Properties

Label 750.2.l.c.257.9
Level $750$
Weight $2$
Character 750.257
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 257.9
Character \(\chi\) \(=\) 750.257
Dual form 750.2.l.c.143.9

$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{17}{20}\right)\) \(-1\)

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 0.999724 0.0234972i \(-0.00748007\pi\)
−0.0234972 + 0.999724i \(0.507480\pi\)
\(8\) −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 0.520340 0.853959i \(-0.325805\pi\)
−0.0809806 + 0.996716i \(0.525805\pi\)
\(12\) −1.57112 0.729092i −0.453544 0.210471i
\(13\) 4.48435 + 2.28489i 1.24373 + 0.633714i 0.946996 0.321245i \(-0.104101\pi\)
0.296738 + 0.954959i \(0.404101\pi\)
\(14\) −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 −0.672870 0.739761i \(-0.734939\pi\)
0.868536 0.495626i \(-0.165061\pi\)
\(18\) −2.27139 1.95979i −0.535372 0.461927i
\(19\) 1.27450 + 1.75421i 0.292391 + 0.402442i 0.929789 0.368093i \(-0.119989\pi\)
−0.637398 + 0.770535i \(0.719989\pi\)
\(20\) 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 −0.930665 0.365873i \(-0.880770\pi\)
−0.251034 + 0.967978i \(0.580770\pi\)
\(24\) −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 −0.0768679 0.997041i \(-0.524492\pi\)
−0.971996 + 0.234997i \(0.924492\pi\)
\(30\) 0 0
\(31\) −5.95310 + 4.32518i −1.06921 + 0.776825i −0.975770 0.218800i \(-0.929786\pi\)
−0.0934378 + 0.995625i \(0.529786\pi\)
\(32\) 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 −0.404637 0.914477i \(-0.632602\pi\)
0.977667 0.210158i \(-0.0673979\pi\)
\(38\) −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 −0.0770993 0.997023i \(-0.524566\pi\)
0.523661 + 0.851927i \(0.324566\pi\)
\(42\) −6.28093 0.759414i −0.969168 0.117180i
\(43\) 3.24693 3.24693i 0.495151 0.495151i −0.414773 0.909925i \(-0.636139\pi\)
0.909925 + 0.414773i \(0.136139\pi\)
\(44\) −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 0.0524505 0.998624i \(-0.483297\pi\)
0.358475 + 0.933539i \(0.383297\pi\)
\(48\) 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 0.996300 0.0859487i \(-0.0273921\pi\)
−0.974097 + 0.226131i \(0.927392\pi\)
\(54\) 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 0.989367 + 0.145439i \(0.0464596\pi\)
−0.714928 + 0.699198i \(0.753540\pi\)
\(60\) 0 0
\(61\) 1.78395 5.49044i 0.228412 0.702979i −0.769516 0.638628i \(-0.779502\pi\)
0.997927 0.0643507i \(-0.0204976\pi\)
\(62\) −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 −0.0503493 0.998732i \(-0.516033\pi\)
−0.356510 + 0.934291i \(0.616033\pi\)
\(68\) 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 −0.918578 0.395241i \(-0.870661\pi\)
0.659752 + 0.751483i \(0.270661\pi\)
\(72\) 2.92059 0.685659i 0.344195 0.0808057i
\(73\) 0.270757 + 0.531390i 0.0316897 + 0.0621945i 0.906309 0.422617i \(-0.138888\pi\)
−0.874619 + 0.484811i \(0.838888\pi\)
\(74\) 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 −0.762745 0.646700i \(-0.776149\pi\)
0.850749 + 0.525572i \(0.176149\pi\)
\(80\) 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 0.304643 0.952467i \(-0.401463\pi\)
−0.00459575 + 0.999989i \(0.501463\pi\)
\(84\) −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 −0.788546 0.614976i \(-0.789166\pi\)
0.999421 0.0340306i \(-0.0108344\pi\)
\(90\) 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 0.819114 + 0.573630i \(0.194465\pi\)
−0.601763 + 0.798675i \(0.705535\pi\)
\(98\) −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 \(0.00232102\pi\)
−0.999973 + 0.00729163i \(0.997679\pi\)
\(102\) 4.34495 + 7.80443i 0.430214 + 0.772754i
\(103\) 15.4311 2.44405i 1.52047 0.240819i 0.660371 0.750939i \(-0.270399\pi\)
0.860103 + 0.510120i \(0.170399\pi\)
\(104\) −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 −0.787528 0.616279i \(-0.788639\pi\)
0.616279 + 0.787528i \(0.288639\pi\)
\(108\) 5.19046 + 0.243156i 0.499452 + 0.0233977i
\(109\) −7.65945 + 2.48870i −0.733642 + 0.238375i −0.651928 0.758281i \(-0.726039\pi\)
−0.0817142 + 0.996656i \(0.526039\pi\)
\(110\) 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 −0.534590 0.845112i \(-0.679534\pi\)
0.997934 0.0642521i \(-0.0204662\pi\)
\(114\) −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 0.470495 0.882403i \(-0.344075\pi\)
0.990429 + 0.138025i \(0.0440754\pi\)
\(128\) 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 0.318712 0.947852i \(-0.396750\pi\)
−0.999948 + 0.0102104i \(0.996750\pi\)
\(132\) −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 0.784159 0.620560i \(-0.213095\pi\)
−0.0411262 + 0.999154i \(0.513095\pi\)
\(138\) 4.63737 9.99308i 0.394760 0.850668i
\(139\) 4.61980 + 1.50106i 0.391846 + 0.127319i 0.498312 0.866998i \(-0.333953\pi\)
−0.106466 + 0.994316i \(0.533953\pi\)
\(140\) 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 0.966271 + 0.257528i \(0.0829078\pi\)
0.257528 + 0.966271i \(0.417092\pi\)
\(158\) 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 0.774335 0.632776i \(-0.218085\pi\)
−0.0567839 + 0.998386i \(0.518085\pi\)
\(164\) −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 0.211311 + 0.977419i \(0.432227\pi\)
−0.503008 + 0.864282i \(0.667773\pi\)
\(168\) 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 0.627869 0.778319i \(-0.283928\pi\)
0.998725 0.0504717i \(-0.0160725\pi\)
\(174\) 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 0.715697 0.698410i \(-0.246109\pi\)
−0.443065 + 0.896489i \(0.646109\pi\)
\(180\) 0 0
\(181\) −11.4405 + 8.31202i −0.850367 + 0.617828i −0.925247 0.379365i \(-0.876143\pi\)
0.0748802 + 0.997193i \(0.476143\pi\)
\(182\) −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 0.167456 0.985880i \(-0.446445\pi\)
0.714960 + 0.699165i \(0.246445\pi\)
\(192\) −0.207905 + 1.71953i −0.0150042 + 0.124096i
\(193\) −9.89879 + 9.89879i −0.712531 + 0.712531i −0.967064 0.254533i \(-0.918078\pi\)
0.254533 + 0.967064i \(0.418078\pi\)
\(194\) −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 −0.391284 0.920270i \(-0.627969\pi\)
−0.0877545 + 0.996142i \(0.527969\pi\)
\(198\) −2.38195 3.93122i −0.169278 0.279380i
\(199\) 5.40490i 0.383143i −0.981479 0.191572i \(-0.938642\pi\)
0.981479 0.191572i \(-0.0613585\pi\)
\(200\) 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 −0.717685 0.696368i \(-0.754798\pi\)
0.989934 0.141529i \(-0.0452017\pi\)
\(212\) −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 −0.650236 0.759732i \(-0.725330\pi\)
−0.232437 0.972611i \(-0.574670\pi\)
\(224\) 3.65271 0.244057
\(225\) 0 0
\(226\) 10.8492 0.721675
\(227\) −1.79400 3.52093i −0.119072 0.233692i 0.823776 0.566916i \(-0.191864\pi\)
−0.942848 + 0.333224i \(0.891864\pi\)
\(228\) −0.723425 3.68530i −0.0479100 0.244065i
\(229\) −7.75981 + 10.6805i −0.512783 + 0.705785i −0.984386 0.176026i \(-0.943676\pi\)
0.471603 + 0.881811i \(0.343676\pi\)
\(230\) 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 −0.133733 0.991017i \(-0.542697\pi\)
−0.433429 + 0.901188i \(0.642697\pi\)
\(234\) −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 −0.562305 0.826930i \(-0.690085\pi\)
0.940971 0.338486i \(-0.109915\pi\)
\(240\) 0 0
\(241\) −7.26464 22.3583i −0.467957 1.44022i −0.855226 0.518256i \(-0.826582\pi\)
0.387269 0.921967i \(-0.373418\pi\)
\(242\) 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 \(0.141752\pi\)
−0.902470 + 0.430752i \(0.858248\pi\)
\(252\) 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 −0.104006 0.994577i \(-0.533166\pi\)
0.994577 + 0.104006i \(0.0331660\pi\)
\(258\) −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 0.542343 + 0.840157i \(0.317537\pi\)
−0.998483 + 0.0550670i \(0.982463\pi\)
\(264\) 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 −0.823668 0.567073i \(-0.808076\pi\)
0.284791 + 0.958590i \(0.408076\pi\)
\(270\) 0 0
\(271\) −2.71650 1.97365i −0.165016 0.119891i 0.502213 0.864744i \(-0.332519\pi\)
−0.667228 + 0.744853i \(0.732519\pi\)
\(272\) −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 −0.995366 0.0961574i \(-0.969345\pi\)
−0.507269 + 0.861788i \(0.669345\pi\)
\(278\) 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 0.821290 0.570510i \(-0.193255\pi\)
−0.796380 + 0.604796i \(0.793255\pi\)
\(282\) −3.36258 + 3.61933i −0.200239 + 0.215528i
\(283\) 1.44181 9.10320i 0.0857064 0.541129i −0.907054 0.421015i \(-0.861674\pi\)
0.992760 0.120114i \(-0.0383260\pi\)
\(284\) −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 0.646982 0.762505i \(-0.276031\pi\)
−0.762505 + 0.646982i \(0.776031\pi\)
\(294\) −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 0.287198 0.957871i \(-0.407276\pi\)
−0.957871 + 0.287198i \(0.907276\pi\)
\(308\) −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 0.213856 0.976865i \(-0.431398\pi\)
−0.401174 + 0.916002i \(0.631398\pi\)
\(312\) 3.66945 7.90730i 0.207742 0.447663i
\(313\) −7.56390 3.85400i −0.427537 0.217841i 0.226962 0.973904i \(-0.427121\pi\)
−0.654499 + 0.756063i \(0.727121\pi\)
\(314\) −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 0.905748 + 0.423817i \(0.139310\pi\)
−0.992384 + 0.123183i \(0.960690\pi\)
\(318\) −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 −0.891435 0.453149i \(-0.850301\pi\)
0.155502 + 0.987836i \(0.450301\pi\)
\(332\) −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 −0.299475 0.954104i \(-0.596811\pi\)
0.947913 0.318528i \(-0.103189\pi\)
\(338\) −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 −0.463768 0.885957i \(-0.653503\pi\)
−0.167293 + 0.985907i \(0.553503\pi\)
\(348\) 5.88218 + 10.5656i 0.315318 + 0.566376i
\(349\) 25.4721i 1.36349i −0.731591 0.681744i \(-0.761222\pi\)
0.731591 0.681744i \(-0.238778\pi\)
\(350\) 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 0.996843 + 0.0794030i \(0.0253014\pi\)
−0.923517 + 0.383558i \(0.874699\pi\)
\(354\) −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 0.991284 0.131742i \(-0.0420571\pi\)
−0.879402 + 0.476080i \(0.842057\pi\)
\(360\) 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 −0.238038 0.971256i \(-0.576504\pi\)
−0.526522 + 0.850162i \(0.676504\pi\)
\(368\) 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 0.999976 0.00685847i \(-0.00218314\pi\)
−0.593320 + 0.804967i \(0.702183\pi\)
\(374\) 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 −0.714494 0.699642i \(-0.753343\pi\)
0.886190 + 0.463323i \(0.153343\pi\)
\(380\) 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 −0.667289 0.744799i \(-0.732545\pi\)
−0.864785 + 0.502143i \(0.832545\pi\)
\(384\) −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 −0.940194 0.340639i \(-0.889357\pi\)
0.960856 + 0.277050i \(0.0893567\pi\)
\(390\) 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 0.992172 + 0.124876i \(0.0398532\pi\)
−0.905023 + 0.425362i \(0.860147\pi\)
\(398\) 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 \(0.409816\pi\)
−0.279545 + 0.960132i \(0.590184\pi\)
\(402\) 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 −0.563817 0.825900i \(-0.690668\pi\)
0.0293144 + 0.999570i \(0.490668\pi\)
\(410\) 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 −0.483996 0.875070i \(-0.660815\pi\)
0.682678 + 0.730719i \(0.260815\pi\)
\(420\) 0 0
\(421\) −7.36850 5.35353i −0.359119 0.260915i 0.393566 0.919296i \(-0.371241\pi\)
−0.752684 + 0.658382i \(0.771241\pi\)
\(422\) 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 0.999946 + 0.0103868i \(0.00330628\pi\)
−0.299122 + 0.954215i \(0.596694\pi\)
\(432\) −3.24759 + 4.05625i −0.156250 + 0.195156i
\(433\) 3.46945 21.9052i 0.166731 1.05270i −0.752388 0.658720i \(-0.771098\pi\)
0.919119 0.393979i \(-0.128902\pi\)
\(434\) −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 0.270089 0.962835i \(-0.412947\pi\)
−0.347434 + 0.937704i \(0.612947\pi\)
\(440\) 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 0.723844 0.689964i \(-0.242374\pi\)
−0.689964 + 0.723844i \(0.742374\pi\)
\(444\) −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 −0.976718 0.214529i \(-0.931178\pi\)
−0.214529 0.976718i \(-0.568822\pi\)
\(458\) −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 −0.648699 0.761045i \(-0.724686\pi\)
−0.972140 + 0.234403i \(0.924686\pi\)
\(462\) −8.79295 4.08044i −0.409085 0.189839i
\(463\) −5.89566 3.00399i −0.273994 0.139607i 0.311595 0.950215i \(-0.399137\pi\)
−0.585589 + 0.810608i \(0.699137\pi\)
\(464\) −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 −0.325043 0.945699i \(-0.605379\pi\)
0.601371 0.798970i \(-0.294621\pi\)
\(468\) 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 0.781785 0.623549i \(-0.214310\pi\)
−0.351445 + 0.936208i \(0.614310\pi\)
\(480\) 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 0.163470 + 0.986548i \(0.447731\pi\)
−0.894219 + 0.447629i \(0.852269\pi\)
\(488\) −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 −0.380043 0.924969i \(-0.624091\pi\)
0.236222 + 0.971699i \(0.424091\pi\)
\(492\) −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 \(0.0182772\pi\)
−0.998352 + 0.0573880i \(0.981723\pi\)
\(500\) 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 −0.985049 0.172275i \(-0.944888\pi\)
0.883601 0.468240i \(-0.155112\pi\)
\(504\) 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 0.994397 0.105712i \(-0.0337122\pi\)
−0.866620 + 0.498969i \(0.833712\pi\)
\(510\) 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 −0.153308 0.988179i \(-0.548993\pi\)
0.987188 0.159560i \(-0.0510075\pi\)
\(522\) 4.78706 + 20.3907i 0.209524 + 0.892476i
\(523\) 10.0842 + 19.7913i 0.440950 + 0.865413i 0.999357 + 0.0358458i \(0.0114125\pi\)
−0.558408 + 0.829567i \(0.688587\pi\)
\(524\) 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 0.938590 0.345036i \(-0.112133\pi\)
−0.962142 + 0.272549i \(0.912133\pi\)
\(542\) 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 −0.993424 0.114497i \(-0.963474\pi\)
0.909420 0.415878i \(-0.136526\pi\)
\(548\) −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 −0.986531 0.163573i \(-0.947698\pi\)
0.163573 + 0.986531i \(0.447698\pi\)
\(558\) 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 0.514125 + 0.857716i \(0.328117\pi\)
−0.996101 + 0.0882171i \(0.971883\pi\)
\(564\) −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 0.0675439 0.997716i \(-0.478484\pi\)
0.969757 + 0.244073i \(0.0784837\pi\)
\(570\) 0 0
\(571\) −8.91080 6.47408i −0.372905 0.270932i 0.385509 0.922704i \(-0.374026\pi\)
−0.758415 + 0.651772i \(0.774026\pi\)
\(572\) −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 −0.380530 0.924768i \(-0.624259\pi\)
0.524483 + 0.851421i \(0.324259\pi\)
\(578\) −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 0.998441 + 0.0558204i \(0.0177774\pi\)
0.632028 + 0.774945i \(0.282223\pi\)
\(588\) 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 0.896843 0.442348i \(-0.145855\pi\)
−0.442348 + 0.896843i \(0.645855\pi\)
\(594\) 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 0.353030 0.935612i \(-0.385152\pi\)
−0.935612 + 0.353030i \(0.885152\pi\)
\(608\) 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 0.880048 0.474885i \(-0.157510\pi\)
0.133089 + 0.991104i \(0.457510\pi\)
\(614\) 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 0.801713 + 0.597709i \(0.203922\pi\)
−0.947177 + 0.320712i \(0.896078\pi\)
\(618\) −18.4187 + 19.8250i −0.740909 + 0.797479i
\(619\) −5.12654 7.05608i −0.206053 0.283608i 0.693466 0.720489i \(-0.256083\pi\)
−0.899519 + 0.436882i \(0.856083\pi\)
\(620\) 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 −0.102063 0.994778i \(-0.532544\pi\)
0.914551 + 0.404471i \(0.132544\pi\)
\(632\) −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 0.354054 0.935225i \(-0.384803\pi\)
0.836147 + 0.548505i \(0.184803\pi\)
\(642\) 0.520834 4.30769i 0.0205557 0.170011i
\(643\) 11.3185 11.3185i 0.446357 0.446357i −0.447785 0.894142i \(-0.647787\pi\)
0.894142 + 0.447785i \(0.147787\pi\)
\(644\) 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 0.482491 0.875901i \(-0.339732\pi\)
0.729545 + 0.683933i \(0.239732\pi\)
\(648\) −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 0.982245 0.187601i \(-0.0600712\pi\)
−0.992143 + 0.125111i \(0.960071\pi\)
\(654\) 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 0.975958 0.217960i \(-0.0699403\pi\)
−0.917680 + 0.397320i \(0.869940\pi\)
\(660\) 0 0
\(661\) −14.5577 + 44.8040i −0.566229 + 1.74267i 0.0980414 + 0.995182i \(0.468742\pi\)
−0.664271 + 0.747492i \(0.731258\pi\)
\(662\) −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 −0.998974 0.0452767i \(-0.985583\pi\)
0.550553 0.834800i \(-0.314417\pi\)
\(674\) 26.2203 1.00997
\(675\) 0 0
\(676\) −12.3301 −0.474234
\(677\) −8.38373 16.4540i −0.322213 0.632379i 0.671910 0.740633i \(-0.265474\pi\)
−0.994123 + 0.108254i \(0.965474\pi\)
\(678\) 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 −0.163353 0.986568i \(-0.552231\pi\)
−0.460224 + 0.887803i \(0.652231\pi\)
\(684\) 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 −0.921658 0.388003i \(-0.873165\pi\)
0.517574 0.855638i \(-0.326835\pi\)
\(692\) −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 \(-0.909295\pi\)
0.959674 0.281116i \(-0.0907045\pi\)
\(702\) 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 −0.924314 0.381632i \(-0.875362\pi\)
−0.523468 + 0.852045i \(0.675362\pi\)
\(710\) 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 −0.869606 0.493746i \(-0.835627\pi\)
0.200858 + 0.979620i \(0.435627\pi\)
\(720\) 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 −0.118172 0.992993i \(-0.537704\pi\)
0.733888 + 0.679270i \(0.237704\pi\)
\(728\) −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 −0.980622 0.195911i \(-0.937234\pi\)
0.993166 + 0.116707i \(0.0372338\pi\)
\(734\) −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 −0.199528 0.979892i \(-0.563941\pi\)
−0.737388 + 0.675470i \(0.763941\pi\)
\(740\) 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 0.989903 + 0.141749i \(0.0452727\pi\)
0.141749 + 0.989903i \(0.454727\pi\)
\(744\) 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 0.753615 0.657316i \(-0.228308\pi\)
−0.657316 + 0.753615i \(0.728308\pi\)
\(758\) 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 −0.468452 0.883489i \(-0.655188\pi\)
−0.898287 + 0.439409i \(0.855188\pi\)
\(762\) −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 0.982179 0.187950i \(-0.0601843\pi\)
−0.482261 + 0.876028i \(0.660184\pi\)
\(770\) 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 −0.967859 0.251495i \(-0.919078\pi\)
−0.365429 + 0.930839i \(0.619078\pi\)
\(774\) −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 + 23.1943i −0.829428 +