Properties

Label 1456.2.r.p.625.5
Level $1456$
Weight $2$
Character 1456.625
Analytic conductor $11.626$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.5
Root \(-0.606661 + 1.05077i\) of defining polynomial
Character \(\chi\) \(=\) 1456.625
Dual form 1456.2.r.p.417.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23721 + 2.14292i) q^{3} +(1.06140 - 1.83839i) q^{5} +(-2.63169 + 0.272389i) q^{7} +(-1.56140 + 2.70442i) q^{9} +O(q^{10})\) \(q+(1.23721 + 2.14292i) q^{3} +(1.06140 - 1.83839i) q^{5} +(-2.63169 + 0.272389i) q^{7} +(-1.56140 + 2.70442i) q^{9} +(2.39448 + 4.14736i) q^{11} +1.00000 q^{13} +5.25271 q^{15} +(1.88914 + 3.27208i) q^{17} +(-1.78362 + 3.08931i) q^{19} +(-3.83967 - 5.30250i) q^{21} +(2.23721 - 3.87497i) q^{23} +(0.246870 + 0.427591i) q^{25} -0.303848 q^{27} -5.90107 q^{29} +(-1.88558 - 3.26592i) q^{31} +(-5.92496 + 10.2623i) q^{33} +(-2.29251 + 5.12720i) q^{35} +(-2.81285 + 4.87200i) q^{37} +(1.23721 + 2.14292i) q^{39} +10.3948 q^{41} -3.40733 q^{43} +(3.31453 + 5.74093i) q^{45} +(-3.55438 + 6.15636i) q^{47} +(6.85161 - 1.43369i) q^{49} +(-4.67454 + 8.09654i) q^{51} +(6.19003 + 10.7214i) q^{53} +10.1660 q^{55} -8.82686 q^{57} +(2.39448 + 4.14736i) q^{59} +(-1.60348 + 2.77732i) q^{61} +(3.37246 - 7.54251i) q^{63} +(1.06140 - 1.83839i) q^{65} +(-1.44978 - 2.51109i) q^{67} +11.0717 q^{69} +2.53876 q^{71} +(-3.85035 - 6.66901i) q^{73} +(-0.610862 + 1.05804i) q^{75} +(-7.43122 - 10.2623i) q^{77} +(-2.58925 + 4.48471i) q^{79} +(4.30827 + 7.46214i) q^{81} -3.46731 q^{83} +8.02051 q^{85} +(-7.30089 - 12.6455i) q^{87} +(-1.83216 + 3.17339i) q^{89} +(-2.63169 + 0.272389i) q^{91} +(4.66574 - 8.08129i) q^{93} +(3.78625 + 6.55798i) q^{95} -5.40733 q^{97} -14.9549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 1.23721 + 2.14292i 0.714306 + 1.23721i 0.963227 + 0.268690i \(0.0865908\pi\)
−0.248921 + 0.968524i \(0.580076\pi\)
\(4\) 0 0
\(5\) 1.06140 1.83839i 0.474671 0.822155i −0.524908 0.851159i \(-0.675900\pi\)
0.999579 + 0.0290040i \(0.00923354\pi\)
\(6\) 0 0
\(7\) −2.63169 + 0.272389i −0.994686 + 0.102953i
\(8\) 0 0
\(9\) −1.56140 + 2.70442i −0.520466 + 0.901473i
\(10\) 0 0
\(11\) 2.39448 + 4.14736i 0.721962 + 1.25048i 0.960212 + 0.279272i \(0.0900930\pi\)
−0.238250 + 0.971204i \(0.576574\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 5.25271 1.35624
\(16\) 0 0
\(17\) 1.88914 + 3.27208i 0.458183 + 0.793597i 0.998865 0.0476304i \(-0.0151670\pi\)
−0.540682 + 0.841227i \(0.681834\pi\)
\(18\) 0 0
\(19\) −1.78362 + 3.08931i −0.409190 + 0.708737i −0.994799 0.101856i \(-0.967522\pi\)
0.585609 + 0.810593i \(0.300855\pi\)
\(20\) 0 0
\(21\) −3.83967 5.30250i −0.837886 1.15710i
\(22\) 0 0
\(23\) 2.23721 3.87497i 0.466491 0.807987i −0.532776 0.846256i \(-0.678851\pi\)
0.999267 + 0.0382695i \(0.0121845\pi\)
\(24\) 0 0
\(25\) 0.246870 + 0.427591i 0.0493740 + 0.0855182i
\(26\) 0 0
\(27\) −0.303848 −0.0584757
\(28\) 0 0
\(29\) −5.90107 −1.09580 −0.547901 0.836543i \(-0.684573\pi\)
−0.547901 + 0.836543i \(0.684573\pi\)
\(30\) 0 0
\(31\) −1.88558 3.26592i −0.338660 0.586577i 0.645521 0.763743i \(-0.276640\pi\)
−0.984181 + 0.177166i \(0.943307\pi\)
\(32\) 0 0
\(33\) −5.92496 + 10.2623i −1.03140 + 1.78644i
\(34\) 0 0
\(35\) −2.29251 + 5.12720i −0.387505 + 0.866655i
\(36\) 0 0
\(37\) −2.81285 + 4.87200i −0.462429 + 0.800951i −0.999081 0.0428524i \(-0.986355\pi\)
0.536652 + 0.843804i \(0.319689\pi\)
\(38\) 0 0
\(39\) 1.23721 + 2.14292i 0.198113 + 0.343141i
\(40\) 0 0
\(41\) 10.3948 1.62340 0.811698 0.584077i \(-0.198543\pi\)
0.811698 + 0.584077i \(0.198543\pi\)
\(42\) 0 0
\(43\) −3.40733 −0.519613 −0.259807 0.965661i \(-0.583659\pi\)
−0.259807 + 0.965661i \(0.583659\pi\)
\(44\) 0 0
\(45\) 3.31453 + 5.74093i 0.494101 + 0.855807i
\(46\) 0 0
\(47\) −3.55438 + 6.15636i −0.518459 + 0.897998i 0.481311 + 0.876550i \(0.340161\pi\)
−0.999770 + 0.0214479i \(0.993172\pi\)
\(48\) 0 0
\(49\) 6.85161 1.43369i 0.978801 0.204813i
\(50\) 0 0
\(51\) −4.67454 + 8.09654i −0.654566 + 1.13374i
\(52\) 0 0
\(53\) 6.19003 + 10.7214i 0.850266 + 1.47270i 0.880968 + 0.473175i \(0.156892\pi\)
−0.0307027 + 0.999529i \(0.509774\pi\)
\(54\) 0 0
\(55\) 10.1660 1.37078
\(56\) 0 0
\(57\) −8.82686 −1.16915
\(58\) 0 0
\(59\) 2.39448 + 4.14736i 0.311734 + 0.539940i 0.978738 0.205115i \(-0.0657567\pi\)
−0.667003 + 0.745055i \(0.732423\pi\)
\(60\) 0 0
\(61\) −1.60348 + 2.77732i −0.205305 + 0.355599i −0.950230 0.311550i \(-0.899152\pi\)
0.744925 + 0.667148i \(0.232485\pi\)
\(62\) 0 0
\(63\) 3.37246 7.54251i 0.424890 0.950267i
\(64\) 0 0
\(65\) 1.06140 1.83839i 0.131650 0.228025i
\(66\) 0 0
\(67\) −1.44978 2.51109i −0.177118 0.306778i 0.763774 0.645484i \(-0.223344\pi\)
−0.940892 + 0.338706i \(0.890011\pi\)
\(68\) 0 0
\(69\) 11.0717 1.33287
\(70\) 0 0
\(71\) 2.53876 0.301295 0.150648 0.988588i \(-0.451864\pi\)
0.150648 + 0.988588i \(0.451864\pi\)
\(72\) 0 0
\(73\) −3.85035 6.66901i −0.450650 0.780548i 0.547777 0.836625i \(-0.315474\pi\)
−0.998426 + 0.0560762i \(0.982141\pi\)
\(74\) 0 0
\(75\) −0.610862 + 1.05804i −0.0705362 + 0.122172i
\(76\) 0 0
\(77\) −7.43122 10.2623i −0.846867 1.16950i
\(78\) 0 0
\(79\) −2.58925 + 4.48471i −0.291313 + 0.504569i −0.974120 0.226029i \(-0.927425\pi\)
0.682807 + 0.730598i \(0.260759\pi\)
\(80\) 0 0
\(81\) 4.30827 + 7.46214i 0.478696 + 0.829126i
\(82\) 0 0
\(83\) −3.46731 −0.380587 −0.190294 0.981727i \(-0.560944\pi\)
−0.190294 + 0.981727i \(0.560944\pi\)
\(84\) 0 0
\(85\) 8.02051 0.869946
\(86\) 0 0
\(87\) −7.30089 12.6455i −0.782738 1.35574i
\(88\) 0 0
\(89\) −1.83216 + 3.17339i −0.194209 + 0.336379i −0.946641 0.322291i \(-0.895547\pi\)
0.752432 + 0.658670i \(0.228881\pi\)
\(90\) 0 0
\(91\) −2.63169 + 0.272389i −0.275876 + 0.0285541i
\(92\) 0 0
\(93\) 4.66574 8.08129i 0.483814 0.837991i
\(94\) 0 0
\(95\) 3.78625 + 6.55798i 0.388461 + 0.672835i
\(96\) 0 0
\(97\) −5.40733 −0.549031 −0.274516 0.961583i \(-0.588518\pi\)
−0.274516 + 0.961583i \(0.588518\pi\)
\(98\) 0 0
\(99\) −14.9549 −1.50303
\(100\) 0 0
\(101\) −4.65862 8.06897i −0.463550 0.802892i 0.535585 0.844482i \(-0.320091\pi\)
−0.999135 + 0.0415891i \(0.986758\pi\)
\(102\) 0 0
\(103\) 3.65318 6.32749i 0.359958 0.623466i −0.627995 0.778217i \(-0.716124\pi\)
0.987953 + 0.154751i \(0.0494576\pi\)
\(104\) 0 0
\(105\) −13.8235 + 1.43078i −1.34904 + 0.139630i
\(106\) 0 0
\(107\) 3.37365 5.84333i 0.326143 0.564896i −0.655600 0.755108i \(-0.727584\pi\)
0.981743 + 0.190212i \(0.0609176\pi\)
\(108\) 0 0
\(109\) −2.08822 3.61691i −0.200016 0.346437i 0.748518 0.663115i \(-0.230766\pi\)
−0.948533 + 0.316678i \(0.897433\pi\)
\(110\) 0 0
\(111\) −13.9204 −1.32126
\(112\) 0 0
\(113\) 5.90107 0.555126 0.277563 0.960707i \(-0.410473\pi\)
0.277563 + 0.960707i \(0.410473\pi\)
\(114\) 0 0
\(115\) −4.74915 8.22577i −0.442860 0.767057i
\(116\) 0 0
\(117\) −1.56140 + 2.70442i −0.144351 + 0.250024i
\(118\) 0 0
\(119\) −5.86291 8.09654i −0.537452 0.742208i
\(120\) 0 0
\(121\) −5.96705 + 10.3352i −0.542459 + 0.939567i
\(122\) 0 0
\(123\) 12.8606 + 22.2752i 1.15960 + 2.00849i
\(124\) 0 0
\(125\) 11.6621 1.04309
\(126\) 0 0
\(127\) 10.5268 0.934100 0.467050 0.884231i \(-0.345317\pi\)
0.467050 + 0.884231i \(0.345317\pi\)
\(128\) 0 0
\(129\) −4.21560 7.30163i −0.371163 0.642873i
\(130\) 0 0
\(131\) 2.71204 4.69740i 0.236952 0.410413i −0.722886 0.690967i \(-0.757185\pi\)
0.959838 + 0.280554i \(0.0905182\pi\)
\(132\) 0 0
\(133\) 3.85243 8.61596i 0.334048 0.747099i
\(134\) 0 0
\(135\) −0.322504 + 0.558593i −0.0277567 + 0.0480761i
\(136\) 0 0
\(137\) −11.1224 19.2645i −0.950248 1.64588i −0.744886 0.667192i \(-0.767496\pi\)
−0.205363 0.978686i \(-0.565837\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −17.5901 −1.48135
\(142\) 0 0
\(143\) 2.39448 + 4.14736i 0.200236 + 0.346819i
\(144\) 0 0
\(145\) −6.26338 + 10.8485i −0.520146 + 0.900919i
\(146\) 0 0
\(147\) 11.5492 + 12.9087i 0.952561 + 1.06469i
\(148\) 0 0
\(149\) −1.47736 + 2.55887i −0.121030 + 0.209630i −0.920174 0.391509i \(-0.871953\pi\)
0.799144 + 0.601140i \(0.205286\pi\)
\(150\) 0 0
\(151\) −9.27736 16.0689i −0.754981 1.30766i −0.945384 0.325959i \(-0.894313\pi\)
0.190403 0.981706i \(-0.439020\pi\)
\(152\) 0 0
\(153\) −11.7988 −0.953875
\(154\) 0 0
\(155\) −8.00541 −0.643010
\(156\) 0 0
\(157\) 4.89982 + 8.48673i 0.391048 + 0.677315i 0.992588 0.121528i \(-0.0387793\pi\)
−0.601540 + 0.798843i \(0.705446\pi\)
\(158\) 0 0
\(159\) −15.3168 + 26.5294i −1.21470 + 2.10392i
\(160\) 0 0
\(161\) −4.83216 + 10.8071i −0.380828 + 0.851720i
\(162\) 0 0
\(163\) 6.91709 11.9808i 0.541788 0.938405i −0.457013 0.889460i \(-0.651081\pi\)
0.998801 0.0489451i \(-0.0155859\pi\)
\(164\) 0 0
\(165\) 12.5775 + 21.7848i 0.979156 + 1.69595i
\(166\) 0 0
\(167\) −17.3534 −1.34285 −0.671424 0.741073i \(-0.734317\pi\)
−0.671424 + 0.741073i \(0.734317\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.56987 9.64730i −0.425939 0.737747i
\(172\) 0 0
\(173\) 1.48069 2.56463i 0.112575 0.194985i −0.804233 0.594314i \(-0.797424\pi\)
0.916808 + 0.399329i \(0.130757\pi\)
\(174\) 0 0
\(175\) −0.766156 1.05804i −0.0579160 0.0799806i
\(176\) 0 0
\(177\) −5.92496 + 10.2623i −0.445348 + 0.771365i
\(178\) 0 0
\(179\) −2.83444 4.90939i −0.211856 0.366945i 0.740440 0.672123i \(-0.234617\pi\)
−0.952295 + 0.305178i \(0.901284\pi\)
\(180\) 0 0
\(181\) 7.17645 0.533421 0.266711 0.963777i \(-0.414063\pi\)
0.266711 + 0.963777i \(0.414063\pi\)
\(182\) 0 0
\(183\) −7.93541 −0.586603
\(184\) 0 0
\(185\) 5.97110 + 10.3423i 0.439004 + 0.760377i
\(186\) 0 0
\(187\) −9.04700 + 15.6699i −0.661582 + 1.14589i
\(188\) 0 0
\(189\) 0.799636 0.0827650i 0.0581649 0.00602027i
\(190\) 0 0
\(191\) 5.94088 10.2899i 0.429867 0.744552i −0.566994 0.823722i \(-0.691894\pi\)
0.996861 + 0.0791703i \(0.0252271\pi\)
\(192\) 0 0
\(193\) −11.4851 19.8927i −0.826714 1.43191i −0.900602 0.434645i \(-0.856874\pi\)
0.0738876 0.997267i \(-0.476459\pi\)
\(194\) 0 0
\(195\) 5.25271 0.376154
\(196\) 0 0
\(197\) 16.9216 1.20561 0.602806 0.797888i \(-0.294049\pi\)
0.602806 + 0.797888i \(0.294049\pi\)
\(198\) 0 0
\(199\) 5.02953 + 8.71140i 0.356534 + 0.617535i 0.987379 0.158374i \(-0.0506251\pi\)
−0.630845 + 0.775909i \(0.717292\pi\)
\(200\) 0 0
\(201\) 3.58737 6.21351i 0.253034 0.438267i
\(202\) 0 0
\(203\) 15.5298 1.60739i 1.08998 0.112817i
\(204\) 0 0
\(205\) 11.0330 19.1098i 0.770580 1.33468i
\(206\) 0 0
\(207\) 6.98636 + 12.1007i 0.485586 + 0.841059i
\(208\) 0 0
\(209\) −17.0833 −1.18168
\(210\) 0 0
\(211\) 24.4609 1.68396 0.841978 0.539512i \(-0.181391\pi\)
0.841978 + 0.539512i \(0.181391\pi\)
\(212\) 0 0
\(213\) 3.14099 + 5.44035i 0.215217 + 0.372767i
\(214\) 0 0
\(215\) −3.61654 + 6.26402i −0.246646 + 0.427203i
\(216\) 0 0
\(217\) 5.85187 + 8.08129i 0.397251 + 0.548594i
\(218\) 0 0
\(219\) 9.52742 16.5020i 0.643804 1.11510i
\(220\) 0 0
\(221\) 1.88914 + 3.27208i 0.127077 + 0.220104i
\(222\) 0 0
\(223\) 29.2625 1.95956 0.979780 0.200076i \(-0.0641188\pi\)
0.979780 + 0.200076i \(0.0641188\pi\)
\(224\) 0 0
\(225\) −1.54185 −0.102790
\(226\) 0 0
\(227\) −5.03685 8.72408i −0.334307 0.579038i 0.649044 0.760751i \(-0.275169\pi\)
−0.983352 + 0.181713i \(0.941836\pi\)
\(228\) 0 0
\(229\) 5.56997 9.64748i 0.368074 0.637523i −0.621190 0.783660i \(-0.713351\pi\)
0.989264 + 0.146137i \(0.0466839\pi\)
\(230\) 0 0
\(231\) 12.7973 28.6212i 0.842003 1.88314i
\(232\) 0 0
\(233\) 8.54166 14.7946i 0.559583 0.969226i −0.437948 0.899000i \(-0.644295\pi\)
0.997531 0.0702257i \(-0.0223720\pi\)
\(234\) 0 0
\(235\) 7.54522 + 13.0687i 0.492196 + 0.852508i
\(236\) 0 0
\(237\) −12.8138 −0.832347
\(238\) 0 0
\(239\) −6.92142 −0.447710 −0.223855 0.974622i \(-0.571864\pi\)
−0.223855 + 0.974622i \(0.571864\pi\)
\(240\) 0 0
\(241\) −3.24812 5.62592i −0.209230 0.362397i 0.742242 0.670132i \(-0.233762\pi\)
−0.951472 + 0.307735i \(0.900429\pi\)
\(242\) 0 0
\(243\) −11.1163 + 19.2539i −0.713109 + 1.23514i
\(244\) 0 0
\(245\) 4.63660 14.1177i 0.296221 0.901945i
\(246\) 0 0
\(247\) −1.78362 + 3.08931i −0.113489 + 0.196568i
\(248\) 0 0
\(249\) −4.28981 7.43017i −0.271856 0.470868i
\(250\) 0 0
\(251\) 9.86804 0.622865 0.311433 0.950268i \(-0.399191\pi\)
0.311433 + 0.950268i \(0.399191\pi\)
\(252\) 0 0
\(253\) 21.4278 1.34716
\(254\) 0 0
\(255\) 9.92309 + 17.1873i 0.621408 + 1.07631i
\(256\) 0 0
\(257\) −3.43234 + 5.94499i −0.214104 + 0.370838i −0.952995 0.302986i \(-0.902016\pi\)
0.738891 + 0.673825i \(0.235350\pi\)
\(258\) 0 0
\(259\) 6.07547 13.5878i 0.377511 0.844304i
\(260\) 0 0
\(261\) 9.21392 15.9590i 0.570327 0.987836i
\(262\) 0 0
\(263\) −0.0632753 0.109596i −0.00390172 0.00675798i 0.864068 0.503375i \(-0.167909\pi\)
−0.867970 + 0.496617i \(0.834575\pi\)
\(264\) 0 0
\(265\) 26.2803 1.61439
\(266\) 0 0
\(267\) −9.06710 −0.554897
\(268\) 0 0
\(269\) 2.12154 + 3.67462i 0.129353 + 0.224045i 0.923426 0.383777i \(-0.125377\pi\)
−0.794073 + 0.607822i \(0.792043\pi\)
\(270\) 0 0
\(271\) 0.783616 1.35726i 0.0476013 0.0824479i −0.841243 0.540657i \(-0.818176\pi\)
0.888844 + 0.458209i \(0.151509\pi\)
\(272\) 0 0
\(273\) −3.83967 5.30250i −0.232388 0.320922i
\(274\) 0 0
\(275\) −1.18225 + 2.04771i −0.0712923 + 0.123482i
\(276\) 0 0
\(277\) 6.37260 + 11.0377i 0.382892 + 0.663189i 0.991474 0.130302i \(-0.0415947\pi\)
−0.608582 + 0.793491i \(0.708261\pi\)
\(278\) 0 0
\(279\) 11.7766 0.705045
\(280\) 0 0
\(281\) 4.62986 0.276194 0.138097 0.990419i \(-0.455901\pi\)
0.138097 + 0.990419i \(0.455901\pi\)
\(282\) 0 0
\(283\) 1.82416 + 3.15954i 0.108435 + 0.187815i 0.915136 0.403144i \(-0.132083\pi\)
−0.806701 + 0.590959i \(0.798749\pi\)
\(284\) 0 0
\(285\) −9.36881 + 16.2273i −0.554960 + 0.961220i
\(286\) 0 0
\(287\) −27.3559 + 2.83143i −1.61477 + 0.167134i
\(288\) 0 0
\(289\) 1.36231 2.35959i 0.0801360 0.138800i
\(290\) 0 0
\(291\) −6.69003 11.5875i −0.392176 0.679269i
\(292\) 0 0
\(293\) −21.0415 −1.22926 −0.614630 0.788816i \(-0.710695\pi\)
−0.614630 + 0.788816i \(0.710695\pi\)
\(294\) 0 0
\(295\) 10.1660 0.591886
\(296\) 0 0
\(297\) −0.727559 1.26017i −0.0422172 0.0731224i
\(298\) 0 0
\(299\) 2.23721 3.87497i 0.129381 0.224095i
\(300\) 0 0
\(301\) 8.96705 0.928120i 0.516852 0.0534960i
\(302\) 0 0
\(303\) 11.5274 19.9661i 0.662233 1.14702i
\(304\) 0 0
\(305\) 3.40387 + 5.89567i 0.194905 + 0.337585i
\(306\) 0 0
\(307\) 4.95861 0.283003 0.141502 0.989938i \(-0.454807\pi\)
0.141502 + 0.989938i \(0.454807\pi\)
\(308\) 0 0
\(309\) 18.0791 1.02848
\(310\) 0 0
\(311\) −1.21079 2.09715i −0.0686575 0.118918i 0.829653 0.558279i \(-0.188538\pi\)
−0.898311 + 0.439361i \(0.855205\pi\)
\(312\) 0 0
\(313\) −6.98026 + 12.0902i −0.394548 + 0.683377i −0.993043 0.117749i \(-0.962432\pi\)
0.598496 + 0.801126i \(0.295765\pi\)
\(314\) 0 0
\(315\) −10.2866 14.2055i −0.579583 0.800390i
\(316\) 0 0
\(317\) −1.53431 + 2.65750i −0.0861753 + 0.149260i −0.905891 0.423510i \(-0.860798\pi\)
0.819716 + 0.572770i \(0.194131\pi\)
\(318\) 0 0
\(319\) −14.1300 24.4739i −0.791127 1.37027i
\(320\) 0 0
\(321\) 16.6957 0.931863
\(322\) 0 0
\(323\) −13.4780 −0.749936
\(324\) 0 0
\(325\) 0.246870 + 0.427591i 0.0136939 + 0.0237185i
\(326\) 0 0
\(327\) 5.16716 8.94978i 0.285745 0.494924i
\(328\) 0 0
\(329\) 7.67710 17.1698i 0.423252 0.946603i
\(330\) 0 0
\(331\) 6.80261 11.7825i 0.373905 0.647623i −0.616257 0.787545i \(-0.711352\pi\)
0.990162 + 0.139922i \(0.0446853\pi\)
\(332\) 0 0
\(333\) −8.78395 15.2142i −0.481358 0.833736i
\(334\) 0 0
\(335\) −6.15516 −0.336292
\(336\) 0 0
\(337\) −35.1646 −1.91554 −0.957769 0.287538i \(-0.907163\pi\)
−0.957769 + 0.287538i \(0.907163\pi\)
\(338\) 0 0
\(339\) 7.30089 + 12.6455i 0.396530 + 0.686810i
\(340\) 0 0
\(341\) 9.02997 15.6404i 0.489000 0.846973i
\(342\) 0 0
\(343\) −17.6408 + 5.63933i −0.952514 + 0.304495i
\(344\) 0 0
\(345\) 11.7514 20.3541i 0.632676 1.09583i
\(346\) 0 0
\(347\) −2.73551 4.73804i −0.146850 0.254351i 0.783212 0.621755i \(-0.213580\pi\)
−0.930062 + 0.367404i \(0.880247\pi\)
\(348\) 0 0
\(349\) 4.34196 0.232420 0.116210 0.993225i \(-0.462925\pi\)
0.116210 + 0.993225i \(0.462925\pi\)
\(350\) 0 0
\(351\) −0.303848 −0.0162182
\(352\) 0 0
\(353\) −13.7996 23.9016i −0.734479 1.27216i −0.954951 0.296762i \(-0.904093\pi\)
0.220472 0.975393i \(-0.429240\pi\)
\(354\) 0 0
\(355\) 2.69463 4.66724i 0.143016 0.247712i
\(356\) 0 0
\(357\) 10.0965 22.5809i 0.534365 1.19511i
\(358\) 0 0
\(359\) 3.31427 5.74049i 0.174921 0.302971i −0.765213 0.643777i \(-0.777366\pi\)
0.940134 + 0.340806i \(0.110700\pi\)
\(360\) 0 0
\(361\) 3.13742 + 5.43418i 0.165128 + 0.286009i
\(362\) 0 0
\(363\) −29.5301 −1.54993
\(364\) 0 0
\(365\) −16.3470 −0.855643
\(366\) 0 0
\(367\) 15.6037 + 27.0264i 0.814506 + 1.41077i 0.909682 + 0.415305i \(0.136325\pi\)
−0.0951768 + 0.995460i \(0.530342\pi\)
\(368\) 0 0
\(369\) −16.2304 + 28.1119i −0.844923 + 1.46345i
\(370\) 0 0
\(371\) −19.2107 26.5294i −0.997368 1.37734i
\(372\) 0 0
\(373\) 7.88730 13.6612i 0.408389 0.707350i −0.586321 0.810079i \(-0.699424\pi\)
0.994709 + 0.102729i \(0.0327574\pi\)
\(374\) 0 0
\(375\) 14.4285 + 24.9909i 0.745084 + 1.29052i
\(376\) 0 0
\(377\) −5.90107 −0.303921
\(378\) 0 0
\(379\) −31.6512 −1.62581 −0.812907 0.582393i \(-0.802116\pi\)
−0.812907 + 0.582393i \(0.802116\pi\)
\(380\) 0 0
\(381\) 13.0239 + 22.5580i 0.667233 + 1.15568i
\(382\) 0 0
\(383\) 6.19675 10.7331i 0.316639 0.548435i −0.663145 0.748491i \(-0.730779\pi\)
0.979785 + 0.200055i \(0.0641122\pi\)
\(384\) 0 0
\(385\) −26.7537 + 2.76910i −1.36350 + 0.141126i
\(386\) 0 0
\(387\) 5.32020 9.21486i 0.270441 0.468418i
\(388\) 0 0
\(389\) 7.03705 + 12.1885i 0.356792 + 0.617983i 0.987423 0.158100i \(-0.0505370\pi\)
−0.630631 + 0.776083i \(0.717204\pi\)
\(390\) 0 0
\(391\) 16.9056 0.854954
\(392\) 0 0
\(393\) 13.4215 0.677026
\(394\) 0 0
\(395\) 5.49644 + 9.52012i 0.276556 + 0.479009i
\(396\) 0 0
\(397\) 3.48652 6.03884i 0.174984 0.303081i −0.765172 0.643826i \(-0.777346\pi\)
0.940156 + 0.340745i \(0.110679\pi\)
\(398\) 0 0
\(399\) 23.2296 2.40434i 1.16293 0.120368i
\(400\) 0 0
\(401\) −1.36841 + 2.37016i −0.0683352 + 0.118360i −0.898169 0.439651i \(-0.855102\pi\)
0.829833 + 0.558011i \(0.188435\pi\)
\(402\) 0 0
\(403\) −1.88558 3.26592i −0.0939275 0.162687i
\(404\) 0 0
\(405\) 18.2911 0.908894
\(406\) 0 0
\(407\) −26.9412 −1.33543
\(408\) 0 0
\(409\) 12.2577 + 21.2309i 0.606104 + 1.04980i 0.991876 + 0.127208i \(0.0406017\pi\)
−0.385772 + 0.922594i \(0.626065\pi\)
\(410\) 0 0
\(411\) 27.5215 47.6686i 1.35754 2.35132i
\(412\) 0 0
\(413\) −7.43122 10.2623i −0.365667 0.504977i
\(414\) 0 0
\(415\) −3.68020 + 6.37429i −0.180654 + 0.312902i
\(416\) 0 0
\(417\) 4.94886 + 8.57167i 0.242347 + 0.419757i
\(418\) 0 0
\(419\) 3.01252 0.147171 0.0735856 0.997289i \(-0.476556\pi\)
0.0735856 + 0.997289i \(0.476556\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) −11.0996 19.2251i −0.539681 0.934755i
\(424\) 0 0
\(425\) −0.932742 + 1.61556i −0.0452447 + 0.0783660i
\(426\) 0 0
\(427\) 3.46337 7.74581i 0.167604 0.374846i
\(428\) 0 0
\(429\) −5.92496 + 10.2623i −0.286060 + 0.495470i
\(430\) 0 0
\(431\) −9.39711 16.2763i −0.452643 0.784001i 0.545906 0.837846i \(-0.316185\pi\)
−0.998549 + 0.0538455i \(0.982852\pi\)
\(432\) 0 0
\(433\) −7.76911 −0.373360 −0.186680 0.982421i \(-0.559773\pi\)
−0.186680 + 0.982421i \(0.559773\pi\)
\(434\) 0 0
\(435\) −30.9966 −1.48617
\(436\) 0 0
\(437\) 7.98066 + 13.8229i 0.381767 + 0.661240i
\(438\) 0 0
\(439\) −18.9841 + 32.8814i −0.906060 + 1.56934i −0.0865713 + 0.996246i \(0.527591\pi\)
−0.819488 + 0.573096i \(0.805742\pi\)
\(440\) 0 0
\(441\) −6.82079 + 20.7682i −0.324799 + 0.988961i
\(442\) 0 0
\(443\) 17.8135 30.8539i 0.846344 1.46591i −0.0381050 0.999274i \(-0.512132\pi\)
0.884449 0.466637i \(-0.154535\pi\)
\(444\) 0 0
\(445\) 3.88930 + 6.73647i 0.184371 + 0.319339i
\(446\) 0 0
\(447\) −7.31125 −0.345810
\(448\) 0 0
\(449\) −8.05285 −0.380038 −0.190019 0.981780i \(-0.560855\pi\)
−0.190019 + 0.981780i \(0.560855\pi\)
\(450\) 0 0
\(451\) 24.8901 + 43.1110i 1.17203 + 2.03002i
\(452\) 0 0
\(453\) 22.9562 39.7612i 1.07857 1.86815i
\(454\) 0 0
\(455\) −2.29251 + 5.12720i −0.107475 + 0.240367i
\(456\) 0 0
\(457\) −7.79881 + 13.5079i −0.364813 + 0.631875i −0.988746 0.149603i \(-0.952200\pi\)
0.623933 + 0.781478i \(0.285534\pi\)
\(458\) 0 0
\(459\) −0.574012 0.994218i −0.0267926 0.0464061i
\(460\) 0 0
\(461\) −25.6991 −1.19692 −0.598462 0.801151i \(-0.704221\pi\)
−0.598462 + 0.801151i \(0.704221\pi\)
\(462\) 0 0
\(463\) 20.5209 0.953685 0.476842 0.878989i \(-0.341781\pi\)
0.476842 + 0.878989i \(0.341781\pi\)
\(464\) 0 0
\(465\) −9.90440 17.1549i −0.459306 0.795541i
\(466\) 0 0
\(467\) 5.91241 10.2406i 0.273594 0.473878i −0.696186 0.717862i \(-0.745121\pi\)
0.969779 + 0.243984i \(0.0784543\pi\)
\(468\) 0 0
\(469\) 4.49936 + 6.21351i 0.207761 + 0.286913i
\(470\) 0 0
\(471\) −12.1242 + 20.9998i −0.558656 + 0.967620i
\(472\) 0 0
\(473\) −8.15878 14.1314i −0.375141 0.649764i
\(474\) 0 0
\(475\) −1.76128 −0.0808133
\(476\) 0 0
\(477\) −38.6604 −1.77014
\(478\) 0 0
\(479\) 11.3276 + 19.6200i 0.517571 + 0.896459i 0.999792 + 0.0204092i \(0.00649690\pi\)
−0.482221 + 0.876050i \(0.660170\pi\)
\(480\) 0 0
\(481\) −2.81285 + 4.87200i −0.128255 + 0.222144i
\(482\) 0 0
\(483\) −29.1372 + 3.01580i −1.32579 + 0.137224i
\(484\) 0 0
\(485\) −5.73933 + 9.94081i −0.260610 + 0.451389i
\(486\) 0 0
\(487\) −16.3584 28.3335i −0.741268 1.28391i −0.951918 0.306353i \(-0.900891\pi\)
0.210650 0.977562i \(-0.432442\pi\)
\(488\) 0 0
\(489\) 34.2317 1.54801
\(490\) 0 0
\(491\) −6.17281 −0.278575 −0.139288 0.990252i \(-0.544481\pi\)
−0.139288 + 0.990252i \(0.544481\pi\)
\(492\) 0 0
\(493\) −11.1479 19.3088i −0.502078 0.869625i
\(494\) 0 0
\(495\) −15.8731 + 27.4931i −0.713444 + 1.23572i
\(496\) 0 0
\(497\) −6.68123 + 0.691531i −0.299694 + 0.0310194i
\(498\) 0 0
\(499\) −7.31934 + 12.6775i −0.327659 + 0.567521i −0.982047 0.188637i \(-0.939593\pi\)
0.654388 + 0.756159i \(0.272926\pi\)
\(500\) 0 0
\(501\) −21.4699 37.1870i −0.959205 1.66139i
\(502\) 0 0
\(503\) −12.7787 −0.569774 −0.284887 0.958561i \(-0.591956\pi\)
−0.284887 + 0.958561i \(0.591956\pi\)
\(504\) 0 0
\(505\) −19.7786 −0.880136
\(506\) 0 0
\(507\) 1.23721 + 2.14292i 0.0549466 + 0.0951703i
\(508\) 0 0
\(509\) −5.84263 + 10.1197i −0.258970 + 0.448549i −0.965966 0.258668i \(-0.916716\pi\)
0.706996 + 0.707217i \(0.250050\pi\)
\(510\) 0 0
\(511\) 11.9495 + 16.5020i 0.528615 + 0.730005i
\(512\) 0 0
\(513\) 0.541949 0.938683i 0.0239276 0.0414439i
\(514\) 0 0
\(515\) −7.75495 13.4320i −0.341724 0.591883i
\(516\) 0 0
\(517\) −34.0435 −1.49723
\(518\) 0 0
\(519\) 7.32772 0.321651
\(520\) 0 0
\(521\) −4.23838 7.34108i −0.185687 0.321619i 0.758121 0.652114i \(-0.226118\pi\)
−0.943808 + 0.330495i \(0.892784\pi\)
\(522\) 0 0
\(523\) 16.3554 28.3284i 0.715172 1.23871i −0.247721 0.968831i \(-0.579682\pi\)
0.962893 0.269883i \(-0.0869849\pi\)
\(524\) 0 0
\(525\) 1.31940 2.95084i 0.0575833 0.128785i
\(526\) 0 0
\(527\) 7.12425 12.3396i 0.310337 0.537520i
\(528\) 0 0
\(529\) 1.48975 + 2.58032i 0.0647716 + 0.112188i
\(530\) 0 0
\(531\) −14.9549 −0.648989
\(532\) 0 0
\(533\) 10.3948 0.450249
\(534\) 0 0
\(535\) −7.16156 12.4042i −0.309621 0.536280i
\(536\) 0 0
\(537\) 7.01361 12.1479i 0.302660 0.524222i
\(538\) 0 0
\(539\) 22.3520 + 24.9831i 0.962771 + 1.07610i
\(540\) 0 0
\(541\) 14.0853 24.3964i 0.605573 1.04888i −0.386388 0.922336i \(-0.626277\pi\)
0.991961 0.126547i \(-0.0403893\pi\)
\(542\) 0 0
\(543\) 8.87880 + 15.3785i 0.381026 + 0.659956i
\(544\) 0 0
\(545\) −8.86574 −0.379767
\(546\) 0 0
\(547\) 18.5377 0.792615 0.396307 0.918118i \(-0.370291\pi\)
0.396307 + 0.918118i \(0.370291\pi\)
\(548\) 0 0
\(549\) −5.00735 8.67299i −0.213709 0.370154i
\(550\) 0 0
\(551\) 10.5252 18.2303i 0.448391 0.776635i
\(552\) 0 0
\(553\) 5.59252 12.5077i 0.237818 0.531880i
\(554\) 0 0
\(555\) −14.7751 + 25.5912i −0.627167 + 1.08628i
\(556\) 0 0
\(557\) −2.00142 3.46655i −0.0848027 0.146883i 0.820504 0.571640i \(-0.193693\pi\)
−0.905307 + 0.424758i \(0.860359\pi\)
\(558\) 0 0
\(559\) −3.40733 −0.144115
\(560\) 0 0
\(561\) −44.7723 −1.89029
\(562\) 0 0
\(563\) −8.93100 15.4689i −0.376397 0.651938i 0.614138 0.789199i \(-0.289504\pi\)
−0.990535 + 0.137260i \(0.956170\pi\)
\(564\) 0 0
\(565\) 6.26338 10.8485i 0.263503 0.456400i
\(566\) 0 0
\(567\) −13.3706 18.4645i −0.561514 0.775437i
\(568\) 0 0
\(569\) 18.7336 32.4475i 0.785353 1.36027i −0.143434 0.989660i \(-0.545815\pi\)
0.928788 0.370612i \(-0.120852\pi\)
\(570\) 0 0
\(571\) 8.78514 + 15.2163i 0.367646 + 0.636782i 0.989197 0.146592i \(-0.0468303\pi\)
−0.621551 + 0.783374i \(0.713497\pi\)
\(572\) 0 0
\(573\) 29.4006 1.22823
\(574\) 0 0
\(575\) 2.20920 0.0921301
\(576\) 0 0
\(577\) 17.1247 + 29.6608i 0.712910 + 1.23480i 0.963760 + 0.266770i \(0.0859565\pi\)
−0.250850 + 0.968026i \(0.580710\pi\)
\(578\) 0 0
\(579\) 28.4190 49.2232i 1.18105 2.04565i
\(580\) 0 0
\(581\) 9.12490 0.944459i 0.378565 0.0391828i
\(582\) 0 0
\(583\) −29.6438 + 51.3445i −1.22772 + 2.12647i
\(584\) 0 0
\(585\) 3.31453 + 5.74093i 0.137039 + 0.237358i
\(586\) 0 0
\(587\) 29.4494 1.21551 0.607754 0.794126i \(-0.292071\pi\)
0.607754 + 0.794126i \(0.292071\pi\)
\(588\) 0 0
\(589\) 13.4526 0.554305
\(590\) 0 0
\(591\) 20.9356 + 36.2616i 0.861176 + 1.49160i
\(592\) 0 0
\(593\) 17.0001 29.4450i 0.698109 1.20916i −0.271013 0.962576i \(-0.587359\pi\)
0.969121 0.246584i \(-0.0793081\pi\)
\(594\) 0 0
\(595\) −21.1075 + 2.18470i −0.865324 + 0.0895640i
\(596\) 0 0
\(597\) −12.4452 + 21.5557i −0.509349 + 0.882218i
\(598\) 0 0
\(599\) 10.7209 + 18.5691i 0.438043 + 0.758713i 0.997539 0.0701203i \(-0.0223383\pi\)
−0.559495 + 0.828834i \(0.689005\pi\)
\(600\) 0 0
\(601\) 40.4039 1.64811 0.824054 0.566511i \(-0.191707\pi\)
0.824054 + 0.566511i \(0.191707\pi\)
\(602\) 0 0
\(603\) 9.05472 0.368737
\(604\) 0 0
\(605\) 12.6668 + 21.9396i 0.514980 + 0.891971i
\(606\) 0 0
\(607\) −21.9456 + 38.0110i −0.890746 + 1.54282i −0.0517636 + 0.998659i \(0.516484\pi\)
−0.838983 + 0.544158i \(0.816849\pi\)
\(608\) 0 0
\(609\) 22.6582 + 31.2904i 0.918156 + 1.26795i
\(610\) 0 0
\(611\) −3.55438 + 6.15636i −0.143795 + 0.249060i
\(612\) 0 0
\(613\) 7.15777 + 12.3976i 0.289100 + 0.500735i 0.973595 0.228282i \(-0.0733108\pi\)
−0.684496 + 0.729017i \(0.739977\pi\)
\(614\) 0 0
\(615\) 54.6009 2.20172
\(616\) 0 0
\(617\) −36.9097 −1.48593 −0.742965 0.669330i \(-0.766581\pi\)
−0.742965 + 0.669330i \(0.766581\pi\)
\(618\) 0 0
\(619\) 7.14646 + 12.3780i 0.287240 + 0.497515i 0.973150 0.230172i \(-0.0739288\pi\)
−0.685910 + 0.727687i \(0.740595\pi\)
\(620\) 0 0
\(621\) −0.679774 + 1.17740i −0.0272784 + 0.0472476i
\(622\) 0 0
\(623\) 3.95728 8.85046i 0.158545 0.354586i
\(624\) 0 0
\(625\) 11.1438 19.3016i 0.445750 0.772062i
\(626\) 0 0
\(627\) −21.1357 36.6082i −0.844080 1.46199i
\(628\) 0 0
\(629\) −21.2554 −0.847510
\(630\) 0 0
\(631\) 0.0431064 0.00171604 0.000858019 1.00000i \(-0.499727\pi\)
0.000858019 1.00000i \(0.499727\pi\)
\(632\) 0 0
\(633\) 30.2633 + 52.4176i 1.20286 + 2.08341i
\(634\) 0 0
\(635\) 11.1731 19.3524i 0.443390 0.767975i
\(636\) 0 0
\(637\) 6.85161 1.43369i 0.271471 0.0568048i
\(638\) 0 0
\(639\) −3.96401 + 6.86587i −0.156814 + 0.271610i
\(640\) 0 0
\(641\) −21.3328 36.9494i −0.842594 1.45942i −0.887695 0.460433i \(-0.847694\pi\)
0.0451008 0.998982i \(-0.485639\pi\)
\(642\) 0 0
\(643\) 5.49737 0.216795 0.108398 0.994108i \(-0.465428\pi\)
0.108398 + 0.994108i \(0.465428\pi\)
\(644\) 0 0
\(645\) −17.8977 −0.704722
\(646\) 0 0
\(647\) −19.0933 33.0706i −0.750637 1.30014i −0.947514 0.319713i \(-0.896413\pi\)
0.196877 0.980428i \(-0.436920\pi\)
\(648\) 0 0
\(649\) −11.4671 + 19.8615i −0.450121 + 0.779633i
\(650\) 0 0
\(651\) −10.0775 + 22.5384i −0.394969 + 0.883348i
\(652\) 0 0
\(653\) −19.2510 + 33.3437i −0.753349 + 1.30484i 0.192843 + 0.981230i \(0.438229\pi\)
−0.946191 + 0.323608i \(0.895104\pi\)
\(654\) 0 0
\(655\) −5.75711 9.97161i −0.224949 0.389623i
\(656\) 0 0
\(657\) 24.0477 0.938192
\(658\) 0 0
\(659\) −19.4843 −0.759002 −0.379501 0.925191i \(-0.623904\pi\)
−0.379501 + 0.925191i \(0.623904\pi\)
\(660\) 0 0
\(661\) 20.8334 + 36.0844i 0.810324 + 1.40352i 0.912638 + 0.408770i \(0.134042\pi\)
−0.102314 + 0.994752i \(0.532625\pi\)
\(662\) 0 0
\(663\) −4.67454 + 8.09654i −0.181544 + 0.314443i
\(664\) 0 0
\(665\) −11.7506 16.2273i −0.455668 0.629266i
\(666\) 0 0
\(667\) −13.2020 + 22.8665i −0.511182 + 0.885393i
\(668\) 0 0
\(669\) 36.2040 + 62.7071i 1.39973 + 2.42440i
\(670\) 0 0
\(671\) −15.3580 −0.592890
\(672\) 0 0
\(673\) −14.3157 −0.551830 −0.275915 0.961182i \(-0.588981\pi\)
−0.275915 + 0.961182i \(0.588981\pi\)
\(674\) 0 0
\(675\) −0.0750110 0.129923i −0.00288718 0.00500073i
\(676\) 0 0
\(677\) 14.7641 25.5721i 0.567429 0.982815i −0.429391 0.903119i \(-0.641272\pi\)
0.996819 0.0796963i \(-0.0253950\pi\)
\(678\) 0 0
\(679\) 14.2304 1.47290i 0.546114 0.0565247i
\(680\) 0 0
\(681\) 12.4633 21.5871i 0.477596 0.827220i
\(682\) 0 0
\(683\) 23.5349 + 40.7637i 0.900539 + 1.55978i 0.826795 + 0.562503i \(0.190161\pi\)
0.0737441 + 0.997277i \(0.476505\pi\)
\(684\) 0 0
\(685\) −47.2210 −1.80422
\(686\) 0 0
\(687\) 27.5650 1.05167
\(688\) 0 0
\(689\) 6.19003 + 10.7214i 0.235821 + 0.408454i
\(690\) 0 0
\(691\) −15.4334 + 26.7314i −0.587113 + 1.01691i 0.407495 + 0.913207i \(0.366402\pi\)
−0.994608 + 0.103703i \(0.966931\pi\)
\(692\) 0 0
\(693\) 39.3568 4.07356i 1.49504 0.154742i
\(694\) 0 0
\(695\) 4.24559 7.35358i 0.161044 0.278937i
\(696\) 0 0
\(697\) 19.6372 + 34.0127i 0.743813 + 1.28832i
\(698\) 0 0
\(699\) 42.2715 1.59885
\(700\) 0 0
\(701\) 6.48958 0.245108 0.122554 0.992462i \(-0.460892\pi\)
0.122554 + 0.992462i \(0.460892\pi\)
\(702\) 0 0
\(703\) −10.0341 17.3795i −0.378443 0.655482i
\(704\) 0 0
\(705\) −18.6701 + 32.3376i −0.703157 + 1.21790i
\(706\) 0 0
\(707\) 14.4580 + 19.9661i 0.543747 + 0.750902i
\(708\) 0 0
\(709\) 6.68689 11.5820i 0.251131 0.434972i −0.712706 0.701463i \(-0.752531\pi\)
0.963838 + 0.266490i \(0.0858641\pi\)
\(710\) 0 0
\(711\) −8.08569 14.0048i −0.303237 0.525222i
\(712\) 0 0
\(713\) −16.8738 −0.631929
\(714\) 0 0
\(715\) 10.1660 0.380186
\(716\) 0 0
\(717\) −8.56328 14.8320i −0.319802 0.553913i
\(718\) 0 0
\(719\) −8.37048 + 14.4981i −0.312166 + 0.540688i −0.978831 0.204670i \(-0.934388\pi\)
0.666665 + 0.745358i \(0.267721\pi\)
\(720\) 0 0
\(721\) −7.89050 + 17.6471i −0.293858 + 0.657212i
\(722\) 0 0
\(723\) 8.03725 13.9209i 0.298909 0.517725i
\(724\) 0 0
\(725\) −1.45680 2.52325i −0.0541041 0.0937110i
\(726\) 0 0
\(727\) −38.8138 −1.43952 −0.719761 0.694221i \(-0.755749\pi\)
−0.719761 + 0.694221i \(0.755749\pi\)
\(728\) 0 0
\(729\) −29.1632 −1.08012
\(730\) 0 0
\(731\) −6.43692 11.1491i −0.238078 0.412364i
\(732\) 0 0
\(733\) −18.8639 + 32.6733i −0.696756 + 1.20682i 0.272830 + 0.962062i \(0.412040\pi\)
−0.969585 + 0.244754i \(0.921293\pi\)
\(734\) 0 0
\(735\) 35.9895 7.53074i 1.32749 0.277776i
\(736\) 0 0
\(737\) 6.94292 12.0255i 0.255746 0.442965i
\(738\) 0 0
\(739\) −4.61476 7.99300i −0.169757 0.294027i 0.768578 0.639757i \(-0.220965\pi\)
−0.938334 + 0.345729i \(0.887632\pi\)
\(740\) 0 0
\(741\) −8.82686 −0.324263
\(742\) 0 0
\(743\) 3.56327 0.130724 0.0653619 0.997862i \(-0.479180\pi\)
0.0653619 + 0.997862i \(0.479180\pi\)
\(744\) 0 0
\(745\) 3.13614 + 5.43195i 0.114899 + 0.199011i
\(746\) 0 0
\(747\) 5.41386 9.37707i 0.198083 0.343089i
\(748\) 0 0
\(749\) −7.28674 + 16.2968i −0.266252 + 0.595472i
\(750\) 0 0
\(751\) 25.6053 44.3496i 0.934350 1.61834i 0.158561 0.987349i \(-0.449315\pi\)
0.775789 0.630992i \(-0.217352\pi\)
\(752\) 0 0
\(753\) 12.2089 + 21.1464i 0.444916 + 0.770618i
\(754\) 0 0
\(755\) −39.3879 −1.43347
\(756\) 0 0
\(757\) 25.2305 0.917019 0.458509 0.888690i \(-0.348384\pi\)
0.458509 + 0.888690i \(0.348384\pi\)
\(758\) 0 0
\(759\) 26.5108 + 45.9181i 0.962282 + 1.66672i
\(760\) 0 0
\(761\) −1.82372 + 3.15878i −0.0661099 + 0.114506i −0.897186 0.441653i \(-0.854392\pi\)
0.831076 + 0.556159i \(0.187725\pi\)
\(762\) 0 0
\(763\) 6.48077 + 8.94978i 0.234620 + 0.324004i
\(764\) 0 0
\(765\) −12.5232 + 21.6908i −0.452777 + 0.784233i
\(766\) 0 0
\(767\) 2.39448 + 4.14736i 0.0864596 + 0.149752i
\(768\) 0 0
\(769\) 21.9882 0.792914 0.396457 0.918053i \(-0.370240\pi\)
0.396457 + 0.918053i \(0.370240\pi\)
\(770\) 0 0
\(771\) −16.9862 −0.611742
\(772\) 0 0
\(773\) −10.9295 18.9305i −0.393108 0.680882i 0.599750 0.800187i \(-0.295267\pi\)
−0.992858 + 0.119305i \(0.961933\pi\)
\(774\) 0 0
\(775\) 0.930986 1.61252i 0.0334420 0.0579233i
\(776\) 0 0
\(777\) 36.6342 3.79176i 1.31424 0.136029i
\(778\) 0 0
\(779\) −18.5404 + 32.1128i −0.664277 + 1.15056i
\(780\) 0 0
\(781\) 6.07900 + 10.5291i 0.217524 + 0.376762i
\(782\) 0 0
\(783\) 1.79303 0.0640777
\(784\) 0 0
\(785\) 20.8026 0.742477
\(786\) 0 0
\(787\) 19.9336 + 34.5261i 0.710557 + 1.23072i 0.964648 + 0.263541i \(0.0848905\pi\)
−0.254091 + 0.967180i \(0.581776\pi\)
\(788\) 0 0
\(789\) 0.156570 0.271188i 0.00557405 0.00965454i
\(790\) 0 0
\(791\) −15.5298 + 1.60739i −0.552176 + 0.0571521i
\(792\) 0 0
\(793\) −1.60348 + 2.77732i −0.0569414 + 0.0986254i
\(794\) 0 0
\(795\) 32.5144 + 56.3166i 1.15317 + 1.99734i
\(796\) 0 0
\(797\) −40.1971 −1.42385