Properties

Label 912.2.ci.b.127.1
Level $912$
Weight $2$
Character 912.127
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [912,2,Mod(79,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("912.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.ci (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 127.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 912.127
Dual form 912.2.ci.b.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{3} +(-0.233956 - 1.32683i) q^{5} +(3.20574 + 1.85083i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{3} +(-0.233956 - 1.32683i) q^{5} +(3.20574 + 1.85083i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-1.31908 + 0.761570i) q^{11} +(0.286989 + 0.788496i) q^{13} +(0.233956 - 1.32683i) q^{15} +(0.124485 - 0.104455i) q^{17} +(4.35844 + 0.0632028i) q^{19} +(2.37939 + 2.83564i) q^{21} +(1.85844 + 0.327693i) q^{23} +(2.99273 - 1.08926i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-6.75150 + 8.04612i) q^{29} +(2.95084 - 5.11100i) q^{31} +(-1.50000 + 0.264490i) q^{33} +(1.70574 - 4.68647i) q^{35} +3.67301i q^{37} +0.839100i q^{39} +(0.788333 - 2.16593i) q^{41} +(-2.89053 + 0.509678i) q^{43} +(0.673648 - 1.16679i) q^{45} +(5.63176 - 6.71167i) q^{47} +(3.35117 + 5.80439i) q^{49} +(0.152704 - 0.0555796i) q^{51} +(-6.69846 - 1.18112i) q^{53} +(1.31908 + 1.57202i) q^{55} +(4.07398 + 1.55007i) q^{57} +(9.06805 - 7.60900i) q^{59} +(0.741230 - 4.20372i) q^{61} +(1.26604 + 3.47843i) q^{63} +(0.979055 - 0.565258i) q^{65} +(8.57398 + 7.19442i) q^{67} +(1.63429 + 0.943555i) q^{69} +(1.29426 + 7.34013i) q^{71} +(6.53849 + 2.37981i) q^{73} +3.18479 q^{75} -5.63816 q^{77} +(-12.9893 - 4.72773i) q^{79} +(0.173648 + 0.984808i) q^{81} +(0.134285 + 0.0775297i) q^{83} +(-0.167718 - 0.140732i) q^{85} +(-9.09627 + 5.25173i) q^{87} +(1.92989 + 5.30234i) q^{89} +(-0.539363 + 3.05888i) q^{91} +(4.52094 - 3.79352i) q^{93} +(-0.935822 - 5.79769i) q^{95} +(-5.19846 - 6.19529i) q^{97} +(-1.50000 - 0.264490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{5} + 9 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 6 q^{13} + 6 q^{15} - 12 q^{17} + 18 q^{19} + 3 q^{21} + 3 q^{23} + 3 q^{27} + 6 q^{31} - 9 q^{33} - 12 q^{41} + 3 q^{45} + 39 q^{47} - 6 q^{49} + 3 q^{51} - 12 q^{53} - 9 q^{55} + 9 q^{57} + 12 q^{59} + 27 q^{61} + 3 q^{63} + 9 q^{65} + 36 q^{67} + 18 q^{71} - 9 q^{73} + 12 q^{75} - 18 q^{79} - 9 q^{83} + 27 q^{85} - 27 q^{87} + 3 q^{89} - 12 q^{91} + 24 q^{93} - 24 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\) \(1\) \(-1\)

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 0
\(3\) 0.939693 + 0.342020i 0.542532 + 0.197465i
\(4\) 0 0
\(5\) −0.233956 1.32683i −0.104628 0.593375i −0.991368 0.131107i \(-0.958147\pi\)
0.886740 0.462268i \(-0.152964\pi\)
\(6\) 0 0
\(7\) 3.20574 + 1.85083i 1.21165 + 0.699549i 0.963120 0.269074i \(-0.0867175\pi\)
0.248535 + 0.968623i \(0.420051\pi\)
\(8\) 0 0
\(9\) 0.766044 + 0.642788i 0.255348 + 0.214263i
\(10\) 0 0
\(11\) −1.31908 + 0.761570i −0.397717 + 0.229622i −0.685498 0.728074i \(-0.740416\pi\)
0.287781 + 0.957696i \(0.407082\pi\)
\(12\) 0 0
\(13\) 0.286989 + 0.788496i 0.0795964 + 0.218689i 0.973107 0.230352i \(-0.0739878\pi\)
−0.893511 + 0.449041i \(0.851766\pi\)
\(14\) 0 0
\(15\) 0.233956 1.32683i 0.0604071 0.342585i
\(16\) 0 0
\(17\) 0.124485 0.104455i 0.0301921 0.0253342i −0.627567 0.778563i \(-0.715949\pi\)
0.657759 + 0.753229i \(0.271505\pi\)
\(18\) 0 0
\(19\) 4.35844 + 0.0632028i 0.999895 + 0.0144997i
\(20\) 0 0
\(21\) 2.37939 + 2.83564i 0.519224 + 0.618788i
\(22\) 0 0
\(23\) 1.85844 + 0.327693i 0.387512 + 0.0683288i 0.364010 0.931395i \(-0.381407\pi\)
0.0235017 + 0.999724i \(0.492519\pi\)
\(24\) 0 0
\(25\) 2.99273 1.08926i 0.598545 0.217853i
\(26\) 0 0
\(27\) 0.500000 + 0.866025i 0.0962250 + 0.166667i
\(28\) 0 0
\(29\) −6.75150 + 8.04612i −1.25372 + 1.49413i −0.457390 + 0.889266i \(0.651216\pi\)
−0.796331 + 0.604861i \(0.793229\pi\)
\(30\) 0 0
\(31\) 2.95084 5.11100i 0.529986 0.917963i −0.469402 0.882985i \(-0.655531\pi\)
0.999388 0.0349781i \(-0.0111361\pi\)
\(32\) 0 0
\(33\) −1.50000 + 0.264490i −0.261116 + 0.0460419i
\(34\) 0 0
\(35\) 1.70574 4.68647i 0.288322 0.792159i
\(36\) 0 0
\(37\) 3.67301i 0.603840i 0.953333 + 0.301920i \(0.0976275\pi\)
−0.953333 + 0.301920i \(0.902373\pi\)
\(38\) 0 0
\(39\) 0.839100i 0.134363i
\(40\) 0 0
\(41\) 0.788333 2.16593i 0.123117 0.338261i −0.862788 0.505565i \(-0.831284\pi\)
0.985905 + 0.167304i \(0.0535062\pi\)
\(42\) 0 0
\(43\) −2.89053 + 0.509678i −0.440802 + 0.0777252i −0.389644 0.920965i \(-0.627402\pi\)
−0.0511572 + 0.998691i \(0.516291\pi\)
\(44\) 0 0
\(45\) 0.673648 1.16679i 0.100422 0.173935i
\(46\) 0 0
\(47\) 5.63176 6.71167i 0.821476 0.978998i −0.178511 0.983938i \(-0.557128\pi\)
0.999988 + 0.00494030i \(0.00157255\pi\)
\(48\) 0 0
\(49\) 3.35117 + 5.80439i 0.478738 + 0.829199i
\(50\) 0 0
\(51\) 0.152704 0.0555796i 0.0213828 0.00778270i
\(52\) 0 0
\(53\) −6.69846 1.18112i −0.920105 0.162239i −0.306516 0.951865i \(-0.599163\pi\)
−0.613588 + 0.789626i \(0.710275\pi\)
\(54\) 0 0
\(55\) 1.31908 + 1.57202i 0.177864 + 0.211971i
\(56\) 0 0
\(57\) 4.07398 + 1.55007i 0.539612 + 0.205311i
\(58\) 0 0
\(59\) 9.06805 7.60900i 1.18056 0.990607i 0.180584 0.983560i \(-0.442201\pi\)
0.999975 0.00704735i \(-0.00224326\pi\)
\(60\) 0 0
\(61\) 0.741230 4.20372i 0.0949047 0.538231i −0.899872 0.436154i \(-0.856340\pi\)
0.994777 0.102077i \(-0.0325488\pi\)
\(62\) 0 0
\(63\) 1.26604 + 3.47843i 0.159507 + 0.438241i
\(64\) 0 0
\(65\) 0.979055 0.565258i 0.121437 0.0701116i
\(66\) 0 0
\(67\) 8.57398 + 7.19442i 1.04748 + 0.878939i 0.992826 0.119567i \(-0.0381506\pi\)
0.0546520 + 0.998505i \(0.482595\pi\)
\(68\) 0 0
\(69\) 1.63429 + 0.943555i 0.196745 + 0.113591i
\(70\) 0 0
\(71\) 1.29426 + 7.34013i 0.153601 + 0.871113i 0.960054 + 0.279815i \(0.0902732\pi\)
−0.806453 + 0.591298i \(0.798616\pi\)
\(72\) 0 0
\(73\) 6.53849 + 2.37981i 0.765272 + 0.278536i 0.695017 0.718993i \(-0.255397\pi\)
0.0702545 + 0.997529i \(0.477619\pi\)
\(74\) 0 0
\(75\) 3.18479 0.367748
\(76\) 0 0
\(77\) −5.63816 −0.642527
\(78\) 0 0
\(79\) −12.9893 4.72773i −1.46141 0.531911i −0.515659 0.856794i \(-0.672453\pi\)
−0.945754 + 0.324883i \(0.894675\pi\)
\(80\) 0 0
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) 0 0
\(83\) 0.134285 + 0.0775297i 0.0147397 + 0.00850999i 0.507352 0.861739i \(-0.330624\pi\)
−0.492612 + 0.870249i \(0.663958\pi\)
\(84\) 0 0
\(85\) −0.167718 0.140732i −0.0181916 0.0152646i
\(86\) 0 0
\(87\) −9.09627 + 5.25173i −0.975222 + 0.563045i
\(88\) 0 0
\(89\) 1.92989 + 5.30234i 0.204568 + 0.562046i 0.998971 0.0453443i \(-0.0144385\pi\)
−0.794403 + 0.607391i \(0.792216\pi\)
\(90\) 0 0
\(91\) −0.539363 + 3.05888i −0.0565406 + 0.320658i
\(92\) 0 0
\(93\) 4.52094 3.79352i 0.468800 0.393370i
\(94\) 0 0
\(95\) −0.935822 5.79769i −0.0960133 0.594830i
\(96\) 0 0
\(97\) −5.19846 6.19529i −0.527824 0.629036i 0.434588 0.900629i \(-0.356894\pi\)
−0.962412 + 0.271593i \(0.912449\pi\)
\(98\) 0 0
\(99\) −1.50000 0.264490i −0.150756 0.0265823i
\(100\) 0 0
\(101\) −16.4153 + 5.97470i −1.63339 + 0.594505i −0.985865 0.167542i \(-0.946417\pi\)
−0.647523 + 0.762046i \(0.724195\pi\)
\(102\) 0 0
\(103\) 3.09240 + 5.35619i 0.304703 + 0.527761i 0.977195 0.212343i \(-0.0681095\pi\)
−0.672492 + 0.740104i \(0.734776\pi\)
\(104\) 0 0
\(105\) 3.20574 3.82045i 0.312848 0.372838i
\(106\) 0 0
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) 0 0
\(109\) −7.19459 + 1.26860i −0.689117 + 0.121510i −0.507232 0.861810i \(-0.669331\pi\)
−0.181885 + 0.983320i \(0.558220\pi\)
\(110\) 0 0
\(111\) −1.25624 + 3.45150i −0.119237 + 0.327602i
\(112\) 0 0
\(113\) 1.51319i 0.142349i 0.997464 + 0.0711744i \(0.0226747\pi\)
−0.997464 + 0.0711744i \(0.977325\pi\)
\(114\) 0 0
\(115\) 2.54250i 0.237089i
\(116\) 0 0
\(117\) −0.286989 + 0.788496i −0.0265321 + 0.0728965i
\(118\) 0 0
\(119\) 0.592396 0.104455i 0.0543049 0.00957541i
\(120\) 0 0
\(121\) −4.34002 + 7.51714i −0.394547 + 0.683376i
\(122\) 0 0
\(123\) 1.48158 1.76568i 0.133590 0.159206i
\(124\) 0 0
\(125\) −5.51367 9.54996i −0.493158 0.854174i
\(126\) 0 0
\(127\) −11.9547 + 4.35116i −1.06081 + 0.386103i −0.812732 0.582638i \(-0.802021\pi\)
−0.248077 + 0.968740i \(0.579798\pi\)
\(128\) 0 0
\(129\) −2.89053 0.509678i −0.254497 0.0448747i
\(130\) 0 0
\(131\) −5.89053 7.02006i −0.514658 0.613345i 0.444651 0.895704i \(-0.353328\pi\)
−0.959309 + 0.282358i \(0.908883\pi\)
\(132\) 0 0
\(133\) 13.8550 + 8.26936i 1.20138 + 0.717044i
\(134\) 0 0
\(135\) 1.03209 0.866025i 0.0888281 0.0745356i
\(136\) 0 0
\(137\) 2.47906 14.0594i 0.211800 1.20118i −0.674574 0.738207i \(-0.735673\pi\)
0.886374 0.462970i \(-0.153216\pi\)
\(138\) 0 0
\(139\) −0.137689 0.378297i −0.0116786 0.0320867i 0.933716 0.358014i \(-0.116546\pi\)
−0.945395 + 0.325927i \(0.894324\pi\)
\(140\) 0 0
\(141\) 7.58765 4.38073i 0.638995 0.368924i
\(142\) 0 0
\(143\) −0.979055 0.821525i −0.0818727 0.0686994i
\(144\) 0 0
\(145\) 12.2554 + 7.07564i 1.01775 + 0.587600i
\(146\) 0 0
\(147\) 1.16385 + 6.60051i 0.0959926 + 0.544401i
\(148\) 0 0
\(149\) −10.4966 3.82045i −0.859915 0.312983i −0.125839 0.992051i \(-0.540162\pi\)
−0.734076 + 0.679067i \(0.762384\pi\)
\(150\) 0 0
\(151\) −7.18984 −0.585101 −0.292551 0.956250i \(-0.594504\pi\)
−0.292551 + 0.956250i \(0.594504\pi\)
\(152\) 0 0
\(153\) 0.162504 0.0131377
\(154\) 0 0
\(155\) −7.47178 2.71951i −0.600148 0.218436i
\(156\) 0 0
\(157\) −2.37686 13.4798i −0.189694 1.07581i −0.919775 0.392447i \(-0.871629\pi\)
0.730081 0.683361i \(-0.239482\pi\)
\(158\) 0 0
\(159\) −5.89053 3.40090i −0.467149 0.269709i
\(160\) 0 0
\(161\) 5.35117 + 4.49016i 0.421731 + 0.353874i
\(162\) 0 0
\(163\) −13.8516 + 7.99724i −1.08494 + 0.626393i −0.932226 0.361877i \(-0.882136\pi\)
−0.152718 + 0.988270i \(0.548803\pi\)
\(164\) 0 0
\(165\) 0.701867 + 1.92836i 0.0546402 + 0.150123i
\(166\) 0 0
\(167\) −0.467911 + 2.65366i −0.0362080 + 0.205346i −0.997545 0.0700288i \(-0.977691\pi\)
0.961337 + 0.275375i \(0.0888020\pi\)
\(168\) 0 0
\(169\) 9.41921 7.90366i 0.724555 0.607974i
\(170\) 0 0
\(171\) 3.29813 + 2.84997i 0.252215 + 0.217942i
\(172\) 0 0
\(173\) −12.8478 15.3114i −0.976797 1.16410i −0.986436 0.164148i \(-0.947512\pi\)
0.00963834 0.999954i \(-0.496932\pi\)
\(174\) 0 0
\(175\) 11.6099 + 2.04715i 0.877629 + 0.154750i
\(176\) 0 0
\(177\) 11.1236 4.04866i 0.836102 0.304316i
\(178\) 0 0
\(179\) −2.06758 3.58116i −0.154538 0.267668i 0.778353 0.627827i \(-0.216056\pi\)
−0.932891 + 0.360159i \(0.882722\pi\)
\(180\) 0 0
\(181\) −0.816552 + 0.973128i −0.0606938 + 0.0723321i −0.795537 0.605905i \(-0.792811\pi\)
0.734843 + 0.678237i \(0.237256\pi\)
\(182\) 0 0
\(183\) 2.13429 3.69669i 0.157771 0.273267i
\(184\) 0 0
\(185\) 4.87346 0.859322i 0.358304 0.0631786i
\(186\) 0 0
\(187\) −0.0846555 + 0.232589i −0.00619062 + 0.0170086i
\(188\) 0 0
\(189\) 3.70167i 0.269257i
\(190\) 0 0
\(191\) 5.95275i 0.430726i 0.976534 + 0.215363i \(0.0690934\pi\)
−0.976534 + 0.215363i \(0.930907\pi\)
\(192\) 0 0
\(193\) 3.23396 8.88522i 0.232785 0.639572i −0.767213 0.641392i \(-0.778357\pi\)
0.999998 + 0.00182013i \(0.000579365\pi\)
\(194\) 0 0
\(195\) 1.11334 0.196312i 0.0797280 0.0140582i
\(196\) 0 0
\(197\) 6.70708 11.6170i 0.477860 0.827677i −0.521818 0.853057i \(-0.674746\pi\)
0.999678 + 0.0253794i \(0.00807938\pi\)
\(198\) 0 0
\(199\) −0.370462 + 0.441500i −0.0262614 + 0.0312971i −0.779015 0.627005i \(-0.784281\pi\)
0.752754 + 0.658302i \(0.228725\pi\)
\(200\) 0 0
\(201\) 5.59627 + 9.69302i 0.394730 + 0.683693i
\(202\) 0 0
\(203\) −36.5355 + 13.2979i −2.56429 + 0.933326i
\(204\) 0 0
\(205\) −3.05825 0.539252i −0.213597 0.0376630i
\(206\) 0 0
\(207\) 1.21301 + 1.44561i 0.0843101 + 0.100477i
\(208\) 0 0
\(209\) −5.79726 + 3.23589i −0.401005 + 0.223831i
\(210\) 0 0
\(211\) 5.79292 4.86084i 0.398801 0.334634i −0.421229 0.906954i \(-0.638401\pi\)
0.820030 + 0.572321i \(0.193957\pi\)
\(212\) 0 0
\(213\) −1.29426 + 7.34013i −0.0886814 + 0.502937i
\(214\) 0 0
\(215\) 1.35251 + 3.71599i 0.0922405 + 0.253429i
\(216\) 0 0
\(217\) 18.9192 10.9230i 1.28432 0.741502i
\(218\) 0 0
\(219\) 5.33022 + 4.47259i 0.360183 + 0.302229i
\(220\) 0 0
\(221\) 0.118089 + 0.0681784i 0.00794349 + 0.00458618i
\(222\) 0 0
\(223\) −1.09121 6.18858i −0.0730731 0.414418i −0.999299 0.0374482i \(-0.988077\pi\)
0.926225 0.376970i \(-0.123034\pi\)
\(224\) 0 0
\(225\) 2.99273 + 1.08926i 0.199515 + 0.0726175i
\(226\) 0 0
\(227\) −13.1480 −0.872660 −0.436330 0.899787i \(-0.643722\pi\)
−0.436330 + 0.899787i \(0.643722\pi\)
\(228\) 0 0
\(229\) −19.3851 −1.28100 −0.640501 0.767958i \(-0.721273\pi\)
−0.640501 + 0.767958i \(0.721273\pi\)
\(230\) 0 0
\(231\) −5.29813 1.92836i −0.348592 0.126877i
\(232\) 0 0
\(233\) −4.05169 22.9783i −0.265435 1.50536i −0.767794 0.640697i \(-0.778645\pi\)
0.502359 0.864659i \(-0.332466\pi\)
\(234\) 0 0
\(235\) −10.2228 5.90214i −0.666863 0.385013i
\(236\) 0 0
\(237\) −10.5890 8.88522i −0.687829 0.577157i
\(238\) 0 0
\(239\) 5.13041 2.96205i 0.331859 0.191599i −0.324807 0.945780i \(-0.605299\pi\)
0.656666 + 0.754181i \(0.271966\pi\)
\(240\) 0 0
\(241\) −3.39187 9.31910i −0.218490 0.600296i 0.781223 0.624252i \(-0.214596\pi\)
−0.999713 + 0.0239560i \(0.992374\pi\)
\(242\) 0 0
\(243\) −0.173648 + 0.984808i −0.0111395 + 0.0631754i
\(244\) 0 0
\(245\) 6.91740 5.80439i 0.441937 0.370829i
\(246\) 0 0
\(247\) 1.20099 + 3.45475i 0.0764171 + 0.219821i
\(248\) 0 0
\(249\) 0.0996702 + 0.118782i 0.00631634 + 0.00752753i
\(250\) 0 0
\(251\) −12.5043 2.20485i −0.789267 0.139169i −0.235537 0.971865i \(-0.575685\pi\)
−0.553730 + 0.832696i \(0.686796\pi\)
\(252\) 0 0
\(253\) −2.70099 + 0.983080i −0.169810 + 0.0618057i
\(254\) 0 0
\(255\) −0.109470 0.189608i −0.00685530 0.0118737i
\(256\) 0 0
\(257\) −19.1652 + 22.8402i −1.19549 + 1.42473i −0.316039 + 0.948746i \(0.602353\pi\)
−0.879453 + 0.475985i \(0.842092\pi\)
\(258\) 0 0
\(259\) −6.79813 + 11.7747i −0.422415 + 0.731645i
\(260\) 0 0
\(261\) −10.3439 + 1.82391i −0.640271 + 0.112897i
\(262\) 0 0
\(263\) 4.50980 12.3906i 0.278086 0.764036i −0.719493 0.694499i \(-0.755626\pi\)
0.997579 0.0695361i \(-0.0221519\pi\)
\(264\) 0 0
\(265\) 9.16404i 0.562942i
\(266\) 0 0
\(267\) 5.64263i 0.345323i
\(268\) 0 0
\(269\) −6.37464 + 17.5142i −0.388669 + 1.06786i 0.578933 + 0.815375i \(0.303469\pi\)
−0.967601 + 0.252483i \(0.918753\pi\)
\(270\) 0 0
\(271\) −7.01707 + 1.23730i −0.426257 + 0.0751606i −0.382661 0.923889i \(-0.624992\pi\)
−0.0435955 + 0.999049i \(0.513881\pi\)
\(272\) 0 0
\(273\) −1.55303 + 2.68993i −0.0939939 + 0.162802i
\(274\) 0 0
\(275\) −3.11809 + 3.71599i −0.188028 + 0.224083i
\(276\) 0 0
\(277\) 5.00640 + 8.67133i 0.300805 + 0.521010i 0.976319 0.216338i \(-0.0694113\pi\)
−0.675513 + 0.737348i \(0.736078\pi\)
\(278\) 0 0
\(279\) 5.54576 2.01849i 0.332016 0.120844i
\(280\) 0 0
\(281\) −19.5981 3.45567i −1.16912 0.206148i −0.444814 0.895623i \(-0.646730\pi\)
−0.724309 + 0.689475i \(0.757841\pi\)
\(282\) 0 0
\(283\) 16.1370 + 19.2313i 0.959244 + 1.14318i 0.989629 + 0.143644i \(0.0458819\pi\)
−0.0303860 + 0.999538i \(0.509674\pi\)
\(284\) 0 0
\(285\) 1.10354 5.76811i 0.0653681 0.341674i
\(286\) 0 0
\(287\) 6.53596 5.48432i 0.385805 0.323729i
\(288\) 0 0
\(289\) −2.94743 + 16.7157i −0.173378 + 0.983278i
\(290\) 0 0
\(291\) −2.76604 7.59964i −0.162148 0.445499i
\(292\) 0 0
\(293\) 0.512326 0.295792i 0.0299304 0.0172803i −0.484960 0.874536i \(-0.661166\pi\)
0.514891 + 0.857256i \(0.327833\pi\)
\(294\) 0 0
\(295\) −12.2173 10.2516i −0.711322 0.596870i
\(296\) 0 0
\(297\) −1.31908 0.761570i −0.0765407 0.0441908i
\(298\) 0 0
\(299\) 0.274967 + 1.55942i 0.0159018 + 0.0901834i
\(300\) 0 0
\(301\) −10.2096 3.71599i −0.588472 0.214186i
\(302\) 0 0
\(303\) −17.4688 −1.00356
\(304\) 0 0
\(305\) −5.75103 −0.329303
\(306\) 0 0
\(307\) −9.20961 3.35202i −0.525620 0.191310i 0.0655615 0.997849i \(-0.479116\pi\)
−0.591182 + 0.806538i \(0.701338\pi\)
\(308\) 0 0
\(309\) 1.07398 + 6.09083i 0.0610965 + 0.346495i
\(310\) 0 0
\(311\) 9.34864 + 5.39744i 0.530113 + 0.306061i 0.741062 0.671436i \(-0.234322\pi\)
−0.210950 + 0.977497i \(0.567656\pi\)
\(312\) 0 0
\(313\) −17.7285 14.8760i −1.00207 0.840840i −0.0148032 0.999890i \(-0.504712\pi\)
−0.987270 + 0.159051i \(0.949157\pi\)
\(314\) 0 0
\(315\) 4.31908 2.49362i 0.243352 0.140500i
\(316\) 0 0
\(317\) 8.54829 + 23.4862i 0.480120 + 1.31912i 0.909391 + 0.415942i \(0.136548\pi\)
−0.429272 + 0.903175i \(0.641230\pi\)
\(318\) 0 0
\(319\) 2.77807 15.7552i 0.155542 0.882122i
\(320\) 0 0
\(321\) 4.59627 3.85673i 0.256539 0.215261i
\(322\) 0 0
\(323\) 0.549163 0.447395i 0.0305562 0.0248937i
\(324\) 0 0
\(325\) 1.71776 + 2.04715i 0.0952841 + 0.113555i
\(326\) 0 0
\(327\) −7.19459 1.26860i −0.397862 0.0701538i
\(328\) 0 0
\(329\) 30.4761 11.0924i 1.68020 0.611544i
\(330\) 0 0
\(331\) −3.48680 6.03931i −0.191652 0.331950i 0.754146 0.656707i \(-0.228051\pi\)
−0.945798 + 0.324756i \(0.894718\pi\)
\(332\) 0 0
\(333\) −2.36097 + 2.81369i −0.129380 + 0.154189i
\(334\) 0 0
\(335\) 7.53983 13.0594i 0.411945 0.713509i
\(336\) 0 0
\(337\) 10.6395 1.87603i 0.579570 0.102194i 0.123825 0.992304i \(-0.460484\pi\)
0.455745 + 0.890110i \(0.349373\pi\)
\(338\) 0 0
\(339\) −0.517541 + 1.42193i −0.0281090 + 0.0772288i
\(340\) 0 0
\(341\) 8.98908i 0.486786i
\(342\) 0 0
\(343\) 1.10186i 0.0594950i
\(344\) 0 0
\(345\) 0.869585 2.38917i 0.0468169 0.128628i
\(346\) 0 0
\(347\) 22.9461 4.04601i 1.23181 0.217201i 0.480408 0.877045i \(-0.340489\pi\)
0.751403 + 0.659844i \(0.229378\pi\)
\(348\) 0 0
\(349\) 9.64590 16.7072i 0.516333 0.894315i −0.483487 0.875351i \(-0.660630\pi\)
0.999820 0.0189635i \(-0.00603665\pi\)
\(350\) 0 0
\(351\) −0.539363 + 0.642788i −0.0287891 + 0.0343095i
\(352\) 0 0
\(353\) 13.4119 + 23.2302i 0.713846 + 1.23642i 0.963403 + 0.268057i \(0.0863815\pi\)
−0.249558 + 0.968360i \(0.580285\pi\)
\(354\) 0 0
\(355\) 9.43629 3.43453i 0.500826 0.182286i
\(356\) 0 0
\(357\) 0.592396 + 0.104455i 0.0313529 + 0.00552837i
\(358\) 0 0
\(359\) 19.0783 + 22.7367i 1.00691 + 1.19999i 0.979721 + 0.200364i \(0.0642126\pi\)
0.0271935 + 0.999630i \(0.491343\pi\)
\(360\) 0 0
\(361\) 18.9920 + 0.550931i 0.999580 + 0.0289964i
\(362\) 0 0
\(363\) −6.64930 + 5.57943i −0.348998 + 0.292844i
\(364\) 0 0
\(365\) 1.62789 9.23222i 0.0852076 0.483236i
\(366\) 0 0
\(367\) 8.13223 + 22.3431i 0.424499 + 1.16630i 0.949106 + 0.314956i \(0.101990\pi\)
−0.524607 + 0.851344i \(0.675788\pi\)
\(368\) 0 0
\(369\) 1.99613 1.15247i 0.103914 0.0599950i
\(370\) 0 0
\(371\) −19.2875 16.1841i −1.00135 0.840236i
\(372\) 0 0
\(373\) −29.4192 16.9852i −1.52327 0.879460i −0.999621 0.0275252i \(-0.991237\pi\)
−0.523648 0.851935i \(-0.675429\pi\)
\(374\) 0 0
\(375\) −1.91488 10.8598i −0.0988839 0.560798i
\(376\) 0 0
\(377\) −8.28194 3.01438i −0.426541 0.155248i
\(378\) 0 0
\(379\) 23.5503 1.20970 0.604848 0.796341i \(-0.293234\pi\)
0.604848 + 0.796341i \(0.293234\pi\)
\(380\) 0 0
\(381\) −12.7219 −0.651764
\(382\) 0 0
\(383\) 34.7422 + 12.6451i 1.77524 + 0.646135i 0.999893 + 0.0146011i \(0.00464785\pi\)
0.775348 + 0.631534i \(0.217574\pi\)
\(384\) 0 0
\(385\) 1.31908 + 7.48086i 0.0672264 + 0.381260i
\(386\) 0 0
\(387\) −2.54189 1.46756i −0.129211 0.0746003i
\(388\) 0 0
\(389\) 24.7861 + 20.7980i 1.25671 + 1.05450i 0.996025 + 0.0890763i \(0.0283915\pi\)
0.260681 + 0.965425i \(0.416053\pi\)
\(390\) 0 0
\(391\) 0.265578 0.153331i 0.0134308 0.00775430i
\(392\) 0 0
\(393\) −3.13429 8.61138i −0.158104 0.434387i
\(394\) 0 0
\(395\) −3.23396 + 18.3407i −0.162718 + 0.922819i
\(396\) 0 0
\(397\) 6.28106 5.27043i 0.315237 0.264516i −0.471415 0.881911i \(-0.656257\pi\)
0.786653 + 0.617396i \(0.211812\pi\)
\(398\) 0 0
\(399\) 10.1912 + 12.5094i 0.510198 + 0.626251i
\(400\) 0 0
\(401\) −11.9500 14.2414i −0.596753 0.711182i 0.380136 0.924931i \(-0.375877\pi\)
−0.976889 + 0.213749i \(0.931433\pi\)
\(402\) 0 0
\(403\) 4.87686 + 0.859922i 0.242934 + 0.0428358i
\(404\) 0 0
\(405\) 1.26604 0.460802i 0.0629103 0.0228975i
\(406\) 0 0
\(407\) −2.79726 4.84499i −0.138655 0.240157i
\(408\) 0 0
\(409\) 0.922618 1.09953i 0.0456205 0.0543685i −0.742752 0.669567i \(-0.766480\pi\)
0.788372 + 0.615199i \(0.210924\pi\)
\(410\) 0 0
\(411\) 7.13816 12.3636i 0.352099 0.609854i
\(412\) 0 0
\(413\) 43.1528 7.60900i 2.12341 0.374414i
\(414\) 0 0
\(415\) 0.0714517 0.196312i 0.00350743 0.00963658i
\(416\) 0 0
\(417\) 0.402575i 0.0197142i
\(418\) 0 0
\(419\) 35.0031i 1.71002i −0.518615 0.855008i \(-0.673552\pi\)
0.518615 0.855008i \(-0.326448\pi\)
\(420\) 0 0
\(421\) −11.1316 + 30.5838i −0.542521 + 1.49056i 0.301083 + 0.953598i \(0.402652\pi\)
−0.843604 + 0.536966i \(0.819570\pi\)
\(422\) 0 0
\(423\) 8.62836 1.52141i 0.419525 0.0739736i
\(424\) 0 0
\(425\) 0.258770 0.448204i 0.0125522 0.0217411i
\(426\) 0 0
\(427\) 10.1566 12.1041i 0.491511 0.585760i
\(428\) 0 0
\(429\) −0.639033 1.10684i −0.0308528 0.0534386i
\(430\) 0 0
\(431\) −21.7297 + 7.90895i −1.04668 + 0.380961i −0.807409 0.589992i \(-0.799131\pi\)
−0.239272 + 0.970953i \(0.576909\pi\)
\(432\) 0 0
\(433\) 11.5869 + 2.04309i 0.556832 + 0.0981846i 0.444980 0.895540i \(-0.353211\pi\)
0.111852 + 0.993725i \(0.464322\pi\)
\(434\) 0 0
\(435\) 9.09627 + 10.8405i 0.436133 + 0.519763i
\(436\) 0 0
\(437\) 8.07919 + 1.54569i 0.386480 + 0.0739404i
\(438\) 0 0
\(439\) 17.2875 14.5059i 0.825085 0.692329i −0.129072 0.991635i \(-0.541200\pi\)
0.954157 + 0.299307i \(0.0967553\pi\)
\(440\) 0 0
\(441\) −1.16385 + 6.60051i −0.0554213 + 0.314310i
\(442\) 0 0
\(443\) 7.23601 + 19.8808i 0.343793 + 0.944565i 0.984283 + 0.176598i \(0.0565092\pi\)
−0.640490 + 0.767967i \(0.721269\pi\)
\(444\) 0 0
\(445\) 6.58378 3.80115i 0.312101 0.180192i
\(446\) 0 0
\(447\) −8.55690 7.18009i −0.404728 0.339607i
\(448\) 0 0
\(449\) 31.2212 + 18.0256i 1.47342 + 0.850680i 0.999552 0.0299162i \(-0.00952405\pi\)
0.473868 + 0.880596i \(0.342857\pi\)
\(450\) 0 0
\(451\) 0.609633 + 3.45740i 0.0287065 + 0.162803i
\(452\) 0 0
\(453\) −6.75624 2.45907i −0.317436 0.115537i
\(454\) 0 0
\(455\) 4.18479 0.196186
\(456\) 0 0
\(457\) −39.1908 −1.83327 −0.916634 0.399728i \(-0.869104\pi\)
−0.916634 + 0.399728i \(0.869104\pi\)
\(458\) 0 0
\(459\) 0.152704 + 0.0555796i 0.00712760 + 0.00259423i
\(460\) 0 0
\(461\) −5.37639 30.4910i −0.250404 1.42011i −0.807601 0.589729i \(-0.799235\pi\)
0.557198 0.830380i \(-0.311877\pi\)
\(462\) 0 0
\(463\) −32.8919 18.9902i −1.52862 0.882548i −0.999420 0.0340491i \(-0.989160\pi\)
−0.529197 0.848499i \(-0.677507\pi\)
\(464\) 0 0
\(465\) −6.09105 5.11100i −0.282466 0.237017i
\(466\) 0 0
\(467\) 27.5077 15.8816i 1.27291 0.734913i 0.297372 0.954762i \(-0.403890\pi\)
0.975534 + 0.219849i \(0.0705564\pi\)
\(468\) 0 0
\(469\) 14.1702 + 38.9324i 0.654321 + 1.79773i
\(470\) 0 0
\(471\) 2.37686 13.4798i 0.109520 0.621118i
\(472\) 0 0
\(473\) 3.42468 2.87365i 0.157467 0.132130i
\(474\) 0 0
\(475\) 13.1125 4.55834i 0.601641 0.209151i
\(476\) 0 0
\(477\) −4.37211 5.21048i −0.200185 0.238571i
\(478\) 0 0
\(479\) 38.4707 + 6.78341i 1.75777 + 0.309942i 0.957228 0.289335i \(-0.0934343\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(480\) 0 0
\(481\) −2.89615 + 1.05411i −0.132053 + 0.0480635i
\(482\) 0 0
\(483\) 3.49273 + 6.04958i 0.158925 + 0.275265i
\(484\) 0 0
\(485\) −7.00387 + 8.34689i −0.318029 + 0.379013i
\(486\) 0 0
\(487\) −10.4697 + 18.1341i −0.474428 + 0.821734i −0.999571 0.0292800i \(-0.990679\pi\)
0.525143 + 0.851014i \(0.324012\pi\)
\(488\) 0 0
\(489\) −15.7515 + 2.77741i −0.712307 + 0.125599i
\(490\) 0 0
\(491\) −13.7144 + 37.6799i −0.618920 + 1.70047i 0.0906940 + 0.995879i \(0.471091\pi\)
−0.709614 + 0.704590i \(0.751131\pi\)
\(492\) 0 0
\(493\) 1.70685i 0.0768728i
\(494\) 0 0
\(495\) 2.05212i 0.0922360i
\(496\) 0 0
\(497\) −9.43629 + 25.9260i −0.423275 + 1.16294i
\(498\) 0 0
\(499\) 24.9873 4.40593i 1.11858 0.197236i 0.416365 0.909198i \(-0.363304\pi\)
0.702219 + 0.711961i \(0.252193\pi\)
\(500\) 0 0
\(501\) −1.34730 + 2.33359i −0.0601928 + 0.104257i
\(502\) 0 0
\(503\) −1.78359 + 2.12559i −0.0795261 + 0.0947756i −0.804340 0.594169i \(-0.797481\pi\)
0.724814 + 0.688944i \(0.241926\pi\)
\(504\) 0 0
\(505\) 11.7679 + 20.3825i 0.523663 + 0.907010i
\(506\) 0 0
\(507\) 11.5544 4.20545i 0.513148 0.186771i
\(508\) 0 0
\(509\) 24.9538 + 4.40003i 1.10606 + 0.195028i 0.696712 0.717351i \(-0.254645\pi\)
0.409347 + 0.912379i \(0.365757\pi\)
\(510\) 0 0
\(511\) 16.5560 + 19.7307i 0.732395 + 0.872835i
\(512\) 0 0
\(513\) 2.12449 + 3.80612i 0.0937983 + 0.168044i
\(514\) 0 0
\(515\) 6.38326 5.35619i 0.281280 0.236022i
\(516\) 0 0
\(517\) −2.31732 + 13.1422i −0.101916 + 0.577993i
\(518\) 0 0
\(519\) −6.83615 18.7822i −0.300074 0.824446i
\(520\) 0 0
\(521\) 4.52078 2.61007i 0.198059 0.114349i −0.397691 0.917520i \(-0.630188\pi\)
0.595750 + 0.803170i \(0.296855\pi\)
\(522\) 0 0
\(523\) 0.657289 + 0.551531i 0.0287413 + 0.0241168i 0.657045 0.753851i \(-0.271806\pi\)
−0.628304 + 0.777968i \(0.716251\pi\)
\(524\) 0 0
\(525\) 10.2096 + 5.89452i 0.445584 + 0.257258i
\(526\) 0 0
\(527\) −0.166536 0.944475i −0.00725444 0.0411420i
\(528\) 0 0
\(529\) −18.2665 6.64847i −0.794196 0.289064i
\(530\) 0 0
\(531\) 11.8375 0.513704
\(532\) 0 0
\(533\) 1.93407 0.0837738
\(534\) 0 0
\(535\) −7.59627 2.76481i −0.328415 0.119533i
\(536\) 0 0
\(537\) −0.718063 4.07234i −0.0309867 0.175734i
\(538\) 0 0
\(539\) −8.84090 5.10430i −0.380805 0.219858i
\(540\) 0 0
\(541\) 6.65839 + 5.58705i 0.286266 + 0.240206i 0.774601 0.632451i \(-0.217951\pi\)
−0.488334 + 0.872657i \(0.662395\pi\)
\(542\) 0 0
\(543\) −1.10014 + 0.635164i −0.0472114 + 0.0272575i
\(544\) 0 0
\(545\) 3.36643 + 9.24919i 0.144202 + 0.396192i
\(546\) 0 0
\(547\) 5.75578 32.6426i 0.246099 1.39570i −0.571827 0.820375i \(-0.693765\pi\)
0.817926 0.575324i \(-0.195124\pi\)
\(548\) 0 0
\(549\) 3.26991 2.74378i 0.139557 0.117102i
\(550\) 0 0
\(551\) −29.9345 + 34.6418i −1.27525 + 1.47579i
\(552\) 0 0
\(553\) −32.8901 39.1969i −1.39863 1.66682i
\(554\) 0 0
\(555\) 4.87346 + 0.859322i 0.206867 + 0.0364762i
\(556\) 0 0
\(557\) −14.0446 + 5.11181i −0.595088 + 0.216594i −0.621966 0.783044i \(-0.713666\pi\)
0.0268779 + 0.999639i \(0.491443\pi\)
\(558\) 0 0
\(559\) −1.23143 2.13290i −0.0520839 0.0902120i
\(560\) 0 0
\(561\) −0.159100 + 0.189608i −0.00671722 + 0.00800527i
\(562\) 0 0
\(563\) −9.00640 + 15.5995i −0.379574 + 0.657442i −0.991000 0.133860i \(-0.957263\pi\)
0.611426 + 0.791302i \(0.290596\pi\)
\(564\) 0 0
\(565\) 2.00774 0.354019i 0.0844663 0.0148937i
\(566\) 0 0
\(567\) −1.26604 + 3.47843i −0.0531689 + 0.146080i
\(568\) 0 0
\(569\) 19.4773i 0.816531i −0.912863 0.408265i \(-0.866134\pi\)
0.912863 0.408265i \(-0.133866\pi\)
\(570\) 0 0
\(571\) 24.2575i 1.01514i −0.861610 0.507572i \(-0.830543\pi\)
0.861610 0.507572i \(-0.169457\pi\)
\(572\) 0 0
\(573\) −2.03596 + 5.59375i −0.0850534 + 0.233682i
\(574\) 0 0
\(575\) 5.91875 1.04363i 0.246829 0.0435226i
\(576\) 0 0
\(577\) −20.1689 + 34.9336i −0.839642 + 1.45430i 0.0505517 + 0.998721i \(0.483902\pi\)
−0.890194 + 0.455582i \(0.849431\pi\)
\(578\) 0 0
\(579\) 6.07785 7.24330i 0.252587 0.301021i
\(580\) 0 0
\(581\) 0.286989 + 0.497079i 0.0119063 + 0.0206223i
\(582\) 0 0
\(583\) 9.73530 3.54336i 0.403195 0.146751i
\(584\) 0 0
\(585\) 1.11334 + 0.196312i 0.0460310 + 0.00811650i
\(586\) 0 0
\(587\) −3.52394 4.19967i −0.145448 0.173339i 0.688402 0.725330i \(-0.258313\pi\)
−0.833850 + 0.551991i \(0.813868\pi\)
\(588\) 0 0
\(589\) 13.1841 22.0895i 0.543240 0.910181i
\(590\) 0 0
\(591\) 10.2758 8.62246i 0.422692 0.354681i
\(592\) 0 0
\(593\) −2.03137 + 11.5205i −0.0834185 + 0.473090i 0.914268 + 0.405110i \(0.132767\pi\)
−0.997687 + 0.0679804i \(0.978344\pi\)
\(594\) 0 0
\(595\) −0.277189 0.761570i −0.0113636 0.0312213i
\(596\) 0 0
\(597\) −0.499123 + 0.288169i −0.0204277 + 0.0117940i
\(598\) 0 0
\(599\) 3.15451 + 2.64695i 0.128890 + 0.108152i 0.704954 0.709253i \(-0.250968\pi\)
−0.576064 + 0.817405i \(0.695412\pi\)
\(600\) 0 0
\(601\) 6.24376 + 3.60483i 0.254688 + 0.147044i 0.621909 0.783090i \(-0.286357\pi\)
−0.367221 + 0.930134i \(0.619691\pi\)
\(602\) 0 0
\(603\) 1.94356 + 11.0225i 0.0791480 + 0.448871i
\(604\) 0 0
\(605\) 10.9893 + 3.99979i 0.446779 + 0.162614i
\(606\) 0 0
\(607\) −15.4953 −0.628933 −0.314466 0.949269i \(-0.601826\pi\)
−0.314466 + 0.949269i \(0.601826\pi\)
\(608\) 0 0
\(609\) −38.8803 −1.57551
\(610\) 0 0
\(611\) 6.90838 + 2.51444i 0.279483 + 0.101723i
\(612\) 0 0
\(613\) −4.32454 24.5257i −0.174667 0.990583i −0.938528 0.345203i \(-0.887810\pi\)
0.763861 0.645380i \(-0.223301\pi\)
\(614\) 0 0
\(615\) −2.68938 1.55271i −0.108446 0.0626114i
\(616\) 0 0
\(617\) 7.19119 + 6.03412i 0.289506 + 0.242925i 0.775961 0.630781i \(-0.217266\pi\)
−0.486454 + 0.873706i \(0.661710\pi\)
\(618\) 0 0
\(619\) 23.1318 13.3552i 0.929746 0.536789i 0.0430149 0.999074i \(-0.486304\pi\)
0.886731 + 0.462285i \(0.152970\pi\)
\(620\) 0 0
\(621\) 0.645430 + 1.77330i 0.0259002 + 0.0711602i
\(622\) 0 0
\(623\) −3.62701 + 20.5698i −0.145313 + 0.824112i
\(624\) 0 0
\(625\) 0.817267 0.685768i 0.0326907 0.0274307i
\(626\) 0 0
\(627\) −6.55438 + 1.05796i −0.261757 + 0.0422509i
\(628\) 0 0
\(629\) 0.383666 + 0.457236i 0.0152978 + 0.0182312i
\(630\) 0 0
\(631\) 2.47044 + 0.435605i 0.0983466 + 0.0173412i 0.222605 0.974909i \(-0.428544\pi\)
−0.124258 + 0.992250i \(0.539655\pi\)
\(632\) 0 0
\(633\) 7.10607 2.58640i 0.282441 0.102800i
\(634\) 0 0
\(635\) 8.57011 + 14.8439i 0.340094 + 0.589061i
\(636\) 0 0
\(637\) −3.61499 + 4.30818i −0.143231 + 0.170696i
\(638\) 0 0
\(639\) −3.72668 + 6.45480i −0.147425 + 0.255348i
\(640\) 0 0
\(641\) 32.2925 5.69404i 1.27548 0.224901i 0.505419 0.862874i \(-0.331338\pi\)
0.770059 + 0.637973i \(0.220227\pi\)
\(642\) 0 0
\(643\) −5.22028 + 14.3426i −0.205868 + 0.565618i −0.999060 0.0433543i \(-0.986196\pi\)
0.793192 + 0.608972i \(0.208418\pi\)
\(644\) 0 0
\(645\) 3.95448i 0.155707i
\(646\) 0 0
\(647\) 13.8107i 0.542953i −0.962445 0.271477i \(-0.912488\pi\)
0.962445 0.271477i \(-0.0875120\pi\)
\(648\) 0 0
\(649\) −6.16668 + 16.9428i −0.242063 + 0.665064i
\(650\) 0 0
\(651\) 21.5141 3.79352i 0.843206 0.148680i
\(652\) 0 0
\(653\) 8.39440 14.5395i 0.328498 0.568976i −0.653716 0.756740i \(-0.726791\pi\)
0.982214 + 0.187764i \(0.0601242\pi\)
\(654\) 0 0
\(655\) −7.93629 + 9.45810i −0.310096 + 0.369559i
\(656\) 0 0
\(657\) 3.47906 + 6.02590i 0.135731 + 0.235093i
\(658\) 0 0
\(659\) 2.23947 0.815102i 0.0872376 0.0317519i −0.298033 0.954556i \(-0.596330\pi\)
0.385270 + 0.922804i \(0.374108\pi\)
\(660\) 0 0
\(661\) −5.44104 0.959402i −0.211632 0.0373164i 0.0668270 0.997765i \(-0.478712\pi\)
−0.278459 + 0.960448i \(0.589824\pi\)
\(662\) 0 0
\(663\) 0.0876485 + 0.104455i 0.00340399 + 0.00405671i
\(664\) 0 0
\(665\) 7.73055 20.3179i 0.299778 0.787895i
\(666\) 0 0
\(667\) −15.1839 + 12.7408i −0.587924 + 0.493326i
\(668\) 0 0
\(669\) 1.09121 6.18858i 0.0421888 0.239264i
\(670\) 0 0
\(671\) 2.22369 + 6.10953i 0.0858445 + 0.235856i
\(672\) 0 0
\(673\) −0.0744448 + 0.0429807i −0.00286964 + 0.00165678i −0.501434 0.865196i \(-0.667194\pi\)
0.498564 + 0.866853i \(0.333861\pi\)
\(674\) 0 0
\(675\) 2.43969 + 2.04715i 0.0939038 + 0.0787947i
\(676\) 0 0
\(677\) 9.80113 + 5.65868i 0.376688 + 0.217481i 0.676376 0.736556i \(-0.263549\pi\)
−0.299688 + 0.954037i \(0.596883\pi\)
\(678\) 0 0
\(679\) −5.19846 29.4819i −0.199499 1.13141i
\(680\) 0 0
\(681\) −12.3550 4.49687i −0.473446 0.172320i
\(682\) 0 0
\(683\) −46.1448 −1.76568 −0.882840 0.469673i \(-0.844372\pi\)
−0.882840 + 0.469673i \(0.844372\pi\)
\(684\) 0 0
\(685\) −19.2344 −0.734910
\(686\) 0 0
\(687\) −18.2160 6.63008i −0.694984 0.252953i
\(688\) 0 0
\(689\) −0.991077 5.62068i −0.0377570 0.214131i
\(690\) 0 0
\(691\) 20.3402 + 11.7434i 0.773777 + 0.446740i 0.834220 0.551431i \(-0.185918\pi\)
−0.0604433 + 0.998172i \(0.519251\pi\)
\(692\) 0 0
\(693\) −4.31908 3.62414i −0.164068 0.137670i
\(694\) 0 0
\(695\) −0.469722 + 0.271194i −0.0178176 + 0.0102870i
\(696\) 0 0
\(697\) −0.128107 0.351972i −0.00485240 0.0133319i
\(698\) 0 0
\(699\) 4.05169 22.9783i 0.153249 0.869118i
\(700\) 0 0
\(701\) 24.1989 20.3053i 0.913981 0.766921i −0.0588912 0.998264i \(-0.518757\pi\)
0.972872 + 0.231343i \(0.0743121\pi\)
\(702\) 0 0
\(703\) −0.232145 + 16.0086i −0.00875550 + 0.603776i
\(704\) 0 0
\(705\) −7.58765 9.04261i −0.285767 0.340564i
\(706\) 0 0
\(707\) −63.6814 11.2288i −2.39499 0.422301i
\(708\) 0 0
\(709\) 36.3203 13.2195i 1.36404 0.496469i 0.446738 0.894665i \(-0.352586\pi\)
0.917300 + 0.398196i \(0.130364\pi\)
\(710\) 0 0
\(711\) −6.91147 11.9710i −0.259201 0.448948i
\(712\) 0 0
\(713\) 7.15880 8.53152i 0.268099 0.319508i
\(714\) 0 0
\(715\) −0.860967 + 1.49124i −0.0321983 + 0.0557692i
\(716\) 0 0
\(717\) 5.83409 1.02871i 0.217878 0.0384178i
\(718\) 0 0
\(719\) 9.61222 26.4093i 0.358475 0.984902i −0.621084 0.783744i \(-0.713307\pi\)
0.979559 0.201158i \(-0.0644705\pi\)
\(720\) 0 0
\(721\) 22.8940i 0.852619i
\(722\) 0 0
\(723\) 9.91718i 0.368824i
\(724\) 0 0
\(725\) −11.4410 + 31.4340i −0.424909 + 1.16743i
\(726\) 0 0
\(727\) 2.43124 0.428693i 0.0901696 0.0158993i −0.128381 0.991725i \(-0.540978\pi\)
0.218551 + 0.975826i \(0.429867\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) −0.306589 + 0.365379i −0.0113396 + 0.0135140i
\(732\) 0 0
\(733\) −9.38532 16.2558i −0.346655 0.600423i 0.638998 0.769208i \(-0.279349\pi\)
−0.985653 + 0.168785i \(0.946016\pi\)
\(734\) 0 0
\(735\) 8.48545 3.08845i 0.312991 0.113919i
\(736\) 0 0
\(737\) −16.7888 2.96032i −0.618423 0.109045i
\(738\) 0 0
\(739\) 19.1043 + 22.7676i 0.702763 + 0.837521i 0.992836 0.119484i \(-0.0381239\pi\)
−0.290073 + 0.957005i \(0.593679\pi\)
\(740\) 0 0
\(741\) −0.0530334 + 3.65717i −0.00194823 + 0.134349i
\(742\) 0 0
\(743\) 3.79813 3.18701i 0.139340 0.116920i −0.570454 0.821330i \(-0.693233\pi\)
0.709794 + 0.704410i \(0.248788\pi\)
\(744\) 0 0
\(745\) −2.61334 + 14.8210i −0.0957454 + 0.542999i
\(746\) 0 0
\(747\) 0.0530334 + 0.145708i 0.00194039 + 0.00533118i
\(748\) 0 0
\(749\) 19.2344 11.1050i 0.702810 0.405768i
\(750\) 0 0
\(751\) −20.1839 16.9363i −0.736522 0.618015i 0.195379 0.980728i \(-0.437406\pi\)
−0.931901 + 0.362713i \(0.881851\pi\)
\(752\) 0 0
\(753\) −10.9961 6.34862i −0.400721 0.231357i
\(754\) 0 0
\(755\) 1.68210 + 9.53969i 0.0612180 + 0.347185i
\(756\) 0 0
\(757\) 3.06448 + 1.11538i 0.111381 + 0.0405392i 0.397109 0.917771i \(-0.370013\pi\)
−0.285729 + 0.958311i \(0.592236\pi\)
\(758\) 0 0
\(759\) −2.87433 −0.104332
\(760\) 0 0
\(761\) −20.0205 −0.725744 −0.362872 0.931839i \(-0.618204\pi\)
−0.362872 + 0.931839i \(0.618204\pi\)
\(762\) 0 0
\(763\) −25.4119 9.24919i −0.919974 0.334843i
\(764\) 0 0
\(765\) −0.0380187 0.215615i −0.00137457 0.00779556i
\(766\) 0 0
\(767\) 8.60209 + 4.96642i 0.310603 + 0.179327i
\(768\) 0 0
\(769\) −39.6259 33.2501i −1.42895 1.19903i −0.946333 0.323195i \(-0.895243\pi\)
−0.482613 0.875833i \(-0.660312\pi\)
\(770\) 0 0
\(771\) −25.8212 + 14.9079i −0.929928 + 0.536894i
\(772\) 0 0
\(773\) 4.76975 + 13.1048i 0.171556 + 0.471346i 0.995438 0.0954157i \(-0.0304180\pi\)
−0.823881 + 0.566762i \(0.808196\pi\)
\(774\) 0 0
\(775\) 3.26382 18.5101i 0.117240 0.664901i
\(776\) 0 0
\(777\) −10.4153 + 8.73951i −0.373648 + 0.313528i
\(778\) 0 0
\(779\) 3.57280 9.39024i 0.128009 0.336440i
\(780\) 0 0
\(781\) −7.29726 8.69653i −0.261116 0.311186i
\(782\) 0 0
\(783\) −10.3439 1.82391i −0.369661 0.0651811i
\(784\) 0 0
\(785\) −17.3293 + 6.30737i −0.618511 + 0.225120i
\(786\) 0 0
\(787\) −7.84776