Properties

Label 770.2.i.e.331.1
Level $770$
Weight $2$
Character 770.331
Analytic conductor $6.148$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.14848095564\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 331.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 770.331
Dual form 770.2.i.e.221.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -3.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(-3.00000 + 5.19615i) q^{19} +1.00000 q^{20} +(2.00000 + 1.73205i) q^{21} -1.00000 q^{22} +(-1.00000 + 1.73205i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.50000 + 2.59808i) q^{26} -5.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -7.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(0.500000 - 2.59808i) q^{35} -2.00000 q^{36} +(3.00000 + 5.19615i) q^{38} +(1.50000 + 2.59808i) q^{39} +(0.500000 - 0.866025i) q^{40} -4.00000 q^{41} +(2.50000 - 0.866025i) q^{42} -6.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.00000 + 1.73205i) q^{45} +(1.00000 + 1.73205i) q^{46} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -1.00000 q^{50} +(1.50000 + 2.59808i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{54} +1.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +6.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +(0.500000 + 0.866025i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(0.500000 - 0.866025i) q^{61} +8.00000 q^{62} +(-1.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(0.500000 + 0.866025i) q^{66} +(2.50000 + 4.33013i) q^{67} +2.00000 q^{69} +(-2.00000 - 1.73205i) q^{70} +8.00000 q^{71} +(-1.00000 + 1.73205i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(-0.500000 + 0.866025i) q^{75} +6.00000 q^{76} +(2.00000 + 1.73205i) q^{77} +3.00000 q^{78} +(6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +(0.500000 - 2.59808i) q^{84} +(-3.00000 + 5.19615i) q^{86} +(3.50000 + 6.06218i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +2.00000 q^{90} +(7.50000 - 2.59808i) q^{91} +2.00000 q^{92} +(4.00000 - 6.92820i) q^{93} +(-3.00000 - 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} - q^{11} - q^{12} - 6 q^{13} - q^{14} + 2 q^{15} - q^{16} - 2 q^{18} - 6 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} + q^{24} - q^{25} - 3 q^{26} - 10 q^{27} + 4 q^{28} - 14 q^{29} + q^{30} + 8 q^{31} + q^{32} - q^{33} + q^{35} - 4 q^{36} + 6 q^{38} + 3 q^{39} + q^{40} - 8 q^{41} + 5 q^{42} - 12 q^{43} - q^{44} + 2 q^{45} + 2 q^{46} + 2 q^{48} + 11 q^{49} - 2 q^{50} + 3 q^{52} - 6 q^{53} - 5 q^{54} + 2 q^{55} + 5 q^{56} + 12 q^{57} - 7 q^{58} + q^{59} - q^{60} + q^{61} + 16 q^{62} - 2 q^{63} + 2 q^{64} + 3 q^{65} + q^{66} + 5 q^{67} + 4 q^{69} - 4 q^{70} + 16 q^{71} - 2 q^{72} - 14 q^{73} - q^{75} + 12 q^{76} + 4 q^{77} + 6 q^{78} + 13 q^{79} - q^{80} - q^{81} - 4 q^{82} - 12 q^{83} + q^{84} - 6 q^{86} + 7 q^{87} + q^{88} + 6 q^{89} + 4 q^{90} + 15 q^{91} + 4 q^{92} + 8 q^{93} - 6 q^{95} + q^{96} - 14 q^{97} - 2 q^{98} - 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −1.00000 −0.408248
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) −0.500000 + 2.59808i −0.133631 + 0.694365i
\(15\) 1.00000 0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.00000 + 1.73205i 0.436436 + 0.377964i
\(22\) −1.00000 −0.213201
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.50000 + 2.59808i −0.294174 + 0.509525i
\(27\) −5.00000 −0.962250
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 4.00000 + 6.92820i 0.718421 + 1.24434i 0.961625 + 0.274367i \(0.0884683\pi\)
−0.243204 + 0.969975i \(0.578198\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 0 0
\(35\) 0.500000 2.59808i 0.0845154 0.439155i
\(36\) −2.00000 −0.333333
\(37\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(38\) 3.00000 + 5.19615i 0.486664 + 0.842927i
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 2.50000 0.866025i 0.385758 0.133631i
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 1.00000 + 1.73205i 0.147442 + 0.255377i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.50000 + 2.59808i 0.208013 + 0.360288i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 1.00000 0.134840
\(56\) 2.50000 0.866025i 0.334077 0.115728i
\(57\) 6.00000 0.794719
\(58\) −3.50000 + 6.06218i −0.459573 + 0.796003i
\(59\) 0.500000 + 0.866025i 0.0650945 + 0.112747i 0.896736 0.442566i \(-0.145932\pi\)
−0.831641 + 0.555313i \(0.812598\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 8.00000 1.01600
\(63\) −1.00000 + 5.19615i −0.125988 + 0.654654i
\(64\) 1.00000 0.125000
\(65\) 1.50000 2.59808i 0.186052 0.322252i
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) 2.00000 0.240772
\(70\) −2.00000 1.73205i −0.239046 0.207020i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 6.00000 0.688247
\(77\) 2.00000 + 1.73205i 0.227921 + 0.197386i
\(78\) 3.00000 0.339683
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.00000 + 3.46410i −0.220863 + 0.382546i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0.500000 2.59808i 0.0545545 0.283473i
\(85\) 0 0
\(86\) −3.00000 + 5.19615i −0.323498 + 0.560316i
\(87\) 3.50000 + 6.06218i 0.375239 + 0.649934i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 2.00000 0.210819
\(91\) 7.50000 2.59808i 0.786214 0.272352i
\(92\) 2.00000 0.208514
\(93\) 4.00000 6.92820i 0.414781 0.718421i
\(94\) 0 0
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) −2.00000 −0.201008
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 3.00000 0.294174
\(105\) −2.50000 + 0.866025i −0.243975 + 0.0845154i
\(106\) −6.00000 −0.582772
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) −9.00000 15.5885i −0.862044 1.49310i −0.869953 0.493135i \(-0.835851\pi\)
0.00790932 0.999969i \(-0.497482\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) −13.0000 −1.22294 −0.611469 0.791269i \(-0.709421\pi\)
−0.611469 + 0.791269i \(0.709421\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) −1.00000 1.73205i −0.0932505 0.161515i
\(116\) 3.50000 + 6.06218i 0.324967 + 0.562859i
\(117\) −3.00000 + 5.19615i −0.277350 + 0.480384i
\(118\) 1.00000 0.0920575
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −0.500000 0.866025i −0.0452679 0.0784063i
\(123\) 2.00000 + 3.46410i 0.180334 + 0.312348i
\(124\) 4.00000 6.92820i 0.359211 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 4.00000 + 3.46410i 0.356348 + 0.308607i
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 3.00000 + 5.19615i 0.264135 + 0.457496i
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) 1.00000 0.0870388
\(133\) 3.00000 15.5885i 0.260133 1.35169i
\(134\) 5.00000 0.431934
\(135\) 2.50000 4.33013i 0.215166 0.372678i
\(136\) 0 0
\(137\) 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 1.00000 1.73205i 0.0851257 0.147442i
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −2.50000 + 0.866025i −0.211289 + 0.0731925i
\(141\) 0 0
\(142\) 4.00000 6.92820i 0.335673 0.581402i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 3.50000 6.06218i 0.290659 0.503436i
\(146\) −14.0000 −1.15865
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) 0 0
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i \(0.0764802\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) 0 0
\(154\) 2.50000 0.866025i 0.201456 0.0697863i
\(155\) −8.00000 −0.642575
\(156\) 1.50000 2.59808i 0.120096 0.208013i
\(157\) −3.00000 5.19615i −0.239426 0.414698i 0.721124 0.692806i \(-0.243626\pi\)
−0.960550 + 0.278108i \(0.910293\pi\)
\(158\) −6.50000 11.2583i −0.517112 0.895665i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) −1.00000 −0.0790569
\(161\) 1.00000 5.19615i 0.0788110 0.409514i
\(162\) −1.00000 −0.0785674
\(163\) 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i \(-0.691567\pi\)
0.996942 + 0.0781474i \(0.0249005\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) −0.500000 0.866025i −0.0389249 0.0674200i
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 19.0000 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(168\) −2.00000 1.73205i −0.154303 0.133631i
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 6.00000 + 10.3923i 0.458831 + 0.794719i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) 7.00000 0.530669
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) 1.00000 0.0753778
\(177\) 0.500000 0.866025i 0.0375823 0.0650945i
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i \(-0.977246\pi\)
0.436870 0.899525i \(-0.356087\pi\)
\(180\) 1.00000 1.73205i 0.0745356 0.129099i
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 1.50000 7.79423i 0.111187 0.577747i
\(183\) −1.00000 −0.0739221
\(184\) 1.00000 1.73205i 0.0737210 0.127688i
\(185\) 0 0
\(186\) −4.00000 6.92820i −0.293294 0.508001i
\(187\) 0 0
\(188\) 0 0
\(189\) 12.5000 4.33013i 0.909241 0.314970i
\(190\) −6.00000 −0.435286
\(191\) −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i \(-0.879560\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −4.00000 6.92820i −0.287926 0.498703i 0.685388 0.728178i \(-0.259632\pi\)
−0.973315 + 0.229475i \(0.926299\pi\)
\(194\) −3.50000 + 6.06218i −0.251285 + 0.435239i
\(195\) −3.00000 −0.214834
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 11.0000 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) 3.00000 + 5.19615i 0.212664 + 0.368345i 0.952548 0.304390i \(-0.0984526\pi\)
−0.739883 + 0.672735i \(0.765119\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 2.50000 4.33013i 0.176336 0.305424i
\(202\) 15.0000 1.05540
\(203\) 17.5000 6.06218i 1.22826 0.425481i
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) 2.00000 + 3.46410i 0.139010 + 0.240772i
\(208\) 1.50000 2.59808i 0.104006 0.180144i
\(209\) 6.00000 0.415029
\(210\) −0.500000 + 2.59808i −0.0345033 + 0.179284i
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) −4.00000 6.92820i −0.274075 0.474713i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 3.00000 5.19615i 0.204598 0.354375i
\(216\) 5.00000 0.340207
\(217\) −16.0000 13.8564i −1.08615 0.940634i
\(218\) −18.0000 −1.21911
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) −0.500000 0.866025i −0.0337100 0.0583874i
\(221\) 0 0
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) −2.00000 1.73205i −0.133631 0.115728i
\(225\) −2.00000 −0.133333
\(226\) −6.50000 + 11.2583i −0.432374 + 0.748893i
\(227\) 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i \(-0.0811332\pi\)
−0.702202 + 0.711977i \(0.747800\pi\)
\(228\) −3.00000 5.19615i −0.198680 0.344124i
\(229\) −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i \(0.495620\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0.500000 2.59808i 0.0328976 0.170941i
\(232\) 7.00000 0.459573
\(233\) 6.00000 10.3923i 0.393073 0.680823i −0.599780 0.800165i \(-0.704745\pi\)
0.992853 + 0.119342i \(0.0380786\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) 0.500000 0.866025i 0.0325472 0.0563735i
\(237\) −13.0000 −0.844441
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) −1.00000 −0.0640184
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 4.00000 0.255031
\(247\) 9.00000 15.5885i 0.572656 0.991870i
\(248\) −4.00000 6.92820i −0.254000 0.439941i
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 5.00000 1.73205i 0.314970 0.109109i
\(253\) 2.00000 0.125739
\(254\) −9.50000 + 16.4545i −0.596083 + 1.03245i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.50000 + 11.2583i −0.405459 + 0.702275i −0.994375 0.105919i \(-0.966222\pi\)
0.588916 + 0.808194i \(0.299555\pi\)
\(258\) 6.00000 0.373544
\(259\) 0 0
\(260\) −3.00000 −0.186052
\(261\) −7.00000 + 12.1244i −0.433289 + 0.750479i
\(262\) −7.00000 12.1244i −0.432461 0.749045i
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 6.00000 0.368577
\(266\) −12.0000 10.3923i −0.735767 0.637193i
\(267\) −6.00000 −0.367194
\(268\) 2.50000 4.33013i 0.152712 0.264505i
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) −2.50000 4.33013i −0.152145 0.263523i
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) 0 0
\(273\) −6.00000 5.19615i −0.363137 0.314485i
\(274\) 3.00000 0.181237
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) −1.00000 1.73205i −0.0601929 0.104257i
\(277\) 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i \(0.00395278\pi\)
−0.489207 + 0.872167i \(0.662714\pi\)
\(278\) −8.00000 + 13.8564i −0.479808 + 0.831052i
\(279\) 16.0000 0.957895
\(280\) −0.500000 + 2.59808i −0.0298807 + 0.155265i
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 0 0
\(283\) −5.00000 8.66025i −0.297219 0.514799i 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) −3.00000 + 5.19615i −0.177705 + 0.307794i
\(286\) 3.00000 0.177394
\(287\) 10.0000 3.46410i 0.590281 0.204479i
\(288\) 2.00000 0.117851
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −3.50000 6.06218i −0.205527 0.355983i
\(291\) 3.50000 + 6.06218i 0.205174 + 0.355371i
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) −5.50000 + 4.33013i −0.320767 + 0.252538i
\(295\) −1.00000 −0.0582223
\(296\) 0 0
\(297\) 2.50000 + 4.33013i 0.145065 + 0.251259i
\(298\) −9.00000 15.5885i −0.521356 0.903015i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 1.00000 0.0577350
\(301\) 15.0000 5.19615i 0.864586 0.299501i
\(302\) 17.0000 0.978240
\(303\) 7.50000 12.9904i 0.430864 0.746278i
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) 0.500000 + 0.866025i 0.0286299 + 0.0495885i
\(306\) 0 0
\(307\) −26.0000 −1.48390 −0.741949 0.670456i \(-0.766098\pi\)
−0.741949 + 0.670456i \(0.766098\pi\)
\(308\) 0.500000 2.59808i 0.0284901 0.148039i
\(309\) 4.00000 0.227552
\(310\) −4.00000 + 6.92820i −0.227185 + 0.393496i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) −1.50000 2.59808i −0.0849208 0.147087i
\(313\) 6.50000 11.2583i 0.367402 0.636358i −0.621757 0.783210i \(-0.713581\pi\)
0.989158 + 0.146852i \(0.0469141\pi\)
\(314\) −6.00000 −0.338600
\(315\) −4.00000 3.46410i −0.225374 0.195180i
\(316\) −13.0000 −0.731307
\(317\) 10.0000 17.3205i 0.561656 0.972817i −0.435696 0.900094i \(-0.643498\pi\)
0.997352 0.0727229i \(-0.0231689\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 3.50000 + 6.06218i 0.195962 + 0.339417i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 6.00000 0.334887
\(322\) −4.00000 3.46410i −0.222911 0.193047i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 1.50000 + 2.59808i 0.0832050 + 0.144115i
\(326\) −5.50000 9.52628i −0.304617 0.527612i
\(327\) −9.00000 + 15.5885i −0.497701 + 0.862044i
\(328\) 4.00000 0.220863
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 0 0
\(334\) 9.50000 16.4545i 0.519817 0.900349i
\(335\) −5.00000 −0.273179
\(336\) −2.50000 + 0.866025i −0.136386 + 0.0472456i
\(337\) −4.00000 −0.217894 −0.108947 0.994048i \(-0.534748\pi\)
−0.108947 + 0.994048i \(0.534748\pi\)
\(338\) −2.00000 + 3.46410i −0.108786 + 0.188422i
\(339\) 6.50000 + 11.2583i 0.353032 + 0.611469i
\(340\) 0 0
\(341\) 4.00000 6.92820i 0.216612 0.375183i
\(342\) 12.0000 0.648886
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 6.00000 0.323498
\(345\) −1.00000 + 1.73205i −0.0538382 + 0.0932505i
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) 13.0000 + 22.5167i 0.697877 + 1.20876i 0.969201 + 0.246270i \(0.0792049\pi\)
−0.271325 + 0.962488i \(0.587462\pi\)
\(348\) 3.50000 6.06218i 0.187620 0.324967i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 2.50000 0.866025i 0.133631 0.0462910i
\(351\) 15.0000 0.800641
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) −0.500000 0.866025i −0.0265747 0.0460287i
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) −15.5000 + 26.8468i −0.818059 + 1.41692i 0.0890519 + 0.996027i \(0.471616\pi\)
−0.907111 + 0.420892i \(0.861717\pi\)
\(360\) −1.00000 1.73205i −0.0527046 0.0912871i
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 6.00000 10.3923i 0.315353 0.546207i
\(363\) 1.00000 0.0524864
\(364\) −6.00000 5.19615i −0.314485 0.272352i
\(365\) 14.0000 0.732793
\(366\) −0.500000 + 0.866025i −0.0261354 + 0.0452679i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) −1.00000 1.73205i −0.0521286 0.0902894i
\(369\) −4.00000 + 6.92820i −0.208232 + 0.360668i
\(370\) 0 0
\(371\) 12.0000 + 10.3923i 0.623009 + 0.539542i
\(372\) −8.00000 −0.414781
\(373\) 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) 0 0
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 0 0
\(377\) 21.0000 1.08156
\(378\) 2.50000 12.9904i 0.128586 0.668153i
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) 9.50000 + 16.4545i 0.486700 + 0.842989i
\(382\) 2.00000 + 3.46410i 0.102329 + 0.177239i
\(383\) −8.00000 + 13.8564i −0.408781 + 0.708029i −0.994753 0.102302i \(-0.967379\pi\)
0.585973 + 0.810331i \(0.300713\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −2.50000 + 0.866025i −0.127412 + 0.0441367i
\(386\) −8.00000 −0.407189
\(387\) −6.00000 + 10.3923i −0.304997 + 0.528271i
\(388\) 3.50000 + 6.06218i 0.177686 + 0.307760i
\(389\) 16.0000 + 27.7128i 0.811232 + 1.40510i 0.912002 + 0.410186i \(0.134536\pi\)
−0.100770 + 0.994910i \(0.532131\pi\)
\(390\) −1.50000 + 2.59808i −0.0759555 + 0.131559i
\(391\) 0 0
\(392\) −5.50000 + 4.33013i −0.277792 + 0.218704i
\(393\) −14.0000 −0.706207
\(394\) 5.50000 9.52628i 0.277086 0.479927i
\(395\) 6.50000 + 11.2583i 0.327050 + 0.566468i
\(396\) 1.00000 + 1.73205i 0.0502519 + 0.0870388i
\(397\) −13.0000 + 22.5167i −0.652451 + 1.13008i 0.330075 + 0.943955i \(0.392926\pi\)
−0.982526 + 0.186124i \(0.940407\pi\)
\(398\) 6.00000 0.300753
\(399\) −15.0000 + 5.19615i −0.750939 + 0.260133i
\(400\) 1.00000 0.0500000
\(401\) 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i \(-0.525087\pi\)
0.902703 0.430263i \(-0.141579\pi\)
\(402\) −2.50000 4.33013i −0.124689 0.215967i
\(403\) −12.0000 20.7846i −0.597763 1.03536i
\(404\) 7.50000 12.9904i 0.373139 0.646296i
\(405\) 1.00000 0.0496904
\(406\) 3.50000 18.1865i 0.173702 0.902583i
\(407\) 0 0
\(408\) 0 0
\(409\) 4.00000 + 6.92820i 0.197787 + 0.342578i 0.947811 0.318834i \(-0.103291\pi\)
−0.750023 + 0.661411i \(0.769958\pi\)
\(410\) −2.00000 3.46410i −0.0987730 0.171080i
\(411\) 1.50000 2.59808i 0.0739895 0.128154i
\(412\) 4.00000 0.197066
\(413\) −2.00000 1.73205i −0.0984136 0.0852286i
\(414\) 4.00000 0.196589
\(415\) 3.00000 5.19615i 0.147264 0.255069i
\(416\) −1.50000 2.59808i −0.0735436 0.127381i
\(417\) 8.00000 + 13.8564i 0.391762 + 0.678551i
\(418\) 3.00000 5.19615i 0.146735 0.254152i
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 2.00000 + 1.73205i 0.0975900 + 0.0845154i
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) −6.00000 + 10.3923i −0.292075 + 0.505889i
\(423\) 0 0
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) 0 0
\(426\) −8.00000 −0.387601
\(427\) −0.500000 + 2.59808i −0.0241967 + 0.125730i
\(428\) 6.00000 0.290021
\(429\) 1.50000 2.59808i 0.0724207 0.125436i
\(430\) −3.00000 5.19615i −0.144673 0.250581i
\(431\) 18.5000 + 32.0429i 0.891114 + 1.54345i 0.838542 + 0.544837i \(0.183408\pi\)
0.0525716 + 0.998617i \(0.483258\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −20.0000 + 6.92820i −0.960031 + 0.332564i
\(435\) −7.00000 −0.335624
\(436\) −9.00000 + 15.5885i −0.431022 + 0.746552i
\(437\) −6.00000 10.3923i −0.287019 0.497131i
\(438\) 7.00000 + 12.1244i 0.334473 + 0.579324i
\(439\) −12.5000 + 21.6506i −0.596592 + 1.03333i 0.396728 + 0.917936i \(0.370146\pi\)
−0.993320 + 0.115392i \(0.963188\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −2.00000 13.8564i −0.0952381 0.659829i
\(442\) 0 0
\(443\) −20.0000 + 34.6410i −0.950229 + 1.64584i −0.205301 + 0.978699i \(0.565817\pi\)
−0.744927 + 0.667146i \(0.767516\pi\)
\(444\) 0 0
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −6.00000 + 10.3923i −0.284108 + 0.492090i
\(447\) −18.0000 −0.851371
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) −1.00000 + 1.73205i −0.0471405 + 0.0816497i
\(451\) 2.00000 + 3.46410i 0.0941763 + 0.163118i
\(452\) 6.50000 + 11.2583i 0.305734 + 0.529547i
\(453\) 8.50000 14.7224i 0.399365 0.691720i
\(454\) 8.00000 0.375459
\(455\) −1.50000 + 7.79423i −0.0703211 + 0.365399i
\(456\) −6.00000 −0.280976
\(457\) 20.0000 34.6410i 0.935561 1.62044i 0.161929 0.986802i \(-0.448228\pi\)
0.773631 0.633636i \(-0.218438\pi\)
\(458\) 13.0000 + 22.5167i 0.607450 + 1.05213i
\(459\) 0 0
\(460\) −1.00000 + 1.73205i −0.0466252 + 0.0807573i
\(461\) −23.0000 −1.07122 −0.535608 0.844466i \(-0.679918\pi\)
−0.535608 + 0.844466i \(0.679918\pi\)
\(462\) −2.00000 1.73205i −0.0930484 0.0805823i
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 3.50000 6.06218i 0.162483 0.281430i
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) −6.00000 10.3923i −0.277945 0.481414i
\(467\) 18.0000 31.1769i 0.832941 1.44270i −0.0627555 0.998029i \(-0.519989\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(468\) 6.00000 0.277350
\(469\) −10.0000 8.66025i −0.461757 0.399893i
\(470\) 0 0
\(471\) −3.00000 + 5.19615i −0.138233 + 0.239426i
\(472\) −0.500000 0.866025i −0.0230144 0.0398621i
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) −6.50000 + 11.2583i −0.298555 + 0.517112i
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 4.50000 7.79423i 0.205825 0.356500i
\(479\) −20.5000 35.5070i −0.936669 1.62236i −0.771631 0.636071i \(-0.780559\pi\)
−0.165038 0.986287i \(-0.552775\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 0 0
\(482\) 10.0000 0.455488
\(483\) −5.00000 + 1.73205i −0.227508 + 0.0788110i
\(484\) 1.00000 0.0454545
\(485\) 3.50000 6.06218i 0.158927 0.275269i
\(486\) 8.00000 + 13.8564i 0.362887 + 0.628539i
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) −0.500000 + 0.866025i −0.0226339 + 0.0392031i
\(489\) −11.0000 −0.497437
\(490\) 6.50000 + 2.59808i 0.293640 + 0.117369i
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) 0 0
\(494\) −9.00000 15.5885i −0.404929 0.701358i
\(495\) 1.00000 1.73205i 0.0449467 0.0778499i
\(496\) −8.00000 −0.359211
\(497\) −20.0000 + 6.92820i −0.897123 + 0.310772i
\(498\) 6.00000 0.268866
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) −9.50000 16.4545i −0.424429 0.735132i
\(502\) 2.00000 3.46410i 0.0892644 0.154610i
\(503\) 3.00000 0.133763 0.0668817 0.997761i \(-0.478695\pi\)
0.0668817 + 0.997761i \(0.478695\pi\)
\(504\) 1.00000 5.19615i 0.0445435 0.231455i
\(505\) −15.0000 −0.667491
\(506\) 1.00000 1.73205i 0.0444554 0.0769991i
\(507\) 2.00000 + 3.46410i 0.0888231 + 0.153846i
\(508\) 9.50000 + 16.4545i 0.421494 + 0.730050i
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) 0 0
\(511\) 28.0000 + 24.2487i 1.23865 + 1.07270i
\(512\) −1.00000 −0.0441942
\(513\) 15.0000 25.9808i 0.662266 1.14708i
\(514\) 6.50000 + 11.2583i 0.286703 + 0.496584i
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) 3.00000 5.19615i 0.132068 0.228748i
\(517\) 0 0
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) 5.00000 + 8.66025i 0.219054 + 0.379413i 0.954519 0.298150i \(-0.0963696\pi\)
−0.735465 + 0.677563i \(0.763036\pi\)
\(522\) 7.00000 + 12.1244i 0.306382 + 0.530669i
\(523\) −17.0000 + 29.4449i −0.743358 + 1.28753i 0.207600 + 0.978214i \(0.433435\pi\)
−0.950958 + 0.309320i \(0.899899\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0.500000 2.59808i 0.0218218 0.113389i
\(526\) 9.00000 0.392419
\(527\) 0 0
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 3.00000 5.19615i 0.130312 0.225706i
\(531\) 2.00000 0.0867926
\(532\) −15.0000 + 5.19615i −0.650332 + 0.225282i
\(533\) 12.0000 0.519778
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) −2.50000 4.33013i −0.107984 0.187033i
\(537\) −7.50000 + 12.9904i −0.323649 + 0.560576i
\(538\) 14.0000 0.603583
\(539\) −6.50000 2.59808i −0.279975 0.111907i
\(540\) −5.00000 −0.215166
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) −0.500000 0.866025i −0.0214768 0.0371990i
\(543\) −6.00000 10.3923i −0.257485 0.445976i
\(544\) 0 0
\(545\) 18.0000 0.771035
\(546\) −7.50000 + 2.59808i −0.320970 + 0.111187i
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 1.50000 2.59808i 0.0640768 0.110984i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0.500000 + 0.866025i 0.0213201 + 0.0369274i
\(551\) 21.0000 36.3731i 0.894630 1.54954i
\(552\) −2.00000 −0.0851257
\(553\) −6.50000 + 33.7750i −0.276408 + 1.43626i
\(554\) 17.0000 0.722261
\(555\) 0 0
\(556\) 8.00000 + 13.8564i 0.339276 + 0.587643i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 8.00000 13.8564i 0.338667 0.586588i
\(559\) 18.0000 0.761319
\(560\) 2.00000 + 1.73205i 0.0845154 + 0.0731925i
\(561\) 0 0
\(562\) −4.00000 + 6.92820i −0.168730 + 0.292249i
\(563\) −19.0000 32.9090i −0.800755 1.38695i −0.919120 0.393977i \(-0.871099\pi\)
0.118366 0.992970i \(-0.462235\pi\)
\(564\) 0 0
\(565\) 6.50000 11.2583i 0.273457 0.473642i
\(566\) −10.0000 −0.420331
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) −8.00000 −0.335673
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 3.00000 + 5.19615i 0.125656 + 0.217643i
\(571\) 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i \(0.0325850\pi\)
−0.408883 + 0.912587i \(0.634082\pi\)
\(572\) 1.50000 2.59808i 0.0627182 0.108631i
\(573\) 4.00000 0.167102
\(574\) 2.00000 10.3923i 0.0834784 0.433766i
\(575\) 2.00000 0.0834058
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) −4.00000 + 6.92820i −0.166234 + 0.287926i
\(580\) −7.00000 −0.290659
\(581\) 15.0000 5.19615i 0.622305 0.215573i
\(582\) 7.00000 0.290159
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) 7.00000 + 12.1244i 0.289662 + 0.501709i
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) 13.0000 22.5167i 0.537025 0.930155i
\(587\) 17.0000 0.701665 0.350833 0.936438i \(-0.385899\pi\)
0.350833 + 0.936438i \(0.385899\pi\)
\(588\) 1.00000 + 6.92820i 0.0412393 + 0.285714i
\(589\) −48.0000 −1.97781
\(590\) −0.500000 + 0.866025i −0.0205847 + 0.0356537i
\(591\) −5.50000 9.52628i −0.226240 0.391859i
\(592\) 0 0
\(593\) −15.0000 + 25.9808i −0.615976 + 1.06690i 0.374236 + 0.927333i \(0.377905\pi\)
−0.990212 + 0.139569i \(0.955428\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 3.00000 5.19615i 0.122782 0.212664i
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −16.0000 27.7128i −0.653742 1.13231i −0.982208 0.187799i \(-0.939865\pi\)
0.328465 0.944516i \(-0.393469\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) 4.00000 0.163163 0.0815817 0.996667i \(-0.474003\pi\)
0.0815817 + 0.996667i \(0.474003\pi\)
\(602\) 3.00000 15.5885i 0.122271 0.635338i
\(603\) 10.0000 0.407231
\(604\) 8.50000 14.7224i 0.345860 0.599047i
\(605\) −0.500000 0.866025i −0.0203279 0.0352089i
\(606\) −7.50000 12.9904i −0.304667 0.527698i
\(607\) 12.0000 20.7846i 0.487065 0.843621i −0.512824 0.858494i \(-0.671401\pi\)
0.999889 + 0.0148722i \(0.00473415\pi\)
\(608\) −6.00000 −0.243332
\(609\) −14.0000 12.1244i −0.567309 0.491304i
\(610\) 1.00000 0.0404888
\(611\) 0 0
\(612\) 0 0
\(613\) −3.00000 5.19615i −0.121169 0.209871i 0.799060 0.601251i \(-0.205331\pi\)
−0.920229 + 0.391381i \(0.871998\pi\)
\(614\) −13.0000 + 22.5167i −0.524637 + 0.908698i
\(615\) −4.00000 −0.161296
\(616\) −2.00000 1.73205i −0.0805823 0.0697863i
\(617\) 27.0000 1.08698 0.543490 0.839416i \(-0.317103\pi\)
0.543490 + 0.839416i \(0.317103\pi\)
\(618\) 2.00000 3.46410i 0.0804518 0.139347i
\(619\) −16.0000 27.7128i −0.643094 1.11387i −0.984738 0.174042i \(-0.944317\pi\)
0.341644 0.939829i \(-0.389016\pi\)
\(620\) 4.00000 + 6.92820i 0.160644 + 0.278243i
\(621\) 5.00000 8.66025i 0.200643 0.347524i
\(622\) −12.0000 −0.481156
\(623\) −3.00000 + 15.5885i −0.120192 + 0.624538i
\(624\) −3.00000 −0.120096
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −6.50000 11.2583i −0.259792 0.449973i
\(627\) −3.00000 5.19615i −0.119808 0.207514i
\(628\) −3.00000 + 5.19615i −0.119713 + 0.207349i
\(629\) 0 0
\(630\) −5.00000 + 1.73205i −0.199205 + 0.0690066i
\(631\) −14.0000 −0.557331 −0.278666 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) −6.50000 + 11.2583i −0.258556 + 0.447832i
\(633\) 6.00000 + 10.3923i 0.238479 + 0.413057i
\(634\) −10.0000 17.3205i −0.397151 0.687885i
\(635\) 9.50000 16.4545i 0.376996 0.652976i
\(636\) 6.00000 0.237915
\(637\) −16.5000 + 12.9904i −0.653754 + 0.514698i
\(638\) 7.00000 0.277133
\(639\) 8.00000 13.8564i 0.316475 0.548151i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −0.500000 0.866025i −0.0197488 0.0342059i 0.855982 0.517005i \(-0.172953\pi\)
−0.875731 + 0.482800i \(0.839620\pi\)
\(642\) 3.00000 5.19615i 0.118401 0.205076i
\(643\) 37.0000 1.45914 0.729569 0.683907i \(-0.239721\pi\)
0.729569 + 0.683907i \(0.239721\pi\)
\(644\) −5.00000 + 1.73205i −0.197028 + 0.0682524i
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 0.500000 0.866025i 0.0196267 0.0339945i
\(650\) 3.00000 0.117670
\(651\) −4.00000 + 20.7846i −0.156772 + 0.814613i
\(652\) −11.0000 −0.430793
\(653\) −11.0000 + 19.0526i −0.430463 + 0.745584i −0.996913 0.0785119i \(-0.974983\pi\)
0.566450 + 0.824096i \(0.308316\pi\)
\(654\) 9.00000 + 15.5885i 0.351928 + 0.609557i
\(655\) 7.00000 + 12.1244i 0.273513 + 0.473738i
\(656\) 2.00000 3.46410i 0.0780869 0.135250i
\(657\) −28.0000 −1.09238
\(658\) 0 0
\(659\) −14.0000 −0.545363 −0.272681 0.962104i \(-0.587910\pi\)
−0.272681 + 0.962104i \(0.587910\pi\)
\(660\) −0.500000 + 0.866025i −0.0194625 + 0.0337100i
\(661\) −17.0000 29.4449i −0.661223 1.14527i −0.980294 0.197542i \(-0.936704\pi\)
0.319071 0.947731i \(-0.396629\pi\)
\(662\) 6.50000 + 11.2583i 0.252630 + 0.437567i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 12.0000 + 10.3923i 0.465340 + 0.402996i
\(666\) 0 0
\(667\) 7.00000 12.1244i 0.271041 0.469457i
\(668\) −9.50000 16.4545i −0.367566 0.636643i
\(669\) 6.00000 + 10.3923i 0.231973 + 0.401790i
\(670\) −2.50000 + 4.33013i −0.0965834 + 0.167287i
\(671\) −1.00000 −0.0386046
\(672\) −0.500000 + 2.59808i −0.0192879 + 0.100223i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −2.00000 + 3.46410i −0.0770371 + 0.133432i
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) 2.00000 + 3.46410i 0.0769231 + 0.133235i
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 13.0000 0.499262
\(679\) 17.5000 6.06218i 0.671588 0.232645i
\(680\) 0 0
\(681\) 4.00000 6.92820i 0.153280 0.265489i
\(682\) −4.00000 6.92820i −0.153168 0.265295i
\(683\) 0.500000 + 0.866025i 0.0191320 + 0.0331375i 0.875433 0.483340i \(-0.160576\pi\)
−0.856301 + 0.516477i \(0.827243\pi\)
\(684\) 6.00000 10.3923i 0.229416 0.397360i
\(685\) −3.00000 −0.114624
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 26.0000 0.991962
\(688\) 3.00000 5.19615i 0.114374 0.198101i
\(689\) 9.00000 + 15.5885i 0.342873 + 0.593873i
\(690\) 1.00000 + 1.73205i 0.0380693 + 0.0659380i
\(691\) 13.5000 23.3827i 0.513564 0.889519i −0.486312 0.873785i \(-0.661658\pi\)
0.999876 0.0157341i \(-0.00500851\pi\)
\(692\) 9.00000 0.342129
\(693\) 5.00000 1.73205i 0.189934 0.0657952i
\(694\) 26.0000 0.986947
\(695\) 8.00000 13.8564i 0.303457 0.525603i
\(696\) −3.50000 6.06218i −0.132667 0.229786i
\(697\) 0 0
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) −12.0000 −0.453882
\(700\) 0.500000 2.59808i 0.0188982 0.0981981i
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 7.50000 12.9904i 0.283069 0.490290i
\(703\) 0 0
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) −30.0000 25.9808i −1.12827 0.977107i
\(708\) −1.00000 −0.0375823
\(709\) 9.00000 15.5885i 0.338002 0.585437i −0.646055 0.763291i \(-0.723582\pi\)
0.984057 + 0.177854i \(0.0569156\pi\)
\(710\) 4.00000 + 6.92820i 0.150117 + 0.260011i
\(711\) −13.0000 22.5167i −0.487538 0.844441i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) −7.50000 + 12.9904i −0.280288 + 0.485473i
\(717\) −4.50000 7.79423i −0.168056 0.291081i
\(718\) 15.5000 + 26.8468i 0.578455 + 1.00191i
\(719\) 2.00000 3.46410i 0.0745874 0.129189i −0.826319 0.563202i \(-0.809569\pi\)
0.900907 + 0.434013i \(0.142903\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 2.00000 10.3923i 0.0744839 0.387030i
\(722\) −17.0000 −0.632674
\(723\) 5.00000 8.66025i 0.185952 0.322078i
\(724\) −6.00000 10.3923i −0.222988 0.386227i
\(725\) 3.50000 + 6.06218i 0.129987 + 0.225144i
\(726\) 0.500000 0.866025i 0.0185567 0.0321412i
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) −7.50000 + 2.59808i −0.277968 + 0.0962911i
\(729\) 13.0000 0.481481
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) 0 0
\(732\) 0.500000 + 0.866025i 0.0184805 + 0.0320092i
\(733\) 23.5000 40.7032i 0.867992 1.50341i 0.00394730 0.999992i \(-0.498744\pi\)
0.864045 0.503415i \(-0.167923\pi\)
\(734\) −8.00000 −0.295285
\(735\) 5.50000 4.33013i 0.202871 0.159719i
\(736\) −2.00000 −0.0737210
\(737\) 2.50000 4.33013i 0.0920887 0.159502i
\(738\) 4.00000 + 6.92820i 0.147242 + 0.255031i
\(739\) 6.00000 + 10.3923i 0.220714 + 0.382287i 0.955025 0.296526i \(-0.0958281\pi\)
−0.734311 + 0.678813i \(0.762495\pi\)
\(740\) 0 0
\(741\) −18.0000 −0.661247
\(742\) 15.0000 5.19615i 0.550667 0.190757i
\(743\) 40.0000 1.46746 0.733729 0.679442i \(-0.237778\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(744\) −4.00000 + 6.92820i −0.146647 + 0.254000i
\(745\) 9.00000 + 15.5885i 0.329734 + 0.571117i
\(746\) −0.500000 0.866025i −0.0183063 0.0317074i
\(747\) −6.00000 + 10.3923i −0.219529 + 0.380235i
\(748\) 0 0
\(749\) 3.00000 15.5885i 0.109618 0.569590i
\(750\) −1.00000 −0.0365148
\(751\) 25.0000 43.3013i 0.912263 1.58009i 0.101403 0.994845i \(-0.467667\pi\)
0.810860 0.585240i \(-0.199000\pi\)
\(752\) 0 0
\(753\) −2.00000 3.46410i −0.0728841 0.126239i
\(754\) 10.5000 18.1865i 0.382387 0.662314i
\(755\) −17.0000 −0.618693
\(756\) −10.0000 8.66025i −0.363696 0.314970i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −3.50000 + 6.06218i −0.127126 + 0.220188i
\(759\) −1.00000 1.73205i −0.0362977 0.0628695i
\(760\) 3.00000 + 5.19615i 0.108821 + 0.188484i
\(761\) 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i \(-0.650337\pi\)
0.998684 0.0512772i \(-0.0163292\pi\)
\(762\) 19.0000 0.688297
\(763\) 36.0000 + 31.1769i 1.30329 + 1.12868i
\(764\) 4.00000 0.144715
\(765\) 0 0
\(766\) 8.00000 + 13.8564i 0.289052 + 0.500652i
\(767\) −1.50000 2.59808i −0.0541619 0.0938111i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −0.500000 + 2.59808i −0.0180187 + 0.0936282i
\(771\) 13.0000 0.468184
\(772\) −4.00000 + 6.92820i −0.143963 + 0.249351i
\(773\) −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i \(-0.271596\pi\)
−0.981250 + 0.192740i \(0.938263\pi\)
\(774\) 6.00000 + 10.3923i 0.215666 + 0.373544i
\(775\) 4.00000 6.92820i 0.143684 0.248868i
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) 32.0000 1.14726
\(779\) 12.0000 20.7846i 0.429945 0.744686i