Properties

Label 378.4.g.b.163.1
Level $378$
Weight $4$
Character 378.163
Analytic conductor $22.303$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,4,Mod(109,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.109");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), 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: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11184604443.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 43x^{4} - 210x^{3} + 1849x^{2} - 4515x + 11025 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.1
Root \(-3.77219 + 6.53362i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.b.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.90212 + 6.75867i) q^{5} +(16.3412 - 8.71578i) q^{7} -8.00000 q^{8} +(7.80425 + 13.5173i) q^{10} +(2.79192 + 4.83575i) q^{11} +12.8042 q^{13} +(1.24504 - 37.0196i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(23.9251 + 41.4394i) q^{17} +(23.4637 - 40.6404i) q^{19} +31.2170 q^{20} +11.1677 q^{22} +(19.0130 - 32.9315i) q^{23} +(32.0469 + 55.5068i) q^{25} +(12.8042 - 22.1776i) q^{26} +(-62.8748 - 39.1761i) q^{28} +290.356 q^{29} +(-126.303 - 218.763i) q^{31} +(16.0000 + 27.7128i) q^{32} +95.7002 q^{34} +(-4.85832 + 144.455i) q^{35} +(205.336 - 355.652i) q^{37} +(-46.9275 - 81.2808i) q^{38} +(31.2170 - 54.0694i) q^{40} +11.7824 q^{41} +242.586 q^{43} +(11.1677 - 19.3430i) q^{44} +(-38.0261 - 65.8631i) q^{46} +(28.4874 - 49.3416i) q^{47} +(191.070 - 284.853i) q^{49} +128.188 q^{50} +(-25.6085 - 44.3552i) q^{52} +(-115.369 - 199.825i) q^{53} -43.5777 q^{55} +(-130.730 + 69.7262i) q^{56} +(290.356 - 502.911i) q^{58} +(259.028 + 448.650i) q^{59} +(129.473 - 224.253i) q^{61} -505.212 q^{62} +64.0000 q^{64} +(-49.9637 + 86.5397i) q^{65} +(-123.139 - 213.283i) q^{67} +(95.7002 - 165.758i) q^{68} +(245.345 + 152.870i) q^{70} -545.724 q^{71} +(143.956 + 249.339i) q^{73} +(-410.672 - 711.304i) q^{74} -187.710 q^{76} +(87.7707 + 54.6883i) q^{77} +(45.1287 - 78.1652i) q^{79} +(-62.4340 - 108.139i) q^{80} +(11.7824 - 20.4077i) q^{82} -372.935 q^{83} -373.434 q^{85} +(242.586 - 420.171i) q^{86} +(-22.3354 - 38.6860i) q^{88} +(-559.424 + 968.951i) q^{89} +(209.237 - 111.599i) q^{91} -152.104 q^{92} +(-56.9747 - 98.6832i) q^{94} +(183.117 + 317.168i) q^{95} +393.762 q^{97} +(-302.309 - 615.796i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} - 12 q^{4} + 5 q^{5} + 8 q^{7} - 48 q^{8} - 10 q^{10} - 29 q^{11} + 20 q^{13} + 20 q^{14} - 48 q^{16} - 38 q^{17} + 57 q^{19} - 40 q^{20} - 116 q^{22} - 14 q^{23} + 134 q^{25} + 20 q^{26}+ \cdots + 720 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −3.90212 + 6.75867i −0.349016 + 0.604514i −0.986075 0.166301i \(-0.946818\pi\)
0.637059 + 0.770815i \(0.280151\pi\)
\(6\) 0 0
\(7\) 16.3412 8.71578i 0.882343 0.470608i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 7.80425 + 13.5173i 0.246792 + 0.427456i
\(11\) 2.79192 + 4.83575i 0.0765269 + 0.132549i 0.901749 0.432259i \(-0.142284\pi\)
−0.825222 + 0.564808i \(0.808950\pi\)
\(12\) 0 0
\(13\) 12.8042 0.273174 0.136587 0.990628i \(-0.456387\pi\)
0.136587 + 0.990628i \(0.456387\pi\)
\(14\) 1.24504 37.0196i 0.0237680 0.706707i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 23.9251 + 41.4394i 0.341334 + 0.591208i 0.984681 0.174367i \(-0.0557879\pi\)
−0.643347 + 0.765575i \(0.722455\pi\)
\(18\) 0 0
\(19\) 23.4637 40.6404i 0.283313 0.490713i −0.688886 0.724870i \(-0.741900\pi\)
0.972199 + 0.234157i \(0.0752331\pi\)
\(20\) 31.2170 0.349016
\(21\) 0 0
\(22\) 11.1677 0.108225
\(23\) 19.0130 32.9315i 0.172369 0.298552i −0.766879 0.641792i \(-0.778191\pi\)
0.939248 + 0.343240i \(0.111524\pi\)
\(24\) 0 0
\(25\) 32.0469 + 55.5068i 0.256375 + 0.444055i
\(26\) 12.8042 22.1776i 0.0965815 0.167284i
\(27\) 0 0
\(28\) −62.8748 39.1761i −0.424365 0.264414i
\(29\) 290.356 1.85923 0.929616 0.368528i \(-0.120138\pi\)
0.929616 + 0.368528i \(0.120138\pi\)
\(30\) 0 0
\(31\) −126.303 218.763i −0.731764 1.26745i −0.956129 0.292947i \(-0.905364\pi\)
0.224365 0.974505i \(-0.427969\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 95.7002 0.482719
\(35\) −4.85832 + 144.455i −0.0234630 + 0.697638i
\(36\) 0 0
\(37\) 205.336 355.652i 0.912351 1.58024i 0.101617 0.994824i \(-0.467598\pi\)
0.810734 0.585415i \(-0.199068\pi\)
\(38\) −46.9275 81.2808i −0.200333 0.346986i
\(39\) 0 0
\(40\) 31.2170 54.0694i 0.123396 0.213728i
\(41\) 11.7824 0.0448806 0.0224403 0.999748i \(-0.492856\pi\)
0.0224403 + 0.999748i \(0.492856\pi\)
\(42\) 0 0
\(43\) 242.586 0.860326 0.430163 0.902751i \(-0.358456\pi\)
0.430163 + 0.902751i \(0.358456\pi\)
\(44\) 11.1677 19.3430i 0.0382635 0.0662743i
\(45\) 0 0
\(46\) −38.0261 65.8631i −0.121883 0.211108i
\(47\) 28.4874 49.3416i 0.0884109 0.153132i −0.818429 0.574608i \(-0.805154\pi\)
0.906840 + 0.421476i \(0.138488\pi\)
\(48\) 0 0
\(49\) 191.070 284.853i 0.557057 0.830474i
\(50\) 128.188 0.362569
\(51\) 0 0
\(52\) −25.6085 44.3552i −0.0682934 0.118288i
\(53\) −115.369 199.825i −0.299003 0.517889i 0.676905 0.736071i \(-0.263321\pi\)
−0.975908 + 0.218181i \(0.929988\pi\)
\(54\) 0 0
\(55\) −43.5777 −0.106837
\(56\) −130.730 + 69.7262i −0.311955 + 0.166385i
\(57\) 0 0
\(58\) 290.356 502.911i 0.657338 1.13854i
\(59\) 259.028 + 448.650i 0.571570 + 0.989988i 0.996405 + 0.0847176i \(0.0269988\pi\)
−0.424835 + 0.905271i \(0.639668\pi\)
\(60\) 0 0
\(61\) 129.473 224.253i 0.271759 0.470700i −0.697554 0.716533i \(-0.745728\pi\)
0.969312 + 0.245833i \(0.0790614\pi\)
\(62\) −505.212 −1.03487
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −49.9637 + 86.5397i −0.0953421 + 0.165137i
\(66\) 0 0
\(67\) −123.139 213.283i −0.224535 0.388906i 0.731645 0.681686i \(-0.238753\pi\)
−0.956180 + 0.292780i \(0.905420\pi\)
\(68\) 95.7002 165.758i 0.170667 0.295604i
\(69\) 0 0
\(70\) 245.345 + 152.870i 0.418919 + 0.261021i
\(71\) −545.724 −0.912191 −0.456096 0.889931i \(-0.650752\pi\)
−0.456096 + 0.889931i \(0.650752\pi\)
\(72\) 0 0
\(73\) 143.956 + 249.339i 0.230805 + 0.399767i 0.958045 0.286617i \(-0.0925306\pi\)
−0.727240 + 0.686383i \(0.759197\pi\)
\(74\) −410.672 711.304i −0.645130 1.11740i
\(75\) 0 0
\(76\) −187.710 −0.283313
\(77\) 87.7707 + 54.6883i 0.129901 + 0.0809391i
\(78\) 0 0
\(79\) 45.1287 78.1652i 0.0642706 0.111320i −0.832100 0.554626i \(-0.812861\pi\)
0.896370 + 0.443306i \(0.146195\pi\)
\(80\) −62.4340 108.139i −0.0872541 0.151129i
\(81\) 0 0
\(82\) 11.7824 20.4077i 0.0158677 0.0274836i
\(83\) −372.935 −0.493192 −0.246596 0.969118i \(-0.579312\pi\)
−0.246596 + 0.969118i \(0.579312\pi\)
\(84\) 0 0
\(85\) −373.434 −0.476525
\(86\) 242.586 420.171i 0.304171 0.526840i
\(87\) 0 0
\(88\) −22.3354 38.6860i −0.0270564 0.0468630i
\(89\) −559.424 + 968.951i −0.666279 + 1.15403i 0.312658 + 0.949866i \(0.398781\pi\)
−0.978937 + 0.204164i \(0.934553\pi\)
\(90\) 0 0
\(91\) 209.237 111.599i 0.241033 0.128558i
\(92\) −152.104 −0.172369
\(93\) 0 0
\(94\) −56.9747 98.6832i −0.0625159 0.108281i
\(95\) 183.117 + 317.168i 0.197762 + 0.342534i
\(96\) 0 0
\(97\) 393.762 0.412170 0.206085 0.978534i \(-0.433928\pi\)
0.206085 + 0.978534i \(0.433928\pi\)
\(98\) −302.309 615.796i −0.311610 0.634743i
\(99\) 0 0
\(100\) 128.188 222.027i 0.128188 0.222027i
\(101\) 547.800 + 948.818i 0.539685 + 0.934762i 0.998921 + 0.0464472i \(0.0147899\pi\)
−0.459236 + 0.888314i \(0.651877\pi\)
\(102\) 0 0
\(103\) 121.111 209.771i 0.115859 0.200673i −0.802264 0.596969i \(-0.796371\pi\)
0.918123 + 0.396296i \(0.129705\pi\)
\(104\) −102.434 −0.0965815
\(105\) 0 0
\(106\) −461.477 −0.422855
\(107\) −49.5638 + 85.8470i −0.0447805 + 0.0775621i −0.887547 0.460717i \(-0.847592\pi\)
0.842766 + 0.538279i \(0.180926\pi\)
\(108\) 0 0
\(109\) 459.570 + 795.998i 0.403842 + 0.699475i 0.994186 0.107677i \(-0.0343412\pi\)
−0.590344 + 0.807152i \(0.701008\pi\)
\(110\) −43.5777 + 75.4788i −0.0377725 + 0.0654238i
\(111\) 0 0
\(112\) −9.96036 + 296.157i −0.00840326 + 0.249859i
\(113\) 2121.07 1.76578 0.882889 0.469581i \(-0.155595\pi\)
0.882889 + 0.469581i \(0.155595\pi\)
\(114\) 0 0
\(115\) 148.382 + 257.006i 0.120319 + 0.208399i
\(116\) −580.712 1005.82i −0.464808 0.805071i
\(117\) 0 0
\(118\) 1036.11 0.808322
\(119\) 752.141 + 468.645i 0.579401 + 0.361013i
\(120\) 0 0
\(121\) 649.910 1125.68i 0.488287 0.845738i
\(122\) −258.945 448.507i −0.192162 0.332835i
\(123\) 0 0
\(124\) −505.212 + 875.052i −0.365882 + 0.633726i
\(125\) −1475.73 −1.05595
\(126\) 0 0
\(127\) −1250.33 −0.873611 −0.436805 0.899556i \(-0.643890\pi\)
−0.436805 + 0.899556i \(0.643890\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 99.9275 + 173.079i 0.0674171 + 0.116770i
\(131\) 56.7324 98.2634i 0.0378376 0.0655367i −0.846486 0.532410i \(-0.821286\pi\)
0.884324 + 0.466874i \(0.154620\pi\)
\(132\) 0 0
\(133\) 29.2134 868.618i 0.0190460 0.566306i
\(134\) −492.556 −0.317540
\(135\) 0 0
\(136\) −191.400 331.515i −0.120680 0.209024i
\(137\) −7.65748 13.2631i −0.00477535 0.00827115i 0.863628 0.504130i \(-0.168187\pi\)
−0.868403 + 0.495859i \(0.834853\pi\)
\(138\) 0 0
\(139\) −2539.81 −1.54981 −0.774905 0.632077i \(-0.782203\pi\)
−0.774905 + 0.632077i \(0.782203\pi\)
\(140\) 510.123 272.080i 0.307952 0.164250i
\(141\) 0 0
\(142\) −545.724 + 945.222i −0.322508 + 0.558601i
\(143\) 35.7485 + 61.9182i 0.0209052 + 0.0362088i
\(144\) 0 0
\(145\) −1133.00 + 1962.42i −0.648903 + 1.12393i
\(146\) 575.825 0.326408
\(147\) 0 0
\(148\) −1642.69 −0.912351
\(149\) −43.5846 + 75.4907i −0.0239637 + 0.0415063i −0.877759 0.479103i \(-0.840962\pi\)
0.853795 + 0.520610i \(0.174295\pi\)
\(150\) 0 0
\(151\) 498.030 + 862.613i 0.268405 + 0.464890i 0.968450 0.249208i \(-0.0801703\pi\)
−0.700045 + 0.714098i \(0.746837\pi\)
\(152\) −187.710 + 325.123i −0.100166 + 0.173493i
\(153\) 0 0
\(154\) 182.494 97.3351i 0.0954919 0.0509317i
\(155\) 1971.40 1.02159
\(156\) 0 0
\(157\) 1081.66 + 1873.48i 0.549844 + 0.952358i 0.998285 + 0.0585451i \(0.0186461\pi\)
−0.448441 + 0.893813i \(0.648021\pi\)
\(158\) −90.2574 156.330i −0.0454462 0.0787151i
\(159\) 0 0
\(160\) −249.736 −0.123396
\(161\) 23.6721 703.854i 0.0115877 0.344543i
\(162\) 0 0
\(163\) −661.783 + 1146.24i −0.318005 + 0.550801i −0.980072 0.198644i \(-0.936346\pi\)
0.662066 + 0.749445i \(0.269680\pi\)
\(164\) −23.5648 40.8155i −0.0112201 0.0194339i
\(165\) 0 0
\(166\) −372.935 + 645.942i −0.174370 + 0.302017i
\(167\) 2071.29 0.959766 0.479883 0.877332i \(-0.340679\pi\)
0.479883 + 0.877332i \(0.340679\pi\)
\(168\) 0 0
\(169\) −2033.05 −0.925376
\(170\) −373.434 + 646.807i −0.168477 + 0.291811i
\(171\) 0 0
\(172\) −485.172 840.342i −0.215081 0.372532i
\(173\) −1542.64 + 2671.93i −0.677946 + 1.17424i 0.297653 + 0.954674i \(0.403796\pi\)
−0.975598 + 0.219562i \(0.929537\pi\)
\(174\) 0 0
\(175\) 1007.47 + 627.735i 0.435186 + 0.271156i
\(176\) −89.3415 −0.0382635
\(177\) 0 0
\(178\) 1118.85 + 1937.90i 0.471131 + 0.816022i
\(179\) −723.786 1253.63i −0.302225 0.523470i 0.674414 0.738353i \(-0.264396\pi\)
−0.976640 + 0.214883i \(0.931063\pi\)
\(180\) 0 0
\(181\) −1683.16 −0.691208 −0.345604 0.938380i \(-0.612326\pi\)
−0.345604 + 0.938380i \(0.612326\pi\)
\(182\) 15.9419 474.008i 0.00649280 0.193054i
\(183\) 0 0
\(184\) −152.104 + 263.452i −0.0609417 + 0.105554i
\(185\) 1602.49 + 2775.60i 0.636851 + 1.10306i
\(186\) 0 0
\(187\) −133.594 + 231.391i −0.0522425 + 0.0904867i
\(188\) −227.899 −0.0884109
\(189\) 0 0
\(190\) 732.467 0.279678
\(191\) 1047.11 1813.66i 0.396684 0.687076i −0.596631 0.802516i \(-0.703494\pi\)
0.993314 + 0.115440i \(0.0368277\pi\)
\(192\) 0 0
\(193\) 1709.71 + 2961.31i 0.637657 + 1.10445i 0.985946 + 0.167067i \(0.0534296\pi\)
−0.348289 + 0.937387i \(0.613237\pi\)
\(194\) 393.762 682.016i 0.145724 0.252401i
\(195\) 0 0
\(196\) −1368.90 92.1821i −0.498870 0.0335941i
\(197\) −3517.08 −1.27199 −0.635993 0.771695i \(-0.719409\pi\)
−0.635993 + 0.771695i \(0.719409\pi\)
\(198\) 0 0
\(199\) 1566.03 + 2712.45i 0.557855 + 0.966233i 0.997675 + 0.0681473i \(0.0217088\pi\)
−0.439820 + 0.898086i \(0.644958\pi\)
\(200\) −256.375 444.055i −0.0906423 0.156997i
\(201\) 0 0
\(202\) 2191.20 0.763230
\(203\) 4744.77 2530.68i 1.64048 0.874969i
\(204\) 0 0
\(205\) −45.9764 + 79.6335i −0.0156641 + 0.0271309i
\(206\) −242.222 419.542i −0.0819245 0.141897i
\(207\) 0 0
\(208\) −102.434 + 177.421i −0.0341467 + 0.0591439i
\(209\) 262.036 0.0867244
\(210\) 0 0
\(211\) −3088.38 −1.00764 −0.503822 0.863807i \(-0.668073\pi\)
−0.503822 + 0.863807i \(0.668073\pi\)
\(212\) −461.477 + 799.302i −0.149502 + 0.258945i
\(213\) 0 0
\(214\) 99.1276 + 171.694i 0.0316646 + 0.0548447i
\(215\) −946.600 + 1639.56i −0.300268 + 0.520079i
\(216\) 0 0
\(217\) −3970.63 2474.03i −1.24214 0.773953i
\(218\) 1838.28 0.571119
\(219\) 0 0
\(220\) 87.1554 + 150.958i 0.0267092 + 0.0462616i
\(221\) 306.342 + 530.600i 0.0932435 + 0.161502i
\(222\) 0 0
\(223\) 4399.79 1.32122 0.660609 0.750730i \(-0.270298\pi\)
0.660609 + 0.750730i \(0.270298\pi\)
\(224\) 502.998 + 313.409i 0.150036 + 0.0934843i
\(225\) 0 0
\(226\) 2121.07 3673.79i 0.624297 1.08131i
\(227\) −1643.69 2846.96i −0.480597 0.832419i 0.519155 0.854680i \(-0.326247\pi\)
−0.999752 + 0.0222611i \(0.992913\pi\)
\(228\) 0 0
\(229\) −1506.76 + 2609.78i −0.434800 + 0.753096i −0.997279 0.0737158i \(-0.976514\pi\)
0.562479 + 0.826811i \(0.309848\pi\)
\(230\) 593.529 0.170157
\(231\) 0 0
\(232\) −2322.85 −0.657338
\(233\) −2540.80 + 4400.80i −0.714393 + 1.23737i 0.248800 + 0.968555i \(0.419964\pi\)
−0.963193 + 0.268811i \(0.913369\pi\)
\(234\) 0 0
\(235\) 222.322 + 385.074i 0.0617137 + 0.106891i
\(236\) 1036.11 1794.60i 0.285785 0.494994i
\(237\) 0 0
\(238\) 1563.86 834.102i 0.425924 0.227171i
\(239\) 3087.38 0.835590 0.417795 0.908541i \(-0.362803\pi\)
0.417795 + 0.908541i \(0.362803\pi\)
\(240\) 0 0
\(241\) 608.325 + 1053.65i 0.162596 + 0.281625i 0.935799 0.352534i \(-0.114680\pi\)
−0.773203 + 0.634159i \(0.781347\pi\)
\(242\) −1299.82 2251.36i −0.345271 0.598027i
\(243\) 0 0
\(244\) −1035.78 −0.271759
\(245\) 1179.65 + 2402.91i 0.307612 + 0.626598i
\(246\) 0 0
\(247\) 300.435 520.369i 0.0773937 0.134050i
\(248\) 1010.42 + 1750.10i 0.258718 + 0.448112i
\(249\) 0 0
\(250\) −1475.73 + 2556.05i −0.373334 + 0.646634i
\(251\) −2649.43 −0.666257 −0.333128 0.942881i \(-0.608104\pi\)
−0.333128 + 0.942881i \(0.608104\pi\)
\(252\) 0 0
\(253\) 212.332 0.0527635
\(254\) −1250.33 + 2165.63i −0.308868 + 0.534975i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −357.989 + 620.055i −0.0868901 + 0.150498i −0.906195 0.422860i \(-0.861026\pi\)
0.819305 + 0.573358i \(0.194360\pi\)
\(258\) 0 0
\(259\) 255.652 7601.45i 0.0613338 1.82367i
\(260\) 399.710 0.0953421
\(261\) 0 0
\(262\) −113.465 196.527i −0.0267553 0.0463415i
\(263\) −3173.49 5496.65i −0.744053 1.28874i −0.950636 0.310309i \(-0.899567\pi\)
0.206582 0.978429i \(-0.433766\pi\)
\(264\) 0 0
\(265\) 1800.74 0.417429
\(266\) −1475.28 919.217i −0.340056 0.211883i
\(267\) 0 0
\(268\) −492.556 + 853.132i −0.112267 + 0.194453i
\(269\) −3919.92 6789.50i −0.888482 1.53890i −0.841670 0.539993i \(-0.818427\pi\)
−0.0468125 0.998904i \(-0.514906\pi\)
\(270\) 0 0
\(271\) −1640.28 + 2841.04i −0.367674 + 0.636831i −0.989202 0.146562i \(-0.953179\pi\)
0.621527 + 0.783393i \(0.286513\pi\)
\(272\) −765.602 −0.170667
\(273\) 0 0
\(274\) −30.6299 −0.00675336
\(275\) −178.945 + 309.942i −0.0392392 + 0.0679643i
\(276\) 0 0
\(277\) −3766.56 6523.88i −0.817006 1.41510i −0.907878 0.419234i \(-0.862299\pi\)
0.0908720 0.995863i \(-0.471035\pi\)
\(278\) −2539.81 + 4399.08i −0.547941 + 0.949062i
\(279\) 0 0
\(280\) 38.8665 1155.64i 0.00829543 0.246652i
\(281\) −3454.53 −0.733380 −0.366690 0.930343i \(-0.619509\pi\)
−0.366690 + 0.930343i \(0.619509\pi\)
\(282\) 0 0
\(283\) 1322.28 + 2290.26i 0.277744 + 0.481066i 0.970824 0.239794i \(-0.0770800\pi\)
−0.693080 + 0.720861i \(0.743747\pi\)
\(284\) 1091.45 + 1890.44i 0.228048 + 0.394990i
\(285\) 0 0
\(286\) 142.994 0.0295643
\(287\) 192.539 102.693i 0.0396000 0.0211211i
\(288\) 0 0
\(289\) 1311.68 2271.90i 0.266982 0.462427i
\(290\) 2266.01 + 3924.84i 0.458844 + 0.794741i
\(291\) 0 0
\(292\) 575.825 997.358i 0.115403 0.199883i
\(293\) −8580.20 −1.71079 −0.855394 0.517978i \(-0.826685\pi\)
−0.855394 + 0.517978i \(0.826685\pi\)
\(294\) 0 0
\(295\) −4043.04 −0.797949
\(296\) −1642.69 + 2845.22i −0.322565 + 0.558699i
\(297\) 0 0
\(298\) 87.1692 + 150.981i 0.0169449 + 0.0293494i
\(299\) 243.447 421.663i 0.0470867 0.0815566i
\(300\) 0 0
\(301\) 3964.15 2114.33i 0.759102 0.404876i
\(302\) 1992.12 0.379581
\(303\) 0 0
\(304\) 375.420 + 650.246i 0.0708283 + 0.122678i
\(305\) 1010.44 + 1750.13i 0.189697 + 0.328564i
\(306\) 0 0
\(307\) 9077.13 1.68749 0.843745 0.536745i \(-0.180346\pi\)
0.843745 + 0.536745i \(0.180346\pi\)
\(308\) 13.9043 413.423i 0.00257230 0.0764837i
\(309\) 0 0
\(310\) 1971.40 3414.56i 0.361187 0.625594i
\(311\) −3620.21 6270.39i −0.660075 1.14328i −0.980596 0.196041i \(-0.937191\pi\)
0.320521 0.947241i \(-0.396142\pi\)
\(312\) 0 0
\(313\) 4977.05 8620.50i 0.898784 1.55674i 0.0697331 0.997566i \(-0.477785\pi\)
0.829051 0.559173i \(-0.188881\pi\)
\(314\) 4326.62 0.777597
\(315\) 0 0
\(316\) −361.030 −0.0642706
\(317\) 2275.80 3941.80i 0.403223 0.698402i −0.590890 0.806752i \(-0.701223\pi\)
0.994113 + 0.108350i \(0.0345567\pi\)
\(318\) 0 0
\(319\) 810.652 + 1404.09i 0.142281 + 0.246439i
\(320\) −249.736 + 432.555i −0.0436271 + 0.0755643i
\(321\) 0 0
\(322\) −1195.44 744.856i −0.206892 0.128910i
\(323\) 2245.48 0.386818
\(324\) 0 0
\(325\) 410.336 + 710.723i 0.0700349 + 0.121304i
\(326\) 1323.57 + 2292.48i 0.224864 + 0.389475i
\(327\) 0 0
\(328\) −94.2593 −0.0158677
\(329\) 35.4681 1054.59i 0.00594352 0.176722i
\(330\) 0 0
\(331\) 4953.58 8579.85i 0.822578 1.42475i −0.0811782 0.996700i \(-0.525868\pi\)
0.903756 0.428047i \(-0.140798\pi\)
\(332\) 745.870 + 1291.88i 0.123298 + 0.213558i
\(333\) 0 0
\(334\) 2071.29 3587.57i 0.339329 0.587734i
\(335\) 1922.01 0.313465
\(336\) 0 0
\(337\) −8206.45 −1.32651 −0.663255 0.748393i \(-0.730826\pi\)
−0.663255 + 0.748393i \(0.730826\pi\)
\(338\) −2033.05 + 3521.35i −0.327170 + 0.566675i
\(339\) 0 0
\(340\) 746.868 + 1293.61i 0.119131 + 0.206341i
\(341\) 705.256 1221.54i 0.111999 0.193988i
\(342\) 0 0
\(343\) 639.611 6320.17i 0.100687 0.994918i
\(344\) −1940.69 −0.304171
\(345\) 0 0
\(346\) 3085.28 + 5343.86i 0.479380 + 0.830311i
\(347\) −980.017 1697.44i −0.151614 0.262603i 0.780207 0.625522i \(-0.215114\pi\)
−0.931821 + 0.362918i \(0.881780\pi\)
\(348\) 0 0
\(349\) 3808.47 0.584134 0.292067 0.956398i \(-0.405657\pi\)
0.292067 + 0.956398i \(0.405657\pi\)
\(350\) 2094.74 1117.25i 0.319910 0.170628i
\(351\) 0 0
\(352\) −89.3415 + 154.744i −0.0135282 + 0.0234315i
\(353\) 4695.51 + 8132.86i 0.707979 + 1.22626i 0.965606 + 0.260011i \(0.0837263\pi\)
−0.257626 + 0.966245i \(0.582940\pi\)
\(354\) 0 0
\(355\) 2129.48 3688.37i 0.318370 0.551433i
\(356\) 4475.39 0.666279
\(357\) 0 0
\(358\) −2895.15 −0.427411
\(359\) 6027.50 10439.9i 0.886126 1.53481i 0.0417077 0.999130i \(-0.486720\pi\)
0.844418 0.535685i \(-0.179946\pi\)
\(360\) 0 0
\(361\) 2328.41 + 4032.92i 0.339467 + 0.587975i
\(362\) −1683.16 + 2915.33i −0.244379 + 0.423277i
\(363\) 0 0
\(364\) −805.064 501.620i −0.115925 0.0722309i
\(365\) −2246.94 −0.322220
\(366\) 0 0
\(367\) 2923.66 + 5063.94i 0.415842 + 0.720260i 0.995516 0.0945886i \(-0.0301536\pi\)
−0.579674 + 0.814848i \(0.696820\pi\)
\(368\) 304.208 + 526.904i 0.0430923 + 0.0746380i
\(369\) 0 0
\(370\) 6409.96 0.900644
\(371\) −3626.91 2259.86i −0.507546 0.316242i
\(372\) 0 0
\(373\) 4066.66 7043.66i 0.564513 0.977766i −0.432581 0.901595i \(-0.642397\pi\)
0.997095 0.0761709i \(-0.0242695\pi\)
\(374\) 267.188 + 462.783i 0.0369410 + 0.0639837i
\(375\) 0 0
\(376\) −227.899 + 394.733i −0.0312580 + 0.0541404i
\(377\) 3717.79 0.507894
\(378\) 0 0
\(379\) −7913.69 −1.07256 −0.536278 0.844041i \(-0.680170\pi\)
−0.536278 + 0.844041i \(0.680170\pi\)
\(380\) 732.467 1268.67i 0.0988810 0.171267i
\(381\) 0 0
\(382\) −2094.23 3627.31i −0.280498 0.485836i
\(383\) 949.004 1643.72i 0.126611 0.219296i −0.795751 0.605624i \(-0.792923\pi\)
0.922361 + 0.386328i \(0.126257\pi\)
\(384\) 0 0
\(385\) −712.112 + 379.813i −0.0942665 + 0.0502782i
\(386\) 6838.85 0.901783
\(387\) 0 0
\(388\) −787.524 1364.03i −0.103042 0.178475i
\(389\) 751.212 + 1301.14i 0.0979124 + 0.169589i 0.910820 0.412803i \(-0.135450\pi\)
−0.812908 + 0.582392i \(0.802117\pi\)
\(390\) 0 0
\(391\) 1819.55 0.235342
\(392\) −1528.56 + 2278.82i −0.196949 + 0.293617i
\(393\) 0 0
\(394\) −3517.08 + 6091.76i −0.449715 + 0.778930i
\(395\) 352.195 + 610.020i 0.0448630 + 0.0777050i
\(396\) 0 0
\(397\) −7327.84 + 12692.2i −0.926382 + 1.60454i −0.137059 + 0.990563i \(0.543765\pi\)
−0.789323 + 0.613978i \(0.789568\pi\)
\(398\) 6264.13 0.788926
\(399\) 0 0
\(400\) −1025.50 −0.128188
\(401\) 85.1443 147.474i 0.0106033 0.0183654i −0.860675 0.509155i \(-0.829958\pi\)
0.871278 + 0.490789i \(0.163291\pi\)
\(402\) 0 0
\(403\) −1617.21 2801.10i −0.199899 0.346235i
\(404\) 2191.20 3795.27i 0.269842 0.467381i
\(405\) 0 0
\(406\) 361.506 10748.9i 0.0441903 1.31393i
\(407\) 2293.13 0.279278
\(408\) 0 0
\(409\) 5733.15 + 9930.11i 0.693120 + 1.20052i 0.970810 + 0.239849i \(0.0770978\pi\)
−0.277690 + 0.960671i \(0.589569\pi\)
\(410\) 91.9528 + 159.267i 0.0110762 + 0.0191845i
\(411\) 0 0
\(412\) −968.890 −0.115859
\(413\) 8143.18 + 5073.86i 0.970217 + 0.604524i
\(414\) 0 0
\(415\) 1455.24 2520.55i 0.172132 0.298142i
\(416\) 204.868 + 354.842i 0.0241454 + 0.0418210i
\(417\) 0 0
\(418\) 262.036 453.859i 0.0306617 0.0531076i
\(419\) −9329.18 −1.08773 −0.543866 0.839172i \(-0.683040\pi\)
−0.543866 + 0.839172i \(0.683040\pi\)
\(420\) 0 0
\(421\) 4184.24 0.484388 0.242194 0.970228i \(-0.422133\pi\)
0.242194 + 0.970228i \(0.422133\pi\)
\(422\) −3088.38 + 5349.23i −0.356256 + 0.617053i
\(423\) 0 0
\(424\) 922.954 + 1598.60i 0.105714 + 0.183101i
\(425\) −1533.45 + 2656.01i −0.175019 + 0.303142i
\(426\) 0 0
\(427\) 161.199 4793.03i 0.0182693 0.543210i
\(428\) 396.510 0.0447805
\(429\) 0 0
\(430\) 1893.20 + 3279.12i 0.212321 + 0.367752i
\(431\) 3643.40 + 6310.56i 0.407185 + 0.705265i 0.994573 0.104041i \(-0.0331772\pi\)
−0.587388 + 0.809305i \(0.699844\pi\)
\(432\) 0 0
\(433\) −5314.89 −0.589879 −0.294939 0.955516i \(-0.595299\pi\)
−0.294939 + 0.955516i \(0.595299\pi\)
\(434\) −8255.77 + 4403.31i −0.913110 + 0.487018i
\(435\) 0 0
\(436\) 1838.28 3183.99i 0.201921 0.349738i
\(437\) −892.233 1545.39i −0.0976689 0.169167i
\(438\) 0 0
\(439\) −4273.05 + 7401.14i −0.464560 + 0.804641i −0.999182 0.0404505i \(-0.987121\pi\)
0.534622 + 0.845091i \(0.320454\pi\)
\(440\) 348.622 0.0377725
\(441\) 0 0
\(442\) 1225.37 0.131866
\(443\) 5398.26 9350.06i 0.578960 1.00279i −0.416639 0.909072i \(-0.636792\pi\)
0.995599 0.0937156i \(-0.0298745\pi\)
\(444\) 0 0
\(445\) −4365.88 7561.93i −0.465085 0.805551i
\(446\) 4399.79 7620.66i 0.467121 0.809078i
\(447\) 0 0
\(448\) 1045.84 557.810i 0.110293 0.0588260i
\(449\) −3617.92 −0.380267 −0.190134 0.981758i \(-0.560892\pi\)
−0.190134 + 0.981758i \(0.560892\pi\)
\(450\) 0 0
\(451\) 32.8956 + 56.9768i 0.00343457 + 0.00594886i
\(452\) −4242.13 7347.59i −0.441445 0.764605i
\(453\) 0 0
\(454\) −6574.76 −0.679667
\(455\) −62.2071 + 1849.64i −0.00640948 + 0.190577i
\(456\) 0 0
\(457\) 3549.67 6148.21i 0.363340 0.629324i −0.625168 0.780490i \(-0.714970\pi\)
0.988508 + 0.151166i \(0.0483029\pi\)
\(458\) 3013.51 + 5219.55i 0.307450 + 0.532519i
\(459\) 0 0
\(460\) 593.529 1028.02i 0.0601597 0.104200i
\(461\) −16652.8 −1.68243 −0.841215 0.540700i \(-0.818159\pi\)
−0.841215 + 0.540700i \(0.818159\pi\)
\(462\) 0 0
\(463\) −15394.4 −1.54523 −0.772614 0.634876i \(-0.781051\pi\)
−0.772614 + 0.634876i \(0.781051\pi\)
\(464\) −2322.85 + 4023.29i −0.232404 + 0.402536i
\(465\) 0 0
\(466\) 5081.61 + 8801.61i 0.505152 + 0.874950i
\(467\) 8307.83 14389.6i 0.823214 1.42585i −0.0800634 0.996790i \(-0.525512\pi\)
0.903277 0.429058i \(-0.141154\pi\)
\(468\) 0 0
\(469\) −3871.17 2412.05i −0.381139 0.237480i
\(470\) 889.290 0.0872763
\(471\) 0 0
\(472\) −2072.23 3589.20i −0.202081 0.350014i
\(473\) 677.281 + 1173.09i 0.0658381 + 0.114035i
\(474\) 0 0
\(475\) 3007.76 0.290538
\(476\) 119.151 3542.78i 0.0114733 0.341141i
\(477\) 0 0
\(478\) 3087.38 5347.50i 0.295426 0.511693i
\(479\) 839.186 + 1453.51i 0.0800489 + 0.138649i 0.903271 0.429071i \(-0.141159\pi\)
−0.823222 + 0.567720i \(0.807826\pi\)
\(480\) 0 0
\(481\) 2629.17 4553.86i 0.249230 0.431680i
\(482\) 2433.30 0.229946
\(483\) 0 0
\(484\) −5199.28 −0.488287
\(485\) −1536.51 + 2661.31i −0.143854 + 0.249163i
\(486\) 0 0
\(487\) 4729.44 + 8191.64i 0.440065 + 0.762214i 0.997694 0.0678758i \(-0.0216222\pi\)
−0.557629 + 0.830090i \(0.688289\pi\)
\(488\) −1035.78 + 1794.03i −0.0960812 + 0.166418i
\(489\) 0 0
\(490\) 5341.61 + 359.706i 0.492468 + 0.0331630i
\(491\) −12084.6 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(492\) 0 0
\(493\) 6946.78 + 12032.2i 0.634620 + 1.09919i
\(494\) −600.871 1040.74i −0.0547256 0.0947876i
\(495\) 0 0
\(496\) 4041.69 0.365882
\(497\) −8917.80 + 4756.41i −0.804865 + 0.429284i
\(498\) 0 0
\(499\) −5576.33 + 9658.48i −0.500262 + 0.866479i 0.499738 + 0.866177i \(0.333430\pi\)
−1.00000 0.000302529i \(0.999904\pi\)
\(500\) 2951.47 + 5112.09i 0.263987 + 0.457239i
\(501\) 0 0
\(502\) −2649.43 + 4588.95i −0.235557 + 0.407997i
\(503\) 18353.8 1.62695 0.813476 0.581598i \(-0.197572\pi\)
0.813476 + 0.581598i \(0.197572\pi\)
\(504\) 0 0
\(505\) −8550.34 −0.753436
\(506\) 212.332 367.769i 0.0186547 0.0323109i
\(507\) 0 0
\(508\) 2500.65 + 4331.26i 0.218403 + 0.378284i
\(509\) −8839.43 + 15310.3i −0.769746 + 1.33324i 0.167954 + 0.985795i \(0.446284\pi\)
−0.937700 + 0.347445i \(0.887049\pi\)
\(510\) 0 0
\(511\) 4525.61 + 2819.82i 0.391783 + 0.244112i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 715.978 + 1240.11i 0.0614405 + 0.106418i
\(515\) 945.182 + 1637.10i 0.0808732 + 0.140076i
\(516\) 0 0
\(517\) 318.138 0.0270633
\(518\) −12910.4 8044.25i −1.09508 0.682324i
\(519\) 0 0
\(520\) 399.710 692.318i 0.0337085 0.0583849i
\(521\) −3844.84 6659.46i −0.323312 0.559993i 0.657857 0.753143i \(-0.271463\pi\)
−0.981169 + 0.193150i \(0.938130\pi\)
\(522\) 0 0
\(523\) −10654.7 + 18454.5i −0.890819 + 1.54294i −0.0519230 + 0.998651i \(0.516535\pi\)
−0.838896 + 0.544292i \(0.816798\pi\)
\(524\) −453.859 −0.0378376
\(525\) 0 0
\(526\) −12694.0 −1.05225
\(527\) 6043.61 10467.8i 0.499552 0.865249i
\(528\) 0 0
\(529\) 5360.51 + 9284.68i 0.440578 + 0.763103i
\(530\) 1800.74 3118.97i 0.147583 0.255622i
\(531\) 0 0
\(532\) −3067.41 + 1636.04i −0.249979 + 0.133329i
\(533\) 150.865 0.0122602
\(534\) 0 0
\(535\) −386.808 669.971i −0.0312583 0.0541409i
\(536\) 985.112 + 1706.26i 0.0793850 + 0.137499i
\(537\) 0 0
\(538\) −15679.7 −1.25650
\(539\) 1910.93 + 128.683i 0.152708 + 0.0102834i
\(540\) 0 0
\(541\) 2262.65 3919.03i 0.179813 0.311446i −0.762003 0.647573i \(-0.775784\pi\)
0.941816 + 0.336128i \(0.109117\pi\)
\(542\) 3280.56 + 5682.09i 0.259985 + 0.450307i
\(543\) 0 0
\(544\) −765.602 + 1326.06i −0.0603399 + 0.104512i
\(545\) −7173.19 −0.563790
\(546\) 0 0
\(547\) −15313.6 −1.19701 −0.598504 0.801120i \(-0.704238\pi\)
−0.598504 + 0.801120i \(0.704238\pi\)
\(548\) −30.6299 + 53.0526i −0.00238767 + 0.00413557i
\(549\) 0 0
\(550\) 357.890 + 619.883i 0.0277463 + 0.0480580i
\(551\) 6812.84 11800.2i 0.526745 0.912349i
\(552\) 0 0
\(553\) 56.1873 1670.65i 0.00432066 0.128469i
\(554\) −15066.2 −1.15542
\(555\) 0 0
\(556\) 5079.62 + 8798.15i 0.387453 + 0.671088i
\(557\) 12455.6 + 21573.7i 0.947503 + 1.64112i 0.750660 + 0.660689i \(0.229736\pi\)
0.196844 + 0.980435i \(0.436931\pi\)
\(558\) 0 0
\(559\) 3106.13 0.235018
\(560\) −1962.76 1222.96i −0.148110 0.0922847i
\(561\) 0 0
\(562\) −3454.53 + 5983.41i −0.259289 + 0.449102i
\(563\) −3212.07 5563.48i −0.240449 0.416470i 0.720393 0.693566i \(-0.243961\pi\)
−0.960842 + 0.277096i \(0.910628\pi\)
\(564\) 0 0
\(565\) −8276.66 + 14335.6i −0.616286 + 1.06744i
\(566\) 5289.13 0.392789
\(567\) 0 0
\(568\) 4365.80 0.322508
\(569\) 4793.27 8302.19i 0.353153 0.611680i −0.633647 0.773623i \(-0.718443\pi\)
0.986800 + 0.161943i \(0.0517760\pi\)
\(570\) 0 0
\(571\) 1521.81 + 2635.86i 0.111534 + 0.193183i 0.916389 0.400289i \(-0.131090\pi\)
−0.804855 + 0.593472i \(0.797757\pi\)
\(572\) 142.994 247.673i 0.0104526 0.0181044i
\(573\) 0 0
\(574\) 14.6696 436.180i 0.00106672 0.0317174i
\(575\) 2437.23 0.176765
\(576\) 0 0
\(577\) 2121.12 + 3673.89i 0.153039 + 0.265071i 0.932343 0.361574i \(-0.117761\pi\)
−0.779304 + 0.626646i \(0.784427\pi\)
\(578\) −2623.37 4543.80i −0.188785 0.326985i
\(579\) 0 0
\(580\) 9064.04 0.648903
\(581\) −6094.21 + 3250.42i −0.435164 + 0.232100i
\(582\) 0 0
\(583\) 644.204 1115.79i 0.0457636 0.0792650i
\(584\) −1151.65 1994.72i −0.0816021 0.141339i
\(585\) 0 0
\(586\) −8580.20 + 14861.3i −0.604855 + 1.04764i
\(587\) −13992.3 −0.983854 −0.491927 0.870637i \(-0.663707\pi\)
−0.491927 + 0.870637i \(0.663707\pi\)
\(588\) 0 0
\(589\) −11854.2 −0.829273
\(590\) −4043.04 + 7002.76i −0.282118 + 0.488642i
\(591\) 0 0
\(592\) 3285.37 + 5690.43i 0.228088 + 0.395060i
\(593\) −9155.07 + 15857.0i −0.633986 + 1.09810i 0.352743 + 0.935720i \(0.385249\pi\)
−0.986729 + 0.162375i \(0.948084\pi\)
\(594\) 0 0
\(595\) −6102.37 + 3254.77i −0.420458 + 0.224256i
\(596\) 348.677 0.0239637
\(597\) 0 0
\(598\) −486.895 843.327i −0.0332953 0.0576692i
\(599\) 4911.78 + 8507.45i 0.335042 + 0.580309i 0.983493 0.180947i \(-0.0579163\pi\)
−0.648451 + 0.761256i \(0.724583\pi\)
\(600\) 0 0
\(601\) 9284.95 0.630184 0.315092 0.949061i \(-0.397965\pi\)
0.315092 + 0.949061i \(0.397965\pi\)
\(602\) 302.030 8980.43i 0.0204482 0.607999i
\(603\) 0 0
\(604\) 1992.12 3450.45i 0.134202 0.232445i
\(605\) 5072.06 + 8785.07i 0.340841 + 0.590353i
\(606\) 0 0
\(607\) −1297.19 + 2246.80i −0.0867403 + 0.150239i −0.906131 0.422996i \(-0.860978\pi\)
0.819391 + 0.573235i \(0.194312\pi\)
\(608\) 1501.68 0.100166
\(609\) 0 0
\(610\) 4041.75 0.268271
\(611\) 364.759 631.782i 0.0241515 0.0418317i
\(612\) 0 0
\(613\) −242.268 419.621i −0.0159627 0.0276482i 0.857934 0.513760i \(-0.171748\pi\)
−0.873896 + 0.486112i \(0.838415\pi\)
\(614\) 9077.13 15722.1i 0.596618 1.03337i
\(615\) 0 0
\(616\) −702.166 437.506i −0.0459271 0.0286163i
\(617\) −14454.7 −0.943154 −0.471577 0.881825i \(-0.656315\pi\)
−0.471577 + 0.881825i \(0.656315\pi\)
\(618\) 0 0
\(619\) −8395.18 14540.9i −0.545122 0.944179i −0.998599 0.0529114i \(-0.983150\pi\)
0.453477 0.891268i \(-0.350183\pi\)
\(620\) −3942.80 6829.12i −0.255398 0.442362i
\(621\) 0 0
\(622\) −14480.8 −0.933487
\(623\) −696.508 + 20709.7i −0.0447914 + 1.33181i
\(624\) 0 0
\(625\) 1752.64 3035.65i 0.112169 0.194282i
\(626\) −9954.09 17241.0i −0.635536 1.10078i
\(627\) 0 0
\(628\) 4326.62 7493.93i 0.274922 0.476179i
\(629\) 19650.7 1.24567
\(630\) 0 0
\(631\) 28338.7 1.78787 0.893935 0.448197i \(-0.147934\pi\)
0.893935 + 0.448197i \(0.147934\pi\)
\(632\) −361.030 + 625.322i −0.0227231 + 0.0393575i
\(633\) 0 0
\(634\) −4551.60 7883.60i −0.285121 0.493845i
\(635\) 4878.93 8450.55i 0.304904 0.528110i
\(636\) 0 0
\(637\) 2446.51 3647.32i 0.152173 0.226864i
\(638\) 3242.61 0.201216
\(639\) 0 0
\(640\) 499.472 + 865.110i 0.0308490 + 0.0534320i
\(641\) 5183.34 + 8977.81i 0.319391 + 0.553201i 0.980361 0.197211i \(-0.0631883\pi\)
−0.660970 + 0.750412i \(0.729855\pi\)
\(642\) 0 0
\(643\) −6466.39 −0.396593 −0.198297 0.980142i \(-0.563541\pi\)
−0.198297 + 0.980142i \(0.563541\pi\)
\(644\) −2485.57 + 1325.71i −0.152089 + 0.0811182i
\(645\) 0 0
\(646\) 2245.48 3889.29i 0.136761 0.236877i
\(647\) −8156.73 14127.9i −0.495632 0.858460i 0.504355 0.863496i \(-0.331730\pi\)
−0.999987 + 0.00503632i \(0.998397\pi\)
\(648\) 0 0
\(649\) −1446.37 + 2505.19i −0.0874810 + 0.151522i
\(650\) 1641.34 0.0990443
\(651\) 0 0
\(652\) 5294.27 0.318005
\(653\) −5052.60 + 8751.35i −0.302792 + 0.524452i −0.976767 0.214302i \(-0.931252\pi\)
0.673975 + 0.738754i \(0.264586\pi\)
\(654\) 0 0
\(655\) 442.753 + 766.872i 0.0264119 + 0.0457468i
\(656\) −94.2593 + 163.262i −0.00561007 + 0.00971693i
\(657\) 0 0
\(658\) −1791.14 1116.02i −0.106118 0.0661202i
\(659\) 13873.0 0.820055 0.410028 0.912073i \(-0.365519\pi\)
0.410028 + 0.912073i \(0.365519\pi\)
\(660\) 0 0
\(661\) 11937.6 + 20676.6i 0.702452 + 1.21668i 0.967603 + 0.252475i \(0.0812446\pi\)
−0.265152 + 0.964207i \(0.585422\pi\)
\(662\) −9907.16 17159.7i −0.581651 1.00745i
\(663\) 0 0
\(664\) 2983.48 0.174370
\(665\) 5756.71 + 3586.90i 0.335693 + 0.209164i
\(666\) 0 0
\(667\) 5520.55 9561.87i 0.320474 0.555078i
\(668\) −4142.57 7175.15i −0.239942 0.415591i
\(669\) 0 0
\(670\) 1922.01 3329.03i 0.110827 0.191958i
\(671\) 1445.91 0.0831875
\(672\) 0 0
\(673\) −19177.0 −1.09839 −0.549196 0.835694i \(-0.685066\pi\)
−0.549196 + 0.835694i \(0.685066\pi\)
\(674\) −8206.45 + 14214.0i −0.468992 + 0.812318i
\(675\) 0 0
\(676\) 4066.10 + 7042.70i 0.231344 + 0.400700i
\(677\) −3088.77 + 5349.90i −0.175349 + 0.303713i −0.940282 0.340397i \(-0.889439\pi\)
0.764933 + 0.644109i \(0.222772\pi\)
\(678\) 0 0
\(679\) 6434.55 3431.94i 0.363675 0.193970i
\(680\) 2987.47 0.168477
\(681\) 0 0
\(682\) −1410.51 2443.08i −0.0791955 0.137171i
\(683\) 11887.8 + 20590.2i 0.665991 + 1.15353i 0.979015 + 0.203786i \(0.0653246\pi\)
−0.313024 + 0.949745i \(0.601342\pi\)
\(684\) 0 0
\(685\) 119.522 0.00666670
\(686\) −10307.2 7428.00i −0.573662 0.413415i
\(687\) 0 0
\(688\) −1940.69 + 3361.37i −0.107541 + 0.186266i
\(689\) −1477.22 2558.61i −0.0816799 0.141474i
\(690\) 0 0
\(691\) 4217.58 7305.06i 0.232192 0.402168i −0.726261 0.687419i \(-0.758744\pi\)
0.958453 + 0.285251i \(0.0920771\pi\)
\(692\) 12341.1 0.677946
\(693\) 0 0
\(694\) −3920.07 −0.214415
\(695\) 9910.64 17165.7i 0.540910 0.936883i
\(696\) 0 0
\(697\) 281.895 + 488.256i 0.0153193 + 0.0265338i
\(698\) 3808.47 6596.46i 0.206522 0.357707i
\(699\) 0 0
\(700\) 159.599 4745.45i 0.00861755 0.256230i
\(701\) −9383.79 −0.505594 −0.252797 0.967519i \(-0.581350\pi\)
−0.252797 + 0.967519i \(0.581350\pi\)
\(702\) 0 0
\(703\) −9635.89 16689.8i −0.516962 0.895405i
\(704\) 178.683 + 309.488i 0.00956587 + 0.0165686i
\(705\) 0 0
\(706\) 18782.0 1.00123
\(707\) 17221.4 + 10730.3i 0.916093 + 0.570800i
\(708\) 0 0
\(709\) 11425.9 19790.3i 0.605233 1.04829i −0.386782 0.922171i \(-0.626413\pi\)
0.992015 0.126122i \(-0.0402532\pi\)
\(710\) −4258.97 7376.75i −0.225121 0.389922i
\(711\) 0 0
\(712\) 4475.39 7751.61i 0.235565 0.408011i
\(713\) −9605.60 −0.504534
\(714\) 0 0
\(715\) −557.980 −0.0291850
\(716\) −2895.15 + 5014.54i −0.151113 + 0.261735i
\(717\) 0 0
\(718\) −12055.0 20879.9i −0.626585 1.08528i
\(719\) 264.286 457.757i 0.0137082 0.0237433i −0.859090 0.511825i \(-0.828970\pi\)
0.872798 + 0.488081i \(0.162303\pi\)
\(720\) 0 0
\(721\) 150.789 4483.49i 0.00778873 0.231586i
\(722\) 9313.63 0.480079
\(723\) 0 0
\(724\) 3366.33 + 5830.65i 0.172802 + 0.299302i
\(725\) 9305.00 + 16116.7i 0.476661 + 0.825601i
\(726\) 0 0
\(727\) −19525.3 −0.996083 −0.498041 0.867153i \(-0.665947\pi\)
−0.498041 + 0.867153i \(0.665947\pi\)
\(728\) −1673.90 + 892.792i −0.0852180 + 0.0454520i
\(729\) 0 0
\(730\) −2246.94 + 3891.81i −0.113922 + 0.197318i
\(731\) 5803.88 + 10052.6i 0.293659 + 0.508631i
\(732\) 0 0
\(733\) 13680.3 23695.0i 0.689351 1.19399i −0.282697 0.959209i \(-0.591229\pi\)
0.972048 0.234782i \(-0.0754377\pi\)
\(734\) 11694.7 0.588090
\(735\) 0 0
\(736\) 1216.83 0.0609417
\(737\) 687.589 1190.94i 0.0343659 0.0595235i
\(738\) 0 0
\(739\) 2265.66 + 3924.24i 0.112779 + 0.195339i 0.916890 0.399140i \(-0.130691\pi\)
−0.804111 + 0.594480i \(0.797358\pi\)
\(740\) 6409.96 11102.4i 0.318426 0.551529i
\(741\) 0 0
\(742\) −7541.09 + 4022.13i −0.373103 + 0.198999i
\(743\) 21343.8 1.05387 0.526937 0.849904i \(-0.323340\pi\)
0.526937 + 0.849904i \(0.323340\pi\)
\(744\) 0 0
\(745\) −340.145 589.148i −0.0167274 0.0289728i
\(746\) −8133.31 14087.3i −0.399171 0.691385i
\(747\) 0 0
\(748\) 1068.75 0.0522425
\(749\) −61.7092 + 1834.83i −0.00301042 + 0.0895104i
\(750\) 0 0
\(751\) −5657.26 + 9798.67i −0.274882 + 0.476110i −0.970105 0.242684i \(-0.921972\pi\)
0.695223 + 0.718794i \(0.255305\pi\)
\(752\) 455.798 + 789.465i 0.0221027 + 0.0382830i
\(753\) 0 0
\(754\) 3717.79 6439.40i 0.179568 0.311020i
\(755\) −7773.49 −0.374711
\(756\) 0 0
\(757\) −10211.6 −0.490285 −0.245142 0.969487i \(-0.578835\pi\)
−0.245142 + 0.969487i \(0.578835\pi\)
\(758\) −7913.69 + 13706.9i −0.379206 + 0.656804i
\(759\) 0 0
\(760\) −1464.93 2537.34i −0.0699194 0.121104i
\(761\) 2493.48 4318.84i 0.118776 0.205726i −0.800507 0.599324i \(-0.795436\pi\)
0.919283 + 0.393597i \(0.128770\pi\)
\(762\) 0 0
\(763\) 14447.7 + 9002.07i 0.685505 + 0.427125i
\(764\) −8376.92 −0.396684
\(765\) 0 0
\(766\) −1898.01 3287.45i −0.0895272 0.155066i
\(767\) 3316.66 + 5744.63i 0.156138 + 0.270439i
\(768\) 0 0
\(769\) −10481.8 −0.491526 −0.245763 0.969330i \(-0.579039\pi\)
−0.245763 + 0.969330i \(0.579039\pi\)
\(770\) −54.2562 + 1613.23i −0.00253930 + 0.0755022i
\(771\) 0 0
\(772\) 6838.85 11845.2i 0.318828 0.552227i
\(773\) −4818.10 8345.19i −0.224185 0.388300i 0.731890 0.681423i \(-0.238639\pi\)
−0.956075 + 0.293123i \(0.905305\pi\)
\(774\) 0 0
\(775\) 8095.23 14021.3i 0.375212 0.649886i
\(776\) −3150.10 −0.145724
\(777\) 0 0
\(778\) 3004.85 0.138469
\(779\) 276.459 478.842i 0.0127153 0.0220235i
\(780\) 0 0
\(781\) −1523.62 2638.99i −0.0698072 0.120910i
\(782\) 1819.55 3151.55i 0.0832059 0.144117i
\(783\) 0 0
\(784\) 2418.47 + 4926.37i 0.110171 + 0.224416i
\(785\) −16883.0 −0.767618
\(786\) 0 0
\(787\) 2946.89 + 5104.17i 0.133476 + 0.231187i 0.925014 0.379933i \(-0.124053\pi\)
−0.791538 + 0.611119i \(0.790720\pi\)
\(788\) 7034.15 + 12183.5i 0.317997 + 0.550786i
\(789\) 0 0
\(790\) 1408.78 0.0634458
\(791\) 34660.8 18486.7i 1.55802 0.830989i
\(792\) 0 0
\(793\) 1657.80 2871.39i 0.0742374 0.128583i
\(794\) 14655.7 + 25384.4i 0.655051 + 1.13458i
\(795\) 0 0
\(796\) 6264.13 10849.8i 0.278927 0.483117i
\(797\) 32641.4 1.45071 0.725357 0.688373i \(-0.241675\pi\)
0.725357 + 0.688373i \(0.241675\pi\)
\(798\) 0 0
\(799\) 2726.25 0.120711
\(800\) −1025.50 + 1776.22i −0.0453211 + 0.0784985i
\(801\) 0 0
\(802\) −170.289 294.949i −0.00749763 0.0129863i
\(803\) −803.829 + 1392.27i −0.0353257 + 0.0611859i
\(804\) 0 0
\(805\) 4664.75 + 2906.52i 0.204237 + 0.127256i
\(806\) −6468.86 −0.282699
\(807\) 0 0
\(808\) −4382.40 7590.54i −0.190807 0.330488i
\(809\) 9017.11 + 15618.1i 0.391872 + 0.678743i 0.992697 0.120638i \(-0.0384942\pi\)
−0.600824 + 0.799381i \(0.705161\pi\)
\(810\) 0 0
\(811\) 39379.6 1.70506 0.852531 0.522677i \(-0.175067\pi\)
0.852531 + 0.522677i \(0.175067\pi\)
\(812\) −18256.1 11375.0i −0.788993 0.491606i
\(813\) 0 0
\(814\) 2293.13 3971.81i 0.0987396 0.171022i
\(815\) −5164.72 8945.56i −0.221978 0.384477i
\(816\) 0 0
\(817\) 5691.97 9858.79i 0.243742 0.422173i
\(818\) 22932.6 0.980220
\(819\) 0 0
\(820\) 367.811 0.0156641
\(821\) 13818.4 23934.2i 0.587413 1.01743i −0.407157 0.913358i \(-0.633480\pi\)
0.994570 0.104071i \(-0.0331870\pi\)
\(822\) 0 0
\(823\) −4696.30 8134.24i −0.198910 0.344522i 0.749265 0.662270i \(-0.230407\pi\)
−0.948175 + 0.317748i \(0.897073\pi\)
\(824\) −968.890 + 1678.17i −0.0409622 + 0.0709487i
\(825\) 0 0
\(826\) 16931.4 9030.54i 0.713217 0.380403i
\(827\) −40070.2 −1.68486 −0.842428 0.538809i \(-0.818874\pi\)
−0.842428 + 0.538809i \(0.818874\pi\)
\(828\) 0 0
\(829\) −14119.9 24456.5i −0.591563 1.02462i −0.994022 0.109180i \(-0.965178\pi\)
0.402459 0.915438i \(-0.368156\pi\)
\(830\) −2910.48 5041.09i −0.121716 0.210818i
\(831\) 0 0
\(832\) 819.472 0.0341467
\(833\) 16375.5 + 1102.73i 0.681126 + 0.0458672i
\(834\) 0 0
\(835\) −8082.41 + 13999.1i −0.334974 + 0.580192i
\(836\) −524.071 907.718i −0.0216811 0.0375527i
\(837\) 0 0
\(838\) −9329.18 + 16158.6i −0.384572 + 0.666098i
\(839\) −24586.0 −1.01168 −0.505842 0.862626i \(-0.668818\pi\)
−0.505842 + 0.862626i \(0.668818\pi\)
\(840\) 0 0
\(841\) 59917.6 2.45675
\(842\) 4184.24 7247.32i 0.171257 0.296626i
\(843\) 0 0
\(844\) 6176.76 + 10698.5i 0.251911 + 0.436323i
\(845\) 7933.22 13740.7i 0.322971 0.559403i
\(846\) 0 0
\(847\) 809.168 24059.4i 0.0328256 0.976023i
\(848\) 3691.82 0.149502
\(849\) 0 0
\(850\) 3066.89 + 5312.02i 0.123757 + 0.214354i
\(851\) −7808.11 13524.0i −0.314522 0.544769i
\(852\) 0 0
\(853\) −150.549 −0.00604303 −0.00302151 0.999995i \(-0.500962\pi\)
−0.00302151 + 0.999995i \(0.500962\pi\)
\(854\) −8140.57 5072.23i −0.326188 0.203241i
\(855\) 0 0
\(856\) 396.510 686.776i 0.0158323 0.0274223i
\(857\) 4332.63 + 7504.33i 0.172695 + 0.299117i 0.939361 0.342929i \(-0.111419\pi\)
−0.766666 + 0.642046i \(0.778086\pi\)
\(858\) 0 0
\(859\) 8006.96 13868.5i 0.318037 0.550856i −0.662041 0.749467i \(-0.730310\pi\)
0.980078 + 0.198611i \(0.0636430\pi\)
\(860\) 7572.80 0.300268
\(861\) 0 0
\(862\) 14573.6 0.575846
\(863\) −19339.0 + 33496.2i −0.762814 + 1.32123i 0.178580 + 0.983925i \(0.442850\pi\)
−0.941394 + 0.337308i \(0.890484\pi\)
\(864\) 0 0
\(865\) −12039.1 20852.4i −0.473229 0.819656i
\(866\) −5314.89 + 9205.66i −0.208554 + 0.361225i
\(867\) 0 0
\(868\) −629.011 + 18702.7i −0.0245968 + 0.731350i
\(869\) 503.983 0.0196737
\(870\) 0 0
\(871\) −1576.70 2730.93i −0.0613370 0.106239i
\(872\) −3676.56 6367.98i −0.142780 0.247302i
\(873\) 0 0
\(874\) −3568.93 −0.138125
\(875\) −24115.3 + 12862.2i −0.931709 + 0.496938i
\(876\) 0 0
\(877\) −14169.4 + 24542.2i −0.545573 + 0.944961i 0.452997 + 0.891512i \(0.350355\pi\)
−0.998571 + 0.0534489i \(0.982979\pi\)
\(878\) 8546.10 + 14802.3i 0.328493 + 0.568967i
\(879\) 0 0
\(880\) 348.622 603.830i 0.0133546 0.0231308i
\(881\) −37656.8 −1.44006 −0.720028 0.693945i \(-0.755871\pi\)
−0.720028 + 0.693945i \(0.755871\pi\)
\(882\) 0 0
\(883\) 41858.7 1.59531 0.797655 0.603114i \(-0.206074\pi\)
0.797655 + 0.603114i \(0.206074\pi\)
\(884\) 1225.37 2122.40i 0.0466218 0.0807512i
\(885\) 0 0
\(886\) −10796.5 18700.1i −0.409386 0.709078i
\(887\) −20573.8 + 35634.8i −0.778805 + 1.34893i 0.153826 + 0.988098i \(0.450841\pi\)
−0.932631 + 0.360832i \(0.882493\pi\)
\(888\) 0 0
\(889\) −20431.9 + 10897.6i −0.770824 + 0.411128i
\(890\) −17463.5 −0.657729
\(891\) 0 0
\(892\) −8799.58 15241.3i −0.330305 0.572104i
\(893\) −1336.84 2315.48i −0.0500959 0.0867687i
\(894\) 0 0
\(895\) 11297.2 0.421926
\(896\) 79.6829 2369.25i 0.00297100 0.0883384i
\(897\) 0 0
\(898\) −3617.92 + 6266.41i −0.134445 + 0.232865i
\(899\) −36672.8 63519.2i −1.36052 2.35649i
\(900\) 0 0
\(901\) 5520.43 9561.67i 0.204120 0.353546i
\(902\) 131.582 0.00485722
\(903\) 0 0
\(904\) −16968.5 −0.624297
\(905\) 6567.91 11376.0i 0.241243 0.417845i
\(906\) 0 0
\(907\) −5874.59 10175.1i −0.215064 0.372501i 0.738229 0.674551i \(-0.235663\pi\)
−0.953292 + 0.302050i \(0.902329\pi\)
\(908\) −6574.76 + 11387.8i −0.240299 + 0.416210i
\(909\) 0 0
\(910\) 3141.46 + 1957.38i 0.114438 + 0.0713040i
\(911\) 48408.6 1.76054 0.880268 0.474477i \(-0.157363\pi\)
0.880268 + 0.474477i \(0.157363\pi\)
\(912\) 0 0
\(913\) −1041.21 1803.42i −0.0377425 0.0653719i
\(914\) −7099.34 12296.4i −0.256920 0.444999i
\(915\) 0 0
\(916\) 12054.0 0.434800
\(917\) 70.6344 2100.21i 0.00254368 0.0756325i
\(918\) 0 0
\(919\) 5070.66 8782.64i 0.182008 0.315248i −0.760556 0.649272i \(-0.775074\pi\)
0.942564 + 0.334025i \(0.108407\pi\)
\(920\) −1187.06 2056.05i −0.0425393 0.0736802i
\(921\) 0 0
\(922\) −16652.8 + 28843.6i −0.594829 + 1.03027i
\(923\) −6987.59 −0.249187
\(924\) 0 0
\(925\) 26321.5 0.935616
\(926\) −15394.4 + 26664.0i −0.546321 + 0.946255i
\(927\) 0 0
\(928\) 4645.70 + 8046.58i 0.164335 + 0.284636i
\(929\) 6798.05 11774.6i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894921\pi\)
\(930\) 0 0
\(931\) −7093.30 14448.9i −0.249703 0.508639i
\(932\) 20326.4 0.714393
\(933\) 0 0
\(934\) −16615.7 28779.2i −0.582100 1.00823i
\(935\) −1042.60 1805.83i −0.0364670 0.0631627i
\(936\) 0 0
\(937\) −46027.4 −1.60475 −0.802374 0.596822i \(-0.796430\pi\)
−0.802374 + 0.596822i \(0.796430\pi\)
\(938\) −8048.97 + 4293.01i −0.280179 + 0.149437i
\(939\) 0 0
\(940\) 889.290 1540.30i 0.0308568 0.0534456i
\(941\) −253.733 439.478i −0.00879006 0.0152248i 0.861597 0.507593i \(-0.169465\pi\)
−0.870387 + 0.492368i \(0.836131\pi\)
\(942\) 0 0
\(943\) 224.019 388.013i 0.00773603 0.0133992i
\(944\) −8288.91 −0.285785
\(945\) 0 0
\(946\) 2709.13 0.0931091
\(947\) −602.414 + 1043.41i −0.0206714 + 0.0358039i −0.876176 0.481991i \(-0.839914\pi\)
0.855505 + 0.517795i \(0.173247\pi\)
\(948\) 0 0
\(949\) 1843.25 + 3192.60i 0.0630500 + 0.109206i
\(950\) 3007.76 5209.59i 0.102721 0.177917i
\(951\) 0 0
\(952\) −6017.13 3749.16i −0.204849 0.127638i
\(953\) −18606.2 −0.632437 −0.316219 0.948686i \(-0.602413\pi\)
−0.316219 + 0.948686i \(0.602413\pi\)
\(954\) 0 0
\(955\) 8171.94 + 14154.2i 0.276898 + 0.479602i
\(956\) −6174.76 10695.0i −0.208898 0.361821i
\(957\) 0 0
\(958\) 3356.75 0.113206
\(959\) −240.731 149.995i −0.00810596 0.00505067i
\(960\) 0 0
\(961\) −17009.4 + 29461.1i −0.570956 + 0.988926i
\(962\) −5258.34 9107.71i −0.176233 0.305244i
\(963\) 0 0
\(964\) 2433.30 4214.60i 0.0812981 0.140812i
\(965\) −26686.0 −0.890211
\(966\) 0 0
\(967\) −39645.1 −1.31841 −0.659204 0.751964i \(-0.729107\pi\)
−0.659204 + 0.751964i \(0.729107\pi\)
\(968\) −5199.28 + 9005.42i −0.172636 + 0.299014i
\(969\) 0 0
\(970\) 3073.02 + 5322.62i 0.101720 + 0.176185i
\(971\) −26704.0 + 46252.7i −0.882567 + 1.52865i −0.0340898 + 0.999419i \(0.510853\pi\)
−0.848477 + 0.529232i \(0.822480\pi\)
\(972\) 0 0
\(973\) −41503.5 + 22136.4i −1.36746 + 0.729353i
\(974\) 18917.8 0.622345
\(975\) 0 0
\(976\) 2071.56 + 3588.05i 0.0679397 + 0.117675i
\(977\) −11856.7 20536.4i −0.388259 0.672484i 0.603957 0.797017i \(-0.293590\pi\)
−0.992215 + 0.124533i \(0.960257\pi\)
\(978\) 0 0
\(979\) −6247.48 −0.203953
\(980\) 5964.64 8892.24i 0.194422 0.289849i
\(981\) 0 0
\(982\) −12084.6 + 20931.1i −0.392703 + 0.680181i
\(983\) 26074.2 + 45161.8i 0.846020 + 1.46535i 0.884733 + 0.466099i \(0.154341\pi\)
−0.0387129 + 0.999250i \(0.512326\pi\)
\(984\) 0 0
\(985\) 13724.1 23770.8i 0.443944 0.768934i
\(986\) 27787.1 0.897488
\(987\) 0 0
\(988\) −2403.48 −0.0773937
\(989\) 4612.29 7988.73i 0.148294 0.256852i
\(990\) 0 0
\(991\) 6416.26 + 11113.3i 0.205670 + 0.356231i 0.950346 0.311195i \(-0.100729\pi\)
−0.744676 + 0.667426i \(0.767396\pi\)
\(992\) 4041.69 7000.42i 0.129359 0.224056i
\(993\) 0 0
\(994\) −679.451 + 20202.5i −0.0216810 + 0.644652i
\(995\) −24443.4 −0.778802
\(996\) 0 0
\(997\) −11795.0 20429.5i −0.374675 0.648955i 0.615604 0.788056i \(-0.288912\pi\)
−0.990278 + 0.139100i \(0.955579\pi\)
\(998\) 11152.7 + 19317.0i 0.353739 + 0.612693i
\(999\) 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 378.4.g.b.163.1 yes 6
3.2 odd 2 378.4.g.a.163.3 yes 6
7.4 even 3 inner 378.4.g.b.109.1 yes 6
21.11 odd 6 378.4.g.a.109.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.4.g.a.109.3 6 21.11 odd 6
378.4.g.a.163.3 yes 6 3.2 odd 2
378.4.g.b.109.1 yes 6 7.4 even 3 inner
378.4.g.b.163.1 yes 6 1.1 even 1 trivial