Properties

Label 230.4.b.a.139.3
Level $230$
Weight $4$
Character 230.139
Analytic conductor $13.570$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,4,Mod(139,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, 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("230.139");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(13.5704393013\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} + 212 x^{12} + 17560 x^{10} + 728073 x^{8} + 16036416 x^{6} + 183184060 x^{4} + 961600400 x^{2} + 1560250000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.3
Root \(-3.85861i\) of defining polynomial
Character \(\chi\) \(=\) 230.139
Dual form 230.4.b.a.139.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{2} -4.85861i q^{3} -4.00000 q^{4} +(8.38650 + 7.39369i) q^{5} -9.71722 q^{6} +11.5462i q^{7} +8.00000i q^{8} +3.39393 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} -4.85861i q^{3} -4.00000 q^{4} +(8.38650 + 7.39369i) q^{5} -9.71722 q^{6} +11.5462i q^{7} +8.00000i q^{8} +3.39393 q^{9} +(14.7874 - 16.7730i) q^{10} +30.5254 q^{11} +19.4344i q^{12} +52.0283i q^{13} +23.0923 q^{14} +(35.9230 - 40.7467i) q^{15} +16.0000 q^{16} +38.0089i q^{17} -6.78787i q^{18} +109.470 q^{19} +(-33.5460 - 29.5747i) q^{20} +56.0983 q^{21} -61.0508i q^{22} +23.0000i q^{23} +38.8689 q^{24} +(15.6668 + 124.014i) q^{25} +104.057 q^{26} -147.672i q^{27} -46.1847i q^{28} -60.9293 q^{29} +(-81.4934 - 71.8460i) q^{30} -63.1074 q^{31} -32.0000i q^{32} -148.311i q^{33} +76.0178 q^{34} +(-85.3687 + 96.8320i) q^{35} -13.5757 q^{36} -386.056i q^{37} -218.939i q^{38} +252.785 q^{39} +(-59.1495 + 67.0920i) q^{40} -92.0091 q^{41} -112.197i q^{42} -181.661i q^{43} -122.102 q^{44} +(28.4632 + 25.0937i) q^{45} +46.0000 q^{46} +207.423i q^{47} -77.7377i q^{48} +209.686 q^{49} +(248.029 - 31.3337i) q^{50} +184.670 q^{51} -208.113i q^{52} +136.696i q^{53} -295.344 q^{54} +(256.001 + 225.695i) q^{55} -92.3694 q^{56} -531.870i q^{57} +121.859i q^{58} +230.608 q^{59} +(-143.692 + 162.987i) q^{60} -241.396 q^{61} +126.215i q^{62} +39.1869i q^{63} -64.0000 q^{64} +(-384.681 + 436.336i) q^{65} -296.622 q^{66} +269.366i q^{67} -152.036i q^{68} +111.748 q^{69} +(193.664 + 170.737i) q^{70} +186.611 q^{71} +27.1515i q^{72} +59.1574i q^{73} -772.113 q^{74} +(602.537 - 76.1190i) q^{75} -437.878 q^{76} +352.451i q^{77} -505.571i q^{78} +941.143 q^{79} +(134.184 + 118.299i) q^{80} -625.845 q^{81} +184.018i q^{82} +94.2803i q^{83} -224.393 q^{84} +(-281.026 + 318.762i) q^{85} -363.321 q^{86} +296.032i q^{87} +244.203i q^{88} +1380.57 q^{89} +(50.1873 - 56.9265i) q^{90} -600.728 q^{91} -92.0000i q^{92} +306.614i q^{93} +414.846 q^{94} +(918.067 + 809.383i) q^{95} -155.475 q^{96} +1253.69i q^{97} -419.372i q^{98} +103.601 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 4.85861i 0.935039i −0.883983 0.467520i \(-0.845148\pi\)
0.883983 0.467520i \(-0.154852\pi\)
\(4\) −4.00000 −0.500000
\(5\) 8.38650 + 7.39369i 0.750112 + 0.661311i
\(6\) −9.71722 −0.661173
\(7\) 11.5462i 0.623435i 0.950175 + 0.311717i \(0.100904\pi\)
−0.950175 + 0.311717i \(0.899096\pi\)
\(8\) 8.00000i 0.353553i
\(9\) 3.39393 0.125701
\(10\) 14.7874 16.7730i 0.467618 0.530409i
\(11\) 30.5254 0.836704 0.418352 0.908285i \(-0.362608\pi\)
0.418352 + 0.908285i \(0.362608\pi\)
\(12\) 19.4344i 0.467520i
\(13\) 52.0283i 1.11000i 0.831849 + 0.555002i \(0.187283\pi\)
−0.831849 + 0.555002i \(0.812717\pi\)
\(14\) 23.0923 0.440835
\(15\) 35.9230 40.7467i 0.618352 0.701384i
\(16\) 16.0000 0.250000
\(17\) 38.0089i 0.542266i 0.962542 + 0.271133i \(0.0873983\pi\)
−0.962542 + 0.271133i \(0.912602\pi\)
\(18\) 6.78787i 0.0888842i
\(19\) 109.470 1.32179 0.660896 0.750478i \(-0.270177\pi\)
0.660896 + 0.750478i \(0.270177\pi\)
\(20\) −33.5460 29.5747i −0.375056 0.330656i
\(21\) 56.0983 0.582936
\(22\) 61.0508i 0.591639i
\(23\) 23.0000i 0.208514i
\(24\) 38.8689 0.330586
\(25\) 15.6668 + 124.014i 0.125335 + 0.992115i
\(26\) 104.057 0.784892
\(27\) 147.672i 1.05258i
\(28\) 46.1847i 0.311717i
\(29\) −60.9293 −0.390148 −0.195074 0.980789i \(-0.562495\pi\)
−0.195074 + 0.980789i \(0.562495\pi\)
\(30\) −81.4934 71.8460i −0.495953 0.437241i
\(31\) −63.1074 −0.365626 −0.182813 0.983148i \(-0.558520\pi\)
−0.182813 + 0.983148i \(0.558520\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 148.311i 0.782352i
\(34\) 76.0178 0.383440
\(35\) −85.3687 + 96.8320i −0.412284 + 0.467645i
\(36\) −13.5757 −0.0628506
\(37\) 386.056i 1.71533i −0.514208 0.857666i \(-0.671914\pi\)
0.514208 0.857666i \(-0.328086\pi\)
\(38\) 218.939i 0.934648i
\(39\) 252.785 1.03790
\(40\) −59.1495 + 67.0920i −0.233809 + 0.265204i
\(41\) −92.0091 −0.350473 −0.175237 0.984526i \(-0.556069\pi\)
−0.175237 + 0.984526i \(0.556069\pi\)
\(42\) 112.197i 0.412198i
\(43\) 181.661i 0.644255i −0.946696 0.322128i \(-0.895602\pi\)
0.946696 0.322128i \(-0.104398\pi\)
\(44\) −122.102 −0.418352
\(45\) 28.4632 + 25.0937i 0.0942899 + 0.0831276i
\(46\) 46.0000 0.147442
\(47\) 207.423i 0.643740i 0.946784 + 0.321870i \(0.104311\pi\)
−0.946784 + 0.321870i \(0.895689\pi\)
\(48\) 77.7377i 0.233760i
\(49\) 209.686 0.611329
\(50\) 248.029 31.3337i 0.701531 0.0886250i
\(51\) 184.670 0.507040
\(52\) 208.113i 0.555002i
\(53\) 136.696i 0.354277i 0.984186 + 0.177138i \(0.0566840\pi\)
−0.984186 + 0.177138i \(0.943316\pi\)
\(54\) −295.344 −0.744283
\(55\) 256.001 + 225.695i 0.627622 + 0.553322i
\(56\) −92.3694 −0.220417
\(57\) 531.870i 1.23593i
\(58\) 121.859i 0.275876i
\(59\) 230.608 0.508859 0.254429 0.967091i \(-0.418112\pi\)
0.254429 + 0.967091i \(0.418112\pi\)
\(60\) −143.692 + 162.987i −0.309176 + 0.350692i
\(61\) −241.396 −0.506681 −0.253341 0.967377i \(-0.581529\pi\)
−0.253341 + 0.967377i \(0.581529\pi\)
\(62\) 126.215i 0.258537i
\(63\) 39.1869i 0.0783665i
\(64\) −64.0000 −0.125000
\(65\) −384.681 + 436.336i −0.734059 + 0.832627i
\(66\) −296.622 −0.553206
\(67\) 269.366i 0.491168i 0.969375 + 0.245584i \(0.0789797\pi\)
−0.969375 + 0.245584i \(0.921020\pi\)
\(68\) 152.036i 0.271133i
\(69\) 111.748 0.194969
\(70\) 193.664 + 170.737i 0.330675 + 0.291529i
\(71\) 186.611 0.311925 0.155963 0.987763i \(-0.450152\pi\)
0.155963 + 0.987763i \(0.450152\pi\)
\(72\) 27.1515i 0.0444421i
\(73\) 59.1574i 0.0948473i 0.998875 + 0.0474236i \(0.0151011\pi\)
−0.998875 + 0.0474236i \(0.984899\pi\)
\(74\) −772.113 −1.21292
\(75\) 602.537 76.1190i 0.927666 0.117193i
\(76\) −437.878 −0.660896
\(77\) 352.451i 0.521631i
\(78\) 505.571i 0.733905i
\(79\) 941.143 1.34034 0.670170 0.742208i \(-0.266221\pi\)
0.670170 + 0.742208i \(0.266221\pi\)
\(80\) 134.184 + 118.299i 0.187528 + 0.165328i
\(81\) −625.845 −0.858498
\(82\) 184.018i 0.247822i
\(83\) 94.2803i 0.124682i 0.998055 + 0.0623410i \(0.0198566\pi\)
−0.998055 + 0.0623410i \(0.980143\pi\)
\(84\) −224.393 −0.291468
\(85\) −281.026 + 318.762i −0.358606 + 0.406760i
\(86\) −363.321 −0.455557
\(87\) 296.032i 0.364804i
\(88\) 244.203i 0.295820i
\(89\) 1380.57 1.64427 0.822135 0.569293i \(-0.192783\pi\)
0.822135 + 0.569293i \(0.192783\pi\)
\(90\) 50.1873 56.9265i 0.0587801 0.0666731i
\(91\) −600.728 −0.692015
\(92\) 92.0000i 0.104257i
\(93\) 306.614i 0.341875i
\(94\) 414.846 0.455193
\(95\) 918.067 + 809.383i 0.991491 + 0.874116i
\(96\) −155.475 −0.165293
\(97\) 1253.69i 1.31230i 0.754632 + 0.656149i \(0.227816\pi\)
−0.754632 + 0.656149i \(0.772184\pi\)
\(98\) 419.372i 0.432275i
\(99\) 103.601 0.105175
\(100\) −62.6673 496.057i −0.0626673 0.496057i
\(101\) −1424.98 −1.40387 −0.701936 0.712240i \(-0.747681\pi\)
−0.701936 + 0.712240i \(0.747681\pi\)
\(102\) 369.341i 0.358531i
\(103\) 498.334i 0.476721i −0.971177 0.238361i \(-0.923390\pi\)
0.971177 0.238361i \(-0.0766100\pi\)
\(104\) −416.227 −0.392446
\(105\) 470.469 + 414.773i 0.437267 + 0.385502i
\(106\) 273.392 0.250511
\(107\) 897.019i 0.810450i −0.914217 0.405225i \(-0.867193\pi\)
0.914217 0.405225i \(-0.132807\pi\)
\(108\) 590.689i 0.526288i
\(109\) −1784.56 −1.56817 −0.784084 0.620655i \(-0.786867\pi\)
−0.784084 + 0.620655i \(0.786867\pi\)
\(110\) 451.390 512.002i 0.391258 0.443796i
\(111\) −1875.70 −1.60390
\(112\) 184.739i 0.155859i
\(113\) 1320.30i 1.09915i −0.835445 0.549574i \(-0.814790\pi\)
0.835445 0.549574i \(-0.185210\pi\)
\(114\) −1063.74 −0.873932
\(115\) −170.055 + 192.890i −0.137893 + 0.156409i
\(116\) 243.717 0.195074
\(117\) 176.581i 0.139529i
\(118\) 461.217i 0.359817i
\(119\) −438.858 −0.338067
\(120\) 325.974 + 287.384i 0.247977 + 0.218621i
\(121\) −399.201 −0.299926
\(122\) 482.791i 0.358278i
\(123\) 447.036i 0.327706i
\(124\) 252.429 0.182813
\(125\) −785.533 + 1155.88i −0.562082 + 0.827082i
\(126\) 78.3739 0.0554135
\(127\) 1464.71i 1.02340i 0.859163 + 0.511702i \(0.170985\pi\)
−0.859163 + 0.511702i \(0.829015\pi\)
\(128\) 128.000i 0.0883883i
\(129\) −882.617 −0.602404
\(130\) 872.671 + 769.362i 0.588757 + 0.519058i
\(131\) −351.211 −0.234240 −0.117120 0.993118i \(-0.537366\pi\)
−0.117120 + 0.993118i \(0.537366\pi\)
\(132\) 593.243i 0.391176i
\(133\) 1263.95i 0.824050i
\(134\) 538.731 0.347308
\(135\) 1091.84 1238.45i 0.696080 0.789549i
\(136\) −304.071 −0.191720
\(137\) 331.895i 0.206976i −0.994631 0.103488i \(-0.967000\pi\)
0.994631 0.103488i \(-0.0330003\pi\)
\(138\) 223.496i 0.137864i
\(139\) 2215.75 1.35207 0.676033 0.736872i \(-0.263698\pi\)
0.676033 + 0.736872i \(0.263698\pi\)
\(140\) 341.475 387.328i 0.206142 0.233823i
\(141\) 1007.79 0.601922
\(142\) 373.223i 0.220564i
\(143\) 1588.18i 0.928746i
\(144\) 54.3029 0.0314253
\(145\) −510.984 450.492i −0.292654 0.258009i
\(146\) 118.315 0.0670672
\(147\) 1018.78i 0.571617i
\(148\) 1544.23i 0.857666i
\(149\) −2477.32 −1.36208 −0.681041 0.732245i \(-0.738473\pi\)
−0.681041 + 0.732245i \(0.738473\pi\)
\(150\) −152.238 1205.07i −0.0828679 0.655959i
\(151\) −1018.32 −0.548806 −0.274403 0.961615i \(-0.588480\pi\)
−0.274403 + 0.961615i \(0.588480\pi\)
\(152\) 875.756i 0.467324i
\(153\) 129.000i 0.0681635i
\(154\) 704.903 0.368848
\(155\) −529.250 466.596i −0.274261 0.241793i
\(156\) −1011.14 −0.518949
\(157\) 1086.32i 0.552216i 0.961127 + 0.276108i \(0.0890447\pi\)
−0.961127 + 0.276108i \(0.910955\pi\)
\(158\) 1882.29i 0.947763i
\(159\) 664.153 0.331263
\(160\) 236.598 268.368i 0.116904 0.132602i
\(161\) −265.562 −0.129995
\(162\) 1251.69i 0.607050i
\(163\) 143.788i 0.0690942i −0.999403 0.0345471i \(-0.989001\pi\)
0.999403 0.0345471i \(-0.0109989\pi\)
\(164\) 368.036 0.175237
\(165\) 1096.56 1243.81i 0.517378 0.586851i
\(166\) 188.561 0.0881635
\(167\) 2265.50i 1.04976i −0.851177 0.524878i \(-0.824111\pi\)
0.851177 0.524878i \(-0.175889\pi\)
\(168\) 448.786i 0.206099i
\(169\) −509.948 −0.232111
\(170\) 637.524 + 562.052i 0.287623 + 0.253573i
\(171\) 371.532 0.166151
\(172\) 726.642i 0.322128i
\(173\) 4159.77i 1.82810i −0.405602 0.914050i \(-0.632938\pi\)
0.405602 0.914050i \(-0.367062\pi\)
\(174\) 592.063 0.257955
\(175\) −1431.89 + 180.892i −0.618519 + 0.0781380i
\(176\) 488.406 0.209176
\(177\) 1120.44i 0.475803i
\(178\) 2761.14i 1.16267i
\(179\) 3483.94 1.45476 0.727379 0.686236i \(-0.240738\pi\)
0.727379 + 0.686236i \(0.240738\pi\)
\(180\) −113.853 100.375i −0.0471450 0.0415638i
\(181\) 2365.09 0.971246 0.485623 0.874168i \(-0.338593\pi\)
0.485623 + 0.874168i \(0.338593\pi\)
\(182\) 1201.46i 0.489329i
\(183\) 1172.85i 0.473767i
\(184\) −184.000 −0.0737210
\(185\) 2854.38 3237.66i 1.13437 1.28669i
\(186\) 613.228 0.241742
\(187\) 1160.24i 0.453716i
\(188\) 829.692i 0.321870i
\(189\) 1705.05 0.656212
\(190\) 1618.77 1836.13i 0.618093 0.701090i
\(191\) −4868.10 −1.84421 −0.922103 0.386944i \(-0.873531\pi\)
−0.922103 + 0.386944i \(0.873531\pi\)
\(192\) 310.951i 0.116880i
\(193\) 1452.53i 0.541737i −0.962616 0.270869i \(-0.912689\pi\)
0.962616 0.270869i \(-0.0873109\pi\)
\(194\) 2507.38 0.927934
\(195\) 2119.98 + 1869.01i 0.778540 + 0.686374i
\(196\) −838.744 −0.305665
\(197\) 4235.47i 1.53180i −0.642960 0.765900i \(-0.722294\pi\)
0.642960 0.765900i \(-0.277706\pi\)
\(198\) 207.202i 0.0743698i
\(199\) −2457.38 −0.875374 −0.437687 0.899128i \(-0.644202\pi\)
−0.437687 + 0.899128i \(0.644202\pi\)
\(200\) −992.115 + 125.335i −0.350765 + 0.0443125i
\(201\) 1308.74 0.459261
\(202\) 2849.97i 0.992687i
\(203\) 703.500i 0.243232i
\(204\) −738.682 −0.253520
\(205\) −771.634 680.286i −0.262894 0.231772i
\(206\) −996.667 −0.337093
\(207\) 78.0605i 0.0262105i
\(208\) 832.453i 0.277501i
\(209\) 3341.60 1.10595
\(210\) 829.546 940.937i 0.272591 0.309194i
\(211\) −2325.90 −0.758871 −0.379435 0.925218i \(-0.623882\pi\)
−0.379435 + 0.925218i \(0.623882\pi\)
\(212\) 546.784i 0.177138i
\(213\) 906.671i 0.291662i
\(214\) −1794.04 −0.573075
\(215\) 1343.14 1523.50i 0.426053 0.483263i
\(216\) 1181.38 0.372141
\(217\) 728.648i 0.227944i
\(218\) 3569.13i 1.10886i
\(219\) 287.423 0.0886859
\(220\) −1024.00 902.780i −0.313811 0.276661i
\(221\) −1977.54 −0.601918
\(222\) 3751.39i 1.13413i
\(223\) 5012.72i 1.50528i 0.658435 + 0.752638i \(0.271219\pi\)
−0.658435 + 0.752638i \(0.728781\pi\)
\(224\) 369.477 0.110209
\(225\) 53.1722 + 420.896i 0.0157547 + 0.124710i
\(226\) −2640.61 −0.777215
\(227\) 3897.60i 1.13962i −0.821778 0.569808i \(-0.807017\pi\)
0.821778 0.569808i \(-0.192983\pi\)
\(228\) 2127.48i 0.617964i
\(229\) −2346.46 −0.677111 −0.338556 0.940946i \(-0.609938\pi\)
−0.338556 + 0.940946i \(0.609938\pi\)
\(230\) 385.779 + 340.110i 0.110598 + 0.0975050i
\(231\) 1712.42 0.487745
\(232\) 487.434i 0.137938i
\(233\) 2476.94i 0.696437i −0.937413 0.348218i \(-0.886787\pi\)
0.937413 0.348218i \(-0.113213\pi\)
\(234\) 353.161 0.0986619
\(235\) −1533.62 + 1739.55i −0.425712 + 0.482877i
\(236\) −922.434 −0.254429
\(237\) 4572.64i 1.25327i
\(238\) 877.715i 0.239050i
\(239\) 5126.70 1.38753 0.693764 0.720203i \(-0.255951\pi\)
0.693764 + 0.720203i \(0.255951\pi\)
\(240\) 574.768 651.948i 0.154588 0.175346i
\(241\) −4672.12 −1.24879 −0.624394 0.781110i \(-0.714654\pi\)
−0.624394 + 0.781110i \(0.714654\pi\)
\(242\) 798.402i 0.212079i
\(243\) 946.414i 0.249846i
\(244\) 965.583 0.253341
\(245\) 1758.53 + 1550.35i 0.458565 + 0.404279i
\(246\) 894.072 0.231723
\(247\) 5695.52i 1.46719i
\(248\) 504.859i 0.129268i
\(249\) 458.071 0.116583
\(250\) 2311.76 + 1571.07i 0.584835 + 0.397452i
\(251\) 3001.39 0.754764 0.377382 0.926058i \(-0.376824\pi\)
0.377382 + 0.926058i \(0.376824\pi\)
\(252\) 156.748i 0.0391832i
\(253\) 702.084i 0.174465i
\(254\) 2929.43 0.723656
\(255\) 1548.74 + 1365.40i 0.380336 + 0.335311i
\(256\) 256.000 0.0625000
\(257\) 1398.04i 0.339329i −0.985502 0.169664i \(-0.945732\pi\)
0.985502 0.169664i \(-0.0542684\pi\)
\(258\) 1765.23i 0.425964i
\(259\) 4457.47 1.06940
\(260\) 1538.72 1745.34i 0.367029 0.416314i
\(261\) −206.790 −0.0490421
\(262\) 702.422i 0.165633i
\(263\) 451.199i 0.105787i −0.998600 0.0528937i \(-0.983156\pi\)
0.998600 0.0528937i \(-0.0168445\pi\)
\(264\) 1186.49 0.276603
\(265\) −1010.69 + 1146.40i −0.234287 + 0.265747i
\(266\) 2527.91 0.582692
\(267\) 6707.64i 1.53746i
\(268\) 1077.46i 0.245584i
\(269\) −4998.42 −1.13293 −0.566467 0.824084i \(-0.691690\pi\)
−0.566467 + 0.824084i \(0.691690\pi\)
\(270\) −2476.91 2183.68i −0.558295 0.492203i
\(271\) −8357.51 −1.87337 −0.936684 0.350176i \(-0.886122\pi\)
−0.936684 + 0.350176i \(0.886122\pi\)
\(272\) 608.143i 0.135566i
\(273\) 2918.70i 0.647062i
\(274\) −663.790 −0.146354
\(275\) 478.236 + 3785.58i 0.104868 + 0.830107i
\(276\) −446.992 −0.0974846
\(277\) 632.582i 0.137214i 0.997644 + 0.0686068i \(0.0218554\pi\)
−0.997644 + 0.0686068i \(0.978145\pi\)
\(278\) 4431.49i 0.956055i
\(279\) −214.182 −0.0459597
\(280\) −774.656 682.950i −0.165338 0.145765i
\(281\) −7414.60 −1.57408 −0.787042 0.616899i \(-0.788389\pi\)
−0.787042 + 0.616899i \(0.788389\pi\)
\(282\) 2015.57i 0.425623i
\(283\) 2450.81i 0.514789i −0.966306 0.257395i \(-0.917136\pi\)
0.966306 0.257395i \(-0.0828640\pi\)
\(284\) −746.445 −0.155963
\(285\) 3932.48 4460.52i 0.817333 0.927083i
\(286\) 3176.37 0.656723
\(287\) 1062.35i 0.218497i
\(288\) 108.606i 0.0222210i
\(289\) 3468.32 0.705948
\(290\) −900.984 + 1021.97i −0.182440 + 0.206938i
\(291\) 6091.18 1.22705
\(292\) 236.630i 0.0474236i
\(293\) 8753.49i 1.74534i 0.488311 + 0.872670i \(0.337613\pi\)
−0.488311 + 0.872670i \(0.662387\pi\)
\(294\) −2037.56 −0.404194
\(295\) 1934.00 + 1705.05i 0.381701 + 0.336514i
\(296\) 3088.45 0.606461
\(297\) 4507.75i 0.880694i
\(298\) 4954.65i 0.963138i
\(299\) −1196.65 −0.231452
\(300\) −2410.15 + 304.476i −0.463833 + 0.0585964i
\(301\) 2097.48 0.401651
\(302\) 2036.64i 0.388064i
\(303\) 6923.43i 1.31268i
\(304\) 1751.51 0.330448
\(305\) −2024.47 1784.80i −0.380067 0.335074i
\(306\) 257.999 0.0481989
\(307\) 7545.31i 1.40272i 0.712809 + 0.701358i \(0.247422\pi\)
−0.712809 + 0.701358i \(0.752578\pi\)
\(308\) 1409.81i 0.260815i
\(309\) −2421.21 −0.445753
\(310\) −933.192 + 1058.50i −0.170973 + 0.193931i
\(311\) −4670.34 −0.851546 −0.425773 0.904830i \(-0.639998\pi\)
−0.425773 + 0.904830i \(0.639998\pi\)
\(312\) 2022.28i 0.366952i
\(313\) 3513.81i 0.634544i −0.948335 0.317272i \(-0.897233\pi\)
0.948335 0.317272i \(-0.102767\pi\)
\(314\) 2172.64 0.390476
\(315\) −289.736 + 328.641i −0.0518246 + 0.0587836i
\(316\) −3764.57 −0.670170
\(317\) 6942.35i 1.23004i −0.788513 0.615018i \(-0.789149\pi\)
0.788513 0.615018i \(-0.210851\pi\)
\(318\) 1328.31i 0.234238i
\(319\) −1859.89 −0.326438
\(320\) −536.736 473.196i −0.0937639 0.0826639i
\(321\) −4358.27 −0.757803
\(322\) 531.124i 0.0919204i
\(323\) 4160.82i 0.716762i
\(324\) 2503.38 0.429249
\(325\) −6452.26 + 815.119i −1.10125 + 0.139122i
\(326\) −287.576 −0.0488570
\(327\) 8670.50i 1.46630i
\(328\) 736.072i 0.123911i
\(329\) −2394.94 −0.401330
\(330\) −2487.62 2193.13i −0.414966 0.365842i
\(331\) 4598.51 0.763616 0.381808 0.924242i \(-0.375302\pi\)
0.381808 + 0.924242i \(0.375302\pi\)
\(332\) 377.121i 0.0623410i
\(333\) 1310.25i 0.215619i
\(334\) −4530.99 −0.742290
\(335\) −1991.60 + 2259.04i −0.324815 + 0.368431i
\(336\) 897.573 0.145734
\(337\) 638.077i 0.103140i 0.998669 + 0.0515702i \(0.0164226\pi\)
−0.998669 + 0.0515702i \(0.983577\pi\)
\(338\) 1019.90i 0.164127i
\(339\) −6414.84 −1.02775
\(340\) 1124.10 1275.05i 0.179303 0.203380i
\(341\) −1926.38 −0.305921
\(342\) 743.065i 0.117486i
\(343\) 6381.41i 1.00456i
\(344\) 1453.28 0.227779
\(345\) 937.175 + 826.229i 0.146249 + 0.128935i
\(346\) −8319.54 −1.29266
\(347\) 302.348i 0.0467750i −0.999726 0.0233875i \(-0.992555\pi\)
0.999726 0.0233875i \(-0.00744515\pi\)
\(348\) 1184.13i 0.182402i
\(349\) −8944.40 −1.37187 −0.685935 0.727663i \(-0.740607\pi\)
−0.685935 + 0.727663i \(0.740607\pi\)
\(350\) 361.784 + 2863.78i 0.0552519 + 0.437359i
\(351\) 7683.14 1.16836
\(352\) 976.812i 0.147910i
\(353\) 11231.8i 1.69351i 0.531981 + 0.846756i \(0.321448\pi\)
−0.531981 + 0.846756i \(0.678552\pi\)
\(354\) −2240.87 −0.336443
\(355\) 1565.02 + 1379.74i 0.233979 + 0.206280i
\(356\) −5522.28 −0.822135
\(357\) 2132.24i 0.316106i
\(358\) 6967.88i 1.02867i
\(359\) −9283.39 −1.36479 −0.682393 0.730985i \(-0.739061\pi\)
−0.682393 + 0.730985i \(0.739061\pi\)
\(360\) −200.749 + 227.706i −0.0293901 + 0.0333365i
\(361\) 5124.58 0.747132
\(362\) 4730.17i 0.686775i
\(363\) 1939.56i 0.280442i
\(364\) 2402.91 0.346008
\(365\) −437.391 + 496.124i −0.0627236 + 0.0711460i
\(366\) 2345.69 0.335004
\(367\) 9662.14i 1.37428i −0.726526 0.687139i \(-0.758866\pi\)
0.726526 0.687139i \(-0.241134\pi\)
\(368\) 368.000i 0.0521286i
\(369\) −312.273 −0.0440549
\(370\) −6475.32 5708.76i −0.909827 0.802119i
\(371\) −1578.32 −0.220868
\(372\) 1226.46i 0.170938i
\(373\) 2630.59i 0.365166i 0.983190 + 0.182583i \(0.0584458\pi\)
−0.983190 + 0.182583i \(0.941554\pi\)
\(374\) 2320.47 0.320826
\(375\) 5615.98 + 3816.60i 0.773354 + 0.525568i
\(376\) −1659.38 −0.227596
\(377\) 3170.05i 0.433066i
\(378\) 3410.10i 0.464012i
\(379\) −3941.24 −0.534164 −0.267082 0.963674i \(-0.586059\pi\)
−0.267082 + 0.963674i \(0.586059\pi\)
\(380\) −3672.27 3237.53i −0.495745 0.437058i
\(381\) 7116.46 0.956923
\(382\) 9736.20i 1.30405i
\(383\) 8146.17i 1.08681i −0.839469 0.543407i \(-0.817134\pi\)
0.839469 0.543407i \(-0.182866\pi\)
\(384\) 621.902 0.0826466
\(385\) −2605.91 + 2955.83i −0.344960 + 0.391281i
\(386\) −2905.06 −0.383066
\(387\) 616.544i 0.0809837i
\(388\) 5014.76i 0.656149i
\(389\) 2668.67 0.347833 0.173917 0.984760i \(-0.444358\pi\)
0.173917 + 0.984760i \(0.444358\pi\)
\(390\) 3738.03 4239.97i 0.485340 0.550511i
\(391\) −874.205 −0.113070
\(392\) 1677.49i 0.216138i
\(393\) 1706.40i 0.219024i
\(394\) −8470.94 −1.08315
\(395\) 7892.89 + 6958.51i 1.00540 + 0.886382i
\(396\) −414.404 −0.0525874
\(397\) 7028.13i 0.888493i −0.895905 0.444247i \(-0.853471\pi\)
0.895905 0.444247i \(-0.146529\pi\)
\(398\) 4914.77i 0.618983i
\(399\) 6141.06 0.770520
\(400\) 250.669 + 1984.23i 0.0313337 + 0.248029i
\(401\) 9420.36 1.17314 0.586572 0.809897i \(-0.300477\pi\)
0.586572 + 0.809897i \(0.300477\pi\)
\(402\) 2617.48i 0.324747i
\(403\) 3283.37i 0.405847i
\(404\) 5699.93 0.701936
\(405\) −5248.65 4627.30i −0.643969 0.567734i
\(406\) −1407.00 −0.171991
\(407\) 11784.5i 1.43523i
\(408\) 1477.36i 0.179266i
\(409\) −10022.5 −1.21169 −0.605847 0.795581i \(-0.707165\pi\)
−0.605847 + 0.795581i \(0.707165\pi\)
\(410\) −1360.57 + 1543.27i −0.163887 + 0.185894i
\(411\) −1612.55 −0.193531
\(412\) 1993.33i 0.238361i
\(413\) 2662.64i 0.317240i
\(414\) 156.121 0.0185336
\(415\) −697.079 + 790.682i −0.0824536 + 0.0935254i
\(416\) 1664.91 0.196223
\(417\) 10765.4i 1.26423i
\(418\) 6683.20i 0.782024i
\(419\) 11177.5 1.30324 0.651621 0.758545i \(-0.274089\pi\)
0.651621 + 0.758545i \(0.274089\pi\)
\(420\) −1881.87 1659.09i −0.218633 0.192751i
\(421\) 8965.60 1.03790 0.518951 0.854804i \(-0.326323\pi\)
0.518951 + 0.854804i \(0.326323\pi\)
\(422\) 4651.81i 0.536603i
\(423\) 703.980i 0.0809189i
\(424\) −1093.57 −0.125256
\(425\) −4713.65 + 595.480i −0.537990 + 0.0679647i
\(426\) −1813.34 −0.206236
\(427\) 2787.20i 0.315883i
\(428\) 3588.08i 0.405225i
\(429\) 7716.37 0.868414
\(430\) −3046.99 2686.28i −0.341719 0.301265i
\(431\) 16553.1 1.84997 0.924984 0.380006i \(-0.124078\pi\)
0.924984 + 0.380006i \(0.124078\pi\)
\(432\) 2362.76i 0.263144i
\(433\) 752.803i 0.0835505i −0.999127 0.0417753i \(-0.986699\pi\)
0.999127 0.0417753i \(-0.0133014\pi\)
\(434\) −1457.30 −0.161181
\(435\) −2188.76 + 2482.67i −0.241249 + 0.273643i
\(436\) 7138.26 0.784084
\(437\) 2517.80i 0.275613i
\(438\) 574.845i 0.0627104i
\(439\) 2672.91 0.290594 0.145297 0.989388i \(-0.453586\pi\)
0.145297 + 0.989388i \(0.453586\pi\)
\(440\) −1805.56 + 2048.01i −0.195629 + 0.221898i
\(441\) 711.660 0.0768448
\(442\) 3955.08i 0.425620i
\(443\) 7311.22i 0.784123i −0.919939 0.392062i \(-0.871762\pi\)
0.919939 0.392062i \(-0.128238\pi\)
\(444\) 7502.78 0.801951
\(445\) 11578.1 + 10207.5i 1.23339 + 1.08737i
\(446\) 10025.4 1.06439
\(447\) 12036.3i 1.27360i
\(448\) 738.955i 0.0779293i
\(449\) −3585.70 −0.376881 −0.188441 0.982085i \(-0.560343\pi\)
−0.188441 + 0.982085i \(0.560343\pi\)
\(450\) 841.793 106.344i 0.0881833 0.0111403i
\(451\) −2808.61 −0.293242
\(452\) 5281.22i 0.549574i
\(453\) 4947.62i 0.513155i
\(454\) −7795.21 −0.805831
\(455\) −5038.01 4441.59i −0.519089 0.457638i
\(456\) 4254.96 0.436966
\(457\) 1222.55i 0.125139i −0.998041 0.0625693i \(-0.980071\pi\)
0.998041 0.0625693i \(-0.0199294\pi\)
\(458\) 4692.92i 0.478790i
\(459\) 5612.86 0.570775
\(460\) 680.219 771.558i 0.0689465 0.0782045i
\(461\) 3845.46 0.388505 0.194252 0.980952i \(-0.437772\pi\)
0.194252 + 0.980952i \(0.437772\pi\)
\(462\) 3424.84i 0.344888i
\(463\) 5113.70i 0.513291i −0.966506 0.256645i \(-0.917383\pi\)
0.966506 0.256645i \(-0.0826173\pi\)
\(464\) −974.869 −0.0975370
\(465\) −2267.01 + 2571.42i −0.226086 + 0.256444i
\(466\) −4953.88 −0.492455
\(467\) 11547.5i 1.14422i 0.820175 + 0.572112i \(0.193876\pi\)
−0.820175 + 0.572112i \(0.806124\pi\)
\(468\) 706.323i 0.0697645i
\(469\) −3110.14 −0.306211
\(470\) 3479.11 + 3067.24i 0.341445 + 0.301024i
\(471\) 5278.01 0.516344
\(472\) 1844.87i 0.179909i
\(473\) 5545.26i 0.539051i
\(474\) −9145.28 −0.886196
\(475\) 1715.04 + 13575.8i 0.165666 + 1.31137i
\(476\) 1755.43 0.169034
\(477\) 463.937i 0.0445330i
\(478\) 10253.4i 0.981130i
\(479\) 4515.48 0.430725 0.215363 0.976534i \(-0.430907\pi\)
0.215363 + 0.976534i \(0.430907\pi\)
\(480\) −1303.90 1149.54i −0.123988 0.109310i
\(481\) 20085.9 1.90403
\(482\) 9344.24i 0.883026i
\(483\) 1290.26i 0.121551i
\(484\) 1596.80 0.149963
\(485\) −9269.38 + 10514.1i −0.867837 + 0.984369i
\(486\) −1892.83 −0.176668
\(487\) 12101.2i 1.12599i 0.826460 + 0.562995i \(0.190351\pi\)
−0.826460 + 0.562995i \(0.809649\pi\)
\(488\) 1931.17i 0.179139i
\(489\) −698.610 −0.0646058
\(490\) 3100.70 3517.06i 0.285868 0.324255i
\(491\) 10133.6 0.931409 0.465705 0.884940i \(-0.345801\pi\)
0.465705 + 0.884940i \(0.345801\pi\)
\(492\) 1788.14i 0.163853i
\(493\) 2315.86i 0.211564i
\(494\) 11391.0 1.03746
\(495\) 868.851 + 765.994i 0.0788928 + 0.0695533i
\(496\) −1009.72 −0.0914066
\(497\) 2154.65i 0.194465i
\(498\) 916.142i 0.0824363i
\(499\) −3383.17 −0.303510 −0.151755 0.988418i \(-0.548493\pi\)
−0.151755 + 0.988418i \(0.548493\pi\)
\(500\) 3142.13 4623.53i 0.281041 0.413541i
\(501\) −11007.2 −0.981564
\(502\) 6002.77i 0.533699i
\(503\) 8508.84i 0.754255i −0.926161 0.377128i \(-0.876912\pi\)
0.926161 0.377128i \(-0.123088\pi\)
\(504\) −313.495 −0.0277067
\(505\) −11950.6 10535.9i −1.05306 0.928396i
\(506\) 1404.17 0.123365
\(507\) 2477.64i 0.217033i
\(508\) 5858.85i 0.511702i
\(509\) 8042.61 0.700359 0.350179 0.936683i \(-0.386121\pi\)
0.350179 + 0.936683i \(0.386121\pi\)
\(510\) 2730.79 3097.48i 0.237101 0.268939i
\(511\) −683.042 −0.0591311
\(512\) 512.000i 0.0441942i
\(513\) 16165.6i 1.39128i
\(514\) −2796.09 −0.239942
\(515\) 3684.52 4179.28i 0.315261 0.357594i
\(516\) 3530.47 0.301202
\(517\) 6331.67i 0.538620i
\(518\) 8914.94i 0.756178i
\(519\) −20210.7 −1.70935
\(520\) −3490.69 3077.45i −0.294378 0.259529i
\(521\) 9066.35 0.762388 0.381194 0.924495i \(-0.375513\pi\)
0.381194 + 0.924495i \(0.375513\pi\)
\(522\) 413.580i 0.0346780i
\(523\) 13818.5i 1.15533i −0.816273 0.577667i \(-0.803963\pi\)
0.816273 0.577667i \(-0.196037\pi\)
\(524\) 1404.84 0.117120
\(525\) 878.883 + 6956.99i 0.0730621 + 0.578339i
\(526\) −902.397 −0.0748030
\(527\) 2398.64i 0.198267i
\(528\) 2372.97i 0.195588i
\(529\) −529.000 −0.0434783
\(530\) 2292.80 + 2021.38i 0.187911 + 0.165666i
\(531\) 782.670 0.0639642
\(532\) 5055.82i 0.412025i
\(533\) 4787.08i 0.389027i
\(534\) −13415.3 −1.08715
\(535\) 6632.28 7522.86i 0.535960 0.607928i
\(536\) −2154.92 −0.173654
\(537\) 16927.1i 1.36026i
\(538\) 9996.85i 0.801105i
\(539\) 6400.74 0.511502
\(540\) −4367.37 + 4953.81i −0.348040 + 0.394774i
\(541\) 14965.2 1.18929 0.594643 0.803990i \(-0.297293\pi\)
0.594643 + 0.803990i \(0.297293\pi\)
\(542\) 16715.0i 1.32467i
\(543\) 11491.0i 0.908153i
\(544\) 1216.29 0.0958600
\(545\) −14966.3 13194.5i −1.17630 1.03705i
\(546\) 5837.40 0.457542
\(547\) 6818.50i 0.532976i −0.963838 0.266488i \(-0.914137\pi\)
0.963838 0.266488i \(-0.0858633\pi\)
\(548\) 1327.58i 0.103488i
\(549\) −819.281 −0.0636905
\(550\) 7571.17 956.472i 0.586974 0.0741529i
\(551\) −6669.90 −0.515694
\(552\) 893.984i 0.0689320i
\(553\) 10866.6i 0.835614i
\(554\) 1265.16 0.0970246
\(555\) −15730.5 13868.3i −1.20311 1.06068i
\(556\) −8862.98 −0.676033
\(557\) 12318.3i 0.937060i 0.883448 + 0.468530i \(0.155216\pi\)
−0.883448 + 0.468530i \(0.844784\pi\)
\(558\) 428.364i 0.0324984i
\(559\) 9451.50 0.715127
\(560\) −1365.90 + 1549.31i −0.103071 + 0.116911i
\(561\) 5637.14 0.424243
\(562\) 14829.2i 1.11305i
\(563\) 19821.4i 1.48379i −0.670516 0.741895i \(-0.733927\pi\)
0.670516 0.741895i \(-0.266073\pi\)
\(564\) −4031.15 −0.300961
\(565\) 9761.91 11072.7i 0.726879 0.824484i
\(566\) −4901.61 −0.364011
\(567\) 7226.11i 0.535217i
\(568\) 1492.89i 0.110282i
\(569\) −4612.33 −0.339822 −0.169911 0.985459i \(-0.554348\pi\)
−0.169911 + 0.985459i \(0.554348\pi\)
\(570\) −8921.05 7864.95i −0.655547 0.577941i
\(571\) −6497.97 −0.476238 −0.238119 0.971236i \(-0.576531\pi\)
−0.238119 + 0.971236i \(0.576531\pi\)
\(572\) 6352.74i 0.464373i
\(573\) 23652.2i 1.72441i
\(574\) −2124.70 −0.154501
\(575\) −2852.33 + 360.337i −0.206870 + 0.0261341i
\(576\) −217.212 −0.0157127
\(577\) 160.102i 0.0115513i 0.999983 + 0.00577567i \(0.00183846\pi\)
−0.999983 + 0.00577567i \(0.998162\pi\)
\(578\) 6936.64i 0.499180i
\(579\) −7057.27 −0.506546
\(580\) 2043.94 + 1801.97i 0.146327 + 0.129005i
\(581\) −1088.58 −0.0777311
\(582\) 12182.4i 0.867655i
\(583\) 4172.70i 0.296425i
\(584\) −473.259 −0.0335336
\(585\) −1305.58 + 1480.89i −0.0922721 + 0.104662i
\(586\) 17507.0 1.23414
\(587\) 7342.71i 0.516296i −0.966105 0.258148i \(-0.916888\pi\)
0.966105 0.258148i \(-0.0831123\pi\)
\(588\) 4075.13i 0.285809i
\(589\) −6908.33 −0.483282
\(590\) 3410.09 3868.00i 0.237951 0.269903i
\(591\) −20578.5 −1.43229
\(592\) 6176.90i 0.428833i
\(593\) 12241.1i 0.847692i −0.905734 0.423846i \(-0.860680\pi\)
0.905734 0.423846i \(-0.139320\pi\)
\(594\) −9015.50 −0.622745
\(595\) −3680.48 3244.77i −0.253588 0.223568i
\(596\) 9909.30 0.681041
\(597\) 11939.5i 0.818509i
\(598\) 2393.30i 0.163661i
\(599\) −1597.64 −0.108978 −0.0544888 0.998514i \(-0.517353\pi\)
−0.0544888 + 0.998514i \(0.517353\pi\)
\(600\) 608.952 + 4820.30i 0.0414339 + 0.327980i
\(601\) −861.146 −0.0584474 −0.0292237 0.999573i \(-0.509304\pi\)
−0.0292237 + 0.999573i \(0.509304\pi\)
\(602\) 4194.97i 0.284010i
\(603\) 914.209i 0.0617404i
\(604\) 4073.28 0.274403
\(605\) −3347.90 2951.57i −0.224978 0.198344i
\(606\) 13846.9 0.928202
\(607\) 24599.3i 1.64490i 0.568838 + 0.822449i \(0.307393\pi\)
−0.568838 + 0.822449i \(0.692607\pi\)
\(608\) 3503.03i 0.233662i
\(609\) −3418.03 −0.227431
\(610\) −3569.61 + 4048.93i −0.236933 + 0.268748i
\(611\) −10791.9 −0.714554
\(612\) 515.999i 0.0340817i
\(613\) 6965.05i 0.458916i 0.973319 + 0.229458i \(0.0736954\pi\)
−0.973319 + 0.229458i \(0.926305\pi\)
\(614\) 15090.6 0.991870
\(615\) −3305.24 + 3749.07i −0.216716 + 0.245816i
\(616\) −2819.61 −0.184424
\(617\) 7486.04i 0.488455i 0.969718 + 0.244227i \(0.0785343\pi\)
−0.969718 + 0.244227i \(0.921466\pi\)
\(618\) 4842.41i 0.315195i
\(619\) 12204.5 0.792472 0.396236 0.918149i \(-0.370316\pi\)
0.396236 + 0.918149i \(0.370316\pi\)
\(620\) 2117.00 + 1866.38i 0.137130 + 0.120896i
\(621\) 3396.46 0.219477
\(622\) 9340.69i 0.602134i
\(623\) 15940.3i 1.02509i
\(624\) 4044.56 0.259475
\(625\) −15134.1 + 3885.82i −0.968582 + 0.248693i
\(626\) −7027.62 −0.448691
\(627\) 16235.5i 1.03411i
\(628\) 4345.29i 0.276108i
\(629\) 14673.6 0.930166
\(630\) 657.283 + 579.472i 0.0415663 + 0.0366456i
\(631\) −9566.26 −0.603529 −0.301764 0.953383i \(-0.597576\pi\)
−0.301764 + 0.953383i \(0.597576\pi\)
\(632\) 7529.14i 0.473882i
\(633\) 11300.6i 0.709574i
\(634\) −13884.7 −0.869767
\(635\) −10829.6 + 12283.8i −0.676788 + 0.767667i
\(636\) −2656.61 −0.165631
\(637\) 10909.6i 0.678579i
\(638\) 3719.78i 0.230827i
\(639\) 633.346 0.0392094
\(640\) −946.392 + 1073.47i −0.0584522 + 0.0663011i
\(641\) −32146.3 −1.98081 −0.990407 0.138183i \(-0.955874\pi\)
−0.990407 + 0.138183i \(0.955874\pi\)
\(642\) 8716.53i 0.535847i
\(643\) 12234.1i 0.750336i 0.926957 + 0.375168i \(0.122415\pi\)
−0.926957 + 0.375168i \(0.877585\pi\)
\(644\) 1062.25 0.0649975
\(645\) −7402.07 6525.80i −0.451870 0.398377i
\(646\) 8321.64 0.506827
\(647\) 18206.2i 1.10627i −0.833091 0.553136i \(-0.813431\pi\)
0.833091 0.553136i \(-0.186569\pi\)
\(648\) 5006.76i 0.303525i
\(649\) 7039.41 0.425764
\(650\) 1630.24 + 12904.5i 0.0983742 + 0.778703i
\(651\) −3540.22 −0.213137
\(652\) 575.152i 0.0345471i
\(653\) 16496.5i 0.988601i −0.869291 0.494301i \(-0.835424\pi\)
0.869291 0.494301i \(-0.164576\pi\)
\(654\) 17341.0 1.03683
\(655\) −2945.43 2596.74i −0.175706 0.154906i
\(656\) −1472.14 −0.0876183
\(657\) 200.776i 0.0119224i
\(658\) 4789.89i 0.283783i
\(659\) −9669.49 −0.571578 −0.285789 0.958293i \(-0.592256\pi\)
−0.285789 + 0.958293i \(0.592256\pi\)
\(660\) −4386.26 + 4975.24i −0.258689 + 0.293426i
\(661\) 19252.4 1.13288 0.566438 0.824105i \(-0.308321\pi\)
0.566438 + 0.824105i \(0.308321\pi\)
\(662\) 9197.02i 0.539958i
\(663\) 9608.10i 0.562817i
\(664\) −754.242 −0.0440817
\(665\) −9345.28 + 10600.2i −0.544954 + 0.618130i
\(666\) −2620.50 −0.152466
\(667\) 1401.37i 0.0813515i
\(668\) 9061.98i 0.524878i
\(669\) 24354.8 1.40749
\(670\) 4518.07 + 3983.21i 0.260520 + 0.229679i
\(671\) −7368.70 −0.423942
\(672\) 1795.15i 0.103049i
\(673\) 23690.9i 1.35693i 0.734631 + 0.678467i \(0.237355\pi\)
−0.734631 + 0.678467i \(0.762645\pi\)
\(674\) 1276.15 0.0729312
\(675\) 18313.5 2313.56i 1.04427 0.131924i
\(676\) 2039.79 0.116055
\(677\) 22913.3i 1.30079i 0.759598 + 0.650393i \(0.225396\pi\)
−0.759598 + 0.650393i \(0.774604\pi\)
\(678\) 12829.7i 0.726727i
\(679\) −14475.3 −0.818131
\(680\) −2550.10 2248.21i −0.143811 0.126787i
\(681\) −18936.9 −1.06559
\(682\) 3852.75i 0.216319i
\(683\) 5932.99i 0.332386i −0.986093 0.166193i \(-0.946853\pi\)
0.986093 0.166193i \(-0.0531475\pi\)
\(684\) −1486.13 −0.0830754
\(685\) 2453.93 2783.44i 0.136876 0.155255i
\(686\) 12762.8 0.710330
\(687\) 11400.5i 0.633126i
\(688\) 2906.57i 0.161064i
\(689\) −7112.07 −0.393249
\(690\) 1652.46 1874.35i 0.0911711 0.103413i
\(691\) 9480.21 0.521917 0.260958 0.965350i \(-0.415961\pi\)
0.260958 + 0.965350i \(0.415961\pi\)
\(692\) 16639.1i 0.914050i
\(693\) 1196.20i 0.0655696i
\(694\) −604.697 −0.0330749
\(695\) 18582.4 + 16382.5i 1.01420 + 0.894136i
\(696\) −2368.25 −0.128978
\(697\) 3497.17i 0.190050i
\(698\) 17888.8i 0.970059i
\(699\) −12034.5 −0.651196
\(700\) 5727.56 723.568i 0.309259 0.0390690i
\(701\) 16240.3 0.875019 0.437510 0.899214i \(-0.355861\pi\)
0.437510 + 0.899214i \(0.355861\pi\)
\(702\) 15366.3i 0.826158i
\(703\) 42261.4i 2.26731i
\(704\) −1953.62 −0.104588
\(705\) 8451.81 + 7451.26i 0.451509 + 0.398058i
\(706\) 22463.7 1.19749
\(707\) 16453.1i 0.875222i
\(708\) 4481.74i 0.237901i
\(709\) −29180.1 −1.54567 −0.772837 0.634605i \(-0.781163\pi\)
−0.772837 + 0.634605i \(0.781163\pi\)
\(710\) 2759.49 3130.03i 0.145862 0.165448i
\(711\) 3194.17 0.168482
\(712\) 11044.6i 0.581337i
\(713\) 1451.47i 0.0762384i
\(714\) 4264.47 0.223521
\(715\) −11742.5 + 13319.3i −0.614190 + 0.696663i
\(716\) −13935.8 −0.727379
\(717\) 24908.6i 1.29739i
\(718\) 18566.8i 0.965050i
\(719\) −18555.0 −0.962427 −0.481214 0.876603i \(-0.659804\pi\)
−0.481214 + 0.876603i \(0.659804\pi\)
\(720\) 455.412 + 401.499i 0.0235725 + 0.0207819i
\(721\) 5753.84 0.297204
\(722\) 10249.2i 0.528302i
\(723\) 22700.0i 1.16767i
\(724\) −9460.35 −0.485623
\(725\) −954.569 7556.11i −0.0488991 0.387071i
\(726\) 3879.12 0.198303
\(727\) 13806.7i 0.704352i −0.935934 0.352176i \(-0.885442\pi\)
0.935934 0.352176i \(-0.114558\pi\)
\(728\) 4805.82i 0.244664i
\(729\) −21496.1 −1.09211
\(730\) 992.247 + 874.783i 0.0503078 + 0.0443523i
\(731\) 6904.72 0.349358
\(732\) 4691.39i 0.236883i
\(733\) 33023.5i 1.66405i 0.554736 + 0.832027i \(0.312819\pi\)
−0.554736 + 0.832027i \(0.687181\pi\)
\(734\) −19324.3 −0.971761
\(735\) 7532.55 8544.02i 0.378017 0.428777i
\(736\) 736.000 0.0368605
\(737\) 8222.49i 0.410962i
\(738\) 624.545i 0.0311515i
\(739\) 9366.48 0.466240 0.233120 0.972448i \(-0.425106\pi\)
0.233120 + 0.972448i \(0.425106\pi\)
\(740\) −11417.5 + 12950.6i −0.567184 + 0.643345i
\(741\) 27672.3 1.37189
\(742\) 3156.63i 0.156177i
\(743\) 4374.71i 0.216006i 0.994151 + 0.108003i \(0.0344456\pi\)
−0.994151 + 0.108003i \(0.965554\pi\)
\(744\) −2452.91 −0.120871
\(745\) −20776.1 18316.6i −1.02171 0.900761i
\(746\) 5261.18 0.258211
\(747\) 319.981i 0.0156727i
\(748\) 4640.95i 0.226858i
\(749\) 10357.1 0.505263
\(750\) 7633.19 11232.0i 0.371633 0.546844i
\(751\) 7114.96 0.345711 0.172855 0.984947i \(-0.444701\pi\)
0.172855 + 0.984947i \(0.444701\pi\)
\(752\) 3318.77i 0.160935i
\(753\) 14582.6i 0.705734i
\(754\) −6340.10 −0.306224
\(755\) −8540.14 7529.13i −0.411666 0.362931i
\(756\) −6820.19 −0.328106
\(757\) 16213.0i 0.778429i 0.921147 + 0.389214i \(0.127253\pi\)
−0.921147 + 0.389214i \(0.872747\pi\)
\(758\) 7882.49i 0.377711i
\(759\) 3411.15 0.163132
\(760\) −6475.07 + 7344.53i −0.309047 + 0.350545i
\(761\) −9766.67 −0.465232 −0.232616 0.972569i \(-0.574728\pi\)
−0.232616 + 0.972569i \(0.574728\pi\)
\(762\) 14232.9i 0.676647i
\(763\) 20604.9i 0.977650i
\(764\) 19472.4 0.922103
\(765\) −953.784 + 1081.86i −0.0450773 + 0.0511302i
\(766\) −16292.3 −0.768494
\(767\) 11998.2i 0.564836i
\(768\) 1243.80i 0.0584400i
\(769\) 42497.5 1.99285 0.996424 0.0844951i \(-0.0269277\pi\)
0.996424 + 0.0844951i \(0.0269277\pi\)
\(770\) 5911.67 + 5211.83i 0.276677 + 0.243924i
\(771\) −6792.54 −0.317286
\(772\) 5810.11i 0.270869i
\(773\) 26248.0i 1.22131i −0.791896 0.610656i \(-0.790906\pi\)
0.791896 0.610656i \(-0.209094\pi\)
\(774\) −1233.09 −0.0572641
\(775\) −988.693 7826.22i −0.0458257 0.362743i
\(776\) −10029.5 −0.463967
\(777\) 21657.1i 0.999928i
\(778\) 5337.35i 0.245955i
\(779\) −10072.2 −0.463252
\(780\) −8479.94 7476.06i −0.389270 0.343187i
\(781\) 5696.38 0.260989
\(782\) 1748.41i 0.0799527i
\(783\) 8997.56i 0.410660i
\(784\) 3354.98 0.152832
\(785\) −8031.92 + 9110.44i −0.365187 + 0.414223i
\(786\) 3412.79 0.154873
\(787\) 13044.9i 0.590852i −0.955366 0.295426i \(-0.904538\pi\)
0.955366 0.295426i \(-0.0954616\pi\)
\(788\) 16941.9i 0.765900i
\(789\) −2192.20 −0.0989154
\(790\) 13917.0 15785.8i 0.626766 0.710928i
\(791\) 15244.5 0.685247
\(792\) 828.809i 0.0371849i
\(793\) 12559.4i 0.562419i
\(794\) −14056.3 −0.628260
\(795\) 5569.92 + 4910.54i 0.248484 + 0.219068i
\(796\) 9829.54 0.437687
\(797\) 13044.8i 0.579764i −0.957062 0.289882i \(-0.906384\pi\)
0.957062 0.289882i \(-0.0936160\pi\)
\(798\) 12282.1i 0.544840i
\(799\) −7883.93 −0.349078
\(800\) 3968.46 501.339i 0.175383 0.0221562i
\(801\) 4685.56 0.206687
\(802\) 18840.7i 0.829538i
\(803\) 1805.80i 0.0793591i
\(804\) −5234.97 −0.229631
\(805\) −2227.14 1963.48i −0.0975108 0.0859672i
\(806\) −6566.74 −0.286977
\(807\) 24285.4i 1.05934i
\(808\) 11399.9i 0.496344i
\(809\) −14991.2 −0.651499 −0.325749 0.945456i \(-0.605617\pi\)
−0.325749 + 0.945456i \(0.605617\pi\)
\(810\) −9254.60 + 10497.3i −0.401449 + 0.455355i
\(811\) −36807.9 −1.59371 −0.796856 0.604169i \(-0.793505\pi\)
−0.796856 + 0.604169i \(0.793505\pi\)
\(812\) 2814.00i 0.121616i
\(813\) 40605.9i 1.75167i
\(814\) −23569.0 −1.01486
\(815\) 1063.12 1205.88i 0.0456928 0.0518283i
\(816\) 2954.73 0.126760
\(817\) 19886.3i 0.851571i
\(818\) 20045.1i 0.856797i
\(819\) −2038.83 −0.0869872
\(820\) 3086.54 + 2721.14i 0.131447 + 0.115886i
\(821\) 533.820 0.0226924 0.0113462 0.999936i \(-0.496388\pi\)
0.0113462 + 0.999936i \(0.496388\pi\)
\(822\) 3225.10i 0.136847i
\(823\) 40071.2i 1.69720i −0.529037 0.848599i \(-0.677447\pi\)
0.529037 0.848599i \(-0.322553\pi\)
\(824\) 3986.67 0.168546
\(825\) 18392.7 2323.56i 0.776182 0.0980558i
\(826\) 5325.29 0.224323
\(827\) 26949.3i 1.13315i −0.824009 0.566577i \(-0.808267\pi\)
0.824009 0.566577i \(-0.191733\pi\)
\(828\) 312.242i 0.0131053i
\(829\) 42875.5 1.79629 0.898147 0.439696i \(-0.144914\pi\)
0.898147 + 0.439696i \(0.144914\pi\)
\(830\) 1581.36 + 1394.16i 0.0661325 + 0.0583035i
\(831\) 3073.47 0.128300
\(832\) 3329.81i 0.138751i
\(833\) 7969.94i 0.331503i
\(834\) −21530.9 −0.893949
\(835\) 16750.4 18999.6i 0.694216 0.787435i
\(836\) −13366.4 −0.552974
\(837\) 9319.20i 0.384849i
\(838\) 22355.1i 0.921531i
\(839\) 32088.5 1.32040 0.660201 0.751089i \(-0.270471\pi\)
0.660201 + 0.751089i \(0.270471\pi\)
\(840\) −3318.19 + 3763.75i −0.136296 + 0.154597i
\(841\) −20676.6 −0.847785
\(842\) 17931.2i 0.733907i
\(843\) 36024.6i 1.47183i
\(844\) 9303.61 0.379435
\(845\) −4276.68 3770.39i −0.174109 0.153498i
\(846\) 1407.96 0.0572183
\(847\) 4609.24i 0.186984i
\(848\) 2187.14i 0.0885691i
\(849\) −11907.5 −0.481348
\(850\) 1190.96 + 9427.30i 0.0480583 + 0.380416i
\(851\) 8879.29 0.357671
\(852\) 3626.68i 0.145831i
\(853\) 5672.84i 0.227707i 0.993498 + 0.113854i \(0.0363195\pi\)
−0.993498 + 0.113854i \(0.963681\pi\)
\(854\) −5574.39 −0.223363
\(855\) 3115.86 + 2746.99i 0.124632 + 0.109877i
\(856\) 7176.16 0.286537
\(857\) 11376.7i 0.453465i 0.973957 + 0.226733i \(0.0728044\pi\)
−0.973957 + 0.226733i \(0.927196\pi\)
\(858\) 15432.7i 0.614062i
\(859\) 23889.6 0.948898 0.474449 0.880283i \(-0.342647\pi\)
0.474449 + 0.880283i \(0.342647\pi\)
\(860\) −5372.56 + 6093.99i −0.213027 + 0.241632i
\(861\) −5161.55 −0.204303
\(862\) 33106.3i 1.30813i
\(863\) 18232.1i 0.719150i −0.933116 0.359575i \(-0.882922\pi\)
0.933116 0.359575i \(-0.117078\pi\)
\(864\) −4725.51 −0.186071
\(865\) 30756.0 34885.9i 1.20894 1.37128i
\(866\) −1505.61 −0.0590792
\(867\) 16851.2i 0.660089i
\(868\) 2914.59i 0.113972i
\(869\) 28728.7 1.12147
\(870\) 4965.34 + 4377.53i 0.193495 + 0.170589i
\(871\) −14014.6 −0.545199
\(872\) 14276.5i 0.554431i
\(873\) 4254.94i 0.164957i
\(874\) 5035.60 0.194887
\(875\) −13346.0 9069.90i −0.515631 0.350421i
\(876\) −1149.69 −0.0443430
\(877\) 12349.2i 0.475487i 0.971328 + 0.237743i \(0.0764078\pi\)
−0.971328 + 0.237743i \(0.923592\pi\)
\(878\) 5345.81i 0.205481i
\(879\) 42529.8 1.63196
\(880\) 4096.02 + 3611.12i 0.156905 + 0.138331i
\(881\) −37347.4 −1.42823 −0.714113 0.700031i \(-0.753170\pi\)
−0.714113 + 0.700031i \(0.753170\pi\)
\(882\) 1423.32i 0.0543375i
\(883\) 3389.21i 0.129169i −0.997912 0.0645844i \(-0.979428\pi\)
0.997912 0.0645844i \(-0.0205722\pi\)
\(884\) 7910.16 0.300959
\(885\) 8284.15 9396.54i 0.314654 0.356905i
\(886\) −14622.4 −0.554459
\(887\) 41902.9i 1.58620i −0.609090 0.793101i \(-0.708465\pi\)
0.609090 0.793101i \(-0.291535\pi\)
\(888\) 15005.6i 0.567065i
\(889\) −16911.8 −0.638025
\(890\) 20415.0 23156.3i 0.768890 0.872136i
\(891\) −19104.2 −0.718309
\(892\) 20050.9i 0.752638i
\(893\) 22706.5i 0.850890i
\(894\) 24072.7 0.900572
\(895\) 29218.1 + 25759.1i 1.09123 + 0.962048i
\(896\) −1477.91 −0.0551044
\(897\) 5814.06i 0.216417i
\(898\) 7171.40i 0.266495i
\(899\) 3845.09 0.142648
\(900\) −212.689 1683.59i −0.00787736 0.0623550i
\(901\) −5195.67 −0.192112
\(902\) 5617.22i 0.207354i
\(903\) 10190.9i 0.375560i
\(904\) 10562.4 0.388608
\(905\) 19834.8 + 17486.7i 0.728543 + 0.642296i
\(906\) 9895.23 0.362855
\(907\) 37106.0i 1.35842i 0.733945 + 0.679209i \(0.237677\pi\)
−0.733945 + 0.679209i \(0.762323\pi\)
\(908\) 15590.4i 0.569808i
\(909\) −4836.30 −0.176468
\(910\) −8883.19 + 10076.0i −0.323599 + 0.367051i
\(911\) −43702.3 −1.58938 −0.794688 0.607018i \(-0.792366\pi\)
−0.794688 + 0.607018i \(0.792366\pi\)
\(912\) 8509.91i 0.308982i
\(913\) 2877.94i 0.104322i
\(914\) −2445.09 −0.0884863
\(915\) −8671.66 + 9836.08i −0.313307 + 0.355378i
\(916\) 9385.84 0.338556
\(917\) 4055.14i 0.146033i
\(918\) 11225.7i 0.403599i
\(919\) −40160.4 −1.44153 −0.720767 0.693178i \(-0.756210\pi\)
−0.720767 + 0.693178i \(0.756210\pi\)
\(920\) −1543.12 1360.44i −0.0552990 0.0487525i
\(921\) 36659.7 1.31159
\(922\) 7690.91i 0.274714i
\(923\) 9709.07i 0.346238i
\(924\) −6849.69 −0.243873
\(925\) 47876.5 6048.28i 1.70181 0.214991i
\(926\) −10227.4 −0.362952
\(927\) 1691.31i 0.0599244i
\(928\) 1949.74i 0.0689691i
\(929\) −11545.6 −0.407748 −0.203874 0.978997i \(-0.565353\pi\)
−0.203874 + 0.978997i \(0.565353\pi\)
\(930\) 5142.84 + 4534.01i 0.181334 + 0.159867i
\(931\) 22954.2 0.808050
\(932\) 9907.76i 0.348218i
\(933\) 22691.4i 0.796230i
\(934\) 23094.9 0.809089
\(935\) −8578.43 + 9730.33i −0.300048 + 0.340338i
\(936\) −1412.65 −0.0493309
\(937\) 5690.42i 0.198397i −0.995068 0.0991985i \(-0.968372\pi\)
0.995068 0.0991985i \(-0.0316279\pi\)
\(938\) 6220.28i 0.216524i
\(939\) −17072.2 −0.593324
\(940\) 6134.48 6958.22i 0.212856 0.241438i
\(941\) 37839.6 1.31088 0.655438 0.755249i \(-0.272484\pi\)
0.655438 + 0.755249i \(0.272484\pi\)
\(942\) 10556.0i 0.365110i
\(943\) 2116.21i 0.0730787i
\(944\) 3689.74 0.127215
\(945\) 14299.4 + 12606.6i 0.492232 + 0.433960i
\(946\) −11090.5 −0.381167
\(947\) 47246.5i 1.62123i 0.585579 + 0.810615i \(0.300867\pi\)
−0.585579 + 0.810615i \(0.699133\pi\)
\(948\) 18290.6i 0.626635i
\(949\) −3077.86 −0.105281
\(950\) 27151.6 3430.08i 0.927277 0.117144i
\(951\) −33730.2 −1.15013
\(952\) 3510.86i 0.119525i
\(953\) 7264.72i 0.246933i 0.992349 + 0.123467i \(0.0394012\pi\)
−0.992349 + 0.123467i \(0.960599\pi\)
\(954\) 927.875 0.0314896
\(955\) −40826.3 35993.2i −1.38336 1.21959i
\(956\) −20506.8 −0.693764
\(957\) 9036.48i 0.305233i
\(958\) 9030.96i 0.304569i
\(959\) 3832.12 0.129036
\(960\) −2299.07 + 2607.79i −0.0772940 + 0.0876730i
\(961\) −25808.5 −0.866317
\(962\) 40171.7i 1.34635i
\(963\) 3044.42i 0.101875i
\(964\) 18688.5 0.624394
\(965\) 10739.5 12181.6i 0.358257 0.406363i
\(966\) 2580.52 0.0859492
\(967\) 47977.9i 1.59552i 0.602976 + 0.797759i \(0.293981\pi\)
−0.602976 + 0.797759i \(0.706019\pi\)
\(968\) 3193.61i 0.106040i
\(969\) 20215.8 0.670201
\(970\) 21028.1 + 18538.8i 0.696054 + 0.613653i
\(971\) −14030.3 −0.463701 −0.231850 0.972751i \(-0.574478\pi\)
−0.231850 + 0.972751i \(0.574478\pi\)
\(972\) 3785.66i 0.124923i
\(973\) 25583.4i 0.842924i
\(974\) 24202.4 0.796195
\(975\) 3960.34 + 31349.0i 0.130085 + 1.02971i
\(976\) −3862.33 −0.126670
\(977\) 29406.7i 0.962950i −0.876460 0.481475i \(-0.840101\pi\)
0.876460 0.481475i \(-0.159899\pi\)
\(978\) 1397.22i 0.0456832i
\(979\) 42142.4 1.37577
\(980\) −7034.13 6201.41i −0.229283 0.202139i
\(981\) −6056.69 −0.197121
\(982\) 20267.2i 0.658606i
\(983\) 50249.5i 1.63043i −0.579161 0.815213i \(-0.696620\pi\)
0.579161 0.815213i \(-0.303380\pi\)
\(984\) −3576.29 −0.115862
\(985\) 31315.7 35520.8i 1.01300 1.14902i
\(986\) −4631.71 −0.149598
\(987\) 11636.1i 0.375259i
\(988\) 22782.1i 0.733597i
\(989\) 4178.19 0.134337
\(990\) 1531.99 1737.70i 0.0491816 0.0557856i
\(991\) 56812.8 1.82111 0.910555 0.413389i \(-0.135655\pi\)
0.910555 + 0.413389i \(0.135655\pi\)
\(992\) 2019.44i 0.0646342i
\(993\) 22342.4i 0.714011i
\(994\) 4309.29 0.137507
\(995\) −20608.9 18169.1i −0.656628 0.578894i
\(996\) −1832.28 −0.0582913
\(997\) 8891.14i 0.282433i 0.989979 + 0.141216i \(0.0451013\pi\)
−0.989979 + 0.141216i \(0.954899\pi\)
\(998\) 6766.35i 0.214614i
\(999\) −57009.8 −1.80552
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 230.4.b.a.139.3 14
5.2 odd 4 1150.4.a.z.1.3 7
5.3 odd 4 1150.4.a.y.1.5 7
5.4 even 2 inner 230.4.b.a.139.12 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.b.a.139.3 14 1.1 even 1 trivial
230.4.b.a.139.12 yes 14 5.4 even 2 inner
1150.4.a.y.1.5 7 5.3 odd 4
1150.4.a.z.1.3 7 5.2 odd 4