Properties

Label 525.2.m.b.307.5
Level 525
Weight 2
Character 525.307
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 307.5
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 \(\chi\) \(=\) 525.307
Dual form 525.2.m.b.118.5

$q$-expansion

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

Character values

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

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

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 0.763699 0.645573i \(-0.223381\pi\)
−0.645573 + 0.763699i \(0.723381\pi\)
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.94418i 0.972092i
\(5\) 0 0
\(6\) 0.236253i 0.0964497i
\(7\) 2.64501 + 0.0627175i 0.999719 + 0.0237050i
\(8\) 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 \(-0.281291\pi\)
−0.773091 + 0.634295i \(0.781291\pi\)
\(14\) 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 \(-0.657062\pi\)
0.880716 + 0.473645i \(0.157062\pi\)
\(18\) −0.167056 + 0.167056i −0.0393754 + 0.0393754i
\(19\) −7.21850 −1.65604 −0.828019 0.560700i \(-0.810532\pi\)
−0.828019 + 0.560700i \(0.810532\pi\)
\(20\) 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 0.0790800 0.996868i \(-0.474802\pi\)
0.996868 0.0790800i \(-0.0251983\pi\)
\(24\) −0.931824 −0.190208
\(25\) 0 0
\(26\) 0.167202i 0.0327910i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0.121934 5.14238i 0.0230434 0.971819i
\(29\) 3.65191i 0.678143i −0.940761 0.339071i \(-0.889887\pi\)
0.940761 0.339071i \(-0.110113\pi\)
\(30\) 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 0.682674 0.730723i \(-0.260817\pi\)
−0.730723 + 0.682674i \(0.760817\pi\)
\(38\) −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 \(0.796777\pi\)
\(42\) 0.0148172 0.624890i 0.00228634 0.0964226i
\(43\) −3.65191 + 3.65191i −0.556911 + 0.556911i −0.928427 0.371516i \(-0.878838\pi\)
0.371516 + 0.928427i \(0.378838\pi\)
\(44\) 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 \(-0.739975\pi\)
0.729023 + 0.684490i \(0.239975\pi\)
\(48\) 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 −0.972822 0.231553i \(-0.925619\pi\)
0.231553 + 0.972822i \(0.425619\pi\)
\(54\) 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 \(-0.369808\pi\)
0.397701 + 0.917515i \(0.369808\pi\)
\(60\) 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
\(63\) −0.0627175 + 2.64501i −0.00790166 + 0.333240i
\(64\) 6.69141i 0.836426i
\(65\) 0 0
\(66\) 0.941708i 0.115916i
\(67\) −0.944185 0.944185i −0.115351 0.115351i 0.647075 0.762426i \(-0.275992\pi\)
−0.762426 + 0.647075i \(0.775992\pi\)
\(68\) −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 \(-0.286513\pi\)
−0.783393 + 0.621527i \(0.786513\pi\)
\(74\) 0.0976524i 0.0113519i
\(75\) 0 0
\(76\) 14.0341i 1.60982i
\(77\) 10.5431 + 0.249993i 1.20149 + 0.0284894i
\(78\) −0.118230 + 0.118230i −0.0133869 + 0.0133869i
\(79\) 8.64027i 0.972106i 0.873929 + 0.486053i \(0.161564\pi\)
−0.873929 + 0.486053i \(0.838436\pi\)
\(80\) 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 0.916898 + 0.399122i \(0.130685\pi\)
0.399122 + 0.916898i \(0.369315\pi\)
\(84\) −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 \(-0.363863\pi\)
0.414767 + 0.909928i \(0.363863\pi\)
\(90\) 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 \(-0.929283\pi\)
0.220340 + 0.975423i \(0.429283\pi\)
\(98\) 1.11265 + 1.22350i 0.112395 + 0.123592i
\(99\) 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 0.961743 + 0.273954i \(0.0883316\pi\)
0.273954 + 0.961743i \(0.411668\pi\)
\(104\) −0.659476 −0.0646669
\(105\) 0 0
\(106\) −1.80304 −0.175127
\(107\) −7.48020 7.48020i −0.723138 0.723138i 0.246105 0.969243i \(-0.420849\pi\)
−0.969243 + 0.246105i \(0.920849\pi\)
\(108\) −1.37475 1.37475i −0.132285 0.132285i
\(109\) 0.668223i 0.0640042i 0.999488 + 0.0320021i \(0.0101883\pi\)
−0.999488 + 0.0320021i \(0.989812\pi\)
\(110\) 0 0
\(111\) 0.413339i 0.0392324i
\(112\) −9.70248 0.230062i −0.916798 0.0217388i
\(113\) 3.39653 3.39653i 0.319518 0.319518i −0.529064 0.848582i \(-0.677457\pi\)
0.848582 + 0.529064i \(0.177457\pi\)
\(114\) 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 0.918328 0.395820i \(-0.129540\pi\)
−0.395820 + 0.918328i \(0.629540\pi\)
\(128\) −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
\(133\) −19.0930 0.452726i −1.65557 0.0392564i
\(134\) 0.315463i 0.0272519i
\(135\) 0 0
\(136\) 2.21179i 0.189659i
\(137\) 0.811977 + 0.811977i 0.0693719 + 0.0693719i 0.740941 0.671570i \(-0.234380\pi\)
−0.671570 + 0.740941i \(0.734380\pi\)
\(138\) −1.21908 1.21908i −0.103775 0.103775i
\(139\) −0.442439 −0.0375272 −0.0187636 0.999824i \(-0.505973\pi\)
−0.0187636 + 0.999824i \(0.505973\pi\)
\(140\) 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
\(147\) −4.70958 5.17879i −0.388440 0.427139i
\(148\) −0.568236 + 0.568236i −0.0467087 + 0.0467087i
\(149\) 3.14114i 0.257332i −0.991688 0.128666i \(-0.958930\pi\)
0.991688 0.128666i \(-0.0410696\pi\)
\(150\) 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 \(-0.601604\pi\)
0.949487 + 0.313805i \(0.101604\pi\)
\(158\) −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 −0.985834 0.167722i \(-0.946359\pi\)
0.167722 + 0.985834i \(0.446359\pi\)
\(164\) 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 \(-0.831642\pi\)
0.504595 + 0.863356i \(0.331642\pi\)
\(168\) −2.46468 0.0584417i −0.190154 0.00450887i
\(169\) 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 \(-0.207343\pi\)
−0.606290 + 0.795244i \(0.707343\pi\)
\(174\) −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 \(0.309570\pi\)
−0.563199 + 0.826321i \(0.690430\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 0.0104865 0.442251i 0.000777310 0.0327818i
\(183\) −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 −0.308562 0.951204i \(-0.599848\pi\)
0.951204 + 0.308562i \(0.0998477\pi\)
\(194\) −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 0.796323 0.604872i \(-0.206776\pi\)
−0.604872 + 0.796323i \(0.706776\pi\)
\(198\) −0.665888 + 0.665888i −0.0473226 + 0.0473226i
\(199\) 0.616637 0.0437122 0.0218561 0.999761i \(-0.493042\pi\)
0.0218561 + 0.999761i \(0.493042\pi\)
\(200\) 0 0
\(201\) 1.33528i 0.0941833i
\(202\) 1.05518 1.05518i 0.0742422 0.0742422i
\(203\) 0.229039 9.65933i 0.0160754 0.677952i
\(204\) 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
\(217\) 0.309712 13.0616i 0.0210246 0.886680i
\(218\) −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 \(-0.229562\pi\)
−0.660279 + 0.751020i \(0.729562\pi\)
\(224\) −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 \(-0.812462\pi\)
0.555668 + 0.831404i \(0.312462\pi\)
\(228\) 9.92361 9.92361i 0.657207 0.657207i
\(229\) 12.9900 0.858403 0.429202 0.903209i \(-0.358795\pi\)
0.429202 + 0.903209i \(0.358795\pi\)
\(230\) 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 0.0819485 0.996637i \(-0.473886\pi\)
0.996637 0.0819485i \(-0.0261143\pi\)
\(234\) 0.167202 0.0109303
\(235\) 0 0
\(236\) 11.8782i 0.773203i
\(237\) 6.10959 6.10959i 0.396861 0.396861i
\(238\) 1.48325 + 0.0351703i 0.0961447 + 0.00227975i
\(239\) 5.48048i 0.354503i 0.984166 + 0.177251i \(0.0567205\pi\)
−0.984166 + 0.177251i \(0.943279\pi\)
\(240\) 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 \(0.767361\pi\)
\(252\) 5.14238 + 0.121934i 0.323940 + 0.00768115i
\(253\) 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 \(-0.614032\pi\)
0.936515 + 0.350628i \(0.114032\pi\)
\(258\) 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 −0.998725 0.0504843i \(-0.983924\pi\)
0.0504843 + 0.998725i \(0.483924\pi\)
\(264\) −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 \(-0.747135\pi\)
−0.700714 + 0.713442i \(0.747135\pi\)
\(270\) 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
\(273\) −0.0443868 + 1.87194i −0.00268641 + 0.113295i
\(274\) 0.271291i 0.0163893i
\(275\) 0 0
\(276\) 14.1876i 0.853991i
\(277\) −4.80771 4.80771i −0.288867 0.288867i 0.547765 0.836632i \(-0.315479\pi\)
−0.836632 + 0.547765i \(0.815479\pi\)
\(278\) −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 \(-0.465592\pi\)
−0.994163 + 0.107885i \(0.965592\pi\)
\(284\) 2.31935i 0.137628i
\(285\) 0 0
\(286\) 0.666471i 0.0394092i
\(287\) −0.478650 + 20.1863i −0.0282538 + 1.19156i
\(288\) 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 \(-0.313435\pi\)
−0.833098 + 0.553125i \(0.813435\pi\)
\(294\) 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 \(-0.880136\pi\)
0.367728 + 0.929933i \(0.380136\pi\)
\(308\) 0.486033 20.4977i 0.0276943 1.16796i
\(309\) 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 −0.998883 0.0472492i \(-0.984955\pi\)
−0.0472492 0.998883i \(-0.515045\pi\)
\(314\) 2.66123 0.150182
\(315\) 0 0
\(316\) 16.7983 0.944977
\(317\) 21.8793 + 21.8793i 1.22887 + 1.22887i 0.964393 + 0.264473i \(0.0851980\pi\)
0.264473 + 0.964393i \(0.414802\pi\)
\(318\) 1.27494 + 1.27494i 0.0714953 + 0.0714953i
\(319\) 14.5566i 0.815013i
\(320\) 0 0
\(321\) 10.5786i 0.590440i
\(322\) 4.56010 + 0.108127i 0.254124 + 0.00602570i
\(323\) −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 0.634525 0.772903i \(-0.281196\pi\)
−0.772903 + 0.634525i \(0.781196\pi\)
\(338\) 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
\(343\) 18.4734 + 1.31608i 0.997472 + 0.0710617i
\(344\) 4.81248i 0.259472i
\(345\) 0 0
\(346\) 0.830370i 0.0446410i
\(347\) −13.6980 13.6980i −0.735348 0.735348i 0.236326 0.971674i \(-0.424057\pi\)
−0.971674 + 0.236326i \(0.924057\pi\)
\(348\) 5.02045 + 5.02045i 0.269124 + 0.269124i
\(349\) 0.508601 0.0272248 0.0136124 0.999907i \(-0.495667\pi\)
0.0136124 + 0.999907i \(0.495667\pi\)
\(350\) 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 \(-0.384836\pi\)
−0.935262 + 0.353957i \(0.884836\pi\)
\(354\) 1.44341i 0.0767162i
\(355\) 0 0
\(356\) 15.2148i 0.806383i
\(357\) −6.27823 0.148867i −0.332279 0.00787888i
\(358\) −3.69375 + 3.69375i −0.195221 + 0.195221i
\(359\) 15.9860i 0.843710i −0.906663 0.421855i \(-0.861379\pi\)
0.906663 0.421855i \(-0.138621\pi\)
\(360\) 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 \(-0.754818\pi\)
0.696324 + 0.717728i \(0.254818\pi\)
\(368\) −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 −0.612273 0.790646i \(-0.709745\pi\)
0.790646 + 0.612273i \(0.209745\pi\)
\(374\) 2.23525 0.115582
\(375\) 0 0
\(376\) 0.402328i 0.0207485i
\(377\) −1.82755 + 1.82755i −0.0941237 + 0.0941237i
\(378\) 0.624890 + 0.0148172i 0.0321409 + 0.000762113i
\(379\) 12.9179i 0.663547i −0.943359 0.331773i \(-0.892353\pi\)
0.943359 0.331773i \(-0.107647\pi\)
\(380\) 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 \(-0.131378\pi\)
−0.401117 + 0.916027i \(0.631378\pi\)
\(384\) 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 \(0.211567\pi\)
−0.787127 + 0.616791i \(0.788433\pi\)
\(390\) 0 0
\(391\) 17.3213i 0.875976i
\(392\) 4.82572 4.38850i 0.243736 0.221653i
\(393\) 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 \(-0.827655\pi\)
0.515369 + 0.856969i \(0.327655\pi\)
\(398\) 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 \(-0.694432\pi\)
−0.573546 + 0.819174i \(0.694432\pi\)
\(410\) 0 0
\(411\) 1.14831i 0.0566419i
\(412\) 24.3819 24.3819i 1.20121 1.20121i
\(413\) 16.1599 + 0.383178i 0.795178 + 0.0188550i
\(414\) 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 \(-0.396819\pi\)
0.318505 + 0.947921i \(0.396819\pi\)
\(420\) 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
\(427\) 0.445951 18.8072i 0.0215811 0.910146i
\(428\) −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 \(-0.0126730\pi\)
−0.0398028 + 0.999208i \(0.512673\pi\)
\(434\) 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 \(-0.243890\pi\)
0.720548 + 0.693405i \(0.243890\pi\)
\(440\) 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 −0.336337 0.941742i \(-0.609188\pi\)
0.941742 + 0.336337i \(0.109188\pi\)
\(444\) 0.803607 0.0381375
\(445\) 0 0
\(446\) 0.452737i 0.0214377i
\(447\) −2.22112 + 2.22112i −0.105056 + 0.105056i
\(448\) −0.419669 + 17.6988i −0.0198275 + 0.836191i
\(449\) 30.4170i 1.43547i 0.696318 + 0.717734i \(0.254820\pi\)
−0.696318 + 0.717734i \(0.745180\pi\)
\(450\) 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 0.675670 0.737204i \(-0.263855\pi\)
−0.737204 + 0.675670i \(0.763855\pi\)
\(458\) 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 \(-0.00963467\pi\)
\(462\) 0.0590616 2.49083i 0.00274779 0.115884i
\(463\) −16.5240 + 16.5240i −0.767934 + 0.767934i −0.977742 0.209809i \(-0.932716\pi\)
0.209809 + 0.977742i \(0.432716\pi\)
\(464\) 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 \(-0.978479\pi\)
0.0675588 + 0.997715i \(0.478479\pi\)
\(468\) −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 \(-0.581487\pi\)
−0.253212 + 0.967411i \(0.581487\pi\)
\(480\) 0 0
\(481\) 0.292530i 0.0133382i
\(482\) 2.44749 2.44749i 0.111480 0.111480i
\(483\) −19.3018 0.457677i −0.878261 0.0208250i
\(484\) 9.50389i 0.431995i
\(485\) 0 0
\(486\) 0.236253i 0.0107166i
\(487\) 13.6519 + 13.6519i 0.618627 + 0.618627i 0.945179 0.326552i \(-0.105887\pi\)
−0.326552 + 0.945179i \(0.605887\pi\)
\(488\) −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
\(497\) 3.15541 + 0.0748201i 0.141540 + 0.00335614i
\(498\) 2.83255 2.83255i 0.126930 0.126930i
\(499\) 4.27431i 0.191344i 0.995413 + 0.0956722i \(0.0305000\pi\)
−0.995413 + 0.0956722i \(0.969500\pi\)
\(500\) 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 \(-0.436806\pi\)
−0.980357 + 0.197229i \(0.936806\pi\)
\(504\) 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 \(-0.712333\pi\)
−0.618682 + 0.785641i \(0.712333\pi\)
\(510\) 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
\(518\) 0.00612451 0.258291i 0.000269096 0.0113487i
\(519\) 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 \(-0.215019\pi\)
−0.625290 + 0.780392i \(0.715019\pi\)
\(524\) 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
\(532\) −0.880184 + 37.1203i −0.0381608 + 1.60937i
\(533\) 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 −0.972121 0.234482i \(-0.924661\pi\)
−0.234482 0.972121i \(-0.575339\pi\)
\(548\) 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
\(553\) −0.541896 + 22.8536i −0.0230438 + 0.971833i
\(554\) 1.60631i 0.0682457i
\(555\) 0 0
\(556\) 0.860184i 0.0364799i
\(557\) −28.1616 28.1616i −1.19325 1.19325i −0.976150 0.217096i \(-0.930342\pi\)
−0.217096 0.976150i \(-0.569658\pi\)
\(558\) 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 0.985891 + 0.167386i \(0.0535326\pi\)
0.167386 + 0.985891i \(0.446467\pi\)
\(564\) 0.839429i 0.0353463i
\(565\) 0 0
\(566\) 4.98144i 0.209386i
\(567\) −2.64501 0.0627175i −0.111080 0.00263389i
\(568\) 0.786047 0.786047i 0.0329818 0.0329818i
\(569\) 17.7767i 0.745240i −0.927984 0.372620i \(-0.878460\pi\)
0.927984 0.372620i \(-0.121540\pi\)
\(570\) 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 \(-0.786594\pi\)
0.621327 + 0.783552i \(0.286594\pi\)
\(578\) −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 \(-0.604670\pi\)
0.946420 + 0.322937i \(0.104670\pi\)
\(588\) −10.0685 + 9.15630i −0.415219 + 0.377599i
\(589\) 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 \(-0.218241\pi\)
−0.633157 + 0.774023i \(0.718241\pi\)
\(594\) 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 \(0.0661608\pi\)
−0.978477 + 0.206357i \(0.933839\pi\)
\(600\) 0 0
\(601\) 38.4063i 1.56663i −0.621628 0.783313i \(-0.713528\pi\)
0.621628 0.783313i \(-0.286472\pi\)
\(602\) −3.22730 0.0765245i −0.131535 0.00311891i
\(603\) 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 \(-0.845459\pi\)
0.466656 + 0.884439i \(0.345459\pi\)
\(608\) 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 −0.353282 0.935517i \(-0.614934\pi\)
0.935517 + 0.353282i \(0.114934\pi\)
\(614\) −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 0.999721 + 0.0236346i \(0.00752382\pi\)
0.0236346 + 0.999721i \(0.492476\pi\)
\(618\) 2.96283 2.96283i 0.119183 0.119183i
\(619\) −11.1991 −0.450129 −0.225064 0.974344i \(-0.572259\pi\)
−0.225064 + 0.974344i \(0.572259\pi\)
\(620\) 0 0
\(621\) 7.29744i 0.292836i
\(622\) 4.56168 4.56168i 0.182907 0.182907i
\(623\) 20.6993 + 0.490815i 0.829301 + 0.0196641i
\(624\) 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
\(637\) −3.33309 3.66516i −0.132062 0.145219i
\(638\) 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 \(-0.351866\pi\)
−0.893652 + 0.448761i \(0.851866\pi\)
\(644\) −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 0.0320982 0.999485i \(-0.489781\pi\)
0.999485 0.0320982i \(-0.0102189\pi\)
\(648\) −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 −0.667377 0.744720i \(-0.732583\pi\)
0.744720 + 0.667377i \(0.232583\pi\)
\(654\) 0.157870 0.00617319
\(655\) 0 0
\(656\) 27.9953i 1.09303i
\(657\) 1.38298 1.38298i 0.0539552 0.0539552i
\(658\) 0.269805 + 0.00639752i 0.0105181 + 0.000249401i
\(659\) 15.1044i 0.588385i −0.955746 0.294193i \(-0.904949\pi\)
0.955746 0.294193i \(-0.0950507\pi\)
\(660\) 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
\(672\) −0.171236 + 7.22160i −0.00660558 + 0.278579i
\(673\) 11.4381 11.4381i 0.440906 0.440906i −0.451411 0.892316i \(-0.649079\pi\)
0.892316 + 0.451411i \(0.149079\pi\)
\(674\) 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 \(-0.516913\pi\)
0.998589 + 0.0531077i \(0.0169127\pi\)
\(678\) −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 −0.390191 0.920734i \(-0.627591\pi\)
0.920734 + 0.390191i \(0.127591\pi\)
\(684\) −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
\(693\) −0.249993 + 10.5431i −0.00949646 + 0.400498i
\(694\) 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
\(707\) 0.396144 16.7067i 0.0148985 0.628322i
\(708\) −8.39914 + 8.39914i −0.315659 + 0.315659i
\(709\) 48.5284i 1.82252i −0.411827 0.911262i \(-0.635109\pi\)
0.411827 0.911262i \(-0.364891\pi\)
\(710\) 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 \(-0.197962\pi\)
0.812764 + 0.582593i \(0.197962\pi\)
\(720\) 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 \(-0.838363\pi\)
0.486254 + 0.873817i \(0.338363\pi\)
\(728\) −1.74432 0.0413607i −0.0646487 0.00153293i
\(729\) 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 \(-0.414029\pi\)
−0.963748 + 0.266815i \(0.914029\pi\)
\(734\) −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 \(0.126032\pi\)
−0.922634 + 0.385677i \(0.873968\pi\)
\(740\) 0 0
\(741\) 5.10872i 0.187673i
\(742\) −4.76906 0.113082i −0.175078 0.00415138i
\(743\) −9.18724 + 9.18724i −0.337047 + 0.337047i −0.855255 0.518208i \(-0.826599\pi\)
0.518208 + 0.855255i \(0.326599\pi\)
\(744\) 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 0.913414 0.407031i \(-0.133436\pi\)
−0.407031 + 0.913414i \(0.633436\pi\)
\(758\) 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
\(763\) −0.0419093 + 1.76746i −0.00151722 + 0.0639862i
\(764\) 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 \(-0.564832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(770\) 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 \(-0.434219\pi\)
−0.978723 + 0.205188i \(0.934219\pi\)
\(774\) 1.22015i 0.0438572i
\(775\) 0 0
\(776\) 9.80008i 0.351802i
\(777\) −0.0259236 + 1.09328i −0.000930003 + 0.0392214i
\(778\) −4.06447 + 4.06447i −0.145718 + 0.145718i
\(779\) 55.0905i 1.97382i
\(780\) 0 0
\(781\) 4.75520 0.170155