Properties

Label 950.2.e.n.201.4
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(0.741409 - 1.28416i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.n.501.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.741409 - 1.28416i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.741409 + 1.28416i) q^{6} +0.482818 q^{7} +1.00000 q^{8} +(0.400626 + 0.693904i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.741409 - 1.28416i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.741409 + 1.28416i) q^{6} +0.482818 q^{7} +1.00000 q^{8} +(0.400626 + 0.693904i) q^{9} -4.43782 q^{11} -1.48282 q^{12} +(2.07118 + 3.58738i) q^{13} +(-0.241409 + 0.418132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.94930 + 6.84039i) q^{17} -0.801252 q^{18} +(4.31875 + 0.590253i) q^{19} +(0.357965 - 0.620014i) q^{21} +(2.21891 - 3.84326i) q^{22} +(2.82977 + 4.90130i) q^{23} +(0.741409 - 1.28416i) q^{24} -4.14235 q^{26} +5.63656 q^{27} +(-0.241409 - 0.418132i) q^{28} +(-1.91196 - 3.31161i) q^{29} +7.58017 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.29024 + 5.69885i) q^{33} +(-3.94930 - 6.84039i) q^{34} +(0.400626 - 0.693904i) q^{36} +3.50579 q^{37} +(-2.67055 + 3.44502i) q^{38} +6.14235 q^{39} +(4.44930 - 7.70641i) q^{41} +(0.357965 + 0.620014i) q^{42} +(-0.318434 + 0.551544i) q^{43} +(2.21891 + 3.84326i) q^{44} -5.65953 q^{46} +(-2.13055 - 3.69022i) q^{47} +(0.741409 + 1.28416i) q^{48} -6.76689 q^{49} +(5.85609 + 10.1430i) q^{51} +(2.07118 - 3.58738i) q^{52} +(1.59368 + 2.76033i) q^{53} +(-2.81828 + 4.88141i) q^{54} +0.482818 q^{56} +(3.95994 - 5.10834i) q^{57} +3.82392 q^{58} +(-0.812584 + 1.40744i) q^{59} +(-0.735243 - 1.27348i) q^{61} +(-3.79008 + 6.56462i) q^{62} +(0.193429 + 0.335029i) q^{63} +1.00000 q^{64} +(-3.29024 - 5.69885i) q^{66} +(6.59750 + 11.4272i) q^{67} +7.89860 q^{68} +8.39206 q^{69} +(-1.41164 + 2.44504i) q^{71} +(0.400626 + 0.693904i) q^{72} +(-3.43828 + 5.95528i) q^{73} +(-1.75289 + 3.03610i) q^{74} +(-1.64820 - 4.03527i) q^{76} -2.14266 q^{77} +(-3.07118 + 5.31943i) q^{78} +(0.576026 - 0.997706i) q^{79} +(2.97712 - 5.15652i) q^{81} +(4.44930 + 7.70641i) q^{82} +12.4044 q^{83} -0.715931 q^{84} +(-0.318434 - 0.551544i) q^{86} -5.67017 q^{87} -4.43782 q^{88} +(-4.37859 - 7.58395i) q^{89} +(1.00000 + 1.73205i) q^{91} +(2.82977 - 4.90130i) q^{92} +(5.62000 - 9.73413i) q^{93} +4.26110 q^{94} -1.48282 q^{96} +(-0.476652 + 0.825585i) q^{97} +(3.38344 - 5.86030i) q^{98} +(-1.77790 - 3.07942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} + O(q^{10}) \) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} - 6q^{11} - 2q^{13} + 5q^{14} - 5q^{16} + 4q^{17} + 10q^{18} + 11q^{19} + 20q^{21} + 3q^{22} + 13q^{23} + 4q^{26} + 36q^{27} + 5q^{28} + 2q^{29} - 8q^{31} - 5q^{32} + 2q^{33} + 4q^{34} - 5q^{36} + 10q^{37} - 13q^{38} + 16q^{39} + q^{41} + 20q^{42} + 3q^{44} - 26q^{46} - 10q^{47} - 20q^{49} + 4q^{51} - 2q^{52} + 5q^{53} - 18q^{54} - 10q^{56} - 10q^{57} - 4q^{58} + 22q^{59} - 2q^{61} + 4q^{62} + 23q^{63} + 10q^{64} + 2q^{66} + 4q^{67} - 8q^{68} - 24q^{69} - 22q^{71} - 5q^{72} + 26q^{73} - 5q^{74} + 2q^{76} + 10q^{77} - 8q^{78} + 2q^{79} - 5q^{81} + q^{82} + 12q^{83} - 40q^{84} - 20q^{87} - 6q^{88} - q^{89} + 10q^{91} + 13q^{92} + 6q^{93} + 20q^{94} + 8q^{97} + 10q^{98} + 13q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.741409 1.28416i 0.428053 0.741409i −0.568647 0.822581i \(-0.692533\pi\)
0.996700 + 0.0811725i \(0.0258665\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.741409 + 1.28416i 0.302679 + 0.524255i
\(7\) 0.482818 0.182488 0.0912440 0.995829i \(-0.470916\pi\)
0.0912440 + 0.995829i \(0.470916\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.400626 + 0.693904i 0.133542 + 0.231301i
\(10\) 0 0
\(11\) −4.43782 −1.33805 −0.669026 0.743239i \(-0.733288\pi\)
−0.669026 + 0.743239i \(0.733288\pi\)
\(12\) −1.48282 −0.428053
\(13\) 2.07118 + 3.58738i 0.574441 + 0.994960i 0.996102 + 0.0882071i \(0.0281137\pi\)
−0.421661 + 0.906753i \(0.638553\pi\)
\(14\) −0.241409 + 0.418132i −0.0645192 + 0.111751i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.94930 + 6.84039i −0.957846 + 1.65904i −0.230129 + 0.973160i \(0.573915\pi\)
−0.727717 + 0.685878i \(0.759419\pi\)
\(18\) −0.801252 −0.188857
\(19\) 4.31875 + 0.590253i 0.990789 + 0.135413i
\(20\) 0 0
\(21\) 0.357965 0.620014i 0.0781144 0.135298i
\(22\) 2.21891 3.84326i 0.473073 0.819386i
\(23\) 2.82977 + 4.90130i 0.590047 + 1.02199i 0.994225 + 0.107311i \(0.0342242\pi\)
−0.404178 + 0.914680i \(0.632443\pi\)
\(24\) 0.741409 1.28416i 0.151339 0.262128i
\(25\) 0 0
\(26\) −4.14235 −0.812382
\(27\) 5.63656 1.08476
\(28\) −0.241409 0.418132i −0.0456220 0.0790196i
\(29\) −1.91196 3.31161i −0.355042 0.614950i 0.632083 0.774900i \(-0.282200\pi\)
−0.987125 + 0.159950i \(0.948867\pi\)
\(30\) 0 0
\(31\) 7.58017 1.36144 0.680719 0.732545i \(-0.261667\pi\)
0.680719 + 0.732545i \(0.261667\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −3.29024 + 5.69885i −0.572756 + 0.992043i
\(34\) −3.94930 6.84039i −0.677299 1.17312i
\(35\) 0 0
\(36\) 0.400626 0.693904i 0.0667710 0.115651i
\(37\) 3.50579 0.576348 0.288174 0.957578i \(-0.406952\pi\)
0.288174 + 0.957578i \(0.406952\pi\)
\(38\) −2.67055 + 3.44502i −0.433220 + 0.558856i
\(39\) 6.14235 0.983563
\(40\) 0 0
\(41\) 4.44930 7.70641i 0.694864 1.20354i −0.275363 0.961340i \(-0.588798\pi\)
0.970227 0.242199i \(-0.0778687\pi\)
\(42\) 0.357965 + 0.620014i 0.0552352 + 0.0956702i
\(43\) −0.318434 + 0.551544i −0.0485607 + 0.0841097i −0.889284 0.457355i \(-0.848797\pi\)
0.840723 + 0.541465i \(0.182130\pi\)
\(44\) 2.21891 + 3.84326i 0.334513 + 0.579393i
\(45\) 0 0
\(46\) −5.65953 −0.834453
\(47\) −2.13055 3.69022i −0.310773 0.538274i 0.667757 0.744379i \(-0.267254\pi\)
−0.978530 + 0.206105i \(0.933921\pi\)
\(48\) 0.741409 + 1.28416i 0.107013 + 0.185352i
\(49\) −6.76689 −0.966698
\(50\) 0 0
\(51\) 5.85609 + 10.1430i 0.820017 + 1.42031i
\(52\) 2.07118 3.58738i 0.287220 0.497480i
\(53\) 1.59368 + 2.76033i 0.218908 + 0.379160i 0.954474 0.298293i \(-0.0964171\pi\)
−0.735566 + 0.677453i \(0.763084\pi\)
\(54\) −2.81828 + 4.88141i −0.383520 + 0.664275i
\(55\) 0 0
\(56\) 0.482818 0.0645192
\(57\) 3.95994 5.10834i 0.524507 0.676616i
\(58\) 3.82392 0.502105
\(59\) −0.812584 + 1.40744i −0.105789 + 0.183233i −0.914060 0.405578i \(-0.867070\pi\)
0.808271 + 0.588811i \(0.200404\pi\)
\(60\) 0 0
\(61\) −0.735243 1.27348i −0.0941382 0.163052i 0.815110 0.579306i \(-0.196676\pi\)
−0.909249 + 0.416253i \(0.863343\pi\)
\(62\) −3.79008 + 6.56462i −0.481341 + 0.833707i
\(63\) 0.193429 + 0.335029i 0.0243698 + 0.0422097i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.29024 5.69885i −0.405000 0.701481i
\(67\) 6.59750 + 11.4272i 0.806013 + 1.39606i 0.915605 + 0.402079i \(0.131712\pi\)
−0.109592 + 0.993977i \(0.534954\pi\)
\(68\) 7.89860 0.957846
\(69\) 8.39206 1.01028
\(70\) 0 0
\(71\) −1.41164 + 2.44504i −0.167531 + 0.290172i −0.937551 0.347847i \(-0.886913\pi\)
0.770020 + 0.638020i \(0.220246\pi\)
\(72\) 0.400626 + 0.693904i 0.0472142 + 0.0817774i
\(73\) −3.43828 + 5.95528i −0.402421 + 0.697013i −0.994017 0.109221i \(-0.965164\pi\)
0.591597 + 0.806234i \(0.298498\pi\)
\(74\) −1.75289 + 3.03610i −0.203770 + 0.352940i
\(75\) 0 0
\(76\) −1.64820 4.03527i −0.189062 0.462878i
\(77\) −2.14266 −0.244178
\(78\) −3.07118 + 5.31943i −0.347742 + 0.602307i
\(79\) 0.576026 0.997706i 0.0648080 0.112251i −0.831801 0.555074i \(-0.812690\pi\)
0.896609 + 0.442824i \(0.146023\pi\)
\(80\) 0 0
\(81\) 2.97712 5.15652i 0.330791 0.572947i
\(82\) 4.44930 + 7.70641i 0.491343 + 0.851031i
\(83\) 12.4044 1.36156 0.680779 0.732489i \(-0.261641\pi\)
0.680779 + 0.732489i \(0.261641\pi\)
\(84\) −0.715931 −0.0781144
\(85\) 0 0
\(86\) −0.318434 0.551544i −0.0343376 0.0594745i
\(87\) −5.67017 −0.607906
\(88\) −4.43782 −0.473073
\(89\) −4.37859 7.58395i −0.464130 0.803897i 0.535032 0.844832i \(-0.320300\pi\)
−0.999162 + 0.0409353i \(0.986966\pi\)
\(90\) 0 0
\(91\) 1.00000 + 1.73205i 0.104828 + 0.181568i
\(92\) 2.82977 4.90130i 0.295024 0.510996i
\(93\) 5.62000 9.73413i 0.582767 1.00938i
\(94\) 4.26110 0.439499
\(95\) 0 0
\(96\) −1.48282 −0.151339
\(97\) −0.476652 + 0.825585i −0.0483967 + 0.0838255i −0.889209 0.457501i \(-0.848744\pi\)
0.840812 + 0.541327i \(0.182078\pi\)
\(98\) 3.38344 5.86030i 0.341779 0.591979i
\(99\) −1.77790 3.07942i −0.178686 0.309493i
\(100\) 0 0
\(101\) 3.32360 + 5.75665i 0.330711 + 0.572808i 0.982651 0.185462i \(-0.0593783\pi\)
−0.651941 + 0.758270i \(0.726045\pi\)
\(102\) −11.7122 −1.15968
\(103\) 4.13171 0.407110 0.203555 0.979064i \(-0.434750\pi\)
0.203555 + 0.979064i \(0.434750\pi\)
\(104\) 2.07118 + 3.58738i 0.203095 + 0.351772i
\(105\) 0 0
\(106\) −3.18735 −0.309583
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −2.81828 4.88141i −0.271189 0.469714i
\(109\) −9.10799 + 15.7755i −0.872387 + 1.51102i −0.0128662 + 0.999917i \(0.504096\pi\)
−0.859521 + 0.511101i \(0.829238\pi\)
\(110\) 0 0
\(111\) 2.59922 4.50198i 0.246707 0.427309i
\(112\) −0.241409 + 0.418132i −0.0228110 + 0.0395098i
\(113\) −8.29703 −0.780519 −0.390260 0.920705i \(-0.627615\pi\)
−0.390260 + 0.920705i \(0.627615\pi\)
\(114\) 2.44398 + 5.98358i 0.228900 + 0.560413i
\(115\) 0 0
\(116\) −1.91196 + 3.31161i −0.177521 + 0.307475i
\(117\) −1.65953 + 2.87440i −0.153424 + 0.265738i
\(118\) −0.812584 1.40744i −0.0748044 0.129565i
\(119\) −1.90679 + 3.30266i −0.174795 + 0.302754i
\(120\) 0 0
\(121\) 8.69420 0.790382
\(122\) 1.47049 0.133132
\(123\) −6.59750 11.4272i −0.594877 1.03036i
\(124\) −3.79008 6.56462i −0.340359 0.589520i
\(125\) 0 0
\(126\) −0.386859 −0.0344641
\(127\) −7.17384 12.4255i −0.636576 1.10258i −0.986179 0.165683i \(-0.947017\pi\)
0.349603 0.936898i \(-0.386316\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0.472180 + 0.817839i 0.0415731 + 0.0720067i
\(130\) 0 0
\(131\) −5.00032 + 8.66080i −0.436880 + 0.756698i −0.997447 0.0714111i \(-0.977250\pi\)
0.560567 + 0.828109i \(0.310583\pi\)
\(132\) 6.58047 0.572756
\(133\) 2.08517 + 0.284985i 0.180807 + 0.0247113i
\(134\) −13.1950 −1.13987
\(135\) 0 0
\(136\) −3.94930 + 6.84039i −0.338650 + 0.586558i
\(137\) 1.82945 + 3.16870i 0.156301 + 0.270720i 0.933532 0.358495i \(-0.116710\pi\)
−0.777231 + 0.629215i \(0.783377\pi\)
\(138\) −4.19603 + 7.26773i −0.357190 + 0.618671i
\(139\) 3.17602 + 5.50103i 0.269387 + 0.466591i 0.968704 0.248220i \(-0.0798457\pi\)
−0.699317 + 0.714812i \(0.746512\pi\)
\(140\) 0 0
\(141\) −6.31843 −0.532108
\(142\) −1.41164 2.44504i −0.118462 0.205183i
\(143\) −9.19149 15.9201i −0.768631 1.33131i
\(144\) −0.801252 −0.0667710
\(145\) 0 0
\(146\) −3.43828 5.95528i −0.284554 0.492863i
\(147\) −5.01703 + 8.68975i −0.413798 + 0.716719i
\(148\) −1.75289 3.03610i −0.144087 0.249566i
\(149\) 6.02101 10.4287i 0.493260 0.854351i −0.506710 0.862117i \(-0.669138\pi\)
0.999970 + 0.00776522i \(0.00247177\pi\)
\(150\) 0 0
\(151\) −1.53484 −0.124903 −0.0624516 0.998048i \(-0.519892\pi\)
−0.0624516 + 0.998048i \(0.519892\pi\)
\(152\) 4.31875 + 0.590253i 0.350297 + 0.0478759i
\(153\) −6.32877 −0.511650
\(154\) 1.07133 1.85559i 0.0863300 0.149528i
\(155\) 0 0
\(156\) −3.07118 5.31943i −0.245891 0.425895i
\(157\) 9.52664 16.5006i 0.760309 1.31689i −0.182383 0.983228i \(-0.558381\pi\)
0.942691 0.333666i \(-0.108286\pi\)
\(158\) 0.576026 + 0.997706i 0.0458262 + 0.0793732i
\(159\) 4.72626 0.374817
\(160\) 0 0
\(161\) 1.36626 + 2.36643i 0.107676 + 0.186501i
\(162\) 2.97712 + 5.15652i 0.233905 + 0.405135i
\(163\) −9.96533 −0.780545 −0.390272 0.920699i \(-0.627619\pi\)
−0.390272 + 0.920699i \(0.627619\pi\)
\(164\) −8.89860 −0.694864
\(165\) 0 0
\(166\) −6.20219 + 10.7425i −0.481384 + 0.833781i
\(167\) −3.70272 6.41331i −0.286525 0.496277i 0.686453 0.727175i \(-0.259167\pi\)
−0.972978 + 0.230898i \(0.925834\pi\)
\(168\) 0.357965 0.620014i 0.0276176 0.0478351i
\(169\) −2.07953 + 3.60186i −0.159964 + 0.277066i
\(170\) 0 0
\(171\) 1.32062 + 3.23327i 0.100991 + 0.247254i
\(172\) 0.636868 0.0485607
\(173\) −7.83274 + 13.5667i −0.595512 + 1.03146i 0.397962 + 0.917402i \(0.369718\pi\)
−0.993474 + 0.114056i \(0.963616\pi\)
\(174\) 2.83509 4.91051i 0.214927 0.372265i
\(175\) 0 0
\(176\) 2.21891 3.84326i 0.167256 0.289697i
\(177\) 1.20491 + 2.08697i 0.0905669 + 0.156866i
\(178\) 8.75719 0.656379
\(179\) 4.61284 0.344780 0.172390 0.985029i \(-0.444851\pi\)
0.172390 + 0.985029i \(0.444851\pi\)
\(180\) 0 0
\(181\) −0.605224 1.04828i −0.0449860 0.0779180i 0.842656 0.538453i \(-0.180991\pi\)
−0.887642 + 0.460535i \(0.847658\pi\)
\(182\) −2.00000 −0.148250
\(183\) −2.18046 −0.161184
\(184\) 2.82977 + 4.90130i 0.208613 + 0.361329i
\(185\) 0 0
\(186\) 5.62000 + 9.73413i 0.412079 + 0.713741i
\(187\) 17.5263 30.3564i 1.28165 2.21988i
\(188\) −2.13055 + 3.69022i −0.155386 + 0.269137i
\(189\) 2.72143 0.197955
\(190\) 0 0
\(191\) −7.64783 −0.553378 −0.276689 0.960960i \(-0.589237\pi\)
−0.276689 + 0.960960i \(0.589237\pi\)
\(192\) 0.741409 1.28416i 0.0535066 0.0926761i
\(193\) 8.96163 15.5220i 0.645072 1.11730i −0.339212 0.940710i \(-0.610161\pi\)
0.984285 0.176588i \(-0.0565061\pi\)
\(194\) −0.476652 0.825585i −0.0342216 0.0592736i
\(195\) 0 0
\(196\) 3.38344 + 5.86030i 0.241675 + 0.418593i
\(197\) −18.5697 −1.32304 −0.661518 0.749929i \(-0.730088\pi\)
−0.661518 + 0.749929i \(0.730088\pi\)
\(198\) 3.55581 0.252700
\(199\) 6.76689 + 11.7206i 0.479692 + 0.830851i 0.999729 0.0232931i \(-0.00741510\pi\)
−0.520037 + 0.854144i \(0.674082\pi\)
\(200\) 0 0
\(201\) 19.5658 1.38006
\(202\) −6.64720 −0.467695
\(203\) −0.923127 1.59890i −0.0647908 0.112221i
\(204\) 5.85609 10.1430i 0.410008 0.710155i
\(205\) 0 0
\(206\) −2.06586 + 3.57817i −0.143935 + 0.249303i
\(207\) −2.26736 + 3.92717i −0.157592 + 0.272958i
\(208\) −4.14235 −0.287220
\(209\) −19.1658 2.61944i −1.32573 0.181190i
\(210\) 0 0
\(211\) 6.67055 11.5537i 0.459220 0.795392i −0.539700 0.841857i \(-0.681462\pi\)
0.998920 + 0.0464656i \(0.0147958\pi\)
\(212\) 1.59368 2.76033i 0.109454 0.189580i
\(213\) 2.09321 + 3.62554i 0.143424 + 0.248418i
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) 0 0
\(216\) 5.63656 0.383520
\(217\) 3.65984 0.248446
\(218\) −9.10799 15.7755i −0.616871 1.06845i
\(219\) 5.09835 + 8.83060i 0.344514 + 0.596716i
\(220\) 0 0
\(221\) −32.7188 −2.20090
\(222\) 2.59922 + 4.50198i 0.174448 + 0.302153i
\(223\) −2.75859 + 4.77802i −0.184729 + 0.319960i −0.943485 0.331415i \(-0.892474\pi\)
0.758756 + 0.651375i \(0.225807\pi\)
\(224\) −0.241409 0.418132i −0.0161298 0.0279376i
\(225\) 0 0
\(226\) 4.14852 7.18544i 0.275955 0.477968i
\(227\) 22.2457 1.47650 0.738248 0.674529i \(-0.235653\pi\)
0.738248 + 0.674529i \(0.235653\pi\)
\(228\) −6.40392 0.875238i −0.424110 0.0579641i
\(229\) 16.4341 1.08599 0.542997 0.839735i \(-0.317290\pi\)
0.542997 + 0.839735i \(0.317290\pi\)
\(230\) 0 0
\(231\) −1.58858 + 2.75151i −0.104521 + 0.181036i
\(232\) −1.91196 3.31161i −0.125526 0.217418i
\(233\) 5.28454 9.15309i 0.346202 0.599639i −0.639370 0.768899i \(-0.720805\pi\)
0.985571 + 0.169261i \(0.0541380\pi\)
\(234\) −1.65953 2.87440i −0.108487 0.187905i
\(235\) 0 0
\(236\) 1.62517 0.105789
\(237\) −0.854141 1.47942i −0.0554824 0.0960984i
\(238\) −1.90679 3.30266i −0.123599 0.214080i
\(239\) −15.8625 −1.02606 −0.513031 0.858370i \(-0.671478\pi\)
−0.513031 + 0.858370i \(0.671478\pi\)
\(240\) 0 0
\(241\) −2.19672 3.80483i −0.141503 0.245091i 0.786560 0.617514i \(-0.211860\pi\)
−0.928063 + 0.372423i \(0.878527\pi\)
\(242\) −4.34710 + 7.52940i −0.279442 + 0.484008i
\(243\) 4.04032 + 6.99804i 0.259187 + 0.448924i
\(244\) −0.735243 + 1.27348i −0.0470691 + 0.0815261i
\(245\) 0 0
\(246\) 13.1950 0.841283
\(247\) 6.82742 + 16.7155i 0.434419 + 1.06358i
\(248\) 7.58017 0.481341
\(249\) 9.19672 15.9292i 0.582819 1.00947i
\(250\) 0 0
\(251\) −7.21853 12.5029i −0.455630 0.789173i 0.543095 0.839671i \(-0.317252\pi\)
−0.998724 + 0.0504980i \(0.983919\pi\)
\(252\) 0.193429 0.335029i 0.0121849 0.0211049i
\(253\) −12.5580 21.7511i −0.789513 1.36748i
\(254\) 14.3477 0.900254
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.51765 + 9.55685i 0.344182 + 0.596140i 0.985205 0.171382i \(-0.0548231\pi\)
−0.641023 + 0.767522i \(0.721490\pi\)
\(258\) −0.944359 −0.0587933
\(259\) 1.69266 0.105177
\(260\) 0 0
\(261\) 1.53196 2.65343i 0.0948259 0.164243i
\(262\) −5.00032 8.66080i −0.308921 0.535066i
\(263\) 10.5630 18.2957i 0.651345 1.12816i −0.331451 0.943472i \(-0.607538\pi\)
0.982797 0.184691i \(-0.0591284\pi\)
\(264\) −3.29024 + 5.69885i −0.202500 + 0.350740i
\(265\) 0 0
\(266\) −1.28939 + 1.66332i −0.0790575 + 0.101984i
\(267\) −12.9853 −0.794688
\(268\) 6.59750 11.4272i 0.403006 0.698028i
\(269\) 14.1483 24.5056i 0.862637 1.49413i −0.00673681 0.999977i \(-0.502144\pi\)
0.869374 0.494154i \(-0.164522\pi\)
\(270\) 0 0
\(271\) 6.15672 10.6638i 0.373994 0.647777i −0.616182 0.787604i \(-0.711321\pi\)
0.990176 + 0.139827i \(0.0446546\pi\)
\(272\) −3.94930 6.84039i −0.239461 0.414759i
\(273\) 2.96564 0.179488
\(274\) −3.65890 −0.221042
\(275\) 0 0
\(276\) −4.19603 7.26773i −0.252571 0.437466i
\(277\) −27.2677 −1.63836 −0.819178 0.573539i \(-0.805570\pi\)
−0.819178 + 0.573539i \(0.805570\pi\)
\(278\) −6.35204 −0.380970
\(279\) 3.03681 + 5.25991i 0.181809 + 0.314903i
\(280\) 0 0
\(281\) −4.63665 8.03092i −0.276600 0.479084i 0.693938 0.720035i \(-0.255874\pi\)
−0.970537 + 0.240950i \(0.922541\pi\)
\(282\) 3.15922 5.47192i 0.188129 0.325848i
\(283\) 13.0034 22.5226i 0.772975 1.33883i −0.162951 0.986634i \(-0.552101\pi\)
0.935926 0.352197i \(-0.114565\pi\)
\(284\) 2.82328 0.167531
\(285\) 0 0
\(286\) 18.3830 1.08701
\(287\) 2.14820 3.72079i 0.126804 0.219631i
\(288\) 0.400626 0.693904i 0.0236071 0.0408887i
\(289\) −22.6939 39.3071i −1.33494 2.31218i
\(290\) 0 0
\(291\) 0.706788 + 1.22419i 0.0414326 + 0.0717634i
\(292\) 6.87657 0.402421
\(293\) −17.4435 −1.01906 −0.509529 0.860453i \(-0.670180\pi\)
−0.509529 + 0.860453i \(0.670180\pi\)
\(294\) −5.01703 8.68975i −0.292599 0.506797i
\(295\) 0 0
\(296\) 3.50579 0.203770
\(297\) −25.0140 −1.45146
\(298\) 6.02101 + 10.4287i 0.348788 + 0.604118i
\(299\) −11.7219 + 20.3029i −0.677894 + 1.17415i
\(300\) 0 0
\(301\) −0.153746 + 0.266295i −0.00886175 + 0.0153490i
\(302\) 0.767418 1.32921i 0.0441600 0.0764873i
\(303\) 9.85659 0.566246
\(304\) −2.67055 + 3.44502i −0.153167 + 0.197585i
\(305\) 0 0
\(306\) 3.16438 5.48087i 0.180896 0.313321i
\(307\) 0.557182 0.965067i 0.0318000 0.0550793i −0.849687 0.527287i \(-0.823209\pi\)
0.881487 + 0.472207i \(0.156543\pi\)
\(308\) 1.07133 + 1.85559i 0.0610446 + 0.105732i
\(309\) 3.06329 5.30577i 0.174264 0.301835i
\(310\) 0 0
\(311\) 33.8032 1.91680 0.958400 0.285427i \(-0.0921354\pi\)
0.958400 + 0.285427i \(0.0921354\pi\)
\(312\) 6.14235 0.347742
\(313\) 7.38095 + 12.7842i 0.417196 + 0.722605i 0.995656 0.0931060i \(-0.0296796\pi\)
−0.578460 + 0.815711i \(0.696346\pi\)
\(314\) 9.52664 + 16.5006i 0.537619 + 0.931184i
\(315\) 0 0
\(316\) −1.15205 −0.0648080
\(317\) 13.0683 + 22.6350i 0.733989 + 1.27131i 0.955165 + 0.296072i \(0.0956770\pi\)
−0.221177 + 0.975234i \(0.570990\pi\)
\(318\) −2.36313 + 4.09306i −0.132518 + 0.229528i
\(319\) 8.48492 + 14.6963i 0.475064 + 0.822835i
\(320\) 0 0
\(321\) −7.41409 + 12.8416i −0.413814 + 0.716747i
\(322\) −2.73252 −0.152278
\(323\) −21.0936 + 27.2108i −1.17368 + 1.51405i
\(324\) −5.95424 −0.330791
\(325\) 0 0
\(326\) 4.98267 8.63023i 0.275964 0.477984i
\(327\) 13.5055 + 23.3922i 0.746855 + 1.29359i
\(328\) 4.44930 7.70641i 0.245671 0.425515i
\(329\) −1.02867 1.78170i −0.0567123 0.0982285i
\(330\) 0 0
\(331\) 2.17127 0.119344 0.0596720 0.998218i \(-0.480995\pi\)
0.0596720 + 0.998218i \(0.480995\pi\)
\(332\) −6.20219 10.7425i −0.340390 0.589572i
\(333\) 1.40451 + 2.43268i 0.0769666 + 0.133310i
\(334\) 7.40545 0.405208
\(335\) 0 0
\(336\) 0.357965 + 0.620014i 0.0195286 + 0.0338245i
\(337\) 6.56430 11.3697i 0.357580 0.619347i −0.629976 0.776615i \(-0.716935\pi\)
0.987556 + 0.157268i \(0.0502686\pi\)
\(338\) −2.07953 3.60186i −0.113112 0.195915i
\(339\) −6.15149 + 10.6547i −0.334103 + 0.578684i
\(340\) 0 0
\(341\) −33.6394 −1.82167
\(342\) −3.46041 0.472942i −0.187117 0.0255738i
\(343\) −6.64690 −0.358899
\(344\) −0.318434 + 0.551544i −0.0171688 + 0.0297373i
\(345\) 0 0
\(346\) −7.83274 13.5667i −0.421091 0.729351i
\(347\) −7.46811 + 12.9352i −0.400909 + 0.694395i −0.993836 0.110861i \(-0.964639\pi\)
0.592927 + 0.805257i \(0.297972\pi\)
\(348\) 2.83509 + 4.91051i 0.151977 + 0.263231i
\(349\) −18.8611 −1.00961 −0.504806 0.863233i \(-0.668436\pi\)
−0.504806 + 0.863233i \(0.668436\pi\)
\(350\) 0 0
\(351\) 11.6743 + 20.2205i 0.623129 + 1.07929i
\(352\) 2.21891 + 3.84326i 0.118268 + 0.204846i
\(353\) 2.01172 0.107073 0.0535366 0.998566i \(-0.482951\pi\)
0.0535366 + 0.998566i \(0.482951\pi\)
\(354\) −2.40983 −0.128081
\(355\) 0 0
\(356\) −4.37859 + 7.58395i −0.232065 + 0.401948i
\(357\) 2.82742 + 4.89724i 0.149643 + 0.259190i
\(358\) −2.30642 + 3.99483i −0.121898 + 0.211134i
\(359\) 3.29938 5.71469i 0.174135 0.301610i −0.765727 0.643166i \(-0.777621\pi\)
0.939861 + 0.341556i \(0.110954\pi\)
\(360\) 0 0
\(361\) 18.3032 + 5.09831i 0.963326 + 0.268332i
\(362\) 1.21045 0.0636197
\(363\) 6.44596 11.1647i 0.338325 0.585996i
\(364\) 1.00000 1.73205i 0.0524142 0.0907841i
\(365\) 0 0
\(366\) 1.09023 1.88834i 0.0569873 0.0987049i
\(367\) −5.59922 9.69814i −0.292277 0.506239i 0.682071 0.731286i \(-0.261080\pi\)
−0.974348 + 0.225048i \(0.927746\pi\)
\(368\) −5.65953 −0.295024
\(369\) 7.13002 0.371174
\(370\) 0 0
\(371\) 0.769455 + 1.33274i 0.0399481 + 0.0691922i
\(372\) −11.2400 −0.582767
\(373\) −3.19437 −0.165398 −0.0826991 0.996575i \(-0.526354\pi\)
−0.0826991 + 0.996575i \(0.526354\pi\)
\(374\) 17.5263 + 30.3564i 0.906261 + 1.56969i
\(375\) 0 0
\(376\) −2.13055 3.69022i −0.109875 0.190309i
\(377\) 7.92000 13.7178i 0.407901 0.706505i
\(378\) −1.36072 + 2.35683i −0.0699877 + 0.121222i
\(379\) 17.2666 0.886927 0.443463 0.896292i \(-0.353750\pi\)
0.443463 + 0.896292i \(0.353750\pi\)
\(380\) 0 0
\(381\) −21.2750 −1.08995
\(382\) 3.82392 6.62322i 0.195649 0.338873i
\(383\) −16.0924 + 27.8729i −0.822285 + 1.42424i 0.0816914 + 0.996658i \(0.473968\pi\)
−0.903977 + 0.427582i \(0.859366\pi\)
\(384\) 0.741409 + 1.28416i 0.0378349 + 0.0655319i
\(385\) 0 0
\(386\) 8.96163 + 15.5220i 0.456135 + 0.790049i
\(387\) −0.510292 −0.0259396
\(388\) 0.953304 0.0483967
\(389\) 5.03587 + 8.72239i 0.255329 + 0.442243i 0.964985 0.262306i \(-0.0844829\pi\)
−0.709656 + 0.704548i \(0.751150\pi\)
\(390\) 0 0
\(391\) −44.7024 −2.26070
\(392\) −6.76689 −0.341779
\(393\) 7.41456 + 12.8424i 0.374015 + 0.647813i
\(394\) 9.28485 16.0818i 0.467764 0.810191i
\(395\) 0 0
\(396\) −1.77790 + 3.07942i −0.0893430 + 0.154747i
\(397\) 17.7217 30.6949i 0.889428 1.54053i 0.0488757 0.998805i \(-0.484436\pi\)
0.840553 0.541730i \(-0.182230\pi\)
\(398\) −13.5338 −0.678387
\(399\) 1.91193 2.46640i 0.0957161 0.123474i
\(400\) 0 0
\(401\) 15.4751 26.8036i 0.772789 1.33851i −0.163239 0.986587i \(-0.552194\pi\)
0.936029 0.351924i \(-0.114472\pi\)
\(402\) −9.78289 + 16.9445i −0.487926 + 0.845113i
\(403\) 15.6999 + 27.1929i 0.782065 + 1.35458i
\(404\) 3.32360 5.75665i 0.165355 0.286404i
\(405\) 0 0
\(406\) 1.84625 0.0916281
\(407\) −15.5580 −0.771183
\(408\) 5.85609 + 10.1430i 0.289920 + 0.502156i
\(409\) −13.5583 23.4837i −0.670417 1.16120i −0.977786 0.209606i \(-0.932782\pi\)
0.307369 0.951590i \(-0.400551\pi\)
\(410\) 0 0
\(411\) 5.42548 0.267619
\(412\) −2.06586 3.57817i −0.101777 0.176284i
\(413\) −0.392330 + 0.679535i −0.0193053 + 0.0334378i
\(414\) −2.26736 3.92717i −0.111434 0.193010i
\(415\) 0 0
\(416\) 2.07118 3.58738i 0.101548 0.175886i
\(417\) 9.41892 0.461246
\(418\) 11.8514 15.2884i 0.579671 0.747778i
\(419\) −8.28108 −0.404557 −0.202279 0.979328i \(-0.564835\pi\)
−0.202279 + 0.979328i \(0.564835\pi\)
\(420\) 0 0
\(421\) −2.95790 + 5.12323i −0.144159 + 0.249691i −0.929059 0.369932i \(-0.879381\pi\)
0.784900 + 0.619623i \(0.212714\pi\)
\(422\) 6.67055 + 11.5537i 0.324717 + 0.562427i
\(423\) 1.70711 2.95680i 0.0830024 0.143764i
\(424\) 1.59368 + 2.76033i 0.0773958 + 0.134053i
\(425\) 0 0
\(426\) −4.18642 −0.202833
\(427\) −0.354988 0.614858i −0.0171791 0.0297551i
\(428\) 5.00000 + 8.66025i 0.241684 + 0.418609i
\(429\) −27.2586 −1.31606
\(430\) 0 0
\(431\) 7.48526 + 12.9649i 0.360552 + 0.624495i 0.988052 0.154122i \(-0.0492548\pi\)
−0.627499 + 0.778617i \(0.715922\pi\)
\(432\) −2.81828 + 4.88141i −0.135595 + 0.234857i
\(433\) −1.67587 2.90269i −0.0805371 0.139494i 0.822944 0.568123i \(-0.192330\pi\)
−0.903481 + 0.428629i \(0.858997\pi\)
\(434\) −1.82992 + 3.16951i −0.0878389 + 0.152141i
\(435\) 0 0
\(436\) 18.2160 0.872387
\(437\) 9.32805 + 22.8378i 0.446221 + 1.09248i
\(438\) −10.1967 −0.487217
\(439\) −6.00116 + 10.3943i −0.286420 + 0.496094i −0.972953 0.231005i \(-0.925799\pi\)
0.686533 + 0.727099i \(0.259132\pi\)
\(440\) 0 0
\(441\) −2.71099 4.69557i −0.129095 0.223599i
\(442\) 16.3594 28.3353i 0.778137 1.34777i
\(443\) 13.3972 + 23.2046i 0.636520 + 1.10248i 0.986191 + 0.165612i \(0.0529600\pi\)
−0.349671 + 0.936873i \(0.613707\pi\)
\(444\) −5.19844 −0.246707
\(445\) 0 0
\(446\) −2.75859 4.77802i −0.130623 0.226246i
\(447\) −8.92805 15.4638i −0.422282 0.731415i
\(448\) 0.482818 0.0228110
\(449\) 3.53608 0.166878 0.0834389 0.996513i \(-0.473410\pi\)
0.0834389 + 0.996513i \(0.473410\pi\)
\(450\) 0 0
\(451\) −19.7452 + 34.1996i −0.929764 + 1.61040i
\(452\) 4.14852 + 7.18544i 0.195130 + 0.337975i
\(453\) −1.13794 + 1.97097i −0.0534651 + 0.0926043i
\(454\) −11.1228 + 19.2653i −0.522020 + 0.904165i
\(455\) 0 0
\(456\) 3.95994 5.10834i 0.185441 0.239220i
\(457\) 21.5147 1.00642 0.503208 0.864166i \(-0.332153\pi\)
0.503208 + 0.864166i \(0.332153\pi\)
\(458\) −8.21703 + 14.2323i −0.383957 + 0.665033i
\(459\) −22.2605 + 38.5563i −1.03903 + 1.79965i
\(460\) 0 0
\(461\) −20.1971 + 34.9825i −0.940675 + 1.62930i −0.176486 + 0.984303i \(0.556473\pi\)
−0.764188 + 0.644993i \(0.776860\pi\)
\(462\) −1.58858 2.75151i −0.0739076 0.128012i
\(463\) −19.6448 −0.912972 −0.456486 0.889731i \(-0.650892\pi\)
−0.456486 + 0.889731i \(0.650892\pi\)
\(464\) 3.82392 0.177521
\(465\) 0 0
\(466\) 5.28454 + 9.15309i 0.244801 + 0.424009i
\(467\) 15.1929 0.703042 0.351521 0.936180i \(-0.385665\pi\)
0.351521 + 0.936180i \(0.385665\pi\)
\(468\) 3.31907 0.153424
\(469\) 3.18539 + 5.51726i 0.147088 + 0.254763i
\(470\) 0 0
\(471\) −14.1263 24.4674i −0.650904 1.12740i
\(472\) −0.812584 + 1.40744i −0.0374022 + 0.0647825i
\(473\) 1.41315 2.44765i 0.0649768 0.112543i
\(474\) 1.70828 0.0784640
\(475\) 0 0
\(476\) 3.81358 0.174795
\(477\) −1.27694 + 2.21172i −0.0584669 + 0.101268i
\(478\) 7.93127 13.7374i 0.362768 0.628332i
\(479\) 2.12032 + 3.67250i 0.0968798 + 0.167801i 0.910392 0.413748i \(-0.135780\pi\)
−0.813512 + 0.581548i \(0.802447\pi\)
\(480\) 0 0
\(481\) 7.26110 + 12.5766i 0.331078 + 0.573443i
\(482\) 4.39344 0.200116
\(483\) 4.05183 0.184365
\(484\) −4.34710 7.52940i −0.197596 0.342245i
\(485\) 0 0
\(486\) −8.08064 −0.366545
\(487\) −8.00831 −0.362891 −0.181446 0.983401i \(-0.558078\pi\)
−0.181446 + 0.983401i \(0.558078\pi\)
\(488\) −0.735243 1.27348i −0.0332829 0.0576477i
\(489\) −7.38838 + 12.7971i −0.334114 + 0.578703i
\(490\) 0 0
\(491\) 8.53834 14.7888i 0.385330 0.667411i −0.606485 0.795095i \(-0.707421\pi\)
0.991815 + 0.127684i \(0.0407543\pi\)
\(492\) −6.59750 + 11.4272i −0.297438 + 0.515178i
\(493\) 30.2036 1.36030
\(494\) −17.8898 2.44504i −0.804899 0.110007i
\(495\) 0 0
\(496\) −3.79008 + 6.56462i −0.170180 + 0.294760i
\(497\) −0.681566 + 1.18051i −0.0305724 + 0.0529530i
\(498\) 9.19672 + 15.9292i 0.412115 + 0.713804i
\(499\) −5.63718 + 9.76389i −0.252355 + 0.437092i −0.964174 0.265272i \(-0.914538\pi\)
0.711819 + 0.702363i \(0.247872\pi\)
\(500\) 0 0
\(501\) −10.9809 −0.490592
\(502\) 14.4371 0.644357
\(503\) 4.25268 + 7.36586i 0.189618 + 0.328427i 0.945123 0.326715i \(-0.105942\pi\)
−0.755505 + 0.655143i \(0.772609\pi\)
\(504\) 0.193429 + 0.335029i 0.00861602 + 0.0149234i
\(505\) 0 0
\(506\) 25.1160 1.11654
\(507\) 3.08357 + 5.34090i 0.136946 + 0.237198i
\(508\) −7.17384 + 12.4255i −0.318288 + 0.551291i
\(509\) −15.4306 26.7265i −0.683948 1.18463i −0.973766 0.227550i \(-0.926928\pi\)
0.289819 0.957082i \(-0.406405\pi\)
\(510\) 0 0
\(511\) −1.66006 + 2.87532i −0.0734369 + 0.127196i
\(512\) 1.00000 0.0441942
\(513\) 24.3429 + 3.32700i 1.07477 + 0.146891i
\(514\) −11.0353 −0.486746
\(515\) 0 0
\(516\) 0.472180 0.817839i 0.0207866 0.0360034i
\(517\) 9.45499 + 16.3765i 0.415830 + 0.720238i
\(518\) −0.846328 + 1.46588i −0.0371855 + 0.0644072i
\(519\) 11.6145 + 20.1170i 0.509821 + 0.883036i
\(520\) 0 0
\(521\) −8.09735 −0.354751 −0.177376 0.984143i \(-0.556761\pi\)
−0.177376 + 0.984143i \(0.556761\pi\)
\(522\) 1.53196 + 2.65343i 0.0670521 + 0.116138i
\(523\) 7.35267 + 12.7352i 0.321510 + 0.556872i 0.980800 0.195017i \(-0.0624763\pi\)
−0.659290 + 0.751889i \(0.729143\pi\)
\(524\) 10.0006 0.436880
\(525\) 0 0
\(526\) 10.5630 + 18.2957i 0.460571 + 0.797732i
\(527\) −29.9363 + 51.8513i −1.30405 + 2.25868i
\(528\) −3.29024 5.69885i −0.143189 0.248011i
\(529\) −4.51516 + 7.82048i −0.196311 + 0.340021i
\(530\) 0 0
\(531\) −1.30217 −0.0565093
\(532\) −0.795780 1.94830i −0.0345015 0.0844696i
\(533\) 36.8611 1.59663
\(534\) 6.49265 11.2456i 0.280965 0.486645i
\(535\) 0 0
\(536\) 6.59750 + 11.4272i 0.284969 + 0.493580i
\(537\) 3.42000 5.92361i 0.147584 0.255623i
\(538\) 14.1483 + 24.5056i 0.609977 + 1.05651i
\(539\) 30.0302 1.29349
\(540\) 0 0
\(541\) −5.50993 9.54347i −0.236890 0.410306i 0.722930 0.690921i \(-0.242795\pi\)
−0.959820 + 0.280615i \(0.909462\pi\)
\(542\) 6.15672 + 10.6638i 0.264454 + 0.458048i
\(543\) −1.79487 −0.0770254
\(544\) 7.89860 0.338650
\(545\) 0 0
\(546\) −1.48282 + 2.56832i −0.0634587 + 0.109914i
\(547\) 1.29610 + 2.24490i 0.0554171 + 0.0959852i 0.892403 0.451239i \(-0.149018\pi\)
−0.836986 + 0.547224i \(0.815684\pi\)
\(548\) 1.82945 3.16870i 0.0781503 0.135360i
\(549\) 0.589115 1.02038i 0.0251428 0.0435486i
\(550\) 0 0
\(551\) −6.30258 15.4305i −0.268499 0.657364i
\(552\) 8.39206 0.357190
\(553\) 0.278115 0.481710i 0.0118267 0.0204844i
\(554\) 13.6338 23.6145i 0.579246 1.00328i
\(555\) 0 0
\(556\) 3.17602 5.50103i 0.134693 0.233296i
\(557\) 4.21791 + 7.30563i 0.178719 + 0.309550i 0.941442 0.337175i \(-0.109472\pi\)
−0.762723 + 0.646725i \(0.776138\pi\)
\(558\) −6.07362 −0.257117
\(559\) −2.63813 −0.111581
\(560\) 0 0
\(561\) −25.9883 45.0130i −1.09722 1.90045i
\(562\) 9.27331 0.391171
\(563\) −27.9415 −1.17760 −0.588798 0.808280i \(-0.700399\pi\)
−0.588798 + 0.808280i \(0.700399\pi\)
\(564\) 3.15922 + 5.47192i 0.133027 + 0.230410i
\(565\) 0 0
\(566\) 13.0034 + 22.5226i 0.546576 + 0.946697i
\(567\) 1.43741 2.48966i 0.0603654 0.104556i
\(568\) −1.41164 + 2.44504i −0.0592312 + 0.102591i
\(569\) 10.7931 0.452472 0.226236 0.974072i \(-0.427358\pi\)
0.226236 + 0.974072i \(0.427358\pi\)
\(570\) 0 0
\(571\) 6.26581 0.262216 0.131108 0.991368i \(-0.458147\pi\)
0.131108 + 0.991368i \(0.458147\pi\)
\(572\) −9.19149 + 15.9201i −0.384316 + 0.665654i
\(573\) −5.67017 + 9.82102i −0.236875 + 0.410279i
\(574\) 2.14820 + 3.72079i 0.0896642 + 0.155303i
\(575\) 0 0
\(576\) 0.400626 + 0.693904i 0.0166927 + 0.0289127i
\(577\) −42.3965 −1.76499 −0.882494 0.470324i \(-0.844137\pi\)
−0.882494 + 0.470324i \(0.844137\pi\)
\(578\) 45.3879 1.88789
\(579\) −13.2885 23.0163i −0.552250 0.956525i
\(580\) 0 0
\(581\) 5.98906 0.248468
\(582\) −1.41358 −0.0585946
\(583\) −7.07244 12.2498i −0.292911 0.507336i
\(584\) −3.43828 + 5.95528i −0.142277 + 0.246431i
\(585\) 0 0
\(586\) 8.72173 15.1065i 0.360291 0.624043i
\(587\) 21.8535 37.8513i 0.901989 1.56229i 0.0770809 0.997025i \(-0.475440\pi\)
0.824908 0.565266i \(-0.191227\pi\)
\(588\) 10.0341 0.413798
\(589\) 32.7368 + 4.47422i 1.34890 + 0.184357i
\(590\) 0 0
\(591\) −13.7677 + 23.8464i −0.566329 + 0.980911i
\(592\) −1.75289 + 3.03610i −0.0720435 + 0.124783i
\(593\) −14.2795 24.7329i −0.586391 1.01566i −0.994700 0.102815i \(-0.967215\pi\)
0.408310 0.912843i \(-0.366118\pi\)
\(594\) 12.5070 21.6628i 0.513169 0.888835i
\(595\) 0 0
\(596\) −12.0420 −0.493260
\(597\) 20.0681 0.821333
\(598\) −11.7219 20.3029i −0.479344 0.830247i
\(599\) −6.25875 10.8405i −0.255726 0.442930i 0.709367 0.704840i \(-0.248981\pi\)
−0.965092 + 0.261910i \(0.915648\pi\)
\(600\) 0 0
\(601\) 9.44734 0.385365 0.192682 0.981261i \(-0.438281\pi\)
0.192682 + 0.981261i \(0.438281\pi\)
\(602\) −0.153746 0.266295i −0.00626620 0.0108534i
\(603\) −5.28626 + 9.15607i −0.215273 + 0.372864i
\(604\) 0.767418 + 1.32921i 0.0312258 + 0.0540847i
\(605\) 0 0
\(606\) −4.92829 + 8.53606i −0.200198 + 0.346754i
\(607\) −15.1486 −0.614864 −0.307432 0.951570i \(-0.599470\pi\)
−0.307432 + 0.951570i \(0.599470\pi\)
\(608\) −1.64820 4.03527i −0.0668434 0.163652i
\(609\) −2.73766 −0.110936
\(610\) 0 0
\(611\) 8.82548 15.2862i 0.357041 0.618413i
\(612\) 3.16438 + 5.48087i 0.127913 + 0.221551i
\(613\) −3.67718 + 6.36907i −0.148520 + 0.257244i −0.930681 0.365833i \(-0.880784\pi\)
0.782161 + 0.623077i \(0.214118\pi\)
\(614\) 0.557182 + 0.965067i 0.0224860 + 0.0389469i
\(615\) 0 0
\(616\) −2.14266 −0.0863300
\(617\) −15.1038 26.1606i −0.608057 1.05319i −0.991560 0.129646i \(-0.958616\pi\)
0.383504 0.923539i \(-0.374717\pi\)
\(618\) 3.06329 + 5.30577i 0.123224 + 0.213429i
\(619\) 32.0889 1.28976 0.644881 0.764283i \(-0.276907\pi\)
0.644881 + 0.764283i \(0.276907\pi\)
\(620\) 0 0
\(621\) 15.9502 + 27.6265i 0.640058 + 1.10861i
\(622\) −16.9016 + 29.2744i −0.677691 + 1.17380i
\(623\) −2.11406 3.66166i −0.0846981 0.146701i
\(624\) −3.07118 + 5.31943i −0.122945 + 0.212948i
\(625\) 0 0
\(626\) −14.7619 −0.590004
\(627\) −17.5735 + 22.6699i −0.701817 + 0.905347i
\(628\) −19.0533 −0.760309
\(629\) −13.8454 + 23.9809i −0.552052 + 0.956183i
\(630\) 0 0
\(631\) −5.03414 8.71938i −0.200406 0.347113i 0.748253 0.663413i \(-0.230893\pi\)
−0.948659 + 0.316300i \(0.897559\pi\)
\(632\) 0.576026 0.997706i 0.0229131 0.0396866i
\(633\) −9.89121 17.1321i −0.393140 0.680939i
\(634\) −26.1366 −1.03802
\(635\) 0 0
\(636\) −2.36313 4.09306i −0.0937043 0.162301i
\(637\) −14.0154 24.2754i −0.555311 0.961826i
\(638\) −16.9698 −0.671842
\(639\) −2.26216 −0.0894897
\(640\) 0 0
\(641\) 15.9198 27.5740i 0.628796 1.08911i −0.358997 0.933339i \(-0.616881\pi\)
0.987794 0.155768i \(-0.0497854\pi\)
\(642\) −7.41409 12.8416i −0.292611 0.506817i
\(643\) 20.0270 34.6879i 0.789790 1.36796i −0.136306 0.990667i \(-0.543523\pi\)
0.926096 0.377289i \(-0.123144\pi\)
\(644\) 1.36626 2.36643i 0.0538382 0.0932506i
\(645\) 0 0
\(646\) −13.0185 31.8730i −0.512205 1.25403i
\(647\) 5.37891 0.211467 0.105733 0.994395i \(-0.466281\pi\)
0.105733 + 0.994395i \(0.466281\pi\)
\(648\) 2.97712 5.15652i 0.116952 0.202567i
\(649\) 3.60610 6.24594i 0.141552 0.245175i
\(650\) 0 0
\(651\) 2.71344 4.69981i 0.106348 0.184200i
\(652\) 4.98267 + 8.63023i 0.195136 + 0.337986i
\(653\) −19.0958 −0.747278 −0.373639 0.927574i \(-0.621890\pi\)
−0.373639 + 0.927574i \(0.621890\pi\)
\(654\) −27.0110 −1.05621
\(655\) 0 0
\(656\) 4.44930 + 7.70641i 0.173716 + 0.300885i
\(657\) −5.50986 −0.214960
\(658\) 2.05733 0.0802032
\(659\) −20.3162 35.1887i −0.791407 1.37076i −0.925096 0.379733i \(-0.876016\pi\)
0.133690 0.991023i \(-0.457317\pi\)
\(660\) 0 0
\(661\) 9.76205 + 16.9084i 0.379700 + 0.657659i 0.991018 0.133725i \(-0.0426940\pi\)
−0.611319 + 0.791384i \(0.709361\pi\)
\(662\) −1.08564 + 1.88038i −0.0421945 + 0.0730830i
\(663\) −24.2580 + 42.0161i −0.942102 + 1.63177i
\(664\) 12.4044 0.481384
\(665\) 0 0
\(666\) −2.80902 −0.108847
\(667\) 10.8208 18.7422i 0.418983 0.725699i
\(668\) −3.70272 + 6.41331i −0.143263 + 0.248138i
\(669\) 4.09049 + 7.08493i 0.158147 + 0.273919i
\(670\) 0 0
\(671\) 3.26287 + 5.65146i 0.125962 + 0.218172i
\(672\) −0.715931 −0.0276176
\(673\) −1.79517 −0.0691988 −0.0345994 0.999401i \(-0.511016\pi\)
−0.0345994 + 0.999401i \(0.511016\pi\)
\(674\) 6.56430 + 11.3697i 0.252847 + 0.437944i
\(675\) 0 0
\(676\) 4.15907 0.159964
\(677\) −6.92605 −0.266190 −0.133095 0.991103i \(-0.542492\pi\)
−0.133095 + 0.991103i \(0.542492\pi\)
\(678\) −6.15149 10.6547i −0.236247 0.409191i
\(679\) −0.230136 + 0.398607i −0.00883181 + 0.0152971i
\(680\) 0 0
\(681\) 16.4931 28.5669i 0.632018 1.09469i
\(682\) 16.8197 29.1326i 0.644059 1.11554i
\(683\) 11.7972 0.451407 0.225704 0.974196i \(-0.427532\pi\)
0.225704 + 0.974196i \(0.427532\pi\)
\(684\) 2.13978 2.76033i 0.0818166 0.105544i
\(685\) 0 0
\(686\) 3.32345 5.75638i 0.126890 0.219780i
\(687\) 12.1844 21.1039i 0.464862 0.805165i
\(688\) −0.318434 0.551544i −0.0121402 0.0210274i
\(689\) −6.60157 + 11.4342i −0.251500 + 0.435610i
\(690\) 0 0
\(691\) 15.3361 0.583413 0.291707 0.956508i \(-0.405777\pi\)
0.291707 + 0.956508i \(0.405777\pi\)
\(692\) 15.6655 0.595512
\(693\) −0.858403 1.48680i −0.0326080 0.0564788i
\(694\) −7.46811 12.9352i −0.283486 0.491012i
\(695\) 0 0
\(696\) −5.67017 −0.214927
\(697\) 35.1432 + 60.8699i 1.33115 + 2.30561i
\(698\) 9.43056 16.3342i 0.356952 0.618259i
\(699\) −7.83601 13.5724i −0.296385 0.513354i
\(700\) 0 0
\(701\) 5.57300 9.65272i 0.210489 0.364578i −0.741378 0.671087i \(-0.765828\pi\)
0.951868 + 0.306509i \(0.0991609\pi\)
\(702\) −23.3486 −0.881237
\(703\) 15.1406 + 2.06930i 0.571039 + 0.0780452i
\(704\) −4.43782 −0.167256
\(705\) 0 0
\(706\) −1.00586 + 1.74220i −0.0378561 + 0.0655686i
\(707\) 1.60469 + 2.77941i 0.0603507 + 0.104530i
\(708\) 1.20491 2.08697i 0.0452834 0.0784332i
\(709\) 8.65757 + 14.9954i 0.325142 + 0.563162i 0.981541 0.191252i \(-0.0612546\pi\)
−0.656399 + 0.754414i \(0.727921\pi\)
\(710\) 0 0
\(711\) 0.923084 0.0346183
\(712\) −4.37859 7.58395i −0.164095 0.284220i
\(713\) 21.4501 + 37.1527i 0.803312 + 1.39138i
\(714\) −5.65485 −0.211627
\(715\) 0 0
\(716\) −2.30642 3.99483i −0.0861949 0.149294i
\(717\) −11.7606 + 20.3700i −0.439209 + 0.760732i
\(718\) 3.29938 + 5.71469i 0.123132 + 0.213270i
\(719\) 18.7052 32.3983i 0.697585 1.20825i −0.271716 0.962377i \(-0.587591\pi\)
0.969301 0.245875i \(-0.0790754\pi\)
\(720\) 0 0
\(721\) 1.99486 0.0742926
\(722\) −13.5669 + 13.3019i −0.504907 + 0.495045i
\(723\) −6.51468 −0.242283
\(724\) −0.605224 + 1.04828i −0.0224930 + 0.0389590i
\(725\) 0 0
\(726\) 6.44596 + 11.1647i 0.239232 + 0.414362i
\(727\) 17.9095 31.0202i 0.664228 1.15048i −0.315266 0.949003i \(-0.602094\pi\)
0.979494 0.201474i \(-0.0645730\pi\)
\(728\) 1.00000 + 1.73205i 0.0370625 + 0.0641941i
\(729\) 29.8448 1.10536
\(730\) 0 0
\(731\) −2.51518 4.35643i −0.0930274 0.161128i
\(732\) 1.09023 + 1.88834i 0.0402961 + 0.0697949i
\(733\) −20.1867 −0.745614 −0.372807 0.927909i \(-0.621605\pi\)
−0.372807 + 0.927909i \(0.621605\pi\)
\(734\) 11.1984 0.413342
\(735\) 0 0
\(736\) 2.82977 4.90130i 0.104307 0.180664i
\(737\) −29.2785 50.7118i −1.07849 1.86799i
\(738\) −3.56501 + 6.17478i −0.131230 + 0.227297i
\(739\) 19.1178 33.1130i 0.703260 1.21808i −0.264056 0.964507i \(-0.585060\pi\)
0.967316 0.253575i \(-0.0816064\pi\)
\(740\) 0 0
\(741\) 26.5273 + 3.62554i 0.974504 + 0.133188i
\(742\) −1.53891 −0.0564952
\(743\) 7.86688 13.6258i 0.288608 0.499884i −0.684870 0.728665i \(-0.740141\pi\)
0.973478 + 0.228782i \(0.0734743\pi\)
\(744\) 5.62000 9.73413i 0.206039 0.356870i
\(745\) 0 0
\(746\) 1.59718 2.76640i 0.0584771 0.101285i
\(747\) 4.96952 + 8.60746i 0.181825 + 0.314930i
\(748\) −35.0525 −1.28165
\(749\) −4.82818 −0.176418
\(750\) 0 0
\(751\) 12.1150 + 20.9838i 0.442083 + 0.765710i 0.997844 0.0656323i \(-0.0209064\pi\)
−0.555761 + 0.831342i \(0.687573\pi\)
\(752\) 4.26110 0.155386
\(753\) −21.4075 −0.780134
\(754\) 7.92000 + 13.7178i 0.288429 + 0.499574i
\(755\) 0 0
\(756\) −1.36072 2.35683i −0.0494888 0.0857171i
\(757\) 7.40312 12.8226i 0.269071 0.466045i −0.699551 0.714582i \(-0.746617\pi\)
0.968622 + 0.248538i \(0.0799500\pi\)
\(758\) −8.63331 + 14.9533i −0.313576 + 0.543130i
\(759\) −37.2424 −1.35181
\(760\) 0 0
\(761\) −1.98843 −0.0720804 −0.0360402 0.999350i \(-0.511474\pi\)
−0.0360402 + 0.999350i \(0.511474\pi\)
\(762\) 10.6375 18.4247i 0.385356 0.667456i
\(763\) −4.39750 + 7.61669i −0.159200 + 0.275743i
\(764\) 3.82392 + 6.62322i 0.138344 + 0.239620i
\(765\) 0 0
\(766\) −16.0924 27.8729i −0.581443 1.00709i
\(767\) −6.73202 −0.243079
\(768\) −1.48282 −0.0535066
\(769\) 14.9388 + 25.8748i 0.538708 + 0.933070i 0.998974 + 0.0452890i \(0.0144209\pi\)
−0.460266 + 0.887781i \(0.652246\pi\)
\(770\) 0 0
\(771\) 16.3633 0.589311
\(772\) −17.9233 −0.645072
\(773\) 6.31979 + 10.9462i 0.227307 + 0.393707i 0.957009 0.290058i \(-0.0936746\pi\)
−0.729702 + 0.683765i \(0.760341\pi\)
\(774\) 0.255146 0.441926i 0.00917103 0.0158847i
\(775\) 0 0
\(776\) −0.476652 + 0.825585i −0.0171108 + 0.0296368i
\(777\) 1.25495 2.17364i 0.0450211 0.0779788i
\(778\) −10.0717 −0.361090
\(779\) 23.7641 30.6559i 0.851439 1.09836i
\(780\) 0 0
\(781\) 6.26461 10.8506i 0.224165 0.388266i
\(782\) 22.3512 38.7134i 0.799277 1.38439i
\(783\) −10.7769 18.6661i −0.385134 0.667072i
\(784\) 3.38344 5.86030i 0.120837 0.209296i
\(785\) 0 0
\(786\) −14.8291