Properties

Label 804.2.s.b.5.16
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.16
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.33701 + 1.10109i) q^{3} +(1.09364 - 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(0.575207 + 2.94434i) q^{9} +O(q^{10})\) \(q+(1.33701 + 1.10109i) q^{3} +(1.09364 - 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(0.575207 + 2.94434i) q^{9} +(3.69014 - 1.08352i) q^{11} +(-1.65469 - 2.57474i) q^{13} +(1.81579 + 0.774850i) q^{15} +(4.10573 + 0.590315i) q^{17} +(-4.90683 - 5.66278i) q^{19} +(0.800501 + 4.72384i) q^{21} +(-1.08727 + 0.496537i) q^{23} +(-3.11334 + 2.00082i) q^{25} +(-2.47292 + 4.56997i) q^{27} +7.40032i q^{29} +(0.00434668 - 0.00676357i) q^{31} +(6.12683 + 2.61449i) q^{33} +(2.86801 + 1.30978i) q^{35} +4.76894 q^{37} +(0.622682 - 5.26442i) q^{39} +(0.919315 - 6.39398i) q^{41} +(-7.53507 - 1.08338i) q^{43} +(1.57456 + 3.03533i) q^{45} +(3.24748 - 1.48308i) q^{47} +(0.0927634 + 0.645184i) q^{49} +(4.83942 + 5.31003i) q^{51} +(-0.624559 - 4.34391i) q^{53} +(3.68774 - 2.36997i) q^{55} +(-0.325269 - 12.9741i) q^{57} +(-7.02119 + 10.9252i) q^{59} +(-0.929884 + 3.16689i) q^{61} +(-4.13109 + 7.19726i) q^{63} +(-2.63643 - 2.28448i) q^{65} +(-4.74764 + 6.66783i) q^{67} +(-2.00042 - 0.533298i) q^{69} +(11.4234 - 1.64244i) q^{71} +(11.3262 + 3.32568i) q^{73} +(-6.36566 - 0.752938i) q^{75} +(9.67720 + 4.41943i) q^{77} +(-0.942057 - 1.46587i) q^{79} +(-8.33827 + 3.38721i) q^{81} +(-2.07934 - 7.08159i) q^{83} +(4.67975 - 0.672846i) q^{85} +(-8.14841 + 9.89432i) q^{87} +(-5.41699 - 2.47386i) q^{89} +(1.20487 - 8.38004i) q^{91} +(0.0132589 - 0.00425690i) q^{93} +(-7.18474 - 4.61735i) q^{95} -6.48460i q^{97} +(5.31286 + 10.2418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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
\(3\) 1.33701 + 1.10109i 0.771925 + 0.635714i
\(4\) 0 0
\(5\) 1.09364 0.321121i 0.489090 0.143610i −0.0278834 0.999611i \(-0.508877\pi\)
0.516974 + 0.856001i \(0.327059\pi\)
\(6\) 0 0
\(7\) 2.09055 + 1.81147i 0.790153 + 0.684672i 0.953332 0.301925i \(-0.0976292\pi\)
−0.163179 + 0.986597i \(0.552175\pi\)
\(8\) 0 0
\(9\) 0.575207 + 2.94434i 0.191736 + 0.981447i
\(10\) 0 0
\(11\) 3.69014 1.08352i 1.11262 0.326695i 0.326765 0.945106i \(-0.394041\pi\)
0.785855 + 0.618411i \(0.212223\pi\)
\(12\) 0 0
\(13\) −1.65469 2.57474i −0.458927 0.714105i 0.532259 0.846582i \(-0.321343\pi\)
−0.991186 + 0.132477i \(0.957707\pi\)
\(14\) 0 0
\(15\) 1.81579 + 0.774850i 0.468836 + 0.200065i
\(16\) 0 0
\(17\) 4.10573 + 0.590315i 0.995785 + 0.143172i 0.620892 0.783896i \(-0.286770\pi\)
0.374893 + 0.927068i \(0.377679\pi\)
\(18\) 0 0
\(19\) −4.90683 5.66278i −1.12570 1.29913i −0.949144 0.314842i \(-0.898048\pi\)
−0.176560 0.984290i \(-0.556497\pi\)
\(20\) 0 0
\(21\) 0.800501 + 4.72384i 0.174684 + 1.03083i
\(22\) 0 0
\(23\) −1.08727 + 0.496537i −0.226710 + 0.103535i −0.525532 0.850774i \(-0.676134\pi\)
0.298822 + 0.954309i \(0.403406\pi\)
\(24\) 0 0
\(25\) −3.11334 + 2.00082i −0.622668 + 0.400164i
\(26\) 0 0
\(27\) −2.47292 + 4.56997i −0.475914 + 0.879492i
\(28\) 0 0
\(29\) 7.40032i 1.37420i 0.726561 + 0.687102i \(0.241118\pi\)
−0.726561 + 0.687102i \(0.758882\pi\)
\(30\) 0 0
\(31\) 0.00434668 0.00676357i 0.000780687 0.00121477i −0.840863 0.541248i \(-0.817952\pi\)
0.841644 + 0.540033i \(0.181588\pi\)
\(32\) 0 0
\(33\) 6.12683 + 2.61449i 1.06654 + 0.455124i
\(34\) 0 0
\(35\) 2.86801 + 1.30978i 0.484782 + 0.221392i
\(36\) 0 0
\(37\) 4.76894 0.784009 0.392004 0.919963i \(-0.371782\pi\)
0.392004 + 0.919963i \(0.371782\pi\)
\(38\) 0 0
\(39\) 0.622682 5.26442i 0.0997090 0.842982i
\(40\) 0 0
\(41\) 0.919315 6.39398i 0.143573 0.998571i −0.782883 0.622169i \(-0.786252\pi\)
0.926456 0.376403i \(-0.122839\pi\)
\(42\) 0 0
\(43\) −7.53507 1.08338i −1.14909 0.165214i −0.458657 0.888613i \(-0.651669\pi\)
−0.690430 + 0.723400i \(0.742578\pi\)
\(44\) 0 0
\(45\) 1.57456 + 3.03533i 0.234722 + 0.452481i
\(46\) 0 0
\(47\) 3.24748 1.48308i 0.473694 0.216329i −0.164239 0.986421i \(-0.552517\pi\)
0.637933 + 0.770092i \(0.279790\pi\)
\(48\) 0 0
\(49\) 0.0927634 + 0.645184i 0.0132519 + 0.0921691i
\(50\) 0 0
\(51\) 4.83942 + 5.31003i 0.677655 + 0.743553i
\(52\) 0 0
\(53\) −0.624559 4.34391i −0.0857898 0.596681i −0.986685 0.162644i \(-0.947998\pi\)
0.900895 0.434037i \(-0.142911\pi\)
\(54\) 0 0
\(55\) 3.68774 2.36997i 0.497255 0.319566i
\(56\) 0 0
\(57\) −0.325269 12.9741i −0.0430829 1.71846i
\(58\) 0 0
\(59\) −7.02119 + 10.9252i −0.914081 + 1.42234i −0.00765668 + 0.999971i \(0.502437\pi\)
−0.906425 + 0.422368i \(0.861199\pi\)
\(60\) 0 0
\(61\) −0.929884 + 3.16689i −0.119059 + 0.405479i −0.997359 0.0726319i \(-0.976860\pi\)
0.878299 + 0.478111i \(0.158678\pi\)
\(62\) 0 0
\(63\) −4.13109 + 7.19726i −0.520468 + 0.906769i
\(64\) 0 0
\(65\) −2.63643 2.28448i −0.327009 0.283355i
\(66\) 0 0
\(67\) −4.74764 + 6.66783i −0.580017 + 0.814605i
\(68\) 0 0
\(69\) −2.00042 0.533298i −0.240822 0.0642016i
\(70\) 0 0
\(71\) 11.4234 1.64244i 1.35571 0.194921i 0.574148 0.818752i \(-0.305333\pi\)
0.781560 + 0.623830i \(0.214424\pi\)
\(72\) 0 0
\(73\) 11.3262 + 3.32568i 1.32563 + 0.389241i 0.866523 0.499137i \(-0.166350\pi\)
0.459111 + 0.888379i \(0.348168\pi\)
\(74\) 0 0
\(75\) −6.36566 0.752938i −0.735043 0.0869418i
\(76\) 0 0
\(77\) 9.67720 + 4.41943i 1.10282 + 0.503640i
\(78\) 0 0
\(79\) −0.942057 1.46587i −0.105990 0.164923i 0.784207 0.620499i \(-0.213070\pi\)
−0.890197 + 0.455576i \(0.849433\pi\)
\(80\) 0 0
\(81\) −8.33827 + 3.38721i −0.926475 + 0.376357i
\(82\) 0 0
\(83\) −2.07934 7.08159i −0.228237 0.777305i −0.991373 0.131067i \(-0.958160\pi\)
0.763136 0.646238i \(-0.223659\pi\)
\(84\) 0 0
\(85\) 4.67975 0.672846i 0.507590 0.0729804i
\(86\) 0 0
\(87\) −8.14841 + 9.89432i −0.873601 + 1.06078i
\(88\) 0 0
\(89\) −5.41699 2.47386i −0.574200 0.262228i 0.107081 0.994250i \(-0.465850\pi\)
−0.681281 + 0.732022i \(0.738577\pi\)
\(90\) 0 0
\(91\) 1.20487 8.38004i 0.126304 0.878467i
\(92\) 0 0
\(93\) 0.0132589 0.00425690i 0.00137488 0.000441420i
\(94\) 0 0
\(95\) −7.18474 4.61735i −0.737139 0.473731i
\(96\) 0 0
\(97\) 6.48460i 0.658412i −0.944258 0.329206i \(-0.893219\pi\)
0.944258 0.329206i \(-0.106781\pi\)
\(98\) 0 0
\(99\) 5.31286 + 10.2418i 0.533963 + 1.02934i
\(100\) 0 0
\(101\) −8.92133 10.2958i −0.887706 1.02447i −0.999527 0.0307386i \(-0.990214\pi\)
0.111822 0.993728i \(-0.464331\pi\)
\(102\) 0 0
\(103\) −11.7843 7.57331i −1.16114 0.746221i −0.189315 0.981916i \(-0.560627\pi\)
−0.971827 + 0.235696i \(0.924263\pi\)
\(104\) 0 0
\(105\) 2.39238 + 4.90912i 0.233473 + 0.479081i
\(106\) 0 0
\(107\) −5.60348 + 19.0837i −0.541709 + 1.84489i −0.00680961 + 0.999977i \(0.502168\pi\)
−0.534900 + 0.844916i \(0.679651\pi\)
\(108\) 0 0
\(109\) 0.920825 + 1.43283i 0.0881990 + 0.137240i 0.882550 0.470219i \(-0.155825\pi\)
−0.794351 + 0.607459i \(0.792189\pi\)
\(110\) 0 0
\(111\) 6.37613 + 5.25102i 0.605196 + 0.498405i
\(112\) 0 0
\(113\) 0.577431 + 0.169549i 0.0543201 + 0.0159498i 0.308780 0.951134i \(-0.400079\pi\)
−0.254460 + 0.967083i \(0.581898\pi\)
\(114\) 0 0
\(115\) −1.02963 + 0.892177i −0.0960132 + 0.0831959i
\(116\) 0 0
\(117\) 6.62913 6.35297i 0.612863 0.587332i
\(118\) 0 0
\(119\) 7.51389 + 8.67149i 0.688797 + 0.794914i
\(120\) 0 0
\(121\) 3.18935 2.04967i 0.289941 0.186334i
\(122\) 0 0
\(123\) 8.26947 7.53658i 0.745633 0.679551i
\(124\) 0 0
\(125\) −6.49445 + 7.49499i −0.580881 + 0.670372i
\(126\) 0 0
\(127\) 13.6009 15.6963i 1.20689 1.39282i 0.309896 0.950770i \(-0.399706\pi\)
0.896990 0.442051i \(-0.145749\pi\)
\(128\) 0 0
\(129\) −8.88159 9.74527i −0.781980 0.858023i
\(130\) 0 0
\(131\) −5.58640 + 2.55122i −0.488086 + 0.222902i −0.644229 0.764833i \(-0.722821\pi\)
0.156142 + 0.987735i \(0.450094\pi\)
\(132\) 0 0
\(133\) 20.7269i 1.79725i
\(134\) 0 0
\(135\) −1.23696 + 5.79201i −0.106461 + 0.498497i
\(136\) 0 0
\(137\) −0.685286 1.50057i −0.0585479 0.128202i 0.878097 0.478483i \(-0.158813\pi\)
−0.936645 + 0.350281i \(0.886086\pi\)
\(138\) 0 0
\(139\) −5.68952 19.3767i −0.482579 1.64351i −0.736611 0.676316i \(-0.763575\pi\)
0.254033 0.967196i \(-0.418243\pi\)
\(140\) 0 0
\(141\) 5.97492 + 1.59288i 0.503179 + 0.134144i
\(142\) 0 0
\(143\) −8.89583 7.70828i −0.743906 0.644599i
\(144\) 0 0
\(145\) 2.37640 + 8.09328i 0.197349 + 0.672110i
\(146\) 0 0
\(147\) −0.586379 + 0.964760i −0.0483637 + 0.0795721i
\(148\) 0 0
\(149\) 12.1484 10.5266i 0.995232 0.862373i 0.00474598 0.999989i \(-0.498489\pi\)
0.990486 + 0.137616i \(0.0439438\pi\)
\(150\) 0 0
\(151\) −1.94375 + 13.5191i −0.158180 + 1.10017i 0.743804 + 0.668397i \(0.233019\pi\)
−0.901984 + 0.431769i \(0.857890\pi\)
\(152\) 0 0
\(153\) 0.623559 + 12.4282i 0.0504117 + 1.00476i
\(154\) 0 0
\(155\) 0.00258177 0.00879272i 0.000207373 0.000706248i
\(156\) 0 0
\(157\) −1.61205 3.52989i −0.128655 0.281716i 0.834332 0.551262i \(-0.185854\pi\)
−0.962987 + 0.269546i \(0.913126\pi\)
\(158\) 0 0
\(159\) 3.94798 6.49555i 0.313095 0.515131i
\(160\) 0 0
\(161\) −3.17244 0.931513i −0.250024 0.0734135i
\(162\) 0 0
\(163\) −11.9476 −0.935806 −0.467903 0.883780i \(-0.654990\pi\)
−0.467903 + 0.883780i \(0.654990\pi\)
\(164\) 0 0
\(165\) 7.54011 + 0.891853i 0.586996 + 0.0694307i
\(166\) 0 0
\(167\) 8.83963 7.65959i 0.684031 0.592717i −0.241949 0.970289i \(-0.577787\pi\)
0.925980 + 0.377573i \(0.123241\pi\)
\(168\) 0 0
\(169\) 1.50908 3.30443i 0.116083 0.254187i
\(170\) 0 0
\(171\) 13.8507 17.7047i 1.05919 1.35391i
\(172\) 0 0
\(173\) 5.21190 8.10988i 0.396253 0.616582i −0.584602 0.811320i \(-0.698749\pi\)
0.980855 + 0.194738i \(0.0623856\pi\)
\(174\) 0 0
\(175\) −10.1330 1.45691i −0.765984 0.110132i
\(176\) 0 0
\(177\) −21.4170 + 6.87616i −1.60980 + 0.516844i
\(178\) 0 0
\(179\) −0.610074 + 1.33588i −0.0455990 + 0.0998480i −0.931060 0.364865i \(-0.881115\pi\)
0.885461 + 0.464713i \(0.153842\pi\)
\(180\) 0 0
\(181\) −3.40577 7.45760i −0.253149 0.554319i 0.739805 0.672822i \(-0.234918\pi\)
−0.992954 + 0.118502i \(0.962191\pi\)
\(182\) 0 0
\(183\) −4.73030 + 3.21029i −0.349674 + 0.237312i
\(184\) 0 0
\(185\) 5.21550 1.53141i 0.383451 0.112591i
\(186\) 0 0
\(187\) 15.7903 2.27031i 1.15470 0.166021i
\(188\) 0 0
\(189\) −13.4481 + 5.07413i −0.978208 + 0.369089i
\(190\) 0 0
\(191\) −8.90948 + 19.5091i −0.644668 + 1.41163i 0.251477 + 0.967863i \(0.419084\pi\)
−0.896145 + 0.443762i \(0.853644\pi\)
\(192\) 0 0
\(193\) −11.8842 7.63752i −0.855444 0.549761i 0.0378242 0.999284i \(-0.487957\pi\)
−0.893268 + 0.449524i \(0.851594\pi\)
\(194\) 0 0
\(195\) −1.00953 5.95733i −0.0722938 0.426613i
\(196\) 0 0
\(197\) 0.402118 + 2.79679i 0.0286497 + 0.199263i 0.999119 0.0419605i \(-0.0133604\pi\)
−0.970470 + 0.241224i \(0.922451\pi\)
\(198\) 0 0
\(199\) 4.32271 4.98868i 0.306429 0.353638i −0.581559 0.813504i \(-0.697557\pi\)
0.887988 + 0.459866i \(0.152103\pi\)
\(200\) 0 0
\(201\) −13.6895 + 3.68740i −0.965585 + 0.260089i
\(202\) 0 0
\(203\) −13.4055 + 15.4707i −0.940879 + 1.08583i
\(204\) 0 0
\(205\) −1.04784 7.28792i −0.0731846 0.509010i
\(206\) 0 0
\(207\) −2.08738 2.91567i −0.145083 0.202653i
\(208\) 0 0
\(209\) −24.2427 15.5798i −1.67690 1.07768i
\(210\) 0 0
\(211\) −4.70976 + 10.3129i −0.324233 + 0.709972i −0.999622 0.0274900i \(-0.991249\pi\)
0.675389 + 0.737462i \(0.263976\pi\)
\(212\) 0 0
\(213\) 17.0817 + 10.3822i 1.17042 + 0.711377i
\(214\) 0 0
\(215\) −8.58854 + 1.23485i −0.585734 + 0.0842158i
\(216\) 0 0
\(217\) 0.0213390 0.00626568i 0.00144858 0.000425342i
\(218\) 0 0
\(219\) 11.4814 + 16.9177i 0.775844 + 1.14319i
\(220\) 0 0
\(221\) −5.27378 11.5480i −0.354753 0.776801i
\(222\) 0 0
\(223\) −2.85396 + 6.24929i −0.191115 + 0.418484i −0.980797 0.195033i \(-0.937519\pi\)
0.789682 + 0.613517i \(0.210246\pi\)
\(224\) 0 0
\(225\) −7.68192 8.01584i −0.512128 0.534390i
\(226\) 0 0
\(227\) −17.6790 2.54186i −1.17340 0.168709i −0.472079 0.881556i \(-0.656496\pi\)
−0.701320 + 0.712847i \(0.747405\pi\)
\(228\) 0 0
\(229\) 9.84576 15.3203i 0.650626 1.01239i −0.346604 0.938012i \(-0.612665\pi\)
0.997230 0.0743824i \(-0.0236985\pi\)
\(230\) 0 0
\(231\) 8.07236 + 16.5643i 0.531122 + 1.08985i
\(232\) 0 0
\(233\) 2.89983 6.34973i 0.189974 0.415985i −0.790547 0.612402i \(-0.790203\pi\)
0.980520 + 0.196417i \(0.0629307\pi\)
\(234\) 0 0
\(235\) 3.07533 2.66479i 0.200612 0.173831i
\(236\) 0 0
\(237\) 0.354510 2.99718i 0.0230279 0.194687i
\(238\) 0 0
\(239\) 1.00374 0.0649266 0.0324633 0.999473i \(-0.489665\pi\)
0.0324633 + 0.999473i \(0.489665\pi\)
\(240\) 0 0
\(241\) 25.1298 + 7.37876i 1.61875 + 0.475308i 0.960682 0.277651i \(-0.0895557\pi\)
0.658068 + 0.752958i \(0.271374\pi\)
\(242\) 0 0
\(243\) −14.8780 4.65243i −0.954424 0.298454i
\(244\) 0 0
\(245\) 0.308632 + 0.675810i 0.0197178 + 0.0431759i
\(246\) 0 0
\(247\) −6.46095 + 22.0040i −0.411100 + 1.40008i
\(248\) 0 0
\(249\) 5.01735 11.7577i 0.317961 0.745115i
\(250\) 0 0
\(251\) 1.74308 12.1234i 0.110022 0.765220i −0.857872 0.513863i \(-0.828214\pi\)
0.967894 0.251357i \(-0.0808768\pi\)
\(252\) 0 0
\(253\) −3.47415 + 3.01037i −0.218418 + 0.189260i
\(254\) 0 0
\(255\) 6.99775 + 4.25321i 0.438216 + 0.266347i
\(256\) 0 0
\(257\) 0.555928 + 1.89332i 0.0346778 + 0.118102i 0.975013 0.222148i \(-0.0713067\pi\)
−0.940335 + 0.340249i \(0.889489\pi\)
\(258\) 0 0
\(259\) 9.96970 + 8.63879i 0.619487 + 0.536788i
\(260\) 0 0
\(261\) −21.7891 + 4.25672i −1.34871 + 0.263484i
\(262\) 0 0
\(263\) −3.92129 13.3547i −0.241797 0.823486i −0.987556 0.157270i \(-0.949731\pi\)
0.745758 0.666216i \(-0.232087\pi\)
\(264\) 0 0
\(265\) −2.07796 4.55011i −0.127648 0.279511i
\(266\) 0 0
\(267\) −4.51865 9.27217i −0.276537 0.567448i
\(268\) 0 0
\(269\) 4.90578i 0.299111i 0.988753 + 0.149555i \(0.0477842\pi\)
−0.988753 + 0.149555i \(0.952216\pi\)
\(270\) 0 0
\(271\) −27.8623 + 12.7243i −1.69251 + 0.772945i −0.693913 + 0.720059i \(0.744115\pi\)
−0.998601 + 0.0528861i \(0.983158\pi\)
\(272\) 0 0
\(273\) 10.8381 9.87756i 0.655951 0.597817i
\(274\) 0 0
\(275\) −9.32073 + 10.7567i −0.562061 + 0.648653i
\(276\) 0 0
\(277\) 7.92339 9.14408i 0.476071 0.549415i −0.466020 0.884774i \(-0.654312\pi\)
0.942090 + 0.335360i \(0.108858\pi\)
\(278\) 0 0
\(279\) 0.0224145 + 0.00890765i 0.00134192 + 0.000533287i
\(280\) 0 0
\(281\) 13.9279 8.95093i 0.830870 0.533968i −0.0546844 0.998504i \(-0.517415\pi\)
0.885554 + 0.464536i \(0.153779\pi\)
\(282\) 0 0
\(283\) −3.29329 3.80066i −0.195766 0.225926i 0.649377 0.760467i \(-0.275030\pi\)
−0.845142 + 0.534541i \(0.820484\pi\)
\(284\) 0 0
\(285\) −4.52198 14.0845i −0.267859 0.834294i
\(286\) 0 0
\(287\) 13.5044 11.7016i 0.797138 0.690724i
\(288\) 0 0
\(289\) 0.197150 + 0.0578886i 0.0115971 + 0.00340521i
\(290\) 0 0
\(291\) 7.14012 8.67000i 0.418561 0.508244i
\(292\) 0 0
\(293\) 6.01047 + 9.35248i 0.351135 + 0.546377i 0.971228 0.238151i \(-0.0765414\pi\)
−0.620093 + 0.784529i \(0.712905\pi\)
\(294\) 0 0
\(295\) −4.17034 + 14.2029i −0.242806 + 0.826923i
\(296\) 0 0
\(297\) −4.17375 + 19.5433i −0.242186 + 1.13402i
\(298\) 0 0
\(299\) 3.07754 + 1.97781i 0.177979 + 0.114380i
\(300\) 0 0
\(301\) −13.7899 15.9144i −0.794837 0.917291i
\(302\) 0 0
\(303\) −0.591385 23.5887i −0.0339742 1.35514i
\(304\) 0 0
\(305\) 3.76204i 0.215414i
\(306\) 0 0
\(307\) −13.2632 8.52373i −0.756969 0.486475i 0.104349 0.994541i \(-0.466724\pi\)
−0.861318 + 0.508066i \(0.830361\pi\)
\(308\) 0 0
\(309\) −7.41688 23.1012i −0.421932 1.31418i
\(310\) 0 0
\(311\) −3.61950 + 25.1742i −0.205243 + 1.42750i 0.583170 + 0.812350i \(0.301812\pi\)
−0.788413 + 0.615146i \(0.789097\pi\)
\(312\) 0 0
\(313\) 20.7512 + 9.47674i 1.17293 + 0.535657i 0.904012 0.427507i \(-0.140608\pi\)
0.268914 + 0.963164i \(0.413335\pi\)
\(314\) 0 0
\(315\) −2.20672 + 9.19778i −0.124335 + 0.518236i
\(316\) 0 0
\(317\) 18.1791 2.61376i 1.02104 0.146803i 0.388595 0.921409i \(-0.372960\pi\)
0.632445 + 0.774605i \(0.282051\pi\)
\(318\) 0 0
\(319\) 8.01842 + 27.3082i 0.448945 + 1.52897i
\(320\) 0 0
\(321\) −28.5048 + 19.3452i −1.59098 + 1.07975i
\(322\) 0 0
\(323\) −16.8033 26.1464i −0.934960 1.45483i
\(324\) 0 0
\(325\) 10.3032 + 4.70532i 0.571519 + 0.261004i
\(326\) 0 0
\(327\) −0.346520 + 2.92962i −0.0191626 + 0.162009i
\(328\) 0 0
\(329\) 9.47557 + 2.78228i 0.522405 + 0.153392i
\(330\) 0 0
\(331\) −8.39413 + 1.20689i −0.461383 + 0.0663369i −0.369087 0.929395i \(-0.620330\pi\)
−0.0922958 + 0.995732i \(0.529421\pi\)
\(332\) 0 0
\(333\) 2.74313 + 14.0414i 0.150323 + 0.769462i
\(334\) 0 0
\(335\) −3.05102 + 8.81676i −0.166695 + 0.481711i
\(336\) 0 0
\(337\) −1.80903 1.56754i −0.0985443 0.0853891i 0.604195 0.796836i \(-0.293495\pi\)
−0.702740 + 0.711447i \(0.748040\pi\)
\(338\) 0 0
\(339\) 0.585344 + 0.862492i 0.0317915 + 0.0468441i
\(340\) 0 0
\(341\) 0.00871139 0.0296683i 0.000471748 0.00160663i
\(342\) 0 0
\(343\) 9.49381 14.7727i 0.512618 0.797648i
\(344\) 0 0
\(345\) −2.35899 + 0.0591414i −0.127004 + 0.00318407i
\(346\) 0 0
\(347\) 15.5069 9.96571i 0.832456 0.534987i −0.0536012 0.998562i \(-0.517070\pi\)
0.886058 + 0.463575i \(0.153434\pi\)
\(348\) 0 0
\(349\) 3.09748 + 21.5434i 0.165804 + 1.15319i 0.887441 + 0.460921i \(0.152481\pi\)
−0.721637 + 0.692272i \(0.756610\pi\)
\(350\) 0 0
\(351\) 15.8584 1.19475i 0.846460 0.0637708i
\(352\) 0 0
\(353\) 0.253361 + 1.76217i 0.0134851 + 0.0937906i 0.995452 0.0952597i \(-0.0303682\pi\)
−0.981967 + 0.189050i \(0.939459\pi\)
\(354\) 0 0
\(355\) 11.9657 5.46453i 0.635071 0.290027i
\(356\) 0 0
\(357\) 0.498087 + 19.8673i 0.0263616 + 1.05149i
\(358\) 0 0
\(359\) 27.8551 + 4.00496i 1.47014 + 0.211374i 0.830378 0.557201i \(-0.188125\pi\)
0.639760 + 0.768575i \(0.279034\pi\)
\(360\) 0 0
\(361\) −5.28616 + 36.7660i −0.278219 + 1.93505i
\(362\) 0 0
\(363\) 6.52107 + 0.771320i 0.342267 + 0.0404838i
\(364\) 0 0
\(365\) 13.4547 0.704254
\(366\) 0 0
\(367\) 15.3338 + 7.00272i 0.800419 + 0.365539i 0.773258 0.634092i \(-0.218626\pi\)
0.0271614 + 0.999631i \(0.491353\pi\)
\(368\) 0 0
\(369\) 19.3548 0.971088i 1.00757 0.0505528i
\(370\) 0 0
\(371\) 6.56319 10.2125i 0.340744 0.530207i
\(372\) 0 0
\(373\) 3.91498i 0.202710i −0.994850 0.101355i \(-0.967682\pi\)
0.994850 0.101355i \(-0.0323178\pi\)
\(374\) 0 0
\(375\) −16.9358 + 2.86994i −0.874561 + 0.148203i
\(376\) 0 0
\(377\) 19.0539 12.2452i 0.981327 0.630660i
\(378\) 0 0
\(379\) −29.4711 + 13.4590i −1.51383 + 0.691343i −0.987308 0.158818i \(-0.949232\pi\)
−0.526523 + 0.850161i \(0.676504\pi\)
\(380\) 0 0
\(381\) 35.4676 6.01034i 1.81706 0.307919i
\(382\) 0 0
\(383\) 19.4053 + 22.3949i 0.991565 + 1.14433i 0.989530 + 0.144329i \(0.0461024\pi\)
0.00203522 + 0.999998i \(0.499352\pi\)
\(384\) 0 0
\(385\) 12.0025 + 1.72570i 0.611706 + 0.0879500i
\(386\) 0 0
\(387\) −1.14439 22.8090i −0.0581727 1.15944i
\(388\) 0 0
\(389\) 17.7489 + 27.6178i 0.899903 + 1.40028i 0.916335 + 0.400412i \(0.131133\pi\)
−0.0164322 + 0.999865i \(0.505231\pi\)
\(390\) 0 0
\(391\) −4.75713 + 1.39682i −0.240578 + 0.0706402i
\(392\) 0 0
\(393\) −10.2782 2.74010i −0.518467 0.138220i
\(394\) 0 0
\(395\) −1.50099 1.30062i −0.0755231 0.0654412i
\(396\) 0 0
\(397\) 24.0828 7.07136i 1.20868 0.354901i 0.385516 0.922701i \(-0.374024\pi\)
0.823166 + 0.567800i \(0.192205\pi\)
\(398\) 0 0
\(399\) 22.8222 27.7121i 1.14254 1.38734i
\(400\) 0 0
\(401\) −20.4141 −1.01943 −0.509717 0.860342i \(-0.670250\pi\)
−0.509717 + 0.860342i \(0.670250\pi\)
\(402\) 0 0
\(403\) −0.0246068 −0.00122575
\(404\) 0 0
\(405\) −8.03135 + 6.38199i −0.399081 + 0.317123i
\(406\) 0 0
\(407\) 17.5981 5.16726i 0.872304 0.256131i
\(408\) 0 0
\(409\) 16.8847 + 14.6307i 0.834896 + 0.723442i 0.963342 0.268275i \(-0.0864535\pi\)
−0.128446 + 0.991716i \(0.540999\pi\)
\(410\) 0 0
\(411\) 0.736021 2.76084i 0.0363052 0.136182i
\(412\) 0 0
\(413\) −34.4688 + 10.1210i −1.69610 + 0.498019i
\(414\) 0 0
\(415\) −4.54810 7.07698i −0.223257 0.347395i
\(416\) 0 0
\(417\) 13.7285 32.1716i 0.672289 1.57545i
\(418\) 0 0
\(419\) 19.2259 + 2.76426i 0.939245 + 0.135043i 0.594900 0.803800i \(-0.297192\pi\)
0.344346 + 0.938843i \(0.388101\pi\)
\(420\) 0 0
\(421\) 3.03310 + 3.50038i 0.147824 + 0.170598i 0.824833 0.565377i \(-0.191269\pi\)
−0.677008 + 0.735975i \(0.736724\pi\)
\(422\) 0 0
\(423\) 6.23466 + 8.70862i 0.303139 + 0.423427i
\(424\) 0 0
\(425\) −13.9636 + 6.37698i −0.677336 + 0.309329i
\(426\) 0 0
\(427\) −7.68070 + 4.93609i −0.371695 + 0.238874i
\(428\) 0 0
\(429\) −3.40634 20.1012i −0.164460 0.970493i
\(430\) 0 0
\(431\) 14.1768i 0.682872i −0.939905 0.341436i \(-0.889087\pi\)
0.939905 0.341436i \(-0.110913\pi\)
\(432\) 0 0
\(433\) −5.01481 + 7.80320i −0.240996 + 0.374998i −0.940591 0.339543i \(-0.889728\pi\)
0.699594 + 0.714540i \(0.253364\pi\)
\(434\) 0 0
\(435\) −5.73414 + 13.4374i −0.274931 + 0.644276i
\(436\) 0 0
\(437\) 8.14681 + 3.72052i 0.389715 + 0.177977i
\(438\) 0 0
\(439\) −19.7692 −0.943531 −0.471766 0.881724i \(-0.656383\pi\)
−0.471766 + 0.881724i \(0.656383\pi\)
\(440\) 0 0
\(441\) −1.84628 + 0.644242i −0.0879182 + 0.0306782i
\(442\) 0 0
\(443\) −2.98481 + 20.7598i −0.141812 + 0.986328i 0.787311 + 0.616557i \(0.211473\pi\)
−0.929123 + 0.369771i \(0.879436\pi\)
\(444\) 0 0
\(445\) −6.71864 0.965995i −0.318494 0.0457926i
\(446\) 0 0
\(447\) 27.8332 0.697797i 1.31647 0.0330047i
\(448\) 0 0
\(449\) −3.28217 + 1.49892i −0.154895 + 0.0707382i −0.491354 0.870960i \(-0.663498\pi\)
0.336459 + 0.941698i \(0.390771\pi\)
\(450\) 0 0
\(451\) −3.53562 24.5908i −0.166486 1.15794i
\(452\) 0 0
\(453\) −17.4845 + 15.9349i −0.821494 + 0.748688i
\(454\) 0 0
\(455\) −1.37332 9.55165i −0.0643822 0.447788i
\(456\) 0 0
\(457\) 3.95969 2.54474i 0.185227 0.119038i −0.444741 0.895659i \(-0.646704\pi\)
0.629968 + 0.776621i \(0.283068\pi\)
\(458\) 0 0
\(459\) −12.8509 + 17.3033i −0.599827 + 0.807648i
\(460\) 0 0
\(461\) −19.9136 + 30.9862i −0.927469 + 1.44317i −0.0312737 + 0.999511i \(0.509956\pi\)
−0.896196 + 0.443659i \(0.853680\pi\)
\(462\) 0 0
\(463\) −1.45589 + 4.95832i −0.0676611 + 0.230433i −0.986381 0.164478i \(-0.947406\pi\)
0.918720 + 0.394910i \(0.129224\pi\)
\(464\) 0 0
\(465\) 0.0131334 0.00891321i 0.000609048 0.000413340i
\(466\) 0 0
\(467\) −3.00536 2.60416i −0.139071 0.120506i 0.582547 0.812797i \(-0.302056\pi\)
−0.721619 + 0.692291i \(0.756602\pi\)
\(468\) 0 0
\(469\) −22.0037 + 5.33920i −1.01604 + 0.246541i
\(470\) 0 0
\(471\) 1.73140 6.49452i 0.0797785 0.299252i
\(472\) 0 0
\(473\) −28.9793 + 4.16660i −1.33247 + 0.191581i
\(474\) 0 0
\(475\) 26.6069 + 7.81248i 1.22081 + 0.358461i
\(476\) 0 0
\(477\) 12.4307 4.33756i 0.569162 0.198603i
\(478\) 0 0
\(479\) 25.6151 + 11.6980i 1.17038 + 0.534495i 0.903229 0.429159i \(-0.141190\pi\)
0.267153 + 0.963654i \(0.413917\pi\)
\(480\) 0 0
\(481\) −7.89110 12.2788i −0.359803 0.559864i
\(482\) 0 0
\(483\) −3.21592 4.73859i −0.146329 0.215613i
\(484\) 0 0
\(485\) −2.08234 7.09181i −0.0945544 0.322023i
\(486\) 0 0
\(487\) −4.01264 + 0.576930i −0.181830 + 0.0261432i −0.232628 0.972566i \(-0.574733\pi\)
0.0507982 + 0.998709i \(0.483823\pi\)
\(488\) 0 0
\(489\) −15.9740 13.1553i −0.722372 0.594905i
\(490\) 0 0
\(491\) 26.9926 + 12.3271i 1.21816 + 0.556315i 0.917622 0.397455i \(-0.130107\pi\)
0.300538 + 0.953770i \(0.402834\pi\)
\(492\) 0 0
\(493\) −4.36852 + 30.3837i −0.196748 + 1.36841i
\(494\) 0 0
\(495\) 9.09921 + 9.49474i 0.408979 + 0.426757i
\(496\) 0 0
\(497\) 26.8564 + 17.2596i 1.20467 + 0.774197i
\(498\) 0 0
\(499\) 29.0682i 1.30127i −0.759391 0.650635i \(-0.774503\pi\)
0.759391 0.650635i \(-0.225497\pi\)
\(500\) 0 0
\(501\) 20.2526 0.507746i 0.904819 0.0226844i
\(502\) 0 0
\(503\) 21.9061 + 25.2810i 0.976744 + 1.12722i 0.991860 + 0.127336i \(0.0406428\pi\)
−0.0151160 + 0.999886i \(0.504812\pi\)
\(504\) 0 0
\(505\) −13.0629 8.39502i −0.581292 0.373573i
\(506\) 0 0
\(507\) 5.65614 2.75643i 0.251198 0.122418i
\(508\) 0 0
\(509\) 11.6770 39.7683i 0.517575 1.76270i −0.120487 0.992715i \(-0.538446\pi\)
0.638062 0.769985i \(-0.279736\pi\)
\(510\) 0 0
\(511\) 17.6537 + 27.4696i 0.780952 + 1.21518i
\(512\) 0 0
\(513\) 38.0130 8.42048i 1.67831 0.371773i
\(514\) 0 0
\(515\) −15.3197 4.49828i −0.675068 0.198218i
\(516\) 0 0
\(517\) 10.3767 8.99149i 0.456368 0.395445i
\(518\) 0 0
\(519\) 15.8981 5.10424i 0.697848 0.224051i
\(520\) 0 0
\(521\) −7.20556 8.31566i −0.315681 0.364315i 0.575628 0.817712i \(-0.304758\pi\)
−0.891309 + 0.453396i \(0.850212\pi\)
\(522\) 0 0
\(523\) −14.9040 + 9.57823i −0.651707 + 0.418827i −0.824290 0.566168i \(-0.808425\pi\)
0.172582 + 0.984995i \(0.444789\pi\)
\(524\) 0 0
\(525\) −11.9438 13.1053i −0.521270 0.571960i
\(526\) 0 0
\(527\) 0.0218389 0.0252035i 0.000951319 0.00109788i
\(528\) 0 0
\(529\) −14.1262 + 16.3025i −0.614183 + 0.708805i
\(530\) 0 0
\(531\) −36.2061 14.3885i −1.57121 0.624409i
\(532\) 0 0
\(533\) −17.9840 + 8.21303i −0.778975 + 0.355746i
\(534\) 0 0
\(535\) 22.6701i 0.980114i
\(536\) 0 0
\(537\) −2.28659 + 1.11434i −0.0986738 + 0.0480872i
\(538\) 0 0
\(539\) 1.04138 + 2.28031i 0.0448555 + 0.0982199i
\(540\) 0 0
\(541\) 8.97688 + 30.5724i 0.385946 + 1.31441i 0.892049 + 0.451939i \(0.149268\pi\)
−0.506103 + 0.862473i \(0.668914\pi\)
\(542\) 0 0
\(543\) 3.65792 13.7210i 0.156976 0.588823i
\(544\) 0 0
\(545\) 1.46716 + 1.27130i 0.0628464 + 0.0544567i
\(546\) 0 0
\(547\) 5.92930 + 20.1934i 0.253519 + 0.863406i 0.983649 + 0.180097i \(0.0576413\pi\)
−0.730130 + 0.683308i \(0.760541\pi\)
\(548\) 0 0
\(549\) −9.85928 0.916273i −0.420784 0.0391056i
\(550\) 0 0
\(551\) 41.9064 36.3121i 1.78527 1.54695i
\(552\) 0 0
\(553\) 0.685963 4.77098i 0.0291701 0.202883i
\(554\) 0 0
\(555\) 8.65940 + 3.69521i 0.367571 + 0.156853i
\(556\) 0 0
\(557\) −3.60071 + 12.2629i −0.152567 + 0.519595i −0.999935 0.0114112i \(-0.996368\pi\)
0.847368 + 0.531006i \(0.178186\pi\)
\(558\) 0 0
\(559\) 9.67875 + 21.1935i 0.409368 + 0.896390i
\(560\) 0 0
\(561\) 23.6117 + 14.3511i 0.996887 + 0.605906i
\(562\) 0 0
\(563\) −43.9639 12.9090i −1.85286 0.544048i −0.999751 0.0223106i \(-0.992898\pi\)
−0.853106 0.521737i \(-0.825284\pi\)
\(564\) 0 0
\(565\) 0.685947 0.0288580
\(566\) 0 0
\(567\) −23.5674 8.02340i −0.989738 0.336951i
\(568\) 0 0
\(569\) −8.34604 + 7.23188i −0.349884 + 0.303176i −0.812016 0.583635i \(-0.801630\pi\)
0.462132 + 0.886811i \(0.347085\pi\)
\(570\) 0 0
\(571\) −8.80710 + 19.2849i −0.368566 + 0.807046i 0.630947 + 0.775826i \(0.282667\pi\)
−0.999513 + 0.0312200i \(0.990061\pi\)
\(572\) 0 0
\(573\) −33.3933 + 16.2737i −1.39502 + 0.679844i
\(574\) 0 0
\(575\) 2.39154 3.72131i 0.0997342 0.155190i
\(576\) 0 0
\(577\) −19.0613 2.74060i −0.793531 0.114093i −0.266385 0.963867i \(-0.585829\pi\)
−0.527147 + 0.849774i \(0.676738\pi\)
\(578\) 0 0
\(579\) −7.47976 23.2970i −0.310848 0.968192i
\(580\) 0 0
\(581\) 8.48112 18.5711i 0.351856 0.770457i
\(582\) 0 0
\(583\) −7.01144 15.3529i −0.290384 0.635853i
\(584\) 0 0
\(585\) 5.20980 9.07661i 0.215399 0.375272i
\(586\) 0 0
\(587\) −14.3810 + 4.22263i −0.593566 + 0.174287i −0.564699 0.825297i \(-0.691008\pi\)
−0.0288662 + 0.999583i \(0.509190\pi\)
\(588\) 0 0
\(589\) −0.0596291 + 0.00857337i −0.00245697 + 0.000353259i
\(590\) 0 0
\(591\) −2.54188 + 4.18211i −0.104559 + 0.172029i
\(592\) 0 0
\(593\) −15.9821 + 34.9959i −0.656306 + 1.43711i 0.229619 + 0.973281i \(0.426252\pi\)
−0.885925 + 0.463829i \(0.846475\pi\)
\(594\) 0 0
\(595\) 11.0021 + 7.07061i 0.451041 + 0.289867i
\(596\) 0 0
\(597\) 11.2725 1.91023i 0.461353 0.0781807i
\(598\) 0 0
\(599\) −4.01145 27.9002i −0.163903 1.13997i −0.891187 0.453636i \(-0.850127\pi\)
0.727284 0.686337i \(-0.240782\pi\)
\(600\) 0 0
\(601\) −2.81122 + 3.24432i −0.114672 + 0.132338i −0.810183 0.586177i \(-0.800632\pi\)
0.695511 + 0.718515i \(0.255178\pi\)
\(602\) 0 0
\(603\) −22.3632 10.1433i −0.910701 0.413067i
\(604\) 0 0
\(605\) 2.82980 3.26577i 0.115048 0.132772i
\(606\) 0 0
\(607\) −0.831144 5.78073i −0.0337351 0.234633i 0.965977 0.258628i \(-0.0832704\pi\)
−0.999712 + 0.0239954i \(0.992361\pi\)
\(608\) 0 0
\(609\) −34.9579 + 5.92396i −1.41657 + 0.240051i
\(610\) 0 0
\(611\) −9.19210 5.90741i −0.371873 0.238988i
\(612\) 0 0
\(613\) 17.4434 38.1957i 0.704531 1.54271i −0.129858 0.991533i \(-0.541452\pi\)
0.834389 0.551176i \(-0.185821\pi\)
\(614\) 0 0
\(615\) 6.62366 10.8978i 0.267092 0.439442i
\(616\) 0 0
\(617\) −32.9759 + 4.74122i −1.32756 + 0.190874i −0.769351 0.638826i \(-0.779420\pi\)
−0.558209 + 0.829701i \(0.688511\pi\)
\(618\) 0 0
\(619\) −1.44894 + 0.425447i −0.0582378 + 0.0171002i −0.310722 0.950501i \(-0.600571\pi\)
0.252484 + 0.967601i \(0.418753\pi\)
\(620\) 0 0
\(621\) 0.419556 6.19667i 0.0168362 0.248664i
\(622\) 0 0
\(623\) −6.84317 14.9844i −0.274166 0.600339i
\(624\) 0 0
\(625\) 2.99113 6.54967i 0.119645 0.261987i
\(626\) 0 0
\(627\) −15.2580 47.5238i −0.609346 1.89792i
\(628\) 0 0
\(629\) 19.5800 + 2.81517i 0.780704 + 0.112248i
\(630\) 0 0
\(631\) 12.0269 18.7142i 0.478784 0.745002i −0.514896 0.857253i \(-0.672170\pi\)
0.993680 + 0.112250i \(0.0358059\pi\)
\(632\) 0 0
\(633\) −17.6525 + 8.60267i −0.701623 + 0.341925i
\(634\) 0 0
\(635\) 9.83408 21.5336i 0.390254 0.854536i
\(636\) 0 0
\(637\) 1.50769 1.30642i 0.0597368 0.0517622i
\(638\) 0 0
\(639\) 11.4067 + 32.6896i 0.451243 + 1.29318i
\(640\) 0 0
\(641\) 18.4942 0.730477 0.365239 0.930914i \(-0.380987\pi\)
0.365239 + 0.930914i \(0.380987\pi\)
\(642\) 0 0
\(643\) −15.6061 4.58236i −0.615444 0.180711i −0.0408714 0.999164i \(-0.513013\pi\)
−0.574572 + 0.818454i \(0.694832\pi\)
\(644\) 0 0
\(645\) −12.8427 7.80574i −0.505679 0.307351i
\(646\) 0 0
\(647\) −17.4739 38.2625i −0.686969 1.50425i −0.855087 0.518485i \(-0.826496\pi\)
0.168117 0.985767i \(-0.446231\pi\)
\(648\) 0 0
\(649\) −14.0715 + 47.9231i −0.552355 + 1.88115i
\(650\) 0 0
\(651\) 0.0354295 + 0.0151188i 0.00138859 + 0.000592552i
\(652\) 0 0
\(653\) −6.03492 + 41.9738i −0.236165 + 1.64256i 0.434406 + 0.900717i \(0.356958\pi\)
−0.670571 + 0.741845i \(0.733951\pi\)
\(654\) 0 0
\(655\) −5.29026 + 4.58403i −0.206707 + 0.179113i
\(656\) 0 0
\(657\) −3.27700 + 35.2612i −0.127848 + 1.37567i
\(658\) 0 0
\(659\) −10.1402 34.5344i −0.395006 1.34527i −0.881748 0.471721i \(-0.843633\pi\)
0.486741 0.873546i \(-0.338185\pi\)
\(660\) 0 0
\(661\) 26.8605 + 23.2748i 1.04475 + 0.905283i 0.995618 0.0935088i \(-0.0298083\pi\)
0.0491342 + 0.998792i \(0.484354\pi\)
\(662\) 0 0
\(663\) 5.66423 21.2467i 0.219980 0.825154i
\(664\) 0 0
\(665\) −6.65585 22.6678i −0.258103 0.879018i
\(666\) 0 0
\(667\) −3.67453 8.04611i −0.142279 0.311547i
\(668\) 0 0
\(669\) −10.6968 + 5.21293i −0.413562 + 0.201543i
\(670\) 0 0
\(671\) 12.6938i 0.490040i
\(672\) 0 0
\(673\) 5.30639 2.42335i 0.204546 0.0934131i −0.310508 0.950571i \(-0.600499\pi\)
0.515054 + 0.857158i \(0.327772\pi\)
\(674\) 0 0
\(675\) −1.44467 19.1758i −0.0556053 0.738075i
\(676\) 0 0
\(677\) 5.62699 6.49390i 0.216263 0.249581i −0.637244 0.770662i \(-0.719926\pi\)
0.853507 + 0.521081i \(0.174471\pi\)
\(678\) 0 0
\(679\) 11.7467 13.5564i 0.450796 0.520246i
\(680\) 0 0
\(681\) −20.8383 22.8647i −0.798525 0.876176i
\(682\) 0 0
\(683\) −1.45684 + 0.936255i −0.0557445 + 0.0358248i −0.568216 0.822879i \(-0.692366\pi\)
0.512472 + 0.858704i \(0.328730\pi\)
\(684\) 0 0
\(685\) −1.23132 1.42102i −0.0470463 0.0542943i
\(686\) 0 0
\(687\) 30.0329 9.64239i 1.14583 0.367880i
\(688\) 0 0
\(689\) −10.1510 + 8.79588i −0.386722 + 0.335096i
\(690\) 0 0
\(691\) 18.8649 + 5.53922i 0.717653 + 0.210722i 0.620116 0.784510i \(-0.287085\pi\)
0.0975370 + 0.995232i \(0.468904\pi\)
\(692\) 0 0
\(693\) −7.44590 + 31.0350i −0.282846 + 1.17892i
\(694\) 0 0
\(695\) −12.4446 19.3641i −0.472049 0.734523i
\(696\) 0 0
\(697\) 7.54892 25.7092i 0.285936 0.973807i
\(698\) 0 0
\(699\) 10.8687 5.29671i 0.411093 0.200340i
\(700\) 0 0
\(701\) 18.3391 + 11.7859i 0.692660 + 0.445145i 0.839031 0.544084i \(-0.183123\pi\)
−0.146371 + 0.989230i \(0.546759\pi\)
\(702\) 0 0
\(703\) −23.4004 27.0055i −0.882562 1.01853i
\(704\) 0 0
\(705\) 7.04592 0.176646i 0.265365 0.00665287i
\(706\) 0 0
\(707\) 37.6845i 1.41727i
\(708\) 0 0
\(709\) 24.2498 + 15.5844i 0.910720 + 0.585284i 0.909951 0.414715i \(-0.136119\pi\)
0.000768915 1.00000i \(0.499755\pi\)
\(710\) 0 0
\(711\) 3.77414 3.61692i 0.141541 0.135645i
\(712\) 0 0
\(713\) −0.00136763 + 0.00951208i −5.12182e−5 + 0.000356230i
\(714\) 0 0
\(715\) −12.2041 5.57343i −0.456408 0.208435i
\(716\) 0 0
\(717\) 1.34201 + 1.10521i 0.0501184 + 0.0412747i
\(718\) 0 0
\(719\) −41.3844 + 5.95018i −1.54338 + 0.221904i −0.860813 0.508921i \(-0.830044\pi\)
−0.682565 + 0.730825i \(0.739135\pi\)
\(720\) 0 0
\(721\) −10.9168 37.1793i −0.406564 1.38463i
\(722\) 0 0
\(723\) 25.4741 + 37.5356i 0.947394 + 1.39596i
\(724\) 0 0
\(725\) −14.8067 23.0397i −0.549908 0.855673i
\(726\) 0 0
\(727\) 19.1137 + 8.72894i 0.708888 + 0.323738i 0.737025 0.675866i \(-0.236230\pi\)
−0.0281366 + 0.999604i \(0.508957\pi\)
\(728\) 0 0
\(729\) −14.7693 22.6024i −0.547013 0.837124i
\(730\) 0 0
\(731\) −30.2974 8.89612i −1.12059 0.329035i
\(732\) 0 0
\(733\) −24.6359 + 3.54211i −0.909948 + 0.130831i −0.581364 0.813644i \(-0.697481\pi\)
−0.328584 + 0.944475i \(0.606571\pi\)
\(734\) 0 0
\(735\) −0.331482 + 1.24340i −0.0122269 + 0.0458634i
\(736\) 0 0
\(737\) −10.2947 + 29.7494i −0.379211 + 1.09583i
\(738\) 0 0
\(739\) 0.277242 + 0.240232i 0.0101985 + 0.00883706i 0.659945 0.751314i \(-0.270580\pi\)
−0.649747 + 0.760151i \(0.725125\pi\)
\(740\) 0 0
\(741\) −32.8667 + 22.3055i −1.20739 + 0.819413i
\(742\) 0 0
\(743\) −0.132950 + 0.452788i −0.00487748 + 0.0166112i −0.961896 0.273416i \(-0.911846\pi\)
0.957018 + 0.290028i \(0.0936645\pi\)
\(744\) 0 0
\(745\) 9.90559 15.4134i 0.362913 0.564703i
\(746\) 0 0
\(747\) 19.6545 10.1957i 0.719122 0.373040i
\(748\) 0 0
\(749\) −46.2839 + 29.7449i −1.69118 + 1.08685i
\(750\) 0 0
\(751\) 3.81484 + 26.5328i 0.139205 + 0.968195i 0.932966 + 0.359965i \(0.117211\pi\)
−0.793761 + 0.608230i \(0.791880\pi\)
\(752\) 0 0
\(753\) 15.6794 14.2898i 0.571389 0.520750i
\(754\) 0 0
\(755\) 2.21550 + 15.4092i 0.0806304 + 0.560797i
\(756\) 0 0
\(757\) −29.0755 + 13.2783i −1.05677 + 0.482609i −0.866528 0.499129i \(-0.833654\pi\)
−0.190239 + 0.981738i \(0.560926\pi\)
\(758\) 0 0
\(759\) −7.95968 + 0.199554i −0.288918 + 0.00724336i
\(760\) 0 0
\(761\) 39.4929 + 5.67822i 1.43162 + 0.205835i 0.814100 0.580724i \(-0.197231\pi\)
0.617515 + 0.786559i \(0.288140\pi\)
\(762\) 0 0
\(763\) −0.670503 + 4.66345i −0.0242738 + 0.168828i
\(764\) 0 0
\(765\) 4.67291 + 13.3917i 0.168950 + 0.484179i
\(766\) 0 0
\(767\) 39.7474 1.43520
\(768\) 0 0
\(769\) 11.1492 + 5.09166i 0.402050 + 0.183610i 0.606169 0.795336i \(-0.292706\pi\)
−0.204119 + 0.978946i \(0.565433\pi\)
\(770\) 0 0
\(771\) −1.34143 + 3.14351i −0.0483103 + 0.113211i
\(772\) 0 0
\(773\) 6.11766 9.51926i 0.220037 0.342384i −0.713632 0.700520i \(-0.752951\pi\)
0.933669 + 0.358136i \(0.116588\pi\)
\(774\) 0 0
\(775\) 0.0297542i 0.00106880i
\(776\) 0 0