Properties

Label 105.4.s.a.101.16
Level $105$
Weight $4$
Character 105.101
Analytic conductor $6.195$
Analytic rank $0$
Dimension $32$
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] = [105,4,Mod(26,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.26");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.s (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: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.16
Character \(\chi\) \(=\) 105.101
Dual form 105.4.s.a.26.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.69077 - 2.70822i) q^{2} +(-2.85230 + 4.34332i) q^{3} +(10.6689 - 18.4790i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-1.61684 + 28.0981i) q^{6} +(14.5222 - 11.4937i) q^{7} -72.2429i q^{8} +(-10.7288 - 24.7769i) q^{9} +O(q^{10})\) \(q+(4.69077 - 2.70822i) q^{2} +(-2.85230 + 4.34332i) q^{3} +(10.6689 - 18.4790i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-1.61684 + 28.0981i) q^{6} +(14.5222 - 11.4937i) q^{7} -72.2429i q^{8} +(-10.7288 - 24.7769i) q^{9} +(-23.4538 - 13.5411i) q^{10} +(38.4696 + 22.2104i) q^{11} +(49.8294 + 99.0459i) q^{12} +22.9471i q^{13} +(36.9928 - 93.2436i) q^{14} +(25.9379 + 1.49253i) q^{15} +(-110.298 - 191.042i) q^{16} +(-32.3140 + 55.9695i) q^{17} +(-117.427 - 87.1667i) q^{18} +(-15.6960 + 9.06207i) q^{19} -106.689 q^{20} +(8.49916 + 95.8580i) q^{21} +240.602 q^{22} +(-76.2989 + 44.0512i) q^{23} +(313.774 + 206.058i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(62.1458 + 107.640i) q^{26} +(138.215 + 24.0726i) q^{27} +(-57.4571 - 390.981i) q^{28} +308.783i q^{29} +(125.711 - 63.2442i) q^{30} +(-82.5212 - 47.6436i) q^{31} +(-534.254 - 308.452i) q^{32} +(-206.194 + 103.735i) q^{33} +350.053i q^{34} +(-86.0748 - 34.1487i) q^{35} +(-572.316 - 66.0838i) q^{36} +(-83.8935 - 145.308i) q^{37} +(-49.0841 + 85.0161i) q^{38} +(-99.6666 - 65.4521i) q^{39} +(-312.821 + 180.607i) q^{40} +271.265 q^{41} +(299.472 + 426.630i) q^{42} +225.930 q^{43} +(820.853 - 473.920i) q^{44} +(-80.4651 + 108.399i) q^{45} +(-238.600 + 413.268i) q^{46} +(-31.1914 - 54.0251i) q^{47} +(1144.36 + 65.8494i) q^{48} +(78.7889 - 333.828i) q^{49} +135.411i q^{50} +(-150.924 - 299.992i) q^{51} +(424.040 + 244.820i) q^{52} +(19.9236 + 11.5029i) q^{53} +(713.530 - 261.398i) q^{54} -222.104i q^{55} +(-830.339 - 1049.13i) q^{56} +(5.41017 - 94.0203i) q^{57} +(836.250 + 1448.43i) q^{58} +(-41.0850 + 71.1613i) q^{59} +(304.308 - 463.382i) q^{60} +(424.943 - 245.341i) q^{61} -516.117 q^{62} +(-440.584 - 236.501i) q^{63} -1576.64 q^{64} +(99.3640 - 57.3678i) q^{65} +(-686.270 + 1045.01i) q^{66} +(-278.306 + 482.040i) q^{67} +(689.508 + 1194.26i) q^{68} +(26.2991 - 457.037i) q^{69} +(-496.239 + 72.9254i) q^{70} -669.023i q^{71} +(-1789.95 + 775.078i) q^{72} +(-184.713 - 106.644i) q^{73} +(-787.050 - 454.404i) q^{74} +(-58.3818 - 116.046i) q^{75} +386.728i q^{76} +(813.943 - 119.614i) q^{77} +(-644.771 - 37.1018i) q^{78} +(288.663 + 499.979i) q^{79} +(-551.492 + 955.212i) q^{80} +(-498.787 + 531.651i) q^{81} +(1272.44 - 734.643i) q^{82} -1281.15 q^{83} +(1862.04 + 865.640i) q^{84} +323.140 q^{85} +(1059.79 - 611.868i) q^{86} +(-1341.14 - 880.741i) q^{87} +(1604.54 - 2779.15i) q^{88} +(-511.382 - 885.739i) q^{89} +(-83.8746 + 726.392i) q^{90} +(263.748 + 333.243i) q^{91} +1879.90i q^{92} +(442.306 - 222.522i) q^{93} +(-292.623 - 168.946i) q^{94} +(78.4798 + 45.3103i) q^{95} +(2863.56 - 1440.64i) q^{96} +472.961i q^{97} +(-534.499 - 1779.29i) q^{98} +(137.573 - 1191.45i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.69077 2.70822i 1.65844 0.957499i 0.685000 0.728543i \(-0.259802\pi\)
0.973437 0.228955i \(-0.0735310\pi\)
\(3\) −2.85230 + 4.34332i −0.548925 + 0.835871i
\(4\) 10.6689 18.4790i 1.33361 2.30988i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) −1.61684 + 28.0981i −0.110012 + 1.91183i
\(7\) 14.5222 11.4937i 0.784125 0.620602i
\(8\) 72.2429i 3.19271i
\(9\) −10.7288 24.7769i −0.397362 0.917662i
\(10\) −23.4538 13.5411i −0.741675 0.428206i
\(11\) 38.4696 + 22.2104i 1.05446 + 0.608790i 0.923893 0.382650i \(-0.124989\pi\)
0.130562 + 0.991440i \(0.458322\pi\)
\(12\) 49.8294 + 99.0459i 1.19871 + 2.38267i
\(13\) 22.9471i 0.489568i 0.969578 + 0.244784i \(0.0787171\pi\)
−0.969578 + 0.244784i \(0.921283\pi\)
\(14\) 36.9928 93.2436i 0.706196 1.78003i
\(15\) 25.9379 + 1.49253i 0.446475 + 0.0256913i
\(16\) −110.298 191.042i −1.72341 2.98504i
\(17\) −32.3140 + 55.9695i −0.461018 + 0.798506i −0.999012 0.0444424i \(-0.985849\pi\)
0.537994 + 0.842949i \(0.319182\pi\)
\(18\) −117.427 87.1667i −1.53766 1.14141i
\(19\) −15.6960 + 9.06207i −0.189521 + 0.109420i −0.591758 0.806115i \(-0.701566\pi\)
0.402237 + 0.915535i \(0.368233\pi\)
\(20\) −106.689 −1.19282
\(21\) 8.49916 + 95.8580i 0.0883176 + 0.996092i
\(22\) 240.602 2.33166
\(23\) −76.2989 + 44.0512i −0.691714 + 0.399361i −0.804254 0.594286i \(-0.797435\pi\)
0.112540 + 0.993647i \(0.464101\pi\)
\(24\) 313.774 + 206.058i 2.66870 + 1.75256i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 62.1458 + 107.640i 0.468761 + 0.811918i
\(27\) 138.215 + 24.0726i 0.985169 + 0.171584i
\(28\) −57.4571 390.981i −0.387799 2.63887i
\(29\) 308.783i 1.97722i 0.150485 + 0.988612i \(0.451916\pi\)
−0.150485 + 0.988612i \(0.548084\pi\)
\(30\) 125.711 63.2442i 0.765050 0.384892i
\(31\) −82.5212 47.6436i −0.478105 0.276034i 0.241522 0.970395i \(-0.422354\pi\)
−0.719626 + 0.694362i \(0.755687\pi\)
\(32\) −534.254 308.452i −2.95137 1.70397i
\(33\) −206.194 + 103.735i −1.08769 + 0.547209i
\(34\) 350.053i 1.76570i
\(35\) −86.0748 34.1487i −0.415694 0.164920i
\(36\) −572.316 66.0838i −2.64961 0.305944i
\(37\) −83.8935 145.308i −0.372757 0.645634i 0.617232 0.786782i \(-0.288254\pi\)
−0.989989 + 0.141147i \(0.954921\pi\)
\(38\) −49.0841 + 85.0161i −0.209539 + 0.362932i
\(39\) −99.6666 65.4521i −0.409216 0.268736i
\(40\) −312.821 + 180.607i −1.23653 + 0.713912i
\(41\) 271.265 1.03328 0.516639 0.856203i \(-0.327183\pi\)
0.516639 + 0.856203i \(0.327183\pi\)
\(42\) 299.472 + 426.630i 1.10023 + 1.56739i
\(43\) 225.930 0.801257 0.400629 0.916241i \(-0.368792\pi\)
0.400629 + 0.916241i \(0.368792\pi\)
\(44\) 820.853 473.920i 2.81246 1.62377i
\(45\) −80.4651 + 108.399i −0.266556 + 0.359093i
\(46\) −238.600 + 413.268i −0.764776 + 1.32463i
\(47\) −31.1914 54.0251i −0.0968029 0.167667i 0.813557 0.581486i \(-0.197528\pi\)
−0.910360 + 0.413818i \(0.864195\pi\)
\(48\) 1144.36 + 65.8494i 3.44113 + 0.198011i
\(49\) 78.7889 333.828i 0.229705 0.973260i
\(50\) 135.411i 0.383000i
\(51\) −150.924 299.992i −0.414384 0.823672i
\(52\) 424.040 + 244.820i 1.13084 + 0.652892i
\(53\) 19.9236 + 11.5029i 0.0516361 + 0.0298121i 0.525596 0.850734i \(-0.323842\pi\)
−0.473960 + 0.880547i \(0.657176\pi\)
\(54\) 713.530 261.398i 1.79813 0.658737i
\(55\) 222.104i 0.544518i
\(56\) −830.339 1049.13i −1.98141 2.50349i
\(57\) 5.41017 94.0203i 0.0125718 0.218479i
\(58\) 836.250 + 1448.43i 1.89319 + 3.27910i
\(59\) −41.0850 + 71.1613i −0.0906578 + 0.157024i −0.907788 0.419429i \(-0.862230\pi\)
0.817130 + 0.576453i \(0.195564\pi\)
\(60\) 304.308 463.382i 0.654766 0.997040i
\(61\) 424.943 245.341i 0.891941 0.514962i 0.0173639 0.999849i \(-0.494473\pi\)
0.874577 + 0.484887i \(0.161139\pi\)
\(62\) −516.117 −1.05721
\(63\) −440.584 236.501i −0.881085 0.472958i
\(64\) −1576.64 −3.07938
\(65\) 99.3640 57.3678i 0.189609 0.109471i
\(66\) −686.270 + 1045.01i −1.27991 + 1.94897i
\(67\) −278.306 + 482.040i −0.507470 + 0.878963i 0.492493 + 0.870316i \(0.336086\pi\)
−0.999963 + 0.00864671i \(0.997248\pi\)
\(68\) 689.508 + 1194.26i 1.22963 + 2.12979i
\(69\) 26.2991 457.037i 0.0458846 0.797404i
\(70\) −496.239 + 72.9254i −0.847312 + 0.124518i
\(71\) 669.023i 1.11829i −0.829071 0.559144i \(-0.811130\pi\)
0.829071 0.559144i \(-0.188870\pi\)
\(72\) −1789.95 + 775.078i −2.92983 + 1.26866i
\(73\) −184.713 106.644i −0.296151 0.170983i 0.344561 0.938764i \(-0.388028\pi\)
−0.640713 + 0.767781i \(0.721361\pi\)
\(74\) −787.050 454.404i −1.23639 0.713829i
\(75\) −58.3818 116.046i −0.0898847 0.178664i
\(76\) 386.728i 0.583694i
\(77\) 813.943 119.614i 1.20464 0.177030i
\(78\) −644.771 37.1018i −0.935974 0.0538583i
\(79\) 288.663 + 499.979i 0.411103 + 0.712050i 0.995011 0.0997694i \(-0.0318105\pi\)
−0.583908 + 0.811820i \(0.698477\pi\)
\(80\) −551.492 + 955.212i −0.770733 + 1.33495i
\(81\) −498.787 + 531.651i −0.684207 + 0.729288i
\(82\) 1272.44 734.643i 1.71363 0.989363i
\(83\) −1281.15 −1.69426 −0.847132 0.531382i \(-0.821673\pi\)
−0.847132 + 0.531382i \(0.821673\pi\)
\(84\) 1862.04 + 865.640i 2.41863 + 1.12439i
\(85\) 323.140 0.412347
\(86\) 1059.79 611.868i 1.32883 0.767203i
\(87\) −1341.14 880.741i −1.65271 1.08535i
\(88\) 1604.54 2779.15i 1.94369 3.36657i
\(89\) −511.382 885.739i −0.609060 1.05492i −0.991396 0.130900i \(-0.958213\pi\)
0.382335 0.924024i \(-0.375120\pi\)
\(90\) −83.8746 + 726.392i −0.0982351 + 0.850760i
\(91\) 263.748 + 333.243i 0.303827 + 0.383883i
\(92\) 1879.90i 2.13037i
\(93\) 442.306 222.522i 0.493173 0.248112i
\(94\) −292.623 168.946i −0.321083 0.185377i
\(95\) 78.4798 + 45.3103i 0.0847564 + 0.0489341i
\(96\) 2863.56 1440.64i 3.04438 1.53161i
\(97\) 472.961i 0.495072i 0.968879 + 0.247536i \(0.0796208\pi\)
−0.968879 + 0.247536i \(0.920379\pi\)
\(98\) −534.499 1779.29i −0.550944 1.83403i
\(99\) 137.573 1191.45i 0.139663 1.20954i
\(100\) 266.722 + 461.975i 0.266722 + 0.461975i
\(101\) −330.855 + 573.058i −0.325954 + 0.564568i −0.981705 0.190409i \(-0.939019\pi\)
0.655751 + 0.754977i \(0.272352\pi\)
\(102\) −1520.39 998.457i −1.47589 0.969235i
\(103\) −1149.63 + 663.739i −1.09977 + 0.634953i −0.936161 0.351572i \(-0.885647\pi\)
−0.163610 + 0.986525i \(0.552314\pi\)
\(104\) 1657.77 1.56305
\(105\) 393.830 276.448i 0.366036 0.256938i
\(106\) 124.609 0.114180
\(107\) −11.2649 + 6.50382i −0.0101778 + 0.00587615i −0.505080 0.863072i \(-0.668537\pi\)
0.494902 + 0.868949i \(0.335204\pi\)
\(108\) 1919.44 2297.26i 1.71017 2.04679i
\(109\) 656.500 1137.09i 0.576893 0.999208i −0.418940 0.908014i \(-0.637598\pi\)
0.995833 0.0911940i \(-0.0290683\pi\)
\(110\) −601.506 1041.84i −0.521376 0.903049i
\(111\) 870.407 + 50.0855i 0.744283 + 0.0428279i
\(112\) −3797.56 1506.62i −3.20389 1.27109i
\(113\) 785.985i 0.654329i 0.944967 + 0.327165i \(0.106093\pi\)
−0.944967 + 0.327165i \(0.893907\pi\)
\(114\) −229.249 455.679i −0.188344 0.374371i
\(115\) 381.495 + 220.256i 0.309344 + 0.178600i
\(116\) 5706.00 + 3294.36i 4.56714 + 2.63684i
\(117\) 568.558 246.195i 0.449258 0.194536i
\(118\) 445.068i 0.347219i
\(119\) 174.027 + 1184.21i 0.134059 + 0.912238i
\(120\) 107.825 1873.82i 0.0820250 1.42547i
\(121\) 321.105 + 556.169i 0.241251 + 0.417858i
\(122\) 1328.87 2301.67i 0.986151 1.70806i
\(123\) −773.728 + 1178.19i −0.567193 + 0.863688i
\(124\) −1760.81 + 1016.61i −1.27521 + 0.736242i
\(125\) 125.000 0.0894427
\(126\) −2707.17 + 83.8237i −1.91408 + 0.0592667i
\(127\) −443.373 −0.309787 −0.154894 0.987931i \(-0.549503\pi\)
−0.154894 + 0.987931i \(0.549503\pi\)
\(128\) −3121.63 + 1802.27i −2.15559 + 1.24453i
\(129\) −644.421 + 981.287i −0.439830 + 0.669748i
\(130\) 310.729 538.198i 0.209636 0.363101i
\(131\) −1234.95 2138.99i −0.823648 1.42660i −0.902948 0.429750i \(-0.858602\pi\)
0.0792995 0.996851i \(-0.474732\pi\)
\(132\) −282.936 + 4916.98i −0.186564 + 3.24219i
\(133\) −123.783 + 312.006i −0.0807020 + 0.203416i
\(134\) 3014.85i 1.94361i
\(135\) −241.301 658.672i −0.153836 0.419922i
\(136\) 4043.40 + 2334.46i 2.54940 + 1.47190i
\(137\) −1584.16 914.618i −0.987915 0.570373i −0.0832645 0.996527i \(-0.526535\pi\)
−0.904650 + 0.426155i \(0.859868\pi\)
\(138\) −1114.39 2215.08i −0.687416 1.36638i
\(139\) 2449.22i 1.49453i −0.664525 0.747266i \(-0.731366\pi\)
0.664525 0.747266i \(-0.268634\pi\)
\(140\) −1549.35 + 1226.25i −0.935317 + 0.740264i
\(141\) 323.615 + 18.6216i 0.193286 + 0.0111222i
\(142\) −1811.86 3138.23i −1.07076 1.85461i
\(143\) −509.665 + 882.766i −0.298044 + 0.516228i
\(144\) −3550.06 + 4782.50i −2.05444 + 2.76765i
\(145\) 1337.07 771.957i 0.765776 0.442121i
\(146\) −1155.26 −0.654864
\(147\) 1225.19 + 1294.38i 0.687429 + 0.726251i
\(148\) −3580.19 −1.98845
\(149\) 733.815 423.668i 0.403466 0.232941i −0.284512 0.958672i \(-0.591832\pi\)
0.687979 + 0.725731i \(0.258498\pi\)
\(150\) −588.132 386.232i −0.320138 0.210238i
\(151\) 209.435 362.753i 0.112872 0.195499i −0.804055 0.594554i \(-0.797328\pi\)
0.916927 + 0.399055i \(0.130662\pi\)
\(152\) 654.670 + 1133.92i 0.349347 + 0.605087i
\(153\) 1733.44 + 200.156i 0.915950 + 0.105762i
\(154\) 3494.08 2765.41i 1.82832 1.44704i
\(155\) 476.436i 0.246892i
\(156\) −2272.82 + 1143.44i −1.16648 + 0.586850i
\(157\) 2635.77 + 1521.76i 1.33985 + 0.773565i 0.986786 0.162032i \(-0.0518047\pi\)
0.353069 + 0.935597i \(0.385138\pi\)
\(158\) 2708.10 + 1563.52i 1.36357 + 0.787260i
\(159\) −106.789 + 53.7247i −0.0532635 + 0.0267965i
\(160\) 3084.52i 1.52408i
\(161\) −601.716 + 1516.68i −0.294546 + 0.742429i
\(162\) −899.867 + 3844.67i −0.436421 + 1.86461i
\(163\) 453.547 + 785.567i 0.217942 + 0.377487i 0.954179 0.299237i \(-0.0967322\pi\)
−0.736237 + 0.676724i \(0.763399\pi\)
\(164\) 2894.08 5012.70i 1.37799 2.38675i
\(165\) 964.668 + 633.507i 0.455147 + 0.298900i
\(166\) −6009.55 + 3469.62i −2.80983 + 1.62226i
\(167\) −1763.11 −0.816967 −0.408483 0.912766i \(-0.633942\pi\)
−0.408483 + 0.912766i \(0.633942\pi\)
\(168\) 6925.06 614.004i 3.18024 0.281973i
\(169\) 1670.43 0.760323
\(170\) 1515.78 875.133i 0.683851 0.394822i
\(171\) 392.928 + 291.672i 0.175719 + 0.130437i
\(172\) 2410.42 4174.97i 1.06856 1.85081i
\(173\) 861.685 + 1492.48i 0.378686 + 0.655904i 0.990871 0.134811i \(-0.0430426\pi\)
−0.612185 + 0.790714i \(0.709709\pi\)
\(174\) −8676.21 499.251i −3.78013 0.217518i
\(175\) 67.3187 + 458.086i 0.0290790 + 0.197875i
\(176\) 9799.08i 4.19678i
\(177\) −191.889 381.418i −0.0814874 0.161973i
\(178\) −4797.55 2769.86i −2.02018 1.16635i
\(179\) 173.172 + 99.9810i 0.0723100 + 0.0417482i 0.535719 0.844396i \(-0.320041\pi\)
−0.463409 + 0.886144i \(0.653374\pi\)
\(180\) 1144.64 + 2643.41i 0.473979 + 1.09460i
\(181\) 266.755i 0.109546i −0.998499 0.0547729i \(-0.982557\pi\)
0.998499 0.0547729i \(-0.0174435\pi\)
\(182\) 2139.67 + 848.879i 0.871446 + 0.345731i
\(183\) −146.472 + 2545.45i −0.0591666 + 1.02822i
\(184\) 3182.38 + 5512.05i 1.27505 + 2.20844i
\(185\) −419.468 + 726.539i −0.166702 + 0.288736i
\(186\) 1472.12 2241.66i 0.580328 0.883690i
\(187\) −2486.21 + 1435.42i −0.972245 + 0.561326i
\(188\) −1331.11 −0.516388
\(189\) 2283.88 1239.02i 0.878982 0.476855i
\(190\) 490.841 0.187418
\(191\) 1178.07 680.162i 0.446296 0.257669i −0.259969 0.965617i \(-0.583712\pi\)
0.706265 + 0.707948i \(0.250379\pi\)
\(192\) 4497.06 6847.86i 1.69035 2.57397i
\(193\) −1749.00 + 3029.35i −0.652308 + 1.12983i 0.330253 + 0.943892i \(0.392866\pi\)
−0.982561 + 0.185939i \(0.940467\pi\)
\(194\) 1280.88 + 2218.55i 0.474031 + 0.821045i
\(195\) −34.2493 + 595.199i −0.0125777 + 0.218580i
\(196\) −5328.23 5017.51i −1.94177 1.82854i
\(197\) 3118.87i 1.12797i −0.825784 0.563986i \(-0.809267\pi\)
0.825784 0.563986i \(-0.190733\pi\)
\(198\) −2581.37 5961.37i −0.926514 2.13968i
\(199\) 3212.10 + 1854.51i 1.14422 + 0.660615i 0.947472 0.319839i \(-0.103629\pi\)
0.196747 + 0.980454i \(0.436962\pi\)
\(200\) 1564.10 + 903.036i 0.552994 + 0.319271i
\(201\) −1299.84 2583.69i −0.456137 0.906664i
\(202\) 3584.11i 1.24840i
\(203\) 3549.06 + 4484.21i 1.22707 + 1.55039i
\(204\) −7153.74 411.644i −2.45521 0.141279i
\(205\) −678.162 1174.61i −0.231048 0.400187i
\(206\) −3595.10 + 6226.89i −1.21593 + 2.10606i
\(207\) 1910.04 + 1417.83i 0.641340 + 0.476069i
\(208\) 4383.87 2531.03i 1.46138 0.843728i
\(209\) −805.089 −0.266455
\(210\) 1098.68 2363.33i 0.361030 0.776595i
\(211\) −3228.76 −1.05344 −0.526722 0.850038i \(-0.676579\pi\)
−0.526722 + 0.850038i \(0.676579\pi\)
\(212\) 425.124 245.445i 0.137725 0.0795154i
\(213\) 2905.78 + 1908.25i 0.934744 + 0.613856i
\(214\) −35.2275 + 61.0158i −0.0112528 + 0.0194904i
\(215\) −564.826 978.307i −0.179167 0.310326i
\(216\) 1739.07 9985.08i 0.547819 3.14536i
\(217\) −1745.99 + 256.585i −0.546201 + 0.0802678i
\(218\) 7111.78i 2.20950i
\(219\) 990.046 498.086i 0.305485 0.153687i
\(220\) −4104.26 2369.60i −1.25777 0.726174i
\(221\) −1284.34 741.514i −0.390923 0.225700i
\(222\) 4218.52 2122.31i 1.27535 0.641623i
\(223\) 573.232i 0.172137i −0.996289 0.0860683i \(-0.972570\pi\)
0.996289 0.0860683i \(-0.0274303\pi\)
\(224\) −11303.8 + 1661.17i −3.37173 + 0.495497i
\(225\) 670.545 + 77.4261i 0.198680 + 0.0229411i
\(226\) 2128.62 + 3686.87i 0.626520 + 1.08516i
\(227\) −599.567 + 1038.48i −0.175307 + 0.303640i −0.940267 0.340437i \(-0.889425\pi\)
0.764961 + 0.644077i \(0.222758\pi\)
\(228\) −1679.68 1103.06i −0.487893 0.320404i
\(229\) 3537.94 2042.63i 1.02093 0.589436i 0.106559 0.994306i \(-0.466017\pi\)
0.914374 + 0.404871i \(0.132683\pi\)
\(230\) 2386.00 0.684036
\(231\) −1802.09 + 3876.39i −0.513284 + 1.10410i
\(232\) 22307.3 6.31271
\(233\) −471.919 + 272.462i −0.132688 + 0.0766077i −0.564875 0.825177i \(-0.691076\pi\)
0.432186 + 0.901784i \(0.357742\pi\)
\(234\) 2000.23 2694.62i 0.558798 0.752790i
\(235\) −155.957 + 270.126i −0.0432916 + 0.0749832i
\(236\) 876.660 + 1518.42i 0.241804 + 0.418817i
\(237\) −2994.92 172.335i −0.820847 0.0472336i
\(238\) 4023.41 + 5083.55i 1.09580 + 1.38453i
\(239\) 2085.41i 0.564411i 0.959354 + 0.282205i \(0.0910659\pi\)
−0.959354 + 0.282205i \(0.908934\pi\)
\(240\) −2575.77 5119.85i −0.692771 1.37702i
\(241\) 733.059 + 423.232i 0.195936 + 0.113124i 0.594758 0.803905i \(-0.297248\pi\)
−0.398823 + 0.917028i \(0.630581\pi\)
\(242\) 3012.45 + 1739.24i 0.800198 + 0.461994i
\(243\) −886.439 3682.82i −0.234013 0.972234i
\(244\) 10470.0i 2.74703i
\(245\) −1642.49 + 493.405i −0.428306 + 0.128663i
\(246\) −438.591 + 7622.03i −0.113673 + 1.97546i
\(247\) −207.948 360.177i −0.0535686 0.0927835i
\(248\) −3441.91 + 5961.57i −0.881297 + 1.52645i
\(249\) 3654.21 5564.42i 0.930025 1.41619i
\(250\) 586.346 338.527i 0.148335 0.0856413i
\(251\) 2920.18 0.734343 0.367172 0.930153i \(-0.380326\pi\)
0.367172 + 0.930153i \(0.380326\pi\)
\(252\) −9070.84 + 5618.35i −2.26750 + 1.40446i
\(253\) −3913.58 −0.972509
\(254\) −2079.76 + 1200.75i −0.513763 + 0.296621i
\(255\) −921.693 + 1403.50i −0.226348 + 0.344669i
\(256\) −3455.32 + 5984.79i −0.843585 + 1.46113i
\(257\) −1596.86 2765.85i −0.387586 0.671318i 0.604538 0.796576i \(-0.293358\pi\)
−0.992124 + 0.125258i \(0.960024\pi\)
\(258\) −365.293 + 6348.22i −0.0881478 + 1.53187i
\(259\) −2888.45 1145.94i −0.692970 0.274924i
\(260\) 2448.20i 0.583965i
\(261\) 7650.67 3312.86i 1.81442 0.785674i
\(262\) −11585.7 6689.01i −2.73194 1.57728i
\(263\) −3540.11 2043.89i −0.830010 0.479207i 0.0238458 0.999716i \(-0.492409\pi\)
−0.853856 + 0.520509i \(0.825742\pi\)
\(264\) 7494.09 + 14896.0i 1.74708 + 3.47267i
\(265\) 115.029i 0.0266648i
\(266\) 264.342 + 1798.78i 0.0609318 + 0.414625i
\(267\) 5305.66 + 305.301i 1.21611 + 0.0699780i
\(268\) 5938.41 + 10285.6i 1.35353 + 2.34438i
\(269\) −2040.61 + 3534.43i −0.462520 + 0.801109i −0.999086 0.0427501i \(-0.986388\pi\)
0.536566 + 0.843859i \(0.319721\pi\)
\(270\) −2915.71 2436.18i −0.657202 0.549116i
\(271\) −3822.65 + 2207.01i −0.856861 + 0.494709i −0.862960 0.505272i \(-0.831392\pi\)
0.00609886 + 0.999981i \(0.498059\pi\)
\(272\) 14256.7 3.17809
\(273\) −2199.67 + 195.031i −0.487655 + 0.0432375i
\(274\) −9907.93 −2.18453
\(275\) −961.739 + 555.260i −0.210891 + 0.121758i
\(276\) −8165.02 5362.05i −1.78071 1.16941i
\(277\) 2349.99 4070.31i 0.509738 0.882892i −0.490199 0.871611i \(-0.663076\pi\)
0.999936 0.0112809i \(-0.00359091\pi\)
\(278\) −6633.01 11488.7i −1.43101 2.47859i
\(279\) −295.109 + 2555.77i −0.0633251 + 0.548424i
\(280\) −2467.00 + 6218.29i −0.526541 + 1.32719i
\(281\) 5240.30i 1.11249i 0.831018 + 0.556246i \(0.187759\pi\)
−0.831018 + 0.556246i \(0.812241\pi\)
\(282\) 1568.44 789.070i 0.331202 0.166626i
\(283\) −3198.19 1846.48i −0.671777 0.387851i 0.124972 0.992160i \(-0.460116\pi\)
−0.796750 + 0.604309i \(0.793449\pi\)
\(284\) −12362.9 7137.71i −2.58310 1.49136i
\(285\) −420.645 + 211.624i −0.0874276 + 0.0439843i
\(286\) 5521.13i 1.14151i
\(287\) 3939.36 3117.84i 0.810220 0.641255i
\(288\) −1910.58 + 16546.5i −0.390909 + 3.38545i
\(289\) 368.108 + 637.582i 0.0749253 + 0.129774i
\(290\) 4181.25 7242.14i 0.846660 1.46646i
\(291\) −2054.22 1349.03i −0.413816 0.271757i
\(292\) −3941.36 + 2275.54i −0.789899 + 0.456048i
\(293\) −3440.35 −0.685964 −0.342982 0.939342i \(-0.611437\pi\)
−0.342982 + 0.939342i \(0.611437\pi\)
\(294\) 9252.56 + 2753.57i 1.83544 + 0.546229i
\(295\) 410.850 0.0810868
\(296\) −10497.5 + 6060.71i −2.06133 + 1.19011i
\(297\) 4782.42 + 3995.88i 0.934358 + 0.780689i
\(298\) 2294.77 3974.66i 0.446082 0.772637i
\(299\) −1010.85 1750.84i −0.195515 0.338641i
\(300\) −2767.27 159.236i −0.532562 0.0306450i
\(301\) 3281.01 2596.78i 0.628286 0.497262i
\(302\) 2268.79i 0.432298i
\(303\) −1545.27 3071.54i −0.292982 0.582361i
\(304\) 3462.48 + 1999.06i 0.653246 + 0.377152i
\(305\) −2124.72 1226.70i −0.398888 0.230298i
\(306\) 8673.23 3755.64i 1.62031 0.701621i
\(307\) 962.266i 0.178891i −0.995992 0.0894453i \(-0.971491\pi\)
0.995992 0.0894453i \(-0.0285094\pi\)
\(308\) 6473.49 16317.0i 1.19760 3.01866i
\(309\) 396.260 6886.39i 0.0729529 1.26781i
\(310\) 1290.29 + 2234.85i 0.236399 + 0.409455i
\(311\) 4433.22 7678.57i 0.808312 1.40004i −0.105721 0.994396i \(-0.533715\pi\)
0.914032 0.405641i \(-0.132952\pi\)
\(312\) −4728.45 + 7200.20i −0.857999 + 1.30651i
\(313\) 6119.35 3533.01i 1.10507 0.638011i 0.167521 0.985869i \(-0.446424\pi\)
0.937548 + 0.347857i \(0.113091\pi\)
\(314\) 16485.0 2.96275
\(315\) 77.3791 + 2499.04i 0.0138407 + 0.446999i
\(316\) 12318.8 2.19300
\(317\) 5750.08 3319.81i 1.01879 0.588200i 0.105038 0.994468i \(-0.466504\pi\)
0.913754 + 0.406269i \(0.133170\pi\)
\(318\) −355.423 + 541.217i −0.0626764 + 0.0954400i
\(319\) −6858.19 + 11878.7i −1.20371 + 2.08489i
\(320\) 3941.61 + 6827.07i 0.688571 + 1.19264i
\(321\) 3.88286 67.4780i 0.000675140 0.0117329i
\(322\) 1284.98 + 8743.96i 0.222389 + 1.51330i
\(323\) 1171.33i 0.201778i
\(324\) 4502.90 + 14889.2i 0.772102 + 2.55302i
\(325\) −496.820 286.839i −0.0847957 0.0489568i
\(326\) 4254.97 + 2456.61i 0.722887 + 0.417359i
\(327\) 3066.21 + 6094.71i 0.518538 + 1.03070i
\(328\) 19596.9i 3.29896i
\(329\) −1073.92 426.058i −0.179960 0.0713962i
\(330\) 6240.71 + 359.106i 1.04103 + 0.0599035i
\(331\) −5714.37 9897.58i −0.948913 1.64357i −0.747720 0.664014i \(-0.768851\pi\)
−0.201194 0.979552i \(-0.564482\pi\)
\(332\) −13668.4 + 23674.3i −2.25948 + 3.91354i
\(333\) −2700.20 + 3637.59i −0.444354 + 0.598616i
\(334\) −8270.33 + 4774.88i −1.35489 + 0.782244i
\(335\) 2783.06 0.453895
\(336\) 17375.5 12196.7i 2.82116 1.98031i
\(337\) −3287.98 −0.531477 −0.265738 0.964045i \(-0.585616\pi\)
−0.265738 + 0.964045i \(0.585616\pi\)
\(338\) 7835.59 4523.88i 1.26095 0.728008i
\(339\) −3413.78 2241.86i −0.546935 0.359178i
\(340\) 3447.54 5971.31i 0.549909 0.952470i
\(341\) −2116.37 3665.66i −0.336093 0.582131i
\(342\) 2633.05 + 304.031i 0.416312 + 0.0480705i
\(343\) −2692.74 5753.50i −0.423890 0.905714i
\(344\) 16321.9i 2.55819i
\(345\) −2044.78 + 1028.72i −0.319093 + 0.160534i
\(346\) 8083.93 + 4667.26i 1.25605 + 0.725183i
\(347\) −4738.46 2735.75i −0.733066 0.423236i 0.0864768 0.996254i \(-0.472439\pi\)
−0.819543 + 0.573018i \(0.805772\pi\)
\(348\) −30583.7 + 15386.5i −4.71108 + 2.37012i
\(349\) 5647.28i 0.866165i −0.901354 0.433083i \(-0.857426\pi\)
0.901354 0.433083i \(-0.142574\pi\)
\(350\) 1556.37 + 1966.46i 0.237690 + 0.300320i
\(351\) −552.397 + 3171.65i −0.0840022 + 0.482308i
\(352\) −13701.7 23732.0i −2.07472 3.59352i
\(353\) −5123.73 + 8874.56i −0.772546 + 1.33809i 0.163618 + 0.986524i \(0.447684\pi\)
−0.936164 + 0.351565i \(0.885650\pi\)
\(354\) −1933.07 1269.47i −0.290230 0.190597i
\(355\) −2896.95 + 1672.56i −0.433111 + 0.250057i
\(356\) −21823.5 −3.24899
\(357\) −5639.77 2621.86i −0.836102 0.388694i
\(358\) 1083.08 0.159895
\(359\) 757.417 437.295i 0.111351 0.0642884i −0.443290 0.896378i \(-0.646189\pi\)
0.554641 + 0.832090i \(0.312856\pi\)
\(360\) 7831.06 + 5813.03i 1.14648 + 0.851037i
\(361\) −3265.26 + 5655.59i −0.476054 + 0.824551i
\(362\) −722.431 1251.29i −0.104890 0.181675i
\(363\) −3331.51 191.703i −0.481704 0.0277185i
\(364\) 8971.89 1318.48i 1.29191 0.189854i
\(365\) 1066.44i 0.152932i
\(366\) 6206.56 + 12336.8i 0.886399 + 1.76190i
\(367\) 2917.76 + 1684.57i 0.415002 + 0.239602i 0.692937 0.720998i \(-0.256316\pi\)
−0.277934 + 0.960600i \(0.589650\pi\)
\(368\) 16831.3 + 9717.55i 2.38422 + 1.37653i
\(369\) −2910.34 6721.09i −0.410586 0.948200i
\(370\) 4544.04i 0.638468i
\(371\) 421.545 61.9488i 0.0589907 0.00866905i
\(372\) 606.927 10547.4i 0.0845905 1.47005i
\(373\) 5197.92 + 9003.06i 0.721549 + 1.24976i 0.960379 + 0.278699i \(0.0899030\pi\)
−0.238829 + 0.971062i \(0.576764\pi\)
\(374\) −7774.83 + 13466.4i −1.07494 + 1.86185i
\(375\) −356.537 + 542.914i −0.0490974 + 0.0747626i
\(376\) −3902.93 + 2253.36i −0.535314 + 0.309064i
\(377\) −7085.68 −0.967987
\(378\) 7357.59 11997.2i 1.00115 1.63246i
\(379\) −10819.1 −1.46634 −0.733169 0.680047i \(-0.761959\pi\)
−0.733169 + 0.680047i \(0.761959\pi\)
\(380\) 1674.58 966.820i 0.226064 0.130518i
\(381\) 1264.63 1925.71i 0.170050 0.258942i
\(382\) 3684.05 6380.96i 0.493435 0.854655i
\(383\) 5329.00 + 9230.09i 0.710964 + 1.23142i 0.964496 + 0.264098i \(0.0850742\pi\)
−0.253532 + 0.967327i \(0.581592\pi\)
\(384\) 1075.98 18698.9i 0.142991 2.48495i
\(385\) −2552.80 3225.44i −0.337929 0.426971i
\(386\) 18946.6i 2.49834i
\(387\) −2423.96 5597.85i −0.318389 0.735283i
\(388\) 8739.86 + 5045.96i 1.14355 + 0.660232i
\(389\) 13027.0 + 7521.13i 1.69793 + 0.980299i 0.947723 + 0.319094i \(0.103379\pi\)
0.750205 + 0.661205i \(0.229955\pi\)
\(390\) 1451.27 + 2884.70i 0.188431 + 0.374544i
\(391\) 5693.89i 0.736451i
\(392\) −24116.7 5691.94i −3.10734 0.733383i
\(393\) 12812.8 + 737.279i 1.64458 + 0.0946331i
\(394\) −8446.58 14629.9i −1.08003 1.87067i
\(395\) 1443.31 2499.89i 0.183851 0.318439i
\(396\) −20549.0 15253.6i −2.60764 1.93566i
\(397\) −241.393 + 139.368i −0.0305168 + 0.0176189i −0.515181 0.857082i \(-0.672275\pi\)
0.484664 + 0.874700i \(0.338942\pi\)
\(398\) 20089.6 2.53015
\(399\) −1002.07 1427.56i −0.125731 0.179117i
\(400\) 5514.92 0.689365
\(401\) 1862.25 1075.17i 0.231911 0.133894i −0.379542 0.925174i \(-0.623919\pi\)
0.611453 + 0.791281i \(0.290585\pi\)
\(402\) −13094.4 8599.25i −1.62460 1.06689i
\(403\) 1093.28 1893.62i 0.135137 0.234065i
\(404\) 7059.70 + 12227.8i 0.869389 + 1.50583i
\(405\) 3549.08 + 830.682i 0.435445 + 0.101918i
\(406\) 28792.0 + 11422.7i 3.51952 + 1.39631i
\(407\) 7453.24i 0.907723i
\(408\) −21672.3 + 10903.2i −2.62975 + 1.32301i
\(409\) 2743.48 + 1583.95i 0.331678 + 0.191494i 0.656586 0.754251i \(-0.272000\pi\)
−0.324908 + 0.945746i \(0.605333\pi\)
\(410\) −6362.20 3673.22i −0.766357 0.442457i
\(411\) 8490.99 4271.76i 1.01905 0.512678i
\(412\) 28325.4i 3.38711i
\(413\) 221.263 + 1505.64i 0.0263623 + 0.179389i
\(414\) 12799.4 + 1477.91i 1.51946 + 0.175448i
\(415\) 3202.86 + 5547.52i 0.378849 + 0.656186i
\(416\) 7078.09 12259.6i 0.834211 1.44490i
\(417\) 10637.7 + 6985.90i 1.24924 + 0.820386i
\(418\) −3776.49 + 2180.35i −0.441899 + 0.255131i
\(419\) −5925.57 −0.690890 −0.345445 0.938439i \(-0.612272\pi\)
−0.345445 + 0.938439i \(0.612272\pi\)
\(420\) −906.764 10227.0i −0.105347 1.18815i
\(421\) −568.868 −0.0658550 −0.0329275 0.999458i \(-0.510483\pi\)
−0.0329275 + 0.999458i \(0.510483\pi\)
\(422\) −15145.3 + 8744.17i −1.74707 + 1.00867i
\(423\) −1003.93 + 1352.45i −0.115396 + 0.155457i
\(424\) 831.001 1439.34i 0.0951816 0.164859i
\(425\) −807.851 1399.24i −0.0922035 0.159701i
\(426\) 18798.3 + 1081.70i 2.13798 + 0.123025i
\(427\) 3351.23 8447.07i 0.379807 0.957336i
\(428\) 277.553i 0.0313459i
\(429\) −2380.41 4731.55i −0.267896 0.532497i
\(430\) −5298.93 3059.34i −0.594273 0.343104i
\(431\) −9170.19 5294.41i −1.02485 0.591700i −0.109348 0.994003i \(-0.534876\pi\)
−0.915506 + 0.402303i \(0.868210\pi\)
\(432\) −10646.0 29060.2i −1.18567 3.23648i
\(433\) 10574.5i 1.17362i −0.809723 0.586812i \(-0.800383\pi\)
0.809723 0.586812i \(-0.199617\pi\)
\(434\) −7495.16 + 5932.10i −0.828984 + 0.656106i
\(435\) −460.868 + 8009.16i −0.0507975 + 0.882781i
\(436\) −14008.2 24263.0i −1.53870 2.66510i
\(437\) 798.390 1382.85i 0.0873963 0.151375i
\(438\) 3295.15 5017.66i 0.359471 0.547382i
\(439\) −939.951 + 542.681i −0.102190 + 0.0589994i −0.550224 0.835017i \(-0.685458\pi\)
0.448034 + 0.894017i \(0.352124\pi\)
\(440\) −16045.4 −1.73849
\(441\) −9116.53 + 1629.43i −0.984400 + 0.175945i
\(442\) −8032.72 −0.864429
\(443\) −257.587 + 148.718i −0.0276260 + 0.0159499i −0.513749 0.857940i \(-0.671744\pi\)
0.486123 + 0.873890i \(0.338411\pi\)
\(444\) 10211.8 15549.9i 1.09151 1.66209i
\(445\) −2556.91 + 4428.70i −0.272380 + 0.471776i
\(446\) −1552.44 2688.90i −0.164821 0.285478i
\(447\) −252.935 + 4395.62i −0.0267638 + 0.465113i
\(448\) −22896.3 + 18121.5i −2.41462 + 1.91107i
\(449\) 8313.87i 0.873843i 0.899500 + 0.436922i \(0.143931\pi\)
−0.899500 + 0.436922i \(0.856069\pi\)
\(450\) 3355.06 1452.79i 0.351464 0.152189i
\(451\) 10435.4 + 6024.90i 1.08955 + 0.629050i
\(452\) 14524.2 + 8385.56i 1.51142 + 0.872619i
\(453\) 978.177 + 1944.32i 0.101454 + 0.201661i
\(454\) 6495.03i 0.671425i
\(455\) 783.615 1975.17i 0.0807394 0.203511i
\(456\) −6792.29 390.846i −0.697540 0.0401382i
\(457\) −2604.24 4510.68i −0.266568 0.461709i 0.701406 0.712762i \(-0.252556\pi\)
−0.967973 + 0.251054i \(0.919223\pi\)
\(458\) 11063.8 19163.0i 1.12877 1.95508i
\(459\) −5813.63 + 6957.97i −0.591192 + 0.707561i
\(460\) 8140.23 4699.76i 0.825087 0.476364i
\(461\) 7763.38 0.784332 0.392166 0.919895i \(-0.371726\pi\)
0.392166 + 0.919895i \(0.371726\pi\)
\(462\) 2044.92 + 23063.7i 0.205927 + 2.32255i
\(463\) 9492.44 0.952810 0.476405 0.879226i \(-0.341940\pi\)
0.476405 + 0.879226i \(0.341940\pi\)
\(464\) 58990.6 34058.2i 5.90209 3.40757i
\(465\) −2069.31 1358.94i −0.206370 0.135525i
\(466\) −1475.77 + 2556.11i −0.146704 + 0.254098i
\(467\) 1807.27 + 3130.28i 0.179080 + 0.310176i 0.941566 0.336829i \(-0.109354\pi\)
−0.762486 + 0.647005i \(0.776021\pi\)
\(468\) 1516.43 13133.0i 0.149780 1.29717i
\(469\) 1498.82 + 10199.0i 0.147567 + 1.00415i
\(470\) 1689.46i 0.165806i
\(471\) −14127.5 + 7107.45i −1.38208 + 0.695317i
\(472\) 5140.89 + 2968.10i 0.501332 + 0.289444i
\(473\) 8691.44 + 5018.01i 0.844890 + 0.487798i
\(474\) −14515.2 + 7302.50i −1.40655 + 0.707626i
\(475\) 453.103i 0.0437680i
\(476\) 23739.7 + 9418.32i 2.28594 + 0.906907i
\(477\) 71.2498 617.056i 0.00683922 0.0592307i
\(478\) 5647.75 + 9782.18i 0.540422 + 0.936039i
\(479\) 44.6749 77.3792i 0.00426148 0.00738110i −0.863887 0.503686i \(-0.831977\pi\)
0.868148 + 0.496305i \(0.165310\pi\)
\(480\) −13397.0 8797.97i −1.27393 0.836605i
\(481\) 3334.40 1925.12i 0.316082 0.182490i
\(482\) 4584.81 0.433263
\(483\) −4871.14 6939.47i −0.458891 0.653740i
\(484\) 13703.3 1.28693
\(485\) 2047.98 1182.40i 0.191740 0.110701i
\(486\) −14131.9 14874.6i −1.31901 1.38832i
\(487\) −4558.91 + 7896.27i −0.424197 + 0.734731i −0.996345 0.0854193i \(-0.972777\pi\)
0.572148 + 0.820151i \(0.306110\pi\)
\(488\) −17724.1 30699.1i −1.64413 2.84771i
\(489\) −4705.62 270.773i −0.435164 0.0250405i
\(490\) −6368.30 + 6762.67i −0.587123 + 0.623482i
\(491\) 8849.23i 0.813361i 0.913570 + 0.406680i \(0.133314\pi\)
−0.913570 + 0.406680i \(0.866686\pi\)
\(492\) 13516.9 + 26867.7i 1.23860 + 2.46197i
\(493\) −17282.4 9978.01i −1.57883 0.911536i
\(494\) −1950.88 1126.34i −0.177680 0.102584i
\(495\) −5503.04 + 2382.91i −0.499684 + 0.216371i
\(496\) 21020.1i 1.90288i
\(497\) −7689.56 9715.68i −0.694012 0.876877i
\(498\) 2071.40 35997.8i 0.186389 3.23915i
\(499\) 8611.60 + 14915.7i 0.772562 + 1.33812i 0.936155 + 0.351588i \(0.114358\pi\)
−0.163593 + 0.986528i \(0.552308\pi\)
\(500\) 1333.61 2309.88i 0.119282 0.206602i
\(501\) 5028.91 7657.74i 0.448454 0.682879i
\(502\) 13697.9 7908.48i 1.21786 0.703133i
\(503\) −3093.21 −0.274193 −0.137097 0.990558i \(-0.543777\pi\)
−0.137097 + 0.990558i \(0.543777\pi\)
\(504\) −17085.5 + 31829.0i −1.51002 + 2.81305i
\(505\) 3308.55 0.291542
\(506\) −18357.7 + 10598.8i −1.61284 + 0.931176i
\(507\) −4764.56 + 7255.20i −0.417360 + 0.635532i
\(508\) −4730.29 + 8193.09i −0.413135 + 0.715570i
\(509\) 9975.53 + 17278.1i 0.868679 + 1.50460i 0.863347 + 0.504610i \(0.168364\pi\)
0.00533139 + 0.999986i \(0.498303\pi\)
\(510\) −522.465 + 9079.63i −0.0453630 + 0.788339i
\(511\) −3908.18 + 574.332i −0.338332 + 0.0497200i
\(512\) 8594.64i 0.741861i
\(513\) −2387.57 + 874.675i −0.205485 + 0.0752785i
\(514\) −14981.0 8649.30i −1.28557 0.742226i
\(515\) 5748.15 + 3318.69i 0.491832 + 0.283960i
\(516\) 11258.0 + 22377.5i 0.960474 + 1.90914i
\(517\) 2771.10i 0.235730i
\(518\) −16652.5 + 2447.19i −1.41249 + 0.207574i
\(519\) −8940.11 514.436i −0.756122 0.0435092i
\(520\) −4144.42 7178.34i −0.349509 0.605367i
\(521\) 6479.49 11222.8i 0.544859 0.943723i −0.453757 0.891125i \(-0.649917\pi\)
0.998616 0.0525977i \(-0.0167501\pi\)
\(522\) 26915.6 36259.5i 2.25682 3.04030i
\(523\) 17989.0 10385.9i 1.50402 0.868347i 0.504033 0.863685i \(-0.331849\pi\)
0.999989 0.00466274i \(-0.00148420\pi\)
\(524\) −52702.0 −4.39370
\(525\) −2181.63 1014.21i −0.181360 0.0843122i
\(526\) −22141.1 −1.83536
\(527\) 5333.18 3079.11i 0.440829 0.254513i
\(528\) 42560.5 + 27949.9i 3.50797 + 2.30372i
\(529\) −2202.48 + 3814.81i −0.181021 + 0.313538i
\(530\) −311.523 539.573i −0.0255315 0.0442218i
\(531\) 2203.95 + 254.484i 0.180119 + 0.0207979i
\(532\) 4444.94 + 5616.14i 0.362242 + 0.457689i
\(533\) 6224.74i 0.505860i
\(534\) 25714.4 12936.8i 2.08384 1.04837i
\(535\) 56.3247 + 32.5191i 0.00455164 + 0.00262789i
\(536\) 34823.9 + 20105.6i 2.80628 + 1.62021i
\(537\) −928.188 + 466.965i −0.0745889 + 0.0375252i
\(538\) 22105.6i 1.77145i
\(539\) 10445.4 11092.3i 0.834725 0.886417i
\(540\) −14746.0 2568.27i −1.17512 0.204668i
\(541\) 5548.29 + 9609.91i 0.440923 + 0.763701i 0.997758 0.0669217i \(-0.0213178\pi\)
−0.556835 + 0.830623i \(0.687984\pi\)
\(542\) −11954.1 + 20705.1i −0.947366 + 1.64089i
\(543\) 1158.60 + 760.867i 0.0915662 + 0.0601324i
\(544\) 34527.8 19934.6i 2.72126 1.57112i
\(545\) −6565.00 −0.515989
\(546\) −9789.94 + 6872.02i −0.767346 + 0.538636i
\(547\) 3805.15 0.297434 0.148717 0.988880i \(-0.452486\pi\)
0.148717 + 0.988880i \(0.452486\pi\)
\(548\) −33802.5 + 19515.9i −2.63498 + 1.52131i
\(549\) −10637.9 7896.55i −0.826985 0.613874i
\(550\) −3007.53 + 5209.19i −0.233166 + 0.403856i
\(551\) −2798.21 4846.64i −0.216348 0.374726i
\(552\) −33017.7 1899.92i −2.54588 0.146496i
\(553\) 9938.63 + 3942.98i 0.764256 + 0.303206i
\(554\) 25457.1i 1.95229i
\(555\) −1959.14 3894.19i −0.149840 0.297836i
\(556\) −45259.1 26130.4i −3.45218 1.99312i
\(557\) 2655.83 + 1533.34i 0.202031 + 0.116643i 0.597602 0.801793i \(-0.296120\pi\)
−0.395572 + 0.918435i \(0.629453\pi\)
\(558\) 5537.30 + 12787.8i 0.420094 + 0.970160i
\(559\) 5184.45i 0.392270i
\(560\) 2970.06 + 20210.5i 0.224121 + 1.52509i
\(561\) 856.960 14892.6i 0.0644936 1.12080i
\(562\) 14191.9 + 24581.0i 1.06521 + 1.84500i
\(563\) 7931.28 13737.4i 0.593718 1.02835i −0.400008 0.916512i \(-0.630993\pi\)
0.993726 0.111839i \(-0.0356741\pi\)
\(564\) 3796.72 5781.42i 0.283459 0.431634i
\(565\) 3403.41 1964.96i 0.253421 0.146312i
\(566\) −20002.6 −1.48547
\(567\) −1132.84 + 13453.7i −0.0839059 + 0.996474i
\(568\) −48332.1 −3.57037
\(569\) −9173.42 + 5296.28i −0.675870 + 0.390213i −0.798297 0.602264i \(-0.794265\pi\)
0.122427 + 0.992477i \(0.460932\pi\)
\(570\) −1400.02 + 2131.88i −0.102878 + 0.156657i
\(571\) 5552.17 9616.64i 0.406920 0.704805i −0.587623 0.809135i \(-0.699936\pi\)
0.994543 + 0.104329i \(0.0332696\pi\)
\(572\) 10875.1 + 18836.2i 0.794948 + 1.37689i
\(573\) −406.065 + 7056.77i −0.0296049 + 0.514487i
\(574\) 10034.8 25293.7i 0.729697 1.83927i
\(575\) 2202.56i 0.159745i
\(576\) 16915.5 + 39064.3i 1.22363 + 2.82583i
\(577\) 16951.9 + 9787.19i 1.22308 + 0.706146i 0.965573 0.260130i \(-0.0837656\pi\)
0.257507 + 0.966276i \(0.417099\pi\)
\(578\) 3453.42 + 1993.83i 0.248518 + 0.143482i
\(579\) −8168.76 16237.1i −0.586325 1.16544i
\(580\) 32943.6i 2.35846i
\(581\) −18605.1 + 14725.1i −1.32852 + 1.05146i
\(582\) −13289.3 764.702i −0.946496 0.0544638i
\(583\) 510.968 + 885.022i 0.0362986 + 0.0628711i
\(584\) −7704.28 + 13344.2i −0.545899 + 0.945526i
\(585\) −2487.45 1846.44i −0.175801 0.130497i
\(586\) −16137.9 + 9317.22i −1.13763 + 0.656810i
\(587\) 4516.62 0.317582 0.158791 0.987312i \(-0.449240\pi\)
0.158791 + 0.987312i \(0.449240\pi\)
\(588\) 36990.3 8830.74i 2.59431 0.619343i
\(589\) 1727.00 0.120815
\(590\) 1927.20 1112.67i 0.134477 0.0776405i
\(591\) 13546.2 + 8895.96i 0.942839 + 0.619172i
\(592\) −18506.6 + 32054.4i −1.28483 + 2.22539i
\(593\) 4634.46 + 8027.12i 0.320935 + 0.555875i 0.980681 0.195613i \(-0.0626696\pi\)
−0.659746 + 0.751488i \(0.729336\pi\)
\(594\) 33255.0 + 5791.92i 2.29708 + 0.400076i
\(595\) 4692.71 3714.08i 0.323332 0.255903i
\(596\) 18080.2i 1.24261i
\(597\) −17216.6 + 8661.55i −1.18028 + 0.593792i
\(598\) −9483.31 5475.19i −0.648497 0.374410i
\(599\) −11438.3 6603.93i −0.780230 0.450466i 0.0562818 0.998415i \(-0.482075\pi\)
−0.836512 + 0.547949i \(0.815409\pi\)
\(600\) −8383.46 + 4217.67i −0.570422 + 0.286976i
\(601\) 20312.8i 1.37866i −0.724446 0.689332i \(-0.757904\pi\)
0.724446 0.689332i \(-0.242096\pi\)
\(602\) 8357.80 21066.6i 0.565845 1.42626i
\(603\) 14929.3 + 1723.85i 1.00824 + 0.116419i
\(604\) −4468.88 7740.32i −0.301053 0.521439i
\(605\) 1605.52 2780.85i 0.107891 0.186872i
\(606\) −15566.9 10223.0i −1.04350 0.685279i
\(607\) −5906.71 + 3410.24i −0.394969 + 0.228035i −0.684311 0.729191i \(-0.739897\pi\)
0.289342 + 0.957226i \(0.406563\pi\)
\(608\) 11180.9 0.745795
\(609\) −29599.3 + 2624.40i −1.96950 + 0.174624i
\(610\) −13288.7 −0.882041
\(611\) 1239.72 715.753i 0.0820847 0.0473916i
\(612\) 22192.5 29896.8i 1.46582 1.97468i
\(613\) −8226.29 + 14248.4i −0.542018 + 0.938802i 0.456770 + 0.889585i \(0.349006\pi\)
−0.998788 + 0.0492177i \(0.984327\pi\)
\(614\) −2606.02 4513.77i −0.171288 0.296679i
\(615\) 7036.02 + 404.871i 0.461333 + 0.0265463i
\(616\) −8641.27 58801.6i −0.565205 3.84608i
\(617\) 12385.4i 0.808130i −0.914730 0.404065i \(-0.867597\pi\)
0.914730 0.404065i \(-0.132403\pi\)
\(618\) −16791.1 33375.6i −1.09294 2.17243i
\(619\) 16122.6 + 9308.36i 1.04688 + 0.604418i 0.921775 0.387725i \(-0.126739\pi\)
0.125108 + 0.992143i \(0.460072\pi\)
\(620\) 8804.07 + 5083.03i 0.570290 + 0.329257i
\(621\) −11606.1 + 4251.84i −0.749980 + 0.274751i
\(622\) 48024.5i 3.09583i
\(623\) −17606.8 6985.21i −1.13227 0.449208i
\(624\) −1511.06 + 26259.8i −0.0969401 + 1.68467i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 19136.3 33145.1i 1.22179 2.11620i
\(627\) 2296.36 3496.76i 0.146264 0.222722i
\(628\) 56241.3 32470.9i 3.57368 2.06327i
\(629\) 10843.7 0.687390
\(630\) 7130.90 + 11512.8i 0.450955 + 0.728068i
\(631\) 2351.97 0.148385 0.0741923 0.997244i \(-0.476362\pi\)
0.0741923 + 0.997244i \(0.476362\pi\)
\(632\) 36119.9 20853.8i 2.27337 1.31253i
\(633\) 9209.38 14023.5i 0.578262 0.880544i
\(634\) 17981.5 31144.9i 1.12640 1.95098i
\(635\) 1108.43 + 1919.86i 0.0692706 + 0.119980i
\(636\) −146.534 + 2546.53i −0.00913592 + 0.158768i
\(637\) 7660.40 + 1807.98i 0.476477 + 0.112456i
\(638\) 74293.8i 4.61022i
\(639\) −16576.3 + 7177.79i −1.02621 + 0.444365i
\(640\) 15608.2 + 9011.37i 0.964010 + 0.556572i
\(641\) 3691.03 + 2131.02i 0.227437 + 0.131311i 0.609389 0.792871i \(-0.291415\pi\)
−0.381952 + 0.924182i \(0.624748\pi\)
\(642\) −164.531 327.039i −0.0101145 0.0201047i
\(643\) 6939.64i 0.425618i −0.977094 0.212809i \(-0.931739\pi\)
0.977094 0.212809i \(-0.0682612\pi\)
\(644\) 21607.1 + 27300.4i 1.32211 + 1.67047i
\(645\) 5860.15 + 337.208i 0.357741 + 0.0205854i
\(646\) −3172.21 5494.42i −0.193203 0.334637i
\(647\) 16226.1 28104.5i 0.985958 1.70773i 0.348358 0.937362i \(-0.386740\pi\)
0.637600 0.770367i \(-0.279927\pi\)
\(648\) 38408.0 + 36033.8i 2.32841 + 2.18448i
\(649\) −3161.04 + 1825.03i −0.191189 + 0.110383i
\(650\) −3107.29 −0.187504
\(651\) 3865.66 8315.25i 0.232730 0.500615i
\(652\) 19355.3 1.16260
\(653\) 15239.5 8798.55i 0.913276 0.527280i 0.0317925 0.999494i \(-0.489878\pi\)
0.881484 + 0.472214i \(0.156545\pi\)
\(654\) 30888.7 + 20284.9i 1.84686 + 1.21285i
\(655\) −6174.74 + 10695.0i −0.368347 + 0.637995i
\(656\) −29920.0 51823.0i −1.78076 3.08437i
\(657\) −660.563 + 5720.77i −0.0392253 + 0.339709i
\(658\) −6191.35 + 909.859i −0.366815 + 0.0539058i
\(659\) 11521.1i 0.681027i −0.940240 0.340514i \(-0.889399\pi\)
0.940240 0.340514i \(-0.110601\pi\)
\(660\) 21998.5 11067.3i 1.29741 0.652719i
\(661\) 23492.6 + 13563.5i 1.38239 + 0.798120i 0.992442 0.122718i \(-0.0391612\pi\)
0.389944 + 0.920839i \(0.372495\pi\)
\(662\) −53609.6 30951.5i −3.14742 1.81717i
\(663\) 6883.95 3463.27i 0.403244 0.202869i
\(664\) 92553.6i 5.40930i
\(665\) 1660.48 244.019i 0.0968283 0.0142295i
\(666\) −2814.61 + 24375.8i −0.163760 + 1.41823i
\(667\) −13602.2 23559.8i −0.789627 1.36767i
\(668\) −18810.4 + 32580.5i −1.08951 + 1.88709i
\(669\) 2489.73 + 1635.03i 0.143884 + 0.0944901i
\(670\) 13054.7 7537.12i 0.752755 0.434604i
\(671\) 21796.5 1.25402
\(672\) 25026.9 53834.2i 1.43666 3.09032i
\(673\) −13645.5 −0.781566 −0.390783 0.920483i \(-0.627796\pi\)
−0.390783 + 0.920483i \(0.627796\pi\)
\(674\) −15423.1 + 8904.56i −0.881420 + 0.508888i
\(675\) −2248.88 + 2691.54i −0.128236 + 0.153478i
\(676\) 17821.6 30867.9i 1.01397 1.75625i
\(677\) −3038.14 5262.22i −0.172475 0.298735i 0.766810 0.641874i \(-0.221843\pi\)
−0.939284 + 0.343140i \(0.888510\pi\)
\(678\) −22084.7 1270.81i −1.25097 0.0719840i
\(679\) 5436.09 + 6868.44i 0.307243 + 0.388198i
\(680\) 23344.6i 1.31651i
\(681\) −2800.30 5566.17i −0.157574 0.313210i
\(682\) −19854.8 11463.2i −1.11478 0.643618i
\(683\) −6220.19 3591.23i −0.348476 0.201193i 0.315538 0.948913i \(-0.397815\pi\)
−0.664014 + 0.747720i \(0.731148\pi\)
\(684\) 9581.91 4149.12i 0.535634 0.231938i
\(685\) 9146.18i 0.510157i
\(686\) −28212.7 19695.8i −1.57021 1.09619i
\(687\) −1219.48 + 21192.6i −0.0677233 + 1.17692i
\(688\) −24919.8 43162.3i −1.38090 2.39178i
\(689\) −263.958 + 457.189i −0.0145951 + 0.0252794i
\(690\) −6805.59 + 10363.2i −0.375485 + 0.571766i
\(691\) −13426.5 + 7751.80i −0.739173 + 0.426762i −0.821769 0.569821i \(-0.807012\pi\)
0.0825954 + 0.996583i \(0.473679\pi\)
\(692\) 36772.8 2.02008
\(693\) −11696.3 18883.6i −0.641132 1.03511i
\(694\) −29636.0 −1.62099
\(695\) −10605.4 + 6123.04i −0.578830 + 0.334187i
\(696\) −63627.2 + 96887.8i −3.46521 + 5.27662i
\(697\) −8765.65 + 15182.6i −0.476360 + 0.825079i
\(698\) −15294.0 26490.1i −0.829352 1.43648i
\(699\) 162.663 2826.84i 0.00880185 0.152962i
\(700\) 9183.20 + 3643.28i 0.495846 + 0.196718i
\(701\) 20937.6i 1.12811i −0.825739 0.564053i \(-0.809241\pi\)
0.825739 0.564053i \(-0.190759\pi\)
\(702\) 5998.34 + 16373.5i 0.322497 + 0.880309i
\(703\) 2633.58 + 1520.50i 0.141291 + 0.0815742i
\(704\) −60652.8 35017.9i −3.24707 1.87470i
\(705\) −728.404 1447.85i −0.0389125 0.0773463i
\(706\) 55504.7i 2.95885i
\(707\) 1781.82 + 12124.8i 0.0947839 + 0.644980i
\(708\) −9095.47 523.377i −0.482809 0.0277821i
\(709\) −2420.87 4193.07i −0.128234 0.222107i 0.794759 0.606926i \(-0.207597\pi\)
−0.922992 + 0.384818i \(0.874264\pi\)
\(710\) −9059.29 + 15691.1i −0.478858 + 0.829406i
\(711\) 9290.91 12516.3i 0.490065 0.660195i
\(712\) −63988.3 + 36943.7i −3.36807 + 1.94456i
\(713\) 8395.04 0.440949
\(714\) −33555.4 + 2975.16i −1.75880 + 0.155942i
\(715\) 5096.65 0.266579
\(716\) 3695.10 2133.37i 0.192866 0.111351i
\(717\) −9057.60 5948.22i −0.471775 0.309819i
\(718\) 2368.58 4102.50i 0.123112 0.213236i
\(719\) 13205.6 + 22872.8i 0.684961 + 1.18639i 0.973449 + 0.228903i \(0.0735140\pi\)
−0.288488 + 0.957483i \(0.593153\pi\)
\(720\) 29584.0 + 3415.99i 1.53129 + 0.176814i
\(721\) −9066.33 + 22852.5i −0.468305 + 1.18040i
\(722\) 35372.1i 1.82329i
\(723\) −3929.13 + 1976.72i −0.202111 + 0.101681i
\(724\) −4929.38 2845.98i −0.253037 0.146091i
\(725\) −6685.34 3859.78i −0.342465 0.197722i
\(726\) −16146.5 + 8123.20i −0.825417 + 0.415262i
\(727\) 16397.6i 0.836524i −0.908326 0.418262i \(-0.862639\pi\)
0.908326 0.418262i \(-0.137361\pi\)
\(728\) 24074.4 19053.9i 1.22563 0.970034i
\(729\) 18524.0 + 6654.41i 0.941118 + 0.338079i
\(730\) 2888.15 + 5002.43i 0.146432 + 0.253628i
\(731\) −7300.72 + 12645.2i −0.369394 + 0.639809i
\(732\) 45474.7 + 29863.7i 2.29616 + 1.50791i
\(733\) −16789.2 + 9693.24i −0.846006 + 0.488442i −0.859301 0.511470i \(-0.829101\pi\)
0.0132952 + 0.999912i \(0.495768\pi\)
\(734\) 18248.7 0.917673
\(735\) 2541.86 8541.19i 0.127562 0.428635i
\(736\) 54350.7 2.72200
\(737\) −21412.6 + 12362.6i −1.07021 + 0.617885i
\(738\) −31853.9 23645.2i −1.58883 1.17939i
\(739\) 15662.9 27129.0i 0.779661 1.35041i −0.152476 0.988307i \(-0.548725\pi\)
0.932137 0.362105i \(-0.117942\pi\)
\(740\) 8950.49 + 15502.7i 0.444630 + 0.770122i
\(741\) 2157.50 + 124.148i 0.106960 + 0.00615477i
\(742\) 1809.60 1432.22i 0.0895317 0.0708606i
\(743\) 21594.1i 1.06623i −0.846042 0.533116i \(-0.821021\pi\)
0.846042 0.533116i \(-0.178979\pi\)
\(744\) −16075.6 31953.5i −0.792151 1.57456i
\(745\) −3669.08 2118.34i −0.180436 0.104175i
\(746\) 48764.4 + 28154.2i 2.39329 + 1.38177i
\(747\) 13745.1 + 31742.8i 0.673237 + 1.55476i
\(748\) 61257.0i 2.99435i
\(749\) −88.8387 + 223.926i −0.00433391 + 0.0109240i
\(750\) −202.105 + 3512.27i −0.00983976 + 0.171000i
\(751\) 4800.78 + 8315.20i 0.233266 + 0.404029i 0.958767 0.284192i \(-0.0917253\pi\)
−0.725501 + 0.688221i \(0.758392\pi\)
\(752\) −6880.72 + 11917.8i −0.333662 + 0.577920i
\(753\) −8329.23 + 12683.3i −0.403100 + 0.613816i
\(754\) −33237.3 + 19189.5i −1.60534 + 0.926846i
\(755\) −2094.35 −0.100955
\(756\) 1470.46 55422.7i 0.0707409 2.66628i
\(757\) −37494.0 −1.80019 −0.900093 0.435697i \(-0.856502\pi\)
−0.900093 + 0.435697i \(0.856502\pi\)
\(758\) −50750.1 + 29300.6i −2.43183 + 1.40402i
\(759\) 11162.7 16997.9i 0.533835 0.812892i
\(760\) 3273.35 5669.61i 0.156233 0.270603i
\(761\) 20075.9 + 34772.5i 0.956309 + 1.65638i 0.731343 + 0.682010i \(0.238894\pi\)
0.224966 + 0.974367i \(0.427773\pi\)
\(762\) 716.862 12457.9i 0.0340803 0.592262i
\(763\) −3535.58 24058.7i −0.167754 1.14153i
\(764\) 29026.2i 1.37452i
\(765\) −3466.90 8006.40i −0.163851 0.378395i
\(766\) 49994.2 + 28864.1i 2.35818 + 1.36149i
\(767\) −1632.95 942.782i −0.0768739 0.0443832i
\(768\) −16138.2 32078.0i −0.758253 1.50718i
\(769\) 10187.4i 0.477722i −0.971054 0.238861i \(-0.923226\pi\)
0.971054 0.238861i \(-0.0767740\pi\)
\(770\) −20709.8 8216.26i −0.969258 0.384537i
\(771\) 16567.7 + 953.346i 0.773892 + 0.0445317i
\(772\) 37319.6 + 64639.5i 1.73985 + 3.01350i
\(773\) −15595.5 + 27012.3i −0.725657 + 1.25687i 0.233047 + 0.972466i \(0.425131\pi\)
−0.958703 + 0.284409i \(0.908203\pi\)
\(774\) −26530.4 19693.6i −1.23206 0.914563i
\(775\) 2063.03 1191.09i 0.0956209 0.0552068i
\(776\) 34168.1 1.58062
\(777\) 13215.9 9276.87i 0.610190 0.428321i
\(778\) 81475.4 3.75454
\(779\) −4257.76 + 2458.22i −0.195828 + 0.113061i
\(780\) 10633.3 + 6982.99i 0.488119 + 0.320553i
\(781\) 14859.3 25737.0i 0.680802 1.17918i
\(782\) −15420.3 26708.7i −0.705150 1.22136i
\(783\) −7433.20 + 42678.5i −0.339260 + 1.94790i
\(784\) −72465.6 + 21768.7i −3.30109 + 0.991649i
\(785\) 15217.6i 0.691898i
\(786\) 62098.4 31241.3i 2.81804 1.41774i
\(787\) 30648.1 + 17694.7i 1.38817 + 0.801459i 0.993109 0.117197i \(-0.0373910\pi\)
0.395059 + 0.918656i \(0.370724\pi\)
\(788\) −57633.7 33274.8i −2.60548 1.50427i
\(789\) 18974.7 9546.06i 0.856169 0.430733i
\(790\) 15635.2i 0.704147i
\(791\) 9033.89 + 11414.2i 0.406078 + 0.513076i
\(792\) −86073.5 9938.68i −3.86173 0.445904i
\(793\) 5629.87 + 9751.22i 0.252109 + 0.436666i
\(794\) −754.880 + 1307.49i −0.0337402 + 0.0584397i
\(795\) 499.607 + 328.097i 0.0222883 + 0.0146370i
\(796\) 68538.9 39570.9i 3.05188 1.76200i
\(797\) −1039.98 −0.0462209 −0.0231104 0.999733i \(-0.507357\pi\)
−0.0231104 + 0.999733i \(0.507357\pi\)
\(798\) −8566.65 3982.54i −0.380020 0.176667i
\(799\) 4031.68 0.178511
\(800\) 13356.4 7711.30i 0.590273 0.340794i
\(801\) −16459.3 + 22173.3i −0.726046 + 0.978098i
\(802\) 5823.58 10086.7i 0.256406 0.444109i
\(803\) −4737.22 8205.11i −0.208185 0.360588i
\(804\) −61611.9 3545.30i −2.70259 0.155514i
\(805\) 8071.70 1186.19i 0.353404 0.0519350i
\(806\) 11843.4i 0.517576i
\(807\) −9530.74 18944.3i −0.415735 0.826356i
\(808\) 41399.4 + 23901.9i 1.80251 + 1.04068i
\(809\) 8457.97 + 4883.21i 0.367573 + 0.212218i 0.672397 0.740190i \(-0.265265\pi\)
−0.304825 + 0.952408i \(0.598598\pi\)
\(810\) 18897.6 5715.15i 0.819745 0.247913i
\(811\) 19662.3i 0.851341i −0.904878 0.425671i \(-0.860038\pi\)
0.904878 0.425671i \(-0.139962\pi\)
\(812\) 120728. 17741.8i 5.21764 0.766766i
\(813\) 1317.61 22898.0i 0.0568396 0.987784i
\(814\) −20185.0 34961.4i −0.869144 1.50540i
\(815\) 2267.74 3927.84i 0.0974667 0.168817i
\(816\) −40664.5 + 61921.5i −1.74454 + 2.65648i
\(817\) −3546.20 + 2047.40i −0.151855 + 0.0876736i
\(818\) 17158.7 0.733422
\(819\) 5427.03 10110.1i 0.231545 0.431351i
\(820\) −28940.8 −1.23251
\(821\) −10679.9 + 6166.06i −0.453998 + 0.262116i −0.709517 0.704688i \(-0.751087\pi\)
0.255519 + 0.966804i \(0.417754\pi\)
\(822\) 28260.4 43033.3i 1.19914 1.82598i
\(823\) −17347.5 + 30046.7i −0.734744 + 1.27261i 0.220091 + 0.975479i \(0.429364\pi\)
−0.954836 + 0.297135i \(0.903969\pi\)
\(824\) 47950.4 + 83052.5i 2.02722 + 3.51125i
\(825\) 331.497 5760.90i 0.0139894 0.243114i
\(826\) 5115.49 + 6463.37i 0.215485 + 0.272263i
\(827\) 28297.8i 1.18986i 0.803779 + 0.594928i \(0.202819\pi\)
−0.803779 + 0.594928i \(0.797181\pi\)
\(828\) 46578.2 20169.1i 1.95496 0.846526i
\(829\) −22663.5 13084.8i −0.949500 0.548194i −0.0565744 0.998398i \(-0.518018\pi\)
−0.892926 + 0.450204i \(0.851351\pi\)
\(830\) 30047.8 + 17348.1i 1.25659 + 0.725495i
\(831\) 10975.7 + 21816.5i 0.458176 + 0.910717i
\(832\) 36179.4i 1.50757i
\(833\) 16138.2 + 15197.1i 0.671256 + 0.632111i
\(834\) 68818.4 + 3959.99i 2.85730 + 0.164416i
\(835\) 4407.77 + 7634.48i 0.182679 + 0.316410i
\(836\) −8589.38 + 14877.3i −0.355347 + 0.615479i
\(837\) −10258.8 8571.59i −0.423651 0.353975i
\(838\) −27795.5 + 16047.7i −1.14580 + 0.661527i
\(839\) −4964.87 −0.204298 −0.102149 0.994769i \(-0.532572\pi\)
−0.102149 + 0.994769i \(0.532572\pi\)
\(840\) −19971.4 28451.4i −0.820330 1.16865i
\(841\) −70957.8 −2.90942
\(842\) −2668.43 + 1540.62i −0.109216 + 0.0630560i
\(843\) −22760.3 14946.9i −0.929900 0.610675i
\(844\) −34447.1 + 59664.2i −1.40488 + 2.43333i
\(845\) −4176.07 7233.17i −0.170013 0.294472i
\(846\) −1046.47 + 9062.87i −0.0425275 + 0.368307i
\(847\) 11055.6 + 4386.12i 0.448495 + 0.177933i
\(848\) 5075.00i 0.205514i
\(849\) 17142.0 8624.06i 0.692949 0.348618i
\(850\) −7578.88 4375.67i −0.305827 0.176570i
\(851\) 12802.0 + 7391.22i 0.515683 + 0.297729i
\(852\) 66264.0 33337.0i 2.66451 1.34050i
\(853\) 37172.7i 1.49211i −0.665885 0.746054i \(-0.731946\pi\)
0.665885 0.746054i \(-0.268054\pi\)
\(854\) −7156.64 48699.1i −0.286763 1.95134i
\(855\) 280.656 2430.61i 0.0112260 0.0972223i
\(856\) 469.854 + 813.811i 0.0187609 + 0.0324947i
\(857\) −3226.39 + 5588.27i −0.128601 + 0.222744i −0.923135 0.384476i \(-0.874382\pi\)
0.794534 + 0.607220i \(0.207715\pi\)
\(858\) −23980.0 15747.9i −0.954154 0.626603i
\(859\) 10830.0 6252.69i 0.430168 0.248358i −0.269250 0.963070i \(-0.586776\pi\)
0.699418 + 0.714713i \(0.253443\pi\)
\(860\) −24104.2 −0.955752
\(861\) 2305.52 + 26002.9i 0.0912567 + 1.02924i
\(862\) −57353.6 −2.26621
\(863\) −8338.96 + 4814.50i −0.328924 + 0.189904i −0.655363 0.755314i \(-0.727484\pi\)
0.326439 + 0.945218i \(0.394151\pi\)
\(864\) −66417.0 55493.7i −2.61522 2.18511i
\(865\) 4308.43 7462.41i 0.169354 0.293329i
\(866\) −28638.1 49602.6i −1.12374 1.94638i
\(867\) −3819.17 219.765i −0.149603 0.00860855i
\(868\) −13886.3 + 35001.7i −0.543010 + 1.36870i
\(869\) 25645.3i 1.00110i
\(870\) 19528.7 + 38817.2i 0.761018 + 1.51268i
\(871\) −11061.4 6386.32i −0.430313 0.248441i
\(872\) −82146.8 47427.5i −3.19018 1.84185i
\(873\) 11718.5 5074.30i 0.454309 0.196723i
\(874\) 8648.85i 0.334727i
\(875\) 1815.28 1436.71i 0.0701343 0.0555084i
\(876\) 1358.53 23609.1i 0.0523977 0.910590i
\(877\) 5716.73 + 9901.67i 0.220114 + 0.381249i 0.954843 0.297112i \(-0.0960236\pi\)
−0.734728 + 0.678362i \(0.762690\pi\)
\(878\) −2939.39 + 5091.18i −0.112984 + 0.195694i
\(879\) 9812.91 14942.5i 0.376543 0.573378i
\(880\) −42431.3 + 24497.7i −1.62541 + 0.938429i
\(881\) −20616.7 −0.788414 −0.394207 0.919022i \(-0.628981\pi\)
−0.394207 + 0.919022i \(0.628981\pi\)
\(882\) −38350.7 + 32332.8i −1.46410 + 1.23436i
\(883\) 9685.44 0.369129 0.184565 0.982820i \(-0.440913\pi\)
0.184565 + 0.982820i \(0.440913\pi\)
\(884\) −27404.9 + 15822.2i −1.04268 + 0.601990i
\(885\) −1171.87 + 1784.45i −0.0445106 + 0.0677781i
\(886\) −805.520 + 1395.20i −0.0305440 + 0.0529037i
\(887\) 16109.0 + 27901.6i 0.609793 + 1.05619i 0.991274 + 0.131816i \(0.0420809\pi\)
−0.381481 + 0.924377i \(0.624586\pi\)
\(888\) 3618.32 62880.7i 0.136737 2.37628i
\(889\) −6438.75 + 5096.00i −0.242912 + 0.192255i
\(890\) 27698.6i 1.04321i
\(891\) −30996.3 + 9374.12i −1.16545 + 0.352463i
\(892\) −10592.8 6115.73i −0.397614 0.229563i
\(893\) 979.159 + 565.317i 0.0366924 + 0.0211844i
\(894\) 10717.8 + 21303.8i 0.400959 + 0.796987i
\(895\) 999.810i 0.0373407i
\(896\) −24618.1 + 62052.2i −0.917895 + 2.31363i
\(897\) 10487.7 + 603.489i 0.390384 + 0.0224637i
\(898\) 22515.7 + 38998.4i 0.836704 + 1.44921i
\(899\) 14711.5 25481.1i 0.545781 0.945320i
\(900\) 8584.71 11565.0i 0.317952 0.428332i
\(901\) −1287.62 + 743.409i −0.0476103 + 0.0274878i
\(902\) 65266.9 2.40926
\(903\) 1920.22 + 21657.2i 0.0707651 + 0.798126i
\(904\) 56781.8 2.08909
\(905\) −1155.09 + 666.889i −0.0424269 + 0.0244952i
\(906\) 9854.05 + 6471.25i 0.361345 + 0.237299i
\(907\) 12636.0 21886.1i 0.462591 0.801231i −0.536498 0.843902i \(-0.680253\pi\)
0.999089 + 0.0426701i \(0.0135864\pi\)
\(908\) 12793.4 + 22158.8i 0.467581 + 0.809875i
\(909\) 17748.3 + 2049.35i 0.647605 + 0.0747772i
\(910\) −1673.43 11387.3i −0.0609601 0.414817i
\(911\) 26490.3i 0.963405i −0.876335 0.481703i \(-0.840019\pi\)
0.876335 0.481703i \(-0.159981\pi\)
\(912\) −18558.6 + 9336.71i −0.673833 + 0.339001i
\(913\) −49285.1 28454.8i −1.78653 1.03145i
\(914\) −24431.8 14105.7i −0.884171 0.510476i
\(915\) 11388.3 5729.38i 0.411459 0.207003i
\(916\) 87170.2i 3.14430i
\(917\) −42519.2 16868.8i −1.53120 0.607476i
\(918\) −8426.69 + 48382.8i −0.302965 + 1.73951i
\(919\) 11986.2 + 20760.6i 0.430236 + 0.745190i 0.996893 0.0787630i \(-0.0250970\pi\)
−0.566657 + 0.823953i \(0.691764\pi\)
\(920\) 15911.9 27560.3i 0.570218 0.987647i
\(921\) 4179.43 + 2744.67i 0.149530 + 0.0981976i
\(922\) 36416.2 21024.9i 1.30076 0.750996i
\(923\) 15352.1 0.547478
\(924\) 52405.6 + 74657.4i 1.86582 + 2.65806i
\(925\) 4194.68 0.149103
\(926\) 44526.8 25707.6i 1.58017 0.912314i
\(927\) 28779.5 + 21363.1i 1.01968 + 0.756911i
\(928\) 95244.6 164969.i 3.36914 5.83551i
\(929\) −8343.21 14450.9i −0.294652 0.510353i 0.680252 0.732979i \(-0.261870\pi\)
−0.974904 + 0.222626i \(0.928537\pi\)
\(930\) −13387.0 770.320i −0.472017 0.0271611i
\(931\) 1788.51 + 5953.75i 0.0629602 + 0.209588i
\(932\) 11627.5i 0.408659i
\(933\) 20705.6 + 41156.4i 0.726548 + 1.44416i
\(934\) 16955.0 + 9788.95i 0.593986 + 0.342938i
\(935\) 12431.1 + 7177.08i 0.434801 + 0.251033i
\(936\) −17785.8 41074.3i −0.621097 1.43435i
\(937\) 8294.49i 0.289188i 0.989491 + 0.144594i \(0.0461876\pi\)
−0.989491 + 0.144594i \(0.953812\pi\)
\(938\) 34651.8 + 43782.2i 1.20621 + 1.52403i
\(939\) −2109.25 + 36655.5i −0.0733043 + 1.27392i
\(940\) 3327.77 + 5763.86i 0.115468 + 0.199996i
\(941\) −12592.5 + 21810.9i −0.436243 + 0.755594i −0.997396 0.0721173i \(-0.977024\pi\)
0.561154 + 0.827712i \(0.310358\pi\)
\(942\) −47020.2 + 71599.7i −1.62633 + 2.47648i
\(943\) −20697.2 + 11949.5i −0.714733 + 0.412651i
\(944\) 18126.4 0.624963
\(945\) −11074.8 6791.92i −0.381232 0.233800i
\(946\) 54359.4 1.86826
\(947\) 29961.5 17298.3i 1.02811 0.593578i 0.111665 0.993746i \(-0.464381\pi\)
0.916442 + 0.400168i \(0.131048\pi\)
\(948\) −35136.9 + 53504.5i −1.20379 + 1.83306i
\(949\) 2447.18 4238.63i 0.0837078 0.144986i
\(950\) −1227.10 2125.40i −0.0419078 0.0725865i
\(951\) −1981.97 + 34443.5i −0.0675812 + 1.17446i
\(952\) 85550.7 12572.2i 2.91251 0.428012i
\(953\) 30037.8i 1.02101i −0.859876 0.510504i \(-0.829459\pi\)
0.859876 0.510504i \(-0.170541\pi\)
\(954\) −1336.90 3087.42i −0.0453709 0.104779i
\(955\) −5890.37 3400.81i −0.199590 0.115233i
\(956\) 38536.4 + 22249.0i 1.30372 + 0.752702i
\(957\) −32031.5 63669.0i −1.08195 2.15060i
\(958\) 483.957i 0.0163214i
\(959\) −33517.9 + 4925.67i −1.12862 + 0.165858i
\(960\) −40894.7 2353.19i −1.37487 0.0791133i
\(961\) −10355.7 17936.5i −0.347611 0.602079i
\(962\) 10427.3 18060.5i 0.349468 0.605296i
\(963\) 282.003 + 209.332i 0.00943658 + 0.00700481i
\(964\) 15641.8 9030.81i 0.522603 0.301725i
\(965\) 17490.0 0.583442
\(966\) −41642.9 19359.3i −1.38700 0.644799i
\(967\) −12240.3 −0.407055 −0.203528 0.979069i \(-0.565241\pi\)
−0.203528 + 0.979069i \(0.565241\pi\)
\(968\) 40179.3 23197.5i 1.33410 0.770244i
\(969\) 5087.45 + 3340.98i 0.168661 + 0.110761i
\(970\) 6404.41 11092.8i 0.211993 0.367183i
\(971\) −23693.7 41038.7i −0.783076 1.35633i −0.930142 0.367201i \(-0.880316\pi\)
0.147065 0.989127i \(-0.453017\pi\)
\(972\) −77512.1 22910.9i −2.55782 0.756038i
\(973\) −28150.6 35568.0i −0.927510 1.17190i
\(974\) 49386.1i 1.62467i
\(975\) 2662.91 1339.69i 0.0874681 0.0440047i
\(976\) −93741.0 54121.4i −3.07436 1.77498i
\(977\) −23011.9 13285.9i −0.753549 0.435061i 0.0734261 0.997301i \(-0.476607\pi\)
−0.826975 + 0.562239i \(0.809940\pi\)
\(978\) −22806.3 + 11473.7i −0.745669 + 0.375141i
\(979\) 45432.0i 1.48316i
\(980\) −8405.88 + 35615.7i −0.273996 + 1.16092i
\(981\) −35217.0 4066.42i −1.14617 0.132345i
\(982\) 23965.6 + 41509.7i 0.778792 + 1.34891i
\(983\) 21278.4 36855.2i 0.690412 1.19583i −0.281291 0.959623i \(-0.590763\pi\)
0.971703 0.236206i \(-0.0759041\pi\)
\(984\) 85115.7 + 55896.3i 2.75751 + 1.81088i
\(985\) −13505.1 + 7797.18i −0.436862 + 0.252222i
\(986\) −108090. −3.49118
\(987\) 4913.64 3449.12i 0.158463 0.111233i
\(988\) −8874.30 −0.285758
\(989\) −17238.2 + 9952.51i −0.554241 + 0.319991i
\(990\) −19360.1 + 26081.1i −0.621519 + 0.837284i
\(991\) −18686.0 + 32365.1i −0.598971 + 1.03745i 0.394002 + 0.919110i \(0.371090\pi\)
−0.992973 + 0.118339i \(0.962243\pi\)
\(992\) 29391.5 + 50907.6i 0.940708 + 1.62935i
\(993\) 59287.4 + 3411.55i 1.89469 + 0.109025i
\(994\) −62382.1 24749.0i −1.99058 0.789730i
\(995\) 18545.1i 0.590872i
\(996\) −63838.7 126892.i −2.03093 4.03688i
\(997\) −32689.2 18873.1i −1.03839 0.599516i −0.119015 0.992892i \(-0.537974\pi\)
−0.919378 + 0.393376i \(0.871307\pi\)
\(998\) 80790.0 + 46644.1i 2.56249 + 1.47945i
\(999\) −8097.45 22103.3i −0.256448 0.700018i
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 105.4.s.a.101.16 yes 32
3.2 odd 2 105.4.s.b.101.1 yes 32
7.5 odd 6 105.4.s.b.26.1 yes 32
21.5 even 6 inner 105.4.s.a.26.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.s.a.26.16 32 21.5 even 6 inner
105.4.s.a.101.16 yes 32 1.1 even 1 trivial
105.4.s.b.26.1 yes 32 7.5 odd 6
105.4.s.b.101.1 yes 32 3.2 odd 2