Properties

Label 105.4.i.c.46.3
Level $105$
Weight $4$
Character 105.46
Analytic conductor $6.195$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,4,Mod(16,105)]
 
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([0, 0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\), 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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.646154928.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 11x^{4} - 8x^{3} + 121x^{2} - 44x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.3
Root \(-1.74267 - 3.01840i\) of defining polynomial
Character \(\chi\) \(=\) 105.46
Dual form 105.4.i.c.16.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24267 + 2.15238i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.911519 - 1.57880i) q^{4} +(-2.50000 - 4.33013i) q^{5} +7.45605 q^{6} +(-8.88380 - 16.2505i) q^{7} +24.4137 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.24267 + 2.15238i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.911519 - 1.57880i) q^{4} +(-2.50000 - 4.33013i) q^{5} +7.45605 q^{6} +(-8.88380 - 16.2505i) q^{7} +24.4137 q^{8} +(-4.50000 - 7.79423i) q^{9} +(6.21337 - 10.7619i) q^{10} +(13.0299 - 22.5684i) q^{11} +(-2.73456 - 4.73639i) q^{12} +3.20425 q^{13} +(23.9375 - 39.3153i) q^{14} -15.0000 q^{15} +(23.0461 + 39.9170i) q^{16} +(9.01624 - 15.6166i) q^{17} +(11.1841 - 19.3714i) q^{18} +(17.1199 + 29.6526i) q^{19} -9.11519 q^{20} +(-55.5457 - 1.29492i) q^{21} +64.7676 q^{22} +(49.5912 + 85.8945i) q^{23} +(36.6205 - 63.4286i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(3.98184 + 6.89675i) q^{26} -27.0000 q^{27} +(-33.7540 - 0.786896i) q^{28} +212.096 q^{29} +(-18.6401 - 32.2856i) q^{30} +(-146.585 + 253.893i) q^{31} +(40.3771 - 69.9352i) q^{32} +(-39.0896 - 67.7052i) q^{33} +44.8170 q^{34} +(-48.1571 + 79.0942i) q^{35} -16.4073 q^{36} +(-10.3520 - 17.9301i) q^{37} +(-42.5490 + 73.6971i) q^{38} +(4.80637 - 8.32488i) q^{39} +(-61.0342 - 105.714i) q^{40} -207.842 q^{41} +(-66.2381 - 121.164i) q^{42} +5.96397 q^{43} +(-23.7540 - 41.1431i) q^{44} +(-22.5000 + 38.9711i) q^{45} +(-123.252 + 213.478i) q^{46} +(-200.949 - 348.055i) q^{47} +138.277 q^{48} +(-185.156 + 288.732i) q^{49} -62.1337 q^{50} +(-27.0487 - 46.8497i) q^{51} +(2.92073 - 5.05886i) q^{52} +(3.65770 - 6.33533i) q^{53} +(-33.5522 - 58.1141i) q^{54} -130.299 q^{55} +(-216.886 - 396.734i) q^{56} +102.720 q^{57} +(263.566 + 456.510i) q^{58} +(-20.2045 + 34.9952i) q^{59} +(-13.6728 + 23.6820i) q^{60} +(179.242 + 310.456i) q^{61} -728.631 q^{62} +(-86.6828 + 142.370i) q^{63} +569.440 q^{64} +(-8.01062 - 13.8748i) q^{65} +(97.1514 - 168.271i) q^{66} +(-293.731 + 508.757i) q^{67} +(-16.4369 - 28.4696i) q^{68} +297.547 q^{69} +(-230.084 - 5.36388i) q^{70} +803.405 q^{71} +(-109.862 - 190.286i) q^{72} +(328.025 - 568.157i) q^{73} +(25.7282 - 44.5626i) q^{74} +(37.5000 + 64.9519i) q^{75} +62.4206 q^{76} +(-482.502 - 11.2484i) q^{77} +23.8910 q^{78} +(637.780 + 1104.67i) q^{79} +(115.231 - 199.585i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-258.280 - 447.354i) q^{82} +244.647 q^{83} +(-52.6754 + 86.5150i) q^{84} -90.1624 q^{85} +(7.41127 + 12.8367i) q^{86} +(318.144 - 551.041i) q^{87} +(318.107 - 550.978i) q^{88} +(705.542 + 1222.03i) q^{89} -111.841 q^{90} +(-28.4659 - 52.0706i) q^{91} +180.813 q^{92} +(439.756 + 761.679i) q^{93} +(499.429 - 865.037i) q^{94} +(85.5997 - 148.263i) q^{95} +(-121.131 - 209.805i) q^{96} -952.212 q^{97} +(-851.549 - 39.7254i) q^{98} -234.538 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24267 + 2.15238i 0.439352 + 0.760980i 0.997640 0.0686676i \(-0.0218748\pi\)
−0.558288 + 0.829647i \(0.688541\pi\)
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 0.911519 1.57880i 0.113940 0.197350i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 7.45605 0.507320
\(7\) −8.88380 16.2505i −0.479680 0.877443i
\(8\) 24.4137 1.07894
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 6.21337 10.7619i 0.196484 0.340320i
\(11\) 13.0299 22.5684i 0.357151 0.618603i −0.630333 0.776325i \(-0.717082\pi\)
0.987484 + 0.157722i \(0.0504150\pi\)
\(12\) −2.73456 4.73639i −0.0657832 0.113940i
\(13\) 3.20425 0.0683614 0.0341807 0.999416i \(-0.489118\pi\)
0.0341807 + 0.999416i \(0.489118\pi\)
\(14\) 23.9375 39.3153i 0.456968 0.750533i
\(15\) −15.0000 −0.258199
\(16\) 23.0461 + 39.9170i 0.360096 + 0.623704i
\(17\) 9.01624 15.6166i 0.128633 0.222799i −0.794514 0.607245i \(-0.792274\pi\)
0.923147 + 0.384447i \(0.125608\pi\)
\(18\) 11.1841 19.3714i 0.146451 0.253660i
\(19\) 17.1199 + 29.6526i 0.206715 + 0.358041i 0.950678 0.310180i \(-0.100389\pi\)
−0.743963 + 0.668221i \(0.767056\pi\)
\(20\) −9.11519 −0.101911
\(21\) −55.5457 1.29492i −0.577193 0.0134559i
\(22\) 64.7676 0.627659
\(23\) 49.5912 + 85.8945i 0.449586 + 0.778706i 0.998359 0.0572653i \(-0.0182381\pi\)
−0.548773 + 0.835972i \(0.684905\pi\)
\(24\) 36.6205 63.4286i 0.311464 0.539471i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 3.98184 + 6.89675i 0.0300347 + 0.0520217i
\(27\) −27.0000 −0.192450
\(28\) −33.7540 0.786896i −0.227818 0.00531105i
\(29\) 212.096 1.35811 0.679055 0.734088i \(-0.262390\pi\)
0.679055 + 0.734088i \(0.262390\pi\)
\(30\) −18.6401 32.2856i −0.113440 0.196484i
\(31\) −146.585 + 253.893i −0.849274 + 1.47099i 0.0325838 + 0.999469i \(0.489626\pi\)
−0.881857 + 0.471516i \(0.843707\pi\)
\(32\) 40.3771 69.9352i 0.223054 0.386341i
\(33\) −39.0896 67.7052i −0.206201 0.357151i
\(34\) 44.8170 0.226060
\(35\) −48.1571 + 79.0942i −0.232573 + 0.381982i
\(36\) −16.4073 −0.0759599
\(37\) −10.3520 17.9301i −0.0459960 0.0796674i 0.842111 0.539304i \(-0.181313\pi\)
−0.888107 + 0.459637i \(0.847979\pi\)
\(38\) −42.5490 + 73.6971i −0.181641 + 0.314612i
\(39\) 4.80637 8.32488i 0.0197342 0.0341807i
\(40\) −61.0342 105.714i −0.241259 0.417873i
\(41\) −207.842 −0.791695 −0.395847 0.918316i \(-0.629549\pi\)
−0.395847 + 0.918316i \(0.629549\pi\)
\(42\) −66.2381 121.164i −0.243351 0.445144i
\(43\) 5.96397 0.0211511 0.0105755 0.999944i \(-0.496634\pi\)
0.0105755 + 0.999944i \(0.496634\pi\)
\(44\) −23.7540 41.1431i −0.0813874 0.140967i
\(45\) −22.5000 + 38.9711i −0.0745356 + 0.129099i
\(46\) −123.252 + 213.478i −0.395053 + 0.684252i
\(47\) −200.949 348.055i −0.623649 1.08019i −0.988801 0.149243i \(-0.952316\pi\)
0.365152 0.930948i \(-0.381017\pi\)
\(48\) 138.277 0.415803
\(49\) −185.156 + 288.732i −0.539814 + 0.841785i
\(50\) −62.1337 −0.175741
\(51\) −27.0487 46.8497i −0.0742662 0.128633i
\(52\) 2.92073 5.05886i 0.00778909 0.0134911i
\(53\) 3.65770 6.33533i 0.00947970 0.0164193i −0.861247 0.508187i \(-0.830316\pi\)
0.870726 + 0.491768i \(0.163649\pi\)
\(54\) −33.5522 58.1141i −0.0845533 0.146451i
\(55\) −130.299 −0.319445
\(56\) −216.886 396.734i −0.517547 0.946711i
\(57\) 102.720 0.238694
\(58\) 263.566 + 456.510i 0.596688 + 1.03349i
\(59\) −20.2045 + 34.9952i −0.0445830 + 0.0772200i −0.887456 0.460893i \(-0.847529\pi\)
0.842873 + 0.538113i \(0.180863\pi\)
\(60\) −13.6728 + 23.6820i −0.0294191 + 0.0509555i
\(61\) 179.242 + 310.456i 0.376223 + 0.651637i 0.990509 0.137446i \(-0.0438895\pi\)
−0.614287 + 0.789083i \(0.710556\pi\)
\(62\) −728.631 −1.49252
\(63\) −86.6828 + 142.370i −0.173349 + 0.284712i
\(64\) 569.440 1.11219
\(65\) −8.01062 13.8748i −0.0152861 0.0264763i
\(66\) 97.1514 168.271i 0.181190 0.313830i
\(67\) −293.731 + 508.757i −0.535597 + 0.927681i 0.463537 + 0.886077i \(0.346580\pi\)
−0.999134 + 0.0416035i \(0.986753\pi\)
\(68\) −16.4369 28.4696i −0.0293128 0.0507713i
\(69\) 297.547 0.519138
\(70\) −230.084 5.36388i −0.392862 0.00915866i
\(71\) 803.405 1.34291 0.671455 0.741045i \(-0.265670\pi\)
0.671455 + 0.741045i \(0.265670\pi\)
\(72\) −109.862 190.286i −0.179824 0.311464i
\(73\) 328.025 568.157i 0.525924 0.910928i −0.473620 0.880729i \(-0.657053\pi\)
0.999544 0.0301981i \(-0.00961381\pi\)
\(74\) 25.7282 44.5626i 0.0404168 0.0700040i
\(75\) 37.5000 + 64.9519i 0.0577350 + 0.100000i
\(76\) 62.4206 0.0942123
\(77\) −482.502 11.2484i −0.714107 0.0166478i
\(78\) 23.8910 0.0346811
\(79\) 637.780 + 1104.67i 0.908302 + 1.57323i 0.816422 + 0.577456i \(0.195955\pi\)
0.0918807 + 0.995770i \(0.470712\pi\)
\(80\) 115.231 199.585i 0.161040 0.278929i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −258.280 447.354i −0.347832 0.602464i
\(83\) 244.647 0.323537 0.161768 0.986829i \(-0.448280\pi\)
0.161768 + 0.986829i \(0.448280\pi\)
\(84\) −52.6754 + 86.5150i −0.0684209 + 0.112376i
\(85\) −90.1624 −0.115053
\(86\) 7.41127 + 12.8367i 0.00929277 + 0.0160955i
\(87\) 318.144 551.041i 0.392053 0.679055i
\(88\) 318.107 550.978i 0.385345 0.667437i
\(89\) 705.542 + 1222.03i 0.840307 + 1.45545i 0.889636 + 0.456671i \(0.150958\pi\)
−0.0493291 + 0.998783i \(0.515708\pi\)
\(90\) −111.841 −0.130989
\(91\) −28.4659 52.0706i −0.0327916 0.0599833i
\(92\) 180.813 0.204903
\(93\) 439.756 + 761.679i 0.490328 + 0.849274i
\(94\) 499.429 865.037i 0.548002 0.949168i
\(95\) 85.5997 148.263i 0.0924458 0.160121i
\(96\) −121.131 209.805i −0.128780 0.223054i
\(97\) −952.212 −0.996727 −0.498363 0.866968i \(-0.666065\pi\)
−0.498363 + 0.866968i \(0.666065\pi\)
\(98\) −851.549 39.7254i −0.877749 0.0409476i
\(99\) −234.538 −0.238100
\(100\) 22.7880 + 39.4699i 0.0227880 + 0.0394699i
\(101\) 720.732 1248.35i 0.710055 1.22985i −0.254781 0.966999i \(-0.582003\pi\)
0.964836 0.262852i \(-0.0846633\pi\)
\(102\) 67.2255 116.438i 0.0652580 0.113030i
\(103\) −569.993 987.257i −0.545273 0.944440i −0.998590 0.0530906i \(-0.983093\pi\)
0.453317 0.891349i \(-0.350241\pi\)
\(104\) 78.2275 0.0737581
\(105\) 133.257 + 243.757i 0.123853 + 0.226555i
\(106\) 18.1813 0.0166597
\(107\) −346.702 600.505i −0.313242 0.542552i 0.665820 0.746113i \(-0.268082\pi\)
−0.979062 + 0.203561i \(0.934749\pi\)
\(108\) −24.6110 + 42.6275i −0.0219277 + 0.0379800i
\(109\) 570.059 987.371i 0.500933 0.867642i −0.499066 0.866564i \(-0.666324\pi\)
0.999999 0.00107792i \(-0.000343113\pi\)
\(110\) −161.919 280.452i −0.140349 0.243091i
\(111\) −62.1117 −0.0531116
\(112\) 443.934 729.126i 0.374534 0.615142i
\(113\) 1154.64 0.961237 0.480618 0.876930i \(-0.340412\pi\)
0.480618 + 0.876930i \(0.340412\pi\)
\(114\) 127.647 + 221.091i 0.104871 + 0.181641i
\(115\) 247.956 429.473i 0.201061 0.348248i
\(116\) 193.329 334.856i 0.154743 0.268022i
\(117\) −14.4191 24.9746i −0.0113936 0.0197342i
\(118\) −100.430 −0.0783505
\(119\) −333.875 7.78353i −0.257196 0.00599593i
\(120\) −366.205 −0.278582
\(121\) 325.945 + 564.552i 0.244887 + 0.424157i
\(122\) −445.479 + 771.592i −0.330588 + 0.572595i
\(123\) −311.763 + 539.990i −0.228543 + 0.395847i
\(124\) 267.230 + 462.857i 0.193532 + 0.335208i
\(125\) 125.000 0.0894427
\(126\) −414.151 9.65498i −0.292822 0.00682646i
\(127\) −1453.32 −1.01544 −0.507722 0.861521i \(-0.669512\pi\)
−0.507722 + 0.861521i \(0.669512\pi\)
\(128\) 384.612 + 666.168i 0.265588 + 0.460012i
\(129\) 8.94595 15.4948i 0.00610579 0.0105755i
\(130\) 19.9092 34.4837i 0.0134319 0.0232648i
\(131\) 769.788 + 1333.31i 0.513410 + 0.889252i 0.999879 + 0.0155543i \(0.00495129\pi\)
−0.486469 + 0.873698i \(0.661715\pi\)
\(132\) −142.524 −0.0939781
\(133\) 329.779 541.635i 0.215003 0.353126i
\(134\) −1460.05 −0.941262
\(135\) 67.5000 + 116.913i 0.0430331 + 0.0745356i
\(136\) 220.120 381.258i 0.138787 0.240387i
\(137\) −1457.77 + 2524.93i −0.909093 + 1.57460i −0.0937658 + 0.995594i \(0.529891\pi\)
−0.815327 + 0.579001i \(0.803443\pi\)
\(138\) 369.755 + 640.434i 0.228084 + 0.395053i
\(139\) −2338.76 −1.42713 −0.713565 0.700589i \(-0.752920\pi\)
−0.713565 + 0.700589i \(0.752920\pi\)
\(140\) 80.9775 + 148.126i 0.0488847 + 0.0894211i
\(141\) −1205.70 −0.720127
\(142\) 998.371 + 1729.23i 0.590010 + 1.02193i
\(143\) 41.7510 72.3148i 0.0244153 0.0422886i
\(144\) 207.415 359.253i 0.120032 0.207901i
\(145\) −530.239 918.401i −0.303683 0.525994i
\(146\) 1630.52 0.924263
\(147\) 472.414 + 914.148i 0.265061 + 0.512909i
\(148\) −37.7440 −0.0209631
\(149\) 246.088 + 426.237i 0.135304 + 0.234354i 0.925714 0.378225i \(-0.123466\pi\)
−0.790409 + 0.612579i \(0.790132\pi\)
\(150\) −93.2006 + 161.428i −0.0507320 + 0.0878704i
\(151\) −540.975 + 936.996i −0.291549 + 0.504978i −0.974176 0.225789i \(-0.927504\pi\)
0.682627 + 0.730767i \(0.260837\pi\)
\(152\) 417.961 + 723.930i 0.223034 + 0.386306i
\(153\) −162.292 −0.0857552
\(154\) −575.383 1052.50i −0.301076 0.550735i
\(155\) 1465.85 0.759613
\(156\) −8.76220 15.1766i −0.00449703 0.00778909i
\(157\) 1445.65 2503.95i 0.734877 1.27284i −0.219900 0.975522i \(-0.570573\pi\)
0.954777 0.297322i \(-0.0960936\pi\)
\(158\) −1585.11 + 2745.49i −0.798129 + 1.38240i
\(159\) −10.9731 19.0060i −0.00547311 0.00947970i
\(160\) −403.771 −0.199506
\(161\) 955.268 1568.95i 0.467613 0.768017i
\(162\) −201.313 −0.0976337
\(163\) −1262.53 2186.76i −0.606680 1.05080i −0.991784 0.127927i \(-0.959168\pi\)
0.385104 0.922873i \(-0.374166\pi\)
\(164\) −189.452 + 328.140i −0.0902056 + 0.156241i
\(165\) −195.448 + 338.526i −0.0922159 + 0.159723i
\(166\) 304.017 + 526.573i 0.142146 + 0.246205i
\(167\) −2891.98 −1.34005 −0.670025 0.742338i \(-0.733717\pi\)
−0.670025 + 0.742338i \(0.733717\pi\)
\(168\) −1356.07 31.6138i −0.622759 0.0145182i
\(169\) −2186.73 −0.995327
\(170\) −112.042 194.063i −0.0505486 0.0875528i
\(171\) 154.080 266.874i 0.0689050 0.119347i
\(172\) 5.43627 9.41589i 0.00240995 0.00417416i
\(173\) 1452.47 + 2515.75i 0.638320 + 1.10560i 0.985801 + 0.167916i \(0.0537037\pi\)
−0.347481 + 0.937687i \(0.612963\pi\)
\(174\) 1581.40 0.688996
\(175\) 462.881 + 10.7910i 0.199946 + 0.00466127i
\(176\) 1201.15 0.514433
\(177\) 60.6134 + 104.985i 0.0257400 + 0.0445830i
\(178\) −1753.52 + 3037.18i −0.738380 + 1.27891i
\(179\) −11.5520 + 20.0087i −0.00482369 + 0.00835487i −0.868427 0.495817i \(-0.834869\pi\)
0.863603 + 0.504172i \(0.168202\pi\)
\(180\) 41.0184 + 71.0459i 0.0169852 + 0.0294191i
\(181\) −3024.01 −1.24184 −0.620919 0.783875i \(-0.713240\pi\)
−0.620919 + 0.783875i \(0.713240\pi\)
\(182\) 76.7016 125.976i 0.0312390 0.0513075i
\(183\) 1075.45 0.434424
\(184\) 1210.70 + 2097.00i 0.485078 + 0.840179i
\(185\) −51.7598 + 89.6506i −0.0205700 + 0.0356283i
\(186\) −1092.95 + 1893.04i −0.430853 + 0.746260i
\(187\) −234.961 406.964i −0.0918826 0.159145i
\(188\) −732.677 −0.284234
\(189\) 239.863 + 438.763i 0.0923145 + 0.168864i
\(190\) 425.490 0.162465
\(191\) −1948.45 3374.81i −0.738140 1.27850i −0.953332 0.301924i \(-0.902371\pi\)
0.215192 0.976572i \(-0.430962\pi\)
\(192\) 854.160 1479.45i 0.321061 0.556094i
\(193\) 2304.64 3991.76i 0.859543 1.48877i −0.0128229 0.999918i \(-0.504082\pi\)
0.872366 0.488854i \(-0.162585\pi\)
\(194\) −1183.29 2049.52i −0.437914 0.758489i
\(195\) −48.0637 −0.0176508
\(196\) 287.076 + 555.509i 0.104620 + 0.202445i
\(197\) 3119.11 1.12806 0.564029 0.825755i \(-0.309251\pi\)
0.564029 + 0.825755i \(0.309251\pi\)
\(198\) −291.454 504.814i −0.104610 0.181190i
\(199\) 2074.47 3593.08i 0.738970 1.27993i −0.213990 0.976836i \(-0.568646\pi\)
0.952960 0.303098i \(-0.0980208\pi\)
\(200\) −305.171 + 528.572i −0.107894 + 0.186878i
\(201\) 881.194 + 1526.27i 0.309227 + 0.535597i
\(202\) 3582.54 1.24786
\(203\) −1884.22 3446.66i −0.651458 1.19166i
\(204\) −98.6216 −0.0338475
\(205\) 519.605 + 899.983i 0.177028 + 0.306622i
\(206\) 1416.63 2453.68i 0.479133 0.829883i
\(207\) 446.321 773.051i 0.149862 0.259569i
\(208\) 73.8455 + 127.904i 0.0246166 + 0.0426373i
\(209\) 892.283 0.295314
\(210\) −359.062 + 589.730i −0.117989 + 0.193787i
\(211\) −3835.74 −1.25148 −0.625742 0.780030i \(-0.715204\pi\)
−0.625742 + 0.780030i \(0.715204\pi\)
\(212\) −6.66813 11.5495i −0.00216023 0.00374163i
\(213\) 1205.11 2087.31i 0.387665 0.671455i
\(214\) 861.675 1492.47i 0.275247 0.476742i
\(215\) −14.9099 25.8247i −0.00472953 0.00819178i
\(216\) −659.169 −0.207643
\(217\) 5428.12 + 126.544i 1.69809 + 0.0395870i
\(218\) 2833.59 0.880344
\(219\) −984.076 1704.47i −0.303643 0.525924i
\(220\) −118.770 + 205.715i −0.0363975 + 0.0630424i
\(221\) 28.8903 50.0394i 0.00879353 0.0152308i
\(222\) −77.1847 133.688i −0.0233347 0.0404168i
\(223\) −750.330 −0.225318 −0.112659 0.993634i \(-0.535937\pi\)
−0.112659 + 0.993634i \(0.535937\pi\)
\(224\) −1495.18 34.8567i −0.445987 0.0103972i
\(225\) 225.000 0.0666667
\(226\) 1434.85 + 2485.23i 0.422321 + 0.731482i
\(227\) 314.420 544.591i 0.0919329 0.159232i −0.816392 0.577499i \(-0.804029\pi\)
0.908324 + 0.418266i \(0.137362\pi\)
\(228\) 93.6309 162.174i 0.0271968 0.0471062i
\(229\) 1223.66 + 2119.45i 0.353109 + 0.611603i 0.986792 0.161989i \(-0.0517910\pi\)
−0.633683 + 0.773593i \(0.718458\pi\)
\(230\) 1232.52 0.353346
\(231\) −752.978 + 1236.71i −0.214469 + 0.352248i
\(232\) 5178.04 1.46532
\(233\) −1580.58 2737.65i −0.444409 0.769739i 0.553602 0.832782i \(-0.313253\pi\)
−0.998011 + 0.0630423i \(0.979920\pi\)
\(234\) 35.8365 62.0707i 0.0100116 0.0173406i
\(235\) −1004.75 + 1740.27i −0.278904 + 0.483076i
\(236\) 36.8335 + 63.7975i 0.0101596 + 0.0175969i
\(237\) 3826.68 1.04882
\(238\) −398.145 728.298i −0.108437 0.198355i
\(239\) −6018.30 −1.62884 −0.814418 0.580279i \(-0.802944\pi\)
−0.814418 + 0.580279i \(0.802944\pi\)
\(240\) −345.692 598.756i −0.0929763 0.161040i
\(241\) −2859.22 + 4952.31i −0.764225 + 1.32368i 0.176430 + 0.984313i \(0.443545\pi\)
−0.940655 + 0.339364i \(0.889788\pi\)
\(242\) −810.086 + 1403.11i −0.215183 + 0.372708i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 653.530 0.171467
\(245\) 1713.14 + 79.9191i 0.446728 + 0.0208402i
\(246\) −1549.68 −0.401642
\(247\) 54.8566 + 95.0143i 0.0141313 + 0.0244762i
\(248\) −3578.69 + 6198.46i −0.916317 + 1.58711i
\(249\) 366.971 635.612i 0.0933970 0.161768i
\(250\) 155.334 + 269.047i 0.0392968 + 0.0680641i
\(251\) 1236.06 0.310834 0.155417 0.987849i \(-0.450328\pi\)
0.155417 + 0.987849i \(0.450328\pi\)
\(252\) 145.760 + 266.627i 0.0364365 + 0.0666505i
\(253\) 2584.67 0.642280
\(254\) −1806.01 3128.09i −0.446137 0.772733i
\(255\) −135.244 + 234.249i −0.0332129 + 0.0575264i
\(256\) 1321.86 2289.54i 0.322721 0.558969i
\(257\) 549.467 + 951.705i 0.133365 + 0.230995i 0.924972 0.380036i \(-0.124088\pi\)
−0.791607 + 0.611031i \(0.790755\pi\)
\(258\) 44.4676 0.0107304
\(259\) −199.408 + 327.512i −0.0478402 + 0.0785737i
\(260\) −29.2073 −0.00696678
\(261\) −954.431 1653.12i −0.226352 0.392053i
\(262\) −1913.19 + 3313.75i −0.451135 + 0.781389i
\(263\) 3361.74 5822.70i 0.788189 1.36518i −0.138886 0.990308i \(-0.544352\pi\)
0.927075 0.374875i \(-0.122314\pi\)
\(264\) −954.322 1652.93i −0.222479 0.385345i
\(265\) −36.5770 −0.00847891
\(266\) 1575.61 + 36.7317i 0.363184 + 0.00846679i
\(267\) 4233.25 0.970302
\(268\) 535.483 + 927.484i 0.122052 + 0.211400i
\(269\) −2570.07 + 4451.49i −0.582527 + 1.00897i 0.412652 + 0.910889i \(0.364603\pi\)
−0.995179 + 0.0980772i \(0.968731\pi\)
\(270\) −167.761 + 290.571i −0.0378134 + 0.0654947i
\(271\) −1457.50 2524.47i −0.326705 0.565870i 0.655151 0.755498i \(-0.272605\pi\)
−0.981856 + 0.189628i \(0.939272\pi\)
\(272\) 831.157 0.185280
\(273\) −177.982 4.14924i −0.0394578 0.000919867i
\(274\) −7246.14 −1.59765
\(275\) 325.747 + 564.210i 0.0714301 + 0.123721i
\(276\) 271.220 469.767i 0.0591505 0.102452i
\(277\) −892.967 + 1546.66i −0.193694 + 0.335488i −0.946472 0.322787i \(-0.895380\pi\)
0.752778 + 0.658275i \(0.228714\pi\)
\(278\) −2906.32 5033.89i −0.627012 1.08602i
\(279\) 2638.53 0.566182
\(280\) −1175.69 + 1930.98i −0.250932 + 0.412136i
\(281\) 1264.76 0.268503 0.134252 0.990947i \(-0.457137\pi\)
0.134252 + 0.990947i \(0.457137\pi\)
\(282\) −1498.29 2595.11i −0.316389 0.548002i
\(283\) −4183.20 + 7245.52i −0.878677 + 1.52191i −0.0258826 + 0.999665i \(0.508240\pi\)
−0.852794 + 0.522247i \(0.825094\pi\)
\(284\) 732.319 1268.41i 0.153011 0.265023i
\(285\) −256.799 444.789i −0.0533736 0.0924458i
\(286\) 207.532 0.0429077
\(287\) 1846.43 + 3377.53i 0.379760 + 0.694667i
\(288\) −726.787 −0.148703
\(289\) 2293.91 + 3973.18i 0.466907 + 0.808707i
\(290\) 1317.83 2282.55i 0.266847 0.462193i
\(291\) −1428.32 + 2473.92i −0.287730 + 0.498363i
\(292\) −598.003 1035.77i −0.119847 0.207582i
\(293\) −1552.76 −0.309602 −0.154801 0.987946i \(-0.549474\pi\)
−0.154801 + 0.987946i \(0.549474\pi\)
\(294\) −1380.53 + 2152.80i −0.273858 + 0.427054i
\(295\) 202.045 0.0398762
\(296\) −252.729 437.740i −0.0496270 0.0859565i
\(297\) −351.807 + 609.347i −0.0687337 + 0.119050i
\(298\) −611.615 + 1059.35i −0.118892 + 0.205927i
\(299\) 158.903 + 275.227i 0.0307344 + 0.0532335i
\(300\) 136.728 0.0263133
\(301\) −52.9827 96.9173i −0.0101458 0.0185589i
\(302\) −2689.02 −0.512370
\(303\) −2162.20 3745.04i −0.409950 0.710055i
\(304\) −789.096 + 1366.76i −0.148874 + 0.257858i
\(305\) 896.210 1552.28i 0.168252 0.291421i
\(306\) −201.676 349.314i −0.0376767 0.0652580i
\(307\) −6847.06 −1.27291 −0.636453 0.771315i \(-0.719599\pi\)
−0.636453 + 0.771315i \(0.719599\pi\)
\(308\) −457.569 + 751.520i −0.0846507 + 0.139032i
\(309\) −3419.96 −0.629627
\(310\) 1821.58 + 3155.06i 0.333738 + 0.578050i
\(311\) −1175.13 + 2035.38i −0.214262 + 0.371113i −0.953044 0.302832i \(-0.902068\pi\)
0.738782 + 0.673944i \(0.235401\pi\)
\(312\) 117.341 203.241i 0.0212921 0.0368790i
\(313\) 2045.92 + 3543.64i 0.369465 + 0.639931i 0.989482 0.144657i \(-0.0462078\pi\)
−0.620017 + 0.784588i \(0.712874\pi\)
\(314\) 7185.91 1.29148
\(315\) 833.185 + 19.4238i 0.149031 + 0.00347431i
\(316\) 2325.40 0.413967
\(317\) 496.845 + 860.562i 0.0880304 + 0.152473i 0.906678 0.421822i \(-0.138609\pi\)
−0.818648 + 0.574295i \(0.805276\pi\)
\(318\) 27.2720 47.2365i 0.00480924 0.00832985i
\(319\) 2763.58 4786.66i 0.485050 0.840131i
\(320\) −1423.60 2465.75i −0.248693 0.430748i
\(321\) −2080.21 −0.361701
\(322\) 4564.06 + 106.401i 0.789892 + 0.0184145i
\(323\) 617.430 0.106361
\(324\) 73.8330 + 127.883i 0.0126600 + 0.0219277i
\(325\) −40.0531 + 69.3740i −0.00683614 + 0.0118405i
\(326\) 3137.82 5434.87i 0.533092 0.923342i
\(327\) −1710.18 2962.11i −0.289214 0.500933i
\(328\) −5074.19 −0.854193
\(329\) −3870.86 + 6357.57i −0.648654 + 1.06536i
\(330\) −971.514 −0.162061
\(331\) −1530.07 2650.16i −0.254079 0.440078i 0.710566 0.703631i \(-0.248439\pi\)
−0.964645 + 0.263553i \(0.915106\pi\)
\(332\) 223.001 386.249i 0.0368637 0.0638498i
\(333\) −93.1676 + 161.371i −0.0153320 + 0.0265558i
\(334\) −3593.80 6224.64i −0.588754 1.01975i
\(335\) 2937.31 0.479052
\(336\) −1228.42 2247.06i −0.199452 0.364843i
\(337\) −2761.72 −0.446411 −0.223205 0.974771i \(-0.571652\pi\)
−0.223205 + 0.974771i \(0.571652\pi\)
\(338\) −2717.40 4706.67i −0.437299 0.757423i
\(339\) 1731.97 2999.85i 0.277485 0.480618i
\(340\) −82.1847 + 142.348i −0.0131091 + 0.0227056i
\(341\) 3819.98 + 6616.39i 0.606637 + 1.05073i
\(342\) 765.883 0.121094
\(343\) 6336.92 + 443.836i 0.997556 + 0.0698684i
\(344\) 145.602 0.0228208
\(345\) −743.868 1288.42i −0.116083 0.201061i
\(346\) −3609.90 + 6252.53i −0.560894 + 0.971497i
\(347\) −6265.03 + 10851.4i −0.969235 + 1.67876i −0.271456 + 0.962451i \(0.587505\pi\)
−0.697779 + 0.716313i \(0.745828\pi\)
\(348\) −579.988 1004.57i −0.0893408 0.154743i
\(349\) 3744.12 0.574263 0.287132 0.957891i \(-0.407298\pi\)
0.287132 + 0.957891i \(0.407298\pi\)
\(350\) 551.984 + 1009.70i 0.0842994 + 0.154203i
\(351\) −86.5147 −0.0131562
\(352\) −1052.22 1822.49i −0.159328 0.275964i
\(353\) 1122.02 1943.39i 0.169175 0.293020i −0.768955 0.639303i \(-0.779223\pi\)
0.938130 + 0.346283i \(0.112556\pi\)
\(354\) −150.645 + 260.926i −0.0226178 + 0.0391752i
\(355\) −2008.51 3478.84i −0.300284 0.520107i
\(356\) 2572.46 0.382978
\(357\) −521.035 + 855.758i −0.0772440 + 0.126867i
\(358\) −57.4217 −0.00847718
\(359\) 470.588 + 815.083i 0.0691830 + 0.119828i 0.898542 0.438888i \(-0.144627\pi\)
−0.829359 + 0.558716i \(0.811294\pi\)
\(360\) −549.308 + 951.429i −0.0804196 + 0.139291i
\(361\) 2843.31 4924.77i 0.414538 0.718001i
\(362\) −3757.86 6508.80i −0.545604 0.945013i
\(363\) 1955.67 0.282771
\(364\) −108.156 2.52141i −0.0155740 0.000363071i
\(365\) −3280.25 −0.470401
\(366\) 1336.44 + 2314.78i 0.190865 + 0.330588i
\(367\) −242.112 + 419.350i −0.0344363 + 0.0596455i −0.882730 0.469881i \(-0.844297\pi\)
0.848294 + 0.529526i \(0.177630\pi\)
\(368\) −2285.77 + 3959.07i −0.323788 + 0.560817i
\(369\) 935.289 + 1619.97i 0.131949 + 0.228543i
\(370\) −257.282 −0.0361499
\(371\) −135.446 3.15762i −0.0189543 0.000441875i
\(372\) 1603.38 0.223472
\(373\) 5211.12 + 9025.93i 0.723383 + 1.25294i 0.959636 + 0.281244i \(0.0907471\pi\)
−0.236253 + 0.971691i \(0.575920\pi\)
\(374\) 583.960 1011.45i 0.0807376 0.139842i
\(375\) 187.500 324.760i 0.0258199 0.0447214i
\(376\) −4905.91 8497.29i −0.672881 1.16546i
\(377\) 679.607 0.0928423
\(378\) −646.311 + 1061.51i −0.0879436 + 0.144440i
\(379\) −6388.05 −0.865784 −0.432892 0.901446i \(-0.642507\pi\)
−0.432892 + 0.901446i \(0.642507\pi\)
\(380\) −156.052 270.289i −0.0210665 0.0364883i
\(381\) −2179.98 + 3775.84i −0.293134 + 0.507722i
\(382\) 4842.57 8387.58i 0.648606 1.12342i
\(383\) 2491.40 + 4315.22i 0.332387 + 0.575712i 0.982979 0.183716i \(-0.0588125\pi\)
−0.650592 + 0.759427i \(0.725479\pi\)
\(384\) 2307.67 0.306674
\(385\) 1157.55 + 2117.42i 0.153232 + 0.280295i
\(386\) 11455.7 1.51057
\(387\) −26.8379 46.4845i −0.00352518 0.00610579i
\(388\) −867.960 + 1503.35i −0.113567 + 0.196704i
\(389\) 3374.32 5844.50i 0.439807 0.761769i −0.557867 0.829930i \(-0.688380\pi\)
0.997674 + 0.0681618i \(0.0217134\pi\)
\(390\) −59.7276 103.451i −0.00775493 0.0134319i
\(391\) 1788.50 0.231326
\(392\) −4520.34 + 7049.01i −0.582428 + 0.908237i
\(393\) 4618.73 0.592835
\(394\) 3876.04 + 6713.49i 0.495614 + 0.858429i
\(395\) 3188.90 5523.34i 0.406205 0.703568i
\(396\) −213.786 + 370.288i −0.0271291 + 0.0469890i
\(397\) −1991.14 3448.76i −0.251720 0.435991i 0.712280 0.701896i \(-0.247663\pi\)
−0.963999 + 0.265904i \(0.914329\pi\)
\(398\) 10311.5 1.29867
\(399\) −912.541 1669.24i −0.114497 0.209440i
\(400\) −1152.31 −0.144038
\(401\) −3284.14 5688.29i −0.408982 0.708378i 0.585794 0.810460i \(-0.300783\pi\)
−0.994776 + 0.102082i \(0.967450\pi\)
\(402\) −2190.07 + 3793.32i −0.271719 + 0.470631i
\(403\) −469.695 + 813.536i −0.0580576 + 0.100559i
\(404\) −1313.92 2275.78i −0.161807 0.280258i
\(405\) 405.000 0.0496904
\(406\) 5077.03 8338.61i 0.620613 1.01931i
\(407\) −539.539 −0.0657100
\(408\) −660.359 1143.77i −0.0801290 0.138787i
\(409\) 2478.39 4292.69i 0.299629 0.518973i −0.676422 0.736514i \(-0.736470\pi\)
0.976051 + 0.217541i \(0.0698037\pi\)
\(410\) −1291.40 + 2236.77i −0.155555 + 0.269430i
\(411\) 4373.31 + 7574.80i 0.524865 + 0.909093i
\(412\) −2078.24 −0.248513
\(413\) 748.180 + 17.4421i 0.0891418 + 0.00207813i
\(414\) 2218.53 0.263369
\(415\) −611.618 1059.35i −0.0723450 0.125305i
\(416\) 129.378 224.090i 0.0152483 0.0264108i
\(417\) −3508.14 + 6076.27i −0.411977 + 0.713565i
\(418\) 1108.82 + 1920.53i 0.129747 + 0.224728i
\(419\) 5778.60 0.673754 0.336877 0.941549i \(-0.390629\pi\)
0.336877 + 0.941549i \(0.390629\pi\)
\(420\) 506.309 + 11.8034i 0.0588223 + 0.00137131i
\(421\) 7463.23 0.863980 0.431990 0.901878i \(-0.357812\pi\)
0.431990 + 0.901878i \(0.357812\pi\)
\(422\) −4766.58 8255.96i −0.549842 0.952355i
\(423\) −1808.54 + 3132.49i −0.207883 + 0.360064i
\(424\) 89.2980 154.669i 0.0102281 0.0177155i
\(425\) 225.406 + 390.414i 0.0257266 + 0.0445597i
\(426\) 5990.22 0.681285
\(427\) 3452.71 5670.80i 0.391308 0.642691i
\(428\) −1264.10 −0.142763
\(429\) −125.253 216.944i −0.0140962 0.0244153i
\(430\) 37.0564 64.1835i 0.00415585 0.00719815i
\(431\) −1520.79 + 2634.09i −0.169963 + 0.294384i −0.938406 0.345533i \(-0.887698\pi\)
0.768444 + 0.639917i \(0.221031\pi\)
\(432\) −622.245 1077.76i −0.0693004 0.120032i
\(433\) 4047.48 0.449214 0.224607 0.974449i \(-0.427890\pi\)
0.224607 + 0.974449i \(0.427890\pi\)
\(434\) 6473.01 + 11840.6i 0.715932 + 1.30960i
\(435\) −3181.44 −0.350662
\(436\) −1039.24 1800.01i −0.114153 0.197718i
\(437\) −1698.00 + 2941.02i −0.185872 + 0.321941i
\(438\) 2445.77 4236.20i 0.266812 0.462132i
\(439\) 1366.46 + 2366.77i 0.148559 + 0.257312i 0.930695 0.365796i \(-0.119203\pi\)
−0.782136 + 0.623108i \(0.785870\pi\)
\(440\) −3181.07 −0.344663
\(441\) 3083.65 + 143.854i 0.332971 + 0.0155334i
\(442\) 143.605 0.0154538
\(443\) −3199.52 5541.73i −0.343146 0.594347i 0.641869 0.766814i \(-0.278159\pi\)
−0.985015 + 0.172468i \(0.944826\pi\)
\(444\) −56.6160 + 98.0618i −0.00605153 + 0.0104816i
\(445\) 3527.71 6110.17i 0.375797 0.650899i
\(446\) −932.416 1614.99i −0.0989937 0.171462i
\(447\) 1476.53 0.156236
\(448\) −5058.79 9253.67i −0.533495 0.975882i
\(449\) −16489.7 −1.73318 −0.866588 0.499024i \(-0.833692\pi\)
−0.866588 + 0.499024i \(0.833692\pi\)
\(450\) 279.602 + 484.285i 0.0292901 + 0.0507320i
\(451\) −2708.16 + 4690.67i −0.282754 + 0.489745i
\(452\) 1052.48 1822.95i 0.109523 0.189700i
\(453\) 1622.92 + 2810.99i 0.168326 + 0.291549i
\(454\) 1562.89 0.161564
\(455\) −154.307 + 253.437i −0.0158990 + 0.0261128i
\(456\) 2507.77 0.257537
\(457\) −7187.97 12449.9i −0.735753 1.27436i −0.954392 0.298556i \(-0.903495\pi\)
0.218639 0.975806i \(-0.429838\pi\)
\(458\) −3041.23 + 5267.57i −0.310278 + 0.537418i
\(459\) −243.438 + 421.648i −0.0247554 + 0.0428776i
\(460\) −452.033 782.945i −0.0458178 0.0793587i
\(461\) 1000.39 0.101069 0.0505346 0.998722i \(-0.483907\pi\)
0.0505346 + 0.998722i \(0.483907\pi\)
\(462\) −3597.56 83.8688i −0.362281 0.00844574i
\(463\) −626.125 −0.0628477 −0.0314239 0.999506i \(-0.510004\pi\)
−0.0314239 + 0.999506i \(0.510004\pi\)
\(464\) 4887.98 + 8466.23i 0.489049 + 0.847058i
\(465\) 2198.78 3808.40i 0.219282 0.379807i
\(466\) 3928.30 6804.01i 0.390504 0.676373i
\(467\) −459.520 795.912i −0.0455333 0.0788659i 0.842361 0.538914i \(-0.181165\pi\)
−0.887894 + 0.460048i \(0.847832\pi\)
\(468\) −52.5732 −0.00519273
\(469\) 10877.0 + 253.572i 1.07090 + 0.0249656i
\(470\) −4994.29 −0.490148
\(471\) −4336.96 7511.84i −0.424282 0.734877i
\(472\) −493.265 + 854.361i −0.0481025 + 0.0833160i
\(473\) 77.7098 134.597i 0.00755412 0.0130841i
\(474\) 4755.32 + 8236.46i 0.460800 + 0.798129i
\(475\) −855.997 −0.0826860
\(476\) −316.622 + 520.027i −0.0304882 + 0.0500743i
\(477\) −65.8387 −0.00631980
\(478\) −7478.80 12953.7i −0.715632 1.23951i
\(479\) 7831.84 13565.1i 0.747068 1.29396i −0.202154 0.979354i \(-0.564794\pi\)
0.949222 0.314606i \(-0.101873\pi\)
\(480\) −605.656 + 1049.03i −0.0575923 + 0.0997528i
\(481\) −33.1702 57.4525i −0.00314435 0.00544618i
\(482\) −14212.3 −1.34305
\(483\) −2643.35 4835.29i −0.249020 0.455514i
\(484\) 1188.42 0.111610
\(485\) 2380.53 + 4123.20i 0.222875 + 0.386031i
\(486\) −301.970 + 523.027i −0.0281844 + 0.0488169i
\(487\) −7220.23 + 12505.8i −0.671827 + 1.16364i 0.305558 + 0.952173i \(0.401157\pi\)
−0.977385 + 0.211466i \(0.932176\pi\)
\(488\) 4375.95 + 7579.38i 0.405922 + 0.703078i
\(489\) −7575.16 −0.700533
\(490\) 1956.86 + 3786.63i 0.180412 + 0.349107i
\(491\) −19320.8 −1.77584 −0.887918 0.460001i \(-0.847849\pi\)
−0.887918 + 0.460001i \(0.847849\pi\)
\(492\) 568.356 + 984.421i 0.0520802 + 0.0902056i
\(493\) 1912.30 3312.21i 0.174698 0.302585i
\(494\) −136.338 + 236.144i −0.0124173 + 0.0215073i
\(495\) 586.345 + 1015.58i 0.0532409 + 0.0922159i
\(496\) −13512.9 −1.22328
\(497\) −7137.29 13055.7i −0.644167 1.17833i
\(498\) 1824.10 0.164137
\(499\) 2266.59 + 3925.86i 0.203340 + 0.352195i 0.949603 0.313456i \(-0.101487\pi\)
−0.746263 + 0.665652i \(0.768154\pi\)
\(500\) 113.940 197.350i 0.0101911 0.0176515i
\(501\) −4337.98 + 7513.60i −0.386839 + 0.670025i
\(502\) 1536.02 + 2660.47i 0.136566 + 0.236539i
\(503\) 1296.32 0.114911 0.0574554 0.998348i \(-0.481701\pi\)
0.0574554 + 0.998348i \(0.481701\pi\)
\(504\) −2116.25 + 3475.76i −0.187034 + 0.307188i
\(505\) −7207.32 −0.635092
\(506\) 3211.90 + 5563.18i 0.282187 + 0.488762i
\(507\) −3280.10 + 5681.30i −0.287326 + 0.497663i
\(508\) −1324.73 + 2294.50i −0.115700 + 0.200398i
\(509\) 3266.81 + 5658.28i 0.284477 + 0.492728i 0.972482 0.232977i \(-0.0748468\pi\)
−0.688005 + 0.725706i \(0.741513\pi\)
\(510\) −672.255 −0.0583685
\(511\) −12146.9 283.178i −1.05156 0.0245148i
\(512\) 12724.4 1.09833
\(513\) −462.239 800.621i −0.0397823 0.0689050i
\(514\) −1365.62 + 2365.32i −0.117188 + 0.202976i
\(515\) −2849.97 + 4936.28i −0.243853 + 0.422366i
\(516\) −16.3088 28.2477i −0.00139139 0.00240995i
\(517\) −10473.4 −0.890946
\(518\) −952.728 22.2107i −0.0808117 0.00188394i
\(519\) 8714.83 0.737068
\(520\) −195.569 338.735i −0.0164928 0.0285664i
\(521\) −411.791 + 713.244i −0.0346275 + 0.0599765i −0.882820 0.469712i \(-0.844358\pi\)
0.848192 + 0.529688i \(0.177691\pi\)
\(522\) 2372.09 4108.59i 0.198896 0.344498i
\(523\) 8626.23 + 14941.1i 0.721221 + 1.24919i 0.960511 + 0.278243i \(0.0897522\pi\)
−0.239289 + 0.970948i \(0.576914\pi\)
\(524\) 2806.71 0.233991
\(525\) 722.357 1186.41i 0.0600500 0.0986272i
\(526\) 16710.2 1.38517
\(527\) 2643.29 + 4578.32i 0.218489 + 0.378434i
\(528\) 1801.73 3120.69i 0.148504 0.257217i
\(529\) 1164.92 2017.70i 0.0957443 0.165834i
\(530\) −45.4534 78.7275i −0.00372522 0.00645228i
\(531\) 363.680 0.0297220
\(532\) −554.532 1014.36i −0.0451918 0.0826660i
\(533\) −665.978 −0.0541214
\(534\) 5260.55 + 9111.55i 0.426304 + 0.738380i
\(535\) −1733.51 + 3002.53i −0.140086 + 0.242637i
\(536\) −7171.06 + 12420.6i −0.577878 + 1.00091i
\(537\) 34.6561 + 60.0261i 0.00278496 + 0.00482369i
\(538\) −12775.0 −1.02374
\(539\) 4103.66 + 7940.82i 0.327936 + 0.634574i
\(540\) 246.110 0.0196128
\(541\) 8572.43 + 14847.9i 0.681252 + 1.17996i 0.974599 + 0.223957i \(0.0718976\pi\)
−0.293347 + 0.956006i \(0.594769\pi\)
\(542\) 3622.41 6274.19i 0.287077 0.497232i
\(543\) −4536.01 + 7856.60i −0.358488 + 0.620919i
\(544\) −728.099 1261.10i −0.0573841 0.0993922i
\(545\) −5700.59 −0.448048
\(546\) −212.243 388.241i −0.0166358 0.0304307i
\(547\) −14217.3 −1.11131 −0.555656 0.831412i \(-0.687533\pi\)
−0.555656 + 0.831412i \(0.687533\pi\)
\(548\) 2657.57 + 4603.05i 0.207164 + 0.358818i
\(549\) 1613.18 2794.10i 0.125408 0.217212i
\(550\) −809.595 + 1402.26i −0.0627659 + 0.108714i
\(551\) 3631.07 + 6289.19i 0.280742 + 0.486259i
\(552\) 7264.23 0.560120
\(553\) 12285.5 20177.9i 0.944722 1.55163i
\(554\) −4438.67 −0.340399
\(555\) 155.279 + 268.952i 0.0118761 + 0.0205700i
\(556\) −2131.82 + 3692.43i −0.162607 + 0.281643i
\(557\) 9695.91 16793.8i 0.737575 1.27752i −0.216010 0.976391i \(-0.569304\pi\)
0.953584 0.301126i \(-0.0973623\pi\)
\(558\) 3278.84 + 5679.12i 0.248753 + 0.430853i
\(559\) 19.1100 0.00144592
\(560\) −4267.04 99.4762i −0.321992 0.00750649i
\(561\) −1409.77 −0.106097
\(562\) 1571.69 + 2722.24i 0.117967 + 0.204325i
\(563\) 2081.20 3604.75i 0.155794 0.269844i −0.777554 0.628817i \(-0.783540\pi\)
0.933348 + 0.358973i \(0.116873\pi\)
\(564\) −1099.02 + 1903.55i −0.0820512 + 0.142117i
\(565\) −2886.61 4999.76i −0.214939 0.372285i
\(566\) −20793.4 −1.54419
\(567\) 1499.73 + 34.9628i 0.111081 + 0.00258960i
\(568\) 19614.1 1.44892
\(569\) 5348.05 + 9263.10i 0.394028 + 0.682477i 0.992977 0.118311i \(-0.0377479\pi\)
−0.598948 + 0.800788i \(0.704415\pi\)
\(570\) 638.236 1105.46i 0.0468996 0.0812324i
\(571\) −6235.48 + 10800.2i −0.456999 + 0.791546i −0.998801 0.0489606i \(-0.984409\pi\)
0.541801 + 0.840506i \(0.317742\pi\)
\(572\) −76.1136 131.833i −0.00556376 0.00963671i
\(573\) −11690.7 −0.852331
\(574\) −4975.21 + 8171.38i −0.361779 + 0.594193i
\(575\) −2479.56 −0.179835
\(576\) −2562.48 4438.35i −0.185365 0.321061i
\(577\) 7851.02 13598.4i 0.566451 0.981122i −0.430462 0.902609i \(-0.641649\pi\)
0.996913 0.0785131i \(-0.0250173\pi\)
\(578\) −5701.18 + 9874.73i −0.410273 + 0.710614i
\(579\) −6913.93 11975.3i −0.496257 0.859543i
\(580\) −1933.29 −0.138406
\(581\) −2173.40 3975.64i −0.155194 0.283885i
\(582\) −7099.74 −0.505659
\(583\) −95.3189 165.097i −0.00677136 0.0117283i
\(584\) 8008.31 13870.8i 0.567442 0.982838i
\(585\) −72.0956 + 124.873i −0.00509536 + 0.00882542i
\(586\) −1929.58 3342.13i −0.136024 0.235601i
\(587\) 22423.3 1.57668 0.788339 0.615241i \(-0.210941\pi\)
0.788339 + 0.615241i \(0.210941\pi\)
\(588\) 1873.87 + 87.4173i 0.131423 + 0.00613100i
\(589\) −10038.1 −0.702230
\(590\) 251.076 + 434.876i 0.0175197 + 0.0303450i
\(591\) 4678.66 8103.68i 0.325642 0.564029i
\(592\) 477.145 826.439i 0.0331259 0.0573757i
\(593\) −266.968 462.403i −0.0184875 0.0320213i 0.856634 0.515925i \(-0.172552\pi\)
−0.875121 + 0.483904i \(0.839218\pi\)
\(594\) −1748.73 −0.120793
\(595\) 800.985 + 1465.18i 0.0551885 + 0.100952i
\(596\) 897.255 0.0616661
\(597\) −6223.40 10779.2i −0.426645 0.738970i
\(598\) −394.929 + 684.036i −0.0270064 + 0.0467765i
\(599\) 2813.30 4872.78i 0.191900 0.332381i −0.753980 0.656898i \(-0.771868\pi\)
0.945880 + 0.324517i \(0.105202\pi\)
\(600\) 915.513 + 1585.72i 0.0622928 + 0.107894i
\(601\) 8563.09 0.581191 0.290596 0.956846i \(-0.406147\pi\)
0.290596 + 0.956846i \(0.406147\pi\)
\(602\) 142.762 234.475i 0.00966537 0.0158746i
\(603\) 5287.16 0.357065
\(604\) 986.217 + 1708.18i 0.0664381 + 0.115074i
\(605\) 1629.72 2822.76i 0.109517 0.189689i
\(606\) 5373.82 9307.72i 0.360225 0.623928i
\(607\) 10366.6 + 17955.5i 0.693194 + 1.20065i 0.970786 + 0.239948i \(0.0771304\pi\)
−0.277592 + 0.960699i \(0.589536\pi\)
\(608\) 2765.01 0.184434
\(609\) −11781.0 274.647i −0.783892 0.0182746i
\(610\) 4454.79 0.295687
\(611\) −643.892 1115.25i −0.0426335 0.0738434i
\(612\) −147.932 + 256.227i −0.00977094 + 0.0169238i
\(613\) −6225.28 + 10782.5i −0.410174 + 0.710443i −0.994909 0.100782i \(-0.967865\pi\)
0.584734 + 0.811225i \(0.301199\pi\)
\(614\) −8508.67 14737.4i −0.559254 0.968656i
\(615\) 3117.63 0.204415
\(616\) −11779.7 274.616i −0.770481 0.0179620i
\(617\) 6173.86 0.402837 0.201418 0.979505i \(-0.435445\pi\)
0.201418 + 0.979505i \(0.435445\pi\)
\(618\) −4249.90 7361.04i −0.276628 0.479133i
\(619\) 13335.8 23098.3i 0.865930 1.49984i −0.000189984 1.00000i \(-0.500060\pi\)
0.866120 0.499835i \(-0.166606\pi\)
\(620\) 1336.15 2314.28i 0.0865503 0.149909i
\(621\) −1338.96 2319.15i −0.0865229 0.149862i
\(622\) −5841.22 −0.376546
\(623\) 13590.7 22321.7i 0.874000 1.43547i
\(624\) 443.073 0.0284249
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −5084.83 + 8807.19i −0.324650 + 0.562310i
\(627\) 1338.42 2318.22i 0.0852497 0.147657i
\(628\) −2635.48 4564.79i −0.167464 0.290056i
\(629\) −373.343 −0.0236664
\(630\) 993.571 + 1817.47i 0.0628330 + 0.114936i
\(631\) 25175.3 1.58829 0.794147 0.607726i \(-0.207918\pi\)
0.794147 + 0.607726i \(0.207918\pi\)
\(632\) 15570.6 + 26969.0i 0.980006 + 1.69742i
\(633\) −5753.61 + 9965.55i −0.361273 + 0.625742i
\(634\) −1234.83 + 2138.80i −0.0773526 + 0.133979i
\(635\) 3633.30 + 6293.07i 0.227060 + 0.393280i
\(636\) −40.0088 −0.00249442
\(637\) −593.286 + 925.169i −0.0369024 + 0.0575456i
\(638\) 13736.9 0.852430
\(639\) −3615.32 6261.92i −0.223818 0.387665i
\(640\) 1923.06 3330.84i 0.118774 0.205723i
\(641\) 3951.07 6843.45i 0.243460 0.421685i −0.718238 0.695798i \(-0.755051\pi\)
0.961697 + 0.274113i \(0.0883842\pi\)
\(642\) −2585.03 4477.40i −0.158914 0.275247i
\(643\) −18223.2 −1.11766 −0.558828 0.829284i \(-0.688749\pi\)
−0.558828 + 0.829284i \(0.688749\pi\)
\(644\) −1606.31 2938.30i −0.0982880 0.179791i
\(645\) −89.4595 −0.00546119
\(646\) 767.264 + 1328.94i 0.0467301 + 0.0809388i
\(647\) 11989.7 20766.8i 0.728539 1.26187i −0.228961 0.973436i \(-0.573533\pi\)
0.957500 0.288432i \(-0.0931338\pi\)
\(648\) −988.754 + 1712.57i −0.0599413 + 0.103821i
\(649\) 526.523 + 911.965i 0.0318457 + 0.0551583i
\(650\) −199.092 −0.0120139
\(651\) 8470.95 13912.8i 0.509989 0.837615i
\(652\) −4603.27 −0.276500
\(653\) −5459.18 9455.57i −0.327158 0.566654i 0.654789 0.755812i \(-0.272758\pi\)
−0.981947 + 0.189158i \(0.939424\pi\)
\(654\) 4250.39 7361.88i 0.254133 0.440172i
\(655\) 3848.94 6666.56i 0.229604 0.397686i
\(656\) −4789.95 8296.44i −0.285086 0.493783i
\(657\) −5904.46 −0.350616
\(658\) −18494.1 431.147i −1.09571 0.0255439i
\(659\) −910.217 −0.0538043 −0.0269021 0.999638i \(-0.508564\pi\)
−0.0269021 + 0.999638i \(0.508564\pi\)
\(660\) 356.309 + 617.146i 0.0210141 + 0.0363975i
\(661\) 5321.44 9217.00i 0.313132 0.542360i −0.665907 0.746035i \(-0.731955\pi\)
0.979039 + 0.203675i \(0.0652886\pi\)
\(662\) 3802.76 6586.57i 0.223260 0.386698i
\(663\) −86.6708 150.118i −0.00507694 0.00879353i
\(664\) 5972.74 0.349077
\(665\) −3169.80 73.8965i −0.184841 0.00430915i
\(666\) −463.108 −0.0269446
\(667\) 10518.1 + 18217.9i 0.610588 + 1.05757i
\(668\) −2636.10 + 4565.86i −0.152685 + 0.264459i
\(669\) −1125.49 + 1949.41i −0.0650436 + 0.112659i
\(670\) 3650.12 + 6322.20i 0.210473 + 0.364549i
\(671\) 9342.00 0.537472
\(672\) −2333.33 + 3832.31i −0.133944 + 0.219992i
\(673\) 12314.8 0.705351 0.352676 0.935746i \(-0.385272\pi\)
0.352676 + 0.935746i \(0.385272\pi\)
\(674\) −3431.92 5944.25i −0.196131 0.339709i
\(675\) 337.500 584.567i 0.0192450 0.0333333i
\(676\) −1993.25 + 3452.41i −0.113407 + 0.196427i
\(677\) −4907.95 8500.81i −0.278623 0.482589i 0.692420 0.721495i \(-0.256545\pi\)
−0.971043 + 0.238906i \(0.923211\pi\)
\(678\) 8609.08 0.487655
\(679\) 8459.27 + 15473.9i 0.478110 + 0.874571i
\(680\) −2201.20 −0.124135
\(681\) −943.259 1633.77i −0.0530775 0.0919329i
\(682\) −9493.97 + 16444.0i −0.533054 + 0.923277i
\(683\) −2177.36 + 3771.29i −0.121983 + 0.211281i −0.920550 0.390626i \(-0.872259\pi\)
0.798567 + 0.601906i \(0.205592\pi\)
\(684\) −280.893 486.521i −0.0157021 0.0271968i
\(685\) 14577.7 0.813117
\(686\) 6919.44 + 14191.0i 0.385110 + 0.789817i
\(687\) 7341.99 0.407735
\(688\) 137.446 + 238.064i 0.00761641 + 0.0131920i
\(689\) 11.7202 20.3000i 0.000648046 0.00112245i
\(690\) 1848.77 3202.17i 0.102002 0.176673i
\(691\) −6744.58 11682.0i −0.371311 0.643130i 0.618456 0.785819i \(-0.287758\pi\)
−0.989768 + 0.142689i \(0.954425\pi\)
\(692\) 5295.82 0.290920
\(693\) 2083.59 + 3811.35i 0.114212 + 0.208920i
\(694\) −31141.6 −1.70334
\(695\) 5846.90 + 10127.1i 0.319116 + 0.552725i
\(696\) 7767.06 13452.9i 0.423002 0.732661i
\(697\) −1873.95 + 3245.78i −0.101838 + 0.176388i
\(698\) 4652.72 + 8058.75i 0.252304 + 0.437003i
\(699\) −9483.49 −0.513160
\(700\) 438.961 720.959i 0.0237017 0.0389281i
\(701\) −17175.4 −0.925399 −0.462700 0.886515i \(-0.653119\pi\)
−0.462700 + 0.886515i \(0.653119\pi\)
\(702\) −107.510 186.212i −0.00578019 0.0100116i
\(703\) 354.450 613.925i 0.0190161 0.0329369i
\(704\) 7419.74 12851.4i 0.397219 0.688003i
\(705\) 3014.24 + 5220.82i 0.161025 + 0.278904i
\(706\) 5577.21 0.297310
\(707\) −26689.0 622.194i −1.41972 0.0330976i
\(708\) 221.001 0.0117313
\(709\) −906.735 1570.51i −0.0480298 0.0831901i 0.841011 0.541018i \(-0.181961\pi\)
−0.889041 + 0.457828i \(0.848628\pi\)
\(710\) 4991.85 8646.14i 0.263860 0.457020i
\(711\) 5740.02 9942.01i 0.302767 0.524409i
\(712\) 17224.9 + 29834.4i 0.906642 + 1.57035i
\(713\) −29077.4 −1.52729
\(714\) −2489.39 58.0344i −0.130481 0.00304185i
\(715\) −417.510 −0.0218377
\(716\) 21.0598 + 36.4766i 0.00109922 + 0.00190391i
\(717\) −9027.46 + 15636.0i −0.470204 + 0.814418i
\(718\) −1169.58 + 2025.77i −0.0607914 + 0.105294i
\(719\) −11350.9 19660.4i −0.588760 1.01976i −0.994395 0.105727i \(-0.966283\pi\)
0.405636 0.914035i \(-0.367050\pi\)
\(720\) −2074.15 −0.107360
\(721\) −10979.7 + 18033.3i −0.567136 + 0.931475i
\(722\) 14133.3 0.728512
\(723\) 8577.65 + 14856.9i 0.441226 + 0.764225i
\(724\) −2756.44 + 4774.29i −0.141495 + 0.245076i
\(725\) −2651.20 + 4592.01i −0.135811 + 0.235232i
\(726\) 2430.26 + 4209.33i 0.124236 + 0.215183i
\(727\) 29667.1 1.51347 0.756734 0.653723i \(-0.226794\pi\)
0.756734 + 0.653723i \(0.226794\pi\)
\(728\) −694.958 1271.23i −0.0353803 0.0647185i
\(729\) 729.000 0.0370370
\(730\) −4076.29 7060.34i −0.206672 0.357966i
\(731\) 53.7725 93.1368i 0.00272072 0.00471243i
\(732\) 980.294 1697.92i 0.0494983 0.0857335i
\(733\) −5287.33 9157.92i −0.266428 0.461467i 0.701509 0.712661i \(-0.252510\pi\)
−0.967937 + 0.251194i \(0.919177\pi\)
\(734\) −1203.46 −0.0605187
\(735\) 2777.34 4330.98i 0.139379 0.217348i
\(736\) 8009.39 0.401128
\(737\) 7654.57 + 13258.1i 0.382577 + 0.662643i
\(738\) −2324.52 + 4026.19i −0.115944 + 0.200821i
\(739\) −15764.8 + 27305.4i −0.784730 + 1.35919i 0.144429 + 0.989515i \(0.453865\pi\)
−0.929160 + 0.369678i \(0.879468\pi\)
\(740\) 94.3600 + 163.436i 0.00468749 + 0.00811897i
\(741\) 329.139 0.0163175
\(742\) −161.520 295.456i −0.00799133 0.0146179i
\(743\) 8886.27 0.438769 0.219385 0.975638i \(-0.429595\pi\)
0.219385 + 0.975638i \(0.429595\pi\)
\(744\) 10736.1 + 18595.4i 0.529036 + 0.916317i
\(745\) 1230.44 2131.18i 0.0605098 0.104806i
\(746\) −12951.5 + 22432.6i −0.635639 + 1.10096i
\(747\) −1100.91 1906.84i −0.0539228 0.0933970i
\(748\) −856.685 −0.0418764
\(749\) −6678.47 + 10968.8i −0.325802 + 0.535104i
\(750\) 932.006 0.0453761
\(751\) 10241.2 + 17738.2i 0.497610 + 0.861886i 0.999996 0.00275714i \(-0.000877627\pi\)
−0.502386 + 0.864644i \(0.667544\pi\)
\(752\) 9262.21 16042.6i 0.449146 0.777944i
\(753\) 1854.09 3211.38i 0.0897301 0.155417i
\(754\) 844.531 + 1462.77i 0.0407905 + 0.0706511i
\(755\) 5409.75 0.260769
\(756\) 911.357 + 21.2462i 0.0438436 + 0.00102211i
\(757\) −9959.68 −0.478191 −0.239096 0.970996i \(-0.576851\pi\)
−0.239096 + 0.970996i \(0.576851\pi\)
\(758\) −7938.27 13749.5i −0.380384 0.658844i
\(759\) 3877.01 6715.17i 0.185410 0.321140i
\(760\) 2089.80 3619.65i 0.0997437 0.172761i
\(761\) 2278.35 + 3946.21i 0.108528 + 0.187976i 0.915174 0.403058i \(-0.132053\pi\)
−0.806646 + 0.591035i \(0.798720\pi\)
\(762\) −10836.0 −0.515155
\(763\) −21109.5 492.120i −1.00159 0.0233499i
\(764\) −7104.19 −0.336414
\(765\) 405.731 + 702.746i 0.0191755 + 0.0332129i
\(766\) −6191.99 + 10724.8i −0.292070 + 0.505880i
\(767\) −64.7401 + 112.133i −0.00304776 + 0.00527887i
\(768\) −3965.59 6868.61i −0.186323 0.322721i
\(769\) −23304.9 −1.09284 −0.546421 0.837511i \(-0.684010\pi\)
−0.546421 + 0.837511i \(0.684010\pi\)
\(770\) −3119.02 + 5122.74i −0.145976 + 0.239754i
\(771\) 3296.80 0.153997
\(772\) −4201.45 7277.12i −0.195872 0.339261i
\(773\) −19795.7 + 34287.2i −0.921090 + 1.59537i −0.123359 + 0.992362i \(0.539367\pi\)
−0.797732 + 0.603013i \(0.793967\pi\)
\(774\) 66.7014 115.530i 0.00309759 0.00536518i
\(775\) −3664.63 6347.33i −0.169855 0.294197i
\(776\) −23247.0 −1.07541
\(777\) 551.788 + 1009.35i 0.0254766 + 0.0466024i
\(778\) 16772.8 0.772921
\(779\) −3558.24 6163.06i −0.163655 0.283459i
\(780\) −43.8110 + 75.8829i −0.00201114 + 0.00348339i
\(781\) 10468.3 18131.6i 0.479621 0.830728i
\(782\) 2222.53 + 3849.53i 0.101634 + 0.176035i
\(783\) −5726.58 −0.261368
\(784\) −15792.5 736.730i −0.719409 0.0335609i
\(785\) −14456.5 −0.657294
\(786\) 5739.58 + 9941.24i 0.260463 + 0.451135i
\(787\) −11195.6 + 19391.3i −0.507089 + 0.878304i 0.492877 + 0.870099i \(0.335945\pi\)
−0.999966 + 0.00820496i \(0.997388\pi\)
\(788\) 2843.13 4924.44i 0.128531 0.222622i
\(789\) −10085.2 17468.1i −0.455061 0.788189i
\(790\) 15851.1 0.713868
\(791\) −10257.6 18763.5i −0.461086 0.843431i
\(792\) −5725.93 −0.256897
\(793\) 574.336 + 994.778i 0.0257191 + 0.0445468i
\(794\) 4948.69 8571.38i 0.221187 0.383107i
\(795\) −54.8656 + 95.0299i −0.00244765 + 0.00423945i
\(796\) −3781.83 6550.32i −0.168396 0.291671i
\(797\) −16409.1 −0.729285 −0.364642 0.931148i \(-0.618809\pi\)
−0.364642 + 0.931148i \(0.618809\pi\)
\(798\) 2458.85 4038.46i 0.109076 0.179148i
\(799\) −7247.23 −0.320887
\(800\) 1009.43 + 1748.38i 0.0446108 + 0.0772682i
\(801\) 6349.88 10998.3i 0.280102 0.485151i
\(802\) 8162.22 14137.4i 0.359374 0.622454i
\(803\) −8548.26 14806.0i −0.375668 0.650677i
\(804\) 3212.90 0.140933
\(805\) −9181.93 214.055i −0.402013 0.00937200i
\(806\) −2334.71 −0.102031
\(807\) 7710.20 + 13354.5i 0.336322 + 0.582527i
\(808\) 17595.7 30476.7i 0.766108 1.32694i
\(809\) −21773.8 + 37713.3i −0.946260 + 1.63897i −0.193052 + 0.981188i \(0.561839\pi\)
−0.753208 + 0.657782i \(0.771495\pi\)
\(810\) 503.283 + 871.712i 0.0218316 + 0.0378134i
\(811\) 23780.0 1.02963 0.514814 0.857302i \(-0.327861\pi\)
0.514814 + 0.857302i \(0.327861\pi\)
\(812\) −7159.07 166.897i −0.309402 0.00721298i
\(813\) −8745.02 −0.377246
\(814\) −670.471 1161.29i −0.0288698 0.0500039i
\(815\) −6312.64 + 10933.8i −0.271315 + 0.469932i
\(816\) 1246.74 2159.41i 0.0534859 0.0926402i
\(817\) 102.103 + 176.847i 0.00437225 + 0.00757295i
\(818\) 12319.3 0.526571
\(819\) −277.753 + 456.187i −0.0118504 + 0.0194633i
\(820\) 1894.52 0.0806823
\(821\) −15615.7 27047.2i −0.663814 1.14976i −0.979605 0.200931i \(-0.935603\pi\)
0.315792 0.948829i \(-0.397730\pi\)
\(822\) −10869.2 + 18826.0i −0.461201 + 0.798823i
\(823\) −1667.96 + 2889.00i −0.0706458 + 0.122362i −0.899185 0.437570i \(-0.855839\pi\)
0.828539 + 0.559932i \(0.189173\pi\)
\(824\) −13915.6 24102.6i −0.588318 1.01900i
\(825\) 1954.48 0.0824804
\(826\) 892.203 + 1632.04i 0.0375832 + 0.0687481i
\(827\) 32281.3 1.35735 0.678677 0.734437i \(-0.262554\pi\)
0.678677 + 0.734437i \(0.262554\pi\)
\(828\) −813.660 1409.30i −0.0341505 0.0591505i
\(829\) 14756.4 25558.9i 0.618230 1.07081i −0.371579 0.928401i \(-0.621184\pi\)
0.989809 0.142404i \(-0.0454831\pi\)
\(830\) 1520.09 2632.87i 0.0635698 0.110106i
\(831\) 2678.90 + 4639.99i 0.111829 + 0.193694i
\(832\) 1824.63 0.0760308
\(833\) 2839.60 + 5494.78i 0.118111 + 0.228551i
\(834\) −17437.9 −0.724011
\(835\) 7229.96 + 12522.7i 0.299644 + 0.518999i
\(836\) 813.333 1408.73i 0.0336480 0.0582800i
\(837\) 3957.80 6855.11i 0.163443 0.283091i
\(838\) 7180.91 + 12437.7i 0.296015 + 0.512713i
\(839\) 17025.0 0.700558 0.350279 0.936645i \(-0.386087\pi\)
0.350279 + 0.936645i \(0.386087\pi\)
\(840\) 3253.30 + 5951.01i 0.133630 + 0.244440i
\(841\) 20595.6 0.844462
\(842\) 9274.37 + 16063.7i 0.379591 + 0.657471i
\(843\) 1897.14 3285.95i 0.0775102 0.134252i
\(844\) −3496.35 + 6055.86i −0.142594 + 0.246980i
\(845\) 5466.83 + 9468.83i 0.222562 + 0.385488i
\(846\) −8989.73 −0.365335
\(847\) 6278.62 10312.1i 0.254706 0.418334i
\(848\) 337.184 0.0136544
\(849\) 12549.6 + 21736.5i 0.507304 + 0.878677i
\(850\) −560.212 + 970.316i −0.0226060 + 0.0391548i
\(851\) 1026.73 1778.35i 0.0413583 0.0716347i
\(852\) −2196.96 3805.24i −0.0883409 0.153011i
\(853\) −19970.0 −0.801593 −0.400796 0.916167i \(-0.631267\pi\)
−0.400796 + 0.916167i \(0.631267\pi\)
\(854\) 16496.3 + 384.573i 0.660997 + 0.0154096i
\(855\) −1540.80 −0.0616305
\(856\) −8464.27 14660.5i −0.337971 0.585382i
\(857\) −2344.96 + 4061.60i −0.0934685 + 0.161892i −0.908968 0.416865i \(-0.863129\pi\)
0.815500 + 0.578757i \(0.196462\pi\)
\(858\) 311.297 539.183i 0.0123864 0.0214538i
\(859\) −17201.2 29793.4i −0.683235 1.18340i −0.973988 0.226600i \(-0.927239\pi\)
0.290753 0.956798i \(-0.406094\pi\)
\(860\) −54.3627 −0.00215553
\(861\) 11544.7 + 269.139i 0.456961 + 0.0106530i
\(862\) −7559.39 −0.298694
\(863\) −1658.93 2873.35i −0.0654351 0.113337i 0.831452 0.555597i \(-0.187510\pi\)
−0.896887 + 0.442260i \(0.854177\pi\)
\(864\) −1090.18 + 1888.25i −0.0429268 + 0.0743513i
\(865\) 7262.36 12578.8i 0.285465 0.494441i
\(866\) 5029.71 + 8711.71i 0.197363 + 0.341843i
\(867\) 13763.5 0.539138
\(868\) 5147.62 8454.55i 0.201292 0.330606i
\(869\) 33240.8 1.29760
\(870\) −3953.49 6847.64i −0.154064 0.266847i
\(871\) −941.188 + 1630.19i −0.0366142 + 0.0634176i
\(872\) 13917.2 24105.4i 0.540478 0.936136i
\(873\) 4284.96 + 7421.76i 0.166121 + 0.287730i
\(874\) −8440.24 −0.326654
\(875\) −1110.48 2031.31i −0.0429039 0.0784809i
\(876\) −3588.02 −0.138388
\(877\) −13434.1 23268.6i −0.517261 0.895922i −0.999799 0.0200472i \(-0.993618\pi\)
0.482538 0.875875i \(-0.339715\pi\)
\(878\) −3396.12 + 5882.25i −0.130539 + 0.226101i
\(879\) −2329.15 + 4034.20i −0.0893744 + 0.154801i
\(880\) −3002.88 5201.14i −0.115031 0.199239i
\(881\) −12933.5 −0.494599 −0.247300 0.968939i \(-0.579543\pi\)
−0.247300 + 0.968939i \(0.579543\pi\)
\(882\) 3522.34 + 6815.93i 0.134471 + 0.260209i
\(883\) −17537.5 −0.668386 −0.334193 0.942505i \(-0.608464\pi\)
−0.334193 + 0.942505i \(0.608464\pi\)
\(884\) −52.6680 91.2237i −0.00200387 0.00347080i
\(885\) 303.067 524.927i 0.0115113 0.0199381i
\(886\) 7951.93 13773.1i 0.301524 0.522255i
\(887\) 17647.2 + 30565.9i 0.668022 + 1.15705i 0.978456 + 0.206453i \(0.0661921\pi\)
−0.310435 + 0.950595i \(0.600475\pi\)
\(888\) −1516.38 −0.0573043
\(889\) 12911.0 + 23617.2i 0.487089 + 0.890995i
\(890\) 17535.2 0.660428
\(891\) 1055.42 + 1828.04i 0.0396834 + 0.0687337i
\(892\) −683.940 + 1184.62i −0.0256726 + 0.0444663i
\(893\) 6880.49 11917.3i 0.257835 0.446583i
\(894\) 1834.84 + 3178.04i 0.0686425 + 0.118892i
\(895\) 115.520 0.00431444
\(896\) 7408.73 12168.2i 0.276237 0.453697i
\(897\) 953.416 0.0354890
\(898\) −20491.3 35492.0i −0.761474 1.31891i
\(899\) −31090.1 + 53849.6i −1.15341 + 1.99776i
\(900\) 205.092 355.229i 0.00759599 0.0131566i
\(901\) −65.9575 114.242i −0.00243880 0.00422413i
\(902\) −13461.4 −0.496914
\(903\) −331.273 7.72286i −0.0122083 0.000284608i
\(904\) 28189.1 1.03712
\(905\) 7560.02 + 13094.3i 0.277683 + 0.480962i
\(906\) −4033.53 + 6986.29i −0.147909 + 0.256185i
\(907\) −15307.9 + 26514.0i −0.560408 + 0.970655i 0.437053 + 0.899436i \(0.356022\pi\)
−0.997461 + 0.0712189i \(0.977311\pi\)
\(908\) −573.199 992.810i −0.0209496 0.0362859i
\(909\) −12973.2 −0.473370
\(910\) −737.247 17.1872i −0.0268566 0.000626099i
\(911\) 28971.0 1.05362 0.526812 0.849982i \(-0.323387\pi\)
0.526812 + 0.849982i \(0.323387\pi\)
\(912\) 2367.29 + 4100.27i 0.0859526 + 0.148874i
\(913\) 3187.73 5521.30i 0.115551 0.200141i
\(914\) 17864.6 30942.4i 0.646509 1.11979i
\(915\) −2688.63 4656.84i −0.0971402 0.168252i
\(916\) 4461.57 0.160933
\(917\) 14828.3 24354.3i 0.533996 0.877045i
\(918\) −1210.06 −0.0435053
\(919\) −13119.7 22724.0i −0.470924 0.815664i 0.528523 0.848919i \(-0.322746\pi\)
−0.999447 + 0.0332552i \(0.989413\pi\)
\(920\) 6053.52 10485.0i 0.216933 0.375740i
\(921\) −10270.6 + 17789.2i −0.367456 + 0.636453i
\(922\) 1243.16 + 2153.22i 0.0444049 + 0.0769116i
\(923\) 2574.31 0.0918032
\(924\) 1266.15 + 2316.08i 0.0450794 + 0.0824604i
\(925\) 517.598 0.0183984
\(926\) −778.070 1347.66i −0.0276123 0.0478258i
\(927\) −5129.94 + 8885.31i −0.181758 + 0.314813i
\(928\) 8563.80 14832.9i 0.302932 0.524693i
\(929\) 8971.61 + 15539.3i 0.316845 + 0.548792i 0.979828 0.199843i \(-0.0640431\pi\)
−0.662983 + 0.748635i \(0.730710\pi\)
\(930\) 10929.5 0.385367
\(931\) −11731.5 547.284i −0.412981 0.0192659i
\(932\) −5762.92 −0.202544
\(933\) 3525.39 + 6106.15i 0.123704 + 0.214262i
\(934\) 1142.07 1978.12i 0.0400103 0.0692998i
\(935\) −1174.80 + 2034.82i −0.0410911 + 0.0711719i
\(936\) −352.024 609.723i −0.0122930 0.0212921i
\(937\) 43418.1 1.51378 0.756888 0.653545i \(-0.226719\pi\)
0.756888 + 0.653545i \(0.226719\pi\)
\(938\) 12970.8 + 23726.5i 0.451505 + 0.825904i
\(939\) 12275.5 0.426621
\(940\) 1831.69 + 3172.58i 0.0635566 + 0.110083i
\(941\) −15447.5 + 26755.8i −0.535146 + 0.926901i 0.464010 + 0.885830i \(0.346410\pi\)
−0.999156 + 0.0410706i \(0.986923\pi\)
\(942\) 10778.9 18669.5i 0.372818 0.645739i
\(943\) −10307.1 17852.5i −0.355935 0.616498i
\(944\) −1862.54 −0.0642166
\(945\) 1300.24 2135.54i 0.0447586 0.0735124i
\(946\) 386.272 0.0132757
\(947\) −3876.31 6713.97i −0.133013 0.230385i 0.791824 0.610750i \(-0.209132\pi\)
−0.924837 + 0.380365i \(0.875798\pi\)
\(948\) 3488.09 6041.55i 0.119502 0.206984i
\(949\) 1051.07 1820.52i 0.0359529 0.0622723i
\(950\) −1063.73 1842.43i −0.0363282 0.0629224i
\(951\) 2981.07 0.101649
\(952\) −8151.13 190.025i −0.277499 0.00646926i
\(953\) 21377.5 0.726638 0.363319 0.931665i \(-0.381644\pi\)
0.363319 + 0.931665i \(0.381644\pi\)
\(954\) −81.8161 141.710i −0.00277662 0.00480924i
\(955\) −9742.24 + 16874.1i −0.330106 + 0.571761i
\(956\) −5485.80 + 9501.68i −0.185589 + 0.321450i
\(957\) −8290.74 14360.0i −0.280044 0.485050i
\(958\) 38929.7 1.31290
\(959\) 53981.9 + 1258.46i 1.81769 + 0.0423753i
\(960\) −8541.60 −0.287166
\(961\) −28079.0 48634.2i −0.942532 1.63251i
\(962\) 82.4396 142.790i 0.00276295 0.00478557i
\(963\) −3120.32 + 5404.55i −0.104414 + 0.180851i
\(964\) 5212.46 + 9028.24i 0.174151 + 0.301639i
\(965\) −23046.4 −0.768798
\(966\) 7122.53 11698.2i 0.237229 0.389630i
\(967\) −47707.3 −1.58652 −0.793259 0.608885i \(-0.791617\pi\)
−0.793259 + 0.608885i \(0.791617\pi\)
\(968\) 7957.51 + 13782.8i 0.264219 + 0.457641i
\(969\) 926.145 1604.13i 0.0307039 0.0531807i
\(970\) −5916.45 + 10247.6i −0.195841 + 0.339207i
\(971\) 21717.3 + 37615.4i 0.717756 + 1.24319i 0.961887 + 0.273447i \(0.0881640\pi\)
−0.244131 + 0.969742i \(0.578503\pi\)
\(972\) 442.998 0.0146185
\(973\) 20777.1 + 38006.0i 0.684566 + 1.25222i
\(974\) −35889.6 −1.18067
\(975\) 120.159 + 208.122i 0.00394685 + 0.00683614i
\(976\) −8261.66 + 14309.6i −0.270952 + 0.469303i
\(977\) 16743.8 29001.1i 0.548292 0.949669i −0.450100 0.892978i \(-0.648612\pi\)
0.998392 0.0566908i \(-0.0180549\pi\)
\(978\) −9413.46 16304.6i −0.307781 0.533092i
\(979\) 36772.5 1.20046
\(980\) 1687.73 2631.85i 0.0550129 0.0857870i
\(981\) −10261.1 −0.333955
\(982\) −24009.5 41585.6i −0.780217 1.35138i
\(983\) −7883.76 + 13655.1i −0.255802 + 0.443061i −0.965113 0.261834i \(-0.915673\pi\)
0.709311 + 0.704895i \(0.249006\pi\)
\(984\) −7611.29 + 13183.1i −0.246584 + 0.427096i
\(985\) −7797.77 13506.1i −0.252241 0.436895i
\(986\) 9505.49 0.307015
\(987\) 10711.2 + 19593.1i 0.345431 + 0.631871i
\(988\) 200.011 0.00644049
\(989\) 295.760 + 512.272i 0.00950924 + 0.0164705i
\(990\) −1457.27 + 2524.07i −0.0467829 + 0.0810304i
\(991\) 1792.30 3104.35i 0.0574512 0.0995084i −0.835869 0.548928i \(-0.815036\pi\)
0.893321 + 0.449420i \(0.148369\pi\)
\(992\) 11837.4 + 20502.9i 0.378868 + 0.656218i
\(993\) −9180.42 −0.293386
\(994\) 19231.5 31586.1i 0.613667 1.00790i
\(995\) −20744.7 −0.660955
\(996\) −669.002 1158.75i −0.0212833 0.0368637i
\(997\) 18006.7 31188.6i 0.571995 0.990724i −0.424366 0.905491i \(-0.639503\pi\)
0.996361 0.0852334i \(-0.0271636\pi\)
\(998\) −5633.28 + 9757.13i −0.178676 + 0.309475i
\(999\) 279.503 + 484.113i 0.00885193 + 0.0153320i
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.i.c.46.3 yes 6
3.2 odd 2 315.4.j.e.46.1 6
7.2 even 3 inner 105.4.i.c.16.3 6
7.3 odd 6 735.4.a.s.1.1 3
7.4 even 3 735.4.a.r.1.1 3
21.2 odd 6 315.4.j.e.226.1 6
21.11 odd 6 2205.4.a.bi.1.3 3
21.17 even 6 2205.4.a.bj.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.i.c.16.3 6 7.2 even 3 inner
105.4.i.c.46.3 yes 6 1.1 even 1 trivial
315.4.j.e.46.1 6 3.2 odd 2
315.4.j.e.226.1 6 21.2 odd 6
735.4.a.r.1.1 3 7.4 even 3
735.4.a.s.1.1 3 7.3 odd 6
2205.4.a.bi.1.3 3 21.11 odd 6
2205.4.a.bj.1.3 3 21.17 even 6