Properties

Label 175.5.g.c.57.7
Level $175$
Weight $5$
Character 175.57
Analytic conductor $18.090$
Analytic rank $0$
Dimension $24$
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] = [175,5,Mod(43,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.43");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.0897435397\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 57.7
Character \(\chi\) \(=\) 175.57
Dual form 175.5.g.c.43.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0151985 + 0.0151985i) q^{2} +(-8.40408 + 8.40408i) q^{3} -15.9995i q^{4} -0.255459 q^{6} +(13.0958 + 13.0958i) q^{7} +(0.486345 - 0.486345i) q^{8} -60.2572i q^{9} +O(q^{10})\) \(q+(0.0151985 + 0.0151985i) q^{2} +(-8.40408 + 8.40408i) q^{3} -15.9995i q^{4} -0.255459 q^{6} +(13.0958 + 13.0958i) q^{7} +(0.486345 - 0.486345i) q^{8} -60.2572i q^{9} +178.541 q^{11} +(134.461 + 134.461i) q^{12} +(-130.151 + 130.151i) q^{13} +0.398073i q^{14} -255.978 q^{16} +(-219.300 - 219.300i) q^{17} +(0.915819 - 0.915819i) q^{18} +255.173i q^{19} -220.116 q^{21} +(2.71356 + 2.71356i) q^{22} +(54.1585 - 54.1585i) q^{23} +8.17456i q^{24} -3.95620 q^{26} +(-174.324 - 174.324i) q^{27} +(209.527 - 209.527i) q^{28} -438.959i q^{29} -1449.39 q^{31} +(-11.6720 - 11.6720i) q^{32} +(-1500.48 + 1500.48i) q^{33} -6.66605i q^{34} -964.087 q^{36} +(-914.326 - 914.326i) q^{37} +(-3.87825 + 3.87825i) q^{38} -2187.60i q^{39} -1734.82 q^{41} +(-3.34544 - 3.34544i) q^{42} +(103.893 - 103.893i) q^{43} -2856.58i q^{44} +1.64625 q^{46} +(-1422.27 - 1422.27i) q^{47} +(2151.26 - 2151.26i) q^{48} +343.000i q^{49} +3686.03 q^{51} +(2082.36 + 2082.36i) q^{52} +(-3305.54 + 3305.54i) q^{53} -5.29893i q^{54} +12.7381 q^{56} +(-2144.50 - 2144.50i) q^{57} +(6.67152 - 6.67152i) q^{58} +4661.12i q^{59} -3974.31 q^{61} +(-22.0285 - 22.0285i) q^{62} +(789.116 - 789.116i) q^{63} +4095.29i q^{64} -45.6100 q^{66} +(3729.40 + 3729.40i) q^{67} +(-3508.69 + 3508.69i) q^{68} +910.305i q^{69} -1249.55 q^{71} +(-29.3058 - 29.3058i) q^{72} +(3437.16 - 3437.16i) q^{73} -27.7928i q^{74} +4082.66 q^{76} +(2338.14 + 2338.14i) q^{77} +(33.2482 - 33.2482i) q^{78} -11135.9i q^{79} +7810.90 q^{81} +(-26.3666 - 26.3666i) q^{82} +(-3632.77 + 3632.77i) q^{83} +3521.76i q^{84} +3.15802 q^{86} +(3689.05 + 3689.05i) q^{87} +(86.8327 - 86.8327i) q^{88} +8157.71i q^{89} -3408.86 q^{91} +(-866.511 - 866.511i) q^{92} +(12180.8 - 12180.8i) q^{93} -43.2326i q^{94} +196.185 q^{96} +(-4381.16 - 4381.16i) q^{97} +(-5.21308 + 5.21308i) q^{98} -10758.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0151985 + 0.0151985i 0.00379962 + 0.00379962i 0.709004 0.705204i \(-0.249145\pi\)
−0.705204 + 0.709004i \(0.749145\pi\)
\(3\) −8.40408 + 8.40408i −0.933787 + 0.933787i −0.997940 0.0641531i \(-0.979565\pi\)
0.0641531 + 0.997940i \(0.479565\pi\)
\(4\) 15.9995i 0.999971i
\(5\) 0 0
\(6\) −0.255459 −0.00709608
\(7\) 13.0958 + 13.0958i 0.267261 + 0.267261i
\(8\) 0.486345 0.486345i 0.00759914 0.00759914i
\(9\) 60.2572i 0.743916i
\(10\) 0 0
\(11\) 178.541 1.47555 0.737774 0.675048i \(-0.235877\pi\)
0.737774 + 0.675048i \(0.235877\pi\)
\(12\) 134.461 + 134.461i 0.933760 + 0.933760i
\(13\) −130.151 + 130.151i −0.770125 + 0.770125i −0.978128 0.208004i \(-0.933303\pi\)
0.208004 + 0.978128i \(0.433303\pi\)
\(14\) 0.398073i 0.00203098i
\(15\) 0 0
\(16\) −255.978 −0.999913
\(17\) −219.300 219.300i −0.758823 0.758823i 0.217285 0.976108i \(-0.430280\pi\)
−0.976108 + 0.217285i \(0.930280\pi\)
\(18\) 0.915819 0.915819i 0.00282660 0.00282660i
\(19\) 255.173i 0.706851i 0.935463 + 0.353426i \(0.114983\pi\)
−0.935463 + 0.353426i \(0.885017\pi\)
\(20\) 0 0
\(21\) −220.116 −0.499130
\(22\) 2.71356 + 2.71356i 0.00560653 + 0.00560653i
\(23\) 54.1585 54.1585i 0.102379 0.102379i −0.654062 0.756441i \(-0.726936\pi\)
0.756441 + 0.654062i \(0.226936\pi\)
\(24\) 8.17456i 0.0141920i
\(25\) 0 0
\(26\) −3.95620 −0.00585237
\(27\) −174.324 174.324i −0.239128 0.239128i
\(28\) 209.527 209.527i 0.267254 0.267254i
\(29\) 438.959i 0.521949i −0.965346 0.260975i \(-0.915956\pi\)
0.965346 0.260975i \(-0.0840439\pi\)
\(30\) 0 0
\(31\) −1449.39 −1.50821 −0.754103 0.656757i \(-0.771928\pi\)
−0.754103 + 0.656757i \(0.771928\pi\)
\(32\) −11.6720 11.6720i −0.0113984 0.0113984i
\(33\) −1500.48 + 1500.48i −1.37785 + 1.37785i
\(34\) 6.66605i 0.00576648i
\(35\) 0 0
\(36\) −964.087 −0.743895
\(37\) −914.326 914.326i −0.667879 0.667879i 0.289346 0.957225i \(-0.406562\pi\)
−0.957225 + 0.289346i \(0.906562\pi\)
\(38\) −3.87825 + 3.87825i −0.00268577 + 0.00268577i
\(39\) 2187.60i 1.43826i
\(40\) 0 0
\(41\) −1734.82 −1.03202 −0.516008 0.856584i \(-0.672582\pi\)
−0.516008 + 0.856584i \(0.672582\pi\)
\(42\) −3.34544 3.34544i −0.00189651 0.00189651i
\(43\) 103.893 103.893i 0.0561885 0.0561885i −0.678454 0.734643i \(-0.737350\pi\)
0.734643 + 0.678454i \(0.237350\pi\)
\(44\) 2856.58i 1.47551i
\(45\) 0 0
\(46\) 1.64625 0.000778003
\(47\) −1422.27 1422.27i −0.643851 0.643851i 0.307649 0.951500i \(-0.400458\pi\)
−0.951500 + 0.307649i \(0.900458\pi\)
\(48\) 2151.26 2151.26i 0.933706 0.933706i
\(49\) 343.000i 0.142857i
\(50\) 0 0
\(51\) 3686.03 1.41716
\(52\) 2082.36 + 2082.36i 0.770102 + 0.770102i
\(53\) −3305.54 + 3305.54i −1.17677 + 1.17677i −0.196204 + 0.980563i \(0.562861\pi\)
−0.980563 + 0.196204i \(0.937139\pi\)
\(54\) 5.29893i 0.00181719i
\(55\) 0 0
\(56\) 12.7381 0.00406191
\(57\) −2144.50 2144.50i −0.660049 0.660049i
\(58\) 6.67152 6.67152i 0.00198321 0.00198321i
\(59\) 4661.12i 1.33902i 0.742804 + 0.669509i \(0.233495\pi\)
−0.742804 + 0.669509i \(0.766505\pi\)
\(60\) 0 0
\(61\) −3974.31 −1.06808 −0.534038 0.845460i \(-0.679326\pi\)
−0.534038 + 0.845460i \(0.679326\pi\)
\(62\) −22.0285 22.0285i −0.00573061 0.00573061i
\(63\) 789.116 789.116i 0.198820 0.198820i
\(64\) 4095.29i 0.999827i
\(65\) 0 0
\(66\) −45.6100 −0.0104706
\(67\) 3729.40 + 3729.40i 0.830786 + 0.830786i 0.987624 0.156838i \(-0.0501302\pi\)
−0.156838 + 0.987624i \(0.550130\pi\)
\(68\) −3508.69 + 3508.69i −0.758801 + 0.758801i
\(69\) 910.305i 0.191200i
\(70\) 0 0
\(71\) −1249.55 −0.247877 −0.123938 0.992290i \(-0.539553\pi\)
−0.123938 + 0.992290i \(0.539553\pi\)
\(72\) −29.3058 29.3058i −0.00565312 0.00565312i
\(73\) 3437.16 3437.16i 0.644992 0.644992i −0.306786 0.951779i \(-0.599254\pi\)
0.951779 + 0.306786i \(0.0992536\pi\)
\(74\) 27.7928i 0.00507538i
\(75\) 0 0
\(76\) 4082.66 0.706831
\(77\) 2338.14 + 2338.14i 0.394357 + 0.394357i
\(78\) 33.2482 33.2482i 0.00546486 0.00546486i
\(79\) 11135.9i 1.78431i −0.451731 0.892154i \(-0.649193\pi\)
0.451731 0.892154i \(-0.350807\pi\)
\(80\) 0 0
\(81\) 7810.90 1.19050
\(82\) −26.3666 26.3666i −0.00392127 0.00392127i
\(83\) −3632.77 + 3632.77i −0.527329 + 0.527329i −0.919775 0.392446i \(-0.871629\pi\)
0.392446 + 0.919775i \(0.371629\pi\)
\(84\) 3521.76i 0.499116i
\(85\) 0 0
\(86\) 3.15802 0.000426990
\(87\) 3689.05 + 3689.05i 0.487389 + 0.487389i
\(88\) 86.8327 86.8327i 0.0112129 0.0112129i
\(89\) 8157.71i 1.02988i 0.857225 + 0.514942i \(0.172186\pi\)
−0.857225 + 0.514942i \(0.827814\pi\)
\(90\) 0 0
\(91\) −3408.86 −0.411649
\(92\) −866.511 866.511i −0.102376 0.102376i
\(93\) 12180.8 12180.8i 1.40834 1.40834i
\(94\) 43.2326i 0.00489278i
\(95\) 0 0
\(96\) 196.185 0.0212874
\(97\) −4381.16 4381.16i −0.465635 0.465635i 0.434862 0.900497i \(-0.356797\pi\)
−0.900497 + 0.434862i \(0.856797\pi\)
\(98\) −5.21308 + 5.21308i −0.000542803 + 0.000542803i
\(99\) 10758.4i 1.09768i
\(100\) 0 0
\(101\) 410.097 0.0402016 0.0201008 0.999798i \(-0.493601\pi\)
0.0201008 + 0.999798i \(0.493601\pi\)
\(102\) 56.0221 + 56.0221i 0.00538466 + 0.00538466i
\(103\) 3073.57 3073.57i 0.289713 0.289713i −0.547254 0.836967i \(-0.684327\pi\)
0.836967 + 0.547254i \(0.184327\pi\)
\(104\) 126.597i 0.0117046i
\(105\) 0 0
\(106\) −100.478 −0.00894254
\(107\) −11506.0 11506.0i −1.00498 1.00498i −0.999988 0.00499151i \(-0.998411\pi\)
−0.00499151 0.999988i \(-0.501589\pi\)
\(108\) −2789.11 + 2789.11i −0.239121 + 0.239121i
\(109\) 13007.3i 1.09480i 0.836871 + 0.547400i \(0.184382\pi\)
−0.836871 + 0.547400i \(0.815618\pi\)
\(110\) 0 0
\(111\) 15368.1 1.24731
\(112\) −3352.23 3352.23i −0.267238 0.267238i
\(113\) 6514.25 6514.25i 0.510162 0.510162i −0.404414 0.914576i \(-0.632525\pi\)
0.914576 + 0.404414i \(0.132525\pi\)
\(114\) 65.1863i 0.00501587i
\(115\) 0 0
\(116\) −7023.15 −0.521934
\(117\) 7842.54 + 7842.54i 0.572908 + 0.572908i
\(118\) −70.8420 + 70.8420i −0.00508777 + 0.00508777i
\(119\) 5743.81i 0.405608i
\(120\) 0 0
\(121\) 17236.0 1.17724
\(122\) −60.4036 60.4036i −0.00405829 0.00405829i
\(123\) 14579.6 14579.6i 0.963683 0.963683i
\(124\) 23189.5i 1.50816i
\(125\) 0 0
\(126\) 23.9868 0.00151088
\(127\) −5300.60 5300.60i −0.328638 0.328638i 0.523430 0.852068i \(-0.324652\pi\)
−0.852068 + 0.523430i \(0.824652\pi\)
\(128\) −248.994 + 248.994i −0.0151974 + 0.0151974i
\(129\) 1746.24i 0.104936i
\(130\) 0 0
\(131\) −3216.78 −0.187447 −0.0937234 0.995598i \(-0.529877\pi\)
−0.0937234 + 0.995598i \(0.529877\pi\)
\(132\) 24006.9 + 24006.9i 1.37781 + 1.37781i
\(133\) −3341.70 + 3341.70i −0.188914 + 0.188914i
\(134\) 113.362i 0.00631335i
\(135\) 0 0
\(136\) −213.311 −0.0115328
\(137\) 9320.99 + 9320.99i 0.496616 + 0.496616i 0.910383 0.413767i \(-0.135787\pi\)
−0.413767 + 0.910383i \(0.635787\pi\)
\(138\) −13.8353 + 13.8353i −0.000726489 + 0.000726489i
\(139\) 10358.2i 0.536111i −0.963404 0.268055i \(-0.913619\pi\)
0.963404 0.268055i \(-0.0863810\pi\)
\(140\) 0 0
\(141\) 23905.7 1.20244
\(142\) −18.9912 18.9912i −0.000941838 0.000941838i
\(143\) −23237.3 + 23237.3i −1.13636 + 1.13636i
\(144\) 15424.5i 0.743852i
\(145\) 0 0
\(146\) 104.479 0.00490146
\(147\) −2882.60 2882.60i −0.133398 0.133398i
\(148\) −14628.8 + 14628.8i −0.667860 + 0.667860i
\(149\) 3719.04i 0.167517i −0.996486 0.0837584i \(-0.973308\pi\)
0.996486 0.0837584i \(-0.0266924\pi\)
\(150\) 0 0
\(151\) −22024.4 −0.965940 −0.482970 0.875637i \(-0.660442\pi\)
−0.482970 + 0.875637i \(0.660442\pi\)
\(152\) 124.102 + 124.102i 0.00537146 + 0.00537146i
\(153\) −13214.4 + 13214.4i −0.564500 + 0.564500i
\(154\) 71.0725i 0.00299682i
\(155\) 0 0
\(156\) −35000.6 −1.43822
\(157\) 11748.5 + 11748.5i 0.476634 + 0.476634i 0.904053 0.427420i \(-0.140577\pi\)
−0.427420 + 0.904053i \(0.640577\pi\)
\(158\) 169.248 169.248i 0.00677970 0.00677970i
\(159\) 55560.0i 2.19770i
\(160\) 0 0
\(161\) 1418.50 0.0547239
\(162\) 118.714 + 118.714i 0.00452347 + 0.00452347i
\(163\) −5346.78 + 5346.78i −0.201241 + 0.201241i −0.800532 0.599290i \(-0.795450\pi\)
0.599290 + 0.800532i \(0.295450\pi\)
\(164\) 27756.3i 1.03199i
\(165\) 0 0
\(166\) −110.425 −0.00400731
\(167\) 6998.41 + 6998.41i 0.250938 + 0.250938i 0.821355 0.570417i \(-0.193218\pi\)
−0.570417 + 0.821355i \(0.693218\pi\)
\(168\) −107.052 + 107.052i −0.00379296 + 0.00379296i
\(169\) 5317.59i 0.186184i
\(170\) 0 0
\(171\) 15376.0 0.525838
\(172\) −1662.23 1662.23i −0.0561869 0.0561869i
\(173\) 32836.2 32836.2i 1.09714 1.09714i 0.102392 0.994744i \(-0.467350\pi\)
0.994744 0.102392i \(-0.0326496\pi\)
\(174\) 112.136i 0.00370379i
\(175\) 0 0
\(176\) −45702.6 −1.47542
\(177\) −39172.5 39172.5i −1.25036 1.25036i
\(178\) −123.985 + 123.985i −0.00391317 + 0.00391317i
\(179\) 4157.69i 0.129761i 0.997893 + 0.0648807i \(0.0206667\pi\)
−0.997893 + 0.0648807i \(0.979333\pi\)
\(180\) 0 0
\(181\) 48603.7 1.48359 0.741793 0.670629i \(-0.233976\pi\)
0.741793 + 0.670629i \(0.233976\pi\)
\(182\) −51.8096 51.8096i −0.00156411 0.00156411i
\(183\) 33400.5 33400.5i 0.997356 0.997356i
\(184\) 52.6794i 0.00155598i
\(185\) 0 0
\(186\) 370.258 0.0107023
\(187\) −39154.1 39154.1i −1.11968 1.11968i
\(188\) −22755.6 + 22755.6i −0.643832 + 0.643832i
\(189\) 4565.83i 0.127819i
\(190\) 0 0
\(191\) −59079.1 −1.61945 −0.809724 0.586811i \(-0.800383\pi\)
−0.809724 + 0.586811i \(0.800383\pi\)
\(192\) −34417.2 34417.2i −0.933625 0.933625i
\(193\) −41523.8 + 41523.8i −1.11476 + 1.11476i −0.122264 + 0.992498i \(0.539016\pi\)
−0.992498 + 0.122264i \(0.960984\pi\)
\(194\) 133.174i 0.00353848i
\(195\) 0 0
\(196\) 5487.84 0.142853
\(197\) −14556.7 14556.7i −0.375085 0.375085i 0.494240 0.869325i \(-0.335446\pi\)
−0.869325 + 0.494240i \(0.835446\pi\)
\(198\) 163.512 163.512i 0.00417079 0.00417079i
\(199\) 68770.5i 1.73658i −0.496053 0.868292i \(-0.665218\pi\)
0.496053 0.868292i \(-0.334782\pi\)
\(200\) 0 0
\(201\) −62684.3 −1.55155
\(202\) 6.23286 + 6.23286i 0.000152751 + 0.000152751i
\(203\) 5748.52 5748.52i 0.139497 0.139497i
\(204\) 58974.7i 1.41712i
\(205\) 0 0
\(206\) 93.4271 0.00220160
\(207\) −3263.44 3263.44i −0.0761614 0.0761614i
\(208\) 33315.8 33315.8i 0.770058 0.770058i
\(209\) 45559.0i 1.04299i
\(210\) 0 0
\(211\) −40600.3 −0.911935 −0.455968 0.889996i \(-0.650707\pi\)
−0.455968 + 0.889996i \(0.650707\pi\)
\(212\) 52887.1 + 52887.1i 1.17673 + 1.17673i
\(213\) 10501.3 10501.3i 0.231464 0.231464i
\(214\) 349.748i 0.00763708i
\(215\) 0 0
\(216\) −169.563 −0.00363433
\(217\) −18980.9 18980.9i −0.403085 0.403085i
\(218\) −197.692 + 197.692i −0.00415983 + 0.00415983i
\(219\) 57772.4i 1.20457i
\(220\) 0 0
\(221\) 57084.2 1.16878
\(222\) 233.573 + 233.573i 0.00473932 + 0.00473932i
\(223\) −21915.3 + 21915.3i −0.440695 + 0.440695i −0.892246 0.451550i \(-0.850871\pi\)
0.451550 + 0.892246i \(0.350871\pi\)
\(224\) 305.708i 0.00609272i
\(225\) 0 0
\(226\) 198.014 0.00387685
\(227\) 30850.1 + 30850.1i 0.598694 + 0.598694i 0.939965 0.341271i \(-0.110857\pi\)
−0.341271 + 0.939965i \(0.610857\pi\)
\(228\) −34311.0 + 34311.0i −0.660029 + 0.660029i
\(229\) 63623.5i 1.21324i −0.794992 0.606620i \(-0.792525\pi\)
0.794992 0.606620i \(-0.207475\pi\)
\(230\) 0 0
\(231\) −39299.9 −0.736491
\(232\) −213.486 213.486i −0.00396636 0.00396636i
\(233\) −29781.5 + 29781.5i −0.548574 + 0.548574i −0.926028 0.377454i \(-0.876800\pi\)
0.377454 + 0.926028i \(0.376800\pi\)
\(234\) 238.390i 0.00435367i
\(235\) 0 0
\(236\) 74575.8 1.33898
\(237\) 93586.8 + 93586.8i 1.66616 + 1.66616i
\(238\) 87.2973 87.2973i 0.00154116 0.00154116i
\(239\) 70756.8i 1.23872i 0.785108 + 0.619359i \(0.212608\pi\)
−0.785108 + 0.619359i \(0.787392\pi\)
\(240\) 0 0
\(241\) 12911.9 0.222308 0.111154 0.993803i \(-0.464545\pi\)
0.111154 + 0.993803i \(0.464545\pi\)
\(242\) 261.962 + 261.962i 0.00447308 + 0.00447308i
\(243\) −51523.2 + 51523.2i −0.872550 + 0.872550i
\(244\) 63587.2i 1.06805i
\(245\) 0 0
\(246\) 443.175 0.00732326
\(247\) −33211.1 33211.1i −0.544364 0.544364i
\(248\) −704.901 + 704.901i −0.0114611 + 0.0114611i
\(249\) 61060.2i 0.984826i
\(250\) 0 0
\(251\) −45510.3 −0.722374 −0.361187 0.932494i \(-0.617628\pi\)
−0.361187 + 0.932494i \(0.617628\pi\)
\(252\) −12625.5 12625.5i −0.198814 0.198814i
\(253\) 9669.53 9669.53i 0.151065 0.151065i
\(254\) 161.122i 0.00249740i
\(255\) 0 0
\(256\) 65517.1 0.999711
\(257\) 28510.9 + 28510.9i 0.431663 + 0.431663i 0.889194 0.457530i \(-0.151266\pi\)
−0.457530 + 0.889194i \(0.651266\pi\)
\(258\) −26.5403 + 26.5403i −0.000398718 + 0.000398718i
\(259\) 23947.7i 0.356996i
\(260\) 0 0
\(261\) −26450.5 −0.388287
\(262\) −48.8902 48.8902i −0.000712228 0.000712228i
\(263\) 28724.4 28724.4i 0.415279 0.415279i −0.468294 0.883573i \(-0.655131\pi\)
0.883573 + 0.468294i \(0.155131\pi\)
\(264\) 1459.50i 0.0209409i
\(265\) 0 0
\(266\) −101.578 −0.00143560
\(267\) −68558.1 68558.1i −0.961692 0.961692i
\(268\) 59668.6 59668.6i 0.830762 0.830762i
\(269\) 56575.8i 0.781855i 0.920422 + 0.390927i \(0.127846\pi\)
−0.920422 + 0.390927i \(0.872154\pi\)
\(270\) 0 0
\(271\) 85972.1 1.17063 0.585314 0.810807i \(-0.300971\pi\)
0.585314 + 0.810807i \(0.300971\pi\)
\(272\) 56135.9 + 56135.9i 0.758757 + 0.758757i
\(273\) 28648.4 28648.4i 0.384392 0.384392i
\(274\) 283.330i 0.00377391i
\(275\) 0 0
\(276\) 14564.5 0.191195
\(277\) 52002.6 + 52002.6i 0.677743 + 0.677743i 0.959489 0.281746i \(-0.0909135\pi\)
−0.281746 + 0.959489i \(0.590913\pi\)
\(278\) 157.429 157.429i 0.00203702 0.00203702i
\(279\) 87335.9i 1.12198i
\(280\) 0 0
\(281\) 48758.7 0.617503 0.308752 0.951143i \(-0.400089\pi\)
0.308752 + 0.951143i \(0.400089\pi\)
\(282\) 363.330 + 363.330i 0.00456881 + 0.00456881i
\(283\) 80206.3 80206.3i 1.00146 1.00146i 0.00146510 0.999999i \(-0.499534\pi\)
0.999999 0.00146510i \(-0.000466356\pi\)
\(284\) 19992.2i 0.247870i
\(285\) 0 0
\(286\) −706.345 −0.00863545
\(287\) −22718.8 22718.8i −0.275818 0.275818i
\(288\) −703.322 + 703.322i −0.00847948 + 0.00847948i
\(289\) 12663.7i 0.151623i
\(290\) 0 0
\(291\) 73639.3 0.869608
\(292\) −54993.1 54993.1i −0.644974 0.644974i
\(293\) 4087.77 4087.77i 0.0476159 0.0476159i −0.682898 0.730514i \(-0.739281\pi\)
0.730514 + 0.682898i \(0.239281\pi\)
\(294\) 87.6224i 0.00101373i
\(295\) 0 0
\(296\) −889.356 −0.0101506
\(297\) −31124.1 31124.1i −0.352845 0.352845i
\(298\) 56.5238 56.5238i 0.000636501 0.000636501i
\(299\) 14097.6i 0.157689i
\(300\) 0 0
\(301\) 2721.11 0.0300340
\(302\) −334.738 334.738i −0.00367021 0.00367021i
\(303\) −3446.49 + 3446.49i −0.0375398 + 0.0375398i
\(304\) 65318.7i 0.706790i
\(305\) 0 0
\(306\) −401.678 −0.00428978
\(307\) 23151.2 + 23151.2i 0.245639 + 0.245639i 0.819178 0.573539i \(-0.194430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(308\) 37409.2 37409.2i 0.394346 0.394346i
\(309\) 51661.0i 0.541060i
\(310\) 0 0
\(311\) 30470.3 0.315033 0.157517 0.987516i \(-0.449651\pi\)
0.157517 + 0.987516i \(0.449651\pi\)
\(312\) −1063.93 1063.93i −0.0109296 0.0109296i
\(313\) −12110.0 + 12110.0i −0.123610 + 0.123610i −0.766206 0.642595i \(-0.777858\pi\)
0.642595 + 0.766206i \(0.277858\pi\)
\(314\) 357.120i 0.00362206i
\(315\) 0 0
\(316\) −178169. −1.78426
\(317\) −52830.9 52830.9i −0.525738 0.525738i 0.393561 0.919299i \(-0.371243\pi\)
−0.919299 + 0.393561i \(0.871243\pi\)
\(318\) 844.429 844.429i 0.00835043 0.00835043i
\(319\) 78372.4i 0.770161i
\(320\) 0 0
\(321\) 193395. 1.87687
\(322\) 21.5590 + 21.5590i 0.000207930 + 0.000207930i
\(323\) 55959.4 55959.4i 0.536375 0.536375i
\(324\) 124971.i 1.19047i
\(325\) 0 0
\(326\) −162.526 −0.00152928
\(327\) −109315. 109315.i −1.02231 1.02231i
\(328\) −843.720 + 843.720i −0.00784243 + 0.00784243i
\(329\) 37251.4i 0.344153i
\(330\) 0 0
\(331\) −67516.0 −0.616241 −0.308121 0.951347i \(-0.599700\pi\)
−0.308121 + 0.951347i \(0.599700\pi\)
\(332\) 58122.7 + 58122.7i 0.527314 + 0.527314i
\(333\) −55094.8 + 55094.8i −0.496846 + 0.496846i
\(334\) 212.730i 0.00190694i
\(335\) 0 0
\(336\) 56344.9 0.499087
\(337\) 135510. + 135510.i 1.19320 + 1.19320i 0.976164 + 0.217033i \(0.0696381\pi\)
0.217033 + 0.976164i \(0.430362\pi\)
\(338\) 80.8194 80.8194i 0.000707428 0.000707428i
\(339\) 109493.i 0.952765i
\(340\) 0 0
\(341\) −258775. −2.22543
\(342\) 233.693 + 233.693i 0.00199799 + 0.00199799i
\(343\) −4491.86 + 4491.86i −0.0381802 + 0.0381802i
\(344\) 101.055i 0.000853968i
\(345\) 0 0
\(346\) 998.121 0.00833741
\(347\) 82622.8 + 82622.8i 0.686185 + 0.686185i 0.961387 0.275202i \(-0.0887446\pi\)
−0.275202 + 0.961387i \(0.588745\pi\)
\(348\) 59023.1 59023.1i 0.487375 0.487375i
\(349\) 41675.4i 0.342160i 0.985257 + 0.171080i \(0.0547256\pi\)
−0.985257 + 0.171080i \(0.945274\pi\)
\(350\) 0 0
\(351\) 45376.9 0.368316
\(352\) −2083.93 2083.93i −0.0168189 0.0168189i
\(353\) −76506.9 + 76506.9i −0.613976 + 0.613976i −0.943980 0.330004i \(-0.892950\pi\)
0.330004 + 0.943980i \(0.392950\pi\)
\(354\) 1190.72i 0.00950178i
\(355\) 0 0
\(356\) 130520. 1.02985
\(357\) 48271.5 + 48271.5i 0.378751 + 0.378751i
\(358\) −63.1906 + 63.1906i −0.000493045 + 0.000493045i
\(359\) 39385.8i 0.305598i 0.988257 + 0.152799i \(0.0488287\pi\)
−0.988257 + 0.152799i \(0.951171\pi\)
\(360\) 0 0
\(361\) 65207.6 0.500361
\(362\) 738.704 + 738.704i 0.00563707 + 0.00563707i
\(363\) −144853. + 144853.i −1.09929 + 1.09929i
\(364\) 54540.3i 0.411637i
\(365\) 0 0
\(366\) 1015.27 0.00757916
\(367\) 59666.2 + 59666.2i 0.442992 + 0.442992i 0.893016 0.450024i \(-0.148585\pi\)
−0.450024 + 0.893016i \(0.648585\pi\)
\(368\) −13863.4 + 13863.4i −0.102370 + 0.102370i
\(369\) 104535.i 0.767733i
\(370\) 0 0
\(371\) −86577.3 −0.629008
\(372\) −194886. 194886.i −1.40830 1.40830i
\(373\) 151950. 151950.i 1.09215 1.09215i 0.0968525 0.995299i \(-0.469122\pi\)
0.995299 0.0968525i \(-0.0308775\pi\)
\(374\) 1190.17i 0.00850872i
\(375\) 0 0
\(376\) −1383.42 −0.00978542
\(377\) 57131.0 + 57131.0i 0.401966 + 0.401966i
\(378\) 69.3937 69.3937i 0.000485665 0.000485665i
\(379\) 200208.i 1.39381i −0.717165 0.696904i \(-0.754561\pi\)
0.717165 0.696904i \(-0.245439\pi\)
\(380\) 0 0
\(381\) 89093.4 0.613756
\(382\) −897.913 897.913i −0.00615330 0.00615330i
\(383\) −108161. + 108161.i −0.737351 + 0.737351i −0.972065 0.234714i \(-0.924585\pi\)
0.234714 + 0.972065i \(0.424585\pi\)
\(384\) 4185.14i 0.0283823i
\(385\) 0 0
\(386\) −1262.20 −0.00847135
\(387\) −6260.27 6260.27i −0.0417995 0.0417995i
\(388\) −70096.6 + 70096.6i −0.465622 + 0.465622i
\(389\) 287702.i 1.90127i 0.310317 + 0.950633i \(0.399565\pi\)
−0.310317 + 0.950633i \(0.600435\pi\)
\(390\) 0 0
\(391\) −23753.9 −0.155375
\(392\) 166.816 + 166.816i 0.00108559 + 0.00108559i
\(393\) 27034.0 27034.0i 0.175035 0.175035i
\(394\) 442.480i 0.00285037i
\(395\) 0 0
\(396\) −172129. −1.09765
\(397\) 15821.3 + 15821.3i 0.100383 + 0.100383i 0.755515 0.655132i \(-0.227387\pi\)
−0.655132 + 0.755515i \(0.727387\pi\)
\(398\) 1045.21 1045.21i 0.00659837 0.00659837i
\(399\) 56167.8i 0.352811i
\(400\) 0 0
\(401\) 37856.9 0.235427 0.117714 0.993048i \(-0.462444\pi\)
0.117714 + 0.993048i \(0.462444\pi\)
\(402\) −952.707 952.707i −0.00589532 0.00589532i
\(403\) 188639. 188639.i 1.16151 1.16151i
\(404\) 6561.36i 0.0402005i
\(405\) 0 0
\(406\) 174.738 0.00106007
\(407\) −163245. 163245.i −0.985488 0.985488i
\(408\) 1792.68 1792.68i 0.0107692 0.0107692i
\(409\) 16990.5i 0.101569i −0.998710 0.0507844i \(-0.983828\pi\)
0.998710 0.0507844i \(-0.0161721\pi\)
\(410\) 0 0
\(411\) −156669. −0.927467
\(412\) −49175.6 49175.6i −0.289705 0.289705i
\(413\) −61041.1 + 61041.1i −0.357868 + 0.357868i
\(414\) 99.1987i 0.000578769i
\(415\) 0 0
\(416\) 3038.24 0.0175564
\(417\) 87051.1 + 87051.1i 0.500613 + 0.500613i
\(418\) −692.428 + 692.428i −0.00396298 + 0.00396298i
\(419\) 291749.i 1.66181i −0.556413 0.830906i \(-0.687823\pi\)
0.556413 0.830906i \(-0.312177\pi\)
\(420\) 0 0
\(421\) 105749. 0.596637 0.298319 0.954466i \(-0.403574\pi\)
0.298319 + 0.954466i \(0.403574\pi\)
\(422\) −617.063 617.063i −0.00346501 0.00346501i
\(423\) −85701.8 + 85701.8i −0.478971 + 0.478971i
\(424\) 3215.26i 0.0178848i
\(425\) 0 0
\(426\) 319.208 0.00175895
\(427\) −52046.8 52046.8i −0.285456 0.285456i
\(428\) −184091. + 184091.i −1.00495 + 1.00495i
\(429\) 390577.i 2.12223i
\(430\) 0 0
\(431\) −193428. −1.04127 −0.520637 0.853778i \(-0.674305\pi\)
−0.520637 + 0.853778i \(0.674305\pi\)
\(432\) 44623.1 + 44623.1i 0.239107 + 0.239107i
\(433\) −123647. + 123647.i −0.659488 + 0.659488i −0.955259 0.295771i \(-0.904424\pi\)
0.295771 + 0.955259i \(0.404424\pi\)
\(434\) 576.961i 0.00306314i
\(435\) 0 0
\(436\) 208111. 1.09477
\(437\) 13819.8 + 13819.8i 0.0723667 + 0.0723667i
\(438\) −878.054 + 878.054i −0.00457692 + 0.00457692i
\(439\) 120323.i 0.624337i 0.950027 + 0.312168i \(0.101055\pi\)
−0.950027 + 0.312168i \(0.898945\pi\)
\(440\) 0 0
\(441\) 20668.2 0.106274
\(442\) 867.594 + 867.594i 0.00444091 + 0.00444091i
\(443\) −42476.7 + 42476.7i −0.216443 + 0.216443i −0.806998 0.590555i \(-0.798909\pi\)
0.590555 + 0.806998i \(0.298909\pi\)
\(444\) 245883.i 1.24728i
\(445\) 0 0
\(446\) −666.160 −0.00334895
\(447\) 31255.1 + 31255.1i 0.156425 + 0.156425i
\(448\) −53631.1 + 53631.1i −0.267215 + 0.267215i
\(449\) 58862.3i 0.291974i −0.989286 0.145987i \(-0.953364\pi\)
0.989286 0.145987i \(-0.0466358\pi\)
\(450\) 0 0
\(451\) −309737. −1.52279
\(452\) −104225. 104225.i −0.510147 0.510147i
\(453\) 185095. 185095.i 0.901983 0.901983i
\(454\) 937.751i 0.00454963i
\(455\) 0 0
\(456\) −2085.93 −0.0100316
\(457\) −273815. 273815.i −1.31107 1.31107i −0.920629 0.390438i \(-0.872324\pi\)
−0.390438 0.920629i \(-0.627676\pi\)
\(458\) 966.981 966.981i 0.00460985 0.00460985i
\(459\) 76458.5i 0.362911i
\(460\) 0 0
\(461\) −361733. −1.70210 −0.851052 0.525082i \(-0.824035\pi\)
−0.851052 + 0.525082i \(0.824035\pi\)
\(462\) −597.299 597.299i −0.00279839 0.00279839i
\(463\) 16249.5 16249.5i 0.0758014 0.0758014i −0.668190 0.743991i \(-0.732931\pi\)
0.743991 + 0.668190i \(0.232931\pi\)
\(464\) 112364.i 0.521904i
\(465\) 0 0
\(466\) −905.269 −0.00416875
\(467\) 188589. + 188589.i 0.864735 + 0.864735i 0.991884 0.127148i \(-0.0405824\pi\)
−0.127148 + 0.991884i \(0.540582\pi\)
\(468\) 125477. 125477.i 0.572892 0.572892i
\(469\) 97678.9i 0.444074i
\(470\) 0 0
\(471\) −197471. −0.890149
\(472\) 2266.91 + 2266.91i 0.0101754 + 0.0101754i
\(473\) 18549.1 18549.1i 0.0829088 0.0829088i
\(474\) 2844.76i 0.0126616i
\(475\) 0 0
\(476\) −91898.3 −0.405596
\(477\) 199183. + 199183.i 0.875416 + 0.875416i
\(478\) −1075.40 + 1075.40i −0.00470666 + 0.00470666i
\(479\) 347260.i 1.51351i 0.653701 + 0.756753i \(0.273215\pi\)
−0.653701 + 0.756753i \(0.726785\pi\)
\(480\) 0 0
\(481\) 238001. 1.02870
\(482\) 196.241 + 196.241i 0.000844689 + 0.000844689i
\(483\) −11921.2 + 11921.2i −0.0511004 + 0.0511004i
\(484\) 275768.i 1.17721i
\(485\) 0 0
\(486\) −1566.15 −0.00663072
\(487\) −35396.5 35396.5i −0.149246 0.149246i 0.628535 0.777781i \(-0.283655\pi\)
−0.777781 + 0.628535i \(0.783655\pi\)
\(488\) −1932.89 + 1932.89i −0.00811646 + 0.00811646i
\(489\) 89869.6i 0.375833i
\(490\) 0 0
\(491\) −180759. −0.749785 −0.374893 0.927068i \(-0.622320\pi\)
−0.374893 + 0.927068i \(0.622320\pi\)
\(492\) −233266. 233266.i −0.963655 0.963655i
\(493\) −96263.7 + 96263.7i −0.396067 + 0.396067i
\(494\) 1009.52i 0.00413675i
\(495\) 0 0
\(496\) 371010. 1.50807
\(497\) −16363.8 16363.8i −0.0662479 0.0662479i
\(498\) 928.023 928.023i 0.00374197 0.00374197i
\(499\) 186215.i 0.747847i −0.927460 0.373923i \(-0.878012\pi\)
0.927460 0.373923i \(-0.121988\pi\)
\(500\) 0 0
\(501\) −117630. −0.468645
\(502\) −691.687 691.687i −0.00274475 0.00274475i
\(503\) 28470.2 28470.2i 0.112526 0.112526i −0.648602 0.761128i \(-0.724646\pi\)
0.761128 + 0.648602i \(0.224646\pi\)
\(504\) 767.565i 0.00302172i
\(505\) 0 0
\(506\) 293.925 0.00114798
\(507\) 44689.5 + 44689.5i 0.173856 + 0.173856i
\(508\) −84807.2 + 84807.2i −0.328629 + 0.328629i
\(509\) 9013.98i 0.0347921i 0.999849 + 0.0173961i \(0.00553762\pi\)
−0.999849 + 0.0173961i \(0.994462\pi\)
\(510\) 0 0
\(511\) 90024.9 0.344763
\(512\) 4979.67 + 4979.67i 0.0189959 + 0.0189959i
\(513\) 44482.9 44482.9i 0.169028 0.169028i
\(514\) 866.647i 0.00328032i
\(515\) 0 0
\(516\) 27939.1 0.104933
\(517\) −253933. 253933.i −0.950033 0.950033i
\(518\) 363.969 363.969i 0.00135645 0.00135645i
\(519\) 551916.i 2.04898i
\(520\) 0 0
\(521\) 123697. 0.455704 0.227852 0.973696i \(-0.426830\pi\)
0.227852 + 0.973696i \(0.426830\pi\)
\(522\) −402.007 402.007i −0.00147534 0.00147534i
\(523\) −82201.1 + 82201.1i −0.300521 + 0.300521i −0.841218 0.540697i \(-0.818161\pi\)
0.540697 + 0.841218i \(0.318161\pi\)
\(524\) 51466.9i 0.187441i
\(525\) 0 0
\(526\) 873.135 0.00315580
\(527\) 317850. + 317850.i 1.14446 + 1.14446i
\(528\) 384089. 384089.i 1.37773 1.37773i
\(529\) 273975.i 0.979037i
\(530\) 0 0
\(531\) 280866. 0.996117
\(532\) 53465.6 + 53465.6i 0.188909 + 0.188909i
\(533\) 225788. 225788.i 0.794780 0.794780i
\(534\) 2083.96i 0.00730814i
\(535\) 0 0
\(536\) 3627.55 0.0126265
\(537\) −34941.5 34941.5i −0.121170 0.121170i
\(538\) −859.867 + 859.867i −0.00297075 + 0.00297075i
\(539\) 61239.7i 0.210793i
\(540\) 0 0
\(541\) 17926.3 0.0612484 0.0306242 0.999531i \(-0.490250\pi\)
0.0306242 + 0.999531i \(0.490250\pi\)
\(542\) 1306.65 + 1306.65i 0.00444795 + 0.00444795i
\(543\) −408470. + 408470.i −1.38535 + 1.38535i
\(544\) 5119.33i 0.0172988i
\(545\) 0 0
\(546\) 870.825 0.00292109
\(547\) 336131. + 336131.i 1.12340 + 1.12340i 0.991227 + 0.132173i \(0.0421956\pi\)
0.132173 + 0.991227i \(0.457804\pi\)
\(548\) 149132. 149132.i 0.496602 0.496602i
\(549\) 239481.i 0.794560i
\(550\) 0 0
\(551\) 112011. 0.368941
\(552\) 442.722 + 442.722i 0.00145296 + 0.00145296i
\(553\) 145833. 145833.i 0.476876 0.476876i
\(554\) 1580.72i 0.00515034i
\(555\) 0 0
\(556\) −165726. −0.536095
\(557\) −178158. 178158.i −0.574241 0.574241i 0.359070 0.933311i \(-0.383094\pi\)
−0.933311 + 0.359070i \(0.883094\pi\)
\(558\) −1327.37 + 1327.37i −0.00426309 + 0.00426309i
\(559\) 27043.4i 0.0865443i
\(560\) 0 0
\(561\) 658108. 2.09108
\(562\) 741.058 + 741.058i 0.00234628 + 0.00234628i
\(563\) −289503. + 289503.i −0.913348 + 0.913348i −0.996534 0.0831863i \(-0.973490\pi\)
0.0831863 + 0.996534i \(0.473490\pi\)
\(564\) 382480.i 1.20240i
\(565\) 0 0
\(566\) 2438.03 0.00761037
\(567\) 102290. + 102290.i 0.318176 + 0.318176i
\(568\) −607.711 + 607.711i −0.00188365 + 0.00188365i
\(569\) 448419.i 1.38503i 0.721403 + 0.692516i \(0.243498\pi\)
−0.721403 + 0.692516i \(0.756502\pi\)
\(570\) 0 0
\(571\) 403775. 1.23842 0.619209 0.785226i \(-0.287453\pi\)
0.619209 + 0.785226i \(0.287453\pi\)
\(572\) 371787. + 371787.i 1.13632 + 1.13632i
\(573\) 496506. 496506.i 1.51222 1.51222i
\(574\) 690.584i 0.00209601i
\(575\) 0 0
\(576\) 246771. 0.743787
\(577\) −314392. 314392.i −0.944321 0.944321i 0.0542087 0.998530i \(-0.482736\pi\)
−0.998530 + 0.0542087i \(0.982736\pi\)
\(578\) −192.470 + 192.470i −0.000576112 + 0.000576112i
\(579\) 697938.i 2.08190i
\(580\) 0 0
\(581\) −95148.1 −0.281869
\(582\) 1119.21 + 1119.21i 0.00330418 + 0.00330418i
\(583\) −590175. + 590175.i −1.73638 + 1.73638i
\(584\) 3343.29i 0.00980277i
\(585\) 0 0
\(586\) 124.256 0.000361845
\(587\) 56100.9 + 56100.9i 0.162815 + 0.162815i 0.783812 0.620998i \(-0.213272\pi\)
−0.620998 + 0.783812i \(0.713272\pi\)
\(588\) −46120.3 + 46120.3i −0.133394 + 0.133394i
\(589\) 369844.i 1.06608i
\(590\) 0 0
\(591\) 244671. 0.700500
\(592\) 234047. + 234047.i 0.667821 + 0.667821i
\(593\) 65402.5 65402.5i 0.185988 0.185988i −0.607971 0.793959i \(-0.708016\pi\)
0.793959 + 0.607971i \(0.208016\pi\)
\(594\) 946.078i 0.00268135i
\(595\) 0 0
\(596\) −59502.9 −0.167512
\(597\) 577953. + 577953.i 1.62160 + 1.62160i
\(598\) −214.262 + 214.262i −0.000599159 + 0.000599159i
\(599\) 519621.i 1.44822i −0.689687 0.724108i \(-0.742252\pi\)
0.689687 0.724108i \(-0.257748\pi\)
\(600\) 0 0
\(601\) −433485. −1.20012 −0.600060 0.799955i \(-0.704857\pi\)
−0.600060 + 0.799955i \(0.704857\pi\)
\(602\) 41.3568 + 41.3568i 0.000114118 + 0.000114118i
\(603\) 224723. 224723.i 0.618035 0.618035i
\(604\) 352380.i 0.965913i
\(605\) 0 0
\(606\) −104.763 −0.000285274
\(607\) −374141. 374141.i −1.01545 1.01545i −0.999879 0.0155710i \(-0.995043\pi\)
−0.0155710 0.999879i \(-0.504957\pi\)
\(608\) 2978.38 2978.38i 0.00805700 0.00805700i
\(609\) 96622.1i 0.260521i
\(610\) 0 0
\(611\) 370219. 0.991690
\(612\) 211424. + 211424.i 0.564484 + 0.564484i
\(613\) 152256. 152256.i 0.405186 0.405186i −0.474870 0.880056i \(-0.657505\pi\)
0.880056 + 0.474870i \(0.157505\pi\)
\(614\) 703.727i 0.00186667i
\(615\) 0 0
\(616\) 2274.29 0.00599355
\(617\) −408731. 408731.i −1.07366 1.07366i −0.997062 0.0766005i \(-0.975593\pi\)
−0.0766005 0.997062i \(-0.524407\pi\)
\(618\) −785.169 + 785.169i −0.00205583 + 0.00205583i
\(619\) 72206.4i 0.188449i 0.995551 + 0.0942247i \(0.0300372\pi\)
−0.995551 + 0.0942247i \(0.969963\pi\)
\(620\) 0 0
\(621\) −18882.3 −0.0489633
\(622\) 463.103 + 463.103i 0.00119701 + 0.00119701i
\(623\) −106832. + 106832.i −0.275248 + 0.275248i
\(624\) 559977.i 1.43814i
\(625\) 0 0
\(626\) −368.107 −0.000939345
\(627\) −382882. 382882.i −0.973934 0.973934i
\(628\) 187971. 187971.i 0.476620 0.476620i
\(629\) 401023.i 1.01360i
\(630\) 0 0
\(631\) −453999. −1.14024 −0.570120 0.821561i \(-0.693103\pi\)
−0.570120 + 0.821561i \(0.693103\pi\)
\(632\) −5415.87 5415.87i −0.0135592 0.0135592i
\(633\) 341208. 341208.i 0.851553 0.851553i
\(634\) 1605.90i 0.00399521i
\(635\) 0 0
\(636\) −888935. −2.19764
\(637\) −44641.8 44641.8i −0.110018 0.110018i
\(638\) 1191.14 1191.14i 0.00292632 0.00292632i
\(639\) 75294.2i 0.184400i
\(640\) 0 0
\(641\) 419719. 1.02151 0.510755 0.859727i \(-0.329366\pi\)
0.510755 + 0.859727i \(0.329366\pi\)
\(642\) 2939.31 + 2939.31i 0.00713141 + 0.00713141i
\(643\) 291772. 291772.i 0.705703 0.705703i −0.259926 0.965629i \(-0.583698\pi\)
0.965629 + 0.259926i \(0.0836982\pi\)
\(644\) 22695.3i 0.0547223i
\(645\) 0 0
\(646\) 1701.00 0.00407604
\(647\) −123334. 123334.i −0.294628 0.294628i 0.544278 0.838905i \(-0.316804\pi\)
−0.838905 + 0.544278i \(0.816804\pi\)
\(648\) 3798.79 3798.79i 0.00904681 0.00904681i
\(649\) 832203.i 1.97579i
\(650\) 0 0
\(651\) 319033. 0.752791
\(652\) 85546.1 + 85546.1i 0.201236 + 0.201236i
\(653\) −140737. + 140737.i −0.330052 + 0.330052i −0.852606 0.522554i \(-0.824979\pi\)
0.522554 + 0.852606i \(0.324979\pi\)
\(654\) 3322.83i 0.00776878i
\(655\) 0 0
\(656\) 444075. 1.03193
\(657\) −207114. 207114.i −0.479820 0.479820i
\(658\) 566.166 566.166i 0.00130765 0.00130765i
\(659\) 38660.5i 0.0890218i −0.999009 0.0445109i \(-0.985827\pi\)
0.999009 0.0445109i \(-0.0141729\pi\)
\(660\) 0 0
\(661\) −252816. −0.578631 −0.289315 0.957234i \(-0.593428\pi\)
−0.289315 + 0.957234i \(0.593428\pi\)
\(662\) −1026.14 1026.14i −0.00234148 0.00234148i
\(663\) −479740. + 479740.i −1.09139 + 1.09139i
\(664\) 3533.56i 0.00801449i
\(665\) 0 0
\(666\) −1674.71 −0.00377566
\(667\) −23773.4 23773.4i −0.0534366 0.0534366i
\(668\) 111971. 111971.i 0.250931 0.250931i
\(669\) 368356.i 0.823031i
\(670\) 0 0
\(671\) −709579. −1.57600
\(672\) 2569.20 + 2569.20i 0.00568930 + 0.00568930i
\(673\) −322576. + 322576.i −0.712199 + 0.712199i −0.966995 0.254796i \(-0.917992\pi\)
0.254796 + 0.966995i \(0.417992\pi\)
\(674\) 4119.10i 0.00906740i
\(675\) 0 0
\(676\) −85079.0 −0.186178
\(677\) −105500. 105500.i −0.230184 0.230184i 0.582586 0.812769i \(-0.302041\pi\)
−0.812769 + 0.582586i \(0.802041\pi\)
\(678\) −1664.12 + 1664.12i −0.00362015 + 0.00362015i
\(679\) 114750.i 0.248893i
\(680\) 0 0
\(681\) −518534. −1.11811
\(682\) −3932.99 3932.99i −0.00845580 0.00845580i
\(683\) 424431. 424431.i 0.909841 0.909841i −0.0864179 0.996259i \(-0.527542\pi\)
0.996259 + 0.0864179i \(0.0275420\pi\)
\(684\) 246009.i 0.525823i
\(685\) 0 0
\(686\) −136.539 −0.000290141
\(687\) 534697. + 534697.i 1.13291 + 1.13291i
\(688\) −26594.2 + 26594.2i −0.0561836 + 0.0561836i
\(689\) 860439.i 1.81251i
\(690\) 0 0
\(691\) 240516. 0.503718 0.251859 0.967764i \(-0.418958\pi\)
0.251859 + 0.967764i \(0.418958\pi\)
\(692\) −525364. 525364.i −1.09710 1.09710i
\(693\) 140890. 140890.i 0.293368 0.293368i
\(694\) 2511.49i 0.00521449i
\(695\) 0 0
\(696\) 3588.30 0.00740748
\(697\) 380445. + 380445.i 0.783117 + 0.783117i
\(698\) −633.403 + 633.403i −0.00130008 + 0.00130008i
\(699\) 500573.i 1.02450i
\(700\) 0 0
\(701\) 451921. 0.919658 0.459829 0.888008i \(-0.347911\pi\)
0.459829 + 0.888008i \(0.347911\pi\)
\(702\) 689.661 + 689.661i 0.00139946 + 0.00139946i
\(703\) 233312. 233312.i 0.472091 0.472091i
\(704\) 731179.i 1.47529i
\(705\) 0 0
\(706\) −2325.58 −0.00466576
\(707\) 5370.55 + 5370.55i 0.0107443 + 0.0107443i
\(708\) −626741. + 626741.i −1.25032 + 1.25032i
\(709\) 567115.i 1.12818i 0.825713 + 0.564091i \(0.190773\pi\)
−0.825713 + 0.564091i \(0.809227\pi\)
\(710\) 0 0
\(711\) −671016. −1.32738
\(712\) 3967.46 + 3967.46i 0.00782623 + 0.00782623i
\(713\) −78496.5 + 78496.5i −0.154409 + 0.154409i
\(714\) 1467.31i 0.00287822i
\(715\) 0 0
\(716\) 66521.1 0.129758
\(717\) −594646. 594646.i −1.15670 1.15670i
\(718\) −598.605 + 598.605i −0.00116116 + 0.00116116i
\(719\) 316359.i 0.611959i −0.952038 0.305979i \(-0.901016\pi\)
0.952038 0.305979i \(-0.0989838\pi\)
\(720\) 0 0
\(721\) 80501.6 0.154858
\(722\) 991.057 + 991.057i 0.00190118 + 0.00190118i
\(723\) −108513. + 108513.i −0.207589 + 0.207589i
\(724\) 777637.i 1.48354i
\(725\) 0 0
\(726\) −4403.09 −0.00835381
\(727\) −9776.49 9776.49i −0.0184975 0.0184975i 0.697798 0.716295i \(-0.254164\pi\)
−0.716295 + 0.697798i \(0.754164\pi\)
\(728\) −1657.88 + 1657.88i −0.00312818 + 0.00312818i
\(729\) 233328.i 0.439047i
\(730\) 0 0
\(731\) −45567.2 −0.0852742
\(732\) −534392. 534392.i −0.997327 0.997327i
\(733\) −160398. + 160398.i −0.298533 + 0.298533i −0.840439 0.541906i \(-0.817703\pi\)
0.541906 + 0.840439i \(0.317703\pi\)
\(734\) 1813.67i 0.00336641i
\(735\) 0 0
\(736\) −1264.28 −0.00233392
\(737\) 665852. + 665852.i 1.22586 + 1.22586i
\(738\) −1588.78 + 1588.78i −0.00291710 + 0.00291710i
\(739\) 754750.i 1.38202i −0.722845 0.691010i \(-0.757166\pi\)
0.722845 0.691010i \(-0.242834\pi\)
\(740\) 0 0
\(741\) 558217. 1.01664
\(742\) −1315.85 1315.85i −0.00239000 0.00239000i
\(743\) −212897. + 212897.i −0.385649 + 0.385649i −0.873132 0.487483i \(-0.837915\pi\)
0.487483 + 0.873132i \(0.337915\pi\)
\(744\) 11848.1i 0.0214044i
\(745\) 0 0
\(746\) 4618.82 0.00829953
\(747\) 218901. + 218901.i 0.392289 + 0.392289i
\(748\) −626447. + 626447.i −1.11965 + 1.11965i
\(749\) 301361.i 0.537184i
\(750\) 0 0
\(751\) −177487. −0.314693 −0.157347 0.987543i \(-0.550294\pi\)
−0.157347 + 0.987543i \(0.550294\pi\)
\(752\) 364069. + 364069.i 0.643795 + 0.643795i
\(753\) 382472. 382472.i 0.674543 0.674543i
\(754\) 1736.61i 0.00305464i
\(755\) 0 0
\(756\) −73051.1 −0.127815
\(757\) 402096. + 402096.i 0.701678 + 0.701678i 0.964771 0.263093i \(-0.0847425\pi\)
−0.263093 + 0.964771i \(0.584742\pi\)
\(758\) 3042.86 3042.86i 0.00529594 0.00529594i
\(759\) 162527.i 0.282125i
\(760\) 0 0
\(761\) 374461. 0.646603 0.323301 0.946296i \(-0.395207\pi\)
0.323301 + 0.946296i \(0.395207\pi\)
\(762\) 1354.09 + 1354.09i 0.00233204 + 0.00233204i
\(763\) −170341. + 170341.i −0.292597 + 0.292597i
\(764\) 945238.i 1.61940i
\(765\) 0 0
\(766\) −3287.78 −0.00560331
\(767\) −606650. 606650.i −1.03121 1.03121i
\(768\) −550611. + 550611.i −0.933517 + 0.933517i
\(769\) 660539.i 1.11698i −0.829511 0.558490i \(-0.811381\pi\)
0.829511 0.558490i \(-0.188619\pi\)
\(770\) 0 0
\(771\) −479217. −0.806163
\(772\) 664361. + 664361.i 1.11473 + 1.11473i
\(773\) −166751. + 166751.i −0.279067 + 0.279067i −0.832737 0.553669i \(-0.813227\pi\)
0.553669 + 0.832737i \(0.313227\pi\)
\(774\) 190.293i 0.000317645i
\(775\) 0 0
\(776\) −4261.51 −0.00707685
\(777\) 201258. + 201258.i 0.333359 + 0.333359i
\(778\) −4372.63 + 4372.63i −0.00722410 + 0.00722410i
\(779\) 442679.i 0.729481i
\(780\) 0 0
\(781\) −223096. −0.365754
\(782\) −361.023 361.023i −0.000590366 0.000590366i
\(783\) −76521.2 + 76521.2i −0.124813 + 0.124813i
\(784\) 87800.4i 0.142845i
\(785\) 0 0
\(786\) 821.754 0.00133014
\(787\) −334297. 334297.i −0.539738 0.539738i 0.383714 0.923452i \(-0.374645\pi\)
−0.923452 + 0.383714i \(0.874645\pi\)
\(788\) −232900. + 232900.i −0.375075 + 0.375075i
\(789\) 482804.i 0.775563i
\(790\) 0 0
\(791\) 170619. 0.272693
\(792\) −5232.29 5232.29i −0.00834145 0.00834145i
\(793\) 517261. 517261.i 0.822552 0.822552i
\(794\) 480.919i 0.000762836i
\(795\) 0 0
\(796\) −1.10030e6 −1.73653
\(797\) −316482. 316482.i −0.498232 0.498232i 0.412655 0.910887i \(-0.364602\pi\)
−0.910887 + 0.412655i \(0.864602\pi\)
\(798\) 853.666 853.666i 0.00134055 0.00134055i
\(799\) 623805.i 0.977137i
\(800\) 0 0
\(801\) 491561. 0.766147
\(802\) 575.368 + 575.368i 0.000894535 + 0.000894535i
\(803\) 613676. 613676.i 0.951718 0.951718i
\(804\) 1.00292e6i 1.55151i
\(805\) 0 0
\(806\) 5734.06 0.00882657
\(807\) −475468. 475468.i −0.730086 0.730086i
\(808\) 199.449 199.449i 0.000305498 0.000305498i
\(809\) 287899.i 0.439889i −0.975512 0.219945i \(-0.929412\pi\)
0.975512 0.219945i \(-0.0705877\pi\)
\(810\) 0 0
\(811\) −265302. −0.403366 −0.201683 0.979451i \(-0.564641\pi\)
−0.201683 + 0.979451i \(0.564641\pi\)
\(812\) −91973.7 91973.7i −0.139493 0.139493i
\(813\) −722517. + 722517.i −1.09312 + 1.09312i
\(814\) 4962.16i 0.00748897i
\(815\) 0 0
\(816\) −943541. −1.41703
\(817\) 26510.6 + 26510.6i 0.0397169 + 0.0397169i
\(818\) 258.230 258.230i 0.000385923 0.000385923i
\(819\) 205409.i 0.306232i
\(820\) 0 0
\(821\) −61802.8 −0.0916899 −0.0458450 0.998949i \(-0.514598\pi\)
−0.0458450 + 0.998949i \(0.514598\pi\)
\(822\) −2381.13 2381.13i −0.00352403 0.00352403i
\(823\) 729615. 729615.i 1.07719 1.07719i 0.0804343 0.996760i \(-0.474369\pi\)
0.996760 0.0804343i \(-0.0256307\pi\)
\(824\) 2989.63i 0.00440314i
\(825\) 0 0
\(826\) −1855.47 −0.00271952
\(827\) −341394. 341394.i −0.499165 0.499165i 0.412013 0.911178i \(-0.364826\pi\)
−0.911178 + 0.412013i \(0.864826\pi\)
\(828\) −52213.5 + 52213.5i −0.0761592 + 0.0761592i
\(829\) 83296.0i 0.121203i −0.998162 0.0606017i \(-0.980698\pi\)
0.998162 0.0606017i \(-0.0193019\pi\)
\(830\) 0 0
\(831\) −874068. −1.26574
\(832\) −533006. 533006.i −0.769991 0.769991i
\(833\) 75219.8 75219.8i 0.108403 0.108403i
\(834\) 2646.09i 0.00380428i
\(835\) 0 0
\(836\) 728923. 1.04296
\(837\) 252663. + 252663.i 0.360654 + 0.360654i
\(838\) 4434.15 4434.15i 0.00631426 0.00631426i
\(839\) 1.16611e6i 1.65659i −0.560296 0.828293i \(-0.689312\pi\)
0.560296 0.828293i \(-0.310688\pi\)
\(840\) 0 0
\(841\) 514596. 0.727569
\(842\) 1607.22 + 1607.22i 0.00226700 + 0.00226700i
\(843\) −409772. + 409772.i −0.576616 + 0.576616i
\(844\) 649586.i 0.911909i
\(845\) 0 0
\(846\) −2605.08 −0.00363982
\(847\) 225719. + 225719.i 0.314632 + 0.314632i
\(848\) 846144. 846144.i 1.17666 1.17666i
\(849\) 1.34812e6i 1.87031i
\(850\) 0 0
\(851\) −99037.1 −0.136754
\(852\) −168016. 168016.i −0.231457 0.231457i
\(853\) 904459. 904459.i 1.24306 1.24306i 0.284330 0.958726i \(-0.408229\pi\)
0.958726 0.284330i \(-0.0917712\pi\)
\(854\) 1582.07i 0.00216925i
\(855\) 0 0
\(856\) −11191.8 −0.0152739
\(857\) 206785. + 206785.i 0.281552 + 0.281552i 0.833728 0.552176i \(-0.186202\pi\)
−0.552176 + 0.833728i \(0.686202\pi\)
\(858\) 5936.19 5936.19i 0.00806367 0.00806367i
\(859\) 428256.i 0.580386i 0.956968 + 0.290193i \(0.0937195\pi\)
−0.956968 + 0.290193i \(0.906280\pi\)
\(860\) 0 0
\(861\) 381862. 0.515110
\(862\) −2939.81 2939.81i −0.00395645 0.00395645i
\(863\) −572263. + 572263.i −0.768376 + 0.768376i −0.977821 0.209444i \(-0.932835\pi\)
0.209444 + 0.977821i \(0.432835\pi\)
\(864\) 4069.42i 0.00545136i
\(865\) 0 0
\(866\) −3758.49 −0.00501161
\(867\) −106427. 106427.i −0.141584 0.141584i
\(868\) −303685. + 303685.i −0.403073 + 0.403073i
\(869\) 1.98821e6i 2.63283i
\(870\) 0 0
\(871\) −970770. −1.27962
\(872\) 6326.04 + 6326.04i 0.00831953 + 0.00831953i
\(873\) −263997. + 263997.i −0.346394 + 0.346394i
\(874\) 420.080i 0.000549933i
\(875\) 0 0
\(876\) 924332. 1.20454
\(877\) −45559.5 45559.5i −0.0592352 0.0592352i 0.676869 0.736104i \(-0.263336\pi\)
−0.736104 + 0.676869i \(0.763336\pi\)
\(878\) −1828.73 + 1828.73i −0.00237225 + 0.00237225i
\(879\) 68708.0i 0.0889261i
\(880\) 0 0
\(881\) −85914.1 −0.110691 −0.0553455 0.998467i \(-0.517626\pi\)
−0.0553455 + 0.998467i \(0.517626\pi\)
\(882\) 314.126 + 314.126i 0.000403800 + 0.000403800i
\(883\) 340402. 340402.i 0.436586 0.436586i −0.454275 0.890861i \(-0.650102\pi\)
0.890861 + 0.454275i \(0.150102\pi\)
\(884\) 913321.i 1.16874i
\(885\) 0 0
\(886\) −1291.16 −0.00164480
\(887\) −97903.9 97903.9i −0.124438 0.124438i 0.642145 0.766583i \(-0.278045\pi\)
−0.766583 + 0.642145i \(0.778045\pi\)
\(888\) 7474.22 7474.22i 0.00947851 0.00947851i
\(889\) 138831.i 0.175664i
\(890\) 0 0
\(891\) 1.39457e6 1.75665
\(892\) 350635. + 350635.i 0.440682 + 0.440682i
\(893\) 362924. 362924.i 0.455107 0.455107i
\(894\) 950.062i 0.00118871i
\(895\) 0 0
\(896\) −6521.56 −0.00812335
\(897\) −118477. 118477.i −0.147248 0.147248i
\(898\) 894.619 894.619i 0.00110939 0.00110939i
\(899\) 636221.i 0.787207i
\(900\) 0 0
\(901\) 1.44981e6 1.78591
\(902\) −4707.53 4707.53i −0.00578602 0.00578602i
\(903\) −22868.4 + 22868.4i −0.0280454 + 0.0280454i
\(904\) 6336.35i 0.00775358i
\(905\) 0 0
\(906\) 5626.33 0.00685439
\(907\) 398218. + 398218.i 0.484068 + 0.484068i 0.906428 0.422360i \(-0.138798\pi\)
−0.422360 + 0.906428i \(0.638798\pi\)
\(908\) 493588. 493588.i 0.598677 0.598677i
\(909\) 24711.3i 0.0299067i
\(910\) 0 0
\(911\) −250366. −0.301674 −0.150837 0.988559i \(-0.548197\pi\)
−0.150837 + 0.988559i \(0.548197\pi\)
\(912\) 548944. + 548944.i 0.659991 + 0.659991i
\(913\) −648600. + 648600.i −0.778100 + 0.778100i
\(914\) 8323.15i 0.00996312i
\(915\) 0 0
\(916\) −1.01795e6 −1.21320
\(917\) −42126.3 42126.3i −0.0500973 0.0500973i
\(918\) −1162.05 + 1162.05i −0.00137893 + 0.00137893i
\(919\) 319536.i 0.378345i −0.981944 0.189173i \(-0.939419\pi\)
0.981944 0.189173i \(-0.0605806\pi\)
\(920\) 0 0
\(921\) −389129. −0.458748
\(922\) −5497.79 5497.79i −0.00646735 0.00646735i
\(923\) 162630. 162630.i 0.190896 0.190896i
\(924\) 628780.i 0.736469i
\(925\) 0 0
\(926\) 493.935 0.000576034
\(927\) −185204. 185204.i −0.215522 0.215522i
\(928\) −5123.53 + 5123.53i −0.00594940 + 0.00594940i
\(929\) 318241.i 0.368744i 0.982857 + 0.184372i \(0.0590251\pi\)
−0.982857 + 0.184372i \(0.940975\pi\)
\(930\) 0 0
\(931\) −87524.4 −0.100979
\(932\) 476491. + 476491.i 0.548558 + 0.548558i
\(933\) −256075. + 256075.i −0.294174 + 0.294174i
\(934\) 5732.55i 0.00657134i
\(935\) 0 0
\(936\) 7628.36 0.00870722
\(937\) 201589. + 201589.i 0.229608 + 0.229608i 0.812529 0.582921i \(-0.198090\pi\)
−0.582921 + 0.812529i \(0.698090\pi\)
\(938\) −1484.57 + 1484.57i −0.00168731 + 0.00168731i
\(939\) 203547.i 0.230851i
\(940\) 0 0
\(941\) −438035. −0.494686 −0.247343 0.968928i \(-0.579557\pi\)
−0.247343 + 0.968928i \(0.579557\pi\)
\(942\) −3001.27 3001.27i −0.00338223 0.00338223i
\(943\) −93955.1 + 93955.1i −0.105657 + 0.105657i
\(944\) 1.19314e6i 1.33890i
\(945\) 0 0
\(946\) 563.837 0.000630045
\(947\) −1.20314e6 1.20314e6i −1.34158 1.34158i −0.894485 0.447098i \(-0.852457\pi\)
−0.447098 0.894485i \(-0.647543\pi\)
\(948\) 1.49734e6 1.49734e6i 1.66612 1.66612i
\(949\) 894701.i 0.993449i
\(950\) 0 0
\(951\) 887990. 0.981855
\(952\) −2793.47 2793.47i −0.00308227 0.00308227i
\(953\) −323897. + 323897.i −0.356633 + 0.356633i −0.862570 0.505937i \(-0.831147\pi\)
0.505937 + 0.862570i \(0.331147\pi\)
\(954\) 6054.55i 0.00665250i
\(955\) 0 0
\(956\) 1.13208e6 1.23868
\(957\) 658648. + 658648.i 0.719167 + 0.719167i
\(958\) −5277.83 + 5277.83i −0.00575075 + 0.00575075i
\(959\) 244132.i 0.265453i
\(960\) 0 0
\(961\) 1.17720e6 1.27468
\(962\) 3617.26 + 3617.26i 0.00390867 + 0.00390867i
\(963\) −693320. + 693320.i −0.747620 + 0.747620i
\(964\) 206584.i 0.222302i
\(965\) 0 0
\(966\) −362.368 −0.000388325
\(967\) −206662. 206662.i −0.221008 0.221008i 0.587915 0.808923i \(-0.299949\pi\)
−0.808923 + 0.587915i \(0.799949\pi\)
\(968\) 8382.65 8382.65i 0.00894603 0.00894603i
\(969\) 940576.i 1.00172i
\(970\) 0 0
\(971\) 772001. 0.818803 0.409402 0.912354i \(-0.365737\pi\)
0.409402 + 0.912354i \(0.365737\pi\)
\(972\) 824348. + 824348.i 0.872525 + 0.872525i
\(973\) 135649. 135649.i 0.143282 0.143282i
\(974\) 1075.95i 0.00113416i
\(975\) 0 0
\(976\) 1.01734e6 1.06798
\(977\) 433267. + 433267.i 0.453907 + 0.453907i 0.896649 0.442742i \(-0.145994\pi\)
−0.442742 + 0.896649i \(0.645994\pi\)
\(978\) 1365.88 1365.88i 0.00142802 0.00142802i
\(979\) 1.45649e6i 1.51964i
\(980\) 0 0
\(981\) 783784. 0.814439
\(982\) −2747.26 2747.26i −0.00284890 0.00284890i
\(983\) −697281. + 697281.i −0.721607 + 0.721607i −0.968933 0.247325i \(-0.920448\pi\)
0.247325 + 0.968933i \(0.420448\pi\)
\(984\) 14181.4i 0.0146463i
\(985\) 0 0
\(986\) −2926.13 −0.00300981
\(987\) 313064. + 313064.i 0.321365 + 0.321365i
\(988\) −531362. + 531362.i −0.544348 + 0.544348i
\(989\) 11253.3i 0.0115050i
\(990\) 0 0
\(991\) 1.67220e6 1.70271 0.851354 0.524591i \(-0.175782\pi\)
0.851354 + 0.524591i \(0.175782\pi\)
\(992\) 16917.2 + 16917.2i 0.0171912 + 0.0171912i
\(993\) 567410. 567410.i 0.575438 0.575438i
\(994\) 497.411i 0.000503434i
\(995\) 0 0
\(996\) −976935. −0.984798
\(997\) 387338. + 387338.i 0.389672 + 0.389672i 0.874571 0.484898i \(-0.161143\pi\)
−0.484898 + 0.874571i \(0.661143\pi\)
\(998\) 2830.18 2830.18i 0.00284154 0.00284154i
\(999\) 318778.i 0.319417i
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 175.5.g.c.57.7 24
5.2 odd 4 35.5.g.a.8.6 24
5.3 odd 4 inner 175.5.g.c.43.7 24
5.4 even 2 35.5.g.a.22.6 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.5.g.a.8.6 24 5.2 odd 4
35.5.g.a.22.6 yes 24 5.4 even 2
175.5.g.c.43.7 24 5.3 odd 4 inner
175.5.g.c.57.7 24 1.1 even 1 trivial