Properties

Label 1014.2.e.b.991.1
Level $1014$
Weight $2$
Character 1014.991
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 991.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1014.991
Dual form 1014.2.e.b.529.1

$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

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

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:
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\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 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 −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) −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 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) −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 0.785872 + 0.618389i \(0.212214\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) −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 0.981236 + 0.192809i \(0.0617599\pi\)
−0.323640 + 0.946180i \(0.604907\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) −5.00000 8.66025i −0.780869 1.35250i −0.931436 0.363905i \(-0.881443\pi\)
0.150567 0.988600i \(-0.451890\pi\)
\(42\) −1.00000 1.73205i −0.154303 0.267261i
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) 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 −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 2.00000 0.258199
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −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 0.920623 0.390453i \(-0.127682\pi\)
−0.798454 + 0.602056i \(0.794348\pi\)
\(68\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −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 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 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 −0.382164 0.924095i \(-0.624821\pi\)
0.991371 0.131084i \(-0.0418458\pi\)
\(98\) 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 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) −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 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) −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 0.322498 + 0.946570i \(0.395477\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(114\) 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 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) −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 −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) −4.00000 −0.340503
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) −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 0.422744 + 0.906249i \(0.361067\pi\)
−0.996207 + 0.0870170i \(0.972267\pi\)
\(150\) 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 0.450110 + 0.892973i \(0.351385\pi\)
−0.998392 + 0.0566798i \(0.981949\pi\)
\(164\) 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 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 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 −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) −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 −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 11.0000 + 19.0526i 0.783718 + 1.35744i 0.929762 + 0.368161i \(0.120012\pi\)
−0.146045 + 0.989278i \(0.546654\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −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 0.582165 0.813070i \(-0.302206\pi\)
−0.995222 + 0.0976347i \(0.968872\pi\)
\(212\) 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 0.999362 0.0357107i \(-0.0113695\pi\)
−0.530607 + 0.847618i \(0.678036\pi\)
\(224\) −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 −0.967692 0.252136i \(-0.918867\pi\)
0.702202 + 0.711977i \(0.252200\pi\)
\(228\) 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 −0.340339 0.940303i \(-0.610542\pi\)
0.984496 0.175409i \(-0.0561248\pi\)
\(242\) −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 −0.0364441 + 0.999336i \(0.511603\pi\)
−0.847228 + 0.531229i \(0.821730\pi\)
\(252\) 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 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 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 −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 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 −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −5.00000 8.66025i −0.303728 0.526073i 0.673249 0.739416i \(-0.264898\pi\)
−0.976977 + 0.213343i \(0.931565\pi\)
\(272\) 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 −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) −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 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 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 −0.994772 0.102123i \(-0.967436\pi\)
0.585827 + 0.810436i \(0.300770\pi\)
\(294\) −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 −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 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 −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 5.00000 + 8.66025i 0.268028 + 0.464238i
\(349\) −8.00000 13.8564i −0.428230 0.741716i 0.568486 0.822693i \(-0.307529\pi\)
−0.996716 + 0.0809766i \(0.974196\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 0 0
\(353\) −13.0000 22.5167i −0.691920 1.19844i −0.971208 0.238233i \(-0.923432\pi\)
0.279288 0.960207i \(-0.409902\pi\)
\(354\) 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 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 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 −0.777847 0.628454i \(-0.783688\pi\)
0.933181 + 0.359408i \(0.117021\pi\)
\(374\) 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 −0.858635 0.512588i \(-0.828687\pi\)
−0.0145964 0.999893i \(-0.504646\pi\)
\(380\) 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 −0.810394 0.585886i \(-0.800747\pi\)
0.912589 + 0.408879i \(0.134080\pi\)
\(384\) −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 −0.748017 0.663679i \(-0.768994\pi\)
0.948772 + 0.315963i \(0.102327\pi\)
\(398\) 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 −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) −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 −0.911227 0.411905i \(-0.864864\pi\)
0.812333 + 0.583193i \(0.198197\pi\)
\(410\) −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 −0.672949 0.739689i \(-0.734973\pi\)
−0.304115 0.952635i \(-0.598361\pi\)
\(420\) −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 0.999779 0.0210230i \(-0.00669232\pi\)
−0.518096 + 0.855323i \(0.673359\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −13.0000 + 22.5167i −0.624740 + 1.08208i 0.363851 + 0.931457i \(0.381462\pi\)
−0.988591 + 0.150624i \(0.951872\pi\)
\(434\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 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 −0.928091 0.372353i \(-0.878551\pi\)
0.786513 + 0.617574i \(0.211885\pi\)
\(450\) −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 −0.981921 0.189292i \(-0.939381\pi\)
0.327028 0.945015i \(-0.393953\pi\)
\(458\) 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 −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 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 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) 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 −0.994646 0.103339i \(-0.967047\pi\)
0.586817 + 0.809719i \(0.300381\pi\)
\(488\) −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 −0.987181 0.159603i \(-0.948978\pi\)
0.355370 0.934726i \(-0.384355\pi\)
\(492\) −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 0.464107 + 0.885779i \(0.346375\pi\)
−0.999161 + 0.0409609i \(0.986958\pi\)
\(504\) −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 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) −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 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) 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 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 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 −0.983897 0.178735i \(-0.942800\pi\)
0.646737 + 0.762713i \(0.276133\pi\)
\(564\) 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 0.951592 0.307364i \(-0.0994469\pi\)
−0.741981 + 0.670421i \(0.766114\pi\)
\(570\) 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 −0.995726 0.0923513i \(-0.970562\pi\)
0.417885 0.908500i \(-0.362772\pi\)
\(588\) 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 0.549602 0.835426i \(-0.314779\pi\)
−0.998302 + 0.0582563i \(0.981446\pi\)
\(602\) 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 −0.333842 0.942629i \(-0.608345\pi\)
0.983262 0.182199i \(-0.0583216\pi\)
\(608\) 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 0.658012 0.753007i \(-0.271397\pi\)
−0.981129 + 0.193352i \(0.938064\pi\)
\(614\) −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 −0.555056 0.831813i \(-0.687303\pi\)
0.997899 + 0.0647859i \(0.0206365\pi\)
\(618\) −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 −0.749173 0.662375i \(-0.769549\pi\)
0.948220 + 0.317615i \(0.102882\pi\)
\(632\) 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 −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) 8.00000 0.315735
\(643\) −3.00000 + 5.19615i −0.118308 + 0.204916i −0.919097 0.394030i \(-0.871080\pi\)
0.800789 + 0.598947i \(0.204414\pi\)
\(644\) 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 −0.987748 0.156059i \(-0.950121\pi\)
0.358723 0.933444i \(-0.383212\pi\)
\(648\) −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 0.999949 + 0.0101092i \(0.00321793\pi\)
−0.491220 + 0.871036i \(0.663449\pi\)
\(654\) −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 −0.992388 0.123148i \(-0.960701\pi\)
0.602844 + 0.797859i \(0.294034\pi\)
\(660\) 0 0
\(661\) −20.0000 34.6410i −0.777910 1.34738i −0.933144 0.359502i \(-0.882947\pi\)
0.155235 0.987878i \(-0.450387\pi\)
\(662\) −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 0.802395 0.596794i \(-0.203559\pi\)
−0.918036 + 0.396497i \(0.870226\pi\)
\(674\) −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 −0.998917 0.0465244i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(684\) −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 0.945319 0.326146i \(-0.105750\pi\)
−0.755110 + 0.655598i \(0.772417\pi\)
\(692\) −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 0.300170 + 0.953886i \(0.402957\pi\)
−0.976174 + 0.216988i \(0.930377\pi\)
\(710\) 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 −0.617079 0.786901i \(-0.711684\pi\)
0.990016 + 0.140955i \(0.0450174\pi\)
\(720\) 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 0.521475 0.853266i \(-0.325382\pi\)
−0.999688 + 0.0249776i \(0.992049\pi\)
\(740\) −16.0000 −0.588172
\(741\) 0 0
\(742\) −12.0000 −0.440534
\(743\) −8.00000 13.8564i −0.293492 0.508342i 0.681141 0.732152i \(-0.261484\pi\)
−0.974633 + 0.223810i \(0.928151\pi\)
\(744\) −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 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −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 0.993701 0.112062i \(-0.0357456\pi\)
−0.593899 + 0.804539i \(0.702412\pi\)
\(758\) −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 −0.454935 0.890525i \(-0.650337\pi\)
0.998684 0.0512772i \(-0.0163292\pi\)
\(762\) −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 0.564376 0.825518i \(-0.309117\pi\)
−0.997107 + 0.0760054i \(0.975783\pi\)
\(770\) 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 −0.914920 0.403634i \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 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