Properties

Label 315.2.p.e.307.5
Level 315
Weight 2
Character 315.307
Analytic conductor 2.515
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
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 \(\chi\) \(=\) 315.307
Dual form 315.2.p.e.118.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.167056 + 0.167056i) q^{2} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +(-2.64501 - 0.0627175i) q^{7} +(0.658899 - 0.658899i) q^{8} +O(q^{10})\) \(q+(0.167056 + 0.167056i) q^{2} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +(-2.64501 - 0.0627175i) q^{7} +(0.658899 - 0.658899i) q^{8} +(-0.359321 - 0.387253i) q^{10} -3.98602 q^{11} +(0.500437 + 0.500437i) q^{13} +(-0.431387 - 0.452341i) q^{14} -3.66822 q^{16} +(1.67840 - 1.67840i) q^{17} -7.21850 q^{19} +(-0.162536 + 4.34429i) q^{20} +(-0.665888 - 0.665888i) q^{22} +(5.16007 - 5.16007i) q^{23} +(4.98602 + 0.373614i) q^{25} +0.167202i q^{26} +(-0.121934 + 5.14238i) q^{28} +3.65191i q^{29} -4.93821i q^{31} +(-1.93060 - 1.93060i) q^{32} +0.560773 q^{34} +(5.90504 + 0.361268i) q^{35} +(0.292275 + 0.292275i) q^{37} +(-1.20589 - 1.20589i) q^{38} +(-1.52740 + 1.41723i) q^{40} -7.63184i q^{41} +(3.65191 - 3.65191i) q^{43} +7.74956i q^{44} +1.72404 q^{46} +(0.305303 - 0.305303i) q^{47} +(6.99213 + 0.331777i) q^{49} +(0.770530 + 0.895358i) q^{50} +(0.972943 - 0.972943i) q^{52} +(-5.39653 + 5.39653i) q^{53} +(8.90678 + 0.333235i) q^{55} +(-1.78412 + 1.70147i) q^{56} +(-0.610073 + 0.610073i) q^{58} -6.10959 q^{59} -7.11047i q^{61} +(0.824957 - 0.824957i) q^{62} +6.69141i q^{64} +(-1.07639 - 1.16007i) q^{65} +(0.944185 + 0.944185i) q^{67} +(-3.26312 - 3.26312i) q^{68} +(0.926119 + 1.04682i) q^{70} -1.19297 q^{71} +(1.38298 + 1.38298i) q^{73} +0.0976524i q^{74} +14.0341i q^{76} +(10.5431 + 0.249993i) q^{77} +8.64027i q^{79} +(8.19666 + 0.306667i) q^{80} +(1.27494 - 1.27494i) q^{82} +(11.9895 + 11.9895i) q^{83} +(-3.89070 + 3.61007i) q^{85} +1.22015 q^{86} +(-2.62639 + 2.62639i) q^{88} -7.82581 q^{89} +(-1.29227 - 1.35505i) q^{91} +(-10.0321 - 10.0321i) q^{92} +0.102005 q^{94} +(16.1298 + 0.603474i) q^{95} +(7.43671 - 7.43671i) q^{97} +(1.11265 + 1.22350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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 0
\(4\) 1.94418i 0.972092i
\(5\) −2.23450 0.0836010i −0.999301 0.0373875i
\(6\) 0 0
\(7\) −2.64501 0.0627175i −0.999719 0.0237050i
\(8\) 0.658899 0.658899i 0.232956 0.232956i
\(9\) 0 0
\(10\) −0.359321 0.387253i −0.113627 0.122460i
\(11\) −3.98602 −1.20183 −0.600915 0.799313i \(-0.705197\pi\)
−0.600915 + 0.799313i \(0.705197\pi\)
\(12\) 0 0
\(13\) 0.500437 + 0.500437i 0.138796 + 0.138796i 0.773091 0.634295i \(-0.218709\pi\)
−0.634295 + 0.773091i \(0.718709\pi\)
\(14\) −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 0
\(19\) −7.21850 −1.65604 −0.828019 0.560700i \(-0.810532\pi\)
−0.828019 + 0.560700i \(0.810532\pi\)
\(20\) −0.162536 + 4.34429i −0.0363441 + 0.971413i
\(21\) 0 0
\(22\) −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 0
\(25\) 4.98602 + 0.373614i 0.997204 + 0.0747227i
\(26\) 0.167202i 0.0327910i
\(27\) 0 0
\(28\) −0.121934 + 5.14238i −0.0230434 + 0.971819i
\(29\) 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
\(33\) 0 0
\(34\) 0.560773 0.0961717
\(35\) 5.90504 + 0.361268i 0.998134 + 0.0610654i
\(36\) 0 0
\(37\) 0.292275 + 0.292275i 0.0480497 + 0.0480497i 0.730723 0.682674i \(-0.239183\pi\)
−0.682674 + 0.730723i \(0.739183\pi\)
\(38\) −1.20589 1.20589i −0.195622 0.195622i
\(39\) 0 0
\(40\) −1.52740 + 1.41723i −0.241503 + 0.224084i
\(41\) 7.63184i 1.19189i −0.803024 0.595947i \(-0.796777\pi\)
0.803024 0.595947i \(-0.203223\pi\)
\(42\) 0 0
\(43\) 3.65191 3.65191i 0.556911 0.556911i −0.371516 0.928427i \(-0.621162\pi\)
0.928427 + 0.371516i \(0.121162\pi\)
\(44\) 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 \(0.239975\pi\)
\(48\) 0 0
\(49\) 6.99213 + 0.331777i 0.998876 + 0.0473967i
\(50\) 0.770530 + 0.895358i 0.108969 + 0.126623i
\(51\) 0 0
\(52\) 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 0
\(55\) 8.90678 + 0.333235i 1.20099 + 0.0449335i
\(56\) −1.78412 + 1.70147i −0.238413 + 0.227368i
\(57\) 0 0
\(58\) −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
\(63\) 0 0
\(64\) 6.69141i 0.836426i
\(65\) −1.07639 1.16007i −0.133510 0.143889i
\(66\) 0 0
\(67\) 0.944185 + 0.944185i 0.115351 + 0.115351i 0.762426 0.647075i \(-0.224008\pi\)
−0.647075 + 0.762426i \(0.724008\pi\)
\(68\) −3.26312 3.26312i −0.395711 0.395711i
\(69\) 0 0
\(70\) 0.926119 + 1.04682i 0.110692 + 0.125119i
\(71\) −1.19297 −0.141579 −0.0707897 0.997491i \(-0.522552\pi\)
−0.0707897 + 0.997491i \(0.522552\pi\)
\(72\) 0 0
\(73\) 1.38298 + 1.38298i 0.161865 + 0.161865i 0.783393 0.621527i \(-0.213487\pi\)
−0.621527 + 0.783393i \(0.713487\pi\)
\(74\) 0.0976524i 0.0113519i
\(75\) 0 0
\(76\) 14.0341i 1.60982i
\(77\) 10.5431 + 0.249993i 1.20149 + 0.0284894i
\(78\) 0 0
\(79\) 8.64027i 0.972106i 0.873929 + 0.486053i \(0.161564\pi\)
−0.873929 + 0.486053i \(0.838436\pi\)
\(80\) 8.19666 + 0.306667i 0.916415 + 0.0342864i
\(81\) 0 0
\(82\) 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 \(0.369315\pi\)
\(84\) 0 0
\(85\) −3.89070 + 3.61007i −0.422006 + 0.391567i
\(86\) 1.22015 0.131572
\(87\) 0 0
\(88\) −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
\(93\) 0 0
\(94\) 0.102005 0.0105211
\(95\) 16.1298 + 0.603474i 1.65488 + 0.0619151i
\(96\) 0 0
\(97\) 7.43671 7.43671i 0.755083 0.755083i −0.220340 0.975423i \(-0.570717\pi\)
0.975423 + 0.220340i \(0.0707167\pi\)
\(98\) 1.11265 + 1.22350i 0.112395 + 0.123592i
\(99\) 0 0
\(100\) 0.726374 9.69375i 0.0726374 0.969375i
\(101\) 6.31633i 0.628498i 0.949341 + 0.314249i \(0.101753\pi\)
−0.949341 + 0.314249i \(0.898247\pi\)
\(102\) 0 0
\(103\) −12.5410 12.5410i −1.23570 1.23570i −0.961743 0.273954i \(-0.911668\pi\)
−0.273954 0.961743i \(-0.588332\pi\)
\(104\) 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 \(0.920849\pi\)
\(108\) 0 0
\(109\) 0.668223i 0.0640042i 0.999488 + 0.0320021i \(0.0101883\pi\)
−0.999488 + 0.0320021i \(0.989812\pi\)
\(110\) 1.43226 + 1.54360i 0.136561 + 0.147176i
\(111\) 0 0
\(112\) 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 \(0.177457\pi\)
\(114\) 0 0
\(115\) −11.9616 + 11.0988i −1.11542 + 1.03497i
\(116\) 7.09999 0.659217
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) −9.60080 −0.862177
\(125\) −11.1101 1.25168i −0.993713 0.111953i
\(126\) 0 0
\(127\) −5.88837 5.88837i −0.522508 0.522508i 0.395820 0.918328i \(-0.370460\pi\)
−0.918328 + 0.395820i \(0.870460\pi\)
\(128\) −4.97903 + 4.97903i −0.440088 + 0.440088i
\(129\) 0 0
\(130\) 0.0139783 0.373614i 0.00122597 0.0327681i
\(131\) 18.8144i 1.64383i −0.569613 0.821913i \(-0.692907\pi\)
0.569613 0.821913i \(-0.307093\pi\)
\(132\) 0 0
\(133\) 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 \(0.734380\pi\)
\(138\) 0 0
\(139\) −0.442439 −0.0375272 −0.0187636 0.999824i \(-0.505973\pi\)
−0.0187636 + 0.999824i \(0.505973\pi\)
\(140\) 0.702371 11.4805i 0.0593612 0.970278i
\(141\) 0 0
\(142\) −0.199293 0.199293i −0.0167243 0.0167243i
\(143\) −1.99475 1.99475i −0.166810 0.166810i
\(144\) 0 0
\(145\) 0.305303 8.16021i 0.0253541 0.677669i
\(146\) 0.462070i 0.0382411i
\(147\) 0 0
\(148\) 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
\(153\) 0 0
\(154\) 1.71952 + 1.80304i 0.138563 + 0.145293i
\(155\) −0.412839 + 11.0345i −0.0331601 + 0.886309i
\(156\) 0 0
\(157\) −7.96508 + 7.96508i −0.635682 + 0.635682i −0.949487 0.313805i \(-0.898396\pi\)
0.313805 + 0.949487i \(0.398396\pi\)
\(158\) −1.44341 + 1.44341i −0.114831 + 0.114831i
\(159\) 0 0
\(160\) 4.15253 + 4.47533i 0.328286 + 0.353806i
\(161\) −13.9720 + 13.3248i −1.10115 + 1.05014i
\(162\) 0 0
\(163\) 10.4450 10.4450i 0.818113 0.818113i −0.167722 0.985834i \(-0.553641\pi\)
0.985834 + 0.167722i \(0.0536410\pi\)
\(164\) −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 \(0.331642\pi\)
\(168\) 0 0
\(169\) 12.4991i 0.961471i
\(170\) −1.25305 0.0468811i −0.0961045 0.00359562i
\(171\) 0 0
\(172\) −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 0
\(175\) −13.1646 1.30092i −0.995153 0.0983404i
\(176\) 14.6216 1.10215
\(177\) 0 0
\(178\) −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 \(0.897877\pi\)
\(182\) 0.0104865 0.442251i 0.000777310 0.0327818i
\(183\) 0 0
\(184\) 6.79993i 0.501297i
\(185\) −0.628655 0.677524i −0.0462196 0.0498125i
\(186\) 0 0
\(187\) −6.69013 + 6.69013i −0.489231 + 0.489231i
\(188\) −0.593566 0.593566i −0.0432903 0.0432903i
\(189\) 0 0
\(190\) 2.59376 + 2.79539i 0.188171 + 0.202799i
\(191\) −15.2898 −1.10633 −0.553167 0.833070i \(-0.686581\pi\)
−0.553167 + 0.833070i \(0.686581\pi\)
\(192\) 0 0
\(193\) −8.92787 + 8.92787i −0.642642 + 0.642642i −0.951204 0.308562i \(-0.900152\pi\)
0.308562 + 0.951204i \(0.400152\pi\)
\(194\) 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 0
\(199\) 0.616637 0.0437122 0.0218561 0.999761i \(-0.493042\pi\)
0.0218561 + 0.999761i \(0.493042\pi\)
\(200\) 3.53146 3.03911i 0.249712 0.214898i
\(201\) 0 0
\(202\) −1.05518 + 1.05518i −0.0742422 + 0.0742422i
\(203\) 0.229039 9.65933i 0.0160754 0.677952i
\(204\) 0 0
\(205\) −0.638029 + 17.0534i −0.0445619 + 1.19106i
\(206\) 4.19008i 0.291937i
\(207\) 0 0
\(208\) −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 0
\(214\) 2.49922i 0.170843i
\(215\) −8.46551 + 7.85491i −0.577343 + 0.535700i
\(216\) 0 0
\(217\) −0.309712 + 13.0616i −0.0210246 + 0.886680i
\(218\) −0.111631 + 0.111631i −0.00756058 + 0.00756058i
\(219\) 0 0
\(220\) 0.647871 17.3164i 0.0436795 1.16747i
\(221\) 1.67987 0.113000
\(222\) 0 0
\(223\) −1.35505 1.35505i −0.0907407 0.0907407i 0.660279 0.751020i \(-0.270438\pi\)
−0.751020 + 0.660279i \(0.770438\pi\)
\(224\) 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 \(0.312462\pi\)
\(228\) 0 0
\(229\) 12.9900 0.858403 0.429202 0.903209i \(-0.358795\pi\)
0.429202 + 0.903209i \(0.358795\pi\)
\(230\) −3.85237 0.144131i −0.254018 0.00950374i
\(231\) 0 0
\(232\) 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 0
\(235\) −0.707725 + 0.656678i −0.0461669 + 0.0428370i
\(236\) 11.8782i 0.773203i
\(237\) 0 0
\(238\) −1.48325 0.0351703i −0.0961447 0.00227975i
\(239\) 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 0
\(244\) −13.8241 −0.884995
\(245\) −15.5962 1.32591i −0.996406 0.0847090i
\(246\) 0 0
\(247\) −3.61241 3.61241i −0.229852 0.229852i
\(248\) −3.25378 3.25378i −0.206615 0.206615i
\(249\) 0 0
\(250\) −1.64690 2.06510i −0.104159 0.130608i
\(251\) 21.1506i 1.33501i −0.744604 0.667507i \(-0.767361\pi\)
0.744604 0.667507i \(-0.232639\pi\)
\(252\) 0 0
\(253\) −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 0
\(259\) −0.754738 0.791399i −0.0468971 0.0491752i
\(260\) −2.25538 + 2.09271i −0.139873 + 0.129784i
\(261\) 0 0
\(262\) 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 \(0.483924\pi\)
\(264\) 0 0
\(265\) 12.5097 11.6074i 0.768466 0.713037i
\(266\) 3.11397 + 3.26523i 0.190929 + 0.200204i
\(267\) 0 0
\(268\) 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
\(273\) 0 0
\(274\) 0.271291i 0.0163893i
\(275\) −19.8744 1.48923i −1.19847 0.0898041i
\(276\) 0 0
\(277\) 4.80771 + 4.80771i 0.288867 + 0.288867i 0.836632 0.547765i \(-0.184521\pi\)
−0.547765 + 0.836632i \(0.684521\pi\)
\(278\) −0.0739121 0.0739121i −0.00443295 0.00443295i
\(279\) 0 0
\(280\) 4.12886 3.65279i 0.246747 0.218296i
\(281\) 9.65658 0.576063 0.288032 0.957621i \(-0.406999\pi\)
0.288032 + 0.957621i \(0.406999\pi\)
\(282\) 0 0
\(283\) 14.9095 + 14.9095i 0.886278 + 0.886278i 0.994163 0.107885i \(-0.0344079\pi\)
−0.107885 + 0.994163i \(0.534408\pi\)
\(284\) 2.31935i 0.137628i
\(285\) 0 0
\(286\) 0.666471i 0.0394092i
\(287\) −0.478650 + 20.1863i −0.0282538 + 1.19156i
\(288\) 0 0
\(289\) 11.3660i 0.668586i
\(290\) 1.41421 1.31221i 0.0830455 0.0770555i
\(291\) 0 0
\(292\) 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 0
\(295\) 13.6519 + 0.510768i 0.794845 + 0.0297381i
\(296\) 0.385159 0.0223869
\(297\) 0 0
\(298\) −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
\(303\) 0 0
\(304\) 26.4791 1.51868
\(305\) −0.594442 + 15.8884i −0.0340377 + 0.909765i
\(306\) 0 0
\(307\) 9.85063 9.85063i 0.562205 0.562205i −0.367728 0.929933i \(-0.619864\pi\)
0.929933 + 0.367728i \(0.119864\pi\)
\(308\) 0.486033 20.4977i 0.0276943 1.16796i
\(309\) 0 0
\(310\) −1.91234 + 1.77440i −0.108614 + 0.100779i
\(311\) 27.3063i 1.54840i 0.632941 + 0.774200i \(0.281848\pi\)
−0.632941 + 0.774200i \(0.718152\pi\)
\(312\) 0 0
\(313\) 18.5080 + 18.5080i 1.04613 + 1.04613i 0.998883 + 0.0472492i \(0.0150455\pi\)
0.0472492 + 0.998883i \(0.484955\pi\)
\(314\) −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 \(0.414802\pi\)
\(318\) 0 0
\(319\) 14.5566i 0.815013i
\(320\) 0.559409 14.9520i 0.0312719 0.835842i
\(321\) 0 0
\(322\) −4.56010 0.108127i −0.254124 0.00602570i
\(323\) −12.1155 + 12.1155i −0.674126 + 0.674126i
\(324\) 0 0
\(325\) 2.30822 + 2.68216i 0.128037 + 0.148780i
\(326\) 3.48978 0.193281
\(327\) 0 0
\(328\) −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 0
\(334\) −1.54901 −0.0847582
\(335\) −2.03085 2.18872i −0.110957 0.119583i
\(336\) 0 0
\(337\) 2.54028 + 2.54028i 0.138378 + 0.138378i 0.772903 0.634525i \(-0.218804\pi\)
−0.634525 + 0.772903i \(0.718804\pi\)
\(338\) 2.08805 2.08805i 0.113575 0.113575i
\(339\) 0 0
\(340\) 7.01865 + 7.56425i 0.380640 + 0.410229i
\(341\) 19.6838i 1.06594i
\(342\) 0 0
\(343\) −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 \(0.924057\pi\)
\(348\) 0 0
\(349\) 0.508601 0.0272248 0.0136124 0.999907i \(-0.495667\pi\)
0.0136124 + 0.999907i \(0.495667\pi\)
\(350\) −1.98190 2.41656i −0.105937 0.129170i
\(351\) 0 0
\(352\) 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 \(0.884836\pi\)
\(354\) 0 0
\(355\) 2.66570 + 0.0997335i 0.141480 + 0.00529330i
\(356\) 15.2148i 0.806383i
\(357\) 0 0
\(358\) 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
\(363\) 0 0
\(364\) −2.63446 + 2.51242i −0.138083 + 0.131687i
\(365\) −2.97465 3.20589i −0.155701 0.167804i
\(366\) 0 0
\(367\) 0.410036 0.410036i 0.0214037 0.0214037i −0.696324 0.717728i \(-0.745182\pi\)
0.717728 + 0.696324i \(0.245182\pi\)
\(368\) −18.9283 + 18.9283i −0.986705 + 0.986705i
\(369\) 0 0
\(370\) 0.00816384 0.218205i 0.000424418 0.0113439i
\(371\) 14.6123 13.9354i 0.758633 0.723490i
\(372\) 0 0
\(373\) −3.44496 + 3.44496i −0.178373 + 0.178373i −0.790646 0.612273i \(-0.790255\pi\)
0.612273 + 0.790646i \(0.290255\pi\)
\(374\) −2.23525 −0.115582
\(375\) 0 0
\(376\) 0.402328i 0.0207485i
\(377\) −1.82755 + 1.82755i −0.0941237 + 0.0941237i
\(378\) 0 0
\(379\) 12.9179i 0.663547i −0.943359 0.331773i \(-0.892353\pi\)
0.943359 0.331773i \(-0.107647\pi\)
\(380\) 1.17326 31.3593i 0.0601872 1.60870i
\(381\) 0 0
\(382\) −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 \(0.631378\pi\)
\(384\) 0 0
\(385\) −23.5376 1.44002i −1.19959 0.0733903i
\(386\) −2.98291 −0.151826
\(387\) 0 0
\(388\) −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
\(392\) 4.82572 4.38850i 0.243736 0.221653i
\(393\) 0 0
\(394\) 0.897808i 0.0452309i
\(395\) 0.722335 19.3067i 0.0363446 0.971426i
\(396\) 0 0
\(397\) 6.80633 6.80633i 0.341600 0.341600i −0.515369 0.856969i \(-0.672345\pi\)
0.856969 + 0.515369i \(0.172345\pi\)
\(398\) 0.103013 + 0.103013i 0.00516356 + 0.00516356i
\(399\) 0 0
\(400\) −18.2898 1.37050i −0.914492 0.0685249i
\(401\) 8.83090 0.440994 0.220497 0.975388i \(-0.429232\pi\)
0.220497 + 0.975388i \(0.429232\pi\)
\(402\) 0 0
\(403\) 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
\(408\) 0 0
\(409\) −23.1985 −1.14709 −0.573546 0.819174i \(-0.694432\pi\)
−0.573546 + 0.819174i \(0.694432\pi\)
\(410\) −2.95545 + 2.74228i −0.145959 + 0.135432i
\(411\) 0 0
\(412\) −24.3819 + 24.3819i −1.20121 + 1.20121i
\(413\) 16.1599 + 0.383178i 0.795178 + 0.0188550i
\(414\) 0 0
\(415\) −25.7883 27.7930i −1.26590 1.36430i
\(416\) 1.93229i 0.0947381i
\(417\) 0 0
\(418\) 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 0
\(424\) 7.11153i 0.345367i
\(425\) 8.99560 7.74146i 0.436351 0.375516i
\(426\) 0 0
\(427\) −0.445951 + 18.8072i −0.0215811 + 0.910146i
\(428\) −14.5429 + 14.5429i −0.702957 + 0.702957i
\(429\) 0 0
\(430\) −2.72642 0.102005i −0.131480 0.00491914i
\(431\) 22.5558 1.08648 0.543238 0.839579i \(-0.317198\pi\)
0.543238 + 0.839579i \(0.317198\pi\)
\(432\) 0 0
\(433\) −19.9639 19.9639i −0.959405 0.959405i 0.0398028 0.999208i \(-0.487327\pi\)
−0.999208 + 0.0398028i \(0.987327\pi\)
\(434\) −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 0
\(439\) 30.1943 1.44110 0.720548 0.693405i \(-0.243890\pi\)
0.720548 + 0.693405i \(0.243890\pi\)
\(440\) 6.08824 5.64910i 0.290246 0.269310i
\(441\) 0 0
\(442\) 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 0
\(445\) 17.4868 + 0.654245i 0.828954 + 0.0310142i
\(446\) 0.452737i 0.0214377i
\(447\) 0 0
\(448\) 0.419669 17.6988i 0.0198275 0.836191i
\(449\) 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
\(453\) 0 0
\(454\) −1.38802 −0.0651432
\(455\) 2.77431 + 3.13589i 0.130062 + 0.147013i
\(456\) 0 0
\(457\) 1.31546 + 1.31546i 0.0615348 + 0.0615348i 0.737204 0.675670i \(-0.236145\pi\)
−0.675670 + 0.737204i \(0.736145\pi\)
\(458\) 2.17005 + 2.17005i 0.101400 + 0.101400i
\(459\) 0 0
\(460\) 21.5781 + 23.2555i 1.00609 + 1.08429i
\(461\) 1.29957i 0.0605272i 0.999542 + 0.0302636i \(0.00963467\pi\)
−0.999542 + 0.0302636i \(0.990365\pi\)
\(462\) 0 0
\(463\) 16.5240 16.5240i 0.767934 0.767934i −0.209809 0.977742i \(-0.567284\pi\)
0.977742 + 0.209809i \(0.0672841\pi\)
\(464\) 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 0
\(469\) −2.43816 2.55659i −0.112584 0.118052i
\(470\) −0.227932 0.00852775i −0.0105137 0.000393356i
\(471\) 0 0
\(472\) −4.02560 + 4.02560i −0.185293 + 0.185293i
\(473\) −14.5566 + 14.5566i −0.669313 + 0.669313i
\(474\) 0 0
\(475\) −35.9916 2.69693i −1.65141 0.123744i
\(476\) 8.42631 + 8.83562i 0.386219 + 0.404980i
\(477\) 0 0
\(478\) 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 0
\(484\) 9.50389i 0.431995i
\(485\) −17.2391 + 15.9956i −0.782786 + 0.726325i
\(486\) 0 0
\(487\) −13.6519 13.6519i −0.618627 0.618627i 0.326552 0.945179i \(-0.394113\pi\)
−0.945179 + 0.326552i \(0.894113\pi\)
\(488\) −4.68508 4.68508i −0.212084 0.212084i
\(489\) 0 0
\(490\) −2.38394 2.82694i −0.107695 0.127708i
\(491\) −32.1155 −1.44935 −0.724677 0.689089i \(-0.758011\pi\)
−0.724677 + 0.689089i \(0.758011\pi\)
\(492\) 0 0
\(493\) 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
\(498\) 0 0
\(499\) 4.27431i 0.191344i 0.995413 + 0.0956722i \(0.0305000\pi\)
−0.995413 + 0.0956722i \(0.969500\pi\)
\(500\) −2.43349 + 21.6000i −0.108829 + 0.965981i
\(501\) 0 0
\(502\) 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 \(0.936806\pi\)
\(504\) 0 0
\(505\) 0.528051 14.1139i 0.0234980 0.628059i
\(506\) −6.87206 −0.305500
\(507\) 0 0
\(508\) −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
\(513\) 0 0
\(514\) 3.13814 0.138417
\(515\) 26.9744 + 29.0713i 1.18863 + 1.28103i
\(516\) 0 0
\(517\) −1.21695 + 1.21695i −0.0535212 + 0.0535212i
\(518\) 0.00612451 0.258291i 0.000269096 0.0113487i
\(519\) 0 0
\(520\) −1.47360 0.0551328i −0.0646217 0.00241773i
\(521\) 28.8647i 1.26458i −0.774730 0.632292i \(-0.782114\pi\)
0.774730 0.632292i \(-0.217886\pi\)
\(522\) 0 0
\(523\) −3.54707 3.54707i −0.155103 0.155103i 0.625290 0.780392i \(-0.284981\pi\)
−0.780392 + 0.625290i \(0.784981\pi\)
\(524\) −36.5788 −1.59795
\(525\) 0 0
\(526\) −5.13793 −0.224024
\(527\) −8.28829 8.28829i −0.361043 0.361043i
\(528\) 0 0
\(529\) 30.2526i 1.31533i
\(530\) 4.02891 + 0.150736i 0.175005 + 0.00654756i
\(531\) 0 0
\(532\) 0.880184 37.1203i 0.0381608 1.60937i
\(533\) 3.81926 3.81926i 0.165430 0.165430i
\(534\) 0 0
\(535\) 16.0892 + 17.3399i 0.695596 + 0.749669i
\(536\) 1.24424 0.0537432
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) −6.48062 −0.277854
\(545\) 0.0558641 1.49315i 0.00239296 0.0639594i
\(546\) 0 0
\(547\) 28.2200 + 28.2200i 1.20660 + 1.20660i 0.972121 + 0.234482i \(0.0753392\pi\)
0.234482 + 0.972121i \(0.424661\pi\)
\(548\) 1.57863 1.57863i 0.0674359 0.0674359i
\(549\) 0 0
\(550\) −3.07135 3.56892i −0.130963 0.152179i
\(551\) 26.3613i 1.12303i
\(552\) 0 0
\(553\) 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 0
\(559\) 3.65510 0.154594
\(560\) −21.6610 1.32521i −0.915344 0.0560004i
\(561\) 0 0
\(562\) 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 0
\(565\) −7.87351 + 7.30560i −0.331241 + 0.307349i
\(566\) 4.98144i 0.209386i
\(567\) 0 0
\(568\) −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
\(573\) 0 0
\(574\) −3.45220 + 3.29227i −0.144092 + 0.137417i
\(575\) 27.6561 23.8003i 1.15334 0.992543i
\(576\) 0 0
\(577\) 3.89677 3.89677i 0.162225 0.162225i −0.621327 0.783552i \(-0.713406\pi\)
0.783552 + 0.621327i \(0.213406\pi\)
\(578\) −1.89875 + 1.89875i −0.0789776 + 0.0789776i
\(579\) 0 0
\(580\) −15.8650 0.593566i −0.658756 0.0246465i
\(581\) −30.9604 32.4643i −1.28445 1.34685i
\(582\) 0 0
\(583\) 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 \(0.104670\pi\)
\(588\) 0 0
\(589\) 35.6465i 1.46879i
\(590\) 2.19530 + 2.36596i 0.0903793 + 0.0974050i
\(591\) 0 0
\(592\) −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 0
\(595\) 10.5174 9.30466i 0.431170 0.381454i
\(596\) 6.10696 0.250151
\(597\) 0 0
\(598\) 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 \(-0.286472\pi\)
\(602\) −3.22730 0.0765245i −0.131535 0.00311891i
\(603\) 0 0
\(604\) 28.6261i 1.16478i
\(605\) −10.9231 0.408673i −0.444087 0.0166149i
\(606\) 0 0
\(607\) 10.2931 10.2931i 0.417783 0.417783i −0.466656 0.884439i \(-0.654541\pi\)
0.884439 + 0.466656i \(0.154541\pi\)
\(608\) 13.9360 + 13.9360i 0.565180 + 0.565180i
\(609\) 0 0
\(610\) −2.75355 + 2.55494i −0.111488 + 0.103447i
\(611\) 0.305570 0.0123621
\(612\) 0 0
\(613\) −14.4155 + 14.4155i −0.582235 + 0.582235i −0.935517 0.353282i \(-0.885066\pi\)
0.353282 + 0.935517i \(0.385066\pi\)
\(614\) 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 \(0.492476\pi\)
\(618\) 0 0
\(619\) −11.1991 −0.450129 −0.225064 0.974344i \(-0.572259\pi\)
−0.225064 + 0.974344i \(0.572259\pi\)
\(620\) 21.4530 + 0.802636i 0.861574 + 0.0322346i
\(621\) 0 0
\(622\) −4.56168 + 4.56168i −0.182907 + 0.182907i
\(623\) 20.6993 + 0.490815i 0.829301 + 0.0196641i
\(624\) 0 0
\(625\) 24.7208 + 3.72569i 0.988833 + 0.149028i
\(626\) 6.18373i 0.247152i
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 7.31014i 0.290323i
\(635\) 12.6653 + 13.6499i 0.502608 + 0.541678i
\(636\) 0 0
\(637\) 3.33309 + 3.66516i 0.132062 + 0.145219i
\(638\) 2.43176 2.43176i 0.0962745 0.0962745i
\(639\) 0 0
\(640\) 11.5419 10.7094i 0.456235 0.423327i
\(641\) 29.8969 1.18086 0.590428 0.807090i \(-0.298959\pi\)
0.590428 + 0.807090i \(0.298959\pi\)
\(642\) 0 0
\(643\) 11.2813 + 11.2813i 0.444891 + 0.444891i 0.893652 0.448761i \(-0.148134\pi\)
−0.448761 + 0.893652i \(0.648134\pi\)
\(644\) 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 0
\(649\) 24.3530 0.955937
\(650\) −0.0624689 + 0.833673i −0.00245023 + 0.0326993i
\(651\) 0 0
\(652\) −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 0
\(655\) −1.57291 + 42.0410i −0.0614585 + 1.64268i
\(656\) 27.9953i 1.09303i
\(657\) 0 0
\(658\) −0.269805 0.00639752i −0.0105181 0.000249401i
\(659\) 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
\(663\) 0 0
\(664\) 15.7998 0.613150
\(665\) −42.6255 2.60781i −1.65295 0.101127i
\(666\) 0 0
\(667\) 18.8441 + 18.8441i 0.729646 + 0.729646i
\(668\) 9.01365 + 9.01365i 0.348749 + 0.348749i
\(669\) 0 0
\(670\) 0.0263730 0.704904i 0.00101888 0.0272328i
\(671\) 28.3425i 1.09415i
\(672\) 0 0
\(673\) −11.4381 + 11.4381i −0.440906 + 0.440906i −0.892316 0.451411i \(-0.850921\pi\)
0.451411 + 0.892316i \(0.350921\pi\)
\(674\) 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 0
\(679\) −20.1366 + 19.2037i −0.772770 + 0.736972i
\(680\) −0.184908 + 4.94226i −0.00709089 + 0.189527i
\(681\) 0 0
\(682\) −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 \(0.127591\pi\)
\(684\) 0 0
\(685\) −1.74648 1.88225i −0.0667297 0.0719170i
\(686\) −2.86624 3.30596i −0.109433 0.126222i
\(687\) 0 0
\(688\) −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 0
\(694\) 4.57667i 0.173728i
\(695\) 0.988633 + 0.0369884i 0.0375010 + 0.00140305i
\(696\) 0 0
\(697\) −12.8093 12.8093i −0.485186 0.485186i
\(698\) 0.0849648 + 0.0849648i 0.00321597 + 0.00321597i
\(699\) 0 0
\(700\) −2.52923 + 25.5945i −0.0955960 + 0.967380i
\(701\) −1.45193 −0.0548388 −0.0274194 0.999624i \(-0.508729\pi\)
−0.0274194 + 0.999624i \(0.508729\pi\)
\(702\) 0 0
\(703\) −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
\(708\) 0 0
\(709\) 48.5284i 1.82252i −0.411827 0.911262i \(-0.635109\pi\)
0.411827 0.911262i \(-0.364891\pi\)
\(710\) 0.428659 + 0.461981i 0.0160873 + 0.0173378i
\(711\) 0 0
\(712\) −5.15642 + 5.15642i −0.193245 + 0.193245i
\(713\) −25.4815 25.4815i −0.954290 0.954290i
\(714\) 0 0
\(715\) 4.29052 + 4.62405i 0.160457 + 0.172930i
\(716\) −42.9876 −1.60652
\(717\) 0 0
\(718\) −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
\(723\) 0 0
\(724\) 16.4970 0.613104
\(725\) −1.36440 + 18.2085i −0.0506727 + 0.676247i
\(726\) 0 0
\(727\) 10.4498 10.4498i 0.387563 0.387563i −0.486254 0.873817i \(-0.661637\pi\)
0.873817 + 0.486254i \(0.161637\pi\)
\(728\) −1.74432 0.0413607i −0.0646487 0.00153293i
\(729\) 0 0
\(730\) 0.0386295 1.03250i 0.00142974 0.0382144i
\(731\) 12.2587i 0.453405i
\(732\) 0 0
\(733\) 18.8687 + 18.8687i 0.696933 + 0.696933i 0.963748 0.266815i \(-0.0859712\pi\)
−0.266815 + 0.963748i \(0.585971\pi\)
\(734\) 0.136998 0.00505669
\(735\) 0 0
\(736\) −19.9240 −0.734409
\(737\) −3.76354 3.76354i −0.138632 0.138632i
\(738\) 0 0
\(739\) 20.9689i 0.771354i 0.922634 + 0.385677i \(0.126032\pi\)
−0.922634 + 0.385677i \(0.873968\pi\)
\(740\) −1.31723 + 1.22222i −0.0484224 + 0.0449297i
\(741\) 0 0
\(742\) 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 \(0.326599\pi\)
\(744\) 0 0
\(745\) 0.262603 7.01890i 0.00962102 0.257152i
\(746\) −1.15100 −0.0421412
\(747\) 0 0
\(748\) 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
\(753\) 0 0
\(754\) −0.610607 −0.0222370
\(755\) 32.9007 + 1.23094i 1.19738 + 0.0447984i
\(756\) 0 0
\(757\) −13.9324 13.9324i −0.506383 0.506383i 0.407031 0.913414i \(-0.366564\pi\)
−0.913414 + 0.407031i \(0.866564\pi\)
\(758\) 2.15801 2.15801i 0.0783824 0.0783824i
\(759\) 0 0
\(760\) 11.0255 10.2303i 0.399938 0.371091i
\(761\) 8.78825i 0.318574i 0.987232 + 0.159287i \(0.0509195\pi\)
−0.987232 + 0.159287i \(0.949081\pi\)
\(762\) 0 0
\(763\) 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
\(768\) 0 0
\(769\) −11.2183 −0.404543 −0.202271 0.979330i \(-0.564832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(770\) −3.69153 4.17266i −0.133034 0.150372i
\(771\) 0 0
\(772\) 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 \(0.934219\pi\)
\(774\) 0 0
\(775\) 1.84498 24.6220i 0.0662738 0.884450i
\(776\) 9.80008i 0.351802i
\(777\) 0 0
\(778\) 4.06447 4.06447i 0.145718 0.145718i
\(779\) 55.0905i 1.97382i
\(780\) 0 0
\(781\) 4.75520 0.170155
\(782\) 2.89362 2.89362i 0.103476 0.103476i
\(783\) 0 0
\(784\) −25.6487 1.21703i −0.916025 0.0434654i
\(785\) 18.4639 17.1321i