Properties

Label 750.2.l.c.143.9
Level $750$
Weight $2$
Character 750.143
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 143.9
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.c.257.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.453990 - 0.891007i) q^{2} +(0.333634 - 1.69961i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.36290 - 1.06888i) q^{6} +(2.58285 - 2.58285i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.77738 - 1.13410i) q^{9} +O(q^{10})\) \(q+(0.453990 - 0.891007i) q^{2} +(0.333634 - 1.69961i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.36290 - 1.06888i) q^{6} +(2.58285 - 2.58285i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.77738 - 1.13410i) q^{9} +(1.45719 - 0.473470i) q^{11} +(-1.57112 + 0.729092i) q^{12} +(4.48435 - 2.28489i) q^{13} +(-1.12875 - 3.47393i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.806752 + 5.09363i) q^{17} +(-2.27139 + 1.95979i) q^{18} +(1.27450 - 1.75421i) q^{19} +(-3.52813 - 5.25158i) q^{21} +(0.239686 - 1.51332i) q^{22} +(-5.66723 - 2.88760i) q^{23} +(-0.0636485 + 1.73088i) q^{24} -5.03290i q^{26} +(-2.85416 + 4.34209i) q^{27} +(-3.60774 - 0.571409i) q^{28} +(-5.64831 + 4.10373i) q^{29} +(-5.95310 - 4.32518i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.318547 - 2.63463i) q^{33} +(4.90472 + 1.59364i) q^{34} +(0.714995 + 2.91355i) q^{36} +(3.48561 + 6.84089i) q^{37} +(-0.984395 - 1.93198i) q^{38} +(-2.38730 - 8.38398i) q^{39} +(2.85939 + 0.929072i) q^{41} +(-6.28093 + 0.759414i) q^{42} +(3.24693 + 3.24693i) q^{43} +(-1.23956 - 0.900593i) q^{44} +(-5.14573 + 3.73859i) q^{46} +(2.81716 + 0.446195i) q^{47} +(1.51333 + 0.842515i) q^{48} -6.34226i q^{49} +(8.92637 + 0.328243i) q^{51} +(-4.48435 - 2.28489i) q^{52} +(0.161639 - 1.02055i) q^{53} +(2.57307 + 4.51434i) q^{54} +(-2.14701 + 2.95510i) q^{56} +(-2.55625 - 2.75143i) q^{57} +(1.09218 + 6.89573i) q^{58} +(2.10801 - 6.48779i) q^{59} +(1.78395 + 5.49044i) q^{61} +(-6.55641 + 3.34066i) q^{62} +(-10.1028 + 4.24434i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-2.49209 - 0.912268i) q^{66} +(-3.33029 + 0.527466i) q^{67} +(3.64664 - 3.64664i) q^{68} +(-6.79858 + 8.66870i) q^{69} +(-2.18090 - 3.00175i) q^{71} +(2.92059 + 0.685659i) q^{72} +(0.270757 - 0.531390i) q^{73} +7.67771 q^{74} -2.16832 q^{76} +(2.54081 - 4.98661i) q^{77} +(-8.55399 - 1.67915i) q^{78} +(0.782199 + 1.07660i) q^{79} +(6.42764 + 6.29964i) q^{81} +(2.12595 - 2.12595i) q^{82} +(2.73356 - 0.432953i) q^{83} +(-2.17484 + 5.94112i) q^{84} +(4.36710 - 1.41896i) q^{86} +(5.09030 + 10.9691i) q^{87} +(-1.36518 + 0.695596i) q^{88} +(1.98939 + 6.12272i) q^{89} +(5.68088 - 17.4839i) q^{91} +(0.994998 + 6.28217i) q^{92} +(-9.33729 + 8.67494i) q^{93} +(1.67653 - 2.30754i) q^{94} +(1.43772 - 0.965894i) q^{96} +(2.14067 - 13.5156i) q^{97} +(-5.65100 - 2.87933i) q^{98} +(-4.58413 - 0.337594i) 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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.453990 0.891007i 0.321020 0.630037i
\(3\) 0.333634 1.69961i 0.192624 0.981273i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) −1.36290 1.06888i −0.556402 0.436368i
\(7\) 2.58285 2.58285i 0.976227 0.976227i −0.0234972 0.999724i \(-0.507480\pi\)
0.999724 + 0.0234972i \(0.00748007\pi\)
\(8\) −0.987688 + 0.156434i −0.349201 + 0.0553079i
\(9\) −2.77738 1.13410i −0.925792 0.378033i
\(10\) 0 0
\(11\) 1.45719 0.473470i 0.439360 0.142757i −0.0809806 0.996716i \(-0.525805\pi\)
0.520340 + 0.853959i \(0.325805\pi\)
\(12\) −1.57112 + 0.729092i −0.453544 + 0.210471i
\(13\) 4.48435 2.28489i 1.24373 0.633714i 0.296738 0.954959i \(-0.404101\pi\)
0.946996 + 0.321245i \(0.104101\pi\)
\(14\) −1.12875 3.47393i −0.301671 0.928447i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.806752 + 5.09363i 0.195666 + 1.23539i 0.868536 + 0.495626i \(0.165061\pi\)
−0.672870 + 0.739761i \(0.734939\pi\)
\(18\) −2.27139 + 1.95979i −0.535372 + 0.461927i
\(19\) 1.27450 1.75421i 0.292391 0.402442i −0.637398 0.770535i \(-0.719989\pi\)
0.929789 + 0.368093i \(0.119989\pi\)
\(20\) 0 0
\(21\) −3.52813 5.25158i −0.769900 1.14599i
\(22\) 0.239686 1.51332i 0.0511012 0.322640i
\(23\) −5.66723 2.88760i −1.18170 0.602105i −0.251034 0.967978i \(-0.580770\pi\)
−0.930665 + 0.365873i \(0.880770\pi\)
\(24\) −0.0636485 + 1.73088i −0.0129922 + 0.353315i
\(25\) 0 0
\(26\) 5.03290i 0.987033i
\(27\) −2.85416 + 4.34209i −0.549283 + 0.835636i
\(28\) −3.60774 0.571409i −0.681798 0.107986i
\(29\) −5.64831 + 4.10373i −1.04886 + 0.762044i −0.971996 0.234997i \(-0.924492\pi\)
−0.0768679 + 0.997041i \(0.524492\pi\)
\(30\) 0 0
\(31\) −5.95310 4.32518i −1.06921 0.776825i −0.0934378 0.995625i \(-0.529786\pi\)
−0.975770 + 0.218800i \(0.929786\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.318547 2.63463i −0.0554520 0.458630i
\(34\) 4.90472 + 1.59364i 0.841152 + 0.273307i
\(35\) 0 0
\(36\) 0.714995 + 2.91355i 0.119166 + 0.485592i
\(37\) 3.48561 + 6.84089i 0.573031 + 1.12464i 0.977667 + 0.210158i \(0.0673979\pi\)
−0.404637 + 0.914477i \(0.632602\pi\)
\(38\) −0.984395 1.93198i −0.159690 0.313409i
\(39\) −2.38730 8.38398i −0.382274 1.34251i
\(40\) 0 0
\(41\) 2.85939 + 0.929072i 0.446562 + 0.145097i 0.523661 0.851927i \(-0.324566\pi\)
−0.0770993 + 0.997023i \(0.524566\pi\)
\(42\) −6.28093 + 0.759414i −0.969168 + 0.117180i
\(43\) 3.24693 + 3.24693i 0.495151 + 0.495151i 0.909925 0.414773i \(-0.136139\pi\)
−0.414773 + 0.909925i \(0.636139\pi\)
\(44\) −1.23956 0.900593i −0.186871 0.135770i
\(45\) 0 0
\(46\) −5.14573 + 3.73859i −0.758697 + 0.551226i
\(47\) 2.81716 + 0.446195i 0.410925 + 0.0650842i 0.358475 0.933539i \(-0.383297\pi\)
0.0524505 + 0.998624i \(0.483297\pi\)
\(48\) 1.51333 + 0.842515i 0.218430 + 0.121607i
\(49\) 6.34226i 0.906037i
\(50\) 0 0
\(51\) 8.92637 + 0.328243i 1.24994 + 0.0459632i
\(52\) −4.48435 2.28489i −0.621867 0.316857i
\(53\) 0.161639 1.02055i 0.0222028 0.140183i −0.974097 0.226131i \(-0.927392\pi\)
0.996300 + 0.0859487i \(0.0273921\pi\)
\(54\) 2.57307 + 4.51434i 0.350151 + 0.614324i
\(55\) 0 0
\(56\) −2.14701 + 2.95510i −0.286906 + 0.394892i
\(57\) −2.55625 2.75143i −0.338584 0.364436i
\(58\) 1.09218 + 6.89573i 0.143410 + 0.905454i
\(59\) 2.10801 6.48779i 0.274439 0.844638i −0.714928 0.699198i \(-0.753540\pi\)
0.989367 0.145439i \(-0.0464596\pi\)
\(60\) 0 0
\(61\) 1.78395 + 5.49044i 0.228412 + 0.702979i 0.997927 + 0.0643507i \(0.0204976\pi\)
−0.769516 + 0.638628i \(0.779502\pi\)
\(62\) −6.55641 + 3.34066i −0.832665 + 0.424264i
\(63\) −10.1028 + 4.24434i −1.27283 + 0.534737i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) −2.49209 0.912268i −0.306755 0.112292i
\(67\) −3.33029 + 0.527466i −0.406859 + 0.0644402i −0.356510 0.934291i \(-0.616033\pi\)
−0.0503493 + 0.998732i \(0.516033\pi\)
\(68\) 3.64664 3.64664i 0.442220 0.442220i
\(69\) −6.79858 + 8.66870i −0.818453 + 1.04359i
\(70\) 0 0
\(71\) −2.18090 3.00175i −0.258825 0.356242i 0.659752 0.751483i \(-0.270661\pi\)
−0.918578 + 0.395241i \(0.870661\pi\)
\(72\) 2.92059 + 0.685659i 0.344195 + 0.0808057i
\(73\) 0.270757 0.531390i 0.0316897 0.0621945i −0.874619 0.484811i \(-0.838888\pi\)
0.906309 + 0.422617i \(0.138888\pi\)
\(74\) 7.67771 0.892516
\(75\) 0 0
\(76\) −2.16832 −0.248723
\(77\) 2.54081 4.98661i 0.289552 0.568277i
\(78\) −8.55399 1.67915i −0.968549 0.190126i
\(79\) 0.782199 + 1.07660i 0.0880042 + 0.121127i 0.850749 0.525572i \(-0.176149\pi\)
−0.762745 + 0.646700i \(0.776149\pi\)
\(80\) 0 0
\(81\) 6.42764 + 6.29964i 0.714182 + 0.699960i
\(82\) 2.12595 2.12595i 0.234771 0.234771i
\(83\) 2.73356 0.432953i 0.300047 0.0475228i −0.00459575 0.999989i \(-0.501463\pi\)
0.304643 + 0.952467i \(0.401463\pi\)
\(84\) −2.17484 + 5.94112i −0.237294 + 0.648229i
\(85\) 0 0
\(86\) 4.36710 1.41896i 0.470917 0.153010i
\(87\) 5.09030 + 10.9691i 0.545737 + 1.17601i
\(88\) −1.36518 + 0.695596i −0.145529 + 0.0741507i
\(89\) 1.98939 + 6.12272i 0.210875 + 0.649007i 0.999421 + 0.0340306i \(0.0108344\pi\)
−0.788546 + 0.614976i \(0.789166\pi\)
\(90\) 0 0
\(91\) 5.68088 17.4839i 0.595518 1.83282i
\(92\) 0.994998 + 6.28217i 0.103736 + 0.654961i
\(93\) −9.33729 + 8.67494i −0.968232 + 0.899549i
\(94\) 1.67653 2.30754i 0.172921 0.238005i
\(95\) 0 0
\(96\) 1.43772 0.965894i 0.146737 0.0985811i
\(97\) 2.14067 13.5156i 0.217352 1.37230i −0.601763 0.798675i \(-0.705535\pi\)
0.819114 0.573630i \(-0.194465\pi\)
\(98\) −5.65100 2.87933i −0.570837 0.290856i
\(99\) −4.58413 0.337594i −0.460722 0.0339295i
\(100\) 0 0
\(101\) 0.146560i 0.0145833i −0.999973 0.00729163i \(-0.997679\pi\)
0.999973 0.00729163i \(-0.00232102\pi\)
\(102\) 4.34495 7.80443i 0.430214 0.772754i
\(103\) 15.4311 + 2.44405i 1.52047 + 0.240819i 0.860103 0.510120i \(-0.170399\pi\)
0.660371 + 0.750939i \(0.270399\pi\)
\(104\) −4.07170 + 2.95827i −0.399263 + 0.290082i
\(105\) 0 0
\(106\) −0.835930 0.607339i −0.0811927 0.0589900i
\(107\) −1.77141 1.77141i −0.171249 0.171249i 0.616279 0.787528i \(-0.288639\pi\)
−0.787528 + 0.616279i \(0.788639\pi\)
\(108\) 5.19046 0.243156i 0.499452 0.0233977i
\(109\) −7.65945 2.48870i −0.733642 0.238375i −0.0817142 0.996656i \(-0.526039\pi\)
−0.651928 + 0.758281i \(0.726039\pi\)
\(110\) 0 0
\(111\) 12.7898 3.64183i 1.21395 0.345668i
\(112\) 1.65829 + 3.25458i 0.156694 + 0.307529i
\(113\) 4.92541 + 9.66667i 0.463344 + 0.909364i 0.997934 + 0.0642521i \(0.0204662\pi\)
−0.534590 + 0.845112i \(0.679534\pi\)
\(114\) −3.61206 + 1.02852i −0.338300 + 0.0963293i
\(115\) 0 0
\(116\) 6.63998 + 2.15746i 0.616507 + 0.200315i
\(117\) −15.0460 + 1.26030i −1.39100 + 0.116515i
\(118\) −4.82364 4.82364i −0.444052 0.444052i
\(119\) 15.2398 + 11.0724i 1.39703 + 1.01500i
\(120\) 0 0
\(121\) −6.99996 + 5.08577i −0.636360 + 0.462342i
\(122\) 5.70191 + 0.903094i 0.516227 + 0.0817623i
\(123\) 2.53305 4.54989i 0.228398 0.410250i
\(124\) 7.35843i 0.660807i
\(125\) 0 0
\(126\) −0.804822 + 10.9285i −0.0716992 + 0.973590i
\(127\) 16.4638 + 8.38871i 1.46092 + 0.744378i 0.990429 0.138025i \(-0.0440754\pi\)
0.470495 + 0.882403i \(0.344075\pi\)
\(128\) 0.156434 0.987688i 0.0138270 0.0873001i
\(129\) 6.60181 4.43523i 0.581257 0.390501i
\(130\) 0 0
\(131\) −7.79711 + 10.7318i −0.681236 + 0.937641i −0.999948 0.0102104i \(-0.996750\pi\)
0.318712 + 0.947852i \(0.396750\pi\)
\(132\) −1.94422 + 1.80631i −0.169223 + 0.157219i
\(133\) −1.23900 7.82271i −0.107435 0.678315i
\(134\) −1.04194 + 3.20677i −0.0900102 + 0.277023i
\(135\) 0 0
\(136\) −1.59364 4.90472i −0.136653 0.420576i
\(137\) 8.69698 4.43133i 0.743033 0.378594i −0.0411262 0.999154i \(-0.513095\pi\)
0.784159 + 0.620560i \(0.213095\pi\)
\(138\) 4.63737 + 9.99308i 0.394760 + 0.850668i
\(139\) 4.61980 1.50106i 0.391846 0.127319i −0.106466 0.994316i \(-0.533953\pi\)
0.498312 + 0.866998i \(0.333953\pi\)
\(140\) 0 0
\(141\) 1.69826 4.63922i 0.143019 0.390693i
\(142\) −3.66469 + 0.580430i −0.307534 + 0.0487086i
\(143\) 5.45272 5.45272i 0.455980 0.455980i
\(144\) 1.93685 2.29099i 0.161404 0.190915i
\(145\) 0 0
\(146\) −0.350551 0.482492i −0.0290118 0.0399313i
\(147\) −10.7794 2.11600i −0.889070 0.174524i
\(148\) 3.48561 6.84089i 0.286515 0.562318i
\(149\) −6.55688 −0.537160 −0.268580 0.963257i \(-0.586554\pi\)
−0.268580 + 0.963257i \(0.586554\pi\)
\(150\) 0 0
\(151\) 1.06618 0.0867647 0.0433824 0.999059i \(-0.486187\pi\)
0.0433824 + 0.999059i \(0.486187\pi\)
\(152\) −0.984395 + 1.93198i −0.0798450 + 0.156705i
\(153\) 3.53603 15.0619i 0.285871 1.21768i
\(154\) −3.28960 4.52775i −0.265084 0.364856i
\(155\) 0 0
\(156\) −5.37956 + 6.85934i −0.430710 + 0.549187i
\(157\) 15.3342 15.3342i 1.22380 1.22380i 0.257528 0.966271i \(-0.417092\pi\)
0.966271 0.257528i \(-0.0829078\pi\)
\(158\) 1.31437 0.208176i 0.104566 0.0165616i
\(159\) −1.68061 0.615212i −0.133281 0.0487895i
\(160\) 0 0
\(161\) −22.0958 + 7.17938i −1.74140 + 0.565814i
\(162\) 8.53111 2.86709i 0.670267 0.225260i
\(163\) 9.16108 4.66780i 0.717551 0.365610i −0.0567839 0.998386i \(-0.518085\pi\)
0.774335 + 0.632776i \(0.218085\pi\)
\(164\) −0.929072 2.85939i −0.0725483 0.223281i
\(165\) 0 0
\(166\) 0.855246 2.63218i 0.0663800 0.204297i
\(167\) −3.76955 23.8000i −0.291697 1.84170i −0.503008 0.864282i \(-0.667773\pi\)
0.211311 0.977419i \(-0.432227\pi\)
\(168\) 4.30622 + 4.63501i 0.332232 + 0.357598i
\(169\) 7.24745 9.97526i 0.557496 0.767327i
\(170\) 0 0
\(171\) −5.52922 + 3.42667i −0.422830 + 0.262044i
\(172\) 0.718323 4.53531i 0.0547716 0.345814i
\(173\) 21.3945 + 10.9010i 1.62659 + 0.828791i 0.998725 + 0.0504717i \(0.0160725\pi\)
0.627869 + 0.778319i \(0.283928\pi\)
\(174\) 12.0845 + 0.444374i 0.916122 + 0.0336879i
\(175\) 0 0
\(176\) 1.53218i 0.115492i
\(177\) −10.3234 5.74735i −0.775956 0.431997i
\(178\) 6.35855 + 1.00709i 0.476593 + 0.0754849i
\(179\) 3.64757 2.65012i 0.272632 0.198079i −0.443065 0.896489i \(-0.646109\pi\)
0.715697 + 0.698410i \(0.246109\pi\)
\(180\) 0 0
\(181\) −11.4405 8.31202i −0.850367 0.617828i 0.0748802 0.997193i \(-0.476143\pi\)
−0.925247 + 0.379365i \(0.876143\pi\)
\(182\) −12.9992 12.9992i −0.963568 0.963568i
\(183\) 9.92681 1.20023i 0.733811 0.0887236i
\(184\) 6.04917 + 1.96550i 0.445951 + 0.144898i
\(185\) 0 0
\(186\) 3.49039 + 12.2579i 0.255928 + 0.898795i
\(187\) 3.58727 + 7.04042i 0.262327 + 0.514846i
\(188\) −1.29491 2.54140i −0.0944409 0.185351i
\(189\) 3.84312 + 18.5869i 0.279546 + 1.35200i
\(190\) 0 0
\(191\) 12.1952 + 3.96247i 0.882416 + 0.286714i 0.714960 0.699165i \(-0.246445\pi\)
0.167456 + 0.985880i \(0.446445\pi\)
\(192\) −0.207905 1.71953i −0.0150042 0.124096i
\(193\) −9.89879 9.89879i −0.712531 0.712531i 0.254533 0.967064i \(-0.418078\pi\)
−0.967064 + 0.254533i \(0.918078\pi\)
\(194\) −11.0707 8.04332i −0.794828 0.577477i
\(195\) 0 0
\(196\) −5.13100 + 3.72789i −0.366500 + 0.266278i
\(197\) −6.72363 1.06492i −0.479039 0.0758723i −0.0877545 0.996142i \(-0.527969\pi\)
−0.391284 + 0.920270i \(0.627969\pi\)
\(198\) −2.38195 + 3.93122i −0.169278 + 0.279380i
\(199\) 5.40490i 0.383143i 0.981479 + 0.191572i \(0.0613585\pi\)
−0.981479 + 0.191572i \(0.938642\pi\)
\(200\) 0 0
\(201\) −0.214610 + 5.83618i −0.0151374 + 0.411653i
\(202\) −0.130586 0.0665368i −0.00918799 0.00468151i
\(203\) −3.98940 + 25.1881i −0.280001 + 1.76786i
\(204\) −4.98123 7.41452i −0.348756 0.519120i
\(205\) 0 0
\(206\) 9.18325 12.6397i 0.639827 0.880647i
\(207\) 12.4652 + 14.4471i 0.866391 + 1.00415i
\(208\) 0.787319 + 4.97094i 0.0545908 + 0.344673i
\(209\) 1.02663 3.15965i 0.0710137 0.218558i
\(210\) 0 0
\(211\) 3.95464 + 12.1711i 0.272249 + 0.837896i 0.989934 + 0.141529i \(0.0452017\pi\)
−0.717685 + 0.696368i \(0.754798\pi\)
\(212\) −0.920647 + 0.469093i −0.0632303 + 0.0322175i
\(213\) −5.82944 + 2.70520i −0.399427 + 0.185357i
\(214\) −2.38255 + 0.774136i −0.162868 + 0.0529189i
\(215\) 0 0
\(216\) 2.13977 4.73512i 0.145593 0.322184i
\(217\) −26.5473 + 4.20467i −1.80215 + 0.285432i
\(218\) −5.69477 + 5.69477i −0.385698 + 0.385698i
\(219\) −0.812824 0.637472i −0.0549256 0.0430763i
\(220\) 0 0
\(221\) 15.2561 + 20.9983i 1.02624 + 1.41250i
\(222\) 2.56155 13.0491i 0.171920 0.875802i
\(223\) −13.1811 + 25.8694i −0.882673 + 1.73234i −0.232437 + 0.972611i \(0.574670\pi\)
−0.650236 + 0.759732i \(0.725330\pi\)
\(224\) 3.65271 0.244057
\(225\) 0 0
\(226\) 10.8492 0.721675
\(227\) −1.79400 + 3.52093i −0.119072 + 0.233692i −0.942848 0.333224i \(-0.891864\pi\)
0.823776 + 0.566916i \(0.191864\pi\)
\(228\) −0.723425 + 3.68530i −0.0479100 + 0.244065i
\(229\) −7.75981 10.6805i −0.512783 0.705785i 0.471603 0.881811i \(-0.343676\pi\)
−0.984386 + 0.176026i \(0.943676\pi\)
\(230\) 0 0
\(231\) −7.62762 5.98209i −0.501860 0.393593i
\(232\) 4.93680 4.93680i 0.324117 0.324117i
\(233\) −8.65736 + 1.37119i −0.567163 + 0.0898297i −0.433429 0.901188i \(-0.642697\pi\)
−0.133733 + 0.991017i \(0.542697\pi\)
\(234\) −5.70781 + 13.9783i −0.373131 + 0.913787i
\(235\) 0 0
\(236\) −6.48779 + 2.10801i −0.422319 + 0.137220i
\(237\) 2.09078 0.970244i 0.135811 0.0630241i
\(238\) 16.7843 8.55203i 1.08796 0.554345i
\(239\) 5.85405 + 18.0169i 0.378667 + 1.16542i 0.940971 + 0.338486i \(0.109915\pi\)
−0.562305 + 0.826930i \(0.690085\pi\)
\(240\) 0 0
\(241\) −7.26464 + 22.3583i −0.467957 + 1.44022i 0.387269 + 0.921967i \(0.373418\pi\)
−0.855226 + 0.518256i \(0.826582\pi\)
\(242\) 1.35354 + 8.54590i 0.0870087 + 0.549351i
\(243\) 12.8514 8.82273i 0.824420 0.565978i
\(244\) 3.39328 4.67045i 0.217232 0.298995i
\(245\) 0 0
\(246\) −2.90400 4.32257i −0.185152 0.275597i
\(247\) 1.70716 10.7786i 0.108624 0.685824i
\(248\) 6.55641 + 3.34066i 0.416332 + 0.212132i
\(249\) 0.176156 4.79044i 0.0111634 0.303582i
\(250\) 0 0
\(251\) 13.6488i 0.861504i −0.902470 0.430752i \(-0.858248\pi\)
0.902470 0.430752i \(-0.141752\pi\)
\(252\) 9.37200 + 5.67855i 0.590381 + 0.357715i
\(253\) −9.62542 1.52452i −0.605145 0.0958455i
\(254\) 14.9488 10.8609i 0.937971 0.681476i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 14.2769 + 14.2769i 0.890571 + 0.890571i 0.994577 0.104006i \(-0.0331660\pi\)
−0.104006 + 0.994577i \(0.533166\pi\)
\(258\) −0.954666 7.89581i −0.0594349 0.491571i
\(259\) 26.6718 + 8.66620i 1.65731 + 0.538492i
\(260\) 0 0
\(261\) 20.3415 4.99188i 1.25911 0.308989i
\(262\) 6.02229 + 11.8194i 0.372058 + 0.730205i
\(263\) −7.39734 14.5181i −0.456139 0.895224i −0.998483 0.0550670i \(-0.982463\pi\)
0.542343 0.840157i \(-0.317537\pi\)
\(264\) 0.726772 + 2.55236i 0.0447297 + 0.157087i
\(265\) 0 0
\(266\) −7.53258 2.44748i −0.461852 0.150065i
\(267\) 11.0700 1.33845i 0.677472 0.0819118i
\(268\) 2.38422 + 2.38422i 0.145640 + 0.145640i
\(269\) −8.83824 6.42136i −0.538877 0.391517i 0.284791 0.958590i \(-0.408076\pi\)
−0.823668 + 0.567073i \(0.808076\pi\)
\(270\) 0 0
\(271\) −2.71650 + 1.97365i −0.165016 + 0.119891i −0.667228 0.744853i \(-0.732519\pi\)
0.502213 + 0.864744i \(0.332519\pi\)
\(272\) −5.09363 0.806752i −0.308847 0.0489165i
\(273\) −27.8206 15.4885i −1.68378 0.937409i
\(274\) 9.76085i 0.589674i
\(275\) 0 0
\(276\) 11.0092 + 0.404835i 0.662678 + 0.0243682i
\(277\) −25.0088 12.7426i −1.50263 0.765631i −0.507269 0.861788i \(-0.669345\pi\)
−0.995366 + 0.0961574i \(0.969345\pi\)
\(278\) 0.759888 4.79774i 0.0455750 0.287749i
\(279\) 11.6288 + 18.7640i 0.696198 + 1.12337i
\(280\) 0 0
\(281\) 0.417572 0.574739i 0.0249103 0.0342861i −0.796380 0.604796i \(-0.793255\pi\)
0.821290 + 0.570510i \(0.193255\pi\)
\(282\) −3.36258 3.61933i −0.200239 0.215528i
\(283\) 1.44181 + 9.10320i 0.0857064 + 0.541129i 0.992760 + 0.120114i \(0.0383260\pi\)
−0.907054 + 0.421015i \(0.861674\pi\)
\(284\) −1.14657 + 3.52877i −0.0680363 + 0.209394i
\(285\) 0 0
\(286\) −2.38293 7.33390i −0.140905 0.433662i
\(287\) 9.78504 4.98573i 0.577593 0.294298i
\(288\) −1.16197 2.76583i −0.0684699 0.162978i
\(289\) −9.12626 + 2.96530i −0.536839 + 0.174430i
\(290\) 0 0
\(291\) −22.2572 8.14759i −1.30474 0.477620i
\(292\) −0.589050 + 0.0932964i −0.0344716 + 0.00545976i
\(293\) −1.97743 + 1.97743i −0.115523 + 0.115523i −0.762505 0.646982i \(-0.776031\pi\)
0.646982 + 0.762505i \(0.276031\pi\)
\(294\) −6.77911 + 8.64387i −0.395366 + 0.504121i
\(295\) 0 0
\(296\) −4.51285 6.21140i −0.262304 0.361030i
\(297\) −2.10320 + 7.67862i −0.122040 + 0.445559i
\(298\) −2.97676 + 5.84222i −0.172439 + 0.338431i
\(299\) −32.0116 −1.85128
\(300\) 0 0
\(301\) 16.7727 0.966760
\(302\) 0.484037 0.949976i 0.0278532 0.0546650i
\(303\) −0.249095 0.0488974i −0.0143102 0.00280908i
\(304\) 1.27450 + 1.75421i 0.0730979 + 0.100611i
\(305\) 0 0
\(306\) −11.8149 9.98857i −0.675413 0.571008i
\(307\) −11.7511 + 11.7511i −0.670673 + 0.670673i −0.957871 0.287198i \(-0.907276\pi\)
0.287198 + 0.957871i \(0.407276\pi\)
\(308\) −5.52770 + 0.875502i −0.314970 + 0.0498864i
\(309\) 9.30230 25.4115i 0.529189 1.44561i
\(310\) 0 0
\(311\) −3.30339 + 1.07334i −0.187318 + 0.0608633i −0.401174 0.916002i \(-0.631398\pi\)
0.213856 + 0.976865i \(0.431398\pi\)
\(312\) 3.66945 + 7.90730i 0.207742 + 0.447663i
\(313\) −7.56390 + 3.85400i −0.427537 + 0.217841i −0.654499 0.756063i \(-0.727121\pi\)
0.226962 + 0.973904i \(0.427121\pi\)
\(314\) −6.70127 20.6244i −0.378175 1.16390i
\(315\) 0 0
\(316\) 0.411226 1.26562i 0.0231333 0.0711969i
\(317\) −1.54252 9.73906i −0.0866363 0.547000i −0.992384 0.123183i \(-0.960690\pi\)
0.905748 0.423817i \(-0.139310\pi\)
\(318\) −1.31114 + 1.21813i −0.0735249 + 0.0683093i
\(319\) −6.28766 + 8.65423i −0.352042 + 0.484544i
\(320\) 0 0
\(321\) −3.60172 + 2.41972i −0.201029 + 0.135055i
\(322\) −3.63443 + 22.9469i −0.202539 + 1.27878i
\(323\) 9.96348 + 5.07665i 0.554383 + 0.282472i
\(324\) 1.31844 8.90290i 0.0732469 0.494606i
\(325\) 0 0
\(326\) 10.2817i 0.569452i
\(327\) −6.78529 + 12.1878i −0.375227 + 0.673986i
\(328\) −2.96952 0.470327i −0.163965 0.0259694i
\(329\) 8.42877 6.12386i 0.464693 0.337619i
\(330\) 0 0
\(331\) −13.3891 9.72777i −0.735933 0.534687i 0.155502 0.987836i \(-0.450301\pi\)
−0.891435 + 0.453149i \(0.850301\pi\)
\(332\) −1.95701 1.95701i −0.107405 0.107405i
\(333\) −1.92260 22.9528i −0.105358 1.25780i
\(334\) −22.9173 7.44629i −1.25398 0.407443i
\(335\) 0 0
\(336\) 6.08480 1.73262i 0.331953 0.0945221i
\(337\) 11.9038 + 23.3624i 0.648439 + 1.27263i 0.947913 + 0.318528i \(0.103189\pi\)
−0.299475 + 0.954104i \(0.596811\pi\)
\(338\) −5.59775 10.9862i −0.304477 0.597570i
\(339\) 18.0729 5.14617i 0.981585 0.279502i
\(340\) 0 0
\(341\) −10.7226 3.48400i −0.580663 0.188669i
\(342\) 0.542974 + 6.48225i 0.0293607 + 0.350520i
\(343\) 1.69884 + 1.69884i 0.0917290 + 0.0917290i
\(344\) −3.71488 2.69902i −0.200293 0.145521i
\(345\) 0 0
\(346\) 19.4258 14.1137i 1.04434 0.758756i
\(347\) −11.7554 1.86187i −0.631061 0.0999502i −0.167293 0.985907i \(-0.553503\pi\)
−0.463768 + 0.885957i \(0.653503\pi\)
\(348\) 5.88218 10.5656i 0.315318 0.566376i
\(349\) 25.4721i 1.36349i 0.731591 + 0.681744i \(0.238778\pi\)
−0.731591 + 0.681744i \(0.761222\pi\)
\(350\) 0 0
\(351\) −2.87784 + 25.9929i −0.153608 + 1.38740i
\(352\) 1.36518 + 0.695596i 0.0727645 + 0.0370754i
\(353\) 1.37767 8.69825i 0.0733258 0.462961i −0.923517 0.383558i \(-0.874699\pi\)
0.996843 0.0794030i \(-0.0253014\pi\)
\(354\) −9.80767 + 6.58900i −0.521272 + 0.350201i
\(355\) 0 0
\(356\) 3.78405 5.20829i 0.200554 0.276039i
\(357\) 23.9033 22.2077i 1.26510 1.17536i
\(358\) −0.705308 4.45314i −0.0372767 0.235356i
\(359\) 2.11987 6.52428i 0.111882 0.344338i −0.879402 0.476080i \(-0.842057\pi\)
0.991284 + 0.131742i \(0.0420571\pi\)
\(360\) 0 0
\(361\) 4.41845 + 13.5986i 0.232550 + 0.715715i
\(362\) −12.6000 + 6.42000i −0.662239 + 0.337428i
\(363\) 6.30841 + 13.5940i 0.331106 + 0.713500i
\(364\) −17.4839 + 5.68088i −0.916408 + 0.297759i
\(365\) 0 0
\(366\) 3.43727 9.38975i 0.179669 0.490810i
\(367\) −14.6468 + 2.31983i −0.764559 + 0.121094i −0.526522 0.850162i \(-0.676504\pi\)
−0.238038 + 0.971256i \(0.576504\pi\)
\(368\) 4.49754 4.49754i 0.234450 0.234450i
\(369\) −6.88794 5.82321i −0.358572 0.303144i
\(370\) 0 0
\(371\) −2.21843 3.05341i −0.115175 0.158525i
\(372\) 12.5065 + 2.45502i 0.648431 + 0.127287i
\(373\) 7.85384 15.4140i 0.406656 0.798108i −0.593320 0.804967i \(-0.702183\pi\)
0.999976 + 0.00685847i \(0.00218314\pi\)
\(374\) 7.90165 0.408584
\(375\) 0 0
\(376\) −2.85228 −0.147095
\(377\) −15.9524 + 31.3083i −0.821590 + 1.61246i
\(378\) 18.3058 + 5.01402i 0.941546 + 0.257893i
\(379\) 3.34257 + 4.60065i 0.171696 + 0.236319i 0.886190 0.463323i \(-0.153343\pi\)
−0.714494 + 0.699642i \(0.753343\pi\)
\(380\) 0 0
\(381\) 19.7505 25.1833i 1.01185 1.29018i
\(382\) 9.06711 9.06711i 0.463914 0.463914i
\(383\) −29.9833 + 4.74888i −1.53207 + 0.242657i −0.864785 0.502143i \(-0.832545\pi\)
−0.667289 + 0.744799i \(0.732545\pi\)
\(384\) −1.62650 0.595405i −0.0830018 0.0303841i
\(385\) 0 0
\(386\) −13.3138 + 4.32593i −0.677657 + 0.220184i
\(387\) −5.33560 12.7003i −0.271224 0.645591i
\(388\) −12.1926 + 6.21246i −0.618987 + 0.315390i
\(389\) 0.407506 + 1.25417i 0.0206613 + 0.0635891i 0.960856 0.277050i \(-0.0893567\pi\)
−0.940194 + 0.340639i \(0.889357\pi\)
\(390\) 0 0
\(391\) 10.1363 31.1963i 0.512615 1.57767i
\(392\) 0.992148 + 6.26418i 0.0501110 + 0.316389i
\(393\) 15.6385 + 16.8326i 0.788860 + 0.849091i
\(394\) −4.00131 + 5.50734i −0.201583 + 0.277456i
\(395\) 0 0
\(396\) 2.42136 + 3.90707i 0.121678 + 0.196338i
\(397\) 1.73643 10.9634i 0.0871491 0.550238i −0.905023 0.425362i \(-0.860147\pi\)
0.992172 0.124876i \(-0.0398532\pi\)
\(398\) 4.81580 + 2.45377i 0.241394 + 0.122997i
\(399\) −13.7090 0.504110i −0.686307 0.0252371i
\(400\) 0 0
\(401\) 38.4533i 1.92026i −0.279545 0.960132i \(-0.590184\pi\)
0.279545 0.960132i \(-0.409816\pi\)
\(402\) 5.10265 + 2.84079i 0.254497 + 0.141686i
\(403\) −36.5783 5.79343i −1.82209 0.288591i
\(404\) −0.118569 + 0.0861458i −0.00589905 + 0.00428591i
\(405\) 0 0
\(406\) 20.6316 + 14.9897i 1.02393 + 0.743928i
\(407\) 8.31815 + 8.31815i 0.412316 + 0.412316i
\(408\) −8.86782 + 1.07219i −0.439022 + 0.0530813i
\(409\) −10.8096 3.51227i −0.534502 0.173670i 0.0293144 0.999570i \(-0.490668\pi\)
−0.563817 + 0.825900i \(0.690668\pi\)
\(410\) 0 0
\(411\) −4.62994 16.2600i −0.228378 0.802044i
\(412\) −7.09291 13.9206i −0.349443 0.685820i
\(413\) −11.3123 22.2017i −0.556643 1.09247i
\(414\) 18.5316 4.54771i 0.910777 0.223508i
\(415\) 0 0
\(416\) 4.78657 + 1.55525i 0.234681 + 0.0762525i
\(417\) −1.00991 8.35269i −0.0494553 0.409033i
\(418\) −2.34919 2.34919i −0.114903 0.114903i
\(419\) 4.06691 + 2.95479i 0.198682 + 0.144351i 0.682678 0.730719i \(-0.260815\pi\)
−0.483996 + 0.875070i \(0.660815\pi\)
\(420\) 0 0
\(421\) −7.36850 + 5.35353i −0.359119 + 0.260915i −0.752684 0.658382i \(-0.771241\pi\)
0.393566 + 0.919296i \(0.371241\pi\)
\(422\) 12.6399 + 2.00197i 0.615303 + 0.0974544i
\(423\) −7.31829 4.43419i −0.355828 0.215598i
\(424\) 1.03327i 0.0501799i
\(425\) 0 0
\(426\) −0.236159 + 6.42221i −0.0114420 + 0.311157i
\(427\) 18.7887 + 9.57331i 0.909248 + 0.463285i
\(428\) −0.391893 + 2.47432i −0.0189429 + 0.119601i
\(429\) −7.44831 11.0867i −0.359608 0.535273i
\(430\) 0 0
\(431\) 14.5495 20.0257i 0.700824 0.964602i −0.299122 0.954215i \(-0.596694\pi\)
0.999946 0.0103868i \(-0.00330628\pi\)
\(432\) −3.24759 4.05625i −0.156250 0.195156i
\(433\) 3.46945 + 21.9052i 0.166731 + 1.05270i 0.919119 + 0.393979i \(0.128902\pi\)
−0.752388 + 0.658720i \(0.771098\pi\)
\(434\) −8.30582 + 25.5627i −0.398692 + 1.22705i
\(435\) 0 0
\(436\) 2.48870 + 7.65945i 0.119187 + 0.366821i
\(437\) −12.2883 + 6.26122i −0.587831 + 0.299515i
\(438\) −0.937006 + 0.434825i −0.0447719 + 0.0207768i
\(439\) −1.62057 + 0.526555i −0.0773456 + 0.0251311i −0.347434 0.937704i \(-0.612947\pi\)
0.270089 + 0.962835i \(0.412947\pi\)
\(440\) 0 0
\(441\) −7.19275 + 17.6148i −0.342512 + 0.838802i
\(442\) 25.6357 4.06030i 1.21937 0.193129i
\(443\) 0.713085 0.713085i 0.0338797 0.0338797i −0.689964 0.723844i \(-0.742374\pi\)
0.723844 + 0.689964i \(0.242374\pi\)
\(444\) −10.4640 8.20655i −0.496598 0.389465i
\(445\) 0 0
\(446\) 17.0657 + 23.4889i 0.808085 + 1.11223i
\(447\) −2.18760 + 11.1442i −0.103470 + 0.527101i
\(448\) 1.65829 3.25458i 0.0783470 0.153765i
\(449\) −12.4310 −0.586657 −0.293329 0.956012i \(-0.594763\pi\)
−0.293329 + 0.956012i \(0.594763\pi\)
\(450\) 0 0
\(451\) 4.60656 0.216915
\(452\) 4.92541 9.66667i 0.231672 0.454682i
\(453\) 0.355715 1.81210i 0.0167130 0.0851398i
\(454\) 2.32271 + 3.19694i 0.109010 + 0.150040i
\(455\) 0 0
\(456\) 2.95520 + 2.31767i 0.138390 + 0.108535i
\(457\) −25.4659 + 25.4659i −1.19125 + 1.19125i −0.214529 + 0.976718i \(0.568822\pi\)
−0.976718 + 0.214529i \(0.931178\pi\)
\(458\) −13.0392 + 2.06521i −0.609284 + 0.0965011i
\(459\) −24.4196 11.0350i −1.13981 0.515071i
\(460\) 0 0
\(461\) −34.8009 + 11.3075i −1.62084 + 0.526642i −0.972140 0.234403i \(-0.924686\pi\)
−0.648699 + 0.761045i \(0.724686\pi\)
\(462\) −8.79295 + 4.08044i −0.409085 + 0.189839i
\(463\) −5.89566 + 3.00399i −0.273994 + 0.139607i −0.585589 0.810608i \(-0.699137\pi\)
0.311595 + 0.950215i \(0.399137\pi\)
\(464\) −2.15746 6.63998i −0.100158 0.308253i
\(465\) 0 0
\(466\) −2.70862 + 8.33627i −0.125474 + 0.386170i
\(467\) 5.97151 + 37.7026i 0.276328 + 1.74467i 0.601371 + 0.798970i \(0.294621\pi\)
−0.325043 + 0.945699i \(0.605379\pi\)
\(468\) 9.86343 + 11.4317i 0.455937 + 0.528430i
\(469\) −7.23928 + 9.96401i −0.334279 + 0.460095i
\(470\) 0 0
\(471\) −20.9461 31.1781i −0.965147 1.43661i
\(472\) −1.06714 + 6.73768i −0.0491192 + 0.310127i
\(473\) 6.26871 + 3.19407i 0.288236 + 0.146863i
\(474\) 0.0847006 2.30338i 0.00389043 0.105798i
\(475\) 0 0
\(476\) 18.8375i 0.863413i
\(477\) −1.60633 + 2.65112i −0.0735488 + 0.121387i
\(478\) 18.7109 + 2.96351i 0.855815 + 0.135548i
\(479\) 9.41843 6.84289i 0.430339 0.312660i −0.351445 0.936208i \(-0.614310\pi\)
0.781785 + 0.623549i \(0.214310\pi\)
\(480\) 0 0
\(481\) 31.2614 + 22.7127i 1.42540 + 1.03561i
\(482\) 16.6233 + 16.6233i 0.757170 + 0.757170i
\(483\) 4.83024 + 39.9497i 0.219783 + 1.81777i
\(484\) 8.22894 + 2.67375i 0.374043 + 0.121534i
\(485\) 0 0
\(486\) −2.02668 15.4561i −0.0919320 0.701105i
\(487\) −16.1262 31.6495i −0.730750 1.43418i −0.894219 0.447629i \(-0.852269\pi\)
0.163470 0.986548i \(-0.447731\pi\)
\(488\) −2.62088 5.14377i −0.118642 0.232848i
\(489\) −4.87701 17.1276i −0.220546 0.774538i
\(490\) 0 0
\(491\) −3.18688 1.03548i −0.143822 0.0467305i 0.236222 0.971699i \(-0.424091\pi\)
−0.380043 + 0.924969i \(0.624091\pi\)
\(492\) −5.16983 + 0.625074i −0.233074 + 0.0281805i
\(493\) −25.4597 25.4597i −1.14665 1.14665i
\(494\) −8.82874 6.41446i −0.397224 0.288600i
\(495\) 0 0
\(496\) 5.95310 4.32518i 0.267302 0.194206i
\(497\) −13.3860 2.12014i −0.600446 0.0951012i
\(498\) −4.18834 2.33177i −0.187684 0.104489i
\(499\) 2.56390i 0.114776i −0.998352 0.0573880i \(-0.981723\pi\)
0.998352 0.0573880i \(-0.0182772\pi\)
\(500\) 0 0
\(501\) −41.7085 1.53372i −1.86340 0.0685214i
\(502\) −12.1612 6.19642i −0.542779 0.276560i
\(503\) −2.27523 + 14.3652i −0.101448 + 0.640515i 0.883601 + 0.468240i \(0.155112\pi\)
−0.985049 + 0.172275i \(0.944888\pi\)
\(504\) 9.31442 5.77251i 0.414897 0.257128i
\(505\) 0 0
\(506\) −5.72820 + 7.88419i −0.254650 + 0.350495i
\(507\) −14.5361 15.6460i −0.645570 0.694861i
\(508\) −2.89055 18.2502i −0.128248 0.809723i
\(509\) 2.88278 8.87228i 0.127777 0.393257i −0.866620 0.498969i \(-0.833712\pi\)
0.994397 + 0.105712i \(0.0337122\pi\)
\(510\) 0 0
\(511\) −0.673177 2.07183i −0.0297796 0.0916522i
\(512\) −0.891007 + 0.453990i −0.0393773 + 0.0200637i
\(513\) 3.97929 + 10.5408i 0.175690 + 0.465388i
\(514\) 19.2024 6.23925i 0.846983 0.275202i
\(515\) 0 0
\(516\) −7.46862 2.73401i −0.328788 0.120358i
\(517\) 4.31640 0.683651i 0.189835 0.0300669i
\(518\) 19.8304 19.8304i 0.871298 0.871298i
\(519\) 25.6655 32.7254i 1.12659 1.43649i
\(520\) 0 0
\(521\) 19.0337 + 26.1976i 0.833881 + 1.14774i 0.987188 + 0.159560i \(0.0510075\pi\)
−0.153308 + 0.988179i \(0.548993\pi\)
\(522\) 4.78706 20.3907i 0.209524 0.892476i
\(523\) 10.0842 19.7913i 0.440950 0.865413i −0.558408 0.829567i \(-0.688587\pi\)
0.999357 0.0358458i \(-0.0114125\pi\)
\(524\) 13.2652 0.579494
\(525\) 0 0
\(526\) −16.2940 −0.710454
\(527\) 17.2282 33.8122i 0.750471 1.47288i
\(528\) 2.60412 + 0.511188i 0.113330 + 0.0222466i
\(529\) 10.2602 + 14.1219i 0.446095 + 0.613997i
\(530\) 0 0
\(531\) −13.2125 + 15.6283i −0.573375 + 0.678212i
\(532\) −5.60044 + 5.60044i −0.242810 + 0.242810i
\(533\) 14.9453 2.36711i 0.647354 0.102531i
\(534\) 3.83310 10.4711i 0.165875 0.453128i
\(535\) 0 0
\(536\) 3.20677 1.04194i 0.138511 0.0450051i
\(537\) −3.28722 7.08363i −0.141854 0.305681i
\(538\) −9.73395 + 4.95969i −0.419660 + 0.213828i
\(539\) −3.00287 9.24188i −0.129343 0.398076i
\(540\) 0 0
\(541\) −0.547811 + 1.68599i −0.0235522 + 0.0724863i −0.962142 0.272549i \(-0.912133\pi\)
0.938590 + 0.345036i \(0.112133\pi\)
\(542\) 0.525272 + 3.31644i 0.0225624 + 0.142453i
\(543\) −17.9442 + 16.6713i −0.770058 + 0.715434i
\(544\) −3.03128 + 4.17220i −0.129965 + 0.178882i
\(545\) 0 0
\(546\) −26.4307 + 17.7567i −1.13113 + 0.759917i
\(547\) −1.96467 + 12.4044i −0.0840033 + 0.530376i 0.909420 + 0.415878i \(0.136526\pi\)
−0.993424 + 0.114497i \(0.963474\pi\)
\(548\) −8.69698 4.43133i −0.371517 0.189297i
\(549\) 1.27200 17.2722i 0.0542875 0.737159i
\(550\) 0 0
\(551\) 15.1385i 0.644922i
\(552\) 5.35879 9.62550i 0.228085 0.409689i
\(553\) 4.80101 + 0.760406i 0.204160 + 0.0323357i
\(554\) −22.7075 + 16.4980i −0.964751 + 0.700933i
\(555\) 0 0
\(556\) −3.92984 2.85519i −0.166662 0.121087i
\(557\) −19.4225 19.4225i −0.822959 0.822959i 0.163573 0.986531i \(-0.447698\pi\)
−0.986531 + 0.163573i \(0.947698\pi\)
\(558\) 21.9983 1.84265i 0.931260 0.0780054i
\(559\) 21.9792 + 7.14148i 0.929621 + 0.302052i
\(560\) 0 0
\(561\) 13.1628 3.74805i 0.555735 0.158243i
\(562\) −0.322522 0.632986i −0.0136048 0.0267009i
\(563\) −11.4362 22.4447i −0.481977 0.945933i −0.996101 0.0882171i \(-0.971883\pi\)
0.514125 0.857716i \(-0.328117\pi\)
\(564\) −4.75142 + 1.35295i −0.200071 + 0.0569693i
\(565\) 0 0
\(566\) 8.76558 + 2.84811i 0.368445 + 0.119715i
\(567\) 32.8727 0.330602i 1.38052 0.0138840i
\(568\) 2.62363 + 2.62363i 0.110085 + 0.110085i
\(569\) 24.7435 + 17.9772i 1.03730 + 0.753643i 0.969757 0.244073i \(-0.0784837\pi\)
0.0675439 + 0.997716i \(0.478484\pi\)
\(570\) 0 0
\(571\) −8.91080 + 6.47408i −0.372905 + 0.270932i −0.758415 0.651772i \(-0.774026\pi\)
0.385509 + 0.922704i \(0.374026\pi\)
\(572\) −7.61638 1.20632i −0.318457 0.0504386i
\(573\) 10.8034 19.4052i 0.451320 0.810663i
\(574\) 10.9820i 0.458380i
\(575\) 0 0
\(576\) −2.99190 0.220336i −0.124662 0.00918066i
\(577\) 3.45787 + 1.76187i 0.143953 + 0.0733478i 0.524483 0.851421i \(-0.324259\pi\)
−0.380530 + 0.924768i \(0.624259\pi\)
\(578\) −1.50113 + 9.47778i −0.0624389 + 0.394224i
\(579\) −20.1267 + 13.5216i −0.836437 + 0.561937i
\(580\) 0 0
\(581\) 5.94213 8.17864i 0.246521 0.339307i
\(582\) −17.3641 + 16.1324i −0.719765 + 0.668708i
\(583\) −0.247659 1.56366i −0.0102570 0.0647602i
\(584\) −0.184296 + 0.567203i −0.00762620 + 0.0234710i
\(585\) 0 0
\(586\) 0.864170 + 2.65964i 0.0356985 + 0.109869i
\(587\) 39.5031 20.1279i 1.63047 0.830766i 0.632028 0.774945i \(-0.282223\pi\)
0.998441 0.0558204i \(-0.0177774\pi\)
\(588\) 4.62409 + 9.96447i 0.190694 + 0.410928i
\(589\) −15.1745 + 4.93049i −0.625254 + 0.203157i
\(590\) 0 0
\(591\) −4.05318 + 11.0723i −0.166726 + 0.455453i
\(592\) −7.58319 + 1.20106i −0.311667 + 0.0493632i
\(593\) 11.0677 11.0677i 0.454495 0.454495i −0.442348 0.896843i \(-0.645855\pi\)
0.896843 + 0.442348i \(0.145855\pi\)
\(594\) 5.88686 + 5.35999i 0.241541 + 0.219923i
\(595\) 0 0
\(596\) 3.85404 + 5.30463i 0.157868 + 0.217286i
\(597\) 9.18625 + 1.80326i 0.375968 + 0.0738026i
\(598\) −14.5330 + 28.5226i −0.594298 + 1.16638i
\(599\) 39.0036 1.59364 0.796822 0.604215i \(-0.206513\pi\)
0.796822 + 0.604215i \(0.206513\pi\)
\(600\) 0 0
\(601\) −25.7471 −1.05025 −0.525123 0.851027i \(-0.675981\pi\)
−0.525123 + 0.851027i \(0.675981\pi\)
\(602\) 7.61463 14.9446i 0.310349 0.609094i
\(603\) 9.84766 + 2.31190i 0.401028 + 0.0941480i
\(604\) −0.626686 0.862560i −0.0254995 0.0350971i
\(605\) 0 0
\(606\) −0.156655 + 0.199747i −0.00636367 + 0.00811415i
\(607\) −14.3533 + 14.3533i −0.582583 + 0.582583i −0.935612 0.353030i \(-0.885152\pi\)
0.353030 + 0.935612i \(0.385152\pi\)
\(608\) 2.14162 0.339200i 0.0868542 0.0137564i
\(609\) 41.4790 + 15.1841i 1.68081 + 0.615289i
\(610\) 0 0
\(611\) 13.6526 4.43601i 0.552327 0.179462i
\(612\) −14.2637 + 5.99244i −0.576577 + 0.242230i
\(613\) 25.0841 12.7810i 1.01314 0.516219i 0.133089 0.991104i \(-0.457510\pi\)
0.880048 + 0.474885i \(0.157510\pi\)
\(614\) 5.13543 + 15.8052i 0.207249 + 0.637848i
\(615\) 0 0
\(616\) −1.72945 + 5.32269i −0.0696814 + 0.214457i
\(617\) −3.61324 22.8131i −0.145464 0.918421i −0.947177 0.320712i \(-0.896078\pi\)
0.801713 0.597709i \(-0.203922\pi\)
\(618\) −18.4187 19.8250i −0.740909 0.797479i
\(619\) −5.12654 + 7.05608i −0.206053 + 0.283608i −0.899519 0.436882i \(-0.856083\pi\)
0.693466 + 0.720489i \(0.256083\pi\)
\(620\) 0 0
\(621\) 28.7134 16.3660i 1.15223 0.656744i
\(622\) −0.543357 + 3.43062i −0.0217866 + 0.137555i
\(623\) 20.9524 + 10.6758i 0.839440 + 0.427716i
\(624\) 8.71135 + 0.320336i 0.348733 + 0.0128237i
\(625\) 0 0
\(626\) 8.48916i 0.339295i
\(627\) −5.02767 2.79905i −0.200786 0.111783i
\(628\) −21.4188 3.39240i −0.854702 0.135372i
\(629\) −32.0330 + 23.2733i −1.27724 + 0.927967i
\(630\) 0 0
\(631\) 20.4095 + 14.8283i 0.812488 + 0.590307i 0.914551 0.404471i \(-0.132544\pi\)
−0.102063 + 0.994778i \(0.532544\pi\)
\(632\) −0.940986 0.940986i −0.0374304 0.0374304i
\(633\) 22.0057 2.66066i 0.874646 0.105752i
\(634\) −9.37785 3.04705i −0.372442 0.121014i
\(635\) 0 0
\(636\) 0.490118 + 1.72125i 0.0194344 + 0.0682520i
\(637\) −14.4914 28.4409i −0.574169 1.12687i
\(638\) 4.85643 + 9.53128i 0.192268 + 0.377347i
\(639\) 2.65290 + 10.8104i 0.104947 + 0.427651i
\(640\) 0 0
\(641\) 30.1335 + 9.79096i 1.19020 + 0.386720i 0.836147 0.548505i \(-0.184803\pi\)
0.354054 + 0.935225i \(0.384803\pi\)
\(642\) 0.520834 + 4.30769i 0.0205557 + 0.170011i
\(643\) 11.3185 + 11.3185i 0.446357 + 0.446357i 0.894142 0.447785i \(-0.147787\pi\)
−0.447785 + 0.894142i \(0.647787\pi\)
\(644\) 18.7959 + 13.6560i 0.740660 + 0.538121i
\(645\) 0 0
\(646\) 9.04665 6.57278i 0.355936 0.258602i
\(647\) 30.8296 + 4.88293i 1.21204 + 0.191968i 0.729545 0.683933i \(-0.239732\pi\)
0.482491 + 0.875901i \(0.339732\pi\)
\(648\) −7.33398 5.21658i −0.288106 0.204926i
\(649\) 10.4520i 0.410278i
\(650\) 0 0
\(651\) −1.71075 + 46.5229i −0.0670498 + 1.82338i
\(652\) −9.16108 4.66780i −0.358775 0.182805i
\(653\) −0.252918 + 1.59686i −0.00989744 + 0.0624900i −0.992143 0.125111i \(-0.960071\pi\)
0.982245 + 0.187601i \(0.0600712\pi\)
\(654\) 7.77894 + 11.5789i 0.304181 + 0.452770i
\(655\) 0 0
\(656\) −1.76720 + 2.43234i −0.0689976 + 0.0949670i
\(657\) −1.35464 + 1.16880i −0.0528496 + 0.0455994i
\(658\) −1.62982 10.2903i −0.0635369 0.401156i
\(659\) 1.49604 4.60434i 0.0582774 0.179360i −0.917680 0.397320i \(-0.869940\pi\)
0.975958 + 0.217960i \(0.0699403\pi\)
\(660\) 0 0
\(661\) −14.5577 44.8040i −0.566229 1.74267i −0.664271 0.747492i \(-0.731258\pi\)
0.0980414 0.995182i \(-0.468742\pi\)
\(662\) −14.7460 + 7.51349i −0.573121 + 0.292020i
\(663\) 40.7789 18.9238i 1.58372 0.734940i
\(664\) −2.63218 + 0.855246i −0.102148 + 0.0331900i
\(665\) 0 0
\(666\) −21.3239 8.70729i −0.826284 0.337401i
\(667\) 43.8601 6.94676i 1.69827 0.268980i
\(668\) −17.0389 + 17.0389i −0.659256 + 0.659256i
\(669\) 39.5703 + 31.0337i 1.52988 + 1.19983i
\(670\) 0 0
\(671\) 5.19911 + 7.15597i 0.200710 + 0.276253i
\(672\) 1.21867 6.20819i 0.0470111 0.239486i
\(673\) −11.6331 + 22.8312i −0.448422 + 0.880077i 0.550553 + 0.834800i \(0.314417\pi\)
−0.998974 + 0.0452767i \(0.985583\pi\)
\(674\) 26.2203 1.00997
\(675\) 0 0
\(676\) −12.3301 −0.474234
\(677\) −8.38373 + 16.4540i −0.322213 + 0.632379i −0.994123 0.108254i \(-0.965474\pi\)
0.671910 + 0.740633i \(0.265474\pi\)
\(678\) 3.61965 18.4394i 0.139012 0.708160i
\(679\) −29.3799 40.4379i −1.12750 1.55187i
\(680\) 0 0
\(681\) 5.38568 + 4.22382i 0.206380 + 0.161857i
\(682\) −7.97224 + 7.97224i −0.305273 + 0.305273i
\(683\) −16.2967 + 2.58115i −0.623578 + 0.0987650i −0.460224 0.887803i \(-0.652231\pi\)
−0.163353 + 0.986568i \(0.552231\pi\)
\(684\) 6.02223 + 2.45909i 0.230266 + 0.0940255i
\(685\) 0 0
\(686\) 2.28494 0.742422i 0.0872394 0.0283458i
\(687\) −20.7416 + 9.62532i −0.791342 + 0.367229i
\(688\) −4.09136 + 2.08465i −0.155982 + 0.0794767i
\(689\) −1.60699 4.94581i −0.0612214 0.188420i
\(690\) 0 0
\(691\) −10.6221 + 32.6914i −0.404084 + 1.24364i 0.517574 + 0.855638i \(0.326835\pi\)
−0.921658 + 0.388003i \(0.873165\pi\)
\(692\) −3.75624 23.7160i −0.142791 0.901547i
\(693\) −12.7121 + 10.9682i −0.482892 + 0.416646i
\(694\) −6.99576 + 9.62884i −0.265555 + 0.365506i
\(695\) 0 0
\(696\) −6.74357 10.0377i −0.255614 0.380480i
\(697\) −2.42553 + 15.3142i −0.0918736 + 0.580067i
\(698\) 22.6958 + 11.5641i 0.859048 + 0.437707i
\(699\) −0.557896 + 15.1717i −0.0211016 + 0.573845i
\(700\) 0 0
\(701\) 14.8859i 0.562232i 0.959674 + 0.281116i \(0.0907045\pi\)
−0.959674 + 0.281116i \(0.909295\pi\)
\(702\) 21.8533 + 14.3647i 0.824801 + 0.542161i
\(703\) 16.4428 + 2.60428i 0.620150 + 0.0982222i
\(704\) 1.23956 0.900593i 0.0467177 0.0339424i
\(705\) 0 0
\(706\) −7.12475 5.17643i −0.268143 0.194818i
\(707\) −0.378543 0.378543i −0.0142366 0.0142366i
\(708\) 1.41825 + 11.7300i 0.0533013 + 0.440842i
\(709\) −38.5502 12.5257i −1.44778 0.470413i −0.523468 0.852045i \(-0.675362\pi\)
−0.924314 + 0.381632i \(0.875362\pi\)
\(710\) 0 0
\(711\) −0.951484 3.87723i −0.0356834 0.145407i
\(712\) −2.92270 5.73613i −0.109533 0.214970i
\(713\) 21.2482 + 41.7019i 0.795750 + 1.56175i
\(714\) −8.93533 31.3801i −0.334396 1.17437i
\(715\) 0 0
\(716\) −4.28798 1.39325i −0.160249 0.0520681i
\(717\) 32.5749 3.93856i 1.21653 0.147088i
\(718\) −4.85077 4.85077i −0.181029 0.181029i
\(719\) −17.9319 13.0283i −0.668748 0.485874i 0.200858 0.979620i \(-0.435627\pi\)
−0.869606 + 0.493746i \(0.835627\pi\)
\(720\) 0 0
\(721\) 46.1690 33.5437i 1.71942 1.24923i
\(722\) 14.1224 + 2.23676i 0.525580 + 0.0832437i
\(723\) 35.5767 + 19.8066i 1.32311 + 0.736614i
\(724\) 14.1413i 0.525556i
\(725\) 0 0
\(726\) 14.9763 + 0.550713i 0.555823 + 0.0204389i
\(727\) 16.6015 + 8.45889i 0.615716 + 0.313723i 0.733888 0.679270i \(-0.237704\pi\)
−0.118172 + 0.992993i \(0.537704\pi\)
\(728\) −2.87585 + 18.1574i −0.106586 + 0.672957i
\(729\) −10.7076 24.7860i −0.396576 0.918002i
\(730\) 0 0
\(731\) −13.9192 + 19.1581i −0.514819 + 0.708588i
\(732\) −6.80584 7.32548i −0.251551 0.270758i
\(733\) 0.339633 + 2.14436i 0.0125446 + 0.0792038i 0.993166 0.116707i \(-0.0372338\pi\)
−0.980622 + 0.195911i \(0.937234\pi\)
\(734\) −4.58254 + 14.1036i −0.169145 + 0.520574i
\(735\) 0 0
\(736\) −1.96550 6.04917i −0.0724491 0.222975i
\(737\) −4.60312 + 2.34541i −0.169558 + 0.0863942i
\(738\) −8.31558 + 3.49352i −0.306101 + 0.128598i
\(739\) −25.4696 + 8.27559i −0.936916 + 0.304423i −0.737388 0.675470i \(-0.763941\pi\)
−0.199528 + 0.979892i \(0.563941\pi\)
\(740\) 0 0
\(741\) −17.7498 6.49761i −0.652057 0.238696i
\(742\) −3.72775 + 0.590418i −0.136850 + 0.0216749i
\(743\) 30.8466 30.8466i 1.13165 1.13165i 0.141749 0.989903i \(-0.454727\pi\)
0.989903 0.141749i \(-0.0452727\pi\)
\(744\) 7.86527 10.0288i 0.288355 0.367674i
\(745\) 0 0
\(746\) −10.1684 13.9956i −0.372293 0.512417i
\(747\) −8.08314 1.89765i −0.295746 0.0694315i
\(748\) 3.58727 7.04042i 0.131164 0.257423i
\(749\) −9.15060 −0.334356
\(750\) 0 0
\(751\) 48.1007 1.75522 0.877610 0.479376i \(-0.159137\pi\)
0.877610 + 0.479376i \(0.159137\pi\)
\(752\) −1.29491 + 2.54140i −0.0472204 + 0.0926753i
\(753\) −23.1977 4.55370i −0.845370 0.165946i
\(754\) 20.6537 + 28.4274i 0.752163 + 1.03526i
\(755\) 0 0
\(756\) 12.7782 14.0342i 0.464737 0.510420i
\(757\) 2.64953 2.64953i 0.0962989 0.0962989i −0.657316 0.753615i \(-0.728308\pi\)
0.753615 + 0.657316i \(0.228308\pi\)
\(758\) 5.61670 0.889598i 0.204008 0.0323117i
\(759\) −5.80246 + 15.8509i −0.210616 + 0.575350i
\(760\) 0 0
\(761\) −37.7032 + 12.2505i −1.36674 + 0.444080i −0.898287 0.439409i \(-0.855188\pi\)
−0.468452 + 0.883489i \(0.655188\pi\)
\(762\) −13.4720 29.0308i −0.488038 1.05167i
\(763\) −26.2112 + 13.3553i −0.948909 + 0.483493i
\(764\) −3.96247 12.1952i −0.143357 0.441208i
\(765\) 0 0
\(766\) −9.38083 + 28.8712i −0.338943 + 1.04316i
\(767\) −5.37083 33.9101i −0.193929 1.22442i
\(768\) −1.26892 + 1.17891i −0.0457883 + 0.0425403i
\(769\) 13.8631 19.0810i 0.499918 0.688078i −0.482261 0.876028i \(-0.660184\pi\)
0.982179 + 0.187950i \(0.0601843\pi\)
\(770\) 0 0
\(771\) 29.0286 19.5020i 1.04544 0.702348i
\(772\) −2.18993 + 13.8267i −0.0788172 + 0.497632i
\(773\) −37.0692 18.8877i −1.33329 0.679344i −0.365429 0.930839i \(-0.619078\pi\)
−0.967859 + 0.251495i \(0.919078\pi\)
\(774\) −13.7383 1.01175i −0.493814 0.0363665i
\(775\) 0 0
\(776\) 13.6841i 0.491231i
\(777\) 23.6278 42.4405i 0.847644 1.52254i
\(778\) 1.30248 + 0.206293i 0.0466962 + 0.00739595i
\(779\) 5.27409 3.83185i 0.188964 0.137290i
\(780\) 0 0
\(781\) −4.59923 3.34153i −0.164573 0.119570i
\(782\) −23.1943