Properties

Label 1050.3.q.e.649.13
Level $1050$
Weight $3$
Character 1050.649
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 649.13
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.e.199.14

$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.532482 0.846441i \(-0.321259\pi\)
−0.999281 + 0.0379228i \(0.987926\pi\)
\(12\) 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 −0.776816 0.629727i \(-0.783167\pi\)
−0.156951 0.987606i \(-0.550167\pi\)
\(18\) −3.67423 + 2.12132i −0.204124 + 0.117851i
\(19\) 26.9408 + 15.5543i 1.41794 + 0.818648i 0.996118 0.0880311i \(-0.0280575\pi\)
0.421822 + 0.906679i \(0.361391\pi\)
\(20\) 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 0.874576 0.484888i \(-0.161140\pi\)
0.0173632 + 0.999849i \(0.494473\pi\)
\(24\) 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 −0.191385 0.981515i \(-0.561298\pi\)
0.754325 + 0.656502i \(0.227965\pi\)
\(32\) −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 0.943266 0.332037i \(-0.107736\pi\)
0.184081 + 0.982911i \(0.441069\pi\)
\(38\) 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 \(-0.707902\pi\)
0.607685 0.794178i \(-0.292098\pi\)
\(42\) 6.35331 15.9259i 0.151269 0.379189i
\(43\) 3.03497i 0.0705807i −0.999377 0.0352904i \(-0.988764\pi\)
0.999377 0.0352904i \(-0.0112356\pi\)
\(44\) 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 0.321869 + 0.946784i \(0.395689\pi\)
−0.980874 + 0.194645i \(0.937644\pi\)
\(48\) 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 −0.488671 0.872468i \(-0.662518\pi\)
0.511244 + 0.859435i \(0.329185\pi\)
\(54\) 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 0.623061 0.782173i \(-0.285889\pi\)
0.988912 0.148500i \(-0.0474445\pi\)
\(60\) 0 0
\(61\) −34.3741 19.8459i −0.563510 0.325343i 0.191043 0.981582i \(-0.438813\pi\)
−0.754553 + 0.656239i \(0.772146\pi\)
\(62\) 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 −0.599342 0.800493i \(-0.704571\pi\)
0.393576 + 0.919292i \(0.371238\pi\)
\(68\) 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 0.999988 0.00489557i \(-0.00155831\pi\)
−0.504234 + 0.863567i \(0.668225\pi\)
\(74\) 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 −0.303138 0.952947i \(-0.598034\pi\)
0.976845 0.213948i \(-0.0686325\pi\)
\(80\) 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 0.990555 + 0.137114i \(0.0437826\pi\)
0.614022 + 0.789289i \(0.289551\pi\)
\(90\) 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 0.206012 0.978549i \(-0.433951\pi\)
0.950455 + 0.310863i \(0.100618\pi\)
\(102\) −67.3479 + 38.8833i −0.660274 + 0.381209i
\(103\) 18.7010 32.3911i 0.181563 0.314477i −0.760850 0.648928i \(-0.775218\pi\)
0.942413 + 0.334451i \(0.108551\pi\)
\(104\) 19.8652i 0.191011i
\(105\) 0 0
\(106\) 1.95374 0.0184315
\(107\) −21.4739 12.3980i −0.200691 0.115869i 0.396287 0.918127i \(-0.370299\pi\)
−0.596978 + 0.802258i \(0.703632\pi\)
\(108\) 5.19615 + 9.00000i 0.0481125 + 0.0833333i
\(109\) −28.1448 48.7483i −0.258209 0.447232i 0.707553 0.706660i \(-0.249799\pi\)
−0.965762 + 0.259429i \(0.916466\pi\)
\(110\) 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 \(0.107662\pi\)
−0.943343 + 0.331818i \(0.892338\pi\)
\(114\) 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 \(-0.831153\pi\)
0.862580 0.505921i \(-0.168847\pi\)
\(128\) −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 0.728341 0.685215i \(-0.240292\pi\)
−0.229243 + 0.973369i \(0.573625\pi\)
\(132\) −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 −0.799723 0.600369i \(-0.795020\pi\)
0.120073 + 0.992765i \(0.461687\pi\)
\(138\) 29.0120 50.2503i 0.210232 0.364133i
\(139\) 272.004i 1.95686i 0.206576 + 0.978431i \(0.433768\pi\)
−0.206576 + 0.978431i \(0.566232\pi\)
\(140\) 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 −0.971374 0.237557i \(-0.923653\pi\)
0.691417 + 0.722456i \(0.256987\pi\)
\(150\) 0 0
\(151\) −63.3973 109.807i −0.419850 0.727201i 0.576074 0.817397i \(-0.304584\pi\)
−0.995924 + 0.0901962i \(0.971251\pi\)
\(152\) −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 0.979658 0.200673i \(-0.0643130\pi\)
−0.663617 + 0.748072i \(0.730980\pi\)
\(158\) 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 −0.482433 0.875933i \(-0.660247\pi\)
−0.999797 + 0.0201678i \(0.993580\pi\)
\(164\) 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 −0.977885 0.209142i \(-0.932933\pi\)
0.670065 + 0.742303i \(0.266266\pi\)
\(174\) 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 −0.977815 0.209471i \(-0.932826\pi\)
0.307500 0.951548i \(-0.400508\pi\)
\(180\) 0 0
\(181\) 309.322i 1.70896i −0.519482 0.854482i \(-0.673875\pi\)
0.519482 0.854482i \(-0.326125\pi\)
\(182\) 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 −0.870041 0.492979i \(-0.835908\pi\)
0.861953 + 0.506988i \(0.169241\pi\)
\(192\) 6.92820 + 12.0000i 0.0360844 + 0.0625000i
\(193\) −206.718 + 119.349i −1.07108 + 0.618387i −0.928476 0.371393i \(-0.878880\pi\)
−0.142602 + 0.989780i \(0.545547\pi\)
\(194\) 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 \(0.265149\pi\)
−0.672666 + 0.739946i \(0.734851\pi\)
\(198\) 37.7328 + 21.7850i 0.190570 + 0.110025i
\(199\) −209.224 + 120.796i −1.05138 + 0.607013i −0.923034 0.384717i \(-0.874299\pi\)
−0.128342 + 0.991730i \(0.540966\pi\)
\(200\) 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 0.806975 0.590585i \(-0.201103\pi\)
−0.914950 + 0.403568i \(0.867770\pi\)
\(228\) 93.3258 53.8817i 0.409324 0.236323i
\(229\) −24.3476 14.0571i −0.106321 0.0613846i 0.445896 0.895085i \(-0.352885\pi\)
−0.552218 + 0.833700i \(0.686218\pi\)
\(230\) 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 0.135420 0.990788i \(-0.456762\pi\)
−0.790338 + 0.612671i \(0.790095\pi\)
\(234\) −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 −0.894266 0.447535i \(-0.852302\pi\)
−0.0595563 + 0.998225i \(0.518969\pi\)
\(242\) 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 \(-0.984667\pi\)
0.998840 0.0481520i \(-0.0153332\pi\)
\(252\) −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 −0.875154 0.483844i \(-0.839240\pi\)
0.856599 + 0.515983i \(0.172573\pi\)
\(258\) −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 −0.701138 0.713026i \(-0.747324\pi\)
0.266929 + 0.963716i \(0.413991\pi\)
\(264\) −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 −0.437785 0.899080i \(-0.644237\pi\)
0.559733 + 0.828673i \(0.310904\pi\)
\(270\) 0 0
\(271\) 313.801 + 181.173i 1.15794 + 0.668535i 0.950809 0.309779i \(-0.100255\pi\)
0.207128 + 0.978314i \(0.433588\pi\)
\(272\) 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 −0.312321 0.949977i \(-0.601106\pi\)
0.666544 + 0.745466i \(0.267773\pi\)
\(278\) −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 0.901638 0.432492i \(-0.142366\pi\)
−0.825368 + 0.564595i \(0.809032\pi\)
\(284\) 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 −0.938947 0.344061i \(-0.888197\pi\)
−0.171508 + 0.985183i \(0.554864\pi\)
\(312\) 29.7978 17.2037i 0.0955056 0.0551402i
\(313\) −64.6002 + 111.891i −0.206390 + 0.357479i −0.950575 0.310495i \(-0.899505\pi\)
0.744184 + 0.667974i \(0.232838\pi\)
\(314\) 140.342i 0.446949i
\(315\) 0 0
\(316\) 212.892 0.673707
\(317\) −348.632 201.283i −1.09979 0.634961i −0.163621 0.986523i \(-0.552317\pi\)
−0.936165 + 0.351562i \(0.885651\pi\)
\(318\) −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 −0.712001 0.702178i \(-0.752211\pi\)
0.964105 + 0.265522i \(0.0855443\pi\)
\(332\) −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 \(0.296899\pi\)
−0.595638 + 0.803253i \(0.703101\pi\)
\(338\) −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 −0.928151 0.372204i \(-0.878602\pi\)
−0.141737 + 0.989904i \(0.545269\pi\)
\(348\) −15.9292 + 27.5902i −0.0457736 + 0.0792822i
\(349\) 74.6851i 0.213998i 0.994259 + 0.106999i \(0.0341241\pi\)
−0.994259 + 0.106999i \(0.965876\pi\)
\(350\) 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 0.999774 + 0.0212499i \(0.00676457\pi\)
−0.481484 + 0.876455i \(0.659902\pi\)
\(354\) −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 0.277828 + 0.960631i \(0.410386\pi\)
−0.970845 + 0.239710i \(0.922948\pi\)
\(360\) 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 0.755330 0.655345i \(-0.227477\pi\)
−0.945210 + 0.326462i \(0.894143\pi\)
\(368\) −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 0.0390009 0.999239i \(-0.487582\pi\)
−0.845866 + 0.533395i \(0.820916\pi\)
\(374\) −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 −0.315382 0.948965i \(-0.602133\pi\)
0.979519 0.201353i \(-0.0645339\pi\)
\(384\) 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 0.734979 0.678090i \(-0.237192\pi\)
−0.954732 + 0.297466i \(0.903859\pi\)
\(390\) 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 −0.116906 0.993143i \(-0.537298\pi\)
0.918540 0.395328i \(-0.129369\pi\)
\(398\) −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 −0.214773 0.976664i \(-0.568901\pi\)
0.953202 0.302333i \(-0.0977654\pi\)
\(402\) 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 −0.168571 0.985690i \(-0.553915\pi\)
0.769347 + 0.638831i \(0.220582\pi\)
\(410\) 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 \(-0.804695\pi\)
0.817599 0.575789i \(-0.195305\pi\)
\(420\) 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 0.678446 0.734650i \(-0.262654\pi\)
−0.975449 + 0.220226i \(0.929320\pi\)
\(432\) −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 0.131414 0.991328i \(-0.458048\pi\)
−0.792808 + 0.609472i \(0.791382\pi\)
\(440\) 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 0.748894 0.662690i \(-0.230585\pi\)
−0.199459 + 0.979906i \(0.563919\pi\)
\(444\) 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 0.940319 0.340294i \(-0.110527\pi\)
0.175456 + 0.984487i \(0.443860\pi\)
\(458\) −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 \(0.0209229\pi\)
−0.997840 + 0.0656839i \(0.979077\pi\)
\(462\) −174.263 + 25.2717i −0.377193 + 0.0547007i
\(463\) 88.7592i 0.191704i 0.995396 + 0.0958522i \(0.0305576\pi\)
−0.995396 + 0.0958522i \(0.969442\pi\)
\(464\) 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 −0.657644 0.753329i \(-0.728447\pi\)
0.981224 + 0.192872i \(0.0617802\pi\)
\(468\) −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 −0.531421 0.847108i \(-0.678342\pi\)
0.467906 + 0.883778i \(0.345009\pi\)
\(480\) 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 −0.556366 0.830937i \(-0.687805\pi\)
0.441430 + 0.897296i \(0.354471\pi\)
\(488\) 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 −0.945916 0.324412i \(-0.894834\pi\)
0.753907 + 0.656981i \(0.228167\pi\)
\(500\) 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 0.232773 0.972531i \(-0.425220\pi\)
−0.725850 + 0.687853i \(0.758553\pi\)
\(510\) 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 −0.971842 0.235634i \(-0.924283\pi\)
−0.281856 + 0.959457i \(0.590950\pi\)
\(522\) 33.7909 19.5092i 0.0647336 0.0373740i
\(523\) −37.8638 + 65.5821i −0.0723974 + 0.125396i −0.899952 0.435990i \(-0.856398\pi\)
0.827554 + 0.561386i \(0.189732\pi\)
\(524\) 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 −0.0998002 + 0.995007i \(0.531820\pi\)
−0.811802 + 0.583933i \(0.801513\pi\)
\(542\) 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 \(-0.897355\pi\)
0.948456 0.316910i \(-0.102645\pi\)
\(548\) −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 −0.375942 0.926643i \(-0.622681\pi\)
0.614525 + 0.788897i \(0.289348\pi\)
\(558\) −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 0.932933 0.360051i \(-0.117241\pi\)
−0.778280 + 0.627918i \(0.783907\pi\)
\(564\) 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 −0.946112 0.323840i \(-0.895026\pi\)
0.753509 + 0.657437i \(0.228359\pi\)
\(570\) 0 0
\(571\) −478.914 829.504i −0.838729 1.45272i −0.890958 0.454087i \(-0.849966\pi\)
0.0522282 0.998635i \(-0.483368\pi\)
\(572\) 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 0.828284 + 0.560309i \(0.189318\pi\)
0.0710997 + 0.997469i \(0.477349\pi\)
\(578\) −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 −0.998368 0.0571059i \(-0.981813\pi\)
0.548639 + 0.836059i \(0.315146\pi\)
\(594\) 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 0.686677 0.726963i \(-0.259069\pi\)
−0.972907 + 0.231198i \(0.925735\pi\)
\(600\) 0 0
\(601\) 418.941i 0.697073i 0.937295 + 0.348536i \(0.113321\pi\)
−0.937295 + 0.348536i \(0.886679\pi\)
\(602\) 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 −0.801807 0.597583i \(-0.796128\pi\)
0.918426 + 0.395594i \(0.129461\pi\)
\(608\) −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 −0.694926 0.719081i \(-0.744563\pi\)
0.275279 + 0.961364i \(0.411230\pi\)
\(614\) 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 \(0.184024\pi\)
−0.837486 + 0.546458i \(0.815976\pi\)
\(618\) −79.3418 45.8080i −0.128385 0.0741230i
\(619\) 833.055 480.965i 1.34581 0.777003i 0.358156 0.933662i \(-0.383406\pi\)
0.987653 + 0.156659i \(0.0500724\pi\)
\(620\) 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 0.662427 0.749126i \(-0.269526\pi\)
−0.979976 + 0.199115i \(0.936193\pi\)
\(642\) −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 −0.814969 0.579504i \(-0.803246\pi\)
−0.0943805 0.995536i \(-0.530087\pi\)
\(648\) 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 0.952715 0.303864i \(-0.0982769\pi\)
0.213204 + 0.977008i \(0.431610\pi\)
\(654\) −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 −0.483237 0.875489i \(-0.660539\pi\)
0.516577 + 0.856241i \(0.327206\pi\)
\(662\) 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 \(0.00548420\pi\)
−0.999852 + 0.0172283i \(0.994516\pi\)
\(674\) −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 −0.913727 0.406330i \(-0.866809\pi\)
0.808755 + 0.588146i \(0.200142\pi\)
\(678\) 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 −0.0220879 0.999756i \(-0.507031\pi\)
0.854770 + 0.519007i \(0.173698\pi\)
\(684\) −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 0.645721 0.763573i \(-0.276557\pi\)
−0.338413 + 0.940998i \(0.609890\pi\)
\(692\) −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 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(710\) 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 0.948542 0.316653i \(-0.102559\pi\)
0.200042 + 0.979787i \(0.435892\pi\)
\(720\) 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 −0.879577 0.475756i \(-0.842175\pi\)
0.851805 + 0.523859i \(0.175508\pi\)
\(734\) 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 0.996357 + 0.0852847i \(0.0271800\pi\)
−0.424320 + 0.905512i \(0.639487\pi\)
\(740\) 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 \(0.0768559\pi\)
−0.970992 + 0.239111i \(0.923144\pi\)
\(744\) 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 −0.929310 0.369300i \(-0.879597\pi\)
0.784479 + 0.620156i \(0.212931\pi\)
\(752\) −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 \(-0.716116\pi\)
0.627975 0.778233i \(-0.283884\pi\)
\(758\) −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 0.888431 0.459010i \(-0.151796\pi\)
0.0467017 + 0.998909i \(0.485129\pi\)
\(762\) −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 \(-0.952033\pi\)
0.988667 0.150122i \(-0.0479667\pi\)
\(770\) 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 0.997398 0.0720908i \(-0.0229671\pi\)
−0.561131 + 0.827727i \(0.689634\pi\)
\(774\) 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 −0.0610314