Properties

Label 864.2.v.b.109.11
Level $864$
Weight $2$
Character 864.109
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.v (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 109.11
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.679990 + 1.24001i) q^{2} +(-1.07523 - 1.68638i) q^{4} +(-3.54476 + 1.46829i) q^{5} +(1.60611 - 1.60611i) q^{7} +(2.82227 - 0.186565i) q^{8} +O(q^{10})\) \(q+(-0.679990 + 1.24001i) q^{2} +(-1.07523 - 1.68638i) q^{4} +(-3.54476 + 1.46829i) q^{5} +(1.60611 - 1.60611i) q^{7} +(2.82227 - 0.186565i) q^{8} +(0.589716 - 5.39394i) q^{10} +(0.347249 + 0.838334i) q^{11} +(-5.66583 - 2.34686i) q^{13} +(0.899444 + 3.08372i) q^{14} +(-1.68777 + 3.62649i) q^{16} -0.593837i q^{17} +(5.16462 + 2.13925i) q^{19} +(6.28751 + 4.39907i) q^{20} +(-1.27566 - 0.139468i) q^{22} +(0.0201157 + 0.0201157i) q^{23} +(6.87390 - 6.87390i) q^{25} +(6.76283 - 5.42982i) q^{26} +(-4.43544 - 0.981580i) q^{28} +(2.80250 - 6.76583i) q^{29} +6.90566 q^{31} +(-3.34920 - 4.55882i) q^{32} +(0.736362 + 0.403803i) q^{34} +(-3.33503 + 8.05148i) q^{35} +(1.45330 - 0.601978i) q^{37} +(-6.16457 + 4.94948i) q^{38} +(-9.73032 + 4.80522i) q^{40} +(8.95213 + 8.95213i) q^{41} +(2.56146 + 6.18392i) q^{43} +(1.04038 - 1.48699i) q^{44} +(-0.0386221 + 0.0112651i) q^{46} -2.63414i q^{47} +1.84085i q^{49} +(3.84949 + 13.1979i) q^{50} +(2.13435 + 12.0782i) q^{52} +(2.47496 + 5.97509i) q^{53} +(-2.46183 - 2.46183i) q^{55} +(4.23322 - 4.83250i) q^{56} +(6.48400 + 8.07581i) q^{58} +(-7.46732 + 3.09307i) q^{59} +(-2.06985 + 4.99706i) q^{61} +(-4.69578 + 8.56306i) q^{62} +(7.93039 - 1.05307i) q^{64} +23.5299 q^{65} +(3.91146 - 9.44309i) q^{67} +(-1.00144 + 0.638510i) q^{68} +(-7.71609 - 9.61038i) q^{70} +(10.7650 - 10.7650i) q^{71} +(-4.07812 - 4.07812i) q^{73} +(-0.241775 + 2.21144i) q^{74} +(-1.94554 - 11.0097i) q^{76} +(1.90417 + 0.788734i) q^{77} +7.64704i q^{79} +(0.658016 - 15.3332i) q^{80} +(-17.1880 + 5.01333i) q^{82} +(2.67059 + 1.10620i) q^{83} +(0.871923 + 2.10501i) q^{85} +(-9.40986 - 1.02877i) q^{86} +(1.13643 + 2.30122i) q^{88} +(-3.74752 + 3.74752i) q^{89} +(-12.8692 + 5.33061i) q^{91} +(0.0122938 - 0.0555518i) q^{92} +(3.26635 + 1.79119i) q^{94} -21.4483 q^{95} +14.4996 q^{97} +(-2.28266 - 1.25176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.679990 + 1.24001i −0.480825 + 0.876816i
\(3\) 0 0
\(4\) −1.07523 1.68638i −0.537614 0.843191i
\(5\) −3.54476 + 1.46829i −1.58526 + 0.656638i −0.989236 0.146327i \(-0.953255\pi\)
−0.596027 + 0.802964i \(0.703255\pi\)
\(6\) 0 0
\(7\) 1.60611 1.60611i 0.607051 0.607051i −0.335123 0.942174i \(-0.608778\pi\)
0.942174 + 0.335123i \(0.108778\pi\)
\(8\) 2.82227 0.186565i 0.997822 0.0659606i
\(9\) 0 0
\(10\) 0.589716 5.39394i 0.186484 1.70571i
\(11\) 0.347249 + 0.838334i 0.104700 + 0.252767i 0.967544 0.252702i \(-0.0813193\pi\)
−0.862845 + 0.505469i \(0.831319\pi\)
\(12\) 0 0
\(13\) −5.66583 2.34686i −1.57142 0.650903i −0.584394 0.811470i \(-0.698668\pi\)
−0.987025 + 0.160567i \(0.948668\pi\)
\(14\) 0.899444 + 3.08372i 0.240387 + 0.824158i
\(15\) 0 0
\(16\) −1.68777 + 3.62649i −0.421943 + 0.906622i
\(17\) 0.593837i 0.144027i −0.997404 0.0720134i \(-0.977058\pi\)
0.997404 0.0720134i \(-0.0229424\pi\)
\(18\) 0 0
\(19\) 5.16462 + 2.13925i 1.18484 + 0.490779i 0.886073 0.463546i \(-0.153423\pi\)
0.298772 + 0.954325i \(0.403423\pi\)
\(20\) 6.28751 + 4.39907i 1.40593 + 0.983663i
\(21\) 0 0
\(22\) −1.27566 0.139468i −0.271973 0.0297346i
\(23\) 0.0201157 + 0.0201157i 0.00419442 + 0.00419442i 0.709201 0.705006i \(-0.249056\pi\)
−0.705006 + 0.709201i \(0.749056\pi\)
\(24\) 0 0
\(25\) 6.87390 6.87390i 1.37478 1.37478i
\(26\) 6.76283 5.42982i 1.32630 1.06487i
\(27\) 0 0
\(28\) −4.43544 0.981580i −0.838219 0.185501i
\(29\) 2.80250 6.76583i 0.520411 1.25638i −0.417237 0.908798i \(-0.637002\pi\)
0.937648 0.347586i \(-0.112998\pi\)
\(30\) 0 0
\(31\) 6.90566 1.24029 0.620147 0.784486i \(-0.287073\pi\)
0.620147 + 0.784486i \(0.287073\pi\)
\(32\) −3.34920 4.55882i −0.592060 0.805894i
\(33\) 0 0
\(34\) 0.736362 + 0.403803i 0.126285 + 0.0692517i
\(35\) −3.33503 + 8.05148i −0.563723 + 1.36095i
\(36\) 0 0
\(37\) 1.45330 0.601978i 0.238921 0.0989645i −0.260010 0.965606i \(-0.583726\pi\)
0.498932 + 0.866641i \(0.333726\pi\)
\(38\) −6.16457 + 4.94948i −1.00003 + 0.802912i
\(39\) 0 0
\(40\) −9.73032 + 4.80522i −1.53850 + 0.759772i
\(41\) 8.95213 + 8.95213i 1.39809 + 1.39809i 0.805524 + 0.592563i \(0.201884\pi\)
0.592563 + 0.805524i \(0.298116\pi\)
\(42\) 0 0
\(43\) 2.56146 + 6.18392i 0.390619 + 0.943039i 0.989805 + 0.142429i \(0.0454912\pi\)
−0.599186 + 0.800610i \(0.704509\pi\)
\(44\) 1.04038 1.48699i 0.156843 0.224173i
\(45\) 0 0
\(46\) −0.0386221 + 0.0112651i −0.00569452 + 0.00166095i
\(47\) 2.63414i 0.384229i −0.981373 0.192115i \(-0.938465\pi\)
0.981373 0.192115i \(-0.0615345\pi\)
\(48\) 0 0
\(49\) 1.84085i 0.262979i
\(50\) 3.84949 + 13.1979i 0.544400 + 1.86646i
\(51\) 0 0
\(52\) 2.13435 + 12.0782i 0.295981 + 1.67494i
\(53\) 2.47496 + 5.97509i 0.339962 + 0.820741i 0.997719 + 0.0675106i \(0.0215056\pi\)
−0.657756 + 0.753231i \(0.728494\pi\)
\(54\) 0 0
\(55\) −2.46183 2.46183i −0.331953 0.331953i
\(56\) 4.23322 4.83250i 0.565687 0.645770i
\(57\) 0 0
\(58\) 6.48400 + 8.07581i 0.851390 + 1.06041i
\(59\) −7.46732 + 3.09307i −0.972163 + 0.402683i −0.811517 0.584329i \(-0.801358\pi\)
−0.160646 + 0.987012i \(0.551358\pi\)
\(60\) 0 0
\(61\) −2.06985 + 4.99706i −0.265017 + 0.639808i −0.999235 0.0391060i \(-0.987549\pi\)
0.734218 + 0.678914i \(0.237549\pi\)
\(62\) −4.69578 + 8.56306i −0.596365 + 1.08751i
\(63\) 0 0
\(64\) 7.93039 1.05307i 0.991298 0.131634i
\(65\) 23.5299 2.91852
\(66\) 0 0
\(67\) 3.91146 9.44309i 0.477860 1.15366i −0.482750 0.875758i \(-0.660362\pi\)
0.960610 0.277899i \(-0.0896380\pi\)
\(68\) −1.00144 + 0.638510i −0.121442 + 0.0774307i
\(69\) 0 0
\(70\) −7.71609 9.61038i −0.922249 1.14866i
\(71\) 10.7650 10.7650i 1.27757 1.27757i 0.335549 0.942023i \(-0.391078\pi\)
0.942023 0.335549i \(-0.108922\pi\)
\(72\) 0 0
\(73\) −4.07812 4.07812i −0.477308 0.477308i 0.426962 0.904270i \(-0.359584\pi\)
−0.904270 + 0.426962i \(0.859584\pi\)
\(74\) −0.241775 + 2.21144i −0.0281058 + 0.257075i
\(75\) 0 0
\(76\) −1.94554 11.0097i −0.223168 1.26290i
\(77\) 1.90417 + 0.788734i 0.217000 + 0.0898845i
\(78\) 0 0
\(79\) 7.64704i 0.860359i 0.902743 + 0.430180i \(0.141550\pi\)
−0.902743 + 0.430180i \(0.858450\pi\)
\(80\) 0.658016 15.3332i 0.0735684 1.71430i
\(81\) 0 0
\(82\) −17.1880 + 5.01333i −1.89810 + 0.553630i
\(83\) 2.67059 + 1.10620i 0.293135 + 0.121421i 0.524405 0.851469i \(-0.324288\pi\)
−0.231269 + 0.972890i \(0.574288\pi\)
\(84\) 0 0
\(85\) 0.871923 + 2.10501i 0.0945734 + 0.228320i
\(86\) −9.40986 1.02877i −1.01469 0.110936i
\(87\) 0 0
\(88\) 1.13643 + 2.30122i 0.121144 + 0.245311i
\(89\) −3.74752 + 3.74752i −0.397236 + 0.397236i −0.877257 0.480021i \(-0.840629\pi\)
0.480021 + 0.877257i \(0.340629\pi\)
\(90\) 0 0
\(91\) −12.8692 + 5.33061i −1.34906 + 0.558800i
\(92\) 0.0122938 0.0555518i 0.00128172 0.00579168i
\(93\) 0 0
\(94\) 3.26635 + 1.79119i 0.336898 + 0.184747i
\(95\) −21.4483 −2.20055
\(96\) 0 0
\(97\) 14.4996 1.47221 0.736106 0.676866i \(-0.236662\pi\)
0.736106 + 0.676866i \(0.236662\pi\)
\(98\) −2.28266 1.25176i −0.230584 0.126447i
\(99\) 0 0
\(100\) −18.9830 4.20102i −1.89830 0.420102i
\(101\) 3.93445 1.62970i 0.391493 0.162162i −0.178249 0.983985i \(-0.557043\pi\)
0.569742 + 0.821824i \(0.307043\pi\)
\(102\) 0 0
\(103\) 10.0464 10.0464i 0.989903 0.989903i −0.0100468 0.999950i \(-0.503198\pi\)
0.999950 + 0.0100468i \(0.00319804\pi\)
\(104\) −16.4283 5.56643i −1.61093 0.545834i
\(105\) 0 0
\(106\) −9.09209 0.994032i −0.883102 0.0965489i
\(107\) −2.72596 6.58106i −0.263529 0.636215i 0.735623 0.677391i \(-0.236890\pi\)
−0.999152 + 0.0411761i \(0.986890\pi\)
\(108\) 0 0
\(109\) 3.05385 + 1.26495i 0.292506 + 0.121160i 0.524111 0.851650i \(-0.324398\pi\)
−0.231605 + 0.972810i \(0.574398\pi\)
\(110\) 4.72670 1.37866i 0.450673 0.131450i
\(111\) 0 0
\(112\) 3.11379 + 8.53527i 0.294225 + 0.806507i
\(113\) 0.622324i 0.0585433i −0.999571 0.0292716i \(-0.990681\pi\)
0.999571 0.0292716i \(-0.00931879\pi\)
\(114\) 0 0
\(115\) −0.100841 0.0417697i −0.00940347 0.00389505i
\(116\) −14.4231 + 2.54872i −1.33915 + 0.236643i
\(117\) 0 0
\(118\) 1.24228 11.3628i 0.114362 1.04603i
\(119\) −0.953766 0.953766i −0.0874316 0.0874316i
\(120\) 0 0
\(121\) 7.19595 7.19595i 0.654178 0.654178i
\(122\) −4.78890 5.96457i −0.433567 0.540007i
\(123\) 0 0
\(124\) −7.42516 11.6456i −0.666799 1.04580i
\(125\) −6.93202 + 16.7354i −0.620018 + 1.49686i
\(126\) 0 0
\(127\) 9.84939 0.873992 0.436996 0.899463i \(-0.356042\pi\)
0.436996 + 0.899463i \(0.356042\pi\)
\(128\) −4.08677 + 10.5498i −0.361223 + 0.932480i
\(129\) 0 0
\(130\) −16.0001 + 29.1772i −1.40330 + 2.55901i
\(131\) 3.55214 8.57563i 0.310352 0.749256i −0.689340 0.724438i \(-0.742099\pi\)
0.999692 0.0248182i \(-0.00790069\pi\)
\(132\) 0 0
\(133\) 11.7308 4.85905i 1.01719 0.421333i
\(134\) 9.04973 + 11.2714i 0.781778 + 0.973704i
\(135\) 0 0
\(136\) −0.110789 1.67597i −0.00950010 0.143713i
\(137\) −7.55484 7.55484i −0.645454 0.645454i 0.306437 0.951891i \(-0.400863\pi\)
−0.951891 + 0.306437i \(0.900863\pi\)
\(138\) 0 0
\(139\) 2.37282 + 5.72849i 0.201260 + 0.485884i 0.991995 0.126273i \(-0.0403017\pi\)
−0.790736 + 0.612158i \(0.790302\pi\)
\(140\) 17.1638 3.03303i 1.45060 0.256338i
\(141\) 0 0
\(142\) 6.02857 + 20.6688i 0.505907 + 1.73448i
\(143\) 5.56480i 0.465352i
\(144\) 0 0
\(145\) 28.0981i 2.33342i
\(146\) 7.82998 2.28381i 0.648014 0.189010i
\(147\) 0 0
\(148\) −2.57780 1.80356i −0.211893 0.148252i
\(149\) −7.03565 16.9856i −0.576383 1.39151i −0.896038 0.443977i \(-0.853567\pi\)
0.319655 0.947534i \(-0.396433\pi\)
\(150\) 0 0
\(151\) −15.9489 15.9489i −1.29790 1.29790i −0.929775 0.368129i \(-0.879998\pi\)
−0.368129 0.929775i \(-0.620002\pi\)
\(152\) 14.9750 + 5.07401i 1.21464 + 0.411557i
\(153\) 0 0
\(154\) −2.27285 + 1.82485i −0.183152 + 0.147051i
\(155\) −24.4789 + 10.1395i −1.96619 + 0.814423i
\(156\) 0 0
\(157\) 0.0755402 0.182370i 0.00602876 0.0145547i −0.920836 0.389949i \(-0.872493\pi\)
0.926865 + 0.375394i \(0.122493\pi\)
\(158\) −9.48237 5.19991i −0.754377 0.413683i
\(159\) 0 0
\(160\) 18.5658 + 11.2423i 1.46775 + 0.888785i
\(161\) 0.0646160 0.00509245
\(162\) 0 0
\(163\) −3.11179 + 7.51254i −0.243735 + 0.588427i −0.997648 0.0685466i \(-0.978164\pi\)
0.753913 + 0.656974i \(0.228164\pi\)
\(164\) 5.47114 24.7223i 0.427224 1.93049i
\(165\) 0 0
\(166\) −3.18766 + 2.55935i −0.247411 + 0.198644i
\(167\) −2.05729 + 2.05729i −0.159198 + 0.159198i −0.782211 0.623013i \(-0.785908\pi\)
0.623013 + 0.782211i \(0.285908\pi\)
\(168\) 0 0
\(169\) 17.4015 + 17.4015i 1.33858 + 1.33858i
\(170\) −3.20312 0.350195i −0.245668 0.0268587i
\(171\) 0 0
\(172\) 7.67430 10.9687i 0.585160 0.836358i
\(173\) 10.0549 + 4.16489i 0.764462 + 0.316650i 0.730627 0.682777i \(-0.239228\pi\)
0.0338350 + 0.999427i \(0.489228\pi\)
\(174\) 0 0
\(175\) 22.0804i 1.66912i
\(176\) −3.62629 0.155621i −0.273342 0.0117303i
\(177\) 0 0
\(178\) −2.09867 7.19522i −0.157302 0.539305i
\(179\) −6.17617 2.55825i −0.461628 0.191213i 0.139734 0.990189i \(-0.455375\pi\)
−0.601362 + 0.798976i \(0.705375\pi\)
\(180\) 0 0
\(181\) 3.25743 + 7.86412i 0.242123 + 0.584536i 0.997493 0.0707622i \(-0.0225431\pi\)
−0.755371 + 0.655298i \(0.772543\pi\)
\(182\) 2.14096 19.5827i 0.158699 1.45157i
\(183\) 0 0
\(184\) 0.0605249 + 0.0530191i 0.00446195 + 0.00390862i
\(185\) −4.26773 + 4.26773i −0.313770 + 0.313770i
\(186\) 0 0
\(187\) 0.497834 0.206210i 0.0364052 0.0150795i
\(188\) −4.44217 + 2.83230i −0.323979 + 0.206567i
\(189\) 0 0
\(190\) 14.5847 26.5961i 1.05808 1.92948i
\(191\) −10.9258 −0.790560 −0.395280 0.918561i \(-0.629352\pi\)
−0.395280 + 0.918561i \(0.629352\pi\)
\(192\) 0 0
\(193\) −1.25358 −0.0902347 −0.0451174 0.998982i \(-0.514366\pi\)
−0.0451174 + 0.998982i \(0.514366\pi\)
\(194\) −9.85959 + 17.9796i −0.707877 + 1.29086i
\(195\) 0 0
\(196\) 3.10438 1.97933i 0.221741 0.141381i
\(197\) 24.4641 10.1334i 1.74300 0.721973i 0.744474 0.667651i \(-0.232700\pi\)
0.998523 0.0543220i \(-0.0172998\pi\)
\(198\) 0 0
\(199\) −10.5918 + 10.5918i −0.750835 + 0.750835i −0.974635 0.223800i \(-0.928154\pi\)
0.223800 + 0.974635i \(0.428154\pi\)
\(200\) 18.1176 20.6824i 1.28110 1.46247i
\(201\) 0 0
\(202\) −0.654547 + 5.98692i −0.0460537 + 0.421239i
\(203\) −6.36553 15.3677i −0.446773 1.07860i
\(204\) 0 0
\(205\) −44.8774 18.5888i −3.13437 1.29830i
\(206\) 5.62615 + 19.2891i 0.391992 + 1.34393i
\(207\) 0 0
\(208\) 18.0735 16.5861i 1.25317 1.15004i
\(209\) 5.07253i 0.350874i
\(210\) 0 0
\(211\) 15.0917 + 6.25117i 1.03895 + 0.430348i 0.835936 0.548827i \(-0.184925\pi\)
0.203017 + 0.979175i \(0.434925\pi\)
\(212\) 7.41513 10.5983i 0.509274 0.727895i
\(213\) 0 0
\(214\) 10.0142 + 1.09484i 0.684555 + 0.0748420i
\(215\) −18.1595 18.1595i −1.23847 1.23847i
\(216\) 0 0
\(217\) 11.0912 11.0912i 0.752921 0.752921i
\(218\) −3.64513 + 2.92664i −0.246879 + 0.198217i
\(219\) 0 0
\(220\) −1.50456 + 6.79861i −0.101437 + 0.458362i
\(221\) −1.39366 + 3.36458i −0.0937474 + 0.226326i
\(222\) 0 0
\(223\) −14.6420 −0.980501 −0.490250 0.871582i \(-0.663095\pi\)
−0.490250 + 0.871582i \(0.663095\pi\)
\(224\) −12.7011 1.94278i −0.848629 0.129808i
\(225\) 0 0
\(226\) 0.771685 + 0.423174i 0.0513317 + 0.0281491i
\(227\) 5.96486 14.4004i 0.395902 0.955791i −0.592726 0.805404i \(-0.701948\pi\)
0.988627 0.150387i \(-0.0480518\pi\)
\(228\) 0 0
\(229\) 1.61192 0.667680i 0.106519 0.0441215i −0.328788 0.944404i \(-0.606640\pi\)
0.435306 + 0.900282i \(0.356640\pi\)
\(230\) 0.120366 0.0966404i 0.00793667 0.00637228i
\(231\) 0 0
\(232\) 6.64713 19.6178i 0.436406 1.28797i
\(233\) −12.0945 12.0945i −0.792340 0.792340i 0.189534 0.981874i \(-0.439302\pi\)
−0.981874 + 0.189534i \(0.939302\pi\)
\(234\) 0 0
\(235\) 3.86767 + 9.33739i 0.252299 + 0.609104i
\(236\) 13.2452 + 9.26701i 0.862187 + 0.603231i
\(237\) 0 0
\(238\) 1.83123 0.534124i 0.118701 0.0346221i
\(239\) 22.9115i 1.48202i 0.671495 + 0.741009i \(0.265653\pi\)
−0.671495 + 0.741009i \(0.734347\pi\)
\(240\) 0 0
\(241\) 16.6684i 1.07371i −0.843676 0.536853i \(-0.819613\pi\)
0.843676 0.536853i \(-0.180387\pi\)
\(242\) 4.02985 + 13.8162i 0.259048 + 0.888139i
\(243\) 0 0
\(244\) 10.6525 1.88242i 0.681957 0.120509i
\(245\) −2.70289 6.52536i −0.172682 0.416890i
\(246\) 0 0
\(247\) −24.2413 24.2413i −1.54244 1.54244i
\(248\) 19.4896 1.28835i 1.23759 0.0818106i
\(249\) 0 0
\(250\) −16.0382 19.9756i −1.01435 1.26337i
\(251\) −2.62614 + 1.08778i −0.165761 + 0.0686603i −0.464021 0.885824i \(-0.653594\pi\)
0.298260 + 0.954485i \(0.403594\pi\)
\(252\) 0 0
\(253\) −0.00987852 + 0.0238489i −0.000621057 + 0.00149937i
\(254\) −6.69748 + 12.2133i −0.420238 + 0.766330i
\(255\) 0 0
\(256\) −10.3029 12.2414i −0.643928 0.765086i
\(257\) 11.2410 0.701196 0.350598 0.936526i \(-0.385978\pi\)
0.350598 + 0.936526i \(0.385978\pi\)
\(258\) 0 0
\(259\) 1.36732 3.30100i 0.0849610 0.205114i
\(260\) −25.2999 39.6803i −1.56904 2.46087i
\(261\) 0 0
\(262\) 8.21841 + 10.2360i 0.507735 + 0.632383i
\(263\) −17.3998 + 17.3998i −1.07292 + 1.07292i −0.0757955 + 0.997123i \(0.524150\pi\)
−0.997123 + 0.0757955i \(0.975850\pi\)
\(264\) 0 0
\(265\) −17.5463 17.5463i −1.07786 1.07786i
\(266\) −1.95157 + 17.8503i −0.119658 + 1.09448i
\(267\) 0 0
\(268\) −20.1304 + 3.55726i −1.22966 + 0.217294i
\(269\) 20.2847 + 8.40222i 1.23678 + 0.512292i 0.902708 0.430254i \(-0.141576\pi\)
0.334075 + 0.942547i \(0.391576\pi\)
\(270\) 0 0
\(271\) 4.06118i 0.246699i −0.992363 0.123350i \(-0.960636\pi\)
0.992363 0.123350i \(-0.0393637\pi\)
\(272\) 2.15355 + 1.00226i 0.130578 + 0.0607711i
\(273\) 0 0
\(274\) 14.5053 4.23083i 0.876295 0.255594i
\(275\) 8.14958 + 3.37567i 0.491438 + 0.203560i
\(276\) 0 0
\(277\) −5.72498 13.8213i −0.343981 0.830443i −0.997305 0.0733652i \(-0.976626\pi\)
0.653324 0.757078i \(-0.273374\pi\)
\(278\) −8.71686 0.953008i −0.522802 0.0571576i
\(279\) 0 0
\(280\) −7.91023 + 23.3456i −0.472726 + 1.39517i
\(281\) 5.96575 5.96575i 0.355887 0.355887i −0.506408 0.862294i \(-0.669027\pi\)
0.862294 + 0.506408i \(0.169027\pi\)
\(282\) 0 0
\(283\) −19.7761 + 8.19155i −1.17557 + 0.486937i −0.883030 0.469316i \(-0.844500\pi\)
−0.292540 + 0.956253i \(0.594500\pi\)
\(284\) −29.7288 6.57909i −1.76408 0.390397i
\(285\) 0 0
\(286\) 6.90039 + 3.78401i 0.408028 + 0.223753i
\(287\) 28.7561 1.69742
\(288\) 0 0
\(289\) 16.6474 0.979256
\(290\) −34.8418 19.1064i −2.04598 1.12197i
\(291\) 0 0
\(292\) −2.49237 + 11.2622i −0.145855 + 0.659070i
\(293\) −11.8575 + 4.91155i −0.692725 + 0.286936i −0.701135 0.713029i \(-0.747323\pi\)
0.00841001 + 0.999965i \(0.497323\pi\)
\(294\) 0 0
\(295\) 21.9283 21.9283i 1.27672 1.27672i
\(296\) 3.98930 1.97008i 0.231873 0.114508i
\(297\) 0 0
\(298\) 25.8464 + 2.82577i 1.49724 + 0.163692i
\(299\) −0.0667634 0.161181i −0.00386103 0.00932135i
\(300\) 0 0
\(301\) 14.0460 + 5.81805i 0.809598 + 0.335347i
\(302\) 30.6218 8.93164i 1.76209 0.513958i
\(303\) 0 0
\(304\) −16.4747 + 15.1189i −0.944888 + 0.867126i
\(305\) 20.7525i 1.18828i
\(306\) 0 0
\(307\) 21.0702 + 8.72756i 1.20254 + 0.498108i 0.891819 0.452393i \(-0.149430\pi\)
0.310721 + 0.950501i \(0.399430\pi\)
\(308\) −0.717311 4.05923i −0.0408726 0.231296i
\(309\) 0 0
\(310\) 4.07238 37.2487i 0.231295 2.11558i
\(311\) −2.17719 2.17719i −0.123457 0.123457i 0.642679 0.766136i \(-0.277823\pi\)
−0.766136 + 0.642679i \(0.777823\pi\)
\(312\) 0 0
\(313\) −9.67647 + 9.67647i −0.546946 + 0.546946i −0.925556 0.378610i \(-0.876402\pi\)
0.378610 + 0.925556i \(0.376402\pi\)
\(314\) 0.174773 + 0.217680i 0.00986303 + 0.0122844i
\(315\) 0 0
\(316\) 12.8958 8.22231i 0.725447 0.462541i
\(317\) −2.56261 + 6.18669i −0.143931 + 0.347479i −0.979362 0.202116i \(-0.935218\pi\)
0.835431 + 0.549596i \(0.185218\pi\)
\(318\) 0 0
\(319\) 6.64519 0.372059
\(320\) −26.5651 + 15.3770i −1.48503 + 0.859598i
\(321\) 0 0
\(322\) −0.0439382 + 0.0801242i −0.00244858 + 0.00446515i
\(323\) 1.27037 3.06694i 0.0706852 0.170649i
\(324\) 0 0
\(325\) −55.0785 + 22.8142i −3.05520 + 1.26551i
\(326\) −7.19960 8.96709i −0.398749 0.496641i
\(327\) 0 0
\(328\) 26.9354 + 23.5951i 1.48726 + 1.30282i
\(329\) −4.23071 4.23071i −0.233247 0.233247i
\(330\) 0 0
\(331\) 8.91192 + 21.5153i 0.489844 + 1.18259i 0.954799 + 0.297253i \(0.0960704\pi\)
−0.464955 + 0.885334i \(0.653930\pi\)
\(332\) −1.00602 5.69305i −0.0552128 0.312447i
\(333\) 0 0
\(334\) −1.15211 3.94998i −0.0630408 0.216133i
\(335\) 39.2166i 2.14263i
\(336\) 0 0
\(337\) 11.4661i 0.624597i −0.949984 0.312299i \(-0.898901\pi\)
0.949984 0.312299i \(-0.101099\pi\)
\(338\) −33.4108 + 9.74510i −1.81731 + 0.530064i
\(339\) 0 0
\(340\) 2.61233 3.73376i 0.141674 0.202492i
\(341\) 2.39799 + 5.78925i 0.129858 + 0.313505i
\(342\) 0 0
\(343\) 14.1993 + 14.1993i 0.766692 + 0.766692i
\(344\) 8.38284 + 16.9748i 0.451972 + 0.915220i
\(345\) 0 0
\(346\) −12.0017 + 9.63608i −0.645217 + 0.518039i
\(347\) 29.6276 12.2721i 1.59049 0.658803i 0.600460 0.799655i \(-0.294984\pi\)
0.990031 + 0.140852i \(0.0449843\pi\)
\(348\) 0 0
\(349\) −10.9206 + 26.3647i −0.584567 + 1.41127i 0.304065 + 0.952651i \(0.401656\pi\)
−0.888633 + 0.458620i \(0.848344\pi\)
\(350\) 27.3798 + 15.0145i 1.46351 + 0.802557i
\(351\) 0 0
\(352\) 2.65881 4.39079i 0.141715 0.234030i
\(353\) −2.15781 −0.114849 −0.0574243 0.998350i \(-0.518289\pi\)
−0.0574243 + 0.998350i \(0.518289\pi\)
\(354\) 0 0
\(355\) −22.3532 + 53.9654i −1.18639 + 2.86419i
\(356\) 10.3492 + 2.29032i 0.548506 + 0.121386i
\(357\) 0 0
\(358\) 7.37198 5.91889i 0.389621 0.312823i
\(359\) 6.11399 6.11399i 0.322684 0.322684i −0.527112 0.849796i \(-0.676725\pi\)
0.849796 + 0.527112i \(0.176725\pi\)
\(360\) 0 0
\(361\) 8.66183 + 8.66183i 0.455886 + 0.455886i
\(362\) −11.9666 1.30830i −0.628949 0.0687626i
\(363\) 0 0
\(364\) 22.8268 + 15.9708i 1.19645 + 0.837099i
\(365\) 20.4438 + 8.46810i 1.07008 + 0.443241i
\(366\) 0 0
\(367\) 10.3243i 0.538924i 0.963011 + 0.269462i \(0.0868459\pi\)
−0.963011 + 0.269462i \(0.913154\pi\)
\(368\) −0.106900 + 0.0389987i −0.00557256 + 0.00203295i
\(369\) 0 0
\(370\) −2.38999 8.19402i −0.124250 0.425987i
\(371\) 13.5717 + 5.62157i 0.704606 + 0.291857i
\(372\) 0 0
\(373\) −3.33636 8.05469i −0.172750 0.417056i 0.813664 0.581336i \(-0.197470\pi\)
−0.986414 + 0.164280i \(0.947470\pi\)
\(374\) −0.0828210 + 0.757537i −0.00428257 + 0.0391713i
\(375\) 0 0
\(376\) −0.491438 7.43425i −0.0253440 0.383392i
\(377\) −31.7570 + 31.7570i −1.63557 + 1.63557i
\(378\) 0 0
\(379\) −5.51425 + 2.28408i −0.283248 + 0.117325i −0.519785 0.854297i \(-0.673988\pi\)
0.236536 + 0.971623i \(0.423988\pi\)
\(380\) 23.0618 + 36.1701i 1.18305 + 1.85549i
\(381\) 0 0
\(382\) 7.42941 13.5480i 0.380122 0.693176i
\(383\) −9.23956 −0.472120 −0.236060 0.971739i \(-0.575856\pi\)
−0.236060 + 0.971739i \(0.575856\pi\)
\(384\) 0 0
\(385\) −7.90791 −0.403024
\(386\) 0.852422 1.55445i 0.0433872 0.0791193i
\(387\) 0 0
\(388\) −15.5904 24.4519i −0.791482 1.24136i
\(389\) 34.6091 14.3355i 1.75475 0.726841i 0.757491 0.652845i \(-0.226425\pi\)
0.997259 0.0739961i \(-0.0235752\pi\)
\(390\) 0 0
\(391\) 0.0119455 0.0119455i 0.000604109 0.000604109i
\(392\) 0.343438 + 5.19537i 0.0173462 + 0.262406i
\(393\) 0 0
\(394\) −4.06992 + 37.2263i −0.205040 + 1.87543i
\(395\) −11.2280 27.1069i −0.564944 1.36390i
\(396\) 0 0
\(397\) −15.6301 6.47420i −0.784452 0.324931i −0.0457415 0.998953i \(-0.514565\pi\)
−0.738711 + 0.674023i \(0.764565\pi\)
\(398\) −5.93159 20.3363i −0.297324 1.01936i
\(399\) 0 0
\(400\) 13.3265 + 36.5297i 0.666327 + 1.82648i
\(401\) 20.6019i 1.02881i 0.857548 + 0.514405i \(0.171987\pi\)
−0.857548 + 0.514405i \(0.828013\pi\)
\(402\) 0 0
\(403\) −39.1263 16.2067i −1.94902 0.807311i
\(404\) −6.97873 4.88269i −0.347205 0.242923i
\(405\) 0 0
\(406\) 23.3846 + 2.55662i 1.16056 + 0.126883i
\(407\) 1.00932 + 1.00932i 0.0500299 + 0.0500299i
\(408\) 0 0
\(409\) −1.39644 + 1.39644i −0.0690496 + 0.0690496i −0.740788 0.671739i \(-0.765548\pi\)
0.671739 + 0.740788i \(0.265548\pi\)
\(410\) 53.5664 43.0080i 2.64546 2.12401i
\(411\) 0 0
\(412\) −27.7443 6.13992i −1.36686 0.302492i
\(413\) −7.02552 + 16.9611i −0.345703 + 0.834601i
\(414\) 0 0
\(415\) −11.0908 −0.544426
\(416\) 8.27706 + 33.6896i 0.405816 + 1.65177i
\(417\) 0 0
\(418\) −6.28996 3.44927i −0.307652 0.168709i
\(419\) −3.15556 + 7.61820i −0.154159 + 0.372173i −0.982024 0.188754i \(-0.939555\pi\)
0.827865 + 0.560927i \(0.189555\pi\)
\(420\) 0 0
\(421\) −19.8735 + 8.23189i −0.968577 + 0.401198i −0.810182 0.586178i \(-0.800632\pi\)
−0.158395 + 0.987376i \(0.550632\pi\)
\(422\) −18.0137 + 14.4630i −0.876892 + 0.704048i
\(423\) 0 0
\(424\) 8.09975 + 16.4016i 0.393358 + 0.796530i
\(425\) −4.08198 4.08198i −0.198005 0.198005i
\(426\) 0 0
\(427\) 4.70141 + 11.3502i 0.227517 + 0.549275i
\(428\) −8.16715 + 11.6732i −0.394774 + 0.564243i
\(429\) 0 0
\(430\) 34.8662 10.1696i 1.68140 0.490423i
\(431\) 19.9125i 0.959153i 0.877500 + 0.479576i \(0.159210\pi\)
−0.877500 + 0.479576i \(0.840790\pi\)
\(432\) 0 0
\(433\) 4.68554i 0.225173i 0.993642 + 0.112586i \(0.0359135\pi\)
−0.993642 + 0.112586i \(0.964086\pi\)
\(434\) 6.21126 + 21.2951i 0.298150 + 1.02220i
\(435\) 0 0
\(436\) −1.15040 6.51007i −0.0550942 0.311776i
\(437\) 0.0608574 + 0.146923i 0.00291120 + 0.00702827i
\(438\) 0 0
\(439\) 19.8658 + 19.8658i 0.948142 + 0.948142i 0.998720 0.0505784i \(-0.0161065\pi\)
−0.0505784 + 0.998720i \(0.516106\pi\)
\(440\) −7.40723 6.48864i −0.353126 0.309334i
\(441\) 0 0
\(442\) −3.22443 4.01602i −0.153370 0.191023i
\(443\) −8.20972 + 3.40058i −0.390056 + 0.161566i −0.569088 0.822277i \(-0.692703\pi\)
0.179032 + 0.983843i \(0.442703\pi\)
\(444\) 0 0
\(445\) 7.78161 18.7865i 0.368884 0.890564i
\(446\) 9.95641 18.1562i 0.471450 0.859719i
\(447\) 0 0
\(448\) 11.0457 14.4284i 0.521860 0.681677i
\(449\) 24.2045 1.14228 0.571141 0.820852i \(-0.306501\pi\)
0.571141 + 0.820852i \(0.306501\pi\)
\(450\) 0 0
\(451\) −4.39625 + 10.6135i −0.207011 + 0.499770i
\(452\) −1.04948 + 0.669140i −0.0493632 + 0.0314737i
\(453\) 0 0
\(454\) 13.8006 + 17.1886i 0.647694 + 0.806702i
\(455\) 37.7914 37.7914i 1.77169 1.77169i
\(456\) 0 0
\(457\) 12.5941 + 12.5941i 0.589128 + 0.589128i 0.937395 0.348267i \(-0.113230\pi\)
−0.348267 + 0.937395i \(0.613230\pi\)
\(458\) −0.268164 + 2.45281i −0.0125305 + 0.114612i
\(459\) 0 0
\(460\) 0.0379873 + 0.214968i 0.00177117 + 0.0100230i
\(461\) 15.2109 + 6.30054i 0.708440 + 0.293446i 0.707659 0.706554i \(-0.249751\pi\)
0.000781253 1.00000i \(0.499751\pi\)
\(462\) 0 0
\(463\) 33.7363i 1.56786i −0.620849 0.783930i \(-0.713212\pi\)
0.620849 0.783930i \(-0.286788\pi\)
\(464\) 19.8062 + 21.5824i 0.919481 + 1.00194i
\(465\) 0 0
\(466\) 23.2215 6.77313i 1.07571 0.313759i
\(467\) 33.4989 + 13.8757i 1.55015 + 0.642091i 0.983343 0.181762i \(-0.0581801\pi\)
0.566803 + 0.823853i \(0.308180\pi\)
\(468\) 0 0
\(469\) −8.88439 21.4488i −0.410243 0.990414i
\(470\) −14.2084 1.55339i −0.655384 0.0716527i
\(471\) 0 0
\(472\) −20.4977 + 10.1226i −0.943484 + 0.465930i
\(473\) −4.29472 + 4.29472i −0.197472 + 0.197472i
\(474\) 0 0
\(475\) 50.2061 20.7960i 2.30361 0.954188i
\(476\) −0.582899 + 2.63393i −0.0267171 + 0.120726i
\(477\) 0 0
\(478\) −28.4103 15.5796i −1.29946 0.712592i
\(479\) −30.0639 −1.37365 −0.686827 0.726821i \(-0.740997\pi\)
−0.686827 + 0.726821i \(0.740997\pi\)
\(480\) 0 0
\(481\) −9.64693 −0.439862
\(482\) 20.6689 + 11.3343i 0.941443 + 0.516265i
\(483\) 0 0
\(484\) −19.8724 4.39784i −0.903292 0.199902i
\(485\) −51.3976 + 21.2896i −2.33384 + 0.966710i
\(486\) 0 0
\(487\) −25.9500 + 25.9500i −1.17590 + 1.17590i −0.195127 + 0.980778i \(0.562512\pi\)
−0.980778 + 0.195127i \(0.937488\pi\)
\(488\) −4.90939 + 14.4892i −0.222238 + 0.655895i
\(489\) 0 0
\(490\) 9.92943 + 1.08558i 0.448566 + 0.0490414i
\(491\) −7.04524 17.0087i −0.317947 0.767592i −0.999363 0.0356955i \(-0.988635\pi\)
0.681416 0.731897i \(-0.261365\pi\)
\(492\) 0 0
\(493\) −4.01780 1.66423i −0.180953 0.0749531i
\(494\) 46.5432 13.5755i 2.09408 0.610791i
\(495\) 0 0
\(496\) −11.6552 + 25.0433i −0.523333 + 1.12448i
\(497\) 34.5795i 1.55110i
\(498\) 0 0
\(499\) −24.3749 10.0964i −1.09117 0.451978i −0.236757 0.971569i \(-0.576084\pi\)
−0.854415 + 0.519591i \(0.826084\pi\)
\(500\) 35.6757 6.30430i 1.59547 0.281937i
\(501\) 0 0
\(502\) 0.436892 3.99611i 0.0194995 0.178355i
\(503\) −2.77268 2.77268i −0.123628 0.123628i 0.642586 0.766214i \(-0.277862\pi\)
−0.766214 + 0.642586i \(0.777862\pi\)
\(504\) 0 0
\(505\) −11.5538 + 11.5538i −0.514138 + 0.514138i
\(506\) −0.0228554 0.0284664i −0.00101605 0.00126549i
\(507\) 0 0
\(508\) −10.5903 16.6098i −0.469870 0.736942i
\(509\) −4.94920 + 11.9484i −0.219369 + 0.529604i −0.994802 0.101826i \(-0.967532\pi\)
0.775433 + 0.631430i \(0.217532\pi\)
\(510\) 0 0
\(511\) −13.0998 −0.579501
\(512\) 22.1852 4.45158i 0.980457 0.196734i
\(513\) 0 0
\(514\) −7.64378 + 13.9389i −0.337153 + 0.614820i
\(515\) −20.8611 + 50.3631i −0.919249 + 2.21926i
\(516\) 0 0
\(517\) 2.20829 0.914703i 0.0971205 0.0402286i
\(518\) 3.16349 + 3.94013i 0.138996 + 0.173119i
\(519\) 0 0
\(520\) 66.4076 4.38984i 2.91216 0.192507i
\(521\) 10.6270 + 10.6270i 0.465580 + 0.465580i 0.900479 0.434899i \(-0.143216\pi\)
−0.434899 + 0.900479i \(0.643216\pi\)
\(522\) 0 0
\(523\) −15.4746 37.3590i −0.676657 1.63360i −0.770064 0.637967i \(-0.779776\pi\)
0.0934064 0.995628i \(-0.470224\pi\)
\(524\) −18.2812 + 3.23048i −0.798616 + 0.141124i
\(525\) 0 0
\(526\) −9.74417 33.4076i −0.424866 1.45664i
\(527\) 4.10084i 0.178635i
\(528\) 0 0
\(529\) 22.9992i 0.999965i
\(530\) 33.6888 9.82619i 1.46335 0.426822i
\(531\) 0 0
\(532\) −20.8075 14.5580i −0.902119 0.631170i
\(533\) −29.7118 71.7306i −1.28696 3.10700i
\(534\) 0 0
\(535\) 19.3258 + 19.3258i 0.835525 + 0.835525i
\(536\) 9.27743 27.3807i 0.400724 1.18266i
\(537\) 0 0
\(538\) −24.2122 + 19.4398i −1.04386 + 0.838108i
\(539\) −1.54325 + 0.639233i −0.0664723 + 0.0275337i
\(540\) 0 0
\(541\) −4.99043 + 12.0480i −0.214555 + 0.517982i −0.994113 0.108348i \(-0.965444\pi\)
0.779558 + 0.626330i \(0.215444\pi\)
\(542\) 5.03589 + 2.76156i 0.216310 + 0.118619i
\(543\) 0 0
\(544\) −2.70720 + 1.98888i −0.116070 + 0.0852725i
\(545\) −12.6825 −0.543257
\(546\) 0 0
\(547\) 5.45215 13.1627i 0.233117 0.562795i −0.763424 0.645898i \(-0.776483\pi\)
0.996541 + 0.0831031i \(0.0264831\pi\)
\(548\) −4.61718 + 20.8635i −0.197236 + 0.891246i
\(549\) 0 0
\(550\) −9.72747 + 7.81010i −0.414781 + 0.333024i
\(551\) 28.9477 28.9477i 1.23321 1.23321i
\(552\) 0 0
\(553\) 12.2820 + 12.2820i 0.522282 + 0.522282i
\(554\) 21.0315 + 2.29936i 0.893541 + 0.0976903i
\(555\) 0 0
\(556\) 7.10911 10.1609i 0.301493 0.430919i
\(557\) −24.1244 9.99266i −1.02218 0.423403i −0.192299 0.981336i \(-0.561594\pi\)
−0.829885 + 0.557934i \(0.811594\pi\)
\(558\) 0 0
\(559\) 41.0484i 1.73616i
\(560\) −23.5698 25.6835i −0.996007 1.08533i
\(561\) 0 0
\(562\) 3.34091 + 11.4542i 0.140928 + 0.483166i
\(563\) 27.9136 + 11.5622i 1.17642 + 0.487288i 0.883309 0.468792i \(-0.155311\pi\)
0.293108 + 0.956079i \(0.405311\pi\)
\(564\) 0 0
\(565\) 0.913749 + 2.20599i 0.0384417 + 0.0928065i
\(566\) 3.29002 30.0927i 0.138290 1.26489i
\(567\) 0 0
\(568\) 28.3734 32.3901i 1.19052 1.35906i
\(569\) 7.42864 7.42864i 0.311425 0.311425i −0.534037 0.845461i \(-0.679326\pi\)
0.845461 + 0.534037i \(0.179326\pi\)
\(570\) 0 0
\(571\) −14.3745 + 5.95413i −0.601556 + 0.249173i −0.662613 0.748962i \(-0.730553\pi\)
0.0610576 + 0.998134i \(0.480553\pi\)
\(572\) −9.38439 + 5.98343i −0.392381 + 0.250180i
\(573\) 0 0
\(574\) −19.5539 + 35.6577i −0.816163 + 1.48833i
\(575\) 0.276547 0.0115328
\(576\) 0 0
\(577\) 28.4266 1.18342 0.591708 0.806153i \(-0.298454\pi\)
0.591708 + 0.806153i \(0.298454\pi\)
\(578\) −11.3200 + 20.6428i −0.470851 + 0.858628i
\(579\) 0 0
\(580\) 47.3841 30.2118i 1.96752 1.25448i
\(581\) 6.06592 2.51259i 0.251657 0.104240i
\(582\) 0 0
\(583\) −4.14969 + 4.14969i −0.171863 + 0.171863i
\(584\) −12.2704 10.7487i −0.507752 0.444785i
\(585\) 0 0
\(586\) 1.97265 18.0432i 0.0814896 0.745359i
\(587\) −3.24243 7.82792i −0.133829 0.323093i 0.842731 0.538334i \(-0.180946\pi\)
−0.976561 + 0.215241i \(0.930946\pi\)
\(588\) 0 0
\(589\) 35.6651 + 14.7730i 1.46956 + 0.608710i
\(590\) 12.2802 + 42.1023i 0.505568 + 1.73332i
\(591\) 0 0
\(592\) −0.269778 + 6.28639i −0.0110878 + 0.258369i
\(593\) 28.4410i 1.16793i 0.811779 + 0.583965i \(0.198500\pi\)
−0.811779 + 0.583965i \(0.801500\pi\)
\(594\) 0 0
\(595\) 4.78127 + 1.98047i 0.196013 + 0.0811912i
\(596\) −21.0792 + 30.1281i −0.863439 + 1.23410i
\(597\) 0 0
\(598\) 0.245264 + 0.0268146i 0.0100296 + 0.00109653i
\(599\) 30.7323 + 30.7323i 1.25569 + 1.25569i 0.953131 + 0.302559i \(0.0978410\pi\)
0.302559 + 0.953131i \(0.402159\pi\)
\(600\) 0 0
\(601\) −8.09508 + 8.09508i −0.330205 + 0.330205i −0.852664 0.522459i \(-0.825015\pi\)
0.522459 + 0.852664i \(0.325015\pi\)
\(602\) −16.7656 + 13.4609i −0.683313 + 0.548626i
\(603\) 0 0
\(604\) −9.74726 + 44.0447i −0.396610 + 1.79215i
\(605\) −14.9422 + 36.0736i −0.607486 + 1.46660i
\(606\) 0 0
\(607\) −27.7849 −1.12775 −0.563877 0.825859i \(-0.690691\pi\)
−0.563877 + 0.825859i \(0.690691\pi\)
\(608\) −7.54485 30.7094i −0.305984 1.24543i
\(609\) 0 0
\(610\) 25.7332 + 14.1115i 1.04191 + 0.571357i
\(611\) −6.18197 + 14.9246i −0.250096 + 0.603785i
\(612\) 0 0
\(613\) −1.11196 + 0.460588i −0.0449115 + 0.0186030i −0.405026 0.914305i \(-0.632738\pi\)
0.360115 + 0.932908i \(0.382738\pi\)
\(614\) −25.1497 + 20.1925i −1.01496 + 0.814903i
\(615\) 0 0
\(616\) 5.52123 + 1.87077i 0.222457 + 0.0753753i
\(617\) −5.18952 5.18952i −0.208922 0.208922i 0.594887 0.803809i \(-0.297197\pi\)
−0.803809 + 0.594887i \(0.797197\pi\)
\(618\) 0 0
\(619\) −12.4653 30.0938i −0.501022 1.20957i −0.948928 0.315493i \(-0.897830\pi\)
0.447906 0.894080i \(-0.352170\pi\)
\(620\) 43.4194 + 30.3785i 1.74377 + 1.22003i
\(621\) 0 0
\(622\) 4.18019 1.21926i 0.167610 0.0488879i
\(623\) 12.0378i 0.482285i
\(624\) 0 0
\(625\) 20.8952i 0.835807i
\(626\) −5.41897 18.5788i −0.216586 0.742557i
\(627\) 0 0
\(628\) −0.388769 + 0.0686997i −0.0155136 + 0.00274142i
\(629\) −0.357477 0.863025i −0.0142535 0.0344111i
\(630\) 0 0
\(631\) −11.7055 11.7055i −0.465990 0.465990i 0.434623 0.900613i \(-0.356882\pi\)
−0.900613 + 0.434623i \(0.856882\pi\)
\(632\) 1.42667 + 21.5820i 0.0567498 + 0.858486i
\(633\) 0 0
\(634\) −5.92898 7.38454i −0.235470 0.293278i
\(635\) −34.9137 + 14.4617i −1.38551 + 0.573896i
\(636\) 0 0
\(637\) 4.32022 10.4299i 0.171173 0.413249i
\(638\) −4.51866 + 8.24007i −0.178895 + 0.326227i
\(639\) 0 0
\(640\) −1.00353 43.3970i −0.0396680 1.71542i
\(641\) 9.09143 0.359090 0.179545 0.983750i \(-0.442537\pi\)
0.179545 + 0.983750i \(0.442537\pi\)
\(642\) 0 0
\(643\) −2.60708 + 6.29406i −0.102813 + 0.248213i −0.966913 0.255108i \(-0.917889\pi\)
0.864099 + 0.503322i \(0.167889\pi\)
\(644\) −0.0694769 0.108967i −0.00273777 0.00429391i
\(645\) 0 0
\(646\) 2.93919 + 3.66076i 0.115641 + 0.144030i
\(647\) −1.17619 + 1.17619i −0.0462409 + 0.0462409i −0.729849 0.683608i \(-0.760410\pi\)
0.683608 + 0.729849i \(0.260410\pi\)
\(648\) 0 0
\(649\) −5.18604 5.18604i −0.203570 0.203570i
\(650\) 9.16301 83.8110i 0.359403 3.28734i
\(651\) 0 0
\(652\) 16.0149 2.83001i 0.627192 0.110832i
\(653\) 21.8087 + 9.03346i 0.853440 + 0.353506i 0.766138 0.642676i \(-0.222176\pi\)
0.0873015 + 0.996182i \(0.472176\pi\)
\(654\) 0 0
\(655\) 35.6141i 1.39156i
\(656\) −47.5739 + 17.3556i −1.85745 + 0.677624i
\(657\) 0 0
\(658\) 8.12294 2.36926i 0.316665 0.0923635i
\(659\) −3.84511 1.59270i −0.149784 0.0620426i 0.306532 0.951860i \(-0.400831\pi\)
−0.456316 + 0.889818i \(0.650831\pi\)
\(660\) 0 0
\(661\) 8.39703 + 20.2722i 0.326607 + 0.788498i 0.998840 + 0.0481584i \(0.0153352\pi\)
−0.672233 + 0.740339i \(0.734665\pi\)
\(662\) −32.7391 3.57934i −1.27244 0.139115i
\(663\) 0 0
\(664\) 7.74350 + 2.62374i 0.300506 + 0.101821i
\(665\) −34.4483 + 34.4483i −1.33585 + 1.33585i
\(666\) 0 0
\(667\) 0.192474 0.0797253i 0.00745262 0.00308698i
\(668\) 5.68143 + 1.25732i 0.219821 + 0.0486472i
\(669\) 0 0
\(670\) −48.6288 26.6669i −1.87869 1.03023i
\(671\) −4.90796 −0.189470
\(672\) 0 0
\(673\) 21.0624 0.811897 0.405949 0.913896i \(-0.366941\pi\)
0.405949 + 0.913896i \(0.366941\pi\)
\(674\) 14.2180 + 7.79682i 0.547657 + 0.300322i
\(675\) 0 0
\(676\) 10.6350 48.0561i 0.409039 1.84831i
\(677\) −23.4192 + 9.70057i −0.900074 + 0.372823i −0.784249 0.620447i \(-0.786951\pi\)
−0.115826 + 0.993270i \(0.536951\pi\)
\(678\) 0 0
\(679\) 23.2879 23.2879i 0.893708 0.893708i
\(680\) 2.85352 + 5.77823i 0.109428 + 0.221585i
\(681\) 0 0
\(682\) −8.80931 0.963116i −0.337326 0.0368796i
\(683\) −9.64199 23.2778i −0.368940 0.890701i −0.993925 0.110064i \(-0.964895\pi\)
0.624984 0.780637i \(-0.285105\pi\)
\(684\) 0 0
\(685\) 37.8728 + 15.6874i 1.44704 + 0.599385i
\(686\) −27.2627 + 7.95185i −1.04089 + 0.303603i
\(687\) 0 0
\(688\) −26.7491 1.14793i −1.01980 0.0437643i
\(689\) 39.6622i 1.51101i
\(690\) 0 0
\(691\) 14.5099 + 6.01021i 0.551984 + 0.228639i 0.641201 0.767373i \(-0.278436\pi\)
−0.0892171 + 0.996012i \(0.528436\pi\)
\(692\) −3.78774 21.4347i −0.143988 0.814823i
\(693\) 0 0
\(694\) −4.92892 + 45.0833i −0.187099 + 1.71134i
\(695\) −16.8221 16.8221i −0.638100 0.638100i
\(696\) 0 0
\(697\) 5.31611 5.31611i 0.201362 0.201362i
\(698\) −25.2665 31.4694i −0.956350 1.19113i
\(699\) 0 0
\(700\) −37.2360 + 23.7415i −1.40739 + 0.897343i
\(701\) 15.0307 36.2872i 0.567700 1.37055i −0.335789 0.941937i \(-0.609003\pi\)
0.903489 0.428612i \(-0.140997\pi\)
\(702\) 0 0
\(703\) 8.79353 0.331654
\(704\) 3.63665 + 6.28263i 0.137061 + 0.236786i
\(705\) 0 0
\(706\) 1.46729 2.67569i 0.0552221 0.100701i
\(707\) 3.70167 8.93662i 0.139216 0.336096i
\(708\) 0 0
\(709\) −17.8505 + 7.39392i −0.670389 + 0.277684i −0.691803 0.722086i \(-0.743183\pi\)
0.0214137 + 0.999771i \(0.493183\pi\)
\(710\) −51.7175 64.4141i −1.94092 2.41742i
\(711\) 0 0
\(712\) −9.87735 + 11.2757i −0.370169 + 0.422573i
\(713\) 0.138912 + 0.138912i 0.00520231 + 0.00520231i
\(714\) 0 0
\(715\) 8.17072 + 19.7259i 0.305568 + 0.737706i
\(716\) 2.32659 + 13.1661i 0.0869488 + 0.492040i
\(717\) 0 0
\(718\) 3.42393 + 11.7388i 0.127780 + 0.438090i
\(719\) 15.1220i 0.563955i −0.959421 0.281977i \(-0.909010\pi\)
0.959421 0.281977i \(-0.0909903\pi\)
\(720\) 0 0
\(721\) 32.2712i 1.20184i
\(722\) −16.6307 + 4.85076i −0.618930 + 0.180527i
\(723\) 0 0
\(724\) 9.75945 13.9490i 0.362707 0.518410i
\(725\) −27.2435 65.7717i −1.01180 2.44270i
\(726\) 0 0
\(727\) −4.29348 4.29348i −0.159236 0.159236i 0.622992 0.782228i \(-0.285917\pi\)
−0.782228 + 0.622992i \(0.785917\pi\)
\(728\) −35.3259 + 17.4454i −1.30927 + 0.646568i
\(729\) 0 0
\(730\) −24.4021 + 19.5922i −0.903161 + 0.725140i
\(731\) 3.67224 1.52109i 0.135823 0.0562597i
\(732\) 0 0
\(733\) −3.86315 + 9.32647i −0.142689 + 0.344481i −0.979026 0.203734i \(-0.934692\pi\)
0.836338 + 0.548215i \(0.184692\pi\)
\(734\) −12.8022 7.02042i −0.472537 0.259128i
\(735\) 0 0
\(736\) 0.0243325 0.159076i 0.000896907 0.00586361i
\(737\) 9.27471 0.341638
\(738\) 0 0
\(739\) −7.81425 + 18.8653i −0.287452 + 0.693970i −0.999970 0.00768326i \(-0.997554\pi\)
0.712519 + 0.701653i \(0.247554\pi\)
\(740\) 11.7858 + 2.60824i 0.433255 + 0.0958809i
\(741\) 0 0
\(742\) −16.1994 + 13.0063i −0.594698 + 0.477478i
\(743\) 30.2898 30.2898i 1.11122 1.11122i 0.118239 0.992985i \(-0.462275\pi\)
0.992985 0.118239i \(-0.0377248\pi\)
\(744\) 0 0
\(745\) 49.8793 + 49.8793i 1.82744 + 1.82744i
\(746\) 12.2565 + 1.34000i 0.448744 + 0.0490609i
\(747\) 0 0
\(748\) −0.883033 0.617816i −0.0322869 0.0225896i
\(749\) −14.9481 6.19169i −0.546190 0.226239i
\(750\) 0 0
\(751\) 24.7308i 0.902439i −0.892413 0.451220i \(-0.850989\pi\)
0.892413 0.451220i \(-0.149011\pi\)
\(752\) 9.55269 + 4.44583i 0.348351 + 0.162123i
\(753\) 0 0
\(754\) −17.7844 60.9732i −0.647669 2.22051i
\(755\) 79.9526 + 33.1174i 2.90977 + 1.20527i
\(756\) 0 0
\(757\) −0.536814 1.29598i −0.0195109 0.0471034i 0.913824 0.406111i \(-0.133115\pi\)
−0.933335 + 0.359007i \(0.883115\pi\)
\(758\) 0.917367 8.39086i 0.0333203 0.304770i
\(759\) 0 0
\(760\) −60.5330 + 4.00151i −2.19576 + 0.145150i
\(761\) 32.7299 32.7299i 1.18646 1.18646i 0.208416 0.978040i \(-0.433169\pi\)
0.978040 0.208416i \(-0.0668308\pi\)
\(762\) 0 0
\(763\) 6.93645 2.87317i 0.251116 0.104016i
\(764\) 11.7477 + 18.4250i 0.425016 + 0.666593i
\(765\) 0 0
\(766\) 6.28281 11.4571i 0.227007 0.413962i
\(767\) 49.5676 1.78978
\(768\) 0 0
\(769\) 9.81757 0.354031 0.177015 0.984208i \(-0.443356\pi\)
0.177015 + 0.984208i \(0.443356\pi\)
\(770\) 5.37730 9.80585i 0.193784 0.353378i
\(771\) 0 0
\(772\) 1.34788 + 2.11402i 0.0485114 + 0.0760851i
\(773\) −21.7629 + 9.01448i −0.782756 + 0.324228i −0.738027 0.674771i \(-0.764242\pi\)
−0.0447290 + 0.998999i \(0.514242\pi\)
\(774\) 0 0
\(775\) 47.4688 47.4688i 1.70513 1.70513i
\(776\) 40.9218 2.70512i 1.46901 0.0971081i
\(777\) 0 0
\(778\) −5.75766 + 52.6635i −0.206422 + 1.88808i
\(779\) 27.0834 + 65.3852i 0.970364 + 2.34267i
\(780\) 0 0
\(781\) 12.7628 + 5.28653i 0.456689 + 0.189167i
\(782\) 0.00668965 + 0.0229353i 0.000239221 + 0.000820163i
\(783\) 0 0
\(784\) −6.67582 3.10693i −0.238422 0.110962i
\(785\) 0.757372i 0.0270318i
\(786\) 0 0
\(787\) −1.27278 0.527202i −0.0453697 0.0187927i 0.359883 0.932997i \(-0.382817\pi\)
−0.405253 + 0.914205i \(0.632817\pi\)
\(788\) −43.3933 30.3602i −1.54582 1.08154i