Properties

Label 1050.2.d.h.1049.12
Level $1050$
Weight $2$
Character 1050.1049
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.d (of order \(2\), degree \(1\), not 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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1049.12
Root \(0.721683 - 1.57454i\) of defining polynomial
Character \(\chi\) \(=\) 1050.1049
Dual form 1050.2.d.h.1049.11

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.57454 + 0.721683i) q^{3} +1.00000 q^{4} +(1.57454 + 0.721683i) q^{6} +(2.29622 - 1.31429i) q^{7} +1.00000 q^{8} +(1.95835 + 2.27264i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.57454 + 0.721683i) q^{3} +1.00000 q^{4} +(1.57454 + 0.721683i) q^{6} +(2.29622 - 1.31429i) q^{7} +1.00000 q^{8} +(1.95835 + 2.27264i) q^{9} +3.91669i q^{11} +(1.57454 + 0.721683i) q^{12} -4.99166 q^{13} +(2.29622 - 1.31429i) q^{14} +1.00000 q^{16} +3.54830i q^{17} +(1.95835 + 2.27264i) q^{18} -3.14908i q^{19} +(4.56399 - 0.412258i) q^{21} +3.91669i q^{22} +7.54528 q^{23} +(1.57454 + 0.721683i) q^{24} -4.99166 q^{26} +(1.44337 + 4.99166i) q^{27} +(2.29622 - 1.31429i) q^{28} -7.54528i q^{29} +4.19323i q^{31} +1.00000 q^{32} +(-2.82661 + 6.16698i) q^{33} +3.54830i q^{34} +(1.95835 + 2.27264i) q^{36} -10.4620i q^{37} -3.14908i q^{38} +(-7.85957 - 3.60240i) q^{39} -9.32176 q^{41} +(4.56399 - 0.412258i) q^{42} +2.91669i q^{43} +3.91669i q^{44} +7.54528 q^{46} -8.00387i q^{47} +(1.57454 + 0.721683i) q^{48} +(3.54528 - 6.03581i) q^{49} +(-2.56075 + 5.58693i) q^{51} -4.99166 q^{52} -0.288109 q^{53} +(1.44337 + 4.99166i) q^{54} +(2.29622 - 1.31429i) q^{56} +(2.27264 - 4.95835i) q^{57} -7.54528i q^{58} -5.89894 q^{59} +2.48752i q^{61} +4.19323i q^{62} +(7.48371 + 2.64464i) q^{63} +1.00000 q^{64} +(-2.82661 + 6.16698i) q^{66} +0.545275i q^{67} +3.54830i q^{68} +(11.8803 + 5.44530i) q^{69} +5.37142i q^{71} +(1.95835 + 2.27264i) q^{72} +4.85479 q^{73} -10.4620i q^{74} -3.14908i q^{76} +(5.14768 + 8.99360i) q^{77} +(-7.85957 - 3.60240i) q^{78} -0.742834 q^{79} +(-1.32976 + 8.90122i) q^{81} -9.32176 q^{82} -4.45557i q^{83} +(4.56399 - 0.412258i) q^{84} +2.91669i q^{86} +(5.44530 - 11.8803i) q^{87} +3.91669i q^{88} -12.3340 q^{89} +(-11.4620 + 6.56050i) q^{91} +7.54528 q^{92} +(-3.02618 + 6.60240i) q^{93} -8.00387i q^{94} +(1.57454 + 0.721683i) q^{96} -0.524688 q^{97} +(3.54528 - 6.03581i) q^{98} +(-8.90122 + 7.67024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 12q + 12q^{2} + 12q^{4} + 12q^{8} + 12q^{16} + 14q^{21} + 20q^{23} + 12q^{32} - 12q^{39} + 14q^{42} + 20q^{46} - 28q^{49} + 28q^{51} + 20q^{53} - 8q^{57} + 30q^{63} + 12q^{64} - 44q^{77} - 12q^{78} - 56q^{79} - 16q^{81} + 14q^{84} - 20q^{91} + 20q^{92} - 48q^{93} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.57454 + 0.721683i 0.909060 + 0.416664i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.57454 + 0.721683i 0.642803 + 0.294626i
\(7\) 2.29622 1.31429i 0.867891 0.496756i
\(8\) 1.00000 0.353553
\(9\) 1.95835 + 2.27264i 0.652782 + 0.757546i
\(10\) 0 0
\(11\) 3.91669i 1.18093i 0.807064 + 0.590464i \(0.201055\pi\)
−0.807064 + 0.590464i \(0.798945\pi\)
\(12\) 1.57454 + 0.721683i 0.454530 + 0.208332i
\(13\) −4.99166 −1.38444 −0.692219 0.721688i \(-0.743367\pi\)
−0.692219 + 0.721688i \(0.743367\pi\)
\(14\) 2.29622 1.31429i 0.613691 0.351259i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.54830i 0.860588i 0.902689 + 0.430294i \(0.141590\pi\)
−0.902689 + 0.430294i \(0.858410\pi\)
\(18\) 1.95835 + 2.27264i 0.461587 + 0.535666i
\(19\) 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
\(22\) 3.91669i 0.835041i
\(23\) 7.54528 1.57330 0.786649 0.617400i \(-0.211814\pi\)
0.786649 + 0.617400i \(0.211814\pi\)
\(24\) 1.57454 + 0.721683i 0.321401 + 0.147313i
\(25\) 0 0
\(26\) −4.99166 −0.978946
\(27\) 1.44337 + 4.99166i 0.277776 + 0.960646i
\(28\) 2.29622 1.31429i 0.433945 0.248378i
\(29\) 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 \(0.122894\pi\)
−0.926391 + 0.376563i \(0.877106\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.82661 + 6.16698i −0.492050 + 1.07353i
\(34\) 3.54830i 0.608528i
\(35\) 0 0
\(36\) 1.95835 + 2.27264i 0.326391 + 0.378773i
\(37\) 10.4620i 1.71994i −0.510347 0.859968i \(-0.670483\pi\)
0.510347 0.859968i \(-0.329517\pi\)
\(38\) 3.14908i 0.510848i
\(39\) −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 \(0.759507\pi\)
\(42\) 4.56399 0.412258i 0.704240 0.0636127i
\(43\) 2.91669i 0.444791i 0.974956 + 0.222396i \(0.0713877\pi\)
−0.974956 + 0.222396i \(0.928612\pi\)
\(44\) 3.91669i 0.590464i
\(45\) 0 0
\(46\) 7.54528 1.11249
\(47\) 8.00387i 1.16748i −0.811939 0.583742i \(-0.801588\pi\)
0.811939 0.583742i \(-0.198412\pi\)
\(48\) 1.57454 + 0.721683i 0.227265 + 0.104166i
\(49\) 3.54528 6.03581i 0.506468 0.862259i
\(50\) 0 0
\(51\) −2.56075 + 5.58693i −0.358576 + 0.782327i
\(52\) −4.99166 −0.692219
\(53\) −0.288109 −0.0395748 −0.0197874 0.999804i \(-0.506299\pi\)
−0.0197874 + 0.999804i \(0.506299\pi\)
\(54\) 1.44337 + 4.99166i 0.196417 + 0.679279i
\(55\) 0 0
\(56\) 2.29622 1.31429i 0.306846 0.175630i
\(57\) 2.27264 4.95835i 0.301018 0.656749i
\(58\) 7.54528i 0.990743i
\(59\) −5.89894 −0.767976 −0.383988 0.923338i \(-0.625450\pi\)
−0.383988 + 0.923338i \(0.625450\pi\)
\(60\) 0 0
\(61\) 2.48752i 0.318494i 0.987239 + 0.159247i \(0.0509066\pi\)
−0.987239 + 0.159247i \(0.949093\pi\)
\(62\) 4.19323i 0.532540i
\(63\) 7.48371 + 2.64464i 0.942858 + 0.333194i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.82661 + 6.16698i −0.347932 + 0.759103i
\(67\) 0.545275i 0.0666160i 0.999445 + 0.0333080i \(0.0106042\pi\)
−0.999445 + 0.0333080i \(0.989396\pi\)
\(68\) 3.54830i 0.430294i
\(69\) 11.8803 + 5.44530i 1.43022 + 0.655537i
\(70\) 0 0
\(71\) 5.37142i 0.637470i 0.947844 + 0.318735i \(0.103258\pi\)
−0.947844 + 0.318735i \(0.896742\pi\)
\(72\) 1.95835 + 2.27264i 0.230793 + 0.267833i
\(73\) 4.85479 0.568210 0.284105 0.958793i \(-0.408304\pi\)
0.284105 + 0.958793i \(0.408304\pi\)
\(74\) 10.4620i 1.21618i
\(75\) 0 0
\(76\) 3.14908i 0.361224i
\(77\) 5.14768 + 8.99360i 0.586632 + 1.02492i
\(78\) −7.85957 3.60240i −0.889921 0.407891i
\(79\) −0.742834 −0.0835753 −0.0417876 0.999127i \(-0.513305\pi\)
−0.0417876 + 0.999127i \(0.513305\pi\)
\(80\) 0 0
\(81\) −1.32976 + 8.90122i −0.147751 + 0.989025i
\(82\) −9.32176 −1.02942
\(83\) 4.45557i 0.489063i −0.969641 0.244531i \(-0.921366\pi\)
0.969641 0.244531i \(-0.0786341\pi\)
\(84\) 4.56399 0.412258i 0.497973 0.0449810i
\(85\) 0 0
\(86\) 2.91669i 0.314515i
\(87\) 5.44530 11.8803i 0.583797 1.27371i
\(88\) 3.91669i 0.417521i
\(89\) −12.3340 −1.30740 −0.653699 0.756755i \(-0.726784\pi\)
−0.653699 + 0.756755i \(0.726784\pi\)
\(90\) 0 0
\(91\) −11.4620 + 6.56050i −1.20154 + 0.687727i
\(92\) 7.54528 0.786649
\(93\) −3.02618 + 6.60240i −0.313801 + 0.684637i
\(94\) 8.00387i 0.825536i
\(95\) 0 0
\(96\) 1.57454 + 0.721683i 0.160701 + 0.0736565i
\(97\) −0.524688 −0.0532740 −0.0266370 0.999645i \(-0.508480\pi\)
−0.0266370 + 0.999645i \(0.508480\pi\)
\(98\) 3.54528 6.03581i 0.358127 0.609709i
\(99\) −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 \(0.630368\pi\)
\(102\) −2.56075 + 5.58693i −0.253552 + 0.553188i
\(103\) 6.17269 0.608213 0.304106 0.952638i \(-0.401642\pi\)
0.304106 + 0.952638i \(0.401642\pi\)
\(104\) −4.99166 −0.489473
\(105\) 0 0
\(106\) −0.288109 −0.0279836
\(107\) 2.65953 0.257106 0.128553 0.991703i \(-0.458967\pi\)
0.128553 + 0.991703i \(0.458967\pi\)
\(108\) 1.44337 + 4.99166i 0.138888 + 0.480323i
\(109\) −14.9239 −1.42945 −0.714727 0.699404i \(-0.753449\pi\)
−0.714727 + 0.699404i \(0.753449\pi\)
\(110\) 0 0
\(111\) 7.55023 16.4728i 0.716636 1.56353i
\(112\) 2.29622 1.31429i 0.216973 0.124189i
\(113\) 11.8024 1.11028 0.555140 0.831757i \(-0.312665\pi\)
0.555140 + 0.831757i \(0.312665\pi\)
\(114\) 2.27264 4.95835i 0.212852 0.464392i
\(115\) 0 0
\(116\) 7.54528i 0.700561i
\(117\) −9.77540 11.3442i −0.903736 1.04878i
\(118\) −5.89894 −0.543041
\(119\) 4.66349 + 8.14768i 0.427502 + 0.746896i
\(120\) 0 0
\(121\) −4.34047 −0.394589
\(122\) 2.48752i 0.225209i
\(123\) −14.6775 6.72736i −1.32342 0.606586i
\(124\) 4.19323i 0.376563i
\(125\) 0 0
\(126\) 7.48371 + 2.64464i 0.666702 + 0.235604i
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 1.00000 0.0883883
\(129\) −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 \(0.721688\pi\)
\(132\) −2.82661 + 6.16698i −0.246025 + 0.536767i
\(133\) −4.13881 7.23098i −0.358880 0.627006i
\(134\) 0.545275i 0.0471046i
\(135\) 0 0
\(136\) 3.54830i 0.304264i
\(137\) −18.3787 −1.57019 −0.785097 0.619372i \(-0.787387\pi\)
−0.785097 + 0.619372i \(0.787387\pi\)
\(138\) 11.8803 + 5.44530i 1.01132 + 0.463535i
\(139\) 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
\(142\) 5.37142i 0.450759i
\(143\) 19.5508i 1.63492i
\(144\) 1.95835 + 2.27264i 0.163195 + 0.189386i
\(145\) 0 0
\(146\) 4.85479 0.401785
\(147\) 9.93812 6.94505i 0.819682 0.572818i
\(148\) 10.4620i 0.859968i
\(149\) 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 \(0.534110\pi\)
\(152\) 3.14908i 0.255424i
\(153\) −8.06399 + 6.94879i −0.651935 + 0.561776i
\(154\) 5.14768 + 8.99360i 0.414811 + 0.724725i
\(155\) 0 0
\(156\) −7.85957 3.60240i −0.629269 0.288423i
\(157\) 24.2853 1.93818 0.969091 0.246704i \(-0.0793476\pi\)
0.969091 + 0.246704i \(0.0793476\pi\)
\(158\) −0.742834 −0.0590967
\(159\) −0.453638 0.207923i −0.0359758 0.0164894i
\(160\) 0 0
\(161\) 17.3256 9.91669i 1.36545 0.781545i
\(162\) −1.32976 + 8.90122i −0.104476 + 0.699346i
\(163\) 13.4620i 1.05442i −0.849734 0.527211i \(-0.823238\pi\)
0.849734 0.527211i \(-0.176762\pi\)
\(164\) −9.32176 −0.727907
\(165\) 0 0
\(166\) 4.45557i 0.345819i
\(167\) 21.7812i 1.68548i 0.538321 + 0.842740i \(0.319059\pi\)
−0.538321 + 0.842740i \(0.680941\pi\)
\(168\) 4.56399 0.412258i 0.352120 0.0318064i
\(169\) 11.9167 0.916669
\(170\) 0 0
\(171\) 7.15671 6.16698i 0.547287 0.471601i
\(172\) 2.91669i 0.222396i
\(173\) 0.907276i 0.0689789i 0.999405 + 0.0344895i \(0.0109805\pi\)
−0.999405 + 0.0344895i \(0.989019\pi\)
\(174\) 5.44530 11.8803i 0.412807 0.900645i
\(175\) 0 0
\(176\) 3.91669i 0.295232i
\(177\) −9.28811 4.25717i −0.698137 0.319988i
\(178\) −12.3340 −0.924470
\(179\) 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 \(-0.630782\pi\)
0.399400 0.916777i \(-0.369218\pi\)
\(182\) −11.4620 + 6.56050i −0.849618 + 0.486297i
\(183\) −1.79520 + 3.91669i −0.132705 + 0.289530i
\(184\) 7.54528 0.556245
\(185\) 0 0
\(186\) −3.02618 + 6.60240i −0.221891 + 0.484111i
\(187\) −13.8976 −1.01629
\(188\) 8.00387i 0.583742i
\(189\) 9.87479 + 9.56496i 0.718285 + 0.695749i
\(190\) 0 0
\(191\) 16.0072i 1.15824i −0.815241 0.579122i \(-0.803396\pi\)
0.815241 0.579122i \(-0.196604\pi\)
\(192\) 1.57454 + 0.721683i 0.113633 + 0.0520830i
\(193\) 26.4310i 1.90255i 0.308349 + 0.951273i \(0.400224\pi\)
−0.308349 + 0.951273i \(0.599776\pi\)
\(194\) −0.524688 −0.0376704
\(195\) 0 0
\(196\) 3.54528 6.03581i 0.253234 0.431129i
\(197\) −17.2644 −1.23004 −0.615019 0.788512i \(-0.710852\pi\)
−0.615019 + 0.788512i \(0.710852\pi\)
\(198\) −8.90122 + 7.67024i −0.632582 + 0.545100i
\(199\) 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
\(202\) −8.00387 −0.563150
\(203\) −9.91669 17.3256i −0.696015 1.21602i
\(204\) −2.56075 + 5.58693i −0.179288 + 0.391163i
\(205\) 0 0
\(206\) 6.17269 0.430071
\(207\) 14.7763 + 17.1477i 1.02702 + 1.19185i
\(208\) −4.99166 −0.346110
\(209\) 12.3340 0.853158
\(210\) 0 0
\(211\) −6.88575 −0.474035 −0.237017 0.971505i \(-0.576170\pi\)
−0.237017 + 0.971505i \(0.576170\pi\)
\(212\) −0.288109 −0.0197874
\(213\) −3.87646 + 8.45750i −0.265611 + 0.579499i
\(214\) 2.65953 0.181801
\(215\) 0 0
\(216\) 1.44337 + 4.99166i 0.0982087 + 0.339640i
\(217\) 5.51112 + 9.62858i 0.374119 + 0.653631i
\(218\) −14.9239 −1.01078
\(219\) 7.64405 + 3.50362i 0.516537 + 0.236753i
\(220\) 0 0
\(221\) 17.7119i 1.19143i
\(222\) 7.55023 16.4728i 0.506738 1.10558i
\(223\) 2.90336 0.194424 0.0972118 0.995264i \(-0.469008\pi\)
0.0972118 + 0.995264i \(0.469008\pi\)
\(224\) 2.29622 1.31429i 0.153423 0.0878148i
\(225\) 0 0
\(226\) 11.8024 0.785087
\(227\) 21.6557i 1.43734i −0.695351 0.718671i \(-0.744751\pi\)
0.695351 0.718671i \(-0.255249\pi\)
\(228\) 2.27264 4.95835i 0.150509 0.328374i
\(229\) 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
\(232\) 7.54528i 0.495372i
\(233\) 5.42378 0.355324 0.177662 0.984092i \(-0.443147\pi\)
0.177662 + 0.984092i \(0.443147\pi\)
\(234\) −9.77540 11.3442i −0.639038 0.741596i
\(235\) 0 0
\(236\) −5.89894 −0.383988
\(237\) −1.16962 0.536091i −0.0759750 0.0348228i
\(238\) 4.66349 + 8.14768i 0.302289 + 0.528135i
\(239\) 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 \(0.203480\pi\)
−0.802543 + 0.596595i \(0.796520\pi\)
\(242\) −4.34047 −0.279016
\(243\) −8.51763 + 13.0557i −0.546406 + 0.837520i
\(244\) 2.48752i 0.159247i
\(245\) 0 0
\(246\) −14.6775 6.72736i −0.935802 0.428921i
\(247\) 15.7191i 1.00018i
\(248\) 4.19323i 0.266270i
\(249\) 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 \(0.262130\pi\)
\(252\) 7.48371 + 2.64464i 0.471429 + 0.166597i
\(253\) 29.5525i 1.85795i
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 31.8900i 1.98924i −0.103575 0.994622i \(-0.533028\pi\)
0.103575 0.994622i \(-0.466972\pi\)
\(258\) −2.10493 + 4.59244i −0.131047 + 0.285913i
\(259\) −13.7501 24.0230i −0.854388 1.49272i
\(260\) 0 0
\(261\) 17.1477 14.7763i 1.06141 0.914627i
\(262\) −14.6846 −0.907218
\(263\) −14.1739 −0.873998 −0.436999 0.899462i \(-0.643959\pi\)
−0.436999 + 0.899462i \(0.643959\pi\)
\(264\) −2.82661 + 6.16698i −0.173966 + 0.379552i
\(265\) 0 0
\(266\) −4.13881 7.23098i −0.253767 0.443360i
\(267\) −19.4203 8.90122i −1.18850 0.544746i
\(268\) 0.545275i 0.0333080i
\(269\) 6.68074 0.407332 0.203666 0.979040i \(-0.434714\pi\)
0.203666 + 0.979040i \(0.434714\pi\)
\(270\) 0 0
\(271\) 9.45864i 0.574571i 0.957845 + 0.287286i \(0.0927529\pi\)
−0.957845 + 0.287286i \(0.907247\pi\)
\(272\) 3.54830i 0.215147i
\(273\) −22.7819 + 2.05785i −1.37882 + 0.124547i
\(274\) −18.3787 −1.11030
\(275\) 0 0
\(276\) 11.8803 + 5.44530i 0.715112 + 0.327769i
\(277\) 11.2048i 0.673231i −0.941642 0.336616i \(-0.890718\pi\)
0.941642 0.336616i \(-0.109282\pi\)
\(278\) 12.6077i 0.756160i
\(279\) −9.52969 + 8.21179i −0.570527 + 0.491627i
\(280\) 0 0
\(281\) 2.90945i 0.173563i 0.996227 + 0.0867816i \(0.0276582\pi\)
−0.996227 + 0.0867816i \(0.972342\pi\)
\(282\) 5.77626 12.6024i 0.343971 0.750462i
\(283\) 24.4056 1.45076 0.725381 0.688348i \(-0.241664\pi\)
0.725381 + 0.688348i \(0.241664\pi\)
\(284\) 5.37142i 0.318735i
\(285\) 0 0
\(286\) 19.5508i 1.15606i
\(287\) −21.4048 + 12.2515i −1.26349 + 0.723184i
\(288\) 1.95835 + 2.27264i 0.115397 + 0.133916i
\(289\) 4.40960 0.259388
\(290\) 0 0
\(291\) −0.826142 0.378659i −0.0484293 0.0221974i
\(292\) 4.85479 0.284105
\(293\) 17.0799i 0.997819i −0.866654 0.498910i \(-0.833734\pi\)
0.866654 0.498910i \(-0.166266\pi\)
\(294\) 9.93812 6.94505i 0.579603 0.405044i
\(295\) 0 0
\(296\) 10.4620i 0.608089i
\(297\) −19.5508 + 5.65322i −1.13445 + 0.328033i
\(298\) 5.65953i 0.327847i
\(299\) −37.6635 −2.17813
\(300\) 0 0
\(301\) 3.83338 + 6.69737i 0.220953 + 0.386030i
\(302\) −2.62858 −0.151258
\(303\) −12.6024 5.77626i −0.723989 0.331837i
\(304\) 3.14908i 0.180612i
\(305\) 0 0
\(306\) −8.06399 + 6.94879i −0.460988 + 0.397236i
\(307\) 11.8093 0.673991 0.336996 0.941506i \(-0.390589\pi\)
0.336996 + 0.941506i \(0.390589\pi\)
\(308\) 5.14768 + 8.99360i 0.293316 + 0.512458i
\(309\) 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 \(0.526082\pi\)
\(312\) −7.85957 3.60240i −0.444960 0.203946i
\(313\) −4.20986 −0.237955 −0.118978 0.992897i \(-0.537962\pi\)
−0.118978 + 0.992897i \(0.537962\pi\)
\(314\) 24.2853 1.37050
\(315\) 0 0
\(316\) −0.742834 −0.0417876
\(317\) 23.2644 1.30666 0.653330 0.757074i \(-0.273372\pi\)
0.653330 + 0.757074i \(0.273372\pi\)
\(318\) −0.453638 0.207923i −0.0254388 0.0116598i
\(319\) 29.5525 1.65462
\(320\) 0 0
\(321\) 4.18753 + 1.91934i 0.233725 + 0.107127i
\(322\) 17.3256 9.91669i 0.965520 0.552636i
\(323\) 11.1739 0.621730
\(324\) −1.32976 + 8.90122i −0.0738757 + 0.494512i
\(325\) 0 0
\(326\) 13.4620i 0.745589i
\(327\) −23.4983 10.7704i −1.29946 0.595602i
\(328\) −9.32176 −0.514708
\(329\) −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 \(0.746709\pi\)
\(332\) 4.45557i 0.244531i
\(333\) 23.7763 20.4881i 1.30293 1.12274i
\(334\) 21.7812i 1.19181i
\(335\) 0 0
\(336\) 4.56399 0.412258i 0.248986 0.0224905i
\(337\) 7.68095i 0.418408i 0.977872 + 0.209204i \(0.0670873\pi\)
−0.977872 + 0.209204i \(0.932913\pi\)
\(338\) 11.9167 0.648183
\(339\) 18.5834 + 8.51763i 1.00931 + 0.462614i
\(340\) 0 0
\(341\) −16.4236 −0.889387
\(342\) 7.15671 6.16698i 0.386991 0.333472i
\(343\) 0.207923 18.5191i 0.0112268 0.999937i
\(344\) 2.91669i 0.157257i
\(345\) 0 0
\(346\) 0.907276i 0.0487755i
\(347\) 8.26441 0.443657 0.221828 0.975086i \(-0.428798\pi\)
0.221828 + 0.975086i \(0.428798\pi\)
\(348\) 5.44530 11.8803i 0.291899 0.636853i
\(349\) 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
\(352\) 3.91669i 0.208760i
\(353\) 18.8945i 1.00565i 0.864388 + 0.502826i \(0.167706\pi\)
−0.864388 + 0.502826i \(0.832294\pi\)
\(354\) −9.28811 4.25717i −0.493657 0.226266i
\(355\) 0 0
\(356\) −12.3340 −0.653699
\(357\) 1.46281 + 16.1944i 0.0774202 + 0.857098i
\(358\) 2.08331i 0.110106i
\(359\) 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
\(362\) 24.6679i 1.29652i
\(363\) −6.83425 3.13245i −0.358705 0.164411i
\(364\) −11.4620 + 6.56050i −0.600770 + 0.343864i
\(365\) 0 0
\(366\) −1.79520 + 3.91669i −0.0938366 + 0.204729i
\(367\) −16.9544 −0.885015 −0.442507 0.896765i \(-0.645911\pi\)
−0.442507 + 0.896765i \(0.645911\pi\)
\(368\) 7.54528 0.393325
\(369\) −18.2552 21.1850i −0.950330 1.10285i
\(370\) 0 0
\(371\) −0.661561 + 0.378659i −0.0343466 + 0.0196590i
\(372\) −3.02618 + 6.60240i −0.156900 + 0.342319i
\(373\) 22.8097i 1.18104i 0.807023 + 0.590520i \(0.201077\pi\)
−0.807023 + 0.590520i \(0.798923\pi\)
\(374\) −13.8976 −0.718627
\(375\) 0 0
\(376\) 8.00387i 0.412768i
\(377\) 37.6635i 1.93977i
\(378\) 9.87479 + 9.56496i 0.507904 + 0.491969i
\(379\) −0.371417 −0.0190784 −0.00953920 0.999955i \(-0.503036\pi\)
−0.00953920 + 0.999955i \(0.503036\pi\)
\(380\) 0 0
\(381\) −1.44337 + 3.14908i −0.0739459 + 0.161332i
\(382\) 16.0072i 0.819002i
\(383\) 32.8367i 1.67788i 0.544226 + 0.838939i \(0.316823\pi\)
−0.544226 + 0.838939i \(0.683177\pi\)
\(384\) 1.57454 + 0.721683i 0.0803504 + 0.0368283i
\(385\) 0 0
\(386\) 26.4310i 1.34530i
\(387\) −6.62858 + 5.71189i −0.336950 + 0.290352i
\(388\) −0.524688 −0.0266370
\(389\) 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
\(392\) 3.54528 6.03581i 0.179063 0.304855i
\(393\) −23.1215 10.5976i −1.16632 0.534580i
\(394\) −17.2644 −0.869768
\(395\) 0 0
\(396\) −8.90122 + 7.67024i −0.447303 + 0.385444i
\(397\) −7.35371 −0.369072 −0.184536 0.982826i \(-0.559078\pi\)
−0.184536 + 0.982826i \(0.559078\pi\)
\(398\) 10.8906i 0.545896i
\(399\) −1.29823 14.3724i −0.0649929 0.719519i
\(400\) 0 0
\(401\) 17.1215i 0.855007i 0.904014 + 0.427503i \(0.140607\pi\)
−0.904014 + 0.427503i \(0.859393\pi\)
\(402\) −0.393516 + 0.858557i −0.0196268 + 0.0428209i
\(403\) 20.9312i 1.04266i
\(404\) −8.00387 −0.398207
\(405\) 0 0
\(406\) −9.91669 17.3256i −0.492157 0.859857i
\(407\) 40.9763 2.03112
\(408\) −2.56075 + 5.58693i −0.126776 + 0.276594i
\(409\) 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
\(412\) 6.17269 0.304106
\(413\) −13.5453 + 7.75293i −0.666519 + 0.381497i
\(414\) 14.7763 + 17.1477i 0.726213 + 0.842762i
\(415\) 0 0
\(416\) −4.99166 −0.244736
\(417\) 9.09878 19.8513i 0.445569 0.972124i
\(418\) 12.3340 0.603274
\(419\) 11.5522 0.564360 0.282180 0.959361i \(-0.408942\pi\)
0.282180 + 0.959361i \(0.408942\pi\)
\(420\) 0 0
\(421\) 36.9239 1.79956 0.899781 0.436341i \(-0.143726\pi\)
0.899781 + 0.436341i \(0.143726\pi\)
\(422\) −6.88575 −0.335193
\(423\) 18.1899 15.6743i 0.884423 0.762112i
\(424\) −0.288109 −0.0139918
\(425\) 0 0
\(426\) −3.87646 + 8.45750i −0.187815 + 0.409767i
\(427\) 3.26932 + 5.71189i 0.158214 + 0.276418i
\(428\) 2.65953 0.128553
\(429\) 14.1095 30.7835i 0.681213 1.48624i
\(430\) 0 0
\(431\) 5.03094i 0.242332i −0.992632 0.121166i \(-0.961337\pi\)
0.992632 0.121166i \(-0.0386633\pi\)
\(432\) 1.44337 + 4.99166i 0.0694440 + 0.240161i
\(433\) −3.04024 −0.146104 −0.0730522 0.997328i \(-0.523274\pi\)
−0.0730522 + 0.997328i \(0.523274\pi\)
\(434\) 5.51112 + 9.62858i 0.264542 + 0.462187i
\(435\) 0 0
\(436\) −14.9239 −0.714727
\(437\) 23.7607i 1.13663i
\(438\) 7.64405 + 3.50362i 0.365247 + 0.167409i
\(439\) 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
\(442\) 17.7119i 0.842469i
\(443\) −10.5976 −0.503509 −0.251755 0.967791i \(-0.581008\pi\)
−0.251755 + 0.967791i \(0.581008\pi\)
\(444\) 7.55023 16.4728i 0.358318 0.781763i
\(445\) 0 0
\(446\) 2.90336 0.137478
\(447\) −4.08439 + 8.91114i −0.193185 + 0.421483i
\(448\) 2.29622 1.31429i 0.108486 0.0620944i
\(449\) 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
\(452\) 11.8024 0.555140
\(453\) −4.13881 1.89701i −0.194458 0.0891291i
\(454\) 21.6557i 1.01635i
\(455\) 0 0
\(456\) 2.27264 4.95835i 0.106426 0.232196i
\(457\) 19.7573i 0.924208i 0.886826 + 0.462104i \(0.152905\pi\)
−0.886826 + 0.462104i \(0.847095\pi\)
\(458\) 16.9378i 0.791452i
\(459\) −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 \(0.284532\pi\)
\(462\) 1.61469 + 17.8758i 0.0751220 + 0.831656i
\(463\) 38.7573i 1.80121i −0.434643 0.900603i \(-0.643126\pi\)
0.434643 0.900603i \(-0.356874\pi\)
\(464\) 7.54528i 0.350281i
\(465\) 0 0
\(466\) 5.42378 0.251252
\(467\) 18.5181i 0.856913i 0.903562 + 0.428457i \(0.140943\pi\)
−0.903562 + 0.428457i \(0.859057\pi\)
\(468\) −9.77540 11.3442i −0.451868 0.524388i
\(469\) 0.716650 + 1.25207i 0.0330918 + 0.0578154i
\(470\) 0 0
\(471\) 38.2382 + 17.5263i 1.76192 + 0.807571i
\(472\) −5.89894 −0.271521
\(473\) −11.4238 −0.525266
\(474\) −1.16962 0.536091i −0.0537224 0.0246235i
\(475\) 0 0
\(476\) 4.66349 + 8.14768i 0.213751 + 0.373448i
\(477\) −0.564216 0.654766i −0.0258337 0.0299797i
\(478\) 13.2572i 0.606369i
\(479\) 14.4337 0.659491 0.329746 0.944070i \(-0.393037\pi\)
0.329746 + 0.944070i \(0.393037\pi\)
\(480\) 0 0
\(481\) 52.2226i 2.38115i
\(482\) 18.5233i 0.843712i
\(483\) 34.4366 3.11060i 1.56692 0.141537i
\(484\) −4.34047 −0.197294
\(485\) 0 0
\(486\) −8.51763 + 13.0557i −0.386367 + 0.592216i
\(487\) 26.2430i 1.18918i 0.804028 + 0.594592i \(0.202686\pi\)
−0.804028 + 0.594592i \(0.797314\pi\)
\(488\) 2.48752i 0.112605i
\(489\) 9.71528 21.1964i 0.439340 0.958534i
\(490\) 0 0
\(491\) 30.0000i 1.35388i 0.736038 + 0.676941i \(0.236695\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(492\) −14.6775 6.72736i −0.661712 0.303293i
\(493\) 26.7729 1.20579
\(494\) 15.7191i 0.707237i
\(495\) 0 0
\(496\) 4.19323i 0.188281i
\(497\) 7.05961 + 12.3340i 0.316667 + 0.553254i
\(498\) 3.21551 7.01547i 0.144091 0.314371i
\(499\) −41.6740 −1.86558 −0.932792 0.360414i \(-0.882635\pi\)
−0.932792 + 0.360414i \(0.882635\pi\)
\(500\) 0 0
\(501\) −15.7191 + 34.2954i −0.702279 + 1.53220i
\(502\) 21.5355 0.961176
\(503\) 0.415846i 0.0185417i 0.999957 + 0.00927084i \(0.00295104\pi\)
−0.999957 + 0.00927084i \(0.997049\pi\)
\(504\) 7.48371 + 2.64464i 0.333351 + 0.117802i
\(505\) 0 0
\(506\) 29.5525i 1.31377i
\(507\) 18.7633 + 8.60008i 0.833307 + 0.381943i
\(508\) 2.00000i 0.0887357i
\(509\) 11.3064 0.501149 0.250575 0.968097i \(-0.419380\pi\)
0.250575 + 0.968097i \(0.419380\pi\)
\(510\) 0 0
\(511\) 11.1477 6.38061i 0.493144 0.282261i
\(512\) 1.00000 0.0441942
\(513\) 15.7191 4.54528i 0.694017 0.200679i
\(514\) 31.8900i 1.40661i
\(515\) 0 0
\(516\) −2.10493 + 4.59244i −0.0926643 + 0.202171i
\(517\) 31.3487 1.37871
\(518\) −13.7501 24.0230i −0.604144 1.05551i
\(519\) −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 \(0.482726\pi\)
\(522\) 17.1477 14.7763i 0.750533 0.646739i
\(523\) −12.0602 −0.527357 −0.263678 0.964611i \(-0.584936\pi\)
−0.263678 + 0.964611i \(0.584936\pi\)
\(524\) −14.6846 −0.641500
\(525\) 0 0
\(526\) −14.1739 −0.618010
\(527\) −14.8788 −0.648131
\(528\) −2.82661 + 6.16698i −0.123012 + 0.268384i
\(529\) 33.9312 1.47527
\(530\) 0 0
\(531\) −11.5522 13.4061i −0.501321 0.581777i
\(532\) −4.13881 7.23098i −0.179440 0.313503i
\(533\) 46.5311 2.01549
\(534\) −19.4203 8.90122i −0.840399 0.385193i
\(535\) 0 0
\(536\) 0.545275i 0.0235523i
\(537\) −1.50349 + 3.28025i −0.0648803 + 0.141553i
\(538\) 6.68074 0.288027
\(539\) 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 \(0.464737\pi\)
\(542\) 9.45864i 0.406283i
\(543\) 17.8024 38.8406i 0.763976 1.66681i
\(544\) 3.54830i 0.152132i
\(545\) 0 0
\(546\) −22.7819 + 2.05785i −0.974976 + 0.0880679i
\(547\) 3.11425i 0.133156i 0.997781 + 0.0665779i \(0.0212081\pi\)
−0.997781 + 0.0665779i \(0.978792\pi\)
\(548\) −18.3787 −0.785097
\(549\) −5.65322 + 4.87142i −0.241274 + 0.207907i
\(550\) 0 0
\(551\) −23.7607 −1.01224
\(552\) 11.8803 + 5.44530i 0.505660 + 0.231767i
\(553\) −1.70571 + 0.976300i −0.0725342 + 0.0415165i
\(554\) 11.2048i 0.476046i
\(555\) 0 0
\(556\) 12.6077i 0.534686i
\(557\) −1.93812 −0.0821206 −0.0410603 0.999157i \(-0.513074\pi\)
−0.0410603 + 0.999157i \(0.513074\pi\)
\(558\) −9.52969 + 8.21179i −0.403424 + 0.347633i
\(559\) 14.5591i 0.615786i
\(560\) 0 0
\(561\) −21.8823 10.0297i −0.923871 0.423452i
\(562\) 2.90945i 0.122728i
\(563\) 25.8656i 1.09010i 0.838402 + 0.545052i \(0.183490\pi\)
−0.838402 + 0.545052i \(0.816510\pi\)
\(564\) 5.77626 12.6024i 0.243224 0.530657i
\(565\) 0 0
\(566\) 24.4056 1.02584
\(567\) 8.64537 + 22.1869i 0.363071 + 0.931761i
\(568\) 5.37142i 0.225380i
\(569\) 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 \(0.469522\pi\)
\(572\) 19.5508i 0.817460i
\(573\) 11.5522 25.2040i 0.482598 1.05291i
\(574\) −21.4048 + 12.2515i −0.893421 + 0.511368i
\(575\) 0 0
\(576\) 1.95835 + 2.27264i 0.0815977 + 0.0946932i
\(577\) 23.7493 0.988694 0.494347 0.869265i \(-0.335407\pi\)
0.494347 + 0.869265i \(0.335407\pi\)
\(578\) 4.40960 0.183415
\(579\) −19.0748 + 41.6167i −0.792723 + 1.72953i
\(580\) 0 0
\(581\) −5.85592 10.2310i −0.242945 0.424453i
\(582\) −0.826142 0.378659i −0.0342447 0.0156959i
\(583\) 1.12843i 0.0467349i
\(584\) 4.85479 0.200893
\(585\) 0 0
\(586\) 17.0799i 0.705565i
\(587\) 28.8726i 1.19170i −0.803096 0.595849i \(-0.796816\pi\)
0.803096 0.595849i \(-0.203184\pi\)
\(588\) 9.93812 6.94505i 0.409841 0.286409i
\(589\) 13.2048 0.544094
\(590\) 0 0
\(591\) −27.1835 12.4594i −1.11818 0.512513i
\(592\) 10.4620i 0.429984i
\(593\) 4.74595i 0.194893i −0.995241 0.0974463i \(-0.968933\pi\)
0.995241 0.0974463i \(-0.0310674\pi\)
\(594\) −19.5508 + 5.65322i −0.802179 + 0.231955i
\(595\) 0 0
\(596\) 5.65953i 0.231823i
\(597\) −7.85957 + 17.1477i −0.321671 + 0.701808i
\(598\) −37.6635 −1.54017
\(599\) 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 \(0.00759397\pi\)
−0.999715 + 0.0238549i \(0.992406\pi\)
\(602\) 3.83338 + 6.69737i 0.156237 + 0.272965i
\(603\) −1.23921 + 1.06784i −0.0504646 + 0.0434857i
\(604\) −2.62858 −0.106956
\(605\) 0 0
\(606\) −12.6024 5.77626i −0.511938 0.234644i
\(607\) −42.5463 −1.72690 −0.863450 0.504434i \(-0.831701\pi\)
−0.863450 + 0.504434i \(0.831701\pi\)
\(608\) 3.14908i 0.127712i
\(609\) −3.11060 34.4366i −0.126048 1.39544i
\(610\) 0 0
\(611\) 39.9526i 1.61631i
\(612\) −8.06399 + 6.94879i −0.325967 + 0.280888i
\(613\) 11.1524i 0.450443i 0.974308 + 0.225221i \(0.0723105\pi\)
−0.974308 + 0.225221i \(0.927689\pi\)
\(614\) 11.8093 0.476584
\(615\) 0 0
\(616\) 5.14768 + 8.99360i 0.207406 + 0.362362i
\(617\) 42.1811 1.69815 0.849074 0.528275i \(-0.177161\pi\)
0.849074 + 0.528275i \(0.177161\pi\)
\(618\) 9.71913 + 4.45472i 0.390961 + 0.179195i
\(619\) 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
\(622\) −2.88673 −0.115747
\(623\) −28.3215 + 16.2104i −1.13468 + 0.649457i
\(624\) −7.85957 3.60240i −0.314634 0.144211i
\(625\) 0 0
\(626\) −4.20986 −0.168260
\(627\) 19.4203 + 8.90122i 0.775573 + 0.355481i
\(628\) 24.2853 0.969091
\(629\) 37.1221 1.48016
\(630\) 0 0
\(631\) 4.46197 0.177628 0.0888140 0.996048i \(-0.471692\pi\)
0.0888140 + 0.996048i \(0.471692\pi\)
\(632\) −0.742834 −0.0295483
\(633\) −10.8419 4.96933i −0.430926 0.197513i
\(634\) 23.2644 0.923948
\(635\) 0 0
\(636\) −0.453638 0.207923i −0.0179879 0.00824469i
\(637\) −17.6968 + 30.1287i −0.701173 + 1.19374i
\(638\) 29.5525 1.17000
\(639\) −12.2073 + 10.5191i −0.482913 + 0.416129i
\(640\) 0 0
\(641\) 2.90945i 0.114916i −0.998348 0.0574582i \(-0.981700\pi\)
0.998348 0.0574582i \(-0.0182996\pi\)
\(642\) 4.18753 + 1.91934i 0.165268 + 0.0757501i
\(643\) 31.7645 1.25267 0.626335 0.779554i \(-0.284554\pi\)
0.626335 + 0.779554i \(0.284554\pi\)
\(644\) 17.3256 9.91669i 0.682725 0.390772i
\(645\) 0 0
\(646\) 11.1739 0.439630
\(647\) 23.3448i 0.917779i 0.888493 + 0.458890i \(0.151753\pi\)
−0.888493 + 0.458890i \(0.848247\pi\)
\(648\) −1.32976 + 8.90122i −0.0522380 + 0.349673i
\(649\) 23.1043i 0.906924i
\(650\) 0 0
\(651\) 1.72869 + 19.1379i 0.0677527 + 0.750072i
\(652\) 13.4620i 0.527211i
\(653\) 2.28087 0.0892572 0.0446286 0.999004i \(-0.485790\pi\)
0.0446286 + 0.999004i \(0.485790\pi\)
\(654\) −23.4983 10.7704i −0.918857 0.421154i
\(655\) 0 0
\(656\) −9.32176 −0.363954
\(657\) 9.50736 + 11.0332i 0.370917 + 0.430445i
\(658\) −10.5194 18.3787i −0.410089 0.716475i
\(659\) 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 \(0.0269077\pi\)
−0.996429 + 0.0844325i \(0.973092\pi\)
\(662\) −25.4620 −0.989607
\(663\) 12.7824 27.8881i 0.496426 1.08308i
\(664\) 4.45557i 0.172910i
\(665\) 0 0
\(666\) 23.7763 20.4881i 0.921311 0.793900i
\(667\) 56.9312i 2.20438i
\(668\) 21.7812i 0.842740i
\(669\) 4.57146 + 2.09531i 0.176743 + 0.0810093i
\(670\) 0 0
\(671\) −9.74284 −0.376118
\(672\) 4.56399 0.412258i 0.176060 0.0159032i
\(673\) 2.00724i 0.0773735i −0.999251 0.0386867i \(-0.987683\pi\)
0.999251 0.0386867i \(-0.0123174\pi\)
\(674\) 7.68095i 0.295859i
\(675\) 0 0
\(676\) 11.9167 0.458334
\(677\) 27.5547i 1.05901i −0.848306 0.529506i \(-0.822377\pi\)
0.848306 0.529506i \(-0.177623\pi\)
\(678\) 18.5834 + 8.51763i 0.713691 + 0.327117i
\(679\) −1.20480 + 0.689593i −0.0462360 + 0.0264642i
\(680\) 0 0
\(681\) 15.6286 34.0978i 0.598889 1.30663i
\(682\) −16.4236 −0.628891
\(683\) 5.75008 0.220021 0.110010 0.993930i \(-0.464912\pi\)
0.110010 + 0.993930i \(0.464912\pi\)
\(684\) 7.15671 6.16698i 0.273644 0.235801i
\(685\) 0 0
\(686\) 0.207923 18.5191i 0.00793854 0.707062i
\(687\) −12.2237 + 26.6693i −0.466365 + 1.01750i
\(688\) 2.91669i 0.111198i
\(689\) 1.43814 0.0547888
\(690\) 0 0
\(691\) 23.6404i 0.899324i −0.893199 0.449662i \(-0.851544\pi\)
0.893199 0.449662i \(-0.148456\pi\)
\(692\) 0.907276i 0.0344895i
\(693\) −10.3583 + 29.3114i −0.393478 + 1.11345i
\(694\) 8.26441 0.313713
\(695\) 0 0
\(696\) 5.44530 11.8803i 0.206404 0.450323i
\(697\) 33.0764i 1.25286i
\(698\) 24.6846i 0.934325i
\(699\) 8.53996 + 3.91425i 0.323011 + 0.148051i
\(700\) 0 0
\(701\) 46.6882i 1.76339i 0.471821 + 0.881694i \(0.343597\pi\)
−0.471821 + 0.881694i \(0.656403\pi\)
\(702\) −7.20480 24.9167i −0.271928 0.940420i
\(703\) −32.9455 −1.24256
\(704\) 3.91669i 0.147616i
\(705\) 0 0
\(706\) 18.8945i 0.711103i
\(707\) −18.3787 + 10.5194i −0.691201 + 0.395623i
\(708\) −9.28811 4.25717i −0.349068 0.159994i
\(709\) −17.8334 −0.669747 −0.334873 0.942263i \(-0.608694\pi\)
−0.334873 + 0.942263i \(0.608694\pi\)
\(710\) 0 0
\(711\) −1.45472 1.68819i −0.0545564 0.0633121i
\(712\) −12.3340 −0.462235
\(713\) 31.6391i 1.18489i
\(714\) 1.46281 + 16.1944i 0.0547443 + 0.606060i
\(715\) 0 0
\(716\) 2.08331i 0.0778569i
\(717\) 9.56748 20.8739i 0.357304 0.779551i
\(718\) 1.49291i 0.0557149i
\(719\) 18.4786 0.689136 0.344568 0.938761i \(-0.388025\pi\)
0.344568 + 0.938761i \(0.388025\pi\)
\(720\) 0 0
\(721\) 14.1739 8.11271i 0.527862 0.302133i
\(722\) 9.08331 0.338046
\(723\) −13.3679 + 29.1656i −0.497159 + 1.08468i
\(724\) 24.6679i 0.916777i
\(725\) 0 0
\(726\) −6.83425 3.13245i −0.253643 0.116256i
\(727\) 8.92777 0.331113 0.165556 0.986200i \(-0.447058\pi\)
0.165556 + 0.986200i \(0.447058\pi\)
\(728\) −11.4620 + 6.56050i −0.424809 + 0.243148i
\(729\) −22.8334 + 14.4096i −0.845681 + 0.533689i
\(730\) 0 0
\(731\) −10.3493 −0.382782
\(732\) −1.79520 + 3.91669i −0.0663525 + 0.144765i
\(733\) 24.7934 0.915765 0.457883 0.889013i \(-0.348608\pi\)
0.457883 + 0.889013i \(0.348608\pi\)
\(734\) −16.9544 −0.625800
\(735\) 0 0
\(736\) 7.54528 0.278123
\(737\) −2.13567 −0.0786686
\(738\) −18.2552 21.1850i −0.671985 0.779830i
\(739\) −5.32629 −0.195931 −0.0979654 0.995190i \(-0.531233\pi\)
−0.0979654 + 0.995190i \(0.531233\pi\)
\(740\) 0 0
\(741\) −11.3442 + 24.7504i −0.416741 + 0.909228i
\(742\) −0.661561 + 0.378659i −0.0242867 + 0.0139010i
\(743\) −45.7409 −1.67807 −0.839035 0.544078i \(-0.816880\pi\)
−0.839035 + 0.544078i \(0.816880\pi\)
\(744\) −3.02618 + 6.60240i −0.110945 + 0.242056i
\(745\) 0 0
\(746\) 22.8097i 0.835122i
\(747\) 10.1259 8.72555i 0.370487 0.319251i
\(748\) −13.8976 −0.508146
\(749\) 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 \(0.630751\pi\)
\(752\) 8.00387i 0.291871i
\(753\) 33.9085 + 15.5418i 1.23569 + 0.566375i
\(754\) 37.6635i 1.37162i
\(755\) 0 0
\(756\) 9.87479 + 9.56496i 0.359143 + 0.347874i
\(757\) 14.0524i 0.510742i −0.966843 0.255371i \(-0.917802\pi\)
0.966843 0.255371i \(-0.0821976\pi\)
\(758\) −0.371417 −0.0134905
\(759\) −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 \(0.144018\pi\)
\(762\) −1.44337 + 3.14908i −0.0522877 + 0.114079i
\(763\) −34.2687 + 19.6144i −1.24061 + 0.710089i
\(764\) 16.0072i 0.579122i
\(765\) 0 0
\(766\) 32.8367i 1.18644i
\(767\) 29.4455 1.06322
\(768\) 1.57454 + 0.721683i 0.0568163 + 0.0260415i
\(769\) 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
\(772\) 26.4310i 0.951273i
\(773\) 29.9500i 1.07723i −0.842553 0.538613i \(-0.818949\pi\)
0.842553 0.538613i \(-0.181051\pi\)
\(774\) −6.62858 + 5.71189i −0.238260 + 0.205310i
\(775\) 0 0
\(776\) −0.524688 −0.0188352
\(777\) −4.31302 47.7484i −0.154729 1.71296i
\(778\) 24.1287i 0.865057i
\(779\) 29.3550i 1.05175i
\(780\) 0 0
\(781\) −21.0382 −0.752805
\(782\) 26.7729i 0.957396i
\(783\) 37.6635 10.8906i 1.34598 0.389198i
\(784\) 3.54528 6.03581i 0.126617 0.215565i
\(785\) 0 0
\(786\) −23.1215 10.5976i −0.824716 0.378005i
\(787\) −1.01612 −0.0362207 −0.0181103 0.999836i \(-0.505765\pi\)
−0.0181103 + 0.999836i \(0.505765\pi\)
\(788\) −17.2644 −0.615019
\(789\) −22.3173 10.2290i −0.794517 0.364163i
\(790\) 0