Properties

Label 315.2.p.e.118.6
Level 315
Weight 2
Character 315.118
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: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
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 defining polynomial
Character \(\chi\) \(=\) 315.118
Dual form 315.2.p.e.307.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.167056 - 0.167056i) q^{2} +1.94418i q^{4} +(2.23450 - 0.0836010i) q^{5} +(-0.0627175 + 2.64501i) q^{7} +(0.658899 + 0.658899i) q^{8} +O(q^{10})\) \(q+(0.167056 - 0.167056i) q^{2} +1.94418i q^{4} +(2.23450 - 0.0836010i) q^{5} +(-0.0627175 + 2.64501i) q^{7} +(0.658899 + 0.658899i) q^{8} +(0.359321 - 0.387253i) q^{10} -3.98602 q^{11} +(-0.500437 + 0.500437i) q^{13} +(0.431387 + 0.452341i) q^{14} -3.66822 q^{16} +(-1.67840 - 1.67840i) q^{17} +7.21850 q^{19} +(0.162536 + 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(5.16007 + 5.16007i) q^{23} +(4.98602 - 0.373614i) q^{25} +0.167202i q^{26} +(-5.14238 - 0.121934i) q^{28} -3.65191i q^{29} -4.93821i q^{31} +(-1.93060 + 1.93060i) q^{32} -0.560773 q^{34} +(0.0809828 + 5.91553i) q^{35} +(0.292275 - 0.292275i) q^{37} +(1.20589 - 1.20589i) q^{38} +(1.52740 + 1.41723i) q^{40} -7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} -7.74956i q^{44} +1.72404 q^{46} +(-0.305303 - 0.305303i) q^{47} +(-6.99213 - 0.331777i) q^{49} +(0.770530 - 0.895358i) q^{50} +(-0.972943 - 0.972943i) q^{52} +(-5.39653 - 5.39653i) q^{53} +(-8.90678 + 0.333235i) q^{55} +(-1.78412 + 1.70147i) q^{56} +(-0.610073 - 0.610073i) q^{58} +6.10959 q^{59} -7.11047i q^{61} +(-0.824957 - 0.824957i) q^{62} -6.69141i q^{64} +(-1.07639 + 1.16007i) q^{65} +(0.944185 - 0.944185i) q^{67} +(3.26312 - 3.26312i) q^{68} +(1.00175 + 0.974695i) q^{70} -1.19297 q^{71} +(-1.38298 + 1.38298i) q^{73} -0.0976524i q^{74} +14.0341i q^{76} +(0.249993 - 10.5431i) q^{77} -8.64027i q^{79} +(-8.19666 + 0.306667i) q^{80} +(-1.27494 - 1.27494i) q^{82} +(-11.9895 + 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +1.22015 q^{86} +(-2.62639 - 2.62639i) q^{88} +7.82581 q^{89} +(-1.29227 - 1.35505i) q^{91} +(-10.0321 + 10.0321i) q^{92} -0.102005 q^{94} +(16.1298 - 0.603474i) q^{95} +(-7.43671 - 7.43671i) q^{97} +(-1.22350 + 1.11265i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 0
\(4\) 1.94418i 0.972092i
\(5\) 2.23450 0.0836010i 0.999301 0.0373875i
\(6\) 0 0
\(7\) −0.0627175 + 2.64501i −0.0237050 + 0.999719i
\(8\) 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 \(-0.781291\pi\)
0.634295 + 0.773091i \(0.281291\pi\)
\(14\) 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 0
\(19\) 7.21850 1.65604 0.828019 0.560700i \(-0.189468\pi\)
0.828019 + 0.560700i \(0.189468\pi\)
\(20\) 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 0.996868 + 0.0790800i \(0.0251983\pi\)
0.0790800 + 0.996868i \(0.474802\pi\)
\(24\) 0 0
\(25\) 4.98602 0.373614i 0.997204 0.0747227i
\(26\) 0.167202i 0.0327910i
\(27\) 0 0
\(28\) −5.14238 0.121934i −0.971819 0.0230434i
\(29\) 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
\(33\) 0 0
\(34\) −0.560773 −0.0961717
\(35\) 0.0809828 + 5.91553i 0.0136886 + 0.999906i
\(36\) 0 0
\(37\) 0.292275 0.292275i 0.0480497 0.0480497i −0.682674 0.730723i \(-0.739183\pi\)
0.730723 + 0.682674i \(0.239183\pi\)
\(38\) 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 0.928427 0.371516i \(-0.121162\pi\)
−0.371516 + 0.928427i \(0.621162\pi\)
\(44\) 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 \(0.760025\pi\)
\(48\) 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 0.231553 0.972822i \(-0.425619\pi\)
−0.972822 + 0.231553i \(0.925619\pi\)
\(54\) 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 \(-0.369808\pi\)
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 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 −0.647075 0.762426i \(-0.724008\pi\)
0.762426 + 0.647075i \(0.224008\pi\)
\(68\) 3.26312 3.26312i 0.395711 0.395711i
\(69\) 0 0
\(70\) 1.00175 + 0.974695i 0.119732 + 0.116498i
\(71\) −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 \(-0.786513\pi\)
0.621527 + 0.783393i \(0.286513\pi\)
\(74\) 0.0976524i 0.0113519i
\(75\) 0 0
\(76\) 14.0341i 1.60982i
\(77\) 0.249993 10.5431i 0.0284894 1.20149i
\(78\) 0 0
\(79\) 8.64027i 0.972106i −0.873929 0.486053i \(-0.838436\pi\)
0.873929 0.486053i \(-0.161564\pi\)
\(80\) −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 −0.399122 + 0.916898i \(0.630685\pi\)
−0.916898 + 0.399122i \(0.869315\pi\)
\(84\) 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 \(-0.363863\pi\)
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
\(93\) 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 \(-0.429283\pi\)
−0.975423 + 0.220340i \(0.929283\pi\)
\(98\) −1.22350 + 1.11265i −0.123592 + 0.112395i
\(99\) 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 0.273954 0.961743i \(-0.411668\pi\)
0.961743 0.273954i \(-0.0883316\pi\)
\(104\) −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 \(0.420849\pi\)
\(108\) 0 0
\(109\) 0.668223i 0.0640042i −0.999488 0.0320021i \(-0.989812\pi\)
0.999488 0.0320021i \(-0.0101883\pi\)
\(110\) −1.43226 + 1.54360i −0.136561 + 0.147176i
\(111\) 0 0
\(112\) 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 \(0.677457\pi\)
\(114\) 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 −0.918328 0.395820i \(-0.870460\pi\)
0.395820 + 0.918328i \(0.370460\pi\)
\(128\) −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
\(133\) −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 \(0.234380\pi\)
\(138\) 0 0
\(139\) 0.442439 0.0375272 0.0187636 0.999824i \(-0.494027\pi\)
0.0187636 + 0.999824i \(0.494027\pi\)
\(140\) −11.5009 + 0.157445i −0.972001 + 0.0133066i
\(141\) 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 \(-0.958930\pi\)
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
\(153\) 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 \(-0.101604\pi\)
−0.313805 + 0.949487i \(0.601604\pi\)
\(158\) −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 0.985834 0.167722i \(-0.0536410\pi\)
−0.167722 + 0.985834i \(0.553641\pi\)
\(164\) 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 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 \(-0.792657\pi\)
0.606290 + 0.795244i \(0.292657\pi\)
\(174\) 0 0
\(175\) 0.675500 + 13.2115i 0.0510630 + 0.998695i
\(176\) 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 \(0.309570\pi\)
−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 \(0.897877\pi\)
\(182\) −0.442251 0.0104865i −0.0327818 0.000777310i
\(183\) 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 0.308562 0.951204i \(-0.400152\pi\)
−0.951204 + 0.308562i \(0.900152\pi\)
\(194\) −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 0
\(199\) −0.616637 −0.0437122 −0.0218561 0.999761i \(-0.506958\pi\)
−0.0218561 + 0.999761i \(0.506958\pi\)
\(200\) 3.53146 + 3.03911i 0.249712 + 0.214898i
\(201\) 0 0
\(202\) 1.05518 + 1.05518i 0.0742422 + 0.0742422i
\(203\) 9.65933 + 0.229039i 0.677952 + 0.0160754i
\(204\) 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
\(217\) 13.0616 + 0.309712i 0.886680 + 0.0210246i
\(218\) −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 \(-0.729562\pi\)
0.751020 + 0.660279i \(0.229562\pi\)
\(224\) −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 \(0.687538\pi\)
\(228\) 0 0
\(229\) −12.9900 −0.858403 −0.429202 0.903209i \(-0.641205\pi\)
−0.429202 + 0.903209i \(0.641205\pi\)
\(230\) 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 0.996637 + 0.0819485i \(0.0261143\pi\)
0.0819485 + 0.996637i \(0.473886\pi\)
\(234\) 0 0
\(235\) −0.707725 0.656678i −0.0461669 0.0428370i
\(236\) 11.8782i 0.773203i
\(237\) 0 0
\(238\) 0.0351703 1.48325i 0.00227975 0.0961447i
\(239\) 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 0
\(244\) 13.8241 0.884995
\(245\) −15.6517 0.156807i −0.999950 0.0100180i
\(246\) 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 \(-0.385968\pi\)
−0.936515 + 0.350628i \(0.885968\pi\)
\(258\) 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 0.0504843 0.998725i \(-0.483924\pi\)
−0.998725 + 0.0504843i \(0.983924\pi\)
\(264\) 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 \(-0.747135\pi\)
−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 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 −0.547765 0.836632i \(-0.684521\pi\)
0.836632 + 0.547765i \(0.184521\pi\)
\(278\) 0.0739121 0.0739121i 0.00443295 0.00443295i
\(279\) 0 0
\(280\) −3.84438 + 3.95109i −0.229745 + 0.236123i
\(281\) 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 \(-0.965592\pi\)
0.107885 + 0.994163i \(0.465592\pi\)
\(284\) 2.31935i 0.137628i
\(285\) 0 0
\(286\) 0.666471i 0.0394092i
\(287\) 20.1863 + 0.478650i 1.19156 + 0.0282538i
\(288\) 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 \(-0.686565\pi\)
0.833098 + 0.553125i \(0.186565\pi\)
\(294\) 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 \(-0.380136\pi\)
−0.929933 + 0.367728i \(0.880136\pi\)
\(308\) 20.4977 + 0.486033i 1.16796 + 0.0276943i
\(309\) 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 −0.0472492 + 0.998883i \(0.515045\pi\)
−0.998883 + 0.0472492i \(0.984955\pi\)
\(314\) 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 \(-0.0851980\pi\)
\(318\) 0 0
\(319\) 14.5566i 0.815013i
\(320\) −0.559409 14.9520i −0.0312719 0.835842i
\(321\) 0 0
\(322\) −0.108127 + 4.56010i −0.00602570 + 0.254124i
\(323\) −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 −0.634525 0.772903i \(-0.718804\pi\)
0.772903 + 0.634525i \(0.218804\pi\)
\(338\) 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
\(343\) 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 \(0.424057\pi\)
\(348\) 0 0
\(349\) −0.508601 −0.0272248 −0.0136124 0.999907i \(-0.504333\pi\)
−0.0136124 + 0.999907i \(0.504333\pi\)
\(350\) 2.31990 + 2.09421i 0.124004 + 0.111940i
\(351\) 0 0
\(352\) 7.69540 7.69540i 0.410166 0.410166i
\(353\) 10.9217 10.9217i 0.581305 0.581305i −0.353957 0.935262i \(-0.615164\pi\)
0.935262 + 0.353957i \(0.115164\pi\)
\(354\) 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 \(-0.861379\pi\)
0.906663 0.421855i \(-0.138621\pi\)
\(360\) 0 0
\(361\) 33.1068 1.74246
\(362\) 1.41752 + 1.41752i 0.0745030 + 0.0745030i
\(363\) 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 \(-0.254818\pi\)
−0.717728 + 0.696324i \(0.754818\pi\)
\(368\) −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 0.612273 0.790646i \(-0.290255\pi\)
−0.790646 + 0.612273i \(0.790255\pi\)
\(374\) 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 \(0.107647\pi\)
−0.943359 + 0.331773i \(0.892353\pi\)
\(380\) 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 \(-0.868622\pi\)
0.401117 + 0.916027i \(0.368622\pi\)
\(384\) 0 0
\(385\) −0.322799 23.5794i −0.0164514 1.20172i
\(386\) −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 \(0.211567\pi\)
−0.787127 + 0.616791i \(0.788433\pi\)
\(390\) 0 0
\(391\) 17.3213i 0.875976i
\(392\) −4.38850 4.82572i −0.221653 0.243736i
\(393\) 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 \(-0.327655\pi\)
−0.856969 + 0.515369i \(0.827655\pi\)
\(398\) −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 \(-0.305568\pi\)
0.573546 + 0.819174i \(0.305568\pi\)
\(410\) −2.95545 2.74228i −0.145959 0.135432i
\(411\) 0 0
\(412\) 24.3819 + 24.3819i 1.20121 + 1.20121i
\(413\) −0.383178 + 16.1599i −0.0188550 + 0.795178i
\(414\) 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 \(-0.396819\pi\)
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 0
\(424\) 7.11153i 0.345367i
\(425\) −8.99560 7.74146i −0.436351 0.375516i
\(426\) 0 0
\(427\) 18.8072 + 0.445951i 0.910146 + 0.0215811i
\(428\) −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 \(-0.512673\pi\)
0.999208 + 0.0398028i \(0.0126730\pi\)
\(434\) 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 \(-0.756110\pi\)
−0.720548 + 0.693405i \(0.756110\pi\)
\(440\) −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 0.941742 0.336337i \(-0.109188\pi\)
−0.336337 + 0.941742i \(0.609188\pi\)
\(444\) 0 0
\(445\) 17.4868 0.654245i 0.828954 0.0310142i
\(446\) 0.452737i 0.0214377i
\(447\) 0 0
\(448\) 17.6988 + 0.419669i 0.836191 + 0.0198275i
\(449\) 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
\(453\) 0 0
\(454\) 1.38802 0.0651432
\(455\) −3.00088 2.91982i −0.140683 0.136883i
\(456\) 0 0
\(457\) 1.31546 1.31546i 0.0615348 0.0615348i −0.675670 0.737204i \(-0.736145\pi\)
0.737204 + 0.675670i \(0.236145\pi\)
\(458\) −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 0.977742 0.209809i \(-0.0672841\pi\)
−0.209809 + 0.977742i \(0.567284\pi\)
\(464\) 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 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 \(-0.581487\pi\)
−0.253212 + 0.967411i \(0.581487\pi\)
\(480\) 0 0
\(481\) 0.292530i 0.0133382i
\(482\) −2.44749 2.44749i −0.111480 0.111480i
\(483\) 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 −0.945179 0.326552i \(-0.894113\pi\)
0.326552 + 0.945179i \(0.394113\pi\)
\(488\) 4.68508 4.68508i 0.212084 0.212084i
\(489\) 0 0
\(490\) −2.64090 + 2.58851i −0.119304 + 0.116937i
\(491\) −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
\(497\) 0.0748201 3.15541i 0.00335614 0.141540i
\(498\) 0 0
\(499\) 4.27431i 0.191344i −0.995413 0.0956722i \(-0.969500\pi\)
0.995413 0.0956722i \(-0.0305000\pi\)
\(500\) 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 \(-0.563194\pi\)
0.980357 + 0.197229i \(0.0631943\pi\)
\(504\) 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 \(-0.712333\pi\)
−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
\(513\) 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
\(518\) 0.258291 + 0.00612451i 0.0113487 + 0.000269096i
\(519\) 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 \(-0.715019\pi\)
0.780392 + 0.625290i \(0.215019\pi\)
\(524\) 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
\(532\) −37.1203 0.880184i −1.60937 0.0381608i
\(533\) 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 0.234482 0.972121i \(-0.424661\pi\)
0.972121 0.234482i \(-0.0753392\pi\)
\(548\) 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
\(553\) 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 0
\(559\) −3.65510 −0.154594
\(560\) −0.297063 21.6995i −0.0125532 0.916970i
\(561\) 0 0
\(562\) 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 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 \(-0.878460\pi\)
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
\(573\) 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 \(-0.286594\pi\)
−0.783552 + 0.621327i \(0.786594\pi\)
\(578\) −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 \(-0.395330\pi\)
−0.946420 + 0.322937i \(0.895330\pi\)
\(588\) 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 \(-0.781759\pi\)
0.633157 + 0.774023i \(0.281759\pi\)
\(594\) 0 0
\(595\) 9.79269 10.0645i 0.401461 0.412605i
\(596\) 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 \(0.0661608\pi\)
−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 \(-0.286472\pi\)
\(602\) −0.0765245 + 3.22730i −0.00311891 + 0.131535i
\(603\) 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 \(-0.345459\pi\)
−0.884439 + 0.466656i \(0.845459\pi\)
\(608\) −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 0.353282 0.935517i \(-0.385066\pi\)
−0.935517 + 0.353282i \(0.885066\pi\)
\(614\) −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 \(-0.00752382\pi\)
\(618\) 0 0
\(619\) 11.1991 0.450129 0.225064 0.974344i \(-0.427741\pi\)
0.225064 + 0.974344i \(0.427741\pi\)
\(620\) 21.4530 0.802636i 0.861574 0.0322346i
\(621\) 0 0
\(622\) 4.56168 + 4.56168i 0.182907 + 0.182907i
\(623\) −0.490815 + 20.6993i −0.0196641 + 0.829301i
\(624\) 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
\(637\) 3.66516 3.33309i 0.145219 0.132062i
\(638\) 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 \(-0.851866\pi\)
0.448761 + 0.893652i \(0.351866\pi\)
\(644\) −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 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 0.744720 0.667377i \(-0.232583\pi\)
−0.667377 + 0.744720i \(0.732583\pi\)
\(654\) 0 0
\(655\) −1.57291 42.0410i −0.0614585 1.64268i
\(656\) 27.9953i 1.09303i
\(657\) 0 0
\(658\) 0.00639752 0.269805i 0.000249401 0.0105181i
\(659\) 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
\(663\) 0 0
\(664\) −15.7998 −0.613150
\(665\) 0.584574 + 42.7012i 0.0226688 + 1.65588i
\(666\) 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 0.451411 0.892316i \(-0.350921\pi\)
−0.892316 + 0.451411i \(0.850921\pi\)
\(674\) 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 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 0.920734 0.390191i \(-0.127591\pi\)
−0.390191 + 0.920734i \(0.627591\pi\)
\(684\) 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
\(700\) −25.6856 + 1.31330i −0.970824 + 0.0496380i
\(701\) −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
\(707\) −16.7067 0.396144i −0.628322 0.0148985i
\(708\) 0 0
\(709\) 48.5284i 1.82252i 0.411827 + 0.911262i \(0.364891\pi\)
−0.411827 + 0.911262i \(0.635109\pi\)
\(710\) −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 \(-0.197962\pi\)
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
\(723\) 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 \(-0.338363\pi\)
−0.873817 + 0.486254i \(0.838363\pi\)
\(728\) 0.0413607 1.74432i 0.00153293 0.0646487i
\(729\) 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 \(-0.914029\pi\)
0.266815 + 0.963748i \(0.414029\pi\)
\(734\) −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 \(-0.873968\pi\)
0.922634 0.385677i \(-0.126032\pi\)
\(740\) 1.31723 + 1.22222i 0.0484224 + 0.0449297i
\(741\) 0 0
\(742\) 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 \(0.826599\pi\)
\(744\) 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 −0.913414 0.407031i \(-0.866564\pi\)
0.407031 + 0.913414i \(0.366564\pi\)
\(758\) 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
\(763\) 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
\(768\) 0 0
\(769\) 11.2183 0.404543 0.202271 0.979330i \(-0.435168\pi\)
0.202271 + 0.979330i \(0.435168\pi\)
\(770\) −3.99300 3.88515i −0.143898 0.140011i
\(771\) 0 0
\(772\) 17.3574 17.3574i 0.624708 0.624708i
\(773\) 21.5065 21.5065i 0.773535 0.773535i −0.205188 0.978723i \(-0.565781\pi\)
0.978723 + 0.205188i \(0.0657806\pi\)
\(774\) 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 0.659004 + 0.611471i
\(786\) 0