Properties

Label 405.2.e.l.271.2
Level $405$
Weight $2$
Character 405.271
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 271.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.2.e.l.136.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 2.36603i) q^{2} +(-2.73205 + 4.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.633975 + 1.09808i) q^{7} -9.46410 q^{8} +O(q^{10})\) \(q+(1.36603 + 2.36603i) q^{2} +(-2.73205 + 4.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.633975 + 1.09808i) q^{7} -9.46410 q^{8} -2.73205 q^{10} +(1.13397 + 1.96410i) q^{11} +(2.73205 - 4.73205i) q^{13} +(-1.73205 + 3.00000i) q^{14} +(-7.46410 - 12.9282i) q^{16} +0.732051 q^{17} -2.46410 q^{19} +(-2.73205 - 4.73205i) q^{20} +(-3.09808 + 5.36603i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +14.9282 q^{26} -6.92820 q^{28} +(3.59808 + 6.23205i) q^{29} +(1.50000 - 2.59808i) q^{31} +(10.9282 - 18.9282i) q^{32} +(1.00000 + 1.73205i) q^{34} -1.26795 q^{35} +0.732051 q^{37} +(-3.36603 - 5.83013i) q^{38} +(4.73205 - 8.19615i) q^{40} +(-1.59808 + 2.76795i) q^{41} +(5.09808 + 8.83013i) q^{43} -12.3923 q^{44} -9.46410 q^{46} +(2.63397 + 4.56218i) q^{47} +(2.69615 - 4.66987i) q^{49} +(1.36603 - 2.36603i) q^{50} +(14.9282 + 25.8564i) q^{52} +3.26795 q^{53} -2.26795 q^{55} +(-6.00000 - 10.3923i) q^{56} +(-9.83013 + 17.0263i) q^{58} +(5.86603 - 10.1603i) q^{59} +(-2.00000 - 3.46410i) q^{61} +8.19615 q^{62} +29.8564 q^{64} +(2.73205 + 4.73205i) q^{65} +(1.73205 - 3.00000i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-1.73205 - 3.00000i) q^{70} -0.267949 q^{71} +9.66025 q^{73} +(1.00000 + 1.73205i) q^{74} +(6.73205 - 11.6603i) q^{76} +(-1.43782 + 2.49038i) q^{77} +(-4.26795 - 7.39230i) q^{79} +14.9282 q^{80} -8.73205 q^{82} +(4.09808 + 7.09808i) q^{83} +(-0.366025 + 0.633975i) q^{85} +(-13.9282 + 24.1244i) q^{86} +(-10.7321 - 18.5885i) q^{88} -5.19615 q^{89} +6.92820 q^{91} +(-9.46410 - 16.3923i) q^{92} +(-7.19615 + 12.4641i) q^{94} +(1.23205 - 2.13397i) q^{95} +(-3.83013 - 6.63397i) q^{97} +14.7321 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 4 q^{4} - 2 q^{5} + 6 q^{7} - 24 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 2.36603i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) 0 0
\(4\) −2.73205 + 4.73205i −1.36603 + 2.36603i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0.633975 + 1.09808i 0.239620 + 0.415034i 0.960605 0.277916i \(-0.0896439\pi\)
−0.720985 + 0.692950i \(0.756311\pi\)
\(8\) −9.46410 −3.34607
\(9\) 0 0
\(10\) −2.73205 −0.863950
\(11\) 1.13397 + 1.96410i 0.341906 + 0.592199i 0.984787 0.173768i \(-0.0555941\pi\)
−0.642880 + 0.765967i \(0.722261\pi\)
\(12\) 0 0
\(13\) 2.73205 4.73205i 0.757735 1.31243i −0.186269 0.982499i \(-0.559640\pi\)
0.944003 0.329936i \(-0.107027\pi\)
\(14\) −1.73205 + 3.00000i −0.462910 + 0.801784i
\(15\) 0 0
\(16\) −7.46410 12.9282i −1.86603 3.23205i
\(17\) 0.732051 0.177548 0.0887742 0.996052i \(-0.471705\pi\)
0.0887742 + 0.996052i \(0.471705\pi\)
\(18\) 0 0
\(19\) −2.46410 −0.565304 −0.282652 0.959223i \(-0.591214\pi\)
−0.282652 + 0.959223i \(0.591214\pi\)
\(20\) −2.73205 4.73205i −0.610905 1.05812i
\(21\) 0 0
\(22\) −3.09808 + 5.36603i −0.660512 + 1.14404i
\(23\) −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i \(-0.950952\pi\)
0.626994 + 0.779024i \(0.284285\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 14.9282 2.92766
\(27\) 0 0
\(28\) −6.92820 −1.30931
\(29\) 3.59808 + 6.23205i 0.668146 + 1.15726i 0.978422 + 0.206616i \(0.0662452\pi\)
−0.310276 + 0.950646i \(0.600421\pi\)
\(30\) 0 0
\(31\) 1.50000 2.59808i 0.269408 0.466628i −0.699301 0.714827i \(-0.746505\pi\)
0.968709 + 0.248199i \(0.0798387\pi\)
\(32\) 10.9282 18.9282i 1.93185 3.34607i
\(33\) 0 0
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) −1.26795 −0.214323
\(36\) 0 0
\(37\) 0.732051 0.120348 0.0601742 0.998188i \(-0.480834\pi\)
0.0601742 + 0.998188i \(0.480834\pi\)
\(38\) −3.36603 5.83013i −0.546041 0.945771i
\(39\) 0 0
\(40\) 4.73205 8.19615i 0.748203 1.29593i
\(41\) −1.59808 + 2.76795i −0.249578 + 0.432281i −0.963409 0.268037i \(-0.913625\pi\)
0.713831 + 0.700318i \(0.246958\pi\)
\(42\) 0 0
\(43\) 5.09808 + 8.83013i 0.777449 + 1.34658i 0.933408 + 0.358818i \(0.116820\pi\)
−0.155958 + 0.987764i \(0.549847\pi\)
\(44\) −12.3923 −1.86821
\(45\) 0 0
\(46\) −9.46410 −1.39541
\(47\) 2.63397 + 4.56218i 0.384205 + 0.665462i 0.991659 0.128893i \(-0.0411424\pi\)
−0.607454 + 0.794355i \(0.707809\pi\)
\(48\) 0 0
\(49\) 2.69615 4.66987i 0.385165 0.667125i
\(50\) 1.36603 2.36603i 0.193185 0.334607i
\(51\) 0 0
\(52\) 14.9282 + 25.8564i 2.07017 + 3.58564i
\(53\) 3.26795 0.448887 0.224444 0.974487i \(-0.427944\pi\)
0.224444 + 0.974487i \(0.427944\pi\)
\(54\) 0 0
\(55\) −2.26795 −0.305810
\(56\) −6.00000 10.3923i −0.801784 1.38873i
\(57\) 0 0
\(58\) −9.83013 + 17.0263i −1.29076 + 2.23566i
\(59\) 5.86603 10.1603i 0.763691 1.32275i −0.177244 0.984167i \(-0.556718\pi\)
0.940936 0.338585i \(-0.109948\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 8.19615 1.04091
\(63\) 0 0
\(64\) 29.8564 3.73205
\(65\) 2.73205 + 4.73205i 0.338869 + 0.586939i
\(66\) 0 0
\(67\) 1.73205 3.00000i 0.211604 0.366508i −0.740613 0.671932i \(-0.765465\pi\)
0.952217 + 0.305424i \(0.0987981\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 0 0
\(70\) −1.73205 3.00000i −0.207020 0.358569i
\(71\) −0.267949 −0.0317997 −0.0158999 0.999874i \(-0.505061\pi\)
−0.0158999 + 0.999874i \(0.505061\pi\)
\(72\) 0 0
\(73\) 9.66025 1.13065 0.565324 0.824869i \(-0.308751\pi\)
0.565324 + 0.824869i \(0.308751\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0 0
\(76\) 6.73205 11.6603i 0.772219 1.33752i
\(77\) −1.43782 + 2.49038i −0.163855 + 0.283805i
\(78\) 0 0
\(79\) −4.26795 7.39230i −0.480182 0.831699i 0.519560 0.854434i \(-0.326096\pi\)
−0.999742 + 0.0227349i \(0.992763\pi\)
\(80\) 14.9282 1.66902
\(81\) 0 0
\(82\) −8.73205 −0.964294
\(83\) 4.09808 + 7.09808i 0.449822 + 0.779115i 0.998374 0.0570015i \(-0.0181540\pi\)
−0.548552 + 0.836117i \(0.684821\pi\)
\(84\) 0 0
\(85\) −0.366025 + 0.633975i −0.0397010 + 0.0687642i
\(86\) −13.9282 + 24.1244i −1.50192 + 2.60140i
\(87\) 0 0
\(88\) −10.7321 18.5885i −1.14404 1.98154i
\(89\) −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
\(92\) −9.46410 16.3923i −0.986701 1.70902i
\(93\) 0 0
\(94\) −7.19615 + 12.4641i −0.742226 + 1.28557i
\(95\) 1.23205 2.13397i 0.126406 0.218941i
\(96\) 0 0
\(97\) −3.83013 6.63397i −0.388890 0.673578i 0.603410 0.797431i \(-0.293808\pi\)
−0.992301 + 0.123853i \(0.960475\pi\)
\(98\) 14.7321 1.48816
\(99\) 0 0
\(100\) 5.46410 0.546410
\(101\) −7.33013 12.6962i −0.729375 1.26331i −0.957148 0.289600i \(-0.906478\pi\)
0.227773 0.973714i \(-0.426856\pi\)
\(102\) 0 0
\(103\) 3.73205 6.46410i 0.367730 0.636927i −0.621480 0.783430i \(-0.713468\pi\)
0.989210 + 0.146503i \(0.0468018\pi\)
\(104\) −25.8564 + 44.7846i −2.53543 + 4.39149i
\(105\) 0 0
\(106\) 4.46410 + 7.73205i 0.433592 + 0.751003i
\(107\) −15.4641 −1.49497 −0.747486 0.664278i \(-0.768739\pi\)
−0.747486 + 0.664278i \(0.768739\pi\)
\(108\) 0 0
\(109\) −19.9282 −1.90878 −0.954388 0.298570i \(-0.903490\pi\)
−0.954388 + 0.298570i \(0.903490\pi\)
\(110\) −3.09808 5.36603i −0.295390 0.511630i
\(111\) 0 0
\(112\) 9.46410 16.3923i 0.894274 1.54893i
\(113\) −2.56218 + 4.43782i −0.241029 + 0.417475i −0.961008 0.276521i \(-0.910818\pi\)
0.719978 + 0.693997i \(0.244152\pi\)
\(114\) 0 0
\(115\) −1.73205 3.00000i −0.161515 0.279751i
\(116\) −39.3205 −3.65082
\(117\) 0 0
\(118\) 32.0526 2.95068
\(119\) 0.464102 + 0.803848i 0.0425441 + 0.0736886i
\(120\) 0 0
\(121\) 2.92820 5.07180i 0.266200 0.461072i
\(122\) 5.46410 9.46410i 0.494697 0.856840i
\(123\) 0 0
\(124\) 8.19615 + 14.1962i 0.736036 + 1.27485i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 16.5885 1.47199 0.735994 0.676988i \(-0.236715\pi\)
0.735994 + 0.676988i \(0.236715\pi\)
\(128\) 18.9282 + 32.7846i 1.67303 + 2.89778i
\(129\) 0 0
\(130\) −7.46410 + 12.9282i −0.654645 + 1.13388i
\(131\) 7.79423 13.5000i 0.680985 1.17950i −0.293696 0.955899i \(-0.594885\pi\)
0.974681 0.223602i \(-0.0717814\pi\)
\(132\) 0 0
\(133\) −1.56218 2.70577i −0.135458 0.234620i
\(134\) 9.46410 0.817574
\(135\) 0 0
\(136\) −6.92820 −0.594089
\(137\) −4.73205 8.19615i −0.404286 0.700245i 0.589952 0.807439i \(-0.299147\pi\)
−0.994238 + 0.107194i \(0.965813\pi\)
\(138\) 0 0
\(139\) −10.6962 + 18.5263i −0.907236 + 1.57138i −0.0893482 + 0.996000i \(0.528478\pi\)
−0.817888 + 0.575378i \(0.804855\pi\)
\(140\) 3.46410 6.00000i 0.292770 0.507093i
\(141\) 0 0
\(142\) −0.366025 0.633975i −0.0307162 0.0532020i
\(143\) 12.3923 1.03630
\(144\) 0 0
\(145\) −7.19615 −0.597608
\(146\) 13.1962 + 22.8564i 1.09212 + 1.89161i
\(147\) 0 0
\(148\) −2.00000 + 3.46410i −0.164399 + 0.284747i
\(149\) 4.00000 6.92820i 0.327693 0.567581i −0.654361 0.756182i \(-0.727062\pi\)
0.982054 + 0.188602i \(0.0603956\pi\)
\(150\) 0 0
\(151\) 7.69615 + 13.3301i 0.626304 + 1.08479i 0.988287 + 0.152606i \(0.0487665\pi\)
−0.361983 + 0.932185i \(0.617900\pi\)
\(152\) 23.3205 1.89154
\(153\) 0 0
\(154\) −7.85641 −0.633087
\(155\) 1.50000 + 2.59808i 0.120483 + 0.208683i
\(156\) 0 0
\(157\) −2.56218 + 4.43782i −0.204484 + 0.354177i −0.949968 0.312347i \(-0.898885\pi\)
0.745484 + 0.666523i \(0.232218\pi\)
\(158\) 11.6603 20.1962i 0.927640 1.60672i
\(159\) 0 0
\(160\) 10.9282 + 18.9282i 0.863950 + 1.49641i
\(161\) −4.39230 −0.346162
\(162\) 0 0
\(163\) 9.26795 0.725922 0.362961 0.931804i \(-0.381766\pi\)
0.362961 + 0.931804i \(0.381766\pi\)
\(164\) −8.73205 15.1244i −0.681859 1.18101i
\(165\) 0 0
\(166\) −11.1962 + 19.3923i −0.868990 + 1.50513i
\(167\) 0.169873 0.294229i 0.0131452 0.0227681i −0.859378 0.511341i \(-0.829149\pi\)
0.872523 + 0.488573i \(0.162482\pi\)
\(168\) 0 0
\(169\) −8.42820 14.5981i −0.648323 1.12293i
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) −55.7128 −4.24806
\(173\) −7.73205 13.3923i −0.587857 1.01820i −0.994513 0.104617i \(-0.966638\pi\)
0.406656 0.913581i \(-0.366695\pi\)
\(174\) 0 0
\(175\) 0.633975 1.09808i 0.0479240 0.0830068i
\(176\) 16.9282 29.3205i 1.27601 2.21012i
\(177\) 0 0
\(178\) −7.09808 12.2942i −0.532023 0.921491i
\(179\) −16.1244 −1.20519 −0.602595 0.798047i \(-0.705867\pi\)
−0.602595 + 0.798047i \(0.705867\pi\)
\(180\) 0 0
\(181\) 19.5359 1.45209 0.726046 0.687646i \(-0.241356\pi\)
0.726046 + 0.687646i \(0.241356\pi\)
\(182\) 9.46410 + 16.3923i 0.701526 + 1.21508i
\(183\) 0 0
\(184\) 16.3923 28.3923i 1.20846 2.09311i
\(185\) −0.366025 + 0.633975i −0.0269107 + 0.0466107i
\(186\) 0 0
\(187\) 0.830127 + 1.43782i 0.0607049 + 0.105144i
\(188\) −28.7846 −2.09933
\(189\) 0 0
\(190\) 6.73205 0.488394
\(191\) −8.06218 13.9641i −0.583359 1.01041i −0.995078 0.0990961i \(-0.968405\pi\)
0.411719 0.911311i \(-0.364928\pi\)
\(192\) 0 0
\(193\) 4.36603 7.56218i 0.314273 0.544337i −0.665009 0.746835i \(-0.731572\pi\)
0.979283 + 0.202498i \(0.0649058\pi\)
\(194\) 10.4641 18.1244i 0.751279 1.30125i
\(195\) 0 0
\(196\) 14.7321 + 25.5167i 1.05229 + 1.82262i
\(197\) 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 \(0.522583\pi\)
\(200\) 4.73205 + 8.19615i 0.334607 + 0.579555i
\(201\) 0 0
\(202\) 20.0263 34.6865i 1.40904 2.44054i
\(203\) −4.56218 + 7.90192i −0.320202 + 0.554606i
\(204\) 0 0
\(205\) −1.59808 2.76795i −0.111614 0.193322i
\(206\) 20.3923 1.42080
\(207\) 0 0
\(208\) −81.5692 −5.65581
\(209\) −2.79423 4.83975i −0.193281 0.334772i
\(210\) 0 0
\(211\) −9.42820 + 16.3301i −0.649064 + 1.12421i 0.334282 + 0.942473i \(0.391506\pi\)
−0.983347 + 0.181739i \(0.941827\pi\)
\(212\) −8.92820 + 15.4641i −0.613192 + 1.06208i
\(213\) 0 0
\(214\) −21.1244 36.5885i −1.44403 2.50114i
\(215\) −10.1962 −0.695372
\(216\) 0 0
\(217\) 3.80385 0.258222
\(218\) −27.2224 47.1506i −1.84374 3.19344i
\(219\) 0 0
\(220\) 6.19615 10.7321i 0.417745 0.723555i
\(221\) 2.00000 3.46410i 0.134535 0.233021i
\(222\) 0 0
\(223\) 12.3923 + 21.4641i 0.829850 + 1.43734i 0.898155 + 0.439678i \(0.144907\pi\)
−0.0683053 + 0.997664i \(0.521759\pi\)
\(224\) 27.7128 1.85164
\(225\) 0 0
\(226\) −14.0000 −0.931266
\(227\) −10.0263 17.3660i −0.665468 1.15262i −0.979158 0.203098i \(-0.934899\pi\)
0.313691 0.949525i \(-0.398434\pi\)
\(228\) 0 0
\(229\) 6.00000 10.3923i 0.396491 0.686743i −0.596799 0.802391i \(-0.703561\pi\)
0.993290 + 0.115648i \(0.0368944\pi\)
\(230\) 4.73205 8.19615i 0.312022 0.540438i
\(231\) 0 0
\(232\) −34.0526 58.9808i −2.23566 3.87228i
\(233\) 10.0526 0.658565 0.329283 0.944231i \(-0.393193\pi\)
0.329283 + 0.944231i \(0.393193\pi\)
\(234\) 0 0
\(235\) −5.26795 −0.343643
\(236\) 32.0526 + 55.5167i 2.08644 + 3.61383i
\(237\) 0 0
\(238\) −1.26795 + 2.19615i −0.0821889 + 0.142355i
\(239\) 3.73205 6.46410i 0.241406 0.418128i −0.719709 0.694276i \(-0.755725\pi\)
0.961115 + 0.276148i \(0.0890580\pi\)
\(240\) 0 0
\(241\) −9.16025 15.8660i −0.590064 1.02202i −0.994223 0.107332i \(-0.965769\pi\)
0.404159 0.914689i \(-0.367564\pi\)
\(242\) 16.0000 1.02852
\(243\) 0 0
\(244\) 21.8564 1.39921
\(245\) 2.69615 + 4.66987i 0.172251 + 0.298347i
\(246\) 0 0
\(247\) −6.73205 + 11.6603i −0.428350 + 0.741924i
\(248\) −14.1962 + 24.5885i −0.901457 + 1.56137i
\(249\) 0 0
\(250\) 1.36603 + 2.36603i 0.0863950 + 0.149641i
\(251\) 10.3923 0.655956 0.327978 0.944685i \(-0.393633\pi\)
0.327978 + 0.944685i \(0.393633\pi\)
\(252\) 0 0
\(253\) −7.85641 −0.493928
\(254\) 22.6603 + 39.2487i 1.42183 + 2.46268i
\(255\) 0 0
\(256\) −21.8564 + 37.8564i −1.36603 + 2.36603i
\(257\) 5.19615 9.00000i 0.324127 0.561405i −0.657208 0.753709i \(-0.728263\pi\)
0.981335 + 0.192304i \(0.0615961\pi\)
\(258\) 0 0
\(259\) 0.464102 + 0.803848i 0.0288379 + 0.0499487i
\(260\) −29.8564 −1.85162
\(261\) 0 0
\(262\) 42.5885 2.63112
\(263\) 6.66025 + 11.5359i 0.410689 + 0.711334i 0.994965 0.100221i \(-0.0319549\pi\)
−0.584276 + 0.811555i \(0.698622\pi\)
\(264\) 0 0
\(265\) −1.63397 + 2.83013i −0.100374 + 0.173853i
\(266\) 4.26795 7.39230i 0.261685 0.453251i
\(267\) 0 0
\(268\) 9.46410 + 16.3923i 0.578112 + 1.00132i
\(269\) −6.66025 −0.406083 −0.203041 0.979170i \(-0.565083\pi\)
−0.203041 + 0.979170i \(0.565083\pi\)
\(270\) 0 0
\(271\) 10.9282 0.663841 0.331921 0.943307i \(-0.392303\pi\)
0.331921 + 0.943307i \(0.392303\pi\)
\(272\) −5.46410 9.46410i −0.331310 0.573845i
\(273\) 0 0
\(274\) 12.9282 22.3923i 0.781021 1.35277i
\(275\) 1.13397 1.96410i 0.0683812 0.118440i
\(276\) 0 0
\(277\) −7.09808 12.2942i −0.426482 0.738689i 0.570075 0.821592i \(-0.306914\pi\)
−0.996558 + 0.0829037i \(0.973581\pi\)
\(278\) −58.4449 −3.50529
\(279\) 0 0
\(280\) 12.0000 0.717137
\(281\) −4.26795 7.39230i −0.254605 0.440988i 0.710184 0.704017i \(-0.248612\pi\)
−0.964788 + 0.263029i \(0.915279\pi\)
\(282\) 0 0
\(283\) −2.66025 + 4.60770i −0.158136 + 0.273899i −0.934196 0.356759i \(-0.883882\pi\)
0.776061 + 0.630658i \(0.217215\pi\)
\(284\) 0.732051 1.26795i 0.0434392 0.0752389i
\(285\) 0 0
\(286\) 16.9282 + 29.3205i 1.00099 + 1.73376i
\(287\) −4.05256 −0.239215
\(288\) 0 0
\(289\) −16.4641 −0.968477
\(290\) −9.83013 17.0263i −0.577245 0.999818i
\(291\) 0 0
\(292\) −26.3923 + 45.7128i −1.54449 + 2.67514i
\(293\) −12.6340 + 21.8827i −0.738085 + 1.27840i 0.215272 + 0.976554i \(0.430936\pi\)
−0.953357 + 0.301846i \(0.902397\pi\)
\(294\) 0 0
\(295\) 5.86603 + 10.1603i 0.341533 + 0.591553i
\(296\) −6.92820 −0.402694
\(297\) 0 0
\(298\) 21.8564 1.26611
\(299\) 9.46410 + 16.3923i 0.547323 + 0.947991i
\(300\) 0 0
\(301\) −6.46410 + 11.1962i −0.372585 + 0.645335i
\(302\) −21.0263 + 36.4186i −1.20993 + 2.09565i
\(303\) 0 0
\(304\) 18.3923 + 31.8564i 1.05487 + 1.82709i
\(305\) 4.00000 0.229039
\(306\) 0 0
\(307\) −24.0526 −1.37275 −0.686376 0.727247i \(-0.740800\pi\)
−0.686376 + 0.727247i \(0.740800\pi\)
\(308\) −7.85641 13.6077i −0.447660 0.775370i
\(309\) 0 0
\(310\) −4.09808 + 7.09808i −0.232755 + 0.403144i
\(311\) −8.13397 + 14.0885i −0.461235 + 0.798883i −0.999023 0.0441973i \(-0.985927\pi\)
0.537787 + 0.843080i \(0.319260\pi\)
\(312\) 0 0
\(313\) 11.4641 + 19.8564i 0.647989 + 1.12235i 0.983602 + 0.180351i \(0.0577232\pi\)
−0.335613 + 0.942000i \(0.608943\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 46.6410 2.62376
\(317\) 2.09808 + 3.63397i 0.117840 + 0.204104i 0.918911 0.394464i \(-0.129070\pi\)
−0.801072 + 0.598568i \(0.795736\pi\)
\(318\) 0 0
\(319\) −8.16025 + 14.1340i −0.456887 + 0.791351i
\(320\) −14.9282 + 25.8564i −0.834512 + 1.44542i
\(321\) 0 0
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) −1.80385 −0.100369
\(324\) 0 0
\(325\) −5.46410 −0.303094
\(326\) 12.6603 + 21.9282i 0.701187 + 1.21449i
\(327\) 0 0
\(328\) 15.1244 26.1962i 0.835103 1.44644i
\(329\) −3.33975 + 5.78461i −0.184126 + 0.318916i
\(330\) 0 0
\(331\) −3.23205 5.59808i −0.177650 0.307698i 0.763425 0.645896i \(-0.223516\pi\)
−0.941075 + 0.338198i \(0.890183\pi\)
\(332\) −44.7846 −2.45787
\(333\) 0 0
\(334\) 0.928203 0.0507890
\(335\) 1.73205 + 3.00000i 0.0946320 + 0.163908i
\(336\) 0 0
\(337\) 3.66025 6.33975i 0.199387 0.345348i −0.748943 0.662634i \(-0.769438\pi\)
0.948330 + 0.317286i \(0.102772\pi\)
\(338\) 23.0263 39.8827i 1.25246 2.16933i
\(339\) 0 0
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) 6.80385 0.368449
\(342\) 0 0
\(343\) 15.7128 0.848412
\(344\) −48.2487 83.5692i −2.60140 4.50575i
\(345\) 0 0
\(346\) 21.1244 36.5885i 1.13565 1.96701i
\(347\) −1.29423 + 2.24167i −0.0694778 + 0.120339i −0.898672 0.438622i \(-0.855467\pi\)
0.829194 + 0.558961i \(0.188800\pi\)
\(348\) 0 0
\(349\) −4.42820 7.66987i −0.237036 0.410559i 0.722826 0.691030i \(-0.242843\pi\)
−0.959863 + 0.280471i \(0.909509\pi\)
\(350\) 3.46410 0.185164
\(351\) 0 0
\(352\) 49.5692 2.64205
\(353\) 9.75833 + 16.9019i 0.519384 + 0.899599i 0.999746 + 0.0225287i \(0.00717171\pi\)
−0.480363 + 0.877070i \(0.659495\pi\)
\(354\) 0 0
\(355\) 0.133975 0.232051i 0.00711063 0.0123160i
\(356\) 14.1962 24.5885i 0.752395 1.30319i
\(357\) 0 0
\(358\) −22.0263 38.1506i −1.16413 2.01632i
\(359\) 18.1244 0.956567 0.478283 0.878206i \(-0.341259\pi\)
0.478283 + 0.878206i \(0.341259\pi\)
\(360\) 0 0
\(361\) −12.9282 −0.680432
\(362\) 26.6865 + 46.2224i 1.40261 + 2.42940i
\(363\) 0 0
\(364\) −18.9282 + 32.7846i −0.992107 + 1.71838i
\(365\) −4.83013 + 8.36603i −0.252820 + 0.437898i
\(366\) 0 0
\(367\) 15.5885 + 27.0000i 0.813711 + 1.40939i 0.910250 + 0.414059i \(0.135889\pi\)
−0.0965390 + 0.995329i \(0.530777\pi\)
\(368\) 51.7128 2.69572
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 2.07180 + 3.58846i 0.107562 + 0.186303i
\(372\) 0 0
\(373\) 9.02628 15.6340i 0.467363 0.809497i −0.531942 0.846781i \(-0.678537\pi\)
0.999305 + 0.0372845i \(0.0118708\pi\)
\(374\) −2.26795 + 3.92820i −0.117273 + 0.203123i
\(375\) 0 0
\(376\) −24.9282 43.1769i −1.28557 2.22668i
\(377\) 39.3205 2.02511
\(378\) 0 0
\(379\) −18.3923 −0.944749 −0.472375 0.881398i \(-0.656603\pi\)
−0.472375 + 0.881398i \(0.656603\pi\)
\(380\) 6.73205 + 11.6603i 0.345347 + 0.598158i
\(381\) 0 0
\(382\) 22.0263 38.1506i 1.12696 1.95196i
\(383\) −4.73205 + 8.19615i −0.241797 + 0.418804i −0.961226 0.275762i \(-0.911070\pi\)
0.719430 + 0.694565i \(0.244403\pi\)
\(384\) 0 0
\(385\) −1.43782 2.49038i −0.0732782 0.126922i
\(386\) 23.8564 1.21426
\(387\) 0 0
\(388\) 41.8564 2.12494
\(389\) −10.2679 17.7846i −0.520606 0.901716i −0.999713 0.0239591i \(-0.992373\pi\)
0.479107 0.877756i \(-0.340960\pi\)
\(390\) 0 0
\(391\) −1.26795 + 2.19615i −0.0641229 + 0.111064i
\(392\) −25.5167 + 44.1962i −1.28879 + 2.23224i
\(393\) 0 0
\(394\) 18.9282 + 32.7846i 0.953589 + 1.65166i
\(395\) 8.53590 0.429488
\(396\) 0 0
\(397\) −6.39230 −0.320821 −0.160410 0.987050i \(-0.551282\pi\)
−0.160410 + 0.987050i \(0.551282\pi\)
\(398\) −2.73205 4.73205i −0.136945 0.237196i
\(399\) 0 0
\(400\) −7.46410 + 12.9282i −0.373205 + 0.646410i
\(401\) −5.53590 + 9.58846i −0.276450 + 0.478825i −0.970500 0.241102i \(-0.922491\pi\)
0.694050 + 0.719927i \(0.255825\pi\)
\(402\) 0 0
\(403\) −8.19615 14.1962i −0.408279 0.707161i
\(404\) 80.1051 3.98538
\(405\) 0 0
\(406\) −24.9282 −1.23717
\(407\) 0.830127 + 1.43782i 0.0411479 + 0.0712702i
\(408\) 0 0
\(409\) −4.92820 + 8.53590i −0.243684 + 0.422073i −0.961761 0.273891i \(-0.911689\pi\)
0.718077 + 0.695964i \(0.245023\pi\)
\(410\) 4.36603 7.56218i 0.215623 0.373469i
\(411\) 0 0
\(412\) 20.3923 + 35.3205i 1.00466 + 1.74012i
\(413\) 14.8756 0.731983
\(414\) 0 0
\(415\) −8.19615 −0.402333
\(416\) −59.7128 103.426i −2.92766 5.07086i
\(417\) 0 0
\(418\) 7.63397 13.2224i 0.373390 0.646730i
\(419\) 0.196152 0.339746i 0.00958267 0.0165977i −0.861194 0.508276i \(-0.830283\pi\)
0.870777 + 0.491678i \(0.163616\pi\)
\(420\) 0 0
\(421\) 3.89230 + 6.74167i 0.189699 + 0.328569i 0.945150 0.326637i \(-0.105915\pi\)
−0.755451 + 0.655206i \(0.772582\pi\)
\(422\) −51.5167 −2.50779
\(423\) 0 0
\(424\) −30.9282 −1.50201
\(425\) −0.366025 0.633975i −0.0177548 0.0307523i
\(426\) 0 0
\(427\) 2.53590 4.39230i 0.122721 0.212559i
\(428\) 42.2487 73.1769i 2.04217 3.53714i
\(429\) 0 0
\(430\) −13.9282 24.1244i −0.671678 1.16338i
\(431\) −38.6603 −1.86220 −0.931099 0.364765i \(-0.881149\pi\)
−0.931099 + 0.364765i \(0.881149\pi\)
\(432\) 0 0
\(433\) −28.5359 −1.37135 −0.685674 0.727909i \(-0.740492\pi\)
−0.685674 + 0.727909i \(0.740492\pi\)
\(434\) 5.19615 + 9.00000i 0.249423 + 0.432014i
\(435\) 0 0
\(436\) 54.4449 94.3013i 2.60744 4.51621i
\(437\) 4.26795 7.39230i 0.204164 0.353622i
\(438\) 0 0
\(439\) 7.69615 + 13.3301i 0.367317 + 0.636212i 0.989145 0.146942i \(-0.0469430\pi\)
−0.621828 + 0.783154i \(0.713610\pi\)
\(440\) 21.4641 1.02326
\(441\) 0 0
\(442\) 10.9282 0.519802
\(443\) 8.83013 + 15.2942i 0.419532 + 0.726651i 0.995892 0.0905449i \(-0.0288609\pi\)
−0.576360 + 0.817196i \(0.695528\pi\)
\(444\) 0 0
\(445\) 2.59808 4.50000i 0.123161 0.213320i
\(446\) −33.8564 + 58.6410i −1.60315 + 2.77673i
\(447\) 0 0
\(448\) 18.9282 + 32.7846i 0.894274 + 1.54893i
\(449\) −16.1244 −0.760955 −0.380478 0.924790i \(-0.624240\pi\)
−0.380478 + 0.924790i \(0.624240\pi\)
\(450\) 0 0
\(451\) −7.24871 −0.341328
\(452\) −14.0000 24.2487i −0.658505 1.14056i
\(453\) 0 0
\(454\) 27.3923 47.4449i 1.28558 2.22670i
\(455\) −3.46410 + 6.00000i −0.162400 + 0.281284i
\(456\) 0 0
\(457\) 0.366025 + 0.633975i 0.0171219 + 0.0296561i 0.874459 0.485099i \(-0.161216\pi\)
−0.857337 + 0.514755i \(0.827883\pi\)
\(458\) 32.7846 1.53192
\(459\) 0 0
\(460\) 18.9282 0.882532
\(461\) −0.526279 0.911543i −0.0245113 0.0424548i 0.853510 0.521077i \(-0.174470\pi\)
−0.878021 + 0.478622i \(0.841136\pi\)
\(462\) 0 0
\(463\) −5.19615 + 9.00000i −0.241486 + 0.418265i −0.961138 0.276069i \(-0.910968\pi\)
0.719652 + 0.694335i \(0.244301\pi\)
\(464\) 53.7128 93.0333i 2.49355 4.31896i
\(465\) 0 0
\(466\) 13.7321 + 23.7846i 0.636125 + 1.10180i
\(467\) −35.3731 −1.63687 −0.818435 0.574599i \(-0.805158\pi\)
−0.818435 + 0.574599i \(0.805158\pi\)
\(468\) 0 0
\(469\) 4.39230 0.202818
\(470\) −7.19615 12.4641i −0.331934 0.574926i
\(471\) 0 0
\(472\) −55.5167 + 96.1577i −2.55536 + 4.42602i
\(473\) −11.5622 + 20.0263i −0.531630 + 0.920809i
\(474\) 0 0
\(475\) 1.23205 + 2.13397i 0.0565304 + 0.0979135i
\(476\) −5.07180 −0.232465
\(477\) 0 0
\(478\) 20.3923 0.932722
\(479\) 18.0622 + 31.2846i 0.825282 + 1.42943i 0.901704 + 0.432355i \(0.142317\pi\)
−0.0764216 + 0.997076i \(0.524350\pi\)
\(480\) 0 0
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) 25.0263 43.3468i 1.13992 1.97439i
\(483\) 0 0
\(484\) 16.0000 + 27.7128i 0.727273 + 1.25967i
\(485\) 7.66025 0.347834
\(486\) 0 0
\(487\) 3.60770 0.163480 0.0817401 0.996654i \(-0.473952\pi\)
0.0817401 + 0.996654i \(0.473952\pi\)
\(488\) 18.9282 + 32.7846i 0.856840 + 1.48409i
\(489\) 0 0
\(490\) −7.36603 + 12.7583i −0.332763 + 0.576363i
\(491\) 19.0622 33.0167i 0.860264 1.49002i −0.0114100 0.999935i \(-0.503632\pi\)
0.871674 0.490086i \(-0.163035\pi\)
\(492\) 0 0
\(493\) 2.63397 + 4.56218i 0.118628 + 0.205470i
\(494\) −36.7846 −1.65502
\(495\) 0 0
\(496\) −44.7846 −2.01089
\(497\) −0.169873 0.294229i −0.00761984 0.0131980i
\(498\) 0 0
\(499\) 5.16025 8.93782i 0.231005 0.400112i −0.727099 0.686532i \(-0.759132\pi\)
0.958104 + 0.286420i \(0.0924654\pi\)
\(500\) −2.73205 + 4.73205i −0.122181 + 0.211624i
\(501\) 0 0
\(502\) 14.1962 + 24.5885i 0.633605 + 1.09744i
\(503\) 27.3205 1.21816 0.609081 0.793108i \(-0.291539\pi\)
0.609081 + 0.793108i \(0.291539\pi\)
\(504\) 0 0
\(505\) 14.6603 0.652373
\(506\) −10.7321 18.5885i −0.477098 0.826358i
\(507\) 0 0
\(508\) −45.3205 + 78.4974i −2.01077 + 3.48276i
\(509\) −17.3923 + 30.1244i −0.770900 + 1.33524i 0.166170 + 0.986097i \(0.446860\pi\)
−0.937070 + 0.349141i \(0.886473\pi\)
\(510\) 0 0
\(511\) 6.12436 + 10.6077i 0.270926 + 0.469257i
\(512\) −43.7128 −1.93185
\(513\) 0 0
\(514\) 28.3923 1.25233
\(515\) 3.73205 + 6.46410i 0.164454 + 0.284842i
\(516\) 0 0
\(517\) −5.97372 + 10.3468i −0.262724 + 0.455051i
\(518\) −1.26795 + 2.19615i −0.0557105 + 0.0964934i
\(519\) 0 0
\(520\) −25.8564 44.7846i −1.13388 1.96394i
\(521\) 12.5359 0.549208 0.274604 0.961557i \(-0.411453\pi\)
0.274604 + 0.961557i \(0.411453\pi\)
\(522\) 0 0
\(523\) −26.2487 −1.14778 −0.573888 0.818934i \(-0.694566\pi\)
−0.573888 + 0.818934i \(0.694566\pi\)
\(524\) 42.5885 + 73.7654i 1.86049 + 3.22246i
\(525\) 0 0
\(526\) −18.1962 + 31.5167i −0.793390 + 1.37419i
\(527\) 1.09808 1.90192i 0.0478330 0.0828491i
\(528\) 0 0
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) −8.92820 −0.387816
\(531\) 0 0
\(532\) 17.0718 0.740156
\(533\) 8.73205 + 15.1244i 0.378227 + 0.655109i
\(534\) 0 0
\(535\) 7.73205 13.3923i 0.334286 0.579000i
\(536\) −16.3923 + 28.3923i −0.708040 + 1.22636i
\(537\) 0 0
\(538\) −9.09808 15.7583i −0.392246 0.679390i
\(539\) 12.2295 0.526761
\(540\) 0 0
\(541\) −17.5359 −0.753927 −0.376964 0.926228i \(-0.623032\pi\)
−0.376964 + 0.926228i \(0.623032\pi\)
\(542\) 14.9282 + 25.8564i 0.641221 + 1.11063i
\(543\) 0 0
\(544\) 8.00000 13.8564i 0.342997 0.594089i
\(545\) 9.96410 17.2583i 0.426815 0.739266i
\(546\) 0 0
\(547\) 3.07180 + 5.32051i 0.131341 + 0.227488i 0.924194 0.381924i \(-0.124739\pi\)
−0.792853 + 0.609413i \(0.791405\pi\)
\(548\) 51.7128 2.20906
\(549\) 0 0
\(550\) 6.19615 0.264205
\(551\) −8.86603 15.3564i −0.377705 0.654205i
\(552\) 0 0
\(553\) 5.41154 9.37307i 0.230122 0.398583i
\(554\) 19.3923 33.5885i 0.823900 1.42704i
\(555\) 0 0
\(556\) −58.4449 101.229i −2.47861 4.29309i
\(557\) −9.46410 −0.401007 −0.200503 0.979693i \(-0.564258\pi\)
−0.200503 + 0.979693i \(0.564258\pi\)
\(558\) 0 0
\(559\) 55.7128 2.35640
\(560\) 9.46410 + 16.3923i 0.399931 + 0.692701i
\(561\) 0 0
\(562\) 11.6603 20.1962i 0.491858 0.851923i
\(563\) 6.63397 11.4904i 0.279589 0.484262i −0.691694 0.722191i \(-0.743135\pi\)
0.971283 + 0.237929i \(0.0764686\pi\)
\(564\) 0 0
\(565\) −2.56218 4.43782i −0.107792 0.186701i
\(566\) −14.5359 −0.610989
\(567\) 0 0
\(568\) 2.53590 0.106404
\(569\) −16.4545 28.5000i −0.689808 1.19478i −0.971900 0.235395i \(-0.924362\pi\)
0.282092 0.959387i \(-0.408972\pi\)
\(570\) 0 0
\(571\) −0.892305 + 1.54552i −0.0373418 + 0.0646779i −0.884092 0.467312i \(-0.845222\pi\)
0.846750 + 0.531990i \(0.178556\pi\)
\(572\) −33.8564 + 58.6410i −1.41561 + 2.45190i
\(573\) 0 0
\(574\) −5.53590 9.58846i −0.231064 0.400214i
\(575\) 3.46410 0.144463
\(576\) 0 0
\(577\) 18.7321 0.779825 0.389913 0.920852i \(-0.372505\pi\)
0.389913 + 0.920852i \(0.372505\pi\)
\(578\) −22.4904 38.9545i −0.935477 1.62029i
\(579\) 0 0
\(580\) 19.6603 34.0526i 0.816348 1.41396i
\(581\) −5.19615 + 9.00000i −0.215573 + 0.373383i
\(582\) 0 0
\(583\) 3.70577 + 6.41858i 0.153477 + 0.265831i
\(584\) −91.4256 −3.78322
\(585\) 0 0
\(586\) −69.0333 −2.85174
\(587\) −2.83013 4.90192i −0.116812 0.202324i 0.801691 0.597739i \(-0.203934\pi\)
−0.918503 + 0.395415i \(0.870601\pi\)
\(588\) 0 0
\(589\) −3.69615 + 6.40192i −0.152297 + 0.263787i
\(590\) −16.0263 + 27.7583i −0.659791 + 1.14279i
\(591\) 0 0
\(592\) −5.46410 9.46410i −0.224573 0.388972i
\(593\) −27.8564 −1.14393 −0.571963 0.820280i \(-0.693818\pi\)
−0.571963 + 0.820280i \(0.693818\pi\)
\(594\) 0 0
\(595\) −0.928203 −0.0380526
\(596\) 21.8564 + 37.8564i 0.895273 + 1.55066i
\(597\) 0 0
\(598\) −25.8564 + 44.7846i −1.05735 + 1.83138i
\(599\) −8.40192 + 14.5526i −0.343293 + 0.594601i −0.985042 0.172313i \(-0.944876\pi\)
0.641749 + 0.766915i \(0.278209\pi\)
\(600\) 0 0
\(601\) −8.62436 14.9378i −0.351795 0.609326i 0.634769 0.772702i \(-0.281095\pi\)
−0.986564 + 0.163375i \(0.947762\pi\)
\(602\) −35.3205 −1.43956
\(603\) 0 0
\(604\) −84.1051 −3.42219
\(605\) 2.92820 + 5.07180i 0.119048 + 0.206198i
\(606\) 0 0
\(607\) 2.90192 5.02628i 0.117785 0.204010i −0.801104 0.598525i \(-0.795754\pi\)
0.918890 + 0.394514i \(0.129087\pi\)
\(608\) −26.9282 + 46.6410i −1.09208 + 1.89154i
\(609\) 0 0
\(610\) 5.46410 + 9.46410i 0.221235 + 0.383190i
\(611\) 28.7846 1.16450
\(612\) 0 0
\(613\) −5.46410 −0.220693 −0.110346 0.993893i \(-0.535196\pi\)
−0.110346 + 0.993893i \(0.535196\pi\)
\(614\) −32.8564 56.9090i −1.32598 2.29666i
\(615\) 0 0
\(616\) 13.6077 23.5692i 0.548270 0.949631i
\(617\) −3.46410 + 6.00000i −0.139459 + 0.241551i −0.927292 0.374338i \(-0.877870\pi\)
0.787833 + 0.615889i \(0.211203\pi\)
\(618\) 0 0
\(619\) −7.92820 13.7321i −0.318661 0.551938i 0.661548 0.749903i \(-0.269900\pi\)
−0.980209 + 0.197965i \(0.936567\pi\)
\(620\) −16.3923 −0.658331
\(621\) 0 0
\(622\) −44.4449 −1.78208
\(623\) −3.29423 5.70577i −0.131980 0.228597i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −31.3205 + 54.2487i −1.25182 + 2.16821i
\(627\) 0 0
\(628\) −14.0000 24.2487i −0.558661 0.967629i
\(629\) 0.535898 0.0213677
\(630\) 0 0
\(631\) 22.7128 0.904183 0.452091 0.891972i \(-0.350678\pi\)
0.452091 + 0.891972i \(0.350678\pi\)
\(632\) 40.3923 + 69.9615i 1.60672 + 2.78292i
\(633\) 0 0
\(634\) −5.73205 + 9.92820i −0.227649 + 0.394299i
\(635\) −8.29423 + 14.3660i −0.329146 + 0.570098i
\(636\) 0 0
\(637\) −14.7321 25.5167i −0.583705 1.01101i
\(638\) −44.5885 −1.76527
\(639\) 0 0
\(640\) −37.8564 −1.49641
\(641\) −13.3301 23.0885i −0.526508 0.911939i −0.999523 0.0308846i \(-0.990168\pi\)
0.473015 0.881055i \(-0.343166\pi\)
\(642\) 0 0
\(643\) −12.1699 + 21.0788i −0.479933 + 0.831268i −0.999735 0.0230185i \(-0.992672\pi\)
0.519802 + 0.854287i \(0.326006\pi\)
\(644\) 12.0000 20.7846i 0.472866 0.819028i
\(645\) 0 0
\(646\) −2.46410 4.26795i −0.0969488 0.167920i
\(647\) 4.53590 0.178325 0.0891623 0.996017i \(-0.471581\pi\)
0.0891623 + 0.996017i \(0.471581\pi\)
\(648\) 0 0
\(649\) 26.6077 1.04444
\(650\) −7.46410 12.9282i −0.292766 0.507086i
\(651\) 0 0
\(652\) −25.3205 + 43.8564i −0.991628 + 1.71755i
\(653\) 5.26795 9.12436i 0.206151 0.357064i −0.744348 0.667792i \(-0.767240\pi\)
0.950499 + 0.310728i \(0.100573\pi\)
\(654\) 0 0
\(655\) 7.79423 + 13.5000i 0.304546 + 0.527489i
\(656\) 47.7128 1.86287
\(657\) 0 0
\(658\) −18.2487 −0.711409
\(659\) −2.73205 4.73205i −0.106426 0.184335i 0.807894 0.589328i \(-0.200607\pi\)
−0.914320 + 0.404993i \(0.867274\pi\)
\(660\) 0 0
\(661\) 8.16025 14.1340i 0.317397 0.549748i −0.662547 0.749020i \(-0.730525\pi\)
0.979944 + 0.199272i \(0.0638579\pi\)
\(662\) 8.83013 15.2942i 0.343193 0.594427i
\(663\) 0 0
\(664\) −38.7846 67.1769i −1.50513 2.60697i
\(665\) 3.12436 0.121157
\(666\) 0 0
\(667\) −24.9282 −0.965224
\(668\) 0.928203 + 1.60770i 0.0359133 + 0.0622036i
\(669\) 0 0
\(670\) −4.73205 + 8.19615i −0.182815 + 0.316645i
\(671\) 4.53590 7.85641i 0.175106 0.303293i
\(672\) 0 0
\(673\) −5.19615 9.00000i −0.200297 0.346925i 0.748327 0.663330i \(-0.230857\pi\)
−0.948624 + 0.316405i \(0.897524\pi\)
\(674\) 20.0000 0.770371
\(675\) 0 0
\(676\) 92.1051 3.54250
\(677\) 9.00000 + 15.5885i 0.345898 + 0.599113i 0.985517 0.169580i \(-0.0542410\pi\)
−0.639618 + 0.768693i \(0.720908\pi\)
\(678\) 0 0
\(679\) 4.85641 8.41154i 0.186372 0.322805i
\(680\) 3.46410 6.00000i 0.132842 0.230089i
\(681\) 0 0
\(682\) 9.29423 + 16.0981i 0.355894 + 0.616427i
\(683\) −40.3923 −1.54557 −0.772784 0.634669i \(-0.781137\pi\)
−0.772784 + 0.634669i \(0.781137\pi\)
\(684\) 0 0
\(685\) 9.46410 0.361605
\(686\) 21.4641 + 37.1769i 0.819503 + 1.41942i
\(687\) 0 0
\(688\) 76.1051 131.818i 2.90148 5.02551i
\(689\) 8.92820 15.4641i 0.340137 0.589135i
\(690\) 0 0
\(691\) −18.8564 32.6603i −0.717332 1.24245i −0.962053 0.272861i \(-0.912030\pi\)
0.244722 0.969593i \(-0.421303\pi\)
\(692\) 84.4974 3.21211
\(693\) 0 0
\(694\) −7.07180 −0.268442
\(695\) −10.6962 18.5263i −0.405728 0.702742i
\(696\) 0 0
\(697\) −1.16987 + 2.02628i −0.0443121 + 0.0767508i
\(698\) 12.0981 20.9545i 0.457919 0.793139i
\(699\) 0 0
\(700\) 3.46410 + 6.00000i 0.130931 + 0.226779i
\(701\) −31.1962 −1.17826 −0.589131 0.808037i \(-0.700530\pi\)
−0.589131 + 0.808037i \(0.700530\pi\)
\(702\) 0 0
\(703\) −1.80385 −0.0680334
\(704\) 33.8564 + 58.6410i 1.27601 + 2.21012i
\(705\) 0 0
\(706\) −26.6603 + 46.1769i −1.00337 + 1.73789i
\(707\) 9.29423 16.0981i 0.349545 0.605430i
\(708\) 0 0
\(709\) 14.7321 + 25.5167i 0.553274 + 0.958298i 0.998036 + 0.0626494i \(0.0199550\pi\)
−0.444762 + 0.895649i \(0.646712\pi\)
\(710\) 0.732051 0.0274734
\(711\) 0 0
\(712\) 49.1769 1.84298
\(713\) 5.19615 + 9.00000i 0.194597 + 0.337053i
\(714\) 0 0
\(715\) −6.19615 + 10.7321i −0.231723 + 0.401356i
\(716\) 44.0526 76.3013i 1.64632 2.85151i
\(717\) 0 0
\(718\) 24.7583 + 42.8827i 0.923973 + 1.60037i
\(719\) 39.5885 1.47640 0.738200 0.674582i \(-0.235676\pi\)
0.738200 + 0.674582i \(0.235676\pi\)
\(720\) 0 0
\(721\) 9.46410 0.352462
\(722\) −17.6603 30.5885i −0.657247 1.13838i
\(723\) 0 0
\(724\) −53.3731 + 92.4449i −1.98359 + 3.43569i
\(725\) 3.59808 6.23205i 0.133629 0.231453i
\(726\) 0 0
\(727\) −6.19615 10.7321i −0.229803 0.398030i 0.727947 0.685633i \(-0.240475\pi\)
−0.957749 + 0.287604i \(0.907141\pi\)
\(728\) −65.5692 −2.43016
\(729\) 0 0
\(730\) −26.3923 −0.976823
\(731\) 3.73205 + 6.46410i 0.138035 + 0.239083i
\(732\) 0 0
\(733\) 3.39230 5.87564i 0.125298 0.217022i −0.796552 0.604571i \(-0.793345\pi\)
0.921849 + 0.387549i \(0.126678\pi\)
\(734\) −42.5885 + 73.7654i −1.57197 + 2.72273i
\(735\) 0 0
\(736\) 37.8564 + 65.5692i 1.39541 + 2.41691i
\(737\) 7.85641 0.289394
\(738\) 0 0
\(739\) 15.5359 0.571497 0.285749 0.958305i \(-0.407758\pi\)
0.285749 + 0.958305i \(0.407758\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) −5.66025 + 9.80385i −0.207794 + 0.359911i
\(743\) 22.9545 39.7583i 0.842118 1.45859i −0.0459822 0.998942i \(-0.514642\pi\)
0.888100 0.459649i \(-0.152025\pi\)
\(744\) 0 0
\(745\) 4.00000 + 6.92820i 0.146549 + 0.253830i
\(746\) 49.3205 1.80575
\(747\) 0 0
\(748\) −9.07180 −0.331698
\(749\) −9.80385 16.9808i −0.358225 0.620464i
\(750\) 0 0
\(751\) −3.60770 + 6.24871i −0.131647 + 0.228019i −0.924311 0.381639i \(-0.875360\pi\)
0.792665 + 0.609658i \(0.208693\pi\)
\(752\) 39.3205 68.1051i 1.43387 2.48354i
\(753\) 0 0
\(754\) 53.7128 + 93.0333i 1.95611 + 3.38807i
\(755\) −15.3923 −0.560183
\(756\) 0 0
\(757\) 53.1769 1.93275 0.966374 0.257141i \(-0.0827805\pi\)
0.966374 + 0.257141i \(0.0827805\pi\)
\(758\) −25.1244 43.5167i −0.912558 1.58060i
\(759\) 0 0
\(760\) −11.6603 + 20.1962i −0.422962 + 0.732591i
\(761\) 17.7224 30.6962i 0.642438 1.11273i −0.342449 0.939536i \(-0.611256\pi\)
0.984887 0.173198i \(-0.0554102\pi\)
\(762\) 0 0
\(763\) −12.6340 21.8827i −0.457381 0.792206i
\(764\) 88.1051 3.18753
\(765\) 0 0
\(766\) −25.8564 −0.934230
\(767\) −32.0526 55.5167i −1.15735 2.00459i
\(768\) 0 0
\(769\) 8.23205 14.2583i 0.296855 0.514169i −0.678559 0.734545i \(-0.737395\pi\)
0.975415 + 0.220377i \(0.0707287\pi\)
\(770\) 3.92820 6.80385i 0.141563 0.245194i
\(771\) 0 0
\(772\) 23.8564 + 41.3205i 0.858611 + 1.48716i
\(773\) −43.5167 −1.56519 −0.782593 0.622534i \(-0.786103\pi\)
−0.782593 + 0.622534i \(0.786103\pi\)
\(774\) 0 0
\(775\) −3.00000 −0.107763
\(776\) 36.2487 + 62.7846i 1.30125 + 2.25384i
\(777\) 0 0
\(778\) 28.0526 48.5885i 1.00573 1.74198i
\(779\) 3.93782 6.82051i 0.141087 0.244370i
\(780\) 0 0
\(781\) −0.303848 0.526279i −0.0108725 0.0188318i
\(782\) −6.92820 −0.247752
\(783\) 0 0
\(784\) −80.4974 −2.87491
\(785\) −2.56218 4.43782i −0.0914480 0.158393i
\(786\) 0 0
\(787\) 4.97372 8.61474i 0.177294 0.307082i −0.763659 0.645620i \(-0.776599\pi\)