Properties

Label 1950.2.z.e.1849.2
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1849.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.e.1699.2

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −1.73205 1.00000i −0.654654 0.377964i 0.135583 0.990766i \(-0.456709\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.46410 1.00000i −0.960769 0.277350i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.73205 1.00000i −0.420084 0.242536i 0.275029 0.961436i \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 4.33013 + 2.50000i 0.923186 + 0.533002i
\(23\) −0.866025 + 0.500000i −0.180579 + 0.104257i −0.587565 0.809177i \(-0.699913\pi\)
0.406986 + 0.913434i \(0.366580\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.50000 + 0.866025i −0.686406 + 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) −1.73205 + 1.00000i −0.327327 + 0.188982i
\(29\) 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) 0 0
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −4.33013 2.50000i −0.753778 0.435194i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −2.59808 + 1.50000i −0.427121 + 0.246598i −0.698119 0.715981i \(-0.745980\pi\)
0.270998 + 0.962580i \(0.412646\pi\)
\(38\) 2.00000i 0.324443i
\(39\) 3.50000 0.866025i 0.560449 0.138675i
\(40\) 0 0
\(41\) 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(42\) 1.73205 1.00000i 0.267261 0.154303i
\(43\) 9.52628 + 5.50000i 1.45274 + 0.838742i 0.998636 0.0522047i \(-0.0166248\pi\)
0.454108 + 0.890947i \(0.349958\pi\)
\(44\) 5.00000 0.753778
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) 9.00000i 1.31278i −0.754420 0.656392i \(-0.772082\pi\)
0.754420 0.656392i \(-0.227918\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) −2.59808 + 2.50000i −0.360288 + 0.346688i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 2.00000i 0.264906i
\(58\) 4.33013 + 2.50000i 0.568574 + 0.328266i
\(59\) −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i \(0.597400\pi\)
−0.675178 + 0.737655i \(0.735933\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) −9.52628 + 5.50000i −1.20984 + 0.698501i
\(63\) −1.73205 + 1.00000i −0.218218 + 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −5.00000 −0.615457
\(67\) −13.8564 + 8.00000i −1.69283 + 0.977356i −0.740613 + 0.671932i \(0.765465\pi\)
−0.952217 + 0.305424i \(0.901202\pi\)
\(68\) −1.73205 + 1.00000i −0.210042 + 0.121268i
\(69\) 0.500000 0.866025i 0.0601929 0.104257i
\(70\) 0 0
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) 0 0
\(76\) 1.00000 + 1.73205i 0.114708 + 0.198680i
\(77\) 10.0000i 1.13961i
\(78\) 2.59808 2.50000i 0.294174 0.283069i
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.73205 + 1.00000i 0.191273 + 0.110432i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 1.00000 1.73205i 0.109109 0.188982i
\(85\) 0 0
\(86\) 11.0000 1.18616
\(87\) −4.33013 2.50000i −0.464238 0.268028i
\(88\) 4.33013 2.50000i 0.461593 0.266501i
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) 0 0
\(91\) 5.00000 + 5.19615i 0.524142 + 0.544705i
\(92\) 1.00000i 0.104257i
\(93\) 9.52628 5.50000i 0.987829 0.570323i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −1.73205 1.00000i −0.175863 0.101535i 0.409484 0.912317i \(-0.365709\pi\)
−0.585348 + 0.810782i \(0.699042\pi\)
\(98\) −2.59808 1.50000i −0.262445 0.151523i
\(99\) 5.00000 0.502519
\(100\) 0 0
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 1.73205 1.00000i 0.171499 0.0990148i
\(103\) 10.0000i 0.985329i 0.870219 + 0.492665i \(0.163977\pi\)
−0.870219 + 0.492665i \(0.836023\pi\)
\(104\) −1.00000 + 3.46410i −0.0980581 + 0.339683i
\(105\) 0 0
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) −8.66025 + 5.00000i −0.837218 + 0.483368i −0.856318 0.516449i \(-0.827253\pi\)
0.0190994 + 0.999818i \(0.493920\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 1.50000 2.59808i 0.142374 0.246598i
\(112\) 2.00000i 0.188982i
\(113\) −9.52628 5.50000i −0.896157 0.517396i −0.0202056 0.999796i \(-0.506432\pi\)
−0.875951 + 0.482399i \(0.839765\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 0 0
\(116\) 5.00000 0.464238
\(117\) −2.59808 + 2.50000i −0.240192 + 0.231125i
\(118\) 15.0000i 1.38086i
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 10.0000i 0.905357i
\(123\) −1.73205 1.00000i −0.156174 0.0901670i
\(124\) −5.50000 + 9.52628i −0.493915 + 0.855485i
\(125\) 0 0
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −1.73205 + 1.00000i −0.153695 + 0.0887357i −0.574875 0.818241i \(-0.694949\pi\)
0.421180 + 0.906977i \(0.361616\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −11.0000 −0.968496
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) −4.33013 + 2.50000i −0.376889 + 0.217597i
\(133\) 3.46410 2.00000i 0.300376 0.173422i
\(134\) −8.00000 + 13.8564i −0.691095 + 1.19701i
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −9.52628 5.50000i −0.813885 0.469897i 0.0344182 0.999408i \(-0.489042\pi\)
−0.848303 + 0.529511i \(0.822376\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) 1.00000 1.73205i 0.0848189 0.146911i −0.820495 0.571654i \(-0.806302\pi\)
0.905314 + 0.424743i \(0.139635\pi\)
\(140\) 0 0
\(141\) 4.50000 + 7.79423i 0.378968 + 0.656392i
\(142\) 0 0
\(143\) −4.33013 17.5000i −0.362103 1.46342i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −3.00000 5.19615i −0.248282 0.430037i
\(147\) 2.59808 + 1.50000i 0.214286 + 0.123718i
\(148\) 3.00000i 0.246598i
\(149\) 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i \(-0.588141\pi\)
0.969724 0.244202i \(-0.0785259\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 1.73205 + 1.00000i 0.140488 + 0.0811107i
\(153\) −1.73205 + 1.00000i −0.140028 + 0.0808452i
\(154\) −5.00000 8.66025i −0.402911 0.697863i
\(155\) 0 0
\(156\) 1.00000 3.46410i 0.0800641 0.277350i
\(157\) 7.00000i 0.558661i 0.960195 + 0.279330i \(0.0901125\pi\)
−0.960195 + 0.279330i \(0.909888\pi\)
\(158\) 9.52628 5.50000i 0.757870 0.437557i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 0 0
\(161\) 2.00000 0.157622
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 12.9904 + 7.50000i 1.01749 + 0.587445i 0.913375 0.407120i \(-0.133467\pi\)
0.104111 + 0.994566i \(0.466800\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −2.59808 + 1.50000i −0.201045 + 0.116073i −0.597143 0.802135i \(-0.703697\pi\)
0.396098 + 0.918208i \(0.370364\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 11.0000 + 6.92820i 0.846154 + 0.532939i
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 9.52628 5.50000i 0.726372 0.419371i
\(173\) −17.3205 10.0000i −1.31685 0.760286i −0.333633 0.942703i \(-0.608275\pi\)
−0.983221 + 0.182417i \(0.941608\pi\)
\(174\) −5.00000 −0.379049
\(175\) 0 0
\(176\) 2.50000 4.33013i 0.188445 0.326396i
\(177\) 15.0000i 1.12747i
\(178\) 1.73205 + 1.00000i 0.129823 + 0.0749532i
\(179\) −6.50000 11.2583i −0.485833 0.841487i 0.514035 0.857769i \(-0.328150\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 6.92820 + 2.00000i 0.513553 + 0.148250i
\(183\) 10.0000i 0.739221i
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) 5.50000 9.52628i 0.403280 0.698501i
\(187\) 10.0000i 0.731272i
\(188\) −7.79423 4.50000i −0.568453 0.328196i
\(189\) 1.00000 1.73205i 0.0727393 0.125988i
\(190\) 0 0
\(191\) −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i \(-0.879560\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −20.7846 + 12.0000i −1.49611 + 0.863779i −0.999990 0.00447566i \(-0.998575\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 6.92820 4.00000i 0.493614 0.284988i −0.232458 0.972606i \(-0.574677\pi\)
0.726073 + 0.687618i \(0.241344\pi\)
\(198\) 4.33013 2.50000i 0.307729 0.177667i
\(199\) 12.0000 20.7846i 0.850657 1.47338i −0.0299585 0.999551i \(-0.509538\pi\)
0.880616 0.473831i \(-0.157129\pi\)
\(200\) 0 0
\(201\) 8.00000 13.8564i 0.564276 0.977356i
\(202\) −1.73205 1.00000i −0.121867 0.0703598i
\(203\) 10.0000i 0.701862i
\(204\) 1.00000 1.73205i 0.0700140 0.121268i
\(205\) 0 0
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) 1.00000i 0.0695048i
\(208\) 0.866025 + 3.50000i 0.0600481 + 0.242681i
\(209\) −10.0000 −0.691714
\(210\) 0 0
\(211\) 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) 5.19615 + 3.00000i 0.356873 + 0.206041i
\(213\) 0 0
\(214\) −5.00000 + 8.66025i −0.341793 + 0.592003i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 19.0526 + 11.0000i 1.29337 + 0.746729i
\(218\) 1.73205 1.00000i 0.117309 0.0677285i
\(219\) 3.00000 + 5.19615i 0.202721 + 0.351123i
\(220\) 0 0
\(221\) 5.00000 + 5.19615i 0.336336 + 0.349531i
\(222\) 3.00000i 0.201347i
\(223\) 22.5167 13.0000i 1.50783 0.870544i 0.507869 0.861435i \(-0.330434\pi\)
0.999959 0.00910984i \(-0.00289979\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 0 0
\(226\) −11.0000 −0.731709
\(227\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) −1.73205 1.00000i −0.114708 0.0662266i
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 5.00000 + 8.66025i 0.328976 + 0.569803i
\(232\) 4.33013 2.50000i 0.284287 0.164133i
\(233\) 1.00000i 0.0655122i 0.999463 + 0.0327561i \(0.0104285\pi\)
−0.999463 + 0.0327561i \(0.989572\pi\)
\(234\) −1.00000 + 3.46410i −0.0653720 + 0.226455i
\(235\) 0 0
\(236\) 7.50000 + 12.9904i 0.488208 + 0.845602i
\(237\) −9.52628 + 5.50000i −0.618798 + 0.357263i
\(238\) 3.46410 + 2.00000i 0.224544 + 0.129641i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) 14.0000i 0.899954i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 5.00000 + 8.66025i 0.320092 + 0.554416i
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 5.19615 5.00000i 0.330623 0.318142i
\(248\) 11.0000i 0.698501i
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) 0 0
\(251\) −12.5000 + 21.6506i −0.788993 + 1.36658i 0.137591 + 0.990489i \(0.456064\pi\)
−0.926584 + 0.376087i \(0.877269\pi\)
\(252\) 2.00000i 0.125988i
\(253\) −4.33013 2.50000i −0.272233 0.157174i
\(254\) −1.00000 + 1.73205i −0.0627456 + 0.108679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 14.7224 8.50000i 0.918360 0.530215i 0.0352486 0.999379i \(-0.488778\pi\)
0.883112 + 0.469163i \(0.155444\pi\)
\(258\) −9.52628 + 5.50000i −0.593080 + 0.342415i
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 5.00000 0.309492
\(262\) −0.866025 + 0.500000i −0.0535032 + 0.0308901i
\(263\) 18.1865 10.5000i 1.12143 0.647458i 0.179664 0.983728i \(-0.442499\pi\)
0.941766 + 0.336270i \(0.109166\pi\)
\(264\) −2.50000 + 4.33013i −0.153864 + 0.266501i
\(265\) 0 0
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) −1.73205 1.00000i −0.106000 0.0611990i
\(268\) 16.0000i 0.977356i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) 0 0
\(271\) 6.50000 + 11.2583i 0.394847 + 0.683895i 0.993082 0.117426i \(-0.0374643\pi\)
−0.598235 + 0.801321i \(0.704131\pi\)
\(272\) 2.00000i 0.121268i
\(273\) −6.92820 2.00000i −0.419314 0.121046i
\(274\) −11.0000 −0.664534
\(275\) 0 0
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) −9.52628 5.50000i −0.572379 0.330463i 0.185720 0.982603i \(-0.440538\pi\)
−0.758099 + 0.652140i \(0.773872\pi\)
\(278\) 2.00000i 0.119952i
\(279\) −5.50000 + 9.52628i −0.329276 + 0.570323i
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 7.79423 + 4.50000i 0.464140 + 0.267971i
\(283\) 16.4545 9.50000i 0.978117 0.564716i 0.0764162 0.997076i \(-0.475652\pi\)
0.901701 + 0.432360i \(0.142319\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −12.5000 12.9904i −0.739140 0.768137i
\(287\) 4.00000i 0.236113i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) 2.00000 0.117242
\(292\) −5.19615 3.00000i −0.304082 0.175562i
\(293\) −5.19615 3.00000i −0.303562 0.175262i 0.340480 0.940252i \(-0.389411\pi\)
−0.644042 + 0.764990i \(0.722744\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) 1.50000 + 2.59808i 0.0871857 + 0.151010i
\(297\) −4.33013 + 2.50000i −0.251259 + 0.145065i
\(298\) 17.0000i 0.984784i
\(299\) 3.50000 0.866025i 0.202410 0.0500835i
\(300\) 0 0
\(301\) −11.0000 19.0526i −0.634029 1.09817i
\(302\) 6.92820 4.00000i 0.398673 0.230174i
\(303\) 1.73205 + 1.00000i 0.0995037 + 0.0574485i
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) −1.00000 + 1.73205i −0.0571662 + 0.0990148i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −8.66025 5.00000i −0.493464 0.284901i
\(309\) −5.00000 8.66025i −0.284440 0.492665i
\(310\) 0 0
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) −0.866025 3.50000i −0.0490290 0.198148i
\(313\) 20.0000i 1.13047i 0.824931 + 0.565233i \(0.191214\pi\)
−0.824931 + 0.565233i \(0.808786\pi\)
\(314\) 3.50000 + 6.06218i 0.197516 + 0.342108i
\(315\) 0 0
\(316\) 5.50000 9.52628i 0.309399 0.535895i
\(317\) 16.0000i 0.898650i −0.893368 0.449325i \(-0.851665\pi\)
0.893368 0.449325i \(-0.148335\pi\)
\(318\) −5.19615 3.00000i −0.291386 0.168232i
\(319\) −12.5000 + 21.6506i −0.699866 + 1.21220i
\(320\) 0 0
\(321\) 5.00000 8.66025i 0.279073 0.483368i
\(322\) 1.73205 1.00000i 0.0965234 0.0557278i
\(323\) 3.46410 2.00000i 0.192748 0.111283i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 15.0000 0.830773
\(327\) −1.73205 + 1.00000i −0.0957826 + 0.0553001i
\(328\) 1.73205 1.00000i 0.0956365 0.0552158i
\(329\) −9.00000 + 15.5885i −0.496186 + 0.859419i
\(330\) 0 0
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) 3.00000i 0.164399i
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) −1.00000 1.73205i −0.0545545 0.0944911i
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) 12.9904 + 0.500000i 0.706584 + 0.0271964i
\(339\) 11.0000 0.597438
\(340\) 0 0
\(341\) −27.5000 47.6314i −1.48921 2.57938i
\(342\) 1.73205 + 1.00000i 0.0936586 + 0.0540738i
\(343\) 20.0000i 1.07990i
\(344\) 5.50000 9.52628i 0.296540 0.513623i
\(345\) 0 0
\(346\) −20.0000 −1.07521
\(347\) 29.4449 + 17.0000i 1.58068 + 0.912608i 0.994760 + 0.102241i \(0.0326014\pi\)
0.585923 + 0.810366i \(0.300732\pi\)
\(348\) −4.33013 + 2.50000i −0.232119 + 0.134014i
\(349\) 10.0000 + 17.3205i 0.535288 + 0.927146i 0.999149 + 0.0412379i \(0.0131301\pi\)
−0.463862 + 0.885908i \(0.653537\pi\)
\(350\) 0 0
\(351\) 1.00000 3.46410i 0.0533761 0.184900i
\(352\) 5.00000i 0.266501i
\(353\) −15.5885 + 9.00000i −0.829690 + 0.479022i −0.853746 0.520689i \(-0.825675\pi\)
0.0240566 + 0.999711i \(0.492342\pi\)
\(354\) −7.50000 12.9904i −0.398621 0.690431i
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) −3.46410 2.00000i −0.183340 0.105851i
\(358\) −11.2583 6.50000i −0.595021 0.343536i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −13.8564 + 8.00000i −0.728277 + 0.420471i
\(363\) 14.0000i 0.734809i
\(364\) 7.00000 1.73205i 0.366900 0.0907841i
\(365\) 0 0
\(366\) −5.00000 8.66025i −0.261354 0.452679i
\(367\) 13.8564 8.00000i 0.723299 0.417597i −0.0926670 0.995697i \(-0.529539\pi\)
0.815966 + 0.578101i \(0.196206\pi\)
\(368\) 0.866025 + 0.500000i 0.0451447 + 0.0260643i
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 11.0000i 0.570323i
\(373\) 16.4545 + 9.50000i 0.851981 + 0.491891i 0.861319 0.508065i \(-0.169639\pi\)
−0.00933789 + 0.999956i \(0.502972\pi\)
\(374\) −5.00000 8.66025i −0.258544 0.447811i
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) −4.33013 17.5000i −0.223013 0.901296i
\(378\) 2.00000i 0.102869i
\(379\) −1.00000 1.73205i −0.0513665 0.0889695i 0.839199 0.543825i \(-0.183024\pi\)
−0.890565 + 0.454855i \(0.849691\pi\)
\(380\) 0 0
\(381\) 1.00000 1.73205i 0.0512316 0.0887357i
\(382\) 4.00000i 0.204658i
\(383\) −26.8468 15.5000i −1.37181 0.792013i −0.380651 0.924719i \(-0.624300\pi\)
−0.991155 + 0.132706i \(0.957633\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) −12.0000 + 20.7846i −0.610784 + 1.05791i
\(387\) 9.52628 5.50000i 0.484248 0.279581i
\(388\) −1.73205 + 1.00000i −0.0879316 + 0.0507673i
\(389\) −5.00000 −0.253510 −0.126755 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) −2.59808 + 1.50000i −0.131223 + 0.0757614i
\(393\) 0.866025 0.500000i 0.0436852 0.0252217i
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 0 0
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) 2.59808 + 1.50000i 0.130394 + 0.0752828i 0.563778 0.825926i \(-0.309347\pi\)
−0.433384 + 0.901209i \(0.642681\pi\)
\(398\) 24.0000i 1.20301i
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) 0 0
\(401\) −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i \(-0.811051\pi\)
−0.0699455 0.997551i \(-0.522283\pi\)
\(402\) 16.0000i 0.798007i
\(403\) 38.1051 + 11.0000i 1.89815 + 0.547949i
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) −5.00000 8.66025i −0.248146 0.429801i
\(407\) −12.9904 7.50000i −0.643909 0.371761i
\(408\) 2.00000i 0.0990148i
\(409\) 15.0000 25.9808i 0.741702 1.28467i −0.210017 0.977698i \(-0.567352\pi\)
0.951720 0.306968i \(-0.0993146\pi\)
\(410\) 0 0
\(411\) 11.0000 0.542590
\(412\) 8.66025 + 5.00000i 0.426660 + 0.246332i
\(413\) 25.9808 15.0000i 1.27843 0.738102i
\(414\) 0.500000 + 0.866025i 0.0245737 + 0.0425628i
\(415\) 0 0
\(416\) 2.50000 + 2.59808i 0.122573 + 0.127381i
\(417\) 2.00000i 0.0979404i
\(418\) −8.66025 + 5.00000i −0.423587 + 0.244558i
\(419\) −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i \(-0.197817\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) 3.46410 + 2.00000i 0.168630 + 0.0973585i
\(423\) −7.79423 4.50000i −0.378968 0.218797i
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 17.3205 10.0000i 0.838198 0.483934i
\(428\) 10.0000i 0.483368i
\(429\) 12.5000 + 12.9904i 0.603506 + 0.627182i
\(430\) 0 0
\(431\) −20.0000 34.6410i −0.963366 1.66860i −0.713942 0.700205i \(-0.753092\pi\)
−0.249424 0.968394i \(-0.580241\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −24.2487 14.0000i −1.16532 0.672797i −0.212746 0.977108i \(-0.568241\pi\)
−0.952573 + 0.304311i \(0.901574\pi\)
\(434\) 22.0000 1.05603
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 2.00000i 0.0956730i
\(438\) 5.19615 + 3.00000i 0.248282 + 0.143346i
\(439\) −2.00000 3.46410i −0.0954548 0.165333i 0.814344 0.580383i \(-0.197097\pi\)
−0.909798 + 0.415051i \(0.863764\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 6.92820 + 2.00000i 0.329541 + 0.0951303i
\(443\) 20.0000i 0.950229i 0.879924 + 0.475114i \(0.157593\pi\)
−0.879924 + 0.475114i \(0.842407\pi\)
\(444\) −1.50000 2.59808i −0.0711868 0.123299i
\(445\) 0 0
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 17.0000i 0.804072i
\(448\) 1.73205 + 1.00000i 0.0818317 + 0.0472456i
\(449\) 6.00000 10.3923i 0.283158 0.490443i −0.689003 0.724758i \(-0.741951\pi\)
0.972161 + 0.234315i \(0.0752847\pi\)
\(450\) 0 0
\(451\) −5.00000 + 8.66025i −0.235441 + 0.407795i
\(452\) −9.52628 + 5.50000i −0.448078 + 0.258698i
\(453\) −6.92820 + 4.00000i −0.325515 + 0.187936i
\(454\) 0 0
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −32.9090 + 19.0000i −1.53942 + 0.888783i −0.540544 + 0.841316i \(0.681781\pi\)
−0.998873 + 0.0474665i \(0.984885\pi\)
\(458\) −8.66025 + 5.00000i −0.404667 + 0.233635i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 0 0
\(461\) 19.5000 33.7750i 0.908206 1.57306i 0.0916500 0.995791i \(-0.470786\pi\)
0.816556 0.577267i \(-0.195881\pi\)
\(462\) 8.66025 + 5.00000i 0.402911 + 0.232621i
\(463\) 14.0000i 0.650635i 0.945605 + 0.325318i \(0.105471\pi\)
−0.945605 + 0.325318i \(0.894529\pi\)
\(464\) 2.50000 4.33013i 0.116060 0.201021i
\(465\) 0 0
\(466\) 0.500000 + 0.866025i 0.0231621 + 0.0401179i
\(467\) 6.00000i 0.277647i −0.990317 0.138823i \(-0.955668\pi\)
0.990317 0.138823i \(-0.0443321\pi\)
\(468\) 0.866025 + 3.50000i 0.0400320 + 0.161788i
\(469\) 32.0000 1.47762
\(470\) 0 0
\(471\) −3.50000 6.06218i −0.161271 0.279330i
\(472\) 12.9904 + 7.50000i 0.597931 + 0.345215i
\(473\) 55.0000i 2.52890i
\(474\) −5.50000 + 9.52628i −0.252623 + 0.437557i
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 5.19615 + 3.00000i 0.237915 + 0.137361i
\(478\) 17.3205 10.0000i 0.792222 0.457389i
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) 0 0
\(481\) 10.5000 2.59808i 0.478759 0.118462i
\(482\) 7.00000i 0.318841i
\(483\) −1.73205 + 1.00000i −0.0788110 + 0.0455016i
\(484\) 7.00000 + 12.1244i 0.318182 + 0.551107i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 1.73205 + 1.00000i 0.0784867 + 0.0453143i 0.538730 0.842479i \(-0.318904\pi\)
−0.460243 + 0.887793i \(0.652238\pi\)
\(488\) 8.66025 + 5.00000i 0.392031 + 0.226339i
\(489\) −15.0000 −0.678323
\(490\) 0 0
\(491\) 8.00000 + 13.8564i 0.361035 + 0.625331i 0.988131 0.153611i \(-0.0490902\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(492\) −1.73205 + 1.00000i −0.0780869 + 0.0450835i
\(493\) 10.0000i 0.450377i
\(494\) 2.00000 6.92820i 0.0899843 0.311715i
\(495\) 0 0
\(496\) 5.50000 + 9.52628i 0.246957 + 0.427743i
\(497\) 0 0
\(498\) −5.19615 3.00000i −0.232845 0.134433i
\(499\) −28.0000 −1.25345 −0.626726 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) 0 0
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) 25.0000i 1.11580i
\(503\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) 0 0
\(506\) −5.00000 −0.222277
\(507\) −12.9904 0.500000i −0.576923 0.0222058i
\(508\) 2.00000i 0.0887357i
\(509\) 14.5000 + 25.1147i 0.642701 + 1.11319i 0.984827 + 0.173537i \(0.0555197\pi\)
−0.342126 + 0.939654i \(0.611147\pi\)
\(510\) 0 0
\(511\) −6.00000 + 10.3923i −0.265424 + 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) −1.73205 1.00000i −0.0764719 0.0441511i
\(514\) 8.50000 14.7224i 0.374919 0.649379i
\(515\) 0 0
\(516\) −5.50000 + 9.52628i −0.242124 + 0.419371i
\(517\) 38.9711 22.5000i 1.71395 0.989549i
\(518\) 5.19615 3.00000i 0.228306 0.131812i
\(519\) 20.0000 0.877903
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 4.33013 2.50000i 0.189525 0.109422i
\(523\) −26.8468 + 15.5000i −1.17393 + 0.677768i −0.954602 0.297884i \(-0.903719\pi\)
−0.219326 + 0.975652i \(0.570386\pi\)
\(524\) −0.500000 + 0.866025i −0.0218426 + 0.0378325i
\(525\) 0 0
\(526\) 10.5000 18.1865i 0.457822 0.792971i
\(527\) 19.0526 + 11.0000i 0.829943 + 0.479168i
\(528\) 5.00000i 0.217597i
\(529\) −11.0000 + 19.0526i −0.478261 + 0.828372i
\(530\) 0 0
\(531\) 7.50000 + 12.9904i 0.325472 + 0.563735i
\(532\) 4.00000i 0.173422i
\(533\) −1.73205 7.00000i −0.0750234 0.303204i
\(534\) −2.00000 −0.0865485
\(535\) 0 0
\(536\) 8.00000 + 13.8564i 0.345547 + 0.598506i
\(537\) 11.2583 + 6.50000i 0.485833 + 0.280496i
\(538\) 14.0000i 0.603583i
\(539\) 7.50000 12.9904i 0.323048 0.559535i
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 11.2583 + 6.50000i 0.483587 + 0.279199i
\(543\) 13.8564 8.00000i 0.594635 0.343313i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) 0 0
\(546\) −7.00000 + 1.73205i −0.299572 + 0.0741249i
\(547\) 12.0000i 0.513083i 0.966533 + 0.256541i \(0.0825830\pi\)
−0.966533 + 0.256541i \(0.917417\pi\)
\(548\) −9.52628 + 5.50000i −0.406942 + 0.234948i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) 0 0
\(551\) −10.0000 −0.426014
\(552\) −0.866025 0.500000i −0.0368605 0.0212814i
\(553\) −19.0526 11.0000i −0.810197 0.467768i
\(554\) −11.0000 −0.467345
\(555\) 0 0
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) −22.5167 + 13.0000i −0.954062 + 0.550828i −0.894340 0.447387i \(-0.852355\pi\)
−0.0597213 + 0.998215i \(0.519021\pi\)
\(558\) 11.0000i 0.465667i
\(559\) −27.5000 28.5788i −1.16313 1.20876i
\(560\) 0 0
\(561\) 5.00000 + 8.66025i 0.211100 + 0.365636i
\(562\) −8.66025 + 5.00000i −0.365311 + 0.210912i
\(563\) −10.3923 6.00000i −0.437983 0.252870i 0.264758 0.964315i \(-0.414708\pi\)
−0.702742 + 0.711445i \(0.748041\pi\)
\(564\) 9.00000 0.378968
\(565\) 0 0
\(566\) 9.50000 16.4545i 0.399315 0.691633i
\(567\) 2.00000i 0.0839921i
\(568\) 0 0
\(569\) −11.0000 19.0526i −0.461144 0.798725i 0.537874 0.843025i \(-0.319228\pi\)
−0.999018 + 0.0443003i \(0.985894\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) −17.3205 5.00000i −0.724207 0.209061i
\(573\) 4.00000i 0.167102i
\(574\) −2.00000 3.46410i −0.0834784 0.144589i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 22.0000i 0.915872i 0.888985 + 0.457936i \(0.151411\pi\)
−0.888985 + 0.457936i \(0.848589\pi\)
\(578\) −11.2583 6.50000i −0.468285 0.270364i
\(579\) 12.0000 20.7846i 0.498703 0.863779i
\(580\) 0 0
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) 1.73205 1.00000i 0.0717958 0.0414513i
\(583\) −25.9808 + 15.0000i −1.07601 + 0.621237i
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 15.5885 9.00000i 0.643404 0.371470i −0.142520 0.989792i \(-0.545521\pi\)
0.785925 + 0.618322i \(0.212187\pi\)
\(588\) 2.59808 1.50000i 0.107143 0.0618590i
\(589\) 11.0000 19.0526i 0.453247 0.785047i
\(590\) 0 0
\(591\) −4.00000 + 6.92820i −0.164538 + 0.284988i
\(592\) 2.59808 + 1.50000i 0.106780 + 0.0616496i
\(593\) 31.0000i 1.27302i 0.771270 + 0.636509i \(0.219622\pi\)
−0.771270 + 0.636509i \(0.780378\pi\)
\(594\) −2.50000 + 4.33013i −0.102576 + 0.177667i
\(595\) 0 0
\(596\) −8.50000 14.7224i −0.348174 0.603054i
\(597\) 24.0000i 0.982255i
\(598\) 2.59808 2.50000i 0.106243 0.102233i
\(599\) −42.0000 −1.71607 −0.858037 0.513588i \(-0.828316\pi\)
−0.858037 + 0.513588i \(0.828316\pi\)
\(600\) 0 0
\(601\) 1.50000 + 2.59808i 0.0611863 + 0.105978i 0.894996 0.446074i \(-0.147178\pi\)
−0.833810 + 0.552052i \(0.813845\pi\)
\(602\) −19.0526 11.0000i −0.776524 0.448327i
\(603\) 16.0000i 0.651570i
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 0 0
\(606\) 2.00000 0.0812444
\(607\) 15.5885 + 9.00000i 0.632716 + 0.365299i 0.781803 0.623525i \(-0.214300\pi\)
−0.149087 + 0.988824i \(0.547634\pi\)
\(608\) 1.73205 1.00000i 0.0702439 0.0405554i
\(609\) 5.00000 + 8.66025i 0.202610 + 0.350931i
\(610\) 0 0
\(611\) −9.00000 + 31.1769i −0.364101 + 1.26128i
\(612\) 2.00000i 0.0808452i
\(613\) −25.1147 + 14.5000i −1.01437 + 0.585649i −0.912470 0.409145i \(-0.865827\pi\)
−0.101905 + 0.994794i \(0.532494\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −10.0000 −0.402911
\(617\) 35.5070 + 20.5000i 1.42946 + 0.825299i 0.997078 0.0763917i \(-0.0243399\pi\)
0.432382 + 0.901691i \(0.357673\pi\)
\(618\) −8.66025 5.00000i −0.348367 0.201129i
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) 17.3205 10.0000i 0.694489 0.400963i
\(623\) 4.00000i 0.160257i
\(624\) −2.50000 2.59808i −0.100080 0.104006i
\(625\) 0 0
\(626\) 10.0000 + 17.3205i 0.399680 + 0.692267i
\(627\) 8.66025 5.00000i 0.345857 0.199681i
\(628\) 6.06218 + 3.50000i 0.241907 + 0.139665i
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −20.0000 + 34.6410i −0.796187 + 1.37904i 0.125895 + 0.992044i \(0.459820\pi\)
−0.922082 + 0.386994i \(0.873514\pi\)
\(632\) 11.0000i 0.437557i
\(633\) −3.46410 2.00000i −0.137686 0.0794929i
\(634\) −8.00000 13.8564i −0.317721 0.550308i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 2.59808 + 10.5000i 0.102940 + 0.416025i
\(638\) 25.0000i 0.989759i
\(639\) 0 0
\(640\) 0 0
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 10.0000i 0.394669i
\(643\) −6.92820 4.00000i −0.273222 0.157745i 0.357129 0.934055i \(-0.383756\pi\)
−0.630351 + 0.776310i \(0.717089\pi\)
\(644\) 1.00000 1.73205i 0.0394055 0.0682524i
\(645\) 0 0
\(646\) 2.00000 3.46410i 0.0786889 0.136293i
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −75.0000 −2.94401
\(650\) 0 0
\(651\) −22.0000 −0.862248
\(652\) 12.9904 7.50000i 0.508743 0.293723i
\(653\) 29.4449 17.0000i 1.15227 0.665261i 0.202828 0.979214i \(-0.434987\pi\)
0.949439 + 0.313953i \(0.101653\pi\)
\(654\) −1.00000 + 1.73205i −0.0391031 + 0.0677285i
\(655\) 0 0
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) −5.19615 3.00000i −0.202721 0.117041i
\(658\) 18.0000i 0.701713i
\(659\) −19.5000 + 33.7750i −0.759612 + 1.31569i 0.183436 + 0.983032i \(0.441278\pi\)
−0.943049 + 0.332655i \(0.892055\pi\)
\(660\) 0 0
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 28.0000i 1.08825i
\(663\) −6.92820 2.00000i −0.269069 0.0776736i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 1.50000 + 2.59808i 0.0581238 + 0.100673i
\(667\) −4.33013 2.50000i −0.167663 0.0968004i
\(668\) 3.00000i 0.116073i
\(669\) −13.0000 + 22.5167i −0.502609 + 0.870544i
\(670\) 0 0
\(671\) −50.0000 −1.93023
\(672\) −1.73205 1.00000i −0.0668153 0.0385758i
\(673\) 6.92820 4.00000i 0.267063 0.154189i −0.360489 0.932763i \(-0.617390\pi\)
0.627552 + 0.778575i \(0.284057\pi\)
\(674\) 1.00000 + 1.73205i 0.0385186 + 0.0667161i
\(675\) 0 0
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 4.00000i 0.153732i 0.997041 + 0.0768662i \(0.0244914\pi\)
−0.997041 + 0.0768662i \(0.975509\pi\)
\(678\) 9.52628 5.50000i 0.365855 0.211226i
\(679\) 2.00000 + 3.46410i 0.0767530 + 0.132940i
\(680\) 0 0
\(681\) 0 0
\(682\) −47.6314 27.5000i −1.82390 1.05303i
\(683\) 10.3923 + 6.00000i 0.397650 + 0.229584i 0.685470 0.728101i \(-0.259597\pi\)
−0.287819 + 0.957685i \(0.592930\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 8.66025 5.00000i 0.330409 0.190762i
\(688\) 11.0000i 0.419371i
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) 15.0000 + 25.9808i 0.570627 + 0.988355i 0.996502 + 0.0835727i \(0.0266331\pi\)
−0.425875 + 0.904782i \(0.640034\pi\)
\(692\) −17.3205 + 10.0000i −0.658427 + 0.380143i
\(693\) −8.66025 5.00000i −0.328976 0.189934i
\(694\) 34.0000 1.29062
\(695\) 0 0
\(696\) −2.50000 + 4.33013i −0.0947623 + 0.164133i
\(697\) 4.00000i 0.151511i
\(698\) 17.3205 + 10.0000i 0.655591 + 0.378506i
\(699\) −0.500000 0.866025i −0.0189117 0.0327561i
\(700\) 0 0
\(701\) 13.0000 0.491003 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(702\) −0.866025 3.50000i −0.0326860 0.132099i
\(703\) 6.00000i 0.226294i
\(704\) −2.50000 4.33013i −0.0942223 0.163198i
\(705\) 0 0
\(706\) −9.00000 + 15.5885i −0.338719 + 0.586679i
\(707\) 4.00000i 0.150435i
\(708\) −12.9904 7.50000i −0.488208 0.281867i
\(709\) −4.00000 + 6.92820i −0.150223 + 0.260194i −0.931309 0.364229i \(-0.881333\pi\)
0.781086 + 0.624423i \(0.214666\pi\)
\(710\) 0 0
\(711\) 5.50000 9.52628i 0.206266 0.357263i
\(712\) 1.73205 1.00000i 0.0649113 0.0374766i
\(713\) 9.52628 5.50000i 0.356762 0.205977i
\(714\) −4.00000 −0.149696
\(715\) 0 0
\(716\) −13.0000 −0.485833
\(717\) −17.3205 + 10.0000i −0.646846 + 0.373457i
\(718\) −10.3923 + 6.00000i −0.387837 + 0.223918i
\(719\) 12.0000 20.7846i 0.447524 0.775135i −0.550700 0.834703i \(-0.685639\pi\)
0.998224 + 0.0595683i \(0.0189724\pi\)
\(720\) 0 0
\(721\) 10.0000 17.3205i 0.372419 0.645049i
\(722\) 12.9904 + 7.50000i 0.483452 + 0.279121i
\(723\) 7.00000i 0.260333i
\(724\) −8.00000 + 13.8564i −0.297318 + 0.514969i
\(725\) 0 0
\(726\) −7.00000 12.1244i −0.259794 0.449977i
\(727\) 40.0000i 1.48352i 0.670667 + 0.741759i \(0.266008\pi\)
−0.670667 + 0.741759i \(0.733992\pi\)
\(728\) 5.19615 5.00000i 0.192582 0.185312i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −11.0000 19.0526i −0.406850 0.704684i
\(732\) −8.66025 5.00000i −0.320092 0.184805i
\(733\) 6.00000i 0.221615i 0.993842 + 0.110808i \(0.0353437\pi\)
−0.993842 + 0.110808i \(0.964656\pi\)
\(734\) 8.00000 13.8564i 0.295285 0.511449i
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −69.2820 40.0000i −2.55204 1.47342i
\(738\) 1.73205 1.00000i 0.0637577 0.0368105i
\(739\) 22.0000 + 38.1051i 0.809283 + 1.40172i 0.913361 + 0.407150i \(0.133477\pi\)
−0.104078 + 0.994569i \(0.533189\pi\)
\(740\) 0 0
\(741\) −2.00000 + 6.92820i −0.0734718 + 0.254514i
\(742\) 12.0000i 0.440534i
\(743\) 44.1673 25.5000i 1.62034 0.935504i 0.633513 0.773732i \(-0.281612\pi\)
0.986828 0.161772i \(-0.0517209\pi\)
\(744\) −5.50000 9.52628i −0.201640 0.349250i
\(745\) 0 0
\(746\) 19.0000 0.695639
\(747\) 5.19615 + 3.00000i 0.190117 + 0.109764i
\(748\) −8.66025 5.00000i −0.316650 0.182818i
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) 11.5000 + 19.9186i 0.419641 + 0.726839i 0.995903 0.0904254i \(-0.0288227\pi\)
−0.576262 + 0.817265i \(0.695489\pi\)
\(752\) −7.79423 + 4.50000i −0.284226 + 0.164098i
\(753\) 25.0000i 0.911051i
\(754\) −12.5000 12.9904i −0.455223 0.473082i
\(755\) 0 0
\(756\) −1.00000 1.73205i −0.0363696 0.0629941i
\(757\) −8.66025 + 5.00000i −0.314762 + 0.181728i −0.649056 0.760741i \(-0.724836\pi\)
0.334293 + 0.942469i \(0.391502\pi\)
\(758\) −1.73205 1.00000i −0.0629109 0.0363216i
\(759\) 5.00000 0.181489
\(760\) 0 0
\(761\) −10.0000 + 17.3205i −0.362500 + 0.627868i −0.988372 0.152058i \(-0.951410\pi\)
0.625872 + 0.779926i \(0.284743\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) −3.46410 2.00000i −0.125409 0.0724049i
\(764\) 2.00000 + 3.46410i 0.0723575 + 0.125327i
\(765\) 0 0
\(766\) −31.0000 −1.12008
\(767\) 38.9711 37.5000i 1.40717 1.35405i
\(768\) 1.00000i 0.0360844i
\(769\) 21.5000 + 37.2391i 0.775310 + 1.34288i 0.934620 + 0.355647i \(0.115740\pi\)
−0.159310 + 0.987229i \(0.550927\pi\)
\(770\) 0 0
\(771\) −8.50000 + 14.7224i −0.306120 + 0.530215i
\(772\) 24.0000i 0.863779i
\(773\) −27.7128 16.0000i −0.996761 0.575480i −0.0894724 0.995989i \(-0.528518\pi\)
−0.907288 + 0.420509i \(0.861851\pi\)
\(774\) 5.50000 9.52628i 0.197693 0.342415i
\(775\) 0 0
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) −5.19615 + 3.00000i −0.186411 + 0.107624i
\(778\) −4.33013 + 2.50000i −0.155243 + 0.0896293i
\(779\) −4.00000 −0.143315
\(780\) 0 0
\(781\) 0 0
\(782\) 1.73205 1.00000i 0.0619380 0.0357599i
\(783\) −4.33013 + 2.50000i −0.154746 + 0.0893427i
\(784\) −1.50000 + 2.59808i −0.0535714 + 0.0927884i
\(785\)