Properties

Label 121.4.c.g.3.2
Level $121$
Weight $4$
Character 121.3
Analytic conductor $7.139$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [121,4,Mod(3,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.3"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\), degree \(4\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.13923111069\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 3.2
Root \(-0.535233 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 121.3
Dual form 121.4.c.g.81.2

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.61153 - 2.62393i) q^{2} +(-2.30653 - 7.09878i) q^{3} +(3.68602 - 11.3444i) q^{4} +(6.84760 + 4.97507i) q^{5} +(-26.9569 - 19.5853i) q^{6} +(6.25720 - 19.2577i) q^{7} +(-5.41889 - 16.6776i) q^{8} +(-23.2292 + 16.8770i) q^{9} +37.7846 q^{10} -89.0333 q^{12} +(-49.7836 + 36.1699i) q^{13} +(-27.9328 - 85.9682i) q^{14} +(19.5227 - 60.0848i) q^{15} +(13.8695 + 10.0768i) q^{16} +(56.1084 + 40.7652i) q^{17} +(-39.6088 + 121.903i) q^{18} +(2.21779 + 6.82565i) q^{19} +(81.6796 - 59.3437i) q^{20} -151.138 q^{21} +50.3154 q^{23} +(-105.892 + 76.9351i) q^{24} +(-16.4888 - 50.7474i) q^{25} +(-84.8877 + 261.258i) q^{26} +(10.3430 + 7.51461i) q^{27} +(-195.402 - 141.968i) q^{28} +(-44.2425 + 136.164i) q^{29} +(-87.1515 - 268.225i) q^{30} +(206.148 - 149.775i) q^{31} +216.818 q^{32} +309.603 q^{34} +(138.655 - 100.739i) q^{35} +(105.836 + 325.730i) q^{36} +(104.035 - 320.187i) q^{37} +(25.9197 + 18.8317i) q^{38} +(371.590 + 269.976i) q^{39} +(45.8660 - 141.161i) q^{40} +(55.0272 + 169.356i) q^{41} +(-545.842 + 396.577i) q^{42} -55.7898 q^{43} -243.028 q^{45} +(181.716 - 132.024i) q^{46} +(-79.2676 - 243.961i) q^{47} +(39.5423 - 121.699i) q^{48} +(-54.2125 - 39.3877i) q^{49} +(-192.708 - 140.010i) q^{50} +(159.967 - 492.328i) q^{51} +(226.822 + 698.088i) q^{52} +(-172.684 + 125.462i) q^{53} +57.0718 q^{54} -355.079 q^{56} +(43.3384 - 31.4872i) q^{57} +(197.503 + 607.852i) q^{58} +(-246.439 + 758.460i) q^{59} +(-609.665 - 442.947i) q^{60} +(-136.479 - 99.1578i) q^{61} +(351.510 - 1081.84i) q^{62} +(179.662 + 552.942i) q^{63} +(672.090 - 488.302i) q^{64} -520.846 q^{65} -366.105 q^{67} +(669.273 - 486.255i) q^{68} +(-116.054 - 357.178i) q^{69} +(236.426 - 727.644i) q^{70} +(632.643 + 459.642i) q^{71} +(407.344 + 295.953i) q^{72} +(-295.896 + 910.673i) q^{73} +(-464.422 - 1429.35i) q^{74} +(-322.213 + 234.101i) q^{75} +85.6077 q^{76} +2050.41 q^{78} +(-473.750 + 344.199i) q^{79} +(44.8399 + 138.003i) q^{80} +(-210.076 + 646.548i) q^{81} +(643.112 + 467.248i) q^{82} +(531.257 + 385.980i) q^{83} +(-557.099 + 1714.57i) q^{84} +(181.398 + 558.287i) q^{85} +(-201.487 + 146.389i) q^{86} +1068.65 q^{87} +72.6819 q^{89} +(-877.705 + 637.690i) q^{90} +(385.042 + 1185.04i) q^{91} +(185.463 - 570.797i) q^{92} +(-1538.71 - 1117.94i) q^{93} +(-926.414 - 673.079i) q^{94} +(-18.7716 + 57.7730i) q^{95} +(-500.098 - 1539.14i) q^{96} +(792.513 - 575.794i) q^{97} -299.141 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9} + 136 q^{10} - 352 q^{12} - 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} + 98 q^{20}+ \cdots + 3288 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.61153 2.62393i 1.27687 0.927700i 0.277416 0.960750i \(-0.410522\pi\)
0.999454 + 0.0330493i \(0.0105218\pi\)
\(3\) −2.30653 7.09878i −0.443893 1.36616i −0.883694 0.468066i \(-0.844951\pi\)
0.439801 0.898095i \(-0.355049\pi\)
\(4\) 3.68602 11.3444i 0.460752 1.41805i
\(5\) 6.84760 + 4.97507i 0.612468 + 0.444984i 0.850283 0.526326i \(-0.176431\pi\)
−0.237814 + 0.971311i \(0.576431\pi\)
\(6\) −26.9569 19.5853i −1.83418 1.33261i
\(7\) 6.25720 19.2577i 0.337857 1.03982i −0.627441 0.778664i \(-0.715898\pi\)
0.965298 0.261152i \(-0.0841024\pi\)
\(8\) −5.41889 16.6776i −0.239483 0.737054i
\(9\) −23.2292 + 16.8770i −0.860339 + 0.625073i
\(10\) 37.7846 1.19485
\(11\) 0 0
\(12\) −89.0333 −2.14181
\(13\) −49.7836 + 36.1699i −1.06211 + 0.771671i −0.974478 0.224482i \(-0.927931\pi\)
−0.0876357 + 0.996153i \(0.527931\pi\)
\(14\) −27.9328 85.9682i −0.533239 1.64114i
\(15\) 19.5227 60.0848i 0.336050 1.03426i
\(16\) 13.8695 + 10.0768i 0.216710 + 0.157449i
\(17\) 56.1084 + 40.7652i 0.800488 + 0.581588i 0.911057 0.412280i \(-0.135267\pi\)
−0.110569 + 0.993868i \(0.535267\pi\)
\(18\) −39.6088 + 121.903i −0.518661 + 1.59627i
\(19\) 2.21779 + 6.82565i 0.0267787 + 0.0824164i 0.963553 0.267519i \(-0.0862037\pi\)
−0.936774 + 0.349935i \(0.886204\pi\)
\(20\) 81.6796 59.3437i 0.913206 0.663483i
\(21\) −151.138 −1.57053
\(22\) 0 0
\(23\) 50.3154 0.456151 0.228076 0.973643i \(-0.426757\pi\)
0.228076 + 0.973643i \(0.426757\pi\)
\(24\) −105.892 + 76.9351i −0.900630 + 0.654346i
\(25\) −16.4888 50.7474i −0.131911 0.405979i
\(26\) −84.8877 + 261.258i −0.640302 + 1.97065i
\(27\) 10.3430 + 7.51461i 0.0737224 + 0.0535625i
\(28\) −195.402 141.968i −1.31884 0.958195i
\(29\) −44.2425 + 136.164i −0.283297 + 0.871900i 0.703606 + 0.710590i \(0.251572\pi\)
−0.986904 + 0.161310i \(0.948428\pi\)
\(30\) −87.1515 268.225i −0.530387 1.63236i
\(31\) 206.148 149.775i 1.19436 0.867755i 0.200644 0.979664i \(-0.435696\pi\)
0.993718 + 0.111909i \(0.0356964\pi\)
\(32\) 216.818 1.19776
\(33\) 0 0
\(34\) 309.603 1.56166
\(35\) 138.655 100.739i 0.669628 0.486513i
\(36\) 105.836 + 325.730i 0.489981 + 1.50801i
\(37\) 104.035 320.187i 0.462250 1.42266i −0.400159 0.916446i \(-0.631045\pi\)
0.862409 0.506212i \(-0.168955\pi\)
\(38\) 25.9197 + 18.8317i 0.110651 + 0.0803924i
\(39\) 371.590 + 269.976i 1.52569 + 1.10848i
\(40\) 45.8660 141.161i 0.181301 0.557988i
\(41\) 55.0272 + 169.356i 0.209605 + 0.645098i 0.999493 + 0.0318465i \(0.0101388\pi\)
−0.789888 + 0.613251i \(0.789861\pi\)
\(42\) −545.842 + 396.577i −2.00536 + 1.45698i
\(43\) −55.7898 −0.197857 −0.0989286 0.995095i \(-0.531542\pi\)
−0.0989286 + 0.995095i \(0.531542\pi\)
\(44\) 0 0
\(45\) −243.028 −0.805078
\(46\) 181.716 132.024i 0.582446 0.423172i
\(47\) −79.2676 243.961i −0.246008 0.757134i −0.995469 0.0950859i \(-0.969687\pi\)
0.749461 0.662048i \(-0.230313\pi\)
\(48\) 39.5423 121.699i 0.118905 0.365952i
\(49\) −54.2125 39.3877i −0.158054 0.114833i
\(50\) −192.708 140.010i −0.545060 0.396009i
\(51\) 159.967 492.328i 0.439213 1.35176i
\(52\) 226.822 + 698.088i 0.604896 + 1.86168i
\(53\) −172.684 + 125.462i −0.447546 + 0.325161i −0.788626 0.614873i \(-0.789207\pi\)
0.341080 + 0.940034i \(0.389207\pi\)
\(54\) 57.0718 0.143824
\(55\) 0 0
\(56\) −355.079 −0.847312
\(57\) 43.3384 31.4872i 0.100707 0.0731681i
\(58\) 197.503 + 607.852i 0.447128 + 1.37612i
\(59\) −246.439 + 758.460i −0.543790 + 1.67361i 0.180061 + 0.983655i \(0.442370\pi\)
−0.723851 + 0.689957i \(0.757630\pi\)
\(60\) −609.665 442.947i −1.31179 0.953071i
\(61\) −136.479 99.1578i −0.286465 0.208129i 0.435268 0.900301i \(-0.356654\pi\)
−0.721732 + 0.692172i \(0.756654\pi\)
\(62\) 351.510 1081.84i 0.720029 2.21602i
\(63\) 179.662 + 552.942i 0.359290 + 1.10578i
\(64\) 672.090 488.302i 1.31268 0.953714i
\(65\) −520.846 −0.993892
\(66\) 0 0
\(67\) −366.105 −0.667565 −0.333783 0.942650i \(-0.608325\pi\)
−0.333783 + 0.942650i \(0.608325\pi\)
\(68\) 669.273 486.255i 1.19355 0.867163i
\(69\) −116.054 357.178i −0.202482 0.623176i
\(70\) 236.426 727.644i 0.403690 1.24243i
\(71\) 632.643 + 459.642i 1.05748 + 0.768302i 0.973620 0.228175i \(-0.0732760\pi\)
0.0838575 + 0.996478i \(0.473276\pi\)
\(72\) 407.344 + 295.953i 0.666749 + 0.484422i
\(73\) −295.896 + 910.673i −0.474410 + 1.46009i 0.372341 + 0.928096i \(0.378555\pi\)
−0.846751 + 0.531989i \(0.821445\pi\)
\(74\) −464.422 1429.35i −0.729568 2.24538i
\(75\) −322.213 + 234.101i −0.496079 + 0.360422i
\(76\) 85.6077 0.129209
\(77\) 0 0
\(78\) 2050.41 2.97645
\(79\) −473.750 + 344.199i −0.674697 + 0.490196i −0.871594 0.490228i \(-0.836913\pi\)
0.196897 + 0.980424i \(0.436913\pi\)
\(80\) 44.8399 + 138.003i 0.0626657 + 0.192865i
\(81\) −210.076 + 646.548i −0.288170 + 0.886896i
\(82\) 643.112 + 467.248i 0.866096 + 0.629256i
\(83\) 531.257 + 385.980i 0.702566 + 0.510444i 0.880767 0.473550i \(-0.157028\pi\)
−0.178201 + 0.983994i \(0.557028\pi\)
\(84\) −557.099 + 1714.57i −0.723625 + 2.22709i
\(85\) 181.398 + 558.287i 0.231476 + 0.712409i
\(86\) −201.487 + 146.389i −0.252638 + 0.183552i
\(87\) 1068.65 1.31691
\(88\) 0 0
\(89\) 72.6819 0.0865648 0.0432824 0.999063i \(-0.486218\pi\)
0.0432824 + 0.999063i \(0.486218\pi\)
\(90\) −877.705 + 637.690i −1.02798 + 0.746871i
\(91\) 385.042 + 1185.04i 0.443554 + 1.36512i
\(92\) 185.463 570.797i 0.210173 0.646845i
\(93\) −1538.71 1117.94i −1.71566 1.24650i
\(94\) −926.414 673.079i −1.01651 0.738540i
\(95\) −18.7716 + 57.7730i −0.0202729 + 0.0623935i
\(96\) −500.098 1539.14i −0.531677 1.63633i
\(97\) 792.513 575.794i 0.829562 0.602712i −0.0898736 0.995953i \(-0.528646\pi\)
0.919435 + 0.393241i \(0.128646\pi\)
\(98\) −299.141 −0.308345
\(99\) 0 0
\(100\) −636.477 −0.636477
\(101\) −828.782 + 602.145i −0.816504 + 0.593225i −0.915709 0.401842i \(-0.868370\pi\)
0.0992051 + 0.995067i \(0.468370\pi\)
\(102\) −714.109 2197.80i −0.693209 2.13348i
\(103\) −229.199 + 705.401i −0.219258 + 0.674808i 0.779565 + 0.626321i \(0.215440\pi\)
−0.998824 + 0.0484872i \(0.984560\pi\)
\(104\) 873.000 + 634.272i 0.823122 + 0.598033i
\(105\) −1034.94 751.925i −0.961899 0.698861i
\(106\) −294.449 + 906.220i −0.269806 + 0.830376i
\(107\) −401.065 1234.35i −0.362359 1.11523i −0.951618 0.307283i \(-0.900580\pi\)
0.589259 0.807944i \(-0.299420\pi\)
\(108\) 123.373 89.6357i 0.109922 0.0798630i
\(109\) −691.844 −0.607951 −0.303975 0.952680i \(-0.598314\pi\)
−0.303975 + 0.952680i \(0.598314\pi\)
\(110\) 0 0
\(111\) −2512.89 −2.14877
\(112\) 280.839 204.041i 0.236935 0.172144i
\(113\) −166.557 512.610i −0.138658 0.426746i 0.857483 0.514512i \(-0.172027\pi\)
−0.996141 + 0.0877666i \(0.972027\pi\)
\(114\) 73.8978 227.434i 0.0607120 0.186852i
\(115\) 344.540 + 250.323i 0.279378 + 0.202980i
\(116\) 1381.62 + 1003.81i 1.10587 + 0.803460i
\(117\) 545.992 1680.39i 0.431428 1.32780i
\(118\) 1100.13 + 3385.84i 0.858262 + 2.64146i
\(119\) 1136.12 825.442i 0.875195 0.635867i
\(120\) −1107.86 −0.842781
\(121\) 0 0
\(122\) −753.082 −0.558859
\(123\) 1075.30 781.252i 0.788266 0.572709i
\(124\) −939.244 2890.70i −0.680215 2.09349i
\(125\) 466.507 1435.76i 0.333805 1.02735i
\(126\) 2099.74 + 1525.55i 1.48460 + 1.07862i
\(127\) −569.345 413.653i −0.397804 0.289022i 0.370842 0.928696i \(-0.379069\pi\)
−0.768646 + 0.639674i \(0.779069\pi\)
\(128\) 610.000 1877.39i 0.421226 1.29640i
\(129\) 128.681 + 396.039i 0.0878274 + 0.270305i
\(130\) −1881.05 + 1366.67i −1.26907 + 0.922034i
\(131\) 446.318 0.297672 0.148836 0.988862i \(-0.452447\pi\)
0.148836 + 0.988862i \(0.452447\pi\)
\(132\) 0 0
\(133\) 145.323 0.0947453
\(134\) −1322.20 + 960.635i −0.852394 + 0.619300i
\(135\) 33.4388 + 102.914i 0.0213182 + 0.0656106i
\(136\) 375.821 1156.66i 0.236959 0.729284i
\(137\) −1593.34 1157.63i −0.993637 0.721919i −0.0329221 0.999458i \(-0.510481\pi\)
−0.960714 + 0.277539i \(0.910481\pi\)
\(138\) −1356.34 985.441i −0.836664 0.607872i
\(139\) −79.9427 + 246.038i −0.0487817 + 0.150135i −0.972480 0.232986i \(-0.925150\pi\)
0.923698 + 0.383120i \(0.125150\pi\)
\(140\) −631.736 1944.28i −0.381367 1.17373i
\(141\) −1548.99 + 1125.41i −0.925166 + 0.672173i
\(142\) 3490.88 2.06302
\(143\) 0 0
\(144\) −492.241 −0.284862
\(145\) −980.383 + 712.290i −0.561492 + 0.407948i
\(146\) 1320.91 + 4065.34i 0.748761 + 2.30445i
\(147\) −154.562 + 475.692i −0.0867213 + 0.266901i
\(148\) −3248.85 2360.43i −1.80442 1.31099i
\(149\) 79.9537 + 58.0898i 0.0439602 + 0.0319389i 0.609548 0.792749i \(-0.291351\pi\)
−0.565588 + 0.824688i \(0.691351\pi\)
\(150\) −549.416 + 1690.93i −0.299064 + 0.920425i
\(151\) −459.679 1414.75i −0.247736 0.762454i −0.995174 0.0981223i \(-0.968716\pi\)
0.747438 0.664331i \(-0.231284\pi\)
\(152\) 101.818 73.9749i 0.0543323 0.0394747i
\(153\) −1991.34 −1.05223
\(154\) 0 0
\(155\) 2156.76 1.11765
\(156\) 4432.40 3220.33i 2.27485 1.65277i
\(157\) 652.647 + 2008.64i 0.331764 + 1.02106i 0.968294 + 0.249812i \(0.0803689\pi\)
−0.636531 + 0.771251i \(0.719631\pi\)
\(158\) −807.808 + 2486.18i −0.406745 + 1.25183i
\(159\) 1288.93 + 936.461i 0.642884 + 0.467083i
\(160\) 1484.68 + 1078.69i 0.733591 + 0.532985i
\(161\) 314.833 968.956i 0.154114 0.474313i
\(162\) 937.801 + 2886.25i 0.454818 + 1.39979i
\(163\) −1120.47 + 814.069i −0.538417 + 0.391183i −0.823497 0.567321i \(-0.807980\pi\)
0.285080 + 0.958504i \(0.407980\pi\)
\(164\) 2124.08 1.01136
\(165\) 0 0
\(166\) 2931.44 1.37062
\(167\) −627.204 + 455.690i −0.290626 + 0.211152i −0.723539 0.690284i \(-0.757486\pi\)
0.432913 + 0.901436i \(0.357486\pi\)
\(168\) 819.003 + 2520.63i 0.376116 + 1.15756i
\(169\) 491.234 1511.86i 0.223593 0.688149i
\(170\) 2120.03 + 1540.30i 0.956466 + 0.694913i
\(171\) −166.714 121.125i −0.0745550 0.0541674i
\(172\) −205.642 + 632.901i −0.0911631 + 0.280571i
\(173\) −138.012 424.757i −0.0606523 0.186669i 0.916140 0.400860i \(-0.131288\pi\)
−0.976792 + 0.214191i \(0.931288\pi\)
\(174\) 3859.46 2804.06i 1.68152 1.22170i
\(175\) −1080.45 −0.466711
\(176\) 0 0
\(177\) 5952.56 2.52781
\(178\) 262.493 190.712i 0.110532 0.0803062i
\(179\) −867.487 2669.85i −0.362229 1.11483i −0.951698 0.307035i \(-0.900663\pi\)
0.589469 0.807791i \(-0.299337\pi\)
\(180\) −895.806 + 2757.01i −0.370941 + 1.14164i
\(181\) 1080.36 + 784.930i 0.443662 + 0.322339i 0.787088 0.616841i \(-0.211588\pi\)
−0.343427 + 0.939180i \(0.611588\pi\)
\(182\) 4500.05 + 3269.48i 1.83278 + 1.33159i
\(183\) −389.106 + 1197.55i −0.157178 + 0.483744i
\(184\) −272.653 839.141i −0.109241 0.336208i
\(185\) 2305.34 1674.93i 0.916173 0.665639i
\(186\) −8490.49 −3.34706
\(187\) 0 0
\(188\) −3059.77 −1.18700
\(189\) 209.432 152.161i 0.0806027 0.0585613i
\(190\) 83.7983 + 257.905i 0.0319967 + 0.0984756i
\(191\) −616.479 + 1897.33i −0.233544 + 0.718774i 0.763767 + 0.645492i \(0.223348\pi\)
−0.997311 + 0.0732826i \(0.976652\pi\)
\(192\) −5016.55 3644.73i −1.88561 1.36998i
\(193\) 1692.19 + 1229.45i 0.631121 + 0.458537i 0.856789 0.515668i \(-0.172456\pi\)
−0.225667 + 0.974204i \(0.572456\pi\)
\(194\) 1351.34 4159.00i 0.500107 1.53917i
\(195\) 1201.35 + 3697.37i 0.441182 + 1.35782i
\(196\) −646.657 + 469.824i −0.235662 + 0.171219i
\(197\) 3777.20 1.36606 0.683032 0.730389i \(-0.260661\pi\)
0.683032 + 0.730389i \(0.260661\pi\)
\(198\) 0 0
\(199\) −1251.15 −0.445688 −0.222844 0.974854i \(-0.571534\pi\)
−0.222844 + 0.974854i \(0.571534\pi\)
\(200\) −756.995 + 549.989i −0.267638 + 0.194451i
\(201\) 844.434 + 2598.90i 0.296327 + 0.912002i
\(202\) −1413.19 + 4349.34i −0.492234 + 1.51494i
\(203\) 2345.38 + 1704.02i 0.810902 + 0.589155i
\(204\) −4995.52 3629.46i −1.71449 1.24565i
\(205\) −465.756 + 1433.45i −0.158682 + 0.488373i
\(206\) 1023.17 + 3148.98i 0.346055 + 1.06505i
\(207\) −1168.78 + 849.171i −0.392445 + 0.285128i
\(208\) −1054.95 −0.351670
\(209\) 0 0
\(210\) −5710.71 −1.87655
\(211\) 3724.95 2706.34i 1.21534 0.882995i 0.219634 0.975582i \(-0.429514\pi\)
0.995705 + 0.0925872i \(0.0295137\pi\)
\(212\) 786.775 + 2421.45i 0.254887 + 0.784460i
\(213\) 1803.69 5551.17i 0.580218 1.78573i
\(214\) −4687.32 3405.54i −1.49728 1.08784i
\(215\) −382.026 277.558i −0.121181 0.0880433i
\(216\) 69.2784 213.217i 0.0218231 0.0671647i
\(217\) −1594.41 4907.10i −0.498783 1.53510i
\(218\) −2498.62 + 1815.35i −0.776274 + 0.563996i
\(219\) 7147.16 2.20530
\(220\) 0 0
\(221\) −4267.75 −1.29900
\(222\) −9075.40 + 6593.67i −2.74370 + 1.99341i
\(223\) −1434.91 4416.19i −0.430890 1.32614i −0.897240 0.441543i \(-0.854431\pi\)
0.466350 0.884600i \(-0.345569\pi\)
\(224\) 1356.67 4175.41i 0.404672 1.24545i
\(225\) 1239.48 + 900.538i 0.367255 + 0.266826i
\(226\) −1946.58 1414.27i −0.572940 0.416266i
\(227\) −1316.40 + 4051.47i −0.384901 + 1.18460i 0.551650 + 0.834075i \(0.313998\pi\)
−0.936552 + 0.350529i \(0.886002\pi\)
\(228\) −197.457 607.710i −0.0573549 0.176520i
\(229\) −4657.01 + 3383.51i −1.34386 + 0.976370i −0.344566 + 0.938762i \(0.611974\pi\)
−0.999293 + 0.0376082i \(0.988026\pi\)
\(230\) 1901.15 0.545034
\(231\) 0 0
\(232\) 2510.65 0.710483
\(233\) 4167.31 3027.73i 1.17172 0.851301i 0.180502 0.983575i \(-0.442228\pi\)
0.991213 + 0.132274i \(0.0422277\pi\)
\(234\) −2437.37 7501.44i −0.680921 2.09566i
\(235\) 670.929 2064.91i 0.186241 0.573190i
\(236\) 7695.90 + 5591.40i 2.12271 + 1.54224i
\(237\) 3536.12 + 2569.14i 0.969179 + 0.704150i
\(238\) 1937.24 5962.22i 0.527617 1.62384i
\(239\) 643.147 + 1979.40i 0.174066 + 0.535720i 0.999590 0.0286478i \(-0.00912014\pi\)
−0.825524 + 0.564367i \(0.809120\pi\)
\(240\) 876.230 636.618i 0.235668 0.171223i
\(241\) −6829.14 −1.82533 −0.912663 0.408714i \(-0.865977\pi\)
−0.912663 + 0.408714i \(0.865977\pi\)
\(242\) 0 0
\(243\) 5419.43 1.43069
\(244\) −1627.95 + 1182.77i −0.427126 + 0.310325i
\(245\) −175.269 539.422i −0.0457042 0.140663i
\(246\) 1833.53 5643.04i 0.475211 1.46255i
\(247\) −357.293 259.588i −0.0920404 0.0668713i
\(248\) −3614.99 2626.44i −0.925613 0.672497i
\(249\) 1514.63 4661.55i 0.385485 1.18640i
\(250\) −2082.53 6409.38i −0.526844 1.62146i
\(251\) −16.2859 + 11.8324i −0.00409545 + 0.00297552i −0.589831 0.807527i \(-0.700806\pi\)
0.585736 + 0.810502i \(0.300806\pi\)
\(252\) 6935.03 1.73359
\(253\) 0 0
\(254\) −3141.60 −0.776070
\(255\) 3544.76 2575.42i 0.870515 0.632466i
\(256\) −669.380 2060.14i −0.163423 0.502964i
\(257\) 46.6586 143.600i 0.0113248 0.0348543i −0.945234 0.326392i \(-0.894167\pi\)
0.956559 + 0.291538i \(0.0941670\pi\)
\(258\) 1503.92 + 1092.66i 0.362906 + 0.263667i
\(259\) −5515.08 4006.94i −1.32313 0.961309i
\(260\) −1919.85 + 5908.68i −0.457938 + 1.40939i
\(261\) −1270.33 3909.66i −0.301269 0.927211i
\(262\) 1611.89 1171.11i 0.380088 0.276150i
\(263\) 2609.68 0.611862 0.305931 0.952054i \(-0.401032\pi\)
0.305931 + 0.952054i \(0.401032\pi\)
\(264\) 0 0
\(265\) −1806.65 −0.418799
\(266\) 524.840 381.319i 0.120977 0.0878953i
\(267\) −167.643 515.953i −0.0384255 0.118261i
\(268\) −1349.47 + 4153.24i −0.307582 + 0.946640i
\(269\) 975.627 + 708.834i 0.221134 + 0.160663i 0.692837 0.721094i \(-0.256361\pi\)
−0.471703 + 0.881757i \(0.656361\pi\)
\(270\) 390.805 + 283.936i 0.0880875 + 0.0639993i
\(271\) −1881.35 + 5790.19i −0.421711 + 1.29789i 0.484398 + 0.874848i \(0.339039\pi\)
−0.906109 + 0.423045i \(0.860961\pi\)
\(272\) 367.413 + 1130.78i 0.0819033 + 0.252072i
\(273\) 7524.21 5466.66i 1.66808 1.21193i
\(274\) −8791.94 −1.93847
\(275\) 0 0
\(276\) −4479.74 −0.976989
\(277\) −6030.04 + 4381.08i −1.30798 + 0.950301i −0.999999 0.00109196i \(-0.999652\pi\)
−0.307978 + 0.951393i \(0.599652\pi\)
\(278\) 356.872 + 1098.34i 0.0769920 + 0.236957i
\(279\) −2260.89 + 6958.30i −0.485147 + 1.49313i
\(280\) −2431.44 1766.55i −0.518952 0.377040i
\(281\) −5436.47 3949.83i −1.15414 0.838530i −0.165112 0.986275i \(-0.552798\pi\)
−0.989025 + 0.147745i \(0.952798\pi\)
\(282\) −2641.24 + 8128.89i −0.557742 + 1.71655i
\(283\) 210.466 + 647.748i 0.0442082 + 0.136059i 0.970724 0.240196i \(-0.0772117\pi\)
−0.926516 + 0.376255i \(0.877212\pi\)
\(284\) 7546.29 5482.70i 1.57673 1.14556i
\(285\) 453.415 0.0942386
\(286\) 0 0
\(287\) 3605.72 0.741600
\(288\) −5036.50 + 3659.23i −1.03048 + 0.748688i
\(289\) −31.8431 98.0029i −0.00648139 0.0199477i
\(290\) −1671.69 + 5144.92i −0.338499 + 1.04179i
\(291\) −5915.40 4297.79i −1.19164 0.865776i
\(292\) 9240.36 + 6713.51i 1.85189 + 1.34547i
\(293\) 1767.77 5440.63i 0.352471 1.08480i −0.604990 0.796233i \(-0.706823\pi\)
0.957461 0.288562i \(-0.0931772\pi\)
\(294\) 689.979 + 2123.54i 0.136872 + 0.421249i
\(295\) −5460.91 + 3967.58i −1.07778 + 0.783056i
\(296\) −5903.71 −1.15928
\(297\) 0 0
\(298\) 441.179 0.0857612
\(299\) −2504.88 + 1819.90i −0.484485 + 0.351999i
\(300\) 1468.06 + 4518.21i 0.282527 + 0.869530i
\(301\) −349.087 + 1074.38i −0.0668474 + 0.205735i
\(302\) −5372.35 3903.24i −1.02366 0.743729i
\(303\) 6186.11 + 4494.47i 1.17288 + 0.852148i
\(304\) −38.0209 + 117.016i −0.00717318 + 0.0220768i
\(305\) −441.237 1357.99i −0.0828365 0.254945i
\(306\) −7191.80 + 5225.15i −1.34356 + 0.976151i
\(307\) −185.674 −0.0345178 −0.0172589 0.999851i \(-0.505494\pi\)
−0.0172589 + 0.999851i \(0.505494\pi\)
\(308\) 0 0
\(309\) 5536.14 1.01922
\(310\) 7789.22 5659.20i 1.42709 1.03684i
\(311\) 784.413 + 2414.18i 0.143022 + 0.440178i 0.996751 0.0805398i \(-0.0256644\pi\)
−0.853729 + 0.520718i \(0.825664\pi\)
\(312\) 2488.95 7660.21i 0.451632 1.38998i
\(313\) 7186.64 + 5221.40i 1.29781 + 0.942911i 0.999932 0.0116947i \(-0.00372262\pi\)
0.297874 + 0.954605i \(0.403723\pi\)
\(314\) 7627.60 + 5541.77i 1.37086 + 0.995988i
\(315\) −1520.67 + 4680.16i −0.272001 + 0.837133i
\(316\) 2158.48 + 6643.13i 0.384254 + 1.18261i
\(317\) 2326.18 1690.07i 0.412150 0.299444i −0.362322 0.932053i \(-0.618016\pi\)
0.774472 + 0.632609i \(0.218016\pi\)
\(318\) 7112.22 1.25419
\(319\) 0 0
\(320\) 7031.54 1.22836
\(321\) −7837.32 + 5694.15i −1.36273 + 0.990082i
\(322\) −1405.45 4325.52i −0.243238 0.748608i
\(323\) −153.812 + 473.385i −0.0264964 + 0.0815475i
\(324\) 6560.35 + 4766.37i 1.12489 + 0.817279i
\(325\) 2656.40 + 1929.99i 0.453387 + 0.329405i
\(326\) −1910.55 + 5880.08i −0.324588 + 0.998979i
\(327\) 1595.76 + 4911.25i 0.269865 + 0.830559i
\(328\) 2526.28 1835.45i 0.425275 0.308981i
\(329\) −5194.10 −0.870396
\(330\) 0 0
\(331\) −8295.55 −1.37754 −0.688769 0.724981i \(-0.741848\pi\)
−0.688769 + 0.724981i \(0.741848\pi\)
\(332\) 6336.94 4604.05i 1.04754 0.761085i
\(333\) 2987.13 + 9193.46i 0.491574 + 1.51291i
\(334\) −1069.47 + 3291.48i −0.175205 + 0.539227i
\(335\) −2506.94 1821.40i −0.408862 0.297056i
\(336\) −2096.21 1522.98i −0.340350 0.247279i
\(337\) 3138.17 9658.30i 0.507261 1.56119i −0.289674 0.957125i \(-0.593547\pi\)
0.796935 0.604065i \(-0.206453\pi\)
\(338\) −2192.92 6749.11i −0.352897 1.08610i
\(339\) −3254.74 + 2364.70i −0.521454 + 0.378859i
\(340\) 7002.07 1.11688
\(341\) 0 0
\(342\) −919.915 −0.145448
\(343\) 4521.14 3284.80i 0.711716 0.517092i
\(344\) 302.319 + 930.441i 0.0473835 + 0.145831i
\(345\) 982.294 3023.19i 0.153290 0.471777i
\(346\) −1612.97 1171.89i −0.250618 0.182084i
\(347\) −9632.18 6998.19i −1.49015 1.08266i −0.974104 0.226099i \(-0.927403\pi\)
−0.516047 0.856560i \(-0.672597\pi\)
\(348\) 3939.06 12123.2i 0.606769 1.86744i
\(349\) −1403.08 4318.22i −0.215200 0.662319i −0.999139 0.0414806i \(-0.986793\pi\)
0.783939 0.620838i \(-0.213207\pi\)
\(350\) −3902.08 + 2835.03i −0.595929 + 0.432968i
\(351\) −786.712 −0.119634
\(352\) 0 0
\(353\) −722.250 −0.108899 −0.0544497 0.998517i \(-0.517340\pi\)
−0.0544497 + 0.998517i \(0.517340\pi\)
\(354\) 21497.9 15619.1i 3.22768 2.34505i
\(355\) 2045.33 + 6294.89i 0.305789 + 0.941121i
\(356\) 267.907 824.532i 0.0398849 0.122753i
\(357\) −8480.14 6161.18i −1.25719 0.913402i
\(358\) −10138.5 7366.02i −1.49674 1.08745i
\(359\) 3770.01 11602.9i 0.554244 1.70579i −0.143688 0.989623i \(-0.545896\pi\)
0.697932 0.716164i \(-0.254104\pi\)
\(360\) 1316.94 + 4053.13i 0.192803 + 0.593386i
\(361\) 5507.38 4001.34i 0.802942 0.583371i
\(362\) 5961.37 0.865532
\(363\) 0 0
\(364\) 14862.8 2.14017
\(365\) −6556.84 + 4763.82i −0.940276 + 0.683151i
\(366\) 1737.01 + 5345.97i 0.248074 + 0.763492i
\(367\) −44.3792 + 136.585i −0.00631219 + 0.0194269i −0.954163 0.299287i \(-0.903251\pi\)
0.947851 + 0.318714i \(0.103251\pi\)
\(368\) 697.847 + 507.015i 0.0988526 + 0.0718207i
\(369\) −4136.46 3005.31i −0.583565 0.423985i
\(370\) 3930.92 12098.1i 0.552321 1.69987i
\(371\) 1335.59 + 4110.52i 0.186901 + 0.575223i
\(372\) −18354.0 + 13335.0i −2.55810 + 1.85857i
\(373\) 3676.93 0.510414 0.255207 0.966886i \(-0.417856\pi\)
0.255207 + 0.966886i \(0.417856\pi\)
\(374\) 0 0
\(375\) −11268.2 −1.55170
\(376\) −3639.14 + 2643.99i −0.499134 + 0.362642i
\(377\) −2722.50 8379.00i −0.371926 1.14467i
\(378\) 357.109 1099.07i 0.0485919 0.149550i
\(379\) −1885.87 1370.17i −0.255596 0.185701i 0.452607 0.891710i \(-0.350494\pi\)
−0.708203 + 0.706009i \(0.750494\pi\)
\(380\) 586.207 + 425.905i 0.0791363 + 0.0574959i
\(381\) −1623.22 + 4995.76i −0.218268 + 0.671760i
\(382\) 2752.03 + 8469.87i 0.368602 + 1.13444i
\(383\) 2998.37 2178.44i 0.400025 0.290635i −0.369526 0.929220i \(-0.620480\pi\)
0.769551 + 0.638585i \(0.220480\pi\)
\(384\) −14734.2 −1.95807
\(385\) 0 0
\(386\) 9337.39 1.23124
\(387\) 1295.95 941.562i 0.170224 0.123675i
\(388\) −3610.82 11113.0i −0.472453 1.45406i
\(389\) 2017.01 6207.72i 0.262896 0.809110i −0.729275 0.684221i \(-0.760142\pi\)
0.992171 0.124889i \(-0.0398576\pi\)
\(390\) 14040.4 + 10200.9i 1.82298 + 1.32447i
\(391\) 2823.12 + 2051.11i 0.365143 + 0.265292i
\(392\) −363.122 + 1117.57i −0.0467868 + 0.143995i
\(393\) −1029.45 3168.32i −0.132134 0.406668i
\(394\) 13641.5 9911.13i 1.74429 1.26730i
\(395\) −4956.47 −0.631359
\(396\) 0 0
\(397\) −11290.7 −1.42736 −0.713682 0.700470i \(-0.752974\pi\)
−0.713682 + 0.700470i \(0.752974\pi\)
\(398\) −4518.58 + 3282.94i −0.569086 + 0.413465i
\(399\) −335.193 1031.62i −0.0420568 0.129437i
\(400\) 282.678 869.993i 0.0353347 0.108749i
\(401\) −11173.1 8117.70i −1.39141 1.01092i −0.995709 0.0925412i \(-0.970501\pi\)
−0.395703 0.918379i \(-0.629499\pi\)
\(402\) 9869.04 + 7170.28i 1.22444 + 0.889605i
\(403\) −4845.43 + 14912.7i −0.598928 + 1.84331i
\(404\) 3776.07 + 11621.5i 0.465016 + 1.43117i
\(405\) −4655.14 + 3382.16i −0.571150 + 0.414965i
\(406\) 12941.6 1.58198
\(407\) 0 0
\(408\) −9077.70 −1.10150
\(409\) 7515.28 5460.17i 0.908573 0.660117i −0.0320802 0.999485i \(-0.510213\pi\)
0.940654 + 0.339368i \(0.110213\pi\)
\(410\) 2079.18 + 6399.06i 0.250447 + 0.770798i
\(411\) −4542.66 + 13980.9i −0.545190 + 1.67792i
\(412\) 7157.52 + 5200.24i 0.855887 + 0.621839i
\(413\) 13064.2 + 9491.67i 1.55653 + 1.13088i
\(414\) −1992.93 + 6133.62i −0.236588 + 0.728142i
\(415\) 1717.55 + 5286.08i 0.203160 + 0.625261i
\(416\) −10794.0 + 7842.28i −1.27216 + 0.924278i
\(417\) 1930.96 0.226762
\(418\) 0 0
\(419\) 3072.83 0.358276 0.179138 0.983824i \(-0.442669\pi\)
0.179138 + 0.983824i \(0.442669\pi\)
\(420\) −12344.9 + 8969.11i −1.43422 + 1.04202i
\(421\) 1846.01 + 5681.45i 0.213704 + 0.657712i 0.999243 + 0.0389005i \(0.0123855\pi\)
−0.785539 + 0.618812i \(0.787614\pi\)
\(422\) 6351.55 19548.1i 0.732674 2.25494i
\(423\) 5958.63 + 4329.20i 0.684914 + 0.497619i
\(424\) 3028.16 + 2200.09i 0.346841 + 0.251995i
\(425\) 1143.56 3519.53i 0.130520 0.401699i
\(426\) −8051.84 24781.0i −0.915758 2.81841i
\(427\) −2763.52 + 2007.82i −0.313200 + 0.227553i
\(428\) −15481.3 −1.74840
\(429\) 0 0
\(430\) −2107.99 −0.236411
\(431\) −188.817 + 137.184i −0.0211021 + 0.0153316i −0.598286 0.801282i \(-0.704151\pi\)
0.577184 + 0.816614i \(0.304151\pi\)
\(432\) 67.7285 + 208.447i 0.00754303 + 0.0232151i
\(433\) −1721.63 + 5298.64i −0.191077 + 0.588075i 0.808923 + 0.587915i \(0.200051\pi\)
−1.00000 0.000160200i \(0.999949\pi\)
\(434\) −18634.2 13538.5i −2.06099 1.49740i
\(435\) 7317.68 + 5316.61i 0.806565 + 0.586004i
\(436\) −2550.15 + 7848.55i −0.280115 + 0.862104i
\(437\) 111.589 + 343.435i 0.0122151 + 0.0375943i
\(438\) 25812.2 18753.7i 2.81588 2.04586i
\(439\) 3533.06 0.384109 0.192054 0.981384i \(-0.438485\pi\)
0.192054 + 0.981384i \(0.438485\pi\)
\(440\) 0 0
\(441\) 1924.05 0.207759
\(442\) −15413.1 + 11198.3i −1.65866 + 1.20509i
\(443\) −4605.16 14173.2i −0.493900 1.52007i −0.818663 0.574274i \(-0.805284\pi\)
0.324763 0.945795i \(-0.394716\pi\)
\(444\) −9262.57 + 28507.3i −0.990050 + 3.04706i
\(445\) 497.697 + 361.598i 0.0530182 + 0.0385200i
\(446\) −16770.0 12184.1i −1.78045 1.29358i
\(447\) 227.951 701.560i 0.0241201 0.0742341i
\(448\) −5198.16 15998.3i −0.548192 1.68716i
\(449\) 5816.95 4226.26i 0.611400 0.444208i −0.238507 0.971141i \(-0.576658\pi\)
0.849907 + 0.526932i \(0.176658\pi\)
\(450\) 6839.39 0.716471
\(451\) 0 0
\(452\) −6429.18 −0.669033
\(453\) −8982.72 + 6526.33i −0.931666 + 0.676895i
\(454\) 5876.55 + 18086.2i 0.607489 + 1.86966i
\(455\) −3259.04 + 10030.3i −0.335793 + 1.03347i
\(456\) −759.978 552.156i −0.0780466 0.0567041i
\(457\) −3189.31 2317.17i −0.326454 0.237183i 0.412470 0.910971i \(-0.364666\pi\)
−0.738925 + 0.673788i \(0.764666\pi\)
\(458\) −7940.82 + 24439.3i −0.810154 + 2.49340i
\(459\) 273.994 + 843.265i 0.0278626 + 0.0857522i
\(460\) 4109.74 2985.90i 0.416560 0.302648i
\(461\) −8254.37 −0.833936 −0.416968 0.908921i \(-0.636907\pi\)
−0.416968 + 0.908921i \(0.636907\pi\)
\(462\) 0 0
\(463\) 7083.97 0.711058 0.355529 0.934665i \(-0.384301\pi\)
0.355529 + 0.934665i \(0.384301\pi\)
\(464\) −1985.71 + 1442.71i −0.198673 + 0.144345i
\(465\) −4974.64 15310.4i −0.496115 1.52689i
\(466\) 7105.83 21869.5i 0.706376 2.17400i
\(467\) 14464.4 + 10509.0i 1.43326 + 1.04132i 0.989398 + 0.145229i \(0.0463919\pi\)
0.443862 + 0.896095i \(0.353608\pi\)
\(468\) −17050.5 12387.9i −1.68410 1.22357i
\(469\) −2290.79 + 7050.33i −0.225541 + 0.694145i
\(470\) −2995.09 9217.95i −0.293943 0.904665i
\(471\) 12753.6 9266.00i 1.24767 0.906486i
\(472\) 13984.7 1.36377
\(473\) 0 0
\(474\) 19512.1 1.89076
\(475\) 309.815 225.094i 0.0299270 0.0217432i
\(476\) −5176.37 15931.2i −0.498442 1.53405i
\(477\) 1893.88 5828.75i 0.181792 0.559497i
\(478\) 7516.57 + 5461.11i 0.719247 + 0.522563i
\(479\) −3485.40 2532.29i −0.332468 0.241552i 0.409009 0.912530i \(-0.365874\pi\)
−0.741477 + 0.670978i \(0.765874\pi\)
\(480\) 4232.88 13027.5i 0.402508 1.23879i
\(481\) 6401.88 + 19703.0i 0.606862 + 1.86773i
\(482\) −24663.7 + 17919.2i −2.33070 + 1.69336i
\(483\) −7604.58 −0.716399
\(484\) 0 0
\(485\) 8291.43 0.776277
\(486\) 19572.5 14220.2i 1.82680 1.32725i
\(487\) 4097.01 + 12609.3i 0.381218 + 1.17327i 0.939187 + 0.343406i \(0.111581\pi\)
−0.557969 + 0.829862i \(0.688419\pi\)
\(488\) −914.152 + 2813.47i −0.0847986 + 0.260983i
\(489\) 8363.30 + 6076.29i 0.773418 + 0.561921i
\(490\) −2048.40 1488.25i −0.188851 0.137209i
\(491\) 283.909 873.783i 0.0260950 0.0803121i −0.937161 0.348897i \(-0.886556\pi\)
0.963256 + 0.268585i \(0.0865561\pi\)
\(492\) −4899.26 15078.4i −0.448934 1.38168i
\(493\) −8033.14 + 5836.42i −0.733863 + 0.533183i
\(494\) −1971.52 −0.179560
\(495\) 0 0
\(496\) 4368.41 0.395458
\(497\) 12810.2 9307.16i 1.15617 0.840006i
\(498\) −6761.46 20809.6i −0.608410 1.87249i
\(499\) 3776.49 11622.8i 0.338795 1.04270i −0.626027 0.779801i \(-0.715320\pi\)
0.964822 0.262903i \(-0.0846800\pi\)
\(500\) −14568.3 10584.5i −1.30303 0.946705i
\(501\) 4681.51 + 3401.32i 0.417474 + 0.303313i
\(502\) −27.7697 + 85.4664i −0.00246897 + 0.00759871i
\(503\) −1696.14 5220.18i −0.150352 0.462736i 0.847308 0.531101i \(-0.178222\pi\)
−0.997660 + 0.0683654i \(0.978222\pi\)
\(504\) 8248.19 5992.66i 0.728976 0.529632i
\(505\) −8670.89 −0.764058
\(506\) 0 0
\(507\) −11865.4 −1.03937
\(508\) −6791.26 + 4934.14i −0.593136 + 0.430939i
\(509\) −28.6897 88.2977i −0.00249832 0.00768905i 0.949800 0.312859i \(-0.101287\pi\)
−0.952298 + 0.305170i \(0.901287\pi\)
\(510\) 6044.29 18602.4i 0.524795 1.61515i
\(511\) 15686.0 + 11396.5i 1.35794 + 0.986599i
\(512\) 4952.85 + 3598.46i 0.427514 + 0.310607i
\(513\) −28.3536 + 87.2633i −0.00244023 + 0.00751027i
\(514\) −208.289 641.047i −0.0178740 0.0550104i
\(515\) −5078.88 + 3690.02i −0.434568 + 0.315732i
\(516\) 4967.15 0.423772
\(517\) 0 0
\(518\) −30431.8 −2.58127
\(519\) −2696.93 + 1959.43i −0.228096 + 0.165722i
\(520\) 2822.41 + 8686.48i 0.238021 + 0.732552i
\(521\) −1359.33 + 4183.60i −0.114306 + 0.351798i −0.991802 0.127787i \(-0.959213\pi\)
0.877496 + 0.479585i \(0.159213\pi\)
\(522\) −14846.5 10786.6i −1.24486 0.904441i
\(523\) 4667.80 + 3391.36i 0.390265 + 0.283544i 0.765564 0.643359i \(-0.222460\pi\)
−0.375299 + 0.926904i \(0.622460\pi\)
\(524\) 1645.14 5063.21i 0.137153 0.422113i
\(525\) 2492.10 + 7669.88i 0.207170 + 0.637602i
\(526\) 9424.95 6847.62i 0.781268 0.567625i
\(527\) 17672.2 1.46075
\(528\) 0 0
\(529\) −9635.37 −0.791926
\(530\) −6524.78 + 4740.53i −0.534752 + 0.388520i
\(531\) −7075.95 21777.5i −0.578286 1.77978i
\(532\) 535.664 1648.60i 0.0436541 0.134354i
\(533\) −8865.05 6440.84i −0.720428 0.523422i
\(534\) −1959.28 1423.50i −0.158776 0.115357i
\(535\) 3394.66 10447.7i 0.274325 0.844285i
\(536\) 1983.88 + 6105.77i 0.159871 + 0.492032i
\(537\) −16951.8 + 12316.2i −1.36224 + 0.989727i
\(538\) 5383.44 0.431407
\(539\) 0 0
\(540\) 1290.75 0.102861
\(541\) −9332.30 + 6780.31i −0.741639 + 0.538832i −0.893224 0.449612i \(-0.851562\pi\)
0.151585 + 0.988444i \(0.451562\pi\)
\(542\) 8398.52 + 25848.0i 0.665585 + 2.04846i
\(543\) 3080.15 9479.73i 0.243429 0.749197i
\(544\) 12165.3 + 8838.62i 0.958793 + 0.696604i
\(545\) −4737.47 3441.97i −0.372350 0.270528i
\(546\) 12829.8 39486.1i 1.00561 3.09496i
\(547\) −1004.60 3091.83i −0.0785254 0.241676i 0.904086 0.427351i \(-0.140553\pi\)
−0.982611 + 0.185674i \(0.940553\pi\)
\(548\) −19005.7 + 13808.4i −1.48154 + 1.07640i
\(549\) 4843.78 0.376552
\(550\) 0 0
\(551\) −1027.53 −0.0794452
\(552\) −5327.99 + 3871.01i −0.410823 + 0.298481i
\(553\) 3664.13 + 11277.0i 0.281763 + 0.867177i
\(554\) −10282.0 + 31644.8i −0.788523 + 2.42682i
\(555\) −17207.3 12501.8i −1.31605 0.956168i
\(556\) 2496.49 + 1813.80i 0.190422 + 0.138350i
\(557\) −6235.51 + 19190.9i −0.474340 + 1.45987i 0.372507 + 0.928029i \(0.378498\pi\)
−0.846846 + 0.531838i \(0.821502\pi\)
\(558\) 10092.8 + 31062.6i 0.765706 + 2.35660i
\(559\) 2777.41 2017.91i 0.210147 0.152681i
\(560\) 2938.19 0.221717
\(561\) 0 0
\(562\) −29998.1 −2.25159
\(563\) 10464.2 7602.67i 0.783326 0.569119i −0.122650 0.992450i \(-0.539139\pi\)
0.905975 + 0.423331i \(0.139139\pi\)
\(564\) 7057.46 + 21720.6i 0.526902 + 1.62164i
\(565\) 1409.76 4338.78i 0.104971 0.323069i
\(566\) 2459.75 + 1787.12i 0.182670 + 0.132717i
\(567\) 11136.5 + 8091.15i 0.824849 + 0.599288i
\(568\) 4237.52 13041.7i 0.313032 0.963414i
\(569\) 4423.73 + 13614.8i 0.325927 + 1.00310i 0.971020 + 0.238997i \(0.0768185\pi\)
−0.645093 + 0.764104i \(0.723182\pi\)
\(570\) 1637.52 1189.73i 0.120330 0.0874252i
\(571\) 2503.96 0.183516 0.0917580 0.995781i \(-0.470751\pi\)
0.0917580 + 0.995781i \(0.470751\pi\)
\(572\) 0 0
\(573\) 14890.7 1.08563
\(574\) 13022.2 9461.18i 0.946927 0.687983i
\(575\) −829.641 2553.37i −0.0601712 0.185188i
\(576\) −7371.02 + 22685.7i −0.533205 + 1.64104i
\(577\) −4303.76 3126.86i −0.310516 0.225603i 0.421602 0.906781i \(-0.361468\pi\)
−0.732118 + 0.681178i \(0.761468\pi\)
\(578\) −372.156 270.387i −0.0267814 0.0194578i
\(579\) 4824.49 14848.2i 0.346285 1.06575i
\(580\) 4466.79 + 13747.4i 0.319782 + 0.984187i
\(581\) 10757.3 7815.61i 0.768135 0.558083i
\(582\) −32640.8 −2.32475
\(583\) 0 0
\(584\) 16791.3 1.18978
\(585\) 12098.8 8790.30i 0.855084 0.621255i
\(586\) −7891.50 24287.5i −0.556305 1.71213i
\(587\) 2232.54 6871.04i 0.156979 0.483132i −0.841377 0.540449i \(-0.818255\pi\)
0.998356 + 0.0573170i \(0.0182546\pi\)
\(588\) 4826.72 + 3506.82i 0.338521 + 0.245950i
\(589\) 1479.51 + 1074.92i 0.103501 + 0.0751977i
\(590\) −9311.59 + 28658.1i −0.649749 + 1.99972i
\(591\) −8712.25 26813.5i −0.606386 1.86626i
\(592\) 4669.35 3392.48i 0.324171 0.235524i
\(593\) −26210.5 −1.81507 −0.907535 0.419976i \(-0.862038\pi\)
−0.907535 + 0.419976i \(0.862038\pi\)
\(594\) 0 0
\(595\) 11886.4 0.818980
\(596\) 953.704 692.907i 0.0655457 0.0476218i
\(597\) 2885.83 + 8881.67i 0.197838 + 0.608882i
\(598\) −4271.16 + 13145.3i −0.292075 + 0.898913i
\(599\) 3292.70 + 2392.29i 0.224601 + 0.163182i 0.694395 0.719594i \(-0.255672\pi\)
−0.469794 + 0.882776i \(0.655672\pi\)
\(600\) 5650.29 + 4105.18i 0.384454 + 0.279322i
\(601\) 514.070 1582.14i 0.0348907 0.107383i −0.932094 0.362215i \(-0.882020\pi\)
0.966985 + 0.254833i \(0.0820204\pi\)
\(602\) 1558.36 + 4796.15i 0.105505 + 0.324711i
\(603\) 8504.31 6178.74i 0.574332 0.417277i
\(604\) −17743.8 −1.19534
\(605\) 0 0
\(606\) 34134.6 2.28815
\(607\) −8958.87 + 6509.00i −0.599060 + 0.435243i −0.845545 0.533904i \(-0.820724\pi\)
0.246485 + 0.969147i \(0.420724\pi\)
\(608\) 480.856 + 1479.92i 0.0320745 + 0.0987152i
\(609\) 6686.74 20579.7i 0.444927 1.36934i
\(610\) −5156.81 3746.64i −0.342284 0.248684i
\(611\) 12770.3 + 9278.13i 0.845547 + 0.614326i
\(612\) −7340.13 + 22590.6i −0.484815 + 1.49211i
\(613\) −4869.77 14987.6i −0.320862 0.987511i −0.973274 0.229647i \(-0.926243\pi\)
0.652412 0.757864i \(-0.273757\pi\)
\(614\) −670.567 + 487.195i −0.0440747 + 0.0320221i
\(615\) 11250.0 0.737634
\(616\) 0 0
\(617\) 19132.5 1.24837 0.624185 0.781277i \(-0.285431\pi\)
0.624185 + 0.781277i \(0.285431\pi\)
\(618\) 19994.0 14526.5i 1.30142 0.945534i
\(619\) 3169.76 + 9755.52i 0.205821 + 0.633453i 0.999679 + 0.0253491i \(0.00806974\pi\)
−0.793857 + 0.608104i \(0.791930\pi\)
\(620\) 7949.86 24467.2i 0.514958 1.58488i
\(621\) 520.410 + 378.100i 0.0336286 + 0.0244326i
\(622\) 9167.57 + 6660.63i 0.590974 + 0.429368i
\(623\) 454.785 1399.68i 0.0292465 0.0900115i
\(624\) 2433.27 + 7488.84i 0.156104 + 0.480438i
\(625\) 4941.43 3590.16i 0.316252 0.229770i
\(626\) 39655.4 2.53187
\(627\) 0 0
\(628\) 25192.5 1.60078
\(629\) 18889.7 13724.2i 1.19743 0.869981i
\(630\) 6788.45 + 20892.7i 0.429299 + 1.32125i
\(631\) −836.092 + 2573.23i −0.0527485 + 0.162343i −0.973960 0.226718i \(-0.927200\pi\)
0.921212 + 0.389061i \(0.127200\pi\)
\(632\) 8307.63 + 6035.85i 0.522879 + 0.379894i
\(633\) −27803.4 20200.4i −1.74579 1.26839i
\(634\) 3966.46 12207.5i 0.248467 0.764703i
\(635\) −1840.69 5665.06i −0.115032 0.354033i
\(636\) 15374.6 11170.3i 0.958557 0.696432i
\(637\) 4123.54 0.256484
\(638\) 0 0
\(639\) −22453.1 −1.39003
\(640\) 13517.2 9820.81i 0.834865 0.606565i
\(641\) 1658.98 + 5105.82i 0.102224 + 0.314614i 0.989069 0.147454i \(-0.0471077\pi\)
−0.886845 + 0.462068i \(0.847108\pi\)
\(642\) −13363.7 + 41129.2i −0.821531 + 2.52841i
\(643\) −24971.4 18142.8i −1.53154 1.11273i −0.955378 0.295387i \(-0.904551\pi\)
−0.576158 0.817339i \(-0.695449\pi\)
\(644\) −9831.74 7143.18i −0.601592 0.437082i
\(645\) −1089.17 + 3352.12i −0.0664899 + 0.204635i
\(646\) 686.633 + 2113.24i 0.0418192 + 0.128706i
\(647\) 7097.43 5156.58i 0.431265 0.313333i −0.350889 0.936417i \(-0.614121\pi\)
0.782155 + 0.623084i \(0.214121\pi\)
\(648\) 11921.3 0.722703
\(649\) 0 0
\(650\) 14657.8 0.884505
\(651\) −31156.9 + 22636.8i −1.87578 + 1.36284i
\(652\) 5105.05 + 15711.7i 0.306640 + 0.943740i
\(653\) −9225.19 + 28392.2i −0.552848 + 1.70149i 0.148713 + 0.988880i \(0.452487\pi\)
−0.701561 + 0.712610i \(0.747513\pi\)
\(654\) 18649.9 + 13550.0i 1.11509 + 0.810162i
\(655\) 3056.21 + 2220.47i 0.182314 + 0.132459i
\(656\) −943.364 + 2903.38i −0.0561466 + 0.172802i
\(657\) −8496.00 26148.0i −0.504506 1.55271i
\(658\) −18758.7 + 13629.0i −1.11138 + 0.807467i
\(659\) −9304.45 −0.550000 −0.275000 0.961444i \(-0.588678\pi\)
−0.275000 + 0.961444i \(0.588678\pi\)
\(660\) 0 0
\(661\) 2078.54 0.122309 0.0611543 0.998128i \(-0.480522\pi\)
0.0611543 + 0.998128i \(0.480522\pi\)
\(662\) −29959.7 + 21767.0i −1.75894 + 1.27794i
\(663\) 9843.71 + 30295.8i 0.576619 + 1.77465i
\(664\) 3558.42 10951.7i 0.207972 0.640072i
\(665\) 995.116 + 722.994i 0.0580285 + 0.0421602i
\(666\) 34911.2 + 25364.4i 2.03120 + 1.47575i
\(667\) −2226.08 + 6851.16i −0.129226 + 0.397718i
\(668\) 2857.64 + 8794.93i 0.165517 + 0.509410i
\(669\) −28039.9 + 20372.2i −1.62046 + 1.17733i
\(670\) −13833.1 −0.797643
\(671\) 0 0
\(672\) −32769.5 −1.88112
\(673\) −12107.3 + 8796.46i −0.693465 + 0.503832i −0.877797 0.479032i \(-0.840988\pi\)
0.184333 + 0.982864i \(0.440988\pi\)
\(674\) −14009.1 43115.6i −0.800610 2.46402i
\(675\) 210.803 648.786i 0.0120205 0.0369952i
\(676\) −15340.5 11145.5i −0.872808 0.634132i
\(677\) −18643.4 13545.2i −1.05838 0.768958i −0.0845923 0.996416i \(-0.526959\pi\)
−0.973788 + 0.227457i \(0.926959\pi\)
\(678\) −5549.76 + 17080.4i −0.314362 + 0.967506i
\(679\) −6129.55 18864.8i −0.346437 1.06622i
\(680\) 8327.93 6050.59i 0.469649 0.341220i
\(681\) 31796.8 1.78922
\(682\) 0 0
\(683\) 17860.8 1.00062 0.500312 0.865845i \(-0.333219\pi\)
0.500312 + 0.865845i \(0.333219\pi\)
\(684\) −1988.59 + 1444.80i −0.111163 + 0.0807650i
\(685\) −5151.27 15854.0i −0.287328 0.884305i
\(686\) 7709.15 23726.3i 0.429062 1.32052i
\(687\) 34760.4 + 25254.9i 1.93041 + 1.40252i
\(688\) −773.774 562.180i −0.0428777 0.0311525i
\(689\) 4058.86 12491.9i 0.224427 0.690716i
\(690\) −4385.06 13495.8i −0.241937 0.744605i
\(691\) −9497.27 + 6900.17i −0.522856 + 0.379877i −0.817679 0.575675i \(-0.804739\pi\)
0.294823 + 0.955552i \(0.404739\pi\)
\(692\) −5327.32 −0.292651
\(693\) 0 0
\(694\) −53149.7 −2.90711
\(695\) −1771.48 + 1287.05i −0.0966847 + 0.0702456i
\(696\) −5790.89 17822.5i −0.315378 0.970634i
\(697\) −3816.35 + 11745.5i −0.207395 + 0.638297i
\(698\) −16398.0 11913.8i −0.889216 0.646053i
\(699\) −31105.2 22599.3i −1.68313 1.22287i
\(700\) −3982.56 + 12257.1i −0.215038 + 0.661819i
\(701\) 9423.54 + 29002.7i 0.507735 + 1.56265i 0.796123 + 0.605134i \(0.206881\pi\)
−0.288388 + 0.957513i \(0.593119\pi\)
\(702\) −2841.24 + 2064.28i −0.152757 + 0.110985i
\(703\) 2416.21 0.129629
\(704\) 0 0
\(705\) −16205.8 −0.865741
\(706\) −2608.43 + 1895.14i −0.139050 + 0.101026i
\(707\) 6410.06 + 19728.1i 0.340983 + 1.04944i
\(708\) 21941.3 67528.2i 1.16469 3.58456i
\(709\) −490.660 356.485i −0.0259903 0.0188831i 0.574714 0.818354i \(-0.305113\pi\)
−0.600705 + 0.799471i \(0.705113\pi\)
\(710\) 23904.2 + 17367.4i 1.26353 + 0.918009i
\(711\) 5195.77 15990.9i 0.274060 0.843469i
\(712\) −393.855 1212.16i −0.0207308 0.0638029i
\(713\) 10372.4 7535.99i 0.544810 0.395828i
\(714\) −46792.8 −2.45263
\(715\) 0 0
\(716\) −33485.4 −1.74778
\(717\) 12567.9 9131.12i 0.654613 0.475604i
\(718\) −16829.7 51796.5i −0.874762 2.69224i
\(719\) 7017.39 21597.3i 0.363984 1.12023i −0.586631 0.809854i \(-0.699546\pi\)
0.950615 0.310373i \(-0.100454\pi\)
\(720\) −3370.67 2448.93i −0.174469 0.126759i
\(721\) 12150.2 + 8827.66i 0.627598 + 0.455977i
\(722\) 9390.82 28902.0i 0.484058 1.48978i
\(723\) 15751.6 + 48478.6i 0.810249 + 2.49369i
\(724\) 12886.8 9362.80i 0.661511 0.480616i
\(725\) 7639.50 0.391343
\(726\) 0 0
\(727\) 34351.1 1.75243 0.876213 0.481925i \(-0.160062\pi\)
0.876213 + 0.481925i \(0.160062\pi\)
\(728\) 17677.1 12843.2i 0.899942 0.653846i
\(729\) −6828.05 21014.6i −0.346901 1.06765i
\(730\) −11180.3 + 34409.4i −0.566851 + 1.74459i
\(731\) −3130.28 2274.28i −0.158382 0.115071i
\(732\) 12151.2 + 8828.35i 0.613553 + 0.445772i
\(733\) 493.821 1519.83i 0.0248836 0.0765840i −0.937844 0.347058i \(-0.887181\pi\)
0.962727 + 0.270474i \(0.0871806\pi\)
\(734\) 198.113 + 609.729i 0.00996252 + 0.0306615i
\(735\) −3424.98 + 2488.39i −0.171881 + 0.124879i
\(736\) 10909.3 0.546360
\(737\) 0 0
\(738\) −22824.7 −1.13847
\(739\) 11473.6 8336.03i 0.571126 0.414947i −0.264388 0.964416i \(-0.585170\pi\)
0.835514 + 0.549469i \(0.185170\pi\)
\(740\) −10503.5 32326.5i −0.521780 1.60587i
\(741\) −1018.65 + 3135.09i −0.0505009 + 0.155426i
\(742\) 15609.3 + 11340.8i 0.772283 + 0.561097i
\(743\) −28113.3 20425.5i −1.38813 1.00853i −0.996068 0.0885912i \(-0.971764\pi\)
−0.392057 0.919941i \(-0.628236\pi\)
\(744\) −10306.5 + 31720.0i −0.507867 + 1.56305i
\(745\) 258.490 + 795.551i 0.0127119 + 0.0391232i
\(746\) 13279.4 9648.02i 0.651732 0.473511i
\(747\) −18854.8 −0.923510
\(748\) 0 0
\(749\) −26280.3 −1.28206
\(750\) −40695.4 + 29566.9i −1.98131 + 1.43951i
\(751\) −8615.14 26514.7i −0.418603 1.28833i −0.908988 0.416822i \(-0.863144\pi\)
0.490385 0.871506i \(-0.336856\pi\)
\(752\) 1358.93 4182.36i 0.0658978 0.202812i
\(753\) 121.560 + 88.3184i 0.00588299 + 0.00427424i
\(754\) −31818.3 23117.4i −1.53681 1.11656i
\(755\) 3890.77 11974.6i 0.187549 0.577217i
\(756\) −954.206 2936.74i −0.0459050 0.141281i
\(757\) 6412.71 4659.11i 0.307892 0.223696i −0.423100 0.906083i \(-0.639058\pi\)
0.730991 + 0.682387i \(0.239058\pi\)
\(758\) −10406.1 −0.498638
\(759\) 0 0
\(760\) 1065.24 0.0508424
\(761\) −7491.48 + 5442.88i −0.356854 + 0.259270i −0.751739 0.659461i \(-0.770785\pi\)
0.394885 + 0.918731i \(0.370785\pi\)
\(762\) 7246.22 + 22301.6i 0.344492 + 1.06024i
\(763\) −4329.00 + 13323.3i −0.205400 + 0.632157i
\(764\) 19251.7 + 13987.2i 0.911652 + 0.662354i
\(765\) −13635.9 9907.08i −0.644455 0.468224i
\(766\) 5112.63 15735.0i 0.241158 0.742207i
\(767\) −15164.8 46672.5i −0.713911 2.19719i
\(768\) −13080.5 + 9503.57i −0.614587 + 0.446524i
\(769\) 30944.5 1.45109 0.725545 0.688175i \(-0.241588\pi\)
0.725545 + 0.688175i \(0.241588\pi\)
\(770\) 0 0
\(771\) −1127.01 −0.0526436
\(772\) 20184.8 14665.1i 0.941018 0.683690i
\(773\) 4645.07 + 14296.1i 0.216134 + 0.665192i 0.999071 + 0.0430912i \(0.0137206\pi\)
−0.782937 + 0.622101i \(0.786279\pi\)
\(774\) 2209.77 6800.97i 0.102621 0.315834i
\(775\) −10999.8 7991.85i −0.509840 0.370420i
\(776\) −13897.4 10097.1i −0.642898 0.467092i
\(777\) −15723.7 + 48392.5i −0.725976 + 2.23433i
\(778\) −9004.14 27711.9i −0.414928 1.27702i
\(779\) −1033.93 + 751.193i −0.0475537 + 0.0345498i
\(780\) 46372.7 2.12873
\(781\) 0 0
\(782\) 15577.8 0.712352
\(783\) −1480.82 + 1075.88i −0.0675865 + 0.0491045i
\(784\) −354.998 1092.57i −0.0161716 0.0497709i
\(785\) −5524.07 + 17001.3i −0.251162 + 0.772999i
\(786\) −12031.3 8741.28i −0.545984 0.396681i
\(787\) −5444.60 3955.73i −0.246606 0.179170i 0.457615 0.889150i \(-0.348704\pi\)
−0.704221 + 0.709981i \(0.748704\pi\)
\(788\) 13922.8 42850.1i 0.629417 1.93715i
\(789\) −6019.31 18525.5i −0.271601 0.835902i
\(790\) −17900.5 + 13005.4i −0.806164 + 0.585712i
\(791\) −10913.8 −0.490584
\(792\) 0 0
\(793\) 10380.9 0.464865
\(794\) −40776.7 + 29626.0i −1.82256 + 1.32417i
\(795\) 4167.10 + 12825.0i 0.185902 + 0.572147i
\(796\) −4611.77 + 14193.6i −0.205352 + 0.632008i
\(797\) 14680.7 + 10666.1i 0.652467 + 0.474045i 0.864111 0.503302i \(-0.167882\pi\)
−0.211644 + 0.977347i \(0.567882\pi\)
\(798\) −3917.46 2846.20i −0.173780 0.126259i
\(799\) 5497.51 16919.6i 0.243414 0.749152i
\(800\) −3575.07 11002.9i −0.157997 0.486266i
\(801\) −1688.34 + 1226.65i −0.0744750 + 0.0541093i
\(802\) −61652.2 −2.71448
\(803\) 0 0
\(804\) 32595.6 1.42980
\(805\) 6976.48 5068.71i 0.305452 0.221924i
\(806\) 21630.5 + 66571.8i 0.945287 + 2.90929i
\(807\) 2781.54 8560.71i 0.121332 0.373422i
\(808\) 14533.4 + 10559.2i 0.632778 + 0.459740i
\(809\) 23426.5 + 17020.3i 1.01808 + 0.739682i 0.965889 0.258955i \(-0.0833781\pi\)
0.0521954 + 0.998637i \(0.483378\pi\)
\(810\) −7937.64 + 24429.5i −0.344321 + 1.05971i
\(811\) 825.006 + 2539.11i 0.0357212 + 0.109938i 0.967327 0.253531i \(-0.0815920\pi\)
−0.931606 + 0.363470i \(0.881592\pi\)
\(812\) 27976.1 20325.8i 1.20908 0.878445i
\(813\) 45442.7 1.96032
\(814\) 0 0
\(815\) −11722.6 −0.503833
\(816\) 7179.72 5216.37i 0.308015 0.223786i
\(817\) −123.730 380.801i −0.00529836 0.0163067i
\(818\) 12814.6 39439.2i 0.547739 1.68577i
\(819\) −28944.1 21029.1i −1.23490 0.897211i
\(820\) 14544.8 + 10567.4i 0.619424 + 0.450038i
\(821\) −2540.72 + 7819.53i −0.108004 + 0.332404i −0.990424 0.138060i \(-0.955913\pi\)
0.882419 + 0.470464i \(0.155913\pi\)
\(822\) 20278.9 + 62412.1i 0.860473 + 2.64826i
\(823\) −13266.6 + 9638.75i −0.561901 + 0.408245i −0.832154 0.554544i \(-0.812893\pi\)
0.270253 + 0.962789i \(0.412893\pi\)
\(824\) 13006.4 0.549879
\(825\) 0 0
\(826\) 72087.2 3.03660
\(827\) 18227.6 13243.1i 0.766427 0.556842i −0.134448 0.990921i \(-0.542926\pi\)
0.900875 + 0.434079i \(0.142926\pi\)
\(828\) 5325.17 + 16389.2i 0.223505 + 0.687879i
\(829\) −4088.07 + 12581.8i −0.171272 + 0.527121i −0.999444 0.0333535i \(-0.989381\pi\)
0.828172 + 0.560475i \(0.189381\pi\)
\(830\) 20073.3 + 14584.1i 0.839464 + 0.609906i
\(831\) 45008.8 + 32700.8i 1.87887 + 1.36508i
\(832\) −15797.2 + 48618.8i −0.658257 + 2.02591i
\(833\) −1436.13 4419.96i −0.0597347 0.183845i
\(834\) 6973.74 5066.72i 0.289545 0.210367i
\(835\) −6561.93 −0.271958
\(836\) 0 0
\(837\) 3257.68 0.134530
\(838\) 11097.6 8062.91i 0.457472 0.332373i
\(839\) 1013.35 + 3118.78i 0.0416983 + 0.128334i 0.969739 0.244146i \(-0.0785076\pi\)
−0.928040 + 0.372480i \(0.878508\pi\)
\(840\) −6932.12 + 21334.9i −0.284739 + 0.876337i
\(841\) 3147.76 + 2286.98i 0.129065 + 0.0937711i
\(842\) 21574.7 + 15674.9i 0.883031 + 0.641560i
\(843\) −15499.6 + 47702.7i −0.633254 + 1.94895i
\(844\) −16971.5 52233.0i −0.692161 2.13025i
\(845\) 10885.4 7908.71i 0.443159 0.321974i
\(846\) 32879.3 1.33619
\(847\) 0 0
\(848\) −3659.28 −0.148184
\(849\) 4112.78 2988.11i 0.166255 0.120791i
\(850\) −5104.98 15711.5i −0.205999 0.634001i
\(851\) 5234.55 16110.3i 0.210856 0.648947i
\(852\) −56326.3 40923.5i −2.26491 1.64556i
\(853\) 27600.1 + 20052.6i 1.10786 + 0.804911i 0.982326 0.187178i \(-0.0599342\pi\)
0.125538 + 0.992089i \(0.459934\pi\)
\(854\) −4712.18 + 14502.6i −0.188814 + 0.581111i
\(855\) −538.985 1658.83i −0.0215589 0.0663516i
\(856\) −18412.7 + 13377.6i −0.735204 + 0.534157i
\(857\) 5029.20 0.200460 0.100230 0.994964i \(-0.468042\pi\)
0.100230 + 0.994964i \(0.468042\pi\)
\(858\) 0 0
\(859\) −3540.39 −0.140625 −0.0703124 0.997525i \(-0.522400\pi\)
−0.0703124 + 0.997525i \(0.522400\pi\)
\(860\) −4556.89 + 3310.77i −0.180684 + 0.131275i
\(861\) −8316.73 25596.3i −0.329191 1.01315i
\(862\) −321.958 + 990.886i −0.0127215 + 0.0391528i
\(863\) 8449.44 + 6138.88i 0.333282 + 0.242143i 0.741822 0.670597i \(-0.233962\pi\)
−0.408540 + 0.912740i \(0.633962\pi\)
\(864\) 2242.54 + 1629.30i 0.0883018 + 0.0641550i
\(865\) 1168.15 3595.18i 0.0459169 0.141318i
\(866\) 7685.55 + 23653.7i 0.301577 + 0.928158i
\(867\) −622.254 + 452.094i −0.0243747 + 0.0177093i
\(868\) −61545.1 −2.40666
\(869\) 0 0
\(870\) 40378.5 1.57352
\(871\) 18226.0 13242.0i 0.709030 0.515141i
\(872\) 3749.03 + 11538.3i 0.145594 + 0.448092i
\(873\) −8691.74 + 26750.4i −0.336965 + 1.03707i
\(874\) 1304.16 + 947.526i 0.0504734 + 0.0366711i
\(875\) −24730.4 17967.7i −0.955474 0.694192i
\(876\) 26344.6 81080.2i 1.01610 3.12722i
\(877\) 5340.72 + 16437.0i 0.205637 + 0.632884i 0.999687 + 0.0250320i \(0.00796876\pi\)
−0.794050 + 0.607852i \(0.792031\pi\)
\(878\) 12759.8 9270.51i 0.490457 0.356338i
\(879\) −42699.3 −1.63847
\(880\) 0 0
\(881\) −6262.31 −0.239481 −0.119740 0.992805i \(-0.538206\pi\)
−0.119740 + 0.992805i \(0.538206\pi\)
\(882\) 6948.79 5048.59i 0.265281 0.192738i
\(883\) 9088.07 + 27970.2i 0.346362 + 1.06599i 0.960850 + 0.277067i \(0.0893626\pi\)
−0.614488 + 0.788926i \(0.710637\pi\)
\(884\) −15731.0 + 48415.0i −0.598519 + 1.84205i
\(885\) 40760.8 + 29614.4i 1.54820 + 1.12483i
\(886\) −53821.3 39103.5i −2.04082 1.48274i
\(887\) 3672.59 11303.1i 0.139023 0.427869i −0.857171 0.515032i \(-0.827780\pi\)
0.996194 + 0.0871630i \(0.0277801\pi\)
\(888\) 13617.1 + 41909.1i 0.514595 + 1.58376i
\(889\) −11528.5 + 8375.94i −0.434931 + 0.315996i
\(890\) 2746.26 0.103432
\(891\) 0 0
\(892\) −55388.1 −2.07907
\(893\) 1489.39 1082.11i 0.0558125 0.0405502i
\(894\) −1017.60 3131.84i −0.0380688 0.117164i
\(895\) 7342.49 22597.9i 0.274226 0.843982i
\(896\) −32337.2 23494.4i −1.20570 0.875995i
\(897\) 18696.7 + 13583.9i 0.695946 + 0.505634i
\(898\) 9918.68 30526.6i 0.368587 1.13439i
\(899\) 11273.6 + 34696.4i 0.418236 + 1.28720i
\(900\) 14784.8 10741.8i 0.547586 0.397844i
\(901\) −14803.5 −0.547365
\(902\) 0 0
\(903\) 8431.98 0.310740
\(904\) −7646.56 + 5555.55i −0.281328 + 0.204397i
\(905\) 3492.81 + 10749.8i 0.128293 + 0.394845i
\(906\) −15316.7 + 47140.1i −0.561661 + 1.72861i
\(907\) −35640.6 25894.4i −1.30477 0.947972i −0.304781 0.952422i \(-0.598583\pi\)
−0.999990 + 0.00445054i \(0.998583\pi\)
\(908\) 41109.2 + 29867.6i 1.50248 + 1.09162i
\(909\) 9089.52 27974.7i 0.331661 1.02075i
\(910\) 14548.7 + 44776.2i 0.529982 + 1.63112i
\(911\) 28867.5 20973.5i 1.04986 0.762768i 0.0776742 0.996979i \(-0.475251\pi\)
0.972186 + 0.234211i \(0.0752506\pi\)
\(912\) 918.369 0.0333446
\(913\) 0 0
\(914\) −17598.4 −0.636874
\(915\) −8622.32 + 6264.48i −0.311525 + 0.226336i
\(916\) 21218.1 + 65302.6i 0.765356 + 2.35552i
\(917\) 2792.70 8595.05i 0.100570 0.309524i
\(918\) 3202.21 + 2326.54i 0.115129 + 0.0836463i
\(919\) 4688.30 + 3406.25i 0.168284 + 0.122265i 0.668739 0.743497i \(-0.266834\pi\)
−0.500456 + 0.865762i \(0.666834\pi\)
\(920\) 2307.77 7102.57i 0.0827009 0.254527i
\(921\) 428.263 + 1318.06i 0.0153222 + 0.0471568i
\(922\) −29810.9 + 21658.9i −1.06483 + 0.773643i
\(923\) −48120.4 −1.71604
\(924\) 0 0
\(925\) −17964.1 −0.638545
\(926\) 25584.0 18587.9i 0.907929 0.659649i
\(927\) −6580.94 20254.0i −0.233168 0.717616i
\(928\) −9592.57 + 29522.9i −0.339323 + 1.04433i
\(929\) 28252.2 + 20526.5i 0.997768 + 0.724921i 0.961608 0.274425i \(-0.0884876\pi\)
0.0361593 + 0.999346i \(0.488488\pi\)
\(930\) −58139.5 42240.8i −2.04997 1.48939i
\(931\) 148.615 457.389i 0.00523163 0.0161013i
\(932\) −18987.0 58435.9i −0.667317 2.05379i
\(933\) 15328.4 11136.8i 0.537867 0.390784i
\(934\) 79813.6 2.79612
\(935\) 0 0
\(936\) −30983.6 −1.08198
\(937\) −16008.2 + 11630.6i −0.558127 + 0.405503i −0.830773 0.556612i \(-0.812101\pi\)
0.272646 + 0.962114i \(0.412101\pi\)
\(938\) 10226.3 + 31473.4i 0.355972 + 1.09557i
\(939\) 20489.4 63059.7i 0.712082 2.19156i
\(940\) −20952.1 15222.6i −0.727001 0.528197i
\(941\) −15027.6 10918.2i −0.520602 0.378239i 0.296229 0.955117i \(-0.404271\pi\)
−0.816831 + 0.576878i \(0.804271\pi\)
\(942\) 21746.5 66928.9i 0.752166 2.31493i
\(943\) 2768.71 + 8521.22i 0.0956116 + 0.294262i
\(944\) −11060.8 + 8036.13i −0.381354 + 0.277070i
\(945\) 2191.12 0.0754255
\(946\) 0 0
\(947\) 24620.0 0.844817 0.422408 0.906406i \(-0.361185\pi\)
0.422408 + 0.906406i \(0.361185\pi\)
\(948\) 42179.5 30645.2i 1.44507 1.04991i
\(949\) −18208.2 56039.1i −0.622827 1.91687i
\(950\) 528.277 1625.87i 0.0180417 0.0555265i
\(951\) −17362.9 12614.9i −0.592040 0.430142i
\(952\) −19922.9 14474.9i −0.678263 0.492787i
\(953\) 8229.75 25328.6i 0.279735 0.860937i −0.708192 0.706020i \(-0.750489\pi\)
0.987927 0.154917i \(-0.0495111\pi\)
\(954\) −8454.45 26020.1i −0.286921 0.883053i
\(955\) −13660.8 + 9925.12i −0.462881 + 0.336303i
\(956\) 24825.8 0.839878
\(957\) 0 0
\(958\) −19232.2 −0.648607
\(959\) −32263.1 + 23440.5i −1.08637 + 0.789294i
\(960\) −16218.5 49915.4i −0.545260 1.67814i
\(961\) 10858.4 33418.7i 0.364486 1.12177i
\(962\) 74819.9 + 54359.8i 2.50758 + 1.82186i
\(963\) 30148.5 + 21904.2i 1.00885 + 0.732972i
\(964\) −25172.3 + 77472.4i −0.841023 + 2.58840i
\(965\) 5470.85 + 16837.5i 0.182500 + 0.561678i
\(966\) −27464.2 + 19953.9i −0.914748 + 0.664603i
\(967\) 20484.3 0.681210 0.340605 0.940207i \(-0.389368\pi\)
0.340605 + 0.940207i \(0.389368\pi\)
\(968\) 0 0
\(969\) 3715.23 0.123169
\(970\) 29944.8 21756.2i 0.991205 0.720153i
\(971\) −17132.3 52727.8i −0.566222 1.74265i −0.664291 0.747474i \(-0.731267\pi\)
0.0980691 0.995180i \(-0.468733\pi\)
\(972\) 19976.1 61480.2i 0.659192 2.02878i
\(973\) 4237.91 + 3079.02i 0.139631 + 0.101448i
\(974\) 47882.4 + 34788.6i 1.57521 + 1.14446i
\(975\) 7573.49 23308.8i 0.248765 0.765620i
\(976\) −893.701 2750.53i −0.0293101 0.0902073i
\(977\) −47418.8 + 34451.8i −1.55278 + 1.12816i −0.611141 + 0.791522i \(0.709289\pi\)
−0.941635 + 0.336635i \(0.890711\pi\)
\(978\) 46148.1 1.50885
\(979\) 0 0
\(980\) −6765.46 −0.220525
\(981\) 16070.9 11676.2i 0.523044 0.380013i
\(982\) −1267.40 3900.65i −0.0411857 0.126757i
\(983\) −9587.60 + 29507.6i −0.311085 + 0.957422i 0.666251 + 0.745728i \(0.267898\pi\)
−0.977336 + 0.211694i \(0.932102\pi\)
\(984\) −18856.4 13700.0i −0.610894 0.443840i
\(985\) 25864.8 + 18791.9i 0.836670 + 0.607877i
\(986\) −13697.6 + 42156.9i −0.442414 + 1.36161i
\(987\) 11980.4 + 36871.8i 0.386362 + 1.18910i
\(988\) −4261.86 + 3096.42i −0.137235 + 0.0997068i
\(989\) −2807.08 −0.0902528
\(990\) 0 0
\(991\) 11965.1 0.383537 0.191769 0.981440i \(-0.438578\pi\)
0.191769 + 0.981440i \(0.438578\pi\)
\(992\) 44696.6 32473.9i 1.43056 1.03936i
\(993\) 19134.0 + 58888.3i 0.611479 + 1.88194i
\(994\) 21843.1 67226.2i 0.697004 2.14516i
\(995\) −8567.40 6224.58i −0.272970 0.198324i
\(996\) −47299.5 34365.1i −1.50476 1.09327i
\(997\) 10273.8 31619.4i 0.326352 1.00441i −0.644475 0.764626i \(-0.722924\pi\)
0.970827 0.239782i \(-0.0770761\pi\)
\(998\) −16858.6 51885.5i −0.534720 1.64570i
\(999\) 3482.10 2529.90i 0.110279 0.0801225i
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 121.4.c.g.3.2 8
11.2 odd 10 121.4.a.e.1.2 yes 2
11.3 even 5 inner 121.4.c.g.27.1 8
11.4 even 5 inner 121.4.c.g.81.2 8
11.5 even 5 inner 121.4.c.g.9.1 8
11.6 odd 10 121.4.c.d.9.2 8
11.7 odd 10 121.4.c.d.81.1 8
11.8 odd 10 121.4.c.d.27.2 8
11.9 even 5 121.4.a.b.1.1 2
11.10 odd 2 121.4.c.d.3.1 8
33.2 even 10 1089.4.a.k.1.1 2
33.20 odd 10 1089.4.a.x.1.2 2
44.31 odd 10 1936.4.a.z.1.2 2
44.35 even 10 1936.4.a.y.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
121.4.a.b.1.1 2 11.9 even 5
121.4.a.e.1.2 yes 2 11.2 odd 10
121.4.c.d.3.1 8 11.10 odd 2
121.4.c.d.9.2 8 11.6 odd 10
121.4.c.d.27.2 8 11.8 odd 10
121.4.c.d.81.1 8 11.7 odd 10
121.4.c.g.3.2 8 1.1 even 1 trivial
121.4.c.g.9.1 8 11.5 even 5 inner
121.4.c.g.27.1 8 11.3 even 5 inner
121.4.c.g.81.2 8 11.4 even 5 inner
1089.4.a.k.1.1 2 33.2 even 10
1089.4.a.x.1.2 2 33.20 odd 10
1936.4.a.y.1.2 2 44.35 even 10
1936.4.a.z.1.2 2 44.31 odd 10