Properties

Label 756.2.ck.a.5.4
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.63242 + 0.578955i) q^{3} +(0.649280 - 3.68225i) q^{5} +(0.647047 - 2.56541i) q^{7} +(2.32962 - 1.89020i) q^{9} +O(q^{10})\) \(q+(-1.63242 + 0.578955i) q^{3} +(0.649280 - 3.68225i) q^{5} +(0.647047 - 2.56541i) q^{7} +(2.32962 - 1.89020i) q^{9} +(0.889725 - 0.156882i) q^{11} +(-0.769375 + 0.916906i) q^{13} +(1.07196 + 6.38690i) q^{15} -7.46688 q^{17} +0.689746i q^{19} +(0.429002 + 4.56245i) q^{21} +(2.84180 - 3.38672i) q^{23} +(-8.43895 - 3.07153i) q^{25} +(-2.70859 + 4.43436i) q^{27} +(-0.230745 - 0.274991i) q^{29} +(3.43265 + 9.43113i) q^{31} +(-1.36158 + 0.771209i) q^{33} +(-9.02637 - 4.04826i) q^{35} +(-4.77757 - 8.27499i) q^{37} +(0.725101 - 1.94221i) q^{39} +(-5.79118 - 4.85938i) q^{41} +(4.12751 + 1.50229i) q^{43} +(-5.44762 - 9.80553i) q^{45} +(-4.35416 - 1.58478i) q^{47} +(-6.16266 - 3.31988i) q^{49} +(12.1891 - 4.32299i) q^{51} +(11.6009 - 6.69781i) q^{53} -3.37805i q^{55} +(-0.399332 - 1.12596i) q^{57} +(0.0113213 + 0.00949971i) q^{59} +(-1.34236 + 3.68810i) q^{61} +(-3.34177 - 7.19949i) q^{63} +(2.87674 + 3.42836i) q^{65} +(-0.323090 + 1.83233i) q^{67} +(-2.67826 + 7.17384i) q^{69} +(-9.69050 - 5.59481i) q^{71} +(-9.63739 - 5.56415i) q^{73} +(15.5542 + 0.128266i) q^{75} +(0.173225 - 2.38402i) q^{77} +(1.78156 + 10.1037i) q^{79} +(1.85428 - 8.80691i) q^{81} +(4.58220 - 3.84492i) q^{83} +(-4.84810 + 27.4949i) q^{85} +(0.535881 + 0.315311i) q^{87} +13.9206 q^{89} +(1.85442 + 2.56704i) q^{91} +(-11.0637 - 13.4083i) q^{93} +(2.53982 + 0.447839i) q^{95} +(1.53264 - 4.21088i) q^{97} +(1.77618 - 2.04723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −1.63242 + 0.578955i −0.942481 + 0.334260i
\(4\) 0 0
\(5\) 0.649280 3.68225i 0.290367 1.64675i −0.395092 0.918642i \(-0.629287\pi\)
0.685459 0.728111i \(-0.259602\pi\)
\(6\) 0 0
\(7\) 0.647047 2.56541i 0.244561 0.969634i
\(8\) 0 0
\(9\) 2.32962 1.89020i 0.776541 0.630067i
\(10\) 0 0
\(11\) 0.889725 0.156882i 0.268262 0.0473018i −0.0378990 0.999282i \(-0.512067\pi\)
0.306161 + 0.951980i \(0.400955\pi\)
\(12\) 0 0
\(13\) −0.769375 + 0.916906i −0.213386 + 0.254304i −0.862111 0.506719i \(-0.830858\pi\)
0.648725 + 0.761023i \(0.275303\pi\)
\(14\) 0 0
\(15\) 1.07196 + 6.38690i 0.276778 + 1.64909i
\(16\) 0 0
\(17\) −7.46688 −1.81098 −0.905492 0.424362i \(-0.860498\pi\)
−0.905492 + 0.424362i \(0.860498\pi\)
\(18\) 0 0
\(19\) 0.689746i 0.158239i 0.996865 + 0.0791193i \(0.0252108\pi\)
−0.996865 + 0.0791193i \(0.974789\pi\)
\(20\) 0 0
\(21\) 0.429002 + 4.56245i 0.0936159 + 0.995608i
\(22\) 0 0
\(23\) 2.84180 3.38672i 0.592555 0.706180i −0.383540 0.923524i \(-0.625295\pi\)
0.976095 + 0.217344i \(0.0697395\pi\)
\(24\) 0 0
\(25\) −8.43895 3.07153i −1.68779 0.614305i
\(26\) 0 0
\(27\) −2.70859 + 4.43436i −0.521269 + 0.853392i
\(28\) 0 0
\(29\) −0.230745 0.274991i −0.0428482 0.0510645i 0.744195 0.667963i \(-0.232833\pi\)
−0.787043 + 0.616898i \(0.788389\pi\)
\(30\) 0 0
\(31\) 3.43265 + 9.43113i 0.616522 + 1.69388i 0.715341 + 0.698776i \(0.246271\pi\)
−0.0988186 + 0.995105i \(0.531506\pi\)
\(32\) 0 0
\(33\) −1.36158 + 0.771209i −0.237021 + 0.134250i
\(34\) 0 0
\(35\) −9.02637 4.04826i −1.52574 0.684281i
\(36\) 0 0
\(37\) −4.77757 8.27499i −0.785427 1.36040i −0.928743 0.370723i \(-0.879110\pi\)
0.143316 0.989677i \(-0.454223\pi\)
\(38\) 0 0
\(39\) 0.725101 1.94221i 0.116109 0.311003i
\(40\) 0 0
\(41\) −5.79118 4.85938i −0.904430 0.758907i 0.0666210 0.997778i \(-0.478778\pi\)
−0.971051 + 0.238871i \(0.923223\pi\)
\(42\) 0 0
\(43\) 4.12751 + 1.50229i 0.629440 + 0.229097i 0.636988 0.770874i \(-0.280180\pi\)
−0.00754750 + 0.999972i \(0.502402\pi\)
\(44\) 0 0
\(45\) −5.44762 9.80553i −0.812083 1.46172i
\(46\) 0 0
\(47\) −4.35416 1.58478i −0.635119 0.231165i 0.00433856 0.999991i \(-0.498619\pi\)
−0.639458 + 0.768826i \(0.720841\pi\)
\(48\) 0 0
\(49\) −6.16266 3.31988i −0.880380 0.474269i
\(50\) 0 0
\(51\) 12.1891 4.32299i 1.70682 0.605339i
\(52\) 0 0
\(53\) 11.6009 6.69781i 1.59351 0.920014i 0.600814 0.799389i \(-0.294843\pi\)
0.992698 0.120625i \(-0.0384900\pi\)
\(54\) 0 0
\(55\) 3.37805i 0.455496i
\(56\) 0 0
\(57\) −0.399332 1.12596i −0.0528928 0.149137i
\(58\) 0 0
\(59\) 0.0113213 + 0.00949971i 0.00147391 + 0.00123676i 0.643524 0.765426i \(-0.277472\pi\)
−0.642050 + 0.766662i \(0.721916\pi\)
\(60\) 0 0
\(61\) −1.34236 + 3.68810i −0.171871 + 0.472213i −0.995483 0.0949418i \(-0.969733\pi\)
0.823612 + 0.567154i \(0.191956\pi\)
\(62\) 0 0
\(63\) −3.34177 7.19949i −0.421023 0.907050i
\(64\) 0 0
\(65\) 2.87674 + 3.42836i 0.356815 + 0.425236i
\(66\) 0 0
\(67\) −0.323090 + 1.83233i −0.0394717 + 0.223855i −0.998162 0.0605954i \(-0.980700\pi\)
0.958691 + 0.284451i \(0.0918112\pi\)
\(68\) 0 0
\(69\) −2.67826 + 7.17384i −0.322425 + 0.863629i
\(70\) 0 0
\(71\) −9.69050 5.59481i −1.15005 0.663982i −0.201151 0.979560i \(-0.564468\pi\)
−0.948899 + 0.315578i \(0.897801\pi\)
\(72\) 0 0
\(73\) −9.63739 5.56415i −1.12797 0.651234i −0.184547 0.982824i \(-0.559082\pi\)
−0.943424 + 0.331589i \(0.892415\pi\)
\(74\) 0 0
\(75\) 15.5542 + 0.128266i 1.79605 + 0.0148108i
\(76\) 0 0
\(77\) 0.173225 2.38402i 0.0197409 0.271684i
\(78\) 0 0
\(79\) 1.78156 + 10.1037i 0.200441 + 1.13676i 0.904455 + 0.426570i \(0.140278\pi\)
−0.704014 + 0.710186i \(0.748611\pi\)
\(80\) 0 0
\(81\) 1.85428 8.80691i 0.206031 0.978545i
\(82\) 0 0
\(83\) 4.58220 3.84492i 0.502962 0.422035i −0.355683 0.934607i \(-0.615752\pi\)
0.858644 + 0.512572i \(0.171307\pi\)
\(84\) 0 0
\(85\) −4.84810 + 27.4949i −0.525850 + 2.98224i
\(86\) 0 0
\(87\) 0.535881 + 0.315311i 0.0574525 + 0.0338049i
\(88\) 0 0
\(89\) 13.9206 1.47558 0.737788 0.675032i \(-0.235870\pi\)
0.737788 + 0.675032i \(0.235870\pi\)
\(90\) 0 0
\(91\) 1.85442 + 2.56704i 0.194396 + 0.269099i
\(92\) 0 0
\(93\) −11.0637 13.4083i −1.14726 1.39037i
\(94\) 0 0
\(95\) 2.53982 + 0.447839i 0.260580 + 0.0459473i
\(96\) 0 0
\(97\) 1.53264 4.21088i 0.155616 0.427550i −0.837245 0.546827i \(-0.815835\pi\)
0.992861 + 0.119277i \(0.0380576\pi\)
\(98\) 0 0
\(99\) 1.77618 2.04723i 0.178513 0.205755i
\(100\) 0 0
\(101\) 3.46818 2.91015i 0.345097 0.289571i −0.453721 0.891144i \(-0.649904\pi\)
0.798818 + 0.601573i \(0.205459\pi\)
\(102\) 0 0
\(103\) −11.5700 2.04010i −1.14002 0.201017i −0.428406 0.903586i \(-0.640925\pi\)
−0.711615 + 0.702570i \(0.752036\pi\)
\(104\) 0 0
\(105\) 17.0786 + 1.38262i 1.66670 + 0.134930i
\(106\) 0 0
\(107\) −5.33302 3.07902i −0.515563 0.297660i 0.219555 0.975600i \(-0.429540\pi\)
−0.735117 + 0.677940i \(0.762873\pi\)
\(108\) 0 0
\(109\) 2.87972 + 4.98782i 0.275827 + 0.477746i 0.970343 0.241730i \(-0.0777150\pi\)
−0.694516 + 0.719477i \(0.744382\pi\)
\(110\) 0 0
\(111\) 12.5899 + 10.7423i 1.19498 + 1.01961i
\(112\) 0 0
\(113\) 1.26420 + 3.47337i 0.118926 + 0.326747i 0.984845 0.173438i \(-0.0554875\pi\)
−0.865919 + 0.500185i \(0.833265\pi\)
\(114\) 0 0
\(115\) −10.6256 12.6631i −0.990846 1.18084i
\(116\) 0 0
\(117\) −0.0592181 + 3.59032i −0.00547471 + 0.331925i
\(118\) 0 0
\(119\) −4.83142 + 19.1556i −0.442896 + 1.75599i
\(120\) 0 0
\(121\) −9.56962 + 3.48306i −0.869966 + 0.316642i
\(122\) 0 0
\(123\) 12.2670 + 4.57974i 1.10608 + 0.412941i
\(124\) 0 0
\(125\) −7.44173 + 12.8895i −0.665609 + 1.15287i
\(126\) 0 0
\(127\) 7.29860 + 12.6416i 0.647646 + 1.12176i 0.983683 + 0.179908i \(0.0575799\pi\)
−0.336037 + 0.941849i \(0.609087\pi\)
\(128\) 0 0
\(129\) −7.60762 0.0627351i −0.669813 0.00552352i
\(130\) 0 0
\(131\) −2.05501 1.72436i −0.179547 0.150658i 0.548585 0.836095i \(-0.315167\pi\)
−0.728132 + 0.685437i \(0.759611\pi\)
\(132\) 0 0
\(133\) 1.76948 + 0.446298i 0.153434 + 0.0386989i
\(134\) 0 0
\(135\) 14.5698 + 12.8529i 1.25397 + 1.10620i
\(136\) 0 0
\(137\) 0.607400 1.66882i 0.0518937 0.142577i −0.911038 0.412323i \(-0.864718\pi\)
0.962931 + 0.269746i \(0.0869398\pi\)
\(138\) 0 0
\(139\) 7.70465 + 1.35854i 0.653500 + 0.115230i 0.490561 0.871407i \(-0.336792\pi\)
0.162938 + 0.986636i \(0.447903\pi\)
\(140\) 0 0
\(141\) 8.02536 + 0.0661799i 0.675857 + 0.00557335i
\(142\) 0 0
\(143\) −0.540686 + 0.936495i −0.0452144 + 0.0783137i
\(144\) 0 0
\(145\) −1.16240 + 0.671114i −0.0965324 + 0.0557330i
\(146\) 0 0
\(147\) 11.9821 + 1.85155i 0.988271 + 0.152713i
\(148\) 0 0
\(149\) 5.08102 + 13.9600i 0.416254 + 1.14365i 0.953808 + 0.300418i \(0.0971262\pi\)
−0.537554 + 0.843229i \(0.680652\pi\)
\(150\) 0 0
\(151\) −2.80728 15.9209i −0.228453 1.29562i −0.855972 0.517022i \(-0.827040\pi\)
0.627518 0.778602i \(-0.284071\pi\)
\(152\) 0 0
\(153\) −17.3950 + 14.1139i −1.40630 + 1.14104i
\(154\) 0 0
\(155\) 36.9565 6.51644i 2.96842 0.523413i
\(156\) 0 0
\(157\) 0.0313116 0.0373157i 0.00249894 0.00297812i −0.764794 0.644275i \(-0.777159\pi\)
0.767292 + 0.641297i \(0.221603\pi\)
\(158\) 0 0
\(159\) −15.0599 + 17.6501i −1.19433 + 1.39974i
\(160\) 0 0
\(161\) −6.84955 9.48174i −0.539820 0.747266i
\(162\) 0 0
\(163\) −2.22231 + 3.84915i −0.174064 + 0.301488i −0.939837 0.341623i \(-0.889023\pi\)
0.765773 + 0.643111i \(0.222357\pi\)
\(164\) 0 0
\(165\) 1.95574 + 5.51441i 0.152254 + 0.429297i
\(166\) 0 0
\(167\) 3.33767 1.21481i 0.258277 0.0940050i −0.209637 0.977779i \(-0.567228\pi\)
0.467913 + 0.883774i \(0.345006\pi\)
\(168\) 0 0
\(169\) 2.00865 + 11.3916i 0.154511 + 0.876278i
\(170\) 0 0
\(171\) 1.30376 + 1.60685i 0.0997009 + 0.122879i
\(172\) 0 0
\(173\) 14.4798 12.1500i 1.10088 0.923749i 0.103397 0.994640i \(-0.467029\pi\)
0.997484 + 0.0708908i \(0.0225842\pi\)
\(174\) 0 0
\(175\) −13.3401 + 19.6619i −1.00842 + 1.48630i
\(176\) 0 0
\(177\) −0.0239811 0.00895304i −0.00180253 0.000672952i
\(178\) 0 0
\(179\) 26.7211i 1.99723i −0.0526473 0.998613i \(-0.516766\pi\)
0.0526473 0.998613i \(-0.483234\pi\)
\(180\) 0 0
\(181\) 6.39653 3.69304i 0.475450 0.274501i −0.243068 0.970009i \(-0.578154\pi\)
0.718519 + 0.695508i \(0.244821\pi\)
\(182\) 0 0
\(183\) 0.0560563 6.79771i 0.00414380 0.502501i
\(184\) 0 0
\(185\) −33.5726 + 12.2194i −2.46831 + 0.898390i
\(186\) 0 0
\(187\) −6.64347 + 1.17142i −0.485819 + 0.0856629i
\(188\) 0 0
\(189\) 9.62336 + 9.81789i 0.699996 + 0.714146i
\(190\) 0 0
\(191\) −1.42440 + 0.251161i −0.103066 + 0.0181733i −0.224943 0.974372i \(-0.572220\pi\)
0.121877 + 0.992545i \(0.461109\pi\)
\(192\) 0 0
\(193\) 16.3927 5.96644i 1.17997 0.429474i 0.323779 0.946133i \(-0.395047\pi\)
0.856191 + 0.516659i \(0.172825\pi\)
\(194\) 0 0
\(195\) −6.68093 3.93104i −0.478431 0.281508i
\(196\) 0 0
\(197\) 13.9252 8.03969i 0.992126 0.572804i 0.0862168 0.996276i \(-0.472522\pi\)
0.905909 + 0.423472i \(0.139189\pi\)
\(198\) 0 0
\(199\) 3.28881i 0.233138i −0.993183 0.116569i \(-0.962810\pi\)
0.993183 0.116569i \(-0.0371896\pi\)
\(200\) 0 0
\(201\) −0.533418 3.17820i −0.0376244 0.224173i
\(202\) 0 0
\(203\) −0.854767 + 0.414023i −0.0599929 + 0.0290587i
\(204\) 0 0
\(205\) −21.6535 + 18.1695i −1.51235 + 1.26901i
\(206\) 0 0
\(207\) 0.218730 13.2613i 0.0152028 0.921727i
\(208\) 0 0
\(209\) 0.108209 + 0.613684i 0.00748498 + 0.0424494i
\(210\) 0 0
\(211\) 23.2958 8.47897i 1.60375 0.583717i 0.623558 0.781777i \(-0.285686\pi\)
0.980190 + 0.198060i \(0.0634642\pi\)
\(212\) 0 0
\(213\) 19.0581 + 3.52275i 1.30584 + 0.241375i
\(214\) 0 0
\(215\) 8.21173 14.2231i 0.560036 0.970010i
\(216\) 0 0
\(217\) 26.4158 2.70378i 1.79322 0.183544i
\(218\) 0 0
\(219\) 18.9537 + 3.50344i 1.28077 + 0.236741i
\(220\) 0 0
\(221\) 5.74484 6.84643i 0.386439 0.460541i
\(222\) 0 0
\(223\) 15.8216 2.78978i 1.05949 0.186817i 0.383362 0.923598i \(-0.374766\pi\)
0.676132 + 0.736781i \(0.263655\pi\)
\(224\) 0 0
\(225\) −25.4654 + 8.79581i −1.69769 + 0.586387i
\(226\) 0 0
\(227\) −1.48157 8.40237i −0.0983349 0.557685i −0.993674 0.112301i \(-0.964178\pi\)
0.895339 0.445385i \(-0.146933\pi\)
\(228\) 0 0
\(229\) 0.302173 + 0.830212i 0.0199681 + 0.0548620i 0.949276 0.314443i \(-0.101818\pi\)
−0.929308 + 0.369305i \(0.879596\pi\)
\(230\) 0 0
\(231\) 1.09746 + 3.99202i 0.0722077 + 0.262656i
\(232\) 0 0
\(233\) 7.90471 4.56379i 0.517855 0.298984i −0.218202 0.975904i \(-0.570019\pi\)
0.736057 + 0.676920i \(0.236686\pi\)
\(234\) 0 0
\(235\) −8.66265 + 15.0041i −0.565089 + 0.978762i
\(236\) 0 0
\(237\) −8.75785 15.4621i −0.568883 1.00437i
\(238\) 0 0
\(239\) −16.4613 2.90258i −1.06480 0.187752i −0.386312 0.922368i \(-0.626251\pi\)
−0.678483 + 0.734616i \(0.737362\pi\)
\(240\) 0 0
\(241\) 8.58860 23.5970i 0.553241 1.52002i −0.276019 0.961152i \(-0.589015\pi\)
0.829259 0.558864i \(-0.188763\pi\)
\(242\) 0 0
\(243\) 2.07183 + 15.4502i 0.132908 + 0.991128i
\(244\) 0 0
\(245\) −16.2259 + 20.5369i −1.03664 + 1.31206i
\(246\) 0 0
\(247\) −0.632433 0.530674i −0.0402407 0.0337660i
\(248\) 0 0
\(249\) −5.25406 + 8.92944i −0.332963 + 0.565880i
\(250\) 0 0
\(251\) −8.73608 15.1313i −0.551417 0.955082i −0.998173 0.0604258i \(-0.980754\pi\)
0.446756 0.894656i \(-0.352579\pi\)
\(252\) 0 0
\(253\) 1.99710 3.45908i 0.125557 0.217470i
\(254\) 0 0
\(255\) −8.00417 47.6903i −0.501241 2.98648i
\(256\) 0 0
\(257\) −21.3751 + 7.77990i −1.33334 + 0.485297i −0.907709 0.419599i \(-0.862171\pi\)
−0.425632 + 0.904896i \(0.639948\pi\)
\(258\) 0 0
\(259\) −24.3201 + 6.90212i −1.51117 + 0.428877i
\(260\) 0 0
\(261\) −1.05734 0.204471i −0.0654475 0.0126564i
\(262\) 0 0
\(263\) −1.78344 2.12542i −0.109972 0.131059i 0.708251 0.705961i \(-0.249485\pi\)
−0.818222 + 0.574902i \(0.805040\pi\)
\(264\) 0 0
\(265\) −17.1307 47.0663i −1.05233 2.89126i
\(266\) 0 0
\(267\) −22.7243 + 8.05937i −1.39070 + 0.493226i
\(268\) 0 0
\(269\) 5.69974 + 9.87224i 0.347519 + 0.601921i 0.985808 0.167876i \(-0.0536908\pi\)
−0.638289 + 0.769797i \(0.720357\pi\)
\(270\) 0 0
\(271\) 3.39054 + 1.95753i 0.205961 + 0.118912i 0.599433 0.800425i \(-0.295393\pi\)
−0.393472 + 0.919337i \(0.628726\pi\)
\(272\) 0 0
\(273\) −4.51340 3.11688i −0.273164 0.188642i
\(274\) 0 0
\(275\) −7.99021 1.40889i −0.481828 0.0849592i
\(276\) 0 0
\(277\) 4.15531 3.48672i 0.249669 0.209497i −0.509361 0.860553i \(-0.670118\pi\)
0.759030 + 0.651056i \(0.225674\pi\)
\(278\) 0 0
\(279\) 25.8235 + 15.4826i 1.54601 + 0.926918i
\(280\) 0 0
\(281\) −6.74746 + 18.5385i −0.402520 + 1.10591i 0.558517 + 0.829493i \(0.311370\pi\)
−0.961037 + 0.276421i \(0.910852\pi\)
\(282\) 0 0
\(283\) 15.3551 + 2.70751i 0.912764 + 0.160945i 0.610258 0.792203i \(-0.291066\pi\)
0.302506 + 0.953147i \(0.402177\pi\)
\(284\) 0 0
\(285\) −4.40534 + 0.739378i −0.260950 + 0.0437970i
\(286\) 0 0
\(287\) −16.2135 + 11.7125i −0.957050 + 0.691368i
\(288\) 0 0
\(289\) 38.7543 2.27967
\(290\) 0 0
\(291\) −0.0640022 + 7.76128i −0.00375188 + 0.454974i
\(292\) 0 0
\(293\) 3.36781 19.0998i 0.196749 1.11582i −0.713156 0.701005i \(-0.752735\pi\)
0.909905 0.414816i \(-0.136154\pi\)
\(294\) 0 0
\(295\) 0.0423310 0.0355200i 0.00246461 0.00206805i
\(296\) 0 0
\(297\) −1.71423 + 4.37029i −0.0994697 + 0.253590i
\(298\) 0 0
\(299\) 0.918896 + 5.21132i 0.0531411 + 0.301378i
\(300\) 0 0
\(301\) 6.52469 9.61672i 0.376077 0.554298i
\(302\) 0 0
\(303\) −3.97670 + 6.75852i −0.228455 + 0.388267i
\(304\) 0 0
\(305\) 12.7089 + 7.33751i 0.727712 + 0.420145i
\(306\) 0 0
\(307\) 15.6946 + 9.06129i 0.895739 + 0.517155i 0.875815 0.482646i \(-0.160324\pi\)
0.0199238 + 0.999802i \(0.493658\pi\)
\(308\) 0 0
\(309\) 20.0682 3.36818i 1.14164 0.191609i
\(310\) 0 0
\(311\) −3.95939 + 22.4548i −0.224516 + 1.27330i 0.639091 + 0.769131i \(0.279311\pi\)
−0.863608 + 0.504165i \(0.831800\pi\)
\(312\) 0 0
\(313\) −16.4418 19.5945i −0.929344 1.10755i −0.993971 0.109639i \(-0.965030\pi\)
0.0646276 0.997909i \(-0.479414\pi\)
\(314\) 0 0
\(315\) −28.6801 + 7.63074i −1.61594 + 0.429944i
\(316\) 0 0
\(317\) 5.90887 16.2345i 0.331875 0.911819i −0.655749 0.754979i \(-0.727647\pi\)
0.987624 0.156840i \(-0.0501307\pi\)
\(318\) 0 0
\(319\) −0.248441 0.208466i −0.0139100 0.0116719i
\(320\) 0 0
\(321\) 10.4884 + 1.93869i 0.585404 + 0.108207i
\(322\) 0 0
\(323\) 5.15025i 0.286568i
\(324\) 0 0
\(325\) 9.30902 5.37457i 0.516372 0.298127i
\(326\) 0 0
\(327\) −7.58865 6.47501i −0.419653 0.358069i
\(328\) 0 0
\(329\) −6.88297 + 10.1448i −0.379470 + 0.559300i
\(330\) 0 0
\(331\) −23.3643 8.50391i −1.28422 0.467417i −0.392393 0.919797i \(-0.628353\pi\)
−0.891825 + 0.452380i \(0.850575\pi\)
\(332\) 0 0
\(333\) −26.7713 10.2470i −1.46706 0.561534i
\(334\) 0 0
\(335\) 6.53734 + 2.37940i 0.357173 + 0.130000i
\(336\) 0 0
\(337\) −5.16317 4.33242i −0.281256 0.236002i 0.491236 0.871027i \(-0.336545\pi\)
−0.772492 + 0.635025i \(0.780990\pi\)
\(338\) 0 0
\(339\) −4.07465 4.93810i −0.221304 0.268201i
\(340\) 0 0
\(341\) 4.53369 + 7.85259i 0.245513 + 0.425241i
\(342\) 0 0
\(343\) −12.5044 + 13.6616i −0.675173 + 0.737659i
\(344\) 0 0
\(345\) 24.6769 + 14.5199i 1.32856 + 0.781723i
\(346\) 0 0
\(347\) 9.44947 + 25.9622i 0.507274 + 1.39372i 0.884038 + 0.467415i \(0.154815\pi\)
−0.376764 + 0.926309i \(0.622963\pi\)
\(348\) 0 0
\(349\) 17.8032 + 21.2170i 0.952981 + 1.13572i 0.990650 + 0.136429i \(0.0435624\pi\)
−0.0376687 + 0.999290i \(0.511993\pi\)
\(350\) 0 0
\(351\) −1.98196 5.89521i −0.105789 0.314663i
\(352\) 0 0
\(353\) −13.2918 4.83782i −0.707451 0.257491i −0.0368622 0.999320i \(-0.511736\pi\)
−0.670589 + 0.741829i \(0.733958\pi\)
\(354\) 0 0
\(355\) −26.8933 + 32.0502i −1.42735 + 1.70105i
\(356\) 0 0
\(357\) −3.20331 34.0673i −0.169537 1.80303i
\(358\) 0 0
\(359\) 14.6085i 0.771006i −0.922707 0.385503i \(-0.874028\pi\)
0.922707 0.385503i \(-0.125972\pi\)
\(360\) 0 0
\(361\) 18.5242 0.974961
\(362\) 0 0
\(363\) 13.6052 11.2262i 0.714085 0.589223i
\(364\) 0 0
\(365\) −26.7460 + 31.8746i −1.39995 + 1.66839i
\(366\) 0 0
\(367\) −2.66648 + 0.470173i −0.139189 + 0.0245428i −0.242809 0.970074i \(-0.578069\pi\)
0.103619 + 0.994617i \(0.466958\pi\)
\(368\) 0 0
\(369\) −22.6765 0.374022i −1.18049 0.0194708i
\(370\) 0 0
\(371\) −9.67627 34.0950i −0.502367 1.77012i
\(372\) 0 0
\(373\) −5.01731 + 28.4546i −0.259786 + 1.47332i 0.523695 + 0.851906i \(0.324553\pi\)
−0.783481 + 0.621415i \(0.786558\pi\)
\(374\) 0 0
\(375\) 4.68566 25.3495i 0.241966 1.30904i
\(376\) 0 0
\(377\) 0.429670 0.0221291
\(378\) 0 0
\(379\) 3.86950 0.198763 0.0993815 0.995049i \(-0.468314\pi\)
0.0993815 + 0.995049i \(0.468314\pi\)
\(380\) 0 0
\(381\) −19.2333 16.4108i −0.985352 0.840752i
\(382\) 0 0
\(383\) −3.64342 + 20.6629i −0.186170 + 1.05582i 0.738273 + 0.674502i \(0.235642\pi\)
−0.924443 + 0.381321i \(0.875469\pi\)
\(384\) 0 0
\(385\) −8.66609 2.18576i −0.441665 0.111396i
\(386\) 0 0
\(387\) 12.4552 4.30206i 0.633133 0.218686i
\(388\) 0 0
\(389\) −14.0482 + 2.47708i −0.712274 + 0.125593i −0.518033 0.855361i \(-0.673336\pi\)
−0.194241 + 0.980954i \(0.562224\pi\)
\(390\) 0 0
\(391\) −21.2194 + 25.2882i −1.07311 + 1.27888i
\(392\) 0 0
\(393\) 4.35298 + 1.62513i 0.219579 + 0.0819769i
\(394\) 0 0
\(395\) 38.3611 1.93016
\(396\) 0 0
\(397\) 28.9198i 1.45144i −0.687989 0.725721i \(-0.741506\pi\)
0.687989 0.725721i \(-0.258494\pi\)
\(398\) 0 0
\(399\) −3.14693 + 0.295903i −0.157544 + 0.0148137i
\(400\) 0 0
\(401\) 9.75159 11.6215i 0.486971 0.580350i −0.465473 0.885062i \(-0.654116\pi\)
0.952444 + 0.304712i \(0.0985603\pi\)
\(402\) 0 0
\(403\) −11.2885 4.10866i −0.562318 0.204667i
\(404\) 0 0
\(405\) −31.2253 12.5461i −1.55160 0.623420i
\(406\) 0 0
\(407\) −5.54892 6.61295i −0.275050 0.327792i
\(408\) 0 0
\(409\) 7.75940 + 21.3188i 0.383678 + 1.05415i 0.969795 + 0.243920i \(0.0784335\pi\)
−0.586117 + 0.810226i \(0.699344\pi\)
\(410\) 0 0
\(411\) −0.0253648 + 3.07588i −0.00125115 + 0.151722i
\(412\) 0 0
\(413\) 0.0316961 0.0228971i 0.00155966 0.00112669i
\(414\) 0 0
\(415\) −11.1828 19.3693i −0.548944 0.950799i
\(416\) 0 0
\(417\) −13.3638 + 2.24293i −0.654427 + 0.109837i
\(418\) 0 0
\(419\) 21.2332 + 17.8168i 1.03731 + 0.870407i 0.991703 0.128552i \(-0.0410329\pi\)
0.0456084 + 0.998959i \(0.485477\pi\)
\(420\) 0 0
\(421\) −10.8260 3.94035i −0.527628 0.192041i 0.0644509 0.997921i \(-0.479470\pi\)
−0.592079 + 0.805880i \(0.701693\pi\)
\(422\) 0 0
\(423\) −13.1391 + 4.53829i −0.638845 + 0.220659i
\(424\) 0 0
\(425\) 63.0126 + 22.9347i 3.05656 + 1.11250i
\(426\) 0 0
\(427\) 8.59292 + 5.83007i 0.415840 + 0.282137i
\(428\) 0 0
\(429\) 0.340441 1.84179i 0.0164366 0.0889225i
\(430\) 0 0
\(431\) 0.198915 0.114844i 0.00958139 0.00553182i −0.495202 0.868778i \(-0.664906\pi\)
0.504783 + 0.863246i \(0.331572\pi\)
\(432\) 0 0
\(433\) 27.7350i 1.33286i −0.745568 0.666429i \(-0.767822\pi\)
0.745568 0.666429i \(-0.232178\pi\)
\(434\) 0 0
\(435\) 1.50899 1.76852i 0.0723506 0.0847942i
\(436\) 0 0
\(437\) 2.33598 + 1.96012i 0.111745 + 0.0937652i
\(438\) 0 0
\(439\) 14.1419 38.8545i 0.674956 1.85443i 0.184841 0.982768i \(-0.440823\pi\)
0.490115 0.871658i \(-0.336955\pi\)
\(440\) 0 0
\(441\) −20.6319 + 3.91460i −0.982472 + 0.186410i
\(442\) 0 0
\(443\) 11.3456 + 13.5212i 0.539045 + 0.642409i 0.964973 0.262348i \(-0.0844968\pi\)
−0.425928 + 0.904757i \(0.640052\pi\)
\(444\) 0 0
\(445\) 9.03834 51.2590i 0.428459 2.42991i
\(446\) 0 0
\(447\) −16.3766 19.8470i −0.774586 0.938729i
\(448\) 0 0
\(449\) −2.02166 1.16721i −0.0954080 0.0550838i 0.451537 0.892252i \(-0.350876\pi\)
−0.546945 + 0.837169i \(0.684209\pi\)
\(450\) 0 0
\(451\) −5.91491 3.41497i −0.278522 0.160805i
\(452\) 0 0
\(453\) 13.8002 + 24.3644i 0.648388 + 1.14474i
\(454\) 0 0
\(455\) 10.6565 5.16170i 0.499586 0.241984i
\(456\) 0 0
\(457\) 0.544911 + 3.09034i 0.0254899 + 0.144560i 0.994897 0.100900i \(-0.0321721\pi\)
−0.969407 + 0.245460i \(0.921061\pi\)
\(458\) 0 0
\(459\) 20.2247 33.1108i 0.944010 1.54548i
\(460\) 0 0
\(461\) 9.62681 8.07785i 0.448365 0.376223i −0.390464 0.920618i \(-0.627685\pi\)
0.838829 + 0.544395i \(0.183241\pi\)
\(462\) 0 0
\(463\) 2.81661 15.9738i 0.130899 0.742364i −0.846729 0.532024i \(-0.821432\pi\)
0.977628 0.210340i \(-0.0674573\pi\)
\(464\) 0 0
\(465\) −56.5561 + 32.0338i −2.62272 + 1.48553i
\(466\) 0 0
\(467\) −10.1387 −0.469162 −0.234581 0.972097i \(-0.575372\pi\)
−0.234581 + 0.972097i \(0.575372\pi\)
\(468\) 0 0
\(469\) 4.49163 + 2.01446i 0.207404 + 0.0930193i
\(470\) 0 0
\(471\) −0.0295097 + 0.0790432i −0.00135974 + 0.00364212i
\(472\) 0 0
\(473\) 3.90803 + 0.689092i 0.179692 + 0.0316845i
\(474\) 0 0
\(475\) 2.11857 5.82073i 0.0972068 0.267074i
\(476\) 0 0
\(477\) 14.3656 37.5315i 0.657756 1.71845i
\(478\) 0 0
\(479\) 19.3092 16.2023i 0.882259 0.740303i −0.0843835 0.996433i \(-0.526892\pi\)
0.966642 + 0.256130i \(0.0824476\pi\)
\(480\) 0 0
\(481\) 11.2631 + 1.98599i 0.513555 + 0.0905535i
\(482\) 0 0
\(483\) 16.6709 + 11.5126i 0.758551 + 0.523843i
\(484\) 0 0
\(485\) −14.5104 8.37760i −0.658884 0.380407i
\(486\) 0 0
\(487\) −4.27727 7.40844i −0.193821 0.335709i 0.752692 0.658373i \(-0.228755\pi\)
−0.946514 + 0.322664i \(0.895422\pi\)
\(488\) 0 0
\(489\) 1.39927 7.57006i 0.0632770 0.342330i
\(490\) 0 0
\(491\) 11.2025 + 30.7785i 0.505560 + 1.38902i 0.885774 + 0.464117i \(0.153628\pi\)
−0.380213 + 0.924899i \(0.624149\pi\)
\(492\) 0 0
\(493\) 1.72294 + 2.05333i 0.0775975 + 0.0924771i
\(494\) 0 0
\(495\) −6.38519 7.86958i −0.286993 0.353711i
\(496\) 0 0
\(497\) −20.6232 + 21.2400i −0.925076 + 0.952744i
\(498\) 0 0
\(499\) 12.7319 4.63403i 0.569958 0.207448i −0.0409339 0.999162i \(-0.513033\pi\)
0.610892 + 0.791714i \(0.290811\pi\)
\(500\) 0 0
\(501\) −4.74517 + 3.91545i −0.211999 + 0.174929i
\(502\) 0 0
\(503\) −19.3212 + 33.4653i −0.861490 + 1.49215i 0.00899970 + 0.999960i \(0.497135\pi\)
−0.870490 + 0.492186i \(0.836198\pi\)
\(504\) 0 0
\(505\) −8.46408 14.6602i −0.376647 0.652371i
\(506\) 0 0
\(507\) −9.87420 17.4330i −0.438528 0.774228i
\(508\) 0 0
\(509\) −0.0630183 0.0528786i −0.00279324 0.00234380i 0.641390 0.767215i \(-0.278358\pi\)
−0.644183 + 0.764871i \(0.722803\pi\)
\(510\) 0 0
\(511\) −20.5102 + 21.1236i −0.907316 + 0.934453i
\(512\) 0 0
\(513\) −3.05858 1.86824i −0.135040 0.0824849i
\(514\) 0 0
\(515\) −15.0243 + 41.2789i −0.662049 + 1.81897i
\(516\) 0 0
\(517\) −4.12263 0.726931i −0.181313 0.0319704i
\(518\) 0 0
\(519\) −16.6029 + 28.2172i −0.728788 + 1.23860i
\(520\) 0 0
\(521\) −1.02550 + 1.77622i −0.0449281 + 0.0778177i −0.887615 0.460586i \(-0.847639\pi\)
0.842687 + 0.538404i \(0.180973\pi\)
\(522\) 0 0
\(523\) 0.666771 0.384961i 0.0291559 0.0168332i −0.485351 0.874319i \(-0.661308\pi\)
0.514507 + 0.857486i \(0.327975\pi\)
\(524\) 0 0
\(525\) 10.3934 39.8200i 0.453603 1.73789i
\(526\) 0 0
\(527\) −25.6312 70.4211i −1.11651 3.06759i
\(528\) 0 0
\(529\) 0.599836 + 3.40184i 0.0260798 + 0.147906i
\(530\) 0 0
\(531\) 0.0443308 0.000731184i 0.00192379 3.17307e-5i
\(532\) 0 0
\(533\) 8.91118 1.57128i 0.385986 0.0680598i
\(534\) 0 0
\(535\) −14.8004 + 17.6384i −0.639875 + 0.762574i
\(536\) 0 0
\(537\) 15.4703 + 43.6201i 0.667592 + 1.88235i
\(538\) 0 0
\(539\) −6.00390 1.98697i −0.258606 0.0855847i
\(540\) 0 0
\(541\) −11.6715 + 20.2156i −0.501796 + 0.869136i 0.498202 + 0.867061i \(0.333994\pi\)
−0.999998 + 0.00207506i \(0.999339\pi\)
\(542\) 0 0
\(543\) −8.30375 + 9.73191i −0.356348 + 0.417636i
\(544\) 0 0
\(545\) 20.2361 7.36535i 0.866821 0.315497i
\(546\) 0 0
\(547\) −5.13973 29.1488i −0.219759 1.24631i −0.872455 0.488695i \(-0.837473\pi\)
0.652696 0.757620i \(-0.273638\pi\)
\(548\) 0 0
\(549\) 3.84406 + 11.1292i 0.164060 + 0.474983i
\(550\) 0 0
\(551\) 0.189674 0.159155i 0.00808038 0.00678025i
\(552\) 0 0
\(553\) 27.0729 + 1.96715i 1.15126 + 0.0836515i
\(554\) 0 0
\(555\) 47.7302 39.3843i 2.02604 1.67177i
\(556\) 0 0
\(557\) 24.7683i 1.04947i −0.851266 0.524734i \(-0.824165\pi\)
0.851266 0.524734i \(-0.175835\pi\)
\(558\) 0 0
\(559\) −4.55307 + 2.62872i −0.192574 + 0.111183i
\(560\) 0 0
\(561\) 10.1668 5.75853i 0.429241 0.243125i
\(562\) 0 0
\(563\) −17.2769 + 6.28829i −0.728136 + 0.265020i −0.679376 0.733791i \(-0.737749\pi\)
−0.0487606 + 0.998810i \(0.515527\pi\)
\(564\) 0 0
\(565\) 13.6107 2.39993i 0.572605 0.100966i
\(566\) 0 0
\(567\) −21.3935 10.4555i −0.898444 0.439089i
\(568\) 0 0
\(569\) −16.9229 + 2.98396i −0.709444 + 0.125094i −0.516714 0.856158i \(-0.672845\pi\)
−0.192729 + 0.981252i \(0.561734\pi\)
\(570\) 0 0
\(571\) −0.968221 + 0.352404i −0.0405188 + 0.0147476i −0.362200 0.932100i \(-0.617974\pi\)
0.321681 + 0.946848i \(0.395752\pi\)
\(572\) 0 0
\(573\) 2.17982 1.23467i 0.0910633 0.0515789i
\(574\) 0 0
\(575\) −34.3842 + 19.8517i −1.43392 + 0.827873i
\(576\) 0 0
\(577\) 39.7208i 1.65360i −0.562498 0.826798i \(-0.690160\pi\)
0.562498 0.826798i \(-0.309840\pi\)
\(578\) 0 0
\(579\) −23.3055 + 19.2304i −0.968543 + 0.799187i
\(580\) 0 0
\(581\) −6.89891 14.2431i −0.286215 0.590902i
\(582\) 0 0
\(583\) 9.27087 7.77919i 0.383960 0.322181i
\(584\) 0 0
\(585\) 13.1820 + 2.54918i 0.545009 + 0.105396i
\(586\) 0 0
\(587\) 1.61600 + 9.16478i 0.0666994 + 0.378271i 0.999825 + 0.0187199i \(0.00595907\pi\)
−0.933125 + 0.359551i \(0.882930\pi\)
\(588\) 0 0
\(589\) −6.50509 + 2.36766i −0.268037 + 0.0975577i
\(590\) 0 0
\(591\) −18.0771 + 21.1862i −0.743594 + 0.871485i
\(592\) 0 0
\(593\) −5.72573 + 9.91725i −0.235127 + 0.407253i −0.959310 0.282356i \(-0.908884\pi\)
0.724182 + 0.689609i \(0.242217\pi\)
\(594\) 0 0
\(595\) 67.3989 + 30.2279i 2.76308 + 1.23922i
\(596\) 0 0
\(597\) 1.90407 + 5.36874i 0.0779286 + 0.219728i
\(598\) 0 0
\(599\) −3.34805 + 3.99005i −0.136798 + 0.163029i −0.830094 0.557624i \(-0.811713\pi\)
0.693296 + 0.720653i \(0.256158\pi\)
\(600\) 0 0
\(601\) 5.98265 1.05490i 0.244037 0.0430304i −0.0502914 0.998735i \(-0.516015\pi\)
0.294329 + 0.955704i \(0.404904\pi\)
\(602\) 0 0
\(603\) 2.71080 + 4.87935i 0.110392 + 0.198703i
\(604\) 0 0
\(605\) 6.61213 + 37.4992i 0.268821 + 1.52456i
\(606\) 0 0
\(607\) −0.0760370 0.208910i −0.00308625 0.00847940i 0.938140 0.346256i \(-0.112547\pi\)
−0.941226 + 0.337777i \(0.890325\pi\)
\(608\) 0 0
\(609\) 1.15564 1.17073i 0.0468290 0.0474405i
\(610\) 0 0
\(611\) 4.80308 2.77306i 0.194312 0.112186i
\(612\) 0 0
\(613\) −14.4222 + 24.9801i −0.582509 + 1.00894i 0.412672 + 0.910880i \(0.364596\pi\)
−0.995181 + 0.0980556i \(0.968738\pi\)
\(614\) 0 0
\(615\) 24.8285 42.1967i 1.00118 1.70154i
\(616\) 0 0
\(617\) 9.68410 + 1.70757i 0.389867 + 0.0687441i 0.365146 0.930950i \(-0.381019\pi\)
0.0247213 + 0.999694i \(0.492130\pi\)
\(618\) 0 0
\(619\) 0.486578 1.33686i 0.0195572 0.0537330i −0.929530 0.368747i \(-0.879787\pi\)
0.949087 + 0.315014i \(0.102009\pi\)
\(620\) 0 0
\(621\) 7.32066 + 21.7748i 0.293768 + 0.873792i
\(622\) 0 0
\(623\) 9.00725 35.7119i 0.360868 1.43077i
\(624\) 0 0
\(625\) 8.23300 + 6.90830i 0.329320 + 0.276332i
\(626\) 0 0
\(627\) −0.531939 0.939145i −0.0212436 0.0375059i
\(628\) 0 0
\(629\) 35.6735 + 61.7884i 1.42240 + 2.46366i
\(630\) 0 0
\(631\) 13.6519 23.6458i 0.543473 0.941323i −0.455228 0.890375i \(-0.650442\pi\)
0.998701 0.0509480i \(-0.0162243\pi\)
\(632\) 0 0
\(633\) −33.1197 + 27.3285i −1.31639 + 1.08621i
\(634\) 0 0
\(635\) 51.2882 18.6674i 2.03531 0.740793i
\(636\) 0 0
\(637\) 7.78542 3.09635i 0.308469 0.122682i
\(638\) 0 0
\(639\) −33.1505 + 5.28319i −1.31141 + 0.209000i
\(640\) 0 0
\(641\) 2.18677 + 2.60610i 0.0863724 + 0.102935i 0.807500 0.589868i \(-0.200820\pi\)
−0.721127 + 0.692803i \(0.756376\pi\)
\(642\) 0 0
\(643\) −0.422932 1.16200i −0.0166788 0.0458247i 0.931074 0.364831i \(-0.118873\pi\)
−0.947753 + 0.319006i \(0.896651\pi\)
\(644\) 0 0
\(645\) −5.17048 + 27.9724i −0.203588 + 1.10141i
\(646\) 0 0
\(647\) −0.766333 1.32733i −0.0301277 0.0521827i 0.850568 0.525864i \(-0.176258\pi\)
−0.880696 + 0.473682i \(0.842925\pi\)
\(648\) 0 0
\(649\) 0.0115632 + 0.00667601i 0.000453895 + 0.000262056i
\(650\) 0 0
\(651\) −41.5565 + 19.7073i −1.62873 + 0.772389i
\(652\) 0 0
\(653\) −29.9964 5.28917i −1.17385 0.206981i −0.447485 0.894291i \(-0.647680\pi\)
−0.726364 + 0.687310i \(0.758791\pi\)
\(654\) 0 0
\(655\) −7.68380 + 6.44747i −0.300231 + 0.251924i
\(656\) 0 0
\(657\) −32.9688 + 5.25423i −1.28624 + 0.204987i
\(658\) 0 0
\(659\) −8.70108 + 23.9060i −0.338946 + 0.931246i 0.646748 + 0.762703i \(0.276128\pi\)
−0.985694 + 0.168543i \(0.946094\pi\)
\(660\) 0 0
\(661\) 30.7559 + 5.42310i 1.19627 + 0.210934i 0.736084 0.676890i \(-0.236673\pi\)
0.460183 + 0.887824i \(0.347784\pi\)
\(662\) 0 0
\(663\) −5.41424 + 14.5023i −0.210272 + 0.563222i
\(664\) 0 0
\(665\) 2.79227 6.22591i 0.108280 0.241430i
\(666\) 0 0
\(667\) −1.58705 −0.0614507
\(668\) 0 0
\(669\) −24.2125 + 13.7141i −0.936108 + 0.530218i
\(670\) 0 0
\(671\) −0.615731 + 3.49198i −0.0237700 + 0.134807i
\(672\) 0 0
\(673\) 21.3263 17.8949i 0.822068 0.689797i −0.131388 0.991331i \(-0.541943\pi\)
0.953455 + 0.301534i \(0.0974988\pi\)
\(674\) 0 0
\(675\) 36.4779 29.1018i 1.40404 1.12013i
\(676\) 0 0
\(677\) 3.13907 + 17.8025i 0.120644 + 0.684207i 0.983800 + 0.179270i \(0.0573734\pi\)
−0.863156 + 0.504938i \(0.831515\pi\)
\(678\) 0 0
\(679\) −9.81096 6.65648i −0.376510 0.255452i
\(680\) 0 0
\(681\) 7.28314 + 12.8585i 0.279091 + 0.492738i
\(682\) 0 0
\(683\) −7.54357 4.35528i −0.288647 0.166650i 0.348685 0.937240i \(-0.386628\pi\)
−0.637331 + 0.770590i \(0.719962\pi\)
\(684\) 0 0
\(685\) −5.75064 3.32013i −0.219721 0.126856i
\(686\) 0 0
\(687\) −0.973930 1.18032i −0.0371577 0.0450318i
\(688\) 0 0
\(689\) −2.78422 + 15.7901i −0.106070 + 0.601555i
\(690\) 0 0
\(691\) 28.1894 + 33.5948i 1.07238 + 1.27801i 0.958678 + 0.284493i \(0.0918252\pi\)
0.113698 + 0.993515i \(0.463730\pi\)
\(692\) 0 0
\(693\) −4.10272 5.88130i −0.155850 0.223412i
\(694\) 0 0
\(695\) 10.0049 27.4884i 0.379509 1.04269i
\(696\) 0 0
\(697\) 43.2421 + 36.2844i 1.63791 + 1.37437i
\(698\) 0 0
\(699\) −10.2616 + 12.0265i −0.388130 + 0.454884i
\(700\) 0 0
\(701\) 24.2340i 0.915305i −0.889131 0.457652i \(-0.848690\pi\)
0.889131 0.457652i \(-0.151310\pi\)
\(702\) 0 0
\(703\) 5.70765 3.29531i 0.215268 0.124285i
\(704\) 0 0
\(705\) 5.45440 29.5084i 0.205425 1.11135i
\(706\) 0 0
\(707\) −5.22165 10.7803i −0.196380 0.405435i
\(708\) 0 0
\(709\) −0.630968 0.229653i −0.0236965 0.00862481i 0.330145 0.943930i \(-0.392902\pi\)
−0.353841 + 0.935306i \(0.615125\pi\)
\(710\) 0 0
\(711\) 23.2484 + 20.1703i 0.871882 + 0.756446i
\(712\) 0 0
\(713\) 41.6955 + 15.1759i 1.56151 + 0.568343i
\(714\) 0 0
\(715\) 3.09735 + 2.59899i 0.115834 + 0.0971967i
\(716\) 0 0
\(717\) 28.5524 4.79213i 1.06631 0.178965i
\(718\) 0 0
\(719\) −9.38852 16.2614i −0.350133 0.606448i 0.636140 0.771574i \(-0.280530\pi\)
−0.986272 + 0.165126i \(0.947197\pi\)
\(720\) 0 0
\(721\) −12.7200 + 28.3616i −0.473717 + 1.05624i
\(722\) 0 0
\(723\) −0.358656 + 43.4927i −0.0133386 + 1.61751i
\(724\) 0 0
\(725\) 1.10260 + 3.02937i 0.0409496 + 0.112508i
\(726\) 0 0
\(727\) −0.400021 0.476727i −0.0148360 0.0176808i 0.758575 0.651585i \(-0.225896\pi\)
−0.773411 + 0.633904i \(0.781451\pi\)
\(728\) 0 0
\(729\) −12.3270 24.0217i −0.456557 0.889694i
\(730\) 0 0
\(731\) −30.8197 11.2174i −1.13991 0.414892i
\(732\) 0 0
\(733\) 23.4542 27.9516i 0.866301 1.03242i −0.132846 0.991137i \(-0.542412\pi\)
0.999148 0.0412808i \(-0.0131438\pi\)
\(734\) 0 0
\(735\) 14.5976 42.9191i 0.538442 1.58309i
\(736\) 0 0
\(737\) 1.68096i 0.0619189i
\(738\) 0 0
\(739\) 42.8175 1.57507 0.787533 0.616272i \(-0.211358\pi\)
0.787533 + 0.616272i \(0.211358\pi\)
\(740\) 0 0
\(741\) 1.33963 + 0.500135i 0.0492127 + 0.0183729i
\(742\) 0 0
\(743\) −8.05809 + 9.60326i −0.295623 + 0.352309i −0.893327 0.449407i \(-0.851635\pi\)
0.597704 + 0.801717i \(0.296080\pi\)
\(744\) 0 0
\(745\) 54.7032 9.64565i 2.00417 0.353389i
\(746\) 0 0
\(747\) 3.40712 17.6185i 0.124660 0.644627i
\(748\) 0 0
\(749\) −11.3497 + 11.6891i −0.414708 + 0.427111i
\(750\) 0 0
\(751\) −8.85692 + 50.2301i −0.323193 + 1.83292i 0.198884 + 0.980023i \(0.436268\pi\)
−0.522077 + 0.852898i \(0.674843\pi\)
\(752\) 0 0
\(753\) 23.0214 + 19.6430i 0.838945 + 0.715830i
\(754\) 0 0
\(755\) −60.4475 −2.19991
\(756\) 0 0
\(757\) −46.4934 −1.68983 −0.844916 0.534899i \(-0.820350\pi\)
−0.844916 + 0.534899i \(0.820350\pi\)
\(758\) 0 0
\(759\) −1.25746 + 6.80291i −0.0456431 + 0.246930i
\(760\) 0 0
\(761\) 4.42847 25.1151i 0.160532 0.910423i −0.793020 0.609195i \(-0.791493\pi\)
0.953552 0.301227i \(-0.0973963\pi\)
\(762\) 0 0
\(763\) 14.6591 4.16031i 0.530695 0.150613i
\(764\) 0 0
\(765\) 40.6767 + 73.2167i 1.47067 + 2.64716i
\(766\) 0 0
\(767\) −0.0174207 + 0.00307174i −0.000629025 + 0.000110914i
\(768\) 0 0
\(769\) −17.0032 + 20.2637i −0.613153 + 0.730727i −0.979877 0.199603i \(-0.936035\pi\)
0.366724 + 0.930330i \(0.380479\pi\)
\(770\) 0 0
\(771\) 30.3890 25.0753i 1.09443 0.903065i
\(772\) 0 0
\(773\) −35.6277 −1.28144 −0.640719 0.767776i \(-0.721364\pi\)
−0.640719 + 0.767776i \(0.721364\pi\)
\(774\) 0 0
\(775\) 90.1323i 3.23765i
\(776\) 0 0
\(777\) 35.7047 25.3474i 1.28090 0.909333i