Properties

Label 390.2.i.f.211.1
Level $390$
Weight $2$
Character 390.211
Analytic conductor $3.114$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
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 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 390.211
Dual form 390.2.i.f.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(-2.50000 + 4.33013i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +1.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-2.50000 - 4.33013i) q^{29} +(-0.500000 + 0.866025i) q^{30} -11.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} +2.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.50000 - 2.59808i) q^{37} +2.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} -1.00000 q^{40} +(1.00000 + 1.73205i) q^{41} +(1.00000 + 1.73205i) q^{42} +(5.50000 - 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +9.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +2.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +6.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 4.33013i) q^{55} +(-1.00000 + 1.73205i) q^{56} +2.00000 q^{57} +(2.50000 - 4.33013i) q^{58} +(7.50000 - 12.9904i) q^{59} -1.00000 q^{60} +(-5.00000 + 8.66025i) q^{61} +(-5.50000 - 9.52628i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 + 3.46410i) q^{65} -5.00000 q^{66} +(-8.00000 - 13.8564i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-0.500000 + 0.866025i) q^{69} +2.00000 q^{70} +(0.500000 - 0.866025i) q^{72} -6.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +(0.500000 + 0.866025i) q^{75} +(1.00000 + 1.73205i) q^{76} +10.0000 q^{77} +(-2.50000 - 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{85} +11.0000 q^{86} +(2.50000 - 4.33013i) q^{87} +(-2.50000 - 4.33013i) q^{88} +(-1.00000 - 1.73205i) q^{89} -1.00000 q^{90} +(5.00000 + 5.19615i) q^{91} -1.00000 q^{92} +(-5.50000 - 9.52628i) q^{93} +(4.50000 + 7.79423i) q^{94} +(1.00000 - 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(-1.50000 + 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + 2q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + 2q^{7} - 2q^{8} - q^{9} + q^{10} + 5q^{11} - 2q^{12} - 2q^{13} + 4q^{14} + q^{15} - q^{16} + 2q^{17} - 2q^{18} + 2q^{19} - q^{20} + 4q^{21} - 5q^{22} + q^{23} - q^{24} + 2q^{25} - 7q^{26} - 2q^{27} + 2q^{28} - 5q^{29} - q^{30} - 22q^{31} + q^{32} - 5q^{33} + 4q^{34} + 2q^{35} - q^{36} - 3q^{37} + 4q^{38} - 7q^{39} - 2q^{40} + 2q^{41} + 2q^{42} + 11q^{43} - 10q^{44} - q^{45} - q^{46} + 18q^{47} + q^{48} + 3q^{49} + q^{50} + 4q^{51} - 5q^{52} + 12q^{53} - q^{54} + 5q^{55} - 2q^{56} + 4q^{57} + 5q^{58} + 15q^{59} - 2q^{60} - 10q^{61} - 11q^{62} + 2q^{63} + 2q^{64} - 2q^{65} - 10q^{66} - 16q^{67} + 2q^{68} - q^{69} + 4q^{70} + q^{72} - 12q^{73} + 3q^{74} + q^{75} + 2q^{76} + 20q^{77} - 5q^{78} - 22q^{79} - q^{80} - q^{81} - 2q^{82} + 12q^{83} - 2q^{84} + 2q^{85} + 22q^{86} + 5q^{87} - 5q^{88} - 2q^{89} - 2q^{90} + 10q^{91} - 2q^{92} - 11q^{93} + 9q^{94} + 2q^{95} + 2q^{96} + 2q^{97} - 3q^{98} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 0.447214
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) 2.00000 0.534522
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 2.00000 0.436436
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 1.00000 0.200000
\(26\) −3.50000 + 0.866025i −0.686406 + 0.169842i
\(27\) −1.00000 −0.192450
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −2.50000 + 4.33013i −0.435194 + 0.753778i
\(34\) 2.00000 0.342997
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 2.00000 0.324443
\(39\) −3.50000 + 0.866025i −0.560449 + 0.138675i
\(40\) −1.00000 −0.158114
\(41\) 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) 5.50000 9.52628i 0.838742 1.45274i −0.0522047 0.998636i \(-0.516625\pi\)
0.890947 0.454108i \(-0.150042\pi\)
\(44\) −5.00000 −0.753778
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 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
\(52\) −2.50000 2.59808i −0.346688 0.360288i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 2.50000 + 4.33013i 0.337100 + 0.583874i
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 2.00000 0.264906
\(58\) 2.50000 4.33013i 0.328266 0.568574i
\(59\) 7.50000 12.9904i 0.976417 1.69120i 0.301239 0.953549i \(-0.402600\pi\)
0.675178 0.737655i \(-0.264067\pi\)
\(60\) −1.00000 −0.129099
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) −5.50000 9.52628i −0.698501 1.20984i
\(63\) 1.00000 + 1.73205i 0.125988 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) −1.00000 + 3.46410i −0.124035 + 0.429669i
\(66\) −5.00000 −0.615457
\(67\) −8.00000 13.8564i −0.977356 1.69283i −0.671932 0.740613i \(-0.734535\pi\)
−0.305424 0.952217i \(-0.598798\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) −0.500000 + 0.866025i −0.0601929 + 0.104257i
\(70\) 2.00000 0.239046
\(71\) 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
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 1.50000 2.59808i 0.174371 0.302020i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 1.00000 + 1.73205i 0.114708 + 0.198680i
\(77\) 10.0000 1.13961
\(78\) −2.50000 2.59808i −0.283069 0.294174i
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.00000 + 1.73205i −0.109109 + 0.188982i
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) 11.0000 1.18616
\(87\) 2.50000 4.33013i 0.268028 0.464238i
\(88\) −2.50000 4.33013i −0.266501 0.461593i
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) −1.00000 −0.105409
\(91\) 5.00000 + 5.19615i 0.524142 + 0.544705i
\(92\) −1.00000 −0.104257
\(93\) −5.50000 9.52628i −0.570323 0.987829i
\(94\) 4.50000 + 7.79423i 0.464140 + 0.803913i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 1.00000 0.102062
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) −5.00000 −0.502519
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 1.00000 + 1.73205i 0.0990148 + 0.171499i
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 1.00000 3.46410i 0.0980581 0.339683i
\(105\) 2.00000 0.195180
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) −5.00000 8.66025i −0.483368 0.837218i 0.516449 0.856318i \(-0.327253\pi\)
−0.999818 + 0.0190994i \(0.993920\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −2.50000 + 4.33013i −0.238366 + 0.412861i
\(111\) 1.50000 2.59808i 0.142374 0.246598i
\(112\) −2.00000 −0.188982
\(113\) −5.50000 + 9.52628i −0.517396 + 0.896157i 0.482399 + 0.875951i \(0.339765\pi\)
−0.999796 + 0.0202056i \(0.993568\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 0.500000 + 0.866025i 0.0466252 + 0.0807573i
\(116\) 5.00000 0.464238
\(117\) −2.50000 2.59808i −0.231125 0.240192i
\(118\) 15.0000 1.38086
\(119\) −2.00000 3.46410i −0.183340 0.317554i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −10.0000 −0.905357
\(123\) −1.00000 + 1.73205i −0.0901670 + 0.156174i
\(124\) 5.50000 9.52628i 0.493915 0.855485i
\(125\) 1.00000 0.0894427
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −1.00000 1.73205i −0.0887357 0.153695i 0.818241 0.574875i \(-0.194949\pi\)
−0.906977 + 0.421180i \(0.861616\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 11.0000 0.968496
\(130\) −3.50000 + 0.866025i −0.306970 + 0.0759555i
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) −2.50000 4.33013i −0.217597 0.376889i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 8.00000 13.8564i 0.691095 1.19701i
\(135\) −1.00000 −0.0860663
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) 5.50000 9.52628i 0.469897 0.813885i −0.529511 0.848303i \(-0.677624\pi\)
0.999408 + 0.0344182i \(0.0109578\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i \(-0.860365\pi\)
0.820495 + 0.571654i \(0.193698\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 4.50000 + 7.79423i 0.378968 + 0.656392i
\(142\) 0 0
\(143\) −17.5000 + 4.33013i −1.46342 + 0.362103i
\(144\) 1.00000 0.0833333
\(145\) −2.50000 4.33013i −0.207614 0.359597i
\(146\) −3.00000 5.19615i −0.248282 0.430037i
\(147\) −1.50000 + 2.59808i −0.123718 + 0.214286i
\(148\) 3.00000 0.246598
\(149\) −8.50000 + 14.7224i −0.696347 + 1.20611i 0.273377 + 0.961907i \(0.411859\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 1.00000 + 1.73205i 0.0808452 + 0.140028i
\(154\) 5.00000 + 8.66025i 0.402911 + 0.697863i
\(155\) −11.0000 −0.883541
\(156\) 1.00000 3.46410i 0.0800641 0.277350i
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) −5.50000 9.52628i −0.437557 0.757870i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 2.00000 0.157622
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 7.50000 12.9904i 0.587445 1.01749i −0.407120 0.913375i \(-0.633467\pi\)
0.994566 0.104111i \(-0.0331996\pi\)
\(164\) −2.00000 −0.156174
\(165\) −2.50000 + 4.33013i −0.194625 + 0.337100i
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −1.50000 2.59808i −0.116073 0.201045i 0.802135 0.597143i \(-0.203697\pi\)
−0.918208 + 0.396098i \(0.870364\pi\)
\(168\) −2.00000 −0.154303
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 2.00000 0.153393
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 5.50000 + 9.52628i 0.419371 + 0.726372i
\(173\) −10.0000 + 17.3205i −0.760286 + 1.31685i 0.182417 + 0.983221i \(0.441608\pi\)
−0.942703 + 0.333633i \(0.891725\pi\)
\(174\) 5.00000 0.379049
\(175\) 1.00000 1.73205i 0.0755929 0.130931i
\(176\) 2.50000 4.33013i 0.188445 0.326396i
\(177\) 15.0000 1.12747
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i \(-0.00518305\pi\)
−0.514035 + 0.857769i \(0.671850\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −2.00000 + 6.92820i −0.148250 + 0.513553i
\(183\) −10.0000 −0.739221
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) −1.50000 2.59808i −0.110282 0.191014i
\(186\) 5.50000 9.52628i 0.403280 0.698501i
\(187\) 10.0000 0.731272
\(188\) −4.50000 + 7.79423i −0.328196 + 0.568453i
\(189\) −1.00000 + 1.73205i −0.0727393 + 0.125988i
\(190\) 2.00000 0.145095
\(191\) −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
\(193\) 12.0000 + 20.7846i 0.863779 + 1.49611i 0.868255 + 0.496119i \(0.165242\pi\)
−0.00447566 + 0.999990i \(0.501425\pi\)
\(194\) 2.00000 0.143592
\(195\) −3.50000 + 0.866025i −0.250640 + 0.0620174i
\(196\) −3.00000 −0.214286
\(197\) 4.00000 + 6.92820i 0.284988 + 0.493614i 0.972606 0.232458i \(-0.0746770\pi\)
−0.687618 + 0.726073i \(0.741344\pi\)
\(198\) −2.50000 4.33013i −0.177667 0.307729i
\(199\) −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i \(0.490462\pi\)
−0.880616 + 0.473831i \(0.842871\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.00000 13.8564i 0.564276 0.977356i
\(202\) 1.00000 1.73205i 0.0703598 0.121867i
\(203\) −10.0000 −0.701862
\(204\) −1.00000 + 1.73205i −0.0700140 + 0.121268i
\(205\) 1.00000 + 1.73205i 0.0698430 + 0.120972i
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) −1.00000 −0.0695048
\(208\) 3.50000 0.866025i 0.242681 0.0600481i
\(209\) 10.0000 0.691714
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) 5.50000 9.52628i 0.375097 0.649687i
\(216\) 1.00000 0.0680414
\(217\) −11.0000 + 19.0526i −0.746729 + 1.29337i
\(218\) −1.00000 1.73205i −0.0677285 0.117309i
\(219\) −3.00000 5.19615i −0.202721 0.351123i
\(220\) −5.00000 −0.337100
\(221\) 5.00000 + 5.19615i 0.336336 + 0.349531i
\(222\) 3.00000 0.201347
\(223\) −13.0000 22.5167i −0.870544 1.50783i −0.861435 0.507869i \(-0.830434\pi\)
−0.00910984 0.999959i \(-0.502900\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −11.0000 −0.731709
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −0.500000 + 0.866025i −0.0329690 + 0.0571040i
\(231\) 5.00000 + 8.66025i 0.328976 + 0.569803i
\(232\) 2.50000 + 4.33013i 0.164133 + 0.284287i
\(233\) 1.00000 0.0655122 0.0327561 0.999463i \(-0.489572\pi\)
0.0327561 + 0.999463i \(0.489572\pi\)
\(234\) 1.00000 3.46410i 0.0653720 0.226455i
\(235\) 9.00000 0.587095
\(236\) 7.50000 + 12.9904i 0.488208 + 0.845602i
\(237\) −5.50000 9.52628i −0.357263 0.618798i
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) −14.0000 −0.899954
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.00000 8.66025i −0.320092 0.554416i
\(245\) 1.50000 + 2.59808i 0.0958315 + 0.165985i
\(246\) −2.00000 −0.127515
\(247\) 5.00000 + 5.19615i 0.318142 + 0.330623i
\(248\) 11.0000 0.698501
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −12.5000 + 21.6506i −0.788993 + 1.36658i 0.137591 + 0.990489i \(0.456064\pi\)
−0.926584 + 0.376087i \(0.877269\pi\)
\(252\) −2.00000 −0.125988
\(253\) −2.50000 + 4.33013i −0.157174 + 0.272233i
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 2.00000 0.125245
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.50000 + 14.7224i 0.530215 + 0.918360i 0.999379 + 0.0352486i \(0.0112223\pi\)
−0.469163 + 0.883112i \(0.655444\pi\)
\(258\) 5.50000 + 9.52628i 0.342415 + 0.593080i
\(259\) −6.00000 −0.372822
\(260\) −2.50000 2.59808i −0.155043 0.161126i
\(261\) 5.00000 0.309492
\(262\) −0.500000 0.866025i −0.0308901 0.0535032i
\(263\) −10.5000 18.1865i −0.647458 1.12143i −0.983728 0.179664i \(-0.942499\pi\)
0.336270 0.941766i \(-0.390834\pi\)
\(264\) 2.50000 4.33013i 0.153864 0.266501i
\(265\) 6.00000 0.368577
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) 1.00000 1.73205i 0.0611990 0.106000i
\(268\) 16.0000 0.977356
\(269\) −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 6.50000 + 11.2583i 0.394847 + 0.683895i 0.993082 0.117426i \(-0.0374643\pi\)
−0.598235 + 0.801321i \(0.704131\pi\)
\(272\) −2.00000 −0.121268
\(273\) −2.00000 + 6.92820i −0.121046 + 0.419314i
\(274\) 11.0000 0.664534
\(275\) 2.50000 + 4.33013i 0.150756 + 0.261116i
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) 5.50000 9.52628i 0.330463 0.572379i −0.652140 0.758099i \(-0.726128\pi\)
0.982603 + 0.185720i \(0.0594618\pi\)
\(278\) −2.00000 −0.119952
\(279\) 5.50000 9.52628i 0.329276 0.570323i
\(280\) −1.00000 + 1.73205i −0.0597614 + 0.103510i
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) −4.50000 + 7.79423i −0.267971 + 0.464140i
\(283\) −9.50000 16.4545i −0.564716 0.978117i −0.997076 0.0764162i \(-0.975652\pi\)
0.432360 0.901701i \(-0.357681\pi\)
\(284\) 0 0
\(285\) 2.00000 0.118470
\(286\) −12.5000 12.9904i −0.739140 0.768137i
\(287\) 4.00000 0.236113
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 2.50000 4.33013i 0.146805 0.254274i
\(291\) 2.00000 0.117242
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) −3.00000 −0.174964
\(295\) 7.50000 12.9904i 0.436667 0.756329i
\(296\) 1.50000 + 2.59808i 0.0871857 + 0.151010i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) −17.0000 −0.984784
\(299\) −3.50000 + 0.866025i −0.202410 + 0.0500835i
\(300\) −1.00000 −0.0577350
\(301\) −11.0000 19.0526i −0.634029 1.09817i
\(302\) 4.00000 + 6.92820i 0.230174 + 0.398673i
\(303\) 1.00000 1.73205i 0.0574485 0.0995037i
\(304\) −2.00000 −0.114708
\(305\) −5.00000 + 8.66025i −0.286299 + 0.495885i
\(306\) −1.00000 + 1.73205i −0.0571662 + 0.0990148i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) −5.00000 + 8.66025i −0.284901 + 0.493464i
\(309\) 5.00000 + 8.66025i 0.284440 + 0.492665i
\(310\) −5.50000 9.52628i −0.312379 0.541056i
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 3.50000 0.866025i 0.198148 0.0490290i
\(313\) 20.0000 1.13047 0.565233 0.824931i \(-0.308786\pi\)
0.565233 + 0.824931i \(0.308786\pi\)
\(314\) −3.50000 6.06218i −0.197516 0.342108i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) 5.50000 9.52628i 0.309399 0.535895i
\(317\) 16.0000 0.898650 0.449325 0.893368i \(-0.351665\pi\)
0.449325 + 0.893368i \(0.351665\pi\)
\(318\) −3.00000 + 5.19615i −0.168232 + 0.291386i
\(319\) 12.5000 21.6506i 0.699866 1.21220i
\(320\) 1.00000 0.0559017
\(321\) 5.00000 8.66025i 0.279073 0.483368i
\(322\) 1.00000 + 1.73205i 0.0557278 + 0.0965234i
\(323\) −2.00000 3.46410i −0.111283 0.192748i
\(324\) 1.00000 0.0555556
\(325\) −1.00000 + 3.46410i −0.0554700 + 0.192154i
\(326\) 15.0000 0.830773
\(327\) −1.00000 1.73205i −0.0553001 0.0957826i
\(328\) −1.00000 1.73205i −0.0552158 0.0956365i
\(329\) 9.00000 15.5885i 0.496186 0.859419i
\(330\) −5.00000 −0.275241
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) 3.00000 0.164399
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) −8.00000 13.8564i −0.437087 0.757056i
\(336\) −1.00000 1.73205i −0.0545545 0.0944911i
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 0.500000 12.9904i 0.0271964 0.706584i
\(339\) −11.0000 −0.597438
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) −27.5000 47.6314i −1.48921 2.57938i
\(342\) −1.00000 + 1.73205i −0.0540738 + 0.0936586i
\(343\) 20.0000 1.07990
\(344\) −5.50000 + 9.52628i −0.296540 + 0.513623i
\(345\) −0.500000 + 0.866025i −0.0269191 + 0.0466252i
\(346\) −20.0000 −1.07521
\(347\) −17.0000 + 29.4449i −0.912608 + 1.58068i −0.102241 + 0.994760i \(0.532601\pi\)
−0.810366 + 0.585923i \(0.800732\pi\)
\(348\) 2.50000 + 4.33013i 0.134014 + 0.232119i
\(349\) −10.0000 17.3205i −0.535288 0.927146i −0.999149 0.0412379i \(-0.986870\pi\)
0.463862 0.885908i \(-0.346463\pi\)
\(350\) 2.00000 0.106904
\(351\) 1.00000 3.46410i 0.0533761 0.184900i
\(352\) 5.00000 0.266501
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 7.50000 + 12.9904i 0.398621 + 0.690431i
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) 2.00000 3.46410i 0.105851 0.183340i
\(358\) −6.50000 + 11.2583i −0.343536 + 0.595021i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −8.00000 13.8564i −0.420471 0.728277i
\(363\) −14.0000 −0.734809
\(364\) −7.00000 + 1.73205i −0.366900 + 0.0907841i
\(365\) −6.00000 −0.314054
\(366\) −5.00000 8.66025i −0.261354 0.452679i
\(367\) 8.00000 + 13.8564i 0.417597 + 0.723299i 0.995697 0.0926670i \(-0.0295392\pi\)
−0.578101 + 0.815966i \(0.696206\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) −2.00000 −0.104116
\(370\) 1.50000 2.59808i 0.0779813 0.135068i
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 11.0000 0.570323
\(373\) 9.50000 16.4545i 0.491891 0.851981i −0.508065 0.861319i \(-0.669639\pi\)
0.999956 + 0.00933789i \(0.00297238\pi\)
\(374\) 5.00000 + 8.66025i 0.258544 + 0.447811i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −9.00000 −0.464140
\(377\) 17.5000 4.33013i 0.901296 0.223013i
\(378\) −2.00000 −0.102869
\(379\) 1.00000 + 1.73205i 0.0513665 + 0.0889695i 0.890565 0.454855i \(-0.150309\pi\)
−0.839199 + 0.543825i \(0.816976\pi\)
\(380\) 1.00000 + 1.73205i 0.0512989 + 0.0888523i
\(381\) 1.00000 1.73205i 0.0512316 0.0887357i
\(382\) −4.00000 −0.204658
\(383\) −15.5000 + 26.8468i −0.792013 + 1.37181i 0.132706 + 0.991155i \(0.457633\pi\)
−0.924719 + 0.380651i \(0.875700\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 10.0000 0.509647
\(386\) −12.0000 + 20.7846i −0.610784 + 1.05791i
\(387\) 5.50000 + 9.52628i 0.279581 + 0.484248i
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) 5.00000 0.253510 0.126755 0.991934i \(-0.459544\pi\)
0.126755 + 0.991934i \(0.459544\pi\)
\(390\) −2.50000 2.59808i −0.126592 0.131559i
\(391\) 2.00000 0.101144
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) −0.500000 0.866025i −0.0252217 0.0436852i
\(394\) −4.00000 + 6.92820i −0.201517 + 0.349038i
\(395\) −11.0000 −0.553470
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) −1.50000 + 2.59808i −0.0752828 + 0.130394i −0.901209 0.433384i \(-0.857319\pi\)
0.825926 + 0.563778i \(0.190653\pi\)
\(398\) −24.0000 −1.20301
\(399\) 2.00000 3.46410i 0.100125 0.173422i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i \(-0.811051\pi\)
−0.0699455 0.997551i \(-0.522283\pi\)
\(402\) 16.0000 0.798007
\(403\) 11.0000 38.1051i 0.547949 1.89815i
\(404\) 2.00000 0.0995037
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) −5.00000 8.66025i −0.248146 0.429801i
\(407\) 7.50000 12.9904i 0.371761 0.643909i
\(408\) −2.00000 −0.0990148
\(409\) −15.0000 + 25.9808i −0.741702 + 1.28467i 0.210017 + 0.977698i \(0.432648\pi\)
−0.951720 + 0.306968i \(0.900685\pi\)
\(410\) −1.00000 + 1.73205i −0.0493865 + 0.0855399i
\(411\) 11.0000 0.542590
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) −15.0000 25.9808i −0.738102 1.27843i
\(414\) −0.500000 0.866025i −0.0245737 0.0425628i
\(415\) 6.00000 0.294528
\(416\) 2.50000 + 2.59808i 0.122573 + 0.127381i
\(417\) −2.00000 −0.0979404
\(418\) 5.00000 + 8.66025i 0.244558 + 0.423587i
\(419\) 2.00000 + 3.46410i 0.0977064 + 0.169232i 0.910735 0.412991i \(-0.135516\pi\)
−0.813029 + 0.582224i \(0.802183\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) −2.00000 + 3.46410i −0.0973585 + 0.168630i
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) −6.00000 −0.291386
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) 10.0000 + 17.3205i 0.483934 + 0.838198i
\(428\) 10.0000 0.483368
\(429\) −12.5000 12.9904i −0.603506 0.627182i
\(430\) 11.0000 0.530467
\(431\) −20.0000 34.6410i −0.963366 1.66860i −0.713942 0.700205i \(-0.753092\pi\)
−0.249424 0.968394i \(-0.580241\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −14.0000 + 24.2487i −0.672797 + 1.16532i 0.304311 + 0.952573i \(0.401574\pi\)
−0.977108 + 0.212746i \(0.931759\pi\)
\(434\) −22.0000 −1.05603
\(435\) 2.50000 4.33013i 0.119866 0.207614i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 2.00000 0.0956730
\(438\) 3.00000 5.19615i 0.143346 0.248282i
\(439\) 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i \(-0.136236\pi\)
−0.814344 + 0.580383i \(0.802903\pi\)
\(440\) −2.50000 4.33013i −0.119183 0.206431i
\(441\) −3.00000 −0.142857
\(442\) −2.00000 + 6.92820i −0.0951303 + 0.329541i
\(443\) 20.0000 0.950229 0.475114 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) 1.50000 + 2.59808i 0.0711868 + 0.123299i
\(445\) −1.00000 1.73205i −0.0474045 0.0821071i
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) −17.0000 −0.804072
\(448\) 1.00000 1.73205i 0.0472456 0.0818317i
\(449\) −6.00000 + 10.3923i −0.283158 + 0.490443i −0.972161 0.234315i \(-0.924715\pi\)
0.689003 + 0.724758i \(0.258049\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −5.00000 + 8.66025i −0.235441 + 0.407795i
\(452\) −5.50000 9.52628i −0.258698 0.448078i
\(453\) 4.00000 + 6.92820i 0.187936 + 0.325515i
\(454\) 0 0
\(455\) 5.00000 + 5.19615i 0.234404 + 0.243599i
\(456\) −2.00000 −0.0936586
\(457\) −19.0000 32.9090i −0.888783 1.53942i −0.841316 0.540544i \(-0.818219\pi\)
−0.0474665 0.998873i \(-0.515115\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) −1.00000 −0.0466252
\(461\) 19.5000 33.7750i 0.908206 1.57306i 0.0916500 0.995791i \(-0.470786\pi\)
0.816556 0.577267i \(-0.195881\pi\)
\(462\) −5.00000 + 8.66025i −0.232621 + 0.402911i
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) −2.50000 + 4.33013i −0.116060 + 0.201021i
\(465\) −5.50000 9.52628i −0.255056 0.441771i
\(466\) 0.500000 + 0.866025i 0.0231621 + 0.0401179i
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 3.50000 0.866025i 0.161788 0.0400320i
\(469\) −32.0000 −1.47762
\(470\) 4.50000 + 7.79423i 0.207570 + 0.359521i
\(471\) −3.50000 6.06218i −0.161271 0.279330i
\(472\) −7.50000 + 12.9904i −0.345215 + 0.597931i
\(473\) 55.0000 2.52890
\(474\) 5.50000 9.52628i 0.252623 0.437557i
\(475\) 1.00000 1.73205i 0.0458831 0.0794719i
\(476\) 4.00000 0.183340
\(477\) −3.00000 + 5.19615i −0.137361 + 0.237915i
\(478\) −10.0000 17.3205i −0.457389 0.792222i
\(479\) 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) 1.00000 0.0456435
\(481\) 10.5000 2.59808i 0.478759 0.118462i
\(482\) 7.00000 0.318841
\(483\) 1.00000 + 1.73205i 0.0455016 + 0.0788110i
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 1.00000 0.0453609
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) 5.00000 8.66025i 0.226339 0.392031i
\(489\) 15.0000 0.678323
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) 8.00000 + 13.8564i 0.361035 + 0.625331i 0.988131 0.153611i \(-0.0490902\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(492\) −1.00000 1.73205i −0.0450835 0.0780869i
\(493\) −10.0000 −0.450377
\(494\) −2.00000 + 6.92820i −0.0899843 + 0.311715i
\(495\) −5.00000 −0.224733
\(496\) 5.50000 + 9.52628i 0.246957 + 0.427743i
\(497\) 0 0
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) −25.0000 −1.11580
\(503\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(504\) −1.00000 1.73205i −0.0445435 0.0771517i
\(505\) −1.00000 1.73205i −0.0444994 0.0770752i
\(506\) −5.00000 −0.222277
\(507\) 0.500000 12.9904i 0.0222058 0.576923i
\(508\) 2.00000 0.0887357
\(509\) −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i \(-0.944480\pi\)
0.342126 0.939654i \(-0.388853\pi\)
\(510\) 1.00000 + 1.73205i 0.0442807 + 0.0766965i
\(511\) −6.00000 + 10.3923i −0.265424 + 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 + 1.73205i −0.0441511 + 0.0764719i
\(514\) −8.50000 + 14.7224i −0.374919 + 0.649379i
\(515\) 10.0000 0.440653
\(516\) −5.50000 + 9.52628i −0.242124 + 0.419371i
\(517\) 22.5000 + 38.9711i 0.989549 + 1.71395i
\(518\) −3.00000 5.19615i −0.131812 0.228306i
\(519\) −20.0000 −0.877903
\(520\) 1.00000 3.46410i 0.0438529 0.151911i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 2.50000 + 4.33013i 0.109422 + 0.189525i
\(523\) 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i \(0.0703858\pi\)
−0.297884 + 0.954602i \(0.596281\pi\)
\(524\) 0.500000 0.866025i 0.0218426 0.0378325i
\(525\) 2.00000 0.0872872
\(526\) 10.5000 18.1865i 0.457822 0.792971i
\(527\) −11.0000 + 19.0526i −0.479168 + 0.829943i
\(528\) 5.00000 0.217597
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 3.00000 + 5.19615i 0.130312 + 0.225706i
\(531\) 7.50000 + 12.9904i 0.325472 + 0.563735i
\(532\) 4.00000 0.173422
\(533\) −7.00000 + 1.73205i −0.303204 + 0.0750234i
\(534\) 2.00000 0.0865485
\(535\) −5.00000 8.66025i −0.216169 0.374415i
\(536\) 8.00000 + 13.8564i 0.345547 + 0.598506i
\(537\) −6.50000 + 11.2583i −0.280496 + 0.485833i
\(538\) −14.0000 −0.603583
\(539\) −7.50000 + 12.9904i −0.323048 + 0.559535i
\(540\) 0.500000 0.866025i 0.0215166 0.0372678i
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) −6.50000 + 11.2583i −0.279199 + 0.483587i
\(543\) −8.00000 13.8564i −0.343313 0.594635i
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) −2.00000 −0.0856706
\(546\) −7.00000 + 1.73205i −0.299572 + 0.0741249i
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 5.50000 + 9.52628i 0.234948 + 0.406942i
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) −2.50000 + 4.33013i −0.106600 + 0.184637i
\(551\) −10.0000 −0.426014
\(552\) 0.500000 0.866025i 0.0212814 0.0368605i
\(553\) −11.0000 + 19.0526i −0.467768 + 0.810197i
\(554\) 11.0000 0.467345
\(555\) 1.50000 2.59808i 0.0636715 0.110282i
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) −13.0000 22.5167i −0.550828 0.954062i −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 11.0000 0.465667
\(559\) 27.5000 + 28.5788i 1.16313 + 1.20876i
\(560\) −2.00000 −0.0845154
\(561\) 5.00000 + 8.66025i 0.211100 + 0.365636i
\(562\) −5.00000 8.66025i −0.210912 0.365311i
\(563\) −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) −9.00000 −0.378968
\(565\) −5.50000 + 9.52628i −0.231387 + 0.400774i
\(566\) 9.50000 16.4545i 0.399315 0.691633i
\(567\) −2.00000 −0.0839921
\(568\) 0 0
\(569\) 11.0000 + 19.0526i 0.461144 + 0.798725i 0.999018 0.0443003i \(-0.0141058\pi\)
−0.537874 + 0.843025i \(0.680772\pi\)
\(570\) 1.00000 + 1.73205i 0.0418854 + 0.0725476i
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 5.00000 17.3205i 0.209061 0.724207i
\(573\) −4.00000 −0.167102
\(574\) 2.00000 + 3.46410i 0.0834784 + 0.144589i
\(575\) 0.500000 + 0.866025i 0.0208514 + 0.0361158i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) −6.50000 + 11.2583i −0.270364 + 0.468285i
\(579\) −12.0000 + 20.7846i −0.498703 + 0.863779i
\(580\) 5.00000 0.207614
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) 1.00000 + 1.73205i 0.0414513 + 0.0717958i
\(583\) 15.0000 + 25.9808i 0.621237 + 1.07601i
\(584\) 6.00000 0.248282
\(585\) −2.50000 2.59808i −0.103362 0.107417i
\(586\) −6.00000 −0.247858
\(587\) 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i \(-0.0455206\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(588\) −1.50000 2.59808i −0.0618590 0.107143i
\(589\) −11.0000 + 19.0526i −0.453247 + 0.785047i
\(590\) 15.0000 0.617540
\(591\) −4.00000 + 6.92820i −0.164538 + 0.284988i
\(592\) −1.50000 + 2.59808i −0.0616496 + 0.106780i
\(593\) 31.0000 1.27302 0.636509 0.771270i \(-0.280378\pi\)
0.636509 + 0.771270i \(0.280378\pi\)
\(594\) 2.50000 4.33013i 0.102576 0.177667i
\(595\) −2.00000 3.46410i −0.0819920 0.142014i
\(596\) −8.50000 14.7224i −0.348174 0.603054i
\(597\) −24.0000 −0.982255
\(598\) −2.50000 2.59808i −0.102233 0.106243i
\(599\) 42.0000 1.71607 0.858037 0.513588i \(-0.171684\pi\)
0.858037 + 0.513588i \(0.171684\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 1.50000 + 2.59808i 0.0611863 + 0.105978i 0.894996 0.446074i \(-0.147178\pi\)
−0.833810 + 0.552052i \(0.813845\pi\)
\(602\) 11.0000 19.0526i 0.448327 0.776524i
\(603\) 16.0000 0.651570
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 2.00000 0.0812444
\(607\) −9.00000 + 15.5885i −0.365299 + 0.632716i −0.988824 0.149087i \(-0.952366\pi\)
0.623525 + 0.781803i \(0.285700\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) −5.00000 8.66025i −0.202610 0.350931i
\(610\) −10.0000 −0.404888
\(611\) −9.00000 + 31.1769i −0.364101 + 1.26128i
\(612\) −2.00000 −0.0808452
\(613\) 14.5000 + 25.1147i 0.585649 + 1.01437i 0.994794 + 0.101905i \(0.0324938\pi\)
−0.409145 + 0.912470i \(0.634173\pi\)
\(614\) 0 0
\(615\) −1.00000 + 1.73205i −0.0403239 + 0.0698430i
\(616\) −10.0000 −0.402911
\(617\) −20.5000 + 35.5070i −0.825299 + 1.42946i 0.0763917 + 0.997078i \(0.475660\pi\)
−0.901691 + 0.432382i \(0.857673\pi\)
\(618\) −5.00000 + 8.66025i −0.201129 + 0.348367i
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 5.50000 9.52628i 0.220885 0.382585i
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) 10.0000 + 17.3205i 0.400963 + 0.694489i
\(623\) −4.00000 −0.160257
\(624\) 2.50000 + 2.59808i 0.100080 + 0.104006i
\(625\) 1.00000 0.0400000
\(626\) 10.0000 + 17.3205i 0.399680 + 0.692267i
\(627\) 5.00000 + 8.66025i 0.199681 + 0.345857i
\(628\) 3.50000 6.06218i 0.139665 0.241907i
\(629\) −6.00000 −0.239236
\(630\) −1.00000 + 1.73205i −0.0398410 + 0.0690066i
\(631\) −20.0000 + 34.6410i −0.796187 + 1.37904i 0.125895 + 0.992044i \(0.459820\pi\)
−0.922082 + 0.386994i \(0.873514\pi\)
\(632\) 11.0000 0.437557
\(633\) −2.00000 + 3.46410i −0.0794929 + 0.137686i
\(634\) 8.00000 + 13.8564i 0.317721 + 0.550308i
\(635\) −1.00000 1.73205i −0.0396838 0.0687343i
\(636\) −6.00000 −0.237915
\(637\) −10.5000 + 2.59808i −0.416025 + 0.102940i
\(638\) 25.0000 0.989759
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 10.0000 0.394669
\(643\) −4.00000 + 6.92820i −0.157745 + 0.273222i −0.934055 0.357129i \(-0.883756\pi\)
0.776310 + 0.630351i \(0.217089\pi\)
\(644\) −1.00000 + 1.73205i −0.0394055 + 0.0682524i
\(645\) 11.0000 0.433125
\(646\) 2.00000 3.46410i 0.0786889 0.136293i
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 75.0000 2.94401
\(650\) −3.50000 + 0.866025i −0.137281 + 0.0339683i
\(651\) −22.0000 −0.862248
\(652\) 7.50000 + 12.9904i 0.293723 + 0.508743i
\(653\) −17.0000 29.4449i −0.665261 1.15227i −0.979214 0.202828i \(-0.934987\pi\)
0.313953 0.949439i \(-0.398347\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) −1.00000 −0.0390732
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 3.00000 5.19615i 0.117041 0.202721i
\(658\) 18.0000 0.701713
\(659\) 19.5000 33.7750i 0.759612 1.31569i −0.183436 0.983032i \(-0.558722\pi\)
0.943049 0.332655i \(-0.107945\pi\)
\(660\) −2.50000 4.33013i −0.0973124 0.168550i
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 28.0000 1.08825
\(663\) −2.00000 + 6.92820i −0.0776736 + 0.269069i
\(664\) −6.00000 −0.232845
\(665\) −2.00000 3.46410i −0.0775567 0.134332i
\(666\) 1.50000 + 2.59808i 0.0581238 + 0.100673i
\(667\) 2.50000 4.33013i 0.0968004 0.167663i
\(668\) 3.00000 0.116073
\(669\) 13.0000 22.5167i 0.502609 0.870544i
\(670\) 8.00000 13.8564i 0.309067 0.535320i
\(671\) −50.0000 −1.93023
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) −4.00000 6.92820i −0.154189 0.267063i 0.778575 0.627552i \(-0.215943\pi\)
−0.932763 + 0.360489i \(0.882610\pi\)
\(674\) −1.00000 1.73205i −0.0385186 0.0667161i
\(675\) −1.00000 −0.0384900
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) −4.00000 −0.153732 −0.0768662 0.997041i \(-0.524491\pi\)
−0.0768662 + 0.997041i \(0.524491\pi\)
\(678\) −5.50000 9.52628i −0.211226 0.365855i
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) −1.00000 + 1.73205i −0.0383482 + 0.0664211i
\(681\) 0 0
\(682\) 27.5000 47.6314i 1.05303 1.82390i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 5.50000 9.52628i 0.210144 0.363980i
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) −11.0000 −0.419371
\(689\) −6.00000 + 20.7846i −0.228582 + 0.791831i
\(690\) −1.00000 −0.0380693
\(691\) 15.0000 + 25.9808i 0.570627 + 0.988355i 0.996502 + 0.0835727i \(0.0266331\pi\)
−0.425875 + 0.904782i \(0.640034\pi\)
\(692\) −10.0000 17.3205i −0.380143 0.658427i
\(693\) −5.00000 + 8.66025i −0.189934 + 0.328976i
\(694\) −34.0000 −1.29062
\(695\) −1.00000 + 1.73205i −0.0379322 + 0.0657004i
\(696\) −2.50000 + 4.33013i −0.0947623 + 0.164133i
\(697\) 4.00000 0.151511
\(698\) 10.0000 17.3205i 0.378506 0.655591i
\(699\) 0.500000 + 0.866025i 0.0189117 + 0.0327561i
\(700\) 1.00000 + 1.73205i 0.0377964 + 0.0654654i
\(701\) 13.0000 0.491003 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(702\) 3.50000 0.866025i 0.132099 0.0326860i
\(703\) −6.00000 −0.226294
\(704\) 2.50000 + 4.33013i 0.0942223 + 0.163198i
\(705\) 4.50000 + 7.79423i 0.169480 + 0.293548i
\(706\) −9.00000 + 15.5885i −0.338719 + 0.586679i
\(707\) −4.00000 −0.150435
\(708\) −7.50000 + 12.9904i −0.281867 + 0.488208i
\(709\) 4.00000 6.92820i 0.150223 0.260194i −0.781086 0.624423i \(-0.785334\pi\)
0.931309 + 0.364229i \(0.118667\pi\)
\(710\) 0 0
\(711\) 5.50000 9.52628i 0.206266 0.357263i
\(712\) 1.00000 + 1.73205i 0.0374766 + 0.0649113i
\(713\) −5.50000 9.52628i −0.205977 0.356762i
\(714\) 4.00000 0.149696
\(715\) −17.5000 + 4.33013i −0.654463 + 0.161938i
\(716\) −13.0000 −0.485833
\(717\) −10.0000 17.3205i −0.373457 0.646846i
\(718\) 6.00000 + 10.3923i 0.223918 + 0.387837i
\(719\) −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i \(-0.981028\pi\)
0.550700 + 0.834703i \(0.314361\pi\)
\(720\) 1.00000 0.0372678
\(721\) 10.0000 17.3205i 0.372419 0.645049i
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) 7.00000 0.260333
\(724\) 8.00000 13.8564i 0.297318 0.514969i
\(725\) −2.50000 4.33013i −0.0928477 0.160817i
\(726\) −7.00000 12.1244i −0.259794 0.449977i
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) −5.00000 5.19615i −0.185312 0.192582i
\(729\) 1.00000 0.0370370
\(730\) −3.00000 5.19615i −0.111035 0.192318i
\(731\) −11.0000 19.0526i −0.406850 0.704684i
\(732\) 5.00000 8.66025i 0.184805 0.320092i
\(733\) 6.00000 0.221615 0.110808 0.993842i \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) −8.00000 + 13.8564i −0.295285 + 0.511449i
\(735\) −1.50000 + 2.59808i −0.0553283 + 0.0958315i
\(736\) 1.00000 0.0368605
\(737\) 40.0000 69.2820i 1.47342 2.55204i
\(738\) −1.00000 1.73205i −0.0368105 0.0637577i
\(739\) −22.0000 38.1051i −0.809283 1.40172i −0.913361 0.407150i \(-0.866523\pi\)
0.104078 0.994569i \(-0.466811\pi\)
\(740\) 3.00000 0.110282
\(741\) −2.00000 + 6.92820i −0.0734718 + 0.254514i
\(742\) 12.0000 0.440534
\(743\) −25.5000 44.1673i −0.935504 1.62034i −0.773732 0.633513i \(-0.781612\pi\)
−0.161772 0.986828i \(-0.551721\pi\)
\(744\) 5.50000 + 9.52628i 0.201640 + 0.349250i
\(745\) −8.50000 + 14.7224i −0.311416 + 0.539388i
\(746\) 19.0000 0.695639
\(747\) −3.00000 + 5.19615i −0.109764 + 0.190117i
\(748\) −5.00000 + 8.66025i −0.182818 + 0.316650i
\(749\) −20.0000 −0.730784
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 11.5000 + 19.9186i 0.419641 + 0.726839i 0.995903 0.0904254i \(-0.0288227\pi\)
−0.576262 + 0.817265i \(0.695489\pi\)
\(752\) −4.50000 7.79423i −0.164098 0.284226i
\(753\) −25.0000 −0.911051
\(754\) 12.5000 + 12.9904i 0.455223 + 0.473082i
\(755\) 8.00000 0.291150
\(756\) −1.00000 1.73205i −0.0363696 0.0629941i
\(757\) −5.00000 8.66025i −0.181728 0.314762i 0.760741 0.649056i \(-0.224836\pi\)
−0.942469 + 0.334293i \(0.891502\pi\)
\(758\) −1.00000 + 1.73205i −0.0363216 + 0.0629109i
\(759\) −5.00000 −0.181489
\(760\) −1.00000 + 1.73205i −0.0362738 + 0.0628281i
\(761\) −10.0000 + 17.3205i −0.362500 + 0.627868i −0.988372 0.152058i \(-0.951410\pi\)
0.625872 + 0.779926i \(0.284743\pi\)
\(762\) 2.00000 0.0724524
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) −31.0000 −1.12008
\(767\) 37.5000 + 38.9711i 1.35405 + 1.40717i
\(768\) −1.00000 −0.0360844
\(769\) −21.5000 37.2391i −0.775310 1.34288i −0.934620 0.355647i \(-0.884260\pi\)
0.159310 0.987229i \(-0.449073\pi\)
\(770\) 5.00000 + 8.66025i 0.180187 + 0.312094i
\(771\) −8.50000 + 14.7224i −0.306120 + 0.530215i
\(772\) −24.0000 −0.863779
\(773\) −16.0000 + 27.7128i −0.575480 + 0.996761i 0.420509 + 0.907288i \(0.361851\pi\)
−0.995989 + 0.0894724i \(0.971482\pi\)
\(774\) −5.50000 + 9.52628i −0.197693 + 0.342415i
\(775\) −11.0000 −0.395132
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) −3.00000 5.19615i −0.107624 0.186411i
\(778\) 2.50000 + 4.33013i 0.0896293 + 0.155243i
\(779\) <