Properties

Label 35.3.d.b.6.1
Level $35$
Weight $3$
Character 35.6
Analytic conductor $0.954$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,3,Mod(6,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.6");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-5}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 6.1
Root \(-2.23607i\) of defining polynomial
Character \(\chi\) \(=\) 35.6
Dual form 35.3.d.b.6.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -2.23607i q^{3} +2.23607i q^{5} -4.47214i q^{6} +(-2.00000 + 6.70820i) q^{7} -8.00000 q^{8} +4.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -2.23607i q^{3} +2.23607i q^{5} -4.47214i q^{6} +(-2.00000 + 6.70820i) q^{7} -8.00000 q^{8} +4.00000 q^{9} +4.47214i q^{10} -1.00000 q^{11} -20.1246i q^{13} +(-4.00000 + 13.4164i) q^{14} +5.00000 q^{15} -16.0000 q^{16} -6.70820i q^{17} +8.00000 q^{18} +13.4164i q^{19} +(15.0000 + 4.47214i) q^{21} -2.00000 q^{22} +8.00000 q^{23} +17.8885i q^{24} -5.00000 q^{25} -40.2492i q^{26} -29.0689i q^{27} +41.0000 q^{29} +10.0000 q^{30} +40.2492i q^{31} +2.23607i q^{33} -13.4164i q^{34} +(-15.0000 - 4.47214i) q^{35} -28.0000 q^{37} +26.8328i q^{38} -45.0000 q^{39} -17.8885i q^{40} +13.4164i q^{41} +(30.0000 + 8.94427i) q^{42} -82.0000 q^{43} +8.94427i q^{45} +16.0000 q^{46} +20.1246i q^{47} +35.7771i q^{48} +(-41.0000 - 26.8328i) q^{49} -10.0000 q^{50} -15.0000 q^{51} +74.0000 q^{53} -58.1378i q^{54} -2.23607i q^{55} +(16.0000 - 53.6656i) q^{56} +30.0000 q^{57} +82.0000 q^{58} -93.9149i q^{59} +80.4984i q^{61} +80.4984i q^{62} +(-8.00000 + 26.8328i) q^{63} +64.0000 q^{64} +45.0000 q^{65} +4.47214i q^{66} +2.00000 q^{67} -17.8885i q^{69} +(-30.0000 - 8.94427i) q^{70} +14.0000 q^{71} -32.0000 q^{72} -67.0820i q^{73} -56.0000 q^{74} +11.1803i q^{75} +(2.00000 - 6.70820i) q^{77} -90.0000 q^{78} -19.0000 q^{79} -35.7771i q^{80} -29.0000 q^{81} +26.8328i q^{82} +93.9149i q^{83} +15.0000 q^{85} -164.000 q^{86} -91.6788i q^{87} +8.00000 q^{88} +107.331i q^{89} +17.8885i q^{90} +(135.000 + 40.2492i) q^{91} +90.0000 q^{93} +40.2492i q^{94} -30.0000 q^{95} -60.3738i q^{97} +(-82.0000 - 53.6656i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} - 4 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{11} - 8 q^{14} + 10 q^{15} - 32 q^{16} + 16 q^{18} + 30 q^{21} - 4 q^{22} + 16 q^{23} - 10 q^{25} + 82 q^{29} + 20 q^{30} - 30 q^{35} - 56 q^{37} - 90 q^{39} + 60 q^{42} - 164 q^{43} + 32 q^{46} - 82 q^{49} - 20 q^{50} - 30 q^{51} + 148 q^{53} + 32 q^{56} + 60 q^{57} + 164 q^{58} - 16 q^{63} + 128 q^{64} + 90 q^{65} + 4 q^{67} - 60 q^{70} + 28 q^{71} - 64 q^{72} - 112 q^{74} + 4 q^{77} - 180 q^{78} - 38 q^{79} - 58 q^{81} + 30 q^{85} - 328 q^{86} + 16 q^{88} + 270 q^{91} + 180 q^{93} - 60 q^{95} - 164 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) 2.23607i 0.745356i −0.927961 0.372678i \(-0.878440\pi\)
0.927961 0.372678i \(-0.121560\pi\)
\(4\) 0 0
\(5\) 2.23607i 0.447214i
\(6\) 4.47214i 0.745356i
\(7\) −2.00000 + 6.70820i −0.285714 + 0.958315i
\(8\) −8.00000 −1.00000
\(9\) 4.00000 0.444444
\(10\) 4.47214i 0.447214i
\(11\) −1.00000 −0.0909091 −0.0454545 0.998966i \(-0.514474\pi\)
−0.0454545 + 0.998966i \(0.514474\pi\)
\(12\) 0 0
\(13\) 20.1246i 1.54805i −0.633157 0.774024i \(-0.718241\pi\)
0.633157 0.774024i \(-0.281759\pi\)
\(14\) −4.00000 + 13.4164i −0.285714 + 0.958315i
\(15\) 5.00000 0.333333
\(16\) −16.0000 −1.00000
\(17\) 6.70820i 0.394600i −0.980343 0.197300i \(-0.936783\pi\)
0.980343 0.197300i \(-0.0632173\pi\)
\(18\) 8.00000 0.444444
\(19\) 13.4164i 0.706127i 0.935599 + 0.353063i \(0.114860\pi\)
−0.935599 + 0.353063i \(0.885140\pi\)
\(20\) 0 0
\(21\) 15.0000 + 4.47214i 0.714286 + 0.212959i
\(22\) −2.00000 −0.0909091
\(23\) 8.00000 0.347826 0.173913 0.984761i \(-0.444359\pi\)
0.173913 + 0.984761i \(0.444359\pi\)
\(24\) 17.8885i 0.745356i
\(25\) −5.00000 −0.200000
\(26\) 40.2492i 1.54805i
\(27\) 29.0689i 1.07663i
\(28\) 0 0
\(29\) 41.0000 1.41379 0.706897 0.707317i \(-0.250095\pi\)
0.706897 + 0.707317i \(0.250095\pi\)
\(30\) 10.0000 0.333333
\(31\) 40.2492i 1.29836i 0.760634 + 0.649181i \(0.224888\pi\)
−0.760634 + 0.649181i \(0.775112\pi\)
\(32\) 0 0
\(33\) 2.23607i 0.0677596i
\(34\) 13.4164i 0.394600i
\(35\) −15.0000 4.47214i −0.428571 0.127775i
\(36\) 0 0
\(37\) −28.0000 −0.756757 −0.378378 0.925651i \(-0.623518\pi\)
−0.378378 + 0.925651i \(0.623518\pi\)
\(38\) 26.8328i 0.706127i
\(39\) −45.0000 −1.15385
\(40\) 17.8885i 0.447214i
\(41\) 13.4164i 0.327229i 0.986524 + 0.163615i \(0.0523154\pi\)
−0.986524 + 0.163615i \(0.947685\pi\)
\(42\) 30.0000 + 8.94427i 0.714286 + 0.212959i
\(43\) −82.0000 −1.90698 −0.953488 0.301430i \(-0.902536\pi\)
−0.953488 + 0.301430i \(0.902536\pi\)
\(44\) 0 0
\(45\) 8.94427i 0.198762i
\(46\) 16.0000 0.347826
\(47\) 20.1246i 0.428183i 0.976814 + 0.214092i \(0.0686791\pi\)
−0.976814 + 0.214092i \(0.931321\pi\)
\(48\) 35.7771i 0.745356i
\(49\) −41.0000 26.8328i −0.836735 0.547608i
\(50\) −10.0000 −0.200000
\(51\) −15.0000 −0.294118
\(52\) 0 0
\(53\) 74.0000 1.39623 0.698113 0.715987i \(-0.254023\pi\)
0.698113 + 0.715987i \(0.254023\pi\)
\(54\) 58.1378i 1.07663i
\(55\) 2.23607i 0.0406558i
\(56\) 16.0000 53.6656i 0.285714 0.958315i
\(57\) 30.0000 0.526316
\(58\) 82.0000 1.41379
\(59\) 93.9149i 1.59178i −0.605443 0.795889i \(-0.707004\pi\)
0.605443 0.795889i \(-0.292996\pi\)
\(60\) 0 0
\(61\) 80.4984i 1.31965i 0.751421 + 0.659823i \(0.229369\pi\)
−0.751421 + 0.659823i \(0.770631\pi\)
\(62\) 80.4984i 1.29836i
\(63\) −8.00000 + 26.8328i −0.126984 + 0.425918i
\(64\) 64.0000 1.00000
\(65\) 45.0000 0.692308
\(66\) 4.47214i 0.0677596i
\(67\) 2.00000 0.0298507 0.0149254 0.999889i \(-0.495249\pi\)
0.0149254 + 0.999889i \(0.495249\pi\)
\(68\) 0 0
\(69\) 17.8885i 0.259254i
\(70\) −30.0000 8.94427i −0.428571 0.127775i
\(71\) 14.0000 0.197183 0.0985915 0.995128i \(-0.468566\pi\)
0.0985915 + 0.995128i \(0.468566\pi\)
\(72\) −32.0000 −0.444444
\(73\) 67.0820i 0.918932i −0.888195 0.459466i \(-0.848041\pi\)
0.888195 0.459466i \(-0.151959\pi\)
\(74\) −56.0000 −0.756757
\(75\) 11.1803i 0.149071i
\(76\) 0 0
\(77\) 2.00000 6.70820i 0.0259740 0.0871195i
\(78\) −90.0000 −1.15385
\(79\) −19.0000 −0.240506 −0.120253 0.992743i \(-0.538371\pi\)
−0.120253 + 0.992743i \(0.538371\pi\)
\(80\) 35.7771i 0.447214i
\(81\) −29.0000 −0.358025
\(82\) 26.8328i 0.327229i
\(83\) 93.9149i 1.13150i 0.824575 + 0.565752i \(0.191414\pi\)
−0.824575 + 0.565752i \(0.808586\pi\)
\(84\) 0 0
\(85\) 15.0000 0.176471
\(86\) −164.000 −1.90698
\(87\) 91.6788i 1.05378i
\(88\) 8.00000 0.0909091
\(89\) 107.331i 1.20597i 0.797753 + 0.602985i \(0.206022\pi\)
−0.797753 + 0.602985i \(0.793978\pi\)
\(90\) 17.8885i 0.198762i
\(91\) 135.000 + 40.2492i 1.48352 + 0.442299i
\(92\) 0 0
\(93\) 90.0000 0.967742
\(94\) 40.2492i 0.428183i
\(95\) −30.0000 −0.315789
\(96\) 0 0
\(97\) 60.3738i 0.622411i −0.950343 0.311205i \(-0.899267\pi\)
0.950343 0.311205i \(-0.100733\pi\)
\(98\) −82.0000 53.6656i −0.836735 0.547608i
\(99\) −4.00000 −0.0404040
\(100\) 0 0
\(101\) 174.413i 1.72686i −0.504465 0.863432i \(-0.668310\pi\)
0.504465 0.863432i \(-0.331690\pi\)
\(102\) −30.0000 −0.294118
\(103\) 6.70820i 0.0651282i 0.999470 + 0.0325641i \(0.0103673\pi\)
−0.999470 + 0.0325641i \(0.989633\pi\)
\(104\) 160.997i 1.54805i
\(105\) −10.0000 + 33.5410i −0.0952381 + 0.319438i
\(106\) 148.000 1.39623
\(107\) −34.0000 −0.317757 −0.158879 0.987298i \(-0.550788\pi\)
−0.158879 + 0.987298i \(0.550788\pi\)
\(108\) 0 0
\(109\) 101.000 0.926606 0.463303 0.886200i \(-0.346664\pi\)
0.463303 + 0.886200i \(0.346664\pi\)
\(110\) 4.47214i 0.0406558i
\(111\) 62.6099i 0.564053i
\(112\) 32.0000 107.331i 0.285714 0.958315i
\(113\) −112.000 −0.991150 −0.495575 0.868565i \(-0.665043\pi\)
−0.495575 + 0.868565i \(0.665043\pi\)
\(114\) 60.0000 0.526316
\(115\) 17.8885i 0.155553i
\(116\) 0 0
\(117\) 80.4984i 0.688021i
\(118\) 187.830i 1.59178i
\(119\) 45.0000 + 13.4164i 0.378151 + 0.112743i
\(120\) −40.0000 −0.333333
\(121\) −120.000 −0.991736
\(122\) 160.997i 1.31965i
\(123\) 30.0000 0.243902
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) −16.0000 + 53.6656i −0.126984 + 0.425918i
\(127\) 62.0000 0.488189 0.244094 0.969751i \(-0.421509\pi\)
0.244094 + 0.969751i \(0.421509\pi\)
\(128\) 128.000 1.00000
\(129\) 183.358i 1.42138i
\(130\) 90.0000 0.692308
\(131\) 134.164i 1.02415i −0.858940 0.512077i \(-0.828876\pi\)
0.858940 0.512077i \(-0.171124\pi\)
\(132\) 0 0
\(133\) −90.0000 26.8328i −0.676692 0.201750i
\(134\) 4.00000 0.0298507
\(135\) 65.0000 0.481481
\(136\) 53.6656i 0.394600i
\(137\) −4.00000 −0.0291971 −0.0145985 0.999893i \(-0.504647\pi\)
−0.0145985 + 0.999893i \(0.504647\pi\)
\(138\) 35.7771i 0.259254i
\(139\) 80.4984i 0.579126i −0.957159 0.289563i \(-0.906490\pi\)
0.957159 0.289563i \(-0.0935099\pi\)
\(140\) 0 0
\(141\) 45.0000 0.319149
\(142\) 28.0000 0.197183
\(143\) 20.1246i 0.140732i
\(144\) −64.0000 −0.444444
\(145\) 91.6788i 0.632267i
\(146\) 134.164i 0.918932i
\(147\) −60.0000 + 91.6788i −0.408163 + 0.623665i
\(148\) 0 0
\(149\) −94.0000 −0.630872 −0.315436 0.948947i \(-0.602151\pi\)
−0.315436 + 0.948947i \(0.602151\pi\)
\(150\) 22.3607i 0.149071i
\(151\) −181.000 −1.19868 −0.599338 0.800496i \(-0.704569\pi\)
−0.599338 + 0.800496i \(0.704569\pi\)
\(152\) 107.331i 0.706127i
\(153\) 26.8328i 0.175378i
\(154\) 4.00000 13.4164i 0.0259740 0.0871195i
\(155\) −90.0000 −0.580645
\(156\) 0 0
\(157\) 174.413i 1.11091i 0.831546 + 0.555456i \(0.187456\pi\)
−0.831546 + 0.555456i \(0.812544\pi\)
\(158\) −38.0000 −0.240506
\(159\) 165.469i 1.04069i
\(160\) 0 0
\(161\) −16.0000 + 53.6656i −0.0993789 + 0.333327i
\(162\) −58.0000 −0.358025
\(163\) 164.000 1.00613 0.503067 0.864247i \(-0.332205\pi\)
0.503067 + 0.864247i \(0.332205\pi\)
\(164\) 0 0
\(165\) −5.00000 −0.0303030
\(166\) 187.830i 1.13150i
\(167\) 154.289i 0.923884i 0.886910 + 0.461942i \(0.152847\pi\)
−0.886910 + 0.461942i \(0.847153\pi\)
\(168\) −120.000 35.7771i −0.714286 0.212959i
\(169\) −236.000 −1.39645
\(170\) 30.0000 0.176471
\(171\) 53.6656i 0.313834i
\(172\) 0 0
\(173\) 73.7902i 0.426533i −0.976994 0.213267i \(-0.931590\pi\)
0.976994 0.213267i \(-0.0684103\pi\)
\(174\) 183.358i 1.05378i
\(175\) 10.0000 33.5410i 0.0571429 0.191663i
\(176\) 16.0000 0.0909091
\(177\) −210.000 −1.18644
\(178\) 214.663i 1.20597i
\(179\) 218.000 1.21788 0.608939 0.793217i \(-0.291596\pi\)
0.608939 + 0.793217i \(0.291596\pi\)
\(180\) 0 0
\(181\) 147.580i 0.815362i −0.913124 0.407681i \(-0.866338\pi\)
0.913124 0.407681i \(-0.133662\pi\)
\(182\) 270.000 + 80.4984i 1.48352 + 0.442299i
\(183\) 180.000 0.983607
\(184\) −64.0000 −0.347826
\(185\) 62.6099i 0.338432i
\(186\) 180.000 0.967742
\(187\) 6.70820i 0.0358727i
\(188\) 0 0
\(189\) 195.000 + 58.1378i 1.03175 + 0.307607i
\(190\) −60.0000 −0.315789
\(191\) 167.000 0.874346 0.437173 0.899378i \(-0.355980\pi\)
0.437173 + 0.899378i \(0.355980\pi\)
\(192\) 143.108i 0.745356i
\(193\) −172.000 −0.891192 −0.445596 0.895234i \(-0.647008\pi\)
−0.445596 + 0.895234i \(0.647008\pi\)
\(194\) 120.748i 0.622411i
\(195\) 100.623i 0.516016i
\(196\) 0 0
\(197\) 302.000 1.53299 0.766497 0.642247i \(-0.221998\pi\)
0.766497 + 0.642247i \(0.221998\pi\)
\(198\) −8.00000 −0.0404040
\(199\) 174.413i 0.876449i −0.898866 0.438224i \(-0.855608\pi\)
0.898866 0.438224i \(-0.144392\pi\)
\(200\) 40.0000 0.200000
\(201\) 4.47214i 0.0222494i
\(202\) 348.827i 1.72686i
\(203\) −82.0000 + 275.036i −0.403941 + 1.35486i
\(204\) 0 0
\(205\) −30.0000 −0.146341
\(206\) 13.4164i 0.0651282i
\(207\) 32.0000 0.154589
\(208\) 321.994i 1.54805i
\(209\) 13.4164i 0.0641933i
\(210\) −20.0000 + 67.0820i −0.0952381 + 0.319438i
\(211\) 107.000 0.507109 0.253555 0.967321i \(-0.418400\pi\)
0.253555 + 0.967321i \(0.418400\pi\)
\(212\) 0 0
\(213\) 31.3050i 0.146972i
\(214\) −68.0000 −0.317757
\(215\) 183.358i 0.852826i
\(216\) 232.551i 1.07663i
\(217\) −270.000 80.4984i −1.24424 0.370961i
\(218\) 202.000 0.926606
\(219\) −150.000 −0.684932
\(220\) 0 0
\(221\) −135.000 −0.610860
\(222\) 125.220i 0.564053i
\(223\) 114.039i 0.511388i 0.966758 + 0.255694i \(0.0823039\pi\)
−0.966758 + 0.255694i \(0.917696\pi\)
\(224\) 0 0
\(225\) −20.0000 −0.0888889
\(226\) −224.000 −0.991150
\(227\) 60.3738i 0.265964i −0.991118 0.132982i \(-0.957545\pi\)
0.991118 0.132982i \(-0.0424553\pi\)
\(228\) 0 0
\(229\) 335.410i 1.46467i 0.680943 + 0.732337i \(0.261570\pi\)
−0.680943 + 0.732337i \(0.738430\pi\)
\(230\) 35.7771i 0.155553i
\(231\) −15.0000 4.47214i −0.0649351 0.0193599i
\(232\) −328.000 −1.41379
\(233\) −52.0000 −0.223176 −0.111588 0.993755i \(-0.535594\pi\)
−0.111588 + 0.993755i \(0.535594\pi\)
\(234\) 160.997i 0.688021i
\(235\) −45.0000 −0.191489
\(236\) 0 0
\(237\) 42.4853i 0.179263i
\(238\) 90.0000 + 26.8328i 0.378151 + 0.112743i
\(239\) −307.000 −1.28452 −0.642259 0.766487i \(-0.722003\pi\)
−0.642259 + 0.766487i \(0.722003\pi\)
\(240\) −80.0000 −0.333333
\(241\) 53.6656i 0.222679i 0.993782 + 0.111339i \(0.0355141\pi\)
−0.993782 + 0.111339i \(0.964486\pi\)
\(242\) −240.000 −0.991736
\(243\) 196.774i 0.809769i
\(244\) 0 0
\(245\) 60.0000 91.6788i 0.244898 0.374199i
\(246\) 60.0000 0.243902
\(247\) 270.000 1.09312
\(248\) 321.994i 1.29836i
\(249\) 210.000 0.843373
\(250\) 22.3607i 0.0894427i
\(251\) 26.8328i 0.106904i 0.998570 + 0.0534518i \(0.0170224\pi\)
−0.998570 + 0.0534518i \(0.982978\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.0316206
\(254\) 124.000 0.488189
\(255\) 33.5410i 0.131533i
\(256\) 0 0
\(257\) 281.745i 1.09628i 0.836386 + 0.548141i \(0.184664\pi\)
−0.836386 + 0.548141i \(0.815336\pi\)
\(258\) 366.715i 1.42138i
\(259\) 56.0000 187.830i 0.216216 0.725211i
\(260\) 0 0
\(261\) 164.000 0.628352
\(262\) 268.328i 1.02415i
\(263\) 98.0000 0.372624 0.186312 0.982491i \(-0.440347\pi\)
0.186312 + 0.982491i \(0.440347\pi\)
\(264\) 17.8885i 0.0677596i
\(265\) 165.469i 0.624411i
\(266\) −180.000 53.6656i −0.676692 0.201750i
\(267\) 240.000 0.898876
\(268\) 0 0
\(269\) 187.830i 0.698252i 0.937076 + 0.349126i \(0.113521\pi\)
−0.937076 + 0.349126i \(0.886479\pi\)
\(270\) 130.000 0.481481
\(271\) 160.997i 0.594084i −0.954864 0.297042i \(-0.904000\pi\)
0.954864 0.297042i \(-0.0960002\pi\)
\(272\) 107.331i 0.394600i
\(273\) 90.0000 301.869i 0.329670 1.10575i
\(274\) −8.00000 −0.0291971
\(275\) 5.00000 0.0181818
\(276\) 0 0
\(277\) 176.000 0.635379 0.317690 0.948195i \(-0.397093\pi\)
0.317690 + 0.948195i \(0.397093\pi\)
\(278\) 160.997i 0.579126i
\(279\) 160.997i 0.577050i
\(280\) 120.000 + 35.7771i 0.428571 + 0.127775i
\(281\) −181.000 −0.644128 −0.322064 0.946718i \(-0.604377\pi\)
−0.322064 + 0.946718i \(0.604377\pi\)
\(282\) 90.0000 0.319149
\(283\) 140.872i 0.497782i 0.968532 + 0.248891i \(0.0800661\pi\)
−0.968532 + 0.248891i \(0.919934\pi\)
\(284\) 0 0
\(285\) 67.0820i 0.235376i
\(286\) 40.2492i 0.140732i
\(287\) −90.0000 26.8328i −0.313589 0.0934941i
\(288\) 0 0
\(289\) 244.000 0.844291
\(290\) 183.358i 0.632267i
\(291\) −135.000 −0.463918
\(292\) 0 0
\(293\) 368.951i 1.25922i −0.776912 0.629610i \(-0.783215\pi\)
0.776912 0.629610i \(-0.216785\pi\)
\(294\) −120.000 + 183.358i −0.408163 + 0.623665i
\(295\) 210.000 0.711864
\(296\) 224.000 0.756757
\(297\) 29.0689i 0.0978750i
\(298\) −188.000 −0.630872
\(299\) 160.997i 0.538451i
\(300\) 0 0
\(301\) 164.000 550.073i 0.544850 1.82748i
\(302\) −362.000 −1.19868
\(303\) −390.000 −1.28713
\(304\) 214.663i 0.706127i
\(305\) −180.000 −0.590164
\(306\) 53.6656i 0.175378i
\(307\) 422.617i 1.37660i 0.725425 + 0.688301i \(0.241643\pi\)
−0.725425 + 0.688301i \(0.758357\pi\)
\(308\) 0 0
\(309\) 15.0000 0.0485437
\(310\) −180.000 −0.580645
\(311\) 254.912i 0.819652i 0.912164 + 0.409826i \(0.134411\pi\)
−0.912164 + 0.409826i \(0.865589\pi\)
\(312\) 360.000 1.15385
\(313\) 46.9574i 0.150024i −0.997183 0.0750119i \(-0.976101\pi\)
0.997183 0.0750119i \(-0.0238995\pi\)
\(314\) 348.827i 1.11091i
\(315\) −60.0000 17.8885i −0.190476 0.0567890i
\(316\) 0 0
\(317\) 122.000 0.384858 0.192429 0.981311i \(-0.438363\pi\)
0.192429 + 0.981311i \(0.438363\pi\)
\(318\) 330.938i 1.04069i
\(319\) −41.0000 −0.128527
\(320\) 143.108i 0.447214i
\(321\) 76.0263i 0.236842i
\(322\) −32.0000 + 107.331i −0.0993789 + 0.333327i
\(323\) 90.0000 0.278638
\(324\) 0 0
\(325\) 100.623i 0.309609i
\(326\) 328.000 1.00613
\(327\) 225.843i 0.690651i
\(328\) 107.331i 0.327229i
\(329\) −135.000 40.2492i −0.410334 0.122338i
\(330\) −10.0000 −0.0303030
\(331\) 14.0000 0.0422961 0.0211480 0.999776i \(-0.493268\pi\)
0.0211480 + 0.999776i \(0.493268\pi\)
\(332\) 0 0
\(333\) −112.000 −0.336336
\(334\) 308.577i 0.923884i
\(335\) 4.47214i 0.0133497i
\(336\) −240.000 71.5542i −0.714286 0.212959i
\(337\) −64.0000 −0.189911 −0.0949555 0.995482i \(-0.530271\pi\)
−0.0949555 + 0.995482i \(0.530271\pi\)
\(338\) −472.000 −1.39645
\(339\) 250.440i 0.738760i
\(340\) 0 0
\(341\) 40.2492i 0.118033i
\(342\) 107.331i 0.313834i
\(343\) 262.000 221.371i 0.763848 0.645396i
\(344\) 656.000 1.90698
\(345\) 40.0000 0.115942
\(346\) 147.580i 0.426533i
\(347\) −448.000 −1.29107 −0.645533 0.763732i \(-0.723365\pi\)
−0.645533 + 0.763732i \(0.723365\pi\)
\(348\) 0 0
\(349\) 147.580i 0.422867i 0.977392 + 0.211433i \(0.0678131\pi\)
−0.977392 + 0.211433i \(0.932187\pi\)
\(350\) 20.0000 67.0820i 0.0571429 0.191663i
\(351\) −585.000 −1.66667
\(352\) 0 0
\(353\) 248.204i 0.703126i 0.936164 + 0.351563i \(0.114350\pi\)
−0.936164 + 0.351563i \(0.885650\pi\)
\(354\) −420.000 −1.18644
\(355\) 31.3050i 0.0881830i
\(356\) 0 0
\(357\) 30.0000 100.623i 0.0840336 0.281857i
\(358\) 436.000 1.21788
\(359\) −334.000 −0.930362 −0.465181 0.885216i \(-0.654011\pi\)
−0.465181 + 0.885216i \(0.654011\pi\)
\(360\) 71.5542i 0.198762i
\(361\) 181.000 0.501385
\(362\) 295.161i 0.815362i
\(363\) 268.328i 0.739196i
\(364\) 0 0
\(365\) 150.000 0.410959
\(366\) 360.000 0.983607
\(367\) 60.3738i 0.164506i −0.996611 0.0822532i \(-0.973788\pi\)
0.996611 0.0822532i \(-0.0262116\pi\)
\(368\) −128.000 −0.347826
\(369\) 53.6656i 0.145435i
\(370\) 125.220i 0.338432i
\(371\) −148.000 + 496.407i −0.398922 + 1.33802i
\(372\) 0 0
\(373\) −412.000 −1.10456 −0.552279 0.833659i \(-0.686242\pi\)
−0.552279 + 0.833659i \(0.686242\pi\)
\(374\) 13.4164i 0.0358727i
\(375\) −25.0000 −0.0666667
\(376\) 160.997i 0.428183i
\(377\) 825.109i 2.18862i
\(378\) 390.000 + 116.276i 1.03175 + 0.307607i
\(379\) 86.0000 0.226913 0.113456 0.993543i \(-0.463808\pi\)
0.113456 + 0.993543i \(0.463808\pi\)
\(380\) 0 0
\(381\) 138.636i 0.363875i
\(382\) 334.000 0.874346
\(383\) 469.574i 1.22604i 0.790066 + 0.613021i \(0.210046\pi\)
−0.790066 + 0.613021i \(0.789954\pi\)
\(384\) 286.217i 0.745356i
\(385\) 15.0000 + 4.47214i 0.0389610 + 0.0116159i
\(386\) −344.000 −0.891192
\(387\) −328.000 −0.847545
\(388\) 0 0
\(389\) 221.000 0.568123 0.284062 0.958806i \(-0.408318\pi\)
0.284062 + 0.958806i \(0.408318\pi\)
\(390\) 201.246i 0.516016i
\(391\) 53.6656i 0.137252i
\(392\) 328.000 + 214.663i 0.836735 + 0.547608i
\(393\) −300.000 −0.763359
\(394\) 604.000 1.53299
\(395\) 42.4853i 0.107558i
\(396\) 0 0
\(397\) 234.787i 0.591403i 0.955280 + 0.295702i \(0.0955534\pi\)
−0.955280 + 0.295702i \(0.904447\pi\)
\(398\) 348.827i 0.876449i
\(399\) −60.0000 + 201.246i −0.150376 + 0.504376i
\(400\) 80.0000 0.200000
\(401\) 599.000 1.49377 0.746883 0.664956i \(-0.231550\pi\)
0.746883 + 0.664956i \(0.231550\pi\)
\(402\) 8.94427i 0.0222494i
\(403\) 810.000 2.00993
\(404\) 0 0
\(405\) 64.8460i 0.160114i
\(406\) −164.000 + 550.073i −0.403941 + 1.35486i
\(407\) 28.0000 0.0687961
\(408\) 120.000 0.294118
\(409\) 13.4164i 0.0328030i 0.999865 + 0.0164015i \(0.00522099\pi\)
−0.999865 + 0.0164015i \(0.994779\pi\)
\(410\) −60.0000 −0.146341
\(411\) 8.94427i 0.0217622i
\(412\) 0 0
\(413\) 630.000 + 187.830i 1.52542 + 0.454793i
\(414\) 64.0000 0.154589
\(415\) −210.000 −0.506024
\(416\) 0 0
\(417\) −180.000 −0.431655
\(418\) 26.8328i 0.0641933i
\(419\) 603.738i 1.44090i −0.693505 0.720451i \(-0.743935\pi\)
0.693505 0.720451i \(-0.256065\pi\)
\(420\) 0 0
\(421\) −61.0000 −0.144893 −0.0724466 0.997372i \(-0.523081\pi\)
−0.0724466 + 0.997372i \(0.523081\pi\)
\(422\) 214.000 0.507109
\(423\) 80.4984i 0.190304i
\(424\) −592.000 −1.39623
\(425\) 33.5410i 0.0789200i
\(426\) 62.6099i 0.146972i
\(427\) −540.000 160.997i −1.26464 0.377042i
\(428\) 0 0
\(429\) 45.0000 0.104895
\(430\) 366.715i 0.852826i
\(431\) 227.000 0.526682 0.263341 0.964703i \(-0.415176\pi\)
0.263341 + 0.964703i \(0.415176\pi\)
\(432\) 465.102i 1.07663i
\(433\) 147.580i 0.340833i −0.985372 0.170416i \(-0.945489\pi\)
0.985372 0.170416i \(-0.0545112\pi\)
\(434\) −540.000 160.997i −1.24424 0.370961i
\(435\) 205.000 0.471264
\(436\) 0 0
\(437\) 107.331i 0.245609i
\(438\) −300.000 −0.684932
\(439\) 724.486i 1.65031i −0.564906 0.825155i \(-0.691088\pi\)
0.564906 0.825155i \(-0.308912\pi\)
\(440\) 17.8885i 0.0406558i
\(441\) −164.000 107.331i −0.371882 0.243382i
\(442\) −270.000 −0.610860
\(443\) −526.000 −1.18736 −0.593679 0.804702i \(-0.702325\pi\)
−0.593679 + 0.804702i \(0.702325\pi\)
\(444\) 0 0
\(445\) −240.000 −0.539326
\(446\) 228.079i 0.511388i
\(447\) 210.190i 0.470225i
\(448\) −128.000 + 429.325i −0.285714 + 0.958315i
\(449\) 161.000 0.358575 0.179287 0.983797i \(-0.442621\pi\)
0.179287 + 0.983797i \(0.442621\pi\)
\(450\) −40.0000 −0.0888889
\(451\) 13.4164i 0.0297481i
\(452\) 0 0
\(453\) 404.728i 0.893440i
\(454\) 120.748i 0.265964i
\(455\) −90.0000 + 301.869i −0.197802 + 0.663449i
\(456\) −240.000 −0.526316
\(457\) 602.000 1.31729 0.658643 0.752455i \(-0.271131\pi\)
0.658643 + 0.752455i \(0.271131\pi\)
\(458\) 670.820i 1.46467i
\(459\) −195.000 −0.424837
\(460\) 0 0
\(461\) 53.6656i 0.116411i 0.998305 + 0.0582057i \(0.0185379\pi\)
−0.998305 + 0.0582057i \(0.981462\pi\)
\(462\) −30.0000 8.94427i −0.0649351 0.0193599i
\(463\) −316.000 −0.682505 −0.341253 0.939972i \(-0.610851\pi\)
−0.341253 + 0.939972i \(0.610851\pi\)
\(464\) −656.000 −1.41379
\(465\) 201.246i 0.432787i
\(466\) −104.000 −0.223176
\(467\) 623.863i 1.33590i −0.744208 0.667948i \(-0.767173\pi\)
0.744208 0.667948i \(-0.232827\pi\)
\(468\) 0 0
\(469\) −4.00000 + 13.4164i −0.00852878 + 0.0286064i
\(470\) −90.0000 −0.191489
\(471\) 390.000 0.828025
\(472\) 751.319i 1.59178i
\(473\) 82.0000 0.173362
\(474\) 84.9706i 0.179263i
\(475\) 67.0820i 0.141225i
\(476\) 0 0
\(477\) 296.000 0.620545
\(478\) −614.000 −1.28452
\(479\) 563.489i 1.17639i −0.808720 0.588193i \(-0.799839\pi\)
0.808720 0.588193i \(-0.200161\pi\)
\(480\) 0 0
\(481\) 563.489i 1.17150i
\(482\) 107.331i 0.222679i
\(483\) 120.000 + 35.7771i 0.248447 + 0.0740726i
\(484\) 0 0
\(485\) 135.000 0.278351
\(486\) 393.548i 0.809769i
\(487\) 332.000 0.681725 0.340862 0.940113i \(-0.389281\pi\)
0.340862 + 0.940113i \(0.389281\pi\)
\(488\) 643.988i 1.31965i
\(489\) 366.715i 0.749929i
\(490\) 120.000 183.358i 0.244898 0.374199i
\(491\) −181.000 −0.368635 −0.184318 0.982867i \(-0.559008\pi\)
−0.184318 + 0.982867i \(0.559008\pi\)
\(492\) 0 0
\(493\) 275.036i 0.557883i
\(494\) 540.000 1.09312
\(495\) 8.94427i 0.0180692i
\(496\) 643.988i 1.29836i
\(497\) −28.0000 + 93.9149i −0.0563380 + 0.188963i
\(498\) 420.000 0.843373
\(499\) 593.000 1.18838 0.594188 0.804326i \(-0.297473\pi\)
0.594188 + 0.804326i \(0.297473\pi\)
\(500\) 0 0
\(501\) 345.000 0.688623
\(502\) 53.6656i 0.106904i
\(503\) 436.033i 0.866865i 0.901186 + 0.433433i \(0.142698\pi\)
−0.901186 + 0.433433i \(0.857302\pi\)
\(504\) 64.0000 214.663i 0.126984 0.425918i
\(505\) 390.000 0.772277
\(506\) −16.0000 −0.0316206
\(507\) 527.712i 1.04085i
\(508\) 0 0
\(509\) 187.830i 0.369017i −0.982831 0.184509i \(-0.940931\pi\)
0.982831 0.184509i \(-0.0590693\pi\)
\(510\) 67.0820i 0.131533i
\(511\) 450.000 + 134.164i 0.880626 + 0.262552i
\(512\) −512.000 −1.00000
\(513\) 390.000 0.760234
\(514\) 563.489i 1.09628i
\(515\) −15.0000 −0.0291262
\(516\) 0 0
\(517\) 20.1246i 0.0389257i
\(518\) 112.000 375.659i 0.216216 0.725211i
\(519\) −165.000 −0.317919
\(520\) −360.000 −0.692308
\(521\) 523.240i 1.00430i 0.864781 + 0.502150i \(0.167457\pi\)
−0.864781 + 0.502150i \(0.832543\pi\)
\(522\) 328.000 0.628352
\(523\) 845.234i 1.61613i −0.589096 0.808063i \(-0.700516\pi\)
0.589096 0.808063i \(-0.299484\pi\)
\(524\) 0 0
\(525\) −75.0000 22.3607i −0.142857 0.0425918i
\(526\) 196.000 0.372624
\(527\) 270.000 0.512334
\(528\) 35.7771i 0.0677596i
\(529\) −465.000 −0.879017
\(530\) 330.938i 0.624411i
\(531\) 375.659i 0.707457i
\(532\) 0 0
\(533\) 270.000 0.506567
\(534\) 480.000 0.898876
\(535\) 76.0263i 0.142105i
\(536\) −16.0000 −0.0298507
\(537\) 487.463i 0.907752i
\(538\) 375.659i 0.698252i
\(539\) 41.0000 + 26.8328i 0.0760668 + 0.0497826i
\(540\) 0 0
\(541\) −1081.00 −1.99815 −0.999076 0.0429834i \(-0.986314\pi\)
−0.999076 + 0.0429834i \(0.986314\pi\)
\(542\) 321.994i 0.594084i
\(543\) −330.000 −0.607735
\(544\) 0 0
\(545\) 225.843i 0.414391i
\(546\) 180.000 603.738i 0.329670 1.10575i
\(547\) 92.0000 0.168190 0.0840951 0.996458i \(-0.473200\pi\)
0.0840951 + 0.996458i \(0.473200\pi\)
\(548\) 0 0
\(549\) 321.994i 0.586510i
\(550\) 10.0000 0.0181818
\(551\) 550.073i 0.998317i
\(552\) 143.108i 0.259254i
\(553\) 38.0000 127.456i 0.0687161 0.230481i
\(554\) 352.000 0.635379
\(555\) −140.000 −0.252252
\(556\) 0 0
\(557\) −928.000 −1.66607 −0.833034 0.553222i \(-0.813398\pi\)
−0.833034 + 0.553222i \(0.813398\pi\)
\(558\) 321.994i 0.577050i
\(559\) 1650.22i 2.95209i
\(560\) 240.000 + 71.5542i 0.428571 + 0.127775i
\(561\) 15.0000 0.0267380
\(562\) −362.000 −0.644128
\(563\) 281.745i 0.500434i −0.968190 0.250217i \(-0.919498\pi\)
0.968190 0.250217i \(-0.0805020\pi\)
\(564\) 0 0
\(565\) 250.440i 0.443256i
\(566\) 281.745i 0.497782i
\(567\) 58.0000 194.538i 0.102293 0.343100i
\(568\) −112.000 −0.197183
\(569\) −574.000 −1.00879 −0.504394 0.863474i \(-0.668284\pi\)
−0.504394 + 0.863474i \(0.668284\pi\)
\(570\) 134.164i 0.235376i
\(571\) −226.000 −0.395797 −0.197898 0.980223i \(-0.563412\pi\)
−0.197898 + 0.980223i \(0.563412\pi\)
\(572\) 0 0
\(573\) 373.423i 0.651699i
\(574\) −180.000 53.6656i −0.313589 0.0934941i
\(575\) −40.0000 −0.0695652
\(576\) 256.000 0.444444
\(577\) 623.863i 1.08122i −0.841274 0.540609i \(-0.818194\pi\)
0.841274 0.540609i \(-0.181806\pi\)
\(578\) 488.000 0.844291
\(579\) 384.604i 0.664255i
\(580\) 0 0
\(581\) −630.000 187.830i −1.08434 0.323287i
\(582\) −270.000 −0.463918
\(583\) −74.0000 −0.126930
\(584\) 536.656i 0.918932i
\(585\) 180.000 0.307692
\(586\) 737.902i 1.25922i
\(587\) 201.246i 0.342838i −0.985198 0.171419i \(-0.945165\pi\)
0.985198 0.171419i \(-0.0548352\pi\)
\(588\) 0 0
\(589\) −540.000 −0.916808
\(590\) 420.000 0.711864
\(591\) 675.293i 1.14263i
\(592\) 448.000 0.756757
\(593\) 194.538i 0.328057i 0.986456 + 0.164029i \(0.0524489\pi\)
−0.986456 + 0.164029i \(0.947551\pi\)
\(594\) 58.1378i 0.0978750i
\(595\) −30.0000 + 100.623i −0.0504202 + 0.169114i
\(596\) 0 0
\(597\) −390.000 −0.653266
\(598\) 321.994i 0.538451i
\(599\) 581.000 0.969950 0.484975 0.874528i \(-0.338829\pi\)
0.484975 + 0.874528i \(0.338829\pi\)
\(600\) 89.4427i 0.149071i
\(601\) 1086.73i 1.80820i 0.427319 + 0.904101i \(0.359458\pi\)
−0.427319 + 0.904101i \(0.640542\pi\)
\(602\) 328.000 1100.15i 0.544850 1.82748i
\(603\) 8.00000 0.0132670
\(604\) 0 0
\(605\) 268.328i 0.443518i
\(606\) −780.000 −1.28713
\(607\) 342.118i 0.563622i 0.959470 + 0.281811i \(0.0909351\pi\)
−0.959470 + 0.281811i \(0.909065\pi\)
\(608\) 0 0
\(609\) 615.000 + 183.358i 1.00985 + 0.301080i
\(610\) −360.000 −0.590164
\(611\) 405.000 0.662848
\(612\) 0 0
\(613\) −922.000 −1.50408 −0.752039 0.659118i \(-0.770930\pi\)
−0.752039 + 0.659118i \(0.770930\pi\)
\(614\) 845.234i 1.37660i
\(615\) 67.0820i 0.109076i
\(616\) −16.0000 + 53.6656i −0.0259740 + 0.0871195i
\(617\) 332.000 0.538088 0.269044 0.963128i \(-0.413292\pi\)
0.269044 + 0.963128i \(0.413292\pi\)
\(618\) 30.0000 0.0485437
\(619\) 107.331i 0.173395i −0.996235 0.0866973i \(-0.972369\pi\)
0.996235 0.0866973i \(-0.0276313\pi\)
\(620\) 0 0
\(621\) 232.551i 0.374478i
\(622\) 509.823i 0.819652i
\(623\) −720.000 214.663i −1.15570 0.344563i
\(624\) 720.000 1.15385
\(625\) 25.0000 0.0400000
\(626\) 93.9149i 0.150024i
\(627\) −30.0000 −0.0478469
\(628\) 0 0
\(629\) 187.830i 0.298616i
\(630\) −120.000 35.7771i −0.190476 0.0567890i
\(631\) 839.000 1.32964 0.664818 0.747006i \(-0.268509\pi\)
0.664818 + 0.747006i \(0.268509\pi\)
\(632\) 152.000 0.240506
\(633\) 239.259i 0.377977i
\(634\) 244.000 0.384858
\(635\) 138.636i 0.218325i
\(636\) 0 0
\(637\) −540.000 + 825.109i −0.847724 + 1.29530i
\(638\) −82.0000 −0.128527
\(639\) 56.0000 0.0876369
\(640\) 286.217i 0.447214i
\(641\) 614.000 0.957878 0.478939 0.877848i \(-0.341021\pi\)
0.478939 + 0.877848i \(0.341021\pi\)
\(642\) 152.053i 0.236842i
\(643\) 476.282i 0.740719i −0.928888 0.370360i \(-0.879234\pi\)
0.928888 0.370360i \(-0.120766\pi\)
\(644\) 0 0
\(645\) −410.000 −0.635659
\(646\) 180.000 0.278638
\(647\) 925.732i 1.43081i −0.698712 0.715404i \(-0.746243\pi\)
0.698712 0.715404i \(-0.253757\pi\)
\(648\) 232.000 0.358025
\(649\) 93.9149i 0.144707i
\(650\) 201.246i 0.309609i
\(651\) −180.000 + 603.738i −0.276498 + 0.927401i
\(652\) 0 0
\(653\) 314.000 0.480858 0.240429 0.970667i \(-0.422712\pi\)
0.240429 + 0.970667i \(0.422712\pi\)
\(654\) 451.686i 0.690651i
\(655\) 300.000 0.458015
\(656\) 214.663i 0.327229i
\(657\) 268.328i 0.408414i
\(658\) −270.000 80.4984i −0.410334 0.122338i
\(659\) −787.000 −1.19423 −0.597117 0.802154i \(-0.703687\pi\)
−0.597117 + 0.802154i \(0.703687\pi\)
\(660\) 0 0
\(661\) 563.489i 0.852480i −0.904610 0.426240i \(-0.859838\pi\)
0.904610 0.426240i \(-0.140162\pi\)
\(662\) 28.0000 0.0422961
\(663\) 301.869i 0.455308i
\(664\) 751.319i 1.13150i
\(665\) 60.0000 201.246i 0.0902256 0.302626i
\(666\) −224.000 −0.336336
\(667\) 328.000 0.491754
\(668\) 0 0
\(669\) 255.000 0.381166
\(670\) 8.94427i 0.0133497i
\(671\) 80.4984i 0.119968i
\(672\) 0 0
\(673\) −76.0000 −0.112927 −0.0564636 0.998405i \(-0.517982\pi\)
−0.0564636 + 0.998405i \(0.517982\pi\)
\(674\) −128.000 −0.189911
\(675\) 145.344i 0.215325i
\(676\) 0 0
\(677\) 1200.77i 1.77366i 0.462095 + 0.886831i \(0.347098\pi\)
−0.462095 + 0.886831i \(0.652902\pi\)
\(678\) 500.879i 0.738760i
\(679\) 405.000 + 120.748i 0.596465 + 0.177832i
\(680\) −120.000 −0.176471
\(681\) −135.000 −0.198238
\(682\) 80.4984i 0.118033i
\(683\) 248.000 0.363104 0.181552 0.983381i \(-0.441888\pi\)
0.181552 + 0.983381i \(0.441888\pi\)
\(684\) 0 0
\(685\) 8.94427i 0.0130573i
\(686\) 524.000 442.741i 0.763848 0.645396i
\(687\) 750.000 1.09170
\(688\) 1312.00 1.90698
\(689\) 1489.22i 2.16142i
\(690\) 80.0000 0.115942
\(691\) 804.984i 1.16496i −0.812847 0.582478i \(-0.802083\pi\)
0.812847 0.582478i \(-0.197917\pi\)
\(692\) 0 0
\(693\) 8.00000 26.8328i 0.0115440 0.0387198i
\(694\) −896.000 −1.29107
\(695\) 180.000 0.258993
\(696\) 733.430i 1.05378i
\(697\) 90.0000 0.129125
\(698\) 295.161i 0.422867i
\(699\) 116.276i 0.166346i
\(700\) 0 0
\(701\) 47.0000 0.0670471 0.0335235 0.999438i \(-0.489327\pi\)
0.0335235 + 0.999438i \(0.489327\pi\)
\(702\) −1170.00 −1.66667
\(703\) 375.659i 0.534366i
\(704\) −64.0000 −0.0909091
\(705\) 100.623i 0.142728i
\(706\) 496.407i 0.703126i
\(707\) 1170.00 + 348.827i 1.65488 + 0.493390i
\(708\) 0 0
\(709\) −247.000 −0.348378 −0.174189 0.984712i \(-0.555730\pi\)
−0.174189 + 0.984712i \(0.555730\pi\)
\(710\) 62.6099i 0.0881830i
\(711\) −76.0000 −0.106892
\(712\) 858.650i 1.20597i
\(713\) 321.994i 0.451604i
\(714\) 60.0000 201.246i 0.0840336 0.281857i
\(715\) −45.0000 −0.0629371
\(716\) 0 0
\(717\) 686.473i 0.957424i
\(718\) −668.000 −0.930362
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 143.108i 0.198762i
\(721\) −45.0000 13.4164i −0.0624133 0.0186081i
\(722\) 362.000 0.501385
\(723\) 120.000 0.165975
\(724\) 0 0
\(725\) −205.000 −0.282759
\(726\) 536.656i 0.739196i
\(727\) 496.407i 0.682816i 0.939915 + 0.341408i \(0.110904\pi\)
−0.939915 + 0.341408i \(0.889096\pi\)
\(728\) −1080.00 321.994i −1.48352 0.442299i
\(729\) −701.000 −0.961591
\(730\) 300.000 0.410959
\(731\) 550.073i 0.752493i
\(732\) 0 0
\(733\) 623.863i 0.851109i 0.904933 + 0.425555i \(0.139921\pi\)
−0.904933 + 0.425555i \(0.860079\pi\)
\(734\) 120.748i 0.164506i
\(735\) −205.000 134.164i −0.278912 0.182536i
\(736\) 0 0
\(737\) −2.00000 −0.00271370
\(738\) 107.331i 0.145435i
\(739\) 581.000 0.786198 0.393099 0.919496i \(-0.371403\pi\)
0.393099 + 0.919496i \(0.371403\pi\)
\(740\) 0 0
\(741\) 603.738i 0.814762i
\(742\) −296.000 + 992.814i −0.398922 + 1.33802i
\(743\) 494.000 0.664872 0.332436 0.943126i \(-0.392129\pi\)
0.332436 + 0.943126i \(0.392129\pi\)
\(744\) −720.000 −0.967742
\(745\) 210.190i 0.282135i
\(746\) −824.000 −1.10456
\(747\) 375.659i 0.502891i
\(748\) 0 0
\(749\) 68.0000 228.079i 0.0907877 0.304511i
\(750\) −50.0000 −0.0666667
\(751\) −1153.00 −1.53529 −0.767643 0.640878i \(-0.778571\pi\)
−0.767643 + 0.640878i \(0.778571\pi\)
\(752\) 321.994i 0.428183i
\(753\) 60.0000 0.0796813
\(754\) 1650.22i 2.18862i
\(755\) 404.728i 0.536064i
\(756\) 0 0
\(757\) −88.0000 −0.116248 −0.0581242 0.998309i \(-0.518512\pi\)
−0.0581242 + 0.998309i \(0.518512\pi\)
\(758\) 172.000 0.226913
\(759\) 17.8885i 0.0235686i
\(760\) 240.000 0.315789
\(761\) 456.158i 0.599419i 0.954031 + 0.299710i \(0.0968898\pi\)
−0.954031 + 0.299710i \(0.903110\pi\)
\(762\) 277.272i 0.363875i
\(763\) −202.000 + 677.529i −0.264744 + 0.887980i
\(764\) 0 0
\(765\) 60.0000 0.0784314
\(766\) 939.149i 1.22604i
\(767\) −1890.00 −2.46415
\(768\) 0 0
\(769\) 898.899i 1.16892i −0.811423 0.584460i \(-0.801306\pi\)
0.811423 0.584460i \(-0.198694\pi\)
\(770\) 30.0000 + 8.94427i 0.0389610 + 0.0116159i
\(771\) 630.000 0.817121
\(772\) 0 0
\(773\) 811.693i 1.05006i 0.851085 + 0.525028i \(0.175945\pi\)
−0.851085 + 0.525028i \(0.824055\pi\)
\(774\) −656.000 −0.847545
\(775\) 201.246i 0.259672i
\(776\) 482.991i 0.622411i
\(777\) −420.000 125.220i −0.540541 0.161158i
\(778\) 442.000 0.568123
\(779\) −180.000 −0.231065
\(780\) 0 0
\(781\) −14.0000 −0.0179257
\(782\) 107.331i 0.137252i
\(783\) 1191.82i 1.52213i
\(784\) 656.000 + 429.325i 0.836735