Properties

Label 300.2.x.a.233.8
Level $300$
Weight $2$
Character 300.233
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 233.8
Character \(\chi\) \(=\) 300.233
Dual form 300.2.x.a.197.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.767407 - 1.55277i) q^{3} +(1.73820 - 1.40665i) q^{5} +(-0.636300 + 0.636300i) q^{7} +(-1.82217 - 2.38321i) q^{9} +O(q^{10})\) \(q+(0.767407 - 1.55277i) q^{3} +(1.73820 - 1.40665i) q^{5} +(-0.636300 + 0.636300i) q^{7} +(-1.82217 - 2.38321i) q^{9} +(2.06892 - 0.672233i) q^{11} +(0.777501 - 0.396157i) q^{13} +(-0.850289 - 3.77849i) q^{15} +(0.108171 + 0.682968i) q^{17} +(-3.00841 + 4.14072i) q^{19} +(0.499725 + 1.47633i) q^{21} +(-4.93053 - 2.51223i) q^{23} +(1.04269 - 4.89007i) q^{25} +(-5.09892 + 1.00052i) q^{27} +(4.84938 - 3.52328i) q^{29} +(6.26107 + 4.54893i) q^{31} +(0.543881 - 3.72843i) q^{33} +(-0.210967 + 2.00107i) q^{35} +(-0.550893 - 1.08119i) q^{37} +(-0.0184796 - 1.51129i) q^{39} +(2.90898 + 0.945186i) q^{41} +(8.01220 + 8.01220i) q^{43} +(-6.51964 - 1.57934i) q^{45} +(-7.69094 - 1.21813i) q^{47} +6.19025i q^{49} +(1.14350 + 0.356149i) q^{51} +(-0.429522 + 2.71189i) q^{53} +(2.65060 - 4.07872i) q^{55} +(4.12090 + 7.84897i) q^{57} +(-3.57345 + 10.9980i) q^{59} +(2.58562 + 7.95771i) q^{61} +(2.67588 + 0.356986i) q^{63} +(0.794201 - 1.78227i) q^{65} +(-9.44650 + 1.49618i) q^{67} +(-7.68464 + 5.72807i) q^{69} +(-3.16602 - 4.35766i) q^{71} +(7.59343 - 14.9030i) q^{73} +(-6.79298 - 5.37172i) q^{75} +(-0.888711 + 1.74419i) q^{77} +(2.00608 + 2.76113i) q^{79} +(-2.35936 + 8.68524i) q^{81} +(-5.95105 + 0.942553i) q^{83} +(1.14872 + 1.03498i) q^{85} +(-1.74939 - 10.2337i) q^{87} +(4.99027 + 15.3585i) q^{89} +(-0.242649 + 0.746798i) q^{91} +(11.8682 - 6.23110i) q^{93} +(0.595312 + 11.4292i) q^{95} +(-0.0903661 + 0.570549i) q^{97} +(-5.37200 - 3.70574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\)

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
\(3\) 0.767407 1.55277i 0.443062 0.896491i
\(4\) 0 0
\(5\) 1.73820 1.40665i 0.777347 0.629072i
\(6\) 0 0
\(7\) −0.636300 + 0.636300i −0.240499 + 0.240499i −0.817056 0.576558i \(-0.804396\pi\)
0.576558 + 0.817056i \(0.304396\pi\)
\(8\) 0 0
\(9\) −1.82217 2.38321i −0.607391 0.794403i
\(10\) 0 0
\(11\) 2.06892 0.672233i 0.623803 0.202686i 0.0199748 0.999800i \(-0.493641\pi\)
0.603828 + 0.797115i \(0.293641\pi\)
\(12\) 0 0
\(13\) 0.777501 0.396157i 0.215640 0.109874i −0.342834 0.939396i \(-0.611387\pi\)
0.558474 + 0.829522i \(0.311387\pi\)
\(14\) 0 0
\(15\) −0.850289 3.77849i −0.219544 0.975603i
\(16\) 0 0
\(17\) 0.108171 + 0.682968i 0.0262354 + 0.165644i 0.997327 0.0730615i \(-0.0232769\pi\)
−0.971092 + 0.238706i \(0.923277\pi\)
\(18\) 0 0
\(19\) −3.00841 + 4.14072i −0.690176 + 0.949945i −1.00000 0.000848557i \(-0.999730\pi\)
0.309824 + 0.950794i \(0.399730\pi\)
\(20\) 0 0
\(21\) 0.499725 + 1.47633i 0.109049 + 0.322161i
\(22\) 0 0
\(23\) −4.93053 2.51223i −1.02809 0.523837i −0.143225 0.989690i \(-0.545747\pi\)
−0.884862 + 0.465853i \(0.845747\pi\)
\(24\) 0 0
\(25\) 1.04269 4.89007i 0.208537 0.978014i
\(26\) 0 0
\(27\) −5.09892 + 1.00052i −0.981287 + 0.192551i
\(28\) 0 0
\(29\) 4.84938 3.52328i 0.900507 0.654256i −0.0380893 0.999274i \(-0.512127\pi\)
0.938596 + 0.345018i \(0.112127\pi\)
\(30\) 0 0
\(31\) 6.26107 + 4.54893i 1.12452 + 0.817012i 0.984888 0.173191i \(-0.0554078\pi\)
0.139633 + 0.990203i \(0.455408\pi\)
\(32\) 0 0
\(33\) 0.543881 3.72843i 0.0946776 0.649036i
\(34\) 0 0
\(35\) −0.210967 + 2.00107i −0.0356600 + 0.338242i
\(36\) 0 0
\(37\) −0.550893 1.08119i −0.0905663 0.177746i 0.841280 0.540600i \(-0.181803\pi\)
−0.931846 + 0.362853i \(0.881803\pi\)
\(38\) 0 0
\(39\) −0.0184796 1.51129i −0.00295911 0.242000i
\(40\) 0 0
\(41\) 2.90898 + 0.945186i 0.454307 + 0.147613i 0.527227 0.849724i \(-0.323232\pi\)
−0.0729199 + 0.997338i \(0.523232\pi\)
\(42\) 0 0
\(43\) 8.01220 + 8.01220i 1.22185 + 1.22185i 0.966974 + 0.254875i \(0.0820344\pi\)
0.254875 + 0.966974i \(0.417966\pi\)
\(44\) 0 0
\(45\) −6.51964 1.57934i −0.971890 0.235434i
\(46\) 0 0
\(47\) −7.69094 1.21813i −1.12184 0.177682i −0.432160 0.901797i \(-0.642248\pi\)
−0.689679 + 0.724115i \(0.742248\pi\)
\(48\) 0 0
\(49\) 6.19025i 0.884321i
\(50\) 0 0
\(51\) 1.14350 + 0.356149i 0.160122 + 0.0498708i
\(52\) 0 0
\(53\) −0.429522 + 2.71189i −0.0589994 + 0.372507i 0.940468 + 0.339881i \(0.110387\pi\)
−0.999468 + 0.0326258i \(0.989613\pi\)
\(54\) 0 0
\(55\) 2.65060 4.07872i 0.357407 0.549974i
\(56\) 0 0
\(57\) 4.12090 + 7.84897i 0.545826 + 1.03962i
\(58\) 0 0
\(59\) −3.57345 + 10.9980i −0.465224 + 1.43181i 0.393477 + 0.919334i \(0.371272\pi\)
−0.858701 + 0.512477i \(0.828728\pi\)
\(60\) 0 0
\(61\) 2.58562 + 7.95771i 0.331054 + 1.01888i 0.968633 + 0.248495i \(0.0799359\pi\)
−0.637579 + 0.770385i \(0.720064\pi\)
\(62\) 0 0
\(63\) 2.67588 + 0.356986i 0.337130 + 0.0449760i
\(64\) 0 0
\(65\) 0.794201 1.78227i 0.0985085 0.221063i
\(66\) 0 0
\(67\) −9.44650 + 1.49618i −1.15407 + 0.182787i −0.703997 0.710203i \(-0.748603\pi\)
−0.450076 + 0.892990i \(0.648603\pi\)
\(68\) 0 0
\(69\) −7.68464 + 5.72807i −0.925122 + 0.689578i
\(70\) 0 0
\(71\) −3.16602 4.35766i −0.375738 0.517159i 0.578711 0.815533i \(-0.303556\pi\)
−0.954449 + 0.298374i \(0.903556\pi\)
\(72\) 0 0
\(73\) 7.59343 14.9030i 0.888744 1.74426i 0.261936 0.965085i \(-0.415639\pi\)
0.626808 0.779174i \(-0.284361\pi\)
\(74\) 0 0
\(75\) −6.79298 5.37172i −0.784386 0.620273i
\(76\) 0 0
\(77\) −0.888711 + 1.74419i −0.101278 + 0.198769i
\(78\) 0 0
\(79\) 2.00608 + 2.76113i 0.225701 + 0.310651i 0.906817 0.421525i \(-0.138505\pi\)
−0.681116 + 0.732176i \(0.738505\pi\)
\(80\) 0 0
\(81\) −2.35936 + 8.68524i −0.262151 + 0.965027i
\(82\) 0 0
\(83\) −5.95105 + 0.942553i −0.653212 + 0.103459i −0.474240 0.880395i \(-0.657277\pi\)
−0.178972 + 0.983854i \(0.557277\pi\)
\(84\) 0 0
\(85\) 1.14872 + 1.03498i 0.124596 + 0.112259i
\(86\) 0 0
\(87\) −1.74939 10.2337i −0.187554 1.09717i
\(88\) 0 0
\(89\) 4.99027 + 15.3585i 0.528968 + 1.62800i 0.756334 + 0.654186i \(0.226989\pi\)
−0.227366 + 0.973809i \(0.573011\pi\)
\(90\) 0 0
\(91\) −0.242649 + 0.746798i −0.0254366 + 0.0782857i
\(92\) 0 0
\(93\) 11.8682 6.23110i 1.23068 0.646135i
\(94\) 0 0
\(95\) 0.595312 + 11.4292i 0.0610778 + 1.17261i
\(96\) 0 0
\(97\) −0.0903661 + 0.570549i −0.00917528 + 0.0579305i −0.991851 0.127402i \(-0.959336\pi\)
0.982676 + 0.185332i \(0.0593362\pi\)
\(98\) 0 0
\(99\) −5.37200 3.70574i −0.539906 0.372441i
\(100\) 0 0
\(101\) 10.1216i 1.00713i −0.863956 0.503567i \(-0.832021\pi\)
0.863956 0.503567i \(-0.167979\pi\)
\(102\) 0 0
\(103\) 3.57836 + 0.566756i 0.352586 + 0.0558442i 0.330215 0.943906i \(-0.392879\pi\)
0.0223707 + 0.999750i \(0.492879\pi\)
\(104\) 0 0
\(105\) 2.94529 + 1.86321i 0.287431 + 0.181831i
\(106\) 0 0
\(107\) −1.76323 1.76323i −0.170458 0.170458i 0.616722 0.787181i \(-0.288460\pi\)
−0.787181 + 0.616722i \(0.788460\pi\)
\(108\) 0 0
\(109\) −5.77632 1.87684i −0.553272 0.179769i 0.0190199 0.999819i \(-0.493945\pi\)
−0.572291 + 0.820050i \(0.693945\pi\)
\(110\) 0 0
\(111\) −2.10159 + 0.0256976i −0.199474 + 0.00243911i
\(112\) 0 0
\(113\) 3.00442 + 5.89650i 0.282632 + 0.554696i 0.988057 0.154088i \(-0.0492439\pi\)
−0.705425 + 0.708784i \(0.749244\pi\)
\(114\) 0 0
\(115\) −12.1041 + 2.56876i −1.12871 + 0.239538i
\(116\) 0 0
\(117\) −2.36087 1.13108i −0.218262 0.104569i
\(118\) 0 0
\(119\) −0.503402 0.365743i −0.0461467 0.0335276i
\(120\) 0 0
\(121\) −5.07066 + 3.68405i −0.460969 + 0.334913i
\(122\) 0 0
\(123\) 3.70003 3.79163i 0.333620 0.341880i
\(124\) 0 0
\(125\) −5.06621 9.96662i −0.453136 0.891442i
\(126\) 0 0
\(127\) −10.3962 5.29711i −0.922510 0.470042i −0.0728321 0.997344i \(-0.523204\pi\)
−0.849678 + 0.527302i \(0.823204\pi\)
\(128\) 0 0
\(129\) 18.5897 6.29247i 1.63673 0.554021i
\(130\) 0 0
\(131\) 11.1367 15.3284i 0.973018 1.33924i 0.0325110 0.999471i \(-0.489650\pi\)
0.940507 0.339773i \(-0.110350\pi\)
\(132\) 0 0
\(133\) −0.720488 4.54898i −0.0624742 0.394447i
\(134\) 0 0
\(135\) −7.45556 + 8.91149i −0.641672 + 0.766979i
\(136\) 0 0
\(137\) 10.5280 5.36426i 0.899464 0.458300i 0.0578166 0.998327i \(-0.481586\pi\)
0.841647 + 0.540027i \(0.181586\pi\)
\(138\) 0 0
\(139\) 5.62085 1.82633i 0.476755 0.154907i −0.0607756 0.998151i \(-0.519357\pi\)
0.537530 + 0.843244i \(0.319357\pi\)
\(140\) 0 0
\(141\) −7.79355 + 11.0075i −0.656335 + 0.926995i
\(142\) 0 0
\(143\) 1.34228 1.34228i 0.112247 0.112247i
\(144\) 0 0
\(145\) 3.47318 12.9455i 0.288432 1.07507i
\(146\) 0 0
\(147\) 9.61201 + 4.75044i 0.792785 + 0.391809i
\(148\) 0 0
\(149\) −8.89212 −0.728471 −0.364236 0.931307i \(-0.618670\pi\)
−0.364236 + 0.931307i \(0.618670\pi\)
\(150\) 0 0
\(151\) 6.58968 0.536260 0.268130 0.963383i \(-0.413594\pi\)
0.268130 + 0.963383i \(0.413594\pi\)
\(152\) 0 0
\(153\) 1.43055 1.50228i 0.115653 0.121452i
\(154\) 0 0
\(155\) 17.2817 0.900156i 1.38810 0.0723023i
\(156\) 0 0
\(157\) 9.41818 9.41818i 0.751653 0.751653i −0.223135 0.974788i \(-0.571629\pi\)
0.974788 + 0.223135i \(0.0716290\pi\)
\(158\) 0 0
\(159\) 3.88132 + 2.74807i 0.307809 + 0.217936i
\(160\) 0 0
\(161\) 4.73583 1.53876i 0.373236 0.121272i
\(162\) 0 0
\(163\) −10.5179 + 5.35912i −0.823823 + 0.419759i −0.814476 0.580198i \(-0.802975\pi\)
−0.00934719 + 0.999956i \(0.502975\pi\)
\(164\) 0 0
\(165\) −4.29921 7.24580i −0.334693 0.564085i
\(166\) 0 0
\(167\) −3.37212 21.2908i −0.260943 1.64753i −0.675394 0.737457i \(-0.736027\pi\)
0.414452 0.910071i \(-0.363973\pi\)
\(168\) 0 0
\(169\) −7.19364 + 9.90120i −0.553357 + 0.761630i
\(170\) 0 0
\(171\) 15.3500 0.375447i 1.17385 0.0287111i
\(172\) 0 0
\(173\) −4.69375 2.39158i −0.356859 0.181829i 0.266365 0.963872i \(-0.414177\pi\)
−0.623224 + 0.782044i \(0.714177\pi\)
\(174\) 0 0
\(175\) 2.44809 + 3.77501i 0.185058 + 0.285364i
\(176\) 0 0
\(177\) 14.3350 + 13.9886i 1.07748 + 1.05145i
\(178\) 0 0
\(179\) 16.3130 11.8521i 1.21929 0.885869i 0.223253 0.974761i \(-0.428332\pi\)
0.996041 + 0.0888915i \(0.0283325\pi\)
\(180\) 0 0
\(181\) −17.8222 12.9486i −1.32471 0.962462i −0.999861 0.0166976i \(-0.994685\pi\)
−0.324854 0.945764i \(-0.605315\pi\)
\(182\) 0 0
\(183\) 14.3407 + 2.09194i 1.06009 + 0.154640i
\(184\) 0 0
\(185\) −2.47841 1.10441i −0.182217 0.0811979i
\(186\) 0 0
\(187\) 0.682911 + 1.34029i 0.0499394 + 0.0980116i
\(188\) 0 0
\(189\) 2.60781 3.88107i 0.189690 0.282306i
\(190\) 0 0
\(191\) −5.98311 1.94403i −0.432922 0.140665i 0.0844455 0.996428i \(-0.473088\pi\)
−0.517368 + 0.855763i \(0.673088\pi\)
\(192\) 0 0
\(193\) −7.45104 7.45104i −0.536338 0.536338i 0.386114 0.922451i \(-0.373817\pi\)
−0.922451 + 0.386114i \(0.873817\pi\)
\(194\) 0 0
\(195\) −2.15798 2.60094i −0.154536 0.186257i
\(196\) 0 0
\(197\) −23.7368 3.75954i −1.69118 0.267856i −0.764749 0.644329i \(-0.777137\pi\)
−0.926428 + 0.376472i \(0.877137\pi\)
\(198\) 0 0
\(199\) 20.1941i 1.43152i −0.698346 0.715760i \(-0.746080\pi\)
0.698346 0.715760i \(-0.253920\pi\)
\(200\) 0 0
\(201\) −4.92609 + 15.8164i −0.347459 + 1.11560i
\(202\) 0 0
\(203\) −0.843796 + 5.32752i −0.0592229 + 0.373918i
\(204\) 0 0
\(205\) 6.38594 2.44899i 0.446014 0.171045i
\(206\) 0 0
\(207\) 2.99712 + 16.3282i 0.208314 + 1.13489i
\(208\) 0 0
\(209\) −3.44063 + 10.5892i −0.237993 + 0.732467i
\(210\) 0 0
\(211\) −0.979151 3.01352i −0.0674075 0.207459i 0.911679 0.410903i \(-0.134787\pi\)
−0.979087 + 0.203444i \(0.934787\pi\)
\(212\) 0 0
\(213\) −9.19606 + 1.57200i −0.630104 + 0.107712i
\(214\) 0 0
\(215\) 25.1972 + 2.65648i 1.71843 + 0.181170i
\(216\) 0 0
\(217\) −6.87840 + 1.08943i −0.466936 + 0.0739554i
\(218\) 0 0
\(219\) −17.3136 23.2275i −1.16994 1.56957i
\(220\) 0 0
\(221\) 0.354666 + 0.488156i 0.0238574 + 0.0328369i
\(222\) 0 0
\(223\) −6.35432 + 12.4711i −0.425517 + 0.835124i 0.574347 + 0.818612i \(0.305256\pi\)
−0.999864 + 0.0165117i \(0.994744\pi\)
\(224\) 0 0
\(225\) −13.5540 + 6.42562i −0.903601 + 0.428375i
\(226\) 0 0
\(227\) −8.70950 + 17.0934i −0.578070 + 1.13453i 0.398064 + 0.917358i \(0.369682\pi\)
−0.976134 + 0.217169i \(0.930318\pi\)
\(228\) 0 0
\(229\) −5.96289 8.20721i −0.394039 0.542348i 0.565197 0.824956i \(-0.308800\pi\)
−0.959235 + 0.282609i \(0.908800\pi\)
\(230\) 0 0
\(231\) 2.02632 + 2.71847i 0.133322 + 0.178862i
\(232\) 0 0
\(233\) −21.7035 + 3.43750i −1.42185 + 0.225198i −0.819519 0.573052i \(-0.805759\pi\)
−0.602326 + 0.798250i \(0.705759\pi\)
\(234\) 0 0
\(235\) −15.0819 + 8.70110i −0.983833 + 0.567597i
\(236\) 0 0
\(237\) 5.82686 0.996063i 0.378495 0.0647012i
\(238\) 0 0
\(239\) 6.69642 + 20.6095i 0.433155 + 1.33312i 0.894965 + 0.446136i \(0.147200\pi\)
−0.461810 + 0.886979i \(0.652800\pi\)
\(240\) 0 0
\(241\) 6.18567 19.0375i 0.398454 1.22631i −0.527785 0.849378i \(-0.676977\pi\)
0.926239 0.376937i \(-0.123023\pi\)
\(242\) 0 0
\(243\) 11.6756 + 10.3287i 0.748988 + 0.662583i
\(244\) 0 0
\(245\) 8.70749 + 10.7599i 0.556301 + 0.687424i
\(246\) 0 0
\(247\) −0.698668 + 4.41121i −0.0444552 + 0.280679i
\(248\) 0 0
\(249\) −3.10331 + 9.96391i −0.196664 + 0.631437i
\(250\) 0 0
\(251\) 11.8785i 0.749764i 0.927073 + 0.374882i \(0.122317\pi\)
−0.927073 + 0.374882i \(0.877683\pi\)
\(252\) 0 0
\(253\) −11.8897 1.88314i −0.747498 0.118392i
\(254\) 0 0
\(255\) 2.48861 0.989445i 0.155843 0.0619615i
\(256\) 0 0
\(257\) 7.36523 + 7.36523i 0.459430 + 0.459430i 0.898468 0.439038i \(-0.144681\pi\)
−0.439038 + 0.898468i \(0.644681\pi\)
\(258\) 0 0
\(259\) 1.03849 + 0.337427i 0.0645288 + 0.0209667i
\(260\) 0 0
\(261\) −17.2331 5.13705i −1.06670 0.317975i
\(262\) 0 0
\(263\) −1.00991 1.98207i −0.0622739 0.122219i 0.857771 0.514031i \(-0.171848\pi\)
−0.920045 + 0.391812i \(0.871848\pi\)
\(264\) 0 0
\(265\) 3.06808 + 5.31800i 0.188471 + 0.326682i
\(266\) 0 0
\(267\) 27.6777 + 4.03747i 1.69385 + 0.247089i
\(268\) 0 0
\(269\) −16.6826 12.1206i −1.01716 0.739006i −0.0514573 0.998675i \(-0.516387\pi\)
−0.965698 + 0.259669i \(0.916387\pi\)
\(270\) 0 0
\(271\) 4.83987 3.51637i 0.294001 0.213604i −0.431000 0.902352i \(-0.641839\pi\)
0.725001 + 0.688748i \(0.241839\pi\)
\(272\) 0 0
\(273\) 0.973393 + 0.949876i 0.0589124 + 0.0574891i
\(274\) 0 0
\(275\) −1.13003 10.8181i −0.0681435 0.652356i
\(276\) 0 0
\(277\) 26.8008 + 13.6557i 1.61030 + 0.820490i 0.999590 + 0.0286381i \(0.00911705\pi\)
0.610713 + 0.791852i \(0.290883\pi\)
\(278\) 0 0
\(279\) −0.567703 23.2104i −0.0339875 1.38957i
\(280\) 0 0
\(281\) −4.52028 + 6.22163i −0.269657 + 0.371151i −0.922274 0.386537i \(-0.873671\pi\)
0.652617 + 0.757688i \(0.273671\pi\)
\(282\) 0 0
\(283\) 1.44567 + 9.12761i 0.0859363 + 0.542580i 0.992668 + 0.120872i \(0.0385692\pi\)
−0.906732 + 0.421708i \(0.861431\pi\)
\(284\) 0 0
\(285\) 18.2037 + 7.84643i 1.07829 + 0.464783i
\(286\) 0 0
\(287\) −2.45241 + 1.24956i −0.144761 + 0.0737594i
\(288\) 0 0
\(289\) 15.7132 5.10553i 0.924307 0.300326i
\(290\) 0 0
\(291\) 0.816582 + 0.578160i 0.0478689 + 0.0338924i
\(292\) 0 0
\(293\) −14.0642 + 14.0642i −0.821637 + 0.821637i −0.986343 0.164706i \(-0.947332\pi\)
0.164706 + 0.986343i \(0.447332\pi\)
\(294\) 0 0
\(295\) 9.25887 + 24.1432i 0.539072 + 1.40567i
\(296\) 0 0
\(297\) −9.87666 + 5.49766i −0.573102 + 0.319007i
\(298\) 0 0
\(299\) −4.82874 −0.279253
\(300\) 0 0
\(301\) −10.1963 −0.587706
\(302\) 0 0
\(303\) −15.7164 7.76735i −0.902885 0.446223i
\(304\) 0 0
\(305\) 15.6880 + 10.1950i 0.898293 + 0.583767i
\(306\) 0 0
\(307\) 15.6968 15.6968i 0.895865 0.895865i −0.0992024 0.995067i \(-0.531629\pi\)
0.995067 + 0.0992024i \(0.0316291\pi\)
\(308\) 0 0
\(309\) 3.62610 5.12143i 0.206281 0.291348i
\(310\) 0 0
\(311\) −2.25244 + 0.731862i −0.127724 + 0.0415001i −0.372182 0.928160i \(-0.621390\pi\)
0.244457 + 0.969660i \(0.421390\pi\)
\(312\) 0 0
\(313\) −8.52093 + 4.34163i −0.481632 + 0.245404i −0.677910 0.735145i \(-0.737114\pi\)
0.196279 + 0.980548i \(0.437114\pi\)
\(314\) 0 0
\(315\) 5.15338 3.14351i 0.290360 0.177117i
\(316\) 0 0
\(317\) −3.90141 24.6325i −0.219125 1.38350i −0.814551 0.580091i \(-0.803017\pi\)
0.595426 0.803410i \(-0.296983\pi\)
\(318\) 0 0
\(319\) 7.66451 10.5493i 0.429130 0.590647i
\(320\) 0 0
\(321\) −4.09101 + 1.38477i −0.228338 + 0.0772906i
\(322\) 0 0
\(323\) −3.15340 1.60674i −0.175460 0.0894013i
\(324\) 0 0
\(325\) −1.12655 4.21511i −0.0624895 0.233812i
\(326\) 0 0
\(327\) −7.34709 + 7.52899i −0.406295 + 0.416354i
\(328\) 0 0
\(329\) 5.66884 4.11865i 0.312533 0.227069i
\(330\) 0 0
\(331\) −3.45492 2.51015i −0.189900 0.137970i 0.488773 0.872411i \(-0.337445\pi\)
−0.678673 + 0.734441i \(0.737445\pi\)
\(332\) 0 0
\(333\) −1.57287 + 3.28301i −0.0861930 + 0.179908i
\(334\) 0 0
\(335\) −14.3153 + 15.8885i −0.782129 + 0.868084i
\(336\) 0 0
\(337\) 16.4657 + 32.3157i 0.896941 + 1.76035i 0.586990 + 0.809594i \(0.300313\pi\)
0.309951 + 0.950753i \(0.399687\pi\)
\(338\) 0 0
\(339\) 11.4615 0.140148i 0.622504 0.00761178i
\(340\) 0 0
\(341\) 16.0116 + 5.20248i 0.867076 + 0.281730i
\(342\) 0 0
\(343\) −8.39295 8.39295i −0.453177 0.453177i
\(344\) 0 0
\(345\) −5.30007 + 20.7661i −0.285346 + 1.11801i
\(346\) 0 0
\(347\) −3.51964 0.557457i −0.188944 0.0299258i 0.0612451 0.998123i \(-0.480493\pi\)
−0.250189 + 0.968197i \(0.580493\pi\)
\(348\) 0 0
\(349\) 6.07476i 0.325174i 0.986694 + 0.162587i \(0.0519839\pi\)
−0.986694 + 0.162587i \(0.948016\pi\)
\(350\) 0 0
\(351\) −3.56805 + 2.79788i −0.190449 + 0.149340i
\(352\) 0 0
\(353\) −3.37712 + 21.3223i −0.179746 + 1.13487i 0.718549 + 0.695476i \(0.244807\pi\)
−0.898295 + 0.439394i \(0.855193\pi\)
\(354\) 0 0
\(355\) −11.6329 3.12101i −0.617409 0.165646i
\(356\) 0 0
\(357\) −0.954227 + 0.500992i −0.0505030 + 0.0265153i
\(358\) 0 0
\(359\) −0.695103 + 2.13931i −0.0366861 + 0.112908i −0.967723 0.252018i \(-0.918906\pi\)
0.931036 + 0.364926i \(0.118906\pi\)
\(360\) 0 0
\(361\) −2.22370 6.84384i −0.117037 0.360202i
\(362\) 0 0
\(363\) 1.82921 + 10.7007i 0.0960088 + 0.561642i
\(364\) 0 0
\(365\) −7.76429 36.5856i −0.406401 1.91498i
\(366\) 0 0
\(367\) 0.0910705 0.0144241i 0.00475384 0.000752934i −0.154057 0.988062i \(-0.549234\pi\)
0.158811 + 0.987309i \(0.449234\pi\)
\(368\) 0 0
\(369\) −3.04810 8.65501i −0.158678 0.450562i
\(370\) 0 0
\(371\) −1.45227 1.99888i −0.0753982 0.103777i
\(372\) 0 0
\(373\) −9.29049 + 18.2336i −0.481043 + 0.944101i 0.515164 + 0.857092i \(0.327731\pi\)
−0.996208 + 0.0870092i \(0.972269\pi\)
\(374\) 0 0
\(375\) −19.3637 + 0.218194i −0.999937 + 0.0112675i
\(376\) 0 0
\(377\) 2.37463 4.66047i 0.122300 0.240026i
\(378\) 0 0
\(379\) −13.7712 18.9544i −0.707377 0.973620i −0.999850 0.0173466i \(-0.994478\pi\)
0.292473 0.956274i \(-0.405522\pi\)
\(380\) 0 0
\(381\) −16.2033 + 12.0778i −0.830118 + 0.618764i
\(382\) 0 0
\(383\) 26.5323 4.20230i 1.35574 0.214728i 0.564093 0.825711i \(-0.309226\pi\)
0.791643 + 0.610984i \(0.209226\pi\)
\(384\) 0 0
\(385\) 0.908707 + 4.28186i 0.0463120 + 0.218224i
\(386\) 0 0
\(387\) 4.49512 33.6944i 0.228500 1.71278i
\(388\) 0 0
\(389\) 6.63326 + 20.4151i 0.336319 + 1.03508i 0.966068 + 0.258286i \(0.0831577\pi\)
−0.629749 + 0.776799i \(0.716842\pi\)
\(390\) 0 0
\(391\) 1.18243 3.63915i 0.0597981 0.184040i
\(392\) 0 0
\(393\) −15.2550 29.0558i −0.769513 1.46567i
\(394\) 0 0
\(395\) 7.37089 + 1.97755i 0.370870 + 0.0995014i
\(396\) 0 0
\(397\) 2.70917 17.1050i 0.135969 0.858477i −0.821556 0.570128i \(-0.806894\pi\)
0.957525 0.288349i \(-0.0931063\pi\)
\(398\) 0 0
\(399\) −7.61642 2.37217i −0.381298 0.118757i
\(400\) 0 0
\(401\) 38.7468i 1.93492i −0.253022 0.967460i \(-0.581425\pi\)
0.253022 0.967460i \(-0.418575\pi\)
\(402\) 0 0
\(403\) 6.67008 + 1.05644i 0.332260 + 0.0526249i
\(404\) 0 0
\(405\) 8.11602 + 18.4155i 0.403288 + 0.915073i
\(406\) 0 0
\(407\) −1.86656 1.86656i −0.0925221 0.0925221i
\(408\) 0 0
\(409\) 23.7030 + 7.70156i 1.17204 + 0.380818i 0.829403 0.558651i \(-0.188681\pi\)
0.342634 + 0.939469i \(0.388681\pi\)
\(410\) 0 0
\(411\) −0.250228 20.4640i −0.0123428 1.00942i
\(412\) 0 0
\(413\) −4.72421 9.27178i −0.232463 0.456234i
\(414\) 0 0
\(415\) −9.01828 + 10.0094i −0.442690 + 0.491341i
\(416\) 0 0
\(417\) 1.47762 10.1294i 0.0723594 0.496040i
\(418\) 0 0
\(419\) −16.0365 11.6512i −0.783434 0.569198i 0.122574 0.992459i \(-0.460885\pi\)
−0.906008 + 0.423261i \(0.860885\pi\)
\(420\) 0 0
\(421\) −28.5140 + 20.7166i −1.38968 + 1.00967i −0.393785 + 0.919203i \(0.628835\pi\)
−0.995900 + 0.0904626i \(0.971165\pi\)
\(422\) 0 0
\(423\) 11.1112 + 20.5488i 0.540245 + 0.999115i
\(424\) 0 0
\(425\) 3.45255 + 0.183155i 0.167473 + 0.00888431i
\(426\) 0 0
\(427\) −6.70871 3.41826i −0.324657 0.165421i
\(428\) 0 0
\(429\) −1.05417 3.11432i −0.0508959 0.150361i
\(430\) 0 0
\(431\) −5.84421 + 8.04387i −0.281506 + 0.387459i −0.926232 0.376954i \(-0.876971\pi\)
0.644726 + 0.764414i \(0.276971\pi\)
\(432\) 0 0
\(433\) −1.00246 6.32931i −0.0481753 0.304167i 0.951822 0.306652i \(-0.0992089\pi\)
−0.999997 + 0.00248534i \(0.999209\pi\)
\(434\) 0 0
\(435\) −17.4361 15.3275i −0.835995 0.734899i
\(436\) 0 0
\(437\) 25.2355 12.8581i 1.20718 0.615087i
\(438\) 0 0
\(439\) 13.3636 4.34210i 0.637811 0.207237i 0.0277788 0.999614i \(-0.491157\pi\)
0.610032 + 0.792377i \(0.291157\pi\)
\(440\) 0 0
\(441\) 14.7526 11.2797i 0.702507 0.537129i
\(442\) 0 0
\(443\) −4.23679 + 4.23679i −0.201296 + 0.201296i −0.800555 0.599259i \(-0.795462\pi\)
0.599259 + 0.800555i \(0.295462\pi\)
\(444\) 0 0
\(445\) 30.2781 + 19.6766i 1.43532 + 0.932759i
\(446\) 0 0
\(447\) −6.82387 + 13.8074i −0.322758 + 0.653068i
\(448\) 0 0
\(449\) 2.90528 0.137109 0.0685544 0.997647i \(-0.478161\pi\)
0.0685544 + 0.997647i \(0.478161\pi\)
\(450\) 0 0
\(451\) 6.65384 0.313317
\(452\) 0 0
\(453\) 5.05696 10.2322i 0.237597 0.480752i
\(454\) 0 0
\(455\) 0.628708 + 1.63941i 0.0294743 + 0.0768566i
\(456\) 0 0
\(457\) −0.266668 + 0.266668i −0.0124742 + 0.0124742i −0.713316 0.700842i \(-0.752808\pi\)
0.700842 + 0.713316i \(0.252808\pi\)
\(458\) 0 0
\(459\) −1.23488 3.37417i −0.0576394 0.157493i
\(460\) 0 0
\(461\) 7.84012 2.54741i 0.365151 0.118645i −0.120694 0.992690i \(-0.538512\pi\)
0.485845 + 0.874045i \(0.338512\pi\)
\(462\) 0 0
\(463\) 25.2437 12.8623i 1.17318 0.597763i 0.244861 0.969558i \(-0.421258\pi\)
0.928315 + 0.371795i \(0.121258\pi\)
\(464\) 0 0
\(465\) 11.8644 27.5253i 0.550198 1.27646i
\(466\) 0 0
\(467\) −2.43120 15.3500i −0.112502 0.710312i −0.977876 0.209185i \(-0.932919\pi\)
0.865374 0.501127i \(-0.167081\pi\)
\(468\) 0 0
\(469\) 5.05878 6.96282i 0.233593 0.321513i
\(470\) 0 0
\(471\) −7.39667 21.8518i −0.340821 1.00688i
\(472\) 0 0
\(473\) 21.9627 + 11.1905i 1.00984 + 0.514541i
\(474\) 0 0
\(475\) 17.1116 + 19.0288i 0.785133 + 0.873101i
\(476\) 0 0
\(477\) 7.24567 3.91790i 0.331757 0.179388i
\(478\) 0 0
\(479\) 27.1035 19.6918i 1.23839 0.899743i 0.240900 0.970550i \(-0.422558\pi\)
0.997490 + 0.0708073i \(0.0225576\pi\)
\(480\) 0 0
\(481\) −0.856641 0.622386i −0.0390594 0.0283783i
\(482\) 0 0
\(483\) 1.24496 8.53450i 0.0566478 0.388333i
\(484\) 0 0
\(485\) 0.645487 + 1.11884i 0.0293100 + 0.0508040i
\(486\) 0 0
\(487\) 4.96474 + 9.74384i 0.224974 + 0.441536i 0.975710 0.219066i \(-0.0703011\pi\)
−0.750736 + 0.660602i \(0.770301\pi\)
\(488\) 0 0
\(489\) 0.249988 + 20.4444i 0.0113048 + 0.924529i
\(490\) 0 0
\(491\) −29.5939 9.61564i −1.33555 0.433948i −0.447746 0.894161i \(-0.647773\pi\)
−0.887809 + 0.460213i \(0.847773\pi\)
\(492\) 0 0
\(493\) 2.93085 + 2.93085i 0.131999 + 0.131999i
\(494\) 0 0
\(495\) −14.5503 + 1.11519i −0.653987 + 0.0501240i
\(496\) 0 0
\(497\) 4.78732 + 0.758236i 0.214740 + 0.0340115i
\(498\) 0 0
\(499\) 18.3818i 0.822881i 0.911437 + 0.411441i \(0.134974\pi\)
−0.911437 + 0.411441i \(0.865026\pi\)
\(500\) 0 0
\(501\) −35.6474 11.1025i −1.59261 0.496025i
\(502\) 0 0
\(503\) 6.37553 40.2535i 0.284271 1.79481i −0.270403 0.962747i \(-0.587157\pi\)
0.554674 0.832068i \(-0.312843\pi\)
\(504\) 0 0
\(505\) −14.2375 17.5933i −0.633559 0.782892i
\(506\) 0 0
\(507\) 9.85381 + 18.7683i 0.437623 + 0.833529i
\(508\) 0 0
\(509\) −8.19240 + 25.2136i −0.363122 + 1.11757i 0.588027 + 0.808841i \(0.299905\pi\)
−0.951149 + 0.308733i \(0.900095\pi\)
\(510\) 0 0
\(511\) 4.65104 + 14.3144i 0.205750 + 0.633234i
\(512\) 0 0
\(513\) 11.1967 24.1231i 0.494348 1.06506i
\(514\) 0 0
\(515\) 7.01713 4.04835i 0.309212 0.178392i
\(516\) 0 0
\(517\) −16.7308 + 2.64990i −0.735820 + 0.116542i
\(518\) 0 0
\(519\) −7.31559 + 5.45298i −0.321119 + 0.239359i
\(520\) 0 0
\(521\) −1.98068 2.72618i −0.0867754 0.119436i 0.763422 0.645900i \(-0.223518\pi\)
−0.850198 + 0.526464i \(0.823518\pi\)
\(522\) 0 0
\(523\) −6.15343 + 12.0768i −0.269071 + 0.528081i −0.985520 0.169558i \(-0.945766\pi\)
0.716449 + 0.697639i \(0.245766\pi\)
\(524\) 0 0
\(525\) 7.74040 0.904346i 0.337819 0.0394689i
\(526\) 0 0
\(527\) −2.42950 + 4.76817i −0.105831 + 0.207705i
\(528\) 0 0
\(529\) 4.47979 + 6.16590i 0.194773 + 0.268083i
\(530\) 0 0
\(531\) 32.7219 11.5239i 1.42001 0.500095i
\(532\) 0 0
\(533\) 2.63618 0.417530i 0.114186 0.0180852i
\(534\) 0 0
\(535\) −5.54510 0.584607i −0.239736 0.0252748i
\(536\) 0 0
\(537\) −5.88485 34.4258i −0.253950 1.48558i
\(538\) 0 0
\(539\) 4.16129 + 12.8071i 0.179239 + 0.551642i
\(540\) 0 0
\(541\) 3.66203 11.2706i 0.157443 0.484559i −0.840957 0.541101i \(-0.818007\pi\)
0.998400 + 0.0565420i \(0.0180075\pi\)
\(542\) 0 0
\(543\) −33.7830 + 17.7369i −1.44977 + 0.761164i
\(544\) 0 0
\(545\) −12.6805 + 4.86292i −0.543172 + 0.208305i
\(546\) 0 0
\(547\) −2.04796 + 12.9303i −0.0875642 + 0.552859i 0.904435 + 0.426612i \(0.140293\pi\)
−0.991999 + 0.126247i \(0.959707\pi\)
\(548\) 0 0
\(549\) 14.2534 20.6624i 0.608322 0.881849i
\(550\) 0 0
\(551\) 30.6793i 1.30698i
\(552\) 0 0
\(553\) −3.03337 0.480438i −0.128992 0.0204303i
\(554\) 0 0
\(555\) −3.61685 + 3.00087i −0.153527 + 0.127380i
\(556\) 0 0
\(557\) 16.6516 + 16.6516i 0.705552 + 0.705552i 0.965597 0.260045i \(-0.0837374\pi\)
−0.260045 + 0.965597i \(0.583737\pi\)
\(558\) 0 0
\(559\) 9.40359 + 3.05541i 0.397729 + 0.129230i
\(560\) 0 0
\(561\) 2.60523 0.0318559i 0.109993 0.00134496i
\(562\) 0 0
\(563\) 9.45734 + 18.5611i 0.398579 + 0.782256i 0.999859 0.0167826i \(-0.00534231\pi\)
−0.601280 + 0.799039i \(0.705342\pi\)
\(564\) 0 0
\(565\) 13.5166 + 6.02315i 0.568647 + 0.253396i
\(566\) 0 0
\(567\) −4.02515 7.02768i −0.169041 0.295135i
\(568\) 0 0
\(569\) −23.7171 17.2314i −0.994271 0.722380i −0.0334184 0.999441i \(-0.510639\pi\)
−0.960852 + 0.277062i \(0.910639\pi\)
\(570\) 0 0
\(571\) 7.34646 5.33751i 0.307440 0.223368i −0.423357 0.905963i \(-0.639149\pi\)
0.730797 + 0.682595i \(0.239149\pi\)
\(572\) 0 0
\(573\) −7.61010 + 7.79851i −0.317917 + 0.325788i
\(574\) 0 0
\(575\) −17.4260 + 21.4912i −0.726714 + 0.896245i
\(576\) 0 0
\(577\) −16.0285 8.16690i −0.667273 0.339993i 0.0873249 0.996180i \(-0.472168\pi\)
−0.754598 + 0.656187i \(0.772168\pi\)
\(578\) 0 0
\(579\) −17.2877 + 5.85176i −0.718453 + 0.243191i
\(580\) 0 0
\(581\) 3.18690 4.38639i 0.132215 0.181978i
\(582\) 0 0
\(583\) 0.934378 + 5.89943i 0.0386980 + 0.244329i
\(584\) 0 0
\(585\) −5.69469 + 1.35486i −0.235447 + 0.0560166i
\(586\) 0 0
\(587\) −12.3163 + 6.27549i −0.508350 + 0.259017i −0.689301 0.724475i \(-0.742082\pi\)
0.180951 + 0.983492i \(0.442082\pi\)
\(588\) 0 0
\(589\) −37.6717 + 12.2403i −1.55223 + 0.504351i
\(590\) 0 0
\(591\) −24.0535 + 33.9726i −0.989427 + 1.39745i
\(592\) 0 0
\(593\) −0.149745 + 0.149745i −0.00614930 + 0.00614930i −0.710175 0.704025i \(-0.751384\pi\)
0.704025 + 0.710175i \(0.251384\pi\)
\(594\) 0 0
\(595\) −1.38948 + 0.0723742i −0.0569633 + 0.00296705i
\(596\) 0 0
\(597\) −31.3567 15.4971i −1.28334 0.634253i
\(598\) 0 0
\(599\) −4.89253 −0.199903 −0.0999517 0.994992i \(-0.531869\pi\)
−0.0999517 + 0.994992i \(0.531869\pi\)
\(600\) 0 0
\(601\) 37.0254 1.51030 0.755148 0.655554i \(-0.227565\pi\)
0.755148 + 0.655554i \(0.227565\pi\)
\(602\) 0 0
\(603\) 20.7789 + 19.7867i 0.846181 + 0.805776i
\(604\) 0 0
\(605\) −3.63166 + 13.5362i −0.147648 + 0.550326i
\(606\) 0 0
\(607\) 25.1008 25.1008i 1.01881 1.01881i 0.0189918 0.999820i \(-0.493954\pi\)
0.999820 0.0189918i \(-0.00604565\pi\)
\(608\) 0 0
\(609\) 7.62486 + 5.39859i 0.308975 + 0.218762i
\(610\) 0 0
\(611\) −6.46229 + 2.09973i −0.261436 + 0.0849458i
\(612\) 0 0
\(613\) 18.3061 9.32741i 0.739375 0.376731i −0.0433812 0.999059i \(-0.513813\pi\)
0.782757 + 0.622328i \(0.213813\pi\)
\(614\) 0 0
\(615\) 1.09790 11.7953i 0.0442717 0.475631i
\(616\) 0 0
\(617\) 5.07305 + 32.0300i 0.204233 + 1.28948i 0.850341 + 0.526232i \(0.176396\pi\)
−0.646108 + 0.763246i \(0.723604\pi\)
\(618\) 0 0
\(619\) −0.306242 + 0.421506i −0.0123089 + 0.0169418i −0.815127 0.579282i \(-0.803333\pi\)
0.802818 + 0.596224i \(0.203333\pi\)
\(620\) 0 0
\(621\) 27.6539 + 7.87655i 1.10971 + 0.316075i
\(622\) 0 0
\(623\) −12.9479 6.59729i −0.518747 0.264315i
\(624\) 0 0
\(625\) −22.8256 10.1976i −0.913024 0.407905i
\(626\) 0 0
\(627\) 13.8021 + 13.4687i 0.551204 + 0.537887i
\(628\) 0 0
\(629\) 0.678826 0.493196i 0.0270666 0.0196650i
\(630\) 0 0
\(631\) −8.26187 6.00260i −0.328900 0.238960i 0.411064 0.911607i \(-0.365157\pi\)
−0.739964 + 0.672647i \(0.765157\pi\)
\(632\) 0 0
\(633\) −5.43070 0.792199i −0.215851 0.0314871i
\(634\) 0 0
\(635\) −25.5218 + 5.41629i −1.01280 + 0.214939i
\(636\) 0 0
\(637\) 2.45231 + 4.81293i 0.0971640 + 0.190695i
\(638\) 0 0
\(639\) −4.61616 + 15.4857i −0.182612 + 0.612605i
\(640\) 0 0
\(641\) 17.1276 + 5.56508i 0.676498 + 0.219807i 0.627061 0.778970i \(-0.284258\pi\)
0.0494363 + 0.998777i \(0.484258\pi\)
\(642\) 0 0
\(643\) −6.99059 6.99059i −0.275682 0.275682i 0.555700 0.831383i \(-0.312450\pi\)
−0.831383 + 0.555700i \(0.812450\pi\)
\(644\) 0 0
\(645\) 23.4614 37.0867i 0.923790 1.46029i
\(646\) 0 0
\(647\) −17.5984 2.78732i −0.691865 0.109581i −0.199407 0.979917i \(-0.563902\pi\)
−0.492458 + 0.870336i \(0.663902\pi\)
\(648\) 0 0
\(649\) 25.1561i 0.987462i
\(650\) 0 0
\(651\) −3.58689 + 11.5166i −0.140581 + 0.451371i
\(652\) 0 0
\(653\) −2.53429 + 16.0009i −0.0991746 + 0.626164i 0.887167 + 0.461449i \(0.152670\pi\)
−0.986341 + 0.164715i \(0.947330\pi\)
\(654\) 0 0
\(655\) −2.20376 42.3092i −0.0861082 1.65316i
\(656\) 0 0
\(657\) −49.3534 + 9.05904i −1.92546 + 0.353427i
\(658\) 0 0
\(659\) 9.69034 29.8238i 0.377482 1.16177i −0.564307 0.825565i \(-0.690856\pi\)
0.941789 0.336205i \(-0.109144\pi\)
\(660\) 0 0
\(661\) 12.1139 + 37.2828i 0.471177 + 1.45013i 0.851046 + 0.525092i \(0.175969\pi\)
−0.379869 + 0.925040i \(0.624031\pi\)
\(662\) 0 0
\(663\) 1.03017 0.176100i 0.0400083 0.00683915i
\(664\) 0 0
\(665\) −7.65117 6.89357i −0.296700 0.267321i
\(666\) 0 0
\(667\) −32.7613 + 5.18888i −1.26852 + 0.200914i
\(668\) 0 0
\(669\) 14.4883 + 19.4372i 0.560150 + 0.751484i
\(670\) 0 0
\(671\) 10.6989 + 14.7257i 0.413025 + 0.568480i
\(672\) 0 0
\(673\) 11.9112 23.3771i 0.459145 0.901122i −0.539120 0.842229i \(-0.681243\pi\)
0.998264 0.0588931i \(-0.0187571\pi\)
\(674\) 0 0
\(675\) −0.423941 + 25.9773i −0.0163175 + 0.999867i
\(676\) 0 0
\(677\) −5.68410 + 11.1557i −0.218458 + 0.428748i −0.974062 0.226281i \(-0.927343\pi\)
0.755604 + 0.655028i \(0.227343\pi\)
\(678\) 0 0
\(679\) −0.305540 0.420540i −0.0117256 0.0161388i
\(680\) 0 0
\(681\) 19.8583 + 26.6414i 0.760971 + 1.02090i
\(682\) 0 0
\(683\) −3.16982 + 0.502051i −0.121290 + 0.0192104i −0.216784 0.976220i \(-0.569557\pi\)
0.0954943 + 0.995430i \(0.469557\pi\)
\(684\) 0 0
\(685\) 10.7541 24.1333i 0.410892 0.922086i
\(686\) 0 0
\(687\) −17.3198 + 2.96071i −0.660793 + 0.112958i
\(688\) 0 0
\(689\) 0.740381 + 2.27866i 0.0282063 + 0.0868100i
\(690\) 0 0
\(691\) −5.16372 + 15.8923i −0.196437 + 0.604571i 0.803520 + 0.595278i \(0.202958\pi\)
−0.999957 + 0.00929313i \(0.997042\pi\)
\(692\) 0 0
\(693\) 5.77616 1.06024i 0.219418 0.0402752i
\(694\) 0 0
\(695\) 7.20118 11.0811i 0.273156 0.420329i
\(696\) 0 0
\(697\) −0.330863 + 2.08899i −0.0125323 + 0.0791260i
\(698\) 0 0
\(699\) −11.3178 + 36.3385i −0.428078 + 1.37445i
\(700\) 0 0
\(701\) 10.1389i 0.382941i 0.981498 + 0.191470i \(0.0613256\pi\)
−0.981498 + 0.191470i \(0.938674\pi\)
\(702\) 0 0
\(703\) 6.13421 + 0.971563i 0.231356 + 0.0366432i
\(704\) 0 0
\(705\) 1.93685 + 30.0959i 0.0729459 + 1.13348i
\(706\) 0 0
\(707\) 6.44035 + 6.44035i 0.242214 + 0.242214i
\(708\) 0 0
\(709\) −4.38945 1.42622i −0.164849 0.0535627i 0.225430 0.974259i \(-0.427621\pi\)
−0.390279 + 0.920697i \(0.627621\pi\)
\(710\) 0 0
\(711\) 2.92492 9.81215i 0.109693 0.367984i
\(712\) 0 0
\(713\) −19.4424 38.1579i −0.728125 1.42903i
\(714\) 0 0
\(715\) 0.445037 4.22126i 0.0166435 0.157866i
\(716\) 0 0
\(717\) 37.1406 + 5.41785i 1.38704 + 0.202333i
\(718\) 0 0
\(719\) −4.62038 3.35690i −0.172311 0.125191i 0.498287 0.867012i \(-0.333963\pi\)
−0.670598 + 0.741821i \(0.733963\pi\)
\(720\) 0 0
\(721\) −2.63754 + 1.91628i −0.0982269 + 0.0713660i
\(722\) 0 0
\(723\) −24.8139 24.2144i −0.922840 0.900544i
\(724\) 0 0
\(725\) −12.1727 27.3875i −0.452083 1.01715i
\(726\) 0 0
\(727\) −19.0304 9.69647i −0.705798 0.359622i 0.0639646 0.997952i \(-0.479626\pi\)
−0.769763 + 0.638330i \(0.779626\pi\)
\(728\) 0 0
\(729\) 24.9979 10.2032i 0.925848 0.377895i
\(730\) 0 0
\(731\) −4.60538 + 6.33877i −0.170336 + 0.234448i
\(732\) 0 0
\(733\) 4.21301 + 26.5999i 0.155611 + 0.982489i 0.934664 + 0.355531i \(0.115700\pi\)
−0.779053 + 0.626958i \(0.784300\pi\)
\(734\) 0 0
\(735\) 23.3898 5.26350i 0.862746 0.194147i
\(736\) 0 0
\(737\) −18.5383 + 9.44572i −0.682866 + 0.347937i
\(738\) 0 0
\(739\) −31.2236 + 10.1452i −1.14858 + 0.373196i −0.820608 0.571491i \(-0.806365\pi\)
−0.327972 + 0.944688i \(0.606365\pi\)
\(740\) 0 0
\(741\) 6.31343 + 4.47006i 0.231930 + 0.164212i
\(742\) 0 0
\(743\) 3.67463 3.67463i 0.134809 0.134809i −0.636482 0.771291i \(-0.719611\pi\)
0.771291 + 0.636482i \(0.219611\pi\)
\(744\) 0 0
\(745\) −15.4563 + 12.5081i −0.566275 + 0.458261i
\(746\) 0 0
\(747\) 13.0901 + 12.4651i 0.478943 + 0.456074i
\(748\) 0 0
\(749\) 2.24389 0.0819899
\(750\) 0 0
\(751\) 30.6986 1.12021 0.560105 0.828422i \(-0.310761\pi\)
0.560105 + 0.828422i \(0.310761\pi\)
\(752\) 0 0
\(753\) 18.4445 + 9.11563i 0.672156 + 0.332192i
\(754\) 0 0
\(755\) 11.4542 9.26935i 0.416860 0.337346i
\(756\) 0 0
\(757\) 12.7050 12.7050i 0.461771 0.461771i −0.437465 0.899236i \(-0.644124\pi\)
0.899236 + 0.437465i \(0.144124\pi\)
\(758\) 0 0
\(759\) −12.0483 + 17.0168i −0.437326 + 0.617670i
\(760\) 0 0
\(761\) 9.26623 3.01078i 0.335901 0.109141i −0.136210 0.990680i \(-0.543492\pi\)
0.472111 + 0.881539i \(0.343492\pi\)
\(762\) 0 0
\(763\) 4.86971 2.48124i 0.176295 0.0898269i
\(764\) 0 0
\(765\) 0.373399 4.62354i 0.0135003 0.167165i
\(766\) 0 0
\(767\) 1.57855 + 9.96657i 0.0569981 + 0.359872i
\(768\) 0 0
\(769\) −12.7156 + 17.5015i −0.458535 + 0.631119i −0.974204 0.225669i \(-0.927543\pi\)
0.515669 + 0.856788i \(0.327543\pi\)
\(770\) 0 0
\(771\) 17.0886 5.78436i 0.615431 0.208319i
\(772\) 0 0
\(773\) 32.7902 + 16.7075i 1.17938 + 0.600926i 0.930029 0.367487i \(-0.119782\pi\)
0.249354 + 0.968412i \(0.419782\pi\)
\(774\) 0 0
\(775\) 28.7729 25.8740i 1.03355 0.929420i
\(776\) 0 0
\(777\) 1.32089 1.35359i 0.0473867 0.0485599i
\(778\) 0 0
\(779\) −12.6652 + 9.20177i −0.453776 + 0.329688i
\(780\) 0 0
\(781\) −9.47961 6.88734i −0.339207 0.246448i
\(782\) 0 0
\(783\) −21.2015 + 22.8168i −0.757678 + 0.815407i
\(784\) 0 0
\(785\) 3.12263 29.6188i 0.111452 1.05714i
\(786\) 0 0
\(787\) −1.07205 2.10401i −0.0382144 0.0750000i 0.871110 0.491088i \(-0.163401\pi\)
−0.909324 + 0.416088i \(0.863401\pi\)
\(788\) 0 0
\(789\) −3.85270 + 0.0471096i −0.137160 + 0.00167715i
\(790\) 0 0
\(791\) −5.66365 1.84023i −0.201376 0.0654311i
\(792\) 0 0
\(793\) 5.16282 + 5.16282i 0.183337 + 0.183337i
\(794\) 0 0
\(795\) 10.6121 0.682950i 0.376372 0.0242217i
\(796\) 0 0