Properties

Label 288.2.w.a.35.2
Level $288$
Weight $2$
Character 288.35
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 35.2
Character \(\chi\) \(=\) 288.35
Dual form 288.2.w.a.107.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.33776 - 0.458699i) q^{2} +(1.57919 + 1.22726i) q^{4} +(-2.70076 + 1.11869i) q^{5} +(-1.06647 - 1.06647i) q^{7} +(-1.54963 - 2.36614i) q^{8} +O(q^{10})\) \(q+(-1.33776 - 0.458699i) q^{2} +(1.57919 + 1.22726i) q^{4} +(-2.70076 + 1.11869i) q^{5} +(-1.06647 - 1.06647i) q^{7} +(-1.54963 - 2.36614i) q^{8} +(4.12611 - 0.257702i) q^{10} +(5.29504 - 2.19328i) q^{11} +(1.67540 - 4.04478i) q^{13} +(0.937494 + 1.91588i) q^{14} +(0.987684 + 3.87614i) q^{16} +3.44484 q^{17} +(3.23205 + 1.33876i) q^{19} +(-5.63794 - 1.54790i) q^{20} +(-8.08953 + 0.505243i) q^{22} +(0.703083 + 0.703083i) q^{23} +(2.50711 - 2.50711i) q^{25} +(-4.09662 + 4.64243i) q^{26} +(-0.375329 - 2.99300i) q^{28} +(3.94721 - 9.52941i) q^{29} +4.23846i q^{31} +(0.456702 - 5.63839i) q^{32} +(-4.60837 - 1.58015i) q^{34} +(4.07335 + 1.68724i) q^{35} +(-2.04600 - 4.93947i) q^{37} +(-3.70961 - 3.27347i) q^{38} +(6.83218 + 4.65683i) q^{40} +(-3.53573 + 3.53573i) q^{41} +(-3.38340 - 8.16825i) q^{43} +(11.0536 + 3.03477i) q^{44} +(-0.618051 - 1.26306i) q^{46} +4.33671i q^{47} -4.72526i q^{49} +(-4.50391 + 2.20390i) q^{50} +(7.60977 - 4.33133i) q^{52} +(-0.541366 - 1.30697i) q^{53} +(-11.8470 + 11.8470i) q^{55} +(-0.870790 + 4.17608i) q^{56} +(-9.65155 + 10.9375i) q^{58} +(3.66093 + 8.83827i) q^{59} +(-1.97197 - 0.816817i) q^{61} +(1.94418 - 5.67003i) q^{62} +(-3.19728 + 7.33331i) q^{64} +12.7983i q^{65} +(-3.55849 + 8.59096i) q^{67} +(5.44006 + 4.22771i) q^{68} +(-4.67522 - 4.12556i) q^{70} +(-1.76501 + 1.76501i) q^{71} +(-1.16342 - 1.16342i) q^{73} +(0.471315 + 7.54631i) q^{74} +(3.46102 + 6.08071i) q^{76} +(-7.98610 - 3.30795i) q^{77} +14.4770 q^{79} +(-7.00371 - 9.36362i) q^{80} +(6.35178 - 3.10811i) q^{82} +(4.27230 - 10.3143i) q^{83} +(-9.30371 + 3.85372i) q^{85} +(0.779399 + 12.4791i) q^{86} +(-13.3950 - 9.13005i) q^{88} +(-7.99481 - 7.99481i) q^{89} +(-6.10044 + 2.52688i) q^{91} +(0.247439 + 1.97317i) q^{92} +(1.98925 - 5.80147i) q^{94} -10.2267 q^{95} +12.8450 q^{97} +(-2.16747 + 6.32126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33776 0.458699i −0.945937 0.324349i
\(3\) 0 0
\(4\) 1.57919 + 1.22726i 0.789595 + 0.613628i
\(5\) −2.70076 + 1.11869i −1.20782 + 0.500294i −0.893517 0.449029i \(-0.851770\pi\)
−0.314300 + 0.949324i \(0.601770\pi\)
\(6\) 0 0
\(7\) −1.06647 1.06647i −0.403090 0.403090i 0.476231 0.879320i \(-0.342003\pi\)
−0.879320 + 0.476231i \(0.842003\pi\)
\(8\) −1.54963 2.36614i −0.547878 0.836558i
\(9\) 0 0
\(10\) 4.12611 0.257702i 1.30479 0.0814925i
\(11\) 5.29504 2.19328i 1.59651 0.661297i 0.605596 0.795772i \(-0.292935\pi\)
0.990917 + 0.134475i \(0.0429346\pi\)
\(12\) 0 0
\(13\) 1.67540 4.04478i 0.464674 1.12182i −0.501783 0.864993i \(-0.667323\pi\)
0.966457 0.256828i \(-0.0826774\pi\)
\(14\) 0.937494 + 1.91588i 0.250556 + 0.512039i
\(15\) 0 0
\(16\) 0.987684 + 3.87614i 0.246921 + 0.969036i
\(17\) 3.44484 0.835498 0.417749 0.908563i \(-0.362819\pi\)
0.417749 + 0.908563i \(0.362819\pi\)
\(18\) 0 0
\(19\) 3.23205 + 1.33876i 0.741483 + 0.307132i 0.721261 0.692663i \(-0.243563\pi\)
0.0202218 + 0.999796i \(0.493563\pi\)
\(20\) −5.63794 1.54790i −1.26068 0.346121i
\(21\) 0 0
\(22\) −8.08953 + 0.505243i −1.72469 + 0.107718i
\(23\) 0.703083 + 0.703083i 0.146603 + 0.146603i 0.776599 0.629996i \(-0.216943\pi\)
−0.629996 + 0.776599i \(0.716943\pi\)
\(24\) 0 0
\(25\) 2.50711 2.50711i 0.501422 0.501422i
\(26\) −4.09662 + 4.64243i −0.803414 + 0.910456i
\(27\) 0 0
\(28\) −0.375329 2.99300i −0.0709304 0.565625i
\(29\) 3.94721 9.52941i 0.732979 1.76957i 0.100574 0.994930i \(-0.467932\pi\)
0.632405 0.774638i \(-0.282068\pi\)
\(30\) 0 0
\(31\) 4.23846i 0.761250i 0.924729 + 0.380625i \(0.124291\pi\)
−0.924729 + 0.380625i \(0.875709\pi\)
\(32\) 0.456702 5.63839i 0.0807343 0.996736i
\(33\) 0 0
\(34\) −4.60837 1.58015i −0.790328 0.270993i
\(35\) 4.07335 + 1.68724i 0.688522 + 0.285195i
\(36\) 0 0
\(37\) −2.04600 4.93947i −0.336360 0.812044i −0.998059 0.0622749i \(-0.980164\pi\)
0.661699 0.749769i \(-0.269836\pi\)
\(38\) −3.70961 3.27347i −0.601778 0.531027i
\(39\) 0 0
\(40\) 6.83218 + 4.65683i 1.08026 + 0.736310i
\(41\) −3.53573 + 3.53573i −0.552188 + 0.552188i −0.927072 0.374884i \(-0.877683\pi\)
0.374884 + 0.927072i \(0.377683\pi\)
\(42\) 0 0
\(43\) −3.38340 8.16825i −0.515963 1.24565i −0.940364 0.340171i \(-0.889515\pi\)
0.424400 0.905475i \(-0.360485\pi\)
\(44\) 11.0536 + 3.03477i 1.66639 + 0.457508i
\(45\) 0 0
\(46\) −0.618051 1.26306i −0.0911267 0.186228i
\(47\) 4.33671i 0.632575i 0.948663 + 0.316287i \(0.102436\pi\)
−0.948663 + 0.316287i \(0.897564\pi\)
\(48\) 0 0
\(49\) 4.72526i 0.675038i
\(50\) −4.50391 + 2.20390i −0.636950 + 0.311678i
\(51\) 0 0
\(52\) 7.60977 4.33133i 1.05529 0.600648i
\(53\) −0.541366 1.30697i −0.0743624 0.179527i 0.882327 0.470636i \(-0.155976\pi\)
−0.956690 + 0.291110i \(0.905976\pi\)
\(54\) 0 0
\(55\) −11.8470 + 11.8470i −1.59745 + 1.59745i
\(56\) −0.870790 + 4.17608i −0.116364 + 0.558052i
\(57\) 0 0
\(58\) −9.65155 + 10.9375i −1.26731 + 1.43616i
\(59\) 3.66093 + 8.83827i 0.476613 + 1.15064i 0.961188 + 0.275895i \(0.0889743\pi\)
−0.484575 + 0.874750i \(0.661026\pi\)
\(60\) 0 0
\(61\) −1.97197 0.816817i −0.252485 0.104583i 0.252851 0.967505i \(-0.418632\pi\)
−0.505336 + 0.862922i \(0.668632\pi\)
\(62\) 1.94418 5.67003i 0.246911 0.720095i
\(63\) 0 0
\(64\) −3.19728 + 7.33331i −0.399660 + 0.916663i
\(65\) 12.7983i 1.58743i
\(66\) 0 0
\(67\) −3.55849 + 8.59096i −0.434739 + 1.04955i 0.543001 + 0.839732i \(0.317288\pi\)
−0.977740 + 0.209821i \(0.932712\pi\)
\(68\) 5.44006 + 4.22771i 0.659705 + 0.512685i
\(69\) 0 0
\(70\) −4.67522 4.12556i −0.558796 0.493098i
\(71\) −1.76501 + 1.76501i −0.209468 + 0.209468i −0.804041 0.594574i \(-0.797321\pi\)
0.594574 + 0.804041i \(0.297321\pi\)
\(72\) 0 0
\(73\) −1.16342 1.16342i −0.136168 0.136168i 0.635737 0.771905i \(-0.280696\pi\)
−0.771905 + 0.635737i \(0.780696\pi\)
\(74\) 0.471315 + 7.54631i 0.0547893 + 0.877241i
\(75\) 0 0
\(76\) 3.46102 + 6.08071i 0.397006 + 0.697505i
\(77\) −7.98610 3.30795i −0.910100 0.376976i
\(78\) 0 0
\(79\) 14.4770 1.62879 0.814393 0.580314i \(-0.197070\pi\)
0.814393 + 0.580314i \(0.197070\pi\)
\(80\) −7.00371 9.36362i −0.783039 1.04689i
\(81\) 0 0
\(82\) 6.35178 3.10811i 0.701437 0.343233i
\(83\) 4.27230 10.3143i 0.468946 1.13214i −0.495678 0.868507i \(-0.665080\pi\)
0.964624 0.263630i \(-0.0849197\pi\)
\(84\) 0 0
\(85\) −9.30371 + 3.85372i −1.00913 + 0.417995i
\(86\) 0.779399 + 12.4791i 0.0840448 + 1.34566i
\(87\) 0 0
\(88\) −13.3950 9.13005i −1.42791 0.973267i
\(89\) −7.99481 7.99481i −0.847448 0.847448i 0.142366 0.989814i \(-0.454529\pi\)
−0.989814 + 0.142366i \(0.954529\pi\)
\(90\) 0 0
\(91\) −6.10044 + 2.52688i −0.639500 + 0.264889i
\(92\) 0.247439 + 1.97317i 0.0257973 + 0.205717i
\(93\) 0 0
\(94\) 1.98925 5.80147i 0.205175 0.598376i
\(95\) −10.2267 −1.04923
\(96\) 0 0
\(97\) 12.8450 1.30421 0.652107 0.758127i \(-0.273885\pi\)
0.652107 + 0.758127i \(0.273885\pi\)
\(98\) −2.16747 + 6.32126i −0.218948 + 0.638543i
\(99\) 0 0
\(100\) 7.03607 0.882337i 0.703607 0.0882337i
\(101\) −0.195046 + 0.0807908i −0.0194078 + 0.00803898i −0.392366 0.919809i \(-0.628343\pi\)
0.372958 + 0.927848i \(0.378343\pi\)
\(102\) 0 0
\(103\) 7.52990 + 7.52990i 0.741943 + 0.741943i 0.972952 0.231009i \(-0.0742026\pi\)
−0.231009 + 0.972952i \(0.574203\pi\)
\(104\) −12.1668 + 2.30368i −1.19305 + 0.225894i
\(105\) 0 0
\(106\) 0.124709 + 1.99674i 0.0121128 + 0.193940i
\(107\) −6.43177 + 2.66413i −0.621783 + 0.257551i −0.671257 0.741225i \(-0.734245\pi\)
0.0494744 + 0.998775i \(0.484245\pi\)
\(108\) 0 0
\(109\) −4.89484 + 11.8172i −0.468840 + 1.13188i 0.495830 + 0.868420i \(0.334864\pi\)
−0.964670 + 0.263461i \(0.915136\pi\)
\(110\) 21.2827 10.4142i 2.02922 0.992958i
\(111\) 0 0
\(112\) 3.08047 5.18715i 0.291077 0.490139i
\(113\) −0.983568 −0.0925263 −0.0462631 0.998929i \(-0.514731\pi\)
−0.0462631 + 0.998929i \(0.514731\pi\)
\(114\) 0 0
\(115\) −2.68539 1.11233i −0.250414 0.103725i
\(116\) 17.9284 10.2045i 1.66461 0.947465i
\(117\) 0 0
\(118\) −0.843332 13.5027i −0.0776350 1.24303i
\(119\) −3.67384 3.67384i −0.336780 0.336780i
\(120\) 0 0
\(121\) 15.4488 15.4488i 1.40443 1.40443i
\(122\) 2.26335 + 1.99724i 0.204914 + 0.180822i
\(123\) 0 0
\(124\) −5.20168 + 6.69334i −0.467125 + 0.601079i
\(125\) 1.62704 3.92802i 0.145527 0.351333i
\(126\) 0 0
\(127\) 5.32766i 0.472754i −0.971661 0.236377i \(-0.924040\pi\)
0.971661 0.236377i \(-0.0759600\pi\)
\(128\) 7.64097 8.34360i 0.675372 0.737477i
\(129\) 0 0
\(130\) 5.87055 17.1210i 0.514882 1.50161i
\(131\) 17.7023 + 7.33252i 1.54666 + 0.640646i 0.982707 0.185165i \(-0.0592820\pi\)
0.563948 + 0.825811i \(0.309282\pi\)
\(132\) 0 0
\(133\) −2.01915 4.87465i −0.175082 0.422686i
\(134\) 8.70107 9.86034i 0.751658 0.851804i
\(135\) 0 0
\(136\) −5.33824 8.15100i −0.457750 0.698943i
\(137\) −10.0787 + 10.0787i −0.861079 + 0.861079i −0.991464 0.130384i \(-0.958379\pi\)
0.130384 + 0.991464i \(0.458379\pi\)
\(138\) 0 0
\(139\) −4.57378 11.0421i −0.387943 0.936578i −0.990375 0.138408i \(-0.955802\pi\)
0.602432 0.798170i \(-0.294198\pi\)
\(140\) 4.36192 + 7.66352i 0.368650 + 0.647685i
\(141\) 0 0
\(142\) 3.17076 1.55154i 0.266084 0.130203i
\(143\) 25.0919i 2.09829i
\(144\) 0 0
\(145\) 30.1524i 2.50402i
\(146\) 1.02271 + 2.09003i 0.0846404 + 0.172972i
\(147\) 0 0
\(148\) 2.83098 10.3113i 0.232705 0.847586i
\(149\) −2.47497 5.97511i −0.202758 0.489500i 0.789492 0.613761i \(-0.210344\pi\)
−0.992250 + 0.124261i \(0.960344\pi\)
\(150\) 0 0
\(151\) −5.28519 + 5.28519i −0.430103 + 0.430103i −0.888663 0.458560i \(-0.848365\pi\)
0.458560 + 0.888663i \(0.348365\pi\)
\(152\) −1.84079 9.72208i −0.149308 0.788565i
\(153\) 0 0
\(154\) 9.16611 + 8.08845i 0.738626 + 0.651786i
\(155\) −4.74153 11.4471i −0.380849 0.919451i
\(156\) 0 0
\(157\) 19.9431 + 8.26070i 1.59163 + 0.659276i 0.990201 0.139649i \(-0.0445973\pi\)
0.601431 + 0.798924i \(0.294597\pi\)
\(158\) −19.3667 6.64057i −1.54073 0.528295i
\(159\) 0 0
\(160\) 5.07418 + 15.7389i 0.401149 + 1.24427i
\(161\) 1.49964i 0.118188i
\(162\) 0 0
\(163\) 4.75817 11.4872i 0.372689 0.899751i −0.620604 0.784124i \(-0.713112\pi\)
0.993293 0.115626i \(-0.0368875\pi\)
\(164\) −9.92283 + 1.24434i −0.774843 + 0.0971668i
\(165\) 0 0
\(166\) −10.4464 + 11.8383i −0.810801 + 0.918828i
\(167\) −13.4711 + 13.4711i −1.04243 + 1.04243i −0.0433679 + 0.999059i \(0.513809\pi\)
−0.999059 + 0.0433679i \(0.986191\pi\)
\(168\) 0 0
\(169\) −4.36092 4.36092i −0.335455 0.335455i
\(170\) 14.2138 0.887743i 1.09015 0.0680868i
\(171\) 0 0
\(172\) 4.68150 17.0515i 0.356961 1.30017i
\(173\) −1.48659 0.615768i −0.113024 0.0468160i 0.325455 0.945558i \(-0.394483\pi\)
−0.438479 + 0.898742i \(0.644483\pi\)
\(174\) 0 0
\(175\) −5.34754 −0.404236
\(176\) 13.7313 + 18.3581i 1.03503 + 1.38379i
\(177\) 0 0
\(178\) 7.02791 + 14.3623i 0.526764 + 1.07650i
\(179\) 0.188898 0.456040i 0.0141189 0.0340860i −0.916663 0.399661i \(-0.869128\pi\)
0.930782 + 0.365575i \(0.119128\pi\)
\(180\) 0 0
\(181\) −20.2286 + 8.37896i −1.50358 + 0.622803i −0.974221 0.225596i \(-0.927567\pi\)
−0.529358 + 0.848398i \(0.677567\pi\)
\(182\) 9.31999 0.582093i 0.690843 0.0431476i
\(183\) 0 0
\(184\) 0.574076 2.75312i 0.0423215 0.202963i
\(185\) 11.0515 + 11.0515i 0.812522 + 0.812522i
\(186\) 0 0
\(187\) 18.2406 7.55549i 1.33388 0.552512i
\(188\) −5.32226 + 6.84850i −0.388166 + 0.499478i
\(189\) 0 0
\(190\) 13.6808 + 4.69096i 0.992509 + 0.340318i
\(191\) −23.3059 −1.68636 −0.843180 0.537632i \(-0.819319\pi\)
−0.843180 + 0.537632i \(0.819319\pi\)
\(192\) 0 0
\(193\) −27.0699 −1.94854 −0.974268 0.225392i \(-0.927634\pi\)
−0.974268 + 0.225392i \(0.927634\pi\)
\(194\) −17.1835 5.89200i −1.23371 0.423021i
\(195\) 0 0
\(196\) 5.79911 7.46209i 0.414222 0.533006i
\(197\) 0.234504 0.0971345i 0.0167077 0.00692055i −0.374314 0.927302i \(-0.622122\pi\)
0.391022 + 0.920381i \(0.372122\pi\)
\(198\) 0 0
\(199\) −2.87064 2.87064i −0.203494 0.203494i 0.598001 0.801495i \(-0.295962\pi\)
−0.801495 + 0.598001i \(0.795962\pi\)
\(200\) −9.81728 2.04709i −0.694187 0.144751i
\(201\) 0 0
\(202\) 0.297983 0.0186110i 0.0209660 0.00130946i
\(203\) −14.3725 + 5.95328i −1.00875 + 0.417838i
\(204\) 0 0
\(205\) 5.59377 13.5045i 0.390686 0.943199i
\(206\) −6.61922 13.5271i −0.461183 0.942480i
\(207\) 0 0
\(208\) 17.3329 + 2.49914i 1.20182 + 0.173284i
\(209\) 20.0501 1.38689
\(210\) 0 0
\(211\) 21.3966 + 8.86277i 1.47300 + 0.610138i 0.967542 0.252710i \(-0.0813219\pi\)
0.505462 + 0.862849i \(0.331322\pi\)
\(212\) 0.749072 2.72836i 0.0514465 0.187384i
\(213\) 0 0
\(214\) 9.82618 0.613708i 0.671704 0.0419522i
\(215\) 18.2755 + 18.2755i 1.24638 + 1.24638i
\(216\) 0 0
\(217\) 4.52021 4.52021i 0.306852 0.306852i
\(218\) 11.9686 13.5633i 0.810618 0.918620i
\(219\) 0 0
\(220\) −33.2481 + 4.16937i −2.24158 + 0.281099i
\(221\) 5.77151 13.9337i 0.388234 0.937279i
\(222\) 0 0
\(223\) 6.32748i 0.423720i 0.977300 + 0.211860i \(0.0679520\pi\)
−0.977300 + 0.211860i \(0.932048\pi\)
\(224\) −6.50026 + 5.52614i −0.434317 + 0.369231i
\(225\) 0 0
\(226\) 1.31578 + 0.451162i 0.0875241 + 0.0300108i
\(227\) −6.62883 2.74575i −0.439971 0.182242i 0.151691 0.988428i \(-0.451528\pi\)
−0.591662 + 0.806186i \(0.701528\pi\)
\(228\) 0 0
\(229\) −2.56839 6.20065i −0.169724 0.409751i 0.816015 0.578031i \(-0.196179\pi\)
−0.985739 + 0.168280i \(0.946179\pi\)
\(230\) 3.08218 + 2.71981i 0.203233 + 0.179339i
\(231\) 0 0
\(232\) −28.6647 + 5.42741i −1.88193 + 0.356327i
\(233\) 4.72679 4.72679i 0.309662 0.309662i −0.535116 0.844779i \(-0.679732\pi\)
0.844779 + 0.535116i \(0.179732\pi\)
\(234\) 0 0
\(235\) −4.85145 11.7124i −0.316474 0.764035i
\(236\) −5.06552 + 18.4502i −0.329737 + 1.20101i
\(237\) 0 0
\(238\) 3.22952 + 6.59989i 0.209339 + 0.427808i
\(239\) 5.76879i 0.373152i 0.982441 + 0.186576i \(0.0597390\pi\)
−0.982441 + 0.186576i \(0.940261\pi\)
\(240\) 0 0
\(241\) 20.1679i 1.29913i 0.760308 + 0.649563i \(0.225048\pi\)
−0.760308 + 0.649563i \(0.774952\pi\)
\(242\) −27.7530 + 13.5804i −1.78403 + 0.872979i
\(243\) 0 0
\(244\) −2.11167 3.71002i −0.135186 0.237510i
\(245\) 5.28612 + 12.7618i 0.337718 + 0.815322i
\(246\) 0 0
\(247\) 10.8300 10.8300i 0.689095 0.689095i
\(248\) 10.0288 6.56806i 0.636830 0.417072i
\(249\) 0 0
\(250\) −3.97836 + 4.50842i −0.251614 + 0.285137i
\(251\) 0.288817 + 0.697266i 0.0182300 + 0.0440110i 0.932732 0.360569i \(-0.117418\pi\)
−0.914502 + 0.404580i \(0.867418\pi\)
\(252\) 0 0
\(253\) 5.26491 + 2.18080i 0.331002 + 0.137105i
\(254\) −2.44379 + 7.12712i −0.153337 + 0.447195i
\(255\) 0 0
\(256\) −14.0490 + 7.65681i −0.878060 + 0.478550i
\(257\) 6.89560i 0.430136i −0.976599 0.215068i \(-0.931003\pi\)
0.976599 0.215068i \(-0.0689973\pi\)
\(258\) 0 0
\(259\) −3.08582 + 7.44983i −0.191743 + 0.462910i
\(260\) −15.7068 + 20.2109i −0.974091 + 1.25343i
\(261\) 0 0
\(262\) −20.3179 17.9292i −1.25525 1.10767i
\(263\) 3.11571 3.11571i 0.192123 0.192123i −0.604490 0.796613i \(-0.706623\pi\)
0.796613 + 0.604490i \(0.206623\pi\)
\(264\) 0 0
\(265\) 2.92420 + 2.92420i 0.179632 + 0.179632i
\(266\) 0.465130 + 7.44728i 0.0285190 + 0.456622i
\(267\) 0 0
\(268\) −16.1628 + 9.19958i −0.987303 + 0.561954i
\(269\) 12.4085 + 5.13977i 0.756560 + 0.313378i 0.727415 0.686198i \(-0.240721\pi\)
0.0291452 + 0.999575i \(0.490721\pi\)
\(270\) 0 0
\(271\) 5.94627 0.361210 0.180605 0.983556i \(-0.442194\pi\)
0.180605 + 0.983556i \(0.442194\pi\)
\(272\) 3.40242 + 13.3527i 0.206302 + 0.809627i
\(273\) 0 0
\(274\) 18.1059 8.85974i 1.09382 0.535237i
\(275\) 7.77645 18.7740i 0.468938 1.13212i
\(276\) 0 0
\(277\) −8.48544 + 3.51479i −0.509841 + 0.211183i −0.622748 0.782423i \(-0.713984\pi\)
0.112907 + 0.993606i \(0.463984\pi\)
\(278\) 1.05362 + 16.8696i 0.0631917 + 1.01177i
\(279\) 0 0
\(280\) −2.31995 12.2527i −0.138643 0.732241i
\(281\) 12.5190 + 12.5190i 0.746823 + 0.746823i 0.973881 0.227058i \(-0.0729107\pi\)
−0.227058 + 0.973881i \(0.572911\pi\)
\(282\) 0 0
\(283\) −16.8466 + 6.97810i −1.00143 + 0.414805i −0.822321 0.569024i \(-0.807321\pi\)
−0.179107 + 0.983830i \(0.557321\pi\)
\(284\) −4.95340 + 0.621166i −0.293930 + 0.0368594i
\(285\) 0 0
\(286\) −11.5096 + 33.5669i −0.680579 + 1.98485i
\(287\) 7.54153 0.445162
\(288\) 0 0
\(289\) −5.13305 −0.301944
\(290\) 13.8309 40.3366i 0.812177 2.36865i
\(291\) 0 0
\(292\) −0.409447 3.26508i −0.0239611 0.191074i
\(293\) 1.86190 0.771224i 0.108773 0.0450554i −0.327633 0.944805i \(-0.606251\pi\)
0.436406 + 0.899750i \(0.356251\pi\)
\(294\) 0 0
\(295\) −19.7746 19.7746i −1.15132 1.15132i
\(296\) −8.51696 + 12.4955i −0.495038 + 0.726285i
\(297\) 0 0
\(298\) 0.570135 + 9.12852i 0.0330270 + 0.528801i
\(299\) 4.02177 1.66587i 0.232585 0.0963398i
\(300\) 0 0
\(301\) −5.10292 + 12.3195i −0.294127 + 0.710086i
\(302\) 9.49462 4.64599i 0.546354 0.267347i
\(303\) 0 0
\(304\) −1.99698 + 13.8502i −0.114534 + 0.794361i
\(305\) 6.23959 0.357278
\(306\) 0 0
\(307\) −3.70099 1.53300i −0.211227 0.0874930i 0.274561 0.961570i \(-0.411467\pi\)
−0.485788 + 0.874077i \(0.661467\pi\)
\(308\) −8.55186 15.0249i −0.487288 0.856121i
\(309\) 0 0
\(310\) 1.09226 + 17.4884i 0.0620362 + 0.993272i
\(311\) 9.17785 + 9.17785i 0.520428 + 0.520428i 0.917701 0.397273i \(-0.130043\pi\)
−0.397273 + 0.917701i \(0.630043\pi\)
\(312\) 0 0
\(313\) −8.66154 + 8.66154i −0.489579 + 0.489579i −0.908173 0.418594i \(-0.862523\pi\)
0.418594 + 0.908173i \(0.362523\pi\)
\(314\) −22.8899 20.1987i −1.29175 1.13988i
\(315\) 0 0
\(316\) 22.8619 + 17.7669i 1.28608 + 0.999469i
\(317\) −7.41379 + 17.8985i −0.416400 + 1.00528i 0.566982 + 0.823730i \(0.308111\pi\)
−0.983382 + 0.181548i \(0.941889\pi\)
\(318\) 0 0
\(319\) 59.1159i 3.30986i
\(320\) 0.431378 23.3823i 0.0241148 1.30711i
\(321\) 0 0
\(322\) −0.687884 + 2.00616i −0.0383343 + 0.111799i
\(323\) 11.1339 + 4.61182i 0.619507 + 0.256608i
\(324\) 0 0
\(325\) −5.94030 14.3411i −0.329508 0.795503i
\(326\) −11.6345 + 13.1846i −0.644374 + 0.730226i
\(327\) 0 0
\(328\) 13.8451 + 2.88697i 0.764469 + 0.159406i
\(329\) 4.62500 4.62500i 0.254984 0.254984i
\(330\) 0 0
\(331\) −3.96293 9.56736i −0.217822 0.525870i 0.776763 0.629793i \(-0.216860\pi\)
−0.994585 + 0.103923i \(0.966860\pi\)
\(332\) 19.4050 11.0450i 1.06499 0.606171i
\(333\) 0 0
\(334\) 24.2003 11.8419i 1.32418 0.647960i
\(335\) 27.1830i 1.48517i
\(336\) 0 0
\(337\) 7.50723i 0.408945i −0.978872 0.204472i \(-0.934452\pi\)
0.978872 0.204472i \(-0.0655479\pi\)
\(338\) 3.83350 + 7.83420i 0.208515 + 0.426124i
\(339\) 0 0
\(340\) −19.4218 5.33227i −1.05330 0.289183i
\(341\) 9.29611 + 22.4428i 0.503413 + 1.21535i
\(342\) 0 0
\(343\) −12.5047 + 12.5047i −0.675190 + 0.675190i
\(344\) −14.0842 + 20.6634i −0.759371 + 1.11410i
\(345\) 0 0
\(346\) 1.70625 + 1.50565i 0.0917286 + 0.0809441i
\(347\) 1.18203 + 2.85368i 0.0634548 + 0.153194i 0.952426 0.304769i \(-0.0985793\pi\)
−0.888971 + 0.457963i \(0.848579\pi\)
\(348\) 0 0
\(349\) 3.41473 + 1.41443i 0.182786 + 0.0757126i 0.472200 0.881492i \(-0.343460\pi\)
−0.289413 + 0.957204i \(0.593460\pi\)
\(350\) 7.15371 + 2.45291i 0.382382 + 0.131114i
\(351\) 0 0
\(352\) −9.94829 30.8571i −0.530245 1.64469i
\(353\) 6.81226i 0.362580i 0.983430 + 0.181290i \(0.0580273\pi\)
−0.983430 + 0.181290i \(0.941973\pi\)
\(354\) 0 0
\(355\) 2.79236 6.74136i 0.148203 0.357794i
\(356\) −2.81365 22.4370i −0.149123 1.18916i
\(357\) 0 0
\(358\) −0.461884 + 0.523423i −0.0244114 + 0.0276638i
\(359\) 5.31414 5.31414i 0.280469 0.280469i −0.552827 0.833296i \(-0.686451\pi\)
0.833296 + 0.552827i \(0.186451\pi\)
\(360\) 0 0
\(361\) −4.78116 4.78116i −0.251640 0.251640i
\(362\) 30.9044 1.93018i 1.62430 0.101448i
\(363\) 0 0
\(364\) −12.7349 3.49637i −0.667489 0.183260i
\(365\) 4.44363 + 1.84061i 0.232590 + 0.0963420i
\(366\) 0 0
\(367\) 29.3775 1.53349 0.766745 0.641951i \(-0.221875\pi\)
0.766745 + 0.641951i \(0.221875\pi\)
\(368\) −2.03083 + 3.41968i −0.105864 + 0.178263i
\(369\) 0 0
\(370\) −9.71491 19.8535i −0.505054 1.03214i
\(371\) −0.816501 + 1.97121i −0.0423906 + 0.102340i
\(372\) 0 0
\(373\) 14.6798 6.08058i 0.760092 0.314840i 0.0312402 0.999512i \(-0.490054\pi\)
0.728852 + 0.684671i \(0.240054\pi\)
\(374\) −27.8672 + 1.74048i −1.44098 + 0.0899982i
\(375\) 0 0
\(376\) 10.2613 6.72031i 0.529186 0.346574i
\(377\) −31.9312 31.9312i −1.64454 1.64454i
\(378\) 0 0
\(379\) −1.25001 + 0.517769i −0.0642085 + 0.0265960i −0.414557 0.910024i \(-0.636063\pi\)
0.350348 + 0.936620i \(0.386063\pi\)
\(380\) −16.1498 12.5507i −0.828469 0.643839i
\(381\) 0 0
\(382\) 31.1777 + 10.6904i 1.59519 + 0.546969i
\(383\) 35.2581 1.80160 0.900802 0.434230i \(-0.142980\pi\)
0.900802 + 0.434230i \(0.142980\pi\)
\(384\) 0 0
\(385\) 25.2691 1.28783
\(386\) 36.2130 + 12.4170i 1.84319 + 0.632006i
\(387\) 0 0
\(388\) 20.2847 + 15.7641i 1.02980 + 0.800303i
\(389\) 3.34556 1.38578i 0.169627 0.0702616i −0.296254 0.955109i \(-0.595738\pi\)
0.465881 + 0.884848i \(0.345738\pi\)
\(390\) 0 0
\(391\) 2.42201 + 2.42201i 0.122486 + 0.122486i
\(392\) −11.1807 + 7.32242i −0.564708 + 0.369838i
\(393\) 0 0
\(394\) −0.358264 + 0.0223759i −0.0180491 + 0.00112728i
\(395\) −39.0988 + 16.1953i −1.96728 + 0.814872i
\(396\) 0 0
\(397\) −2.21822 + 5.35526i −0.111329 + 0.268773i −0.969718 0.244227i \(-0.921466\pi\)
0.858389 + 0.513000i \(0.171466\pi\)
\(398\) 2.52346 + 5.15698i 0.126490 + 0.258496i
\(399\) 0 0
\(400\) 12.1941 + 7.24168i 0.609707 + 0.362084i
\(401\) −5.97617 −0.298436 −0.149218 0.988804i \(-0.547676\pi\)
−0.149218 + 0.988804i \(0.547676\pi\)
\(402\) 0 0
\(403\) 17.1437 + 7.10114i 0.853987 + 0.353733i
\(404\) −0.407166 0.111788i −0.0202573 0.00556164i
\(405\) 0 0
\(406\) 21.9577 1.37140i 1.08974 0.0680612i
\(407\) −21.6672 21.6672i −1.07401 1.07401i
\(408\) 0 0
\(409\) −5.91961 + 5.91961i −0.292706 + 0.292706i −0.838148 0.545443i \(-0.816362\pi\)
0.545443 + 0.838148i \(0.316362\pi\)
\(410\) −13.6776 + 15.5000i −0.675490 + 0.765488i
\(411\) 0 0
\(412\) 2.65003 + 21.1323i 0.130557 + 1.04111i
\(413\) 5.52150 13.3301i 0.271695 0.655931i
\(414\) 0 0
\(415\) 32.6357i 1.60203i
\(416\) −22.0409 11.2938i −1.08064 0.553726i
\(417\) 0 0
\(418\) −26.8222 9.19696i −1.31191 0.449838i
\(419\) −30.7382 12.7322i −1.50166 0.622007i −0.527841 0.849343i \(-0.676998\pi\)
−0.973816 + 0.227336i \(0.926998\pi\)
\(420\) 0 0
\(421\) 7.98264 + 19.2718i 0.389050 + 0.939249i 0.990142 + 0.140069i \(0.0447326\pi\)
−0.601092 + 0.799180i \(0.705267\pi\)
\(422\) −24.5582 21.6709i −1.19547 1.05492i
\(423\) 0 0
\(424\) −2.25357 + 3.30628i −0.109443 + 0.160567i
\(425\) 8.63660 8.63660i 0.418937 0.418937i
\(426\) 0 0
\(427\) 1.23194 + 2.97417i 0.0596179 + 0.143930i
\(428\) −13.4266 3.68627i −0.648997 0.178183i
\(429\) 0 0
\(430\) −16.0652 32.8312i −0.774735 1.58326i
\(431\) 29.2128i 1.40713i 0.710630 + 0.703565i \(0.248410\pi\)
−0.710630 + 0.703565i \(0.751590\pi\)
\(432\) 0 0
\(433\) 17.9410i 0.862190i −0.902306 0.431095i \(-0.858127\pi\)
0.902306 0.431095i \(-0.141873\pi\)
\(434\) −8.12037 + 3.97353i −0.389790 + 0.190736i
\(435\) 0 0
\(436\) −22.2326 + 12.6544i −1.06475 + 0.606034i
\(437\) 1.33114 + 3.21366i 0.0636771 + 0.153730i
\(438\) 0 0
\(439\) −8.96708 + 8.96708i −0.427975 + 0.427975i −0.887938 0.459963i \(-0.847863\pi\)
0.459963 + 0.887938i \(0.347863\pi\)
\(440\) 46.3903 + 9.67325i 2.21157 + 0.461154i
\(441\) 0 0
\(442\) −14.1122 + 15.9925i −0.671251 + 0.760684i
\(443\) 6.09257 + 14.7088i 0.289467 + 0.698835i 0.999988 0.00484090i \(-0.00154091\pi\)
−0.710522 + 0.703675i \(0.751541\pi\)
\(444\) 0 0
\(445\) 30.5358 + 12.6484i 1.44754 + 0.599589i
\(446\) 2.90241 8.46464i 0.137433 0.400812i
\(447\) 0 0
\(448\) 11.2306 4.41097i 0.530596 0.208399i
\(449\) 3.66413i 0.172921i 0.996255 + 0.0864604i \(0.0275556\pi\)
−0.996255 + 0.0864604i \(0.972444\pi\)
\(450\) 0 0
\(451\) −10.9670 + 26.4766i −0.516415 + 1.24674i
\(452\) −1.55324 1.20709i −0.0730583 0.0567767i
\(453\) 0 0
\(454\) 7.60829 + 6.71379i 0.357075 + 0.315094i
\(455\) 13.6490 13.6490i 0.639876 0.639876i
\(456\) 0 0
\(457\) −13.9728 13.9728i −0.653622 0.653622i 0.300241 0.953863i \(-0.402933\pi\)
−0.953863 + 0.300241i \(0.902933\pi\)
\(458\) 0.591655 + 9.47309i 0.0276462 + 0.442648i
\(459\) 0 0
\(460\) −2.87564 5.05224i −0.134077 0.235562i
\(461\) 2.25638 + 0.934623i 0.105090 + 0.0435297i 0.434609 0.900619i \(-0.356887\pi\)
−0.329519 + 0.944149i \(0.606887\pi\)
\(462\) 0 0
\(463\) 16.4302 0.763575 0.381788 0.924250i \(-0.375309\pi\)
0.381788 + 0.924250i \(0.375309\pi\)
\(464\) 40.8360 + 5.88791i 1.89576 + 0.273339i
\(465\) 0 0
\(466\) −8.49148 + 4.15513i −0.393360 + 0.192482i
\(467\) −8.14599 + 19.6662i −0.376951 + 0.910041i 0.615582 + 0.788072i \(0.288921\pi\)
−0.992534 + 0.121969i \(0.961079\pi\)
\(468\) 0 0
\(469\) 12.9571 5.36700i 0.598303 0.247825i
\(470\) 1.11758 + 17.8938i 0.0515501 + 0.825377i
\(471\) 0 0
\(472\) 15.2395 22.3584i 0.701456 1.02913i
\(473\) −35.8304 35.8304i −1.64748 1.64748i
\(474\) 0 0
\(475\) 11.4595 4.74669i 0.525799 0.217793i
\(476\) −1.29295 10.3104i −0.0592622 0.472578i
\(477\) 0 0
\(478\) 2.64614 7.71724i 0.121032 0.352978i
\(479\) 4.35772 0.199109 0.0995545 0.995032i \(-0.468258\pi\)
0.0995545 + 0.995032i \(0.468258\pi\)
\(480\) 0 0
\(481\) −23.4070 −1.06727
\(482\) 9.25098 26.9797i 0.421370 1.22889i
\(483\) 0 0
\(484\) 43.3562 5.43695i 1.97073 0.247134i
\(485\) −34.6914 + 14.3696i −1.57525 + 0.652491i
\(486\) 0 0
\(487\) 10.1865 + 10.1865i 0.461594 + 0.461594i 0.899178 0.437584i \(-0.144166\pi\)
−0.437584 + 0.899178i \(0.644166\pi\)
\(488\) 1.12312 + 5.93174i 0.0508414 + 0.268517i
\(489\) 0 0
\(490\) −1.21771 19.4969i −0.0550105 0.880782i
\(491\) 28.0848 11.6331i 1.26745 0.524994i 0.355260 0.934768i \(-0.384392\pi\)
0.912187 + 0.409774i \(0.134392\pi\)
\(492\) 0 0
\(493\) 13.5975 32.8273i 0.612402 1.47847i
\(494\) −19.4556 + 9.52019i −0.875349 + 0.428333i
\(495\) 0 0
\(496\) −16.4289 + 4.18626i −0.737679 + 0.187969i
\(497\) 3.76467 0.168869
\(498\) 0 0
\(499\) −20.5327 8.50493i −0.919170 0.380733i −0.127610 0.991824i \(-0.540731\pi\)
−0.791560 + 0.611092i \(0.790731\pi\)
\(500\) 7.39009 4.20630i 0.330495 0.188111i
\(501\) 0 0
\(502\) −0.0665318 1.06525i −0.00296946 0.0475446i
\(503\) 6.66355 + 6.66355i 0.297113 + 0.297113i 0.839882 0.542769i \(-0.182624\pi\)
−0.542769 + 0.839882i \(0.682624\pi\)
\(504\) 0 0
\(505\) 0.436393 0.436393i 0.0194192 0.0194192i
\(506\) −6.04284 5.33238i −0.268637 0.237053i
\(507\) 0 0
\(508\) 6.53841 8.41339i 0.290095 0.373284i
\(509\) 4.13590 9.98494i 0.183320 0.442575i −0.805327 0.592831i \(-0.798010\pi\)
0.988647 + 0.150257i \(0.0480101\pi\)
\(510\) 0 0
\(511\) 2.48152i 0.109776i
\(512\) 22.3063 3.79870i 0.985807 0.167881i
\(513\) 0 0
\(514\) −3.16301 + 9.22464i −0.139514 + 0.406882i
\(515\) −28.7601 11.9128i −1.26732 0.524942i
\(516\) 0 0
\(517\) 9.51161 + 22.9631i 0.418320 + 1.00991i
\(518\) 7.54531 8.55060i 0.331522 0.375692i
\(519\) 0 0
\(520\) 30.2825 19.8326i 1.32798 0.869717i
\(521\) −2.91587 + 2.91587i −0.127746 + 0.127746i −0.768089 0.640343i \(-0.778792\pi\)
0.640343 + 0.768089i \(0.278792\pi\)
\(522\) 0 0
\(523\) 14.2159 + 34.3201i 0.621616 + 1.50071i 0.849805 + 0.527097i \(0.176720\pi\)
−0.228189 + 0.973617i \(0.573280\pi\)
\(524\) 18.9564 + 33.3047i 0.828113 + 1.45492i
\(525\) 0 0
\(526\) −5.59724 + 2.73889i −0.244051 + 0.119421i
\(527\) 14.6008i 0.636023i
\(528\) 0 0
\(529\) 22.0113i 0.957015i
\(530\) −2.57055 5.25320i −0.111657 0.228185i
\(531\) 0 0
\(532\) 2.79383 10.1760i 0.121128 0.441186i
\(533\) 8.37748 + 20.2250i 0.362869 + 0.876043i
\(534\) 0 0
\(535\) 14.3903 14.3903i 0.622149 0.622149i
\(536\) 25.8418 4.89292i 1.11620 0.211342i
\(537\) 0 0
\(538\) −14.2420 12.5675i −0.614015 0.541825i
\(539\) −10.3638 25.0204i −0.446401 1.07771i
\(540\) 0 0
\(541\) −29.5435 12.2373i −1.27017 0.526123i −0.357157 0.934044i \(-0.616254\pi\)
−0.913017 + 0.407921i \(0.866254\pi\)
\(542\) −7.95467 2.72755i −0.341682 0.117158i
\(543\) 0 0
\(544\) 1.57327 19.4234i 0.0674533 0.832770i
\(545\) 37.3912i 1.60166i
\(546\) 0 0
\(547\) −11.8740 + 28.6664i −0.507696 + 1.22569i 0.437510 + 0.899213i \(0.355860\pi\)
−0.945206 + 0.326474i \(0.894140\pi\)
\(548\) −28.2853 + 3.54703i −1.20829 + 0.151521i
\(549\) 0 0
\(550\) −19.0146 + 21.5480i −0.810787 + 0.918811i
\(551\) 25.5152 25.5152i 1.08698 1.08698i
\(552\) 0 0
\(553\) −15.4393 15.4393i −0.656546 0.656546i
\(554\) 12.9637 0.809665i 0.550775 0.0343994i
\(555\) 0 0
\(556\) 6.32860 23.0508i 0.268392 0.977570i
\(557\) −16.2393 6.72656i −0.688083 0.285013i 0.0111181 0.999938i \(-0.496461\pi\)
−0.699201 + 0.714925i \(0.746461\pi\)
\(558\) 0 0
\(559\) −38.7074 −1.63715
\(560\) −2.51679 + 17.4553i −0.106354 + 0.737623i
\(561\) 0 0
\(562\) −11.0050 22.4899i −0.464216 0.948679i
\(563\) −15.7698 + 38.0718i −0.664620 + 1.60453i 0.125862 + 0.992048i \(0.459830\pi\)
−0.790481 + 0.612486i \(0.790170\pi\)
\(564\) 0 0
\(565\) 2.65638 1.10031i 0.111755 0.0462904i
\(566\) 25.7375 1.60747i 1.08183 0.0675672i
\(567\) 0 0
\(568\) 6.91137 + 1.44115i 0.289995 + 0.0604693i
\(569\) 11.0276 + 11.0276i 0.462302 + 0.462302i 0.899409 0.437107i \(-0.143997\pi\)
−0.437107 + 0.899409i \(0.643997\pi\)
\(570\) 0 0
\(571\) −31.3409 + 12.9818i −1.31157 + 0.543272i −0.925343 0.379130i \(-0.876223\pi\)
−0.386231 + 0.922402i \(0.626223\pi\)
\(572\) 30.7942 39.6249i 1.28757 1.65680i
\(573\) 0 0
\(574\) −10.0887 3.45929i −0.421096 0.144388i
\(575\) 3.52541 0.147020
\(576\) 0 0
\(577\) −2.28631 −0.0951802 −0.0475901 0.998867i \(-0.515154\pi\)
−0.0475901 + 0.998867i \(0.515154\pi\)
\(578\) 6.86677 + 2.35452i 0.285620 + 0.0979353i
\(579\) 0 0
\(580\) −37.0047 + 47.6164i −1.53654 + 1.97716i
\(581\) −15.5562 + 6.44359i −0.645380 + 0.267325i
\(582\) 0 0
\(583\) −5.73311 5.73311i −0.237441 0.237441i
\(584\) −0.949947 + 4.55569i −0.0393091 + 0.188516i
\(585\) 0 0
\(586\) −2.84453 + 0.177659i −0.117506 + 0.00733903i
\(587\) −5.89005 + 2.43974i −0.243108 + 0.100699i −0.500911 0.865499i \(-0.667002\pi\)
0.257803 + 0.966198i \(0.417002\pi\)
\(588\) 0 0
\(589\) −5.67428 + 13.6989i −0.233805 + 0.564454i
\(590\) 17.3830 + 35.5242i 0.715648 + 1.46251i
\(591\) 0 0
\(592\) 17.1253 12.8092i 0.703845 0.526455i
\(593\) −10.9801 −0.450897 −0.225449 0.974255i \(-0.572385\pi\)
−0.225449 + 0.974255i \(0.572385\pi\)
\(594\) 0 0
\(595\) 14.0321 + 5.81227i 0.575259 + 0.238280i
\(596\) 3.42454 12.4733i 0.140275 0.510925i
\(597\) 0 0
\(598\) −6.14429 + 0.383750i −0.251259 + 0.0156927i
\(599\) 3.54515 + 3.54515i 0.144851 + 0.144851i 0.775813 0.630962i \(-0.217340\pi\)
−0.630962 + 0.775813i \(0.717340\pi\)
\(600\) 0 0
\(601\) 0.844578 0.844578i 0.0344511 0.0344511i −0.689671 0.724122i \(-0.742245\pi\)
0.724122 + 0.689671i \(0.242245\pi\)
\(602\) 12.4774 14.1398i 0.508542 0.576297i
\(603\) 0 0
\(604\) −14.8326 + 1.86004i −0.603531 + 0.0756839i
\(605\) −24.4410 + 59.0059i −0.993669 + 2.39893i
\(606\) 0 0
\(607\) 17.9859i 0.730024i 0.931003 + 0.365012i \(0.118935\pi\)
−0.931003 + 0.365012i \(0.881065\pi\)
\(608\) 9.02453 17.6121i 0.365993 0.714266i
\(609\) 0 0
\(610\) −8.34706 2.86210i −0.337963 0.115883i
\(611\) 17.5411 + 7.26575i 0.709636 + 0.293941i
\(612\) 0 0
\(613\) −6.72419 16.2336i −0.271588 0.655671i 0.727964 0.685615i \(-0.240467\pi\)
−0.999552 + 0.0299448i \(0.990467\pi\)
\(614\) 4.24784 + 3.74843i 0.171429 + 0.151274i
\(615\) 0 0
\(616\) 4.54842 + 24.0224i 0.183261 + 0.967888i
\(617\) −8.70935 + 8.70935i −0.350625 + 0.350625i −0.860342 0.509717i \(-0.829750\pi\)
0.509717 + 0.860342i \(0.329750\pi\)
\(618\) 0 0
\(619\) −3.38639 8.17546i −0.136110 0.328600i 0.841098 0.540883i \(-0.181910\pi\)
−0.977208 + 0.212284i \(0.931910\pi\)
\(620\) 6.56071 23.8962i 0.263485 0.959694i
\(621\) 0 0
\(622\) −8.06786 16.4876i −0.323492 0.661093i
\(623\) 17.0525i 0.683195i
\(624\) 0 0
\(625\) 30.1567i 1.20627i
\(626\) 15.5601 7.61400i 0.621906 0.304317i
\(627\) 0 0
\(628\) 21.3559 + 37.5205i 0.852195 + 1.49723i
\(629\) −7.04814 17.0157i −0.281028 0.678461i
\(630\) 0 0
\(631\) 2.69060 2.69060i 0.107111 0.107111i −0.651520 0.758631i \(-0.725868\pi\)
0.758631 + 0.651520i \(0.225868\pi\)
\(632\) −22.4340 34.2546i −0.892375 1.36257i
\(633\) 0 0
\(634\) 18.1279 20.5431i 0.719949 0.815871i
\(635\) 5.96002 + 14.3888i 0.236516 + 0.571000i
\(636\) 0 0
\(637\) −19.1127 7.91673i −0.757272 0.313672i
\(638\) −27.1164 + 79.0827i −1.07355 + 3.13092i
\(639\) 0 0
\(640\) −11.3025 + 31.0820i −0.446771 + 1.22862i
\(641\) 37.2166i 1.46997i −0.678084 0.734984i \(-0.737189\pi\)
0.678084 0.734984i \(-0.262811\pi\)
\(642\) 0 0
\(643\) −11.0037 + 26.5652i −0.433942 + 1.04763i 0.544063 + 0.839044i \(0.316885\pi\)
−0.978005 + 0.208583i \(0.933115\pi\)
\(644\) 1.84044 2.36822i 0.0725237 0.0933209i
\(645\) 0 0
\(646\) −12.7790 11.2766i −0.502784 0.443672i
\(647\) −30.0988 + 30.0988i −1.18331 + 1.18331i −0.204426 + 0.978882i \(0.565533\pi\)
−0.978882 + 0.204426i \(0.934467\pi\)
\(648\) 0 0
\(649\) 38.7695 + 38.7695i 1.52184 + 1.52184i
\(650\) 1.36841 + 21.9098i 0.0536733 + 0.859372i
\(651\) 0 0
\(652\) 21.6119 12.3011i 0.846386 0.481746i
\(653\) 4.00245 + 1.65787i 0.156628 + 0.0648775i 0.459620 0.888116i \(-0.347986\pi\)
−0.302992 + 0.952993i \(0.597986\pi\)
\(654\) 0 0
\(655\) −56.0125 −2.18859
\(656\) −17.1972 10.2128i −0.671436 0.398743i
\(657\) 0 0
\(658\) −8.30861 + 4.06564i −0.323903 + 0.158495i
\(659\) 2.32569 5.61472i 0.0905962 0.218719i −0.872086 0.489352i \(-0.837233\pi\)
0.962682 + 0.270634i \(0.0872332\pi\)
\(660\) 0 0
\(661\) 37.0965 15.3659i 1.44288 0.597662i 0.482389 0.875957i \(-0.339769\pi\)
0.960496 + 0.278295i \(0.0897692\pi\)
\(662\) 0.912900 + 14.6166i 0.0354809 + 0.568090i
\(663\) 0 0
\(664\) −31.0255 + 5.87441i −1.20402 + 0.227971i
\(665\) 10.9065 + 10.9065i 0.422935 + 0.422935i
\(666\) 0 0
\(667\) 9.47519 3.92475i 0.366881 0.151967i
\(668\) −37.8060 + 4.74095i −1.46276 + 0.183433i
\(669\) 0 0
\(670\) −12.4688 + 36.3643i −0.481712 + 1.40487i
\(671\) −12.2332 −0.472256
\(672\) 0 0
\(673\) −13.6208 −0.525043 −0.262521 0.964926i \(-0.584554\pi\)
−0.262521 + 0.964926i \(0.584554\pi\)
\(674\) −3.44356 + 10.0429i −0.132641 + 0.386836i
\(675\) 0 0
\(676\) −1.53475 12.2387i −0.0590290 0.470718i
\(677\) 11.5314 4.77647i 0.443189 0.183575i −0.149918 0.988698i \(-0.547901\pi\)
0.593107 + 0.805124i \(0.297901\pi\)
\(678\) 0 0
\(679\) −13.6989 13.6989i −0.525715 0.525715i
\(680\) 23.5358 + 16.0421i 0.902556 + 0.615185i
\(681\) 0 0
\(682\) −2.14145 34.2872i −0.0820004 1.31292i
\(683\) 37.0003 15.3260i 1.41578 0.586435i 0.461982 0.886889i \(-0.347138\pi\)
0.953796 + 0.300454i \(0.0971383\pi\)
\(684\) 0 0
\(685\) 15.9452 38.4950i 0.609233 1.47082i
\(686\) 22.4641 10.9924i 0.857685 0.419690i
\(687\) 0 0
\(688\) 28.3196 21.1822i 1.07967 0.807563i
\(689\) −6.19344 −0.235951
\(690\) 0 0
\(691\) 6.40367 + 2.65249i 0.243607 + 0.100905i 0.501147 0.865362i \(-0.332912\pi\)
−0.257539 + 0.966268i \(0.582912\pi\)
\(692\) −1.59191 2.79685i −0.0605154 0.106320i
\(693\) 0 0
\(694\) −0.272293 4.35973i −0.0103361 0.165493i
\(695\) 24.7054 + 24.7054i 0.937129 + 0.937129i
\(696\) 0 0
\(697\) −12.1800 + 12.1800i −0.461352 + 0.461352i
\(698\) −3.91929 3.45850i −0.148347 0.130906i
\(699\) 0 0
\(700\) −8.44478 6.56280i −0.319183 0.248051i
\(701\) 7.95095 19.1953i 0.300303 0.724996i −0.699642 0.714494i \(-0.746657\pi\)
0.999945 0.0105021i \(-0.00334297\pi\)
\(702\) 0 0
\(703\) 18.7037i 0.705424i
\(704\) −0.845748 + 45.8426i −0.0318753 + 1.72776i
\(705\) 0 0
\(706\) 3.12478 9.11315i 0.117603 0.342978i
\(707\) 0.294173 + 0.121850i 0.0110635 + 0.00458266i
\(708\) 0 0
\(709\) 0.602133 + 1.45368i 0.0226136 + 0.0545940i 0.934783 0.355219i \(-0.115594\pi\)
−0.912169 + 0.409813i \(0.865594\pi\)
\(710\) −6.82776 + 7.73745i −0.256241 + 0.290381i
\(711\) 0 0
\(712\) −6.52786 + 31.3059i −0.244642 + 1.17324i
\(713\) −2.97999 + 2.97999i −0.111602 + 0.111602i
\(714\) 0 0
\(715\) 28.0701 + 67.7673i 1.04976 + 2.53435i
\(716\) 0.857983 0.488347i 0.0320643 0.0182504i
\(717\) 0 0
\(718\) −9.54662 + 4.67144i −0.356277 + 0.174337i
\(719\) 36.1660i 1.34877i −0.738382 0.674383i \(-0.764410\pi\)
0.738382 0.674383i \(-0.235590\pi\)
\(720\) 0 0
\(721\) 16.0609i 0.598139i
\(722\) 4.20292 + 8.58915i 0.156416 + 0.319655i
\(723\) 0 0
\(724\) −42.2279 11.5937i −1.56939 0.430876i
\(725\) −13.9952 33.7874i −0.519768 1.25483i
\(726\) 0 0
\(727\) −3.48345 + 3.48345i −0.129194 + 0.129194i −0.768747 0.639553i \(-0.779119\pi\)
0.639553 + 0.768747i \(0.279119\pi\)
\(728\) 15.4324 + 10.5188i 0.571963 + 0.389852i
\(729\) 0 0
\(730\) −5.10021 4.50058i −0.188767 0.166574i
\(731\) −11.6553 28.1383i −0.431086 1.04073i
\(732\) 0 0
\(733\) −9.32567 3.86282i −0.344452 0.142677i 0.203750 0.979023i \(-0.434687\pi\)
−0.548201 + 0.836347i \(0.684687\pi\)
\(734\) −39.2999 13.4754i −1.45059 0.497387i
\(735\) 0 0
\(736\) 4.28536 3.64316i 0.157960 0.134289i
\(737\) 53.2942i 1.96312i
\(738\) 0 0
\(739\) 18.2859 44.1460i 0.672657 1.62394i −0.104421 0.994533i \(-0.533299\pi\)
0.777078 0.629404i \(-0.216701\pi\)
\(740\) 3.88940 + 31.0154i 0.142977 + 1.14015i
\(741\) 0 0
\(742\) 1.99647 2.26247i 0.0732928 0.0830579i
\(743\) 26.3660 26.3660i 0.967273 0.967273i −0.0322079 0.999481i \(-0.510254\pi\)
0.999481 + 0.0322079i \(0.0102539\pi\)
\(744\) 0 0
\(745\) 13.3686 + 13.3686i 0.489789 + 0.489789i
\(746\) −22.4272 + 1.40072i −0.821118 + 0.0512841i
\(747\) 0 0
\(748\) 38.0779 + 10.4543i 1.39226 + 0.382247i
\(749\) 9.70055 + 4.01810i 0.354450 + 0.146818i
\(750\) 0 0
\(751\) 31.9193 1.16475 0.582377 0.812919i \(-0.302123\pi\)
0.582377 + 0.812919i \(0.302123\pi\)
\(752\) −16.8097 + 4.28330i −0.612988 + 0.156196i
\(753\) 0 0
\(754\) 28.0694 + 57.3631i 1.02223 + 2.08904i
\(755\) 8.36155 20.1866i 0.304308 0.734664i
\(756\) 0 0
\(757\) 25.8156 10.6932i 0.938284 0.388650i 0.139469 0.990226i \(-0.455461\pi\)
0.798815 + 0.601577i \(0.205461\pi\)
\(758\) 1.90970 0.119273i 0.0693636 0.00433220i
\(759\) 0 0
\(760\) 15.8476 + 24.1977i 0.574851 + 0.877745i
\(761\) 14.4436 + 14.4436i 0.523579 + 0.523579i 0.918650 0.395072i \(-0.129280\pi\)
−0.395072 + 0.918650i \(0.629280\pi\)
\(762\) 0 0
\(763\) 17.8229 7.38250i 0.645234 0.267265i
\(764\) −36.8045 28.6024i −1.33154 1.03480i
\(765\) 0 0
\(766\) −47.1668 16.1729i −1.70420 0.584349i
\(767\) 41.8824 1.51229
\(768\) 0 0
\(769\) 21.6737 0.781574 0.390787 0.920481i \(-0.372203\pi\)
0.390787 + 0.920481i \(0.372203\pi\)
\(770\) −33.8040 11.5909i −1.21821 0.417708i
\(771\) 0 0
\(772\) −42.7486 33.2217i −1.53855 1.19568i
\(773\) −5.45257 + 2.25853i −0.196115 + 0.0812336i −0.478580 0.878044i \(-0.658848\pi\)
0.282464 + 0.959278i \(0.408848\pi\)
\(774\) 0 0
\(775\) 10.6263 + 10.6263i 0.381708 + 0.381708i
\(776\) −19.9051 30.3932i −0.714550 1.09105i
\(777\) 0 0
\(778\) −5.11120 + 0.319227i −0.183245 + 0.0114448i
\(779\) −16.1611 + 6.69416i −0.579033 + 0.239843i
\(780\) 0 0
\(781\) −5.47463 + 13.2169i −0.195898 + 0.472939i
\(782\) −2.12909 4.35104i −0.0761361 0.155593i
\(783\) 0 0
\(784\) 18.3158 4.66707i 0.654135 0.166681i
\(785\) −63.1027 −2.25223
\(786\) 0 0
\(787\) −38.9288 16.1249i −1.38766 0.574789i −0.441144 0.897436i \(-0.645427\pi\)
−0.946519 + 0.322647i \(0.895427\pi\)