(-0.300536\pi\)
−0.810005 + 0.586423i \(0.800536\pi\)
\(14\) −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 \(-0.487499\pi\)
−0.999229 + 0.0392622i \(0.987499\pi\)
\(18\) 10.5294 7.15070i 0.584965 0.397261i
\(19\) −8.66094 −0.455839 −0.227919 0.973680i \(-0.573192\pi\)
−0.227919 + 0.973680i \(0.573192\pi\)
\(20\) 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 \(-0.183566\pi\)
−0.545252 + 0.838272i \(0.683566\pi\)
\(24\) 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
\(28\) −11.9137 + 7.35279i −0.425490 + 0.262600i
\(29\) 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
\(35\) 10.3898 33.4223i 0.296851 0.954924i
\(36\) 3.37866 17.6801i 0.0938518 0.491113i
\(37\) −25.1721 25.1721i −0.680326 0.680326i 0.279747 0.960074i \(-0.409749\pi\)
−0.960074 + 0.279747i \(0.909749\pi\)
\(38\) −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 \(0.244730\pi\)
\(42\) 28.1261 + 9.53535i 0.669669 + 0.227032i
\(43\) 10.5096 10.5096i 0.244409 0.244409i −0.574262 0.818671i \(-0.694711\pi\)
0.818671 + 0.574262i \(0.194711\pi\)
\(44\) −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 \(-0.105111\pi\)
−0.324247 + 0.945972i \(0.605111\pi\)
\(48\) 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 0.798019 0.602633i \(-0.205882\pi\)
−0.602633 + 0.798019i \(0.705882\pi\)
\(54\) −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
\(63\) −22.4363 58.8694i −0.356132 0.934436i
\(64\) 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 0.902060 + 0.431611i \(0.142055\pi\)
0.431611 + 0.902060i \(0.357945\pi\)
\(68\) −32.6389 + 32.6389i −0.479983 + 0.479983i
\(69\) −18.2224 22.0344i −0.264092 0.319339i
\(70\) −23.0325 43.8121i −0.329036 0.625887i
\(71\) 47.3026i 0.666233i −0.942886 0.333117i \(-0.891900\pi\)
0.942886 0.333117i \(-0.108100\pi\)
\(72\) −14.3014 21.0587i −0.198631 0.292482i
\(73\) −89.3562 89.3562i −1.22406 1.22406i −0.966177 0.257880i \(-0.916976\pi\)
−0.257880 0.966177i \(-0.583024\pi\)
\(74\) −50.3442 −0.680326
\(75\) 17.2663 72.9855i 0.230217 0.973139i
\(76\) 17.3219i 0.227919i
\(77\) −116.502 + 71.9016i −1.51301 + 0.933787i
\(78\) 17.3617 + 1.64404i 0.222586 + 0.0210774i
\(79\) 41.4668i 0.524896i 0.964946 + 0.262448i \(0.0845298\pi\)
−0.964946 + 0.262448i \(0.915470\pi\)
\(80\) −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 \(-0.875023\pi\)
0.382617 + 0.923907i \(0.375023\pi\)
\(84\) 37.6614 18.5907i 0.448350 0.221318i
\(85\) 7.94959 115.122i 0.0935246 1.35437i
\(86\) 21.0192i 0.244409i
\(87\) −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 \(-0.754672\pi\)
0.696653 + 0.717408i \(0.254672\pi\)
\(98\) 21.8312 + 65.7678i 0.222768 + 0.671100i
\(99\) 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 \(0.227509\pi\)
\(102\) 97.4805 + 9.23076i 0.955691 + 0.0904976i
\(103\) −58.4473 58.4473i −0.567450 0.567450i 0.363963 0.931413i \(-0.381423\pi\)
−0.931413 + 0.363963i \(0.881423\pi\)
\(104\) 11.6263i 0.111791i
\(105\) −40.4829 + 96.8821i −0.385551 + 0.922686i
\(106\) 20.7109 0.195386
\(107\) 31.9911 31.9911i 0.298982 0.298982i −0.541633 0.840615i \(-0.682194\pi\)
0.840615 + 0.541633i \(0.182194\pi\)
\(108\) −15.0910 + 51.8484i −0.139732 + 0.480078i
\(109\) 0.710351i 0.00651698i 0.999995 + 0.00325849i \(0.00103721\pi\)
−0.999995 + 0.00325849i \(0.998963\pi\)
\(110\) 9.52700 137.965i 0.0866090 1.25423i
\(111\) 68.0609 + 82.2990i 0.613161 + 0.741432i
\(112\) 14.7056 + 23.8274i 0.131300 + 0.212745i
\(113\) 59.6020 + 59.6020i 0.527451 + 0.527451i 0.919812 0.392360i \(-0.128341\pi\)
−0.392360 + 0.919812i \(0.628341\pi\)
\(114\) 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
\(126\) −81.3058 36.4331i −0.645284 0.289152i
\(127\) −116.358 116.358i −0.916202 0.916202i 0.0805491 0.996751i \(-0.474333\pi\)
−0.996751 + 0.0805491i \(0.974333\pi\)
\(128\) 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 \(0.416446\pi\)
\(132\) 116.823 + 11.0624i 0.885025 + 0.0838059i
\(133\) 31.8410 + 51.5920i 0.239406 + 0.387909i
\(134\) 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 −0.847016 0.531568i \(-0.821603\pi\)
0.531568 + 0.847016i \(0.321603\pi\)
\(138\) −40.2568 3.81205i −0.291716 0.0276235i
\(139\) −16.4136 −0.118083 −0.0590417 0.998256i \(-0.518804\pi\)
−0.0590417 + 0.998256i \(0.518804\pi\)
\(140\) −66.8447 20.7796i −0.477462 0.148426i
\(141\) −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
\(147\) 77.9984 124.600i 0.530602 0.847621i
\(148\) −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 0.00339453 0.999994i \(-0.498919\pi\)
0.999994 0.00339453i \(-0.00108051\pi\)
\(158\) 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 −0.181022 0.983479i \(-0.557941\pi\)
0.983479 + 0.181022i \(0.0579405\pi\)
\(164\) 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 \(-0.297461\pi\)
−0.804304 + 0.594219i \(0.797461\pi\)
\(168\) 19.0707 56.2522i 0.113516 0.334834i
\(169\) 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 0.370032 0.929019i \(-0.379347\pi\)
0.929019 0.370032i \(-0.120653\pi\)
\(174\) −102.463 + 84.7367i −0.588869 + 0.486992i
\(175\) 160.141 70.5679i 0.915092 0.403245i
\(176\) 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 \(0.783124\pi\)
\(182\) 21.3714 + 34.6280i 0.117425 + 0.190264i
\(183\) 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
\(189\) 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 \(-0.0202996\pi\)
\(192\) 2.26252 23.8931i 0.0117840 0.124443i
\(193\) −119.177 + 119.177i −0.617497 + 0.617497i −0.944889 0.327392i \(-0.893830\pi\)
0.327392 + 0.944889i \(0.393830\pi\)
\(194\) 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 −0.765392 0.643565i \(-0.777455\pi\)
0.643565 + 0.765392i \(0.277455\pi\)
\(198\) −139.851 205.930i −0.706317 1.04005i
\(199\) 146.804 0.737706 0.368853 0.929488i \(-0.379751\pi\)
0.368853 + 0.929488i \(0.379751\pi\)
\(200\) 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
\(203\) −115.217 186.685i −0.567569 0.919632i
\(204\) 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
\(210\) 56.3992 + 137.365i 0.268568 + 0.654119i
\(211\) 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
\(217\) −235.003 + 145.037i −1.08296 + 0.668372i
\(218\) 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 \(-0.340426\pi\)
−0.876950 + 0.480581i \(0.840426\pi\)
\(224\) 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 \(-0.269798\pi\)
−0.749692 + 0.661787i \(0.769798\pi\)
\(228\) 4.89888 51.7342i 0.0214863 0.226904i
\(229\) 291.903 1.27468 0.637342 0.770581i \(-0.280034\pi\)
0.637342 + 0.770581i \(0.280034\pi\)
\(230\) 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 0.989726 + 0.142978i \(0.0456679\pi\)
0.142978 + 0.989726i \(0.454332\pi\)
\(234\) −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
\(238\) 119.993 + 194.425i 0.504174 + 0.816912i
\(239\) −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
\(245\) −237.289 + 60.9832i −0.968526 + 0.248911i
\(246\) −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 \(0.558128\pi\)
\(252\) −117.739 + 44.8726i −0.467218 + 0.178066i
\(253\) 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 \(-0.0412045\pi\)
−0.129086 + 0.991633i \(0.541204\pi\)
\(258\) −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 0.999834 0.0182309i \(-0.00580340\pi\)
−0.0182309 + 0.999834i \(0.505803\pi\)
\(264\) 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
\(273\) 27.7151 81.7503i 0.101521 0.299452i
\(274\) 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 0.871430 0.490520i \(-0.163193\pi\)
−0.490520 + 0.871430i \(0.663193\pi\)
\(278\) −16.4136 + 16.4136i −0.0590417 + 0.0590417i
\(279\) 66.6456 348.747i 0.238873 1.24999i
\(280\) −87.6242 + 46.0651i −0.312944 + 0.164518i
\(281\) 237.031i 0.843525i −0.906706 0.421762i \(-0.861412\pi\)
0.906706 0.421762i \(-0.138588\pi\)
\(282\) −174.546 16.5283i −0.618956 0.0586111i
\(283\) 286.765 + 286.765i 1.01330 + 1.01330i 0.999910 + 0.0133925i \(0.00426309\pi\)
0.0133925 + 0.999910i \(0.495737\pi\)
\(284\) −94.6051 −0.333117
\(285\) 75.7004 + 105.580i 0.265615 + 0.370456i
\(286\) 113.691i 0.397521i
\(287\) −216.667 351.066i −0.754939 1.22323i
\(288\) −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 0.233635 0.972324i \(-0.424938\pi\)
0.972324 0.233635i \(-0.0750619\pi\)
\(294\) −46.6019 202.599i −0.158510 0.689111i
\(295\) −160.480 + 139.748i −0.544001 + 0.473723i
\(296\) 100.688i 0.340163i
\(297\) −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 \(-0.537307\pi\)
0.993140 + 0.116935i \(0.0373069\pi\)
\(308\) 143.803 + 233.004i 0.466893 + 0.756507i
\(309\) 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 \(0.548077\pi\)
\(312\) 3.28808 34.7234i 0.0105387 0.111293i
\(313\) −65.0697 65.0697i −0.207890 0.207890i 0.595480 0.803370i \(-0.296962\pi\)
−0.803370 + 0.595480i \(0.796962\pi\)
\(314\) 315.064i 1.00339i
\(315\) 148.308 277.903i 0.470817 0.882231i
\(316\) 82.9336 0.262448
\(317\) −183.110 + 183.110i −0.577633 + 0.577633i −0.934251 0.356617i \(-0.883930\pi\)
0.356617 + 0.934251i \(0.383930\pi\)
\(318\) −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
\(322\) −49.5539 80.2921i −0.153894 0.249354i
\(323\) 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
\(336\) −37.1815 75.3229i −0.110659 0.224175i
\(337\) 201.311 + 201.311i 0.597362 + 0.597362i 0.939610 0.342248i \(-0.111188\pi\)
−0.342248 + 0.939610i \(0.611188\pi\)
\(338\) −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
\(343\) 341.671 30.1624i 0.996126 0.0879370i
\(344\) −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 0.0782023 0.996938i \(-0.475082\pi\)
0.996938 0.0782023i \(-0.0249180\pi\)
\(348\) −17.7266 + 187.200i −0.0509385 + 0.537931i
\(349\) −413.538 −1.18492 −0.592461 0.805599i \(-0.701843\pi\)
−0.592461 + 0.805599i \(0.701843\pi\)
\(350\) 89.5732 230.709i 0.255923 0.659169i
\(351\) 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 \(-0.754796\pi\)
0.696372 + 0.717681i \(0.254796\pi\)
\(354\) −115.074 139.147i −0.325069 0.393072i
\(355\) 178.364 155.321i 0.502433 0.437525i
\(356\) −9.60857 −0.0269904
\(357\) 155.611 459.002i 0.435886 1.28572i
\(358\) −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 \(-0.886898\pi\)
0.347890 + 0.937535i \(0.386898\pi\)
\(368\) −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 −0.788703 0.614775i \(-0.789247\pi\)
0.614775 + 0.788703i \(0.289247\pi\)
\(374\) 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
\(378\) 232.527 + 131.807i 0.615151 + 0.348696i
\(379\) 44.8235i 0.118268i −0.998250 0.0591339i \(-0.981166\pi\)
0.998250 0.0591339i \(-0.0188339\pi\)
\(380\) −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 −0.247315 + 0.968935i \(0.579548\pi\)
−0.968935 + 0.247315i \(0.920452\pi\)
\(384\) −21.6306 26.1556i −0.0563297 0.0681136i
\(385\) −653.662 203.200i −1.69782 0.527792i
\(386\) 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
\(392\) 131.536 43.6625i 0.335550 0.111384i
\(393\) −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 \(-0.874599\pi\)
0.383847 + 0.923397i \(0.374599\pi\)
\(398\) 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 \(-0.112767\pi\)
\(402\) −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 \(-0.299646\pi\)
0.588684 + 0.808364i \(0.299646\pi\)
\(410\) 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
\(413\) 253.523 156.467i 0.613856 0.378854i
\(414\) 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 \(0.995304\pi\)
\(420\) 193.764 + 80.9658i 0.461343 + 0.192776i
\(421\) 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
\(427\) 268.732 165.853i 0.629349 0.388416i
\(428\) −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 \(0.997154\pi\)
\(432\) 103.697 + 30.1821i 0.240039 + 0.0698659i
\(433\) −16.6929 16.6929i −0.0385516 0.0385516i 0.687568 0.726120i \(-0.258678\pi\)
−0.726120 + 0.687568i \(0.758678\pi\)
\(434\) −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 \(-0.804532\pi\)
−0.817303 + 0.576208i \(0.804532\pi\)
\(440\) −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 \(-0.166198\pi\)
−0.498725 + 0.866760i \(0.666198\pi\)
\(444\) 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
\(448\) 47.6548 29.4111i 0.106372 0.0656499i
\(449\) −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
\(455\) −127.343 + 66.9456i −0.279874 + 0.147133i
\(456\) −46.8353 56.6331i −0.102709 0.124195i
\(457\) 201.532 + 201.532i 0.440990 + 0.440990i 0.892345 0.451355i \(-0.149059\pi\)
−0.451355 + 0.892345i \(0.649059\pi\)
\(458\) 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 \(0.571583\pi\)
\(462\) 186.489 550.080i 0.403656 1.19065i
\(463\) −172.047 + 172.047i −0.371592 + 0.371592i −0.868057 0.496465i \(-0.834631\pi\)
0.496465 + 0.868057i \(0.334631\pi\)
\(464\) −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 \(-0.0824436\pi\)
−0.256118 + 0.966645i \(0.582444\pi\)
\(468\) −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
\(483\) −64.2632 + 189.555i −0.133050 + 0.392454i
\(484\) 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 0.356069 0.934460i \(-0.384117\pi\)
−0.934460 + 0.356069i \(0.884117\pi\)
\(488\) 90.2262 90.2262i 0.184890 0.184890i
\(489\) −427.646 + 353.662i −0.874532 + 0.723234i
\(490\) −176.306 + 298.272i −0.359808 + 0.608719i
\(491\) 896.974i 1.82683i 0.407029 + 0.913415i \(0.366565\pi\)
−0.407029 + 0.913415i \(0.633435\pi\)
\(492\) −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
\(497\) −281.774 + 173.903i −0.566951 + 0.349905i
\(498\) 25.4121 268.362i 0.0510283 0.538880i
\(499\) 0.286254i 0.000573655i −1.00000 0.000286827i \(-0.999909\pi\)
1.00000 0.000286827i \(-9.13000e-5\pi\)
\(500\) 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 \(-0.825570\pi\)
0.520970 + 0.853575i \(0.325570\pi\)
\(504\) −72.8662 + 162.612i −0.144576 + 0.322642i
\(505\) 500.952 + 575.269i 0.991983 + 1.13915i
\(506\) 263.616i 0.520981i
\(507\) −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
\(518\) 185.085 + 299.893i 0.357307 + 0.578944i
\(519\) −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 \(0.448410\pi\)
\(522\) 329.986 224.100i 0.632156 0.429310i
\(523\) −4.84540 4.84540i −0.00926463 0.00926463i 0.702459 0.711724i \(-0.252085\pi\)
−0.711724 + 0.702459i \(0.752085\pi\)
\(524\) 135.972i 0.259489i
\(525\) −498.241 + 165.471i −0.949031 + 0.315182i
\(526\) 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
\(532\) 103.184 63.6820i 0.193955 0.119703i
\(533\) −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
\(546\) −54.0352 109.465i −0.0989656 0.200486i
\(547\) 367.452 + 367.452i 0.671758 + 0.671758i 0.958121 0.286363i \(-0.0924464\pi\)
−0.286363 + 0.958121i \(0.592446\pi\)
\(548\) 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
\(553\) 247.012 152.448i 0.446676 0.275675i
\(554\) 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 −0.777922 0.628361i \(-0.783726\pi\)
0.628361 + 0.777922i \(0.283726\pi\)
\(558\) −282.101 415.392i −0.505557 0.744430i
\(559\) −61.0936 −0.109291
\(560\) −41.5592 + 133.689i −0.0742128 + 0.238731i
\(561\) 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 \(-0.728875\pi\)
0.752445 + 0.658656i \(0.228875\pi\)
\(564\) −191.074 + 158.017i −0.338784 + 0.280173i
\(565\) −29.0336 + 420.448i −0.0513868 + 0.744157i
\(566\) 573.529 1.01330
\(567\) −98.8878 558.310i −0.174405 0.984674i
\(568\) −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 0.193852 0.981031i \(-0.437902\pi\)
0.981031 0.193852i \(-0.0620983\pi\)
\(578\) 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 \(-0.199609\pi\)
−0.586792 + 0.809738i \(0.699609\pi\)
\(588\) −249.201 155.997i −0.423811 0.265301i
\(589\) 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 \(-0.763448\pi\)
0.676611 + 0.736341i \(0.263448\pi\)
\(594\) 359.444 + 654.589i 0.605125 + 1.10200i
\(595\) −714.989 + 375.878i −1.20166 + 0.631728i
\(596\) 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 \(0.872542\pi\)
\(602\) −125.208 + 77.2747i −0.207987 + 0.128363i
\(603\) 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 −0.0260927 + 0.999660i \(0.508306\pi\)
−0.999660 + 0.0260927i \(0.991694\pi\)
\(608\) 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
\(612\) −343.667 + 233.391i −0.561547 + 0.381357i
\(613\) 140.330 140.330i 0.228923 0.228923i −0.583319 0.812243i \(-0.698246\pi\)
0.812243 + 0.583319i \(0.198246\pi\)
\(614\) 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 −0.358647 0.933473i \(-0.616762\pi\)
0.933473 + 0.358647i \(0.116762\pi\)
\(618\) 349.122 + 33.0596i 0.564923 + 0.0534944i
\(619\) −802.714 −1.29679 −0.648396 0.761304i \(-0.724560\pi\)
−0.648396 + 0.761304i \(0.724560\pi\)
\(620\) −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
\(623\) −28.6184 + 17.6624i −0.0459365 + 0.0283506i
\(624\) −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
\(630\) −129.595 426.210i −0.205707 0.676524i
\(631\) −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
\(637\) 191.158 63.4539i 0.300091 0.0996136i
\(638\) −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 \(-0.139210\pi\)
\(642\) −18.0951 + 191.092i −0.0281855 + 0.297651i
\(643\) 487.269 + 487.269i 0.757806 + 0.757806i 0.975923 0.218117i \(-0.0699913\pi\)
−0.218117 + 0.975923i \(0.569991\pi\)
\(644\) −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 \(-0.0938052\pi\)
−0.290451 + 0.956890i \(0.593805\pi\)
\(648\) −90.8496 210.320i −0.140200 0.324567i
\(649\) 832.370 1.28254
\(650\) 19.9757 143.949i 0.0307318 0.221460i
\(651\) 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 −0.997385 0.0722752i \(-0.976974\pi\)
−0.0722752 0.997385i \(-0.523026\pi\)
\(654\) −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
\(658\) −214.856 348.132i −0.326530 0.529075i
\(659\) 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
\(665\) −89.9853 + 289.469i −0.135316 + 0.435291i
\(666\) −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
\(672\) −112.504 38.1414i −0.167417 0.0567580i
\(673\) 369.528 369.528i 0.549076 0.549076i −0.377098 0.926174i \(-0.623078\pi\)
0.926174 + 0.377098i \(0.123078\pi\)
\(674\) 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 \(-0.170030\pi\)
−0.509123 + 0.860694i \(0.670030\pi\)
\(678\) −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 0.936245 0.351349i \(-0.114277\pi\)
−0.351349 + 0.936245i \(0.614277\pi\)
\(684\) −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
\(693\) −1151.35 + 438.802i −1.66140 + 0.633191i
\(694\) 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
\(700\) −141.136 320.282i −0.201623 0.457546i
\(701\) 256.614i 0.366069i 0.983106 + 0.183035i \(0.0585920\pi\)
−0.983106 + 0.183035i \(0.941408\pi\)
\(702\) 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
\(707\) −560.882 908.796i −0.793326 1.28543i
\(708\) −254.222 24.0731i −0.359070 0.0340016i
\(709\) 271.653i 0.383149i 0.981478 + 0.191575i \(0.0613594\pi\)
−0.981478 + 0.191575i \(0.938641\pi\)
\(710\) 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
\(717\) 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 \(-0.698662\pi\)
0.811480 + 0.584380i \(0.198662\pi\)
\(728\) 69.2560 42.7427i 0.0951318 0.0587125i
\(729\) 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 −0.948184 0.317721i \(-0.897082\pi\)
−0.317721 0.948184i \(-0.602918\pi\)
\(734\) 432.800i 0.589646i
\(735\) 725.944 115.026i 0.987678 0.156498i
\(736\) −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 \(0.225107\pi\)
−0.760188 + 0.649703i \(0.774893\pi\)
\(740\) −355.141 24.5238i −0.479921 0.0331403i
\(741\) −68.0649 82.3039i −0.0918555 0.111071i
\(742\) −76.1414 123.372i −0.102616 0.166269i
\(743\) −197.378 197.378i −0.265650 0.265650i 0.561695 0.827345i \(-0.310150\pi\)
−0.827345 + 0.561695i \(0.810150\pi\)
\(744\) 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
\(756\) 364.334 100.720i 0.481924 0.133228i
\(757\) 230.964 + 230.964i 0.305105 + 0.305105i 0.843007 0.537902i \(-0.180783\pi\)
−0.537902 + 0.843007i \(0.680783\pi\)
\(758\) −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 \(0.492708\pi\)
\(762\) 695.036 + 65.8153i 0.912121 + 0.0863718i
\(763\) 4.23146 2.61153i 0.00554582 0.00342271i
\(764\) −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