Properties

Label 1050.3.q.e.199.14
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.14
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.e.649.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.50174 - 2.59373i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.50174 - 2.59373i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.13478 + 8.89370i) q^{11} +(1.73205 + 3.00000i) q^{12} +7.02340 q^{13} +(6.12892 - 7.77408i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-15.8741 + 27.4947i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(26.9408 - 15.5543i) q^{19} +(-1.74007 + 11.9988i) q^{21} +14.5234i q^{22} +(20.5146 - 11.8441i) q^{23} +(4.24264 + 2.44949i) q^{24} +(8.60187 - 4.96629i) q^{26} +5.19615 q^{27} +(2.00927 - 13.8551i) q^{28} -9.19673 q^{29} +(17.4511 + 10.0754i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-8.89370 - 15.4043i) q^{33} +44.8986i q^{34} -6.00000 q^{36} +(41.7118 - 24.0823i) q^{37} +(21.9971 - 38.1001i) q^{38} +(-6.08244 + 10.5351i) q^{39} +65.1226i q^{41} +(6.35331 + 15.9259i) q^{42} +3.03497i q^{43} +(10.2696 + 17.7874i) q^{44} +(16.7501 - 29.0120i) q^{46} +(-30.9732 - 53.6472i) q^{47} +6.92820 q^{48} +(35.5451 - 33.7275i) q^{49} +(-27.4947 - 47.6222i) q^{51} +(7.02340 - 12.1649i) q^{52} +(1.19642 + 0.690751i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-7.33617 - 18.3897i) q^{56} +53.8817i q^{57} +(-11.2636 + 6.50307i) q^{58} +(95.1064 + 54.9097i) q^{59} +(-34.3741 + 19.8459i) q^{61} +28.4976 q^{62} +(-16.4913 - 13.0014i) q^{63} -8.00000 q^{64} +(-21.7850 - 12.5776i) q^{66} +(-13.7863 - 7.95952i) q^{67} +(31.7481 + 54.9893i) q^{68} +41.0292i q^{69} +53.3489 q^{71} +(-7.34847 + 4.24264i) q^{72} +(36.1901 - 62.6830i) q^{73} +(34.0576 - 58.9894i) q^{74} -62.2172i q^{76} +(-10.3171 + 71.1427i) q^{77} +17.2037i q^{78} +(53.2229 + 92.1847i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(46.0486 + 79.7586i) q^{82} -49.4298 q^{83} +(19.0425 + 15.0127i) q^{84} +(2.14605 + 3.71707i) q^{86} +(7.96460 - 13.7951i) q^{87} +(25.1552 + 14.5234i) q^{88} +(142.807 - 82.4499i) q^{89} +(45.6643 - 18.2168i) q^{91} -47.3765i q^{92} +(-30.2262 + 17.4511i) q^{93} +(-75.8686 - 43.8027i) q^{94} +(8.48528 - 4.89898i) q^{96} +49.4799 q^{97} +(19.6848 - 66.4418i) q^{98} +30.8087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) −0.866025 + 1.50000i −0.288675 + 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 6.50174 2.59373i 0.928819 0.370533i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) −5.13478 + 8.89370i −0.466798 + 0.808518i −0.999281 0.0379228i \(-0.987926\pi\)
0.532482 + 0.846441i \(0.321259\pi\)
\(12\) 1.73205 + 3.00000i 0.144338 + 0.250000i
\(13\) 7.02340 0.540261 0.270131 0.962824i \(-0.412933\pi\)
0.270131 + 0.962824i \(0.412933\pi\)
\(14\) 6.12892 7.77408i 0.437780 0.555291i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −15.8741 + 27.4947i −0.933768 + 1.61733i −0.156951 + 0.987606i \(0.550167\pi\)
−0.776816 + 0.629727i \(0.783167\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) 26.9408 15.5543i 1.41794 0.818648i 0.421822 0.906679i \(-0.361391\pi\)
0.996118 + 0.0880311i \(0.0280575\pi\)
\(20\) 0 0
\(21\) −1.74007 + 11.9988i −0.0828607 + 0.571373i
\(22\) 14.5234i 0.660152i
\(23\) 20.5146 11.8441i 0.891940 0.514962i 0.0173632 0.999849i \(-0.494473\pi\)
0.874576 + 0.484888i \(0.161140\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 8.60187 4.96629i 0.330841 0.191011i
\(27\) 5.19615 0.192450
\(28\) 2.00927 13.8551i 0.0717595 0.494824i
\(29\) −9.19673 −0.317129 −0.158564 0.987349i \(-0.550687\pi\)
−0.158564 + 0.987349i \(0.550687\pi\)
\(30\) 0 0
\(31\) 17.4511 + 10.0754i 0.562940 + 0.325013i 0.754325 0.656502i \(-0.227965\pi\)
−0.191385 + 0.981515i \(0.561298\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) −8.89370 15.4043i −0.269506 0.466798i
\(34\) 44.8986i 1.32055i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 41.7118 24.0823i 1.12735 0.650874i 0.184081 0.982911i \(-0.441069\pi\)
0.943266 + 0.332037i \(0.107736\pi\)
\(38\) 21.9971 38.1001i 0.578871 1.00263i
\(39\) −6.08244 + 10.5351i −0.155960 + 0.270131i
\(40\) 0 0
\(41\) 65.1226i 1.58836i 0.607685 + 0.794178i \(0.292098\pi\)
−0.607685 + 0.794178i \(0.707902\pi\)
\(42\) 6.35331 + 15.9259i 0.151269 + 0.379189i
\(43\) 3.03497i 0.0705807i 0.999377 + 0.0352904i \(0.0112356\pi\)
−0.999377 + 0.0352904i \(0.988764\pi\)
\(44\) 10.2696 + 17.7874i 0.233399 + 0.404259i
\(45\) 0 0
\(46\) 16.7501 29.0120i 0.364133 0.630697i
\(47\) −30.9732 53.6472i −0.659005 1.14143i −0.980874 0.194645i \(-0.937644\pi\)
0.321869 0.946784i \(-0.395689\pi\)
\(48\) 6.92820 0.144338
\(49\) 35.5451 33.7275i 0.725411 0.688316i
\(50\) 0 0
\(51\) −27.4947 47.6222i −0.539111 0.933768i
\(52\) 7.02340 12.1649i 0.135065 0.233940i
\(53\) 1.19642 + 0.690751i 0.0225739 + 0.0130330i 0.511244 0.859435i \(-0.329185\pi\)
−0.488671 + 0.872468i \(0.662518\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −7.33617 18.3897i −0.131003 0.328387i
\(57\) 53.8817i 0.945293i
\(58\) −11.2636 + 6.50307i −0.194201 + 0.112122i
\(59\) 95.1064 + 54.9097i 1.61197 + 0.930673i 0.988912 + 0.148500i \(0.0474445\pi\)
0.623061 + 0.782173i \(0.285889\pi\)
\(60\) 0 0
\(61\) −34.3741 + 19.8459i −0.563510 + 0.325343i −0.754553 0.656239i \(-0.772146\pi\)
0.191043 + 0.981582i \(0.438813\pi\)
\(62\) 28.4976 0.459638
\(63\) −16.4913 13.0014i −0.261767 0.206372i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −21.7850 12.5776i −0.330076 0.190570i
\(67\) −13.7863 7.95952i −0.205765 0.118799i 0.393576 0.919292i \(-0.371238\pi\)
−0.599342 + 0.800493i \(0.704571\pi\)
\(68\) 31.7481 + 54.9893i 0.466884 + 0.808667i
\(69\) 41.0292i 0.594626i
\(70\) 0 0
\(71\) 53.3489 0.751393 0.375696 0.926743i \(-0.377404\pi\)
0.375696 + 0.926743i \(0.377404\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) 36.1901 62.6830i 0.495754 0.858672i −0.504234 0.863567i \(-0.668225\pi\)
0.999988 + 0.00489557i \(0.00155831\pi\)
\(74\) 34.0576 58.9894i 0.460237 0.797155i
\(75\) 0 0
\(76\) 62.2172i 0.818648i
\(77\) −10.3171 + 71.1427i −0.133989 + 0.923931i
\(78\) 17.2037i 0.220561i
\(79\) 53.2229 + 92.1847i 0.673707 + 1.16690i 0.976845 + 0.213948i \(0.0686325\pi\)
−0.303138 + 0.952947i \(0.598034\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 46.0486 + 79.7586i 0.561569 + 0.972666i
\(83\) −49.4298 −0.595540 −0.297770 0.954638i \(-0.596243\pi\)
−0.297770 + 0.954638i \(0.596243\pi\)
\(84\) 19.0425 + 15.0127i 0.226697 + 0.178723i
\(85\) 0 0
\(86\) 2.14605 + 3.71707i 0.0249541 + 0.0432217i
\(87\) 7.96460 13.7951i 0.0915472 0.158564i
\(88\) 25.1552 + 14.5234i 0.285854 + 0.165038i
\(89\) 142.807 82.4499i 1.60458 0.926403i 0.614022 0.789289i \(-0.289551\pi\)
0.990555 0.137114i \(-0.0437826\pi\)
\(90\) 0 0
\(91\) 45.6643 18.2168i 0.501805 0.200185i
\(92\) 47.3765i 0.514962i
\(93\) −30.2262 + 17.4511i −0.325013 + 0.187647i
\(94\) −75.8686 43.8027i −0.807113 0.465987i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 49.4799 0.510102 0.255051 0.966928i \(-0.417908\pi\)
0.255051 + 0.966928i \(0.417908\pi\)
\(98\) 19.6848 66.4418i 0.200865 0.677977i
\(99\) 30.8087 0.311199
\(100\) 0 0
\(101\) 116.803 + 67.4364i 1.15647 + 0.667687i 0.950455 0.310863i \(-0.100618\pi\)
0.206012 + 0.978549i \(0.433951\pi\)
\(102\) −67.3479 38.8833i −0.660274 0.381209i
\(103\) 18.7010 + 32.3911i 0.181563 + 0.314477i 0.942413 0.334451i \(-0.108551\pi\)
−0.760850 + 0.648928i \(0.775218\pi\)
\(104\) 19.8652i 0.191011i
\(105\) 0 0
\(106\) 1.95374 0.0184315
\(107\) −21.4739 + 12.3980i −0.200691 + 0.115869i −0.596978 0.802258i \(-0.703632\pi\)
0.396287 + 0.918127i \(0.370299\pi\)
\(108\) 5.19615 9.00000i 0.0481125 0.0833333i
\(109\) −28.1448 + 48.7483i −0.258209 + 0.447232i −0.965762 0.259429i \(-0.916466\pi\)
0.707553 + 0.706660i \(0.249799\pi\)
\(110\) 0 0
\(111\) 83.4237i 0.751565i
\(112\) −21.9884 17.3352i −0.196325 0.154779i
\(113\) 74.9910i 0.663637i −0.943343 0.331818i \(-0.892338\pi\)
0.943343 0.331818i \(-0.107662\pi\)
\(114\) 38.1001 + 65.9913i 0.334212 + 0.578871i
\(115\) 0 0
\(116\) −9.19673 + 15.9292i −0.0792822 + 0.137321i
\(117\) −10.5351 18.2473i −0.0900436 0.155960i
\(118\) 155.308 1.31617
\(119\) −31.8952 + 219.936i −0.268027 + 1.84820i
\(120\) 0 0
\(121\) 7.76807 + 13.4547i 0.0641989 + 0.111196i
\(122\) −28.0664 + 48.6124i −0.230052 + 0.398462i
\(123\) −97.6839 56.3978i −0.794178 0.458519i
\(124\) 34.9023 20.1508i 0.281470 0.162507i
\(125\) 0 0
\(126\) −29.3910 4.26229i −0.233262 0.0338277i
\(127\) 128.504i 1.01184i 0.862580 + 0.505921i \(0.168847\pi\)
−0.862580 + 0.505921i \(0.831153\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) −4.55246 2.62836i −0.0352904 0.0203749i
\(130\) 0 0
\(131\) 65.3818 37.7482i 0.499098 0.288154i −0.229243 0.973369i \(-0.573625\pi\)
0.728341 + 0.685215i \(0.240292\pi\)
\(132\) −35.5748 −0.269506
\(133\) 134.819 171.007i 1.01367 1.28577i
\(134\) −22.5129 −0.168007
\(135\) 0 0
\(136\) 77.7667 + 44.8986i 0.571814 + 0.330137i
\(137\) −93.1121 53.7583i −0.679650 0.392396i 0.120073 0.992765i \(-0.461687\pi\)
−0.799723 + 0.600369i \(0.795020\pi\)
\(138\) 29.0120 + 50.2503i 0.210232 + 0.364133i
\(139\) 272.004i 1.95686i −0.206576 0.978431i \(-0.566232\pi\)
0.206576 0.978431i \(-0.433768\pi\)
\(140\) 0 0
\(141\) 107.294 0.760953
\(142\) 65.3388 37.7234i 0.460132 0.265658i
\(143\) −36.0636 + 62.4640i −0.252193 + 0.436811i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 102.361i 0.701102i
\(147\) 19.8082 + 82.5266i 0.134750 + 0.561405i
\(148\) 96.3294i 0.650874i
\(149\) −41.7135 72.2498i −0.279956 0.484898i 0.691417 0.722456i \(-0.256987\pi\)
−0.971374 + 0.237557i \(0.923653\pi\)
\(150\) 0 0
\(151\) −63.3973 + 109.807i −0.419850 + 0.727201i −0.995924 0.0901962i \(-0.971251\pi\)
0.576074 + 0.817397i \(0.304584\pi\)
\(152\) −43.9942 76.2002i −0.289436 0.501317i
\(153\) 95.2443 0.622512
\(154\) 37.6696 + 94.4270i 0.244608 + 0.613162i
\(155\) 0 0
\(156\) 12.1649 + 21.0702i 0.0779800 + 0.135065i
\(157\) 49.6184 85.9416i 0.316041 0.547399i −0.663617 0.748072i \(-0.730980\pi\)
0.979658 + 0.200673i \(0.0643130\pi\)
\(158\) 130.369 + 75.2685i 0.825120 + 0.476383i
\(159\) −2.07225 + 1.19642i −0.0130330 + 0.00752463i
\(160\) 0 0
\(161\) 102.660 130.217i 0.637641 0.808799i
\(162\) 12.7279i 0.0785674i
\(163\) −241.603 + 139.490i −1.48223 + 0.855765i −0.999797 0.0201678i \(-0.993580\pi\)
−0.482433 + 0.875933i \(0.660247\pi\)
\(164\) 112.796 + 65.1226i 0.687779 + 0.397089i
\(165\) 0 0
\(166\) −60.5389 + 34.9522i −0.364692 + 0.210555i
\(167\) −29.9435 −0.179302 −0.0896511 0.995973i \(-0.528575\pi\)
−0.0896511 + 0.995973i \(0.528575\pi\)
\(168\) 33.9378 + 4.92167i 0.202011 + 0.0292957i
\(169\) −119.672 −0.708118
\(170\) 0 0
\(171\) −80.8225 46.6629i −0.472646 0.272883i
\(172\) 5.25673 + 3.03497i 0.0305624 + 0.0176452i
\(173\) −53.2530 92.2369i −0.307821 0.533161i 0.670065 0.742303i \(-0.266266\pi\)
−0.977885 + 0.209142i \(0.932933\pi\)
\(174\) 22.5273i 0.129467i
\(175\) 0 0
\(176\) 41.0782 0.233399
\(177\) −164.729 + 95.1064i −0.930673 + 0.537324i
\(178\) 116.602 201.960i 0.655066 1.13461i
\(179\) −119.986 + 207.822i −0.670315 + 1.16102i 0.307500 + 0.951548i \(0.400508\pi\)
−0.977815 + 0.209471i \(0.932826\pi\)
\(180\) 0 0
\(181\) 309.322i 1.70896i 0.519482 + 0.854482i \(0.326125\pi\)
−0.519482 + 0.854482i \(0.673875\pi\)
\(182\) 43.0459 54.6004i 0.236516 0.300002i
\(183\) 68.7483i 0.375674i
\(184\) −33.5002 58.0241i −0.182066 0.315348i
\(185\) 0 0
\(186\) −24.6796 + 42.7464i −0.132686 + 0.229819i
\(187\) −163.020 282.358i −0.871762 1.50994i
\(188\) −123.893 −0.659005
\(189\) 33.7840 13.4774i 0.178751 0.0713091i
\(190\) 0 0
\(191\) −1.54480 2.67567i −0.00808796 0.0140088i 0.861953 0.506988i \(-0.169241\pi\)
−0.870041 + 0.492979i \(0.835908\pi\)
\(192\) 6.92820 12.0000i 0.0360844 0.0625000i
\(193\) −206.718 119.349i −1.07108 0.618387i −0.142602 0.989780i \(-0.545547\pi\)
−0.928476 + 0.371393i \(0.878880\pi\)
\(194\) 60.6002 34.9875i 0.312372 0.180348i
\(195\) 0 0
\(196\) −22.8726 95.2935i −0.116697 0.486191i
\(197\) 291.539i 1.47989i −0.672666 0.739946i \(-0.734851\pi\)
0.672666 0.739946i \(-0.265149\pi\)
\(198\) 37.7328 21.7850i 0.190570 0.110025i
\(199\) −209.224 120.796i −1.05138 0.607013i −0.128342 0.991730i \(-0.540966\pi\)
−0.923034 + 0.384717i \(0.874299\pi\)
\(200\) 0 0
\(201\) 23.8785 13.7863i 0.118799 0.0685885i
\(202\) 190.739 0.944252
\(203\) −59.7947 + 23.8538i −0.294555 + 0.117507i
\(204\) −109.979 −0.539111
\(205\) 0 0
\(206\) 45.8080 + 26.4473i 0.222369 + 0.128385i
\(207\) −61.5438 35.5324i −0.297313 0.171654i
\(208\) −14.0468 24.3298i −0.0675327 0.116970i
\(209\) 319.472i 1.52857i
\(210\) 0 0
\(211\) −263.018 −1.24653 −0.623266 0.782010i \(-0.714195\pi\)
−0.623266 + 0.782010i \(0.714195\pi\)
\(212\) 2.39283 1.38150i 0.0112869 0.00651652i
\(213\) −46.2015 + 80.0234i −0.216908 + 0.375696i
\(214\) −17.5334 + 30.3688i −0.0819318 + 0.141910i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 139.596 + 20.2442i 0.643297 + 0.0932911i
\(218\) 79.6056i 0.365163i
\(219\) 62.6830 + 108.570i 0.286224 + 0.495754i
\(220\) 0 0
\(221\) −111.490 + 193.106i −0.504479 + 0.873783i
\(222\) 58.9894 + 102.173i 0.265718 + 0.460237i
\(223\) 112.658 0.505193 0.252597 0.967572i \(-0.418715\pi\)
0.252597 + 0.967572i \(0.418715\pi\)
\(224\) −39.1880 5.68306i −0.174947 0.0253708i
\(225\) 0 0
\(226\) −53.0266 91.8448i −0.234631 0.406393i
\(227\) −24.5102 + 42.4529i −0.107974 + 0.187017i −0.914950 0.403568i \(-0.867770\pi\)
0.806975 + 0.590585i \(0.201103\pi\)
\(228\) 93.3258 + 53.8817i 0.409324 + 0.236323i
\(229\) −24.3476 + 14.0571i −0.106321 + 0.0613846i −0.552218 0.833700i \(-0.686218\pi\)
0.445896 + 0.895085i \(0.352885\pi\)
\(230\) 0 0
\(231\) −97.7792 77.0871i −0.423286 0.333710i
\(232\) 26.0123i 0.112122i
\(233\) −152.596 + 88.1014i −0.654919 + 0.378117i −0.790338 0.612671i \(-0.790095\pi\)
0.135420 + 0.990788i \(0.456762\pi\)
\(234\) −25.8056 14.8989i −0.110280 0.0636704i
\(235\) 0 0
\(236\) 190.213 109.819i 0.805987 0.465337i
\(237\) −184.369 −0.777930
\(238\) 116.455 + 291.919i 0.489306 + 1.22655i
\(239\) −34.7150 −0.145251 −0.0726255 0.997359i \(-0.523138\pi\)
−0.0726255 + 0.997359i \(0.523138\pi\)
\(240\) 0 0
\(241\) −229.871 132.716i −0.953823 0.550690i −0.0595563 0.998225i \(-0.518969\pi\)
−0.894266 + 0.447535i \(0.852302\pi\)
\(242\) 19.0278 + 10.9857i 0.0786273 + 0.0453955i
\(243\) −7.79423 13.5000i −0.0320750 0.0555556i
\(244\) 79.3837i 0.325343i
\(245\) 0 0
\(246\) −159.517 −0.648444
\(247\) 189.216 109.244i 0.766058 0.442284i
\(248\) 28.4976 49.3592i 0.114910 0.199029i
\(249\) 42.8075 74.1447i 0.171918 0.297770i
\(250\) 0 0
\(251\) 24.1723i 0.0963040i 0.998840 + 0.0481520i \(0.0153332\pi\)
−0.998840 + 0.0481520i \(0.984667\pi\)
\(252\) −39.0104 + 15.5624i −0.154803 + 0.0617555i
\(253\) 243.268i 0.961533i
\(254\) 90.8659 + 157.384i 0.357740 + 0.619624i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −4.76874 8.25969i −0.0185554 0.0321389i 0.856599 0.515983i \(-0.172573\pi\)
−0.875154 + 0.483844i \(0.839240\pi\)
\(258\) −7.43413 −0.0288145
\(259\) 208.736 264.766i 0.805932 1.02226i
\(260\) 0 0
\(261\) 13.7951 + 23.8938i 0.0528548 + 0.0915472i
\(262\) 53.3840 92.4639i 0.203756 0.352916i
\(263\) −114.197 65.9316i −0.434209 0.250691i 0.266929 0.963716i \(-0.413991\pi\)
−0.701138 + 0.713026i \(0.747324\pi\)
\(264\) −43.5701 + 25.1552i −0.165038 + 0.0952848i
\(265\) 0 0
\(266\) 44.1980 304.771i 0.166158 1.14576i
\(267\) 285.615i 1.06972i
\(268\) −27.5726 + 15.9190i −0.102883 + 0.0593994i
\(269\) 32.8041 + 18.9395i 0.121949 + 0.0704070i 0.559733 0.828673i \(-0.310904\pi\)
−0.437785 + 0.899080i \(0.644237\pi\)
\(270\) 0 0
\(271\) 313.801 181.173i 1.15794 0.668535i 0.207128 0.978314i \(-0.433588\pi\)
0.950809 + 0.309779i \(0.100255\pi\)
\(272\) 126.992 0.466884
\(273\) −12.2212 + 84.2726i −0.0447664 + 0.308691i
\(274\) −152.051 −0.554932
\(275\) 0 0
\(276\) 71.0647 + 41.0292i 0.257481 + 0.148657i
\(277\) 98.1197 + 56.6495i 0.354223 + 0.204511i 0.666544 0.745466i \(-0.267773\pi\)
−0.312321 + 0.949977i \(0.601106\pi\)
\(278\) −192.336 333.135i −0.691855 1.19833i
\(279\) 60.4525i 0.216676i
\(280\) 0 0
\(281\) −178.735 −0.636069 −0.318034 0.948079i \(-0.603023\pi\)
−0.318034 + 0.948079i \(0.603023\pi\)
\(282\) 131.408 75.8686i 0.465987 0.269038i
\(283\) 21.5843 37.3850i 0.0762695 0.132103i −0.825368 0.564595i \(-0.809032\pi\)
0.901638 + 0.432492i \(0.142366\pi\)
\(284\) 53.3489 92.4030i 0.187848 0.325363i
\(285\) 0 0
\(286\) 102.003i 0.356655i
\(287\) 168.910 + 423.410i 0.588538 + 1.47530i
\(288\) 16.9706i 0.0589256i
\(289\) −359.471 622.622i −1.24384 2.15440i
\(290\) 0 0
\(291\) −42.8508 + 74.2198i −0.147254 + 0.255051i
\(292\) −72.3801 125.366i −0.247877 0.429336i
\(293\) 15.4426 0.0527050 0.0263525 0.999653i \(-0.491611\pi\)
0.0263525 + 0.999653i \(0.491611\pi\)
\(294\) 82.6151 + 87.0675i 0.281004 + 0.296148i
\(295\) 0 0
\(296\) −68.1151 117.979i −0.230119 0.398577i
\(297\) −26.6811 + 46.2130i −0.0898354 + 0.155599i
\(298\) −102.177 58.9917i −0.342875 0.197959i
\(299\) 144.082 83.1859i 0.481881 0.278214i
\(300\) 0 0
\(301\) 7.87189 + 19.7326i 0.0261525 + 0.0655568i
\(302\) 179.315i 0.593757i
\(303\) −202.309 + 116.803i −0.667687 + 0.385489i
\(304\) −107.763 62.2172i −0.354485 0.204662i
\(305\) 0 0
\(306\) 116.650 67.3479i 0.381209 0.220091i
\(307\) 234.648 0.764327 0.382163 0.924095i \(-0.375179\pi\)
0.382163 + 0.924095i \(0.375179\pi\)
\(308\) 112.906 + 89.0125i 0.366577 + 0.289002i
\(309\) −64.7823 −0.209651
\(310\) 0 0
\(311\) −345.352 199.389i −1.11045 0.641121i −0.171508 0.985183i \(-0.554864\pi\)
−0.938947 + 0.344061i \(0.888197\pi\)
\(312\) 29.7978 + 17.2037i 0.0955056 + 0.0551402i
\(313\) −64.6002 111.891i −0.206390 0.357479i 0.744184 0.667974i \(-0.232838\pi\)
−0.950575 + 0.310495i \(0.899505\pi\)
\(314\) 140.342i 0.446949i
\(315\) 0 0
\(316\) 212.892 0.673707
\(317\) −348.632 + 201.283i −1.09979 + 0.634961i −0.936165 0.351562i \(-0.885651\pi\)
−0.163621 + 0.986523i \(0.552317\pi\)
\(318\) −1.69199 + 2.93061i −0.00532072 + 0.00921575i
\(319\) 47.2232 81.7930i 0.148035 0.256404i
\(320\) 0 0
\(321\) 42.9479i 0.133794i
\(322\) 33.6554 232.074i 0.104520 0.720726i
\(323\) 987.640i 3.05771i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −197.268 + 341.679i −0.605118 + 1.04809i
\(327\) −48.7483 84.4345i −0.149077 0.258209i
\(328\) 184.195 0.561569
\(329\) −340.526 268.464i −1.03503 0.815999i
\(330\) 0 0
\(331\) 83.4463 + 144.533i 0.252104 + 0.436656i 0.964105 0.265522i \(-0.0855443\pi\)
−0.712001 + 0.702178i \(0.752211\pi\)
\(332\) −49.4298 + 85.6150i −0.148885 + 0.257876i
\(333\) −125.136 72.2470i −0.375782 0.216958i
\(334\) −36.6731 + 21.1732i −0.109800 + 0.0633929i
\(335\) 0 0
\(336\) 45.0453 17.9699i 0.134064 0.0534818i
\(337\) 541.392i 1.60651i −0.595638 0.803253i \(-0.703101\pi\)
0.595638 0.803253i \(-0.296899\pi\)
\(338\) −146.568 + 84.6208i −0.433632 + 0.250357i
\(339\) 112.486 + 64.9441i 0.331818 + 0.191575i
\(340\) 0 0
\(341\) −179.215 + 103.470i −0.525558 + 0.303431i
\(342\) −131.983 −0.385914
\(343\) 143.625 311.482i 0.418732 0.908110i
\(344\) 8.58420 0.0249541
\(345\) 0 0
\(346\) −130.443 75.3111i −0.377002 0.217662i
\(347\) −371.251 214.342i −1.06989 0.617700i −0.141737 0.989904i \(-0.545269\pi\)
−0.928151 + 0.372204i \(0.878602\pi\)
\(348\) −15.9292 27.5902i −0.0457736 0.0792822i
\(349\) 74.6851i 0.213998i −0.994259 0.106999i \(-0.965876\pi\)
0.994259 0.106999i \(-0.0341241\pi\)
\(350\) 0 0
\(351\) 36.4946 0.103973
\(352\) 50.3104 29.0467i 0.142927 0.0825190i
\(353\) 182.956 316.890i 0.518290 0.897705i −0.481484 0.876455i \(-0.659902\pi\)
0.999774 0.0212499i \(-0.00676457\pi\)
\(354\) −134.501 + 232.962i −0.379946 + 0.658085i
\(355\) 0 0
\(356\) 329.799i 0.926403i
\(357\) −302.282 238.313i −0.846728 0.667543i
\(358\) 339.373i 0.947968i
\(359\) −248.793 430.922i −0.693017 1.20034i −0.970845 0.239710i \(-0.922948\pi\)
0.277828 0.960631i \(-0.410386\pi\)
\(360\) 0 0
\(361\) 303.373 525.457i 0.840368 1.45556i
\(362\) 218.724 + 378.841i 0.604210 + 1.04652i
\(363\) −26.9094 −0.0741305
\(364\) 14.1119 97.3096i 0.0387689 0.267334i
\(365\) 0 0
\(366\) −48.6124 84.1991i −0.132821 0.230052i
\(367\) −69.6861 + 120.700i −0.189880 + 0.328882i −0.945210 0.326462i \(-0.894143\pi\)
0.755330 + 0.655345i \(0.227477\pi\)
\(368\) −82.0584 47.3765i −0.222985 0.128740i
\(369\) 169.194 97.6839i 0.458519 0.264726i
\(370\) 0 0
\(371\) 9.57040 + 1.38790i 0.0257962 + 0.00374098i
\(372\) 69.8045i 0.187647i
\(373\) −300.961 + 173.760i −0.806865 + 0.465844i −0.845866 0.533395i \(-0.820916\pi\)
0.0390009 + 0.999239i \(0.487582\pi\)
\(374\) −399.315 230.544i −1.06769 0.616429i
\(375\) 0 0
\(376\) −151.737 + 87.6055i −0.403556 + 0.232993i
\(377\) −64.5923 −0.171332
\(378\) 31.8468 40.3953i 0.0842509 0.106866i
\(379\) −307.387 −0.811048 −0.405524 0.914084i \(-0.632911\pi\)
−0.405524 + 0.914084i \(0.632911\pi\)
\(380\) 0 0
\(381\) −192.756 111.288i −0.505921 0.292093i
\(382\) −3.78397 2.18468i −0.00990569 0.00571905i
\(383\) 254.364 + 440.572i 0.664136 + 1.15032i 0.979519 + 0.201353i \(0.0645339\pi\)
−0.315382 + 0.948965i \(0.602133\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −337.569 −0.874531
\(387\) 7.88509 4.55246i 0.0203749 0.0117635i
\(388\) 49.4799 85.7016i 0.127525 0.220880i
\(389\) −85.4840 + 148.063i −0.219753 + 0.380624i −0.954732 0.297466i \(-0.903859\pi\)
0.734979 + 0.678090i \(0.237192\pi\)
\(390\) 0 0
\(391\) 752.057i 1.92342i
\(392\) −95.3957 100.537i −0.243356 0.256472i
\(393\) 130.764i 0.332732i
\(394\) −206.149 357.061i −0.523221 0.906245i
\(395\) 0 0
\(396\) 30.8087 53.3622i 0.0777997 0.134753i
\(397\) 318.249 + 551.223i 0.801634 + 1.38847i 0.918540 + 0.395328i \(0.129369\pi\)
−0.116906 + 0.993143i \(0.537298\pi\)
\(398\) −341.661 −0.858446
\(399\) 139.755 + 350.325i 0.350262 + 0.878006i
\(400\) 0 0
\(401\) 296.110 + 512.878i 0.738429 + 1.27900i 0.953202 + 0.302333i \(0.0977654\pi\)
−0.214773 + 0.976664i \(0.568901\pi\)
\(402\) 19.4968 33.7694i 0.0484994 0.0840034i
\(403\) 122.566 + 70.7636i 0.304135 + 0.175592i
\(404\) 233.606 134.873i 0.578234 0.333843i
\(405\) 0 0
\(406\) −56.3661 + 71.4961i −0.138833 + 0.176099i
\(407\) 494.630i 1.21531i
\(408\) −134.696 + 77.7667i −0.330137 + 0.190605i
\(409\) 245.717 + 141.865i 0.600776 + 0.346858i 0.769347 0.638831i \(-0.220582\pi\)
−0.168571 + 0.985690i \(0.553915\pi\)
\(410\) 0 0
\(411\) 161.275 93.1121i 0.392396 0.226550i
\(412\) 74.8041 0.181563
\(413\) 760.778 + 110.328i 1.84208 + 0.267138i
\(414\) −100.501 −0.242755
\(415\) 0 0
\(416\) −34.4075 19.8652i −0.0827103 0.0477528i
\(417\) 408.006 + 235.562i 0.978431 + 0.564897i
\(418\) 225.901 + 391.271i 0.540432 + 0.936056i
\(419\) 482.511i 1.15158i 0.817599 + 0.575789i \(0.195305\pi\)
−0.817599 + 0.575789i \(0.804695\pi\)
\(420\) 0 0
\(421\) 762.080 1.81017 0.905083 0.425234i \(-0.139808\pi\)
0.905083 + 0.425234i \(0.139808\pi\)
\(422\) −322.130 + 185.982i −0.763342 + 0.440716i
\(423\) −92.9197 + 160.942i −0.219668 + 0.380476i
\(424\) 1.95374 3.38397i 0.00460787 0.00798107i
\(425\) 0 0
\(426\) 130.678i 0.306755i
\(427\) −172.017 + 218.190i −0.402849 + 0.510984i
\(428\) 49.5920i 0.115869i
\(429\) −62.4640 108.191i −0.145604 0.252193i
\(430\) 0 0
\(431\) −128.008 + 221.717i −0.297003 + 0.514424i −0.975449 0.220226i \(-0.929320\pi\)
0.678446 + 0.734650i \(0.262654\pi\)
\(432\) −10.3923 18.0000i −0.0240563 0.0416667i
\(433\) −646.579 −1.49325 −0.746627 0.665243i \(-0.768328\pi\)
−0.746627 + 0.665243i \(0.768328\pi\)
\(434\) 185.284 73.9150i 0.426921 0.170311i
\(435\) 0 0
\(436\) 56.2897 + 97.4966i 0.129105 + 0.223616i
\(437\) 368.454 638.181i 0.843144 1.46037i
\(438\) 153.541 + 88.6472i 0.350551 + 0.202391i
\(439\) −290.352 + 167.635i −0.661394 + 0.381856i −0.792808 0.609472i \(-0.791382\pi\)
0.131414 + 0.991328i \(0.458048\pi\)
\(440\) 0 0
\(441\) −140.944 41.7578i −0.319602 0.0946888i
\(442\) 315.341i 0.713441i
\(443\) 243.400 140.527i 0.549435 0.317216i −0.199459 0.979906i \(-0.563919\pi\)
0.748894 + 0.662690i \(0.230585\pi\)
\(444\) 144.494 + 83.4237i 0.325437 + 0.187891i
\(445\) 0 0
\(446\) 137.977 79.6613i 0.309366 0.178613i
\(447\) 144.500 0.323265
\(448\) −52.0139 + 20.7498i −0.116102 + 0.0463166i
\(449\) −47.2320 −0.105194 −0.0525969 0.998616i \(-0.516750\pi\)
−0.0525969 + 0.998616i \(0.516750\pi\)
\(450\) 0 0
\(451\) −579.181 334.390i −1.28422 0.741442i
\(452\) −129.888 74.9910i −0.287363 0.165909i
\(453\) −109.807 190.192i −0.242400 0.419850i
\(454\) 69.3253i 0.152699i
\(455\) 0 0
\(456\) 152.400 0.334212
\(457\) 509.909 294.396i 1.11578 0.644193i 0.175456 0.984487i \(-0.443860\pi\)
0.940319 + 0.340294i \(0.110527\pi\)
\(458\) −19.8797 + 34.4327i −0.0434055 + 0.0751805i
\(459\) −82.4840 + 142.866i −0.179704 + 0.311256i
\(460\) 0 0
\(461\) 60.5606i 0.131368i −0.997840 0.0656839i \(-0.979077\pi\)
0.997840 0.0656839i \(-0.0209229\pi\)
\(462\) −174.263 25.2717i −0.377193 0.0547007i
\(463\) 88.7592i 0.191704i −0.995396 0.0958522i \(-0.969442\pi\)
0.995396 0.0958522i \(-0.0305576\pi\)
\(464\) 18.3935 + 31.8584i 0.0396411 + 0.0686604i
\(465\) 0 0
\(466\) −124.594 + 215.803i −0.267369 + 0.463097i
\(467\) 151.112 + 261.733i 0.323580 + 0.560457i 0.981224 0.192872i \(-0.0617802\pi\)
−0.657644 + 0.753329i \(0.728447\pi\)
\(468\) −42.1404 −0.0900436
\(469\) −110.280 15.9928i −0.235138 0.0340997i
\(470\) 0 0
\(471\) 85.9416 + 148.855i 0.182466 + 0.316041i
\(472\) 155.308 269.002i 0.329043 0.569919i
\(473\) −26.9921 15.5839i −0.0570658 0.0329470i
\(474\) −225.806 + 130.369i −0.476383 + 0.275040i
\(475\) 0 0
\(476\) 349.045 + 275.180i 0.733288 + 0.578110i
\(477\) 4.14451i 0.00868869i
\(478\) −42.5170 + 24.5472i −0.0889478 + 0.0513540i
\(479\) −30.4237 17.5651i −0.0635151 0.0366704i 0.467906 0.883778i \(-0.345009\pi\)
−0.531421 + 0.847108i \(0.678342\pi\)
\(480\) 0 0
\(481\) 292.959 169.140i 0.609062 0.351642i
\(482\) −375.378 −0.778793
\(483\) 106.419 + 266.761i 0.220329 + 0.552301i
\(484\) 31.0723 0.0641989
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −55.9741 32.3167i −0.114937 0.0663586i 0.441430 0.897296i \(-0.354471\pi\)
−0.556366 + 0.830937i \(0.687805\pi\)
\(488\) 56.1327 + 97.2247i 0.115026 + 0.199231i
\(489\) 483.207i 0.988153i
\(490\) 0 0
\(491\) 241.365 0.491578 0.245789 0.969323i \(-0.420953\pi\)
0.245789 + 0.969323i \(0.420953\pi\)
\(492\) −195.368 + 112.796i −0.397089 + 0.229260i
\(493\) 145.989 252.861i 0.296125 0.512903i
\(494\) 154.494 267.592i 0.312742 0.541685i
\(495\) 0 0
\(496\) 80.6033i 0.162507i
\(497\) 346.860 138.373i 0.697908 0.278416i
\(498\) 121.078i 0.243128i
\(499\) −95.8123 165.952i −0.192009 0.332569i 0.753907 0.656981i \(-0.228167\pi\)
−0.945916 + 0.324412i \(0.894834\pi\)
\(500\) 0 0
\(501\) 25.9318 44.9152i 0.0517601 0.0896511i
\(502\) 17.0924 + 29.6049i 0.0340486 + 0.0589739i
\(503\) −919.711 −1.82845 −0.914226 0.405205i \(-0.867200\pi\)
−0.914226 + 0.405205i \(0.867200\pi\)
\(504\) −36.7735 + 46.6445i −0.0729634 + 0.0925485i
\(505\) 0 0
\(506\) 172.016 + 297.941i 0.339953 + 0.588816i
\(507\) 103.639 179.508i 0.204416 0.354059i
\(508\) 222.575 + 128.504i 0.438140 + 0.252960i
\(509\) −250.976 + 144.901i −0.493076 + 0.284678i −0.725850 0.687853i \(-0.758553\pi\)
0.232773 + 0.972531i \(0.425220\pi\)
\(510\) 0 0
\(511\) 72.7154 501.416i 0.142300 0.981244i
\(512\) 22.6274i 0.0441942i
\(513\) 139.989 80.8225i 0.272883 0.157549i
\(514\) −11.6810 6.74401i −0.0227256 0.0131206i
\(515\) 0 0
\(516\) −9.10492 + 5.25673i −0.0176452 + 0.0101875i
\(517\) 636.163 1.23049
\(518\) 68.4307 471.870i 0.132106 0.910946i
\(519\) 184.474 0.355441
\(520\) 0 0
\(521\) −653.176 377.112i −1.25370 0.723823i −0.281856 0.959457i \(-0.590950\pi\)
−0.971842 + 0.235634i \(0.924283\pi\)
\(522\) 33.7909 + 19.5092i 0.0647336 + 0.0373740i
\(523\) −37.8638 65.5821i −0.0723974 0.125396i 0.827554 0.561386i \(-0.189732\pi\)
−0.899952 + 0.435990i \(0.856398\pi\)
\(524\) 150.993i 0.288154i
\(525\) 0 0
\(526\) −186.483 −0.354530
\(527\) −554.040 + 319.875i −1.05131 + 0.606974i
\(528\) −35.5748 + 61.6174i −0.0673765 + 0.116700i
\(529\) 16.0662 27.8275i 0.0303709 0.0526039i
\(530\) 0 0
\(531\) 329.458i 0.620449i
\(532\) −161.375 404.520i −0.303336 0.760376i
\(533\) 457.382i 0.858128i
\(534\) 201.960 + 349.805i 0.378202 + 0.655066i
\(535\) 0 0
\(536\) −22.5129 + 38.9935i −0.0420017 + 0.0727491i
\(537\) −207.822 359.959i −0.387007 0.670315i
\(538\) 53.5689 0.0995705
\(539\) 117.446 + 489.311i 0.217895 + 0.907813i
\(540\) 0 0
\(541\) −493.177 854.207i −0.911602 1.57894i −0.811802 0.583933i \(-0.801513\pi\)
−0.0998002 0.995007i \(-0.531820\pi\)
\(542\) 256.217 443.782i 0.472726 0.818785i
\(543\) −463.984 267.881i −0.854482 0.493335i
\(544\) 155.533 89.7972i 0.285907 0.165068i
\(545\) 0 0
\(546\) 44.6218 + 111.854i 0.0817250 + 0.204861i
\(547\) 346.700i 0.633820i 0.948456 + 0.316910i \(0.102645\pi\)
−0.948456 + 0.316910i \(0.897355\pi\)
\(548\) −186.224 + 107.517i −0.339825 + 0.196198i
\(549\) 103.122 + 59.5377i 0.187837 + 0.108448i
\(550\) 0 0
\(551\) −247.768 + 143.049i −0.449669 + 0.259617i
\(552\) 116.048 0.210232
\(553\) 585.143 + 461.315i 1.05813 + 0.834204i
\(554\) 160.229 0.289222
\(555\) 0 0
\(556\) −471.124 272.004i −0.847346 0.489215i
\(557\) 132.891 + 76.7246i 0.238583 + 0.137746i 0.614525 0.788897i \(-0.289348\pi\)
−0.375942 + 0.926643i \(0.622681\pi\)
\(558\) −42.7464 74.0389i −0.0766064 0.132686i
\(559\) 21.3158i 0.0381320i
\(560\) 0 0
\(561\) 564.716 1.00662
\(562\) −218.905 + 126.385i −0.389511 + 0.224884i
\(563\) 87.0695 150.809i 0.154653 0.267866i −0.778280 0.627918i \(-0.783907\pi\)
0.932933 + 0.360051i \(0.117241\pi\)
\(564\) 107.294 185.839i 0.190238 0.329502i
\(565\) 0 0
\(566\) 61.0495i 0.107861i
\(567\) −9.04169 + 62.3478i −0.0159465 + 0.109961i
\(568\) 150.893i 0.265658i
\(569\) −109.591 189.817i −0.192603 0.333597i 0.753509 0.657437i \(-0.228359\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(570\) 0 0
\(571\) −478.914 + 829.504i −0.838729 + 1.45272i 0.0522282 + 0.998635i \(0.483368\pi\)
−0.890958 + 0.454087i \(0.849966\pi\)
\(572\) 72.1272 + 124.928i 0.126097 + 0.218406i
\(573\) 5.35135 0.00933917
\(574\) 506.268 + 399.132i 0.882001 + 0.695351i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 518.944 898.838i 0.899384 1.55778i 0.0710997 0.997469i \(-0.477349\pi\)
0.828284 0.560309i \(-0.189318\pi\)
\(578\) −880.521 508.369i −1.52339 0.879531i
\(579\) 358.046 206.718i 0.618387 0.357026i
\(580\) 0 0
\(581\) −321.380 + 128.208i −0.553149 + 0.220667i
\(582\) 121.200i 0.208248i
\(583\) −12.2867 + 7.09371i −0.0210749 + 0.0121676i
\(584\) −177.294 102.361i −0.303586 0.175276i
\(585\) 0 0
\(586\) 18.9132 10.9195i 0.0322751 0.0186340i
\(587\) −819.162 −1.39551 −0.697753 0.716339i \(-0.745817\pi\)
−0.697753 + 0.716339i \(0.745817\pi\)
\(588\) 162.748 + 48.2177i 0.276783 + 0.0820029i
\(589\) 626.864 1.06429
\(590\) 0 0
\(591\) 437.308 + 252.480i 0.739946 + 0.427208i
\(592\) −166.847 96.3294i −0.281837 0.162719i
\(593\) −266.689 461.919i −0.449729 0.778953i 0.548639 0.836059i \(-0.315146\pi\)
−0.998368 + 0.0571059i \(0.981813\pi\)
\(594\) 75.4655i 0.127046i
\(595\) 0 0
\(596\) −166.854 −0.279956
\(597\) 362.387 209.224i 0.607013 0.350459i
\(598\) 117.643 203.763i 0.196727 0.340741i
\(599\) −171.452 + 296.963i −0.286230 + 0.495765i −0.972907 0.231198i \(-0.925735\pi\)
0.686677 + 0.726963i \(0.259069\pi\)
\(600\) 0 0
\(601\) 418.941i 0.697073i −0.937295 0.348536i \(-0.886679\pi\)
0.937295 0.348536i \(-0.113321\pi\)
\(602\) 23.5941 + 18.6011i 0.0391929 + 0.0308989i
\(603\) 47.7571i 0.0791992i
\(604\) 126.795 + 219.615i 0.209925 + 0.363601i
\(605\) 0 0
\(606\) −165.185 + 286.108i −0.272582 + 0.472126i
\(607\) 70.7875 + 122.608i 0.116619 + 0.201989i 0.918426 0.395594i \(-0.129461\pi\)
−0.801807 + 0.597583i \(0.796128\pi\)
\(608\) −175.977 −0.289436
\(609\) 16.0030 110.350i 0.0262775 0.181199i
\(610\) 0 0
\(611\) −217.537 376.786i −0.356035 0.616670i
\(612\) 95.2443 164.968i 0.155628 0.269556i
\(613\) −257.244 148.520i −0.419647 0.242284i 0.275279 0.961364i \(-0.411230\pi\)
−0.694926 + 0.719081i \(0.744563\pi\)
\(614\) 287.384 165.921i 0.468053 0.270230i
\(615\) 0 0
\(616\) 201.222 + 29.1813i 0.326659 + 0.0473722i
\(617\) 674.329i 1.09292i −0.837486 0.546458i \(-0.815976\pi\)
0.837486 0.546458i \(-0.184024\pi\)
\(618\) −79.3418 + 45.8080i −0.128385 + 0.0741230i
\(619\) 833.055 + 480.965i 1.34581 + 0.777003i 0.987653 0.156659i \(-0.0500724\pi\)
0.358156 + 0.933662i \(0.383406\pi\)
\(620\) 0 0
\(621\) 106.597 61.5438i 0.171654 0.0991044i
\(622\) −563.957 −0.906683
\(623\) 714.643 906.471i 1.14710 1.45501i
\(624\) 48.6595 0.0779800
\(625\) 0 0
\(626\) −158.238 91.3585i −0.252776 0.145940i
\(627\) −479.208 276.671i −0.764287 0.441261i
\(628\) −99.2368 171.883i −0.158020 0.273699i
\(629\) 1529.14i 2.43106i
\(630\) 0 0
\(631\) 1185.17 1.87824 0.939122 0.343584i \(-0.111641\pi\)
0.939122 + 0.343584i \(0.111641\pi\)
\(632\) 260.738 150.537i 0.412560 0.238191i
\(633\) 227.781 394.527i 0.359843 0.623266i
\(634\) −284.657 + 493.040i −0.448985 + 0.777666i
\(635\) 0 0
\(636\) 4.78566i 0.00752463i
\(637\) 249.648 236.882i 0.391912 0.371871i
\(638\) 133.567i 0.209353i
\(639\) −80.0234 138.605i −0.125232 0.216908i
\(640\) 0 0
\(641\) −203.549 + 352.557i −0.317549 + 0.550011i −0.979976 0.199115i \(-0.936193\pi\)
0.662427 + 0.749126i \(0.269526\pi\)
\(642\) −30.3688 52.6002i −0.0473034 0.0819318i
\(643\) 1077.83 1.67626 0.838128 0.545474i \(-0.183650\pi\)
0.838128 + 0.545474i \(0.183650\pi\)
\(644\) −122.882 308.029i −0.190810 0.478306i
\(645\) 0 0
\(646\) 698.367 + 1209.61i 1.08106 + 1.87246i
\(647\) −588.349 + 1019.05i −0.909350 + 1.57504i −0.0943805 + 0.995536i \(0.530087\pi\)
−0.814969 + 0.579504i \(0.803246\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) −976.701 + 563.899i −1.50493 + 0.868873i
\(650\) 0 0
\(651\) −151.260 + 191.861i −0.232349 + 0.294718i
\(652\) 557.959i 0.855765i
\(653\) 761.345 439.563i 1.16592 0.673144i 0.213204 0.977008i \(-0.431610\pi\)
0.952715 + 0.303864i \(0.0982769\pi\)
\(654\) −119.408 68.9405i −0.182582 0.105414i
\(655\) 0 0
\(656\) 225.591 130.245i 0.343889 0.198545i
\(657\) −217.140 −0.330503
\(658\) −606.890 88.0113i −0.922325 0.133756i
\(659\) −65.1550 −0.0988696 −0.0494348 0.998777i \(-0.515742\pi\)
−0.0494348 + 0.998777i \(0.515742\pi\)
\(660\) 0 0
\(661\) 22.0376 + 12.7234i 0.0333397 + 0.0192487i 0.516577 0.856241i \(-0.327206\pi\)
−0.483237 + 0.875489i \(0.660539\pi\)
\(662\) 204.401 + 118.011i 0.308762 + 0.178264i
\(663\) −193.106 334.469i −0.291261 0.504479i
\(664\) 139.809i 0.210555i
\(665\) 0 0
\(666\) −204.345 −0.306825
\(667\) −188.667 + 108.927i −0.282860 + 0.163309i
\(668\) −29.9435 + 51.8636i −0.0448256 + 0.0776401i
\(669\) −97.5647 + 168.987i −0.145837 + 0.252597i
\(670\) 0 0
\(671\) 407.618i 0.607478i
\(672\) 42.4624 53.8604i 0.0631881 0.0801494i
\(673\) 23.1893i 0.0344566i −0.999852 0.0172283i \(-0.994516\pi\)
0.999852 0.0172283i \(-0.00548420\pi\)
\(674\) −382.822 663.068i −0.567986 0.983780i
\(675\) 0 0
\(676\) −119.672 + 207.278i −0.177029 + 0.306624i
\(677\) −71.0658 123.090i −0.104972 0.181816i 0.808755 0.588146i \(-0.200142\pi\)
−0.913727 + 0.406330i \(0.866809\pi\)
\(678\) 183.690 0.270929
\(679\) 321.705 128.337i 0.473792 0.189009i
\(680\) 0 0
\(681\) −42.4529 73.5306i −0.0623391 0.107974i
\(682\) −146.329 + 253.449i −0.214558 + 0.371626i
\(683\) 568.722 + 328.352i 0.832682 + 0.480749i 0.854770 0.519007i \(-0.173698\pi\)
−0.0220879 + 0.999756i \(0.507031\pi\)
\(684\) −161.645 + 93.3258i −0.236323 + 0.136441i
\(685\) 0 0
\(686\) −44.3466 483.044i −0.0646452 0.704146i
\(687\) 48.6951i 0.0708808i
\(688\) 10.5135 6.06994i 0.0152812 0.00882259i
\(689\) 8.40290 + 4.85142i 0.0121958 + 0.00704125i
\(690\) 0 0
\(691\) 212.350 122.600i 0.307308 0.177425i −0.338413 0.940998i \(-0.609890\pi\)
0.645721 + 0.763573i \(0.276557\pi\)
\(692\) −213.012 −0.307821
\(693\) 200.310 79.9094i 0.289047 0.115309i
\(694\) −606.250 −0.873560
\(695\) 0 0
\(696\) −39.0184 22.5273i −0.0560610 0.0323668i
\(697\) −1790.52 1033.76i −2.56890 1.48316i
\(698\) −52.8104 91.4702i −0.0756595 0.131046i
\(699\) 305.192i 0.436612i
\(700\) 0 0
\(701\) 379.419 0.541254 0.270627 0.962684i \(-0.412769\pi\)
0.270627 + 0.962684i \(0.412769\pi\)
\(702\) 44.6966 25.8056i 0.0636704 0.0367601i
\(703\) 749.168 1297.60i 1.06567 1.84580i
\(704\) 41.0782 71.1496i 0.0583498 0.101065i
\(705\) 0 0
\(706\) 517.479i 0.732973i
\(707\) 934.335 + 135.498i 1.32155 + 0.191651i
\(708\) 380.426i 0.537324i
\(709\) −442.054 765.661i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(710\) 0 0
\(711\) 159.669 276.554i 0.224569 0.388965i
\(712\) −233.203 403.920i −0.327533 0.567304i
\(713\) 477.337 0.669477
\(714\) −538.731 78.1269i −0.754525 0.109421i
\(715\) 0 0
\(716\) 239.973 + 415.645i 0.335157 + 0.580510i
\(717\) 30.0641 52.0725i 0.0419304 0.0726255i
\(718\) −609.416 351.847i −0.848769 0.490037i
\(719\) 825.831 476.794i 1.14858 0.663135i 0.200042 0.979787i \(-0.435892\pi\)
0.948542 + 0.316653i \(0.102559\pi\)
\(720\) 0 0
\(721\) 205.603 + 162.093i 0.285164 + 0.224817i
\(722\) 858.068i 1.18846i
\(723\) 398.149 229.871i 0.550690 0.317941i
\(724\) 535.762 + 309.322i 0.740003 + 0.427241i
\(725\) 0 0
\(726\) −32.9571 + 19.0278i −0.0453955 + 0.0262091i
\(727\) −1110.82 −1.52795 −0.763974 0.645248i \(-0.776754\pi\)
−0.763974 + 0.645248i \(0.776754\pi\)
\(728\) −51.5249 129.158i −0.0707759 0.177415i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −83.4455 48.1773i −0.114153 0.0659060i
\(732\) −119.075 68.7483i −0.162671 0.0939184i
\(733\) −20.3571 35.2595i −0.0277722 0.0481029i 0.851805 0.523859i \(-0.175508\pi\)
−0.879577 + 0.475756i \(0.842175\pi\)
\(734\) 197.102i 0.268531i
\(735\) 0 0
\(736\) −134.001 −0.182066
\(737\) 141.579 81.7407i 0.192102 0.110910i
\(738\) 138.146 239.276i 0.187190 0.324222i
\(739\) 422.735 732.199i 0.572037 0.990797i −0.424320 0.905512i \(-0.639487\pi\)
0.996357 0.0852847i \(-0.0271800\pi\)
\(740\) 0 0
\(741\) 378.433i 0.510705i
\(742\) 12.7027 5.06747i 0.0171195 0.00682947i
\(743\) 355.319i 0.478222i −0.970992 0.239111i \(-0.923144\pi\)
0.970992 0.239111i \(-0.0768559\pi\)
\(744\) 49.3592 + 85.4927i 0.0663431 + 0.114910i
\(745\) 0 0
\(746\) −245.733 + 425.623i −0.329401 + 0.570540i
\(747\) 74.1447 + 128.422i 0.0992567 + 0.171918i
\(748\) −652.078 −0.871762
\(749\) −107.461 + 136.306i −0.143473 + 0.181984i
\(750\) 0 0
\(751\) −108.768 188.392i −0.144831 0.250855i 0.784479 0.620156i \(-0.212931\pi\)
−0.929310 + 0.369300i \(0.879597\pi\)
\(752\) −123.893 + 214.589i −0.164751 + 0.285357i
\(753\) −36.2584 20.9338i −0.0481520 0.0278006i
\(754\) −79.1091 + 45.6737i −0.104919 + 0.0605751i
\(755\) 0 0
\(756\) 10.4404 71.9930i 0.0138101 0.0952289i
\(757\) 1178.25i 1.55647i 0.627975 + 0.778233i \(0.283884\pi\)
−0.627975 + 0.778233i \(0.716116\pi\)
\(758\) −376.471 + 217.356i −0.496663 + 0.286749i
\(759\) −364.902 210.676i −0.480766 0.277571i
\(760\) 0 0
\(761\) 711.636 410.863i 0.935133 0.539899i 0.0467017 0.998909i \(-0.485129\pi\)
0.888431 + 0.459010i \(0.151796\pi\)
\(762\) −314.769 −0.413082
\(763\) −56.5504 + 389.948i −0.0741159 + 0.511073i
\(764\) −6.17920 −0.00808796
\(765\) 0 0
\(766\) 623.063 + 359.725i 0.813398 + 0.469615i
\(767\) 667.970 + 385.653i 0.870887 + 0.502807i
\(768\) −13.8564 24.0000i −0.0180422 0.0312500i
\(769\) 230.888i 0.300244i 0.988667 + 0.150122i \(0.0479667\pi\)
−0.988667 + 0.150122i \(0.952033\pi\)
\(770\) 0 0
\(771\) 16.5194 0.0214259
\(772\) −413.436 + 238.697i −0.535539 + 0.309193i
\(773\) 337.234 584.107i 0.436267 0.755636i −0.561131 0.827727i \(-0.689634\pi\)
0.997398 + 0.0720908i \(0.0229671\pi\)
\(774\) 6.43815 11.1512i 0.00831802 0.0144072i
\(775\) 0 0
\(776\) 139.950i 0.180348i
\(777\) 216.378 + 542.399i 0.278479 + 0.698068i
\(778\) 241.785i 0.310778i
\(779\) 1012.94 + 1754.46i 1.30030 + 2.25219i
\(780\) 0 0
\(781\) −273.935 + 474.469i −0.350749 + 0.607515i
\(782\) 531.784 + 921.077i 0.680031 + 1.17785i
\(783\) −47.7876