Properties

Label 35.4.b.a.29.4
Level $35$
Weight $4$
Character 35.29
Analytic conductor $2.065$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,4,Mod(29,35)]
 
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([1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.29");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.06506685020\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.4
Root \(-2.67516i\) of defining polynomial
Character \(\chi\) \(=\) 35.29
Dual form 35.4.b.a.29.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.67516i q^{2} +2.49396i q^{3} +5.19383 q^{4} +(6.35505 - 9.19855i) q^{5} +4.17779 q^{6} +7.00000i q^{7} -22.1018i q^{8} +20.7802 q^{9} +(-15.4091 - 10.6457i) q^{10} -57.5880 q^{11} +12.9532i q^{12} +45.5159i q^{13} +11.7261 q^{14} +(22.9408 + 15.8492i) q^{15} +4.52655 q^{16} +92.0051i q^{17} -34.8101i q^{18} -125.177 q^{19} +(33.0070 - 47.7757i) q^{20} -17.4577 q^{21} +96.4692i q^{22} -158.496i q^{23} +55.1211 q^{24} +(-44.2268 - 116.914i) q^{25} +76.2466 q^{26} +119.162i q^{27} +36.3568i q^{28} +40.1708 q^{29} +(26.5500 - 38.4296i) q^{30} +49.5590 q^{31} -184.397i q^{32} -143.622i q^{33} +154.123 q^{34} +(64.3899 + 44.4853i) q^{35} +107.929 q^{36} +231.307i q^{37} +209.692i q^{38} -113.515 q^{39} +(-203.305 - 140.458i) q^{40} +169.556 q^{41} +29.2445i q^{42} +147.428i q^{43} -299.102 q^{44} +(132.059 - 191.147i) q^{45} -265.507 q^{46} -67.0327i q^{47} +11.2890i q^{48} -49.0000 q^{49} +(-195.851 + 74.0870i) q^{50} -229.457 q^{51} +236.402i q^{52} -268.647i q^{53} +199.615 q^{54} +(-365.974 + 529.726i) q^{55} +154.713 q^{56} -312.187i q^{57} -67.2926i q^{58} +240.843 q^{59} +(119.151 + 82.3183i) q^{60} +90.4579 q^{61} -83.0194i q^{62} +145.461i q^{63} -272.683 q^{64} +(418.681 + 289.256i) q^{65} -240.591 q^{66} -406.498i q^{67} +477.859i q^{68} +395.283 q^{69} +(74.5201 - 107.863i) q^{70} +330.782 q^{71} -459.279i q^{72} -546.255i q^{73} +387.477 q^{74} +(291.580 - 110.300i) q^{75} -650.149 q^{76} -403.116i q^{77} +190.156i q^{78} +25.3087 q^{79} +(28.7664 - 41.6377i) q^{80} +263.879 q^{81} -284.034i q^{82} -376.255i q^{83} -90.6725 q^{84} +(846.314 + 584.697i) q^{85} +246.965 q^{86} +100.184i q^{87} +1272.80i q^{88} -1026.44 q^{89} +(-320.203 - 221.220i) q^{90} -318.612 q^{91} -823.203i q^{92} +123.598i q^{93} -112.291 q^{94} +(-795.506 + 1151.45i) q^{95} +459.879 q^{96} -942.660i q^{97} +82.0829i q^{98} -1196.69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} - 16 q^{10} + 84 q^{11} - 56 q^{14} + 8 q^{15} + 148 q^{16} + 72 q^{19} - 68 q^{20} + 140 q^{21} + 72 q^{24} - 362 q^{25} - 620 q^{26} + 88 q^{29} + 52 q^{30}+ \cdots - 5304 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67516i 0.592259i −0.955148 0.296130i \(-0.904304\pi\)
0.955148 0.296130i \(-0.0956960\pi\)
\(3\) 2.49396i 0.479963i 0.970777 + 0.239982i \(0.0771414\pi\)
−0.970777 + 0.239982i \(0.922859\pi\)
\(4\) 5.19383 0.649229
\(5\) 6.35505 9.19855i 0.568413 0.822744i
\(6\) 4.17779 0.284263
\(7\) 7.00000i 0.377964i
\(8\) 22.1018i 0.976771i
\(9\) 20.7802 0.769635
\(10\) −15.4091 10.6457i −0.487278 0.336648i
\(11\) −57.5880 −1.57849 −0.789247 0.614076i \(-0.789529\pi\)
−0.789247 + 0.614076i \(0.789529\pi\)
\(12\) 12.9532i 0.311606i
\(13\) 45.5159i 0.971066i 0.874218 + 0.485533i \(0.161374\pi\)
−0.874218 + 0.485533i \(0.838626\pi\)
\(14\) 11.7261 0.223853
\(15\) 22.9408 + 15.8492i 0.394887 + 0.272817i
\(16\) 4.52655 0.0707273
\(17\) 92.0051i 1.31262i 0.754492 + 0.656309i \(0.227883\pi\)
−0.754492 + 0.656309i \(0.772117\pi\)
\(18\) 34.8101i 0.455824i
\(19\) −125.177 −1.51145 −0.755726 0.654888i \(-0.772716\pi\)
−0.755726 + 0.654888i \(0.772716\pi\)
\(20\) 33.0070 47.7757i 0.369030 0.534149i
\(21\) −17.4577 −0.181409
\(22\) 96.4692i 0.934878i
\(23\) 158.496i 1.43690i −0.695578 0.718451i \(-0.744851\pi\)
0.695578 0.718451i \(-0.255149\pi\)
\(24\) 55.1211 0.468814
\(25\) −44.2268 116.914i −0.353814 0.935316i
\(26\) 76.2466 0.575123
\(27\) 119.162i 0.849360i
\(28\) 36.3568i 0.245386i
\(29\) 40.1708 0.257225 0.128613 0.991695i \(-0.458948\pi\)
0.128613 + 0.991695i \(0.458948\pi\)
\(30\) 26.5500 38.4296i 0.161578 0.233875i
\(31\) 49.5590 0.287131 0.143566 0.989641i \(-0.454143\pi\)
0.143566 + 0.989641i \(0.454143\pi\)
\(32\) 184.397i 1.01866i
\(33\) 143.622i 0.757619i
\(34\) 154.123 0.777410
\(35\) 64.3899 + 44.4853i 0.310968 + 0.214840i
\(36\) 107.929 0.499670
\(37\) 231.307i 1.02775i 0.857866 + 0.513874i \(0.171790\pi\)
−0.857866 + 0.513874i \(0.828210\pi\)
\(38\) 209.692i 0.895171i
\(39\) −113.515 −0.466076
\(40\) −203.305 140.458i −0.803632 0.555209i
\(41\) 169.556 0.645859 0.322929 0.946423i \(-0.395332\pi\)
0.322929 + 0.946423i \(0.395332\pi\)
\(42\) 29.2445i 0.107441i
\(43\) 147.428i 0.522849i 0.965224 + 0.261425i \(0.0841923\pi\)
−0.965224 + 0.261425i \(0.915808\pi\)
\(44\) −299.102 −1.02480
\(45\) 132.059 191.147i 0.437470 0.633213i
\(46\) −265.507 −0.851018
\(47\) 67.0327i 0.208037i −0.994575 0.104018i \(-0.966830\pi\)
0.994575 0.104018i \(-0.0331701\pi\)
\(48\) 11.2890i 0.0339465i
\(49\) −49.0000 −0.142857
\(50\) −195.851 + 74.0870i −0.553949 + 0.209550i
\(51\) −229.457 −0.630008
\(52\) 236.402i 0.630444i
\(53\) 268.647i 0.696254i −0.937447 0.348127i \(-0.886818\pi\)
0.937447 0.348127i \(-0.113182\pi\)
\(54\) 199.615 0.503041
\(55\) −365.974 + 529.726i −0.897236 + 1.29870i
\(56\) 154.713 0.369185
\(57\) 312.187i 0.725441i
\(58\) 67.2926i 0.152344i
\(59\) 240.843 0.531442 0.265721 0.964050i \(-0.414390\pi\)
0.265721 + 0.964050i \(0.414390\pi\)
\(60\) 119.151 + 82.3183i 0.256372 + 0.177121i
\(61\) 90.4579 0.189868 0.0949340 0.995484i \(-0.469736\pi\)
0.0949340 + 0.995484i \(0.469736\pi\)
\(62\) 83.0194i 0.170056i
\(63\) 145.461i 0.290895i
\(64\) −272.683 −0.532583
\(65\) 418.681 + 289.256i 0.798938 + 0.551966i
\(66\) −240.591 −0.448707
\(67\) 406.498i 0.741218i −0.928789 0.370609i \(-0.879149\pi\)
0.928789 0.370609i \(-0.120851\pi\)
\(68\) 477.859i 0.852190i
\(69\) 395.283 0.689660
\(70\) 74.5201 107.863i 0.127241 0.184174i
\(71\) 330.782 0.552910 0.276455 0.961027i \(-0.410840\pi\)
0.276455 + 0.961027i \(0.410840\pi\)
\(72\) 459.279i 0.751758i
\(73\) 546.255i 0.875812i −0.899021 0.437906i \(-0.855720\pi\)
0.899021 0.437906i \(-0.144280\pi\)
\(74\) 387.477 0.608693
\(75\) 291.580 110.300i 0.448917 0.169818i
\(76\) −650.149 −0.981279
\(77\) 403.116i 0.596615i
\(78\) 190.156i 0.276038i
\(79\) 25.3087 0.0360436 0.0180218 0.999838i \(-0.494263\pi\)
0.0180218 + 0.999838i \(0.494263\pi\)
\(80\) 28.7664 41.6377i 0.0402023 0.0581905i
\(81\) 263.879 0.361974
\(82\) 284.034i 0.382516i
\(83\) 376.255i 0.497582i −0.968557 0.248791i \(-0.919967\pi\)
0.968557 0.248791i \(-0.0800333\pi\)
\(84\) −90.6725 −0.117776
\(85\) 846.314 + 584.697i 1.07995 + 0.746109i
\(86\) 246.965 0.309662
\(87\) 100.184i 0.123459i
\(88\) 1272.80i 1.54183i
\(89\) −1026.44 −1.22250 −0.611248 0.791439i \(-0.709332\pi\)
−0.611248 + 0.791439i \(0.709332\pi\)
\(90\) −320.203 221.220i −0.375026 0.259096i
\(91\) −318.612 −0.367028
\(92\) 823.203i 0.932878i
\(93\) 123.598i 0.137812i
\(94\) −112.291 −0.123212
\(95\) −795.506 + 1151.45i −0.859128 + 1.24354i
\(96\) 459.879 0.488919
\(97\) 942.660i 0.986728i −0.869823 0.493364i \(-0.835767\pi\)
0.869823 0.493364i \(-0.164233\pi\)
\(98\) 82.0829i 0.0846085i
\(99\) −1196.69 −1.21487
\(100\) −229.706 607.234i −0.229706 0.607234i
\(101\) −604.617 −0.595659 −0.297830 0.954619i \(-0.596263\pi\)
−0.297830 + 0.954619i \(0.596263\pi\)
\(102\) 384.378i 0.373128i
\(103\) 300.967i 0.287914i 0.989584 + 0.143957i \(0.0459828\pi\)
−0.989584 + 0.143957i \(0.954017\pi\)
\(104\) 1005.98 0.948509
\(105\) −110.945 + 160.586i −0.103115 + 0.149253i
\(106\) −450.027 −0.412363
\(107\) 1511.66i 1.36577i 0.730525 + 0.682886i \(0.239276\pi\)
−0.730525 + 0.682886i \(0.760724\pi\)
\(108\) 618.907i 0.551429i
\(109\) 1767.09 1.55281 0.776406 0.630233i \(-0.217041\pi\)
0.776406 + 0.630233i \(0.217041\pi\)
\(110\) 887.377 + 613.066i 0.769165 + 0.531396i
\(111\) −576.871 −0.493281
\(112\) 31.6858i 0.0267324i
\(113\) 1045.27i 0.870182i −0.900387 0.435091i \(-0.856716\pi\)
0.900387 0.435091i \(-0.143284\pi\)
\(114\) −522.963 −0.429649
\(115\) −1457.94 1007.25i −1.18220 0.816753i
\(116\) 208.640 0.166998
\(117\) 945.828i 0.747366i
\(118\) 403.451i 0.314751i
\(119\) −644.036 −0.496123
\(120\) 350.297 507.034i 0.266480 0.385714i
\(121\) 1985.38 1.49164
\(122\) 151.532i 0.112451i
\(123\) 422.866i 0.309988i
\(124\) 257.401 0.186414
\(125\) −1356.51 336.174i −0.970638 0.240547i
\(126\) 243.671 0.172285
\(127\) 260.727i 0.182171i 0.995843 + 0.0910857i \(0.0290337\pi\)
−0.995843 + 0.0910857i \(0.970966\pi\)
\(128\) 1018.39i 0.703233i
\(129\) −367.679 −0.250948
\(130\) 484.551 701.358i 0.326907 0.473178i
\(131\) −723.522 −0.482553 −0.241276 0.970456i \(-0.577566\pi\)
−0.241276 + 0.970456i \(0.577566\pi\)
\(132\) 745.950i 0.491868i
\(133\) 876.240i 0.571275i
\(134\) −680.950 −0.438993
\(135\) 1096.12 + 757.279i 0.698805 + 0.482787i
\(136\) 2033.48 1.28213
\(137\) 773.693i 0.482490i 0.970464 + 0.241245i \(0.0775557\pi\)
−0.970464 + 0.241245i \(0.922444\pi\)
\(138\) 662.164i 0.408457i
\(139\) 2952.97 1.80192 0.900961 0.433899i \(-0.142863\pi\)
0.900961 + 0.433899i \(0.142863\pi\)
\(140\) 334.430 + 231.049i 0.201889 + 0.139480i
\(141\) 167.177 0.0998499
\(142\) 554.114i 0.327466i
\(143\) 2621.17i 1.53282i
\(144\) 94.0624 0.0544343
\(145\) 255.287 369.513i 0.146210 0.211630i
\(146\) −915.066 −0.518708
\(147\) 122.204i 0.0685662i
\(148\) 1201.37i 0.667244i
\(149\) −2514.00 −1.38225 −0.691124 0.722736i \(-0.742884\pi\)
−0.691124 + 0.722736i \(0.742884\pi\)
\(150\) −184.770 488.444i −0.100576 0.265875i
\(151\) 101.052 0.0544605 0.0272302 0.999629i \(-0.491331\pi\)
0.0272302 + 0.999629i \(0.491331\pi\)
\(152\) 2766.64i 1.47634i
\(153\) 1911.88i 1.01024i
\(154\) −675.285 −0.353351
\(155\) 314.950 455.872i 0.163209 0.236235i
\(156\) −589.578 −0.302590
\(157\) 2338.35i 1.18867i 0.804219 + 0.594333i \(0.202584\pi\)
−0.804219 + 0.594333i \(0.797416\pi\)
\(158\) 42.3961i 0.0213472i
\(159\) 669.995 0.334176
\(160\) −1696.19 1171.85i −0.838096 0.579019i
\(161\) 1109.47 0.543098
\(162\) 442.040i 0.214383i
\(163\) 1325.20i 0.636798i 0.947957 + 0.318399i \(0.103145\pi\)
−0.947957 + 0.318399i \(0.896855\pi\)
\(164\) 880.646 0.419310
\(165\) −1321.12 912.726i −0.623326 0.430640i
\(166\) −630.288 −0.294698
\(167\) 2086.20i 0.966675i 0.875434 + 0.483338i \(0.160576\pi\)
−0.875434 + 0.483338i \(0.839424\pi\)
\(168\) 385.847i 0.177195i
\(169\) 125.299 0.0570317
\(170\) 979.462 1417.71i 0.441890 0.639609i
\(171\) −2601.20 −1.16327
\(172\) 765.715i 0.339449i
\(173\) 1918.19i 0.842990i −0.906831 0.421495i \(-0.861505\pi\)
0.906831 0.421495i \(-0.138495\pi\)
\(174\) 167.825 0.0731195
\(175\) 818.401 309.587i 0.353516 0.133729i
\(176\) −260.675 −0.111643
\(177\) 600.652i 0.255072i
\(178\) 1719.45i 0.724035i
\(179\) −629.046 −0.262665 −0.131333 0.991338i \(-0.541926\pi\)
−0.131333 + 0.991338i \(0.541926\pi\)
\(180\) 685.891 992.787i 0.284019 0.411100i
\(181\) −2800.85 −1.15020 −0.575099 0.818084i \(-0.695036\pi\)
−0.575099 + 0.818084i \(0.695036\pi\)
\(182\) 533.726i 0.217376i
\(183\) 225.599i 0.0911296i
\(184\) −3503.05 −1.40352
\(185\) 2127.69 + 1469.97i 0.845573 + 0.584185i
\(186\) 207.047 0.0816207
\(187\) 5298.39i 2.07196i
\(188\) 348.157i 0.135063i
\(189\) −834.133 −0.321028
\(190\) 1928.86 + 1332.60i 0.736497 + 0.508827i
\(191\) 740.255 0.280434 0.140217 0.990121i \(-0.455220\pi\)
0.140217 + 0.990121i \(0.455220\pi\)
\(192\) 680.060i 0.255620i
\(193\) 4082.57i 1.52264i −0.648375 0.761321i \(-0.724551\pi\)
0.648375 0.761321i \(-0.275449\pi\)
\(194\) −1579.11 −0.584399
\(195\) −721.393 + 1044.17i −0.264923 + 0.383461i
\(196\) −254.498 −0.0927470
\(197\) 3414.89i 1.23503i 0.786559 + 0.617515i \(0.211860\pi\)
−0.786559 + 0.617515i \(0.788140\pi\)
\(198\) 2004.65i 0.719515i
\(199\) 3392.44 1.20846 0.604231 0.796809i \(-0.293480\pi\)
0.604231 + 0.796809i \(0.293480\pi\)
\(200\) −2584.02 + 977.492i −0.913589 + 0.345596i
\(201\) 1013.79 0.355757
\(202\) 1012.83i 0.352785i
\(203\) 281.196i 0.0972220i
\(204\) −1191.76 −0.409020
\(205\) 1077.54 1559.67i 0.367114 0.531376i
\(206\) 504.169 0.170520
\(207\) 3293.58i 1.10589i
\(208\) 206.030i 0.0686809i
\(209\) 7208.70 2.38582
\(210\) 269.007 + 185.850i 0.0883965 + 0.0610709i
\(211\) 3398.04 1.10867 0.554337 0.832292i \(-0.312972\pi\)
0.554337 + 0.832292i \(0.312972\pi\)
\(212\) 1395.31i 0.452029i
\(213\) 824.958i 0.265376i
\(214\) 2532.28 0.808892
\(215\) 1356.12 + 936.910i 0.430171 + 0.297194i
\(216\) 2633.69 0.829630
\(217\) 346.913i 0.108525i
\(218\) 2960.16i 0.919667i
\(219\) 1362.34 0.420358
\(220\) −1900.81 + 2751.31i −0.582512 + 0.843151i
\(221\) −4187.70 −1.27464
\(222\) 966.353i 0.292150i
\(223\) 182.611i 0.0548365i −0.999624 0.0274183i \(-0.991271\pi\)
0.999624 0.0274183i \(-0.00872860\pi\)
\(224\) 1290.78 0.385017
\(225\) −919.040 2429.50i −0.272308 0.719852i
\(226\) −1750.99 −0.515373
\(227\) 3152.33i 0.921707i −0.887476 0.460854i \(-0.847543\pi\)
0.887476 0.460854i \(-0.152457\pi\)
\(228\) 1621.45i 0.470977i
\(229\) −6012.35 −1.73497 −0.867483 0.497466i \(-0.834264\pi\)
−0.867483 + 0.497466i \(0.834264\pi\)
\(230\) −1687.31 + 2442.28i −0.483730 + 0.700170i
\(231\) 1005.36 0.286353
\(232\) 887.848i 0.251250i
\(233\) 940.660i 0.264484i 0.991217 + 0.132242i \(0.0422175\pi\)
−0.991217 + 0.132242i \(0.957782\pi\)
\(234\) 1584.42 0.442635
\(235\) −616.604 425.996i −0.171161 0.118251i
\(236\) 1250.90 0.345027
\(237\) 63.1188i 0.0172996i
\(238\) 1078.86i 0.293833i
\(239\) −5158.82 −1.39622 −0.698109 0.715991i \(-0.745975\pi\)
−0.698109 + 0.715991i \(0.745975\pi\)
\(240\) 103.843 + 71.7423i 0.0279293 + 0.0192956i
\(241\) −463.836 −0.123976 −0.0619882 0.998077i \(-0.519744\pi\)
−0.0619882 + 0.998077i \(0.519744\pi\)
\(242\) 3325.83i 0.883440i
\(243\) 3875.47i 1.02309i
\(244\) 469.823 0.123268
\(245\) −311.397 + 450.729i −0.0812018 + 0.117535i
\(246\) 708.370 0.183594
\(247\) 5697.55i 1.46772i
\(248\) 1095.34i 0.280461i
\(249\) 938.365 0.238821
\(250\) −563.146 + 2272.37i −0.142466 + 0.574869i
\(251\) 2290.25 0.575934 0.287967 0.957640i \(-0.407021\pi\)
0.287967 + 0.957640i \(0.407021\pi\)
\(252\) 755.501i 0.188857i
\(253\) 9127.48i 2.26814i
\(254\) 436.760 0.107893
\(255\) −1458.21 + 2110.67i −0.358105 + 0.518335i
\(256\) −3887.43 −0.949079
\(257\) 802.202i 0.194708i −0.995250 0.0973541i \(-0.968962\pi\)
0.995250 0.0973541i \(-0.0310379\pi\)
\(258\) 615.922i 0.148627i
\(259\) −1619.15 −0.388452
\(260\) 2174.56 + 1502.35i 0.518694 + 0.358352i
\(261\) 834.756 0.197970
\(262\) 1212.02i 0.285796i
\(263\) 286.978i 0.0672845i 0.999434 + 0.0336423i \(0.0107107\pi\)
−0.999434 + 0.0336423i \(0.989289\pi\)
\(264\) −3174.31 −0.740020
\(265\) −2471.16 1707.26i −0.572839 0.395760i
\(266\) −1467.84 −0.338343
\(267\) 2559.90i 0.586753i
\(268\) 2111.28i 0.481221i
\(269\) −3561.22 −0.807180 −0.403590 0.914940i \(-0.632238\pi\)
−0.403590 + 0.914940i \(0.632238\pi\)
\(270\) 1268.57 1836.17i 0.285935 0.413874i
\(271\) 1928.81 0.432349 0.216175 0.976355i \(-0.430642\pi\)
0.216175 + 0.976355i \(0.430642\pi\)
\(272\) 416.466i 0.0928380i
\(273\) 794.605i 0.176160i
\(274\) 1296.06 0.285759
\(275\) 2546.93 + 6732.87i 0.558494 + 1.47639i
\(276\) 2053.04 0.447747
\(277\) 6588.69i 1.42916i 0.699556 + 0.714578i \(0.253381\pi\)
−0.699556 + 0.714578i \(0.746619\pi\)
\(278\) 4946.70i 1.06721i
\(279\) 1029.84 0.220986
\(280\) 983.206 1423.13i 0.209849 0.303744i
\(281\) 815.552 0.173138 0.0865689 0.996246i \(-0.472410\pi\)
0.0865689 + 0.996246i \(0.472410\pi\)
\(282\) 280.049i 0.0591371i
\(283\) 6513.49i 1.36815i 0.729411 + 0.684076i \(0.239794\pi\)
−0.729411 + 0.684076i \(0.760206\pi\)
\(284\) 1718.03 0.358965
\(285\) −2871.67 1983.96i −0.596852 0.412350i
\(286\) −4390.89 −0.907828
\(287\) 1186.89i 0.244112i
\(288\) 3831.80i 0.783997i
\(289\) −3551.94 −0.722967
\(290\) −618.995 427.648i −0.125340 0.0865943i
\(291\) 2350.96 0.473593
\(292\) 2837.16i 0.568603i
\(293\) 435.520i 0.0868373i −0.999057 0.0434186i \(-0.986175\pi\)
0.999057 0.0434186i \(-0.0138249\pi\)
\(294\) −204.712 −0.0406089
\(295\) 1530.57 2215.40i 0.302078 0.437240i
\(296\) 5112.31 1.00387
\(297\) 6862.29i 1.34071i
\(298\) 4211.36i 0.818650i
\(299\) 7214.10 1.39533
\(300\) 1514.42 572.879i 0.291450 0.110251i
\(301\) −1031.99 −0.197618
\(302\) 169.279i 0.0322547i
\(303\) 1507.89i 0.285895i
\(304\) −566.620 −0.106901
\(305\) 574.864 832.082i 0.107923 0.156213i
\(306\) 3202.71 0.598323
\(307\) 4915.99i 0.913910i −0.889490 0.456955i \(-0.848940\pi\)
0.889490 0.456955i \(-0.151060\pi\)
\(308\) 2093.72i 0.387340i
\(309\) −750.601 −0.138188
\(310\) −763.659 527.592i −0.139913 0.0966620i
\(311\) −1831.11 −0.333868 −0.166934 0.985968i \(-0.553387\pi\)
−0.166934 + 0.985968i \(0.553387\pi\)
\(312\) 2508.89i 0.455249i
\(313\) 2442.96i 0.441163i 0.975369 + 0.220582i \(0.0707955\pi\)
−0.975369 + 0.220582i \(0.929204\pi\)
\(314\) 3917.11 0.703998
\(315\) 1338.03 + 924.412i 0.239332 + 0.165348i
\(316\) 131.449 0.0234006
\(317\) 1666.19i 0.295214i 0.989046 + 0.147607i \(0.0471570\pi\)
−0.989046 + 0.147607i \(0.952843\pi\)
\(318\) 1122.35i 0.197919i
\(319\) −2313.36 −0.406029
\(320\) −1732.91 + 2508.29i −0.302727 + 0.438180i
\(321\) −3770.02 −0.655521
\(322\) 1858.55i 0.321655i
\(323\) 11516.9i 1.98396i
\(324\) 1370.54 0.235004
\(325\) 5321.47 2013.02i 0.908253 0.343577i
\(326\) 2219.93 0.377149
\(327\) 4407.05i 0.745292i
\(328\) 3747.50i 0.630856i
\(329\) 469.229 0.0786305
\(330\) −1528.96 + 2213.09i −0.255051 + 0.369171i
\(331\) −5466.38 −0.907732 −0.453866 0.891070i \(-0.649956\pi\)
−0.453866 + 0.891070i \(0.649956\pi\)
\(332\) 1954.20i 0.323045i
\(333\) 4806.60i 0.790991i
\(334\) 3494.72 0.572522
\(335\) −3739.19 2583.31i −0.609833 0.421318i
\(336\) −79.0233 −0.0128306
\(337\) 10650.5i 1.72157i 0.508970 + 0.860784i \(0.330027\pi\)
−0.508970 + 0.860784i \(0.669973\pi\)
\(338\) 209.896i 0.0337776i
\(339\) 2606.86 0.417655
\(340\) 4395.61 + 3036.82i 0.701134 + 0.484395i
\(341\) −2854.01 −0.453235
\(342\) 4357.43i 0.688956i
\(343\) 343.000i 0.0539949i
\(344\) 3258.42 0.510704
\(345\) 2512.04 3636.04i 0.392011 0.567413i
\(346\) −3213.28 −0.499269
\(347\) 4019.13i 0.621782i 0.950446 + 0.310891i \(0.100627\pi\)
−0.950446 + 0.310891i \(0.899373\pi\)
\(348\) 520.341i 0.0801529i
\(349\) −10544.9 −1.61735 −0.808674 0.588256i \(-0.799815\pi\)
−0.808674 + 0.588256i \(0.799815\pi\)
\(350\) −518.609 1370.95i −0.0792024 0.209373i
\(351\) −5423.76 −0.824784
\(352\) 10619.1i 1.60795i
\(353\) 2959.98i 0.446300i −0.974784 0.223150i \(-0.928366\pi\)
0.974784 0.223150i \(-0.0716340\pi\)
\(354\) 1006.19 0.151069
\(355\) 2102.14 3042.72i 0.314281 0.454903i
\(356\) −5331.14 −0.793680
\(357\) 1606.20i 0.238121i
\(358\) 1053.75i 0.155566i
\(359\) −2170.17 −0.319045 −0.159523 0.987194i \(-0.550995\pi\)
−0.159523 + 0.987194i \(0.550995\pi\)
\(360\) −4224.70 2918.74i −0.618504 0.427309i
\(361\) 8810.30 1.28449
\(362\) 4691.88i 0.681215i
\(363\) 4951.46i 0.715934i
\(364\) −1654.82 −0.238285
\(365\) −5024.76 3471.48i −0.720569 0.497823i
\(366\) 377.914 0.0539724
\(367\) 1252.20i 0.178105i −0.996027 0.0890523i \(-0.971616\pi\)
0.996027 0.0890523i \(-0.0283838\pi\)
\(368\) 717.441i 0.101628i
\(369\) 3523.40 0.497076
\(370\) 2462.43 3564.23i 0.345989 0.500798i
\(371\) 1880.53 0.263159
\(372\) 641.949i 0.0894718i
\(373\) 4646.02i 0.644938i −0.946580 0.322469i \(-0.895487\pi\)
0.946580 0.322469i \(-0.104513\pi\)
\(374\) −8875.66 −1.22714
\(375\) 838.406 3383.08i 0.115454 0.465870i
\(376\) −1481.54 −0.203204
\(377\) 1828.41i 0.249783i
\(378\) 1397.31i 0.190132i
\(379\) −1434.84 −0.194466 −0.0972331 0.995262i \(-0.530999\pi\)
−0.0972331 + 0.995262i \(0.530999\pi\)
\(380\) −4131.72 + 5980.43i −0.557771 + 0.807341i
\(381\) −650.242 −0.0874355
\(382\) 1240.05i 0.166090i
\(383\) 13216.7i 1.76330i 0.471905 + 0.881649i \(0.343566\pi\)
−0.471905 + 0.881649i \(0.656434\pi\)
\(384\) 2539.82 0.337526
\(385\) −3708.08 2561.82i −0.490861 0.339123i
\(386\) −6838.97 −0.901799
\(387\) 3063.57i 0.402403i
\(388\) 4896.02i 0.640612i
\(389\) 7755.01 1.01078 0.505391 0.862890i \(-0.331348\pi\)
0.505391 + 0.862890i \(0.331348\pi\)
\(390\) 1749.16 + 1208.45i 0.227108 + 0.156903i
\(391\) 14582.5 1.88610
\(392\) 1082.99i 0.139539i
\(393\) 1804.44i 0.231607i
\(394\) 5720.49 0.731457
\(395\) 160.838 232.803i 0.0204876 0.0296547i
\(396\) −6215.40 −0.788726
\(397\) 3560.83i 0.450158i −0.974341 0.225079i \(-0.927736\pi\)
0.974341 0.225079i \(-0.0722640\pi\)
\(398\) 5682.89i 0.715723i
\(399\) 2185.31 0.274191
\(400\) −200.195 529.219i −0.0250243 0.0661524i
\(401\) −5430.61 −0.676288 −0.338144 0.941094i \(-0.609799\pi\)
−0.338144 + 0.941094i \(0.609799\pi\)
\(402\) 1698.26i 0.210701i
\(403\) 2255.73i 0.278823i
\(404\) −3140.28 −0.386719
\(405\) 1676.96 2427.31i 0.205751 0.297812i
\(406\) 471.048 0.0575806
\(407\) 13320.5i 1.62229i
\(408\) 5071.42i 0.615374i
\(409\) 9698.79 1.17255 0.586277 0.810111i \(-0.300593\pi\)
0.586277 + 0.810111i \(0.300593\pi\)
\(410\) −2612.70 1805.05i −0.314713 0.217427i
\(411\) −1929.56 −0.231577
\(412\) 1563.17i 0.186922i
\(413\) 1685.90i 0.200866i
\(414\) −5517.27 −0.654974
\(415\) −3461.00 2391.12i −0.409383 0.282832i
\(416\) 8393.01 0.989186
\(417\) 7364.58i 0.864856i
\(418\) 12075.7i 1.41302i
\(419\) −13830.9 −1.61261 −0.806307 0.591498i \(-0.798537\pi\)
−0.806307 + 0.591498i \(0.798537\pi\)
\(420\) −576.228 + 834.056i −0.0669453 + 0.0968994i
\(421\) 16703.0 1.93362 0.966810 0.255498i \(-0.0822393\pi\)
0.966810 + 0.255498i \(0.0822393\pi\)
\(422\) 5692.26i 0.656623i
\(423\) 1392.95i 0.160112i
\(424\) −5937.58 −0.680081
\(425\) 10756.7 4069.09i 1.22771 0.464423i
\(426\) 1381.94 0.157172
\(427\) 633.205i 0.0717634i
\(428\) 7851.31i 0.886699i
\(429\) 6537.10 0.735698
\(430\) 1569.48 2271.72i 0.176016 0.254773i
\(431\) 8174.07 0.913530 0.456765 0.889588i \(-0.349008\pi\)
0.456765 + 0.889588i \(0.349008\pi\)
\(432\) 539.392i 0.0600729i
\(433\) 14222.8i 1.57853i −0.614051 0.789267i \(-0.710461\pi\)
0.614051 0.789267i \(-0.289539\pi\)
\(434\) 581.136 0.0642752
\(435\) 921.552 + 636.677i 0.101575 + 0.0701755i
\(436\) 9177.96 1.00813
\(437\) 19840.1i 2.17181i
\(438\) 2282.14i 0.248961i
\(439\) −5537.38 −0.602016 −0.301008 0.953622i \(-0.597323\pi\)
−0.301008 + 0.953622i \(0.597323\pi\)
\(440\) 11707.9 + 8088.70i 1.26853 + 0.876394i
\(441\) −1018.23 −0.109948
\(442\) 7015.07i 0.754916i
\(443\) 3974.09i 0.426218i −0.977028 0.213109i \(-0.931641\pi\)
0.977028 0.213109i \(-0.0683589\pi\)
\(444\) −2996.17 −0.320252
\(445\) −6523.06 + 9441.74i −0.694882 + 1.00580i
\(446\) −305.903 −0.0324774
\(447\) 6269.82i 0.663428i
\(448\) 1908.78i 0.201298i
\(449\) 15243.1 1.60216 0.801078 0.598559i \(-0.204260\pi\)
0.801078 + 0.598559i \(0.204260\pi\)
\(450\) −4069.81 + 1539.54i −0.426339 + 0.161277i
\(451\) −9764.40 −1.01948
\(452\) 5428.95i 0.564947i
\(453\) 252.021i 0.0261390i
\(454\) −5280.67 −0.545890
\(455\) −2024.79 + 2930.77i −0.208623 + 0.301970i
\(456\) −6899.89 −0.708590
\(457\) 10768.9i 1.10229i −0.834410 0.551145i \(-0.814191\pi\)
0.834410 0.551145i \(-0.185809\pi\)
\(458\) 10071.7i 1.02755i
\(459\) −10963.5 −1.11489
\(460\) −7572.27 5231.49i −0.767520 0.530260i
\(461\) −332.605 −0.0336029 −0.0168015 0.999859i \(-0.505348\pi\)
−0.0168015 + 0.999859i \(0.505348\pi\)
\(462\) 1684.13i 0.169595i
\(463\) 8205.35i 0.823618i 0.911270 + 0.411809i \(0.135103\pi\)
−0.911270 + 0.411809i \(0.864897\pi\)
\(464\) 181.835 0.0181929
\(465\) 1136.93 + 785.473i 0.113384 + 0.0783343i
\(466\) 1575.76 0.156643
\(467\) 167.628i 0.0166100i −0.999966 0.00830501i \(-0.997356\pi\)
0.999966 0.00830501i \(-0.00264360\pi\)
\(468\) 4912.47i 0.485212i
\(469\) 2845.49 0.280154
\(470\) −713.612 + 1032.91i −0.0700351 + 0.101372i
\(471\) −5831.75 −0.570515
\(472\) 5323.06i 0.519097i
\(473\) 8490.07i 0.825315i
\(474\) 105.734 0.0102459
\(475\) 5536.18 + 14635.0i 0.534773 + 1.41368i
\(476\) −3345.01 −0.322098
\(477\) 5582.52i 0.535862i
\(478\) 8641.86i 0.826924i
\(479\) −6628.58 −0.632292 −0.316146 0.948711i \(-0.602389\pi\)
−0.316146 + 0.948711i \(0.602389\pi\)
\(480\) 2922.55 4230.23i 0.277908 0.402255i
\(481\) −10528.2 −0.998010
\(482\) 777.001i 0.0734262i
\(483\) 2766.98i 0.260667i
\(484\) 10311.7 0.968419
\(485\) −8671.11 5990.65i −0.811824 0.560868i
\(486\) 6492.05 0.605937
\(487\) 20641.6i 1.92065i −0.278875 0.960327i \(-0.589961\pi\)
0.278875 0.960327i \(-0.410039\pi\)
\(488\) 1999.28i 0.185458i
\(489\) −3305.01 −0.305640
\(490\) 755.044 + 521.641i 0.0696111 + 0.0480925i
\(491\) −16710.8 −1.53594 −0.767972 0.640484i \(-0.778734\pi\)
−0.767972 + 0.640484i \(0.778734\pi\)
\(492\) 2196.30i 0.201253i
\(493\) 3695.92i 0.337639i
\(494\) −9544.32 −0.869270
\(495\) −7605.01 + 11007.8i −0.690545 + 0.999523i
\(496\) 224.331 0.0203080
\(497\) 2315.47i 0.208980i
\(498\) 1571.91i 0.141444i
\(499\) 13728.7 1.23162 0.615812 0.787893i \(-0.288828\pi\)
0.615812 + 0.787893i \(0.288828\pi\)
\(500\) −7045.47 1746.03i −0.630166 0.156170i
\(501\) −5202.90 −0.463969
\(502\) 3836.54i 0.341102i
\(503\) 19523.7i 1.73065i 0.501209 + 0.865326i \(0.332889\pi\)
−0.501209 + 0.865326i \(0.667111\pi\)
\(504\) 3214.95 0.284138
\(505\) −3842.37 + 5561.60i −0.338580 + 0.490075i
\(506\) 15290.0 1.34333
\(507\) 312.490i 0.0273731i
\(508\) 1354.17i 0.118271i
\(509\) 8688.17 0.756574 0.378287 0.925688i \(-0.376513\pi\)
0.378287 + 0.925688i \(0.376513\pi\)
\(510\) 3535.72 + 2442.74i 0.306989 + 0.212091i
\(511\) 3823.78 0.331026
\(512\) 1635.04i 0.141131i
\(513\) 14916.3i 1.28377i
\(514\) −1343.82 −0.115318
\(515\) 2768.46 + 1912.66i 0.236880 + 0.163654i
\(516\) −1909.66 −0.162923
\(517\) 3860.28i 0.328385i
\(518\) 2712.34i 0.230064i
\(519\) 4783.89 0.404604
\(520\) 6393.08 9253.60i 0.539144 0.780380i
\(521\) 6771.36 0.569402 0.284701 0.958616i \(-0.408106\pi\)
0.284701 + 0.958616i \(0.408106\pi\)
\(522\) 1398.35i 0.117249i
\(523\) 1365.89i 0.114200i 0.998368 + 0.0570998i \(0.0181853\pi\)
−0.998368 + 0.0570998i \(0.981815\pi\)
\(524\) −3757.85 −0.313287
\(525\) 772.099 + 2041.06i 0.0641851 + 0.169675i
\(526\) 480.735 0.0398499
\(527\) 4559.68i 0.376894i
\(528\) 650.113i 0.0535844i
\(529\) −12954.0 −1.06469
\(530\) −2859.94 + 4139.60i −0.234392 + 0.339269i
\(531\) 5004.75 0.409016
\(532\) 4551.04i 0.370888i
\(533\) 7717.51i 0.627171i
\(534\) −4288.24 −0.347510
\(535\) 13905.1 + 9606.67i 1.12368 + 0.776322i
\(536\) −8984.34 −0.724001
\(537\) 1568.82i 0.126070i
\(538\) 5965.62i 0.478060i
\(539\) 2821.81 0.225499
\(540\) 5693.05 + 3933.18i 0.453685 + 0.313439i
\(541\) −23250.1 −1.84769 −0.923844 0.382770i \(-0.874970\pi\)
−0.923844 + 0.382770i \(0.874970\pi\)
\(542\) 3231.06i 0.256063i
\(543\) 6985.22i 0.552052i
\(544\) 16965.5 1.33711
\(545\) 11229.9 16254.7i 0.882638 1.27757i
\(546\) −1331.09 −0.104332
\(547\) 11552.7i 0.903033i −0.892263 0.451516i \(-0.850883\pi\)
0.892263 0.451516i \(-0.149117\pi\)
\(548\) 4018.43i 0.313246i
\(549\) 1879.73 0.146129
\(550\) 11278.6 4266.52i 0.874406 0.330773i
\(551\) −5028.47 −0.388784
\(552\) 8736.48i 0.673640i
\(553\) 177.161i 0.0136232i
\(554\) 11037.1 0.846430
\(555\) −3666.04 + 5306.38i −0.280387 + 0.405844i
\(556\) 15337.2 1.16986
\(557\) 16406.2i 1.24803i −0.781413 0.624014i \(-0.785501\pi\)
0.781413 0.624014i \(-0.214499\pi\)
\(558\) 1725.16i 0.130881i
\(559\) −6710.31 −0.507721
\(560\) 291.464 + 201.365i 0.0219939 + 0.0151950i
\(561\) 13214.0 0.994465
\(562\) 1366.18i 0.102542i
\(563\) 13631.9i 1.02045i −0.860040 0.510227i \(-0.829561\pi\)
0.860040 0.510227i \(-0.170439\pi\)
\(564\) 868.289 0.0648255
\(565\) −9614.95 6642.72i −0.715936 0.494622i
\(566\) 10911.2 0.810300
\(567\) 1847.15i 0.136813i
\(568\) 7310.88i 0.540067i
\(569\) 3086.83 0.227428 0.113714 0.993514i \(-0.463725\pi\)
0.113714 + 0.993514i \(0.463725\pi\)
\(570\) −3323.46 + 4810.51i −0.244218 + 0.353491i
\(571\) −3258.06 −0.238784 −0.119392 0.992847i \(-0.538095\pi\)
−0.119392 + 0.992847i \(0.538095\pi\)
\(572\) 13613.9i 0.995152i
\(573\) 1846.17i 0.134598i
\(574\) 1988.24 0.144577
\(575\) −18530.5 + 7009.78i −1.34396 + 0.508396i
\(576\) −5666.39 −0.409895
\(577\) 23758.4i 1.71417i 0.515178 + 0.857083i \(0.327726\pi\)
−0.515178 + 0.857083i \(0.672274\pi\)
\(578\) 5950.07i 0.428184i
\(579\) 10181.8 0.730812
\(580\) 1325.92 1919.19i 0.0949238 0.137397i
\(581\) 2633.78 0.188068
\(582\) 3938.23i 0.280490i
\(583\) 15470.8i 1.09903i
\(584\) −12073.2 −0.855468
\(585\) 8700.25 + 6010.78i 0.614891 + 0.424812i
\(586\) −729.566 −0.0514302
\(587\) 596.893i 0.0419701i 0.999780 + 0.0209850i \(0.00668023\pi\)
−0.999780 + 0.0209850i \(0.993320\pi\)
\(588\) 634.708i 0.0445151i
\(589\) −6203.66 −0.433985
\(590\) −3711.16 2563.95i −0.258960 0.178909i
\(591\) −8516.60 −0.592768
\(592\) 1047.02i 0.0726898i
\(593\) 19496.3i 1.35012i −0.737765 0.675058i \(-0.764119\pi\)
0.737765 0.675058i \(-0.235881\pi\)
\(594\) −11495.5 −0.794047
\(595\) −4092.88 + 5924.20i −0.282003 + 0.408182i
\(596\) −13057.3 −0.897396
\(597\) 8460.62i 0.580017i
\(598\) 12084.8i 0.826395i
\(599\) −3797.02 −0.259001 −0.129501 0.991579i \(-0.541337\pi\)
−0.129501 + 0.991579i \(0.541337\pi\)
\(600\) −2437.83 6444.45i −0.165873 0.438489i
\(601\) 5789.33 0.392931 0.196466 0.980511i \(-0.437054\pi\)
0.196466 + 0.980511i \(0.437054\pi\)
\(602\) 1728.76i 0.117041i
\(603\) 8447.09i 0.570468i
\(604\) 524.850 0.0353573
\(605\) 12617.2 18262.6i 0.847869 1.22724i
\(606\) −2525.96 −0.169324
\(607\) 18536.4i 1.23949i 0.784803 + 0.619745i \(0.212764\pi\)
−0.784803 + 0.619745i \(0.787236\pi\)
\(608\) 23082.3i 1.53966i
\(609\) −701.291 −0.0466630
\(610\) −1393.87 962.991i −0.0925184 0.0639186i
\(611\) 3051.06 0.202017
\(612\) 9929.98i 0.655876i
\(613\) 2163.47i 0.142548i −0.997457 0.0712738i \(-0.977294\pi\)
0.997457 0.0712738i \(-0.0227064\pi\)
\(614\) −8235.08 −0.541272
\(615\) 3889.76 + 2687.34i 0.255041 + 0.176201i
\(616\) −8909.59 −0.582756
\(617\) 22964.9i 1.49843i 0.662327 + 0.749215i \(0.269569\pi\)
−0.662327 + 0.749215i \(0.730431\pi\)
\(618\) 1257.38i 0.0818433i
\(619\) 1386.67 0.0900401 0.0450200 0.998986i \(-0.485665\pi\)
0.0450200 + 0.998986i \(0.485665\pi\)
\(620\) 1635.80 2367.72i 0.105960 0.153371i
\(621\) 18886.7 1.22045
\(622\) 3067.41i 0.197736i
\(623\) 7185.06i 0.462060i
\(624\) −513.831 −0.0329643
\(625\) −11713.0 + 10341.5i −0.749631 + 0.661856i
\(626\) 4092.35 0.261283
\(627\) 17978.2i 1.14510i
\(628\) 12145.0i 0.771716i
\(629\) −21281.4 −1.34904
\(630\) 1548.54 2241.42i 0.0979291 0.141747i
\(631\) 5969.39 0.376605 0.188303 0.982111i \(-0.439701\pi\)
0.188303 + 0.982111i \(0.439701\pi\)
\(632\) 559.367i 0.0352064i
\(633\) 8474.57i 0.532123i
\(634\) 2791.14 0.174843
\(635\) 2398.31 + 1656.93i 0.149880 + 0.103548i
\(636\) 3479.84 0.216957
\(637\) 2230.28i 0.138724i
\(638\) 3875.25i 0.240474i
\(639\) 6873.70 0.425539
\(640\) −9367.71 6471.91i −0.578580 0.399726i
\(641\) 30367.1 1.87118 0.935592 0.353084i \(-0.114867\pi\)
0.935592 + 0.353084i \(0.114867\pi\)
\(642\) 6315.40i 0.388238i
\(643\) 28592.2i 1.75360i −0.480851 0.876802i \(-0.659672\pi\)
0.480851 0.876802i \(-0.340328\pi\)
\(644\) 5762.42 0.352595
\(645\) −2336.62 + 3382.12i −0.142642 + 0.206466i
\(646\) −19292.7 −1.17502
\(647\) 14507.9i 0.881555i −0.897616 0.440778i \(-0.854703\pi\)
0.897616 0.440778i \(-0.145297\pi\)
\(648\) 5832.21i 0.353566i
\(649\) −13869.7 −0.838877
\(650\) −3372.14 8914.33i −0.203487 0.537921i
\(651\) −865.188 −0.0520882
\(652\) 6882.89i 0.413428i
\(653\) 6999.85i 0.419488i −0.977756 0.209744i \(-0.932737\pi\)
0.977756 0.209744i \(-0.0672630\pi\)
\(654\) 7382.53 0.441406
\(655\) −4598.01 + 6655.35i −0.274289 + 0.397017i
\(656\) 767.504 0.0456799
\(657\) 11351.3i 0.674056i
\(658\) 786.035i 0.0465696i
\(659\) −7308.92 −0.432041 −0.216020 0.976389i \(-0.569308\pi\)
−0.216020 + 0.976389i \(0.569308\pi\)
\(660\) −6861.66 4740.55i −0.404681 0.279584i
\(661\) −30097.2 −1.77102 −0.885512 0.464617i \(-0.846192\pi\)
−0.885512 + 0.464617i \(0.846192\pi\)
\(662\) 9157.07i 0.537613i
\(663\) 10444.0i 0.611779i
\(664\) −8315.91 −0.486024
\(665\) −8060.14 5568.54i −0.470013 0.324720i
\(666\) 8051.83 0.468472
\(667\) 6366.92i 0.369608i
\(668\) 10835.4i 0.627594i
\(669\) 455.425 0.0263195
\(670\) −4327.47 + 6263.76i −0.249529 + 0.361179i
\(671\) −5209.29 −0.299706
\(672\) 3219.16i 0.184794i
\(673\) 5400.26i 0.309309i 0.987969 + 0.154654i \(0.0494264\pi\)
−0.987969 + 0.154654i \(0.950574\pi\)
\(674\) 17841.3 1.01962
\(675\) 13931.7 5270.15i 0.794419 0.300516i
\(676\) 650.781 0.0370267
\(677\) 6431.09i 0.365091i 0.983197 + 0.182546i \(0.0584338\pi\)
−0.983197 + 0.182546i \(0.941566\pi\)
\(678\) 4366.91i 0.247360i
\(679\) 6598.62 0.372948
\(680\) 12922.9 18705.1i 0.728778 1.05486i
\(681\) 7861.79 0.442385
\(682\) 4780.92i 0.268433i
\(683\) 20865.8i 1.16897i 0.811404 + 0.584486i \(0.198704\pi\)
−0.811404 + 0.584486i \(0.801296\pi\)
\(684\) −13510.2 −0.755227
\(685\) 7116.86 + 4916.86i 0.396965 + 0.274253i
\(686\) −574.581 −0.0319790
\(687\) 14994.6i 0.832720i
\(688\) 667.339i 0.0369797i
\(689\) 12227.7 0.676109
\(690\) −6090.95 4208.08i −0.336056 0.232172i
\(691\) 18450.3 1.01575 0.507873 0.861432i \(-0.330432\pi\)
0.507873 + 0.861432i \(0.330432\pi\)
\(692\) 9962.76i 0.547294i
\(693\) 8376.81i 0.459176i
\(694\) 6732.70 0.368256
\(695\) 18766.2 27163.0i 1.02424 1.48252i
\(696\) 2214.26 0.120591
\(697\) 15600.0i 0.847766i
\(698\) 17664.4i 0.957890i
\(699\) −2345.97 −0.126942
\(700\) 4250.64 1607.95i 0.229513 0.0868209i
\(701\) 12639.3 0.680996 0.340498 0.940245i \(-0.389404\pi\)
0.340498 + 0.940245i \(0.389404\pi\)
\(702\) 9085.69i 0.488486i
\(703\) 28954.4i 1.55339i
\(704\) 15703.3 0.840680
\(705\) 1062.42 1537.79i 0.0567560 0.0821509i
\(706\) −4958.45 −0.264325
\(707\) 4232.32i 0.225138i
\(708\) 3119.69i 0.165600i
\(709\) 23126.8 1.22503 0.612514 0.790460i \(-0.290158\pi\)
0.612514 + 0.790460i \(0.290158\pi\)
\(710\) −5097.04 3521.42i −0.269421 0.186136i
\(711\) 525.918 0.0277404
\(712\) 22686.1i 1.19410i
\(713\) 7854.92i 0.412579i
\(714\) −2690.65 −0.141029
\(715\) −24111.0 16657.7i −1.26112 0.871275i
\(716\) −3267.16 −0.170530
\(717\) 12865.9i 0.670134i
\(718\) 3635.39i 0.188957i
\(719\) 24093.1 1.24968 0.624841 0.780752i \(-0.285164\pi\)
0.624841 + 0.780752i \(0.285164\pi\)
\(720\) 597.771 865.238i 0.0309411 0.0447854i
\(721\) −2106.77 −0.108821
\(722\) 14758.7i 0.760750i
\(723\) 1156.79i 0.0595041i
\(724\) −14547.2 −0.746741
\(725\) −1776.63 4696.55i −0.0910100 0.240587i
\(726\) 8294.49 0.424019
\(727\) 35983.4i 1.83570i 0.396931 + 0.917849i \(0.370075\pi\)
−0.396931 + 0.917849i \(0.629925\pi\)
\(728\) 7041.89i 0.358503i
\(729\) −2540.55 −0.129073
\(730\) −5815.28 + 8417.28i −0.294840 + 0.426764i
\(731\) −13564.1 −0.686302
\(732\) 1171.72i 0.0591640i
\(733\) 1451.50i 0.0731413i 0.999331 + 0.0365706i \(0.0116434\pi\)
−0.999331 + 0.0365706i \(0.988357\pi\)
\(734\) −2097.64 −0.105484
\(735\) −1124.10 776.613i −0.0564124 0.0389739i
\(736\) −29226.3 −1.46371
\(737\) 23409.4i 1.17001i
\(738\) 5902.27i 0.294398i
\(739\) 5891.67 0.293273 0.146636 0.989190i \(-0.453155\pi\)
0.146636 + 0.989190i \(0.453155\pi\)
\(740\) 11050.9 + 7634.77i 0.548970 + 0.379270i
\(741\) 14209.5 0.704451
\(742\) 3150.19i 0.155859i
\(743\) 7438.65i 0.367292i −0.982992 0.183646i \(-0.941210\pi\)
0.982992 0.183646i \(-0.0587900\pi\)
\(744\) 2731.75 0.134611
\(745\) −15976.6 + 23125.2i −0.785688 + 1.13724i
\(746\) −7782.84 −0.381970
\(747\) 7818.64i 0.382957i
\(748\) 27518.9i 1.34518i
\(749\) −10581.6 −0.516214
\(750\) −5667.20 1404.47i −0.275916 0.0683784i
\(751\) 20272.4 0.985018 0.492509 0.870307i \(-0.336080\pi\)
0.492509 + 0.870307i \(0.336080\pi\)
\(752\) 303.427i 0.0147139i
\(753\) 5711.80i 0.276427i
\(754\) 3062.89 0.147936
\(755\) 642.193 929.537i 0.0309560 0.0448070i
\(756\) −4332.35 −0.208421
\(757\) 10193.8i 0.489432i −0.969595 0.244716i \(-0.921305\pi\)
0.969595 0.244716i \(-0.0786947\pi\)
\(758\) 2403.59i 0.115174i
\(759\) −22763.6 −1.08862
\(760\) 25449.1 + 17582.1i 1.21465 + 0.839172i
\(761\) −41117.6 −1.95862 −0.979311 0.202362i \(-0.935138\pi\)
−0.979311 + 0.202362i \(0.935138\pi\)
\(762\) 1089.26i 0.0517845i
\(763\) 12369.6i 0.586908i
\(764\) 3844.76 0.182066
\(765\) 17586.5 + 12150.1i 0.831167 + 0.574232i
\(766\) 22140.2 1.04433
\(767\) 10962.2i 0.516065i
\(768\) 9695.10i 0.455523i
\(769\) −11486.6 −0.538642 −0.269321 0.963050i \(-0.586799\pi\)
−0.269321 + 0.963050i \(0.586799\pi\)
\(770\) −4291.47 + 6211.64i −0.200849 + 0.290717i
\(771\) 2000.66 0.0934527
\(772\) 21204.2i 0.988544i
\(773\) 21799.2i 1.01431i 0.861854 + 0.507156i \(0.169303\pi\)
−0.861854 + 0.507156i \(0.830697\pi\)
\(774\) 5131.98 0.238327
\(775\) −2191.84 5794.17i −0.101591 0.268558i
\(776\) −20834.5 −0.963807
\(777\) 4038.10i 0.186443i
\(778\) 12990.9i 0.598645i
\(779\) −21224.5 −0.976185