Properties

Label 225.4.f.b.107.1
Level $225$
Weight $4$
Character 225.107
Analytic conductor $13.275$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.4.f.b.143.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.12132 + 2.12132i) q^{2} -1.00000i q^{4} +(9.00000 + 9.00000i) q^{7} +(-14.8492 - 14.8492i) q^{8} +O(q^{10})\) \(q+(-2.12132 + 2.12132i) q^{2} -1.00000i q^{4} +(9.00000 + 9.00000i) q^{7} +(-14.8492 - 14.8492i) q^{8} -38.1838i q^{11} +(-63.0000 + 63.0000i) q^{13} -38.1838 q^{14} +71.0000 q^{16} +(-29.6985 + 29.6985i) q^{17} -70.0000i q^{19} +(81.0000 + 81.0000i) q^{22} +(-72.1249 - 72.1249i) q^{23} -267.286i q^{26} +(9.00000 - 9.00000i) q^{28} -229.103 q^{29} +196.000 q^{31} +(-31.8198 + 31.8198i) q^{32} -126.000i q^{34} +(-207.000 - 207.000i) q^{37} +(148.492 + 148.492i) q^{38} -267.286i q^{41} +(144.000 - 144.000i) q^{43} -38.1838 q^{44} +306.000 q^{46} +(356.382 - 356.382i) q^{47} -181.000i q^{49} +(63.0000 + 63.0000i) q^{52} +(224.860 + 224.860i) q^{53} -267.286i q^{56} +(486.000 - 486.000i) q^{58} -267.286 q^{59} -322.000 q^{61} +(-415.779 + 415.779i) q^{62} +433.000i q^{64} +(-378.000 - 378.000i) q^{67} +(29.6985 + 29.6985i) q^{68} +840.043i q^{71} +(-378.000 + 378.000i) q^{73} +878.227 q^{74} -70.0000 q^{76} +(343.654 - 343.654i) q^{77} -488.000i q^{79} +(567.000 + 567.000i) q^{82} +(-772.161 - 772.161i) q^{83} +610.940i q^{86} +(-567.000 + 567.000i) q^{88} -267.286 q^{89} -1134.00 q^{91} +(-72.1249 + 72.1249i) q^{92} +1512.00i q^{94} +(252.000 + 252.000i) q^{97} +(383.959 + 383.959i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 36 q^{7} + O(q^{10}) \) \( 4 q + 36 q^{7} - 252 q^{13} + 284 q^{16} + 324 q^{22} + 36 q^{28} + 784 q^{31} - 828 q^{37} + 576 q^{43} + 1224 q^{46} + 252 q^{52} + 1944 q^{58} - 1288 q^{61} - 1512 q^{67} - 1512 q^{73} - 280 q^{76} + 2268 q^{82} - 2268 q^{88} - 4536 q^{91} + 1008 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12132 + 2.12132i −0.750000 + 0.750000i −0.974479 0.224479i \(-0.927932\pi\)
0.224479 + 0.974479i \(0.427932\pi\)
\(3\) 0 0
\(4\) 1.00000i 0.125000i
\(5\) 0 0
\(6\) 0 0
\(7\) 9.00000 + 9.00000i 0.485954 + 0.485954i 0.907027 0.421073i \(-0.138346\pi\)
−0.421073 + 0.907027i \(0.638346\pi\)
\(8\) −14.8492 14.8492i −0.656250 0.656250i
\(9\) 0 0
\(10\) 0 0
\(11\) 38.1838i 1.04662i −0.852142 0.523311i \(-0.824697\pi\)
0.852142 0.523311i \(-0.175303\pi\)
\(12\) 0 0
\(13\) −63.0000 + 63.0000i −1.34408 + 1.34408i −0.452128 + 0.891953i \(0.649335\pi\)
−0.891953 + 0.452128i \(0.850665\pi\)
\(14\) −38.1838 −0.728931
\(15\) 0 0
\(16\) 71.0000 1.10938
\(17\) −29.6985 + 29.6985i −0.423702 + 0.423702i −0.886476 0.462774i \(-0.846854\pi\)
0.462774 + 0.886476i \(0.346854\pi\)
\(18\) 0 0
\(19\) 70.0000i 0.845216i −0.906313 0.422608i \(-0.861115\pi\)
0.906313 0.422608i \(-0.138885\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 81.0000 + 81.0000i 0.784966 + 0.784966i
\(23\) −72.1249 72.1249i −0.653873 0.653873i 0.300050 0.953923i \(-0.402997\pi\)
−0.953923 + 0.300050i \(0.902997\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 267.286i 2.01612i
\(27\) 0 0
\(28\) 9.00000 9.00000i 0.0607443 0.0607443i
\(29\) −229.103 −1.46701 −0.733505 0.679684i \(-0.762117\pi\)
−0.733505 + 0.679684i \(0.762117\pi\)
\(30\) 0 0
\(31\) 196.000 1.13557 0.567785 0.823177i \(-0.307801\pi\)
0.567785 + 0.823177i \(0.307801\pi\)
\(32\) −31.8198 + 31.8198i −0.175781 + 0.175781i
\(33\) 0 0
\(34\) 126.000i 0.635554i
\(35\) 0 0
\(36\) 0 0
\(37\) −207.000 207.000i −0.919746 0.919746i 0.0772649 0.997011i \(-0.475381\pi\)
−0.997011 + 0.0772649i \(0.975381\pi\)
\(38\) 148.492 + 148.492i 0.633912 + 0.633912i
\(39\) 0 0
\(40\) 0 0
\(41\) 267.286i 1.01812i −0.860730 0.509062i \(-0.829992\pi\)
0.860730 0.509062i \(-0.170008\pi\)
\(42\) 0 0
\(43\) 144.000 144.000i 0.510693 0.510693i −0.404046 0.914739i \(-0.632396\pi\)
0.914739 + 0.404046i \(0.132396\pi\)
\(44\) −38.1838 −0.130828
\(45\) 0 0
\(46\) 306.000 0.980810
\(47\) 356.382 356.382i 1.10603 1.10603i 0.112368 0.993667i \(-0.464156\pi\)
0.993667 0.112368i \(-0.0358436\pi\)
\(48\) 0 0
\(49\) 181.000i 0.527697i
\(50\) 0 0
\(51\) 0 0
\(52\) 63.0000 + 63.0000i 0.168010 + 0.168010i
\(53\) 224.860 + 224.860i 0.582772 + 0.582772i 0.935664 0.352892i \(-0.114802\pi\)
−0.352892 + 0.935664i \(0.614802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 267.286i 0.637815i
\(57\) 0 0
\(58\) 486.000 486.000i 1.10026 1.10026i
\(59\) −267.286 −0.589792 −0.294896 0.955529i \(-0.595285\pi\)
−0.294896 + 0.955529i \(0.595285\pi\)
\(60\) 0 0
\(61\) −322.000 −0.675867 −0.337933 0.941170i \(-0.609728\pi\)
−0.337933 + 0.941170i \(0.609728\pi\)
\(62\) −415.779 + 415.779i −0.851677 + 0.851677i
\(63\) 0 0
\(64\) 433.000i 0.845703i
\(65\) 0 0
\(66\) 0 0
\(67\) −378.000 378.000i −0.689254 0.689254i 0.272813 0.962067i \(-0.412046\pi\)
−0.962067 + 0.272813i \(0.912046\pi\)
\(68\) 29.6985 + 29.6985i 0.0529628 + 0.0529628i
\(69\) 0 0
\(70\) 0 0
\(71\) 840.043i 1.40415i 0.712102 + 0.702076i \(0.247743\pi\)
−0.712102 + 0.702076i \(0.752257\pi\)
\(72\) 0 0
\(73\) −378.000 + 378.000i −0.606049 + 0.606049i −0.941911 0.335862i \(-0.890972\pi\)
0.335862 + 0.941911i \(0.390972\pi\)
\(74\) 878.227 1.37962
\(75\) 0 0
\(76\) −70.0000 −0.105652
\(77\) 343.654 343.654i 0.508610 0.508610i
\(78\) 0 0
\(79\) 488.000i 0.694991i −0.937682 0.347496i \(-0.887032\pi\)
0.937682 0.347496i \(-0.112968\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 567.000 + 567.000i 0.763594 + 0.763594i
\(83\) −772.161 772.161i −1.02115 1.02115i −0.999771 0.0213809i \(-0.993194\pi\)
−0.0213809 0.999771i \(-0.506806\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 610.940i 0.766039i
\(87\) 0 0
\(88\) −567.000 + 567.000i −0.686845 + 0.686845i
\(89\) −267.286 −0.318340 −0.159170 0.987251i \(-0.550882\pi\)
−0.159170 + 0.987251i \(0.550882\pi\)
\(90\) 0 0
\(91\) −1134.00 −1.30632
\(92\) −72.1249 + 72.1249i −0.0817341 + 0.0817341i
\(93\) 0 0
\(94\) 1512.00i 1.65905i
\(95\) 0 0
\(96\) 0 0
\(97\) 252.000 + 252.000i 0.263781 + 0.263781i 0.826588 0.562807i \(-0.190279\pi\)
−0.562807 + 0.826588i \(0.690279\pi\)
\(98\) 383.959 + 383.959i 0.395773 + 0.395773i
\(99\) 0 0
\(100\) 0 0
\(101\) 1603.72i 1.57996i 0.613133 + 0.789980i \(0.289909\pi\)
−0.613133 + 0.789980i \(0.710091\pi\)
\(102\) 0 0
\(103\) −945.000 + 945.000i −0.904016 + 0.904016i −0.995781 0.0917650i \(-0.970749\pi\)
0.0917650 + 0.995781i \(0.470749\pi\)
\(104\) 1871.00 1.76411
\(105\) 0 0
\(106\) −954.000 −0.874157
\(107\) −1323.70 + 1323.70i −1.19596 + 1.19596i −0.220589 + 0.975367i \(0.570798\pi\)
−0.975367 + 0.220589i \(0.929202\pi\)
\(108\) 0 0
\(109\) 70.0000i 0.0615118i 0.999527 + 0.0307559i \(0.00979145\pi\)
−0.999527 + 0.0307559i \(0.990209\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 639.000 + 639.000i 0.539106 + 0.539106i
\(113\) −521.845 521.845i −0.434434 0.434434i 0.455700 0.890134i \(-0.349389\pi\)
−0.890134 + 0.455700i \(0.849389\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 229.103i 0.183376i
\(117\) 0 0
\(118\) 567.000 567.000i 0.442344 0.442344i
\(119\) −534.573 −0.411800
\(120\) 0 0
\(121\) −127.000 −0.0954170
\(122\) 683.065 683.065i 0.506900 0.506900i
\(123\) 0 0
\(124\) 196.000i 0.141946i
\(125\) 0 0
\(126\) 0 0
\(127\) −315.000 315.000i −0.220092 0.220092i 0.588445 0.808537i \(-0.299740\pi\)
−0.808537 + 0.588445i \(0.799740\pi\)
\(128\) −1173.09 1173.09i −0.810059 0.810059i
\(129\) 0 0
\(130\) 0 0
\(131\) 1336.43i 0.891333i 0.895199 + 0.445666i \(0.147033\pi\)
−0.895199 + 0.445666i \(0.852967\pi\)
\(132\) 0 0
\(133\) 630.000 630.000i 0.410736 0.410736i
\(134\) 1603.72 1.03388
\(135\) 0 0
\(136\) 882.000 0.556109
\(137\) 1294.01 1294.01i 0.806966 0.806966i −0.177208 0.984174i \(-0.556706\pi\)
0.984174 + 0.177208i \(0.0567064\pi\)
\(138\) 0 0
\(139\) 308.000i 0.187944i 0.995575 + 0.0939720i \(0.0299564\pi\)
−0.995575 + 0.0939720i \(0.970044\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1782.00 1782.00i −1.05311 1.05311i
\(143\) 2405.58 + 2405.58i 1.40674 + 1.40674i
\(144\) 0 0
\(145\) 0 0
\(146\) 1603.72i 0.909073i
\(147\) 0 0
\(148\) −207.000 + 207.000i −0.114968 + 0.114968i
\(149\) −2443.76 −1.34363 −0.671814 0.740719i \(-0.734485\pi\)
−0.671814 + 0.740719i \(0.734485\pi\)
\(150\) 0 0
\(151\) −2072.00 −1.11667 −0.558334 0.829616i \(-0.688559\pi\)
−0.558334 + 0.829616i \(0.688559\pi\)
\(152\) −1039.45 + 1039.45i −0.554673 + 0.554673i
\(153\) 0 0
\(154\) 1458.00i 0.762916i
\(155\) 0 0
\(156\) 0 0
\(157\) 315.000 + 315.000i 0.160126 + 0.160126i 0.782622 0.622497i \(-0.213882\pi\)
−0.622497 + 0.782622i \(0.713882\pi\)
\(158\) 1035.20 + 1035.20i 0.521243 + 0.521243i
\(159\) 0 0
\(160\) 0 0
\(161\) 1298.25i 0.635505i
\(162\) 0 0
\(163\) 2394.00 2394.00i 1.15038 1.15038i 0.163908 0.986476i \(-0.447590\pi\)
0.986476 0.163908i \(-0.0524101\pi\)
\(164\) −267.286 −0.127266
\(165\) 0 0
\(166\) 3276.00 1.53173
\(167\) 742.462 742.462i 0.344033 0.344033i −0.513848 0.857881i \(-0.671781\pi\)
0.857881 + 0.513848i \(0.171781\pi\)
\(168\) 0 0
\(169\) 5741.00i 2.61311i
\(170\) 0 0
\(171\) 0 0
\(172\) −144.000 144.000i −0.0638366 0.0638366i
\(173\) 326.683 + 326.683i 0.143568 + 0.143568i 0.775238 0.631670i \(-0.217630\pi\)
−0.631670 + 0.775238i \(0.717630\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2711.05i 1.16110i
\(177\) 0 0
\(178\) 567.000 567.000i 0.238755 0.238755i
\(179\) −1565.53 −0.653707 −0.326853 0.945075i \(-0.605988\pi\)
−0.326853 + 0.945075i \(0.605988\pi\)
\(180\) 0 0
\(181\) 3094.00 1.27058 0.635291 0.772273i \(-0.280880\pi\)
0.635291 + 0.772273i \(0.280880\pi\)
\(182\) 2405.58 2405.58i 0.979743 0.979743i
\(183\) 0 0
\(184\) 2142.00i 0.858208i
\(185\) 0 0
\(186\) 0 0
\(187\) 1134.00 + 1134.00i 0.443456 + 0.443456i
\(188\) −356.382 356.382i −0.138254 0.138254i
\(189\) 0 0
\(190\) 0 0
\(191\) 840.043i 0.318238i −0.987259 0.159119i \(-0.949135\pi\)
0.987259 0.159119i \(-0.0508653\pi\)
\(192\) 0 0
\(193\) 1242.00 1242.00i 0.463218 0.463218i −0.436491 0.899709i \(-0.643779\pi\)
0.899709 + 0.436491i \(0.143779\pi\)
\(194\) −1069.15 −0.395671
\(195\) 0 0
\(196\) −181.000 −0.0659621
\(197\) −3725.04 + 3725.04i −1.34720 + 1.34720i −0.458507 + 0.888691i \(0.651616\pi\)
−0.888691 + 0.458507i \(0.848384\pi\)
\(198\) 0 0
\(199\) 700.000i 0.249355i 0.992197 + 0.124678i \(0.0397897\pi\)
−0.992197 + 0.124678i \(0.960210\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −3402.00 3402.00i −1.18497 1.18497i
\(203\) −2061.92 2061.92i −0.712900 0.712900i
\(204\) 0 0
\(205\) 0 0
\(206\) 4009.30i 1.35602i
\(207\) 0 0
\(208\) −4473.00 + 4473.00i −1.49109 + 1.49109i
\(209\) −2672.86 −0.884621
\(210\) 0 0
\(211\) 1316.00 0.429371 0.214685 0.976683i \(-0.431127\pi\)
0.214685 + 0.976683i \(0.431127\pi\)
\(212\) 224.860 224.860i 0.0728464 0.0728464i
\(213\) 0 0
\(214\) 5616.00i 1.79393i
\(215\) 0 0
\(216\) 0 0
\(217\) 1764.00 + 1764.00i 0.551835 + 0.551835i
\(218\) −148.492 148.492i −0.0461338 0.0461338i
\(219\) 0 0
\(220\) 0 0
\(221\) 3742.01i 1.13898i
\(222\) 0 0
\(223\) −2205.00 + 2205.00i −0.662142 + 0.662142i −0.955885 0.293742i \(-0.905099\pi\)
0.293742 + 0.955885i \(0.405099\pi\)
\(224\) −572.756 −0.170843
\(225\) 0 0
\(226\) 2214.00 0.651651
\(227\) 653.367 653.367i 0.191037 0.191037i −0.605107 0.796144i \(-0.706870\pi\)
0.796144 + 0.605107i \(0.206870\pi\)
\(228\) 0 0
\(229\) 3206.00i 0.925146i 0.886581 + 0.462573i \(0.153074\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3402.00 + 3402.00i 0.962725 + 0.962725i
\(233\) 12.7279 + 12.7279i 0.00357869 + 0.00357869i 0.708894 0.705315i \(-0.249195\pi\)
−0.705315 + 0.708894i \(0.749195\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 267.286i 0.0737240i
\(237\) 0 0
\(238\) 1134.00 1134.00i 0.308850 0.308850i
\(239\) 1298.25 0.351367 0.175683 0.984447i \(-0.443786\pi\)
0.175683 + 0.984447i \(0.443786\pi\)
\(240\) 0 0
\(241\) −700.000 −0.187099 −0.0935497 0.995615i \(-0.529821\pi\)
−0.0935497 + 0.995615i \(0.529821\pi\)
\(242\) 269.408 269.408i 0.0715627 0.0715627i
\(243\) 0 0
\(244\) 322.000i 0.0844834i
\(245\) 0 0
\(246\) 0 0
\(247\) 4410.00 + 4410.00i 1.13604 + 1.13604i
\(248\) −2910.45 2910.45i −0.745217 0.745217i
\(249\) 0 0
\(250\) 0 0
\(251\) 5078.44i 1.27709i 0.769587 + 0.638543i \(0.220462\pi\)
−0.769587 + 0.638543i \(0.779538\pi\)
\(252\) 0 0
\(253\) −2754.00 + 2754.00i −0.684358 + 0.684358i
\(254\) 1336.43 0.330139
\(255\) 0 0
\(256\) 1513.00 0.369385
\(257\) −2880.75 + 2880.75i −0.699208 + 0.699208i −0.964240 0.265032i \(-0.914618\pi\)
0.265032 + 0.964240i \(0.414618\pi\)
\(258\) 0 0
\(259\) 3726.00i 0.893909i
\(260\) 0 0
\(261\) 0 0
\(262\) −2835.00 2835.00i −0.668500 0.668500i
\(263\) 1412.80 + 1412.80i 0.331243 + 0.331243i 0.853058 0.521815i \(-0.174745\pi\)
−0.521815 + 0.853058i \(0.674745\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2672.86i 0.616104i
\(267\) 0 0
\(268\) −378.000 + 378.000i −0.0861568 + 0.0861568i
\(269\) −1603.72 −0.363496 −0.181748 0.983345i \(-0.558176\pi\)
−0.181748 + 0.983345i \(0.558176\pi\)
\(270\) 0 0
\(271\) −2716.00 −0.608802 −0.304401 0.952544i \(-0.598456\pi\)
−0.304401 + 0.952544i \(0.598456\pi\)
\(272\) −2108.59 + 2108.59i −0.470045 + 0.470045i
\(273\) 0 0
\(274\) 5490.00i 1.21045i
\(275\) 0 0
\(276\) 0 0
\(277\) −3843.00 3843.00i −0.833587 0.833587i 0.154419 0.988005i \(-0.450649\pi\)
−0.988005 + 0.154419i \(0.950649\pi\)
\(278\) −653.367 653.367i −0.140958 0.140958i
\(279\) 0 0
\(280\) 0 0
\(281\) 3780.19i 0.802517i −0.915965 0.401259i \(-0.868573\pi\)
0.915965 0.401259i \(-0.131427\pi\)
\(282\) 0 0
\(283\) −126.000 + 126.000i −0.0264662 + 0.0264662i −0.720216 0.693750i \(-0.755957\pi\)
0.693750 + 0.720216i \(0.255957\pi\)
\(284\) 840.043 0.175519
\(285\) 0 0
\(286\) −10206.0 −2.11012
\(287\) 2405.58 2405.58i 0.494762 0.494762i
\(288\) 0 0
\(289\) 3149.00i 0.640953i
\(290\) 0 0
\(291\) 0 0
\(292\) 378.000 + 378.000i 0.0757561 + 0.0757561i
\(293\) 772.161 + 772.161i 0.153959 + 0.153959i 0.779884 0.625924i \(-0.215278\pi\)
−0.625924 + 0.779884i \(0.715278\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6147.59i 1.20717i
\(297\) 0 0
\(298\) 5184.00 5184.00i 1.00772 1.00772i
\(299\) 9087.74 1.75772
\(300\) 0 0
\(301\) 2592.00 0.496347
\(302\) 4395.38 4395.38i 0.837501 0.837501i
\(303\) 0 0
\(304\) 4970.00i 0.937661i
\(305\) 0 0
\(306\) 0 0
\(307\) −3024.00 3024.00i −0.562178 0.562178i 0.367747 0.929926i \(-0.380129\pi\)
−0.929926 + 0.367747i \(0.880129\pi\)
\(308\) −343.654 343.654i −0.0635763 0.0635763i
\(309\) 0 0
\(310\) 0 0
\(311\) 10156.9i 1.85191i 0.377634 + 0.925955i \(0.376738\pi\)
−0.377634 + 0.925955i \(0.623262\pi\)
\(312\) 0 0
\(313\) 5418.00 5418.00i 0.978414 0.978414i −0.0213583 0.999772i \(-0.506799\pi\)
0.999772 + 0.0213583i \(0.00679906\pi\)
\(314\) −1336.43 −0.240189
\(315\) 0 0
\(316\) −488.000 −0.0868739
\(317\) 1977.07 1977.07i 0.350294 0.350294i −0.509925 0.860219i \(-0.670327\pi\)
0.860219 + 0.509925i \(0.170327\pi\)
\(318\) 0 0
\(319\) 8748.00i 1.53540i
\(320\) 0 0
\(321\) 0 0
\(322\) 2754.00 + 2754.00i 0.476629 + 0.476629i
\(323\) 2078.89 + 2078.89i 0.358120 + 0.358120i
\(324\) 0 0
\(325\) 0 0
\(326\) 10156.9i 1.72558i
\(327\) 0 0
\(328\) −3969.00 + 3969.00i −0.668144 + 0.668144i
\(329\) 6414.87 1.07496
\(330\) 0 0
\(331\) −6622.00 −1.09963 −0.549816 0.835286i \(-0.685302\pi\)
−0.549816 + 0.835286i \(0.685302\pi\)
\(332\) −772.161 + 772.161i −0.127644 + 0.127644i
\(333\) 0 0
\(334\) 3150.00i 0.516049i
\(335\) 0 0
\(336\) 0 0
\(337\) −2790.00 2790.00i −0.450982 0.450982i 0.444698 0.895680i \(-0.353311\pi\)
−0.895680 + 0.444698i \(0.853311\pi\)
\(338\) 12178.5 + 12178.5i 1.95983 + 1.95983i
\(339\) 0 0
\(340\) 0 0
\(341\) 7484.02i 1.18851i
\(342\) 0 0
\(343\) 4716.00 4716.00i 0.742391 0.742391i
\(344\) −4276.58 −0.670284
\(345\) 0 0
\(346\) −1386.00 −0.215352
\(347\) −1858.28 + 1858.28i −0.287486 + 0.287486i −0.836085 0.548600i \(-0.815161\pi\)
0.548600 + 0.836085i \(0.315161\pi\)
\(348\) 0 0
\(349\) 5614.00i 0.861062i −0.902576 0.430531i \(-0.858326\pi\)
0.902576 0.430531i \(-0.141674\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1215.00 + 1215.00i 0.183976 + 0.183976i
\(353\) −1514.62 1514.62i −0.228372 0.228372i 0.583640 0.812012i \(-0.301628\pi\)
−0.812012 + 0.583640i \(0.801628\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 267.286i 0.0397926i
\(357\) 0 0
\(358\) 3321.00 3321.00i 0.490280 0.490280i
\(359\) 11455.1 1.68406 0.842032 0.539428i \(-0.181360\pi\)
0.842032 + 0.539428i \(0.181360\pi\)
\(360\) 0 0
\(361\) 1959.00 0.285610
\(362\) −6563.37 + 6563.37i −0.952936 + 0.952936i
\(363\) 0 0
\(364\) 1134.00i 0.163291i
\(365\) 0 0
\(366\) 0 0
\(367\) −5481.00 5481.00i −0.779580 0.779580i 0.200179 0.979759i \(-0.435848\pi\)
−0.979759 + 0.200179i \(0.935848\pi\)
\(368\) −5120.87 5120.87i −0.725390 0.725390i
\(369\) 0 0
\(370\) 0 0
\(371\) 4047.48i 0.566401i
\(372\) 0 0
\(373\) −2709.00 + 2709.00i −0.376050 + 0.376050i −0.869675 0.493625i \(-0.835672\pi\)
0.493625 + 0.869675i \(0.335672\pi\)
\(374\) −4811.15 −0.665184
\(375\) 0 0
\(376\) −10584.0 −1.45167
\(377\) 14433.5 14433.5i 1.97178 1.97178i
\(378\) 0 0
\(379\) 13916.0i 1.88606i 0.332707 + 0.943030i \(0.392038\pi\)
−0.332707 + 0.943030i \(0.607962\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1782.00 + 1782.00i 0.238678 + 0.238678i
\(383\) −6890.05 6890.05i −0.919230 0.919230i 0.0777435 0.996973i \(-0.475228\pi\)
−0.996973 + 0.0777435i \(0.975228\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5269.36i 0.694827i
\(387\) 0 0
\(388\) 252.000 252.000i 0.0329726 0.0329726i
\(389\) −6720.34 −0.875925 −0.437963 0.898993i \(-0.644300\pi\)
−0.437963 + 0.898993i \(0.644300\pi\)
\(390\) 0 0
\(391\) 4284.00 0.554095
\(392\) −2687.71 + 2687.71i −0.346301 + 0.346301i
\(393\) 0 0
\(394\) 15804.0i 2.02080i
\(395\) 0 0
\(396\) 0 0
\(397\) 5607.00 + 5607.00i 0.708834 + 0.708834i 0.966290 0.257456i \(-0.0828841\pi\)
−0.257456 + 0.966290i \(0.582884\pi\)
\(398\) −1484.92 1484.92i −0.187016 0.187016i
\(399\) 0 0
\(400\) 0 0
\(401\) 8056.77i 1.00333i −0.865061 0.501666i \(-0.832721\pi\)
0.865061 0.501666i \(-0.167279\pi\)
\(402\) 0 0
\(403\) −12348.0 + 12348.0i −1.52630 + 1.52630i
\(404\) 1603.72 0.197495
\(405\) 0 0
\(406\) 8748.00 1.06935
\(407\) −7904.04 + 7904.04i −0.962626 + 0.962626i
\(408\) 0 0
\(409\) 1694.00i 0.204799i 0.994743 + 0.102400i \(0.0326521\pi\)
−0.994743 + 0.102400i \(0.967348\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 945.000 + 945.000i 0.113002 + 0.113002i
\(413\) −2405.58 2405.58i −0.286612 0.286612i
\(414\) 0 0
\(415\) 0 0
\(416\) 4009.30i 0.472529i
\(417\) 0 0
\(418\) 5670.00 5670.00i 0.663466 0.663466i
\(419\) −267.286 −0.0311642 −0.0155821 0.999879i \(-0.504960\pi\)
−0.0155821 + 0.999879i \(0.504960\pi\)
\(420\) 0 0
\(421\) 12850.0 1.48758 0.743789 0.668414i \(-0.233027\pi\)
0.743789 + 0.668414i \(0.233027\pi\)
\(422\) −2791.66 + 2791.66i −0.322028 + 0.322028i
\(423\) 0 0
\(424\) 6678.00i 0.764888i
\(425\) 0 0
\(426\) 0 0
\(427\) −2898.00 2898.00i −0.328440 0.328440i
\(428\) 1323.70 + 1323.70i 0.149494 + 0.149494i
\(429\) 0 0
\(430\) 0 0
\(431\) 7178.55i 0.802270i −0.916019 0.401135i \(-0.868616\pi\)
0.916019 0.401135i \(-0.131384\pi\)
\(432\) 0 0
\(433\) −11214.0 + 11214.0i −1.24460 + 1.24460i −0.286524 + 0.958073i \(0.592500\pi\)
−0.958073 + 0.286524i \(0.907500\pi\)
\(434\) −7484.02 −0.827752
\(435\) 0 0
\(436\) 70.0000 0.00768897
\(437\) −5048.74 + 5048.74i −0.552664 + 0.552664i
\(438\) 0 0
\(439\) 2324.00i 0.252662i −0.991988 0.126331i \(-0.959680\pi\)
0.991988 0.126331i \(-0.0403201\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 7938.00 + 7938.00i 0.854236 + 0.854236i
\(443\) 5685.14 + 5685.14i 0.609727 + 0.609727i 0.942875 0.333148i \(-0.108111\pi\)
−0.333148 + 0.942875i \(0.608111\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 9355.02i 0.993213i
\(447\) 0 0
\(448\) −3897.00 + 3897.00i −0.410973 + 0.410973i
\(449\) −3703.83 −0.389297 −0.194648 0.980873i \(-0.562357\pi\)
−0.194648 + 0.980873i \(0.562357\pi\)
\(450\) 0 0
\(451\) −10206.0 −1.06559
\(452\) −521.845 + 521.845i −0.0543042 + 0.0543042i
\(453\) 0 0
\(454\) 2772.00i 0.286556i
\(455\) 0 0
\(456\) 0 0
\(457\) 7200.00 + 7200.00i 0.736984 + 0.736984i 0.971993 0.235009i \(-0.0755120\pi\)
−0.235009 + 0.971993i \(0.575512\pi\)
\(458\) −6800.95 6800.95i −0.693860 0.693860i
\(459\) 0 0
\(460\) 0 0
\(461\) 13898.9i 1.40420i −0.712079 0.702100i \(-0.752246\pi\)
0.712079 0.702100i \(-0.247754\pi\)
\(462\) 0 0
\(463\) 4095.00 4095.00i 0.411038 0.411038i −0.471062 0.882100i \(-0.656129\pi\)
0.882100 + 0.471062i \(0.156129\pi\)
\(464\) −16266.3 −1.62746
\(465\) 0 0
\(466\) −54.0000 −0.00536803
\(467\) 9919.29 9919.29i 0.982891 0.982891i −0.0169649 0.999856i \(-0.505400\pi\)
0.999856 + 0.0169649i \(0.00540036\pi\)
\(468\) 0 0
\(469\) 6804.00i 0.669892i
\(470\) 0 0
\(471\) 0 0
\(472\) 3969.00 + 3969.00i 0.387051 + 0.387051i
\(473\) −5498.46 5498.46i −0.534502 0.534502i
\(474\) 0 0
\(475\) 0 0
\(476\) 534.573i 0.0514750i
\(477\) 0 0
\(478\) −2754.00 + 2754.00i −0.263525 + 0.263525i
\(479\) 15502.6 1.47877 0.739387 0.673281i \(-0.235116\pi\)
0.739387 + 0.673281i \(0.235116\pi\)
\(480\) 0 0
\(481\) 26082.0 2.47243
\(482\) 1484.92 1484.92i 0.140325 0.140325i
\(483\) 0 0
\(484\) 127.000i 0.0119271i
\(485\) 0 0
\(486\) 0 0
\(487\) −6975.00 6975.00i −0.649009 0.649009i 0.303744 0.952754i \(-0.401763\pi\)
−0.952754 + 0.303744i \(0.901763\pi\)
\(488\) 4781.46 + 4781.46i 0.443538 + 0.443538i
\(489\) 0 0
\(490\) 0 0
\(491\) 2100.11i 0.193028i −0.995332 0.0965138i \(-0.969231\pi\)
0.995332 0.0965138i \(-0.0307692\pi\)
\(492\) 0 0
\(493\) 6804.00 6804.00i 0.621576 0.621576i
\(494\) −18710.0 −1.70406
\(495\) 0 0
\(496\) 13916.0 1.25977
\(497\) −7560.39 + 7560.39i −0.682353 + 0.682353i
\(498\) 0 0
\(499\) 574.000i 0.0514945i 0.999668 + 0.0257473i \(0.00819651\pi\)
−0.999668 + 0.0257473i \(0.991803\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −10773.0 10773.0i −0.957814 0.957814i
\(503\) −8077.99 8077.99i −0.716063 0.716063i 0.251734 0.967797i \(-0.418999\pi\)
−0.967797 + 0.251734i \(0.918999\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 11684.2i 1.02654i
\(507\) 0 0
\(508\) −315.000 + 315.000i −0.0275115 + 0.0275115i
\(509\) 4811.15 0.418960 0.209480 0.977813i \(-0.432823\pi\)
0.209480 + 0.977813i \(0.432823\pi\)
\(510\) 0 0
\(511\) −6804.00 −0.589024
\(512\) 6175.16 6175.16i 0.533020 0.533020i
\(513\) 0 0
\(514\) 12222.0i 1.04881i
\(515\) 0 0
\(516\) 0 0
\(517\) −13608.0 13608.0i −1.15760 1.15760i
\(518\) 7904.04 + 7904.04i 0.670432 + 0.670432i
\(519\) 0 0
\(520\) 0 0
\(521\) 14166.2i 1.19123i −0.803270 0.595616i \(-0.796908\pi\)
0.803270 0.595616i \(-0.203092\pi\)
\(522\) 0 0
\(523\) 8694.00 8694.00i 0.726887 0.726887i −0.243111 0.969998i \(-0.578168\pi\)
0.969998 + 0.243111i \(0.0781680\pi\)
\(524\) 1336.43 0.111417
\(525\) 0 0
\(526\) −5994.00 −0.496865
\(527\) −5820.90 + 5820.90i −0.481143 + 0.481143i
\(528\) 0 0
\(529\) 1763.00i 0.144900i
\(530\) 0 0
\(531\) 0 0
\(532\) −630.000 630.000i −0.0513420 0.0513420i
\(533\) 16839.0 + 16839.0i 1.36844 + 1.36844i
\(534\) 0 0
\(535\) 0 0
\(536\) 11226.0i 0.904647i
\(537\) 0 0
\(538\) 3402.00 3402.00i 0.272622 0.272622i
\(539\) −6911.26 −0.552299
\(540\) 0 0
\(541\) −646.000 −0.0513377 −0.0256689 0.999671i \(-0.508172\pi\)
−0.0256689 + 0.999671i \(0.508172\pi\)
\(542\) 5761.51 5761.51i 0.456601 0.456601i
\(543\) 0 0
\(544\) 1890.00i 0.148958i
\(545\) 0 0
\(546\) 0 0
\(547\) 11340.0 + 11340.0i 0.886405 + 0.886405i 0.994176 0.107771i \(-0.0343713\pi\)
−0.107771 + 0.994176i \(0.534371\pi\)
\(548\) −1294.01 1294.01i −0.100871 0.100871i
\(549\) 0 0
\(550\) 0 0
\(551\) 16037.2i 1.23994i
\(552\) 0 0
\(553\) 4392.00 4392.00i 0.337734 0.337734i
\(554\) 16304.5 1.25038
\(555\) 0 0
\(556\) 308.000 0.0234930
\(557\) 5867.57 5867.57i 0.446350 0.446350i −0.447789 0.894139i \(-0.647788\pi\)
0.894139 + 0.447789i \(0.147788\pi\)
\(558\) 0 0
\(559\) 18144.0i 1.37283i
\(560\) 0 0
\(561\) 0 0
\(562\) 8019.00 + 8019.00i 0.601888 + 0.601888i
\(563\) 2672.86 + 2672.86i 0.200085 + 0.200085i 0.800036 0.599952i \(-0.204813\pi\)
−0.599952 + 0.800036i \(0.704813\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 534.573i 0.0396992i
\(567\) 0 0
\(568\) 12474.0 12474.0i 0.921474 0.921474i
\(569\) −20886.5 −1.53885 −0.769427 0.638734i \(-0.779458\pi\)
−0.769427 + 0.638734i \(0.779458\pi\)
\(570\) 0 0
\(571\) −12238.0 −0.896925 −0.448463 0.893802i \(-0.648028\pi\)
−0.448463 + 0.893802i \(0.648028\pi\)
\(572\) 2405.58 2405.58i 0.175843 0.175843i
\(573\) 0 0
\(574\) 10206.0i 0.742143i
\(575\) 0 0
\(576\) 0 0
\(577\) −4536.00 4536.00i −0.327272 0.327272i 0.524276 0.851548i \(-0.324336\pi\)
−0.851548 + 0.524276i \(0.824336\pi\)
\(578\) −6680.04 6680.04i −0.480714 0.480714i
\(579\) 0 0
\(580\) 0 0
\(581\) 13898.9i 0.992467i
\(582\) 0 0
\(583\) 8586.00 8586.00i 0.609941 0.609941i
\(584\) 11226.0 0.795439
\(585\) 0 0
\(586\) −3276.00 −0.230939
\(587\) 9147.13 9147.13i 0.643173 0.643173i −0.308161 0.951334i \(-0.599714\pi\)
0.951334 + 0.308161i \(0.0997136\pi\)
\(588\) 0 0
\(589\) 13720.0i 0.959801i
\(590\) 0 0
\(591\) 0 0
\(592\) −14697.0 14697.0i −1.02034 1.02034i
\(593\) 14285.0 + 14285.0i 0.989230 + 0.989230i 0.999943 0.0107125i \(-0.00340996\pi\)
−0.0107125 + 0.999943i \(0.503410\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2443.76i 0.167954i
\(597\) 0 0
\(598\) −19278.0 + 19278.0i −1.31829 + 1.31829i
\(599\) 7789.49 0.531335 0.265668 0.964065i \(-0.414408\pi\)
0.265668 + 0.964065i \(0.414408\pi\)
\(600\) 0 0
\(601\) 6748.00 0.457998 0.228999 0.973427i \(-0.426455\pi\)
0.228999 + 0.973427i \(0.426455\pi\)
\(602\) −5498.46 + 5498.46i −0.372260 + 0.372260i
\(603\) 0 0
\(604\) 2072.00i 0.139584i
\(605\) 0 0
\(606\) 0 0
\(607\) 13671.0 + 13671.0i 0.914150 + 0.914150i 0.996596 0.0824460i \(-0.0262732\pi\)
−0.0824460 + 0.996596i \(0.526273\pi\)
\(608\) 2227.39 + 2227.39i 0.148573 + 0.148573i
\(609\) 0 0
\(610\) 0 0
\(611\) 44904.1i 2.97320i
\(612\) 0 0
\(613\) −3213.00 + 3213.00i −0.211700 + 0.211700i −0.804989 0.593290i \(-0.797829\pi\)
0.593290 + 0.804989i \(0.297829\pi\)
\(614\) 12829.7 0.843268
\(615\) 0 0
\(616\) −10206.0 −0.667551
\(617\) −9906.57 + 9906.57i −0.646391 + 0.646391i −0.952119 0.305728i \(-0.901100\pi\)
0.305728 + 0.952119i \(0.401100\pi\)
\(618\) 0 0
\(619\) 2828.00i 0.183630i −0.995776 0.0918150i \(-0.970733\pi\)
0.995776 0.0918150i \(-0.0292668\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −21546.0 21546.0i −1.38893 1.38893i
\(623\) −2405.58 2405.58i −0.154699 0.154699i
\(624\) 0 0
\(625\) 0 0
\(626\) 22986.6i 1.46762i
\(627\) 0 0
\(628\) 315.000 315.000i 0.0200157 0.0200157i
\(629\) 12295.2 0.779397
\(630\) 0 0
\(631\) −12220.0 −0.770952 −0.385476 0.922718i \(-0.625963\pi\)
−0.385476 + 0.922718i \(0.625963\pi\)
\(632\) −7246.43 + 7246.43i −0.456088 + 0.456088i
\(633\) 0 0
\(634\) 8388.00i 0.525442i
\(635\) 0 0
\(636\) 0 0
\(637\) 11403.0 + 11403.0i 0.709267 + 0.709267i
\(638\) −18557.3 18557.3i −1.15155 1.15155i
\(639\) 0 0
\(640\) 0 0
\(641\) 2176.47i 0.134112i 0.997749 + 0.0670558i \(0.0213606\pi\)
−0.997749 + 0.0670558i \(0.978639\pi\)
\(642\) 0 0
\(643\) −4914.00 + 4914.00i −0.301383 + 0.301383i −0.841555 0.540172i \(-0.818359\pi\)
0.540172 + 0.841555i \(0.318359\pi\)
\(644\) −1298.25 −0.0794381
\(645\) 0 0
\(646\) −8820.00 −0.537180
\(647\) −2375.88 + 2375.88i −0.144367 + 0.144367i −0.775596 0.631229i \(-0.782551\pi\)
0.631229 + 0.775596i \(0.282551\pi\)
\(648\) 0 0
\(649\) 10206.0i 0.617289i
\(650\) 0 0
\(651\) 0 0
\(652\) −2394.00 2394.00i −0.143798 0.143798i
\(653\) −21603.5 21603.5i −1.29466 1.29466i −0.931873 0.362784i \(-0.881826\pi\)
−0.362784 0.931873i \(-0.618174\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 18977.3i 1.12948i
\(657\) 0 0
\(658\) −13608.0 + 13608.0i −0.806224 + 0.806224i
\(659\) 14395.3 0.850926 0.425463 0.904976i \(-0.360111\pi\)
0.425463 + 0.904976i \(0.360111\pi\)
\(660\) 0 0
\(661\) −22610.0 −1.33045 −0.665225 0.746643i \(-0.731664\pi\)
−0.665225 + 0.746643i \(0.731664\pi\)
\(662\) 14047.4 14047.4i 0.824724 0.824724i
\(663\) 0 0
\(664\) 22932.0i 1.34026i
\(665\) 0 0
\(666\) 0 0
\(667\) 16524.0 + 16524.0i 0.959238 + 0.959238i
\(668\) −742.462 742.462i −0.0430041 0.0430041i
\(669\) 0 0
\(670\) 0 0
\(671\) 12295.2i 0.707377i
\(672\) 0 0
\(673\) −1278.00 + 1278.00i −0.0731995 + 0.0731995i −0.742759 0.669559i \(-0.766483\pi\)
0.669559 + 0.742759i \(0.266483\pi\)
\(674\) 11837.0 0.676473
\(675\) 0 0
\(676\) −5741.00 −0.326639
\(677\) −7840.40 + 7840.40i −0.445098 + 0.445098i −0.893721 0.448623i \(-0.851914\pi\)
0.448623 + 0.893721i \(0.351914\pi\)
\(678\) 0 0
\(679\) 4536.00i 0.256371i
\(680\) 0 0
\(681\) 0 0
\(682\) 15876.0 + 15876.0i 0.891383 + 0.891383i
\(683\) 5125.11 + 5125.11i 0.287126 + 0.287126i 0.835943 0.548817i \(-0.184922\pi\)
−0.548817 + 0.835943i \(0.684922\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 20008.3i 1.11359i
\(687\) 0 0
\(688\) 10224.0 10224.0i 0.566550 0.566550i
\(689\) −28332.4 −1.56658
\(690\) 0 0
\(691\) 12418.0 0.683651 0.341826 0.939763i \(-0.388955\pi\)
0.341826 + 0.939763i \(0.388955\pi\)
\(692\) 326.683 326.683i 0.0179460 0.0179460i
\(693\) 0 0
\(694\) 7884.00i 0.431228i
\(695\) 0 0
\(696\) 0 0
\(697\) 7938.00 + 7938.00i 0.431382 + 0.431382i
\(698\) 11909.1 + 11909.1i 0.645796 + 0.645796i
\(699\) 0 0
\(700\) 0 0
\(701\) 7254.92i 0.390891i 0.980715 + 0.195445i \(0.0626152\pi\)
−0.980715 + 0.195445i \(0.937385\pi\)
\(702\) 0 0
\(703\) −14490.0 + 14490.0i −0.777384 + 0.777384i
\(704\) 16533.6 0.885131
\(705\) 0 0
\(706\) 6426.00 0.342558
\(707\) −14433.5 + 14433.5i −0.767788 + 0.767788i
\(708\) 0 0
\(709\) 2086.00i 0.110496i −0.998473 0.0552478i \(-0.982405\pi\)
0.998473 0.0552478i \(-0.0175949\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3969.00 + 3969.00i 0.208911 + 0.208911i
\(713\) −14136.5 14136.5i −0.742518 0.742518i
\(714\) 0 0
\(715\) 0 0
\(716\) 1565.53i 0.0817134i
\(717\) 0 0
\(718\) −24300.0 + 24300.0i −1.26305 + 1.26305i
\(719\) 10691.5 0.554554 0.277277 0.960790i \(-0.410568\pi\)
0.277277 + 0.960790i \(0.410568\pi\)
\(720\) 0 0
\(721\) −17010.0 −0.878621
\(722\) −4155.67 + 4155.67i −0.214208 + 0.214208i
\(723\) 0 0
\(724\) 3094.00i 0.158823i
\(725\) 0 0
\(726\) 0 0
\(727\) −14931.0 14931.0i −0.761706 0.761706i 0.214925 0.976631i \(-0.431049\pi\)
−0.976631 + 0.214925i \(0.931049\pi\)
\(728\) 16839.0 + 16839.0i 0.857275 + 0.857275i
\(729\) 0 0
\(730\) 0 0
\(731\) 8553.16i 0.432764i
\(732\) 0 0
\(733\) 8757.00 8757.00i 0.441265 0.441265i −0.451172 0.892437i \(-0.648994\pi\)
0.892437 + 0.451172i \(0.148994\pi\)
\(734\) 23253.9 1.16937
\(735\) 0 0
\(736\) 4590.00 0.229877
\(737\) −14433.5 + 14433.5i −0.721389 + 0.721389i
\(738\) 0 0
\(739\) 33010.0i 1.64316i −0.570096 0.821578i \(-0.693094\pi\)
0.570096 0.821578i \(-0.306906\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −8586.00 8586.00i −0.424801 0.424801i
\(743\) 4734.79 + 4734.79i 0.233785 + 0.233785i 0.814271 0.580485i \(-0.197137\pi\)
−0.580485 + 0.814271i \(0.697137\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 11493.3i 0.564075i
\(747\) 0 0
\(748\) 1134.00 1134.00i 0.0554320 0.0554320i
\(749\) −23826.7 −1.16236
\(750\) 0 0
\(751\) −18704.0 −0.908813 −0.454407 0.890794i \(-0.650149\pi\)
−0.454407 + 0.890794i \(0.650149\pi\)
\(752\) 25303.1 25303.1i 1.22701 1.22701i
\(753\) 0 0
\(754\) 61236.0i 2.95767i
\(755\) 0 0
\(756\) 0 0
\(757\) 2187.00 + 2187.00i 0.105004 + 0.105004i 0.757657 0.652653i \(-0.226344\pi\)
−0.652653 + 0.757657i \(0.726344\pi\)
\(758\) −29520.3 29520.3i −1.41455 1.41455i
\(759\) 0 0
\(760\) 0 0
\(761\) 4543.87i 0.216446i −0.994127 0.108223i \(-0.965484\pi\)
0.994127 0.108223i \(-0.0345160\pi\)
\(762\) 0 0
\(763\) −630.000 + 630.000i −0.0298919 + 0.0298919i
\(764\) −840.043 −0.0397797
\(765\) 0 0
\(766\) 29232.0 1.37884
\(767\) 16839.0 16839.0i 0.792728 0.792728i
\(768\) 0 0
\(769\) 35336.0i 1.65702i −0.559974 0.828510i \(-0.689189\pi\)
0.559974 0.828510i \(-0.310811\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1242.00 1242.00i −0.0579023 0.0579023i
\(773\) 9919.29 + 9919.29i 0.461542 + 0.461542i 0.899161 0.437618i \(-0.144178\pi\)
−0.437618 + 0.899161i \(0.644178\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 7484.02i 0.346212i
\(777\) 0 0
\(778\) 14256.0 14256.0i 0.656944 0.656944i
\(779\) −18710.0 −0.860535
\(780\) 0 0
\(781\) 32076.0 1.46962
\(782\) −9087.74 + 9087.74i −0.415571 + 0.415571i
\(783\) 0 0
\(784\) 12851.0i 0.585414i
\(785\) 0 0
\(786\) 0 0
\(787\) −19278.0 19278.0i −0.873172 0.873172i 0.119645 0.992817i \(-0.461824\pi\)
−0.992817 + 0.119645i \(0.961824\pi\)
\(788\) 3725.04 + 3725.04i 0.168400 + 0.168400i
\(789\) 0 0
\(790\) 0 0
\(791\) 9393.21i 0.422230i
\(792\) 0 0
\(793\) 20286.0 20286.0i 0.908420