Properties

Label 405.2.e.i.136.2
Level $405$
Weight $2$
Character 405.136
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.2.e.i.271.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 - 0.633975i) q^{2} +(0.732051 + 1.26795i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.36603 - 4.09808i) q^{7} +2.53590 q^{8} +O(q^{10})\) \(q+(0.366025 - 0.633975i) q^{2} +(0.732051 + 1.26795i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.36603 - 4.09808i) q^{7} +2.53590 q^{8} +0.732051 q^{10} +(-2.86603 + 4.96410i) q^{11} +(-0.732051 - 1.26795i) q^{13} +(-1.73205 - 3.00000i) q^{14} +(-0.535898 + 0.928203i) q^{16} +2.73205 q^{17} +4.46410 q^{19} +(-0.732051 + 1.26795i) q^{20} +(2.09808 + 3.63397i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.07180 q^{26} +6.92820 q^{28} +(1.59808 - 2.76795i) q^{29} +(1.50000 + 2.59808i) q^{31} +(2.92820 + 5.07180i) q^{32} +(1.00000 - 1.73205i) q^{34} +4.73205 q^{35} -2.73205 q^{37} +(1.63397 - 2.83013i) q^{38} +(1.26795 + 2.19615i) q^{40} +(-3.59808 - 6.23205i) q^{41} +(-0.0980762 + 0.169873i) q^{43} -8.39230 q^{44} -2.53590 q^{46} +(-4.36603 + 7.56218i) q^{47} +(-7.69615 - 13.3301i) q^{49} +(0.366025 + 0.633975i) q^{50} +(1.07180 - 1.85641i) q^{52} -6.73205 q^{53} -5.73205 q^{55} +(6.00000 - 10.3923i) q^{56} +(-1.16987 - 2.02628i) q^{58} +(-4.13397 - 7.16025i) q^{59} +(-2.00000 + 3.46410i) q^{61} +2.19615 q^{62} +2.14359 q^{64} +(0.732051 - 1.26795i) q^{65} +(-1.73205 - 3.00000i) q^{67} +(2.00000 + 3.46410i) q^{68} +(1.73205 - 3.00000i) q^{70} +3.73205 q^{71} -7.66025 q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.26795 + 5.66025i) q^{76} +(13.5622 + 23.4904i) q^{77} +(-7.73205 + 13.3923i) q^{79} -1.07180 q^{80} -5.26795 q^{82} +(1.09808 - 1.90192i) q^{83} +(1.36603 + 2.36603i) q^{85} +(0.0717968 + 0.124356i) q^{86} +(-7.26795 + 12.5885i) q^{88} -5.19615 q^{89} -6.92820 q^{91} +(2.53590 - 4.39230i) q^{92} +(3.19615 + 5.53590i) q^{94} +(2.23205 + 3.86603i) q^{95} +(4.83013 - 8.36603i) q^{97} -11.2679 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 6 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 6 q^{7} + 24 q^{8} - 4 q^{10} - 8 q^{11} + 4 q^{13} - 16 q^{16} + 4 q^{17} + 4 q^{19} + 4 q^{20} - 2 q^{22} - 2 q^{25} - 32 q^{26} - 4 q^{29} + 6 q^{31} - 16 q^{32} + 4 q^{34} + 12 q^{35} - 4 q^{37} + 10 q^{38} + 12 q^{40} - 4 q^{41} + 10 q^{43} + 8 q^{44} - 24 q^{46} - 14 q^{47} - 10 q^{49} - 2 q^{50} + 32 q^{52} - 20 q^{53} - 16 q^{55} + 24 q^{56} - 22 q^{58} - 20 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} - 4 q^{65} + 8 q^{68} + 8 q^{71} + 4 q^{73} - 4 q^{74} + 20 q^{76} + 30 q^{77} - 24 q^{79} - 32 q^{80} - 28 q^{82} - 6 q^{83} + 2 q^{85} + 28 q^{86} - 36 q^{88} + 24 q^{92} - 8 q^{94} + 2 q^{95} + 2 q^{97} - 52 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 0.633975i 0.258819 0.448288i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) 0 0
\(4\) 0.732051 + 1.26795i 0.366025 + 0.633975i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.36603 4.09808i 0.894274 1.54893i 0.0595724 0.998224i \(-0.481026\pi\)
0.834701 0.550703i \(-0.185640\pi\)
\(8\) 2.53590 0.896575
\(9\) 0 0
\(10\) 0.732051 0.231495
\(11\) −2.86603 + 4.96410i −0.864139 + 1.49673i 0.00376022 + 0.999993i \(0.498803\pi\)
−0.867899 + 0.496740i \(0.834530\pi\)
\(12\) 0 0
\(13\) −0.732051 1.26795i −0.203034 0.351666i 0.746470 0.665419i \(-0.231747\pi\)
−0.949505 + 0.313753i \(0.898414\pi\)
\(14\) −1.73205 3.00000i −0.462910 0.801784i
\(15\) 0 0
\(16\) −0.535898 + 0.928203i −0.133975 + 0.232051i
\(17\) 2.73205 0.662620 0.331310 0.943522i \(-0.392509\pi\)
0.331310 + 0.943522i \(0.392509\pi\)
\(18\) 0 0
\(19\) 4.46410 1.02414 0.512068 0.858945i \(-0.328880\pi\)
0.512068 + 0.858945i \(0.328880\pi\)
\(20\) −0.732051 + 1.26795i −0.163692 + 0.283522i
\(21\) 0 0
\(22\) 2.09808 + 3.63397i 0.447311 + 0.774766i
\(23\) −1.73205 3.00000i −0.361158 0.625543i 0.626994 0.779024i \(-0.284285\pi\)
−0.988152 + 0.153481i \(0.950952\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.07180 −0.210197
\(27\) 0 0
\(28\) 6.92820 1.30931
\(29\) 1.59808 2.76795i 0.296755 0.513995i −0.678636 0.734474i \(-0.737429\pi\)
0.975392 + 0.220479i \(0.0707621\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 2.92820 + 5.07180i 0.517638 + 0.896575i
\(33\) 0 0
\(34\) 1.00000 1.73205i 0.171499 0.297044i
\(35\) 4.73205 0.799863
\(36\) 0 0
\(37\) −2.73205 −0.449146 −0.224573 0.974457i \(-0.572099\pi\)
−0.224573 + 0.974457i \(0.572099\pi\)
\(38\) 1.63397 2.83013i 0.265066 0.459107i
\(39\) 0 0
\(40\) 1.26795 + 2.19615i 0.200480 + 0.347242i
\(41\) −3.59808 6.23205i −0.561925 0.973283i −0.997328 0.0730473i \(-0.976728\pi\)
0.435403 0.900235i \(-0.356606\pi\)
\(42\) 0 0
\(43\) −0.0980762 + 0.169873i −0.0149565 + 0.0259054i −0.873407 0.486991i \(-0.838094\pi\)
0.858450 + 0.512897i \(0.171428\pi\)
\(44\) −8.39230 −1.26519
\(45\) 0 0
\(46\) −2.53590 −0.373898
\(47\) −4.36603 + 7.56218i −0.636850 + 1.10306i 0.349270 + 0.937022i \(0.386430\pi\)
−0.986120 + 0.166035i \(0.946904\pi\)
\(48\) 0 0
\(49\) −7.69615 13.3301i −1.09945 1.90430i
\(50\) 0.366025 + 0.633975i 0.0517638 + 0.0896575i
\(51\) 0 0
\(52\) 1.07180 1.85641i 0.148631 0.257437i
\(53\) −6.73205 −0.924718 −0.462359 0.886693i \(-0.652997\pi\)
−0.462359 + 0.886693i \(0.652997\pi\)
\(54\) 0 0
\(55\) −5.73205 −0.772910
\(56\) 6.00000 10.3923i 0.801784 1.38873i
\(57\) 0 0
\(58\) −1.16987 2.02628i −0.153612 0.266064i
\(59\) −4.13397 7.16025i −0.538198 0.932186i −0.999001 0.0446835i \(-0.985772\pi\)
0.460804 0.887502i \(-0.347561\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 2.19615 0.278912
\(63\) 0 0
\(64\) 2.14359 0.267949
\(65\) 0.732051 1.26795i 0.0907997 0.157270i
\(66\) 0 0
\(67\) −1.73205 3.00000i −0.211604 0.366508i 0.740613 0.671932i \(-0.234535\pi\)
−0.952217 + 0.305424i \(0.901202\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 0 0
\(70\) 1.73205 3.00000i 0.207020 0.358569i
\(71\) 3.73205 0.442913 0.221456 0.975170i \(-0.428919\pi\)
0.221456 + 0.975170i \(0.428919\pi\)
\(72\) 0 0
\(73\) −7.66025 −0.896565 −0.448282 0.893892i \(-0.647964\pi\)
−0.448282 + 0.893892i \(0.647964\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0 0
\(76\) 3.26795 + 5.66025i 0.374859 + 0.649276i
\(77\) 13.5622 + 23.4904i 1.54555 + 2.67698i
\(78\) 0 0
\(79\) −7.73205 + 13.3923i −0.869924 + 1.50675i −0.00784992 + 0.999969i \(0.502499\pi\)
−0.862074 + 0.506783i \(0.830835\pi\)
\(80\) −1.07180 −0.119831
\(81\) 0 0
\(82\) −5.26795 −0.581748
\(83\) 1.09808 1.90192i 0.120530 0.208763i −0.799447 0.600737i \(-0.794874\pi\)
0.919977 + 0.391973i \(0.128207\pi\)
\(84\) 0 0
\(85\) 1.36603 + 2.36603i 0.148166 + 0.256631i
\(86\) 0.0717968 + 0.124356i 0.00774204 + 0.0134096i
\(87\) 0 0
\(88\) −7.26795 + 12.5885i −0.774766 + 1.34193i
\(89\) −5.19615 −0.550791 −0.275396 0.961331i \(-0.588809\pi\)
−0.275396 + 0.961331i \(0.588809\pi\)
\(90\) 0 0
\(91\) −6.92820 −0.726273
\(92\) 2.53590 4.39230i 0.264386 0.457929i
\(93\) 0 0
\(94\) 3.19615 + 5.53590i 0.329658 + 0.570984i
\(95\) 2.23205 + 3.86603i 0.229004 + 0.396646i
\(96\) 0 0
\(97\) 4.83013 8.36603i 0.490425 0.849441i −0.509514 0.860462i \(-0.670175\pi\)
0.999939 + 0.0110211i \(0.00350819\pi\)
\(98\) −11.2679 −1.13823
\(99\) 0 0
\(100\) −1.46410 −0.146410
\(101\) −1.33013 + 2.30385i −0.132353 + 0.229241i −0.924583 0.380981i \(-0.875586\pi\)
0.792230 + 0.610222i \(0.208920\pi\)
\(102\) 0 0
\(103\) 0.267949 + 0.464102i 0.0264018 + 0.0457293i 0.878924 0.476961i \(-0.158262\pi\)
−0.852523 + 0.522690i \(0.824928\pi\)
\(104\) −1.85641 3.21539i −0.182036 0.315295i
\(105\) 0 0
\(106\) −2.46410 + 4.26795i −0.239335 + 0.414540i
\(107\) 8.53590 0.825196 0.412598 0.910913i \(-0.364621\pi\)
0.412598 + 0.910913i \(0.364621\pi\)
\(108\) 0 0
\(109\) −6.07180 −0.581573 −0.290786 0.956788i \(-0.593917\pi\)
−0.290786 + 0.956788i \(0.593917\pi\)
\(110\) −2.09808 + 3.63397i −0.200044 + 0.346486i
\(111\) 0 0
\(112\) 2.53590 + 4.39230i 0.239620 + 0.415034i
\(113\) −9.56218 16.5622i −0.899534 1.55804i −0.828091 0.560594i \(-0.810573\pi\)
−0.0714432 0.997445i \(-0.522760\pi\)
\(114\) 0 0
\(115\) 1.73205 3.00000i 0.161515 0.279751i
\(116\) 4.67949 0.434480
\(117\) 0 0
\(118\) −6.05256 −0.557183
\(119\) 6.46410 11.1962i 0.592563 1.02635i
\(120\) 0 0
\(121\) −10.9282 18.9282i −0.993473 1.72075i
\(122\) 1.46410 + 2.53590i 0.132554 + 0.229589i
\(123\) 0 0
\(124\) −2.19615 + 3.80385i −0.197220 + 0.341596i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −14.5885 −1.29452 −0.647258 0.762271i \(-0.724084\pi\)
−0.647258 + 0.762271i \(0.724084\pi\)
\(128\) −5.07180 + 8.78461i −0.448288 + 0.776457i
\(129\) 0 0
\(130\) −0.535898 0.928203i −0.0470014 0.0814088i
\(131\) 7.79423 + 13.5000i 0.680985 + 1.17950i 0.974681 + 0.223602i \(0.0717814\pi\)
−0.293696 + 0.955899i \(0.594885\pi\)
\(132\) 0 0
\(133\) 10.5622 18.2942i 0.915857 1.58631i
\(134\) −2.53590 −0.219068
\(135\) 0 0
\(136\) 6.92820 0.594089
\(137\) 1.26795 2.19615i 0.108328 0.187630i −0.806765 0.590873i \(-0.798784\pi\)
0.915093 + 0.403243i \(0.132117\pi\)
\(138\) 0 0
\(139\) −0.303848 0.526279i −0.0257720 0.0446384i 0.852852 0.522153i \(-0.174871\pi\)
−0.878624 + 0.477515i \(0.841538\pi\)
\(140\) 3.46410 + 6.00000i 0.292770 + 0.507093i
\(141\) 0 0
\(142\) 1.36603 2.36603i 0.114634 0.198552i
\(143\) 8.39230 0.701800
\(144\) 0 0
\(145\) 3.19615 0.265426
\(146\) −2.80385 + 4.85641i −0.232048 + 0.401919i
\(147\) 0 0
\(148\) −2.00000 3.46410i −0.164399 0.284747i
\(149\) −4.00000 6.92820i −0.327693 0.567581i 0.654361 0.756182i \(-0.272938\pi\)
−0.982054 + 0.188602i \(0.939604\pi\)
\(150\) 0 0
\(151\) −2.69615 + 4.66987i −0.219410 + 0.380029i −0.954628 0.297802i \(-0.903746\pi\)
0.735218 + 0.677831i \(0.237080\pi\)
\(152\) 11.3205 0.918214
\(153\) 0 0
\(154\) 19.8564 1.60007
\(155\) −1.50000 + 2.59808i −0.120483 + 0.208683i
\(156\) 0 0
\(157\) 9.56218 + 16.5622i 0.763145 + 1.32181i 0.941222 + 0.337789i \(0.109679\pi\)
−0.178077 + 0.984017i \(0.556988\pi\)
\(158\) 5.66025 + 9.80385i 0.450306 + 0.779952i
\(159\) 0 0
\(160\) −2.92820 + 5.07180i −0.231495 + 0.400961i
\(161\) −16.3923 −1.29189
\(162\) 0 0
\(163\) 12.7321 0.997251 0.498626 0.866817i \(-0.333838\pi\)
0.498626 + 0.866817i \(0.333838\pi\)
\(164\) 5.26795 9.12436i 0.411358 0.712492i
\(165\) 0 0
\(166\) −0.803848 1.39230i −0.0623907 0.108064i
\(167\) −8.83013 15.2942i −0.683296 1.18350i −0.973969 0.226681i \(-0.927213\pi\)
0.290673 0.956822i \(-0.406121\pi\)
\(168\) 0 0
\(169\) 5.42820 9.40192i 0.417554 0.723225i
\(170\) 2.00000 0.153393
\(171\) 0 0
\(172\) −0.287187 −0.0218978
\(173\) 4.26795 7.39230i 0.324486 0.562027i −0.656922 0.753958i \(-0.728142\pi\)
0.981408 + 0.191932i \(0.0614753\pi\)
\(174\) 0 0
\(175\) 2.36603 + 4.09808i 0.178855 + 0.309785i
\(176\) −3.07180 5.32051i −0.231545 0.401048i
\(177\) 0 0
\(178\) −1.90192 + 3.29423i −0.142555 + 0.246913i
\(179\) −8.12436 −0.607243 −0.303621 0.952793i \(-0.598196\pi\)
−0.303621 + 0.952793i \(0.598196\pi\)
\(180\) 0 0
\(181\) 26.4641 1.96706 0.983531 0.180742i \(-0.0578498\pi\)
0.983531 + 0.180742i \(0.0578498\pi\)
\(182\) −2.53590 + 4.39230i −0.187973 + 0.325579i
\(183\) 0 0
\(184\) −4.39230 7.60770i −0.323805 0.560847i
\(185\) −1.36603 2.36603i −0.100432 0.173954i
\(186\) 0 0
\(187\) −7.83013 + 13.5622i −0.572596 + 0.991765i
\(188\) −12.7846 −0.932413
\(189\) 0 0
\(190\) 3.26795 0.237082
\(191\) −4.06218 + 7.03590i −0.293929 + 0.509100i −0.974735 0.223364i \(-0.928296\pi\)
0.680806 + 0.732464i \(0.261630\pi\)
\(192\) 0 0
\(193\) 2.63397 + 4.56218i 0.189598 + 0.328393i 0.945116 0.326735i \(-0.105948\pi\)
−0.755519 + 0.655127i \(0.772615\pi\)
\(194\) −3.53590 6.12436i −0.253863 0.439703i
\(195\) 0 0
\(196\) 11.2679 19.5167i 0.804854 1.39405i
\(197\) 13.8564 0.987228 0.493614 0.869681i \(-0.335676\pi\)
0.493614 + 0.869681i \(0.335676\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) −1.26795 + 2.19615i −0.0896575 + 0.155291i
\(201\) 0 0
\(202\) 0.973721 + 1.68653i 0.0685107 + 0.118664i
\(203\) −7.56218 13.0981i −0.530761 0.919305i
\(204\) 0 0
\(205\) 3.59808 6.23205i 0.251301 0.435265i
\(206\) 0.392305 0.0273332
\(207\) 0 0
\(208\) 1.56922 0.108806
\(209\) −12.7942 + 22.1603i −0.884995 + 1.53286i
\(210\) 0 0
\(211\) 4.42820 + 7.66987i 0.304850 + 0.528016i 0.977228 0.212192i \(-0.0680603\pi\)
−0.672378 + 0.740208i \(0.734727\pi\)
\(212\) −4.92820 8.53590i −0.338470 0.586248i
\(213\) 0 0
\(214\) 3.12436 5.41154i 0.213577 0.369925i
\(215\) −0.196152 −0.0133775
\(216\) 0 0
\(217\) 14.1962 0.963698
\(218\) −2.22243 + 3.84936i −0.150522 + 0.260712i
\(219\) 0 0
\(220\) −4.19615 7.26795i −0.282905 0.490005i
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) 0 0
\(223\) −8.39230 + 14.5359i −0.561990 + 0.973396i 0.435332 + 0.900270i \(0.356631\pi\)
−0.997323 + 0.0731260i \(0.976702\pi\)
\(224\) 27.7128 1.85164
\(225\) 0 0
\(226\) −14.0000 −0.931266
\(227\) −9.02628 + 15.6340i −0.599095 + 1.03766i 0.393860 + 0.919171i \(0.371140\pi\)
−0.992955 + 0.118493i \(0.962194\pi\)
\(228\) 0 0
\(229\) 6.00000 + 10.3923i 0.396491 + 0.686743i 0.993290 0.115648i \(-0.0368944\pi\)
−0.596799 + 0.802391i \(0.703561\pi\)
\(230\) −1.26795 2.19615i −0.0836061 0.144810i
\(231\) 0 0
\(232\) 4.05256 7.01924i 0.266064 0.460836i
\(233\) 28.0526 1.83778 0.918892 0.394509i \(-0.129085\pi\)
0.918892 + 0.394509i \(0.129085\pi\)
\(234\) 0 0
\(235\) −8.73205 −0.569616
\(236\) 6.05256 10.4833i 0.393988 0.682407i
\(237\) 0 0
\(238\) −4.73205 8.19615i −0.306733 0.531278i
\(239\) −0.267949 0.464102i −0.0173322 0.0300202i 0.857229 0.514935i \(-0.172184\pi\)
−0.874561 + 0.484915i \(0.838851\pi\)
\(240\) 0 0
\(241\) 8.16025 14.1340i 0.525648 0.910449i −0.473906 0.880576i \(-0.657156\pi\)
0.999554 0.0298736i \(-0.00951049\pi\)
\(242\) −16.0000 −1.02852
\(243\) 0 0
\(244\) −5.85641 −0.374918
\(245\) 7.69615 13.3301i 0.491689 0.851631i
\(246\) 0 0
\(247\) −3.26795 5.66025i −0.207935 0.360153i
\(248\) 3.80385 + 6.58846i 0.241545 + 0.418367i
\(249\) 0 0
\(250\) −0.366025 + 0.633975i −0.0231495 + 0.0400961i
\(251\) 10.3923 0.655956 0.327978 0.944685i \(-0.393633\pi\)
0.327978 + 0.944685i \(0.393633\pi\)
\(252\) 0 0
\(253\) 19.8564 1.24836
\(254\) −5.33975 + 9.24871i −0.335045 + 0.580316i
\(255\) 0 0
\(256\) 5.85641 + 10.1436i 0.366025 + 0.633975i
\(257\) 5.19615 + 9.00000i 0.324127 + 0.561405i 0.981335 0.192304i \(-0.0615961\pi\)
−0.657208 + 0.753709i \(0.728263\pi\)
\(258\) 0 0
\(259\) −6.46410 + 11.1962i −0.401660 + 0.695695i
\(260\) 2.14359 0.132940
\(261\) 0 0
\(262\) 11.4115 0.705007
\(263\) 10.6603 18.4641i 0.657339 1.13855i −0.323962 0.946070i \(-0.605015\pi\)
0.981302 0.192475i \(-0.0616515\pi\)
\(264\) 0 0
\(265\) −3.36603 5.83013i −0.206773 0.358142i
\(266\) −7.73205 13.3923i −0.474082 0.821135i
\(267\) 0 0
\(268\) 2.53590 4.39230i 0.154905 0.268303i
\(269\) −10.6603 −0.649967 −0.324984 0.945720i \(-0.605359\pi\)
−0.324984 + 0.945720i \(0.605359\pi\)
\(270\) 0 0
\(271\) −2.92820 −0.177876 −0.0889378 0.996037i \(-0.528347\pi\)
−0.0889378 + 0.996037i \(0.528347\pi\)
\(272\) −1.46410 + 2.53590i −0.0887742 + 0.153761i
\(273\) 0 0
\(274\) −0.928203 1.60770i −0.0560748 0.0971244i
\(275\) −2.86603 4.96410i −0.172828 0.299347i
\(276\) 0 0
\(277\) −1.90192 + 3.29423i −0.114276 + 0.197931i −0.917490 0.397759i \(-0.869788\pi\)
0.803214 + 0.595690i \(0.203121\pi\)
\(278\) −0.444864 −0.0266812
\(279\) 0 0
\(280\) 12.0000 0.717137
\(281\) 7.73205 13.3923i 0.461255 0.798918i −0.537768 0.843093i \(-0.680732\pi\)
0.999024 + 0.0441747i \(0.0140658\pi\)
\(282\) 0 0
\(283\) 14.6603 + 25.3923i 0.871462 + 1.50942i 0.860485 + 0.509476i \(0.170161\pi\)
0.0109768 + 0.999940i \(0.496506\pi\)
\(284\) 2.73205 + 4.73205i 0.162117 + 0.280796i
\(285\) 0 0
\(286\) 3.07180 5.32051i 0.181639 0.314608i
\(287\) −34.0526 −2.01006
\(288\) 0 0
\(289\) −9.53590 −0.560935
\(290\) 1.16987 2.02628i 0.0686973 0.118987i
\(291\) 0 0
\(292\) −5.60770 9.71281i −0.328166 0.568399i
\(293\) 14.3660 + 24.8827i 0.839272 + 1.45366i 0.890504 + 0.454975i \(0.150352\pi\)
−0.0512319 + 0.998687i \(0.516315\pi\)
\(294\) 0 0
\(295\) 4.13397 7.16025i 0.240689 0.416886i
\(296\) −6.92820 −0.402694
\(297\) 0 0
\(298\) −5.85641 −0.339253
\(299\) −2.53590 + 4.39230i −0.146655 + 0.254014i
\(300\) 0 0
\(301\) 0.464102 + 0.803848i 0.0267504 + 0.0463330i
\(302\) 1.97372 + 3.41858i 0.113575 + 0.196717i
\(303\) 0 0
\(304\) −2.39230 + 4.14359i −0.137208 + 0.237651i
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) 14.0526 0.802022 0.401011 0.916073i \(-0.368659\pi\)
0.401011 + 0.916073i \(0.368659\pi\)
\(308\) −19.8564 + 34.3923i −1.13142 + 1.95968i
\(309\) 0 0
\(310\) 1.09808 + 1.90192i 0.0623665 + 0.108022i
\(311\) 9.86603 + 17.0885i 0.559451 + 0.968998i 0.997542 + 0.0700670i \(0.0223213\pi\)
−0.438091 + 0.898930i \(0.644345\pi\)
\(312\) 0 0
\(313\) 4.53590 7.85641i 0.256384 0.444070i −0.708886 0.705323i \(-0.750802\pi\)
0.965271 + 0.261252i \(0.0841355\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −22.6410 −1.27366
\(317\) 3.09808 5.36603i 0.174005 0.301386i −0.765811 0.643065i \(-0.777662\pi\)
0.939817 + 0.341679i \(0.110996\pi\)
\(318\) 0 0
\(319\) 9.16025 + 15.8660i 0.512876 + 0.888327i
\(320\) 1.07180 + 1.85641i 0.0599153 + 0.103776i
\(321\) 0 0
\(322\) −6.00000 + 10.3923i −0.334367 + 0.579141i
\(323\) 12.1962 0.678612
\(324\) 0 0
\(325\) 1.46410 0.0812137
\(326\) 4.66025 8.07180i 0.258108 0.447055i
\(327\) 0 0
\(328\) −9.12436 15.8038i −0.503808 0.872622i
\(329\) 20.6603 + 35.7846i 1.13904 + 1.97287i
\(330\) 0 0
\(331\) 0.232051 0.401924i 0.0127547 0.0220917i −0.859578 0.511005i \(-0.829273\pi\)
0.872332 + 0.488913i \(0.162607\pi\)
\(332\) 3.21539 0.176467
\(333\) 0 0
\(334\) −12.9282 −0.707400
\(335\) 1.73205 3.00000i 0.0946320 0.163908i
\(336\) 0 0
\(337\) −13.6603 23.6603i −0.744121 1.28886i −0.950604 0.310406i \(-0.899535\pi\)
0.206483 0.978450i \(-0.433798\pi\)
\(338\) −3.97372 6.88269i −0.216142 0.374369i
\(339\) 0 0
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) −17.1962 −0.931224
\(342\) 0 0
\(343\) −39.7128 −2.14429
\(344\) −0.248711 + 0.430781i −0.0134096 + 0.0232261i
\(345\) 0 0
\(346\) −3.12436 5.41154i −0.167966 0.290926i
\(347\) −14.2942 24.7583i −0.767354 1.32910i −0.938993 0.343937i \(-0.888239\pi\)
0.171638 0.985160i \(-0.445094\pi\)
\(348\) 0 0
\(349\) 9.42820 16.3301i 0.504680 0.874132i −0.495305 0.868719i \(-0.664944\pi\)
0.999985 0.00541263i \(-0.00172290\pi\)
\(350\) 3.46410 0.185164
\(351\) 0 0
\(352\) −33.5692 −1.78925
\(353\) 12.7583 22.0981i 0.679057 1.17616i −0.296208 0.955124i \(-0.595722\pi\)
0.975265 0.221038i \(-0.0709446\pi\)
\(354\) 0 0
\(355\) 1.86603 + 3.23205i 0.0990383 + 0.171539i
\(356\) −3.80385 6.58846i −0.201604 0.349188i
\(357\) 0 0
\(358\) −2.97372 + 5.15064i −0.157166 + 0.272220i
\(359\) 6.12436 0.323231 0.161616 0.986854i \(-0.448330\pi\)
0.161616 + 0.986854i \(0.448330\pi\)
\(360\) 0 0
\(361\) 0.928203 0.0488528
\(362\) 9.68653 16.7776i 0.509113 0.881809i
\(363\) 0 0
\(364\) −5.07180 8.78461i −0.265834 0.460439i
\(365\) −3.83013 6.63397i −0.200478 0.347238i
\(366\) 0 0
\(367\) −15.5885 + 27.0000i −0.813711 + 1.40939i 0.0965390 + 0.995329i \(0.469223\pi\)
−0.910250 + 0.414059i \(0.864111\pi\)
\(368\) 3.71281 0.193544
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) −15.9282 + 27.5885i −0.826951 + 1.43232i
\(372\) 0 0
\(373\) −10.0263 17.3660i −0.519141 0.899179i −0.999753 0.0222451i \(-0.992919\pi\)
0.480611 0.876934i \(-0.340415\pi\)
\(374\) 5.73205 + 9.92820i 0.296397 + 0.513375i
\(375\) 0 0
\(376\) −11.0718 + 19.1769i −0.570984 + 0.988974i
\(377\) −4.67949 −0.241006
\(378\) 0 0
\(379\) 2.39230 0.122884 0.0614422 0.998111i \(-0.480430\pi\)
0.0614422 + 0.998111i \(0.480430\pi\)
\(380\) −3.26795 + 5.66025i −0.167642 + 0.290365i
\(381\) 0 0
\(382\) 2.97372 + 5.15064i 0.152149 + 0.263529i
\(383\) 1.26795 + 2.19615i 0.0647892 + 0.112218i 0.896600 0.442840i \(-0.146029\pi\)
−0.831811 + 0.555059i \(0.812696\pi\)
\(384\) 0 0
\(385\) −13.5622 + 23.4904i −0.691193 + 1.19718i
\(386\) 3.85641 0.196286
\(387\) 0 0
\(388\) 14.1436 0.718032
\(389\) 13.7321 23.7846i 0.696243 1.20593i −0.273517 0.961867i \(-0.588187\pi\)
0.969760 0.244061i \(-0.0784796\pi\)
\(390\) 0 0
\(391\) −4.73205 8.19615i −0.239310 0.414497i
\(392\) −19.5167 33.8038i −0.985740 1.70735i
\(393\) 0 0
\(394\) 5.07180 8.78461i 0.255513 0.442562i
\(395\) −15.4641 −0.778083
\(396\) 0 0
\(397\) 14.3923 0.722329 0.361165 0.932502i \(-0.382379\pi\)
0.361165 + 0.932502i \(0.382379\pi\)
\(398\) −0.732051 + 1.26795i −0.0366944 + 0.0635566i
\(399\) 0 0
\(400\) −0.535898 0.928203i −0.0267949 0.0464102i
\(401\) 12.4641 + 21.5885i 0.622428 + 1.07808i 0.989032 + 0.147699i \(0.0471868\pi\)
−0.366605 + 0.930377i \(0.619480\pi\)
\(402\) 0 0
\(403\) 2.19615 3.80385i 0.109398 0.189483i
\(404\) −3.89488 −0.193778
\(405\) 0 0
\(406\) −11.0718 −0.549484
\(407\) 7.83013 13.5622i 0.388125 0.672252i
\(408\) 0 0
\(409\) 8.92820 + 15.4641i 0.441471 + 0.764651i 0.997799 0.0663124i \(-0.0211234\pi\)
−0.556328 + 0.830963i \(0.687790\pi\)
\(410\) −2.63397 4.56218i −0.130083 0.225310i
\(411\) 0 0
\(412\) −0.392305 + 0.679492i −0.0193275 + 0.0334762i
\(413\) −39.1244 −1.92518
\(414\) 0 0
\(415\) 2.19615 0.107805
\(416\) 4.28719 7.42563i 0.210197 0.364071i
\(417\) 0 0
\(418\) 9.36603 + 16.2224i 0.458107 + 0.793465i
\(419\) 10.1962 + 17.6603i 0.498115 + 0.862760i 0.999998 0.00217566i \(-0.000692534\pi\)
−0.501883 + 0.864936i \(0.667359\pi\)
\(420\) 0 0
\(421\) −16.8923 + 29.2583i −0.823281 + 1.42596i 0.0799458 + 0.996799i \(0.474525\pi\)
−0.903226 + 0.429165i \(0.858808\pi\)
\(422\) 6.48334 0.315604
\(423\) 0 0
\(424\) −17.0718 −0.829080
\(425\) −1.36603 + 2.36603i −0.0662620 + 0.114769i
\(426\) 0 0
\(427\) 9.46410 + 16.3923i 0.458000 + 0.793279i
\(428\) 6.24871 + 10.8231i 0.302043 + 0.523154i
\(429\) 0 0
\(430\) −0.0717968 + 0.124356i −0.00346235 + 0.00599696i
\(431\) 21.3397 1.02790 0.513950 0.857820i \(-0.328182\pi\)
0.513950 + 0.857820i \(0.328182\pi\)
\(432\) 0 0
\(433\) −35.4641 −1.70430 −0.852148 0.523301i \(-0.824700\pi\)
−0.852148 + 0.523301i \(0.824700\pi\)
\(434\) 5.19615 9.00000i 0.249423 0.432014i
\(435\) 0 0
\(436\) −4.44486 7.69873i −0.212870 0.368702i
\(437\) −7.73205 13.3923i −0.369874 0.640641i
\(438\) 0 0
\(439\) −2.69615 + 4.66987i −0.128680 + 0.222881i −0.923166 0.384403i \(-0.874407\pi\)
0.794485 + 0.607284i \(0.207741\pi\)
\(440\) −14.5359 −0.692972
\(441\) 0 0
\(442\) −2.92820 −0.139280
\(443\) −0.169873 + 0.294229i −0.00807091 + 0.0139792i −0.870033 0.492994i \(-0.835902\pi\)
0.861962 + 0.506973i \(0.169236\pi\)
\(444\) 0 0
\(445\) −2.59808 4.50000i −0.123161 0.213320i
\(446\) 6.14359 + 10.6410i 0.290908 + 0.503867i
\(447\) 0 0
\(448\) 5.07180 8.78461i 0.239620 0.415034i
\(449\) −8.12436 −0.383412 −0.191706 0.981452i \(-0.561402\pi\)
−0.191706 + 0.981452i \(0.561402\pi\)
\(450\) 0 0
\(451\) 41.2487 1.94233
\(452\) 14.0000 24.2487i 0.658505 1.14056i
\(453\) 0 0
\(454\) 6.60770 + 11.4449i 0.310114 + 0.537134i
\(455\) −3.46410 6.00000i −0.162400 0.281284i
\(456\) 0 0
\(457\) −1.36603 + 2.36603i −0.0639000 + 0.110678i −0.896206 0.443639i \(-0.853687\pi\)
0.832306 + 0.554317i \(0.187021\pi\)
\(458\) 8.78461 0.410478
\(459\) 0 0
\(460\) 5.07180 0.236474
\(461\) −18.5263 + 32.0885i −0.862855 + 1.49451i 0.00630665 + 0.999980i \(0.497993\pi\)
−0.869162 + 0.494528i \(0.835341\pi\)
\(462\) 0 0
\(463\) 5.19615 + 9.00000i 0.241486 + 0.418265i 0.961138 0.276069i \(-0.0890320\pi\)
−0.719652 + 0.694335i \(0.755699\pi\)
\(464\) 1.71281 + 2.96668i 0.0795153 + 0.137725i
\(465\) 0 0
\(466\) 10.2679 17.7846i 0.475654 0.823856i
\(467\) −37.3731 −1.72942 −0.864710 0.502272i \(-0.832498\pi\)
−0.864710 + 0.502272i \(0.832498\pi\)
\(468\) 0 0
\(469\) −16.3923 −0.756926
\(470\) −3.19615 + 5.53590i −0.147428 + 0.255352i
\(471\) 0 0
\(472\) −10.4833 18.1577i −0.482535 0.835775i
\(473\) −0.562178 0.973721i −0.0258490 0.0447717i
\(474\) 0 0
\(475\) −2.23205 + 3.86603i −0.102414 + 0.177385i
\(476\) 18.9282 0.867573
\(477\) 0 0
\(478\) −0.392305 −0.0179436
\(479\) −5.93782 + 10.2846i −0.271306 + 0.469916i −0.969197 0.246289i \(-0.920789\pi\)
0.697890 + 0.716204i \(0.254122\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −5.97372 10.3468i −0.272096 0.471283i
\(483\) 0 0
\(484\) 16.0000 27.7128i 0.727273 1.25967i
\(485\) 9.66025 0.438650
\(486\) 0 0
\(487\) 24.3923 1.10532 0.552660 0.833407i \(-0.313613\pi\)
0.552660 + 0.833407i \(0.313613\pi\)
\(488\) −5.07180 + 8.78461i −0.229589 + 0.397661i
\(489\) 0 0
\(490\) −5.63397 9.75833i −0.254517 0.440836i
\(491\) −6.93782 12.0167i −0.313100 0.542304i 0.665932 0.746012i \(-0.268034\pi\)
−0.979032 + 0.203708i \(0.934701\pi\)
\(492\) 0 0
\(493\) 4.36603 7.56218i 0.196636 0.340583i
\(494\) −4.78461 −0.215270
\(495\) 0 0
\(496\) −3.21539 −0.144375
\(497\) 8.83013 15.2942i 0.396085 0.686040i
\(498\) 0 0
\(499\) −12.1603 21.0622i −0.544368 0.942873i −0.998646 0.0520129i \(-0.983436\pi\)
0.454279 0.890860i \(-0.349897\pi\)
\(500\) −0.732051 1.26795i −0.0327383 0.0567044i
\(501\) 0 0
\(502\) 3.80385 6.58846i 0.169774 0.294057i
\(503\) 7.32051 0.326405 0.163203 0.986593i \(-0.447818\pi\)
0.163203 + 0.986593i \(0.447818\pi\)
\(504\) 0 0
\(505\) −2.66025 −0.118380
\(506\) 7.26795 12.5885i 0.323100 0.559625i
\(507\) 0 0
\(508\) −10.6795 18.4974i −0.473826 0.820690i
\(509\) −3.39230 5.87564i −0.150361 0.260433i 0.780999 0.624532i \(-0.214710\pi\)
−0.931360 + 0.364099i \(0.881377\pi\)
\(510\) 0 0
\(511\) −18.1244 + 31.3923i −0.801774 + 1.38871i
\(512\) −11.7128 −0.517638
\(513\) 0 0
\(514\) 7.60770 0.335561
\(515\) −0.267949 + 0.464102i −0.0118073 + 0.0204508i
\(516\) 0 0
\(517\) −25.0263 43.3468i −1.10065 1.90639i
\(518\) 4.73205 + 8.19615i 0.207914 + 0.360118i
\(519\) 0 0
\(520\) 1.85641 3.21539i 0.0814088 0.141004i
\(521\) −19.4641 −0.852738 −0.426369 0.904549i \(-0.640207\pi\)
−0.426369 + 0.904549i \(0.640207\pi\)
\(522\) 0 0
\(523\) 22.2487 0.972868 0.486434 0.873717i \(-0.338297\pi\)
0.486434 + 0.873717i \(0.338297\pi\)
\(524\) −11.4115 + 19.7654i −0.498516 + 0.863454i
\(525\) 0 0
\(526\) −7.80385 13.5167i −0.340264 0.589354i
\(527\) 4.09808 + 7.09808i 0.178515 + 0.309197i
\(528\) 0 0
\(529\) 5.50000 9.52628i 0.239130 0.414186i
\(530\) −4.92820 −0.214067
\(531\) 0 0
\(532\) 30.9282 1.34091
\(533\) −5.26795 + 9.12436i −0.228180 + 0.395220i
\(534\) 0 0
\(535\) 4.26795 + 7.39230i 0.184520 + 0.319597i
\(536\) −4.39230 7.60770i −0.189719 0.328602i
\(537\) 0 0
\(538\) −3.90192 + 6.75833i −0.168224 + 0.291372i
\(539\) 88.2295 3.80031
\(540\) 0 0
\(541\) −24.4641 −1.05179 −0.525897 0.850548i \(-0.676270\pi\)
−0.525897 + 0.850548i \(0.676270\pi\)
\(542\) −1.07180 + 1.85641i −0.0460376 + 0.0797395i
\(543\) 0 0
\(544\) 8.00000 + 13.8564i 0.342997 + 0.594089i
\(545\) −3.03590 5.25833i −0.130044 0.225242i
\(546\) 0 0
\(547\) 16.9282 29.3205i 0.723798 1.25365i −0.235669 0.971833i \(-0.575728\pi\)
0.959467 0.281821i \(-0.0909385\pi\)
\(548\) 3.71281 0.158604
\(549\) 0 0
\(550\) −4.19615 −0.178925
\(551\) 7.13397 12.3564i 0.303918 0.526401i
\(552\) 0 0
\(553\) 36.5885 + 63.3731i 1.55590 + 2.69490i
\(554\) 1.39230 + 2.41154i 0.0591534 + 0.102457i
\(555\) 0 0
\(556\) 0.444864 0.770527i 0.0188664 0.0326776i
\(557\) 2.53590 0.107449 0.0537247 0.998556i \(-0.482891\pi\)
0.0537247 + 0.998556i \(0.482891\pi\)
\(558\) 0 0
\(559\) 0.287187 0.0121467
\(560\) −2.53590 + 4.39230i −0.107161 + 0.185609i
\(561\) 0 0
\(562\) −5.66025 9.80385i −0.238763 0.413550i
\(563\) −8.36603 14.4904i −0.352586 0.610697i 0.634116 0.773238i \(-0.281364\pi\)
−0.986702 + 0.162541i \(0.948031\pi\)
\(564\) 0 0
\(565\) 9.56218 16.5622i 0.402284 0.696776i
\(566\) 21.4641 0.902203
\(567\) 0 0
\(568\) 9.46410 0.397105
\(569\) −16.4545 + 28.5000i −0.689808 + 1.19478i 0.282092 + 0.959387i \(0.408972\pi\)
−0.971900 + 0.235395i \(0.924362\pi\)
\(570\) 0 0
\(571\) 19.8923 + 34.4545i 0.832467 + 1.44188i 0.896076 + 0.443900i \(0.146406\pi\)
−0.0636091 + 0.997975i \(0.520261\pi\)
\(572\) 6.14359 + 10.6410i 0.256877 + 0.444923i
\(573\) 0 0
\(574\) −12.4641 + 21.5885i −0.520242 + 0.901085i
\(575\) 3.46410 0.144463
\(576\) 0 0
\(577\) 15.2679 0.635613 0.317807 0.948156i \(-0.397054\pi\)
0.317807 + 0.948156i \(0.397054\pi\)
\(578\) −3.49038 + 6.04552i −0.145181 + 0.251460i
\(579\) 0 0
\(580\) 2.33975 + 4.05256i 0.0971527 + 0.168273i
\(581\) −5.19615 9.00000i −0.215573 0.373383i
\(582\) 0 0
\(583\) 19.2942 33.4186i 0.799085 1.38406i
\(584\) −19.4256 −0.803838
\(585\) 0 0
\(586\) 21.0333 0.868878
\(587\) −5.83013 + 10.0981i −0.240635 + 0.416792i −0.960895 0.276912i \(-0.910689\pi\)
0.720260 + 0.693704i \(0.244022\pi\)
\(588\) 0 0
\(589\) 6.69615 + 11.5981i 0.275910 + 0.477890i
\(590\) −3.02628 5.24167i −0.124590 0.215796i
\(591\) 0 0
\(592\) 1.46410 2.53590i 0.0601742 0.104225i
\(593\) 0.143594 0.00589668 0.00294834 0.999996i \(-0.499062\pi\)
0.00294834 + 0.999996i \(0.499062\pi\)
\(594\) 0 0
\(595\) 12.9282 0.530005
\(596\) 5.85641 10.1436i 0.239888 0.415498i
\(597\) 0 0
\(598\) 1.85641 + 3.21539i 0.0759141 + 0.131487i
\(599\) 13.5981 + 23.5526i 0.555602 + 0.962331i 0.997856 + 0.0654417i \(0.0208456\pi\)
−0.442254 + 0.896890i \(0.645821\pi\)
\(600\) 0 0
\(601\) 15.6244 27.0622i 0.637331 1.10389i −0.348685 0.937240i \(-0.613372\pi\)
0.986016 0.166649i \(-0.0532948\pi\)
\(602\) 0.679492 0.0276940
\(603\) 0 0
\(604\) −7.89488 −0.321238
\(605\) 10.9282 18.9282i 0.444295 0.769541i
\(606\) 0 0
\(607\) 8.09808 + 14.0263i 0.328691 + 0.569309i 0.982252 0.187564i \(-0.0600593\pi\)
−0.653562 + 0.756873i \(0.726726\pi\)
\(608\) 13.0718 + 22.6410i 0.530131 + 0.918214i
\(609\) 0 0
\(610\) −1.46410 + 2.53590i −0.0592797 + 0.102676i
\(611\) 12.7846 0.517210
\(612\) 0 0
\(613\) 1.46410 0.0591345 0.0295673 0.999563i \(-0.490587\pi\)
0.0295673 + 0.999563i \(0.490587\pi\)
\(614\) 5.14359 8.90897i 0.207579 0.359537i
\(615\) 0 0
\(616\) 34.3923 + 59.5692i 1.38571 + 2.40011i
\(617\) −3.46410 6.00000i −0.139459 0.241551i 0.787833 0.615889i \(-0.211203\pi\)
−0.927292 + 0.374338i \(0.877870\pi\)
\(618\) 0 0
\(619\) 5.92820 10.2679i 0.238275 0.412704i −0.721945 0.691951i \(-0.756752\pi\)
0.960219 + 0.279247i \(0.0900848\pi\)
\(620\) −4.39230 −0.176399
\(621\) 0 0
\(622\) 14.4449 0.579186
\(623\) −12.2942 + 21.2942i −0.492558 + 0.853135i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −3.32051 5.75129i −0.132714 0.229868i
\(627\) 0 0
\(628\) −14.0000 + 24.2487i −0.558661 + 0.967629i
\(629\) −7.46410 −0.297613
\(630\) 0 0
\(631\) −32.7128 −1.30228 −0.651138 0.758959i \(-0.725708\pi\)
−0.651138 + 0.758959i \(0.725708\pi\)
\(632\) −19.6077 + 33.9615i −0.779952 + 1.35092i
\(633\) 0 0
\(634\) −2.26795 3.92820i −0.0900718 0.156009i
\(635\) −7.29423 12.6340i −0.289463 0.501364i
\(636\) 0 0
\(637\) −11.2679 + 19.5167i −0.446452 + 0.773278i
\(638\) 13.4115 0.530968
\(639\) 0 0
\(640\) −10.1436 −0.400961
\(641\) 4.66987 8.08846i 0.184449 0.319475i −0.758942 0.651158i \(-0.774283\pi\)
0.943391 + 0.331684i \(0.107617\pi\)
\(642\) 0 0
\(643\) −20.8301 36.0788i −0.821460 1.42281i −0.904595 0.426272i \(-0.859827\pi\)
0.0831349 0.996538i \(-0.473507\pi\)
\(644\) −12.0000 20.7846i −0.472866 0.819028i
\(645\) 0 0
\(646\) 4.46410 7.73205i 0.175638 0.304213i
\(647\) −11.4641 −0.450700 −0.225350 0.974278i \(-0.572353\pi\)
−0.225350 + 0.974278i \(0.572353\pi\)
\(648\) 0 0
\(649\) 47.3923 1.86031
\(650\) 0.535898 0.928203i 0.0210197 0.0364071i
\(651\) 0 0
\(652\) 9.32051 + 16.1436i 0.365019 + 0.632232i
\(653\) −8.73205 15.1244i −0.341712 0.591862i 0.643039 0.765833i \(-0.277673\pi\)
−0.984751 + 0.173972i \(0.944340\pi\)
\(654\) 0 0
\(655\) −7.79423 + 13.5000i −0.304546 + 0.527489i
\(656\) 7.71281 0.301135
\(657\) 0 0
\(658\) 30.2487 1.17922
\(659\) −0.732051 + 1.26795i −0.0285167 + 0.0493923i −0.879932 0.475101i \(-0.842412\pi\)
0.851415 + 0.524493i \(0.175745\pi\)
\(660\) 0 0
\(661\) −9.16025 15.8660i −0.356293 0.617117i 0.631046 0.775746i \(-0.282626\pi\)
−0.987338 + 0.158629i \(0.949293\pi\)
\(662\) −0.169873 0.294229i −0.00660230 0.0114355i
\(663\) 0 0
\(664\) 2.78461 4.82309i 0.108064 0.187172i
\(665\) 21.1244 0.819167
\(666\) 0 0
\(667\) −11.0718 −0.428702
\(668\) 12.9282 22.3923i 0.500207 0.866384i
\(669\) 0 0
\(670\) −1.26795 2.19615i −0.0489852 0.0848448i
\(671\) −11.4641 19.8564i −0.442567 0.766548i
\(672\) 0 0
\(673\) 5.19615 9.00000i 0.200297 0.346925i −0.748327 0.663330i \(-0.769143\pi\)
0.948624 + 0.316405i \(0.102476\pi\)
\(674\) −20.0000 −0.770371
\(675\) 0 0
\(676\) 15.8949 0.611342
\(677\) −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i \(-0.945759\pi\)
0.639618 + 0.768693i \(0.279092\pi\)
\(678\) 0 0
\(679\) −22.8564 39.5885i −0.877148 1.51927i
\(680\) 3.46410 + 6.00000i 0.132842 + 0.230089i
\(681\) 0 0
\(682\) −6.29423 + 10.9019i −0.241018 + 0.417456i
\(683\) 19.6077 0.750268 0.375134 0.926971i \(-0.377597\pi\)
0.375134 + 0.926971i \(0.377597\pi\)
\(684\) 0 0
\(685\) 2.53590 0.0968917
\(686\) −14.5359 + 25.1769i −0.554983 + 0.961259i
\(687\) 0 0
\(688\) −0.105118 0.182069i −0.00400758 0.00694133i
\(689\) 4.92820 + 8.53590i 0.187750 + 0.325192i
\(690\) 0 0
\(691\) 8.85641 15.3397i 0.336914 0.583551i −0.646937 0.762544i \(-0.723950\pi\)
0.983851 + 0.178992i \(0.0572836\pi\)
\(692\) 12.4974 0.475081
\(693\) 0 0
\(694\) −20.9282 −0.794424
\(695\) 0.303848 0.526279i 0.0115256 0.0199629i
\(696\) 0 0
\(697\) −9.83013 17.0263i −0.372343 0.644916i
\(698\) −6.90192 11.9545i −0.261242 0.452484i
\(699\) 0 0
\(700\) −3.46410 + 6.00000i −0.130931 + 0.226779i
\(701\) 20.8038 0.785750 0.392875 0.919592i \(-0.371480\pi\)
0.392875 + 0.919592i \(0.371480\pi\)
\(702\) 0 0
\(703\) −12.1962 −0.459987
\(704\) −6.14359 + 10.6410i −0.231545 + 0.401048i
\(705\) 0 0
\(706\) −9.33975 16.1769i −0.351506 0.608826i
\(707\) 6.29423 + 10.9019i 0.236719 + 0.410009i
\(708\) 0 0
\(709\) 11.2679 19.5167i 0.423177 0.732964i −0.573072 0.819505i \(-0.694248\pi\)
0.996248 + 0.0865418i \(0.0275816\pi\)
\(710\) 2.73205 0.102532
\(711\) 0 0
\(712\) −13.1769 −0.493826
\(713\) 5.19615 9.00000i 0.194597 0.337053i
\(714\) 0 0
\(715\) 4.19615 + 7.26795i 0.156927 + 0.271806i
\(716\) −5.94744 10.3013i −0.222266 0.384977i
\(717\) 0 0
\(718\) 2.24167 3.88269i 0.0836584 0.144901i
\(719\) −8.41154 −0.313698 −0.156849 0.987623i \(-0.550134\pi\)
−0.156849 + 0.987623i \(0.550134\pi\)
\(720\) 0 0
\(721\) 2.53590 0.0944418
\(722\) 0.339746 0.588457i 0.0126440 0.0219001i
\(723\) 0 0
\(724\) 19.3731 + 33.5551i 0.719994 + 1.24707i
\(725\) 1.59808 + 2.76795i 0.0593511 + 0.102799i
\(726\) 0 0
\(727\) 4.19615 7.26795i 0.155627 0.269553i −0.777660 0.628685i \(-0.783594\pi\)
0.933287 + 0.359131i \(0.116927\pi\)
\(728\) −17.5692 −0.651159
\(729\) 0 0
\(730\) −5.60770 −0.207550
\(731\) −0.267949 + 0.464102i −0.00991046 + 0.0171654i
\(732\) 0 0
\(733\) −17.3923 30.1244i −0.642399 1.11267i −0.984896 0.173149i \(-0.944606\pi\)
0.342496 0.939519i \(-0.388728\pi\)
\(734\) 11.4115 + 19.7654i 0.421208 + 0.729553i
\(735\) 0 0
\(736\) 10.1436 17.5692i 0.373898 0.647610i
\(737\) 19.8564 0.731420
\(738\) 0 0
\(739\) 22.4641 0.826355 0.413178 0.910650i \(-0.364419\pi\)
0.413178 + 0.910650i \(0.364419\pi\)
\(740\) 2.00000 3.46410i 0.0735215 0.127343i
\(741\) 0 0
\(742\) 11.6603 + 20.1962i 0.428061 + 0.741424i
\(743\) 9.95448 + 17.2417i 0.365195 + 0.632536i 0.988807 0.149198i \(-0.0476691\pi\)
−0.623613 + 0.781733i \(0.714336\pi\)
\(744\) 0 0
\(745\) 4.00000 6.92820i 0.146549 0.253830i
\(746\) −14.6795 −0.537454
\(747\) 0 0
\(748\) −22.9282 −0.838338
\(749\) 20.1962 34.9808i 0.737951 1.27817i
\(750\) 0 0
\(751\) −24.3923 42.2487i −0.890088 1.54168i −0.839769 0.542944i \(-0.817310\pi\)
−0.0503191 0.998733i \(-0.516024\pi\)
\(752\) −4.67949 8.10512i −0.170644 0.295563i
\(753\) 0 0
\(754\) −1.71281 + 2.96668i −0.0623770 + 0.108040i
\(755\) −5.39230 −0.196246
\(756\) 0 0
\(757\) −9.17691 −0.333541 −0.166770 0.985996i \(-0.553334\pi\)
−0.166770 + 0.985996i \(0.553334\pi\)
\(758\) 0.875644 1.51666i 0.0318048 0.0550876i
\(759\) 0 0
\(760\) 5.66025 + 9.80385i 0.205319 + 0.355623i
\(761\) 11.7224 + 20.3038i 0.424938 + 0.736014i 0.996415 0.0846043i \(-0.0269626\pi\)
−0.571477 + 0.820618i \(0.693629\pi\)
\(762\) 0 0
\(763\) −14.3660 + 24.8827i −0.520085 + 0.900814i
\(764\) −11.8949 −0.430342
\(765\) 0 0
\(766\) 1.85641 0.0670747
\(767\) −6.05256 + 10.4833i −0.218545 + 0.378531i
\(768\) 0 0
\(769\) 4.76795 + 8.25833i 0.171937 + 0.297803i 0.939097 0.343653i \(-0.111664\pi\)
−0.767160 + 0.641456i \(0.778331\pi\)
\(770\) 9.92820 + 17.1962i 0.357788 + 0.619706i
\(771\) 0 0
\(772\) −3.85641 + 6.67949i −0.138795 + 0.240400i
\(773\) −1.51666 −0.0545505 −0.0272752 0.999628i \(-0.508683\pi\)
−0.0272752 + 0.999628i \(0.508683\pi\)
\(774\) 0 0
\(775\) −3.00000 −0.107763
\(776\) 12.2487 21.2154i 0.439703 0.761588i
\(777\) 0 0
\(778\) −10.0526 17.4115i −0.360402 0.624234i
\(779\) −16.0622 27.8205i −0.575487 0.996773i
\(780\) 0 0
\(781\) −10.6962 + 18.5263i −0.382738 + 0.662922i
\(782\) −6.92820 −0.247752
\(783\) 0 0
\(784\) 16.4974 0.589194
\(785\) −9.56218 + 16.5622i −0.341289 + 0.591129i
\(786\) 0 0
\(787\) 24.0263 + 41.6147i 0.856444 + 1.48341i 0.875299 + 0.483583i \(0.160665\pi\)