Properties

Label 864.2.w.a.107.11
Level $864$
Weight $2$
Character 864.107
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.11
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.649337 + 1.25633i) q^{2} +(-1.15672 - 1.63156i) q^{4} +(3.53205 + 1.46302i) q^{5} +(-2.51075 + 2.51075i) q^{7} +(2.80088 - 0.393792i) q^{8} +O(q^{10})\) \(q+(-0.649337 + 1.25633i) q^{2} +(-1.15672 - 1.63156i) q^{4} +(3.53205 + 1.46302i) q^{5} +(-2.51075 + 2.51075i) q^{7} +(2.80088 - 0.393792i) q^{8} +(-4.13152 + 3.48742i) q^{10} +(-5.60551 - 2.32188i) q^{11} +(-0.868013 - 2.09557i) q^{13} +(-1.52400 - 4.78464i) q^{14} +(-1.32398 + 3.77453i) q^{16} -5.57376 q^{17} +(-5.18048 + 2.14582i) q^{19} +(-1.69859 - 7.45506i) q^{20} +(6.55691 - 5.53468i) q^{22} +(0.739154 - 0.739154i) q^{23} +(6.79939 + 6.79939i) q^{25} +(3.19636 + 0.270220i) q^{26} +(7.00067 + 1.19220i) q^{28} +(0.987514 + 2.38407i) q^{29} +7.29884i q^{31} +(-3.88234 - 4.11430i) q^{32} +(3.61925 - 7.00247i) q^{34} +(-12.5413 + 5.19479i) q^{35} +(0.441498 - 1.06587i) q^{37} +(0.668014 - 7.90174i) q^{38} +(10.4690 + 2.70686i) q^{40} +(0.383180 + 0.383180i) q^{41} +(-2.39337 + 5.77810i) q^{43} +(2.69574 + 11.8315i) q^{44} +(0.448661 + 1.40858i) q^{46} -8.10998i q^{47} -5.60769i q^{49} +(-12.9574 + 4.12717i) q^{50} +(-2.41500 + 3.84021i) q^{52} +(0.0479059 - 0.115655i) q^{53} +(-16.4020 - 16.4020i) q^{55} +(-6.04358 + 8.02101i) q^{56} +(-3.63640 - 0.307422i) q^{58} +(0.590646 - 1.42595i) q^{59} +(-6.20097 + 2.56852i) q^{61} +(-9.16975 - 4.73941i) q^{62} +(7.68986 - 2.20593i) q^{64} -8.67157i q^{65} +(0.495417 + 1.19604i) q^{67} +(6.44730 + 9.09393i) q^{68} +(1.61719 - 19.1292i) q^{70} +(3.91505 + 3.91505i) q^{71} +(-7.21185 + 7.21185i) q^{73} +(1.05240 + 1.24678i) q^{74} +(9.49342 + 5.97014i) q^{76} +(19.9037 - 8.24437i) q^{77} +6.53923 q^{79} +(-10.1986 + 11.3948i) q^{80} +(-0.730214 + 0.232587i) q^{82} +(0.667667 + 1.61189i) q^{83} +(-19.6868 - 8.15453i) q^{85} +(-5.70509 - 6.75879i) q^{86} +(-16.6147 - 4.29590i) q^{88} +(11.5889 - 11.5889i) q^{89} +(7.44080 + 3.08208i) q^{91} +(-2.06097 - 0.350978i) q^{92} +(10.1888 + 5.26611i) q^{94} -21.4371 q^{95} -16.2214 q^{97} +(7.04510 + 3.64128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.649337 + 1.25633i −0.459150 + 0.888359i
\(3\) 0 0
\(4\) −1.15672 1.63156i −0.578362 0.815780i
\(5\) 3.53205 + 1.46302i 1.57958 + 0.654283i 0.988347 0.152218i \(-0.0486416\pi\)
0.591232 + 0.806501i \(0.298642\pi\)
\(6\) 0 0
\(7\) −2.51075 + 2.51075i −0.948973 + 0.948973i −0.998760 0.0497873i \(-0.984146\pi\)
0.0497873 + 0.998760i \(0.484146\pi\)
\(8\) 2.80088 0.393792i 0.990261 0.139227i
\(9\) 0 0
\(10\) −4.13152 + 3.48742i −1.30650 + 1.10282i
\(11\) −5.60551 2.32188i −1.69013 0.700073i −0.690398 0.723430i \(-0.742565\pi\)
−0.999727 + 0.0233568i \(0.992565\pi\)
\(12\) 0 0
\(13\) −0.868013 2.09557i −0.240744 0.581206i 0.756613 0.653862i \(-0.226852\pi\)
−0.997357 + 0.0726560i \(0.976852\pi\)
\(14\) −1.52400 4.78464i −0.407307 1.27875i
\(15\) 0 0
\(16\) −1.32398 + 3.77453i −0.330996 + 0.943632i
\(17\) −5.57376 −1.35184 −0.675918 0.736977i \(-0.736252\pi\)
−0.675918 + 0.736977i \(0.736252\pi\)
\(18\) 0 0
\(19\) −5.18048 + 2.14582i −1.18848 + 0.492286i −0.887261 0.461268i \(-0.847395\pi\)
−0.301222 + 0.953554i \(0.597395\pi\)
\(20\) −1.69859 7.45506i −0.379817 1.66700i
\(21\) 0 0
\(22\) 6.55691 5.53468i 1.39794 1.18000i
\(23\) 0.739154 0.739154i 0.154124 0.154124i −0.625833 0.779957i \(-0.715241\pi\)
0.779957 + 0.625833i \(0.215241\pi\)
\(24\) 0 0
\(25\) 6.79939 + 6.79939i 1.35988 + 1.35988i
\(26\) 3.19636 + 0.270220i 0.626857 + 0.0529946i
\(27\) 0 0
\(28\) 7.00067 + 1.19220i 1.32300 + 0.225304i
\(29\) 0.987514 + 2.38407i 0.183377 + 0.442711i 0.988658 0.150182i \(-0.0479859\pi\)
−0.805282 + 0.592892i \(0.797986\pi\)
\(30\) 0 0
\(31\) 7.29884i 1.31091i 0.755234 + 0.655456i \(0.227523\pi\)
−0.755234 + 0.655456i \(0.772477\pi\)
\(32\) −3.88234 4.11430i −0.686307 0.727312i
\(33\) 0 0
\(34\) 3.61925 7.00247i 0.620696 1.20091i
\(35\) −12.5413 + 5.19479i −2.11987 + 0.878081i
\(36\) 0 0
\(37\) 0.441498 1.06587i 0.0725818 0.175228i −0.883425 0.468573i \(-0.844768\pi\)
0.956007 + 0.293345i \(0.0947684\pi\)
\(38\) 0.668014 7.90174i 0.108366 1.28183i
\(39\) 0 0
\(40\) 10.4690 + 2.70686i 1.65529 + 0.427991i
\(41\) 0.383180 + 0.383180i 0.0598427 + 0.0598427i 0.736395 0.676552i \(-0.236527\pi\)
−0.676552 + 0.736395i \(0.736527\pi\)
\(42\) 0 0
\(43\) −2.39337 + 5.77810i −0.364985 + 0.881153i 0.629570 + 0.776944i \(0.283231\pi\)
−0.994555 + 0.104209i \(0.966769\pi\)
\(44\) 2.69574 + 11.8315i 0.406398 + 1.78367i
\(45\) 0 0
\(46\) 0.448661 + 1.40858i 0.0661514 + 0.207684i
\(47\) 8.10998i 1.18296i −0.806319 0.591481i \(-0.798544\pi\)
0.806319 0.591481i \(-0.201456\pi\)
\(48\) 0 0
\(49\) 5.60769i 0.801098i
\(50\) −12.9574 + 4.12717i −1.83245 + 0.583670i
\(51\) 0 0
\(52\) −2.41500 + 3.84021i −0.334900 + 0.532541i
\(53\) 0.0479059 0.115655i 0.00658038 0.0158864i −0.920555 0.390613i \(-0.872263\pi\)
0.927136 + 0.374726i \(0.122263\pi\)
\(54\) 0 0
\(55\) −16.4020 16.4020i −2.21164 2.21164i
\(56\) −6.04358 + 8.02101i −0.807608 + 1.07185i
\(57\) 0 0
\(58\) −3.63640 0.307422i −0.477483 0.0403665i
\(59\) 0.590646 1.42595i 0.0768956 0.185642i −0.880757 0.473568i \(-0.842966\pi\)
0.957653 + 0.287926i \(0.0929657\pi\)
\(60\) 0 0
\(61\) −6.20097 + 2.56852i −0.793952 + 0.328866i −0.742531 0.669811i \(-0.766375\pi\)
−0.0514209 + 0.998677i \(0.516375\pi\)
\(62\) −9.16975 4.73941i −1.16456 0.601905i
\(63\) 0 0
\(64\) 7.68986 2.20593i 0.961232 0.275741i
\(65\) 8.67157i 1.07558i
\(66\) 0 0
\(67\) 0.495417 + 1.19604i 0.0605249 + 0.146120i 0.951249 0.308425i \(-0.0998019\pi\)
−0.890724 + 0.454545i \(0.849802\pi\)
\(68\) 6.44730 + 9.09393i 0.781850 + 1.10280i
\(69\) 0 0
\(70\) 1.61719 19.1292i 0.193291 2.28638i
\(71\) 3.91505 + 3.91505i 0.464630 + 0.464630i 0.900170 0.435539i \(-0.143442\pi\)
−0.435539 + 0.900170i \(0.643442\pi\)
\(72\) 0 0
\(73\) −7.21185 + 7.21185i −0.844083 + 0.844083i −0.989387 0.145304i \(-0.953584\pi\)
0.145304 + 0.989387i \(0.453584\pi\)
\(74\) 1.05240 + 1.24678i 0.122339 + 0.144935i
\(75\) 0 0
\(76\) 9.49342 + 5.97014i 1.08897 + 0.684822i
\(77\) 19.9037 8.24437i 2.26823 0.939533i
\(78\) 0 0
\(79\) 6.53923 0.735721 0.367860 0.929881i \(-0.380090\pi\)
0.367860 + 0.929881i \(0.380090\pi\)
\(80\) −10.1986 + 11.3948i −1.14024 + 1.27398i
\(81\) 0 0
\(82\) −0.730214 + 0.232587i −0.0806386 + 0.0256850i
\(83\) 0.667667 + 1.61189i 0.0732860 + 0.176928i 0.956277 0.292461i \(-0.0944742\pi\)
−0.882991 + 0.469389i \(0.844474\pi\)
\(84\) 0 0
\(85\) −19.6868 8.15453i −2.13533 0.884483i
\(86\) −5.70509 6.75879i −0.615196 0.728819i
\(87\) 0 0
\(88\) −16.6147 4.29590i −1.77113 0.457944i
\(89\) 11.5889 11.5889i 1.22842 1.22842i 0.263864 0.964560i \(-0.415003\pi\)
0.964560 0.263864i \(-0.0849970\pi\)
\(90\) 0 0
\(91\) 7.44080 + 3.08208i 0.780008 + 0.323090i
\(92\) −2.06097 0.350978i −0.214871 0.0365920i
\(93\) 0 0
\(94\) 10.1888 + 5.26611i 1.05089 + 0.543157i
\(95\) −21.4371 −2.19940
\(96\) 0 0
\(97\) −16.2214 −1.64704 −0.823519 0.567289i \(-0.807992\pi\)
−0.823519 + 0.567289i \(0.807992\pi\)
\(98\) 7.04510 + 3.64128i 0.711662 + 0.367824i
\(99\) 0 0
\(100\) 3.22860 18.9586i 0.322860 1.89586i
\(101\) −8.52695 3.53198i −0.848463 0.351445i −0.0842784 0.996442i \(-0.526859\pi\)
−0.764185 + 0.644997i \(0.776859\pi\)
\(102\) 0 0
\(103\) 3.31041 3.31041i 0.326184 0.326184i −0.524949 0.851133i \(-0.675916\pi\)
0.851133 + 0.524949i \(0.175916\pi\)
\(104\) −3.25642 5.52762i −0.319318 0.542028i
\(105\) 0 0
\(106\) 0.114194 + 0.135285i 0.0110915 + 0.0131400i
\(107\) 3.61441 + 1.49714i 0.349418 + 0.144734i 0.550488 0.834843i \(-0.314442\pi\)
−0.201070 + 0.979577i \(0.564442\pi\)
\(108\) 0 0
\(109\) 1.85232 + 4.47190i 0.177420 + 0.428330i 0.987424 0.158094i \(-0.0505351\pi\)
−0.810004 + 0.586425i \(0.800535\pi\)
\(110\) 31.2567 9.95586i 2.98021 0.949254i
\(111\) 0 0
\(112\) −6.15270 12.8011i −0.581375 1.20959i
\(113\) −5.96978 −0.561590 −0.280795 0.959768i \(-0.590598\pi\)
−0.280795 + 0.959768i \(0.590598\pi\)
\(114\) 0 0
\(115\) 3.69213 1.52933i 0.344292 0.142611i
\(116\) 2.74747 4.36890i 0.255097 0.405642i
\(117\) 0 0
\(118\) 1.40793 + 1.66796i 0.129610 + 0.153549i
\(119\) 13.9943 13.9943i 1.28285 1.28285i
\(120\) 0 0
\(121\) 18.2525 + 18.2525i 1.65931 + 1.65931i
\(122\) 0.799605 9.45829i 0.0723928 0.856313i
\(123\) 0 0
\(124\) 11.9085 8.44274i 1.06942 0.758181i
\(125\) 6.75299 + 16.3032i 0.604006 + 1.45820i
\(126\) 0 0
\(127\) 16.4206i 1.45709i 0.684998 + 0.728545i \(0.259803\pi\)
−0.684998 + 0.728545i \(0.740197\pi\)
\(128\) −2.22194 + 11.0934i −0.196393 + 0.980525i
\(129\) 0 0
\(130\) 10.8943 + 5.63077i 0.955497 + 0.493851i
\(131\) 5.57826 2.31059i 0.487375 0.201877i −0.125444 0.992101i \(-0.540035\pi\)
0.612819 + 0.790223i \(0.290035\pi\)
\(132\) 0 0
\(133\) 7.61924 18.3945i 0.660672 1.59500i
\(134\) −1.82432 0.154228i −0.157597 0.0133233i
\(135\) 0 0
\(136\) −15.6114 + 2.19490i −1.33867 + 0.188211i
\(137\) 10.4513 + 10.4513i 0.892917 + 0.892917i 0.994797 0.101880i \(-0.0324857\pi\)
−0.101880 + 0.994797i \(0.532486\pi\)
\(138\) 0 0
\(139\) 8.23647 19.8846i 0.698608 1.68659i −0.0280653 0.999606i \(-0.508935\pi\)
0.726673 0.686983i \(-0.241065\pi\)
\(140\) 22.9825 + 14.4530i 1.94237 + 1.22150i
\(141\) 0 0
\(142\) −7.46077 + 2.37640i −0.626094 + 0.199423i
\(143\) 13.7622i 1.15085i
\(144\) 0 0
\(145\) 9.86540i 0.819277i
\(146\) −4.37754 13.7434i −0.362287 1.13741i
\(147\) 0 0
\(148\) −2.24972 + 0.512586i −0.184926 + 0.0421343i
\(149\) −3.70094 + 8.93485i −0.303192 + 0.731971i 0.696701 + 0.717362i \(0.254651\pi\)
−0.999893 + 0.0146095i \(0.995349\pi\)
\(150\) 0 0
\(151\) 5.51555 + 5.51555i 0.448849 + 0.448849i 0.894972 0.446123i \(-0.147196\pi\)
−0.446123 + 0.894972i \(0.647196\pi\)
\(152\) −13.6649 + 8.05022i −1.10837 + 0.652959i
\(153\) 0 0
\(154\) −2.56655 + 30.3589i −0.206818 + 2.44639i
\(155\) −10.6784 + 25.7799i −0.857707 + 2.07069i
\(156\) 0 0
\(157\) −9.30584 + 3.85461i −0.742687 + 0.307631i −0.721754 0.692150i \(-0.756664\pi\)
−0.0209332 + 0.999781i \(0.506664\pi\)
\(158\) −4.24616 + 8.21542i −0.337807 + 0.653584i
\(159\) 0 0
\(160\) −7.69330 20.2118i −0.608208 1.59789i
\(161\) 3.71166i 0.292519i
\(162\) 0 0
\(163\) −4.44931 10.7416i −0.348496 0.841345i −0.996798 0.0799612i \(-0.974520\pi\)
0.648301 0.761384i \(-0.275480\pi\)
\(164\) 0.181948 1.06842i 0.0142078 0.0834293i
\(165\) 0 0
\(166\) −2.45861 0.207851i −0.190825 0.0161324i
\(167\) −3.22354 3.22354i −0.249445 0.249445i 0.571298 0.820743i \(-0.306440\pi\)
−0.820743 + 0.571298i \(0.806440\pi\)
\(168\) 0 0
\(169\) 5.55442 5.55442i 0.427263 0.427263i
\(170\) 23.0281 19.4380i 1.76618 1.49083i
\(171\) 0 0
\(172\) 12.1958 2.77874i 0.929921 0.211877i
\(173\) −2.90445 + 1.20306i −0.220821 + 0.0914672i −0.490351 0.871525i \(-0.663132\pi\)
0.269530 + 0.962992i \(0.413132\pi\)
\(174\) 0 0
\(175\) −34.1431 −2.58097
\(176\) 16.1856 18.0840i 1.22004 1.36314i
\(177\) 0 0
\(178\) 7.03438 + 22.0846i 0.527249 + 1.65531i
\(179\) 1.65524 + 3.99611i 0.123719 + 0.298683i 0.973589 0.228309i \(-0.0733196\pi\)
−0.849870 + 0.526992i \(0.823320\pi\)
\(180\) 0 0
\(181\) 17.3324 + 7.17932i 1.28831 + 0.533635i 0.918481 0.395466i \(-0.129417\pi\)
0.369827 + 0.929100i \(0.379417\pi\)
\(182\) −8.70369 + 7.34678i −0.645161 + 0.544580i
\(183\) 0 0
\(184\) 1.77921 2.36136i 0.131165 0.174081i
\(185\) 3.11878 3.11878i 0.229297 0.229297i
\(186\) 0 0
\(187\) 31.2438 + 12.9416i 2.28477 + 0.946383i
\(188\) −13.2319 + 9.38100i −0.965037 + 0.684180i
\(189\) 0 0
\(190\) 13.9199 26.9320i 1.00985 1.95385i
\(191\) −19.0737 −1.38012 −0.690061 0.723751i \(-0.742416\pi\)
−0.690061 + 0.723751i \(0.742416\pi\)
\(192\) 0 0
\(193\) −15.2555 −1.09812 −0.549059 0.835783i \(-0.685014\pi\)
−0.549059 + 0.835783i \(0.685014\pi\)
\(194\) 10.5332 20.3795i 0.756238 1.46316i
\(195\) 0 0
\(196\) −9.14928 + 6.48654i −0.653520 + 0.463324i
\(197\) −4.50554 1.86625i −0.321006 0.132965i 0.216361 0.976313i \(-0.430581\pi\)
−0.537367 + 0.843348i \(0.680581\pi\)
\(198\) 0 0
\(199\) −13.7213 + 13.7213i −0.972675 + 0.972675i −0.999636 0.0269615i \(-0.991417\pi\)
0.0269615 + 0.999636i \(0.491417\pi\)
\(200\) 21.7218 + 16.3667i 1.53596 + 1.15730i
\(201\) 0 0
\(202\) 9.97419 8.41921i 0.701781 0.592373i
\(203\) −8.46519 3.50640i −0.594140 0.246101i
\(204\) 0 0
\(205\) 0.792810 + 1.91401i 0.0553722 + 0.133680i
\(206\) 2.00939 + 6.30852i 0.140001 + 0.439536i
\(207\) 0 0
\(208\) 9.05902 0.501845i 0.628130 0.0347967i
\(209\) 34.0216 2.35332
\(210\) 0 0
\(211\) −3.32806 + 1.37853i −0.229113 + 0.0949018i −0.494287 0.869299i \(-0.664571\pi\)
0.265174 + 0.964201i \(0.414571\pi\)
\(212\) −0.244112 + 0.0556195i −0.0167657 + 0.00381996i
\(213\) 0 0
\(214\) −4.22786 + 3.56874i −0.289011 + 0.243954i
\(215\) −16.9070 + 16.9070i −1.15305 + 1.15305i
\(216\) 0 0
\(217\) −18.3255 18.3255i −1.24402 1.24402i
\(218\) −6.82095 0.576644i −0.461973 0.0390553i
\(219\) 0 0
\(220\) −7.78827 + 45.7334i −0.525085 + 3.08334i
\(221\) 4.83810 + 11.6802i 0.325446 + 0.785695i
\(222\) 0 0
\(223\) 6.11094i 0.409219i 0.978844 + 0.204609i \(0.0655924\pi\)
−0.978844 + 0.204609i \(0.934408\pi\)
\(224\) 20.0775 + 0.582389i 1.34149 + 0.0389125i
\(225\) 0 0
\(226\) 3.87640 7.50001i 0.257854 0.498893i
\(227\) 5.17260 2.14256i 0.343318 0.142207i −0.204361 0.978896i \(-0.565512\pi\)
0.547679 + 0.836689i \(0.315512\pi\)
\(228\) 0 0
\(229\) 4.17236 10.0730i 0.275717 0.665641i −0.723990 0.689810i \(-0.757694\pi\)
0.999708 + 0.0241692i \(0.00769404\pi\)
\(230\) −0.476094 + 5.63157i −0.0313927 + 0.371335i
\(231\) 0 0
\(232\) 3.70474 + 6.28862i 0.243228 + 0.412868i
\(233\) 3.06232 + 3.06232i 0.200619 + 0.200619i 0.800265 0.599646i \(-0.204692\pi\)
−0.599646 + 0.800265i \(0.704692\pi\)
\(234\) 0 0
\(235\) 11.8651 28.6448i 0.773992 1.86858i
\(236\) −3.00973 + 0.685750i −0.195917 + 0.0446385i
\(237\) 0 0
\(238\) 8.49442 + 26.6684i 0.550611 + 1.72866i
\(239\) 8.00090i 0.517535i −0.965940 0.258767i \(-0.916684\pi\)
0.965940 0.258767i \(-0.0833163\pi\)
\(240\) 0 0
\(241\) 30.6409i 1.97375i 0.161481 + 0.986876i \(0.448373\pi\)
−0.161481 + 0.986876i \(0.551627\pi\)
\(242\) −34.7831 + 11.0791i −2.23594 + 0.712191i
\(243\) 0 0
\(244\) 11.3635 + 7.14618i 0.727474 + 0.457487i
\(245\) 8.20416 19.8066i 0.524145 1.26540i
\(246\) 0 0
\(247\) 8.99344 + 8.99344i 0.572239 + 0.572239i
\(248\) 2.87423 + 20.4432i 0.182514 + 1.29814i
\(249\) 0 0
\(250\) −24.8671 2.10227i −1.57273 0.132959i
\(251\) 0.765150 1.84724i 0.0482958 0.116596i −0.897890 0.440219i \(-0.854901\pi\)
0.946186 + 0.323623i \(0.104901\pi\)
\(252\) 0 0
\(253\) −5.85956 + 2.42711i −0.368388 + 0.152591i
\(254\) −20.6296 10.6625i −1.29442 0.669023i
\(255\) 0 0
\(256\) −12.4941 9.99482i −0.780884 0.624676i
\(257\) 20.3873i 1.27173i 0.771802 + 0.635863i \(0.219356\pi\)
−0.771802 + 0.635863i \(0.780644\pi\)
\(258\) 0 0
\(259\) 1.56764 + 3.78462i 0.0974084 + 0.235165i
\(260\) −14.1482 + 10.0306i −0.877434 + 0.622072i
\(261\) 0 0
\(262\) −0.719309 + 8.50849i −0.0444390 + 0.525656i
\(263\) 15.5570 + 15.5570i 0.959283 + 0.959283i 0.999203 0.0399195i \(-0.0127101\pi\)
−0.0399195 + 0.999203i \(0.512710\pi\)
\(264\) 0 0
\(265\) 0.338412 0.338412i 0.0207885 0.0207885i
\(266\) 18.1621 + 21.5165i 1.11359 + 1.31926i
\(267\) 0 0
\(268\) 1.37836 2.19179i 0.0841965 0.133885i
\(269\) 16.3872 6.78780i 0.999145 0.413860i 0.177662 0.984092i \(-0.443147\pi\)
0.821484 + 0.570232i \(0.193147\pi\)
\(270\) 0 0
\(271\) −2.76808 −0.168149 −0.0840743 0.996459i \(-0.526793\pi\)
−0.0840743 + 0.996459i \(0.526793\pi\)
\(272\) 7.37956 21.0383i 0.447451 1.27564i
\(273\) 0 0
\(274\) −19.9167 + 6.34387i −1.20321 + 0.383247i
\(275\) −22.3267 53.9014i −1.34635 3.25038i
\(276\) 0 0
\(277\) 3.01233 + 1.24775i 0.180993 + 0.0749698i 0.471340 0.881952i \(-0.343771\pi\)
−0.290347 + 0.956922i \(0.593771\pi\)
\(278\) 19.6333 + 23.2595i 1.17753 + 1.39501i
\(279\) 0 0
\(280\) −33.0811 + 19.4887i −1.97698 + 1.16467i
\(281\) 9.71631 9.71631i 0.579626 0.579626i −0.355174 0.934800i \(-0.615578\pi\)
0.934800 + 0.355174i \(0.115578\pi\)
\(282\) 0 0
\(283\) −17.1498 7.10366i −1.01945 0.422269i −0.190554 0.981677i \(-0.561029\pi\)
−0.828893 + 0.559408i \(0.811029\pi\)
\(284\) 1.85901 10.9163i 0.110312 0.647761i
\(285\) 0 0
\(286\) −17.2898 8.93628i −1.02237 0.528413i
\(287\) −1.92414 −0.113578
\(288\) 0 0
\(289\) 14.0668 0.827458
\(290\) −12.3942 6.40597i −0.727811 0.376171i
\(291\) 0 0
\(292\) 20.1087 + 3.42446i 1.17677 + 0.200401i
\(293\) 19.6509 + 8.13967i 1.14802 + 0.475524i 0.873868 0.486163i \(-0.161604\pi\)
0.274149 + 0.961687i \(0.411604\pi\)
\(294\) 0 0
\(295\) 4.17238 4.17238i 0.242925 0.242925i
\(296\) 0.816851 3.15923i 0.0474785 0.183627i
\(297\) 0 0
\(298\) −8.82195 10.4513i −0.511042 0.605429i
\(299\) −2.19054 0.907353i −0.126682 0.0524736i
\(300\) 0 0
\(301\) −8.49821 20.5165i −0.489829 1.18255i
\(302\) −10.5108 + 3.34789i −0.604828 + 0.192650i
\(303\) 0 0
\(304\) −1.24062 22.3949i −0.0711542 1.28444i
\(305\) −25.6599 −1.46928
\(306\) 0 0
\(307\) 24.4403 10.1235i 1.39488 0.577780i 0.446466 0.894801i \(-0.352682\pi\)
0.948419 + 0.317021i \(0.102682\pi\)
\(308\) −36.4742 22.9376i −2.07831 1.30699i
\(309\) 0 0
\(310\) −25.4541 30.1553i −1.44570 1.71271i
\(311\) −4.43894 + 4.43894i −0.251709 + 0.251709i −0.821671 0.569962i \(-0.806958\pi\)
0.569962 + 0.821671i \(0.306958\pi\)
\(312\) 0 0
\(313\) 13.9499 + 13.9499i 0.788492 + 0.788492i 0.981247 0.192755i \(-0.0617421\pi\)
−0.192755 + 0.981247i \(0.561742\pi\)
\(314\) 1.19997 14.1941i 0.0677185 0.801021i
\(315\) 0 0
\(316\) −7.56408 10.6692i −0.425513 0.600187i
\(317\) −10.3082 24.8861i −0.578964 1.39774i −0.893743 0.448579i \(-0.851930\pi\)
0.314779 0.949165i \(-0.398070\pi\)
\(318\) 0 0
\(319\) 15.6568i 0.876613i
\(320\) 30.3882 + 3.45898i 1.69875 + 0.193363i
\(321\) 0 0
\(322\) −4.66306 2.41011i −0.259862 0.134310i
\(323\) 28.8747 11.9603i 1.60663 0.665489i
\(324\) 0 0
\(325\) 8.34663 20.1505i 0.462988 1.11775i
\(326\) 16.3840 + 1.38511i 0.907428 + 0.0767141i
\(327\) 0 0
\(328\) 1.22414 + 0.922349i 0.0675916 + 0.0509282i
\(329\) 20.3621 + 20.3621i 1.12260 + 1.12260i
\(330\) 0 0
\(331\) −3.08779 + 7.45457i −0.169720 + 0.409740i −0.985738 0.168286i \(-0.946177\pi\)
0.816018 + 0.578026i \(0.196177\pi\)
\(332\) 1.85759 2.95385i 0.101949 0.162114i
\(333\) 0 0
\(334\) 6.14300 1.95666i 0.336130 0.107064i
\(335\) 4.94929i 0.270408i
\(336\) 0 0
\(337\) 6.48428i 0.353221i −0.984281 0.176611i \(-0.943487\pi\)
0.984281 0.176611i \(-0.0565134\pi\)
\(338\) 3.37149 + 10.5849i 0.183385 + 0.575741i
\(339\) 0 0
\(340\) 9.46754 + 41.5527i 0.513450 + 2.25351i
\(341\) 16.9470 40.9138i 0.917733 2.21560i
\(342\) 0 0
\(343\) −3.49575 3.49575i −0.188753 0.188753i
\(344\) −4.42817 + 17.1263i −0.238751 + 0.923386i
\(345\) 0 0
\(346\) 0.374524 4.43014i 0.0201346 0.238166i
\(347\) 2.92830 7.06955i 0.157200 0.379513i −0.825583 0.564281i \(-0.809153\pi\)
0.982782 + 0.184768i \(0.0591534\pi\)
\(348\) 0 0
\(349\) 1.49118 0.617665i 0.0798208 0.0330629i −0.342416 0.939549i \(-0.611245\pi\)
0.422237 + 0.906486i \(0.361245\pi\)
\(350\) 22.1703 42.8949i 1.18505 2.29283i
\(351\) 0 0
\(352\) 12.2096 + 32.0771i 0.650774 + 1.70971i
\(353\) 36.9316i 1.96567i 0.184489 + 0.982835i \(0.440937\pi\)
−0.184489 + 0.982835i \(0.559063\pi\)
\(354\) 0 0
\(355\) 8.10033 + 19.5559i 0.429921 + 1.03792i
\(356\) −32.3132 5.50286i −1.71260 0.291651i
\(357\) 0 0
\(358\) −6.09524 0.515292i −0.322143 0.0272340i
\(359\) −6.75852 6.75852i −0.356701 0.356701i 0.505895 0.862595i \(-0.331162\pi\)
−0.862595 + 0.505895i \(0.831162\pi\)
\(360\) 0 0
\(361\) 8.79775 8.79775i 0.463039 0.463039i
\(362\) −20.2742 + 17.1134i −1.06559 + 0.899461i
\(363\) 0 0
\(364\) −3.57835 15.7052i −0.187556 0.823178i
\(365\) −36.0237 + 14.9215i −1.88557 + 0.781027i
\(366\) 0 0
\(367\) −2.80609 −0.146477 −0.0732384 0.997314i \(-0.523333\pi\)
−0.0732384 + 0.997314i \(0.523333\pi\)
\(368\) 1.81133 + 3.76859i 0.0944222 + 0.196451i
\(369\) 0 0
\(370\) 1.89308 + 5.94336i 0.0984163 + 0.308980i
\(371\) 0.170101 + 0.410660i 0.00883120 + 0.0213204i
\(372\) 0 0
\(373\) −6.31254 2.61474i −0.326851 0.135386i 0.213223 0.977003i \(-0.431604\pi\)
−0.540074 + 0.841617i \(0.681604\pi\)
\(374\) −36.5466 + 30.8490i −1.88978 + 1.59516i
\(375\) 0 0
\(376\) −3.19364 22.7151i −0.164700 1.17144i
\(377\) 4.13881 4.13881i 0.213159 0.213159i
\(378\) 0 0
\(379\) 25.4489 + 10.5413i 1.30722 + 0.541468i 0.924072 0.382219i \(-0.124840\pi\)
0.383148 + 0.923687i \(0.374840\pi\)
\(380\) 24.7968 + 34.9759i 1.27205 + 1.79423i
\(381\) 0 0
\(382\) 12.3852 23.9628i 0.633684 1.22604i
\(383\) −7.86327 −0.401794 −0.200897 0.979612i \(-0.564386\pi\)
−0.200897 + 0.979612i \(0.564386\pi\)
\(384\) 0 0
\(385\) 82.3623 4.19757
\(386\) 9.90599 19.1660i 0.504202 0.975523i
\(387\) 0 0
\(388\) 18.7637 + 26.4663i 0.952583 + 1.34362i
\(389\) −32.2453 13.3564i −1.63490 0.677198i −0.639133 0.769096i \(-0.720707\pi\)
−0.995768 + 0.0918978i \(0.970707\pi\)
\(390\) 0 0
\(391\) −4.11987 + 4.11987i −0.208351 + 0.208351i
\(392\) −2.20826 15.7065i −0.111534 0.793296i
\(393\) 0 0
\(394\) 5.27024 4.44861i 0.265511 0.224118i
\(395\) 23.0969 + 9.56704i 1.16213 + 0.481370i
\(396\) 0 0
\(397\) −11.3411 27.3798i −0.569193 1.37415i −0.902236 0.431242i \(-0.858075\pi\)
0.333043 0.942912i \(-0.391925\pi\)
\(398\) −8.32870 26.1481i −0.417480 1.31069i
\(399\) 0 0
\(400\) −34.6667 + 16.6622i −1.73334 + 0.833111i
\(401\) −10.9457 −0.546600 −0.273300 0.961929i \(-0.588115\pi\)
−0.273300 + 0.961929i \(0.588115\pi\)
\(402\) 0 0
\(403\) 15.2952 6.33549i 0.761910 0.315593i
\(404\) 4.10068 + 17.9978i 0.204017 + 0.895422i
\(405\) 0 0
\(406\) 9.90194 8.35823i 0.491425 0.414812i
\(407\) −4.94964 + 4.94964i −0.245345 + 0.245345i
\(408\) 0 0
\(409\) 15.9557 + 15.9557i 0.788956 + 0.788956i 0.981323 0.192367i \(-0.0616163\pi\)
−0.192367 + 0.981323i \(0.561616\pi\)
\(410\) −2.91943 0.246809i −0.144180 0.0121890i
\(411\) 0 0
\(412\) −9.23035 1.57190i −0.454747 0.0774422i
\(413\) 2.09722 + 5.06315i 0.103198 + 0.249141i
\(414\) 0 0
\(415\) 6.67008i 0.327422i
\(416\) −5.25187 + 11.7070i −0.257494 + 0.573982i
\(417\) 0 0
\(418\) −22.0915 + 42.7423i −1.08053 + 2.09059i
\(419\) −6.71862 + 2.78294i −0.328226 + 0.135956i −0.540710 0.841209i \(-0.681844\pi\)
0.212485 + 0.977164i \(0.431844\pi\)
\(420\) 0 0
\(421\) 4.87375 11.7663i 0.237532 0.573453i −0.759494 0.650514i \(-0.774554\pi\)
0.997026 + 0.0770610i \(0.0245536\pi\)
\(422\) 0.429149 5.07627i 0.0208906 0.247109i
\(423\) 0 0
\(424\) 0.0886346 0.342801i 0.00430448 0.0166479i
\(425\) −37.8981 37.8981i −1.83833 1.83833i
\(426\) 0 0
\(427\) 9.12014 22.0180i 0.441354 1.06552i
\(428\) −1.73820 7.62890i −0.0840191 0.368757i
\(429\) 0 0
\(430\) −10.2624 32.2190i −0.494897 1.55374i
\(431\) 9.92174i 0.477914i 0.971030 + 0.238957i \(0.0768054\pi\)
−0.971030 + 0.238957i \(0.923195\pi\)
\(432\) 0 0
\(433\) 10.1916i 0.489776i −0.969551 0.244888i \(-0.921249\pi\)
0.969551 0.244888i \(-0.0787512\pi\)
\(434\) 34.9223 11.1235i 1.67633 0.533943i
\(435\) 0 0
\(436\) 5.15355 8.19492i 0.246810 0.392466i
\(437\) −2.24308 + 5.41527i −0.107301 + 0.259047i
\(438\) 0 0
\(439\) −15.7711 15.7711i −0.752715 0.752715i 0.222270 0.974985i \(-0.428653\pi\)
−0.974985 + 0.222270i \(0.928653\pi\)
\(440\) −52.3989 39.4810i −2.49802 1.88218i
\(441\) 0 0
\(442\) −17.8157 1.50614i −0.847408 0.0716400i
\(443\) −10.7283 + 25.9005i −0.509718 + 1.23057i 0.434327 + 0.900755i \(0.356986\pi\)
−0.944046 + 0.329814i \(0.893014\pi\)
\(444\) 0 0
\(445\) 57.8875 23.9778i 2.74413 1.13666i
\(446\) −7.67734 3.96806i −0.363533 0.187893i
\(447\) 0 0
\(448\) −13.7687 + 24.8458i −0.650512 + 1.17385i
\(449\) 4.82450i 0.227682i 0.993499 + 0.113841i \(0.0363155\pi\)
−0.993499 + 0.113841i \(0.963685\pi\)
\(450\) 0 0
\(451\) −1.25822 3.03762i −0.0592474 0.143036i
\(452\) 6.90538 + 9.74006i 0.324802 + 0.458134i
\(453\) 0 0
\(454\) −0.666999 + 7.88973i −0.0313038 + 0.370284i
\(455\) 21.7721 + 21.7721i 1.02069 + 1.02069i
\(456\) 0 0
\(457\) −6.21109 + 6.21109i −0.290542 + 0.290542i −0.837294 0.546752i \(-0.815864\pi\)
0.546752 + 0.837294i \(0.315864\pi\)
\(458\) 9.94570 + 11.7826i 0.464732 + 0.550565i
\(459\) 0 0
\(460\) −6.76596 4.25492i −0.315465 0.198387i
\(461\) 7.88931 3.26786i 0.367442 0.152199i −0.191320 0.981528i \(-0.561277\pi\)
0.558761 + 0.829328i \(0.311277\pi\)
\(462\) 0 0
\(463\) −8.48040 −0.394118 −0.197059 0.980392i \(-0.563139\pi\)
−0.197059 + 0.980392i \(0.563139\pi\)
\(464\) −10.3062 + 0.570935i −0.478453 + 0.0265050i
\(465\) 0 0
\(466\) −5.83575 + 1.85880i −0.270336 + 0.0861073i
\(467\) −9.27447 22.3906i −0.429171 1.03611i −0.979551 0.201197i \(-0.935517\pi\)
0.550379 0.834915i \(-0.314483\pi\)
\(468\) 0 0
\(469\) −4.24683 1.75909i −0.196100 0.0812274i
\(470\) 28.2829 + 33.5066i 1.30459 + 1.54554i
\(471\) 0 0
\(472\) 1.09280 4.22649i 0.0503003 0.194540i
\(473\) 26.8321 26.8321i 1.23374 1.23374i
\(474\) 0 0
\(475\) −49.8143 20.6338i −2.28564 0.946743i
\(476\) −39.0201 6.64501i −1.78848 0.304574i
\(477\) 0 0
\(478\) 10.0518 + 5.19528i 0.459757 + 0.237626i
\(479\) −23.9869 −1.09599 −0.547995 0.836482i \(-0.684609\pi\)
−0.547995 + 0.836482i \(0.684609\pi\)
\(480\) 0 0
\(481\) −2.61683 −0.119317
\(482\) −38.4950 19.8962i −1.75340 0.906249i
\(483\) 0 0
\(484\) 8.66696 50.8931i 0.393953 2.31332i
\(485\) −57.2949 23.7323i −2.60163 1.07763i
\(486\) 0 0
\(487\) −23.4325 + 23.4325i −1.06183 + 1.06183i −0.0638687 + 0.997958i \(0.520344\pi\)
−0.997958 + 0.0638687i \(0.979656\pi\)
\(488\) −16.3567 + 9.63602i −0.740433 + 0.436202i
\(489\) 0 0
\(490\) 19.5563 + 23.1683i 0.883465 + 1.04664i
\(491\) 14.6291 + 6.05958i 0.660203 + 0.273465i 0.687524 0.726162i \(-0.258698\pi\)
−0.0273208 + 0.999627i \(0.508698\pi\)
\(492\) 0 0
\(493\) −5.50416 13.2882i −0.247895 0.598472i
\(494\) −17.1385 + 5.45895i −0.771097 + 0.245610i
\(495\) 0 0
\(496\) −27.5497 9.66354i −1.23702 0.433906i
\(497\) −19.6594 −0.881843
\(498\) 0 0
\(499\) −13.3018 + 5.50979i −0.595470 + 0.246652i −0.660002 0.751264i \(-0.729445\pi\)
0.0645317 + 0.997916i \(0.479445\pi\)
\(500\) 18.7883 29.8762i 0.840237 1.33610i
\(501\) 0 0
\(502\) 1.82389 + 2.16076i 0.0814044 + 0.0964393i
\(503\) 22.0806 22.0806i 0.984523 0.984523i −0.0153587 0.999882i \(-0.504889\pi\)
0.999882 + 0.0153587i \(0.00488901\pi\)
\(504\) 0 0
\(505\) −24.9502 24.9502i −1.11027 1.11027i
\(506\) 0.755582 8.93755i 0.0335897 0.397323i
\(507\) 0 0
\(508\) 26.7912 18.9941i 1.18867 0.842725i
\(509\) 13.4106 + 32.3760i 0.594413 + 1.43504i 0.879202 + 0.476449i \(0.158076\pi\)
−0.284790 + 0.958590i \(0.591924\pi\)
\(510\) 0 0
\(511\) 36.2142i 1.60202i
\(512\) 20.6697 9.20674i 0.913480 0.406884i
\(513\) 0 0
\(514\) −25.6132 13.2382i −1.12975 0.583914i
\(515\) 16.5357 6.84931i 0.728650 0.301817i
\(516\) 0 0
\(517\) −18.8304 + 45.4606i −0.828159 + 1.99935i
\(518\) −5.77265 0.488021i −0.253636 0.0214424i
\(519\) 0 0
\(520\) −3.41480 24.2880i −0.149749 1.06510i
\(521\) −11.6079 11.6079i −0.508551 0.508551i 0.405531 0.914082i \(-0.367087\pi\)
−0.914082 + 0.405531i \(0.867087\pi\)
\(522\) 0 0
\(523\) −15.2533 + 36.8247i −0.666979 + 1.61023i 0.119659 + 0.992815i \(0.461820\pi\)
−0.786638 + 0.617415i \(0.788180\pi\)
\(524\) −10.2224 6.42856i −0.446567 0.280833i
\(525\) 0 0
\(526\) −29.6464 + 9.44295i −1.29264 + 0.411732i
\(527\) 40.6820i 1.77214i
\(528\) 0 0
\(529\) 21.9073i 0.952491i
\(530\) 0.205413 + 0.644899i 0.00892257 + 0.0280126i
\(531\) 0 0
\(532\) −38.8251 + 8.84606i −1.68328 + 0.383525i
\(533\) 0.470375 1.13559i 0.0203742 0.0491877i
\(534\) 0 0
\(535\) 10.5759 + 10.5759i 0.457237 + 0.457237i
\(536\) 1.85860 + 3.15488i 0.0802792 + 0.136270i
\(537\) 0 0
\(538\) −2.11310 + 24.9953i −0.0911024 + 1.07762i
\(539\) −13.0204 + 31.4339i −0.560827 + 1.35396i
\(540\) 0 0
\(541\) −8.53566 + 3.53558i −0.366976 + 0.152007i −0.558548 0.829472i \(-0.688641\pi\)
0.191572 + 0.981479i \(0.438641\pi\)
\(542\) 1.79741 3.47761i 0.0772055 0.149376i
\(543\) 0 0
\(544\) 21.6392 + 22.9321i 0.927774 + 0.983206i
\(545\) 18.5049i 0.792664i
\(546\) 0 0
\(547\) 1.00707 + 2.43127i 0.0430591 + 0.103954i 0.943946 0.330100i \(-0.107083\pi\)
−0.900887 + 0.434054i \(0.857083\pi\)
\(548\) 4.96268 29.1413i 0.211995 1.24485i
\(549\) 0 0
\(550\) 82.2154 + 6.95050i 3.50568 + 0.296370i
\(551\) −10.2316 10.2316i −0.435880 0.435880i
\(552\) 0 0
\(553\) −16.4183 + 16.4183i −0.698179 + 0.698179i
\(554\) −3.52359 + 2.97426i −0.149703 + 0.126364i
\(555\) 0 0
\(556\) −41.9702 + 9.56267i −1.77993 + 0.405548i
\(557\) −28.8901 + 11.9667i −1.22411 + 0.507044i −0.898715 0.438533i \(-0.855498\pi\)
−0.325398 + 0.945577i \(0.605498\pi\)
\(558\) 0 0
\(559\) 14.1859 0.599999
\(560\) −3.00339 54.2155i −0.126916 2.29102i
\(561\) 0 0
\(562\) 5.89772 + 18.5160i 0.248780 + 0.781052i
\(563\) −4.36887 10.5474i −0.184126 0.444519i 0.804683 0.593704i \(-0.202335\pi\)
−0.988809 + 0.149185i \(0.952335\pi\)
\(564\) 0 0
\(565\) −21.0855 8.73392i −0.887075 0.367439i
\(566\) 20.0605 16.9331i 0.843206 0.711749i
\(567\) 0 0
\(568\) 12.5073 + 9.42386i 0.524794 + 0.395416i
\(569\) −19.3660 + 19.3660i −0.811863 + 0.811863i −0.984913 0.173050i \(-0.944638\pi\)
0.173050 + 0.984913i \(0.444638\pi\)
\(570\) 0 0
\(571\) 25.4123 + 10.5261i 1.06347 + 0.440504i 0.844682 0.535268i \(-0.179789\pi\)
0.218789 + 0.975772i \(0.429789\pi\)
\(572\) 22.4538 15.9190i 0.938841 0.665607i
\(573\) 0 0
\(574\) 1.24941 2.41735i 0.0521495 0.100898i
\(575\) 10.0516 0.419180
\(576\) 0 0
\(577\) −28.6830 −1.19409 −0.597045 0.802208i \(-0.703659\pi\)
−0.597045 + 0.802208i \(0.703659\pi\)
\(578\) −9.13408 + 17.6725i −0.379928 + 0.735079i
\(579\) 0 0
\(580\) 16.0960 11.4115i 0.668350 0.473838i
\(581\) −5.72339 2.37071i −0.237446 0.0983534i
\(582\) 0 0
\(583\) −0.537074 + 0.537074i −0.0222433 + 0.0222433i
\(584\) −17.3596 + 23.0395i −0.718344 + 0.953381i
\(585\) 0 0
\(586\) −22.9862 + 19.4026i −0.949549 + 0.801514i
\(587\) 22.8287 + 9.45596i 0.942241 + 0.390289i 0.800309 0.599587i \(-0.204669\pi\)
0.141932 + 0.989876i \(0.454669\pi\)
\(588\) 0 0
\(589\) −15.6620 37.8115i −0.645343 1.55800i
\(590\) 2.53260 + 7.95116i 0.104265 + 0.327344i
\(591\) 0 0
\(592\) 3.43862 + 3.07764i 0.141327 + 0.126490i
\(593\) −39.0642 −1.60417 −0.802086 0.597208i \(-0.796277\pi\)
−0.802086 + 0.597208i \(0.796277\pi\)
\(594\) 0 0
\(595\) 69.9024 28.9545i 2.86572 1.18702i
\(596\) 18.8587 4.29685i 0.772483 0.176006i
\(597\) 0 0
\(598\) 2.56234 2.16287i 0.104782 0.0884462i
\(599\) 10.9019 10.9019i 0.445440 0.445440i −0.448395 0.893835i \(-0.648004\pi\)
0.893835 + 0.448395i \(0.148004\pi\)
\(600\) 0 0
\(601\) 7.61396 + 7.61396i 0.310580 + 0.310580i 0.845134 0.534554i \(-0.179521\pi\)
−0.534554 + 0.845134i \(0.679521\pi\)
\(602\) 31.2936 + 2.64557i 1.27543 + 0.107825i
\(603\) 0 0
\(604\) 2.61899 15.3789i 0.106565 0.625759i
\(605\) 37.7648 + 91.1723i 1.53536 + 3.70668i
\(606\) 0 0
\(607\) 35.9004i 1.45715i −0.684966 0.728575i \(-0.740183\pi\)
0.684966 0.728575i \(-0.259817\pi\)
\(608\) 28.9409 + 12.9832i 1.17371 + 0.526539i
\(609\) 0 0
\(610\) 16.6619 32.2373i 0.674621 1.30525i
\(611\) −16.9950 + 7.03957i −0.687545 + 0.284790i
\(612\) 0 0
\(613\) −9.05139 + 21.8520i −0.365582 + 0.882593i 0.628881 + 0.777502i \(0.283513\pi\)
−0.994463 + 0.105091i \(0.966487\pi\)
\(614\) −3.15155 + 37.2787i −0.127186 + 1.50445i
\(615\) 0 0
\(616\) 52.5012 30.9294i 2.11533 1.24618i
\(617\) −16.8704 16.8704i −0.679178 0.679178i 0.280636 0.959814i \(-0.409455\pi\)
−0.959814 + 0.280636i \(0.909455\pi\)
\(618\) 0 0
\(619\) −6.82536 + 16.4779i −0.274334 + 0.662301i −0.999659 0.0261052i \(-0.991690\pi\)
0.725325 + 0.688407i \(0.241690\pi\)
\(620\) 54.4133 12.3978i 2.18529 0.497906i
\(621\) 0 0
\(622\) −2.69440 8.45914i −0.108036 0.339180i
\(623\) 58.1937i 2.33148i
\(624\) 0 0
\(625\) 19.3844i 0.775375i
\(626\) −26.5838 + 8.46745i −1.06250 + 0.338427i
\(627\) 0 0
\(628\) 17.0533 + 10.7243i 0.680501 + 0.427948i
\(629\) −2.46080 + 5.94090i −0.0981186 + 0.236879i
\(630\) 0 0
\(631\) 21.2734 + 21.2734i 0.846882 + 0.846882i 0.989743 0.142861i \(-0.0456301\pi\)
−0.142861 + 0.989743i \(0.545630\pi\)
\(632\) 18.3156 2.57510i 0.728555 0.102432i
\(633\) 0 0
\(634\) 37.9586 + 3.20903i 1.50753 + 0.127447i
\(635\) −24.0236 + 57.9982i −0.953349 + 2.30159i
\(636\) 0 0
\(637\) −11.7513 + 4.86755i −0.465603 + 0.192859i
\(638\) 19.6701 + 10.1665i 0.778747 + 0.402497i
\(639\) 0 0
\(640\) −24.0778 + 35.9316i −0.951760 + 1.42032i
\(641\) 32.3465i 1.27761i −0.769368 0.638806i \(-0.779429\pi\)
0.769368 0.638806i \(-0.220571\pi\)
\(642\) 0 0
\(643\) 3.66614 + 8.85085i 0.144579 + 0.349043i 0.979535 0.201272i \(-0.0645075\pi\)
−0.834957 + 0.550315i \(0.814507\pi\)
\(644\) 6.05579 4.29336i 0.238632 0.169182i
\(645\) 0 0
\(646\) −3.72335 + 44.0424i −0.146493 + 1.73283i
\(647\) 6.34519 + 6.34519i 0.249455 + 0.249455i 0.820747 0.571292i \(-0.193558\pi\)
−0.571292 + 0.820747i \(0.693558\pi\)
\(648\) 0 0
\(649\) −6.62175 + 6.62175i −0.259926 + 0.259926i
\(650\) 19.8959 + 23.5706i 0.780383 + 0.924515i
\(651\) 0 0
\(652\) −12.3789 + 19.6843i −0.484796 + 0.770898i
\(653\) 24.5959 10.1880i 0.962513 0.398686i 0.154593 0.987978i \(-0.450593\pi\)
0.807920 + 0.589292i \(0.200593\pi\)
\(654\) 0 0
\(655\) 23.0831 0.901933
\(656\) −1.95365 + 0.939002i −0.0762772 + 0.0366619i
\(657\) 0 0
\(658\) −38.8033 + 12.3596i −1.51271 + 0.481828i
\(659\) 0.582111 + 1.40534i 0.0226758 + 0.0547443i 0.934812 0.355143i \(-0.115568\pi\)
−0.912136 + 0.409888i \(0.865568\pi\)
\(660\) 0 0
\(661\) −11.8390 4.90388i −0.460484 0.190739i 0.140367 0.990099i \(-0.455172\pi\)
−0.600851 + 0.799361i \(0.705172\pi\)
\(662\) −7.36038 8.71980i −0.286069 0.338905i
\(663\) 0 0
\(664\) 2.50480 + 4.25179i 0.0972053 + 0.165001i
\(665\) 53.8230 53.8230i 2.08717 2.08717i
\(666\) 0 0
\(667\) 2.49212 + 1.03227i 0.0964953 + 0.0399696i
\(668\) −1.53066 + 8.98816i −0.0592230 + 0.347762i
\(669\) 0 0
\(670\) −6.21793 3.21375i −0.240220 0.124158i
\(671\) 40.7234 1.57211
\(672\) 0 0
\(673\) −12.1970 −0.470158 −0.235079 0.971976i \(-0.575535\pi\)
−0.235079 + 0.971976i \(0.575535\pi\)
\(674\) 8.14639 + 4.21048i 0.313787 + 0.162182i
\(675\) 0 0
\(676\) −15.4873 2.63745i −0.595666 0.101440i
\(677\) 11.7841 + 4.88114i 0.452900 + 0.187597i 0.597460 0.801899i \(-0.296177\pi\)
−0.144560 + 0.989496i \(0.546177\pi\)
\(678\) 0 0
\(679\) 40.7279 40.7279i 1.56299 1.56299i
\(680\) −58.3515 15.0874i −2.23768 0.578574i
\(681\) 0 0
\(682\) 40.3968 + 47.8578i 1.54687 + 1.83257i
\(683\) −4.12594 1.70902i −0.157875 0.0653939i 0.302347 0.953198i \(-0.402230\pi\)
−0.460221 + 0.887804i \(0.652230\pi\)
\(684\) 0 0
\(685\) 21.6240 + 52.2051i 0.826212 + 1.99465i
\(686\) 6.66173 2.12189i 0.254346 0.0810142i
\(687\) 0 0
\(688\) −18.6408 16.6839i −0.710675 0.636070i
\(689\) −0.283946 −0.0108175
\(690\) 0 0
\(691\) 10.7178 4.43945i 0.407724 0.168885i −0.169389 0.985549i \(-0.554179\pi\)
0.577113 + 0.816665i \(0.304179\pi\)
\(692\) 5.32251 + 3.34718i 0.202332 + 0.127241i
\(693\) 0 0
\(694\) 6.98022 + 8.26943i 0.264966 + 0.313903i
\(695\) 58.1832 58.1832i 2.20701 2.20701i
\(696\) 0 0
\(697\) −2.13576 2.13576i −0.0808975 0.0808975i
\(698\) −0.192285 + 2.27448i −0.00727809 + 0.0860903i
\(699\) 0 0
\(700\) 39.4941 + 55.7065i 1.49274 + 2.10551i
\(701\) −16.9379 40.8917i −0.639735 1.54446i −0.827032 0.562154i \(-0.809973\pi\)
0.187297 0.982303i \(-0.440027\pi\)
\(702\) 0 0
\(703\) 6.46909i 0.243986i
\(704\) −48.2275 5.48956i −1.81764 0.206895i
\(705\) 0 0
\(706\) −46.3982 23.9810i −1.74622 0.902538i
\(707\) 30.2769 12.5411i 1.13868 0.471657i
\(708\) 0 0
\(709\) −14.9301 + 36.0446i −0.560714 + 1.35368i 0.348483 + 0.937315i \(0.386697\pi\)
−0.909197 + 0.416367i \(0.863303\pi\)
\(710\) −29.8285 2.52171i −1.11944 0.0946379i
\(711\) 0 0
\(712\) 27.8956 37.0228i 1.04543 1.38749i
\(713\) 5.39497 + 5.39497i 0.202043 + 0.202043i
\(714\) 0 0
\(715\) −20.1343 + 48.6086i −0.752982 + 1.81786i
\(716\) 4.60524 7.32302i 0.172106 0.273674i
\(717\) 0 0
\(718\) 12.8795 4.10236i 0.480658 0.153099i
\(719\) 52.7335i 1.96663i −0.181913 0.983315i \(-0.558229\pi\)
0.181913 0.983315i \(-0.441771\pi\)
\(720\) 0 0
\(721\) 16.6232i 0.619079i
\(722\) 5.34016 + 16.7656i 0.198740 + 0.623950i
\(723\) 0 0
\(724\) −8.33531 36.5834i −0.309779 1.35961i
\(725\) −9.49572 + 22.9247i −0.352662 + 0.851402i
\(726\) 0 0
\(727\) 11.4355 + 11.4355i 0.424119 + 0.424119i 0.886619 0.462500i \(-0.153048\pi\)
−0.462500 + 0.886619i \(0.653048\pi\)
\(728\) 22.0545 + 5.70241i 0.817394 + 0.211345i
\(729\) 0 0
\(730\) 4.64520 54.9467i 0.171927 2.03367i
\(731\) 13.3401 32.2058i 0.493400 1.19117i
\(732\) 0 0
\(733\) 10.3641 4.29294i 0.382806 0.158563i −0.182978 0.983117i \(-0.558574\pi\)
0.565784 + 0.824554i \(0.308574\pi\)
\(734\) 1.82210 3.52538i 0.0672549 0.130124i
\(735\) 0 0
\(736\) −5.91075 0.171453i −0.217873 0.00631985i
\(737\) 7.85473i 0.289333i
\(738\) 0 0
\(739\) −18.5384 44.7556i −0.681946 1.64636i −0.760408 0.649446i \(-0.775001\pi\)
0.0784620 0.996917i \(-0.474999\pi\)
\(740\) −8.69605 1.48091i −0.319673 0.0544395i
\(741\) 0 0
\(742\) −0.626377 0.0529540i −0.0229950 0.00194400i
\(743\) −14.2285 14.2285i −0.521994 0.521994i 0.396179 0.918173i \(-0.370336\pi\)
−0.918173 + 0.396179i \(0.870336\pi\)
\(744\) 0 0
\(745\) −26.1438 + 26.1438i −0.957833 + 0.957833i
\(746\) 7.38393 6.23277i 0.270345 0.228198i
\(747\) 0 0
\(748\) −15.0254 65.9460i −0.549383 2.41122i
\(749\) −12.8338 + 5.31593i −0.468936 + 0.194240i
\(750\) 0 0
\(751\) 15.1432 0.552583 0.276292 0.961074i \(-0.410894\pi\)
0.276292 + 0.961074i \(0.410894\pi\)
\(752\) 30.6113 + 10.7375i 1.11628 + 0.391555i
\(753\) 0 0
\(754\) 2.51222 + 7.88718i 0.0914897 + 0.287234i
\(755\) 11.4118 + 27.5505i 0.415318 + 1.00267i
\(756\) 0 0
\(757\) −18.5440 7.68118i −0.673993 0.279177i 0.0193201 0.999813i \(-0.493850\pi\)
−0.693313 + 0.720636i \(0.743850\pi\)
\(758\) −29.7682 + 25.1273i −1.08123 + 0.912665i
\(759\) 0 0
\(760\) −60.0427 + 8.44175i −2.17798 + 0.306214i
\(761\) −12.4579 + 12.4579i −0.451600 + 0.451600i −0.895885 0.444285i \(-0.853458\pi\)
0.444285 + 0.895885i \(0.353458\pi\)
\(762\) 0 0
\(763\) −15.8785 6.57709i −0.574840 0.238107i
\(764\) 22.0630 + 31.1199i 0.798210 + 1.12588i
\(765\) 0 0
\(766\) 5.10591 9.87885i 0.184484 0.356937i
\(767\) −3.50086 −0.126409
\(768\) 0 0
\(769\) 30.2721 1.09164 0.545819 0.837903i \(-0.316219\pi\)
0.545819 + 0.837903i \(0.316219\pi\)
\(770\) −53.4809 + 103.474i −1.92732 + 3.72895i
\(771\) 0 0
\(772\) 17.6464 + 24.8904i 0.635110 + 0.895823i
\(773\) 35.8692 + 14.8575i 1.29013 + 0.534387i 0.919023 0.394204i \(-0.128980\pi\)
0.371103 + 0.928592i \(0.378980\pi\)
\(774\) 0 0
\(775\) −49.6277 + 49.6277i −1.78268 + 1.78268i
\(776\) −45.4343 + 6.38787i −1.63100 + 0.229311i
\(777\) 0 0
\(778\) 37.7181 31.8379i 1.35226 1.14144i
\(779\) −2.80729 1.16282i −0.100582 0.0416623i
\(780\) 0 0
\(781\) −12.8556 31.0361i −0.460009 1.11056i
\(782\) −2.50073 7.85109i −0.0894258 0.280754i
\(783\) 0 0
\(784\) 21.1664 + 7.42448i 0.755942 + 0.265160i
\(785\) −38.5080 −1.37441
\(786\) 0 0
\(787\) 12.2284 5.06518i 0.435897 0.180554i −0.153934 0.988081i \(-0.549194\pi\)
0.589831 + 0.807527i \(0.299194\pi\)
\(788\) 2.16675 + 9.50980i 0.0771873 + 0.338773i
\(789\)