Properties

Label 756.2.ck.a.5.20
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 5.20
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37168 - 1.05759i) q^{3} +(-0.403931 + 2.29081i) q^{5} +(2.60966 + 0.435529i) q^{7} +(0.762996 - 2.90135i) q^{9} +O(q^{10})\) \(q+(1.37168 - 1.05759i) q^{3} +(-0.403931 + 2.29081i) q^{5} +(2.60966 + 0.435529i) q^{7} +(0.762996 - 2.90135i) q^{9} +(1.79103 - 0.315807i) q^{11} +(-2.58138 + 3.07637i) q^{13} +(1.86868 + 3.56944i) q^{15} +1.25468 q^{17} +5.76919i q^{19} +(4.04022 - 2.16255i) q^{21} +(5.50076 - 6.55555i) q^{23} +(-0.386172 - 0.140555i) q^{25} +(-2.02186 - 4.78666i) q^{27} +(-4.11192 - 4.90039i) q^{29} +(2.63669 + 7.24423i) q^{31} +(2.12272 - 2.32737i) q^{33} +(-2.05183 + 5.80230i) q^{35} +(2.04970 + 3.55019i) q^{37} +(-0.287275 + 6.94984i) q^{39} +(-1.98773 - 1.66790i) q^{41} +(-4.77434 - 1.73772i) q^{43} +(6.33824 + 2.91982i) q^{45} +(5.64657 + 2.05518i) q^{47} +(6.62063 + 2.27316i) q^{49} +(1.72101 - 1.32694i) q^{51} +(-2.91534 + 1.68317i) q^{53} +4.23047i q^{55} +(6.10145 + 7.91347i) q^{57} +(-7.51642 - 6.30702i) q^{59} +(3.74706 - 10.2950i) q^{61} +(3.25478 - 7.23923i) q^{63} +(-6.00468 - 7.15609i) q^{65} +(1.64220 - 9.31340i) q^{67} +(0.612165 - 14.8097i) q^{69} +(4.63046 + 2.67340i) q^{71} +(-7.35335 - 4.24546i) q^{73} +(-0.678353 + 0.215616i) q^{75} +(4.81152 - 0.0441033i) q^{77} +(0.709479 + 4.02366i) q^{79} +(-7.83567 - 4.42744i) q^{81} +(-7.74206 + 6.49636i) q^{83} +(-0.506802 + 2.87422i) q^{85} +(-10.8228 - 2.37302i) q^{87} +6.53549 q^{89} +(-8.07638 + 6.90402i) q^{91} +(11.2781 + 7.14821i) q^{93} +(-13.2161 - 2.33036i) q^{95} +(3.30745 - 9.08716i) q^{97} +(0.450282 - 5.43737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) 1.37168 1.05759i 0.791938 0.610601i
\(4\) 0 0
\(5\) −0.403931 + 2.29081i −0.180643 + 1.02448i 0.750783 + 0.660549i \(0.229677\pi\)
−0.931426 + 0.363931i \(0.881435\pi\)
\(6\) 0 0
\(7\) 2.60966 + 0.435529i 0.986358 + 0.164614i
\(8\) 0 0
\(9\) 0.762996 2.90135i 0.254332 0.967117i
\(10\) 0 0
\(11\) 1.79103 0.315807i 0.540016 0.0952194i 0.103014 0.994680i \(-0.467151\pi\)
0.437002 + 0.899460i \(0.356040\pi\)
\(12\) 0 0
\(13\) −2.58138 + 3.07637i −0.715947 + 0.853233i −0.994230 0.107267i \(-0.965790\pi\)
0.278283 + 0.960499i \(0.410235\pi\)
\(14\) 0 0
\(15\) 1.86868 + 3.56944i 0.482490 + 0.921626i
\(16\) 0 0
\(17\) 1.25468 0.304304 0.152152 0.988357i \(-0.451380\pi\)
0.152152 + 0.988357i \(0.451380\pi\)
\(18\) 0 0
\(19\) 5.76919i 1.32354i 0.749706 + 0.661772i \(0.230195\pi\)
−0.749706 + 0.661772i \(0.769805\pi\)
\(20\) 0 0
\(21\) 4.04022 2.16255i 0.881648 0.471907i
\(22\) 0 0
\(23\) 5.50076 6.55555i 1.14699 1.36693i 0.227515 0.973775i \(-0.426940\pi\)
0.919473 0.393152i \(-0.128616\pi\)
\(24\) 0 0
\(25\) −0.386172 0.140555i −0.0772343 0.0281110i
\(26\) 0 0
\(27\) −2.02186 4.78666i −0.389108 0.921192i
\(28\) 0 0
\(29\) −4.11192 4.90039i −0.763564 0.909980i 0.234504 0.972115i \(-0.424653\pi\)
−0.998068 + 0.0621353i \(0.980209\pi\)
\(30\) 0 0
\(31\) 2.63669 + 7.24423i 0.473563 + 1.30110i 0.914871 + 0.403747i \(0.132292\pi\)
−0.441308 + 0.897356i \(0.645485\pi\)
\(32\) 0 0
\(33\) 2.12272 2.32737i 0.369518 0.405142i
\(34\) 0 0
\(35\) −2.05183 + 5.80230i −0.346823 + 0.980767i
\(36\) 0 0
\(37\) 2.04970 + 3.55019i 0.336969 + 0.583648i 0.983861 0.178934i \(-0.0572648\pi\)
−0.646892 + 0.762582i \(0.723931\pi\)
\(38\) 0 0
\(39\) −0.287275 + 6.94984i −0.0460009 + 1.11287i
\(40\) 0 0
\(41\) −1.98773 1.66790i −0.310431 0.260482i 0.474239 0.880396i \(-0.342723\pi\)
−0.784670 + 0.619914i \(0.787168\pi\)
\(42\) 0 0
\(43\) −4.77434 1.73772i −0.728079 0.264999i −0.0487278 0.998812i \(-0.515517\pi\)
−0.679352 + 0.733813i \(0.737739\pi\)
\(44\) 0 0
\(45\) 6.33824 + 2.91982i 0.944848 + 0.435261i
\(46\) 0 0
\(47\) 5.64657 + 2.05518i 0.823637 + 0.299779i 0.719245 0.694757i \(-0.244488\pi\)
0.104392 + 0.994536i \(0.466710\pi\)
\(48\) 0 0
\(49\) 6.62063 + 2.27316i 0.945804 + 0.324737i
\(50\) 0 0
\(51\) 1.72101 1.32694i 0.240990 0.185808i
\(52\) 0 0
\(53\) −2.91534 + 1.68317i −0.400453 + 0.231202i −0.686679 0.726960i \(-0.740932\pi\)
0.286226 + 0.958162i \(0.407599\pi\)
\(54\) 0 0
\(55\) 4.23047i 0.570436i
\(56\) 0 0
\(57\) 6.10145 + 7.91347i 0.808157 + 1.04816i
\(58\) 0 0
\(59\) −7.51642 6.30702i −0.978554 0.821104i 0.00531667 0.999986i \(-0.498308\pi\)
−0.983871 + 0.178882i \(0.942752\pi\)
\(60\) 0 0
\(61\) 3.74706 10.2950i 0.479762 1.31814i −0.429934 0.902860i \(-0.641463\pi\)
0.909696 0.415275i \(-0.136315\pi\)
\(62\) 0 0
\(63\) 3.25478 7.23923i 0.410064 0.912057i
\(64\) 0 0
\(65\) −6.00468 7.15609i −0.744788 0.887604i
\(66\) 0 0
\(67\) 1.64220 9.31340i 0.200627 1.13781i −0.703547 0.710649i \(-0.748402\pi\)
0.904174 0.427164i \(-0.140487\pi\)
\(68\) 0 0
\(69\) 0.612165 14.8097i 0.0736960 1.78287i
\(70\) 0 0
\(71\) 4.63046 + 2.67340i 0.549534 + 0.317274i 0.748934 0.662644i \(-0.230566\pi\)
−0.199400 + 0.979918i \(0.563899\pi\)
\(72\) 0 0
\(73\) −7.35335 4.24546i −0.860644 0.496893i 0.00358383 0.999994i \(-0.498859\pi\)
−0.864228 + 0.503100i \(0.832193\pi\)
\(74\) 0 0
\(75\) −0.678353 + 0.215616i −0.0783294 + 0.0248972i
\(76\) 0 0
\(77\) 4.81152 0.0441033i 0.548324 0.00502604i
\(78\) 0 0
\(79\) 0.709479 + 4.02366i 0.0798227 + 0.452697i 0.998354 + 0.0573491i \(0.0182648\pi\)
−0.918532 + 0.395348i \(0.870624\pi\)
\(80\) 0 0
\(81\) −7.83567 4.42744i −0.870631 0.491938i
\(82\) 0 0
\(83\) −7.74206 + 6.49636i −0.849802 + 0.713068i −0.959746 0.280869i \(-0.909377\pi\)
0.109944 + 0.993938i \(0.464933\pi\)
\(84\) 0 0
\(85\) −0.506802 + 2.87422i −0.0549704 + 0.311753i
\(86\) 0 0
\(87\) −10.8228 2.37302i −1.16033 0.254415i
\(88\) 0 0
\(89\) 6.53549 0.692760 0.346380 0.938094i \(-0.387411\pi\)
0.346380 + 0.938094i \(0.387411\pi\)
\(90\) 0 0
\(91\) −8.07638 + 6.90402i −0.846634 + 0.723738i
\(92\) 0 0
\(93\) 11.2781 + 7.14821i 1.16949 + 0.741235i
\(94\) 0 0
\(95\) −13.2161 2.33036i −1.35594 0.239089i
\(96\) 0 0
\(97\) 3.30745 9.08716i 0.335821 0.922661i −0.650745 0.759297i \(-0.725543\pi\)
0.986566 0.163364i \(-0.0522346\pi\)
\(98\) 0 0
\(99\) 0.450282 5.43737i 0.0452551 0.546476i
\(100\) 0 0
\(101\) 1.10030 0.923260i 0.109484 0.0918678i −0.586402 0.810020i \(-0.699456\pi\)
0.695886 + 0.718152i \(0.255012\pi\)
\(102\) 0 0
\(103\) 1.55330 + 0.273888i 0.153051 + 0.0269870i 0.249649 0.968336i \(-0.419685\pi\)
−0.0965976 + 0.995324i \(0.530796\pi\)
\(104\) 0 0
\(105\) 3.32201 + 10.1289i 0.324195 + 0.988478i
\(106\) 0 0
\(107\) −13.8232 7.98083i −1.33634 0.771536i −0.350078 0.936721i \(-0.613845\pi\)
−0.986263 + 0.165184i \(0.947178\pi\)
\(108\) 0 0
\(109\) 3.77704 + 6.54202i 0.361774 + 0.626612i 0.988253 0.152827i \(-0.0488378\pi\)
−0.626479 + 0.779439i \(0.715504\pi\)
\(110\) 0 0
\(111\) 6.56619 + 2.70196i 0.623235 + 0.256459i
\(112\) 0 0
\(113\) −2.00364 5.50496i −0.188487 0.517863i 0.809071 0.587711i \(-0.199971\pi\)
−0.997558 + 0.0698478i \(0.977749\pi\)
\(114\) 0 0
\(115\) 12.7956 + 15.2492i 1.19319 + 1.42199i
\(116\) 0 0
\(117\) 6.95605 + 9.83676i 0.643087 + 0.909409i
\(118\) 0 0
\(119\) 3.27427 + 0.546447i 0.300152 + 0.0500927i
\(120\) 0 0
\(121\) −7.22856 + 2.63098i −0.657142 + 0.239180i
\(122\) 0 0
\(123\) −4.49048 0.185616i −0.404893 0.0167364i
\(124\) 0 0
\(125\) −5.33739 + 9.24464i −0.477391 + 0.826866i
\(126\) 0 0
\(127\) −3.42823 5.93786i −0.304206 0.526900i 0.672878 0.739753i \(-0.265058\pi\)
−0.977084 + 0.212853i \(0.931724\pi\)
\(128\) 0 0
\(129\) −8.38664 + 2.66572i −0.738403 + 0.234703i
\(130\) 0 0
\(131\) −10.3553 8.68914i −0.904748 0.759174i 0.0663648 0.997795i \(-0.478860\pi\)
−0.971113 + 0.238622i \(0.923304\pi\)
\(132\) 0 0
\(133\) −2.51265 + 15.0556i −0.217874 + 1.30549i
\(134\) 0 0
\(135\) 11.7820 2.69822i 1.01403 0.232226i
\(136\) 0 0
\(137\) −7.18160 + 19.7313i −0.613566 + 1.68576i 0.108642 + 0.994081i \(0.465350\pi\)
−0.722207 + 0.691677i \(0.756872\pi\)
\(138\) 0 0
\(139\) −20.1849 3.55915i −1.71206 0.301883i −0.770180 0.637826i \(-0.779834\pi\)
−0.941882 + 0.335944i \(0.890945\pi\)
\(140\) 0 0
\(141\) 9.91882 3.15272i 0.835315 0.265507i
\(142\) 0 0
\(143\) −3.65180 + 6.32510i −0.305379 + 0.528931i
\(144\) 0 0
\(145\) 12.8868 7.44019i 1.07019 0.617874i
\(146\) 0 0
\(147\) 11.4854 3.88389i 0.947303 0.320337i
\(148\) 0 0
\(149\) −2.36927 6.50950i −0.194098 0.533279i 0.804020 0.594602i \(-0.202690\pi\)
−0.998118 + 0.0613227i \(0.980468\pi\)
\(150\) 0 0
\(151\) 0.184744 + 1.04774i 0.0150343 + 0.0852635i 0.991402 0.130854i \(-0.0417718\pi\)
−0.976367 + 0.216117i \(0.930661\pi\)
\(152\) 0 0
\(153\) 0.957312 3.64025i 0.0773941 0.294297i
\(154\) 0 0
\(155\) −17.6602 + 3.11397i −1.41850 + 0.250120i
\(156\) 0 0
\(157\) −4.42188 + 5.26979i −0.352904 + 0.420575i −0.913068 0.407807i \(-0.866294\pi\)
0.560164 + 0.828382i \(0.310738\pi\)
\(158\) 0 0
\(159\) −2.21880 + 5.39201i −0.175962 + 0.427614i
\(160\) 0 0
\(161\) 17.2102 14.7120i 1.35636 1.15947i
\(162\) 0 0
\(163\) −11.1280 + 19.2742i −0.871609 + 1.50967i −0.0112777 + 0.999936i \(0.503590\pi\)
−0.860331 + 0.509735i \(0.829743\pi\)
\(164\) 0 0
\(165\) 4.47411 + 5.80284i 0.348309 + 0.451750i
\(166\) 0 0
\(167\) 0.764681 0.278321i 0.0591728 0.0215371i −0.312264 0.949995i \(-0.601087\pi\)
0.371437 + 0.928458i \(0.378865\pi\)
\(168\) 0 0
\(169\) −0.543105 3.08010i −0.0417773 0.236931i
\(170\) 0 0
\(171\) 16.7384 + 4.40187i 1.28002 + 0.336619i
\(172\) 0 0
\(173\) 6.59740 5.53588i 0.501591 0.420885i −0.356567 0.934270i \(-0.616053\pi\)
0.858159 + 0.513384i \(0.171609\pi\)
\(174\) 0 0
\(175\) −0.946560 0.534989i −0.0715532 0.0404414i
\(176\) 0 0
\(177\) −16.9804 0.701891i −1.27632 0.0527574i
\(178\) 0 0
\(179\) 21.6297i 1.61668i −0.588716 0.808340i \(-0.700366\pi\)
0.588716 0.808340i \(-0.299634\pi\)
\(180\) 0 0
\(181\) 6.59068 3.80513i 0.489882 0.282833i −0.234644 0.972081i \(-0.575392\pi\)
0.724525 + 0.689248i \(0.242059\pi\)
\(182\) 0 0
\(183\) −5.74812 18.0842i −0.424913 1.33682i
\(184\) 0 0
\(185\) −8.96074 + 3.26144i −0.658807 + 0.239786i
\(186\) 0 0
\(187\) 2.24716 0.396235i 0.164329 0.0289756i
\(188\) 0 0
\(189\) −3.19165 13.3721i −0.232158 0.972678i
\(190\) 0 0
\(191\) −11.3970 + 2.00960i −0.824660 + 0.145410i −0.570025 0.821628i \(-0.693066\pi\)
−0.254635 + 0.967037i \(0.581955\pi\)
\(192\) 0 0
\(193\) −10.6308 + 3.86929i −0.765220 + 0.278517i −0.694996 0.719014i \(-0.744594\pi\)
−0.0702244 + 0.997531i \(0.522372\pi\)
\(194\) 0 0
\(195\) −15.8047 3.46535i −1.13180 0.248159i
\(196\) 0 0
\(197\) −3.98585 + 2.30123i −0.283980 + 0.163956i −0.635224 0.772328i \(-0.719092\pi\)
0.351244 + 0.936284i \(0.385759\pi\)
\(198\) 0 0
\(199\) 23.8528i 1.69088i 0.534070 + 0.845440i \(0.320662\pi\)
−0.534070 + 0.845440i \(0.679338\pi\)
\(200\) 0 0
\(201\) −7.59721 14.5118i −0.535866 1.02358i
\(202\) 0 0
\(203\) −8.59644 14.5792i −0.603351 1.02326i
\(204\) 0 0
\(205\) 4.62374 3.87978i 0.322936 0.270976i
\(206\) 0 0
\(207\) −14.8229 20.9615i −1.03026 1.45692i
\(208\) 0 0
\(209\) 1.82195 + 10.3328i 0.126027 + 0.714735i
\(210\) 0 0
\(211\) 7.50376 2.73115i 0.516580 0.188020i −0.0705562 0.997508i \(-0.522477\pi\)
0.587136 + 0.809488i \(0.300255\pi\)
\(212\) 0 0
\(213\) 9.17886 1.23010i 0.628925 0.0842852i
\(214\) 0 0
\(215\) 5.90927 10.2352i 0.403009 0.698032i
\(216\) 0 0
\(217\) 3.72578 + 20.0533i 0.252922 + 1.36131i
\(218\) 0 0
\(219\) −14.5764 + 1.95345i −0.984980 + 0.132002i
\(220\) 0 0
\(221\) −3.23880 + 3.85985i −0.217865 + 0.259642i
\(222\) 0 0
\(223\) −6.24957 + 1.10197i −0.418502 + 0.0737932i −0.378934 0.925424i \(-0.623709\pi\)
−0.0395680 + 0.999217i \(0.512598\pi\)
\(224\) 0 0
\(225\) −0.702447 + 1.01318i −0.0468298 + 0.0675451i
\(226\) 0 0
\(227\) 0.624196 + 3.53999i 0.0414293 + 0.234957i 0.998490 0.0549295i \(-0.0174934\pi\)
−0.957061 + 0.289887i \(0.906382\pi\)
\(228\) 0 0
\(229\) −8.36647 22.9867i −0.552872 1.51900i −0.829771 0.558104i \(-0.811529\pi\)
0.276900 0.960899i \(-0.410693\pi\)
\(230\) 0 0
\(231\) 6.55321 5.14912i 0.431170 0.338788i
\(232\) 0 0
\(233\) 20.9694 12.1067i 1.37375 0.793136i 0.382353 0.924016i \(-0.375114\pi\)
0.991398 + 0.130880i \(0.0417804\pi\)
\(234\) 0 0
\(235\) −6.98885 + 12.1050i −0.455902 + 0.789646i
\(236\) 0 0
\(237\) 5.22857 + 4.76882i 0.339632 + 0.309768i
\(238\) 0 0
\(239\) 2.42563 + 0.427703i 0.156901 + 0.0276658i 0.251547 0.967845i \(-0.419061\pi\)
−0.0946460 + 0.995511i \(0.530172\pi\)
\(240\) 0 0
\(241\) 2.20492 6.05798i 0.142032 0.390229i −0.848197 0.529681i \(-0.822312\pi\)
0.990229 + 0.139452i \(0.0445340\pi\)
\(242\) 0 0
\(243\) −15.4304 + 2.21394i −0.989863 + 0.142024i
\(244\) 0 0
\(245\) −7.88165 + 14.2484i −0.503540 + 0.910296i
\(246\) 0 0
\(247\) −17.7482 14.8925i −1.12929 0.947587i
\(248\) 0 0
\(249\) −3.74911 + 17.0989i −0.237590 + 1.08360i
\(250\) 0 0
\(251\) 5.67332 + 9.82648i 0.358097 + 0.620242i 0.987643 0.156721i \(-0.0500924\pi\)
−0.629546 + 0.776963i \(0.716759\pi\)
\(252\) 0 0
\(253\) 7.78174 13.4784i 0.489234 0.847378i
\(254\) 0 0
\(255\) 2.34458 + 4.47849i 0.146824 + 0.280454i
\(256\) 0 0
\(257\) 19.1682 6.97665i 1.19568 0.435191i 0.333964 0.942586i \(-0.391614\pi\)
0.861714 + 0.507395i \(0.169391\pi\)
\(258\) 0 0
\(259\) 3.80282 + 10.1575i 0.236296 + 0.631156i
\(260\) 0 0
\(261\) −17.3551 + 8.19113i −1.07426 + 0.507018i
\(262\) 0 0
\(263\) −18.9725 22.6105i −1.16989 1.39422i −0.902530 0.430627i \(-0.858293\pi\)
−0.267362 0.963596i \(-0.586152\pi\)
\(264\) 0 0
\(265\) −2.67823 7.35837i −0.164522 0.452021i
\(266\) 0 0
\(267\) 8.96458 6.91188i 0.548623 0.423000i
\(268\) 0 0
\(269\) 14.8916 + 25.7929i 0.907954 + 1.57262i 0.816902 + 0.576777i \(0.195690\pi\)
0.0910522 + 0.995846i \(0.470977\pi\)
\(270\) 0 0
\(271\) −22.2490 12.8455i −1.35153 0.780307i −0.363068 0.931763i \(-0.618271\pi\)
−0.988464 + 0.151455i \(0.951604\pi\)
\(272\) 0 0
\(273\) −3.77655 + 18.0116i −0.228567 + 1.09011i
\(274\) 0 0
\(275\) −0.736033 0.129783i −0.0443845 0.00782618i
\(276\) 0 0
\(277\) 13.8688 11.6373i 0.833294 0.699216i −0.122751 0.992437i \(-0.539172\pi\)
0.956045 + 0.293221i \(0.0947272\pi\)
\(278\) 0 0
\(279\) 23.0298 2.12263i 1.37876 0.127078i
\(280\) 0 0
\(281\) 3.92202 10.7757i 0.233968 0.642822i −0.766032 0.642802i \(-0.777772\pi\)
1.00000 1.93050e-5i \(-6.14496e-6\pi\)
\(282\) 0 0
\(283\) 8.31293 + 1.46579i 0.494152 + 0.0871324i 0.415170 0.909744i \(-0.363722\pi\)
0.0789820 + 0.996876i \(0.474833\pi\)
\(284\) 0 0
\(285\) −20.5928 + 10.7808i −1.21981 + 0.638597i
\(286\) 0 0
\(287\) −4.46087 5.21836i −0.263317 0.308030i
\(288\) 0 0
\(289\) −15.4258 −0.907399
\(290\) 0 0
\(291\) −5.07375 15.9626i −0.297428 0.935743i
\(292\) 0 0
\(293\) 3.30387 18.7372i 0.193014 1.09464i −0.722204 0.691680i \(-0.756871\pi\)
0.915218 0.402958i \(-0.132018\pi\)
\(294\) 0 0
\(295\) 17.4843 14.6711i 1.01797 0.854182i
\(296\) 0 0
\(297\) −5.13288 7.93453i −0.297840 0.460408i
\(298\) 0 0
\(299\) 5.96775 + 33.8448i 0.345124 + 1.95729i
\(300\) 0 0
\(301\) −11.7026 6.61420i −0.674524 0.381236i
\(302\) 0 0
\(303\) 0.532821 2.43008i 0.0306098 0.139604i
\(304\) 0 0
\(305\) 22.0702 + 12.7422i 1.26374 + 0.729619i
\(306\) 0 0
\(307\) 23.5264 + 13.5830i 1.34272 + 0.775223i 0.987207 0.159447i \(-0.0509710\pi\)
0.355518 + 0.934669i \(0.384304\pi\)
\(308\) 0 0
\(309\) 2.42029 1.26707i 0.137685 0.0720811i
\(310\) 0 0
\(311\) −4.24642 + 24.0826i −0.240792 + 1.36560i 0.589273 + 0.807934i \(0.299414\pi\)
−0.830065 + 0.557666i \(0.811697\pi\)
\(312\) 0 0
\(313\) −8.71127 10.3817i −0.492390 0.586807i 0.461434 0.887175i \(-0.347335\pi\)
−0.953824 + 0.300367i \(0.902891\pi\)
\(314\) 0 0
\(315\) 15.2690 + 10.3802i 0.860309 + 0.584859i
\(316\) 0 0
\(317\) 6.46678 17.7673i 0.363210 0.997912i −0.614677 0.788779i \(-0.710714\pi\)
0.977887 0.209133i \(-0.0670643\pi\)
\(318\) 0 0
\(319\) −8.91215 7.47818i −0.498984 0.418698i
\(320\) 0 0
\(321\) −27.4015 + 3.67220i −1.52940 + 0.204962i
\(322\) 0 0
\(323\) 7.23846i 0.402759i
\(324\) 0 0
\(325\) 1.42926 0.825182i 0.0792809 0.0457728i
\(326\) 0 0
\(327\) 12.0997 + 4.97897i 0.669113 + 0.275338i
\(328\) 0 0
\(329\) 13.8405 + 7.82257i 0.763053 + 0.431272i
\(330\) 0 0
\(331\) 17.0985 + 6.22336i 0.939820 + 0.342067i 0.766095 0.642728i \(-0.222197\pi\)
0.173725 + 0.984794i \(0.444420\pi\)
\(332\) 0 0
\(333\) 11.8643 3.23813i 0.650158 0.177448i
\(334\) 0 0
\(335\) 20.6719 + 7.52394i 1.12942 + 0.411077i
\(336\) 0 0
\(337\) 4.58257 + 3.84523i 0.249629 + 0.209463i 0.759012 0.651076i \(-0.225682\pi\)
−0.509384 + 0.860539i \(0.670127\pi\)
\(338\) 0 0
\(339\) −8.57036 5.43199i −0.465478 0.295025i
\(340\) 0 0
\(341\) 7.01016 + 12.1420i 0.379622 + 0.657524i
\(342\) 0 0
\(343\) 16.2876 + 8.81565i 0.879445 + 0.476000i
\(344\) 0 0
\(345\) 33.6788 + 7.38443i 1.81321 + 0.397565i
\(346\) 0 0
\(347\) 9.25708 + 25.4336i 0.496946 + 1.36535i 0.894211 + 0.447645i \(0.147737\pi\)
−0.397265 + 0.917704i \(0.630041\pi\)
\(348\) 0 0
\(349\) 10.3811 + 12.3717i 0.555686 + 0.662241i 0.968628 0.248517i \(-0.0799431\pi\)
−0.412942 + 0.910757i \(0.635499\pi\)
\(350\) 0 0
\(351\) 19.9447 + 6.13619i 1.06457 + 0.327526i
\(352\) 0 0
\(353\) −14.7706 5.37608i −0.786162 0.286140i −0.0824224 0.996597i \(-0.526266\pi\)
−0.703740 + 0.710458i \(0.748488\pi\)
\(354\) 0 0
\(355\) −7.99462 + 9.52762i −0.424310 + 0.505673i
\(356\) 0 0
\(357\) 5.06917 2.71330i 0.268289 0.143603i
\(358\) 0 0
\(359\) 2.52187i 0.133099i 0.997783 + 0.0665496i \(0.0211991\pi\)
−0.997783 + 0.0665496i \(0.978801\pi\)
\(360\) 0 0
\(361\) −14.2836 −0.751767
\(362\) 0 0
\(363\) −7.13275 + 11.2537i −0.374372 + 0.590668i
\(364\) 0 0
\(365\) 12.6958 15.1302i 0.664527 0.791952i
\(366\) 0 0
\(367\) 34.5407 6.09046i 1.80301 0.317920i 0.831609 0.555361i \(-0.187420\pi\)
0.971402 + 0.237442i \(0.0763088\pi\)
\(368\) 0 0
\(369\) −6.35579 + 4.49449i −0.330869 + 0.233974i
\(370\) 0 0
\(371\) −8.34111 + 3.12279i −0.433049 + 0.162127i
\(372\) 0 0
\(373\) 5.32884 30.2213i 0.275917 1.56480i −0.460118 0.887858i \(-0.652193\pi\)
0.736035 0.676944i \(-0.236696\pi\)
\(374\) 0 0
\(375\) 2.45588 + 18.3254i 0.126821 + 0.946322i
\(376\) 0 0
\(377\) 25.6899 1.32310
\(378\) 0 0
\(379\) 25.4637 1.30798 0.653991 0.756502i \(-0.273093\pi\)
0.653991 + 0.756502i \(0.273093\pi\)
\(380\) 0 0
\(381\) −10.9823 4.51916i −0.562638 0.231524i
\(382\) 0 0
\(383\) −1.77070 + 10.0421i −0.0904786 + 0.513130i 0.905561 + 0.424216i \(0.139450\pi\)
−0.996039 + 0.0889131i \(0.971661\pi\)
\(384\) 0 0
\(385\) −1.84249 + 11.0401i −0.0939020 + 0.562655i
\(386\) 0 0
\(387\) −8.68452 + 12.5262i −0.441459 + 0.636740i
\(388\) 0 0
\(389\) −19.5100 + 3.44014i −0.989196 + 0.174422i −0.644758 0.764387i \(-0.723042\pi\)
−0.344438 + 0.938809i \(0.611931\pi\)
\(390\) 0 0
\(391\) 6.90167 8.22509i 0.349033 0.415961i
\(392\) 0 0
\(393\) −23.3937 0.966991i −1.18006 0.0487782i
\(394\) 0 0
\(395\) −9.50400 −0.478198
\(396\) 0 0
\(397\) 6.94762i 0.348691i 0.984685 + 0.174346i \(0.0557810\pi\)
−0.984685 + 0.174346i \(0.944219\pi\)
\(398\) 0 0
\(399\) 12.4762 + 23.3088i 0.624590 + 1.16690i
\(400\) 0 0
\(401\) 21.7144 25.8782i 1.08436 1.29229i 0.130699 0.991422i \(-0.458278\pi\)
0.953665 0.300872i \(-0.0972776\pi\)
\(402\) 0 0
\(403\) −29.0923 10.5887i −1.44919 0.527462i
\(404\) 0 0
\(405\) 13.3075 16.1616i 0.661254 0.803078i
\(406\) 0 0
\(407\) 4.79226 + 5.71119i 0.237543 + 0.283093i
\(408\) 0 0
\(409\) 5.58263 + 15.3382i 0.276043 + 0.758423i 0.997801 + 0.0662772i \(0.0211122\pi\)
−0.721758 + 0.692146i \(0.756666\pi\)
\(410\) 0 0
\(411\) 11.0168 + 34.6602i 0.543420 + 1.70966i
\(412\) 0 0
\(413\) −16.8684 19.7328i −0.830039 0.970987i
\(414\) 0 0
\(415\) −11.7546 20.3596i −0.577013 0.999416i
\(416\) 0 0
\(417\) −31.4513 + 16.4654i −1.54018 + 0.806315i
\(418\) 0 0
\(419\) −18.4928 15.5173i −0.903431 0.758069i 0.0674271 0.997724i \(-0.478521\pi\)
−0.970858 + 0.239656i \(0.922965\pi\)
\(420\) 0 0
\(421\) 0.657830 + 0.239431i 0.0320607 + 0.0116691i 0.358001 0.933721i \(-0.383459\pi\)
−0.325940 + 0.945390i \(0.605681\pi\)
\(422\) 0 0
\(423\) 10.2711 14.8146i 0.499399 0.720310i
\(424\) 0 0
\(425\) −0.484520 0.176351i −0.0235027 0.00855427i
\(426\) 0 0
\(427\) 14.2623 25.2344i 0.690201 1.22118i
\(428\) 0 0
\(429\) 1.68029 + 12.5381i 0.0811252 + 0.605346i
\(430\) 0 0
\(431\) 14.9907 8.65486i 0.722074 0.416890i −0.0934413 0.995625i \(-0.529787\pi\)
0.815516 + 0.578735i \(0.196453\pi\)
\(432\) 0 0
\(433\) 27.8478i 1.33828i −0.743136 0.669141i \(-0.766662\pi\)
0.743136 0.669141i \(-0.233338\pi\)
\(434\) 0 0
\(435\) 9.80781 23.8345i 0.470249 1.14278i
\(436\) 0 0
\(437\) 37.8202 + 31.7349i 1.80919 + 1.51809i
\(438\) 0 0
\(439\) 2.94890 8.10204i 0.140743 0.386689i −0.849215 0.528047i \(-0.822924\pi\)
0.989959 + 0.141358i \(0.0451467\pi\)
\(440\) 0 0
\(441\) 11.6468 17.4744i 0.554607 0.832112i
\(442\) 0 0
\(443\) 13.2210 + 15.7562i 0.628148 + 0.748598i 0.982449 0.186534i \(-0.0597253\pi\)
−0.354300 + 0.935132i \(0.615281\pi\)
\(444\) 0 0
\(445\) −2.63989 + 14.9715i −0.125143 + 0.709719i
\(446\) 0 0
\(447\) −10.1343 6.42322i −0.479335 0.303808i
\(448\) 0 0
\(449\) 0.162556 + 0.0938518i 0.00767150 + 0.00442914i 0.503831 0.863802i \(-0.331923\pi\)
−0.496159 + 0.868231i \(0.665257\pi\)
\(450\) 0 0
\(451\) −4.08682 2.35952i −0.192441 0.111106i
\(452\) 0 0
\(453\) 1.36149 + 1.24177i 0.0639682 + 0.0583435i
\(454\) 0 0
\(455\) −12.5535 21.2902i −0.588516 0.998098i
\(456\) 0 0
\(457\) 0.844709 + 4.79058i 0.0395138 + 0.224094i 0.998170 0.0604736i \(-0.0192611\pi\)
−0.958656 + 0.284568i \(0.908150\pi\)
\(458\) 0 0
\(459\) −2.53678 6.00570i −0.118407 0.280322i
\(460\) 0 0
\(461\) −23.6098 + 19.8110i −1.09962 + 0.922690i −0.997399 0.0720715i \(-0.977039\pi\)
−0.102220 + 0.994762i \(0.532595\pi\)
\(462\) 0 0
\(463\) −1.71296 + 9.71467i −0.0796080 + 0.451479i 0.918782 + 0.394764i \(0.129174\pi\)
−0.998390 + 0.0567150i \(0.981937\pi\)
\(464\) 0 0
\(465\) −20.9308 + 22.9486i −0.970640 + 1.06422i
\(466\) 0 0
\(467\) 3.30666 0.153014 0.0765070 0.997069i \(-0.475623\pi\)
0.0765070 + 0.997069i \(0.475623\pi\)
\(468\) 0 0
\(469\) 8.34184 23.5896i 0.385190 1.08926i
\(470\) 0 0
\(471\) −0.492099 + 11.9050i −0.0226747 + 0.548553i
\(472\) 0 0
\(473\) −9.09977 1.60453i −0.418408 0.0737766i
\(474\) 0 0
\(475\) 0.810888 2.22790i 0.0372061 0.102223i
\(476\) 0 0
\(477\) 2.65908 + 9.74268i 0.121751 + 0.446087i
\(478\) 0 0
\(479\) −11.0256 + 9.25158i −0.503773 + 0.422716i −0.858932 0.512090i \(-0.828871\pi\)
0.355159 + 0.934806i \(0.384427\pi\)
\(480\) 0 0
\(481\) −16.2128 2.85875i −0.739239 0.130348i
\(482\) 0 0
\(483\) 8.04757 38.3815i 0.366177 1.74642i
\(484\) 0 0
\(485\) 19.4809 + 11.2473i 0.884584 + 0.510715i
\(486\) 0 0
\(487\) 16.1563 + 27.9836i 0.732113 + 1.26806i 0.955979 + 0.293436i \(0.0947989\pi\)
−0.223866 + 0.974620i \(0.571868\pi\)
\(488\) 0 0
\(489\) 5.12028 + 38.2068i 0.231547 + 1.72777i
\(490\) 0 0
\(491\) −7.74489 21.2789i −0.349522 0.960303i −0.982521 0.186151i \(-0.940399\pi\)
0.632999 0.774152i \(-0.281824\pi\)
\(492\) 0 0
\(493\) −5.15912 6.14840i −0.232355 0.276910i
\(494\) 0 0
\(495\) 12.2741 + 3.22783i 0.551679 + 0.145080i
\(496\) 0 0
\(497\) 10.9196 + 8.99335i 0.489810 + 0.403407i
\(498\) 0 0
\(499\) −17.2967 + 6.29549i −0.774307 + 0.281825i −0.698797 0.715320i \(-0.746281\pi\)
−0.0755104 + 0.997145i \(0.524059\pi\)
\(500\) 0 0
\(501\) 0.754545 1.19049i 0.0337106 0.0531871i
\(502\) 0 0
\(503\) 12.3813 21.4450i 0.552053 0.956184i −0.446073 0.894997i \(-0.647178\pi\)
0.998126 0.0611879i \(-0.0194889\pi\)
\(504\) 0 0
\(505\) 1.67056 + 2.89350i 0.0743391 + 0.128759i
\(506\) 0 0
\(507\) −4.00246 3.65052i −0.177755 0.162125i
\(508\) 0 0
\(509\) 1.25802 + 1.05560i 0.0557608 + 0.0467888i 0.670242 0.742143i \(-0.266190\pi\)
−0.614481 + 0.788931i \(0.710635\pi\)
\(510\) 0 0
\(511\) −17.3407 14.2818i −0.767107 0.631789i
\(512\) 0 0
\(513\) 27.6151 11.6645i 1.21924 0.515001i
\(514\) 0 0
\(515\) −1.25485 + 3.44768i −0.0552953 + 0.151923i
\(516\) 0 0
\(517\) 10.7622 + 1.89767i 0.473322 + 0.0834594i
\(518\) 0 0
\(519\) 3.19480 14.5708i 0.140236 0.639587i
\(520\) 0 0
\(521\) −7.46457 + 12.9290i −0.327029 + 0.566430i −0.981921 0.189292i \(-0.939381\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(522\) 0 0
\(523\) 32.3259 18.6633i 1.41351 0.816091i 0.417794 0.908542i \(-0.362804\pi\)
0.995717 + 0.0924512i \(0.0294702\pi\)
\(524\) 0 0
\(525\) −1.86418 + 0.267243i −0.0813593 + 0.0116634i
\(526\) 0 0
\(527\) 3.30818 + 9.08916i 0.144107 + 0.395930i
\(528\) 0 0
\(529\) −8.72298 49.4705i −0.379260 2.15089i
\(530\) 0 0
\(531\) −24.0339 + 16.9955i −1.04298 + 0.737543i
\(532\) 0 0
\(533\) 10.2622 1.80950i 0.444504 0.0783781i
\(534\) 0 0
\(535\) 23.8662 28.4426i 1.03182 1.22968i
\(536\) 0 0
\(537\) −22.8754 29.6690i −0.987147 1.28031i
\(538\) 0 0
\(539\) 12.5756 + 1.98046i 0.541671 + 0.0853045i
\(540\) 0 0
\(541\) −1.30807 + 2.26565i −0.0562385 + 0.0974080i −0.892774 0.450505i \(-0.851244\pi\)
0.836536 + 0.547913i \(0.184577\pi\)
\(542\) 0 0
\(543\) 5.01601 12.1897i 0.215258 0.523109i
\(544\) 0 0
\(545\) −16.5122 + 6.00993i −0.707303 + 0.257437i
\(546\) 0 0
\(547\) 0.140528 + 0.796974i 0.00600855 + 0.0340762i 0.987665 0.156584i \(-0.0500482\pi\)
−0.981656 + 0.190660i \(0.938937\pi\)
\(548\) 0 0
\(549\) −27.0103 18.7266i −1.15277 0.799230i
\(550\) 0 0
\(551\) 28.2713 23.7224i 1.20440 1.01061i
\(552\) 0 0
\(553\) 0.0990807 + 10.8094i 0.00421334 + 0.459661i
\(554\) 0 0
\(555\) −8.84196 + 13.9505i −0.375320 + 0.592164i
\(556\) 0 0
\(557\) 12.8849i 0.545952i 0.962021 + 0.272976i \(0.0880080\pi\)
−0.962021 + 0.272976i \(0.911992\pi\)
\(558\) 0 0
\(559\) 17.6703 10.2019i 0.747372 0.431496i
\(560\) 0 0
\(561\) 2.66333 2.92009i 0.112446 0.123286i
\(562\) 0 0
\(563\) −29.0171 + 10.5614i −1.22292 + 0.445108i −0.871169 0.490984i \(-0.836638\pi\)
−0.351756 + 0.936092i \(0.614415\pi\)
\(564\) 0 0
\(565\) 13.4201 2.36633i 0.564590 0.0995524i
\(566\) 0 0
\(567\) −18.5202 14.9668i −0.777773 0.628545i
\(568\) 0 0
\(569\) 2.93023 0.516678i 0.122842 0.0216603i −0.111889 0.993721i \(-0.535690\pi\)
0.234731 + 0.972060i \(0.424579\pi\)
\(570\) 0 0
\(571\) 3.81131 1.38720i 0.159498 0.0580526i −0.261037 0.965329i \(-0.584064\pi\)
0.420535 + 0.907276i \(0.361842\pi\)
\(572\) 0 0
\(573\) −13.5077 + 14.8099i −0.564292 + 0.618694i
\(574\) 0 0
\(575\) −3.04565 + 1.75841i −0.127013 + 0.0733307i
\(576\) 0 0
\(577\) 3.81347i 0.158757i −0.996845 0.0793785i \(-0.974706\pi\)
0.996845 0.0793785i \(-0.0252936\pi\)
\(578\) 0 0
\(579\) −10.4899 + 16.5504i −0.435944 + 0.687813i
\(580\) 0 0
\(581\) −23.0335 + 13.5814i −0.955590 + 0.563451i
\(582\) 0 0
\(583\) −4.68991 + 3.93530i −0.194236 + 0.162983i
\(584\) 0 0
\(585\) −25.3439 + 11.9616i −1.04784 + 0.494551i
\(586\) 0 0
\(587\) 3.89708 + 22.1014i 0.160850 + 0.912223i 0.953241 + 0.302211i \(0.0977246\pi\)
−0.792392 + 0.610013i \(0.791164\pi\)
\(588\) 0 0
\(589\) −41.7934 + 15.2115i −1.72207 + 0.626781i
\(590\) 0 0
\(591\) −3.03354 + 7.37196i −0.124783 + 0.303242i
\(592\) 0 0
\(593\) −11.6564 + 20.1895i −0.478672 + 0.829085i −0.999701 0.0244543i \(-0.992215\pi\)
0.521028 + 0.853539i \(0.325549\pi\)
\(594\) 0 0
\(595\) −2.57439 + 7.28000i −0.105540 + 0.298451i
\(596\) 0 0
\(597\) 25.2265 + 32.7183i 1.03245 + 1.33907i
\(598\) 0 0
\(599\) 25.7163 30.6474i 1.05074 1.25222i 0.0839964 0.996466i \(-0.473232\pi\)
0.966742 0.255755i \(-0.0823240\pi\)
\(600\) 0 0
\(601\) −7.62355 + 1.34424i −0.310971 + 0.0548326i −0.326956 0.945040i \(-0.606023\pi\)
0.0159848 + 0.999872i \(0.494912\pi\)
\(602\) 0 0
\(603\) −25.7684 11.8707i −1.04937 0.483412i
\(604\) 0 0
\(605\) −3.10723 17.6220i −0.126327 0.716435i
\(606\) 0 0
\(607\) 8.96428 + 24.6291i 0.363849 + 0.999666i 0.977656 + 0.210211i \(0.0674149\pi\)
−0.613807 + 0.789456i \(0.710363\pi\)
\(608\) 0 0
\(609\) −27.2104 10.9064i −1.10262 0.441951i
\(610\) 0 0
\(611\) −20.8985 + 12.0657i −0.845462 + 0.488128i
\(612\) 0 0
\(613\) −3.43863 + 5.95588i −0.138885 + 0.240556i −0.927075 0.374876i \(-0.877685\pi\)
0.788190 + 0.615432i \(0.211018\pi\)
\(614\) 0 0
\(615\) 2.23905 10.2118i 0.0902874 0.411781i
\(616\) 0 0
\(617\) 17.2432 + 3.04044i 0.694185 + 0.122404i 0.509598 0.860413i \(-0.329794\pi\)
0.184587 + 0.982816i \(0.440905\pi\)
\(618\) 0 0
\(619\) −1.26081 + 3.46404i −0.0506762 + 0.139232i −0.962448 0.271464i \(-0.912492\pi\)
0.911772 + 0.410696i \(0.134714\pi\)
\(620\) 0 0
\(621\) −42.5010 13.0758i −1.70550 0.524715i
\(622\) 0 0
\(623\) 17.0554 + 2.84639i 0.683310 + 0.114038i
\(624\) 0 0
\(625\) −20.5958 17.2819i −0.823832 0.691277i
\(626\) 0 0
\(627\) 13.4270 + 12.2464i 0.536224 + 0.489073i
\(628\) 0 0
\(629\) 2.57171 + 4.45434i 0.102541 + 0.177606i
\(630\) 0 0
\(631\) −22.6990 + 39.3158i −0.903633 + 1.56514i −0.0808913 + 0.996723i \(0.525777\pi\)
−0.822742 + 0.568415i \(0.807557\pi\)
\(632\) 0 0
\(633\) 7.40430 11.6822i 0.294294 0.464325i
\(634\) 0 0
\(635\) 14.9873 5.45492i 0.594751 0.216472i
\(636\) 0 0
\(637\) −24.0835 + 14.4996i −0.954222 + 0.574496i
\(638\) 0 0
\(639\) 11.2895 11.3948i 0.446605 0.450771i
\(640\) 0 0
\(641\) −2.73662 3.26137i −0.108090 0.128817i 0.709287 0.704920i \(-0.249017\pi\)
−0.817377 + 0.576103i \(0.804573\pi\)
\(642\) 0 0
\(643\) 5.17807 + 14.2266i 0.204203 + 0.561044i 0.998946 0.0459029i \(-0.0146165\pi\)
−0.794743 + 0.606946i \(0.792394\pi\)
\(644\) 0 0
\(645\) −2.71902 20.2889i −0.107061 0.798876i
\(646\) 0 0
\(647\) 9.64047 + 16.6978i 0.379006 + 0.656458i 0.990918 0.134468i \(-0.0429326\pi\)
−0.611912 + 0.790926i \(0.709599\pi\)
\(648\) 0 0
\(649\) −15.4539 8.92233i −0.606620 0.350232i
\(650\) 0 0
\(651\) 26.3188 + 23.5663i 1.03152 + 0.923637i
\(652\) 0 0
\(653\) 3.06019 + 0.539594i 0.119755 + 0.0211160i 0.233204 0.972428i \(-0.425079\pi\)
−0.113450 + 0.993544i \(0.536190\pi\)
\(654\) 0 0
\(655\) 24.0880 20.2122i 0.941195 0.789756i
\(656\) 0 0
\(657\) −17.9281 + 18.0954i −0.699443 + 0.705968i
\(658\) 0 0
\(659\) −3.25069 + 8.93121i −0.126629 + 0.347911i −0.986766 0.162153i \(-0.948156\pi\)
0.860136 + 0.510064i \(0.170378\pi\)
\(660\) 0 0
\(661\) 17.2839 + 3.04761i 0.672265 + 0.118538i 0.499353 0.866399i \(-0.333571\pi\)
0.172912 + 0.984937i \(0.444682\pi\)
\(662\) 0 0
\(663\) −0.360437 + 8.71980i −0.0139982 + 0.338649i
\(664\) 0 0
\(665\) −33.4746 11.8374i −1.29809 0.459035i
\(666\) 0 0
\(667\) −54.7434 −2.11967
\(668\) 0 0
\(669\) −7.40696 + 8.12104i −0.286370 + 0.313978i
\(670\) 0 0
\(671\) 3.45988 19.6219i 0.133567 0.757497i
\(672\) 0 0
\(673\) 7.62458 6.39778i 0.293906 0.246616i −0.483896 0.875125i \(-0.660779\pi\)
0.777802 + 0.628509i \(0.216334\pi\)
\(674\) 0 0
\(675\) 0.107998 + 2.13265i 0.00415684 + 0.0820859i
\(676\) 0 0
\(677\) 0.187175 + 1.06152i 0.00719371 + 0.0407975i 0.988193 0.153212i \(-0.0489618\pi\)
−0.981000 + 0.194010i \(0.937851\pi\)
\(678\) 0 0
\(679\) 12.5890 22.2739i 0.483123 0.854793i
\(680\) 0 0
\(681\) 4.60006 + 4.19558i 0.176275 + 0.160775i
\(682\) 0 0
\(683\) 19.7773 + 11.4184i 0.756758 + 0.436914i 0.828130 0.560535i \(-0.189405\pi\)
−0.0713727 + 0.997450i \(0.522738\pi\)
\(684\) 0 0
\(685\) −42.2997 24.4217i −1.61619 0.933107i
\(686\) 0 0
\(687\) −35.7866 22.6820i −1.36535 0.865372i
\(688\) 0 0
\(689\) 2.34755 13.3136i 0.0894344 0.507208i
\(690\) 0 0
\(691\) 2.69196 + 3.20816i 0.102407 + 0.122044i 0.814814 0.579723i \(-0.196839\pi\)
−0.712407 + 0.701767i \(0.752395\pi\)
\(692\) 0 0
\(693\) 3.54321 13.9936i 0.134595 0.531571i
\(694\) 0 0
\(695\) 16.3066 44.8021i 0.618546 1.69944i
\(696\) 0 0
\(697\) −2.49395 2.09267i −0.0944652 0.0792657i
\(698\) 0 0
\(699\) 15.9593 38.7836i 0.603636 1.46693i
\(700\) 0 0
\(701\) 19.8279i 0.748890i 0.927249 + 0.374445i \(0.122167\pi\)
−0.927249 + 0.374445i \(0.877833\pi\)
\(702\) 0 0
\(703\) −20.4817 + 11.8251i −0.772483 + 0.445993i
\(704\) 0 0
\(705\) 3.21576 + 23.9956i 0.121113 + 0.903726i
\(706\) 0 0
\(707\) 3.27351 1.93018i 0.123113 0.0725919i
\(708\) 0 0
\(709\) −36.3221 13.2202i −1.36411 0.496494i −0.446785 0.894641i \(-0.647431\pi\)
−0.917322 + 0.398147i \(0.869653\pi\)
\(710\) 0 0
\(711\) 12.2154 + 1.01159i 0.458112 + 0.0379374i
\(712\) 0 0
\(713\) 61.9937 + 22.5639i 2.32168 + 0.845024i
\(714\) 0 0
\(715\) −13.0145 10.9205i −0.486715 0.408402i
\(716\) 0 0
\(717\) 3.77951 1.97865i 0.141148 0.0738942i
\(718\) 0 0
\(719\) 13.9956 + 24.2411i 0.521949 + 0.904041i 0.999674 + 0.0255322i \(0.00812804\pi\)
−0.477725 + 0.878509i \(0.658539\pi\)
\(720\) 0 0
\(721\) 3.93429 + 1.39126i 0.146521 + 0.0518133i
\(722\) 0 0
\(723\) −3.38243 10.6415i −0.125794 0.395762i
\(724\) 0 0
\(725\) 0.899131 + 2.47034i 0.0333929 + 0.0917462i
\(726\) 0 0
\(727\) −0.372280 0.443665i −0.0138071 0.0164546i 0.759097 0.650978i \(-0.225641\pi\)
−0.772904 + 0.634523i \(0.781196\pi\)
\(728\) 0 0
\(729\) −18.8241 + 19.3559i −0.697190 + 0.716886i
\(730\) 0 0
\(731\) −5.99024 2.18027i −0.221557 0.0806402i
\(732\) 0 0
\(733\) 19.4025 23.1230i 0.716646 0.854066i −0.277654 0.960681i \(-0.589557\pi\)
0.994300 + 0.106615i \(0.0340013\pi\)
\(734\) 0 0
\(735\) 4.25790 + 27.8798i 0.157055 + 1.02836i
\(736\) 0 0
\(737\) 17.1992i 0.633541i
\(738\) 0 0
\(739\) −14.3822 −0.529058 −0.264529 0.964378i \(-0.585217\pi\)
−0.264529 + 0.964378i \(0.585217\pi\)
\(740\) 0 0
\(741\) −40.0950 1.65735i −1.47293 0.0608841i
\(742\) 0 0
\(743\) −18.5207 + 22.0721i −0.679459 + 0.809747i −0.990038 0.140800i \(-0.955033\pi\)
0.310579 + 0.950547i \(0.399477\pi\)
\(744\) 0 0
\(745\) 15.8690 2.79814i 0.581396 0.102516i
\(746\) 0 0
\(747\) 12.9411 + 27.4191i 0.473489 + 1.00321i
\(748\) 0 0
\(749\) −32.5980 26.8477i −1.19110 0.980992i
\(750\) 0 0
\(751\) −4.38064 + 24.8439i −0.159852 + 0.906566i 0.794363 + 0.607444i \(0.207805\pi\)
−0.954215 + 0.299122i \(0.903306\pi\)
\(752\) 0 0
\(753\) 18.1744 + 7.47870i 0.662311 + 0.272539i
\(754\) 0 0
\(755\) −2.47478 −0.0900666
\(756\) 0 0
\(757\) 34.3865 1.24980 0.624899 0.780706i \(-0.285140\pi\)
0.624899 + 0.780706i \(0.285140\pi\)
\(758\) 0 0
\(759\) −3.58059 26.7179i −0.129967 0.969798i
\(760\) 0 0
\(761\) −0.659485 + 3.74012i −0.0239063 + 0.135579i −0.994425 0.105447i \(-0.966373\pi\)
0.970519 + 0.241026i \(0.0774839\pi\)
\(762\) 0 0
\(763\) 7.00753 + 18.7174i 0.253690 + 0.677617i
\(764\) 0 0
\(765\) 7.95243 + 3.66343i 0.287521 + 0.132452i
\(766\) 0 0
\(767\) 38.8055 6.84246i 1.40119 0.247067i
\(768\) 0 0
\(769\) 9.13219 10.8833i 0.329315 0.392463i −0.575827 0.817572i \(-0.695320\pi\)
0.905142 + 0.425109i \(0.139764\pi\)
\(770\) 0 0
\(771\) 18.9141 29.8418i 0.681175 1.07473i
\(772\) 0 0
\(773\) −45.9757 −1.65363 −0.826816 0.562472i \(-0.809850\pi\)
−0.826816 + 0.562472i \(0.809850\pi\)
\(774\) 0 0
\(775\) 3.16812i 0.113802i
\(776\) 0 0
\(777\) 15.9587 + 9.91096i 0.572516 + 0.355554i
\(778\) 0