Properties

Label 2070.2.j.f.737.2
Level $2070$
Weight $2$
Character 2070.737
Analytic conductor $16.529$
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] = [2070,2,Mod(323,2070)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2070.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.j (of order \(4\), degree \(2\), 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: \(16.5290332184\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 737.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2070.737
Dual form 2070.2.j.f.323.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.707107 - 2.12132i) q^{10} -4.82843i q^{11} +(-1.41421 + 1.41421i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(2.58579 - 2.58579i) q^{17} +0.585786i q^{19} +(-1.00000 - 2.00000i) q^{20} +(-3.41421 - 3.41421i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000i q^{26} +(2.00000 - 2.00000i) q^{28} -0.828427 q^{29} +0.828427 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.65685i q^{34} +(6.00000 + 2.00000i) q^{35} +(-1.41421 - 1.41421i) q^{37} +(0.414214 + 0.414214i) q^{38} +(-2.12132 - 0.707107i) q^{40} -5.41421i q^{41} +(2.24264 - 2.24264i) q^{43} -4.82843 q^{44} -1.00000 q^{46} +1.00000i q^{49} +(-0.707107 - 4.94975i) q^{50} +(1.41421 + 1.41421i) q^{52} +(8.65685 + 8.65685i) q^{53} +(-4.82843 - 9.65685i) q^{55} -2.82843i q^{56} +(-0.585786 + 0.585786i) q^{58} -2.82843 q^{59} +5.41421 q^{61} +(0.585786 - 0.585786i) q^{62} +1.00000i q^{64} +(-1.41421 + 4.24264i) q^{65} +(6.82843 + 6.82843i) q^{67} +(-2.58579 - 2.58579i) q^{68} +(5.65685 - 2.82843i) q^{70} -7.41421i q^{71} +(-9.82843 + 9.82843i) q^{73} -2.00000 q^{74} +0.585786 q^{76} +(9.65685 - 9.65685i) q^{77} +1.17157i q^{79} +(-2.00000 + 1.00000i) q^{80} +(-3.82843 - 3.82843i) q^{82} +(-0.757359 - 0.757359i) q^{83} +(2.58579 - 7.75736i) q^{85} -3.17157i q^{86} +(-3.41421 + 3.41421i) q^{88} +14.0000 q^{89} -5.65685 q^{91} +(-0.707107 + 0.707107i) q^{92} +(0.585786 + 1.17157i) q^{95} +(-9.07107 - 9.07107i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{5} + 8 q^{7} - 4 q^{16} + 16 q^{17} - 4 q^{20} - 8 q^{22} + 12 q^{25} + 8 q^{28} + 8 q^{29} - 8 q^{31} + 24 q^{35} - 4 q^{38} - 8 q^{43} - 8 q^{44} - 4 q^{46} + 12 q^{53} - 8 q^{55} - 8 q^{58} + 16 q^{61} + 8 q^{62} + 16 q^{67} - 16 q^{68} - 28 q^{73} - 8 q^{74} + 8 q^{76} + 16 q^{77} - 8 q^{80} - 4 q^{82} - 20 q^{83} + 16 q^{85} - 8 q^{88} + 56 q^{89} + 8 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).

\(n\) \(461\) \(1657\) \(1891\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 0 0
\(7\) 2.00000 + 2.00000i 0.755929 + 0.755929i 0.975579 0.219650i \(-0.0704915\pi\)
−0.219650 + 0.975579i \(0.570491\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) 0.707107 2.12132i 0.223607 0.670820i
\(11\) 4.82843i 1.45583i −0.685670 0.727913i \(-0.740491\pi\)
0.685670 0.727913i \(-0.259509\pi\)
\(12\) 0 0
\(13\) −1.41421 + 1.41421i −0.392232 + 0.392232i −0.875482 0.483250i \(-0.839456\pi\)
0.483250 + 0.875482i \(0.339456\pi\)
\(14\) 2.82843 0.755929
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 2.58579 2.58579i 0.627145 0.627145i −0.320203 0.947349i \(-0.603751\pi\)
0.947349 + 0.320203i \(0.103751\pi\)
\(18\) 0 0
\(19\) 0.585786i 0.134389i 0.997740 + 0.0671943i \(0.0214047\pi\)
−0.997740 + 0.0671943i \(0.978595\pi\)
\(20\) −1.00000 2.00000i −0.223607 0.447214i
\(21\) 0 0
\(22\) −3.41421 3.41421i −0.727913 0.727913i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 2.00000i 0.392232i
\(27\) 0 0
\(28\) 2.00000 2.00000i 0.377964 0.377964i
\(29\) −0.828427 −0.153835 −0.0769175 0.997037i \(-0.524508\pi\)
−0.0769175 + 0.997037i \(0.524508\pi\)
\(30\) 0 0
\(31\) 0.828427 0.148790 0.0743950 0.997229i \(-0.476297\pi\)
0.0743950 + 0.997229i \(0.476297\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 3.65685i 0.627145i
\(35\) 6.00000 + 2.00000i 1.01419 + 0.338062i
\(36\) 0 0
\(37\) −1.41421 1.41421i −0.232495 0.232495i 0.581238 0.813733i \(-0.302568\pi\)
−0.813733 + 0.581238i \(0.802568\pi\)
\(38\) 0.414214 + 0.414214i 0.0671943 + 0.0671943i
\(39\) 0 0
\(40\) −2.12132 0.707107i −0.335410 0.111803i
\(41\) 5.41421i 0.845558i −0.906233 0.422779i \(-0.861055\pi\)
0.906233 0.422779i \(-0.138945\pi\)
\(42\) 0 0
\(43\) 2.24264 2.24264i 0.341999 0.341999i −0.515119 0.857119i \(-0.672252\pi\)
0.857119 + 0.515119i \(0.172252\pi\)
\(44\) −4.82843 −0.727913
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) −0.707107 4.94975i −0.100000 0.700000i
\(51\) 0 0
\(52\) 1.41421 + 1.41421i 0.196116 + 0.196116i
\(53\) 8.65685 + 8.65685i 1.18911 + 1.18911i 0.977314 + 0.211797i \(0.0679314\pi\)
0.211797 + 0.977314i \(0.432069\pi\)
\(54\) 0 0
\(55\) −4.82843 9.65685i −0.651065 1.30213i
\(56\) 2.82843i 0.377964i
\(57\) 0 0
\(58\) −0.585786 + 0.585786i −0.0769175 + 0.0769175i
\(59\) −2.82843 −0.368230 −0.184115 0.982905i \(-0.558942\pi\)
−0.184115 + 0.982905i \(0.558942\pi\)
\(60\) 0 0
\(61\) 5.41421 0.693219 0.346610 0.938010i \(-0.387333\pi\)
0.346610 + 0.938010i \(0.387333\pi\)
\(62\) 0.585786 0.585786i 0.0743950 0.0743950i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −1.41421 + 4.24264i −0.175412 + 0.526235i
\(66\) 0 0
\(67\) 6.82843 + 6.82843i 0.834225 + 0.834225i 0.988092 0.153866i \(-0.0491726\pi\)
−0.153866 + 0.988092i \(0.549173\pi\)
\(68\) −2.58579 2.58579i −0.313573 0.313573i
\(69\) 0 0
\(70\) 5.65685 2.82843i 0.676123 0.338062i
\(71\) 7.41421i 0.879905i −0.898021 0.439953i \(-0.854995\pi\)
0.898021 0.439953i \(-0.145005\pi\)
\(72\) 0 0
\(73\) −9.82843 + 9.82843i −1.15033 + 1.15033i −0.163844 + 0.986486i \(0.552389\pi\)
−0.986486 + 0.163844i \(0.947611\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 0.585786 0.0671943
\(77\) 9.65685 9.65685i 1.10050 1.10050i
\(78\) 0 0
\(79\) 1.17157i 0.131812i 0.997826 + 0.0659061i \(0.0209938\pi\)
−0.997826 + 0.0659061i \(0.979006\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 0 0
\(82\) −3.82843 3.82843i −0.422779 0.422779i
\(83\) −0.757359 0.757359i −0.0831310 0.0831310i 0.664319 0.747450i \(-0.268722\pi\)
−0.747450 + 0.664319i \(0.768722\pi\)
\(84\) 0 0
\(85\) 2.58579 7.75736i 0.280468 0.841404i
\(86\) 3.17157i 0.341999i
\(87\) 0 0
\(88\) −3.41421 + 3.41421i −0.363956 + 0.363956i
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) −5.65685 −0.592999
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.585786 + 1.17157i 0.0601004 + 0.120201i
\(96\) 0 0
\(97\) −9.07107 9.07107i −0.921027 0.921027i 0.0760747 0.997102i \(-0.475761\pi\)
−0.997102 + 0.0760747i \(0.975761\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) −4.00000 3.00000i −0.400000 0.300000i
\(101\) 3.65685i 0.363871i 0.983311 + 0.181935i \(0.0582361\pi\)
−0.983311 + 0.181935i \(0.941764\pi\)
\(102\) 0 0
\(103\) −5.17157 + 5.17157i −0.509570 + 0.509570i −0.914394 0.404824i \(-0.867333\pi\)
0.404824 + 0.914394i \(0.367333\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 12.2426 1.18911
\(107\) −4.07107 + 4.07107i −0.393565 + 0.393565i −0.875956 0.482391i \(-0.839768\pi\)
0.482391 + 0.875956i \(0.339768\pi\)
\(108\) 0 0
\(109\) 19.0711i 1.82668i −0.407201 0.913339i \(-0.633495\pi\)
0.407201 0.913339i \(-0.366505\pi\)
\(110\) −10.2426 3.41421i −0.976597 0.325532i
\(111\) 0 0
\(112\) −2.00000 2.00000i −0.188982 0.188982i
\(113\) 12.2426 + 12.2426i 1.15169 + 1.15169i 0.986214 + 0.165477i \(0.0529164\pi\)
0.165477 + 0.986214i \(0.447084\pi\)
\(114\) 0 0
\(115\) −2.12132 0.707107i −0.197814 0.0659380i
\(116\) 0.828427i 0.0769175i
\(117\) 0 0
\(118\) −2.00000 + 2.00000i −0.184115 + 0.184115i
\(119\) 10.3431 0.948155
\(120\) 0 0
\(121\) −12.3137 −1.11943
\(122\) 3.82843 3.82843i 0.346610 0.346610i
\(123\) 0 0
\(124\) 0.828427i 0.0743950i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) −1.58579 1.58579i −0.140716 0.140716i 0.633240 0.773956i \(-0.281725\pi\)
−0.773956 + 0.633240i \(0.781725\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 2.00000 + 4.00000i 0.175412 + 0.350823i
\(131\) 5.65685i 0.494242i 0.968985 + 0.247121i \(0.0794845\pi\)
−0.968985 + 0.247121i \(0.920516\pi\)
\(132\) 0 0
\(133\) −1.17157 + 1.17157i −0.101588 + 0.101588i
\(134\) 9.65685 0.834225
\(135\) 0 0
\(136\) −3.65685 −0.313573
\(137\) 1.07107 1.07107i 0.0915075 0.0915075i −0.659871 0.751379i \(-0.729389\pi\)
0.751379 + 0.659871i \(0.229389\pi\)
\(138\) 0 0
\(139\) 6.82843i 0.579180i 0.957151 + 0.289590i \(0.0935189\pi\)
−0.957151 + 0.289590i \(0.906481\pi\)
\(140\) 2.00000 6.00000i 0.169031 0.507093i
\(141\) 0 0
\(142\) −5.24264 5.24264i −0.439953 0.439953i
\(143\) 6.82843 + 6.82843i 0.571022 + 0.571022i
\(144\) 0 0
\(145\) −1.65685 + 0.828427i −0.137594 + 0.0687971i
\(146\) 13.8995i 1.15033i
\(147\) 0 0
\(148\) −1.41421 + 1.41421i −0.116248 + 0.116248i
\(149\) −11.6569 −0.954967 −0.477483 0.878641i \(-0.658451\pi\)
−0.477483 + 0.878641i \(0.658451\pi\)
\(150\) 0 0
\(151\) −16.9706 −1.38104 −0.690522 0.723311i \(-0.742619\pi\)
−0.690522 + 0.723311i \(0.742619\pi\)
\(152\) 0.414214 0.414214i 0.0335972 0.0335972i
\(153\) 0 0
\(154\) 13.6569i 1.10050i
\(155\) 1.65685 0.828427i 0.133082 0.0665409i
\(156\) 0 0
\(157\) −4.24264 4.24264i −0.338600 0.338600i 0.517241 0.855840i \(-0.326959\pi\)
−0.855840 + 0.517241i \(0.826959\pi\)
\(158\) 0.828427 + 0.828427i 0.0659061 + 0.0659061i
\(159\) 0 0
\(160\) −0.707107 + 2.12132i −0.0559017 + 0.167705i
\(161\) 2.82843i 0.222911i
\(162\) 0 0
\(163\) −6.48528 + 6.48528i −0.507966 + 0.507966i −0.913902 0.405935i \(-0.866946\pi\)
0.405935 + 0.913902i \(0.366946\pi\)
\(164\) −5.41421 −0.422779
\(165\) 0 0
\(166\) −1.07107 −0.0831310
\(167\) 15.8995 15.8995i 1.23034 1.23034i 0.266507 0.963833i \(-0.414131\pi\)
0.963833 0.266507i \(-0.0858695\pi\)
\(168\) 0 0
\(169\) 9.00000i 0.692308i
\(170\) −3.65685 7.31371i −0.280468 0.560936i
\(171\) 0 0
\(172\) −2.24264 2.24264i −0.171000 0.171000i
\(173\) −9.89949 9.89949i −0.752645 0.752645i 0.222327 0.974972i \(-0.428635\pi\)
−0.974972 + 0.222327i \(0.928635\pi\)
\(174\) 0 0
\(175\) 14.0000 2.00000i 1.05830 0.151186i
\(176\) 4.82843i 0.363956i
\(177\) 0 0
\(178\) 9.89949 9.89949i 0.741999 0.741999i
\(179\) −23.3137 −1.74255 −0.871274 0.490797i \(-0.836706\pi\)
−0.871274 + 0.490797i \(0.836706\pi\)
\(180\) 0 0
\(181\) 13.4142 0.997071 0.498535 0.866869i \(-0.333871\pi\)
0.498535 + 0.866869i \(0.333871\pi\)
\(182\) −4.00000 + 4.00000i −0.296500 + 0.296500i
\(183\) 0 0
\(184\) 1.00000i 0.0737210i
\(185\) −4.24264 1.41421i −0.311925 0.103975i
\(186\) 0 0
\(187\) −12.4853 12.4853i −0.913014 0.913014i
\(188\) 0 0
\(189\) 0 0
\(190\) 1.24264 + 0.414214i 0.0901506 + 0.0300502i
\(191\) 9.17157i 0.663632i 0.943344 + 0.331816i \(0.107661\pi\)
−0.943344 + 0.331816i \(0.892339\pi\)
\(192\) 0 0
\(193\) −5.00000 + 5.00000i −0.359908 + 0.359908i −0.863779 0.503871i \(-0.831909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −12.8284 −0.921027
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 7.07107 7.07107i 0.503793 0.503793i −0.408822 0.912614i \(-0.634060\pi\)
0.912614 + 0.408822i \(0.134060\pi\)
\(198\) 0 0
\(199\) 6.34315i 0.449654i −0.974399 0.224827i \(-0.927818\pi\)
0.974399 0.224827i \(-0.0721816\pi\)
\(200\) −4.94975 + 0.707107i −0.350000 + 0.0500000i
\(201\) 0 0
\(202\) 2.58579 + 2.58579i 0.181935 + 0.181935i
\(203\) −1.65685 1.65685i −0.116288 0.116288i
\(204\) 0 0
\(205\) −5.41421 10.8284i −0.378145 0.756290i
\(206\) 7.31371i 0.509570i
\(207\) 0 0
\(208\) 1.41421 1.41421i 0.0980581 0.0980581i
\(209\) 2.82843 0.195646
\(210\) 0 0
\(211\) −14.8284 −1.02083 −0.510416 0.859928i \(-0.670508\pi\)
−0.510416 + 0.859928i \(0.670508\pi\)
\(212\) 8.65685 8.65685i 0.594555 0.594555i
\(213\) 0 0
\(214\) 5.75736i 0.393565i
\(215\) 2.24264 6.72792i 0.152947 0.458840i
\(216\) 0 0
\(217\) 1.65685 + 1.65685i 0.112475 + 0.112475i
\(218\) −13.4853 13.4853i −0.913339 0.913339i
\(219\) 0 0
\(220\) −9.65685 + 4.82843i −0.651065 + 0.325532i
\(221\) 7.31371i 0.491973i
\(222\) 0 0
\(223\) −3.24264 + 3.24264i −0.217143 + 0.217143i −0.807293 0.590150i \(-0.799069\pi\)
0.590150 + 0.807293i \(0.299069\pi\)
\(224\) −2.82843 −0.188982
\(225\) 0 0
\(226\) 17.3137 1.15169
\(227\) 4.89949 4.89949i 0.325191 0.325191i −0.525563 0.850754i \(-0.676145\pi\)
0.850754 + 0.525563i \(0.176145\pi\)
\(228\) 0 0
\(229\) 13.4142i 0.886436i 0.896414 + 0.443218i \(0.146163\pi\)
−0.896414 + 0.443218i \(0.853837\pi\)
\(230\) −2.00000 + 1.00000i −0.131876 + 0.0659380i
\(231\) 0 0
\(232\) 0.585786 + 0.585786i 0.0384588 + 0.0384588i
\(233\) 13.1716 + 13.1716i 0.862898 + 0.862898i 0.991674 0.128775i \(-0.0411046\pi\)
−0.128775 + 0.991674i \(0.541105\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.82843i 0.184115i
\(237\) 0 0
\(238\) 7.31371 7.31371i 0.474077 0.474077i
\(239\) −9.55635 −0.618149 −0.309074 0.951038i \(-0.600019\pi\)
−0.309074 + 0.951038i \(0.600019\pi\)
\(240\) 0 0
\(241\) 13.7990 0.888871 0.444436 0.895811i \(-0.353404\pi\)
0.444436 + 0.895811i \(0.353404\pi\)
\(242\) −8.70711 + 8.70711i −0.559714 + 0.559714i
\(243\) 0 0
\(244\) 5.41421i 0.346610i
\(245\) 1.00000 + 2.00000i 0.0638877 + 0.127775i
\(246\) 0 0
\(247\) −0.828427 0.828427i −0.0527116 0.0527116i
\(248\) −0.585786 0.585786i −0.0371975 0.0371975i
\(249\) 0 0
\(250\) −6.36396 9.19239i −0.402492 0.581378i
\(251\) 28.8284i 1.81963i 0.415009 + 0.909817i \(0.363778\pi\)
−0.415009 + 0.909817i \(0.636222\pi\)
\(252\) 0 0
\(253\) −3.41421 + 3.41421i −0.214650 + 0.214650i
\(254\) −2.24264 −0.140716
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.8284 10.8284i 0.675459 0.675459i −0.283510 0.958969i \(-0.591499\pi\)
0.958969 + 0.283510i \(0.0914991\pi\)
\(258\) 0 0
\(259\) 5.65685i 0.351500i
\(260\) 4.24264 + 1.41421i 0.263117 + 0.0877058i
\(261\) 0 0
\(262\) 4.00000 + 4.00000i 0.247121 + 0.247121i
\(263\) 12.1421 + 12.1421i 0.748716 + 0.748716i 0.974238 0.225522i \(-0.0724087\pi\)
−0.225522 + 0.974238i \(0.572409\pi\)
\(264\) 0 0
\(265\) 25.9706 + 8.65685i 1.59536 + 0.531786i
\(266\) 1.65685i 0.101588i
\(267\) 0 0
\(268\) 6.82843 6.82843i 0.417113 0.417113i
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 0 0
\(271\) 8.97056 0.544923 0.272461 0.962167i \(-0.412162\pi\)
0.272461 + 0.962167i \(0.412162\pi\)
\(272\) −2.58579 + 2.58579i −0.156786 + 0.156786i
\(273\) 0 0
\(274\) 1.51472i 0.0915075i
\(275\) −19.3137 14.4853i −1.16466 0.873495i
\(276\) 0 0
\(277\) 22.7279 + 22.7279i 1.36559 + 1.36559i 0.866620 + 0.498968i \(0.166288\pi\)
0.498968 + 0.866620i \(0.333712\pi\)
\(278\) 4.82843 + 4.82843i 0.289590 + 0.289590i
\(279\) 0 0
\(280\) −2.82843 5.65685i −0.169031 0.338062i
\(281\) 30.9706i 1.84755i 0.382937 + 0.923774i \(0.374913\pi\)
−0.382937 + 0.923774i \(0.625087\pi\)
\(282\) 0 0
\(283\) −2.82843 + 2.82843i −0.168133 + 0.168133i −0.786158 0.618026i \(-0.787933\pi\)
0.618026 + 0.786158i \(0.287933\pi\)
\(284\) −7.41421 −0.439953
\(285\) 0 0
\(286\) 9.65685 0.571022
\(287\) 10.8284 10.8284i 0.639182 0.639182i
\(288\) 0 0
\(289\) 3.62742i 0.213377i
\(290\) −0.585786 + 1.75736i −0.0343986 + 0.103196i
\(291\) 0 0
\(292\) 9.82843 + 9.82843i 0.575165 + 0.575165i
\(293\) −7.34315 7.34315i −0.428991 0.428991i 0.459293 0.888285i \(-0.348103\pi\)
−0.888285 + 0.459293i \(0.848103\pi\)
\(294\) 0 0
\(295\) −5.65685 + 2.82843i −0.329355 + 0.164677i
\(296\) 2.00000i 0.116248i
\(297\) 0 0
\(298\) −8.24264 + 8.24264i −0.477483 + 0.477483i
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) 8.97056 0.517055
\(302\) −12.0000 + 12.0000i −0.690522 + 0.690522i
\(303\) 0 0
\(304\) 0.585786i 0.0335972i
\(305\) 10.8284 5.41421i 0.620034 0.310017i
\(306\) 0 0
\(307\) 10.8284 + 10.8284i 0.618011 + 0.618011i 0.945021 0.327010i \(-0.106041\pi\)
−0.327010 + 0.945021i \(0.606041\pi\)
\(308\) −9.65685 9.65685i −0.550250 0.550250i
\(309\) 0 0
\(310\) 0.585786 1.75736i 0.0332704 0.0998113i
\(311\) 31.2132i 1.76994i 0.465650 + 0.884969i \(0.345821\pi\)
−0.465650 + 0.884969i \(0.654179\pi\)
\(312\) 0 0
\(313\) 0.928932 0.928932i 0.0525064 0.0525064i −0.680366 0.732872i \(-0.738179\pi\)
0.732872 + 0.680366i \(0.238179\pi\)
\(314\) −6.00000 −0.338600
\(315\) 0 0
\(316\) 1.17157 0.0659061
\(317\) 10.7279 10.7279i 0.602540 0.602540i −0.338446 0.940986i \(-0.609901\pi\)
0.940986 + 0.338446i \(0.109901\pi\)
\(318\) 0 0
\(319\) 4.00000i 0.223957i
\(320\) 1.00000 + 2.00000i 0.0559017 + 0.111803i
\(321\) 0 0
\(322\) −2.00000 2.00000i −0.111456 0.111456i
\(323\) 1.51472 + 1.51472i 0.0842812 + 0.0842812i
\(324\) 0 0
\(325\) 1.41421 + 9.89949i 0.0784465 + 0.549125i
\(326\) 9.17157i 0.507966i
\(327\) 0 0
\(328\) −3.82843 + 3.82843i −0.211390 + 0.211390i
\(329\) 0 0
\(330\) 0 0
\(331\) −31.7990 −1.74783 −0.873915 0.486078i \(-0.838427\pi\)
−0.873915 + 0.486078i \(0.838427\pi\)
\(332\) −0.757359 + 0.757359i −0.0415655 + 0.0415655i
\(333\) 0 0
\(334\) 22.4853i 1.23034i
\(335\) 20.4853 + 6.82843i 1.11923 + 0.373077i
\(336\) 0 0
\(337\) 2.24264 + 2.24264i 0.122164 + 0.122164i 0.765546 0.643381i \(-0.222469\pi\)
−0.643381 + 0.765546i \(0.722469\pi\)
\(338\) 6.36396 + 6.36396i 0.346154 + 0.346154i
\(339\) 0 0
\(340\) −7.75736 2.58579i −0.420702 0.140234i
\(341\) 4.00000i 0.216612i
\(342\) 0 0
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) −3.17157 −0.171000
\(345\) 0 0
\(346\) −14.0000 −0.752645
\(347\) −10.0000 + 10.0000i −0.536828 + 0.536828i −0.922596 0.385768i \(-0.873937\pi\)
0.385768 + 0.922596i \(0.373937\pi\)
\(348\) 0 0
\(349\) 23.6569i 1.26632i 0.774020 + 0.633161i \(0.218243\pi\)
−0.774020 + 0.633161i \(0.781757\pi\)
\(350\) 8.48528 11.3137i 0.453557 0.604743i
\(351\) 0 0
\(352\) 3.41421 + 3.41421i 0.181978 + 0.181978i
\(353\) 5.89949 + 5.89949i 0.313998 + 0.313998i 0.846456 0.532458i \(-0.178732\pi\)
−0.532458 + 0.846456i \(0.678732\pi\)
\(354\) 0 0
\(355\) −7.41421 14.8284i −0.393506 0.787011i
\(356\) 14.0000i 0.741999i
\(357\) 0 0
\(358\) −16.4853 + 16.4853i −0.871274 + 0.871274i
\(359\) 6.82843 0.360391 0.180195 0.983631i \(-0.442327\pi\)
0.180195 + 0.983631i \(0.442327\pi\)
\(360\) 0 0
\(361\) 18.6569 0.981940
\(362\) 9.48528 9.48528i 0.498535 0.498535i
\(363\) 0 0
\(364\) 5.65685i 0.296500i
\(365\) −9.82843 + 29.4853i −0.514443 + 1.54333i
\(366\) 0 0
\(367\) 6.00000 + 6.00000i 0.313197 + 0.313197i 0.846147 0.532950i \(-0.178916\pi\)
−0.532950 + 0.846147i \(0.678916\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) 0 0
\(370\) −4.00000 + 2.00000i −0.207950 + 0.103975i
\(371\) 34.6274i 1.79777i
\(372\) 0 0
\(373\) 4.24264 4.24264i 0.219676 0.219676i −0.588686 0.808362i \(-0.700355\pi\)
0.808362 + 0.588686i \(0.200355\pi\)
\(374\) −17.6569 −0.913014
\(375\) 0 0
\(376\) 0 0
\(377\) 1.17157 1.17157i 0.0603391 0.0603391i
\(378\) 0 0
\(379\) 30.0416i 1.54313i 0.636148 + 0.771567i \(0.280527\pi\)
−0.636148 + 0.771567i \(0.719473\pi\)
\(380\) 1.17157 0.585786i 0.0601004 0.0300502i
\(381\) 0 0
\(382\) 6.48528 + 6.48528i 0.331816 + 0.331816i
\(383\) −16.8284 16.8284i −0.859892 0.859892i 0.131433 0.991325i \(-0.458042\pi\)
−0.991325 + 0.131433i \(0.958042\pi\)
\(384\) 0 0
\(385\) 9.65685 28.9706i 0.492159 1.47648i
\(386\) 7.07107i 0.359908i
\(387\) 0 0
\(388\) −9.07107 + 9.07107i −0.460514 + 0.460514i
\(389\) −20.2843 −1.02845 −0.514227 0.857654i \(-0.671921\pi\)
−0.514227 + 0.857654i \(0.671921\pi\)
\(390\) 0 0
\(391\) −3.65685 −0.184935
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) 0 0
\(394\) 10.0000i 0.503793i
\(395\) 1.17157 + 2.34315i 0.0589482 + 0.117896i
\(396\) 0 0
\(397\) 5.41421 + 5.41421i 0.271732 + 0.271732i 0.829797 0.558065i \(-0.188456\pi\)
−0.558065 + 0.829797i \(0.688456\pi\)
\(398\) −4.48528 4.48528i −0.224827 0.224827i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) 34.0000i 1.69788i −0.528490 0.848939i \(-0.677242\pi\)
0.528490 0.848939i \(-0.322758\pi\)
\(402\) 0 0
\(403\) −1.17157 + 1.17157i −0.0583602 + 0.0583602i
\(404\) 3.65685 0.181935
\(405\) 0 0
\(406\) −2.34315 −0.116288
\(407\) −6.82843 + 6.82843i −0.338473 + 0.338473i
\(408\) 0 0
\(409\) 5.31371i 0.262746i −0.991333 0.131373i \(-0.958061\pi\)
0.991333 0.131373i \(-0.0419386\pi\)
\(410\) −11.4853 3.82843i −0.567218 0.189073i
\(411\) 0 0
\(412\) 5.17157 + 5.17157i 0.254785 + 0.254785i
\(413\) −5.65685 5.65685i −0.278356 0.278356i
\(414\) 0 0
\(415\) −2.27208 0.757359i −0.111532 0.0371773i
\(416\) 2.00000i 0.0980581i
\(417\) 0 0
\(418\) 2.00000 2.00000i 0.0978232 0.0978232i
\(419\) −33.6569 −1.64424 −0.822122 0.569311i \(-0.807210\pi\)
−0.822122 + 0.569311i \(0.807210\pi\)
\(420\) 0 0
\(421\) −3.27208 −0.159471 −0.0797357 0.996816i \(-0.525408\pi\)
−0.0797357 + 0.996816i \(0.525408\pi\)
\(422\) −10.4853 + 10.4853i −0.510416 + 0.510416i
\(423\) 0 0
\(424\) 12.2426i 0.594555i
\(425\) −2.58579 18.1005i −0.125429 0.878003i
\(426\) 0 0
\(427\) 10.8284 + 10.8284i 0.524024 + 0.524024i
\(428\) 4.07107 + 4.07107i 0.196782 + 0.196782i
\(429\) 0 0
\(430\) −3.17157 6.34315i −0.152947 0.305894i
\(431\) 10.8284i 0.521587i 0.965395 + 0.260793i \(0.0839842\pi\)
−0.965395 + 0.260793i \(0.916016\pi\)
\(432\) 0 0
\(433\) −20.5858 + 20.5858i −0.989290 + 0.989290i −0.999943 0.0106535i \(-0.996609\pi\)
0.0106535 + 0.999943i \(0.496609\pi\)
\(434\) 2.34315 0.112475
\(435\) 0 0
\(436\) −19.0711 −0.913339
\(437\) 0.414214 0.414214i 0.0198145 0.0198145i
\(438\) 0 0
\(439\) 4.14214i 0.197693i −0.995103 0.0988467i \(-0.968485\pi\)
0.995103 0.0988467i \(-0.0315153\pi\)
\(440\) −3.41421 + 10.2426i −0.162766 + 0.488299i
\(441\) 0 0
\(442\) 5.17157 + 5.17157i 0.245987 + 0.245987i
\(443\) 4.82843 + 4.82843i 0.229405 + 0.229405i 0.812444 0.583039i \(-0.198136\pi\)
−0.583039 + 0.812444i \(0.698136\pi\)
\(444\) 0 0
\(445\) 28.0000 14.0000i 1.32733 0.663664i
\(446\) 4.58579i 0.217143i
\(447\) 0 0
\(448\) −2.00000 + 2.00000i −0.0944911 + 0.0944911i
\(449\) −4.92893 −0.232611 −0.116305 0.993214i \(-0.537105\pi\)
−0.116305 + 0.993214i \(0.537105\pi\)
\(450\) 0 0
\(451\) −26.1421 −1.23099
\(452\) 12.2426 12.2426i 0.575845 0.575845i
\(453\) 0 0
\(454\) 6.92893i 0.325191i
\(455\) −11.3137 + 5.65685i −0.530395 + 0.265197i
\(456\) 0 0
\(457\) −1.27208 1.27208i −0.0595053 0.0595053i 0.676728 0.736233i \(-0.263397\pi\)
−0.736233 + 0.676728i \(0.763397\pi\)
\(458\) 9.48528 + 9.48528i 0.443218 + 0.443218i
\(459\) 0 0
\(460\) −0.707107 + 2.12132i −0.0329690 + 0.0989071i
\(461\) 13.5147i 0.629443i −0.949184 0.314722i \(-0.898089\pi\)
0.949184 0.314722i \(-0.101911\pi\)
\(462\) 0 0
\(463\) −25.8701 + 25.8701i −1.20228 + 1.20228i −0.228813 + 0.973470i \(0.573484\pi\)
−0.973470 + 0.228813i \(0.926516\pi\)
\(464\) 0.828427 0.0384588
\(465\) 0 0
\(466\) 18.6274 0.862898
\(467\) −7.92893 + 7.92893i −0.366907 + 0.366907i −0.866348 0.499441i \(-0.833539\pi\)
0.499441 + 0.866348i \(0.333539\pi\)
\(468\) 0 0
\(469\) 27.3137i 1.26123i
\(470\) 0 0
\(471\) 0 0
\(472\) 2.00000 + 2.00000i 0.0920575 + 0.0920575i
\(473\) −10.8284 10.8284i −0.497892 0.497892i
\(474\) 0 0
\(475\) 2.34315 + 1.75736i 0.107511 + 0.0806332i
\(476\) 10.3431i 0.474077i
\(477\) 0 0
\(478\) −6.75736 + 6.75736i −0.309074 + 0.309074i
\(479\) −18.6274 −0.851108 −0.425554 0.904933i \(-0.639921\pi\)
−0.425554 + 0.904933i \(0.639921\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 9.75736 9.75736i 0.444436 0.444436i
\(483\) 0 0
\(484\) 12.3137i 0.559714i
\(485\) −27.2132 9.07107i −1.23569 0.411896i
\(486\) 0 0
\(487\) 28.2132 + 28.2132i 1.27846 + 1.27846i 0.941528 + 0.336934i \(0.109390\pi\)
0.336934 + 0.941528i \(0.390610\pi\)
\(488\) −3.82843 3.82843i −0.173305 0.173305i
\(489\) 0 0
\(490\) 2.12132 + 0.707107i 0.0958315 + 0.0319438i
\(491\) 9.17157i 0.413907i −0.978351 0.206954i \(-0.933645\pi\)
0.978351 0.206954i \(-0.0663549\pi\)
\(492\) 0 0
\(493\) −2.14214 + 2.14214i −0.0964769 + 0.0964769i
\(494\) −1.17157 −0.0527116
\(495\) 0 0
\(496\) −0.828427 −0.0371975
\(497\) 14.8284 14.8284i 0.665146 0.665146i
\(498\) 0 0
\(499\) 12.9706i 0.580642i 0.956929 + 0.290321i \(0.0937621\pi\)
−0.956929 + 0.290321i \(0.906238\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) 0 0
\(502\) 20.3848 + 20.3848i 0.909817 + 0.909817i
\(503\) 25.7990 + 25.7990i 1.15032 + 1.15032i 0.986488 + 0.163832i \(0.0523854\pi\)
0.163832 + 0.986488i \(0.447615\pi\)
\(504\) 0 0
\(505\) 3.65685 + 7.31371i 0.162728 + 0.325456i
\(506\) 4.82843i 0.214650i
\(507\) 0 0
\(508\) −1.58579 + 1.58579i −0.0703579 + 0.0703579i
\(509\) 11.4558 0.507771 0.253886 0.967234i \(-0.418291\pi\)
0.253886 + 0.967234i \(0.418291\pi\)
\(510\) 0 0
\(511\) −39.3137 −1.73914
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 15.3137i 0.675459i
\(515\) −5.17157 + 15.5147i −0.227887 + 0.683660i
\(516\) 0 0
\(517\) 0 0
\(518\) −4.00000 4.00000i −0.175750 0.175750i
\(519\) 0 0
\(520\) 4.00000 2.00000i 0.175412 0.0877058i
\(521\) 12.1421i 0.531957i −0.963979 0.265978i \(-0.914305\pi\)
0.963979 0.265978i \(-0.0856950\pi\)
\(522\) 0 0
\(523\) 15.2132 15.2132i 0.665227 0.665227i −0.291380 0.956607i \(-0.594115\pi\)
0.956607 + 0.291380i \(0.0941145\pi\)
\(524\) 5.65685 0.247121
\(525\) 0 0
\(526\) 17.1716 0.748716
\(527\) 2.14214 2.14214i 0.0933129 0.0933129i
\(528\) 0 0
\(529\) 1.00000i 0.0434783i
\(530\) 24.4853 12.2426i 1.06357 0.531786i
\(531\) 0 0
\(532\) 1.17157 + 1.17157i 0.0507941 + 0.0507941i
\(533\) 7.65685 + 7.65685i 0.331655 + 0.331655i
\(534\) 0 0
\(535\) −4.07107 + 12.2132i −0.176008 + 0.528023i
\(536\) 9.65685i 0.417113i
\(537\) 0 0
\(538\) 1.41421 1.41421i 0.0609711 0.0609711i
\(539\) 4.82843 0.207975
\(540\) 0 0
\(541\) 21.3137 0.916348 0.458174 0.888863i \(-0.348504\pi\)
0.458174 + 0.888863i \(0.348504\pi\)
\(542\) 6.34315 6.34315i 0.272461 0.272461i
\(543\) 0 0
\(544\) 3.65685i 0.156786i
\(545\) −19.0711 38.1421i −0.816915 1.63383i
\(546\) 0 0
\(547\) −0.142136 0.142136i −0.00607728 0.00607728i 0.704062 0.710139i \(-0.251368\pi\)
−0.710139 + 0.704062i \(0.751368\pi\)
\(548\) −1.07107 1.07107i −0.0457537 0.0457537i
\(549\) 0 0
\(550\) −23.8995 + 3.41421i −1.01908 + 0.145583i
\(551\) 0.485281i 0.0206737i
\(552\) 0 0
\(553\) −2.34315 + 2.34315i −0.0996407 + 0.0996407i
\(554\) 32.1421 1.36559
\(555\) 0 0
\(556\) 6.82843 0.289590
\(557\) −14.1716 + 14.1716i −0.600469 + 0.600469i −0.940437 0.339968i \(-0.889584\pi\)
0.339968 + 0.940437i \(0.389584\pi\)
\(558\) 0 0
\(559\) 6.34315i 0.268286i
\(560\) −6.00000 2.00000i −0.253546 0.0845154i
\(561\) 0 0
\(562\) 21.8995 + 21.8995i 0.923774 + 0.923774i
\(563\) −28.0711 28.0711i −1.18305 1.18305i −0.978949 0.204106i \(-0.934571\pi\)
−0.204106 0.978949i \(-0.565429\pi\)
\(564\) 0 0
\(565\) 36.7279 + 12.2426i 1.54516 + 0.515052i
\(566\) 4.00000i 0.168133i
\(567\) 0 0
\(568\) −5.24264 + 5.24264i −0.219976 + 0.219976i
\(569\) −5.31371 −0.222762 −0.111381 0.993778i \(-0.535527\pi\)
−0.111381 + 0.993778i \(0.535527\pi\)
\(570\) 0 0
\(571\) −17.7574 −0.743122 −0.371561 0.928408i \(-0.621177\pi\)
−0.371561 + 0.928408i \(0.621177\pi\)
\(572\) 6.82843 6.82843i 0.285511 0.285511i
\(573\) 0 0
\(574\) 15.3137i 0.639182i
\(575\) −4.94975 + 0.707107i −0.206419 + 0.0294884i
\(576\) 0 0
\(577\) 1.14214 + 1.14214i 0.0475477 + 0.0475477i 0.730481 0.682933i \(-0.239296\pi\)
−0.682933 + 0.730481i \(0.739296\pi\)
\(578\) 2.56497 + 2.56497i 0.106689 + 0.106689i
\(579\) 0 0
\(580\) 0.828427 + 1.65685i 0.0343986 + 0.0687971i
\(581\) 3.02944i 0.125682i
\(582\) 0 0
\(583\) 41.7990 41.7990i 1.73114 1.73114i
\(584\) 13.8995 0.575165
\(585\) 0 0
\(586\) −10.3848 −0.428991
\(587\) 18.6274 18.6274i 0.768836 0.768836i −0.209066 0.977902i \(-0.567042\pi\)
0.977902 + 0.209066i \(0.0670423\pi\)
\(588\) 0 0
\(589\) 0.485281i 0.0199957i
\(590\) −2.00000 + 6.00000i −0.0823387 + 0.247016i
\(591\) 0 0
\(592\) 1.41421 + 1.41421i 0.0581238 + 0.0581238i
\(593\) −16.4853 16.4853i −0.676969 0.676969i 0.282344 0.959313i \(-0.408888\pi\)
−0.959313 + 0.282344i \(0.908888\pi\)
\(594\) 0 0
\(595\) 20.6863 10.3431i 0.848055 0.424028i
\(596\) 11.6569i 0.477483i
\(597\) 0 0
\(598\) 1.41421 1.41421i 0.0578315 0.0578315i
\(599\) −17.5563 −0.717333 −0.358666 0.933466i \(-0.616768\pi\)
−0.358666 + 0.933466i \(0.616768\pi\)
\(600\) 0 0
\(601\) 14.3431 0.585069 0.292535 0.956255i \(-0.405501\pi\)
0.292535 + 0.956255i \(0.405501\pi\)
\(602\) 6.34315 6.34315i 0.258527 0.258527i
\(603\) 0 0
\(604\) 16.9706i 0.690522i
\(605\) −24.6274 + 12.3137i −1.00125 + 0.500623i
\(606\) 0 0
\(607\) 0.0710678 + 0.0710678i 0.00288455 + 0.00288455i 0.708548 0.705663i \(-0.249351\pi\)
−0.705663 + 0.708548i \(0.749351\pi\)
\(608\) −0.414214 0.414214i −0.0167986 0.0167986i
\(609\) 0 0
\(610\) 3.82843 11.4853i 0.155008 0.465025i
\(611\) 0 0
\(612\) 0 0
\(613\) 17.4558 17.4558i 0.705035 0.705035i −0.260452 0.965487i \(-0.583872\pi\)
0.965487 + 0.260452i \(0.0838715\pi\)
\(614\) 15.3137 0.618011
\(615\) 0 0
\(616\) −13.6569 −0.550250
\(617\) 23.2132 23.2132i 0.934528 0.934528i −0.0634562 0.997985i \(-0.520212\pi\)
0.997985 + 0.0634562i \(0.0202123\pi\)
\(618\) 0 0
\(619\) 7.41421i 0.298002i 0.988837 + 0.149001i \(0.0476058\pi\)
−0.988837 + 0.149001i \(0.952394\pi\)
\(620\) −0.828427 1.65685i −0.0332704 0.0665409i
\(621\) 0 0
\(622\) 22.0711 + 22.0711i 0.884969 + 0.884969i
\(623\) 28.0000 + 28.0000i 1.12180 + 1.12180i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 1.31371i 0.0525064i
\(627\) 0 0
\(628\) −4.24264 + 4.24264i −0.169300 + 0.169300i
\(629\) −7.31371 −0.291617
\(630\) 0 0
\(631\) 29.6569 1.18062 0.590310 0.807176i \(-0.299005\pi\)
0.590310 + 0.807176i \(0.299005\pi\)
\(632\) 0.828427 0.828427i 0.0329531 0.0329531i
\(633\) 0 0
\(634\) 15.1716i 0.602540i
\(635\) −4.75736 1.58579i −0.188790 0.0629300i
\(636\) 0 0
\(637\) −1.41421 1.41421i −0.0560332 0.0560332i
\(638\) 2.82843 + 2.82843i 0.111979 + 0.111979i
\(639\) 0 0
\(640\) 2.12132 + 0.707107i 0.0838525 + 0.0279508i
\(641\) 22.4853i 0.888115i 0.895998 + 0.444058i \(0.146461\pi\)
−0.895998 + 0.444058i \(0.853539\pi\)
\(642\) 0 0
\(643\) −7.79899 + 7.79899i −0.307562 + 0.307562i −0.843963 0.536401i \(-0.819783\pi\)
0.536401 + 0.843963i \(0.319783\pi\)
\(644\) −2.82843 −0.111456
\(645\) 0 0
\(646\) 2.14214 0.0842812
\(647\) 2.72792 2.72792i 0.107246 0.107246i −0.651448 0.758693i \(-0.725838\pi\)
0.758693 + 0.651448i \(0.225838\pi\)
\(648\) 0 0
\(649\) 13.6569i 0.536078i
\(650\) 8.00000 + 6.00000i 0.313786 + 0.235339i
\(651\) 0 0
\(652\) 6.48528 + 6.48528i 0.253983 + 0.253983i
\(653\) −28.2426 28.2426i −1.10522 1.10522i −0.993770 0.111450i \(-0.964451\pi\)
−0.111450 0.993770i \(-0.535549\pi\)
\(654\) 0 0
\(655\) 5.65685 + 11.3137i 0.221032 + 0.442063i
\(656\) 5.41421i 0.211390i
\(657\) 0 0
\(658\) 0 0
\(659\) 37.9411 1.47798 0.738988 0.673718i \(-0.235304\pi\)
0.738988 + 0.673718i \(0.235304\pi\)
\(660\) 0 0
\(661\) 44.5269 1.73190 0.865948 0.500134i \(-0.166716\pi\)
0.865948 + 0.500134i \(0.166716\pi\)
\(662\) −22.4853 + 22.4853i −0.873915 + 0.873915i
\(663\) 0 0
\(664\) 1.07107i 0.0415655i
\(665\) −1.17157 + 3.51472i −0.0454316 + 0.136295i
\(666\) 0 0
\(667\) 0.585786 + 0.585786i 0.0226817 + 0.0226817i
\(668\) −15.8995 15.8995i −0.615170 0.615170i
\(669\) 0 0
\(670\) 19.3137 9.65685i 0.746154 0.373077i
\(671\) 26.1421i 1.00921i
\(672\) 0 0
\(673\) 1.48528 1.48528i 0.0572534 0.0572534i −0.677900 0.735154i \(-0.737110\pi\)
0.735154 + 0.677900i \(0.237110\pi\)
\(674\) 3.17157 0.122164
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) −11.3431 + 11.3431i −0.435953 + 0.435953i −0.890647 0.454695i \(-0.849748\pi\)
0.454695 + 0.890647i \(0.349748\pi\)
\(678\) 0 0
\(679\) 36.2843i 1.39246i
\(680\) −7.31371 + 3.65685i −0.280468 + 0.140234i
\(681\) 0 0
\(682\) −2.82843 2.82843i −0.108306 0.108306i
\(683\) 28.2843 + 28.2843i 1.08227 + 1.08227i 0.996298 + 0.0859698i \(0.0273989\pi\)
0.0859698 + 0.996298i \(0.472601\pi\)
\(684\) 0 0
\(685\) 1.07107 3.21320i 0.0409234 0.122770i
\(686\) 16.9706i 0.647939i
\(687\) 0 0
\(688\) −2.24264 + 2.24264i −0.0854999 + 0.0854999i
\(689\) −24.4853 −0.932815
\(690\) 0 0
\(691\) −12.6863 −0.482609 −0.241305 0.970449i \(-0.577575\pi\)
−0.241305 + 0.970449i \(0.577575\pi\)
\(692\) −9.89949 + 9.89949i −0.376322 + 0.376322i
\(693\) 0 0
\(694\) 14.1421i 0.536828i
\(695\) 6.82843 + 13.6569i 0.259017 + 0.518034i
\(696\) 0 0
\(697\) −14.0000 14.0000i −0.530288 0.530288i
\(698\) 16.7279 + 16.7279i 0.633161 + 0.633161i
\(699\) 0 0
\(700\) −2.00000 14.0000i −0.0755929 0.529150i
\(701\) 19.9411i 0.753166i 0.926383 + 0.376583i \(0.122901\pi\)
−0.926383 + 0.376583i \(0.877099\pi\)
\(702\) 0 0
\(703\) 0.828427 0.828427i 0.0312447 0.0312447i
\(704\) 4.82843 0.181978
\(705\) 0 0
\(706\) 8.34315 0.313998
\(707\) −7.31371 + 7.31371i −0.275060 + 0.275060i
\(708\) 0 0
\(709\) 6.10051i 0.229109i 0.993417 + 0.114555i \(0.0365441\pi\)
−0.993417 + 0.114555i \(0.963456\pi\)
\(710\) −15.7279 5.24264i −0.590258 0.196753i
\(711\) 0 0
\(712\) −9.89949 9.89949i −0.370999 0.370999i
\(713\) −0.585786 0.585786i −0.0219379 0.0219379i
\(714\) 0 0
\(715\) 20.4853 + 6.82843i 0.766106 + 0.255369i
\(716\) 23.3137i 0.871274i
\(717\) 0 0
\(718\) 4.82843 4.82843i 0.180195 0.180195i
\(719\) −34.5269 −1.28764 −0.643818 0.765178i \(-0.722651\pi\)
−0.643818 + 0.765178i \(0.722651\pi\)
\(720\) 0 0
\(721\) −20.6863 −0.770398
\(722\) 13.1924 13.1924i 0.490970 0.490970i
\(723\) 0 0
\(724\) 13.4142i 0.498535i
\(725\) −2.48528 + 3.31371i −0.0923010 + 0.123068i
\(726\) 0 0
\(727\) −13.6569 13.6569i −0.506505 0.506505i 0.406947 0.913452i \(-0.366593\pi\)
−0.913452 + 0.406947i \(0.866593\pi\)
\(728\) 4.00000 + 4.00000i 0.148250 + 0.148250i
\(729\) 0 0
\(730\) 13.8995 + 27.7990i 0.514443 + 1.02889i
\(731\) 11.5980i 0.428967i
\(732\) 0 0
\(733\) −32.0000 + 32.0000i −1.18195 + 1.18195i −0.202708 + 0.979239i \(0.564974\pi\)
−0.979239 + 0.202708i \(0.935026\pi\)
\(734\) 8.48528 0.313197
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 32.9706 32.9706i 1.21449 1.21449i
\(738\) 0 0
\(739\) 18.1421i 0.667369i −0.942685 0.333685i \(-0.891708\pi\)
0.942685 0.333685i \(-0.108292\pi\)
\(740\) −1.41421 + 4.24264i −0.0519875 + 0.155963i
\(741\) 0 0
\(742\) 24.4853 + 24.4853i 0.898883 + 0.898883i
\(743\) −13.5147 13.5147i −0.495807 0.495807i 0.414323 0.910130i \(-0.364018\pi\)
−0.910130 + 0.414323i \(0.864018\pi\)
\(744\) 0 0
\(745\) −23.3137 + 11.6569i −0.854148 + 0.427074i
\(746\) 6.00000i 0.219676i
\(747\) 0 0
\(748\) −12.4853 + 12.4853i −0.456507 + 0.456507i
\(749\) −16.2843 −0.595014
\(750\) 0 0
\(751\) −10.1421 −0.370092 −0.185046 0.982730i \(-0.559243\pi\)
−0.185046 + 0.982730i \(0.559243\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 1.65685i 0.0603391i
\(755\) −33.9411 + 16.9706i −1.23524 + 0.617622i
\(756\) 0 0
\(757\) −27.1127 27.1127i −0.985428 0.985428i 0.0144676 0.999895i \(-0.495395\pi\)
−0.999895 + 0.0144676i \(0.995395\pi\)
\(758\) 21.2426 + 21.2426i 0.771567 + 0.771567i
\(759\) 0 0
\(760\) 0.414214 1.24264i 0.0150251 0.0450753i
\(761\) 7.55635i 0.273917i −0.990577 0.136959i \(-0.956267\pi\)
0.990577 0.136959i \(-0.0437328\pi\)
\(762\) 0 0
\(763\) 38.1421 38.1421i 1.38084 1.38084i
\(764\) 9.17157 0.331816
\(765\) 0 0
\(766\) −23.7990 −0.859892
\(767\) 4.00000 4.00000i 0.144432 0.144432i
\(768\) 0 0
\(769\) 17.3137i 0.624348i 0.950025 + 0.312174i \(0.101057\pi\)
−0.950025 + 0.312174i \(0.898943\pi\)
\(770\) −13.6569 27.3137i −0.492159 0.984318i
\(771\) 0 0
\(772\) 5.00000 + 5.00000i 0.179954 + 0.179954i
\(773\) −20.1716 20.1716i −0.725521 0.725521i 0.244203 0.969724i \(-0.421474\pi\)
−0.969724 + 0.244203i \(0.921474\pi\)
\(774\) 0 0
\(775\) 2.48528 3.31371i 0.0892739 0.119032i
\(776\) 12.8284i 0.460514i
\(777\) 0 0
\(778\) −14.3431 + 14.3431i −0.514227 + 0.514227i
\(779\) 3.17157 0.113633
\(780\) 0 0
\(781\) −35.7990 −1.28099
\(782\) −2.58579 + 2.58579i −0.0924675 + 0.0924675i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) −12.7279 4.24264i −0.454279 0.151426i
\(786\) 0 0
\(787\) −2.82843 2.82843i −0.100823 0.100823i 0.654896 0.755719i \(-0.272712\pi\)
−0.755719 + 0.654896i \(0.772712\pi\)
\(788\) −7.07107 7.07107i −0.251896 0.251896i
\(789\) 0 0
\(790\) 2.48528 + 0.828427i 0.0884223 + 0.0294741i
\(791\) 48.9706i 1.74119i
\(792\) 0 0
\(793\) −7.65685 + 7.65685i −0.271903 + 0.271903i
\(794\) 7.65685 0.271732
\(795\) 0 0
\(796\) −6.34315 −0.224827
\(797\) 29.4853 29.4853i 1.04442 1.04442i 0.0454559 0.998966i \(-0.485526\pi\)
0.998966 0.0454559i \(-0.0144741\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.707107 + 4.94975i 0.0250000 + 0.175000i
\(801\) 0 0
\(802\) −24.0416 24.0416i −0.848939 0.848939i
\(803\) 47.4558 + 47.4558i 1.67468 + 1.67468i
\(804\) 0 0
\(805\) −2.82843 5.65685i −0.0996890 0.199378i
\(806\) 1.65685i 0.0583602i
\(807\) 0 0
\(808\) 2.58579 2.58579i 0.0909676 0.0909676i
\(809\) 20.2426 0.711693 0.355847 0.934544i \(-0.384193\pi\)
0.355847 + 0.934544i \(0.384193\pi\)
\(810\) 0 0
\(811\) −16.9706 −0.595917 −0.297959 0.954579i \(-0.596306\pi\)
−0.297959 + 0.954579i \(0.596306\pi\)
\(812\) −1.65685 + 1.65685i −0.0581442 + 0.0581442i
\(813\) 0 0
\(814\) 9.65685i 0.338473i
\(815\) −6.48528 + 19.4558i −0.227169 + 0.681508i
\(816\) 0 0
\(817\) 1.31371 + 1.31371i 0.0459608 + 0.0459608i
\(818\) −3.75736 3.75736i −0.131373 0.131373i
\(819\) 0 0
\(820\) −10.8284 + 5.41421i −0.378145 + 0.189073i
\(821\) 50.4853i 1.76195i −0.473164 0.880974i \(-0.656888\pi\)
0.473164 0.880974i \(-0.343112\pi\)
\(822\) 0 0
\(823\) 25.5858 25.5858i 0.891864 0.891864i −0.102834 0.994699i \(-0.532791\pi\)
0.994699 + 0.102834i \(0.0327911\pi\)
\(824\) 7.31371 0.254785
\(825\) 0 0
\(826\) −8.00000 −0.278356
\(827\) −39.2426 + 39.2426i −1.36460 + 1.36460i −0.496649 + 0.867952i \(0.665436\pi\)
−0.867952 + 0.496649i \(0.834564\pi\)
\(828\) 0 0
\(829\) 10.2843i 0.357188i −0.983923 0.178594i \(-0.942845\pi\)
0.983923 0.178594i \(-0.0571548\pi\)
\(830\) −2.14214 + 1.07107i −0.0743546 + 0.0371773i
\(831\) 0 0
\(832\) −1.41421 1.41421i −0.0490290 0.0490290i
\(833\) 2.58579 + 2.58579i 0.0895922 + 0.0895922i
\(834\) 0 0
\(835\) 15.8995 47.6985i 0.550225 1.65067i
\(836\) 2.82843i 0.0978232i
\(837\) 0 0
\(838\) −23.7990 + 23.7990i −0.822122 + 0.822122i
\(839\) −11.5147 −0.397532 −0.198766 0.980047i \(-0.563693\pi\)
−0.198766 + 0.980047i \(0.563693\pi\)
\(840\) 0 0
\(841\) −28.3137 −0.976335
\(842\) −2.31371 + 2.31371i −0.0797357 + 0.0797357i
\(843\) 0 0
\(844\) 14.8284i 0.510416i
\(845\) 9.00000 + 18.0000i 0.309609 + 0.619219i
\(846\) 0 0
\(847\) −24.6274 24.6274i −0.846208 0.846208i
\(848\) −8.65685 8.65685i −0.297278 0.297278i
\(849\) 0 0
\(850\) −14.6274 10.9706i −0.501716 0.376287i
\(851\) 2.00000i 0.0685591i
\(852\) 0 0
\(853\) 37.2132 37.2132i 1.27416 1.27416i 0.330269 0.943887i \(-0.392861\pi\)
0.943887 0.330269i \(-0.107139\pi\)
\(854\) 15.3137 0.524024
\(855\) 0 0
\(856\) 5.75736 0.196782
\(857\) 20.2426 20.2426i 0.691475 0.691475i −0.271081 0.962557i \(-0.587381\pi\)
0.962557 + 0.271081i \(0.0873812\pi\)
\(858\) 0 0
\(859\) 1.17157i 0.0399736i −0.999800 0.0199868i \(-0.993638\pi\)
0.999800 0.0199868i \(-0.00636241\pi\)
\(860\) −6.72792 2.24264i −0.229420 0.0764734i
\(861\) 0 0
\(862\) 7.65685 + 7.65685i 0.260793 + 0.260793i
\(863\) 29.7574 + 29.7574i 1.01295 + 1.01295i 0.999915 + 0.0130373i \(0.00415001\pi\)
0.0130373 + 0.999915i \(0.495850\pi\)
\(864\) 0 0
\(865\) −29.6985 9.89949i −1.00978 0.336593i
\(866\) 29.1127i 0.989290i
\(867\) 0 0
\(868\) 1.65685 1.65685i 0.0562373 0.0562373i
\(869\) 5.65685 0.191896
\(870\) 0 0
\(871\) −19.3137 −0.654420
\(872\) −13.4853 + 13.4853i −0.456669 + 0.456669i
\(873\) 0 0
\(874\) 0.585786i 0.0198145i
\(875\) 26.0000 18.0000i 0.878960 0.608511i
\(876\) 0 0
\(877\) −30.0416 30.0416i −1.01443 1.01443i −0.999894 0.0145395i \(-0.995372\pi\)
−0.0145395 0.999894i \(-0.504628\pi\)
\(878\) −2.92893 2.92893i −0.0988467 0.0988467i
\(879\) 0 0
\(880\) 4.82843 + 9.65685i 0.162766 + 0.325532i
\(881\) 14.9706i 0.504371i −0.967679 0.252186i \(-0.918851\pi\)
0.967679 0.252186i \(-0.0811493\pi\)
\(882\) 0 0
\(883\) −20.9706 + 20.9706i −0.705716 + 0.705716i −0.965631 0.259916i \(-0.916305\pi\)
0.259916 + 0.965631i \(0.416305\pi\)
\(884\) 7.31371 0.245987
\(885\) 0 0
\(886\) 6.82843 0.229405
\(887\) 36.2843 36.2843i 1.21831 1.21831i 0.250082 0.968225i \(-0.419542\pi\)
0.968225 0.250082i \(-0.0804576\pi\)
\(888\) 0 0
\(889\) 6.34315i 0.212742i
\(890\) 9.89949 29.6985i 0.331832 0.995495i
\(891\) 0 0
\(892\) 3.24264 + 3.24264i 0.108572 + 0.108572i
\(893\) 0 0
\(894\) 0 0
\(895\) −46.6274 + 23.3137i −1.55858 + 0.779291i
\(896\) 2.82843i 0.0944911i
\(897\) 0 0
\(898\) −3.48528 + 3.48528i −0.116305 + 0.116305i
\(899\) −0.686292 −0.0228891
\(900\) 0 0
\(901\) 44.7696 1.49149
\(902\) −18.4853 + 18.4853i −0.615493 + 0.615493i
\(903\) 0 0
\(904\) 17.3137i 0.575845i
\(905\) 26.8284 13.4142i 0.891807 0.445904i
\(906\) 0 0
\(907\) −33.3553 33.3553i −1.10755 1.10755i −0.993472 0.114074i \(-0.963610\pi\)
−0.114074 0.993472i \(-0.536390\pi\)
\(908\) −4.89949 4.89949i −0.162595 0.162595i
\(909\) 0 0
\(910\) −4.00000 + 12.0000i −0.132599 + 0.397796i
\(911\) 48.2843i 1.59973i −0.600180 0.799865i \(-0.704905\pi\)
0.600180 0.799865i \(-0.295095\pi\)
\(912\) 0 0
\(913\) −3.65685 + 3.65685i −0.121024 + 0.121024i
\(914\) −1.79899 −0.0595053
\(915\) 0 0
\(916\) 13.4142 0.443218
\(917\) −11.3137 + 11.3137i −0.373612 + 0.373612i
\(918\) 0 0
\(919\) 28.9706i 0.955651i 0.878455 + 0.477825i \(0.158575\pi\)
−0.878455 + 0.477825i \(0.841425\pi\)
\(920\) 1.00000 + 2.00000i 0.0329690 + 0.0659380i
\(921\) 0 0
\(922\) −9.55635 9.55635i −0.314722 0.314722i
\(923\) 10.4853 + 10.4853i 0.345127 + 0.345127i
\(924\) 0 0
\(925\) −9.89949 + 1.41421i −0.325493 + 0.0464991i
\(926\) 36.5858i 1.20228i
\(927\) 0 0
\(928\) 0.585786 0.585786i 0.0192294 0.0192294i
\(929\) 9.69848 0.318197 0.159098 0.987263i \(-0.449141\pi\)
0.159098 + 0.987263i \(0.449141\pi\)
\(930\) 0 0
\(931\) −0.585786 −0.0191984
\(932\) 13.1716 13.1716i 0.431449 0.431449i
\(933\) 0 0
\(934\) 11.2132i 0.366907i
\(935\) −37.4558 12.4853i −1.22494 0.408312i
\(936\) 0 0
\(937\) 36.5269 + 36.5269i 1.19328 + 1.19328i 0.976140 + 0.217142i \(0.0696735\pi\)
0.217142 + 0.976140i \(0.430326\pi\)
\(938\) 19.3137 + 19.3137i 0.630615 + 0.630615i
\(939\) 0 0
\(940\) 0 0
\(941\) 45.9411i 1.49764i −0.662775 0.748819i \(-0.730621\pi\)
0.662775 0.748819i \(-0.269379\pi\)
\(942\) 0 0
\(943\) −3.82843 + 3.82843i −0.124671 + 0.124671i
\(944\) 2.82843 0.0920575
\(945\) 0 0
\(946\) −15.3137 −0.497892
\(947\) −25.4558 + 25.4558i −0.827204 + 0.827204i −0.987129 0.159925i \(-0.948875\pi\)
0.159925 + 0.987129i \(0.448875\pi\)
\(948\) 0 0
\(949\) 27.7990i 0.902393i
\(950\) 2.89949 0.414214i 0.0940720 0.0134389i
\(951\) 0 0
\(952\) −7.31371 7.31371i −0.237039 0.237039i
\(953\) 29.0711 + 29.0711i 0.941704 + 0.941704i 0.998392 0.0566877i \(-0.0180539\pi\)
−0.0566877 + 0.998392i \(0.518054\pi\)
\(954\) 0 0
\(955\) 9.17157 + 18.3431i 0.296785 + 0.593570i
\(956\) 9.55635i 0.309074i
\(957\) 0 0
\(958\) −13.1716 + 13.1716i −0.425554 + 0.425554i
\(959\) 4.28427 0.138346
\(960\) 0 0
\(961\) −30.3137 −0.977862
\(962\) 2.82843 2.82843i 0.0911922 0.0911922i
\(963\) 0 0
\(964\) 13.7990i 0.444436i
\(965\) −5.00000 + 15.0000i −0.160956 + 0.482867i
\(966\) 0 0
\(967\) −2.41421 2.41421i −0.0776359 0.0776359i 0.667223 0.744858i \(-0.267483\pi\)
−0.744858 + 0.667223i \(0.767483\pi\)
\(968\) 8.70711 + 8.70711i 0.279857 + 0.279857i
\(969\) 0 0
\(970\) −25.6569 + 12.8284i −0.823792 + 0.411896i
\(971\) 50.6274i 1.62471i 0.583162 + 0.812356i \(0.301815\pi\)
−0.583162 + 0.812356i \(0.698185\pi\)
\(972\) 0 0
\(973\) −13.6569 + 13.6569i −0.437819 + 0.437819i
\(974\) 39.8995 1.27846
\(975\) 0 0
\(976\) −5.41421 −0.173305
\(977\) 35.5563 35.5563i 1.13755 1.13755i 0.148660 0.988888i \(-0.452504\pi\)
0.988888 0.148660i \(-0.0474960\pi\)
\(978\) 0 0
\(979\) 67.5980i 2.16044i
\(980\) 2.00000 1.00000i 0.0638877 0.0319438i
\(981\) 0 0
\(982\) −6.48528 6.48528i −0.206954 0.206954i
\(983\) 29.9411 + 29.9411i 0.954974 + 0.954974i 0.999029 0.0440555i \(-0.0140278\pi\)
−0.0440555 + 0.999029i \(0.514028\pi\)
\(984\) 0 0
\(985\) 7.07107 21.2132i 0.225303 0.675909i
\(986\) 3.02944i 0.0964769i
\(987\) 0 0
\(988\) −0.828427 + 0.828427i −0.0263558 + 0.0263558i
\(989\) −3.17157 −0.100850
\(990\) 0 0
\(991\) 41.9411 1.33230 0.666152 0.745816i \(-0.267940\pi\)
0.666152 + 0.745816i \(0.267940\pi\)
\(992\) −0.585786 + 0.585786i −0.0185987 + 0.0185987i
\(993\) 0 0
\(994\) 20.9706i 0.665146i
\(995\) −6.34315 12.6863i −0.201091 0.402182i
\(996\) 0 0
\(997\) 5.07107 + 5.07107i 0.160602 + 0.160602i 0.782834 0.622231i \(-0.213774\pi\)
−0.622231 + 0.782834i \(0.713774\pi\)
\(998\) 9.17157 + 9.17157i 0.290321 + 0.290321i
\(999\) 0 0
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 2070.2.j.f.737.2 yes 4
3.2 odd 2 2070.2.j.a.737.1 yes 4
5.3 odd 4 2070.2.j.a.323.1 4
15.8 even 4 inner 2070.2.j.f.323.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2070.2.j.a.323.1 4 5.3 odd 4
2070.2.j.a.737.1 yes 4 3.2 odd 2
2070.2.j.f.323.2 yes 4 15.8 even 4 inner
2070.2.j.f.737.2 yes 4 1.1 even 1 trivial