Properties

Label 525.2.m.b.118.6
Level 525
Weight 2
Character 525.118
Analytic conductor 4.192
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 118.6
Root \(-1.40927 - 0.118126i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 525.118
Dual form 525.2.m.b.307.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.167056 - 0.167056i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.94418i q^{4} -0.236253i q^{6} +(0.0627175 - 2.64501i) q^{7} +(0.658899 + 0.658899i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.167056 - 0.167056i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.94418i q^{4} -0.236253i q^{6} +(0.0627175 - 2.64501i) q^{7} +(0.658899 + 0.658899i) q^{8} -1.00000i q^{9} +3.98602 q^{11} +(1.37475 + 1.37475i) q^{12} +(0.500437 - 0.500437i) q^{13} +(-0.431387 - 0.452341i) q^{14} -3.66822 q^{16} +(-1.67840 - 1.67840i) q^{17} +(-0.167056 - 0.167056i) q^{18} +7.21850 q^{19} +(-1.82596 - 1.91465i) q^{21} +(0.665888 - 0.665888i) q^{22} +(5.16007 + 5.16007i) q^{23} +0.931824 q^{24} -0.167202i q^{26} +(-0.707107 - 0.707107i) q^{27} +(5.14238 + 0.121934i) q^{28} +3.65191i q^{29} -4.93821i q^{31} +(-1.93060 + 1.93060i) q^{32} +(2.81854 - 2.81854i) q^{33} -0.560773 q^{34} +1.94418 q^{36} +(-0.292275 + 0.292275i) q^{37} +(1.20589 - 1.20589i) q^{38} -0.707725i q^{39} +7.63184i q^{41} +(-0.624890 - 0.0148172i) q^{42} +(-3.65191 - 3.65191i) q^{43} +7.74956i q^{44} +1.72404 q^{46} +(-0.305303 - 0.305303i) q^{47} +(-2.59383 + 2.59383i) q^{48} +(-6.99213 - 0.331777i) q^{49} -2.37361 q^{51} +(0.972943 + 0.972943i) q^{52} +(-5.39653 - 5.39653i) q^{53} -0.236253 q^{54} +(1.78412 - 1.70147i) q^{56} +(5.10425 - 5.10425i) q^{57} +(0.610073 + 0.610073i) q^{58} -6.10959 q^{59} -7.11047i q^{61} +(-0.824957 - 0.824957i) q^{62} +(-2.64501 - 0.0627175i) q^{63} -6.69141i q^{64} -0.941708i q^{66} +(-0.944185 + 0.944185i) q^{67} +(3.26312 - 3.26312i) q^{68} +7.29744 q^{69} +1.19297 q^{71} +(0.658899 - 0.658899i) q^{72} +(1.38298 - 1.38298i) q^{73} +0.0976524i q^{74} +14.0341i q^{76} +(0.249993 - 10.5431i) q^{77} +(-0.118230 - 0.118230i) q^{78} -8.64027i q^{79} -1.00000 q^{81} +(1.27494 + 1.27494i) q^{82} +(-11.9895 + 11.9895i) q^{83} +(3.72244 - 3.54999i) q^{84} -1.22015 q^{86} +(2.58229 + 2.58229i) q^{87} +(2.62639 + 2.62639i) q^{88} -7.82581 q^{89} +(-1.29227 - 1.35505i) q^{91} +(-10.0321 + 10.0321i) q^{92} +(-3.49184 - 3.49184i) q^{93} -0.102005 q^{94} +2.73028i q^{96} +(7.43671 + 7.43671i) q^{97} +(-1.22350 + 1.11265i) q^{98} -3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q + 8q^{7} - 24q^{8} - 16q^{11} - 48q^{16} + 8q^{21} + 16q^{22} + 40q^{23} - 24q^{28} - 48q^{32} - 16q^{36} - 32q^{37} + 16q^{42} + 16q^{43} + 64q^{46} - 16q^{51} - 24q^{53} + 24q^{56} - 8q^{57} - 32q^{58} - 8q^{63} + 32q^{67} + 64q^{71} - 24q^{72} + 24q^{77} + 8q^{78} - 16q^{81} + 64q^{86} + 64q^{88} - 48q^{91} + 40q^{92} - 24q^{93} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.167056 0.167056i 0.118126 0.118126i −0.645573 0.763699i \(-0.723381\pi\)
0.763699 + 0.645573i \(0.223381\pi\)
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.94418i 0.972092i
\(5\) 0 0
\(6\) 0.236253i 0.0964497i
\(7\) 0.0627175 2.64501i 0.0237050 0.999719i
\(8\) 0.658899 + 0.658899i 0.232956 + 0.232956i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 3.98602 1.20183 0.600915 0.799313i \(-0.294803\pi\)
0.600915 + 0.799313i \(0.294803\pi\)
\(12\) 1.37475 + 1.37475i 0.396855 + 0.396855i
\(13\) 0.500437 0.500437i 0.138796 0.138796i −0.634295 0.773091i \(-0.718709\pi\)
0.773091 + 0.634295i \(0.218709\pi\)
\(14\) −0.431387 0.452341i −0.115293 0.120893i
\(15\) 0 0
\(16\) −3.66822 −0.917056
\(17\) −1.67840 1.67840i −0.407071 0.407071i 0.473645 0.880716i \(-0.342938\pi\)
−0.880716 + 0.473645i \(0.842938\pi\)
\(18\) −0.167056 0.167056i −0.0393754 0.0393754i
\(19\) 7.21850 1.65604 0.828019 0.560700i \(-0.189468\pi\)
0.828019 + 0.560700i \(0.189468\pi\)
\(20\) 0 0
\(21\) −1.82596 1.91465i −0.398456 0.417811i
\(22\) 0.665888 0.665888i 0.141968 0.141968i
\(23\) 5.16007 + 5.16007i 1.07595 + 1.07595i 0.996868 + 0.0790800i \(0.0251983\pi\)
0.0790800 + 0.996868i \(0.474802\pi\)
\(24\) 0.931824 0.190208
\(25\) 0 0
\(26\) 0.167202i 0.0327910i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 5.14238 + 0.121934i 0.971819 + 0.0230434i
\(29\) 3.65191i 0.678143i 0.940761 + 0.339071i \(0.110113\pi\)
−0.940761 + 0.339071i \(0.889887\pi\)
\(30\) 0 0
\(31\) 4.93821i 0.886929i −0.896292 0.443465i \(-0.853749\pi\)
0.896292 0.443465i \(-0.146251\pi\)
\(32\) −1.93060 + 1.93060i −0.341284 + 0.341284i
\(33\) 2.81854 2.81854i 0.490645 0.490645i
\(34\) −0.560773 −0.0961717
\(35\) 0 0
\(36\) 1.94418 0.324031
\(37\) −0.292275 + 0.292275i −0.0480497 + 0.0480497i −0.730723 0.682674i \(-0.760817\pi\)
0.682674 + 0.730723i \(0.260817\pi\)
\(38\) 1.20589 1.20589i 0.195622 0.195622i
\(39\) 0.707725i 0.113327i
\(40\) 0 0
\(41\) 7.63184i 1.19189i 0.803024 + 0.595947i \(0.203223\pi\)
−0.803024 + 0.595947i \(0.796777\pi\)
\(42\) −0.624890 0.0148172i −0.0964226 0.00228634i
\(43\) −3.65191 3.65191i −0.556911 0.556911i 0.371516 0.928427i \(-0.378838\pi\)
−0.928427 + 0.371516i \(0.878838\pi\)
\(44\) 7.74956i 1.16829i
\(45\) 0 0
\(46\) 1.72404 0.254196
\(47\) −0.305303 0.305303i −0.0445331 0.0445331i 0.684490 0.729023i \(-0.260025\pi\)
−0.729023 + 0.684490i \(0.760025\pi\)
\(48\) −2.59383 + 2.59383i −0.374386 + 0.374386i
\(49\) −6.99213 0.331777i −0.998876 0.0473967i
\(50\) 0 0
\(51\) −2.37361 −0.332372
\(52\) 0.972943 + 0.972943i 0.134923 + 0.134923i
\(53\) −5.39653 5.39653i −0.741270 0.741270i 0.231553 0.972822i \(-0.425619\pi\)
−0.972822 + 0.231553i \(0.925619\pi\)
\(54\) −0.236253 −0.0321499
\(55\) 0 0
\(56\) 1.78412 1.70147i 0.238413 0.227368i
\(57\) 5.10425 5.10425i 0.676075 0.676075i
\(58\) 0.610073 + 0.610073i 0.0801065 + 0.0801065i
\(59\) −6.10959 −0.795401 −0.397701 0.917515i \(-0.630192\pi\)
−0.397701 + 0.917515i \(0.630192\pi\)
\(60\) 0 0
\(61\) 7.11047i 0.910402i −0.890389 0.455201i \(-0.849567\pi\)
0.890389 0.455201i \(-0.150433\pi\)
\(62\) −0.824957 0.824957i −0.104770 0.104770i
\(63\) −2.64501 0.0627175i −0.333240 0.00790166i
\(64\) 6.69141i 0.836426i
\(65\) 0 0
\(66\) 0.941708i 0.115916i
\(67\) −0.944185 + 0.944185i −0.115351 + 0.115351i −0.762426 0.647075i \(-0.775992\pi\)
0.647075 + 0.762426i \(0.275992\pi\)
\(68\) 3.26312 3.26312i 0.395711 0.395711i
\(69\) 7.29744 0.878508
\(70\) 0 0
\(71\) 1.19297 0.141579 0.0707897 0.997491i \(-0.477448\pi\)
0.0707897 + 0.997491i \(0.477448\pi\)
\(72\) 0.658899 0.658899i 0.0776520 0.0776520i
\(73\) 1.38298 1.38298i 0.161865 0.161865i −0.621527 0.783393i \(-0.713487\pi\)
0.783393 + 0.621527i \(0.213487\pi\)
\(74\) 0.0976524i 0.0113519i
\(75\) 0 0
\(76\) 14.0341i 1.60982i
\(77\) 0.249993 10.5431i 0.0284894 1.20149i
\(78\) −0.118230 0.118230i −0.0133869 0.0133869i
\(79\) 8.64027i 0.972106i −0.873929 0.486053i \(-0.838436\pi\)
0.873929 0.486053i \(-0.161564\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 1.27494 + 1.27494i 0.140794 + 0.140794i
\(83\) −11.9895 + 11.9895i −1.31602 + 1.31602i −0.399122 + 0.916898i \(0.630685\pi\)
−0.916898 + 0.399122i \(0.869315\pi\)
\(84\) 3.72244 3.54999i 0.406151 0.387336i
\(85\) 0 0
\(86\) −1.22015 −0.131572
\(87\) 2.58229 + 2.58229i 0.276851 + 0.276851i
\(88\) 2.62639 + 2.62639i 0.279974 + 0.279974i
\(89\) −7.82581 −0.829534 −0.414767 0.909928i \(-0.636137\pi\)
−0.414767 + 0.909928i \(0.636137\pi\)
\(90\) 0 0
\(91\) −1.29227 1.35505i −0.135467 0.142048i
\(92\) −10.0321 + 10.0321i −1.04592 + 1.04592i
\(93\) −3.49184 3.49184i −0.362087 0.362087i
\(94\) −0.102005 −0.0105211
\(95\) 0 0
\(96\) 2.73028i 0.278658i
\(97\) 7.43671 + 7.43671i 0.755083 + 0.755083i 0.975423 0.220340i \(-0.0707167\pi\)
−0.220340 + 0.975423i \(0.570717\pi\)
\(98\) −1.22350 + 1.11265i −0.123592 + 0.112395i
\(99\) 3.98602i 0.400610i
\(100\) 0 0
\(101\) 6.31633i 0.628498i −0.949341 0.314249i \(-0.898247\pi\)
0.949341 0.314249i \(-0.101753\pi\)
\(102\) −0.396526 + 0.396526i −0.0392619 + 0.0392619i
\(103\) −12.5410 + 12.5410i −1.23570 + 1.23570i −0.273954 + 0.961743i \(0.588332\pi\)
−0.961743 + 0.273954i \(0.911668\pi\)
\(104\) 0.659476 0.0646669
\(105\) 0 0
\(106\) −1.80304 −0.175127
\(107\) −7.48020 + 7.48020i −0.723138 + 0.723138i −0.969243 0.246105i \(-0.920849\pi\)
0.246105 + 0.969243i \(0.420849\pi\)
\(108\) 1.37475 1.37475i 0.132285 0.132285i
\(109\) 0.668223i 0.0640042i −0.999488 0.0320021i \(-0.989812\pi\)
0.999488 0.0320021i \(-0.0101883\pi\)
\(110\) 0 0
\(111\) 0.413339i 0.0392324i
\(112\) −0.230062 + 9.70248i −0.0217388 + 0.916798i
\(113\) 3.39653 + 3.39653i 0.319518 + 0.319518i 0.848582 0.529064i \(-0.177457\pi\)
−0.529064 + 0.848582i \(0.677457\pi\)
\(114\) 1.70539i 0.159724i
\(115\) 0 0
\(116\) −7.09999 −0.659217
\(117\) −0.500437 0.500437i −0.0462655 0.0462655i
\(118\) −1.02064 + 1.02064i −0.0939578 + 0.0939578i
\(119\) −4.54464 + 4.33411i −0.416607 + 0.397307i
\(120\) 0 0
\(121\) 4.88837 0.444397
\(122\) −1.18785 1.18785i −0.107542 0.107542i
\(123\) 5.39653 + 5.39653i 0.486588 + 0.486588i
\(124\) 9.60080 0.862177
\(125\) 0 0
\(126\) −0.452341 + 0.431387i −0.0402978 + 0.0384310i
\(127\) 5.88837 5.88837i 0.522508 0.522508i −0.395820 0.918328i \(-0.629540\pi\)
0.918328 + 0.395820i \(0.129540\pi\)
\(128\) −4.97903 4.97903i −0.440088 0.440088i
\(129\) −5.16458 −0.454716
\(130\) 0 0
\(131\) 18.8144i 1.64383i 0.569613 + 0.821913i \(0.307093\pi\)
−0.569613 + 0.821913i \(0.692907\pi\)
\(132\) 5.47977 + 5.47977i 0.476953 + 0.476953i
\(133\) 0.452726 19.0930i 0.0392564 1.65557i
\(134\) 0.315463i 0.0272519i
\(135\) 0 0
\(136\) 2.21179i 0.189659i
\(137\) 0.811977 0.811977i 0.0693719 0.0693719i −0.671570 0.740941i \(-0.734380\pi\)
0.740941 + 0.671570i \(0.234380\pi\)
\(138\) 1.21908 1.21908i 0.103775 0.103775i
\(139\) 0.442439 0.0375272 0.0187636 0.999824i \(-0.494027\pi\)
0.0187636 + 0.999824i \(0.494027\pi\)
\(140\) 0 0
\(141\) −0.431764 −0.0363611
\(142\) 0.199293 0.199293i 0.0167243 0.0167243i
\(143\) 1.99475 1.99475i 0.166810 0.166810i
\(144\) 3.66822i 0.305685i
\(145\) 0 0
\(146\) 0.462070i 0.0382411i
\(147\) −5.17879 + 4.70958i −0.427139 + 0.388440i
\(148\) −0.568236 0.568236i −0.0467087 0.0467087i
\(149\) 3.14114i 0.257332i 0.991688 + 0.128666i \(0.0410696\pi\)
−0.991688 + 0.128666i \(0.958930\pi\)
\(150\) 0 0
\(151\) −14.7239 −1.19822 −0.599109 0.800668i \(-0.704478\pi\)
−0.599109 + 0.800668i \(0.704478\pi\)
\(152\) 4.75626 + 4.75626i 0.385784 + 0.385784i
\(153\) −1.67840 + 1.67840i −0.135690 + 0.135690i
\(154\) −1.71952 1.80304i −0.138563 0.145293i
\(155\) 0 0
\(156\) 1.37595 0.110164
\(157\) −7.96508 7.96508i −0.635682 0.635682i 0.313805 0.949487i \(-0.398396\pi\)
−0.949487 + 0.313805i \(0.898396\pi\)
\(158\) −1.44341 1.44341i −0.114831 0.114831i
\(159\) −7.63184 −0.605244
\(160\) 0 0
\(161\) 13.9720 13.3248i 1.10115 1.05014i
\(162\) −0.167056 + 0.167056i −0.0131251 + 0.0131251i
\(163\) −10.4450 10.4450i −0.818113 0.818113i 0.167722 0.985834i \(-0.446359\pi\)
−0.985834 + 0.167722i \(0.946359\pi\)
\(164\) −14.8377 −1.15863
\(165\) 0 0
\(166\) 4.00584i 0.310913i
\(167\) 4.63621 + 4.63621i 0.358761 + 0.358761i 0.863356 0.504595i \(-0.168358\pi\)
−0.504595 + 0.863356i \(0.668358\pi\)
\(168\) 0.0584417 2.46468i 0.00450887 0.190154i
\(169\) 12.4991i 0.961471i
\(170\) 0 0
\(171\) 7.21850i 0.552013i
\(172\) 7.09999 7.09999i 0.541369 0.541369i
\(173\) −2.48531 + 2.48531i −0.188954 + 0.188954i −0.795244 0.606290i \(-0.792657\pi\)
0.606290 + 0.795244i \(0.292657\pi\)
\(174\) 0.862773 0.0654067
\(175\) 0 0
\(176\) −14.6216 −1.10215
\(177\) −4.32013 + 4.32013i −0.324721 + 0.324721i
\(178\) −1.30735 + 1.30735i −0.0979898 + 0.0979898i
\(179\) 22.1109i 1.65264i −0.563199 0.826321i \(-0.690430\pi\)
0.563199 0.826321i \(-0.309570\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) −0.442251 0.0104865i −0.0327818 0.000777310i
\(183\) −5.02786 5.02786i −0.371670 0.371670i
\(184\) 6.79993i 0.501297i
\(185\) 0 0
\(186\) −1.16667 −0.0855441
\(187\) −6.69013 6.69013i −0.489231 0.489231i
\(188\) 0.593566 0.593566i 0.0432903 0.0432903i
\(189\) −1.91465 + 1.82596i −0.139270 + 0.132819i
\(190\) 0 0
\(191\) 15.2898 1.10633 0.553167 0.833070i \(-0.313419\pi\)
0.553167 + 0.833070i \(0.313419\pi\)
\(192\) −4.73154 4.73154i −0.341470 0.341470i
\(193\) 8.92787 + 8.92787i 0.642642 + 0.642642i 0.951204 0.308562i \(-0.0998477\pi\)
−0.308562 + 0.951204i \(0.599848\pi\)
\(194\) 2.48469 0.178390
\(195\) 0 0
\(196\) 0.645035 13.5940i 0.0460739 0.971000i
\(197\) 2.68715 2.68715i 0.191451 0.191451i −0.604872 0.796323i \(-0.706776\pi\)
0.796323 + 0.604872i \(0.206776\pi\)
\(198\) −0.665888 0.665888i −0.0473226 0.0473226i
\(199\) −0.616637 −0.0437122 −0.0218561 0.999761i \(-0.506958\pi\)
−0.0218561 + 0.999761i \(0.506958\pi\)
\(200\) 0 0
\(201\) 1.33528i 0.0941833i
\(202\) −1.05518 1.05518i −0.0742422 0.0742422i
\(203\) 9.65933 + 0.229039i 0.677952 + 0.0160754i
\(204\) 4.61474i 0.323097i
\(205\) 0 0
\(206\) 4.19008i 0.291937i
\(207\) 5.16007 5.16007i 0.358649 0.358649i
\(208\) −1.83572 + 1.83572i −0.127284 + 0.127284i
\(209\) 28.7731 1.99028
\(210\) 0 0
\(211\) 9.30849 0.640823 0.320411 0.947278i \(-0.396179\pi\)
0.320411 + 0.947278i \(0.396179\pi\)
\(212\) 10.4918 10.4918i 0.720583 0.720583i
\(213\) 0.843557 0.843557i 0.0577996 0.0577996i
\(214\) 2.49922i 0.170843i
\(215\) 0 0
\(216\) 0.931824i 0.0634026i
\(217\) −13.0616 0.309712i −0.886680 0.0210246i
\(218\) −0.111631 0.111631i −0.00756058 0.00756058i
\(219\) 1.95583i 0.132163i
\(220\) 0 0
\(221\) −1.67987 −0.113000
\(222\) 0.0690507 + 0.0690507i 0.00463438 + 0.00463438i
\(223\) −1.35505 + 1.35505i −0.0907407 + 0.0907407i −0.751020 0.660279i \(-0.770438\pi\)
0.660279 + 0.751020i \(0.270438\pi\)
\(224\) 4.98536 + 5.22753i 0.333098 + 0.349279i
\(225\) 0 0
\(226\) 1.13482 0.0754870
\(227\) 4.15437 + 4.15437i 0.275735 + 0.275735i 0.831404 0.555668i \(-0.187538\pi\)
−0.555668 + 0.831404i \(0.687538\pi\)
\(228\) 9.92361 + 9.92361i 0.657207 + 0.657207i
\(229\) −12.9900 −0.858403 −0.429202 0.903209i \(-0.641205\pi\)
−0.429202 + 0.903209i \(0.641205\pi\)
\(230\) 0 0
\(231\) −7.27830 7.63184i −0.478877 0.502138i
\(232\) −2.40624 + 2.40624i −0.157977 + 0.157977i
\(233\) 16.4639 + 16.4639i 1.07859 + 1.07859i 0.996637 + 0.0819485i \(0.0261143\pi\)
0.0819485 + 0.996637i \(0.473886\pi\)
\(234\) −0.167202 −0.0109303
\(235\) 0 0
\(236\) 11.8782i 0.773203i
\(237\) −6.10959 6.10959i −0.396861 0.396861i
\(238\) −0.0351703 + 1.48325i −0.00227975 + 0.0961447i
\(239\) 5.48048i 0.354503i −0.984166 0.177251i \(-0.943279\pi\)
0.984166 0.177251i \(-0.0567205\pi\)
\(240\) 0 0
\(241\) 14.6507i 0.943737i −0.881669 0.471868i \(-0.843580\pi\)
0.881669 0.471868i \(-0.156420\pi\)
\(242\) 0.816631 0.816631i 0.0524950 0.0524950i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 13.8241 0.884995
\(245\) 0 0
\(246\) 1.80304 0.114958
\(247\) 3.61241 3.61241i 0.229852 0.229852i
\(248\) 3.25378 3.25378i 0.206615 0.206615i
\(249\) 16.9557i 1.07453i
\(250\) 0 0
\(251\) 21.1506i 1.33501i 0.744604 + 0.667507i \(0.232639\pi\)
−0.744604 + 0.667507i \(0.767361\pi\)
\(252\) 0.121934 5.14238i 0.00768115 0.323940i
\(253\) 20.5681 + 20.5681i 1.29311 + 1.29311i
\(254\) 1.96737i 0.123444i
\(255\) 0 0
\(256\) 11.7193 0.732454
\(257\) −9.39248 9.39248i −0.585887 0.585887i 0.350628 0.936515i \(-0.385968\pi\)
−0.936515 + 0.350628i \(0.885968\pi\)
\(258\) −0.862773 + 0.862773i −0.0537139 + 0.0537139i
\(259\) 0.754738 + 0.791399i 0.0468971 + 0.0491752i
\(260\) 0 0
\(261\) 3.65191 0.226048
\(262\) 3.14306 + 3.14306i 0.194179 + 0.194179i
\(263\) −15.3779 15.3779i −0.948241 0.948241i 0.0504843 0.998725i \(-0.483924\pi\)
−0.998725 + 0.0504843i \(0.983924\pi\)
\(264\) 3.71427 0.228598
\(265\) 0 0
\(266\) −3.11397 3.26523i −0.190929 0.200204i
\(267\) −5.53368 + 5.53368i −0.338656 + 0.338656i
\(268\) −1.83567 1.83567i −0.112131 0.112131i
\(269\) 22.9851 1.40143 0.700714 0.713442i \(-0.252865\pi\)
0.700714 + 0.713442i \(0.252865\pi\)
\(270\) 0 0
\(271\) 15.7596i 0.957330i 0.877998 + 0.478665i \(0.158879\pi\)
−0.877998 + 0.478665i \(0.841121\pi\)
\(272\) 6.15674 + 6.15674i 0.373307 + 0.373307i
\(273\) −1.87194 0.0443868i −0.113295 0.00268641i
\(274\) 0.271291i 0.0163893i
\(275\) 0 0
\(276\) 14.1876i 0.853991i
\(277\) −4.80771 + 4.80771i −0.288867 + 0.288867i −0.836632 0.547765i \(-0.815479\pi\)
0.547765 + 0.836632i \(0.315479\pi\)
\(278\) 0.0739121 0.0739121i 0.00443295 0.00443295i
\(279\) −4.93821 −0.295643
\(280\) 0 0
\(281\) −9.65658 −0.576063 −0.288032 0.957621i \(-0.593001\pi\)
−0.288032 + 0.957621i \(0.593001\pi\)
\(282\) −0.0721287 + 0.0721287i −0.00429520 + 0.00429520i
\(283\) 14.9095 14.9095i 0.886278 0.886278i −0.107885 0.994163i \(-0.534408\pi\)
0.994163 + 0.107885i \(0.0344079\pi\)
\(284\) 2.31935i 0.137628i
\(285\) 0 0
\(286\) 0.666471i 0.0394092i
\(287\) 20.1863 + 0.478650i 1.19156 + 0.0282538i
\(288\) 1.93060 + 1.93060i 0.113761 + 0.113761i
\(289\) 11.3660i 0.668586i
\(290\) 0 0
\(291\) 10.5171 0.616523
\(292\) 2.68877 + 2.68877i 0.157348 + 0.157348i
\(293\) 4.79236 4.79236i 0.279973 0.279973i −0.553125 0.833098i \(-0.686565\pi\)
0.833098 + 0.553125i \(0.186565\pi\)
\(294\) −0.0783831 + 1.65191i −0.00457140 + 0.0963413i
\(295\) 0 0
\(296\) −0.385159 −0.0223869
\(297\) −2.81854 2.81854i −0.163548 0.163548i
\(298\) 0.524746 + 0.524746i 0.0303977 + 0.0303977i
\(299\) 5.16458 0.298675
\(300\) 0 0
\(301\) −9.88837 + 9.43029i −0.569956 + 0.543553i
\(302\) −2.45972 + 2.45972i −0.141541 + 0.141541i
\(303\) −4.46632 4.46632i −0.256583 0.256583i
\(304\) −26.4791 −1.51868
\(305\) 0 0
\(306\) 0.560773i 0.0320572i
\(307\) 9.85063 + 9.85063i 0.562205 + 0.562205i 0.929933 0.367728i \(-0.119864\pi\)
−0.367728 + 0.929933i \(0.619864\pi\)
\(308\) 20.4977 + 0.486033i 1.16796 + 0.0276943i
\(309\) 17.7356i 1.00894i
\(310\) 0 0
\(311\) 27.3063i 1.54840i −0.632941 0.774200i \(-0.718152\pi\)
0.632941 0.774200i \(-0.281848\pi\)
\(312\) 0.466320 0.466320i 0.0264002 0.0264002i
\(313\) 18.5080 18.5080i 1.04613 1.04613i 0.0472492 0.998883i \(-0.484955\pi\)
0.998883 0.0472492i \(-0.0150455\pi\)
\(314\) −2.66123 −0.150182
\(315\) 0 0
\(316\) 16.7983 0.944977
\(317\) 21.8793 21.8793i 1.22887 1.22887i 0.264473 0.964393i \(-0.414802\pi\)
0.964393 0.264473i \(-0.0851980\pi\)
\(318\) −1.27494 + 1.27494i −0.0714953 + 0.0714953i
\(319\) 14.5566i 0.815013i
\(320\) 0 0
\(321\) 10.5786i 0.590440i
\(322\) 0.108127 4.56010i 0.00602570 0.254124i
\(323\) −12.1155 12.1155i −0.674126 0.674126i
\(324\) 1.94418i 0.108010i
\(325\) 0 0
\(326\) −3.48978 −0.193281
\(327\) −0.472505 0.472505i −0.0261296 0.0261296i
\(328\) −5.02861 + 5.02861i −0.277659 + 0.277659i
\(329\) −0.826678 + 0.788382i −0.0455762 + 0.0434649i
\(330\) 0 0
\(331\) −16.6913 −0.917438 −0.458719 0.888581i \(-0.651691\pi\)
−0.458719 + 0.888581i \(0.651691\pi\)
\(332\) −23.3098 23.3098i −1.27929 1.27929i
\(333\) 0.292275 + 0.292275i 0.0160166 + 0.0160166i
\(334\) 1.54901 0.0847582
\(335\) 0 0
\(336\) 6.69801 + 7.02337i 0.365406 + 0.383156i
\(337\) −2.54028 + 2.54028i −0.138378 + 0.138378i −0.772903 0.634525i \(-0.781196\pi\)
0.634525 + 0.772903i \(0.281196\pi\)
\(338\) 2.08805 + 2.08805i 0.113575 + 0.113575i
\(339\) 4.80341 0.260886
\(340\) 0 0
\(341\) 19.6838i 1.06594i
\(342\) −1.20589 1.20589i −0.0652072 0.0652072i
\(343\) −1.31608 + 18.4734i −0.0710617 + 0.997472i
\(344\) 4.81248i 0.259472i
\(345\) 0 0
\(346\) 0.830370i 0.0446410i
\(347\) −13.6980 + 13.6980i −0.735348 + 0.735348i −0.971674 0.236326i \(-0.924057\pi\)
0.236326 + 0.971674i \(0.424057\pi\)
\(348\) −5.02045 + 5.02045i −0.269124 + 0.269124i
\(349\) −0.508601 −0.0272248 −0.0136124 0.999907i \(-0.504333\pi\)
−0.0136124 + 0.999907i \(0.504333\pi\)
\(350\) 0 0
\(351\) −0.707725 −0.0377756
\(352\) −7.69540 + 7.69540i −0.410166 + 0.410166i
\(353\) 10.9217 10.9217i 0.581305 0.581305i −0.353957 0.935262i \(-0.615164\pi\)
0.935262 + 0.353957i \(0.115164\pi\)
\(354\) 1.44341i 0.0767162i
\(355\) 0 0
\(356\) 15.2148i 0.806383i
\(357\) −0.148867 + 6.27823i −0.00787888 + 0.332279i
\(358\) −3.69375 3.69375i −0.195221 0.195221i
\(359\) 15.9860i 0.843710i 0.906663 + 0.421855i \(0.138621\pi\)
−0.906663 + 0.421855i \(0.861379\pi\)
\(360\) 0 0
\(361\) 33.1068 1.74246
\(362\) 1.41752 + 1.41752i 0.0745030 + 0.0745030i
\(363\) 3.45660 3.45660i 0.181424 0.181424i
\(364\) 2.63446 2.51242i 0.138083 0.131687i
\(365\) 0 0
\(366\) −1.67987 −0.0878080
\(367\) 0.410036 + 0.410036i 0.0214037 + 0.0214037i 0.717728 0.696324i \(-0.245182\pi\)
−0.696324 + 0.717728i \(0.745182\pi\)
\(368\) −18.9283 18.9283i −0.986705 0.986705i
\(369\) 7.63184 0.397298
\(370\) 0 0
\(371\) −14.6123 + 13.9354i −0.758633 + 0.723490i
\(372\) 6.78879 6.78879i 0.351982 0.351982i
\(373\) 3.44496 + 3.44496i 0.178373 + 0.178373i 0.790646 0.612273i \(-0.209745\pi\)
−0.612273 + 0.790646i \(0.709745\pi\)
\(374\) −2.23525 −0.115582
\(375\) 0 0
\(376\) 0.402328i 0.0207485i
\(377\) 1.82755 + 1.82755i 0.0941237 + 0.0941237i
\(378\) −0.0148172 + 0.624890i −0.000762113 + 0.0321409i
\(379\) 12.9179i 0.663547i 0.943359 + 0.331773i \(0.107647\pi\)
−0.943359 + 0.331773i \(0.892353\pi\)
\(380\) 0 0
\(381\) 8.32741i 0.426626i
\(382\) 2.55426 2.55426i 0.130687 0.130687i
\(383\) −10.0770 + 10.0770i −0.514910 + 0.514910i −0.916027 0.401117i \(-0.868622\pi\)
0.401117 + 0.916027i \(0.368622\pi\)
\(384\) −7.04142 −0.359331
\(385\) 0 0
\(386\) 2.98291 0.151826
\(387\) −3.65191 + 3.65191i −0.185637 + 0.185637i
\(388\) −14.4583 + 14.4583i −0.734011 + 0.734011i
\(389\) 24.3300i 1.23358i −0.787127 0.616791i \(-0.788433\pi\)
0.787127 0.616791i \(-0.211567\pi\)
\(390\) 0 0
\(391\) 17.3213i 0.875976i
\(392\) −4.38850 4.82572i −0.221653 0.243736i
\(393\) 13.3038 + 13.3038i 0.671089 + 0.671089i
\(394\) 0.897808i 0.0452309i
\(395\) 0 0
\(396\) 7.74956 0.389430
\(397\) 6.80633 + 6.80633i 0.341600 + 0.341600i 0.856969 0.515369i \(-0.172345\pi\)
−0.515369 + 0.856969i \(0.672345\pi\)
\(398\) −0.103013 + 0.103013i −0.00516356 + 0.00516356i
\(399\) −13.1807 13.8209i −0.659858 0.691911i
\(400\) 0 0
\(401\) −8.83090 −0.440994 −0.220497 0.975388i \(-0.570768\pi\)
−0.220497 + 0.975388i \(0.570768\pi\)
\(402\) 0.223066 + 0.223066i 0.0111255 + 0.0111255i
\(403\) −2.47127 2.47127i −0.123103 0.123103i
\(404\) 12.2801 0.610958
\(405\) 0 0
\(406\) 1.65191 1.57539i 0.0819829 0.0781851i
\(407\) −1.16501 + 1.16501i −0.0577476 + 0.0577476i
\(408\) −1.56397 1.56397i −0.0774282 0.0774282i
\(409\) 23.1985 1.14709 0.573546 0.819174i \(-0.305568\pi\)
0.573546 + 0.819174i \(0.305568\pi\)
\(410\) 0 0
\(411\) 1.14831i 0.0566419i
\(412\) −24.3819 24.3819i −1.20121 1.20121i
\(413\) −0.383178 + 16.1599i −0.0188550 + 0.795178i
\(414\) 1.72404i 0.0847319i
\(415\) 0 0
\(416\) 1.93229i 0.0947381i
\(417\) 0.312852 0.312852i 0.0153204 0.0153204i
\(418\) 4.80672 4.80672i 0.235104 0.235104i
\(419\) −13.0393 −0.637009 −0.318505 0.947921i \(-0.603181\pi\)
−0.318505 + 0.947921i \(0.603181\pi\)
\(420\) 0 0
\(421\) −31.3549 −1.52814 −0.764071 0.645132i \(-0.776802\pi\)
−0.764071 + 0.645132i \(0.776802\pi\)
\(422\) 1.55504 1.55504i 0.0756981 0.0756981i
\(423\) −0.305303 + 0.305303i −0.0148444 + 0.0148444i
\(424\) 7.11153i 0.345367i
\(425\) 0 0
\(426\) 0.281842i 0.0136553i
\(427\) −18.8072 0.445951i −0.910146 0.0215811i
\(428\) −14.5429 14.5429i −0.702957 0.702957i
\(429\) 2.82101i 0.136200i
\(430\) 0 0
\(431\) −22.5558 −1.08648 −0.543238 0.839579i \(-0.682802\pi\)
−0.543238 + 0.839579i \(0.682802\pi\)
\(432\) 2.59383 + 2.59383i 0.124795 + 0.124795i
\(433\) −19.9639 + 19.9639i −0.959405 + 0.959405i −0.999208 0.0398028i \(-0.987327\pi\)
0.0398028 + 0.999208i \(0.487327\pi\)
\(434\) −2.23376 + 2.13028i −0.107224 + 0.102257i
\(435\) 0 0
\(436\) 1.29915 0.0622180
\(437\) 37.2479 + 37.2479i 1.78181 + 1.78181i
\(438\) −0.326732 0.326732i −0.0156119 0.0156119i
\(439\) −30.1943 −1.44110 −0.720548 0.693405i \(-0.756110\pi\)
−0.720548 + 0.693405i \(0.756110\pi\)
\(440\) 0 0
\(441\) −0.331777 + 6.99213i −0.0157989 + 0.332959i
\(442\) −0.280632 + 0.280632i −0.0133483 + 0.0133483i
\(443\) 12.7423 + 12.7423i 0.605404 + 0.605404i 0.941742 0.336337i \(-0.109188\pi\)
−0.336337 + 0.941742i \(0.609188\pi\)
\(444\) −0.803607 −0.0381375
\(445\) 0 0
\(446\) 0.452737i 0.0214377i
\(447\) 2.22112 + 2.22112i 0.105056 + 0.105056i
\(448\) −17.6988 0.419669i −0.836191 0.0198275i
\(449\) 30.4170i 1.43547i −0.696318 0.717734i \(-0.745180\pi\)
0.696318 0.717734i \(-0.254820\pi\)
\(450\) 0 0
\(451\) 30.4207i 1.43245i
\(452\) −6.60347 + 6.60347i −0.310601 + 0.310601i
\(453\) −10.4114 + 10.4114i −0.489170 + 0.489170i
\(454\) 1.38802 0.0651432
\(455\) 0 0
\(456\) 6.72637 0.314991
\(457\) −1.31546 + 1.31546i −0.0615348 + 0.0615348i −0.737204 0.675670i \(-0.763855\pi\)
0.675670 + 0.737204i \(0.263855\pi\)
\(458\) −2.17005 + 2.17005i −0.101400 + 0.101400i
\(459\) 2.37361i 0.110791i
\(460\) 0 0
\(461\) 1.29957i 0.0605272i −0.999542 0.0302636i \(-0.990365\pi\)
0.999542 0.0302636i \(-0.00963467\pi\)
\(462\) −2.49083 0.0590616i −0.115884 0.00274779i
\(463\) −16.5240 16.5240i −0.767934 0.767934i 0.209809 0.977742i \(-0.432716\pi\)
−0.977742 + 0.209809i \(0.932716\pi\)
\(464\) 13.3960i 0.621895i
\(465\) 0 0
\(466\) 5.50078 0.254819
\(467\) 20.1009 + 20.1009i 0.930157 + 0.930157i 0.997715 0.0675588i \(-0.0215210\pi\)
−0.0675588 + 0.997715i \(0.521521\pi\)
\(468\) 0.972943 0.972943i 0.0449743 0.0449743i
\(469\) 2.43816 + 2.55659i 0.112584 + 0.118052i
\(470\) 0 0
\(471\) −11.2643 −0.519032
\(472\) −4.02560 4.02560i −0.185293 0.185293i
\(473\) −14.5566 14.5566i −0.669313 0.669313i
\(474\) −2.04129 −0.0937594
\(475\) 0 0
\(476\) −8.42631 8.83562i −0.386219 0.404980i
\(477\) −5.39653 + 5.39653i −0.247090 + 0.247090i
\(478\) −0.915546 0.915546i −0.0418761 0.0418761i
\(479\) 11.0836 0.506425 0.253212 0.967411i \(-0.418513\pi\)
0.253212 + 0.967411i \(0.418513\pi\)
\(480\) 0 0
\(481\) 0.292530i 0.0133382i
\(482\) −2.44749 2.44749i −0.111480 0.111480i
\(483\) 0.457677 19.3018i 0.0208250 0.878261i
\(484\) 9.50389i 0.431995i
\(485\) 0 0
\(486\) 0.236253i 0.0107166i
\(487\) 13.6519 13.6519i 0.618627 0.618627i −0.326552 0.945179i \(-0.605887\pi\)
0.945179 + 0.326552i \(0.105887\pi\)
\(488\) 4.68508 4.68508i 0.212084 0.212084i
\(489\) −14.7714 −0.667986
\(490\) 0 0
\(491\) 32.1155 1.44935 0.724677 0.689089i \(-0.241989\pi\)
0.724677 + 0.689089i \(0.241989\pi\)
\(492\) −10.4918 + 10.4918i −0.473009 + 0.473009i
\(493\) 6.12936 6.12936i 0.276052 0.276052i
\(494\) 1.20695i 0.0543032i
\(495\) 0 0
\(496\) 18.1145i 0.813364i
\(497\) 0.0748201 3.15541i 0.00335614 0.141540i
\(498\) 2.83255 + 2.83255i 0.126930 + 0.126930i
\(499\) 4.27431i 0.191344i −0.995413 0.0956722i \(-0.969500\pi\)
0.995413 0.0956722i \(-0.0305000\pi\)
\(500\) 0 0
\(501\) 6.55659 0.292927
\(502\) 3.53333 + 3.53333i 0.157700 + 0.157700i
\(503\) 17.5637 17.5637i 0.783128 0.783128i −0.197229 0.980357i \(-0.563194\pi\)
0.980357 + 0.197229i \(0.0631943\pi\)
\(504\) −1.70147 1.78412i −0.0757894 0.0794709i
\(505\) 0 0
\(506\) 6.87206 0.305500
\(507\) 8.83822 + 8.83822i 0.392519 + 0.392519i
\(508\) 11.4481 + 11.4481i 0.507926 + 0.507926i
\(509\) 27.9162 1.23736 0.618682 0.785641i \(-0.287667\pi\)
0.618682 + 0.785641i \(0.287667\pi\)
\(510\) 0 0
\(511\) −3.57125 3.74473i −0.157983 0.165657i
\(512\) 11.9158 11.9158i 0.526611 0.526611i
\(513\) −5.10425 5.10425i −0.225358 0.225358i
\(514\) −3.13814 −0.138417
\(515\) 0 0
\(516\) 10.0409i 0.442026i
\(517\) −1.21695 1.21695i −0.0535212 0.0535212i
\(518\) 0.258291 + 0.00612451i 0.0113487 + 0.000269096i
\(519\) 3.51476i 0.154281i
\(520\) 0 0
\(521\) 28.8647i 1.26458i 0.774730 + 0.632292i \(0.217886\pi\)
−0.774730 + 0.632292i \(0.782114\pi\)
\(522\) 0.610073 0.610073i 0.0267022 0.0267022i
\(523\) −3.54707 + 3.54707i −0.155103 + 0.155103i −0.780392 0.625290i \(-0.784981\pi\)
0.625290 + 0.780392i \(0.284981\pi\)
\(524\) −36.5788 −1.59795
\(525\) 0 0
\(526\) −5.13793 −0.224024
\(527\) −8.28829 + 8.28829i −0.361043 + 0.361043i
\(528\) −10.3390 + 10.3390i −0.449949 + 0.449949i
\(529\) 30.2526i 1.31533i
\(530\) 0 0
\(531\) 6.10959i 0.265134i
\(532\) 37.1203 + 0.880184i 1.60937 + 0.0381608i
\(533\) 3.81926 + 3.81926i 0.165430 + 0.165430i
\(534\) 1.84887i 0.0800083i
\(535\) 0 0
\(536\) −1.24424 −0.0537432
\(537\) −15.6347 15.6347i −0.674688 0.674688i
\(538\) 3.83980 3.83980i 0.165546 0.165546i
\(539\) −27.8708 1.32247i −1.20048 0.0569628i
\(540\) 0 0
\(541\) −4.08698 −0.175713 −0.0878565 0.996133i \(-0.528002\pi\)
−0.0878565 + 0.996133i \(0.528002\pi\)
\(542\) 2.63274 + 2.63274i 0.113086 + 0.113086i
\(543\) 6.00000 + 6.00000i 0.257485 + 0.257485i
\(544\) 6.48062 0.277854
\(545\) 0 0
\(546\) −0.320133 + 0.305303i −0.0137004 + 0.0130658i
\(547\) −28.2200 + 28.2200i −1.20660 + 1.20660i −0.234482 + 0.972121i \(0.575339\pi\)
−0.972121 + 0.234482i \(0.924661\pi\)
\(548\) 1.57863 + 1.57863i 0.0674359 + 0.0674359i
\(549\) −7.11047 −0.303467
\(550\) 0 0
\(551\) 26.3613i 1.12303i
\(552\) 4.80827 + 4.80827i 0.204654 + 0.204654i
\(553\) −22.8536 0.541896i −0.971833 0.0230438i
\(554\) 1.60631i 0.0682457i
\(555\) 0 0
\(556\) 0.860184i 0.0364799i
\(557\) −28.1616 + 28.1616i −1.19325 + 1.19325i −0.217096 + 0.976150i \(0.569658\pi\)
−0.976150 + 0.217096i \(0.930342\pi\)
\(558\) −0.824957 + 0.824957i −0.0349232 + 0.0349232i
\(559\) −3.65510 −0.154594
\(560\) 0 0
\(561\) −9.46128 −0.399455
\(562\) −1.61319 + 1.61319i −0.0680482 + 0.0680482i
\(563\) −27.3645 + 27.3645i −1.15328 + 1.15328i −0.167386 + 0.985891i \(0.553533\pi\)
−0.985891 + 0.167386i \(0.946467\pi\)
\(564\) 0.839429i 0.0353463i
\(565\) 0 0
\(566\) 4.98144i 0.209386i
\(567\) −0.0627175 + 2.64501i −0.00263389 + 0.111080i
\(568\) 0.786047 + 0.786047i 0.0329818 + 0.0329818i
\(569\) 17.7767i 0.745240i 0.927984 + 0.372620i \(0.121540\pi\)
−0.927984 + 0.372620i \(0.878460\pi\)
\(570\) 0 0
\(571\) −16.8866 −0.706683 −0.353342 0.935494i \(-0.614955\pi\)
−0.353342 + 0.935494i \(0.614955\pi\)
\(572\) 3.87817 + 3.87817i 0.162154 + 0.162154i
\(573\) 10.8116 10.8116i 0.451659 0.451659i
\(574\) 3.45220 3.29227i 0.144092 0.137417i
\(575\) 0 0
\(576\) −6.69141 −0.278809
\(577\) 3.89677 + 3.89677i 0.162225 + 0.162225i 0.783552 0.621327i \(-0.213406\pi\)
−0.621327 + 0.783552i \(0.713406\pi\)
\(578\) −1.89875 1.89875i −0.0789776 0.0789776i
\(579\) 12.6259 0.524715
\(580\) 0 0
\(581\) 30.9604 + 32.4643i 1.28445 + 1.34685i
\(582\) 1.75694 1.75694i 0.0728276 0.0728276i
\(583\) −21.5107 21.5107i −0.890881 0.890881i
\(584\) 1.82249 0.0754151
\(585\) 0 0
\(586\) 1.60118i 0.0661443i
\(587\) −15.1058 15.1058i −0.623484 0.623484i 0.322937 0.946420i \(-0.395330\pi\)
−0.946420 + 0.322937i \(0.895330\pi\)
\(588\) −9.15630 10.0685i −0.377599 0.415219i
\(589\) 35.6465i 1.46879i
\(590\) 0 0
\(591\) 3.80020i 0.156319i
\(592\) 1.07213 1.07213i 0.0440642 0.0440642i
\(593\) −3.43032 + 3.43032i −0.140866 + 0.140866i −0.774023 0.633157i \(-0.781759\pi\)
0.633157 + 0.774023i \(0.281759\pi\)
\(594\) −0.941708 −0.0386388
\(595\) 0 0
\(596\) −6.10696 −0.250151
\(597\) −0.436028 + 0.436028i −0.0178454 + 0.0178454i
\(598\) 0.862773 0.862773i 0.0352814 0.0352814i
\(599\) 10.1010i 0.412714i −0.978477 0.206357i \(-0.933839\pi\)
0.978477 0.206357i \(-0.0661608\pi\)
\(600\) 0 0
\(601\) 38.4063i 1.56663i −0.621628 0.783313i \(-0.713528\pi\)
0.621628 0.783313i \(-0.286472\pi\)
\(602\) −0.0765245 + 3.22730i −0.00311891 + 0.131535i
\(603\) 0.944185 + 0.944185i 0.0384502 + 0.0384502i
\(604\) 28.6261i 1.16478i
\(605\) 0 0
\(606\) −1.49225 −0.0606185
\(607\) 10.2931 + 10.2931i 0.417783 + 0.417783i 0.884439 0.466656i \(-0.154541\pi\)
−0.466656 + 0.884439i \(0.654541\pi\)
\(608\) −13.9360 + 13.9360i −0.565180 + 0.565180i
\(609\) 6.99213 6.66822i 0.283336 0.270210i
\(610\) 0 0
\(611\) −0.305570 −0.0123621
\(612\) −3.26312 3.26312i −0.131904 0.131904i
\(613\) 14.4155 + 14.4155i 0.582235 + 0.582235i 0.935517 0.353282i \(-0.114934\pi\)
−0.353282 + 0.935517i \(0.614934\pi\)
\(614\) 3.29121 0.132822
\(615\) 0 0
\(616\) 7.11153 6.78209i 0.286532 0.273258i
\(617\) 25.4196 25.4196i 1.02336 1.02336i 0.0236346 0.999721i \(-0.492476\pi\)
0.999721 0.0236346i \(-0.00752382\pi\)
\(618\) 2.96283 + 2.96283i 0.119183 + 0.119183i
\(619\) 11.1991 0.450129 0.225064 0.974344i \(-0.427741\pi\)
0.225064 + 0.974344i \(0.427741\pi\)
\(620\) 0 0
\(621\) 7.29744i 0.292836i
\(622\) −4.56168 4.56168i −0.182907 0.182907i
\(623\) −0.490815 + 20.6993i −0.0196641 + 0.829301i
\(624\) 2.59609i 0.103927i
\(625\) 0 0
\(626\) 6.18373i 0.247152i
\(627\) 20.3457 20.3457i 0.812527 0.812527i
\(628\) 15.4856 15.4856i 0.617942 0.617942i
\(629\) 0.981107 0.0391193
\(630\) 0 0
\(631\) 21.2015 0.844020 0.422010 0.906591i \(-0.361325\pi\)
0.422010 + 0.906591i \(0.361325\pi\)
\(632\) 5.69306 5.69306i 0.226458 0.226458i
\(633\) 6.58210 6.58210i 0.261615 0.261615i
\(634\) 7.31014i 0.290323i
\(635\) 0 0
\(636\) 14.8377i 0.588353i
\(637\) −3.66516 + 3.33309i −0.145219 + 0.132062i
\(638\) 2.43176 + 2.43176i 0.0962745 + 0.0962745i
\(639\) 1.19297i 0.0471931i
\(640\) 0 0
\(641\) −29.8969 −1.18086 −0.590428 0.807090i \(-0.701041\pi\)
−0.590428 + 0.807090i \(0.701041\pi\)
\(642\) 1.76722 + 1.76722i 0.0697465 + 0.0697465i
\(643\) 11.2813 11.2813i 0.444891 0.444891i −0.448761 0.893652i \(-0.648134\pi\)
0.893652 + 0.448761i \(0.148134\pi\)
\(644\) 25.9059 + 27.1642i 1.02083 + 1.07042i
\(645\) 0 0
\(646\) −4.04794 −0.159264
\(647\) −26.2395 26.2395i −1.03158 1.03158i −0.999485 0.0320982i \(-0.989781\pi\)
−0.0320982 0.999485i \(-0.510219\pi\)
\(648\) −0.658899 0.658899i −0.0258840 0.0258840i
\(649\) −24.3530 −0.955937
\(650\) 0 0
\(651\) −9.45495 + 9.01695i −0.370569 + 0.353402i
\(652\) 20.3069 20.3069i 0.795281 0.795281i
\(653\) 1.97641 + 1.97641i 0.0773427 + 0.0773427i 0.744720 0.667377i \(-0.232583\pi\)
−0.667377 + 0.744720i \(0.732583\pi\)
\(654\) −0.157870 −0.00617319
\(655\) 0 0
\(656\) 27.9953i 1.09303i
\(657\) −1.38298 1.38298i −0.0539552 0.0539552i
\(658\) −0.00639752 + 0.269805i −0.000249401 + 0.0105181i
\(659\) 15.1044i 0.588385i 0.955746 + 0.294193i \(0.0950507\pi\)
−0.955746 + 0.294193i \(0.904949\pi\)
\(660\) 0 0
\(661\) 1.10054i 0.0428062i −0.999771 0.0214031i \(-0.993187\pi\)
0.999771 0.0214031i \(-0.00681333\pi\)
\(662\) −2.78838 + 2.78838i −0.108374 + 0.108374i
\(663\) −1.18785 + 1.18785i −0.0461321 + 0.0461321i
\(664\) −15.7998 −0.613150
\(665\) 0 0
\(666\) 0.0976524 0.00378395
\(667\) −18.8441 + 18.8441i −0.729646 + 0.729646i
\(668\) −9.01365 + 9.01365i −0.348749 + 0.348749i
\(669\) 1.91633i 0.0740894i
\(670\) 0 0
\(671\) 28.3425i 1.09415i
\(672\) 7.22160 + 0.171236i 0.278579 + 0.00660558i
\(673\) 11.4381 + 11.4381i 0.440906 + 0.440906i 0.892316 0.451411i \(-0.149079\pi\)
−0.451411 + 0.892316i \(0.649079\pi\)
\(674\) 0.848737i 0.0326921i
\(675\) 0 0
\(676\) −24.3006 −0.934639
\(677\) −24.6007 24.6007i −0.945481 0.945481i 0.0531077 0.998589i \(-0.483087\pi\)
−0.998589 + 0.0531077i \(0.983087\pi\)
\(678\) 0.802438 0.802438i 0.0308175 0.0308175i
\(679\) 20.1366 19.2037i 0.772770 0.736972i
\(680\) 0 0
\(681\) 5.87517 0.225137
\(682\) −3.28830 3.28830i −0.125915 0.125915i
\(683\) 13.8654 + 13.8654i 0.530543 + 0.530543i 0.920734 0.390191i \(-0.127591\pi\)
−0.390191 + 0.920734i \(0.627591\pi\)
\(684\) 14.0341 0.536607
\(685\) 0 0
\(686\) 2.86624 + 3.30596i 0.109433 + 0.126222i
\(687\) −9.18531 + 9.18531i −0.350442 + 0.350442i
\(688\) 13.3960 + 13.3960i 0.510719 + 0.510719i
\(689\) −5.40125 −0.205771
\(690\) 0 0
\(691\) 12.4060i 0.471947i −0.971759 0.235974i \(-0.924172\pi\)
0.971759 0.235974i \(-0.0758279\pi\)
\(692\) −4.83190 4.83190i −0.183681 0.183681i
\(693\) −10.5431 0.249993i −0.400498 0.00949646i
\(694\) 4.57667i 0.173728i
\(695\) 0 0
\(696\) 3.40294i 0.128988i
\(697\) 12.8093 12.8093i 0.485186 0.485186i
\(698\) −0.0849648 + 0.0849648i −0.00321597 + 0.00321597i
\(699\) 23.2835 0.880661
\(700\) 0 0
\(701\) 1.45193 0.0548388 0.0274194 0.999624i \(-0.491271\pi\)
0.0274194 + 0.999624i \(0.491271\pi\)
\(702\) −0.118230 + 0.118230i −0.00446229 + 0.00446229i
\(703\) −2.10979 + 2.10979i −0.0795720 + 0.0795720i
\(704\) 26.6721i 1.00524i
\(705\) 0 0
\(706\) 3.64907i 0.137335i
\(707\) −16.7067 0.396144i −0.628322 0.0148985i
\(708\) −8.39914 8.39914i −0.315659 0.315659i
\(709\) 48.5284i 1.82252i 0.411827 + 0.911262i \(0.364891\pi\)
−0.411827 + 0.911262i \(0.635109\pi\)
\(710\) 0 0
\(711\) −8.64027 −0.324035
\(712\) −5.15642 5.15642i −0.193245 0.193245i
\(713\) 25.4815 25.4815i 0.954290 0.954290i
\(714\) 1.02395 + 1.07368i 0.0383202 + 0.0401816i
\(715\) 0 0
\(716\) 42.9876 1.60652
\(717\) −3.87528 3.87528i −0.144725 0.144725i
\(718\) 2.67056 + 2.67056i 0.0996644 + 0.0996644i
\(719\) −43.5872 −1.62553 −0.812764 0.582593i \(-0.802038\pi\)
−0.812764 + 0.582593i \(0.802038\pi\)
\(720\) 0 0
\(721\) 32.3844 + 33.9575i 1.20606 + 1.26464i
\(722\) 5.53068 5.53068i 0.205831 0.205831i
\(723\) −10.3596 10.3596i −0.385279 0.385279i
\(724\) −16.4970 −0.613104
\(725\) 0 0
\(726\) 1.15489i 0.0428620i
\(727\) 10.4498 + 10.4498i 0.387563 + 0.387563i 0.873817 0.486254i \(-0.161637\pi\)
−0.486254 + 0.873817i \(0.661637\pi\)
\(728\) 0.0413607 1.74432i 0.00153293 0.0646487i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 12.2587i 0.453405i
\(732\) 9.77509 9.77509i 0.361298 0.361298i
\(733\) 18.8687 18.8687i 0.696933 0.696933i −0.266815 0.963748i \(-0.585971\pi\)
0.963748 + 0.266815i \(0.0859712\pi\)
\(734\) 0.136998 0.00505669
\(735\) 0 0
\(736\) −19.9240 −0.734409
\(737\) −3.76354 + 3.76354i −0.138632 + 0.138632i
\(738\) 1.27494 1.27494i 0.0469313 0.0469313i
\(739\) 20.9689i 0.771354i −0.922634 0.385677i \(-0.873968\pi\)
0.922634 0.385677i \(-0.126032\pi\)
\(740\) 0 0
\(741\) 5.10872i 0.187673i
\(742\) −0.113082 + 4.76906i −0.00415138 + 0.175078i
\(743\) −9.18724 9.18724i −0.337047 0.337047i 0.518208 0.855255i \(-0.326599\pi\)
−0.855255 + 0.518208i \(0.826599\pi\)
\(744\) 4.60155i 0.168701i
\(745\) 0 0
\(746\) 1.15100 0.0421412
\(747\) 11.9895 + 11.9895i 0.438673 + 0.438673i
\(748\) 13.0069 13.0069i 0.475578 0.475578i
\(749\) 19.3160 + 20.2543i 0.705793 + 0.740077i
\(750\) 0 0
\(751\) 11.1969 0.408579 0.204290 0.978910i \(-0.434512\pi\)
0.204290 + 0.978910i \(0.434512\pi\)
\(752\) 1.11992 + 1.11992i 0.0408393 + 0.0408393i
\(753\) 14.9557 + 14.9557i 0.545017 + 0.545017i
\(754\) 0.610607 0.0222370
\(755\) 0 0
\(756\) −3.54999 3.72244i −0.129112 0.135384i
\(757\) 13.9324 13.9324i 0.506383 0.506383i −0.407031 0.913414i \(-0.633436\pi\)
0.913414 + 0.407031i \(0.133436\pi\)
\(758\) 2.15801 + 2.15801i 0.0783824 + 0.0783824i
\(759\) 29.0877 1.05582
\(760\) 0 0
\(761\) 8.78825i 0.318574i −0.987232 0.159287i \(-0.949081\pi\)
0.987232 0.159287i \(-0.0509195\pi\)
\(762\) −1.39114 1.39114i −0.0503958 0.0503958i
\(763\) −1.76746 0.0419093i −0.0639862 0.00151722i
\(764\) 29.7263i 1.07546i
\(765\) 0 0
\(766\) 3.36684i 0.121649i
\(767\) −3.05747 + 3.05747i −0.110399 + 0.110399i
\(768\) 8.28678 8.28678i 0.299023 0.299023i
\(769\) 11.2183 0.404543 0.202271 0.979330i \(-0.435168\pi\)
0.202271 + 0.979330i \(0.435168\pi\)
\(770\) 0 0
\(771\) −13.2830 −0.478374
\(772\) −17.3574 + 17.3574i −0.624708 + 0.624708i
\(773\) 21.5065 21.5065i 0.773535 0.773535i −0.205188 0.978723i \(-0.565781\pi\)
0.978723 + 0.205188i \(0.0657806\pi\)
\(774\) 1.22015i 0.0438572i
\(775\) 0 0
\(776\) 9.80008i 0.351802i
\(777\) 1.09328 + 0.0259236i 0.0392214 + 0.000930003i
\(778\) −4.06447 4.06447i −0.145718 0.145718i
\(779\) 55.0905i 1.97382i
\(780\) 0 0
\(781\) 4.75520 0.170155