Properties

Label 1050.2.b.e.251.4
Level $1050$
Weight $2$
Character 1050.251
Analytic conductor $8.384$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 4 x^{8} - 30 x^{6} + 36 x^{4} + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.4
Root \(0.721683 - 1.57454i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.e.251.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.721683 + 1.57454i) q^{3} -1.00000 q^{4} +(1.57454 - 0.721683i) q^{6} +(1.31429 - 2.29622i) q^{7} +1.00000i q^{8} +(-1.95835 + 2.27264i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.721683 + 1.57454i) q^{3} -1.00000 q^{4} +(1.57454 - 0.721683i) q^{6} +(1.31429 - 2.29622i) q^{7} +1.00000i q^{8} +(-1.95835 + 2.27264i) q^{9} -3.91669i q^{11} +(-0.721683 - 1.57454i) q^{12} -4.99166i q^{13} +(-2.29622 - 1.31429i) q^{14} +1.00000 q^{16} -3.54830 q^{17} +(2.27264 + 1.95835i) q^{18} -3.14908i q^{19} +(4.56399 + 0.412258i) q^{21} -3.91669 q^{22} +7.54528i q^{23} +(-1.57454 + 0.721683i) q^{24} -4.99166 q^{26} +(-4.99166 - 1.44337i) q^{27} +(-1.31429 + 2.29622i) q^{28} -7.54528i q^{29} -4.19323i q^{31} -1.00000i q^{32} +(6.16698 - 2.82661i) q^{33} +3.54830i q^{34} +(1.95835 - 2.27264i) q^{36} +10.4620 q^{37} -3.14908 q^{38} +(7.85957 - 3.60240i) q^{39} -9.32176 q^{41} +(0.412258 - 4.56399i) q^{42} +2.91669 q^{43} +3.91669i q^{44} +7.54528 q^{46} +8.00387 q^{47} +(0.721683 + 1.57454i) q^{48} +(-3.54528 - 6.03581i) q^{49} +(-2.56075 - 5.58693i) q^{51} +4.99166i q^{52} -0.288109i q^{53} +(-1.44337 + 4.99166i) q^{54} +(2.29622 + 1.31429i) q^{56} +(4.95835 - 2.27264i) q^{57} -7.54528 q^{58} +5.89894 q^{59} -2.48752i q^{61} -4.19323 q^{62} +(2.64464 + 7.48371i) q^{63} -1.00000 q^{64} +(-2.82661 - 6.16698i) q^{66} -0.545275 q^{67} +3.54830 q^{68} +(-11.8803 + 5.44530i) q^{69} -5.37142i q^{71} +(-2.27264 - 1.95835i) q^{72} +4.85479i q^{73} -10.4620i q^{74} +3.14908i q^{76} +(-8.99360 - 5.14768i) q^{77} +(-3.60240 - 7.85957i) q^{78} +0.742834 q^{79} +(-1.32976 - 8.90122i) q^{81} +9.32176i q^{82} -4.45557 q^{83} +(-4.56399 - 0.412258i) q^{84} -2.91669i q^{86} +(11.8803 - 5.44530i) q^{87} +3.91669 q^{88} +12.3340 q^{89} +(-11.4620 - 6.56050i) q^{91} -7.54528i q^{92} +(6.60240 - 3.02618i) q^{93} -8.00387i q^{94} +(1.57454 - 0.721683i) q^{96} +0.524688i q^{97} +(-6.03581 + 3.54528i) q^{98} +(8.90122 + 7.67024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{4} + 4q^{7} + O(q^{10}) \) \( 12q - 12q^{4} + 4q^{7} + 12q^{16} - 8q^{18} + 14q^{21} - 4q^{28} + 8q^{37} + 12q^{39} - 14q^{42} - 12q^{43} + 20q^{46} + 28q^{49} + 28q^{51} + 36q^{57} - 20q^{58} + 22q^{63} - 12q^{64} + 64q^{67} + 8q^{72} - 8q^{78} + 56q^{79} - 16q^{81} - 14q^{84} - 20q^{91} + 44q^{93} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.721683 + 1.57454i 0.416664 + 0.909060i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) 1.57454 0.721683i 0.642803 0.294626i
\(7\) 1.31429 2.29622i 0.496756 0.867891i
\(8\) 1.00000i 0.353553i
\(9\) −1.95835 + 2.27264i −0.652782 + 0.757546i
\(10\) 0 0
\(11\) 3.91669i 1.18093i −0.807064 0.590464i \(-0.798945\pi\)
0.807064 0.590464i \(-0.201055\pi\)
\(12\) −0.721683 1.57454i −0.208332 0.454530i
\(13\) 4.99166i 1.38444i −0.721688 0.692219i \(-0.756633\pi\)
0.721688 0.692219i \(-0.243367\pi\)
\(14\) −2.29622 1.31429i −0.613691 0.351259i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.54830 −0.860588 −0.430294 0.902689i \(-0.641590\pi\)
−0.430294 + 0.902689i \(0.641590\pi\)
\(18\) 2.27264 + 1.95835i 0.535666 + 0.461587i
\(19\) 3.14908i 0.722448i −0.932479 0.361224i \(-0.882359\pi\)
0.932479 0.361224i \(-0.117641\pi\)
\(20\) 0 0
\(21\) 4.56399 + 0.412258i 0.995945 + 0.0899620i
\(22\) −3.91669 −0.835041
\(23\) 7.54528i 1.57330i 0.617400 + 0.786649i \(0.288186\pi\)
−0.617400 + 0.786649i \(0.711814\pi\)
\(24\) −1.57454 + 0.721683i −0.321401 + 0.147313i
\(25\) 0 0
\(26\) −4.99166 −0.978946
\(27\) −4.99166 1.44337i −0.960646 0.277776i
\(28\) −1.31429 + 2.29622i −0.248378 + 0.433945i
\(29\) 7.54528i 1.40112i −0.713592 0.700561i \(-0.752933\pi\)
0.713592 0.700561i \(-0.247067\pi\)
\(30\) 0 0
\(31\) 4.19323i 0.753126i −0.926391 0.376563i \(-0.877106\pi\)
0.926391 0.376563i \(-0.122894\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.16698 2.82661i 1.07353 0.492050i
\(34\) 3.54830i 0.608528i
\(35\) 0 0
\(36\) 1.95835 2.27264i 0.326391 0.378773i
\(37\) 10.4620 1.71994 0.859968 0.510347i \(-0.170483\pi\)
0.859968 + 0.510347i \(0.170483\pi\)
\(38\) −3.14908 −0.510848
\(39\) 7.85957 3.60240i 1.25854 0.576846i
\(40\) 0 0
\(41\) −9.32176 −1.45581 −0.727907 0.685675i \(-0.759507\pi\)
−0.727907 + 0.685675i \(0.759507\pi\)
\(42\) 0.412258 4.56399i 0.0636127 0.704240i
\(43\) 2.91669 0.444791 0.222396 0.974956i \(-0.428612\pi\)
0.222396 + 0.974956i \(0.428612\pi\)
\(44\) 3.91669i 0.590464i
\(45\) 0 0
\(46\) 7.54528 1.11249
\(47\) 8.00387 1.16748 0.583742 0.811939i \(-0.301588\pi\)
0.583742 + 0.811939i \(0.301588\pi\)
\(48\) 0.721683 + 1.57454i 0.104166 + 0.227265i
\(49\) −3.54528 6.03581i −0.506468 0.862259i
\(50\) 0 0
\(51\) −2.56075 5.58693i −0.358576 0.782327i
\(52\) 4.99166i 0.692219i
\(53\) 0.288109i 0.0395748i −0.999804 0.0197874i \(-0.993701\pi\)
0.999804 0.0197874i \(-0.00629893\pi\)
\(54\) −1.44337 + 4.99166i −0.196417 + 0.679279i
\(55\) 0 0
\(56\) 2.29622 + 1.31429i 0.306846 + 0.175630i
\(57\) 4.95835 2.27264i 0.656749 0.301018i
\(58\) −7.54528 −0.990743
\(59\) 5.89894 0.767976 0.383988 0.923338i \(-0.374550\pi\)
0.383988 + 0.923338i \(0.374550\pi\)
\(60\) 0 0
\(61\) 2.48752i 0.318494i −0.987239 0.159247i \(-0.949093\pi\)
0.987239 0.159247i \(-0.0509066\pi\)
\(62\) −4.19323 −0.532540
\(63\) 2.64464 + 7.48371i 0.333194 + 0.942858i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −2.82661 6.16698i −0.347932 0.759103i
\(67\) −0.545275 −0.0666160 −0.0333080 0.999445i \(-0.510604\pi\)
−0.0333080 + 0.999445i \(0.510604\pi\)
\(68\) 3.54830 0.430294
\(69\) −11.8803 + 5.44530i −1.43022 + 0.655537i
\(70\) 0 0
\(71\) 5.37142i 0.637470i −0.947844 0.318735i \(-0.896742\pi\)
0.947844 0.318735i \(-0.103258\pi\)
\(72\) −2.27264 1.95835i −0.267833 0.230793i
\(73\) 4.85479i 0.568210i 0.958793 + 0.284105i \(0.0916964\pi\)
−0.958793 + 0.284105i \(0.908304\pi\)
\(74\) 10.4620i 1.21618i
\(75\) 0 0
\(76\) 3.14908i 0.361224i
\(77\) −8.99360 5.14768i −1.02492 0.586632i
\(78\) −3.60240 7.85957i −0.407891 0.889921i
\(79\) 0.742834 0.0835753 0.0417876 0.999127i \(-0.486695\pi\)
0.0417876 + 0.999127i \(0.486695\pi\)
\(80\) 0 0
\(81\) −1.32976 8.90122i −0.147751 0.989025i
\(82\) 9.32176i 1.02942i
\(83\) −4.45557 −0.489063 −0.244531 0.969641i \(-0.578634\pi\)
−0.244531 + 0.969641i \(0.578634\pi\)
\(84\) −4.56399 0.412258i −0.497973 0.0449810i
\(85\) 0 0
\(86\) 2.91669i 0.314515i
\(87\) 11.8803 5.44530i 1.27371 0.583797i
\(88\) 3.91669 0.417521
\(89\) 12.3340 1.30740 0.653699 0.756755i \(-0.273216\pi\)
0.653699 + 0.756755i \(0.273216\pi\)
\(90\) 0 0
\(91\) −11.4620 6.56050i −1.20154 0.687727i
\(92\) 7.54528i 0.786649i
\(93\) 6.60240 3.02618i 0.684637 0.313801i
\(94\) 8.00387i 0.825536i
\(95\) 0 0
\(96\) 1.57454 0.721683i 0.160701 0.0736565i
\(97\) 0.524688i 0.0532740i 0.999645 + 0.0266370i \(0.00847982\pi\)
−0.999645 + 0.0266370i \(0.991520\pi\)
\(98\) −6.03581 + 3.54528i −0.609709 + 0.358127i
\(99\) 8.90122 + 7.67024i 0.894606 + 0.770888i
\(100\) 0 0
\(101\) −8.00387 −0.796415 −0.398207 0.917295i \(-0.630368\pi\)
−0.398207 + 0.917295i \(0.630368\pi\)
\(102\) −5.58693 + 2.56075i −0.553188 + 0.253552i
\(103\) 6.17269i 0.608213i 0.952638 + 0.304106i \(0.0983578\pi\)
−0.952638 + 0.304106i \(0.901642\pi\)
\(104\) 4.99166 0.489473
\(105\) 0 0
\(106\) −0.288109 −0.0279836
\(107\) 2.65953i 0.257106i −0.991703 0.128553i \(-0.958967\pi\)
0.991703 0.128553i \(-0.0410332\pi\)
\(108\) 4.99166 + 1.44337i 0.480323 + 0.138888i
\(109\) 14.9239 1.42945 0.714727 0.699404i \(-0.246551\pi\)
0.714727 + 0.699404i \(0.246551\pi\)
\(110\) 0 0
\(111\) 7.55023 + 16.4728i 0.716636 + 1.56353i
\(112\) 1.31429 2.29622i 0.124189 0.216973i
\(113\) 11.8024i 1.11028i 0.831757 + 0.555140i \(0.187335\pi\)
−0.831757 + 0.555140i \(0.812665\pi\)
\(114\) −2.27264 4.95835i −0.212852 0.464392i
\(115\) 0 0
\(116\) 7.54528i 0.700561i
\(117\) 11.3442 + 9.77540i 1.04878 + 0.903736i
\(118\) 5.89894i 0.543041i
\(119\) −4.66349 + 8.14768i −0.427502 + 0.746896i
\(120\) 0 0
\(121\) −4.34047 −0.394589
\(122\) −2.48752 −0.225209
\(123\) −6.72736 14.6775i −0.606586 1.32342i
\(124\) 4.19323i 0.376563i
\(125\) 0 0
\(126\) 7.48371 2.64464i 0.666702 0.235604i
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.10493 + 4.59244i 0.185329 + 0.404342i
\(130\) 0 0
\(131\) −14.6846 −1.28300 −0.641500 0.767123i \(-0.721688\pi\)
−0.641500 + 0.767123i \(0.721688\pi\)
\(132\) −6.16698 + 2.82661i −0.536767 + 0.246025i
\(133\) −7.23098 4.13881i −0.627006 0.358880i
\(134\) 0.545275i 0.0471046i
\(135\) 0 0
\(136\) 3.54830i 0.304264i
\(137\) 18.3787i 1.57019i 0.619372 + 0.785097i \(0.287387\pi\)
−0.619372 + 0.785097i \(0.712613\pi\)
\(138\) 5.44530 + 11.8803i 0.463535 + 1.01132i
\(139\) 12.6077i 1.06937i −0.845051 0.534686i \(-0.820430\pi\)
0.845051 0.534686i \(-0.179570\pi\)
\(140\) 0 0
\(141\) 5.77626 + 12.6024i 0.486449 + 1.06131i
\(142\) −5.37142 −0.450759
\(143\) −19.5508 −1.63492
\(144\) −1.95835 + 2.27264i −0.163195 + 0.189386i
\(145\) 0 0
\(146\) 4.85479 0.401785
\(147\) 6.94505 9.93812i 0.572818 0.819682i
\(148\) −10.4620 −0.859968
\(149\) 5.65953i 0.463646i 0.972758 + 0.231823i \(0.0744691\pi\)
−0.972758 + 0.231823i \(0.925531\pi\)
\(150\) 0 0
\(151\) −2.62858 −0.213911 −0.106956 0.994264i \(-0.534110\pi\)
−0.106956 + 0.994264i \(0.534110\pi\)
\(152\) 3.14908 0.255424
\(153\) 6.94879 8.06399i 0.561776 0.651935i
\(154\) −5.14768 + 8.99360i −0.414811 + 0.724725i
\(155\) 0 0
\(156\) −7.85957 + 3.60240i −0.629269 + 0.288423i
\(157\) 24.2853i 1.93818i −0.246704 0.969091i \(-0.579348\pi\)
0.246704 0.969091i \(-0.420652\pi\)
\(158\) 0.742834i 0.0590967i
\(159\) 0.453638 0.207923i 0.0359758 0.0164894i
\(160\) 0 0
\(161\) 17.3256 + 9.91669i 1.36545 + 0.781545i
\(162\) −8.90122 + 1.32976i −0.699346 + 0.104476i
\(163\) −13.4620 −1.05442 −0.527211 0.849734i \(-0.676762\pi\)
−0.527211 + 0.849734i \(0.676762\pi\)
\(164\) 9.32176 0.727907
\(165\) 0 0
\(166\) 4.45557i 0.345819i
\(167\) −21.7812 −1.68548 −0.842740 0.538321i \(-0.819059\pi\)
−0.842740 + 0.538321i \(0.819059\pi\)
\(168\) −0.412258 + 4.56399i −0.0318064 + 0.352120i
\(169\) −11.9167 −0.916669
\(170\) 0 0
\(171\) 7.15671 + 6.16698i 0.547287 + 0.471601i
\(172\) −2.91669 −0.222396
\(173\) 0.907276 0.0689789 0.0344895 0.999405i \(-0.489019\pi\)
0.0344895 + 0.999405i \(0.489019\pi\)
\(174\) −5.44530 11.8803i −0.412807 0.900645i
\(175\) 0 0
\(176\) 3.91669i 0.295232i
\(177\) 4.25717 + 9.28811i 0.319988 + 0.698137i
\(178\) 12.3340i 0.924470i
\(179\) 2.08331i 0.155714i 0.996965 + 0.0778569i \(0.0248077\pi\)
−0.996965 + 0.0778569i \(0.975192\pi\)
\(180\) 0 0
\(181\) 24.6679i 1.83355i 0.399400 + 0.916777i \(0.369218\pi\)
−0.399400 + 0.916777i \(0.630782\pi\)
\(182\) −6.56050 + 11.4620i −0.486297 + 0.849618i
\(183\) 3.91669 1.79520i 0.289530 0.132705i
\(184\) −7.54528 −0.556245
\(185\) 0 0
\(186\) −3.02618 6.60240i −0.221891 0.484111i
\(187\) 13.8976i 1.01629i
\(188\) −8.00387 −0.583742
\(189\) −9.87479 + 9.56496i −0.718285 + 0.695749i
\(190\) 0 0
\(191\) 16.0072i 1.15824i 0.815241 + 0.579122i \(0.196604\pi\)
−0.815241 + 0.579122i \(0.803396\pi\)
\(192\) −0.721683 1.57454i −0.0520830 0.113633i
\(193\) 26.4310 1.90255 0.951273 0.308349i \(-0.0997764\pi\)
0.951273 + 0.308349i \(0.0997764\pi\)
\(194\) 0.524688 0.0376704
\(195\) 0 0
\(196\) 3.54528 + 6.03581i 0.253234 + 0.431129i
\(197\) 17.2644i 1.23004i 0.788512 + 0.615019i \(0.210852\pi\)
−0.788512 + 0.615019i \(0.789148\pi\)
\(198\) 7.67024 8.90122i 0.545100 0.632582i
\(199\) 10.8906i 0.772014i 0.922496 + 0.386007i \(0.126146\pi\)
−0.922496 + 0.386007i \(0.873854\pi\)
\(200\) 0 0
\(201\) −0.393516 0.858557i −0.0277565 0.0605579i
\(202\) 8.00387i 0.563150i
\(203\) −17.3256 9.91669i −1.21602 0.696015i
\(204\) 2.56075 + 5.58693i 0.179288 + 0.391163i
\(205\) 0 0
\(206\) 6.17269 0.430071
\(207\) −17.1477 14.7763i −1.19185 1.02702i
\(208\) 4.99166i 0.346110i
\(209\) −12.3340 −0.853158
\(210\) 0 0
\(211\) −6.88575 −0.474035 −0.237017 0.971505i \(-0.576170\pi\)
−0.237017 + 0.971505i \(0.576170\pi\)
\(212\) 0.288109i 0.0197874i
\(213\) 8.45750 3.87646i 0.579499 0.265611i
\(214\) −2.65953 −0.181801
\(215\) 0 0
\(216\) 1.44337 4.99166i 0.0982087 0.339640i
\(217\) −9.62858 5.51112i −0.653631 0.374119i
\(218\) 14.9239i 1.01078i
\(219\) −7.64405 + 3.50362i −0.516537 + 0.236753i
\(220\) 0 0
\(221\) 17.7119i 1.19143i
\(222\) 16.4728 7.55023i 1.10558 0.506738i
\(223\) 2.90336i 0.194424i 0.995264 + 0.0972118i \(0.0309924\pi\)
−0.995264 + 0.0972118i \(0.969008\pi\)
\(224\) −2.29622 1.31429i −0.153423 0.0878148i
\(225\) 0 0
\(226\) 11.8024 0.785087
\(227\) 21.6557 1.43734 0.718671 0.695351i \(-0.244751\pi\)
0.718671 + 0.695351i \(0.244751\pi\)
\(228\) −4.95835 + 2.27264i −0.328374 + 0.150509i
\(229\) 16.9378i 1.11928i 0.828735 + 0.559641i \(0.189061\pi\)
−0.828735 + 0.559641i \(0.810939\pi\)
\(230\) 0 0
\(231\) 1.61469 17.8758i 0.106239 1.17614i
\(232\) 7.54528 0.495372
\(233\) 5.42378i 0.355324i 0.984092 + 0.177662i \(0.0568533\pi\)
−0.984092 + 0.177662i \(0.943147\pi\)
\(234\) 9.77540 11.3442i 0.639038 0.741596i
\(235\) 0 0
\(236\) −5.89894 −0.383988
\(237\) 0.536091 + 1.16962i 0.0348228 + 0.0759750i
\(238\) 8.14768 + 4.66349i 0.528135 + 0.302289i
\(239\) 13.2572i 0.857535i −0.903415 0.428767i \(-0.858948\pi\)
0.903415 0.428767i \(-0.141052\pi\)
\(240\) 0 0
\(241\) 18.5233i 1.19319i −0.802543 0.596595i \(-0.796520\pi\)
0.802543 0.596595i \(-0.203480\pi\)
\(242\) 4.34047i 0.279016i
\(243\) 13.0557 8.51763i 0.837520 0.546406i
\(244\) 2.48752i 0.159247i
\(245\) 0 0
\(246\) −14.6775 + 6.72736i −0.935802 + 0.428921i
\(247\) −15.7191 −1.00018
\(248\) 4.19323 0.266270
\(249\) −3.21551 7.01547i −0.203775 0.444587i
\(250\) 0 0
\(251\) 21.5355 1.35931 0.679654 0.733533i \(-0.262130\pi\)
0.679654 + 0.733533i \(0.262130\pi\)
\(252\) −2.64464 7.48371i −0.166597 0.471429i
\(253\) 29.5525 1.85795
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 31.8900 1.98924 0.994622 0.103575i \(-0.0330281\pi\)
0.994622 + 0.103575i \(0.0330281\pi\)
\(258\) 4.59244 2.10493i 0.285913 0.131047i
\(259\) 13.7501 24.0230i 0.854388 1.49272i
\(260\) 0 0
\(261\) 17.1477 + 14.7763i 1.06141 + 0.914627i
\(262\) 14.6846i 0.907218i
\(263\) 14.1739i 0.873998i −0.899462 0.436999i \(-0.856041\pi\)
0.899462 0.436999i \(-0.143959\pi\)
\(264\) 2.82661 + 6.16698i 0.173966 + 0.379552i
\(265\) 0 0
\(266\) −4.13881 + 7.23098i −0.253767 + 0.443360i
\(267\) 8.90122 + 19.4203i 0.544746 + 1.18850i
\(268\) 0.545275 0.0333080
\(269\) −6.68074 −0.407332 −0.203666 0.979040i \(-0.565286\pi\)
−0.203666 + 0.979040i \(0.565286\pi\)
\(270\) 0 0
\(271\) 9.45864i 0.574571i −0.957845 0.287286i \(-0.907247\pi\)
0.957845 0.287286i \(-0.0927529\pi\)
\(272\) −3.54830 −0.215147
\(273\) 2.05785 22.7819i 0.124547 1.37882i
\(274\) 18.3787 1.11030
\(275\) 0 0
\(276\) 11.8803 5.44530i 0.715112 0.327769i
\(277\) 11.2048 0.673231 0.336616 0.941642i \(-0.390718\pi\)
0.336616 + 0.941642i \(0.390718\pi\)
\(278\) −12.6077 −0.756160
\(279\) 9.52969 + 8.21179i 0.570527 + 0.491627i
\(280\) 0 0
\(281\) 2.90945i 0.173563i −0.996227 0.0867816i \(-0.972342\pi\)
0.996227 0.0867816i \(-0.0276582\pi\)
\(282\) 12.6024 5.77626i 0.750462 0.343971i
\(283\) 24.4056i 1.45076i 0.688348 + 0.725381i \(0.258336\pi\)
−0.688348 + 0.725381i \(0.741664\pi\)
\(284\) 5.37142i 0.318735i
\(285\) 0 0
\(286\) 19.5508i 1.15606i
\(287\) −12.2515 + 21.4048i −0.723184 + 1.26349i
\(288\) 2.27264 + 1.95835i 0.133916 + 0.115397i
\(289\) −4.40960 −0.259388
\(290\) 0 0
\(291\) −0.826142 + 0.378659i −0.0484293 + 0.0221974i
\(292\) 4.85479i 0.284105i
\(293\) −17.0799 −0.997819 −0.498910 0.866654i \(-0.666266\pi\)
−0.498910 + 0.866654i \(0.666266\pi\)
\(294\) −9.93812 6.94505i −0.579603 0.405044i
\(295\) 0 0
\(296\) 10.4620i 0.608089i
\(297\) −5.65322 + 19.5508i −0.328033 + 1.13445i
\(298\) 5.65953 0.327847
\(299\) 37.6635 2.17813
\(300\) 0 0
\(301\) 3.83338 6.69737i 0.220953 0.386030i
\(302\) 2.62858i 0.151258i
\(303\) −5.77626 12.6024i −0.331837 0.723989i
\(304\) 3.14908i 0.180612i
\(305\) 0 0
\(306\) −8.06399 6.94879i −0.460988 0.397236i
\(307\) 11.8093i 0.673991i −0.941506 0.336996i \(-0.890589\pi\)
0.941506 0.336996i \(-0.109411\pi\)
\(308\) 8.99360 + 5.14768i 0.512458 + 0.293316i
\(309\) −9.71913 + 4.45472i −0.552902 + 0.253420i
\(310\) 0 0
\(311\) −2.88673 −0.163692 −0.0818458 0.996645i \(-0.526082\pi\)
−0.0818458 + 0.996645i \(0.526082\pi\)
\(312\) 3.60240 + 7.85957i 0.203946 + 0.444960i
\(313\) 4.20986i 0.237955i −0.992897 0.118978i \(-0.962038\pi\)
0.992897 0.118978i \(-0.0379617\pi\)
\(314\) −24.2853 −1.37050
\(315\) 0 0
\(316\) −0.742834 −0.0417876
\(317\) 23.2644i 1.30666i −0.757074 0.653330i \(-0.773372\pi\)
0.757074 0.653330i \(-0.226628\pi\)
\(318\) −0.207923 0.453638i −0.0116598 0.0254388i
\(319\) −29.5525 −1.65462
\(320\) 0 0
\(321\) 4.18753 1.91934i 0.233725 0.107127i
\(322\) 9.91669 17.3256i 0.552636 0.965520i
\(323\) 11.1739i 0.621730i
\(324\) 1.32976 + 8.90122i 0.0738757 + 0.494512i
\(325\) 0 0
\(326\) 13.4620i 0.745589i
\(327\) 10.7704 + 23.4983i 0.595602 + 1.29946i
\(328\) 9.32176i 0.514708i
\(329\) 10.5194 18.3787i 0.579954 1.01325i
\(330\) 0 0
\(331\) −25.4620 −1.39952 −0.699758 0.714380i \(-0.746709\pi\)
−0.699758 + 0.714380i \(0.746709\pi\)
\(332\) 4.45557 0.244531
\(333\) −20.4881 + 23.7763i −1.12274 + 1.30293i
\(334\) 21.7812i 1.19181i
\(335\) 0 0
\(336\) 4.56399 + 0.412258i 0.248986 + 0.0224905i
\(337\) −7.68095 −0.418408 −0.209204 0.977872i \(-0.567087\pi\)
−0.209204 + 0.977872i \(0.567087\pi\)
\(338\) 11.9167i 0.648183i
\(339\) −18.5834 + 8.51763i −1.00931 + 0.462614i
\(340\) 0 0
\(341\) −16.4236 −0.889387
\(342\) 6.16698 7.15671i 0.333472 0.386991i
\(343\) −18.5191 + 0.207923i −0.999937 + 0.0112268i
\(344\) 2.91669i 0.157257i
\(345\) 0 0
\(346\) 0.907276i 0.0487755i
\(347\) 8.26441i 0.443657i −0.975086 0.221828i \(-0.928798\pi\)
0.975086 0.221828i \(-0.0712025\pi\)
\(348\) −11.8803 + 5.44530i −0.636853 + 0.291899i
\(349\) 24.6846i 1.32133i 0.750679 + 0.660667i \(0.229727\pi\)
−0.750679 + 0.660667i \(0.770273\pi\)
\(350\) 0 0
\(351\) −7.20480 + 24.9167i −0.384564 + 1.32995i
\(352\) −3.91669 −0.208760
\(353\) 18.8945 1.00565 0.502826 0.864388i \(-0.332294\pi\)
0.502826 + 0.864388i \(0.332294\pi\)
\(354\) 9.28811 4.25717i 0.493657 0.226266i
\(355\) 0 0
\(356\) −12.3340 −0.653699
\(357\) −16.1944 1.46281i −0.857098 0.0774202i
\(358\) 2.08331 0.110106
\(359\) 1.49291i 0.0787927i −0.999224 0.0393964i \(-0.987457\pi\)
0.999224 0.0393964i \(-0.0125435\pi\)
\(360\) 0 0
\(361\) 9.08331 0.478069
\(362\) 24.6679 1.29652
\(363\) −3.13245 6.83425i −0.164411 0.358705i
\(364\) 11.4620 + 6.56050i 0.600770 + 0.343864i
\(365\) 0 0
\(366\) −1.79520 3.91669i −0.0938366 0.204729i
\(367\) 16.9544i 0.885015i 0.896765 + 0.442507i \(0.145911\pi\)
−0.896765 + 0.442507i \(0.854089\pi\)
\(368\) 7.54528i 0.393325i
\(369\) 18.2552 21.1850i 0.950330 1.10285i
\(370\) 0 0
\(371\) −0.661561 0.378659i −0.0343466 0.0196590i
\(372\) −6.60240 + 3.02618i −0.342319 + 0.156900i
\(373\) 22.8097 1.18104 0.590520 0.807023i \(-0.298923\pi\)
0.590520 + 0.807023i \(0.298923\pi\)
\(374\) 13.8976 0.718627
\(375\) 0 0
\(376\) 8.00387i 0.412768i
\(377\) −37.6635 −1.93977
\(378\) 9.56496 + 9.87479i 0.491969 + 0.507904i
\(379\) 0.371417 0.0190784 0.00953920 0.999955i \(-0.496964\pi\)
0.00953920 + 0.999955i \(0.496964\pi\)
\(380\) 0 0
\(381\) −1.44337 3.14908i −0.0739459 0.161332i
\(382\) 16.0072 0.819002
\(383\) 32.8367 1.67788 0.838939 0.544226i \(-0.183177\pi\)
0.838939 + 0.544226i \(0.183177\pi\)
\(384\) −1.57454 + 0.721683i −0.0803504 + 0.0368283i
\(385\) 0 0
\(386\) 26.4310i 1.34530i
\(387\) −5.71189 + 6.62858i −0.290352 + 0.336950i
\(388\) 0.524688i 0.0266370i
\(389\) 24.1287i 1.22338i 0.791099 + 0.611688i \(0.209509\pi\)
−0.791099 + 0.611688i \(0.790491\pi\)
\(390\) 0 0
\(391\) 26.7729i 1.35396i
\(392\) 6.03581 3.54528i 0.304855 0.179063i
\(393\) −10.5976 23.1215i −0.534580 1.16632i
\(394\) 17.2644 0.869768
\(395\) 0 0
\(396\) −8.90122 7.67024i −0.447303 0.385444i
\(397\) 7.35371i 0.369072i 0.982826 + 0.184536i \(0.0590782\pi\)
−0.982826 + 0.184536i \(0.940922\pi\)
\(398\) 10.8906 0.545896
\(399\) 1.29823 14.3724i 0.0649929 0.719519i
\(400\) 0 0
\(401\) 17.1215i 0.855007i −0.904014 0.427503i \(-0.859393\pi\)
0.904014 0.427503i \(-0.140607\pi\)
\(402\) −0.858557 + 0.393516i −0.0428209 + 0.0196268i
\(403\) −20.9312 −1.04266
\(404\) 8.00387 0.398207
\(405\) 0 0
\(406\) −9.91669 + 17.3256i −0.492157 + 0.859857i
\(407\) 40.9763i 2.03112i
\(408\) 5.58693 2.56075i 0.276594 0.126776i
\(409\) 23.2246i 1.14838i 0.818722 + 0.574191i \(0.194683\pi\)
−0.818722 + 0.574191i \(0.805317\pi\)
\(410\) 0 0
\(411\) −28.9379 + 13.2636i −1.42740 + 0.654244i
\(412\) 6.17269i 0.304106i
\(413\) 7.75293 13.5453i 0.381497 0.666519i
\(414\) −14.7763 + 17.1477i −0.726213 + 0.842762i
\(415\) 0 0
\(416\) −4.99166 −0.244736
\(417\) 19.8513 9.09878i 0.972124 0.445569i
\(418\) 12.3340i 0.603274i
\(419\) −11.5522 −0.564360 −0.282180 0.959361i \(-0.591058\pi\)
−0.282180 + 0.959361i \(0.591058\pi\)
\(420\) 0 0
\(421\) 36.9239 1.79956 0.899781 0.436341i \(-0.143726\pi\)
0.899781 + 0.436341i \(0.143726\pi\)
\(422\) 6.88575i 0.335193i
\(423\) −15.6743 + 18.1899i −0.762112 + 0.884423i
\(424\) 0.288109 0.0139918
\(425\) 0 0
\(426\) −3.87646 8.45750i −0.187815 0.409767i
\(427\) −5.71189 3.26932i −0.276418 0.158214i
\(428\) 2.65953i 0.128553i
\(429\) −14.1095 30.7835i −0.681213 1.48624i
\(430\) 0 0
\(431\) 5.03094i 0.242332i 0.992632 + 0.121166i \(0.0386633\pi\)
−0.992632 + 0.121166i \(0.961337\pi\)
\(432\) −4.99166 1.44337i −0.240161 0.0694440i
\(433\) 3.04024i 0.146104i −0.997328 0.0730522i \(-0.976726\pi\)
0.997328 0.0730522i \(-0.0232740\pi\)
\(434\) −5.51112 + 9.62858i −0.264542 + 0.462187i
\(435\) 0 0
\(436\) −14.9239 −0.714727
\(437\) 23.7607 1.13663
\(438\) 3.50362 + 7.64405i 0.167409 + 0.365247i
\(439\) 19.8184i 0.945879i −0.881095 0.472940i \(-0.843193\pi\)
0.881095 0.472940i \(-0.156807\pi\)
\(440\) 0 0
\(441\) 20.6601 + 3.76308i 0.983814 + 0.179194i
\(442\) 17.7119 0.842469
\(443\) 10.5976i 0.503509i −0.967791 0.251755i \(-0.918992\pi\)
0.967791 0.251755i \(-0.0810076\pi\)
\(444\) −7.55023 16.4728i −0.358318 0.781763i
\(445\) 0 0
\(446\) 2.90336 0.137478
\(447\) −8.91114 + 4.08439i −0.421483 + 0.193185i
\(448\) −1.31429 + 2.29622i −0.0620944 + 0.108486i
\(449\) 6.19756i 0.292481i −0.989249 0.146240i \(-0.953283\pi\)
0.989249 0.146240i \(-0.0467173\pi\)
\(450\) 0 0
\(451\) 36.5105i 1.71921i
\(452\) 11.8024i 0.555140i
\(453\) −1.89701 4.13881i −0.0891291 0.194458i
\(454\) 21.6557i 1.01635i
\(455\) 0 0
\(456\) 2.27264 + 4.95835i 0.106426 + 0.232196i
\(457\) −19.7573 −0.924208 −0.462104 0.886826i \(-0.652905\pi\)
−0.462104 + 0.886826i \(0.652905\pi\)
\(458\) 16.9378 0.791452
\(459\) 17.7119 + 5.12149i 0.826720 + 0.239051i
\(460\) 0 0
\(461\) 26.8983 1.25278 0.626390 0.779510i \(-0.284532\pi\)
0.626390 + 0.779510i \(0.284532\pi\)
\(462\) −17.8758 1.61469i −0.831656 0.0751220i
\(463\) −38.7573 −1.80121 −0.900603 0.434643i \(-0.856874\pi\)
−0.900603 + 0.434643i \(0.856874\pi\)
\(464\) 7.54528i 0.350281i
\(465\) 0 0
\(466\) 5.42378 0.251252
\(467\) −18.5181 −0.856913 −0.428457 0.903562i \(-0.640943\pi\)
−0.428457 + 0.903562i \(0.640943\pi\)
\(468\) −11.3442 9.77540i −0.524388 0.451868i
\(469\) −0.716650 + 1.25207i −0.0330918 + 0.0578154i
\(470\) 0 0
\(471\) 38.2382 17.5263i 1.76192 0.807571i
\(472\) 5.89894i 0.271521i
\(473\) 11.4238i 0.525266i
\(474\) 1.16962 0.536091i 0.0537224 0.0246235i
\(475\) 0 0
\(476\) 4.66349 8.14768i 0.213751 0.373448i
\(477\) 0.654766 + 0.564216i 0.0299797 + 0.0258337i
\(478\) −13.2572 −0.606369
\(479\) −14.4337 −0.659491 −0.329746 0.944070i \(-0.606963\pi\)
−0.329746 + 0.944070i \(0.606963\pi\)
\(480\) 0 0
\(481\) 52.2226i 2.38115i
\(482\) −18.5233 −0.843712
\(483\) −3.11060 + 34.4366i −0.141537 + 1.56692i
\(484\) 4.34047 0.197294
\(485\) 0 0
\(486\) −8.51763 13.0557i −0.386367 0.592216i
\(487\) −26.2430 −1.18918 −0.594592 0.804028i \(-0.702686\pi\)
−0.594592 + 0.804028i \(0.702686\pi\)
\(488\) 2.48752 0.112605
\(489\) −9.71528 21.1964i −0.439340 0.958534i
\(490\) 0 0
\(491\) 30.0000i 1.35388i −0.736038 0.676941i \(-0.763305\pi\)
0.736038 0.676941i \(-0.236695\pi\)
\(492\) 6.72736 + 14.6775i 0.303293 + 0.661712i
\(493\) 26.7729i 1.20579i
\(494\) 15.7191i 0.707237i
\(495\) 0 0
\(496\) 4.19323i 0.188281i
\(497\) −12.3340 7.05961i −0.553254 0.316667i
\(498\) −7.01547 + 3.21551i −0.314371 + 0.144091i
\(499\) 41.6740 1.86558 0.932792 0.360414i \(-0.117365\pi\)
0.932792 + 0.360414i \(0.117365\pi\)
\(500\) 0 0
\(501\) −15.7191 34.2954i −0.702279 1.53220i
\(502\) 21.5355i 0.961176i
\(503\) 0.415846 0.0185417 0.00927084 0.999957i \(-0.497049\pi\)
0.00927084 + 0.999957i \(0.497049\pi\)
\(504\) −7.48371 + 2.64464i −0.333351 + 0.117802i
\(505\) 0 0
\(506\) 29.5525i 1.31377i
\(507\) −8.60008 18.7633i −0.381943 0.833307i
\(508\) 2.00000 0.0887357
\(509\) −11.3064 −0.501149 −0.250575 0.968097i \(-0.580620\pi\)
−0.250575 + 0.968097i \(0.580620\pi\)
\(510\) 0 0
\(511\) 11.1477 + 6.38061i 0.493144 + 0.282261i
\(512\) 1.00000i 0.0441942i
\(513\) −4.54528 + 15.7191i −0.200679 + 0.694017i
\(514\) 31.8900i 1.40661i
\(515\) 0 0
\(516\) −2.10493 4.59244i −0.0926643 0.202171i
\(517\) 31.3487i 1.37871i
\(518\) −24.0230 13.7501i −1.05551 0.604144i
\(519\) 0.654766 + 1.42854i 0.0287411 + 0.0627060i
\(520\) 0 0
\(521\) 2.47611 0.108481 0.0542403 0.998528i \(-0.482726\pi\)
0.0542403 + 0.998528i \(0.482726\pi\)
\(522\) 14.7763 17.1477i 0.646739 0.750533i
\(523\) 12.0602i 0.527357i −0.964611 0.263678i \(-0.915064\pi\)
0.964611 0.263678i \(-0.0849357\pi\)
\(524\) 14.6846 0.641500
\(525\) 0 0
\(526\) −14.1739 −0.618010
\(527\) 14.8788i 0.648131i
\(528\) 6.16698 2.82661i 0.268384 0.123012i
\(529\) −33.9312 −1.47527
\(530\) 0 0
\(531\) −11.5522 + 13.4061i −0.501321 + 0.581777i
\(532\) 7.23098 + 4.13881i 0.313503 + 0.179440i
\(533\) 46.5311i 2.01549i
\(534\) 19.4203 8.90122i 0.840399 0.385193i
\(535\) 0 0
\(536\) 0.545275i 0.0235523i
\(537\) −3.28025 + 1.50349i −0.141553 + 0.0648803i
\(538\) 6.68074i 0.288027i
\(539\) −23.6404 + 13.8857i −1.01826 + 0.598102i
\(540\) 0 0
\(541\) 5.14292 0.221111 0.110556 0.993870i \(-0.464737\pi\)
0.110556 + 0.993870i \(0.464737\pi\)
\(542\) −9.45864 −0.406283
\(543\) −38.8406 + 17.8024i −1.66681 + 0.763976i
\(544\) 3.54830i 0.152132i
\(545\) 0 0
\(546\) −22.7819 2.05785i −0.974976 0.0880679i
\(547\) −3.11425 −0.133156 −0.0665779 0.997781i \(-0.521208\pi\)
−0.0665779 + 0.997781i \(0.521208\pi\)
\(548\) 18.3787i 0.785097i
\(549\) 5.65322 + 4.87142i 0.241274 + 0.207907i
\(550\) 0 0
\(551\) −23.7607 −1.01224
\(552\) −5.44530 11.8803i −0.231767 0.505660i
\(553\) 0.976300 1.70571i 0.0415165 0.0725342i
\(554\) 11.2048i 0.476046i
\(555\) 0 0
\(556\) 12.6077i 0.534686i
\(557\) 1.93812i 0.0821206i 0.999157 + 0.0410603i \(0.0130736\pi\)
−0.999157 + 0.0410603i \(0.986926\pi\)
\(558\) 8.21179 9.52969i 0.347633 0.403424i
\(559\) 14.5591i 0.615786i
\(560\) 0 0
\(561\) −21.8823 + 10.0297i −0.923871 + 0.423452i
\(562\) −2.90945 −0.122728
\(563\) 25.8656 1.09010 0.545052 0.838402i \(-0.316510\pi\)
0.545052 + 0.838402i \(0.316510\pi\)
\(564\) −5.77626 12.6024i −0.243224 0.530657i
\(565\) 0 0
\(566\) 24.4056 1.02584
\(567\) −22.1869 8.64537i −0.931761 0.363071i
\(568\) 5.37142 0.225380
\(569\) 30.3787i 1.27354i −0.771054 0.636770i \(-0.780270\pi\)
0.771054 0.636770i \(-0.219730\pi\)
\(570\) 0 0
\(571\) 4.56898 0.191206 0.0956028 0.995420i \(-0.469522\pi\)
0.0956028 + 0.995420i \(0.469522\pi\)
\(572\) 19.5508 0.817460
\(573\) −25.2040 + 11.5522i −1.05291 + 0.482598i
\(574\) 21.4048 + 12.2515i 0.893421 + 0.511368i
\(575\) 0 0
\(576\) 1.95835 2.27264i 0.0815977 0.0946932i
\(577\) 23.7493i 0.988694i −0.869265 0.494347i \(-0.835407\pi\)
0.869265 0.494347i \(-0.164593\pi\)
\(578\) 4.40960i 0.183415i
\(579\) 19.0748 + 41.6167i 0.792723 + 1.72953i
\(580\) 0 0
\(581\) −5.85592 + 10.2310i −0.242945 + 0.424453i
\(582\) 0.378659 + 0.826142i 0.0156959 + 0.0342447i
\(583\) −1.12843 −0.0467349
\(584\) −4.85479 −0.200893
\(585\) 0 0
\(586\) 17.0799i 0.705565i
\(587\) 28.8726 1.19170 0.595849 0.803096i \(-0.296816\pi\)
0.595849 + 0.803096i \(0.296816\pi\)
\(588\) −6.94505 + 9.93812i −0.286409 + 0.409841i
\(589\) −13.2048 −0.544094
\(590\) 0 0
\(591\) −27.1835 + 12.4594i −1.11818 + 0.512513i
\(592\) 10.4620 0.429984
\(593\) −4.74595 −0.194893 −0.0974463 0.995241i \(-0.531067\pi\)
−0.0974463 + 0.995241i \(0.531067\pi\)
\(594\) 19.5508 + 5.65322i 0.802179 + 0.231955i
\(595\) 0 0
\(596\) 5.65953i 0.231823i
\(597\) −17.1477 + 7.85957i −0.701808 + 0.321671i
\(598\) 37.6635i 1.54017i
\(599\) 3.19756i 0.130649i 0.997864 + 0.0653243i \(0.0208082\pi\)
−0.997864 + 0.0653243i \(0.979192\pi\)
\(600\) 0 0
\(601\) 1.16962i 0.0477098i −0.999715 0.0238549i \(-0.992406\pi\)
0.999715 0.0238549i \(-0.00759397\pi\)
\(602\) −6.69737 3.83338i −0.272965 0.156237i
\(603\) 1.06784 1.23921i 0.0434857 0.0504646i
\(604\) 2.62858 0.106956
\(605\) 0 0
\(606\) −12.6024 + 5.77626i −0.511938 + 0.234644i
\(607\) 42.5463i 1.72690i 0.504434 + 0.863450i \(0.331701\pi\)
−0.504434 + 0.863450i \(0.668299\pi\)
\(608\) −3.14908 −0.127712
\(609\) 3.11060 34.4366i 0.126048 1.39544i
\(610\) 0 0
\(611\) 39.9526i 1.61631i
\(612\) −6.94879 + 8.06399i −0.280888 + 0.325967i
\(613\) 11.1524 0.450443 0.225221 0.974308i \(-0.427689\pi\)
0.225221 + 0.974308i \(0.427689\pi\)
\(614\) −11.8093 −0.476584
\(615\) 0 0
\(616\) 5.14768 8.99360i 0.207406 0.362362i
\(617\) 42.1811i 1.69815i −0.528275 0.849074i \(-0.677161\pi\)
0.528275 0.849074i \(-0.322839\pi\)
\(618\) 4.45472 + 9.71913i 0.179195 + 0.390961i
\(619\) 11.0327i 0.443442i 0.975110 + 0.221721i \(0.0711674\pi\)
−0.975110 + 0.221721i \(0.928833\pi\)
\(620\) 0 0
\(621\) 10.8906 37.6635i 0.437025 1.51138i
\(622\) 2.88673i 0.115747i
\(623\) 16.2104 28.3215i 0.649457 1.13468i
\(624\) 7.85957 3.60240i 0.314634 0.144211i
\(625\) 0 0
\(626\) −4.20986 −0.168260
\(627\) −8.90122 19.4203i −0.355481 0.775573i
\(628\) 24.2853i 0.969091i
\(629\) −37.1221 −1.48016
\(630\) 0 0
\(631\) 4.46197 0.177628 0.0888140 0.996048i \(-0.471692\pi\)
0.0888140 + 0.996048i \(0.471692\pi\)
\(632\) 0.742834i 0.0295483i
\(633\) −4.96933 10.8419i −0.197513 0.430926i
\(634\) −23.2644 −0.923948
\(635\) 0 0
\(636\) −0.453638 + 0.207923i −0.0179879 + 0.00824469i
\(637\) −30.1287 + 17.6968i −1.19374 + 0.701173i
\(638\) 29.5525i 1.17000i
\(639\) 12.2073 + 10.5191i 0.482913 + 0.416129i
\(640\) 0 0
\(641\) 2.90945i 0.114916i 0.998348 + 0.0574582i \(0.0182996\pi\)
−0.998348 + 0.0574582i \(0.981700\pi\)
\(642\) −1.91934 4.18753i −0.0757501 0.165268i
\(643\) 31.7645i 1.25267i 0.779554 + 0.626335i \(0.215446\pi\)
−0.779554 + 0.626335i \(0.784554\pi\)
\(644\) −17.3256 9.91669i −0.682725 0.390772i
\(645\) 0 0
\(646\) 11.1739 0.439630
\(647\) −23.3448 −0.917779 −0.458890 0.888493i \(-0.651753\pi\)
−0.458890 + 0.888493i \(0.651753\pi\)
\(648\) 8.90122 1.32976i 0.349673 0.0522380i
\(649\) 23.1043i 0.906924i
\(650\) 0 0
\(651\) 1.72869 19.1379i 0.0677527 0.750072i
\(652\) 13.4620 0.527211
\(653\) 2.28087i 0.0892572i 0.999004 + 0.0446286i \(0.0142104\pi\)
−0.999004 + 0.0446286i \(0.985790\pi\)
\(654\) 23.4983 10.7704i 0.918857 0.421154i
\(655\) 0 0
\(656\) −9.32176 −0.363954
\(657\) −11.0332 9.50736i −0.430445 0.370917i
\(658\) −18.3787 10.5194i −0.716475 0.410089i
\(659\) 2.08331i 0.0811542i 0.999176 + 0.0405771i \(0.0129196\pi\)
−0.999176 + 0.0405771i \(0.987080\pi\)
\(660\) 0 0
\(661\) 4.34150i 0.168865i −0.996429 0.0844325i \(-0.973092\pi\)
0.996429 0.0844325i \(-0.0269077\pi\)
\(662\) 25.4620i 0.989607i
\(663\) −27.8881 + 12.7824i −1.08308 + 0.496426i
\(664\) 4.45557i 0.172910i
\(665\) 0 0
\(666\) 23.7763 + 20.4881i 0.921311 + 0.793900i
\(667\) 56.9312 2.20438
\(668\) 21.7812 0.842740
\(669\) −4.57146 + 2.09531i −0.176743 + 0.0810093i
\(670\) 0 0
\(671\) −9.74284 −0.376118
\(672\) 0.412258 4.56399i 0.0159032 0.176060i
\(673\) −2.00724 −0.0773735 −0.0386867 0.999251i \(-0.512317\pi\)
−0.0386867 + 0.999251i \(0.512317\pi\)
\(674\) 7.68095i 0.295859i
\(675\) 0 0
\(676\) 11.9167 0.458334
\(677\) 27.5547 1.05901 0.529506 0.848306i \(-0.322377\pi\)
0.529506 + 0.848306i \(0.322377\pi\)
\(678\) 8.51763 + 18.5834i 0.327117 + 0.713691i
\(679\) 1.20480 + 0.689593i 0.0462360 + 0.0264642i
\(680\) 0 0
\(681\) 15.6286 + 34.0978i 0.598889 + 1.30663i
\(682\) 16.4236i 0.628891i
\(683\) 5.75008i 0.220021i 0.993930 + 0.110010i \(0.0350884\pi\)
−0.993930 + 0.110010i \(0.964912\pi\)
\(684\) −7.15671 6.16698i −0.273644 0.235801i
\(685\) 0 0
\(686\) 0.207923 + 18.5191i 0.00793854 + 0.707062i
\(687\) −26.6693 + 12.2237i −1.01750 + 0.466365i
\(688\) 2.91669 0.111198
\(689\) −1.43814 −0.0547888
\(690\) 0 0
\(691\) 23.6404i 0.899324i 0.893199 + 0.449662i \(0.148456\pi\)
−0.893199 + 0.449662i \(0.851544\pi\)
\(692\) −0.907276 −0.0344895
\(693\) 29.3114 10.3583i 1.11345 0.393478i
\(694\) −8.26441 −0.313713
\(695\) 0 0
\(696\) 5.44530 + 11.8803i 0.206404 + 0.450323i
\(697\) 33.0764 1.25286
\(698\) 24.6846 0.934325
\(699\) −8.53996 + 3.91425i −0.323011 + 0.148051i
\(700\) 0 0
\(701\) 46.6882i 1.76339i −0.471821 0.881694i \(-0.656403\pi\)
0.471821 0.881694i \(-0.343597\pi\)
\(702\) 24.9167 + 7.20480i 0.940420 + 0.271928i
\(703\) 32.9455i 1.24256i
\(704\) 3.91669i 0.147616i
\(705\) 0 0
\(706\) 18.8945i 0.711103i
\(707\) −10.5194 + 18.3787i −0.395623 + 0.691201i
\(708\) −4.25717 9.28811i −0.159994 0.349068i
\(709\) 17.8334 0.669747 0.334873 0.942263i \(-0.391306\pi\)
0.334873 + 0.942263i \(0.391306\pi\)
\(710\) 0 0
\(711\) −1.45472 + 1.68819i −0.0545564 + 0.0633121i
\(712\) 12.3340i 0.462235i
\(713\) 31.6391 1.18489
\(714\) −1.46281 + 16.1944i −0.0547443 + 0.606060i
\(715\) 0 0
\(716\) 2.08331i 0.0778569i
\(717\) 20.8739 9.56748i 0.779551 0.357304i
\(718\) −1.49291 −0.0557149
\(719\) −18.4786 −0.689136 −0.344568 0.938761i \(-0.611975\pi\)
−0.344568 + 0.938761i \(0.611975\pi\)
\(720\) 0 0
\(721\) 14.1739 + 8.11271i 0.527862 + 0.302133i
\(722\) 9.08331i 0.338046i
\(723\) 29.1656 13.3679i 1.08468 0.497159i
\(724\) 24.6679i 0.916777i
\(725\) 0 0
\(726\) −6.83425 + 3.13245i −0.253643 + 0.116256i
\(727\) 8.92777i 0.331113i −0.986200 0.165556i \(-0.947058\pi\)
0.986200 0.165556i \(-0.0529420\pi\)
\(728\) 6.56050 11.4620i 0.243148 0.424809i
\(729\) 22.8334 + 14.4096i 0.845681 + 0.533689i
\(730\) 0 0
\(731\) −10.3493 −0.382782
\(732\) −3.91669 + 1.79520i −0.144765 + 0.0663525i
\(733\) 24.7934i 0.915765i 0.889013 + 0.457883i \(0.151392\pi\)
−0.889013 + 0.457883i \(0.848608\pi\)
\(734\) 16.9544 0.625800
\(735\) 0 0
\(736\) 7.54528 0.278123
\(737\) 2.13567i 0.0786686i
\(738\) −21.1850 18.2552i −0.779830 0.671985i
\(739\) 5.32629 0.195931 0.0979654 0.995190i \(-0.468767\pi\)
0.0979654 + 0.995190i \(0.468767\pi\)
\(740\) 0 0
\(741\) −11.3442 24.7504i −0.416741 0.909228i
\(742\) −0.378659 + 0.661561i −0.0139010 + 0.0242867i
\(743\) 45.7409i 1.67807i −0.544078 0.839035i \(-0.683120\pi\)
0.544078 0.839035i \(-0.316880\pi\)
\(744\) 3.02618 + 6.60240i 0.110945 + 0.242056i
\(745\) 0 0
\(746\) 22.8097i 0.835122i
\(747\) 8.72555 10.1259i 0.319251 0.370487i
\(748\) 13.8976i 0.508146i
\(749\) −6.10686 3.49539i −0.223140 0.127719i
\(750\) 0 0
\(751\) −21.8857 −0.798622 −0.399311 0.916815i \(-0.630751\pi\)
−0.399311 + 0.916815i \(0.630751\pi\)
\(752\) 8.00387 0.291871
\(753\) 15.5418 + 33.9085i 0.566375 + 1.23569i
\(754\) 37.6635i 1.37162i
\(755\) 0 0
\(756\) 9.87479 9.56496i 0.359143 0.347874i
\(757\) 14.0524 0.510742 0.255371 0.966843i \(-0.417802\pi\)
0.255371 + 0.966843i \(0.417802\pi\)
\(758\) 0.371417i 0.0134905i
\(759\) 21.3276 + 46.5316i 0.774142 + 1.68899i
\(760\) 0 0
\(761\) 49.6210 1.79876 0.899380 0.437167i \(-0.144018\pi\)
0.899380 + 0.437167i \(0.144018\pi\)
\(762\) −3.14908 + 1.44337i −0.114079 + 0.0522877i
\(763\) 19.6144 34.2687i 0.710089 1.24061i
\(764\) 16.0072i 0.579122i
\(765\) 0 0
\(766\) 32.8367i 1.18644i
\(767\) 29.4455i 1.06322i
\(768\) 0.721683 + 1.57454i 0.0260415 + 0.0568163i
\(769\) 12.9903i 0.468442i 0.972183 + 0.234221i \(0.0752540\pi\)
−0.972183 + 0.234221i \(0.924746\pi\)
\(770\) 0 0
\(771\) 23.0145 + 50.2120i 0.828846 + 1.80834i
\(772\) −26.4310 −0.951273
\(773\) −29.9500 −1.07723 −0.538613 0.842553i \(-0.681051\pi\)
−0.538613 + 0.842553i \(0.681051\pi\)
\(774\) 6.62858 + 5.71189i 0.238260 + 0.205310i
\(775\) 0 0
\(776\) −0.524688 −0.0188352
\(777\) 47.7484 + 4.31302i 1.71296 + 0.154729i
\(778\) 24.1287 0.865057
\(779\) 29.3550i 1.05175i
\(780\) 0 0
\(781\) −21.0382 −0.752805
\(782\) −26.7729 −0.957396
\(783\) −10.8906 + 37.6635i −0.389198 + 1.34598i
\(784\) −3.54528 6.03581i −0.126617 0.215565i
\(785\) 0 0
\(786\) −23.1215 + 10.5976i −0.824716 + 0.378005i
\(787\) 1.01612i 0.0362207i 0.999836 + 0.0181103i \(0.00576502\pi\)
−0.999836 + 0.0181103i \(0.994235\pi\)
\(788\) 17.2644i