Properties

Label 950.2.e.o.201.2
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 201.2
Root \(0.741409 - 1.28416i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.o.501.2

$q$-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 −0.996700 0.0811725i \(-0.974134\pi\)
0.568647 + 0.822581i \(0.307467\pi\)
\(4\) −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 \(-0.529084\pi\)
−0.0912440 + 0.995829i \(0.529084\pi\)
\(8\) −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 \(-0.971886\pi\)
0.421661 0.906753i \(-0.361447\pi\)
\(14\) −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 \(-0.426085\pi\)
0.727717 0.685878i \(-0.240581\pi\)
\(18\) 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 \(-0.965776\pi\)
0.404178 0.914680i \(-0.367557\pi\)
\(24\) 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 \(-0.593048\pi\)
−0.288174 + 0.957578i \(0.593048\pi\)
\(38\) 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 −0.840723 0.541465i \(-0.817870\pi\)
0.889284 + 0.457355i \(0.151203\pi\)
\(44\) 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 0.978530 0.206105i \(-0.0660789\pi\)
−0.667757 + 0.744379i \(0.732746\pi\)
\(48\) −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 0.735566 0.677453i \(-0.236916\pi\)
−0.954474 + 0.298293i \(0.903583\pi\)
\(54\) −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 \(-0.868288\pi\)
0.109592 0.993977i \(-0.465046\pi\)
\(68\) −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 −0.591597 0.806234i \(-0.701502\pi\)
0.994017 + 0.109221i \(0.0348356\pi\)
\(74\) −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 \(-0.738359\pi\)
−0.680779 + 0.732489i \(0.738359\pi\)
\(84\) −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 −0.840812 0.541327i \(-0.817922\pi\)
0.889209 + 0.457501i \(0.151256\pi\)
\(98\) −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 \(-0.565250\pi\)
−0.203555 + 0.979064i \(0.565250\pi\)
\(104\) 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 \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 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 \(-0.372385\pi\)
0.390260 + 0.920705i \(0.372385\pi\)
\(114\) 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 \(0.0529830\pi\)
−0.349603 + 0.936898i \(0.613684\pi\)
\(128\) 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 0.777231 0.629215i \(-0.216623\pi\)
−0.933532 + 0.358495i \(0.883290\pi\)
\(138\) 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 \(0.441619\pi\)
−0.942691 + 0.333666i \(0.891714\pi\)
\(158\) −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 \(-0.372381\pi\)
0.390272 + 0.920699i \(0.372381\pi\)
\(164\) −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 0.972978 0.230898i \(-0.0741664\pi\)
−0.686453 + 0.727175i \(0.740833\pi\)
\(168\) −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 \(-0.630282\pi\)
0.993474 0.114056i \(-0.0363843\pi\)
\(174\) 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 \(0.389839\pi\)
−0.984285 + 0.176588i \(0.943494\pi\)
\(194\) −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 \(-0.269912\pi\)
0.661518 + 0.749929i \(0.269912\pi\)
\(198\) −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 −0.758756 0.651375i \(-0.774193\pi\)
0.943485 + 0.331415i \(0.107526\pi\)
\(224\) −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 \(-0.764347\pi\)
−0.738248 + 0.674529i \(0.764347\pi\)
\(228\) 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 −0.985571 0.169261i \(-0.945862\pi\)
0.639370 + 0.768899i \(0.279195\pi\)
\(234\) −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 0.641023 0.767522i \(-0.278510\pi\)
−0.985205 + 0.171382i \(0.945177\pi\)
\(258\) 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 \(0.392462\pi\)
−0.982797 + 0.184691i \(0.940872\pi\)
\(264\) −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 \(-0.194430\pi\)
0.819178 + 0.573539i \(0.194430\pi\)
\(278\) 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 \(0.447899\pi\)
−0.935926 + 0.352197i \(0.885435\pi\)
\(284\) 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 \(-0.329820\pi\)
0.509529 + 0.860453i \(0.329820\pi\)
\(294\) −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 −0.881487 0.472207i \(-0.843457\pi\)
0.849687 + 0.527287i \(0.176791\pi\)
\(308\) −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 0.578460 0.815711i \(-0.303654\pi\)
−0.995656 + 0.0931060i \(0.970320\pi\)
\(314\) 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 \(-0.904323\pi\)
0.221177 0.975234i \(-0.429010\pi\)
\(318\) 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 −0.987556 0.157268i \(-0.949731\pi\)
0.629976 + 0.776615i \(0.283065\pi\)
\(338\) 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 −0.592927 0.805257i \(-0.702028\pi\)
0.993836 + 0.110861i \(0.0353609\pi\)
\(348\) −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 \(-0.517049\pi\)
−0.0535366 + 0.998566i \(0.517049\pi\)
\(354\) −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 0.974348 0.225048i \(-0.0722537\pi\)
−0.682071 + 0.731286i \(0.738920\pi\)
\(368\) 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 \(-0.473646\pi\)
0.0826991 + 0.996575i \(0.473646\pi\)
\(374\) 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 \(-0.526032\pi\)
0.903977 0.427582i \(-0.140634\pi\)
\(384\) 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 \(0.515564\pi\)
−0.840553 + 0.541730i \(0.817770\pi\)
\(398\) 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 0.903481 0.428629i \(-0.141003\pi\)
−0.822944 + 0.568123i \(0.807670\pi\)
\(434\) −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 \(-0.947040\pi\)
0.349671 0.936873i \(-0.386293\pi\)
\(444\) −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 \(-0.667847\pi\)
−0.503208 + 0.864166i \(0.667847\pi\)
\(458\) 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 \(-0.349108\pi\)
0.456486 + 0.889731i \(0.349108\pi\)
\(464\) 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 \(-0.614335\pi\)
−0.351521 + 0.936180i \(0.614335\pi\)
\(468\) −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 \(-0.441922\pi\)
0.181446 + 0.983401i \(0.441922\pi\)
\(488\) 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 0.755505 0.655143i \(-0.227391\pi\)
−0.945123 + 0.326715i \(0.894058\pi\)
\(504\) 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 0.659290 0.751889i \(-0.270857\pi\)
−0.980800 + 0.195017i \(0.937524\pi\)
\(524\) 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 0.836986 0.547224i \(-0.184316\pi\)
−0.892403 + 0.451239i \(0.850982\pi\)
\(548\) −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 0.762723 0.646725i \(-0.223862\pi\)
−0.941442 + 0.337175i \(0.890528\pi\)
\(558\) 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 \(-0.299601\pi\)
0.588798 + 0.808280i \(0.299601\pi\)
\(564\) 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 \(-0.155863\pi\)
0.882494 + 0.470324i \(0.155863\pi\)
\(578\) −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 \(0.524560\pi\)
−0.824908 + 0.565266i \(0.808773\pi\)
\(588\) −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 \(0.0327850\pi\)
−0.408310 + 0.912843i \(0.633882\pi\)
\(594\) 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 \(-0.400530\pi\)
0.307432 + 0.951570i \(0.400530\pi\)
\(608\) 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 −0.782161 0.623077i \(-0.785882\pi\)
0.930681 + 0.365833i \(0.119216\pi\)
\(614\) 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 \(0.0413841\pi\)
−0.383504 + 0.923539i \(0.625283\pi\)
\(618\) −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 \(0.456477\pi\)
−0.926096 + 0.377289i \(0.876856\pi\)
\(644\) 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 \(-0.533719\pi\)
−0.105733 + 0.994395i \(0.533719\pi\)
\(648\) −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 \(-0.378110\pi\)
0.373639 + 0.927574i \(0.378110\pi\)
\(654\) −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 \(-0.488984\pi\)
0.0345994 + 0.999401i \(0.488984\pi\)
\(674\) 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 \(-0.457508\pi\)
0.133095 + 0.991103i \(0.457508\pi\)
\(678\) 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 \(-0.572468\pi\)
−0.225704 + 0.974196i \(0.572468\pi\)
\(684\) 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 \(0.397906\pi\)
−0.979494 + 0.201474i \(0.935427\pi\)
\(728\) −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 \(-0.378395\pi\)
0.372807 + 0.927909i \(0.378395\pi\)
\(734\) 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 −0.973478 0.228782i \(-0.926526\pi\)
0.684870 + 0.728665i \(0.259859\pi\)
\(744\) 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 −0.968622 0.248538i \(-0.920050\pi\)
0.699551 + 0.714582i \(0.253383\pi\)
\(758\) 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 0.729702 0.683765i \(-0.239659\pi\)
−0.957009 + 0.290058i \(0.906325\pi\)
\(774\) 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