Properties

Label 1470.2.i.x.361.1
Level $1470$
Weight $2$
Character 1470.361
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(361,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\), degree \(2\), not 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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1470.361
Dual form 1470.2.i.x.961.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.12132 + 1.94218i) q^{11} +(0.500000 + 0.866025i) q^{12} +5.65685 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.29289 + 2.23936i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.41421 + 5.91359i) q^{19} +1.00000 q^{20} -2.24264 q^{22} +(-1.58579 - 2.74666i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.82843 + 4.89898i) q^{26} -1.00000 q^{27} +2.58579 q^{29} +(-0.500000 - 0.866025i) q^{30} +(5.12132 - 8.87039i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.12132 + 1.94218i) q^{33} -2.58579 q^{34} +1.00000 q^{36} +(0.121320 + 0.210133i) q^{37} +(-3.41421 + 5.91359i) q^{38} +(2.82843 - 4.89898i) q^{39} +(0.500000 + 0.866025i) q^{40} +10.4853 q^{41} +9.07107 q^{43} +(-1.12132 - 1.94218i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(1.58579 - 2.74666i) q^{46} +(1.12132 + 1.94218i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.29289 + 2.23936i) q^{51} +(-2.82843 + 4.89898i) q^{52} +(-0.171573 + 0.297173i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.24264 q^{55} +6.82843 q^{57} +(1.29289 + 2.23936i) q^{58} +(1.58579 - 2.74666i) q^{59} +(0.500000 - 0.866025i) q^{60} +(5.82843 + 10.0951i) q^{61} +10.2426 q^{62} +1.00000 q^{64} +(-2.82843 - 4.89898i) q^{65} +(-1.12132 + 1.94218i) q^{66} +(-4.53553 + 7.85578i) q^{67} +(-1.29289 - 2.23936i) q^{68} -3.17157 q^{69} -4.48528 q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-0.121320 + 0.210133i) q^{74} +(0.500000 + 0.866025i) q^{75} -6.82843 q^{76} +5.65685 q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.24264 + 9.08052i) q^{82} +5.17157 q^{83} +2.58579 q^{85} +(4.53553 + 7.85578i) q^{86} +(1.29289 - 2.23936i) q^{87} +(1.12132 - 1.94218i) q^{88} +(0.414214 + 0.717439i) q^{89} -1.00000 q^{90} +3.17157 q^{92} +(-5.12132 - 8.87039i) q^{93} +(-1.12132 + 1.94218i) q^{94} +(3.41421 - 5.91359i) q^{95} +(-0.500000 - 0.866025i) q^{96} -6.48528 q^{97} +2.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} + 4 q^{20} + 8 q^{22} - 12 q^{23} - 2 q^{24} - 2 q^{25} - 4 q^{27} + 16 q^{29} - 2 q^{30} + 12 q^{31} + 2 q^{32} - 4 q^{33} - 16 q^{34} + 4 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 8 q^{41} + 8 q^{43} + 4 q^{44} - 2 q^{45} + 12 q^{46} - 4 q^{47} - 4 q^{48} - 4 q^{50} + 8 q^{51} - 12 q^{53} - 2 q^{54} - 8 q^{55} + 16 q^{57} + 8 q^{58} + 12 q^{59} + 2 q^{60} + 12 q^{61} + 24 q^{62} + 4 q^{64} + 4 q^{66} - 4 q^{67} - 8 q^{68} - 24 q^{69} + 16 q^{71} + 2 q^{72} + 4 q^{73} + 8 q^{74} + 2 q^{75} - 16 q^{76} - 16 q^{79} - 2 q^{80} - 2 q^{81} + 4 q^{82} + 32 q^{83} + 16 q^{85} + 4 q^{86} + 8 q^{87} - 4 q^{88} - 4 q^{89} - 4 q^{90} + 24 q^{92} - 12 q^{93} + 4 q^{94} + 8 q^{95} - 2 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −1.12132 + 1.94218i −0.338091 + 0.585590i −0.984074 0.177762i \(-0.943114\pi\)
0.645983 + 0.763352i \(0.276448\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 5.65685 1.56893 0.784465 0.620174i \(-0.212938\pi\)
0.784465 + 0.620174i \(0.212938\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.29289 + 2.23936i −0.313573 + 0.543124i −0.979133 0.203220i \(-0.934859\pi\)
0.665560 + 0.746344i \(0.268193\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 3.41421 + 5.91359i 0.783274 + 1.35667i 0.930025 + 0.367497i \(0.119785\pi\)
−0.146750 + 0.989174i \(0.546881\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −2.24264 −0.478133
\(23\) −1.58579 2.74666i −0.330659 0.572719i 0.651982 0.758234i \(-0.273938\pi\)
−0.982641 + 0.185516i \(0.940604\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.82843 + 4.89898i 0.554700 + 0.960769i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.58579 0.480168 0.240084 0.970752i \(-0.422825\pi\)
0.240084 + 0.970752i \(0.422825\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 5.12132 8.87039i 0.919816 1.59317i 0.120124 0.992759i \(-0.461671\pi\)
0.799693 0.600410i \(-0.204996\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.12132 + 1.94218i 0.195197 + 0.338091i
\(34\) −2.58579 −0.443459
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 0.121320 + 0.210133i 0.0199449 + 0.0345457i 0.875826 0.482628i \(-0.160318\pi\)
−0.855881 + 0.517173i \(0.826984\pi\)
\(38\) −3.41421 + 5.91359i −0.553859 + 0.959311i
\(39\) 2.82843 4.89898i 0.452911 0.784465i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 10.4853 1.63753 0.818763 0.574132i \(-0.194660\pi\)
0.818763 + 0.574132i \(0.194660\pi\)
\(42\) 0 0
\(43\) 9.07107 1.38332 0.691662 0.722221i \(-0.256879\pi\)
0.691662 + 0.722221i \(0.256879\pi\)
\(44\) −1.12132 1.94218i −0.169045 0.292795i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 1.58579 2.74666i 0.233811 0.404973i
\(47\) 1.12132 + 1.94218i 0.163561 + 0.283297i 0.936143 0.351618i \(-0.114368\pi\)
−0.772582 + 0.634915i \(0.781035\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 1.29289 + 2.23936i 0.181041 + 0.313573i
\(52\) −2.82843 + 4.89898i −0.392232 + 0.679366i
\(53\) −0.171573 + 0.297173i −0.0235673 + 0.0408198i −0.877569 0.479451i \(-0.840836\pi\)
0.854001 + 0.520271i \(0.174169\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 2.24264 0.302398
\(56\) 0 0
\(57\) 6.82843 0.904447
\(58\) 1.29289 + 2.23936i 0.169765 + 0.294042i
\(59\) 1.58579 2.74666i 0.206452 0.357585i −0.744143 0.668021i \(-0.767142\pi\)
0.950594 + 0.310436i \(0.100475\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) 5.82843 + 10.0951i 0.746254 + 1.29255i 0.949607 + 0.313444i \(0.101483\pi\)
−0.203353 + 0.979105i \(0.565184\pi\)
\(62\) 10.2426 1.30082
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.82843 4.89898i −0.350823 0.607644i
\(66\) −1.12132 + 1.94218i −0.138025 + 0.239066i
\(67\) −4.53553 + 7.85578i −0.554104 + 0.959736i 0.443869 + 0.896092i \(0.353606\pi\)
−0.997973 + 0.0636440i \(0.979728\pi\)
\(68\) −1.29289 2.23936i −0.156786 0.271562i
\(69\) −3.17157 −0.381813
\(70\) 0 0
\(71\) −4.48528 −0.532305 −0.266152 0.963931i \(-0.585752\pi\)
−0.266152 + 0.963931i \(0.585752\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −0.121320 + 0.210133i −0.0141032 + 0.0244275i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) −6.82843 −0.783274
\(77\) 0 0
\(78\) 5.65685 0.640513
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.24264 + 9.08052i 0.578953 + 1.00278i
\(83\) 5.17157 0.567654 0.283827 0.958876i \(-0.408396\pi\)
0.283827 + 0.958876i \(0.408396\pi\)
\(84\) 0 0
\(85\) 2.58579 0.280468
\(86\) 4.53553 + 7.85578i 0.489079 + 0.847110i
\(87\) 1.29289 2.23936i 0.138613 0.240084i
\(88\) 1.12132 1.94218i 0.119533 0.207037i
\(89\) 0.414214 + 0.717439i 0.0439065 + 0.0760484i 0.887144 0.461494i \(-0.152686\pi\)
−0.843237 + 0.537542i \(0.819353\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 3.17157 0.330659
\(93\) −5.12132 8.87039i −0.531056 0.919816i
\(94\) −1.12132 + 1.94218i −0.115655 + 0.200321i
\(95\) 3.41421 5.91359i 0.350291 0.606722i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −6.48528 −0.658481 −0.329240 0.944246i \(-0.606793\pi\)
−0.329240 + 0.944246i \(0.606793\pi\)
\(98\) 0 0
\(99\) 2.24264 0.225394
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −8.82843 + 15.2913i −0.878461 + 1.52154i −0.0254321 + 0.999677i \(0.508096\pi\)
−0.853029 + 0.521863i \(0.825237\pi\)
\(102\) −1.29289 + 2.23936i −0.128016 + 0.221729i
\(103\) −7.41421 12.8418i −0.730544 1.26534i −0.956651 0.291237i \(-0.905933\pi\)
0.226107 0.974103i \(-0.427400\pi\)
\(104\) −5.65685 −0.554700
\(105\) 0 0
\(106\) −0.343146 −0.0333293
\(107\) −4.82843 8.36308i −0.466782 0.808490i 0.532498 0.846431i \(-0.321253\pi\)
−0.999280 + 0.0379415i \(0.987920\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 1.82843 3.16693i 0.175132 0.303337i −0.765075 0.643941i \(-0.777298\pi\)
0.940207 + 0.340604i \(0.110632\pi\)
\(110\) 1.12132 + 1.94218i 0.106914 + 0.185180i
\(111\) 0.242641 0.0230304
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 3.41421 + 5.91359i 0.319770 + 0.553859i
\(115\) −1.58579 + 2.74666i −0.147875 + 0.256128i
\(116\) −1.29289 + 2.23936i −0.120042 + 0.207919i
\(117\) −2.82843 4.89898i −0.261488 0.452911i
\(118\) 3.17157 0.291967
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 2.98528 + 5.17066i 0.271389 + 0.470060i
\(122\) −5.82843 + 10.0951i −0.527681 + 0.913970i
\(123\) 5.24264 9.08052i 0.472713 0.818763i
\(124\) 5.12132 + 8.87039i 0.459908 + 0.796584i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.82843 0.250982 0.125491 0.992095i \(-0.459949\pi\)
0.125491 + 0.992095i \(0.459949\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 4.53553 7.85578i 0.399331 0.691662i
\(130\) 2.82843 4.89898i 0.248069 0.429669i
\(131\) 1.58579 + 2.74666i 0.138551 + 0.239977i 0.926948 0.375189i \(-0.122422\pi\)
−0.788397 + 0.615166i \(0.789089\pi\)
\(132\) −2.24264 −0.195197
\(133\) 0 0
\(134\) −9.07107 −0.783621
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 1.29289 2.23936i 0.110865 0.192023i
\(137\) −6.82843 + 11.8272i −0.583392 + 1.01046i 0.411682 + 0.911328i \(0.364941\pi\)
−0.995074 + 0.0991368i \(0.968392\pi\)
\(138\) −1.58579 2.74666i −0.134991 0.233811i
\(139\) −2.34315 −0.198743 −0.0993715 0.995050i \(-0.531683\pi\)
−0.0993715 + 0.995050i \(0.531683\pi\)
\(140\) 0 0
\(141\) 2.24264 0.188864
\(142\) −2.24264 3.88437i −0.188198 0.325969i
\(143\) −6.34315 + 10.9867i −0.530440 + 0.918750i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −1.29289 2.23936i −0.107369 0.185968i
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) −0.242641 −0.0199449
\(149\) −11.1924 19.3858i −0.916916 1.58815i −0.804071 0.594533i \(-0.797337\pi\)
−0.112845 0.993613i \(-0.535996\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −10.0711 + 17.4436i −0.819572 + 1.41954i 0.0864262 + 0.996258i \(0.472455\pi\)
−0.905998 + 0.423282i \(0.860878\pi\)
\(152\) −3.41421 5.91359i −0.276929 0.479656i
\(153\) 2.58579 0.209048
\(154\) 0 0
\(155\) −10.2426 −0.822709
\(156\) 2.82843 + 4.89898i 0.226455 + 0.392232i
\(157\) 4.17157 7.22538i 0.332928 0.576648i −0.650157 0.759800i \(-0.725297\pi\)
0.983085 + 0.183152i \(0.0586301\pi\)
\(158\) 4.00000 6.92820i 0.318223 0.551178i
\(159\) 0.171573 + 0.297173i 0.0136066 + 0.0235673i
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 8.53553 + 14.7840i 0.668555 + 1.15797i 0.978308 + 0.207154i \(0.0664200\pi\)
−0.309754 + 0.950817i \(0.600247\pi\)
\(164\) −5.24264 + 9.08052i −0.409381 + 0.709069i
\(165\) 1.12132 1.94218i 0.0872947 0.151199i
\(166\) 2.58579 + 4.47871i 0.200696 + 0.347616i
\(167\) 2.24264 0.173541 0.0867704 0.996228i \(-0.472345\pi\)
0.0867704 + 0.996228i \(0.472345\pi\)
\(168\) 0 0
\(169\) 19.0000 1.46154
\(170\) 1.29289 + 2.23936i 0.0991604 + 0.171751i
\(171\) 3.41421 5.91359i 0.261091 0.452224i
\(172\) −4.53553 + 7.85578i −0.345831 + 0.598997i
\(173\) −10.4142 18.0379i −0.791778 1.37140i −0.924865 0.380295i \(-0.875822\pi\)
0.133087 0.991104i \(-0.457511\pi\)
\(174\) 2.58579 0.196028
\(175\) 0 0
\(176\) 2.24264 0.169045
\(177\) −1.58579 2.74666i −0.119195 0.206452i
\(178\) −0.414214 + 0.717439i −0.0310466 + 0.0537743i
\(179\) −13.1213 + 22.7268i −0.980734 + 1.69868i −0.321188 + 0.947015i \(0.604082\pi\)
−0.659545 + 0.751665i \(0.729251\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 18.4853 1.37400 0.687000 0.726657i \(-0.258927\pi\)
0.687000 + 0.726657i \(0.258927\pi\)
\(182\) 0 0
\(183\) 11.6569 0.861699
\(184\) 1.58579 + 2.74666i 0.116906 + 0.202487i
\(185\) 0.121320 0.210133i 0.00891965 0.0154493i
\(186\) 5.12132 8.87039i 0.375513 0.650408i
\(187\) −2.89949 5.02207i −0.212032 0.367250i
\(188\) −2.24264 −0.163561
\(189\) 0 0
\(190\) 6.82843 0.495386
\(191\) −2.00000 3.46410i −0.144715 0.250654i 0.784552 0.620063i \(-0.212893\pi\)
−0.929267 + 0.369410i \(0.879560\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 2.41421 4.18154i 0.173779 0.300994i −0.765959 0.642889i \(-0.777736\pi\)
0.939738 + 0.341895i \(0.111069\pi\)
\(194\) −3.24264 5.61642i −0.232808 0.403235i
\(195\) −5.65685 −0.405096
\(196\) 0 0
\(197\) −25.7990 −1.83810 −0.919051 0.394139i \(-0.871043\pi\)
−0.919051 + 0.394139i \(0.871043\pi\)
\(198\) 1.12132 + 1.94218i 0.0796888 + 0.138025i
\(199\) 2.87868 4.98602i 0.204064 0.353450i −0.745770 0.666204i \(-0.767918\pi\)
0.949834 + 0.312754i \(0.101252\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 4.53553 + 7.85578i 0.319912 + 0.554104i
\(202\) −17.6569 −1.24233
\(203\) 0 0
\(204\) −2.58579 −0.181041
\(205\) −5.24264 9.08052i −0.366162 0.634211i
\(206\) 7.41421 12.8418i 0.516573 0.894730i
\(207\) −1.58579 + 2.74666i −0.110220 + 0.190906i
\(208\) −2.82843 4.89898i −0.196116 0.339683i
\(209\) −15.3137 −1.05927
\(210\) 0 0
\(211\) −23.3137 −1.60498 −0.802491 0.596664i \(-0.796492\pi\)
−0.802491 + 0.596664i \(0.796492\pi\)
\(212\) −0.171573 0.297173i −0.0117837 0.0204099i
\(213\) −2.24264 + 3.88437i −0.153663 + 0.266152i
\(214\) 4.82843 8.36308i 0.330064 0.571688i
\(215\) −4.53553 7.85578i −0.309321 0.535759i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 3.65685 0.247673
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) −1.12132 + 1.94218i −0.0755994 + 0.130942i
\(221\) −7.31371 + 12.6677i −0.491973 + 0.852123i
\(222\) 0.121320 + 0.210133i 0.00814249 + 0.0141032i
\(223\) −7.31371 −0.489762 −0.244881 0.969553i \(-0.578749\pi\)
−0.244881 + 0.969553i \(0.578749\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 5.00000 + 8.66025i 0.332595 + 0.576072i
\(227\) 12.4853 21.6251i 0.828677 1.43531i −0.0703990 0.997519i \(-0.522427\pi\)
0.899076 0.437792i \(-0.144239\pi\)
\(228\) −3.41421 + 5.91359i −0.226112 + 0.391637i
\(229\) 8.07107 + 13.9795i 0.533351 + 0.923791i 0.999241 + 0.0389487i \(0.0124009\pi\)
−0.465890 + 0.884843i \(0.654266\pi\)
\(230\) −3.17157 −0.209127
\(231\) 0 0
\(232\) −2.58579 −0.169765
\(233\) −9.48528 16.4290i −0.621401 1.07630i −0.989225 0.146403i \(-0.953230\pi\)
0.367824 0.929896i \(-0.380103\pi\)
\(234\) 2.82843 4.89898i 0.184900 0.320256i
\(235\) 1.12132 1.94218i 0.0731469 0.126694i
\(236\) 1.58579 + 2.74666i 0.103226 + 0.178793i
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) −19.3137 −1.24930 −0.624650 0.780905i \(-0.714758\pi\)
−0.624650 + 0.780905i \(0.714758\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) 9.77817 16.9363i 0.629868 1.09096i −0.357710 0.933833i \(-0.616442\pi\)
0.987578 0.157130i \(-0.0502242\pi\)
\(242\) −2.98528 + 5.17066i −0.191901 + 0.332383i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −11.6569 −0.746254
\(245\) 0 0
\(246\) 10.4853 0.668517
\(247\) 19.3137 + 33.4523i 1.22890 + 2.12852i
\(248\) −5.12132 + 8.87039i −0.325204 + 0.563270i
\(249\) 2.58579 4.47871i 0.163868 0.283827i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −12.9706 −0.818695 −0.409347 0.912379i \(-0.634244\pi\)
−0.409347 + 0.912379i \(0.634244\pi\)
\(252\) 0 0
\(253\) 7.11270 0.447172
\(254\) 1.41421 + 2.44949i 0.0887357 + 0.153695i
\(255\) 1.29289 2.23936i 0.0809641 0.140234i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.29289 + 16.0958i 0.579675 + 1.00403i 0.995516 + 0.0945891i \(0.0301537\pi\)
−0.415842 + 0.909437i \(0.636513\pi\)
\(258\) 9.07107 0.564740
\(259\) 0 0
\(260\) 5.65685 0.350823
\(261\) −1.29289 2.23936i −0.0800281 0.138613i
\(262\) −1.58579 + 2.74666i −0.0979702 + 0.169689i
\(263\) 6.07107 10.5154i 0.374358 0.648407i −0.615873 0.787846i \(-0.711196\pi\)
0.990231 + 0.139439i \(0.0445298\pi\)
\(264\) −1.12132 1.94218i −0.0690125 0.119533i
\(265\) 0.343146 0.0210793
\(266\) 0 0
\(267\) 0.828427 0.0506989
\(268\) −4.53553 7.85578i −0.277052 0.479868i
\(269\) −6.17157 + 10.6895i −0.376287 + 0.651749i −0.990519 0.137377i \(-0.956133\pi\)
0.614231 + 0.789126i \(0.289466\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −15.8492 27.4517i −0.962773 1.66757i −0.715483 0.698630i \(-0.753793\pi\)
−0.247290 0.968942i \(-0.579540\pi\)
\(272\) 2.58579 0.156786
\(273\) 0 0
\(274\) −13.6569 −0.825041
\(275\) −1.12132 1.94218i −0.0676182 0.117118i
\(276\) 1.58579 2.74666i 0.0954531 0.165330i
\(277\) 7.77817 13.4722i 0.467345 0.809466i −0.531959 0.846770i \(-0.678544\pi\)
0.999304 + 0.0373046i \(0.0118772\pi\)
\(278\) −1.17157 2.02922i −0.0702663 0.121705i
\(279\) −10.2426 −0.613211
\(280\) 0 0
\(281\) −23.4558 −1.39926 −0.699629 0.714506i \(-0.746651\pi\)
−0.699629 + 0.714506i \(0.746651\pi\)
\(282\) 1.12132 + 1.94218i 0.0667737 + 0.115655i
\(283\) −4.75736 + 8.23999i −0.282796 + 0.489816i −0.972072 0.234682i \(-0.924595\pi\)
0.689277 + 0.724498i \(0.257928\pi\)
\(284\) 2.24264 3.88437i 0.133076 0.230495i
\(285\) −3.41421 5.91359i −0.202241 0.350291i
\(286\) −12.6863 −0.750156
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 5.15685 + 8.93193i 0.303344 + 0.525408i
\(290\) 1.29289 2.23936i 0.0759213 0.131500i
\(291\) −3.24264 + 5.61642i −0.190087 + 0.329240i
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) 21.3137 1.24516 0.622580 0.782556i \(-0.286084\pi\)
0.622580 + 0.782556i \(0.286084\pi\)
\(294\) 0 0
\(295\) −3.17157 −0.184656
\(296\) −0.121320 0.210133i −0.00705160 0.0122137i
\(297\) 1.12132 1.94218i 0.0650656 0.112697i
\(298\) 11.1924 19.3858i 0.648358 1.12299i
\(299\) −8.97056 15.5375i −0.518781 0.898555i
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) −20.1421 −1.15905
\(303\) 8.82843 + 15.2913i 0.507180 + 0.878461i
\(304\) 3.41421 5.91359i 0.195819 0.339168i
\(305\) 5.82843 10.0951i 0.333735 0.578046i
\(306\) 1.29289 + 2.23936i 0.0739098 + 0.128016i
\(307\) −7.31371 −0.417415 −0.208708 0.977978i \(-0.566926\pi\)
−0.208708 + 0.977978i \(0.566926\pi\)
\(308\) 0 0
\(309\) −14.8284 −0.843560
\(310\) −5.12132 8.87039i −0.290871 0.503804i
\(311\) 5.41421 9.37769i 0.307012 0.531760i −0.670695 0.741733i \(-0.734004\pi\)
0.977707 + 0.209973i \(0.0673375\pi\)
\(312\) −2.82843 + 4.89898i −0.160128 + 0.277350i
\(313\) −15.2426 26.4010i −0.861565 1.49227i −0.870418 0.492314i \(-0.836151\pi\)
0.00885295 0.999961i \(-0.497182\pi\)
\(314\) 8.34315 0.470831
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 12.6569 + 21.9223i 0.710880 + 1.23128i 0.964527 + 0.263983i \(0.0850363\pi\)
−0.253648 + 0.967297i \(0.581630\pi\)
\(318\) −0.171573 + 0.297173i −0.00962133 + 0.0166646i
\(319\) −2.89949 + 5.02207i −0.162341 + 0.281182i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −9.65685 −0.538993
\(322\) 0 0
\(323\) −17.6569 −0.982454
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −2.82843 + 4.89898i −0.156893 + 0.271746i
\(326\) −8.53553 + 14.7840i −0.472740 + 0.818809i
\(327\) −1.82843 3.16693i −0.101112 0.175132i
\(328\) −10.4853 −0.578953
\(329\) 0 0
\(330\) 2.24264 0.123453
\(331\) 3.17157 + 5.49333i 0.174325 + 0.301940i 0.939928 0.341374i \(-0.110892\pi\)
−0.765602 + 0.643314i \(0.777559\pi\)
\(332\) −2.58579 + 4.47871i −0.141913 + 0.245801i
\(333\) 0.121320 0.210133i 0.00664831 0.0115152i
\(334\) 1.12132 + 1.94218i 0.0613559 + 0.106272i
\(335\) 9.07107 0.495605
\(336\) 0 0
\(337\) 33.1127 1.80376 0.901882 0.431983i \(-0.142186\pi\)
0.901882 + 0.431983i \(0.142186\pi\)
\(338\) 9.50000 + 16.4545i 0.516732 + 0.895006i
\(339\) 5.00000 8.66025i 0.271563 0.470360i
\(340\) −1.29289 + 2.23936i −0.0701170 + 0.121446i
\(341\) 11.4853 + 19.8931i 0.621963 + 1.07727i
\(342\) 6.82843 0.369239
\(343\) 0 0
\(344\) −9.07107 −0.489079
\(345\) 1.58579 + 2.74666i 0.0853759 + 0.147875i
\(346\) 10.4142 18.0379i 0.559872 0.969726i
\(347\) 11.1716 19.3497i 0.599721 1.03875i −0.393140 0.919478i \(-0.628611\pi\)
0.992862 0.119270i \(-0.0380553\pi\)
\(348\) 1.29289 + 2.23936i 0.0693064 + 0.120042i
\(349\) 23.4558 1.25556 0.627781 0.778390i \(-0.283963\pi\)
0.627781 + 0.778390i \(0.283963\pi\)
\(350\) 0 0
\(351\) −5.65685 −0.301941
\(352\) 1.12132 + 1.94218i 0.0597666 + 0.103519i
\(353\) −8.02082 + 13.8925i −0.426905 + 0.739421i −0.996596 0.0824378i \(-0.973729\pi\)
0.569691 + 0.821859i \(0.307063\pi\)
\(354\) 1.58579 2.74666i 0.0842836 0.145983i
\(355\) 2.24264 + 3.88437i 0.119027 + 0.206161i
\(356\) −0.828427 −0.0439065
\(357\) 0 0
\(358\) −26.2426 −1.38697
\(359\) 14.2426 + 24.6690i 0.751698 + 1.30198i 0.946999 + 0.321236i \(0.104098\pi\)
−0.195301 + 0.980743i \(0.562569\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) −13.8137 + 23.9260i −0.727037 + 1.25927i
\(362\) 9.24264 + 16.0087i 0.485782 + 0.841400i
\(363\) 5.97056 0.313373
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 5.82843 + 10.0951i 0.304657 + 0.527681i
\(367\) 5.41421 9.37769i 0.282620 0.489512i −0.689410 0.724372i \(-0.742130\pi\)
0.972029 + 0.234860i \(0.0754632\pi\)
\(368\) −1.58579 + 2.74666i −0.0826648 + 0.143180i
\(369\) −5.24264 9.08052i −0.272921 0.472713i
\(370\) 0.242641 0.0126143
\(371\) 0 0
\(372\) 10.2426 0.531056
\(373\) −3.29289 5.70346i −0.170500 0.295314i 0.768095 0.640336i \(-0.221205\pi\)
−0.938595 + 0.345022i \(0.887871\pi\)
\(374\) 2.89949 5.02207i 0.149929 0.259685i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) −1.12132 1.94218i −0.0578277 0.100160i
\(377\) 14.6274 0.753350
\(378\) 0 0
\(379\) 0.485281 0.0249272 0.0124636 0.999922i \(-0.496033\pi\)
0.0124636 + 0.999922i \(0.496033\pi\)
\(380\) 3.41421 + 5.91359i 0.175145 + 0.303361i
\(381\) 1.41421 2.44949i 0.0724524 0.125491i
\(382\) 2.00000 3.46410i 0.102329 0.177239i
\(383\) −9.70711 16.8132i −0.496010 0.859114i 0.503979 0.863716i \(-0.331869\pi\)
−0.999989 + 0.00460116i \(0.998535\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 4.82843 0.245760
\(387\) −4.53553 7.85578i −0.230554 0.399331i
\(388\) 3.24264 5.61642i 0.164620 0.285130i
\(389\) 14.9497 25.8937i 0.757982 1.31286i −0.185896 0.982569i \(-0.559519\pi\)
0.943878 0.330294i \(-0.107148\pi\)
\(390\) −2.82843 4.89898i −0.143223 0.248069i
\(391\) 8.20101 0.414743
\(392\) 0 0
\(393\) 3.17157 0.159985
\(394\) −12.8995 22.3426i −0.649867 1.12560i
\(395\) −4.00000 + 6.92820i −0.201262 + 0.348596i
\(396\) −1.12132 + 1.94218i −0.0563485 + 0.0975984i
\(397\) −3.34315 5.79050i −0.167788 0.290617i 0.769854 0.638220i \(-0.220329\pi\)
−0.937642 + 0.347603i \(0.886996\pi\)
\(398\) 5.75736 0.288590
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) −4.53553 + 7.85578i −0.226212 + 0.391810i
\(403\) 28.9706 50.1785i 1.44313 2.49957i
\(404\) −8.82843 15.2913i −0.439231 0.760770i
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −0.544156 −0.0269728
\(408\) −1.29289 2.23936i −0.0640078 0.110865i
\(409\) −2.12132 + 3.67423i −0.104893 + 0.181679i −0.913694 0.406402i \(-0.866783\pi\)
0.808802 + 0.588081i \(0.200117\pi\)
\(410\) 5.24264 9.08052i 0.258916 0.448455i
\(411\) 6.82843 + 11.8272i 0.336821 + 0.583392i
\(412\) 14.8284 0.730544
\(413\) 0 0
\(414\) −3.17157 −0.155874
\(415\) −2.58579 4.47871i −0.126931 0.219851i
\(416\) 2.82843 4.89898i 0.138675 0.240192i
\(417\) −1.17157 + 2.02922i −0.0573722 + 0.0993715i
\(418\) −7.65685 13.2621i −0.374509 0.648669i
\(419\) −36.9706 −1.80613 −0.903065 0.429504i \(-0.858689\pi\)
−0.903065 + 0.429504i \(0.858689\pi\)
\(420\) 0 0
\(421\) −3.65685 −0.178224 −0.0891121 0.996022i \(-0.528403\pi\)
−0.0891121 + 0.996022i \(0.528403\pi\)
\(422\) −11.6569 20.1903i −0.567447 0.982847i
\(423\) 1.12132 1.94218i 0.0545205 0.0944322i
\(424\) 0.171573 0.297173i 0.00833232 0.0144320i
\(425\) −1.29289 2.23936i −0.0627145 0.108625i
\(426\) −4.48528 −0.217313
\(427\) 0 0
\(428\) 9.65685 0.466782
\(429\) 6.34315 + 10.9867i 0.306250 + 0.530440i
\(430\) 4.53553 7.85578i 0.218723 0.378839i
\(431\) −6.72792 + 11.6531i −0.324073 + 0.561310i −0.981324 0.192361i \(-0.938386\pi\)
0.657252 + 0.753671i \(0.271719\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −17.7990 −0.855365 −0.427682 0.903929i \(-0.640670\pi\)
−0.427682 + 0.903929i \(0.640670\pi\)
\(434\) 0 0
\(435\) −2.58579 −0.123979
\(436\) 1.82843 + 3.16693i 0.0875658 + 0.151668i
\(437\) 10.8284 18.7554i 0.517994 0.897192i
\(438\) 1.00000 1.73205i 0.0477818 0.0827606i
\(439\) 11.8492 + 20.5235i 0.565533 + 0.979533i 0.997000 + 0.0774037i \(0.0246630\pi\)
−0.431466 + 0.902129i \(0.642004\pi\)
\(440\) −2.24264 −0.106914
\(441\) 0 0
\(442\) −14.6274 −0.695755
\(443\) −18.1421 31.4231i −0.861959 1.49296i −0.870035 0.492989i \(-0.835904\pi\)
0.00807656 0.999967i \(-0.497429\pi\)
\(444\) −0.121320 + 0.210133i −0.00575761 + 0.00997247i
\(445\) 0.414214 0.717439i 0.0196356 0.0340099i
\(446\) −3.65685 6.33386i −0.173157 0.299917i
\(447\) −22.3848 −1.05876
\(448\) 0 0
\(449\) −10.4853 −0.494831 −0.247416 0.968909i \(-0.579581\pi\)
−0.247416 + 0.968909i \(0.579581\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) −11.7574 + 20.3643i −0.553632 + 0.958919i
\(452\) −5.00000 + 8.66025i −0.235180 + 0.407344i
\(453\) 10.0711 + 17.4436i 0.473180 + 0.819572i
\(454\) 24.9706 1.17193
\(455\) 0 0
\(456\) −6.82843 −0.319770
\(457\) −1.24264 2.15232i −0.0581283 0.100681i 0.835497 0.549495i \(-0.185180\pi\)
−0.893625 + 0.448814i \(0.851847\pi\)
\(458\) −8.07107 + 13.9795i −0.377136 + 0.653219i
\(459\) 1.29289 2.23936i 0.0603471 0.104524i
\(460\) −1.58579 2.74666i −0.0739377 0.128064i
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −25.6569 −1.19238 −0.596188 0.802845i \(-0.703319\pi\)
−0.596188 + 0.802845i \(0.703319\pi\)
\(464\) −1.29289 2.23936i −0.0600211 0.103960i
\(465\) −5.12132 + 8.87039i −0.237496 + 0.411354i
\(466\) 9.48528 16.4290i 0.439397 0.761058i
\(467\) −6.24264 10.8126i −0.288875 0.500346i 0.684667 0.728856i \(-0.259948\pi\)
−0.973541 + 0.228510i \(0.926615\pi\)
\(468\) 5.65685 0.261488
\(469\) 0 0
\(470\) 2.24264 0.103445
\(471\) −4.17157 7.22538i −0.192216 0.332928i
\(472\) −1.58579 + 2.74666i −0.0729917 + 0.126425i
\(473\) −10.1716 + 17.6177i −0.467689 + 0.810062i
\(474\) −4.00000 6.92820i −0.183726 0.318223i
\(475\) −6.82843 −0.313310
\(476\) 0 0
\(477\) 0.343146 0.0157116
\(478\) −9.65685 16.7262i −0.441694 0.765037i
\(479\) 4.24264 7.34847i 0.193851 0.335760i −0.752672 0.658396i \(-0.771235\pi\)
0.946523 + 0.322635i \(0.104569\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 0.686292 + 1.18869i 0.0312922 + 0.0541997i
\(482\) 19.5563 0.890767
\(483\) 0 0
\(484\) −5.97056 −0.271389
\(485\) 3.24264 + 5.61642i 0.147241 + 0.255028i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −5.41421 + 9.37769i −0.245341 + 0.424944i −0.962228 0.272246i \(-0.912233\pi\)
0.716886 + 0.697190i \(0.245567\pi\)
\(488\) −5.82843 10.0951i −0.263840 0.456985i
\(489\) 17.0711 0.771980
\(490\) 0 0
\(491\) −17.0711 −0.770407 −0.385203 0.922832i \(-0.625869\pi\)
−0.385203 + 0.922832i \(0.625869\pi\)
\(492\) 5.24264 + 9.08052i 0.236356 + 0.409381i
\(493\) −3.34315 + 5.79050i −0.150568 + 0.260791i
\(494\) −19.3137 + 33.4523i −0.868965 + 1.50509i
\(495\) −1.12132 1.94218i −0.0503996 0.0872947i
\(496\) −10.2426 −0.459908
\(497\) 0 0
\(498\) 5.17157 0.231744
\(499\) −3.41421 5.91359i −0.152841 0.264729i 0.779430 0.626490i \(-0.215509\pi\)
−0.932271 + 0.361761i \(0.882176\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 1.12132 1.94218i 0.0500969 0.0867704i
\(502\) −6.48528 11.2328i −0.289452 0.501346i
\(503\) −4.58579 −0.204470 −0.102235 0.994760i \(-0.532599\pi\)
−0.102235 + 0.994760i \(0.532599\pi\)
\(504\) 0 0
\(505\) 17.6569 0.785720
\(506\) 3.55635 + 6.15978i 0.158099 + 0.273836i
\(507\) 9.50000 16.4545i 0.421910 0.730769i
\(508\) −1.41421 + 2.44949i −0.0627456 + 0.108679i
\(509\) 8.48528 + 14.6969i 0.376103 + 0.651430i 0.990492 0.137574i \(-0.0439304\pi\)
−0.614388 + 0.789004i \(0.710597\pi\)
\(510\) 2.58579 0.114501
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −3.41421 5.91359i −0.150741 0.261091i
\(514\) −9.29289 + 16.0958i −0.409892 + 0.709954i
\(515\) −7.41421 + 12.8418i −0.326709 + 0.565877i
\(516\) 4.53553 + 7.85578i 0.199666 + 0.345831i
\(517\) −5.02944 −0.221194
\(518\) 0 0
\(519\) −20.8284 −0.914266
\(520\) 2.82843 + 4.89898i 0.124035 + 0.214834i
\(521\) −19.3848 + 33.5754i −0.849262 + 1.47097i 0.0326050 + 0.999468i \(0.489620\pi\)
−0.881867 + 0.471497i \(0.843714\pi\)
\(522\) 1.29289 2.23936i 0.0565884 0.0980140i
\(523\) −20.8995 36.1990i −0.913871 1.58287i −0.808546 0.588433i \(-0.799745\pi\)
−0.105325 0.994438i \(-0.533588\pi\)
\(524\) −3.17157 −0.138551
\(525\) 0 0
\(526\) 12.1421 0.529422
\(527\) 13.2426 + 22.9369i 0.576858 + 0.999148i
\(528\) 1.12132 1.94218i 0.0487992 0.0845227i
\(529\) 6.47056 11.2073i 0.281329 0.487276i
\(530\) 0.171573 + 0.297173i 0.00745265 + 0.0129084i
\(531\) −3.17157 −0.137635
\(532\) 0 0
\(533\) 59.3137 2.56916
\(534\) 0.414214 + 0.717439i 0.0179248 + 0.0310466i
\(535\) −4.82843 + 8.36308i −0.208751 + 0.361568i
\(536\) 4.53553 7.85578i 0.195905 0.339318i
\(537\) 13.1213 + 22.7268i 0.566227 + 0.980734i
\(538\) −12.3431 −0.532151
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 14.8995 + 25.8067i 0.640579 + 1.10952i 0.985304 + 0.170812i \(0.0546391\pi\)
−0.344724 + 0.938704i \(0.612028\pi\)
\(542\) 15.8492 27.4517i 0.680783 1.17915i
\(543\) 9.24264 16.0087i 0.396640 0.687000i
\(544\) 1.29289 + 2.23936i 0.0554323 + 0.0960116i
\(545\) −3.65685 −0.156642
\(546\) 0 0
\(547\) −28.3848 −1.21365 −0.606823 0.794837i \(-0.707556\pi\)
−0.606823 + 0.794837i \(0.707556\pi\)
\(548\) −6.82843 11.8272i −0.291696 0.505232i
\(549\) 5.82843 10.0951i 0.248751 0.430850i
\(550\) 1.12132 1.94218i 0.0478133 0.0828150i
\(551\) 8.82843 + 15.2913i 0.376104 + 0.651431i
\(552\) 3.17157 0.134991
\(553\) 0 0
\(554\) 15.5563 0.660926
\(555\) −0.121320 0.210133i −0.00514976 0.00891965i
\(556\) 1.17157 2.02922i 0.0496858 0.0860583i
\(557\) 19.0000 32.9090i 0.805056 1.39440i −0.111198 0.993798i \(-0.535469\pi\)
0.916253 0.400599i \(-0.131198\pi\)
\(558\) −5.12132 8.87039i −0.216803 0.375513i
\(559\) 51.3137 2.17034
\(560\) 0 0
\(561\) −5.79899 −0.244834
\(562\) −11.7279 20.3134i −0.494713 0.856867i
\(563\) 10.2426 17.7408i 0.431676 0.747684i −0.565342 0.824857i \(-0.691256\pi\)
0.997018 + 0.0771722i \(0.0245891\pi\)
\(564\) −1.12132 + 1.94218i −0.0472161 + 0.0817807i
\(565\) −5.00000 8.66025i −0.210352 0.364340i
\(566\) −9.51472 −0.399933
\(567\) 0 0
\(568\) 4.48528 0.188198
\(569\) −4.51472 7.81972i −0.189267 0.327820i 0.755739 0.654873i \(-0.227278\pi\)
−0.945006 + 0.327053i \(0.893944\pi\)
\(570\) 3.41421 5.91359i 0.143006 0.247693i
\(571\) −2.34315 + 4.05845i −0.0980576 + 0.169841i −0.910881 0.412670i \(-0.864596\pi\)
0.812823 + 0.582511i \(0.197930\pi\)
\(572\) −6.34315 10.9867i −0.265220 0.459375i
\(573\) −4.00000 −0.167102
\(574\) 0 0
\(575\) 3.17157 0.132264
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 1.92893 3.34101i 0.0803025 0.139088i −0.823077 0.567929i \(-0.807745\pi\)
0.903380 + 0.428841i \(0.141078\pi\)
\(578\) −5.15685 + 8.93193i −0.214497 + 0.371519i
\(579\) −2.41421 4.18154i −0.100331 0.173779i
\(580\) 2.58579 0.107369
\(581\) 0 0
\(582\) −6.48528 −0.268824
\(583\) −0.384776 0.666452i −0.0159358 0.0276016i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) −2.82843 + 4.89898i −0.116941 + 0.202548i
\(586\) 10.6569 + 18.4582i 0.440231 + 0.762502i
\(587\) −5.17157 −0.213454 −0.106727 0.994288i \(-0.534037\pi\)
−0.106727 + 0.994288i \(0.534037\pi\)
\(588\) 0 0
\(589\) 69.9411 2.88187
\(590\) −1.58579 2.74666i −0.0652858 0.113078i
\(591\) −12.8995 + 22.3426i −0.530614 + 0.919051i
\(592\) 0.121320 0.210133i 0.00498624 0.00863641i
\(593\) 20.6066 + 35.6917i 0.846212 + 1.46568i 0.884565 + 0.466417i \(0.154456\pi\)
−0.0383530 + 0.999264i \(0.512211\pi\)
\(594\) 2.24264 0.0920167
\(595\) 0 0
\(596\) 22.3848 0.916916
\(597\) −2.87868 4.98602i −0.117817 0.204064i
\(598\) 8.97056 15.5375i 0.366834 0.635374i
\(599\) −2.00000 + 3.46410i −0.0817178 + 0.141539i −0.903988 0.427558i \(-0.859374\pi\)
0.822270 + 0.569097i \(0.192707\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) −31.7574 −1.29541 −0.647705 0.761891i \(-0.724271\pi\)
−0.647705 + 0.761891i \(0.724271\pi\)
\(602\) 0 0
\(603\) 9.07107 0.369402
\(604\) −10.0711 17.4436i −0.409786 0.709770i
\(605\) 2.98528 5.17066i 0.121369 0.210217i
\(606\) −8.82843 + 15.2913i −0.358630 + 0.621166i
\(607\) −2.00000 3.46410i −0.0811775 0.140604i 0.822578 0.568652i \(-0.192535\pi\)
−0.903756 + 0.428048i \(0.859201\pi\)
\(608\) 6.82843 0.276929
\(609\) 0 0
\(610\) 11.6569 0.471972
\(611\) 6.34315 + 10.9867i 0.256616 + 0.444472i
\(612\) −1.29289 + 2.23936i −0.0522621 + 0.0905206i
\(613\) 5.53553 9.58783i 0.223578 0.387249i −0.732314 0.680967i \(-0.761560\pi\)
0.955892 + 0.293719i \(0.0948929\pi\)
\(614\) −3.65685 6.33386i −0.147579 0.255614i
\(615\) −10.4853 −0.422807
\(616\) 0 0
\(617\) 33.9411 1.36642 0.683209 0.730223i \(-0.260584\pi\)
0.683209 + 0.730223i \(0.260584\pi\)
\(618\) −7.41421 12.8418i −0.298243 0.516573i
\(619\) −9.55635 + 16.5521i −0.384102 + 0.665284i −0.991644 0.129003i \(-0.958822\pi\)
0.607542 + 0.794287i \(0.292156\pi\)
\(620\) 5.12132 8.87039i 0.205677 0.356243i
\(621\) 1.58579 + 2.74666i 0.0636354 + 0.110220i
\(622\) 10.8284 0.434180
\(623\) 0 0
\(624\) −5.65685 −0.226455
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 15.2426 26.4010i 0.609218 1.05520i
\(627\) −7.65685 + 13.2621i −0.305785 + 0.529636i
\(628\) 4.17157 + 7.22538i 0.166464 + 0.288324i
\(629\) −0.627417 −0.0250168
\(630\) 0 0
\(631\) −8.14214 −0.324133 −0.162067 0.986780i \(-0.551816\pi\)
−0.162067 + 0.986780i \(0.551816\pi\)
\(632\) 4.00000 + 6.92820i 0.159111 + 0.275589i
\(633\) −11.6569 + 20.1903i −0.463318 + 0.802491i
\(634\) −12.6569 + 21.9223i −0.502668 + 0.870646i
\(635\) −1.41421 2.44949i −0.0561214 0.0972050i
\(636\) −0.343146 −0.0136066
\(637\) 0 0
\(638\) −5.79899 −0.229584
\(639\) 2.24264 + 3.88437i 0.0887175 + 0.153663i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i \(0.338307\pi\)
−0.999878 + 0.0156233i \(0.995027\pi\)
\(642\) −4.82843 8.36308i −0.190563 0.330064i
\(643\) 28.8284 1.13688 0.568441 0.822724i \(-0.307547\pi\)
0.568441 + 0.822724i \(0.307547\pi\)
\(644\) 0 0
\(645\) −9.07107 −0.357173
\(646\) −8.82843 15.2913i −0.347350 0.601628i
\(647\) −4.43503 + 7.68170i −0.174359 + 0.301999i −0.939939 0.341342i \(-0.889119\pi\)
0.765580 + 0.643340i \(0.222452\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 3.55635 + 6.15978i 0.139599 + 0.241792i
\(650\) −5.65685 −0.221880
\(651\) 0 0
\(652\) −17.0711 −0.668555
\(653\) 0.899495 + 1.55797i 0.0352000 + 0.0609681i 0.883089 0.469206i \(-0.155460\pi\)
−0.847889 + 0.530174i \(0.822127\pi\)
\(654\) 1.82843 3.16693i 0.0714972 0.123837i
\(655\) 1.58579 2.74666i 0.0619618 0.107321i
\(656\) −5.24264 9.08052i −0.204691 0.354535i
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) 20.3848 0.794078 0.397039 0.917802i \(-0.370038\pi\)
0.397039 + 0.917802i \(0.370038\pi\)
\(660\) 1.12132 + 1.94218i 0.0436473 + 0.0755994i
\(661\) 2.51472 4.35562i 0.0978112 0.169414i −0.812967 0.582309i \(-0.802149\pi\)
0.910778 + 0.412895i \(0.135483\pi\)
\(662\) −3.17157 + 5.49333i −0.123267 + 0.213504i
\(663\) 7.31371 + 12.6677i 0.284041 + 0.491973i
\(664\) −5.17157 −0.200696
\(665\) 0 0
\(666\) 0.242641 0.00940214
\(667\) −4.10051 7.10228i −0.158772 0.275002i
\(668\) −1.12132 + 1.94218i −0.0433852 + 0.0751453i
\(669\) −3.65685 + 6.33386i −0.141382 + 0.244881i
\(670\) 4.53553 + 7.85578i 0.175223 + 0.303495i
\(671\) −26.1421 −1.00921
\(672\) 0 0
\(673\) −26.2843 −1.01318 −0.506592 0.862186i \(-0.669095\pi\)
−0.506592 + 0.862186i \(0.669095\pi\)
\(674\) 16.5563 + 28.6764i 0.637727 + 1.10458i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) −9.50000 + 16.4545i −0.365385 + 0.632865i
\(677\) 22.2132 + 38.4744i 0.853723 + 1.47869i 0.877825 + 0.478982i \(0.158994\pi\)
−0.0241021 + 0.999710i \(0.507673\pi\)
\(678\) 10.0000 0.384048
\(679\) 0 0
\(680\) −2.58579 −0.0991604
\(681\) −12.4853 21.6251i −0.478437 0.828677i
\(682\) −11.4853 + 19.8931i −0.439794 + 0.761746i
\(683\) 15.8995 27.5387i 0.608377 1.05374i −0.383131 0.923694i \(-0.625154\pi\)
0.991508 0.130046i \(-0.0415126\pi\)
\(684\) 3.41421 + 5.91359i 0.130546 + 0.226112i
\(685\) 13.6569 0.521802
\(686\) 0 0
\(687\) 16.1421 0.615861
\(688\) −4.53553 7.85578i −0.172916 0.299499i
\(689\) −0.970563 + 1.68106i −0.0369755 + 0.0640434i
\(690\) −1.58579 + 2.74666i −0.0603699 + 0.104564i
\(691\) −1.51472 2.62357i −0.0576226 0.0998053i 0.835775 0.549072i \(-0.185019\pi\)
−0.893398 + 0.449267i \(0.851685\pi\)
\(692\) 20.8284 0.791778
\(693\) 0 0
\(694\) 22.3431 0.848134
\(695\) 1.17157 + 2.02922i 0.0444403 + 0.0769728i
\(696\) −1.29289 + 2.23936i −0.0490070 + 0.0848826i
\(697\) −13.5563 + 23.4803i −0.513483 + 0.889379i
\(698\) 11.7279 + 20.3134i 0.443908 + 0.768872i
\(699\) −18.9706 −0.717533
\(700\) 0 0
\(701\) −17.2132 −0.650134 −0.325067 0.945691i \(-0.605387\pi\)
−0.325067 + 0.945691i \(0.605387\pi\)
\(702\) −2.82843 4.89898i −0.106752 0.184900i
\(703\) −0.828427 + 1.43488i −0.0312447 + 0.0541174i
\(704\) −1.12132 + 1.94218i −0.0422614 + 0.0731988i
\(705\) −1.12132 1.94218i −0.0422314 0.0731469i
\(706\) −16.0416 −0.603735
\(707\) 0 0
\(708\) 3.17157 0.119195
\(709\) −5.92893 10.2692i −0.222666 0.385668i 0.732951 0.680282i \(-0.238143\pi\)
−0.955617 + 0.294613i \(0.904809\pi\)
\(710\) −2.24264 + 3.88437i −0.0841648 + 0.145778i
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) −0.414214 0.717439i −0.0155233 0.0268872i
\(713\) −32.4853 −1.21658
\(714\) 0 0
\(715\) 12.6863 0.474440
\(716\) −13.1213 22.7268i −0.490367 0.849340i
\(717\) −9.65685 + 16.7262i −0.360642 + 0.624650i
\(718\) −14.2426 + 24.6690i −0.531531 + 0.920638i
\(719\) −8.97056 15.5375i −0.334546 0.579450i 0.648852 0.760915i \(-0.275249\pi\)
−0.983397 + 0.181465i \(0.941916\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) −27.6274 −1.02819
\(723\) −9.77817 16.9363i −0.363654 0.629868i
\(724\) −9.24264 + 16.0087i −0.343500 + 0.594960i
\(725\) −1.29289 + 2.23936i −0.0480168 + 0.0831676i
\(726\) 2.98528 + 5.17066i 0.110794 + 0.191901i
\(727\) −30.6274 −1.13591 −0.567954 0.823060i \(-0.692265\pi\)
−0.567954 + 0.823060i \(0.692265\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) −11.7279 + 20.3134i −0.433773 + 0.751317i
\(732\) −5.82843 + 10.0951i −0.215425 + 0.373127i
\(733\) 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) 10.8284 0.399685
\(735\) 0 0
\(736\) −3.17157 −0.116906
\(737\) −10.1716 17.6177i −0.374675 0.648956i
\(738\) 5.24264 9.08052i 0.192984 0.334259i
\(739\) −5.55635 + 9.62388i −0.204394 + 0.354020i −0.949939 0.312434i \(-0.898856\pi\)
0.745546 + 0.666454i \(0.232189\pi\)
\(740\) 0.121320 + 0.210133i 0.00445982 + 0.00772464i
\(741\) 38.6274 1.41901
\(742\) 0 0
\(743\) 28.2843 1.03765 0.518825 0.854881i \(-0.326370\pi\)
0.518825 + 0.854881i \(0.326370\pi\)
\(744\) 5.12132 + 8.87039i 0.187757 + 0.325204i
\(745\) −11.1924 + 19.3858i −0.410057 + 0.710240i
\(746\) 3.29289 5.70346i 0.120561 0.208818i
\(747\) −2.58579 4.47871i −0.0946090 0.163868i
\(748\) 5.79899 0.212032
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) −10.8995 18.8785i −0.397728 0.688885i 0.595717 0.803194i \(-0.296868\pi\)
−0.993445 + 0.114309i \(0.963535\pi\)
\(752\) 1.12132 1.94218i 0.0408903 0.0708242i
\(753\) −6.48528 + 11.2328i −0.236337 + 0.409347i
\(754\) 7.31371 + 12.6677i 0.266350 + 0.461331i
\(755\) 20.1421 0.733047
\(756\) 0 0
\(757\) 25.8995 0.941333 0.470667 0.882311i \(-0.344013\pi\)
0.470667 + 0.882311i \(0.344013\pi\)
\(758\) 0.242641 + 0.420266i 0.00881311 + 0.0152647i
\(759\) 3.55635 6.15978i 0.129087 0.223586i
\(760\) −3.41421 + 5.91359i −0.123847 + 0.214509i
\(761\) 13.4853 + 23.3572i 0.488841 + 0.846698i 0.999918 0.0128376i \(-0.00408646\pi\)
−0.511077 + 0.859535i \(0.670753\pi\)
\(762\) 2.82843 0.102463
\(763\) 0 0
\(764\) 4.00000 0.144715
\(765\) −1.29289 2.23936i −0.0467447 0.0809641i
\(766\) 9.70711 16.8132i 0.350732 0.607486i
\(767\) 8.97056 15.5375i 0.323908 0.561026i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 4.72792 0.170493 0.0852466 0.996360i \(-0.472832\pi\)
0.0852466 + 0.996360i \(0.472832\pi\)
\(770\) 0 0
\(771\) 18.5858 0.669351
\(772\) 2.41421 + 4.18154i 0.0868894 + 0.150497i
\(773\) 11.4853 19.8931i 0.413097 0.715505i −0.582130 0.813096i \(-0.697780\pi\)
0.995227 + 0.0975912i \(0.0311138\pi\)
\(774\) 4.53553 7.85578i 0.163026 0.282370i
\(775\) 5.12132 + 8.87039i 0.183963 + 0.318634i
\(776\) 6.48528 0.232808
\(777\) 0 0
\(778\) 29.8995 1.07195
\(779\) 35.7990 + 62.0057i 1.28263 + 2.22158i
\(780\) 2.82843 4.89898i 0.101274 0.175412i
\(781\) 5.02944 8.71124i 0.179967 0.311713i
\(782\) 4.10051 + 7.10228i 0.146634 + 0.253977i
\(783\) −2.58579 −0.0924085
\(784\) 0 0
\(785\) −8.34315 −0.297780
\(786\) 1.58579 + 2.74666i 0.0565631 + 0.0979702i
\(787\) −19.1716 + 33.2061i −0.683393 + 1.18367i 0.290546 + 0.956861i \(0.406163\pi\)
−0.973939 + 0.226810i \(0.927170\pi\)
\(788\) 12.8995 22.3426i 0.459525 0.795921i
\(789\) −6.07107 10.5154i −0.216136 0.374358i
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) −2.24264 −0.0796888
\(793\) 32.9706 + 57.1067i 1.17082 + 2.02792i
\(794\) 3.34315 5.79050i 0.118644 0.205497i
\(795\) 0.171573 0.297173i 0.00608506 0.0105396i
\(796\) 2.87868 + 4.98602i 0.102032 + 0.176725i
\(797\) 0.142136 0.00503470 0.00251735 0.999997i \(-0.499199\pi\)
0.00251735 + 0.999997i \(0.499199\pi\)
\(798\) 0 0
\(799\) −5.79899 −0.205154
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) 0.414214 0.717439i 0.0146355 0.0253495i
\(802\) −3.00000 + 5.19615i −0.105934 + 0.183483i
\(803\) 2.24264 + 3.88437i 0.0791411 + 0.137076i
\(804\) −9.07107 −0.319912
\(805\) 0 0
\(806\) 57.9411 2.04089
\(807\) 6.17157 + 10.6895i 0.217250 + 0.376287i
\(808\) 8.82843 15.2913i 0.310583 0.537946i
\(809\) −17.2426 + 29.8651i −0.606219 + 1.05000i 0.385639 + 0.922650i \(0.373981\pi\)
−0.991858 + 0.127352i \(0.959352\pi\)
\(810\) 0.500000 + 0.866025i 0.0175682 + 0.0304290i
\(811\) 10.3431 0.363197 0.181598 0.983373i \(-0.441873\pi\)
0.181598 + 0.983373i \(0.441873\pi\)
\(812\) 0 0
\(813\) −31.6985 −1.11171
\(814\) −0.272078 0.471253i −0.00953633 0.0165174i
\(815\) 8.53553 14.7840i 0.298987 0.517860i
\(816\) 1.29289 2.23936i 0.0452603 0.0783932i
\(817\) 30.9706 + 53.6426i 1.08352 + 1.87672i
\(818\) −4.24264 −0.148340
\(819\) 0 0
\(820\) 10.4853 0.366162
\(821\) −0.606602 1.05066i −0.0211705 0.0366685i 0.855246 0.518222i \(-0.173406\pi\)
−0.876417 + 0.481554i \(0.840073\pi\)
\(822\) −6.82843 + 11.8272i −0.238169 + 0.412520i
\(823\) −14.4853 + 25.0892i −0.504925 + 0.874556i 0.495059 + 0.868860i \(0.335147\pi\)
−0.999984 + 0.00569646i \(0.998187\pi\)
\(824\) 7.41421 + 12.8418i 0.258286 + 0.447365i
\(825\) −2.24264 −0.0780787
\(826\) 0 0
\(827\) 35.5147 1.23497 0.617484 0.786584i \(-0.288152\pi\)
0.617484 + 0.786584i \(0.288152\pi\)
\(828\) −1.58579 2.74666i −0.0551099 0.0954531i
\(829\) −16.6569 + 28.8505i −0.578516 + 1.00202i 0.417133 + 0.908845i \(0.363035\pi\)
−0.995650 + 0.0931746i \(0.970299\pi\)
\(830\) 2.58579 4.47871i 0.0897540 0.155458i
\(831\) −7.77817 13.4722i −0.269822 0.467345i
\(832\) 5.65685 0.196116
\(833\) 0 0
\(834\) −2.34315 −0.0811365
\(835\) −1.12132 1.94218i −0.0388049 0.0672120i
\(836\) 7.65685 13.2621i 0.264818 0.458678i
\(837\) −5.12132 + 8.87039i −0.177019 + 0.306605i
\(838\) −18.4853 32.0174i −0.638563 1.10602i
\(839\) 8.48528 0.292944 0.146472 0.989215i \(-0.453208\pi\)
0.146472 + 0.989215i \(0.453208\pi\)
\(840\) 0 0
\(841\) −22.3137 −0.769438
\(842\) −1.82843 3.16693i −0.0630118 0.109140i
\(843\) −11.7279 + 20.3134i −0.403931 + 0.699629i
\(844\) 11.6569 20.1903i 0.401245 0.694978i
\(845\) −9.50000 16.4545i −0.326810 0.566051i
\(846\) 2.24264 0.0771036
\(847\) 0 0
\(848\) 0.343146 0.0117837
\(849\) 4.75736 + 8.23999i 0.163272 + 0.282796i
\(850\) 1.29289 2.23936i 0.0443459 0.0768093i
\(851\) 0.384776 0.666452i 0.0131900 0.0228457i
\(852\) −2.24264 3.88437i −0.0768316 0.133076i
\(853\) −40.6274 −1.39106 −0.695528 0.718499i \(-0.744830\pi\)
−0.695528 + 0.718499i \(0.744830\pi\)
\(854\) 0 0
\(855\) −6.82843 −0.233527
\(856\) 4.82843 + 8.36308i 0.165032 + 0.285844i
\(857\) −12.3640 + 21.4150i −0.422345 + 0.731523i −0.996168 0.0874562i \(-0.972126\pi\)
0.573823 + 0.818979i \(0.305460\pi\)
\(858\) −6.34315 + 10.9867i −0.216551 + 0.375078i
\(859\) 17.7990 + 30.8288i 0.607294 + 1.05186i 0.991684 + 0.128693i \(0.0410782\pi\)
−0.384391 + 0.923170i \(0.625588\pi\)
\(860\) 9.07107 0.309321
\(861\) 0 0
\(862\) −13.4558 −0.458308
\(863\) −22.8284 39.5400i −0.777089 1.34596i −0.933613 0.358283i \(-0.883362\pi\)
0.156524 0.987674i \(-0.449971\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) −10.4142 + 18.0379i −0.354094 + 0.613309i
\(866\) −8.89949 15.4144i −0.302417 0.523802i
\(867\) 10.3137 0.350272
\(868\) 0 0
\(869\) 17.9411 0.608611
\(870\) −1.29289 2.23936i −0.0438332 0.0759213i
\(871\) −25.6569 + 44.4390i −0.869349 + 1.50576i
\(872\) −1.82843 + 3.16693i −0.0619184 + 0.107246i
\(873\) 3.24264 + 5.61642i 0.109747 + 0.190087i
\(874\) 21.6569 0.732554
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −2.12132 3.67423i −0.0716319 0.124070i 0.827985 0.560751i \(-0.189487\pi\)
−0.899617 + 0.436681i \(0.856154\pi\)
\(878\) −11.8492 + 20.5235i −0.399893 + 0.692634i
\(879\) 10.6569 18.4582i 0.359447 0.622580i
\(880\) −1.12132 1.94218i −0.0377997 0.0654710i
\(881\) 26.0000 0.875962 0.437981 0.898984i \(-0.355694\pi\)
0.437981 + 0.898984i \(0.355694\pi\)
\(882\) 0 0
\(883\) −34.2426 −1.15236 −0.576178 0.817324i \(-0.695457\pi\)
−0.576178 + 0.817324i \(0.695457\pi\)
\(884\) −7.31371 12.6677i −0.245987 0.426061i
\(885\) −1.58579 + 2.74666i −0.0533056 + 0.0923281i
\(886\) 18.1421 31.4231i 0.609497 1.05568i
\(887\) 16.4350 + 28.4663i 0.551834 + 0.955805i 0.998142 + 0.0609256i \(0.0194052\pi\)
−0.446308 + 0.894879i \(0.647261\pi\)
\(888\) −0.242641 −0.00814249
\(889\) 0 0
\(890\) 0.828427 0.0277689
\(891\) −1.12132 1.94218i −0.0375656 0.0650656i
\(892\) 3.65685 6.33386i 0.122441 0.212073i
\(893\) −7.65685 + 13.2621i −0.256227 + 0.443798i
\(894\) −11.1924 19.3858i −0.374329 0.648358i
\(895\) 26.2426 0.877195
\(896\) 0 0
\(897\) −17.9411 −0.599037
\(898\) −5.24264 9.08052i −0.174949 0.303021i
\(899\) 13.2426 22.9369i 0.441667 0.764989i
\(900\) −0.500000 + 0.866025i −0.0166667 + 0.0288675i
\(901\) −0.443651 0.768426i −0.0147802 0.0256000i
\(902\) −23.5147 −0.782954
\(903\) 0 0
\(904\) −10.0000 −0.332595
\(905\) −9.24264 16.0087i −0.307236 0.532148i
\(906\) −10.0711 + 17.4436i −0.334589 + 0.579525i
\(907\) 8.43503 14.6099i 0.280081 0.485114i −0.691324 0.722545i \(-0.742972\pi\)
0.971404 + 0.237431i \(0.0763055\pi\)
\(908\) 12.4853 + 21.6251i 0.414339 + 0.717656i
\(909\) 17.6569 0.585641
\(910\) 0 0
\(911\) 44.9706 1.48994 0.744971 0.667097i \(-0.232463\pi\)
0.744971 + 0.667097i \(0.232463\pi\)
\(912\) −3.41421 5.91359i −0.113056 0.195819i
\(913\) −5.79899 + 10.0441i −0.191919 + 0.332413i
\(914\) 1.24264 2.15232i 0.0411029 0.0711923i
\(915\) −5.82843 10.0951i −0.192682 0.333735i
\(916\) −16.1421 −0.533351
\(917\) 0 0
\(918\) 2.58579 0.0853437
\(919\) 15.3848 + 26.6472i 0.507497 + 0.879010i 0.999962 + 0.00867847i \(0.00276248\pi\)
−0.492465 + 0.870332i \(0.663904\pi\)
\(920\) 1.58579 2.74666i 0.0522818 0.0905548i
\(921\) −3.65685 + 6.33386i −0.120497 + 0.208708i
\(922\) 1.00000 + 1.73205i 0.0329332 + 0.0570421i
\(923\) −25.3726 −0.835149
\(924\) 0 0
\(925\) −0.242641 −0.00797798
\(926\) −12.8284 22.2195i −0.421568 0.730178i
\(927\) −7.41421 + 12.8418i −0.243515 + 0.421780i
\(928\) 1.29289 2.23936i 0.0424413 0.0735105i
\(929\) −27.8284 48.2002i −0.913021 1.58140i −0.809773 0.586743i \(-0.800410\pi\)
−0.103248 0.994656i \(-0.532924\pi\)
\(930\) −10.2426 −0.335869
\(931\) 0 0
\(932\) 18.9706 0.621401
\(933\) −5.41421 9.37769i −0.177253 0.307012i
\(934\) 6.24264 10.8126i 0.204265 0.353798i
\(935\) −2.89949 + 5.02207i −0.0948236 + 0.164239i
\(936\) 2.82843 + 4.89898i 0.0924500 + 0.160128i
\(937\) 36.3431 1.18728 0.593639 0.804731i \(-0.297691\pi\)
0.593639 + 0.804731i \(0.297691\pi\)
\(938\) 0 0
\(939\) −30.4853 −0.994850
\(940\) 1.12132 + 1.94218i 0.0365734 + 0.0633471i
\(941\) 14.1421 24.4949i 0.461020 0.798511i −0.537992 0.842950i \(-0.680817\pi\)
0.999012 + 0.0444393i \(0.0141501\pi\)
\(942\) 4.17157 7.22538i 0.135917 0.235415i
\(943\) −16.6274 28.7995i −0.541463 0.937842i
\(944\) −3.17157 −0.103226
\(945\) 0 0
\(946\) −20.3431 −0.661413
\(947\) 4.58579 + 7.94282i 0.149018 + 0.258107i 0.930865 0.365364i \(-0.119055\pi\)
−0.781847 + 0.623471i \(0.785722\pi\)
\(948\) 4.00000 6.92820i 0.129914 0.225018i
\(949\) 5.65685 9.79796i 0.183629 0.318055i
\(950\) −3.41421 5.91359i −0.110772 0.191862i
\(951\) 25.3137 0.820853
\(952\) 0 0
\(953\) 4.68629 0.151804 0.0759019 0.997115i \(-0.475816\pi\)
0.0759019 + 0.997115i \(0.475816\pi\)
\(954\) 0.171573 + 0.297173i 0.00555488 + 0.00962133i
\(955\) −2.00000 + 3.46410i −0.0647185 + 0.112096i
\(956\) 9.65685 16.7262i 0.312325 0.540963i
\(957\) 2.89949 + 5.02207i 0.0937274 + 0.162341i
\(958\) 8.48528 0.274147
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −36.9558 64.0094i −1.19212 2.06482i
\(962\) −0.686292 + 1.18869i −0.0221269 + 0.0383250i
\(963\) −4.82843 + 8.36308i −0.155594 + 0.269497i
\(964\) 9.77817 + 16.9363i 0.314934 + 0.545481i
\(965\) −4.82843 −0.155433
\(966\) 0 0
\(967\) −10.3431 −0.332613 −0.166307 0.986074i \(-0.553184\pi\)
−0.166307 + 0.986074i \(0.553184\pi\)
\(968\) −2.98528 5.17066i −0.0959506 0.166191i
\(969\) −8.82843 + 15.2913i −0.283610 + 0.491227i
\(970\) −3.24264 + 5.61642i −0.104115 + 0.180332i
\(971\) 2.48528 + 4.30463i 0.0797565 + 0.138142i 0.903145 0.429336i \(-0.141252\pi\)
−0.823388 + 0.567478i \(0.807919\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −10.8284 −0.346965
\(975\) 2.82843 + 4.89898i 0.0905822 + 0.156893i
\(976\) 5.82843 10.0951i 0.186563 0.323137i
\(977\) 14.6569 25.3864i 0.468914 0.812183i −0.530454 0.847714i \(-0.677979\pi\)
0.999369 + 0.0355301i \(0.0113120\pi\)
\(978\) 8.53553 + 14.7840i 0.272936 + 0.472740i
\(979\) −1.85786 −0.0593776
\(980\) 0 0
\(981\) −3.65685 −0.116754
\(982\) −8.53553 14.7840i −0.272380 0.471776i
\(983\) 8.53553 14.7840i 0.272241 0.471536i −0.697194 0.716882i \(-0.745568\pi\)
0.969435 + 0.245347i \(0.0789018\pi\)
\(984\) −5.24264 + 9.08052i −0.167129 + 0.289476i
\(985\) 12.8995 + 22.3426i 0.411012 + 0.711894i
\(986\) −6.68629 −0.212935
\(987\) 0 0
\(988\) −38.6274 −1.22890
\(989\) −14.3848 24.9152i −0.457409 0.792256i
\(990\) 1.12132 1.94218i 0.0356379 0.0617267i
\(991\) 5.10051 8.83433i 0.162023 0.280632i −0.773571 0.633709i \(-0.781531\pi\)
0.935594 + 0.353078i \(0.114865\pi\)
\(992\) −5.12132 8.87039i −0.162602 0.281635i
\(993\) 6.34315 0.201294
\(994\) 0 0
\(995\) −5.75736 −0.182521
\(996\) 2.58579 + 4.47871i 0.0819338 + 0.141913i
\(997\) 28.3137 49.0408i 0.896704 1.55314i 0.0650229 0.997884i \(-0.479288\pi\)
0.831681 0.555253i \(-0.187379\pi\)
\(998\) 3.41421 5.91359i 0.108075 0.187191i
\(999\) −0.121320 0.210133i −0.00383841 0.00664831i
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 1470.2.i.x.361.1 4
7.2 even 3 inner 1470.2.i.x.961.1 4
7.3 odd 6 1470.2.a.t.1.2 yes 2
7.4 even 3 1470.2.a.s.1.2 2
7.5 odd 6 1470.2.i.w.961.1 4
7.6 odd 2 1470.2.i.w.361.1 4
21.11 odd 6 4410.2.a.bw.1.1 2
21.17 even 6 4410.2.a.bz.1.1 2
35.4 even 6 7350.2.a.dl.1.2 2
35.24 odd 6 7350.2.a.dh.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.a.s.1.2 2 7.4 even 3
1470.2.a.t.1.2 yes 2 7.3 odd 6
1470.2.i.w.361.1 4 7.6 odd 2
1470.2.i.w.961.1 4 7.5 odd 6
1470.2.i.x.361.1 4 1.1 even 1 trivial
1470.2.i.x.961.1 4 7.2 even 3 inner
4410.2.a.bw.1.1 2 21.11 odd 6
4410.2.a.bz.1.1 2 21.17 even 6
7350.2.a.dh.1.2 2 35.24 odd 6
7350.2.a.dl.1.2 2 35.4 even 6