Properties

Label 1014.2.e.b.529.1
Level $1014$
Weight $2$
Character 1014.529
Analytic conductor $8.097$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.b.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +1.00000 q^{12} +2.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(3.00000 + 5.19615i) q^{19} +(-1.00000 - 1.73205i) q^{20} +2.00000 q^{21} +(2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(5.00000 - 8.66025i) q^{29} +(-1.00000 - 1.73205i) q^{30} +10.0000 q^{31} +(-0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(-2.00000 - 3.46410i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.00000 - 6.92820i) q^{37} -6.00000 q^{38} +2.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-1.00000 - 1.73205i) q^{45} +(2.00000 + 3.46410i) q^{46} +12.0000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +2.00000 q^{51} -6.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} -6.00000 q^{57} +(5.00000 + 8.66025i) q^{58} +(2.00000 + 3.46410i) q^{59} +2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-5.00000 + 8.66025i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(2.00000 + 3.46410i) q^{69} +4.00000 q^{70} +(-0.500000 - 0.866025i) q^{72} +4.00000 q^{73} +(4.00000 + 6.92820i) q^{74} +(0.500000 - 0.866025i) q^{75} +(3.00000 - 5.19615i) q^{76} +(-1.00000 + 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.00000 - 8.66025i) q^{82} -4.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +(-2.00000 - 3.46410i) q^{85} -4.00000 q^{86} +(5.00000 + 8.66025i) q^{87} +(-3.00000 + 5.19615i) q^{89} +2.00000 q^{90} -4.00000 q^{92} +(-5.00000 + 8.66025i) q^{93} +(-6.00000 + 10.3923i) q^{94} +(6.00000 + 10.3923i) q^{95} +1.00000 q^{96} +(6.00000 + 10.3923i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - 2 q^{10} + 2 q^{12} + 4 q^{14} - 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + 6 q^{19} - 2 q^{20} + 4 q^{21} + 4 q^{23} - q^{24} - 2 q^{25} + 2 q^{27} - 2 q^{28} + 10 q^{29} - 2 q^{30} + 20 q^{31} - q^{32} + 4 q^{34} - 4 q^{35} - q^{36} + 8 q^{37} - 12 q^{38} + 4 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} - 2 q^{45} + 4 q^{46} + 24 q^{47} - q^{48} + 3 q^{49} + q^{50} + 4 q^{51} - 12 q^{53} - q^{54} - 2 q^{56} - 12 q^{57} + 10 q^{58} + 4 q^{59} + 4 q^{60} - 2 q^{61} - 10 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{67} - 2 q^{68} + 4 q^{69} + 8 q^{70} - q^{72} + 8 q^{73} + 8 q^{74} + q^{75} + 6 q^{76} - 2 q^{80} - q^{81} - 10 q^{82} - 8 q^{83} - 2 q^{84} - 4 q^{85} - 8 q^{86} + 10 q^{87} - 6 q^{89} + 4 q^{90} - 8 q^{92} - 10 q^{93} - 12 q^{94} + 12 q^{95} + 2 q^{96} + 12 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 2.00000 0.534522
\(15\) −1.00000 + 1.73205i −0.258199 + 0.447214i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) −1.00000 1.73205i −0.223607 0.387298i
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.00000 + 1.73205i −0.188982 + 0.327327i
\(29\) 5.00000 8.66025i 0.928477 1.60817i 0.142605 0.989780i \(-0.454452\pi\)
0.785872 0.618389i \(-0.212214\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −2.00000 3.46410i −0.338062 0.585540i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) −5.00000 + 8.66025i −0.780869 + 1.35250i 0.150567 + 0.988600i \(0.451890\pi\)
−0.931436 + 0.363905i \(0.881443\pi\)
\(42\) −1.00000 + 1.73205i −0.154303 + 0.267261i
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 2.00000 0.280056
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) −6.00000 −0.794719
\(58\) 5.00000 + 8.66025i 0.656532 + 1.13715i
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 2.00000 0.258199
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) −5.00000 + 8.66025i −0.635001 + 1.09985i
\(63\) −1.00000 + 1.73205i −0.125988 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 2.00000 + 3.46410i 0.240772 + 0.417029i
\(70\) 4.00000 0.478091
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 3.00000 5.19615i 0.344124 0.596040i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.00000 8.66025i −0.552158 0.956365i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) −1.00000 1.73205i −0.109109 0.188982i
\(85\) −2.00000 3.46410i −0.216930 0.375735i
\(86\) −4.00000 −0.431331
\(87\) 5.00000 + 8.66025i 0.536056 + 0.928477i
\(88\) 0 0
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) −5.00000 + 8.66025i −0.518476 + 0.898027i
\(94\) −6.00000 + 10.3923i −0.618853 + 1.07188i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 1.00000 0.102062
\(97\) 6.00000 + 10.3923i 0.609208 + 1.05518i 0.991371 + 0.131084i \(0.0418458\pi\)
−0.382164 + 0.924095i \(0.624821\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) −1.00000 + 1.73205i −0.0990148 + 0.171499i
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 4.00000 0.390360
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) −4.00000 + 6.92820i −0.386695 + 0.669775i −0.992003 0.126217i \(-0.959717\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 4.00000 + 6.92820i 0.379663 + 0.657596i
\(112\) 2.00000 0.188982
\(113\) −7.00000 12.1244i −0.658505 1.14056i −0.981003 0.193993i \(-0.937856\pi\)
0.322498 0.946570i \(-0.395477\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) −10.0000 −0.928477
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) −2.00000 + 3.46410i −0.183340 + 0.317554i
\(120\) −1.00000 + 1.73205i −0.0912871 + 0.158114i
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 2.00000 0.181071
\(123\) −5.00000 8.66025i −0.450835 0.780869i
\(124\) −5.00000 8.66025i −0.449013 0.777714i
\(125\) −12.0000 −1.07331
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) 4.00000 6.92820i 0.354943 0.614779i −0.632166 0.774833i \(-0.717834\pi\)
0.987108 + 0.160055i \(0.0511671\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 6.00000 10.3923i 0.520266 0.901127i
\(134\) 1.00000 + 1.73205i 0.0863868 + 0.149626i
\(135\) 2.00000 0.172133
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) −4.00000 −0.340503
\(139\) 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i \(0.155640\pi\)
−0.0346338 + 0.999400i \(0.511026\pi\)
\(140\) −2.00000 + 3.46410i −0.169031 + 0.292770i
\(141\) −6.00000 + 10.3923i −0.505291 + 0.875190i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 10.0000 17.3205i 0.830455 1.43839i
\(146\) −2.00000 + 3.46410i −0.165521 + 0.286691i
\(147\) 1.50000 + 2.59808i 0.123718 + 0.214286i
\(148\) −8.00000 −0.657596
\(149\) −7.00000 12.1244i −0.573462 0.993266i −0.996207 0.0870170i \(-0.972267\pi\)
0.422744 0.906249i \(-0.361067\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) −1.00000 + 1.73205i −0.0808452 + 0.140028i
\(154\) 0 0
\(155\) 20.0000 1.60644
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) −1.00000 1.73205i −0.0790569 0.136931i
\(161\) −8.00000 −0.630488
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −7.00000 12.1244i −0.548282 0.949653i −0.998392 0.0566798i \(-0.981949\pi\)
0.450110 0.892973i \(-0.351385\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 2.00000 0.154303
\(169\) 0 0
\(170\) 4.00000 0.306786
\(171\) 3.00000 5.19615i 0.229416 0.397360i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) −10.0000 −0.758098
\(175\) 1.00000 + 1.73205i 0.0755929 + 0.130931i
\(176\) 0 0
\(177\) −4.00000 −0.300658
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) −1.00000 + 1.73205i −0.0745356 + 0.129099i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 8.00000 13.8564i 0.588172 1.01874i
\(186\) −5.00000 8.66025i −0.366618 0.635001i
\(187\) 0 0
\(188\) −6.00000 10.3923i −0.437595 0.757937i
\(189\) −1.00000 1.73205i −0.0727393 0.125988i
\(190\) −12.0000 −0.870572
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 11.0000 19.0526i 0.783718 1.35744i −0.146045 0.989278i \(-0.546654\pi\)
0.929762 0.368161i \(-0.120012\pi\)
\(198\) 0 0
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 1.00000 + 1.73205i 0.0705346 + 0.122169i
\(202\) 1.00000 + 1.73205i 0.0703598 + 0.121867i
\(203\) −20.0000 −1.40372
\(204\) −1.00000 1.73205i −0.0700140 0.121268i
\(205\) −10.0000 + 17.3205i −0.698430 + 1.20972i
\(206\) −8.00000 + 13.8564i −0.557386 + 0.965422i
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 0 0
\(210\) −2.00000 + 3.46410i −0.138013 + 0.239046i
\(211\) −6.00000 + 10.3923i −0.413057 + 0.715436i −0.995222 0.0976347i \(-0.968872\pi\)
0.582165 + 0.813070i \(0.302206\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) −4.00000 6.92820i −0.273434 0.473602i
\(215\) 4.00000 + 6.92820i 0.272798 + 0.472500i
\(216\) 1.00000 0.0680414
\(217\) −10.0000 17.3205i −0.678844 1.17579i
\(218\) −2.00000 + 3.46410i −0.135457 + 0.234619i
\(219\) −2.00000 + 3.46410i −0.135147 + 0.234082i
\(220\) 0 0
\(221\) 0 0
\(222\) −8.00000 −0.536925
\(223\) 7.00000 12.1244i 0.468755 0.811907i −0.530607 0.847618i \(-0.678036\pi\)
0.999362 + 0.0357107i \(0.0113695\pi\)
\(224\) −1.00000 + 1.73205i −0.0668153 + 0.115728i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 14.0000 0.931266
\(227\) −4.00000 6.92820i −0.265489 0.459841i 0.702202 0.711977i \(-0.252200\pi\)
−0.967692 + 0.252136i \(0.918867\pi\)
\(228\) 3.00000 + 5.19615i 0.198680 + 0.344124i
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 4.00000 + 6.92820i 0.263752 + 0.456832i
\(231\) 0 0
\(232\) 5.00000 8.66025i 0.328266 0.568574i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 24.0000 1.56559
\(236\) 2.00000 3.46410i 0.130189 0.225494i
\(237\) 0 0
\(238\) −2.00000 3.46410i −0.129641 0.224544i
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) −1.00000 1.73205i −0.0645497 0.111803i
\(241\) 10.0000 + 17.3205i 0.644157 + 1.11571i 0.984496 + 0.175409i \(0.0561248\pi\)
−0.340339 + 0.940303i \(0.610542\pi\)
\(242\) −11.0000 −0.707107
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 10.0000 0.637577
\(247\) 0 0
\(248\) 10.0000 0.635001
\(249\) 2.00000 3.46410i 0.126745 0.219529i
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −14.0000 24.2487i −0.883672 1.53057i −0.847228 0.531229i \(-0.821730\pi\)
−0.0364441 0.999336i \(-0.511603\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 4.00000 + 6.92820i 0.250982 + 0.434714i
\(255\) 4.00000 0.250490
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 2.00000 3.46410i 0.124515 0.215666i
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) −10.0000 −0.618984
\(262\) 4.00000 6.92820i 0.247121 0.428026i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 6.00000 + 10.3923i 0.367884 + 0.637193i
\(267\) −3.00000 5.19615i −0.183597 0.317999i
\(268\) −2.00000 −0.122169
\(269\) 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i \(-0.0680585\pi\)
−0.672374 + 0.740212i \(0.734725\pi\)
\(270\) −1.00000 + 1.73205i −0.0608581 + 0.105409i
\(271\) −5.00000 + 8.66025i −0.303728 + 0.526073i −0.976977 0.213343i \(-0.931565\pi\)
0.673249 + 0.739416i \(0.264898\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 2.00000 3.46410i 0.120386 0.208514i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −20.0000 −1.19952
\(279\) −5.00000 8.66025i −0.299342 0.518476i
\(280\) −2.00000 3.46410i −0.119523 0.207020i
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) −6.00000 10.3923i −0.357295 0.618853i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 0 0
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 20.0000 1.18056
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 10.0000 + 17.3205i 0.587220 + 1.01710i
\(291\) −12.0000 −0.703452
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) −7.00000 12.1244i −0.408944 0.708312i 0.585827 0.810436i \(-0.300770\pi\)
−0.994772 + 0.102123i \(0.967436\pi\)
\(294\) −3.00000 −0.174964
\(295\) 4.00000 + 6.92820i 0.232889 + 0.403376i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) 14.0000 0.810998
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 4.00000 6.92820i 0.230556 0.399335i
\(302\) 5.00000 8.66025i 0.287718 0.498342i
\(303\) 1.00000 + 1.73205i 0.0574485 + 0.0995037i
\(304\) −6.00000 −0.344124
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) −8.00000 + 13.8564i −0.455104 + 0.788263i
\(310\) −10.0000 + 17.3205i −0.567962 + 0.983739i
\(311\) 28.0000 1.58773 0.793867 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 1.00000 1.73205i 0.0564333 0.0977453i
\(315\) −2.00000 + 3.46410i −0.112687 + 0.195180i
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 0 0
\(320\) 2.00000 0.111803
\(321\) −4.00000 6.92820i −0.223258 0.386695i
\(322\) 4.00000 6.92820i 0.222911 0.386094i
\(323\) 6.00000 10.3923i 0.333849 0.578243i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 14.0000 0.775388
\(327\) −2.00000 + 3.46410i −0.110600 + 0.191565i
\(328\) −5.00000 + 8.66025i −0.276079 + 0.478183i
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) 2.00000 + 3.46410i 0.109764 + 0.190117i
\(333\) −8.00000 −0.438397
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) −1.00000 + 1.73205i −0.0545545 + 0.0944911i
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) 14.0000 0.760376
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) 0 0
\(342\) 3.00000 + 5.19615i 0.162221 + 0.280976i
\(343\) −20.0000 −1.07990
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 4.00000 + 6.92820i 0.215353 + 0.373002i
\(346\) 6.00000 0.322562
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 5.00000 8.66025i 0.268028 0.464238i
\(349\) −8.00000 + 13.8564i −0.428230 + 0.741716i −0.996716 0.0809766i \(-0.974196\pi\)
0.568486 + 0.822693i \(0.307529\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 0 0
\(353\) −13.0000 + 22.5167i −0.691920 + 1.19844i 0.279288 + 0.960207i \(0.409902\pi\)
−0.971208 + 0.238233i \(0.923432\pi\)
\(354\) 2.00000 3.46410i 0.106299 0.184115i
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) −2.00000 3.46410i −0.105851 0.183340i
\(358\) 0 0
\(359\) −4.00000 −0.211112 −0.105556 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) −1.00000 1.73205i −0.0527046 0.0912871i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 11.0000 19.0526i 0.578147 1.00138i
\(363\) −11.0000 −0.577350
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) −1.00000 + 1.73205i −0.0522708 + 0.0905357i
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 10.0000 0.520579
\(370\) 8.00000 + 13.8564i 0.415900 + 0.720360i
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) 10.0000 0.518476
\(373\) 3.00000 + 5.19615i 0.155334 + 0.269047i 0.933181 0.359408i \(-0.117021\pi\)
−0.777847 + 0.628454i \(0.783688\pi\)
\(374\) 0 0
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 12.0000 0.618853
\(377\) 0 0
\(378\) 2.00000 0.102869
\(379\) −17.0000 + 29.4449i −0.873231 + 1.51248i −0.0145964 + 0.999893i \(0.504646\pi\)
−0.858635 + 0.512588i \(0.828687\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 12.0000 0.613973
\(383\) 2.00000 + 3.46410i 0.102195 + 0.177007i 0.912589 0.408879i \(-0.134080\pi\)
−0.810394 + 0.585886i \(0.800747\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) 8.00000 + 13.8564i 0.407189 + 0.705273i
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) 4.00000 6.92820i 0.201773 0.349482i
\(394\) 11.0000 + 19.0526i 0.554172 + 0.959854i
\(395\) 0 0
\(396\) 0 0
\(397\) 4.00000 + 6.92820i 0.200754 + 0.347717i 0.948772 0.315963i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(398\) 0 0
\(399\) 6.00000 + 10.3923i 0.300376 + 0.520266i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) −2.00000 −0.0997509
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) −1.00000 + 1.73205i −0.0496904 + 0.0860663i
\(406\) 10.0000 17.3205i 0.496292 0.859602i
\(407\) 0 0
\(408\) 2.00000 0.0990148
\(409\) −2.00000 3.46410i −0.0988936 0.171289i 0.812333 0.583193i \(-0.198197\pi\)
−0.911227 + 0.411905i \(0.864864\pi\)
\(410\) −10.0000 17.3205i −0.493865 0.855399i
\(411\) 2.00000 0.0986527
\(412\) −8.00000 13.8564i −0.394132 0.682656i
\(413\) 4.00000 6.92820i 0.196827 0.340915i
\(414\) 2.00000 3.46410i 0.0982946 0.170251i
\(415\) −8.00000 −0.392705
\(416\) 0 0
\(417\) −20.0000 −0.979404
\(418\) 0 0
\(419\) −20.0000 + 34.6410i −0.977064 + 1.69232i −0.304115 + 0.952635i \(0.598361\pi\)
−0.672949 + 0.739689i \(0.734973\pi\)
\(420\) −2.00000 3.46410i −0.0975900 0.169031i
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) −6.00000 10.3923i −0.292075 0.505889i
\(423\) −6.00000 10.3923i −0.291730 0.505291i
\(424\) −6.00000 −0.291386
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) −2.00000 + 3.46410i −0.0967868 + 0.167640i
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 10.0000 17.3205i 0.481683 0.834300i −0.518096 0.855323i \(-0.673359\pi\)
0.999779 + 0.0210230i \(0.00669232\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −13.0000 22.5167i −0.624740 1.08208i −0.988591 0.150624i \(-0.951872\pi\)
0.363851 0.931457i \(-0.381462\pi\)
\(434\) 20.0000 0.960031
\(435\) 10.0000 + 17.3205i 0.479463 + 0.830455i
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) 24.0000 1.14808
\(438\) −2.00000 3.46410i −0.0955637 0.165521i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −16.0000 −0.760183 −0.380091 0.924949i \(-0.624107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(444\) 4.00000 6.92820i 0.189832 0.328798i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 7.00000 + 12.1244i 0.331460 + 0.574105i
\(447\) 14.0000 0.662177
\(448\) −1.00000 1.73205i −0.0472456 0.0818317i
\(449\) −3.00000 5.19615i −0.141579 0.245222i 0.786513 0.617574i \(-0.211885\pi\)
−0.928091 + 0.372353i \(0.878551\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) −7.00000 + 12.1244i −0.329252 + 0.570282i
\(453\) 5.00000 8.66025i 0.234920 0.406894i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) −14.0000 + 24.2487i −0.654892 + 1.13431i 0.327028 + 0.945015i \(0.393953\pi\)
−0.981921 + 0.189292i \(0.939381\pi\)
\(458\) 2.00000 3.46410i 0.0934539 0.161867i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) −8.00000 −0.373002
\(461\) 15.0000 + 25.9808i 0.698620 + 1.21004i 0.968945 + 0.247276i \(0.0795353\pi\)
−0.270326 + 0.962769i \(0.587131\pi\)
\(462\) 0 0
\(463\) −6.00000 −0.278844 −0.139422 0.990233i \(-0.544524\pi\)
−0.139422 + 0.990233i \(0.544524\pi\)
\(464\) 5.00000 + 8.66025i 0.232119 + 0.402042i
\(465\) −10.0000 + 17.3205i −0.463739 + 0.803219i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) −12.0000 + 20.7846i −0.553519 + 0.958723i
\(471\) 1.00000 1.73205i 0.0460776 0.0798087i
\(472\) 2.00000 + 3.46410i 0.0920575 + 0.159448i
\(473\) 0 0
\(474\) 0 0
\(475\) −3.00000 5.19615i −0.137649 0.238416i
\(476\) 4.00000 0.183340
\(477\) 3.00000 + 5.19615i 0.137361 + 0.237915i
\(478\) 8.00000 13.8564i 0.365911 0.633777i
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 2.00000 0.0912871
\(481\) 0 0
\(482\) −20.0000 −0.910975
\(483\) 4.00000 6.92820i 0.182006 0.315244i
\(484\) 5.50000 9.52628i 0.250000 0.433013i
\(485\) 12.0000 + 20.7846i 0.544892 + 0.943781i
\(486\) 1.00000 0.0453609
\(487\) −9.00000 15.5885i −0.407829 0.706380i 0.586817 0.809719i \(-0.300381\pi\)
−0.994646 + 0.103339i \(0.967047\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) 14.0000 0.633102
\(490\) 3.00000 + 5.19615i 0.135526 + 0.234738i
\(491\) −14.0000 + 24.2487i −0.631811 + 1.09433i 0.355370 + 0.934726i \(0.384355\pi\)
−0.987181 + 0.159603i \(0.948978\pi\)
\(492\) −5.00000 + 8.66025i −0.225417 + 0.390434i
\(493\) −20.0000 −0.900755
\(494\) 0 0
\(495\) 0 0
\(496\) −5.00000 + 8.66025i −0.224507 + 0.388857i
\(497\) 0 0
\(498\) 2.00000 + 3.46410i 0.0896221 + 0.155230i
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 28.0000 1.24970
\(503\) −12.0000 20.7846i −0.535054 0.926740i −0.999161 0.0409609i \(-0.986958\pi\)
0.464107 0.885779i \(-0.346375\pi\)
\(504\) −1.00000 + 1.73205i −0.0445435 + 0.0771517i
\(505\) 2.00000 3.46410i 0.0889988 0.154150i
\(506\) 0 0
\(507\) 0 0
\(508\) −8.00000 −0.354943
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) −2.00000 + 3.46410i −0.0885615 + 0.153393i
\(511\) −4.00000 6.92820i −0.176950 0.306486i
\(512\) 1.00000 0.0441942
\(513\) 3.00000 + 5.19615i 0.132453 + 0.229416i
\(514\) 9.00000 + 15.5885i 0.396973 + 0.687577i
\(515\) 32.0000 1.41009
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 0 0
\(518\) 8.00000 13.8564i 0.351500 0.608816i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 5.00000 8.66025i 0.218844 0.379049i
\(523\) −2.00000 + 3.46410i −0.0874539 + 0.151475i −0.906434 0.422347i \(-0.861206\pi\)
0.818980 + 0.573822i \(0.194540\pi\)
\(524\) 4.00000 + 6.92820i 0.174741 + 0.302660i
\(525\) −2.00000 −0.0872872
\(526\) −12.0000 20.7846i −0.523225 0.906252i
\(527\) −10.0000 17.3205i −0.435607 0.754493i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 6.00000 10.3923i 0.260623 0.451413i
\(531\) 2.00000 3.46410i 0.0867926 0.150329i
\(532\) −12.0000 −0.520266
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) −8.00000 + 13.8564i −0.345870 + 0.599065i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 0 0
\(538\) −10.0000 −0.431131
\(539\) 0 0
\(540\) −1.00000 1.73205i −0.0430331 0.0745356i
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −5.00000 8.66025i −0.214768 0.371990i
\(543\) 11.0000 19.0526i 0.472055 0.817624i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 60.0000 2.55609
\(552\) 2.00000 + 3.46410i 0.0851257 + 0.147442i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 8.00000 + 13.8564i 0.339581 + 0.588172i
\(556\) 10.0000 17.3205i 0.424094 0.734553i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 10.0000 0.423334
\(559\) 0 0
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) −5.00000 + 8.66025i −0.210912 + 0.365311i
\(563\) −8.00000 13.8564i −0.337160 0.583978i 0.646737 0.762713i \(-0.276133\pi\)
−0.983897 + 0.178735i \(0.942800\pi\)
\(564\) 12.0000 0.505291
\(565\) −14.0000 24.2487i −0.588984 1.02015i
\(566\) 2.00000 + 3.46410i 0.0840663 + 0.145607i
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) 5.00000 8.66025i 0.209611 0.363057i −0.741981 0.670421i \(-0.766114\pi\)
0.951592 + 0.307364i \(0.0994469\pi\)
\(570\) 6.00000 10.3923i 0.251312 0.435286i
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) −10.0000 + 17.3205i −0.417392 + 0.722944i
\(575\) −2.00000 + 3.46410i −0.0834058 + 0.144463i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 8.00000 0.333044 0.166522 0.986038i \(-0.446746\pi\)
0.166522 + 0.986038i \(0.446746\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 8.00000 + 13.8564i 0.332469 + 0.575853i
\(580\) −20.0000 −0.830455
\(581\) 4.00000 + 6.92820i 0.165948 + 0.287430i
\(582\) 6.00000 10.3923i 0.248708 0.430775i
\(583\) 0 0
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −14.0000 + 24.2487i −0.577842 + 1.00085i 0.417885 + 0.908500i \(0.362772\pi\)
−0.995726 + 0.0923513i \(0.970562\pi\)
\(588\) 1.50000 2.59808i 0.0618590 0.107143i
\(589\) 30.0000 + 51.9615i 1.23613 + 2.14104i
\(590\) −8.00000 −0.329355
\(591\) 11.0000 + 19.0526i 0.452480 + 0.783718i
\(592\) 4.00000 + 6.92820i 0.164399 + 0.284747i
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −4.00000 + 6.92820i −0.163984 + 0.284029i
\(596\) −7.00000 + 12.1244i −0.286731 + 0.496633i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) −11.0000 + 19.0526i −0.448699 + 0.777170i −0.998302 0.0582563i \(-0.981446\pi\)
0.549602 + 0.835426i \(0.314779\pi\)
\(602\) 4.00000 + 6.92820i 0.163028 + 0.282372i
\(603\) −2.00000 −0.0814463
\(604\) 5.00000 + 8.66025i 0.203447 + 0.352381i
\(605\) 11.0000 + 19.0526i 0.447214 + 0.774597i
\(606\) −2.00000 −0.0812444
\(607\) 16.0000 + 27.7128i 0.649420 + 1.12483i 0.983262 + 0.182199i \(0.0583216\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(608\) 3.00000 5.19615i 0.121666 0.210732i
\(609\) 10.0000 17.3205i 0.405220 0.701862i
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) 2.00000 0.0808452
\(613\) −8.00000 + 13.8564i −0.323117 + 0.559655i −0.981129 0.193352i \(-0.938064\pi\)
0.658012 + 0.753007i \(0.271397\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) −10.0000 17.3205i −0.403239 0.698430i
\(616\) 0 0
\(617\) 11.0000 + 19.0526i 0.442843 + 0.767027i 0.997899 0.0647859i \(-0.0206365\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(618\) −8.00000 13.8564i −0.321807 0.557386i
\(619\) 26.0000 1.04503 0.522514 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) −10.0000 17.3205i −0.401610 0.695608i
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) −14.0000 + 24.2487i −0.561349 + 0.972285i
\(623\) 12.0000 0.480770
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 13.0000 22.5167i 0.519584 0.899947i
\(627\) 0 0
\(628\) 1.00000 + 1.73205i 0.0399043 + 0.0691164i
\(629\) −16.0000 −0.637962
\(630\) −2.00000 3.46410i −0.0796819 0.138013i
\(631\) 5.00000 + 8.66025i 0.199047 + 0.344759i 0.948220 0.317615i \(-0.102882\pi\)
−0.749173 + 0.662375i \(0.769549\pi\)
\(632\) 0 0
\(633\) −6.00000 10.3923i −0.238479 0.413057i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 8.00000 13.8564i 0.317470 0.549875i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 8.00000 0.315735
\(643\) −3.00000 5.19615i −0.118308 0.204916i 0.800789 0.598947i \(-0.204414\pi\)
−0.919097 + 0.394030i \(0.871080\pi\)
\(644\) 4.00000 + 6.92820i 0.157622 + 0.273009i
\(645\) −8.00000 −0.315000
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −16.0000 + 27.7128i −0.629025 + 1.08950i 0.358723 + 0.933444i \(0.383212\pi\)
−0.987748 + 0.156059i \(0.950121\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 0 0
\(651\) 20.0000 0.783862
\(652\) −7.00000 + 12.1244i −0.274141 + 0.474826i
\(653\) 13.0000 22.5167i 0.508729 0.881145i −0.491220 0.871036i \(-0.663449\pi\)
0.999949 0.0101092i \(-0.00321793\pi\)
\(654\) −2.00000 3.46410i −0.0782062 0.135457i
\(655\) −16.0000 −0.625172
\(656\) −5.00000 8.66025i −0.195217 0.338126i
\(657\) −2.00000 3.46410i −0.0780274 0.135147i
\(658\) 24.0000 0.935617
\(659\) −10.0000 17.3205i −0.389545 0.674711i 0.602844 0.797859i \(-0.294034\pi\)
−0.992388 + 0.123148i \(0.960701\pi\)
\(660\) 0 0
\(661\) −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i \(0.450387\pi\)
−0.933144 + 0.359502i \(0.882947\pi\)
\(662\) −10.0000 −0.388661
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) 12.0000 20.7846i 0.465340 0.805993i
\(666\) 4.00000 6.92820i 0.154997 0.268462i
\(667\) −20.0000 34.6410i −0.774403 1.34131i
\(668\) 12.0000 0.464294
\(669\) 7.00000 + 12.1244i 0.270636 + 0.468755i
\(670\) 2.00000 + 3.46410i 0.0772667 + 0.133830i
\(671\) 0 0
\(672\) −1.00000 1.73205i −0.0385758 0.0668153i
\(673\) −3.00000 + 5.19615i −0.115642 + 0.200297i −0.918036 0.396497i \(-0.870226\pi\)
0.802395 + 0.596794i \(0.203559\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −7.00000 + 12.1244i −0.268833 + 0.465633i
\(679\) 12.0000 20.7846i 0.460518 0.797640i
\(680\) −2.00000 3.46410i −0.0766965 0.132842i
\(681\) 8.00000 0.306561
\(682\) 0 0
\(683\) −12.0000 20.7846i −0.459167 0.795301i 0.539750 0.841825i \(-0.318519\pi\)
−0.998917 + 0.0465244i \(0.985185\pi\)
\(684\) −6.00000 −0.229416
\(685\) −2.00000 3.46410i −0.0764161 0.132357i
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 2.00000 3.46410i 0.0763048 0.132164i
\(688\) −4.00000 −0.152499
\(689\) 0 0
\(690\) −8.00000 −0.304555
\(691\) 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i \(-0.772417\pi\)
0.945319 + 0.326146i \(0.105750\pi\)
\(692\) −3.00000 + 5.19615i −0.114043 + 0.197528i
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 20.0000 + 34.6410i 0.758643 + 1.31401i
\(696\) 5.00000 + 8.66025i 0.189525 + 0.328266i
\(697\) 20.0000 0.757554
\(698\) −8.00000 13.8564i −0.302804 0.524473i
\(699\) −3.00000 + 5.19615i −0.113470 + 0.196537i
\(700\) 1.00000 1.73205i 0.0377964 0.0654654i
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 0 0
\(703\) 48.0000 1.81035
\(704\) 0 0
\(705\) −12.0000 + 20.7846i −0.451946 + 0.782794i
\(706\) −13.0000 22.5167i −0.489261 0.847426i
\(707\) −4.00000 −0.150435
\(708\) 2.00000 + 3.46410i 0.0751646 + 0.130189i
\(709\) −18.0000 31.1769i −0.676004 1.17087i −0.976174 0.216988i \(-0.930377\pi\)
0.300170 0.953886i \(-0.402957\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 20.0000 34.6410i 0.749006 1.29732i
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) 0 0
\(717\) 8.00000 13.8564i 0.298765 0.517477i
\(718\) 2.00000 3.46410i 0.0746393 0.129279i
\(719\) 10.0000 + 17.3205i 0.372937 + 0.645946i 0.990016 0.140955i \(-0.0450174\pi\)
−0.617079 + 0.786901i \(0.711684\pi\)
\(720\) 2.00000 0.0745356
\(721\) −16.0000 27.7128i −0.595871 1.03208i
\(722\) −8.50000 14.7224i −0.316337 0.547912i
\(723\) −20.0000 −0.743808
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) −5.00000 + 8.66025i −0.185695 + 0.321634i
\(726\) 5.50000 9.52628i 0.204124 0.353553i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −4.00000 + 6.92820i −0.148047 + 0.256424i
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) −44.0000 −1.62518 −0.812589 0.582838i \(-0.801942\pi\)
−0.812589 + 0.582838i \(0.801942\pi\)
\(734\) −4.00000 6.92820i −0.147643 0.255725i
\(735\) 3.00000 + 5.19615i 0.110657 + 0.191663i
\(736\) −4.00000 −0.147442
\(737\) 0 0
\(738\) −5.00000 + 8.66025i −0.184053 + 0.318788i
\(739\) −13.0000 + 22.5167i −0.478213 + 0.828289i −0.999688 0.0249776i \(-0.992049\pi\)
0.521475 + 0.853266i \(0.325382\pi\)
\(740\) −16.0000 −0.588172
\(741\) 0 0
\(742\) −12.0000 −0.440534
\(743\) −8.00000 + 13.8564i −0.293492 + 0.508342i −0.974633 0.223810i \(-0.928151\pi\)
0.681141 + 0.732152i \(0.261484\pi\)
\(744\) −5.00000 + 8.66025i −0.183309 + 0.317500i
\(745\) −14.0000 24.2487i −0.512920 0.888404i
\(746\) −6.00000 −0.219676
\(747\) 2.00000 + 3.46410i 0.0731762 + 0.126745i
\(748\) 0 0
\(749\) 16.0000 0.584627
\(750\) 6.00000 + 10.3923i 0.219089 + 0.379473i
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) −6.00000 + 10.3923i −0.218797 + 0.378968i
\(753\) 28.0000 1.02038
\(754\) 0 0
\(755\) −20.0000 −0.727875
\(756\) −1.00000 + 1.73205i −0.0363696 + 0.0629941i
\(757\) 11.0000 19.0526i 0.399802 0.692477i −0.593899 0.804539i \(-0.702412\pi\)
0.993701 + 0.112062i \(0.0357456\pi\)
\(758\) −17.0000 29.4449i −0.617468 1.06949i
\(759\) 0 0
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) −8.00000 −0.289809
\(763\) −4.00000 6.92820i −0.144810 0.250818i
\(764\) −6.00000 + 10.3923i −0.217072 + 0.375980i
\(765\) −2.00000 + 3.46410i −0.0723102 + 0.125245i
\(766\) −4.00000 −0.144526
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −12.0000 + 20.7846i −0.432731 + 0.749512i −0.997107 0.0760054i \(-0.975783\pi\)
0.564376 + 0.825518i \(0.309117\pi\)
\(770\) 0 0
\(771\) 9.00000 + 15.5885i 0.324127 + 0.561405i
\(772\) −16.0000 −0.575853
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) −10.0000 −0.359211
\(776\) 6.00000 + 10.3923i 0.215387 + 0.373062i
\(777\) 8.00000 13.8564i 0.286998 0.497096i
\(778\) 15.0000 25.9808i 0.537776 0.931455i
\(779\) −60.0000 −2.14972
\(780\) 0 0
\(781\) 0 0
\(782\) 4.00000 6.92820i 0.143040 0.247752i
\(783\) 5.00000