Properties

Label 1110.2.e.a.739.1
Level $1110$
Weight $2$
Character 1110.739
Analytic conductor $8.863$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 739.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1110.739
Dual form 1110.2.e.a.739.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{6} +3.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{6} +3.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} -3.00000 q^{11} -1.00000i q^{12} -4.00000 q^{13} -3.00000i q^{14} +(-1.00000 - 2.00000i) q^{15} +1.00000 q^{16} +7.00000 q^{17} +1.00000 q^{18} -4.00000i q^{19} +(2.00000 - 1.00000i) q^{20} +3.00000 q^{21} +3.00000 q^{22} +6.00000 q^{23} +1.00000i q^{24} +(3.00000 - 4.00000i) q^{25} +4.00000 q^{26} +1.00000i q^{27} +3.00000i q^{28} -9.00000i q^{29} +(1.00000 + 2.00000i) q^{30} -5.00000i q^{31} -1.00000 q^{32} +3.00000i q^{33} -7.00000 q^{34} +(3.00000 + 6.00000i) q^{35} -1.00000 q^{36} +(6.00000 - 1.00000i) q^{37} +4.00000i q^{38} +4.00000i q^{39} +(-2.00000 + 1.00000i) q^{40} +7.00000 q^{41} -3.00000 q^{42} +1.00000 q^{43} -3.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} -6.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} -2.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} -7.00000i q^{51} -4.00000 q^{52} +1.00000i q^{53} -1.00000i q^{54} +(-6.00000 + 3.00000i) q^{55} -3.00000i q^{56} -4.00000 q^{57} +9.00000i q^{58} +6.00000i q^{59} +(-1.00000 - 2.00000i) q^{60} -5.00000i q^{61} +5.00000i q^{62} -3.00000i q^{63} +1.00000 q^{64} +(-8.00000 + 4.00000i) q^{65} -3.00000i q^{66} -2.00000i q^{67} +7.00000 q^{68} -6.00000i q^{69} +(-3.00000 - 6.00000i) q^{70} +12.0000 q^{71} +1.00000 q^{72} -4.00000i q^{73} +(-6.00000 + 1.00000i) q^{74} +(-4.00000 - 3.00000i) q^{75} -4.00000i q^{76} -9.00000i q^{77} -4.00000i q^{78} -4.00000i q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -7.00000 q^{82} -14.0000i q^{83} +3.00000 q^{84} +(14.0000 - 7.00000i) q^{85} -1.00000 q^{86} -9.00000 q^{87} +3.00000 q^{88} +6.00000i q^{89} +(2.00000 - 1.00000i) q^{90} -12.0000i q^{91} +6.00000 q^{92} -5.00000 q^{93} -8.00000i q^{94} +(-4.00000 - 8.00000i) q^{95} +1.00000i q^{96} +7.00000 q^{97} +2.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} + 2q^{4} + 4q^{5} - 2q^{8} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} + 2q^{4} + 4q^{5} - 2q^{8} - 2q^{9} - 4q^{10} - 6q^{11} - 8q^{13} - 2q^{15} + 2q^{16} + 14q^{17} + 2q^{18} + 4q^{20} + 6q^{21} + 6q^{22} + 12q^{23} + 6q^{25} + 8q^{26} + 2q^{30} - 2q^{32} - 14q^{34} + 6q^{35} - 2q^{36} + 12q^{37} - 4q^{40} + 14q^{41} - 6q^{42} + 2q^{43} - 6q^{44} - 4q^{45} - 12q^{46} - 4q^{49} - 6q^{50} - 8q^{52} - 12q^{55} - 8q^{57} - 2q^{60} + 2q^{64} - 16q^{65} + 14q^{68} - 6q^{70} + 24q^{71} + 2q^{72} - 12q^{74} - 8q^{75} + 4q^{80} + 2q^{81} - 14q^{82} + 6q^{84} + 28q^{85} - 2q^{86} - 18q^{87} + 6q^{88} + 4q^{90} + 12q^{92} - 10q^{93} - 8q^{95} + 14q^{97} + 4q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 1.00000i 0.408248i
\(7\) 3.00000i 1.13389i 0.823754 + 0.566947i \(0.191875\pi\)
−0.823754 + 0.566947i \(0.808125\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 3.00000i 0.801784i
\(15\) −1.00000 2.00000i −0.258199 0.516398i
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) 3.00000 0.654654
\(22\) 3.00000 0.639602
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 4.00000 0.784465
\(27\) 1.00000i 0.192450i
\(28\) 3.00000i 0.566947i
\(29\) 9.00000i 1.67126i −0.549294 0.835629i \(-0.685103\pi\)
0.549294 0.835629i \(-0.314897\pi\)
\(30\) 1.00000 + 2.00000i 0.182574 + 0.365148i
\(31\) 5.00000i 0.898027i −0.893525 0.449013i \(-0.851776\pi\)
0.893525 0.449013i \(-0.148224\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.00000i 0.522233i
\(34\) −7.00000 −1.20049
\(35\) 3.00000 + 6.00000i 0.507093 + 1.01419i
\(36\) −1.00000 −0.166667
\(37\) 6.00000 1.00000i 0.986394 0.164399i
\(38\) 4.00000i 0.648886i
\(39\) 4.00000i 0.640513i
\(40\) −2.00000 + 1.00000i −0.316228 + 0.158114i
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) −3.00000 −0.462910
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −3.00000 −0.452267
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) −6.00000 −0.884652
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −2.00000 −0.285714
\(50\) −3.00000 + 4.00000i −0.424264 + 0.565685i
\(51\) 7.00000i 0.980196i
\(52\) −4.00000 −0.554700
\(53\) 1.00000i 0.137361i 0.997639 + 0.0686803i \(0.0218788\pi\)
−0.997639 + 0.0686803i \(0.978121\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −6.00000 + 3.00000i −0.809040 + 0.404520i
\(56\) 3.00000i 0.400892i
\(57\) −4.00000 −0.529813
\(58\) 9.00000i 1.18176i
\(59\) 6.00000i 0.781133i 0.920575 + 0.390567i \(0.127721\pi\)
−0.920575 + 0.390567i \(0.872279\pi\)
\(60\) −1.00000 2.00000i −0.129099 0.258199i
\(61\) 5.00000i 0.640184i −0.947386 0.320092i \(-0.896286\pi\)
0.947386 0.320092i \(-0.103714\pi\)
\(62\) 5.00000i 0.635001i
\(63\) 3.00000i 0.377964i
\(64\) 1.00000 0.125000
\(65\) −8.00000 + 4.00000i −0.992278 + 0.496139i
\(66\) 3.00000i 0.369274i
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) 7.00000 0.848875
\(69\) 6.00000i 0.722315i
\(70\) −3.00000 6.00000i −0.358569 0.717137i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000 0.117851
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) −6.00000 + 1.00000i −0.697486 + 0.116248i
\(75\) −4.00000 3.00000i −0.461880 0.346410i
\(76\) 4.00000i 0.458831i
\(77\) 9.00000i 1.02565i
\(78\) 4.00000i 0.452911i
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) −7.00000 −0.773021
\(83\) 14.0000i 1.53670i −0.640030 0.768350i \(-0.721078\pi\)
0.640030 0.768350i \(-0.278922\pi\)
\(84\) 3.00000 0.327327
\(85\) 14.0000 7.00000i 1.51851 0.759257i
\(86\) −1.00000 −0.107833
\(87\) −9.00000 −0.964901
\(88\) 3.00000 0.319801
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 2.00000 1.00000i 0.210819 0.105409i
\(91\) 12.0000i 1.25794i
\(92\) 6.00000 0.625543
\(93\) −5.00000 −0.518476
\(94\) 8.00000i 0.825137i
\(95\) −4.00000 8.00000i −0.410391 0.820783i
\(96\) 1.00000i 0.102062i
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 2.00000 0.202031
\(99\) 3.00000 0.301511
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 7.00000i 0.693103i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 4.00000 0.392232
\(105\) 6.00000 3.00000i 0.585540 0.292770i
\(106\) 1.00000i 0.0971286i
\(107\) 18.0000i 1.74013i 0.492941 + 0.870063i \(0.335922\pi\)
−0.492941 + 0.870063i \(0.664078\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 11.0000i 1.05361i 0.849987 + 0.526804i \(0.176610\pi\)
−0.849987 + 0.526804i \(0.823390\pi\)
\(110\) 6.00000 3.00000i 0.572078 0.286039i
\(111\) −1.00000 6.00000i −0.0949158 0.569495i
\(112\) 3.00000i 0.283473i
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 4.00000 0.374634
\(115\) 12.0000 6.00000i 1.11901 0.559503i
\(116\) 9.00000i 0.835629i
\(117\) 4.00000 0.369800
\(118\) 6.00000i 0.552345i
\(119\) 21.0000i 1.92507i
\(120\) 1.00000 + 2.00000i 0.0912871 + 0.182574i
\(121\) −2.00000 −0.181818
\(122\) 5.00000i 0.452679i
\(123\) 7.00000i 0.631169i
\(124\) 5.00000i 0.449013i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 3.00000i 0.267261i
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000i 0.0880451i
\(130\) 8.00000 4.00000i 0.701646 0.350823i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 3.00000i 0.261116i
\(133\) 12.0000 1.04053
\(134\) 2.00000i 0.172774i
\(135\) 1.00000 + 2.00000i 0.0860663 + 0.172133i
\(136\) −7.00000 −0.600245
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 6.00000i 0.510754i
\(139\) −15.0000 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(140\) 3.00000 + 6.00000i 0.253546 + 0.507093i
\(141\) 8.00000 0.673722
\(142\) −12.0000 −1.00702
\(143\) 12.0000 1.00349
\(144\) −1.00000 −0.0833333
\(145\) −9.00000 18.0000i −0.747409 1.49482i
\(146\) 4.00000i 0.331042i
\(147\) 2.00000i 0.164957i
\(148\) 6.00000 1.00000i 0.493197 0.0821995i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 4.00000 + 3.00000i 0.326599 + 0.244949i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 4.00000i 0.324443i
\(153\) −7.00000 −0.565916
\(154\) 9.00000i 0.725241i
\(155\) −5.00000 10.0000i −0.401610 0.803219i
\(156\) 4.00000i 0.320256i
\(157\) 7.00000i 0.558661i −0.960195 0.279330i \(-0.909888\pi\)
0.960195 0.279330i \(-0.0901125\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 1.00000 0.0793052
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 18.0000i 1.41860i
\(162\) −1.00000 −0.0785674
\(163\) −9.00000 −0.704934 −0.352467 0.935824i \(-0.614657\pi\)
−0.352467 + 0.935824i \(0.614657\pi\)
\(164\) 7.00000 0.546608
\(165\) 3.00000 + 6.00000i 0.233550 + 0.467099i
\(166\) 14.0000i 1.08661i
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −3.00000 −0.231455
\(169\) 3.00000 0.230769
\(170\) −14.0000 + 7.00000i −1.07375 + 0.536875i
\(171\) 4.00000i 0.305888i
\(172\) 1.00000 0.0762493
\(173\) 9.00000i 0.684257i −0.939653 0.342129i \(-0.888852\pi\)
0.939653 0.342129i \(-0.111148\pi\)
\(174\) 9.00000 0.682288
\(175\) 12.0000 + 9.00000i 0.907115 + 0.680336i
\(176\) −3.00000 −0.226134
\(177\) 6.00000 0.450988
\(178\) 6.00000i 0.449719i
\(179\) 4.00000i 0.298974i −0.988764 0.149487i \(-0.952238\pi\)
0.988764 0.149487i \(-0.0477622\pi\)
\(180\) −2.00000 + 1.00000i −0.149071 + 0.0745356i
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 12.0000i 0.889499i
\(183\) −5.00000 −0.369611
\(184\) −6.00000 −0.442326
\(185\) 11.0000 8.00000i 0.808736 0.588172i
\(186\) 5.00000 0.366618
\(187\) −21.0000 −1.53567
\(188\) 8.00000i 0.583460i
\(189\) −3.00000 −0.218218
\(190\) 4.00000 + 8.00000i 0.290191 + 0.580381i
\(191\) 15.0000i 1.08536i −0.839939 0.542681i \(-0.817409\pi\)
0.839939 0.542681i \(-0.182591\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −7.00000 −0.502571
\(195\) 4.00000 + 8.00000i 0.286446 + 0.572892i
\(196\) −2.00000 −0.142857
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) −3.00000 −0.213201
\(199\) 16.0000i 1.13421i 0.823646 + 0.567105i \(0.191937\pi\)
−0.823646 + 0.567105i \(0.808063\pi\)
\(200\) −3.00000 + 4.00000i −0.212132 + 0.282843i
\(201\) −2.00000 −0.141069
\(202\) −2.00000 −0.140720
\(203\) 27.0000 1.89503
\(204\) 7.00000i 0.490098i
\(205\) 14.0000 7.00000i 0.977802 0.488901i
\(206\) 14.0000 0.975426
\(207\) −6.00000 −0.417029
\(208\) −4.00000 −0.277350
\(209\) 12.0000i 0.830057i
\(210\) −6.00000 + 3.00000i −0.414039 + 0.207020i
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 1.00000i 0.0686803i
\(213\) 12.0000i 0.822226i
\(214\) 18.0000i 1.23045i
\(215\) 2.00000 1.00000i 0.136399 0.0681994i
\(216\) 1.00000i 0.0680414i
\(217\) 15.0000 1.01827
\(218\) 11.0000i 0.745014i
\(219\) −4.00000 −0.270295
\(220\) −6.00000 + 3.00000i −0.404520 + 0.202260i
\(221\) −28.0000 −1.88348
\(222\) 1.00000 + 6.00000i 0.0671156 + 0.402694i
\(223\) 11.0000i 0.736614i 0.929704 + 0.368307i \(0.120063\pi\)
−0.929704 + 0.368307i \(0.879937\pi\)
\(224\) 3.00000i 0.200446i
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) −1.00000 −0.0665190
\(227\) −13.0000 −0.862840 −0.431420 0.902151i \(-0.641987\pi\)
−0.431420 + 0.902151i \(0.641987\pi\)
\(228\) −4.00000 −0.264906
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −12.0000 + 6.00000i −0.791257 + 0.395628i
\(231\) −9.00000 −0.592157
\(232\) 9.00000i 0.590879i
\(233\) 6.00000i 0.393073i 0.980497 + 0.196537i \(0.0629694\pi\)
−0.980497 + 0.196537i \(0.937031\pi\)
\(234\) −4.00000 −0.261488
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) 6.00000i 0.390567i
\(237\) −4.00000 −0.259828
\(238\) 21.0000i 1.36123i
\(239\) 9.00000i 0.582162i −0.956698 0.291081i \(-0.905985\pi\)
0.956698 0.291081i \(-0.0940149\pi\)
\(240\) −1.00000 2.00000i −0.0645497 0.129099i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 2.00000 0.128565
\(243\) 1.00000i 0.0641500i
\(244\) 5.00000i 0.320092i
\(245\) −4.00000 + 2.00000i −0.255551 + 0.127775i
\(246\) 7.00000i 0.446304i
\(247\) 16.0000i 1.01806i
\(248\) 5.00000i 0.317500i
\(249\) −14.0000 −0.887214
\(250\) −2.00000 + 11.0000i −0.126491 + 0.695701i
\(251\) 20.0000i 1.26239i 0.775625 + 0.631194i \(0.217435\pi\)
−0.775625 + 0.631194i \(0.782565\pi\)
\(252\) 3.00000i 0.188982i
\(253\) −18.0000 −1.13165
\(254\) 8.00000i 0.501965i
\(255\) −7.00000 14.0000i −0.438357 0.876714i
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 1.00000i 0.0622573i
\(259\) 3.00000 + 18.0000i 0.186411 + 1.11847i
\(260\) −8.00000 + 4.00000i −0.496139 + 0.248069i
\(261\) 9.00000i 0.557086i
\(262\) 0 0
\(263\) 31.0000i 1.91154i 0.294112 + 0.955771i \(0.404976\pi\)
−0.294112 + 0.955771i \(0.595024\pi\)
\(264\) 3.00000i 0.184637i
\(265\) 1.00000 + 2.00000i 0.0614295 + 0.122859i
\(266\) −12.0000 −0.735767
\(267\) 6.00000 0.367194
\(268\) 2.00000i 0.122169i
\(269\) 20.0000 1.21942 0.609711 0.792624i \(-0.291286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) −1.00000 2.00000i −0.0608581 0.121716i
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 7.00000 0.424437
\(273\) −12.0000 −0.726273
\(274\) 12.0000i 0.724947i
\(275\) −9.00000 + 12.0000i −0.542720 + 0.723627i
\(276\) 6.00000i 0.361158i
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 15.0000 0.899640
\(279\) 5.00000i 0.299342i
\(280\) −3.00000 6.00000i −0.179284 0.358569i
\(281\) 30.0000i 1.78965i −0.446417 0.894825i \(-0.647300\pi\)
0.446417 0.894825i \(-0.352700\pi\)
\(282\) −8.00000 −0.476393
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 12.0000 0.712069
\(285\) −8.00000 + 4.00000i −0.473879 + 0.236940i
\(286\) −12.0000 −0.709575
\(287\) 21.0000i 1.23959i
\(288\) 1.00000 0.0589256
\(289\) 32.0000 1.88235
\(290\) 9.00000 + 18.0000i 0.528498 + 1.05700i
\(291\) 7.00000i 0.410347i
\(292\) 4.00000i 0.234082i
\(293\) 29.0000i 1.69420i −0.531435 0.847099i \(-0.678347\pi\)
0.531435 0.847099i \(-0.321653\pi\)
\(294\) 2.00000i 0.116642i
\(295\) 6.00000 + 12.0000i 0.349334 + 0.698667i
\(296\) −6.00000 + 1.00000i −0.348743 + 0.0581238i
\(297\) 3.00000i 0.174078i
\(298\) 0 0
\(299\) −24.0000 −1.38796
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 3.00000i 0.172917i
\(302\) −2.00000 −0.115087
\(303\) 2.00000i 0.114897i
\(304\) 4.00000i 0.229416i
\(305\) −5.00000 10.0000i −0.286299 0.572598i
\(306\) 7.00000 0.400163
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) 9.00000i 0.512823i
\(309\) 14.0000i 0.796432i
\(310\) 5.00000 + 10.0000i 0.283981 + 0.567962i
\(311\) 15.0000i 0.850572i 0.905059 + 0.425286i \(0.139826\pi\)
−0.905059 + 0.425286i \(0.860174\pi\)
\(312\) 4.00000i 0.226455i
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 7.00000i 0.395033i
\(315\) −3.00000 6.00000i −0.169031 0.338062i
\(316\) 4.00000i 0.225018i
\(317\) 27.0000i 1.51647i −0.651981 0.758236i \(-0.726062\pi\)
0.651981 0.758236i \(-0.273938\pi\)
\(318\) −1.00000 −0.0560772
\(319\) 27.0000i 1.51171i
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) 18.0000 1.00466
\(322\) 18.0000i 1.00310i
\(323\) 28.0000i 1.55796i
\(324\) 1.00000 0.0555556
\(325\) −12.0000 + 16.0000i −0.665640 + 0.887520i
\(326\) 9.00000 0.498464
\(327\) 11.0000 0.608301
\(328\) −7.00000 −0.386510
\(329\) −24.0000 −1.32316
\(330\) −3.00000 6.00000i −0.165145 0.330289i
\(331\) 20.0000i 1.09930i −0.835395 0.549650i \(-0.814761\pi\)
0.835395 0.549650i \(-0.185239\pi\)
\(332\) 14.0000i 0.768350i
\(333\) −6.00000 + 1.00000i −0.328798 + 0.0547997i
\(334\) −12.0000 −0.656611
\(335\) −2.00000 4.00000i −0.109272 0.218543i
\(336\) 3.00000 0.163663
\(337\) 18.0000i 0.980522i 0.871576 + 0.490261i \(0.163099\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −3.00000 −0.163178
\(339\) 1.00000i 0.0543125i
\(340\) 14.0000 7.00000i 0.759257 0.379628i
\(341\) 15.0000i 0.812296i
\(342\) 4.00000i 0.216295i
\(343\) 15.0000i 0.809924i
\(344\) −1.00000 −0.0539164
\(345\) −6.00000 12.0000i −0.323029 0.646058i
\(346\) 9.00000i 0.483843i
\(347\) −28.0000 −1.50312 −0.751559 0.659665i \(-0.770698\pi\)
−0.751559 + 0.659665i \(0.770698\pi\)
\(348\) −9.00000 −0.482451
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −12.0000 9.00000i −0.641427 0.481070i
\(351\) 4.00000i 0.213504i
\(352\) 3.00000 0.159901
\(353\) 31.0000 1.64996 0.824982 0.565159i \(-0.191185\pi\)
0.824982 + 0.565159i \(0.191185\pi\)
\(354\) −6.00000 −0.318896
\(355\) 24.0000 12.0000i 1.27379 0.636894i
\(356\) 6.00000i 0.317999i
\(357\) 21.0000 1.11144
\(358\) 4.00000i 0.211407i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 2.00000 1.00000i 0.105409 0.0527046i
\(361\) 3.00000 0.157895
\(362\) 18.0000 0.946059
\(363\) 2.00000i 0.104973i
\(364\) 12.0000i 0.628971i
\(365\) −4.00000 8.00000i −0.209370 0.418739i
\(366\) 5.00000 0.261354
\(367\) 23.0000i 1.20059i 0.799779 + 0.600295i \(0.204950\pi\)
−0.799779 + 0.600295i \(0.795050\pi\)
\(368\) 6.00000 0.312772
\(369\) −7.00000 −0.364405
\(370\) −11.0000 + 8.00000i −0.571863 + 0.415900i
\(371\) −3.00000 −0.155752
\(372\) −5.00000 −0.259238
\(373\) 14.0000i 0.724893i −0.932005 0.362446i \(-0.881942\pi\)
0.932005 0.362446i \(-0.118058\pi\)
\(374\) 21.0000 1.08588
\(375\) −11.0000 2.00000i −0.568038 0.103280i
\(376\) 8.00000i 0.412568i
\(377\) 36.0000i 1.85409i
\(378\) 3.00000 0.154303
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −4.00000 8.00000i −0.205196 0.410391i
\(381\) 8.00000 0.409852
\(382\) 15.0000i 0.767467i
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −9.00000 18.0000i −0.458682 0.917365i
\(386\) 14.0000 0.712581
\(387\) −1.00000 −0.0508329
\(388\) 7.00000 0.355371
\(389\) 31.0000i 1.57176i 0.618378 + 0.785881i \(0.287790\pi\)
−0.618378 + 0.785881i \(0.712210\pi\)
\(390\) −4.00000 8.00000i −0.202548 0.405096i
\(391\) 42.0000 2.12403
\(392\) 2.00000 0.101015
\(393\) 0 0
\(394\) 18.0000i 0.906827i
\(395\) −4.00000 8.00000i −0.201262 0.402524i
\(396\) 3.00000 0.150756
\(397\) 38.0000i 1.90717i 0.301131 + 0.953583i \(0.402636\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 12.0000i 0.600751i
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 10.0000i 0.499376i −0.968326 0.249688i \(-0.919672\pi\)
0.968326 0.249688i \(-0.0803281\pi\)
\(402\) 2.00000 0.0997509
\(403\) 20.0000i 0.996271i
\(404\) 2.00000 0.0995037
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) −27.0000 −1.33999
\(407\) −18.0000 + 3.00000i −0.892227 + 0.148704i
\(408\) 7.00000i 0.346552i
\(409\) 14.0000i 0.692255i −0.938187 0.346128i \(-0.887496\pi\)
0.938187 0.346128i \(-0.112504\pi\)
\(410\) −14.0000 + 7.00000i −0.691411 + 0.345705i
\(411\) −12.0000 −0.591916
\(412\) −14.0000 −0.689730
\(413\) −18.0000 −0.885722
\(414\) 6.00000 0.294884
\(415\) −14.0000 28.0000i −0.687233 1.37447i
\(416\) 4.00000 0.196116
\(417\) 15.0000i 0.734553i
\(418\) 12.0000i 0.586939i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 6.00000 3.00000i 0.292770 0.146385i
\(421\) 30.0000i 1.46211i 0.682318 + 0.731055i \(0.260972\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 13.0000 0.632830
\(423\) 8.00000i 0.388973i
\(424\) 1.00000i 0.0485643i
\(425\) 21.0000 28.0000i 1.01865 1.35820i
\(426\) 12.0000i 0.581402i
\(427\) 15.0000 0.725901
\(428\) 18.0000i 0.870063i
\(429\) 12.0000i 0.579365i
\(430\) −2.00000 + 1.00000i −0.0964486 + 0.0482243i
\(431\) 25.0000i 1.20421i −0.798418 0.602104i \(-0.794329\pi\)
0.798418 0.602104i \(-0.205671\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) −15.0000 −0.720023
\(435\) −18.0000 + 9.00000i −0.863034 + 0.431517i
\(436\) 11.0000i 0.526804i
\(437\) 24.0000i 1.14808i
\(438\) 4.00000 0.191127
\(439\) 9.00000i 0.429547i −0.976664 0.214773i \(-0.931099\pi\)
0.976664 0.214773i \(-0.0689013\pi\)
\(440\) 6.00000 3.00000i 0.286039 0.143019i
\(441\) 2.00000 0.0952381
\(442\) 28.0000 1.33182
\(443\) 36.0000i 1.71041i 0.518289 + 0.855206i \(0.326569\pi\)
−0.518289 + 0.855206i \(0.673431\pi\)
\(444\) −1.00000 6.00000i −0.0474579 0.284747i
\(445\) 6.00000 + 12.0000i 0.284427 + 0.568855i
\(446\) 11.0000i 0.520865i
\(447\) 0 0
\(448\) 3.00000i 0.141737i
\(449\) 6.00000i 0.283158i 0.989927 + 0.141579i \(0.0452178\pi\)
−0.989927 + 0.141579i \(0.954782\pi\)
\(450\) 3.00000 4.00000i 0.141421 0.188562i
\(451\) −21.0000 −0.988851
\(452\) 1.00000 0.0470360
\(453\) 2.00000i 0.0939682i
\(454\) 13.0000 0.610120
\(455\) −12.0000 24.0000i −0.562569 1.12514i
\(456\) 4.00000 0.187317
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) −10.0000 −0.467269
\(459\) 7.00000i 0.326732i
\(460\) 12.0000 6.00000i 0.559503 0.279751i
\(461\) 25.0000i 1.16437i 0.813058 + 0.582183i \(0.197801\pi\)
−0.813058 + 0.582183i \(0.802199\pi\)
\(462\) 9.00000 0.418718
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) 9.00000i 0.417815i
\(465\) −10.0000 + 5.00000i −0.463739 + 0.231869i
\(466\) 6.00000i 0.277945i
\(467\) −23.0000 −1.06431 −0.532157 0.846646i \(-0.678618\pi\)
−0.532157 + 0.846646i \(0.678618\pi\)
\(468\) 4.00000 0.184900
\(469\) 6.00000 0.277054
\(470\) −8.00000 16.0000i −0.369012 0.738025i
\(471\) −7.00000 −0.322543
\(472\) 6.00000i 0.276172i
\(473\) −3.00000 −0.137940
\(474\) 4.00000 0.183726
\(475\) −16.0000 12.0000i −0.734130 0.550598i
\(476\) 21.0000i 0.962533i
\(477\) 1.00000i 0.0457869i
\(478\) 9.00000i 0.411650i
\(479\) 24.0000i 1.09659i −0.836286 0.548294i \(-0.815277\pi\)
0.836286 0.548294i \(-0.184723\pi\)
\(480\) 1.00000 + 2.00000i 0.0456435 + 0.0912871i
\(481\) −24.0000 + 4.00000i −1.09431 + 0.182384i
\(482\) 0 0
\(483\) 18.0000 0.819028
\(484\) −2.00000 −0.0909091
\(485\) 14.0000 7.00000i 0.635707 0.317854i
\(486\) 1.00000i 0.0453609i
\(487\) 22.0000 0.996915 0.498458 0.866914i \(-0.333900\pi\)
0.498458 + 0.866914i \(0.333900\pi\)
\(488\) 5.00000i 0.226339i
\(489\) 9.00000i 0.406994i
\(490\) 4.00000 2.00000i 0.180702 0.0903508i
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 7.00000i 0.315584i
\(493\) 63.0000i 2.83738i
\(494\) 16.0000i 0.719874i
\(495\) 6.00000 3.00000i 0.269680 0.134840i
\(496\) 5.00000i 0.224507i
\(497\) 36.0000i 1.61482i
\(498\) 14.0000 0.627355
\(499\) 24.0000i 1.07439i −0.843459 0.537194i \(-0.819484\pi\)
0.843459 0.537194i \(-0.180516\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) 12.0000i 0.536120i
\(502\) 20.0000i 0.892644i
\(503\) −14.0000 −0.624229 −0.312115 0.950044i \(-0.601037\pi\)
−0.312115 + 0.950044i \(0.601037\pi\)
\(504\) 3.00000i 0.133631i
\(505\) 4.00000 2.00000i 0.177998 0.0889988i
\(506\) 18.0000 0.800198
\(507\) 3.00000i 0.133235i
\(508\) 8.00000i 0.354943i
\(509\) −10.0000 −0.443242 −0.221621 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 7.00000 + 14.0000i 0.309965 + 0.619930i
\(511\) 12.0000 0.530849
\(512\) −1.00000 −0.0441942
\(513\) 4.00000 0.176604
\(514\) 18.0000 0.793946
\(515\) −28.0000 + 14.0000i −1.23383 + 0.616914i
\(516\) 1.00000i 0.0440225i
\(517\) 24.0000i 1.05552i
\(518\) −3.00000 18.0000i −0.131812 0.790875i
\(519\) −9.00000 −0.395056
\(520\) 8.00000 4.00000i 0.350823 0.175412i
\(521\) 37.0000 1.62100 0.810500 0.585739i \(-0.199196\pi\)
0.810500 + 0.585739i \(0.199196\pi\)
\(522\) 9.00000i 0.393919i
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 0 0
\(525\) 9.00000 12.0000i 0.392792 0.523723i
\(526\) 31.0000i 1.35166i
\(527\) 35.0000i 1.52462i
\(528\) 3.00000i 0.130558i
\(529\) 13.0000 0.565217
\(530\) −1.00000 2.00000i −0.0434372 0.0868744i
\(531\) 6.00000i 0.260378i
\(532\) 12.0000 0.520266
\(533\) −28.0000 −1.21281
\(534\) −6.00000 −0.259645
\(535\) 18.0000 + 36.0000i 0.778208 + 1.55642i
\(536\) 2.00000i 0.0863868i
\(537\) −4.00000 −0.172613
\(538\) −20.0000 −0.862261
\(539\) 6.00000 0.258438
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) 30.0000i 1.28980i 0.764267 + 0.644900i \(0.223101\pi\)
−0.764267 + 0.644900i \(0.776899\pi\)
\(542\) −22.0000 −0.944981
\(543\) 18.0000i 0.772454i
\(544\) −7.00000 −0.300123
\(545\) 11.0000 + 22.0000i 0.471188 + 0.942376i
\(546\) 12.0000 0.513553
\(547\) −23.0000 −0.983409 −0.491704 0.870762i \(-0.663626\pi\)
−0.491704 + 0.870762i \(0.663626\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 5.00000i 0.213395i
\(550\) 9.00000 12.0000i 0.383761 0.511682i
\(551\) −36.0000 −1.53365
\(552\) 6.00000i 0.255377i
\(553\) 12.0000 0.510292
\(554\) 28.0000 1.18961
\(555\) −8.00000 11.0000i −0.339581 0.466924i
\(556\) −15.0000 −0.636142
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 5.00000i 0.211667i
\(559\) −4.00000 −0.169182
\(560\) 3.00000 + 6.00000i 0.126773 + 0.253546i
\(561\) 21.0000i 0.886621i
\(562\) 30.0000i 1.26547i
\(563\) 21.0000 0.885044 0.442522 0.896758i \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 8.00000 0.336861
\(565\) 2.00000 1.00000i 0.0841406 0.0420703i
\(566\) 4.00000 0.168133
\(567\) 3.00000i 0.125988i
\(568\) −12.0000 −0.503509
\(569\) 24.0000i 1.00613i −0.864248 0.503066i \(-0.832205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(570\) 8.00000 4.00000i 0.335083 0.167542i
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) 12.0000 0.501745
\(573\) −15.0000 −0.626634
\(574\) 21.0000i 0.876523i
\(575\) 18.0000 24.0000i 0.750652 1.00087i
\(576\) −1.00000 −0.0416667
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) −32.0000 −1.33102
\(579\) 14.0000i 0.581820i
\(580\) −9.00000 18.0000i −0.373705 0.747409i
\(581\) 42.0000 1.74245
\(582\) 7.00000i 0.290159i
\(583\) 3.00000i 0.124247i
\(584\) 4.00000i 0.165521i
\(585\) 8.00000 4.00000i 0.330759 0.165380i
\(586\) 29.0000i 1.19798i
\(587\) 47.0000 1.93990 0.969949 0.243309i \(-0.0782329\pi\)
0.969949 + 0.243309i \(0.0782329\pi\)
\(588\) 2.00000i 0.0824786i
\(589\) −20.0000 −0.824086
\(590\) −6.00000 12.0000i −0.247016 0.494032i
\(591\) 18.0000 0.740421
\(592\) 6.00000 1.00000i 0.246598 0.0410997i
\(593\) 46.0000i 1.88899i 0.328521 + 0.944497i \(0.393450\pi\)
−0.328521 + 0.944497i \(0.606550\pi\)
\(594\) 3.00000i 0.123091i
\(595\) 21.0000 + 42.0000i 0.860916 + 1.72183i
\(596\) 0 0
\(597\) 16.0000 0.654836
\(598\) 24.0000 0.981433
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 4.00000 + 3.00000i 0.163299 + 0.122474i
\(601\) −23.0000 −0.938190 −0.469095 0.883148i \(-0.655420\pi\)
−0.469095 + 0.883148i \(0.655420\pi\)
\(602\) 3.00000i 0.122271i
\(603\) 2.00000i 0.0814463i
\(604\) 2.00000 0.0813788
\(605\) −4.00000 + 2.00000i −0.162623 + 0.0813116i
\(606\) 2.00000i 0.0812444i
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 27.0000i 1.09410i
\(610\) 5.00000 + 10.0000i 0.202444 + 0.404888i
\(611\) 32.0000i 1.29458i
\(612\) −7.00000 −0.282958
\(613\) 31.0000i 1.25208i 0.779792 + 0.626039i \(0.215325\pi\)
−0.779792 + 0.626039i \(0.784675\pi\)
\(614\) 18.0000i 0.726421i
\(615\) −7.00000 14.0000i −0.282267 0.564534i
\(616\) 9.00000i 0.362620i
\(617\) 8.00000i 0.322068i 0.986949 + 0.161034i \(0.0514829\pi\)
−0.986949 + 0.161034i \(0.948517\pi\)
\(618\) 14.0000i 0.563163i
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) −5.00000 10.0000i −0.200805 0.401610i
\(621\) 6.00000i 0.240772i
\(622\) 15.0000i 0.601445i
\(623\) −18.0000 −0.721155
\(624\) 4.00000i 0.160128i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −6.00000 −0.239808
\(627\) 12.0000 0.479234
\(628\) 7.00000i 0.279330i
\(629\) 42.0000 7.00000i 1.67465 0.279108i
\(630\) 3.00000 + 6.00000i 0.119523 + 0.239046i
\(631\) 25.0000i 0.995234i −0.867397 0.497617i \(-0.834208\pi\)
0.867397 0.497617i \(-0.165792\pi\)
\(632\) 4.00000i 0.159111i
\(633\) 13.0000i 0.516704i
\(634\) 27.0000i 1.07231i
\(635\) 8.00000 + 16.0000i 0.317470 + 0.634941i
\(636\) 1.00000 0.0396526
\(637\) 8.00000 0.316972
\(638\) 27.0000i 1.06894i
\(639\) −12.0000 −0.474713
\(640\) −2.00000 + 1.00000i −0.0790569 + 0.0395285i
\(641\) 17.0000 0.671460 0.335730 0.941958i \(-0.391017\pi\)
0.335730 + 0.941958i \(0.391017\pi\)
\(642\) −18.0000 −0.710403
\(643\) 31.0000 1.22252 0.611260 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 18.0000i 0.709299i
\(645\) −1.00000 2.00000i −0.0393750 0.0787499i
\(646\) 28.0000i 1.10165i
\(647\) −48.0000 −1.88707 −0.943537 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 18.0000i 0.706562i
\(650\) 12.0000 16.0000i 0.470679 0.627572i
\(651\) 15.0000i 0.587896i
\(652\) −9.00000 −0.352467
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) −11.0000 −0.430134
\(655\) 0 0
\(656\) 7.00000 0.273304
\(657\) 4.00000i 0.156055i
\(658\) 24.0000 0.935617
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 3.00000 + 6.00000i 0.116775 + 0.233550i
\(661\) 35.0000i 1.36134i −0.732589 0.680671i \(-0.761688\pi\)
0.732589 0.680671i \(-0.238312\pi\)
\(662\) 20.0000i 0.777322i
\(663\) 28.0000i 1.08743i
\(664\) 14.0000i 0.543305i
\(665\) 24.0000 12.0000i 0.930680 0.465340i
\(666\) 6.00000 1.00000i 0.232495 0.0387492i
\(667\) 54.0000i 2.09089i
\(668\) 12.0000 0.464294
\(669\) 11.0000 0.425285
\(670\) 2.00000 + 4.00000i 0.0772667 + 0.154533i
\(671\) 15.0000i 0.579069i
\(672\) −3.00000 −0.115728
\(673\) 26.0000i 1.00223i 0.865382 + 0.501113i \(0.167076\pi\)
−0.865382 + 0.501113i \(0.832924\pi\)
\(674\) 18.0000i 0.693334i
\(675\) 4.00000 + 3.00000i 0.153960 + 0.115470i
\(676\) 3.00000 0.115385
\(677\) 42.0000i 1.61419i −0.590421 0.807096i \(-0.701038\pi\)
0.590421 0.807096i \(-0.298962\pi\)
\(678\) 1.00000i 0.0384048i
\(679\) 21.0000i 0.805906i
\(680\) −14.0000 + 7.00000i −0.536875 + 0.268438i
\(681\) 13.0000i 0.498161i
\(682\) 15.0000i 0.574380i
\(683\) 1.00000 0.0382639 0.0191320 0.999817i \(-0.493910\pi\)
0.0191320 + 0.999817i \(0.493910\pi\)
\(684\) 4.00000i 0.152944i
\(685\) −12.0000 24.0000i −0.458496 0.916993i
\(686\) 15.0000i 0.572703i
\(687\) 10.0000i 0.381524i
\(688\) 1.00000 0.0381246
\(689\) 4.00000i 0.152388i
\(690\) 6.00000 + 12.0000i 0.228416 + 0.456832i
\(691\) −43.0000 −1.63580 −0.817899 0.575362i \(-0.804861\pi\)
−0.817899 + 0.575362i \(0.804861\pi\)
\(692\) 9.00000i 0.342129i
\(693\) 9.00000i 0.341882i
\(694\) 28.0000 1.06287
\(695\) −30.0000 + 15.0000i −1.13796 + 0.568982i
\(696\) 9.00000 0.341144
\(697\) 49.0000 1.85601
\(698\) 0 0
\(699\) 6.00000 0.226941
\(700\) 12.0000 + 9.00000i 0.453557 + 0.340168i
\(701\) 10.0000i 0.377695i −0.982006 0.188847i \(-0.939525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) 4.00000i 0.150970i
\(703\) −4.00000 24.0000i −0.150863 0.905177i
\(704\) −3.00000 −0.113067
\(705\) 16.0000 8.00000i 0.602595 0.301297i
\(706\) −31.0000 −1.16670
\(707\) 6.00000i 0.225653i
\(708\) 6.00000 0.225494
\(709\) 11.0000i 0.413114i 0.978435 + 0.206557i \(0.0662258\pi\)
−0.978435 + 0.206557i \(0.933774\pi\)
\(710\) −24.0000 + 12.0000i −0.900704 + 0.450352i
\(711\) 4.00000i 0.150012i
\(712\) 6.00000i 0.224860i
\(713\) 30.0000i 1.12351i
\(714\) −21.0000 −0.785905
\(715\) 24.0000 12.0000i 0.897549 0.448775i
\(716\) 4.00000i 0.149487i
\(717\) −9.00000 −0.336111
\(718\) 0 0
\(719\) 50.0000 1.86469 0.932343 0.361576i \(-0.117761\pi\)
0.932343 + 0.361576i \(0.117761\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) 42.0000i 1.56416i
\(722\) −3.00000 −0.111648
\(723\) 0 0
\(724\) −18.0000 −0.668965
\(725\) −36.0000 27.0000i −1.33701 1.00275i
\(726\) 2.00000i 0.0742270i
\(727\) −18.0000 −0.667583 −0.333792 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 12.0000i 0.444750i
\(729\) −1.00000 −0.0370370
\(730\) 4.00000 + 8.00000i 0.148047 + 0.296093i
\(731\) 7.00000 0.258904
\(732\) −5.00000 −0.184805
\(733\) 11.0000i 0.406294i 0.979148 + 0.203147i \(0.0651170\pi\)
−0.979148 + 0.203147i \(0.934883\pi\)
\(734\) 23.0000i 0.848945i
\(735\) 2.00000 + 4.00000i 0.0737711 + 0.147542i
\(736\) −6.00000 −0.221163
\(737\) 6.00000i 0.221013i
\(738\) 7.00000 0.257674
\(739\) 5.00000 0.183928 0.0919640 0.995762i \(-0.470686\pi\)
0.0919640 + 0.995762i \(0.470686\pi\)
\(740\) 11.0000 8.00000i 0.404368 0.294086i
\(741\) 16.0000 0.587775
\(742\) 3.00000 0.110133
\(743\) 51.0000i 1.87101i 0.353315 + 0.935504i \(0.385054\pi\)
−0.353315 + 0.935504i \(0.614946\pi\)
\(744\) 5.00000 0.183309
\(745\) 0 0
\(746\) 14.0000i 0.512576i
\(747\) 14.0000i 0.512233i
\(748\) −21.0000 −0.767836
\(749\) −54.0000 −1.97312
\(750\) 11.0000 + 2.00000i 0.401663 + 0.0730297i
\(751\) −18.0000 −0.656829 −0.328415 0.944534i \(-0.606514\pi\)
−0.328415 + 0.944534i \(0.606514\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 20.0000 0.728841
\(754\) 36.0000i 1.31104i
\(755\) 4.00000 2.00000i 0.145575 0.0727875i
\(756\) −3.00000 −0.109109
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −20.0000 −0.726433
\(759\) 18.0000i 0.653359i
\(760\) 4.00000 + 8.00000i 0.145095 + 0.290191i
\(761\) −13.0000 −0.471250 −0.235625 0.971844i \(-0.575714\pi\)
−0.235625 + 0.971844i \(0.575714\pi\)
\(762\) −8.00000 −0.289809
\(763\) −33.0000 −1.19468
\(764\) 15.0000i 0.542681i
\(765\) −14.0000 + 7.00000i −0.506171 + 0.253086i
\(766\) −6.00000 −0.216789
\(767\) 24.0000i 0.866590i
\(768\) 1.00000i 0.0360844i
\(769\) 26.0000i 0.937584i 0.883309 + 0.468792i \(0.155311\pi\)
−0.883309 + 0.468792i \(0.844689\pi\)
\(770\) 9.00000 + 18.0000i 0.324337 + 0.648675i
\(771\) 18.0000i 0.648254i
\(772\) −14.0000 −0.503871
\(773\) 11.0000i 0.395643i 0.980238 + 0.197821i \(0.0633866\pi\)
−0.980238 + 0.197821i \(0.936613\pi\)
\(774\) 1.00000 0.0359443
\(775\) −20.0000 15.0000i −0.718421 0.538816i
\(776\) −7.00000 −0.251285
\(777\) 18.0000 3.00000i 0.645746 0.107624i
\(778\) 31.0000i 1.11140i
\(779\) 28.0000i 1.00320i
\(780\) 4.00000 + 8.00000i 0.143223 + 0.286446i
\(781\) −36.0000 −1.28818
\(782\) −42.0000 −1.50192
\(783\) 9.00000 0.321634
\(784\) −2.00000 −0.0714286
\(785\) −7.00000 14.0000i −0.249841 0.499681i
\(786\) 0 0
\(787\) 28.0000i 0.998092i 0.866575 + 0.499046i \(0.166316\pi\)
−0.866575 + 0.499046i