Properties

Label 378.4.g.b.163.2
Level $378$
Weight $4$
Character 378.163
Analytic conductor $22.303$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,4,Mod(109,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.109");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), 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: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11184604443.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 43x^{4} - 210x^{3} + 1849x^{2} - 4515x + 11025 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(1.60692 - 2.78326i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.b.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-0.301070 + 0.521469i) q^{5} +(-17.6665 - 5.55825i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-0.301070 + 0.521469i) q^{5} +(-17.6665 - 5.55825i) q^{7} -8.00000 q^{8} +(0.602141 + 1.04294i) q^{10} +(4.52503 + 7.83758i) q^{11} +5.60214 q^{13} +(-27.2937 + 25.0411i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-6.61646 - 11.4601i) q^{17} +(-24.8134 + 42.9780i) q^{19} +2.40856 q^{20} +18.1001 q^{22} +(-65.0049 + 112.592i) q^{23} +(62.3187 + 107.939i) q^{25} +(5.60214 - 9.70319i) q^{26} +(16.0787 + 72.3151i) q^{28} -50.2607 q^{29} +(124.287 + 215.272i) q^{31} +(16.0000 + 27.7128i) q^{32} -26.4659 q^{34} +(8.21732 - 7.53912i) q^{35} +(-15.1176 + 26.1845i) q^{37} +(49.6267 + 85.9560i) q^{38} +(2.40856 - 4.17175i) q^{40} -277.880 q^{41} -48.9644 q^{43} +(18.1001 - 31.3503i) q^{44} +(130.010 + 225.184i) q^{46} +(-121.813 + 210.986i) q^{47} +(281.212 + 196.390i) q^{49} +249.275 q^{50} +(-11.2043 - 19.4064i) q^{52} +(-243.524 - 421.796i) q^{53} -5.44941 q^{55} +(141.332 + 44.4660i) q^{56} +(-50.2607 + 87.0541i) q^{58} +(-44.7885 - 77.5759i) q^{59} +(-339.433 + 587.916i) q^{61} +497.150 q^{62} +64.0000 q^{64} +(-1.68664 + 2.92134i) q^{65} +(350.562 + 607.191i) q^{67} +(-26.4659 + 45.8402i) q^{68} +(-4.84082 - 21.7719i) q^{70} +376.105 q^{71} +(134.482 + 232.929i) q^{73} +(30.2352 + 52.3689i) q^{74} +198.507 q^{76} +(-36.3783 - 163.614i) q^{77} +(-19.6704 + 34.0701i) q^{79} +(-4.81712 - 8.34351i) q^{80} +(-277.880 + 481.303i) q^{82} -491.595 q^{83} +7.96808 q^{85} +(-48.9644 + 84.8089i) q^{86} +(-36.2002 - 62.7006i) q^{88} +(342.378 - 593.015i) q^{89} +(-98.9703 - 31.1381i) q^{91} +520.039 q^{92} +(243.626 + 421.972i) q^{94} +(-14.9411 - 25.8788i) q^{95} -328.527 q^{97} +(621.369 - 290.683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} - 12 q^{4} + 5 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} - 12 q^{4} + 5 q^{5} + 8 q^{7} - 48 q^{8} - 10 q^{10} - 29 q^{11} + 20 q^{13} + 20 q^{14} - 48 q^{16} - 38 q^{17} + 57 q^{19} - 40 q^{20} - 116 q^{22} - 14 q^{23} + 134 q^{25} + 20 q^{26} + 8 q^{28} + 362 q^{29} - 88 q^{31} + 96 q^{32} - 152 q^{34} + 490 q^{35} + 384 q^{37} - 114 q^{38} - 40 q^{40} - 432 q^{41} - 726 q^{43} - 116 q^{44} + 28 q^{46} - 183 q^{47} + 372 q^{49} + 536 q^{50} - 40 q^{52} - 396 q^{53} - 1268 q^{55} - 64 q^{56} + 362 q^{58} - 427 q^{59} - 427 q^{61} - 352 q^{62} + 384 q^{64} - 216 q^{65} - 32 q^{67} - 152 q^{68} + 1162 q^{70} + 790 q^{71} + 373 q^{73} - 768 q^{74} - 456 q^{76} + 1211 q^{77} + 1364 q^{79} + 80 q^{80} - 432 q^{82} + 154 q^{83} - 2678 q^{85} - 726 q^{86} + 232 q^{88} - 1233 q^{89} + 131 q^{91} + 112 q^{92} + 366 q^{94} - 464 q^{95} + 1180 q^{97} + 720 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −0.301070 + 0.521469i −0.0269285 + 0.0466416i −0.879176 0.476498i \(-0.841906\pi\)
0.852247 + 0.523139i \(0.175239\pi\)
\(6\) 0 0
\(7\) −17.6665 5.55825i −0.953902 0.300117i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 0.602141 + 1.04294i 0.0190414 + 0.0329806i
\(11\) 4.52503 + 7.83758i 0.124032 + 0.214829i 0.921354 0.388725i \(-0.127084\pi\)
−0.797322 + 0.603554i \(0.793751\pi\)
\(12\) 0 0
\(13\) 5.60214 0.119520 0.0597598 0.998213i \(-0.480967\pi\)
0.0597598 + 0.998213i \(0.480967\pi\)
\(14\) −27.2937 + 25.0411i −0.521039 + 0.478036i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −6.61646 11.4601i −0.0943958 0.163498i 0.814960 0.579517i \(-0.196759\pi\)
−0.909356 + 0.416018i \(0.863425\pi\)
\(18\) 0 0
\(19\) −24.8134 + 42.9780i −0.299609 + 0.518938i −0.976047 0.217562i \(-0.930190\pi\)
0.676437 + 0.736500i \(0.263523\pi\)
\(20\) 2.40856 0.0269285
\(21\) 0 0
\(22\) 18.1001 0.175407
\(23\) −65.0049 + 112.592i −0.589324 + 1.02074i 0.404997 + 0.914318i \(0.367273\pi\)
−0.994321 + 0.106422i \(0.966061\pi\)
\(24\) 0 0
\(25\) 62.3187 + 107.939i 0.498550 + 0.863513i
\(26\) 5.60214 9.70319i 0.0422565 0.0731905i
\(27\) 0 0
\(28\) 16.0787 + 72.3151i 0.108521 + 0.488081i
\(29\) −50.2607 −0.321834 −0.160917 0.986968i \(-0.551445\pi\)
−0.160917 + 0.986968i \(0.551445\pi\)
\(30\) 0 0
\(31\) 124.287 + 215.272i 0.720087 + 1.24723i 0.960965 + 0.276671i \(0.0892313\pi\)
−0.240878 + 0.970555i \(0.577435\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −26.4659 −0.133496
\(35\) 8.21732 7.53912i 0.0396852 0.0364098i
\(36\) 0 0
\(37\) −15.1176 + 26.1845i −0.0671708 + 0.116343i −0.897655 0.440699i \(-0.854731\pi\)
0.830484 + 0.557042i \(0.188064\pi\)
\(38\) 49.6267 + 85.9560i 0.211856 + 0.366945i
\(39\) 0 0
\(40\) 2.40856 4.17175i 0.00952068 0.0164903i
\(41\) −277.880 −1.05848 −0.529239 0.848473i \(-0.677522\pi\)
−0.529239 + 0.848473i \(0.677522\pi\)
\(42\) 0 0
\(43\) −48.9644 −0.173651 −0.0868256 0.996224i \(-0.527672\pi\)
−0.0868256 + 0.996224i \(0.527672\pi\)
\(44\) 18.1001 31.3503i 0.0620158 0.107414i
\(45\) 0 0
\(46\) 130.010 + 225.184i 0.416715 + 0.721772i
\(47\) −121.813 + 210.986i −0.378048 + 0.654798i −0.990778 0.135494i \(-0.956738\pi\)
0.612730 + 0.790292i \(0.290071\pi\)
\(48\) 0 0
\(49\) 281.212 + 196.390i 0.819859 + 0.572565i
\(50\) 249.275 0.705056
\(51\) 0 0
\(52\) −11.2043 19.4064i −0.0298799 0.0517535i
\(53\) −243.524 421.796i −0.631143 1.09317i −0.987318 0.158752i \(-0.949253\pi\)
0.356176 0.934419i \(-0.384081\pi\)
\(54\) 0 0
\(55\) −5.44941 −0.0133600
\(56\) 141.332 + 44.4660i 0.337255 + 0.106107i
\(57\) 0 0
\(58\) −50.2607 + 87.0541i −0.113785 + 0.197082i
\(59\) −44.7885 77.5759i −0.0988299 0.171178i 0.812371 0.583141i \(-0.198177\pi\)
−0.911201 + 0.411963i \(0.864843\pi\)
\(60\) 0 0
\(61\) −339.433 + 587.916i −0.712459 + 1.23402i 0.251473 + 0.967864i \(0.419085\pi\)
−0.963931 + 0.266151i \(0.914248\pi\)
\(62\) 497.150 1.01836
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −1.68664 + 2.92134i −0.00321849 + 0.00557458i
\(66\) 0 0
\(67\) 350.562 + 607.191i 0.639223 + 1.10717i 0.985604 + 0.169073i \(0.0540773\pi\)
−0.346380 + 0.938094i \(0.612589\pi\)
\(68\) −26.4659 + 45.8402i −0.0471979 + 0.0817491i
\(69\) 0 0
\(70\) −4.84082 21.7719i −0.00826555 0.0371749i
\(71\) 376.105 0.628669 0.314334 0.949312i \(-0.398219\pi\)
0.314334 + 0.949312i \(0.398219\pi\)
\(72\) 0 0
\(73\) 134.482 + 232.929i 0.215615 + 0.373456i 0.953463 0.301511i \(-0.0974911\pi\)
−0.737848 + 0.674967i \(0.764158\pi\)
\(74\) 30.2352 + 52.3689i 0.0474969 + 0.0822671i
\(75\) 0 0
\(76\) 198.507 0.299609
\(77\) −36.3783 163.614i −0.0538401 0.242150i
\(78\) 0 0
\(79\) −19.6704 + 34.0701i −0.0280138 + 0.0485213i −0.879692 0.475543i \(-0.842252\pi\)
0.851679 + 0.524064i \(0.175585\pi\)
\(80\) −4.81712 8.34351i −0.00673214 0.0116604i
\(81\) 0 0
\(82\) −277.880 + 481.303i −0.374228 + 0.648183i
\(83\) −491.595 −0.650115 −0.325058 0.945694i \(-0.605384\pi\)
−0.325058 + 0.945694i \(0.605384\pi\)
\(84\) 0 0
\(85\) 7.96808 0.0101678
\(86\) −48.9644 + 84.8089i −0.0613950 + 0.106339i
\(87\) 0 0
\(88\) −36.2002 62.7006i −0.0438518 0.0759535i
\(89\) 342.378 593.015i 0.407775 0.706286i −0.586865 0.809685i \(-0.699638\pi\)
0.994640 + 0.103398i \(0.0329716\pi\)
\(90\) 0 0
\(91\) −98.9703 31.1381i −0.114010 0.0358699i
\(92\) 520.039 0.589324
\(93\) 0 0
\(94\) 243.626 + 421.972i 0.267320 + 0.463012i
\(95\) −14.9411 25.8788i −0.0161361 0.0279485i
\(96\) 0 0
\(97\) −328.527 −0.343885 −0.171942 0.985107i \(-0.555004\pi\)
−0.171942 + 0.985107i \(0.555004\pi\)
\(98\) 621.369 290.683i 0.640487 0.299627i
\(99\) 0 0
\(100\) 249.275 431.757i 0.249275 0.431757i
\(101\) −189.567 328.339i −0.186758 0.323475i 0.757409 0.652940i \(-0.226465\pi\)
−0.944168 + 0.329466i \(0.893131\pi\)
\(102\) 0 0
\(103\) 130.161 225.446i 0.124516 0.215669i −0.797027 0.603943i \(-0.793595\pi\)
0.921544 + 0.388274i \(0.126929\pi\)
\(104\) −44.8171 −0.0422565
\(105\) 0 0
\(106\) −974.095 −0.892571
\(107\) 544.146 942.488i 0.491631 0.851530i −0.508322 0.861167i \(-0.669734\pi\)
0.999954 + 0.00963652i \(0.00306745\pi\)
\(108\) 0 0
\(109\) −251.781 436.097i −0.221250 0.383216i 0.733938 0.679217i \(-0.237680\pi\)
−0.955188 + 0.296001i \(0.904347\pi\)
\(110\) −5.44941 + 9.43865i −0.00472346 + 0.00818127i
\(111\) 0 0
\(112\) 218.349 200.328i 0.184215 0.169011i
\(113\) −1280.25 −1.06580 −0.532901 0.846178i \(-0.678898\pi\)
−0.532901 + 0.846178i \(0.678898\pi\)
\(114\) 0 0
\(115\) −39.1421 67.7961i −0.0317393 0.0549741i
\(116\) 100.521 + 174.108i 0.0804584 + 0.139358i
\(117\) 0 0
\(118\) −179.154 −0.139767
\(119\) 53.1921 + 239.235i 0.0409757 + 0.184291i
\(120\) 0 0
\(121\) 624.548 1081.75i 0.469232 0.812734i
\(122\) 678.867 + 1175.83i 0.503785 + 0.872580i
\(123\) 0 0
\(124\) 497.150 861.089i 0.360043 0.623613i
\(125\) −150.317 −0.107558
\(126\) 0 0
\(127\) −920.069 −0.642857 −0.321429 0.946934i \(-0.604163\pi\)
−0.321429 + 0.946934i \(0.604163\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 3.37328 + 5.84269i 0.00227581 + 0.00394183i
\(131\) −1392.23 + 2411.42i −0.928551 + 1.60830i −0.142802 + 0.989751i \(0.545611\pi\)
−0.785749 + 0.618545i \(0.787722\pi\)
\(132\) 0 0
\(133\) 677.248 621.353i 0.441540 0.405099i
\(134\) 1402.25 0.903998
\(135\) 0 0
\(136\) 52.9317 + 91.6804i 0.0333740 + 0.0578054i
\(137\) −1207.94 2092.22i −0.753295 1.30475i −0.946217 0.323532i \(-0.895130\pi\)
0.192922 0.981214i \(-0.438204\pi\)
\(138\) 0 0
\(139\) −94.5986 −0.0577248 −0.0288624 0.999583i \(-0.509188\pi\)
−0.0288624 + 0.999583i \(0.509188\pi\)
\(140\) −42.5509 13.3874i −0.0256872 0.00808172i
\(141\) 0 0
\(142\) 376.105 651.433i 0.222268 0.384979i
\(143\) 25.3498 + 43.9072i 0.0148242 + 0.0256763i
\(144\) 0 0
\(145\) 15.1320 26.2094i 0.00866651 0.0150108i
\(146\) 537.926 0.304925
\(147\) 0 0
\(148\) 120.941 0.0671708
\(149\) −1172.33 + 2030.53i −0.644569 + 1.11643i 0.339831 + 0.940486i \(0.389630\pi\)
−0.984401 + 0.175941i \(0.943703\pi\)
\(150\) 0 0
\(151\) 113.816 + 197.135i 0.0613391 + 0.106242i 0.895064 0.445937i \(-0.147130\pi\)
−0.833725 + 0.552180i \(0.813796\pi\)
\(152\) 198.507 343.824i 0.105928 0.183472i
\(153\) 0 0
\(154\) −319.766 100.605i −0.167321 0.0526427i
\(155\) −149.677 −0.0775635
\(156\) 0 0
\(157\) −172.605 298.961i −0.0877414 0.151973i 0.818815 0.574058i \(-0.194632\pi\)
−0.906556 + 0.422085i \(0.861298\pi\)
\(158\) 39.3408 + 68.1402i 0.0198088 + 0.0343098i
\(159\) 0 0
\(160\) −19.2685 −0.00952068
\(161\) 1774.22 1627.79i 0.868499 0.796820i
\(162\) 0 0
\(163\) 1645.72 2850.47i 0.790813 1.36973i −0.134651 0.990893i \(-0.542991\pi\)
0.925464 0.378836i \(-0.123675\pi\)
\(164\) 555.760 + 962.605i 0.264619 + 0.458334i
\(165\) 0 0
\(166\) −491.595 + 851.468i −0.229850 + 0.398113i
\(167\) −3657.31 −1.69468 −0.847338 0.531054i \(-0.821796\pi\)
−0.847338 + 0.531054i \(0.821796\pi\)
\(168\) 0 0
\(169\) −2165.62 −0.985715
\(170\) 7.96808 13.8011i 0.00359485 0.00622646i
\(171\) 0 0
\(172\) 97.9289 + 169.618i 0.0434128 + 0.0751932i
\(173\) −1325.61 + 2296.03i −0.582569 + 1.00904i 0.412605 + 0.910910i \(0.364619\pi\)
−0.995174 + 0.0981286i \(0.968714\pi\)
\(174\) 0 0
\(175\) −501.002 2253.29i −0.216413 0.973331i
\(176\) −144.801 −0.0620158
\(177\) 0 0
\(178\) −684.755 1186.03i −0.288340 0.499420i
\(179\) −700.967 1214.11i −0.292697 0.506965i 0.681750 0.731585i \(-0.261219\pi\)
−0.974446 + 0.224620i \(0.927886\pi\)
\(180\) 0 0
\(181\) −2.91675 −0.00119779 −0.000598897 1.00000i \(-0.500191\pi\)
−0.000598897 1.00000i \(0.500191\pi\)
\(182\) −152.903 + 140.284i −0.0622743 + 0.0571347i
\(183\) 0 0
\(184\) 520.039 900.734i 0.208358 0.360886i
\(185\) −9.10293 15.7667i −0.00361762 0.00626591i
\(186\) 0 0
\(187\) 59.8794 103.714i 0.0234161 0.0405579i
\(188\) 974.503 0.378048
\(189\) 0 0
\(190\) −59.7645 −0.0228199
\(191\) −126.055 + 218.334i −0.0477540 + 0.0827124i −0.888914 0.458073i \(-0.848540\pi\)
0.841160 + 0.540786i \(0.181873\pi\)
\(192\) 0 0
\(193\) −986.702 1709.02i −0.368002 0.637398i 0.621251 0.783612i \(-0.286625\pi\)
−0.989253 + 0.146213i \(0.953291\pi\)
\(194\) −328.527 + 569.025i −0.121582 + 0.210586i
\(195\) 0 0
\(196\) 117.891 1366.93i 0.0429631 0.498151i
\(197\) 1788.56 0.646850 0.323425 0.946254i \(-0.395166\pi\)
0.323425 + 0.946254i \(0.395166\pi\)
\(198\) 0 0
\(199\) −461.066 798.589i −0.164242 0.284475i 0.772144 0.635447i \(-0.219184\pi\)
−0.936386 + 0.350973i \(0.885851\pi\)
\(200\) −498.550 863.513i −0.176264 0.305298i
\(201\) 0 0
\(202\) −758.266 −0.264116
\(203\) 887.931 + 279.361i 0.306998 + 0.0965878i
\(204\) 0 0
\(205\) 83.6615 144.906i 0.0285033 0.0493691i
\(206\) −260.323 450.892i −0.0880464 0.152501i
\(207\) 0 0
\(208\) −44.8171 + 77.6255i −0.0149399 + 0.0258767i
\(209\) −449.125 −0.148644
\(210\) 0 0
\(211\) −5130.61 −1.67396 −0.836981 0.547232i \(-0.815682\pi\)
−0.836981 + 0.547232i \(0.815682\pi\)
\(212\) −974.095 + 1687.18i −0.315571 + 0.546586i
\(213\) 0 0
\(214\) −1088.29 1884.98i −0.347636 0.602123i
\(215\) 14.7417 25.5334i 0.00467618 0.00809938i
\(216\) 0 0
\(217\) −999.190 4493.93i −0.312578 1.40584i
\(218\) −1007.12 −0.312895
\(219\) 0 0
\(220\) 10.8988 + 18.8773i 0.00333999 + 0.00578503i
\(221\) −37.0664 64.2008i −0.0112821 0.0195412i
\(222\) 0 0
\(223\) 3777.82 1.13445 0.567223 0.823564i \(-0.308018\pi\)
0.567223 + 0.823564i \(0.308018\pi\)
\(224\) −128.630 578.521i −0.0383680 0.172563i
\(225\) 0 0
\(226\) −1280.25 + 2217.45i −0.376818 + 0.652667i
\(227\) 1661.63 + 2878.02i 0.485842 + 0.841502i 0.999868 0.0162724i \(-0.00517988\pi\)
−0.514026 + 0.857775i \(0.671847\pi\)
\(228\) 0 0
\(229\) 477.230 826.587i 0.137713 0.238526i −0.788918 0.614499i \(-0.789358\pi\)
0.926631 + 0.375973i \(0.122692\pi\)
\(230\) −156.568 −0.0448861
\(231\) 0 0
\(232\) 402.086 0.113785
\(233\) 2002.14 3467.80i 0.562937 0.975035i −0.434301 0.900768i \(-0.643005\pi\)
0.997238 0.0742678i \(-0.0236619\pi\)
\(234\) 0 0
\(235\) −73.3485 127.043i −0.0203605 0.0352655i
\(236\) −179.154 + 310.304i −0.0494150 + 0.0855892i
\(237\) 0 0
\(238\) 467.560 + 147.104i 0.127342 + 0.0400644i
\(239\) 2768.29 0.749230 0.374615 0.927181i \(-0.377775\pi\)
0.374615 + 0.927181i \(0.377775\pi\)
\(240\) 0 0
\(241\) 3568.69 + 6181.15i 0.953857 + 1.65213i 0.736962 + 0.675935i \(0.236260\pi\)
0.216896 + 0.976195i \(0.430407\pi\)
\(242\) −1249.10 2163.50i −0.331797 0.574690i
\(243\) 0 0
\(244\) 2715.47 0.712459
\(245\) −187.076 + 87.5161i −0.0487830 + 0.0228212i
\(246\) 0 0
\(247\) −139.008 + 240.769i −0.0358092 + 0.0620233i
\(248\) −994.300 1722.18i −0.254589 0.440961i
\(249\) 0 0
\(250\) −150.317 + 260.356i −0.0380275 + 0.0658655i
\(251\) 3925.58 0.987172 0.493586 0.869697i \(-0.335686\pi\)
0.493586 + 0.869697i \(0.335686\pi\)
\(252\) 0 0
\(253\) −1176.60 −0.292379
\(254\) −920.069 + 1593.61i −0.227284 + 0.393668i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1123.14 1945.33i 0.272605 0.472165i −0.696923 0.717146i \(-0.745448\pi\)
0.969528 + 0.244980i \(0.0787815\pi\)
\(258\) 0 0
\(259\) 412.615 378.561i 0.0989910 0.0908210i
\(260\) 13.4931 0.00321849
\(261\) 0 0
\(262\) 2784.47 + 4822.84i 0.656584 + 1.13724i
\(263\) 641.744 + 1111.53i 0.150463 + 0.260609i 0.931398 0.364003i \(-0.118590\pi\)
−0.780935 + 0.624612i \(0.785257\pi\)
\(264\) 0 0
\(265\) 293.271 0.0679830
\(266\) −398.967 1794.38i −0.0919632 0.413611i
\(267\) 0 0
\(268\) 1402.25 2428.76i 0.319612 0.553583i
\(269\) −2360.33 4088.22i −0.534989 0.926629i −0.999164 0.0408850i \(-0.986982\pi\)
0.464174 0.885744i \(-0.346351\pi\)
\(270\) 0 0
\(271\) −2568.52 + 4448.81i −0.575744 + 0.997217i 0.420217 + 0.907424i \(0.361954\pi\)
−0.995960 + 0.0897933i \(0.971379\pi\)
\(272\) 211.727 0.0471979
\(273\) 0 0
\(274\) −4831.77 −1.06532
\(275\) −563.988 + 976.855i −0.123672 + 0.214206i
\(276\) 0 0
\(277\) 2885.47 + 4997.79i 0.625889 + 1.08407i 0.988368 + 0.152080i \(0.0485971\pi\)
−0.362479 + 0.931992i \(0.618070\pi\)
\(278\) −94.5986 + 163.850i −0.0204088 + 0.0353491i
\(279\) 0 0
\(280\) −65.7385 + 60.3130i −0.0140308 + 0.0128728i
\(281\) 3594.63 0.763123 0.381562 0.924343i \(-0.375386\pi\)
0.381562 + 0.924343i \(0.375386\pi\)
\(282\) 0 0
\(283\) 3765.14 + 6521.41i 0.790863 + 1.36982i 0.925433 + 0.378911i \(0.123701\pi\)
−0.134570 + 0.990904i \(0.542965\pi\)
\(284\) −752.211 1302.87i −0.157167 0.272222i
\(285\) 0 0
\(286\) 101.399 0.0209646
\(287\) 4909.18 + 1544.53i 1.00968 + 0.317667i
\(288\) 0 0
\(289\) 2368.94 4103.13i 0.482179 0.835158i
\(290\) −30.2640 52.4188i −0.00612815 0.0106143i
\(291\) 0 0
\(292\) 537.926 931.716i 0.107807 0.186728i
\(293\) −4469.73 −0.891209 −0.445605 0.895230i \(-0.647011\pi\)
−0.445605 + 0.895230i \(0.647011\pi\)
\(294\) 0 0
\(295\) 53.9379 0.0106454
\(296\) 120.941 209.476i 0.0237485 0.0411335i
\(297\) 0 0
\(298\) 2344.66 + 4061.06i 0.455779 + 0.789433i
\(299\) −364.167 + 630.755i −0.0704358 + 0.121998i
\(300\) 0 0
\(301\) 865.031 + 272.156i 0.165646 + 0.0521157i
\(302\) 455.264 0.0867466
\(303\) 0 0
\(304\) −397.014 687.648i −0.0749023 0.129735i
\(305\) −204.387 354.008i −0.0383710 0.0664605i
\(306\) 0 0
\(307\) 2811.31 0.522638 0.261319 0.965252i \(-0.415843\pi\)
0.261319 + 0.965252i \(0.415843\pi\)
\(308\) −494.019 + 453.246i −0.0913939 + 0.0838509i
\(309\) 0 0
\(310\) −149.677 + 259.248i −0.0274229 + 0.0474978i
\(311\) 2580.95 + 4470.33i 0.470585 + 0.815077i 0.999434 0.0336386i \(-0.0107095\pi\)
−0.528849 + 0.848716i \(0.677376\pi\)
\(312\) 0 0
\(313\) −3358.55 + 5817.18i −0.606506 + 1.05050i 0.385306 + 0.922789i \(0.374096\pi\)
−0.991812 + 0.127710i \(0.959237\pi\)
\(314\) −690.421 −0.124085
\(315\) 0 0
\(316\) 157.363 0.0280138
\(317\) 4091.97 7087.51i 0.725010 1.25575i −0.233960 0.972246i \(-0.575168\pi\)
0.958970 0.283508i \(-0.0914982\pi\)
\(318\) 0 0
\(319\) −227.431 393.922i −0.0399175 0.0691392i
\(320\) −19.2685 + 33.3740i −0.00336607 + 0.00583020i
\(321\) 0 0
\(322\) −1045.19 4700.84i −0.180889 0.813563i
\(323\) 656.707 0.113127
\(324\) 0 0
\(325\) 349.118 + 604.690i 0.0595864 + 0.103207i
\(326\) −3291.44 5700.93i −0.559189 0.968545i
\(327\) 0 0
\(328\) 2223.04 0.374228
\(329\) 3324.72 3050.32i 0.557137 0.511155i
\(330\) 0 0
\(331\) −1774.96 + 3074.32i −0.294745 + 0.510514i −0.974926 0.222531i \(-0.928568\pi\)
0.680180 + 0.733045i \(0.261902\pi\)
\(332\) 983.190 + 1702.94i 0.162529 + 0.281508i
\(333\) 0 0
\(334\) −3657.31 + 6334.64i −0.599158 + 1.03777i
\(335\) −422.175 −0.0688534
\(336\) 0 0
\(337\) −7152.10 −1.15608 −0.578041 0.816008i \(-0.696183\pi\)
−0.578041 + 0.816008i \(0.696183\pi\)
\(338\) −2165.62 + 3750.96i −0.348503 + 0.603625i
\(339\) 0 0
\(340\) −15.9362 27.6023i −0.00254194 0.00440277i
\(341\) −1124.81 + 1948.22i −0.178627 + 0.309391i
\(342\) 0 0
\(343\) −3876.45 5032.57i −0.610229 0.792225i
\(344\) 391.715 0.0613950
\(345\) 0 0
\(346\) 2651.22 + 4592.05i 0.411938 + 0.713498i
\(347\) 3138.58 + 5436.18i 0.485555 + 0.841007i 0.999862 0.0165996i \(-0.00528406\pi\)
−0.514307 + 0.857606i \(0.671951\pi\)
\(348\) 0 0
\(349\) 5735.43 0.879686 0.439843 0.898075i \(-0.355034\pi\)
0.439843 + 0.898075i \(0.355034\pi\)
\(350\) −4403.82 1385.53i −0.672554 0.211599i
\(351\) 0 0
\(352\) −144.801 + 250.802i −0.0219259 + 0.0379767i
\(353\) −1308.40 2266.21i −0.197278 0.341695i 0.750367 0.661021i \(-0.229877\pi\)
−0.947645 + 0.319326i \(0.896543\pi\)
\(354\) 0 0
\(355\) −113.234 + 196.127i −0.0169291 + 0.0293221i
\(356\) −2739.02 −0.407775
\(357\) 0 0
\(358\) −2803.87 −0.413936
\(359\) −5826.07 + 10091.0i −0.856513 + 1.48352i 0.0187217 + 0.999825i \(0.494040\pi\)
−0.875234 + 0.483699i \(0.839293\pi\)
\(360\) 0 0
\(361\) 2198.09 + 3807.21i 0.320469 + 0.555068i
\(362\) −2.91675 + 5.05197i −0.000423484 + 0.000733496i
\(363\) 0 0
\(364\) 90.0751 + 405.119i 0.0129704 + 0.0583352i
\(365\) −161.954 −0.0232248
\(366\) 0 0
\(367\) 6237.16 + 10803.1i 0.887132 + 1.53656i 0.843251 + 0.537520i \(0.180639\pi\)
0.0438807 + 0.999037i \(0.486028\pi\)
\(368\) −1040.08 1801.47i −0.147331 0.255185i
\(369\) 0 0
\(370\) −36.4117 −0.00511609
\(371\) 1957.77 + 8805.23i 0.273969 + 1.23220i
\(372\) 0 0
\(373\) −963.950 + 1669.61i −0.133811 + 0.231767i −0.925143 0.379620i \(-0.876055\pi\)
0.791332 + 0.611387i \(0.209388\pi\)
\(374\) −119.759 207.428i −0.0165577 0.0286788i
\(375\) 0 0
\(376\) 974.503 1687.89i 0.133660 0.231506i
\(377\) −281.567 −0.0384654
\(378\) 0 0
\(379\) −2946.20 −0.399304 −0.199652 0.979867i \(-0.563981\pi\)
−0.199652 + 0.979867i \(0.563981\pi\)
\(380\) −59.7645 + 103.515i −0.00806804 + 0.0139743i
\(381\) 0 0
\(382\) 252.110 + 436.667i 0.0337672 + 0.0584865i
\(383\) −1558.73 + 2699.80i −0.207956 + 0.360191i −0.951071 0.308974i \(-0.900015\pi\)
0.743114 + 0.669164i \(0.233348\pi\)
\(384\) 0 0
\(385\) 96.2720 + 30.2891i 0.0127441 + 0.00400955i
\(386\) −3946.81 −0.520433
\(387\) 0 0
\(388\) 657.053 + 1138.05i 0.0859712 + 0.148906i
\(389\) −918.419 1590.75i −0.119706 0.207337i 0.799945 0.600073i \(-0.204862\pi\)
−0.919651 + 0.392736i \(0.871529\pi\)
\(390\) 0 0
\(391\) 1720.41 0.222519
\(392\) −2249.69 1571.12i −0.289864 0.202432i
\(393\) 0 0
\(394\) 1788.56 3097.87i 0.228696 0.396113i
\(395\) −11.8443 20.5150i −0.00150874 0.00261322i
\(396\) 0 0
\(397\) −677.402 + 1173.30i −0.0856369 + 0.148327i −0.905662 0.423999i \(-0.860626\pi\)
0.820026 + 0.572327i \(0.193959\pi\)
\(398\) −1844.26 −0.232273
\(399\) 0 0
\(400\) −1994.20 −0.249275
\(401\) 6128.83 10615.4i 0.763240 1.32197i −0.177932 0.984043i \(-0.556941\pi\)
0.941172 0.337928i \(-0.109726\pi\)
\(402\) 0 0
\(403\) 696.276 + 1205.98i 0.0860644 + 0.149068i
\(404\) −758.266 + 1313.36i −0.0933791 + 0.161737i
\(405\) 0 0
\(406\) 1371.80 1258.58i 0.167688 0.153848i
\(407\) −273.630 −0.0333252
\(408\) 0 0
\(409\) 3807.82 + 6595.34i 0.460354 + 0.797356i 0.998978 0.0451896i \(-0.0143892\pi\)
−0.538625 + 0.842546i \(0.681056\pi\)
\(410\) −167.323 289.812i −0.0201549 0.0349092i
\(411\) 0 0
\(412\) −1041.29 −0.124516
\(413\) 360.070 + 1619.44i 0.0429005 + 0.192948i
\(414\) 0 0
\(415\) 148.005 256.352i 0.0175067 0.0303224i
\(416\) 89.6342 + 155.251i 0.0105641 + 0.0182976i
\(417\) 0 0
\(418\) −449.125 + 777.907i −0.0525536 + 0.0910255i
\(419\) 8575.60 0.999870 0.499935 0.866063i \(-0.333357\pi\)
0.499935 + 0.866063i \(0.333357\pi\)
\(420\) 0 0
\(421\) −14776.6 −1.71061 −0.855303 0.518128i \(-0.826629\pi\)
−0.855303 + 0.518128i \(0.826629\pi\)
\(422\) −5130.61 + 8886.48i −0.591835 + 1.02509i
\(423\) 0 0
\(424\) 1948.19 + 3374.37i 0.223143 + 0.386494i
\(425\) 824.659 1428.35i 0.0941220 0.163024i
\(426\) 0 0
\(427\) 9264.39 8499.77i 1.04997 0.963309i
\(428\) −4353.17 −0.491631
\(429\) 0 0
\(430\) −29.4835 51.0669i −0.00330656 0.00572712i
\(431\) 8168.58 + 14148.4i 0.912916 + 1.58122i 0.809924 + 0.586534i \(0.199508\pi\)
0.102992 + 0.994682i \(0.467159\pi\)
\(432\) 0 0
\(433\) 6150.96 0.682670 0.341335 0.939942i \(-0.389121\pi\)
0.341335 + 0.939942i \(0.389121\pi\)
\(434\) −8782.91 2763.28i −0.971412 0.305626i
\(435\) 0 0
\(436\) −1007.12 + 1744.39i −0.110625 + 0.191608i
\(437\) −3225.98 5587.56i −0.353134 0.611646i
\(438\) 0 0
\(439\) −1299.24 + 2250.35i −0.141252 + 0.244655i −0.927968 0.372659i \(-0.878446\pi\)
0.786717 + 0.617314i \(0.211779\pi\)
\(440\) 43.5952 0.00472346
\(441\) 0 0
\(442\) −148.265 −0.0159554
\(443\) 4915.60 8514.08i 0.527195 0.913129i −0.472303 0.881436i \(-0.656577\pi\)
0.999498 0.0316922i \(-0.0100896\pi\)
\(444\) 0 0
\(445\) 206.159 + 357.079i 0.0219616 + 0.0380385i
\(446\) 3777.82 6543.38i 0.401088 0.694704i
\(447\) 0 0
\(448\) −1130.66 355.728i −0.119238 0.0375146i
\(449\) −13649.3 −1.43463 −0.717317 0.696747i \(-0.754630\pi\)
−0.717317 + 0.696747i \(0.754630\pi\)
\(450\) 0 0
\(451\) −1257.42 2177.91i −0.131285 0.227392i
\(452\) 2560.49 + 4434.91i 0.266450 + 0.461505i
\(453\) 0 0
\(454\) 6646.51 0.687084
\(455\) 46.0346 42.2352i 0.00474315 0.00435169i
\(456\) 0 0
\(457\) 6155.95 10662.4i 0.630117 1.09139i −0.357411 0.933947i \(-0.616340\pi\)
0.987527 0.157447i \(-0.0503263\pi\)
\(458\) −954.461 1653.17i −0.0973778 0.168663i
\(459\) 0 0
\(460\) −156.568 + 271.184i −0.0158696 + 0.0274870i
\(461\) −6291.03 −0.635580 −0.317790 0.948161i \(-0.602941\pi\)
−0.317790 + 0.948161i \(0.602941\pi\)
\(462\) 0 0
\(463\) −5964.10 −0.598651 −0.299326 0.954151i \(-0.596762\pi\)
−0.299326 + 0.954151i \(0.596762\pi\)
\(464\) 402.086 696.433i 0.0402292 0.0696790i
\(465\) 0 0
\(466\) −4004.27 6935.60i −0.398057 0.689454i
\(467\) −4290.20 + 7430.85i −0.425111 + 0.736314i −0.996431 0.0844134i \(-0.973098\pi\)
0.571320 + 0.820728i \(0.306432\pi\)
\(468\) 0 0
\(469\) −2818.29 12675.5i −0.277477 1.24797i
\(470\) −293.394 −0.0287942
\(471\) 0 0
\(472\) 358.308 + 620.608i 0.0349417 + 0.0605207i
\(473\) −221.565 383.762i −0.0215382 0.0373053i
\(474\) 0 0
\(475\) −6185.35 −0.597480
\(476\) 722.351 662.733i 0.0695565 0.0638158i
\(477\) 0 0
\(478\) 2768.29 4794.82i 0.264893 0.458808i
\(479\) 7089.88 + 12280.0i 0.676294 + 1.17138i 0.976089 + 0.217372i \(0.0697486\pi\)
−0.299794 + 0.954004i \(0.596918\pi\)
\(480\) 0 0
\(481\) −84.6910 + 146.689i −0.00802822 + 0.0139053i
\(482\) 14274.8 1.34896
\(483\) 0 0
\(484\) −4996.39 −0.469232
\(485\) 98.9096 171.316i 0.00926031 0.0160393i
\(486\) 0 0
\(487\) −2794.43 4840.09i −0.260016 0.450360i 0.706230 0.707982i \(-0.250394\pi\)
−0.966246 + 0.257622i \(0.917061\pi\)
\(488\) 2715.47 4703.33i 0.251892 0.436290i
\(489\) 0 0
\(490\) −35.4934 + 411.541i −0.00327230 + 0.0379419i
\(491\) 9149.11 0.840924 0.420462 0.907310i \(-0.361868\pi\)
0.420462 + 0.907310i \(0.361868\pi\)
\(492\) 0 0
\(493\) 332.548 + 575.990i 0.0303797 + 0.0526193i
\(494\) 278.016 + 481.538i 0.0253209 + 0.0438571i
\(495\) 0 0
\(496\) −3977.20 −0.360043
\(497\) −6644.47 2090.49i −0.599689 0.188674i
\(498\) 0 0
\(499\) 10709.1 18548.8i 0.960735 1.66404i 0.240075 0.970754i \(-0.422828\pi\)
0.720661 0.693288i \(-0.243839\pi\)
\(500\) 300.634 + 520.713i 0.0268895 + 0.0465740i
\(501\) 0 0
\(502\) 3925.58 6799.30i 0.349018 0.604517i
\(503\) −11552.6 −1.02407 −0.512034 0.858965i \(-0.671108\pi\)
−0.512034 + 0.858965i \(0.671108\pi\)
\(504\) 0 0
\(505\) 228.292 0.0201165
\(506\) −1176.60 + 2037.92i −0.103372 + 0.179045i
\(507\) 0 0
\(508\) 1840.14 + 3187.21i 0.160714 + 0.278365i
\(509\) 9713.19 16823.7i 0.845834 1.46503i −0.0390601 0.999237i \(-0.512436\pi\)
0.884895 0.465791i \(-0.154230\pi\)
\(510\) 0 0
\(511\) −1081.14 4862.53i −0.0935950 0.420950i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −2246.28 3890.66i −0.192761 0.333871i
\(515\) 78.3755 + 135.750i 0.00670609 + 0.0116153i
\(516\) 0 0
\(517\) −2204.83 −0.187559
\(518\) −243.072 1093.23i −0.0206177 0.0927294i
\(519\) 0 0
\(520\) 13.4931 23.3707i 0.00113791 0.00197091i
\(521\) −3458.28 5989.91i −0.290806 0.503691i 0.683195 0.730236i \(-0.260590\pi\)
−0.974001 + 0.226546i \(0.927257\pi\)
\(522\) 0 0
\(523\) −7971.04 + 13806.2i −0.666442 + 1.15431i 0.312450 + 0.949934i \(0.398850\pi\)
−0.978892 + 0.204377i \(0.934483\pi\)
\(524\) 11137.9 0.928551
\(525\) 0 0
\(526\) 2566.98 0.212786
\(527\) 1644.69 2848.68i 0.135946 0.235466i
\(528\) 0 0
\(529\) −2367.78 4101.11i −0.194606 0.337068i
\(530\) 293.271 507.961i 0.0240356 0.0416309i
\(531\) 0 0
\(532\) −3506.93 1103.35i −0.285798 0.0899179i
\(533\) −1556.72 −0.126509
\(534\) 0 0
\(535\) 327.652 + 567.510i 0.0264778 + 0.0458610i
\(536\) −2804.49 4857.53i −0.225999 0.391443i
\(537\) 0 0
\(538\) −9441.34 −0.756589
\(539\) −266.729 + 3092.69i −0.0213151 + 0.247146i
\(540\) 0 0
\(541\) 8881.02 15382.4i 0.705776 1.22244i −0.260634 0.965438i \(-0.583932\pi\)
0.966411 0.257003i \(-0.0827350\pi\)
\(542\) 5137.04 + 8897.62i 0.407112 + 0.705139i
\(543\) 0 0
\(544\) 211.727 366.722i 0.0166870 0.0289027i
\(545\) 303.215 0.0238317
\(546\) 0 0
\(547\) −9998.28 −0.781527 −0.390764 0.920491i \(-0.627789\pi\)
−0.390764 + 0.920491i \(0.627789\pi\)
\(548\) −4831.77 + 8368.87i −0.376648 + 0.652373i
\(549\) 0 0
\(550\) 1127.98 + 1953.71i 0.0874492 + 0.151466i
\(551\) 1247.14 2160.10i 0.0964243 0.167012i
\(552\) 0 0
\(553\) 536.877 492.567i 0.0412845 0.0378772i
\(554\) 11541.9 0.885141
\(555\) 0 0
\(556\) 189.197 + 327.699i 0.0144312 + 0.0249956i
\(557\) 1558.09 + 2698.69i 0.118525 + 0.205291i 0.919183 0.393830i \(-0.128850\pi\)
−0.800658 + 0.599121i \(0.795517\pi\)
\(558\) 0 0
\(559\) −274.306 −0.0207547
\(560\) 38.7266 + 174.175i 0.00292231 + 0.0131433i
\(561\) 0 0
\(562\) 3594.63 6226.08i 0.269805 0.467316i
\(563\) −11072.6 19178.4i −0.828875 1.43565i −0.898922 0.438109i \(-0.855648\pi\)
0.0700470 0.997544i \(-0.477685\pi\)
\(564\) 0 0
\(565\) 385.444 667.609i 0.0287005 0.0497107i
\(566\) 15060.6 1.11845
\(567\) 0 0
\(568\) −3008.84 −0.222268
\(569\) 10360.5 17944.9i 0.763331 1.32213i −0.177794 0.984068i \(-0.556896\pi\)
0.941125 0.338060i \(-0.109771\pi\)
\(570\) 0 0
\(571\) 1524.28 + 2640.12i 0.111715 + 0.193495i 0.916462 0.400123i \(-0.131032\pi\)
−0.804747 + 0.593618i \(0.797699\pi\)
\(572\) 101.399 175.629i 0.00741210 0.0128381i
\(573\) 0 0
\(574\) 7584.37 6958.41i 0.551508 0.505991i
\(575\) −16204.1 −1.17523
\(576\) 0 0
\(577\) −5648.14 9782.86i −0.407513 0.705834i 0.587097 0.809516i \(-0.300271\pi\)
−0.994610 + 0.103683i \(0.966937\pi\)
\(578\) −4737.89 8206.27i −0.340952 0.590546i
\(579\) 0 0
\(580\) −121.056 −0.00866651
\(581\) 8684.77 + 2732.41i 0.620147 + 0.195111i
\(582\) 0 0
\(583\) 2203.90 3817.27i 0.156563 0.271175i
\(584\) −1075.85 1863.43i −0.0762314 0.132037i
\(585\) 0 0
\(586\) −4469.73 + 7741.79i −0.315090 + 0.545752i
\(587\) −5531.46 −0.388940 −0.194470 0.980908i \(-0.562299\pi\)
−0.194470 + 0.980908i \(0.562299\pi\)
\(588\) 0 0
\(589\) −12336.0 −0.862978
\(590\) 53.9379 93.4233i 0.00376371 0.00651894i
\(591\) 0 0
\(592\) −241.882 418.951i −0.0167927 0.0290858i
\(593\) −2880.05 + 4988.40i −0.199443 + 0.345445i −0.948348 0.317232i \(-0.897247\pi\)
0.748905 + 0.662677i \(0.230580\pi\)
\(594\) 0 0
\(595\) −140.768 44.2886i −0.00969906 0.00305152i
\(596\) 9378.62 0.644569
\(597\) 0 0
\(598\) 728.333 + 1261.51i 0.0498056 + 0.0862659i
\(599\) 8560.31 + 14826.9i 0.583915 + 1.01137i 0.995010 + 0.0997775i \(0.0318131\pi\)
−0.411095 + 0.911592i \(0.634854\pi\)
\(600\) 0 0
\(601\) −2611.63 −0.177255 −0.0886277 0.996065i \(-0.528248\pi\)
−0.0886277 + 0.996065i \(0.528248\pi\)
\(602\) 1336.42 1226.12i 0.0904791 0.0830116i
\(603\) 0 0
\(604\) 455.264 788.540i 0.0306696 0.0531212i
\(605\) 376.066 + 651.365i 0.0252715 + 0.0437715i
\(606\) 0 0
\(607\) 13815.8 23929.7i 0.923831 1.60012i 0.130402 0.991461i \(-0.458373\pi\)
0.793430 0.608662i \(-0.208293\pi\)
\(608\) −1588.06 −0.105928
\(609\) 0 0
\(610\) −817.547 −0.0542647
\(611\) −682.413 + 1181.97i −0.0451841 + 0.0782611i
\(612\) 0 0
\(613\) −823.643 1426.59i −0.0542686 0.0939959i 0.837615 0.546261i \(-0.183949\pi\)
−0.891883 + 0.452265i \(0.850616\pi\)
\(614\) 2811.31 4869.33i 0.184780 0.320049i
\(615\) 0 0
\(616\) 291.026 + 1308.91i 0.0190354 + 0.0856129i
\(617\) −15808.0 −1.03145 −0.515727 0.856753i \(-0.672478\pi\)
−0.515727 + 0.856753i \(0.672478\pi\)
\(618\) 0 0
\(619\) −2005.62 3473.83i −0.130230 0.225566i 0.793535 0.608525i \(-0.208238\pi\)
−0.923765 + 0.382959i \(0.874905\pi\)
\(620\) 299.354 + 518.496i 0.0193909 + 0.0335860i
\(621\) 0 0
\(622\) 10323.8 0.665508
\(623\) −9344.74 + 8573.50i −0.600946 + 0.551348i
\(624\) 0 0
\(625\) −7744.58 + 13414.0i −0.495653 + 0.858497i
\(626\) 6717.10 + 11634.4i 0.428864 + 0.742815i
\(627\) 0 0
\(628\) −690.421 + 1195.84i −0.0438707 + 0.0759863i
\(629\) 400.100 0.0253626
\(630\) 0 0
\(631\) −11682.4 −0.737036 −0.368518 0.929621i \(-0.620135\pi\)
−0.368518 + 0.929621i \(0.620135\pi\)
\(632\) 157.363 272.561i 0.00990438 0.0171549i
\(633\) 0 0
\(634\) −8183.95 14175.0i −0.512659 0.887952i
\(635\) 277.005 479.787i 0.0173112 0.0299839i
\(636\) 0 0
\(637\) 1575.39 + 1100.20i 0.0979892 + 0.0684327i
\(638\) −909.724 −0.0564519
\(639\) 0 0
\(640\) 38.5370 + 66.7480i 0.00238017 + 0.00412257i
\(641\) 5405.96 + 9363.40i 0.333109 + 0.576961i 0.983120 0.182964i \(-0.0585690\pi\)
−0.650011 + 0.759925i \(0.725236\pi\)
\(642\) 0 0
\(643\) −2335.44 −0.143236 −0.0716180 0.997432i \(-0.522816\pi\)
−0.0716180 + 0.997432i \(0.522816\pi\)
\(644\) −9187.28 2890.51i −0.562158 0.176866i
\(645\) 0 0
\(646\) 656.707 1137.45i 0.0399966 0.0692761i
\(647\) −12753.8 22090.2i −0.774965 1.34228i −0.934814 0.355137i \(-0.884434\pi\)
0.159850 0.987141i \(-0.448899\pi\)
\(648\) 0 0
\(649\) 405.338 702.067i 0.0245161 0.0424631i
\(650\) 1396.47 0.0842680
\(651\) 0 0
\(652\) −13165.7 −0.790813
\(653\) 2171.15 3760.54i 0.130113 0.225362i −0.793607 0.608431i \(-0.791799\pi\)
0.923720 + 0.383069i \(0.125133\pi\)
\(654\) 0 0
\(655\) −838.321 1452.01i −0.0500090 0.0866182i
\(656\) 2223.04 3850.42i 0.132310 0.229167i
\(657\) 0 0
\(658\) −1958.59 8808.91i −0.116039 0.521896i
\(659\) 4148.85 0.245245 0.122622 0.992453i \(-0.460870\pi\)
0.122622 + 0.992453i \(0.460870\pi\)
\(660\) 0 0
\(661\) 8975.78 + 15546.5i 0.528165 + 0.914809i 0.999461 + 0.0328337i \(0.0104532\pi\)
−0.471296 + 0.881975i \(0.656213\pi\)
\(662\) 3549.92 + 6148.65i 0.208417 + 0.360988i
\(663\) 0 0
\(664\) 3932.76 0.229850
\(665\) 120.117 + 540.235i 0.00700442 + 0.0315029i
\(666\) 0 0
\(667\) 3267.19 5658.94i 0.189664 0.328508i
\(668\) 7314.61 + 12669.3i 0.423669 + 0.733816i
\(669\) 0 0
\(670\) −422.175 + 731.229i −0.0243434 + 0.0421639i
\(671\) −6143.78 −0.353470
\(672\) 0 0
\(673\) 13667.9 0.782850 0.391425 0.920210i \(-0.371982\pi\)
0.391425 + 0.920210i \(0.371982\pi\)
\(674\) −7152.10 + 12387.8i −0.408737 + 0.707953i
\(675\) 0 0
\(676\) 4331.23 + 7501.91i 0.246429 + 0.426827i
\(677\) 8632.32 14951.6i 0.490054 0.848799i −0.509880 0.860246i \(-0.670310\pi\)
0.999934 + 0.0114463i \(0.00364355\pi\)
\(678\) 0 0
\(679\) 5803.92 + 1826.03i 0.328032 + 0.103206i
\(680\) −63.7447 −0.00359485
\(681\) 0 0
\(682\) 2249.62 + 3896.45i 0.126308 + 0.218772i
\(683\) 9857.82 + 17074.3i 0.552268 + 0.956556i 0.998110 + 0.0614450i \(0.0195709\pi\)
−0.445842 + 0.895112i \(0.647096\pi\)
\(684\) 0 0
\(685\) 1454.70 0.0811406
\(686\) −12593.1 + 1681.64i −0.700885 + 0.0935937i
\(687\) 0 0
\(688\) 391.715 678.471i 0.0217064 0.0375966i
\(689\) −1364.25 2362.96i −0.0754339 0.130655i
\(690\) 0 0
\(691\) −5806.90 + 10057.8i −0.319689 + 0.553717i −0.980423 0.196903i \(-0.936912\pi\)
0.660734 + 0.750620i \(0.270245\pi\)
\(692\) 10604.9 0.582569
\(693\) 0 0
\(694\) 12554.3 0.686679
\(695\) 28.4808 49.3302i 0.00155444 0.00269238i
\(696\) 0 0
\(697\) 1838.58 + 3184.52i 0.0999158 + 0.173059i
\(698\) 5735.43 9934.05i 0.311016 0.538695i
\(699\) 0 0
\(700\) −6803.63 + 6242.11i −0.367361 + 0.337042i
\(701\) −16100.4 −0.867481 −0.433740 0.901038i \(-0.642806\pi\)
−0.433740 + 0.901038i \(0.642806\pi\)
\(702\) 0 0
\(703\) −750.237 1299.45i −0.0402500 0.0697150i
\(704\) 289.602 + 501.605i 0.0155039 + 0.0268536i
\(705\) 0 0
\(706\) −5233.59 −0.278993
\(707\) 1523.99 + 6854.27i 0.0810688 + 0.364613i
\(708\) 0 0
\(709\) −1098.83 + 1903.22i −0.0582049 + 0.100814i −0.893660 0.448745i \(-0.851871\pi\)
0.835455 + 0.549559i \(0.185204\pi\)
\(710\) 226.468 + 392.255i 0.0119707 + 0.0207339i
\(711\) 0 0
\(712\) −2739.02 + 4744.12i −0.144170 + 0.249710i
\(713\) −32317.2 −1.69746
\(714\) 0 0
\(715\) −30.5283 −0.00159678
\(716\) −2803.87 + 4856.44i −0.146348 + 0.253483i
\(717\) 0 0
\(718\) 11652.1 + 20182.1i 0.605646 + 1.04901i
\(719\) −4950.87 + 8575.16i −0.256796 + 0.444784i −0.965382 0.260841i \(-0.916000\pi\)
0.708586 + 0.705625i \(0.249333\pi\)
\(720\) 0 0
\(721\) −3552.58 + 3259.38i −0.183502 + 0.168357i
\(722\) 8792.38 0.453211
\(723\) 0 0
\(724\) 5.83351 + 10.1039i 0.000299448 + 0.000518660i
\(725\) −3132.18 5425.10i −0.160450 0.277908i
\(726\) 0 0
\(727\) 24524.8 1.25114 0.625568 0.780170i \(-0.284867\pi\)
0.625568 + 0.780170i \(0.284867\pi\)
\(728\) 791.763 + 249.105i 0.0403086 + 0.0126819i
\(729\) 0 0
\(730\) −161.954 + 280.512i −0.00821120 + 0.0142222i
\(731\) 323.971 + 561.135i 0.0163920 + 0.0283917i
\(732\) 0 0
\(733\) −4870.58 + 8436.09i −0.245428 + 0.425094i −0.962252 0.272160i \(-0.912262\pi\)
0.716824 + 0.697255i \(0.245595\pi\)
\(734\) 24948.7 1.25459
\(735\) 0 0
\(736\) −4160.31 −0.208358
\(737\) −3172.60 + 5495.11i −0.158568 + 0.274647i
\(738\) 0 0
\(739\) 16049.5 + 27798.6i 0.798905 + 1.38374i 0.920330 + 0.391143i \(0.127920\pi\)
−0.121426 + 0.992601i \(0.538747\pi\)
\(740\) −36.4117 + 63.0669i −0.00180881 + 0.00313295i
\(741\) 0 0
\(742\) 17208.9 + 5414.26i 0.851425 + 0.267876i
\(743\) −21404.8 −1.05688 −0.528442 0.848970i \(-0.677223\pi\)
−0.528442 + 0.848970i \(0.677223\pi\)
\(744\) 0 0
\(745\) −705.906 1222.67i −0.0347146 0.0601275i
\(746\) 1927.90 + 3339.22i 0.0946186 + 0.163884i
\(747\) 0 0
\(748\) −479.035 −0.0234161
\(749\) −14851.7 + 13626.0i −0.724527 + 0.664730i
\(750\) 0 0
\(751\) −12218.6 + 21163.2i −0.593692 + 1.02830i 0.400038 + 0.916498i \(0.368997\pi\)
−0.993730 + 0.111806i \(0.964337\pi\)
\(752\) −1949.01 3375.78i −0.0945119 0.163699i
\(753\) 0 0
\(754\) −281.567 + 487.689i −0.0135996 + 0.0235552i
\(755\) −137.066 −0.00660709
\(756\) 0 0
\(757\) 35339.6 1.69675 0.848375 0.529395i \(-0.177581\pi\)
0.848375 + 0.529395i \(0.177581\pi\)
\(758\) −2946.20 + 5102.97i −0.141175 + 0.244523i
\(759\) 0 0
\(760\) 119.529 + 207.030i 0.00570497 + 0.00988129i
\(761\) −12995.4 + 22508.7i −0.619033 + 1.07220i 0.370630 + 0.928781i \(0.379142\pi\)
−0.989663 + 0.143415i \(0.954192\pi\)
\(762\) 0 0
\(763\) 2024.15 + 9103.78i 0.0960410 + 0.431951i
\(764\) 1008.44 0.0477540
\(765\) 0 0
\(766\) 3117.46 + 5399.59i 0.147047 + 0.254693i
\(767\) −250.911 434.591i −0.0118121 0.0204592i
\(768\) 0 0
\(769\) −19140.3 −0.897551 −0.448776 0.893645i \(-0.648140\pi\)
−0.448776 + 0.893645i \(0.648140\pi\)
\(770\) 148.734 136.459i 0.00696106 0.00638654i
\(771\) 0 0
\(772\) −3946.81 + 6836.07i −0.184001 + 0.318699i
\(773\) −14103.5 24428.0i −0.656232 1.13663i −0.981583 0.191034i \(-0.938816\pi\)
0.325351 0.945593i \(-0.394517\pi\)
\(774\) 0 0
\(775\) −15490.9 + 26831.0i −0.717998 + 1.24361i
\(776\) 2628.21 0.121582
\(777\) 0 0
\(778\) −3673.68 −0.169290
\(779\) 6895.14 11942.7i 0.317130 0.549285i