Properties

Label 105.2.m.a.97.3
Level 105
Weight 2
Character 105.97
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 97.3
Root \(1.40927 - 0.118126i\)
Character \(\chi\) = 105.97
Dual form 105.2.m.a.13.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.167056 - 0.167056i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-0.0627175 - 2.64501i) q^{7} +(-0.658899 + 0.658899i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.167056 - 0.167056i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-0.0627175 - 2.64501i) 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} +(-5.14238 + 0.121934i) 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} +(-0.0809828 + 5.91553i) 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} +(0.624890 - 0.0148172i) 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} +(2.64501 - 0.0627175i) 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} +(1.00175 - 0.974695i) 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} +(-0.249993 - 10.5431i) 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} +(1.22350 + 1.11265i) q^{98} +3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} + 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} + 24q^{8} - 16q^{11} + 8q^{15} - 48q^{16} + 8q^{21} - 16q^{22} - 40q^{23} + 24q^{28} - 8q^{30} + 48q^{32} - 8q^{35} - 16q^{36} + 32q^{37} - 16q^{42} - 16q^{43} + 64q^{46} - 72q^{50} - 16q^{51} + 24q^{53} + 24q^{56} + 8q^{57} + 32q^{58} + 40q^{60} + 8q^{63} + 40q^{65} - 32q^{67} - 40q^{70} + 64q^{71} + 24q^{72} - 24q^{77} - 8q^{78} - 16q^{81} + 48q^{85} + 64q^{86} - 64q^{88} - 48q^{91} - 40q^{92} + 24q^{93} - 72q^{95} - 96q^{98} + O(q^{100}) \)

Character values

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

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

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 0.645573 0.763699i \(-0.276619\pi\)
−0.763699 + 0.645573i \(0.776619\pi\)
\(3\) −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
\(7\) −0.0627175 2.64501i −0.0237050 0.999719i
\(8\) −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 \(-0.281291\pi\)
−0.773091 + 0.634295i \(0.781291\pi\)
\(14\) −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 \(-0.657062\pi\)
0.880716 + 0.473645i \(0.157062\pi\)
\(18\) 0.167056 0.167056i 0.0393754 0.0393754i
\(19\) 7.21850 1.65604 0.828019 0.560700i \(-0.189468\pi\)
0.828019 + 0.560700i \(0.189468\pi\)
\(20\) −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 −0.0790800 + 0.996868i \(0.525198\pi\)
−0.996868 + 0.0790800i \(0.974802\pi\)
\(24\) 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
\(28\) −5.14238 + 0.121934i −0.971819 + 0.0230434i
\(29\) 3.65191i 0.678143i −0.940761 0.339071i \(-0.889887\pi\)
0.940761 0.339071i \(-0.110113\pi\)
\(30\) 0.0197510 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
\(35\) −0.0809828 + 5.91553i −0.0136886 + 0.999906i
\(36\) 1.94418 0.324031
\(37\) 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
\(39\) 0.707725i 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 \(-0.203223\pi\)
\(42\) 0.624890 0.0148172i 0.0964226 0.00228634i
\(43\) 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
\(45\) 0.0836010 2.23450i 0.0124625 0.333100i
\(46\) 1.72404 0.254196
\(47\) 0.305303 0.305303i 0.0445331 0.0445331i −0.684490 0.729023i \(-0.739975\pi\)
0.729023 + 0.684490i \(0.239975\pi\)
\(48\) 2.59383 + 2.59383i 0.374386 + 0.374386i
\(49\) −6.99213 + 0.331777i −0.998876 + 0.0473967i
\(50\) −0.770530 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 −0.231553 0.972822i \(-0.574381\pi\)
0.972822 + 0.231553i \(0.0743805\pi\)
\(54\) −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 \(-0.630192\pi\)
−0.397701 + 0.917515i \(0.630192\pi\)
\(60\) 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
\(63\) 2.64501 0.0627175i 0.333240 0.00790166i
\(64\) 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 0.762426 0.647075i \(-0.224008\pi\)
−0.647075 + 0.762426i \(0.724008\pi\)
\(68\) −3.26312 3.26312i −0.395711 0.395711i
\(69\) 7.29744 0.878508
\(70\) 1.00175 0.974695i 0.119732 0.116498i
\(71\) 1.19297 0.141579 0.0707897 0.997491i \(-0.477448\pi\)
0.0707897 + 0.997491i \(0.477448\pi\)
\(72\) −0.658899 0.658899i −0.0776520 0.0776520i
\(73\) −1.38298 1.38298i −0.161865 0.161865i 0.621527 0.783393i \(-0.286513\pi\)
−0.783393 + 0.621527i \(0.786513\pi\)
\(74\) 0.0976524i 0.0113519i
\(75\) −3.26147 3.78983i −0.376602 0.437612i
\(76\) 14.0341i 1.60982i
\(77\) −0.249993 10.5431i −0.0284894 1.20149i
\(78\) 0.118230 0.118230i 0.0133869 0.0133869i
\(79\) 8.64027i 0.972106i 0.873929 + 0.486053i \(0.161564\pi\)
−0.873929 + 0.486053i \(0.838436\pi\)
\(80\) 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 0.916898 + 0.399122i \(0.130685\pi\)
0.399122 + 0.916898i \(0.369315\pi\)
\(84\) 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 \(-0.636137\pi\)
−0.414767 + 0.909928i \(0.636137\pi\)
\(90\) −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 \(-0.929283\pi\)
0.220340 + 0.975423i \(0.429283\pi\)
\(98\) 1.22350 + 1.11265i 0.123592 + 0.112395i
\(99\) 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 0.961743 + 0.273954i \(0.0883316\pi\)
0.273954 + 0.961743i \(0.411668\pi\)
\(104\) 0.659476 0.0646669
\(105\) 4.24017 4.12564i 0.413798 0.402622i
\(106\) −1.80304 −0.175127
\(107\) 7.48020 + 7.48020i 0.723138 + 0.723138i 0.969243 0.246105i \(-0.0791508\pi\)
−0.246105 + 0.969243i \(0.579151\pi\)
\(108\) −1.37475 1.37475i −0.132285 0.132285i
\(109\) 0.668223i 0.0640042i 0.999488 + 0.0320021i \(0.0101883\pi\)
−0.999488 + 0.0320021i \(0.989812\pi\)
\(110\) 1.43226 + 1.54360i 0.136561 + 0.147176i
\(111\) 0.413339i 0.0392324i
\(112\) 0.230062 + 9.70248i 0.0217388 + 0.916798i
\(113\) −3.39653 + 3.39653i −0.319518 + 0.319518i −0.848582 0.529064i \(-0.822543\pi\)
0.529064 + 0.848582i \(0.322543\pi\)
\(114\) 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 0.395820 0.918328i \(-0.370460\pi\)
−0.918328 + 0.395820i \(0.870460\pi\)
\(128\) 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
\(133\) −0.452726 19.0930i −0.0392564 1.65557i
\(134\) 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 0.671570 0.740941i \(-0.265620\pi\)
−0.740941 + 0.671570i \(0.765620\pi\)
\(138\) −1.21908 1.21908i −0.103775 0.103775i
\(139\) 0.442439 0.0375272 0.0187636 0.999824i \(-0.494027\pi\)
0.0187636 + 0.999824i \(0.494027\pi\)
\(140\) 11.5009 + 0.157445i 0.972001 + 0.0133066i
\(141\) −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
\(147\) 5.17879 + 4.70958i 0.427139 + 0.388440i
\(148\) 0.568236 0.568236i 0.0467087 0.0467087i
\(149\) 3.14114i 0.257332i −0.991688 0.128666i \(-0.958930\pi\)
0.991688 0.128666i \(-0.0410696\pi\)
\(150\) −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 \(-0.601604\pi\)
0.949487 + 0.313805i \(0.101604\pi\)
\(158\) 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 −0.167722 0.985834i \(-0.553641\pi\)
0.985834 + 0.167722i \(0.0536410\pi\)
\(164\) −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 \(-0.831642\pi\)
0.504595 + 0.863356i \(0.331642\pi\)
\(168\) −0.0584417 2.46468i −0.00450887 0.190154i
\(169\) 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 \(-0.207343\pi\)
−0.606290 + 0.795244i \(0.707343\pi\)
\(174\) 0.862773 0.0654067
\(175\) 0.675500 13.2115i 0.0510630 0.998695i
\(176\) −14.6216 −1.10215
\(177\) 4.32013 + 4.32013i 0.324721 + 0.324721i
\(178\) 1.30735 + 1.30735i 0.0979898 + 0.0979898i
\(179\) 22.1109i 1.65264i 0.563199 + 0.826321i \(0.309570\pi\)
−0.563199 + 0.826321i \(0.690430\pi\)
\(180\) −4.34429 0.162536i −0.323804 0.0121147i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 0.442251 0.0104865i 0.0327818 0.000777310i
\(183\) 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 −0.951204 0.308562i \(-0.900152\pi\)
0.308562 + 0.951204i \(0.400152\pi\)
\(194\) 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 0.604872 0.796323i \(-0.293224\pi\)
−0.796323 + 0.604872i \(0.793224\pi\)
\(198\) 0.665888 0.665888i 0.0473226 0.0473226i
\(199\) −0.616637 −0.0437122 −0.0218561 0.999761i \(-0.506958\pi\)
−0.0218561 + 0.999761i \(0.506958\pi\)
\(200\) −3.53146 + 3.03911i −0.249712 + 0.214898i
\(201\) 1.33528i 0.0941833i
\(202\) 1.05518 1.05518i 0.0742422 0.0742422i
\(203\) −9.65933 + 0.229039i −0.677952 + 0.0160754i
\(204\) 4.61474i 0.323097i
\(205\) −0.638029 + 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
\(210\) −1.39756 0.0191324i −0.0964407 0.00132026i
\(211\) 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
\(217\) 13.0616 0.309712i 0.886680 0.0210246i
\(218\) 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 \(-0.229562\pi\)
−0.660279 + 0.751020i \(0.729562\pi\)
\(224\) 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 \(-0.812462\pi\)
0.555668 + 0.831404i \(0.312462\pi\)
\(228\) −9.92361 + 9.92361i −0.657207 + 0.657207i
\(229\) −12.9900 −0.858403 −0.429202 0.903209i \(-0.641205\pi\)
−0.429202 + 0.903209i \(0.641205\pi\)
\(230\) −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 −0.0819485 + 0.996637i \(0.526114\pi\)
−0.996637 + 0.0819485i \(0.973886\pi\)
\(234\) −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
\(238\) 0.0351703 + 1.48325i 0.00227975 + 0.0961447i
\(239\) 5.48048i 0.354503i 0.984166 + 0.177251i \(0.0567205\pi\)
−0.984166 + 0.177251i \(0.943279\pi\)
\(240\) −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
\(245\) 15.6517 0.156807i 0.999950 0.0100180i
\(246\) 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 \(-0.232639\pi\)
\(252\) −0.121934 5.14238i −0.00768115 0.323940i
\(253\) −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 \(-0.614032\pi\)
0.936515 + 0.350628i \(0.114032\pi\)
\(258\) 0.862773 + 0.862773i 0.0537139 + 0.0537139i
\(259\) 0.754738 0.791399i 0.0468971 0.0491752i
\(260\) 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 −0.0504843 0.998725i \(-0.516076\pi\)
0.998725 + 0.0504843i \(0.0160765\pi\)
\(264\) 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 \(-0.252865\pi\)
0.700714 + 0.713442i \(0.252865\pi\)
\(270\) 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
\(273\) 1.87194 0.0443868i 0.113295 0.00268641i
\(274\) 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 0.836632 0.547765i \(-0.184521\pi\)
−0.547765 + 0.836632i \(0.684521\pi\)
\(278\) −0.0739121 0.0739121i −0.00443295 0.00443295i
\(279\) −4.93821 −0.295643
\(280\) −3.84438 3.95109i −0.229745 0.236123i
\(281\) −9.65658 −0.576063 −0.288032 0.957621i \(-0.593001\pi\)
−0.288032 + 0.957621i \(0.593001\pi\)
\(282\) 0.0721287 + 0.0721287i 0.00429520 + 0.00429520i
\(283\) −14.9095 14.9095i −0.886278 0.886278i 0.107885 0.994163i \(-0.465592\pi\)
−0.994163 + 0.107885i \(0.965592\pi\)
\(284\) 2.31935i 0.137628i
\(285\) 10.9788 + 11.8322i 0.650325 + 0.700879i
\(286\) 0.666471i 0.0394092i
\(287\) −20.1863 + 0.478650i −1.19156 + 0.0282538i
\(288\) −1.93060 + 1.93060i −0.113761 + 0.113761i
\(289\) 11.3660i 0.668586i
\(290\) 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 \(-0.313435\pi\)
−0.833098 + 0.553125i \(0.813435\pi\)
\(294\) −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 \(-0.880136\pi\)
0.367728 + 0.929933i \(0.380136\pi\)
\(308\) −20.4977 + 0.486033i −1.16796 + 0.0276943i
\(309\) 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 −0.998883 0.0472492i \(-0.984955\pi\)
−0.0472492 0.998883i \(-0.515045\pi\)
\(314\) −2.66123 −0.150182
\(315\) −5.91553 0.0809828i −0.333302 0.00456286i
\(316\) 16.7983 0.944977
\(317\) −21.8793 21.8793i −1.22887 1.22887i −0.964393 0.264473i \(-0.914802\pi\)
−0.264473 0.964393i \(-0.585198\pi\)
\(318\) 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
\(322\) −0.108127 4.56010i −0.00602570 0.254124i
\(323\) 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 0.772903 0.634525i \(-0.218804\pi\)
−0.634525 + 0.772903i \(0.718804\pi\)
\(338\) −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
\(343\) 1.31608 + 18.4734i 0.0710617 + 0.997472i
\(344\) 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 0.971674 0.236326i \(-0.0759433\pi\)
−0.236326 + 0.971674i \(0.575943\pi\)
\(348\) 5.02045 + 5.02045i 0.269124 + 0.269124i
\(349\) −0.508601 −0.0272248 −0.0136124 0.999907i \(-0.504333\pi\)
−0.0136124 + 0.999907i \(0.504333\pi\)
\(350\) −2.31990 + 2.09421i −0.124004 + 0.111940i
\(351\) −0.707725 −0.0377756
\(352\) 7.69540 + 7.69540i 0.410166 + 0.410166i
\(353\) −10.9217 10.9217i −0.581305 0.581305i 0.353957 0.935262i \(-0.384836\pi\)
−0.935262 + 0.353957i \(0.884836\pi\)
\(354\) 1.44341i 0.0767162i
\(355\) −2.66570 0.0997335i −0.141480 0.00529330i
\(356\) 15.2148i 0.806383i
\(357\) 0.148867 + 6.27823i 0.00787888 + 0.332279i
\(358\) 3.69375 3.69375i 0.195221 0.195221i
\(359\) 15.9860i 0.843710i −0.906663 0.421855i \(-0.861379\pi\)
0.906663 0.421855i \(-0.138621\pi\)
\(360\) 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 \(-0.754818\pi\)
0.696324 + 0.717728i \(0.254818\pi\)
\(368\) 18.9283 18.9283i 0.986705 0.986705i
\(369\) 7.63184 0.397298
\(370\) −0.00816384 + 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 −0.790646 0.612273i \(-0.790255\pi\)
0.612273 + 0.790646i \(0.290255\pi\)
\(374\) −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
\(378\) 0.0148172 + 0.624890i 0.000762113 + 0.0321409i
\(379\) 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
\(381\) 8.32741i 0.426626i
\(382\) −2.55426 2.55426i −0.130687 0.130687i
\(383\) 10.0770 + 10.0770i 0.514910 + 0.514910i 0.916027 0.401117i \(-0.131378\pi\)
−0.401117 + 0.916027i \(0.631378\pi\)
\(384\) −7.04142 −0.359331
\(385\) −0.322799 + 23.5794i −0.0164514 + 1.20172i
\(386\) 2.98291 0.151826
\(387\) 3.65191 + 3.65191i 0.185637 + 0.185637i
\(388\) 14.4583 + 14.4583i 0.734011 + 0.734011i
\(389\) 24.3300i 1.23358i 0.787127 + 0.616791i \(0.211567\pi\)
−0.787127 + 0.616791i \(0.788433\pi\)
\(390\) −0.274069 + 0.254301i −0.0138780 + 0.0128770i
\(391\) 17.3213i 0.875976i
\(392\) 4.38850 4.82572i 0.221653 0.243736i
\(393\) −13.3038 + 13.3038i −0.671089 + 0.671089i
\(394\) 0.897808i 0.0452309i
\(395\) 0.722335 19.3067i 0.0363446 0.971426i
\(396\) 7.74956 0.389430
\(397\) −6.80633 + 6.80633i −0.341600 + 0.341600i −0.856969 0.515369i \(-0.827655\pi\)
0.515369 + 0.856969i \(0.327655\pi\)
\(398\) 0.103013 + 0.103013i 0.00516356 + 0.00516356i
\(399\) −13.1807 + 13.8209i −0.659858 + 0.691911i
\(400\) −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 \(-0.305568\pi\)
0.573546 + 0.819174i \(0.305568\pi\)
\(410\) 2.95545 2.74228i 0.145959 0.135432i
\(411\) 1.14831i 0.0566419i
\(412\) 24.3819 24.3819i 1.20121 1.20121i
\(413\) 0.383178 + 16.1599i 0.0188550 + 0.795178i
\(414\) 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 \(-0.603181\pi\)
−0.318505 + 0.947921i \(0.603181\pi\)
\(420\) −8.02102 8.24368i −0.391385 0.402250i
\(421\) −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
\(427\) 18.8072 0.445951i 0.910146 0.0215811i
\(428\) 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 \(-0.0126730\pi\)
−0.0398028 + 0.999208i \(0.512673\pi\)
\(434\) −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 \(-0.756110\pi\)
−0.720548 + 0.693405i \(0.756110\pi\)
\(440\) 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 −0.941742 0.336337i \(-0.890812\pi\)
0.336337 + 0.941742i \(0.390812\pi\)
\(444\) −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
\(448\) 17.6988 0.419669i 0.836191 0.0198275i
\(449\) 30.4170i 1.43547i 0.696318 + 0.717734i \(0.254820\pi\)
−0.696318 + 0.717734i \(0.745180\pi\)
\(450\) 0.895358 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
\(455\) 3.00088 2.91982i 0.140683 0.136883i
\(456\) 6.72637 0.314991
\(457\) 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
\(459\) 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 \(0.990365\pi\)
\(462\) 2.49083 0.0590616i 0.115884 0.00274779i
\(463\) 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
\(465\) −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 \(-0.978479\pi\)
0.0675588 + 0.997715i \(0.478479\pi\)
\(468\) −0.972943 0.972943i −0.0449743 0.0449743i
\(469\) 2.43816 2.55659i 0.112584 0.118052i
\(470\) 0.227932 + 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 \(-0.418513\pi\)
0.253212 + 0.967411i \(0.418513\pi\)
\(480\) −0.228254 + 6.10081i −0.0104183 + 0.278463i
\(481\) 0.292530i 0.0133382i
\(482\) 2.44749 2.44749i 0.111480 0.111480i
\(483\) −0.457677 19.3018i −0.0208250 0.878261i
\(484\) 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 0.326552 0.945179i \(-0.394113\pi\)
−0.945179 + 0.326552i \(0.894113\pi\)
\(488\) −4.68508 4.68508i −0.212084 0.212084i
\(489\) −14.7714 −0.667986
\(490\) −2.64090 2.58851i −0.119304 0.116937i
\(491\) 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
\(497\) −0.0748201 3.15541i −0.00335614 0.141540i
\(498\) −2.83255 + 2.83255i −0.126930 + 0.126930i
\(499\) 4.27431i 0.191344i 0.995413 + 0.0956722i \(0.0305000\pi\)
−0.995413 + 0.0956722i \(0.969500\pi\)
\(500\) −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 \(-0.436806\pi\)
−0.980357 + 0.197229i \(0.936806\pi\)
\(504\) −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 \(-0.287667\pi\)
0.618682 + 0.785641i \(0.287667\pi\)
\(510\) −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
\(518\) −0.258291 + 0.00612451i −0.0113487 + 0.000269096i
\(519\) 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 \(-0.215019\pi\)
−0.625290 + 0.780392i \(0.715019\pi\)
\(524\) −36.5788 −1.59795
\(525\) −9.81959 + 8.86429i −0.428562 + 0.386869i
\(526\) −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
\(532\) −37.1203 + 0.880184i −1.60937 + 0.0381608i
\(533\) −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 0.972121 + 0.234482i \(0.0753392\pi\)
0.234482 + 0.972121i \(0.424661\pi\)
\(548\) −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
\(553\) 22.8536 0.541896i 0.971833 0.0230438i
\(554\) 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 0.976150 + 0.217096i \(0.0696584\pi\)
0.217096 + 0.976150i \(0.430342\pi\)
\(558\) 0.824957 + 0.824957i 0.0349232 + 0.0349232i
\(559\) −3.65510 −0.154594
\(560\) 0.297063 21.6995i 0.0125532 0.916970i
\(561\) −9.46128 −0.399455
\(562\) 1.61319 + 1.61319i 0.0680482 + 0.0680482i
\(563\) 27.3645 + 27.3645i 1.15328 + 1.15328i 0.985891 + 0.167386i \(0.0535326\pi\)
0.167386 + 0.985891i \(0.446467\pi\)
\(564\) 0.839429i 0.0353463i
\(565\) 7.87351 7.30560i 0.331241 0.307349i
\(566\) 4.98144i 0.209386i
\(567\) 0.0627175 + 2.64501i 0.00263389 + 0.111080i
\(568\) −0.786047 + 0.786047i −0.0329818 + 0.0329818i
\(569\) 17.7767i 0.745240i −0.927984 0.372620i \(-0.878460\pi\)
0.927984 0.372620i \(-0.121540\pi\)
\(570\) 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 \(-0.786594\pi\)
0.621327 + 0.783552i \(0.286594\pi\)
\(578\) 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 \(-0.604670\pi\)
0.946420 + 0.322937i \(0.104670\pi\)
\(588\) 9.15630 10.0685i 0.377599 0.415219i
\(589\) 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 \(-0.218241\pi\)
−0.633157 + 0.774023i \(0.718241\pi\)
\(594\) −0.941708 −0.0386388
\(595\) 9.79269 + 10.0645i 0.401461 + 0.412605i
\(596\) −6.10696 −0.250151
\(597\) 0.436028 + 0.436028i 0.0178454 + 0.0178454i
\(598\) −0.862773 0.862773i −0.0352814 0.0352814i
\(599\) 10.1010i 0.412714i 0.978477 + 0.206357i \(0.0661608\pi\)
−0.978477 + 0.206357i \(0.933839\pi\)
\(600\) 4.64610 + 0.348142i 0.189676 + 0.0142128i
\(601\) 38.4063i 1.56663i 0.621628 + 0.783313i \(0.286472\pi\)
−0.621628 + 0.783313i \(0.713528\pi\)
\(602\) 0.0765245 + 3.22730i 0.00311891 + 0.131535i
\(603\) −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 \(-0.845459\pi\)
0.466656 + 0.884439i \(0.345459\pi\)
\(608\) 13.9360 + 13.9360i 0.565180 + 0.565180i
\(609\) 6.99213 + 6.66822i 0.283336 + 0.270210i
\(610\) −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 −0.935517 0.353282i \(-0.885066\pi\)
0.353282 + 0.935517i \(0.385066\pi\)
\(614\) 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 −0.999721 0.0236346i \(-0.992476\pi\)
−0.0236346 0.999721i \(-0.507524\pi\)
\(618\) −2.96283 + 2.96283i −0.119183 + 0.119183i
\(619\) 11.1991 0.450129 0.225064 0.974344i \(-0.427741\pi\)
0.225064 + 0.974344i \(0.427741\pi\)
\(620\) −21.4530 0.802636i −0.861574 0.0322346i
\(621\) 7.29744i 0.292836i
\(622\) 4.56168 4.56168i 0.182907 0.182907i
\(623\) 0.490815 + 20.6993i 0.0196641 + 0.829301i
\(624\) 2.59609i 0.103927i
\(625\) 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
\(630\) 0.974695 + 1.00175i 0.0388328 + 0.0399107i
\(631\) 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
\(637\) 3.66516 + 3.33309i 0.145219 + 0.132062i
\(638\) −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 \(-0.351866\pi\)
−0.893652 + 0.448761i \(0.851866\pi\)
\(644\) 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 0.0320982 0.999485i \(-0.489781\pi\)
0.999485 0.0320982i \(-0.0102189\pi\)
\(648\) 0.658899 0.658899i 0.0258840 0.0258840i
\(649\) −24.3530 −0.955937
\(650\) −0.0624689 + 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 −0.744720 0.667377i \(-0.767417\pi\)
0.667377 + 0.744720i \(0.267417\pi\)
\(654\) −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
\(658\) 0.00639752 + 0.269805i 0.000249401 + 0.0105181i
\(659\) 15.1044i 0.588385i −0.955746 0.294193i \(-0.904949\pi\)
0.955746 0.294193i \(-0.0950507\pi\)
\(660\) 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
\(665\) −0.584574 + 42.7012i −0.0226688 + 1.65588i
\(666\) 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
\(672\) −7.22160 + 0.171236i −0.278579 + 0.00660558i
\(673\) −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
\(675\) 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 \(-0.516913\pi\)
0.998589 + 0.0531077i \(0.0169127\pi\)
\(678\) −0.802438 0.802438i −0.0308175 0.0308175i
\(679\) 20.1366 + 19.2037i 0.772770 + 0.736972i
\(680\) 0.184908 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 −0.920734 0.390191i \(-0.872409\pi\)
0.390191 + 0.920734i \(0.372409\pi\)
\(684\) 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
\(693\) 10.5431 0.249993i 0.400498 0.00949646i
\(694\) 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
\(700\) −25.6856 1.31330i −0.970824 0.0496380i
\(701\) 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
\(707\) 16.7067 0.396144i 0.628322 0.0148985i
\(708\) 8.39914 8.39914i 0.315659 0.315659i
\(709\) 48.5284i 1.82252i −0.411827 0.911262i \(-0.635109\pi\)
0.411827 0.911262i \(-0.364891\pi\)
\(710\) 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 \(-0.802038\pi\)
−0.812764 + 0.582593i \(0.802038\pi\)
\(720\) −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 \(-0.838363\pi\)
0.486254 + 0.873817i \(0.338363\pi\)
\(728\) −0.0413607 1.74432i −0.00153293 0.0646487i
\(729\) 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 \(-0.414029\pi\)
−0.963748 + 0.266815i \(0.914029\pi\)
\(734\) 0.136998 0.00505669
\(735\) −11.1783 10.9565i −0.412318 0.404138i
\(736\) −19.9240 −0.734409
\(737\) 3.76354 + 3.76354i 0.138632 + 0.138632i
\(738\) −1.27494 1.27494i −0.0469313 0.0469313i
\(739\) 20.9689i 0.771354i 0.922634 + 0.385677i \(0.126032\pi\)
−0.922634 + 0.385677i \(0.873968\pi\)
\(740\) −1.31723 + 1.22222i −0.0484224 + 0.0449297i
\(741\) 5.10872i 0.187673i
\(742\) 0.113082 + 4.76906i 0.00415138 + 0.175078i
\(743\) 9.18724 9.18724i 0.337047 0.337047i −0.518208 0.855255i \(-0.673401\pi\)
0.855255 + 0.518208i \(0.173401\pi\)
\(744\) 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 0.407031 0.913414i \(-0.366564\pi\)
−0.913414 + 0.407031i \(0.866564\pi\)
\(758\) −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
\(763\) 1.76746 0.0419093i 0.0639862 0.00151722i
\(764\) 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 \(-0.435168\pi\)
0.202271 + 0.979330i \(0.435168\pi\)
\(770\) 3.99300 3.88515i 0.143898 0.140011i
\(771\) −13.2830 −0.478374
\(772\) 17.3574 + 17.3574i 0.624708 + 0.624708i
\(773\)