Properties

Label 1960.2.q.y.361.2
Level $1960$
Weight $2$
Character 1960.361
Analytic conductor $15.651$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 361.2
Root \(-0.591990 + 1.02536i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.y.961.2

$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.984764 0.173894i \(-0.944365\pi\)
0.642979 + 0.765884i \(0.277698\pi\)
\(4\) 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 −0.882858 0.469640i \(-0.844384\pi\)
0.848149 + 0.529758i \(0.177717\pi\)
\(12\) 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 −0.132376 0.991200i \(-0.542261\pi\)
0.924592 0.380958i \(-0.124406\pi\)
\(18\) 0 0
\(19\) −0.130093 0.225328i −0.0298454 0.0516937i 0.850717 0.525624i \(-0.176168\pi\)
−0.880562 + 0.473930i \(0.842835\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.43539 + 7.68233i 0.924843 + 1.60188i 0.791813 + 0.610764i \(0.209137\pi\)
0.133030 + 0.991112i \(0.457529\pi\)
\(24\) 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 −0.560079 0.828439i \(-0.689229\pi\)
0.997489 + 0.0708235i \(0.0225627\pi\)
\(32\) 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 0.909550 0.415594i \(-0.136426\pi\)
−0.814690 + 0.579897i \(0.803093\pi\)
\(38\) 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 0.897745 0.440516i \(-0.145204\pi\)
−0.830370 + 0.557212i \(0.811871\pi\)
\(48\) 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 −0.783354 0.621576i \(-0.786493\pi\)
0.929977 + 0.367617i \(0.119826\pi\)
\(54\) 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 −0.982531 0.186100i \(-0.940415\pi\)
0.652432 + 0.757847i \(0.273749\pi\)
\(60\) 0 0
\(61\) 4.44417 + 7.69752i 0.569017 + 0.985566i 0.996663 + 0.0816204i \(0.0260095\pi\)
−0.427646 + 0.903946i \(0.640657\pi\)
\(62\) 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 −0.999998 0.00180980i \(-0.999424\pi\)
0.501567 + 0.865119i \(0.332757\pi\)
\(68\) 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 −0.634862 0.772626i \(-0.718943\pi\)
0.986544 + 0.163494i \(0.0522764\pi\)
\(74\) 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 0.862832 0.505491i \(-0.168689\pi\)
−0.869184 + 0.494489i \(0.835355\pi\)
\(80\) 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 0.886830 + 0.462095i \(0.152902\pi\)
−0.0432288 + 0.999065i \(0.513764\pi\)
\(90\) 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 −0.621655 0.783291i \(-0.713539\pi\)
0.989178 + 0.146723i \(0.0468726\pi\)
\(102\) 0 0
\(103\) −5.29032 9.16311i −0.521271 0.902868i −0.999694 0.0247384i \(-0.992125\pi\)
0.478423 0.878130i \(-0.341209\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.73306 + 11.6620i 0.650910 + 1.12741i 0.982903 + 0.184127i \(0.0589456\pi\)
−0.331993 + 0.943282i \(0.607721\pi\)
\(108\) 0 0
\(109\) −4.25284 + 7.36614i −0.407348 + 0.705548i −0.994592 0.103862i \(-0.966880\pi\)
0.587243 + 0.809410i \(0.300213\pi\)
\(110\) 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 0.824470 0.565906i \(-0.191474\pi\)
−0.902324 + 0.431058i \(0.858140\pi\)
\(132\) 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 −0.516518 0.856276i \(-0.672772\pi\)
0.999816 + 0.0191800i \(0.00610555\pi\)
\(138\) 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 −0.737470 0.675380i \(-0.763980\pi\)
−0.216161 0.976358i \(-0.569354\pi\)
\(150\) 0 0
\(151\) −11.1699 + 19.3468i −0.908992 + 1.57442i −0.0935251 + 0.995617i \(0.529814\pi\)
−0.815467 + 0.578804i \(0.803520\pi\)
\(152\) 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 −0.927762 0.373173i \(-0.878270\pi\)
0.787058 + 0.616879i \(0.211603\pi\)
\(158\) 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 0.986198 + 0.165568i \(0.0529456\pi\)
−0.349714 + 0.936857i \(0.613721\pi\)
\(164\) 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 0.977942 + 0.208878i \(0.0669813\pi\)
−0.308077 + 0.951361i \(0.599685\pi\)
\(174\) 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 −0.188646 + 0.982045i \(0.560410\pi\)
−0.756153 + 0.654395i \(0.772923\pi\)
\(180\) 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 −0.961508 0.274779i \(-0.911395\pi\)
0.242788 0.970079i \(-0.421938\pi\)
\(192\) 0 0
\(193\) 5.71676 9.90172i 0.411501 0.712741i −0.583553 0.812075i \(-0.698338\pi\)
0.995054 + 0.0993341i \(0.0316712\pi\)
\(194\) 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 0.487989 + 0.872850i \(0.337731\pi\)
−0.999905 + 0.0138143i \(0.995603\pi\)
\(200\) 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 −0.129171 0.991622i \(-0.541231\pi\)
0.923355 0.383946i \(-0.125435\pi\)
\(228\) 0 0
\(229\) 1.29767 + 2.24763i 0.0857523 + 0.148527i 0.905712 0.423895i \(-0.139337\pi\)
−0.819959 + 0.572422i \(0.806004\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.58189 + 13.1322i 0.496706 + 0.860320i 0.999993 0.00379927i \(-0.00120935\pi\)
−0.503287 + 0.864120i \(0.667876\pi\)
\(234\) 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 −0.353057 0.935602i \(-0.614858\pi\)
0.986783 0.162044i \(-0.0518088\pi\)
\(242\) 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 0.891530 0.452961i \(-0.149632\pi\)
−0.838041 + 0.545607i \(0.816299\pi\)
\(258\) 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 −0.292492 0.956268i \(-0.594485\pi\)
0.974398 0.224828i \(-0.0721821\pi\)
\(264\) 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 −0.287796 + 0.957692i \(0.592922\pi\)
−0.685488 + 0.728084i \(0.740411\pi\)
\(270\) 0 0
\(271\) −12.8883 22.3232i −0.782910 1.35604i −0.930239 0.366953i \(-0.880401\pi\)
0.147329 0.989088i \(-0.452932\pi\)
\(272\) 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 −0.720097 0.693874i \(-0.755903\pi\)
0.960961 + 0.276685i \(0.0892360\pi\)
\(278\) 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 −0.815056 0.579383i \(-0.803294\pi\)
0.909288 + 0.416167i \(0.136627\pi\)
\(284\) 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 −0.404058 0.914733i \(-0.632401\pi\)
0.994211 0.107442i \(-0.0342659\pi\)
\(312\) 0 0
\(313\) −10.6930 18.5208i −0.604405 1.04686i −0.992145 0.125091i \(-0.960078\pi\)
0.387741 0.921769i \(-0.373256\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.74547 13.4155i −0.435029 0.753492i 0.562269 0.826954i \(-0.309928\pi\)
−0.997298 + 0.0734623i \(0.976595\pi\)
\(318\) 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 0.959054 0.283222i \(-0.0914033\pi\)
−0.724805 + 0.688954i \(0.758070\pi\)
\(332\) 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 −0.915815 0.401601i \(-0.868454\pi\)
0.805704 + 0.592318i \(0.201787\pi\)
\(348\) 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 −0.117191 0.993109i \(-0.537389\pi\)
0.918653 0.395064i \(-0.129278\pi\)
\(354\) 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 −0.728528 0.685016i \(-0.759795\pi\)
−0.228977 0.973432i \(-0.573538\pi\)
\(360\) 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 −0.971277 0.237951i \(-0.923524\pi\)
0.691710 + 0.722175i \(0.256858\pi\)
\(368\) 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 0.783682 0.621162i \(-0.213339\pi\)
−0.929783 + 0.368108i \(0.880006\pi\)
\(374\) 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 −0.953355 0.301852i \(-0.902395\pi\)
0.215266 0.976555i \(-0.430938\pi\)
\(384\) 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 −0.397036 0.917803i \(-0.629961\pi\)
0.993359 0.115058i \(-0.0367055\pi\)
\(390\) 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 0.579462 0.814999i \(-0.303263\pi\)
−0.995541 + 0.0943288i \(0.969930\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.760807 + 1.31776i 0.0379929 + 0.0658056i 0.884397 0.466736i \(-0.154570\pi\)
−0.846404 + 0.532542i \(0.821237\pi\)
\(402\) 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 −0.925303 0.379228i \(-0.876189\pi\)
0.791073 + 0.611722i \(0.209523\pi\)
\(410\) 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 −0.180692 0.983540i \(-0.557834\pi\)
0.942117 0.335286i \(-0.108833\pi\)
\(432\) 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 0.868927 0.494941i \(-0.164810\pi\)
−0.863095 + 0.505042i \(0.831477\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.72741 + 2.99196i 0.0820716 + 0.142152i 0.904140 0.427237i \(-0.140513\pi\)
−0.822068 + 0.569389i \(0.807180\pi\)
\(444\) 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 0.962544 0.271124i \(-0.0873955\pi\)
−0.716073 + 0.698026i \(0.754062\pi\)
\(458\) 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 0.998744 0.0501059i \(-0.0159559\pi\)
−0.542765 + 0.839885i \(0.682623\pi\)
\(468\) 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 −0.862282 0.506428i \(-0.830966\pi\)
0.869721 + 0.493544i \(0.164299\pi\)
\(480\) 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 −0.608173 0.793805i \(-0.708097\pi\)
0.991541 + 0.129791i \(0.0414306\pi\)
\(488\) 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 −0.801437 0.598079i \(-0.795931\pi\)
−0.117233 0.993104i \(-0.537402\pi\)
\(500\) 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 0.946273 0.323369i \(-0.104815\pi\)
−0.753182 + 0.657812i \(0.771482\pi\)
\(510\) 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 0.399961 + 0.916532i \(0.369024\pi\)
−0.993721 + 0.111890i \(0.964310\pi\)
\(522\) 0 0
\(523\) −0.685928 1.18806i −0.0299935 0.0519503i 0.850639 0.525750i \(-0.176215\pi\)
−0.880633 + 0.473800i \(0.842882\pi\)
\(524\) 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 0.759152 0.650913i \(-0.225614\pi\)
−0.943284 + 0.331988i \(0.892281\pi\)
\(542\) 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 −0.689435 0.724347i \(-0.742141\pi\)
0.972021 + 0.234895i \(0.0754745\pi\)
\(558\) 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 −0.361716 0.932288i \(-0.617809\pi\)
0.988243 0.152889i \(-0.0488578\pi\)
\(564\) 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 0.505592 0.862773i \(-0.331274\pi\)
−0.999979 + 0.00646948i \(0.997941\pi\)
\(570\) 0 0
\(571\) −16.3217 + 28.2700i −0.683042 + 1.18306i 0.291006 + 0.956721i \(0.406010\pi\)
−0.974048 + 0.226342i \(0.927323\pi\)
\(572\) 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 0.392951 + 0.919559i \(0.371454\pi\)
−0.992837 + 0.119474i \(0.961879\pi\)
\(578\) 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 0.986470 + 0.163941i \(0.0524207\pi\)
−0.351258 + 0.936279i \(0.614246\pi\)
\(594\) 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 −0.321005 0.947077i \(-0.604021\pi\)
0.980696 0.195540i \(-0.0626460\pi\)
\(600\) 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 0.756247 0.654286i \(-0.227031\pi\)
−0.944752 + 0.327786i \(0.893697\pi\)
\(608\) 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 0.104518 + 0.994523i \(0.466670\pi\)
−0.913541 + 0.406746i \(0.866663\pi\)
\(614\) 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 −0.121920 + 0.992540i \(0.538905\pi\)
−0.798605 + 0.601856i \(0.794428\pi\)
\(620\) 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 −0.318301 0.947990i \(-0.603112\pi\)
0.980134 0.198338i \(-0.0635543\pi\)
\(642\) 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 −0.881096 0.472937i \(-0.843194\pi\)
0.850124 + 0.526583i \(0.176527\pi\)
\(648\) 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 0.722593 0.691273i \(-0.242950\pi\)
−0.959957 + 0.280148i \(0.909617\pi\)
\(654\) 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 −0.881387 0.472395i \(-0.843390\pi\)
0.849799 + 0.527106i \(0.176723\pi\)
\(662\) 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 0.958860 0.283880i \(-0.0916218\pi\)
−0.725277 + 0.688457i \(0.758288\pi\)
\(678\) 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 −0.367004 0.930219i \(-0.619617\pi\)
0.989096 0.147275i \(-0.0470501\pi\)
\(684\) 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 0.992006 0.126194i \(-0.0402761\pi\)
−0.605290 + 0.796005i \(0.706943\pi\)
\(692\) 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 0.954509 0.298183i \(-0.0963805\pi\)
−0.735488 + 0.677538i \(0.763047\pi\)
\(710\) 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 0.808134 0.588998i \(-0.200478\pi\)
−0.914155 + 0.405365i \(0.867144\pi\)
\(720\) 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 0.882489 0.470333i \(-0.155866\pi\)
−0.848565 + 0.529092i \(0.822533\pi\)
\(734\) 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 −0.546708 0.837323i \(-0.684119\pi\)
0.998497 + 0.0548012i \(0.0174525\pi\)
\(740\) 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 0.863013 0.505181i \(-0.168574\pi\)
−0.869006 + 0.494801i \(0.835241\pi\)
\(752\) 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 0.784117 0.620613i \(-0.213116\pi\)
−0.929525 + 0.368759i \(0.879783\pi\)
\(762\) 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 0.0543350 0.998523i \(-0.482696\pi\)
0.837579 0.546317i \(-0.183971\pi\)
\(774\) 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 −0.609187 0.793027i \(-0.708504\pi\)
0.991375 + 0.131058i \(0.0418373\pi\)
\(788\) 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