Properties

Label 225.4.e.e.151.7
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.7
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.e.76.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.238017 - 0.412258i) q^{2} +(-3.09012 - 4.17746i) q^{3} +(3.88670 + 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(6.34045 - 10.9820i) q^{7} +7.50869 q^{8} +(-7.90234 + 25.8177i) q^{9} +O(q^{10})\) \(q+(0.238017 - 0.412258i) q^{2} +(-3.09012 - 4.17746i) q^{3} +(3.88670 + 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(6.34045 - 10.9820i) q^{7} +7.50869 q^{8} +(-7.90234 + 25.8177i) q^{9} +(0.794994 - 1.37697i) q^{11} +(16.1121 - 37.0390i) q^{12} +(5.36718 + 9.29622i) q^{13} +(-3.01828 - 5.22781i) q^{14} +(-29.3064 + 50.7601i) q^{16} +69.7787 q^{17} +(8.76266 + 9.40287i) q^{18} +98.5661 q^{19} +(-65.4695 + 7.44864i) q^{21} +(-0.378445 - 0.655486i) q^{22} +(-15.7777 - 27.3278i) q^{23} +(-23.2027 - 31.3672i) q^{24} +5.10993 q^{26} +(132.272 - 46.7680i) q^{27} +98.5736 q^{28} +(150.627 - 260.893i) q^{29} +(58.6364 + 101.561i) q^{31} +(43.9856 + 76.1853i) q^{32} +(-8.20886 + 0.933944i) q^{33} +(16.6086 - 28.7669i) q^{34} +(-204.517 + 47.1473i) q^{36} +169.562 q^{37} +(23.4605 - 40.6347i) q^{38} +(22.2494 - 51.1476i) q^{39} +(-70.9376 - 122.868i) q^{41} +(-12.5121 + 28.7633i) q^{42} +(150.121 - 260.018i) q^{43} +12.3596 q^{44} -15.0215 q^{46} +(243.712 - 422.122i) q^{47} +(302.608 - 34.4286i) q^{48} +(91.0974 + 157.785i) q^{49} +(-215.625 - 291.498i) q^{51} +(-41.7212 + 72.2632i) q^{52} -459.166 q^{53} +(12.2024 - 65.6616i) q^{54} +(47.6084 - 82.4602i) q^{56} +(-304.581 - 411.756i) q^{57} +(-71.7037 - 124.194i) q^{58} +(250.099 + 433.185i) q^{59} +(-290.915 + 503.880i) q^{61} +55.8259 q^{62} +(233.425 + 250.479i) q^{63} -427.024 q^{64} +(-1.56883 + 3.60647i) q^{66} +(250.468 + 433.823i) q^{67} +(271.209 + 469.747i) q^{68} +(-65.4059 + 150.357i) q^{69} +1066.69 q^{71} +(-59.3362 + 193.857i) q^{72} -435.288 q^{73} +(40.3588 - 69.9034i) q^{74} +(383.096 + 663.542i) q^{76} +(-10.0812 - 17.4612i) q^{77} +(-15.7903 - 21.3465i) q^{78} +(-187.644 + 325.009i) q^{79} +(-604.106 - 408.040i) q^{81} -67.5375 q^{82} +(-646.617 + 1119.97i) q^{83} +(-304.604 - 411.787i) q^{84} +(-71.4630 - 123.778i) q^{86} +(-1555.33 + 176.954i) q^{87} +(5.96936 - 10.3392i) q^{88} -403.296 q^{89} +136.121 q^{91} +(122.646 - 212.430i) q^{92} +(243.074 - 558.787i) q^{93} +(-116.016 - 200.945i) q^{94} +(182.340 - 419.170i) q^{96} +(-790.735 + 1369.59i) q^{97} +86.7311 q^{98} +(29.2679 + 31.4062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9} - 29 q^{11} - 77 q^{12} + 24 q^{13} + 69 q^{14} - 192 q^{16} + 158 q^{17} + 125 q^{18} - 150 q^{19} - 60 q^{21} - 18 q^{22} - 318 q^{23} + 342 q^{24} - 308 q^{26} - 394 q^{27} - 192 q^{28} - 106 q^{29} - 60 q^{31} - 914 q^{32} - 80 q^{33} + 108 q^{34} + 1303 q^{36} + 168 q^{37} - 640 q^{38} - 410 q^{39} + 353 q^{41} + 1521 q^{42} - 426 q^{43} + 1142 q^{44} + 540 q^{46} - 1210 q^{47} + 2680 q^{48} - 666 q^{49} - 1369 q^{51} - 75 q^{52} + 896 q^{53} - 2128 q^{54} + 570 q^{56} + 1544 q^{57} + 594 q^{58} - 482 q^{59} - 402 q^{61} + 5088 q^{62} - 1038 q^{63} + 1950 q^{64} + 2041 q^{66} - 201 q^{67} - 3437 q^{68} + 2856 q^{69} - 1888 q^{71} - 5493 q^{72} + 906 q^{73} - 10 q^{74} + 462 q^{76} - 2652 q^{77} - 4589 q^{78} - 258 q^{79} + 3071 q^{81} - 1746 q^{82} - 3012 q^{83} - 2703 q^{84} - 1952 q^{86} + 2708 q^{87} - 216 q^{88} - 1476 q^{89} - 1236 q^{91} - 5232 q^{92} + 3024 q^{93} - 63 q^{94} - 10424 q^{96} - 318 q^{97} + 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.238017 0.412258i 0.0841519 0.145755i −0.820878 0.571104i \(-0.806515\pi\)
0.905030 + 0.425349i \(0.139849\pi\)
\(3\) −3.09012 4.17746i −0.594694 0.803953i
\(4\) 3.88670 + 6.73195i 0.485837 + 0.841494i
\(5\) 0 0
\(6\) −2.45769 + 0.279619i −0.167225 + 0.0190256i
\(7\) 6.34045 10.9820i 0.342352 0.592971i −0.642517 0.766271i \(-0.722110\pi\)
0.984869 + 0.173300i \(0.0554431\pi\)
\(8\) 7.50869 0.331840
\(9\) −7.90234 + 25.8177i −0.292679 + 0.956211i
\(10\) 0 0
\(11\) 0.794994 1.37697i 0.0217909 0.0377429i −0.854924 0.518753i \(-0.826397\pi\)
0.876715 + 0.481010i \(0.159730\pi\)
\(12\) 16.1121 37.0390i 0.387597 0.891021i
\(13\) 5.36718 + 9.29622i 0.114507 + 0.198331i 0.917582 0.397546i \(-0.130138\pi\)
−0.803076 + 0.595877i \(0.796805\pi\)
\(14\) −3.01828 5.22781i −0.0576191 0.0997993i
\(15\) 0 0
\(16\) −29.3064 + 50.7601i −0.457912 + 0.793127i
\(17\) 69.7787 0.995519 0.497760 0.867315i \(-0.334156\pi\)
0.497760 + 0.867315i \(0.334156\pi\)
\(18\) 8.76266 + 9.40287i 0.114743 + 0.123127i
\(19\) 98.5661 1.19014 0.595069 0.803675i \(-0.297125\pi\)
0.595069 + 0.803675i \(0.297125\pi\)
\(20\) 0 0
\(21\) −65.4695 + 7.44864i −0.680315 + 0.0774013i
\(22\) −0.378445 0.655486i −0.00366749 0.00635227i
\(23\) −15.7777 27.3278i −0.143038 0.247750i 0.785601 0.618734i \(-0.212354\pi\)
−0.928639 + 0.370984i \(0.879021\pi\)
\(24\) −23.2027 31.3672i −0.197343 0.266784i
\(25\) 0 0
\(26\) 5.10993 0.0385438
\(27\) 132.272 46.7680i 0.942802 0.333352i
\(28\) 98.5736 0.665309
\(29\) 150.627 260.893i 0.964507 1.67058i 0.253574 0.967316i \(-0.418394\pi\)
0.710933 0.703260i \(-0.248273\pi\)
\(30\) 0 0
\(31\) 58.6364 + 101.561i 0.339723 + 0.588417i 0.984380 0.176054i \(-0.0563334\pi\)
−0.644658 + 0.764471i \(0.723000\pi\)
\(32\) 43.9856 + 76.1853i 0.242988 + 0.420868i
\(33\) −8.20886 + 0.933944i −0.0433024 + 0.00492663i
\(34\) 16.6086 28.7669i 0.0837748 0.145102i
\(35\) 0 0
\(36\) −204.517 + 47.1473i −0.946840 + 0.218275i
\(37\) 169.562 0.753402 0.376701 0.926335i \(-0.377059\pi\)
0.376701 + 0.926335i \(0.377059\pi\)
\(38\) 23.4605 40.6347i 0.100152 0.173469i
\(39\) 22.2494 51.1476i 0.0913526 0.210004i
\(40\) 0 0
\(41\) −70.9376 122.868i −0.270210 0.468017i 0.698706 0.715409i \(-0.253760\pi\)
−0.968915 + 0.247392i \(0.920426\pi\)
\(42\) −12.5121 + 28.7633i −0.0459682 + 0.105673i
\(43\) 150.121 260.018i 0.532402 0.922147i −0.466882 0.884319i \(-0.654623\pi\)
0.999284 0.0378277i \(-0.0120438\pi\)
\(44\) 12.3596 0.0423472
\(45\) 0 0
\(46\) −15.0215 −0.0481478
\(47\) 243.712 422.122i 0.756364 1.31006i −0.188330 0.982106i \(-0.560307\pi\)
0.944694 0.327954i \(-0.106359\pi\)
\(48\) 302.608 34.4286i 0.909953 0.103528i
\(49\) 91.0974 + 157.785i 0.265590 + 0.460016i
\(50\) 0 0
\(51\) −215.625 291.498i −0.592029 0.800350i
\(52\) −41.7212 + 72.2632i −0.111263 + 0.192713i
\(53\) −459.166 −1.19002 −0.595012 0.803717i \(-0.702853\pi\)
−0.595012 + 0.803717i \(0.702853\pi\)
\(54\) 12.2024 65.6616i 0.0307508 0.165471i
\(55\) 0 0
\(56\) 47.6084 82.4602i 0.113606 0.196772i
\(57\) −304.581 411.756i −0.707767 0.956814i
\(58\) −71.7037 124.194i −0.162330 0.281164i
\(59\) 250.099 + 433.185i 0.551867 + 0.955862i 0.998140 + 0.0609650i \(0.0194178\pi\)
−0.446273 + 0.894897i \(0.647249\pi\)
\(60\) 0 0
\(61\) −290.915 + 503.880i −0.610621 + 1.05763i 0.380515 + 0.924775i \(0.375747\pi\)
−0.991136 + 0.132852i \(0.957587\pi\)
\(62\) 55.8259 0.114353
\(63\) 233.425 + 250.479i 0.466806 + 0.500911i
\(64\) −427.024 −0.834032
\(65\) 0 0
\(66\) −1.56883 + 3.60647i −0.00292589 + 0.00672614i
\(67\) 250.468 + 433.823i 0.456709 + 0.791044i 0.998785 0.0492862i \(-0.0156946\pi\)
−0.542075 + 0.840330i \(0.682361\pi\)
\(68\) 271.209 + 469.747i 0.483660 + 0.837724i
\(69\) −65.4059 + 150.357i −0.114115 + 0.262331i
\(70\) 0 0
\(71\) 1066.69 1.78299 0.891495 0.453031i \(-0.149657\pi\)
0.891495 + 0.453031i \(0.149657\pi\)
\(72\) −59.3362 + 193.857i −0.0971227 + 0.317309i
\(73\) −435.288 −0.697899 −0.348950 0.937141i \(-0.613462\pi\)
−0.348950 + 0.937141i \(0.613462\pi\)
\(74\) 40.3588 69.9034i 0.0634002 0.109812i
\(75\) 0 0
\(76\) 383.096 + 663.542i 0.578213 + 1.00149i
\(77\) −10.0812 17.4612i −0.0149203 0.0258427i
\(78\) −15.7903 21.3465i −0.0229218 0.0309874i
\(79\) −187.644 + 325.009i −0.267236 + 0.462866i −0.968147 0.250383i \(-0.919444\pi\)
0.700911 + 0.713248i \(0.252777\pi\)
\(80\) 0 0
\(81\) −604.106 408.040i −0.828678 0.559726i
\(82\) −67.5375 −0.0909546
\(83\) −646.617 + 1119.97i −0.855126 + 1.48112i 0.0214014 + 0.999771i \(0.493187\pi\)
−0.876528 + 0.481351i \(0.840146\pi\)
\(84\) −304.604 411.787i −0.395655 0.534877i
\(85\) 0 0
\(86\) −71.4630 123.778i −0.0896053 0.155201i
\(87\) −1555.33 + 176.954i −1.91665 + 0.218062i
\(88\) 5.96936 10.3392i 0.00723109 0.0125246i
\(89\) −403.296 −0.480330 −0.240165 0.970732i \(-0.577201\pi\)
−0.240165 + 0.970732i \(0.577201\pi\)
\(90\) 0 0
\(91\) 136.121 0.156806
\(92\) 122.646 212.430i 0.138987 0.240732i
\(93\) 243.074 558.787i 0.271028 0.623049i
\(94\) −116.016 200.945i −0.127299 0.220488i
\(95\) 0 0
\(96\) 182.340 419.170i 0.193854 0.445639i
\(97\) −790.735 + 1369.59i −0.827700 + 1.43362i 0.0721373 + 0.997395i \(0.477018\pi\)
−0.899838 + 0.436225i \(0.856315\pi\)
\(98\) 86.7311 0.0893996
\(99\) 29.2679 + 31.4062i 0.0297124 + 0.0318832i
\(100\) 0 0
\(101\) 577.422 1000.12i 0.568867 0.985307i −0.427811 0.903868i \(-0.640715\pi\)
0.996678 0.0814388i \(-0.0259515\pi\)
\(102\) −171.495 + 19.5114i −0.166476 + 0.0189404i
\(103\) −725.615 1256.80i −0.694145 1.20229i −0.970468 0.241230i \(-0.922449\pi\)
0.276323 0.961065i \(-0.410884\pi\)
\(104\) 40.3004 + 69.8024i 0.0379979 + 0.0658143i
\(105\) 0 0
\(106\) −109.290 + 189.295i −0.100143 + 0.173452i
\(107\) −136.728 −0.123533 −0.0617664 0.998091i \(-0.519673\pi\)
−0.0617664 + 0.998091i \(0.519673\pi\)
\(108\) 828.939 + 708.673i 0.738562 + 0.631408i
\(109\) 40.1176 0.0352529 0.0176265 0.999845i \(-0.494389\pi\)
0.0176265 + 0.999845i \(0.494389\pi\)
\(110\) 0 0
\(111\) −523.967 708.339i −0.448043 0.605699i
\(112\) 371.631 + 643.684i 0.313534 + 0.543057i
\(113\) −989.231 1713.40i −0.823531 1.42640i −0.903037 0.429564i \(-0.858667\pi\)
0.0795054 0.996834i \(-0.474666\pi\)
\(114\) −242.245 + 27.5609i −0.199021 + 0.0226431i
\(115\) 0 0
\(116\) 2341.76 1.87437
\(117\) −282.420 + 65.1062i −0.223160 + 0.0514450i
\(118\) 238.112 0.185763
\(119\) 442.428 766.309i 0.340818 0.590314i
\(120\) 0 0
\(121\) 664.236 + 1150.49i 0.499050 + 0.864381i
\(122\) 138.486 + 239.865i 0.102770 + 0.178003i
\(123\) −294.069 + 676.014i −0.215571 + 0.495562i
\(124\) −455.804 + 789.475i −0.330100 + 0.571750i
\(125\) 0 0
\(126\) 158.821 36.6130i 0.112293 0.0258869i
\(127\) −1318.35 −0.921142 −0.460571 0.887623i \(-0.652355\pi\)
−0.460571 + 0.887623i \(0.652355\pi\)
\(128\) −453.524 + 785.527i −0.313174 + 0.542433i
\(129\) −1550.11 + 176.360i −1.05798 + 0.120369i
\(130\) 0 0
\(131\) −792.463 1372.59i −0.528533 0.915446i −0.999447 0.0332667i \(-0.989409\pi\)
0.470913 0.882179i \(-0.343924\pi\)
\(132\) −38.1926 51.6317i −0.0251836 0.0340452i
\(133\) 624.953 1082.45i 0.407446 0.705717i
\(134\) 238.463 0.153732
\(135\) 0 0
\(136\) 523.947 0.330353
\(137\) 190.760 330.406i 0.118961 0.206047i −0.800395 0.599473i \(-0.795377\pi\)
0.919356 + 0.393426i \(0.128710\pi\)
\(138\) 46.4182 + 62.7517i 0.0286332 + 0.0387086i
\(139\) 1231.19 + 2132.49i 0.751283 + 1.30126i 0.947201 + 0.320641i \(0.103898\pi\)
−0.195918 + 0.980620i \(0.562769\pi\)
\(140\) 0 0
\(141\) −2516.50 + 286.309i −1.50303 + 0.171004i
\(142\) 253.890 439.750i 0.150042 0.259880i
\(143\) 17.0675 0.00998080
\(144\) −1078.92 1157.75i −0.624375 0.669992i
\(145\) 0 0
\(146\) −103.606 + 179.451i −0.0587295 + 0.101723i
\(147\) 377.640 868.131i 0.211886 0.487090i
\(148\) 659.037 + 1141.48i 0.366030 + 0.633983i
\(149\) −192.172 332.852i −0.105660 0.183008i 0.808348 0.588705i \(-0.200362\pi\)
−0.914008 + 0.405697i \(0.867029\pi\)
\(150\) 0 0
\(151\) −398.550 + 690.308i −0.214792 + 0.372030i −0.953208 0.302315i \(-0.902241\pi\)
0.738417 + 0.674345i \(0.235574\pi\)
\(152\) 740.102 0.394935
\(153\) −551.415 + 1801.53i −0.291368 + 0.951926i
\(154\) −9.59804 −0.00502229
\(155\) 0 0
\(156\) 430.800 49.0133i 0.221100 0.0251551i
\(157\) −435.496 754.300i −0.221378 0.383438i 0.733849 0.679313i \(-0.237722\pi\)
−0.955227 + 0.295875i \(0.904389\pi\)
\(158\) 89.3252 + 154.716i 0.0449768 + 0.0779021i
\(159\) 1418.88 + 1918.15i 0.707700 + 0.956723i
\(160\) 0 0
\(161\) −400.152 −0.195878
\(162\) −312.006 + 151.927i −0.151318 + 0.0736822i
\(163\) 31.2604 0.0150215 0.00751074 0.999972i \(-0.497609\pi\)
0.00751074 + 0.999972i \(0.497609\pi\)
\(164\) 551.426 955.097i 0.262556 0.454759i
\(165\) 0 0
\(166\) 307.813 + 533.147i 0.143921 + 0.249278i
\(167\) −18.6415 32.2881i −0.00863787 0.0149612i 0.861674 0.507462i \(-0.169416\pi\)
−0.870312 + 0.492501i \(0.836083\pi\)
\(168\) −491.590 + 55.9295i −0.225756 + 0.0256849i
\(169\) 1040.89 1802.87i 0.473776 0.820605i
\(170\) 0 0
\(171\) −778.903 + 2544.75i −0.348329 + 1.13802i
\(172\) 2333.90 1.03464
\(173\) −590.590 + 1022.93i −0.259548 + 0.449550i −0.966121 0.258090i \(-0.916907\pi\)
0.706573 + 0.707640i \(0.250240\pi\)
\(174\) −297.244 + 683.315i −0.129506 + 0.297712i
\(175\) 0 0
\(176\) 46.5967 + 80.7079i 0.0199566 + 0.0345658i
\(177\) 1036.78 2383.37i 0.440276 1.01212i
\(178\) −95.9916 + 166.262i −0.0404206 + 0.0700106i
\(179\) −429.484 −0.179336 −0.0896680 0.995972i \(-0.528581\pi\)
−0.0896680 + 0.995972i \(0.528581\pi\)
\(180\) 0 0
\(181\) −1787.97 −0.734246 −0.367123 0.930172i \(-0.619657\pi\)
−0.367123 + 0.930172i \(0.619657\pi\)
\(182\) 32.3992 56.1171i 0.0131956 0.0228554i
\(183\) 3003.90 341.762i 1.21341 0.138053i
\(184\) −118.470 205.196i −0.0474659 0.0822134i
\(185\) 0 0
\(186\) −172.509 233.211i −0.0680051 0.0919346i
\(187\) 55.4736 96.0832i 0.0216932 0.0375738i
\(188\) 3788.94 1.46988
\(189\) 325.056 1749.13i 0.125102 0.673178i
\(190\) 0 0
\(191\) −392.583 + 679.974i −0.148724 + 0.257598i −0.930756 0.365640i \(-0.880850\pi\)
0.782032 + 0.623238i \(0.214183\pi\)
\(192\) 1319.56 + 1783.88i 0.495994 + 0.670522i
\(193\) −238.539 413.162i −0.0889659 0.154093i 0.818108 0.575064i \(-0.195023\pi\)
−0.907074 + 0.420971i \(0.861690\pi\)
\(194\) 376.417 + 651.974i 0.139305 + 0.241284i
\(195\) 0 0
\(196\) −708.136 + 1226.53i −0.258067 + 0.446985i
\(197\) 4628.37 1.67390 0.836949 0.547281i \(-0.184337\pi\)
0.836949 + 0.547281i \(0.184337\pi\)
\(198\) 19.9137 4.59070i 0.00714751 0.00164771i
\(199\) 2533.85 0.902611 0.451305 0.892370i \(-0.350958\pi\)
0.451305 + 0.892370i \(0.350958\pi\)
\(200\) 0 0
\(201\) 1038.30 2386.88i 0.364359 0.837601i
\(202\) −274.873 476.094i −0.0957425 0.165831i
\(203\) −1910.08 3308.36i −0.660402 1.14385i
\(204\) 1124.28 2584.54i 0.385861 0.887029i
\(205\) 0 0
\(206\) −690.836 −0.233654
\(207\) 830.222 191.391i 0.278765 0.0642636i
\(208\) −629.170 −0.209736
\(209\) 78.3594 135.722i 0.0259341 0.0449192i
\(210\) 0 0
\(211\) −1382.70 2394.90i −0.451131 0.781382i 0.547325 0.836920i \(-0.315646\pi\)
−0.998457 + 0.0555378i \(0.982313\pi\)
\(212\) −1784.64 3091.08i −0.578158 1.00140i
\(213\) −3296.18 4456.03i −1.06033 1.43344i
\(214\) −32.5437 + 56.3673i −0.0103955 + 0.0180056i
\(215\) 0 0
\(216\) 993.185 351.166i 0.312860 0.110620i
\(217\) 1487.12 0.465219
\(218\) 9.54869 16.5388i 0.00296660 0.00513830i
\(219\) 1345.09 + 1818.40i 0.415036 + 0.561078i
\(220\) 0 0
\(221\) 374.515 + 648.679i 0.113994 + 0.197443i
\(222\) −416.732 + 47.4128i −0.125988 + 0.0143339i
\(223\) 234.694 406.502i 0.0704767 0.122069i −0.828634 0.559791i \(-0.810881\pi\)
0.899110 + 0.437722i \(0.144215\pi\)
\(224\) 1115.55 0.332750
\(225\) 0 0
\(226\) −941.817 −0.277207
\(227\) −2143.99 + 3713.50i −0.626879 + 1.08579i 0.361295 + 0.932452i \(0.382335\pi\)
−0.988174 + 0.153335i \(0.950999\pi\)
\(228\) 1588.11 3650.79i 0.461294 1.06044i
\(229\) −2052.30 3554.69i −0.592227 1.02577i −0.993932 0.109998i \(-0.964916\pi\)
0.401705 0.915769i \(-0.368418\pi\)
\(230\) 0 0
\(231\) −41.7913 + 96.0711i −0.0119033 + 0.0273637i
\(232\) 1131.01 1958.97i 0.320062 0.554364i
\(233\) 4272.57 1.20131 0.600656 0.799508i \(-0.294906\pi\)
0.600656 + 0.799508i \(0.294906\pi\)
\(234\) −40.3804 + 131.927i −0.0112810 + 0.0368560i
\(235\) 0 0
\(236\) −1944.12 + 3367.31i −0.536235 + 0.928786i
\(237\) 1937.56 220.441i 0.531045 0.0604185i
\(238\) −210.611 364.790i −0.0573610 0.0993521i
\(239\) 780.619 + 1352.07i 0.211272 + 0.365934i 0.952113 0.305747i \(-0.0989061\pi\)
−0.740841 + 0.671681i \(0.765573\pi\)
\(240\) 0 0
\(241\) 2410.77 4175.58i 0.644362 1.11607i −0.340086 0.940394i \(-0.610456\pi\)
0.984448 0.175674i \(-0.0562105\pi\)
\(242\) 632.399 0.167984
\(243\) 162.187 + 3784.52i 0.0428161 + 0.999083i
\(244\) −4522.80 −1.18665
\(245\) 0 0
\(246\) 208.699 + 282.135i 0.0540901 + 0.0731232i
\(247\) 529.021 + 916.292i 0.136279 + 0.236042i
\(248\) 440.282 + 762.591i 0.112734 + 0.195260i
\(249\) 6676.77 759.634i 1.69929 0.193333i
\(250\) 0 0
\(251\) −3487.72 −0.877063 −0.438532 0.898716i \(-0.644501\pi\)
−0.438532 + 0.898716i \(0.644501\pi\)
\(252\) −778.962 + 2544.94i −0.194722 + 0.636176i
\(253\) −50.1728 −0.0124677
\(254\) −313.791 + 543.503i −0.0775158 + 0.134261i
\(255\) 0 0
\(256\) −1492.20 2584.57i −0.364308 0.631000i
\(257\) −2460.87 4262.35i −0.597295 1.03454i −0.993219 0.116261i \(-0.962909\pi\)
0.395924 0.918283i \(-0.370424\pi\)
\(258\) −296.247 + 681.021i −0.0714865 + 0.164335i
\(259\) 1075.10 1862.13i 0.257929 0.446745i
\(260\) 0 0
\(261\) 5545.36 + 5950.51i 1.31513 + 1.41121i
\(262\) −754.480 −0.177908
\(263\) −2758.58 + 4777.99i −0.646772 + 1.12024i 0.337117 + 0.941463i \(0.390548\pi\)
−0.983889 + 0.178780i \(0.942785\pi\)
\(264\) −61.6377 + 7.01269i −0.0143695 + 0.00163485i
\(265\) 0 0
\(266\) −297.500 515.284i −0.0685747 0.118775i
\(267\) 1246.23 + 1684.75i 0.285649 + 0.386162i
\(268\) −1946.98 + 3372.28i −0.443772 + 0.768636i
\(269\) −7844.13 −1.77794 −0.888969 0.457968i \(-0.848577\pi\)
−0.888969 + 0.457968i \(0.848577\pi\)
\(270\) 0 0
\(271\) 4301.35 0.964164 0.482082 0.876126i \(-0.339881\pi\)
0.482082 + 0.876126i \(0.339881\pi\)
\(272\) −2044.96 + 3541.98i −0.455860 + 0.789573i
\(273\) −420.631 568.641i −0.0932517 0.126065i
\(274\) −90.8083 157.285i −0.0200216 0.0346785i
\(275\) 0 0
\(276\) −1266.41 + 144.083i −0.276192 + 0.0314231i
\(277\) 925.922 1603.74i 0.200842 0.347869i −0.747958 0.663746i \(-0.768966\pi\)
0.948800 + 0.315877i \(0.102299\pi\)
\(278\) 1172.18 0.252888
\(279\) −3085.44 + 711.285i −0.662081 + 0.152629i
\(280\) 0 0
\(281\) −3470.93 + 6011.82i −0.736862 + 1.27628i 0.217040 + 0.976163i \(0.430360\pi\)
−0.953902 + 0.300119i \(0.902974\pi\)
\(282\) −480.937 + 1105.59i −0.101558 + 0.233465i
\(283\) 3216.21 + 5570.64i 0.675562 + 1.17011i 0.976304 + 0.216402i \(0.0694321\pi\)
−0.300743 + 0.953705i \(0.597235\pi\)
\(284\) 4145.88 + 7180.87i 0.866242 + 1.50038i
\(285\) 0 0
\(286\) 4.06236 7.03621i 0.000839903 0.00145476i
\(287\) −1799.10 −0.370027
\(288\) −2314.52 + 533.564i −0.473556 + 0.109169i
\(289\) −43.9287 −0.00894133
\(290\) 0 0
\(291\) 8164.88 928.941i 1.64479 0.187132i
\(292\) −1691.83 2930.34i −0.339065 0.587278i
\(293\) −3820.89 6617.98i −0.761840 1.31955i −0.941901 0.335890i \(-0.890963\pi\)
0.180062 0.983655i \(-0.442370\pi\)
\(294\) −268.009 362.316i −0.0531654 0.0718731i
\(295\) 0 0
\(296\) 1273.19 0.250009
\(297\) 40.7569 219.314i 0.00796281 0.0428481i
\(298\) −182.961 −0.0355660
\(299\) 169.364 293.347i 0.0327577 0.0567380i
\(300\) 0 0
\(301\) −1903.67 3297.26i −0.364538 0.631398i
\(302\) 189.724 + 328.611i 0.0361502 + 0.0626140i
\(303\) −5962.28 + 678.344i −1.13044 + 0.128613i
\(304\) −2888.61 + 5003.23i −0.544978 + 0.943930i
\(305\) 0 0
\(306\) 611.448 + 656.120i 0.114229 + 0.122575i
\(307\) −4517.66 −0.839857 −0.419929 0.907557i \(-0.637945\pi\)
−0.419929 + 0.907557i \(0.637945\pi\)
\(308\) 78.3654 135.733i 0.0144977 0.0251107i
\(309\) −3008.00 + 6914.89i −0.553784 + 1.27306i
\(310\) 0 0
\(311\) −1966.54 3406.15i −0.358560 0.621044i 0.629160 0.777275i \(-0.283399\pi\)
−0.987721 + 0.156231i \(0.950066\pi\)
\(312\) 167.064 384.051i 0.0303145 0.0696879i
\(313\) −1583.09 + 2742.00i −0.285884 + 0.495165i −0.972823 0.231549i \(-0.925620\pi\)
0.686939 + 0.726715i \(0.258954\pi\)
\(314\) −414.622 −0.0745175
\(315\) 0 0
\(316\) −2917.26 −0.519332
\(317\) −3920.86 + 6791.13i −0.694692 + 1.20324i 0.275592 + 0.961275i \(0.411126\pi\)
−0.970284 + 0.241967i \(0.922207\pi\)
\(318\) 1128.49 128.391i 0.199002 0.0226410i
\(319\) −239.495 414.817i −0.0420349 0.0728066i
\(320\) 0 0
\(321\) 422.506 + 571.176i 0.0734641 + 0.0993145i
\(322\) −95.2431 + 164.966i −0.0164835 + 0.0285503i
\(323\) 6877.82 1.18480
\(324\) 398.932 5652.74i 0.0684040 0.969263i
\(325\) 0 0
\(326\) 7.44051 12.8873i 0.00126409 0.00218946i
\(327\) −123.968 167.590i −0.0209647 0.0283417i
\(328\) −532.648 922.574i −0.0896664 0.155307i
\(329\) −3090.49 5352.89i −0.517885 0.897004i
\(330\) 0 0
\(331\) 5426.53 9399.03i 0.901115 1.56078i 0.0750663 0.997179i \(-0.476083\pi\)
0.826049 0.563599i \(-0.190584\pi\)
\(332\) −10052.8 −1.66181
\(333\) −1339.94 + 4377.70i −0.220505 + 0.720411i
\(334\) −17.7480 −0.00290757
\(335\) 0 0
\(336\) 1540.58 3541.53i 0.250135 0.575019i
\(337\) −3258.64 5644.13i −0.526735 0.912331i −0.999515 0.0311507i \(-0.990083\pi\)
0.472780 0.881180i \(-0.343251\pi\)
\(338\) −495.499 858.229i −0.0797384 0.138111i
\(339\) −4100.81 + 9427.08i −0.657008 + 1.51035i
\(340\) 0 0
\(341\) 186.462 0.0296114
\(342\) 863.701 + 926.804i 0.136560 + 0.146537i
\(343\) 6659.94 1.04841
\(344\) 1127.21 1952.39i 0.176672 0.306005i
\(345\) 0 0
\(346\) 281.142 + 486.952i 0.0436829 + 0.0756609i
\(347\) 2969.27 + 5142.93i 0.459363 + 0.795640i 0.998927 0.0463041i \(-0.0147443\pi\)
−0.539564 + 0.841944i \(0.681411\pi\)
\(348\) −7236.33 9782.62i −1.11468 1.50691i
\(349\) 3648.27 6318.99i 0.559563 0.969192i −0.437970 0.898990i \(-0.644302\pi\)
0.997533 0.0702022i \(-0.0223644\pi\)
\(350\) 0 0
\(351\) 1144.69 + 978.613i 0.174071 + 0.148816i
\(352\) 139.873 0.0211797
\(353\) 625.356 1083.15i 0.0942900 0.163315i −0.815022 0.579430i \(-0.803275\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(354\) −735.795 994.704i −0.110472 0.149344i
\(355\) 0 0
\(356\) −1567.49 2714.97i −0.233362 0.404195i
\(357\) −4568.38 + 519.757i −0.677267 + 0.0770545i
\(358\) −102.225 + 177.058i −0.0150915 + 0.0261392i
\(359\) −10928.3 −1.60661 −0.803303 0.595570i \(-0.796926\pi\)
−0.803303 + 0.595570i \(0.796926\pi\)
\(360\) 0 0
\(361\) 2856.27 0.416427
\(362\) −425.567 + 737.104i −0.0617882 + 0.107020i
\(363\) 2753.56 6329.97i 0.398139 0.915254i
\(364\) 529.062 + 916.362i 0.0761823 + 0.131952i
\(365\) 0 0
\(366\) 574.087 1319.73i 0.0819891 0.188479i
\(367\) −3215.66 + 5569.68i −0.457373 + 0.792194i −0.998821 0.0485405i \(-0.984543\pi\)
0.541448 + 0.840734i \(0.317876\pi\)
\(368\) 1849.55 0.261996
\(369\) 3732.73 860.504i 0.526607 0.121398i
\(370\) 0 0
\(371\) −2911.32 + 5042.55i −0.407407 + 0.705650i
\(372\) 4706.49 535.470i 0.655968 0.0746312i
\(373\) 2455.85 + 4253.66i 0.340909 + 0.590472i 0.984602 0.174812i \(-0.0559317\pi\)
−0.643693 + 0.765284i \(0.722598\pi\)
\(374\) −26.4074 45.7389i −0.00365105 0.00632381i
\(375\) 0 0
\(376\) 1829.96 3169.58i 0.250992 0.434731i
\(377\) 3233.76 0.441770
\(378\) −643.726 550.331i −0.0875918 0.0748836i
\(379\) 4805.81 0.651340 0.325670 0.945483i \(-0.394410\pi\)
0.325670 + 0.945483i \(0.394410\pi\)
\(380\) 0 0
\(381\) 4073.87 + 5507.37i 0.547797 + 0.740554i
\(382\) 186.883 + 323.691i 0.0250308 + 0.0433547i
\(383\) −2116.08 3665.15i −0.282314 0.488983i 0.689640 0.724152i \(-0.257769\pi\)
−0.971954 + 0.235170i \(0.924435\pi\)
\(384\) 4682.95 532.792i 0.622333 0.0708045i
\(385\) 0 0
\(386\) −227.106 −0.0299466
\(387\) 5526.75 + 5930.53i 0.725944 + 0.778982i
\(388\) −12293.4 −1.60851
\(389\) 1758.54 3045.89i 0.229208 0.396999i −0.728366 0.685188i \(-0.759720\pi\)
0.957573 + 0.288189i \(0.0930532\pi\)
\(390\) 0 0
\(391\) −1100.95 1906.90i −0.142398 0.246640i
\(392\) 684.022 + 1184.76i 0.0881335 + 0.152652i
\(393\) −3285.12 + 7551.94i −0.421660 + 0.969325i
\(394\) 1101.63 1908.09i 0.140862 0.243980i
\(395\) 0 0
\(396\) −97.6697 + 319.096i −0.0123942 + 0.0404929i
\(397\) −3925.05 −0.496203 −0.248101 0.968734i \(-0.579807\pi\)
−0.248101 + 0.968734i \(0.579807\pi\)
\(398\) 603.100 1044.60i 0.0759564 0.131560i
\(399\) −6453.07 + 734.184i −0.809669 + 0.0921182i
\(400\) 0 0
\(401\) −403.676 699.188i −0.0502709 0.0870718i 0.839795 0.542904i \(-0.182675\pi\)
−0.890066 + 0.455832i \(0.849342\pi\)
\(402\) −736.879 996.169i −0.0914233 0.123593i
\(403\) −629.424 + 1090.19i −0.0778011 + 0.134755i
\(404\) 8977.05 1.10551
\(405\) 0 0
\(406\) −1818.53 −0.222296
\(407\) 134.801 233.482i 0.0164173 0.0284356i
\(408\) −1619.06 2188.77i −0.196459 0.265588i
\(409\) −404.224 700.137i −0.0488694 0.0846444i 0.840556 0.541725i \(-0.182228\pi\)
−0.889425 + 0.457080i \(0.848895\pi\)
\(410\) 0 0
\(411\) −1969.73 + 224.101i −0.236398 + 0.0268956i
\(412\) 5640.49 9769.61i 0.674482 1.16824i
\(413\) 6342.97 0.755732
\(414\) 118.705 387.821i 0.0140919 0.0460395i
\(415\) 0 0
\(416\) −472.157 + 817.800i −0.0556476 + 0.0963844i
\(417\) 5103.85 11732.9i 0.599369 1.37785i
\(418\) −37.3018 64.6086i −0.00436481 0.00756008i
\(419\) −880.089 1524.36i −0.102614 0.177732i 0.810147 0.586227i \(-0.199387\pi\)
−0.912761 + 0.408495i \(0.866054\pi\)
\(420\) 0 0
\(421\) −7287.86 + 12622.9i −0.843678 + 1.46129i 0.0430868 + 0.999071i \(0.486281\pi\)
−0.886765 + 0.462221i \(0.847053\pi\)
\(422\) −1316.42 −0.151854
\(423\) 8972.32 + 9627.84i 1.03132 + 1.10667i
\(424\) −3447.73 −0.394898
\(425\) 0 0
\(426\) −2621.59 + 298.265i −0.298160 + 0.0339225i
\(427\) 3689.07 + 6389.65i 0.418095 + 0.724161i
\(428\) −531.421 920.447i −0.0600168 0.103952i
\(429\) −52.7405 71.2987i −0.00593552 0.00802409i
\(430\) 0 0
\(431\) 5715.34 0.638743 0.319371 0.947630i \(-0.396528\pi\)
0.319371 + 0.947630i \(0.396528\pi\)
\(432\) −1502.45 + 8084.72i −0.167330 + 0.900408i
\(433\) 12751.4 1.41523 0.707614 0.706599i \(-0.249772\pi\)
0.707614 + 0.706599i \(0.249772\pi\)
\(434\) 353.962 613.079i 0.0391491 0.0678082i
\(435\) 0 0
\(436\) 155.925 + 270.070i 0.0171272 + 0.0296651i
\(437\) −1555.15 2693.60i −0.170235 0.294856i
\(438\) 1069.81 121.715i 0.116706 0.0132780i
\(439\) −2420.51 + 4192.44i −0.263154 + 0.455796i −0.967078 0.254479i \(-0.918096\pi\)
0.703924 + 0.710275i \(0.251429\pi\)
\(440\) 0 0
\(441\) −4793.54 + 1105.05i −0.517605 + 0.119323i
\(442\) 356.564 0.0383711
\(443\) −4472.98 + 7747.43i −0.479724 + 0.830907i −0.999730 0.0232564i \(-0.992597\pi\)
0.520005 + 0.854163i \(0.325930\pi\)
\(444\) 2732.01 6280.42i 0.292016 0.671297i
\(445\) 0 0
\(446\) −111.723 193.509i −0.0118615 0.0205447i
\(447\) −796.640 + 1831.34i −0.0842948 + 0.193780i
\(448\) −2707.53 + 4689.57i −0.285533 + 0.494557i
\(449\) −2743.57 −0.288367 −0.144184 0.989551i \(-0.546056\pi\)
−0.144184 + 0.989551i \(0.546056\pi\)
\(450\) 0 0
\(451\) −225.580 −0.0235524
\(452\) 7689.68 13318.9i 0.800204 1.38599i
\(453\) 4115.30 468.209i 0.426829 0.0485615i
\(454\) 1020.61 + 1767.76i 0.105506 + 0.182742i
\(455\) 0 0
\(456\) −2287.00 3091.75i −0.234865 0.317509i
\(457\) 2806.35 4860.74i 0.287255 0.497540i −0.685899 0.727697i \(-0.740591\pi\)
0.973153 + 0.230157i \(0.0739240\pi\)
\(458\) −1953.93 −0.199348
\(459\) 9229.74 3263.41i 0.938578 0.331858i
\(460\) 0 0
\(461\) −6273.50 + 10866.0i −0.633809 + 1.09779i 0.352957 + 0.935640i \(0.385176\pi\)
−0.986766 + 0.162150i \(0.948157\pi\)
\(462\) 29.6591 + 40.0954i 0.00298672 + 0.00403768i
\(463\) −5361.12 9285.74i −0.538126 0.932062i −0.999005 0.0445990i \(-0.985799\pi\)
0.460879 0.887463i \(-0.347534\pi\)
\(464\) 8828.65 + 15291.7i 0.883319 + 1.52995i
\(465\) 0 0
\(466\) 1016.95 1761.40i 0.101093 0.175098i
\(467\) 12798.4 1.26818 0.634089 0.773260i \(-0.281375\pi\)
0.634089 + 0.773260i \(0.281375\pi\)
\(468\) −1535.97 1648.19i −0.151710 0.162794i
\(469\) 6352.31 0.625421
\(470\) 0 0
\(471\) −1805.33 + 4150.14i −0.176614 + 0.406005i
\(472\) 1877.92 + 3252.65i 0.183132 + 0.317193i
\(473\) −238.691 413.425i −0.0232030 0.0401888i
\(474\) 370.293 851.242i 0.0358822 0.0824870i
\(475\) 0 0
\(476\) 6878.34 0.662328
\(477\) 3628.49 11854.6i 0.348296 1.13791i
\(478\) 743.203 0.0711158
\(479\) −1207.38 + 2091.25i −0.115171 + 0.199481i −0.917848 0.396932i \(-0.870075\pi\)
0.802677 + 0.596413i \(0.203408\pi\)
\(480\) 0 0
\(481\) 910.070 + 1576.29i 0.0862695 + 0.149423i
\(482\) −1147.61 1987.72i −0.108449 0.187839i
\(483\) 1236.52 + 1671.62i 0.116487 + 0.157477i
\(484\) −5163.37 + 8943.21i −0.484914 + 0.839896i
\(485\) 0 0
\(486\) 1598.80 + 833.919i 0.149225 + 0.0778340i
\(487\) 16386.9 1.52477 0.762384 0.647125i \(-0.224029\pi\)
0.762384 + 0.647125i \(0.224029\pi\)
\(488\) −2184.39 + 3783.48i −0.202629 + 0.350963i
\(489\) −96.5982 130.589i −0.00893317 0.0120766i
\(490\) 0 0
\(491\) −7935.54 13744.8i −0.729381 1.26332i −0.957145 0.289609i \(-0.906475\pi\)
0.227764 0.973716i \(-0.426858\pi\)
\(492\) −5693.85 + 647.805i −0.521745 + 0.0593604i
\(493\) 10510.6 18204.8i 0.960186 1.66309i
\(494\) 503.665 0.0458724
\(495\) 0 0
\(496\) −6873.68 −0.622252
\(497\) 6763.26 11714.3i 0.610410 1.05726i
\(498\) 1276.02 2933.36i 0.114819 0.263950i
\(499\) −5730.39 9925.33i −0.514083 0.890419i −0.999867 0.0163392i \(-0.994799\pi\)
0.485783 0.874079i \(-0.338534\pi\)
\(500\) 0 0
\(501\) −77.2776 + 177.648i −0.00689123 + 0.0158418i
\(502\) −830.138 + 1437.84i −0.0738065 + 0.127837i
\(503\) −1038.52 −0.0920585 −0.0460293 0.998940i \(-0.514657\pi\)
−0.0460293 + 0.998940i \(0.514657\pi\)
\(504\) 1752.71 + 1880.77i 0.154905 + 0.166222i
\(505\) 0 0
\(506\) −11.9420 + 20.6841i −0.00104918 + 0.00181724i
\(507\) −10747.9 + 1222.81i −0.941479 + 0.107115i
\(508\) −5124.04 8875.10i −0.447525 0.775135i
\(509\) 2514.44 + 4355.14i 0.218960 + 0.379249i 0.954490 0.298242i \(-0.0964003\pi\)
−0.735530 + 0.677492i \(0.763067\pi\)
\(510\) 0 0
\(511\) −2759.92 + 4780.33i −0.238927 + 0.413834i
\(512\) −8677.07 −0.748976
\(513\) 13037.5 4609.74i 1.12206 0.396735i
\(514\) −2342.92 −0.201054
\(515\) 0 0
\(516\) −7212.04 9749.79i −0.615295 0.831803i
\(517\) −387.499 671.169i −0.0329636 0.0570947i
\(518\) −511.785 886.438i −0.0434104 0.0751889i
\(519\) 6098.25 693.815i 0.515768 0.0586803i
\(520\) 0 0
\(521\) 7057.78 0.593487 0.296744 0.954957i \(-0.404099\pi\)
0.296744 + 0.954957i \(0.404099\pi\)
\(522\) 3773.04 869.797i 0.316363 0.0729310i
\(523\) −14453.5 −1.20843 −0.604215 0.796821i \(-0.706513\pi\)
−0.604215 + 0.796821i \(0.706513\pi\)
\(524\) 6160.13 10669.7i 0.513562 0.889515i
\(525\) 0 0
\(526\) 1313.18 + 2274.49i 0.108854 + 0.188541i
\(527\) 4091.57 + 7086.81i 0.338201 + 0.585781i
\(528\) 193.165 444.053i 0.0159212 0.0366002i
\(529\) 5585.63 9674.59i 0.459080 0.795150i
\(530\) 0 0
\(531\) −13160.2 + 3033.81i −1.07553 + 0.247940i
\(532\) 9716.01 0.791809
\(533\) 761.469 1318.90i 0.0618816 0.107182i
\(534\) 991.180 112.769i 0.0803231 0.00913858i
\(535\) 0 0
\(536\) 1880.68 + 3257.44i 0.151554 + 0.262500i
\(537\) 1327.16 + 1794.15i 0.106650 + 0.144178i
\(538\) −1867.04 + 3233.81i −0.149617 + 0.259144i
\(539\) 289.687 0.0231498
\(540\) 0 0
\(541\) 4101.59 0.325954 0.162977 0.986630i \(-0.447890\pi\)
0.162977 + 0.986630i \(0.447890\pi\)
\(542\) 1023.80 1773.27i 0.0811362 0.140532i
\(543\) 5525.03 + 7469.16i 0.436651 + 0.590299i
\(544\) 3069.26 + 5316.11i 0.241900 + 0.418982i
\(545\) 0 0
\(546\) −334.544 + 38.0620i −0.0262219 + 0.00298334i
\(547\) −8410.52 + 14567.4i −0.657418 + 1.13868i 0.323863 + 0.946104i \(0.395018\pi\)
−0.981282 + 0.192578i \(0.938315\pi\)
\(548\) 2965.70 0.231183
\(549\) −10710.1 11492.6i −0.832598 0.893428i
\(550\) 0 0
\(551\) 14846.7 25715.2i 1.14790 1.98821i
\(552\) −491.112 + 1128.98i −0.0378680 + 0.0870521i
\(553\) 2379.50 + 4121.41i 0.182977 + 0.316926i
\(554\) −440.771 763.438i −0.0338025 0.0585476i
\(555\) 0 0
\(556\) −9570.54 + 16576.7i −0.730002 + 1.26440i
\(557\) 12248.8 0.931771 0.465885 0.884845i \(-0.345736\pi\)
0.465885 + 0.884845i \(0.345736\pi\)
\(558\) −441.156 + 1441.30i −0.0334688 + 0.109346i
\(559\) 3222.91 0.243854
\(560\) 0 0
\(561\) −572.804 + 65.1694i −0.0431084 + 0.00490455i
\(562\) 1652.28 + 2861.84i 0.124017 + 0.214803i
\(563\) 4422.86 + 7660.62i 0.331086 + 0.573457i 0.982725 0.185072i \(-0.0592517\pi\)
−0.651639 + 0.758529i \(0.725918\pi\)
\(564\) −11708.3 15828.1i −0.874127 1.18171i
\(565\) 0 0
\(566\) 3062.06 0.227399
\(567\) −8311.39 + 4047.12i −0.615601 + 0.299759i
\(568\) 8009.40 0.591667
\(569\) 4049.35 7013.68i 0.298344 0.516747i −0.677413 0.735603i \(-0.736899\pi\)
0.975757 + 0.218856i \(0.0702325\pi\)
\(570\) 0 0
\(571\) 8189.02 + 14183.8i 0.600175 + 1.03953i 0.992794 + 0.119832i \(0.0382356\pi\)
−0.392619 + 0.919701i \(0.628431\pi\)
\(572\) 66.3361 + 114.897i 0.00484904 + 0.00839879i
\(573\) 4053.69 461.200i 0.295542 0.0336246i
\(574\) −428.218 + 741.696i −0.0311385 + 0.0539334i
\(575\) 0 0
\(576\) 3374.49 11024.8i 0.244104 0.797510i
\(577\) −24920.9 −1.79804 −0.899020 0.437907i \(-0.855720\pi\)
−0.899020 + 0.437907i \(0.855720\pi\)
\(578\) −10.4558 + 18.1100i −0.000752430 + 0.00130325i
\(579\) −988.853 + 2273.21i −0.0709764 + 0.163163i
\(580\) 0 0
\(581\) 8199.69 + 14202.3i 0.585509 + 1.01413i
\(582\) 1560.42 3587.15i 0.111137 0.255484i
\(583\) −365.034 + 632.257i −0.0259317 + 0.0449150i
\(584\) −3268.44 −0.231591
\(585\) 0 0
\(586\) −3637.76 −0.256441
\(587\) −4182.25 + 7243.86i −0.294071 + 0.509346i −0.974768 0.223219i \(-0.928344\pi\)
0.680697 + 0.732565i \(0.261677\pi\)
\(588\) 7311.99 831.905i 0.512826 0.0583456i
\(589\) 5779.56 + 10010.5i 0.404317 + 0.700297i
\(590\) 0 0
\(591\) −14302.2 19334.8i −0.995456 1.34573i
\(592\) −4969.25 + 8607.00i −0.344992 + 0.597543i
\(593\) −27169.7 −1.88150 −0.940749 0.339105i \(-0.889876\pi\)
−0.940749 + 0.339105i \(0.889876\pi\)
\(594\) −80.7132 69.0030i −0.00557526 0.00476637i
\(595\) 0 0
\(596\) 1493.83 2587.39i 0.102667 0.177825i
\(597\) −7829.88 10585.0i −0.536777 0.725656i
\(598\) −80.6231 139.643i −0.00551325 0.00954923i
\(599\) −10666.2 18474.4i −0.727560 1.26017i −0.957911 0.287064i \(-0.907321\pi\)
0.230351 0.973108i \(-0.426013\pi\)
\(600\) 0 0
\(601\) −292.016 + 505.786i −0.0198196 + 0.0343285i −0.875765 0.482738i \(-0.839643\pi\)
0.855946 + 0.517066i \(0.172976\pi\)
\(602\) −1812.43 −0.122706
\(603\) −13179.6 + 3038.28i −0.890074 + 0.205188i
\(604\) −6196.17 −0.417415
\(605\) 0 0
\(606\) −1139.47 + 2619.46i −0.0763827 + 0.175591i
\(607\) 5635.12 + 9760.32i 0.376808 + 0.652651i 0.990596 0.136820i \(-0.0436883\pi\)
−0.613788 + 0.789471i \(0.710355\pi\)
\(608\) 4335.49 + 7509.29i 0.289190 + 0.500891i
\(609\) −7918.17 + 18202.5i −0.526864 + 1.21117i
\(610\) 0 0
\(611\) 5232.19 0.346435
\(612\) −14271.0 + 3289.88i −0.942598 + 0.217297i
\(613\) −4271.02 −0.281411 −0.140706 0.990051i \(-0.544937\pi\)
−0.140706 + 0.990051i \(0.544937\pi\)
\(614\) −1075.28 + 1862.44i −0.0706756 + 0.122414i
\(615\) 0 0
\(616\) −75.6968 131.111i −0.00495115 0.00857565i
\(617\) −3598.08 6232.06i −0.234770 0.406634i 0.724436 0.689342i \(-0.242100\pi\)
−0.959206 + 0.282708i \(0.908767\pi\)
\(618\) 2134.76 + 2885.94i 0.138953 + 0.187847i
\(619\) −5128.24 + 8882.36i −0.332991 + 0.576757i −0.983097 0.183087i \(-0.941391\pi\)
0.650106 + 0.759843i \(0.274724\pi\)
\(620\) 0 0
\(621\) −3365.01 2876.80i −0.217445 0.185897i
\(622\) −1872.28 −0.120694
\(623\) −2557.08 + 4428.99i −0.164442 + 0.284822i
\(624\) 1944.21 + 2628.33i 0.124729 + 0.168618i
\(625\) 0 0
\(626\) 753.607 + 1305.29i 0.0481153 + 0.0833382i
\(627\) −809.115 + 92.0552i −0.0515358 + 0.00586337i
\(628\) 3385.28 5863.47i 0.215107 0.372576i
\(629\) 11831.8 0.750026
\(630\) 0 0
\(631\) 15187.7 0.958183 0.479091 0.877765i \(-0.340966\pi\)
0.479091 + 0.877765i \(0.340966\pi\)
\(632\) −1408.96 + 2440.39i −0.0886795 + 0.153597i
\(633\) −5731.90 + 13176.7i −0.359909 + 0.827371i
\(634\) 1866.47 + 3232.81i 0.116919 + 0.202510i
\(635\) 0 0
\(636\) −7398.14 + 17007.1i −0.461250 + 1.06034i
\(637\) −977.872 + 1693.72i −0.0608237 + 0.105350i
\(638\) −228.016 −0.0141493
\(639\) −8429.31 + 27539.3i −0.521844 + 1.70491i
\(640\) 0 0
\(641\) 14196.7 24589.4i 0.874783 1.51517i 0.0177891 0.999842i \(-0.494337\pi\)
0.856994 0.515327i \(-0.172329\pi\)
\(642\) 336.036 38.2317i 0.0206578 0.00235029i
\(643\) −5844.00 10122.1i −0.358421 0.620804i 0.629276 0.777182i \(-0.283351\pi\)
−0.987697 + 0.156378i \(0.950018\pi\)
\(644\) −1555.27 2693.80i −0.0951648 0.164830i
\(645\) 0 0
\(646\) 1637.04 2835.44i 0.0997036 0.172692i
\(647\) 12800.8 0.777822 0.388911 0.921275i \(-0.372851\pi\)
0.388911 + 0.921275i \(0.372851\pi\)
\(648\) −4536.04 3063.85i −0.274989 0.185740i
\(649\) 795.310 0.0481027
\(650\) 0 0
\(651\) −4595.39 6212.40i −0.276663 0.374014i
\(652\) 121.500 + 210.443i 0.00729799 + 0.0126405i
\(653\) −3079.46 5333.78i −0.184546 0.319643i 0.758877 0.651233i \(-0.225748\pi\)
−0.943423 + 0.331590i \(0.892415\pi\)
\(654\) −98.5968 + 11.2176i −0.00589517 + 0.000670709i
\(655\) 0 0
\(656\) 8315.69 0.494929
\(657\) 3439.80 11238.1i 0.204261 0.667339i
\(658\) −2942.36 −0.174324
\(659\) −8289.10 + 14357.1i −0.489981 + 0.848672i −0.999934 0.0115307i \(-0.996330\pi\)
0.509953 + 0.860202i \(0.329663\pi\)
\(660\) 0 0
\(661\) 11469.8 + 19866.4i 0.674925 + 1.16900i 0.976491 + 0.215559i \(0.0691573\pi\)
−0.301566 + 0.953445i \(0.597509\pi\)
\(662\) −2583.22 4474.27i −0.151661 0.262685i
\(663\) 1552.53 3569.01i 0.0909433 0.209063i
\(664\) −4855.25 + 8409.53i −0.283765 + 0.491496i
\(665\) 0 0
\(666\) 1485.82 + 1594.37i 0.0864478 + 0.0927637i
\(667\) −9506.20 −0.551847
\(668\) 144.908 250.988i 0.00839319 0.0145374i
\(669\) −2423.38 + 275.715i −0.140050 + 0.0159338i
\(670\) 0 0
\(671\) 462.552 + 801.163i 0.0266119 + 0.0460932i
\(672\) −3447.19 4660.18i −0.197884 0.267515i
\(673\) 1181.62 2046.62i 0.0676790 0.117223i −0.830200 0.557465i \(-0.811774\pi\)
0.897879 + 0.440242i \(0.145107\pi\)
\(674\) −3102.46 −0.177303
\(675\) 0 0
\(676\) 16182.4 0.920712
\(677\) −7824.09 + 13551.7i −0.444172 + 0.769328i −0.997994 0.0633068i \(-0.979835\pi\)
0.553822 + 0.832635i \(0.313169\pi\)
\(678\) 2910.33 + 3934.40i 0.164853 + 0.222861i
\(679\) 10027.2 + 17367.7i 0.566730 + 0.981605i
\(680\) 0 0
\(681\) 22138.2 2518.72i 1.24572 0.141729i
\(682\) 44.3813 76.8706i 0.00249186 0.00431602i
\(683\) −19626.7 −1.09955 −0.549777 0.835311i \(-0.685287\pi\)
−0.549777 + 0.835311i \(0.685287\pi\)
\(684\) −20158.5 + 4647.12i −1.12687 + 0.259777i
\(685\) 0 0
\(686\) 1585.18 2745.62i 0.0882253 0.152811i
\(687\) −8507.72 + 19557.8i −0.472474 + 1.08614i
\(688\) 8799.02 + 15240.3i 0.487586 + 0.844524i
\(689\) −2464.42 4268.51i −0.136266 0.236019i
\(690\) 0 0
\(691\) 51.5955 89.3660i 0.00284050 0.00491989i −0.864602 0.502458i \(-0.832429\pi\)
0.867442 + 0.497538i \(0.165763\pi\)
\(692\) −9181.78 −0.504391
\(693\) 530.473 122.290i 0.0290779 0.00670332i
\(694\) 2826.96 0.154625
\(695\) 0 0
\(696\) −11678.5 + 1328.69i −0.636021 + 0.0723619i
\(697\) −4949.93 8573.54i −0.268999 0.465920i
\(698\) −1736.71 3008.06i −0.0941766 0.163119i
\(699\) −13202.8 17848.5i −0.714412 0.965797i
\(700\) 0 0
\(701\) −17977.8 −0.968631 −0.484316 0.874893i \(-0.660931\pi\)
−0.484316 + 0.874893i \(0.660931\pi\)
\(702\) 675.898 238.981i 0.0363392 0.0128487i
\(703\) 16713.1 0.896651
\(704\) −339.482 + 588.000i −0.0181743 + 0.0314788i
\(705\) 0 0
\(706\) −297.692 515.617i −0.0158694 0.0274865i
\(707\) −7322.22 12682.5i −0.389506 0.674644i
\(708\) 20074.4 2283.92i 1.06560 0.121236i
\(709\) −5385.10 + 9327.26i −0.285249 + 0.494066i −0.972670 0.232194i \(-0.925410\pi\)
0.687421 + 0.726260i \(0.258743\pi\)
\(710\) 0 0
\(711\) −6908.16 7412.87i −0.364383 0.391005i
\(712\) −3028.23 −0.159393
\(713\) 1850.30 3204.81i 0.0971868 0.168333i
\(714\) −873.080 + 2007.06i −0.0457622 + 0.105200i
\(715\) 0 0
\(716\) −1669.27 2891.27i −0.0871280 0.150910i
\(717\) 3236.02 7439.06i 0.168551 0.387471i
\(718\) −2601.12 + 4505.27i −0.135199 + 0.234171i
\(719\) 24138.7 1.25205 0.626023 0.779804i \(-0.284681\pi\)
0.626023 + 0.779804i \(0.284681\pi\)
\(720\) 0 0
\(721\) −18402.9 −0.950568
\(722\) 679.843 1177.52i 0.0350431 0.0606964i
\(723\) −24892.9 + 2832.13i −1.28046 + 0.145682i
\(724\) −6949.28 12036.5i −0.356724 0.617864i
\(725\) 0 0
\(726\) −1954.19 2641.82i −0.0998991 0.135051i
\(727\) −5395.46 + 9345.20i −0.275250 + 0.476746i −0.970198 0.242313i \(-0.922094\pi\)
0.694949 + 0.719059i \(0.255427\pi\)
\(728\) 1022.09 0.0520347
\(729\) 15308.5 12372.1i 0.777753 0.628570i
\(730\) 0 0
\(731\) 10475.3 18143.7i 0.530016 0.918015i
\(732\) 13976.0 + 18893.8i 0.705692 + 0.954009i
\(733\) −10492.9 18174.3i −0.528738 0.915801i −0.999438 0.0335082i \(-0.989332\pi\)
0.470700 0.882293i \(-0.344001\pi\)
\(734\) 1530.77 + 2651.36i 0.0769776 + 0.133329i
\(735\) 0 0
\(736\) 1387.99 2404.06i 0.0695134 0.120401i
\(737\) 796.481 0.0398084
\(738\) 533.705 1743.66i 0.0266205 0.0869717i
\(739\) 1773.47 0.0882790 0.0441395 0.999025i \(-0.485945\pi\)
0.0441395 + 0.999025i \(0.485945\pi\)
\(740\) 0 0
\(741\) 2193.03 5041.42i 0.108722 0.249934i
\(742\) 1385.89 + 2400.43i 0.0685682 + 0.118764i
\(743\) −2640.39 4573.28i −0.130372 0.225811i 0.793448 0.608638i \(-0.208284\pi\)
−0.923820 + 0.382827i \(0.874950\pi\)
\(744\) 1825.17 4195.76i 0.0899381 0.206753i
\(745\) 0 0
\(746\) 2338.14 0.114753
\(747\) −23805.4 25544.6i −1.16599 1.25117i
\(748\) 862.437 0.0421575
\(749\) −866.918 + 1501.55i −0.0422917 + 0.0732514i
\(750\) 0 0
\(751\) −5514.51 9551.40i −0.267946 0.464095i 0.700386 0.713765i \(-0.253011\pi\)
−0.968331 + 0.249669i \(0.919678\pi\)
\(752\) 14284.6 + 24741.7i 0.692696 + 1.19978i
\(753\) 10777.5 + 14569.8i 0.521584 + 0.705117i
\(754\) 769.692 1333.15i 0.0371758 0.0643904i
\(755\) 0 0
\(756\) 13038.5 4610.09i 0.627255 0.221782i
\(757\) 19897.2 0.955318 0.477659 0.878545i \(-0.341486\pi\)
0.477659 + 0.878545i \(0.341486\pi\)
\(758\) 1143.87 1981.24i 0.0548115 0.0949363i
\(759\) 155.040 + 209.595i 0.00741448 + 0.0100235i
\(760\) 0 0
\(761\) 12636.2 + 21886.5i 0.601920 + 1.04256i 0.992530 + 0.122000i \(0.0389307\pi\)
−0.390610 + 0.920556i \(0.627736\pi\)
\(762\) 3240.11 368.636i 0.154038 0.0175253i
\(763\) 254.364 440.571i 0.0120689 0.0209040i
\(764\) −6103.40 −0.289023
\(765\) 0 0
\(766\) −2014.65 −0.0950292
\(767\) −2684.65 + 4649.96i −0.126385 + 0.218905i
\(768\) −6185.87 + 14220.3i −0.290642 + 0.668137i
\(769\) −15167.1 26270.1i −0.711233 1.23189i −0.964395 0.264467i \(-0.914804\pi\)
0.253162 0.967424i \(-0.418529\pi\)
\(770\) 0 0
\(771\) −10201.4 + 23451.3i −0.476517 + 1.09543i
\(772\) 1854.26 3211.67i 0.0864458 0.149729i
\(773\) −6671.36 −0.310417 −0.155208 0.987882i \(-0.549605\pi\)
−0.155208 + 0.987882i \(0.549605\pi\)
\(774\) 3760.37 866.877i 0.174630 0.0402574i
\(775\) 0 0
\(776\) −5937.38 + 10283.8i −0.274664 + 0.475732i
\(777\) −11101.2 + 1263.01i −0.512551 + 0.0583143i
\(778\) −837.129 1449.95i −0.0385765 0.0668165i
\(779\) −6992.04 12110.6i −0.321586 0.557004i
\(780\) 0 0
\(781\) 848.008 1468.79i 0.0388529 0.0672952i
\(782\) −1048.18 −0.0479321
\(783\) 7722.18 41553.3i 0.352450 1.89654i
\(784\) −10678.9 −0.486468
\(785\) 0 0
\(786\) 2331.43 + 3151.81i 0.105801 + 0.143030i
\(787\) 10503.1 + 18192.0i 0.475726 + 0.823981i 0.999613 0.0278064i \(-0.00885218\pi\)
−0.523888 + 0.851787i \(0.675519\pi\)
\(788\) 17989.1 + 31158.0i 0.813241 + 1.40858i
\(789\) 28484.2 3240.73i 1.28525 0.146227i
\(790\) 0 0
\(791\) −25088.7 −1.12775
\(792\) 219.763 + 235.819i 0.00985978 + 0.0105801i
\(793\) −6245.57 −0.279681
\(794\) −934.230 + 1618.13i −0.0417564 + 0.0723242i
\(795\) 0 0
\(796\) 9848.29 + 17057.7i 0.438522 + 0.759542i
\(797\) −4566.27 7909.00i −0.202943 0.351507i 0.746533 0.665349i \(-0.231717\pi\)
−0.949475 + 0.313842i \(0.898384\pi\)
\(798\) −1233.27 + 2835.08i −0.0547084 + 0.125765i
\(799\) 17005.9 29455.1i 0.752975 1.30419i
\(800\) 0 0
\(801\) 3186.99 10412.2i 0.140583 0.459296i
\(802\) −384.328 −0.0169216
\(803\) −346.051 + 599.379i −0.0152078 + 0.0263407i
\(804\) 20104.0 2287.28i 0.881856 0.100331i
\(805\) 0 0
\(806\) 299.628 + 518.970i 0.0130942 + 0.0226798i
\(807\) 24239.3 + 32768.5i 1.05733 + 1.42938i
\(808\) 4335.68 7509.61i 0.188773 0.326964i
\(809\) 17687.6 0.768681 0.384341 0.923191i \(-0.374429\pi\)
0.384341 + 0.923191i \(0.374429\pi\)
\(810\) 0 0
\(811\) −7211.00 −0.312223 −0.156111 0.987739i \(-0.549896\pi\)
−0.156111 + 0.987739i \(0.549896\pi\)
\(812\) 14847.8 25717.2i 0.641695 1.11145i
\(813\) −13291.7 17968.7i −0.573382 0.775142i
\(814\) −64.1699 111.146i −0.00276309 0.00478581i
\(815\) 0 0
\(816\) 21115.6 2402.38i 0.905876 0.103064i
\(817\) 14796.9 25628.9i 0.633631 1.09748i
\(818\) −384.850 −0.0164498
\(819\) −1075.68 + 3514.34i −0.0458940 + 0.149940i
\(820\) 0 0
\(821\) −21037.2 + 36437.6i −0.894281 + 1.54894i −0.0595894 + 0.998223i \(0.518979\pi\)
−0.834692 + 0.550717i \(0.814354\pi\)
\(822\) −376.442 + 865.376i −0.0159731 + 0.0367195i
\(823\) 10437.6 + 18078.5i 0.442081 + 0.765707i 0.997844 0.0656341i \(-0.0209070\pi\)
−0.555763 + 0.831341i \(0.687574\pi\)
\(824\) −5448.41 9436.93i −0.230345 0.398970i
\(825\) 0 0
\(826\) 1509.74 2614.94i 0.0635962 0.110152i
\(827\) −3128.34 −0.131540 −0.0657698 0.997835i \(-0.520950\pi\)
−0.0657698 + 0.997835i \(0.520950\pi\)
\(828\) 4515.26 + 4845.14i 0.189512 + 0.203358i
\(829\) −6854.35 −0.287167 −0.143583 0.989638i \(-0.545863\pi\)
−0.143583 + 0.989638i \(0.545863\pi\)
\(830\) 0 0
\(831\) −9560.78 + 1087.76i −0.399109 + 0.0454078i
\(832\) −2291.92 3969.71i −0.0955022 0.165415i
\(833\) 6356.66 + 11010.1i 0.264400 + 0.457954i
\(834\) −3622.18 4896.74i −0.150391 0.203310i
\(835\) 0 0
\(836\) 1218.24 0.0503990
\(837\) 12505.7 + 10691.3i 0.516442 + 0.441514i
\(838\) −837.906 −0.0345405
\(839\) −20793.2 + 36014.9i −0.855615 + 1.48197i 0.0204588 + 0.999791i \(0.493487\pi\)
−0.876074 + 0.482178i \(0.839846\pi\)
\(840\) 0 0
\(841\) −33182.4 57473.6i −1.36055 2.35654i
\(842\) 3469.27 + 6008.96i 0.141994 + 0.245941i
\(843\) 35839.7 4077.58i 1.46428 0.166595i
\(844\) 10748.2 18616.5i 0.438352 0.759249i
\(845\) 0 0
\(846\) 6104.73 1407.32i 0.248091 0.0571922i
\(847\) 16846.2 0.683404
\(848\) 13456.5 23307.3i 0.544926 0.943840i
\(849\) 13332.7 30649.5i 0.538958 1.23897i
\(850\) 0 0
\(851\) −2675.31 4633.77i −0.107765 0.186655i
\(852\) 17186.6 39509.0i 0.691082 1.58868i
\(853\) −9160.28 + 15866.1i −0.367693 + 0.636863i −0.989204 0.146542i \(-0.953186\pi\)
0.621512 + 0.783405i \(0.286519\pi\)
\(854\) 3512.25 0.140734
\(855\) 0 0
\(856\) −1026.65 −0.0409931
\(857\) 6189.48 10720.5i 0.246708 0.427310i −0.715903 0.698200i \(-0.753985\pi\)
0.962610 + 0.270890i \(0.0873179\pi\)
\(858\) −41.9467 + 4.77239i −0.00166904 + 0.000189891i
\(859\) 14758.5 + 25562.5i 0.586210 + 1.01534i 0.994723 + 0.102593i \(0.0327139\pi\)
−0.408514 + 0.912752i \(0.633953\pi\)
\(860\) 0 0
\(861\) 5559.45 + 7515.69i 0.220053 + 0.297484i
\(862\) 1360.35 2356.19i 0.0537514 0.0931001i
\(863\) 41307.0 1.62932 0.814661 0.579937i \(-0.196923\pi\)
0.814661 + 0.579937i \(0.196923\pi\)
\(864\) 9381.08 + 8020.03i 0.369387 + 0.315795i
\(865\) 0 0
\(866\) 3035.06 5256.88i 0.119094 0.206277i
\(867\) 135.745 + 183.511i 0.00531735 + 0.00718840i
\(868\) 5780.00 + 10011.3i 0.226021 + 0.391479i
\(869\) 298.352 + 516.760i 0.0116466 + 0.0201725i
\(870\) 0 0
\(871\) −2688.61 + 4656.81i −0.104593 + 0.181160i
\(872\) 301.230 0.0116983
\(873\) −29111.1 31237.9i −1.12859 1.21105i
\(874\) −1480.61 −0.0573025
\(875\) 0 0
\(876\) −7013.42 + 16122.7i −0.270504 + 0.621843i
\(877\) −19153.4 33174.7i −0.737475 1.27734i −0.953629 0.300984i \(-0.902685\pi\)
0.216155 0.976359i \(-0.430648\pi\)
\(878\) 1152.25 + 1995.75i 0.0442898 + 0.0767122i
\(879\) −15839.3 + 36412.0i −0.607790 + 1.39721i
\(880\) 0 0
\(881\) −47903.1 −1.83189 −0.915946 0.401301i \(-0.868558\pi\)
−0.915946 + 0.401301i \(0.868558\pi\)
\(882\) −685.379 + 2239.20i −0.0261654 + 0.0854849i
\(883\) −39098.9 −1.49013 −0.745064 0.666993i \(-0.767581\pi\)
−0.745064 + 0.666993i \(0.767581\pi\)
\(884\) −2911.25 + 5042.43i −0.110765 + 0.191850i
\(885\) 0 0
\(886\) 2129.30 + 3688.05i 0.0807394 + 0.139845i
\(887\) −14117.0 24451.4i −0.534389 0.925590i −0.999193 0.0401756i \(-0.987208\pi\)
0.464803 0.885414i \(-0.346125\pi\)
\(888\) −3934.31 5318.70i −0.148679 0.200995i
\(889\) −8358.96 + 14478.1i −0.315355 + 0.546211i
\(890\) 0 0
\(891\) −1042.12 + 507.446i −0.0391833 + 0.0190798i
\(892\) 3648.74 0.136961
\(893\) 24021.8 41606.9i 0.900177 1.55915i
\(894\) 565.371 + 764.313i 0.0211508 + 0.0285933i
\(895\) 0 0
\(896\) 5751.09 + 9961.18i 0.214431 + 0.371406i
\(897\) −1748.80 + 198.965i −0.0650955 + 0.00740609i
\(898\) −653.016 + 1131.06i −0.0242666 + 0.0420311i
\(899\) 35328.9 1.31066
\(900\) 0 0
\(901\) −32040.0 −1.18469
\(902\) −53.6919 + 92.9971i −0.00198198 + 0.00343289i
\(903\) −7891.59 + 18141.4i −0.290826 + 0.668559i
\(904\) −7427.83 12865.4i −0.273281 0.473336i
\(905\) 0 0
\(906\) 786.491 1808.01i 0.0288404 0.0662992i
\(907\) 9530.28 16506.9i 0.348895 0.604304i −0.637159 0.770733i \(-0.719890\pi\)
0.986053 + 0.166429i \(0.0532237\pi\)
\(908\) −33332.1 −1.21824
\(909\) 21257.9 + 22811.0i 0.775665 + 0.832336i
\(910\) 0 0
\(911\) 727.041 1259.27i 0.0264412 0.0457975i −0.852502 0.522724i \(-0.824916\pi\)
0.878943 + 0.476926i \(0.158249\pi\)
\(912\) 29826.9 3393.49i 1.08297 0.123212i
\(913\) 1028.11 + 1780.74i 0.0372679 + 0.0645499i
\(914\) −1335.92 2313.88i −0.0483461 0.0837379i
\(915\) 0 0
\(916\) 15953.3 27632.0i 0.575451 0.996711i
\(917\) −20098.3 −0.723778
\(918\) 851.470 4581.79i 0.0306130 0.164729i
\(919\) −6383.04 −0.229115 −0.114558 0.993417i \(-0.536545\pi\)
−0.114558 + 0.993417i \(0.536545\pi\)
\(920\) 0 0
\(921\) 13960.1 + 18872.3i 0.499458 + 0.675205i
\(922\) 2986.41 + 5172.61i 0.106673 + 0.184762i
\(923\) 5725.09 + 9916.14i 0.204164 + 0.353623i
\(924\) −809.176 + 92.0622i −0.0288095 + 0.00327773i
\(925\) 0 0
\(926\) −5104.16 −0.181137
\(927\) 38181.8 8802.02i 1.35281 0.311862i
\(928\) 26501.7 0.937456
\(929\) −14466.9 + 25057.5i −0.510920 + 0.884939i 0.489000 + 0.872284i \(0.337362\pi\)
−0.999920 + 0.0126553i \(0.995972\pi\)
\(930\) 0 0
\(931\) 8979.11 + 15552.3i 0.316089 + 0.547482i
\(932\) 16606.2 + 28762.8i 0.583641 + 1.01090i
\(933\) −8152.20 + 18740.5i −0.286057 + 0.657596i
\(934\) 3046.24 5276.25i 0.106720 0.184844i
\(935\) 0 0
\(936\) −2120.60 + 488.862i −0.0740536 + 0.0170715i
\(937\) 8282.43 0.288768 0.144384 0.989522i \(-0.453880\pi\)
0.144384 + 0.989522i \(0.453880\pi\)
\(938\) 1511.96 2618.80i 0.0526304 0.0911585i
\(939\) 16346.5 1859.79i 0.568103 0.0646346i
\(940\) 0 0
\(941\) 18408.2 + 31883.9i 0.637715 + 1.10455i 0.985933 + 0.167141i \(0.0534534\pi\)
−0.348219 + 0.937413i \(0.613213\pi\)
\(942\) 1281.23 + 1732.07i 0.0443151 + 0.0599085i
\(943\) −2238.47 + 3877.14i −0.0773007 + 0.133889i
\(944\) −29318.0 −1.01083
\(945\) 0 0
\(946\) −227.250 −0.00781031
\(947\) 465.404 806.104i 0.0159700 0.0276609i −0.857930 0.513767i \(-0.828250\pi\)
0.873900 + 0.486106i \(0.161583\pi\)
\(948\) 9014.69 + 12186.7i 0.308843 + 0.417518i
\(949\) −2336.27 4046.54i −0.0799141 0.138415i
\(950\) 0 0
\(951\) 40485.6 4606.15i 1.38048 0.157061i
\(952\) 3322.06 5753.97i 0.113097 0.195890i
\(953\) −11327.1 −0.385016 −0.192508 0.981295i \(-0.561662\pi\)
−0.192508 + 0.981295i \(0.561662\pi\)
\(954\) −4023.52 4317.48i −0.136547 0.146524i
\(955\) 0 0
\(956\) −6068.05 + 10510.2i −0.205287 + 0.355568i
\(957\) −992.815 + 2282.31i −0.0335352 + 0.0770917i
\(958\) 574.756 + 995.507i 0.0193836 + 0.0335734i
\(959\) −2419.00 4189.84i −0.0814533 0.141081i
\(960\) 0 0
\(961\) 8019.05 13889.4i 0.269177 0.466228i
\(962\) 866.451 0.0290390
\(963\) 1080.47 3530.00i 0.0361555 0.118123i
\(964\) 37479.7 1.25222
\(965\) 0 0
\(966\) 983.451 111.890i 0.0327557 0.00372670i
\(967\) −20908.9 36215.3i −0.695330 1.20435i −0.970069 0.242829i \(-0.921925\pi\)
0.274739 0.961519i \(-0.411409\pi\)
\(968\) 4987.54 + 8638.67i 0.165605 + 0.286836i
\(969\) −21253.3 28731.8i −0.704596 0.952527i
\(970\) 0 0
\(971\) −40444.6 −1.33669 −0.668346 0.743850i \(-0.732997\pi\)
−0.668346 + 0.743850i \(0.732997\pi\)
\(972\) −24846.9 + 15801.1i −0.819921 + 0.521421i
\(973\) 31225.3 1.02881
\(974\) 3900.37 6755.64i 0.128312 0.222243i
\(975\) 0 0
\(976\) −17051.3 29533.8i −0.559221 0.968600i
\(977\) 21271.4 + 36843.1i 0.696553 + 1.20646i 0.969655 + 0.244479i \(0.0786170\pi\)
−0.273102 + 0.961985i \(0.588050\pi\)
\(978\) −76.8284 + 8.74098i −0.00251197 + 0.000285793i
\(979\) −320.618 + 555.327i −0.0104668 + 0.0181290i
\(980\) 0 0
\(981\) −317.023 + 1035.74i −0.0103178 + 0.0337092i
\(982\) −7555.19 −0.245515
\(983\) 8943.52 15490.6i 0.290187 0.502619i −0.683667 0.729794i \(-0.739616\pi\)
0.973854 + 0.227175i \(0.0729491\pi\)
\(984\) −2208.07 + 5075.98i −0.0715352 + 0.164447i
\(985\) 0 0
\(986\) −5003.39 8666.13i −0.161603 0.279904i
\(987\) −12811.5 + 29451.5i −0.413165 + 0.949797i
\(988\) −4112.29 + 7122.70i −0.132418 + 0.229355i
\(989\) −9474.29 −0.304616
\(990\) 0 0
\(991\) 41046.0 1.31571 0.657856 0.753144i \(-0.271464\pi\)
0.657856 + 0.753144i \(0.271464\pi\)
\(992\) −5158.31 + 8934.46i −0.165097 + 0.285957i
\(993\) −56032.7 + 6374.99i −1.79068 + 0.203730i
\(994\) −3219.55 5576.42i −0.102734 0.177941i
\(995\) 0 0
\(996\) 31064.4 + 41995.3i 0.988266 + 1.33601i
\(997\) −12415.4 + 21504.2i −0.394384 + 0.683093i −0.993022 0.117926i \(-0.962375\pi\)
0.598638 + 0.801019i \(0.295709\pi\)
\(998\) −5455.74 −0.173044
\(999\) 22428.3 7930.09i 0.710309 0.251148i
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 225.4.e.e.151.7 yes 24
5.2 odd 4 225.4.k.e.124.13 48
5.3 odd 4 225.4.k.e.124.12 48
5.4 even 2 225.4.e.f.151.6 yes 24
9.2 odd 6 2025.4.a.be.1.7 12
9.4 even 3 inner 225.4.e.e.76.7 24
9.7 even 3 2025.4.a.bi.1.6 12
45.4 even 6 225.4.e.f.76.6 yes 24
45.13 odd 12 225.4.k.e.49.13 48
45.22 odd 12 225.4.k.e.49.12 48
45.29 odd 6 2025.4.a.bj.1.6 12
45.34 even 6 2025.4.a.bf.1.7 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.4.e.e.76.7 24 9.4 even 3 inner
225.4.e.e.151.7 yes 24 1.1 even 1 trivial
225.4.e.f.76.6 yes 24 45.4 even 6
225.4.e.f.151.6 yes 24 5.4 even 2
225.4.k.e.49.12 48 45.22 odd 12
225.4.k.e.49.13 48 45.13 odd 12
225.4.k.e.124.12 48 5.3 odd 4
225.4.k.e.124.13 48 5.2 odd 4
2025.4.a.be.1.7 12 9.2 odd 6
2025.4.a.bf.1.7 12 45.34 even 6
2025.4.a.bi.1.6 12 9.7 even 3
2025.4.a.bj.1.6 12 45.29 odd 6