Properties

Label 1960.2.q.y.961.2
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.21913473024.16
Defining polynomial: \(x^{8} - 2 x^{7} + 11 x^{6} - 2 x^{5} + 51 x^{4} + 162 x^{2} + 112 x + 196\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.2
Root \(-0.591990 - 1.02536i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.y.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.591990 - 1.02536i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.799096 - 1.38408i) q^{9} +O(q^{10})\) \(q+(-0.591990 - 1.02536i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.799096 - 1.38408i) q^{9} +(-0.115117 - 0.199389i) q^{11} +2.27259 q^{13} -1.18398 q^{15} +(3.26639 + 5.65755i) q^{17} +(-0.130093 + 0.225328i) q^{19} +(4.43539 - 7.68233i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.44417 q^{27} +5.42662 q^{29} +(2.43539 + 4.21822i) q^{31} +(-0.136296 + 0.236072i) q^{33} +(0.577014 - 0.999417i) q^{37} +(-1.34535 - 2.33022i) q^{39} -4.43337 q^{41} +4.17723 q^{43} +(-0.799096 - 1.38408i) q^{45} +(0.461897 - 0.800028i) q^{47} +(3.86734 - 6.69843i) q^{51} +(1.06743 + 1.84885i) q^{53} -0.230234 q^{55} +0.308055 q^{57} +(-2.53553 - 4.39167i) q^{59} +(4.44417 - 7.69752i) q^{61} +(1.13630 - 1.96812i) q^{65} +(-4.07984 - 7.06649i) q^{67} -10.5028 q^{69} -9.06556 q^{71} +(3.00478 + 5.20442i) q^{73} +(-0.591990 + 1.02536i) q^{75} +(-0.0564558 + 0.0977843i) q^{79} +(0.825600 + 1.42998i) q^{81} -8.72065 q^{83} +6.53278 q^{85} +(-3.21250 - 5.56422i) q^{87} +(7.95852 - 13.7846i) q^{89} +(2.88345 - 4.99429i) q^{93} +(0.130093 + 0.225328i) q^{95} -4.29565 q^{97} -0.367959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 4q^{5} - 6q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{5} - 6q^{9} - 2q^{11} - 20q^{13} + 4q^{15} + 6q^{17} + 4q^{23} - 4q^{25} - 28q^{27} - 4q^{29} - 12q^{31} + 18q^{33} - 14q^{39} - 24q^{41} - 16q^{43} + 6q^{45} - 2q^{47} - 2q^{51} + 4q^{53} - 4q^{55} - 16q^{57} + 8q^{59} + 20q^{61} - 10q^{65} + 8q^{67} - 48q^{69} + 8q^{71} + 16q^{73} + 2q^{75} - 22q^{79} + 20q^{81} - 72q^{83} + 12q^{85} - 18q^{87} + 40q^{89} + 32q^{93} - 52q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.591990 1.02536i −0.341785 0.591990i 0.642979 0.765884i \(-0.277698\pi\)
−0.984764 + 0.173894i \(0.944365\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.799096 1.38408i 0.266365 0.461359i
\(10\) 0 0
\(11\) −0.115117 0.199389i −0.0347091 0.0601179i 0.848149 0.529758i \(-0.177717\pi\)
−0.882858 + 0.469640i \(0.844384\pi\)
\(12\) 0 0
\(13\) 2.27259 0.630304 0.315152 0.949041i \(-0.397945\pi\)
0.315152 + 0.949041i \(0.397945\pi\)
\(14\) 0 0
\(15\) −1.18398 −0.305702
\(16\) 0 0
\(17\) 3.26639 + 5.65755i 0.792216 + 1.37216i 0.924592 + 0.380958i \(0.124406\pi\)
−0.132376 + 0.991200i \(0.542261\pi\)
\(18\) 0 0
\(19\) −0.130093 + 0.225328i −0.0298454 + 0.0516937i −0.880562 0.473930i \(-0.842835\pi\)
0.850717 + 0.525624i \(0.176168\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.43539 7.68233i 0.924843 1.60188i 0.133030 0.991112i \(-0.457529\pi\)
0.791813 0.610764i \(-0.209137\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −5.44417 −1.04773
\(28\) 0 0
\(29\) 5.42662 1.00770 0.503849 0.863792i \(-0.331917\pi\)
0.503849 + 0.863792i \(0.331917\pi\)
\(30\) 0 0
\(31\) 2.43539 + 4.21822i 0.437409 + 0.757615i 0.997489 0.0708235i \(-0.0225627\pi\)
−0.560079 + 0.828439i \(0.689229\pi\)
\(32\) 0 0
\(33\) −0.136296 + 0.236072i −0.0237261 + 0.0410949i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.577014 0.999417i 0.0948605 0.164303i −0.814690 0.579897i \(-0.803093\pi\)
0.909550 + 0.415594i \(0.136426\pi\)
\(38\) 0 0
\(39\) −1.34535 2.33022i −0.215429 0.373133i
\(40\) 0 0
\(41\) −4.43337 −0.692377 −0.346188 0.938165i \(-0.612524\pi\)
−0.346188 + 0.938165i \(0.612524\pi\)
\(42\) 0 0
\(43\) 4.17723 0.637021 0.318511 0.947919i \(-0.396817\pi\)
0.318511 + 0.947919i \(0.396817\pi\)
\(44\) 0 0
\(45\) −0.799096 1.38408i −0.119122 0.206326i
\(46\) 0 0
\(47\) 0.461897 0.800028i 0.0673745 0.116696i −0.830370 0.557212i \(-0.811871\pi\)
0.897745 + 0.440516i \(0.145204\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3.86734 6.69843i 0.541536 0.937967i
\(52\) 0 0
\(53\) 1.06743 + 1.84885i 0.146623 + 0.253959i 0.929977 0.367617i \(-0.119826\pi\)
−0.783354 + 0.621576i \(0.786493\pi\)
\(54\) 0 0
\(55\) −0.230234 −0.0310448
\(56\) 0 0
\(57\) 0.308055 0.0408029
\(58\) 0 0
\(59\) −2.53553 4.39167i −0.330098 0.571747i 0.652432 0.757847i \(-0.273749\pi\)
−0.982531 + 0.186100i \(0.940415\pi\)
\(60\) 0 0
\(61\) 4.44417 7.69752i 0.569017 0.985566i −0.427646 0.903946i \(-0.640657\pi\)
0.996663 0.0816204i \(-0.0260095\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.13630 1.96812i 0.140940 0.244116i
\(66\) 0 0
\(67\) −4.07984 7.06649i −0.498432 0.863309i 0.501567 0.865119i \(-0.332757\pi\)
−0.999998 + 0.00180980i \(0.999424\pi\)
\(68\) 0 0
\(69\) −10.5028 −1.26439
\(70\) 0 0
\(71\) −9.06556 −1.07588 −0.537942 0.842982i \(-0.680798\pi\)
−0.537942 + 0.842982i \(0.680798\pi\)
\(72\) 0 0
\(73\) 3.00478 + 5.20442i 0.351682 + 0.609132i 0.986544 0.163494i \(-0.0522764\pi\)
−0.634862 + 0.772626i \(0.718943\pi\)
\(74\) 0 0
\(75\) −0.591990 + 1.02536i −0.0683571 + 0.118398i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.0564558 + 0.0977843i −0.00635177 + 0.0110016i −0.869184 0.494489i \(-0.835355\pi\)
0.862832 + 0.505491i \(0.168689\pi\)
\(80\) 0 0
\(81\) 0.825600 + 1.42998i 0.0917334 + 0.158887i
\(82\) 0 0
\(83\) −8.72065 −0.957216 −0.478608 0.878029i \(-0.658859\pi\)
−0.478608 + 0.878029i \(0.658859\pi\)
\(84\) 0 0
\(85\) 6.53278 0.708579
\(86\) 0 0
\(87\) −3.21250 5.56422i −0.344416 0.596547i
\(88\) 0 0
\(89\) 7.95852 13.7846i 0.843601 1.46116i −0.0432288 0.999065i \(-0.513764\pi\)
0.886830 0.462095i \(-0.152902\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.88345 4.99429i 0.299000 0.517884i
\(94\) 0 0
\(95\) 0.130093 + 0.225328i 0.0133473 + 0.0231181i
\(96\) 0 0
\(97\) −4.29565 −0.436157 −0.218079 0.975931i \(-0.569979\pi\)
−0.218079 + 0.975931i \(0.569979\pi\)
\(98\) 0 0
\(99\) −0.367959 −0.0369812
\(100\) 0 0
\(101\) 3.69356 + 6.39743i 0.367523 + 0.636568i 0.989178 0.146723i \(-0.0468726\pi\)
−0.621655 + 0.783291i \(0.713539\pi\)
\(102\) 0 0
\(103\) −5.29032 + 9.16311i −0.521271 + 0.902868i 0.478423 + 0.878130i \(0.341209\pi\)
−0.999694 + 0.0247384i \(0.992125\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.73306 11.6620i 0.650910 1.12741i −0.331993 0.943282i \(-0.607721\pi\)
0.982903 0.184127i \(-0.0589456\pi\)
\(108\) 0 0
\(109\) −4.25284 7.36614i −0.407348 0.705548i 0.587243 0.809410i \(-0.300213\pi\)
−0.994592 + 0.103862i \(0.966880\pi\)
\(110\) 0 0
\(111\) −1.36634 −0.129688
\(112\) 0 0
\(113\) 18.3968 1.73063 0.865313 0.501232i \(-0.167120\pi\)
0.865313 + 0.501232i \(0.167120\pi\)
\(114\) 0 0
\(115\) −4.43539 7.68233i −0.413603 0.716381i
\(116\) 0 0
\(117\) 1.81602 3.14544i 0.167891 0.290796i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.47350 9.48037i 0.497591 0.861852i
\(122\) 0 0
\(123\) 2.62451 + 4.54579i 0.236644 + 0.409880i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 8.41032 0.746295 0.373147 0.927772i \(-0.378279\pi\)
0.373147 + 0.927772i \(0.378279\pi\)
\(128\) 0 0
\(129\) −2.47287 4.28314i −0.217724 0.377110i
\(130\) 0 0
\(131\) −0.891086 + 1.54341i −0.0778546 + 0.134848i −0.902324 0.431058i \(-0.858140\pi\)
0.824470 + 0.565906i \(0.191474\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.72208 + 4.71479i −0.234280 + 0.405784i
\(136\) 0 0
\(137\) 5.65685 + 9.79796i 0.483298 + 0.837096i 0.999816 0.0191800i \(-0.00610555\pi\)
−0.516518 + 0.856276i \(0.672772\pi\)
\(138\) 0 0
\(139\) −15.4390 −1.30952 −0.654761 0.755836i \(-0.727231\pi\)
−0.654761 + 0.755836i \(0.727231\pi\)
\(140\) 0 0
\(141\) −1.09375 −0.0921105
\(142\) 0 0
\(143\) −0.261614 0.453129i −0.0218773 0.0378926i
\(144\) 0 0
\(145\) 2.71331 4.69959i 0.225328 0.390280i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.6406 + 20.1620i −0.953631 + 1.65174i −0.216161 + 0.976358i \(0.569354\pi\)
−0.737470 + 0.675380i \(0.763980\pi\)
\(150\) 0 0
\(151\) −11.1699 19.3468i −0.908992 1.57442i −0.815467 0.578804i \(-0.803520\pi\)
−0.0935251 0.995617i \(-0.529814\pi\)
\(152\) 0 0
\(153\) 10.4406 0.844076
\(154\) 0 0
\(155\) 4.87079 0.391231
\(156\) 0 0
\(157\) −1.76301 3.05363i −0.140704 0.243706i 0.787058 0.616879i \(-0.211603\pi\)
−0.927762 + 0.373173i \(0.878270\pi\)
\(158\) 0 0
\(159\) 1.26382 2.18900i 0.100227 0.173599i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.12610 14.0748i 0.636485 1.10242i −0.349714 0.936857i \(-0.613721\pi\)
0.986198 0.165568i \(-0.0529456\pi\)
\(164\) 0 0
\(165\) 0.136296 + 0.236072i 0.0106107 + 0.0183782i
\(166\) 0 0
\(167\) 3.99714 0.309308 0.154654 0.987969i \(-0.450574\pi\)
0.154654 + 0.987969i \(0.450574\pi\)
\(168\) 0 0
\(169\) −7.83532 −0.602717
\(170\) 0 0
\(171\) 0.207914 + 0.360117i 0.0158996 + 0.0275389i
\(172\) 0 0
\(173\) 8.81070 15.2606i 0.669865 1.16024i −0.308077 0.951361i \(-0.599685\pi\)
0.977942 0.208878i \(-0.0669813\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.00202 + 5.19965i −0.225646 + 0.390830i
\(178\) 0 0
\(179\) −12.6406 21.8941i −0.944799 1.63644i −0.756153 0.654395i \(-0.772923\pi\)
−0.188646 0.982045i \(-0.560410\pi\)
\(180\) 0 0
\(181\) −18.4950 −1.37473 −0.687363 0.726315i \(-0.741232\pi\)
−0.687363 + 0.726315i \(0.741232\pi\)
\(182\) 0 0
\(183\) −10.5236 −0.777927
\(184\) 0 0
\(185\) −0.577014 0.999417i −0.0424229 0.0734786i
\(186\) 0 0
\(187\) 0.752035 1.30256i 0.0549942 0.0952528i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.93289 + 17.2043i −0.718719 + 1.24486i 0.242788 + 0.970079i \(0.421938\pi\)
−0.961508 + 0.274779i \(0.911395\pi\)
\(192\) 0 0
\(193\) 5.71676 + 9.90172i 0.411501 + 0.712741i 0.995054 0.0993341i \(-0.0316712\pi\)
−0.583553 + 0.812075i \(0.698338\pi\)
\(194\) 0 0
\(195\) −2.69070 −0.192685
\(196\) 0 0
\(197\) −4.56273 −0.325081 −0.162541 0.986702i \(-0.551969\pi\)
−0.162541 + 0.986702i \(0.551969\pi\)
\(198\) 0 0
\(199\) −7.22146 12.5079i −0.511916 0.886664i −0.999905 0.0138143i \(-0.995603\pi\)
0.487989 0.872850i \(-0.337731\pi\)
\(200\) 0 0
\(201\) −4.83045 + 8.36658i −0.340713 + 0.590133i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.21669 + 3.83941i −0.154820 + 0.268156i
\(206\) 0 0
\(207\) −7.08861 12.2778i −0.492693 0.853369i
\(208\) 0 0
\(209\) 0.0599037 0.00414363
\(210\) 0 0
\(211\) 6.63651 0.456876 0.228438 0.973558i \(-0.426638\pi\)
0.228438 + 0.973558i \(0.426638\pi\)
\(212\) 0 0
\(213\) 5.36672 + 9.29543i 0.367721 + 0.636912i
\(214\) 0 0
\(215\) 2.08861 3.61758i 0.142442 0.246717i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 3.55759 6.16193i 0.240400 0.416385i
\(220\) 0 0
\(221\) 7.42317 + 12.8573i 0.499337 + 0.864876i
\(222\) 0 0
\(223\) 20.3325 1.36156 0.680782 0.732486i \(-0.261640\pi\)
0.680782 + 0.732486i \(0.261640\pi\)
\(224\) 0 0
\(225\) −1.59819 −0.106546
\(226\) 0 0
\(227\) 11.9656 + 20.7250i 0.794185 + 1.37557i 0.923355 + 0.383946i \(0.125435\pi\)
−0.129171 + 0.991622i \(0.541231\pi\)
\(228\) 0 0
\(229\) 1.29767 2.24763i 0.0857523 0.148527i −0.819959 0.572422i \(-0.806004\pi\)
0.905712 + 0.423895i \(0.139337\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.58189 13.1322i 0.496706 0.860320i −0.503287 0.864120i \(-0.667876\pi\)
0.999993 + 0.00379927i \(0.00120935\pi\)
\(234\) 0 0
\(235\) −0.461897 0.800028i −0.0301308 0.0521881i
\(236\) 0 0
\(237\) 0.133685 0.00868377
\(238\) 0 0
\(239\) 10.5656 0.683431 0.341716 0.939803i \(-0.388992\pi\)
0.341716 + 0.939803i \(0.388992\pi\)
\(240\) 0 0
\(241\) 9.83808 + 17.0401i 0.633726 + 1.09765i 0.986783 + 0.162044i \(0.0518088\pi\)
−0.353057 + 0.935602i \(0.614858\pi\)
\(242\) 0 0
\(243\) −7.18875 + 12.4513i −0.461159 + 0.798750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.295648 + 0.512078i −0.0188117 + 0.0325828i
\(248\) 0 0
\(249\) 5.16254 + 8.94178i 0.327163 + 0.566662i
\(250\) 0 0
\(251\) 25.0498 1.58113 0.790564 0.612380i \(-0.209788\pi\)
0.790564 + 0.612380i \(0.209788\pi\)
\(252\) 0 0
\(253\) −2.04236 −0.128402
\(254\) 0 0
\(255\) −3.86734 6.69843i −0.242182 0.419472i
\(256\) 0 0
\(257\) 0.857500 1.48523i 0.0534894 0.0926464i −0.838041 0.545607i \(-0.816299\pi\)
0.891530 + 0.452961i \(0.149632\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 4.33639 7.51085i 0.268416 0.464910i
\(262\) 0 0
\(263\) 11.0587 + 19.1542i 0.681906 + 1.18110i 0.974398 + 0.224828i \(0.0721821\pi\)
−0.292492 + 0.956268i \(0.594485\pi\)
\(264\) 0 0
\(265\) 2.13487 0.131144
\(266\) 0 0
\(267\) −18.8454 −1.15332
\(268\) 0 0
\(269\) −15.9630 27.6488i −0.973283 1.68578i −0.685488 0.728084i \(-0.740411\pi\)
−0.287796 0.957692i \(-0.592922\pi\)
\(270\) 0 0
\(271\) −12.8883 + 22.3232i −0.782910 + 1.35604i 0.147329 + 0.989088i \(0.452932\pi\)
−0.930239 + 0.366953i \(0.880401\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.115117 + 0.199389i −0.00694182 + 0.0120236i
\(276\) 0 0
\(277\) 4.00877 + 6.94340i 0.240864 + 0.417188i 0.960961 0.276685i \(-0.0892360\pi\)
−0.720097 + 0.693874i \(0.755903\pi\)
\(278\) 0 0
\(279\) 7.78445 0.466043
\(280\) 0 0
\(281\) −3.13207 −0.186844 −0.0934218 0.995627i \(-0.529781\pi\)
−0.0934218 + 0.995627i \(0.529781\pi\)
\(282\) 0 0
\(283\) 1.58524 + 2.74571i 0.0942325 + 0.163216i 0.909288 0.416167i \(-0.136627\pi\)
−0.815056 + 0.579383i \(0.803294\pi\)
\(284\) 0 0
\(285\) 0.154027 0.266783i 0.00912380 0.0158029i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −12.8386 + 22.2371i −0.755212 + 1.30806i
\(290\) 0 0
\(291\) 2.54298 + 4.40457i 0.149072 + 0.258200i
\(292\) 0 0
\(293\) 17.5264 1.02390 0.511952 0.859014i \(-0.328923\pi\)
0.511952 + 0.859014i \(0.328923\pi\)
\(294\) 0 0
\(295\) −5.07107 −0.295249
\(296\) 0 0
\(297\) 0.626717 + 1.08550i 0.0363658 + 0.0629874i
\(298\) 0 0
\(299\) 10.0798 17.4588i 0.582932 1.00967i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 4.37310 7.57443i 0.251228 0.435139i
\(304\) 0 0
\(305\) −4.44417 7.69752i −0.254472 0.440759i
\(306\) 0 0
\(307\) −2.11063 −0.120460 −0.0602300 0.998185i \(-0.519183\pi\)
−0.0602300 + 0.998185i \(0.519183\pi\)
\(308\) 0 0
\(309\) 12.5273 0.712651
\(310\) 0 0
\(311\) 10.4075 + 18.0263i 0.590153 + 1.02217i 0.994211 + 0.107442i \(0.0342659\pi\)
−0.404058 + 0.914733i \(0.632401\pi\)
\(312\) 0 0
\(313\) −10.6930 + 18.5208i −0.604405 + 1.04686i 0.387741 + 0.921769i \(0.373256\pi\)
−0.992145 + 0.125091i \(0.960078\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.74547 + 13.4155i −0.435029 + 0.753492i −0.997298 0.0734623i \(-0.976595\pi\)
0.562269 + 0.826954i \(0.309928\pi\)
\(318\) 0 0
\(319\) −0.624697 1.08201i −0.0349763 0.0605807i
\(320\) 0 0
\(321\) −15.9436 −0.889886
\(322\) 0 0
\(323\) −1.69974 −0.0945760
\(324\) 0 0
\(325\) −1.13630 1.96812i −0.0630304 0.109172i
\(326\) 0 0
\(327\) −5.03528 + 8.72135i −0.278451 + 0.482292i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.26180 7.38165i 0.234250 0.405732i −0.724805 0.688954i \(-0.758070\pi\)
0.959054 + 0.283222i \(0.0914033\pi\)
\(332\) 0 0
\(333\) −0.922179 1.59726i −0.0505351 0.0875294i
\(334\) 0 0
\(335\) −8.15968 −0.445811
\(336\) 0 0
\(337\) −18.1246 −0.987309 −0.493655 0.869658i \(-0.664339\pi\)
−0.493655 + 0.869658i \(0.664339\pi\)
\(338\) 0 0
\(339\) −10.8907 18.8633i −0.591503 1.02451i
\(340\) 0 0
\(341\) 0.560711 0.971179i 0.0303642 0.0525923i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −5.25141 + 9.09571i −0.282727 + 0.489697i
\(346\) 0 0
\(347\) −2.05113 3.55266i −0.110110 0.190717i 0.805704 0.592318i \(-0.201787\pi\)
−0.915815 + 0.401601i \(0.868454\pi\)
\(348\) 0 0
\(349\) 8.67850 0.464549 0.232275 0.972650i \(-0.425383\pi\)
0.232275 + 0.972650i \(0.425383\pi\)
\(350\) 0 0
\(351\) −12.3724 −0.660388
\(352\) 0 0
\(353\) 15.0581 + 26.0814i 0.801462 + 1.38817i 0.918653 + 0.395064i \(0.129278\pi\)
−0.117191 + 0.993109i \(0.537389\pi\)
\(354\) 0 0
\(355\) −4.53278 + 7.85100i −0.240575 + 0.416688i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.1421 + 31.4231i −0.957505 + 1.65845i −0.228977 + 0.973432i \(0.573538\pi\)
−0.728528 + 0.685016i \(0.759795\pi\)
\(360\) 0 0
\(361\) 9.46615 + 16.3959i 0.498219 + 0.862940i
\(362\) 0 0
\(363\) −12.9610 −0.680277
\(364\) 0 0
\(365\) 6.00955 0.314554
\(366\) 0 0
\(367\) −5.35574 9.27641i −0.279567 0.484225i 0.691710 0.722175i \(-0.256858\pi\)
−0.971277 + 0.237951i \(0.923524\pi\)
\(368\) 0 0
\(369\) −3.54269 + 6.13612i −0.184425 + 0.319434i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −2.82167 + 4.88728i −0.146101 + 0.253054i −0.929783 0.368108i \(-0.880006\pi\)
0.783682 + 0.621162i \(0.213339\pi\)
\(374\) 0 0
\(375\) 0.591990 + 1.02536i 0.0305702 + 0.0529492i
\(376\) 0 0
\(377\) 12.3325 0.635156
\(378\) 0 0
\(379\) −1.59944 −0.0821575 −0.0410787 0.999156i \(-0.513079\pi\)
−0.0410787 + 0.999156i \(0.513079\pi\)
\(380\) 0 0
\(381\) −4.97882 8.62357i −0.255073 0.441799i
\(382\) 0 0
\(383\) −14.4447 + 25.0189i −0.738089 + 1.27841i 0.215266 + 0.976555i \(0.430938\pi\)
−0.953355 + 0.301852i \(0.902395\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.33801 5.78160i 0.169680 0.293895i
\(388\) 0 0
\(389\) 11.7613 + 20.3712i 0.596323 + 1.03286i 0.993359 + 0.115058i \(0.0367055\pi\)
−0.397036 + 0.917803i \(0.629961\pi\)
\(390\) 0 0
\(391\) 57.9509 2.93070
\(392\) 0 0
\(393\) 2.11006 0.106438
\(394\) 0 0
\(395\) 0.0564558 + 0.0977843i 0.00284060 + 0.00492006i
\(396\) 0 0
\(397\) −8.29032 + 14.3593i −0.416079 + 0.720671i −0.995541 0.0943288i \(-0.969930\pi\)
0.579462 + 0.814999i \(0.303263\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.760807 1.31776i 0.0379929 0.0658056i −0.846404 0.532542i \(-0.821237\pi\)
0.884397 + 0.466736i \(0.154570\pi\)
\(402\) 0 0
\(403\) 5.53466 + 9.58630i 0.275701 + 0.477528i
\(404\) 0 0
\(405\) 1.65120 0.0820488
\(406\) 0 0
\(407\) −0.265697 −0.0131701
\(408\) 0 0
\(409\) −2.71464 4.70189i −0.134230 0.232493i 0.791073 0.611722i \(-0.209523\pi\)
−0.925303 + 0.379228i \(0.876189\pi\)
\(410\) 0 0
\(411\) 6.69760 11.6006i 0.330368 0.572214i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4.36033 + 7.55231i −0.214040 + 0.370728i
\(416\) 0 0
\(417\) 9.13974 + 15.8305i 0.447575 + 0.775223i
\(418\) 0 0
\(419\) −12.4199 −0.606750 −0.303375 0.952871i \(-0.598114\pi\)
−0.303375 + 0.952871i \(0.598114\pi\)
\(420\) 0 0
\(421\) −20.6804 −1.00790 −0.503951 0.863732i \(-0.668121\pi\)
−0.503951 + 0.863732i \(0.668121\pi\)
\(422\) 0 0
\(423\) −0.738200 1.27860i −0.0358925 0.0621676i
\(424\) 0 0
\(425\) 3.26639 5.65755i 0.158443 0.274432i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.309746 + 0.536496i −0.0149547 + 0.0259023i
\(430\) 0 0
\(431\) 15.8076 + 27.3795i 0.761424 + 1.31883i 0.942117 + 0.335286i \(0.108833\pi\)
−0.180692 + 0.983540i \(0.557834\pi\)
\(432\) 0 0
\(433\) 31.1247 1.49576 0.747880 0.663834i \(-0.231072\pi\)
0.747880 + 0.663834i \(0.231072\pi\)
\(434\) 0 0
\(435\) −6.42501 −0.308055
\(436\) 0 0
\(437\) 1.15403 + 1.99883i 0.0552046 + 0.0956172i
\(438\) 0 0
\(439\) 0.122199 0.211655i 0.00583223 0.0101017i −0.863095 0.505042i \(-0.831477\pi\)
0.868927 + 0.494941i \(0.164810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.72741 2.99196i 0.0820716 0.142152i −0.822068 0.569389i \(-0.807180\pi\)
0.904140 + 0.427237i \(0.140513\pi\)
\(444\) 0 0
\(445\) −7.95852 13.7846i −0.377270 0.653451i
\(446\) 0 0
\(447\) 27.5643 1.30375
\(448\) 0 0
\(449\) −15.5329 −0.733044 −0.366522 0.930409i \(-0.619452\pi\)
−0.366522 + 0.930409i \(0.619452\pi\)
\(450\) 0 0
\(451\) 0.510357 + 0.883964i 0.0240318 + 0.0416243i
\(452\) 0 0
\(453\) −13.2249 + 22.9062i −0.621360 + 1.07623i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.26896 9.12610i 0.246471 0.426901i −0.716073 0.698026i \(-0.754062\pi\)
0.962544 + 0.271124i \(0.0873955\pi\)
\(458\) 0 0
\(459\) −17.7828 30.8007i −0.830028 1.43765i
\(460\) 0 0
\(461\) −5.98972 −0.278969 −0.139485 0.990224i \(-0.544545\pi\)
−0.139485 + 0.990224i \(0.544545\pi\)
\(462\) 0 0
\(463\) −33.3601 −1.55038 −0.775188 0.631731i \(-0.782345\pi\)
−0.775188 + 0.631731i \(0.782345\pi\)
\(464\) 0 0
\(465\) −2.88345 4.99429i −0.133717 0.231605i
\(466\) 0 0
\(467\) 9.85379 17.0673i 0.455979 0.789779i −0.542765 0.839885i \(-0.682623\pi\)
0.998744 + 0.0501059i \(0.0159559\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.08737 + 3.61543i −0.0961810 + 0.166590i
\(472\) 0 0
\(473\) −0.480870 0.832892i −0.0221104 0.0382964i
\(474\) 0 0
\(475\) 0.260186 0.0119382
\(476\) 0 0
\(477\) 3.41193 0.156222
\(478\) 0 0
\(479\) 0.162800 + 0.281978i 0.00743853 + 0.0128839i 0.869721 0.493544i \(-0.164299\pi\)
−0.862282 + 0.506428i \(0.830966\pi\)
\(480\) 0 0
\(481\) 1.31132 2.27127i 0.0597909 0.103561i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.14782 + 3.72014i −0.0975277 + 0.168923i
\(486\) 0 0
\(487\) 8.46021 + 14.6535i 0.383369 + 0.664014i 0.991541 0.129791i \(-0.0414306\pi\)
−0.608173 + 0.793805i \(0.708097\pi\)
\(488\) 0 0
\(489\) −19.2423 −0.870165
\(490\) 0 0
\(491\) 15.0203 0.677859 0.338929 0.940812i \(-0.389935\pi\)
0.338929 + 0.940812i \(0.389935\pi\)
\(492\) 0 0
\(493\) 17.7255 + 30.7014i 0.798314 + 1.38272i
\(494\) 0 0
\(495\) −0.183979 + 0.318662i −0.00826926 + 0.0143228i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −20.5215 + 35.5443i −0.918670 + 1.59118i −0.117233 + 0.993104i \(0.537402\pi\)
−0.801437 + 0.598079i \(0.795931\pi\)
\(500\) 0 0
\(501\) −2.36627 4.09850i −0.105717 0.183107i
\(502\) 0 0
\(503\) −8.29741 −0.369963 −0.184982 0.982742i \(-0.559223\pi\)
−0.184982 + 0.982742i \(0.559223\pi\)
\(504\) 0 0
\(505\) 7.38712 0.328722
\(506\) 0 0
\(507\) 4.63843 + 8.03400i 0.206000 + 0.356802i
\(508\) 0 0
\(509\) 4.35633 7.54538i 0.193091 0.334443i −0.753182 0.657812i \(-0.771482\pi\)
0.946273 + 0.323369i \(0.104815\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.708248 1.22672i 0.0312699 0.0541611i
\(514\) 0 0
\(515\) 5.29032 + 9.16311i 0.233120 + 0.403775i
\(516\) 0 0
\(517\) −0.212689 −0.00935404
\(518\) 0 0
\(519\) −20.8634 −0.915800
\(520\) 0 0
\(521\) −13.5528 23.4742i −0.593760 1.02842i −0.993721 0.111890i \(-0.964310\pi\)
0.399961 0.916532i \(-0.369024\pi\)
\(522\) 0 0
\(523\) −0.685928 + 1.18806i −0.0299935 + 0.0519503i −0.880633 0.473800i \(-0.842882\pi\)
0.850639 + 0.525750i \(0.176215\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15.9099 + 27.5567i −0.693045 + 1.20039i
\(528\) 0 0
\(529\) −27.8454 48.2297i −1.21067 2.09694i
\(530\) 0 0
\(531\) −8.10454 −0.351707
\(532\) 0 0
\(533\) −10.0753 −0.436408
\(534\) 0 0
\(535\) −6.73306 11.6620i −0.291096 0.504192i
\(536\) 0 0
\(537\) −14.9662 + 25.9221i −0.645837 + 1.11862i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −4.28279 + 7.41802i −0.184132 + 0.318925i −0.943284 0.331988i \(-0.892281\pi\)
0.759152 + 0.650913i \(0.225614\pi\)
\(542\) 0 0
\(543\) 10.9489 + 18.9640i 0.469861 + 0.813823i
\(544\) 0 0
\(545\) −8.50568 −0.364343
\(546\) 0 0
\(547\) 44.2056 1.89009 0.945046 0.326936i \(-0.106016\pi\)
0.945046 + 0.326936i \(0.106016\pi\)
\(548\) 0 0
\(549\) −7.10263 12.3021i −0.303133 0.525042i
\(550\) 0 0
\(551\) −0.705966 + 1.22277i −0.0300751 + 0.0520917i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.683172 + 1.18329i −0.0289991 + 0.0502278i
\(556\) 0 0
\(557\) 6.66926 + 11.5515i 0.282586 + 0.489453i 0.972021 0.234895i \(-0.0754745\pi\)
−0.689435 + 0.724347i \(0.742141\pi\)
\(558\) 0 0
\(559\) 9.49313 0.401517
\(560\) 0 0
\(561\) −1.78079 −0.0751849
\(562\) 0 0
\(563\) 14.8660 + 25.7487i 0.626528 + 1.08518i 0.988243 + 0.152889i \(0.0488578\pi\)
−0.361716 + 0.932288i \(0.617809\pi\)
\(564\) 0 0
\(565\) 9.19841 15.9321i 0.386980 0.670269i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11.7930 + 20.4260i −0.494387 + 0.856303i −0.999979 0.00646948i \(-0.997941\pi\)
0.505592 + 0.862773i \(0.331274\pi\)
\(570\) 0 0
\(571\) −16.3217 28.2700i −0.683042 1.18306i −0.974048 0.226342i \(-0.927323\pi\)
0.291006 0.956721i \(-0.406010\pi\)
\(572\) 0 0
\(573\) 23.5207 0.982591
\(574\) 0 0
\(575\) −8.87079 −0.369937
\(576\) 0 0
\(577\) −14.4098 24.9584i −0.599886 1.03903i −0.992837 0.119474i \(-0.961879\pi\)
0.392951 0.919559i \(-0.371454\pi\)
\(578\) 0 0
\(579\) 6.76852 11.7234i 0.281290 0.487209i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.245760 0.425669i 0.0101783 0.0176294i
\(584\) 0 0
\(585\) −1.81602 3.14544i −0.0750832 0.130048i
\(586\) 0 0
\(587\) 1.82205 0.0752039 0.0376019 0.999293i \(-0.488028\pi\)
0.0376019 + 0.999293i \(0.488028\pi\)
\(588\) 0 0
\(589\) −1.26731 −0.0522186
\(590\) 0 0
\(591\) 2.70109 + 4.67842i 0.111108 + 0.192445i
\(592\) 0 0
\(593\) 15.4684 26.7921i 0.635212 1.10022i −0.351258 0.936279i \(-0.614246\pi\)
0.986470 0.163941i \(-0.0524207\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.55006 + 14.8091i −0.349931 + 0.606098i
\(598\) 0 0
\(599\) 16.1456 + 27.9650i 0.659691 + 1.14262i 0.980696 + 0.195540i \(0.0626460\pi\)
−0.321005 + 0.947077i \(0.604021\pi\)
\(600\) 0 0
\(601\) 25.2829 1.03131 0.515655 0.856797i \(-0.327549\pi\)
0.515655 + 0.856797i \(0.327549\pi\)
\(602\) 0 0
\(603\) −13.0407 −0.531060
\(604\) 0 0
\(605\) −5.47350 9.48037i −0.222529 0.385432i
\(606\) 0 0
\(607\) −4.64426 + 8.04410i −0.188505 + 0.326500i −0.944752 0.327786i \(-0.893697\pi\)
0.756247 + 0.654286i \(0.227031\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.04970 1.81814i 0.0424664 0.0735540i
\(612\) 0 0
\(613\) −20.0305 34.6938i −0.809023 1.40127i −0.913541 0.406746i \(-0.866663\pi\)
0.104518 0.994523i \(-0.466670\pi\)
\(614\) 0 0
\(615\) 5.24902 0.211661
\(616\) 0 0
\(617\) 27.9860 1.12667 0.563336 0.826228i \(-0.309518\pi\)
0.563336 + 0.826228i \(0.309518\pi\)
\(618\) 0 0
\(619\) −22.9024 39.6681i −0.920525 1.59440i −0.798605 0.601856i \(-0.794428\pi\)
−0.121920 0.992540i \(-0.538905\pi\)
\(620\) 0 0
\(621\) −24.1470 + 41.8239i −0.968986 + 1.67833i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −0.0354624 0.0614227i −0.00141623 0.00245299i
\(628\) 0 0
\(629\) 7.53901 0.300600
\(630\) 0 0
\(631\) 22.5847 0.899082 0.449541 0.893260i \(-0.351588\pi\)
0.449541 + 0.893260i \(0.351588\pi\)
\(632\) 0 0
\(633\) −3.92875 6.80479i −0.156154 0.270466i
\(634\) 0 0
\(635\) 4.20516 7.28355i 0.166877 0.289039i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −7.24425 + 12.5474i −0.286578 + 0.496368i
\(640\) 0 0
\(641\) 16.7563 + 29.0227i 0.661832 + 1.14633i 0.980134 + 0.198338i \(0.0635543\pi\)
−0.318301 + 0.947990i \(0.603112\pi\)
\(642\) 0 0
\(643\) −46.4980 −1.83370 −0.916851 0.399231i \(-0.869277\pi\)
−0.916851 + 0.399231i \(0.869277\pi\)
\(644\) 0 0
\(645\) −4.94575 −0.194739
\(646\) 0 0
\(647\) −0.787826 1.36455i −0.0309726 0.0536462i 0.850124 0.526583i \(-0.176527\pi\)
−0.881096 + 0.472937i \(0.843194\pi\)
\(648\) 0 0
\(649\) −0.583767 + 1.01111i −0.0229148 + 0.0396897i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.06556 + 10.5059i −0.237364 + 0.411126i −0.959957 0.280148i \(-0.909617\pi\)
0.722593 + 0.691273i \(0.242950\pi\)
\(654\) 0 0
\(655\) 0.891086 + 1.54341i 0.0348176 + 0.0603059i
\(656\) 0 0
\(657\) 9.60442 0.374704
\(658\) 0 0
\(659\) 35.1682 1.36996 0.684979 0.728563i \(-0.259811\pi\)
0.684979 + 0.728563i \(0.259811\pi\)
\(660\) 0 0
\(661\) −0.812124 1.40664i −0.0315880 0.0547120i 0.849799 0.527106i \(-0.176723\pi\)
−0.881387 + 0.472395i \(0.843390\pi\)
\(662\) 0 0
\(663\) 8.78888 15.2228i 0.341332 0.591204i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 24.0692 41.6891i 0.931963 1.61421i
\(668\) 0 0
\(669\) −12.0366 20.8481i −0.465363 0.806032i
\(670\) 0 0
\(671\) −2.04640 −0.0790003
\(672\) 0 0
\(673\) −24.3194 −0.937443 −0.468721 0.883346i \(-0.655285\pi\)
−0.468721 + 0.883346i \(0.655285\pi\)
\(674\) 0 0
\(675\) 2.72208 + 4.71479i 0.104773 + 0.181472i
\(676\) 0 0
\(677\) 6.07763 10.5268i 0.233582 0.404577i −0.725277 0.688457i \(-0.758288\pi\)
0.958860 + 0.283880i \(0.0916218\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 14.1670 24.5380i 0.542882 0.940299i
\(682\) 0 0
\(683\) 16.2579 + 28.1595i 0.622091 + 1.07749i 0.989096 + 0.147275i \(0.0470501\pi\)
−0.367004 + 0.930219i \(0.619617\pi\)
\(684\) 0 0
\(685\) 11.3137 0.432275
\(686\) 0 0
\(687\) −3.07282 −0.117236
\(688\) 0 0
\(689\) 2.42584 + 4.20168i 0.0924172 + 0.160071i
\(690\) 0 0
\(691\) 10.1656 17.6073i 0.386716 0.669812i −0.605290 0.796005i \(-0.706943\pi\)
0.992006 + 0.126194i \(0.0402761\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.71951 + 13.3706i −0.292818 + 0.507175i
\(696\) 0 0
\(697\) −14.4811 25.0820i −0.548512 0.950050i
\(698\) 0 0
\(699\) −17.9536 −0.679068
\(700\) 0 0
\(701\) 7.35321 0.277727 0.138863 0.990312i \(-0.455655\pi\)
0.138863 + 0.990312i \(0.455655\pi\)
\(702\) 0 0
\(703\) 0.150131 + 0.260034i 0.00566230 + 0.00980738i
\(704\) 0 0
\(705\) −0.546876 + 0.947217i −0.0205965 + 0.0356743i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 5.83188 10.1011i 0.219021 0.379355i −0.735488 0.677538i \(-0.763047\pi\)
0.954509 + 0.298183i \(0.0963805\pi\)
\(710\) 0 0
\(711\) 0.0902272 + 0.156278i 0.00338378 + 0.00586089i
\(712\) 0 0
\(713\) 43.2077 1.61814
\(714\) 0 0
\(715\) −0.523229 −0.0195676
\(716\) 0 0
\(717\) −6.25472 10.8335i −0.233587 0.404584i
\(718\) 0 0
\(719\) −2.84285 + 4.92397i −0.106021 + 0.183633i −0.914155 0.405365i \(-0.867144\pi\)
0.808134 + 0.588998i \(0.200478\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 11.6481 20.1751i 0.433197 0.750319i
\(724\) 0 0
\(725\) −2.71331 4.69959i −0.100770 0.174538i
\(726\) 0 0
\(727\) −18.6873 −0.693074 −0.346537 0.938036i \(-0.612643\pi\)
−0.346537 + 0.938036i \(0.612643\pi\)
\(728\) 0 0
\(729\) 21.9763 0.813936
\(730\) 0 0
\(731\) 13.6444 + 23.6329i 0.504658 + 0.874094i
\(732\) 0 0
\(733\) 0.918469 1.59083i 0.0339244 0.0587588i −0.848565 0.529092i \(-0.822533\pi\)
0.882489 + 0.470333i \(0.155866\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.939319 + 1.62695i −0.0346003 + 0.0599294i
\(738\) 0 0
\(739\) 12.2817 + 21.2725i 0.451789 + 0.782522i 0.998497 0.0548012i \(-0.0174525\pi\)
−0.546708 + 0.837323i \(0.684119\pi\)
\(740\) 0 0
\(741\) 0.700083 0.0257182
\(742\) 0 0
\(743\) −27.1926 −0.997601 −0.498800 0.866717i \(-0.666226\pi\)
−0.498800 + 0.866717i \(0.666226\pi\)
\(744\) 0 0
\(745\) 11.6406 + 20.1620i 0.426477 + 0.738679i
\(746\) 0 0
\(747\) −6.96864 + 12.0700i −0.254969 + 0.441620i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.164228 + 0.284452i −0.00599278 + 0.0103798i −0.869006 0.494801i \(-0.835241\pi\)
0.863013 + 0.505181i \(0.168574\pi\)
\(752\) 0 0
\(753\) −14.8292 25.6849i −0.540406 0.936011i
\(754\) 0 0
\(755\) −22.3398 −0.813027
\(756\) 0 0
\(757\) −48.6331 −1.76760 −0.883801 0.467864i \(-0.845024\pi\)
−0.883801 + 0.467864i \(0.845024\pi\)
\(758\) 0 0
\(759\) 1.20906 + 2.09414i 0.0438859 + 0.0760126i
\(760\) 0 0
\(761\) −4.01127 + 6.94772i −0.145408 + 0.251854i −0.929525 0.368759i \(-0.879783\pi\)
0.784117 + 0.620613i \(0.213116\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 5.22032 9.04186i 0.188741 0.326909i
\(766\) 0 0
\(767\) −5.76224 9.98048i −0.208062 0.360374i
\(768\) 0 0
\(769\) −35.6370 −1.28510 −0.642552 0.766242i \(-0.722124\pi\)
−0.642552 + 0.766242i \(0.722124\pi\)
\(770\) 0 0
\(771\) −2.03053 −0.0731276
\(772\) 0 0
\(773\) 24.7978 + 42.9510i 0.891914 + 1.54484i 0.837579 + 0.546317i \(0.183971\pi\)
0.0543350 + 0.998523i \(0.482696\pi\)
\(774\) 0 0
\(775\) 2.43539 4.21822i 0.0874819 0.151523i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.576751 0.998962i 0.0206642 0.0357915i
\(780\) 0 0
\(781\) 1.04360 + 1.80757i 0.0373430 + 0.0646799i
\(782\) 0 0
\(783\) −29.5434 −1.05580
\(784\) 0 0
\(785\) −3.52603 −0.125849
\(786\) 0 0
\(787\) 10.7217 + 18.5706i 0.382188 + 0.661969i 0.991375 0.131058i \(-0.0418373\pi\)
−0.609187 + 0.793027i \(0.708504\pi\)
\(788\) 0 0
\(789\) 13.0932 22.6781i 0.466131 0.807363i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 10.0998 17.4933i 0.358654 0.621206i
\(794\) 0 0
\(795\) −1.26382 2.18900i −0.0448231 0.0776358i
\(796\) 0 0
\(797\) −35.1429 −1.24482 −0.622412 0.782690i \(-0.713847\pi\)
−0.622412 + 0.782690i \(0.713847\pi\)
\(798\) 0 0
\(799\) 6.03494 0.213501
\(800\) 0