Properties

Label 804.2.s.b.5.11
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 5.11
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0434100 - 1.73151i) q^{3} +(-1.09364 + 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(-2.99623 - 0.150329i) q^{9} +O(q^{10})\) \(q+(0.0434100 - 1.73151i) q^{3} +(-1.09364 + 0.321121i) q^{5} +(2.09055 + 1.81147i) q^{7} +(-2.99623 - 0.150329i) q^{9} +(-3.69014 + 1.08352i) q^{11} +(-1.65469 - 2.57474i) q^{13} +(0.508549 + 1.90758i) q^{15} +(-4.10573 - 0.590315i) q^{17} +(-4.90683 - 5.66278i) q^{19} +(3.22732 - 3.54116i) q^{21} +(1.08727 - 0.496537i) q^{23} +(-3.11334 + 2.00082i) q^{25} +(-0.390363 + 5.18147i) q^{27} -7.40032i q^{29} +(0.00434668 - 0.00676357i) q^{31} +(1.71594 + 6.43654i) q^{33} +(-2.86801 - 1.30978i) q^{35} +4.76894 q^{37} +(-4.53001 + 2.75333i) q^{39} +(-0.919315 + 6.39398i) q^{41} +(-7.53507 - 1.08338i) q^{43} +(3.32507 - 0.797748i) q^{45} +(-3.24748 + 1.48308i) q^{47} +(0.0927634 + 0.645184i) q^{49} +(-1.20036 + 7.08347i) q^{51} +(0.624559 + 4.34391i) q^{53} +(3.68774 - 2.36997i) q^{55} +(-10.0182 + 8.25039i) q^{57} +(7.02119 - 10.9252i) q^{59} +(-0.929884 + 3.16689i) q^{61} +(-5.99145 - 5.74186i) q^{63} +(2.63643 + 2.28448i) q^{65} +(-4.74764 + 6.66783i) q^{67} +(-0.812560 - 1.90416i) q^{69} +(-11.4234 + 1.64244i) q^{71} +(11.3262 + 3.32568i) q^{73} +(3.32929 + 5.47763i) q^{75} +(-9.67720 - 4.41943i) q^{77} +(-0.942057 - 1.46587i) q^{79} +(8.95480 + 0.900844i) q^{81} +(2.07934 + 7.08159i) q^{83} +(4.67975 - 0.672846i) q^{85} +(-12.8137 - 0.321248i) q^{87} +(5.41699 + 2.47386i) q^{89} +(1.20487 - 8.38004i) q^{91} +(-0.0115225 - 0.00781992i) q^{93} +(7.18474 + 4.61735i) q^{95} -6.48460i q^{97} +(11.2194 - 2.69175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) 0.0434100 1.73151i 0.0250628 0.999686i
\(4\) 0 0
\(5\) −1.09364 + 0.321121i −0.489090 + 0.143610i −0.516974 0.856001i \(-0.672941\pi\)
0.0278834 + 0.999611i \(0.491123\pi\)
\(6\) 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
\(9\) −2.99623 0.150329i −0.998744 0.0501098i
\(10\) 0 0
\(11\) −3.69014 + 1.08352i −1.11262 + 0.326695i −0.785855 0.618411i \(-0.787777\pi\)
−0.326765 + 0.945106i \(0.605959\pi\)
\(12\) 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
\(15\) 0.508549 + 1.90758i 0.131307 + 0.492536i
\(16\) 0 0
\(17\) −4.10573 0.590315i −0.995785 0.143172i −0.374893 0.927068i \(-0.622321\pi\)
−0.620892 + 0.783896i \(0.713230\pi\)
\(18\) 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
\(21\) 3.22732 3.54116i 0.704260 0.772745i
\(22\) 0 0
\(23\) 1.08727 0.496537i 0.226710 0.103535i −0.298822 0.954309i \(-0.596594\pi\)
0.525532 + 0.850774i \(0.323866\pi\)
\(24\) 0 0
\(25\) −3.11334 + 2.00082i −0.622668 + 0.400164i
\(26\) 0 0
\(27\) −0.390363 + 5.18147i −0.0751254 + 0.997174i
\(28\) 0 0
\(29\) 7.40032i 1.37420i −0.726561 0.687102i \(-0.758882\pi\)
0.726561 0.687102i \(-0.241118\pi\)
\(30\) 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
\(33\) 1.71594 + 6.43654i 0.298707 + 1.12046i
\(34\) 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
\(39\) −4.53001 + 2.75333i −0.725383 + 0.440886i
\(40\) 0 0
\(41\) −0.919315 + 6.39398i −0.143573 + 0.998571i 0.782883 + 0.622169i \(0.213748\pi\)
−0.926456 + 0.376403i \(0.877161\pi\)
\(42\) 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
\(45\) 3.32507 0.797748i 0.495672 0.118921i
\(46\) 0 0
\(47\) −3.24748 + 1.48308i −0.473694 + 0.216329i −0.637933 0.770092i \(-0.720210\pi\)
0.164239 + 0.986421i \(0.447483\pi\)
\(48\) 0 0
\(49\) 0.0927634 + 0.645184i 0.0132519 + 0.0921691i
\(50\) 0 0
\(51\) −1.20036 + 7.08347i −0.168084 + 0.991884i
\(52\) 0 0
\(53\) 0.624559 + 4.34391i 0.0857898 + 0.596681i 0.986685 + 0.162644i \(0.0520023\pi\)
−0.900895 + 0.434037i \(0.857089\pi\)
\(54\) 0 0
\(55\) 3.68774 2.36997i 0.497255 0.319566i
\(56\) 0 0
\(57\) −10.0182 + 8.25039i −1.32694 + 1.09279i
\(58\) 0 0
\(59\) 7.02119 10.9252i 0.914081 1.42234i 0.00765668 0.999971i \(-0.497563\pi\)
0.906425 0.422368i \(-0.138801\pi\)
\(60\) 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
\(63\) −5.99145 5.74186i −0.754852 0.723406i
\(64\) 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
\(69\) −0.812560 1.90416i −0.0978207 0.229234i
\(70\) 0 0
\(71\) −11.4234 + 1.64244i −1.35571 + 0.194921i −0.781560 0.623830i \(-0.785576\pi\)
−0.574148 + 0.818752i \(0.694667\pi\)
\(72\) 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
\(75\) 3.32929 + 5.47763i 0.384433 + 0.632502i
\(76\) 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
\(81\) 8.95480 + 0.900844i 0.994978 + 0.100094i
\(82\) 0 0
\(83\) 2.07934 + 7.08159i 0.228237 + 0.777305i 0.991373 + 0.131067i \(0.0418404\pi\)
−0.763136 + 0.646238i \(0.776341\pi\)
\(84\) 0 0
\(85\) 4.67975 0.672846i 0.507590 0.0729804i
\(86\) 0 0
\(87\) −12.8137 0.321248i −1.37377 0.0344414i
\(88\) 0 0
\(89\) 5.41699 + 2.47386i 0.574200 + 0.262228i 0.681281 0.732022i \(-0.261423\pi\)
−0.107081 + 0.994250i \(0.534150\pi\)
\(90\) 0 0
\(91\) 1.20487 8.38004i 0.126304 0.878467i
\(92\) 0 0
\(93\) −0.0115225 0.00781992i −0.00119483 0.000810888i
\(94\) 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
\(99\) 11.2194 2.69175i 1.12759 0.270531i
\(100\) 0 0
\(101\) 8.92133 + 10.2958i 0.887706 + 1.02447i 0.999527 + 0.0307386i \(0.00978593\pi\)
−0.111822 + 0.993728i \(0.535669\pi\)
\(102\) 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 \(-0.497832\pi\)
0.534900 0.844916i \(-0.320349\pi\)
\(108\) 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
\(111\) 0.207020 8.25745i 0.0196494 0.783762i
\(112\) 0 0
\(113\) −0.577431 0.169549i −0.0543201 0.0159498i 0.254460 0.967083i \(-0.418102\pi\)
−0.308780 + 0.951134i \(0.599921\pi\)
\(114\) 0 0
\(115\) −1.02963 + 0.892177i −0.0960132 + 0.0831959i
\(116\) 0 0
\(117\) 4.57076 + 7.96327i 0.422567 + 0.736205i
\(118\) 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
\(123\) 11.0313 + 1.86936i 0.994659 + 0.168555i
\(124\) 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
\(129\) −2.20298 + 13.0000i −0.193961 + 1.14459i
\(130\) 0 0
\(131\) 5.58640 2.55122i 0.488086 0.222902i −0.156142 0.987735i \(-0.549906\pi\)
0.644229 + 0.764833i \(0.277179\pi\)
\(132\) 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 0.936645 0.350281i \(-0.113914\pi\)
−0.878097 + 0.478483i \(0.841187\pi\)
\(138\) 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
\(141\) 2.42698 + 5.68742i 0.204389 + 0.478967i
\(142\) 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
\(147\) 1.12117 0.132613i 0.0924723 0.0109377i
\(148\) 0 0
\(149\) −12.1484 + 10.5266i −0.995232 + 0.862373i −0.990486 0.137616i \(-0.956056\pi\)
−0.00474598 + 0.999989i \(0.501511\pi\)
\(150\) 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
\(153\) 12.2130 + 2.38593i 0.987360 + 0.192891i
\(154\) 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
\(159\) 7.54861 0.892860i 0.598644 0.0708084i
\(160\) 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
\(165\) −3.94353 6.48823i −0.307003 0.505108i
\(166\) 0 0
\(167\) −8.83963 + 7.65959i −0.684031 + 0.592717i −0.925980 0.377573i \(-0.876759\pi\)
0.241949 + 0.970289i \(0.422213\pi\)
\(168\) 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 −0.980855 0.194738i \(-0.937614\pi\)
0.584602 + 0.811320i \(0.301251\pi\)
\(174\) 0 0
\(175\) −10.1330 1.45691i −0.765984 0.110132i
\(176\) 0 0
\(177\) −18.6122 12.6315i −1.39898 0.949442i
\(178\) 0 0
\(179\) 0.610074 1.33588i 0.0455990 0.0998480i −0.885461 0.464713i \(-0.846158\pi\)
0.931060 + 0.364865i \(0.118885\pi\)
\(180\) 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
\(183\) 5.44313 + 1.74757i 0.402368 + 0.129184i
\(184\) 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
\(189\) −10.2022 + 10.1250i −0.742097 + 0.736484i
\(190\) 0 0
\(191\) 8.90948 19.5091i 0.644668 1.41163i −0.251477 0.967863i \(-0.580916\pi\)
0.896145 0.443762i \(-0.146356\pi\)
\(192\) 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
\(195\) 4.07005 4.46584i 0.291462 0.319805i
\(196\) 0 0
\(197\) −0.402118 2.79679i −0.0286497 0.199263i 0.970470 0.241224i \(-0.0775487\pi\)
−0.999119 + 0.0419605i \(0.986640\pi\)
\(198\) 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
\(201\) 11.3393 + 8.51002i 0.799812 + 0.600251i
\(202\) 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
\(207\) −3.33234 + 1.32429i −0.231614 + 0.0920447i
\(208\) 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
\(213\) 2.34800 + 19.8510i 0.160882 + 1.36017i
\(214\) 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
\(219\) 6.25011 19.4671i 0.422343 1.31546i
\(220\) 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
\(225\) 9.62907 5.52690i 0.641938 0.368460i
\(226\) 0 0
\(227\) 17.6790 + 2.54186i 1.17340 + 0.168709i 0.701320 0.712847i \(-0.252595\pi\)
0.472079 + 0.881556i \(0.343504\pi\)
\(228\) 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 −0.980520 0.196417i \(-0.937069\pi\)
0.790547 + 0.612402i \(0.209797\pi\)
\(234\) 0 0
\(235\) 3.07533 2.66479i 0.200612 0.173831i
\(236\) 0 0
\(237\) −2.57906 + 1.56755i −0.167528 + 0.101823i
\(238\) 0 0
\(239\) −1.00374 −0.0649266 −0.0324633 0.999473i \(-0.510335\pi\)
−0.0324633 + 0.999473i \(0.510335\pi\)
\(240\) 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
\(243\) 1.94855 15.4662i 0.124999 0.992157i
\(244\) 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
\(249\) 12.3521 3.29298i 0.782781 0.208684i
\(250\) 0 0
\(251\) −1.74308 + 12.1234i −0.110022 + 0.765220i 0.857872 + 0.513863i \(0.171786\pi\)
−0.967894 + 0.251357i \(0.919123\pi\)
\(252\) 0 0
\(253\) −3.47415 + 3.01037i −0.218418 + 0.189260i
\(254\) 0 0
\(255\) −0.961890 8.13222i −0.0602359 0.509260i
\(256\) 0 0
\(257\) −0.555928 1.89332i −0.0346778 0.118102i 0.940335 0.340249i \(-0.110511\pi\)
−0.975013 + 0.222148i \(0.928693\pi\)
\(258\) 0 0
\(259\) 9.96970 + 8.63879i 0.619487 + 0.536788i
\(260\) 0 0
\(261\) −1.11249 + 22.1731i −0.0688612 + 1.37248i
\(262\) 0 0
\(263\) 3.92129 + 13.3547i 0.241797 + 0.823486i 0.987556 + 0.157270i \(0.0502691\pi\)
−0.745758 + 0.666216i \(0.767913\pi\)
\(264\) 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 \(-0.952216\pi\)
0.988753 0.149555i \(-0.0477842\pi\)
\(270\) 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
\(273\) −14.4578 2.45001i −0.875025 0.148282i
\(274\) 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
\(279\) −0.0140404 + 0.0196118i −0.000840578 + 0.00117413i
\(280\) 0 0
\(281\) −13.9279 + 8.95093i −0.830870 + 0.533968i −0.885554 0.464536i \(-0.846221\pi\)
0.0546844 + 0.998504i \(0.482585\pi\)
\(282\) 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
\(285\) 8.30687 12.2400i 0.492056 0.725035i
\(286\) 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
\(291\) −11.2281 0.281497i −0.658205 0.0165016i
\(292\) 0 0
\(293\) −6.01047 9.35248i −0.351135 0.546377i 0.620093 0.784529i \(-0.287095\pi\)
−0.971228 + 0.238151i \(0.923459\pi\)
\(294\) 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
\(303\) 18.2145 15.0004i 1.04639 0.861751i
\(304\) 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
\(309\) −13.6248 + 20.0758i −0.775088 + 1.14208i
\(310\) 0 0
\(311\) 3.61950 25.1742i 0.205243 1.42750i −0.583170 0.812350i \(-0.698188\pi\)
0.788413 0.615146i \(-0.210903\pi\)
\(312\) 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
\(315\) 8.39632 + 4.35554i 0.473079 + 0.245407i
\(316\) 0 0
\(317\) −18.1791 + 2.61376i −1.02104 + 0.146803i −0.632445 0.774605i \(-0.717949\pi\)
−0.388595 + 0.921409i \(0.627040\pi\)
\(318\) 0 0
\(319\) 8.01842 + 27.3082i 0.448945 + 1.52897i
\(320\) 0 0
\(321\) −32.8003 10.5309i −1.83074 0.587777i
\(322\) 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
\(327\) 2.52093 1.53222i 0.139408 0.0847317i
\(328\) 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
\(333\) −14.2888 0.716912i −0.783024 0.0392865i
\(334\) 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
\(339\) −0.318642 + 0.992466i −0.0173062 + 0.0539033i
\(340\) 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
\(345\) 1.50011 + 1.82154i 0.0807634 + 0.0980682i
\(346\) 0 0
\(347\) −15.5069 + 9.96571i −0.832456 + 0.534987i −0.886058 0.463575i \(-0.846566\pi\)
0.0536012 + 0.998562i \(0.482930\pi\)
\(348\) 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
\(351\) 13.9869 7.56862i 0.746564 0.403983i
\(352\) 0 0
\(353\) −0.253361 1.76217i −0.0134851 0.0937906i 0.981967 0.189050i \(-0.0605409\pi\)
−0.995452 + 0.0952597i \(0.969632\pi\)
\(354\) 0 0
\(355\) 11.9657 5.46453i 0.635071 0.290027i
\(356\) 0 0
\(357\) −15.3409 + 12.6339i −0.811927 + 0.668658i
\(358\) 0 0
\(359\) −27.8551 4.00496i −1.47014 0.211374i −0.639760 0.768575i \(-0.720966\pi\)
−0.830378 + 0.557201i \(0.811875\pi\)
\(360\) 0 0
\(361\) −5.28616 + 36.7660i −0.278219 + 1.93505i
\(362\) 0 0
\(363\) −3.41057 5.61135i −0.179008 0.294520i
\(364\) 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
\(369\) 3.71568 19.0196i 0.193431 0.990123i
\(370\) 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
\(375\) −12.6957 11.5705i −0.655603 0.597500i
\(376\) 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
\(381\) −26.5878 24.2315i −1.36214 1.24142i
\(382\) 0 0
\(383\) −19.4053 22.3949i −0.991565 1.14433i −0.989530 0.144329i \(-0.953898\pi\)
−0.00203522 0.999998i \(-0.500648\pi\)
\(384\) 0 0
\(385\) 12.0025 + 1.72570i 0.611706 + 0.0879500i
\(386\) 0 0
\(387\) 22.4139 + 4.37880i 1.13936 + 0.222587i
\(388\) 0 0
\(389\) −17.7489 27.6178i −0.899903 1.40028i −0.916335 0.400412i \(-0.868867\pi\)
0.0164322 0.999865i \(-0.494769\pi\)
\(390\) 0 0
\(391\) −4.75713 + 1.39682i −0.240578 + 0.0706402i
\(392\) 0 0
\(393\) −4.17496 9.78364i −0.210599 0.493519i
\(394\) 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
\(399\) −35.8888 0.899755i −1.79669 0.0450441i
\(400\) 0 0
\(401\) 20.4141 1.01943 0.509717 0.860342i \(-0.329750\pi\)
0.509717 + 0.860342i \(0.329750\pi\)
\(402\) 0 0
\(403\) −0.0246068 −0.00122575
\(404\) 0 0
\(405\) −10.0826 + 1.89038i −0.501009 + 0.0939338i
\(406\) 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
\(411\) 2.62799 1.12144i 0.129629 0.0553164i
\(412\) 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
\(417\) −33.7979 + 9.01029i −1.65509 + 0.441236i
\(418\) 0 0
\(419\) −19.2259 2.76426i −0.939245 0.135043i −0.344346 0.938843i \(-0.611899\pi\)
−0.594900 + 0.803800i \(0.702808\pi\)
\(420\) 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
\(423\) 9.95316 3.95545i 0.483939 0.192320i
\(424\) 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
\(429\) 13.7331 15.0686i 0.663040 0.727517i
\(430\) 0 0
\(431\) 14.1768i 0.682872i 0.939905 + 0.341436i \(0.110913\pi\)
−0.939905 + 0.341436i \(0.889087\pi\)
\(432\) 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
\(435\) 14.1167 3.76342i 0.676845 0.180442i
\(436\) 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
\(441\) −0.180951 1.94706i −0.00861669 0.0927174i
\(442\) 0 0
\(443\) 2.98481 20.7598i 0.141812 0.986328i −0.787311 0.616557i \(-0.788527\pi\)
0.929123 0.369771i \(-0.120564\pi\)
\(444\) 0 0
\(445\) −6.71864 0.965995i −0.318494 0.0457926i
\(446\) 0 0
\(447\) 17.6995 + 21.4919i 0.837159 + 1.01653i
\(448\) 0 0
\(449\) 3.28217 1.49892i 0.154895 0.0707382i −0.336459 0.941698i \(-0.609229\pi\)
0.491354 + 0.870960i \(0.336502\pi\)
\(450\) 0 0
\(451\) −3.53562 24.5908i −0.166486 1.15794i
\(452\) 0 0
\(453\) 23.3240 + 3.95248i 1.09586 + 0.185704i
\(454\) 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
\(459\) 4.66142 21.0433i 0.217576 0.982215i
\(460\) 0 0
\(461\) 19.9136 30.9862i 0.927469 1.44317i 0.0312737 0.999511i \(-0.490044\pi\)
0.896196 0.443659i \(-0.146320\pi\)
\(462\) 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
\(465\) 0.0151126 + 0.00485205i 0.000700829 + 0.000225009i
\(466\) 0 0
\(467\) 3.00536 + 2.60416i 0.139071 + 0.120506i 0.721619 0.692291i \(-0.243398\pi\)
−0.582547 + 0.812797i \(0.697944\pi\)
\(468\) 0 0
\(469\) −22.0037 + 5.33920i −1.01604 + 0.246541i
\(470\) 0 0
\(471\) −6.18201 + 2.63804i −0.284852 + 0.121554i
\(472\) 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
\(477\) −1.21831 13.1092i −0.0557824 0.600231i
\(478\) 0 0
\(479\) −25.6151 11.6980i −1.17038 0.534495i −0.267153 0.963654i \(-0.586083\pi\)
−0.903229 + 0.429159i \(0.858810\pi\)
\(480\) 0 0
\(481\) −7.89110 12.2788i −0.359803 0.559864i
\(482\) 0 0
\(483\) 1.75064 5.45267i 0.0796568 0.248105i
\(484\) 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
\(489\) −0.518644 + 20.6873i −0.0234539 + 0.935512i
\(490\) 0 0
\(491\) −26.9926 12.3271i −1.21816 0.556315i −0.300538 0.953770i \(-0.597166\pi\)
−0.917622 + 0.397455i \(0.869893\pi\)
\(492\) 0 0
\(493\) −4.36852 + 30.3837i −0.196748 + 1.36841i
\(494\) 0 0
\(495\) −11.4056 + 6.54660i −0.512644 + 0.294248i
\(496\) 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
\(501\) 12.8789 + 15.6384i 0.575387 + 0.698672i
\(502\) 0 0
\(503\) −21.9061 25.2810i −0.976744 1.12722i −0.991860 0.127336i \(-0.959357\pi\)
0.0151160 0.999886i \(-0.495188\pi\)
\(504\) 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 \(0.461554\pi\)
−0.638062 + 0.769985i \(0.720264\pi\)
\(510\) 0 0
\(511\) 17.6537 + 27.4696i 0.780952 + 1.21518i
\(512\) 0 0
\(513\) 31.2570 23.2140i 1.38003 1.02493i
\(514\) 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
\(519\) 13.8161 + 9.37649i 0.606458 + 0.411582i
\(520\) 0 0
\(521\) 7.20556 + 8.31566i 0.315681 + 0.364315i 0.891309 0.453396i \(-0.149788\pi\)
−0.575628 + 0.817712i \(0.695242\pi\)
\(522\) 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
\(525\) −2.96252 + 17.4821i −0.129295 + 0.762983i
\(526\) 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
\(531\) −22.6795 + 31.6789i −0.984206 + 1.37475i
\(532\) 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
\(543\) −13.0607 + 5.57338i −0.560490 + 0.239177i
\(544\) 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
\(549\) 3.26222 9.34895i 0.139228 0.399004i
\(550\) 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
\(555\) 2.42524 + 9.09715i 0.102946 + 0.386152i
\(556\) 0 0
\(557\) 3.60071 12.2629i 0.152567 0.519595i −0.847368 0.531006i \(-0.821814\pi\)
0.999935 + 0.0114112i \(0.00363236\pi\)
\(558\) 0 0
\(559\) 9.67875 + 21.1935i 0.409368 + 0.896390i
\(560\) 0 0
\(561\) −3.24560 27.4396i −0.137029 1.15850i
\(562\) 0 0
\(563\) 43.9639 + 12.9090i 1.85286 + 0.544048i 0.999751 + 0.0223106i \(0.00710228\pi\)
0.853106 + 0.521737i \(0.174716\pi\)
\(564\) 0 0
\(565\) 0.685947 0.0288580
\(566\) 0 0
\(567\) 17.0886 + 18.1046i 0.717654 + 0.760322i
\(568\) 0 0
\(569\) 8.34604 7.23188i 0.349884 0.303176i −0.462132 0.886811i \(-0.652915\pi\)
0.812016 + 0.583635i \(0.198370\pi\)
\(570\) 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
\(579\) −13.7403 + 20.2460i −0.571028 + 0.841397i
\(580\) 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
\(585\) −7.55594 7.24118i −0.312400 0.299386i
\(586\) 0 0
\(587\) 14.3810 4.22263i 0.593566 0.174287i 0.0288662 0.999583i \(-0.490810\pi\)
0.564699 + 0.825297i \(0.308992\pi\)
\(588\) 0 0
\(589\) −0.0596291 + 0.00857337i −0.00245697 + 0.000353259i
\(590\) 0 0
\(591\) −4.86012 + 0.574861i −0.199919 + 0.0236466i
\(592\) 0 0
\(593\) 15.9821 34.9959i 0.656306 1.43711i −0.229619 0.973281i \(-0.573748\pi\)
0.885925 0.463829i \(-0.153525\pi\)
\(594\) 0 0
\(595\) 11.0021 + 7.07061i 0.451041 + 0.289867i
\(596\) 0 0
\(597\) −8.45028 7.70136i −0.345847 0.315196i
\(598\) 0 0
\(599\) 4.01145 + 27.9002i 0.163903 + 1.13997i 0.891187 + 0.453636i \(0.149873\pi\)
−0.727284 + 0.686337i \(0.759218\pi\)
\(600\) 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
\(603\) 15.2274 19.2646i 0.620108 0.784517i
\(604\) 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
\(609\) −26.2057 23.8832i −1.06191 0.967797i
\(610\) 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
\(615\) −12.6646 + 1.49798i −0.510684 + 0.0604044i
\(616\) 0 0
\(617\) 32.9759 4.74122i 1.32756 0.190874i 0.558209 0.829701i \(-0.311489\pi\)
0.769351 + 0.638826i \(0.220580\pi\)
\(618\) 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
\(621\) 2.14836 + 5.82746i 0.0862109 + 0.233848i
\(622\) 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
\(627\) 28.0289 41.3000i 1.11937 1.64936i
\(628\) 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
\(639\) 34.4740 3.20385i 1.36377 0.126742i
\(640\) 0 0
\(641\) −18.4942 −0.730477 −0.365239 0.930914i \(-0.619013\pi\)
−0.365239 + 0.930914i \(0.619013\pi\)
\(642\) 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
\(645\) −1.76531 14.9247i −0.0695092 0.587660i
\(646\) 0 0
\(647\) 17.4739 + 38.2625i 0.686969 + 1.50425i 0.855087 + 0.518485i \(0.173504\pi\)
−0.168117 + 0.985767i \(0.553769\pi\)
\(648\) 0 0
\(649\) −14.0715 + 47.9231i −0.552355 + 1.88115i
\(650\) 0 0
\(651\) −0.00992275 0.0372205i −0.000388903 0.00145879i
\(652\) 0 0
\(653\) 6.03492 41.9738i 0.236165 1.64256i −0.434406 0.900717i \(-0.643042\pi\)
0.670571 0.741845i \(-0.266049\pi\)
\(654\) 0 0
\(655\) −5.29026 + 4.58403i −0.206707 + 0.179113i
\(656\) 0 0
\(657\) −33.4360 11.6672i −1.30446 0.455180i
\(658\) 0 0
\(659\) 10.1402 + 34.5344i 0.395006 + 1.34527i 0.881748 + 0.471721i \(0.156367\pi\)
−0.486741 + 0.873546i \(0.661815\pi\)
\(660\) 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
\(663\) 20.2243 8.63030i 0.785448 0.335173i
\(664\) 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
\(675\) −9.15186 16.9127i −0.352255 0.650971i
\(676\) 0 0
\(677\) −5.62699 + 6.49390i −0.216263 + 0.249581i −0.853507 0.521081i \(-0.825529\pi\)
0.637244 + 0.770662i \(0.280074\pi\)
\(678\) 0 0
\(679\) 11.7467 13.5564i 0.450796 0.520246i
\(680\) 0 0
\(681\) 5.16870 30.5010i 0.198065 1.16880i
\(682\) 0 0
\(683\) 1.45684 0.936255i 0.0557445 0.0358248i −0.512472 0.858704i \(-0.671270\pi\)
0.568216 + 0.822879i \(0.307634\pi\)
\(684\) 0 0
\(685\) −1.23132 1.42102i −0.0470463 0.0542943i
\(686\) 0 0
\(687\) −26.0998 17.7131i −0.995770 0.675795i
\(688\) 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
\(693\) 28.3307 + 14.6964i 1.07620 + 0.558270i
\(694\) 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 0.146371 0.989230i \(-0.453241\pi\)
−0.839031 + 0.544084i \(0.816877\pi\)
\(702\) 0 0
\(703\) −23.4004 27.0055i −0.882562 1.01853i
\(704\) 0 0
\(705\) −4.48059 5.44063i −0.168749 0.204906i
\(706\) 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
\(711\) 2.60226 + 4.53370i 0.0975923 + 0.170027i
\(712\) 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
\(717\) −0.0435724 + 1.73798i −0.00162724 + 0.0649062i
\(718\) 0 0
\(719\) 41.3844 5.95018i 1.54338 0.221904i 0.682565 0.730825i \(-0.260865\pi\)
0.860813 + 0.508921i \(0.169956\pi\)
\(720\) 0 0
\(721\) −10.9168 37.1793i −0.406564 1.38463i
\(722\) 0 0
\(723\) 13.8673 43.1920i 0.515729 1.60633i
\(724\) 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
\(729\) −26.6952 4.04531i −0.988712 0.149826i
\(730\) 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
\(735\) −1.18357 + 0.505062i −0.0436565 + 0.0186295i
\(736\) 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
\(741\) 37.8195 + 12.1424i 1.38934 + 0.446061i
\(742\) 0 0
\(743\) 0.132950 0.452788i 0.00487748 0.0166112i −0.957018 0.290028i \(-0.906336\pi\)
0.961896 + 0.273416i \(0.0881537\pi\)
\(744\) 0 0
\(745\) 9.90559 15.4134i 0.362913 0.564703i
\(746\) 0 0
\(747\) −5.16562 21.5307i −0.189000 0.787765i
\(748\) 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
\(753\) 20.9160 + 3.54442i 0.762222 + 0.129166i
\(754\) 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
\(759\) 5.06167 + 6.14620i 0.183727 + 0.223093i
\(760\) 0 0
\(761\) −39.4929 5.67822i −1.43162 0.205835i −0.617515 0.786559i \(-0.711860\pi\)
−0.814100 + 0.580724i \(0.802769\pi\)
\(762\) 0 0
\(763\) −0.670503 + 4.66345i −0.0242738 + 0.168828i
\(764\) 0 0
\(765\) −14.1228 + 1.31250i −0.510609 + 0.0474535i
\(766\) 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
\(771\) −3.30242 + 0.880404i −0.118934 + 0.0317070i
\(772\) 0 0
\(773\) −6.11766 + 9.51926i −0.220037 + 0.342384i −0.933669 0.358136i \(-0.883412\pi\)
0.713632 + 0.700520i \(0.247049\pi\)
\(774\) 0 0
\(775\) 0.0297542i 0.00106880i
\(776\) 0 0