Properties

Label 35.5.i.a.24.4
Level $35$
Weight $5$
Character 35.24
Analytic conductor $3.618$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,5,Mod(19,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.i (of order \(6\), 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: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 24.4
Character \(\chi\) \(=\) 35.24
Dual form 35.5.i.a.19.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.03096 + 2.32728i) q^{2} +(7.86751 - 13.6269i) q^{3} +(2.83245 - 4.90594i) q^{4} +(-24.7840 + 3.27931i) q^{5} +73.2395i q^{6} +(-45.1600 + 19.0150i) q^{7} -48.1053i q^{8} +(-83.2953 - 144.272i) q^{9} +O(q^{10})\) \(q+(-4.03096 + 2.32728i) q^{2} +(7.86751 - 13.6269i) q^{3} +(2.83245 - 4.90594i) q^{4} +(-24.7840 + 3.27931i) q^{5} +73.2395i q^{6} +(-45.1600 + 19.0150i) q^{7} -48.1053i q^{8} +(-83.2953 - 144.272i) q^{9} +(92.2715 - 70.8980i) q^{10} +(21.2220 - 36.7575i) q^{11} +(-44.5686 - 77.1950i) q^{12} -247.023 q^{13} +(137.785 - 181.749i) q^{14} +(-150.301 + 363.529i) q^{15} +(157.274 + 272.406i) q^{16} +(152.237 - 263.681i) q^{17} +(671.521 + 387.703i) q^{18} +(-10.5557 + 6.09436i) q^{19} +(-54.1112 + 130.877i) q^{20} +(-96.1806 + 764.993i) q^{21} +197.558i q^{22} +(32.1169 - 18.5427i) q^{23} +(-655.528 - 378.469i) q^{24} +(603.492 - 162.549i) q^{25} +(995.742 - 574.892i) q^{26} -1346.77 q^{27} +(-34.6268 + 275.411i) q^{28} +1094.49 q^{29} +(-240.175 - 1815.17i) q^{30} +(-502.352 - 290.033i) q^{31} +(-601.362 - 347.196i) q^{32} +(-333.928 - 578.380i) q^{33} +1417.19i q^{34} +(1056.89 - 619.362i) q^{35} -943.718 q^{36} +(-362.484 + 209.280i) q^{37} +(28.3665 - 49.1323i) q^{38} +(-1943.46 + 3366.17i) q^{39} +(157.752 + 1192.24i) q^{40} -1149.43i q^{41} +(-1392.65 - 3307.50i) q^{42} +354.717i q^{43} +(-120.220 - 208.227i) q^{44} +(2537.50 + 3302.48i) q^{45} +(-86.3081 + 149.490i) q^{46} +(-426.210 - 738.218i) q^{47} +4949.41 q^{48} +(1677.86 - 1717.44i) q^{49} +(-2054.36 + 2059.72i) q^{50} +(-2395.44 - 4149.03i) q^{51} +(-699.680 + 1211.88i) q^{52} +(-2944.64 - 1700.09i) q^{53} +(5428.78 - 3134.31i) q^{54} +(-405.426 + 980.591i) q^{55} +(914.724 + 2172.44i) q^{56} +191.790i q^{57} +(-4411.87 + 2547.19i) q^{58} +(-4396.62 - 2538.39i) q^{59} +(1357.73 + 1767.05i) q^{60} +(165.555 - 95.5833i) q^{61} +2699.95 q^{62} +(6504.95 + 4931.45i) q^{63} -1800.67 q^{64} +(6122.22 - 810.065i) q^{65} +(2692.10 + 1554.29i) q^{66} +(1485.00 + 857.362i) q^{67} +(-862.404 - 1493.73i) q^{68} -583.540i q^{69} +(-2818.86 + 4956.30i) q^{70} -1021.27 q^{71} +(-6940.24 + 4006.95i) q^{72} +(-3355.88 + 5812.56i) q^{73} +(974.106 - 1687.20i) q^{74} +(2532.94 - 9502.60i) q^{75} +69.0477i q^{76} +(-259.439 + 2063.51i) q^{77} -18091.9i q^{78} +(276.955 + 479.700i) q^{79} +(-4791.17 - 6235.56i) q^{80} +(-3848.81 + 6666.33i) q^{81} +(2675.05 + 4633.33i) q^{82} +5185.78 q^{83} +(3480.58 + 2638.66i) q^{84} +(-2908.34 + 7034.31i) q^{85} +(-825.526 - 1429.85i) q^{86} +(8610.94 - 14914.6i) q^{87} +(-1768.23 - 1020.89i) q^{88} +(-8123.42 + 4690.06i) q^{89} +(-17914.4 - 7406.70i) q^{90} +(11155.6 - 4697.15i) q^{91} -210.085i q^{92} +(-7904.52 + 4563.68i) q^{93} +(3436.08 + 1983.82i) q^{94} +(241.628 - 185.658i) q^{95} +(-9462.43 + 5463.14i) q^{96} +333.185 q^{97} +(-2766.42 + 10827.8i) q^{98} -7070.76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.03096 + 2.32728i −1.00774 + 0.581820i −0.910529 0.413444i \(-0.864326\pi\)
−0.0972115 + 0.995264i \(0.530992\pi\)
\(3\) 7.86751 13.6269i 0.874167 1.51410i 0.0165205 0.999864i \(-0.494741\pi\)
0.857647 0.514239i \(-0.171926\pi\)
\(4\) 2.83245 4.90594i 0.177028 0.306621i
\(5\) −24.7840 + 3.27931i −0.991360 + 0.131172i
\(6\) 73.2395i 2.03443i
\(7\) −45.1600 + 19.0150i −0.921633 + 0.388062i
\(8\) 48.1053i 0.751646i
\(9\) −83.2953 144.272i −1.02834 1.78113i
\(10\) 92.2715 70.8980i 0.922715 0.708980i
\(11\) 21.2220 36.7575i 0.175388 0.303781i −0.764907 0.644140i \(-0.777215\pi\)
0.940296 + 0.340359i \(0.110549\pi\)
\(12\) −44.5686 77.1950i −0.309504 0.536077i
\(13\) −247.023 −1.46168 −0.730838 0.682551i \(-0.760870\pi\)
−0.730838 + 0.682551i \(0.760870\pi\)
\(14\) 137.785 181.749i 0.702986 0.927290i
\(15\) −150.301 + 363.529i −0.668006 + 1.61569i
\(16\) 157.274 + 272.406i 0.614350 + 1.06409i
\(17\) 152.237 263.681i 0.526770 0.912393i −0.472743 0.881200i \(-0.656736\pi\)
0.999513 0.0311923i \(-0.00993044\pi\)
\(18\) 671.521 + 387.703i 2.07260 + 1.19661i
\(19\) −10.5557 + 6.09436i −0.0292403 + 0.0168819i −0.514549 0.857461i \(-0.672041\pi\)
0.485309 + 0.874343i \(0.338707\pi\)
\(20\) −54.1112 + 130.877i −0.135278 + 0.327193i
\(21\) −96.1806 + 764.993i −0.218097 + 1.73468i
\(22\) 197.558i 0.408177i
\(23\) 32.1169 18.5427i 0.0607126 0.0350524i −0.469336 0.883019i \(-0.655507\pi\)
0.530049 + 0.847967i \(0.322174\pi\)
\(24\) −655.528 378.469i −1.13807 0.657064i
\(25\) 603.492 162.549i 0.965588 0.260078i
\(26\) 995.742 574.892i 1.47299 0.850431i
\(27\) −1346.77 −1.84742
\(28\) −34.6268 + 275.411i −0.0441668 + 0.351290i
\(29\) 1094.49 1.30142 0.650710 0.759326i \(-0.274471\pi\)
0.650710 + 0.759326i \(0.274471\pi\)
\(30\) −240.175 1815.17i −0.266861 2.01685i
\(31\) −502.352 290.033i −0.522739 0.301803i 0.215316 0.976545i \(-0.430922\pi\)
−0.738055 + 0.674741i \(0.764255\pi\)
\(32\) −601.362 347.196i −0.587267 0.339059i
\(33\) −333.928 578.380i −0.306637 0.531111i
\(34\) 1417.19i 1.22594i
\(35\) 1056.89 619.362i 0.862767 0.505602i
\(36\) −943.718 −0.728178
\(37\) −362.484 + 209.280i −0.264780 + 0.152871i −0.626513 0.779411i \(-0.715518\pi\)
0.361733 + 0.932282i \(0.382185\pi\)
\(38\) 28.3665 49.1323i 0.0196444 0.0340251i
\(39\) −1943.46 + 3366.17i −1.27775 + 2.21313i
\(40\) 157.752 + 1192.24i 0.0985952 + 0.745151i
\(41\) 1149.43i 0.683780i −0.939740 0.341890i \(-0.888933\pi\)
0.939740 0.341890i \(-0.111067\pi\)
\(42\) −1392.65 3307.50i −0.789485 1.87500i
\(43\) 354.717i 0.191843i 0.995389 + 0.0959214i \(0.0305798\pi\)
−0.995389 + 0.0959214i \(0.969420\pi\)
\(44\) −120.220 208.227i −0.0620972 0.107555i
\(45\) 2537.50 + 3302.48i 1.25309 + 1.63085i
\(46\) −86.3081 + 149.490i −0.0407883 + 0.0706475i
\(47\) −426.210 738.218i −0.192943 0.334186i 0.753282 0.657698i \(-0.228470\pi\)
−0.946224 + 0.323512i \(0.895136\pi\)
\(48\) 4949.41 2.14818
\(49\) 1677.86 1717.44i 0.698816 0.715301i
\(50\) −2054.36 + 2059.72i −0.821744 + 0.823889i
\(51\) −2395.44 4149.03i −0.920971 1.59517i
\(52\) −699.680 + 1211.88i −0.258757 + 0.448181i
\(53\) −2944.64 1700.09i −1.04829 0.605229i −0.126118 0.992015i \(-0.540252\pi\)
−0.922169 + 0.386787i \(0.873585\pi\)
\(54\) 5428.78 3134.31i 1.86172 1.07487i
\(55\) −405.426 + 980.591i −0.134025 + 0.324162i
\(56\) 914.724 + 2172.44i 0.291685 + 0.692742i
\(57\) 191.790i 0.0590303i
\(58\) −4411.87 + 2547.19i −1.31149 + 0.757191i
\(59\) −4396.62 2538.39i −1.26303 0.729213i −0.289374 0.957216i \(-0.593447\pi\)
−0.973660 + 0.228003i \(0.926780\pi\)
\(60\) 1357.73 + 1767.05i 0.377148 + 0.490846i
\(61\) 165.555 95.5833i 0.0444921 0.0256875i −0.477589 0.878583i \(-0.658489\pi\)
0.522081 + 0.852896i \(0.325156\pi\)
\(62\) 2699.95 0.702380
\(63\) 6504.95 + 4931.45i 1.63894 + 1.24249i
\(64\) −1800.67 −0.439616
\(65\) 6122.22 810.065i 1.44905 0.191731i
\(66\) 2692.10 + 1554.29i 0.618022 + 0.356815i
\(67\) 1485.00 + 857.362i 0.330808 + 0.190992i 0.656200 0.754587i \(-0.272163\pi\)
−0.325392 + 0.945579i \(0.605496\pi\)
\(68\) −862.404 1493.73i −0.186506 0.323038i
\(69\) 583.540i 0.122567i
\(70\) −2818.86 + 4956.30i −0.575277 + 1.01149i
\(71\) −1021.27 −0.202593 −0.101297 0.994856i \(-0.532299\pi\)
−0.101297 + 0.994856i \(0.532299\pi\)
\(72\) −6940.24 + 4006.95i −1.33878 + 0.772946i
\(73\) −3355.88 + 5812.56i −0.629739 + 1.09074i 0.357865 + 0.933773i \(0.383505\pi\)
−0.987604 + 0.156967i \(0.949828\pi\)
\(74\) 974.106 1687.20i 0.177886 0.308108i
\(75\) 2532.94 9502.60i 0.450301 1.68935i
\(76\) 69.0477i 0.0119542i
\(77\) −259.439 + 2063.51i −0.0437577 + 0.348036i
\(78\) 18091.9i 2.97368i
\(79\) 276.955 + 479.700i 0.0443767 + 0.0768627i 0.887361 0.461076i \(-0.152536\pi\)
−0.842984 + 0.537939i \(0.819203\pi\)
\(80\) −4791.17 6235.56i −0.748621 0.974306i
\(81\) −3848.81 + 6666.33i −0.586619 + 1.01605i
\(82\) 2675.05 + 4633.33i 0.397836 + 0.689073i
\(83\) 5185.78 0.752763 0.376381 0.926465i \(-0.377168\pi\)
0.376381 + 0.926465i \(0.377168\pi\)
\(84\) 3480.58 + 2638.66i 0.493280 + 0.373959i
\(85\) −2908.34 + 7034.31i −0.402538 + 0.973607i
\(86\) −825.526 1429.85i −0.111618 0.193328i
\(87\) 8610.94 14914.6i 1.13766 1.97048i
\(88\) −1768.23 1020.89i −0.228336 0.131830i
\(89\) −8123.42 + 4690.06i −1.02555 + 0.592104i −0.915708 0.401844i \(-0.868369\pi\)
−0.109847 + 0.993949i \(0.535036\pi\)
\(90\) −17914.4 7406.70i −2.21165 0.914407i
\(91\) 11155.6 4697.15i 1.34713 0.567221i
\(92\) 210.085i 0.0248210i
\(93\) −7904.52 + 4563.68i −0.913923 + 0.527653i
\(94\) 3436.08 + 1983.82i 0.388872 + 0.224516i
\(95\) 241.628 185.658i 0.0267732 0.0205715i
\(96\) −9462.43 + 5463.14i −1.02674 + 0.592788i
\(97\) 333.185 0.0354113 0.0177056 0.999843i \(-0.494364\pi\)
0.0177056 + 0.999843i \(0.494364\pi\)
\(98\) −2766.42 + 10827.8i −0.288049 + 1.12742i
\(99\) −7070.76 −0.721433
\(100\) 911.905 3421.11i 0.0911905 0.342111i
\(101\) 2358.29 + 1361.56i 0.231182 + 0.133473i 0.611117 0.791540i \(-0.290720\pi\)
−0.379935 + 0.925013i \(0.624054\pi\)
\(102\) 19311.9 + 11149.7i 1.85620 + 1.07168i
\(103\) −7799.39 13508.9i −0.735167 1.27335i −0.954650 0.297730i \(-0.903770\pi\)
0.219483 0.975616i \(-0.429563\pi\)
\(104\) 11883.1i 1.09866i
\(105\) −124.911 19275.0i −0.0113298 1.74830i
\(106\) 15826.3 1.40854
\(107\) 4460.99 2575.55i 0.389640 0.224959i −0.292364 0.956307i \(-0.594442\pi\)
0.682004 + 0.731348i \(0.261109\pi\)
\(108\) −3814.66 + 6607.18i −0.327045 + 0.566459i
\(109\) 9316.28 16136.3i 0.784132 1.35816i −0.145384 0.989375i \(-0.546442\pi\)
0.929516 0.368782i \(-0.120225\pi\)
\(110\) −647.853 4896.27i −0.0535415 0.404650i
\(111\) 6586.05i 0.534539i
\(112\) −12282.3 9311.30i −0.979137 0.742291i
\(113\) 3398.92i 0.266185i 0.991104 + 0.133092i \(0.0424907\pi\)
−0.991104 + 0.133092i \(0.957509\pi\)
\(114\) −446.348 773.097i −0.0343450 0.0594873i
\(115\) −735.179 + 564.884i −0.0555901 + 0.0427133i
\(116\) 3100.10 5369.52i 0.230388 0.399043i
\(117\) 20575.9 + 35638.5i 1.50310 + 2.60344i
\(118\) 23630.2 1.69708
\(119\) −1861.10 + 14802.6i −0.131424 + 1.04531i
\(120\) 17487.7 + 7230.30i 1.21442 + 0.502104i
\(121\) 6419.76 + 11119.3i 0.438478 + 0.759466i
\(122\) −444.898 + 770.585i −0.0298910 + 0.0517727i
\(123\) −15663.2 9043.18i −1.03531 0.597738i
\(124\) −2845.77 + 1643.01i −0.185079 + 0.106855i
\(125\) −14423.9 + 6007.64i −0.923129 + 0.384489i
\(126\) −37698.1 4739.68i −2.37453 0.298544i
\(127\) 20807.8i 1.29009i 0.764145 + 0.645044i \(0.223161\pi\)
−0.764145 + 0.645044i \(0.776839\pi\)
\(128\) 16880.2 9745.79i 1.03029 0.594836i
\(129\) 4833.71 + 2790.74i 0.290470 + 0.167703i
\(130\) −22793.2 + 17513.5i −1.34871 + 1.03630i
\(131\) 22650.4 13077.2i 1.31988 0.762032i 0.336169 0.941802i \(-0.390869\pi\)
0.983709 + 0.179770i \(0.0575353\pi\)
\(132\) −3783.33 −0.217133
\(133\) 360.813 475.939i 0.0203976 0.0269059i
\(134\) −7981.28 −0.444491
\(135\) 33378.4 4416.48i 1.83146 0.242331i
\(136\) −12684.5 7323.39i −0.685796 0.395945i
\(137\) −21398.2 12354.2i −1.14008 0.658226i −0.193630 0.981075i \(-0.562026\pi\)
−0.946451 + 0.322849i \(0.895359\pi\)
\(138\) 1358.06 + 2352.23i 0.0713117 + 0.123515i
\(139\) 27975.2i 1.44792i −0.689843 0.723959i \(-0.742320\pi\)
0.689843 0.723959i \(-0.257680\pi\)
\(140\) −44.9701 6939.35i −0.00229440 0.354048i
\(141\) −13412.8 −0.674657
\(142\) 4116.71 2376.78i 0.204161 0.117873i
\(143\) −5242.32 + 9079.96i −0.256361 + 0.444029i
\(144\) 26200.3 45380.3i 1.26352 2.18848i
\(145\) −27125.9 + 3589.18i −1.29017 + 0.170710i
\(146\) 31240.3i 1.46558i
\(147\) −10202.8 36376.0i −0.472157 1.68337i
\(148\) 2371.10i 0.108250i
\(149\) 6735.81 + 11666.8i 0.303401 + 0.525506i 0.976904 0.213678i \(-0.0685445\pi\)
−0.673503 + 0.739185i \(0.735211\pi\)
\(150\) 11905.0 + 44199.5i 0.529111 + 1.96442i
\(151\) −5571.47 + 9650.07i −0.244352 + 0.423230i −0.961949 0.273228i \(-0.911909\pi\)
0.717597 + 0.696458i \(0.245242\pi\)
\(152\) 293.171 + 507.787i 0.0126892 + 0.0219783i
\(153\) −50722.4 −2.16679
\(154\) −3756.56 8921.71i −0.158398 0.376189i
\(155\) 13401.4 + 5540.81i 0.557810 + 0.230627i
\(156\) 11009.5 + 19069.0i 0.452395 + 0.783570i
\(157\) 14546.2 25194.8i 0.590134 1.02214i −0.404080 0.914724i \(-0.632408\pi\)
0.994214 0.107418i \(-0.0342585\pi\)
\(158\) −2232.79 1289.10i −0.0894404 0.0516385i
\(159\) −46333.9 + 26750.9i −1.83276 + 1.05814i
\(160\) 16042.7 + 6632.86i 0.626668 + 0.259096i
\(161\) −1097.81 + 1448.09i −0.0423522 + 0.0558657i
\(162\) 35829.0i 1.36522i
\(163\) −162.453 + 93.7920i −0.00611437 + 0.00353013i −0.503054 0.864255i \(-0.667790\pi\)
0.496940 + 0.867785i \(0.334457\pi\)
\(164\) −5639.05 3255.71i −0.209661 0.121048i
\(165\) 10172.8 + 13239.5i 0.373655 + 0.486300i
\(166\) −20903.7 + 12068.8i −0.758590 + 0.437972i
\(167\) 24709.4 0.885992 0.442996 0.896524i \(-0.353916\pi\)
0.442996 + 0.896524i \(0.353916\pi\)
\(168\) 36800.3 + 4626.80i 1.30386 + 0.163931i
\(169\) 32459.5 1.13650
\(170\) −4647.39 35123.6i −0.160810 1.21535i
\(171\) 1758.49 + 1015.26i 0.0601377 + 0.0347205i
\(172\) 1740.22 + 1004.72i 0.0588231 + 0.0339615i
\(173\) 20561.5 + 35613.6i 0.687009 + 1.18993i 0.972801 + 0.231643i \(0.0744101\pi\)
−0.285792 + 0.958292i \(0.592257\pi\)
\(174\) 80160.2i 2.64765i
\(175\) −24162.9 + 18816.1i −0.788991 + 0.614404i
\(176\) 13350.6 0.430999
\(177\) −69180.9 + 39941.6i −2.20821 + 1.27491i
\(178\) 21830.1 37810.9i 0.688996 1.19338i
\(179\) −5988.39 + 10372.2i −0.186898 + 0.323716i −0.944214 0.329332i \(-0.893177\pi\)
0.757317 + 0.653048i \(0.226510\pi\)
\(180\) 23389.1 3094.74i 0.721886 0.0955168i
\(181\) 9776.20i 0.298410i −0.988806 0.149205i \(-0.952329\pi\)
0.988806 0.149205i \(-0.0476714\pi\)
\(182\) −34036.1 + 44896.2i −1.02754 + 1.35540i
\(183\) 3008.01i 0.0898208i
\(184\) −892.004 1545.00i −0.0263470 0.0456343i
\(185\) 8297.50 6375.49i 0.242440 0.186282i
\(186\) 21241.9 36792.0i 0.613998 1.06348i
\(187\) −6461.52 11191.7i −0.184778 0.320046i
\(188\) −4828.87 −0.136625
\(189\) 60820.2 25608.9i 1.70265 0.716914i
\(190\) −541.916 + 1310.72i −0.0150115 + 0.0363079i
\(191\) −5536.64 9589.74i −0.151768 0.262869i 0.780110 0.625643i \(-0.215163\pi\)
−0.931877 + 0.362773i \(0.881830\pi\)
\(192\) −14166.8 + 24537.6i −0.384298 + 0.665624i
\(193\) 53200.5 + 30715.3i 1.42824 + 0.824595i 0.996982 0.0776335i \(-0.0247364\pi\)
0.431258 + 0.902228i \(0.358070\pi\)
\(194\) −1343.05 + 775.413i −0.0356854 + 0.0206030i
\(195\) 37127.9 89800.2i 0.976408 2.36161i
\(196\) −3673.21 13096.0i −0.0956167 0.340900i
\(197\) 39953.3i 1.02949i −0.857344 0.514743i \(-0.827887\pi\)
0.857344 0.514743i \(-0.172113\pi\)
\(198\) 28502.0 16455.6i 0.727017 0.419744i
\(199\) −63018.9 36384.0i −1.59135 0.918764i −0.993076 0.117470i \(-0.962522\pi\)
−0.598270 0.801295i \(-0.704145\pi\)
\(200\) −7819.46 29031.2i −0.195487 0.725780i
\(201\) 23366.4 13490.6i 0.578363 0.333918i
\(202\) −12674.9 −0.310629
\(203\) −49427.4 + 20811.8i −1.19943 + 0.505031i
\(204\) −27139.9 −0.652150
\(205\) 3769.35 + 28487.6i 0.0896930 + 0.677872i
\(206\) 62878.1 + 36302.7i 1.48172 + 0.855469i
\(207\) −5350.38 3089.05i −0.124866 0.0720914i
\(208\) −38850.2 67290.6i −0.897981 1.55535i
\(209\) 517.337i 0.0118435i
\(210\) 45361.8 + 77406.1i 1.02861 + 1.75524i
\(211\) −55326.3 −1.24270 −0.621350 0.783533i \(-0.713416\pi\)
−0.621350 + 0.783533i \(0.713416\pi\)
\(212\) −16681.1 + 9630.81i −0.371152 + 0.214285i
\(213\) −8034.87 + 13916.8i −0.177100 + 0.306747i
\(214\) −11988.1 + 20763.9i −0.261771 + 0.453400i
\(215\) −1163.23 8791.31i −0.0251645 0.190185i
\(216\) 64786.9i 1.38861i
\(217\) 28201.2 + 3545.67i 0.598892 + 0.0752971i
\(218\) 86726.3i 1.82489i
\(219\) 52804.8 + 91460.6i 1.10100 + 1.90698i
\(220\) 3662.38 + 4766.47i 0.0756689 + 0.0984807i
\(221\) −37606.0 + 65135.4i −0.769967 + 1.33362i
\(222\) −15327.6 26548.1i −0.311005 0.538677i
\(223\) 245.690 0.00494058 0.00247029 0.999997i \(-0.499214\pi\)
0.00247029 + 0.999997i \(0.499214\pi\)
\(224\) 33759.5 + 4244.49i 0.672821 + 0.0845920i
\(225\) −73719.3 73527.3i −1.45618 1.45239i
\(226\) −7910.22 13700.9i −0.154872 0.268245i
\(227\) 38803.7 67210.0i 0.753046 1.30431i −0.193294 0.981141i \(-0.561917\pi\)
0.946340 0.323173i \(-0.104750\pi\)
\(228\) 940.908 + 543.234i 0.0181000 + 0.0104500i
\(229\) 74555.2 43044.5i 1.42170 0.820817i 0.425253 0.905074i \(-0.360185\pi\)
0.996444 + 0.0842572i \(0.0268517\pi\)
\(230\) 1648.84 3987.99i 0.0311689 0.0753874i
\(231\) 26078.1 + 19770.0i 0.488711 + 0.370496i
\(232\) 52651.0i 0.978207i
\(233\) 33227.4 19183.9i 0.612047 0.353365i −0.161719 0.986837i \(-0.551704\pi\)
0.773766 + 0.633471i \(0.218371\pi\)
\(234\) −165881. 95771.6i −3.02946 1.74906i
\(235\) 12984.0 + 16898.3i 0.235112 + 0.305990i
\(236\) −24906.4 + 14379.7i −0.447184 + 0.258182i
\(237\) 8715.78 0.155171
\(238\) −26947.9 64000.2i −0.475741 1.12987i
\(239\) −15743.1 −0.275610 −0.137805 0.990459i \(-0.544005\pi\)
−0.137805 + 0.990459i \(0.544005\pi\)
\(240\) −122666. + 16230.6i −2.12962 + 0.281782i
\(241\) 63240.2 + 36511.7i 1.08883 + 0.628635i 0.933264 0.359191i \(-0.116947\pi\)
0.155563 + 0.987826i \(0.450281\pi\)
\(242\) −51755.6 29881.1i −0.883745 0.510230i
\(243\) 6016.80 + 10421.4i 0.101895 + 0.176487i
\(244\) 1082.94i 0.0181896i
\(245\) −35952.0 + 48067.2i −0.598950 + 0.800786i
\(246\) 84184.0 1.39110
\(247\) 2607.51 1505.45i 0.0427398 0.0246758i
\(248\) −13952.1 + 24165.8i −0.226849 + 0.392915i
\(249\) 40799.2 70666.3i 0.658041 1.13976i
\(250\) 44160.8 57785.0i 0.706572 0.924560i
\(251\) 47793.8i 0.758620i −0.925270 0.379310i \(-0.876161\pi\)
0.925270 0.379310i \(-0.123839\pi\)
\(252\) 42618.3 17944.8i 0.671113 0.282578i
\(253\) 1574.05i 0.0245911i
\(254\) −48425.6 83875.6i −0.750598 1.30007i
\(255\) 72974.6 + 94974.1i 1.12225 + 1.46058i
\(256\) −30957.0 + 53619.1i −0.472366 + 0.818163i
\(257\) 17844.1 + 30906.9i 0.270165 + 0.467939i 0.968904 0.247438i \(-0.0795886\pi\)
−0.698739 + 0.715376i \(0.746255\pi\)
\(258\) −25979.3 −0.390291
\(259\) 12390.3 16343.7i 0.184707 0.243642i
\(260\) 13366.7 32329.7i 0.197733 0.478250i
\(261\) −91166.3 157905.i −1.33830 2.31800i
\(262\) −60868.7 + 105428.i −0.886730 + 1.53586i
\(263\) 11718.3 + 6765.57i 0.169416 + 0.0978122i 0.582310 0.812967i \(-0.302149\pi\)
−0.412895 + 0.910779i \(0.635482\pi\)
\(264\) −27823.2 + 16063.7i −0.399208 + 0.230483i
\(265\) 78555.0 + 32478.6i 1.11862 + 0.462493i
\(266\) −346.782 + 2758.20i −0.00490109 + 0.0389819i
\(267\) 147596.i 2.07039i
\(268\) 8412.34 4856.87i 0.117124 0.0676218i
\(269\) 37550.5 + 21679.8i 0.518933 + 0.299606i 0.736498 0.676440i \(-0.236478\pi\)
−0.217565 + 0.976046i \(0.569811\pi\)
\(270\) −124269. + 95483.4i −1.70464 + 1.30979i
\(271\) −9881.32 + 5704.99i −0.134548 + 0.0776812i −0.565763 0.824568i \(-0.691418\pi\)
0.431215 + 0.902249i \(0.358085\pi\)
\(272\) 95771.2 1.29449
\(273\) 23758.8 188971.i 0.318786 2.53554i
\(274\) 115007. 1.53187
\(275\) 6832.40 25632.5i 0.0903458 0.338942i
\(276\) −2862.81 1652.85i −0.0375816 0.0216977i
\(277\) 46200.6 + 26673.9i 0.602127 + 0.347638i 0.769878 0.638191i \(-0.220317\pi\)
−0.167751 + 0.985829i \(0.553650\pi\)
\(278\) 65106.1 + 112767.i 0.842427 + 1.45913i
\(279\) 96633.6i 1.24142i
\(280\) −29794.6 50842.0i −0.380033 0.648495i
\(281\) −109120. −1.38195 −0.690975 0.722878i \(-0.742819\pi\)
−0.690975 + 0.722878i \(0.742819\pi\)
\(282\) 54066.7 31215.4i 0.679879 0.392528i
\(283\) −23560.8 + 40808.6i −0.294183 + 0.509540i −0.974795 0.223104i \(-0.928381\pi\)
0.680611 + 0.732645i \(0.261714\pi\)
\(284\) −2892.70 + 5010.30i −0.0358646 + 0.0621194i
\(285\) −628.937 4753.31i −0.00774315 0.0585203i
\(286\) 48801.3i 0.596622i
\(287\) 21856.5 + 51908.5i 0.265349 + 0.630194i
\(288\) 115679.i 1.39467i
\(289\) −4591.43 7952.60i −0.0549734 0.0952167i
\(290\) 100991. 77597.4i 1.20084 0.922681i
\(291\) 2621.33 4540.28i 0.0309554 0.0536163i
\(292\) 19010.7 + 32927.5i 0.222963 + 0.386183i
\(293\) −159569. −1.85872 −0.929359 0.369177i \(-0.879640\pi\)
−0.929359 + 0.369177i \(0.879640\pi\)
\(294\) 125784. + 122885.i 1.45523 + 1.42169i
\(295\) 117290. + 48493.6i 1.34777 + 0.557237i
\(296\) 10067.5 + 17437.4i 0.114905 + 0.199021i
\(297\) −28581.1 + 49503.9i −0.324016 + 0.561212i
\(298\) −54303.6 31352.2i −0.611499 0.353049i
\(299\) −7933.63 + 4580.48i −0.0887421 + 0.0512353i
\(300\) −39444.8 39342.0i −0.438275 0.437134i
\(301\) −6744.96 16019.1i −0.0744469 0.176809i
\(302\) 51865.4i 0.568675i
\(303\) 37107.7 21424.1i 0.404183 0.233355i
\(304\) −3320.28 1916.96i −0.0359275 0.0207428i
\(305\) −3789.67 + 2911.84i −0.0407382 + 0.0313017i
\(306\) 204460. 118045.i 2.18356 1.26068i
\(307\) −35369.2 −0.375274 −0.187637 0.982238i \(-0.560083\pi\)
−0.187637 + 0.982238i \(0.560083\pi\)
\(308\) 9388.59 + 7117.57i 0.0989690 + 0.0750292i
\(309\) −245447. −2.57064
\(310\) −66915.5 + 8853.97i −0.696312 + 0.0921329i
\(311\) −118276. 68286.6i −1.22286 0.706017i −0.257331 0.966323i \(-0.582843\pi\)
−0.965526 + 0.260307i \(0.916176\pi\)
\(312\) 161931. + 93490.6i 1.66349 + 0.960415i
\(313\) −22073.3 38232.1i −0.225309 0.390247i 0.731103 0.682267i \(-0.239006\pi\)
−0.956412 + 0.292020i \(0.905673\pi\)
\(314\) 135412.i 1.37341i
\(315\) −177390. 100889.i −1.78776 1.01677i
\(316\) 3137.84 0.0314236
\(317\) 141333. 81598.8i 1.40645 0.812017i 0.411411 0.911450i \(-0.365036\pi\)
0.995044 + 0.0994330i \(0.0317029\pi\)
\(318\) 124514. 215664.i 1.23130 2.13267i
\(319\) 23227.3 40230.9i 0.228254 0.395347i
\(320\) 44627.7 5904.95i 0.435818 0.0576655i
\(321\) 81052.7i 0.786606i
\(322\) 1055.12 8392.13i 0.0101763 0.0809395i
\(323\) 3711.13i 0.0355715i
\(324\) 21803.1 + 37764.0i 0.207696 + 0.359740i
\(325\) −149077. + 40153.3i −1.41138 + 0.380150i
\(326\) 436.560 756.145i 0.00410780 0.00711491i
\(327\) −146592. 253904.i −1.37093 2.37451i
\(328\) −55293.9 −0.513960
\(329\) 33284.9 + 25233.5i 0.307507 + 0.233124i
\(330\) −71818.0 29693.2i −0.659486 0.272665i
\(331\) 104688. + 181324.i 0.955520 + 1.65501i 0.733174 + 0.680041i \(0.238038\pi\)
0.222346 + 0.974968i \(0.428628\pi\)
\(332\) 14688.4 25441.1i 0.133260 0.230813i
\(333\) 60386.4 + 34864.1i 0.544566 + 0.314406i
\(334\) −99602.8 + 57505.7i −0.892850 + 0.515487i
\(335\) −39615.7 16379.1i −0.353002 0.145949i
\(336\) −223515. + 94113.1i −1.97983 + 0.833626i
\(337\) 62550.8i 0.550773i 0.961334 + 0.275387i \(0.0888059\pi\)
−0.961334 + 0.275387i \(0.911194\pi\)
\(338\) −130843. + 75542.2i −1.14529 + 0.661235i
\(339\) 46316.8 + 26741.0i 0.403031 + 0.232690i
\(340\) 26272.2 + 34192.4i 0.227268 + 0.295782i
\(341\) −21321.8 + 12310.1i −0.183364 + 0.105865i
\(342\) −9451.20 −0.0808043
\(343\) −43114.9 + 109464.i −0.366471 + 0.930429i
\(344\) 17063.8 0.144198
\(345\) 1913.61 + 14462.5i 0.0160774 + 0.121508i
\(346\) −165765. 95704.6i −1.38465 0.799431i
\(347\) −127193. 73435.2i −1.05634 0.609881i −0.131926 0.991260i \(-0.542116\pi\)
−0.924419 + 0.381379i \(0.875449\pi\)
\(348\) −48780.0 84489.5i −0.402795 0.697661i
\(349\) 143297.i 1.17648i 0.808685 + 0.588242i \(0.200180\pi\)
−0.808685 + 0.588242i \(0.799820\pi\)
\(350\) 53609.3 132081.i 0.437627 1.07821i
\(351\) 332684. 2.70033
\(352\) −25524.1 + 14736.4i −0.205999 + 0.118934i
\(353\) −12842.2 + 22243.3i −0.103060 + 0.178505i −0.912944 0.408085i \(-0.866197\pi\)
0.809884 + 0.586590i \(0.199530\pi\)
\(354\) 185910. 322006.i 1.48353 2.56956i
\(355\) 25311.2 3349.07i 0.200843 0.0265746i
\(356\) 53137.3i 0.419276i
\(357\) 187072. + 141821.i 1.46782 + 1.11277i
\(358\) 55746.6i 0.434963i
\(359\) −82866.0 143528.i −0.642965 1.11365i −0.984767 0.173876i \(-0.944371\pi\)
0.341802 0.939772i \(-0.388963\pi\)
\(360\) 158867. 122067.i 1.22582 0.941878i
\(361\) −65086.2 + 112733.i −0.499430 + 0.865038i
\(362\) 22751.9 + 39407.5i 0.173621 + 0.300720i
\(363\) 202030. 1.53321
\(364\) 8553.61 68033.0i 0.0645575 0.513472i
\(365\) 64110.9 155063.i 0.481223 1.16392i
\(366\) 7000.47 + 12125.2i 0.0522595 + 0.0905161i
\(367\) −23636.1 + 40939.0i −0.175487 + 0.303952i −0.940330 0.340265i \(-0.889483\pi\)
0.764843 + 0.644217i \(0.222817\pi\)
\(368\) 10102.3 + 5832.56i 0.0745975 + 0.0430689i
\(369\) −165831. + 95742.5i −1.21790 + 0.703156i
\(370\) −18609.4 + 45010.0i −0.135934 + 0.328780i
\(371\) 165307. + 20783.6i 1.20100 + 0.150999i
\(372\) 51705.5i 0.373638i
\(373\) −11241.1 + 6490.06i −0.0807963 + 0.0466478i −0.539854 0.841759i \(-0.681521\pi\)
0.459058 + 0.888407i \(0.348187\pi\)
\(374\) 52092.3 + 30075.5i 0.372418 + 0.215015i
\(375\) −31614.4 + 243819.i −0.224814 + 1.73382i
\(376\) −35512.2 + 20503.0i −0.251190 + 0.145025i
\(377\) −270365. −1.90225
\(378\) −185565. + 244774.i −1.29871 + 1.71310i
\(379\) −92246.9 −0.642204 −0.321102 0.947045i \(-0.604053\pi\)
−0.321102 + 0.947045i \(0.604053\pi\)
\(380\) −226.429 1711.28i −0.00156807 0.0118510i
\(381\) 283547. + 163706.i 1.95333 + 1.12775i
\(382\) 44636.0 + 25770.6i 0.305885 + 0.176603i
\(383\) 59350.3 + 102798.i 0.404599 + 0.700787i 0.994275 0.106854i \(-0.0340776\pi\)
−0.589675 + 0.807640i \(0.700744\pi\)
\(384\) 306700.i 2.07995i
\(385\) −336.937 51992.7i −0.00227314 0.350769i
\(386\) −285933. −1.91906
\(387\) 51175.7 29546.3i 0.341698 0.197279i
\(388\) 943.727 1634.58i 0.00626878 0.0108578i
\(389\) 131252. 227335.i 0.867374 1.50234i 0.00270360 0.999996i \(-0.499139\pi\)
0.864670 0.502340i \(-0.167527\pi\)
\(390\) 59328.8 + 448388.i 0.390064 + 2.94798i
\(391\) 11291.5i 0.0738582i
\(392\) −82618.0 80713.9i −0.537653 0.525262i
\(393\) 411541.i 2.66457i
\(394\) 92982.5 + 161050.i 0.598975 + 1.03746i
\(395\) −8437.13 10980.7i −0.0540755 0.0703776i
\(396\) −20027.6 + 34688.7i −0.127714 + 0.221207i
\(397\) 64554.8 + 111812.i 0.409588 + 0.709428i 0.994844 0.101422i \(-0.0323391\pi\)
−0.585255 + 0.810849i \(0.699006\pi\)
\(398\) 338703. 2.13822
\(399\) −3646.88 8661.22i −0.0229074 0.0544043i
\(400\) 139193. + 138830.i 0.869954 + 0.867689i
\(401\) 79376.2 + 137484.i 0.493630 + 0.854992i 0.999973 0.00733998i \(-0.00233641\pi\)
−0.506343 + 0.862332i \(0.669003\pi\)
\(402\) −62792.8 + 108760.i −0.388560 + 0.673005i
\(403\) 124093. + 71644.9i 0.764075 + 0.441139i
\(404\) 13359.4 7713.08i 0.0818513 0.0472569i
\(405\) 73527.8 177840.i 0.448272 1.08422i
\(406\) 150805. 198923.i 0.914879 1.20679i
\(407\) 17765.3i 0.107247i
\(408\) −199591. + 115234.i −1.19900 + 0.692244i
\(409\) −203623. 117562.i −1.21725 0.702780i −0.252922 0.967487i \(-0.581392\pi\)
−0.964329 + 0.264707i \(0.914725\pi\)
\(410\) −81492.6 106060.i −0.484786 0.630934i
\(411\) −336701. + 194394.i −1.99324 + 1.15080i
\(412\) −88365.4 −0.520580
\(413\) 246819. + 31031.9i 1.44703 + 0.181932i
\(414\) 28756.3 0.167777
\(415\) −128524. + 17005.8i −0.746259 + 0.0987417i
\(416\) 148550. + 85765.5i 0.858394 + 0.495594i
\(417\) −381216. 220095.i −2.19230 1.26572i
\(418\) −1203.99 2085.37i −0.00689079 0.0119352i
\(419\) 120989.i 0.689157i −0.938757 0.344579i \(-0.888022\pi\)
0.938757 0.344579i \(-0.111978\pi\)
\(420\) −94915.7 53982.6i −0.538071 0.306024i
\(421\) 182388. 1.02904 0.514519 0.857479i \(-0.327970\pi\)
0.514519 + 0.857479i \(0.327970\pi\)
\(422\) 223018. 128760.i 1.25232 0.723027i
\(423\) −71002.7 + 122980.i −0.396820 + 0.687313i
\(424\) −81783.3 + 141653.i −0.454918 + 0.787941i
\(425\) 49012.5 183876.i 0.271349 1.01800i
\(426\) 74797.5i 0.412162i
\(427\) −5658.95 + 7464.58i −0.0310370 + 0.0409402i
\(428\) 29180.5i 0.159296i
\(429\) 82487.9 + 142873.i 0.448204 + 0.776312i
\(430\) 25148.8 + 32730.3i 0.136013 + 0.177016i
\(431\) 133916. 231949.i 0.720905 1.24864i −0.239732 0.970839i \(-0.577060\pi\)
0.960637 0.277805i \(-0.0896070\pi\)
\(432\) −211812. 366868.i −1.13496 1.96582i
\(433\) 86077.3 0.459106 0.229553 0.973296i \(-0.426274\pi\)
0.229553 + 0.973296i \(0.426274\pi\)
\(434\) −121930. + 51339.6i −0.647337 + 0.272567i
\(435\) −164504. + 397881.i −0.869356 + 2.10269i
\(436\) −52775.7 91410.2i −0.277627 0.480863i
\(437\) −226.012 + 391.464i −0.00118350 + 0.00204988i
\(438\) −425709. 245783.i −2.21904 1.28116i
\(439\) 157393. 90871.0i 0.816689 0.471516i −0.0325841 0.999469i \(-0.510374\pi\)
0.849273 + 0.527953i \(0.177040\pi\)
\(440\) 47171.7 + 19503.1i 0.243655 + 0.100739i
\(441\) −387536. 99012.8i −1.99267 0.509113i
\(442\) 350078.i 1.79193i
\(443\) −89816.0 + 51855.3i −0.457663 + 0.264232i −0.711061 0.703130i \(-0.751785\pi\)
0.253398 + 0.967362i \(0.418452\pi\)
\(444\) 32310.8 + 18654.6i 0.163901 + 0.0946283i
\(445\) 185951. 142878.i 0.939026 0.721513i
\(446\) −990.369 + 571.790i −0.00497883 + 0.00287453i
\(447\) 211976. 1.06089
\(448\) 81318.2 34239.7i 0.405165 0.170598i
\(449\) 122949. 0.609865 0.304933 0.952374i \(-0.401366\pi\)
0.304933 + 0.952374i \(0.401366\pi\)
\(450\) 468278. + 124821.i 2.31249 + 0.616399i
\(451\) −42250.3 24393.2i −0.207719 0.119927i
\(452\) 16674.9 + 9627.24i 0.0816180 + 0.0471222i
\(453\) 87667.1 + 151844.i 0.427209 + 0.739948i
\(454\) 361228.i 1.75255i
\(455\) −261076. + 152997.i −1.26109 + 0.739026i
\(456\) 9226.10 0.0443699
\(457\) 71816.8 41463.5i 0.343870 0.198533i −0.318112 0.948053i \(-0.603049\pi\)
0.661982 + 0.749520i \(0.269716\pi\)
\(458\) −200353. + 347021.i −0.955135 + 1.65434i
\(459\) −205028. + 355118.i −0.973167 + 1.68557i
\(460\) 688.934 + 5206.75i 0.00325583 + 0.0246065i
\(461\) 38947.3i 0.183263i −0.995793 0.0916316i \(-0.970792\pi\)
0.995793 0.0916316i \(-0.0292082\pi\)
\(462\) −151130. 19001.2i −0.708056 0.0890220i
\(463\) 421547.i 1.96646i −0.182378 0.983229i \(-0.558379\pi\)
0.182378 0.983229i \(-0.441621\pi\)
\(464\) 172135. + 298147.i 0.799527 + 1.38482i
\(465\) 180940. 139027.i 0.836812 0.642976i
\(466\) −89292.3 + 154659.i −0.411190 + 0.712202i
\(467\) 14660.4 + 25392.6i 0.0672223 + 0.116432i 0.897678 0.440653i \(-0.145253\pi\)
−0.830455 + 0.557085i \(0.811920\pi\)
\(468\) 233120. 1.06436
\(469\) −83365.2 10481.3i −0.379000 0.0476507i
\(470\) −91665.2 37899.0i −0.414963 0.171566i
\(471\) −228885. 396440.i −1.03175 1.78705i
\(472\) −122110. + 211501.i −0.548110 + 0.949354i
\(473\) 13038.5 + 7527.80i 0.0582782 + 0.0336470i
\(474\) −35133.0 + 20284.0i −0.156372 + 0.0902813i
\(475\) −5379.67 + 5393.72i −0.0238434 + 0.0239057i
\(476\) 67349.4 + 51058.1i 0.297249 + 0.225347i
\(477\) 566437.i 2.48952i
\(478\) 63460.0 36638.7i 0.277744 0.160356i
\(479\) −100876. 58240.8i −0.439660 0.253838i 0.263793 0.964579i \(-0.415026\pi\)
−0.703453 + 0.710741i \(0.748360\pi\)
\(480\) 216602. 166429.i 0.940111 0.722346i
\(481\) 89541.9 51697.0i 0.387022 0.223448i
\(482\) −339892. −1.46301
\(483\) 11096.0 + 26352.7i 0.0475635 + 0.112962i
\(484\) 72734.5 0.310491
\(485\) −8257.64 + 1092.62i −0.0351053 + 0.00464498i
\(486\) −48507.0 28005.5i −0.205368 0.118569i
\(487\) −182358. 105284.i −0.768895 0.443922i 0.0635854 0.997976i \(-0.479746\pi\)
−0.832480 + 0.554055i \(0.813080\pi\)
\(488\) −4598.06 7964.08i −0.0193079 0.0334423i
\(489\) 2951.64i 0.0123437i
\(490\) 33055.4 277427.i 0.137674 1.15547i
\(491\) −198076. −0.821618 −0.410809 0.911721i \(-0.634754\pi\)
−0.410809 + 0.911721i \(0.634754\pi\)
\(492\) −88730.6 + 51228.6i −0.366558 + 0.211633i
\(493\) 166622. 288598.i 0.685549 1.18741i
\(494\) −7007.19 + 12136.8i −0.0287137 + 0.0497337i
\(495\) 175242. 23187.2i 0.715199 0.0946320i
\(496\) 182458.i 0.741652i
\(497\) 46120.7 19419.5i 0.186717 0.0786187i
\(498\) 379804.i 1.53144i
\(499\) 37817.6 + 65501.9i 0.151877 + 0.263059i 0.931918 0.362670i \(-0.118135\pi\)
−0.780040 + 0.625729i \(0.784802\pi\)
\(500\) −11381.8 + 87779.1i −0.0455271 + 0.351116i
\(501\) 194402. 336713.i 0.774505 1.34148i
\(502\) 111230. + 192655.i 0.441380 + 0.764493i
\(503\) −68106.8 −0.269187 −0.134594 0.990901i \(-0.542973\pi\)
−0.134594 + 0.990901i \(0.542973\pi\)
\(504\) 237229. 312923.i 0.933915 1.23190i
\(505\) −62912.7 26011.3i −0.246692 0.101995i
\(506\) 3663.26 + 6344.95i 0.0143076 + 0.0247815i
\(507\) 255375. 442323.i 0.993488 1.72077i
\(508\) 102082. + 58937.1i 0.395568 + 0.228382i
\(509\) −79228.5 + 45742.6i −0.305806 + 0.176557i −0.645048 0.764142i \(-0.723163\pi\)
0.339242 + 0.940699i \(0.389829\pi\)
\(510\) −515189. 213005.i −1.98074 0.818935i
\(511\) 41025.8 326307.i 0.157114 1.24964i
\(512\) 23683.2i 0.0903442i
\(513\) 14216.2 8207.70i 0.0540191 0.0311879i
\(514\) −143858. 83056.4i −0.544512 0.314374i
\(515\) 237600. + 309229.i 0.895843 + 1.16591i
\(516\) 27382.4 15809.3i 0.102842 0.0593761i
\(517\) −36180.1 −0.135359
\(518\) −11908.5 + 94716.7i −0.0443810 + 0.352994i
\(519\) 647071. 2.40224
\(520\) −38968.5 294511.i −0.144114 1.08917i
\(521\) 158501. + 91510.4i 0.583923 + 0.337128i 0.762691 0.646763i \(-0.223878\pi\)
−0.178768 + 0.983891i \(0.557211\pi\)
\(522\) 734976. + 424338.i 2.69732 + 1.55730i
\(523\) 3792.47 + 6568.74i 0.0138649 + 0.0240148i 0.872875 0.487945i \(-0.162253\pi\)
−0.859010 + 0.511959i \(0.828920\pi\)
\(524\) 148162.i 0.539604i
\(525\) 66304.4 + 477301.i 0.240560 + 1.73171i
\(526\) −62981.5 −0.227636
\(527\) −152953. + 88307.3i −0.550726 + 0.317962i
\(528\) 105036. 181928.i 0.376765 0.652576i
\(529\) −139233. + 241158.i −0.497543 + 0.861769i
\(530\) −392239. + 51899.3i −1.39637 + 0.184761i
\(531\) 845744.i 2.99951i
\(532\) −1312.94 3118.20i −0.00463899 0.0110174i
\(533\) 283937.i 0.999464i
\(534\) −343498. 594955.i −1.20460 2.08642i
\(535\) −102115. + 78461.4i −0.356765 + 0.274125i
\(536\) 41243.7 71436.2i 0.143558 0.248650i
\(537\) 94227.3 + 163207.i 0.326760 + 0.565964i
\(538\) −201820. −0.697267
\(539\) −27521.4 98121.3i −0.0947310 0.337742i
\(540\) 72875.4 176262.i 0.249916 0.604464i
\(541\) 131921. + 228494.i 0.450733 + 0.780693i 0.998432 0.0559830i \(-0.0178293\pi\)
−0.547699 + 0.836676i \(0.684496\pi\)
\(542\) 26554.2 45993.2i 0.0903929 0.156565i
\(543\) −133219. 76914.3i −0.451823 0.260860i
\(544\) −183098. + 105712.i −0.618709 + 0.357212i
\(545\) −177979. + 430472.i −0.599204 + 1.44928i
\(546\) 344017. + 817029.i 1.15397 + 2.74064i
\(547\) 232914.i 0.778431i −0.921147 0.389216i \(-0.872746\pi\)
0.921147 0.389216i \(-0.127254\pi\)
\(548\) −121218. + 69985.4i −0.403652 + 0.233049i
\(549\) −27579.9 15923.3i −0.0915058 0.0528309i
\(550\) 32112.7 + 119224.i 0.106158 + 0.394131i
\(551\) −11553.2 + 6670.24i −0.0380539 + 0.0219704i
\(552\) −28071.4 −0.0921268
\(553\) −21628.8 16397.0i −0.0707265 0.0536183i
\(554\) −248311. −0.809051
\(555\) −21597.7 163229.i −0.0701167 0.529920i
\(556\) −137245. 79238.3i −0.443963 0.256322i
\(557\) 394668. + 227862.i 1.27210 + 0.734447i 0.975383 0.220518i \(-0.0707748\pi\)
0.296717 + 0.954965i \(0.404108\pi\)
\(558\) −224893. 389527.i −0.722284 1.25103i
\(559\) 87623.4i 0.280412i
\(560\) 334939. + 190494.i 1.06804 + 0.607442i
\(561\) −203344. −0.646109
\(562\) 439860. 253953.i 1.39265 0.804046i
\(563\) 4036.10 6990.74i 0.0127334 0.0220550i −0.859588 0.510987i \(-0.829280\pi\)
0.872322 + 0.488932i \(0.162613\pi\)
\(564\) −37991.2 + 65802.6i −0.119433 + 0.206864i
\(565\) −11146.1 84238.7i −0.0349161 0.263885i
\(566\) 219330.i 0.684646i
\(567\) 47051.8 374237.i 0.146356 1.16407i
\(568\) 49128.6i 0.152278i
\(569\) −212776. 368539.i −0.657200 1.13830i −0.981337 0.192294i \(-0.938407\pi\)
0.324137 0.946010i \(-0.394926\pi\)
\(570\) 13597.5 + 17696.7i 0.0418513 + 0.0544682i
\(571\) −129907. + 225006.i −0.398438 + 0.690114i −0.993533 0.113540i \(-0.963781\pi\)
0.595096 + 0.803655i \(0.297114\pi\)
\(572\) 29697.2 + 51437.0i 0.0907659 + 0.157211i
\(573\) −174238. −0.530682
\(574\) −208908. 158375.i −0.634062 0.480687i
\(575\) 16368.2 16411.0i 0.0495069 0.0496362i
\(576\) 149987. + 259785.i 0.452074 + 0.783015i
\(577\) 89864.4 155650.i 0.269920 0.467516i −0.698921 0.715199i \(-0.746336\pi\)
0.968841 + 0.247683i \(0.0796692\pi\)
\(578\) 37015.8 + 21371.1i 0.110798 + 0.0639692i
\(579\) 837111. 483306.i 2.49704 1.44167i
\(580\) −59224.4 + 143244.i −0.176054 + 0.425816i
\(581\) −234190. + 98607.8i −0.693771 + 0.292118i
\(582\) 24402.3i 0.0720418i
\(583\) −124982. + 72158.4i −0.367714 + 0.212300i
\(584\) 279615. + 161436.i 0.819851 + 0.473341i
\(585\) −626822. 815789.i −1.83161 2.38378i
\(586\) 643217. 371362.i 1.87311 1.08144i
\(587\) 166789. 0.484050 0.242025 0.970270i \(-0.422188\pi\)
0.242025 + 0.970270i \(0.422188\pi\)
\(588\) −207357. 52978.5i −0.599743 0.153230i
\(589\) 7070.26 0.0203800
\(590\) −585650. + 77490.6i −1.68242 + 0.222610i
\(591\) −544441. 314333.i −1.55875 0.899943i
\(592\) −114018. 65828.5i −0.325335 0.187832i
\(593\) −159004. 275403.i −0.452167 0.783177i 0.546353 0.837555i \(-0.316016\pi\)
−0.998520 + 0.0543780i \(0.982682\pi\)
\(594\) 266065.i 0.754075i
\(595\) −2417.03 372972.i −0.00682728 1.05352i
\(596\) 76315.3 0.214842
\(597\) −991603. + 572503.i −2.78221 + 1.60631i
\(598\) 21320.1 36927.5i 0.0596193 0.103264i
\(599\) 33345.0 57755.3i 0.0929346 0.160967i −0.815810 0.578320i \(-0.803709\pi\)
0.908745 + 0.417352i \(0.137042\pi\)
\(600\) −457126. 121848.i −1.26979 0.338467i
\(601\) 274568.i 0.760154i −0.924955 0.380077i \(-0.875897\pi\)
0.924955 0.380077i \(-0.124103\pi\)
\(602\) 64469.5 + 48874.8i 0.177894 + 0.134863i
\(603\) 285657.i 0.785616i
\(604\) 31561.8 + 54666.6i 0.0865142 + 0.149847i
\(605\) −195571. 254529.i −0.534310 0.695388i
\(606\) −99719.8 + 172720.i −0.271541 + 0.470324i
\(607\) 74923.8 + 129772.i 0.203349 + 0.352211i 0.949605 0.313448i \(-0.101484\pi\)
−0.746256 + 0.665659i \(0.768151\pi\)
\(608\) 8463.75 0.0228958
\(609\) −105269. + 837280.i −0.283835 + 2.25754i
\(610\) 8499.35 20557.1i 0.0228416 0.0552463i
\(611\) 105284. + 182357.i 0.282020 + 0.488472i
\(612\) −143668. + 248841.i −0.383582 + 0.664384i
\(613\) 212122. + 122469.i 0.564500 + 0.325914i 0.754950 0.655783i \(-0.227661\pi\)
−0.190449 + 0.981697i \(0.560995\pi\)
\(614\) 142572. 82313.9i 0.378179 0.218342i
\(615\) 417853. + 172761.i 1.10477 + 0.456769i
\(616\) 99265.7 + 12480.4i 0.261600 + 0.0328903i
\(617\) 316663.i 0.831816i 0.909407 + 0.415908i \(0.136536\pi\)
−0.909407 + 0.415908i \(0.863464\pi\)
\(618\) 989388. 571223.i 2.59054 1.49565i
\(619\) 29834.0 + 17224.7i 0.0778630 + 0.0449542i 0.538426 0.842673i \(-0.319019\pi\)
−0.460563 + 0.887627i \(0.652352\pi\)
\(620\) 65141.6 50052.4i 0.169463 0.130209i
\(621\) −43254.2 + 24972.8i −0.112162 + 0.0647566i
\(622\) 635688. 1.64310
\(623\) 277672. 366270.i 0.715412 0.943682i
\(624\) −1.22262e6 −3.13994
\(625\) 337781. 196194.i 0.864719 0.502256i
\(626\) 177954. + 102742.i 0.454107 + 0.262179i
\(627\) 7049.71 + 4070.15i 0.0179323 + 0.0103532i
\(628\) −82402.7 142726.i −0.208940 0.361895i
\(629\) 127440.i 0.322111i
\(630\) 949852. 6155.48i 2.39318 0.0155089i
\(631\) 70700.7 0.177568 0.0887840 0.996051i \(-0.471702\pi\)
0.0887840 + 0.996051i \(0.471702\pi\)
\(632\) 23076.1 13323.0i 0.0577735 0.0333556i
\(633\) −435280. + 753927.i −1.08633 + 1.88158i
\(634\) −379806. + 657843.i −0.944895 + 1.63661i
\(635\) −68235.3 515701.i −0.169224 1.27894i
\(636\) 303082.i 0.749283i
\(637\) −414470. + 424247.i −1.02144 + 1.04554i
\(638\) 216226.i 0.531209i
\(639\) 85067.2 + 147341.i 0.208334 + 0.360845i
\(640\) −386399. + 296895.i −0.943358 + 0.724842i
\(641\) −45782.4 + 79297.5i −0.111425 + 0.192994i −0.916345 0.400390i \(-0.868875\pi\)
0.804920 + 0.593383i \(0.202208\pi\)
\(642\) 188632. + 326721.i 0.457663 + 0.792696i
\(643\) −578869. −1.40010 −0.700049 0.714095i \(-0.746839\pi\)
−0.700049 + 0.714095i \(0.746839\pi\)
\(644\) 3994.77 + 9487.45i 0.00963209 + 0.0228759i
\(645\) −128950. 53314.5i −0.309958 0.128152i
\(646\) −8636.84 14959.4i −0.0206962 0.0358468i
\(647\) 175425. 303844.i 0.419066 0.725843i −0.576780 0.816900i \(-0.695691\pi\)
0.995846 + 0.0910563i \(0.0290243\pi\)
\(648\) 320686. + 185148.i 0.763712 + 0.440930i
\(649\) −186610. + 107739.i −0.443042 + 0.255791i
\(650\) 507474. 508799.i 1.20112 1.20426i
\(651\) 270190. 356400.i 0.637539 0.840962i
\(652\) 1062.64i 0.00249973i
\(653\) −433487. + 250274.i −1.01660 + 0.586934i −0.913117 0.407698i \(-0.866332\pi\)
−0.103482 + 0.994631i \(0.532998\pi\)
\(654\) 1.18181e6 + 682319.i 2.76308 + 1.59526i
\(655\) −518484. + 398384.i −1.20852 + 0.928579i
\(656\) 313113. 180776.i 0.727600 0.420080i
\(657\) 1.11812e6 2.59034
\(658\) −192896. 24252.3i −0.445524 0.0560145i
\(659\) 300083. 0.690987 0.345494 0.938421i \(-0.387712\pi\)
0.345494 + 0.938421i \(0.387712\pi\)
\(660\) 93766.0 12406.7i 0.215257 0.0284819i
\(661\) 127498. + 73610.9i 0.291810 + 0.168476i 0.638758 0.769408i \(-0.279449\pi\)
−0.346948 + 0.937884i \(0.612782\pi\)
\(662\) −843985. 487275.i −1.92583 1.11188i
\(663\) 591730. + 1.02491e6i 1.34616 + 2.33162i
\(664\) 249464.i 0.565811i
\(665\) −7381.63 + 12978.9i −0.0166920 + 0.0293490i
\(666\) −324554. −0.731709
\(667\) 35151.8 20294.9i 0.0790125 0.0456179i
\(668\) 69988.1 121223.i 0.156845 0.271664i
\(669\) 1932.97 3348.00i 0.00431890 0.00748055i
\(670\) 197808. 26173.1i 0.440651 0.0583050i
\(671\) 8113.86i 0.0180211i
\(672\) 323442. 426644.i 0.716239 0.944772i
\(673\) 226218.i 0.499457i 0.968316 + 0.249728i \(0.0803413\pi\)
−0.968316 + 0.249728i \(0.919659\pi\)
\(674\) −145573. 252140.i −0.320451 0.555037i
\(675\) −812766. + 218916.i −1.78385 + 0.480474i
\(676\) 91939.7 159244.i 0.201191 0.348474i
\(677\) 101310. + 175473.i 0.221041 + 0.382855i 0.955124 0.296205i \(-0.0957211\pi\)
−0.734083 + 0.679060i \(0.762388\pi\)
\(678\) −248935. −0.541535
\(679\) −15046.6 + 6335.51i −0.0326362 + 0.0137418i
\(680\) 338388. + 139906.i 0.731808 + 0.302566i
\(681\) −610577. 1.05755e6i −1.31658 2.28038i
\(682\) 57298.2 99243.5i 0.123189 0.213370i
\(683\) −162026. 93545.9i −0.347331 0.200532i 0.316178 0.948700i \(-0.397600\pi\)
−0.663509 + 0.748168i \(0.730934\pi\)
\(684\) 9961.64 5751.35i 0.0212921 0.0122930i
\(685\) 570845. + 236016.i 1.21657 + 0.502991i
\(686\) −80958.6 541586.i −0.172034 1.15085i
\(687\) 1.35461e6i 2.87013i
\(688\) −96627.1 + 55787.7i −0.204137 + 0.117859i
\(689\) 727394. + 419961.i 1.53226 + 0.884648i
\(690\) −41371.8 53844.1i −0.0868974 0.113094i
\(691\) −552053. + 318728.i −1.15618 + 0.667520i −0.950385 0.311076i \(-0.899311\pi\)
−0.205793 + 0.978596i \(0.565977\pi\)
\(692\) 232957. 0.486479
\(693\) 319316. 134451.i 0.664896 0.279960i
\(694\) 683616. 1.41936
\(695\) 91739.4 + 693338.i 0.189927 + 1.43541i
\(696\) −717471. 414232.i −1.48111 0.855117i
\(697\) −303084. 174986.i −0.623876 0.360195i
\(698\) −333492. 577625.i −0.684501 1.18559i
\(699\) 603716.i 1.23560i
\(700\) 23870.8 + 171837.i 0.0487159 + 0.350688i
\(701\) 555633. 1.13071 0.565356 0.824847i \(-0.308739\pi\)
0.565356 + 0.824847i \(0.308739\pi\)
\(702\) −1.34104e6 + 774247.i −2.72124 + 1.57111i
\(703\) 2550.85 4418.21i 0.00516149 0.00893996i
\(704\) −38213.7 + 66188.1i −0.0771034 + 0.133547i
\(705\) 332424. 43984.9i 0.668827 0.0884963i
\(706\) 119549.i 0.239849i
\(707\) −132390. 16645.1i −0.264861 0.0333002i
\(708\) 452530.i 0.902777i
\(709\) −208472. 361083.i −0.414719 0.718315i 0.580680 0.814132i \(-0.302787\pi\)
−0.995399 + 0.0958171i \(0.969454\pi\)
\(710\) −94234.3 + 72406.2i −0.186936 + 0.143635i
\(711\) 46138.1 79913.6i 0.0912684 0.158082i
\(712\) 225617. + 390780.i 0.445053 + 0.770854i
\(713\) −21512.0 −0.0423157
\(714\) −1.08414e6 136306.i −2.12661 0.267373i
\(715\) 100150. 242229.i 0.195901 0.473820i
\(716\) 33923.6 + 58757.3i 0.0661722 + 0.114614i
\(717\) −123859. + 214531.i −0.240930 + 0.417302i
\(718\) 668060. + 385704.i 1.29588 + 0.748179i
\(719\) −739037. + 426683.i −1.42958 + 0.825369i −0.997087 0.0762684i \(-0.975699\pi\)
−0.432493 + 0.901637i \(0.642366\pi\)
\(720\) −500533. + 1.21062e6i −0.965533 + 2.33531i
\(721\) 609093. + 461758.i 1.17169 + 0.888269i
\(722\) 605895.i 1.16231i
\(723\) 995085. 574513.i 1.90363 1.09906i
\(724\) −47961.4 27690.6i −0.0914987 0.0528268i
\(725\) 660519. 177909.i 1.25663 0.338471i
\(726\) −814375. + 470180.i −1.54508 + 0.892053i
\(727\) −535853. −1.01386 −0.506929 0.861988i \(-0.669219\pi\)
−0.506929 + 0.861988i \(0.669219\pi\)
\(728\) −225958. 536643.i −0.426349 1.01256i
\(729\) −434158. −0.816944
\(730\) 102446. + 774258.i 0.192243 + 1.45292i
\(731\) 93532.4 + 54001.0i 0.175036 + 0.101057i
\(732\) −14757.1 8520.02i −0.0275410 0.0159008i
\(733\) −446381. 773154.i −0.830802 1.43899i −0.897403 0.441211i \(-0.854549\pi\)
0.0666014 0.997780i \(-0.478784\pi\)
\(734\) 220032.i 0.408407i
\(735\) 372155. + 868084.i 0.688890 + 1.60689i
\(736\) −25751.9 −0.0475393
\(737\) 63029.0 36389.8i 0.116039 0.0669954i
\(738\) 445639. 771869.i 0.818220 1.41720i
\(739\) 288389. 499504.i 0.528068 0.914640i −0.471397 0.881921i \(-0.656250\pi\)
0.999465 0.0327191i \(-0.0104167\pi\)
\(740\) −7775.57 58765.3i −0.0141994 0.107314i
\(741\) 47376.5i 0.0862832i
\(742\) −714716. + 300938.i −1.29815 + 0.546599i
\(743\) 428933.i 0.776984i 0.921452 + 0.388492i \(0.127004\pi\)
−0.921452 + 0.388492i \(0.872996\pi\)
\(744\) 219537. + 380249.i 0.396609 + 0.686946i
\(745\) −205199. 267060.i −0.369712 0.481168i
\(746\) 30208.3 52322.4i 0.0542812 0.0940177i
\(747\) −431952. 748162.i −0.774094 1.34077i
\(748\) −73207.6 −0.130844
\(749\) −152484. + 201138.i −0.271807 + 0.358534i
\(750\) −439997. 1.05640e6i −0.782217 1.87804i
\(751\) 121543. + 210519.i 0.215502 + 0.373260i 0.953428 0.301622i \(-0.0975280\pi\)
−0.737926 + 0.674882i \(0.764195\pi\)
\(752\) 134063. 232204.i 0.237069 0.410615i
\(753\) −651283. 376018.i −1.14863 0.663161i
\(754\) 1.08983e6 629215.i 1.91698 1.10677i
\(755\) 106438. 257438.i 0.186725 0.451625i
\(756\) 46634.3 370916.i 0.0815947 0.648981i
\(757\) 156953.i 0.273892i 0.990579 + 0.136946i \(0.0437287\pi\)
−0.990579 + 0.136946i \(0.956271\pi\)
\(758\) 371844. 214684.i 0.647176 0.373647i
\(759\) −21449.5 12383.9i −0.0372334 0.0214967i
\(760\) −8931.14 11623.6i −0.0154625 0.0201239i
\(761\) −368455. + 212727.i −0.636231 + 0.367328i −0.783161 0.621819i \(-0.786394\pi\)
0.146930 + 0.989147i \(0.453061\pi\)
\(762\) −1.52396e6 −2.62459
\(763\) −113892. + 905863.i −0.195634 + 1.55601i
\(764\) −62728.9 −0.107469
\(765\) 1.25710e6 166334.i 2.14807 0.284223i
\(766\) −478478. 276249.i −0.815463 0.470808i
\(767\) 1.08607e6 + 627041.i 1.84615 + 1.06587i
\(768\) 487109. + 843697.i 0.825855 + 1.43042i
\(769\) 737777.i 1.24759i −0.781587 0.623796i \(-0.785590\pi\)
0.781587 0.623796i \(-0.214410\pi\)
\(770\) 122360. + 208797.i 0.206375 + 0.352162i
\(771\) 561554. 0.944676
\(772\) 301375. 173999.i 0.505677 0.291953i
\(773\) 423005. 732666.i 0.707924 1.22616i −0.257702 0.966224i \(-0.582965\pi\)
0.965626 0.259935i \(-0.0837012\pi\)
\(774\) −137525. + 238200.i −0.229562 + 0.397613i
\(775\) −350310. 93376.0i −0.583243 0.155465i
\(776\) 16028.0i 0.0266167i
\(777\) −125234. 297426.i −0.207434 0.492649i
\(778\) 1.22184e6i 2.01862i
\(779\) 7005.06 + 12133.1i 0.0115435 + 0.0199939i
\(780\) −335392. 436502.i −0.551268 0.717458i
\(781\) −21673.4 + 37539.4i −0.0355324 + 0.0615440i
\(782\) 26278.5 + 45515.7i 0.0429722 + 0.0744300i
\(783\) −1.47403e6 −2.40427
\(784\) 731723. + 186950.i 1.19046 + 0.304155i
\(785\) −277892. + 672129.i −0.450958 + 1.09072i
\(786\) 957770. + 1.65891e6i 1.55030 + 2.68520i
\(787\) −162785. + 281951.i −0.262824 + 0.455224i −0.966991 0.254810i \(-0.917987\pi\)
0.704168 + 0.710034i \(0.251320\pi\)
\(788\) −196009. 113166.i −0.315662 0.182248i
\(789\) 184388. 106456.i 0.296195 0.171009i
\(790\) 59564.8 + 24627.1i 0.0954412 + 0.0394602i
\(791\) −64630.5 153495.i −0.103296 0.245325i
\(792\) 340141.i 0.542262i
\(793\) −40895.9 + 23611.3i −0.0650330 + 0.0375468i
\(794\) −520436. 300474.i −0.825518 0.476613i
\(795\) 1.06061e6 814937.i 1.67812 1.28941i
\(796\) −356995. + 206111.i −0.563425 + 0.325294i
\(797\) −34880.5 −0.0549119 −0.0274560 0.999623i \(-0.508741\pi\)
−0.0274560 + 0.999623i \(0.508741\pi\)
\(798\) 34857.5 + 26425.8i 0.0547382 + 0.0414975i
\(799\) −259539. −0.406546
\(800\) −419353. 111780.i −0.655240 0.174656i
\(801\) 1.35329e6 + 781320.i 2.10923 + 1.21777i
\(802\) −639925. 369461.i −0.994902 0.574407i
\(803\) 142437. + 246708.i 0.220898 + 0.382606i
\(804\) 152846.i 0.236451i
\(805\) 22459.4 39489.6i 0.0346582 0.0609384i
\(806\) −666950. −1.02665
\(807\) 590858. 341132.i 0.907269 0.523812i
\(808\) 65498.2 113446.i 0.100324 0.173767i
\(809\) −93144.6 + 161331.i −0.142318 + 0.246503i −0.928369 0.371659i \(-0.878789\pi\)
0.786051 + 0.618162i \(0.212122\pi\)
\(810\) 117494. + 887985.i 0.179080 + 1.35343i
\(811\) 1.27617e6i 1.94030i 0.242510 + 0.970149i \(0.422029\pi\)
−0.242510 + 0.970149i \(0.577971\pi\)
\(812\) −37898.8 + 301436.i −0.0574795 + 0.457176i
\(813\) 179536.i 0.271626i
\(814\) −41344.9 71611.4i −0.0623983 0.108077i
\(815\) 3718.65 2857.27i 0.00559848 0.00430166i
\(816\) 753480. 1.30507e6i 1.13160 1.95998i
\(817\) −2161.77 3744.30i −0.00323867 0.00560954i
\(818\) 1.09440e6 1.63556
\(819\) −1.60687e6 1.21818e6i −2.39560 1.81612i
\(820\) 150435. + 62197.3i 0.223728 + 0.0925004i
\(821\) −584760. 1.01283e6i −0.867544 1.50263i −0.864499 0.502635i \(-0.832364\pi\)
−0.00304500 0.999995i \(-0.500969\pi\)
\(822\) 904819. 1.56719e6i 1.33911 2.31942i
\(823\) 852565. + 492228.i 1.25872 + 0.726720i 0.972825 0.231542i \(-0.0743772\pi\)
0.285891 + 0.958262i \(0.407711\pi\)
\(824\) −649852. + 375192.i −0.957106 + 0.552585i
\(825\) −295538. 294768.i −0.434215 0.433085i
\(826\) −1.06714e6 + 449328.i −1.56409 + 0.658572i
\(827\) 124621.i 0.182213i 0.995841 + 0.0911064i \(0.0290403\pi\)
−0.995841 + 0.0911064i \(0.970960\pi\)
\(828\) −30309.3 + 17499.1i −0.0442095 + 0.0255244i
\(829\) −14134.6 8160.64i −0.0205672 0.0118745i 0.489681 0.871902i \(-0.337113\pi\)
−0.510248 + 0.860027i \(0.670447\pi\)
\(830\) 478500. 367662.i 0.694585 0.533694i
\(831\) 726967. 419715.i 1.05272 0.607788i
\(832\) 444807. 0.642576
\(833\) −197425. 703877.i −0.284520 1.01439i
\(834\) 2.04889e6 2.94569
\(835\) −612398. + 81029.9i −0.878337 + 0.116218i
\(836\) 2538.02 + 1465.33i 0.00363147 + 0.00209663i
\(837\) 676553. + 390608.i 0.965719 + 0.557558i
\(838\) 281575. + 487703.i 0.400965 + 0.694492i
\(839\) 1.12002e6i 1.59112i 0.605878 + 0.795558i \(0.292822\pi\)
−0.605878 + 0.795558i \(0.707178\pi\)
\(840\) −927230. + 6008.87i −1.31410 + 0.00851598i
\(841\) 490636. 0.693693
\(842\) −735199. + 424467.i −1.03700 + 0.598715i
\(843\) −858504. + 1.48697e6i −1.20806 + 2.09241i
\(844\) −156709. + 271427.i −0.219993 + 0.381038i
\(845\) −804475. + 106445.i −1.12668 + 0.149077i
\(846\) 660972.i 0.923511i
\(847\) −501351. 380078.i −0.698836 0.529793i
\(848\) 1.06952e6i 1.48729i
\(849\) 370730. + 642123.i 0.514331 + 0.890847i
\(850\) 230362. + 855261.i 0.318840 + 1.18375i
\(851\) −7761.25 + 13442.9i −0.0107170 + 0.0185624i
\(852\) 45516.7 + 78837.2i 0.0627034 + 0.108605i
\(853\) 84342.4 0.115917 0.0579586 0.998319i \(-0.481541\pi\)
0.0579586 + 0.998319i \(0.481541\pi\)
\(854\) 5438.89 43259.4i 0.00745752 0.0593150i
\(855\) −46911.7 19395.6i −0.0641725 0.0265321i
\(856\) −123898. 214597.i −0.169089 0.292871i
\(857\) −260279. + 450816.i −0.354387 + 0.613816i −0.987013 0.160642i \(-0.948644\pi\)
0.632626 + 0.774457i \(0.281977\pi\)
\(858\) −665012. 383945.i −0.903347 0.521548i
\(859\) 400501. 231230.i 0.542772 0.313370i −0.203429 0.979090i \(-0.565209\pi\)
0.746202 + 0.665720i \(0.231875\pi\)
\(860\) −46424.4 19194.2i −0.0627697 0.0259521i
\(861\) 879309. + 110553.i 1.18614 + 0.149130i
\(862\) 1.24664e6i 1.67775i
\(863\) 480890. 277642.i 0.645691 0.372790i −0.141113 0.989994i \(-0.545068\pi\)
0.786803 + 0.617204i \(0.211735\pi\)
\(864\) 809896. + 467594.i 1.08493 + 0.626385i
\(865\) −626384. 815218.i −0.837160 1.08954i
\(866\) −346975. + 200326.i −0.462660 + 0.267117i
\(867\) −144493. −0.192224
\(868\) 97273.3 128311.i 0.129108 0.170303i
\(869\) 23510.1 0.0311326
\(870\) −262870. 1.98669e6i −0.347298 2.62477i
\(871\) −366828. 211788.i −0.483533 0.279168i
\(872\) −776240. 448163.i −1.02085 0.589390i
\(873\) −27752.7 48069.1i −0.0364147 0.0630722i
\(874\) 2103.97i 0.00275433i
\(875\) 537148. 545576.i 0.701581 0.712589i
\(876\) 598267. 0.779627
\(877\) 1.13396e6 654695.i 1.47435 0.851216i 0.474767 0.880112i \(-0.342532\pi\)
0.999582 + 0.0288957i \(0.00919908\pi\)
\(878\) −422964. + 732595.i −0.548674 + 0.950332i
\(879\) −1.25541e6 + 2.17444e6i −1.62483 + 2.81429i
\(880\) −330882. + 43780.8i −0.427275 + 0.0565351i
\(881\) 361213.i 0.465384i 0.972550 + 0.232692i \(0.0747534\pi\)
−0.972550 + 0.232692i \(0.925247\pi\)
\(882\) 1.79257e6 502786.i 2.30430 0.646318i
\(883\) 1.11366e6i 1.42833i −0.699975 0.714167i \(-0.746806\pi\)
0.699975 0.714167i \(-0.253194\pi\)
\(884\) 213034. + 368985.i 0.272611 + 0.472177i
\(885\) 1.58360e6 1.21678e6i 2.02189 1.55355i
\(886\) 241363. 418054.i 0.307471 0.532555i
\(887\) 208559. + 361236.i 0.265083 + 0.459138i 0.967585 0.252544i \(-0.0812671\pi\)
−0.702502 + 0.711682i \(0.747934\pi\)
\(888\) 316824. 0.401784
\(889\) −395662. 939682.i −0.500634 1.18899i
\(890\) −417044. + 1.00869e6i −0.526505 + 1.27344i
\(891\) 163358. + 282945.i 0.205772 + 0.356407i
\(892\) 695.905 1205.34i 0.000874621 0.00151489i
\(893\) 8997.92 + 5194.95i 0.0112834 + 0.00651447i
\(894\) −854468. + 493327.i −1.06911 + 0.617249i
\(895\) 114402. 276702.i 0.142820 0.345435i
\(896\) −576994. + 761098.i −0.718713 + 0.948036i
\(897\) 144148.i 0.179153i
\(898\) −495605. + 286138.i −0.614586 + 0.354831i
\(899\) −549821. 317439.i −0.680303 0.392773i
\(900\) −569527. + 153400.i −0.703119 + 0.189383i
\(901\) −896563. + 517631.i −1.10441 + 0.637633i
\(902\) 227079. 0.279103
\(903\) −271356. 34116.9i −0.332786 0.0418403i
\(904\) 163506. 0.200077
\(905\) 32059.2 + 242293.i 0.0391431 + 0.295831i
\(906\) −706766. 408052.i −0.861032 0.497117i
\(907\) −969958. 560006.i −1.17907 0.680735i −0.223268 0.974757i \(-0.571673\pi\)
−0.955799 + 0.294022i \(0.905006\pi\)
\(908\) −219819. 380737.i −0.266620 0.461800i
\(909\) 453646.i 0.549021i
\(910\) 696323. 1.22432e6i 0.840868 1.47847i
\(911\) −878004. −1.05794 −0.528968 0.848642i \(-0.677421\pi\)
−0.528968 + 0.848642i \(0.677421\pi\)
\(912\) −52244.6 + 30163.4i −0.0628133 + 0.0362653i
\(913\) 110052. 190616.i 0.132026 0.228675i
\(914\) −192994. + 334275.i −0.231021 + 0.400140i
\(915\) 9864.19 + 74550.4i 0.0117820 + 0.0890447i
\(916\) 487685.i 0.581230i
\(917\) −774230. + 1.02127e6i −0.920728 + 1.21451i
\(918\) 1.90863e6i 2.26483i
\(919\) 511986. + 886785.i 0.606215 + 1.05000i 0.991858 + 0.127347i \(0.0406463\pi\)
−0.385643 + 0.922648i \(0.626020\pi\)
\(920\) 27173.9 + 35366.0i 0.0321053 + 0.0417840i
\(921\) −278267. + 481973.i −0.328052 + 0.568203i
\(922\) 90641.2 + 156995.i 0.106626 + 0.184682i
\(923\) 252278. 0.296126
\(924\) 170855. 71940.1i 0.200117 0.0842611i
\(925\) −184738. + 185220.i −0.215910 + 0.216474i
\(926\) 981058. + 1.69924e6i 1.14412 + 1.98168i
\(927\) −1.29931e6 + 2.25046e6i −1.51200 + 2.61886i
\(928\) −658187. 380004.i −0.764281 0.441258i
\(929\) 735341. 424549.i 0.852034 0.491922i −0.00930233 0.999957i \(-0.502961\pi\)
0.861337 + 0.508034i \(0.169628\pi\)
\(930\) −405806. + 981512.i −0.469194 + 1.13483i
\(931\) −7244.33 + 28354.3i −0.00835794 + 0.0327129i
\(932\) 217349.i 0.250222i
\(933\) −1.86107e6 + 1.07449e6i −2.13796 + 1.23435i
\(934\) −118191. 68237.8i −0.135485 0.0782225i
\(935\) 196843. + 256185.i 0.225163 + 0.293042i
\(936\) 1.71440e6 989810.i 1.95686 1.12980i
\(937\) 739900. 0.842741 0.421370 0.906889i \(-0.361549\pi\)
0.421370 + 0.906889i \(0.361549\pi\)
\(938\) 360435. 151764.i 0.409658 0.172490i
\(939\) −694649. −0.787833
\(940\) 119679. 15835.4i 0.135444 0.0179214i
\(941\) −465455. 268730.i −0.525652 0.303485i 0.213592 0.976923i \(-0.431484\pi\)
−0.739244 + 0.673438i \(0.764817\pi\)
\(942\) 1.84525e6 + 1.06536e6i 2.07948 + 1.20059i
\(943\) −21313.6 36916.3i −0.0239681 0.0415140i
\(944\) 1.59689e6i 1.79197i
\(945\) −1.42339e6 + 834139.i −1.59389 + 0.934060i
\(946\) −70077.1 −0.0783058
\(947\) 1.03060e6 595020.i 1.14919 0.663486i 0.200501 0.979694i \(-0.435743\pi\)
0.948690 + 0.316208i \(0.102410\pi\)
\(948\) 24687.0 42759.1i 0.0274695 0.0475786i
\(949\) 828980. 1.43584e6i 0.920475 1.59431i
\(950\) 9132.59 34261.9i 0.0101192 0.0379633i
\(951\) 2.56792e6i 2.83936i
\(952\) 712086. + 89528.7i 0.785704 + 0.0987844i
\(953\) 230956.i 0.254298i 0.991884 + 0.127149i \(0.0405826\pi\)
−0.991884 + 0.127149i \(0.959417\pi\)
\(954\) −1.31826e6 2.28329e6i −1.44845 2.50879i
\(955\) 168668. + 219516.i 0.184938 + 0.240690i
\(956\) −44591.6 + 77234.9i −0.0487907 + 0.0845080i
\(957\) −365482. 633033.i −0.399064 0.691199i
\(958\) 542170. 0.590751
\(959\) 1.20126e6 + 151031.i 1.30617 + 0.164221i
\(960\) 270643. 654596.i 0.293666 0.710282i
\(961\) −293522. 508395.i −0.317829 0.550497i
\(962\) −240627. + 416778.i −0.260012 + 0.450354i
\(963\) −743159. 429063.i −0.801363 0.462667i
\(964\) 358249. 206835.i 0.385506 0.222572i
\(965\) −1.41925e6 586788.i −1.52406 0.630124i
\(966\) −106058. 80403.2i −0.113655 0.0861626i
\(967\) 1.12804e6i 1.20635i −0.797610 0.603173i \(-0.793903\pi\)
0.797610 0.603173i \(-0.206097\pi\)
\(968\) 534900. 308825.i 0.570850 0.329580i
\(969\) 50571.3 + 29197.4i 0.0538588 + 0.0310954i
\(970\) 30743.4 23622.1i 0.0326745 0.0251059i
\(971\) 1.27656e6 737020.i 1.35395 0.781701i 0.365146 0.930950i \(-0.381019\pi\)
0.988800 + 0.149249i \(0.0476856\pi\)
\(972\) 68169.0 0.0721530
\(973\) 531950. + 1.26336e6i 0.561882 + 1.33445i
\(974\) 980105. 1.03313
\(975\) −625695. + 2.34736e6i −0.658193 + 2.46928i
\(976\) 52074.9 + 30065.5i 0.0546674 + 0.0315623i
\(977\) −569827. 328990.i −0.596972 0.344662i 0.170877 0.985292i \(-0.445340\pi\)
−0.767850 + 0.640630i \(0.778673\pi\)
\(978\) −6869.28 11897.9i −0.00718181 0.0124393i
\(979\) 398129.i 0.415392i
\(980\) 133983. + 312526.i 0.139507 + 0.325412i
\(981\) −3.10401e6 −3.22541
\(982\) 798439. 460979.i 0.827978 0.478033i
\(983\) 135356. 234444.i 0.140078 0.242623i −0.787448 0.616382i \(-0.788598\pi\)
0.927526 + 0.373759i \(0.121931\pi\)
\(984\) −435025. + 753486.i −0.449287 + 0.778189i
\(985\) 131019. + 990203.i 0.135040 + 1.02059i
\(986\) 1.55110e6i 1.59546i
\(987\) 605725. 255046.i 0.621786 0.261809i
\(988\) 17056.4i 0.0174732i
\(989\) 6577.43 + 11392.4i 0.00672455 + 0.0116473i
\(990\) −652430. + 501303.i −0.665677 + 0.511481i
\(991\) −290534. + 503220.i −0.295835 + 0.512402i −0.975179 0.221418i \(-0.928931\pi\)
0.679343 + 0.733820i \(0.262265\pi\)
\(992\) 201397. + 348829.i 0.204658 + 0.354478i
\(993\) 3.29453e6 3.34114
\(994\) −140716. + 185615.i −0.142420 + 0.187863i
\(995\) 1.68117e6 + 695082.i 1.69811 + 0.702085i
\(996\) −231123. 400317.i −0.232983 0.403539i
\(997\) 436452. 755956.i 0.439082 0.760513i −0.558537 0.829480i \(-0.688637\pi\)
0.997619 + 0.0689671i \(0.0219704\pi\)
\(998\) −304882. 176024.i −0.306106 0.176730i
\(999\) 488183. 281852.i 0.489160 0.282417i
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 35.5.i.a.24.4 yes 28
5.2 odd 4 175.5.i.e.101.4 28
5.3 odd 4 175.5.i.e.101.11 28
5.4 even 2 inner 35.5.i.a.24.11 yes 28
7.3 odd 6 245.5.c.a.244.1 28
7.4 even 3 245.5.c.a.244.27 28
7.5 odd 6 inner 35.5.i.a.19.11 yes 28
35.4 even 6 245.5.c.a.244.2 28
35.12 even 12 175.5.i.e.26.4 28
35.19 odd 6 inner 35.5.i.a.19.4 28
35.24 odd 6 245.5.c.a.244.28 28
35.33 even 12 175.5.i.e.26.11 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.5.i.a.19.4 28 35.19 odd 6 inner
35.5.i.a.19.11 yes 28 7.5 odd 6 inner
35.5.i.a.24.4 yes 28 1.1 even 1 trivial
35.5.i.a.24.11 yes 28 5.4 even 2 inner
175.5.i.e.26.4 28 35.12 even 12
175.5.i.e.26.11 28 35.33 even 12
175.5.i.e.101.4 28 5.2 odd 4
175.5.i.e.101.11 28 5.3 odd 4
245.5.c.a.244.1 28 7.3 odd 6
245.5.c.a.244.2 28 35.4 even 6
245.5.c.a.244.27 28 7.4 even 3
245.5.c.a.244.28 28 35.24 odd 6