Properties

Label 2268.2.t.b.1781.4
Level $2268$
Weight $2$
Character 2268.1781
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1781.4
Root \(1.08696 - 1.34852i\) of defining polynomial
Character \(\chi\) \(=\) 2268.1781
Dual form 2268.2.t.b.2105.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0382122 + 0.0661855i) q^{5} +(2.16592 - 1.51947i) q^{7} +O(q^{10})\) \(q+(0.0382122 + 0.0661855i) q^{5} +(2.16592 - 1.51947i) q^{7} +(-4.66300 - 2.69219i) q^{11} +5.31524i q^{13} +(1.89092 - 3.27516i) q^{17} +(-4.33939 + 2.50535i) q^{19} +(2.02463 - 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} -10.2125i q^{29} +(-4.97636 - 2.87310i) q^{31} +(0.183331 + 0.0852905i) q^{35} +(0.354486 + 0.613988i) q^{37} +6.59821 q^{41} -1.43304 q^{43} +(1.46192 + 2.53213i) q^{47} +(2.38244 - 6.58209i) q^{49} +(-10.4835 - 6.05264i) q^{53} -0.411498i q^{55} +(0.289951 - 0.502210i) q^{59} +(2.40641 - 1.38934i) q^{61} +(-0.351792 + 0.203107i) q^{65} +(-2.63593 + 4.56556i) q^{67} -3.32103i q^{71} +(-6.17326 - 3.56413i) q^{73} +(-14.1904 + 1.25421i) q^{77} +(-0.469123 - 0.812544i) q^{79} -12.9958 q^{83} +0.289025 q^{85} +(1.51794 + 2.62915i) q^{89} +(8.07632 + 11.5124i) q^{91} +(-0.331636 - 0.191470i) q^{95} +7.13816i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{7} + O(q^{10}) \) \( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.0382122 + 0.0661855i 0.0170890 + 0.0295991i 0.874443 0.485127i \(-0.161227\pi\)
−0.857354 + 0.514727i \(0.827893\pi\)
\(6\) 0 0
\(7\) 2.16592 1.51947i 0.818642 0.574304i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.66300 2.69219i −1.40595 0.811725i −0.410954 0.911656i \(-0.634804\pi\)
−0.994994 + 0.0999316i \(0.968138\pi\)
\(12\) 0 0
\(13\) 5.31524i 1.47418i 0.675794 + 0.737091i \(0.263801\pi\)
−0.675794 + 0.737091i \(0.736199\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.89092 3.27516i 0.458615 0.794344i −0.540273 0.841490i \(-0.681679\pi\)
0.998888 + 0.0471458i \(0.0150125\pi\)
\(18\) 0 0
\(19\) −4.33939 + 2.50535i −0.995525 + 0.574767i −0.906921 0.421300i \(-0.861574\pi\)
−0.0886040 + 0.996067i \(0.528241\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.02463 1.16892i 0.422164 0.243737i −0.273839 0.961776i \(-0.588293\pi\)
0.696003 + 0.718039i \(0.254960\pi\)
\(24\) 0 0
\(25\) 2.49708 4.32507i 0.499416 0.865014i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 10.2125i 1.89642i −0.317648 0.948209i \(-0.602893\pi\)
0.317648 0.948209i \(-0.397107\pi\)
\(30\) 0 0
\(31\) −4.97636 2.87310i −0.893780 0.516024i −0.0186031 0.999827i \(-0.505922\pi\)
−0.875177 + 0.483803i \(0.839255\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.183331 + 0.0852905i 0.0309887 + 0.0144167i
\(36\) 0 0
\(37\) 0.354486 + 0.613988i 0.0582771 + 0.100939i 0.893692 0.448681i \(-0.148106\pi\)
−0.835415 + 0.549620i \(0.814773\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.59821 1.03047 0.515234 0.857050i \(-0.327705\pi\)
0.515234 + 0.857050i \(0.327705\pi\)
\(42\) 0 0
\(43\) −1.43304 −0.218537 −0.109268 0.994012i \(-0.534851\pi\)
−0.109268 + 0.994012i \(0.534851\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.46192 + 2.53213i 0.213244 + 0.369349i 0.952728 0.303825i \(-0.0982639\pi\)
−0.739484 + 0.673174i \(0.764931\pi\)
\(48\) 0 0
\(49\) 2.38244 6.58209i 0.340349 0.940299i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.4835 6.05264i −1.44002 0.831394i −0.442167 0.896933i \(-0.645790\pi\)
−0.997850 + 0.0655390i \(0.979123\pi\)
\(54\) 0 0
\(55\) 0.411498i 0.0554863i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.289951 0.502210i 0.0377484 0.0653822i −0.846534 0.532335i \(-0.821315\pi\)
0.884282 + 0.466953i \(0.154648\pi\)
\(60\) 0 0
\(61\) 2.40641 1.38934i 0.308109 0.177887i −0.337971 0.941156i \(-0.609741\pi\)
0.646080 + 0.763270i \(0.276407\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.351792 + 0.203107i −0.0436344 + 0.0251923i
\(66\) 0 0
\(67\) −2.63593 + 4.56556i −0.322030 + 0.557771i −0.980907 0.194479i \(-0.937698\pi\)
0.658877 + 0.752251i \(0.271032\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.32103i 0.394134i −0.980390 0.197067i \(-0.936858\pi\)
0.980390 0.197067i \(-0.0631416\pi\)
\(72\) 0 0
\(73\) −6.17326 3.56413i −0.722525 0.417150i 0.0931564 0.995651i \(-0.470304\pi\)
−0.815681 + 0.578502i \(0.803638\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −14.1904 + 1.25421i −1.61714 + 0.142930i
\(78\) 0 0
\(79\) −0.469123 0.812544i −0.0527804 0.0914184i 0.838428 0.545012i \(-0.183475\pi\)
−0.891208 + 0.453594i \(0.850142\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.9958 −1.42648 −0.713238 0.700922i \(-0.752772\pi\)
−0.713238 + 0.700922i \(0.752772\pi\)
\(84\) 0 0
\(85\) 0.289025 0.0313491
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.51794 + 2.62915i 0.160901 + 0.278689i 0.935192 0.354141i \(-0.115227\pi\)
−0.774291 + 0.632830i \(0.781893\pi\)
\(90\) 0 0
\(91\) 8.07632 + 11.5124i 0.846629 + 1.20683i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.331636 0.191470i −0.0340251 0.0196444i
\(96\) 0 0
\(97\) 7.13816i 0.724771i 0.932028 + 0.362385i \(0.118038\pi\)
−0.932028 + 0.362385i \(0.881962\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.08628 7.07765i 0.406600 0.704252i −0.587906 0.808929i \(-0.700048\pi\)
0.994506 + 0.104677i \(0.0333808\pi\)
\(102\) 0 0
\(103\) 6.46599 3.73314i 0.637113 0.367837i −0.146389 0.989227i \(-0.546765\pi\)
0.783502 + 0.621390i \(0.213432\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.99991 + 2.30935i −0.386686 + 0.223253i −0.680723 0.732541i \(-0.738334\pi\)
0.294037 + 0.955794i \(0.405001\pi\)
\(108\) 0 0
\(109\) 5.22792 9.05503i 0.500744 0.867314i −0.499256 0.866455i \(-0.666393\pi\)
1.00000 0.000859385i \(-0.000273551\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 19.2118i 1.80730i −0.428275 0.903648i \(-0.640879\pi\)
0.428275 0.903648i \(-0.359121\pi\)
\(114\) 0 0
\(115\) 0.154731 + 0.0893340i 0.0144287 + 0.00833044i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.880922 9.96693i −0.0807540 0.913667i
\(120\) 0 0
\(121\) 8.99573 + 15.5811i 0.817793 + 1.41646i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.763798 0.0683162
\(126\) 0 0
\(127\) 1.26488 0.112240 0.0561198 0.998424i \(-0.482127\pi\)
0.0561198 + 0.998424i \(0.482127\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.24394 12.5469i −0.632906 1.09623i −0.986955 0.160998i \(-0.948529\pi\)
0.354049 0.935227i \(-0.384805\pi\)
\(132\) 0 0
\(133\) −5.59200 + 12.0200i −0.484888 + 1.04226i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.3414 + 7.70264i 1.13983 + 0.658081i 0.946389 0.323030i \(-0.104702\pi\)
0.193442 + 0.981112i \(0.438035\pi\)
\(138\) 0 0
\(139\) 0.432667i 0.0366983i 0.999832 + 0.0183492i \(0.00584105\pi\)
−0.999832 + 0.0183492i \(0.994159\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 14.3096 24.7850i 1.19663 2.07262i
\(144\) 0 0
\(145\) 0.675921 0.390243i 0.0561322 0.0324079i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.04535 2.33558i 0.331408 0.191338i −0.325058 0.945694i \(-0.605384\pi\)
0.656466 + 0.754356i \(0.272051\pi\)
\(150\) 0 0
\(151\) 4.12276 7.14083i 0.335506 0.581113i −0.648076 0.761575i \(-0.724426\pi\)
0.983582 + 0.180463i \(0.0577595\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.439151i 0.0352734i
\(156\) 0 0
\(157\) −15.2334 8.79500i −1.21576 0.701917i −0.251749 0.967793i \(-0.581006\pi\)
−0.964007 + 0.265875i \(0.914339\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.60905 5.60814i 0.205622 0.441984i
\(162\) 0 0
\(163\) −5.27097 9.12959i −0.412854 0.715085i 0.582346 0.812941i \(-0.302135\pi\)
−0.995201 + 0.0978563i \(0.968801\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.18293 −0.710596 −0.355298 0.934753i \(-0.615621\pi\)
−0.355298 + 0.934753i \(0.615621\pi\)
\(168\) 0 0
\(169\) −15.2517 −1.17321
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.22358 + 2.11931i 0.0930274 + 0.161128i 0.908784 0.417268i \(-0.137012\pi\)
−0.815756 + 0.578396i \(0.803679\pi\)
\(174\) 0 0
\(175\) −1.16332 13.1620i −0.0879384 0.994953i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −5.05509 2.91856i −0.377835 0.218143i 0.299041 0.954240i \(-0.403333\pi\)
−0.676876 + 0.736097i \(0.736667\pi\)
\(180\) 0 0
\(181\) 16.0704i 1.19451i −0.802053 0.597253i \(-0.796259\pi\)
0.802053 0.597253i \(-0.203741\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.0270914 + 0.0469237i −0.00199180 + 0.00344990i
\(186\) 0 0
\(187\) −17.6347 + 10.1814i −1.28958 + 0.744537i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.90415 + 3.98611i −0.499567 + 0.288425i −0.728535 0.685009i \(-0.759798\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(192\) 0 0
\(193\) −0.359027 + 0.621853i −0.0258433 + 0.0447620i −0.878658 0.477452i \(-0.841560\pi\)
0.852814 + 0.522214i \(0.174894\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.5035i 0.962083i 0.876698 + 0.481042i \(0.159741\pi\)
−0.876698 + 0.481042i \(0.840259\pi\)
\(198\) 0 0
\(199\) 21.2568 + 12.2726i 1.50685 + 0.869983i 0.999968 + 0.00796947i \(0.00253679\pi\)
0.506886 + 0.862013i \(0.330797\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −15.5176 22.1195i −1.08912 1.55249i
\(204\) 0 0
\(205\) 0.252132 + 0.436706i 0.0176097 + 0.0305009i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 26.9795 1.86621
\(210\) 0 0
\(211\) 23.5675 1.62245 0.811227 0.584731i \(-0.198800\pi\)
0.811227 + 0.584731i \(0.198800\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.0547597 0.0948465i −0.00373458 0.00646848i
\(216\) 0 0
\(217\) −15.1440 + 1.33849i −1.02804 + 0.0908628i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.4083 + 10.0507i 1.17101 + 0.676081i
\(222\) 0 0
\(223\) 7.47655i 0.500667i −0.968160 0.250334i \(-0.919460\pi\)
0.968160 0.250334i \(-0.0805403\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.318701 0.552006i 0.0211529 0.0366379i −0.855255 0.518207i \(-0.826600\pi\)
0.876408 + 0.481569i \(0.159933\pi\)
\(228\) 0 0
\(229\) 1.58351 0.914239i 0.104641 0.0604146i −0.446766 0.894651i \(-0.647424\pi\)
0.551407 + 0.834236i \(0.314091\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −17.4232 + 10.0593i −1.14143 + 0.659007i −0.946785 0.321866i \(-0.895690\pi\)
−0.194649 + 0.980873i \(0.562357\pi\)
\(234\) 0 0
\(235\) −0.111727 + 0.193516i −0.00728825 + 0.0126236i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.78808i 0.180346i −0.995926 0.0901730i \(-0.971258\pi\)
0.995926 0.0901730i \(-0.0287420\pi\)
\(240\) 0 0
\(241\) 20.0304 + 11.5645i 1.29027 + 0.744938i 0.978702 0.205286i \(-0.0658126\pi\)
0.311568 + 0.950224i \(0.399146\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.526678 0.0938333i 0.0336482 0.00599479i
\(246\) 0 0
\(247\) −13.3165 23.0649i −0.847310 1.46758i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.6541 −1.17743 −0.588717 0.808339i \(-0.700367\pi\)
−0.588717 + 0.808339i \(0.700367\pi\)
\(252\) 0 0
\(253\) −12.5878 −0.791388
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.43687 + 9.41694i 0.339143 + 0.587413i 0.984272 0.176661i \(-0.0565297\pi\)
−0.645129 + 0.764074i \(0.723196\pi\)
\(258\) 0 0
\(259\) 1.70072 + 0.791220i 0.105678 + 0.0491640i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −16.4519 9.49852i −1.01447 0.585704i −0.101972 0.994787i \(-0.532515\pi\)
−0.912497 + 0.409083i \(0.865849\pi\)
\(264\) 0 0
\(265\) 0.925140i 0.0568309i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.29788 7.44415i 0.262046 0.453878i −0.704739 0.709467i \(-0.748936\pi\)
0.966786 + 0.255589i \(0.0822693\pi\)
\(270\) 0 0
\(271\) 1.58706 0.916292i 0.0964073 0.0556608i −0.451021 0.892513i \(-0.648940\pi\)
0.547429 + 0.836852i \(0.315607\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −23.2878 + 13.4452i −1.40431 + 0.810776i
\(276\) 0 0
\(277\) −7.90931 + 13.6993i −0.475224 + 0.823113i −0.999597 0.0283760i \(-0.990966\pi\)
0.524373 + 0.851489i \(0.324300\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.4998i 0.686023i 0.939331 + 0.343012i \(0.111447\pi\)
−0.939331 + 0.343012i \(0.888553\pi\)
\(282\) 0 0
\(283\) 8.59806 + 4.96409i 0.511101 + 0.295085i 0.733286 0.679920i \(-0.237986\pi\)
−0.222185 + 0.975005i \(0.571319\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.2912 10.0258i 0.843584 0.591802i
\(288\) 0 0
\(289\) 1.34887 + 2.33631i 0.0793454 + 0.137430i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 17.2720 1.00904 0.504520 0.863400i \(-0.331670\pi\)
0.504520 + 0.863400i \(0.331670\pi\)
\(294\) 0 0
\(295\) 0.0443187 0.00258034
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.21308 + 10.7614i 0.359312 + 0.622346i
\(300\) 0 0
\(301\) −3.10385 + 2.17746i −0.178903 + 0.125507i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.183908 + 0.106180i 0.0105306 + 0.00607982i
\(306\) 0 0
\(307\) 21.6425i 1.23520i 0.786490 + 0.617602i \(0.211896\pi\)
−0.786490 + 0.617602i \(0.788104\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −10.1016 + 17.4964i −0.572808 + 0.992133i 0.423468 + 0.905911i \(0.360813\pi\)
−0.996276 + 0.0862215i \(0.972521\pi\)
\(312\) 0 0
\(313\) 18.9146 10.9203i 1.06911 0.617254i 0.141175 0.989985i \(-0.454912\pi\)
0.927939 + 0.372731i \(0.121579\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.5288 + 12.4297i −1.20918 + 0.698120i −0.962580 0.270997i \(-0.912647\pi\)
−0.246599 + 0.969117i \(0.579313\pi\)
\(318\) 0 0
\(319\) −27.4940 + 47.6210i −1.53937 + 2.66626i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 18.9496i 1.05439i
\(324\) 0 0
\(325\) 22.9888 + 13.2726i 1.27519 + 0.736230i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.01390 + 3.26305i 0.386689 + 0.179898i
\(330\) 0 0
\(331\) −8.07219 13.9814i −0.443688 0.768490i 0.554272 0.832336i \(-0.312997\pi\)
−0.997960 + 0.0638459i \(0.979663\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.402898 −0.0220127
\(336\) 0 0
\(337\) 15.6304 0.851444 0.425722 0.904854i \(-0.360020\pi\)
0.425722 + 0.904854i \(0.360020\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.4698 + 26.7946i 0.837739 + 1.45101i
\(342\) 0 0
\(343\) −4.84108 17.8764i −0.261394 0.965232i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.0445 + 16.1915i 1.50551 + 0.869206i 0.999980 + 0.00639573i \(0.00203584\pi\)
0.505529 + 0.862810i \(0.331297\pi\)
\(348\) 0 0
\(349\) 30.0708i 1.60965i −0.593510 0.804827i \(-0.702258\pi\)
0.593510 0.804827i \(-0.297742\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.50607 14.7329i 0.452733 0.784156i −0.545822 0.837901i \(-0.683783\pi\)
0.998555 + 0.0537453i \(0.0171159\pi\)
\(354\) 0 0
\(355\) 0.219804 0.126904i 0.0116660 0.00673537i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −25.2692 + 14.5892i −1.33366 + 0.769987i −0.985858 0.167583i \(-0.946404\pi\)
−0.347798 + 0.937570i \(0.613070\pi\)
\(360\) 0 0
\(361\) 3.05356 5.28892i 0.160714 0.278364i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.544774i 0.0285148i
\(366\) 0 0
\(367\) 15.6981 + 9.06329i 0.819433 + 0.473100i 0.850221 0.526426i \(-0.176468\pi\)
−0.0307880 + 0.999526i \(0.509802\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −31.9032 + 2.81975i −1.65633 + 0.146394i
\(372\) 0 0
\(373\) 10.1823 + 17.6362i 0.527219 + 0.913170i 0.999497 + 0.0317200i \(0.0100985\pi\)
−0.472278 + 0.881450i \(0.656568\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 54.2820 2.79566
\(378\) 0 0
\(379\) −21.9961 −1.12986 −0.564931 0.825138i \(-0.691097\pi\)
−0.564931 + 0.825138i \(0.691097\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.3127 + 28.2544i 0.833538 + 1.44373i 0.895215 + 0.445634i \(0.147022\pi\)
−0.0616774 + 0.998096i \(0.519645\pi\)
\(384\) 0 0
\(385\) −0.625257 0.891272i −0.0318660 0.0454234i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13.6400 + 7.87504i 0.691574 + 0.399280i 0.804201 0.594357i \(-0.202593\pi\)
−0.112628 + 0.993637i \(0.535927\pi\)
\(390\) 0 0
\(391\) 8.84131i 0.447124i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.0358524 0.0620983i 0.00180393 0.00312450i
\(396\) 0 0
\(397\) −2.95864 + 1.70817i −0.148490 + 0.0857308i −0.572404 0.819972i \(-0.693989\pi\)
0.423914 + 0.905702i \(0.360656\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.851348 0.491526i 0.0425143 0.0245456i −0.478592 0.878037i \(-0.658853\pi\)
0.521106 + 0.853492i \(0.325519\pi\)
\(402\) 0 0
\(403\) 15.2712 26.4505i 0.760713 1.31759i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.81737i 0.189220i
\(408\) 0 0
\(409\) −25.0195 14.4450i −1.23714 0.714260i −0.268627 0.963244i \(-0.586570\pi\)
−0.968508 + 0.248984i \(0.919903\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.135080 1.52832i −0.00664684 0.0752037i
\(414\) 0 0
\(415\) −0.496599 0.860135i −0.0243771 0.0422223i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.5785 0.614501 0.307251 0.951629i \(-0.400591\pi\)
0.307251 + 0.951629i \(0.400591\pi\)
\(420\) 0 0
\(421\) 26.0463 1.26942 0.634710 0.772750i \(-0.281120\pi\)
0.634710 + 0.772750i \(0.281120\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −9.44354 16.3567i −0.458079 0.793416i
\(426\) 0 0
\(427\) 3.10104 6.66566i 0.150070 0.322574i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.28454 3.62838i −0.302716 0.174773i 0.340947 0.940083i \(-0.389252\pi\)
−0.643662 + 0.765310i \(0.722586\pi\)
\(432\) 0 0
\(433\) 8.29113i 0.398446i 0.979954 + 0.199223i \(0.0638419\pi\)
−0.979954 + 0.199223i \(0.936158\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.85710 + 10.1448i −0.280183 + 0.485292i
\(438\) 0 0
\(439\) 2.83357 1.63596i 0.135239 0.0780802i −0.430854 0.902422i \(-0.641788\pi\)
0.566093 + 0.824341i \(0.308454\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.46737 1.42454i 0.117228 0.0676817i −0.440239 0.897880i \(-0.645106\pi\)
0.557468 + 0.830199i \(0.311773\pi\)
\(444\) 0 0
\(445\) −0.116008 + 0.200931i −0.00549929 + 0.00952505i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.9802i 0.942925i −0.881886 0.471463i \(-0.843726\pi\)
0.881886 0.471463i \(-0.156274\pi\)
\(450\) 0 0
\(451\) −30.7675 17.7636i −1.44878 0.836455i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.453339 + 0.974450i −0.0212529 + 0.0456829i
\(456\) 0 0
\(457\) −9.15008 15.8484i −0.428023 0.741357i 0.568675 0.822563i \(-0.307456\pi\)
−0.996697 + 0.0812053i \(0.974123\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.05908 0.421923 0.210962 0.977494i \(-0.432340\pi\)
0.210962 + 0.977494i \(0.432340\pi\)
\(462\) 0 0
\(463\) −21.6454 −1.00595 −0.502974 0.864302i \(-0.667761\pi\)
−0.502974 + 0.864302i \(0.667761\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.7761 + 23.8610i 0.637484 + 1.10415i 0.985983 + 0.166845i \(0.0533580\pi\)
−0.348500 + 0.937309i \(0.613309\pi\)
\(468\) 0 0
\(469\) 1.22800 + 13.8938i 0.0567038 + 0.641558i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6.68227 + 3.85801i 0.307251 + 0.177392i
\(474\) 0 0
\(475\) 25.0242i 1.14819i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.47325 4.28380i 0.113006 0.195732i −0.803975 0.594663i \(-0.797285\pi\)
0.916981 + 0.398931i \(0.130619\pi\)
\(480\) 0 0
\(481\) −3.26349 + 1.88418i −0.148802 + 0.0859110i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.472443 + 0.272765i −0.0214525 + 0.0123856i
\(486\) 0 0
\(487\) −4.78573 + 8.28913i −0.216862 + 0.375616i −0.953847 0.300293i \(-0.902916\pi\)
0.736985 + 0.675909i \(0.236249\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 38.1062i 1.71971i −0.510538 0.859855i \(-0.670554\pi\)
0.510538 0.859855i \(-0.329446\pi\)
\(492\) 0 0
\(493\) −33.4477 19.3110i −1.50641 0.869725i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.04620 7.19310i −0.226353 0.322655i
\(498\) 0 0
\(499\) 12.4192 + 21.5107i 0.555960 + 0.962951i 0.997828 + 0.0658709i \(0.0209825\pi\)
−0.441868 + 0.897080i \(0.645684\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.2820 −1.21645 −0.608223 0.793766i \(-0.708117\pi\)
−0.608223 + 0.793766i \(0.708117\pi\)
\(504\) 0 0
\(505\) 0.624584 0.0277936
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 20.8860 + 36.1757i 0.925758 + 1.60346i 0.790338 + 0.612671i \(0.209905\pi\)
0.135420 + 0.990788i \(0.456762\pi\)
\(510\) 0 0
\(511\) −18.7864 + 1.66042i −0.831060 + 0.0734528i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.494160 + 0.285303i 0.0217753 + 0.0125720i
\(516\) 0 0
\(517\) 15.7431i 0.692380i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.02629 3.50963i 0.0887732 0.153760i −0.818220 0.574906i \(-0.805039\pi\)
0.906993 + 0.421146i \(0.138372\pi\)
\(522\) 0 0
\(523\) 26.2429 15.1514i 1.14752 0.662523i 0.199241 0.979951i \(-0.436152\pi\)
0.948282 + 0.317428i \(0.102819\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −18.8198 + 10.8656i −0.819801 + 0.473312i
\(528\) 0 0
\(529\) −8.76726 + 15.1853i −0.381185 + 0.660232i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 35.0710i 1.51910i
\(534\) 0 0
\(535\) −0.305691 0.176491i −0.0132162 0.00763037i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −28.8296 + 24.2783i −1.24178 + 1.04574i
\(540\) 0 0
\(541\) 8.82681 + 15.2885i 0.379494 + 0.657303i 0.990989 0.133946i \(-0.0427647\pi\)
−0.611495 + 0.791249i \(0.709431\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.799082 0.0342289
\(546\) 0 0
\(547\) 4.36639 0.186693 0.0933466 0.995634i \(-0.470244\pi\)
0.0933466 + 0.995634i \(0.470244\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 25.5859 + 44.3161i 1.09000 + 1.88793i
\(552\) 0 0
\(553\) −2.25072 1.04709i −0.0957102 0.0445269i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.7527 + 8.51750i 0.625094 + 0.360898i 0.778849 0.627211i \(-0.215804\pi\)
−0.153756 + 0.988109i \(0.549137\pi\)
\(558\) 0 0
\(559\) 7.61695i 0.322163i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.45992 11.1889i 0.272253 0.471556i −0.697185 0.716891i \(-0.745564\pi\)
0.969438 + 0.245335i \(0.0788978\pi\)
\(564\) 0 0
\(565\) 1.27155 0.734127i 0.0534943 0.0308850i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.8280 + 10.8704i −0.789313 + 0.455710i −0.839720 0.543019i \(-0.817281\pi\)
0.0504079 + 0.998729i \(0.483948\pi\)
\(570\) 0 0
\(571\) 16.8254 29.1425i 0.704122 1.21958i −0.262885 0.964827i \(-0.584674\pi\)
0.967007 0.254748i \(-0.0819925\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 11.6755i 0.486904i
\(576\) 0 0
\(577\) 12.5598 + 7.25141i 0.522871 + 0.301880i 0.738109 0.674682i \(-0.235719\pi\)
−0.215237 + 0.976562i \(0.569052\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −28.1479 + 19.7467i −1.16777 + 0.819231i
\(582\) 0 0
\(583\) 32.5897 + 56.4469i 1.34973 + 2.33779i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 31.6834 1.30771 0.653857 0.756618i \(-0.273150\pi\)
0.653857 + 0.756618i \(0.273150\pi\)
\(588\) 0 0
\(589\) 28.7925 1.18637
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.54101 + 6.13320i 0.145412 + 0.251860i 0.929526 0.368755i \(-0.120216\pi\)
−0.784115 + 0.620616i \(0.786883\pi\)
\(594\) 0 0
\(595\) 0.626005 0.439163i 0.0256637 0.0180039i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.20178 3.00325i −0.212539 0.122709i 0.389952 0.920835i \(-0.372492\pi\)
−0.602491 + 0.798126i \(0.705825\pi\)
\(600\) 0 0
\(601\) 0.612087i 0.0249675i −0.999922 0.0124838i \(-0.996026\pi\)
0.999922 0.0124838i \(-0.00397381\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.687494 + 1.19077i −0.0279506 + 0.0484119i
\(606\) 0 0
\(607\) −1.77500 + 1.02480i −0.0720450 + 0.0415952i −0.535590 0.844478i \(-0.679911\pi\)
0.463545 + 0.886073i \(0.346577\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13.4588 + 7.77047i −0.544487 + 0.314360i
\(612\) 0 0
\(613\) −4.93166 + 8.54189i −0.199188 + 0.345003i −0.948265 0.317479i \(-0.897164\pi\)
0.749077 + 0.662482i \(0.230497\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.8055i 1.07915i 0.841937 + 0.539575i \(0.181415\pi\)
−0.841937 + 0.539575i \(0.818585\pi\)
\(618\) 0 0
\(619\) −0.0603011 0.0348148i −0.00242370 0.00139933i 0.498788 0.866724i \(-0.333779\pi\)
−0.501211 + 0.865325i \(0.667112\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.28264 + 3.38807i 0.291773 + 0.135740i
\(624\) 0 0
\(625\) −12.4562 21.5748i −0.498248 0.862992i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.68121 0.106907
\(630\) 0 0
\(631\) 11.8214 0.470603 0.235301 0.971922i \(-0.424392\pi\)
0.235301 + 0.971922i \(0.424392\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.0483338 + 0.0837165i 0.00191807 + 0.00332219i
\(636\) 0 0
\(637\) 34.9854 + 12.6632i 1.38617 + 0.501736i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 17.7673 + 10.2580i 0.701766 + 0.405165i 0.808005 0.589176i \(-0.200547\pi\)
−0.106239 + 0.994341i \(0.533881\pi\)
\(642\) 0 0
\(643\) 18.0226i 0.710743i 0.934725 + 0.355372i \(0.115646\pi\)
−0.934725 + 0.355372i \(0.884354\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.11827 15.7933i 0.358476 0.620899i −0.629230 0.777219i \(-0.716630\pi\)
0.987706 + 0.156320i \(0.0499631\pi\)
\(648\) 0 0
\(649\) −2.70409 + 1.56121i −0.106145 + 0.0612827i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.79559 4.50079i 0.305065 0.176129i −0.339651 0.940552i \(-0.610309\pi\)
0.644716 + 0.764422i \(0.276976\pi\)
\(654\) 0 0
\(655\) 0.553614 0.958888i 0.0216315 0.0374669i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 35.1959i 1.37104i −0.728055 0.685519i \(-0.759575\pi\)
0.728055 0.685519i \(-0.240425\pi\)
\(660\) 0 0
\(661\) 10.8797 + 6.28141i 0.423172 + 0.244318i 0.696433 0.717621i \(-0.254769\pi\)
−0.273262 + 0.961940i \(0.588102\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.00923 + 0.0892002i −0.0391363 + 0.00345904i
\(666\) 0 0
\(667\) −11.9376 20.6765i −0.462226 0.800599i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14.9614 −0.577580
\(672\) 0 0
\(673\) −47.7826 −1.84188 −0.920942 0.389699i \(-0.872579\pi\)
−0.920942 + 0.389699i \(0.872579\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.5235 + 32.0837i 0.711918 + 1.23308i 0.964136 + 0.265407i \(0.0855064\pi\)
−0.252219 + 0.967670i \(0.581160\pi\)
\(678\) 0 0
\(679\) 10.8462 + 15.4607i 0.416239 + 0.593328i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.6844 + 12.5195i 0.829732 + 0.479046i 0.853761 0.520665i \(-0.174316\pi\)
−0.0240289 + 0.999711i \(0.507649\pi\)
\(684\) 0 0
\(685\) 1.17734i 0.0449839i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 32.1712 55.7222i 1.22563 2.12285i
\(690\) 0 0
\(691\) −40.2655 + 23.2473i −1.53177 + 0.884370i −0.532493 + 0.846434i \(0.678745\pi\)
−0.999280 + 0.0379352i \(0.987922\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.0286363 + 0.0165332i −0.00108624 + 0.000627139i
\(696\) 0 0
\(697\) 12.4767 21.6102i 0.472587 0.818545i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 36.0041i 1.35986i 0.733279 + 0.679928i \(0.237989\pi\)
−0.733279 + 0.679928i \(0.762011\pi\)
\(702\) 0 0
\(703\) −3.07651 1.77622i −0.116033 0.0669915i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.90368 21.5386i −0.0715952 0.810043i
\(708\) 0 0
\(709\) −15.9158 27.5670i −0.597731 1.03530i −0.993155 0.116802i \(-0.962736\pi\)
0.395424 0.918499i \(-0.370598\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −13.4337 −0.503096
\(714\) 0 0
\(715\) 2.18721 0.0817969
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20.0271 + 34.6879i 0.746883 + 1.29364i 0.949310 + 0.314342i \(0.101784\pi\)
−0.202427 + 0.979297i \(0.564883\pi\)
\(720\) 0 0
\(721\) 8.33245 17.9106i 0.310317 0.667024i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −44.1699 25.5015i −1.64043 0.947101i
\(726\) 0 0
\(727\) 3.91723i 0.145282i −0.997358 0.0726411i \(-0.976857\pi\)
0.997358 0.0726411i \(-0.0231428\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.70976 + 4.69344i −0.100224 + 0.173593i
\(732\) 0 0
\(733\) −20.4239 + 11.7918i −0.754376 + 0.435539i −0.827273 0.561800i \(-0.810109\pi\)
0.0728971 + 0.997339i \(0.476776\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.5827 14.1928i 0.905514 0.522798i
\(738\) 0 0
\(739\) 16.8641 29.2094i 0.620355 1.07449i −0.369065 0.929404i \(-0.620322\pi\)
0.989420 0.145083i \(-0.0463448\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 33.9485i 1.24545i 0.782441 + 0.622725i \(0.213975\pi\)
−0.782441 + 0.622725i \(0.786025\pi\)
\(744\) 0 0
\(745\) 0.309164 + 0.178496i 0.0113269 + 0.00653958i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.15452 + 11.0796i −0.188342 + 0.404840i
\(750\) 0 0
\(751\) −1.69831 2.94157i −0.0619724 0.107339i 0.833375 0.552709i \(-0.186406\pi\)
−0.895347 + 0.445369i \(0.853072\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.630160 0.0229339
\(756\) 0 0
\(757\) 29.1344 1.05891 0.529454 0.848339i \(-0.322397\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.36288 + 14.4849i 0.303154 + 0.525079i 0.976849 0.213931i \(-0.0686269\pi\)
−0.673694 + 0.739010i \(0.735294\pi\)
\(762\) 0 0
\(763\) −2.43553 27.5561i −0.0881723 0.997599i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.66937 + 1.54116i 0.0963852 + 0.0556480i
\(768\) 0 0
\(769\) 27.8070i 1.00275i 0.865231 + 0.501373i \(0.167172\pi\)
−0.865231 + 0.501373i \(0.832828\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.42238 11.1239i 0.230997 0.400098i −0.727105 0.686526i \(-0.759135\pi\)
0.958102 + 0.286428i \(0.0924679\pi\)
\(774\) 0 0
\(775\) −24.8527 + 14.3487i −0.892736 + 0.515421i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −28.6322 + 16.5308i −1.02586 + 0.592278i
\(780\) 0 0
\(781\) −8.94083 + 15.4860i −0.319928 + 0.554132i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.34431i 0.0479804i
\(786\) 0 0
\(787\) −6.55243 3.78305i −0.233569 0.134851i 0.378648 0.925541i \(-0.376389\pi\)
−0.612217 + 0.790689i \(0.709722\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −29.1917 41.6113i −1.03794 1.47953i
\(792\) 0 0
\(793\) 7.38467 + 12.7906i 0.262237 + 0.454208i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.06724 −0.285756 −0.142878 0.989740i \(-0.545636\pi\)
−0.142878 + 0.989740i \(0.545636\pi\)
\(798\) 0 0
\(799\) 11.0575 0.391186
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 19.1906 + 33.2391i 0.677222 + 1.17298i