Properties

Label 74.5.g.a.45.5
Level $74$
Weight $5$
Character 74.45
Analytic conductor $7.649$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,5,Mod(23,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.23");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.g (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.64937726820\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 45.5
Character \(\chi\) \(=\) 74.45
Dual form 74.5.g.a.51.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.73205 - 0.732051i) q^{2} +(6.38646 + 3.68723i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-43.6075 + 11.6846i) q^{5} +(-14.7489 - 14.7489i) q^{6} +(39.7034 - 68.7683i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(-13.3087 - 23.0514i) q^{9} +O(q^{10})\) \(q+(-2.73205 - 0.732051i) q^{2} +(6.38646 + 3.68723i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-43.6075 + 11.6846i) q^{5} +(-14.7489 - 14.7489i) q^{6} +(39.7034 - 68.7683i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(-13.3087 - 23.0514i) q^{9} +127.692 q^{10} +23.6627i q^{11} +(29.4978 + 51.0917i) q^{12} +(240.572 - 64.4610i) q^{13} +(-158.814 + 158.814i) q^{14} +(-321.581 - 86.1675i) q^{15} +(32.0000 + 55.4256i) q^{16} +(122.681 - 457.851i) q^{17} +(19.4853 + 72.7202i) q^{18} +(-126.519 + 33.9007i) q^{19} +(-348.860 - 93.4767i) q^{20} +(507.129 - 292.791i) q^{21} +(17.3223 - 64.6476i) q^{22} +(-496.506 - 496.506i) q^{23} +(-43.1878 - 161.179i) q^{24} +(1223.82 - 706.571i) q^{25} -704.443 q^{26} -793.620i q^{27} +(550.147 - 317.627i) q^{28} +(-503.438 + 503.438i) q^{29} +(815.498 + 470.828i) q^{30} +(-358.102 + 358.102i) q^{31} +(-46.8513 - 174.851i) q^{32} +(-87.2496 + 151.121i) q^{33} +(-670.340 + 1161.06i) q^{34} +(-927.837 + 3462.73i) q^{35} -212.940i q^{36} +(-1348.59 + 235.514i) q^{37} +370.474 q^{38} +(1774.08 + 475.364i) q^{39} +(884.673 + 510.766i) q^{40} +(646.276 + 373.127i) q^{41} +(-1599.84 + 428.676i) q^{42} +(-553.213 - 553.213i) q^{43} +(-94.6506 + 163.940i) q^{44} +(849.706 + 849.706i) q^{45} +(993.011 + 1719.95i) q^{46} +2648.46 q^{47} +471.965i q^{48} +(-1952.22 - 3381.35i) q^{49} +(-3860.78 + 1034.49i) q^{50} +(2471.69 - 2471.69i) q^{51} +(1924.57 + 515.688i) q^{52} +(-104.046 - 180.213i) q^{53} +(-580.970 + 2168.21i) q^{54} +(-276.489 - 1031.87i) q^{55} +(-1735.55 + 465.039i) q^{56} +(-933.009 - 249.999i) q^{57} +(1743.96 - 1006.88i) q^{58} +(57.1818 - 213.405i) q^{59} +(-1883.31 - 1883.31i) q^{60} +(1128.84 + 4212.87i) q^{61} +(1240.50 - 716.205i) q^{62} -2113.61 q^{63} +512.000i q^{64} +(-9737.52 + 5621.96i) q^{65} +(348.998 - 348.998i) q^{66} +(1832.80 + 1058.17i) q^{67} +(2681.36 - 2681.36i) q^{68} +(-1340.19 - 5001.64i) q^{69} +(5069.79 - 8781.14i) q^{70} +(1611.83 - 2791.77i) q^{71} +(-155.883 + 581.762i) q^{72} -9197.34i q^{73} +(3856.82 + 343.801i) q^{74} +10421.2 q^{75} +(-1012.15 - 271.206i) q^{76} +(1627.24 + 939.489i) q^{77} +(-4498.90 - 2597.44i) q^{78} +(-10618.7 + 2845.28i) q^{79} +(-2043.07 - 2043.07i) q^{80} +(1848.25 - 3201.26i) q^{81} +(-1492.51 - 1492.51i) q^{82} +(2785.13 + 4823.98i) q^{83} +4684.66 q^{84} +21399.2i q^{85} +(1106.43 + 1916.39i) q^{86} +(-5071.48 + 1358.90i) q^{87} +(378.603 - 378.603i) q^{88} +(1026.15 + 274.955i) q^{89} +(-1699.41 - 2943.47i) q^{90} +(5118.64 - 19103.0i) q^{91} +(-1453.87 - 5425.91i) q^{92} +(-3607.41 + 966.603i) q^{93} +(-7235.74 - 1938.81i) q^{94} +(5121.07 - 2956.65i) q^{95} +(345.502 - 1289.43i) q^{96} +(6808.20 + 6808.20i) q^{97} +(2858.25 + 10667.1i) q^{98} +(545.457 - 314.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73205 0.732051i −0.683013 0.183013i
\(3\) 6.38646 + 3.68723i 0.709607 + 0.409692i 0.810915 0.585163i \(-0.198970\pi\)
−0.101309 + 0.994855i \(0.532303\pi\)
\(4\) 6.92820 + 4.00000i 0.433013 + 0.250000i
\(5\) −43.6075 + 11.6846i −1.74430 + 0.467384i −0.983395 0.181480i \(-0.941911\pi\)
−0.760905 + 0.648863i \(0.775245\pi\)
\(6\) −14.7489 14.7489i −0.409692 0.409692i
\(7\) 39.7034 68.7683i 0.810274 1.40344i −0.102398 0.994743i \(-0.532652\pi\)
0.912672 0.408692i \(-0.134015\pi\)
\(8\) −16.0000 16.0000i −0.250000 0.250000i
\(9\) −13.3087 23.0514i −0.164305 0.284585i
\(10\) 127.692 1.27692
\(11\) 23.6627i 0.195559i 0.995208 + 0.0977796i \(0.0311740\pi\)
−0.995208 + 0.0977796i \(0.968826\pi\)
\(12\) 29.4978 + 51.0917i 0.204846 + 0.354803i
\(13\) 240.572 64.4610i 1.42350 0.381426i 0.536776 0.843725i \(-0.319642\pi\)
0.886724 + 0.462299i \(0.152975\pi\)
\(14\) −158.814 + 158.814i −0.810274 + 0.810274i
\(15\) −321.581 86.1675i −1.42925 0.382966i
\(16\) 32.0000 + 55.4256i 0.125000 + 0.216506i
\(17\) 122.681 457.851i 0.424501 1.58426i −0.340510 0.940241i \(-0.610600\pi\)
0.765011 0.644017i \(-0.222734\pi\)
\(18\) 19.4853 + 72.7202i 0.0601399 + 0.224445i
\(19\) −126.519 + 33.9007i −0.350469 + 0.0939078i −0.429759 0.902944i \(-0.641401\pi\)
0.0792901 + 0.996852i \(0.474735\pi\)
\(20\) −348.860 93.4767i −0.872150 0.233692i
\(21\) 507.129 292.791i 1.14995 0.663925i
\(22\) 17.3223 64.6476i 0.0357898 0.133569i
\(23\) −496.506 496.506i −0.938574 0.938574i 0.0596457 0.998220i \(-0.481003\pi\)
−0.998220 + 0.0596457i \(0.981003\pi\)
\(24\) −43.1878 161.179i −0.0749788 0.279825i
\(25\) 1223.82 706.571i 1.95811 1.13051i
\(26\) −704.443 −1.04207
\(27\) 793.620i 1.08864i
\(28\) 550.147 317.627i 0.701718 0.405137i
\(29\) −503.438 + 503.438i −0.598619 + 0.598619i −0.939945 0.341326i \(-0.889124\pi\)
0.341326 + 0.939945i \(0.389124\pi\)
\(30\) 815.498 + 470.828i 0.906108 + 0.523142i
\(31\) −358.102 + 358.102i −0.372635 + 0.372635i −0.868436 0.495801i \(-0.834875\pi\)
0.495801 + 0.868436i \(0.334875\pi\)
\(32\) −46.8513 174.851i −0.0457532 0.170753i
\(33\) −87.2496 + 151.121i −0.0801190 + 0.138770i
\(34\) −670.340 + 1161.06i −0.579879 + 1.00438i
\(35\) −927.837 + 3462.73i −0.757418 + 2.82672i
\(36\) 212.940i 0.164305i
\(37\) −1348.59 + 235.514i −0.985091 + 0.172033i
\(38\) 370.474 0.256561
\(39\) 1774.08 + 475.364i 1.16639 + 0.312534i
\(40\) 884.673 + 510.766i 0.552921 + 0.319229i
\(41\) 646.276 + 373.127i 0.384459 + 0.221968i 0.679757 0.733438i \(-0.262085\pi\)
−0.295298 + 0.955405i \(0.595419\pi\)
\(42\) −1599.84 + 428.676i −0.906939 + 0.243013i
\(43\) −553.213 553.213i −0.299196 0.299196i 0.541503 0.840699i \(-0.317855\pi\)
−0.840699 + 0.541503i \(0.817855\pi\)
\(44\) −94.6506 + 163.940i −0.0488898 + 0.0846796i
\(45\) 849.706 + 849.706i 0.419608 + 0.419608i
\(46\) 993.011 + 1719.95i 0.469287 + 0.812829i
\(47\) 2648.46 1.19894 0.599471 0.800396i \(-0.295378\pi\)
0.599471 + 0.800396i \(0.295378\pi\)
\(48\) 471.965i 0.204846i
\(49\) −1952.22 3381.35i −0.813088 1.40831i
\(50\) −3860.78 + 1034.49i −1.54431 + 0.413797i
\(51\) 2471.69 2471.69i 0.950286 0.950286i
\(52\) 1924.57 + 515.688i 0.711750 + 0.190713i
\(53\) −104.046 180.213i −0.0370401 0.0641554i 0.846911 0.531735i \(-0.178460\pi\)
−0.883951 + 0.467579i \(0.845126\pi\)
\(54\) −580.970 + 2168.21i −0.199235 + 0.743556i
\(55\) −276.489 1031.87i −0.0914012 0.341114i
\(56\) −1735.55 + 465.039i −0.553427 + 0.148290i
\(57\) −933.009 249.999i −0.287168 0.0769465i
\(58\) 1743.96 1006.88i 0.518419 0.299309i
\(59\) 57.1818 213.405i 0.0164268 0.0613057i −0.957226 0.289342i \(-0.906564\pi\)
0.973653 + 0.228036i \(0.0732303\pi\)
\(60\) −1883.31 1883.31i −0.523142 0.523142i
\(61\) 1128.84 + 4212.87i 0.303369 + 1.13219i 0.934340 + 0.356382i \(0.115990\pi\)
−0.630971 + 0.775806i \(0.717343\pi\)
\(62\) 1240.50 716.205i 0.322712 0.186318i
\(63\) −2113.61 −0.532529
\(64\) 512.000i 0.125000i
\(65\) −9737.52 + 5621.96i −2.30474 + 1.33064i
\(66\) 348.998 348.998i 0.0801190 0.0801190i
\(67\) 1832.80 + 1058.17i 0.408287 + 0.235725i 0.690054 0.723758i \(-0.257587\pi\)
−0.281766 + 0.959483i \(0.590920\pi\)
\(68\) 2681.36 2681.36i 0.579879 0.579879i
\(69\) −1340.19 5001.64i −0.281493 1.05054i
\(70\) 5069.79 8781.14i 1.03465 1.79207i
\(71\) 1611.83 2791.77i 0.319744 0.553814i −0.660690 0.750659i \(-0.729736\pi\)
0.980435 + 0.196845i \(0.0630696\pi\)
\(72\) −155.883 + 581.762i −0.0300700 + 0.112223i
\(73\) 9197.34i 1.72590i −0.505287 0.862952i \(-0.668613\pi\)
0.505287 0.862952i \(-0.331387\pi\)
\(74\) 3856.82 + 343.801i 0.704314 + 0.0627832i
\(75\) 10421.2 1.85265
\(76\) −1012.15 271.206i −0.175234 0.0469539i
\(77\) 1627.24 + 939.489i 0.274455 + 0.158457i
\(78\) −4498.90 2597.44i −0.739463 0.426929i
\(79\) −10618.7 + 2845.28i −1.70145 + 0.455902i −0.973303 0.229522i \(-0.926284\pi\)
−0.728145 + 0.685424i \(0.759617\pi\)
\(80\) −2043.07 2043.07i −0.319229 0.319229i
\(81\) 1848.25 3201.26i 0.281702 0.487923i
\(82\) −1492.51 1492.51i −0.221968 0.221968i
\(83\) 2785.13 + 4823.98i 0.404286 + 0.700244i 0.994238 0.107194i \(-0.0341867\pi\)
−0.589952 + 0.807438i \(0.700853\pi\)
\(84\) 4684.66 0.663925
\(85\) 21399.2i 2.96183i
\(86\) 1106.43 + 1916.39i 0.149598 + 0.259111i
\(87\) −5071.48 + 1358.90i −0.670033 + 0.179535i
\(88\) 378.603 378.603i 0.0488898 0.0488898i
\(89\) 1026.15 + 274.955i 0.129548 + 0.0347122i 0.323010 0.946395i \(-0.395305\pi\)
−0.193463 + 0.981108i \(0.561972\pi\)
\(90\) −1699.41 2943.47i −0.209804 0.363391i
\(91\) 5118.64 19103.0i 0.618119 2.30685i
\(92\) −1453.87 5425.91i −0.171771 0.641058i
\(93\) −3607.41 + 966.603i −0.417090 + 0.111759i
\(94\) −7235.74 1938.81i −0.818893 0.219422i
\(95\) 5121.07 2956.65i 0.567431 0.327607i
\(96\) 345.502 1289.43i 0.0374894 0.139912i
\(97\) 6808.20 + 6808.20i 0.723584 + 0.723584i 0.969333 0.245749i \(-0.0790340\pi\)
−0.245749 + 0.969333i \(0.579034\pi\)
\(98\) 2858.25 + 10667.1i 0.297611 + 1.11070i
\(99\) 545.457 314.920i 0.0556532 0.0321314i
\(100\) 11305.1 1.13051
\(101\) 2577.51i 0.252672i 0.991987 + 0.126336i \(0.0403218\pi\)
−0.991987 + 0.126336i \(0.959678\pi\)
\(102\) −8562.20 + 4943.39i −0.822972 + 0.475143i
\(103\) 421.911 421.911i 0.0397691 0.0397691i −0.686943 0.726712i \(-0.741048\pi\)
0.726712 + 0.686943i \(0.241048\pi\)
\(104\) −4880.52 2817.77i −0.451232 0.260519i
\(105\) −18693.5 + 18693.5i −1.69555 + 1.69555i
\(106\) 152.334 + 568.517i 0.0135576 + 0.0505978i
\(107\) 2307.80 3997.22i 0.201572 0.349133i −0.747463 0.664303i \(-0.768728\pi\)
0.949035 + 0.315171i \(0.102062\pi\)
\(108\) 3174.48 5498.36i 0.272160 0.471396i
\(109\) 3403.55 12702.2i 0.286470 1.06912i −0.661288 0.750132i \(-0.729990\pi\)
0.947758 0.318990i \(-0.103344\pi\)
\(110\) 3021.52i 0.249713i
\(111\) −9481.11 3468.46i −0.769508 0.281508i
\(112\) 5082.04 0.405137
\(113\) −3575.81 958.137i −0.280039 0.0750361i 0.116066 0.993242i \(-0.462972\pi\)
−0.396105 + 0.918205i \(0.629638\pi\)
\(114\) 2366.02 + 1366.02i 0.182057 + 0.105111i
\(115\) 27452.8 + 15849.9i 2.07583 + 1.19848i
\(116\) −5501.68 + 1474.17i −0.408864 + 0.109555i
\(117\) −4687.62 4687.62i −0.342437 0.342437i
\(118\) −312.447 + 541.174i −0.0224395 + 0.0388663i
\(119\) −26614.8 26614.8i −1.87944 1.87944i
\(120\) 3766.62 + 6523.98i 0.261571 + 0.453054i
\(121\) 14081.1 0.961757
\(122\) 12336.1i 0.828819i
\(123\) 2751.61 + 4765.93i 0.181877 + 0.315019i
\(124\) −3913.42 + 1048.60i −0.254515 + 0.0681970i
\(125\) −25159.8 + 25159.8i −1.61023 + 1.61023i
\(126\) 5774.49 + 1547.27i 0.363724 + 0.0974596i
\(127\) −6402.95 11090.2i −0.396984 0.687596i 0.596368 0.802711i \(-0.296610\pi\)
−0.993352 + 0.115115i \(0.963276\pi\)
\(128\) 374.810 1398.81i 0.0228766 0.0853766i
\(129\) −1493.25 5572.89i −0.0897333 0.334889i
\(130\) 30719.0 8231.12i 1.81769 0.487049i
\(131\) 13341.2 + 3574.77i 0.777416 + 0.208308i 0.625645 0.780108i \(-0.284836\pi\)
0.151771 + 0.988416i \(0.451502\pi\)
\(132\) −1208.97 + 697.997i −0.0693851 + 0.0400595i
\(133\) −2691.95 + 10046.5i −0.152182 + 0.567951i
\(134\) −4232.68 4232.68i −0.235725 0.235725i
\(135\) 9273.12 + 34607.8i 0.508813 + 1.89892i
\(136\) −9288.50 + 5362.72i −0.502190 + 0.289939i
\(137\) 8360.31 0.445432 0.222716 0.974883i \(-0.428508\pi\)
0.222716 + 0.974883i \(0.428508\pi\)
\(138\) 14645.8i 0.769052i
\(139\) −17897.4 + 10333.1i −0.926317 + 0.534810i −0.885645 0.464363i \(-0.846283\pi\)
−0.0406724 + 0.999173i \(0.512950\pi\)
\(140\) −20279.2 + 20279.2i −1.03465 + 1.03465i
\(141\) 16914.3 + 9765.48i 0.850778 + 0.491197i
\(142\) −6447.33 + 6447.33i −0.319744 + 0.319744i
\(143\) 1525.32 + 5692.56i 0.0745913 + 0.278379i
\(144\) 851.759 1475.29i 0.0410763 0.0711463i
\(145\) 16071.2 27836.1i 0.764386 1.32395i
\(146\) −6732.92 + 25127.6i −0.315862 + 1.17881i
\(147\) 28793.2i 1.33246i
\(148\) −10285.4 3762.67i −0.469565 0.171780i
\(149\) 7002.63 0.315420 0.157710 0.987485i \(-0.449589\pi\)
0.157710 + 0.987485i \(0.449589\pi\)
\(150\) −28471.1 7628.81i −1.26538 0.339058i
\(151\) 30099.1 + 17377.7i 1.32008 + 0.762148i 0.983741 0.179593i \(-0.0574779\pi\)
0.336339 + 0.941741i \(0.390811\pi\)
\(152\) 2566.72 + 1481.89i 0.111094 + 0.0641402i
\(153\) −12186.8 + 3265.45i −0.520604 + 0.139495i
\(154\) −3757.95 3757.95i −0.158457 0.158457i
\(155\) 11431.7 19800.2i 0.475824 0.824151i
\(156\) 10389.8 + 10389.8i 0.426929 + 0.426929i
\(157\) −17524.5 30353.2i −0.710960 1.23142i −0.964497 0.264093i \(-0.914927\pi\)
0.253537 0.967326i \(-0.418406\pi\)
\(158\) 31093.8 1.24555
\(159\) 1534.56i 0.0607002i
\(160\) 4086.13 + 7077.39i 0.159614 + 0.276460i
\(161\) −53856.8 + 14430.9i −2.07773 + 0.556726i
\(162\) −7392.99 + 7392.99i −0.281702 + 0.281702i
\(163\) 24350.9 + 6524.80i 0.916515 + 0.245579i 0.686095 0.727512i \(-0.259323\pi\)
0.230420 + 0.973091i \(0.425990\pi\)
\(164\) 2985.02 + 5170.20i 0.110984 + 0.192230i
\(165\) 2038.95 7609.47i 0.0748926 0.279503i
\(166\) −4077.71 15218.2i −0.147979 0.552265i
\(167\) −1342.48 + 359.716i −0.0481365 + 0.0128981i −0.282807 0.959177i \(-0.591266\pi\)
0.234670 + 0.972075i \(0.424599\pi\)
\(168\) −12798.7 3429.41i −0.453469 0.121507i
\(169\) 28984.9 16734.5i 1.01484 0.585920i
\(170\) 15665.3 58463.7i 0.542052 2.02296i
\(171\) 2465.27 + 2465.27i 0.0843086 + 0.0843086i
\(172\) −1619.92 6045.62i −0.0547566 0.204354i
\(173\) −33415.9 + 19292.7i −1.11651 + 0.644614i −0.940506 0.339776i \(-0.889649\pi\)
−0.175999 + 0.984390i \(0.556315\pi\)
\(174\) 14850.3 0.490498
\(175\) 112213.i 3.66410i
\(176\) −1311.52 + 757.205i −0.0423398 + 0.0244449i
\(177\) 1152.06 1152.06i 0.0367730 0.0367730i
\(178\) −2602.20 1502.38i −0.0821298 0.0474177i
\(179\) 41819.1 41819.1i 1.30517 1.30517i 0.380318 0.924856i \(-0.375815\pi\)
0.924856 0.380318i \(-0.124185\pi\)
\(180\) 2488.11 + 9285.76i 0.0767936 + 0.286598i
\(181\) −18497.1 + 32038.0i −0.564608 + 0.977930i 0.432478 + 0.901645i \(0.357639\pi\)
−0.997086 + 0.0762857i \(0.975694\pi\)
\(182\) −27968.8 + 48443.3i −0.844366 + 1.46248i
\(183\) −8324.55 + 31067.6i −0.248576 + 0.927696i
\(184\) 15888.2i 0.469287i
\(185\) 56056.7 26027.9i 1.63789 0.760493i
\(186\) 10563.2 0.305331
\(187\) 10834.0 + 2902.95i 0.309816 + 0.0830150i
\(188\) 18349.1 + 10593.9i 0.519157 + 0.299736i
\(189\) −54575.9 31509.4i −1.52784 0.882098i
\(190\) −16155.4 + 4328.83i −0.447519 + 0.119912i
\(191\) −6845.27 6845.27i −0.187639 0.187639i 0.607035 0.794675i \(-0.292359\pi\)
−0.794675 + 0.607035i \(0.792359\pi\)
\(192\) −1887.86 + 3269.87i −0.0512115 + 0.0887009i
\(193\) 46468.5 + 46468.5i 1.24751 + 1.24751i 0.956816 + 0.290696i \(0.0938867\pi\)
0.290696 + 0.956816i \(0.406113\pi\)
\(194\) −13616.4 23584.3i −0.361792 0.626642i
\(195\) −82917.8 −2.18061
\(196\) 31235.6i 0.813088i
\(197\) 2911.48 + 5042.82i 0.0750206 + 0.129940i 0.901095 0.433621i \(-0.142764\pi\)
−0.826075 + 0.563561i \(0.809431\pi\)
\(198\) −1720.75 + 461.075i −0.0438923 + 0.0117609i
\(199\) 7387.55 7387.55i 0.186550 0.186550i −0.607653 0.794203i \(-0.707889\pi\)
0.794203 + 0.607653i \(0.207889\pi\)
\(200\) −30886.2 8275.94i −0.772156 0.206898i
\(201\) 7803.42 + 13515.9i 0.193149 + 0.334544i
\(202\) 1886.87 7041.89i 0.0462422 0.172578i
\(203\) 14632.4 + 54608.8i 0.355078 + 1.32517i
\(204\) 27011.2 7237.62i 0.649058 0.173914i
\(205\) −32542.3 8719.68i −0.774356 0.207488i
\(206\) −1461.54 + 843.821i −0.0344411 + 0.0198846i
\(207\) −4837.29 + 18053.0i −0.112892 + 0.421317i
\(208\) 11271.1 + 11271.1i 0.260519 + 0.260519i
\(209\) −802.181 2993.78i −0.0183645 0.0685373i
\(210\) 64756.1 37386.9i 1.46839 0.847777i
\(211\) −165.278 −0.00371236 −0.00185618 0.999998i \(-0.500591\pi\)
−0.00185618 + 0.999998i \(0.500591\pi\)
\(212\) 1664.73i 0.0370401i
\(213\) 20587.8 11886.4i 0.453786 0.261993i
\(214\) −9231.18 + 9231.18i −0.201572 + 0.201572i
\(215\) 30588.3 + 17660.2i 0.661726 + 0.382048i
\(216\) −12697.9 + 12697.9i −0.272160 + 0.272160i
\(217\) 10408.2 + 38844.0i 0.221033 + 0.824906i
\(218\) −18597.4 + 32211.6i −0.391326 + 0.677796i
\(219\) 33912.7 58738.5i 0.707088 1.22471i
\(220\) 2211.91 8254.95i 0.0457006 0.170557i
\(221\) 118054.i 2.41711i
\(222\) 23363.8 + 16416.7i 0.474064 + 0.333103i
\(223\) 17804.5 0.358030 0.179015 0.983846i \(-0.442709\pi\)
0.179015 + 0.983846i \(0.442709\pi\)
\(224\) −13884.4 3720.31i −0.276714 0.0741452i
\(225\) −32574.9 18807.1i −0.643455 0.371499i
\(226\) 9067.90 + 5235.36i 0.177537 + 0.102501i
\(227\) 44745.1 11989.4i 0.868348 0.232673i 0.202974 0.979184i \(-0.434939\pi\)
0.665373 + 0.746511i \(0.268272\pi\)
\(228\) −5464.08 5464.08i −0.105111 0.105111i
\(229\) −25747.3 + 44595.7i −0.490977 + 0.850397i −0.999946 0.0103877i \(-0.996693\pi\)
0.508969 + 0.860785i \(0.330027\pi\)
\(230\) −63399.6 63399.6i −1.19848 1.19848i
\(231\) 6928.21 + 12000.0i 0.129837 + 0.224884i
\(232\) 16110.0 0.299309
\(233\) 24235.7i 0.446419i 0.974770 + 0.223210i \(0.0716534\pi\)
−0.974770 + 0.223210i \(0.928347\pi\)
\(234\) 9375.23 + 16238.4i 0.171218 + 0.296559i
\(235\) −115493. + 30946.2i −2.09131 + 0.560366i
\(236\) 1249.79 1249.79i 0.0224395 0.0224395i
\(237\) −78307.4 20982.4i −1.39414 0.373558i
\(238\) 53229.6 + 92196.3i 0.939721 + 1.62765i
\(239\) −12582.0 + 46956.6i −0.220269 + 0.822055i 0.763976 + 0.645245i \(0.223245\pi\)
−0.984245 + 0.176810i \(0.943422\pi\)
\(240\) −5514.72 20581.2i −0.0957416 0.357313i
\(241\) −8229.58 + 2205.11i −0.141691 + 0.0379661i −0.328968 0.944341i \(-0.606701\pi\)
0.187276 + 0.982307i \(0.440034\pi\)
\(242\) −38470.2 10308.1i −0.656892 0.176014i
\(243\) −32063.3 + 18511.8i −0.542996 + 0.313499i
\(244\) −9030.69 + 33703.0i −0.151684 + 0.566094i
\(245\) 124641. + 124641.i 2.07649 + 2.07649i
\(246\) −4028.64 15035.1i −0.0665714 0.248448i
\(247\) −28251.6 + 16311.1i −0.463073 + 0.267355i
\(248\) 11459.3 0.186318
\(249\) 41077.6i 0.662531i
\(250\) 87156.1 50319.6i 1.39450 0.805114i
\(251\) 26642.1 26642.1i 0.422884 0.422884i −0.463312 0.886195i \(-0.653339\pi\)
0.886195 + 0.463312i \(0.153339\pi\)
\(252\) −14643.5 8454.43i −0.230592 0.133132i
\(253\) 11748.6 11748.6i 0.183547 0.183547i
\(254\) 9374.57 + 34986.4i 0.145306 + 0.542290i
\(255\) −78903.7 + 136665.i −1.21344 + 2.10173i
\(256\) −2048.00 + 3547.24i −0.0312500 + 0.0541266i
\(257\) −1821.16 + 6796.68i −0.0275729 + 0.102904i −0.978341 0.207000i \(-0.933630\pi\)
0.950768 + 0.309903i \(0.100297\pi\)
\(258\) 16318.6i 0.245156i
\(259\) −37347.7 + 102091.i −0.556756 + 1.52191i
\(260\) −89951.4 −1.33064
\(261\) 18305.1 + 4904.83i 0.268714 + 0.0720017i
\(262\) −33832.0 19532.9i −0.492862 0.284554i
\(263\) 97555.0 + 56323.4i 1.41039 + 0.814287i 0.995424 0.0955522i \(-0.0304617\pi\)
0.414962 + 0.909839i \(0.363795\pi\)
\(264\) 3813.92 1021.94i 0.0547223 0.0146628i
\(265\) 6642.88 + 6642.88i 0.0945943 + 0.0945943i
\(266\) 14709.1 25476.9i 0.207884 0.360067i
\(267\) 5539.62 + 5539.62i 0.0777065 + 0.0777065i
\(268\) 8465.35 + 14662.4i 0.117862 + 0.204144i
\(269\) −19015.0 −0.262780 −0.131390 0.991331i \(-0.541944\pi\)
−0.131390 + 0.991331i \(0.541944\pi\)
\(270\) 101339.i 1.39010i
\(271\) −39396.4 68236.6i −0.536437 0.929135i −0.999092 0.0425974i \(-0.986437\pi\)
0.462656 0.886538i \(-0.346897\pi\)
\(272\) 29302.4 7851.57i 0.396065 0.106125i
\(273\) 103127. 103127.i 1.38372 1.38372i
\(274\) −22840.8 6120.17i −0.304235 0.0815197i
\(275\) 16719.4 + 28958.8i 0.221082 + 0.382926i
\(276\) 10721.5 40013.1i 0.140746 0.525272i
\(277\) 23042.4 + 85995.3i 0.300309 + 1.12077i 0.936909 + 0.349573i \(0.113673\pi\)
−0.636601 + 0.771194i \(0.719660\pi\)
\(278\) 56460.9 15128.6i 0.730563 0.195754i
\(279\) 13020.7 + 3488.87i 0.167272 + 0.0448205i
\(280\) 70249.1 40558.3i 0.896035 0.517326i
\(281\) −3171.64 + 11836.7i −0.0401672 + 0.149906i −0.983097 0.183086i \(-0.941391\pi\)
0.942930 + 0.332992i \(0.108058\pi\)
\(282\) −39061.9 39061.9i −0.491197 0.491197i
\(283\) −24519.3 91507.1i −0.306150 1.14257i −0.931951 0.362585i \(-0.881894\pi\)
0.625801 0.779983i \(-0.284772\pi\)
\(284\) 22334.2 12894.7i 0.276907 0.159872i
\(285\) 43607.3 0.536871
\(286\) 16669.0i 0.203787i
\(287\) 51318.7 29628.9i 0.623034 0.359709i
\(288\) −3407.03 + 3407.03i −0.0410763 + 0.0410763i
\(289\) −122245. 70578.4i −1.46365 0.845038i
\(290\) −64284.8 + 64284.8i −0.764386 + 0.764386i
\(291\) 18377.0 + 68583.7i 0.217014 + 0.809907i
\(292\) 36789.4 63721.0i 0.431476 0.747338i
\(293\) 30435.0 52715.0i 0.354518 0.614043i −0.632517 0.774546i \(-0.717978\pi\)
0.987035 + 0.160503i \(0.0513116\pi\)
\(294\) −21078.1 + 78664.4i −0.243857 + 0.910088i
\(295\) 9974.21i 0.114613i
\(296\) 25345.7 + 17809.2i 0.289281 + 0.203264i
\(297\) 18779.2 0.212894
\(298\) −19131.5 5126.28i −0.215436 0.0577258i
\(299\) −151450. 87439.9i −1.69406 0.978064i
\(300\) 72199.9 + 41684.6i 0.802221 + 0.463162i
\(301\) −60008.0 + 16079.1i −0.662332 + 0.177471i
\(302\) −69511.0 69511.0i −0.762148 0.762148i
\(303\) −9503.86 + 16461.2i −0.103518 + 0.179298i
\(304\) −5927.58 5927.58i −0.0641402 0.0641402i
\(305\) −98451.4 170523.i −1.05833 1.83309i
\(306\) 35685.5 0.381109
\(307\) 8323.80i 0.0883171i 0.999025 + 0.0441586i \(0.0140607\pi\)
−0.999025 + 0.0441586i \(0.985939\pi\)
\(308\) 7515.91 + 13017.9i 0.0792283 + 0.137227i
\(309\) 4250.20 1138.84i 0.0445135 0.0119274i
\(310\) −45726.7 + 45726.7i −0.475824 + 0.475824i
\(311\) −108541. 29083.6i −1.12221 0.300695i −0.350433 0.936588i \(-0.613966\pi\)
−0.771778 + 0.635892i \(0.780632\pi\)
\(312\) −20779.5 35991.2i −0.213465 0.369732i
\(313\) −18785.4 + 70107.9i −0.191748 + 0.715614i 0.801337 + 0.598214i \(0.204123\pi\)
−0.993085 + 0.117400i \(0.962544\pi\)
\(314\) 25657.6 + 95755.4i 0.260229 + 0.971190i
\(315\) 92169.2 24696.7i 0.928890 0.248895i
\(316\) −84949.9 22762.3i −0.850724 0.227951i
\(317\) −17647.3 + 10188.7i −0.175615 + 0.101391i −0.585231 0.810867i \(-0.698996\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(318\) −1123.38 + 4192.50i −0.0111089 + 0.0414590i
\(319\) −11912.7 11912.7i −0.117065 0.117065i
\(320\) −5982.51 22327.0i −0.0584230 0.218037i
\(321\) 29477.3 17018.7i 0.286074 0.165165i
\(322\) 157704. 1.52100
\(323\) 62085.8i 0.595097i
\(324\) 25610.1 14786.0i 0.243961 0.140851i
\(325\) 248869. 248869.i 2.35616 2.35616i
\(326\) −61751.4 35652.2i −0.581047 0.335468i
\(327\) 68572.7 68572.7i 0.641292 0.641292i
\(328\) −4370.37 16310.4i −0.0406229 0.151607i
\(329\) 105153. 182130.i 0.971471 1.68264i
\(330\) −11141.0 + 19296.8i −0.102305 + 0.177198i
\(331\) 27718.0 103445.i 0.252992 0.944178i −0.716205 0.697890i \(-0.754122\pi\)
0.969197 0.246288i \(-0.0792108\pi\)
\(332\) 44562.0i 0.404286i
\(333\) 23376.9 + 27952.5i 0.210814 + 0.252076i
\(334\) 3931.05 0.0352383
\(335\) −92288.2 24728.5i −0.822350 0.220348i
\(336\) 32456.2 + 18738.6i 0.287488 + 0.165981i
\(337\) −7047.82 4069.06i −0.0620576 0.0358290i 0.468650 0.883384i \(-0.344740\pi\)
−0.530708 + 0.847555i \(0.678074\pi\)
\(338\) −91438.8 + 24500.9i −0.800381 + 0.214461i
\(339\) −19303.9 19303.9i −0.167976 0.167976i
\(340\) −85596.8 + 148258.i −0.740456 + 1.28251i
\(341\) −8473.66 8473.66i −0.0728723 0.0728723i
\(342\) −4930.53 8539.94i −0.0421543 0.0730134i
\(343\) −119384. −1.01475
\(344\) 17702.8i 0.149598i
\(345\) 116884. + 202450.i 0.982015 + 1.70090i
\(346\) 105417. 28246.4i 0.880560 0.235945i
\(347\) 11850.1 11850.1i 0.0984150 0.0984150i −0.656185 0.754600i \(-0.727831\pi\)
0.754600 + 0.656185i \(0.227831\pi\)
\(348\) −40571.8 10871.2i −0.335017 0.0897674i
\(349\) 21225.1 + 36762.9i 0.174260 + 0.301827i 0.939905 0.341436i \(-0.110913\pi\)
−0.765645 + 0.643264i \(0.777580\pi\)
\(350\) −82145.8 + 306572.i −0.670578 + 2.50263i
\(351\) −51157.5 190922.i −0.415236 1.54968i
\(352\) 4137.45 1108.63i 0.0333924 0.00894745i
\(353\) 55303.5 + 14818.5i 0.443816 + 0.118920i 0.473805 0.880630i \(-0.342880\pi\)
−0.0299882 + 0.999550i \(0.509547\pi\)
\(354\) −3990.86 + 2304.12i −0.0318464 + 0.0183865i
\(355\) −37667.2 + 140576.i −0.298887 + 1.11546i
\(356\) 6009.53 + 6009.53i 0.0474177 + 0.0474177i
\(357\) −71839.6 268109.i −0.563673 2.10366i
\(358\) −144866. + 83638.1i −1.13031 + 0.652587i
\(359\) 250770. 1.94575 0.972876 0.231329i \(-0.0743074\pi\)
0.972876 + 0.231329i \(0.0743074\pi\)
\(360\) 27190.6i 0.209804i
\(361\) −98003.5 + 56582.3i −0.752016 + 0.434177i
\(362\) 73988.5 73988.5i 0.564608 0.564608i
\(363\) 89928.3 + 51920.1i 0.682469 + 0.394024i
\(364\) 111875. 111875.i 0.844366 0.844366i
\(365\) 107467. + 401073.i 0.806659 + 3.01049i
\(366\) 45486.2 78784.3i 0.339560 0.588136i
\(367\) −3655.93 + 6332.26i −0.0271435 + 0.0470139i −0.879278 0.476309i \(-0.841974\pi\)
0.852135 + 0.523323i \(0.175308\pi\)
\(368\) 11631.0 43407.3i 0.0858855 0.320529i
\(369\) 19863.4i 0.145882i
\(370\) −172204. + 30073.1i −1.25788 + 0.219672i
\(371\) −16523.9 −0.120051
\(372\) −28859.3 7732.83i −0.208545 0.0558795i
\(373\) 82552.3 + 47661.6i 0.593351 + 0.342571i 0.766421 0.642338i \(-0.222035\pi\)
−0.173070 + 0.984909i \(0.555369\pi\)
\(374\) −27473.8 15862.0i −0.196416 0.113401i
\(375\) −253452. + 67912.3i −1.80233 + 0.482932i
\(376\) −42375.4 42375.4i −0.299736 0.299736i
\(377\) −88660.8 + 153565.i −0.623805 + 1.08046i
\(378\) 126038. + 126038.i 0.882098 + 0.882098i
\(379\) 46750.0 + 80973.4i 0.325464 + 0.563721i 0.981606 0.190917i \(-0.0611460\pi\)
−0.656142 + 0.754638i \(0.727813\pi\)
\(380\) 47306.4 0.327607
\(381\) 94436.5i 0.650564i
\(382\) 13690.5 + 23712.7i 0.0938196 + 0.162500i
\(383\) −49257.8 + 13198.6i −0.335797 + 0.0899766i −0.422778 0.906233i \(-0.638945\pi\)
0.0869804 + 0.996210i \(0.472278\pi\)
\(384\) 7551.44 7551.44i 0.0512115 0.0512115i
\(385\) −81937.5 21955.1i −0.552791 0.148120i
\(386\) −92937.1 160972.i −0.623756 1.08038i
\(387\) −5389.77 + 20114.9i −0.0359872 + 0.134306i
\(388\) 19935.8 + 74401.4i 0.132425 + 0.494217i
\(389\) −133806. + 35853.3i −0.884256 + 0.236936i −0.672242 0.740331i \(-0.734669\pi\)
−0.212013 + 0.977267i \(0.568002\pi\)
\(390\) 226536. + 60700.0i 1.48939 + 0.399080i
\(391\) −288237. + 166414.i −1.88537 + 1.08852i
\(392\) −22866.0 + 85337.2i −0.148805 + 0.555349i
\(393\) 72022.3 + 72022.3i 0.466318 + 0.466318i
\(394\) −4262.70 15908.6i −0.0274595 0.102480i
\(395\) 429811. 248151.i 2.75475 1.59046i
\(396\) 5038.72 0.0321314
\(397\) 125916.i 0.798914i −0.916752 0.399457i \(-0.869199\pi\)
0.916752 0.399457i \(-0.130801\pi\)
\(398\) −25591.2 + 14775.1i −0.161557 + 0.0932748i
\(399\) −54235.7 + 54235.7i −0.340674 + 0.340674i
\(400\) 78324.3 + 45220.6i 0.489527 + 0.282629i
\(401\) 6608.59 6608.59i 0.0410979 0.0410979i −0.686259 0.727357i \(-0.740748\pi\)
0.727357 + 0.686259i \(0.240748\pi\)
\(402\) −11425.0 42638.7i −0.0706975 0.263847i
\(403\) −63065.7 + 109233.i −0.388314 + 0.672579i
\(404\) −10310.0 + 17857.5i −0.0631681 + 0.109410i
\(405\) −43192.1 + 161195.i −0.263326 + 0.982746i
\(406\) 159906.i 0.970090i
\(407\) −5572.88 31911.2i −0.0336427 0.192644i
\(408\) −79094.2 −0.475143
\(409\) 201785. + 54068.2i 1.20627 + 0.323218i 0.805296 0.592873i \(-0.202007\pi\)
0.400970 + 0.916091i \(0.368673\pi\)
\(410\) 82524.0 + 47645.2i 0.490922 + 0.283434i
\(411\) 53392.8 + 30826.3i 0.316081 + 0.182490i
\(412\) 4610.72 1235.44i 0.0271628 0.00727825i
\(413\) −12405.2 12405.2i −0.0727284 0.0727284i
\(414\) 26431.4 45780.6i 0.154213 0.267104i
\(415\) −177819. 177819.i −1.03248 1.03248i
\(416\) −22542.2 39044.2i −0.130259 0.225616i
\(417\) −152401. −0.876428
\(418\) 8766.40i 0.0501728i
\(419\) −88582.6 153430.i −0.504569 0.873939i −0.999986 0.00528379i \(-0.998318\pi\)
0.495417 0.868655i \(-0.335015\pi\)
\(420\) −204286. + 54738.3i −1.15808 + 0.310308i
\(421\) 15323.1 15323.1i 0.0864536 0.0864536i −0.662557 0.749011i \(-0.730529\pi\)
0.749011 + 0.662557i \(0.230529\pi\)
\(422\) 451.548 + 120.992i 0.00253559 + 0.000679410i
\(423\) −35247.7 61050.8i −0.196993 0.341201i
\(424\) −1218.67 + 4548.13i −0.00677882 + 0.0252989i
\(425\) −173365. 647008.i −0.959808 3.58205i
\(426\) −64948.4 + 17402.9i −0.357890 + 0.0958962i
\(427\) 334531. + 89637.3i 1.83477 + 0.491624i
\(428\) 31977.8 18462.4i 0.174566 0.100786i
\(429\) −11248.4 + 41979.5i −0.0611189 + 0.228099i
\(430\) −70640.6 70640.6i −0.382048 0.382048i
\(431\) 71479.1 + 266764.i 0.384791 + 1.43606i 0.838496 + 0.544907i \(0.183435\pi\)
−0.453705 + 0.891152i \(0.649898\pi\)
\(432\) 43986.9 25395.8i 0.235698 0.136080i
\(433\) −54416.2 −0.290237 −0.145118 0.989414i \(-0.546356\pi\)
−0.145118 + 0.989414i \(0.546356\pi\)
\(434\) 113743.i 0.603873i
\(435\) 205276. 118516.i 1.08483 0.626325i
\(436\) 74389.5 74389.5i 0.391326 0.391326i
\(437\) 79649.3 + 45985.6i 0.417080 + 0.240801i
\(438\) −135651. + 135651.i −0.707088 + 0.707088i
\(439\) −23033.9 85963.5i −0.119519 0.446052i 0.880066 0.474851i \(-0.157498\pi\)
−0.999585 + 0.0287997i \(0.990831\pi\)
\(440\) −12086.1 + 20933.7i −0.0624282 + 0.108129i
\(441\) −51963.2 + 90002.9i −0.267189 + 0.462785i
\(442\) −86421.5 + 322529.i −0.442361 + 1.65092i
\(443\) 124255.i 0.633149i 0.948568 + 0.316574i \(0.102533\pi\)
−0.948568 + 0.316574i \(0.897467\pi\)
\(444\) −51813.2 61954.6i −0.262830 0.314273i
\(445\) −47960.4 −0.242194
\(446\) −48642.7 13033.8i −0.244539 0.0655240i
\(447\) 44722.1 + 25820.3i 0.223824 + 0.129225i
\(448\) 35209.4 + 20328.2i 0.175429 + 0.101284i
\(449\) 265772. 71213.4i 1.31831 0.353240i 0.469964 0.882685i \(-0.344267\pi\)
0.848344 + 0.529446i \(0.177600\pi\)
\(450\) 75228.5 + 75228.5i 0.371499 + 0.371499i
\(451\) −8829.19 + 15292.6i −0.0434078 + 0.0751845i
\(452\) −20941.4 20941.4i −0.102501 0.102501i
\(453\) 128151. + 221965.i 0.624492 + 1.08165i
\(454\) −131023. −0.635674
\(455\) 892844.i 4.31274i
\(456\) 10928.2 + 18928.1i 0.0525554 + 0.0910287i
\(457\) −257063. + 68879.9i −1.23086 + 0.329807i −0.814913 0.579583i \(-0.803215\pi\)
−0.415944 + 0.909390i \(0.636549\pi\)
\(458\) 102989. 102989.i 0.490977 0.490977i
\(459\) −363359. 97361.8i −1.72469 0.462129i
\(460\) 126799. + 219623.i 0.599240 + 1.03791i
\(461\) 91736.8 342366.i 0.431660 1.61098i −0.317276 0.948333i \(-0.602768\pi\)
0.748936 0.662643i \(-0.230565\pi\)
\(462\) −10143.6 37856.5i −0.0475235 0.177360i
\(463\) 305237. 81788.0i 1.42389 0.381529i 0.537026 0.843566i \(-0.319548\pi\)
0.886861 + 0.462037i \(0.152881\pi\)
\(464\) −44013.4 11793.4i −0.204432 0.0547774i
\(465\) 146016. 84302.3i 0.675296 0.389882i
\(466\) 17741.7 66213.0i 0.0817004 0.304910i
\(467\) 22323.5 + 22323.5i 0.102359 + 0.102359i 0.756432 0.654072i \(-0.226941\pi\)
−0.654072 + 0.756432i \(0.726941\pi\)
\(468\) −13726.3 51227.2i −0.0626703 0.233889i
\(469\) 145537. 84025.9i 0.661649 0.382003i
\(470\) 338186. 1.53095
\(471\) 258467.i 1.16510i
\(472\) −4329.39 + 2499.58i −0.0194331 + 0.0112197i
\(473\) 13090.5 13090.5i 0.0585105 0.0585105i
\(474\) 198580. + 114650.i 0.883848 + 0.510290i
\(475\) −130883. + 130883.i −0.580091 + 0.580091i
\(476\) −77933.5 290852.i −0.343962 1.28368i
\(477\) −2769.43 + 4796.80i −0.0121718 + 0.0210821i
\(478\) 68749.3 119077.i 0.300893 0.521162i
\(479\) −55066.6 + 205511.i −0.240003 + 0.895705i 0.735826 + 0.677171i \(0.236794\pi\)
−0.975829 + 0.218534i \(0.929873\pi\)
\(480\) 60266.0i 0.261571i
\(481\) −309251. + 143589.i −1.33666 + 0.620629i
\(482\) 24097.9 0.103725
\(483\) −397165. 106420.i −1.70246 0.456172i
\(484\) 97556.6 + 56324.3i 0.416453 + 0.240439i
\(485\) −376440. 217338.i −1.60034 0.923956i
\(486\) 101150. 27103.1i 0.428247 0.114748i
\(487\) −180349. 180349.i −0.760422 0.760422i 0.215976 0.976399i \(-0.430707\pi\)
−0.976399 + 0.215976i \(0.930707\pi\)
\(488\) 49344.6 85467.3i 0.207205 0.358889i
\(489\) 131458. + 131458.i 0.549753 + 0.549753i
\(490\) −249283. 431770.i −1.03824 1.79829i
\(491\) 440636. 1.82775 0.913876 0.405994i \(-0.133075\pi\)
0.913876 + 0.405994i \(0.133075\pi\)
\(492\) 44025.8i 0.181877i
\(493\) 168737. + 292262.i 0.694252 + 1.20248i
\(494\) 89125.5 23881.1i 0.365214 0.0978589i
\(495\) −20106.3 + 20106.3i −0.0820582 + 0.0820582i
\(496\) −31307.3 8388.78i −0.127257 0.0340985i
\(497\) −127990. 221686.i −0.518161 0.897481i
\(498\) 30070.9 112226.i 0.121252 0.452517i
\(499\) −10387.3 38765.9i −0.0417158 0.155686i 0.941926 0.335820i \(-0.109013\pi\)
−0.983642 + 0.180134i \(0.942347\pi\)
\(500\) −274951. + 73673.0i −1.09981 + 0.294692i
\(501\) −9900.04 2652.71i −0.0394422 0.0105685i
\(502\) −92290.9 + 53284.2i −0.366228 + 0.211442i
\(503\) −7896.18 + 29469.0i −0.0312091 + 0.116474i −0.979773 0.200111i \(-0.935870\pi\)
0.948564 + 0.316585i \(0.102536\pi\)
\(504\) 33817.7 + 33817.7i 0.133132 + 0.133132i
\(505\) −30117.1 112399.i −0.118095 0.440736i
\(506\) −40698.5 + 23497.3i −0.158956 + 0.0917734i
\(507\) 246815. 0.960186
\(508\) 102447.i 0.396984i
\(509\) 110400. 63739.7i 0.426123 0.246022i −0.271570 0.962419i \(-0.587543\pi\)
0.697694 + 0.716396i \(0.254210\pi\)
\(510\) 315615. 315615.i 1.21344 1.21344i
\(511\) −632486. 365166.i −2.42219 1.39845i
\(512\) 8192.00 8192.00i 0.0312500 0.0312500i
\(513\) 26904.3 + 100408.i 0.102232 + 0.381535i
\(514\) 9951.03 17235.7i 0.0376653 0.0652383i
\(515\) −13468.6 + 23328.3i −0.0507818 + 0.0879567i
\(516\) 11946.0 44583.1i 0.0448667 0.167445i
\(517\) 62669.7i 0.234464i
\(518\) 176772. 251577.i 0.658799 0.937588i
\(519\) −284546. −1.05637
\(520\) 245752. + 65849.0i 0.908845 + 0.243524i
\(521\) 63176.1 + 36474.8i 0.232744 + 0.134375i 0.611837 0.790984i \(-0.290431\pi\)
−0.379094 + 0.925358i \(0.623764\pi\)
\(522\) −46419.8 26800.5i −0.170358 0.0983562i
\(523\) −8057.10 + 2158.89i −0.0294561 + 0.00789274i −0.273517 0.961867i \(-0.588187\pi\)
0.244061 + 0.969760i \(0.421520\pi\)
\(524\) 78131.7 + 78131.7i 0.284554 + 0.284554i
\(525\) 413755. 716646.i 1.50115 2.60007i
\(526\) −225294. 225294.i −0.814287 0.814287i
\(527\) 120025. + 207890.i 0.432167 + 0.748534i
\(528\) −11167.9 −0.0400595
\(529\) 213195.i 0.761842i
\(530\) −13285.8 23011.6i −0.0472971 0.0819211i
\(531\) −5680.30 + 1522.03i −0.0201457 + 0.00539803i
\(532\) −58836.3 + 58836.3i −0.207884 + 0.207884i
\(533\) 179528. + 48104.3i 0.631942 + 0.169328i
\(534\) −11079.2 19189.8i −0.0388533 0.0672958i
\(535\) −53931.3 + 201274.i −0.188423 + 0.703203i
\(536\) −12394.1 46255.5i −0.0431406 0.161003i
\(537\) 421272. 112880.i 1.46088 0.391441i
\(538\) 51950.1 + 13920.0i 0.179482 + 0.0480921i
\(539\) 80011.7 46194.8i 0.275408 0.159007i
\(540\) −74185.0 + 276862.i −0.254407 + 0.949459i
\(541\) −124056. 124056.i −0.423862 0.423862i 0.462669 0.886531i \(-0.346892\pi\)
−0.886531 + 0.462669i \(0.846892\pi\)
\(542\) 57680.4 + 215266.i 0.196349 + 0.732786i
\(543\) −236263. + 136406.i −0.801300 + 0.462631i
\(544\) −85803.5 −0.289939
\(545\) 593682.i 1.99876i
\(546\) −357243. + 206254.i −1.19834 + 0.691860i
\(547\) 357891. 357891.i 1.19612 1.19612i 0.220806 0.975318i \(-0.429131\pi\)
0.975318 0.220806i \(-0.0708687\pi\)
\(548\) 57921.9 + 33441.2i 0.192878 + 0.111358i
\(549\) 82089.2 82089.2i 0.272359 0.272359i
\(550\) −24478.8 91356.3i −0.0809218 0.302004i
\(551\) 46627.7 80761.5i 0.153582 0.266012i
\(552\) −58583.3 + 101469.i −0.192263 + 0.333009i
\(553\) −225935. + 843200.i −0.738810 + 2.75728i
\(554\) 251812.i 0.820458i
\(555\) 453975. + 40467.7i 1.47382 + 0.131378i
\(556\) −165329. −0.534810
\(557\) −536150. 143661.i −1.72813 0.463051i −0.748378 0.663272i \(-0.769167\pi\)
−0.979751 + 0.200221i \(0.935834\pi\)
\(558\) −33019.0 19063.6i −0.106046 0.0612259i
\(559\) −168748. 97426.6i −0.540026 0.311784i
\(560\) −221615. + 59381.5i −0.706680 + 0.189354i
\(561\) 58486.9 + 58486.9i 0.185837 + 0.185837i
\(562\) 17330.2 30016.7i 0.0548694 0.0950366i
\(563\) −102838. 102838.i −0.324442 0.324442i 0.526026 0.850468i \(-0.323681\pi\)
−0.850468 + 0.526026i \(0.823681\pi\)
\(564\) 78123.9 + 135314.i 0.245598 + 0.425389i
\(565\) 167128. 0.523542
\(566\) 267951.i 0.836418i
\(567\) −146764. 254202.i −0.456512 0.790702i
\(568\) −70457.7 + 18879.1i −0.218389 + 0.0585173i
\(569\) 100260. 100260.i 0.309674 0.309674i −0.535109 0.844783i \(-0.679730\pi\)
0.844783 + 0.535109i \(0.179730\pi\)
\(570\) −119137. 31922.8i −0.366690 0.0982542i
\(571\) 126878. + 219760.i 0.389148 + 0.674025i 0.992335 0.123575i \(-0.0394360\pi\)
−0.603187 + 0.797600i \(0.706103\pi\)
\(572\) −12202.5 + 45540.5i −0.0372957 + 0.139189i
\(573\) −18477.0 68957.1i −0.0562759 0.210024i
\(574\) −161895. + 43379.7i −0.491372 + 0.131663i
\(575\) −958449. 256816.i −2.89890 0.776758i
\(576\) 11802.3 6814.07i 0.0355731 0.0205382i
\(577\) −48666.0 + 181624.i −0.146175 + 0.545533i 0.853525 + 0.521052i \(0.174460\pi\)
−0.999700 + 0.0244816i \(0.992206\pi\)
\(578\) 282314. + 282314.i 0.845038 + 0.845038i
\(579\) 125430. + 468110.i 0.374148 + 1.39634i
\(580\) 222689. 128570.i 0.661977 0.382193i
\(581\) 442316. 1.31033
\(582\) 200827.i 0.592893i
\(583\) 4264.31 2462.00i 0.0125462 0.00724354i
\(584\) −147157. + 147157.i −0.431476 + 0.431476i
\(585\) 259188. + 149642.i 0.757362 + 0.437263i
\(586\) −121740. + 121740.i −0.354518 + 0.354518i
\(587\) −143947. 537216.i −0.417759 1.55910i −0.779245 0.626719i \(-0.784397\pi\)
0.361486 0.932377i \(-0.382269\pi\)
\(588\) 115173. 199485.i 0.333115 0.576973i
\(589\) 33166.9 57446.7i 0.0956036 0.165590i
\(590\) 7301.63 27250.1i 0.0209757 0.0782823i
\(591\) 42941.1i 0.122941i
\(592\) −56208.4 67210.0i −0.160383 0.191774i
\(593\) −674610. −1.91842 −0.959210 0.282695i \(-0.908772\pi\)
−0.959210 + 0.282695i \(0.908772\pi\)
\(594\) −51305.6 13747.3i −0.145409 0.0389623i
\(595\) 1.47159e6 + 849621.i 4.15673 + 2.39989i
\(596\) 48515.7 + 28010.5i 0.136581 + 0.0788549i
\(597\) 74419.9 19940.7i 0.208805 0.0559491i
\(598\) 349760. + 349760.i 0.978064 + 0.978064i
\(599\) 144517. 250311.i 0.402777 0.697631i −0.591283 0.806464i \(-0.701378\pi\)
0.994060 + 0.108834i \(0.0347116\pi\)
\(600\) −166738. 166738.i −0.463162 0.463162i
\(601\) −295558. 511922.i −0.818265 1.41728i −0.906959 0.421218i \(-0.861603\pi\)
0.0886941 0.996059i \(-0.471731\pi\)
\(602\) 175716. 0.484861
\(603\) 56331.5i 0.154923i
\(604\) 139022. + 240793.i 0.381074 + 0.660040i
\(605\) −614040. + 164532.i −1.67759 + 0.449509i
\(606\) 38015.4 38015.4i 0.103518 0.103518i
\(607\) 292148. + 78280.9i 0.792914 + 0.212461i 0.632470 0.774585i \(-0.282041\pi\)
0.160443 + 0.987045i \(0.448708\pi\)
\(608\) 11855.2 + 20533.7i 0.0320701 + 0.0555470i
\(609\) −107906. + 402710.i −0.290945 + 1.08582i
\(610\) 144143. + 537948.i 0.387377 + 1.44571i
\(611\) 637145. 170722.i 1.70669 0.457307i
\(612\) −97494.6 26123.6i −0.260302 0.0697477i
\(613\) −457797. + 264309.i −1.21829 + 0.703382i −0.964553 0.263890i \(-0.914994\pi\)
−0.253741 + 0.967272i \(0.581661\pi\)
\(614\) 6093.44 22741.0i 0.0161632 0.0603217i
\(615\) −175679. 175679.i −0.464482 0.464482i
\(616\) −11004.1 41067.7i −0.0289996 0.108228i
\(617\) −445642. + 257292.i −1.17062 + 0.675858i −0.953826 0.300359i \(-0.902893\pi\)
−0.216794 + 0.976217i \(0.569560\pi\)
\(618\) −12445.4 −0.0325862
\(619\) 208300.i 0.543635i −0.962349 0.271817i \(-0.912375\pi\)
0.962349 0.271817i \(-0.0876247\pi\)
\(620\) 158402. 91453.4i 0.412076 0.237912i
\(621\) −394037. + 394037.i −1.02177 + 1.02177i
\(622\) 275250. + 158916.i 0.711453 + 0.410758i
\(623\) 59649.7 59649.7i 0.153685 0.153685i
\(624\) 30423.3 + 113541.i 0.0781335 + 0.291598i
\(625\) 361567. 626252.i 0.925611 1.60320i
\(626\) 102645. 177787.i 0.261933 0.453681i
\(627\) 5915.64 22077.5i 0.0150476 0.0561584i
\(628\) 280391.i 0.710960i
\(629\) −57615.9 + 646346.i −0.145627 + 1.63367i
\(630\) −269890. −0.679995
\(631\) 85248.6 + 22842.3i 0.214106 + 0.0573695i 0.364277 0.931290i \(-0.381316\pi\)
−0.150172 + 0.988660i \(0.547983\pi\)
\(632\) 215424. + 124375.i 0.539337 + 0.311387i
\(633\) −1055.54 609.418i −0.00263432 0.00152092i
\(634\) 55672.1 14917.3i 0.138503 0.0371117i
\(635\) 408801. + 408801.i 1.01383 + 1.01383i
\(636\) 6138.24 10631.8i 0.0151750 0.0262839i
\(637\) −687615. 687615.i −1.69460 1.69460i
\(638\) 23825.4 + 41266.8i 0.0585327 + 0.101382i
\(639\) −85805.7 −0.210143
\(640\) 65378.1i 0.159614i
\(641\) 361270. + 625738.i 0.879257 + 1.52292i 0.852158 + 0.523285i \(0.175294\pi\)
0.0270995 + 0.999633i \(0.491373\pi\)
\(642\) −92992.1 + 24917.2i −0.225619 + 0.0604545i
\(643\) 370460. 370460.i 0.896023 0.896023i −0.0990586 0.995082i \(-0.531583\pi\)
0.995082 + 0.0990586i \(0.0315831\pi\)
\(644\) −430855. 115447.i −1.03887 0.278363i
\(645\) 130234. + 225572.i 0.313044 + 0.542207i
\(646\) 45450.0 169622.i 0.108910 0.406459i
\(647\) −141741. 528986.i −0.338601 1.26368i −0.899912 0.436071i \(-0.856370\pi\)
0.561311 0.827605i \(-0.310297\pi\)
\(648\) −80792.1 + 21648.2i −0.192406 + 0.0515551i
\(649\) 5049.74 + 1353.07i 0.0119889 + 0.00321242i
\(650\) −862109. + 497739.i −2.04050 + 1.17808i
\(651\) −76754.9 + 286453.i −0.181111 + 0.675915i
\(652\) 142609. + 142609.i 0.335468 + 0.335468i
\(653\) 23021.3 + 85916.5i 0.0539887 + 0.201488i 0.987652 0.156663i \(-0.0500737\pi\)
−0.933663 + 0.358152i \(0.883407\pi\)
\(654\) −237543. + 137145.i −0.555375 + 0.320646i
\(655\) −623548. −1.45341
\(656\) 47760.3i 0.110984i
\(657\) −212011. + 122405.i −0.491166 + 0.283575i
\(658\) −420612. + 420612.i −0.971471 + 0.971471i
\(659\) −411803. 237755.i −0.948242 0.547468i −0.0557074 0.998447i \(-0.517741\pi\)
−0.892534 + 0.450980i \(0.851075\pi\)
\(660\) 44564.2 44564.2i 0.102305 0.102305i
\(661\) 138046. + 515193.i 0.315951 + 1.17914i 0.923101 + 0.384558i \(0.125646\pi\)
−0.607150 + 0.794587i \(0.707687\pi\)
\(662\) −151454. + 262326.i −0.345593 + 0.598585i
\(663\) 435292. 753947.i 0.990269 1.71520i
\(664\) 32621.7 121746.i 0.0739895 0.276132i
\(665\) 469556.i 1.06180i
\(666\) −43404.3 93480.7i −0.0978554 0.210753i
\(667\) 499920. 1.12370
\(668\) −10739.8 2877.73i −0.0240682 0.00644906i
\(669\) 113708. + 65649.1i 0.254061 + 0.146682i
\(670\) 234033. + 135119.i 0.521349 + 0.301001i
\(671\) −99687.8 + 26711.3i −0.221410 + 0.0593266i
\(672\) −74954.5 74954.5i −0.165981 0.165981i
\(673\) 409341. 708999.i 0.903764 1.56536i 0.0811959 0.996698i \(-0.474126\pi\)
0.822568 0.568667i \(-0.192541\pi\)
\(674\) 16276.2 + 16276.2i 0.0358290 + 0.0358290i
\(675\) −560749. 971246.i −1.23072 2.13168i
\(676\) 267751. 0.585920
\(677\) 451334.i 0.984738i −0.870386 0.492369i \(-0.836131\pi\)
0.870386 0.492369i \(-0.163869\pi\)
\(678\) 38607.9 + 66870.8i 0.0839879 + 0.145471i
\(679\) 738498. 197880.i 1.60181 0.429202i
\(680\) 342387. 342387.i 0.740456 0.740456i
\(681\) 329970. + 88415.3i 0.711510 + 0.190648i
\(682\) 16947.3 + 29353.6i 0.0364361 + 0.0631092i
\(683\) 151823. 566611.i 0.325459 1.21463i −0.588391 0.808577i \(-0.700238\pi\)
0.913850 0.406052i \(-0.133095\pi\)
\(684\) 7218.80 + 26940.9i 0.0154295 + 0.0575838i
\(685\) −364572. + 97686.8i −0.776966 + 0.208187i
\(686\) 326163. + 87395.1i 0.693085 + 0.185712i
\(687\) −328869. + 189872.i −0.696801 + 0.402298i
\(688\) 12959.4 48365.0i 0.0273783 0.102177i
\(689\) −36647.1 36647.1i −0.0771972 0.0771972i
\(690\) −171131. 638668.i −0.359442 1.34146i
\(691\) 294693. 170141.i 0.617182 0.356330i −0.158589 0.987345i \(-0.550694\pi\)
0.775771 + 0.631014i \(0.217361\pi\)
\(692\) −308683. −0.644614
\(693\) 50013.6i 0.104141i
\(694\) −41049.8 + 23700.1i −0.0852299 + 0.0492075i
\(695\) 659722. 659722.i 1.36581 1.36581i
\(696\) 102886. + 59401.3i 0.212392 + 0.122625i
\(697\) 250122. 250122.i 0.514857 0.514857i
\(698\) −31075.6 115976.i −0.0637836 0.238044i
\(699\) −89362.3 + 154780.i −0.182894 + 0.316782i
\(700\) 448853. 777436.i 0.916026 1.58660i
\(701\) 78737.6 293853.i 0.160231 0.597989i −0.838370 0.545102i \(-0.816491\pi\)
0.998600 0.0528874i \(-0.0168424\pi\)
\(702\) 559060.i 1.13445i
\(703\) 162638. 75515.1i 0.329088 0.152800i
\(704\) −12115.3 −0.0244449
\(705\) −851696. 228211.i −1.71359 0.459155i
\(706\) −140244. 80970.0i −0.281368 0.162448i
\(707\) 177251. + 102336.i 0.354609 + 0.204734i
\(708\) 12590.0 3373.47i 0.0251165 0.00672993i
\(709\) −139680. 139680.i −0.277869 0.277869i 0.554389 0.832258i \(-0.312952\pi\)
−0.832258 + 0.554389i \(0.812952\pi\)
\(710\) 205817. 356486.i 0.408287 0.707173i
\(711\) 206910. + 206910.i 0.409300 + 0.409300i
\(712\) −12019.1 20817.6i −0.0237088 0.0410649i
\(713\) 355600. 0.699492
\(714\) 785078.i 1.53998i
\(715\) −133031. 230416.i −0.260219 0.450713i
\(716\) 457007. 122455.i 0.891450 0.238863i
\(717\) −253494. + 253494.i −0.493094 + 0.493094i
\(718\) −685117. 183577.i −1.32897 0.356097i
\(719\) 279522. + 484147.i 0.540703 + 0.936525i 0.998864 + 0.0476560i \(0.0151751\pi\)
−0.458161 + 0.888869i \(0.651492\pi\)
\(720\) −19904.9 + 74286.1i −0.0383968 + 0.143299i
\(721\) −12262.8 45765.4i −0.0235895 0.0880373i
\(722\) 309172. 82842.3i 0.593096 0.158920i
\(723\) −60688.6 16261.5i −0.116100 0.0311088i
\(724\) −256304. + 147977.i −0.488965 + 0.282304i
\(725\) −260402. + 971832.i −0.495413 + 1.84891i
\(726\) −207680. 207680.i −0.394024 0.394024i
\(727\) 96328.9 + 359504.i 0.182259 + 0.680198i 0.995201 + 0.0978538i \(0.0311977\pi\)
−0.812942 + 0.582344i \(0.802136\pi\)
\(728\) −387547. + 223750.i −0.731242 + 0.422183i
\(729\) −572445. −1.07716
\(730\) 1.17442e6i 2.20383i
\(731\) −321157. + 185420.i −0.601012 + 0.346994i
\(732\) −181945. + 181945.i −0.339560 + 0.339560i
\(733\) −218052. 125893.i −0.405838 0.234311i 0.283162 0.959072i \(-0.408617\pi\)
−0.689000 + 0.724761i \(0.741950\pi\)
\(734\) 14623.7 14623.7i 0.0271435 0.0271435i
\(735\) 336436. + 1.25560e6i 0.622771 + 2.32421i
\(736\) −63552.7 + 110077.i −0.117322 + 0.203207i
\(737\) −25039.1 + 43369.0i −0.0460982 + 0.0798444i
\(738\) −14541.0 + 54267.8i −0.0266982 + 0.0996391i
\(739\) 473919.i 0.867792i 0.900963 + 0.433896i \(0.142861\pi\)
−0.900963 + 0.433896i \(0.857139\pi\)
\(740\) 492484. + 43900.5i 0.899350 + 0.0801689i
\(741\) −240571. −0.438133
\(742\) 45144.1 + 12096.3i 0.0819961 + 0.0219708i
\(743\) 610593. + 352526.i 1.10605 + 0.638578i 0.937803 0.347168i \(-0.112856\pi\)
0.168246 + 0.985745i \(0.446190\pi\)
\(744\) 73184.3 + 42253.0i 0.132212 + 0.0763328i
\(745\) −305367. + 81822.9i −0.550186 + 0.147422i
\(746\) −190646. 190646.i −0.342571 0.342571i
\(747\) 74133.0 128402.i 0.132853 0.230108i
\(748\) 63448.1 + 63448.1i 0.113401 + 0.113401i
\(749\) −183255. 317407.i −0.326657 0.565786i
\(750\) 742159. 1.31939
\(751\) 197292.i 0.349808i 0.984585 + 0.174904i \(0.0559616\pi\)
−0.984585 + 0.174904i \(0.944038\pi\)
\(752\) 84750.8 + 146793.i 0.149868 + 0.259579i
\(753\) 268384. 71913.3i 0.473333 0.126829i
\(754\) 354643. 354643.i 0.623805 0.623805i
\(755\) −1.51560e6 406104.i −2.65883 0.712432i
\(756\) −252075. 436607.i −0.441049 0.763919i
\(757\) 79572.7 296969.i 0.138858 0.518227i −0.861094 0.508446i \(-0.830220\pi\)
0.999952 0.00978045i \(-0.00311326\pi\)
\(758\) −68446.8 255447.i −0.119128 0.444593i
\(759\) 118352. 31712.4i 0.205444 0.0550485i
\(760\) −129243. 34630.7i −0.223759 0.0599562i
\(761\) 562405. 324705.i 0.971135 0.560685i 0.0715531 0.997437i \(-0.477204\pi\)
0.899582 + 0.436752i \(0.143871\pi\)
\(762\) −69132.3 + 258005.i −0.119061 + 0.444343i
\(763\) −738379. 738379.i −1.26832 1.26832i
\(764\) −20044.3 74806.5i −0.0343404 0.128160i
\(765\) 493281. 284796.i 0.842892 0.486644i
\(766\) 144237. 0.245821
\(767\) 55025.2i 0.0935343i
\(768\) −26159.0 + 15102.9i −0.0443504 + 0.0256057i
\(769\) 405138. 405138.i 0.685094 0.685094i −0.276049 0.961143i \(-0.589025\pi\)
0.961143 + 0.276049i \(0.0890253\pi\)
\(770\) 207785. + 119965.i 0.350456 + 0.202336i
\(771\) −36691.7 + 36691.7i −0.0617247 + 0.0617247i
\(772\) 136069. + 507818.i 0.228310 + 0.852066i
\(773\) −499650. + 865420.i −0.836194 + 1.44833i 0.0568605 + 0.998382i \(0.481891\pi\)
−0.893055 + 0.449948i \(0.851442\pi\)
\(774\) 29450.2 51009.3i 0.0491594 0.0851466i
\(775\) −185227. + 691277.i −0.308391 + 1.15093i
\(776\) 217863.i 0.361792i
\(777\) −614952. + 514291.i −1.01859 + 0.851857i
\(778\) 391812. 0.647320
\(779\) −94415.5 25298.6i −0.155585 0.0416889i
\(780\) −574471. 331671.i −0.944233 0.545153i
\(781\) 66060.8 + 38140.2i 0.108303 + 0.0625290i
\(782\) 909302. 243647.i 1.48694 0.398425i
\(783\) 399539. + 399539.i 0.651681 + 0.651681i
\(784\) 124942. 216406.i 0.203272 0.352077i
\(785\) 1.11886e6 + 1.11886e6i 1.81567 + 1.81567i
\(786\) −144045. 249493.i −0.233159 0.403843i
\(787\) −1.13706e6 −1.83584 −0.917920 0.396765i \(-0.870133\pi\)
−0.917920 + 0.396765i \(0.870133\pi\)
\(788\) 46583.6i 0.0750206i
\(789\) 415354. + 719415.i 0.667213 + 1.15565i
\(790\) −1.35592e6 + 363319.i −2.17261 + 0.582148i
\(791\) −207862. + 207862.i −0.332216 + 0.332216i
\(792\) −13766.0 3688.60i −0.0219462 0.00588046i
\(793\) 543132. + 940732.i 0.863692 + 1.49596i
\(794\) −92177.0 + 344009.i −0.146211 + 0.545669i
\(795\) 17930.7 + 66918.4i 0.0283703 + 0.105879i
\(796\) 80732.7 21632.3i 0.127416 0.0341409i
\(797\) 256458. + 68717.6i 0.403737 + 0.108181i 0.454972 0.890506i \(-0.349649\pi\)
−0.0512350 + 0.998687i \(0.516316\pi\)
\(798\) 187878. 108471.i 0.295033 0.170337i
\(799\) 324915. 1.21260e6i 0.508952 1.89943i
\(800\) −180882. 180882.i −0.282629 0.282629i
\(801\) −7318.60 27313.4i −0.0114068 0.0425707i
\(802\) −22892.8 + 13217.2i −0.0355919 + 0.0205490i
\(803\) 217634. 0.337516
\(804\) 124855.i 0.193149i
\(805\) 2.17994e6 1.25859e6i 3.36398 1.94219i
\(806\) 252263. 252263.i 0.388314 0.388314i
\(807\) −121439. 70112.8i −0.186471 0.107659i
\(808\) 41240.2 41240.2i 0.0631681 0.0631681i
\(809\) −274732. 1.02531e6i −0.419771 1.56661i −0.775084 0.631858i \(-0.782292\pi\)
0.355313 0.934747i \(-0.384374\pi\)
\(810\) 236006. 408774.i 0.359710 0.623036i
\(811\) −491948. + 852079.i −0.747959 + 1.29550i 0.200841 + 0.979624i \(0.435633\pi\)
−0.948800 + 0.315878i \(0.897701\pi\)
\(812\) −117059. + 436871.i −0.177539 + 0.662584i
\(813\) 581054.i 0.879095i
\(814\) −8135.24 + 91262.7i −0.0122778 + 0.137735i
\(815\) −1.13812e6 −1.71346
\(816\) 216089. + 57901.0i 0.324529 + 0.0869572i
\(817\) 88746.3 + 51237.7i 0.132955 + 0.0767619i
\(818\) −511707. 295434.i −0.764742 0.441524i
\(819\) −508474. + 136245.i −0.758056 + 0.203120i
\(820\) −190581. 190581.i −0.283434 0.283434i
\(821\) −341399. + 591320.i −0.506496 + 0.877276i 0.493476 + 0.869759i \(0.335726\pi\)
−0.999972 + 0.00751686i \(0.997607\pi\)
\(822\) −123305. 123305.i −0.182490 0.182490i
\(823\) 161297. + 279374.i 0.238137 + 0.412465i 0.960180 0.279384i \(-0.0901301\pi\)
−0.722043 + 0.691848i \(0.756797\pi\)
\(824\) −13501.1 −0.0198846
\(825\) 246592.i 0.362303i
\(826\) 24810.4 + 42972.9i 0.0363642 + 0.0629847i
\(827\) −729319. + 195421.i −1.06637 + 0.285732i −0.749000 0.662570i \(-0.769466\pi\)
−0.317367 + 0.948303i \(0.602799\pi\)
\(828\) −105726. + 105726.i −0.154213 + 0.154213i
\(829\) 922914. + 247294.i 1.34293 + 0.359836i 0.857519 0.514452i \(-0.172005\pi\)
0.485407 + 0.874288i \(0.338671\pi\)
\(830\) 355637. + 615982.i 0.516239 + 0.894152i
\(831\) −169925. + 634168.i −0.246068 + 0.918338i
\(832\) 33004.0 + 123173.i 0.0476782 + 0.177938i
\(833\) −1.78765e6 + 479000.i −2.57628 + 0.690313i
\(834\) 416368. + 111565.i 0.598612 + 0.160398i
\(835\) 54339.0 31372.6i 0.0779360 0.0449964i
\(836\) 6417.45 23950.2i 0.00918226 0.0342687i
\(837\) 284197. + 284197.i 0.405666 + 0.405666i
\(838\) 129694. + 484024.i 0.184685 + 0.689254i
\(839\) −603772. + 348588.i −0.857727 + 0.495209i −0.863250 0.504776i \(-0.831575\pi\)
0.00552358 + 0.999985i \(0.498242\pi\)
\(840\) 598191. 0.847777
\(841\) 200381.i 0.283312i
\(842\) −53080.9 + 30646.2i −0.0748710 + 0.0432268i
\(843\) −63900.3 + 63900.3i −0.0899182 + 0.0899182i
\(844\) −1145.08 661.113i −0.00160750 0.000928091i
\(845\) −1.06842e6 + 1.06842e6i −1.49634 + 1.49634i
\(846\) 51606.2 + 192597.i 0.0721043 + 0.269097i
\(847\) 559067. 968332.i 0.779286 1.34976i
\(848\) 6658.93 11533.6i 0.00926004 0.0160389i
\(849\) 180816. 674815.i 0.250854 0.936201i
\(850\) 1.89457e6i 2.62225i
\(851\) 786516. + 552649.i 1.08605 + 0.763115i
\(852\) 190182. 0.261993
\(853\) 142224. + 38108.7i 0.195467 + 0.0523753i 0.355224 0.934781i \(-0.384404\pi\)
−0.159757 + 0.987156i \(0.551071\pi\)
\(854\) −848336. 489787.i −1.16319 0.671571i
\(855\) −136310. 78698.5i −0.186464 0.107655i
\(856\) −100880. + 27030.8i −0.137676 + 0.0368902i
\(857\) −521580. 521580.i −0.710165 0.710165i 0.256405 0.966570i \(-0.417462\pi\)
−0.966570 + 0.256405i \(0.917462\pi\)
\(858\) 61462.3 106456.i 0.0834900 0.144609i
\(859\) 737920. + 737920.i 1.00005 + 1.00005i 1.00000 5.34024e-5i \(1.69985e-5\pi\)
5.34024e−5 1.00000i \(0.499983\pi\)
\(860\) 141281. + 244706.i 0.191024 + 0.330863i
\(861\) 436993. 0.589479
\(862\) 781139.i 1.05127i
\(863\) −121321. 210135.i −0.162898 0.282148i 0.773009 0.634395i \(-0.218751\pi\)
−0.935907 + 0.352248i \(0.885418\pi\)
\(864\) −138765. + 37182.1i −0.185889 + 0.0498088i
\(865\) 1.23176e6 1.23176e6i 1.64624 1.64624i
\(866\) 148668. + 39835.4i 0.198235 + 0.0531170i
\(867\) −520477. 901493.i −0.692410 1.19929i
\(868\) −83265.8 + 310752.i −0.110516 + 0.412453i
\(869\) −67326.9 251268.i −0.0891558 0.332734i
\(870\) −647585. + 173520.i −0.855576 + 0.229251i
\(871\) 509131. + 136421.i 0.671109 + 0.179823i
\(872\) −257693. + 148779.i −0.338898 + 0.195663i
\(873\) 66330.1 247547.i 0.0870326 0.324810i
\(874\) −183942. 183942.i −0.240801 0.240801i
\(875\) 731268. + 2.72913e6i 0.955125 + 3.56458i
\(876\) 469908. 271301.i 0.612356 0.353544i
\(877\) 977479. 1.27089 0.635446 0.772146i \(-0.280816\pi\)
0.635446 + 0.772146i \(0.280816\pi\)
\(878\) 251719.i 0.326532i
\(879\) 388744. 224442.i 0.503137 0.290486i
\(880\) 48344.4 48344.4i 0.0624282 0.0624282i
\(881\) −983731. 567957.i −1.26743 0.731752i −0.292930 0.956134i \(-0.594630\pi\)
−0.974501 + 0.224382i \(0.927964\pi\)
\(882\) 207853. 207853.i 0.267189 0.267189i
\(883\) −192599. 718790.i −0.247020 0.921893i −0.972357 0.233499i \(-0.924983\pi\)
0.725337 0.688394i \(-0.241684\pi\)
\(884\) 472216. 817902.i 0.604277 1.04664i
\(885\) −36777.2 + 63699.9i −0.0469561 + 0.0813303i
\(886\) 90960.8 339470.i 0.115874 0.432449i
\(887\) 668201.i 0.849298i −0.905358 0.424649i \(-0.860398\pi\)
0.905358 0.424649i \(-0.139602\pi\)
\(888\) 96202.5 + 207193.i 0.122000 + 0.262754i
\(889\) −1.01688e6 −1.28666
\(890\) 131030. + 35109.4i 0.165421 + 0.0443245i
\(891\) 75750.3 + 43734.5i 0.0954177 + 0.0550895i
\(892\) 123353. + 71217.9i 0.155032 + 0.0895075i
\(893\) −335081. + 89784.8i −0.420191 + 0.112590i
\(894\) −103281. 103281.i −0.129225 0.129225i
\(895\) −1.33499e6 + 2.31226e6i −1.66660 + 2.88663i
\(896\) −81312.6 81312.6i −0.101284 0.101284i
\(897\) −644821. 1.11686e6i −0.801410 1.38808i
\(898\) −778235. −0.965068
\(899\) 360565.i 0.446133i
\(900\) −150457. 260599.i −0.185749 0.321728i
\(901\) −95274.8 + 25528.8i −0.117362 + 0.0314471i
\(902\) 35316.8 35316.8i 0.0434078 0.0434078i
\(903\) −442526. 118574.i −0.542704 0.145417i
\(904\) 41882.8 + 72543.2i 0.0512506 + 0.0887687i
\(905\) 432263. 1.61323e6i 0.527777 1.96969i
\(906\) −187627. 700232.i −0.228580 0.853072i
\(907\) 1.31389e6 352054.i 1.59714 0.427952i 0.652962 0.757390i \(-0.273526\pi\)
0.944177 + 0.329438i \(0.106859\pi\)
\(908\) 357961. + 95915.3i 0.434174 + 0.116337i
\(909\) 59415.2 34303.4i 0.0719068 0.0415154i
\(910\) 653608. 2.43930e6i 0.789286 2.94565i
\(911\) 265206. + 265206.i 0.319556 + 0.319556i 0.848597 0.529040i \(-0.177448\pi\)
−0.529040 + 0.848597i \(0.677448\pi\)
\(912\) −15999.9 59712.6i −0.0192366 0.0717920i
\(913\) −114148. + 65903.5i −0.136939 + 0.0790618i
\(914\) 752734. 0.901050
\(915\) 1.45205e6i 1.73436i
\(916\) −356765. + 205979.i −0.425199 + 0.245489i
\(917\) 775524. 775524.i 0.922267 0.922267i
\(918\) 921442. + 531995.i 1.09341 + 0.631280i
\(919\) 740422. 740422.i 0.876694 0.876694i −0.116497 0.993191i \(-0.537166\pi\)
0.993191 + 0.116497i \(0.0371664\pi\)
\(920\) −185647. 692844.i −0.219337 0.818577i
\(921\) −30691.7 + 53159.6i −0.0361828 + 0.0626704i
\(922\) −501259. + 868206.i −0.589658 + 1.02132i
\(923\) 207800. 775522.i 0.243918 0.910313i
\(924\) 110851.i 0.129837i
\(925\) −1.48402e6 + 1.24110e6i −1.73443 + 1.45052i
\(926\) −893796. −1.04236
\(927\) −15340.7 4110.53i −0.0178520 0.00478342i
\(928\) 111614. + 64440.1i 0.129605 + 0.0748273i
\(929\) −357768. 206558.i −0.414544 0.239337i 0.278196 0.960524i \(-0.410263\pi\)
−0.692740 + 0.721187i \(0.743597\pi\)
\(930\) −460636. + 123427.i −0.532589 + 0.142707i
\(931\) 361624. + 361624.i 0.417213 + 0.417213i
\(932\) −96942.6 + 167910.i −0.111605 + 0.193305i
\(933\) −585958. 585958.i −0.673136 0.673136i
\(934\) −44646.9 77330.7i −0.0511797 0.0886458i
\(935\) −506362. −0.579212
\(936\) 150004.i 0.171218i
\(937\) 607759. + 1.05267e6i 0.692233 + 1.19898i 0.971105 + 0.238655i \(0.0767064\pi\)
−0.278871 + 0.960328i \(0.589960\pi\)
\(938\) −459126. + 123022.i −0.521826 + 0.139823i
\(939\) −378476. + 378476.i −0.429247 + 0.429247i
\(940\) −923943. 247570.i −1.04566 0.280183i
\(941\) 738032. + 1.27831e6i 0.833481 + 1.44363i 0.895261 + 0.445542i \(0.146989\pi\)
−0.0617802 + 0.998090i \(0.519678\pi\)
\(942\) −189211. + 706144.i −0.213228 + 0.795777i
\(943\) −135620. 506139.i −0.152510 0.569176i
\(944\) 13657.9 3659.63i 0.0153264 0.00410670i
\(945\) 2.74809e6 + 736349.i 3.07729 + 0.824556i
\(946\) −45346.8 + 26181.0i −0.0506715 + 0.0292552i
\(947\) −240252. + 896634.i −0.267897 + 0.999805i 0.692556 + 0.721364i \(0.256484\pi\)
−0.960453 + 0.278441i \(0.910182\pi\)
\(948\) −458600. 458600.i −0.510290 0.510290i
\(949\) −592869. 2.21262e6i −0.658304 2.45682i
\(950\) 453392. 261766.i 0.502374 0.290046i
\(951\) −150272. −0.166156
\(952\) 851673.i 0.939721i
\(953\) 788093. 455006.i 0.867744 0.500992i 0.00114632 0.999999i \(-0.499635\pi\)
0.866598 + 0.499007i \(0.166302\pi\)
\(954\) 11077.7 11077.7i 0.0121718 0.0121718i
\(955\) 378489. + 218521.i 0.414999 + 0.239600i
\(956\) −274997. + 274997.i −0.300893 + 0.300893i
\(957\) −32155.2 120005.i −0.0351097 0.131031i
\(958\) 300889. 521156.i 0.327851 0.567854i
\(959\) 331933. 574924.i 0.360922 0.625135i
\(960\) 44117.7 164650.i 0.0478708 0.178656i
\(961\) 667046.i 0.722286i
\(962\) 950004. 165906.i 1.02654 0.179272i
\(963\) −122855. −0.132477
\(964\) −65836.6 17640.9i −0.0708457 0.0189830i
\(965\) −2.56934e6 1.48341e6i −2.75910 1.59297i
\(966\) 1.00717e6 + 581489.i 1.07932 + 0.623143i
\(967\) −1.40705e6 + 377019.i −1.50473 + 0.403190i −0.914680 0.404180i \(-0.867557\pi\)
−0.590046 + 0.807370i \(0.700890\pi\)
\(968\) −225297. 225297.i −0.240439 0.240439i
\(969\) −228924. + 396509.i −0.243806 + 0.422285i
\(970\) 869350. + 869350.i 0.923956 + 0.923956i
\(971\) −393371. 681338.i −0.417219 0.722644i 0.578440 0.815725i \(-0.303662\pi\)
−0.995659 + 0.0930811i \(0.970328\pi\)
\(972\) −296189. −0.313499
\(973\) 1.64103e6i 1.73337i
\(974\) 360697. + 624746.i 0.380211 + 0.658545i
\(975\) 2.50703e6 671758.i 2.63725 0.706648i
\(976\) −197378. + 197378.i −0.207205 + 0.207205i
\(977\) −695361. 186321.i −0.728486 0.195197i −0.124531 0.992216i \(-0.539743\pi\)
−0.603955 + 0.797018i \(0.706409\pi\)
\(978\) −262915. 455382.i −0.274877 0.476100i
\(979\) −6506.17 + 24281.3i −0.00678828 + 0.0253342i
\(980\) 364975. + 1.36211e6i 0.380024 + 1.41827i
\(981\) −338101. + 90594.0i −0.351325 + 0.0941372i
\(982\) −1.20384e6 322568.i −1.24838 0.334502i
\(983\) 1.09781e6 633818.i 1.13610 0.655930i 0.190641 0.981660i \(-0.438943\pi\)
0.945463 + 0.325730i \(0.105610\pi\)
\(984\) 32229.1 120281.i 0.0332857 0.124224i
\(985\) −185886. 185886.i −0.191590 0.191590i
\(986\) −247049. 921998.i −0.254114 0.948366i
\(987\) 1.34311e6 775446.i 1.37873 0.796008i
\(988\) −260977. −0.267355
\(989\) 549346.i 0.561634i
\(990\) 69650.3 40212.6i 0.0710645 0.0410291i
\(991\) −575248. + 575248.i −0.585744 + 0.585744i −0.936476 0.350732i \(-0.885933\pi\)
0.350732 + 0.936476i \(0.385933\pi\)
\(992\) 79392.2 + 45837.1i 0.0806779 + 0.0465794i
\(993\) 558445. 558445.i 0.566346 0.566346i
\(994\) 187391. + 699353.i 0.189660 + 0.707821i
\(995\) −235832. + 408473.i −0.238208 + 0.412589i
\(996\) −164310. + 284594.i −0.165633 + 0.286884i
\(997\) −126440. + 471882.i −0.127203 + 0.474726i −0.999909 0.0135196i \(-0.995696\pi\)
0.872706 + 0.488246i \(0.162363\pi\)
\(998\) 113514.i 0.113970i
\(999\) 186908. + 1.07027e6i 0.187283 + 1.07241i
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 74.5.g.a.45.5 28
37.14 odd 12 inner 74.5.g.a.51.5 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.5.g.a.45.5 28 1.1 even 1 trivial
74.5.g.a.51.5 yes 28 37.14 odd 12 inner