Properties

Label 930.2.d.e.559.1
Level $930$
Weight $2$
Character 930.559
Analytic conductor $7.426$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 930.559
Dual form 930.2.d.e.559.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} -2.00000i q^{13} -2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -6.00000i q^{17} +1.00000i q^{18} -8.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +2.00000 q^{21} +6.00000i q^{22} +4.00000i q^{23} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} -2.00000 q^{26} -1.00000i q^{27} +2.00000i q^{28} +4.00000 q^{29} +(2.00000 - 1.00000i) q^{30} -1.00000 q^{31} -1.00000i q^{32} -6.00000i q^{33} -6.00000 q^{34} +(-2.00000 - 4.00000i) q^{35} +1.00000 q^{36} -2.00000i q^{37} +8.00000i q^{38} +2.00000 q^{39} +(1.00000 + 2.00000i) q^{40} +2.00000 q^{41} -2.00000i q^{42} -4.00000i q^{43} +6.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +4.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +2.00000i q^{52} +10.0000i q^{53} -1.00000 q^{54} +(-12.0000 + 6.00000i) q^{55} +2.00000 q^{56} -8.00000i q^{57} -4.00000i q^{58} -6.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} -14.0000 q^{61} +1.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} -6.00000 q^{66} -4.00000i q^{67} +6.00000i q^{68} -4.00000 q^{69} +(-4.00000 + 2.00000i) q^{70} +16.0000 q^{71} -1.00000i q^{72} -8.00000i q^{73} -2.00000 q^{74} +(4.00000 + 3.00000i) q^{75} +8.00000 q^{76} +12.0000i q^{77} -2.00000i q^{78} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -2.00000i q^{82} -4.00000i q^{83} -2.00000 q^{84} +(-6.00000 - 12.0000i) q^{85} -4.00000 q^{86} +4.00000i q^{87} -6.00000i q^{88} -10.0000 q^{89} +(1.00000 + 2.00000i) q^{90} -4.00000 q^{91} -4.00000i q^{92} -1.00000i q^{93} -8.00000 q^{94} +(-16.0000 + 8.00000i) q^{95} +1.00000 q^{96} -16.0000i q^{97} -3.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} - 12 q^{11} - 4 q^{14} + 2 q^{15} + 2 q^{16} - 16 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} + 6 q^{25} - 4 q^{26} + 8 q^{29} + 4 q^{30} - 2 q^{31} - 12 q^{34} - 4 q^{35} + 2 q^{36} + 4 q^{39} + 2 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{45} + 8 q^{46} + 6 q^{49} - 8 q^{50} + 12 q^{51} - 2 q^{54} - 24 q^{55} + 4 q^{56} - 12 q^{59} - 2 q^{60} - 28 q^{61} - 2 q^{64} - 4 q^{65} - 12 q^{66} - 8 q^{69} - 8 q^{70} + 32 q^{71} - 4 q^{74} + 8 q^{75} + 16 q^{76} + 4 q^{80} + 2 q^{81} - 4 q^{84} - 12 q^{85} - 8 q^{86} - 20 q^{89} + 2 q^{90} - 8 q^{91} - 16 q^{94} - 32 q^{95} + 2 q^{96} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 1.00000 0.408248
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 6.00000i 1.45521i −0.685994 0.727607i \(-0.740633\pi\)
0.685994 0.727607i \(-0.259367\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 2.00000 0.436436
\(22\) 6.00000i 1.27920i
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) −1.00000 −0.204124
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −2.00000 −0.392232
\(27\) 1.00000i 0.192450i
\(28\) 2.00000i 0.377964i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 2.00000 1.00000i 0.365148 0.182574i
\(31\) −1.00000 −0.179605
\(32\) 1.00000i 0.176777i
\(33\) 6.00000i 1.04447i
\(34\) −6.00000 −1.02899
\(35\) −2.00000 4.00000i −0.338062 0.676123i
\(36\) 1.00000 0.166667
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 8.00000i 1.29777i
\(39\) 2.00000 0.320256
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 6.00000 0.904534
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 4.00000 0.589768
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 3.00000 0.428571
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 6.00000 0.840168
\(52\) 2.00000i 0.277350i
\(53\) 10.0000i 1.37361i 0.726844 + 0.686803i \(0.240986\pi\)
−0.726844 + 0.686803i \(0.759014\pi\)
\(54\) −1.00000 −0.136083
\(55\) −12.0000 + 6.00000i −1.61808 + 0.809040i
\(56\) 2.00000 0.267261
\(57\) 8.00000i 1.05963i
\(58\) 4.00000i 0.525226i
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) −1.00000 2.00000i −0.129099 0.258199i
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 2.00000i 0.251976i
\(64\) −1.00000 −0.125000
\(65\) −2.00000 4.00000i −0.248069 0.496139i
\(66\) −6.00000 −0.738549
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 6.00000i 0.727607i
\(69\) −4.00000 −0.481543
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 8.00000i 0.936329i −0.883641 0.468165i \(-0.844915\pi\)
0.883641 0.468165i \(-0.155085\pi\)
\(74\) −2.00000 −0.232495
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) 8.00000 0.917663
\(77\) 12.0000i 1.36753i
\(78\) 2.00000i 0.226455i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) −2.00000 −0.218218
\(85\) −6.00000 12.0000i −0.650791 1.30158i
\(86\) −4.00000 −0.431331
\(87\) 4.00000i 0.428845i
\(88\) 6.00000i 0.639602i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 1.00000 + 2.00000i 0.105409 + 0.210819i
\(91\) −4.00000 −0.419314
\(92\) 4.00000i 0.417029i
\(93\) 1.00000i 0.103695i
\(94\) −8.00000 −0.825137
\(95\) −16.0000 + 8.00000i −1.64157 + 0.820783i
\(96\) 1.00000 0.102062
\(97\) 16.0000i 1.62455i −0.583272 0.812277i \(-0.698228\pi\)
0.583272 0.812277i \(-0.301772\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 6.00000 0.603023
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 6.00000i 0.594089i
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 2.00000 0.196116
\(105\) 4.00000 2.00000i 0.390360 0.195180i
\(106\) 10.0000 0.971286
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 6.00000 + 12.0000i 0.572078 + 1.14416i
\(111\) 2.00000 0.189832
\(112\) 2.00000i 0.188982i
\(113\) 18.0000i 1.69330i 0.532152 + 0.846649i \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) −8.00000 −0.749269
\(115\) 4.00000 + 8.00000i 0.373002 + 0.746004i
\(116\) −4.00000 −0.371391
\(117\) 2.00000i 0.184900i
\(118\) 6.00000i 0.552345i
\(119\) −12.0000 −1.10004
\(120\) −2.00000 + 1.00000i −0.182574 + 0.0912871i
\(121\) 25.0000 2.27273
\(122\) 14.0000i 1.26750i
\(123\) 2.00000i 0.180334i
\(124\) 1.00000 0.0898027
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 2.00000 0.178174
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.00000 0.352180
\(130\) −4.00000 + 2.00000i −0.350823 + 0.175412i
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 16.0000i 1.38738i
\(134\) −4.00000 −0.345547
\(135\) −1.00000 2.00000i −0.0860663 0.172133i
\(136\) 6.00000 0.514496
\(137\) 14.0000i 1.19610i 0.801459 + 0.598050i \(0.204058\pi\)
−0.801459 + 0.598050i \(0.795942\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 2.00000 + 4.00000i 0.169031 + 0.338062i
\(141\) 8.00000 0.673722
\(142\) 16.0000i 1.34269i
\(143\) 12.0000i 1.00349i
\(144\) −1.00000 −0.0833333
\(145\) 8.00000 4.00000i 0.664364 0.332182i
\(146\) −8.00000 −0.662085
\(147\) 3.00000i 0.247436i
\(148\) 2.00000i 0.164399i
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 3.00000 4.00000i 0.244949 0.326599i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 8.00000i 0.648886i
\(153\) 6.00000i 0.485071i
\(154\) 12.0000 0.966988
\(155\) −2.00000 + 1.00000i −0.160644 + 0.0803219i
\(156\) −2.00000 −0.160128
\(157\) 6.00000i 0.478852i 0.970915 + 0.239426i \(0.0769593\pi\)
−0.970915 + 0.239426i \(0.923041\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) −1.00000 2.00000i −0.0790569 0.158114i
\(161\) 8.00000 0.630488
\(162\) 1.00000i 0.0785674i
\(163\) 20.0000i 1.56652i −0.621694 0.783260i \(-0.713555\pi\)
0.621694 0.783260i \(-0.286445\pi\)
\(164\) −2.00000 −0.156174
\(165\) −6.00000 12.0000i −0.467099 0.934199i
\(166\) −4.00000 −0.310460
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 9.00000 0.692308
\(170\) −12.0000 + 6.00000i −0.920358 + 0.460179i
\(171\) 8.00000 0.611775
\(172\) 4.00000i 0.304997i
\(173\) 14.0000i 1.06440i 0.846619 + 0.532200i \(0.178635\pi\)
−0.846619 + 0.532200i \(0.821365\pi\)
\(174\) 4.00000 0.303239
\(175\) −8.00000 6.00000i −0.604743 0.453557i
\(176\) −6.00000 −0.452267
\(177\) 6.00000i 0.450988i
\(178\) 10.0000i 0.749532i
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 2.00000 1.00000i 0.149071 0.0745356i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 14.0000i 1.03491i
\(184\) −4.00000 −0.294884
\(185\) −2.00000 4.00000i −0.147043 0.294086i
\(186\) −1.00000 −0.0733236
\(187\) 36.0000i 2.63258i
\(188\) 8.00000i 0.583460i
\(189\) −2.00000 −0.145479
\(190\) 8.00000 + 16.0000i 0.580381 + 1.16076i
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 20.0000i 1.43963i −0.694165 0.719816i \(-0.744226\pi\)
0.694165 0.719816i \(-0.255774\pi\)
\(194\) −16.0000 −1.14873
\(195\) 4.00000 2.00000i 0.286446 0.143223i
\(196\) −3.00000 −0.214286
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 6.00000i 0.426401i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 4.00000 + 3.00000i 0.282843 + 0.212132i
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) 8.00000i 0.561490i
\(204\) −6.00000 −0.420084
\(205\) 4.00000 2.00000i 0.279372 0.139686i
\(206\) −6.00000 −0.418040
\(207\) 4.00000i 0.278019i
\(208\) 2.00000i 0.138675i
\(209\) 48.0000 3.32023
\(210\) −2.00000 4.00000i −0.138013 0.276026i
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 16.0000i 1.09630i
\(214\) 4.00000 0.273434
\(215\) −4.00000 8.00000i −0.272798 0.545595i
\(216\) 1.00000 0.0680414
\(217\) 2.00000i 0.135769i
\(218\) 2.00000i 0.135457i
\(219\) 8.00000 0.540590
\(220\) 12.0000 6.00000i 0.809040 0.404520i
\(221\) −12.0000 −0.807207
\(222\) 2.00000i 0.134231i
\(223\) 14.0000i 0.937509i 0.883328 + 0.468755i \(0.155297\pi\)
−0.883328 + 0.468755i \(0.844703\pi\)
\(224\) −2.00000 −0.133631
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) 18.0000 1.19734
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 8.00000i 0.529813i
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 8.00000 4.00000i 0.527504 0.263752i
\(231\) −12.0000 −0.789542
\(232\) 4.00000i 0.262613i
\(233\) 18.0000i 1.17922i −0.807688 0.589610i \(-0.799282\pi\)
0.807688 0.589610i \(-0.200718\pi\)
\(234\) 2.00000 0.130744
\(235\) −8.00000 16.0000i −0.521862 1.04372i
\(236\) 6.00000 0.390567
\(237\) 0 0
\(238\) 12.0000i 0.777844i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 1.00000 + 2.00000i 0.0645497 + 0.129099i
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 1.00000i 0.0641500i
\(244\) 14.0000 0.896258
\(245\) 6.00000 3.00000i 0.383326 0.191663i
\(246\) 2.00000 0.127515
\(247\) 16.0000i 1.01806i
\(248\) 1.00000i 0.0635001i
\(249\) 4.00000 0.253490
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 24.0000i 1.50887i
\(254\) 2.00000 0.125491
\(255\) 12.0000 6.00000i 0.751469 0.375735i
\(256\) 1.00000 0.0625000
\(257\) 14.0000i 0.873296i 0.899632 + 0.436648i \(0.143834\pi\)
−0.899632 + 0.436648i \(0.856166\pi\)
\(258\) 4.00000i 0.249029i
\(259\) −4.00000 −0.248548
\(260\) 2.00000 + 4.00000i 0.124035 + 0.248069i
\(261\) −4.00000 −0.247594
\(262\) 10.0000i 0.617802i
\(263\) 12.0000i 0.739952i −0.929041 0.369976i \(-0.879366\pi\)
0.929041 0.369976i \(-0.120634\pi\)
\(264\) 6.00000 0.369274
\(265\) 10.0000 + 20.0000i 0.614295 + 1.22859i
\(266\) 16.0000 0.981023
\(267\) 10.0000i 0.611990i
\(268\) 4.00000i 0.244339i
\(269\) 4.00000 0.243884 0.121942 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(270\) −2.00000 + 1.00000i −0.121716 + 0.0608581i
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 6.00000i 0.363803i
\(273\) 4.00000i 0.242091i
\(274\) 14.0000 0.845771
\(275\) −18.0000 + 24.0000i −1.08544 + 1.44725i
\(276\) 4.00000 0.240772
\(277\) 10.0000i 0.600842i −0.953807 0.300421i \(-0.902873\pi\)
0.953807 0.300421i \(-0.0971271\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 1.00000 0.0598684
\(280\) 4.00000 2.00000i 0.239046 0.119523i
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 20.0000i 1.18888i −0.804141 0.594438i \(-0.797374\pi\)
0.804141 0.594438i \(-0.202626\pi\)
\(284\) −16.0000 −0.949425
\(285\) −8.00000 16.0000i −0.473879 0.947758i
\(286\) 12.0000 0.709575
\(287\) 4.00000i 0.236113i
\(288\) 1.00000i 0.0589256i
\(289\) −19.0000 −1.11765
\(290\) −4.00000 8.00000i −0.234888 0.469776i
\(291\) 16.0000 0.937937
\(292\) 8.00000i 0.468165i
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 3.00000 0.174964
\(295\) −12.0000 + 6.00000i −0.698667 + 0.349334i
\(296\) 2.00000 0.116248
\(297\) 6.00000i 0.348155i
\(298\) 12.0000i 0.695141i
\(299\) 8.00000 0.462652
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) −8.00000 −0.461112
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −8.00000 −0.458831
\(305\) −28.0000 + 14.0000i −1.60328 + 0.801638i
\(306\) 6.00000 0.342997
\(307\) 8.00000i 0.456584i 0.973593 + 0.228292i \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) 12.0000i 0.683763i
\(309\) 6.00000 0.341328
\(310\) 1.00000 + 2.00000i 0.0567962 + 0.113592i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 2.00000i 0.113228i
\(313\) 24.0000i 1.35656i 0.734803 + 0.678280i \(0.237274\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 6.00000 0.338600
\(315\) 2.00000 + 4.00000i 0.112687 + 0.225374i
\(316\) 0 0
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 10.0000i 0.560772i
\(319\) −24.0000 −1.34374
\(320\) −2.00000 + 1.00000i −0.111803 + 0.0559017i
\(321\) −4.00000 −0.223258
\(322\) 8.00000i 0.445823i
\(323\) 48.0000i 2.67079i
\(324\) −1.00000 −0.0555556
\(325\) −8.00000 6.00000i −0.443760 0.332820i
\(326\) −20.0000 −1.10770
\(327\) 2.00000i 0.110600i
\(328\) 2.00000i 0.110432i
\(329\) −16.0000 −0.882109
\(330\) −12.0000 + 6.00000i −0.660578 + 0.330289i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 2.00000i 0.109599i
\(334\) 12.0000 0.656611
\(335\) −4.00000 8.00000i −0.218543 0.437087i
\(336\) 2.00000 0.109109
\(337\) 8.00000i 0.435788i 0.975972 + 0.217894i \(0.0699187\pi\)
−0.975972 + 0.217894i \(0.930081\pi\)
\(338\) 9.00000i 0.489535i
\(339\) −18.0000 −0.977626
\(340\) 6.00000 + 12.0000i 0.325396 + 0.650791i
\(341\) 6.00000 0.324918
\(342\) 8.00000i 0.432590i
\(343\) 20.0000i 1.07990i
\(344\) 4.00000 0.215666
\(345\) −8.00000 + 4.00000i −0.430706 + 0.215353i
\(346\) 14.0000 0.752645
\(347\) 4.00000i 0.214731i −0.994220 0.107366i \(-0.965758\pi\)
0.994220 0.107366i \(-0.0342415\pi\)
\(348\) 4.00000i 0.214423i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) −6.00000 + 8.00000i −0.320713 + 0.427618i
\(351\) −2.00000 −0.106752
\(352\) 6.00000i 0.319801i
\(353\) 18.0000i 0.958043i −0.877803 0.479022i \(-0.840992\pi\)
0.877803 0.479022i \(-0.159008\pi\)
\(354\) −6.00000 −0.318896
\(355\) 32.0000 16.0000i 1.69838 0.849192i
\(356\) 10.0000 0.529999
\(357\) 12.0000i 0.635107i
\(358\) 18.0000i 0.951330i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) −1.00000 2.00000i −0.0527046 0.105409i
\(361\) 45.0000 2.36842
\(362\) 10.0000i 0.525588i
\(363\) 25.0000i 1.31216i
\(364\) 4.00000 0.209657
\(365\) −8.00000 16.0000i −0.418739 0.837478i
\(366\) −14.0000 −0.731792
\(367\) 26.0000i 1.35719i 0.734513 + 0.678594i \(0.237411\pi\)
−0.734513 + 0.678594i \(0.762589\pi\)
\(368\) 4.00000i 0.208514i
\(369\) −2.00000 −0.104116
\(370\) −4.00000 + 2.00000i −0.207950 + 0.103975i
\(371\) 20.0000 1.03835
\(372\) 1.00000i 0.0518476i
\(373\) 22.0000i 1.13912i −0.821951 0.569558i \(-0.807114\pi\)
0.821951 0.569558i \(-0.192886\pi\)
\(374\) 36.0000 1.86152
\(375\) 11.0000 + 2.00000i 0.568038 + 0.103280i
\(376\) 8.00000 0.412568
\(377\) 8.00000i 0.412021i
\(378\) 2.00000i 0.102869i
\(379\) −36.0000 −1.84920 −0.924598 0.380945i \(-0.875599\pi\)
−0.924598 + 0.380945i \(0.875599\pi\)
\(380\) 16.0000 8.00000i 0.820783 0.410391i
\(381\) −2.00000 −0.102463
\(382\) 8.00000i 0.409316i
\(383\) 16.0000i 0.817562i −0.912633 0.408781i \(-0.865954\pi\)
0.912633 0.408781i \(-0.134046\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 12.0000 + 24.0000i 0.611577 + 1.22315i
\(386\) −20.0000 −1.01797
\(387\) 4.00000i 0.203331i
\(388\) 16.0000i 0.812277i
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) −2.00000 4.00000i −0.101274 0.202548i
\(391\) 24.0000 1.21373
\(392\) 3.00000i 0.151523i
\(393\) 10.0000i 0.504433i
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) −6.00000 −0.301511
\(397\) 22.0000i 1.10415i −0.833795 0.552074i \(-0.813837\pi\)
0.833795 0.552074i \(-0.186163\pi\)
\(398\) 0 0
\(399\) −16.0000 −0.801002
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 2.00000i 0.0996271i
\(404\) 0 0
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) −8.00000 −0.397033
\(407\) 12.0000i 0.594818i
\(408\) 6.00000i 0.297044i
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) −2.00000 4.00000i −0.0987730 0.197546i
\(411\) −14.0000 −0.690569
\(412\) 6.00000i 0.295599i
\(413\) 12.0000i 0.590481i
\(414\) −4.00000 −0.196589
\(415\) −4.00000 8.00000i −0.196352 0.392705i
\(416\) −2.00000 −0.0980581
\(417\) 20.0000i 0.979404i
\(418\) 48.0000i 2.34776i
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) −4.00000 + 2.00000i −0.195180 + 0.0975900i
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 20.0000i 0.973585i
\(423\) 8.00000i 0.388973i
\(424\) −10.0000 −0.485643
\(425\) −24.0000 18.0000i −1.16417 0.873128i
\(426\) 16.0000 0.775203
\(427\) 28.0000i 1.35501i
\(428\) 4.00000i 0.193347i
\(429\) −12.0000 −0.579365
\(430\) −8.00000 + 4.00000i −0.385794 + 0.192897i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 8.00000i 0.384455i 0.981350 + 0.192228i \(0.0615712\pi\)
−0.981350 + 0.192228i \(0.938429\pi\)
\(434\) 2.00000 0.0960031
\(435\) 4.00000 + 8.00000i 0.191785 + 0.383571i
\(436\) 2.00000 0.0957826
\(437\) 32.0000i 1.53077i
\(438\) 8.00000i 0.382255i
\(439\) −32.0000 −1.52728 −0.763638 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) −6.00000 12.0000i −0.286039 0.572078i
\(441\) −3.00000 −0.142857
\(442\) 12.0000i 0.570782i
\(443\) 4.00000i 0.190046i 0.995475 + 0.0950229i \(0.0302924\pi\)
−0.995475 + 0.0950229i \(0.969708\pi\)
\(444\) −2.00000 −0.0949158
\(445\) −20.0000 + 10.0000i −0.948091 + 0.474045i
\(446\) 14.0000 0.662919
\(447\) 12.0000i 0.567581i
\(448\) 2.00000i 0.0944911i
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 4.00000 + 3.00000i 0.188562 + 0.141421i
\(451\) −12.0000 −0.565058
\(452\) 18.0000i 0.846649i
\(453\) 8.00000i 0.375873i
\(454\) 12.0000 0.563188
\(455\) −8.00000 + 4.00000i −0.375046 + 0.187523i
\(456\) 8.00000 0.374634
\(457\) 12.0000i 0.561336i 0.959805 + 0.280668i \(0.0905560\pi\)
−0.959805 + 0.280668i \(0.909444\pi\)
\(458\) 6.00000i 0.280362i
\(459\) −6.00000 −0.280056
\(460\) −4.00000 8.00000i −0.186501 0.373002i
\(461\) −32.0000 −1.49039 −0.745194 0.666847i \(-0.767643\pi\)
−0.745194 + 0.666847i \(0.767643\pi\)
\(462\) 12.0000i 0.558291i
\(463\) 26.0000i 1.20832i 0.796862 + 0.604161i \(0.206492\pi\)
−0.796862 + 0.604161i \(0.793508\pi\)
\(464\) 4.00000 0.185695
\(465\) −1.00000 2.00000i −0.0463739 0.0927478i
\(466\) −18.0000 −0.833834
\(467\) 4.00000i 0.185098i 0.995708 + 0.0925490i \(0.0295015\pi\)
−0.995708 + 0.0925490i \(0.970499\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) −8.00000 −0.369406
\(470\) −16.0000 + 8.00000i −0.738025 + 0.369012i
\(471\) −6.00000 −0.276465
\(472\) 6.00000i 0.276172i
\(473\) 24.0000i 1.10352i
\(474\) 0 0
\(475\) −24.0000 + 32.0000i −1.10120 + 1.46826i
\(476\) 12.0000 0.550019
\(477\) 10.0000i 0.457869i
\(478\) 20.0000i 0.914779i
\(479\) 40.0000 1.82765 0.913823 0.406112i \(-0.133116\pi\)
0.913823 + 0.406112i \(0.133116\pi\)
\(480\) 2.00000 1.00000i 0.0912871 0.0456435i
\(481\) −4.00000 −0.182384
\(482\) 18.0000i 0.819878i
\(483\) 8.00000i 0.364013i
\(484\) −25.0000 −1.13636
\(485\) −16.0000 32.0000i −0.726523 1.45305i
\(486\) 1.00000 0.0453609
\(487\) 14.0000i 0.634401i 0.948359 + 0.317200i \(0.102743\pi\)
−0.948359 + 0.317200i \(0.897257\pi\)
\(488\) 14.0000i 0.633750i
\(489\) 20.0000 0.904431
\(490\) −3.00000 6.00000i −0.135526 0.271052i
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 2.00000i 0.0901670i
\(493\) 24.0000i 1.08091i
\(494\) 16.0000 0.719874
\(495\) 12.0000 6.00000i 0.539360 0.269680i
\(496\) −1.00000 −0.0449013
\(497\) 32.0000i 1.43540i
\(498\) 4.00000i 0.179244i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) −2.00000 + 11.0000i −0.0894427 + 0.491935i
\(501\) −12.0000 −0.536120
\(502\) 6.00000i 0.267793i
\(503\) 8.00000i 0.356702i −0.983967 0.178351i \(-0.942924\pi\)
0.983967 0.178351i \(-0.0570763\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) −24.0000 −1.06693
\(507\) 9.00000i 0.399704i
\(508\) 2.00000i 0.0887357i
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) −6.00000 12.0000i −0.265684 0.531369i
\(511\) −16.0000 −0.707798
\(512\) 1.00000i 0.0441942i
\(513\) 8.00000i 0.353209i
\(514\) 14.0000 0.617514
\(515\) −6.00000 12.0000i −0.264392 0.528783i
\(516\) −4.00000 −0.176090
\(517\) 48.0000i 2.11104i
\(518\) 4.00000i 0.175750i
\(519\) −14.0000 −0.614532
\(520\) 4.00000 2.00000i 0.175412 0.0877058i
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) 4.00000i 0.175075i
\(523\) 40.0000i 1.74908i −0.484955 0.874539i \(-0.661164\pi\)
0.484955 0.874539i \(-0.338836\pi\)
\(524\) −10.0000 −0.436852
\(525\) 6.00000 8.00000i 0.261861 0.349149i
\(526\) −12.0000 −0.523225
\(527\) 6.00000i 0.261364i
\(528\) 6.00000i 0.261116i
\(529\) 7.00000 0.304348
\(530\) 20.0000 10.0000i 0.868744 0.434372i
\(531\) 6.00000 0.260378
\(532\) 16.0000i 0.693688i
\(533\) 4.00000i 0.173259i
\(534\) −10.0000 −0.432742
\(535\) 4.00000 + 8.00000i 0.172935 + 0.345870i
\(536\) 4.00000 0.172774
\(537\) 18.0000i 0.776757i
\(538\) 4.00000i 0.172452i
\(539\) −18.0000 −0.775315
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) 18.0000 0.773880 0.386940 0.922105i \(-0.373532\pi\)
0.386940 + 0.922105i \(0.373532\pi\)
\(542\) 0 0
\(543\) 10.0000i 0.429141i
\(544\) −6.00000 −0.257248
\(545\) −4.00000 + 2.00000i −0.171341 + 0.0856706i
\(546\) −4.00000 −0.171184
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 14.0000i 0.598050i
\(549\) 14.0000 0.597505
\(550\) 24.0000 + 18.0000i 1.02336 + 0.767523i
\(551\) −32.0000 −1.36325
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) −10.0000 −0.424859
\(555\) 4.00000 2.00000i 0.169791 0.0848953i
\(556\) −20.0000 −0.848189
\(557\) 30.0000i 1.27114i 0.772043 + 0.635570i \(0.219235\pi\)
−0.772043 + 0.635570i \(0.780765\pi\)
\(558\) 1.00000i 0.0423334i
\(559\) −8.00000 −0.338364
\(560\) −2.00000 4.00000i −0.0845154 0.169031i
\(561\) −36.0000 −1.51992
\(562\) 22.0000i 0.928014i
\(563\) 36.0000i 1.51722i −0.651546 0.758610i \(-0.725879\pi\)
0.651546 0.758610i \(-0.274121\pi\)
\(564\) −8.00000 −0.336861
\(565\) 18.0000 + 36.0000i 0.757266 + 1.51453i
\(566\) −20.0000 −0.840663
\(567\) 2.00000i 0.0839921i
\(568\) 16.0000i 0.671345i
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) −16.0000 + 8.00000i −0.670166 + 0.335083i
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 8.00000i 0.334205i
\(574\) −4.00000 −0.166957
\(575\) 16.0000 + 12.0000i 0.667246 + 0.500435i
\(576\) 1.00000 0.0416667
\(577\) 16.0000i 0.666089i −0.942911 0.333044i \(-0.891924\pi\)
0.942911 0.333044i \(-0.108076\pi\)
\(578\) 19.0000i 0.790296i
\(579\) 20.0000 0.831172
\(580\) −8.00000 + 4.00000i −0.332182 + 0.166091i
\(581\) −8.00000 −0.331896
\(582\) 16.0000i 0.663221i
\(583\) 60.0000i 2.48495i
\(584\) 8.00000 0.331042
\(585\) 2.00000 + 4.00000i 0.0826898 + 0.165380i
\(586\) −6.00000 −0.247858
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 3.00000i 0.123718i
\(589\) 8.00000 0.329634
\(590\) 6.00000 + 12.0000i 0.247016 + 0.494032i
\(591\) 18.0000 0.740421
\(592\) 2.00000i 0.0821995i
\(593\) 30.0000i 1.23195i −0.787765 0.615976i \(-0.788762\pi\)
0.787765 0.615976i \(-0.211238\pi\)
\(594\) 6.00000 0.246183
\(595\) −24.0000 + 12.0000i −0.983904 + 0.491952i
\(596\) −12.0000 −0.491539
\(597\) 0 0
\(598\) 8.00000i 0.327144i
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) −3.00000 + 4.00000i −0.122474 + 0.163299i
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 4.00000i 0.162893i
\(604\) −8.00000 −0.325515
\(605\) 50.0000 25.0000i 2.03279 1.01639i
\(606\) 0 0
\(607\) 6.00000i 0.243532i −0.992559 0.121766i \(-0.961144\pi\)
0.992559 0.121766i \(-0.0388558\pi\)
\(608\) 8.00000i 0.324443i
\(609\) 8.00000 0.324176
\(610\) 14.0000 + 28.0000i 0.566843 + 1.13369i
\(611\) −16.0000 −0.647291
\(612\) 6.00000i 0.242536i
\(613\) 30.0000i 1.21169i −0.795583 0.605844i \(-0.792835\pi\)
0.795583 0.605844i \(-0.207165\pi\)
\(614\) 8.00000 0.322854
\(615\) 2.00000 + 4.00000i 0.0806478 + 0.161296i
\(616\) −12.0000 −0.483494
\(617\) 22.0000i 0.885687i −0.896599 0.442843i \(-0.853970\pi\)
0.896599 0.442843i \(-0.146030\pi\)
\(618\) 6.00000i 0.241355i
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 2.00000 1.00000i 0.0803219 0.0401610i
\(621\) 4.00000 0.160514
\(622\) 8.00000i 0.320771i
\(623\) 20.0000i 0.801283i
\(624\) 2.00000 0.0800641
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 24.0000 0.959233
\(627\) 48.0000i 1.91694i
\(628\) 6.00000i 0.239426i
\(629\) −12.0000 −0.478471
\(630\) 4.00000 2.00000i 0.159364 0.0796819i
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 20.0000i 0.794929i
\(634\) 18.0000 0.714871
\(635\) 2.00000 + 4.00000i 0.0793676 + 0.158735i
\(636\) 10.0000 0.396526
\(637\) 6.00000i 0.237729i
\(638\) 24.0000i 0.950169i
\(639\) −16.0000 −0.632950
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 4.00000i 0.157867i
\(643\) 32.0000i 1.26196i −0.775800 0.630978i \(-0.782654\pi\)
0.775800 0.630978i \(-0.217346\pi\)
\(644\) −8.00000 −0.315244
\(645\) 8.00000 4.00000i 0.315000 0.157500i
\(646\) 48.0000 1.88853
\(647\) 32.0000i 1.25805i −0.777385 0.629025i \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 36.0000 1.41312
\(650\) −6.00000 + 8.00000i −0.235339 + 0.313786i
\(651\) −2.00000 −0.0783862
\(652\) 20.0000i 0.783260i
\(653\) 42.0000i 1.64359i −0.569785 0.821794i \(-0.692974\pi\)
0.569785 0.821794i \(-0.307026\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 20.0000 10.0000i 0.781465 0.390732i
\(656\) 2.00000 0.0780869
\(657\) 8.00000i 0.312110i
\(658\) 16.0000i 0.623745i
\(659\) −18.0000 −0.701180 −0.350590 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) 6.00000 + 12.0000i 0.233550 + 0.467099i
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 12.0000i 0.466041i
\(664\) 4.00000 0.155230
\(665\) 16.0000 + 32.0000i 0.620453 + 1.24091i
\(666\) 2.00000 0.0774984
\(667\) 16.0000i 0.619522i
\(668\) 12.0000i 0.464294i
\(669\) −14.0000 −0.541271
\(670\) −8.00000 + 4.00000i −0.309067 + 0.154533i
\(671\) 84.0000 3.24278
\(672\) 2.00000i 0.0771517i
\(673\) 24.0000i 0.925132i 0.886585 + 0.462566i \(0.153071\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 8.00000 0.308148
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) −9.00000 −0.346154
\(677\) 10.0000i 0.384331i 0.981363 + 0.192166i \(0.0615511\pi\)
−0.981363 + 0.192166i \(0.938449\pi\)
\(678\) 18.0000i 0.691286i
\(679\) −32.0000 −1.22805
\(680\) 12.0000 6.00000i 0.460179 0.230089i
\(681\) −12.0000 −0.459841
\(682\) 6.00000i 0.229752i
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) −8.00000 −0.305888
\(685\) 14.0000 + 28.0000i 0.534913 + 1.06983i
\(686\) −20.0000 −0.763604
\(687\) 6.00000i 0.228914i
\(688\) 4.00000i 0.152499i
\(689\) 20.0000 0.761939
\(690\) 4.00000 + 8.00000i 0.152277 + 0.304555i
\(691\) −32.0000 −1.21734 −0.608669 0.793424i \(-0.708296\pi\)
−0.608669 + 0.793424i \(0.708296\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 12.0000i 0.455842i
\(694\) −4.00000 −0.151838
\(695\) 40.0000 20.0000i 1.51729 0.758643i
\(696\) −4.00000 −0.151620
\(697\) 12.0000i 0.454532i
\(698\) 2.00000i 0.0757011i
\(699\) 18.0000 0.680823
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) 16.0000 0.604312 0.302156 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 2.00000i 0.0754851i
\(703\) 16.0000i 0.603451i
\(704\) 6.00000 0.226134
\(705\) 16.0000 8.00000i 0.602595 0.301297i
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) 6.00000i 0.225494i
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) −16.0000 32.0000i −0.600469 1.20094i
\(711\) 0 0
\(712\) 10.0000i 0.374766i
\(713\) 4.00000i 0.149801i
\(714\) −12.0000 −0.449089
\(715\) 12.0000 + 24.0000i 0.448775 + 0.897549i
\(716\) 18.0000 0.672692
\(717\) 20.0000i 0.746914i
\(718\) 12.0000i 0.447836i
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) −12.0000 −0.446903
\(722\) 45.0000i 1.67473i
\(723\) 18.0000i 0.669427i
\(724\) −10.0000 −0.371647
\(725\) 12.0000 16.0000i 0.445669 0.594225i
\(726\) 25.0000 0.927837
\(727\) 38.0000i 1.40934i −0.709534 0.704671i \(-0.751095\pi\)
0.709534 0.704671i \(-0.248905\pi\)
\(728\) 4.00000i 0.148250i
\(729\) −1.00000 −0.0370370
\(730\) −16.0000 + 8.00000i −0.592187 + 0.296093i
\(731\) −24.0000 −0.887672
\(732\) 14.0000i 0.517455i
\(733\) 22.0000i 0.812589i 0.913742 + 0.406294i \(0.133179\pi\)
−0.913742 + 0.406294i \(0.866821\pi\)
\(734\) 26.0000 0.959678
\(735\) 3.00000 + 6.00000i 0.110657 + 0.221313i
\(736\) 4.00000 0.147442
\(737\) 24.0000i 0.884051i
\(738\) 2.00000i 0.0736210i
\(739\) 24.0000 0.882854 0.441427 0.897297i \(-0.354472\pi\)
0.441427 + 0.897297i \(0.354472\pi\)
\(740\) 2.00000 + 4.00000i 0.0735215 + 0.147043i
\(741\) −16.0000 −0.587775
\(742\) 20.0000i 0.734223i
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) 1.00000 0.0366618
\(745\) 24.0000 12.0000i 0.879292 0.439646i
\(746\) −22.0000 −0.805477
\(747\) 4.00000i 0.146352i
\(748\) 36.0000i 1.31629i
\(749\) 8.00000 0.292314
\(750\) 2.00000 11.0000i 0.0730297 0.401663i
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 6.00000i 0.218652i
\(754\) −8.00000 −0.291343
\(755\) 16.0000 8.00000i 0.582300 0.291150i
\(756\) 2.00000 0.0727393
\(757\) 34.0000i 1.23575i −0.786276 0.617876i \(-0.787994\pi\)
0.786276 0.617876i \(-0.212006\pi\)
\(758\) 36.0000i 1.30758i
\(759\) 24.0000 0.871145
\(760\) −8.00000 16.0000i −0.290191 0.580381i
\(761\) −54.0000 −1.95750 −0.978749 0.205061i \(-0.934261\pi\)
−0.978749 + 0.205061i \(0.934261\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 4.00000i 0.144810i
\(764\) −8.00000 −0.289430
\(765\) 6.00000 + 12.0000i 0.216930 + 0.433861i
\(766\) −16.0000 −0.578103
\(767\) 12.0000i 0.433295i
\(768\) 1.00000i 0.0360844i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 24.0000 12.0000i 0.864900 0.432450i
\(771\) −14.0000 −0.504198
\(772\) 20.0000i 0.719816i
\(773\) 34.0000i 1.22290i −0.791285 0.611448i \(-0.790588\pi\)
0.791285 0.611448i \(-0.209412\pi\)
\(774\) 4.00000 0.143777
\(775\) −3.00000 + 4.00000i −0.107763 + 0.143684i
\(776\) 16.0000 0.574367
\(777\) 4.00000i 0.143499i
\(778\) 16.0000i 0.573628i
\(779\) −16.0000 −0.573259
\(780\) −4.00000 + 2.00000i −0.143223 + 0.0716115i
\(781\) −96.0000 −3.43515
\(782\) 24.0000i 0.858238i
\(783\) 4.00000i 0.142948i
\(784\) 3.00000 0.107143
\(785\) 6.00000 + 12.0000i 0.214149 + 0.428298i
\(786\) 10.0000 0.356688