Properties

Label 43.5.f.a.2.10
Level $43$
Weight $5$
Character 43.2
Analytic conductor $4.445$
Analytic rank $0$
Dimension $78$
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] = [43,5,Mod(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), degree \(6\), 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: \(4.44490841261\)
Analytic rank: \(0\)
Dimension: \(78\)
Relative dimension: \(13\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 2.10
Character \(\chi\) \(=\) 43.2
Dual form 43.5.f.a.22.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.83585 + 3.81219i) q^{2} +(5.21899 - 10.8373i) q^{3} +(-1.18660 + 1.48795i) q^{4} +(-1.25492 - 0.286428i) q^{5} +50.8953 q^{6} -55.1541i q^{7} +(58.1513 + 13.2726i) q^{8} +(-39.7075 - 49.7916i) q^{9} +O(q^{10})\) \(q+(1.83585 + 3.81219i) q^{2} +(5.21899 - 10.8373i) q^{3} +(-1.18660 + 1.48795i) q^{4} +(-1.25492 - 0.286428i) q^{5} +50.8953 q^{6} -55.1541i q^{7} +(58.1513 + 13.2726i) q^{8} +(-39.7075 - 49.7916i) q^{9} +(-1.21194 - 5.30985i) q^{10} +(23.3205 + 29.2430i) q^{11} +(9.93258 + 20.6252i) q^{12} +(-56.3787 + 247.011i) q^{13} +(210.258 - 101.255i) q^{14} +(-9.65355 + 12.1052i) q^{15} +(62.9353 + 275.737i) q^{16} +(24.6816 + 108.137i) q^{17} +(116.918 - 242.783i) q^{18} +(-71.0668 - 56.6739i) q^{19} +(1.91528 - 1.52739i) q^{20} +(-597.724 - 287.849i) q^{21} +(-68.6669 + 142.588i) q^{22} +(-269.161 - 337.517i) q^{23} +(447.331 - 560.935i) q^{24} +(-561.613 - 270.458i) q^{25} +(-1045.16 + 238.550i) q^{26} +(203.042 - 46.3431i) q^{27} +(82.0666 + 65.4459i) q^{28} +(387.428 + 804.503i) q^{29} +(-63.8697 - 14.5779i) q^{30} +(26.0743 - 12.5567i) q^{31} +(-189.485 + 151.109i) q^{32} +(438.626 - 100.114i) q^{33} +(-366.928 + 292.616i) q^{34} +(-15.7977 + 69.2141i) q^{35} +121.204 q^{36} +1793.33i q^{37} +(85.5834 - 374.965i) q^{38} +(2382.71 + 1900.14i) q^{39} +(-69.1737 - 33.3123i) q^{40} +(-1040.33 + 500.997i) q^{41} -2807.08i q^{42} +(-1727.43 + 659.381i) q^{43} -71.1844 q^{44} +(35.5681 + 73.8580i) q^{45} +(792.539 - 1645.72i) q^{46} +(2219.97 - 2783.75i) q^{47} +(3316.72 + 757.020i) q^{48} -640.972 q^{49} -2637.50i q^{50} +(1300.73 + 296.884i) q^{51} +(-300.642 - 376.993i) q^{52} +(-419.195 - 1836.61i) q^{53} +(549.425 + 688.957i) q^{54} +(-20.8895 - 43.3774i) q^{55} +(732.040 - 3207.28i) q^{56} +(-985.092 + 474.395i) q^{57} +(-2355.66 + 2953.90i) q^{58} +(935.219 + 4097.46i) q^{59} +(-6.55698 - 28.7280i) q^{60} +(-1733.25 + 3599.12i) q^{61} +(95.7371 + 76.3478i) q^{62} +(-2746.21 + 2190.03i) q^{63} +(3153.19 + 1518.50i) q^{64} +(141.502 - 293.832i) q^{65} +(1186.91 + 1488.33i) q^{66} +(4427.17 - 5551.50i) q^{67} +(-190.190 - 91.5909i) q^{68} +(-5062.53 + 1155.49i) q^{69} +(-292.860 + 66.8433i) q^{70} +(-4654.84 - 3712.11i) q^{71} +(-1648.17 - 3422.47i) q^{72} +(3060.01 + 698.427i) q^{73} +(-6836.50 + 3292.29i) q^{74} +(-5862.10 + 4674.87i) q^{75} +(168.656 - 38.4946i) q^{76} +(1612.87 - 1286.22i) q^{77} +(-2869.41 + 12571.7i) q^{78} -3238.19 q^{79} -364.056i q^{80} +(1705.33 - 7471.52i) q^{81} +(-3819.79 - 3046.18i) q^{82} +(-4632.98 - 2231.13i) q^{83} +(1137.56 - 547.822i) q^{84} -142.774i q^{85} +(-5685.00 - 5374.77i) q^{86} +10740.7 q^{87} +(967.986 + 2010.04i) q^{88} +(4293.30 - 8915.14i) q^{89} +(-216.263 + 271.185i) q^{90} +(13623.7 + 3109.51i) q^{91} +821.595 q^{92} -348.109i q^{93} +(14687.7 + 3352.37i) q^{94} +(72.9504 + 91.4770i) q^{95} +(648.702 + 2842.15i) q^{96} +(-2634.89 - 3304.04i) q^{97} +(-1176.73 - 2443.51i) q^{98} +(530.058 - 2322.33i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78 q - 7 q^{2} - 7 q^{3} + 69 q^{4} - 7 q^{5} - 140 q^{6} - 343 q^{8} + 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 78 q - 7 q^{2} - 7 q^{3} + 69 q^{4} - 7 q^{5} - 140 q^{6} - 343 q^{8} + 486 q^{9} - 189 q^{10} - 26 q^{11} - 119 q^{12} + 608 q^{13} + 45 q^{14} - 797 q^{15} + 593 q^{16} - 188 q^{17} - 574 q^{18} + 1421 q^{19} - 2107 q^{20} + 2952 q^{21} - 2359 q^{22} + 652 q^{23} - 253 q^{24} + 1264 q^{25} - 2023 q^{26} - 7 q^{27} + 1785 q^{28} - 2317 q^{29} - 252 q^{30} + 5714 q^{31} - 6517 q^{32} + 9023 q^{33} - 679 q^{34} + 1374 q^{35} - 8544 q^{36} + 95 q^{38} - 10339 q^{39} - 5901 q^{40} - 3611 q^{41} + 7001 q^{43} + 8148 q^{44} + 8862 q^{45} - 2660 q^{46} + 6268 q^{47} + 11081 q^{48} - 1074 q^{49} - 17353 q^{51} + 8277 q^{52} - 200 q^{53} - 8147 q^{54} + 9863 q^{55} + 15927 q^{56} - 25075 q^{57} + 13045 q^{58} + 1468 q^{59} - 357 q^{60} - 8239 q^{61} + 10073 q^{62} - 875 q^{63} + 1173 q^{64} - 19159 q^{65} - 24551 q^{66} + 42658 q^{67} + 3910 q^{68} - 903 q^{69} + 37870 q^{70} + 8960 q^{71} - 40586 q^{72} + 13342 q^{73} + 37116 q^{74} - 44996 q^{75} - 60438 q^{76} + 2625 q^{77} - 13562 q^{78} - 48318 q^{79} + 1048 q^{81} - 57211 q^{82} + 17014 q^{83} - 50382 q^{84} + 21461 q^{86} - 6174 q^{87} + 34909 q^{88} + 51590 q^{89} - 6494 q^{90} + 35840 q^{91} + 105420 q^{92} - 38115 q^{94} + 65915 q^{95} + 101606 q^{96} - 18427 q^{97} + 63455 q^{98} + 36377 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.83585 + 3.81219i 0.458964 + 0.953048i 0.994119 + 0.108294i \(0.0345388\pi\)
−0.535155 + 0.844754i \(0.679747\pi\)
\(3\) 5.21899 10.8373i 0.579888 1.20415i −0.380318 0.924856i \(-0.624185\pi\)
0.960206 0.279294i \(-0.0901002\pi\)
\(4\) −1.18660 + 1.48795i −0.0741626 + 0.0929969i
\(5\) −1.25492 0.286428i −0.0501969 0.0114571i 0.197349 0.980333i \(-0.436767\pi\)
−0.247546 + 0.968876i \(0.579624\pi\)
\(6\) 50.8953 1.41376
\(7\) 55.1541i 1.12559i −0.826595 0.562797i \(-0.809725\pi\)
0.826595 0.562797i \(-0.190275\pi\)
\(8\) 58.1513 + 13.2726i 0.908613 + 0.207385i
\(9\) −39.7075 49.7916i −0.490216 0.614711i
\(10\) −1.21194 5.30985i −0.0121194 0.0530985i
\(11\) 23.3205 + 29.2430i 0.192732 + 0.241678i 0.868803 0.495159i \(-0.164890\pi\)
−0.676071 + 0.736837i \(0.736319\pi\)
\(12\) 9.93258 + 20.6252i 0.0689762 + 0.143231i
\(13\) −56.3787 + 247.011i −0.333602 + 1.46160i 0.478499 + 0.878088i \(0.341181\pi\)
−0.812101 + 0.583517i \(0.801676\pi\)
\(14\) 210.258 101.255i 1.07274 0.516606i
\(15\) −9.65355 + 12.1052i −0.0429047 + 0.0538008i
\(16\) 62.9353 + 275.737i 0.245841 + 1.07710i
\(17\) 24.6816 + 108.137i 0.0854036 + 0.374178i 0.999510 0.0312964i \(-0.00996359\pi\)
−0.914107 + 0.405474i \(0.867106\pi\)
\(18\) 116.918 242.783i 0.360858 0.749329i
\(19\) −71.0668 56.6739i −0.196861 0.156991i 0.520098 0.854106i \(-0.325895\pi\)
−0.716959 + 0.697115i \(0.754467\pi\)
\(20\) 1.91528 1.52739i 0.00478821 0.00381847i
\(21\) −597.724 287.849i −1.35538 0.652718i
\(22\) −68.6669 + 142.588i −0.141874 + 0.294604i
\(23\) −269.161 337.517i −0.508810 0.638028i 0.459381 0.888239i \(-0.348071\pi\)
−0.968191 + 0.250211i \(0.919500\pi\)
\(24\) 447.331 560.935i 0.776616 0.973846i
\(25\) −561.613 270.458i −0.898580 0.432734i
\(26\) −1045.16 + 238.550i −1.54609 + 0.352885i
\(27\) 203.042 46.3431i 0.278522 0.0635707i
\(28\) 82.0666 + 65.4459i 0.104677 + 0.0834769i
\(29\) 387.428 + 804.503i 0.460675 + 0.956602i 0.993864 + 0.110606i \(0.0352792\pi\)
−0.533189 + 0.845996i \(0.679006\pi\)
\(30\) −63.8697 14.5779i −0.0709664 0.0161976i
\(31\) 26.0743 12.5567i 0.0271324 0.0130663i −0.420268 0.907400i \(-0.638064\pi\)
0.447401 + 0.894334i \(0.352350\pi\)
\(32\) −189.485 + 151.109i −0.185044 + 0.147567i
\(33\) 438.626 100.114i 0.402779 0.0919317i
\(34\) −366.928 + 292.616i −0.317412 + 0.253128i
\(35\) −15.7977 + 69.2141i −0.0128961 + 0.0565013i
\(36\) 121.204 0.0935220
\(37\) 1793.33i 1.30995i 0.755649 + 0.654977i \(0.227322\pi\)
−0.755649 + 0.654977i \(0.772678\pi\)
\(38\) 85.5834 374.965i 0.0592683 0.259671i
\(39\) 2382.71 + 1900.14i 1.56654 + 1.24927i
\(40\) −69.1737 33.3123i −0.0432336 0.0208202i
\(41\) −1040.33 + 500.997i −0.618876 + 0.298035i −0.716929 0.697146i \(-0.754453\pi\)
0.0980530 + 0.995181i \(0.468739\pi\)
\(42\) 2807.08i 1.59132i
\(43\) −1727.43 + 659.381i −0.934251 + 0.356615i
\(44\) −71.1844 −0.0367688
\(45\) 35.5681 + 73.8580i 0.0175645 + 0.0364731i
\(46\) 792.539 1645.72i 0.374546 0.777752i
\(47\) 2219.97 2783.75i 1.00496 1.26018i 0.0396169 0.999215i \(-0.487386\pi\)
0.965347 0.260970i \(-0.0840423\pi\)
\(48\) 3316.72 + 757.020i 1.43955 + 0.328568i
\(49\) −640.972 −0.266960
\(50\) 2637.50i 1.05500i
\(51\) 1300.73 + 296.884i 0.500090 + 0.114142i
\(52\) −300.642 376.993i −0.111184 0.139420i
\(53\) −419.195 1836.61i −0.149233 0.653831i −0.993099 0.117278i \(-0.962583\pi\)
0.843866 0.536553i \(-0.180274\pi\)
\(54\) 549.425 + 688.957i 0.188417 + 0.236268i
\(55\) −20.8895 43.3774i −0.00690561 0.0143396i
\(56\) 732.040 3207.28i 0.233431 1.02273i
\(57\) −985.092 + 474.395i −0.303198 + 0.146013i
\(58\) −2355.66 + 2953.90i −0.700255 + 0.878091i
\(59\) 935.219 + 4097.46i 0.268664 + 1.17709i 0.911569 + 0.411148i \(0.134872\pi\)
−0.642905 + 0.765946i \(0.722271\pi\)
\(60\) −6.55698 28.7280i −0.00182138 0.00798001i
\(61\) −1733.25 + 3599.12i −0.465801 + 0.967247i 0.527266 + 0.849700i \(0.323217\pi\)
−0.993067 + 0.117546i \(0.962497\pi\)
\(62\) 95.7371 + 76.3478i 0.0249056 + 0.0198615i
\(63\) −2746.21 + 2190.03i −0.691915 + 0.551784i
\(64\) 3153.19 + 1518.50i 0.769822 + 0.370727i
\(65\) 141.502 293.832i 0.0334916 0.0695460i
\(66\) 1186.91 + 1488.33i 0.272476 + 0.341674i
\(67\) 4427.17 5551.50i 0.986227 1.23669i 0.0146683 0.999892i \(-0.495331\pi\)
0.971559 0.236798i \(-0.0760978\pi\)
\(68\) −190.190 91.5909i −0.0411311 0.0198077i
\(69\) −5062.53 + 1155.49i −1.06333 + 0.242699i
\(70\) −292.860 + 66.8433i −0.0597673 + 0.0136415i
\(71\) −4654.84 3712.11i −0.923395 0.736383i 0.0414668 0.999140i \(-0.486797\pi\)
−0.964862 + 0.262757i \(0.915368\pi\)
\(72\) −1648.17 3422.47i −0.317935 0.660198i
\(73\) 3060.01 + 698.427i 0.574218 + 0.131062i 0.499762 0.866163i \(-0.333421\pi\)
0.0744561 + 0.997224i \(0.476278\pi\)
\(74\) −6836.50 + 3292.29i −1.24845 + 0.601221i
\(75\) −5862.10 + 4674.87i −1.04215 + 0.831088i
\(76\) 168.656 38.4946i 0.0291995 0.00666458i
\(77\) 1612.87 1286.22i 0.272031 0.216938i
\(78\) −2869.41 + 12571.7i −0.471632 + 2.06636i
\(79\) −3238.19 −0.518857 −0.259429 0.965762i \(-0.583534\pi\)
−0.259429 + 0.965762i \(0.583534\pi\)
\(80\) 364.056i 0.0568837i
\(81\) 1705.33 7471.52i 0.259919 1.13878i
\(82\) −3819.79 3046.18i −0.568083 0.453031i
\(83\) −4632.98 2231.13i −0.672519 0.323868i 0.0662732 0.997802i \(-0.478889\pi\)
−0.738792 + 0.673934i \(0.764603\pi\)
\(84\) 1137.56 547.822i 0.161219 0.0776392i
\(85\) 142.774i 0.0197611i
\(86\) −5685.00 5374.77i −0.768659 0.726713i
\(87\) 10740.7 1.41903
\(88\) 967.986 + 2010.04i 0.124998 + 0.259561i
\(89\) 4293.30 8915.14i 0.542015 1.12551i −0.432593 0.901589i \(-0.642401\pi\)
0.974608 0.223917i \(-0.0718845\pi\)
\(90\) −216.263 + 271.185i −0.0266991 + 0.0334796i
\(91\) 13623.7 + 3109.51i 1.64517 + 0.375500i
\(92\) 821.595 0.0970694
\(93\) 348.109i 0.0402485i
\(94\) 14687.7 + 3352.37i 1.66226 + 0.379400i
\(95\) 72.9504 + 91.4770i 0.00808315 + 0.0101360i
\(96\) 648.702 + 2842.15i 0.0703887 + 0.308393i
\(97\) −2634.89 3304.04i −0.280039 0.351158i 0.621842 0.783143i \(-0.286385\pi\)
−0.901881 + 0.431985i \(0.857813\pi\)
\(98\) −1176.73 2443.51i −0.122525 0.254426i
\(99\) 530.058 2322.33i 0.0540820 0.236949i
\(100\) 1068.84 514.726i 0.106884 0.0514726i
\(101\) 1719.84 2156.61i 0.168595 0.211412i −0.690355 0.723471i \(-0.742546\pi\)
0.858950 + 0.512059i \(0.171117\pi\)
\(102\) 1256.18 + 5503.69i 0.120740 + 0.528997i
\(103\) 1786.94 + 7829.10i 0.168436 + 0.737967i 0.986623 + 0.163016i \(0.0521221\pi\)
−0.818187 + 0.574952i \(0.805021\pi\)
\(104\) −6556.98 + 13615.7i −0.606230 + 1.25885i
\(105\) 667.650 + 532.433i 0.0605578 + 0.0482932i
\(106\) 6231.93 4969.80i 0.554640 0.442311i
\(107\) −12878.6 6201.98i −1.12486 0.541705i −0.223471 0.974711i \(-0.571739\pi\)
−0.901391 + 0.433005i \(0.857453\pi\)
\(108\) −171.974 + 357.108i −0.0147440 + 0.0306162i
\(109\) −12631.7 15839.6i −1.06318 1.33319i −0.940141 0.340785i \(-0.889307\pi\)
−0.123039 0.992402i \(-0.539264\pi\)
\(110\) 127.013 159.269i 0.0104969 0.0131627i
\(111\) 19434.9 + 9359.35i 1.57738 + 0.759626i
\(112\) 15208.0 3471.14i 1.21238 0.276717i
\(113\) −3263.35 + 744.838i −0.255568 + 0.0583318i −0.348385 0.937351i \(-0.613270\pi\)
0.0928172 + 0.995683i \(0.470413\pi\)
\(114\) −3616.97 2884.44i −0.278314 0.221948i
\(115\) 241.102 + 500.653i 0.0182308 + 0.0378566i
\(116\) −1656.78 378.150i −0.123126 0.0281027i
\(117\) 14537.7 7001.01i 1.06200 0.511433i
\(118\) −13903.4 + 11087.6i −0.998519 + 0.796293i
\(119\) 5964.22 1361.29i 0.421172 0.0961297i
\(120\) −722.034 + 575.803i −0.0501412 + 0.0399863i
\(121\) 2946.62 12910.0i 0.201258 0.881770i
\(122\) −16902.5 −1.13562
\(123\) 13889.1i 0.918046i
\(124\) −12.2560 + 53.6970i −0.000797086 + 0.00349226i
\(125\) 1256.30 + 1001.86i 0.0804029 + 0.0641192i
\(126\) −13390.5 6448.50i −0.843440 0.406179i
\(127\) 118.686 57.1564i 0.00735858 0.00354370i −0.430201 0.902733i \(-0.641557\pi\)
0.437559 + 0.899190i \(0.355843\pi\)
\(128\) 18686.1i 1.14051i
\(129\) −1869.50 + 22162.1i −0.112343 + 1.33177i
\(130\) 1379.92 0.0816520
\(131\) −7786.31 16168.4i −0.453721 0.942161i −0.994863 0.101230i \(-0.967722\pi\)
0.541142 0.840931i \(-0.317992\pi\)
\(132\) −371.511 + 771.450i −0.0213218 + 0.0442751i
\(133\) −3125.80 + 3919.63i −0.176709 + 0.221586i
\(134\) 29291.0 + 6685.49i 1.63127 + 0.372326i
\(135\) −268.076 −0.0147093
\(136\) 6615.91i 0.357694i
\(137\) −19118.9 4363.76i −1.01864 0.232498i −0.319579 0.947560i \(-0.603542\pi\)
−0.699062 + 0.715061i \(0.746399\pi\)
\(138\) −13699.0 17178.0i −0.719335 0.902018i
\(139\) 7382.95 + 32346.8i 0.382121 + 1.67418i 0.690825 + 0.723022i \(0.257247\pi\)
−0.308705 + 0.951158i \(0.599896\pi\)
\(140\) −84.2417 105.636i −0.00429805 0.00538958i
\(141\) −18582.5 38586.9i −0.934684 1.94089i
\(142\) 5605.66 24560.0i 0.278004 1.21801i
\(143\) −8538.14 + 4111.75i −0.417533 + 0.201073i
\(144\) 11230.4 14082.5i 0.541590 0.679132i
\(145\) −255.760 1120.56i −0.0121646 0.0532965i
\(146\) 2955.19 + 12947.5i 0.138637 + 0.607410i
\(147\) −3345.23 + 6946.43i −0.154807 + 0.321460i
\(148\) −2668.38 2127.96i −0.121822 0.0971496i
\(149\) 26010.8 20742.9i 1.17161 0.934324i 0.172888 0.984942i \(-0.444690\pi\)
0.998718 + 0.0506171i \(0.0161188\pi\)
\(150\) −28583.5 13765.1i −1.27038 0.611781i
\(151\) −18847.7 + 39137.6i −0.826615 + 1.71648i −0.139144 + 0.990272i \(0.544435\pi\)
−0.687471 + 0.726212i \(0.741279\pi\)
\(152\) −3380.41 4238.90i −0.146313 0.183471i
\(153\) 4404.29 5522.80i 0.188145 0.235926i
\(154\) 7864.32 + 3787.26i 0.331604 + 0.159692i
\(155\) −36.3178 + 8.28930i −0.00151167 + 0.000345028i
\(156\) −5654.64 + 1290.64i −0.232357 + 0.0530340i
\(157\) 20991.5 + 16740.2i 0.851617 + 0.679142i 0.948715 0.316133i \(-0.102384\pi\)
−0.0970976 + 0.995275i \(0.530956\pi\)
\(158\) −5944.84 12344.6i −0.238137 0.494496i
\(159\) −22091.8 5042.30i −0.873848 0.199450i
\(160\) 281.071 135.357i 0.0109793 0.00528737i
\(161\) −18615.4 + 14845.3i −0.718160 + 0.572714i
\(162\) 31613.6 7215.60i 1.20460 0.274943i
\(163\) 8776.06 6998.68i 0.330312 0.263415i −0.444264 0.895896i \(-0.646535\pi\)
0.774576 + 0.632481i \(0.217963\pi\)
\(164\) 488.999 2142.44i 0.0181811 0.0796566i
\(165\) −579.118 −0.0212715
\(166\) 21757.8i 0.789586i
\(167\) −9047.35 + 39639.0i −0.324406 + 1.42131i 0.505219 + 0.862991i \(0.331412\pi\)
−0.829624 + 0.558322i \(0.811445\pi\)
\(168\) −30937.9 24672.1i −1.09615 0.874154i
\(169\) −32103.4 15460.2i −1.12403 0.541304i
\(170\) 544.280 262.112i 0.0188332 0.00906960i
\(171\) 5788.91i 0.197972i
\(172\) 1068.65 3352.76i 0.0361224 0.113330i
\(173\) 39819.1 1.33045 0.665227 0.746641i \(-0.268335\pi\)
0.665227 + 0.746641i \(0.268335\pi\)
\(174\) 19718.3 + 40945.4i 0.651284 + 1.35241i
\(175\) −14916.9 + 30975.2i −0.487082 + 1.01144i
\(176\) −6595.71 + 8270.76i −0.212930 + 0.267006i
\(177\) 49286.5 + 11249.3i 1.57319 + 0.359071i
\(178\) 41868.1 1.32143
\(179\) 49891.9i 1.55713i −0.627566 0.778563i \(-0.715949\pi\)
0.627566 0.778563i \(-0.284051\pi\)
\(180\) −152.102 34.7164i −0.00469452 0.00107149i
\(181\) −13606.8 17062.4i −0.415335 0.520814i 0.529522 0.848296i \(-0.322371\pi\)
−0.944857 + 0.327482i \(0.893800\pi\)
\(182\) 13157.0 + 57644.7i 0.397205 + 1.74027i
\(183\) 29959.1 + 37567.6i 0.894597 + 1.12179i
\(184\) −11172.3 23199.5i −0.329994 0.685241i
\(185\) 513.659 2250.49i 0.0150083 0.0657557i
\(186\) 1327.06 639.078i 0.0383587 0.0184726i
\(187\) −2586.67 + 3243.59i −0.0739705 + 0.0927561i
\(188\) 1507.87 + 6606.40i 0.0426626 + 0.186917i
\(189\) −2556.01 11198.6i −0.0715548 0.313502i
\(190\) −214.801 + 446.039i −0.00595017 + 0.0123557i
\(191\) 21666.3 + 17278.3i 0.593906 + 0.473624i 0.873720 0.486430i \(-0.161701\pi\)
−0.279813 + 0.960054i \(0.590273\pi\)
\(192\) 32913.0 26247.2i 0.892821 0.712001i
\(193\) −17539.6 8446.63i −0.470874 0.226761i 0.183371 0.983044i \(-0.441299\pi\)
−0.654245 + 0.756283i \(0.727013\pi\)
\(194\) 7758.38 16110.4i 0.206142 0.428059i
\(195\) −2445.86 3067.01i −0.0643224 0.0806577i
\(196\) 760.578 953.735i 0.0197985 0.0248265i
\(197\) 57819.6 + 27844.4i 1.48985 + 0.717474i 0.988980 0.148049i \(-0.0472994\pi\)
0.500869 + 0.865523i \(0.333014\pi\)
\(198\) 9826.29 2242.79i 0.250645 0.0572081i
\(199\) 10128.2 2311.69i 0.255755 0.0583745i −0.0927207 0.995692i \(-0.529556\pi\)
0.348476 + 0.937318i \(0.386699\pi\)
\(200\) −29068.8 23181.6i −0.726720 0.579540i
\(201\) −37058.1 76952.0i −0.917258 1.90471i
\(202\) 11378.8 + 2597.13i 0.278864 + 0.0636489i
\(203\) 44371.6 21368.2i 1.07675 0.518533i
\(204\) −1985.20 + 1583.15i −0.0477029 + 0.0380418i
\(205\) 1449.03 330.733i 0.0344803 0.00786990i
\(206\) −26565.4 + 21185.2i −0.626012 + 0.499228i
\(207\) −6117.81 + 26803.9i −0.142776 + 0.625543i
\(208\) −71658.4 −1.65631
\(209\) 3399.88i 0.0778342i
\(210\) −804.028 + 3522.68i −0.0182319 + 0.0798793i
\(211\) −63275.1 50460.2i −1.42124 1.13340i −0.970600 0.240698i \(-0.922624\pi\)
−0.450642 0.892705i \(-0.648805\pi\)
\(212\) 3230.21 + 1555.58i 0.0718718 + 0.0346116i
\(213\) −64522.9 + 31072.6i −1.42218 + 0.684886i
\(214\) 60481.4i 1.32067i
\(215\) 2356.66 332.688i 0.0509823 0.00719715i
\(216\) 12422.3 0.266252
\(217\) −692.553 1438.10i −0.0147073 0.0305401i
\(218\) 37193.7 77233.4i 0.782629 1.62515i
\(219\) 23539.2 29517.3i 0.490800 0.615443i
\(220\) 89.3309 + 20.3892i 0.00184568 + 0.000421265i
\(221\) −28102.7 −0.575391
\(222\) 91272.0i 1.85196i
\(223\) 25139.4 + 5737.90i 0.505527 + 0.115383i 0.467676 0.883900i \(-0.345091\pi\)
0.0378516 + 0.999283i \(0.487949\pi\)
\(224\) 8334.28 + 10450.9i 0.166101 + 0.208284i
\(225\) 8833.67 + 38702.8i 0.174492 + 0.764500i
\(226\) −8830.50 11073.1i −0.172889 0.216796i
\(227\) 15369.0 + 31914.1i 0.298260 + 0.619343i 0.995208 0.0977786i \(-0.0311737\pi\)
−0.696949 + 0.717121i \(0.745459\pi\)
\(228\) 463.034 2028.69i 0.00890725 0.0390252i
\(229\) −82940.8 + 39942.2i −1.58160 + 0.761659i −0.998704 0.0508864i \(-0.983795\pi\)
−0.582897 + 0.812546i \(0.698081\pi\)
\(230\) −1465.96 + 1838.25i −0.0277119 + 0.0347496i
\(231\) −5521.67 24192.0i −0.103478 0.453365i
\(232\) 11851.6 + 51925.0i 0.220191 + 0.964719i
\(233\) −331.105 + 687.546i −0.00609892 + 0.0126645i −0.903996 0.427541i \(-0.859380\pi\)
0.897897 + 0.440205i \(0.145094\pi\)
\(234\) 53378.4 + 42567.8i 0.974840 + 0.777409i
\(235\) −3583.23 + 2857.53i −0.0648842 + 0.0517434i
\(236\) −7206.56 3470.49i −0.129391 0.0623114i
\(237\) −16900.1 + 35093.3i −0.300879 + 0.624781i
\(238\) 16138.9 + 20237.6i 0.284919 + 0.357277i
\(239\) −27424.2 + 34388.8i −0.480107 + 0.602035i −0.961613 0.274408i \(-0.911518\pi\)
0.481507 + 0.876442i \(0.340090\pi\)
\(240\) −3945.40 1900.00i −0.0684965 0.0329862i
\(241\) −104925. + 23948.4i −1.80653 + 0.412328i −0.987001 0.160712i \(-0.948621\pi\)
−0.819527 + 0.573040i \(0.805764\pi\)
\(242\) 54624.9 12467.8i 0.932739 0.212892i
\(243\) −58882.4 46957.1i −0.997178 0.795223i
\(244\) −3298.65 6849.71i −0.0554059 0.115052i
\(245\) 804.371 + 183.592i 0.0134006 + 0.00305860i
\(246\) −52948.0 + 25498.4i −0.874942 + 0.421350i
\(247\) 18005.7 14359.1i 0.295133 0.235360i
\(248\) 1682.91 384.114i 0.0273626 0.00624534i
\(249\) −48359.0 + 38565.0i −0.779971 + 0.622006i
\(250\) −1512.91 + 6628.51i −0.0242066 + 0.106056i
\(251\) 67988.0 1.07916 0.539579 0.841935i \(-0.318584\pi\)
0.539579 + 0.841935i \(0.318584\pi\)
\(252\) 6684.92i 0.105268i
\(253\) 3593.04 15742.1i 0.0561334 0.245937i
\(254\) 435.782 + 347.525i 0.00675464 + 0.00538664i
\(255\) −1547.29 745.134i −0.0237953 0.0114592i
\(256\) −20783.8 + 10009.0i −0.317136 + 0.152725i
\(257\) 39236.5i 0.594051i −0.954870 0.297025i \(-0.904005\pi\)
0.954870 0.297025i \(-0.0959946\pi\)
\(258\) −87918.2 + 33559.4i −1.32081 + 0.504168i
\(259\) 98909.3 1.47448
\(260\) 269.301 + 559.209i 0.00398374 + 0.00827232i
\(261\) 24673.7 51235.4i 0.362204 0.752124i
\(262\) 47342.6 59365.8i 0.689683 0.864836i
\(263\) 122034. + 27853.6i 1.76429 + 0.402688i 0.976889 0.213748i \(-0.0685673\pi\)
0.787404 + 0.616437i \(0.211424\pi\)
\(264\) 26835.4 0.385036
\(265\) 2424.88i 0.0345301i
\(266\) −20680.9 4720.27i −0.292284 0.0667120i
\(267\) −74209.7 93056.0i −1.04097 1.30534i
\(268\) 3007.07 + 13174.8i 0.0418672 + 0.183432i
\(269\) 23347.2 + 29276.5i 0.322649 + 0.404589i 0.916531 0.399963i \(-0.130977\pi\)
−0.593882 + 0.804552i \(0.702406\pi\)
\(270\) −492.149 1021.96i −0.00675102 0.0140186i
\(271\) 1089.06 4771.50i 0.0148291 0.0649705i −0.966972 0.254883i \(-0.917963\pi\)
0.981801 + 0.189912i \(0.0608203\pi\)
\(272\) −28264.2 + 13611.3i −0.382031 + 0.183976i
\(273\) 104801. 131416.i 1.40617 1.76329i
\(274\) −18464.0 80896.0i −0.245937 1.07752i
\(275\) −5188.09 22730.5i −0.0686028 0.300569i
\(276\) 4287.90 8903.91i 0.0562893 0.116886i
\(277\) 32861.0 + 26205.7i 0.428273 + 0.341536i 0.813785 0.581167i \(-0.197404\pi\)
−0.385512 + 0.922703i \(0.625975\pi\)
\(278\) −109758. + 87529.3i −1.42019 + 1.13257i
\(279\) −1660.56 799.685i −0.0213327 0.0102733i
\(280\) −1837.31 + 3815.21i −0.0234351 + 0.0486634i
\(281\) 24196.3 + 30341.2i 0.306433 + 0.384255i 0.911074 0.412243i \(-0.135255\pi\)
−0.604640 + 0.796499i \(0.706683\pi\)
\(282\) 112986. 141680.i 1.42078 1.78160i
\(283\) −13109.8 6313.32i −0.163690 0.0788289i 0.350245 0.936658i \(-0.386098\pi\)
−0.513935 + 0.857829i \(0.671813\pi\)
\(284\) 11046.9 2521.38i 0.136963 0.0312609i
\(285\) 1372.09 313.172i 0.0168925 0.00385561i
\(286\) −31349.6 25000.4i −0.383265 0.305644i
\(287\) 27632.0 + 57378.5i 0.335466 + 0.696603i
\(288\) 15047.9 + 3434.59i 0.181423 + 0.0414086i
\(289\) 64165.3 30900.4i 0.768254 0.369971i
\(290\) 3802.25 3032.19i 0.0452110 0.0360546i
\(291\) −49558.5 + 11311.4i −0.585238 + 0.133577i
\(292\) −4670.24 + 3724.39i −0.0547738 + 0.0436807i
\(293\) −1953.83 + 8560.31i −0.0227590 + 0.0997136i −0.985032 0.172373i \(-0.944857\pi\)
0.962273 + 0.272087i \(0.0877137\pi\)
\(294\) −32622.5 −0.377418
\(295\) 5409.87i 0.0621646i
\(296\) −23802.2 + 104284.i −0.271665 + 1.19024i
\(297\) 6090.27 + 4856.82i 0.0690436 + 0.0550604i
\(298\) 126828. + 61077.2i 1.42818 + 0.687775i
\(299\) 98545.4 47457.0i 1.10228 0.530832i
\(300\) 14269.7i 0.158553i
\(301\) 36367.6 + 95274.9i 0.401403 + 1.05159i
\(302\) −183801. −2.01528
\(303\) −14396.1 29893.8i −0.156805 0.325609i
\(304\) 11154.5 23162.6i 0.120699 0.250634i
\(305\) 3205.98 4020.17i 0.0344637 0.0432161i
\(306\) 29139.6 + 6650.92i 0.311201 + 0.0710296i
\(307\) 44674.7 0.474007 0.237003 0.971509i \(-0.423835\pi\)
0.237003 + 0.971509i \(0.423835\pi\)
\(308\) 3926.11i 0.0413867i
\(309\) 94172.6 + 21494.3i 0.986297 + 0.225116i
\(310\) −98.2746 123.232i −0.00102263 0.00128234i
\(311\) −11477.6 50286.8i −0.118668 0.519916i −0.998965 0.0454935i \(-0.985514\pi\)
0.880297 0.474423i \(-0.157343\pi\)
\(312\) 113337. + 142121.i 1.16430 + 1.45998i
\(313\) 50907.4 + 105710.i 0.519628 + 1.07902i 0.981392 + 0.192015i \(0.0615023\pi\)
−0.461764 + 0.887003i \(0.652783\pi\)
\(314\) −25279.4 + 110756.i −0.256394 + 1.12333i
\(315\) 4073.57 1961.73i 0.0410539 0.0197705i
\(316\) 3842.44 4818.26i 0.0384798 0.0482521i
\(317\) 10737.5 + 47043.9i 0.106852 + 0.468149i 0.999837 + 0.0180626i \(0.00574981\pi\)
−0.892985 + 0.450087i \(0.851393\pi\)
\(318\) −21335.0 93474.9i −0.210979 0.924360i
\(319\) −14491.1 + 30091.0i −0.142403 + 0.295703i
\(320\) −3522.07 2808.76i −0.0343953 0.0274293i
\(321\) −134426. + 107201.i −1.30459 + 1.04037i
\(322\) −90768.4 43711.7i −0.875433 0.421586i
\(323\) 4374.52 9083.79i 0.0419301 0.0870687i
\(324\) 9093.72 + 11403.2i 0.0866266 + 0.108626i
\(325\) 98469.3 123477.i 0.932253 1.16901i
\(326\) 42791.9 + 20607.5i 0.402649 + 0.193905i
\(327\) −237584. + 54226.9i −2.22188 + 0.507130i
\(328\) −67146.1 + 15325.7i −0.624127 + 0.142453i
\(329\) −153535. 122440.i −1.41846 1.13118i
\(330\) −1063.18 2207.71i −0.00976287 0.0202728i
\(331\) −144924. 33077.9i −1.32277 0.301913i −0.497898 0.867236i \(-0.665895\pi\)
−0.824870 + 0.565322i \(0.808752\pi\)
\(332\) 8817.31 4246.19i 0.0799945 0.0385233i
\(333\) 89292.6 71208.5i 0.805244 0.642160i
\(334\) −167721. + 38281.3i −1.50347 + 0.343157i
\(335\) −7145.87 + 5698.64i −0.0636745 + 0.0507787i
\(336\) 41752.7 182931.i 0.369833 1.62035i
\(337\) 8670.64 0.0763469 0.0381734 0.999271i \(-0.487846\pi\)
0.0381734 + 0.999271i \(0.487846\pi\)
\(338\) 150767.i 1.31969i
\(339\) −8959.32 + 39253.3i −0.0779607 + 0.341568i
\(340\) 212.440 + 169.415i 0.00183772 + 0.00146553i
\(341\) 975.262 + 469.661i 0.00838711 + 0.00403902i
\(342\) −22068.4 + 10627.6i −0.188677 + 0.0908621i
\(343\) 97072.7i 0.825104i
\(344\) −109204. + 15416.3i −0.922830 + 0.130275i
\(345\) 6684.06 0.0561567
\(346\) 73102.2 + 151798.i 0.610630 + 1.26799i
\(347\) −13739.3 + 28530.0i −0.114106 + 0.236943i −0.950199 0.311645i \(-0.899120\pi\)
0.836093 + 0.548588i \(0.184834\pi\)
\(348\) −12744.9 + 15981.6i −0.105239 + 0.131966i
\(349\) −10230.9 2335.15i −0.0839972 0.0191718i 0.180316 0.983609i \(-0.442288\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(350\) −145469. −1.18750
\(351\) 52766.5i 0.428296i
\(352\) −8837.78 2017.16i −0.0713276 0.0162801i
\(353\) 107208. + 134434.i 0.860354 + 1.07885i 0.996111 + 0.0881078i \(0.0280820\pi\)
−0.135757 + 0.990742i \(0.543347\pi\)
\(354\) 47598.3 + 208542.i 0.379826 + 1.66413i
\(355\) 4778.21 + 5991.69i 0.0379148 + 0.0475436i
\(356\) 8170.85 + 16966.9i 0.0644714 + 0.133876i
\(357\) 16374.4 71740.8i 0.128478 0.562898i
\(358\) 190197. 91594.3i 1.48402 0.714664i
\(359\) 152738. 191528.i 1.18511 1.48608i 0.349344 0.936995i \(-0.386404\pi\)
0.835766 0.549086i \(-0.185024\pi\)
\(360\) 1088.04 + 4767.02i 0.00839538 + 0.0367826i
\(361\) −27160.6 118998.i −0.208413 0.913117i
\(362\) 40064.9 83195.7i 0.305737 0.634869i
\(363\) −124532. 99310.7i −0.945075 0.753673i
\(364\) −20792.7 + 16581.6i −0.156931 + 0.125148i
\(365\) −3640.03 1752.94i −0.0273224 0.0131578i
\(366\) −88214.2 + 183179.i −0.658531 + 1.36745i
\(367\) −249.174 312.454i −0.00185000 0.00231982i 0.780906 0.624649i \(-0.214758\pi\)
−0.782756 + 0.622329i \(0.786187\pi\)
\(368\) 76126.3 95459.4i 0.562133 0.704893i
\(369\) 66254.3 + 31906.4i 0.486588 + 0.234329i
\(370\) 9522.29 2173.40i 0.0695566 0.0158758i
\(371\) −101297. + 23120.3i −0.735948 + 0.167975i
\(372\) 517.969 + 413.067i 0.00374299 + 0.00298493i
\(373\) 75279.4 + 156319.i 0.541076 + 1.12356i 0.974917 + 0.222567i \(0.0714435\pi\)
−0.433841 + 0.900989i \(0.642842\pi\)
\(374\) −17113.9 3906.14i −0.122351 0.0279258i
\(375\) 17414.1 8386.20i 0.123834 0.0596352i
\(376\) 166041. 132414.i 1.17447 0.936606i
\(377\) −220564. + 50342.3i −1.55186 + 0.354201i
\(378\) 37998.8 30303.0i 0.265941 0.212081i
\(379\) −14925.5 + 65393.0i −0.103909 + 0.455253i 0.896028 + 0.443997i \(0.146440\pi\)
−0.999937 + 0.0112557i \(0.996417\pi\)
\(380\) −222.676 −0.00154208
\(381\) 1584.54i 0.0109158i
\(382\) −26092.0 + 114316.i −0.178805 + 0.783397i
\(383\) −105246. 83931.1i −0.717479 0.572171i 0.195241 0.980755i \(-0.437451\pi\)
−0.912720 + 0.408585i \(0.866022\pi\)
\(384\) 202507. + 97522.4i 1.37334 + 0.661366i
\(385\) −2392.44 + 1152.14i −0.0161406 + 0.00777291i
\(386\) 82371.1i 0.552841i
\(387\) 101424. + 59829.2i 0.677200 + 0.399477i
\(388\) 8042.82 0.0534250
\(389\) 11463.2 + 23803.7i 0.0757545 + 0.157306i 0.935406 0.353574i \(-0.115034\pi\)
−0.859652 + 0.510880i \(0.829320\pi\)
\(390\) 7201.78 14954.7i 0.0473490 0.0983212i
\(391\) 29854.9 37436.8i 0.195282 0.244875i
\(392\) −37273.3 8507.40i −0.242564 0.0553636i
\(393\) −215860. −1.39761
\(394\) 271538.i 1.74919i
\(395\) 4063.68 + 927.508i 0.0260450 + 0.00594461i
\(396\) 2826.55 + 3544.39i 0.0180246 + 0.0226022i
\(397\) −24730.2 108350.i −0.156908 0.687460i −0.990778 0.135498i \(-0.956736\pi\)
0.833869 0.551962i \(-0.186121\pi\)
\(398\) 27406.4 + 34366.6i 0.173016 + 0.216955i
\(399\) 26164.8 + 54331.8i 0.164351 + 0.341278i
\(400\) 39230.3 171879.i 0.245189 1.07424i
\(401\) −131315. + 63238.0i −0.816631 + 0.393269i −0.795084 0.606499i \(-0.792573\pi\)
−0.0215471 + 0.999768i \(0.506859\pi\)
\(402\) 225323. 282545.i 1.39429 1.74838i
\(403\) 1631.61 + 7148.57i 0.0100463 + 0.0440158i
\(404\) 1168.17 + 5118.07i 0.00715718 + 0.0313577i
\(405\) −4280.11 + 8887.73i −0.0260942 + 0.0541852i
\(406\) 162920. + 129924.i 0.988374 + 0.788202i
\(407\) −52442.3 + 41821.3i −0.316587 + 0.252470i
\(408\) 71698.9 + 34528.4i 0.430717 + 0.207423i
\(409\) 54755.6 113701.i 0.327327 0.679702i −0.670750 0.741684i \(-0.734028\pi\)
0.998077 + 0.0619814i \(0.0197419\pi\)
\(410\) 3921.03 + 4916.82i 0.0233256 + 0.0292494i
\(411\) −147073. + 184423.i −0.870660 + 1.09177i
\(412\) −13769.7 6631.14i −0.0811204 0.0390655i
\(413\) 225992. 51581.1i 1.32493 0.302406i
\(414\) −113413. + 25885.8i −0.661701 + 0.151029i
\(415\) 5174.98 + 4126.91i 0.0300478 + 0.0239623i
\(416\) −26642.7 55324.2i −0.153954 0.319690i
\(417\) 389085. + 88806.2i 2.23755 + 0.510706i
\(418\) 12961.0 6241.68i 0.0741797 0.0357231i
\(419\) 62172.5 49580.9i 0.354136 0.282414i −0.430221 0.902724i \(-0.641564\pi\)
0.784357 + 0.620309i \(0.212993\pi\)
\(420\) −1584.47 + 361.644i −0.00898224 + 0.00205014i
\(421\) −204638. + 163193.i −1.15458 + 0.920743i −0.997761 0.0668852i \(-0.978694\pi\)
−0.156814 + 0.987628i \(0.550122\pi\)
\(422\) 76200.1 333854.i 0.427888 1.87470i
\(423\) −226757. −1.26730
\(424\) 112365.i 0.625028i
\(425\) 15385.1 67406.7i 0.0851772 0.373186i
\(426\) −236909. 188929.i −1.30546 1.04107i
\(427\) 198506. + 95595.6i 1.08873 + 0.524303i
\(428\) 24510.0 11803.4i 0.133800 0.0644345i
\(429\) 113990.i 0.619372i
\(430\) 5594.75 + 8373.27i 0.0302583 + 0.0452854i
\(431\) −51750.1 −0.278584 −0.139292 0.990251i \(-0.544483\pi\)
−0.139292 + 0.990251i \(0.544483\pi\)
\(432\) 25557.0 + 53069.7i 0.136944 + 0.284367i
\(433\) −51826.2 + 107618.i −0.276423 + 0.573998i −0.992247 0.124283i \(-0.960337\pi\)
0.715824 + 0.698281i \(0.246051\pi\)
\(434\) 4210.89 5280.29i 0.0223560 0.0280336i
\(435\) −13478.7 3076.43i −0.0712311 0.0162580i
\(436\) 38557.3 0.202831
\(437\) 39240.7i 0.205482i
\(438\) 155740. + 35546.7i 0.811806 + 0.185289i
\(439\) −4677.69 5865.64i −0.0242718 0.0304359i 0.769547 0.638590i \(-0.220482\pi\)
−0.793819 + 0.608154i \(0.791910\pi\)
\(440\) −639.015 2799.71i −0.00330070 0.0144613i
\(441\) 25451.4 + 31915.0i 0.130868 + 0.164104i
\(442\) −51592.4 107133.i −0.264083 0.548375i
\(443\) −29196.5 + 127918.i −0.148773 + 0.651816i 0.844454 + 0.535628i \(0.179925\pi\)
−0.993227 + 0.116189i \(0.962932\pi\)
\(444\) −36987.7 + 17812.4i −0.187626 + 0.0903557i
\(445\) −7941.31 + 9958.09i −0.0401026 + 0.0502871i
\(446\) 24278.3 + 106370.i 0.122053 + 0.534749i
\(447\) −89048.1 390145.i −0.445666 1.95259i
\(448\) 83751.3 173911.i 0.417288 0.866507i
\(449\) 118534. + 94527.6i 0.587962 + 0.468884i 0.871715 0.490013i \(-0.163008\pi\)
−0.283753 + 0.958898i \(0.591579\pi\)
\(450\) −131325. + 104728.i −0.648520 + 0.517177i
\(451\) −38911.7 18738.9i −0.191305 0.0921279i
\(452\) 2764.01 5739.53i 0.0135289 0.0280931i
\(453\) 325781. + 408517.i 1.58756 + 1.99074i
\(454\) −93447.4 + 117179.i −0.453373 + 0.568511i
\(455\) −16206.0 7804.41i −0.0782805 0.0376979i
\(456\) −63580.8 + 14511.9i −0.305771 + 0.0697902i
\(457\) 138942. 31712.6i 0.665275 0.151845i 0.123469 0.992348i \(-0.460598\pi\)
0.541806 + 0.840504i \(0.317741\pi\)
\(458\) −304534. 242858.i −1.45180 1.15777i
\(459\) 10022.8 + 20812.6i 0.0475735 + 0.0987874i
\(460\) −1031.04 235.328i −0.00487259 0.00111214i
\(461\) 264425. 127340.i 1.24423 0.599189i 0.308271 0.951299i \(-0.400250\pi\)
0.935959 + 0.352109i \(0.114535\pi\)
\(462\) 82087.7 65462.7i 0.384586 0.306697i
\(463\) −99056.4 + 22609.0i −0.462084 + 0.105468i −0.447224 0.894422i \(-0.647587\pi\)
−0.0148597 + 0.999890i \(0.504730\pi\)
\(464\) −197449. + 157460.i −0.917103 + 0.731365i
\(465\) −99.7082 + 436.850i −0.000461132 + 0.00202035i
\(466\) −3228.92 −0.0148691
\(467\) 95657.0i 0.438614i −0.975656 0.219307i \(-0.929620\pi\)
0.975656 0.219307i \(-0.0703797\pi\)
\(468\) −6833.35 + 29938.9i −0.0311991 + 0.136692i
\(469\) −306188. 244177.i −1.39201 1.11009i
\(470\) −17471.7 8413.95i −0.0790934 0.0380894i
\(471\) 290974. 140125.i 1.31163 0.631648i
\(472\) 250685.i 1.12524i
\(473\) −59566.9 35138.2i −0.266246 0.157057i
\(474\) −164809. −0.733539
\(475\) 24584.1 + 51049.4i 0.108960 + 0.226258i
\(476\) −5051.61 + 10489.8i −0.0222954 + 0.0462969i
\(477\) −74802.7 + 93799.6i −0.328761 + 0.412253i
\(478\) −181444. 41413.3i −0.794119 0.181253i
\(479\) 335880. 1.46391 0.731953 0.681355i \(-0.238609\pi\)
0.731953 + 0.681355i \(0.238609\pi\)
\(480\) 3752.49i 0.0162868i
\(481\) −442972. 101105.i −1.91463 0.437003i
\(482\) −283923. 356028.i −1.22210 1.53246i
\(483\) 63730.0 + 279219.i 0.273180 + 1.19688i
\(484\) 15713.0 + 19703.4i 0.0670761 + 0.0841107i
\(485\) 2360.21 + 4901.03i 0.0100338 + 0.0208355i
\(486\) 70910.1 310677.i 0.300217 1.31534i
\(487\) −129440. + 62335.0i −0.545771 + 0.262830i −0.686389 0.727234i \(-0.740805\pi\)
0.140618 + 0.990064i \(0.455091\pi\)
\(488\) −148560. + 186289.i −0.623826 + 0.782253i
\(489\) −30044.9 131635.i −0.125647 0.550496i
\(490\) 776.819 + 3403.46i 0.00323540 + 0.0141752i
\(491\) 89073.9 184964.i 0.369477 0.767227i −0.630483 0.776203i \(-0.717143\pi\)
0.999960 + 0.00897625i \(0.00285727\pi\)
\(492\) −20666.3 16480.8i −0.0853755 0.0680847i
\(493\) −77434.4 + 61751.9i −0.318596 + 0.254072i
\(494\) 87795.6 + 42280.1i 0.359765 + 0.173254i
\(495\) −1330.36 + 2762.53i −0.00542950 + 0.0112745i
\(496\) 5103.34 + 6399.39i 0.0207440 + 0.0260121i
\(497\) −204738. + 256733.i −0.828868 + 1.03937i
\(498\) −235797. 113554.i −0.950780 0.457871i
\(499\) −62000.3 + 14151.2i −0.248996 + 0.0568317i −0.345197 0.938530i \(-0.612188\pi\)
0.0962011 + 0.995362i \(0.469331\pi\)
\(500\) −2981.44 + 680.495i −0.0119258 + 0.00272198i
\(501\) 382364. + 304925.i 1.52336 + 1.21484i
\(502\) 124816. + 259183.i 0.495294 + 1.02849i
\(503\) −92921.2 21208.6i −0.367264 0.0838257i 0.0349059 0.999391i \(-0.488887\pi\)
−0.402170 + 0.915565i \(0.631744\pi\)
\(504\) −188763. + 90903.5i −0.743115 + 0.357865i
\(505\) −2775.98 + 2213.77i −0.0108851 + 0.00868060i
\(506\) 66608.4 15202.9i 0.260152 0.0593781i
\(507\) −335095. + 267229.i −1.30362 + 1.03960i
\(508\) −55.7876 + 244.422i −0.000216177 + 0.000947135i
\(509\) −272684. −1.05250 −0.526252 0.850329i \(-0.676403\pi\)
−0.526252 + 0.850329i \(0.676403\pi\)
\(510\) 7266.51i 0.0279374i
\(511\) 38521.1 168772.i 0.147522 0.646336i
\(512\) 157438. + 125552.i 0.600577 + 0.478944i
\(513\) −17056.0 8213.74i −0.0648101 0.0312109i
\(514\) 149577. 72032.4i 0.566159 0.272648i
\(515\) 10336.7i 0.0389735i
\(516\) −30757.7 29079.3i −0.115519 0.109215i
\(517\) 133176. 0.498247
\(518\) 181583. + 377061.i 0.676731 + 1.40525i
\(519\) 207816. 431534.i 0.771514 1.60206i
\(520\) 12128.4 15208.6i 0.0448537 0.0562447i
\(521\) −168704. 38505.5i −0.621511 0.141856i −0.0998413 0.995003i \(-0.531834\pi\)
−0.521670 + 0.853148i \(0.674691\pi\)
\(522\) 240617. 0.883049
\(523\) 3836.13i 0.0140246i 0.999975 + 0.00701229i \(0.00223210\pi\)
−0.999975 + 0.00701229i \(0.997768\pi\)
\(524\) 33297.1 + 7599.84i 0.121267 + 0.0276785i
\(525\) 257838. + 323319.i 0.935467 + 1.17304i
\(526\) 117854. + 516353.i 0.425965 + 1.86627i
\(527\) 2001.40 + 2509.68i 0.00720632 + 0.00903644i
\(528\) 55210.1 + 114645.i 0.198039 + 0.411233i
\(529\) 20800.3 91132.2i 0.0743291 0.325657i
\(530\) −9244.09 + 4451.72i −0.0329088 + 0.0158481i
\(531\) 166884. 209266.i 0.591869 0.742181i
\(532\) −2123.14 9302.07i −0.00750161 0.0328667i
\(533\) −65099.3 285219.i −0.229151 1.00398i
\(534\) 218509. 453739.i 0.766279 1.59120i
\(535\) 14385.2 + 11471.8i 0.0502583 + 0.0400796i
\(536\) 331129. 264066.i 1.15257 0.919144i
\(537\) −540696. 260385.i −1.87501 0.902959i
\(538\) −68745.4 + 142751.i −0.237508 + 0.493191i
\(539\) −14947.8 18744.0i −0.0514517 0.0645185i
\(540\) 318.100 398.885i 0.00109088 0.00136792i
\(541\) 514395. + 247720.i 1.75753 + 0.846381i 0.974498 + 0.224397i \(0.0720413\pi\)
0.783030 + 0.621984i \(0.213673\pi\)
\(542\) 20189.2 4608.06i 0.0687260 0.0156863i
\(543\) −255925. + 58413.1i −0.867985 + 0.198112i
\(544\) −21017.3 16760.8i −0.0710199 0.0566365i
\(545\) 11314.9 + 23495.5i 0.0380939 + 0.0791029i
\(546\) 693381. + 158260.i 2.32588 + 0.530866i
\(547\) −65811.8 + 31693.3i −0.219953 + 0.105924i −0.540616 0.841270i \(-0.681809\pi\)
0.320663 + 0.947193i \(0.396094\pi\)
\(548\) 29179.5 23269.9i 0.0971667 0.0774878i
\(549\) 248029. 56611.0i 0.822921 0.187826i
\(550\) 77128.4 61507.9i 0.254970 0.203332i
\(551\) 18061.0 79130.5i 0.0594894 0.260640i
\(552\) −309729. −1.01649
\(553\) 178599.i 0.584022i
\(554\) −39573.4 + 173382.i −0.128939 + 0.564917i
\(555\) −21708.5 17312.0i −0.0704765 0.0562031i
\(556\) −56891.1 27397.3i −0.184033 0.0886254i
\(557\) 232232. 111837.i 0.748536 0.360476i −0.0204085 0.999792i \(-0.506497\pi\)
0.768944 + 0.639316i \(0.220782\pi\)
\(558\) 7798.48i 0.0250462i
\(559\) −65484.2 463870.i −0.209562 1.48447i
\(560\) −20079.2 −0.0640279
\(561\) 21652.0 + 44960.9i 0.0687976 + 0.142860i
\(562\) −71245.5 + 147943.i −0.225572 + 0.468405i
\(563\) 199228. 249824.i 0.628541 0.788165i −0.360977 0.932575i \(-0.617557\pi\)
0.989518 + 0.144409i \(0.0461282\pi\)
\(564\) 79465.4 + 18137.5i 0.249816 + 0.0570188i
\(565\) 4308.60 0.0134971
\(566\) 61567.2i 0.192184i
\(567\) −412085. 94055.7i −1.28180 0.292563i
\(568\) −221415. 277646.i −0.686295 0.860586i
\(569\) −82205.5 360166.i −0.253908 1.11244i −0.927642 0.373470i \(-0.878168\pi\)
0.673734 0.738974i \(-0.264689\pi\)
\(570\) 3712.84 + 4655.75i 0.0114276 + 0.0143298i
\(571\) −111720. 231989.i −0.342657 0.711534i 0.656425 0.754392i \(-0.272068\pi\)
−0.999081 + 0.0428579i \(0.986354\pi\)
\(572\) 4013.28 17583.3i 0.0122661 0.0537414i
\(573\) 300327. 144630.i 0.914713 0.440503i
\(574\) −168009. + 210677.i −0.509929 + 0.639431i
\(575\) 59879.8 + 262351.i 0.181111 + 0.793499i
\(576\) −49596.9 217298.i −0.149489 0.654955i
\(577\) 86100.7 178790.i 0.258616 0.537021i −0.730720 0.682678i \(-0.760815\pi\)
0.989335 + 0.145657i \(0.0465295\pi\)
\(578\) 235596. + 187882.i 0.705201 + 0.562379i
\(579\) −183078. + 146000.i −0.546109 + 0.435507i
\(580\) 1970.82 + 949.099i 0.00585857 + 0.00282134i
\(581\) −123056. + 255528.i −0.364544 + 0.756983i
\(582\) −134103. 168160.i −0.395908 0.496453i
\(583\) 43932.2 55089.3i 0.129255 0.162080i
\(584\) 168673. + 81228.8i 0.494562 + 0.238169i
\(585\) −20249.0 + 4621.71i −0.0591688 + 0.0135049i
\(586\) −36220.5 + 8267.09i −0.105477 + 0.0240745i
\(587\) 455985. + 363636.i 1.32335 + 1.05534i 0.993798 + 0.111199i \(0.0354690\pi\)
0.329552 + 0.944138i \(0.393102\pi\)
\(588\) −6366.51 13220.2i −0.0184139 0.0382369i
\(589\) −2564.65 585.365i −0.00739261 0.00168732i
\(590\) 20623.5 9931.74i 0.0592458 0.0285313i
\(591\) 603519. 481291.i 1.72789 1.37795i
\(592\) −494487. + 112864.i −1.41095 + 0.322040i
\(593\) −422877. + 337233.i −1.20255 + 0.959004i −0.999795 0.0202247i \(-0.993562\pi\)
−0.202758 + 0.979229i \(0.564990\pi\)
\(594\) −7334.30 + 32133.7i −0.0207867 + 0.0910726i
\(595\) −7874.55 −0.0222429
\(596\) 63316.4i 0.178248i
\(597\) 27806.2 121827.i 0.0780178 0.341818i
\(598\) 361830. + 288550.i 1.01182 + 0.806897i
\(599\) −151928. 73164.9i −0.423434 0.203915i 0.210017 0.977698i \(-0.432648\pi\)
−0.633451 + 0.773783i \(0.718362\pi\)
\(600\) −402937. + 194044.i −1.11927 + 0.539011i
\(601\) 409845.i 1.13467i −0.823486 0.567336i \(-0.807974\pi\)
0.823486 0.567336i \(-0.192026\pi\)
\(602\) −296440. + 313551.i −0.817983 + 0.865197i
\(603\) −452210. −1.24367
\(604\) −35870.1 74485.1i −0.0983239 0.204172i
\(605\) −7395.57 + 15357.1i −0.0202051 + 0.0419563i
\(606\) 87531.7 109761.i 0.238353 0.298885i
\(607\) 504987. + 115260.i 1.37057 + 0.312825i 0.843562 0.537032i \(-0.180455\pi\)
0.527013 + 0.849857i \(0.323312\pi\)
\(608\) 22030.0 0.0595947
\(609\) 592391.i 1.59725i
\(610\) 21211.4 + 4841.36i 0.0570045 + 0.0130109i
\(611\) 562458. + 705300.i 1.50663 + 1.88926i
\(612\) 2991.53 + 13106.7i 0.00798711 + 0.0349938i
\(613\) −353935. 443820.i −0.941894 1.18110i −0.983307 0.181956i \(-0.941757\pi\)
0.0414123 0.999142i \(-0.486814\pi\)
\(614\) 82016.2 + 170308.i 0.217552 + 0.451751i
\(615\) 3978.23 17429.8i 0.0105182 0.0460831i
\(616\) 110862. 53388.4i 0.292161 0.140697i
\(617\) −262838. + 329588.i −0.690427 + 0.865768i −0.996268 0.0863147i \(-0.972491\pi\)
0.305841 + 0.952083i \(0.401062\pi\)
\(618\) 90946.9 + 398464.i 0.238128 + 1.04331i
\(619\) 27009.9 + 118338.i 0.0704924 + 0.308847i 0.997866 0.0652882i \(-0.0207967\pi\)
−0.927374 + 0.374135i \(0.877940\pi\)
\(620\) 30.7607 63.8752i 8.00226e−5 0.000166169i
\(621\) −70292.6 56056.4i −0.182275 0.145359i
\(622\) 170632. 136074.i 0.441041 0.351718i
\(623\) −491706. 236793.i −1.26686 0.610089i
\(624\) −373985. + 776587.i −0.960472 + 1.99444i
\(625\) 241615. + 302976.i 0.618536 + 0.775619i
\(626\) −309529. + 388137.i −0.789865 + 0.990460i
\(627\) −36845.6 17743.9i −0.0937240 0.0451351i
\(628\) −49817.1 + 11370.4i −0.126316 + 0.0288309i
\(629\) −193926. + 44262.3i −0.490156 + 0.111875i
\(630\) 14957.0 + 11927.8i 0.0376845 + 0.0300524i
\(631\) 89763.5 + 186396.i 0.225445 + 0.468142i 0.982755 0.184914i \(-0.0592008\pi\)
−0.757309 + 0.653056i \(0.773487\pi\)
\(632\) −188305. 42979.3i −0.471440 0.107603i
\(633\) −877087. + 422383.i −2.18895 + 1.05414i
\(634\) −159628. + 127299.i −0.397127 + 0.316699i
\(635\) −165.314 + 37.7318i −0.000409979 + 9.35750e-5i
\(636\) 33716.8 26888.3i 0.0833551 0.0664735i
\(637\) 36137.2 158327.i 0.0890585 0.390191i
\(638\) −141316. −0.347177
\(639\) 379170.i 0.928608i
\(640\) 5352.22 23449.6i 0.0130669 0.0572500i
\(641\) 48188.8 + 38429.3i 0.117282 + 0.0935291i 0.680374 0.732865i \(-0.261817\pi\)
−0.563093 + 0.826394i \(0.690389\pi\)
\(642\) −655458. 315652.i −1.59028 0.765841i
\(643\) 543860. 261909.i 1.31542 0.633473i 0.361176 0.932498i \(-0.382375\pi\)
0.954245 + 0.299024i \(0.0966612\pi\)
\(644\) 45314.3i 0.109261i
\(645\) 8693.92 27276.2i 0.0208976 0.0655639i
\(646\) 42660.1 0.102225
\(647\) 60784.9 + 126221.i 0.145207 + 0.301525i 0.960869 0.277003i \(-0.0893413\pi\)
−0.815662 + 0.578529i \(0.803627\pi\)
\(648\) 198334. 411844.i 0.472331 0.980806i
\(649\) −98012.4 + 122904.i −0.232697 + 0.291793i
\(650\) 651491. + 148699.i 1.54199 + 0.351949i
\(651\) −19199.6 −0.0453034
\(652\) 21363.0i 0.0502536i
\(653\) 713686. + 162894.i 1.67371 + 0.382014i 0.951013 0.309150i \(-0.100045\pi\)
0.722698 + 0.691164i \(0.242902\pi\)
\(654\) −642892. 806161.i −1.50308 1.88480i
\(655\) 5140.13 + 22520.4i 0.0119809 + 0.0524920i
\(656\) −203617. 255328.i −0.473158 0.593322i
\(657\) −86729.4 180096.i −0.200926 0.417227i
\(658\) 184897. 810087.i 0.427050 1.87103i
\(659\) 439530. 211667.i 1.01209 0.487396i 0.147064 0.989127i \(-0.453018\pi\)
0.865024 + 0.501731i \(0.167303\pi\)
\(660\) 687.182 861.699i 0.00157755 0.00197819i
\(661\) 23986.4 + 105091.i 0.0548988 + 0.240527i 0.994931 0.100558i \(-0.0320627\pi\)
−0.940032 + 0.341085i \(0.889206\pi\)
\(662\) −139960. 613203.i −0.319365 1.39923i
\(663\) −146667. + 304558.i −0.333662 + 0.692856i
\(664\) −239801. 191235.i −0.543894 0.433741i
\(665\) 5045.33 4023.51i 0.0114090 0.00909834i
\(666\) 435389. + 209672.i 0.981587 + 0.472707i
\(667\) 167253. 347304.i 0.375943 0.780653i
\(668\) −48245.3 60497.7i −0.108119 0.135577i
\(669\) 193386. 242498.i 0.432088 0.541821i
\(670\) −34843.1 16779.5i −0.0776188 0.0373793i
\(671\) −145670. + 33248.1i −0.323537 + 0.0738452i
\(672\) 156756. 35778.6i 0.347125 0.0792290i
\(673\) −332382. 265066.i −0.733850 0.585226i 0.183636 0.982994i \(-0.441213\pi\)
−0.917486 + 0.397769i \(0.869785\pi\)
\(674\) 15918.0 + 33054.1i 0.0350404 + 0.0727622i
\(675\) −126565. 28887.6i −0.277783 0.0634022i
\(676\) 61097.9 29423.2i 0.133701 0.0643868i
\(677\) −520941. + 415437.i −1.13661 + 0.906416i −0.996489 0.0837186i \(-0.973320\pi\)
−0.140120 + 0.990135i \(0.544749\pi\)
\(678\) −166089. + 37908.8i −0.361312 + 0.0824671i
\(679\) −182232. + 145325.i −0.395261 + 0.315210i
\(680\) 1894.98 8302.46i 0.00409815 0.0179552i
\(681\) 426075. 0.918738
\(682\) 4580.11i 0.00984708i
\(683\) 150038. 657359.i 0.321632 1.40916i −0.513016 0.858379i \(-0.671472\pi\)
0.834648 0.550783i \(-0.185671\pi\)
\(684\) −8613.62 6869.13i −0.0184108 0.0146821i
\(685\) 22742.8 + 10952.4i 0.0484689 + 0.0233414i
\(686\) 370060. 178211.i 0.786364 0.378693i
\(687\) 1.10732e6i 2.34616i
\(688\) −290532. 434819.i −0.613787 0.918611i
\(689\) 477297. 1.00543
\(690\) 12271.0 + 25480.9i 0.0257739 + 0.0535201i
\(691\) −240642. + 499698.i −0.503982 + 1.04653i 0.481452 + 0.876473i \(0.340110\pi\)
−0.985434 + 0.170058i \(0.945605\pi\)
\(692\) −47249.5 + 59248.9i −0.0986699 + 0.123728i
\(693\) −128086. 29234.8i −0.266708 0.0608743i
\(694\) −133985. −0.278188
\(695\) 42707.5i 0.0884167i
\(696\) 624583. + 142557.i 1.28935 + 0.294286i
\(697\) −79853.5 100133.i −0.164372 0.206116i
\(698\) −9880.50 43289.3i −0.0202800 0.0888525i
\(699\) 5723.14 + 7176.59i 0.0117133 + 0.0146880i
\(700\) −28389.2 58950.9i −0.0579372 0.120308i
\(701\) 63660.5 278915.i 0.129549 0.567591i −0.867934 0.496680i \(-0.834552\pi\)
0.997483 0.0709109i \(-0.0225906\pi\)
\(702\) −201156. + 96871.5i −0.408186 + 0.196572i
\(703\) 101635. 127446.i 0.205652 0.257879i
\(704\) 29128.7 + 127621.i 0.0587727 + 0.257500i
\(705\) 12267.2 + 53746.1i 0.0246813 + 0.108136i
\(706\) −315672. + 655499.i −0.633324 + 1.31511i
\(707\) −118946. 94856.1i −0.237963 0.189769i
\(708\) −75221.9 + 59987.5i −0.150064 + 0.119672i
\(709\) −275023. 132444.i −0.547112 0.263475i 0.139845 0.990173i \(-0.455340\pi\)
−0.686957 + 0.726698i \(0.741054\pi\)
\(710\) −14069.4 + 29215.3i −0.0279098 + 0.0579554i
\(711\) 128580. + 161235.i 0.254352 + 0.318947i
\(712\) 367989. 461443.i 0.725896 0.910245i
\(713\) −11256.3 5420.73i −0.0221419 0.0106630i
\(714\) 303551. 69283.5i 0.595436 0.135904i
\(715\) 11892.4 2714.37i 0.0232626 0.00530954i
\(716\) 74236.7 + 59201.8i 0.144808 + 0.115481i
\(717\) 229557. + 476680.i 0.446532 + 0.927233i
\(718\) 1.01054e6 + 230650.i 1.96023 + 0.447409i
\(719\) 164280. 79113.2i 0.317781 0.153035i −0.268193 0.963365i \(-0.586426\pi\)
0.585974 + 0.810330i \(0.300712\pi\)
\(720\) −18126.9 + 14455.7i −0.0349671 + 0.0278853i
\(721\) 431807. 98557.0i 0.830651 0.189591i
\(722\) 403781. 322005.i 0.774590 0.617715i
\(723\) −288065. + 1.26209e6i −0.551079 + 2.41443i
\(724\) 41533.8 0.0792364
\(725\) 556602.i 1.05893i
\(726\) 149969. 657058.i 0.284531 1.24661i
\(727\) 261073. + 208198.i 0.493961 + 0.393921i 0.838543 0.544836i \(-0.183408\pi\)
−0.344582 + 0.938756i \(0.611979\pi\)
\(728\) 750962. + 361644.i 1.41695 + 0.682368i
\(729\) −256914. + 123723.i −0.483429 + 0.232807i
\(730\) 17094.6i 0.0320785i
\(731\) −113940. 170525.i −0.213226 0.319120i
\(732\) −91448.3 −0.170669
\(733\) 120619. + 250469.i 0.224496 + 0.466172i 0.982545 0.186027i \(-0.0595611\pi\)
−0.758048 + 0.652199i \(0.773847\pi\)
\(734\) 733.688 1523.52i 0.00136182 0.00282785i
\(735\) 6187.66 7759.08i 0.0114539 0.0143627i
\(736\) 102004. + 23281.7i 0.188304 + 0.0429793i
\(737\) 265587. 0.488958
\(738\) 311150.i 0.571290i
\(739\) −56238.6 12836.1i −0.102978 0.0235041i 0.170721 0.985319i \(-0.445390\pi\)
−0.273700 + 0.961815i \(0.588247\pi\)
\(740\) 2739.11 + 3434.73i 0.00500202 + 0.00627234i
\(741\) −61642.7 270074.i −0.112265 0.491866i
\(742\) −274105. 343717.i −0.497862 0.624299i
\(743\) 88689.8 + 184166.i 0.160656 + 0.333605i 0.965721 0.259581i \(-0.0835844\pi\)
−0.805066 + 0.593185i \(0.797870\pi\)
\(744\) 4620.33 20243.0i 0.00834693 0.0365703i
\(745\) −38582.9 + 18580.6i −0.0695157 + 0.0334770i
\(746\) −457717. + 573959.i −0.822468 + 1.03134i
\(747\) 72872.7 + 319276.i 0.130594 + 0.572170i
\(748\) −1756.95 7697.69i −0.00314019 0.0137581i
\(749\) −342065. + 710305.i −0.609740 + 1.26614i
\(750\) 63939.6 + 50990.1i 0.113670 + 0.0906491i
\(751\) −345411. + 275456.i −0.612431 + 0.488397i −0.879893 0.475171i \(-0.842386\pi\)
0.267463 + 0.963568i \(0.413815\pi\)
\(752\) 907298. + 436932.i 1.60441 + 0.772641i
\(753\) 354829. 736809.i 0.625790 1.29947i
\(754\) −596837. 748410.i −1.04982 1.31643i
\(755\) 34862.5 43716.1i 0.0611595 0.0766916i
\(756\) 19695.9 + 9485.07i 0.0344614 + 0.0165957i
\(757\) 405337. 92515.6i 0.707335 0.161444i 0.146304 0.989240i \(-0.453262\pi\)
0.561030 + 0.827795i \(0.310405\pi\)
\(758\) −276692. + 63153.1i −0.481568 + 0.109915i
\(759\) −151851. 121097.i −0.263593 0.210209i
\(760\) 3028.02 + 6287.75i 0.00524241 + 0.0108860i
\(761\) −731145. 166879.i −1.26251 0.288159i −0.461677 0.887048i \(-0.652752\pi\)
−0.800832 + 0.598889i \(0.795609\pi\)
\(762\) 6040.59 2908.99i 0.0104033 0.00500994i
\(763\) −873618. + 696687.i −1.50063 + 1.19671i
\(764\) −51418.5 + 11735.9i −0.0880913 + 0.0201063i
\(765\) −7108.93 + 5669.18i −0.0121473 + 0.00968718i
\(766\) 126745. 555304.i 0.216009 0.946397i
\(767\) −1.06485e6 −1.81007
\(768\) 277478.i 0.470442i
\(769\) −77415.2 + 339178.i −0.130910 + 0.573555i 0.866341 + 0.499454i \(0.166466\pi\)
−0.997251 + 0.0741012i \(0.976391\pi\)
\(770\) −8784.35 7005.28i −0.0148159 0.0118153i
\(771\) −425219. 204775.i −0.715326 0.344483i
\(772\) 33380.7 16075.3i 0.0560094 0.0269727i
\(773\) 875235.i 1.46476i −0.680898 0.732378i \(-0.738410\pi\)
0.680898 0.732378i \(-0.261590\pi\)
\(774\) −41881.4 + 496484.i −0.0699100 + 0.828749i
\(775\) −18039.7 −0.0300349
\(776\) −109369. 227106.i −0.181622 0.377143i
\(777\) 516207. 1.07191e6i 0.855030 1.77549i
\(778\) −69699.3 + 87400.2i −0.115151 + 0.144395i
\(779\) 102326. + 23355.3i 0.168622 + 0.0384868i
\(780\) 7465.82 0.0122712
\(781\) 222690.i 0.365089i
\(782\) 197525. + 45083.9i 0.323005 + 0.0737238i
\(783\) 115947. + 145393.i 0.189120 + 0.237149i
\(784\) −40339.8 176740.i −0.0656298 0.287543i
\(785\) −21547.9 27020.2i −0.0349676 0.0438479i
\(786\) −396287. 822898.i −0.641452 1.33199i
\(787\) −148439. + 650353.i −0.239662 + 1.05003i 0.701659 + 0.712513i \(0.252443\pi\)
−0.941321 + 0.337513i \(0.890414\pi\)
\(788\) −110040. + 52992.4i −0.177214 + 0.0853417i
\(789\) 938755. 1.17716e6i 1.50799 1.89096i
\(790\) 3924.48 + 17194.3i 0.00628823 + 0.0275505i
\(791\) 41080.9 + 179987.i 0.0656578 + 0.287666i
\(792\) 61647.0 128011.i 0.0982793 0.204079i
\(793\) −791306. 631045.i −1.25834 1.00349i
\(794\) 367650. 293191.i 0.583167 0.465060i
\(795\) 26279.2 + 12655.4i 0.0415794 + 0.0200236i
\(796\) −8578.42 + 17813.3i −0.0135388 + 0.0281137i
\(797\) 71589.3 + 89770.1i 0.112702 + 0.141324i 0.834983 0.550276i \(-0.185478\pi\)
−0.722281 + 0.691600i \(0.756906\pi\)
\(798\) −159088. + 199491.i −0.249823 + 0.313269i
\(799\) 355820. + 171354.i 0.557361 + 0.268411i
\(800\) 147286. 33617.0i 0.230134 0.0525266i
\(801\) −614375. + 140227.i −0.957566 + 0.218558i
\(802\) −482151. 384503.i −0.749608 0.597793i
\(803\) 50936.9 + 105772.i 0.0789954 + 0.164036i
\(804\) 158474. + 36170.7i 0.245158 + 0.0559557i
\(805\) 27613.1 13297.7i 0.0426111 0.0205204i
\(806\) −24256.3 + 19343.7i −0.0373383 + 0.0297763i
\(807\) 439128. 100228.i 0.674286 0.153901i
\(808\) 128635. 102583.i 0.197031 0.157127i
\(809\) −74805.9 + 327746.i −0.114298 + 0.500773i 0.885078 + 0.465443i \(0.154105\pi\)
−0.999376 + 0.0353292i \(0.988752\pi\)
\(810\) −41739.4 −0.0636174
\(811\) 919015.i 1.39727i 0.715477 + 0.698636i \(0.246209\pi\)
−0.715477 + 0.698636i \(0.753791\pi\)
\(812\) −20856.5 + 91378.4i −0.0316322 + 0.138590i
\(813\) −46026.6 36705.0i −0.0696350 0.0555321i
\(814\) −255707. 123142.i −0.385918 0.185848i
\(815\) −13017.9 + 6269.09i −0.0195986 + 0.00943821i
\(816\) 377346.i 0.566708i
\(817\) 160133. + 51040.1i 0.239903 + 0.0764659i
\(818\) 533974. 0.798020
\(819\) −386134. 801816.i −0.575666 1.19538i
\(820\) −1227.31 + 2548.54i −0.00182527 + 0.00379022i
\(821\) −232366. + 291378.i −0.344735 + 0.432285i −0.923728 0.383048i \(-0.874874\pi\)
0.578993 + 0.815332i \(0.303446\pi\)
\(822\) −973061. 222095.i −1.44011 0.328696i
\(823\) −664874. −0.981612 −0.490806 0.871269i \(-0.663298\pi\)
−0.490806 + 0.871269i \(0.663298\pi\)
\(824\) 478989.i 0.705458i
\(825\) −273415. 62405.1i −0.401711 0.0916880i
\(826\) 611525. + 766828.i 0.896302 + 1.12393i
\(827\) 6943.95 + 30423.5i 0.0101530 + 0.0444834i 0.979751 0.200221i \(-0.0641661\pi\)
−0.969598 + 0.244705i \(0.921309\pi\)
\(828\) −32623.5 40908.5i −0.0475849 0.0596696i
\(829\) 344668. + 715710.i 0.501524 + 1.04142i 0.986019 + 0.166631i \(0.0532889\pi\)
−0.484496 + 0.874794i \(0.660997\pi\)
\(830\) −6232.06 + 27304.4i −0.00904639 + 0.0396348i
\(831\) 455502. 219358.i 0.659611 0.317652i
\(832\) −552859. + 693263.i −0.798670 + 1.00150i
\(833\) −15820.2 69313.0i −0.0227994 0.0998907i
\(834\) 375758. + 1.64630e6i 0.540226 + 2.36689i
\(835\) 22707.5 47152.5i 0.0325683 0.0676288i
\(836\) 5058.85 + 4034.30i 0.00723834 + 0.00577239i
\(837\) 4712.26 3757.90i 0.00672633 0.00536407i
\(838\) 303152. + 145990.i 0.431690 + 0.207891i
\(839\) −57595.7 + 119599.i −0.0818212 + 0.169904i −0.937866 0.346999i \(-0.887201\pi\)
0.856044 + 0.516902i \(0.172915\pi\)
\(840\) 31757.9 + 39823.1i 0.0450083 + 0.0564386i
\(841\) −56141.5 + 70399.3i −0.0793766 + 0.0995351i
\(842\) −997810. 480520.i −1.40742 0.677778i
\(843\) 455098. 103873.i 0.640398 0.146167i
\(844\) 150165. 34274.1i 0.210806 0.0481151i
\(845\) 35859.1 + 28596.7i 0.0502210 + 0.0400499i
\(846\) −416292. 864439.i −0.581644 1.20780i
\(847\) −712039. 162518.i −0.992514 0.226535i
\(848\) 480040. 231175.i 0.667554 0.321477i
\(849\) −136839. + 109126.i −0.189843 + 0.151395i
\(850\) 285212. 65097.8i 0.394757 0.0901007i
\(851\) 605278. 482693.i 0.835787 0.666518i
\(852\) 30328.5 132878.i 0.0417803 0.183051i
\(853\) 317662. 0.436583 0.218292 0.975884i \(-0.429952\pi\)
0.218292 + 0.975884i \(0.429952\pi\)
\(854\) 932244.i 1.27824i
\(855\) 1658.11 7264.64i 0.00226819 0.00993761i
\(856\) −666587. 531586.i −0.909724 0.725480i
\(857\) 114687. + 55230.4i 0.156154 + 0.0751998i 0.510328 0.859980i \(-0.329524\pi\)
−0.354175 + 0.935179i \(0.615238\pi\)
\(858\) −434551. + 209269.i −0.590291 + 0.284269i
\(859\) 105532.i 0.143020i −0.997440 0.0715102i \(-0.977218\pi\)
0.997440 0.0715102i \(-0.0227819\pi\)
\(860\) −2301.39 + 3901.36i −0.00311167 + 0.00527496i
\(861\) 766041. 1.03335
\(862\) −95005.6 197281.i −0.127860 0.265504i
\(863\) −35203.4 + 73100.7i −0.0472676 + 0.0981522i −0.923265 0.384163i \(-0.874490\pi\)
0.875997 + 0.482316i \(0.160204\pi\)
\(864\) −31470.6 + 39462.8i −0.0421577 + 0.0528641i
\(865\) −49970.0 11405.3i −0.0667847 0.0152432i
\(866\) −505407. −0.673915
\(867\) 856650.i 1.13963i
\(868\) 2961.61 + 675.968i 0.00393087 + 0.000897195i
\(869\) −75516.3 94694.4i −0.100000 0.125396i
\(870\) −13017.0 57031.2i −0.0171978 0.0753485i
\(871\) 1.12168e6 + 1.40655e6i 1.47854 + 1.85404i
\(872\) −524313. 1.08875e6i −0.689537 1.43184i
\(873\) −59888.9 + 262391.i −0.0785811 + 0.344286i
\(874\) −149593. + 72040.1i −0.195834 + 0.0943087i
\(875\) 55256.8 69289.8i 0.0721721 0.0905010i
\(876\) 15988.6 + 70050.5i 0.0208354 + 0.0912857i
\(877\) 159704. + 699710.i 0.207643 + 0.909744i 0.966130 + 0.258056i \(0.0830818\pi\)
−0.758487 + 0.651688i \(0.774061\pi\)
\(878\) 13773.4 28600.7i 0.0178670 0.0371012i
\(879\) 82574.0 + 65850.5i 0.106872 + 0.0852279i
\(880\) 10646.1 8489.98i 0.0137475 0.0109633i
\(881\) −441703. 212713.i −0.569087 0.274058i 0.127134 0.991886i \(-0.459422\pi\)
−0.696221 + 0.717828i \(0.745136\pi\)
\(882\) −74941.2 + 155617.i −0.0963348 + 0.200041i
\(883\) −423929. 531591.i −0.543716 0.681798i 0.431739 0.901999i \(-0.357900\pi\)
−0.975455 + 0.220200i \(0.929329\pi\)
\(884\) 33346.7 41815.4i 0.0426725 0.0535096i
\(885\) −58628.7 28234.1i −0.0748555 0.0360485i
\(886\) −541250. + 123537.i −0.689494 + 0.157372i
\(887\) 580796. 132563.i 0.738204 0.168490i 0.163145 0.986602i \(-0.447836\pi\)
0.575059 + 0.818112i \(0.304979\pi\)
\(888\) 1.00594e6 + 802211.i 1.27569 + 1.01733i
\(889\) −3152.41 6546.04i −0.00398877 0.00828277i
\(890\) −52541.3 11992.2i −0.0663316 0.0151398i
\(891\) 258259. 124371.i 0.325312 0.156662i
\(892\) −38368.1 + 30597.6i −0.0482215 + 0.0384554i
\(893\) −315532. + 72018.1i −0.395676 + 0.0903106i
\(894\) 1.32383e6 1.05572e6i 1.65637 1.32091i
\(895\) −14290.4 + 62610.5i −0.0178402 + 0.0781630i
\(896\) 1.03061e6 1.28375
\(897\) 1.31565e6i 1.63514i
\(898\) −142746. + 625412.i −0.177016 + 0.775557i
\(899\) 20203.8 + 16112.0i 0.0249985 + 0.0199356i
\(900\) −68070.0 32780.8i −0.0840370 0.0404701i
\(901\) 188260. 90661.2i 0.231904 0.111679i
\(902\) 182741.i 0.224607i
\(903\) 1.22233e6 + 103111.i 1.49904 + 0.126453i
\(904\) −199654. −0.244310
\(905\) 12188.3 + 25309.3i 0.0148815 + 0.0309018i
\(906\) −959257. + 1.99192e6i −1.16863 + 2.42669i
\(907\) 626215. 785249.i 0.761218 0.954537i −0.238645 0.971107i \(-0.576703\pi\)
0.999863 + 0.0165702i \(0.00527469\pi\)
\(908\) −65723.5 15001.0i −0.0797167 0.0181948i
\(909\) −175671. −0.212605
\(910\) 76108.2i 0.0919070i
\(911\) −799382. 182454.i −0.963202 0.219845i −0.288126 0.957592i \(-0.593032\pi\)
−0.675076 + 0.737748i \(0.735889\pi\)
\(912\) −192806. 241771.i −0.231809 0.290679i
\(913\) −42798.7 187513.i −0.0513440 0.224953i
\(914\) 375972. + 471454.i 0.450052 + 0.564348i
\(915\) −26836.0 55725.6i −0.0320535 0.0665599i
\(916\) 38985.6 170807.i 0.0464637 0.203571i
\(917\) −891755. + 429447.i −1.06049 + 0.510705i
\(918\) −60941.2 + 76417.9i −0.0723146 + 0.0906796i
\(919\) −51085.9 223822.i −0.0604881 0.265015i 0.935637 0.352964i \(-0.114826\pi\)
−0.996125 + 0.0879483i \(0.971969\pi\)
\(920\) 7375.38 + 32313.7i 0.00871383 + 0.0381778i
\(921\) 233157. 484155.i 0.274871 0.570775i
\(922\) 970891. + 774260.i 1.14211 + 0.910804i
\(923\) 1.17937e6 940513.i 1.38435 1.10398i
\(924\) 42548.6 + 20490.3i 0.0498358 + 0.0239996i
\(925\) 485020. 1.00716e6i 0.566861 1.17710i
\(926\) −268043. 336115.i −0.312595 0.391982i
\(927\) 318868. 399848.i 0.371067 0.465303i
\(928\) −194979. 93897.1i −0.226409 0.109033i
\(929\) −655577. + 149631.i −0.759613 + 0.173377i −0.584747 0.811216i \(-0.698806\pi\)
−0.174866 + 0.984592i \(0.555949\pi\)
\(930\) −1848.41 + 421.887i −0.00213713 + 0.000487787i
\(931\) 45551.9 + 36326.4i 0.0525541 + 0.0419105i
\(932\) −630.145 1308.51i −0.000725452 0.00150642i
\(933\) −604877. 138059.i −0.694871 0.158600i
\(934\) 364663. 175612.i 0.418020 0.201308i
\(935\) 4175.13 3329.56i 0.00477581 0.00380858i
\(936\) 938310. 214163.i 1.07101 0.244452i
\(937\) −302367. + 241129.i −0.344393 + 0.274645i −0.780376 0.625311i \(-0.784972\pi\)
0.435983 + 0.899955i \(0.356401\pi\)
\(938\) 368732. 1.61552e6i 0.419088 1.83614i
\(939\) 1.41130e6 1.60062
\(940\) 8722.42i 0.00987146i
\(941\) −204267. + 894954.i −0.230685 + 1.01070i 0.718388 + 0.695642i \(0.244880\pi\)
−0.949073 + 0.315055i \(0.897977\pi\)
\(942\) 1.06837e6 + 851997.i 1.20398 + 0.960144i
\(943\) 449111. + 216280.i 0.505045 + 0.243217i
\(944\) −1.07097e6 + 515750.i −1.20180 + 0.578755i
\(945\) 14785.5i 0.0165567i
\(946\) 24597.3 291589.i 0.0274856 0.325828i
\(947\) −896567. −0.999731 −0.499865 0.866103i \(-0.666617\pi\)
−0.499865 + 0.866103i \(0.666617\pi\)
\(948\) −32163.5 66788.3i −0.0357888 0.0743162i
\(949\) −345039. + 716480.i −0.383120 + 0.795557i
\(950\) −149477. + 187439.i −0.165626 + 0.207688i
\(951\) 565869. + 129156.i 0.625684 + 0.142808i
\(952\) 364895. 0.402618
\(953\) 490682.i 0.540275i −0.962822 0.270137i \(-0.912931\pi\)
0.962822 0.270137i \(-0.0870691\pi\)
\(954\) −494909. 112960.i −0.543787 0.124116i
\(955\) −22240.6 27888.8i −0.0243859 0.0305790i
\(956\) −18627.3 81611.7i −0.0203814 0.0892969i
\(957\) 250478. + 314089.i 0.273493 + 0.342949i
\(958\) 616627. + 1.28044e6i 0.671879 + 1.39517i
\(959\) −240679. + 1.05448e6i −0.261698 + 1.14658i
\(960\) −48821.2 + 23511.0i −0.0529744 + 0.0255111i
\(961\) −575284. + 721383.i −0.622924 + 0.781122i
\(962\) −427799. 1.87431e6i −0.462263 2.02531i
\(963\) 202568. + 887509.i 0.218433 + 0.957018i
\(964\) 88870.0 184540.i 0.0956316 0.198581i
\(965\) 19591.5 + 15623.7i 0.0210384 + 0.0167776i
\(966\) −947438. + 755557.i −1.01531 + 0.809679i
\(967\) −206840. 99608.8i −0.221198 0.106523i 0.320003 0.947416i \(-0.396316\pi\)
−0.541201 + 0.840893i \(0.682030\pi\)
\(968\) 342700. 711623.i 0.365732 0.759450i
\(969\) −75613.5 94816.4i −0.0805289 0.100980i
\(970\) −14350.7 + 17995.2i −0.0152520 + 0.0191255i
\(971\) −287305. 138359.i −0.304722 0.146747i 0.275274 0.961366i \(-0.411232\pi\)
−0.579996 + 0.814619i \(0.696946\pi\)
\(972\) 139740. 31894.7i 0.147907 0.0337587i
\(973\) 1.78406e6 407200.i 1.88445 0.430112i
\(974\) −475266. 379012.i −0.500978 0.399517i
\(975\) −824248. 1.71157e6i −0.867059 1.80047i
\(976\) −1.10150e6 251409.i −1.15633 0.263926i
\(977\) 287267. 138340.i 0.300952 0.144931i −0.277314 0.960779i \(-0.589444\pi\)
0.578265 + 0.815849i \(0.303730\pi\)
\(978\) 446661. 356200.i 0.466982 0.372406i
\(979\) 360828. 82356.6i 0.376474 0.0859277i
\(980\) −1227.64 + 979.014i −0.00127826 + 0.00101938i
\(981\) −287108. + 1.25790e6i −0.298337 + 1.30710i
\(982\) 868644. 0.900781
\(983\) 1.43895e6i 1.48915i −0.667537 0.744577i \(-0.732651\pi\)
0.667537 0.744577i \(-0.267349\pi\)
\(984\) −184345. + 807670.i −0.190389 + 0.834149i
\(985\) −64583.7 51503.8i −0.0665657 0.0530844i
\(986\) −377568. 181827.i −0.388366 0.187027i
\(987\) −2.12822e6 + 1.02490e6i −2.18466 + 1.05207i
\(988\) 43830.2i 0.0449014i
\(989\) 687509. + 405558.i 0.702887 + 0.414629i
\(990\) −12973.6 −0.0132371
\(991\) −297628. 618030.i −0.303058 0.629307i 0.692709 0.721217i \(-0.256417\pi\)
−0.995767 + 0.0919102i \(0.970703\pi\)
\(992\) −3043.25 + 6319.36i −0.00309253 + 0.00642170i
\(993\) −1.11483e6 + 1.39796e6i −1.13061 + 1.41773i
\(994\) −1.35458e6 309175.i −1.37099 0.312919i
\(995\) −13372.2 −0.0135069
\(996\) 117717.i 0.118664i
\(997\) −543846. 124129.i −0.547123 0.124877i −0.0599804 0.998200i \(-0.519104\pi\)
−0.487143 + 0.873322i \(0.661961\pi\)
\(998\) −167770. 210377.i −0.168443 0.211221i
\(999\) 83108.3 + 364121.i 0.0832747 + 0.364850i
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 43.5.f.a.2.10 78
43.22 odd 14 inner 43.5.f.a.22.10 yes 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.5.f.a.2.10 78 1.1 even 1 trivial
43.5.f.a.22.10 yes 78 43.22 odd 14 inner