Properties

Label 117.4.g.f.100.1
Level $117$
Weight $4$
Character 117.100
Analytic conductor $6.903$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,4,Mod(55,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.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: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + 21016320 x^{2} + 24920064 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.1
Root \(-2.69794 + 4.67298i\) of defining polynomial
Character \(\chi\) \(=\) 117.100
Dual form 117.4.g.f.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.69794 + 4.67298i) q^{2} +(-10.5578 - 18.2867i) q^{4} +13.0421 q^{5} +(3.21247 + 5.56416i) q^{7} +70.7705 q^{8} +O(q^{10})\) \(q+(-2.69794 + 4.67298i) q^{2} +(-10.5578 - 18.2867i) q^{4} +13.0421 q^{5} +(3.21247 + 5.56416i) q^{7} +70.7705 q^{8} +(-35.1870 + 60.9457i) q^{10} +(-13.1028 + 22.6947i) q^{11} +(43.2448 + 18.0800i) q^{13} -34.6683 q^{14} +(-106.472 + 184.416i) q^{16} +(61.9384 + 107.280i) q^{17} +(-54.8333 - 94.9741i) q^{19} +(-137.697 - 238.497i) q^{20} +(-70.7012 - 122.458i) q^{22} +(31.7047 - 54.9141i) q^{23} +45.0976 q^{25} +(-201.160 + 153.303i) q^{26} +(67.8333 - 117.491i) q^{28} +(-112.705 + 195.211i) q^{29} +200.732 q^{31} +(-291.431 - 504.774i) q^{32} -668.426 q^{34} +(41.8975 + 72.5686i) q^{35} +(-126.254 + 218.679i) q^{37} +591.749 q^{38} +922.999 q^{40} +(-113.712 + 196.955i) q^{41} +(192.016 + 332.581i) q^{43} +553.348 q^{44} +(171.075 + 296.311i) q^{46} +34.6646 q^{47} +(150.860 - 261.297i) q^{49} +(-121.671 + 210.740i) q^{50} +(-125.948 - 981.689i) q^{52} -61.0601 q^{53} +(-170.889 + 295.988i) q^{55} +(227.348 + 393.778i) q^{56} +(-608.144 - 1053.34i) q^{58} +(40.2781 + 69.7637i) q^{59} +(13.0692 + 22.6364i) q^{61} +(-541.563 + 938.014i) q^{62} +1441.50 q^{64} +(564.005 + 235.802i) q^{65} +(465.755 - 806.711i) q^{67} +(1307.87 - 2265.29i) q^{68} -452.149 q^{70} +(-213.804 - 370.320i) q^{71} +108.518 q^{73} +(-681.255 - 1179.97i) q^{74} +(-1157.84 + 2005.44i) q^{76} -168.369 q^{77} +384.590 q^{79} +(-1388.63 + 2405.17i) q^{80} +(-613.576 - 1062.74i) q^{82} -85.9758 q^{83} +(807.810 + 1399.17i) q^{85} -2072.19 q^{86} +(-927.291 + 1606.12i) q^{88} +(247.952 - 429.465i) q^{89} +(38.3226 + 298.703i) q^{91} -1338.93 q^{92} +(-93.5232 + 161.987i) q^{94} +(-715.144 - 1238.67i) q^{95} +(-95.4286 - 165.287i) q^{97} +(814.024 + 1409.93i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69794 + 4.67298i −0.953868 + 1.65215i −0.216929 + 0.976187i \(0.569604\pi\)
−0.736939 + 0.675960i \(0.763729\pi\)
\(3\) 0 0
\(4\) −10.5578 18.2867i −1.31973 2.28583i
\(5\) 13.0421 1.16653 0.583263 0.812284i \(-0.301776\pi\)
0.583263 + 0.812284i \(0.301776\pi\)
\(6\) 0 0
\(7\) 3.21247 + 5.56416i 0.173457 + 0.300437i 0.939626 0.342202i \(-0.111173\pi\)
−0.766169 + 0.642639i \(0.777840\pi\)
\(8\) 70.7705 3.12764
\(9\) 0 0
\(10\) −35.1870 + 60.9457i −1.11271 + 1.92727i
\(11\) −13.1028 + 22.6947i −0.359149 + 0.622065i −0.987819 0.155608i \(-0.950266\pi\)
0.628670 + 0.777672i \(0.283600\pi\)
\(12\) 0 0
\(13\) 43.2448 + 18.0800i 0.922612 + 0.385730i
\(14\) −34.6683 −0.661820
\(15\) 0 0
\(16\) −106.472 + 184.416i −1.66363 + 2.88149i
\(17\) 61.9384 + 107.280i 0.883663 + 1.53055i 0.847239 + 0.531213i \(0.178263\pi\)
0.0364243 + 0.999336i \(0.488403\pi\)
\(18\) 0 0
\(19\) −54.8333 94.9741i −0.662086 1.14677i −0.980067 0.198669i \(-0.936338\pi\)
0.317981 0.948097i \(-0.396995\pi\)
\(20\) −137.697 238.497i −1.53949 2.66648i
\(21\) 0 0
\(22\) −70.7012 122.458i −0.685162 1.18673i
\(23\) 31.7047 54.9141i 0.287430 0.497843i −0.685766 0.727822i \(-0.740533\pi\)
0.973196 + 0.229979i \(0.0738658\pi\)
\(24\) 0 0
\(25\) 45.0976 0.360781
\(26\) −201.160 + 153.303i −1.51733 + 1.15635i
\(27\) 0 0
\(28\) 67.8333 117.491i 0.457832 0.792988i
\(29\) −112.705 + 195.211i −0.721683 + 1.24999i 0.238642 + 0.971108i \(0.423298\pi\)
−0.960325 + 0.278884i \(0.910036\pi\)
\(30\) 0 0
\(31\) 200.732 1.16298 0.581491 0.813553i \(-0.302470\pi\)
0.581491 + 0.813553i \(0.302470\pi\)
\(32\) −291.431 504.774i −1.60995 2.78851i
\(33\) 0 0
\(34\) −668.426 −3.37159
\(35\) 41.8975 + 72.5686i 0.202342 + 0.350467i
\(36\) 0 0
\(37\) −126.254 + 218.679i −0.560976 + 0.971638i 0.436436 + 0.899735i \(0.356241\pi\)
−0.997412 + 0.0719031i \(0.977093\pi\)
\(38\) 591.749 2.52617
\(39\) 0 0
\(40\) 922.999 3.64847
\(41\) −113.712 + 196.955i −0.433141 + 0.750223i −0.997142 0.0755517i \(-0.975928\pi\)
0.564001 + 0.825774i \(0.309262\pi\)
\(42\) 0 0
\(43\) 192.016 + 332.581i 0.680980 + 1.17949i 0.974682 + 0.223595i \(0.0717794\pi\)
−0.293702 + 0.955897i \(0.594887\pi\)
\(44\) 553.348 1.89592
\(45\) 0 0
\(46\) 171.075 + 296.311i 0.548340 + 0.949753i
\(47\) 34.6646 0.107582 0.0537910 0.998552i \(-0.482870\pi\)
0.0537910 + 0.998552i \(0.482870\pi\)
\(48\) 0 0
\(49\) 150.860 261.297i 0.439825 0.761800i
\(50\) −121.671 + 210.740i −0.344137 + 0.596063i
\(51\) 0 0
\(52\) −125.948 981.689i −0.335881 2.61800i
\(53\) −61.0601 −0.158250 −0.0791251 0.996865i \(-0.525213\pi\)
−0.0791251 + 0.996865i \(0.525213\pi\)
\(54\) 0 0
\(55\) −170.889 + 295.988i −0.418957 + 0.725654i
\(56\) 227.348 + 393.778i 0.542512 + 0.939658i
\(57\) 0 0
\(58\) −608.144 1053.34i −1.37678 2.38465i
\(59\) 40.2781 + 69.7637i 0.0888774 + 0.153940i 0.907037 0.421051i \(-0.138339\pi\)
−0.818159 + 0.574991i \(0.805005\pi\)
\(60\) 0 0
\(61\) 13.0692 + 22.6364i 0.0274317 + 0.0475131i 0.879415 0.476055i \(-0.157934\pi\)
−0.851984 + 0.523568i \(0.824600\pi\)
\(62\) −541.563 + 938.014i −1.10933 + 1.92142i
\(63\) 0 0
\(64\) 1441.50 2.81544
\(65\) 564.005 + 235.802i 1.07625 + 0.449964i
\(66\) 0 0
\(67\) 465.755 806.711i 0.849269 1.47098i −0.0325921 0.999469i \(-0.510376\pi\)
0.881861 0.471509i \(-0.156290\pi\)
\(68\) 1307.87 2265.29i 2.33239 4.03981i
\(69\) 0 0
\(70\) −452.149 −0.772030
\(71\) −213.804 370.320i −0.357379 0.618998i 0.630143 0.776479i \(-0.282996\pi\)
−0.987522 + 0.157481i \(0.949663\pi\)
\(72\) 0 0
\(73\) 108.518 0.173987 0.0869935 0.996209i \(-0.472274\pi\)
0.0869935 + 0.996209i \(0.472274\pi\)
\(74\) −681.255 1179.97i −1.07019 1.85363i
\(75\) 0 0
\(76\) −1157.84 + 2005.44i −1.74754 + 3.02684i
\(77\) −168.369 −0.249188
\(78\) 0 0
\(79\) 384.590 0.547718 0.273859 0.961770i \(-0.411700\pi\)
0.273859 + 0.961770i \(0.411700\pi\)
\(80\) −1388.63 + 2405.17i −1.94067 + 3.36133i
\(81\) 0 0
\(82\) −613.576 1062.74i −0.826319 1.43123i
\(83\) −85.9758 −0.113700 −0.0568498 0.998383i \(-0.518106\pi\)
−0.0568498 + 0.998383i \(0.518106\pi\)
\(84\) 0 0
\(85\) 807.810 + 1399.17i 1.03081 + 1.78542i
\(86\) −2072.19 −2.59826
\(87\) 0 0
\(88\) −927.291 + 1606.12i −1.12329 + 1.94560i
\(89\) 247.952 429.465i 0.295313 0.511497i −0.679745 0.733449i \(-0.737910\pi\)
0.975058 + 0.221952i \(0.0712428\pi\)
\(90\) 0 0
\(91\) 38.3226 + 298.703i 0.0441462 + 0.344094i
\(92\) −1338.93 −1.51732
\(93\) 0 0
\(94\) −93.5232 + 161.987i −0.102619 + 0.177741i
\(95\) −715.144 1238.67i −0.772340 1.33773i
\(96\) 0 0
\(97\) −95.4286 165.287i −0.0998898 0.173014i 0.811749 0.584006i \(-0.198516\pi\)
−0.911639 + 0.410992i \(0.865182\pi\)
\(98\) 814.024 + 1409.93i 0.839070 + 1.45331i
\(99\) 0 0
\(100\) −476.132 824.685i −0.476132 0.824685i
\(101\) 425.490 736.970i 0.419186 0.726052i −0.576671 0.816976i \(-0.695649\pi\)
0.995858 + 0.0909241i \(0.0289821\pi\)
\(102\) 0 0
\(103\) −1309.50 −1.25270 −0.626352 0.779540i \(-0.715453\pi\)
−0.626352 + 0.779540i \(0.715453\pi\)
\(104\) 3060.46 + 1279.53i 2.88560 + 1.20643i
\(105\) 0 0
\(106\) 164.737 285.333i 0.150950 0.261452i
\(107\) 481.151 833.378i 0.434716 0.752951i −0.562556 0.826759i \(-0.690182\pi\)
0.997272 + 0.0738085i \(0.0235153\pi\)
\(108\) 0 0
\(109\) 891.973 0.783812 0.391906 0.920005i \(-0.371816\pi\)
0.391906 + 0.920005i \(0.371816\pi\)
\(110\) −922.096 1597.12i −0.799258 1.38436i
\(111\) 0 0
\(112\) −1368.16 −1.15427
\(113\) 131.920 + 228.491i 0.109823 + 0.190218i 0.915698 0.401867i \(-0.131638\pi\)
−0.805876 + 0.592085i \(0.798305\pi\)
\(114\) 0 0
\(115\) 413.497 716.198i 0.335294 0.580746i
\(116\) 4759.68 3.80970
\(117\) 0 0
\(118\) −434.673 −0.339109
\(119\) −397.951 + 689.271i −0.306555 + 0.530969i
\(120\) 0 0
\(121\) 322.133 + 557.952i 0.242024 + 0.419197i
\(122\) −141.039 −0.104665
\(123\) 0 0
\(124\) −2119.29 3670.71i −1.53482 2.65838i
\(125\) −1042.10 −0.745665
\(126\) 0 0
\(127\) 771.986 1337.12i 0.539391 0.934252i −0.459546 0.888154i \(-0.651988\pi\)
0.998937 0.0460984i \(-0.0146788\pi\)
\(128\) −1557.65 + 2697.93i −1.07561 + 1.86301i
\(129\) 0 0
\(130\) −2623.55 + 1999.40i −1.77001 + 1.34892i
\(131\) 776.790 0.518080 0.259040 0.965867i \(-0.416594\pi\)
0.259040 + 0.965867i \(0.416594\pi\)
\(132\) 0 0
\(133\) 352.301 610.203i 0.229687 0.397829i
\(134\) 2513.16 + 4352.93i 1.62018 + 2.80624i
\(135\) 0 0
\(136\) 4383.41 + 7592.29i 2.76378 + 4.78701i
\(137\) −1217.36 2108.52i −0.759166 1.31491i −0.943276 0.332009i \(-0.892274\pi\)
0.184110 0.982906i \(-0.441060\pi\)
\(138\) 0 0
\(139\) −625.700 1083.74i −0.381807 0.661310i 0.609513 0.792776i \(-0.291365\pi\)
−0.991321 + 0.131466i \(0.958032\pi\)
\(140\) 884.692 1532.33i 0.534072 0.925041i
\(141\) 0 0
\(142\) 2307.33 1.36357
\(143\) −976.948 + 744.530i −0.571304 + 0.435390i
\(144\) 0 0
\(145\) −1469.92 + 2545.97i −0.841861 + 1.45815i
\(146\) −292.775 + 507.101i −0.165961 + 0.287452i
\(147\) 0 0
\(148\) 5331.88 2.96134
\(149\) −391.810 678.634i −0.215425 0.373127i 0.737979 0.674824i \(-0.235780\pi\)
−0.953404 + 0.301697i \(0.902447\pi\)
\(150\) 0 0
\(151\) 162.220 0.0874255 0.0437128 0.999044i \(-0.486081\pi\)
0.0437128 + 0.999044i \(0.486081\pi\)
\(152\) −3880.58 6721.37i −2.07077 3.58668i
\(153\) 0 0
\(154\) 454.251 786.786i 0.237692 0.411695i
\(155\) 2617.97 1.35665
\(156\) 0 0
\(157\) −2355.76 −1.19752 −0.598758 0.800930i \(-0.704339\pi\)
−0.598758 + 0.800930i \(0.704339\pi\)
\(158\) −1037.60 + 1797.18i −0.522451 + 0.904911i
\(159\) 0 0
\(160\) −3800.89 6583.33i −1.87804 3.25286i
\(161\) 407.402 0.199427
\(162\) 0 0
\(163\) −787.143 1363.37i −0.378244 0.655138i 0.612563 0.790422i \(-0.290139\pi\)
−0.990807 + 0.135284i \(0.956805\pi\)
\(164\) 4802.19 2.28651
\(165\) 0 0
\(166\) 231.958 401.763i 0.108454 0.187849i
\(167\) −1787.28 + 3095.66i −0.828166 + 1.43443i 0.0713090 + 0.997454i \(0.477282\pi\)
−0.899475 + 0.436972i \(0.856051\pi\)
\(168\) 0 0
\(169\) 1543.23 + 1563.73i 0.702425 + 0.711758i
\(170\) −8717.70 −3.93304
\(171\) 0 0
\(172\) 4054.54 7022.66i 1.79742 3.11322i
\(173\) −0.720540 1.24801i −0.000316657 0.000548466i 0.865867 0.500274i \(-0.166767\pi\)
−0.866184 + 0.499726i \(0.833434\pi\)
\(174\) 0 0
\(175\) 144.875 + 250.930i 0.0625800 + 0.108392i
\(176\) −2790.17 4832.72i −1.19498 2.06977i
\(177\) 0 0
\(178\) 1337.92 + 2317.35i 0.563378 + 0.975800i
\(179\) 1041.14 1803.30i 0.434739 0.752990i −0.562535 0.826773i \(-0.690174\pi\)
0.997274 + 0.0737830i \(0.0235072\pi\)
\(180\) 0 0
\(181\) −464.500 −0.190751 −0.0953756 0.995441i \(-0.530405\pi\)
−0.0953756 + 0.995441i \(0.530405\pi\)
\(182\) −1499.22 626.802i −0.610603 0.255284i
\(183\) 0 0
\(184\) 2243.76 3886.30i 0.898978 1.55708i
\(185\) −1646.63 + 2852.04i −0.654392 + 1.13344i
\(186\) 0 0
\(187\) −3246.26 −1.26947
\(188\) −365.982 633.900i −0.141979 0.245914i
\(189\) 0 0
\(190\) 7717.68 2.94684
\(191\) 2433.14 + 4214.32i 0.921758 + 1.59653i 0.796693 + 0.604384i \(0.206581\pi\)
0.125065 + 0.992149i \(0.460086\pi\)
\(192\) 0 0
\(193\) 428.169 741.611i 0.159691 0.276592i −0.775066 0.631880i \(-0.782284\pi\)
0.934757 + 0.355287i \(0.115617\pi\)
\(194\) 1029.84 0.381127
\(195\) 0 0
\(196\) −6371.01 −2.32180
\(197\) 785.965 1361.33i 0.284252 0.492339i −0.688175 0.725544i \(-0.741588\pi\)
0.972428 + 0.233205i \(0.0749214\pi\)
\(198\) 0 0
\(199\) −1563.30 2707.72i −0.556883 0.964549i −0.997754 0.0669791i \(-0.978664\pi\)
0.440872 0.897570i \(-0.354669\pi\)
\(200\) 3191.58 1.12839
\(201\) 0 0
\(202\) 2295.90 + 3976.61i 0.799697 + 1.38512i
\(203\) −1448.25 −0.500724
\(204\) 0 0
\(205\) −1483.05 + 2568.71i −0.505270 + 0.875153i
\(206\) 3532.95 6119.25i 1.19491 2.06965i
\(207\) 0 0
\(208\) −7938.61 + 6050.00i −2.64636 + 2.01679i
\(209\) 2873.88 0.951150
\(210\) 0 0
\(211\) −61.6959 + 106.860i −0.0201295 + 0.0348653i −0.875915 0.482466i \(-0.839741\pi\)
0.855785 + 0.517331i \(0.173075\pi\)
\(212\) 644.662 + 1116.59i 0.208847 + 0.361733i
\(213\) 0 0
\(214\) 2596.24 + 4496.82i 0.829323 + 1.43643i
\(215\) 2504.30 + 4337.57i 0.794380 + 1.37591i
\(216\) 0 0
\(217\) 644.844 + 1116.90i 0.201728 + 0.349402i
\(218\) −2406.49 + 4168.17i −0.747653 + 1.29497i
\(219\) 0 0
\(220\) 7216.84 2.21163
\(221\) 738.884 + 5759.17i 0.224899 + 1.75296i
\(222\) 0 0
\(223\) 1251.84 2168.26i 0.375918 0.651109i −0.614546 0.788881i \(-0.710661\pi\)
0.990464 + 0.137772i \(0.0439941\pi\)
\(224\) 1872.43 3243.14i 0.558513 0.967373i
\(225\) 0 0
\(226\) −1423.65 −0.419025
\(227\) −289.635 501.662i −0.0846861 0.146681i 0.820571 0.571544i \(-0.193655\pi\)
−0.905257 + 0.424864i \(0.860322\pi\)
\(228\) 0 0
\(229\) −768.922 −0.221886 −0.110943 0.993827i \(-0.535387\pi\)
−0.110943 + 0.993827i \(0.535387\pi\)
\(230\) 2231.19 + 3864.53i 0.639652 + 1.10791i
\(231\) 0 0
\(232\) −7976.19 + 13815.2i −2.25717 + 3.90953i
\(233\) 845.695 0.237783 0.118891 0.992907i \(-0.462066\pi\)
0.118891 + 0.992907i \(0.462066\pi\)
\(234\) 0 0
\(235\) 452.101 0.125497
\(236\) 850.498 1473.11i 0.234588 0.406318i
\(237\) 0 0
\(238\) −2147.30 3719.23i −0.584826 1.01295i
\(239\) −6552.78 −1.77349 −0.886744 0.462260i \(-0.847039\pi\)
−0.886744 + 0.462260i \(0.847039\pi\)
\(240\) 0 0
\(241\) −2588.38 4483.20i −0.691834 1.19829i −0.971236 0.238118i \(-0.923470\pi\)
0.279402 0.960174i \(-0.409864\pi\)
\(242\) −3476.39 −0.923434
\(243\) 0 0
\(244\) 275.963 477.983i 0.0724047 0.125409i
\(245\) 1967.54 3407.88i 0.513067 0.888658i
\(246\) 0 0
\(247\) −654.125 5098.52i −0.168506 1.31341i
\(248\) 14205.9 3.63739
\(249\) 0 0
\(250\) 2811.53 4869.70i 0.711266 1.23195i
\(251\) −2148.41 3721.15i −0.540264 0.935765i −0.998889 0.0471349i \(-0.984991\pi\)
0.458624 0.888630i \(-0.348342\pi\)
\(252\) 0 0
\(253\) 830.840 + 1439.06i 0.206460 + 0.357600i
\(254\) 4165.55 + 7214.94i 1.02901 + 1.78231i
\(255\) 0 0
\(256\) −2638.88 4570.68i −0.644259 1.11589i
\(257\) 691.970 1198.53i 0.167953 0.290903i −0.769747 0.638349i \(-0.779618\pi\)
0.937700 + 0.347446i \(0.112951\pi\)
\(258\) 0 0
\(259\) −1622.35 −0.389221
\(260\) −1642.63 12803.3i −0.391813 3.05396i
\(261\) 0 0
\(262\) −2095.74 + 3629.92i −0.494180 + 0.855944i
\(263\) 1239.34 2146.60i 0.290574 0.503288i −0.683372 0.730070i \(-0.739487\pi\)
0.973945 + 0.226782i \(0.0728206\pi\)
\(264\) 0 0
\(265\) −796.355 −0.184603
\(266\) 1900.98 + 3292.59i 0.438182 + 0.758953i
\(267\) 0 0
\(268\) −19669.4 −4.48321
\(269\) 1226.32 + 2124.05i 0.277956 + 0.481433i 0.970877 0.239580i \(-0.0770099\pi\)
−0.692921 + 0.721014i \(0.743677\pi\)
\(270\) 0 0
\(271\) 2990.37 5179.47i 0.670302 1.16100i −0.307516 0.951543i \(-0.599498\pi\)
0.977818 0.209455i \(-0.0671689\pi\)
\(272\) −26378.9 −5.88036
\(273\) 0 0
\(274\) 13137.4 2.89658
\(275\) −590.905 + 1023.48i −0.129574 + 0.224429i
\(276\) 0 0
\(277\) 3689.00 + 6389.53i 0.800182 + 1.38596i 0.919496 + 0.393099i \(0.128597\pi\)
−0.119314 + 0.992857i \(0.538070\pi\)
\(278\) 6752.42 1.45677
\(279\) 0 0
\(280\) 2965.11 + 5135.72i 0.632854 + 1.09613i
\(281\) −5937.17 −1.26043 −0.630217 0.776419i \(-0.717034\pi\)
−0.630217 + 0.776419i \(0.717034\pi\)
\(282\) 0 0
\(283\) −743.259 + 1287.36i −0.156121 + 0.270409i −0.933467 0.358664i \(-0.883232\pi\)
0.777346 + 0.629074i \(0.216566\pi\)
\(284\) −4514.61 + 7819.53i −0.943284 + 1.63382i
\(285\) 0 0
\(286\) −843.419 6573.96i −0.174379 1.35918i
\(287\) −1461.18 −0.300526
\(288\) 0 0
\(289\) −5216.23 + 9034.78i −1.06172 + 1.83895i
\(290\) −7931.50 13737.8i −1.60605 2.78176i
\(291\) 0 0
\(292\) −1145.71 1984.43i −0.229615 0.397705i
\(293\) −1790.02 3100.41i −0.356909 0.618185i 0.630534 0.776162i \(-0.282836\pi\)
−0.987443 + 0.157977i \(0.949503\pi\)
\(294\) 0 0
\(295\) 525.313 + 909.869i 0.103678 + 0.179575i
\(296\) −8935.09 + 15476.0i −1.75453 + 3.03894i
\(297\) 0 0
\(298\) 4228.32 0.821947
\(299\) 2363.91 1801.53i 0.457219 0.348446i
\(300\) 0 0
\(301\) −1233.69 + 2136.81i −0.236242 + 0.409183i
\(302\) −437.660 + 758.049i −0.0833924 + 0.144440i
\(303\) 0 0
\(304\) 23352.9 4.40587
\(305\) 170.450 + 295.228i 0.0319998 + 0.0554252i
\(306\) 0 0
\(307\) −415.013 −0.0771533 −0.0385767 0.999256i \(-0.512282\pi\)
−0.0385767 + 0.999256i \(0.512282\pi\)
\(308\) 1777.61 + 3078.92i 0.328860 + 0.569602i
\(309\) 0 0
\(310\) −7063.14 + 12233.7i −1.29406 + 2.24138i
\(311\) −3009.05 −0.548642 −0.274321 0.961638i \(-0.588453\pi\)
−0.274321 + 0.961638i \(0.588453\pi\)
\(312\) 0 0
\(313\) 3760.84 0.679154 0.339577 0.940578i \(-0.389716\pi\)
0.339577 + 0.940578i \(0.389716\pi\)
\(314\) 6355.70 11008.4i 1.14227 1.97847i
\(315\) 0 0
\(316\) −4060.43 7032.87i −0.722838 1.25199i
\(317\) −2772.04 −0.491146 −0.245573 0.969378i \(-0.578976\pi\)
−0.245573 + 0.969378i \(0.578976\pi\)
\(318\) 0 0
\(319\) −2953.50 5115.62i −0.518384 0.897867i
\(320\) 18800.3 3.28428
\(321\) 0 0
\(322\) −1099.15 + 1903.78i −0.190227 + 0.329483i
\(323\) 6792.58 11765.1i 1.17012 2.02671i
\(324\) 0 0
\(325\) 1950.24 + 815.365i 0.332861 + 0.139164i
\(326\) 8494.67 1.44318
\(327\) 0 0
\(328\) −8047.44 + 13938.6i −1.35471 + 2.34643i
\(329\) 111.359 + 192.879i 0.0186608 + 0.0323215i
\(330\) 0 0
\(331\) −3279.08 5679.53i −0.544515 0.943128i −0.998637 0.0521882i \(-0.983380\pi\)
0.454122 0.890939i \(-0.349953\pi\)
\(332\) 907.716 + 1572.21i 0.150052 + 0.259898i
\(333\) 0 0
\(334\) −9643.96 16703.8i −1.57992 2.73650i
\(335\) 6074.45 10521.2i 0.990694 1.71593i
\(336\) 0 0
\(337\) 9509.17 1.53708 0.768542 0.639799i \(-0.220983\pi\)
0.768542 + 0.639799i \(0.220983\pi\)
\(338\) −11470.8 + 2992.60i −1.84595 + 0.481586i
\(339\) 0 0
\(340\) 17057.4 29544.3i 2.72079 4.71254i
\(341\) −2630.14 + 4555.54i −0.417684 + 0.723450i
\(342\) 0 0
\(343\) 4142.29 0.652077
\(344\) 13589.1 + 23536.9i 2.12986 + 3.68903i
\(345\) 0 0
\(346\) 7.77591 0.00120820
\(347\) 4904.39 + 8494.66i 0.758736 + 1.31417i 0.943495 + 0.331386i \(0.107516\pi\)
−0.184759 + 0.982784i \(0.559150\pi\)
\(348\) 0 0
\(349\) −397.476 + 688.449i −0.0609639 + 0.105593i −0.894897 0.446274i \(-0.852751\pi\)
0.833933 + 0.551866i \(0.186084\pi\)
\(350\) −1563.46 −0.238772
\(351\) 0 0
\(352\) 15274.3 2.31284
\(353\) 3557.80 6162.29i 0.536438 0.929138i −0.462654 0.886539i \(-0.653103\pi\)
0.999092 0.0425989i \(-0.0135638\pi\)
\(354\) 0 0
\(355\) −2788.46 4829.76i −0.416891 0.722077i
\(356\) −10471.3 −1.55893
\(357\) 0 0
\(358\) 5617.87 + 9730.43i 0.829367 + 1.43651i
\(359\) −6907.19 −1.01545 −0.507726 0.861518i \(-0.669514\pi\)
−0.507726 + 0.861518i \(0.669514\pi\)
\(360\) 0 0
\(361\) −2583.89 + 4475.43i −0.376715 + 0.652490i
\(362\) 1253.19 2170.60i 0.181951 0.315149i
\(363\) 0 0
\(364\) 5057.67 3854.44i 0.728280 0.555021i
\(365\) 1415.31 0.202960
\(366\) 0 0
\(367\) 229.767 397.967i 0.0326804 0.0566042i −0.849223 0.528035i \(-0.822929\pi\)
0.881903 + 0.471431i \(0.156262\pi\)
\(368\) 6751.35 + 11693.7i 0.956354 + 1.65645i
\(369\) 0 0
\(370\) −8885.03 15389.3i −1.24841 2.16230i
\(371\) −196.154 339.749i −0.0274496 0.0475441i
\(372\) 0 0
\(373\) −2679.96 4641.83i −0.372019 0.644355i 0.617857 0.786290i \(-0.288001\pi\)
−0.989876 + 0.141935i \(0.954668\pi\)
\(374\) 8758.24 15169.7i 1.21090 2.09735i
\(375\) 0 0
\(376\) 2453.23 0.336478
\(377\) −8403.32 + 6404.15i −1.14799 + 0.874882i
\(378\) 0 0
\(379\) −4297.03 + 7442.68i −0.582384 + 1.00872i 0.412812 + 0.910816i \(0.364547\pi\)
−0.995196 + 0.0979028i \(0.968787\pi\)
\(380\) −15100.7 + 26155.2i −2.03855 + 3.53088i
\(381\) 0 0
\(382\) −26257.9 −3.51694
\(383\) −4668.24 8085.63i −0.622810 1.07874i −0.988960 0.148182i \(-0.952658\pi\)
0.366151 0.930556i \(-0.380676\pi\)
\(384\) 0 0
\(385\) −2195.90 −0.290684
\(386\) 2310.35 + 4001.65i 0.304648 + 0.527665i
\(387\) 0 0
\(388\) −2015.04 + 3490.14i −0.263654 + 0.456663i
\(389\) 12792.1 1.66732 0.833659 0.552279i \(-0.186242\pi\)
0.833659 + 0.552279i \(0.186242\pi\)
\(390\) 0 0
\(391\) 7854.95 1.01596
\(392\) 10676.4 18492.1i 1.37562 2.38264i
\(393\) 0 0
\(394\) 4240.98 + 7345.59i 0.542278 + 0.939253i
\(395\) 5015.88 0.638927
\(396\) 0 0
\(397\) 6692.24 + 11591.3i 0.846030 + 1.46537i 0.884723 + 0.466116i \(0.154347\pi\)
−0.0386932 + 0.999251i \(0.512319\pi\)
\(398\) 16870.8 2.12477
\(399\) 0 0
\(400\) −4801.65 + 8316.70i −0.600206 + 1.03959i
\(401\) 3178.71 5505.68i 0.395853 0.685637i −0.597357 0.801976i \(-0.703782\pi\)
0.993210 + 0.116338i \(0.0371157\pi\)
\(402\) 0 0
\(403\) 8680.60 + 3629.23i 1.07298 + 0.448597i
\(404\) −17969.0 −2.21285
\(405\) 0 0
\(406\) 3907.29 6767.62i 0.477624 0.827270i
\(407\) −3308.57 5730.62i −0.402948 0.697926i
\(408\) 0 0
\(409\) 2650.81 + 4591.35i 0.320475 + 0.555079i 0.980586 0.196089i \(-0.0628241\pi\)
−0.660111 + 0.751168i \(0.729491\pi\)
\(410\) −8002.35 13860.5i −0.963922 1.66956i
\(411\) 0 0
\(412\) 13825.4 + 23946.3i 1.65323 + 2.86347i
\(413\) −258.785 + 448.228i −0.0308328 + 0.0534040i
\(414\) 0 0
\(415\) −1121.31 −0.132633
\(416\) −3476.58 27097.9i −0.409744 3.19371i
\(417\) 0 0
\(418\) −7753.57 + 13429.6i −0.907272 + 1.57144i
\(419\) −8197.92 + 14199.2i −0.955835 + 1.65555i −0.223388 + 0.974730i \(0.571712\pi\)
−0.732447 + 0.680824i \(0.761622\pi\)
\(420\) 0 0
\(421\) 8484.68 0.982227 0.491114 0.871095i \(-0.336590\pi\)
0.491114 + 0.871095i \(0.336590\pi\)
\(422\) −332.904 576.607i −0.0384017 0.0665137i
\(423\) 0 0
\(424\) −4321.26 −0.494950
\(425\) 2793.27 + 4838.09i 0.318809 + 0.552193i
\(426\) 0 0
\(427\) −83.9685 + 145.438i −0.00951645 + 0.0164830i
\(428\) −20319.6 −2.29483
\(429\) 0 0
\(430\) −27025.8 −3.03094
\(431\) −797.370 + 1381.09i −0.0891136 + 0.154349i −0.907137 0.420836i \(-0.861737\pi\)
0.818023 + 0.575185i \(0.195070\pi\)
\(432\) 0 0
\(433\) 1693.79 + 2933.73i 0.187987 + 0.325602i 0.944579 0.328285i \(-0.106471\pi\)
−0.756592 + 0.653887i \(0.773137\pi\)
\(434\) −6959.02 −0.769685
\(435\) 0 0
\(436\) −9417.29 16311.2i −1.03442 1.79166i
\(437\) −6953.90 −0.761213
\(438\) 0 0
\(439\) 3605.77 6245.37i 0.392014 0.678987i −0.600701 0.799473i \(-0.705112\pi\)
0.992715 + 0.120486i \(0.0384453\pi\)
\(440\) −12093.9 + 20947.2i −1.31035 + 2.26959i
\(441\) 0 0
\(442\) −28905.9 12085.1i −3.11067 1.30052i
\(443\) −7500.66 −0.804441 −0.402220 0.915543i \(-0.631761\pi\)
−0.402220 + 0.915543i \(0.631761\pi\)
\(444\) 0 0
\(445\) 3233.82 5601.15i 0.344490 0.596674i
\(446\) 6754.82 + 11699.7i 0.717152 + 1.24214i
\(447\) 0 0
\(448\) 4630.79 + 8020.76i 0.488358 + 0.845860i
\(449\) 3824.77 + 6624.69i 0.402009 + 0.696299i 0.993968 0.109668i \(-0.0349789\pi\)
−0.591960 + 0.805968i \(0.701646\pi\)
\(450\) 0 0
\(451\) −2979.88 5161.31i −0.311125 0.538884i
\(452\) 2785.56 4824.74i 0.289871 0.502072i
\(453\) 0 0
\(454\) 3125.67 0.323117
\(455\) 499.809 + 3895.72i 0.0514976 + 0.401394i
\(456\) 0 0
\(457\) 4500.90 7795.78i 0.460707 0.797968i −0.538290 0.842760i \(-0.680929\pi\)
0.998996 + 0.0447924i \(0.0142626\pi\)
\(458\) 2074.51 3593.16i 0.211649 0.366588i
\(459\) 0 0
\(460\) −17462.5 −1.76999
\(461\) 673.916 + 1167.26i 0.0680854 + 0.117927i 0.898059 0.439876i \(-0.144978\pi\)
−0.829973 + 0.557803i \(0.811644\pi\)
\(462\) 0 0
\(463\) −94.9035 −0.00952600 −0.00476300 0.999989i \(-0.501516\pi\)
−0.00476300 + 0.999989i \(0.501516\pi\)
\(464\) −24000.0 41569.1i −2.40123 4.15905i
\(465\) 0 0
\(466\) −2281.64 + 3951.92i −0.226813 + 0.392852i
\(467\) 13290.9 1.31698 0.658489 0.752591i \(-0.271196\pi\)
0.658489 + 0.752591i \(0.271196\pi\)
\(468\) 0 0
\(469\) 5984.90 0.589247
\(470\) −1219.74 + 2112.66i −0.119708 + 0.207340i
\(471\) 0 0
\(472\) 2850.50 + 4937.21i 0.277977 + 0.481470i
\(473\) −10063.8 −0.978294
\(474\) 0 0
\(475\) −2472.85 4283.10i −0.238868 0.413731i
\(476\) 16806.0 1.61828
\(477\) 0 0
\(478\) 17679.0 30621.0i 1.69167 2.93006i
\(479\) 1900.79 3292.27i 0.181314 0.314045i −0.761014 0.648735i \(-0.775298\pi\)
0.942328 + 0.334690i \(0.108632\pi\)
\(480\) 0 0
\(481\) −9413.57 + 7174.06i −0.892353 + 0.680060i
\(482\) 27933.2 2.63967
\(483\) 0 0
\(484\) 6802.05 11781.5i 0.638810 1.10645i
\(485\) −1244.59 2155.70i −0.116524 0.201825i
\(486\) 0 0
\(487\) 4373.67 + 7575.42i 0.406961 + 0.704877i 0.994548 0.104284i \(-0.0332552\pi\)
−0.587587 + 0.809161i \(0.699922\pi\)
\(488\) 924.911 + 1601.99i 0.0857966 + 0.148604i
\(489\) 0 0
\(490\) 10616.6 + 18388.5i 0.978796 + 1.69533i
\(491\) −7542.69 + 13064.3i −0.693273 + 1.20078i 0.277487 + 0.960729i \(0.410499\pi\)
−0.970759 + 0.240054i \(0.922835\pi\)
\(492\) 0 0
\(493\) −27923.1 −2.55090
\(494\) 25590.1 + 10698.8i 2.33067 + 0.974419i
\(495\) 0 0
\(496\) −21372.4 + 37018.0i −1.93477 + 3.35113i
\(497\) 1373.68 2379.28i 0.123980 0.214739i
\(498\) 0 0
\(499\) 14593.9 1.30925 0.654623 0.755955i \(-0.272827\pi\)
0.654623 + 0.755955i \(0.272827\pi\)
\(500\) 11002.3 + 19056.5i 0.984074 + 1.70447i
\(501\) 0 0
\(502\) 23185.2 2.06136
\(503\) 9102.46 + 15765.9i 0.806876 + 1.39755i 0.915017 + 0.403414i \(0.132177\pi\)
−0.108142 + 0.994135i \(0.534490\pi\)
\(504\) 0 0
\(505\) 5549.30 9611.67i 0.488991 0.846958i
\(506\) −8966.25 −0.787744
\(507\) 0 0
\(508\) −32601.9 −2.84739
\(509\) 3945.96 6834.61i 0.343618 0.595164i −0.641483 0.767137i \(-0.721681\pi\)
0.985102 + 0.171973i \(0.0550140\pi\)
\(510\) 0 0
\(511\) 348.610 + 603.811i 0.0301793 + 0.0522721i
\(512\) 3555.88 0.306932
\(513\) 0 0
\(514\) 3733.79 + 6467.12i 0.320410 + 0.554966i
\(515\) −17078.6 −1.46131
\(516\) 0 0
\(517\) −454.203 + 786.703i −0.0386380 + 0.0669229i
\(518\) 4377.02 7581.23i 0.371265 0.643050i
\(519\) 0 0
\(520\) 39914.9 + 16687.8i 3.36613 + 1.40733i
\(521\) 647.902 0.0544820 0.0272410 0.999629i \(-0.491328\pi\)
0.0272410 + 0.999629i \(0.491328\pi\)
\(522\) 0 0
\(523\) −4634.99 + 8028.04i −0.387522 + 0.671208i −0.992116 0.125326i \(-0.960002\pi\)
0.604593 + 0.796534i \(0.293336\pi\)
\(524\) −8201.20 14204.9i −0.683724 1.18424i
\(525\) 0 0
\(526\) 6687.33 + 11582.8i 0.554337 + 0.960141i
\(527\) 12433.0 + 21534.6i 1.02768 + 1.78000i
\(528\) 0 0
\(529\) 4073.12 + 7054.86i 0.334768 + 0.579835i
\(530\) 2148.52 3721.35i 0.176087 0.304991i
\(531\) 0 0
\(532\) −14878.1 −1.21250
\(533\) −8478.38 + 6461.35i −0.689005 + 0.525089i
\(534\) 0 0
\(535\) 6275.24 10869.0i 0.507107 0.878336i
\(536\) 32961.7 57091.4i 2.65621 4.60069i
\(537\) 0 0
\(538\) −13234.2 −1.06053
\(539\) 3953.38 + 6847.45i 0.315926 + 0.547200i
\(540\) 0 0
\(541\) 3844.83 0.305549 0.152775 0.988261i \(-0.451179\pi\)
0.152775 + 0.988261i \(0.451179\pi\)
\(542\) 16135.7 + 27947.8i 1.27876 + 2.21488i
\(543\) 0 0
\(544\) 36101.6 62529.8i 2.84530 4.92820i
\(545\) 11633.2 0.914337
\(546\) 0 0
\(547\) −20245.4 −1.58251 −0.791253 0.611489i \(-0.790571\pi\)
−0.791253 + 0.611489i \(0.790571\pi\)
\(548\) −25705.2 + 44522.8i −2.00378 + 3.47065i
\(549\) 0 0
\(550\) −3188.46 5522.57i −0.247193 0.428151i
\(551\) 24720.0 1.91126
\(552\) 0 0
\(553\) 1235.48 + 2139.92i 0.0950056 + 0.164555i
\(554\) −39810.8 −3.05307
\(555\) 0 0
\(556\) −13212.1 + 22884.0i −1.00776 + 1.74550i
\(557\) 3611.67 6255.60i 0.274742 0.475868i −0.695328 0.718693i \(-0.744741\pi\)
0.970070 + 0.242825i \(0.0780741\pi\)
\(558\) 0 0
\(559\) 2290.62 + 17854.1i 0.173315 + 1.35089i
\(560\) −17843.7 −1.34649
\(561\) 0 0
\(562\) 16018.2 27744.3i 1.20229 2.08242i
\(563\) −8645.13 14973.8i −0.647156 1.12091i −0.983799 0.179275i \(-0.942625\pi\)
0.336643 0.941632i \(-0.390708\pi\)
\(564\) 0 0
\(565\) 1720.51 + 2980.02i 0.128111 + 0.221894i
\(566\) −4010.54 6946.47i −0.297837 0.515869i
\(567\) 0 0
\(568\) −15131.0 26207.7i −1.11775 1.93600i
\(569\) 8682.00 15037.7i 0.639663 1.10793i −0.345843 0.938292i \(-0.612407\pi\)
0.985507 0.169637i \(-0.0542595\pi\)
\(570\) 0 0
\(571\) 158.149 0.0115908 0.00579540 0.999983i \(-0.498155\pi\)
0.00579540 + 0.999983i \(0.498155\pi\)
\(572\) 23929.4 + 10004.5i 1.74919 + 0.731311i
\(573\) 0 0
\(574\) 3942.19 6828.07i 0.286662 0.496513i
\(575\) 1429.81 2476.50i 0.103699 0.179612i
\(576\) 0 0
\(577\) 9627.04 0.694591 0.347295 0.937756i \(-0.387100\pi\)
0.347295 + 0.937756i \(0.387100\pi\)
\(578\) −28146.2 48750.7i −2.02548 3.50824i
\(579\) 0 0
\(580\) 62076.4 4.44411
\(581\) −276.195 478.383i −0.0197220 0.0341595i
\(582\) 0 0
\(583\) 800.059 1385.74i 0.0568354 0.0984418i
\(584\) 7679.86 0.544169
\(585\) 0 0
\(586\) 19317.6 1.36178
\(587\) −6660.59 + 11536.5i −0.468334 + 0.811179i −0.999345 0.0361864i \(-0.988479\pi\)
0.531011 + 0.847365i \(0.321812\pi\)
\(588\) 0 0
\(589\) −11006.8 19064.3i −0.769994 1.33367i
\(590\) −5669.06 −0.395579
\(591\) 0 0
\(592\) −26885.2 46566.6i −1.86651 3.23290i
\(593\) −16723.4 −1.15809 −0.579044 0.815296i \(-0.696574\pi\)
−0.579044 + 0.815296i \(0.696574\pi\)
\(594\) 0 0
\(595\) −5190.13 + 8989.57i −0.357604 + 0.619389i
\(596\) −8273.31 + 14329.8i −0.568604 + 0.984850i
\(597\) 0 0
\(598\) 2040.81 + 15906.9i 0.139557 + 1.08776i
\(599\) −17160.0 −1.17051 −0.585256 0.810849i \(-0.699006\pi\)
−0.585256 + 0.810849i \(0.699006\pi\)
\(600\) 0 0
\(601\) −5524.29 + 9568.34i −0.374942 + 0.649419i −0.990318 0.138814i \(-0.955671\pi\)
0.615376 + 0.788234i \(0.289004\pi\)
\(602\) −6656.86 11530.0i −0.450687 0.780612i
\(603\) 0 0
\(604\) −1712.69 2966.46i −0.115378 0.199840i
\(605\) 4201.31 + 7276.89i 0.282327 + 0.489004i
\(606\) 0 0
\(607\) −10559.8 18290.1i −0.706110 1.22302i −0.966290 0.257458i \(-0.917115\pi\)
0.260180 0.965560i \(-0.416218\pi\)
\(608\) −31960.3 + 55356.9i −2.13184 + 3.69246i
\(609\) 0 0
\(610\) −1839.46 −0.122094
\(611\) 1499.06 + 626.736i 0.0992563 + 0.0414976i
\(612\) 0 0
\(613\) 3116.91 5398.65i 0.205369 0.355709i −0.744881 0.667197i \(-0.767494\pi\)
0.950250 + 0.311488i \(0.100827\pi\)
\(614\) 1119.68 1939.35i 0.0735940 0.127469i
\(615\) 0 0
\(616\) −11915.6 −0.779371
\(617\) −2799.18 4848.32i −0.182643 0.316347i 0.760137 0.649763i \(-0.225132\pi\)
−0.942780 + 0.333416i \(0.891799\pi\)
\(618\) 0 0
\(619\) −15874.3 −1.03076 −0.515382 0.856961i \(-0.672350\pi\)
−0.515382 + 0.856961i \(0.672350\pi\)
\(620\) −27640.0 47874.0i −1.79040 3.10107i
\(621\) 0 0
\(622\) 8118.25 14061.2i 0.523332 0.906437i
\(623\) 3186.15 0.204896
\(624\) 0 0
\(625\) −19228.4 −1.23062
\(626\) −10146.5 + 17574.3i −0.647823 + 1.12206i
\(627\) 0 0
\(628\) 24871.6 + 43079.0i 1.58039 + 2.73732i
\(629\) −31280.0 −1.98285
\(630\) 0 0
\(631\) −5624.51 9741.93i −0.354846 0.614612i 0.632245 0.774768i \(-0.282133\pi\)
−0.987092 + 0.160156i \(0.948800\pi\)
\(632\) 27217.6 1.71307
\(633\) 0 0
\(634\) 7478.81 12953.7i 0.468488 0.811445i
\(635\) 10068.3 17438.9i 0.629213 1.08983i
\(636\) 0 0
\(637\) 11248.2 8572.20i 0.699637 0.533192i
\(638\) 31873.6 1.97788
\(639\) 0 0
\(640\) −20315.1 + 35186.8i −1.25473 + 2.17325i
\(641\) 11884.2 + 20584.0i 0.732287 + 1.26836i 0.955903 + 0.293681i \(0.0948804\pi\)
−0.223616 + 0.974677i \(0.571786\pi\)
\(642\) 0 0
\(643\) 2184.48 + 3783.63i 0.133977 + 0.232055i 0.925206 0.379465i \(-0.123892\pi\)
−0.791229 + 0.611520i \(0.790558\pi\)
\(644\) −4301.27 7450.02i −0.263189 0.455857i
\(645\) 0 0
\(646\) 36652.0 + 63483.1i 2.23228 + 3.86642i
\(647\) 10652.6 18450.8i 0.647290 1.12114i −0.336477 0.941692i \(-0.609235\pi\)
0.983767 0.179448i \(-0.0574312\pi\)
\(648\) 0 0
\(649\) −2111.02 −0.127681
\(650\) −9071.81 + 6913.61i −0.547424 + 0.417191i
\(651\) 0 0
\(652\) −16621.0 + 28788.5i −0.998358 + 1.72921i
\(653\) 13979.2 24212.6i 0.837744 1.45101i −0.0540335 0.998539i \(-0.517208\pi\)
0.891777 0.452475i \(-0.149459\pi\)
\(654\) 0 0
\(655\) 10131.0 0.604353
\(656\) −24214.3 41940.4i −1.44117 2.49619i
\(657\) 0 0
\(658\) −1201.76 −0.0711999
\(659\) −4809.73 8330.70i −0.284310 0.492440i 0.688131 0.725586i \(-0.258431\pi\)
−0.972442 + 0.233146i \(0.925098\pi\)
\(660\) 0 0
\(661\) −2207.20 + 3822.99i −0.129879 + 0.224958i −0.923630 0.383286i \(-0.874792\pi\)
0.793750 + 0.608244i \(0.208126\pi\)
\(662\) 35387.1 2.07758
\(663\) 0 0
\(664\) −6084.55 −0.355612
\(665\) 4594.76 7958.36i 0.267936 0.464078i
\(666\) 0 0
\(667\) 7146.56 + 12378.2i 0.414866 + 0.718570i
\(668\) 75479.0 4.37181
\(669\) 0 0
\(670\) 32777.0 + 56771.5i 1.88998 + 3.27354i
\(671\) −684.970 −0.0394083
\(672\) 0 0
\(673\) 9000.88 15590.0i 0.515540 0.892942i −0.484297 0.874904i \(-0.660925\pi\)
0.999837 0.0180383i \(-0.00574207\pi\)
\(674\) −25655.2 + 44436.1i −1.46617 + 2.53949i
\(675\) 0 0
\(676\) 12302.4 44730.1i 0.699952 2.54495i
\(677\) −11192.0 −0.635369 −0.317684 0.948197i \(-0.602905\pi\)
−0.317684 + 0.948197i \(0.602905\pi\)
\(678\) 0 0
\(679\) 613.123 1061.96i 0.0346532 0.0600211i
\(680\) 57169.1 + 99019.8i 3.22402 + 5.58417i
\(681\) 0 0
\(682\) −14192.0 24581.2i −0.796831 1.38015i
\(683\) −17561.2 30416.8i −0.983835 1.70405i −0.647002 0.762488i \(-0.723978\pi\)
−0.336833 0.941564i \(-0.609356\pi\)
\(684\) 0 0
\(685\) −15876.9 27499.7i −0.885586 1.53388i
\(686\) −11175.7 + 19356.8i −0.621996 + 1.07733i
\(687\) 0 0
\(688\) −81777.5 −4.53160
\(689\) −2640.53 1103.97i −0.146003 0.0610418i
\(690\) 0 0
\(691\) −14767.3 + 25577.7i −0.812987 + 1.40813i 0.0977773 + 0.995208i \(0.468827\pi\)
−0.910764 + 0.412926i \(0.864507\pi\)
\(692\) −15.2147 + 26.3526i −0.000835802 + 0.00144765i
\(693\) 0 0
\(694\) −52927.1 −2.89494
\(695\) −8160.48 14134.4i −0.445388 0.771434i
\(696\) 0 0
\(697\) −28172.5 −1.53100
\(698\) −2144.74 3714.79i −0.116303 0.201443i
\(699\) 0 0
\(700\) 3059.12 5298.55i 0.165177 0.286095i
\(701\) 8804.19 0.474365 0.237182 0.971465i \(-0.423776\pi\)
0.237182 + 0.971465i \(0.423776\pi\)
\(702\) 0 0
\(703\) 27691.8 1.48566
\(704\) −18887.7 + 32714.5i −1.01116 + 1.75138i
\(705\) 0 0
\(706\) 19197.5 + 33251.0i 1.02338 + 1.77255i
\(707\) 5467.49 0.290843
\(708\) 0 0
\(709\) −13569.1 23502.4i −0.718758 1.24492i −0.961492 0.274832i \(-0.911378\pi\)
0.242735 0.970093i \(-0.421956\pi\)
\(710\) 30092.5 1.59064
\(711\) 0 0
\(712\) 17547.7 30393.4i 0.923633 1.59978i
\(713\) 6364.13 11023.0i 0.334276 0.578983i
\(714\) 0 0
\(715\) −12741.5 + 9710.27i −0.666441 + 0.507893i
\(716\) −43968.6 −2.29495
\(717\) 0 0
\(718\) 18635.2 32277.1i 0.968607 1.67768i
\(719\) −8668.72 15014.7i −0.449637 0.778794i 0.548725 0.836003i \(-0.315113\pi\)
−0.998362 + 0.0572088i \(0.981780\pi\)
\(720\) 0 0
\(721\) −4206.72 7286.25i −0.217290 0.376358i
\(722\) −13942.4 24148.9i −0.718673 1.24478i
\(723\) 0 0
\(724\) 4904.10 + 8494.15i 0.251740 + 0.436026i
\(725\) −5082.73 + 8803.54i −0.260369 + 0.450973i
\(726\) 0 0
\(727\) 25771.3 1.31473 0.657363 0.753574i \(-0.271672\pi\)
0.657363 + 0.753574i \(0.271672\pi\)
\(728\) 2712.11 + 21139.3i 0.138074 + 1.07620i
\(729\) 0 0
\(730\) −3818.42 + 6613.69i −0.193597 + 0.335320i
\(731\) −23786.3 + 41199.1i −1.20351 + 2.08455i
\(732\) 0 0
\(733\) 21784.2 1.09771 0.548853 0.835919i \(-0.315065\pi\)
0.548853 + 0.835919i \(0.315065\pi\)
\(734\) 1239.80 + 2147.39i 0.0623456 + 0.107986i
\(735\) 0 0
\(736\) −36959.0 −1.85099
\(737\) 12205.4 + 21140.4i 0.610029 + 1.05660i
\(738\) 0 0
\(739\) −11176.9 + 19359.0i −0.556360 + 0.963643i 0.441437 + 0.897292i \(0.354469\pi\)
−0.997796 + 0.0663507i \(0.978864\pi\)
\(740\) 69539.2 3.45448
\(741\) 0 0
\(742\) 2116.85 0.104733
\(743\) 9191.31 15919.8i 0.453831 0.786059i −0.544789 0.838573i \(-0.683390\pi\)
0.998620 + 0.0525145i \(0.0167236\pi\)
\(744\) 0 0
\(745\) −5110.04 8850.85i −0.251298 0.435262i
\(746\) 28921.5 1.41943
\(747\) 0 0
\(748\) 34273.5 + 59363.4i 1.67535 + 2.90179i
\(749\) 6182.74 0.301618
\(750\) 0 0
\(751\) −6891.39 + 11936.2i −0.334847 + 0.579972i −0.983455 0.181150i \(-0.942018\pi\)
0.648608 + 0.761122i \(0.275351\pi\)
\(752\) −3690.82 + 6392.69i −0.178977 + 0.309997i
\(753\) 0 0
\(754\) −7254.75 56546.6i −0.350401 2.73117i
\(755\) 2115.69 0.101984
\(756\) 0 0
\(757\) −12819.7 + 22204.4i −0.615510 + 1.06609i 0.374785 + 0.927112i \(0.377717\pi\)
−0.990295 + 0.138983i \(0.955617\pi\)
\(758\) −23186.3 40159.9i −1.11104 1.92437i
\(759\) 0 0
\(760\) −50611.1 87661.0i −2.41560 4.18395i
\(761\) −21.7379 37.6511i −0.00103548 0.00179350i 0.865507 0.500896i \(-0.166996\pi\)
−0.866543 + 0.499103i \(0.833663\pi\)
\(762\) 0 0
\(763\) 2865.44 + 4963.08i 0.135958 + 0.235486i
\(764\) 51377.3 88988.1i 2.43294 4.21397i
\(765\) 0 0
\(766\) 50378.7 2.37631
\(767\) 480.491 + 3745.15i 0.0226200 + 0.176310i
\(768\) 0 0
\(769\) 10242.8 17741.1i 0.480321 0.831940i −0.519425 0.854516i \(-0.673854\pi\)
0.999745 + 0.0225767i \(0.00718701\pi\)
\(770\) 5924.41 10261.4i 0.277274 0.480253i
\(771\) 0 0
\(772\) −18082.1 −0.842992
\(773\) −14725.1 25504.7i −0.685157 1.18673i −0.973387 0.229166i \(-0.926400\pi\)
0.288230 0.957561i \(-0.406933\pi\)
\(774\) 0 0
\(775\) 9052.51 0.419582
\(776\) −6753.53 11697.5i −0.312420 0.541127i
\(777\) 0 0
\(778\) −34512.5 + 59777.4i −1.59040 + 2.75466i
\(779\) 24940.8 1.14711
\(780\) 0 0
\(781\) 11205.7 0.513409
\(782\) −21192.2 + 36706.0i −0.969095 + 1.67852i
\(783\) 0 0
\(784\) 32124.9 + 55641.9i 1.46341 + 2.53471i
\(785\) −30724.1 −1.39693
\(786\) 0 0
\(787\) −4875.55 8444.70i −0.220832 0.382492i 0.734229 0.678902i \(-0.237544\pi\)
−0.955061 + 0.296410i \(0.904211\pi\)
\(788\) −33192.3 −1.50054
\(789\) 0 0
\(790\) −13532.6 + 23439.1i −0.609452 + 1.05560i
\(791\) −847.575 + 1468.04i −0.0380990 + 0.0659894i
\(792\) 0 0
\(793\) 155.906 + 1215.20i 0.00698158 + 0.0544174i
\(794\) −72221.2 −3.22800
\(795\) 0 0
\(796\) −33010.1 + 57175.2i −1.46987 + 2.54588i
\(797\) 18875.4 + 32693.1i 0.838896 + 1.45301i 0.890818 + 0.454360i \(0.150132\pi\)
−0.0519216 + 0.998651i \(0.516535\pi\)
\(798\) 0 0
\(799\) 2147.07 + 3718.83i 0.0950661 + 0.164659i
\(800\) −13142.9 22764.1i −0.580837 1.00604i
\(801\) 0 0
\(802\) 17152.0 + 29708.1i 0.755183 + 1.30801i
\(803\) −1421.89 + 2462.78i −0.0624873 + 0.108231i
\(804\) 0 0
\(805\) 5313.39 0.232637
\(806\) −40379.1 + 30772.8i −1.76463 + 1.34482i
\(807\) 0 0
\(808\) 30112.1 52155.7i 1.31107 2.27083i
\(809\) 3499.72 6061.70i 0.152094 0.263434i −0.779903 0.625900i \(-0.784732\pi\)
0.931997 + 0.362466i \(0.118065\pi\)
\(810\) 0 0
\(811\) −35792.1 −1.54973 −0.774864 0.632128i \(-0.782182\pi\)
−0.774864 + 0.632128i \(0.782182\pi\)
\(812\) 15290.3 + 26483.6i 0.660819 + 1.14457i
\(813\) 0 0
\(814\) 35705.4 1.53744
\(815\) −10266.0 17781.3i −0.441231 0.764235i
\(816\) 0 0
\(817\) 21057.7 36473.1i 0.901735 1.56185i
\(818\) −28607.0 −1.22276
\(819\) 0 0
\(820\) 62630.9 2.66727
\(821\) −4888.31 + 8466.80i −0.207799 + 0.359919i −0.951021 0.309126i \(-0.899963\pi\)
0.743222 + 0.669045i \(0.233297\pi\)
\(822\) 0 0
\(823\) −9831.02 17027.8i −0.416389 0.721206i 0.579185 0.815196i \(-0.303371\pi\)
−0.995573 + 0.0939904i \(0.970038\pi\)
\(824\) −92673.7 −3.91801
\(825\) 0 0
\(826\) −1396.37 2418.59i −0.0588209 0.101881i
\(827\) 5281.22 0.222063 0.111032 0.993817i \(-0.464585\pi\)
0.111032 + 0.993817i \(0.464585\pi\)
\(828\) 0 0
\(829\) −10867.7 + 18823.5i −0.455310 + 0.788621i −0.998706 0.0508562i \(-0.983805\pi\)
0.543396 + 0.839477i \(0.317138\pi\)
\(830\) 3025.23 5239.85i 0.126515 0.219130i
\(831\) 0 0
\(832\) 62337.6 + 26062.4i 2.59756 + 1.08600i
\(833\) 37376.1 1.55463
\(834\) 0 0
\(835\) −23309.9 + 40374.0i −0.966077 + 1.67329i
\(836\) −30341.9 52553.7i −1.25526 2.17417i
\(837\) 0 0
\(838\) −44235.1 76617.4i −1.82348 3.15836i
\(839\) 14287.4 + 24746.5i 0.587908 + 1.01829i 0.994506 + 0.104679i \(0.0333816\pi\)
−0.406598 + 0.913607i \(0.633285\pi\)
\(840\) 0 0
\(841\) −13210.4 22881.0i −0.541652 0.938169i
\(842\) −22891.2 + 39648.7i −0.936915 + 1.62278i
\(843\) 0 0
\(844\) 2605.49 0.106262
\(845\) 20127.0 + 20394.4i 0.819396 + 0.830284i
\(846\) 0 0
\(847\) −2069.69 + 3584.81i −0.0839614 + 0.145425i
\(848\) 6501.22 11260.4i 0.263270 0.455997i
\(849\) 0 0
\(850\) −30144.4 −1.21640
\(851\) 8005.72 + 13866.3i 0.322482 + 0.558556i
\(852\) 0 0
\(853\) 5251.39 0.210791 0.105395 0.994430i \(-0.466389\pi\)
0.105395 + 0.994430i \(0.466389\pi\)
\(854\) −453.085 784.766i −0.0181549 0.0314451i
\(855\) 0 0
\(856\) 34051.3 58978.6i 1.35964 2.35496i
\(857\) −34851.0 −1.38913 −0.694566 0.719429i \(-0.744404\pi\)
−0.694566 + 0.719429i \(0.744404\pi\)
\(858\) 0 0
\(859\) 41697.5 1.65623 0.828114 0.560559i \(-0.189414\pi\)
0.828114 + 0.560559i \(0.189414\pi\)
\(860\) 52879.9 91590.6i 2.09673 3.63164i
\(861\) 0 0
\(862\) −4302.52 7452.19i −0.170005 0.294458i
\(863\) 28648.9 1.13004 0.565018 0.825079i \(-0.308869\pi\)
0.565018 + 0.825079i \(0.308869\pi\)
\(864\) 0 0
\(865\) −9.39739 16.2768i −0.000369388 0.000639799i
\(866\) −18279.0 −0.717257
\(867\) 0 0
\(868\) 13616.3 23584.1i 0.532450 0.922231i
\(869\) −5039.20 + 8728.15i −0.196713 + 0.340716i
\(870\) 0 0
\(871\) 34726.8 26465.2i 1.35095 1.02955i
\(872\) 63125.4 2.45149
\(873\) 0 0
\(874\) 18761.2 32495.4i 0.726096 1.25764i
\(875\) −3347.71 5798.41i −0.129341 0.224025i
\(876\) 0 0
\(877\) 15758.4 + 27294.3i 0.606754 + 1.05093i 0.991772 + 0.128020i \(0.0408621\pi\)
−0.385018 + 0.922909i \(0.625805\pi\)
\(878\) 19456.3 + 33699.4i 0.747858 + 1.29533i
\(879\) 0 0
\(880\) −36389.8 63029.0i −1.39398 2.41444i
\(881\) −15623.1 + 27059.9i −0.597451 + 1.03482i 0.395745 + 0.918360i \(0.370486\pi\)
−0.993196 + 0.116455i \(0.962847\pi\)
\(882\) 0 0
\(883\) −16181.8 −0.616718 −0.308359 0.951270i \(-0.599780\pi\)
−0.308359 + 0.951270i \(0.599780\pi\)
\(884\) 97515.0 74316.0i 3.71016 2.82751i
\(885\) 0 0
\(886\) 20236.4 35050.4i 0.767330 1.32905i
\(887\) 6644.52 11508.6i 0.251523 0.435651i −0.712422 0.701751i \(-0.752402\pi\)
0.963945 + 0.266100i \(0.0857352\pi\)
\(888\) 0 0
\(889\) 9919.92 0.374245
\(890\) 17449.4 + 30223.2i 0.657195 + 1.13830i
\(891\) 0 0
\(892\) −52867.0 −1.98444
\(893\) −1900.78 3292.24i −0.0712285 0.123371i
\(894\) 0 0
\(895\) 13578.7 23519.0i 0.507134 0.878382i
\(896\) −20015.6 −0.746288
\(897\) 0 0
\(898\) −41276.0 −1.53385
\(899\) −22623.5 + 39185.0i −0.839304 + 1.45372i
\(900\) 0 0
\(901\) −3781.97 6550.56i −0.139840 0.242210i
\(902\) 32158.2 1.18709
\(903\) 0 0
\(904\) 9336.01 + 16170.4i 0.343486 + 0.594935i
\(905\) −6058.07 −0.222516
\(906\) 0 0
\(907\) −23564.2 + 40814.4i −0.862664 + 1.49418i 0.00668479 + 0.999978i \(0.497872\pi\)
−0.869348 + 0.494200i \(0.835461\pi\)
\(908\) −6115.82 + 10592.9i −0.223525 + 0.387157i
\(909\) 0 0
\(910\) −19553.1 8174.85i −0.712284 0.297795i
\(911\) −2884.69 −0.104911 −0.0524556 0.998623i \(-0.516705\pi\)
−0.0524556 + 0.998623i \(0.516705\pi\)
\(912\) 0 0
\(913\) 1126.52 1951.20i 0.0408351 0.0707285i
\(914\) 24286.3 + 42065.2i 0.878907 + 1.52231i
\(915\) 0 0
\(916\) 8118.14 + 14061.0i 0.292828 + 0.507194i
\(917\) 2495.41 + 4322.18i 0.0898646 + 0.155650i
\(918\) 0 0
\(919\) 12876.1 + 22302.0i 0.462179 + 0.800518i 0.999069 0.0431343i \(-0.0137343\pi\)
−0.536890 + 0.843652i \(0.680401\pi\)
\(920\) 29263.4 50685.7i 1.04868 1.81637i
\(921\) 0 0
\(922\) −7272.75 −0.259778
\(923\) −2550.54 19880.0i −0.0909556 0.708946i
\(924\) 0 0
\(925\) −5693.77 + 9861.90i −0.202389 + 0.350548i
\(926\) 256.044 443.482i 0.00908655 0.0157384i
\(927\) 0 0
\(928\) 131383. 4.64748
\(929\) 25697.4 + 44509.2i 0.907539 + 1.57190i 0.817473 + 0.575967i \(0.195374\pi\)
0.0900658 + 0.995936i \(0.471292\pi\)
\(930\) 0 0
\(931\) −33088.6 −1.16481
\(932\) −8928.69 15465.0i −0.313808 0.543532i
\(933\) 0 0
\(934\) −35858.1 + 62108.0i −1.25622 + 2.17584i
\(935\) −42338.3 −1.48087
\(936\) 0 0
\(937\) 6781.86 0.236450 0.118225 0.992987i \(-0.462280\pi\)
0.118225 + 0.992987i \(0.462280\pi\)
\(938\) −16146.9 + 27967.3i −0.562064 + 0.973523i
\(939\) 0 0
\(940\) −4773.19 8267.42i −0.165622 0.286865i
\(941\) 22038.2 0.763470 0.381735 0.924272i \(-0.375327\pi\)
0.381735 + 0.924272i \(0.375327\pi\)
\(942\) 0 0
\(943\) 7210.39 + 12488.8i 0.248995 + 0.431273i
\(944\) −17154.0 −0.591436
\(945\) 0 0
\(946\) 27151.5 47027.8i 0.933163 1.61629i
\(947\) −22765.5 + 39431.0i −0.781182 + 1.35305i 0.150072 + 0.988675i \(0.452049\pi\)
−0.931254 + 0.364371i \(0.881284\pi\)
\(948\) 0 0
\(949\) 4692.83 + 1962.00i 0.160522 + 0.0671120i
\(950\) 26686.5 0.911393
\(951\) 0 0
\(952\) −28163.2 + 48780.0i −0.958795 + 1.66068i
\(953\) −13270.6 22985.3i −0.451077 0.781288i 0.547376 0.836887i \(-0.315627\pi\)
−0.998453 + 0.0555985i \(0.982293\pi\)
\(954\) 0 0
\(955\) 31733.4 + 54963.8i 1.07525 + 1.86240i
\(956\) 69183.0 + 119828.i 2.34052 + 4.05390i
\(957\) 0 0
\(958\) 10256.5 + 17764.7i 0.345900 + 0.599116i
\(959\) 7821.44 13547.1i 0.263365 0.456162i
\(960\) 0 0
\(961\) 10502.1 0.352527
\(962\) −8126.92 63344.6i −0.272372 2.12299i
\(963\) 0 0
\(964\) −54655.2 + 94665.6i −1.82606 + 3.16284i
\(965\) 5584.25 9672.20i 0.186283 0.322652i
\(966\) 0 0
\(967\) 48269.6 1.60522 0.802609 0.596506i \(-0.203445\pi\)
0.802609 + 0.596506i \(0.203445\pi\)
\(968\) 22797.5 + 39486.5i 0.756964 + 1.31110i
\(969\) 0 0
\(970\) 13431.4 0.444594
\(971\) 17080.7 + 29584.6i 0.564515 + 0.977769i 0.997095 + 0.0761732i \(0.0242702\pi\)
−0.432579 + 0.901596i \(0.642396\pi\)
\(972\) 0 0
\(973\) 4020.09 6963.00i 0.132454 0.229418i
\(974\) −47199.7 −1.55275
\(975\) 0 0
\(976\) −5566.02 −0.182545
\(977\) 12062.1 20892.2i 0.394985 0.684135i −0.598114 0.801411i \(-0.704083\pi\)
0.993099 + 0.117276i \(0.0374164\pi\)
\(978\) 0 0
\(979\) 6497.72 + 11254.4i 0.212123 + 0.367407i
\(980\) −83091.7 −2.70843
\(981\) 0 0
\(982\) −40699.5 70493.7i −1.32258 2.29078i
\(983\) 19023.4 0.617246 0.308623 0.951185i \(-0.400132\pi\)
0.308623 + 0.951185i \(0.400132\pi\)
\(984\) 0 0
\(985\) 10250.7 17754.7i 0.331587 0.574326i
\(986\) 75334.9 130484.i 2.43322 4.21446i
\(987\) 0 0
\(988\) −86328.9 + 65791.0i −2.77985 + 2.11851i
\(989\) 24351.2 0.782936
\(990\) 0 0
\(991\) 114.981 199.153i 0.00368566 0.00638374i −0.864177 0.503188i \(-0.832160\pi\)
0.867862 + 0.496805i \(0.165493\pi\)
\(992\) −58499.4 101324.i −1.87234 3.24298i
\(993\) 0 0
\(994\) 7412.22 + 12838.3i 0.236520 + 0.409665i
\(995\) −20388.8 35314.5i −0.649618 1.12517i
\(996\) 0 0
\(997\) −13495.6 23375.0i −0.428694 0.742521i 0.568063 0.822985i \(-0.307693\pi\)
−0.996757 + 0.0804645i \(0.974360\pi\)
\(998\) −39373.6 + 68197.1i −1.24885 + 2.16307i
\(999\) 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 117.4.g.f.100.1 yes 16
3.2 odd 2 inner 117.4.g.f.100.8 yes 16
13.3 even 3 inner 117.4.g.f.55.1 16
13.4 even 6 1521.4.a.bd.1.1 8
13.9 even 3 1521.4.a.bc.1.8 8
39.17 odd 6 1521.4.a.bd.1.8 8
39.29 odd 6 inner 117.4.g.f.55.8 yes 16
39.35 odd 6 1521.4.a.bc.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.g.f.55.1 16 13.3 even 3 inner
117.4.g.f.55.8 yes 16 39.29 odd 6 inner
117.4.g.f.100.1 yes 16 1.1 even 1 trivial
117.4.g.f.100.8 yes 16 3.2 odd 2 inner
1521.4.a.bc.1.1 8 39.35 odd 6
1521.4.a.bc.1.8 8 13.9 even 3
1521.4.a.bd.1.1 8 13.4 even 6
1521.4.a.bd.1.8 8 39.17 odd 6