Properties

Label 3150.2.m.f.2843.2
Level 3150
Weight 2
Character 3150.2843
Analytic conductor 25.153
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.2
Root \(-0.707107 - 0.707107i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.f.1457.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.828427i q^{11} +(0.585786 + 0.585786i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-4.41421 - 4.41421i) q^{17} -7.07107i q^{19} +(0.585786 - 0.585786i) q^{22} +(0.828427 - 0.828427i) q^{23} +0.828427i q^{26} +(0.707107 + 0.707107i) q^{28} -8.82843 q^{29} -3.17157 q^{31} +(-0.707107 - 0.707107i) q^{32} -6.24264i q^{34} +(-8.07107 + 8.07107i) q^{37} +(5.00000 - 5.00000i) q^{38} +0.828427i q^{41} +(-3.58579 - 3.58579i) q^{43} +0.828427 q^{44} +1.17157 q^{46} +(-3.58579 - 3.58579i) q^{47} -1.00000i q^{49} +(-0.585786 + 0.585786i) q^{52} +(-0.828427 + 0.828427i) q^{53} +1.00000i q^{56} +(-6.24264 - 6.24264i) q^{58} -8.00000 q^{59} +9.41421 q^{61} +(-2.24264 - 2.24264i) q^{62} -1.00000i q^{64} +(2.41421 - 2.41421i) q^{67} +(4.41421 - 4.41421i) q^{68} -3.75736i q^{71} +(6.00000 + 6.00000i) q^{73} -11.4142 q^{74} +7.07107 q^{76} +(-0.585786 - 0.585786i) q^{77} -9.31371i q^{79} +(-0.585786 + 0.585786i) q^{82} +(-1.65685 + 1.65685i) q^{83} -5.07107i q^{86} +(0.585786 + 0.585786i) q^{88} +9.31371 q^{89} +0.828427 q^{91} +(0.828427 + 0.828427i) q^{92} -5.07107i q^{94} +(-0.242641 + 0.242641i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q + 8q^{13} + 4q^{14} - 4q^{16} - 12q^{17} + 8q^{22} - 8q^{23} - 24q^{29} - 24q^{31} - 4q^{37} + 20q^{38} - 20q^{43} - 8q^{44} + 16q^{46} - 20q^{47} - 8q^{52} + 8q^{53} - 8q^{58} - 32q^{59} + 32q^{61} + 8q^{62} + 4q^{67} + 12q^{68} + 24q^{73} - 40q^{74} - 8q^{77} - 8q^{82} + 16q^{83} + 8q^{88} - 8q^{89} - 8q^{91} - 8q^{92} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.828427i 0.249780i −0.992171 0.124890i \(-0.960142\pi\)
0.992171 0.124890i \(-0.0398578\pi\)
\(12\) 0 0
\(13\) 0.585786 + 0.585786i 0.162468 + 0.162468i 0.783659 0.621191i \(-0.213351\pi\)
−0.621191 + 0.783659i \(0.713351\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −4.41421 4.41421i −1.07060 1.07060i −0.997310 0.0732936i \(-0.976649\pi\)
−0.0732936 0.997310i \(-0.523351\pi\)
\(18\) 0 0
\(19\) 7.07107i 1.62221i −0.584898 0.811107i \(-0.698865\pi\)
0.584898 0.811107i \(-0.301135\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.585786 0.585786i 0.124890 0.124890i
\(23\) 0.828427 0.828427i 0.172739 0.172739i −0.615443 0.788182i \(-0.711023\pi\)
0.788182 + 0.615443i \(0.211023\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.828427i 0.162468i
\(27\) 0 0
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) −8.82843 −1.63940 −0.819699 0.572795i \(-0.805859\pi\)
−0.819699 + 0.572795i \(0.805859\pi\)
\(30\) 0 0
\(31\) −3.17157 −0.569631 −0.284816 0.958582i \(-0.591932\pi\)
−0.284816 + 0.958582i \(0.591932\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 6.24264i 1.07060i
\(35\) 0 0
\(36\) 0 0
\(37\) −8.07107 + 8.07107i −1.32688 + 1.32688i −0.418794 + 0.908081i \(0.637547\pi\)
−0.908081 + 0.418794i \(0.862453\pi\)
\(38\) 5.00000 5.00000i 0.811107 0.811107i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.828427i 0.129379i 0.997905 + 0.0646893i \(0.0206056\pi\)
−0.997905 + 0.0646893i \(0.979394\pi\)
\(42\) 0 0
\(43\) −3.58579 3.58579i −0.546827 0.546827i 0.378694 0.925522i \(-0.376373\pi\)
−0.925522 + 0.378694i \(0.876373\pi\)
\(44\) 0.828427 0.124890
\(45\) 0 0
\(46\) 1.17157 0.172739
\(47\) −3.58579 3.58579i −0.523041 0.523041i 0.395448 0.918488i \(-0.370589\pi\)
−0.918488 + 0.395448i \(0.870589\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.585786 + 0.585786i −0.0812340 + 0.0812340i
\(53\) −0.828427 + 0.828427i −0.113793 + 0.113793i −0.761711 0.647917i \(-0.775640\pi\)
0.647917 + 0.761711i \(0.275640\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) −6.24264 6.24264i −0.819699 0.819699i
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) 9.41421 1.20537 0.602683 0.797981i \(-0.294098\pi\)
0.602683 + 0.797981i \(0.294098\pi\)
\(62\) −2.24264 2.24264i −0.284816 0.284816i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 2.41421 2.41421i 0.294943 0.294943i −0.544086 0.839029i \(-0.683124\pi\)
0.839029 + 0.544086i \(0.183124\pi\)
\(68\) 4.41421 4.41421i 0.535302 0.535302i
\(69\) 0 0
\(70\) 0 0
\(71\) 3.75736i 0.445917i −0.974828 0.222958i \(-0.928429\pi\)
0.974828 0.222958i \(-0.0715714\pi\)
\(72\) 0 0
\(73\) 6.00000 + 6.00000i 0.702247 + 0.702247i 0.964892 0.262646i \(-0.0845950\pi\)
−0.262646 + 0.964892i \(0.584595\pi\)
\(74\) −11.4142 −1.32688
\(75\) 0 0
\(76\) 7.07107 0.811107
\(77\) −0.585786 0.585786i −0.0667566 0.0667566i
\(78\) 0 0
\(79\) 9.31371i 1.04787i −0.851757 0.523937i \(-0.824463\pi\)
0.851757 0.523937i \(-0.175537\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.585786 + 0.585786i −0.0646893 + 0.0646893i
\(83\) −1.65685 + 1.65685i −0.181863 + 0.181863i −0.792167 0.610304i \(-0.791047\pi\)
0.610304 + 0.792167i \(0.291047\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.07107i 0.546827i
\(87\) 0 0
\(88\) 0.585786 + 0.585786i 0.0624450 + 0.0624450i
\(89\) 9.31371 0.987251 0.493626 0.869675i \(-0.335671\pi\)
0.493626 + 0.869675i \(0.335671\pi\)
\(90\) 0 0
\(91\) 0.828427 0.0868428
\(92\) 0.828427 + 0.828427i 0.0863695 + 0.0863695i
\(93\) 0 0
\(94\) 5.07107i 0.523041i
\(95\) 0 0
\(96\) 0 0
\(97\) −0.242641 + 0.242641i −0.0246364 + 0.0246364i −0.719318 0.694681i \(-0.755545\pi\)
0.694681 + 0.719318i \(0.255545\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 15.6569i 1.55792i −0.627077 0.778958i \(-0.715749\pi\)
0.627077 0.778958i \(-0.284251\pi\)
\(102\) 0 0
\(103\) −0.585786 0.585786i −0.0577193 0.0577193i 0.677658 0.735377i \(-0.262995\pi\)
−0.735377 + 0.677658i \(0.762995\pi\)
\(104\) −0.828427 −0.0812340
\(105\) 0 0
\(106\) −1.17157 −0.113793
\(107\) 5.07107 + 5.07107i 0.490239 + 0.490239i 0.908381 0.418143i \(-0.137319\pi\)
−0.418143 + 0.908381i \(0.637319\pi\)
\(108\) 0 0
\(109\) 8.14214i 0.779875i −0.920841 0.389938i \(-0.872497\pi\)
0.920841 0.389938i \(-0.127503\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) −2.58579 + 2.58579i −0.243250 + 0.243250i −0.818193 0.574943i \(-0.805024\pi\)
0.574943 + 0.818193i \(0.305024\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 8.82843i 0.819699i
\(117\) 0 0
\(118\) −5.65685 5.65685i −0.520756 0.520756i
\(119\) −6.24264 −0.572262
\(120\) 0 0
\(121\) 10.3137 0.937610
\(122\) 6.65685 + 6.65685i 0.602683 + 0.602683i
\(123\) 0 0
\(124\) 3.17157i 0.284816i
\(125\) 0 0
\(126\) 0 0
\(127\) −6.82843 + 6.82843i −0.605925 + 0.605925i −0.941879 0.335954i \(-0.890941\pi\)
0.335954 + 0.941879i \(0.390941\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000i 0.524222i 0.965038 + 0.262111i \(0.0844187\pi\)
−0.965038 + 0.262111i \(0.915581\pi\)
\(132\) 0 0
\(133\) −5.00000 5.00000i −0.433555 0.433555i
\(134\) 3.41421 0.294943
\(135\) 0 0
\(136\) 6.24264 0.535302
\(137\) −13.0711 13.0711i −1.11674 1.11674i −0.992217 0.124520i \(-0.960261\pi\)
−0.124520 0.992217i \(-0.539739\pi\)
\(138\) 0 0
\(139\) 8.24264i 0.699132i −0.936912 0.349566i \(-0.886329\pi\)
0.936912 0.349566i \(-0.113671\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.65685 2.65685i 0.222958 0.222958i
\(143\) 0.485281 0.485281i 0.0405813 0.0405813i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.48528i 0.702247i
\(147\) 0 0
\(148\) −8.07107 8.07107i −0.663438 0.663438i
\(149\) −17.3137 −1.41839 −0.709197 0.705010i \(-0.750942\pi\)
−0.709197 + 0.705010i \(0.750942\pi\)
\(150\) 0 0
\(151\) 9.31371 0.757939 0.378969 0.925409i \(-0.376279\pi\)
0.378969 + 0.925409i \(0.376279\pi\)
\(152\) 5.00000 + 5.00000i 0.405554 + 0.405554i
\(153\) 0 0
\(154\) 0.828427i 0.0667566i
\(155\) 0 0
\(156\) 0 0
\(157\) −5.41421 + 5.41421i −0.432101 + 0.432101i −0.889343 0.457241i \(-0.848838\pi\)
0.457241 + 0.889343i \(0.348838\pi\)
\(158\) 6.58579 6.58579i 0.523937 0.523937i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.17157i 0.0923329i
\(162\) 0 0
\(163\) 14.8995 + 14.8995i 1.16702 + 1.16702i 0.982905 + 0.184114i \(0.0589414\pi\)
0.184114 + 0.982905i \(0.441059\pi\)
\(164\) −0.828427 −0.0646893
\(165\) 0 0
\(166\) −2.34315 −0.181863
\(167\) −12.8995 12.8995i −0.998193 0.998193i 0.00180548 0.999998i \(-0.499425\pi\)
−0.999998 + 0.00180548i \(0.999425\pi\)
\(168\) 0 0
\(169\) 12.3137i 0.947208i
\(170\) 0 0
\(171\) 0 0
\(172\) 3.58579 3.58579i 0.273414 0.273414i
\(173\) −8.00000 + 8.00000i −0.608229 + 0.608229i −0.942483 0.334254i \(-0.891516\pi\)
0.334254 + 0.942483i \(0.391516\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.828427i 0.0624450i
\(177\) 0 0
\(178\) 6.58579 + 6.58579i 0.493626 + 0.493626i
\(179\) −9.31371 −0.696139 −0.348070 0.937469i \(-0.613163\pi\)
−0.348070 + 0.937469i \(0.613163\pi\)
\(180\) 0 0
\(181\) 3.07107 0.228271 0.114135 0.993465i \(-0.463590\pi\)
0.114135 + 0.993465i \(0.463590\pi\)
\(182\) 0.585786 + 0.585786i 0.0434214 + 0.0434214i
\(183\) 0 0
\(184\) 1.17157i 0.0863695i
\(185\) 0 0
\(186\) 0 0
\(187\) −3.65685 + 3.65685i −0.267416 + 0.267416i
\(188\) 3.58579 3.58579i 0.261520 0.261520i
\(189\) 0 0
\(190\) 0 0
\(191\) 10.5858i 0.765961i −0.923757 0.382980i \(-0.874898\pi\)
0.923757 0.382980i \(-0.125102\pi\)
\(192\) 0 0
\(193\) −6.00000 6.00000i −0.431889 0.431889i 0.457381 0.889271i \(-0.348787\pi\)
−0.889271 + 0.457381i \(0.848787\pi\)
\(194\) −0.343146 −0.0246364
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −8.82843 8.82843i −0.628999 0.628999i 0.318817 0.947816i \(-0.396714\pi\)
−0.947816 + 0.318817i \(0.896714\pi\)
\(198\) 0 0
\(199\) 11.6569i 0.826332i −0.910656 0.413166i \(-0.864423\pi\)
0.910656 0.413166i \(-0.135577\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 11.0711 11.0711i 0.778958 0.778958i
\(203\) −6.24264 + 6.24264i −0.438147 + 0.438147i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.828427i 0.0577193i
\(207\) 0 0
\(208\) −0.585786 0.585786i −0.0406170 0.0406170i
\(209\) −5.85786 −0.405197
\(210\) 0 0
\(211\) 20.4853 1.41026 0.705132 0.709076i \(-0.250888\pi\)
0.705132 + 0.709076i \(0.250888\pi\)
\(212\) −0.828427 0.828427i −0.0568966 0.0568966i
\(213\) 0 0
\(214\) 7.17157i 0.490239i
\(215\) 0 0
\(216\) 0 0
\(217\) −2.24264 + 2.24264i −0.152240 + 0.152240i
\(218\) 5.75736 5.75736i 0.389938 0.389938i
\(219\) 0 0
\(220\) 0 0
\(221\) 5.17157i 0.347878i
\(222\) 0 0
\(223\) 11.8995 + 11.8995i 0.796849 + 0.796849i 0.982597 0.185748i \(-0.0594709\pi\)
−0.185748 + 0.982597i \(0.559471\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −3.65685 −0.243250
\(227\) 15.6569 + 15.6569i 1.03918 + 1.03918i 0.999200 + 0.0399815i \(0.0127299\pi\)
0.0399815 + 0.999200i \(0.487270\pi\)
\(228\) 0 0
\(229\) 19.0711i 1.26025i −0.776493 0.630126i \(-0.783003\pi\)
0.776493 0.630126i \(-0.216997\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.24264 6.24264i 0.409849 0.409849i
\(233\) 2.58579 2.58579i 0.169401 0.169401i −0.617315 0.786716i \(-0.711780\pi\)
0.786716 + 0.617315i \(0.211780\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 8.00000i 0.520756i
\(237\) 0 0
\(238\) −4.41421 4.41421i −0.286131 0.286131i
\(239\) 17.2132 1.11343 0.556715 0.830704i \(-0.312062\pi\)
0.556715 + 0.830704i \(0.312062\pi\)
\(240\) 0 0
\(241\) 3.65685 0.235559 0.117779 0.993040i \(-0.462422\pi\)
0.117779 + 0.993040i \(0.462422\pi\)
\(242\) 7.29289 + 7.29289i 0.468805 + 0.468805i
\(243\) 0 0
\(244\) 9.41421i 0.602683i
\(245\) 0 0
\(246\) 0 0
\(247\) 4.14214 4.14214i 0.263558 0.263558i
\(248\) 2.24264 2.24264i 0.142408 0.142408i
\(249\) 0 0
\(250\) 0 0
\(251\) 26.9706i 1.70237i −0.524868 0.851183i \(-0.675885\pi\)
0.524868 0.851183i \(-0.324115\pi\)
\(252\) 0 0
\(253\) −0.686292 0.686292i −0.0431468 0.0431468i
\(254\) −9.65685 −0.605925
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 12.8995 + 12.8995i 0.804648 + 0.804648i 0.983818 0.179170i \(-0.0573411\pi\)
−0.179170 + 0.983818i \(0.557341\pi\)
\(258\) 0 0
\(259\) 11.4142i 0.709245i
\(260\) 0 0
\(261\) 0 0
\(262\) −4.24264 + 4.24264i −0.262111 + 0.262111i
\(263\) −22.0000 + 22.0000i −1.35658 + 1.35658i −0.478479 + 0.878099i \(0.658812\pi\)
−0.878099 + 0.478479i \(0.841188\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 7.07107i 0.433555i
\(267\) 0 0
\(268\) 2.41421 + 2.41421i 0.147472 + 0.147472i
\(269\) −1.31371 −0.0800982 −0.0400491 0.999198i \(-0.512751\pi\)
−0.0400491 + 0.999198i \(0.512751\pi\)
\(270\) 0 0
\(271\) 12.8284 0.779271 0.389636 0.920969i \(-0.372601\pi\)
0.389636 + 0.920969i \(0.372601\pi\)
\(272\) 4.41421 + 4.41421i 0.267651 + 0.267651i
\(273\) 0 0
\(274\) 18.4853i 1.11674i
\(275\) 0 0
\(276\) 0 0
\(277\) 3.92893 3.92893i 0.236067 0.236067i −0.579153 0.815219i \(-0.696616\pi\)
0.815219 + 0.579153i \(0.196616\pi\)
\(278\) 5.82843 5.82843i 0.349566 0.349566i
\(279\) 0 0
\(280\) 0 0
\(281\) 27.0711i 1.61492i 0.589919 + 0.807462i \(0.299160\pi\)
−0.589919 + 0.807462i \(0.700840\pi\)
\(282\) 0 0
\(283\) 18.0000 + 18.0000i 1.06999 + 1.06999i 0.997359 + 0.0726300i \(0.0231392\pi\)
0.0726300 + 0.997359i \(0.476861\pi\)
\(284\) 3.75736 0.222958
\(285\) 0 0
\(286\) 0.686292 0.0405813
\(287\) 0.585786 + 0.585786i 0.0345779 + 0.0345779i
\(288\) 0 0
\(289\) 21.9706i 1.29239i
\(290\) 0 0
\(291\) 0 0
\(292\) −6.00000 + 6.00000i −0.351123 + 0.351123i
\(293\) −5.51472 + 5.51472i −0.322173 + 0.322173i −0.849600 0.527427i \(-0.823157\pi\)
0.527427 + 0.849600i \(0.323157\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 11.4142i 0.663438i
\(297\) 0 0
\(298\) −12.2426 12.2426i −0.709197 0.709197i
\(299\) 0.970563 0.0561291
\(300\) 0 0
\(301\) −5.07107 −0.292291
\(302\) 6.58579 + 6.58579i 0.378969 + 0.378969i
\(303\) 0 0
\(304\) 7.07107i 0.405554i
\(305\) 0 0
\(306\) 0 0
\(307\) 24.4853 24.4853i 1.39745 1.39745i 0.590169 0.807279i \(-0.299061\pi\)
0.807279 0.590169i \(-0.200939\pi\)
\(308\) 0.585786 0.585786i 0.0333783 0.0333783i
\(309\) 0 0
\(310\) 0 0
\(311\) 16.0000i 0.907277i 0.891186 + 0.453638i \(0.149874\pi\)
−0.891186 + 0.453638i \(0.850126\pi\)
\(312\) 0 0
\(313\) 8.34315 + 8.34315i 0.471582 + 0.471582i 0.902426 0.430844i \(-0.141784\pi\)
−0.430844 + 0.902426i \(0.641784\pi\)
\(314\) −7.65685 −0.432101
\(315\) 0 0
\(316\) 9.31371 0.523937
\(317\) −3.75736 3.75736i −0.211034 0.211034i 0.593672 0.804707i \(-0.297677\pi\)
−0.804707 + 0.593672i \(0.797677\pi\)
\(318\) 0 0
\(319\) 7.31371i 0.409489i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.828427 0.828427i 0.0461664 0.0461664i
\(323\) −31.2132 + 31.2132i −1.73675 + 1.73675i
\(324\) 0 0
\(325\) 0 0
\(326\) 21.0711i 1.16702i
\(327\) 0 0
\(328\) −0.585786 0.585786i −0.0323446 0.0323446i
\(329\) −5.07107 −0.279577
\(330\) 0 0
\(331\) −30.1421 −1.65676 −0.828381 0.560165i \(-0.810738\pi\)
−0.828381 + 0.560165i \(0.810738\pi\)
\(332\) −1.65685 1.65685i −0.0909317 0.0909317i
\(333\) 0 0
\(334\) 18.2426i 0.998193i
\(335\) 0 0
\(336\) 0 0
\(337\) 18.4853 18.4853i 1.00696 1.00696i 0.00698181 0.999976i \(-0.497778\pi\)
0.999976 0.00698181i \(-0.00222240\pi\)
\(338\) 8.70711 8.70711i 0.473604 0.473604i
\(339\) 0 0
\(340\) 0 0
\(341\) 2.62742i 0.142283i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 5.07107 0.273414
\(345\) 0 0
\(346\) −11.3137 −0.608229
\(347\) 9.17157 + 9.17157i 0.492356 + 0.492356i 0.909048 0.416692i \(-0.136811\pi\)
−0.416692 + 0.909048i \(0.636811\pi\)
\(348\) 0 0
\(349\) 16.7279i 0.895425i −0.894178 0.447713i \(-0.852239\pi\)
0.894178 0.447713i \(-0.147761\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.585786 + 0.585786i −0.0312225 + 0.0312225i
\(353\) 21.3848 21.3848i 1.13820 1.13820i 0.149424 0.988773i \(-0.452258\pi\)
0.988773 0.149424i \(-0.0477418\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 9.31371i 0.493626i
\(357\) 0 0
\(358\) −6.58579 6.58579i −0.348070 0.348070i
\(359\) −4.72792 −0.249530 −0.124765 0.992186i \(-0.539818\pi\)
−0.124765 + 0.992186i \(0.539818\pi\)
\(360\) 0 0
\(361\) −31.0000 −1.63158
\(362\) 2.17157 + 2.17157i 0.114135 + 0.114135i
\(363\) 0 0
\(364\) 0.828427i 0.0434214i
\(365\) 0 0
\(366\) 0 0
\(367\) −20.0000 + 20.0000i −1.04399 + 1.04399i −0.0450047 + 0.998987i \(0.514330\pi\)
−0.998987 + 0.0450047i \(0.985670\pi\)
\(368\) −0.828427 + 0.828427i −0.0431847 + 0.0431847i
\(369\) 0 0
\(370\) 0 0
\(371\) 1.17157i 0.0608250i
\(372\) 0 0
\(373\) 2.75736 + 2.75736i 0.142771 + 0.142771i 0.774880 0.632109i \(-0.217810\pi\)
−0.632109 + 0.774880i \(0.717810\pi\)
\(374\) −5.17157 −0.267416
\(375\) 0 0
\(376\) 5.07107 0.261520
\(377\) −5.17157 5.17157i −0.266350 0.266350i
\(378\) 0 0
\(379\) 5.65685i 0.290573i −0.989390 0.145287i \(-0.953590\pi\)
0.989390 0.145287i \(-0.0464104\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7.48528 7.48528i 0.382980 0.382980i
\(383\) 3.24264 3.24264i 0.165691 0.165691i −0.619391 0.785082i \(-0.712621\pi\)
0.785082 + 0.619391i \(0.212621\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.48528i 0.431889i
\(387\) 0 0
\(388\) −0.242641 0.242641i −0.0123182 0.0123182i
\(389\) −17.3137 −0.877840 −0.438920 0.898526i \(-0.644639\pi\)
−0.438920 + 0.898526i \(0.644639\pi\)
\(390\) 0 0
\(391\) −7.31371 −0.369870
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 12.4853i 0.628999i
\(395\) 0 0
\(396\) 0 0
\(397\) −22.5858 + 22.5858i −1.13355 + 1.13355i −0.143965 + 0.989583i \(0.545985\pi\)
−0.989583 + 0.143965i \(0.954015\pi\)
\(398\) 8.24264 8.24264i 0.413166 0.413166i
\(399\) 0 0
\(400\) 0 0
\(401\) 16.9289i 0.845391i 0.906272 + 0.422695i \(0.138916\pi\)
−0.906272 + 0.422695i \(0.861084\pi\)
\(402\) 0 0
\(403\) −1.85786 1.85786i −0.0925468 0.0925468i
\(404\) 15.6569 0.778958
\(405\) 0 0
\(406\) −8.82843 −0.438147
\(407\) 6.68629 + 6.68629i 0.331427 + 0.331427i
\(408\) 0 0
\(409\) 14.6863i 0.726190i 0.931752 + 0.363095i \(0.118280\pi\)
−0.931752 + 0.363095i \(0.881720\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.585786 0.585786i 0.0288596 0.0288596i
\(413\) −5.65685 + 5.65685i −0.278356 + 0.278356i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.828427i 0.0406170i
\(417\) 0 0
\(418\) −4.14214 4.14214i −0.202598 0.202598i
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −0.142136 −0.00692727 −0.00346363 0.999994i \(-0.501103\pi\)
−0.00346363 + 0.999994i \(0.501103\pi\)
\(422\) 14.4853 + 14.4853i 0.705132 + 0.705132i
\(423\) 0 0
\(424\) 1.17157i 0.0568966i
\(425\) 0 0
\(426\) 0 0
\(427\) 6.65685 6.65685i 0.322148 0.322148i
\(428\) −5.07107 + 5.07107i −0.245119 + 0.245119i
\(429\) 0 0
\(430\) 0 0
\(431\) 29.2132i 1.40715i −0.710621 0.703575i \(-0.751586\pi\)
0.710621 0.703575i \(-0.248414\pi\)
\(432\) 0 0
\(433\) −15.7574 15.7574i −0.757250 0.757250i 0.218571 0.975821i \(-0.429861\pi\)
−0.975821 + 0.218571i \(0.929861\pi\)
\(434\) −3.17157 −0.152240
\(435\) 0 0
\(436\) 8.14214 0.389938
\(437\) −5.85786 5.85786i −0.280220 0.280220i
\(438\) 0 0
\(439\) 13.7990i 0.658590i 0.944227 + 0.329295i \(0.106811\pi\)
−0.944227 + 0.329295i \(0.893189\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3.65685 3.65685i 0.173939 0.173939i
\(443\) −7.51472 + 7.51472i −0.357035 + 0.357035i −0.862719 0.505684i \(-0.831240\pi\)
0.505684 + 0.862719i \(0.331240\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 16.8284i 0.796849i
\(447\) 0 0
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) 23.7574 1.12118 0.560590 0.828094i \(-0.310575\pi\)
0.560590 + 0.828094i \(0.310575\pi\)
\(450\) 0 0
\(451\) 0.686292 0.0323162
\(452\) −2.58579 2.58579i −0.121625 0.121625i
\(453\) 0 0
\(454\) 22.1421i 1.03918i
\(455\) 0 0
\(456\) 0 0
\(457\) −24.4853 + 24.4853i −1.14537 + 1.14537i −0.157921 + 0.987452i \(0.550479\pi\)
−0.987452 + 0.157921i \(0.949521\pi\)
\(458\) 13.4853 13.4853i 0.630126 0.630126i
\(459\) 0 0
\(460\) 0 0
\(461\) 14.6863i 0.684009i 0.939698 + 0.342004i \(0.111106\pi\)
−0.939698 + 0.342004i \(0.888894\pi\)
\(462\) 0 0
\(463\) −22.4853 22.4853i −1.04498 1.04498i −0.998940 0.0460401i \(-0.985340\pi\)
−0.0460401 0.998940i \(-0.514660\pi\)
\(464\) 8.82843 0.409849
\(465\) 0 0
\(466\) 3.65685 0.169401
\(467\) −1.65685 1.65685i −0.0766701 0.0766701i 0.667732 0.744402i \(-0.267265\pi\)
−0.744402 + 0.667732i \(0.767265\pi\)
\(468\) 0 0
\(469\) 3.41421i 0.157654i
\(470\) 0 0
\(471\) 0 0
\(472\) 5.65685 5.65685i 0.260378 0.260378i
\(473\) −2.97056 + 2.97056i −0.136587 + 0.136587i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.24264i 0.286131i
\(477\) 0 0
\(478\) 12.1716 + 12.1716i 0.556715 + 0.556715i
\(479\) 1.65685 0.0757036 0.0378518 0.999283i \(-0.487949\pi\)
0.0378518 + 0.999283i \(0.487949\pi\)
\(480\) 0 0
\(481\) −9.45584 −0.431149
\(482\) 2.58579 + 2.58579i 0.117779 + 0.117779i
\(483\) 0 0
\(484\) 10.3137i 0.468805i
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0000 20.0000i 0.906287 0.906287i −0.0896838 0.995970i \(-0.528586\pi\)
0.995970 + 0.0896838i \(0.0285856\pi\)
\(488\) −6.65685 + 6.65685i −0.301342 + 0.301342i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.9706i 0.495095i 0.968876 + 0.247547i \(0.0796246\pi\)
−0.968876 + 0.247547i \(0.920375\pi\)
\(492\) 0 0
\(493\) 38.9706 + 38.9706i 1.75515 + 1.75515i
\(494\) 5.85786 0.263558
\(495\) 0 0
\(496\) 3.17157 0.142408
\(497\) −2.65685 2.65685i −0.119176 0.119176i
\(498\) 0 0
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 19.0711 19.0711i 0.851183 0.851183i
\(503\) −17.5858 + 17.5858i −0.784111 + 0.784111i −0.980522 0.196410i \(-0.937072\pi\)
0.196410 + 0.980522i \(0.437072\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.970563i 0.0431468i
\(507\) 0 0
\(508\) −6.82843 6.82843i −0.302962 0.302962i
\(509\) 29.6569 1.31452 0.657258 0.753665i \(-0.271716\pi\)
0.657258 + 0.753665i \(0.271716\pi\)
\(510\) 0 0
\(511\) 8.48528 0.375367
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 18.2426i 0.804648i
\(515\) 0 0
\(516\) 0 0
\(517\) −2.97056 + 2.97056i −0.130645 + 0.130645i
\(518\) −8.07107 + 8.07107i −0.354622 + 0.354622i
\(519\) 0 0
\(520\) 0 0
\(521\) 26.9706i 1.18160i −0.806817 0.590801i \(-0.798812\pi\)
0.806817 0.590801i \(-0.201188\pi\)
\(522\) 0 0
\(523\) 26.2843 + 26.2843i 1.14933 + 1.14933i 0.986684 + 0.162647i \(0.0520030\pi\)
0.162647 + 0.986684i \(0.447997\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −31.1127 −1.35658
\(527\) 14.0000 + 14.0000i 0.609850 + 0.609850i
\(528\) 0 0
\(529\) 21.6274i 0.940322i
\(530\) 0 0
\(531\) 0 0
\(532\) 5.00000 5.00000i 0.216777 0.216777i
\(533\) −0.485281 + 0.485281i −0.0210199 + 0.0210199i
\(534\) 0 0
\(535\) 0 0
\(536\) 3.41421i 0.147472i
\(537\) 0 0
\(538\) −0.928932 0.928932i −0.0400491 0.0400491i
\(539\) −0.828427 −0.0356829
\(540\) 0 0
\(541\) 26.4853 1.13869 0.569346 0.822098i \(-0.307197\pi\)
0.569346 + 0.822098i \(0.307197\pi\)
\(542\) 9.07107 + 9.07107i 0.389636 + 0.389636i
\(543\) 0 0
\(544\) 6.24264i 0.267651i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.72792 + 1.72792i −0.0738806 + 0.0738806i −0.743082 0.669201i \(-0.766637\pi\)
0.669201 + 0.743082i \(0.266637\pi\)
\(548\) 13.0711 13.0711i 0.558368 0.558368i
\(549\) 0 0
\(550\) 0 0
\(551\) 62.4264i 2.65945i
\(552\) 0 0
\(553\) −6.58579 6.58579i −0.280056 0.280056i
\(554\) 5.55635 0.236067
\(555\) 0 0
\(556\) 8.24264 0.349566
\(557\) −21.8995 21.8995i −0.927911 0.927911i 0.0696594 0.997571i \(-0.477809\pi\)
−0.997571 + 0.0696594i \(0.977809\pi\)
\(558\) 0 0
\(559\) 4.20101i 0.177684i
\(560\) 0 0
\(561\) 0 0
\(562\) −19.1421 + 19.1421i −0.807462 + 0.807462i
\(563\) 8.14214 8.14214i 0.343150 0.343150i −0.514400 0.857550i \(-0.671985\pi\)
0.857550 + 0.514400i \(0.171985\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 25.4558i 1.06999i
\(567\) 0 0
\(568\) 2.65685 + 2.65685i 0.111479 + 0.111479i
\(569\) −26.3848 −1.10611 −0.553054 0.833146i \(-0.686538\pi\)
−0.553054 + 0.833146i \(0.686538\pi\)
\(570\) 0 0
\(571\) −24.9706 −1.04499 −0.522493 0.852644i \(-0.674998\pi\)
−0.522493 + 0.852644i \(0.674998\pi\)
\(572\) 0.485281 + 0.485281i 0.0202906 + 0.0202906i
\(573\) 0 0
\(574\) 0.828427i 0.0345779i
\(575\) 0 0
\(576\) 0 0
\(577\) −16.8284 + 16.8284i −0.700577 + 0.700577i −0.964534 0.263958i \(-0.914972\pi\)
0.263958 + 0.964534i \(0.414972\pi\)
\(578\) −15.5355 + 15.5355i −0.646193 + 0.646193i
\(579\) 0 0
\(580\) 0 0
\(581\) 2.34315i 0.0972101i
\(582\) 0 0
\(583\) 0.686292 + 0.686292i 0.0284233 + 0.0284233i
\(584\) −8.48528 −0.351123
\(585\) 0 0
\(586\) −7.79899 −0.322173
\(587\) 14.0000 + 14.0000i 0.577842 + 0.577842i 0.934308 0.356466i \(-0.116019\pi\)
−0.356466 + 0.934308i \(0.616019\pi\)
\(588\) 0 0
\(589\) 22.4264i 0.924064i
\(590\) 0 0
\(591\) 0 0
\(592\) 8.07107 8.07107i 0.331719 0.331719i
\(593\) 11.5858 11.5858i 0.475771 0.475771i −0.428005 0.903776i \(-0.640783\pi\)
0.903776 + 0.428005i \(0.140783\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 17.3137i 0.709197i
\(597\) 0 0
\(598\) 0.686292 + 0.686292i 0.0280645 + 0.0280645i
\(599\) −19.0711 −0.779223 −0.389611 0.920979i \(-0.627391\pi\)
−0.389611 + 0.920979i \(0.627391\pi\)
\(600\) 0 0
\(601\) −18.0000 −0.734235 −0.367118 0.930175i \(-0.619655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(602\) −3.58579 3.58579i −0.146146 0.146146i
\(603\) 0 0
\(604\) 9.31371i 0.378969i
\(605\) 0 0
\(606\) 0 0
\(607\) 24.3848 24.3848i 0.989748 0.989748i −0.0102004 0.999948i \(-0.503247\pi\)
0.999948 + 0.0102004i \(0.00324696\pi\)
\(608\) −5.00000 + 5.00000i −0.202777 + 0.202777i
\(609\) 0 0
\(610\) 0 0
\(611\) 4.20101i 0.169955i
\(612\) 0 0
\(613\) −6.41421 6.41421i −0.259068 0.259068i 0.565607 0.824675i \(-0.308642\pi\)
−0.824675 + 0.565607i \(0.808642\pi\)
\(614\) 34.6274 1.39745
\(615\) 0 0
\(616\) 0.828427 0.0333783
\(617\) −27.4142 27.4142i −1.10365 1.10365i −0.993966 0.109689i \(-0.965015\pi\)
−0.109689 0.993966i \(-0.534985\pi\)
\(618\) 0 0
\(619\) 18.8701i 0.758452i 0.925304 + 0.379226i \(0.123810\pi\)
−0.925304 + 0.379226i \(0.876190\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −11.3137 + 11.3137i −0.453638 + 0.453638i
\(623\) 6.58579 6.58579i 0.263854 0.263854i
\(624\) 0 0
\(625\) 0 0
\(626\) 11.7990i 0.471582i
\(627\) 0 0
\(628\) −5.41421 5.41421i −0.216051 0.216051i
\(629\) 71.2548 2.84112
\(630\) 0 0
\(631\) −28.9706 −1.15330 −0.576650 0.816991i \(-0.695640\pi\)
−0.576650 + 0.816991i \(0.695640\pi\)
\(632\) 6.58579 + 6.58579i 0.261969 + 0.261969i
\(633\) 0 0
\(634\) 5.31371i 0.211034i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.585786 0.585786i 0.0232097 0.0232097i
\(638\) −5.17157 + 5.17157i −0.204745 + 0.204745i
\(639\) 0 0
\(640\) 0 0
\(641\) 24.5269i 0.968755i −0.874859 0.484377i \(-0.839046\pi\)
0.874859 0.484377i \(-0.160954\pi\)
\(642\) 0 0
\(643\) −28.1421 28.1421i −1.10982 1.10982i −0.993174 0.116644i \(-0.962786\pi\)
−0.116644 0.993174i \(-0.537214\pi\)
\(644\) 1.17157 0.0461664
\(645\) 0 0
\(646\) −44.1421 −1.73675
\(647\) 24.2132 + 24.2132i 0.951919 + 0.951919i 0.998896 0.0469767i \(-0.0149587\pi\)
−0.0469767 + 0.998896i \(0.514959\pi\)
\(648\) 0 0
\(649\) 6.62742i 0.260149i
\(650\) 0 0
\(651\) 0 0
\(652\) −14.8995 + 14.8995i −0.583509 + 0.583509i
\(653\) −5.41421 + 5.41421i −0.211875 + 0.211875i −0.805063 0.593189i \(-0.797869\pi\)
0.593189 + 0.805063i \(0.297869\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.828427i 0.0323446i
\(657\) 0 0
\(658\) −3.58579 3.58579i −0.139789 0.139789i
\(659\) −21.7990 −0.849168 −0.424584 0.905389i \(-0.639580\pi\)
−0.424584 + 0.905389i \(0.639580\pi\)
\(660\) 0 0
\(661\) −36.2426 −1.40968 −0.704838 0.709369i \(-0.748980\pi\)
−0.704838 + 0.709369i \(0.748980\pi\)
\(662\) −21.3137 21.3137i −0.828381 0.828381i
\(663\) 0 0
\(664\) 2.34315i 0.0909317i
\(665\) 0 0
\(666\) 0 0
\(667\) −7.31371 + 7.31371i −0.283188 + 0.283188i
\(668\) 12.8995 12.8995i 0.499096 0.499096i
\(669\) 0 0
\(670\) 0 0
\(671\) 7.79899i 0.301077i
\(672\) 0 0
\(673\) −25.7990 25.7990i −0.994478 0.994478i 0.00550686 0.999985i \(-0.498247\pi\)
−0.999985 + 0.00550686i \(0.998247\pi\)
\(674\) 26.1421 1.00696
\(675\) 0 0
\(676\) 12.3137 0.473604
\(677\) −24.4853 24.4853i −0.941046 0.941046i 0.0573106 0.998356i \(-0.481747\pi\)
−0.998356 + 0.0573106i \(0.981747\pi\)
\(678\) 0 0
\(679\) 0.343146i 0.0131687i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.85786 + 1.85786i −0.0711413 + 0.0711413i
\(683\) 15.8995 15.8995i 0.608377 0.608377i −0.334145 0.942522i \(-0.608447\pi\)
0.942522 + 0.334145i \(0.108447\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) 3.58579 + 3.58579i 0.136707 + 0.136707i
\(689\) −0.970563 −0.0369755
\(690\) 0 0
\(691\) 25.2132 0.959155 0.479578 0.877499i \(-0.340790\pi\)
0.479578 + 0.877499i \(0.340790\pi\)
\(692\) −8.00000 8.00000i −0.304114 0.304114i
\(693\) 0 0
\(694\) 12.9706i 0.492356i
\(695\) 0 0
\(696\) 0 0
\(697\) 3.65685 3.65685i 0.138513 0.138513i
\(698\) 11.8284 11.8284i 0.447713 0.447713i
\(699\) 0 0
\(700\) 0 0
\(701\) 9.51472i 0.359366i −0.983725 0.179683i \(-0.942493\pi\)
0.983725 0.179683i \(-0.0575072\pi\)
\(702\) 0 0
\(703\) 57.0711 + 57.0711i 2.15248 + 2.15248i
\(704\) −0.828427 −0.0312225
\(705\) 0 0
\(706\) 30.2426 1.13820
\(707\) −11.0711 11.0711i −0.416370 0.416370i
\(708\) 0 0
\(709\) 17.3137i 0.650230i 0.945674 + 0.325115i \(0.105403\pi\)
−0.945674 + 0.325115i \(0.894597\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.58579 + 6.58579i −0.246813 + 0.246813i
\(713\) −2.62742 + 2.62742i −0.0983975 + 0.0983975i
\(714\) 0 0
\(715\) 0 0
\(716\) 9.31371i 0.348070i
\(717\) 0 0
\(718\) −3.34315 3.34315i −0.124765 0.124765i
\(719\) 45.4558 1.69522 0.847608 0.530622i \(-0.178042\pi\)
0.847608 + 0.530622i \(0.178042\pi\)
\(720\) 0 0
\(721\) −0.828427 −0.0308522
\(722\) −21.9203 21.9203i −0.815789 0.815789i
\(723\) 0 0
\(724\) 3.07107i 0.114135i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.75736 + 1.75736i −0.0651768 + 0.0651768i −0.738944 0.673767i \(-0.764675\pi\)
0.673767 + 0.738944i \(0.264675\pi\)
\(728\) −0.585786 + 0.585786i −0.0217107 + 0.0217107i
\(729\) 0 0
\(730\) 0 0
\(731\) 31.6569i 1.17087i
\(732\) 0 0
\(733\) −4.72792 4.72792i −0.174630 0.174630i 0.614380 0.789010i \(-0.289406\pi\)
−0.789010 + 0.614380i \(0.789406\pi\)
\(734\) −28.2843 −1.04399
\(735\) 0 0
\(736\) −1.17157 −0.0431847
\(737\) −2.00000 2.00000i −0.0736709 0.0736709i
\(738\) 0 0
\(739\) 42.6274i 1.56807i 0.620714 + 0.784037i \(0.286843\pi\)
−0.620714 + 0.784037i \(0.713157\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.828427 + 0.828427i −0.0304125 + 0.0304125i
\(743\) −10.1421 + 10.1421i −0.372079 + 0.372079i −0.868234 0.496155i \(-0.834745\pi\)
0.496155 + 0.868234i \(0.334745\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.89949i 0.142771i
\(747\) 0 0
\(748\) −3.65685 3.65685i −0.133708 0.133708i
\(749\) 7.17157 0.262044
\(750\) 0 0
\(751\) 11.0294 0.402470 0.201235 0.979543i \(-0.435505\pi\)
0.201235 + 0.979543i \(0.435505\pi\)
\(752\) 3.58579 + 3.58579i 0.130760 + 0.130760i
\(753\) 0 0
\(754\) 7.31371i 0.266350i
\(755\) 0 0
\(756\) 0 0
\(757\) 9.92893 9.92893i 0.360873 0.360873i −0.503261 0.864134i \(-0.667867\pi\)
0.864134 + 0.503261i \(0.167867\pi\)
\(758\) 4.00000 4.00000i 0.145287 0.145287i
\(759\) 0 0
\(760\) 0 0
\(761\) 4.34315i 0.157439i 0.996897 + 0.0787195i \(0.0250831\pi\)
−0.996897 + 0.0787195i \(0.974917\pi\)
\(762\) 0 0
\(763\) −5.75736 5.75736i −0.208430 0.208430i
\(764\) 10.5858 0.382980
\(765\) 0 0
\(766\) 4.58579 0.165691
\(767\) −4.68629 4.68629i −0.169212 0.169212i
\(768\) 0 0
\(769\) 16.1421i 0.582100i 0.956708 + 0.291050i \(0.0940047\pi\)
−0.956708 + 0.291050i \(0.905995\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000 6.00000i 0.215945 0.215945i
\(773\) 35.9411 35.9411i 1.29271 1.29271i 0.359610 0.933103i \(-0.382910\pi\)
0.933103 0.359610i \(-0.117090\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0.343146i 0.0123182i
\(777\) 0 0
\(778\) −12.2426 12.2426i −0.438920 0.438920i
\(779\) 5.85786 0.209880
\(780\) 0 0
\(781\) −3.11270 −0.111381
\(782\) −5.17157 5.17157i −0.184935 0.184935i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) −12.6863 + 12.6863i −0.452217 + 0.452217i −0.896090 0.443872i \(-0.853604\pi\)
0.443872 + 0.896090i \(0.353604\pi\)
\(788\) 8.82843 8.82843i 0.314500 0.314500i
\(789\) 0 0
\(790\) 0 0
\(791\) 3.65685i 0.130023i
\(792\) 0 0
\(793\) 5.51472 + 5.51472i 0.195833 + 0.195833i
\(794\) −31.9411 −1.13355
\(795\) 0 0
\(796\) 11.6569 0.413166
\(797\) −35.7990 35.7990i −1.26807 1.26807i −0.947086 0.320979i \(-0.895988\pi\)
−0.320979 0.947086i \(-0.604012\pi\)
\(798\) 0 0
\(799\) 31.6569i 1.11994i
\(800\) 0 0
\(801\) 0 0
\(802\) −11.9706 + 11.9706i −0.422695 + 0.422695i
\(803\) 4.97056 4.97056i 0.175407 0.175407i
\(804\) 0 0
\(