Properties

Label 1170.2.i.a.451.1
Level $1170$
Weight $2$
Character 1170.451
Analytic conductor $9.342$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1170.451
Dual form 1170.2.i.a.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-1.00000 - 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{22} +(-0.500000 + 0.866025i) q^{23} +1.00000 q^{25} +(3.50000 + 0.866025i) q^{26} +(1.00000 - 1.73205i) q^{28} +(2.50000 - 4.33013i) q^{29} -11.0000 q^{31} +(-0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-1.50000 + 2.59808i) q^{37} -2.00000 q^{38} -1.00000 q^{40} +(-1.00000 + 1.73205i) q^{41} +(5.50000 + 9.52628i) q^{43} +5.00000 q^{44} +(-0.500000 - 0.866025i) q^{46} -9.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.50000 + 2.59808i) q^{52} -6.00000 q^{53} +(2.50000 - 4.33013i) q^{55} +(1.00000 + 1.73205i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-7.50000 - 12.9904i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(5.50000 - 9.52628i) q^{62} +1.00000 q^{64} +(1.00000 + 3.46410i) q^{65} +(-8.00000 + 13.8564i) q^{67} +(-1.00000 + 1.73205i) q^{68} +2.00000 q^{70} -6.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} +(1.00000 - 1.73205i) q^{76} -10.0000 q^{77} -11.0000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-1.00000 - 1.73205i) q^{82} -6.00000 q^{83} +(1.00000 + 1.73205i) q^{85} -11.0000 q^{86} +(-2.50000 + 4.33013i) q^{88} +(1.00000 - 1.73205i) q^{89} +(5.00000 - 5.19615i) q^{91} +1.00000 q^{92} +(4.50000 - 7.79423i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(1.00000 + 1.73205i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - 2q^{5} + 2q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 2q^{5} + 2q^{7} + 2q^{8} + q^{10} - 5q^{11} - 2q^{13} - 4q^{14} - q^{16} - 2q^{17} + 2q^{19} + q^{20} - 5q^{22} - q^{23} + 2q^{25} + 7q^{26} + 2q^{28} + 5q^{29} - 22q^{31} - q^{32} + 4q^{34} - 2q^{35} - 3q^{37} - 4q^{38} - 2q^{40} - 2q^{41} + 11q^{43} + 10q^{44} - q^{46} - 18q^{47} + 3q^{49} - q^{50} - 5q^{52} - 12q^{53} + 5q^{55} + 2q^{56} + 5q^{58} - 15q^{59} - 10q^{61} + 11q^{62} + 2q^{64} + 2q^{65} - 16q^{67} - 2q^{68} + 4q^{70} - 12q^{73} - 3q^{74} + 2q^{76} - 20q^{77} - 22q^{79} + q^{80} - 2q^{82} - 12q^{83} + 2q^{85} - 22q^{86} - 5q^{88} + 2q^{89} + 10q^{91} + 2q^{92} + 9q^{94} - 2q^{95} + 2q^{97} + 3q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) −2.50000 4.33013i −0.533002 0.923186i
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 3.50000 + 0.866025i 0.686406 + 0.169842i
\(27\) 0 0
\(28\) 1.00000 1.73205i 0.188982 0.327327i
\(29\) 2.50000 4.33013i 0.464238 0.804084i −0.534928 0.844897i \(-0.679661\pi\)
0.999167 + 0.0408130i \(0.0129948\pi\)
\(30\) 0 0
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −1.00000 1.73205i −0.169031 0.292770i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −1.00000 + 1.73205i −0.156174 + 0.270501i −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 0 0
\(43\) 5.50000 + 9.52628i 0.838742 + 1.45274i 0.890947 + 0.454108i \(0.150042\pi\)
−0.0522047 + 0.998636i \(0.516625\pi\)
\(44\) 5.00000 0.753778
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −2.50000 + 2.59808i −0.346688 + 0.360288i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 2.50000 4.33013i 0.337100 0.583874i
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) 0 0
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 5.50000 9.52628i 0.698501 1.20984i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 + 3.46410i 0.124035 + 0.429669i
\(66\) 0 0
\(67\) −8.00000 + 13.8564i −0.977356 + 1.69283i −0.305424 + 0.952217i \(0.598798\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 0 0
\(73\) −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 0
\(76\) 1.00000 1.73205i 0.114708 0.198680i
\(77\) −10.0000 −1.13961
\(78\) 0 0
\(79\) −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 0
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 1.00000 + 1.73205i 0.108465 + 0.187867i
\(86\) −11.0000 −1.18616
\(87\) 0 0
\(88\) −2.50000 + 4.33013i −0.266501 + 0.461593i
\(89\) 1.00000 1.73205i 0.106000 0.183597i −0.808146 0.588982i \(-0.799529\pi\)
0.914146 + 0.405385i \(0.132862\pi\)
\(90\) 0 0
\(91\) 5.00000 5.19615i 0.524142 0.544705i
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) 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
\(105\) 0 0
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) 5.00000 8.66025i 0.483368 0.837218i −0.516449 0.856318i \(-0.672747\pi\)
0.999818 + 0.0190994i \(0.00607989\pi\)
\(108\) 0 0
\(109\) −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
\(111\) 0 0
\(112\) −2.00000 −0.188982
\(113\) 5.50000 + 9.52628i 0.517396 + 0.896157i 0.999796 + 0.0202056i \(0.00643208\pi\)
−0.482399 + 0.875951i \(0.660235\pi\)
\(114\) 0 0
\(115\) 0.500000 0.866025i 0.0466252 0.0807573i
\(116\) −5.00000 −0.464238
\(117\) 0 0
\(118\) 15.0000 1.38086
\(119\) 2.00000 3.46410i 0.183340 0.317554i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) 5.50000 + 9.52628i 0.493915 + 0.855485i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −3.50000 0.866025i −0.306970 0.0759555i
\(131\) 1.00000 0.0873704 0.0436852 0.999045i \(-0.486090\pi\)
0.0436852 + 0.999045i \(0.486090\pi\)
\(132\) 0 0
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) −8.00000 13.8564i −0.691095 1.19701i
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −5.50000 9.52628i −0.469897 0.813885i 0.529511 0.848303i \(-0.322376\pi\)
−0.999408 + 0.0344182i \(0.989042\pi\)
\(138\) 0 0
\(139\) −1.00000 1.73205i −0.0848189 0.146911i 0.820495 0.571654i \(-0.193698\pi\)
−0.905314 + 0.424743i \(0.860365\pi\)
\(140\) −1.00000 + 1.73205i −0.0845154 + 0.146385i
\(141\) 0 0
\(142\) 0 0
\(143\) 17.5000 + 4.33013i 1.46342 + 0.362103i
\(144\) 0 0
\(145\) −2.50000 + 4.33013i −0.207614 + 0.359597i
\(146\) 3.00000 5.19615i 0.248282 0.430037i
\(147\) 0 0
\(148\) 3.00000 0.246598
\(149\) 8.50000 + 14.7224i 0.696347 + 1.20611i 0.969724 + 0.244202i \(0.0785259\pi\)
−0.273377 + 0.961907i \(0.588141\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 0 0
\(154\) 5.00000 8.66025i 0.402911 0.697863i
\(155\) 11.0000 0.883541
\(156\) 0 0
\(157\) −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
\(159\) 0 0
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) −2.00000 −0.157622
\(162\) 0 0
\(163\) 7.50000 + 12.9904i 0.587445 + 1.01749i 0.994566 + 0.104111i \(0.0331996\pi\)
−0.407120 + 0.913375i \(0.633467\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 1.50000 2.59808i 0.116073 0.201045i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) 5.50000 9.52628i 0.419371 0.726372i
\(173\) 10.0000 + 17.3205i 0.760286 + 1.31685i 0.942703 + 0.333633i \(0.108275\pi\)
−0.182417 + 0.983221i \(0.558392\pi\)
\(174\) 0 0
\(175\) 1.00000 + 1.73205i 0.0755929 + 0.130931i
\(176\) −2.50000 4.33013i −0.188445 0.326396i
\(177\) 0 0
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i \(-0.994817\pi\)
0.514035 + 0.857769i \(0.328150\pi\)
\(180\) 0 0
\(181\) −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
\(183\) 0 0
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) 10.0000 0.731272
\(188\) 4.50000 + 7.79423i 0.328196 + 0.568453i
\(189\) 0 0
\(190\) 2.00000 0.145095
\(191\) 2.00000 + 3.46410i 0.144715 + 0.250654i 0.929267 0.369410i \(-0.120440\pi\)
−0.784552 + 0.620063i \(0.787107\pi\)
\(192\) 0 0
\(193\) 12.0000 20.7846i 0.863779 1.49611i −0.00447566 0.999990i \(-0.501425\pi\)
0.868255 0.496119i \(-0.165242\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −4.00000 + 6.92820i −0.284988 + 0.493614i −0.972606 0.232458i \(-0.925323\pi\)
0.687618 + 0.726073i \(0.258656\pi\)
\(198\) 0 0
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) 1.00000 + 1.73205i 0.0703598 + 0.121867i
\(203\) 10.0000 0.701862
\(204\) 0 0
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) −5.00000 + 8.66025i −0.348367 + 0.603388i
\(207\) 0 0
\(208\) 3.50000 + 0.866025i 0.242681 + 0.0600481i
\(209\) −10.0000 −0.691714
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 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
\(216\) 0 0
\(217\) −11.0000 19.0526i −0.746729 1.29337i
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) 0 0
\(220\) −5.00000 −0.337100
\(221\) −5.00000 + 5.19615i −0.336336 + 0.349531i
\(222\) 0 0
\(223\) −13.0000 + 22.5167i −0.870544 + 1.50783i −0.00910984 + 0.999959i \(0.502900\pi\)
−0.861435 + 0.507869i \(0.830434\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) 0 0
\(226\) −11.0000 −0.731709
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 0 0
\(229\) 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
\(231\) 0 0
\(232\) 2.50000 4.33013i 0.164133 0.284287i
\(233\) −1.00000 −0.0655122 −0.0327561 0.999463i \(-0.510428\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) 0 0
\(235\) 9.00000 0.587095
\(236\) −7.50000 + 12.9904i −0.488208 + 0.845602i
\(237\) 0 0
\(238\) 2.00000 + 3.46410i 0.129641 + 0.224544i
\(239\) 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 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 14.0000 0.899954
\(243\) 0 0
\(244\) −5.00000 + 8.66025i −0.320092 + 0.554416i
\(245\) −1.50000 + 2.59808i −0.0958315 + 0.165985i
\(246\) 0 0
\(247\) 5.00000 5.19615i 0.318142 0.330623i
\(248\) −11.0000 −0.698501
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 12.5000 + 21.6506i 0.788993 + 1.36658i 0.926584 + 0.376087i \(0.122731\pi\)
−0.137591 + 0.990489i \(0.543936\pi\)
\(252\) 0 0
\(253\) −2.50000 4.33013i −0.157174 0.272233i
\(254\) −1.00000 1.73205i −0.0627456 0.108679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.50000 + 14.7224i −0.530215 + 0.918360i 0.469163 + 0.883112i \(0.344556\pi\)
−0.999379 + 0.0352486i \(0.988778\pi\)
\(258\) 0 0
\(259\) −6.00000 −0.372822
\(260\) 2.50000 2.59808i 0.155043 0.161126i
\(261\) 0 0
\(262\) −0.500000 + 0.866025i −0.0308901 + 0.0535032i
\(263\) 10.5000 18.1865i 0.647458 1.12143i −0.336270 0.941766i \(-0.609166\pi\)
0.983728 0.179664i \(-0.0575011\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) −2.00000 3.46410i −0.122628 0.212398i
\(267\) 0 0
\(268\) 16.0000 0.977356
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) 0 0
\(271\) 6.50000 11.2583i 0.394847 0.683895i −0.598235 0.801321i \(-0.704131\pi\)
0.993082 + 0.117426i \(0.0374643\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 11.0000 0.664534
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 0 0
\(277\) 5.50000 + 9.52628i 0.330463 + 0.572379i 0.982603 0.185720i \(-0.0594618\pi\)
−0.652140 + 0.758099i \(0.726128\pi\)
\(278\) 2.00000 0.119952
\(279\) 0 0
\(280\) −1.00000 1.73205i −0.0597614 0.103510i
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i \(0.357681\pi\)
−0.997076 + 0.0764162i \(0.975652\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −12.5000 + 12.9904i −0.739140 + 0.768137i
\(287\) −4.00000 −0.236113
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −2.50000 4.33013i −0.146805 0.254274i
\(291\) 0 0
\(292\) 3.00000 + 5.19615i 0.175562 + 0.304082i
\(293\) 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 0 0
\(295\) 7.50000 + 12.9904i 0.436667 + 0.756329i
\(296\) −1.50000 + 2.59808i −0.0871857 + 0.151010i
\(297\) 0 0
\(298\) −17.0000 −0.984784
\(299\) 3.50000 + 0.866025i 0.202410 + 0.0500835i
\(300\) 0 0
\(301\) −11.0000 + 19.0526i −0.634029 + 1.09817i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) 0 0
\(304\) −2.00000 −0.114708
\(305\) 5.00000 + 8.66025i 0.286299 + 0.495885i
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 5.00000 + 8.66025i 0.284901 + 0.493464i
\(309\) 0 0
\(310\) −5.50000 + 9.52628i −0.312379 + 0.541056i
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) 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
\(315\) 0 0
\(316\) 5.50000 + 9.52628i 0.309399 + 0.535895i
\(317\) −16.0000 −0.898650 −0.449325 0.893368i \(-0.648335\pi\)
−0.449325 + 0.893368i \(0.648335\pi\)
\(318\) 0 0
\(319\) 12.5000 + 21.6506i 0.699866 + 1.21220i
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 1.00000 1.73205i 0.0557278 0.0965234i
\(323\) 2.00000 3.46410i 0.111283 0.192748i
\(324\) 0 0
\(325\) −1.00000 3.46410i −0.0554700 0.192154i
\(326\) −15.0000 −0.830773
\(327\) 0 0
\(328\) −1.00000 + 1.73205i −0.0552158 + 0.0956365i
\(329\) −9.00000 15.5885i −0.496186 0.859419i
\(330\) 0 0
\(331\) 14.0000 + 24.2487i 0.769510 + 1.33283i 0.937829 + 0.347097i \(0.112833\pi\)
−0.168320 + 0.985732i \(0.553834\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 0 0
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) 8.00000 13.8564i 0.437087 0.757056i
\(336\) 0 0
\(337\) −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
\(339\) 0 0
\(340\) 1.00000 1.73205i 0.0542326 0.0939336i
\(341\) 27.5000 47.6314i 1.48921 2.57938i
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 5.50000 + 9.52628i 0.296540 + 0.513623i
\(345\) 0 0
\(346\) −20.0000 −1.07521
\(347\) 17.0000 + 29.4449i 0.912608 + 1.58068i 0.810366 + 0.585923i \(0.199268\pi\)
0.102241 + 0.994760i \(0.467399\pi\)
\(348\) 0 0
\(349\) −10.0000 + 17.3205i −0.535288 + 0.927146i 0.463862 + 0.885908i \(0.346463\pi\)
−0.999149 + 0.0412379i \(0.986870\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) −6.50000 11.2583i −0.343536 0.595021i
\(359\) −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
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) 0 0
\(364\) −7.00000 1.73205i −0.366900 0.0907841i
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) 0 0
\(370\) 1.50000 + 2.59808i 0.0779813 + 0.135068i
\(371\) −6.00000 10.3923i −0.311504 0.539542i
\(372\) 0 0
\(373\) 9.50000 + 16.4545i 0.491891 + 0.851981i 0.999956 0.00933789i \(-0.00297238\pi\)
−0.508065 + 0.861319i \(0.669639\pi\)
\(374\) −5.00000 + 8.66025i −0.258544 + 0.447811i
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) −17.5000 4.33013i −0.901296 0.223013i
\(378\) 0 0
\(379\) 1.00000 1.73205i 0.0513665 0.0889695i −0.839199 0.543825i \(-0.816976\pi\)
0.890565 + 0.454855i \(0.150309\pi\)
\(380\) −1.00000 + 1.73205i −0.0512989 + 0.0888523i
\(381\) 0 0
\(382\) −4.00000 −0.204658
\(383\) 15.5000 + 26.8468i 0.792013 + 1.37181i 0.924719 + 0.380651i \(0.124300\pi\)
−0.132706 + 0.991155i \(0.542367\pi\)
\(384\) 0 0
\(385\) 10.0000 0.509647
\(386\) 12.0000 + 20.7846i 0.610784 + 1.05791i
\(387\) 0 0
\(388\) 1.00000 1.73205i 0.0507673 0.0879316i
\(389\) −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
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) 0 0
\(394\) −4.00000 6.92820i −0.201517 0.349038i
\(395\) 11.0000 0.553470
\(396\) 0 0
\(397\) −1.50000 2.59808i −0.0752828 0.130394i 0.825926 0.563778i \(-0.190653\pi\)
−0.901209 + 0.433384i \(0.857319\pi\)
\(398\) 24.0000 1.20301
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 18.0000 31.1769i 0.898877 1.55690i 0.0699455 0.997551i \(-0.477717\pi\)
0.828932 0.559350i \(-0.188949\pi\)
\(402\) 0 0
\(403\) 11.0000 + 38.1051i 0.547949 + 1.89815i
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) −5.00000 + 8.66025i −0.248146 + 0.429801i
\(407\) −7.50000 12.9904i −0.371761 0.643909i
\(408\) 0 0
\(409\) −15.0000 25.9808i −0.741702 1.28467i −0.951720 0.306968i \(-0.900685\pi\)
0.210017 0.977698i \(-0.432648\pi\)
\(410\) 1.00000 + 1.73205i 0.0493865 + 0.0855399i
\(411\) 0 0
\(412\) −5.00000 8.66025i −0.246332 0.426660i
\(413\) 15.0000 25.9808i 0.738102 1.27843i
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) −2.50000 + 2.59808i −0.122573 + 0.127381i
\(417\) 0 0
\(418\) 5.00000 8.66025i 0.244558 0.423587i
\(419\) −2.00000 + 3.46410i −0.0977064 + 0.169232i −0.910735 0.412991i \(-0.864484\pi\)
0.813029 + 0.582224i \(0.197817\pi\)
\(420\) 0 0
\(421\) −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
\(423\) 0 0
\(424\) −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
\(429\) 0 0
\(430\) 11.0000 0.530467
\(431\) 20.0000 34.6410i 0.963366 1.66860i 0.249424 0.968394i \(-0.419759\pi\)
0.713942 0.700205i \(-0.246908\pi\)
\(432\) 0 0
\(433\) −14.0000 24.2487i −0.672797 1.16532i −0.977108 0.212746i \(-0.931759\pi\)
0.304311 0.952573i \(-0.401574\pi\)
\(434\) 22.0000 1.05603
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) 2.00000 3.46410i 0.0954548 0.165333i −0.814344 0.580383i \(-0.802903\pi\)
0.909798 + 0.415051i \(0.136236\pi\)
\(440\) 2.50000 4.33013i 0.119183 0.206431i
\(441\) 0 0
\(442\) −2.00000 6.92820i −0.0951303 0.329541i
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) −1.00000 + 1.73205i −0.0474045 + 0.0821071i
\(446\) −13.0000 22.5167i −0.615568 1.06619i
\(447\) 0 0
\(448\) 1.00000 + 1.73205i 0.0472456 + 0.0818317i
\(449\) 6.00000 + 10.3923i 0.283158 + 0.490443i 0.972161 0.234315i \(-0.0752847\pi\)
−0.689003 + 0.724758i \(0.741951\pi\)
\(450\) 0 0
\(451\) −5.00000 8.66025i −0.235441 0.407795i
\(452\) 5.50000 9.52628i 0.258698 0.448078i
\(453\) 0 0
\(454\) 0 0
\(455\) −5.00000 + 5.19615i −0.234404 + 0.243599i
\(456\) 0 0
\(457\) −19.0000 + 32.9090i −0.888783 + 1.53942i −0.0474665 + 0.998873i \(0.515115\pi\)
−0.841316 + 0.540544i \(0.818219\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) 0 0
\(460\) −1.00000 −0.0466252
\(461\) −19.5000 33.7750i −0.908206 1.57306i −0.816556 0.577267i \(-0.804119\pi\)
−0.0916500 0.995791i \(-0.529214\pi\)
\(462\) 0 0
\(463\) 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
\(465\) 0 0
\(466\) 0.500000 0.866025i 0.0231621 0.0401179i
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0 0
\(469\) −32.0000 −1.47762
\(470\) −4.50000 + 7.79423i −0.207570 + 0.359521i
\(471\) 0 0
\(472\) −7.50000 12.9904i −0.345215 0.597931i
\(473\) −55.0000 −2.52890
\(474\) 0 0
\(475\) 1.00000 + 1.73205i 0.0458831 + 0.0794719i
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) −10.0000 + 17.3205i −0.457389 + 0.792222i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) 10.5000 + 2.59808i 0.478759 + 0.118462i
\(482\) −7.00000 −0.318841
\(483\) 0 0
\(484\) −7.00000 + 12.1244i −0.318182 + 0.551107i
\(485\) −1.00000 1.73205i −0.0454077 0.0786484i
\(486\) 0 0
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) −5.00000 8.66025i −0.226339 0.392031i
\(489\) 0 0
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) −8.00000 + 13.8564i −0.361035 + 0.625331i −0.988131 0.153611i \(-0.950910\pi\)
0.627096 + 0.778942i \(0.284243\pi\)
\(492\) 0 0
\(493\) −10.0000 −0.450377
\(494\) 2.00000 + 6.92820i 0.0899843 + 0.311715i
\(495\) 0 0
\(496\) 5.50000 9.52628i 0.246957 0.427743i
\(497\) 0 0
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) −25.0000 −1.11580
\(503\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(504\) 0 0
\(505\) −1.00000 + 1.73205i −0.0444994 + 0.0770752i
\(506\) 5.00000 0.222277
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) 14.5000 25.1147i 0.642701 1.11319i −0.342126 0.939654i \(-0.611147\pi\)
0.984827 0.173537i \(-0.0555197\pi\)
\(510\) 0 0
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −8.50000 14.7224i −0.374919 0.649379i
\(515\) −10.0000 −0.440653
\(516\) 0 0
\(517\) 22.5000 38.9711i 0.989549 1.71395i
\(518\) 3.00000 5.19615i 0.131812 0.228306i
\(519\) 0 0
\(520\) 1.00000 + 3.46410i 0.0438529 + 0.151911i
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) −0.500000 0.866025i −0.0218426 0.0378325i
\(525\) 0 0
\(526\) 10.5000 + 18.1865i 0.457822 + 0.792971i
\(527\) 11.0000 + 19.0526i 0.479168 + 0.829943i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −3.00000 + 5.19615i −0.130312 + 0.225706i
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 7.00000 + 1.73205i 0.303204 + 0.0750234i
\(534\) 0 0
\(535\) −5.00000 + 8.66025i −0.216169 + 0.374415i
\(536\) −8.00000 + 13.8564i −0.345547 + 0.598506i
\(537\) 0 0
\(538\) −14.0000 −0.603583
\(539\) 7.50000 + 12.9904i 0.323048 + 0.559535i
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 6.50000 + 11.2583i 0.279199 + 0.483587i
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −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
\(549\) 0 0
\(550\) −2.50000 4.33013i −0.106600 0.184637i
\(551\) 10.0000 0.426014
\(552\) 0 0
\(553\) −11.0000 19.0526i −0.467768 0.810197i
\(554\) −11.0000 −0.467345
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 13.0000 22.5167i 0.550828 0.954062i −0.447387 0.894340i \(-0.647645\pi\)
0.998215 0.0597213i \(-0.0190212\pi\)
\(558\) 0 0
\(559\) 27.5000 28.5788i 1.16313 1.20876i
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) −5.00000 + 8.66025i −0.210912 + 0.365311i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 0 0
\(565\) −5.50000 9.52628i −0.231387 0.400774i
\(566\) −9.50000 16.4545i −0.399315 0.691633i
\(567\) 0 0
\(568\) 0 0
\(569\) −11.0000 + 19.0526i −0.461144 + 0.798725i −0.999018 0.0443003i \(-0.985894\pi\)
0.537874 + 0.843025i \(0.319228\pi\)
\(570\) 0 0
\(571\) −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
\(573\) 0 0
\(574\) 2.00000 3.46410i 0.0834784 0.144589i
\(575\) −0.500000 + 0.866025i −0.0208514 + 0.0361158i
\(576\) 0 0
\(577\) −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
\(579\) 0 0
\(580\) 5.00000 0.207614
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) 15.0000 25.9808i 0.621237 1.07601i
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 0 0
\(589\) −11.0000 19.0526i −0.453247 0.785047i
\(590\) −15.0000 −0.617540
\(591\) 0 0
\(592\) −1.50000 2.59808i −0.0616496 0.106780i
\(593\) −31.0000 −1.27302 −0.636509 0.771270i \(-0.719622\pi\)
−0.636509 + 0.771270i \(0.719622\pi\)
\(594\) 0 0
\(595\) −2.00000 + 3.46410i −0.0819920 + 0.142014i
\(596\) 8.50000 14.7224i 0.348174 0.603054i
\(597\) 0 0
\(598\) −2.50000 + 2.59808i −0.102233 + 0.106243i
\(599\) −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 −0.833810 0.552052i \(-0.813845\pi\)
0.894996 + 0.446074i \(0.147178\pi\)
\(602\) −11.0000 19.0526i −0.448327 0.776524i
\(603\) 0 0
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) −9.00000 15.5885i −0.365299 0.632716i 0.623525 0.781803i \(-0.285700\pi\)
−0.988824 + 0.149087i \(0.952366\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) 9.00000 + 31.1769i 0.364101 + 1.26128i
\(612\) 0 0
\(613\) 14.5000 25.1147i 0.585649 1.01437i −0.409145 0.912470i \(-0.634173\pi\)
0.994794 0.101905i \(-0.0324938\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −10.0000 −0.402911
\(617\) 20.5000 + 35.5070i 0.825299 + 1.42946i 0.901691 + 0.432382i \(0.142327\pi\)
−0.0763917 + 0.997078i \(0.524340\pi\)
\(618\) 0 0
\(619\) −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 0
\(622\) 10.0000 17.3205i 0.400963 0.694489i
\(623\) 4.00000 0.160257
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −10.0000 + 17.3205i −0.399680 + 0.692267i
\(627\) 0 0
\(628\) 3.50000 + 6.06218i 0.139665 + 0.241907i
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −20.0000 34.6410i −0.796187 1.37904i −0.922082 0.386994i \(-0.873514\pi\)
0.125895 0.992044i \(-0.459820\pi\)
\(632\) −11.0000 −0.437557
\(633\) 0 0
\(634\) 8.00000 13.8564i 0.317721 0.550308i
\(635\) 1.00000 1.73205i 0.0396838 0.0687343i
\(636\) 0 0
\(637\) −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 −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 0 0
\(643\) −4.00000 6.92820i −0.157745 0.273222i 0.776310 0.630351i \(-0.217089\pi\)
−0.934055 + 0.357129i \(0.883756\pi\)
\(644\) 1.00000 + 1.73205i 0.0394055 + 0.0682524i
\(645\) 0 0
\(646\) 2.00000 + 3.46410i 0.0786889 + 0.136293i
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0 0
\(649\) 75.0000 2.94401
\(650\) 3.50000 + 0.866025i 0.137281 + 0.0339683i
\(651\) 0 0
\(652\) 7.50000 12.9904i 0.293723 0.508743i
\(653\) 17.0000 29.4449i 0.665261 1.15227i −0.313953 0.949439i \(-0.601653\pi\)
0.979214 0.202828i \(-0.0650132\pi\)
\(654\) 0 0
\(655\) −1.00000 −0.0390732
\(656\) −1.00000 1.73205i −0.0390434 0.0676252i
\(657\) 0 0
\(658\) 18.0000 0.701713
\(659\) −19.5000 33.7750i −0.759612 1.31569i −0.943049 0.332655i \(-0.892055\pi\)
0.183436 0.983032i \(-0.441278\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 2.00000 3.46410i 0.0775567 0.134332i
\(666\) 0 0
\(667\) 2.50000 + 4.33013i 0.0968004 + 0.167663i
\(668\) −3.00000 −0.116073
\(669\) 0 0
\(670\) 8.00000 + 13.8564i 0.309067 + 0.535320i
\(671\) 50.0000 1.93023
\(672\) 0 0
\(673\) −4.00000 + 6.92820i −0.154189 + 0.267063i −0.932763 0.360489i \(-0.882610\pi\)
0.778575 + 0.627552i \(0.215943\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 0 0
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 4.00000 0.153732 0.0768662 0.997041i \(-0.475509\pi\)
0.0768662 + 0.997041i \(0.475509\pi\)
\(678\) 0 0
\(679\) −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 \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) 5.50000 + 9.52628i 0.210144 + 0.363980i
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) 0 0
\(688\) −11.0000 −0.419371
\(689\) 6.00000 + 20.7846i 0.228582 + 0.791831i
\(690\) 0 0
\(691\) 15.0000 25.9808i 0.570627 0.988355i −0.425875 0.904782i \(-0.640034\pi\)
0.996502 0.0835727i \(-0.0266331\pi\)
\(692\) 10.0000 17.3205i 0.380143 0.658427i
\(693\) 0 0
\(694\) −34.0000 −1.29062
\(695\) 1.00000 + 1.73205i 0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) 4.00000 0.151511
\(698\) −10.0000 17.3205i −0.378506 0.655591i
\(699\) 0 0
\(700\) 1.00000 1.73205i 0.0377964 0.0654654i
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 0 0
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) 4.00000 0.150435
\(708\) 0 0
\(709\) 4.00000 + 6.92820i 0.150223 + 0.260194i 0.931309 0.364229i \(-0.118667\pi\)
−0.781086 + 0.624423i \(0.785334\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.00000 1.73205i 0.0374766 0.0649113i
\(713\) 5.50000 9.52628i 0.205977 0.356762i
\(714\) 0 0
\(715\) −17.5000 4.33013i −0.654463 0.161938i
\(716\) 13.0000 0.485833
\(717\) 0 0
\(718\) 6.00000 10.3923i 0.223918 0.387837i
\(719\) 12.0000 + 20.7846i 0.447524 + 0.775135i 0.998224 0.0595683i \(-0.0189724\pi\)
−0.550700 + 0.834703i \(0.685639\pi\)
\(720\) 0 0
\(721\) 10.0000 + 17.3205i 0.372419 + 0.645049i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) 0 0
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) 0 0
\(727\) −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
\(729\) 0 0
\(730\) −3.00000 + 5.19615i −0.111035 + 0.192318i
\(731\) 11.0000 19.0526i 0.406850 0.704684i
\(732\) 0 0
\(733\) 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
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −40.0000 69.2820i −1.47342 2.55204i
\(738\) 0 0
\(739\) −22.0000 + 38.1051i −0.809283 + 1.40172i 0.104078 + 0.994569i \(0.466811\pi\)
−0.913361 + 0.407150i \(0.866523\pi\)
\(740\) −3.00000 −0.110282
\(741\) 0 0
\(742\) 12.0000 0.440534
\(743\) 25.5000 44.1673i 0.935504 1.62034i 0.161772 0.986828i \(-0.448279\pi\)
0.773732 0.633513i \(-0.218388\pi\)
\(744\) 0 0
\(745\) −8.50000 14.7224i −0.311416 0.539388i
\(746\) −19.0000 −0.695639
\(747\) 0 0
\(748\) −5.00000 8.66025i −0.182818 0.316650i
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) 11.5000 19.9186i 0.419641 0.726839i −0.576262 0.817265i \(-0.695489\pi\)
0.995903 + 0.0904254i \(0.0288227\pi\)
\(752\) 4.50000 7.79423i 0.164098 0.284226i
\(753\) 0 0
\(754\) 12.5000 12.9904i 0.455223 0.473082i
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −5.00000 + 8.66025i −0.181728 + 0.314762i −0.942469 0.334293i \(-0.891502\pi\)
0.760741 + 0.649056i \(0.224836\pi\)
\(758\) 1.00000 + 1.73205i 0.0363216 + 0.0629109i
\(759\) 0 0
\(760\) −1.00000 1.73205i −0.0362738 0.0628281i
\(761\) 10.0000 + 17.3205i 0.362500 + 0.627868i 0.988372 0.152058i \(-0.0485900\pi\)
−0.625872 + 0.779926i \(0.715257\pi\)
\(762\) 0 0
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) 2.00000 3.46410i 0.0723575 0.125327i
\(765\) 0 0
\(766\) −31.0000 −1.12008
\(767\) −37.5000 + 38.9711i −1.35405 + 1.40717i
\(768\) 0 0
\(769\) −21.5000 + 37.2391i −0.775310 + 1.34288i 0.159310 + 0.987229i \(0.449073\pi\)
−0.934620 + 0.355647i \(0.884260\pi\)
\(770\) −5.00000 + 8.66025i −0.180187 + 0.312094i
\(771\) 0 0
\(772\) −24.0000 −0.863779
\(773\) 16.0000 + 27.7128i 0.575480 + 0.996761i 0.995989 + 0.0894724i \(0.0285181\pi\)
−0.420509 + 0.907288i \(0.638149\pi\)
\(774\) 0 0
\(775\) −11.0000 −0.395132
\(776\) 1.00000 + 1.73205i 0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) 2.50000 4.33013i 0.0896293 0.155243i
\(779\) −4.00000 −0.143315
\(780\) 0 0
\(781\) 0 0
\(782\) −1.00000 + 1.73205i −0.0357599 + 0.0619380i
\(783\) 0 0
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) 7.00000 0.249841
\(786\) 0 0
\(787\) 15.5000 + 26.8468i 0.552515 + 0.956985i 0.998092 + 0.0617409i \(0.0196653\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)
\(788\) 8.00000 0.284988
\(789\) 0 0
\(790\) −5.50000 + 9.52628i −0.195681 + 0.338930i
\(791\) −11.0000