Properties

Label 210.3.k.a.83.7
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 83.7
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-0.282815 + 2.98664i) q^{3} +2.00000i q^{4} +(-3.28357 + 3.77070i) q^{5} +(3.26945 - 2.70382i) q^{6} +(-3.67639 + 5.95686i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-8.84003 - 1.68933i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-0.282815 + 2.98664i) 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} +(-5.97328 - 0.565630i) q^{12} +(-2.90656 + 2.90656i) q^{13} +(9.63325 - 2.28046i) q^{14} +(-10.3331 - 10.8733i) q^{15} -4.00000 q^{16} +(16.3194 - 16.3194i) q^{17} +(7.15070 + 10.5294i) q^{18} -8.66094 q^{19} +(-7.54139 - 6.56714i) q^{20} +(-16.7512 - 12.6647i) q^{21} +(-19.5576 + 19.5576i) q^{22} +(-6.73947 + 6.73947i) q^{23} +(5.40765 + 6.53891i) q^{24} +(-3.43630 - 24.7627i) q^{25} +5.81313 q^{26} +(7.54552 - 25.9242i) q^{27} +(-11.9137 - 7.35279i) q^{28} -31.3396 q^{29} +(-0.540189 + 21.2063i) q^{30} +39.4508i q^{31} +(4.00000 + 4.00000i) q^{32} +(58.4116 + 5.53119i) q^{33} -32.6389 q^{34} +(-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} +(4.08649 + 29.4160i) q^{42} +(10.5096 + 10.5096i) q^{43} +39.1153 q^{44} +(35.3968 - 27.7860i) q^{45} +13.4789 q^{46} +(-29.2211 + 29.2211i) q^{47} +(1.13126 - 11.9466i) q^{48} +(-21.9683 - 43.7995i) q^{49} +(-21.3264 + 28.1990i) q^{50} +(44.1249 + 53.3556i) q^{51} +(-5.81313 - 5.81313i) q^{52} +(-10.3554 + 10.3554i) q^{53} +(-33.4697 + 18.3787i) q^{54} +(73.7459 + 64.2189i) q^{55} +(4.56092 + 19.2665i) q^{56} +(2.44944 - 25.8671i) q^{57} +(31.3396 + 31.3396i) q^{58} +42.5598i q^{59} +(21.7465 - 20.6661i) q^{60} -45.1131i q^{61} +(39.4508 - 39.4508i) q^{62} +(42.5625 - 46.4481i) 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} +(-21.0587 + 14.3014i) q^{72} +(-89.3562 + 89.3562i) q^{73} +50.3442 q^{74} +(74.9291 - 3.25974i) q^{75} -17.3219i q^{76} +(116.502 + 71.9016i) q^{77} +(-1.64404 + 17.3617i) q^{78} -41.4668i q^{79} +(13.1343 - 15.0828i) q^{80} +(75.2923 + 29.8675i) q^{81} +(58.9348 + 58.9348i) q^{82} +(44.9271 + 44.9271i) q^{83} +(25.3295 - 33.5025i) q^{84} +(7.94959 + 115.122i) q^{85} -21.0192i q^{86} +(8.86329 - 93.6000i) q^{87} +(-39.1153 - 39.1153i) q^{88} -4.80429i q^{89} +(-63.1829 - 7.61081i) q^{90} +(-6.62831 - 27.9997i) q^{91} +(-13.4789 - 13.4789i) q^{92} +(-117.825 - 11.1573i) q^{93} +58.4422 q^{94} +(28.4388 - 32.6578i) q^{95} +(-13.0778 + 10.8153i) q^{96} +(-2.01325 - 2.01325i) q^{97} +(-21.8312 + 65.7678i) q^{98} +(-33.0394 + 172.890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −0.282815 + 2.98664i −0.0942716 + 0.995547i
\(4\) 2.00000i 0.500000i
\(5\) −3.28357 + 3.77070i −0.656714 + 0.754139i
\(6\) 3.26945 2.70382i 0.544909 0.450637i
\(7\) −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 \(-0.348588\pi\)
\(12\) −5.97328 0.565630i −0.497773 0.0471358i
\(13\) −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
\(15\) −10.3331 10.8733i −0.688871 0.724884i
\(16\) −4.00000 −0.250000
\(17\) 16.3194 16.3194i 0.959967 0.959967i −0.0392622 0.999229i \(-0.512501\pi\)
0.999229 + 0.0392622i \(0.0125008\pi\)
\(18\) 7.15070 + 10.5294i 0.397261 + 0.584965i
\(19\) −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
\(21\) −16.7512 12.6647i −0.797678 0.603083i
\(22\) −19.5576 + 19.5576i −0.888984 + 0.888984i
\(23\) −6.73947 + 6.73947i −0.293021 + 0.293021i −0.838272 0.545252i \(-0.816434\pi\)
0.545252 + 0.838272i \(0.316434\pi\)
\(24\) 5.40765 + 6.53891i 0.225319 + 0.272455i
\(25\) −3.43630 24.7627i −0.137452 0.990508i
\(26\) 5.81313 0.223582
\(27\) 7.54552 25.9242i 0.279464 0.960156i
\(28\) −11.9137 7.35279i −0.425490 0.262600i
\(29\) −31.3396 −1.08067 −0.540337 0.841449i \(-0.681703\pi\)
−0.540337 + 0.841449i \(0.681703\pi\)
\(30\) −0.540189 + 21.2063i −0.0180063 + 0.706877i
\(31\) 39.4508i 1.27261i 0.771439 + 0.636304i \(0.219537\pi\)
−0.771439 + 0.636304i \(0.780463\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 58.4116 + 5.53119i 1.77005 + 0.167612i
\(34\) −32.6389 −0.959967
\(35\) −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 \(-0.755270\pi\)
−0.718717 + 0.695303i \(0.755270\pi\)
\(42\) 4.08649 + 29.4160i 0.0972974 + 0.700381i
\(43\) 10.5096 + 10.5096i 0.244409 + 0.244409i 0.818671 0.574262i \(-0.194711\pi\)
−0.574262 + 0.818671i \(0.694711\pi\)
\(44\) 39.1153 0.888984
\(45\) 35.3968 27.7860i 0.786597 0.617467i
\(46\) 13.4789 0.293021
\(47\) −29.2211 + 29.2211i −0.621725 + 0.621725i −0.945972 0.324247i \(-0.894889\pi\)
0.324247 + 0.945972i \(0.394889\pi\)
\(48\) 1.13126 11.9466i 0.0235679 0.248887i
\(49\) −21.9683 43.7995i −0.448332 0.893867i
\(50\) −21.3264 + 28.1990i −0.426528 + 0.563980i
\(51\) 44.1249 + 53.3556i 0.865194 + 1.04619i
\(52\) −5.81313 5.81313i −0.111791 0.111791i
\(53\) −10.3554 + 10.3554i −0.195386 + 0.195386i −0.798019 0.602633i \(-0.794118\pi\)
0.602633 + 0.798019i \(0.294118\pi\)
\(54\) −33.4697 + 18.3787i −0.619810 + 0.340346i
\(55\) 73.7459 + 64.2189i 1.34084 + 1.16762i
\(56\) 4.56092 + 19.2665i 0.0814451 + 0.344045i
\(57\) 2.44944 25.8671i 0.0429727 0.453809i
\(58\) 31.3396 + 31.3396i 0.540337 + 0.540337i
\(59\) 42.5598i 0.721353i 0.932691 + 0.360676i \(0.117454\pi\)
−0.932691 + 0.360676i \(0.882546\pi\)
\(60\) 21.7465 20.6661i 0.362442 0.344436i
\(61\) 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
\(63\) 42.5625 46.4481i 0.675596 0.737272i
\(64\) 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 \(-0.891900\pi\)
0.942886 0.333117i \(-0.108100\pi\)
\(72\) −21.0587 + 14.3014i −0.292482 + 0.198631i
\(73\) −89.3562 + 89.3562i −1.22406 + 1.22406i −0.257880 + 0.966177i \(0.583024\pi\)
−0.966177 + 0.257880i \(0.916976\pi\)
\(74\) 50.3442 0.680326
\(75\) 74.9291 3.25974i 0.999055 0.0434631i
\(76\) 17.3219i 0.227919i
\(77\) 116.502 + 71.9016i 1.51301 + 0.933787i
\(78\) −1.64404 + 17.3617i −0.0210774 + 0.222586i
\(79\) 41.4668i 0.524896i −0.964946 0.262448i \(-0.915470\pi\)
0.964946 0.262448i \(-0.0845298\pi\)
\(80\) 13.1343 15.0828i 0.164179 0.188535i
\(81\) 75.2923 + 29.8675i 0.929535 + 0.368735i
\(82\) 58.9348 + 58.9348i 0.718717 + 0.718717i
\(83\) 44.9271 + 44.9271i 0.541290 + 0.541290i 0.923907 0.382617i \(-0.124977\pi\)
−0.382617 + 0.923907i \(0.624977\pi\)
\(84\) 25.3295 33.5025i 0.301542 0.398839i
\(85\) 7.94959 + 115.122i 0.0935246 + 1.35437i
\(86\) 21.0192i 0.244409i
\(87\) 8.86329 93.6000i 0.101877 1.07586i
\(88\) −39.1153 39.1153i −0.444492 0.444492i
\(89\) 4.80429i 0.0539807i −0.999636 0.0269904i \(-0.991408\pi\)
0.999636 0.0269904i \(-0.00859234\pi\)
\(90\) −63.1829 7.61081i −0.702032 0.0845646i
\(91\) −6.62831 27.9997i −0.0728386 0.307689i
\(92\) −13.4789 13.4789i −0.146510 0.146510i
\(93\) −117.825 11.1573i −1.26694 0.119971i
\(94\) 58.4422 0.621725
\(95\) 28.4388 32.6578i 0.299356 0.343766i
\(96\) −13.0778 + 10.8153i −0.136227 + 0.112659i
\(97\) −2.01325 2.01325i −0.0207551 0.0207551i 0.696653 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 \(-0.772491\pi\)
−0.755262 + 0.655423i \(0.772491\pi\)
\(102\) 9.23076 97.4805i 0.0904976 0.955691i
\(103\) −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
\(105\) 102.759 21.5782i 0.978656 0.205507i
\(106\) 20.7109 0.195386
\(107\) −31.9911 31.9911i −0.298982 0.298982i 0.541633 0.840615i \(-0.317806\pi\)
−0.840615 + 0.541633i \(0.817806\pi\)
\(108\) 51.8484 + 15.0910i 0.480078 + 0.139732i
\(109\) 0.710351i 0.00651698i −0.999995 0.00325849i \(-0.998963\pi\)
0.999995 0.00325849i \(-0.00103721\pi\)
\(110\) −9.52700 137.965i −0.0866090 1.25423i
\(111\) −68.0609 82.2990i −0.613161 0.741432i
\(112\) 14.7056 23.8274i 0.131300 0.212745i
\(113\) −59.6020 + 59.6020i −0.527451 + 0.527451i −0.919812 0.392360i \(-0.871659\pi\)
0.392360 + 0.919812i \(0.371659\pi\)
\(114\) −28.3165 + 23.4177i −0.248391 + 0.205418i
\(115\) −3.28296 47.5421i −0.0285475 0.413409i
\(116\) 62.6791i 0.540337i
\(117\) 30.6043 20.7840i 0.261575 0.177641i
\(118\) 42.5598 42.5598i 0.360676 0.360676i
\(119\) 37.2159 + 157.209i 0.312738 + 1.32109i
\(120\) −42.4126 1.08038i −0.353439 0.00900315i
\(121\) −261.501 −2.16117
\(122\) −45.1131 + 45.1131i −0.369779 + 0.369779i
\(123\) 16.6676 176.017i 0.135509 1.43103i
\(124\) −78.9016 −0.636304
\(125\) 104.656 + 68.3529i 0.837248 + 0.546823i
\(126\) −89.0107 + 3.88560i −0.706434 + 0.0308381i
\(127\) −116.358 + 116.358i −0.916202 + 0.916202i −0.996751 0.0805491i \(-0.974333\pi\)
0.0805491 + 0.996751i \(0.474333\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) −34.3606 + 28.4161i −0.266361 + 0.220280i
\(130\) −19.0878 + 21.9195i −0.146829 + 0.168612i
\(131\) −67.9862 −0.518978 −0.259489 0.965746i \(-0.583554\pi\)
−0.259489 + 0.965746i \(0.583554\pi\)
\(132\) −11.0624 + 116.823i −0.0838059 + 0.885025i
\(133\) 31.8410 51.5920i 0.239406 0.387909i
\(134\) −178.712 −1.33367
\(135\) 72.9761 + 113.576i 0.540564 + 0.841303i
\(136\) 65.2777i 0.479983i
\(137\) 43.2163 + 43.2163i 0.315448 + 0.315448i 0.847016 0.531568i \(-0.178397\pi\)
−0.531568 + 0.847016i \(0.678397\pi\)
\(138\) −3.81205 + 40.2568i −0.0276235 + 0.291716i
\(139\) −16.4136 −0.118083 −0.0590417 0.998256i \(-0.518804\pi\)
−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
\(147\) 137.026 53.2241i 0.932151 0.362069i
\(148\) −50.3442 50.3442i −0.340163 0.340163i
\(149\) −63.8210 −0.428329 −0.214165 0.976798i \(-0.568703\pi\)
−0.214165 + 0.976798i \(0.568703\pi\)
\(150\) −78.1889 71.6694i −0.521259 0.477796i
\(151\) 100.225 0.663739 0.331869 0.943325i \(-0.392321\pi\)
0.331869 + 0.943325i \(0.392321\pi\)
\(152\) −17.3219 + 17.3219i −0.113960 + 0.113960i
\(153\) −171.833 + 116.695i −1.12309 + 0.762715i
\(154\) −44.6005 188.404i −0.289613 1.22340i
\(155\) −148.757 129.540i −0.959723 0.835740i
\(156\) 19.0058 15.7177i 0.121832 0.100754i
\(157\) 157.532 + 157.532i 1.00339 + 1.00339i 0.999994 + 0.00339453i \(0.00108051\pi\)
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
\(162\) −45.4248 105.160i −0.280400 0.649135i
\(163\) 130.800 + 130.800i 0.802457 + 0.802457i 0.983479 0.181022i \(-0.0579405\pi\)
−0.181022 + 0.983479i \(0.557941\pi\)
\(164\) 117.870i 0.718717i
\(165\) −212.655 + 202.090i −1.28882 + 1.22479i
\(166\) 89.8542i 0.541290i
\(167\) 35.0842 35.0842i 0.210085 0.210085i −0.594219 0.804304i \(-0.702539\pi\)
0.804304 + 0.594219i \(0.202539\pi\)
\(168\) −58.8320 + 8.17299i −0.350190 + 0.0486487i
\(169\) 152.104i 0.900022i
\(170\) 107.172 123.071i 0.630424 0.723949i
\(171\) 76.5630 + 14.6312i 0.447737 + 0.0855626i
\(172\) −21.0192 + 21.0192i −0.122204 + 0.122204i
\(173\) −224.736 224.736i −1.29905 1.29905i −0.929019 0.370032i \(-0.879347\pi\)
−0.370032 0.929019i \(-0.620653\pi\)
\(174\) −102.463 + 84.7367i −0.588869 + 0.486992i
\(175\) 160.141 + 70.5679i 0.915092 + 0.403245i
\(176\) 78.2306i 0.444492i
\(177\) −127.111 12.0366i −0.718140 0.0680031i
\(178\) −4.80429 + 4.80429i −0.0269904 + 0.0269904i
\(179\) 209.136 1.16836 0.584179 0.811625i \(-0.301417\pi\)
0.584179 + 0.811625i \(0.301417\pi\)
\(180\) 55.5721 + 70.7937i 0.308734 + 0.393298i
\(181\) 227.999i 1.25966i −0.776731 0.629832i \(-0.783124\pi\)
0.776731 0.629832i \(-0.216876\pi\)
\(182\) −21.3714 + 34.6280i −0.117425 + 0.190264i
\(183\) 134.737 + 12.7587i 0.736265 + 0.0697194i
\(184\) 26.9579i 0.146510i
\(185\) −12.2619 177.571i −0.0662807 0.959841i
\(186\) 106.668 + 128.983i 0.573484 + 0.693455i
\(187\) −319.170 319.170i −1.70679 1.70679i
\(188\) −58.4422 58.4422i −0.310863 0.310863i
\(189\) 126.687 + 140.255i 0.670299 + 0.742091i
\(190\) −61.0966 + 4.21895i −0.321561 + 0.0222050i
\(191\) 24.3448i 0.127460i −0.997967 0.0637298i \(-0.979700\pi\)
0.997967 0.0637298i \(-0.0202996\pi\)
\(192\) 23.8931 + 2.26252i 0.124443 + 0.0117840i
\(193\) −119.177 119.177i −0.617497 0.617497i 0.327392 0.944889i \(-0.393830\pi\)
−0.944889 + 0.327392i \(0.893830\pi\)
\(194\) 4.02649i 0.0207551i
\(195\) 61.6376 + 1.57009i 0.316090 + 0.00805176i
\(196\) 87.5990 43.9365i 0.446934 0.224166i
\(197\) 24.0000 + 24.0000i 0.121827 + 0.121827i 0.765392 0.643565i \(-0.222545\pi\)
−0.643565 + 0.765392i \(0.722545\pi\)
\(198\) 205.930 139.851i 1.04005 0.706317i
\(199\) 146.804 0.737706 0.368853 0.929488i \(-0.379751\pi\)
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
\(207\) 70.9624 48.1919i 0.342813 0.232811i
\(208\) 11.6263 11.6263i 0.0558955 0.0558955i
\(209\) 169.388i 0.810467i
\(210\) −124.337 81.1806i −0.592081 0.386574i
\(211\) 123.187 0.583825 0.291912 0.956445i \(-0.405708\pi\)
0.291912 + 0.956445i \(0.405708\pi\)
\(212\) −20.7109 20.7109i −0.0976929 0.0976929i
\(213\) 141.276 + 13.3779i 0.663266 + 0.0628069i
\(214\) 63.9822i 0.298982i
\(215\) −74.1374 + 5.11947i −0.344825 + 0.0238115i
\(216\) −36.7574 66.9395i −0.170173 0.309905i
\(217\) −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
\(222\) −14.2381 + 150.360i −0.0641355 + 0.677297i
\(223\) −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
\(225\) −11.4554 + 224.708i −0.0509130 + 0.998703i
\(226\) 119.204 0.527451
\(227\) 19.9546 19.9546i 0.0879055 0.0879055i −0.661787 0.749692i \(-0.730202\pi\)
0.749692 + 0.661787i \(0.230202\pi\)
\(228\) 51.7342 + 4.89888i 0.226904 + 0.0214863i
\(229\) 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
\(231\) −247.693 + 327.615i −1.07226 + 1.41825i
\(232\) −62.6791 + 62.6791i −0.270169 + 0.270169i
\(233\) −263.920 + 263.920i −1.13270 + 1.13270i −0.142978 + 0.989726i \(0.545668\pi\)
−0.989726 + 0.142978i \(0.954332\pi\)
\(234\) −51.3883 9.82031i −0.219608 0.0419671i
\(235\) −14.2343 206.133i −0.0605714 0.877163i
\(236\) −85.1196 −0.360676
\(237\) 123.846 + 11.7274i 0.522558 + 0.0494828i
\(238\) 119.993 194.425i 0.504174 0.816912i
\(239\) 407.365 1.70446 0.852228 0.523171i \(-0.175251\pi\)
0.852228 + 0.523171i \(0.175251\pi\)
\(240\) 41.3323 + 43.4930i 0.172218 + 0.181221i
\(241\) 311.118i 1.29095i 0.763783 + 0.645474i \(0.223340\pi\)
−0.763783 + 0.645474i \(0.776660\pi\)
\(242\) 261.501 + 261.501i 1.08058 + 1.08058i
\(243\) −110.497 + 216.424i −0.454721 + 0.890634i
\(244\) 90.2262 0.369779
\(245\) 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 \(-0.441872\pi\)
0.181600 + 0.983373i \(0.441872\pi\)
\(252\) 92.8963 + 85.1251i 0.368636 + 0.337798i
\(253\) 131.808 + 131.808i 0.520981 + 0.520981i
\(254\) 232.715 0.916202
\(255\) −346.075 8.81557i −1.35716 0.0345709i
\(256\) 16.0000 0.0625000
\(257\) −221.675 + 221.675i −0.862547 + 0.862547i −0.991633 0.129086i \(-0.958796\pi\)
0.129086 + 0.991633i \(0.458796\pi\)
\(258\) 62.7767 + 5.94453i 0.243320 + 0.0230408i
\(259\) −57.4040 242.489i −0.221637 0.936251i
\(260\) 41.0074 2.83171i 0.157721 0.0108912i
\(261\) 277.043 + 52.9429i 1.06147 + 0.202846i
\(262\) 67.9862 + 67.9862i 0.259489 + 0.259489i
\(263\) −258.162 + 258.162i −0.981603 + 0.981603i −0.999834 0.0182309i \(-0.994197\pi\)
0.0182309 + 0.999834i \(0.494197\pi\)
\(264\) 127.886 105.761i 0.484415 0.400609i
\(265\) −5.04439 73.0501i −0.0190354 0.275661i
\(266\) −83.4330 + 19.7509i −0.313658 + 0.0742517i
\(267\) 14.3487 + 1.35872i 0.0537403 + 0.00508885i
\(268\) 178.712 + 178.712i 0.666835 + 0.666835i
\(269\) 138.071i 0.513275i −0.966508 0.256637i \(-0.917385\pi\)
0.966508 0.256637i \(-0.0826146\pi\)
\(270\) 40.5998 186.552i 0.150370 0.690933i
\(271\) 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
\(273\) 85.4995 11.8777i 0.313185 0.0435079i
\(274\) 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 \(-0.861412\pi\)
0.906706 0.421762i \(-0.138588\pi\)
\(282\) −16.5283 + 174.546i −0.0586111 + 0.618956i
\(283\) 286.765 286.765i 1.01330 1.01330i 0.0133925 0.999910i \(-0.495737\pi\)
0.999910 0.0133925i \(-0.00426309\pi\)
\(284\) 94.6051 0.333117
\(285\) 89.4941 + 94.1726i 0.314014 + 0.330430i
\(286\) 113.691i 0.397521i
\(287\) 216.667 351.066i 0.754939 1.22323i
\(288\) −28.6028 42.1175i −0.0993153 0.146241i
\(289\) 243.648i 0.843072i
\(290\) −221.078 + 15.2662i −0.762337 + 0.0526422i
\(291\) 6.58222 5.44346i 0.0226193 0.0187061i
\(292\) −178.712 178.712i −0.612029 0.612029i
\(293\) −353.346 353.346i −1.20596 1.20596i −0.972324 0.233635i \(-0.924938\pi\)
−0.233635 0.972324i \(-0.575062\pi\)
\(294\) −190.250 83.8021i −0.647110 0.285041i
\(295\) −160.480 139.748i −0.544001 0.473723i
\(296\) 100.688i 0.340163i
\(297\) −507.017 147.573i −1.70713 0.496877i
\(298\) 63.8210 + 63.8210i 0.214165 + 0.214165i
\(299\) 39.1774i 0.131028i
\(300\) 6.51947 + 149.858i 0.0217316 + 0.499528i
\(301\) −101.241 + 23.9667i −0.336350 + 0.0796236i
\(302\) −100.225 100.225i −0.331869 0.331869i
\(303\) 43.1471 455.651i 0.142400 1.50380i
\(304\) 34.6437 0.113960
\(305\) 170.108 + 148.132i 0.557730 + 0.485679i
\(306\) 288.529 + 55.1379i 0.942904 + 0.180189i
\(307\) 268.995 + 268.995i 0.876204 + 0.876204i 0.993140 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 \(-0.451923\pi\)
0.150464 + 0.988615i \(0.451923\pi\)
\(312\) −34.7234 3.28808i −0.111293 0.0105387i
\(313\) −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
\(315\) 35.3847 + 313.006i 0.112332 + 0.993671i
\(316\) 82.9336 0.262448
\(317\) 183.110 + 183.110i 0.577633 + 0.577633i 0.934251 0.356617i \(-0.116070\pi\)
−0.356617 + 0.934251i \(0.616070\pi\)
\(318\) −5.85735 + 61.8560i −0.0184193 + 0.194516i
\(319\) 612.928i 1.92140i
\(320\) 30.1656 + 26.2686i 0.0942674 + 0.0820893i
\(321\) 104.593 86.4983i 0.325836 0.269465i
\(322\) −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
\(327\) 2.12156 + 0.200898i 0.00648796 + 0.000614367i
\(328\) −117.870 + 117.870i −0.359358 + 0.359358i
\(329\) −66.6376 281.494i −0.202546 0.855605i
\(330\) 414.746 + 10.5648i 1.25681 + 0.0320146i
\(331\) −389.930 −1.17804 −0.589018 0.808120i \(-0.700485\pi\)
−0.589018 + 0.808120i \(0.700485\pi\)
\(332\) −89.8542 + 89.8542i −0.270645 + 0.270645i
\(333\) 265.046 179.998i 0.795934 0.540534i
\(334\) −70.1684 −0.210085
\(335\) 43.5274 + 630.341i 0.129933 + 1.88161i
\(336\) 67.0050 + 50.6590i 0.199420 + 0.150771i
\(337\) 201.311 201.311i 0.597362 0.597362i −0.342248 0.939610i \(-0.611188\pi\)
0.939610 + 0.342248i \(0.111188\pi\)
\(338\) 152.104 152.104i 0.450011 0.450011i
\(339\) −161.153 194.866i −0.475379 0.574826i
\(340\) −230.243 + 15.8992i −0.677186 + 0.0467623i
\(341\) 771.565 2.26265
\(342\) −61.9318 91.1942i −0.181087 0.266650i
\(343\) 341.671 + 30.1624i 0.996126 + 0.0879370i
\(344\) 42.0383 0.122204
\(345\) 142.919 + 3.64059i 0.414259 + 0.0105524i
\(346\) 449.472i 1.29905i
\(347\) −373.074 373.074i −1.07514 1.07514i −0.996938 0.0782023i \(-0.975082\pi\)
−0.0782023 0.996938i \(-0.524918\pi\)
\(348\) 187.200 + 17.7266i 0.537931 + 0.0509385i
\(349\) −413.538 −1.18492 −0.592461 0.805599i \(-0.701843\pi\)
−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 \(-0.245204\pi\)
−0.696372 + 0.717681i \(0.745204\pi\)
\(354\) 115.074 + 139.147i 0.325069 + 0.393072i
\(355\) 178.364 + 155.321i 0.502433 + 0.437525i
\(356\) 9.60857 0.0269904
\(357\) −480.052 + 66.6892i −1.34468 + 0.186805i
\(358\) −209.136 209.136i −0.584179 0.584179i
\(359\) 166.966 0.465085 0.232543 0.972586i \(-0.425295\pi\)
0.232543 + 0.972586i \(0.425295\pi\)
\(360\) 15.2216 126.366i 0.0422823 0.351016i
\(361\) −285.988 −0.792211
\(362\) −227.999 + 227.999i −0.629832 + 0.629832i
\(363\) 73.9565 781.010i 0.203737 2.15154i
\(364\) 55.9993 13.2566i 0.153844 0.0364193i
\(365\) −43.5275 630.342i −0.119254 1.72697i
\(366\) −121.978 147.495i −0.333273 0.402992i
\(367\) −216.400 216.400i −0.589646 0.589646i 0.347890 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
\(372\) 22.3146 235.651i 0.0599854 0.633470i
\(373\) −64.8753 64.8753i −0.173928 0.173928i 0.614775 0.788703i \(-0.289247\pi\)
−0.788703 + 0.614775i \(0.789247\pi\)
\(374\) 638.339i 1.70679i
\(375\) −233.744 + 293.239i −0.623317 + 0.781970i
\(376\) 116.884i 0.310863i
\(377\) 91.0905 91.0905i 0.241619 0.241619i
\(378\) 13.5687 266.942i 0.0358959 0.706195i
\(379\) 44.8235i 0.118268i 0.998250 + 0.0591339i \(0.0188339\pi\)
−0.998250 + 0.0591339i \(0.981166\pi\)
\(380\) 65.3155 + 56.8776i 0.171883 + 0.149678i
\(381\) −314.611 380.426i −0.825749 0.998493i
\(382\) −24.3448 + 24.3448i −0.0637298 + 0.0637298i
\(383\) 465.824 + 465.824i 1.21625 + 1.21625i 0.968935 + 0.247315i \(0.0795483\pi\)
0.247315 + 0.968935i \(0.420452\pi\)
\(384\) −21.6306 26.1556i −0.0563297 0.0681136i
\(385\) −653.662 + 203.200i −1.69782 + 0.527792i
\(386\) 238.354i 0.617497i
\(387\) −75.1509 110.659i −0.194188 0.285941i
\(388\) 4.02649 4.02649i 0.0103776 0.0103776i
\(389\) −341.962 −0.879079 −0.439540 0.898223i \(-0.644858\pi\)
−0.439540 + 0.898223i \(0.644858\pi\)
\(390\) −60.0675 63.2077i −0.154019 0.162071i
\(391\) 219.969i 0.562580i
\(392\) −131.536 43.6625i −0.335550 0.111384i
\(393\) 19.2275 203.050i 0.0489249 0.516667i
\(394\) 48.0000i 0.121827i
\(395\) 156.359 + 136.159i 0.395845 + 0.344707i
\(396\) −345.780 66.0787i −0.873183 0.166865i
\(397\) −214.201 214.201i −0.539549 0.539549i 0.383847 0.923397i \(-0.374599\pi\)
−0.923397 + 0.383847i \(0.874599\pi\)
\(398\) −146.804 146.804i −0.368853 0.368853i
\(399\) 145.081 + 109.689i 0.363613 + 0.274909i
\(400\) 13.7452 + 99.0508i 0.0343630 + 0.247627i
\(401\) 278.216i 0.693806i −0.937901 0.346903i \(-0.887233\pi\)
0.937901 0.346903i \(-0.112767\pi\)
\(402\) 50.5424 533.748i 0.125727 1.32773i
\(403\) −114.666 114.666i −0.284532 0.284532i
\(404\) 305.126i 0.755262i
\(405\) −359.849 + 185.832i −0.888516 + 0.458845i
\(406\) −301.902 + 71.4687i −0.743600 + 0.176031i
\(407\) 492.307 + 492.307i 1.20960 + 1.20960i
\(408\) 194.961 + 18.4615i 0.477846 + 0.0452488i
\(409\) 481.543 1.17737 0.588684 0.808364i \(-0.299646\pi\)
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
\(417\) 4.64201 49.0215i 0.0111319 0.117557i
\(418\) 169.388 169.388i 0.405233 0.405233i
\(419\) 12.3613i 0.0295020i 0.999891 + 0.0147510i \(0.00469556\pi\)
−0.999891 + 0.0147510i \(0.995304\pi\)
\(420\) 43.1565 + 205.518i 0.102753 + 0.489328i
\(421\) 10.9249 0.0259498 0.0129749 0.999916i \(-0.495870\pi\)
0.0129749 + 0.999916i \(0.495870\pi\)
\(422\) −123.187 123.187i −0.291912 0.291912i
\(423\) 307.679 208.951i 0.727375 0.493974i
\(424\) 41.4218i 0.0976929i
\(425\) −460.192 348.035i −1.08280 0.818906i
\(426\) −127.898 154.654i −0.300230 0.363036i
\(427\) 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 \(0.997154\pi\)
\(432\) −30.1821 + 103.697i −0.0698659 + 0.240039i
\(433\) −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
\(435\) 323.834 + 340.763i 0.744445 + 0.783363i
\(436\) 1.42070 0.00325849
\(437\) 58.3702 58.3702i 0.133570 0.133570i
\(438\) −50.5425 + 533.749i −0.115394 + 1.21861i
\(439\) −717.592 −1.63461 −0.817303 0.576208i \(-0.804532\pi\)
−0.817303 + 0.576208i \(0.804532\pi\)
\(440\) 275.930 19.0540i 0.627113 0.0433045i
\(441\) 120.208 + 424.301i 0.272581 + 0.962133i
\(442\) 94.8670 94.8670i 0.214631 0.214631i
\(443\) −163.039 + 163.039i −0.368035 + 0.368035i −0.866760 0.498725i \(-0.833802\pi\)
0.498725 + 0.866760i \(0.333802\pi\)
\(444\) 164.598 136.122i 0.370716 0.306581i
\(445\) 18.1155 + 15.7752i 0.0407090 + 0.0354499i
\(446\) 176.781 0.396369
\(447\) 18.0495 190.610i 0.0403793 0.426422i
\(448\) 47.6548 + 29.4111i 0.106372 + 0.0656499i
\(449\) 681.871 1.51864 0.759322 0.650715i \(-0.225531\pi\)
0.759322 + 0.650715i \(0.225531\pi\)
\(450\) 236.164 213.253i 0.524808 0.473895i
\(451\) 1152.63i 2.55571i
\(452\) −119.204 119.204i −0.263726 0.263726i
\(453\) −28.3450 + 299.335i −0.0625717 + 0.660783i
\(454\) −39.9091 −0.0879055
\(455\) 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 \(-0.428417\pi\)
0.222993 + 0.974820i \(0.428417\pi\)
\(462\) 575.307 79.9222i 1.24525 0.172992i
\(463\) −172.047 172.047i −0.371592 0.371592i 0.496465 0.868057i \(-0.334631\pi\)
−0.868057 + 0.496465i \(0.834631\pi\)
\(464\) 125.358 0.270169
\(465\) 428.959 407.648i 0.922492 0.876662i
\(466\) 527.840 1.13270
\(467\) −331.816 + 331.816i −0.710527 + 0.710527i −0.966645 0.256118i \(-0.917556\pi\)
0.256118 + 0.966645i \(0.417556\pi\)
\(468\) 41.5679 + 61.2086i 0.0888204 + 0.130788i
\(469\) 203.773 + 860.788i 0.434484 + 1.83537i
\(470\) −191.899 + 220.368i −0.408296 + 0.468867i
\(471\) −515.044 + 425.939i −1.09351 + 0.904329i
\(472\) 85.1196 + 85.1196i 0.180338 + 0.180338i
\(473\) 205.543 205.543i 0.434551 0.434551i
\(474\) −112.119 135.574i −0.236538 0.286021i
\(475\) 29.7616 + 214.468i 0.0626560 + 0.451512i
\(476\) −314.418 + 74.4317i −0.660543 + 0.156369i
\(477\) 109.036 74.0487i 0.228588 0.155238i
\(478\) −407.365 407.365i −0.852228 0.852228i
\(479\) 449.861i 0.939167i −0.882888 0.469584i \(-0.844404\pi\)
0.882888 0.469584i \(-0.155596\pi\)
\(480\) 2.16076 84.8253i 0.00450157 0.176719i
\(481\) 146.329i 0.304217i
\(482\) 311.118 311.118i 0.645474 0.645474i
\(483\) 198.248 27.5408i 0.410452 0.0570203i
\(484\) 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 \(0.366565\pi\)
−0.407029 + 0.913415i \(0.633435\pi\)
\(492\) 352.034 + 33.3353i 0.715516 + 0.0677546i
\(493\) −511.444 + 511.444i −1.03741 + 1.03741i
\(494\) −50.3472 −0.101917
\(495\) −543.429 692.279i −1.09784 1.39854i
\(496\) 157.803i 0.318152i
\(497\) 281.774 + 173.903i 0.566951 + 0.349905i
\(498\) 268.362 + 25.4121i 0.538880 + 0.0510283i
\(499\) 0.286254i 0.000573655i 1.00000 0.000286827i \(9.13000e-5\pi\)
−1.00000 0.000286827i \(0.999909\pi\)
\(500\) −136.706 + 209.312i −0.273412 + 0.418624i
\(501\) 94.8615 + 114.706i 0.189344 + 0.228954i
\(502\) −91.1631 91.1631i −0.181600 0.181600i
\(503\) 167.300 + 167.300i 0.332605 + 0.332605i 0.853575 0.520970i \(-0.174430\pi\)
−0.520970 + 0.853575i \(0.674430\pi\)
\(504\) −7.77120 178.021i −0.0154190 0.353217i
\(505\) 500.952 575.269i 0.991983 1.13915i
\(506\) 263.616i 0.520981i
\(507\) −454.279 43.0172i −0.896014 0.0848466i
\(508\) −232.715 232.715i −0.458101 0.458101i
\(509\) 480.263i 0.943543i −0.881721 0.471771i \(-0.843615\pi\)
0.881721 0.471771i \(-0.156385\pi\)
\(510\) 337.260 + 354.891i 0.661293 + 0.695864i
\(511\) −203.773 860.790i −0.398774 1.68452i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −65.3513 + 224.528i −0.127390 + 0.437676i
\(514\) 443.349 0.862547
\(515\) −28.4711 412.303i −0.0552837 0.800589i
\(516\) −56.8321 68.7212i −0.110140 0.133181i
\(517\) 571.496 + 571.496i 1.10541 + 1.10541i
\(518\) −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 \(-0.551590\pi\)
−0.161366 + 0.986895i \(0.551590\pi\)
\(522\) −224.100 329.986i −0.429310 0.632156i
\(523\) −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
\(525\) −256.051 + 458.326i −0.487717 + 0.873002i
\(526\) 516.323 0.981603
\(527\) 643.815 + 643.815i 1.22166 + 1.22166i
\(528\) −233.646 22.1248i −0.442512 0.0419030i
\(529\) 438.159i 0.828278i
\(530\) −68.0057 + 78.0945i −0.128313 + 0.147348i
\(531\) 71.8977 376.230i 0.135401 0.708531i
\(532\) 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
\(537\) −59.1468 + 624.614i −0.110143 + 1.16315i
\(538\) −138.071 + 138.071i −0.256637 + 0.256637i
\(539\) −856.615 + 429.647i −1.58927 + 0.797119i
\(540\) −227.152 + 145.952i −0.420652 + 0.270282i
\(541\) 664.777 1.22879 0.614397 0.788997i \(-0.289400\pi\)
0.614397 + 0.788997i \(0.289400\pi\)
\(542\) 95.9122 95.9122i 0.176960 0.176960i
\(543\) 680.952 + 64.4816i 1.25405 + 0.118751i
\(544\) 130.555 0.239992
\(545\) 2.67852 + 2.33249i 0.00491471 + 0.00427980i
\(546\) −97.3771 73.6218i −0.178346 0.134839i
\(547\) 367.452 367.452i 0.671758 0.671758i −0.286363 0.958121i \(-0.592446\pi\)
0.958121 + 0.286363i \(0.0924464\pi\)
\(548\) −86.4327 + 86.4327i −0.157724 + 0.157724i
\(549\) −76.2110 + 398.801i −0.138818 + 0.726414i
\(550\) 551.506 + 417.094i 1.00274 + 0.758353i
\(551\) 271.430 0.492613
\(552\) −80.5135 7.62409i −0.145858 0.0138118i
\(553\) 247.012 + 152.448i 0.446676 + 0.275675i
\(554\) −211.024 −0.380910
\(555\) 533.807 + 13.5977i 0.961815 + 0.0245003i
\(556\) 32.8272i 0.0590417i
\(557\) 83.3059 + 83.3059i 0.149562 + 0.149562i 0.777922 0.628361i \(-0.216274\pi\)
−0.628361 + 0.777922i \(0.716274\pi\)
\(558\) −415.392 + 282.101i −0.744430 + 0.505557i
\(559\) −61.0936 −0.109291
\(560\) 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 \(-0.271125\pi\)
−0.752445 + 0.658656i \(0.771125\pi\)
\(564\) 191.074 158.017i 0.338784 0.280173i
\(565\) −29.0336 420.448i −0.0513868 0.744157i
\(566\) −573.529 −1.01330
\(567\) −454.721 + 338.701i −0.801976 + 0.597356i
\(568\) −94.6051 94.6051i −0.166558 0.166558i
\(569\) 354.050 0.622233 0.311116 0.950372i \(-0.399297\pi\)
0.311116 + 0.950372i \(0.399297\pi\)
\(570\) 4.67854 183.667i 0.00820797 0.322222i
\(571\) 490.557 0.859119 0.429559 0.903039i \(-0.358669\pi\)
0.429559 + 0.903039i \(0.358669\pi\)
\(572\) −113.691 + 113.691i −0.198761 + 0.198761i
\(573\) 72.7090 + 6.88506i 0.126892 + 0.0120158i
\(574\) −567.733 + 134.399i −0.989083 + 0.234144i
\(575\) 190.047 + 143.729i 0.330516 + 0.249963i
\(576\) −13.5147 + 70.7203i −0.0234629 + 0.122778i
\(577\) 677.908 + 677.908i 1.17488 + 1.17488i 0.981031 + 0.193852i \(0.0620983\pi\)
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
\(582\) −12.0257 1.13875i −0.0206627 0.00195662i
\(583\) 202.528 + 202.528i 0.347390 + 0.347390i
\(584\) 357.425i 0.612029i
\(585\) −22.1213 + 183.645i −0.0378142 + 0.313923i
\(586\) 706.692i 1.20596i
\(587\) −130.869 + 130.869i −0.222946 + 0.222946i −0.809738 0.586792i \(-0.800391\pi\)
0.586792 + 0.809738i \(0.300391\pi\)
\(588\) 106.448 + 274.052i 0.181034 + 0.466076i
\(589\) 341.681i 0.580104i
\(590\) 20.7319 + 300.228i 0.0351388 + 0.508862i
\(591\) −78.4668 + 64.8917i −0.132770 + 0.109800i
\(592\) 100.688 100.688i 0.170082 0.170082i
\(593\) 35.4197 + 35.4197i 0.0597296 + 0.0597296i 0.736341 0.676611i \(-0.236552\pi\)
−0.676611 + 0.736341i \(0.736552\pi\)
\(594\) 359.444 + 654.589i 0.605125 + 1.10200i
\(595\) −714.989 375.878i −1.20166 0.631728i
\(596\) 127.642i 0.214165i
\(597\) −41.5182 + 438.449i −0.0695448 + 0.734421i
\(598\) −39.1774 + 39.1774i −0.0655141 + 0.0655141i
\(599\) −442.029 −0.737946 −0.368973 0.929440i \(-0.620290\pi\)
−0.368973 + 0.929440i \(0.620290\pi\)
\(600\) 143.339 156.378i 0.238898 0.260630i
\(601\) 468.548i 0.779614i −0.920897 0.389807i \(-0.872542\pi\)
0.920897 0.389807i \(-0.127458\pi\)
\(602\) 125.208 + 77.2747i 0.207987 + 0.128363i
\(603\) −940.861 + 638.957i −1.56030 + 1.05963i
\(604\) 200.449i 0.331869i
\(605\) 858.659 986.042i 1.41927 1.62982i
\(606\) −498.798 + 412.504i −0.823099 + 0.680699i
\(607\) −622.632 622.632i −1.02575 1.02575i −0.999660 0.0260927i \(-0.991694\pi\)
−0.0260927 0.999660i \(-0.508306\pi\)
\(608\) −34.6437 34.6437i −0.0569798 0.0569798i
\(609\) 524.976 + 396.908i 0.862030 + 0.651737i
\(610\) −21.9757 318.240i −0.0360257 0.521705i
\(611\) 169.866i 0.278013i
\(612\) −233.391 343.667i −0.381357 0.561547i
\(613\) 140.330 + 140.330i 0.228923 + 0.228923i 0.812243 0.583319i \(-0.198246\pi\)
−0.583319 + 0.812243i \(0.698246\pi\)
\(614\) 537.990i 0.876204i
\(615\) 608.977 + 640.813i 0.990207 + 1.04197i
\(616\) 376.807 89.2009i 0.611700 0.144807i
\(617\) −354.668 354.668i −0.574826 0.574826i 0.358647 0.933473i \(-0.383238\pi\)
−0.933473 + 0.358647i \(0.883238\pi\)
\(618\) −33.0596 + 349.122i −0.0534944 + 0.564923i
\(619\) −802.714 −1.29679 −0.648396 0.761304i \(-0.724560\pi\)
−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
\(627\) −505.899 47.9053i −0.806857 0.0764040i
\(628\) −315.064 + 315.064i −0.501694 + 0.501694i
\(629\) 821.588i 1.30618i
\(630\) 277.622 348.391i 0.440669 0.553001i
\(631\) −1193.86 −1.89202 −0.946010 0.324137i \(-0.894926\pi\)
−0.946010 + 0.324137i \(0.894926\pi\)
\(632\) −82.9336 82.9336i −0.131224 0.131224i
\(633\) −34.8391 + 367.915i −0.0550381 + 0.581225i
\(634\) 366.220i 0.577633i
\(635\) −56.6806 820.818i −0.0892607 1.29263i
\(636\) 67.7133 55.9986i 0.106467 0.0880482i
\(637\) 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 \(-0.139210\pi\)
\(642\) −191.092 18.0951i −0.297651 0.0281855i
\(643\) 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
\(645\) 5.67716 222.870i 0.00880180 0.345534i
\(646\) 282.683 0.437590
\(647\) −431.186 + 431.186i −0.666439 + 0.666439i −0.956890 0.290451i \(-0.906195\pi\)
0.290451 + 0.956890i \(0.406195\pi\)
\(648\) 210.320 90.8496i 0.324567 0.140200i
\(649\) 832.370 1.28254
\(650\) −19.9757 143.949i −0.0307318 0.221460i
\(651\) 499.635 660.850i 0.767488 1.01513i
\(652\) −261.601 + 261.601i −0.401229 + 0.401229i
\(653\) 698.488 698.488i 1.06966 1.06966i 0.0722752 0.997385i \(-0.476974\pi\)
0.997385 0.0722752i \(-0.0230260\pi\)
\(654\) −1.92067 2.32246i −0.00293680 0.00355116i
\(655\) 223.238 256.355i 0.340821 0.391382i
\(656\) 235.739 0.359358
\(657\) 940.864 638.959i 1.43206 0.972541i
\(658\) −214.856 + 348.132i −0.326530 + 0.529075i
\(659\) −433.424 −0.657699 −0.328850 0.944382i \(-0.606661\pi\)
−0.328850 + 0.944382i \(0.606661\pi\)
\(660\) −404.181 425.311i −0.612395 0.644410i
\(661\) 797.271i 1.20616i −0.797681 0.603079i \(-0.793940\pi\)
0.797681 0.603079i \(-0.206060\pi\)
\(662\) 389.930 + 389.930i 0.589018 + 0.589018i
\(663\) −283.334 26.8298i −0.427351 0.0404673i
\(664\) 179.708 0.270645
\(665\) 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
\(672\) −16.3460 117.664i −0.0243244 0.175095i
\(673\) 369.528 + 369.528i 0.549076 + 0.549076i 0.926174 0.377098i \(-0.123078\pi\)
−0.377098 + 0.926174i \(0.623078\pi\)
\(674\) −402.622 −0.597362
\(675\) −667.883 97.7640i −0.989456 0.144836i
\(676\) −304.208 −0.450011
\(677\) −238.013 + 238.013i −0.351570 + 0.351570i −0.860694 0.509123i \(-0.829970\pi\)
0.509123 + 0.860694i \(0.329970\pi\)
\(678\) −33.7127 + 356.019i −0.0497237 + 0.525102i
\(679\) 19.3941 4.59113i 0.0285627 0.00676161i
\(680\) 246.143 + 214.344i 0.361974 + 0.315212i
\(681\) 53.9536 + 65.2405i 0.0792270 + 0.0958010i
\(682\) −771.565 771.565i −1.13133 1.13133i
\(683\) −399.484 + 399.484i −0.584896 + 0.584896i −0.936245 0.351349i \(-0.885723\pi\)
0.351349 + 0.936245i \(0.385723\pi\)
\(684\) −29.2624 + 153.126i −0.0427813 + 0.223868i
\(685\) −304.860 + 21.0517i −0.445051 + 0.0307324i
\(686\) −311.509 371.834i −0.454095 0.542032i
\(687\) −82.5544 + 871.808i −0.120167 + 1.26901i
\(688\) −42.0383 42.0383i −0.0611022 0.0611022i
\(689\) 60.1976i 0.0873695i
\(690\) −139.279 146.560i −0.201853 0.212406i
\(691\) 964.818i 1.39626i −0.715969 0.698132i \(-0.754015\pi\)
0.715969 0.698132i \(-0.245985\pi\)
\(692\) 449.472 449.472i 0.649526 0.649526i
\(693\) −908.416 832.423i −1.31085 1.20119i
\(694\) 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 \(0.941408\pi\)
\(702\) 43.8631 150.701i 0.0624830 0.214674i
\(703\) 218.014 218.014i 0.310119 0.310119i
\(704\) −156.461 −0.222246
\(705\) 619.672 + 15.7849i 0.878967 + 0.0223899i
\(706\) 15.0443i 0.0213092i
\(707\) 560.882 908.796i 0.793326 1.28543i
\(708\) 24.0731 254.222i 0.0340016 0.359070i
\(709\) 271.653i 0.383149i −0.981478 0.191575i \(-0.938641\pi\)
0.981478 0.191575i \(-0.0613594\pi\)
\(710\) −23.0422 333.685i −0.0324538 0.469979i
\(711\) −70.0512 + 366.568i −0.0985249 + 0.515566i
\(712\) −9.60857 9.60857i −0.0134952 0.0134952i
\(713\) −265.878 265.878i −0.372900 0.372900i
\(714\) 546.742 + 413.363i 0.765745 + 0.578940i
\(715\) −401.004 + 27.6908i −0.560845 + 0.0387284i
\(716\) 418.272i 0.584179i
\(717\) −115.209 + 1216.65i −0.160682 + 1.69686i
\(718\) −166.966 166.966i −0.232543 0.232543i
\(719\) 648.915i 0.902524i 0.892391 + 0.451262i \(0.149026\pi\)
−0.892391 + 0.451262i \(0.850974\pi\)
\(720\) −141.587 + 111.144i −0.196649 + 0.154367i
\(721\) −133.287 563.038i −0.184864 0.780912i
\(722\) 285.988 + 285.988i 0.396105 + 0.396105i
\(723\) −929.198 87.9889i −1.28520 0.121700i
\(724\) 455.999 0.629832
\(725\) 107.692 + 776.052i 0.148541 + 1.07042i
\(726\) −854.967 + 707.054i −1.17764 + 0.973903i
\(727\) 165.102 + 165.102i 0.227100 + 0.227100i 0.811480 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
\(732\) −25.5173 + 269.473i −0.0348597 + 0.368133i
\(733\) −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
\(735\) −249.244 + 691.450i −0.339107 + 0.940748i
\(736\) −53.9158 −0.0732551
\(737\) −1747.59 1747.59i −2.37122 2.37122i
\(738\) −421.425 620.546i −0.571036 0.840848i
\(739\) 960.261i 1.29941i −0.760188 0.649703i \(-0.774893\pi\)
0.760188 0.649703i \(-0.225107\pi\)
\(740\) 355.141 24.5238i 0.479921 0.0331403i
\(741\) 68.0649 + 82.3039i 0.0918555 + 0.111071i
\(742\) −76.1414 + 123.372i −0.102616 + 0.166269i
\(743\) 197.378 197.378i 0.265650 0.265650i −0.561695 0.827345i \(-0.689850\pi\)
0.827345 + 0.561695i \(0.189850\pi\)
\(744\) −257.965 + 213.336i −0.346728 + 0.286742i
\(745\) 209.561 240.650i 0.281290 0.323020i
\(746\) 129.751i 0.173928i
\(747\) −321.260 473.054i −0.430067 0.633271i
\(748\) 638.339 638.339i 0.853395 0.853395i
\(749\) 308.178 72.9545i 0.411453 0.0974026i
\(750\) 526.982 59.4948i 0.702643 0.0793264i
\(751\) 1038.60 1.38295 0.691477 0.722398i \(-0.256960\pi\)
0.691477 + 0.722398i \(0.256960\pi\)
\(752\) 116.884 116.884i 0.155431 0.155431i
\(753\) −25.7823 + 272.271i −0.0342394 + 0.361582i
\(754\) −182.181 −0.241619
\(755\) −329.095 + 377.916i −0.435887 + 0.500552i
\(756\) −280.510 + 253.373i −0.371046 + 0.335150i
\(757\) 230.964 230.964i 0.305105 0.305105i −0.537902 0.843007i \(-0.680783\pi\)
0.843007 + 0.537902i \(0.180783\pi\)
\(758\) 44.8235 44.8235i 0.0591339 0.0591339i
\(759\) −430.941 + 356.386i −0.567775 + 0.469547i
\(760\) −8.43790 122.193i −0.0111025 0.160780i
\(761\) −34.8617 −0.0458103 −0.0229052 0.999738i \(-0.507292\pi\)
−0.0229052 + 0.999738i \(0.507292\pi\)
\(762\) −65.8153 + 695.036i −0.0863718 + 0.912121i
\(763\) 4.23146 + 2.61153i 0.00554582 + 0.00342271i
\(764\) 48.6895 0.0637298
\(765\) 124.204 1031.11i 0.162358 1.34785i
\(766\) 931.648i 1.21625i