Properties

Label 756.2.ck.a.5.3
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 5.3
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.63320 + 0.576754i) q^{3} +(0.109190 - 0.619249i) q^{5} +(-2.49443 + 0.881937i) q^{7} +(2.33471 - 1.88391i) q^{9} +O(q^{10})\) \(q+(-1.63320 + 0.576754i) q^{3} +(0.109190 - 0.619249i) q^{5} +(-2.49443 + 0.881937i) q^{7} +(2.33471 - 1.88391i) q^{9} +(-1.84753 + 0.325769i) q^{11} +(0.235703 - 0.280900i) q^{13} +(0.178824 + 1.07434i) q^{15} +3.97503 q^{17} -1.40905i q^{19} +(3.56525 - 2.87906i) q^{21} +(3.12882 - 3.72878i) q^{23} +(4.32692 + 1.57487i) q^{25} +(-2.72650 + 4.42337i) q^{27} +(2.85223 + 3.39915i) q^{29} +(-3.24035 - 8.90279i) q^{31} +(2.82950 - 1.59762i) q^{33} +(0.273771 + 1.64097i) q^{35} +(-0.196473 - 0.340302i) q^{37} +(-0.222941 + 0.594710i) q^{39} +(-0.337003 - 0.282779i) q^{41} +(8.15803 + 2.96928i) q^{43} +(-0.911684 - 1.65147i) q^{45} +(9.21115 + 3.35258i) q^{47} +(5.44437 - 4.39986i) q^{49} +(-6.49203 + 2.29261i) q^{51} +(8.64238 - 4.98968i) q^{53} +1.17965i q^{55} +(0.812676 + 2.30127i) q^{57} +(0.442479 + 0.371284i) q^{59} +(1.99861 - 5.49113i) q^{61} +(-4.16228 + 6.75836i) q^{63} +(-0.148210 - 0.176630i) q^{65} +(0.618194 - 3.50595i) q^{67} +(-2.95941 + 7.89443i) q^{69} +(12.2893 + 7.09525i) q^{71} +(-5.51091 - 3.18172i) q^{73} +(-7.97505 - 0.0765143i) q^{75} +(4.32122 - 2.44201i) q^{77} +(-1.75512 - 9.95378i) q^{79} +(1.90173 - 8.79678i) q^{81} +(-3.38160 + 2.83750i) q^{83} +(0.434034 - 2.46153i) q^{85} +(-6.61875 - 3.90648i) q^{87} -6.22400 q^{89} +(-0.340209 + 0.908561i) q^{91} +(10.4269 + 12.6712i) q^{93} +(-0.872552 - 0.153855i) q^{95} +(2.12529 - 5.83919i) q^{97} +(-3.69972 + 4.24116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) −1.63320 + 0.576754i −0.942931 + 0.332989i
\(4\) 0 0
\(5\) 0.109190 0.619249i 0.0488314 0.276936i −0.950609 0.310391i \(-0.899540\pi\)
0.999440 + 0.0334549i \(0.0106510\pi\)
\(6\) 0 0
\(7\) −2.49443 + 0.881937i −0.942806 + 0.333341i
\(8\) 0 0
\(9\) 2.33471 1.88391i 0.778236 0.627971i
\(10\) 0 0
\(11\) −1.84753 + 0.325769i −0.557050 + 0.0982230i −0.445084 0.895489i \(-0.646826\pi\)
−0.111967 + 0.993712i \(0.535715\pi\)
\(12\) 0 0
\(13\) 0.235703 0.280900i 0.0653723 0.0779077i −0.732367 0.680910i \(-0.761585\pi\)
0.797740 + 0.603002i \(0.206029\pi\)
\(14\) 0 0
\(15\) 0.178824 + 1.07434i 0.0461722 + 0.277392i
\(16\) 0 0
\(17\) 3.97503 0.964086 0.482043 0.876148i \(-0.339895\pi\)
0.482043 + 0.876148i \(0.339895\pi\)
\(18\) 0 0
\(19\) 1.40905i 0.323258i −0.986852 0.161629i \(-0.948325\pi\)
0.986852 0.161629i \(-0.0516748\pi\)
\(20\) 0 0
\(21\) 3.56525 2.87906i 0.778002 0.628262i
\(22\) 0 0
\(23\) 3.12882 3.72878i 0.652404 0.777505i −0.333870 0.942619i \(-0.608355\pi\)
0.986275 + 0.165114i \(0.0527991\pi\)
\(24\) 0 0
\(25\) 4.32692 + 1.57487i 0.865383 + 0.314974i
\(26\) 0 0
\(27\) −2.72650 + 4.42337i −0.524715 + 0.851278i
\(28\) 0 0
\(29\) 2.85223 + 3.39915i 0.529646 + 0.631207i 0.962833 0.270097i \(-0.0870557\pi\)
−0.433188 + 0.901304i \(0.642611\pi\)
\(30\) 0 0
\(31\) −3.24035 8.90279i −0.581984 1.59899i −0.784785 0.619768i \(-0.787227\pi\)
0.202801 0.979220i \(-0.434996\pi\)
\(32\) 0 0
\(33\) 2.82950 1.59762i 0.492553 0.278109i
\(34\) 0 0
\(35\) 0.273771 + 1.64097i 0.0462757 + 0.277375i
\(36\) 0 0
\(37\) −0.196473 0.340302i −0.0323000 0.0559452i 0.849424 0.527712i \(-0.176950\pi\)
−0.881724 + 0.471766i \(0.843617\pi\)
\(38\) 0 0
\(39\) −0.222941 + 0.594710i −0.0356991 + 0.0952298i
\(40\) 0 0
\(41\) −0.337003 0.282779i −0.0526311 0.0441627i 0.616093 0.787674i \(-0.288715\pi\)
−0.668724 + 0.743511i \(0.733159\pi\)
\(42\) 0 0
\(43\) 8.15803 + 2.96928i 1.24409 + 0.452811i 0.878400 0.477926i \(-0.158611\pi\)
0.365688 + 0.930737i \(0.380834\pi\)
\(44\) 0 0
\(45\) −0.911684 1.65147i −0.135906 0.246187i
\(46\) 0 0
\(47\) 9.21115 + 3.35258i 1.34358 + 0.489024i 0.910939 0.412540i \(-0.135358\pi\)
0.432644 + 0.901565i \(0.357581\pi\)
\(48\) 0 0
\(49\) 5.44437 4.39986i 0.777768 0.628552i
\(50\) 0 0
\(51\) −6.49203 + 2.29261i −0.909066 + 0.321030i
\(52\) 0 0
\(53\) 8.64238 4.98968i 1.18712 0.685385i 0.229471 0.973316i \(-0.426300\pi\)
0.957651 + 0.287930i \(0.0929671\pi\)
\(54\) 0 0
\(55\) 1.17965i 0.159064i
\(56\) 0 0
\(57\) 0.812676 + 2.30127i 0.107642 + 0.304810i
\(58\) 0 0
\(59\) 0.442479 + 0.371284i 0.0576058 + 0.0483370i 0.671136 0.741334i \(-0.265807\pi\)
−0.613530 + 0.789671i \(0.710251\pi\)
\(60\) 0 0
\(61\) 1.99861 5.49113i 0.255895 0.703067i −0.743515 0.668720i \(-0.766843\pi\)
0.999410 0.0343471i \(-0.0109352\pi\)
\(62\) 0 0
\(63\) −4.16228 + 6.75836i −0.524398 + 0.851473i
\(64\) 0 0
\(65\) −0.148210 0.176630i −0.0183832 0.0219083i
\(66\) 0 0
\(67\) 0.618194 3.50595i 0.0755244 0.428320i −0.923477 0.383653i \(-0.874666\pi\)
0.999002 0.0446676i \(-0.0142229\pi\)
\(68\) 0 0
\(69\) −2.95941 + 7.89443i −0.356271 + 0.950377i
\(70\) 0 0
\(71\) 12.2893 + 7.09525i 1.45848 + 0.842051i 0.998937 0.0461059i \(-0.0146812\pi\)
0.459539 + 0.888157i \(0.348014\pi\)
\(72\) 0 0
\(73\) −5.51091 3.18172i −0.645003 0.372392i 0.141536 0.989933i \(-0.454796\pi\)
−0.786539 + 0.617541i \(0.788129\pi\)
\(74\) 0 0
\(75\) −7.97505 0.0765143i −0.920879 0.00883511i
\(76\) 0 0
\(77\) 4.32122 2.44201i 0.492449 0.278293i
\(78\) 0 0
\(79\) −1.75512 9.95378i −0.197466 1.11989i −0.908862 0.417096i \(-0.863048\pi\)
0.711396 0.702791i \(-0.248063\pi\)
\(80\) 0 0
\(81\) 1.90173 8.79678i 0.211304 0.977420i
\(82\) 0 0
\(83\) −3.38160 + 2.83750i −0.371178 + 0.311456i −0.809228 0.587495i \(-0.800114\pi\)
0.438049 + 0.898951i \(0.355670\pi\)
\(84\) 0 0
\(85\) 0.434034 2.46153i 0.0470776 0.266990i
\(86\) 0 0
\(87\) −6.61875 3.90648i −0.709604 0.418818i
\(88\) 0 0
\(89\) −6.22400 −0.659742 −0.329871 0.944026i \(-0.607005\pi\)
−0.329871 + 0.944026i \(0.607005\pi\)
\(90\) 0 0
\(91\) −0.340209 + 0.908561i −0.0356636 + 0.0952431i
\(92\) 0 0
\(93\) 10.4269 + 12.6712i 1.08122 + 1.31394i
\(94\) 0 0
\(95\) −0.872552 0.153855i −0.0895220 0.0157851i
\(96\) 0 0
\(97\) 2.12529 5.83919i 0.215791 0.592880i −0.783814 0.620996i \(-0.786728\pi\)
0.999605 + 0.0281157i \(0.00895069\pi\)
\(98\) 0 0
\(99\) −3.69972 + 4.24116i −0.371836 + 0.426252i
\(100\) 0 0
\(101\) −12.8654 + 10.7953i −1.28015 + 1.07418i −0.286930 + 0.957952i \(0.592635\pi\)
−0.993223 + 0.116224i \(0.962921\pi\)
\(102\) 0 0
\(103\) −3.84869 0.678628i −0.379223 0.0668672i −0.0192122 0.999815i \(-0.506116\pi\)
−0.360011 + 0.932948i \(0.617227\pi\)
\(104\) 0 0
\(105\) −1.39356 2.52214i −0.135998 0.246136i
\(106\) 0 0
\(107\) 10.8698 + 6.27569i 1.05082 + 0.606693i 0.922880 0.385088i \(-0.125829\pi\)
0.127944 + 0.991781i \(0.459162\pi\)
\(108\) 0 0
\(109\) −0.894424 1.54919i −0.0856703 0.148385i 0.820006 0.572354i \(-0.193970\pi\)
−0.905677 + 0.423969i \(0.860636\pi\)
\(110\) 0 0
\(111\) 0.517151 + 0.442465i 0.0490858 + 0.0419969i
\(112\) 0 0
\(113\) 3.18174 + 8.74175i 0.299313 + 0.822355i 0.994615 + 0.103638i \(0.0330483\pi\)
−0.695302 + 0.718717i \(0.744730\pi\)
\(114\) 0 0
\(115\) −1.96741 2.34467i −0.183462 0.218641i
\(116\) 0 0
\(117\) 0.0211066 1.09986i 0.00195131 0.101683i
\(118\) 0 0
\(119\) −9.91543 + 3.50572i −0.908946 + 0.321369i
\(120\) 0 0
\(121\) −7.02939 + 2.55849i −0.639035 + 0.232590i
\(122\) 0 0
\(123\) 0.713489 + 0.267468i 0.0643331 + 0.0241168i
\(124\) 0 0
\(125\) 3.01970 5.23027i 0.270090 0.467809i
\(126\) 0 0
\(127\) −1.10888 1.92063i −0.0983971 0.170429i 0.812624 0.582788i \(-0.198038\pi\)
−0.911021 + 0.412359i \(0.864705\pi\)
\(128\) 0 0
\(129\) −15.0363 0.144261i −1.32387 0.0127015i
\(130\) 0 0
\(131\) 2.30973 + 1.93809i 0.201802 + 0.169332i 0.738088 0.674704i \(-0.235729\pi\)
−0.536286 + 0.844036i \(0.680173\pi\)
\(132\) 0 0
\(133\) 1.24269 + 3.51478i 0.107755 + 0.304770i
\(134\) 0 0
\(135\) 2.44146 + 2.17137i 0.210127 + 0.186882i
\(136\) 0 0
\(137\) 4.52151 12.4228i 0.386299 1.06135i −0.582355 0.812934i \(-0.697869\pi\)
0.968654 0.248413i \(-0.0799090\pi\)
\(138\) 0 0
\(139\) −21.1007 3.72062i −1.78974 0.315579i −0.822368 0.568956i \(-0.807347\pi\)
−0.967367 + 0.253378i \(0.918459\pi\)
\(140\) 0 0
\(141\) −16.9773 0.162884i −1.42975 0.0137173i
\(142\) 0 0
\(143\) −0.343959 + 0.595755i −0.0287633 + 0.0498196i
\(144\) 0 0
\(145\) 2.41636 1.39508i 0.200668 0.115855i
\(146\) 0 0
\(147\) −6.35413 + 10.3259i −0.524080 + 0.851669i
\(148\) 0 0
\(149\) −5.55270 15.2559i −0.454895 1.24981i −0.929241 0.369475i \(-0.879538\pi\)
0.474346 0.880339i \(-0.342685\pi\)
\(150\) 0 0
\(151\) −2.53282 14.3643i −0.206118 1.16895i −0.895671 0.444717i \(-0.853304\pi\)
0.689553 0.724235i \(-0.257807\pi\)
\(152\) 0 0
\(153\) 9.28053 7.48861i 0.750287 0.605418i
\(154\) 0 0
\(155\) −5.86686 + 1.03448i −0.471237 + 0.0830918i
\(156\) 0 0
\(157\) 4.78689 5.70479i 0.382035 0.455292i −0.540420 0.841395i \(-0.681735\pi\)
0.922455 + 0.386103i \(0.126179\pi\)
\(158\) 0 0
\(159\) −11.2369 + 13.1337i −0.891148 + 1.04157i
\(160\) 0 0
\(161\) −4.51608 + 12.0606i −0.355917 + 0.950510i
\(162\) 0 0
\(163\) −10.6878 + 18.5118i −0.837134 + 1.44996i 0.0551466 + 0.998478i \(0.482437\pi\)
−0.892281 + 0.451481i \(0.850896\pi\)
\(164\) 0 0
\(165\) −0.680368 1.92661i −0.0529666 0.149986i
\(166\) 0 0
\(167\) 3.47846 1.26606i 0.269172 0.0979704i −0.203908 0.978990i \(-0.565364\pi\)
0.473080 + 0.881020i \(0.343142\pi\)
\(168\) 0 0
\(169\) 2.23408 + 12.6701i 0.171852 + 0.974622i
\(170\) 0 0
\(171\) −2.65453 3.28972i −0.202997 0.251571i
\(172\) 0 0
\(173\) −0.900056 + 0.755236i −0.0684300 + 0.0574196i −0.676361 0.736570i \(-0.736444\pi\)
0.607931 + 0.793990i \(0.292000\pi\)
\(174\) 0 0
\(175\) −12.1821 0.112334i −0.920883 0.00849168i
\(176\) 0 0
\(177\) −0.936798 0.351181i −0.0704140 0.0263964i
\(178\) 0 0
\(179\) 4.19541i 0.313579i −0.987632 0.156790i \(-0.949886\pi\)
0.987632 0.156790i \(-0.0501145\pi\)
\(180\) 0 0
\(181\) −1.69261 + 0.977228i −0.125811 + 0.0726368i −0.561585 0.827419i \(-0.689808\pi\)
0.435774 + 0.900056i \(0.356475\pi\)
\(182\) 0 0
\(183\) −0.0971014 + 10.1208i −0.00717794 + 0.748154i
\(184\) 0 0
\(185\) −0.232184 + 0.0845082i −0.0170705 + 0.00621316i
\(186\) 0 0
\(187\) −7.34397 + 1.29494i −0.537044 + 0.0946954i
\(188\) 0 0
\(189\) 2.89993 13.4384i 0.210939 0.977499i
\(190\) 0 0
\(191\) 1.09300 0.192725i 0.0790864 0.0139451i −0.133965 0.990986i \(-0.542771\pi\)
0.213051 + 0.977041i \(0.431660\pi\)
\(192\) 0 0
\(193\) 2.16408 0.787661i 0.155774 0.0566971i −0.262956 0.964808i \(-0.584698\pi\)
0.418730 + 0.908111i \(0.362475\pi\)
\(194\) 0 0
\(195\) 0.343930 + 0.202992i 0.0246294 + 0.0145366i
\(196\) 0 0
\(197\) −16.4656 + 9.50640i −1.17312 + 0.677303i −0.954414 0.298488i \(-0.903518\pi\)
−0.218709 + 0.975790i \(0.570185\pi\)
\(198\) 0 0
\(199\) 3.52524i 0.249897i 0.992163 + 0.124949i \(0.0398766\pi\)
−0.992163 + 0.124949i \(0.960123\pi\)
\(200\) 0 0
\(201\) 1.01244 + 6.08248i 0.0714117 + 0.429025i
\(202\) 0 0
\(203\) −10.1125 5.96347i −0.709760 0.418554i
\(204\) 0 0
\(205\) −0.211908 + 0.177812i −0.0148003 + 0.0124189i
\(206\) 0 0
\(207\) 0.280178 14.6001i 0.0194737 1.01477i
\(208\) 0 0
\(209\) 0.459025 + 2.60326i 0.0317514 + 0.180071i
\(210\) 0 0
\(211\) 9.65706 3.51488i 0.664820 0.241975i 0.0125038 0.999922i \(-0.496020\pi\)
0.652316 + 0.757947i \(0.273798\pi\)
\(212\) 0 0
\(213\) −24.1632 4.50007i −1.65564 0.308339i
\(214\) 0 0
\(215\) 2.72950 4.72763i 0.186150 0.322422i
\(216\) 0 0
\(217\) 15.9345 + 19.3496i 1.08171 + 1.31354i
\(218\) 0 0
\(219\) 10.8355 + 2.01796i 0.732195 + 0.136361i
\(220\) 0 0
\(221\) 0.936926 1.11659i 0.0630245 0.0751097i
\(222\) 0 0
\(223\) 27.8071 4.90315i 1.86210 0.328339i 0.874465 0.485088i \(-0.161212\pi\)
0.987638 + 0.156749i \(0.0501013\pi\)
\(224\) 0 0
\(225\) 13.0690 4.47468i 0.871267 0.298312i
\(226\) 0 0
\(227\) −1.30132 7.38017i −0.0863718 0.489839i −0.997052 0.0767270i \(-0.975553\pi\)
0.910680 0.413112i \(-0.135558\pi\)
\(228\) 0 0
\(229\) 0.533350 + 1.46537i 0.0352448 + 0.0968342i 0.956067 0.293149i \(-0.0947031\pi\)
−0.920822 + 0.389983i \(0.872481\pi\)
\(230\) 0 0
\(231\) −5.64900 + 6.48058i −0.371677 + 0.426391i
\(232\) 0 0
\(233\) 11.5533 6.67028i 0.756879 0.436984i −0.0712949 0.997455i \(-0.522713\pi\)
0.828174 + 0.560471i \(0.189380\pi\)
\(234\) 0 0
\(235\) 3.08185 5.33792i 0.201038 0.348208i
\(236\) 0 0
\(237\) 8.60735 + 15.2443i 0.559107 + 0.990222i
\(238\) 0 0
\(239\) 8.46669 + 1.49291i 0.547665 + 0.0965680i 0.440633 0.897688i \(-0.354754\pi\)
0.107032 + 0.994256i \(0.465865\pi\)
\(240\) 0 0
\(241\) 3.63407 9.98452i 0.234091 0.643160i −0.765909 0.642949i \(-0.777711\pi\)
1.00000 0.000210696i \(-6.70668e-5\pi\)
\(242\) 0 0
\(243\) 1.96766 + 15.4638i 0.126226 + 0.992002i
\(244\) 0 0
\(245\) −2.13014 3.85184i −0.136089 0.246085i
\(246\) 0 0
\(247\) −0.395802 0.332118i −0.0251843 0.0211321i
\(248\) 0 0
\(249\) 3.88630 6.58456i 0.246284 0.417280i
\(250\) 0 0
\(251\) 11.6262 + 20.1372i 0.733839 + 1.27105i 0.955231 + 0.295862i \(0.0956068\pi\)
−0.221391 + 0.975185i \(0.571060\pi\)
\(252\) 0 0
\(253\) −4.56586 + 7.90830i −0.287053 + 0.497191i
\(254\) 0 0
\(255\) 0.710832 + 4.27051i 0.0445140 + 0.267430i
\(256\) 0 0
\(257\) 11.3456 4.12947i 0.707721 0.257589i 0.0370171 0.999315i \(-0.488214\pi\)
0.670704 + 0.741725i \(0.265992\pi\)
\(258\) 0 0
\(259\) 0.790214 + 0.675582i 0.0491015 + 0.0419786i
\(260\) 0 0
\(261\) 13.0628 + 2.56268i 0.808570 + 0.158626i
\(262\) 0 0
\(263\) 16.0766 + 19.1593i 0.991325 + 1.18142i 0.983401 + 0.181446i \(0.0580779\pi\)
0.00792406 + 0.999969i \(0.497478\pi\)
\(264\) 0 0
\(265\) −2.14619 5.89661i −0.131839 0.362226i
\(266\) 0 0
\(267\) 10.1651 3.58972i 0.622091 0.219687i
\(268\) 0 0
\(269\) 7.62612 + 13.2088i 0.464973 + 0.805356i 0.999200 0.0399844i \(-0.0127308\pi\)
−0.534228 + 0.845341i \(0.679397\pi\)
\(270\) 0 0
\(271\) −18.4322 10.6418i −1.11967 0.646444i −0.178356 0.983966i \(-0.557078\pi\)
−0.941318 + 0.337522i \(0.890411\pi\)
\(272\) 0 0
\(273\) 0.0316143 1.68008i 0.00191339 0.101683i
\(274\) 0 0
\(275\) −8.50714 1.50004i −0.513000 0.0904557i
\(276\) 0 0
\(277\) −0.961066 + 0.806430i −0.0577449 + 0.0484537i −0.671203 0.741273i \(-0.734222\pi\)
0.613458 + 0.789727i \(0.289778\pi\)
\(278\) 0 0
\(279\) −24.3374 14.6809i −1.45704 0.878921i
\(280\) 0 0
\(281\) 3.55922 9.77886i 0.212325 0.583358i −0.787115 0.616806i \(-0.788426\pi\)
0.999440 + 0.0334475i \(0.0106487\pi\)
\(282\) 0 0
\(283\) −9.41503 1.66012i −0.559665 0.0986841i −0.113342 0.993556i \(-0.536156\pi\)
−0.446323 + 0.894872i \(0.647267\pi\)
\(284\) 0 0
\(285\) 1.51379 0.251972i 0.0896693 0.0149256i
\(286\) 0 0
\(287\) 1.09002 + 0.408158i 0.0643421 + 0.0240928i
\(288\) 0 0
\(289\) −1.19916 −0.0705388
\(290\) 0 0
\(291\) −0.103256 + 10.7624i −0.00605299 + 0.630901i
\(292\) 0 0
\(293\) 3.33317 18.9033i 0.194726 1.10435i −0.718083 0.695958i \(-0.754980\pi\)
0.912809 0.408388i \(-0.133909\pi\)
\(294\) 0 0
\(295\) 0.278231 0.233464i 0.0161993 0.0135928i
\(296\) 0 0
\(297\) 3.59629 9.06050i 0.208678 0.525744i
\(298\) 0 0
\(299\) −0.309943 1.75777i −0.0179244 0.101655i
\(300\) 0 0
\(301\) −22.9684 0.211797i −1.32387 0.0122078i
\(302\) 0 0
\(303\) 14.7855 25.0511i 0.849407 1.43915i
\(304\) 0 0
\(305\) −3.18215 1.83721i −0.182209 0.105198i
\(306\) 0 0
\(307\) 21.9964 + 12.6996i 1.25540 + 0.724807i 0.972177 0.234246i \(-0.0752622\pi\)
0.283225 + 0.959053i \(0.408596\pi\)
\(308\) 0 0
\(309\) 6.67710 1.11141i 0.379847 0.0632259i
\(310\) 0 0
\(311\) 2.27297 12.8907i 0.128888 0.730962i −0.850034 0.526728i \(-0.823419\pi\)
0.978922 0.204234i \(-0.0654703\pi\)
\(312\) 0 0
\(313\) −3.81819 4.55034i −0.215817 0.257200i 0.647264 0.762266i \(-0.275913\pi\)
−0.863081 + 0.505065i \(0.831468\pi\)
\(314\) 0 0
\(315\) 3.73063 + 3.31543i 0.210197 + 0.186803i
\(316\) 0 0
\(317\) −10.5297 + 28.9300i −0.591404 + 1.62487i 0.176497 + 0.984301i \(0.443524\pi\)
−0.767901 + 0.640569i \(0.778699\pi\)
\(318\) 0 0
\(319\) −6.37691 5.35086i −0.357038 0.299591i
\(320\) 0 0
\(321\) −21.3721 3.98027i −1.19288 0.222157i
\(322\) 0 0
\(323\) 5.60101i 0.311649i
\(324\) 0 0
\(325\) 1.46225 0.844230i 0.0811110 0.0468294i
\(326\) 0 0
\(327\) 2.35428 + 2.01428i 0.130192 + 0.111390i
\(328\) 0 0
\(329\) −25.9333 0.239138i −1.42975 0.0131841i
\(330\) 0 0
\(331\) 16.0263 + 5.83309i 0.880885 + 0.320616i 0.742567 0.669772i \(-0.233608\pi\)
0.138318 + 0.990388i \(0.455830\pi\)
\(332\) 0 0
\(333\) −1.09981 0.424367i −0.0602691 0.0232551i
\(334\) 0 0
\(335\) −2.10356 0.765631i −0.114929 0.0418309i
\(336\) 0 0
\(337\) 13.1848 + 11.0634i 0.718221 + 0.602659i 0.926893 0.375327i \(-0.122469\pi\)
−0.208671 + 0.977986i \(0.566914\pi\)
\(338\) 0 0
\(339\) −10.2383 12.4420i −0.556067 0.675756i
\(340\) 0 0
\(341\) 8.88689 + 15.3925i 0.481252 + 0.833553i
\(342\) 0 0
\(343\) −9.70022 + 15.7767i −0.523762 + 0.851864i
\(344\) 0 0
\(345\) 4.56547 + 2.69461i 0.245797 + 0.145073i
\(346\) 0 0
\(347\) −0.845241 2.32228i −0.0453749 0.124667i 0.914935 0.403600i \(-0.132241\pi\)
−0.960310 + 0.278934i \(0.910019\pi\)
\(348\) 0 0
\(349\) −9.60242 11.4437i −0.514006 0.612568i 0.445147 0.895458i \(-0.353152\pi\)
−0.959153 + 0.282889i \(0.908707\pi\)
\(350\) 0 0
\(351\) 0.599880 + 1.80848i 0.0320192 + 0.0965293i
\(352\) 0 0
\(353\) −22.6470 8.24284i −1.20538 0.438722i −0.340281 0.940324i \(-0.610522\pi\)
−0.865099 + 0.501602i \(0.832744\pi\)
\(354\) 0 0
\(355\) 5.73560 6.83542i 0.304414 0.362787i
\(356\) 0 0
\(357\) 14.1720 11.4443i 0.750061 0.605698i
\(358\) 0 0
\(359\) 27.6871i 1.46127i −0.682768 0.730635i \(-0.739224\pi\)
0.682768 0.730635i \(-0.260776\pi\)
\(360\) 0 0
\(361\) 17.0146 0.895504
\(362\) 0 0
\(363\) 10.0048 8.23276i 0.525116 0.432108i
\(364\) 0 0
\(365\) −2.57201 + 3.06521i −0.134625 + 0.160440i
\(366\) 0 0
\(367\) 30.1123 5.30961i 1.57185 0.277159i 0.681285 0.732018i \(-0.261421\pi\)
0.890564 + 0.454859i \(0.150310\pi\)
\(368\) 0 0
\(369\) −1.31954 0.0253221i −0.0686923 0.00131822i
\(370\) 0 0
\(371\) −17.1572 + 20.0684i −0.890760 + 1.04190i
\(372\) 0 0
\(373\) −0.955166 + 5.41701i −0.0494566 + 0.280482i −0.999499 0.0316373i \(-0.989928\pi\)
0.950043 + 0.312120i \(0.101039\pi\)
\(374\) 0 0
\(375\) −1.91520 + 10.2837i −0.0989005 + 0.531049i
\(376\) 0 0
\(377\) 1.62710 0.0838000
\(378\) 0 0
\(379\) −20.4096 −1.04837 −0.524185 0.851604i \(-0.675630\pi\)
−0.524185 + 0.851604i \(0.675630\pi\)
\(380\) 0 0
\(381\) 2.91876 + 2.49724i 0.149533 + 0.127937i
\(382\) 0 0
\(383\) 2.82778 16.0371i 0.144493 0.819459i −0.823280 0.567635i \(-0.807859\pi\)
0.967773 0.251824i \(-0.0810304\pi\)
\(384\) 0 0
\(385\) −1.04038 2.94255i −0.0530225 0.149966i
\(386\) 0 0
\(387\) 24.6405 8.43663i 1.25255 0.428858i
\(388\) 0 0
\(389\) −16.0873 + 2.83663i −0.815661 + 0.143823i −0.565889 0.824482i \(-0.691467\pi\)
−0.249772 + 0.968305i \(0.580356\pi\)
\(390\) 0 0
\(391\) 12.4372 14.8220i 0.628974 0.749582i
\(392\) 0 0
\(393\) −4.89005 1.83315i −0.246671 0.0924703i
\(394\) 0 0
\(395\) −6.35550 −0.319780
\(396\) 0 0
\(397\) 9.16393i 0.459924i 0.973200 + 0.229962i \(0.0738603\pi\)
−0.973200 + 0.229962i \(0.926140\pi\)
\(398\) 0 0
\(399\) −4.05674 5.02362i −0.203091 0.251496i
\(400\) 0 0
\(401\) 12.5976 15.0132i 0.629092 0.749722i −0.353513 0.935429i \(-0.615013\pi\)
0.982605 + 0.185707i \(0.0594576\pi\)
\(402\) 0 0
\(403\) −3.26456 1.18820i −0.162619 0.0591885i
\(404\) 0 0
\(405\) −5.23975 2.13817i −0.260365 0.106246i
\(406\) 0 0
\(407\) 0.473849 + 0.564712i 0.0234878 + 0.0279917i
\(408\) 0 0
\(409\) 5.57617 + 15.3204i 0.275724 + 0.757544i 0.997835 + 0.0657676i \(0.0209496\pi\)
−0.722111 + 0.691777i \(0.756828\pi\)
\(410\) 0 0
\(411\) −0.219676 + 22.8967i −0.0108358 + 1.12941i
\(412\) 0 0
\(413\) −1.43118 0.535904i −0.0704239 0.0263701i
\(414\) 0 0
\(415\) 1.38788 + 2.40388i 0.0681283 + 0.118002i
\(416\) 0 0
\(417\) 36.6076 6.09337i 1.79268 0.298394i
\(418\) 0 0
\(419\) 6.43393 + 5.39871i 0.314318 + 0.263744i 0.786274 0.617878i \(-0.212007\pi\)
−0.471956 + 0.881622i \(0.656452\pi\)
\(420\) 0 0
\(421\) 20.1286 + 7.32622i 0.981009 + 0.357058i 0.782232 0.622987i \(-0.214081\pi\)
0.198777 + 0.980045i \(0.436303\pi\)
\(422\) 0 0
\(423\) 27.8213 9.52570i 1.35272 0.463156i
\(424\) 0 0
\(425\) 17.1996 + 6.26015i 0.834304 + 0.303662i
\(426\) 0 0
\(427\) −0.142559 + 15.4599i −0.00689893 + 0.748156i
\(428\) 0 0
\(429\) 0.218152 1.17137i 0.0105325 0.0565543i
\(430\) 0 0
\(431\) 23.7130 13.6907i 1.14222 0.659459i 0.195237 0.980756i \(-0.437452\pi\)
0.946978 + 0.321297i \(0.104119\pi\)
\(432\) 0 0
\(433\) 9.79725i 0.470826i 0.971895 + 0.235413i \(0.0756443\pi\)
−0.971895 + 0.235413i \(0.924356\pi\)
\(434\) 0 0
\(435\) −3.14178 + 3.67210i −0.150637 + 0.176064i
\(436\) 0 0
\(437\) −5.25404 4.40867i −0.251335 0.210895i
\(438\) 0 0
\(439\) −8.14845 + 22.3877i −0.388904 + 1.06851i 0.578591 + 0.815618i \(0.303603\pi\)
−0.967495 + 0.252888i \(0.918619\pi\)
\(440\) 0 0
\(441\) 4.42207 20.5291i 0.210575 0.977578i
\(442\) 0 0
\(443\) −20.8243 24.8175i −0.989394 1.17911i −0.983826 0.179129i \(-0.942672\pi\)
−0.00556848 0.999984i \(-0.501773\pi\)
\(444\) 0 0
\(445\) −0.679600 + 3.85420i −0.0322161 + 0.182707i
\(446\) 0 0
\(447\) 17.8676 + 21.7135i 0.845109 + 1.02701i
\(448\) 0 0
\(449\) −27.4242 15.8334i −1.29423 0.747223i −0.314827 0.949149i \(-0.601946\pi\)
−0.979401 + 0.201927i \(0.935280\pi\)
\(450\) 0 0
\(451\) 0.714743 + 0.412657i 0.0336559 + 0.0194313i
\(452\) 0 0
\(453\) 12.4213 + 21.9990i 0.583603 + 1.03361i
\(454\) 0 0
\(455\) 0.525478 + 0.309880i 0.0246348 + 0.0145274i
\(456\) 0 0
\(457\) 6.17622 + 35.0271i 0.288911 + 1.63850i 0.690970 + 0.722883i \(0.257184\pi\)
−0.402059 + 0.915614i \(0.631705\pi\)
\(458\) 0 0
\(459\) −10.8379 + 17.5830i −0.505870 + 0.820705i
\(460\) 0 0
\(461\) 20.6320 17.3123i 0.960927 0.806313i −0.0201766 0.999796i \(-0.506423\pi\)
0.981104 + 0.193483i \(0.0619784\pi\)
\(462\) 0 0
\(463\) 5.46034 30.9671i 0.253763 1.43916i −0.545464 0.838134i \(-0.683647\pi\)
0.799227 0.601029i \(-0.205242\pi\)
\(464\) 0 0
\(465\) 8.98513 5.07326i 0.416675 0.235267i
\(466\) 0 0
\(467\) 36.1290 1.67185 0.835926 0.548841i \(-0.184931\pi\)
0.835926 + 0.548841i \(0.184931\pi\)
\(468\) 0 0
\(469\) 1.54999 + 9.29056i 0.0715717 + 0.428998i
\(470\) 0 0
\(471\) −4.52770 + 12.0779i −0.208625 + 0.556522i
\(472\) 0 0
\(473\) −16.0395 2.82819i −0.737496 0.130040i
\(474\) 0 0
\(475\) 2.21907 6.09684i 0.101818 0.279742i
\(476\) 0 0
\(477\) 10.7773 27.9310i 0.493459 1.27887i
\(478\) 0 0
\(479\) −7.55786 + 6.34179i −0.345327 + 0.289764i −0.798910 0.601450i \(-0.794590\pi\)
0.453583 + 0.891214i \(0.350145\pi\)
\(480\) 0 0
\(481\) −0.141900 0.0250208i −0.00647009 0.00114085i
\(482\) 0 0
\(483\) 0.419662 22.3021i 0.0190953 1.01478i
\(484\) 0 0
\(485\) −3.38385 1.95367i −0.153653 0.0887114i
\(486\) 0 0
\(487\) −5.29343 9.16849i −0.239868 0.415464i 0.720808 0.693135i \(-0.243771\pi\)
−0.960676 + 0.277671i \(0.910438\pi\)
\(488\) 0 0
\(489\) 6.77860 36.3978i 0.306539 1.64597i
\(490\) 0 0
\(491\) 1.98343 + 5.44942i 0.0895107 + 0.245929i 0.976368 0.216115i \(-0.0693386\pi\)
−0.886857 + 0.462044i \(0.847116\pi\)
\(492\) 0 0
\(493\) 11.3377 + 13.5117i 0.510624 + 0.608538i
\(494\) 0 0
\(495\) 2.22236 + 2.75414i 0.0998876 + 0.123789i
\(496\) 0 0
\(497\) −36.9125 6.86020i −1.65575 0.307722i
\(498\) 0 0
\(499\) −19.0968 + 6.95065i −0.854888 + 0.311154i −0.732032 0.681271i \(-0.761428\pi\)
−0.122856 + 0.992424i \(0.539205\pi\)
\(500\) 0 0
\(501\) −4.95084 + 4.07395i −0.221187 + 0.182011i
\(502\) 0 0
\(503\) −6.84793 + 11.8610i −0.305334 + 0.528854i −0.977336 0.211695i \(-0.932102\pi\)
0.672001 + 0.740550i \(0.265435\pi\)
\(504\) 0 0
\(505\) 5.28022 + 9.14561i 0.234967 + 0.406974i
\(506\) 0 0
\(507\) −10.9562 19.4043i −0.486583 0.861776i
\(508\) 0 0
\(509\) 3.01278 + 2.52802i 0.133539 + 0.112053i 0.707111 0.707103i \(-0.249998\pi\)
−0.573572 + 0.819155i \(0.694443\pi\)
\(510\) 0 0
\(511\) 16.5527 + 3.07632i 0.732246 + 0.136088i
\(512\) 0 0
\(513\) 6.23275 + 3.84178i 0.275183 + 0.169619i
\(514\) 0 0
\(515\) −0.840479 + 2.30920i −0.0370359 + 0.101755i
\(516\) 0 0
\(517\) −18.1100 3.19328i −0.796477 0.140440i
\(518\) 0 0
\(519\) 1.03439 1.75257i 0.0454046 0.0769291i
\(520\) 0 0
\(521\) −19.2670 + 33.3713i −0.844100 + 1.46202i 0.0422996 + 0.999105i \(0.486532\pi\)
−0.886400 + 0.462920i \(0.846802\pi\)
\(522\) 0 0
\(523\) −24.8394 + 14.3410i −1.08615 + 0.627090i −0.932549 0.361043i \(-0.882421\pi\)
−0.153602 + 0.988133i \(0.549088\pi\)
\(524\) 0 0
\(525\) 19.9607 6.84263i 0.871156 0.298637i
\(526\) 0 0
\(527\) −12.8805 35.3888i −0.561083 1.54156i
\(528\) 0 0
\(529\) −0.120400 0.682823i −0.00523479 0.0296880i
\(530\) 0 0
\(531\) 1.73253 + 0.0332475i 0.0751853 + 0.00144282i
\(532\) 0 0
\(533\) −0.158865 + 0.0280123i −0.00688122 + 0.00121335i
\(534\) 0 0
\(535\) 5.07309 6.04587i 0.219329 0.261386i
\(536\) 0 0
\(537\) 2.41972 + 6.85195i 0.104419 + 0.295684i
\(538\) 0 0
\(539\) −8.62529 + 9.90247i −0.371518 + 0.426530i
\(540\) 0 0
\(541\) −6.07663 + 10.5250i −0.261255 + 0.452507i −0.966576 0.256382i \(-0.917470\pi\)
0.705321 + 0.708888i \(0.250803\pi\)
\(542\) 0 0
\(543\) 2.20076 2.57223i 0.0944434 0.110385i
\(544\) 0 0
\(545\) −1.05699 + 0.384715i −0.0452767 + 0.0164794i
\(546\) 0 0
\(547\) 0.380983 + 2.16066i 0.0162897 + 0.0923832i 0.991869 0.127265i \(-0.0406200\pi\)
−0.975579 + 0.219649i \(0.929509\pi\)
\(548\) 0 0
\(549\) −5.67865 16.5854i −0.242359 0.707847i
\(550\) 0 0
\(551\) 4.78958 4.01893i 0.204043 0.171212i
\(552\) 0 0
\(553\) 13.1566 + 23.2811i 0.559477 + 0.990013i
\(554\) 0 0
\(555\) 0.330464 0.271932i 0.0140274 0.0115429i
\(556\) 0 0
\(557\) 21.0683i 0.892694i −0.894860 0.446347i \(-0.852725\pi\)
0.894860 0.446347i \(-0.147275\pi\)
\(558\) 0 0
\(559\) 2.75694 1.59172i 0.116606 0.0673227i
\(560\) 0 0
\(561\) 11.2473 6.35057i 0.474863 0.268121i
\(562\) 0 0
\(563\) −39.4456 + 14.3570i −1.66243 + 0.605076i −0.990742 0.135756i \(-0.956654\pi\)
−0.671691 + 0.740832i \(0.734432\pi\)
\(564\) 0 0
\(565\) 5.76073 1.01577i 0.242356 0.0427339i
\(566\) 0 0
\(567\) 3.01447 + 23.6202i 0.126596 + 0.991954i
\(568\) 0 0
\(569\) −16.1479 + 2.84732i −0.676957 + 0.119366i −0.501548 0.865130i \(-0.667236\pi\)
−0.175409 + 0.984496i \(0.556125\pi\)
\(570\) 0 0
\(571\) 15.3637 5.59193i 0.642951 0.234015i 9.25327e−5 1.00000i \(-0.499971\pi\)
0.642858 + 0.765985i \(0.277748\pi\)
\(572\) 0 0
\(573\) −1.67393 + 0.945149i −0.0699295 + 0.0394842i
\(574\) 0 0
\(575\) 19.4105 11.2067i 0.809474 0.467350i
\(576\) 0 0
\(577\) 3.58396i 0.149202i 0.997213 + 0.0746011i \(0.0237683\pi\)
−0.997213 + 0.0746011i \(0.976232\pi\)
\(578\) 0 0
\(579\) −3.08010 + 2.53455i −0.128004 + 0.105332i
\(580\) 0 0
\(581\) 5.93267 10.0603i 0.246129 0.417371i
\(582\) 0 0
\(583\) −14.3416 + 12.0340i −0.593966 + 0.498397i
\(584\) 0 0
\(585\) −0.678785 0.133165i −0.0280643 0.00550568i
\(586\) 0 0
\(587\) 6.72409 + 38.1342i 0.277533 + 1.57397i 0.730799 + 0.682593i \(0.239148\pi\)
−0.453266 + 0.891375i \(0.649741\pi\)
\(588\) 0 0
\(589\) −12.5445 + 4.56582i −0.516886 + 0.188131i
\(590\) 0 0
\(591\) 21.4088 25.0225i 0.880639 1.02929i
\(592\) 0 0
\(593\) 3.48794 6.04130i 0.143233 0.248086i −0.785479 0.618888i \(-0.787584\pi\)
0.928712 + 0.370801i \(0.120917\pi\)
\(594\) 0 0
\(595\) 1.08825 + 6.52291i 0.0446137 + 0.267413i
\(596\) 0 0
\(597\) −2.03320 5.75743i −0.0832131 0.235636i
\(598\) 0 0
\(599\) 4.57709 5.45477i 0.187015 0.222876i −0.664388 0.747388i \(-0.731308\pi\)
0.851403 + 0.524512i \(0.175752\pi\)
\(600\) 0 0
\(601\) 17.0560 3.00744i 0.695730 0.122676i 0.185411 0.982661i \(-0.440638\pi\)
0.510319 + 0.859985i \(0.329527\pi\)
\(602\) 0 0
\(603\) −5.16161 9.35000i −0.210197 0.380762i
\(604\) 0 0
\(605\) 0.816800 + 4.63230i 0.0332076 + 0.188330i
\(606\) 0 0
\(607\) −14.4488 39.6977i −0.586457 1.61128i −0.776931 0.629586i \(-0.783225\pi\)
0.190474 0.981692i \(-0.438998\pi\)
\(608\) 0 0
\(609\) 19.9553 + 3.90712i 0.808629 + 0.158324i
\(610\) 0 0
\(611\) 3.11284 1.79720i 0.125932 0.0727068i
\(612\) 0 0
\(613\) −1.48185 + 2.56665i −0.0598515 + 0.103666i −0.894399 0.447271i \(-0.852396\pi\)
0.834547 + 0.550937i \(0.185729\pi\)
\(614\) 0 0
\(615\) 0.243535 0.412622i 0.00982029 0.0166385i
\(616\) 0 0
\(617\) −22.7707 4.01508i −0.916713 0.161641i −0.304663 0.952460i \(-0.598544\pi\)
−0.612050 + 0.790819i \(0.709655\pi\)
\(618\) 0 0
\(619\) 0.908965 2.49736i 0.0365344 0.100377i −0.920084 0.391721i \(-0.871880\pi\)
0.956619 + 0.291343i \(0.0941022\pi\)
\(620\) 0 0
\(621\) 7.96306 + 24.0065i 0.319547 + 0.963346i
\(622\) 0 0
\(623\) 15.5253 5.48917i 0.622009 0.219919i
\(624\) 0 0
\(625\) 14.7276 + 12.3579i 0.589102 + 0.494316i
\(626\) 0 0
\(627\) −2.25112 3.98691i −0.0899011 0.159222i
\(628\) 0 0
\(629\) −0.780987 1.35271i −0.0311400 0.0539360i
\(630\) 0 0
\(631\) −10.8636 + 18.8163i −0.432473 + 0.749065i −0.997086 0.0762910i \(-0.975692\pi\)
0.564613 + 0.825356i \(0.309026\pi\)
\(632\) 0 0
\(633\) −13.7447 + 11.3103i −0.546304 + 0.449543i
\(634\) 0 0
\(635\) −1.31043 + 0.476957i −0.0520028 + 0.0189275i
\(636\) 0 0
\(637\) 0.0473346 2.56639i 0.00187546 0.101684i
\(638\) 0 0
\(639\) 42.0589 6.58671i 1.66382 0.260566i
\(640\) 0 0
\(641\) 10.3126 + 12.2900i 0.407321 + 0.485427i 0.930238 0.366957i \(-0.119600\pi\)
−0.522916 + 0.852384i \(0.675156\pi\)
\(642\) 0 0
\(643\) −6.32054 17.3655i −0.249258 0.684830i −0.999714 0.0239099i \(-0.992389\pi\)
0.750456 0.660920i \(-0.229834\pi\)
\(644\) 0 0
\(645\) −1.73115 + 9.29544i −0.0681639 + 0.366008i
\(646\) 0 0
\(647\) 12.7137 + 22.0208i 0.499828 + 0.865727i 1.00000 0.000199058i \(-6.33620e-5\pi\)
−0.500172 + 0.865926i \(0.666730\pi\)
\(648\) 0 0
\(649\) −0.938445 0.541811i −0.0368372 0.0212680i
\(650\) 0 0
\(651\) −37.1843 22.4116i −1.45737 0.878378i
\(652\) 0 0
\(653\) −15.8052 2.78688i −0.618505 0.109059i −0.144388 0.989521i \(-0.546121\pi\)
−0.474117 + 0.880462i \(0.657233\pi\)
\(654\) 0 0
\(655\) 1.45236 1.21867i 0.0567484 0.0476175i
\(656\) 0 0
\(657\) −18.8605 + 2.95368i −0.735816 + 0.115234i
\(658\) 0 0
\(659\) −2.85356 + 7.84009i −0.111159 + 0.305407i −0.982782 0.184771i \(-0.940846\pi\)
0.871623 + 0.490177i \(0.163068\pi\)
\(660\) 0 0
\(661\) 18.6628 + 3.29075i 0.725898 + 0.127995i 0.524374 0.851488i \(-0.324299\pi\)
0.201524 + 0.979484i \(0.435411\pi\)
\(662\) 0 0
\(663\) −0.886196 + 2.36399i −0.0344170 + 0.0918097i
\(664\) 0 0
\(665\) 2.31221 0.385757i 0.0896637 0.0149590i
\(666\) 0 0
\(667\) 21.5988 0.836310
\(668\) 0 0
\(669\) −42.5868 + 24.0457i −1.64650 + 0.929662i
\(670\) 0 0
\(671\) −1.90364 + 10.7961i −0.0734893 + 0.416779i
\(672\) 0 0
\(673\) −29.7861 + 24.9935i −1.14817 + 0.963428i −0.999675 0.0254859i \(-0.991887\pi\)
−0.148493 + 0.988913i \(0.547442\pi\)
\(674\) 0 0
\(675\) −18.7636 + 14.8457i −0.722210 + 0.571410i
\(676\) 0 0
\(677\) −6.83083 38.7396i −0.262530 1.48888i −0.775977 0.630761i \(-0.782743\pi\)
0.513447 0.858121i \(-0.328368\pi\)
\(678\) 0 0
\(679\) −0.151596 + 16.4398i −0.00581771 + 0.630903i
\(680\) 0 0
\(681\) 6.38187 + 11.3028i 0.244554 + 0.433123i
\(682\) 0 0
\(683\) 13.4133 + 7.74417i 0.513246 + 0.296323i 0.734167 0.678969i \(-0.237573\pi\)
−0.220921 + 0.975292i \(0.570906\pi\)
\(684\) 0 0
\(685\) −7.19907 4.15638i −0.275062 0.158807i
\(686\) 0 0
\(687\) −1.71623 2.08563i −0.0654781 0.0795718i
\(688\) 0 0
\(689\) 0.635435 3.60373i 0.0242081 0.137291i
\(690\) 0 0
\(691\) −25.3848 30.2524i −0.965683 1.15086i −0.988516 0.151117i \(-0.951713\pi\)
0.0228327 0.999739i \(-0.492731\pi\)
\(692\) 0 0
\(693\) 5.48826 13.8422i 0.208482 0.525822i
\(694\) 0 0
\(695\) −4.60797 + 12.6603i −0.174790 + 0.480233i
\(696\) 0 0
\(697\) −1.33960 1.12406i −0.0507408 0.0425766i
\(698\) 0 0
\(699\) −15.0217 + 17.5573i −0.568174 + 0.664079i
\(700\) 0 0
\(701\) 17.7766i 0.671415i 0.941966 + 0.335707i \(0.108975\pi\)
−0.941966 + 0.335707i \(0.891025\pi\)
\(702\) 0 0
\(703\) −0.479502 + 0.276841i −0.0180848 + 0.0104412i
\(704\) 0 0
\(705\) −1.95462 + 10.4954i −0.0736153 + 0.395279i
\(706\) 0 0
\(707\) 22.5710 38.2747i 0.848870 1.43947i
\(708\) 0 0
\(709\) −44.5363 16.2099i −1.67260 0.608775i −0.680331 0.732905i \(-0.738164\pi\)
−0.992266 + 0.124130i \(0.960386\pi\)
\(710\) 0 0
\(711\) −22.8498 19.9327i −0.856933 0.747534i
\(712\) 0 0
\(713\) −43.3351 15.7727i −1.62291 0.590691i
\(714\) 0 0
\(715\) 0.331364 + 0.278047i 0.0123923 + 0.0103984i
\(716\) 0 0
\(717\) −14.6889 + 2.44498i −0.548566 + 0.0913094i
\(718\) 0 0
\(719\) −23.7545 41.1440i −0.885894 1.53441i −0.844686 0.535262i \(-0.820213\pi\)
−0.0412079 0.999151i \(-0.513121\pi\)
\(720\) 0 0
\(721\) 10.1988 1.70151i 0.379823 0.0633676i
\(722\) 0 0
\(723\) −0.176560 + 18.4027i −0.00656632 + 0.684405i
\(724\) 0 0
\(725\) 6.98814 + 19.1997i 0.259533 + 0.713061i
\(726\) 0 0
\(727\) 8.50270 + 10.1331i 0.315348 + 0.375817i 0.900314 0.435241i \(-0.143337\pi\)
−0.584966 + 0.811057i \(0.698892\pi\)
\(728\) 0 0
\(729\) −12.1324 24.1206i −0.449348 0.893357i
\(730\) 0 0
\(731\) 32.4284 + 11.8030i 1.19941 + 0.436549i
\(732\) 0 0
\(733\) −13.9826 + 16.6638i −0.516458 + 0.615491i −0.959739 0.280892i \(-0.909370\pi\)
0.443281 + 0.896382i \(0.353814\pi\)
\(734\) 0 0
\(735\) 5.70051 + 5.06228i 0.210267 + 0.186725i
\(736\) 0 0
\(737\) 6.67873i 0.246014i
\(738\) 0 0
\(739\) −8.14348 −0.299563 −0.149781 0.988719i \(-0.547857\pi\)
−0.149781 + 0.988719i \(0.547857\pi\)
\(740\) 0 0
\(741\) 0.837976 + 0.314135i 0.0307838 + 0.0115400i
\(742\) 0 0
\(743\) −20.7786 + 24.7630i −0.762294 + 0.908466i −0.997991 0.0633603i \(-0.979818\pi\)
0.235697 + 0.971827i \(0.424263\pi\)
\(744\) 0 0
\(745\) −10.0535 + 1.77270i −0.368332 + 0.0649469i
\(746\) 0 0
\(747\) −2.54944 + 12.9954i −0.0932793 + 0.475476i
\(748\) 0 0
\(749\) −32.6487 6.06778i −1.19296 0.221712i
\(750\) 0 0
\(751\) −2.29857 + 13.0358i −0.0838759 + 0.475684i 0.913718 + 0.406350i \(0.133199\pi\)
−0.997594 + 0.0693340i \(0.977913\pi\)
\(752\) 0 0
\(753\) −30.6022 26.1826i −1.11520 0.954148i
\(754\) 0 0
\(755\) −9.17164 −0.333790
\(756\) 0 0
\(757\) −11.8523 −0.430780 −0.215390 0.976528i \(-0.569102\pi\)
−0.215390 + 0.976528i \(0.569102\pi\)
\(758\) 0 0
\(759\) 2.89583 15.5493i 0.105112 0.564402i
\(760\) 0 0
\(761\) −6.93204 + 39.3135i −0.251286 + 1.42511i 0.554142 + 0.832422i \(0.313046\pi\)
−0.805428 + 0.592693i \(0.798065\pi\)
\(762\) 0 0
\(763\) 3.59736 + 3.07552i 0.130233 + 0.111341i
\(764\) 0 0
\(765\) −3.62397 6.56464i −0.131025 0.237345i
\(766\) 0 0
\(767\) 0.208587 0.0367796i 0.00753165 0.00132803i
\(768\) 0 0
\(769\) −14.9148 + 17.7747i −0.537840 + 0.640973i −0.964702 0.263344i \(-0.915175\pi\)
0.426862 + 0.904317i \(0.359619\pi\)
\(770\) 0 0
\(771\) −16.1480 + 13.2879i −0.581557 + 0.478552i
\(772\) 0 0
\(773\) 17.4609 0.628024 0.314012 0.949419i \(-0.398327\pi\)
0.314012 + 0.949419i \(0.398327\pi\)
\(774\) 0 0
\(775\) 43.6248i 1.56705i
\(776\) 0 0
\(777\) −1.68022 0.647604i −0.0602777 0.0232327i