Properties

Label 750.2.l.c.107.10
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.10
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.891007 + 0.453990i) q^{2} +(1.65131 - 0.522656i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(0.712495 + 0.712495i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.45366 - 1.72614i) q^{9} +O(q^{10})\) \(q+(0.891007 + 0.453990i) q^{2} +(1.65131 - 0.522656i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(0.712495 + 0.712495i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.45366 - 1.72614i) q^{9} +(0.348148 - 0.113120i) q^{11} +(1.39345 + 1.02873i) q^{12} +(-1.19006 - 2.33563i) q^{13} +(0.311372 + 0.958303i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(5.80242 - 0.919013i) q^{17} +(2.96988 - 0.424059i) q^{18} +(-0.341785 + 0.470426i) q^{19} +(1.54894 + 0.804162i) q^{21} +(0.361558 + 0.0572652i) q^{22} +(-3.08387 + 6.05243i) q^{23} +(0.774543 + 1.54922i) q^{24} -2.62134i q^{26} +(3.14959 - 4.13281i) q^{27} +(-0.157626 + 0.995214i) q^{28} +(0.368253 - 0.267552i) q^{29} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.515779 - 0.368759i) q^{33} +(5.58722 + 1.81540i) q^{34} +(2.83870 + 0.970457i) q^{36} +(-8.53839 + 4.35053i) q^{37} +(-0.518102 + 0.263986i) q^{38} +(-3.18589 - 3.23486i) q^{39} +(10.0917 + 3.27898i) q^{41} +(1.01503 + 1.41972i) q^{42} +(-7.18512 + 7.18512i) q^{43} +(0.296153 + 0.215168i) q^{44} +(-5.49549 + 3.99271i) q^{46} +(1.29277 - 8.16222i) q^{47} +(-0.0132082 + 1.73200i) q^{48} -5.98470i q^{49} +(9.10128 - 4.55025i) q^{51} +(1.19006 - 2.33563i) q^{52} +(-8.72670 - 1.38217i) q^{53} +(4.68256 - 2.25248i) q^{54} +(-0.592264 + 0.815182i) q^{56} +(-0.318522 + 0.955457i) q^{57} +(0.449582 - 0.0712068i) q^{58} +(2.91096 - 8.95903i) q^{59} +(-0.335312 - 1.03198i) q^{61} +(-1.32890 - 2.60811i) q^{62} +(2.97808 + 0.518359i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(0.626975 - 0.0944078i) q^{66} +(2.07319 + 13.0896i) q^{67} +(4.15407 + 4.15407i) q^{68} +(-1.92909 + 11.6062i) q^{69} +(-0.755873 - 1.04037i) q^{71} +(2.08872 + 2.15343i) q^{72} +(-8.50497 - 4.33350i) q^{73} -9.58285 q^{74} -0.581479 q^{76} +(0.328652 + 0.167456i) q^{77} +(-1.37006 - 4.32864i) q^{78} +(-7.17322 - 9.87309i) q^{79} +(3.04091 - 8.47071i) q^{81} +(7.50310 + 7.50310i) q^{82} +(-0.148436 - 0.937190i) q^{83} +(0.259864 + 1.72579i) q^{84} +(-9.66396 + 3.14001i) q^{86} +(0.468264 - 0.634281i) q^{87} +(0.166190 + 0.326166i) q^{88} +(0.626378 + 1.92779i) q^{89} +(0.816210 - 2.51204i) q^{91} +(-6.70917 + 1.06263i) q^{92} +(-4.80974 - 1.60343i) q^{93} +(4.85743 - 6.68568i) q^{94} +(-0.798080 + 1.53723i) q^{96} +(-17.7876 - 2.81727i) q^{97} +(2.71700 - 5.33241i) q^{98} +(0.658978 - 0.878510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.891007 + 0.453990i 0.630037 + 0.321020i
\(3\) 1.65131 0.522656i 0.953385 0.301755i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 1.70861 + 0.283990i 0.697537 + 0.115939i
\(7\) 0.712495 + 0.712495i 0.269298 + 0.269298i 0.828817 0.559519i \(-0.189014\pi\)
−0.559519 + 0.828817i \(0.689014\pi\)
\(8\) 0.156434 + 0.987688i 0.0553079 + 0.349201i
\(9\) 2.45366 1.72614i 0.817887 0.575378i
\(10\) 0 0
\(11\) 0.348148 0.113120i 0.104971 0.0341070i −0.256061 0.966661i \(-0.582425\pi\)
0.361031 + 0.932554i \(0.382425\pi\)
\(12\) 1.39345 + 1.02873i 0.402256 + 0.296969i
\(13\) −1.19006 2.33563i −0.330064 0.647787i 0.665020 0.746826i \(-0.268423\pi\)
−0.995084 + 0.0990392i \(0.968423\pi\)
\(14\) 0.311372 + 0.958303i 0.0832176 + 0.256117i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 5.80242 0.919013i 1.40729 0.222893i 0.593868 0.804562i \(-0.297600\pi\)
0.813426 + 0.581669i \(0.197600\pi\)
\(18\) 2.96988 0.424059i 0.700007 0.0999516i
\(19\) −0.341785 + 0.470426i −0.0784108 + 0.107923i −0.846421 0.532515i \(-0.821247\pi\)
0.768010 + 0.640438i \(0.221247\pi\)
\(20\) 0 0
\(21\) 1.54894 + 0.804162i 0.338007 + 0.175482i
\(22\) 0.361558 + 0.0572652i 0.0770844 + 0.0122090i
\(23\) −3.08387 + 6.05243i −0.643031 + 1.26202i 0.307548 + 0.951533i \(0.400492\pi\)
−0.950578 + 0.310486i \(0.899508\pi\)
\(24\) 0.774543 + 1.54922i 0.158103 + 0.316233i
\(25\) 0 0
\(26\) 2.62134i 0.514086i
\(27\) 3.14959 4.13281i 0.606138 0.795359i
\(28\) −0.157626 + 0.995214i −0.0297886 + 0.188078i
\(29\) 0.368253 0.267552i 0.0683830 0.0496831i −0.553069 0.833136i \(-0.686543\pi\)
0.621452 + 0.783453i \(0.286543\pi\)
\(30\) 0 0
\(31\) −2.36811 1.72054i −0.425326 0.309017i 0.354451 0.935074i \(-0.384668\pi\)
−0.779777 + 0.626057i \(0.784668\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0.515779 0.368759i 0.0897855 0.0641926i
\(34\) 5.58722 + 1.81540i 0.958200 + 0.311338i
\(35\) 0 0
\(36\) 2.83870 + 0.970457i 0.473117 + 0.161743i
\(37\) −8.53839 + 4.35053i −1.40370 + 0.715222i −0.981533 0.191295i \(-0.938731\pi\)
−0.422169 + 0.906517i \(0.638731\pi\)
\(38\) −0.518102 + 0.263986i −0.0840472 + 0.0428242i
\(39\) −3.18589 3.23486i −0.510151 0.517992i
\(40\) 0 0
\(41\) 10.0917 + 3.27898i 1.57605 + 0.512090i 0.961036 0.276425i \(-0.0891497\pi\)
0.615016 + 0.788515i \(0.289150\pi\)
\(42\) 1.01503 + 1.41972i 0.156623 + 0.219067i
\(43\) −7.18512 + 7.18512i −1.09572 + 1.09572i −0.100815 + 0.994905i \(0.532145\pi\)
−0.994905 + 0.100815i \(0.967855\pi\)
\(44\) 0.296153 + 0.215168i 0.0446467 + 0.0324377i
\(45\) 0 0
\(46\) −5.49549 + 3.99271i −0.810266 + 0.588693i
\(47\) 1.29277 8.16222i 0.188570 1.19058i −0.693850 0.720119i \(-0.744087\pi\)
0.882420 0.470463i \(-0.155913\pi\)
\(48\) −0.0132082 + 1.73200i −0.00190644 + 0.249993i
\(49\) 5.98470i 0.854957i
\(50\) 0 0
\(51\) 9.10128 4.55025i 1.27443 0.637162i
\(52\) 1.19006 2.33563i 0.165032 0.323893i
\(53\) −8.72670 1.38217i −1.19870 0.189856i −0.475012 0.879979i \(-0.657556\pi\)
−0.723692 + 0.690123i \(0.757556\pi\)
\(54\) 4.68256 2.25248i 0.637215 0.306523i
\(55\) 0 0
\(56\) −0.592264 + 0.815182i −0.0791446 + 0.108933i
\(57\) −0.318522 + 0.955457i −0.0421893 + 0.126553i
\(58\) 0.449582 0.0712068i 0.0590330 0.00934992i
\(59\) 2.91096 8.95903i 0.378975 1.16637i −0.561782 0.827285i \(-0.689884\pi\)
0.940757 0.339081i \(-0.110116\pi\)
\(60\) 0 0
\(61\) −0.335312 1.03198i −0.0429323 0.132132i 0.927293 0.374337i \(-0.122130\pi\)
−0.970225 + 0.242205i \(0.922130\pi\)
\(62\) −1.32890 2.60811i −0.168770 0.331230i
\(63\) 2.97808 + 0.518359i 0.375203 + 0.0653071i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 0.626975 0.0944078i 0.0771753 0.0116208i
\(67\) 2.07319 + 13.0896i 0.253280 + 1.59915i 0.706476 + 0.707737i \(0.250284\pi\)
−0.453196 + 0.891411i \(0.649716\pi\)
\(68\) 4.15407 + 4.15407i 0.503756 + 0.503756i
\(69\) −1.92909 + 11.6062i −0.232235 + 1.39723i
\(70\) 0 0
\(71\) −0.755873 1.04037i −0.0897056 0.123469i 0.761805 0.647806i \(-0.224313\pi\)
−0.851511 + 0.524337i \(0.824313\pi\)
\(72\) 2.08872 + 2.15343i 0.246158 + 0.253784i
\(73\) −8.50497 4.33350i −0.995432 0.507198i −0.121159 0.992633i \(-0.538661\pi\)
−0.874273 + 0.485435i \(0.838661\pi\)
\(74\) −9.58285 −1.11398
\(75\) 0 0
\(76\) −0.581479 −0.0667002
\(77\) 0.328652 + 0.167456i 0.0374533 + 0.0190834i
\(78\) −1.37006 4.32864i −0.155128 0.490122i
\(79\) −7.17322 9.87309i −0.807050 1.11081i −0.991772 0.128018i \(-0.959138\pi\)
0.184722 0.982791i \(-0.440862\pi\)
\(80\) 0 0
\(81\) 3.04091 8.47071i 0.337879 0.941189i
\(82\) 7.50310 + 7.50310i 0.828579 + 0.828579i
\(83\) −0.148436 0.937190i −0.0162930 0.102870i 0.978202 0.207657i \(-0.0665838\pi\)
−0.994495 + 0.104787i \(0.966584\pi\)
\(84\) 0.259864 + 1.72579i 0.0283535 + 0.188300i
\(85\) 0 0
\(86\) −9.66396 + 3.14001i −1.04209 + 0.338596i
\(87\) 0.468264 0.634281i 0.0502032 0.0680021i
\(88\) 0.166190 + 0.326166i 0.0177159 + 0.0347694i
\(89\) 0.626378 + 1.92779i 0.0663960 + 0.204346i 0.978750 0.205056i \(-0.0657375\pi\)
−0.912354 + 0.409401i \(0.865738\pi\)
\(90\) 0 0
\(91\) 0.816210 2.51204i 0.0855620 0.263333i
\(92\) −6.70917 + 1.06263i −0.699479 + 0.110787i
\(93\) −4.80974 1.60343i −0.498747 0.166268i
\(94\) 4.85743 6.68568i 0.501006 0.689576i
\(95\) 0 0
\(96\) −0.798080 + 1.53723i −0.0814537 + 0.156893i
\(97\) −17.7876 2.81727i −1.80605 0.286051i −0.839658 0.543115i \(-0.817245\pi\)
−0.966394 + 0.257065i \(0.917245\pi\)
\(98\) 2.71700 5.33241i 0.274458 0.538655i
\(99\) 0.658978 0.878510i 0.0662297 0.0882936i
\(100\) 0 0
\(101\) 0.362340i 0.0360542i 0.999837 + 0.0180271i \(0.00573851\pi\)
−0.999837 + 0.0180271i \(0.994261\pi\)
\(102\) 10.1751 + 0.0775950i 1.00748 + 0.00768305i
\(103\) −1.24118 + 7.83651i −0.122297 + 0.772154i 0.847957 + 0.530065i \(0.177833\pi\)
−0.970254 + 0.242089i \(0.922167\pi\)
\(104\) 2.12071 1.54078i 0.207952 0.151086i
\(105\) 0 0
\(106\) −7.14805 5.19336i −0.694280 0.504424i
\(107\) −9.06892 + 9.06892i −0.876725 + 0.876725i −0.993194 0.116469i \(-0.962842\pi\)
0.116469 + 0.993194i \(0.462842\pi\)
\(108\) 5.19479 + 0.118865i 0.499869 + 0.0114378i
\(109\) 4.33696 + 1.40916i 0.415405 + 0.134973i 0.509260 0.860613i \(-0.329919\pi\)
−0.0938551 + 0.995586i \(0.529919\pi\)
\(110\) 0 0
\(111\) −11.8257 + 11.6467i −1.12245 + 1.10546i
\(112\) −0.897796 + 0.457450i −0.0848337 + 0.0432249i
\(113\) 12.1221 6.17652i 1.14035 0.581038i 0.221311 0.975203i \(-0.428966\pi\)
0.919039 + 0.394166i \(0.128966\pi\)
\(114\) −0.717574 + 0.706712i −0.0672069 + 0.0661896i
\(115\) 0 0
\(116\) 0.432908 + 0.140660i 0.0401945 + 0.0130600i
\(117\) −6.95162 3.67663i −0.642677 0.339905i
\(118\) 6.66100 6.66100i 0.613195 0.613195i
\(119\) 4.78899 + 3.47940i 0.439006 + 0.318956i
\(120\) 0 0
\(121\) −8.79078 + 6.38687i −0.799161 + 0.580625i
\(122\) 0.169746 1.07173i 0.0153681 0.0970301i
\(123\) 18.3782 + 0.140152i 1.65711 + 0.0126371i
\(124\) 2.92715i 0.262866i
\(125\) 0 0
\(126\) 2.41816 + 1.81388i 0.215427 + 0.161594i
\(127\) 8.95420 17.5736i 0.794557 1.55941i −0.0339477 0.999424i \(-0.510808\pi\)
0.828505 0.559982i \(-0.189192\pi\)
\(128\) −0.987688 0.156434i −0.0873001 0.0138270i
\(129\) −8.10953 + 15.6202i −0.714004 + 1.37528i
\(130\) 0 0
\(131\) −6.37019 + 8.76782i −0.556566 + 0.766048i −0.990885 0.134711i \(-0.956989\pi\)
0.434318 + 0.900759i \(0.356989\pi\)
\(132\) 0.601499 + 0.200523i 0.0523538 + 0.0174533i
\(133\) −0.578696 + 0.0916565i −0.0501793 + 0.00794763i
\(134\) −4.09532 + 12.6041i −0.353782 + 1.08883i
\(135\) 0 0
\(136\) 1.81540 + 5.58722i 0.155669 + 0.479100i
\(137\) 3.95032 + 7.75294i 0.337498 + 0.662378i 0.995917 0.0902740i \(-0.0287743\pi\)
−0.658419 + 0.752652i \(0.728774\pi\)
\(138\) −6.98796 + 9.46545i −0.594854 + 0.805753i
\(139\) 2.91069 0.945741i 0.246882 0.0802167i −0.182962 0.983120i \(-0.558569\pi\)
0.429844 + 0.902903i \(0.358569\pi\)
\(140\) 0 0
\(141\) −2.13127 14.1540i −0.179485 1.19199i
\(142\) −0.201170 1.27013i −0.0168818 0.106587i
\(143\) −0.678525 0.678525i −0.0567411 0.0567411i
\(144\) 0.883429 + 2.86698i 0.0736191 + 0.238915i
\(145\) 0 0
\(146\) −5.61062 7.72236i −0.464338 0.639107i
\(147\) −3.12794 9.88261i −0.257988 0.815104i
\(148\) −8.53839 4.35053i −0.701851 0.357611i
\(149\) 5.85789 0.479897 0.239948 0.970786i \(-0.422869\pi\)
0.239948 + 0.970786i \(0.422869\pi\)
\(150\) 0 0
\(151\) 3.64976 0.297013 0.148507 0.988911i \(-0.452553\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(152\) −0.518102 0.263986i −0.0420236 0.0214121i
\(153\) 12.6508 12.2707i 1.02276 0.992028i
\(154\) 0.216807 + 0.298409i 0.0174708 + 0.0240465i
\(155\) 0 0
\(156\) 0.744434 4.47884i 0.0596024 0.358594i
\(157\) 2.27502 + 2.27502i 0.181567 + 0.181567i 0.792038 0.610472i \(-0.209020\pi\)
−0.610472 + 0.792038i \(0.709020\pi\)
\(158\) −1.90910 12.0536i −0.151880 0.958930i
\(159\) −15.1329 + 2.27866i −1.20012 + 0.180709i
\(160\) 0 0
\(161\) −6.50956 + 2.11508i −0.513025 + 0.166692i
\(162\) 6.55509 6.16691i 0.515017 0.484518i
\(163\) 1.67923 + 3.29567i 0.131527 + 0.258137i 0.947372 0.320134i \(-0.103728\pi\)
−0.815845 + 0.578270i \(0.803728\pi\)
\(164\) 3.27898 + 10.0917i 0.256045 + 0.788026i
\(165\) 0 0
\(166\) 0.293218 0.902431i 0.0227581 0.0700422i
\(167\) −9.02439 + 1.42932i −0.698328 + 0.110604i −0.495497 0.868610i \(-0.665014\pi\)
−0.202831 + 0.979214i \(0.565014\pi\)
\(168\) −0.551953 + 1.65567i −0.0425841 + 0.127738i
\(169\) 3.60230 4.95814i 0.277100 0.381395i
\(170\) 0 0
\(171\) −0.0266046 + 1.74423i −0.00203450 + 0.133385i
\(172\) −10.0362 1.58958i −0.765252 0.121204i
\(173\) −4.18400 + 8.21156i −0.318104 + 0.624313i −0.993588 0.113061i \(-0.963935\pi\)
0.675485 + 0.737374i \(0.263935\pi\)
\(174\) 0.705184 0.352561i 0.0534598 0.0267276i
\(175\) 0 0
\(176\) 0.366065i 0.0275932i
\(177\) 0.124423 16.3156i 0.00935217 1.22635i
\(178\) −0.317093 + 2.00205i −0.0237671 + 0.150060i
\(179\) −10.9316 + 7.94230i −0.817069 + 0.593635i −0.915871 0.401472i \(-0.868499\pi\)
0.0988026 + 0.995107i \(0.468499\pi\)
\(180\) 0 0
\(181\) −13.0973 9.51573i −0.973514 0.707299i −0.0172639 0.999851i \(-0.505496\pi\)
−0.956250 + 0.292552i \(0.905496\pi\)
\(182\) 1.86769 1.86769i 0.138442 0.138442i
\(183\) −1.09308 1.52887i −0.0808026 0.113018i
\(184\) −6.46034 2.09909i −0.476262 0.154747i
\(185\) 0 0
\(186\) −3.55757 3.61225i −0.260854 0.264863i
\(187\) 1.91614 0.976324i 0.140122 0.0713959i
\(188\) 7.36324 3.75176i 0.537020 0.273625i
\(189\) 5.18867 0.700541i 0.377420 0.0509568i
\(190\) 0 0
\(191\) 14.6868 + 4.77202i 1.06270 + 0.345291i 0.787639 0.616136i \(-0.211303\pi\)
0.275058 + 0.961428i \(0.411303\pi\)
\(192\) −1.40898 + 1.00736i −0.101684 + 0.0726998i
\(193\) 6.05387 6.05387i 0.435767 0.435767i −0.454817 0.890585i \(-0.650296\pi\)
0.890585 + 0.454817i \(0.150296\pi\)
\(194\) −14.5698 10.5856i −1.04605 0.760001i
\(195\) 0 0
\(196\) 4.84173 3.51772i 0.345838 0.251266i
\(197\) 0.990925 6.25646i 0.0706005 0.445754i −0.926913 0.375277i \(-0.877548\pi\)
0.997513 0.0704774i \(-0.0224523\pi\)
\(198\) 0.985989 0.483589i 0.0700712 0.0343672i
\(199\) 10.3976i 0.737069i 0.929614 + 0.368535i \(0.120140\pi\)
−0.929614 + 0.368535i \(0.879860\pi\)
\(200\) 0 0
\(201\) 10.2648 + 20.5314i 0.724025 + 1.44817i
\(202\) −0.164499 + 0.322847i −0.0115741 + 0.0227155i
\(203\) 0.453008 + 0.0717494i 0.0317949 + 0.00503582i
\(204\) 9.03082 + 4.68852i 0.632284 + 0.328262i
\(205\) 0 0
\(206\) −4.66360 + 6.41889i −0.324928 + 0.447225i
\(207\) 2.88055 + 20.1738i 0.200212 + 1.40217i
\(208\) 2.58906 0.410067i 0.179519 0.0284331i
\(209\) −0.0657771 + 0.202441i −0.00454990 + 0.0140031i
\(210\) 0 0
\(211\) 1.12958 + 3.47648i 0.0777632 + 0.239331i 0.982380 0.186896i \(-0.0598427\pi\)
−0.904617 + 0.426226i \(0.859843\pi\)
\(212\) −4.01122 7.87247i −0.275492 0.540683i
\(213\) −1.79194 1.32291i −0.122781 0.0906445i
\(214\) −12.1977 + 3.96326i −0.833815 + 0.270923i
\(215\) 0 0
\(216\) 4.57463 + 2.46430i 0.311264 + 0.167674i
\(217\) −0.461396 2.91314i −0.0313216 0.197757i
\(218\) 3.22451 + 3.22451i 0.218391 + 0.218391i
\(219\) −16.3093 2.71079i −1.10208 0.183178i
\(220\) 0 0
\(221\) −9.05171 12.4586i −0.608884 0.838057i
\(222\) −15.8243 + 5.00853i −1.06206 + 0.336151i
\(223\) 1.88406 + 0.959975i 0.126166 + 0.0642847i 0.515934 0.856628i \(-0.327445\pi\)
−0.389768 + 0.920913i \(0.627445\pi\)
\(224\) −1.00762 −0.0673244
\(225\) 0 0
\(226\) 13.6049 0.904987
\(227\) 13.7998 + 7.03137i 0.915928 + 0.466689i 0.847397 0.530960i \(-0.178169\pi\)
0.0685314 + 0.997649i \(0.478169\pi\)
\(228\) −0.960203 + 0.303913i −0.0635910 + 0.0201272i
\(229\) 0.971347 + 1.33694i 0.0641884 + 0.0883477i 0.839904 0.542735i \(-0.182611\pi\)
−0.775716 + 0.631082i \(0.782611\pi\)
\(230\) 0 0
\(231\) 0.630228 + 0.104751i 0.0414660 + 0.00689211i
\(232\) 0.321865 + 0.321865i 0.0211315 + 0.0211315i
\(233\) −2.73209 17.2497i −0.178985 1.13007i −0.899594 0.436726i \(-0.856138\pi\)
0.720609 0.693342i \(-0.243862\pi\)
\(234\) −4.52478 6.43187i −0.295794 0.420465i
\(235\) 0 0
\(236\) 8.95903 2.91096i 0.583183 0.189488i
\(237\) −17.0054 12.5544i −1.10462 0.815497i
\(238\) 2.68740 + 5.27432i 0.174198 + 0.341884i
\(239\) −1.97435 6.07643i −0.127710 0.393052i 0.866675 0.498873i \(-0.166253\pi\)
−0.994385 + 0.105822i \(0.966253\pi\)
\(240\) 0 0
\(241\) 5.94510 18.2971i 0.382958 1.17862i −0.554993 0.831855i \(-0.687279\pi\)
0.937951 0.346768i \(-0.112721\pi\)
\(242\) −10.7322 + 1.69982i −0.689893 + 0.109268i
\(243\) 0.594232 15.5771i 0.0381200 0.999273i
\(244\) 0.637801 0.877858i 0.0408310 0.0561991i
\(245\) 0 0
\(246\) 16.3115 + 8.46842i 1.03998 + 0.539927i
\(247\) 1.50549 + 0.238446i 0.0957918 + 0.0151719i
\(248\) 1.32890 2.60811i 0.0843851 0.165615i
\(249\) −0.734942 1.47001i −0.0465751 0.0931582i
\(250\) 0 0
\(251\) 10.1849i 0.642864i −0.946933 0.321432i \(-0.895836\pi\)
0.946933 0.321432i \(-0.104164\pi\)
\(252\) 1.33111 + 2.71400i 0.0838522 + 0.170966i
\(253\) −0.388991 + 2.45599i −0.0244556 + 0.154407i
\(254\) 15.9565 11.5931i 1.00120 0.727414i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −1.62811 + 1.62811i −0.101558 + 0.101558i −0.756060 0.654502i \(-0.772878\pi\)
0.654502 + 0.756060i \(0.272878\pi\)
\(258\) −14.3171 + 10.2361i −0.891342 + 0.637270i
\(259\) −9.18328 2.98383i −0.570621 0.185406i
\(260\) 0 0
\(261\) 0.441739 1.29214i 0.0273429 0.0799813i
\(262\) −9.65639 + 4.92018i −0.596574 + 0.303970i
\(263\) −14.9902 + 7.63791i −0.924338 + 0.470973i −0.850310 0.526283i \(-0.823585\pi\)
−0.0740278 + 0.997256i \(0.523585\pi\)
\(264\) 0.444904 + 0.451742i 0.0273820 + 0.0278028i
\(265\) 0 0
\(266\) −0.557233 0.181056i −0.0341662 0.0111013i
\(267\) 2.04192 + 2.85601i 0.124963 + 0.174785i
\(268\) −9.37111 + 9.37111i −0.572432 + 0.572432i
\(269\) 4.85348 + 3.52626i 0.295922 + 0.215000i 0.725832 0.687872i \(-0.241455\pi\)
−0.429910 + 0.902872i \(0.641455\pi\)
\(270\) 0 0
\(271\) −10.0235 + 7.28250i −0.608885 + 0.442380i −0.849021 0.528359i \(-0.822808\pi\)
0.240137 + 0.970739i \(0.422808\pi\)
\(272\) −0.919013 + 5.80242i −0.0557234 + 0.351823i
\(273\) 0.0348870 4.57475i 0.00211146 0.276876i
\(274\) 8.70132i 0.525666i
\(275\) 0 0
\(276\) −10.5235 + 5.26132i −0.633443 + 0.316694i
\(277\) −2.80135 + 5.49796i −0.168317 + 0.330340i −0.959722 0.280952i \(-0.909350\pi\)
0.791405 + 0.611292i \(0.209350\pi\)
\(278\) 3.02280 + 0.478765i 0.181296 + 0.0287144i
\(279\) −8.78043 0.133927i −0.525671 0.00801799i
\(280\) 0 0
\(281\) 5.28744 7.27753i 0.315422 0.434141i −0.621640 0.783303i \(-0.713533\pi\)
0.937063 + 0.349161i \(0.113533\pi\)
\(282\) 4.52683 13.5789i 0.269569 0.808613i
\(283\) 12.9466 2.05054i 0.769594 0.121892i 0.240723 0.970594i \(-0.422615\pi\)
0.528871 + 0.848702i \(0.322615\pi\)
\(284\) 0.397386 1.22303i 0.0235805 0.0725733i
\(285\) 0 0
\(286\) −0.296526 0.912614i −0.0175340 0.0539640i
\(287\) 4.85400 + 9.52650i 0.286522 + 0.562332i
\(288\) −0.514439 + 2.95556i −0.0303136 + 0.174158i
\(289\) 16.6555 5.41171i 0.979737 0.318336i
\(290\) 0 0
\(291\) −30.8453 + 4.64457i −1.80818 + 0.272270i
\(292\) −1.49322 9.42784i −0.0873842 0.551722i
\(293\) 9.52977 + 9.52977i 0.556735 + 0.556735i 0.928376 0.371641i \(-0.121205\pi\)
−0.371641 + 0.928376i \(0.621205\pi\)
\(294\) 1.69960 10.2255i 0.0991225 0.596365i
\(295\) 0 0
\(296\) −5.63266 7.75269i −0.327392 0.450616i
\(297\) 0.629019 1.79511i 0.0364994 0.104163i
\(298\) 5.21941 + 2.65942i 0.302353 + 0.154056i
\(299\) 17.8062 1.02976
\(300\) 0 0
\(301\) −10.2387 −0.590150
\(302\) 3.25196 + 1.65696i 0.187129 + 0.0953472i
\(303\) 0.189379 + 0.598336i 0.0108795 + 0.0343735i
\(304\) −0.341785 0.470426i −0.0196027 0.0269808i
\(305\) 0 0
\(306\) 16.8428 5.18992i 0.962837 0.296688i
\(307\) 13.4223 + 13.4223i 0.766053 + 0.766053i 0.977409 0.211356i \(-0.0677880\pi\)
−0.211356 + 0.977409i \(0.567788\pi\)
\(308\) 0.0577015 + 0.364313i 0.00328785 + 0.0207587i
\(309\) 2.04622 + 13.5892i 0.116405 + 0.773064i
\(310\) 0 0
\(311\) 20.3576 6.61457i 1.15437 0.375078i 0.331583 0.943426i \(-0.392417\pi\)
0.822788 + 0.568348i \(0.192417\pi\)
\(312\) 2.69665 3.65271i 0.152668 0.206794i
\(313\) −5.79816 11.3795i −0.327732 0.643210i 0.667075 0.744990i \(-0.267546\pi\)
−0.994807 + 0.101781i \(0.967546\pi\)
\(314\) 0.994222 + 3.05990i 0.0561072 + 0.172680i
\(315\) 0 0
\(316\) 3.77118 11.6065i 0.212146 0.652917i
\(317\) 27.3883 4.33787i 1.53828 0.243639i 0.670997 0.741460i \(-0.265866\pi\)
0.867280 + 0.497821i \(0.165866\pi\)
\(318\) −14.5180 4.83989i −0.814129 0.271408i
\(319\) 0.0979413 0.134805i 0.00548366 0.00754761i
\(320\) 0 0
\(321\) −10.2357 + 19.7155i −0.571300 + 1.10041i
\(322\) −6.76029 1.07072i −0.376736 0.0596692i
\(323\) −1.55085 + 3.04372i −0.0862917 + 0.169357i
\(324\) 8.64035 2.51881i 0.480019 0.139934i
\(325\) 0 0
\(326\) 3.69881i 0.204858i
\(327\) 7.89818 + 0.0602315i 0.436770 + 0.00333081i
\(328\) −1.65992 + 10.4804i −0.0916540 + 0.578681i
\(329\) 6.73663 4.89445i 0.371402 0.269840i
\(330\) 0 0
\(331\) 15.0534 + 10.9369i 0.827410 + 0.601149i 0.918826 0.394664i \(-0.129139\pi\)
−0.0914151 + 0.995813i \(0.529139\pi\)
\(332\) 0.670954 0.670954i 0.0368234 0.0368234i
\(333\) −13.4407 + 25.4131i −0.736547 + 1.39263i
\(334\) −8.68968 2.82345i −0.475478 0.154492i
\(335\) 0 0
\(336\) −1.24345 + 1.22463i −0.0678359 + 0.0668091i
\(337\) 18.4916 9.42193i 1.00730 0.513245i 0.129148 0.991625i \(-0.458776\pi\)
0.878153 + 0.478380i \(0.158776\pi\)
\(338\) 5.46062 2.78232i 0.297019 0.151339i
\(339\) 16.7892 16.5350i 0.911862 0.898060i
\(340\) 0 0
\(341\) −1.01908 0.331120i −0.0551864 0.0179312i
\(342\) −0.815571 + 1.54205i −0.0441010 + 0.0833843i
\(343\) 9.25153 9.25153i 0.499536 0.499536i
\(344\) −8.22066 5.97266i −0.443228 0.322024i
\(345\) 0 0
\(346\) −7.45594 + 5.41706i −0.400834 + 0.291223i
\(347\) −1.16592 + 7.36133i −0.0625898 + 0.395177i 0.936428 + 0.350861i \(0.114111\pi\)
−0.999018 + 0.0443161i \(0.985889\pi\)
\(348\) 0.788383 + 0.00601220i 0.0422618 + 0.000322288i
\(349\) 16.1042i 0.862040i 0.902342 + 0.431020i \(0.141846\pi\)
−0.902342 + 0.431020i \(0.858154\pi\)
\(350\) 0 0
\(351\) −13.4009 2.43796i −0.715287 0.130129i
\(352\) −0.166190 + 0.326166i −0.00885796 + 0.0173847i
\(353\) 0.427472 + 0.0677049i 0.0227520 + 0.00360357i 0.167800 0.985821i \(-0.446334\pi\)
−0.145048 + 0.989425i \(0.546334\pi\)
\(354\) 7.51798 14.4808i 0.399576 0.769646i
\(355\) 0 0
\(356\) −1.19144 + 1.63988i −0.0631463 + 0.0869135i
\(357\) 9.72664 + 3.24259i 0.514788 + 0.171616i
\(358\) −13.3459 + 2.11378i −0.705352 + 0.111717i
\(359\) 0.0683480 0.210354i 0.00360727 0.0111020i −0.949237 0.314563i \(-0.898142\pi\)
0.952844 + 0.303461i \(0.0981421\pi\)
\(360\) 0 0
\(361\) 5.76684 + 17.7485i 0.303518 + 0.934132i
\(362\) −7.34971 14.4246i −0.386292 0.758141i
\(363\) −11.1782 + 15.1413i −0.586702 + 0.794710i
\(364\) 2.51204 0.816210i 0.131666 0.0427810i
\(365\) 0 0
\(366\) −0.279844 1.85848i −0.0146277 0.0971445i
\(367\) 2.61239 + 16.4940i 0.136366 + 0.860980i 0.957119 + 0.289697i \(0.0935544\pi\)
−0.820753 + 0.571284i \(0.806446\pi\)
\(368\) −4.80323 4.80323i −0.250386 0.250386i
\(369\) 30.4215 9.37406i 1.58368 0.487994i
\(370\) 0 0
\(371\) −5.23293 7.20252i −0.271680 0.373936i
\(372\) −1.52989 4.83364i −0.0793212 0.250612i
\(373\) −0.0941389 0.0479661i −0.00487433 0.00248359i 0.451552 0.892245i \(-0.350871\pi\)
−0.456426 + 0.889761i \(0.650871\pi\)
\(374\) 2.15054 0.111202
\(375\) 0 0
\(376\) 8.26396 0.426181
\(377\) −1.06315 0.541700i −0.0547548 0.0278990i
\(378\) 4.94118 + 1.73142i 0.254147 + 0.0890546i
\(379\) 5.78536 + 7.96287i 0.297174 + 0.409025i 0.931328 0.364182i \(-0.118651\pi\)
−0.634154 + 0.773207i \(0.718651\pi\)
\(380\) 0 0
\(381\) 5.60123 33.6995i 0.286960 1.72648i
\(382\) 10.9196 + 10.9196i 0.558693 + 0.558693i
\(383\) 5.20561 + 32.8669i 0.265994 + 1.67942i 0.653010 + 0.757349i \(0.273506\pi\)
−0.387016 + 0.922073i \(0.626494\pi\)
\(384\) −1.71274 + 0.257899i −0.0874030 + 0.0131609i
\(385\) 0 0
\(386\) 8.14244 2.64564i 0.414439 0.134659i
\(387\) −5.22736 + 30.0323i −0.265722 + 1.52663i
\(388\) −8.17604 16.0464i −0.415076 0.814632i
\(389\) −10.3312 31.7962i −0.523814 1.61213i −0.766650 0.642066i \(-0.778078\pi\)
0.242836 0.970067i \(-0.421922\pi\)
\(390\) 0 0
\(391\) −12.3316 + 37.9528i −0.623637 + 1.91936i
\(392\) 5.91102 0.936214i 0.298552 0.0472859i
\(393\) −5.93662 + 17.8078i −0.299463 + 0.898286i
\(394\) 3.72329 5.12467i 0.187577 0.258177i
\(395\) 0 0
\(396\) 1.09807 + 0.0167487i 0.0551799 + 0.000841653i
\(397\) 13.5583 + 2.14742i 0.680471 + 0.107776i 0.487096 0.873349i \(-0.338056\pi\)
0.193376 + 0.981125i \(0.438056\pi\)
\(398\) −4.72043 + 9.26436i −0.236614 + 0.464381i
\(399\) −0.907703 + 0.453812i −0.0454420 + 0.0227190i
\(400\) 0 0
\(401\) 8.63025i 0.430974i 0.976507 + 0.215487i \(0.0691339\pi\)
−0.976507 + 0.215487i \(0.930866\pi\)
\(402\) −0.175045 + 22.9538i −0.00873046 + 1.14483i
\(403\) −1.20033 + 7.57858i −0.0597926 + 0.377516i
\(404\) −0.293139 + 0.212978i −0.0145842 + 0.0105961i
\(405\) 0 0
\(406\) 0.371060 + 0.269591i 0.0184154 + 0.0133796i
\(407\) −2.48049 + 2.48049i −0.122953 + 0.122953i
\(408\) 5.91798 + 8.27741i 0.292984 + 0.409793i
\(409\) 25.9908 + 8.44492i 1.28516 + 0.417574i 0.870395 0.492353i \(-0.163863\pi\)
0.414767 + 0.909928i \(0.363863\pi\)
\(410\) 0 0
\(411\) 10.5753 + 10.7379i 0.521642 + 0.529660i
\(412\) −7.06941 + 3.60205i −0.348285 + 0.177460i
\(413\) 8.45731 4.30921i 0.416157 0.212043i
\(414\) −6.59212 + 19.2827i −0.323985 + 0.947694i
\(415\) 0 0
\(416\) 2.49304 + 0.810037i 0.122231 + 0.0397154i
\(417\) 4.31216 3.08300i 0.211167 0.150975i
\(418\) −0.150514 + 0.150514i −0.00736189 + 0.00736189i
\(419\) 20.8362 + 15.1384i 1.01791 + 0.739557i 0.965854 0.259087i \(-0.0834215\pi\)
0.0520594 + 0.998644i \(0.483421\pi\)
\(420\) 0 0
\(421\) 28.5994 20.7787i 1.39385 1.01269i 0.398419 0.917203i \(-0.369559\pi\)
0.995431 0.0954876i \(-0.0304410\pi\)
\(422\) −0.571828 + 3.61038i −0.0278362 + 0.175751i
\(423\) −10.9171 22.2588i −0.530806 1.08226i
\(424\) 8.83548i 0.429089i
\(425\) 0 0
\(426\) −0.996037 1.99225i −0.0482582 0.0965246i
\(427\) 0.496375 0.974191i 0.0240213 0.0471444i
\(428\) −12.6675 2.00633i −0.612306 0.0969797i
\(429\) −1.47509 0.765821i −0.0712181 0.0369742i
\(430\) 0 0
\(431\) −19.9752 + 27.4935i −0.962171 + 1.32432i −0.0162678 + 0.999868i \(0.505178\pi\)
−0.945904 + 0.324448i \(0.894822\pi\)
\(432\) 2.95726 + 4.27254i 0.142281 + 0.205563i
\(433\) 18.8393 2.98384i 0.905357 0.143394i 0.313641 0.949541i \(-0.398451\pi\)
0.591715 + 0.806147i \(0.298451\pi\)
\(434\) 0.911432 2.80510i 0.0437501 0.134649i
\(435\) 0 0
\(436\) 1.40916 + 4.33696i 0.0674867 + 0.207703i
\(437\) −1.79320 3.51936i −0.0857806 0.168354i
\(438\) −13.3010 9.81959i −0.635547 0.469198i
\(439\) −33.6517 + 10.9341i −1.60611 + 0.521856i −0.968607 0.248596i \(-0.920031\pi\)
−0.637499 + 0.770451i \(0.720031\pi\)
\(440\) 0 0
\(441\) −10.3304 14.6844i −0.491924 0.699259i
\(442\) −2.40904 15.2101i −0.114586 0.723470i
\(443\) 10.2497 + 10.2497i 0.486977 + 0.486977i 0.907351 0.420374i \(-0.138101\pi\)
−0.420374 + 0.907351i \(0.638101\pi\)
\(444\) −16.3734 2.72144i −0.777046 0.129154i
\(445\) 0 0
\(446\) 1.24289 + 1.71069i 0.0588524 + 0.0810034i
\(447\) 9.67320 3.06166i 0.457526 0.144811i
\(448\) −0.897796 0.457450i −0.0424169 0.0216125i
\(449\) −9.47944 −0.447362 −0.223681 0.974662i \(-0.571807\pi\)
−0.223681 + 0.974662i \(0.571807\pi\)
\(450\) 0 0
\(451\) 3.88431 0.182905
\(452\) 12.1221 + 6.17652i 0.570175 + 0.290519i
\(453\) 6.02689 1.90757i 0.283168 0.0896254i
\(454\) 9.10358 + 12.5300i 0.427252 + 0.588062i
\(455\) 0 0
\(456\) −0.993521 0.165134i −0.0465259 0.00773312i
\(457\) −25.4852 25.4852i −1.19215 1.19215i −0.976464 0.215682i \(-0.930803\pi\)
−0.215682 0.976464i \(-0.569197\pi\)
\(458\) 0.258516 + 1.63221i 0.0120797 + 0.0762681i
\(459\) 14.4771 26.8748i 0.675734 1.25441i
\(460\) 0 0
\(461\) 21.4340 6.96431i 0.998279 0.324360i 0.236101 0.971728i \(-0.424130\pi\)
0.762178 + 0.647368i \(0.224130\pi\)
\(462\) 0.513982 + 0.379451i 0.0239126 + 0.0176537i
\(463\) −2.57463 5.05300i −0.119653 0.234833i 0.823409 0.567448i \(-0.192069\pi\)
−0.943063 + 0.332615i \(0.892069\pi\)
\(464\) 0.140660 + 0.432908i 0.00652999 + 0.0200972i
\(465\) 0 0
\(466\) 5.39691 16.6100i 0.250007 0.769442i
\(467\) −11.4802 + 1.81829i −0.531242 + 0.0841404i −0.416292 0.909231i \(-0.636671\pi\)
−0.114950 + 0.993371i \(0.536671\pi\)
\(468\) −1.11160 7.78505i −0.0513838 0.359864i
\(469\) −7.84913 + 10.8034i −0.362439 + 0.498854i
\(470\) 0 0
\(471\) 4.94583 + 2.56772i 0.227892 + 0.118314i
\(472\) 9.30410 + 1.47363i 0.428256 + 0.0678291i
\(473\) −1.68871 + 3.31427i −0.0776467 + 0.152390i
\(474\) −9.45238 18.9064i −0.434162 0.868399i
\(475\) 0 0
\(476\) 5.91951i 0.271320i
\(477\) −23.7982 + 11.6721i −1.08964 + 0.534428i
\(478\) 0.999482 6.31048i 0.0457152 0.288635i
\(479\) 2.20406 1.60135i 0.100706 0.0731673i −0.536293 0.844032i \(-0.680176\pi\)
0.636999 + 0.770865i \(0.280176\pi\)
\(480\) 0 0
\(481\) 20.3224 + 14.7651i 0.926622 + 0.673230i
\(482\) 13.6039 13.6039i 0.619639 0.619639i
\(483\) −9.64386 + 6.89493i −0.438811 + 0.313730i
\(484\) −10.3342 3.35778i −0.469735 0.152626i
\(485\) 0 0
\(486\) 7.60133 13.6095i 0.344803 0.617342i
\(487\) 24.1563 12.3082i 1.09462 0.557739i 0.189068 0.981964i \(-0.439453\pi\)
0.905557 + 0.424225i \(0.139453\pi\)
\(488\) 0.966824 0.492622i 0.0437661 0.0222999i
\(489\) 4.49543 + 4.56452i 0.203290 + 0.206415i
\(490\) 0 0
\(491\) 37.5268 + 12.1932i 1.69356 + 0.550271i 0.987464 0.157846i \(-0.0504550\pi\)
0.706095 + 0.708117i \(0.250455\pi\)
\(492\) 10.6891 + 14.9507i 0.481901 + 0.674029i
\(493\) 1.89088 1.89088i 0.0851609 0.0851609i
\(494\) 1.23315 + 0.895933i 0.0554819 + 0.0403099i
\(495\) 0 0
\(496\) 2.36811 1.72054i 0.106331 0.0772543i
\(497\) 0.202702 1.27981i 0.00909245 0.0574075i
\(498\) 0.0125329 1.64345i 0.000561613 0.0736446i
\(499\) 11.3155i 0.506552i 0.967394 + 0.253276i \(0.0815081\pi\)
−0.967394 + 0.253276i \(0.918492\pi\)
\(500\) 0 0
\(501\) −14.1550 + 7.07690i −0.632400 + 0.316173i
\(502\) 4.62384 9.07480i 0.206372 0.405028i
\(503\) −8.50269 1.34669i −0.379116 0.0600461i −0.0360317 0.999351i \(-0.511472\pi\)
−0.343084 + 0.939305i \(0.611472\pi\)
\(504\) −0.0461019 + 3.02251i −0.00205354 + 0.134633i
\(505\) 0 0
\(506\) −1.46159 + 2.01171i −0.0649756 + 0.0894312i
\(507\) 3.35712 10.0702i 0.149095 0.447233i
\(508\) 19.4805 3.08541i 0.864307 0.136893i
\(509\) 0.697725 2.14738i 0.0309261 0.0951808i −0.934402 0.356220i \(-0.884065\pi\)
0.965328 + 0.261039i \(0.0840653\pi\)
\(510\) 0 0
\(511\) −2.97215 9.14735i −0.131480 0.404655i
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) 0.867702 + 2.89418i 0.0383100 + 0.127781i
\(514\) −2.18980 + 0.711508i −0.0965878 + 0.0313833i
\(515\) 0 0
\(516\) −17.4037 + 2.62059i −0.766154 + 0.115365i
\(517\) −0.473237 2.98790i −0.0208129 0.131408i
\(518\) −6.82773 6.82773i −0.299993 0.299993i
\(519\) −2.61727 + 15.7466i −0.114885 + 0.691201i
\(520\) 0 0
\(521\) −13.0319 17.9369i −0.570938 0.785829i 0.421727 0.906723i \(-0.361424\pi\)
−0.992665 + 0.120894i \(0.961424\pi\)
\(522\) 0.980210 0.950757i 0.0429026 0.0416135i
\(523\) 9.99457 + 5.09249i 0.437032 + 0.222679i 0.658642 0.752456i \(-0.271131\pi\)
−0.221610 + 0.975135i \(0.571131\pi\)
\(524\) −10.8376 −0.473444
\(525\) 0 0
\(526\) −16.8239 −0.733558
\(527\) −15.3220 7.80694i −0.667436 0.340076i
\(528\) 0.191326 + 0.604487i 0.00832639 + 0.0263069i
\(529\) −13.6026 18.7224i −0.591417 0.814016i
\(530\) 0 0
\(531\) −8.32197 27.0071i −0.361143 1.17201i
\(532\) −0.414301 0.414301i −0.0179622 0.0179622i
\(533\) −4.35122 27.4725i −0.188472 1.18997i
\(534\) 0.522762 + 3.47174i 0.0226221 + 0.150237i
\(535\) 0 0
\(536\) −12.6041 + 4.09532i −0.544415 + 0.176891i
\(537\) −13.9005 + 18.8287i −0.599849 + 0.812518i
\(538\) 2.72359 + 5.34536i 0.117423 + 0.230455i
\(539\) −0.676991 2.08356i −0.0291601 0.0897455i
\(540\) 0 0
\(541\) 3.02125 9.29846i 0.129894 0.399772i −0.864867 0.502001i \(-0.832597\pi\)
0.994761 + 0.102229i \(0.0325974\pi\)
\(542\) −12.2372 + 1.93818i −0.525632 + 0.0832520i
\(543\) −26.6012 8.86807i −1.14156 0.380565i
\(544\) −3.45309 + 4.75277i −0.148050 + 0.203773i
\(545\) 0 0
\(546\) 2.10798 4.06029i 0.0902131 0.173765i
\(547\) −10.4482 1.65483i −0.446732 0.0707555i −0.0709846 0.997477i \(-0.522614\pi\)
−0.375748 + 0.926722i \(0.622614\pi\)
\(548\) −3.95032 + 7.75294i −0.168749 + 0.331189i
\(549\) −2.60409 1.95335i −0.111140 0.0833668i
\(550\) 0 0
\(551\) 0.264681i 0.0112758i
\(552\) −11.7651 0.0897208i −0.500757 0.00381877i
\(553\) 1.92364 12.1454i 0.0818016 0.516475i
\(554\) −4.99204 + 3.62693i −0.212092 + 0.154094i
\(555\) 0 0
\(556\) 2.47598 + 1.79891i 0.105005 + 0.0762906i
\(557\) 2.23937 2.23937i 0.0948850 0.0948850i −0.658071 0.752956i \(-0.728627\pi\)
0.752956 + 0.658071i \(0.228627\pi\)
\(558\) −7.76262 4.10556i −0.328618 0.173802i
\(559\) 25.3325 + 8.23103i 1.07145 + 0.348135i
\(560\) 0 0
\(561\) 2.65387 2.61370i 0.112047 0.110351i
\(562\) 8.01507 4.08388i 0.338095 0.172268i
\(563\) −9.06485 + 4.61877i −0.382038 + 0.194658i −0.634454 0.772961i \(-0.718775\pi\)
0.252416 + 0.967619i \(0.418775\pi\)
\(564\) 10.1981 10.0438i 0.429419 0.422919i
\(565\) 0 0
\(566\) 12.4664 + 4.05058i 0.524002 + 0.170259i
\(567\) 8.20197 3.86870i 0.344450 0.162470i
\(568\) 0.909316 0.909316i 0.0381541 0.0381541i
\(569\) −10.0063 7.26997i −0.419484 0.304773i 0.357946 0.933742i \(-0.383477\pi\)
−0.777430 + 0.628969i \(0.783477\pi\)
\(570\) 0 0
\(571\) 22.7821 16.5522i 0.953402 0.692687i 0.00179324 0.999998i \(-0.499429\pi\)
0.951609 + 0.307311i \(0.0994292\pi\)
\(572\) 0.150111 0.947765i 0.00627647 0.0396281i
\(573\) 26.7466 + 0.203969i 1.11735 + 0.00852093i
\(574\) 10.6918i 0.446269i
\(575\) 0 0
\(576\) −1.80017 + 2.39988i −0.0750069 + 0.0999948i
\(577\) 5.07813 9.96640i 0.211405 0.414907i −0.760817 0.648967i \(-0.775201\pi\)
0.972222 + 0.234060i \(0.0752013\pi\)
\(578\) 17.2971 + 2.73958i 0.719463 + 0.113952i
\(579\) 6.83274 13.1609i 0.283959 0.546949i
\(580\) 0 0
\(581\) 0.561983 0.773503i 0.0233150 0.0320903i
\(582\) −29.5919 9.86511i −1.22662 0.408922i
\(583\) −3.19454 + 0.505965i −0.132304 + 0.0209549i
\(584\) 2.94968 9.07817i 0.122059 0.375657i
\(585\) 0 0
\(586\) 4.16466 + 12.8175i 0.172041 + 0.529487i
\(587\) 0.272317 + 0.534451i 0.0112397 + 0.0220592i 0.896558 0.442926i \(-0.146060\pi\)
−0.885318 + 0.464985i \(0.846060\pi\)
\(588\) 6.15664 8.33941i 0.253896 0.343911i
\(589\) 1.61877 0.525971i 0.0667003 0.0216722i
\(590\) 0 0
\(591\) −1.63365 10.8493i −0.0671992 0.446279i
\(592\) −1.49909 9.46487i −0.0616122 0.389004i
\(593\) 1.69633 + 1.69633i 0.0696598 + 0.0696598i 0.741078 0.671419i \(-0.234315\pi\)
−0.671419 + 0.741078i \(0.734315\pi\)
\(594\) 1.37542 1.31389i 0.0564343 0.0539095i
\(595\) 0 0
\(596\) 3.44318 + 4.73913i 0.141038 + 0.194122i
\(597\) 5.43439 + 17.1697i 0.222415 + 0.702711i
\(598\) 15.8654 + 8.08385i 0.648786 + 0.330573i
\(599\) −12.0681 −0.493088 −0.246544 0.969132i \(-0.579295\pi\)
−0.246544 + 0.969132i \(0.579295\pi\)
\(600\) 0 0
\(601\) 8.03062 0.327576 0.163788 0.986496i \(-0.447629\pi\)
0.163788 + 0.986496i \(0.447629\pi\)
\(602\) −9.12277 4.64828i −0.371816 0.189450i
\(603\) 27.6813 + 28.5388i 1.12727 + 1.16219i
\(604\) 2.14528 + 2.95272i 0.0872900 + 0.120144i
\(605\) 0 0
\(606\) −0.102901 + 0.619098i −0.00418007 + 0.0251491i
\(607\) −27.1756 27.1756i −1.10302 1.10302i −0.994044 0.108980i \(-0.965242\pi\)
−0.108980 0.994044i \(-0.534758\pi\)
\(608\) −0.0909634 0.574320i −0.00368905 0.0232918i
\(609\) 0.785558 0.118287i 0.0318324 0.00479321i
\(610\) 0 0
\(611\) −20.6024 + 6.69412i −0.833483 + 0.270815i
\(612\) 17.3632 + 3.02220i 0.701865 + 0.122165i
\(613\) 13.2287 + 25.9627i 0.534300 + 1.04862i 0.987560 + 0.157245i \(0.0502612\pi\)
−0.453259 + 0.891379i \(0.649739\pi\)
\(614\) 5.86577 + 18.0530i 0.236723 + 0.728560i
\(615\) 0 0
\(616\) −0.113982 + 0.350801i −0.00459248 + 0.0141342i
\(617\) 18.9443 3.00048i 0.762667 0.120795i 0.237029 0.971503i \(-0.423826\pi\)
0.525639 + 0.850708i \(0.323826\pi\)
\(618\) −4.34618 + 13.0371i −0.174829 + 0.524427i
\(619\) −11.4117 + 15.7069i −0.458676 + 0.631314i −0.974234 0.225541i \(-0.927585\pi\)
0.515557 + 0.856855i \(0.327585\pi\)
\(620\) 0 0
\(621\) 15.3006 + 31.8077i 0.613993 + 1.27640i
\(622\) 21.1417 + 3.34851i 0.847704 + 0.134263i
\(623\) −0.927252 + 1.81984i −0.0371496 + 0.0729102i
\(624\) 4.06103 2.03034i 0.162571 0.0812786i
\(625\) 0 0
\(626\) 12.7716i 0.510454i
\(627\) −0.00281149 + 0.368672i −0.000112280 + 0.0147233i
\(628\) −0.503308 + 3.17776i −0.0200842 + 0.126806i
\(629\) −45.5451 + 33.0905i −1.81600 + 1.31940i
\(630\) 0 0
\(631\) 8.91070 + 6.47400i 0.354729 + 0.257726i 0.750850 0.660472i \(-0.229644\pi\)
−0.396121 + 0.918198i \(0.629644\pi\)
\(632\) 8.62939 8.62939i 0.343259 0.343259i
\(633\) 3.68228 + 5.15037i 0.146358 + 0.204709i
\(634\) 26.3725 + 8.56893i 1.04738 + 0.340316i
\(635\) 0 0
\(636\) −10.7384 10.9034i −0.425804 0.432348i
\(637\) −13.9780 + 7.12216i −0.553830 + 0.282190i
\(638\) 0.148466 0.0756474i 0.00587784 0.00299491i
\(639\) −3.65047 1.24798i −0.144411 0.0493692i
\(640\) 0 0
\(641\) −41.8679 13.6037i −1.65368 0.537314i −0.674148 0.738596i \(-0.735489\pi\)
−0.979533 + 0.201283i \(0.935489\pi\)
\(642\) −18.0707 + 12.9198i −0.713195 + 0.509902i
\(643\) 21.0709 21.0709i 0.830957 0.830957i −0.156691 0.987648i \(-0.550083\pi\)
0.987648 + 0.156691i \(0.0500826\pi\)
\(644\) −5.53736 4.02313i −0.218203 0.158534i
\(645\) 0 0
\(646\) −2.76364 + 2.00790i −0.108734 + 0.0789998i
\(647\) 5.07470 32.0404i 0.199507 1.25964i −0.661073 0.750322i \(-0.729899\pi\)
0.860580 0.509316i \(-0.170101\pi\)
\(648\) 8.84212 + 1.67836i 0.347351 + 0.0659324i
\(649\) 3.44836i 0.135360i
\(650\) 0 0
\(651\) −2.28448 4.56935i −0.0895358 0.179087i
\(652\) −1.67923 + 3.29567i −0.0657636 + 0.129068i
\(653\) −30.5859 4.84433i −1.19692 0.189573i −0.474012 0.880518i \(-0.657195\pi\)
−0.722907 + 0.690945i \(0.757195\pi\)
\(654\) 7.00998 + 3.63936i 0.274112 + 0.142310i
\(655\) 0 0
\(656\) −6.23698 + 8.58447i −0.243513 + 0.335167i
\(657\) −28.3485 + 4.04779i −1.10598 + 0.157919i
\(658\) 8.22441 1.30262i 0.320621 0.0507814i
\(659\) −6.85074 + 21.0844i −0.266867 + 0.821332i 0.724390 + 0.689390i \(0.242121\pi\)
−0.991257 + 0.131942i \(0.957879\pi\)
\(660\) 0 0
\(661\) −9.91334 30.5101i −0.385584 1.18671i −0.936056 0.351852i \(-0.885552\pi\)
0.550471 0.834854i \(-0.314448\pi\)
\(662\) 8.44742 + 16.5790i 0.328318 + 0.644361i
\(663\) −21.4588 15.8421i −0.833389 0.615257i
\(664\) 0.902431 0.293218i 0.0350211 0.0113790i
\(665\) 0 0
\(666\) −23.5131 + 16.5413i −0.911114 + 0.640963i
\(667\) 0.483694 + 3.05392i 0.0187287 + 0.118248i
\(668\) −6.46075 6.46075i −0.249974 0.249974i
\(669\) 3.61290 + 0.600505i 0.139683 + 0.0232169i
\(670\) 0 0
\(671\) −0.233477 0.321353i −0.00901327 0.0124057i
\(672\) −1.66389 + 0.526638i −0.0641861 + 0.0203155i
\(673\) −33.4118 17.0242i −1.28793 0.656234i −0.330204 0.943910i \(-0.607117\pi\)
−0.957728 + 0.287676i \(0.907117\pi\)
\(674\) 20.7536 0.799398
\(675\) 0 0
\(676\) 6.12860 0.235715
\(677\) −26.7784 13.6443i −1.02918 0.524391i −0.143966 0.989583i \(-0.545985\pi\)
−0.885210 + 0.465192i \(0.845985\pi\)
\(678\) 22.4660 7.11070i 0.862802 0.273085i
\(679\) −10.6662 14.6808i −0.409333 0.563399i
\(680\) 0 0
\(681\) 26.4628 + 4.39842i 1.01406 + 0.168548i
\(682\) −0.757684 0.757684i −0.0290132 0.0290132i
\(683\) −5.21701 32.9389i −0.199623 1.26037i −0.860334 0.509731i \(-0.829745\pi\)
0.660711 0.750640i \(-0.270255\pi\)
\(684\) −1.42675 + 1.00371i −0.0545533 + 0.0383779i
\(685\) 0 0
\(686\) 12.4433 4.04307i 0.475087 0.154365i
\(687\) 2.30276 + 1.70003i 0.0878557 + 0.0648602i
\(688\) −4.61313 9.05378i −0.175874 0.345172i
\(689\) 7.15707 + 22.0272i 0.272663 + 0.839169i
\(690\) 0 0
\(691\) 0.495555 1.52516i 0.0188518 0.0580199i −0.941188 0.337883i \(-0.890289\pi\)
0.960040 + 0.279863i \(0.0902891\pi\)
\(692\) −9.10259 + 1.44171i −0.346028 + 0.0548055i
\(693\) 1.09545 0.156416i 0.0416128 0.00594175i
\(694\) −4.38081 + 6.02967i −0.166293 + 0.228883i
\(695\) 0 0
\(696\) 0.699725 + 0.363275i 0.0265230 + 0.0137699i
\(697\) 61.5694 + 9.75164i 2.33211 + 0.369370i
\(698\) −7.31117 + 14.3490i −0.276732 + 0.543117i
\(699\) −13.5272 27.0568i −0.511646 1.02338i
\(700\) 0 0
\(701\) 17.1529i 0.647855i 0.946082 + 0.323928i \(0.105003\pi\)
−0.946082 + 0.323928i \(0.894997\pi\)
\(702\) −10.8335 8.25612i −0.408883 0.311607i
\(703\) 0.871689 5.50363i 0.0328764 0.207573i
\(704\) −0.296153 + 0.215168i −0.0111617 + 0.00810943i
\(705\) 0 0
\(706\) 0.350143 + 0.254394i 0.0131778 + 0.00957423i
\(707\) −0.258165 + 0.258165i −0.00970931 + 0.00970931i
\(708\) 13.2727 9.48940i 0.498819 0.356633i
\(709\) −43.3999 14.1015i −1.62992 0.529592i −0.655664 0.755052i \(-0.727611\pi\)
−0.974252 + 0.225460i \(0.927611\pi\)
\(710\) 0 0
\(711\) −34.6429 11.8433i −1.29921 0.444157i
\(712\) −1.80607 + 0.920240i −0.0676855 + 0.0344875i
\(713\) 17.7164 9.02694i 0.663483 0.338062i
\(714\) 7.19440 + 7.30497i 0.269244 + 0.273382i
\(715\) 0 0
\(716\) −12.8509 4.17551i −0.480261 0.156046i
\(717\) −6.43616 9.00218i −0.240363 0.336193i
\(718\) 0.156397 0.156397i 0.00583669 0.00583669i
\(719\) 18.8277 + 13.6791i 0.702155 + 0.510145i 0.880633 0.473798i \(-0.157117\pi\)
−0.178478 + 0.983944i \(0.557117\pi\)
\(720\) 0 0
\(721\) −6.46780 + 4.69913i −0.240874 + 0.175005i
\(722\) −2.91936 + 18.4321i −0.108647 + 0.685973i
\(723\) 0.254110 33.3215i 0.00945044 1.23924i
\(724\) 16.1891i 0.601664i
\(725\) 0 0
\(726\) −16.8338 + 8.41618i −0.624762 + 0.312354i
\(727\) −12.3793 + 24.2957i −0.459122 + 0.901077i 0.539144 + 0.842213i \(0.318748\pi\)
−0.998266 + 0.0588635i \(0.981252\pi\)
\(728\) 2.60879 + 0.413192i 0.0966882 + 0.0153139i
\(729\) −7.16021 26.0333i −0.265193 0.964195i
\(730\) 0 0
\(731\) −35.0879 + 48.2943i −1.29777 + 1.78623i
\(732\) 0.594391 1.78297i 0.0219693 0.0659004i
\(733\) −5.78324 + 0.915975i −0.213609 + 0.0338323i −0.262322 0.964981i \(-0.584488\pi\)
0.0487128 + 0.998813i \(0.484488\pi\)
\(734\) −5.16046 + 15.8823i −0.190476 + 0.586225i
\(735\) 0 0
\(736\) −2.09909 6.46034i −0.0773735 0.238131i
\(737\) 2.20247 + 4.32260i 0.0811292 + 0.159225i
\(738\) 31.3615 + 5.45871i 1.15443 + 0.200938i
\(739\) −10.9906 + 3.57105i −0.404295 + 0.131363i −0.504103 0.863643i \(-0.668177\pi\)
0.0998086 + 0.995007i \(0.468177\pi\)
\(740\) 0 0
\(741\) 2.61065 0.393103i 0.0959047 0.0144410i
\(742\) −1.39270 8.79319i −0.0511278 0.322808i
\(743\) 5.09866 + 5.09866i 0.187052 + 0.187052i 0.794420 0.607369i \(-0.207775\pi\)
−0.607369 + 0.794420i \(0.707775\pi\)
\(744\) 0.831282 5.00136i 0.0304763 0.183359i
\(745\) 0 0
\(746\) −0.0621022 0.0854763i −0.00227372 0.00312951i
\(747\) −1.98193 2.04333i −0.0725150 0.0747614i
\(748\) 1.91614 + 0.976324i 0.0700612 + 0.0356980i
\(749\) −12.9231 −0.472200
\(750\) 0 0
\(751\) −19.8804 −0.725445 −0.362723 0.931897i \(-0.618153\pi\)
−0.362723 + 0.931897i \(0.618153\pi\)
\(752\) 7.36324 + 3.75176i 0.268510 + 0.136813i
\(753\) −5.32319 16.8184i −0.193988 0.612897i
\(754\) −0.701343 0.965316i −0.0255414 0.0351547i
\(755\) 0 0
\(756\) 3.61657 + 3.78595i 0.131533 + 0.137694i
\(757\) −16.4335 16.4335i −0.597285 0.597285i 0.342304 0.939589i \(-0.388793\pi\)
−0.939589 + 0.342304i \(0.888793\pi\)
\(758\) 1.53973 + 9.72147i 0.0559255 + 0.353100i
\(759\) 0.641293 + 4.25892i 0.0232775 + 0.154589i
\(760\) 0 0
\(761\) −4.02479 + 1.30773i −0.145898 + 0.0474052i −0.381056 0.924552i \(-0.624439\pi\)
0.235157 + 0.971957i \(0.424439\pi\)
\(762\) 20.2900 27.4835i 0.735028 0.995624i
\(763\) 2.08604 + 4.09408i 0.0755197 + 0.148216i
\(764\) 4.77202 + 14.6868i 0.172646 + 0.531349i
\(765\) 0 0
\(766\) −10.2830 + 31.6480i −0.371542 + 1.14349i
\(767\) −24.3892 + 3.86287i −0.880642 + 0.139480i
\(768\) −1.64315 0.547779i −0.0592920 0.0197663i
\(769\) −4.46592 + 6.14681i −0.161045 + 0.221660i −0.881912 0.471414i \(-0.843744\pi\)
0.720867 + 0.693073i \(0.243744\pi\)
\(770\) 0 0
\(771\) −1.83757 + 3.53945i −0.0661785 + 0.127470i
\(772\) 8.45606 + 1.33931i 0.304340 + 0.0482028i
\(773\) 6.27822 12.3217i 0.225812 0.443181i −0.750106 0.661317i \(-0.769998\pi\)
0.975918 + 0.218136i \(0.0699977\pi\)
\(774\) −18.2920 + 24.3858i −0.657493 + 0.876531i
\(775\) 0 0
\(776\) 18.0093i 0.646495i
\(777\) −16.7240 0.127537i −0.599969 0.00457536i
\(778\) 5.23000 33.0209i 0.187505 1.18386i
\(779\) −4.99169 + 3.62668i −0.178846 + 0.129939i
\(780\) 0 0
\(781\) −0.380843 0.276698i −0.0136276 0.00990105i
\(782\) −28.2178 + 28.2178i −1.00907 + 1.00907i