Properties

Label 153.4.l.a.100.1
Level $153$
Weight $4$
Character 153.100
Analytic conductor $9.027$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [153,4,Mod(19,153)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(153, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("153.19");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 153.l (of order \(8\), degree \(4\), 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: \(9.02729223088\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 17)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 100.1
Root \(2.49971i\) of defining polynomial
Character \(\chi\) \(=\) 153.100
Dual form 153.4.l.a.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.47467 - 2.47467i) q^{2} +4.24796i q^{4} +(8.05561 - 3.33674i) q^{5} +(-6.33320 - 2.62330i) q^{7} +(-9.28506 + 9.28506i) q^{8} +O(q^{10})\) \(q+(-2.47467 - 2.47467i) q^{2} +4.24796i q^{4} +(8.05561 - 3.33674i) q^{5} +(-6.33320 - 2.62330i) q^{7} +(-9.28506 + 9.28506i) q^{8} +(-28.1923 - 11.6776i) q^{10} +(23.6471 - 57.0891i) q^{11} +5.37363i q^{13} +(9.18078 + 22.1644i) q^{14} +79.9385 q^{16} +(-44.2970 - 54.3210i) q^{17} +(-68.4392 - 68.4392i) q^{19} +(14.1743 + 34.2199i) q^{20} +(-199.795 + 82.7579i) q^{22} +(-44.5923 + 107.655i) q^{23} +(-34.6294 + 34.6294i) q^{25} +(13.2979 - 13.2979i) q^{26} +(11.1437 - 26.9032i) q^{28} +(-182.351 + 75.5321i) q^{29} +(-52.8371 - 127.560i) q^{31} +(-123.541 - 123.541i) q^{32} +(-24.8060 + 244.047i) q^{34} -59.7710 q^{35} +(42.6416 + 102.946i) q^{37} +338.729i q^{38} +(-43.8149 + 105.779i) q^{40} +(153.814 + 63.7117i) q^{41} +(-117.300 + 117.300i) q^{43} +(242.512 + 100.452i) q^{44} +(376.762 - 156.060i) q^{46} -130.994i q^{47} +(-209.310 - 209.310i) q^{49} +171.392 q^{50} -22.8269 q^{52} +(-505.038 - 505.038i) q^{53} -538.792i q^{55} +(83.1616 - 34.4467i) q^{56} +(638.174 + 264.340i) q^{58} +(598.365 - 598.365i) q^{59} +(4.61209 + 1.91039i) q^{61} +(-184.915 + 446.423i) q^{62} -28.0634i q^{64} +(17.9304 + 43.2878i) q^{65} +314.069 q^{67} +(230.753 - 188.172i) q^{68} +(147.913 + 147.913i) q^{70} +(45.3357 + 109.450i) q^{71} +(601.028 - 248.954i) q^{73} +(149.233 - 360.280i) q^{74} +(290.727 - 290.727i) q^{76} +(-299.524 + 299.524i) q^{77} +(-79.7533 + 192.542i) q^{79} +(643.953 - 266.734i) q^{80} +(-222.972 - 538.303i) q^{82} +(524.977 + 524.977i) q^{83} +(-538.095 - 289.781i) q^{85} +580.555 q^{86} +(310.511 + 749.640i) q^{88} -215.527i q^{89} +(14.0966 - 34.0323i) q^{91} +(-457.315 - 189.426i) q^{92} +(-324.167 + 324.167i) q^{94} +(-779.683 - 322.955i) q^{95} +(651.973 - 270.056i) q^{97} +1035.94i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(137\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47467 2.47467i −0.874927 0.874927i 0.118077 0.993004i \(-0.462327\pi\)
−0.993004 + 0.118077i \(0.962327\pi\)
\(3\) 0 0
\(4\) 4.24796i 0.530995i
\(5\) 8.05561 3.33674i 0.720515 0.298447i 0.00786742 0.999969i \(-0.497496\pi\)
0.712648 + 0.701522i \(0.247496\pi\)
\(6\) 0 0
\(7\) −6.33320 2.62330i −0.341961 0.141645i 0.205093 0.978743i \(-0.434250\pi\)
−0.547053 + 0.837098i \(0.684250\pi\)
\(8\) −9.28506 + 9.28506i −0.410345 + 0.410345i
\(9\) 0 0
\(10\) −28.1923 11.6776i −0.891518 0.369279i
\(11\) 23.6471 57.0891i 0.648170 1.56482i −0.167227 0.985918i \(-0.553481\pi\)
0.815397 0.578902i \(-0.196519\pi\)
\(12\) 0 0
\(13\) 5.37363i 0.114644i 0.998356 + 0.0573221i \(0.0182562\pi\)
−0.998356 + 0.0573221i \(0.981744\pi\)
\(14\) 9.18078 + 22.1644i 0.175262 + 0.423120i
\(15\) 0 0
\(16\) 79.9385 1.24904
\(17\) −44.2970 54.3210i −0.631977 0.774987i
\(18\) 0 0
\(19\) −68.4392 68.4392i −0.826370 0.826370i 0.160643 0.987013i \(-0.448643\pi\)
−0.987013 + 0.160643i \(0.948643\pi\)
\(20\) 14.1743 + 34.2199i 0.158474 + 0.382590i
\(21\) 0 0
\(22\) −199.795 + 82.7579i −1.93620 + 0.802002i
\(23\) −44.5923 + 107.655i −0.404267 + 0.975986i 0.582351 + 0.812937i \(0.302133\pi\)
−0.986618 + 0.163049i \(0.947867\pi\)
\(24\) 0 0
\(25\) −34.6294 + 34.6294i −0.277035 + 0.277035i
\(26\) 13.2979 13.2979i 0.100305 0.100305i
\(27\) 0 0
\(28\) 11.1437 26.9032i 0.0752126 0.181579i
\(29\) −182.351 + 75.5321i −1.16764 + 0.483653i −0.880413 0.474208i \(-0.842734\pi\)
−0.287230 + 0.957862i \(0.592734\pi\)
\(30\) 0 0
\(31\) −52.8371 127.560i −0.306123 0.739047i −0.999824 0.0187835i \(-0.994021\pi\)
0.693700 0.720264i \(-0.255979\pi\)
\(32\) −123.541 123.541i −0.682473 0.682473i
\(33\) 0 0
\(34\) −24.8060 + 244.047i −0.125123 + 1.23099i
\(35\) −59.7710 −0.288661
\(36\) 0 0
\(37\) 42.6416 + 102.946i 0.189466 + 0.457411i 0.989857 0.142067i \(-0.0453749\pi\)
−0.800391 + 0.599478i \(0.795375\pi\)
\(38\) 338.729i 1.44603i
\(39\) 0 0
\(40\) −43.8149 + 105.779i −0.173194 + 0.418127i
\(41\) 153.814 + 63.7117i 0.585894 + 0.242685i 0.655883 0.754862i \(-0.272296\pi\)
−0.0699888 + 0.997548i \(0.522296\pi\)
\(42\) 0 0
\(43\) −117.300 + 117.300i −0.416000 + 0.416000i −0.883823 0.467822i \(-0.845039\pi\)
0.467822 + 0.883823i \(0.345039\pi\)
\(44\) 242.512 + 100.452i 0.830911 + 0.344175i
\(45\) 0 0
\(46\) 376.762 156.060i 1.20762 0.500213i
\(47\) 130.994i 0.406541i −0.979123 0.203271i \(-0.934843\pi\)
0.979123 0.203271i \(-0.0651571\pi\)
\(48\) 0 0
\(49\) −209.310 209.310i −0.610233 0.610233i
\(50\) 171.392 0.484771
\(51\) 0 0
\(52\) −22.8269 −0.0608755
\(53\) −505.038 505.038i −1.30891 1.30891i −0.922201 0.386711i \(-0.873611\pi\)
−0.386711 0.922201i \(-0.626389\pi\)
\(54\) 0 0
\(55\) 538.792i 1.32092i
\(56\) 83.1616 34.4467i 0.198445 0.0821987i
\(57\) 0 0
\(58\) 638.174 + 264.340i 1.44476 + 0.598441i
\(59\) 598.365 598.365i 1.32035 1.32035i 0.406855 0.913493i \(-0.366625\pi\)
0.913493 0.406855i \(-0.133375\pi\)
\(60\) 0 0
\(61\) 4.61209 + 1.91039i 0.00968061 + 0.00400984i 0.387518 0.921862i \(-0.373332\pi\)
−0.377838 + 0.925872i \(0.623332\pi\)
\(62\) −184.915 + 446.423i −0.378777 + 0.914448i
\(63\) 0 0
\(64\) 28.0634i 0.0548113i
\(65\) 17.9304 + 43.2878i 0.0342153 + 0.0826030i
\(66\) 0 0
\(67\) 314.069 0.572681 0.286341 0.958128i \(-0.407561\pi\)
0.286341 + 0.958128i \(0.407561\pi\)
\(68\) 230.753 188.172i 0.411514 0.335576i
\(69\) 0 0
\(70\) 147.913 + 147.913i 0.252558 + 0.252558i
\(71\) 45.3357 + 109.450i 0.0757796 + 0.182948i 0.957230 0.289329i \(-0.0934322\pi\)
−0.881450 + 0.472277i \(0.843432\pi\)
\(72\) 0 0
\(73\) 601.028 248.954i 0.963630 0.399149i 0.155293 0.987868i \(-0.450368\pi\)
0.808337 + 0.588720i \(0.200368\pi\)
\(74\) 149.233 360.280i 0.234432 0.565969i
\(75\) 0 0
\(76\) 290.727 290.727i 0.438798 0.438798i
\(77\) −299.524 + 299.524i −0.443297 + 0.443297i
\(78\) 0 0
\(79\) −79.7533 + 192.542i −0.113582 + 0.274210i −0.970440 0.241341i \(-0.922413\pi\)
0.856859 + 0.515551i \(0.172413\pi\)
\(80\) 643.953 266.734i 0.899952 0.372772i
\(81\) 0 0
\(82\) −222.972 538.303i −0.300283 0.724947i
\(83\) 524.977 + 524.977i 0.694262 + 0.694262i 0.963167 0.268905i \(-0.0866618\pi\)
−0.268905 + 0.963167i \(0.586662\pi\)
\(84\) 0 0
\(85\) −538.095 289.781i −0.686642 0.369778i
\(86\) 580.555 0.727940
\(87\) 0 0
\(88\) 310.511 + 749.640i 0.376143 + 0.908090i
\(89\) 215.527i 0.256695i −0.991729 0.128348i \(-0.959033\pi\)
0.991729 0.128348i \(-0.0409673\pi\)
\(90\) 0 0
\(91\) 14.0966 34.0323i 0.0162388 0.0392038i
\(92\) −457.315 189.426i −0.518244 0.214663i
\(93\) 0 0
\(94\) −324.167 + 324.167i −0.355694 + 0.355694i
\(95\) −779.683 322.955i −0.842040 0.348784i
\(96\) 0 0
\(97\) 651.973 270.056i 0.682452 0.282681i −0.0143996 0.999896i \(-0.504584\pi\)
0.696851 + 0.717216i \(0.254584\pi\)
\(98\) 1035.94i 1.06782i
\(99\) 0 0
\(100\) −147.104 147.104i −0.147104 0.147104i
\(101\) −546.988 −0.538884 −0.269442 0.963017i \(-0.586839\pi\)
−0.269442 + 0.963017i \(0.586839\pi\)
\(102\) 0 0
\(103\) 1550.96 1.48369 0.741846 0.670570i \(-0.233950\pi\)
0.741846 + 0.670570i \(0.233950\pi\)
\(104\) −49.8944 49.8944i −0.0470438 0.0470438i
\(105\) 0 0
\(106\) 2499.60i 2.29041i
\(107\) −227.070 + 94.0554i −0.205156 + 0.0849783i −0.482895 0.875678i \(-0.660415\pi\)
0.277739 + 0.960656i \(0.410415\pi\)
\(108\) 0 0
\(109\) −1841.65 762.836i −1.61833 0.670334i −0.624477 0.781043i \(-0.714688\pi\)
−0.993853 + 0.110708i \(0.964688\pi\)
\(110\) −1333.33 + 1333.33i −1.15571 + 1.15571i
\(111\) 0 0
\(112\) −506.267 209.703i −0.427122 0.176920i
\(113\) 414.351 1000.33i 0.344946 0.832773i −0.652255 0.758000i \(-0.726177\pi\)
0.997201 0.0747730i \(-0.0238232\pi\)
\(114\) 0 0
\(115\) 1016.02i 0.823865i
\(116\) −320.857 774.617i −0.256817 0.620012i
\(117\) 0 0
\(118\) −2961.51 −2.31042
\(119\) 138.042 + 460.230i 0.106338 + 0.354531i
\(120\) 0 0
\(121\) −1758.83 1758.83i −1.32143 1.32143i
\(122\) −6.68580 16.1410i −0.00496151 0.0119781i
\(123\) 0 0
\(124\) 541.870 224.450i 0.392430 0.162550i
\(125\) −580.504 + 1401.46i −0.415375 + 1.00280i
\(126\) 0 0
\(127\) 718.468 718.468i 0.501998 0.501998i −0.410061 0.912058i \(-0.634492\pi\)
0.912058 + 0.410061i \(0.134492\pi\)
\(128\) −1057.77 + 1057.77i −0.730429 + 0.730429i
\(129\) 0 0
\(130\) 62.7512 151.495i 0.0423357 0.102207i
\(131\) 1024.45 424.340i 0.683255 0.283014i −0.0139317 0.999903i \(-0.504435\pi\)
0.697187 + 0.716889i \(0.254435\pi\)
\(132\) 0 0
\(133\) 253.903 + 612.976i 0.165535 + 0.399637i
\(134\) −777.217 777.217i −0.501054 0.501054i
\(135\) 0 0
\(136\) 915.674 + 93.0731i 0.577341 + 0.0586835i
\(137\) 1975.27 1.23182 0.615909 0.787818i \(-0.288789\pi\)
0.615909 + 0.787818i \(0.288789\pi\)
\(138\) 0 0
\(139\) 397.418 + 959.451i 0.242507 + 0.585465i 0.997531 0.0702334i \(-0.0223744\pi\)
−0.755023 + 0.655698i \(0.772374\pi\)
\(140\) 253.905i 0.153278i
\(141\) 0 0
\(142\) 158.662 383.043i 0.0937647 0.226368i
\(143\) 306.776 + 127.071i 0.179398 + 0.0743090i
\(144\) 0 0
\(145\) −1216.91 + 1216.91i −0.696960 + 0.696960i
\(146\) −2103.42 871.266i −1.19233 0.493880i
\(147\) 0 0
\(148\) −437.310 + 181.140i −0.242883 + 0.100605i
\(149\) 119.562i 0.0657377i 0.999460 + 0.0328689i \(0.0104644\pi\)
−0.999460 + 0.0328689i \(0.989536\pi\)
\(150\) 0 0
\(151\) −1108.64 1108.64i −0.597481 0.597481i 0.342160 0.939642i \(-0.388841\pi\)
−0.939642 + 0.342160i \(0.888841\pi\)
\(152\) 1270.92 0.678194
\(153\) 0 0
\(154\) 1482.44 0.775705
\(155\) −851.270 851.270i −0.441133 0.441133i
\(156\) 0 0
\(157\) 2121.62i 1.07850i 0.842147 + 0.539248i \(0.181291\pi\)
−0.842147 + 0.539248i \(0.818709\pi\)
\(158\) 673.839 279.113i 0.339290 0.140538i
\(159\) 0 0
\(160\) −1407.42 582.972i −0.695414 0.288050i
\(161\) 564.824 564.824i 0.276487 0.276487i
\(162\) 0 0
\(163\) 409.544 + 169.639i 0.196797 + 0.0815160i 0.478905 0.877867i \(-0.341034\pi\)
−0.282108 + 0.959383i \(0.591034\pi\)
\(164\) −270.645 + 653.394i −0.128865 + 0.311107i
\(165\) 0 0
\(166\) 2598.29i 1.21486i
\(167\) −900.241 2173.37i −0.417142 1.00707i −0.983171 0.182685i \(-0.941521\pi\)
0.566029 0.824385i \(-0.308479\pi\)
\(168\) 0 0
\(169\) 2168.12 0.986857
\(170\) 614.494 + 2048.72i 0.277233 + 0.924291i
\(171\) 0 0
\(172\) −498.284 498.284i −0.220894 0.220894i
\(173\) 727.203 + 1755.62i 0.319585 + 0.771547i 0.999276 + 0.0380481i \(0.0121140\pi\)
−0.679691 + 0.733499i \(0.737886\pi\)
\(174\) 0 0
\(175\) 310.158 128.472i 0.133976 0.0554945i
\(176\) 1890.31 4563.62i 0.809590 1.95452i
\(177\) 0 0
\(178\) −533.359 + 533.359i −0.224589 + 0.224589i
\(179\) 70.5199 70.5199i 0.0294464 0.0294464i −0.692230 0.721677i \(-0.743372\pi\)
0.721677 + 0.692230i \(0.243372\pi\)
\(180\) 0 0
\(181\) 1484.36 3583.56i 0.609567 1.47162i −0.253906 0.967229i \(-0.581715\pi\)
0.863473 0.504395i \(-0.168285\pi\)
\(182\) −119.103 + 49.3341i −0.0485082 + 0.0200928i
\(183\) 0 0
\(184\) −585.544 1413.63i −0.234602 0.566380i
\(185\) 687.007 + 687.007i 0.273026 + 0.273026i
\(186\) 0 0
\(187\) −4148.64 + 1244.35i −1.62234 + 0.486607i
\(188\) 556.457 0.215871
\(189\) 0 0
\(190\) 1130.25 + 2728.66i 0.431563 + 1.04188i
\(191\) 2326.90i 0.881511i 0.897627 + 0.440756i \(0.145289\pi\)
−0.897627 + 0.440756i \(0.854711\pi\)
\(192\) 0 0
\(193\) −534.412 + 1290.18i −0.199315 + 0.481189i −0.991660 0.128885i \(-0.958860\pi\)
0.792345 + 0.610074i \(0.208860\pi\)
\(194\) −2281.72 945.117i −0.844421 0.349770i
\(195\) 0 0
\(196\) 889.140 889.140i 0.324030 0.324030i
\(197\) 1869.77 + 774.486i 0.676223 + 0.280101i 0.694247 0.719737i \(-0.255738\pi\)
−0.0180240 + 0.999838i \(0.505738\pi\)
\(198\) 0 0
\(199\) 3827.94 1585.59i 1.36360 0.564820i 0.423552 0.905872i \(-0.360783\pi\)
0.940045 + 0.341052i \(0.110783\pi\)
\(200\) 643.072i 0.227360i
\(201\) 0 0
\(202\) 1353.61 + 1353.61i 0.471484 + 0.471484i
\(203\) 1353.01 0.467795
\(204\) 0 0
\(205\) 1451.65 0.494575
\(206\) −3838.10 3838.10i −1.29812 1.29812i
\(207\) 0 0
\(208\) 429.560i 0.143195i
\(209\) −5525.52 + 2288.75i −1.82875 + 0.757493i
\(210\) 0 0
\(211\) 2171.62 + 899.516i 0.708535 + 0.293485i 0.707698 0.706515i \(-0.249734\pi\)
0.000836499 1.00000i \(0.499734\pi\)
\(212\) 2145.38 2145.38i 0.695025 0.695025i
\(213\) 0 0
\(214\) 794.678 + 329.166i 0.253846 + 0.105147i
\(215\) −553.521 + 1336.32i −0.175581 + 0.423889i
\(216\) 0 0
\(217\) 946.471i 0.296086i
\(218\) 2669.70 + 6445.24i 0.829427 + 2.00241i
\(219\) 0 0
\(220\) 2288.77 0.701402
\(221\) 291.901 238.036i 0.0888478 0.0724526i
\(222\) 0 0
\(223\) −291.603 291.603i −0.0875657 0.0875657i 0.661967 0.749533i \(-0.269722\pi\)
−0.749533 + 0.661967i \(0.769722\pi\)
\(224\) 458.324 + 1106.49i 0.136710 + 0.330048i
\(225\) 0 0
\(226\) −3500.87 + 1450.11i −1.03042 + 0.426813i
\(227\) 733.181 1770.05i 0.214374 0.517545i −0.779712 0.626138i \(-0.784635\pi\)
0.994086 + 0.108593i \(0.0346346\pi\)
\(228\) 0 0
\(229\) −3439.04 + 3439.04i −0.992394 + 0.992394i −0.999971 0.00757695i \(-0.997588\pi\)
0.00757695 + 0.999971i \(0.497588\pi\)
\(230\) 2514.32 2514.32i 0.720822 0.720822i
\(231\) 0 0
\(232\) 991.815 2394.45i 0.280672 0.677602i
\(233\) −513.374 + 212.646i −0.144344 + 0.0597894i −0.453686 0.891162i \(-0.649891\pi\)
0.309342 + 0.950951i \(0.399891\pi\)
\(234\) 0 0
\(235\) −437.093 1055.24i −0.121331 0.292919i
\(236\) 2541.83 + 2541.83i 0.701098 + 0.701098i
\(237\) 0 0
\(238\) 797.309 1480.52i 0.217151 0.403228i
\(239\) 3205.56 0.867575 0.433787 0.901015i \(-0.357177\pi\)
0.433787 + 0.901015i \(0.357177\pi\)
\(240\) 0 0
\(241\) −341.888 825.391i −0.0913815 0.220614i 0.871580 0.490253i \(-0.163096\pi\)
−0.962962 + 0.269639i \(0.913096\pi\)
\(242\) 8705.02i 2.31231i
\(243\) 0 0
\(244\) −8.11525 + 19.5920i −0.00212920 + 0.00514035i
\(245\) −2384.53 987.705i −0.621805 0.257560i
\(246\) 0 0
\(247\) 367.767 367.767i 0.0947386 0.0947386i
\(248\) 1675.00 + 693.807i 0.428881 + 0.177648i
\(249\) 0 0
\(250\) 4904.70 2031.60i 1.24080 0.513957i
\(251\) 2431.39i 0.611427i −0.952124 0.305713i \(-0.901105\pi\)
0.952124 0.305713i \(-0.0988949\pi\)
\(252\) 0 0
\(253\) 5091.47 + 5091.47i 1.26521 + 1.26521i
\(254\) −3555.94 −0.878422
\(255\) 0 0
\(256\) 5010.77 1.22333
\(257\) −2273.66 2273.66i −0.551856 0.551856i 0.375120 0.926976i \(-0.377601\pi\)
−0.926976 + 0.375120i \(0.877601\pi\)
\(258\) 0 0
\(259\) 763.838i 0.183253i
\(260\) −183.885 + 76.1676i −0.0438617 + 0.0181681i
\(261\) 0 0
\(262\) −3585.27 1485.07i −0.845415 0.350182i
\(263\) −1880.31 + 1880.31i −0.440856 + 0.440856i −0.892300 0.451444i \(-0.850909\pi\)
0.451444 + 0.892300i \(0.350909\pi\)
\(264\) 0 0
\(265\) −5753.57 2383.21i −1.33373 0.552450i
\(266\) 888.586 2145.24i 0.204822 0.494484i
\(267\) 0 0
\(268\) 1334.15i 0.304091i
\(269\) −2186.04 5277.57i −0.495484 1.19620i −0.951892 0.306434i \(-0.900864\pi\)
0.456408 0.889771i \(-0.349136\pi\)
\(270\) 0 0
\(271\) 250.885 0.0562369 0.0281185 0.999605i \(-0.491048\pi\)
0.0281185 + 0.999605i \(0.491048\pi\)
\(272\) −3541.04 4342.34i −0.789364 0.967989i
\(273\) 0 0
\(274\) −4888.14 4888.14i −1.07775 1.07775i
\(275\) 1158.08 + 2795.85i 0.253944 + 0.613076i
\(276\) 0 0
\(277\) −3407.52 + 1411.44i −0.739126 + 0.306156i −0.720296 0.693667i \(-0.755994\pi\)
−0.0188299 + 0.999823i \(0.505994\pi\)
\(278\) 1390.85 3357.80i 0.300063 0.724415i
\(279\) 0 0
\(280\) 554.978 554.978i 0.118451 0.118451i
\(281\) 2497.50 2497.50i 0.530208 0.530208i −0.390426 0.920634i \(-0.627672\pi\)
0.920634 + 0.390426i \(0.127672\pi\)
\(282\) 0 0
\(283\) −301.639 + 728.220i −0.0633589 + 0.152962i −0.952388 0.304889i \(-0.901381\pi\)
0.889029 + 0.457851i \(0.151381\pi\)
\(284\) −464.939 + 192.584i −0.0971445 + 0.0402386i
\(285\) 0 0
\(286\) −444.710 1073.63i −0.0919450 0.221975i
\(287\) −806.998 806.998i −0.165978 0.165978i
\(288\) 0 0
\(289\) −988.544 + 4812.52i −0.201210 + 0.979548i
\(290\) 6022.91 1.21958
\(291\) 0 0
\(292\) 1057.55 + 2553.14i 0.211946 + 0.511683i
\(293\) 1413.82i 0.281899i 0.990017 + 0.140949i \(0.0450154\pi\)
−0.990017 + 0.140949i \(0.954985\pi\)
\(294\) 0 0
\(295\) 2823.61 6816.79i 0.557277 1.34539i
\(296\) −1351.79 559.929i −0.265443 0.109950i
\(297\) 0 0
\(298\) 295.877 295.877i 0.0575157 0.0575157i
\(299\) −578.499 239.622i −0.111891 0.0463469i
\(300\) 0 0
\(301\) 1050.59 435.170i 0.201180 0.0833315i
\(302\) 5487.02i 1.04551i
\(303\) 0 0
\(304\) −5470.93 5470.93i −1.03217 1.03217i
\(305\) 43.5276 0.00817175
\(306\) 0 0
\(307\) 4499.58 0.836498 0.418249 0.908333i \(-0.362644\pi\)
0.418249 + 0.908333i \(0.362644\pi\)
\(308\) −1272.36 1272.36i −0.235388 0.235388i
\(309\) 0 0
\(310\) 4213.22i 0.771919i
\(311\) 4357.74 1805.04i 0.794550 0.329113i 0.0517785 0.998659i \(-0.483511\pi\)
0.742771 + 0.669545i \(0.233511\pi\)
\(312\) 0 0
\(313\) −5701.55 2361.66i −1.02962 0.426482i −0.197044 0.980395i \(-0.563134\pi\)
−0.832575 + 0.553913i \(0.813134\pi\)
\(314\) 5250.30 5250.30i 0.943605 0.943605i
\(315\) 0 0
\(316\) −817.908 338.789i −0.145604 0.0603113i
\(317\) −454.194 + 1096.52i −0.0804735 + 0.194280i −0.958995 0.283422i \(-0.908530\pi\)
0.878522 + 0.477702i \(0.158530\pi\)
\(318\) 0 0
\(319\) 12196.3i 2.14064i
\(320\) −93.6403 226.068i −0.0163583 0.0394924i
\(321\) 0 0
\(322\) −2795.50 −0.483811
\(323\) −686.033 + 6749.34i −0.118179 + 1.16267i
\(324\) 0 0
\(325\) −186.085 186.085i −0.0317605 0.0317605i
\(326\) −593.685 1433.28i −0.100863 0.243504i
\(327\) 0 0
\(328\) −2019.74 + 836.602i −0.340004 + 0.140834i
\(329\) −343.636 + 829.611i −0.0575844 + 0.139021i
\(330\) 0 0
\(331\) 2170.88 2170.88i 0.360491 0.360491i −0.503503 0.863994i \(-0.667956\pi\)
0.863994 + 0.503503i \(0.167956\pi\)
\(332\) −2230.08 + 2230.08i −0.368649 + 0.368649i
\(333\) 0 0
\(334\) −3150.58 + 7606.18i −0.516144 + 1.24608i
\(335\) 2530.02 1047.97i 0.412626 0.170915i
\(336\) 0 0
\(337\) −1698.14 4099.67i −0.274491 0.662681i 0.725173 0.688566i \(-0.241760\pi\)
−0.999665 + 0.0258852i \(0.991760\pi\)
\(338\) −5365.39 5365.39i −0.863428 0.863428i
\(339\) 0 0
\(340\) 1230.98 2285.80i 0.196350 0.364603i
\(341\) −8531.74 −1.35490
\(342\) 0 0
\(343\) 1676.31 + 4046.97i 0.263884 + 0.637073i
\(344\) 2178.27i 0.341408i
\(345\) 0 0
\(346\) 2545.00 6144.17i 0.395434 0.954661i
\(347\) −8050.88 3334.79i −1.24552 0.515910i −0.340082 0.940396i \(-0.610455\pi\)
−0.905434 + 0.424486i \(0.860455\pi\)
\(348\) 0 0
\(349\) 71.3677 71.3677i 0.0109462 0.0109462i −0.701612 0.712559i \(-0.747536\pi\)
0.712559 + 0.701612i \(0.247536\pi\)
\(350\) −1085.46 449.613i −0.165773 0.0686653i
\(351\) 0 0
\(352\) −9974.22 + 4131.46i −1.51031 + 0.625589i
\(353\) 8688.88i 1.31009i 0.755589 + 0.655046i \(0.227351\pi\)
−0.755589 + 0.655046i \(0.772649\pi\)
\(354\) 0 0
\(355\) 730.412 + 730.412i 0.109201 + 0.109201i
\(356\) 915.551 0.136304
\(357\) 0 0
\(358\) −349.026 −0.0515269
\(359\) 1705.20 + 1705.20i 0.250688 + 0.250688i 0.821253 0.570565i \(-0.193276\pi\)
−0.570565 + 0.821253i \(0.693276\pi\)
\(360\) 0 0
\(361\) 2508.85i 0.365775i
\(362\) −12541.4 + 5194.82i −1.82089 + 0.754237i
\(363\) 0 0
\(364\) 144.568 + 59.8818i 0.0208170 + 0.00862270i
\(365\) 4010.95 4010.95i 0.575186 0.575186i
\(366\) 0 0
\(367\) −2101.09 870.300i −0.298845 0.123786i 0.228223 0.973609i \(-0.426709\pi\)
−0.527068 + 0.849823i \(0.676709\pi\)
\(368\) −3564.64 + 8605.81i −0.504945 + 1.21905i
\(369\) 0 0
\(370\) 3400.23i 0.477755i
\(371\) 1873.64 + 4523.37i 0.262196 + 0.632997i
\(372\) 0 0
\(373\) −9493.93 −1.31790 −0.658951 0.752186i \(-0.728999\pi\)
−0.658951 + 0.752186i \(0.728999\pi\)
\(374\) 13345.8 + 7187.15i 1.84518 + 0.993687i
\(375\) 0 0
\(376\) 1216.29 + 1216.29i 0.166822 + 0.166822i
\(377\) −405.881 979.883i −0.0554481 0.133864i
\(378\) 0 0
\(379\) 4931.39 2042.65i 0.668360 0.276844i −0.0225917 0.999745i \(-0.507192\pi\)
0.690952 + 0.722901i \(0.257192\pi\)
\(380\) 1371.90 3312.06i 0.185203 0.447119i
\(381\) 0 0
\(382\) 5758.31 5758.31i 0.771258 0.771258i
\(383\) −551.137 + 551.137i −0.0735295 + 0.0735295i −0.742915 0.669386i \(-0.766557\pi\)
0.669386 + 0.742915i \(0.266557\pi\)
\(384\) 0 0
\(385\) −1413.41 + 3412.28i −0.187102 + 0.451703i
\(386\) 4515.27 1870.28i 0.595391 0.246619i
\(387\) 0 0
\(388\) 1147.19 + 2769.55i 0.150102 + 0.362378i
\(389\) 7655.19 + 7655.19i 0.997772 + 0.997772i 0.999998 0.00222529i \(-0.000708332\pi\)
−0.00222529 + 0.999998i \(0.500708\pi\)
\(390\) 0 0
\(391\) 7823.25 2346.51i 1.01186 0.303499i
\(392\) 3886.91 0.500813
\(393\) 0 0
\(394\) −2710.48 6543.67i −0.346578 0.836714i
\(395\) 1817.16i 0.231471i
\(396\) 0 0
\(397\) −2337.00 + 5642.01i −0.295442 + 0.713260i 0.704551 + 0.709653i \(0.251148\pi\)
−0.999993 + 0.00360730i \(0.998852\pi\)
\(398\) −13396.7 5549.09i −1.68722 0.698871i
\(399\) 0 0
\(400\) −2768.22 + 2768.22i −0.346028 + 0.346028i
\(401\) −10579.9 4382.32i −1.31754 0.545743i −0.390464 0.920618i \(-0.627686\pi\)
−0.927075 + 0.374875i \(0.877686\pi\)
\(402\) 0 0
\(403\) 685.460 283.927i 0.0847276 0.0350953i
\(404\) 2323.58i 0.286145i
\(405\) 0 0
\(406\) −3348.24 3348.24i −0.409286 0.409286i
\(407\) 6885.44 0.838571
\(408\) 0 0
\(409\) −7597.11 −0.918466 −0.459233 0.888316i \(-0.651876\pi\)
−0.459233 + 0.888316i \(0.651876\pi\)
\(410\) −3592.36 3592.36i −0.432717 0.432717i
\(411\) 0 0
\(412\) 6588.40i 0.787833i
\(413\) −5359.26 + 2219.88i −0.638527 + 0.264487i
\(414\) 0 0
\(415\) 5980.72 + 2477.30i 0.707427 + 0.293026i
\(416\) 663.862 663.862i 0.0782416 0.0782416i
\(417\) 0 0
\(418\) 19337.7 + 8009.95i 2.26277 + 0.937271i
\(419\) −2635.75 + 6363.26i −0.307315 + 0.741923i 0.692476 + 0.721441i \(0.256520\pi\)
−0.999790 + 0.0204818i \(0.993480\pi\)
\(420\) 0 0
\(421\) 13586.7i 1.57286i −0.617678 0.786431i \(-0.711927\pi\)
0.617678 0.786431i \(-0.288073\pi\)
\(422\) −3148.04 7600.05i −0.363138 0.876694i
\(423\) 0 0
\(424\) 9378.62 1.07421
\(425\) 3415.08 + 347.124i 0.389778 + 0.0396188i
\(426\) 0 0
\(427\) −24.1978 24.1978i −0.00274242 0.00274242i
\(428\) −399.543 964.583i −0.0451230 0.108937i
\(429\) 0 0
\(430\) 4676.72 1937.16i 0.524492 0.217252i
\(431\) 6434.61 15534.5i 0.719128 1.73613i 0.0433099 0.999062i \(-0.486210\pi\)
0.675819 0.737068i \(-0.263790\pi\)
\(432\) 0 0
\(433\) −175.945 + 175.945i −0.0195274 + 0.0195274i −0.716803 0.697276i \(-0.754395\pi\)
0.697276 + 0.716803i \(0.254395\pi\)
\(434\) 2342.20 2342.20i 0.259054 0.259054i
\(435\) 0 0
\(436\) 3240.50 7823.25i 0.355944 0.859325i
\(437\) 10419.7 4315.98i 1.14060 0.472452i
\(438\) 0 0
\(439\) 3777.10 + 9118.74i 0.410641 + 0.991375i 0.984966 + 0.172748i \(0.0552645\pi\)
−0.574325 + 0.818627i \(0.694735\pi\)
\(440\) 5002.71 + 5002.71i 0.542034 + 0.542034i
\(441\) 0 0
\(442\) −1311.42 133.298i −0.141126 0.0143447i
\(443\) 10000.3 1.07253 0.536264 0.844051i \(-0.319835\pi\)
0.536264 + 0.844051i \(0.319835\pi\)
\(444\) 0 0
\(445\) −719.159 1736.20i −0.0766099 0.184953i
\(446\) 1443.24i 0.153227i
\(447\) 0 0
\(448\) −73.6186 + 177.731i −0.00776373 + 0.0187433i
\(449\) 7927.24 + 3283.57i 0.833206 + 0.345125i 0.758171 0.652056i \(-0.226093\pi\)
0.0750349 + 0.997181i \(0.476093\pi\)
\(450\) 0 0
\(451\) 7274.50 7274.50i 0.759518 0.759518i
\(452\) 4249.37 + 1760.15i 0.442198 + 0.183164i
\(453\) 0 0
\(454\) −6194.67 + 2565.92i −0.640375 + 0.265252i
\(455\) 321.187i 0.0330934i
\(456\) 0 0
\(457\) 5901.41 + 5901.41i 0.604062 + 0.604062i 0.941388 0.337326i \(-0.109522\pi\)
−0.337326 + 0.941388i \(0.609522\pi\)
\(458\) 17021.0 1.73655
\(459\) 0 0
\(460\) −4316.02 −0.437468
\(461\) −6081.73 6081.73i −0.614435 0.614435i 0.329663 0.944099i \(-0.393065\pi\)
−0.944099 + 0.329663i \(0.893065\pi\)
\(462\) 0 0
\(463\) 15888.5i 1.59482i −0.603440 0.797408i \(-0.706204\pi\)
0.603440 0.797408i \(-0.293796\pi\)
\(464\) −14576.8 + 6037.92i −1.45843 + 0.604102i
\(465\) 0 0
\(466\) 1796.66 + 744.200i 0.178602 + 0.0739794i
\(467\) 4201.42 4201.42i 0.416314 0.416314i −0.467617 0.883931i \(-0.654887\pi\)
0.883931 + 0.467617i \(0.154887\pi\)
\(468\) 0 0
\(469\) −1989.06 823.897i −0.195835 0.0811173i
\(470\) −1529.70 + 3693.02i −0.150127 + 0.362439i
\(471\) 0 0
\(472\) 11111.7i 1.08360i
\(473\) 3922.74 + 9470.33i 0.381327 + 0.920605i
\(474\) 0 0
\(475\) 4740.02 0.457867
\(476\) −1955.04 + 586.396i −0.188254 + 0.0564652i
\(477\) 0 0
\(478\) −7932.69 7932.69i −0.759064 0.759064i
\(479\) −5707.77 13779.8i −0.544456 1.31443i −0.921551 0.388258i \(-0.873077\pi\)
0.377094 0.926175i \(-0.376923\pi\)
\(480\) 0 0
\(481\) −553.192 + 229.140i −0.0524395 + 0.0217212i
\(482\) −1196.51 + 2888.63i −0.113069 + 0.272974i
\(483\) 0 0
\(484\) 7471.42 7471.42i 0.701673 0.701673i
\(485\) 4350.93 4350.93i 0.407352 0.407352i
\(486\) 0 0
\(487\) −3146.75 + 7596.92i −0.292798 + 0.706878i −1.00000 0.000134144i \(-0.999957\pi\)
0.707202 + 0.707012i \(0.249957\pi\)
\(488\) −60.5616 + 25.0854i −0.00561781 + 0.00232697i
\(489\) 0 0
\(490\) 3456.68 + 8345.16i 0.318688 + 0.769380i
\(491\) 1863.67 + 1863.67i 0.171295 + 0.171295i 0.787548 0.616253i \(-0.211350\pi\)
−0.616253 + 0.787548i \(0.711350\pi\)
\(492\) 0 0
\(493\) 12180.6 + 6559.62i 1.11275 + 0.599250i
\(494\) −1820.20 −0.165779
\(495\) 0 0
\(496\) −4223.72 10197.0i −0.382360 0.923099i
\(497\) 812.097i 0.0732949i
\(498\) 0 0
\(499\) 4884.55 11792.3i 0.438201 1.05791i −0.538368 0.842710i \(-0.680959\pi\)
0.976570 0.215202i \(-0.0690409\pi\)
\(500\) −5953.35 2465.96i −0.532484 0.220562i
\(501\) 0 0
\(502\) −6016.89 + 6016.89i −0.534954 + 0.534954i
\(503\) −5915.75 2450.38i −0.524394 0.217211i 0.104752 0.994498i \(-0.466595\pi\)
−0.629146 + 0.777287i \(0.716595\pi\)
\(504\) 0 0
\(505\) −4406.32 + 1825.16i −0.388274 + 0.160828i
\(506\) 25199.4i 2.21393i
\(507\) 0 0
\(508\) 3052.02 + 3052.02i 0.266558 + 0.266558i
\(509\) −7892.36 −0.687274 −0.343637 0.939103i \(-0.611659\pi\)
−0.343637 + 0.939103i \(0.611659\pi\)
\(510\) 0 0
\(511\) −4459.51 −0.386061
\(512\) −3937.80 3937.80i −0.339898 0.339898i
\(513\) 0 0
\(514\) 11253.1i 0.965667i
\(515\) 12493.9 5175.14i 1.06902 0.442804i
\(516\) 0 0
\(517\) −7478.33 3097.63i −0.636164 0.263508i
\(518\) −1890.25 + 1890.25i −0.160333 + 0.160333i
\(519\) 0 0
\(520\) −568.415 235.445i −0.0479358 0.0198557i
\(521\) −3255.41 + 7859.25i −0.273747 + 0.660883i −0.999637 0.0269270i \(-0.991428\pi\)
0.725891 + 0.687810i \(0.241428\pi\)
\(522\) 0 0
\(523\) 18757.8i 1.56830i −0.620571 0.784150i \(-0.713099\pi\)
0.620571 0.784150i \(-0.286901\pi\)
\(524\) 1802.58 + 4351.81i 0.150279 + 0.362805i
\(525\) 0 0
\(526\) 9306.30 0.771433
\(527\) −4588.67 + 8520.70i −0.379289 + 0.704303i
\(528\) 0 0
\(529\) −997.824 997.824i −0.0820107 0.0820107i
\(530\) 8340.53 + 20135.8i 0.683565 + 1.65027i
\(531\) 0 0
\(532\) −2603.89 + 1078.57i −0.212205 + 0.0878983i
\(533\) −342.363 + 826.537i −0.0278225 + 0.0671694i
\(534\) 0 0
\(535\) −1515.35 + 1515.35i −0.122456 + 0.122456i
\(536\) −2916.15 + 2916.15i −0.234997 + 0.234997i
\(537\) 0 0
\(538\) −7650.50 + 18470.0i −0.613079 + 1.48010i
\(539\) −16898.9 + 6999.75i −1.35044 + 0.559370i
\(540\) 0 0
\(541\) −5127.75 12379.5i −0.407503 0.983800i −0.985792 0.167968i \(-0.946279\pi\)
0.578289 0.815832i \(-0.303721\pi\)
\(542\) −620.858 620.858i −0.0492032 0.0492032i
\(543\) 0 0
\(544\) −1238.37 + 12183.4i −0.0976005 + 0.960215i
\(545\) −17381.0 −1.36609
\(546\) 0 0
\(547\) 2729.96 + 6590.70i 0.213391 + 0.515170i 0.993940 0.109924i \(-0.0350606\pi\)
−0.780549 + 0.625094i \(0.785061\pi\)
\(548\) 8390.88i 0.654089i
\(549\) 0 0
\(550\) 4052.93 9784.65i 0.314214 0.758579i
\(551\) 17649.3 + 7310.57i 1.36458 + 0.565228i
\(552\) 0 0
\(553\) 1010.19 1010.19i 0.0776809 0.0776809i
\(554\) 11925.3 + 4939.63i 0.914546 + 0.378817i
\(555\) 0 0
\(556\) −4075.71 + 1688.21i −0.310879 + 0.128770i
\(557\) 5175.60i 0.393712i 0.980432 + 0.196856i \(0.0630731\pi\)
−0.980432 + 0.196856i \(0.936927\pi\)
\(558\) 0 0
\(559\) −630.324 630.324i −0.0476921 0.0476921i
\(560\) −4778.01 −0.360550
\(561\) 0 0
\(562\) −12361.0 −0.927787
\(563\) 3938.10 + 3938.10i 0.294798 + 0.294798i 0.838972 0.544174i \(-0.183157\pi\)
−0.544174 + 0.838972i \(0.683157\pi\)
\(564\) 0 0
\(565\) 9440.87i 0.702974i
\(566\) 2548.56 1055.65i 0.189265 0.0783961i
\(567\) 0 0
\(568\) −1437.19 595.305i −0.106168 0.0439761i
\(569\) 10840.0 10840.0i 0.798660 0.798660i −0.184224 0.982884i \(-0.558977\pi\)
0.982884 + 0.184224i \(0.0589773\pi\)
\(570\) 0 0
\(571\) −20588.7 8528.10i −1.50895 0.625026i −0.533606 0.845733i \(-0.679164\pi\)
−0.975340 + 0.220707i \(0.929164\pi\)
\(572\) −539.791 + 1303.17i −0.0394577 + 0.0952592i
\(573\) 0 0
\(574\) 3994.11i 0.290437i
\(575\) −2183.83 5272.24i −0.158386 0.382378i
\(576\) 0 0
\(577\) 19321.1 1.39401 0.697007 0.717064i \(-0.254515\pi\)
0.697007 + 0.717064i \(0.254515\pi\)
\(578\) 14355.7 9463.07i 1.03308 0.680989i
\(579\) 0 0
\(580\) −5169.40 5169.40i −0.370082 0.370082i
\(581\) −1947.61 4701.96i −0.139072 0.335749i
\(582\) 0 0
\(583\) −40774.9 + 16889.5i −2.89661 + 1.19981i
\(584\) −3269.03 + 7892.13i −0.231632 + 0.559210i
\(585\) 0 0
\(586\) 3498.74 3498.74i 0.246641 0.246641i
\(587\) −16667.4 + 16667.4i −1.17195 + 1.17195i −0.190210 + 0.981743i \(0.560917\pi\)
−0.981743 + 0.190210i \(0.939083\pi\)
\(588\) 0 0
\(589\) −5113.98 + 12346.2i −0.357755 + 0.863698i
\(590\) −23856.8 + 9881.80i −1.66469 + 0.689537i
\(591\) 0 0
\(592\) 3408.70 + 8229.34i 0.236650 + 0.571324i
\(593\) −19330.9 19330.9i −1.33866 1.33866i −0.897359 0.441302i \(-0.854517\pi\)
−0.441302 0.897359i \(-0.645483\pi\)
\(594\) 0 0
\(595\) 2647.68 + 3246.82i 0.182427 + 0.223709i
\(596\) −507.895 −0.0349064
\(597\) 0 0
\(598\) 838.608 + 2024.58i 0.0573465 + 0.138447i
\(599\) 3930.83i 0.268129i 0.990973 + 0.134064i \(0.0428029\pi\)
−0.990973 + 0.134064i \(0.957197\pi\)
\(600\) 0 0
\(601\) −8595.04 + 20750.3i −0.583359 + 1.40835i 0.306391 + 0.951906i \(0.400879\pi\)
−0.889750 + 0.456448i \(0.849121\pi\)
\(602\) −3676.77 1522.97i −0.248927 0.103109i
\(603\) 0 0
\(604\) 4709.45 4709.45i 0.317259 0.317259i
\(605\) −20037.2 8299.66i −1.34649 0.557734i
\(606\) 0 0
\(607\) 2057.72 852.335i 0.137595 0.0569938i −0.312823 0.949811i \(-0.601275\pi\)
0.450419 + 0.892818i \(0.351275\pi\)
\(608\) 16910.1i 1.12795i
\(609\) 0 0
\(610\) −107.716 107.716i −0.00714969 0.00714969i
\(611\) 703.913 0.0466076
\(612\) 0 0
\(613\) 721.642 0.0475479 0.0237739 0.999717i \(-0.492432\pi\)
0.0237739 + 0.999717i \(0.492432\pi\)
\(614\) −11135.0 11135.0i −0.731874 0.731874i
\(615\) 0 0
\(616\) 5562.19i 0.363810i
\(617\) −6311.56 + 2614.33i −0.411821 + 0.170582i −0.578968 0.815350i \(-0.696545\pi\)
0.167147 + 0.985932i \(0.446545\pi\)
\(618\) 0 0
\(619\) 14869.8 + 6159.26i 0.965536 + 0.399938i 0.809048 0.587742i \(-0.199983\pi\)
0.156487 + 0.987680i \(0.449983\pi\)
\(620\) 3616.16 3616.16i 0.234240 0.234240i
\(621\) 0 0
\(622\) −15250.8 6317.10i −0.983123 0.407223i
\(623\) −565.393 + 1364.98i −0.0363595 + 0.0877796i
\(624\) 0 0
\(625\) 7104.94i 0.454716i
\(626\) 8265.11 + 19953.8i 0.527700 + 1.27398i
\(627\) 0 0
\(628\) −9012.55 −0.572675
\(629\) 3703.23 6876.53i 0.234749 0.435906i
\(630\) 0 0
\(631\) 19184.5 + 19184.5i 1.21034 + 1.21034i 0.970916 + 0.239421i \(0.0769578\pi\)
0.239421 + 0.970916i \(0.423042\pi\)
\(632\) −1047.25 2528.27i −0.0659132 0.159129i
\(633\) 0 0
\(634\) 3837.51 1589.55i 0.240389 0.0995725i
\(635\) 3390.35 8185.03i 0.211877 0.511517i
\(636\) 0 0
\(637\) 1124.75 1124.75i 0.0699597 0.0699597i
\(638\) 30181.9 30181.9i 1.87290 1.87290i
\(639\) 0 0
\(640\) −4991.49 + 12050.5i −0.308291 + 0.744280i
\(641\) 12843.5 5319.95i 0.791400 0.327809i 0.0498939 0.998755i \(-0.484112\pi\)
0.741506 + 0.670946i \(0.234112\pi\)
\(642\) 0 0
\(643\) −3378.07 8155.37i −0.207182 0.500181i 0.785795 0.618487i \(-0.212254\pi\)
−0.992977 + 0.118305i \(0.962254\pi\)
\(644\) 2399.35 + 2399.35i 0.146813 + 0.146813i
\(645\) 0 0
\(646\) 18400.1 15004.7i 1.12065 0.913856i
\(647\) 14695.4 0.892946 0.446473 0.894797i \(-0.352680\pi\)
0.446473 + 0.894797i \(0.352680\pi\)
\(648\) 0 0
\(649\) −20010.6 48309.8i −1.21030 2.92192i
\(650\) 920.999i 0.0555762i
\(651\) 0 0
\(652\) −720.617 + 1739.72i −0.0432846 + 0.104498i
\(653\) −6413.85 2656.70i −0.384370 0.159211i 0.182127 0.983275i \(-0.441702\pi\)
−0.566497 + 0.824064i \(0.691702\pi\)
\(654\) 0 0
\(655\) 6836.64 6836.64i 0.407831 0.407831i
\(656\) 12295.6 + 5093.02i 0.731805 + 0.303124i
\(657\) 0 0
\(658\) 2903.40 1202.63i 0.172016 0.0712512i
\(659\) 11804.8i 0.697800i −0.937160 0.348900i \(-0.886555\pi\)
0.937160 0.348900i \(-0.113445\pi\)
\(660\) 0 0
\(661\) 2731.80 + 2731.80i 0.160748 + 0.160748i 0.782898 0.622150i \(-0.213741\pi\)
−0.622150 + 0.782898i \(0.713741\pi\)
\(662\) −10744.4 −0.630806
\(663\) 0 0
\(664\) −9748.88 −0.569774
\(665\) 4090.68 + 4090.68i 0.238541 + 0.238541i
\(666\) 0 0
\(667\) 22999.1i 1.33513i
\(668\) 9232.40 3824.19i 0.534749 0.221500i
\(669\) 0 0
\(670\) −8854.32 3667.58i −0.510556 0.211479i
\(671\) 218.125 218.125i 0.0125494 0.0125494i
\(672\) 0 0
\(673\) 809.824 + 335.440i 0.0463840 + 0.0192129i 0.405755 0.913982i \(-0.367009\pi\)
−0.359371 + 0.933195i \(0.617009\pi\)
\(674\) −5943.00 + 14347.7i −0.339638 + 0.819958i
\(675\) 0 0
\(676\) 9210.10i 0.524016i
\(677\) 7784.19 + 18792.7i 0.441906 + 1.06686i 0.975279 + 0.220976i \(0.0709243\pi\)
−0.533373 + 0.845880i \(0.679076\pi\)
\(678\) 0 0
\(679\) −4837.51 −0.273412
\(680\) 7686.87 2305.61i 0.433497 0.130024i
\(681\) 0 0
\(682\) 21113.2 + 21113.2i 1.18544 + 1.18544i
\(683\) −11493.8 27748.5i −0.643922 1.55456i −0.821346 0.570430i \(-0.806777\pi\)
0.177425 0.984134i \(-0.443223\pi\)
\(684\) 0 0
\(685\) 15912.0 6590.98i 0.887543 0.367633i
\(686\) 5866.60 14163.2i 0.326513 0.788272i
\(687\) 0 0
\(688\) −9376.76 + 9376.76i −0.519601 + 0.519601i
\(689\) 2713.89 2713.89i 0.150059 0.150059i
\(690\) 0 0
\(691\) 4132.11 9975.80i 0.227486 0.549200i −0.768384 0.639989i \(-0.778939\pi\)
0.995870 + 0.0907888i \(0.0289388\pi\)
\(692\) −7457.82 + 3089.13i −0.409687 + 0.169698i
\(693\) 0 0
\(694\) 11670.8 + 28175.7i 0.638352 + 1.54112i
\(695\) 6402.88 + 6402.88i 0.349461 + 0.349461i
\(696\) 0 0
\(697\) −3352.61 11177.6i −0.182194 0.607432i
\(698\) −353.223 −0.0191543
\(699\) 0 0
\(700\) 545.742 + 1317.54i 0.0294673 + 0.0711404i
\(701\) 328.897i 0.0177208i 0.999961 + 0.00886039i \(0.00282039\pi\)
−0.999961 + 0.00886039i \(0.997180\pi\)
\(702\) 0 0
\(703\) 4127.18 9963.88i 0.221422 0.534559i
\(704\) −1602.11 663.618i −0.0857698 0.0355270i
\(705\) 0 0
\(706\) 21502.1 21502.1i 1.14624 1.14624i
\(707\) 3464.18 + 1434.91i 0.184277 + 0.0763301i
\(708\) 0 0
\(709\) 4480.97 1856.08i 0.237357 0.0983167i −0.260834 0.965384i \(-0.583998\pi\)
0.498192 + 0.867067i \(0.333998\pi\)
\(710\) 3615.06i 0.191085i
\(711\) 0 0
\(712\) 2001.18 + 2001.18i 0.105334 + 0.105334i
\(713\) 16088.7 0.845056
\(714\) 0 0
\(715\) 2895.27 0.151436
\(716\) 299.565 + 299.565i 0.0156359 + 0.0156359i
\(717\) 0 0
\(718\) 8439.60i 0.438667i
\(719\) −30379.9 + 12583.8i −1.57577 + 0.652705i −0.987736 0.156131i \(-0.950098\pi\)
−0.588034 + 0.808836i \(0.700098\pi\)
\(720\) 0 0
\(721\) −9822.52 4068.62i −0.507365 0.210157i
\(722\) 6208.57 6208.57i 0.320026 0.320026i
\(723\) 0 0
\(724\) 15222.8 + 6305.50i 0.781425 + 0.323677i
\(725\) 3699.06 8930.31i 0.189489 0.457467i
\(726\) 0 0
\(727\) 16213.2i 0.827116i 0.910478 + 0.413558i \(0.135714\pi\)
−0.910478 + 0.413558i \(0.864286\pi\)
\(728\) 185.103 + 446.879i 0.00942361 + 0.0227506i
\(729\) 0 0
\(730\) −19851.5 −1.00649
\(731\) 11567.9 + 1175.81i 0.585298 + 0.0594922i
\(732\) 0 0
\(733\) 17579.4 + 17579.4i 0.885826 + 0.885826i 0.994119 0.108293i \(-0.0345384\pi\)
−0.108293 + 0.994119i \(0.534538\pi\)
\(734\) 3045.80 + 7353.20i 0.153164 + 0.369771i
\(735\) 0 0
\(736\) 18808.8 7790.86i 0.941985 0.390183i
\(737\) 7426.82 17929.9i 0.371195 0.896143i
\(738\) 0 0
\(739\) 724.084 724.084i 0.0360431 0.0360431i −0.688856 0.724899i \(-0.741887\pi\)
0.724899 + 0.688856i \(0.241887\pi\)
\(740\) −2918.38 + 2918.38i −0.144975 + 0.144975i
\(741\) 0 0
\(742\) 6557.20 15830.5i 0.324424 0.783229i
\(743\) −6347.67 + 2629.29i −0.313423 + 0.129824i −0.533849 0.845580i \(-0.679255\pi\)
0.220426 + 0.975404i \(0.429255\pi\)
\(744\) 0 0
\(745\) 398.948 + 963.146i 0.0196192 + 0.0473650i
\(746\) 23494.3 + 23494.3i 1.15307 + 1.15307i
\(747\) 0 0
\(748\) −5285.93 17623.2i −0.258386 0.861456i
\(749\) 1684.81 0.0821919
\(750\) 0 0
\(751\) 4656.89 + 11242.7i 0.226275 + 0.546275i 0.995718 0.0924395i \(-0.0294665\pi\)
−0.769444 + 0.638715i \(0.779466\pi\)
\(752\) 10471.5i 0.507786i
\(753\) 0 0
\(754\) −1420.46 + 3429.31i −0.0686078 + 0.165634i
\(755\) −12630.0 5231.51i −0.608811 0.252178i
\(756\) 0 0
\(757\) −19971.1 + 19971.1i −0.958866 + 0.958866i −0.999187 0.0403208i \(-0.987162\pi\)
0.0403208 + 0.999187i \(0.487162\pi\)
\(758\) −17258.4 7148.67i −0.826984 0.342548i
\(759\) 0 0
\(760\) 10238.1 4240.74i 0.488649 0.202405i
\(761\) 30505.2i 1.45310i 0.687112 + 0.726552i \(0.258878\pi\)
−0.687112 + 0.726552i \(0.741122\pi\)
\(762\) 0 0
\(763\) 9662.39 + 9662.39i 0.458456 + 0.458456i
\(764\) −9884.58 −0.468078
\(765\) 0 0
\(766\) 2727.76 0.128666
\(767\) 3215.39 + 3215.39i 0.151370 + 0.151370i
\(768\) 0 0
\(769\) 20404.5i 0.956834i 0.878133 + 0.478417i \(0.158789\pi\)
−0.878133 + 0.478417i \(0.841211\pi\)
\(770\) 11942.0 4946.53i 0.558908 0.231507i
\(771\) 0 0
\(772\) −5480.65 2270.16i −0.255509 0.105835i
\(773\) −21642.1 + 21642.1i −1.00700 + 1.00700i −0.00702854 + 0.999975i \(0.502237\pi\)
−0.999975 + 0.00702854i \(0.997763\pi\)
\(774\) 0 0
\(775\) 6247.05 + 2587.61i 0.289549 + 0.119935i
\(776\) −3546.12 + 8561.09i −0.164044 + 0.396038i
\(777\) 0 0
\(778\) 37888.1i 1.74596i
\(779\) −6166.51 14887.3i −0.283618 0.684713i
\(780\) 0 0
\(781\) 7320.46 0.335399
\(782\) −25166.8 13553.1i −1.15085 0.619767i
\(783\) 0 0
\(784\) −16731.9 16731.9i −0.762205 0.762205i
\(785\) 7079.30 + 17090.9i 0.321874 + 0.777072i
\(786\) 0 0
\(787\) −33344.2 + 13811.6i −1.51028 + 0.625580i −0.975617 0.219482i \(-0.929563\pi\)
−0.534668 + 0.845062i \(0.679563\pi\)
\(788\) −3289.98 + 7942.73i −0.148732 + 0.359071i
\(789\) 0 0
\(790\) 4496.86 4496.86i 0.202520 0.202520i
\(791\) −5248.34 + 5248.34i −0.235916 + 0.235916i
\(792\) 0 0
\(793\) −10.2657 + 24.7836i −0.000459705 + 0.00110983i
\(794\) 19745.4 8178.81i 0.882541 0.365560i
\(795\) 0 0
\(796\) 6735.50 + 16260.9i 0.299917 + 0.724063i
\(797\) 15101.8 + 15101.8i 0.671185 + 0.671185i 0.957989 0.286804i \(-0.0925930\pi\)
−0.286804 + 0.957989i \(0.592593\pi\)
\(798\) 0 0
\(799\) −7115.72 + 5802.65i −0.315064 + 0.256925i
\(800\) 8556.28 0.378138
\(801\) 0 0
\(802\) 15336.9 + 37026.5i 0.675266 + 1.63024i
\(803\) 40199.2i 1.76662i
\(804\) 0 0
\(805\) 2665.33 6434.67i 0.116696 0.281730i
\(806\) −2398.91 993.661i −0.104836 0.0434246i
\(807\) 0 0
\(808\) 5078.81 5078.81i 0.221129 0.221129i
\(809\) 24176.9 + 10014.4i 1.05070 + 0.435213i 0.840140 0.542369i \(-0.182473\pi\)
0.210556 + 0.977582i \(0.432473\pi\)
\(810\) 0 0
\(811\) −18503.7 + 7664.48i −0.801174 + 0.331857i −0.745427 0.666588i \(-0.767754\pi\)
−0.0557475 + 0.998445i \(0.517754\pi\)
\(812\) 5747.51i 0.248397i
\(813\) 0 0
\(814\) −17039.2 17039.2i −0.733689 0.733689i
\(815\) 3865.16 0.166124
\(816\) 0 0
\(817\) 16055.8 0.687541
\(818\) 18800.3 + 18800.3i 0.803591 + 0.803591i
\(819\) 0 0
\(820\) 6166.56i 0.262617i
\(821\) −1997.50 + 827.392i −0.0849126 + 0.0351719i −0.424735 0.905318i \(-0.639633\pi\)
0.339823 + 0.940489i \(0.389633\pi\)
\(822\) 0 0
\(823\) 36378.3 + 15068.4i 1.54079 + 0.638214i 0.981621 0.190842i \(-0.0611218\pi\)
0.559165 + 0.829056i \(0.311122\pi\)
\(824\) −14400.7 + 14400.7i −0.608826 + 0.608826i
\(825\) 0 0
\(826\) 18755.8 + 7768.92i 0.790072 + 0.327258i
\(827\) 8644.75 20870.3i 0.363492 0.877546i −0.631293 0.775545i \(-0.717475\pi\)
0.994784 0.102002i \(-0.0325247\pi\)
\(828\) 0 0
\(829\) 10977.3i 0.459898i 0.973203 + 0.229949i \(0.0738560\pi\)
−0.973203 + 0.229949i \(0.926144\pi\)
\(830\) −8669.81 20930.8i −0.362571 0.875323i
\(831\) 0 0
\(832\) 150.802 0.00628380
\(833\) −2098.12 + 20641.7i −0.0872694 + 0.858576i
\(834\) 0 0
\(835\) −14504.0 14504.0i −0.601115 0.601115i
\(836\) −9722.50 23472.2i −0.402225 0.971056i
\(837\) 0 0
\(838\) 22269.6 9224.36i 0.918006 0.380251i
\(839\) −17065.4 + 41199.4i −0.702219 + 1.69531i 0.0163657 + 0.999866i \(0.494790\pi\)
−0.718584 + 0.695440i \(0.755210\pi\)
\(840\) 0 0
\(841\) 10301.0 10301.0i 0.422362 0.422362i
\(842\) −33622.5 + 33622.5i −1.37614 + 1.37614i
\(843\) 0 0
\(844\) −3821.11 + 9224.97i −0.155839 + 0.376228i
\(845\) 17465.6 7234.47i 0.711045 0.294525i
\(846\) 0 0
\(847\) 6525.07 + 15752.9i 0.264704 + 0.639052i
\(848\) −40372.0 40372.0i −1.63488 1.63488i
\(849\) 0 0
\(850\) −7592.18 9310.21i −0.306364 0.375691i
\(851\) −12984.1 −0.523021
\(852\) 0 0
\(853\) −14188.3 34253.7i −0.569519 1.37494i −0.901961 0.431817i \(-0.857873\pi\)
0.332443 0.943123i \(-0.392127\pi\)
\(854\) 119.763i 0.00479883i
\(855\) 0 0
\(856\) 1235.05 2981.67i 0.0493143 0.119055i
\(857\) 42102.6 + 17439.5i 1.67818 + 0.695123i 0.999236 0.0390702i \(-0.0124396\pi\)
0.678940 + 0.734194i \(0.262440\pi\)
\(858\) 0 0
\(859\) −48.4609 + 48.4609i −0.00192487 + 0.00192487i −0.708069 0.706144i \(-0.750433\pi\)
0.706144 + 0.708069i \(0.250433\pi\)
\(860\) −5676.62 2351.33i −0.225083 0.0932324i
\(861\) 0 0
\(862\) −54366.3 + 22519.3i −2.14817 + 0.889802i
\(863\) 5064.23i 0.199755i −0.995000 0.0998774i \(-0.968155\pi\)
0.995000 0.0998774i \(-0.0318451\pi\)
\(864\) 0 0
\(865\) 11716.1 + 11716.1i 0.460532 + 0.460532i
\(866\) 870.810 0.0341701
\(867\) 0 0
\(868\) −4020.57 −0.157220
\(869\) 9106.10 + 9106.10i 0.355470 + 0.355470i
\(870\) 0 0
\(871\) 1687.69i 0.0656546i
\(872\) 24182.8 10016.8i 0.939143 0.389006i
\(873\) 0 0
\(874\) −36465.9 15104.7i −1.41130 0.584581i
\(875\) 7352.90 7352.90i 0.284084 0.284084i
\(876\) 0 0
\(877\) −3535.56 1464.48i −0.136131 0.0563875i 0.313578 0.949563i \(-0.398472\pi\)
−0.449709 + 0.893175i \(0.648472\pi\)
\(878\) 13218.8 31912.9i 0.508100 1.22666i
\(879\) 0 0
\(880\) 43070.2i 1.64988i
\(881\) −15695.8 37893.0i −0.600232 1.44909i −0.873343 0.487105i \(-0.838053\pi\)
0.273112 0.961982i \(-0.411947\pi\)
\(882\) 0 0
\(883\) −7085.32 −0.270034 −0.135017 0.990843i \(-0.543109\pi\)
−0.135017 + 0.990843i \(0.543109\pi\)
\(884\) 1011.17 + 1239.98i 0.0384719 + 0.0471777i
\(885\) 0 0
\(886\) −24747.5 24747.5i −0.938383 0.938383i
\(887\) 6602.86 + 15940.7i 0.249946 + 0.603424i 0.998199 0.0599902i \(-0.0191070\pi\)
−0.748253 + 0.663414i \(0.769107\pi\)
\(888\) 0 0
\(889\) −6434.95 + 2665.45i −0.242769 + 0.100558i
\(890\) −2516.85 + 6076.21i −0.0947921 + 0.228848i
\(891\) 0 0
\(892\) 1238.72 1238.72i 0.0464969 0.0464969i
\(893\) −8965.12 + 8965.12i −0.335953 + 0.335953i
\(894\) 0 0
\(895\) 332.774 803.387i 0.0124284 0.0300048i
\(896\) 9473.95 3924.24i 0.353239 0.146317i
\(897\) 0 0
\(898\) −11491.5 27743.0i −0.427035 1.03095i
\(899\) 19269.8 + 19269.8i 0.714886 + 0.714886i
\(900\) 0 0
\(901\) −5062.49 + 49805.9i −0.187188 + 1.84159i
\(902\) −36003.9 −1.32905
\(903\) 0 0
\(904\) 5440.87 + 13135.4i 0.200178 + 0.483271i
\(905\) 33820.7i 1.24225i
\(906\) 0 0
\(907\) 6929.04 16728.2i 0.253666 0.612404i −0.744828 0.667256i \(-0.767469\pi\)
0.998494 + 0.0548519i \(0.0174687\pi\)
\(908\) 7519.12 + 3114.52i 0.274813 + 0.113831i
\(909\) 0 0
\(910\) −794.832 + 794.832i −0.0289543 + 0.0289543i
\(911\) 17702.1 + 7332.47i 0.643796 + 0.266669i 0.680602 0.732653i \(-0.261718\pi\)
−0.0368060 + 0.999322i \(0.511718\pi\)
\(912\) 0 0
\(913\) 42384.7 17556.3i 1.53639 0.636395i
\(914\) 29208.1i 1.05702i
\(915\) 0 0
\(916\) −14608.9 14608.9i −0.526956 0.526956i
\(917\) −7601.21 −0.273734
\(918\) 0 0
\(919\) −13214.6 −0.474329 −0.237165 0.971469i \(-0.576218\pi\)
−0.237165 + 0.971469i \(0.576218\pi\)
\(920\) −9433.82 9433.82i −0.338069 0.338069i
\(921\) 0 0
\(922\) 30100.5i 1.07517i
\(923\) −588.143 + 243.617i −0.0209740 + 0.00868770i
\(924\) 0 0
\(925\) −5041.60 2088.30i −0.179207 0.0742301i
\(926\) −39318.7 + 39318.7i −1.39535 + 1.39535i
\(927\) 0 0
\(928\) 31859.0 + 13196.4i 1.12696 + 0.466804i
\(929\) 3109.06 7505.93i 0.109801 0.265082i −0.859422 0.511266i \(-0.829177\pi\)
0.969223 + 0.246184i \(0.0791767\pi\)
\(930\) 0 0
\(931\) 28650.0i 1.00856i
\(932\) −903.313 2180.79i −0.0317479 0.0766461i
\(933\) 0 0
\(934\) −20794.2 −0.728489
\(935\) −29267.7 + 23866.9i −1.02370 + 0.834792i
\(936\) 0 0
\(937\) 8214.97 + 8214.97i 0.286415 + 0.286415i 0.835661 0.549246i \(-0.185085\pi\)
−0.549246 + 0.835661i \(0.685085\pi\)
\(938\) 2883.40 + 6961.14i 0.100369 + 0.242313i
\(939\) 0 0
\(940\) 4482.60 1856.75i 0.155539 0.0644262i
\(941\) −4902.44 + 11835.5i −0.169835 + 0.410019i −0.985764 0.168133i \(-0.946226\pi\)
0.815929 + 0.578152i \(0.196226\pi\)
\(942\) 0 0
\(943\) −13717.8 + 13717.8i −0.473715 + 0.473715i
\(944\) 47832.4 47832.4i 1.64917 1.64917i
\(945\) 0 0
\(946\) 13728.4 33143.4i 0.471829 1.13910i
\(947\) −19835.0 + 8215.93i −0.680624 + 0.281924i −0.696088 0.717957i \(-0.745078\pi\)
0.0154635 + 0.999880i \(0.495078\pi\)
\(948\) 0 0
\(949\) 1337.79 + 3229.70i 0.0457601 + 0.110475i
\(950\) −11730.0 11730.0i −0.400600 0.400600i
\(951\) 0 0
\(952\) −5554.99 2991.54i −0.189116 0.101845i
\(953\) −15897.5 −0.540369 −0.270184 0.962809i \(-0.587085\pi\)
−0.270184 + 0.962809i \(0.587085\pi\)
\(954\) 0 0
\(955\) 7764.27 + 18744.6i 0.263085 + 0.635142i
\(956\) 13617.1i 0.460678i
\(957\) 0 0
\(958\) −19975.5 + 48225.2i −0.673674 + 1.62639i
\(959\) −12509.8 5181.73i −0.421233 0.174480i
\(960\) 0 0
\(961\) 7585.60 7585.60i 0.254627 0.254627i
\(962\) 1936.01 + 801.922i 0.0648852 + 0.0268763i
\(963\) 0 0
\(964\) 3506.22 1452.33i 0.117145 0.0485231i
\(965\) 12176.4i 0.406189i
\(966\) 0 0
\(967\) −23469.7 23469.7i −0.780492 0.780492i 0.199421 0.979914i \(-0.436094\pi\)
−0.979914 + 0.199421i \(0.936094\pi\)
\(968\) 32661.6 1.08449
\(969\) 0 0
\(970\) −21534.2 −0.712806
\(971\) 22510.4 + 22510.4i 0.743968 + 0.743968i 0.973339 0.229371i \(-0.0736670\pi\)
−0.229371 + 0.973339i \(0.573667\pi\)
\(972\) 0 0
\(973\) 7118.94i 0.234556i
\(974\) 26587.0 11012.7i 0.874644 0.362289i
\(975\) 0 0
\(976\) 368.683 + 152.714i 0.0120915 + 0.00500845i
\(977\) 10216.1 10216.1i 0.334536 0.334536i −0.519770 0.854306i \(-0.673982\pi\)
0.854306 + 0.519770i \(0.173982\pi\)
\(978\) 0 0
\(979\) −12304.3 5096.60i −0.401682 0.166382i
\(980\) 4195.73 10129.4i 0.136763 0.330175i
\(981\) 0 0
\(982\) 9223.90i 0.299742i
\(983\) −2996.76 7234.81i −0.0972347 0.234745i 0.867776 0.496955i \(-0.165549\pi\)
−0.965011 + 0.262210i \(0.915549\pi\)
\(984\) 0 0
\(985\) 17646.4 0.570824
\(986\) −13910.0 46375.7i −0.449274 1.49787i
\(987\) 0 0
\(988\) 1562.26 + 1562.26i 0.0503057 + 0.0503057i
\(989\) −7397.27 17858.6i −0.237836 0.574186i
\(990\) 0 0
\(991\) 13532.7 5605.45i 0.433786 0.179680i −0.155095 0.987899i \(-0.549569\pi\)
0.588881 + 0.808219i \(0.299569\pi\)
\(992\) −9231.34 + 22286.4i −0.295459 + 0.713301i
\(993\) 0 0
\(994\) −2009.67 + 2009.67i −0.0641277 + 0.0641277i
\(995\) 25545.7 25545.7i 0.813923 0.813923i
\(996\) 0 0
\(997\) 18818.3 45431.4i 0.597775 1.44316i −0.278068 0.960561i \(-0.589694\pi\)
0.875843 0.482596i \(-0.160306\pi\)
\(998\) −41269.8 + 17094.5i −1.30899 + 0.542201i
\(999\) 0 0
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 153.4.l.a.100.1 12
3.2 odd 2 17.4.d.a.15.3 yes 12
17.8 even 8 inner 153.4.l.a.127.1 12
51.5 even 16 289.4.a.g.1.4 12
51.8 odd 8 17.4.d.a.8.3 12
51.14 even 16 289.4.b.e.288.10 12
51.20 even 16 289.4.b.e.288.9 12
51.29 even 16 289.4.a.g.1.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.8.3 12 51.8 odd 8
17.4.d.a.15.3 yes 12 3.2 odd 2
153.4.l.a.100.1 12 1.1 even 1 trivial
153.4.l.a.127.1 12 17.8 even 8 inner
289.4.a.g.1.3 12 51.29 even 16
289.4.a.g.1.4 12 51.5 even 16
289.4.b.e.288.9 12 51.20 even 16
289.4.b.e.288.10 12 51.14 even 16