Properties

Label 190.2.b.a.39.2
Level $190$
Weight $2$
Character 190.39
Analytic conductor $1.517$
Analytic rank $0$
Dimension $4$
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] = [190,2,Mod(39,190)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(190, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("190.39");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.b (of order \(2\), degree \(1\), 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: \(1.51715763840\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 190.39
Dual form 190.2.b.a.39.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +0.414214i q^{3} -1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +0.414214 q^{6} +4.41421i q^{7} +1.00000i q^{8} +2.82843 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +0.414214i q^{3} -1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +0.414214 q^{6} +4.41421i q^{7} +1.00000i q^{8} +2.82843 q^{9} +(2.12132 - 0.707107i) q^{10} -1.41421 q^{11} -0.414214i q^{12} -5.82843i q^{13} +4.41421 q^{14} +(-0.878680 + 0.292893i) q^{15} +1.00000 q^{16} +1.00000i q^{17} -2.82843i q^{18} +1.00000 q^{19} +(-0.707107 - 2.12132i) q^{20} -1.82843 q^{21} +1.41421i q^{22} -0.757359i q^{23} -0.414214 q^{24} +(-4.00000 + 3.00000i) q^{25} -5.82843 q^{26} +2.41421i q^{27} -4.41421i q^{28} +0.171573 q^{29} +(0.292893 + 0.878680i) q^{30} +6.24264 q^{31} -1.00000i q^{32} -0.585786i q^{33} +1.00000 q^{34} +(-9.36396 + 3.12132i) q^{35} -2.82843 q^{36} -8.48528i q^{37} -1.00000i q^{38} +2.41421 q^{39} +(-2.12132 + 0.707107i) q^{40} -4.24264 q^{41} +1.82843i q^{42} -1.75736i q^{43} +1.41421 q^{44} +(2.00000 + 6.00000i) q^{45} -0.757359 q^{46} +0.414214i q^{48} -12.4853 q^{49} +(3.00000 + 4.00000i) q^{50} -0.414214 q^{51} +5.82843i q^{52} -5.48528i q^{53} +2.41421 q^{54} +(-1.00000 - 3.00000i) q^{55} -4.41421 q^{56} +0.414214i q^{57} -0.171573i q^{58} -6.89949 q^{59} +(0.878680 - 0.292893i) q^{60} +14.2426 q^{61} -6.24264i q^{62} +12.4853i q^{63} -1.00000 q^{64} +(12.3640 - 4.12132i) q^{65} -0.585786 q^{66} +4.75736i q^{67} -1.00000i q^{68} +0.313708 q^{69} +(3.12132 + 9.36396i) q^{70} -13.4142 q^{71} +2.82843i q^{72} -11.4853i q^{73} -8.48528 q^{74} +(-1.24264 - 1.65685i) q^{75} -1.00000 q^{76} -6.24264i q^{77} -2.41421i q^{78} +6.48528 q^{79} +(0.707107 + 2.12132i) q^{80} +7.48528 q^{81} +4.24264i q^{82} -14.4853i q^{83} +1.82843 q^{84} +(-2.12132 + 0.707107i) q^{85} -1.75736 q^{86} +0.0710678i q^{87} -1.41421i q^{88} -7.07107 q^{89} +(6.00000 - 2.00000i) q^{90} +25.7279 q^{91} +0.757359i q^{92} +2.58579i q^{93} +(0.707107 + 2.12132i) q^{95} +0.414214 q^{96} -0.343146i q^{97} +12.4853i q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} - 4 q^{6} + 12 q^{14} - 12 q^{15} + 4 q^{16} + 4 q^{19} + 4 q^{21} + 4 q^{24} - 16 q^{25} - 12 q^{26} + 12 q^{29} + 4 q^{30} + 8 q^{31} + 4 q^{34} - 12 q^{35} + 4 q^{39} + 8 q^{45} - 20 q^{46} - 16 q^{49} + 12 q^{50} + 4 q^{51} + 4 q^{54} - 4 q^{55} - 12 q^{56} + 12 q^{59} + 12 q^{60} + 40 q^{61} - 4 q^{64} + 24 q^{65} - 8 q^{66} - 44 q^{69} + 4 q^{70} - 48 q^{71} + 12 q^{75} - 4 q^{76} - 8 q^{79} - 4 q^{81} - 4 q^{84} - 24 q^{86} + 24 q^{90} + 52 q^{91} - 4 q^{96} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/190\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.414214i 0.239146i 0.992825 + 0.119573i \(0.0381526\pi\)
−0.992825 + 0.119573i \(0.961847\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.707107 + 2.12132i 0.316228 + 0.948683i
\(6\) 0.414214 0.169102
\(7\) 4.41421i 1.66842i 0.551450 + 0.834208i \(0.314075\pi\)
−0.551450 + 0.834208i \(0.685925\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.82843 0.942809
\(10\) 2.12132 0.707107i 0.670820 0.223607i
\(11\) −1.41421 −0.426401 −0.213201 0.977008i \(-0.568389\pi\)
−0.213201 + 0.977008i \(0.568389\pi\)
\(12\) 0.414214i 0.119573i
\(13\) 5.82843i 1.61651i −0.588829 0.808257i \(-0.700411\pi\)
0.588829 0.808257i \(-0.299589\pi\)
\(14\) 4.41421 1.17975
\(15\) −0.878680 + 0.292893i −0.226874 + 0.0756247i
\(16\) 1.00000 0.250000
\(17\) 1.00000i 0.242536i 0.992620 + 0.121268i \(0.0386960\pi\)
−0.992620 + 0.121268i \(0.961304\pi\)
\(18\) 2.82843i 0.666667i
\(19\) 1.00000 0.229416
\(20\) −0.707107 2.12132i −0.158114 0.474342i
\(21\) −1.82843 −0.398996
\(22\) 1.41421i 0.301511i
\(23\) 0.757359i 0.157920i −0.996878 0.0789602i \(-0.974840\pi\)
0.996878 0.0789602i \(-0.0251600\pi\)
\(24\) −0.414214 −0.0845510
\(25\) −4.00000 + 3.00000i −0.800000 + 0.600000i
\(26\) −5.82843 −1.14305
\(27\) 2.41421i 0.464616i
\(28\) 4.41421i 0.834208i
\(29\) 0.171573 0.0318603 0.0159301 0.999873i \(-0.494929\pi\)
0.0159301 + 0.999873i \(0.494929\pi\)
\(30\) 0.292893 + 0.878680i 0.0534747 + 0.160424i
\(31\) 6.24264 1.12121 0.560606 0.828083i \(-0.310568\pi\)
0.560606 + 0.828083i \(0.310568\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.585786i 0.101972i
\(34\) 1.00000 0.171499
\(35\) −9.36396 + 3.12132i −1.58280 + 0.527599i
\(36\) −2.82843 −0.471405
\(37\) 8.48528i 1.39497i −0.716599 0.697486i \(-0.754302\pi\)
0.716599 0.697486i \(-0.245698\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 2.41421 0.386584
\(40\) −2.12132 + 0.707107i −0.335410 + 0.111803i
\(41\) −4.24264 −0.662589 −0.331295 0.943527i \(-0.607485\pi\)
−0.331295 + 0.943527i \(0.607485\pi\)
\(42\) 1.82843i 0.282132i
\(43\) 1.75736i 0.267995i −0.990982 0.133997i \(-0.957219\pi\)
0.990982 0.133997i \(-0.0427814\pi\)
\(44\) 1.41421 0.213201
\(45\) 2.00000 + 6.00000i 0.298142 + 0.894427i
\(46\) −0.757359 −0.111667
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.414214i 0.0597866i
\(49\) −12.4853 −1.78361
\(50\) 3.00000 + 4.00000i 0.424264 + 0.565685i
\(51\) −0.414214 −0.0580015
\(52\) 5.82843i 0.808257i
\(53\) 5.48528i 0.753461i −0.926323 0.376731i \(-0.877048\pi\)
0.926323 0.376731i \(-0.122952\pi\)
\(54\) 2.41421 0.328533
\(55\) −1.00000 3.00000i −0.134840 0.404520i
\(56\) −4.41421 −0.589874
\(57\) 0.414214i 0.0548639i
\(58\) 0.171573i 0.0225286i
\(59\) −6.89949 −0.898238 −0.449119 0.893472i \(-0.648262\pi\)
−0.449119 + 0.893472i \(0.648262\pi\)
\(60\) 0.878680 0.292893i 0.113437 0.0378124i
\(61\) 14.2426 1.82358 0.911792 0.410653i \(-0.134699\pi\)
0.911792 + 0.410653i \(0.134699\pi\)
\(62\) 6.24264i 0.792816i
\(63\) 12.4853i 1.57300i
\(64\) −1.00000 −0.125000
\(65\) 12.3640 4.12132i 1.53356 0.511187i
\(66\) −0.585786 −0.0721053
\(67\) 4.75736i 0.581204i 0.956844 + 0.290602i \(0.0938555\pi\)
−0.956844 + 0.290602i \(0.906144\pi\)
\(68\) 1.00000i 0.121268i
\(69\) 0.313708 0.0377661
\(70\) 3.12132 + 9.36396i 0.373069 + 1.11921i
\(71\) −13.4142 −1.59197 −0.795987 0.605314i \(-0.793048\pi\)
−0.795987 + 0.605314i \(0.793048\pi\)
\(72\) 2.82843i 0.333333i
\(73\) 11.4853i 1.34425i −0.740437 0.672125i \(-0.765382\pi\)
0.740437 0.672125i \(-0.234618\pi\)
\(74\) −8.48528 −0.986394
\(75\) −1.24264 1.65685i −0.143488 0.191317i
\(76\) −1.00000 −0.114708
\(77\) 6.24264i 0.711415i
\(78\) 2.41421i 0.273356i
\(79\) 6.48528 0.729651 0.364826 0.931076i \(-0.381129\pi\)
0.364826 + 0.931076i \(0.381129\pi\)
\(80\) 0.707107 + 2.12132i 0.0790569 + 0.237171i
\(81\) 7.48528 0.831698
\(82\) 4.24264i 0.468521i
\(83\) 14.4853i 1.58997i −0.606632 0.794983i \(-0.707480\pi\)
0.606632 0.794983i \(-0.292520\pi\)
\(84\) 1.82843 0.199498
\(85\) −2.12132 + 0.707107i −0.230089 + 0.0766965i
\(86\) −1.75736 −0.189501
\(87\) 0.0710678i 0.00761927i
\(88\) 1.41421i 0.150756i
\(89\) −7.07107 −0.749532 −0.374766 0.927119i \(-0.622277\pi\)
−0.374766 + 0.927119i \(0.622277\pi\)
\(90\) 6.00000 2.00000i 0.632456 0.210819i
\(91\) 25.7279 2.69702
\(92\) 0.757359i 0.0789602i
\(93\) 2.58579i 0.268134i
\(94\) 0 0
\(95\) 0.707107 + 2.12132i 0.0725476 + 0.217643i
\(96\) 0.414214 0.0422755
\(97\) 0.343146i 0.0348412i −0.999848 0.0174206i \(-0.994455\pi\)
0.999848 0.0174206i \(-0.00554543\pi\)
\(98\) 12.4853i 1.26120i
\(99\) −4.00000 −0.402015
\(100\) 4.00000 3.00000i 0.400000 0.300000i
\(101\) 13.0711 1.30062 0.650310 0.759669i \(-0.274639\pi\)
0.650310 + 0.759669i \(0.274639\pi\)
\(102\) 0.414214i 0.0410133i
\(103\) 4.24264i 0.418040i −0.977911 0.209020i \(-0.932973\pi\)
0.977911 0.209020i \(-0.0670273\pi\)
\(104\) 5.82843 0.571524
\(105\) −1.29289 3.87868i −0.126173 0.378520i
\(106\) −5.48528 −0.532778
\(107\) 19.7279i 1.90717i 0.301124 + 0.953585i \(0.402638\pi\)
−0.301124 + 0.953585i \(0.597362\pi\)
\(108\) 2.41421i 0.232308i
\(109\) 17.9706 1.72127 0.860634 0.509224i \(-0.170068\pi\)
0.860634 + 0.509224i \(0.170068\pi\)
\(110\) −3.00000 + 1.00000i −0.286039 + 0.0953463i
\(111\) 3.51472 0.333602
\(112\) 4.41421i 0.417104i
\(113\) 10.2426i 0.963547i 0.876296 + 0.481773i \(0.160007\pi\)
−0.876296 + 0.481773i \(0.839993\pi\)
\(114\) 0.414214 0.0387947
\(115\) 1.60660 0.535534i 0.149816 0.0499388i
\(116\) −0.171573 −0.0159301
\(117\) 16.4853i 1.52406i
\(118\) 6.89949i 0.635150i
\(119\) −4.41421 −0.404650
\(120\) −0.292893 0.878680i −0.0267374 0.0802121i
\(121\) −9.00000 −0.818182
\(122\) 14.2426i 1.28947i
\(123\) 1.75736i 0.158456i
\(124\) −6.24264 −0.560606
\(125\) −9.19239 6.36396i −0.822192 0.569210i
\(126\) 12.4853 1.11228
\(127\) 2.48528i 0.220533i −0.993902 0.110267i \(-0.964830\pi\)
0.993902 0.110267i \(-0.0351704\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.727922 0.0640900
\(130\) −4.12132 12.3640i −0.361464 1.08439i
\(131\) −16.9706 −1.48272 −0.741362 0.671105i \(-0.765820\pi\)
−0.741362 + 0.671105i \(0.765820\pi\)
\(132\) 0.585786i 0.0509862i
\(133\) 4.41421i 0.382761i
\(134\) 4.75736 0.410973
\(135\) −5.12132 + 1.70711i −0.440773 + 0.146924i
\(136\) −1.00000 −0.0857493
\(137\) 13.0000i 1.11066i 0.831628 + 0.555332i \(0.187409\pi\)
−0.831628 + 0.555332i \(0.812591\pi\)
\(138\) 0.313708i 0.0267046i
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 9.36396 3.12132i 0.791399 0.263800i
\(141\) 0 0
\(142\) 13.4142i 1.12570i
\(143\) 8.24264i 0.689284i
\(144\) 2.82843 0.235702
\(145\) 0.121320 + 0.363961i 0.0100751 + 0.0302253i
\(146\) −11.4853 −0.950529
\(147\) 5.17157i 0.426544i
\(148\) 8.48528i 0.697486i
\(149\) −17.6569 −1.44651 −0.723253 0.690583i \(-0.757354\pi\)
−0.723253 + 0.690583i \(0.757354\pi\)
\(150\) −1.65685 + 1.24264i −0.135282 + 0.101461i
\(151\) −10.4853 −0.853280 −0.426640 0.904422i \(-0.640303\pi\)
−0.426640 + 0.904422i \(0.640303\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 2.82843i 0.228665i
\(154\) −6.24264 −0.503046
\(155\) 4.41421 + 13.2426i 0.354558 + 1.06367i
\(156\) −2.41421 −0.193292
\(157\) 11.6569i 0.930318i 0.885227 + 0.465159i \(0.154003\pi\)
−0.885227 + 0.465159i \(0.845997\pi\)
\(158\) 6.48528i 0.515941i
\(159\) 2.27208 0.180188
\(160\) 2.12132 0.707107i 0.167705 0.0559017i
\(161\) 3.34315 0.263477
\(162\) 7.48528i 0.588099i
\(163\) 10.2426i 0.802266i 0.916020 + 0.401133i \(0.131383\pi\)
−0.916020 + 0.401133i \(0.868617\pi\)
\(164\) 4.24264 0.331295
\(165\) 1.24264 0.414214i 0.0967394 0.0322465i
\(166\) −14.4853 −1.12428
\(167\) 18.2426i 1.41166i −0.708382 0.705829i \(-0.750575\pi\)
0.708382 0.705829i \(-0.249425\pi\)
\(168\) 1.82843i 0.141066i
\(169\) −20.9706 −1.61312
\(170\) 0.707107 + 2.12132i 0.0542326 + 0.162698i
\(171\) 2.82843 0.216295
\(172\) 1.75736i 0.133997i
\(173\) 0.485281i 0.0368953i −0.999830 0.0184476i \(-0.994128\pi\)
0.999830 0.0184476i \(-0.00587240\pi\)
\(174\) 0.0710678 0.00538764
\(175\) −13.2426 17.6569i −1.00105 1.33473i
\(176\) −1.41421 −0.106600
\(177\) 2.85786i 0.214810i
\(178\) 7.07107i 0.529999i
\(179\) 11.6569 0.871274 0.435637 0.900122i \(-0.356523\pi\)
0.435637 + 0.900122i \(0.356523\pi\)
\(180\) −2.00000 6.00000i −0.149071 0.447214i
\(181\) −8.48528 −0.630706 −0.315353 0.948974i \(-0.602123\pi\)
−0.315353 + 0.948974i \(0.602123\pi\)
\(182\) 25.7279i 1.90708i
\(183\) 5.89949i 0.436103i
\(184\) 0.757359 0.0558333
\(185\) 18.0000 6.00000i 1.32339 0.441129i
\(186\) 2.58579 0.189599
\(187\) 1.41421i 0.103418i
\(188\) 0 0
\(189\) −10.6569 −0.775172
\(190\) 2.12132 0.707107i 0.153897 0.0512989i
\(191\) 12.5563 0.908546 0.454273 0.890863i \(-0.349899\pi\)
0.454273 + 0.890863i \(0.349899\pi\)
\(192\) 0.414214i 0.0298933i
\(193\) 0.343146i 0.0247002i 0.999924 + 0.0123501i \(0.00393125\pi\)
−0.999924 + 0.0123501i \(0.996069\pi\)
\(194\) −0.343146 −0.0246364
\(195\) 1.70711 + 5.12132i 0.122248 + 0.366745i
\(196\) 12.4853 0.891806
\(197\) 11.7574i 0.837677i −0.908061 0.418839i \(-0.862437\pi\)
0.908061 0.418839i \(-0.137563\pi\)
\(198\) 4.00000i 0.284268i
\(199\) −9.24264 −0.655193 −0.327597 0.944818i \(-0.606239\pi\)
−0.327597 + 0.944818i \(0.606239\pi\)
\(200\) −3.00000 4.00000i −0.212132 0.282843i
\(201\) −1.97056 −0.138993
\(202\) 13.0711i 0.919677i
\(203\) 0.757359i 0.0531562i
\(204\) 0.414214 0.0290008
\(205\) −3.00000 9.00000i −0.209529 0.628587i
\(206\) −4.24264 −0.295599
\(207\) 2.14214i 0.148889i
\(208\) 5.82843i 0.404129i
\(209\) −1.41421 −0.0978232
\(210\) −3.87868 + 1.29289i −0.267654 + 0.0892181i
\(211\) −19.7279 −1.35813 −0.679063 0.734080i \(-0.737614\pi\)
−0.679063 + 0.734080i \(0.737614\pi\)
\(212\) 5.48528i 0.376731i
\(213\) 5.55635i 0.380715i
\(214\) 19.7279 1.34857
\(215\) 3.72792 1.24264i 0.254242 0.0847474i
\(216\) −2.41421 −0.164266
\(217\) 27.5563i 1.87065i
\(218\) 17.9706i 1.21712i
\(219\) 4.75736 0.321473
\(220\) 1.00000 + 3.00000i 0.0674200 + 0.202260i
\(221\) 5.82843 0.392062
\(222\) 3.51472i 0.235892i
\(223\) 15.1716i 1.01596i 0.861368 + 0.507982i \(0.169608\pi\)
−0.861368 + 0.507982i \(0.830392\pi\)
\(224\) 4.41421 0.294937
\(225\) −11.3137 + 8.48528i −0.754247 + 0.565685i
\(226\) 10.2426 0.681330
\(227\) 16.7574i 1.11223i −0.831107 0.556113i \(-0.812292\pi\)
0.831107 0.556113i \(-0.187708\pi\)
\(228\) 0.414214i 0.0274320i
\(229\) −14.9706 −0.989283 −0.494641 0.869097i \(-0.664701\pi\)
−0.494641 + 0.869097i \(0.664701\pi\)
\(230\) −0.535534 1.60660i −0.0353121 0.105936i
\(231\) 2.58579 0.170132
\(232\) 0.171573i 0.0112643i
\(233\) 24.9706i 1.63588i 0.575306 + 0.817938i \(0.304883\pi\)
−0.575306 + 0.817938i \(0.695117\pi\)
\(234\) −16.4853 −1.07768
\(235\) 0 0
\(236\) 6.89949 0.449119
\(237\) 2.68629i 0.174493i
\(238\) 4.41421i 0.286131i
\(239\) 6.89949 0.446291 0.223146 0.974785i \(-0.428367\pi\)
0.223146 + 0.974785i \(0.428367\pi\)
\(240\) −0.878680 + 0.292893i −0.0567185 + 0.0189062i
\(241\) 8.97056 0.577845 0.288922 0.957353i \(-0.406703\pi\)
0.288922 + 0.957353i \(0.406703\pi\)
\(242\) 9.00000i 0.578542i
\(243\) 10.3431i 0.663513i
\(244\) −14.2426 −0.911792
\(245\) −8.82843 26.4853i −0.564028 1.69208i
\(246\) −1.75736 −0.112045
\(247\) 5.82843i 0.370854i
\(248\) 6.24264i 0.396408i
\(249\) 6.00000 0.380235
\(250\) −6.36396 + 9.19239i −0.402492 + 0.581378i
\(251\) 3.55635 0.224475 0.112237 0.993681i \(-0.464198\pi\)
0.112237 + 0.993681i \(0.464198\pi\)
\(252\) 12.4853i 0.786499i
\(253\) 1.07107i 0.0673375i
\(254\) −2.48528 −0.155940
\(255\) −0.292893 0.878680i −0.0183417 0.0550251i
\(256\) 1.00000 0.0625000
\(257\) 20.7279i 1.29297i 0.762926 + 0.646486i \(0.223762\pi\)
−0.762926 + 0.646486i \(0.776238\pi\)
\(258\) 0.727922i 0.0453184i
\(259\) 37.4558 2.32739
\(260\) −12.3640 + 4.12132i −0.766780 + 0.255593i
\(261\) 0.485281 0.0300382
\(262\) 16.9706i 1.04844i
\(263\) 26.9706i 1.66308i 0.555468 + 0.831538i \(0.312539\pi\)
−0.555468 + 0.831538i \(0.687461\pi\)
\(264\) 0.585786 0.0360527
\(265\) 11.6360 3.87868i 0.714796 0.238265i
\(266\) 4.41421 0.270653
\(267\) 2.92893i 0.179248i
\(268\) 4.75736i 0.290602i
\(269\) 16.6274 1.01379 0.506896 0.862007i \(-0.330793\pi\)
0.506896 + 0.862007i \(0.330793\pi\)
\(270\) 1.70711 + 5.12132i 0.103891 + 0.311674i
\(271\) −27.2426 −1.65487 −0.827436 0.561560i \(-0.810202\pi\)
−0.827436 + 0.561560i \(0.810202\pi\)
\(272\) 1.00000i 0.0606339i
\(273\) 10.6569i 0.644982i
\(274\) 13.0000 0.785359
\(275\) 5.65685 4.24264i 0.341121 0.255841i
\(276\) −0.313708 −0.0188830
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 17.6569 1.05709
\(280\) −3.12132 9.36396i −0.186535 0.559604i
\(281\) 4.24264 0.253095 0.126547 0.991961i \(-0.459610\pi\)
0.126547 + 0.991961i \(0.459610\pi\)
\(282\) 0 0
\(283\) 32.1421i 1.91065i −0.295555 0.955326i \(-0.595504\pi\)
0.295555 0.955326i \(-0.404496\pi\)
\(284\) 13.4142 0.795987
\(285\) −0.878680 + 0.292893i −0.0520485 + 0.0173495i
\(286\) 8.24264 0.487398
\(287\) 18.7279i 1.10547i
\(288\) 2.82843i 0.166667i
\(289\) 16.0000 0.941176
\(290\) 0.363961 0.121320i 0.0213725 0.00712418i
\(291\) 0.142136 0.00833214
\(292\) 11.4853i 0.672125i
\(293\) 5.48528i 0.320454i 0.987080 + 0.160227i \(0.0512226\pi\)
−0.987080 + 0.160227i \(0.948777\pi\)
\(294\) −5.17157 −0.301612
\(295\) −4.87868 14.6360i −0.284048 0.852143i
\(296\) 8.48528 0.493197
\(297\) 3.41421i 0.198113i
\(298\) 17.6569i 1.02283i
\(299\) −4.41421 −0.255281
\(300\) 1.24264 + 1.65685i 0.0717439 + 0.0956585i
\(301\) 7.75736 0.447127
\(302\) 10.4853i 0.603360i
\(303\) 5.41421i 0.311038i
\(304\) 1.00000 0.0573539
\(305\) 10.0711 + 30.2132i 0.576668 + 1.73000i
\(306\) 2.82843 0.161690
\(307\) 17.6569i 1.00773i −0.863782 0.503865i \(-0.831911\pi\)
0.863782 0.503865i \(-0.168089\pi\)
\(308\) 6.24264i 0.355707i
\(309\) 1.75736 0.0999727
\(310\) 13.2426 4.41421i 0.752131 0.250710i
\(311\) −4.75736 −0.269765 −0.134883 0.990862i \(-0.543066\pi\)
−0.134883 + 0.990862i \(0.543066\pi\)
\(312\) 2.41421i 0.136678i
\(313\) 7.97056i 0.450523i 0.974298 + 0.225261i \(0.0723236\pi\)
−0.974298 + 0.225261i \(0.927676\pi\)
\(314\) 11.6569 0.657834
\(315\) −26.4853 + 8.82843i −1.49228 + 0.497426i
\(316\) −6.48528 −0.364826
\(317\) 9.48528i 0.532746i −0.963870 0.266373i \(-0.914175\pi\)
0.963870 0.266373i \(-0.0858254\pi\)
\(318\) 2.27208i 0.127412i
\(319\) −0.242641 −0.0135853
\(320\) −0.707107 2.12132i −0.0395285 0.118585i
\(321\) −8.17157 −0.456093
\(322\) 3.34315i 0.186306i
\(323\) 1.00000i 0.0556415i
\(324\) −7.48528 −0.415849
\(325\) 17.4853 + 23.3137i 0.969909 + 1.29321i
\(326\) 10.2426 0.567287
\(327\) 7.44365i 0.411635i
\(328\) 4.24264i 0.234261i
\(329\) 0 0
\(330\) −0.414214 1.24264i −0.0228017 0.0684051i
\(331\) −19.2426 −1.05767 −0.528836 0.848724i \(-0.677371\pi\)
−0.528836 + 0.848724i \(0.677371\pi\)
\(332\) 14.4853i 0.794983i
\(333\) 24.0000i 1.31519i
\(334\) −18.2426 −0.998193
\(335\) −10.0919 + 3.36396i −0.551378 + 0.183793i
\(336\) −1.82843 −0.0997489
\(337\) 14.1005i 0.768103i 0.923312 + 0.384052i \(0.125472\pi\)
−0.923312 + 0.384052i \(0.874528\pi\)
\(338\) 20.9706i 1.14065i
\(339\) −4.24264 −0.230429
\(340\) 2.12132 0.707107i 0.115045 0.0383482i
\(341\) −8.82843 −0.478086
\(342\) 2.82843i 0.152944i
\(343\) 24.2132i 1.30739i
\(344\) 1.75736 0.0947505
\(345\) 0.221825 + 0.665476i 0.0119427 + 0.0358280i
\(346\) −0.485281 −0.0260889
\(347\) 5.51472i 0.296046i −0.988984 0.148023i \(-0.952709\pi\)
0.988984 0.148023i \(-0.0472909\pi\)
\(348\) 0.0710678i 0.00380963i
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) −17.6569 + 13.2426i −0.943799 + 0.707849i
\(351\) 14.0711 0.751058
\(352\) 1.41421i 0.0753778i
\(353\) 2.51472i 0.133845i 0.997758 + 0.0669225i \(0.0213180\pi\)
−0.997758 + 0.0669225i \(0.978682\pi\)
\(354\) −2.85786 −0.151894
\(355\) −9.48528 28.4558i −0.503426 1.51028i
\(356\) 7.07107 0.374766
\(357\) 1.82843i 0.0967706i
\(358\) 11.6569i 0.616084i
\(359\) 22.7574 1.20109 0.600544 0.799592i \(-0.294951\pi\)
0.600544 + 0.799592i \(0.294951\pi\)
\(360\) −6.00000 + 2.00000i −0.316228 + 0.105409i
\(361\) 1.00000 0.0526316
\(362\) 8.48528i 0.445976i
\(363\) 3.72792i 0.195665i
\(364\) −25.7279 −1.34851
\(365\) 24.3640 8.12132i 1.27527 0.425089i
\(366\) 5.89949 0.308372
\(367\) 25.4558i 1.32878i −0.747384 0.664392i \(-0.768691\pi\)
0.747384 0.664392i \(-0.231309\pi\)
\(368\) 0.757359i 0.0394801i
\(369\) −12.0000 −0.624695
\(370\) −6.00000 18.0000i −0.311925 0.935775i
\(371\) 24.2132 1.25709
\(372\) 2.58579i 0.134067i
\(373\) 9.00000i 0.466002i −0.972476 0.233001i \(-0.925145\pi\)
0.972476 0.233001i \(-0.0748546\pi\)
\(374\) −1.41421 −0.0731272
\(375\) 2.63604 3.80761i 0.136124 0.196624i
\(376\) 0 0
\(377\) 1.00000i 0.0515026i
\(378\) 10.6569i 0.548129i
\(379\) −11.2426 −0.577496 −0.288748 0.957405i \(-0.593239\pi\)
−0.288748 + 0.957405i \(0.593239\pi\)
\(380\) −0.707107 2.12132i −0.0362738 0.108821i
\(381\) 1.02944 0.0527397
\(382\) 12.5563i 0.642439i
\(383\) 12.2426i 0.625570i −0.949824 0.312785i \(-0.898738\pi\)
0.949824 0.312785i \(-0.101262\pi\)
\(384\) −0.414214 −0.0211377
\(385\) 13.2426 4.41421i 0.674907 0.224969i
\(386\) 0.343146 0.0174657
\(387\) 4.97056i 0.252668i
\(388\) 0.343146i 0.0174206i
\(389\) −22.9289 −1.16254 −0.581272 0.813710i \(-0.697445\pi\)
−0.581272 + 0.813710i \(0.697445\pi\)
\(390\) 5.12132 1.70711i 0.259328 0.0864427i
\(391\) 0.757359 0.0383013
\(392\) 12.4853i 0.630602i
\(393\) 7.02944i 0.354588i
\(394\) −11.7574 −0.592327
\(395\) 4.58579 + 13.7574i 0.230736 + 0.692208i
\(396\) 4.00000 0.201008
\(397\) 24.0000i 1.20453i 0.798298 + 0.602263i \(0.205734\pi\)
−0.798298 + 0.602263i \(0.794266\pi\)
\(398\) 9.24264i 0.463292i
\(399\) −1.82843 −0.0915358
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) −25.4142 −1.26913 −0.634563 0.772871i \(-0.718820\pi\)
−0.634563 + 0.772871i \(0.718820\pi\)
\(402\) 1.97056i 0.0982827i
\(403\) 36.3848i 1.81245i
\(404\) −13.0711 −0.650310
\(405\) 5.29289 + 15.8787i 0.263006 + 0.789018i
\(406\) 0.757359 0.0375871
\(407\) 12.0000i 0.594818i
\(408\) 0.414214i 0.0205066i
\(409\) −25.2132 −1.24671 −0.623356 0.781938i \(-0.714231\pi\)
−0.623356 + 0.781938i \(0.714231\pi\)
\(410\) −9.00000 + 3.00000i −0.444478 + 0.148159i
\(411\) −5.38478 −0.265611
\(412\) 4.24264i 0.209020i
\(413\) 30.4558i 1.49863i
\(414\) −2.14214 −0.105280
\(415\) 30.7279 10.2426i 1.50837 0.502791i
\(416\) −5.82843 −0.285762
\(417\) 4.97056i 0.243410i
\(418\) 1.41421i 0.0691714i
\(419\) −19.4142 −0.948446 −0.474223 0.880405i \(-0.657271\pi\)
−0.474223 + 0.880405i \(0.657271\pi\)
\(420\) 1.29289 + 3.87868i 0.0630867 + 0.189260i
\(421\) 19.4853 0.949655 0.474827 0.880079i \(-0.342511\pi\)
0.474827 + 0.880079i \(0.342511\pi\)
\(422\) 19.7279i 0.960340i
\(423\) 0 0
\(424\) 5.48528 0.266389
\(425\) −3.00000 4.00000i −0.145521 0.194029i
\(426\) −5.55635 −0.269206
\(427\) 62.8701i 3.04250i
\(428\) 19.7279i 0.953585i
\(429\) −3.41421 −0.164840
\(430\) −1.24264 3.72792i −0.0599255 0.179776i
\(431\) −6.38478 −0.307544 −0.153772 0.988106i \(-0.549142\pi\)
−0.153772 + 0.988106i \(0.549142\pi\)
\(432\) 2.41421i 0.116154i
\(433\) 9.55635i 0.459249i 0.973279 + 0.229624i \(0.0737498\pi\)
−0.973279 + 0.229624i \(0.926250\pi\)
\(434\) 27.5563 1.32275
\(435\) −0.150758 + 0.0502525i −0.00722827 + 0.00240942i
\(436\) −17.9706 −0.860634
\(437\) 0.757359i 0.0362294i
\(438\) 4.75736i 0.227315i
\(439\) 5.75736 0.274784 0.137392 0.990517i \(-0.456128\pi\)
0.137392 + 0.990517i \(0.456128\pi\)
\(440\) 3.00000 1.00000i 0.143019 0.0476731i
\(441\) −35.3137 −1.68161
\(442\) 5.82843i 0.277230i
\(443\) 4.24264i 0.201574i −0.994908 0.100787i \(-0.967864\pi\)
0.994908 0.100787i \(-0.0321361\pi\)
\(444\) −3.51472 −0.166801
\(445\) −5.00000 15.0000i −0.237023 0.711068i
\(446\) 15.1716 0.718395
\(447\) 7.31371i 0.345927i
\(448\) 4.41421i 0.208552i
\(449\) −17.3137 −0.817084 −0.408542 0.912739i \(-0.633963\pi\)
−0.408542 + 0.912739i \(0.633963\pi\)
\(450\) 8.48528 + 11.3137i 0.400000 + 0.533333i
\(451\) 6.00000 0.282529
\(452\) 10.2426i 0.481773i
\(453\) 4.34315i 0.204059i
\(454\) −16.7574 −0.786462
\(455\) 18.1924 + 54.5772i 0.852872 + 2.55862i
\(456\) −0.414214 −0.0193973
\(457\) 3.00000i 0.140334i −0.997535 0.0701670i \(-0.977647\pi\)
0.997535 0.0701670i \(-0.0223532\pi\)
\(458\) 14.9706i 0.699528i
\(459\) −2.41421 −0.112686
\(460\) −1.60660 + 0.535534i −0.0749082 + 0.0249694i
\(461\) −3.55635 −0.165636 −0.0828178 0.996565i \(-0.526392\pi\)
−0.0828178 + 0.996565i \(0.526392\pi\)
\(462\) 2.58579i 0.120302i
\(463\) 14.1421i 0.657241i −0.944462 0.328620i \(-0.893416\pi\)
0.944462 0.328620i \(-0.106584\pi\)
\(464\) 0.171573 0.00796507
\(465\) −5.48528 + 1.82843i −0.254374 + 0.0847913i
\(466\) 24.9706 1.15674
\(467\) 0.727922i 0.0336842i 0.999858 + 0.0168421i \(0.00536126\pi\)
−0.999858 + 0.0168421i \(0.994639\pi\)
\(468\) 16.4853i 0.762032i
\(469\) −21.0000 −0.969690
\(470\) 0 0
\(471\) −4.82843 −0.222482
\(472\) 6.89949i 0.317575i
\(473\) 2.48528i 0.114273i
\(474\) 2.68629 0.123385
\(475\) −4.00000 + 3.00000i −0.183533 + 0.137649i
\(476\) 4.41421 0.202325
\(477\) 15.5147i 0.710370i
\(478\) 6.89949i 0.315576i
\(479\) 31.1127 1.42158 0.710788 0.703407i \(-0.248339\pi\)
0.710788 + 0.703407i \(0.248339\pi\)
\(480\) 0.292893 + 0.878680i 0.0133687 + 0.0401061i
\(481\) −49.4558 −2.25499
\(482\) 8.97056i 0.408598i
\(483\) 1.38478i 0.0630095i
\(484\) 9.00000 0.409091
\(485\) 0.727922 0.242641i 0.0330532 0.0110177i
\(486\) 10.3431 0.469175
\(487\) 37.7990i 1.71284i 0.516283 + 0.856418i \(0.327315\pi\)
−0.516283 + 0.856418i \(0.672685\pi\)
\(488\) 14.2426i 0.644734i
\(489\) −4.24264 −0.191859
\(490\) −26.4853 + 8.82843i −1.19648 + 0.398828i
\(491\) −33.5563 −1.51438 −0.757188 0.653197i \(-0.773428\pi\)
−0.757188 + 0.653197i \(0.773428\pi\)
\(492\) 1.75736i 0.0792279i
\(493\) 0.171573i 0.00772725i
\(494\) −5.82843 −0.262233
\(495\) −2.82843 8.48528i −0.127128 0.381385i
\(496\) 6.24264 0.280303
\(497\) 59.2132i 2.65608i
\(498\) 6.00000i 0.268866i
\(499\) 25.7574 1.15306 0.576529 0.817077i \(-0.304407\pi\)
0.576529 + 0.817077i \(0.304407\pi\)
\(500\) 9.19239 + 6.36396i 0.411096 + 0.284605i
\(501\) 7.55635 0.337593
\(502\) 3.55635i 0.158728i
\(503\) 14.2721i 0.636361i −0.948030 0.318180i \(-0.896928\pi\)
0.948030 0.318180i \(-0.103072\pi\)
\(504\) −12.4853 −0.556139
\(505\) 9.24264 + 27.7279i 0.411292 + 1.23388i
\(506\) 1.07107 0.0476148
\(507\) 8.68629i 0.385772i
\(508\) 2.48528i 0.110267i
\(509\) −28.9706 −1.28410 −0.642049 0.766664i \(-0.721915\pi\)
−0.642049 + 0.766664i \(0.721915\pi\)
\(510\) −0.878680 + 0.292893i −0.0389086 + 0.0129695i
\(511\) 50.6985 2.24277
\(512\) 1.00000i 0.0441942i
\(513\) 2.41421i 0.106590i
\(514\) 20.7279 0.914269
\(515\) 9.00000 3.00000i 0.396587 0.132196i
\(516\) −0.727922 −0.0320450
\(517\) 0 0
\(518\) 37.4558i 1.64572i
\(519\) 0.201010 0.00882337
\(520\) 4.12132 + 12.3640i 0.180732 + 0.542196i
\(521\) 23.3137 1.02139 0.510696 0.859761i \(-0.329388\pi\)
0.510696 + 0.859761i \(0.329388\pi\)
\(522\) 0.485281i 0.0212402i
\(523\) 2.27208i 0.0993510i 0.998765 + 0.0496755i \(0.0158187\pi\)
−0.998765 + 0.0496755i \(0.984181\pi\)
\(524\) 16.9706 0.741362
\(525\) 7.31371 5.48528i 0.319196 0.239397i
\(526\) 26.9706 1.17597
\(527\) 6.24264i 0.271934i
\(528\) 0.585786i 0.0254931i
\(529\) 22.4264 0.975061
\(530\) −3.87868 11.6360i −0.168479 0.505437i
\(531\) −19.5147 −0.846867
\(532\) 4.41421i 0.191380i
\(533\) 24.7279i 1.07109i
\(534\) −2.92893 −0.126747
\(535\) −41.8492 + 13.9497i −1.80930 + 0.603100i
\(536\) −4.75736 −0.205487
\(537\) 4.82843i 0.208362i
\(538\) 16.6274i 0.716859i
\(539\) 17.6569 0.760535
\(540\) 5.12132 1.70711i 0.220387 0.0734622i
\(541\) 9.75736 0.419502 0.209751 0.977755i \(-0.432735\pi\)
0.209751 + 0.977755i \(0.432735\pi\)
\(542\) 27.2426i 1.17017i
\(543\) 3.51472i 0.150831i
\(544\) 1.00000 0.0428746
\(545\) 12.7071 + 38.1213i 0.544313 + 1.63294i
\(546\) 10.6569 0.456071
\(547\) 17.3137i 0.740281i −0.928976 0.370140i \(-0.879310\pi\)
0.928976 0.370140i \(-0.120690\pi\)
\(548\) 13.0000i 0.555332i
\(549\) 40.2843 1.71929
\(550\) −4.24264 5.65685i −0.180907 0.241209i
\(551\) 0.171573 0.00730925
\(552\) 0.313708i 0.0133523i
\(553\) 28.6274i 1.21736i
\(554\) 0 0
\(555\) 2.48528 + 7.45584i 0.105494 + 0.316483i
\(556\) −12.0000 −0.508913
\(557\) 16.0000i 0.677942i 0.940797 + 0.338971i \(0.110079\pi\)
−0.940797 + 0.338971i \(0.889921\pi\)
\(558\) 17.6569i 0.747474i
\(559\) −10.2426 −0.433218
\(560\) −9.36396 + 3.12132i −0.395700 + 0.131900i
\(561\) 0.585786 0.0247319
\(562\) 4.24264i 0.178965i
\(563\) 4.97056i 0.209484i −0.994499 0.104742i \(-0.966598\pi\)
0.994499 0.104742i \(-0.0334017\pi\)
\(564\) 0 0
\(565\) −21.7279 + 7.24264i −0.914101 + 0.304700i
\(566\) −32.1421 −1.35103
\(567\) 33.0416i 1.38762i
\(568\) 13.4142i 0.562848i
\(569\) 28.2843 1.18574 0.592869 0.805299i \(-0.297995\pi\)
0.592869 + 0.805299i \(0.297995\pi\)
\(570\) 0.292893 + 0.878680i 0.0122679 + 0.0368038i
\(571\) −2.24264 −0.0938516 −0.0469258 0.998898i \(-0.514942\pi\)
−0.0469258 + 0.998898i \(0.514942\pi\)
\(572\) 8.24264i 0.344642i
\(573\) 5.20101i 0.217275i
\(574\) −18.7279 −0.781688
\(575\) 2.27208 + 3.02944i 0.0947522 + 0.126336i
\(576\) −2.82843 −0.117851
\(577\) 20.3137i 0.845671i −0.906207 0.422835i \(-0.861035\pi\)
0.906207 0.422835i \(-0.138965\pi\)
\(578\) 16.0000i 0.665512i
\(579\) −0.142136 −0.00590695
\(580\) −0.121320 0.363961i −0.00503755 0.0151127i
\(581\) 63.9411 2.65272
\(582\) 0.142136i 0.00589171i
\(583\) 7.75736i 0.321277i
\(584\) 11.4853 0.475264
\(585\) 34.9706 11.6569i 1.44585 0.481952i
\(586\) 5.48528 0.226595
\(587\) 30.2426i 1.24825i 0.781326 + 0.624124i \(0.214544\pi\)
−0.781326 + 0.624124i \(0.785456\pi\)
\(588\) 5.17157i 0.213272i
\(589\) 6.24264 0.257224
\(590\) −14.6360 + 4.87868i −0.602556 + 0.200852i
\(591\) 4.87006 0.200327
\(592\) 8.48528i 0.348743i
\(593\) 22.0000i 0.903432i −0.892162 0.451716i \(-0.850812\pi\)
0.892162 0.451716i \(-0.149188\pi\)
\(594\) −3.41421 −0.140087
\(595\) −3.12132 9.36396i −0.127962 0.383885i
\(596\) 17.6569 0.723253
\(597\) 3.82843i 0.156687i
\(598\) 4.41421i 0.180511i
\(599\) 15.2132 0.621595 0.310797 0.950476i \(-0.399404\pi\)
0.310797 + 0.950476i \(0.399404\pi\)
\(600\) 1.65685 1.24264i 0.0676408 0.0507306i
\(601\) −20.2426 −0.825715 −0.412857 0.910796i \(-0.635469\pi\)
−0.412857 + 0.910796i \(0.635469\pi\)
\(602\) 7.75736i 0.316166i
\(603\) 13.4558i 0.547964i
\(604\) 10.4853 0.426640
\(605\) −6.36396 19.0919i −0.258732 0.776195i
\(606\) 5.41421 0.219937
\(607\) 3.17157i 0.128730i 0.997926 + 0.0643651i \(0.0205022\pi\)
−0.997926 + 0.0643651i \(0.979498\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −0.313708 −0.0127121
\(610\) 30.2132 10.0711i 1.22330 0.407766i
\(611\) 0 0
\(612\) 2.82843i 0.114332i
\(613\) 11.6985i 0.472497i 0.971693 + 0.236249i \(0.0759180\pi\)
−0.971693 + 0.236249i \(0.924082\pi\)
\(614\) −17.6569 −0.712573
\(615\) 3.72792 1.24264i 0.150324 0.0501081i
\(616\) 6.24264 0.251523
\(617\) 4.48528i 0.180571i −0.995916 0.0902853i \(-0.971222\pi\)
0.995916 0.0902853i \(-0.0287779\pi\)
\(618\) 1.75736i 0.0706914i
\(619\) −7.75736 −0.311795 −0.155897 0.987773i \(-0.549827\pi\)
−0.155897 + 0.987773i \(0.549827\pi\)
\(620\) −4.41421 13.2426i −0.177279 0.531837i
\(621\) 1.82843 0.0733723
\(622\) 4.75736i 0.190753i
\(623\) 31.2132i 1.25053i
\(624\) 2.41421 0.0966459
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 7.97056 0.318568
\(627\) 0.585786i 0.0233941i
\(628\) 11.6569i 0.465159i
\(629\) 8.48528 0.338330
\(630\) 8.82843 + 26.4853i 0.351733 + 1.05520i
\(631\) −38.9706 −1.55139 −0.775697 0.631106i \(-0.782601\pi\)
−0.775697 + 0.631106i \(0.782601\pi\)
\(632\) 6.48528i 0.257971i
\(633\) 8.17157i 0.324791i
\(634\) −9.48528 −0.376709
\(635\) 5.27208 1.75736i 0.209216 0.0697387i
\(636\) −2.27208 −0.0900938
\(637\) 72.7696i 2.88323i
\(638\) 0.242641i 0.00960624i
\(639\) −37.9411 −1.50093
\(640\) −2.12132 + 0.707107i −0.0838525 + 0.0279508i
\(641\) −18.0416 −0.712602 −0.356301 0.934371i \(-0.615962\pi\)
−0.356301 + 0.934371i \(0.615962\pi\)
\(642\) 8.17157i 0.322506i
\(643\) 14.4853i 0.571244i 0.958342 + 0.285622i \(0.0922001\pi\)
−0.958342 + 0.285622i \(0.907800\pi\)
\(644\) −3.34315 −0.131738
\(645\) 0.514719 + 1.54416i 0.0202670 + 0.0608011i
\(646\) 1.00000 0.0393445
\(647\) 18.7574i 0.737428i −0.929543 0.368714i \(-0.879798\pi\)
0.929543 0.368714i \(-0.120202\pi\)
\(648\) 7.48528i 0.294050i
\(649\) 9.75736 0.383010
\(650\) 23.3137 17.4853i 0.914439 0.685829i
\(651\) −11.4142 −0.447358
\(652\) 10.2426i 0.401133i
\(653\) 28.9706i 1.13371i 0.823819 + 0.566853i \(0.191839\pi\)
−0.823819 + 0.566853i \(0.808161\pi\)
\(654\) 7.44365 0.291070
\(655\) −12.0000 36.0000i −0.468879 1.40664i
\(656\) −4.24264 −0.165647
\(657\) 32.4853i 1.26737i
\(658\) 0 0
\(659\) −18.8995 −0.736220 −0.368110 0.929782i \(-0.619995\pi\)
−0.368110 + 0.929782i \(0.619995\pi\)
\(660\) −1.24264 + 0.414214i −0.0483697 + 0.0161232i
\(661\) −18.4558 −0.717849 −0.358925 0.933367i \(-0.616856\pi\)
−0.358925 + 0.933367i \(0.616856\pi\)
\(662\) 19.2426i 0.747886i
\(663\) 2.41421i 0.0937603i
\(664\) 14.4853 0.562138
\(665\) −9.36396 + 3.12132i −0.363119 + 0.121040i
\(666\) −24.0000 −0.929981
\(667\) 0.129942i 0.00503139i
\(668\) 18.2426i 0.705829i
\(669\) −6.28427 −0.242964
\(670\) 3.36396 + 10.0919i 0.129961 + 0.389883i
\(671\) −20.1421 −0.777579
\(672\) 1.82843i 0.0705331i
\(673\) 12.0000i 0.462566i 0.972887 + 0.231283i \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) 14.1005 0.543131
\(675\) −7.24264 9.65685i −0.278769 0.371692i
\(676\) 20.9706 0.806560
\(677\) 40.9411i 1.57350i −0.617275 0.786748i \(-0.711763\pi\)
0.617275 0.786748i \(-0.288237\pi\)
\(678\) 4.24264i 0.162938i
\(679\) 1.51472 0.0581296
\(680\) −0.707107 2.12132i −0.0271163 0.0813489i
\(681\) 6.94113 0.265985
\(682\) 8.82843i 0.338058i
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) −2.82843 −0.108148
\(685\) −27.5772 + 9.19239i −1.05367 + 0.351223i
\(686\) −24.2132 −0.924464
\(687\) 6.20101i 0.236583i
\(688\) 1.75736i 0.0669987i
\(689\) −31.9706 −1.21798
\(690\) 0.665476 0.221825i 0.0253342 0.00844475i
\(691\) 22.4853 0.855380 0.427690 0.903925i \(-0.359327\pi\)
0.427690 + 0.903925i \(0.359327\pi\)
\(692\) 0.485281i 0.0184476i
\(693\) 17.6569i 0.670728i
\(694\) −5.51472 −0.209336
\(695\) 8.48528 + 25.4558i 0.321865 + 0.965595i
\(696\) −0.0710678 −0.00269382
\(697\) 4.24264i 0.160701i
\(698\) 6.00000i 0.227103i
\(699\) −10.3431 −0.391214
\(700\) 13.2426 + 17.6569i 0.500525 + 0.667366i
\(701\) 16.9706 0.640969 0.320485 0.947254i \(-0.396154\pi\)
0.320485 + 0.947254i \(0.396154\pi\)
\(702\) 14.0711i 0.531078i
\(703\) 8.48528i 0.320028i
\(704\) 1.41421 0.0533002
\(705\) 0 0
\(706\) 2.51472 0.0946427
\(707\) 57.6985i 2.16997i
\(708\) 2.85786i 0.107405i
\(709\) 34.0000 1.27690 0.638448 0.769665i \(-0.279577\pi\)
0.638448 + 0.769665i \(0.279577\pi\)
\(710\) −28.4558 + 9.48528i −1.06793 + 0.355976i
\(711\) 18.3431 0.687922
\(712\) 7.07107i 0.264999i
\(713\) 4.72792i 0.177062i
\(714\) −1.82843 −0.0684272
\(715\) −17.4853 + 5.82843i −0.653912 + 0.217971i
\(716\) −11.6569 −0.435637
\(717\) 2.85786i 0.106729i
\(718\) 22.7574i 0.849297i
\(719\) 5.10051 0.190217 0.0951084 0.995467i \(-0.469680\pi\)
0.0951084 + 0.995467i \(0.469680\pi\)
\(720\) 2.00000 + 6.00000i 0.0745356 + 0.223607i
\(721\) 18.7279 0.697464
\(722\) 1.00000i 0.0372161i
\(723\) 3.71573i 0.138189i
\(724\) 8.48528 0.315353
\(725\) −0.686292 + 0.514719i −0.0254882 + 0.0191162i
\(726\) −3.72792 −0.138356
\(727\) 9.72792i 0.360789i 0.983594 + 0.180394i \(0.0577374\pi\)
−0.983594 + 0.180394i \(0.942263\pi\)
\(728\) 25.7279i 0.953540i
\(729\) 18.1716 0.673021
\(730\) −8.12132 24.3640i −0.300584 0.901751i
\(731\) 1.75736 0.0649983
\(732\) 5.89949i 0.218052i
\(733\) 12.0000i 0.443230i −0.975134 0.221615i \(-0.928867\pi\)
0.975134 0.221615i \(-0.0711328\pi\)
\(734\) −25.4558 −0.939592
\(735\) 10.9706 3.65685i 0.404655 0.134885i
\(736\) −0.757359 −0.0279166
\(737\) 6.72792i 0.247826i
\(738\) 12.0000i 0.441726i
\(739\) −1.27208 −0.0467941 −0.0233971 0.999726i \(-0.507448\pi\)
−0.0233971 + 0.999726i \(0.507448\pi\)
\(740\) −18.0000 + 6.00000i −0.661693 + 0.220564i
\(741\) 2.41421 0.0886884
\(742\) 24.2132i 0.888895i
\(743\) 6.72792i 0.246824i −0.992356 0.123412i \(-0.960616\pi\)
0.992356 0.123412i \(-0.0393836\pi\)
\(744\) −2.58579 −0.0947995
\(745\) −12.4853 37.4558i −0.457425 1.37228i
\(746\) −9.00000 −0.329513
\(747\) 40.9706i 1.49903i
\(748\) 1.41421i 0.0517088i
\(749\) −87.0833 −3.18195
\(750\) −3.80761 2.63604i −0.139034 0.0962545i
\(751\) −26.7279 −0.975316 −0.487658 0.873035i \(-0.662149\pi\)
−0.487658 + 0.873035i \(0.662149\pi\)
\(752\) 0 0
\(753\) 1.47309i 0.0536823i
\(754\) −1.00000 −0.0364179
\(755\) −7.41421 22.2426i −0.269831 0.809493i
\(756\) 10.6569 0.387586
\(757\) 12.3431i 0.448619i 0.974518 + 0.224310i \(0.0720127\pi\)
−0.974518 + 0.224310i \(0.927987\pi\)
\(758\) 11.2426i 0.408351i
\(759\) −0.443651 −0.0161035
\(760\) −2.12132 + 0.707107i −0.0769484 + 0.0256495i
\(761\) 43.9706 1.59393 0.796966 0.604024i \(-0.206437\pi\)
0.796966 + 0.604024i \(0.206437\pi\)
\(762\) 1.02944i 0.0372926i
\(763\) 79.3259i 2.87179i
\(764\) −12.5563 −0.454273
\(765\) −6.00000 + 2.00000i −0.216930 + 0.0723102i
\(766\) −12.2426 −0.442345
\(767\) 40.2132i 1.45201i
\(768\) 0.414214i 0.0149466i
\(769\) 36.4558 1.31463 0.657316 0.753615i \(-0.271692\pi\)
0.657316 + 0.753615i \(0.271692\pi\)
\(770\) −4.41421 13.2426i −0.159077 0.477232i
\(771\) −8.58579 −0.309210
\(772\) 0.343146i 0.0123501i
\(773\) 13.9706i 0.502486i −0.967924 0.251243i \(-0.919161\pi\)
0.967924 0.251243i \(-0.0808394\pi\)
\(774\) −4.97056 −0.178663
\(775\) −24.9706 + 18.7279i −0.896969 + 0.672727i
\(776\) 0.343146 0.0123182
\(777\) 15.5147i 0.556587i
\(778\) 22.9289i 0.822042i
\(779\) −4.24264 −0.152008
\(780\) −1.70711 5.12132i −0.0611242 0.183373i
\(781\) 18.9706 0.678820
\(782\) 0.757359i 0.0270831i
\(783\) 0.414214i 0.0148028i
\(784\) −12.4853 −0.445903
\(785\) −24.7279 + 8.24264i −0.882577 + 0.294192i
\(786\) −7.02944 −0.250732
\(787\) 41.1838i 1.46804i −0.679126 0.734021i \(-0.737641\pi\)
0.679126 0.734021i \(-0.262359\pi\)
\(788\) 11.7574i 0.418839i
\(789\) −11.1716 −0.397719
\(790\) 13.7574 4.58579i 0.489465 0.163155i
\(791\) −45.2132 −1.60760
\(792\) 4.00000i 0.142134i
\(793\) 83.0122i 2.94785i
\(794\) 24.0000 0.851728
\(795\) 1.60660 + 4.81981i 0.0569803 + 0.170941i
\(796\) 9.24264 0.327597
\(797\) 47.4853i 1.68201i −0.541023 0.841007i \(-0.681963\pi\)
0.541023 0.841007i \(-0.318037\pi\)
\(798\) 1.82843i 0.0647256i
\(799\) 0 0
\(800\) 3.00000 + 4.00000i 0.106066 + 0.141421i
\(801\) −20.0000 −0.706665
\(802\) 25.4142i 0.897407i
\(803\) 16.2426i 0.573190i
\(804\) 1.97056 0.0694964
\(805\) 2.36396 + 7.09188i 0.0833187 + 0.249956i
\(806\) −36.3848 −1.28160
\(807\) 6.88730i 0.242444i
\(808\) 13.0711i 0.459839i
\(809\) 28.7990 1.01252 0.506259 0.862381i \(-0.331028\pi\)
0.506259 + 0.862381i \(0.331028\pi\)
\(810\) 15.8787 5.29289i 0.557920 0.185973i
\(811\) 52.6985 1.85049 0.925247 0.379365i \(-0.123858\pi\)
0.925247 + 0.379365i \(0.123858\pi\)
\(812\) 0.757359i 0.0265781i
\(813\) 11.2843i 0.395757i
\(814\) 12.0000 0.420600
\(815\) −21.7279 + 7.24264i −0.761096 + 0.253699i
\(816\) −0.414214 −0.0145004
\(817\) 1.75736i 0.0614822i
\(818\) 25.2132i 0.881559i
\(819\) 72.7696 2.54277
\(820\) 3.00000 + 9.00000i 0.104765 + 0.314294i
\(821\) 6.34315 0.221377 0.110689 0.993855i \(-0.464694\pi\)
0.110689 + 0.993855i \(0.464694\pi\)
\(822\) 5.38478i 0.187816i
\(823\) 15.7279i 0.548241i 0.961695 + 0.274120i \(0.0883867\pi\)
−0.961695 + 0.274120i \(0.911613\pi\)
\(824\) 4.24264 0.147799
\(825\) 1.75736 + 2.34315i 0.0611834 + 0.0815779i
\(826\) −30.4558 −1.05969
\(827\) 20.6985i 0.719757i −0.932999 0.359878i \(-0.882818\pi\)
0.932999 0.359878i \(-0.117182\pi\)
\(828\) 2.14214i 0.0744444i
\(829\) −10.4558 −0.363146 −0.181573 0.983377i \(-0.558119\pi\)
−0.181573 + 0.983377i \(0.558119\pi\)
\(830\) −10.2426 30.7279i −0.355527 1.06658i
\(831\) 0 0
\(832\) 5.82843i 0.202064i
\(833\) 12.4853i 0.432589i
\(834\) 4.97056 0.172117
\(835\) 38.6985 12.8995i 1.33922 0.446405i
\(836\) 1.41421 0.0489116
\(837\) 15.0711i 0.520932i
\(838\) 19.4142i 0.670653i
\(839\) −22.6274 −0.781185 −0.390593 0.920564i \(-0.627730\pi\)
−0.390593 + 0.920564i \(0.627730\pi\)
\(840\) 3.87868 1.29289i 0.133827 0.0446091i
\(841\) −28.9706 −0.998985
\(842\) 19.4853i 0.671507i
\(843\) 1.75736i 0.0605267i
\(844\) 19.7279 0.679063
\(845\) −14.8284 44.4853i −0.510113 1.53034i
\(846\) 0 0
\(847\) 39.7279i 1.36507i
\(848\) 5.48528i 0.188365i
\(849\) 13.3137 0.456925
\(850\) −4.00000 + 3.00000i −0.137199 + 0.102899i
\(851\) −6.42641 −0.220294
\(852\) 5.55635i 0.190357i
\(853\) 27.9411i 0.956686i 0.878173 + 0.478343i \(0.158762\pi\)
−0.878173 + 0.478343i \(0.841238\pi\)
\(854\) 62.8701 2.15137
\(855\) 2.00000 + 6.00000i 0.0683986 + 0.205196i
\(856\) −19.7279 −0.674286
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 3.41421i 0.116559i
\(859\) −4.72792 −0.161315 −0.0806573 0.996742i \(-0.525702\pi\)
−0.0806573 + 0.996742i \(0.525702\pi\)
\(860\) −3.72792 + 1.24264i −0.127121 + 0.0423737i
\(861\) 7.75736 0.264370
\(862\) 6.38478i 0.217466i
\(863\) 0.727922i 0.0247788i −0.999923 0.0123894i \(-0.996056\pi\)
0.999923 0.0123894i \(-0.00394376\pi\)
\(864\) 2.41421 0.0821332
\(865\) 1.02944 0.343146i 0.0350019 0.0116673i
\(866\) 9.55635 0.324738
\(867\) 6.62742i 0.225079i
\(868\) 27.5563i 0.935323i
\(869\) −9.17157 −0.311124
\(870\) 0.0502525 + 0.150758i 0.00170372 + 0.00511116i
\(871\) 27.7279 0.939525
\(872\) 17.9706i 0.608560i
\(873\) 0.970563i 0.0328486i
\(874\) −0.757359 −0.0256181
\(875\) 28.0919 40.5772i 0.949679 1.37176i
\(876\) −4.75736 −0.160736
\(877\) 18.8579i 0.636785i −0.947959 0.318392i \(-0.896857\pi\)
0.947959 0.318392i \(-0.103143\pi\)
\(878\) 5.75736i 0.194301i
\(879\) −2.27208 −0.0766353
\(880\) −1.00000 3.00000i −0.0337100 0.101130i
\(881\) −39.5980 −1.33409 −0.667045 0.745018i \(-0.732441\pi\)
−0.667045 + 0.745018i \(0.732441\pi\)
\(882\) 35.3137i 1.18907i
\(883\) 14.4853i 0.487469i −0.969842 0.243734i \(-0.921628\pi\)
0.969842 0.243734i \(-0.0783725\pi\)
\(884\) −5.82843 −0.196031
\(885\) 6.06245 2.02082i 0.203787 0.0679290i
\(886\) −4.24264 −0.142534
\(887\) 45.2132i 1.51811i −0.651026 0.759055i \(-0.725661\pi\)
0.651026 0.759055i \(-0.274339\pi\)
\(888\) 3.51472i 0.117946i
\(889\) 10.9706 0.367941
\(890\) −15.0000 + 5.00000i −0.502801 + 0.167600i
\(891\) −10.5858 −0.354637
\(892\) 15.1716i 0.507982i
\(893\) 0 0
\(894\) −7.31371 −0.244607
\(895\) 8.24264 + 24.7279i 0.275521 + 0.826563i
\(896\) −4.41421 −0.147469
\(897\) 1.82843i 0.0610494i
\(898\) 17.3137i 0.577766i
\(899\) 1.07107 0.0357221
\(900\) 11.3137 8.48528i 0.377124 0.282843i
\(901\) 5.48528 0.182741
\(902\) 6.00000i 0.199778i
\(903\) 3.21320i 0.106929i
\(904\) −10.2426 −0.340665
\(905\) −6.00000 18.0000i −0.199447 0.598340i
\(906\) −4.34315 −0.144291
\(907\) 38.6985i 1.28496i 0.766302 + 0.642481i \(0.222095\pi\)
−0.766302 + 0.642481i \(0.777905\pi\)
\(908\) 16.7574i 0.556113i
\(909\) 36.9706 1.22624
\(910\) 54.5772 18.1924i 1.80922 0.603072i
\(911\) 40.2843 1.33468 0.667339 0.744754i \(-0.267433\pi\)
0.667339 + 0.744754i \(0.267433\pi\)
\(912\) 0.414214i 0.0137160i
\(913\) 20.4853i 0.677964i
\(914\) −3.00000 −0.0992312
\(915\) −12.5147 + 4.17157i −0.413724 + 0.137908i
\(916\) 14.9706 0.494641
\(917\) 74.9117i 2.47380i
\(918\) 2.41421i 0.0796809i
\(919\) 6.21320 0.204955 0.102477 0.994735i \(-0.467323\pi\)
0.102477 + 0.994735i \(0.467323\pi\)
\(920\) 0.535534 + 1.60660i 0.0176560 + 0.0529681i
\(921\) 7.31371 0.240995
\(922\) 3.55635i 0.117122i
\(923\) 78.1838i 2.57345i
\(924\) −2.58579 −0.0850661
\(925\) 25.4558 + 33.9411i 0.836983 + 1.11598i
\(926\) −14.1421 −0.464739
\(927\) 12.0000i 0.394132i
\(928\) 0.171573i 0.00563216i
\(929\) 12.1716 0.399336 0.199668 0.979864i \(-0.436014\pi\)
0.199668 + 0.979864i \(0.436014\pi\)
\(930\) 1.82843 + 5.48528i 0.0599565 + 0.179869i
\(931\) −12.4853 −0.409189
\(932\) 24.9706i 0.817938i
\(933\) 1.97056i 0.0645133i
\(934\) 0.727922 0.0238183
\(935\) 3.00000 1.00000i 0.0981105 0.0327035i
\(936\) 16.4853 0.538838
\(937\) 27.0000i 0.882052i 0.897494 + 0.441026i \(0.145385\pi\)
−0.897494 + 0.441026i \(0.854615\pi\)
\(938\) 21.0000i 0.685674i
\(939\) −3.30152 −0.107741
\(940\) 0 0
\(941\) 53.1421 1.73238 0.866192 0.499711i \(-0.166561\pi\)
0.866192 + 0.499711i \(0.166561\pi\)
\(942\) 4.82843i 0.157319i
\(943\) 3.21320i 0.104636i
\(944\) −6.89949 −0.224559
\(945\) −7.53553 22.6066i −0.245131 0.735393i
\(946\) 2.48528 0.0808035
\(947\) 12.0000i 0.389948i −0.980808 0.194974i \(-0.937538\pi\)
0.980808 0.194974i \(-0.0624622\pi\)
\(948\) 2.68629i 0.0872467i
\(949\) −66.9411 −2.17300
\(950\) 3.00000 + 4.00000i 0.0973329 + 0.129777i
\(951\) 3.92893 0.127404
\(952\) 4.41421i 0.143065i
\(953\) 18.7279i 0.606657i −0.952886 0.303328i \(-0.901902\pi\)
0.952886 0.303328i \(-0.0980979\pi\)
\(954\) −15.5147 −0.502308
\(955\) 8.87868 + 26.6360i 0.287307 + 0.861922i
\(956\) −6.89949 −0.223146
\(957\) 0.100505i 0.00324887i
\(958\) 31.1127i 1.00521i
\(959\) −57.3848 −1.85305
\(960\) 0.878680 0.292893i 0.0283593 0.00945309i
\(961\) 7.97056 0.257115
\(962\) 49.4558i 1.59452i
\(963\) 55.7990i 1.79810i
\(964\) −8.97056 −0.288922
\(965\) −0.727922 + 0.242641i −0.0234326 + 0.00781088i
\(966\) 1.38478 0.0445544
\(967\) 43.1127i 1.38641i 0.720740 + 0.693205i \(0.243802\pi\)
−0.720740 + 0.693205i \(0.756198\pi\)
\(968\) 9.00000i 0.289271i
\(969\) −0.414214 −0.0133065
\(970\) −0.242641 0.727922i −0.00779072 0.0233722i
\(971\) 41.6569 1.33683 0.668416 0.743788i \(-0.266973\pi\)
0.668416 + 0.743788i \(0.266973\pi\)
\(972\) 10.3431i 0.331757i
\(973\) 52.9706i 1.69816i
\(974\) 37.7990 1.21116
\(975\) −9.65685 + 7.24264i −0.309267 + 0.231950i
\(976\) 14.2426 0.455896
\(977\) 0.242641i 0.00776276i 0.999992 + 0.00388138i \(0.00123549\pi\)
−0.999992 + 0.00388138i \(0.998765\pi\)
\(978\) 4.24264i 0.135665i
\(979\) 10.0000 0.319601
\(980\) 8.82843 + 26.4853i 0.282014 + 0.846041i
\(981\) 50.8284 1.62283
\(982\) 33.5563i 1.07083i
\(983\) 51.4558i 1.64119i 0.571513 + 0.820593i \(0.306357\pi\)
−0.571513 + 0.820593i \(0.693643\pi\)
\(984\) 1.75736 0.0560226
\(985\) 24.9411 8.31371i 0.794690 0.264897i
\(986\) 0.171573 0.00546399
\(987\) 0 0
\(988\) 5.82843i 0.185427i
\(989\) −1.33095 −0.0423218
\(990\) −8.48528 + 2.82843i −0.269680 + 0.0898933i
\(991\) 13.7574 0.437017 0.218508 0.975835i \(-0.429881\pi\)
0.218508 + 0.975835i \(0.429881\pi\)
\(992\) 6.24264i 0.198204i
\(993\) 7.97056i 0.252938i
\(994\) −59.2132 −1.87813
\(995\) −6.53553 19.6066i −0.207190 0.621571i
\(996\) −6.00000 −0.190117
\(997\) 48.7279i 1.54323i 0.636091 + 0.771614i \(0.280550\pi\)
−0.636091 + 0.771614i \(0.719450\pi\)
\(998\) 25.7574i 0.815335i
\(999\) 20.4853 0.648126
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 190.2.b.a.39.2 4
3.2 odd 2 1710.2.d.c.1369.3 4
4.3 odd 2 1520.2.d.e.609.2 4
5.2 odd 4 950.2.a.g.1.2 2
5.3 odd 4 950.2.a.f.1.1 2
5.4 even 2 inner 190.2.b.a.39.3 yes 4
15.2 even 4 8550.2.a.bn.1.1 2
15.8 even 4 8550.2.a.cb.1.2 2
15.14 odd 2 1710.2.d.c.1369.1 4
20.3 even 4 7600.2.a.v.1.2 2
20.7 even 4 7600.2.a.bg.1.1 2
20.19 odd 2 1520.2.d.e.609.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.b.a.39.2 4 1.1 even 1 trivial
190.2.b.a.39.3 yes 4 5.4 even 2 inner
950.2.a.f.1.1 2 5.3 odd 4
950.2.a.g.1.2 2 5.2 odd 4
1520.2.d.e.609.2 4 4.3 odd 2
1520.2.d.e.609.3 4 20.19 odd 2
1710.2.d.c.1369.1 4 15.14 odd 2
1710.2.d.c.1369.3 4 3.2 odd 2
7600.2.a.v.1.2 2 20.3 even 4
7600.2.a.bg.1.1 2 20.7 even 4
8550.2.a.bn.1.1 2 15.2 even 4
8550.2.a.cb.1.2 2 15.8 even 4