Properties

Label 731.2.j.a.135.4
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 135.4
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.4

$q$-expansion

\(f(q)\) \(=\) \(q-2.53253 q^{2} +(1.51123 + 0.872510i) q^{3} +4.41371 q^{4} +(3.60596 + 2.08190i) q^{5} +(-3.82724 - 2.20966i) q^{6} +(-0.435566 + 0.251474i) q^{7} -6.11280 q^{8} +(0.0225487 + 0.0390554i) q^{9} +O(q^{10})\) \(q-2.53253 q^{2} +(1.51123 + 0.872510i) q^{3} +4.41371 q^{4} +(3.60596 + 2.08190i) q^{5} +(-3.82724 - 2.20966i) q^{6} +(-0.435566 + 0.251474i) q^{7} -6.11280 q^{8} +(0.0225487 + 0.0390554i) q^{9} +(-9.13221 - 5.27248i) q^{10} -1.59267i q^{11} +(6.67015 + 3.85101i) q^{12} +(0.640573 + 1.10950i) q^{13} +(1.10309 - 0.636867i) q^{14} +(3.63296 + 6.29248i) q^{15} +6.65344 q^{16} +(4.03682 + 0.839103i) q^{17} +(-0.0571052 - 0.0989090i) q^{18} +(-0.250258 + 0.433460i) q^{19} +(15.9157 + 9.18892i) q^{20} -0.877656 q^{21} +4.03349i q^{22} +(3.28971 + 1.89932i) q^{23} +(-9.23786 - 5.33348i) q^{24} +(6.16864 + 10.6844i) q^{25} +(-1.62227 - 2.80985i) q^{26} -5.15637i q^{27} +(-1.92247 + 1.10994i) q^{28} +(-1.95615 + 1.12938i) q^{29} +(-9.20059 - 15.9359i) q^{30} +(-1.63893 - 0.946238i) q^{31} -4.62443 q^{32} +(1.38962 - 2.40689i) q^{33} +(-10.2234 - 2.12505i) q^{34} -2.09418 q^{35} +(0.0995233 + 0.172379i) q^{36} +(5.81239 + 3.35579i) q^{37} +(0.633787 - 1.09775i) q^{38} +2.23563i q^{39} +(-22.0425 - 12.7263i) q^{40} -6.19755i q^{41} +2.22269 q^{42} +(-6.53940 - 0.485992i) q^{43} -7.02959i q^{44} +0.187776i q^{45} +(-8.33130 - 4.81008i) q^{46} -6.41023 q^{47} +(10.0549 + 5.80519i) q^{48} +(-3.37352 + 5.84311i) q^{49} +(-15.6223 - 27.0586i) q^{50} +(5.36845 + 4.79025i) q^{51} +(2.82730 + 4.89703i) q^{52} +(3.53023 - 6.11455i) q^{53} +13.0587i q^{54} +(3.31578 - 5.74311i) q^{55} +(2.66253 - 1.53721i) q^{56} +(-0.756397 + 0.436706i) q^{57} +(4.95400 - 2.86020i) q^{58} +14.3759 q^{59} +(16.0349 + 27.7732i) q^{60} +(-7.69058 + 4.44016i) q^{61} +(4.15065 + 2.39638i) q^{62} +(-0.0196429 - 0.0113408i) q^{63} -1.59537 q^{64} +5.33444i q^{65} +(-3.51926 + 6.09553i) q^{66} +(2.31291 - 4.00608i) q^{67} +(17.8174 + 3.70356i) q^{68} +(3.31435 + 5.74062i) q^{69} +5.30358 q^{70} +(-5.91339 + 3.41410i) q^{71} +(-0.137835 - 0.238738i) q^{72} +(-4.59813 + 2.65473i) q^{73} +(-14.7201 - 8.49864i) q^{74} +21.5288i q^{75} +(-1.10457 + 1.91317i) q^{76} +(0.400516 + 0.693714i) q^{77} -5.66179i q^{78} +(-6.53529 + 3.77315i) q^{79} +(23.9920 + 13.8518i) q^{80} +(4.56663 - 7.90963i) q^{81} +15.6955i q^{82} +(5.31315 - 9.20265i) q^{83} -3.87372 q^{84} +(12.8097 + 11.4300i) q^{85} +(16.5612 + 1.23079i) q^{86} -3.94159 q^{87} +9.73568i q^{88} +(-5.12917 + 8.88398i) q^{89} -0.475550i q^{90} +(-0.558024 - 0.322175i) q^{91} +(14.5199 + 8.38304i) q^{92} +(-1.65120 - 2.85997i) q^{93} +16.2341 q^{94} +(-1.80484 + 1.04203i) q^{95} +(-6.98858 - 4.03486i) q^{96} +6.75116i q^{97} +(8.54355 - 14.7979i) q^{98} +(0.0622024 - 0.0359126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53253 −1.79077 −0.895385 0.445293i \(-0.853100\pi\)
−0.895385 + 0.445293i \(0.853100\pi\)
\(3\) 1.51123 + 0.872510i 0.872510 + 0.503744i 0.868182 0.496247i \(-0.165289\pi\)
0.00432871 + 0.999991i \(0.498622\pi\)
\(4\) 4.41371 2.20686
\(5\) 3.60596 + 2.08190i 1.61264 + 0.931055i 0.988757 + 0.149534i \(0.0477774\pi\)
0.623879 + 0.781521i \(0.285556\pi\)
\(6\) −3.82724 2.20966i −1.56247 0.902090i
\(7\) −0.435566 + 0.251474i −0.164629 + 0.0950484i −0.580051 0.814580i \(-0.696967\pi\)
0.415422 + 0.909629i \(0.363634\pi\)
\(8\) −6.11280 −2.16120
\(9\) 0.0225487 + 0.0390554i 0.00751622 + 0.0130185i
\(10\) −9.13221 5.27248i −2.88786 1.66731i
\(11\) 1.59267i 0.480208i −0.970747 0.240104i \(-0.922818\pi\)
0.970747 0.240104i \(-0.0771816\pi\)
\(12\) 6.67015 + 3.85101i 1.92551 + 1.11169i
\(13\) 0.640573 + 1.10950i 0.177663 + 0.307721i 0.941080 0.338185i \(-0.109813\pi\)
−0.763417 + 0.645906i \(0.776480\pi\)
\(14\) 1.10309 0.636867i 0.294812 0.170210i
\(15\) 3.63296 + 6.29248i 0.938027 + 1.62471i
\(16\) 6.65344 1.66336
\(17\) 4.03682 + 0.839103i 0.979072 + 0.203512i
\(18\) −0.0571052 0.0989090i −0.0134598 0.0233131i
\(19\) −0.250258 + 0.433460i −0.0574132 + 0.0994426i −0.893304 0.449454i \(-0.851619\pi\)
0.835890 + 0.548897i \(0.184952\pi\)
\(20\) 15.9157 + 9.18892i 3.55885 + 2.05471i
\(21\) −0.877656 −0.191520
\(22\) 4.03349i 0.859942i
\(23\) 3.28971 + 1.89932i 0.685953 + 0.396035i 0.802094 0.597198i \(-0.203719\pi\)
−0.116141 + 0.993233i \(0.537053\pi\)
\(24\) −9.23786 5.33348i −1.88567 1.08869i
\(25\) 6.16864 + 10.6844i 1.23373 + 2.13688i
\(26\) −1.62227 2.80985i −0.318153 0.551058i
\(27\) 5.15637i 0.992343i
\(28\) −1.92247 + 1.10994i −0.363312 + 0.209758i
\(29\) −1.95615 + 1.12938i −0.363247 + 0.209721i −0.670504 0.741906i \(-0.733922\pi\)
0.307257 + 0.951627i \(0.400589\pi\)
\(30\) −9.20059 15.9359i −1.67979 2.90948i
\(31\) −1.63893 0.946238i −0.294361 0.169949i 0.345546 0.938402i \(-0.387694\pi\)
−0.639907 + 0.768452i \(0.721027\pi\)
\(32\) −4.62443 −0.817491
\(33\) 1.38962 2.40689i 0.241902 0.418987i
\(34\) −10.2234 2.12505i −1.75329 0.364444i
\(35\) −2.09418 −0.353981
\(36\) 0.0995233 + 0.172379i 0.0165872 + 0.0287299i
\(37\) 5.81239 + 3.35579i 0.955552 + 0.551688i 0.894801 0.446465i \(-0.147317\pi\)
0.0607506 + 0.998153i \(0.480651\pi\)
\(38\) 0.633787 1.09775i 0.102814 0.178079i
\(39\) 2.23563i 0.357987i
\(40\) −22.0425 12.7263i −3.48523 2.01220i
\(41\) 6.19755i 0.967895i −0.875097 0.483948i \(-0.839202\pi\)
0.875097 0.483948i \(-0.160798\pi\)
\(42\) 2.22269 0.342969
\(43\) −6.53940 0.485992i −0.997250 0.0741130i
\(44\) 7.02959i 1.05975i
\(45\) 0.187776i 0.0279921i
\(46\) −8.33130 4.81008i −1.22838 0.709208i
\(47\) −6.41023 −0.935028 −0.467514 0.883986i \(-0.654850\pi\)
−0.467514 + 0.883986i \(0.654850\pi\)
\(48\) 10.0549 + 5.80519i 1.45130 + 0.837907i
\(49\) −3.37352 + 5.84311i −0.481932 + 0.834730i
\(50\) −15.6223 27.0586i −2.20932 3.82666i
\(51\) 5.36845 + 4.79025i 0.751733 + 0.670769i
\(52\) 2.82730 + 4.89703i 0.392077 + 0.679096i
\(53\) 3.53023 6.11455i 0.484915 0.839897i −0.514935 0.857229i \(-0.672184\pi\)
0.999850 + 0.0173319i \(0.00551720\pi\)
\(54\) 13.0587i 1.77706i
\(55\) 3.31578 5.74311i 0.447100 0.774401i
\(56\) 2.66253 1.53721i 0.355796 0.205419i
\(57\) −0.756397 + 0.436706i −0.100187 + 0.0578431i
\(58\) 4.95400 2.86020i 0.650493 0.375562i
\(59\) 14.3759 1.87158 0.935792 0.352553i \(-0.114686\pi\)
0.935792 + 0.352553i \(0.114686\pi\)
\(60\) 16.0349 + 27.7732i 2.07009 + 3.58550i
\(61\) −7.69058 + 4.44016i −0.984678 + 0.568504i −0.903679 0.428210i \(-0.859144\pi\)
−0.0809987 + 0.996714i \(0.525811\pi\)
\(62\) 4.15065 + 2.39638i 0.527133 + 0.304340i
\(63\) −0.0196429 0.0113408i −0.00247477 0.00142881i
\(64\) −1.59537 −0.199421
\(65\) 5.33444i 0.661656i
\(66\) −3.51926 + 6.09553i −0.433191 + 0.750308i
\(67\) 2.31291 4.00608i 0.282567 0.489420i −0.689449 0.724334i \(-0.742147\pi\)
0.972016 + 0.234914i \(0.0754807\pi\)
\(68\) 17.8174 + 3.70356i 2.16067 + 0.449122i
\(69\) 3.31435 + 5.74062i 0.399001 + 0.691089i
\(70\) 5.30358 0.633899
\(71\) −5.91339 + 3.41410i −0.701790 + 0.405179i −0.808014 0.589163i \(-0.799457\pi\)
0.106223 + 0.994342i \(0.466124\pi\)
\(72\) −0.137835 0.238738i −0.0162441 0.0281355i
\(73\) −4.59813 + 2.65473i −0.538171 + 0.310713i −0.744337 0.667804i \(-0.767235\pi\)
0.206166 + 0.978517i \(0.433901\pi\)
\(74\) −14.7201 8.49864i −1.71117 0.987946i
\(75\) 21.5288i 2.48593i
\(76\) −1.10457 + 1.91317i −0.126703 + 0.219456i
\(77\) 0.400516 + 0.693714i 0.0456430 + 0.0790560i
\(78\) 5.66179i 0.641071i
\(79\) −6.53529 + 3.77315i −0.735278 + 0.424513i −0.820350 0.571862i \(-0.806221\pi\)
0.0850721 + 0.996375i \(0.472888\pi\)
\(80\) 23.9920 + 13.8518i 2.68239 + 1.54868i
\(81\) 4.56663 7.90963i 0.507403 0.878848i
\(82\) 15.6955i 1.73328i
\(83\) 5.31315 9.20265i 0.583194 1.01012i −0.411904 0.911227i \(-0.635136\pi\)
0.995098 0.0988944i \(-0.0315306\pi\)
\(84\) −3.87372 −0.422658
\(85\) 12.8097 + 11.4300i 1.38941 + 1.23976i
\(86\) 16.5612 + 1.23079i 1.78584 + 0.132719i
\(87\) −3.94159 −0.422583
\(88\) 9.73568i 1.03783i
\(89\) −5.12917 + 8.88398i −0.543691 + 0.941700i 0.454997 + 0.890493i \(0.349640\pi\)
−0.998688 + 0.0512072i \(0.983693\pi\)
\(90\) 0.475550i 0.0501273i
\(91\) −0.558024 0.322175i −0.0584968 0.0337731i
\(92\) 14.5199 + 8.38304i 1.51380 + 0.873993i
\(93\) −1.65120 2.85997i −0.171222 0.296565i
\(94\) 16.2341 1.67442
\(95\) −1.80484 + 1.04203i −0.185173 + 0.106910i
\(96\) −6.98858 4.03486i −0.713269 0.411806i
\(97\) 6.75116i 0.685477i 0.939431 + 0.342738i \(0.111354\pi\)
−0.939431 + 0.342738i \(0.888646\pi\)
\(98\) 8.54355 14.7979i 0.863029 1.49481i
\(99\) 0.0622024 0.0359126i 0.00625158 0.00360935i
\(100\) 27.2266 + 47.1579i 2.72266 + 4.71579i
\(101\) −3.98297 6.89870i −0.396320 0.686446i 0.596949 0.802279i \(-0.296380\pi\)
−0.993269 + 0.115833i \(0.963046\pi\)
\(102\) −13.5958 12.1314i −1.34618 1.20119i
\(103\) −1.64180 2.84368i −0.161771 0.280196i 0.773733 0.633512i \(-0.218387\pi\)
−0.935504 + 0.353316i \(0.885054\pi\)
\(104\) −3.91569 6.78218i −0.383965 0.665048i
\(105\) −3.16479 1.82720i −0.308852 0.178316i
\(106\) −8.94043 + 15.4853i −0.868371 + 1.50406i
\(107\) 15.4594i 1.49451i −0.664536 0.747256i \(-0.731371\pi\)
0.664536 0.747256i \(-0.268629\pi\)
\(108\) 22.7587i 2.18996i
\(109\) 5.53619 + 3.19632i 0.530271 + 0.306152i 0.741127 0.671365i \(-0.234292\pi\)
−0.210856 + 0.977517i \(0.567625\pi\)
\(110\) −8.39733 + 14.5446i −0.800654 + 1.38677i
\(111\) 5.85592 + 10.1427i 0.555819 + 0.962707i
\(112\) −2.89801 + 1.67317i −0.273837 + 0.158100i
\(113\) 12.2841i 1.15559i −0.816181 0.577796i \(-0.803913\pi\)
0.816181 0.577796i \(-0.196087\pi\)
\(114\) 1.91560 1.10597i 0.179412 0.103584i
\(115\) 7.90839 + 13.6977i 0.737461 + 1.27732i
\(116\) −8.63387 + 4.98477i −0.801635 + 0.462824i
\(117\) −0.0288881 + 0.0500357i −0.00267071 + 0.00462580i
\(118\) −36.4074 −3.35158
\(119\) −1.96932 + 0.649672i −0.180527 + 0.0595553i
\(120\) −22.2076 38.4647i −2.02727 3.51133i
\(121\) 8.46340 0.769400
\(122\) 19.4766 11.2448i 1.76333 1.01806i
\(123\) 5.40743 9.36594i 0.487572 0.844499i
\(124\) −7.23378 4.17642i −0.649612 0.375054i
\(125\) 30.5510i 2.73257i
\(126\) 0.0497462 + 0.0287210i 0.00443174 + 0.00255867i
\(127\) −13.7804 −1.22282 −0.611408 0.791316i \(-0.709397\pi\)
−0.611408 + 0.791316i \(0.709397\pi\)
\(128\) 13.2892 1.17461
\(129\) −9.45853 6.44014i −0.832777 0.567023i
\(130\) 13.5096i 1.18487i
\(131\) 15.7380i 1.37503i 0.726169 + 0.687516i \(0.241299\pi\)
−0.726169 + 0.687516i \(0.758701\pi\)
\(132\) 6.13339 10.6233i 0.533843 0.924643i
\(133\) 0.251734i 0.0218281i
\(134\) −5.85752 + 10.1455i −0.506013 + 0.876439i
\(135\) 10.7351 18.5937i 0.923926 1.60029i
\(136\) −24.6763 5.12927i −2.11597 0.439831i
\(137\) −4.92454 −0.420731 −0.210366 0.977623i \(-0.567465\pi\)
−0.210366 + 0.977623i \(0.567465\pi\)
\(138\) −8.39369 14.5383i −0.714518 1.23758i
\(139\) −4.39223 2.53586i −0.372544 0.215088i 0.302025 0.953300i \(-0.402337\pi\)
−0.674569 + 0.738211i \(0.735671\pi\)
\(140\) −9.24312 −0.781186
\(141\) −9.68735 5.59299i −0.815822 0.471015i
\(142\) 14.9758 8.64631i 1.25675 0.725582i
\(143\) 1.76707 1.02022i 0.147770 0.0853152i
\(144\) 0.150026 + 0.259853i 0.0125022 + 0.0216544i
\(145\) −9.40506 −0.781048
\(146\) 11.6449 6.72320i 0.963740 0.556416i
\(147\) −10.1963 + 5.88686i −0.840981 + 0.485540i
\(148\) 25.6542 + 14.8115i 2.10877 + 1.21750i
\(149\) 6.55062 11.3460i 0.536648 0.929502i −0.462434 0.886654i \(-0.653024\pi\)
0.999082 0.0428478i \(-0.0136431\pi\)
\(150\) 54.5224i 4.45173i
\(151\) −14.8659 −1.20977 −0.604884 0.796314i \(-0.706780\pi\)
−0.604884 + 0.796314i \(0.706780\pi\)
\(152\) 1.52978 2.64966i 0.124082 0.214916i
\(153\) 0.0582533 + 0.176580i 0.00470950 + 0.0142757i
\(154\) −1.01432 1.75685i −0.0817361 0.141571i
\(155\) −3.93995 6.82420i −0.316465 0.548133i
\(156\) 9.86741i 0.790025i
\(157\) 10.2813 + 17.8077i 0.820536 + 1.42121i 0.905284 + 0.424808i \(0.139658\pi\)
−0.0847476 + 0.996402i \(0.527008\pi\)
\(158\) 16.5508 9.55562i 1.31671 0.760205i
\(159\) 10.6700 6.16033i 0.846187 0.488546i
\(160\) −16.6755 9.62761i −1.31831 0.761129i
\(161\) −1.91052 −0.150570
\(162\) −11.5651 + 20.0314i −0.908642 + 1.57381i
\(163\) 14.5428 8.39628i 1.13908 0.657648i 0.192877 0.981223i \(-0.438218\pi\)
0.946202 + 0.323575i \(0.104885\pi\)
\(164\) 27.3542i 2.13601i
\(165\) 10.0218 5.78611i 0.780199 0.450448i
\(166\) −13.4557 + 23.3060i −1.04437 + 1.80890i
\(167\) −2.36815 1.36725i −0.183253 0.105801i 0.405567 0.914065i \(-0.367074\pi\)
−0.588820 + 0.808264i \(0.700407\pi\)
\(168\) 5.36494 0.413914
\(169\) 5.67933 9.83689i 0.436872 0.756684i
\(170\) −32.4409 28.9469i −2.48811 2.22013i
\(171\) −0.0225720 −0.00172612
\(172\) −28.8631 2.14503i −2.20079 0.163557i
\(173\) 11.4314i 0.869116i −0.900644 0.434558i \(-0.856905\pi\)
0.900644 0.434558i \(-0.143095\pi\)
\(174\) 9.98220 0.756749
\(175\) −5.37371 3.10251i −0.406214 0.234528i
\(176\) 10.5967i 0.798758i
\(177\) 21.7253 + 12.5431i 1.63298 + 0.942799i
\(178\) 12.9898 22.4990i 0.973625 1.68637i
\(179\) −3.44720 5.97073i −0.257656 0.446273i 0.707958 0.706255i \(-0.249617\pi\)
−0.965614 + 0.259982i \(0.916283\pi\)
\(180\) 0.828791i 0.0617745i
\(181\) −12.9078 + 7.45234i −0.959432 + 0.553928i −0.895998 0.444058i \(-0.853538\pi\)
−0.0634335 + 0.997986i \(0.520205\pi\)
\(182\) 1.41321 + 0.815919i 0.104754 + 0.0604799i
\(183\) −15.4963 −1.14552
\(184\) −20.1094 11.6102i −1.48248 0.855912i
\(185\) 13.9728 + 24.2017i 1.02730 + 1.77934i
\(186\) 4.18173 + 7.24296i 0.306619 + 0.531080i
\(187\) 1.33641 6.42932i 0.0977283 0.470159i
\(188\) −28.2929 −2.06347
\(189\) 1.29669 + 2.24594i 0.0943206 + 0.163368i
\(190\) 4.57083 2.63897i 0.331603 0.191451i
\(191\) −10.1588 + 17.5956i −0.735066 + 1.27317i 0.219629 + 0.975583i \(0.429515\pi\)
−0.954695 + 0.297588i \(0.903818\pi\)
\(192\) −2.41097 1.39198i −0.173997 0.100457i
\(193\) 3.73303i 0.268710i 0.990933 + 0.134355i \(0.0428962\pi\)
−0.990933 + 0.134355i \(0.957104\pi\)
\(194\) 17.0975i 1.22753i
\(195\) −4.65436 + 8.06158i −0.333305 + 0.577302i
\(196\) −14.8898 + 25.7898i −1.06355 + 1.84213i
\(197\) −14.5933 + 8.42545i −1.03973 + 0.600288i −0.919757 0.392489i \(-0.871614\pi\)
−0.119973 + 0.992777i \(0.538281\pi\)
\(198\) −0.157529 + 0.0909497i −0.0111951 + 0.00646351i
\(199\) 19.0783i 1.35242i −0.736707 0.676212i \(-0.763620\pi\)
0.736707 0.676212i \(-0.236380\pi\)
\(200\) −37.7077 65.3116i −2.66634 4.61823i
\(201\) 6.99069 4.03608i 0.493085 0.284683i
\(202\) 10.0870 + 17.4712i 0.709718 + 1.22927i
\(203\) 0.568021 0.983842i 0.0398673 0.0690522i
\(204\) 23.6948 + 21.1428i 1.65897 + 1.48029i
\(205\) 12.9027 22.3481i 0.901164 1.56086i
\(206\) 4.15790 + 7.20170i 0.289695 + 0.501766i
\(207\) 0.171308i 0.0119067i
\(208\) 4.26201 + 7.38202i 0.295517 + 0.511851i
\(209\) 0.690359 + 0.398579i 0.0477532 + 0.0275703i
\(210\) 8.01494 + 4.62743i 0.553083 + 0.319323i
\(211\) 20.0310i 1.37899i −0.724291 0.689494i \(-0.757833\pi\)
0.724291 0.689494i \(-0.242167\pi\)
\(212\) 15.5814 26.9878i 1.07014 1.85353i
\(213\) −11.9153 −0.816426
\(214\) 39.1513i 2.67633i
\(215\) −22.5691 15.3669i −1.53920 1.04801i
\(216\) 31.5198i 2.14465i
\(217\) 0.951819 0.0646137
\(218\) −14.0206 8.09478i −0.949593 0.548248i
\(219\) −9.26513 −0.626080
\(220\) 14.6349 25.3484i 0.986686 1.70899i
\(221\) 1.65489 + 5.01637i 0.111320 + 0.337438i
\(222\) −14.8303 25.6868i −0.995344 1.72399i
\(223\) 4.00116 0.267938 0.133969 0.990986i \(-0.457228\pi\)
0.133969 + 0.990986i \(0.457228\pi\)
\(224\) 2.01424 1.16292i 0.134582 0.0777012i
\(225\) −0.278189 + 0.481838i −0.0185459 + 0.0321225i
\(226\) 31.1099i 2.06940i
\(227\) 18.1922 + 10.5033i 1.20746 + 0.697126i 0.962203 0.272333i \(-0.0877952\pi\)
0.245254 + 0.969459i \(0.421129\pi\)
\(228\) −3.33852 + 1.92750i −0.221099 + 0.127652i
\(229\) −9.69715 16.7960i −0.640806 1.10991i −0.985253 0.171103i \(-0.945267\pi\)
0.344447 0.938806i \(-0.388066\pi\)
\(230\) −20.0282 34.6899i −1.32062 2.28739i
\(231\) 1.39782i 0.0919696i
\(232\) 11.9575 6.90369i 0.785051 0.453249i
\(233\) −9.57116 + 5.52591i −0.627028 + 0.362015i −0.779600 0.626278i \(-0.784578\pi\)
0.152572 + 0.988292i \(0.451244\pi\)
\(234\) 0.0731600 0.126717i 0.00478262 0.00828374i
\(235\) −23.1151 13.3455i −1.50786 0.870563i
\(236\) 63.4511 4.13032
\(237\) −13.1685 −0.855383
\(238\) 4.98735 1.64531i 0.323282 0.106650i
\(239\) −3.40393 + 5.89578i −0.220182 + 0.381367i −0.954863 0.297046i \(-0.903998\pi\)
0.734681 + 0.678413i \(0.237332\pi\)
\(240\) 24.1717 + 41.8666i 1.56028 + 2.70248i
\(241\) −6.33917 + 3.65992i −0.408342 + 0.235756i −0.690077 0.723736i \(-0.742423\pi\)
0.281735 + 0.959492i \(0.409090\pi\)
\(242\) −21.4338 −1.37782
\(243\) 0.405842 0.234313i 0.0260347 0.0150312i
\(244\) −33.9440 + 19.5976i −2.17304 + 1.25461i
\(245\) −24.3296 + 14.0467i −1.55436 + 0.897410i
\(246\) −13.6945 + 23.7195i −0.873128 + 1.51230i
\(247\) −0.641235 −0.0408008
\(248\) 10.0185 + 5.78417i 0.636173 + 0.367295i
\(249\) 16.0588 9.27156i 1.01769 0.587561i
\(250\) 77.3714i 4.89340i
\(251\) 6.72823 + 11.6536i 0.424682 + 0.735571i 0.996391 0.0848857i \(-0.0270525\pi\)
−0.571709 + 0.820457i \(0.693719\pi\)
\(252\) −0.0866980 0.0500551i −0.00546146 0.00315318i
\(253\) 3.02499 5.23943i 0.190179 0.329400i
\(254\) 34.8994 2.18978
\(255\) 9.38558 + 28.4500i 0.587748 + 1.78161i
\(256\) −30.4645 −1.90403
\(257\) 18.6693 1.16456 0.582280 0.812988i \(-0.302161\pi\)
0.582280 + 0.812988i \(0.302161\pi\)
\(258\) 23.9540 + 16.3099i 1.49131 + 1.01541i
\(259\) −3.37558 −0.209748
\(260\) 23.5447i 1.46018i
\(261\) −0.0882170 0.0509321i −0.00546049 0.00315262i
\(262\) 39.8569i 2.46237i
\(263\) 7.27677 12.6037i 0.448705 0.777180i −0.549597 0.835430i \(-0.685219\pi\)
0.998302 + 0.0582500i \(0.0185521\pi\)
\(264\) −8.49448 + 14.7129i −0.522799 + 0.905515i
\(265\) 25.4598 14.6992i 1.56398 0.902965i
\(266\) 0.637525i 0.0390892i
\(267\) −15.5027 + 8.95051i −0.948752 + 0.547762i
\(268\) 10.2085 17.6817i 0.623585 1.08008i
\(269\) 3.39014i 0.206700i 0.994645 + 0.103350i \(0.0329562\pi\)
−0.994645 + 0.103350i \(0.967044\pi\)
\(270\) −27.1869 + 47.0890i −1.65454 + 2.86575i
\(271\) 9.92048 + 17.1828i 0.602626 + 1.04378i 0.992422 + 0.122878i \(0.0392124\pi\)
−0.389795 + 0.920902i \(0.627454\pi\)
\(272\) 26.8587 + 5.58292i 1.62855 + 0.338514i
\(273\) −0.562203 0.973763i −0.0340260 0.0589348i
\(274\) 12.4715 0.753433
\(275\) 17.0167 9.82461i 1.02615 0.592446i
\(276\) 14.6286 + 25.3374i 0.880537 + 1.52514i
\(277\) −1.93134 1.11506i −0.116043 0.0669975i 0.440855 0.897578i \(-0.354675\pi\)
−0.556898 + 0.830581i \(0.688009\pi\)
\(278\) 11.1235 + 6.42213i 0.667141 + 0.385174i
\(279\) 0.0853456i 0.00510951i
\(280\) 12.8013 0.765025
\(281\) 8.21770 14.2335i 0.490227 0.849098i −0.509710 0.860346i \(-0.670247\pi\)
0.999937 + 0.0112482i \(0.00358050\pi\)
\(282\) 24.5335 + 14.1644i 1.46095 + 0.843479i
\(283\) 6.45071 3.72432i 0.383455 0.221388i −0.295865 0.955230i \(-0.595608\pi\)
0.679321 + 0.733842i \(0.262275\pi\)
\(284\) −26.1000 + 15.0688i −1.54875 + 0.894172i
\(285\) −3.63672 −0.215421
\(286\) −4.47517 + 2.58374i −0.264622 + 0.152780i
\(287\) 1.55853 + 2.69945i 0.0919969 + 0.159343i
\(288\) −0.104275 0.180609i −0.00614444 0.0106425i
\(289\) 15.5918 + 6.77461i 0.917165 + 0.398507i
\(290\) 23.8186 1.39868
\(291\) −5.89046 + 10.2026i −0.345305 + 0.598086i
\(292\) −20.2948 + 11.7172i −1.18767 + 0.685699i
\(293\) 33.5326 1.95899 0.979497 0.201458i \(-0.0645681\pi\)
0.979497 + 0.201458i \(0.0645681\pi\)
\(294\) 25.8226 14.9087i 1.50600 0.869491i
\(295\) 51.8390 + 29.9293i 3.01818 + 1.74255i
\(296\) −35.5300 20.5133i −2.06514 1.19231i
\(297\) −8.21239 −0.476531
\(298\) −16.5897 + 28.7341i −0.961013 + 1.66452i
\(299\) 4.86660i 0.281443i
\(300\) 95.0220i 5.48610i
\(301\) 2.97056 1.43281i 0.171220 0.0825859i
\(302\) 37.6483 2.16641
\(303\) 13.9007i 0.798575i
\(304\) −1.66508 + 2.88400i −0.0954988 + 0.165409i
\(305\) −36.9759 −2.11723
\(306\) −0.147528 0.447195i −0.00843363 0.0255644i
\(307\) 12.2093 21.1472i 0.696823 1.20693i −0.272739 0.962088i \(-0.587929\pi\)
0.969562 0.244845i \(-0.0787372\pi\)
\(308\) 1.76776 + 3.06185i 0.100728 + 0.174465i
\(309\) 5.72994i 0.325965i
\(310\) 9.97805 + 17.2825i 0.566715 + 0.981579i
\(311\) −21.5893 12.4646i −1.22422 0.706803i −0.258404 0.966037i \(-0.583197\pi\)
−0.965815 + 0.259234i \(0.916530\pi\)
\(312\) 13.6659i 0.773681i
\(313\) −26.2247 15.1408i −1.48231 0.855809i −0.482507 0.875892i \(-0.660274\pi\)
−0.999798 + 0.0200826i \(0.993607\pi\)
\(314\) −26.0377 45.0986i −1.46939 2.54506i
\(315\) −0.0472210 0.0817891i −0.00266060 0.00460829i
\(316\) −28.8449 + 16.6536i −1.62265 + 0.936839i
\(317\) 5.16335i 0.290002i −0.989431 0.145001i \(-0.953681\pi\)
0.989431 0.145001i \(-0.0463186\pi\)
\(318\) −27.0221 + 15.6012i −1.51533 + 0.874874i
\(319\) 1.79873 + 3.11550i 0.100710 + 0.174434i
\(320\) −5.75284 3.32141i −0.321594 0.185672i
\(321\) 13.4884 23.3627i 0.752852 1.30398i
\(322\) 4.83845 0.269636
\(323\) −1.37397 + 1.53981i −0.0764495 + 0.0856772i
\(324\) 20.1558 34.9109i 1.11977 1.93949i
\(325\) −7.90293 + 13.6883i −0.438376 + 0.759289i
\(326\) −36.8301 + 21.2638i −2.03983 + 1.17770i
\(327\) 5.57764 + 9.66076i 0.308444 + 0.534241i
\(328\) 37.8844i 2.09182i
\(329\) 2.79208 1.61201i 0.153932 0.0888729i
\(330\) −25.3806 + 14.6535i −1.39716 + 0.806649i
\(331\) −8.32138 14.4131i −0.457385 0.792213i 0.541437 0.840741i \(-0.317880\pi\)
−0.998822 + 0.0485278i \(0.984547\pi\)
\(332\) 23.4507 40.6178i 1.28703 2.22919i
\(333\) 0.302674i 0.0165864i
\(334\) 5.99740 + 3.46260i 0.328163 + 0.189465i
\(335\) 16.6805 9.63051i 0.911355 0.526171i
\(336\) −5.83943 −0.318567
\(337\) −18.0058 + 10.3957i −0.980841 + 0.566289i −0.902524 0.430640i \(-0.858288\pi\)
−0.0783169 + 0.996929i \(0.524955\pi\)
\(338\) −14.3831 + 24.9122i −0.782337 + 1.35505i
\(339\) 10.7180 18.5641i 0.582123 1.00827i
\(340\) 56.5383 + 50.4489i 3.06622 + 2.73598i
\(341\) −1.50705 + 2.61028i −0.0816111 + 0.141355i
\(342\) 0.0571642 0.00309109
\(343\) 6.91406i 0.373324i
\(344\) 39.9741 + 2.97077i 2.15526 + 0.160173i
\(345\) 27.6006i 1.48597i
\(346\) 28.9505i 1.55639i
\(347\) −5.58740 3.22589i −0.299947 0.173175i 0.342472 0.939528i \(-0.388736\pi\)
−0.642419 + 0.766353i \(0.722069\pi\)
\(348\) −17.3970 −0.932580
\(349\) 7.29552 12.6362i 0.390520 0.676400i −0.601998 0.798497i \(-0.705629\pi\)
0.992518 + 0.122097i \(0.0389619\pi\)
\(350\) 13.6091 + 7.85721i 0.727436 + 0.419985i
\(351\) 5.72101 3.30303i 0.305365 0.176303i
\(352\) 7.36518i 0.392566i
\(353\) 2.48695 + 4.30752i 0.132367 + 0.229266i 0.924588 0.380967i \(-0.124409\pi\)
−0.792222 + 0.610233i \(0.791076\pi\)
\(354\) −55.0201 31.7659i −2.92428 1.68834i
\(355\) −28.4313 −1.50898
\(356\) −22.6387 + 39.2113i −1.19985 + 2.07820i
\(357\) −3.54294 0.736444i −0.187512 0.0389767i
\(358\) 8.73014 + 15.1211i 0.461402 + 0.799173i
\(359\) 0.197646 + 0.342333i 0.0104313 + 0.0180676i 0.871194 0.490939i \(-0.163346\pi\)
−0.860763 + 0.509007i \(0.830013\pi\)
\(360\) 1.14784i 0.0604965i
\(361\) 9.37474 + 16.2375i 0.493407 + 0.854607i
\(362\) 32.6895 18.8733i 1.71812 0.991958i
\(363\) 12.7902 + 7.38441i 0.671310 + 0.387581i
\(364\) −2.46296 1.42199i −0.129094 0.0745325i
\(365\) −22.1076 −1.15716
\(366\) 39.2450 2.05137
\(367\) −19.8449 11.4574i −1.03589 0.598073i −0.117226 0.993105i \(-0.537400\pi\)
−0.918667 + 0.395032i \(0.870734\pi\)
\(368\) 21.8879 + 12.6370i 1.14099 + 0.658748i
\(369\) 0.242048 0.139746i 0.0126005 0.00727491i
\(370\) −35.3867 61.2915i −1.83967 3.18639i
\(371\) 3.55105i 0.184362i
\(372\) −7.28794 12.6231i −0.377862 0.654477i
\(373\) −4.32677 7.49418i −0.224032 0.388034i 0.731997 0.681308i \(-0.238589\pi\)
−0.956028 + 0.293274i \(0.905255\pi\)
\(374\) −3.38451 + 16.2825i −0.175009 + 0.841946i
\(375\) −26.6561 + 46.1697i −1.37651 + 2.38419i
\(376\) 39.1845 2.02079
\(377\) −2.50611 1.44690i −0.129071 0.0745193i
\(378\) −3.28392 5.68791i −0.168907 0.292555i
\(379\) 12.1411i 0.623647i −0.950140 0.311824i \(-0.899060\pi\)
0.950140 0.311824i \(-0.100940\pi\)
\(380\) −7.96607 + 4.59921i −0.408651 + 0.235935i
\(381\) −20.8254 12.0236i −1.06692 0.615986i
\(382\) 25.7275 44.5613i 1.31633 2.27996i
\(383\) 37.3898 1.91053 0.955266 0.295748i \(-0.0955689\pi\)
0.955266 + 0.295748i \(0.0955689\pi\)
\(384\) 20.0830 + 11.5949i 1.02486 + 0.591702i
\(385\) 3.33534i 0.169985i
\(386\) 9.45402i 0.481197i
\(387\) −0.128474 0.266358i −0.00653071 0.0135397i
\(388\) 29.7977i 1.51275i
\(389\) −1.64357 −0.0833324 −0.0416662 0.999132i \(-0.513267\pi\)
−0.0416662 + 0.999132i \(0.513267\pi\)
\(390\) 11.7873 20.4162i 0.596873 1.03381i
\(391\) 11.6863 + 10.4276i 0.591000 + 0.527347i
\(392\) 20.6217 35.7178i 1.04155 1.80402i
\(393\) −13.7315 + 23.7837i −0.692664 + 1.19973i
\(394\) 36.9580 21.3377i 1.86192 1.07498i
\(395\) −31.4213 −1.58098
\(396\) 0.274543 0.158508i 0.0137963 0.00796531i
\(397\) −22.6148 13.0566i −1.13500 0.655294i −0.189815 0.981820i \(-0.560789\pi\)
−0.945188 + 0.326526i \(0.894122\pi\)
\(398\) 48.3164i 2.42188i
\(399\) 0.219641 0.380429i 0.0109958 0.0190453i
\(400\) 41.0427 + 71.0880i 2.05213 + 3.55440i
\(401\) −3.75130 + 2.16582i −0.187331 + 0.108156i −0.590733 0.806867i \(-0.701161\pi\)
0.403401 + 0.915023i \(0.367828\pi\)
\(402\) −17.7041 + 10.2215i −0.883002 + 0.509802i
\(403\) 2.42454i 0.120775i
\(404\) −17.5797 30.4489i −0.874621 1.51489i
\(405\) 32.9342 19.0146i 1.63651 0.944841i
\(406\) −1.43853 + 2.49161i −0.0713931 + 0.123657i
\(407\) 5.34466 9.25723i 0.264925 0.458864i
\(408\) −32.8162 29.2818i −1.62465 1.44967i
\(409\) −35.3131 −1.74612 −0.873059 0.487614i \(-0.837867\pi\)
−0.873059 + 0.487614i \(0.837867\pi\)
\(410\) −32.6765 + 56.5974i −1.61378 + 2.79514i
\(411\) −7.44212 4.29671i −0.367093 0.211941i
\(412\) −7.24642 12.5512i −0.357006 0.618352i
\(413\) −6.26166 + 3.61517i −0.308116 + 0.177891i
\(414\) 0.433843i 0.0213222i
\(415\) 38.3180 22.1229i 1.88096 1.08597i
\(416\) −2.96228 5.13082i −0.145238 0.251559i
\(417\) −4.42512 7.66453i −0.216699 0.375334i
\(418\) −1.74836 1.00941i −0.0855149 0.0493720i
\(419\) 37.9431i 1.85364i −0.375502 0.926822i \(-0.622530\pi\)
0.375502 0.926822i \(-0.377470\pi\)
\(420\) −13.9685 8.06471i −0.681593 0.393518i
\(421\) 2.57467 + 4.45947i 0.125482 + 0.217341i 0.921921 0.387377i \(-0.126619\pi\)
−0.796439 + 0.604719i \(0.793286\pi\)
\(422\) 50.7290i 2.46945i
\(423\) −0.144542 0.250354i −0.00702788 0.0121726i
\(424\) −21.5796 + 37.3770i −1.04800 + 1.81519i
\(425\) 15.9364 + 48.3071i 0.773028 + 2.34324i
\(426\) 30.1760 1.46203
\(427\) 2.23317 3.86797i 0.108071 0.187184i
\(428\) 68.2331i 3.29817i
\(429\) 3.56061 0.171908
\(430\) 57.1568 + 38.9171i 2.75635 + 1.87675i
\(431\) 24.6897i 1.18926i −0.803999 0.594630i \(-0.797299\pi\)
0.803999 0.594630i \(-0.202701\pi\)
\(432\) 34.3075i 1.65062i
\(433\) 12.6006 21.8249i 0.605546 1.04884i −0.386418 0.922324i \(-0.626288\pi\)
0.991965 0.126514i \(-0.0403787\pi\)
\(434\) −2.41051 −0.115708
\(435\) −14.2132 8.20601i −0.681472 0.393448i
\(436\) 24.4351 + 14.1076i 1.17023 + 0.675633i
\(437\) −1.64656 + 0.950640i −0.0787655 + 0.0454753i
\(438\) 23.4642 1.12116
\(439\) 32.5010 18.7644i 1.55119 0.895578i 0.553140 0.833088i \(-0.313429\pi\)
0.998046 0.0624894i \(-0.0199040\pi\)
\(440\) −20.2687 + 35.1065i −0.966274 + 1.67364i
\(441\) −0.304273 −0.0144892
\(442\) −4.19105 12.7041i −0.199348 0.604274i
\(443\) −10.6516 18.4491i −0.506073 0.876544i −0.999975 0.00702687i \(-0.997763\pi\)
0.493902 0.869517i \(-0.335570\pi\)
\(444\) 25.8463 + 44.7672i 1.22661 + 2.12456i
\(445\) −36.9912 + 21.3569i −1.75355 + 1.01241i
\(446\) −10.1331 −0.479815
\(447\) 19.7990 11.4310i 0.936462 0.540667i
\(448\) 0.694890 0.401195i 0.0328304 0.0189547i
\(449\) 30.3385 + 17.5159i 1.43176 + 0.826628i 0.997255 0.0740405i \(-0.0235894\pi\)
0.434507 + 0.900669i \(0.356923\pi\)
\(450\) 0.704523 1.22027i 0.0332115 0.0575240i
\(451\) −9.87066 −0.464791
\(452\) 54.2185i 2.55023i
\(453\) −22.4658 12.9706i −1.05553 0.609413i
\(454\) −46.0723 26.5998i −2.16228 1.24839i
\(455\) −1.34148 2.32350i −0.0628893 0.108928i
\(456\) 4.62371 2.66950i 0.216525 0.125011i
\(457\) 30.7370 1.43782 0.718909 0.695104i \(-0.244642\pi\)
0.718909 + 0.695104i \(0.244642\pi\)
\(458\) 24.5583 + 42.5363i 1.14754 + 1.98759i
\(459\) 4.32672 20.8153i 0.201954 0.971576i
\(460\) 34.9054 + 60.4579i 1.62747 + 2.81886i
\(461\) −10.5994 + 18.3586i −0.493661 + 0.855046i −0.999973 0.00730419i \(-0.997675\pi\)
0.506312 + 0.862350i \(0.331008\pi\)
\(462\) 3.54001i 0.164696i
\(463\) 1.03672 1.79565i 0.0481804 0.0834509i −0.840929 0.541145i \(-0.817991\pi\)
0.889110 + 0.457694i \(0.151324\pi\)
\(464\) −13.0151 + 7.51427i −0.604211 + 0.348841i
\(465\) 13.7506i 0.637669i
\(466\) 24.2393 13.9945i 1.12286 0.648285i
\(467\) −16.7924 + 29.0853i −0.777061 + 1.34591i 0.156568 + 0.987667i \(0.449957\pi\)
−0.933629 + 0.358242i \(0.883376\pi\)
\(468\) −0.127504 + 0.220843i −0.00589386 + 0.0102085i
\(469\) 2.32655i 0.107430i
\(470\) 58.5396 + 33.7978i 2.70023 + 1.55898i
\(471\) 35.8821i 1.65336i
\(472\) −87.8771 −4.04487
\(473\) −0.774024 + 10.4151i −0.0355897 + 0.478887i
\(474\) 33.3495 1.53179
\(475\) −6.17502 −0.283329
\(476\) −8.69199 + 2.86746i −0.398397 + 0.131430i
\(477\) 0.318408 0.0145789
\(478\) 8.62056 14.9313i 0.394295 0.682940i
\(479\) −1.48883 0.859574i −0.0680262 0.0392750i 0.465601 0.884995i \(-0.345838\pi\)
−0.533627 + 0.845720i \(0.679171\pi\)
\(480\) −16.8004 29.0991i −0.766829 1.32819i
\(481\) 8.59850i 0.392058i
\(482\) 16.0542 9.26887i 0.731247 0.422185i
\(483\) −2.88724 1.66695i −0.131374 0.0758487i
\(484\) 37.3550 1.69796
\(485\) −14.0553 + 24.3444i −0.638217 + 1.10542i
\(486\) −1.02781 + 0.593404i −0.0466222 + 0.0269174i
\(487\) 0.383541 0.221437i 0.0173799 0.0100343i −0.491285 0.870999i \(-0.663473\pi\)
0.508665 + 0.860965i \(0.330139\pi\)
\(488\) 47.0110 27.1418i 2.12809 1.22865i
\(489\) 29.3034 1.32514
\(490\) 61.6154 35.5737i 2.78350 1.60705i
\(491\) 0.447768 + 0.775557i 0.0202075 + 0.0350004i 0.875952 0.482398i \(-0.160234\pi\)
−0.855745 + 0.517398i \(0.826901\pi\)
\(492\) 23.8668 41.3386i 1.07600 1.86369i
\(493\) −8.84428 + 2.91770i −0.398326 + 0.131407i
\(494\) 1.62395 0.0730648
\(495\) 0.299066 0.0134420
\(496\) −10.9045 6.29573i −0.489628 0.282687i
\(497\) 1.71712 2.97413i 0.0770232 0.133408i
\(498\) −40.6694 + 23.4805i −1.82244 + 1.05219i
\(499\) −18.9922 + 10.9652i −0.850209 + 0.490869i −0.860722 0.509076i \(-0.829987\pi\)
0.0105121 + 0.999945i \(0.496654\pi\)
\(500\) 134.843i 6.03038i
\(501\) −2.38588 4.13246i −0.106593 0.184625i
\(502\) −17.0395 29.5132i −0.760508 1.31724i
\(503\) −17.4813 + 10.0928i −0.779452 + 0.450017i −0.836236 0.548369i \(-0.815249\pi\)
0.0567838 + 0.998386i \(0.481915\pi\)
\(504\) 0.120073 + 0.0693242i 0.00534848 + 0.00308794i
\(505\) 33.1686i 1.47598i
\(506\) −7.66087 + 13.2690i −0.340567 + 0.589880i
\(507\) 17.1656 9.91055i 0.762350 0.440143i
\(508\) −60.8229 −2.69858
\(509\) −15.2103 26.3449i −0.674183 1.16772i −0.976707 0.214577i \(-0.931163\pi\)
0.302524 0.953142i \(-0.402171\pi\)
\(510\) −23.7693 72.0506i −1.05252 3.19045i
\(511\) 1.33520 2.31263i 0.0590656 0.102305i
\(512\) 50.5740 2.23507
\(513\) 2.23508 + 1.29042i 0.0986812 + 0.0569736i
\(514\) −47.2806 −2.08546
\(515\) 13.6723i 0.602472i
\(516\) −41.7472 28.4249i −1.83782 1.25134i
\(517\) 10.2094i 0.449008i
\(518\) 8.54876 0.375611
\(519\) 9.97404 17.2755i 0.437812 0.758312i
\(520\) 32.6084i 1.42997i
\(521\) −17.0070 9.81901i −0.745091 0.430179i 0.0788261 0.996888i \(-0.474883\pi\)
−0.823918 + 0.566710i \(0.808216\pi\)
\(522\) 0.223412 + 0.128987i 0.00977849 + 0.00564561i
\(523\) 13.1292 + 22.7405i 0.574101 + 0.994372i 0.996139 + 0.0877935i \(0.0279816\pi\)
−0.422038 + 0.906578i \(0.638685\pi\)
\(524\) 69.4629i 3.03450i
\(525\) −5.41395 9.37723i −0.236284 0.409256i
\(526\) −18.4287 + 31.9194i −0.803527 + 1.39175i
\(527\) −5.82208 5.19502i −0.253614 0.226299i
\(528\) 9.24575 16.0141i 0.402370 0.696925i
\(529\) −4.28519 7.42216i −0.186312 0.322703i
\(530\) −64.4777 + 37.2262i −2.80073 + 1.61700i
\(531\) 0.324157 + 0.561457i 0.0140672 + 0.0243652i
\(532\) 1.11108i 0.0481716i
\(533\) 6.87621 3.96998i 0.297842 0.171959i
\(534\) 39.2611 22.6674i 1.69900 0.980916i
\(535\) 32.1849 55.7458i 1.39147 2.41010i
\(536\) −14.1384 + 24.4884i −0.610684 + 1.05774i
\(537\) 12.0309i 0.519171i
\(538\) 8.58562i 0.370153i
\(539\) 9.30615 + 5.37291i 0.400844 + 0.231427i
\(540\) 47.3815 82.0671i 2.03897 3.53160i
\(541\) −31.5196 + 18.1979i −1.35514 + 0.782388i −0.988963 0.148160i \(-0.952665\pi\)
−0.366172 + 0.930547i \(0.619332\pi\)
\(542\) −25.1239 43.5159i −1.07917 1.86917i
\(543\) −26.0090 −1.11615
\(544\) −18.6680 3.88037i −0.800383 0.166369i
\(545\) 13.3089 + 23.0516i 0.570089 + 0.987423i
\(546\) 1.42380 + 2.46609i 0.0609328 + 0.105539i
\(547\) −2.33008 1.34527i −0.0996270 0.0575197i 0.449359 0.893351i \(-0.351653\pi\)
−0.548986 + 0.835832i \(0.684986\pi\)
\(548\) −21.7355 −0.928494
\(549\) −0.346824 0.200239i −0.0148021 0.00854600i
\(550\) −43.0954 + 24.8811i −1.83759 + 1.06094i
\(551\) 1.13055i 0.0481630i
\(552\) −20.2600 35.0913i −0.862321 1.49358i
\(553\) 1.89770 3.28692i 0.0806985 0.139774i
\(554\) 4.89118 + 2.82393i 0.207806 + 0.119977i
\(555\) 48.7658i 2.06999i
\(556\) −19.3860 11.1925i −0.822151 0.474669i
\(557\) −7.33622 −0.310846 −0.155423 0.987848i \(-0.549674\pi\)
−0.155423 + 0.987848i \(0.549674\pi\)
\(558\) 0.216140i 0.00914995i
\(559\) −3.64975 7.56681i −0.154368 0.320042i
\(560\) −13.9335 −0.588798
\(561\) 7.62928 8.55016i 0.322108 0.360988i
\(562\) −20.8116 + 36.0467i −0.877884 + 1.52054i
\(563\) −8.01087 −0.337618 −0.168809 0.985649i \(-0.553992\pi\)
−0.168809 + 0.985649i \(0.553992\pi\)
\(564\) −42.7572 24.6859i −1.80040 1.03946i
\(565\) 25.5743 44.2960i 1.07592 1.86355i
\(566\) −16.3366 + 9.43196i −0.686680 + 0.396455i
\(567\) 4.59356i 0.192911i
\(568\) 36.1474 20.8697i 1.51671 0.875673i
\(569\) 5.73091 9.92622i 0.240252 0.416129i −0.720534 0.693420i \(-0.756103\pi\)
0.960786 + 0.277291i \(0.0894366\pi\)
\(570\) 9.21010 0.385769
\(571\) −6.89431 3.98043i −0.288518 0.166576i 0.348755 0.937214i \(-0.386604\pi\)
−0.637273 + 0.770638i \(0.719938\pi\)
\(572\) 7.79936 4.50296i 0.326108 0.188278i
\(573\) −30.7046 + 17.7273i −1.28270 + 0.740570i
\(574\) −3.94702 6.83643i −0.164745 0.285347i
\(575\) 46.8648i 1.95440i
\(576\) −0.0359734 0.0623078i −0.00149889 0.00259616i
\(577\) −11.1793 19.3631i −0.465400 0.806096i 0.533819 0.845598i \(-0.320756\pi\)
−0.999219 + 0.0395020i \(0.987423\pi\)
\(578\) −39.4867 17.1569i −1.64243 0.713634i
\(579\) −3.25711 + 5.64148i −0.135361 + 0.234452i
\(580\) −41.5112 −1.72366
\(581\) 5.34449i 0.221727i
\(582\) 14.9178 25.8383i 0.618362 1.07103i
\(583\) −9.73845 5.62250i −0.403326 0.232860i
\(584\) 28.1075 16.2279i 1.16310 0.671514i
\(585\) −0.208339 + 0.120284i −0.00861375 + 0.00497315i
\(586\) −84.9223 −3.50811
\(587\) −2.29525 3.97549i −0.0947352 0.164086i 0.814763 0.579794i \(-0.196867\pi\)
−0.909498 + 0.415708i \(0.863534\pi\)
\(588\) −45.0038 + 25.9829i −1.85592 + 1.07152i
\(589\) 0.820313 0.473608i 0.0338004 0.0195147i
\(590\) −131.284 75.7968i −5.40487 3.12050i
\(591\) −29.4052 −1.20957
\(592\) 38.6724 + 22.3275i 1.58943 + 0.917655i
\(593\) 22.8766 + 39.6234i 0.939429 + 1.62714i 0.766539 + 0.642198i \(0.221977\pi\)
0.172891 + 0.984941i \(0.444689\pi\)
\(594\) 20.7981 0.853358
\(595\) −8.45383 1.75723i −0.346573 0.0720395i
\(596\) 28.9126 50.0781i 1.18431 2.05128i
\(597\) 16.6460 28.8317i 0.681276 1.18000i
\(598\) 12.3248i 0.504000i
\(599\) −9.63970 + 16.6965i −0.393867 + 0.682198i −0.992956 0.118484i \(-0.962196\pi\)
0.599088 + 0.800683i \(0.295530\pi\)
\(600\) 131.601i 5.37260i
\(601\) 15.9252i 0.649604i −0.945782 0.324802i \(-0.894702\pi\)
0.945782 0.324802i \(-0.105298\pi\)
\(602\) −7.52303 + 3.62864i −0.306616 + 0.147892i
\(603\) 0.208612 0.00849534
\(604\) −65.6137 −2.66978
\(605\) 30.5187 + 17.6200i 1.24076 + 0.716354i
\(606\) 35.2040i 1.43006i
\(607\) 29.4844 + 17.0228i 1.19674 + 0.690936i 0.959826 0.280596i \(-0.0905321\pi\)
0.236910 + 0.971532i \(0.423865\pi\)
\(608\) 1.15730 2.00450i 0.0469348 0.0812934i
\(609\) 1.71682 0.991209i 0.0695693 0.0401658i
\(610\) 93.6427 3.79148
\(611\) −4.10622 7.11218i −0.166120 0.287728i
\(612\) 0.257113 + 0.779375i 0.0103932 + 0.0315043i
\(613\) 32.5892 1.31627 0.658133 0.752902i \(-0.271347\pi\)
0.658133 + 0.752902i \(0.271347\pi\)
\(614\) −30.9205 + 53.5559i −1.24785 + 2.16134i
\(615\) 38.9980 22.5155i 1.57255 0.907912i
\(616\) −2.44827 4.24053i −0.0986438 0.170856i
\(617\) 29.0497 16.7718i 1.16950 0.675209i 0.215935 0.976408i \(-0.430720\pi\)
0.953561 + 0.301199i \(0.0973868\pi\)
\(618\) 14.5113i 0.583728i
\(619\) −35.9765 + 20.7710i −1.44602 + 0.834858i −0.998241 0.0592881i \(-0.981117\pi\)
−0.447775 + 0.894146i \(0.647784\pi\)
\(620\) −17.3898 30.1200i −0.698392 1.20965i
\(621\) 9.79358 16.9630i 0.393003 0.680701i
\(622\) 54.6756 + 31.5670i 2.19229 + 1.26572i
\(623\) 5.15942i 0.206708i
\(624\) 14.8746i 0.595460i
\(625\) −32.7611 + 56.7438i −1.31044 + 2.26975i
\(626\) 66.4148 + 38.3446i 2.65447 + 1.53256i
\(627\) 0.695529 + 1.20469i 0.0277767 + 0.0481107i
\(628\) 45.3786 + 78.5981i 1.81081 + 3.13641i
\(629\) 20.6477 + 18.4239i 0.823279 + 0.734609i
\(630\) 0.119589 + 0.207133i 0.00476452 + 0.00825240i
\(631\) 5.55331 + 9.61862i 0.221074 + 0.382911i 0.955134 0.296173i \(-0.0957104\pi\)
−0.734060 + 0.679084i \(0.762377\pi\)
\(632\) 39.9489 23.0645i 1.58908 0.917458i
\(633\) 17.4772 30.2714i 0.694657 1.20318i
\(634\) 13.0763i 0.519327i
\(635\) −49.6917 28.6895i −1.97196 1.13851i
\(636\) 47.0944 27.1899i 1.86741 1.07815i
\(637\) −8.64394 −0.342485
\(638\) −4.55535 7.89009i −0.180348 0.312372i
\(639\) −0.266678 0.153967i −0.0105496 0.00609083i
\(640\) 47.9203 + 27.6668i 1.89421 + 1.09363i
\(641\) 10.0094i 0.395348i −0.980268 0.197674i \(-0.936661\pi\)
0.980268 0.197674i \(-0.0633388\pi\)
\(642\) −34.1599 + 59.1667i −1.34818 + 2.33512i
\(643\) 1.30626i 0.0515140i −0.999668 0.0257570i \(-0.991800\pi\)
0.999668 0.0257570i \(-0.00819961\pi\)
\(644\) −8.43248 −0.332286
\(645\) −20.6993 42.9147i −0.815035 1.68976i
\(646\) 3.47961 3.89961i 0.136903 0.153428i
\(647\) 13.0005 0.511102 0.255551 0.966796i \(-0.417743\pi\)
0.255551 + 0.966796i \(0.417743\pi\)
\(648\) −27.9149 + 48.3500i −1.09660 + 1.89937i
\(649\) 22.8961i 0.898750i
\(650\) 20.0144 34.6660i 0.785030 1.35971i
\(651\) 1.43842 + 0.830472i 0.0563761 + 0.0325487i
\(652\) 64.1877 37.0588i 2.51378 1.45133i
\(653\) 17.1551i 0.671331i −0.941981 0.335666i \(-0.891039\pi\)
0.941981 0.335666i \(-0.108961\pi\)
\(654\) −14.1256 24.4662i −0.552353 0.956703i
\(655\) −32.7649 + 56.7505i −1.28023 + 2.21743i
\(656\) 41.2350i 1.60996i
\(657\) −0.207363 0.119721i −0.00809002 0.00467077i
\(658\) −7.07103 + 4.08246i −0.275658 + 0.159151i
\(659\) 1.98073 + 3.43072i 0.0771582 + 0.133642i 0.902023 0.431688i \(-0.142082\pi\)
−0.824865 + 0.565330i \(0.808749\pi\)
\(660\) 44.2335 25.5382i 1.72179 0.994075i
\(661\) 19.1043 0.743073 0.371537 0.928418i \(-0.378831\pi\)
0.371537 + 0.928418i \(0.378831\pi\)
\(662\) 21.0742 + 36.5015i 0.819070 + 1.41867i
\(663\) −1.87592 + 9.02481i −0.0728547 + 0.350495i
\(664\) −32.4782 + 56.2540i −1.26040 + 2.18308i
\(665\) 0.524087 0.907745i 0.0203232 0.0352008i
\(666\) 0.766531i 0.0297025i
\(667\) −8.58022 −0.332228
\(668\) −10.4523 6.03465i −0.404412 0.233488i
\(669\) 6.04669 + 3.49106i 0.233778 + 0.134972i
\(670\) −42.2440 + 24.3896i −1.63203 + 0.942251i
\(671\) 7.07171 + 12.2486i 0.273000 + 0.472850i
\(672\) 4.05866 0.156566
\(673\) −1.60714 + 0.927883i −0.0619507 + 0.0357673i −0.530655 0.847588i \(-0.678054\pi\)
0.468705 + 0.883355i \(0.344721\pi\)
\(674\) 45.6004 26.3274i 1.75646 1.01409i
\(675\) 55.0927 31.8078i 2.12052 1.22428i
\(676\) 25.0669 43.4172i 0.964113 1.66989i
\(677\) 49.4628i 1.90101i 0.310712 + 0.950504i \(0.399433\pi\)
−0.310712 + 0.950504i \(0.600567\pi\)
\(678\) −27.1437 + 47.0143i −1.04245 + 1.80557i
\(679\) −1.69774 2.94058i −0.0651535 0.112849i
\(680\) −78.3031 69.8696i −3.00279 2.67938i
\(681\) 18.3284 + 31.7457i 0.702346 + 1.21650i
\(682\) 3.81664 6.61061i 0.146147 0.253133i
\(683\) −32.1586 18.5668i −1.23051 0.710437i −0.263376 0.964693i \(-0.584836\pi\)
−0.967137 + 0.254256i \(0.918169\pi\)
\(684\) −0.0996262 −0.00380930
\(685\) −17.7577 10.2524i −0.678486 0.391724i
\(686\) 17.5101i 0.668538i
\(687\) 33.8435i 1.29121i
\(688\) −43.5095 3.23351i −1.65878 0.123277i
\(689\) 9.04549 0.344606
\(690\) 69.8994i 2.66102i
\(691\) −9.60398 5.54486i −0.365353 0.210936i 0.306074 0.952008i \(-0.400985\pi\)
−0.671426 + 0.741071i \(0.734318\pi\)
\(692\) 50.4551i 1.91801i
\(693\) −0.0180622 + 0.0312846i −0.000686126 + 0.00118840i
\(694\) 14.1503 + 8.16966i 0.537137 + 0.310116i
\(695\) −10.5588 18.2884i −0.400519 0.693718i
\(696\) 24.0942 0.913287
\(697\) 5.20038 25.0184i 0.196979 0.947640i
\(698\) −18.4761 + 32.0016i −0.699331 + 1.21128i
\(699\) −19.2857 −0.729451
\(700\) −23.7180 13.6936i −0.896456 0.517569i
\(701\) −4.58771 7.94615i −0.173275 0.300122i 0.766288 0.642498i \(-0.222102\pi\)
−0.939563 + 0.342376i \(0.888768\pi\)
\(702\) −14.4886 + 8.36502i −0.546838 + 0.315717i
\(703\) −2.90920 + 1.67963i −0.109723 + 0.0633484i
\(704\) 2.54090i 0.0957637i
\(705\) −23.2881 40.3362i −0.877082 1.51915i
\(706\) −6.29827 10.9089i −0.237039 0.410563i
\(707\) 3.46969 + 2.00323i 0.130491 + 0.0753392i
\(708\) 95.8894 + 55.3618i 3.60374 + 2.08062i
\(709\) 48.4338i 1.81897i 0.415736 + 0.909485i \(0.363524\pi\)
−0.415736 + 0.909485i \(0.636476\pi\)
\(710\) 72.0031 2.70223
\(711\) −0.294724 0.170159i −0.0110530 0.00638146i
\(712\) 31.3536 54.3060i 1.17503 2.03520i
\(713\) −3.59441 6.22571i −0.134612 0.233155i
\(714\) 8.97260 + 1.86507i 0.335791 + 0.0697984i
\(715\) 8.49601 0.317733
\(716\) −15.2150 26.3531i −0.568610 0.984861i
\(717\) −10.2883 + 5.93993i −0.384222 + 0.221831i
\(718\) −0.500544 0.866968i −0.0186801 0.0323549i
\(719\) −25.1135 14.4993i −0.936574 0.540731i −0.0476893 0.998862i \(-0.515186\pi\)
−0.888885 + 0.458131i \(0.848519\pi\)
\(720\) 1.24936i 0.0465608i
\(721\) 1.43022 + 0.825740i 0.0532643 + 0.0307522i
\(722\) −23.7418 41.1220i −0.883579 1.53040i
\(723\) −12.7733 −0.475044
\(724\) −56.9715 + 32.8925i −2.11733 + 1.22244i
\(725\) −24.1335 13.9335i −0.896297 0.517478i
\(726\) −32.3915 18.7012i −1.20216 0.694068i
\(727\) −10.9901 −0.407602 −0.203801 0.979012i \(-0.565330\pi\)
−0.203801 + 0.979012i \(0.565330\pi\)
\(728\) 3.41109 + 1.96939i 0.126423 + 0.0729906i
\(729\) −26.5820 −0.984519
\(730\) 55.9882 2.07222
\(731\) −25.9906 7.44909i −0.961297 0.275515i
\(732\) −68.3964 −2.52800
\(733\) 21.9052 0.809086 0.404543 0.914519i \(-0.367431\pi\)
0.404543 + 0.914519i \(0.367431\pi\)
\(734\) 50.2577 + 29.0163i 1.85505 + 1.07101i
\(735\) −49.0235 −1.80826
\(736\) −15.2130 8.78325i −0.560760 0.323755i
\(737\) −6.38036 3.68370i −0.235024 0.135691i
\(738\) −0.612994 + 0.353912i −0.0225646 + 0.0130277i
\(739\) 15.8611 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(740\) 61.6721 + 106.819i 2.26711 + 3.92675i
\(741\) −0.969055 0.559484i −0.0355991 0.0205532i
\(742\) 8.99316i 0.330149i
\(743\) −5.39527 3.11496i −0.197933 0.114277i 0.397758 0.917490i \(-0.369788\pi\)
−0.595691 + 0.803214i \(0.703122\pi\)
\(744\) 10.0935 + 17.4824i 0.370045 + 0.640937i
\(745\) 47.2426 27.2755i 1.73084 0.999298i
\(746\) 10.9577 + 18.9793i 0.401189 + 0.694880i
\(747\) 0.479218 0.0175337
\(748\) 5.89855 28.3772i 0.215672 1.03757i
\(749\) 3.88763 + 6.73357i 0.142051 + 0.246039i
\(750\) 67.5074 116.926i 2.46502 4.26954i
\(751\) 15.6392 + 9.02929i 0.570682 + 0.329484i 0.757422 0.652926i \(-0.226459\pi\)
−0.186739 + 0.982409i \(0.559792\pi\)
\(752\) −42.6501 −1.55529
\(753\) 23.4818i 0.855724i
\(754\) 6.34680 + 3.66433i 0.231137 + 0.133447i
\(755\) −53.6058 30.9493i −1.95091 1.12636i
\(756\) 5.72324 + 9.91294i 0.208152 + 0.360530i
\(757\) 17.0420 + 29.5176i 0.619402 + 1.07284i 0.989595 + 0.143881i \(0.0459583\pi\)
−0.370193 + 0.928955i \(0.620708\pi\)
\(758\) 30.7478i 1.11681i
\(759\) 9.14291 5.27866i 0.331867 0.191603i
\(760\) 11.0327 6.36971i 0.400197 0.231054i
\(761\) 22.6287 + 39.1941i 0.820290 + 1.42078i 0.905467 + 0.424418i \(0.139521\pi\)
−0.0851768 + 0.996366i \(0.527146\pi\)
\(762\) 52.7411