Properties

Label 1960.2.q.x.361.3
Level $1960$
Weight $2$
Character 1960.361
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 361.3
Root \(-0.591990 + 1.02536i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.x.961.3

$q$-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 −0.642979 0.765884i \(-0.722302\pi\)
0.984764 + 0.173894i \(0.0556351\pi\)
\(4\) 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 \(-0.602055\pi\)
−0.315152 + 0.949041i \(0.602055\pi\)
\(14\) 0 0
\(15\) −1.18398 −0.305702
\(16\) 0 0
\(17\) −3.26639 + 5.65755i −0.792216 + 1.37216i 0.132376 + 0.991200i \(0.457739\pi\)
−0.924592 + 0.380958i \(0.875594\pi\)
\(18\) 0 0
\(19\) 0.130093 + 0.225328i 0.0298454 + 0.0516937i 0.880562 0.473930i \(-0.157165\pi\)
−0.850717 + 0.525624i \(0.823832\pi\)
\(20\) 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 −0.997489 0.0708235i \(-0.977437\pi\)
0.560079 + 0.828439i \(0.310771\pi\)
\(32\) 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 \(-0.387476\pi\)
0.346188 + 0.938165i \(0.387476\pi\)
\(42\) 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 \(-0.188129\pi\)
−0.897745 + 0.440516i \(0.854796\pi\)
\(48\) 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 −0.652432 0.757847i \(-0.726251\pi\)
0.982531 + 0.186100i \(0.0595847\pi\)
\(60\) 0 0
\(61\) −4.44417 7.69752i −0.569017 0.985566i −0.996663 0.0816204i \(-0.973990\pi\)
0.427646 0.903946i \(-0.359343\pi\)
\(62\) 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 −0.986544 0.163494i \(-0.947724\pi\)
0.634862 + 0.772626i \(0.281057\pi\)
\(74\) 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 \(-0.341141\pi\)
0.478608 + 0.878029i \(0.341141\pi\)
\(84\) 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 \(-0.847098\pi\)
0.0432288 0.999065i \(-0.486236\pi\)
\(90\) 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 \(-0.430021\pi\)
0.218079 + 0.975931i \(0.430021\pi\)
\(98\) 0 0
\(99\) −0.367959 −0.0369812
\(100\) 0 0
\(101\) −3.69356 + 6.39743i −0.367523 + 0.636568i −0.989178 0.146723i \(-0.953127\pi\)
0.621655 + 0.783291i \(0.286461\pi\)
\(102\) 0 0
\(103\) 5.29032 + 9.16311i 0.521271 + 0.902868i 0.999694 + 0.0247384i \(0.00787529\pi\)
−0.478423 + 0.878130i \(0.658791\pi\)
\(104\) 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 0.902324 0.431058i \(-0.141860\pi\)
−0.824470 + 0.565906i \(0.808526\pi\)
\(132\) 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 \(-0.272769\pi\)
0.654761 + 0.755836i \(0.272769\pi\)
\(140\) 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 −0.787058 0.616879i \(-0.788397\pi\)
0.927762 + 0.373173i \(0.121730\pi\)
\(158\) 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 \(-0.549426\pi\)
−0.154654 + 0.987969i \(0.549426\pi\)
\(168\) 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 \(-0.933019\pi\)
0.308077 0.951361i \(-0.400315\pi\)
\(174\) 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 \(-0.258768\pi\)
0.687363 + 0.726315i \(0.258768\pi\)
\(182\) 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 \(-0.662269\pi\)
0.999905 0.0138143i \(-0.00439737\pi\)
\(200\) 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 \(-0.738360\pi\)
−0.680782 + 0.732486i \(0.738360\pi\)
\(224\) 0 0
\(225\) −1.59819 −0.106546
\(226\) 0 0
\(227\) −11.9656 + 20.7250i −0.794185 + 1.37557i 0.129171 + 0.991622i \(0.458769\pi\)
−0.923355 + 0.383946i \(0.874565\pi\)
\(228\) 0 0
\(229\) −1.29767 2.24763i −0.0857523 0.148527i 0.819959 0.572422i \(-0.193996\pi\)
−0.905712 + 0.423895i \(0.860663\pi\)
\(230\) 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 \(0.385142\pi\)
−0.986783 + 0.162044i \(0.948191\pi\)
\(242\) 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 \(-0.790212\pi\)
−0.790564 + 0.612380i \(0.790212\pi\)
\(252\) 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 \(-0.183701\pi\)
−0.891530 + 0.452961i \(0.850368\pi\)
\(258\) 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 \(-0.407078\pi\)
0.685488 0.728084i \(-0.259589\pi\)
\(270\) 0 0
\(271\) 12.8883 + 22.3232i 0.782910 + 1.35604i 0.930239 + 0.366953i \(0.119599\pi\)
−0.147329 + 0.989088i \(0.547068\pi\)
\(272\) 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 −0.909288 0.416167i \(-0.863373\pi\)
0.815056 + 0.579383i \(0.196706\pi\)
\(284\) 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 \(-0.671077\pi\)
−0.511952 + 0.859014i \(0.671077\pi\)
\(294\) 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 \(-0.480817\pi\)
0.0602300 + 0.998185i \(0.480817\pi\)
\(308\) 0 0
\(309\) 12.5273 0.712651
\(310\) 0 0
\(311\) −10.4075 + 18.0263i −0.590153 + 1.02217i 0.404058 + 0.914733i \(0.367599\pi\)
−0.994211 + 0.107442i \(0.965734\pi\)
\(312\) 0 0
\(313\) 10.6930 + 18.5208i 0.604405 + 1.04686i 0.992145 + 0.125091i \(0.0399223\pi\)
−0.387741 + 0.921769i \(0.626744\pi\)
\(314\) 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 \(-0.574617\pi\)
−0.232275 + 0.972650i \(0.574617\pi\)
\(350\) 0 0
\(351\) −12.3724 −0.660388
\(352\) 0 0
\(353\) −15.0581 + 26.0814i −0.801462 + 1.38817i 0.117191 + 0.993109i \(0.462611\pi\)
−0.918653 + 0.395064i \(0.870722\pi\)
\(354\) 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 −0.691710 0.722175i \(-0.743142\pi\)
0.971277 + 0.237951i \(0.0764757\pi\)
\(368\) 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 \(0.0976047\pi\)
−0.215266 + 0.976555i \(0.569062\pi\)
\(384\) 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 0.995541 0.0943288i \(-0.0300705\pi\)
−0.579462 + 0.814999i \(0.696737\pi\)
\(398\) 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 −0.791073 0.611722i \(-0.790477\pi\)
0.925303 + 0.379228i \(0.123811\pi\)
\(410\) 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 \(-0.401886\pi\)
0.303375 + 0.952871i \(0.401886\pi\)
\(420\) 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 \(-0.768928\pi\)
−0.747880 + 0.663834i \(0.768928\pi\)
\(434\) 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 \(-0.168523\pi\)
−0.868927 + 0.494941i \(0.835190\pi\)
\(440\) 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 \(-0.455455\pi\)
0.139485 + 0.990224i \(0.455455\pi\)
\(462\) 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 \(-0.317377\pi\)
−0.998744 + 0.0501059i \(0.984044\pi\)
\(468\) 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 \(-0.835701\pi\)
0.862282 + 0.506428i \(0.169034\pi\)
\(480\) 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 \(-0.440777\pi\)
0.184982 + 0.982742i \(0.440777\pi\)
\(504\) 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 \(-0.228518\pi\)
−0.946273 + 0.323369i \(0.895185\pi\)
\(510\) 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 \(-0.630976\pi\)
0.993721 0.111890i \(-0.0356903\pi\)
\(522\) 0 0
\(523\) 0.685928 + 1.18806i 0.0299935 + 0.0519503i 0.880633 0.473800i \(-0.157118\pi\)
−0.850639 + 0.525750i \(0.823785\pi\)
\(524\) 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 \(0.382191\pi\)
−0.988243 + 0.152889i \(0.951142\pi\)
\(564\) 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 \(-0.628546\pi\)
0.992837 0.119474i \(-0.0381209\pi\)
\(578\) 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 \(-0.511972\pi\)
−0.0376019 + 0.999293i \(0.511972\pi\)
\(588\) 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 \(-0.947579\pi\)
0.351258 0.936279i \(-0.385754\pi\)
\(594\) 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 \(-0.672451\pi\)
−0.515655 + 0.856797i \(0.672451\pi\)
\(602\) 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 \(-0.106303\pi\)
−0.756247 + 0.654286i \(0.772969\pi\)
\(608\) 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 \(-0.461095\pi\)
0.798605 0.601856i \(-0.205572\pi\)
\(620\) 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 \(-0.130723\pi\)
0.916851 + 0.399231i \(0.130723\pi\)
\(644\) 0 0
\(645\) −4.94575 −0.194739
\(646\) 0 0
\(647\) 0.787826 1.36455i 0.0309726 0.0536462i −0.850124 0.526583i \(-0.823473\pi\)
0.881096 + 0.472937i \(0.156806\pi\)
\(648\) 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 −0.849799 0.527106i \(-0.823277\pi\)
0.881387 + 0.472395i \(0.156610\pi\)
\(662\) 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 \(-0.241712\pi\)
−0.958860 + 0.283880i \(0.908378\pi\)
\(678\) 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 0.605290 0.796005i \(-0.293057\pi\)
−0.992006 + 0.126194i \(0.959724\pi\)
\(692\) 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 0.914155 0.405365i \(-0.132856\pi\)
−0.808134 + 0.588998i \(0.799522\pi\)
\(720\) 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 \(-0.387357\pi\)
0.346537 + 0.938036i \(0.387357\pi\)
\(728\) 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 \(-0.177467\pi\)
−0.882489 + 0.470333i \(0.844134\pi\)
\(734\) 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 0.929525 0.368759i \(-0.120217\pi\)
−0.784117 + 0.620613i \(0.786884\pi\)
\(762\) 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 \(-0.277876\pi\)
0.642552 + 0.766242i \(0.277876\pi\)
\(770\) 0 0
\(771\) −2.03053 −0.0731276
\(772\) 0 0
\(773\) −24.7978 + 42.9510i −0.891914 + 1.54484i −0.0543350 + 0.998523i \(0.517304\pi\)
−0.837579 + 0.546317i \(0.816029\pi\)
\(774\) 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 \(-0.958163\pi\)
0.609187 + 0.793027i \(0.291496\pi\)
\(788\) 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 \(-0.286153\pi\)
0.622412 + 0.782690i \(0.286153\pi\)
\(798\) 0 0
\(799\) 6.03494 0.213501