Properties

Label 210.3.k.b.83.2
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 83.2
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.2

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −2.98664 + 0.282815i −0.995547 + 0.0942716i
\(4\) 2.00000i 0.500000i
\(5\) 3.28357 3.77070i 0.656714 0.754139i
\(6\) −3.26945 2.70382i −0.544909 0.450637i
\(7\) −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 \(0.348588\pi\)
−0.457939 + 0.888984i \(0.651412\pi\)
\(12\) −0.565630 5.97328i −0.0471358 0.497773i
\(13\) −2.90656 + 2.90656i −0.223582 + 0.223582i −0.810005 0.586423i \(-0.800536\pi\)
0.586423 + 0.810005i \(0.300536\pi\)
\(14\) −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 −0.999229 0.0392622i \(-0.987499\pi\)
0.0392622 + 0.999229i \(0.487499\pi\)
\(18\) 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 −0.545252 0.838272i \(-0.683566\pi\)
0.838272 + 0.545252i \(0.183566\pi\)
\(24\) 5.40765 6.53891i 0.225319 0.272455i
\(25\) −3.43630 24.7627i −0.137452 0.990508i
\(26\) −5.81313 −0.223582
\(27\) −25.9242 + 7.54552i −0.960156 + 0.279464i
\(28\) −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 \(0.219537\pi\)
−0.771439 + 0.636304i \(0.780463\pi\)
\(32\) −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 −0.960074 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 \(0.244730\pi\)
\(42\) 28.1261 9.53535i 0.669669 0.227032i
\(43\) 10.5096 + 10.5096i 0.244409 + 0.244409i 0.818671 0.574262i \(-0.194711\pi\)
−0.574262 + 0.818671i \(0.694711\pi\)
\(44\) −39.1153 −0.888984
\(45\) 22.6569 38.8801i 0.503487 0.864003i
\(46\) 13.4789 0.293021
\(47\) 29.2211 29.2211i 0.621725 0.621725i −0.324247 0.945972i \(-0.605111\pi\)
0.945972 + 0.324247i \(0.105111\pi\)
\(48\) 11.9466 1.13126i 0.248887 0.0235679i
\(49\) −21.9683 43.7995i −0.448332 0.893867i
\(50\) 21.3264 28.1990i 0.426528 0.563980i
\(51\) 44.1249 53.3556i 0.865194 1.04619i
\(52\) −5.81313 5.81313i −0.111791 0.111791i
\(53\) 10.3554 10.3554i 0.195386 0.195386i −0.602633 0.798019i \(-0.705882\pi\)
0.798019 + 0.602633i \(0.205882\pi\)
\(54\) −33.4697 18.3787i −0.619810 0.340346i
\(55\) 73.7459 + 64.2189i 1.34084 + 1.16762i
\(56\) −4.56092 19.2665i −0.0814451 0.344045i
\(57\) 25.8671 2.44944i 0.453809 0.0429727i
\(58\) 31.3396 + 31.3396i 0.540337 + 0.540337i
\(59\) 42.5598i 0.721353i −0.932691 0.360676i \(-0.882546\pi\)
0.932691 0.360676i \(-0.117454\pi\)
\(60\) −24.3807 17.4809i −0.406345 0.291348i
\(61\) 45.1131i 0.739559i −0.929120 0.369779i \(-0.879433\pi\)
0.929120 0.369779i \(-0.120567\pi\)
\(62\) −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 0.431611 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
\(70\) −23.0325 + 43.8121i −0.329036 + 0.625887i
\(71\) 47.3026i 0.666233i 0.942886 + 0.333117i \(0.108100\pi\)
−0.942886 + 0.333117i \(0.891900\pi\)
\(72\) −14.3014 + 21.0587i −0.198631 + 0.292482i
\(73\) −89.3562 + 89.3562i −1.22406 + 1.22406i −0.257880 + 0.966177i \(0.583024\pi\)
−0.966177 + 0.257880i \(0.916976\pi\)
\(74\) −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 \(-0.915470\pi\)
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
\(87\) −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 \(0.00859234\pi\)
−0.999636 + 0.0269904i \(0.991408\pi\)
\(90\) 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 0.696653 0.717408i \(-0.254672\pi\)
−0.717408 + 0.696653i \(0.754672\pi\)
\(98\) 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 −0.931413 0.363963i \(-0.881423\pi\)
0.363963 + 0.931413i \(0.381423\pi\)
\(104\) 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 0.840615 0.541633i \(-0.182194\pi\)
−0.541633 + 0.840615i \(0.682194\pi\)
\(108\) −15.0910 51.8484i −0.139732 0.480078i
\(109\) 0.710351i 0.00651698i −0.999995 0.00325849i \(-0.998963\pi\)
0.999995 0.00325849i \(-0.00103721\pi\)
\(110\) 9.52700 + 137.965i 0.0866090 + 1.25423i
\(111\) 68.0609 82.2990i 0.613161 0.741432i
\(112\) 14.7056 23.8274i 0.131300 0.212745i
\(113\) 59.6020 59.6020i 0.527451 0.527451i −0.392360 0.919812i \(-0.628341\pi\)
0.919812 + 0.392360i \(0.128341\pi\)
\(114\) 28.3165 + 23.4177i 0.248391 + 0.205418i
\(115\) −3.28296 47.5421i −0.0285475 0.413409i
\(116\) 62.6791i 0.540337i
\(117\) −20.7840 + 30.6043i −0.177641 + 0.261575i
\(118\) 42.5598 42.5598i 0.360676 0.360676i
\(119\) −37.2159 157.209i −0.312738 1.32109i
\(120\) −6.89983 41.8616i −0.0574986 0.348847i
\(121\) −261.501 −2.16117
\(122\) 45.1131 45.1131i 0.369779 0.369779i
\(123\) −176.017 + 16.6676i −1.43103 + 0.135509i
\(124\) −78.9016 −0.636304
\(125\) −104.656 68.3529i −0.837248 0.546823i
\(126\) −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 \(0.416446\pi\)
\(132\) 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 0.531568 0.847016i \(-0.321603\pi\)
−0.847016 + 0.531568i \(0.821603\pi\)
\(138\) −40.2568 + 3.81205i −0.291716 + 0.0276235i
\(139\) −16.4136 −0.118083 −0.0590417 0.998256i \(-0.518804\pi\)
−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 0.999994 + 0.00339453i \(0.00108051\pi\)
0.00339453 + 0.999994i \(0.498919\pi\)
\(158\) 41.4668 41.4668i 0.262448 0.262448i
\(159\) −27.9993 + 33.8567i −0.176096 + 0.212935i
\(160\) −28.2171 + 1.94850i −0.176357 + 0.0121781i
\(161\) 15.3691 + 64.9230i 0.0954604 + 0.403249i
\(162\) 105.160 + 45.4248i 0.649135 + 0.280400i
\(163\) 130.800 + 130.800i 0.802457 + 0.802457i 0.983479 0.181022i \(-0.0579405\pi\)
−0.181022 + 0.983479i \(0.557941\pi\)
\(164\) 117.870i 0.718717i
\(165\) −238.415 170.942i −1.44494 1.03601i
\(166\) 89.8542i 0.541290i
\(167\) −35.0842 + 35.0842i −0.210085 + 0.210085i −0.804304 0.594219i \(-0.797461\pi\)
0.594219 + 0.804304i \(0.297461\pi\)
\(168\) 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 0.929019 + 0.370032i \(0.120653\pi\)
0.370032 + 0.929019i \(0.379347\pi\)
\(174\) −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 \(-0.783124\pi\)
0.776731 0.629832i \(-0.216876\pi\)
\(182\) 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 \(0.0202996\pi\)
−0.997967 + 0.0637298i \(0.979700\pi\)
\(192\) 2.26252 + 23.8931i 0.0117840 + 0.124443i
\(193\) −119.177 119.177i −0.617497 0.617497i 0.327392 0.944889i \(-0.393830\pi\)
−0.944889 + 0.327392i \(0.893830\pi\)
\(194\) 4.02649i 0.0207551i
\(195\) −10.0274 60.8367i −0.0514226 0.311983i
\(196\) 87.5990 43.9365i 0.446934 0.224166i
\(197\) −24.0000 24.0000i −0.121827 0.121827i 0.643565 0.765392i \(-0.277455\pi\)
−0.765392 + 0.643565i \(0.777455\pi\)
\(198\) −139.851 + 205.930i −0.706317 + 1.04005i
\(199\) 146.804 0.737706 0.368853 0.929488i \(-0.379751\pi\)
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 −0.876950 0.480581i \(-0.840426\pi\)
0.480581 + 0.876950i \(0.340426\pi\)
\(224\) 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 −0.749692 0.661787i \(-0.769798\pi\)
0.661787 + 0.749692i \(0.269798\pi\)
\(228\) 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 0.142978 0.989726i \(-0.454332\pi\)
0.989726 0.142978i \(-0.0456679\pi\)
\(234\) −51.3883 + 9.82031i −0.219608 + 0.0419671i
\(235\) −14.2343 206.133i −0.0605714 0.877163i
\(236\) 85.1196 0.360676
\(237\) 11.7274 + 123.846i 0.0494828 + 0.522558i
\(238\) 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 \(0.223340\pi\)
−0.763783 + 0.645474i \(0.776660\pi\)
\(242\) −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 −0.129086 0.991633i \(-0.541204\pi\)
0.991633 + 0.129086i \(0.0412045\pi\)
\(258\) −5.94453 62.7767i −0.0230408 0.243320i
\(259\) −57.4040 242.489i −0.221637 0.936251i
\(260\) −41.0074 + 2.83171i −0.157721 + 0.0108912i
\(261\) 277.043 52.9429i 1.06147 0.202846i
\(262\) 67.9862 + 67.9862i 0.259489 + 0.259489i
\(263\) 258.162 258.162i 0.981603 0.981603i −0.0182309 0.999834i \(-0.505803\pi\)
0.999834 + 0.0182309i \(0.00580340\pi\)
\(264\) 127.886 + 105.761i 0.484415 + 0.400609i
\(265\) −5.04439 73.0501i −0.0190354 0.275661i
\(266\) 83.4330 19.7509i 0.313658 0.0742517i
\(267\) −1.35872 14.3487i −0.00508885 0.0537403i
\(268\) 178.712 + 178.712i 0.666835 + 0.666835i
\(269\) 138.071i 0.513275i 0.966508 + 0.256637i \(0.0826146\pi\)
−0.966508 + 0.256637i \(0.917385\pi\)
\(270\) −179.201 + 65.8564i −0.663707 + 0.243913i
\(271\) 95.9122i 0.353920i 0.984218 + 0.176960i \(0.0566263\pi\)
−0.984218 + 0.176960i \(0.943374\pi\)
\(272\) 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 −0.490520 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
\(280\) −87.6242 46.0651i −0.312944 0.164518i
\(281\) 237.031i 0.843525i 0.906706 + 0.421762i \(0.138588\pi\)
−0.906706 + 0.421762i \(0.861412\pi\)
\(282\) −174.546 + 16.5283i −0.618956 + 0.0586111i
\(283\) 286.765 286.765i 1.01330 1.01330i 0.0133925 0.999910i \(-0.495737\pi\)
0.999910 0.0133925i \(-0.00426309\pi\)
\(284\) −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 0.972324 + 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
\(297\) −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 0.993140 0.116935i \(-0.0373069\pi\)
−0.116935 + 0.993140i \(0.537307\pi\)
\(308\) 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 −0.803370 0.595480i \(-0.796962\pi\)
0.595480 + 0.803370i \(0.296962\pi\)
\(314\) 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 0.356617 0.934251i \(-0.383930\pi\)
−0.934251 + 0.356617i \(0.883930\pi\)
\(318\) −61.8560 + 5.85735i −0.194516 + 0.0184193i
\(319\) 612.928i 1.92140i
\(320\) −30.1656 26.2686i −0.0942674 0.0820893i
\(321\) −104.593 86.4983i −0.325836 0.269465i
\(322\) −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 −0.342248 0.939610i \(-0.611188\pi\)
0.939610 + 0.342248i \(0.111188\pi\)
\(338\) −152.104 + 152.104i −0.450011 + 0.450011i
\(339\) −161.153 + 194.866i −0.475379 + 0.574826i
\(340\) −230.243 + 15.8992i −0.677186 + 0.0467623i
\(341\) −771.565 −2.26265
\(342\) −91.1942 61.9318i −0.266650 0.181087i
\(343\) 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 0.996938 + 0.0782023i \(0.0249180\pi\)
0.0782023 + 0.996938i \(0.475082\pi\)
\(348\) −17.7266 187.200i −0.0509385 0.537931i
\(349\) −413.538 −1.18492 −0.592461 0.805599i \(-0.701843\pi\)
−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 0.696372 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
\(357\) 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 0.347890 0.937535i \(-0.386898\pi\)
−0.937535 + 0.347890i \(0.886898\pi\)
\(368\) −26.9579 + 26.9579i −0.0732551 + 0.0732551i
\(369\) 520.985 99.5604i 1.41188 0.269811i
\(370\) −165.309 + 189.833i −0.446780 + 0.513061i
\(371\) 23.6152 + 99.7566i 0.0636529 + 0.268886i
\(372\) 235.651 22.3146i 0.633470 0.0599854i
\(373\) −64.8753 64.8753i −0.173928 0.173928i 0.614775 0.788703i \(-0.289247\pi\)
−0.788703 + 0.614775i \(0.789247\pi\)
\(374\) 638.339i 1.70679i
\(375\) 331.901 + 174.547i 0.885069 + 0.465459i
\(376\) 116.884i 0.310863i
\(377\) −91.0905 + 91.0905i −0.241619 + 0.241619i
\(378\) 232.527 131.807i 0.615151 0.348696i
\(379\) 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
\(385\) −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 0.383847 0.923397i \(-0.374599\pi\)
−0.923397 + 0.383847i \(0.874599\pi\)
\(398\) 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 \(0.112767\pi\)
−0.937901 + 0.346903i \(0.887233\pi\)
\(402\) −533.748 + 50.5424i −1.32773 + 0.125727i
\(403\) −114.666 114.666i −0.284532 0.284532i
\(404\) 305.126i 0.755262i
\(405\) 134.606 381.977i 0.332362 0.943152i
\(406\) −301.902 + 71.4687i −0.743600 + 0.176031i
\(407\) −492.307 492.307i −1.20960 1.20960i
\(408\) 18.4615 + 194.961i 0.0452488 + 0.477846i
\(409\) 481.543 1.17737 0.588684 0.808364i \(-0.299646\pi\)
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 \(-0.995304\pi\)
0.999891 0.0147510i \(-0.00469556\pi\)
\(420\) 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 \(-0.997154\pi\)
0.999960 0.00893932i \(-0.00284551\pi\)
\(432\) 103.697 30.1821i 0.240039 0.0698659i
\(433\) −16.6929 + 16.6929i −0.0385516 + 0.0385516i −0.726120 0.687568i \(-0.758678\pi\)
0.687568 + 0.726120i \(0.258678\pi\)
\(434\) −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 −0.498725 0.866760i \(-0.666198\pi\)
0.866760 + 0.498725i \(0.166198\pi\)
\(444\) 164.598 + 136.122i 0.370716 + 0.306581i
\(445\) 18.1155 + 15.7752i 0.0407090 + 0.0354499i
\(446\) −176.781 −0.396369
\(447\) −190.610 + 18.0495i −0.426422 + 0.0403793i
\(448\) 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 −0.451355 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 \(0.571583\pi\)
\(462\) 186.489 + 550.080i 0.403656 + 1.19065i
\(463\) −172.047 172.047i −0.371592 0.371592i 0.496465 0.868057i \(-0.334631\pi\)
−0.868057 + 0.496465i \(0.834631\pi\)
\(464\) −125.358 −0.270169
\(465\) −480.920 344.817i −1.03424 0.741543i
\(466\) 527.840 1.13270
\(467\) 331.816 331.816i 0.710527 0.710527i −0.256118 0.966645i \(-0.582444\pi\)
0.966645 + 0.256118i \(0.0824436\pi\)
\(468\) −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 \(0.155596\pi\)
−0.882888 + 0.469584i \(0.844404\pi\)
\(480\) 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 −0.934460 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
\(490\) −176.306 298.272i −0.359808 0.608719i
\(491\) 896.974i 1.82683i −0.407029 0.913415i \(-0.633435\pi\)
0.407029 0.913415i \(-0.366565\pi\)
\(492\) −33.3353 352.034i −0.0677546 0.715516i
\(493\) −511.444 + 511.444i −1.03741 + 1.03741i
\(494\) 50.3472 0.101917
\(495\) 760.403 + 443.116i 1.53617 + 0.895184i
\(496\) 157.803i 0.318152i
\(497\) −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 \(9.13000e-5\pi\)
−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
\(507\) −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 \(0.156385\pi\)
−0.881721 + 0.471771i \(0.843615\pi\)
\(510\) 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 −0.711724 0.702459i \(-0.752085\pi\)
0.702459 + 0.711724i \(0.252085\pi\)
\(524\) 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 −0.286363 0.958121i \(-0.592446\pi\)
0.958121 + 0.286363i \(0.0924464\pi\)
\(548\) 86.4327 86.4327i 0.157724 0.157724i
\(549\) −76.2110 398.801i −0.138818 0.726414i
\(550\) 551.506 + 417.094i 1.00274 + 0.758353i
\(551\) −271.430 −0.492613
\(552\) −7.62409 80.5135i −0.0138118 0.145858i
\(553\) 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 0.628361 0.777922i \(-0.283726\pi\)
−0.777922 + 0.628361i \(0.783726\pi\)
\(558\) −282.101 + 415.392i −0.505557 + 0.744430i
\(559\) −61.0936 −0.109291
\(560\) −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 0.752445 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
\(567\) −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 0.981031 + 0.193852i \(0.0620983\pi\)
0.193852 + 0.981031i \(0.437902\pi\)
\(578\) 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 −0.586792 0.809738i \(-0.699609\pi\)
0.809738 + 0.586792i \(0.199609\pi\)
\(588\) −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 0.676611 0.736341i \(-0.263448\pi\)
−0.736341 + 0.676611i \(0.763448\pi\)
\(594\) 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 \(-0.872542\pi\)
0.920897 0.389807i \(-0.127458\pi\)
\(602\) −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 −0.999660 0.0260927i \(-0.991694\pi\)
−0.0260927 0.999660i \(-0.508306\pi\)
\(608\) 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 0.812243 0.583319i \(-0.198246\pi\)
−0.583319 + 0.812243i \(0.698246\pi\)
\(614\) 537.990i 0.876204i
\(615\) −515.116 + 718.436i −0.837587 + 1.16819i
\(616\) 376.807 89.2009i 0.611700 0.144807i
\(617\) 354.668 + 354.668i 0.574826 + 0.574826i 0.933473 0.358647i \(-0.116762\pi\)
−0.358647 + 0.933473i \(0.616762\pi\)
\(618\) 349.122 33.0596i 0.564923 0.0534944i
\(619\) −802.714 −1.29679 −0.648396 0.761304i \(-0.724560\pi\)
−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 \(0.139210\pi\)
−0.905881 + 0.423533i \(0.860790\pi\)
\(642\) −18.0951 191.092i −0.0281855 0.297651i
\(643\) 487.269 487.269i 0.757806 0.757806i −0.218117 0.975923i \(-0.569991\pi\)
0.975923 + 0.218117i \(0.0699913\pi\)
\(644\) −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 −0.290451 0.956890i \(-0.593805\pi\)
0.956890 + 0.290451i \(0.0938052\pi\)
\(648\) −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 −0.0722752 + 0.997385i \(0.523026\pi\)
−0.997385 + 0.0722752i \(0.976974\pi\)
\(654\) −1.92067 + 2.32246i −0.00293680 + 0.00355116i
\(655\) 223.238 256.355i 0.340821 0.391382i
\(656\) −235.739 −0.359358
\(657\) −638.959 + 940.864i −0.972541 + 1.43206i
\(658\) −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 \(-0.793940\pi\)
0.797681 0.603079i \(-0.206060\pi\)
\(662\) −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 0.926174 0.377098i \(-0.123078\pi\)
−0.377098 + 0.926174i \(0.623078\pi\)
\(674\) 402.622 0.597362
\(675\) 275.931 + 616.025i 0.408787 + 0.912630i
\(676\) −304.208 −0.450011
\(677\) 238.013 238.013i 0.351570 0.351570i −0.509123 0.860694i \(-0.670030\pi\)
0.860694 + 0.509123i \(0.170030\pi\)
\(678\) −356.019 + 33.7127i −0.525102 + 0.0497237i
\(679\) 19.3941 4.59113i 0.0285627 0.00676161i
\(680\) −246.143 214.344i −0.361974 0.315212i
\(681\) 53.9536 65.2405i 0.0792270 0.0958010i
\(682\) −771.565 771.565i −1.13133 1.13133i
\(683\) 399.484 399.484i 0.584896 0.584896i −0.351349 0.936245i \(-0.614277\pi\)
0.936245 + 0.351349i \(0.114277\pi\)
\(684\) −29.2624 153.126i −0.0427813 0.223868i
\(685\) −304.860 + 21.0517i −0.445051 + 0.0307324i
\(686\) 311.509 + 371.834i 0.454095 + 0.542032i
\(687\) −871.808 + 82.5544i −1.26901 + 0.120167i
\(688\) −42.0383 42.0383i −0.0611022 0.0611022i
\(689\) 60.1976i 0.0873695i
\(690\) −117.812 + 164.313i −0.170742 + 0.238135i
\(691\) 964.818i 1.39626i −0.715969 0.698132i \(-0.754015\pi\)
0.715969 0.698132i \(-0.245985\pi\)
\(692\) −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 \(-0.941408\pi\)
0.983106 0.183035i \(-0.0585920\pi\)
\(702\) 150.701 43.8631i 0.214674 0.0624830i
\(703\) 218.014 218.014i 0.310119 0.310119i
\(704\) 156.461 0.222246
\(705\) 100.810 + 611.620i 0.142993 + 0.867547i
\(706\) 15.0443i 0.0213092i
\(707\) −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 \(-0.938641\pi\)
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
\(717\) 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 \(-0.850974\pi\)
0.892391 0.451262i \(-0.149026\pi\)
\(720\) −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 0.811480 0.584380i \(-0.198662\pi\)
−0.584380 + 0.811480i \(0.698662\pi\)
\(728\) 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 −0.317721 + 0.948184i \(0.602918\pi\)
−0.948184 + 0.317721i \(0.897082\pi\)
\(734\) 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 \(-0.774893\pi\)
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
\(742\) −76.1414 + 123.372i −0.102616 + 0.166269i
\(743\) −197.378 + 197.378i −0.265650 + 0.265650i −0.827345 0.561695i \(-0.810150\pi\)
0.561695 + 0.827345i \(0.310150\pi\)
\(744\) 257.965 + 213.336i 0.346728 + 0.286742i
\(745\) 209.561 240.650i 0.281290 0.323020i
\(746\) 129.751i 0.173928i
\(747\) −473.054 321.260i −0.633271 0.430067i
\(748\) 638.339 638.339i 0.853395 0.853395i
\(749\) −308.178 + 72.9545i −0.411453 + 0.0974026i
\(750\) 157.354 + 506.448i 0.209805 + 0.675264i
\(751\) 1038.60 1.38295 0.691477 0.722398i \(-0.256960\pi\)
0.691477 + 0.722398i \(0.256960\pi\)
\(752\) −116.884 + 116.884i −0.155431 + 0.155431i
\(753\) 272.271 25.7823i 0.361582 0.0342394i
\(754\) −182.181 −0.241619
\(755\) 329.095 377.916i 0.435887 0.500552i
\(756\) 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 \(0.492708\pi\)
\(762\) 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