Properties

Label 300.2.x.a.77.10
Level $300$
Weight $2$
Character 300.77
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 77.10
Character \(\chi\) \(=\) 300.77
Dual form 300.2.x.a.113.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71709 + 0.227126i) q^{3} +(-0.0496546 + 2.23552i) q^{5} +(-2.02060 - 2.02060i) q^{7} +(2.89683 + 0.779992i) q^{9} +O(q^{10})\) \(q+(1.71709 + 0.227126i) q^{3} +(-0.0496546 + 2.23552i) q^{5} +(-2.02060 - 2.02060i) q^{7} +(2.89683 + 0.779992i) q^{9} +(2.82802 + 3.89243i) q^{11} +(5.74634 - 0.910130i) q^{13} +(-0.593005 + 3.82732i) q^{15} +(-1.36348 - 0.694729i) q^{17} +(-3.53381 + 1.14820i) q^{19} +(-3.01063 - 3.92848i) q^{21} +(-2.52651 - 0.400161i) q^{23} +(-4.99507 - 0.222007i) q^{25} +(4.79697 + 1.99726i) q^{27} +(-0.0334412 + 0.102921i) q^{29} +(-3.13145 - 9.63760i) q^{31} +(3.97190 + 7.32598i) q^{33} +(4.61741 - 4.41674i) q^{35} +(-0.418876 - 2.64468i) q^{37} +(10.0737 - 0.257640i) q^{39} +(-2.26109 + 3.11213i) q^{41} +(-1.86113 + 1.86113i) q^{43} +(-1.88753 + 6.43718i) q^{45} +(-4.48724 - 8.80670i) q^{47} +1.16562i q^{49} +(-2.18344 - 1.50260i) q^{51} +(9.81020 - 4.99855i) q^{53} +(-8.84201 + 6.12880i) q^{55} +(-6.32867 + 1.16896i) q^{57} +(-0.210836 - 0.153181i) q^{59} +(-4.36920 + 3.17441i) q^{61} +(-4.27727 - 7.42937i) q^{63} +(1.74928 + 12.8912i) q^{65} +(1.74449 - 3.42375i) q^{67} +(-4.24738 - 1.26095i) q^{69} +(-14.1996 - 4.61373i) q^{71} +(-0.320861 + 2.02584i) q^{73} +(-8.52658 - 1.51572i) q^{75} +(2.15075 - 13.5793i) q^{77} +(8.17124 + 2.65500i) q^{79} +(7.78322 + 4.51901i) q^{81} +(3.16454 - 6.21076i) q^{83} +(1.62078 - 3.01359i) q^{85} +(-0.0807978 + 0.169131i) q^{87} +(-3.84520 + 2.79370i) q^{89} +(-13.4500 - 9.77202i) q^{91} +(-3.18805 - 17.2599i) q^{93} +(-2.39136 - 7.95690i) q^{95} +(14.9764 - 7.63086i) q^{97} +(5.15621 + 13.4815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\)

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 0
\(3\) 1.71709 + 0.227126i 0.991365 + 0.131131i
\(4\) 0 0
\(5\) −0.0496546 + 2.23552i −0.0222062 + 0.999753i
\(6\) 0 0
\(7\) −2.02060 2.02060i −0.763714 0.763714i 0.213278 0.976992i \(-0.431586\pi\)
−0.976992 + 0.213278i \(0.931586\pi\)
\(8\) 0 0
\(9\) 2.89683 + 0.779992i 0.965609 + 0.259997i
\(10\) 0 0
\(11\) 2.82802 + 3.89243i 0.852679 + 1.17361i 0.983266 + 0.182175i \(0.0583137\pi\)
−0.130587 + 0.991437i \(0.541686\pi\)
\(12\) 0 0
\(13\) 5.74634 0.910130i 1.59375 0.252425i 0.704450 0.709754i \(-0.251194\pi\)
0.889297 + 0.457329i \(0.151194\pi\)
\(14\) 0 0
\(15\) −0.593005 + 3.82732i −0.153113 + 0.988209i
\(16\) 0 0
\(17\) −1.36348 0.694729i −0.330693 0.168497i 0.280758 0.959778i \(-0.409414\pi\)
−0.611451 + 0.791282i \(0.709414\pi\)
\(18\) 0 0
\(19\) −3.53381 + 1.14820i −0.810711 + 0.263416i −0.684899 0.728638i \(-0.740154\pi\)
−0.125812 + 0.992054i \(0.540154\pi\)
\(20\) 0 0
\(21\) −3.01063 3.92848i −0.656972 0.857265i
\(22\) 0 0
\(23\) −2.52651 0.400161i −0.526815 0.0834393i −0.112639 0.993636i \(-0.535930\pi\)
−0.414176 + 0.910197i \(0.635930\pi\)
\(24\) 0 0
\(25\) −4.99507 0.222007i −0.999014 0.0444015i
\(26\) 0 0
\(27\) 4.79697 + 1.99726i 0.923178 + 0.384374i
\(28\) 0 0
\(29\) −0.0334412 + 0.102921i −0.00620988 + 0.0191120i −0.954113 0.299445i \(-0.903198\pi\)
0.947904 + 0.318557i \(0.103198\pi\)
\(30\) 0 0
\(31\) −3.13145 9.63760i −0.562425 1.73096i −0.675482 0.737376i \(-0.736064\pi\)
0.113058 0.993588i \(-0.463936\pi\)
\(32\) 0 0
\(33\) 3.97190 + 7.32598i 0.691419 + 1.27529i
\(34\) 0 0
\(35\) 4.61741 4.41674i 0.780484 0.746566i
\(36\) 0 0
\(37\) −0.418876 2.64468i −0.0688628 0.434782i −0.997899 0.0647929i \(-0.979361\pi\)
0.929036 0.369989i \(-0.120639\pi\)
\(38\) 0 0
\(39\) 10.0737 0.257640i 1.61309 0.0412554i
\(40\) 0 0
\(41\) −2.26109 + 3.11213i −0.353123 + 0.486032i −0.948217 0.317624i \(-0.897115\pi\)
0.595093 + 0.803656i \(0.297115\pi\)
\(42\) 0 0
\(43\) −1.86113 + 1.86113i −0.283820 + 0.283820i −0.834631 0.550810i \(-0.814319\pi\)
0.550810 + 0.834631i \(0.314319\pi\)
\(44\) 0 0
\(45\) −1.88753 + 6.43718i −0.281376 + 0.959598i
\(46\) 0 0
\(47\) −4.48724 8.80670i −0.654531 1.28459i −0.944801 0.327644i \(-0.893745\pi\)
0.290271 0.956945i \(-0.406255\pi\)
\(48\) 0 0
\(49\) 1.16562i 0.166517i
\(50\) 0 0
\(51\) −2.18344 1.50260i −0.305742 0.210406i
\(52\) 0 0
\(53\) 9.81020 4.99855i 1.34754 0.686604i 0.376696 0.926337i \(-0.377060\pi\)
0.970839 + 0.239733i \(0.0770600\pi\)
\(54\) 0 0
\(55\) −8.84201 + 6.12880i −1.19226 + 0.826407i
\(56\) 0 0
\(57\) −6.32867 + 1.16896i −0.838253 + 0.154832i
\(58\) 0 0
\(59\) −0.210836 0.153181i −0.0274485 0.0199425i 0.573976 0.818872i \(-0.305400\pi\)
−0.601425 + 0.798929i \(0.705400\pi\)
\(60\) 0 0
\(61\) −4.36920 + 3.17441i −0.559418 + 0.406441i −0.831246 0.555905i \(-0.812372\pi\)
0.271828 + 0.962346i \(0.412372\pi\)
\(62\) 0 0
\(63\) −4.27727 7.42937i −0.538885 0.936012i
\(64\) 0 0
\(65\) 1.74928 + 12.8912i 0.216971 + 1.59896i
\(66\) 0 0
\(67\) 1.74449 3.42375i 0.213123 0.418278i −0.759552 0.650446i \(-0.774582\pi\)
0.972676 + 0.232168i \(0.0745819\pi\)
\(68\) 0 0
\(69\) −4.24738 1.26095i −0.511324 0.151801i
\(70\) 0 0
\(71\) −14.1996 4.61373i −1.68518 0.547549i −0.699277 0.714851i \(-0.746495\pi\)
−0.985906 + 0.167302i \(0.946495\pi\)
\(72\) 0 0
\(73\) −0.320861 + 2.02584i −0.0375539 + 0.237106i −0.999324 0.0367504i \(-0.988299\pi\)
0.961771 + 0.273857i \(0.0882993\pi\)
\(74\) 0 0
\(75\) −8.52658 1.51572i −0.984565 0.175020i
\(76\) 0 0
\(77\) 2.15075 13.5793i 0.245101 1.54751i
\(78\) 0 0
\(79\) 8.17124 + 2.65500i 0.919337 + 0.298711i 0.730195 0.683239i \(-0.239429\pi\)
0.189142 + 0.981950i \(0.439429\pi\)
\(80\) 0 0
\(81\) 7.78322 + 4.51901i 0.864803 + 0.502112i
\(82\) 0 0
\(83\) 3.16454 6.21076i 0.347353 0.681719i −0.649553 0.760316i \(-0.725044\pi\)
0.996906 + 0.0785968i \(0.0250440\pi\)
\(84\) 0 0
\(85\) 1.62078 3.01359i 0.175798 0.326870i
\(86\) 0 0
\(87\) −0.0807978 + 0.169131i −0.00866243 + 0.0181327i
\(88\) 0 0
\(89\) −3.84520 + 2.79370i −0.407590 + 0.296132i −0.772625 0.634862i \(-0.781057\pi\)
0.365035 + 0.930994i \(0.381057\pi\)
\(90\) 0 0
\(91\) −13.4500 9.77202i −1.40995 1.02439i
\(92\) 0 0
\(93\) −3.18805 17.2599i −0.330585 1.78977i
\(94\) 0 0
\(95\) −2.39136 7.95690i −0.245348 0.816361i
\(96\) 0 0
\(97\) 14.9764 7.63086i 1.52062 0.774797i 0.523606 0.851961i \(-0.324587\pi\)
0.997018 + 0.0771640i \(0.0245865\pi\)
\(98\) 0 0
\(99\) 5.15621 + 13.4815i 0.518219 + 1.35494i
\(100\) 0 0
\(101\) 17.3569i 1.72707i 0.504288 + 0.863536i \(0.331755\pi\)
−0.504288 + 0.863536i \(0.668245\pi\)
\(102\) 0 0
\(103\) −2.15137 4.22231i −0.211981 0.416036i 0.760393 0.649463i \(-0.225006\pi\)
−0.972374 + 0.233426i \(0.925006\pi\)
\(104\) 0 0
\(105\) 8.93168 6.53524i 0.871643 0.637774i
\(106\) 0 0
\(107\) −12.4265 + 12.4265i −1.20132 + 1.20132i −0.227550 + 0.973766i \(0.573072\pi\)
−0.973766 + 0.227550i \(0.926928\pi\)
\(108\) 0 0
\(109\) −10.0321 + 13.8080i −0.960904 + 1.32257i −0.0143943 + 0.999896i \(0.504582\pi\)
−0.946510 + 0.322675i \(0.895418\pi\)
\(110\) 0 0
\(111\) −0.118576 4.63630i −0.0112547 0.440058i
\(112\) 0 0
\(113\) 0.324731 + 2.05027i 0.0305481 + 0.192873i 0.998243 0.0592504i \(-0.0188710\pi\)
−0.967695 + 0.252124i \(0.918871\pi\)
\(114\) 0 0
\(115\) 1.02002 5.62820i 0.0951172 0.524832i
\(116\) 0 0
\(117\) 17.3560 + 1.84561i 1.60457 + 0.170626i
\(118\) 0 0
\(119\) 1.35128 + 4.15881i 0.123872 + 0.381238i
\(120\) 0 0
\(121\) −3.75415 + 11.5541i −0.341286 + 1.05037i
\(122\) 0 0
\(123\) −4.58935 + 4.83026i −0.413808 + 0.435530i
\(124\) 0 0
\(125\) 0.744329 11.1555i 0.0665748 0.997781i
\(126\) 0 0
\(127\) −1.50225 0.237933i −0.133303 0.0211132i 0.0894262 0.995993i \(-0.471497\pi\)
−0.222729 + 0.974880i \(0.571497\pi\)
\(128\) 0 0
\(129\) −3.61846 + 2.77303i −0.318587 + 0.244152i
\(130\) 0 0
\(131\) 5.58648 1.81516i 0.488093 0.158591i −0.0546233 0.998507i \(-0.517396\pi\)
0.542717 + 0.839916i \(0.317396\pi\)
\(132\) 0 0
\(133\) 9.46045 + 4.82034i 0.820325 + 0.417977i
\(134\) 0 0
\(135\) −4.70311 + 10.6245i −0.404779 + 0.914415i
\(136\) 0 0
\(137\) −8.72702 + 1.38222i −0.745599 + 0.118091i −0.517663 0.855585i \(-0.673198\pi\)
−0.227936 + 0.973676i \(0.573198\pi\)
\(138\) 0 0
\(139\) 2.77543 + 3.82005i 0.235409 + 0.324012i 0.910335 0.413873i \(-0.135824\pi\)
−0.674926 + 0.737886i \(0.735824\pi\)
\(140\) 0 0
\(141\) −5.70478 16.1411i −0.480429 1.35933i
\(142\) 0 0
\(143\) 19.7933 + 19.7933i 1.65520 + 1.65520i
\(144\) 0 0
\(145\) −0.228422 0.0798689i −0.0189694 0.00663275i
\(146\) 0 0
\(147\) −0.264741 + 2.00148i −0.0218355 + 0.165079i
\(148\) 0 0
\(149\) −1.98633 −0.162726 −0.0813632 0.996685i \(-0.525927\pi\)
−0.0813632 + 0.996685i \(0.525927\pi\)
\(150\) 0 0
\(151\) 21.4868 1.74857 0.874284 0.485415i \(-0.161332\pi\)
0.874284 + 0.485415i \(0.161332\pi\)
\(152\) 0 0
\(153\) −3.40789 3.07602i −0.275512 0.248681i
\(154\) 0 0
\(155\) 21.7005 6.52185i 1.74303 0.523848i
\(156\) 0 0
\(157\) 7.63307 + 7.63307i 0.609185 + 0.609185i 0.942733 0.333548i \(-0.108246\pi\)
−0.333548 + 0.942733i \(0.608246\pi\)
\(158\) 0 0
\(159\) 17.9803 6.35483i 1.42593 0.503971i
\(160\) 0 0
\(161\) 4.29650 + 5.91363i 0.338612 + 0.466059i
\(162\) 0 0
\(163\) −4.19979 + 0.665182i −0.328953 + 0.0521011i −0.318727 0.947847i \(-0.603255\pi\)
−0.0102264 + 0.999948i \(0.503255\pi\)
\(164\) 0 0
\(165\) −16.5746 + 8.51548i −1.29033 + 0.662929i
\(166\) 0 0
\(167\) 9.52908 + 4.85531i 0.737383 + 0.375715i 0.781991 0.623289i \(-0.214204\pi\)
−0.0446088 + 0.999005i \(0.514204\pi\)
\(168\) 0 0
\(169\) 19.8283 6.44261i 1.52525 0.495585i
\(170\) 0 0
\(171\) −11.1324 + 0.569807i −0.851318 + 0.0435742i
\(172\) 0 0
\(173\) −2.32976 0.368997i −0.177128 0.0280543i 0.0672403 0.997737i \(-0.478581\pi\)
−0.244368 + 0.969682i \(0.578581\pi\)
\(174\) 0 0
\(175\) 9.64443 + 10.5416i 0.729050 + 0.796870i
\(176\) 0 0
\(177\) −0.327234 0.310913i −0.0245964 0.0233697i
\(178\) 0 0
\(179\) 1.36907 4.21356i 0.102329 0.314936i −0.886765 0.462220i \(-0.847053\pi\)
0.989094 + 0.147284i \(0.0470531\pi\)
\(180\) 0 0
\(181\) 2.45027 + 7.54116i 0.182127 + 0.560530i 0.999887 0.0150298i \(-0.00478432\pi\)
−0.817760 + 0.575559i \(0.804784\pi\)
\(182\) 0 0
\(183\) −8.22331 + 4.45840i −0.607885 + 0.329574i
\(184\) 0 0
\(185\) 5.93302 0.805083i 0.436204 0.0591909i
\(186\) 0 0
\(187\) −1.15177 7.27196i −0.0842254 0.531779i
\(188\) 0 0
\(189\) −5.65708 13.7284i −0.411492 0.998595i
\(190\) 0 0
\(191\) −4.93725 + 6.79554i −0.357247 + 0.491708i −0.949379 0.314133i \(-0.898286\pi\)
0.592132 + 0.805841i \(0.298286\pi\)
\(192\) 0 0
\(193\) 9.74578 9.74578i 0.701517 0.701517i −0.263219 0.964736i \(-0.584784\pi\)
0.964736 + 0.263219i \(0.0847843\pi\)
\(194\) 0 0
\(195\) 0.0757523 + 22.5328i 0.00542473 + 1.61360i
\(196\) 0 0
\(197\) −7.05689 13.8499i −0.502783 0.986766i −0.993325 0.115349i \(-0.963201\pi\)
0.490543 0.871417i \(-0.336799\pi\)
\(198\) 0 0
\(199\) 10.6381i 0.754117i −0.926189 0.377059i \(-0.876936\pi\)
0.926189 0.377059i \(-0.123064\pi\)
\(200\) 0 0
\(201\) 3.77308 5.48269i 0.266132 0.386719i
\(202\) 0 0
\(203\) 0.275534 0.140392i 0.0193387 0.00985355i
\(204\) 0 0
\(205\) −6.84494 5.20924i −0.478071 0.363829i
\(206\) 0 0
\(207\) −7.00676 3.12986i −0.487003 0.217540i
\(208\) 0 0
\(209\) −14.4630 10.5080i −1.00042 0.726851i
\(210\) 0 0
\(211\) 8.87487 6.44797i 0.610971 0.443897i −0.238785 0.971072i \(-0.576749\pi\)
0.849756 + 0.527176i \(0.176749\pi\)
\(212\) 0 0
\(213\) −23.3342 11.1473i −1.59883 0.763801i
\(214\) 0 0
\(215\) −4.06818 4.25301i −0.277448 0.290053i
\(216\) 0 0
\(217\) −13.1463 + 25.8011i −0.892430 + 1.75149i
\(218\) 0 0
\(219\) −1.01107 + 3.40568i −0.0683216 + 0.230134i
\(220\) 0 0
\(221\) −8.46732 2.75120i −0.569574 0.185066i
\(222\) 0 0
\(223\) −2.83443 + 17.8959i −0.189807 + 1.19840i 0.690265 + 0.723557i \(0.257494\pi\)
−0.880072 + 0.474840i \(0.842506\pi\)
\(224\) 0 0
\(225\) −14.2967 4.53923i −0.953113 0.302615i
\(226\) 0 0
\(227\) −0.381413 + 2.40815i −0.0253153 + 0.159834i −0.997107 0.0760044i \(-0.975784\pi\)
0.971792 + 0.235839i \(0.0757837\pi\)
\(228\) 0 0
\(229\) −13.9452 4.53107i −0.921524 0.299421i −0.190432 0.981700i \(-0.560989\pi\)
−0.731092 + 0.682279i \(0.760989\pi\)
\(230\) 0 0
\(231\) 6.77725 22.8285i 0.445910 1.50200i
\(232\) 0 0
\(233\) −8.99659 + 17.6568i −0.589386 + 1.15674i 0.383085 + 0.923713i \(0.374861\pi\)
−0.972471 + 0.233022i \(0.925139\pi\)
\(234\) 0 0
\(235\) 19.9103 9.59400i 1.29881 0.625843i
\(236\) 0 0
\(237\) 13.4278 + 6.41478i 0.872228 + 0.416685i
\(238\) 0 0
\(239\) −18.6744 + 13.5678i −1.20795 + 0.877625i −0.995043 0.0994482i \(-0.968292\pi\)
−0.212904 + 0.977073i \(0.568292\pi\)
\(240\) 0 0
\(241\) 7.99196 + 5.80650i 0.514807 + 0.374029i 0.814644 0.579961i \(-0.196932\pi\)
−0.299837 + 0.953990i \(0.596932\pi\)
\(242\) 0 0
\(243\) 12.3382 + 9.52733i 0.791493 + 0.611178i
\(244\) 0 0
\(245\) −2.60576 0.0578783i −0.166476 0.00369771i
\(246\) 0 0
\(247\) −19.2614 + 9.81419i −1.22558 + 0.624462i
\(248\) 0 0
\(249\) 6.84444 9.94571i 0.433749 0.630284i
\(250\) 0 0
\(251\) 16.9633i 1.07071i 0.844626 + 0.535357i \(0.179823\pi\)
−0.844626 + 0.535357i \(0.820177\pi\)
\(252\) 0 0
\(253\) −5.58743 10.9659i −0.351278 0.689423i
\(254\) 0 0
\(255\) 3.46750 4.80650i 0.217143 0.300995i
\(256\) 0 0
\(257\) 17.5417 17.5417i 1.09422 1.09422i 0.0991458 0.995073i \(-0.468389\pi\)
0.995073 0.0991458i \(-0.0316110\pi\)
\(258\) 0 0
\(259\) −4.49745 + 6.19020i −0.279458 + 0.384641i
\(260\) 0 0
\(261\) −0.177151 + 0.272062i −0.0109654 + 0.0168402i
\(262\) 0 0
\(263\) −2.55900 16.1569i −0.157795 0.996277i −0.931767 0.363057i \(-0.881733\pi\)
0.773972 0.633220i \(-0.218267\pi\)
\(264\) 0 0
\(265\) 10.6872 + 22.1791i 0.656511 + 1.36245i
\(266\) 0 0
\(267\) −7.23709 + 3.92370i −0.442903 + 0.240127i
\(268\) 0 0
\(269\) −2.50454 7.70819i −0.152705 0.469977i 0.845216 0.534424i \(-0.179472\pi\)
−0.997921 + 0.0644474i \(0.979472\pi\)
\(270\) 0 0
\(271\) −2.83005 + 8.70999i −0.171913 + 0.529094i −0.999479 0.0322745i \(-0.989725\pi\)
0.827566 + 0.561368i \(0.189725\pi\)
\(272\) 0 0
\(273\) −20.8755 19.8343i −1.26344 1.20043i
\(274\) 0 0
\(275\) −13.2620 20.0708i −0.799728 1.21031i
\(276\) 0 0
\(277\) −3.90301 0.618177i −0.234509 0.0371426i 0.0380735 0.999275i \(-0.487878\pi\)
−0.272583 + 0.962132i \(0.587878\pi\)
\(278\) 0 0
\(279\) −1.55401 30.3610i −0.0930361 1.81766i
\(280\) 0 0
\(281\) 24.5537 7.97798i 1.46475 0.475926i 0.535233 0.844704i \(-0.320224\pi\)
0.929517 + 0.368778i \(0.120224\pi\)
\(282\) 0 0
\(283\) −1.20672 0.614853i −0.0717319 0.0365492i 0.417757 0.908559i \(-0.362816\pi\)
−0.489489 + 0.872010i \(0.662816\pi\)
\(284\) 0 0
\(285\) −2.29897 14.2059i −0.136179 0.841484i
\(286\) 0 0
\(287\) 10.8571 1.71960i 0.640875 0.101505i
\(288\) 0 0
\(289\) −8.61591 11.8588i −0.506818 0.697576i
\(290\) 0 0
\(291\) 27.4491 9.70139i 1.60909 0.568705i
\(292\) 0 0
\(293\) 9.43835 + 9.43835i 0.551395 + 0.551395i 0.926843 0.375449i \(-0.122511\pi\)
−0.375449 + 0.926843i \(0.622511\pi\)
\(294\) 0 0
\(295\) 0.352909 0.463722i 0.0205471 0.0269989i
\(296\) 0 0
\(297\) 5.79170 + 24.3202i 0.336069 + 1.41120i
\(298\) 0 0
\(299\) −14.8824 −0.860672
\(300\) 0 0
\(301\) 7.52120 0.433515
\(302\) 0 0
\(303\) −3.94218 + 29.8034i −0.226473 + 1.71216i
\(304\) 0 0
\(305\) −6.87949 9.92503i −0.393918 0.568306i
\(306\) 0 0
\(307\) −9.42497 9.42497i −0.537911 0.537911i 0.385004 0.922915i \(-0.374200\pi\)
−0.922915 + 0.385004i \(0.874200\pi\)
\(308\) 0 0
\(309\) −2.73512 7.73874i −0.155595 0.440241i
\(310\) 0 0
\(311\) 7.79335 + 10.7266i 0.441920 + 0.608251i 0.970637 0.240547i \(-0.0773269\pi\)
−0.528717 + 0.848798i \(0.677327\pi\)
\(312\) 0 0
\(313\) 0.0874904 0.0138571i 0.00494525 0.000783251i −0.153961 0.988077i \(-0.549203\pi\)
0.158907 + 0.987294i \(0.449203\pi\)
\(314\) 0 0
\(315\) 16.8209 9.19301i 0.947748 0.517967i
\(316\) 0 0
\(317\) −25.7112 13.1005i −1.44409 0.735799i −0.456041 0.889959i \(-0.650733\pi\)
−0.988046 + 0.154160i \(0.950733\pi\)
\(318\) 0 0
\(319\) −0.495187 + 0.160896i −0.0277251 + 0.00900844i
\(320\) 0 0
\(321\) −24.1599 + 18.5151i −1.34847 + 1.03341i
\(322\) 0 0
\(323\) 5.61597 + 0.889483i 0.312481 + 0.0494922i
\(324\) 0 0
\(325\) −28.9054 + 3.27043i −1.60338 + 0.181411i
\(326\) 0 0
\(327\) −20.3623 + 21.4312i −1.12604 + 1.18515i
\(328\) 0 0
\(329\) −8.72788 + 26.8617i −0.481184 + 1.48093i
\(330\) 0 0
\(331\) 1.58196 + 4.86878i 0.0869525 + 0.267612i 0.985073 0.172137i \(-0.0550672\pi\)
−0.898120 + 0.439750i \(0.855067\pi\)
\(332\) 0 0
\(333\) 0.849417 7.98790i 0.0465477 0.437734i
\(334\) 0 0
\(335\) 7.56724 + 4.06984i 0.413442 + 0.222359i
\(336\) 0 0
\(337\) 2.34521 + 14.8070i 0.127752 + 0.806591i 0.965475 + 0.260496i \(0.0838862\pi\)
−0.837723 + 0.546095i \(0.816114\pi\)
\(338\) 0 0
\(339\) 0.0919250 + 3.59426i 0.00499268 + 0.195214i
\(340\) 0 0
\(341\) 28.6579 39.4442i 1.55191 2.13602i
\(342\) 0 0
\(343\) −11.7889 + 11.7889i −0.636542 + 0.636542i
\(344\) 0 0
\(345\) 3.02978 9.43247i 0.163118 0.507827i
\(346\) 0 0
\(347\) 4.06670 + 7.98136i 0.218312 + 0.428462i 0.974025 0.226442i \(-0.0727093\pi\)
−0.755713 + 0.654903i \(0.772709\pi\)
\(348\) 0 0
\(349\) 31.6418i 1.69375i −0.531793 0.846874i \(-0.678482\pi\)
0.531793 0.846874i \(-0.321518\pi\)
\(350\) 0 0
\(351\) 29.3828 + 7.11108i 1.56834 + 0.379561i
\(352\) 0 0
\(353\) 16.4179 8.36532i 0.873834 0.445241i 0.0412563 0.999149i \(-0.486864\pi\)
0.832578 + 0.553908i \(0.186864\pi\)
\(354\) 0 0
\(355\) 11.0191 31.5144i 0.584836 1.67261i
\(356\) 0 0
\(357\) 1.37570 + 7.44799i 0.0728100 + 0.394189i
\(358\) 0 0
\(359\) −3.85147 2.79826i −0.203273 0.147686i 0.481492 0.876450i \(-0.340095\pi\)
−0.684765 + 0.728764i \(0.740095\pi\)
\(360\) 0 0
\(361\) −4.20190 + 3.05286i −0.221153 + 0.160677i
\(362\) 0 0
\(363\) −9.07045 + 18.9868i −0.476075 + 0.996547i
\(364\) 0 0
\(365\) −4.51286 0.817882i −0.236214 0.0428099i
\(366\) 0 0
\(367\) 2.16114 4.24147i 0.112810 0.221403i −0.827698 0.561174i \(-0.810350\pi\)
0.940508 + 0.339771i \(0.110350\pi\)
\(368\) 0 0
\(369\) −8.97743 + 7.25166i −0.467346 + 0.377506i
\(370\) 0 0
\(371\) −29.9225 9.72241i −1.55350 0.504763i
\(372\) 0 0
\(373\) −3.54113 + 22.3578i −0.183353 + 1.15765i 0.708631 + 0.705579i \(0.249313\pi\)
−0.891984 + 0.452066i \(0.850687\pi\)
\(374\) 0 0
\(375\) 3.81179 18.9861i 0.196840 0.980436i
\(376\) 0 0
\(377\) −0.0984925 + 0.621857i −0.00507262 + 0.0320273i
\(378\) 0 0
\(379\) −2.26244 0.735112i −0.116214 0.0377601i 0.250333 0.968160i \(-0.419460\pi\)
−0.366547 + 0.930400i \(0.619460\pi\)
\(380\) 0 0
\(381\) −2.52547 0.749754i −0.129384 0.0384110i
\(382\) 0 0
\(383\) −13.1453 + 25.7992i −0.671696 + 1.31828i 0.263676 + 0.964611i \(0.415065\pi\)
−0.935372 + 0.353666i \(0.884935\pi\)
\(384\) 0 0
\(385\) 30.2500 + 5.48231i 1.54168 + 0.279405i
\(386\) 0 0
\(387\) −6.84306 + 3.93972i −0.347852 + 0.200267i
\(388\) 0 0
\(389\) 15.3567 11.1573i 0.778614 0.565697i −0.125948 0.992037i \(-0.540197\pi\)
0.904563 + 0.426340i \(0.140197\pi\)
\(390\) 0 0
\(391\) 3.16685 + 2.30085i 0.160155 + 0.116359i
\(392\) 0 0
\(393\) 10.0048 1.84797i 0.504675 0.0932175i
\(394\) 0 0
\(395\) −6.34103 + 18.1351i −0.319052 + 0.912477i
\(396\) 0 0
\(397\) −1.51760 + 0.773254i −0.0761660 + 0.0388085i −0.491659 0.870788i \(-0.663609\pi\)
0.415493 + 0.909597i \(0.363609\pi\)
\(398\) 0 0
\(399\) 15.1497 + 10.4257i 0.758432 + 0.521937i
\(400\) 0 0
\(401\) 35.0603i 1.75083i 0.483376 + 0.875413i \(0.339411\pi\)
−0.483376 + 0.875413i \(0.660589\pi\)
\(402\) 0 0
\(403\) −26.7658 52.5309i −1.33330 2.61675i
\(404\) 0 0
\(405\) −10.4888 + 17.1751i −0.521192 + 0.853439i
\(406\) 0 0
\(407\) 9.10963 9.10963i 0.451548 0.451548i
\(408\) 0 0
\(409\) 18.8051 25.8830i 0.929853 1.27983i −0.0300633 0.999548i \(-0.509571\pi\)
0.959917 0.280285i \(-0.0904291\pi\)
\(410\) 0 0
\(411\) −15.2991 + 0.391281i −0.754647 + 0.0193004i
\(412\) 0 0
\(413\) 0.116497 + 0.735533i 0.00573244 + 0.0361932i
\(414\) 0 0
\(415\) 13.7271 + 7.38277i 0.673838 + 0.362406i
\(416\) 0 0
\(417\) 3.89804 + 7.18976i 0.190888 + 0.352084i
\(418\) 0 0
\(419\) 2.91963 + 8.98569i 0.142633 + 0.438980i 0.996699 0.0811851i \(-0.0258705\pi\)
−0.854066 + 0.520165i \(0.825870\pi\)
\(420\) 0 0
\(421\) −1.74189 + 5.36098i −0.0848945 + 0.261278i −0.984489 0.175449i \(-0.943862\pi\)
0.899594 + 0.436727i \(0.143862\pi\)
\(422\) 0 0
\(423\) −6.12960 29.0115i −0.298031 1.41059i
\(424\) 0 0
\(425\) 6.65645 + 3.77292i 0.322885 + 0.183014i
\(426\) 0 0
\(427\) 15.2426 + 2.41419i 0.737640 + 0.116831i
\(428\) 0 0
\(429\) 29.4915 + 38.4826i 1.42386 + 1.85796i
\(430\) 0 0
\(431\) −11.7037 + 3.80275i −0.563745 + 0.183172i −0.577006 0.816740i \(-0.695779\pi\)
0.0132603 + 0.999912i \(0.495779\pi\)
\(432\) 0 0
\(433\) −26.3686 13.4355i −1.26719 0.645667i −0.314400 0.949291i \(-0.601803\pi\)
−0.952792 + 0.303624i \(0.901803\pi\)
\(434\) 0 0
\(435\) −0.374082 0.189023i −0.0179359 0.00906296i
\(436\) 0 0
\(437\) 9.38768 1.48686i 0.449074 0.0711263i
\(438\) 0 0
\(439\) 10.9368 + 15.0532i 0.521984 + 0.718449i 0.985882 0.167439i \(-0.0535497\pi\)
−0.463898 + 0.885888i \(0.653550\pi\)
\(440\) 0 0
\(441\) −0.909172 + 3.37659i −0.0432939 + 0.160790i
\(442\) 0 0
\(443\) −1.48265 1.48265i −0.0704427 0.0704427i 0.671008 0.741450i \(-0.265862\pi\)
−0.741450 + 0.671008i \(0.765862\pi\)
\(444\) 0 0
\(445\) −6.05443 8.73472i −0.287007 0.414066i
\(446\) 0 0
\(447\) −3.41071 0.451146i −0.161321 0.0213385i
\(448\) 0 0
\(449\) −33.3934 −1.57593 −0.787967 0.615718i \(-0.788866\pi\)
−0.787967 + 0.615718i \(0.788866\pi\)
\(450\) 0 0
\(451\) −18.5081 −0.871514
\(452\) 0 0
\(453\) 36.8948 + 4.88019i 1.73347 + 0.229291i
\(454\) 0 0
\(455\) 22.5134 29.5825i 1.05544 1.38685i
\(456\) 0 0
\(457\) 14.4358 + 14.4358i 0.675278 + 0.675278i 0.958928 0.283650i \(-0.0915453\pi\)
−0.283650 + 0.958928i \(0.591545\pi\)
\(458\) 0 0
\(459\) −5.15303 6.05583i −0.240523 0.282662i
\(460\) 0 0
\(461\) −1.12640 1.55036i −0.0524617 0.0722073i 0.781980 0.623303i \(-0.214210\pi\)
−0.834442 + 0.551096i \(0.814210\pi\)
\(462\) 0 0
\(463\) −2.40651 + 0.381153i −0.111840 + 0.0177137i −0.212103 0.977247i \(-0.568031\pi\)
0.100264 + 0.994961i \(0.468031\pi\)
\(464\) 0 0
\(465\) 38.7431 6.26989i 1.79667 0.290759i
\(466\) 0 0
\(467\) 13.9849 + 7.12568i 0.647146 + 0.329737i 0.746569 0.665308i \(-0.231700\pi\)
−0.0994231 + 0.995045i \(0.531700\pi\)
\(468\) 0 0
\(469\) −10.4429 + 3.39312i −0.482210 + 0.156680i
\(470\) 0 0
\(471\) 11.3730 + 14.8404i 0.524042 + 0.683808i
\(472\) 0 0
\(473\) −12.5077 1.98102i −0.575102 0.0910873i
\(474\) 0 0
\(475\) 17.9065 4.95082i 0.821607 0.227159i
\(476\) 0 0
\(477\) 32.3173 6.82805i 1.47971 0.312635i
\(478\) 0 0
\(479\) 3.70860 11.4139i 0.169450 0.521514i −0.829886 0.557932i \(-0.811595\pi\)
0.999337 + 0.0364182i \(0.0115948\pi\)
\(480\) 0 0
\(481\) −4.81400 14.8160i −0.219500 0.675550i
\(482\) 0 0
\(483\) 6.03437 + 11.1301i 0.274573 + 0.506437i
\(484\) 0 0
\(485\) 16.3153 + 33.8589i 0.740838 + 1.53745i
\(486\) 0 0
\(487\) 0.279897 + 1.76720i 0.0126833 + 0.0800794i 0.993218 0.116266i \(-0.0370926\pi\)
−0.980535 + 0.196346i \(0.937093\pi\)
\(488\) 0 0
\(489\) −7.36252 + 0.188300i −0.332945 + 0.00851522i
\(490\) 0 0
\(491\) 3.20544 4.41191i 0.144660 0.199107i −0.730539 0.682871i \(-0.760731\pi\)
0.875198 + 0.483765i \(0.160731\pi\)
\(492\) 0 0
\(493\) 0.117099 0.117099i 0.00527387 0.00527387i
\(494\) 0 0
\(495\) −30.3942 + 10.8574i −1.36612 + 0.488003i
\(496\) 0 0
\(497\) 19.3692 + 38.0141i 0.868826 + 1.70517i
\(498\) 0 0
\(499\) 15.8865i 0.711177i 0.934643 + 0.355588i \(0.115719\pi\)
−0.934643 + 0.355588i \(0.884281\pi\)
\(500\) 0 0
\(501\) 15.2596 + 10.5013i 0.681747 + 0.469165i
\(502\) 0 0
\(503\) 12.2021 6.21728i 0.544065 0.277215i −0.160282 0.987071i \(-0.551240\pi\)
0.704346 + 0.709857i \(0.251240\pi\)
\(504\) 0 0
\(505\) −38.8015 0.861848i −1.72665 0.0383517i
\(506\) 0 0
\(507\) 35.5104 6.55905i 1.57707 0.291298i
\(508\) 0 0
\(509\) 14.7649 + 10.7273i 0.654441 + 0.475479i 0.864781 0.502149i \(-0.167457\pi\)
−0.210340 + 0.977628i \(0.567457\pi\)
\(510\) 0 0
\(511\) 4.74173 3.44507i 0.209762 0.152401i
\(512\) 0 0
\(513\) −19.2448 1.55005i −0.849680 0.0684362i
\(514\) 0 0
\(515\) 9.54587 4.59978i 0.420641 0.202690i
\(516\) 0 0
\(517\) 21.5895 42.3717i 0.949504 1.86351i
\(518\) 0 0
\(519\) −3.91660 1.16275i −0.171920 0.0510391i
\(520\) 0 0
\(521\) 34.6323 + 11.2527i 1.51727 + 0.492991i 0.944999 0.327073i \(-0.106062\pi\)
0.572272 + 0.820064i \(0.306062\pi\)
\(522\) 0 0
\(523\) −3.57185 + 22.5518i −0.156186 + 0.986120i 0.777722 + 0.628608i \(0.216375\pi\)
−0.933908 + 0.357512i \(0.883625\pi\)
\(524\) 0 0
\(525\) 14.1661 + 20.2914i 0.618261 + 0.885591i
\(526\) 0 0
\(527\) −2.42585 + 15.3162i −0.105672 + 0.667185i
\(528\) 0 0
\(529\) −15.6512 5.08537i −0.680485 0.221103i
\(530\) 0 0
\(531\) −0.491276 0.608191i −0.0213196 0.0263932i
\(532\) 0 0
\(533\) −10.1606 + 19.9412i −0.440103 + 0.863750i
\(534\) 0 0
\(535\) −27.1626 28.3967i −1.17434 1.22770i
\(536\) 0 0
\(537\) 3.30782 6.92412i 0.142743 0.298798i
\(538\) 0 0
\(539\) −4.53708 + 3.29638i −0.195426 + 0.141985i
\(540\) 0 0
\(541\) −14.4743 10.5162i −0.622299 0.452126i 0.231425 0.972853i \(-0.425661\pi\)
−0.853724 + 0.520726i \(0.825661\pi\)
\(542\) 0 0
\(543\) 2.49456 + 13.5054i 0.107052 + 0.579572i
\(544\) 0 0
\(545\) −30.3700 23.1126i −1.30091 0.990037i
\(546\) 0 0
\(547\) −13.1268 + 6.68845i −0.561263 + 0.285978i −0.711516 0.702670i \(-0.751991\pi\)
0.150253 + 0.988648i \(0.451991\pi\)
\(548\) 0 0
\(549\) −15.1328 + 5.78777i −0.645853 + 0.247016i
\(550\) 0 0
\(551\) 0.402102i 0.0171301i
\(552\) 0 0
\(553\) −11.1461 21.8755i −0.473981 0.930239i
\(554\) 0 0
\(555\) 10.3704 0.0348640i 0.440199 0.00147989i
\(556\) 0 0
\(557\) −15.7568 + 15.7568i −0.667638 + 0.667638i −0.957169 0.289531i \(-0.906501\pi\)
0.289531 + 0.957169i \(0.406501\pi\)
\(558\) 0 0
\(559\) −9.00083 + 12.3886i −0.380695 + 0.523981i
\(560\) 0 0
\(561\) −0.326042 12.7482i −0.0137655 0.538231i
\(562\) 0 0
\(563\) −3.16190 19.9634i −0.133258 0.841358i −0.960249 0.279143i \(-0.909950\pi\)
0.826991 0.562215i \(-0.190050\pi\)
\(564\) 0 0
\(565\) −4.59954 + 0.624136i −0.193504 + 0.0262576i
\(566\) 0 0
\(567\) −6.59567 24.8578i −0.276992 1.04393i
\(568\) 0 0
\(569\) −10.5620 32.5066i −0.442783 1.36275i −0.884896 0.465788i \(-0.845771\pi\)
0.442113 0.896959i \(-0.354229\pi\)
\(570\) 0 0
\(571\) −4.84382 + 14.9078i −0.202708 + 0.623870i 0.797092 + 0.603858i \(0.206371\pi\)
−0.999800 + 0.0200122i \(0.993629\pi\)
\(572\) 0 0
\(573\) −10.0212 + 10.5472i −0.418640 + 0.440616i
\(574\) 0 0
\(575\) 12.5313 + 2.55973i 0.522590 + 0.106748i
\(576\) 0 0
\(577\) −34.5289 5.46884i −1.43746 0.227671i −0.611428 0.791300i \(-0.709405\pi\)
−0.826028 + 0.563629i \(0.809405\pi\)
\(578\) 0 0
\(579\) 18.9479 14.5209i 0.787450 0.603468i
\(580\) 0 0
\(581\) −18.9437 + 6.15518i −0.785917 + 0.255360i
\(582\) 0 0
\(583\) 47.1999 + 24.0496i 1.95482 + 0.996031i
\(584\) 0 0
\(585\) −4.98769 + 38.7081i −0.206216 + 1.60038i
\(586\) 0 0
\(587\) −38.6761 + 6.12569i −1.59633 + 0.252834i −0.890310 0.455355i \(-0.849512\pi\)
−0.706023 + 0.708189i \(0.749512\pi\)
\(588\) 0 0
\(589\) 22.1319 + 30.4619i 0.911927 + 1.25516i
\(590\) 0 0
\(591\) −8.97167 25.3844i −0.369045 1.04418i
\(592\) 0 0
\(593\) −18.8322 18.8322i −0.773348 0.773348i 0.205343 0.978690i \(-0.434169\pi\)
−0.978690 + 0.205343i \(0.934169\pi\)
\(594\) 0 0
\(595\) −9.36419 + 2.81431i −0.383895 + 0.115375i
\(596\) 0 0
\(597\) 2.41619 18.2667i 0.0988881 0.747605i
\(598\) 0 0
\(599\) 29.8132 1.21813 0.609066 0.793119i \(-0.291544\pi\)
0.609066 + 0.793119i \(0.291544\pi\)
\(600\) 0 0
\(601\) 12.3924 0.505498 0.252749 0.967532i \(-0.418665\pi\)
0.252749 + 0.967532i \(0.418665\pi\)
\(602\) 0 0
\(603\) 7.72399 8.55734i 0.314545 0.348482i
\(604\) 0 0
\(605\) −25.6429 8.96617i −1.04253 0.364527i
\(606\) 0 0
\(607\) −16.4938 16.4938i −0.669464 0.669464i 0.288128 0.957592i \(-0.406967\pi\)
−0.957592 + 0.288128i \(0.906967\pi\)
\(608\) 0 0
\(609\) 0.505004 0.178485i 0.0204638 0.00723257i
\(610\) 0 0
\(611\) −33.8004 46.5223i −1.36742 1.88209i
\(612\) 0 0
\(613\) 34.2415 5.42333i 1.38300 0.219046i 0.579803 0.814756i \(-0.303129\pi\)
0.803199 + 0.595710i \(0.203129\pi\)
\(614\) 0 0
\(615\) −10.5703 10.4994i −0.426234 0.423377i
\(616\) 0 0
\(617\) −24.8462 12.6598i −1.00027 0.509662i −0.124410 0.992231i \(-0.539704\pi\)
−0.875858 + 0.482568i \(0.839704\pi\)
\(618\) 0 0
\(619\) 11.8893 3.86308i 0.477872 0.155270i −0.0601697 0.998188i \(-0.519164\pi\)
0.538042 + 0.842918i \(0.319164\pi\)
\(620\) 0 0
\(621\) −11.3204 6.96568i −0.454272 0.279523i
\(622\) 0 0
\(623\) 13.4145 + 2.12465i 0.537442 + 0.0851224i
\(624\) 0 0
\(625\) 24.9014 + 2.21788i 0.996057 + 0.0887154i
\(626\) 0 0
\(627\) −22.4476 21.3281i −0.896473 0.851761i
\(628\) 0 0
\(629\) −1.26620 + 3.89698i −0.0504869 + 0.155383i
\(630\) 0 0
\(631\) 5.26220 + 16.1954i 0.209485 + 0.644728i 0.999499 + 0.0316401i \(0.0100730\pi\)
−0.790014 + 0.613088i \(0.789927\pi\)
\(632\) 0 0
\(633\) 16.7035 9.05607i 0.663904 0.359946i
\(634\) 0 0
\(635\) 0.606497 3.34649i 0.0240681 0.132802i
\(636\) 0 0
\(637\) 1.06086 + 6.69803i 0.0420329 + 0.265386i
\(638\) 0 0
\(639\) −37.5351 24.4408i −1.48487 0.966861i
\(640\) 0 0
\(641\) 2.68121 3.69037i 0.105901 0.145761i −0.752777 0.658276i \(-0.771286\pi\)
0.858678 + 0.512515i \(0.171286\pi\)
\(642\) 0 0
\(643\) 1.57617 1.57617i 0.0621582 0.0621582i −0.675344 0.737503i \(-0.736005\pi\)
0.737503 + 0.675344i \(0.236005\pi\)
\(644\) 0 0
\(645\) −6.01949 8.22681i −0.237017 0.323930i
\(646\) 0 0
\(647\) −10.6313 20.8650i −0.417958 0.820289i −0.999975 0.00711204i \(-0.997736\pi\)
0.582017 0.813177i \(-0.302264\pi\)
\(648\) 0 0
\(649\) 1.25386i 0.0492185i
\(650\) 0 0
\(651\) −28.4336 + 41.3171i −1.11440 + 1.61934i
\(652\) 0 0
\(653\) −1.68056 + 0.856287i −0.0657653 + 0.0335091i −0.486564 0.873645i \(-0.661750\pi\)
0.420799 + 0.907154i \(0.361750\pi\)
\(654\) 0 0
\(655\) 3.78042 + 12.5788i 0.147713 + 0.491495i
\(656\) 0 0
\(657\) −2.50961 + 5.61823i −0.0979094 + 0.219188i
\(658\) 0 0
\(659\) 39.3347 + 28.5783i 1.53226 + 1.11325i 0.954965 + 0.296719i \(0.0958925\pi\)
0.577297 + 0.816534i \(0.304107\pi\)
\(660\) 0 0
\(661\) 10.8497 7.88279i 0.422006 0.306605i −0.356439 0.934319i \(-0.616009\pi\)
0.778444 + 0.627714i \(0.216009\pi\)
\(662\) 0 0
\(663\) −13.9143 6.64722i −0.540388 0.258156i
\(664\) 0 0
\(665\) −11.2457 + 20.9096i −0.436090 + 0.810841i
\(666\) 0 0
\(667\) 0.125675 0.246651i 0.00486615 0.00955035i
\(668\) 0 0
\(669\) −8.93159 + 30.0851i −0.345315 + 1.16316i
\(670\) 0 0
\(671\) −24.7123 8.02951i −0.954008 0.309976i
\(672\) 0 0
\(673\) 1.34636 8.50057i 0.0518983 0.327673i −0.948056 0.318104i \(-0.896954\pi\)
0.999954 0.00956929i \(-0.00304604\pi\)
\(674\) 0 0
\(675\) −23.5178 11.0414i −0.905200 0.424985i
\(676\) 0 0
\(677\) 0.116734 0.737029i 0.00448645 0.0283263i −0.985344 0.170582i \(-0.945435\pi\)
0.989830 + 0.142255i \(0.0454354\pi\)
\(678\) 0 0
\(679\) −45.6802 14.8424i −1.75304 0.569599i
\(680\) 0 0
\(681\) −1.20187 + 4.04839i −0.0460559 + 0.155134i
\(682\) 0 0
\(683\) 16.4590 32.3026i 0.629785 1.23602i −0.326944 0.945044i \(-0.606019\pi\)
0.956729 0.290980i \(-0.0939812\pi\)
\(684\) 0 0
\(685\) −2.65665 19.5780i −0.101505 0.748038i
\(686\) 0 0
\(687\) −22.9161 10.9476i −0.874303 0.417676i
\(688\) 0 0
\(689\) 51.8234 37.6519i 1.97431 1.43442i
\(690\) 0 0
\(691\) −25.1665 18.2845i −0.957378 0.695576i −0.00483787 0.999988i \(-0.501540\pi\)
−0.952540 + 0.304412i \(0.901540\pi\)
\(692\) 0 0
\(693\) 16.8221 37.6593i 0.639019 1.43056i
\(694\) 0 0
\(695\) −8.67760 + 6.01484i −0.329160 + 0.228156i
\(696\) 0 0
\(697\) 5.24504 2.67248i 0.198670 0.101228i
\(698\) 0 0
\(699\) −19.4583 + 28.2750i −0.735981 + 1.06946i
\(700\) 0 0
\(701\) 0.173863i 0.00656672i −0.999995 0.00328336i \(-0.998955\pi\)
0.999995 0.00328336i \(-0.00104513\pi\)
\(702\) 0 0
\(703\) 4.51685 + 8.86483i 0.170356 + 0.334343i
\(704\) 0 0
\(705\) 36.3670 11.9517i 1.36966 0.450125i
\(706\) 0 0
\(707\) 35.0712 35.0712i 1.31899 1.31899i
\(708\) 0 0
\(709\) −27.9112 + 38.4165i −1.04823 + 1.44276i −0.157891 + 0.987457i \(0.550469\pi\)
−0.890336 + 0.455304i \(0.849531\pi\)
\(710\) 0 0
\(711\) 21.5998 + 14.0646i 0.810056 + 0.527463i
\(712\) 0 0
\(713\) 4.05506 + 25.6026i 0.151863 + 0.958826i
\(714\) 0 0
\(715\) −45.2312 + 43.2655i −1.69155 + 1.61804i
\(716\) 0 0
\(717\) −35.1473 + 19.0557i −1.31260 + 0.711647i
\(718\) 0 0
\(719\) 1.22324 + 3.76475i 0.0456192 + 0.140401i 0.971272 0.237973i \(-0.0764831\pi\)
−0.925653 + 0.378375i \(0.876483\pi\)
\(720\) 0 0
\(721\) −4.18452 + 12.8786i −0.155840 + 0.479626i
\(722\) 0 0
\(723\) 12.4041 + 11.7855i 0.461315 + 0.438307i
\(724\) 0 0
\(725\) 0.189890 0.506676i 0.00705235 0.0188175i
\(726\) 0 0
\(727\) 8.95795 + 1.41880i 0.332232 + 0.0526204i 0.320322 0.947309i \(-0.396209\pi\)
0.0119099 + 0.999929i \(0.496209\pi\)
\(728\) 0 0
\(729\) 19.0219 + 19.1616i 0.704514 + 0.709690i
\(730\) 0 0
\(731\) 3.83061 1.24464i 0.141680 0.0460347i
\(732\) 0 0
\(733\) 20.9011 + 10.6496i 0.772000 + 0.393353i 0.795177 0.606378i \(-0.207378\pi\)
−0.0231770 + 0.999731i \(0.507378\pi\)
\(734\) 0 0
\(735\) −4.46119 0.691216i −0.164553 0.0254959i
\(736\) 0 0
\(737\) 18.2602 2.89213i 0.672622 0.106533i
\(738\) 0 0
\(739\) 6.02439 + 8.29186i 0.221611 + 0.305021i 0.905317 0.424736i \(-0.139633\pi\)
−0.683706 + 0.729757i \(0.739633\pi\)
\(740\) 0 0
\(741\) −35.3028 + 12.4771i −1.29688 + 0.458359i
\(742\) 0 0
\(743\) −21.7690 21.7690i −0.798626 0.798626i 0.184253 0.982879i \(-0.441013\pi\)
−0.982879 + 0.184253i \(0.941013\pi\)
\(744\) 0 0
\(745\) 0.0986303 4.44047i 0.00361354 0.162686i
\(746\) 0 0
\(747\) 14.0115 15.5232i 0.512653 0.567964i
\(748\) 0 0
\(749\) 50.2179 1.83492
\(750\) 0 0
\(751\) 7.73768 0.282352 0.141176 0.989985i \(-0.454912\pi\)
0.141176 + 0.989985i \(0.454912\pi\)
\(752\) 0 0
\(753\) −3.85280 + 29.1276i −0.140404 + 1.06147i
\(754\) 0 0
\(755\) −1.06692 + 48.0340i −0.0388291 + 1.74814i
\(756\) 0 0
\(757\) 4.50352 + 4.50352i 0.163683 + 0.163683i 0.784196 0.620513i \(-0.213076\pi\)
−0.620513 + 0.784196i \(0.713076\pi\)
\(758\) 0 0
\(759\) −7.10349 20.0986i −0.257840 0.729533i
\(760\) 0 0
\(761\) 7.27565 + 10.0141i 0.263742 + 0.363010i 0.920265 0.391297i \(-0.127973\pi\)
−0.656523 + 0.754306i \(0.727973\pi\)
\(762\) 0 0
\(763\) 48.1714 7.62960i 1.74392 0.276210i
\(764\) 0 0
\(765\) 7.04570 7.46566i 0.254738 0.269921i
\(766\) 0 0
\(767\) −1.35095 0.688344i −0.0487800 0.0248547i
\(768\) 0 0
\(769\) 28.2227 9.17010i 1.01774 0.330682i 0.247805 0.968810i \(-0.420291\pi\)
0.769931 + 0.638128i \(0.220291\pi\)
\(770\) 0 0
\(771\) 34.1049 26.1365i 1.22826 0.941284i
\(772\) 0 0
\(773\) −0.378278 0.0599133i −0.0136057 0.00215493i 0.149628 0.988742i \(-0.452192\pi\)
−0.163234 + 0.986587i \(0.552192\pi\)
\(774\) 0 0
\(775\) 13.5022 + 48.8357i 0.485012 + 1.75423i
\(776\) 0 0
\(777\) −9.12850 + 9.60768i −0.327483 + 0.344674i
\(778\) 0 0
\(779\) 4.41691 13.5938i 0.158252 0.487050i
\(780\) 0 0
\(781\) −22.1981 68.3186i −0.794309 2.44463i
\(782\) 0 0
\(783\) −0.365978 + 0.426920i −0.0130790 + 0.0152569i
\(784\) 0 0
\(785\) −17.4429 + 16.6848i −0.622563 + 0.595507i
\(786\) 0 0
\(787\) −0.702867 4.43773i −0.0250545 0.158188i 0.971989 0.235026i \(-0.0755175\pi\)
−0.997044 + 0.0768381i \(0.975518\pi\)
\(788\) 0 0
\(789\) −0.724403 28.3241i −0.0257894 1.00837i
\(790\) 0 0
\(791\) 3.48662 4.79892i 0.123970 0.170630i
\(792\) 0 0
\(793\) −22.2177 + 22.2177i −0.788975 + 0.788975i
\(794\) 0 0
\(795\) 13.3135 + 40.5109i 0.472182 + 1.43677i
\(796\) 0 0