Properties

Label 105.2.m.a.13.4
Level 105
Weight 2
Character 105.13
Analytic conductor 0.838
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
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: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.4
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 \(\chi\) \(=\) 105.13
Dual form 105.2.m.a.97.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.167056 + 0.167056i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.94418i q^{4} +(2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-2.64501 + 0.0627175i) q^{7} +(-0.658899 - 0.658899i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.167056 + 0.167056i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.94418i q^{4} +(2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-2.64501 + 0.0627175i) q^{7} +(-0.658899 - 0.658899i) q^{8} -1.00000i q^{9} +(-0.359321 + 0.387253i) q^{10} +3.98602 q^{11} +(1.37475 + 1.37475i) q^{12} +(0.500437 - 0.500437i) q^{13} +(0.431387 - 0.452341i) q^{14} +(1.52092 - 1.63915i) q^{15} -3.66822 q^{16} +(-1.67840 - 1.67840i) q^{17} +(0.167056 + 0.167056i) q^{18} -7.21850 q^{19} +(0.162536 + 4.34429i) q^{20} +(-1.82596 + 1.91465i) q^{21} +(-0.665888 + 0.665888i) q^{22} +(-5.16007 - 5.16007i) q^{23} -0.931824 q^{24} +(4.98602 - 0.373614i) q^{25} +0.167202i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.121934 - 5.14238i) q^{28} +3.65191i q^{29} +(0.0197510 + 0.527908i) q^{30} +4.93821i q^{31} +(1.93060 - 1.93060i) q^{32} +(2.81854 - 2.81854i) q^{33} +0.560773 q^{34} +(-5.90504 + 0.361268i) q^{35} +1.94418 q^{36} +(0.292275 - 0.292275i) q^{37} +(1.20589 - 1.20589i) q^{38} -0.707725i q^{39} +(-1.52740 - 1.41723i) q^{40} -7.63184i q^{41} +(-0.0148172 - 0.624890i) q^{42} +(3.65191 + 3.65191i) q^{43} +7.74956i q^{44} +(-0.0836010 - 2.23450i) q^{45} +1.72404 q^{46} +(-0.305303 - 0.305303i) q^{47} +(-2.59383 + 2.59383i) q^{48} +(6.99213 - 0.331777i) q^{49} +(-0.770530 + 0.895358i) q^{50} -2.37361 q^{51} +(0.972943 + 0.972943i) q^{52} +(5.39653 + 5.39653i) q^{53} +0.236253 q^{54} +(8.90678 - 0.333235i) q^{55} +(1.78412 + 1.70147i) q^{56} +(-5.10425 + 5.10425i) q^{57} +(-0.610073 - 0.610073i) q^{58} +6.10959 q^{59} +(3.18681 + 2.95695i) q^{60} +7.11047i q^{61} +(-0.824957 - 0.824957i) q^{62} +(0.0627175 + 2.64501i) q^{63} -6.69141i q^{64} +(1.07639 - 1.16007i) q^{65} +0.941708i q^{66} +(0.944185 - 0.944185i) q^{67} +(3.26312 - 3.26312i) q^{68} -7.29744 q^{69} +(0.926119 - 1.04682i) q^{70} +1.19297 q^{71} +(-0.658899 + 0.658899i) q^{72} +(1.38298 - 1.38298i) q^{73} +0.0976524i q^{74} +(3.26147 - 3.78983i) q^{75} -14.0341i q^{76} +(-10.5431 + 0.249993i) q^{77} +(0.118230 + 0.118230i) q^{78} -8.64027i q^{79} +(-8.19666 + 0.306667i) q^{80} -1.00000 q^{81} +(1.27494 + 1.27494i) q^{82} +(-11.9895 + 11.9895i) q^{83} +(-3.72244 - 3.54999i) q^{84} +(-3.89070 - 3.61007i) q^{85} -1.22015 q^{86} +(2.58229 + 2.58229i) q^{87} +(-2.62639 - 2.62639i) q^{88} +7.82581 q^{89} +(0.387253 + 0.359321i) q^{90} +(-1.29227 + 1.35505i) q^{91} +(10.0321 - 10.0321i) q^{92} +(3.49184 + 3.49184i) q^{93} +0.102005 q^{94} +(-16.1298 + 0.603474i) q^{95} -2.73028i q^{96} +(7.43671 + 7.43671i) q^{97} +(-1.11265 + 1.22350i) q^{98} -3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} + 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} + 24q^{8} - 16q^{11} + 8q^{15} - 48q^{16} + 8q^{21} - 16q^{22} - 40q^{23} + 24q^{28} - 8q^{30} + 48q^{32} - 8q^{35} - 16q^{36} + 32q^{37} - 16q^{42} - 16q^{43} + 64q^{46} - 72q^{50} - 16q^{51} + 24q^{53} + 24q^{56} + 8q^{57} + 32q^{58} + 40q^{60} + 8q^{63} + 40q^{65} - 32q^{67} - 40q^{70} + 64q^{71} + 24q^{72} - 24q^{77} - 8q^{78} - 16q^{81} + 48q^{85} + 64q^{86} - 64q^{88} - 48q^{91} - 40q^{92} + 24q^{93} - 72q^{95} - 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 −0.763699 0.645573i \(-0.776619\pi\)
0.645573 + 0.763699i \(0.276619\pi\)
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.94418i 0.972092i
\(5\) 2.23450 0.0836010i 0.999301 0.0373875i
\(6\) 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
\(10\) −0.359321 + 0.387253i −0.113627 + 0.122460i
\(11\) 3.98602 1.20183 0.600915 0.799313i \(-0.294803\pi\)
0.600915 + 0.799313i \(0.294803\pi\)
\(12\) 1.37475 + 1.37475i 0.396855 + 0.396855i
\(13\) 0.500437 0.500437i 0.138796 0.138796i −0.634295 0.773091i \(-0.718709\pi\)
0.773091 + 0.634295i \(0.218709\pi\)
\(14\) 0.431387 0.452341i 0.115293 0.120893i
\(15\) 1.52092 1.63915i 0.392699 0.423226i
\(16\) −3.66822 −0.917056
\(17\) −1.67840 1.67840i −0.407071 0.407071i 0.473645 0.880716i \(-0.342938\pi\)
−0.880716 + 0.473645i \(0.842938\pi\)
\(18\) 0.167056 + 0.167056i 0.0393754 + 0.0393754i
\(19\) −7.21850 −1.65604 −0.828019 0.560700i \(-0.810532\pi\)
−0.828019 + 0.560700i \(0.810532\pi\)
\(20\) 0.162536 + 4.34429i 0.0363441 + 0.971413i
\(21\) −1.82596 + 1.91465i −0.398456 + 0.417811i
\(22\) −0.665888 + 0.665888i −0.141968 + 0.141968i
\(23\) −5.16007 5.16007i −1.07595 1.07595i −0.996868 0.0790800i \(-0.974802\pi\)
−0.0790800 0.996868i \(-0.525198\pi\)
\(24\) −0.931824 −0.190208
\(25\) 4.98602 0.373614i 0.997204 0.0747227i
\(26\) 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 \(0.110113\pi\)
−0.940761 + 0.339071i \(0.889887\pi\)
\(30\) 0.0197510 + 0.527908i 0.00360602 + 0.0963823i
\(31\) 4.93821i 0.886929i 0.896292 + 0.443465i \(0.146251\pi\)
−0.896292 + 0.443465i \(0.853749\pi\)
\(32\) 1.93060 1.93060i 0.341284 0.341284i
\(33\) 2.81854 2.81854i 0.490645 0.490645i
\(34\) 0.560773 0.0961717
\(35\) −5.90504 + 0.361268i −0.998134 + 0.0610654i
\(36\) 1.94418 0.324031
\(37\) 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
\(39\) 0.707725i 0.113327i
\(40\) −1.52740 1.41723i −0.241503 0.224084i
\(41\) 7.63184i 1.19189i −0.803024 0.595947i \(-0.796777\pi\)
0.803024 0.595947i \(-0.203223\pi\)
\(42\) −0.0148172 0.624890i −0.00228634 0.0964226i
\(43\) 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
\(45\) −0.0836010 2.23450i −0.0124625 0.333100i
\(46\) 1.72404 0.254196
\(47\) −0.305303 0.305303i −0.0445331 0.0445331i 0.684490 0.729023i \(-0.260025\pi\)
−0.729023 + 0.684490i \(0.760025\pi\)
\(48\) −2.59383 + 2.59383i −0.374386 + 0.374386i
\(49\) 6.99213 0.331777i 0.998876 0.0473967i
\(50\) −0.770530 + 0.895358i −0.108969 + 0.126623i
\(51\) −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 \(-0.0743805\pi\)
−0.231553 + 0.972822i \(0.574381\pi\)
\(54\) 0.236253 0.0321499
\(55\) 8.90678 0.333235i 1.20099 0.0449335i
\(56\) 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 \(0.369808\pi\)
\(60\) 3.18681 + 2.95695i 0.411415 + 0.381740i
\(61\) 7.11047i 0.910402i 0.890389 + 0.455201i \(0.150433\pi\)
−0.890389 + 0.455201i \(0.849567\pi\)
\(62\) −0.824957 0.824957i −0.104770 0.104770i
\(63\) 0.0627175 + 2.64501i 0.00790166 + 0.333240i
\(64\) 6.69141i 0.836426i
\(65\) 1.07639 1.16007i 0.133510 0.143889i
\(66\) 0.941708i 0.115916i
\(67\) 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
\(69\) −7.29744 −0.878508
\(70\) 0.926119 1.04682i 0.110692 0.125119i
\(71\) 1.19297 0.141579 0.0707897 0.997491i \(-0.477448\pi\)
0.0707897 + 0.997491i \(0.477448\pi\)
\(72\) −0.658899 + 0.658899i −0.0776520 + 0.0776520i
\(73\) 1.38298 1.38298i 0.161865 0.161865i −0.621527 0.783393i \(-0.713487\pi\)
0.783393 + 0.621527i \(0.213487\pi\)
\(74\) 0.0976524i 0.0113519i
\(75\) 3.26147 3.78983i 0.376602 0.437612i
\(76\) 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 \(-0.838436\pi\)
0.873929 0.486053i \(-0.161564\pi\)
\(80\) −8.19666 + 0.306667i −0.916415 + 0.0342864i
\(81\) −1.00000 −0.111111
\(82\) 1.27494 + 1.27494i 0.140794 + 0.140794i
\(83\) −11.9895 + 11.9895i −1.31602 + 1.31602i −0.399122 + 0.916898i \(0.630685\pi\)
−0.916898 + 0.399122i \(0.869315\pi\)
\(84\) −3.72244 3.54999i −0.406151 0.387336i
\(85\) −3.89070 3.61007i −0.422006 0.391567i
\(86\) −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 \(0.363863\pi\)
\(90\) 0.387253 + 0.359321i 0.0408201 + 0.0378758i
\(91\) −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
\(95\) −16.1298 + 0.603474i −1.65488 + 0.0619151i
\(96\) 2.73028i 0.278658i
\(97\) 7.43671 + 7.43671i 0.755083 + 0.755083i 0.975423 0.220340i \(-0.0707167\pi\)
−0.220340 + 0.975423i \(0.570717\pi\)
\(98\) −1.11265 + 1.22350i −0.112395 + 0.123592i
\(99\) 3.98602i 0.400610i
\(100\) 0.726374 + 9.69375i 0.0726374 + 0.969375i
\(101\) 6.31633i 0.628498i 0.949341 + 0.314249i \(0.101753\pi\)
−0.949341 + 0.314249i \(0.898247\pi\)
\(102\) 0.396526 0.396526i 0.0392619 0.0392619i
\(103\) −12.5410 + 12.5410i −1.23570 + 1.23570i −0.273954 + 0.961743i \(0.588332\pi\)
−0.961743 + 0.273954i \(0.911668\pi\)
\(104\) −0.659476 −0.0646669
\(105\) −3.92004 + 4.43095i −0.382557 + 0.432416i
\(106\) −1.80304 −0.175127
\(107\) 7.48020 7.48020i 0.723138 0.723138i −0.246105 0.969243i \(-0.579151\pi\)
0.969243 + 0.246105i \(0.0791508\pi\)
\(108\) 1.37475 1.37475i 0.132285 0.132285i
\(109\) 0.668223i 0.0640042i −0.999488 0.0320021i \(-0.989812\pi\)
0.999488 0.0320021i \(-0.0101883\pi\)
\(110\) −1.43226 + 1.54360i −0.136561 + 0.147176i
\(111\) 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 \(-0.322543\pi\)
−0.848582 + 0.529064i \(0.822543\pi\)
\(114\) 1.70539i 0.159724i
\(115\) −11.9616 11.0988i −1.11542 1.03497i
\(116\) −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
\(120\) −2.08217 + 0.0779014i −0.190075 + 0.00711139i
\(121\) 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
\(125\) 11.1101 1.25168i 0.993713 0.111953i
\(126\) −0.452341 0.431387i −0.0402978 0.0384310i
\(127\) −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
\(129\) 5.16458 0.454716
\(130\) 0.0139783 + 0.373614i 0.00122597 + 0.0327681i
\(131\) 18.8144i 1.64383i −0.569613 0.821913i \(-0.692907\pi\)
0.569613 0.821913i \(-0.307093\pi\)
\(132\) 5.47977 + 5.47977i 0.476953 + 0.476953i
\(133\) 19.0930 0.452726i 1.65557 0.0392564i
\(134\) 0.315463i 0.0272519i
\(135\) −1.63915 1.52092i −0.141075 0.130900i
\(136\) 2.21179i 0.189659i
\(137\) −0.811977 + 0.811977i −0.0693719 + 0.0693719i −0.740941 0.671570i \(-0.765620\pi\)
0.671570 + 0.740941i \(0.265620\pi\)
\(138\) 1.21908 1.21908i 0.103775 0.103775i
\(139\) −0.442439 −0.0375272 −0.0187636 0.999824i \(-0.505973\pi\)
−0.0187636 + 0.999824i \(0.505973\pi\)
\(140\) −0.702371 11.4805i −0.0593612 0.970278i
\(141\) −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
\(145\) 0.305303 + 8.16021i 0.0253541 + 0.677669i
\(146\) 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 \(0.0410696\pi\)
−0.991688 + 0.128666i \(0.958930\pi\)
\(150\) 0.0882672 + 1.17796i 0.00720699 + 0.0961801i
\(151\) −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
\(155\) 0.412839 + 11.0345i 0.0331601 + 0.886309i
\(156\) 1.37595 0.110164
\(157\) −7.96508 7.96508i −0.635682 0.635682i 0.313805 0.949487i \(-0.398396\pi\)
−0.949487 + 0.313805i \(0.898396\pi\)
\(158\) 1.44341 + 1.44341i 0.114831 + 0.114831i
\(159\) 7.63184 0.605244
\(160\) 4.15253 4.47533i 0.328286 0.353806i
\(161\) 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 \(-0.0536410\pi\)
−0.167722 + 0.985834i \(0.553641\pi\)
\(164\) 14.8377 1.15863
\(165\) 6.06241 6.53368i 0.471958 0.508646i
\(166\) 4.00584i 0.310913i
\(167\) 4.63621 + 4.63621i 0.358761 + 0.358761i 0.863356 0.504595i \(-0.168358\pi\)
−0.504595 + 0.863356i \(0.668358\pi\)
\(168\) 2.46468 0.0584417i 0.190154 0.00450887i
\(169\) 12.4991i 0.961471i
\(170\) 1.25305 0.0468811i 0.0961045 0.00359562i
\(171\) 7.21850i 0.552013i
\(172\) −7.09999 + 7.09999i −0.541369 + 0.541369i
\(173\) −2.48531 + 2.48531i −0.188954 + 0.188954i −0.795244 0.606290i \(-0.792657\pi\)
0.606290 + 0.795244i \(0.292657\pi\)
\(174\) −0.862773 −0.0654067
\(175\) −13.1646 + 1.30092i −0.995153 + 0.0983404i
\(176\) −14.6216 −1.10215
\(177\) 4.32013 4.32013i 0.324721 0.324721i
\(178\) −1.30735 + 1.30735i −0.0979898 + 0.0979898i
\(179\) 22.1109i 1.65264i −0.563199 0.826321i \(-0.690430\pi\)
0.563199 0.826321i \(-0.309570\pi\)
\(180\) 4.34429 0.162536i 0.323804 0.0121147i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) −0.0104865 0.442251i −0.000777310 0.0327818i
\(183\) 5.02786 + 5.02786i 0.371670 + 0.371670i
\(184\) 6.79993i 0.501297i
\(185\) 0.628655 0.677524i 0.0462196 0.0498125i
\(186\) −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
\(190\) 2.59376 2.79539i 0.188171 0.202799i
\(191\) 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 \(-0.400152\pi\)
−0.951204 + 0.308562i \(0.900152\pi\)
\(194\) −2.48469 −0.178390
\(195\) −0.0591665 1.58142i −0.00423700 0.113248i
\(196\) 0.645035 + 13.5940i 0.0460739 + 0.971000i
\(197\) −2.68715 + 2.68715i −0.191451 + 0.191451i −0.796323 0.604872i \(-0.793224\pi\)
0.604872 + 0.796323i \(0.293224\pi\)
\(198\) 0.665888 + 0.665888i 0.0473226 + 0.0473226i
\(199\) 0.616637 0.0437122 0.0218561 0.999761i \(-0.493042\pi\)
0.0218561 + 0.999761i \(0.493042\pi\)
\(200\) −3.53146 3.03911i −0.249712 0.214898i
\(201\) 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
\(205\) −0.638029 17.0534i −0.0445619 1.19106i
\(206\) 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
\(210\) −0.0853505 1.39508i −0.00588974 0.0962697i
\(211\) 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
\(215\) 8.46551 + 7.85491i 0.577343 + 0.535700i
\(216\) 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
\(220\) 0.647871 + 17.3164i 0.0436795 + 1.16747i
\(221\) −1.67987 −0.113000
\(222\) 0.0690507 + 0.0690507i 0.00463438 + 0.00463438i
\(223\) −1.35505 + 1.35505i −0.0907407 + 0.0907407i −0.751020 0.660279i \(-0.770438\pi\)
0.660279 + 0.751020i \(0.270438\pi\)
\(224\) −4.98536 + 5.22753i −0.333098 + 0.349279i
\(225\) −0.373614 4.98602i −0.0249076 0.332401i
\(226\) 1.13482 0.0754870
\(227\) 4.15437 + 4.15437i 0.275735 + 0.275735i 0.831404 0.555668i \(-0.187538\pi\)
−0.555668 + 0.831404i \(0.687538\pi\)
\(228\) −9.92361 9.92361i −0.657207 0.657207i
\(229\) 12.9900 0.858403 0.429202 0.903209i \(-0.358795\pi\)
0.429202 + 0.903209i \(0.358795\pi\)
\(230\) 3.85237 0.144131i 0.254018 0.00950374i
\(231\) −7.27830 + 7.63184i −0.478877 + 0.502138i
\(232\) 2.40624 2.40624i 0.157977 0.157977i
\(233\) −16.4639 16.4639i −1.07859 1.07859i −0.996637 0.0819485i \(-0.973886\pi\)
−0.0819485 0.996637i \(-0.526114\pi\)
\(234\) 0.167202 0.0109303
\(235\) −0.707725 0.656678i −0.0461669 0.0428370i
\(236\) 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 \(-0.943279\pi\)
0.984166 0.177251i \(-0.0567205\pi\)
\(240\) −5.57907 + 6.01276i −0.360127 + 0.388122i
\(241\) 14.6507i 0.943737i 0.881669 + 0.471868i \(0.156420\pi\)
−0.881669 + 0.471868i \(0.843580\pi\)
\(242\) −0.816631 + 0.816631i −0.0524950 + 0.0524950i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −13.8241 −0.884995
\(245\) 15.5962 1.32591i 0.996406 0.0847090i
\(246\) 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
\(250\) −1.64690 + 2.06510i −0.104159 + 0.130608i
\(251\) 21.1506i 1.33501i −0.744604 0.667507i \(-0.767361\pi\)
0.744604 0.667507i \(-0.232639\pi\)
\(252\) −5.14238 + 0.121934i −0.323940 + 0.00768115i
\(253\) −20.5681 20.5681i −1.29311 1.29311i
\(254\) 1.96737i 0.123444i
\(255\) −5.30385 + 0.198436i −0.332140 + 0.0124266i
\(256\) 11.7193 0.732454
\(257\) −9.39248 9.39248i −0.585887 0.585887i 0.350628 0.936515i \(-0.385968\pi\)
−0.936515 + 0.350628i \(0.885968\pi\)
\(258\) −0.862773 + 0.862773i −0.0537139 + 0.0537139i
\(259\) −0.754738 + 0.791399i −0.0468971 + 0.0491752i
\(260\) 2.25538 + 2.09271i 0.139873 + 0.129784i
\(261\) 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 \(-0.0160765\pi\)
−0.0504843 + 0.998725i \(0.516076\pi\)
\(264\) −3.71427 −0.228598
\(265\) 12.5097 + 11.6074i 0.768466 + 0.713037i
\(266\) −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 \(0.747135\pi\)
\(270\) 0.527908 0.0197510i 0.0321274 0.00120201i
\(271\) 15.7596i 0.957330i −0.877998 0.478665i \(-0.841121\pi\)
0.877998 0.478665i \(-0.158879\pi\)
\(272\) 6.15674 + 6.15674i 0.373307 + 0.373307i
\(273\) 0.0443868 + 1.87194i 0.00268641 + 0.113295i
\(274\) 0.271291i 0.0163893i
\(275\) 19.8744 1.48923i 1.19847 0.0898041i
\(276\) 14.1876i 0.853991i
\(277\) 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
\(279\) 4.93821 0.295643
\(280\) 4.12886 + 3.65279i 0.246747 + 0.218296i
\(281\) −9.65658 −0.576063 −0.288032 0.957621i \(-0.593001\pi\)
−0.288032 + 0.957621i \(0.593001\pi\)
\(282\) 0.0721287 0.0721287i 0.00429520 0.00429520i
\(283\) 14.9095 14.9095i 0.886278 0.886278i −0.107885 0.994163i \(-0.534408\pi\)
0.994163 + 0.107885i \(0.0344079\pi\)
\(284\) 2.31935i 0.137628i
\(285\) −10.9788 + 11.8322i −0.650325 + 0.700879i
\(286\) 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
\(290\) −1.41421 1.31221i −0.0830455 0.0770555i
\(291\) 10.5171 0.616523
\(292\) 2.68877 + 2.68877i 0.157348 + 0.157348i
\(293\) 4.79236 4.79236i 0.279973 0.279973i −0.553125 0.833098i \(-0.686565\pi\)
0.833098 + 0.553125i \(0.186565\pi\)
\(294\) 0.0783831 + 1.65191i 0.00457140 + 0.0963413i
\(295\) 13.6519 0.510768i 0.794845 0.0297381i
\(296\) −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
\(300\) 7.36814 + 6.34089i 0.425400 + 0.366091i
\(301\) −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
\(305\) 0.594442 + 15.8884i 0.0340377 + 0.909765i
\(306\) 0.560773i 0.0320572i
\(307\) 9.85063 + 9.85063i 0.562205 + 0.562205i 0.929933 0.367728i \(-0.119864\pi\)
−0.367728 + 0.929933i \(0.619864\pi\)
\(308\) −0.486033 20.4977i −0.0276943 1.16796i
\(309\) 17.7356i 1.00894i
\(310\) −1.91234 1.77440i −0.108614 0.100779i
\(311\) 27.3063i 1.54840i 0.632941 + 0.774200i \(0.281848\pi\)
−0.632941 + 0.774200i \(0.718152\pi\)
\(312\) −0.466320 + 0.466320i −0.0264002 + 0.0264002i
\(313\) 18.5080 18.5080i 1.04613 1.04613i 0.0472492 0.998883i \(-0.484955\pi\)
0.998883 0.0472492i \(-0.0150455\pi\)
\(314\) 2.66123 0.150182
\(315\) 0.361268 + 5.90504i 0.0203551 + 0.332711i
\(316\) 16.7983 0.944977
\(317\) −21.8793 + 21.8793i −1.22887 + 1.22887i −0.264473 + 0.964393i \(0.585198\pi\)
−0.964393 + 0.264473i \(0.914802\pi\)
\(318\) −1.27494 + 1.27494i −0.0714953 + 0.0714953i
\(319\) 14.5566i 0.815013i
\(320\) −0.559409 14.9520i −0.0312719 0.835842i
\(321\) 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
\(325\) 2.30822 2.68216i 0.128037 0.148780i
\(326\) −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
\(330\) 0.0787277 + 2.10425i 0.00433382 + 0.115835i
\(331\) −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
\(335\) 2.03085 2.18872i 0.110957 0.119583i
\(336\) 6.69801 7.02337i 0.365406 0.383156i
\(337\) 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
\(339\) −4.80341 −0.260886
\(340\) 7.01865 7.56425i 0.380640 0.410229i
\(341\) 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
\(345\) −16.3062 + 0.610073i −0.877894 + 0.0328452i
\(346\) 0.830370i 0.0446410i
\(347\) 13.6980 13.6980i 0.735348 0.735348i −0.236326 0.971674i \(-0.575943\pi\)
0.971674 + 0.236326i \(0.0759433\pi\)
\(348\) −5.02045 + 5.02045i −0.269124 + 0.269124i
\(349\) 0.508601 0.0272248 0.0136124 0.999907i \(-0.495667\pi\)
0.0136124 + 0.999907i \(0.495667\pi\)
\(350\) 1.98190 2.41656i 0.105937 0.129170i
\(351\) −0.707725 −0.0377756
\(352\) 7.69540 7.69540i 0.410166 0.410166i
\(353\) 10.9217 10.9217i 0.581305 0.581305i −0.353957 0.935262i \(-0.615164\pi\)
0.935262 + 0.353957i \(0.115164\pi\)
\(354\) 1.44341i 0.0767162i
\(355\) 2.66570 0.0997335i 0.141480 0.00529330i
\(356\) 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 \(0.138621\pi\)
−0.906663 + 0.421855i \(0.861379\pi\)
\(360\) −1.41723 + 1.52740i −0.0746945 + 0.0805009i
\(361\) 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
\(365\) 2.97465 3.20589i 0.155701 0.167804i
\(366\) −1.67987 −0.0878080
\(367\) 0.410036 + 0.410036i 0.0214037 + 0.0214037i 0.717728 0.696324i \(-0.245182\pi\)
−0.696324 + 0.717728i \(0.745182\pi\)
\(368\) 18.9283 + 18.9283i 0.986705 + 0.986705i
\(369\) −7.63184 −0.397298
\(370\) 0.00816384 + 0.218205i 0.000424418 + 0.0113439i
\(371\) −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 \(-0.290255\pi\)
−0.790646 + 0.612273i \(0.790255\pi\)
\(374\) 2.23525 0.115582
\(375\) 6.97092 8.74106i 0.359977 0.451387i
\(376\) 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 \(0.107647\pi\)
−0.943359 + 0.331773i \(0.892353\pi\)
\(380\) −1.17326 31.3593i −0.0601872 1.60870i
\(381\) 8.32741i 0.426626i
\(382\) −2.55426 + 2.55426i −0.130687 + 0.130687i
\(383\) −10.0770 + 10.0770i −0.514910 + 0.514910i −0.916027 0.401117i \(-0.868622\pi\)
0.401117 + 0.916027i \(0.368622\pi\)
\(384\) 7.04142 0.359331
\(385\) −23.5376 + 1.44002i −1.19959 + 0.0733903i
\(386\) 2.98291 0.151826
\(387\) 3.65191 3.65191i 0.185637 0.185637i
\(388\) −14.4583 + 14.4583i −0.734011 + 0.734011i
\(389\) 24.3300i 1.23358i −0.787127 0.616791i \(-0.788433\pi\)
0.787127 0.616791i \(-0.211567\pi\)
\(390\) 0.274069 + 0.254301i 0.0138780 + 0.0128770i
\(391\) 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
\(395\) −0.722335 19.3067i −0.0363446 0.971426i
\(396\) 7.74956 0.389430
\(397\) 6.80633 + 6.80633i 0.341600 + 0.341600i 0.856969 0.515369i \(-0.172345\pi\)
−0.515369 + 0.856969i \(0.672345\pi\)
\(398\) −0.103013 + 0.103013i −0.00516356 + 0.00516356i
\(399\) 13.1807 13.8209i 0.659858 0.691911i
\(400\) −18.2898 + 1.37050i −0.914492 + 0.0685249i
\(401\) −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
\(405\) −2.23450 + 0.0836010i −0.111033 + 0.00415417i
\(406\) 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 \(0.694432\pi\)
\(410\) 2.95545 + 2.74228i 0.145959 + 0.135432i
\(411\) 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
\(415\) −25.7883 + 27.7930i −1.26590 + 1.36430i
\(416\) 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 \(0.396819\pi\)
\(420\) −8.61458 7.62128i −0.420349 0.371880i
\(421\) −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
\(425\) −8.99560 7.74146i −0.436351 0.375516i
\(426\) 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
\(430\) −2.72642 + 0.102005i −0.131480 + 0.00491914i
\(431\) −22.5558 −1.08648 −0.543238 0.839579i \(-0.682802\pi\)
−0.543238 + 0.839579i \(0.682802\pi\)
\(432\) 2.59383 + 2.59383i 0.124795 + 0.124795i
\(433\) −19.9639 + 19.9639i −0.959405 + 0.959405i −0.999208 0.0398028i \(-0.987327\pi\)
0.0398028 + 0.999208i \(0.487327\pi\)
\(434\) 2.23376 + 2.13028i 0.107224 + 0.102257i
\(435\) 5.98602 + 5.55426i 0.287008 + 0.266306i
\(436\) 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 \(0.243890\pi\)
\(440\) −6.08824 5.64910i −0.290246 0.269310i
\(441\) −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 \(-0.390812\pi\)
−0.941742 + 0.336337i \(0.890812\pi\)
\(444\) 0.803607 0.0381375
\(445\) 17.4868 0.654245i 0.828954 0.0310142i
\(446\) 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 \(-0.745180\pi\)
0.696318 0.717734i \(-0.254820\pi\)
\(450\) 0.895358 + 0.770530i 0.0422076 + 0.0363231i
\(451\) 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
\(455\) −2.77431 + 3.13589i −0.130062 + 0.147013i
\(456\) 6.72637 0.314991
\(457\) 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
\(459\) 2.37361i 0.110791i
\(460\) 21.5781 23.2555i 1.00609 1.08429i
\(461\) 1.29957i 0.0605272i 0.999542 + 0.0302636i \(0.00963467\pi\)
−0.999542 + 0.0302636i \(0.990365\pi\)
\(462\) −0.0590616 2.49083i −0.00274779 0.115884i
\(463\) 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
\(465\) 8.09446 + 7.51062i 0.375372 + 0.348297i
\(466\) 5.50078 0.254819
\(467\) 20.1009 + 20.1009i 0.930157 + 0.930157i 0.997715 0.0675588i \(-0.0215210\pi\)
−0.0675588 + 0.997715i \(0.521521\pi\)
\(468\) 0.972943 0.972943i 0.0449743 0.0449743i
\(469\) −2.43816 + 2.55659i −0.112584 + 0.118052i
\(470\) 0.227932 0.00852775i 0.0105137 0.000393356i
\(471\) −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
\(475\) −35.9916 + 2.69693i −1.65141 + 0.123744i
\(476\) −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 \(0.581487\pi\)
\(480\) −0.228254 6.10081i −0.0104183 0.278463i
\(481\) 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
\(485\) 17.2391 + 15.9956i 0.782786 + 0.726325i
\(486\) 0.236253i 0.0107166i
\(487\) −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
\(489\) 14.7714 0.667986
\(490\) −2.38394 + 2.82694i −0.107695 + 0.127708i
\(491\) 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
\(495\) −0.333235 8.90678i −0.0149778 0.400330i
\(496\) 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 \(-0.969500\pi\)
0.995413 0.0956722i \(-0.0305000\pi\)
\(500\) 2.43349 + 21.6000i 0.108829 + 0.965981i
\(501\) 6.55659 0.292927
\(502\) 3.53333 + 3.53333i 0.157700 + 0.157700i
\(503\) 17.5637 17.5637i 0.783128 0.783128i −0.197229 0.980357i \(-0.563194\pi\)
0.980357 + 0.197229i \(0.0631943\pi\)
\(504\) 1.70147 1.78412i 0.0757894 0.0794709i
\(505\) 0.528051 + 14.1139i 0.0234980 + 0.628059i
\(506\) 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 \(0.712333\pi\)
\(510\) 0.852889 0.919189i 0.0377666 0.0407024i
\(511\) −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
\(515\) −26.9744 + 29.0713i −1.18863 + 1.28103i
\(516\) 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
\(520\) −1.47360 + 0.0551328i −0.0646217 + 0.00241773i
\(521\) 28.8647i 1.26458i −0.774730 0.632292i \(-0.782114\pi\)
0.774730 0.632292i \(-0.217886\pi\)
\(522\) −0.610073 + 0.610073i −0.0267022 + 0.0267022i
\(523\) −3.54707 + 3.54707i −0.155103 + 0.155103i −0.780392 0.625290i \(-0.784981\pi\)
0.625290 + 0.780392i \(0.284981\pi\)
\(524\) 36.5788 1.59795
\(525\) −8.38891 + 10.2287i −0.366122 + 0.446417i
\(526\) −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
\(530\) −4.02891 + 0.150736i −0.175005 + 0.00654756i
\(531\) 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
\(535\) 16.0892 17.3399i 0.695596 0.749669i
\(536\) −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
\(540\) 2.95695 3.18681i 0.127247 0.137138i
\(541\) −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
\(545\) −0.0558641 1.49315i −0.00239296 0.0639594i
\(546\) −0.320133 0.305303i −0.0137004 0.0130658i
\(547\) 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
\(549\) 7.11047 0.303467
\(550\) −3.07135 + 3.56892i −0.130963 + 0.152179i
\(551\) 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
\(555\) −0.0345555 0.923607i −0.00146680 0.0392050i
\(556\) 0.860184i 0.0364799i
\(557\) 28.1616 28.1616i 1.19325 1.19325i 0.217096 0.976150i \(-0.430342\pi\)
0.976150 0.217096i \(-0.0696584\pi\)
\(558\) −0.824957 + 0.824957i −0.0349232 + 0.0349232i
\(559\) 3.65510 0.154594
\(560\) 21.6610 1.32521i 0.915344 0.0560004i
\(561\) −9.46128 −0.399455
\(562\) 1.61319 1.61319i 0.0680482 0.0680482i
\(563\) −27.3645 + 27.3645i −1.15328 + 1.15328i −0.167386 + 0.985891i \(0.553533\pi\)
−0.985891 + 0.167386i \(0.946467\pi\)
\(564\) 0.839429i 0.0353463i
\(565\) −7.87351 7.30560i −0.331241 0.307349i
\(566\) 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 \(0.121540\pi\)
−0.927984 + 0.372620i \(0.878460\pi\)
\(570\) −0.142572 3.81070i −0.00597170 0.159613i
\(571\) −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
\(575\) −27.6561 23.8003i −1.15334 0.992543i
\(576\) −6.69141 −0.278809
\(577\) 3.89677 + 3.89677i 0.162225 + 0.162225i 0.783552 0.621327i \(-0.213406\pi\)
−0.621327 + 0.783552i \(0.713406\pi\)
\(578\) 1.89875 + 1.89875i 0.0789776 + 0.0789776i
\(579\) −12.6259 −0.524715
\(580\) −15.8650 + 0.593566i −0.658756 + 0.0246465i
\(581\) 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
\(585\) −1.16007 1.07639i −0.0479629 0.0445034i
\(586\) 1.60118i 0.0661443i
\(587\) −15.1058 15.1058i −0.623484 0.623484i 0.322937 0.946420i \(-0.395330\pi\)
−0.946420 + 0.322937i \(0.895330\pi\)
\(588\) 10.0685 + 9.15630i 0.415219 + 0.377599i
\(589\) 35.6465i 1.46879i
\(590\) −2.19530 + 2.36596i −0.0903793 + 0.0974050i
\(591\) 3.80020i 0.156319i
\(592\) −1.07213 + 1.07213i −0.0440642 + 0.0440642i
\(593\) −3.43032 + 3.43032i −0.140866 + 0.140866i −0.774023 0.633157i \(-0.781759\pi\)
0.633157 + 0.774023i \(0.281759\pi\)
\(594\) 0.941708 0.0386388
\(595\) 10.5174 + 9.30466i 0.431170 + 0.381454i
\(596\) −6.10696 −0.250151
\(597\) 0.436028 0.436028i 0.0178454 0.0178454i
\(598\) 0.862773 0.862773i 0.0352814 0.0352814i
\(599\) 10.1010i 0.412714i −0.978477 0.206357i \(-0.933839\pi\)
0.978477 0.206357i \(-0.0661608\pi\)
\(600\) −4.64610 + 0.348142i −0.189676 + 0.0142128i
\(601\) 38.4063i 1.56663i 0.621628 + 0.783313i \(0.286472\pi\)
−0.621628 + 0.783313i \(0.713528\pi\)
\(602\) 3.22730 0.0765245i 0.131535 0.00311891i
\(603\) −0.944185 0.944185i −0.0384502 0.0384502i
\(604\) 28.6261i 1.16478i
\(605\) 10.9231 0.408673i 0.444087 0.0166149i
\(606\) −1.49225 −0.0606185
\(607\) 10.2931 + 10.2931i 0.417783 + 0.417783i 0.884439 0.466656i \(-0.154541\pi\)
−0.466656 + 0.884439i \(0.654541\pi\)
\(608\) −13.9360 + 13.9360i −0.565180 + 0.565180i
\(609\) −6.99213 6.66822i −0.283336 0.270210i
\(610\) −2.75355 2.55494i −0.111488 0.103447i
\(611\) −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 \(-0.385066\pi\)
−0.935517 + 0.353282i \(0.885066\pi\)
\(614\) −3.29121 −0.132822
\(615\) −12.5097 11.6074i −0.504440 0.468056i
\(616\) 7.11153 + 6.78209i 0.286532 + 0.273258i
\(617\) −25.4196 + 25.4196i −1.02336 + 1.02336i −0.0236346 + 0.999721i \(0.507524\pi\)
−0.999721 + 0.0236346i \(0.992476\pi\)
\(618\) −2.96283 2.96283i −0.119183 0.119183i
\(619\) −11.1991 −0.450129 −0.225064 0.974344i \(-0.572259\pi\)
−0.225064 + 0.974344i \(0.572259\pi\)
\(620\) −21.4530 + 0.802636i −0.861574 + 0.0322346i
\(621\) 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
\(625\) 24.7208 3.72569i 0.988833 0.149028i
\(626\) 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
\(630\) −1.04682 0.926119i −0.0417064 0.0368975i
\(631\) 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
\(635\) −12.6653 + 13.6499i −0.502608 + 0.541678i
\(636\) 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
\(640\) 11.5419 + 10.7094i 0.456235 + 0.423327i
\(641\) −29.8969 −1.18086 −0.590428 0.807090i \(-0.701041\pi\)
−0.590428 + 0.807090i \(0.701041\pi\)
\(642\) 1.76722 + 1.76722i 0.0697465 + 0.0697465i
\(643\) 11.2813 11.2813i 0.444891 0.444891i −0.448761 0.893652i \(-0.648134\pi\)
0.893652 + 0.448761i \(0.148134\pi\)
\(644\) −25.9059 + 27.1642i −1.02083 + 1.07042i
\(645\) 11.5403 0.431764i 0.454398 0.0170007i
\(646\) −4.04794 −0.159264
\(647\) −26.2395 26.2395i −1.03158 1.03158i −0.999485 0.0320982i \(-0.989781\pi\)
−0.0320982 0.999485i \(-0.510219\pi\)
\(648\) 0.658899 + 0.658899i 0.0258840 + 0.0258840i
\(649\) 24.3530 0.955937
\(650\) 0.0624689 + 0.833673i 0.00245023 + 0.0326993i
\(651\) −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 \(-0.267417\pi\)
−0.744720 + 0.667377i \(0.767417\pi\)
\(654\) 0.157870 0.00617319
\(655\) −1.57291 42.0410i −0.0614585 1.64268i
\(656\) 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 \(0.0950507\pi\)
−0.955746 + 0.294193i \(0.904949\pi\)
\(660\) 12.7027 + 11.7865i 0.494451 + 0.458787i
\(661\) 1.10054i 0.0428062i 0.999771 + 0.0214031i \(0.00681333\pi\)
−0.999771 + 0.0214031i \(0.993187\pi\)
\(662\) 2.78838 2.78838i 0.108374 0.108374i
\(663\) −1.18785 + 1.18785i −0.0461321 + 0.0461321i
\(664\) 15.7998 0.613150
\(665\) 42.6255 2.60781i 1.65295 0.101127i
\(666\) 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
\(670\) 0.0263730 + 0.704904i 0.00101888 + 0.0272328i
\(671\) 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 \(-0.350921\pi\)
−0.892316 + 0.451411i \(0.850921\pi\)
\(674\) 0.848737i 0.0326921i
\(675\) −3.78983 3.26147i −0.145871 0.125534i
\(676\) −24.3006 −0.934639
\(677\) −24.6007 24.6007i −0.945481 0.945481i 0.0531077 0.998589i \(-0.483087\pi\)
−0.998589 + 0.0531077i \(0.983087\pi\)
\(678\) 0.802438 0.802438i 0.0308175 0.0308175i
\(679\) −20.1366 19.2037i −0.772770 0.736972i
\(680\) 0.184908 + 4.94226i 0.00709089 + 0.189527i
\(681\) 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 \(-0.372409\pi\)
−0.920734 + 0.390191i \(0.872409\pi\)
\(684\) −14.0341 −0.536607
\(685\) −1.74648 + 1.88225i −0.0667297 + 0.0719170i
\(686\) 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
\(690\) 2.62212 2.82596i 0.0998225 0.107582i
\(691\) 12.4060i 0.471947i 0.971759 + 0.235974i \(0.0758279\pi\)
−0.971759 + 0.235974i \(0.924172\pi\)
\(692\) −4.83190 4.83190i −0.183681 0.183681i
\(693\) 0.249993 + 10.5431i 0.00949646 + 0.400498i
\(694\) 4.57667i 0.173728i
\(695\) −0.988633 + 0.0369884i −0.0375010 + 0.00140305i
\(696\) 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
\(700\) −2.52923 25.5945i −0.0955960 0.967380i
\(701\) 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
\(705\) −0.964779 + 0.0360959i −0.0363357 + 0.00135945i
\(706\) 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 \(0.364891\pi\)
−0.411827 + 0.911262i \(0.635109\pi\)
\(710\) −0.428659 + 0.461981i −0.0160873 + 0.0173378i
\(711\) −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
\(715\) 4.29052 4.62405i 0.160457 0.172930i
\(716\) 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 \(0.197962\pi\)
\(720\) 0.306667 + 8.19666i 0.0114288 + 0.305472i
\(721\) 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
\(725\) 1.36440 + 18.2085i 0.0506727 + 0.676247i
\(726\) 1.15489i 0.0428620i
\(727\) 10.4498 + 10.4498i 0.387563 + 0.387563i 0.873817 0.486254i \(-0.161637\pi\)
−0.486254 + 0.873817i \(0.661637\pi\)
\(728\) 1.74432 0.0413607i 0.0646487 0.00153293i
\(729\) 1.00000i 0.0370370i
\(730\) 0.0386295 + 1.03250i 0.00142974 + 0.0382144i
\(731\) 12.2587i 0.453405i
\(732\) −9.77509 + 9.77509i −0.361298 + 0.361298i
\(733\) 18.8687 18.8687i 0.696933 0.696933i −0.266815 0.963748i \(-0.585971\pi\)
0.963748 + 0.266815i \(0.0859712\pi\)
\(734\) −0.136998 −0.00505669
\(735\) 10.0906 11.9657i 0.372199 0.441363i
\(736\) −19.9240 −0.734409
\(737\) 3.76354 3.76354i 0.138632 0.138632i
\(738\) 1.27494 1.27494i 0.0469313 0.0469313i
\(739\) 20.9689i 0.771354i −0.922634 0.385677i \(-0.873968\pi\)
0.922634 0.385677i \(-0.126032\pi\)
\(740\) 1.31723 + 1.22222i 0.0484224 + 0.0449297i
\(741\) 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 \(-0.173401\pi\)
−0.518208 + 0.855255i \(0.673401\pi\)
\(744\) 4.60155i 0.168701i
\(745\) 0.262603 + 7.01890i 0.00962102 + 0.257152i
\(746\) 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
\(750\) 0.295712 + 2.62478i 0.0107979 + 0.0958434i
\(751\) 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
\(755\) −32.9007 + 1.23094i −1.19738 + 0.0447984i
\(756\) −3.54999 + 3.72244i −0.129112 + 0.135384i
\(757\) −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
\(759\) −29.0877 −1.05582
\(760\) 11.0255 + 10.2303i 0.399938 + 0.371091i
\(761\) 8.78825i 0.318574i 0.987232 + 0.159287i \(0.0509195\pi\)
−0.987232 + 0.159287i \(0.949081\pi\)
\(762\) −1.39114 1.39114i −0.0503958 0.0503958i
\(763\) 0.0419093 + 1.76746i 0.00151722 + 0.0639862i
\(764\) 29.7263i 1.07546i
\(765\) −3.61007 + 3.89070i −0.130522 + 0.140669i
\(766\) 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 \(0.564832\pi\)
\(770\) 3.69153 4.17266i 0.133034 0.150372i
\(771\) −13.2830 −0.478374
\(772\) 17.3574 17.3574i 0.624708 0.624708i