Properties

Label 105.4.s.b.26.14
Level $105$
Weight $4$
Character 105.26
Analytic conductor $6.195$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,4,Mod(26,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.26");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.14
Character \(\chi\) \(=\) 105.26
Dual form 105.4.s.b.101.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.31734 + 1.91526i) q^{2} +(-0.144315 - 5.19415i) q^{3} +(3.33648 + 5.77895i) q^{4} +(2.50000 - 4.33013i) q^{5} +(9.46943 - 17.5071i) q^{6} +(8.94735 - 16.2156i) q^{7} -5.08329i q^{8} +(-26.9583 + 1.49918i) q^{9} +O(q^{10})\) \(q+(3.31734 + 1.91526i) q^{2} +(-0.144315 - 5.19415i) q^{3} +(3.33648 + 5.77895i) q^{4} +(2.50000 - 4.33013i) q^{5} +(9.46943 - 17.5071i) q^{6} +(8.94735 - 16.2156i) q^{7} -5.08329i q^{8} +(-26.9583 + 1.49918i) q^{9} +(16.5867 - 9.57632i) q^{10} +(12.9526 - 7.47816i) q^{11} +(29.5352 - 18.1641i) q^{12} +63.8636i q^{13} +(60.7385 - 36.6560i) q^{14} +(-22.8521 - 12.3605i) q^{15} +(36.4277 - 63.0946i) q^{16} +(11.0025 + 19.0569i) q^{17} +(-92.3012 - 46.6591i) q^{18} +(137.229 + 79.2293i) q^{19} +33.3648 q^{20} +(-85.5173 - 44.1337i) q^{21} +57.2906 q^{22} +(-162.564 - 93.8566i) q^{23} +(-26.4033 + 0.733593i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-122.316 + 211.857i) q^{26} +(11.6775 + 139.809i) q^{27} +(123.562 - 2.39660i) q^{28} +179.589i q^{29} +(-52.1345 - 84.7717i) q^{30} +(64.0984 - 37.0072i) q^{31} +(206.467 - 119.204i) q^{32} +(-40.7119 - 66.1983i) q^{33} +84.2908i q^{34} +(-47.8471 - 79.2821i) q^{35} +(-98.6096 - 150.789i) q^{36} +(-182.983 + 316.935i) q^{37} +(303.490 + 525.660i) q^{38} +(331.717 - 9.21645i) q^{39} +(-22.0113 - 12.7082i) q^{40} -168.976 q^{41} +(-199.162 - 310.195i) q^{42} -60.4265 q^{43} +(86.4318 + 49.9014i) q^{44} +(-60.9042 + 120.481i) q^{45} +(-359.521 - 622.708i) q^{46} +(5.05040 - 8.74755i) q^{47} +(-332.979 - 180.105i) q^{48} +(-182.890 - 290.173i) q^{49} -95.7632i q^{50} +(97.3965 - 59.8988i) q^{51} +(-369.064 + 213.079i) q^{52} +(467.597 - 269.967i) q^{53} +(-229.034 + 486.160i) q^{54} -74.7816i q^{55} +(-82.4284 - 45.4820i) q^{56} +(391.724 - 724.222i) q^{57} +(-343.961 + 595.757i) q^{58} +(165.592 + 286.813i) q^{59} +(-4.81503 - 173.302i) q^{60} +(-15.5603 - 8.98375i) q^{61} +283.515 q^{62} +(-216.896 + 450.559i) q^{63} +330.387 q^{64} +(276.537 + 159.659i) q^{65} +(-8.26788 - 297.576i) q^{66} +(-111.665 - 193.410i) q^{67} +(-73.4192 + 127.166i) q^{68} +(-464.045 + 857.929i) q^{69} +(-6.87870 - 354.645i) q^{70} +563.097i q^{71} +(7.62078 + 137.037i) q^{72} +(525.173 - 303.209i) q^{73} +(-1214.03 + 700.920i) q^{74} +(-110.653 + 68.0514i) q^{75} +1057.39i q^{76} +(-5.37159 - 276.943i) q^{77} +(1118.07 + 604.751i) q^{78} +(88.0028 - 152.425i) q^{79} +(-182.138 - 315.473i) q^{80} +(724.505 - 80.8310i) q^{81} +(-560.551 - 323.634i) q^{82} +635.008 q^{83} +(-30.2801 - 641.451i) q^{84} +110.025 q^{85} +(-200.455 - 115.733i) q^{86} +(932.812 - 25.9173i) q^{87} +(-38.0136 - 65.8416i) q^{88} +(-388.869 + 673.540i) q^{89} +(-432.793 + 283.028i) q^{90} +(1035.58 + 571.410i) q^{91} -1252.60i q^{92} +(-201.471 - 327.596i) q^{93} +(33.5077 - 19.3457i) q^{94} +(686.146 - 396.146i) q^{95} +(-648.960 - 1055.22i) q^{96} -1032.16i q^{97} +(-50.9485 - 1312.88i) q^{98} +(-337.968 + 221.017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9} - 36 q^{11} + 84 q^{12} - 18 q^{14} + 20 q^{15} - 376 q^{16} + 72 q^{17} + 260 q^{18} - 198 q^{19} + 640 q^{20} - 256 q^{21} + 204 q^{22} - 72 q^{23} - 94 q^{24} - 400 q^{25} + 312 q^{26} - 508 q^{27} + 350 q^{28} + 100 q^{30} + 510 q^{31} - 810 q^{32} + 454 q^{33} + 70 q^{35} - 612 q^{36} - 658 q^{37} + 192 q^{38} + 576 q^{39} + 1404 q^{41} - 1790 q^{42} + 332 q^{43} - 2034 q^{44} - 500 q^{45} - 468 q^{46} - 408 q^{47} - 2810 q^{48} + 980 q^{49} + 2748 q^{51} + 3378 q^{52} - 1152 q^{53} + 3322 q^{54} + 3354 q^{56} - 816 q^{57} - 1080 q^{58} + 48 q^{59} + 1230 q^{60} - 1662 q^{61} + 2076 q^{62} - 2306 q^{63} - 1952 q^{64} - 870 q^{65} - 3808 q^{66} - 1298 q^{67} - 1182 q^{68} - 2450 q^{69} - 450 q^{70} + 7678 q^{72} + 378 q^{73} - 2898 q^{74} + 50 q^{75} + 3528 q^{77} - 1896 q^{78} - 326 q^{79} + 1880 q^{80} + 1774 q^{81} - 2916 q^{82} + 1536 q^{83} - 10680 q^{84} + 720 q^{85} - 5202 q^{86} - 5666 q^{87} + 1668 q^{88} + 1590 q^{89} - 910 q^{90} + 2082 q^{91} + 4086 q^{93} - 1152 q^{94} - 990 q^{95} + 3996 q^{96} + 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.31734 + 1.91526i 1.17286 + 0.677148i 0.954351 0.298688i \(-0.0965489\pi\)
0.218504 + 0.975836i \(0.429882\pi\)
\(3\) −0.144315 5.19415i −0.0277734 0.999614i
\(4\) 3.33648 + 5.77895i 0.417060 + 0.722368i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 9.46943 17.5071i 0.644313 1.19121i
\(7\) 8.94735 16.2156i 0.483112 0.875559i
\(8\) 5.08329i 0.224652i
\(9\) −26.9583 + 1.49918i −0.998457 + 0.0555253i
\(10\) 16.5867 9.57632i 0.524517 0.302830i
\(11\) 12.9526 7.47816i 0.355031 0.204977i −0.311868 0.950126i \(-0.600955\pi\)
0.666899 + 0.745148i \(0.267621\pi\)
\(12\) 29.5352 18.1641i 0.710507 0.436961i
\(13\) 63.8636i 1.36251i 0.732048 + 0.681253i \(0.238564\pi\)
−0.732048 + 0.681253i \(0.761436\pi\)
\(14\) 60.7385 36.6560i 1.15950 0.699765i
\(15\) −22.8521 12.3605i −0.393359 0.212764i
\(16\) 36.4277 63.0946i 0.569182 0.985852i
\(17\) 11.0025 + 19.0569i 0.156970 + 0.271881i 0.933775 0.357861i \(-0.116494\pi\)
−0.776804 + 0.629742i \(0.783161\pi\)
\(18\) −92.3012 46.6591i −1.20864 0.610980i
\(19\) 137.229 + 79.2293i 1.65697 + 0.956655i 0.974099 + 0.226120i \(0.0726041\pi\)
0.682875 + 0.730535i \(0.260729\pi\)
\(20\) 33.3648 0.373029
\(21\) −85.5173 44.1337i −0.888639 0.458608i
\(22\) 57.2906 0.555200
\(23\) −162.564 93.8566i −1.47378 0.850889i −0.474219 0.880407i \(-0.657270\pi\)
−0.999564 + 0.0295172i \(0.990603\pi\)
\(24\) −26.4033 + 0.733593i −0.224565 + 0.00623934i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −122.316 + 211.857i −0.922618 + 1.59802i
\(27\) 11.6775 + 139.809i 0.0832344 + 0.996530i
\(28\) 123.562 2.39660i 0.833962 0.0161755i
\(29\) 179.589i 1.14996i 0.818167 + 0.574980i \(0.194990\pi\)
−0.818167 + 0.574980i \(0.805010\pi\)
\(30\) −52.1345 84.7717i −0.317281 0.515904i
\(31\) 64.0984 37.0072i 0.371368 0.214410i −0.302688 0.953090i \(-0.597884\pi\)
0.674056 + 0.738680i \(0.264551\pi\)
\(32\) 206.467 119.204i 1.14058 0.658516i
\(33\) −40.7119 66.1983i −0.214759 0.349201i
\(34\) 84.2908i 0.425169i
\(35\) −47.8471 79.2821i −0.231075 0.382889i
\(36\) −98.6096 150.789i −0.456526 0.698097i
\(37\) −182.983 + 316.935i −0.813031 + 1.40821i 0.0977017 + 0.995216i \(0.468851\pi\)
−0.910733 + 0.412996i \(0.864482\pi\)
\(38\) 303.490 + 525.660i 1.29559 + 2.24404i
\(39\) 331.717 9.21645i 1.36198 0.0378414i
\(40\) −22.0113 12.7082i −0.0870072 0.0502336i
\(41\) −168.976 −0.643650 −0.321825 0.946799i \(-0.604296\pi\)
−0.321825 + 0.946799i \(0.604296\pi\)
\(42\) −199.162 310.195i −0.731699 1.13962i
\(43\) −60.4265 −0.214301 −0.107151 0.994243i \(-0.534173\pi\)
−0.107151 + 0.994243i \(0.534173\pi\)
\(44\) 86.4318 + 49.9014i 0.296138 + 0.170976i
\(45\) −60.9042 + 120.481i −0.201757 + 0.399117i
\(46\) −359.521 622.708i −1.15236 1.99594i
\(47\) 5.05040 8.74755i 0.0156740 0.0271481i −0.858082 0.513513i \(-0.828344\pi\)
0.873756 + 0.486365i \(0.161677\pi\)
\(48\) −332.979 180.105i −1.00128 0.541582i
\(49\) −182.890 290.173i −0.533206 0.845985i
\(50\) 95.7632i 0.270859i
\(51\) 97.3965 59.8988i 0.267416 0.164461i
\(52\) −369.064 + 213.079i −0.984231 + 0.568246i
\(53\) 467.597 269.967i 1.21188 0.699676i 0.248708 0.968579i \(-0.419994\pi\)
0.963168 + 0.268902i \(0.0866608\pi\)
\(54\) −229.034 + 486.160i −0.577177 + 1.22515i
\(55\) 74.7816i 0.183337i
\(56\) −82.4284 45.4820i −0.196696 0.108532i
\(57\) 391.724 724.222i 0.910266 1.68291i
\(58\) −343.961 + 595.757i −0.778694 + 1.34874i
\(59\) 165.592 + 286.813i 0.365393 + 0.632879i 0.988839 0.148987i \(-0.0476013\pi\)
−0.623446 + 0.781866i \(0.714268\pi\)
\(60\) −4.81503 173.302i −0.0103603 0.372886i
\(61\) −15.5603 8.98375i −0.0326606 0.0188566i 0.483581 0.875300i \(-0.339336\pi\)
−0.516241 + 0.856443i \(0.672669\pi\)
\(62\) 283.515 0.580748
\(63\) −216.896 + 450.559i −0.433751 + 0.901033i
\(64\) 330.387 0.645287
\(65\) 276.537 + 159.659i 0.527696 + 0.304665i
\(66\) −8.26788 297.576i −0.0154198 0.554986i
\(67\) −111.665 193.410i −0.203613 0.352668i 0.746077 0.665860i \(-0.231935\pi\)
−0.949690 + 0.313192i \(0.898602\pi\)
\(68\) −73.4192 + 127.166i −0.130932 + 0.226781i
\(69\) −464.045 + 857.929i −0.809629 + 1.49685i
\(70\) −6.87870 354.645i −0.0117452 0.605546i
\(71\) 563.097i 0.941230i 0.882339 + 0.470615i \(0.155968\pi\)
−0.882339 + 0.470615i \(0.844032\pi\)
\(72\) 7.62078 + 137.037i 0.0124739 + 0.224305i
\(73\) 525.173 303.209i 0.842012 0.486136i −0.0159358 0.999873i \(-0.505073\pi\)
0.857948 + 0.513737i \(0.171739\pi\)
\(74\) −1214.03 + 700.920i −1.90714 + 1.10109i
\(75\) −110.653 + 68.0514i −0.170361 + 0.104772i
\(76\) 1057.39i 1.59593i
\(77\) −5.37159 276.943i −0.00794999 0.409878i
\(78\) 1118.07 + 604.751i 1.62303 + 0.877880i
\(79\) 88.0028 152.425i 0.125330 0.217078i −0.796532 0.604597i \(-0.793334\pi\)
0.921862 + 0.387518i \(0.126668\pi\)
\(80\) −182.138 315.473i −0.254546 0.440887i
\(81\) 724.505 80.8310i 0.993834 0.110879i
\(82\) −560.551 323.634i −0.754908 0.435847i
\(83\) 635.008 0.839773 0.419887 0.907577i \(-0.362070\pi\)
0.419887 + 0.907577i \(0.362070\pi\)
\(84\) −30.2801 641.451i −0.0393312 0.833191i
\(85\) 110.025 0.140399
\(86\) −200.455 115.733i −0.251344 0.145114i
\(87\) 932.812 25.9173i 1.14952 0.0319383i
\(88\) −38.0136 65.8416i −0.0460485 0.0797583i
\(89\) −388.869 + 673.540i −0.463146 + 0.802193i −0.999116 0.0420446i \(-0.986613\pi\)
0.535970 + 0.844237i \(0.319946\pi\)
\(90\) −432.793 + 283.028i −0.506893 + 0.331487i
\(91\) 1035.58 + 571.410i 1.19295 + 0.658242i
\(92\) 1252.60i 1.41949i
\(93\) −201.471 327.596i −0.224641 0.365270i
\(94\) 33.5077 19.3457i 0.0367666 0.0212272i
\(95\) 686.146 396.146i 0.741022 0.427829i
\(96\) −648.960 1055.22i −0.689939 1.12185i
\(97\) 1032.16i 1.08041i −0.841533 0.540206i \(-0.818346\pi\)
0.841533 0.540206i \(-0.181654\pi\)
\(98\) −50.9485 1312.88i −0.0525161 1.35328i
\(99\) −337.968 + 221.017i −0.343102 + 0.224374i
\(100\) 83.4119 144.474i 0.0834119 0.144474i
\(101\) −16.5291 28.6292i −0.0162842 0.0282050i 0.857768 0.514036i \(-0.171850\pi\)
−0.874053 + 0.485831i \(0.838517\pi\)
\(102\) 437.819 12.1644i 0.425005 0.0118084i
\(103\) −814.812 470.432i −0.779474 0.450030i 0.0567697 0.998387i \(-0.481920\pi\)
−0.836244 + 0.548358i \(0.815253\pi\)
\(104\) 324.637 0.306089
\(105\) −404.898 + 259.967i −0.376324 + 0.241620i
\(106\) 2068.23 1.89514
\(107\) −374.880 216.437i −0.338701 0.195549i 0.320997 0.947080i \(-0.395982\pi\)
−0.659697 + 0.751531i \(0.729316\pi\)
\(108\) −768.989 + 533.954i −0.685148 + 0.475738i
\(109\) −389.652 674.896i −0.342402 0.593058i 0.642476 0.766306i \(-0.277907\pi\)
−0.984878 + 0.173248i \(0.944574\pi\)
\(110\) 143.227 248.076i 0.124147 0.215028i
\(111\) 1672.62 + 904.700i 1.43025 + 0.773607i
\(112\) −697.183 1155.22i −0.588193 0.974629i
\(113\) 489.634i 0.407619i −0.979011 0.203809i \(-0.934668\pi\)
0.979011 0.203809i \(-0.0653323\pi\)
\(114\) 2686.56 1652.23i 2.20719 1.35742i
\(115\) −812.822 + 469.283i −0.659096 + 0.380529i
\(116\) −1037.84 + 599.195i −0.830695 + 0.479602i
\(117\) −95.7432 1721.66i −0.0756535 1.36040i
\(118\) 1268.61i 0.989701i
\(119\) 407.462 7.90313i 0.313882 0.00608805i
\(120\) −62.8318 + 116.164i −0.0477978 + 0.0883688i
\(121\) −553.654 + 958.957i −0.415969 + 0.720479i
\(122\) −34.4125 59.6042i −0.0255374 0.0442321i
\(123\) 24.3858 + 877.688i 0.0178763 + 0.643402i
\(124\) 427.726 + 246.948i 0.309765 + 0.178843i
\(125\) −125.000 −0.0894427
\(126\) −1582.46 + 1079.24i −1.11886 + 0.763068i
\(127\) 435.222 0.304092 0.152046 0.988373i \(-0.451414\pi\)
0.152046 + 0.988373i \(0.451414\pi\)
\(128\) −555.736 320.854i −0.383755 0.221561i
\(129\) 8.72043 + 313.864i 0.00595187 + 0.214219i
\(130\) 611.578 + 1059.28i 0.412607 + 0.714657i
\(131\) −16.9758 + 29.4029i −0.0113220 + 0.0196103i −0.871631 0.490163i \(-0.836937\pi\)
0.860309 + 0.509773i \(0.170271\pi\)
\(132\) 246.722 456.141i 0.162685 0.300773i
\(133\) 2512.59 1516.36i 1.63811 0.988608i
\(134\) 855.474i 0.551505i
\(135\) 634.586 + 298.958i 0.404566 + 0.190594i
\(136\) 96.8716 55.9289i 0.0610785 0.0352637i
\(137\) −2721.27 + 1571.13i −1.69704 + 0.979784i −0.748488 + 0.663149i \(0.769220\pi\)
−0.948547 + 0.316635i \(0.897447\pi\)
\(138\) −3182.55 + 1957.27i −1.96317 + 1.20735i
\(139\) 2399.79i 1.46437i 0.681106 + 0.732185i \(0.261499\pi\)
−0.681106 + 0.732185i \(0.738501\pi\)
\(140\) 298.526 541.029i 0.180215 0.326609i
\(141\) −46.1649 24.9701i −0.0275730 0.0149139i
\(142\) −1078.48 + 1867.98i −0.637352 + 1.10393i
\(143\) 477.582 + 827.196i 0.279283 + 0.483732i
\(144\) −887.439 + 1755.54i −0.513564 + 1.01594i
\(145\) 777.643 + 448.973i 0.445378 + 0.257139i
\(146\) 2322.90 1.31674
\(147\) −1480.81 + 991.832i −0.830850 + 0.556496i
\(148\) −2442.07 −1.35633
\(149\) −687.647 397.013i −0.378082 0.218286i 0.298901 0.954284i \(-0.403380\pi\)
−0.676984 + 0.735998i \(0.736713\pi\)
\(150\) −497.408 + 13.8200i −0.270755 + 0.00752268i
\(151\) −288.851 500.304i −0.155671 0.269630i 0.777632 0.628720i \(-0.216421\pi\)
−0.933303 + 0.359089i \(0.883087\pi\)
\(152\) 402.745 697.575i 0.214914 0.372242i
\(153\) −325.179 497.247i −0.171825 0.262746i
\(154\) 512.600 929.000i 0.268224 0.486110i
\(155\) 370.072i 0.191774i
\(156\) 1160.03 + 1886.22i 0.595362 + 0.968069i
\(157\) −1228.62 + 709.343i −0.624550 + 0.360584i −0.778638 0.627473i \(-0.784089\pi\)
0.154088 + 0.988057i \(0.450756\pi\)
\(158\) 583.870 337.097i 0.293989 0.169734i
\(159\) −1469.73 2389.81i −0.733064 1.19198i
\(160\) 1192.04i 0.588994i
\(161\) −2976.46 + 1796.31i −1.45701 + 0.879310i
\(162\) 2558.24 + 1119.47i 1.24071 + 0.542928i
\(163\) 1060.60 1837.02i 0.509649 0.882737i −0.490289 0.871560i \(-0.663109\pi\)
0.999938 0.0111775i \(-0.00355797\pi\)
\(164\) −563.785 976.505i −0.268440 0.464953i
\(165\) −388.427 + 10.7921i −0.183267 + 0.00509190i
\(166\) 2106.53 + 1216.21i 0.984932 + 0.568651i
\(167\) −2298.28 −1.06495 −0.532473 0.846447i \(-0.678737\pi\)
−0.532473 + 0.846447i \(0.678737\pi\)
\(168\) −224.344 + 434.709i −0.103027 + 0.199634i
\(169\) −1881.56 −0.856421
\(170\) 364.990 + 210.727i 0.164667 + 0.0950707i
\(171\) −3818.25 1930.16i −1.70754 0.863175i
\(172\) −201.612 349.202i −0.0893764 0.154804i
\(173\) 602.351 1043.30i 0.264716 0.458502i −0.702773 0.711414i \(-0.748055\pi\)
0.967489 + 0.252912i \(0.0813884\pi\)
\(174\) 3144.09 + 1700.61i 1.36984 + 0.740934i
\(175\) −462.919 + 8.97879i −0.199962 + 0.00387847i
\(176\) 1089.65i 0.466678i
\(177\) 1465.85 901.498i 0.622487 0.382829i
\(178\) −2580.02 + 1489.57i −1.08641 + 0.627237i
\(179\) −956.963 + 552.503i −0.399591 + 0.230704i −0.686308 0.727311i \(-0.740770\pi\)
0.286716 + 0.958015i \(0.407436\pi\)
\(180\) −899.459 + 50.0199i −0.372454 + 0.0207126i
\(181\) 2923.49i 1.20056i −0.799789 0.600281i \(-0.795056\pi\)
0.799789 0.600281i \(-0.204944\pi\)
\(182\) 2340.98 + 3878.98i 0.953434 + 1.57983i
\(183\) −44.4173 + 82.1191i −0.0179422 + 0.0331717i
\(184\) −477.100 + 826.362i −0.191154 + 0.331088i
\(185\) 914.913 + 1584.68i 0.363599 + 0.629771i
\(186\) −40.9153 1472.62i −0.0161293 0.580524i
\(187\) 285.021 + 164.557i 0.111459 + 0.0643508i
\(188\) 67.4022 0.0261479
\(189\) 2371.57 + 1061.57i 0.912732 + 0.408559i
\(190\) 3034.90 1.15881
\(191\) −832.436 480.607i −0.315356 0.182071i 0.333965 0.942586i \(-0.391613\pi\)
−0.649321 + 0.760515i \(0.724947\pi\)
\(192\) −47.6797 1716.08i −0.0179218 0.645038i
\(193\) −590.830 1023.35i −0.220357 0.381669i 0.734560 0.678544i \(-0.237389\pi\)
−0.954916 + 0.296875i \(0.904055\pi\)
\(194\) 1976.86 3424.02i 0.731599 1.26717i
\(195\) 789.384 1459.42i 0.289892 0.535954i
\(196\) 1066.69 2025.07i 0.388734 0.737998i
\(197\) 3727.40i 1.34805i −0.738708 0.674025i \(-0.764564\pi\)
0.738708 0.674025i \(-0.235436\pi\)
\(198\) −1544.46 + 85.8892i −0.554344 + 0.0308277i
\(199\) −2229.58 + 1287.25i −0.794225 + 0.458546i −0.841448 0.540339i \(-0.818296\pi\)
0.0472231 + 0.998884i \(0.484963\pi\)
\(200\) −110.056 + 63.5411i −0.0389108 + 0.0224652i
\(201\) −988.484 + 607.917i −0.346877 + 0.213329i
\(202\) 126.630i 0.0441072i
\(203\) 2912.14 + 1606.85i 1.00686 + 0.555559i
\(204\) 671.113 + 362.998i 0.230330 + 0.124583i
\(205\) −422.441 + 731.689i −0.143925 + 0.249285i
\(206\) −1802.00 3121.16i −0.609474 1.05564i
\(207\) 4523.18 + 2286.51i 1.51876 + 0.767744i
\(208\) 4029.44 + 2326.40i 1.34323 + 0.775514i
\(209\) 2369.96 0.784370
\(210\) −1841.09 + 86.9095i −0.604986 + 0.0285587i
\(211\) −1310.06 −0.427434 −0.213717 0.976896i \(-0.568557\pi\)
−0.213717 + 0.976896i \(0.568557\pi\)
\(212\) 3120.25 + 1801.48i 1.01085 + 0.583614i
\(213\) 2924.81 81.2631i 0.940866 0.0261411i
\(214\) −829.068 1435.99i −0.264831 0.458701i
\(215\) −151.066 + 261.654i −0.0479192 + 0.0829985i
\(216\) 710.691 59.3599i 0.223872 0.0186988i
\(217\) −26.5824 1370.51i −0.00831581 0.428738i
\(218\) 2985.14i 0.927429i
\(219\) −1650.70 2684.07i −0.509334 0.828185i
\(220\) 432.159 249.507i 0.132437 0.0764626i
\(221\) −1217.04 + 702.659i −0.370439 + 0.213873i
\(222\) 3815.89 + 6204.70i 1.15363 + 1.87582i
\(223\) 1484.59i 0.445809i −0.974840 0.222904i \(-0.928446\pi\)
0.974840 0.222904i \(-0.0715538\pi\)
\(224\) −85.6246 4414.55i −0.0255403 1.31678i
\(225\) 369.438 + 564.926i 0.109463 + 0.167385i
\(226\) 937.779 1624.28i 0.276018 0.478078i
\(227\) 1387.78 + 2403.71i 0.405773 + 0.702819i 0.994411 0.105577i \(-0.0336691\pi\)
−0.588638 + 0.808397i \(0.700336\pi\)
\(228\) 5492.22 152.596i 1.59531 0.0443243i
\(229\) −3258.94 1881.55i −0.940422 0.542953i −0.0503294 0.998733i \(-0.516027\pi\)
−0.890093 + 0.455780i \(0.849360\pi\)
\(230\) −3595.21 −1.03070
\(231\) −1437.71 + 67.8677i −0.409499 + 0.0193306i
\(232\) 912.903 0.258341
\(233\) −3132.07 1808.30i −0.880640 0.508438i −0.00977035 0.999952i \(-0.503110\pi\)
−0.870869 + 0.491515i \(0.836443\pi\)
\(234\) 2979.82 5894.69i 0.832464 1.64678i
\(235\) −25.2520 43.7378i −0.00700961 0.0121410i
\(236\) −1104.98 + 1913.89i −0.304781 + 0.527897i
\(237\) −804.420 435.103i −0.220476 0.119253i
\(238\) 1366.82 + 754.179i 0.372261 + 0.205404i
\(239\) 4715.60i 1.27626i 0.769928 + 0.638131i \(0.220292\pi\)
−0.769928 + 0.638131i \(0.779708\pi\)
\(240\) −1612.33 + 991.581i −0.433647 + 0.266693i
\(241\) 6330.88 3655.14i 1.69215 0.976963i 0.739369 0.673300i \(-0.235124\pi\)
0.952780 0.303662i \(-0.0982095\pi\)
\(242\) −3673.31 + 2120.79i −0.975742 + 0.563345i
\(243\) −524.405 3751.52i −0.138439 0.990371i
\(244\) 119.896i 0.0314573i
\(245\) −1713.71 + 66.5033i −0.446877 + 0.0173418i
\(246\) −1600.11 + 2958.29i −0.414712 + 0.766722i
\(247\) −5059.86 + 8763.94i −1.30345 + 2.25764i
\(248\) −188.118 325.831i −0.0481675 0.0834285i
\(249\) −91.6410 3298.32i −0.0233233 0.839449i
\(250\) −414.667 239.408i −0.104903 0.0605660i
\(251\) −2817.02 −0.708402 −0.354201 0.935169i \(-0.615247\pi\)
−0.354201 + 0.935169i \(0.615247\pi\)
\(252\) −3327.42 + 249.850i −0.831778 + 0.0624566i
\(253\) −2807.50 −0.697652
\(254\) 1443.78 + 833.565i 0.356656 + 0.205916i
\(255\) −15.8782 571.486i −0.00389934 0.140344i
\(256\) −2550.59 4417.75i −0.622702 1.07855i
\(257\) −1583.48 + 2742.67i −0.384338 + 0.665693i −0.991677 0.128750i \(-0.958904\pi\)
0.607339 + 0.794443i \(0.292237\pi\)
\(258\) −572.204 + 1057.89i −0.138077 + 0.255278i
\(259\) 3502.08 + 5802.90i 0.840187 + 1.39218i
\(260\) 2130.79i 0.508255i
\(261\) −269.237 4841.42i −0.0638519 1.14819i
\(262\) −112.629 + 65.0263i −0.0265581 + 0.0153333i
\(263\) 4281.12 2471.71i 1.00375 0.579513i 0.0943917 0.995535i \(-0.469909\pi\)
0.909355 + 0.416022i \(0.136576\pi\)
\(264\) −336.505 + 206.950i −0.0784487 + 0.0482459i
\(265\) 2699.67i 0.625810i
\(266\) 11239.3 217.998i 2.59070 0.0502493i
\(267\) 3554.59 + 1922.64i 0.814746 + 0.440688i
\(268\) 745.137 1290.61i 0.169838 0.294167i
\(269\) 2686.98 + 4653.99i 0.609026 + 1.05486i 0.991401 + 0.130857i \(0.0417730\pi\)
−0.382375 + 0.924007i \(0.624894\pi\)
\(270\) 1532.55 + 2207.14i 0.345437 + 0.497491i
\(271\) 3808.34 + 2198.74i 0.853653 + 0.492857i 0.861882 0.507109i \(-0.169286\pi\)
−0.00822876 + 0.999966i \(0.502619\pi\)
\(272\) 1603.18 0.357379
\(273\) 2818.54 5461.44i 0.624856 1.21077i
\(274\) −12036.5 −2.65384
\(275\) −323.814 186.954i −0.0710062 0.0409955i
\(276\) −6506.20 + 180.769i −1.41894 + 0.0394239i
\(277\) 1386.56 + 2401.60i 0.300760 + 0.520931i 0.976308 0.216384i \(-0.0694264\pi\)
−0.675548 + 0.737316i \(0.736093\pi\)
\(278\) −4596.23 + 7960.90i −0.991596 + 1.71749i
\(279\) −1672.51 + 1093.75i −0.358890 + 0.234699i
\(280\) −403.014 + 243.221i −0.0860167 + 0.0519115i
\(281\) 2638.82i 0.560208i −0.959970 0.280104i \(-0.909631\pi\)
0.959970 0.280104i \(-0.0903690\pi\)
\(282\) −105.320 171.252i −0.0222402 0.0361629i
\(283\) −6563.91 + 3789.67i −1.37874 + 0.796017i −0.992008 0.126175i \(-0.959730\pi\)
−0.386733 + 0.922192i \(0.626397\pi\)
\(284\) −3254.11 + 1878.76i −0.679915 + 0.392549i
\(285\) −2156.66 3506.77i −0.448245 0.728854i
\(286\) 3658.78i 0.756463i
\(287\) −1511.89 + 2740.05i −0.310955 + 0.563553i
\(288\) −5387.31 + 3523.08i −1.10226 + 0.720831i
\(289\) 2214.39 3835.44i 0.450721 0.780671i
\(290\) 1719.80 + 2978.79i 0.348242 + 0.603174i
\(291\) −5361.19 + 148.956i −1.08000 + 0.0300067i
\(292\) 3504.46 + 2023.30i 0.702338 + 0.405495i
\(293\) 116.449 0.0232186 0.0116093 0.999933i \(-0.496305\pi\)
0.0116093 + 0.999933i \(0.496305\pi\)
\(294\) −6811.96 + 454.103i −1.35130 + 0.0900810i
\(295\) 1655.92 0.326817
\(296\) 1611.07 + 930.153i 0.316357 + 0.182649i
\(297\) 1196.77 + 1723.56i 0.233817 + 0.336738i
\(298\) −1520.77 2634.05i −0.295624 0.512036i
\(299\) 5994.02 10381.9i 1.15934 2.00804i
\(300\) −762.455 412.404i −0.146735 0.0793672i
\(301\) −540.657 + 979.850i −0.103531 + 0.187633i
\(302\) 2212.90i 0.421650i
\(303\) −146.319 + 89.9860i −0.0277419 + 0.0170612i
\(304\) 9997.87 5772.27i 1.88624 1.08902i
\(305\) −77.8016 + 44.9188i −0.0146062 + 0.00843292i
\(306\) −126.367 2272.34i −0.0236077 0.424513i
\(307\) 7885.43i 1.46595i −0.680258 0.732973i \(-0.738132\pi\)
0.680258 0.732973i \(-0.261868\pi\)
\(308\) 1582.52 955.056i 0.292767 0.176686i
\(309\) −2325.90 + 4300.15i −0.428207 + 0.791672i
\(310\) 708.787 1227.65i 0.129859 0.224923i
\(311\) 4926.79 + 8533.45i 0.898304 + 1.55591i 0.829662 + 0.558266i \(0.188533\pi\)
0.0686420 + 0.997641i \(0.478133\pi\)
\(312\) −46.8499 1686.21i −0.00850113 0.305971i
\(313\) 4182.59 + 2414.82i 0.755316 + 0.436082i 0.827612 0.561301i \(-0.189699\pi\)
−0.0722952 + 0.997383i \(0.523032\pi\)
\(314\) −5434.32 −0.976676
\(315\) 1408.74 + 2065.58i 0.251979 + 0.369468i
\(316\) 1174.48 0.209081
\(317\) 1492.49 + 861.692i 0.264438 + 0.152673i 0.626357 0.779536i \(-0.284545\pi\)
−0.361919 + 0.932209i \(0.617878\pi\)
\(318\) −298.477 10742.7i −0.0526344 1.89441i
\(319\) 1343.00 + 2326.14i 0.235716 + 0.408272i
\(320\) 825.967 1430.62i 0.144290 0.249918i
\(321\) −1070.10 + 1978.42i −0.186067 + 0.344001i
\(322\) −13314.3 + 258.245i −2.30428 + 0.0446938i
\(323\) 3486.88i 0.600666i
\(324\) 2884.41 + 3917.19i 0.494584 + 0.671671i
\(325\) 1382.69 798.295i 0.235993 0.136251i
\(326\) 7036.74 4062.67i 1.19549 0.690216i
\(327\) −3449.28 + 2121.31i −0.583320 + 0.358741i
\(328\) 858.955i 0.144597i
\(329\) −96.6588 160.163i −0.0161975 0.0268391i
\(330\) −1309.21 708.139i −0.218393 0.118127i
\(331\) −2957.83 + 5123.10i −0.491168 + 0.850729i −0.999948 0.0101679i \(-0.996763\pi\)
0.508780 + 0.860897i \(0.330097\pi\)
\(332\) 2118.69 + 3669.68i 0.350235 + 0.606626i
\(333\) 4457.76 8818.37i 0.733586 1.45118i
\(334\) −7624.15 4401.81i −1.24903 0.721126i
\(335\) −1116.65 −0.182117
\(336\) −5899.79 + 3787.99i −0.957917 + 0.615035i
\(337\) 10105.7 1.63350 0.816752 0.576989i \(-0.195773\pi\)
0.816752 + 0.576989i \(0.195773\pi\)
\(338\) −6241.75 3603.68i −1.00446 0.579924i
\(339\) −2543.23 + 70.6614i −0.407461 + 0.0113209i
\(340\) 367.096 + 635.829i 0.0585546 + 0.101420i
\(341\) 553.492 958.677i 0.0878982 0.152244i
\(342\) −8969.65 13715.9i −1.41820 2.16864i
\(343\) −6341.70 + 369.382i −0.998308 + 0.0581479i
\(344\) 307.165i 0.0481431i
\(345\) 2554.83 + 4154.19i 0.398688 + 0.648273i
\(346\) 3996.40 2307.32i 0.620947 0.358504i
\(347\) 7526.30 4345.31i 1.16436 0.672244i 0.212015 0.977266i \(-0.431997\pi\)
0.952345 + 0.305023i \(0.0986640\pi\)
\(348\) 3262.08 + 5304.20i 0.502488 + 0.817054i
\(349\) 1429.22i 0.219210i 0.993975 + 0.109605i \(0.0349586\pi\)
−0.993975 + 0.109605i \(0.965041\pi\)
\(350\) −1552.86 856.828i −0.237153 0.130855i
\(351\) −8928.72 + 745.765i −1.35778 + 0.113407i
\(352\) 1782.85 3087.99i 0.269962 0.467587i
\(353\) 4132.48 + 7157.66i 0.623087 + 1.07922i 0.988907 + 0.148533i \(0.0474551\pi\)
−0.365821 + 0.930685i \(0.619212\pi\)
\(354\) 6589.33 183.079i 0.989319 0.0274873i
\(355\) 2438.28 + 1407.74i 0.364537 + 0.210465i
\(356\) −5189.81 −0.772638
\(357\) −99.8527 2115.28i −0.0148033 0.313592i
\(358\) −4232.76 −0.624883
\(359\) −256.265 147.955i −0.0376745 0.0217514i 0.481044 0.876696i \(-0.340258\pi\)
−0.518719 + 0.854945i \(0.673591\pi\)
\(360\) 612.440 + 309.594i 0.0896622 + 0.0453250i
\(361\) 9125.06 + 15805.1i 1.33038 + 2.30428i
\(362\) 5599.26 9698.21i 0.812958 1.40808i
\(363\) 5060.87 + 2737.37i 0.731754 + 0.395798i
\(364\) 153.056 + 7891.09i 0.0220393 + 1.13628i
\(365\) 3032.09i 0.434813i
\(366\) −304.627 + 187.345i −0.0435058 + 0.0267560i
\(367\) −2372.36 + 1369.68i −0.337428 + 0.194814i −0.659134 0.752025i \(-0.729077\pi\)
0.321706 + 0.946840i \(0.395744\pi\)
\(368\) −11843.7 + 6837.95i −1.67770 + 0.968622i
\(369\) 4555.32 253.326i 0.642657 0.0357389i
\(370\) 7009.20i 0.984841i
\(371\) −193.918 9997.85i −0.0271368 1.39909i
\(372\) 1220.96 2257.31i 0.170171 0.314613i
\(373\) 3659.18 6337.88i 0.507949 0.879793i −0.492009 0.870590i \(-0.663737\pi\)
0.999958 0.00920295i \(-0.00292943\pi\)
\(374\) 630.340 + 1091.78i 0.0871500 + 0.150948i
\(375\) 18.0393 + 649.268i 0.00248413 + 0.0894082i
\(376\) −44.4663 25.6726i −0.00609887 0.00352118i
\(377\) −11469.2 −1.56683
\(378\) 5834.11 + 8063.76i 0.793848 + 1.09724i
\(379\) 6215.46 0.842392 0.421196 0.906970i \(-0.361610\pi\)
0.421196 + 0.906970i \(0.361610\pi\)
\(380\) 4578.62 + 2643.47i 0.618100 + 0.356860i
\(381\) −62.8089 2260.61i −0.00844567 0.303975i
\(382\) −1840.98 3188.67i −0.246578 0.427085i
\(383\) −3384.88 + 5862.78i −0.451590 + 0.782177i −0.998485 0.0550240i \(-0.982476\pi\)
0.546895 + 0.837201i \(0.315810\pi\)
\(384\) −1586.36 + 2932.88i −0.210817 + 0.389760i
\(385\) −1212.63 669.098i −0.160523 0.0885724i
\(386\) 4526.38i 0.596857i
\(387\) 1629.00 90.5904i 0.213971 0.0118991i
\(388\) 5964.80 3443.78i 0.780456 0.450596i
\(389\) −6822.93 + 3939.22i −0.889297 + 0.513436i −0.873712 0.486443i \(-0.838294\pi\)
−0.0155842 + 0.999879i \(0.504961\pi\)
\(390\) 5413.82 3329.50i 0.702922 0.432297i
\(391\) 4130.63i 0.534258i
\(392\) −1475.03 + 929.681i −0.190052 + 0.119786i
\(393\) 155.173 + 83.9315i 0.0199172 + 0.0107730i
\(394\) 7138.95 12365.0i 0.912830 1.58107i
\(395\) −440.014 762.127i −0.0560494 0.0970804i
\(396\) −2404.87 1215.68i −0.305175 0.154269i
\(397\) −6608.87 3815.63i −0.835490 0.482370i 0.0202386 0.999795i \(-0.493557\pi\)
−0.855729 + 0.517425i \(0.826891\pi\)
\(398\) −9861.68 −1.24201
\(399\) −8238.78 12831.9i −1.03372 1.61002i
\(400\) −1821.38 −0.227673
\(401\) −13358.9 7712.79i −1.66363 0.960495i −0.970962 0.239234i \(-0.923104\pi\)
−0.692664 0.721261i \(-0.743563\pi\)
\(402\) −4443.46 + 123.457i −0.551292 + 0.0153172i
\(403\) 2363.41 + 4093.55i 0.292134 + 0.505991i
\(404\) 110.298 191.041i 0.0135829 0.0235264i
\(405\) 1461.25 3339.28i 0.179285 0.409704i
\(406\) 6583.01 + 10908.0i 0.804702 + 1.33338i
\(407\) 5473.49i 0.666612i
\(408\) −304.483 495.094i −0.0369464 0.0600755i
\(409\) 157.429 90.8918i 0.0190327 0.0109885i −0.490453 0.871467i \(-0.663169\pi\)
0.509486 + 0.860479i \(0.329836\pi\)
\(410\) −2802.75 + 1618.17i −0.337605 + 0.194917i
\(411\) 8553.38 + 13907.9i 1.02654 + 1.66917i
\(412\) 6278.34i 0.750757i
\(413\) 6132.44 118.945i 0.730649 0.0141717i
\(414\) 10625.6 + 16248.2i 1.26140 + 1.92888i
\(415\) 1587.52 2749.66i 0.187779 0.325243i
\(416\) 7612.80 + 13185.8i 0.897231 + 1.55405i
\(417\) 12464.9 346.325i 1.46381 0.0406705i
\(418\) 7861.94 + 4539.10i 0.919953 + 0.531135i
\(419\) 7479.61 0.872084 0.436042 0.899926i \(-0.356380\pi\)
0.436042 + 0.899926i \(0.356380\pi\)
\(420\) −2853.27 1472.51i −0.331488 0.171074i
\(421\) −9069.56 −1.04994 −0.524968 0.851122i \(-0.675923\pi\)
−0.524968 + 0.851122i \(0.675923\pi\)
\(422\) −4345.92 2509.12i −0.501318 0.289436i
\(423\) −123.036 + 243.391i −0.0141424 + 0.0279765i
\(424\) −1372.32 2376.93i −0.157184 0.272250i
\(425\) 275.062 476.422i 0.0313941 0.0543762i
\(426\) 9858.21 + 5332.20i 1.12120 + 0.606446i
\(427\) −284.900 + 171.939i −0.0322887 + 0.0194864i
\(428\) 2888.55i 0.326222i
\(429\) 4227.66 2600.01i 0.475789 0.292610i
\(430\) −1002.27 + 578.664i −0.112405 + 0.0648968i
\(431\) 7258.46 4190.67i 0.811201 0.468347i −0.0361715 0.999346i \(-0.511516\pi\)
0.847373 + 0.530998i \(0.178183\pi\)
\(432\) 9246.59 + 4356.14i 1.02981 + 0.485150i
\(433\) 5640.66i 0.626034i −0.949747 0.313017i \(-0.898660\pi\)
0.949747 0.313017i \(-0.101340\pi\)
\(434\) 2536.71 4597.35i 0.280566 0.508479i
\(435\) 2219.80 4103.99i 0.244670 0.452348i
\(436\) 2600.13 4503.55i 0.285604 0.494681i
\(437\) −14872.4 25759.7i −1.62802 2.81980i
\(438\) −335.229 12065.5i −0.0365704 1.31624i
\(439\) 1828.10 + 1055.45i 0.198748 + 0.114747i 0.596071 0.802931i \(-0.296727\pi\)
−0.397323 + 0.917679i \(0.630061\pi\)
\(440\) −380.136 −0.0411870
\(441\) 5365.43 + 7548.40i 0.579357 + 0.815074i
\(442\) −5383.11 −0.579295
\(443\) −825.998 476.890i −0.0885877 0.0511462i 0.455052 0.890465i \(-0.349621\pi\)
−0.543639 + 0.839319i \(0.682954\pi\)
\(444\) 352.426 + 12684.5i 0.0376699 + 1.35581i
\(445\) 1944.34 + 3367.70i 0.207125 + 0.358751i
\(446\) 2843.38 4924.88i 0.301879 0.522869i
\(447\) −1962.91 + 3629.04i −0.207701 + 0.383999i
\(448\) 2956.09 5357.41i 0.311745 0.564986i
\(449\) 3666.11i 0.385332i 0.981264 + 0.192666i \(0.0617135\pi\)
−0.981264 + 0.192666i \(0.938287\pi\)
\(450\) 143.567 + 2581.62i 0.0150396 + 0.270441i
\(451\) −2188.67 + 1263.63i −0.228516 + 0.131934i
\(452\) 2829.57 1633.65i 0.294451 0.170001i
\(453\) −2556.97 + 1572.53i −0.265203 + 0.163100i
\(454\) 10631.9i 1.09907i
\(455\) 5063.24 3055.69i 0.521689 0.314841i
\(456\) −3681.43 1991.25i −0.378068 0.204493i
\(457\) −4313.23 + 7470.73i −0.441497 + 0.764696i −0.997801 0.0662833i \(-0.978886\pi\)
0.556303 + 0.830979i \(0.312219\pi\)
\(458\) −7207.33 12483.5i −0.735319 1.27361i
\(459\) −2535.85 + 1760.79i −0.257872 + 0.179056i
\(460\) −5423.92 3131.50i −0.549765 0.317407i
\(461\) 7189.28 0.726330 0.363165 0.931725i \(-0.381696\pi\)
0.363165 + 0.931725i \(0.381696\pi\)
\(462\) −4899.34 2528.45i −0.493372 0.254619i
\(463\) −2282.41 −0.229099 −0.114549 0.993418i \(-0.536542\pi\)
−0.114549 + 0.993418i \(0.536542\pi\)
\(464\) 11331.1 + 6542.01i 1.13369 + 0.654537i
\(465\) −1922.21 + 53.4069i −0.191700 + 0.00532620i
\(466\) −6926.76 11997.5i −0.688575 1.19265i
\(467\) 3228.56 5592.04i 0.319915 0.554108i −0.660555 0.750777i \(-0.729679\pi\)
0.980470 + 0.196669i \(0.0630125\pi\)
\(468\) 9629.92 6297.56i 0.951160 0.622019i
\(469\) −4135.36 + 80.2094i −0.407150 + 0.00789707i
\(470\) 193.457i 0.0189862i
\(471\) 3861.74 + 6279.25i 0.377791 + 0.614294i
\(472\) 1457.95 841.750i 0.142177 0.0820862i
\(473\) −782.677 + 451.879i −0.0760836 + 0.0439269i
\(474\) −1835.20 2984.06i −0.177834 0.289161i
\(475\) 3961.46i 0.382662i
\(476\) 1405.16 + 2328.33i 0.135305 + 0.224199i
\(477\) −12200.9 + 7978.88i −1.17116 + 0.765887i
\(478\) −9031.62 + 15643.2i −0.864219 + 1.49687i
\(479\) −6881.73 11919.5i −0.656439 1.13699i −0.981531 0.191303i \(-0.938729\pi\)
0.325092 0.945682i \(-0.394605\pi\)
\(480\) −6191.64 + 172.029i −0.588767 + 0.0163584i
\(481\) −20240.6 11685.9i −1.91870 1.10776i
\(482\) 28002.2 2.64619
\(483\) 9759.83 + 15200.9i 0.919436 + 1.43202i
\(484\) −7389.02 −0.693935
\(485\) −4469.38 2580.40i −0.418442 0.241587i
\(486\) 5445.53 13449.4i 0.508260 1.25531i
\(487\) −3315.76 5743.07i −0.308525 0.534380i 0.669515 0.742798i \(-0.266502\pi\)
−0.978040 + 0.208418i \(0.933169\pi\)
\(488\) −45.6670 + 79.0975i −0.00423616 + 0.00733725i
\(489\) −9694.79 5243.81i −0.896552 0.484936i
\(490\) −5812.32 3061.59i −0.535865 0.282263i
\(491\) 1848.57i 0.169908i 0.996385 + 0.0849540i \(0.0270743\pi\)
−0.996385 + 0.0849540i \(0.972926\pi\)
\(492\) −4990.75 + 3069.31i −0.457318 + 0.281250i
\(493\) −3422.41 + 1975.93i −0.312652 + 0.180510i
\(494\) −33570.5 + 19382.0i −3.05751 + 1.76525i
\(495\) 112.111 + 2015.99i 0.0101799 + 0.183054i
\(496\) 5392.35i 0.488152i
\(497\) 9130.94 + 5038.23i 0.824102 + 0.454719i
\(498\) 6013.16 11117.2i 0.541077 1.00035i
\(499\) 6454.39 11179.3i 0.579034 1.00292i −0.416556 0.909110i \(-0.636763\pi\)
0.995590 0.0938066i \(-0.0299035\pi\)
\(500\) −417.060 722.368i −0.0373029 0.0646106i
\(501\) 331.675 + 11937.6i 0.0295771 + 1.06453i
\(502\) −9345.00 5395.34i −0.830853 0.479693i
\(503\) 16082.5 1.42562 0.712808 0.701359i \(-0.247423\pi\)
0.712808 + 0.701359i \(0.247423\pi\)
\(504\) 2290.32 + 1102.54i 0.202419 + 0.0974428i
\(505\) −165.291 −0.0145650
\(506\) −9313.42 5377.10i −0.818245 0.472414i
\(507\) 271.536 + 9773.08i 0.0237857 + 0.856090i
\(508\) 1452.11 + 2515.13i 0.126825 + 0.219667i
\(509\) −4553.38 + 7886.69i −0.396513 + 0.686781i −0.993293 0.115624i \(-0.963113\pi\)
0.596780 + 0.802405i \(0.296446\pi\)
\(510\) 1041.87 1926.22i 0.0904607 0.167244i
\(511\) −217.796 11228.9i −0.0188546 0.972089i
\(512\) 14406.5i 1.24353i
\(513\) −9474.50 + 20111.1i −0.815418 + 1.73085i
\(514\) −10505.9 + 6065.57i −0.901545 + 0.520507i
\(515\) −4074.06 + 2352.16i −0.348591 + 0.201259i
\(516\) −1784.71 + 1097.60i −0.152262 + 0.0936414i
\(517\) 151.071i 0.0128512i
\(518\) 503.473 + 25957.6i 0.0427053 + 2.20176i
\(519\) −5505.99 2978.14i −0.465677 0.251880i
\(520\) 811.592 1405.72i 0.0684436 0.118548i
\(521\) 2366.98 + 4099.73i 0.199039 + 0.344745i 0.948217 0.317623i \(-0.102885\pi\)
−0.749178 + 0.662368i \(0.769551\pi\)
\(522\) 8379.46 16576.3i 0.702603 1.38989i
\(523\) −1342.45 775.065i −0.112240 0.0648016i 0.442829 0.896606i \(-0.353975\pi\)
−0.555069 + 0.831804i \(0.687308\pi\)
\(524\) −226.557 −0.0188878
\(525\) 113.443 + 2403.18i 0.00943061 + 0.199778i
\(526\) 18935.9 1.56967
\(527\) 1410.49 + 814.344i 0.116588 + 0.0673119i
\(528\) −5659.79 + 157.252i −0.466498 + 0.0129612i
\(529\) 11534.6 + 19978.6i 0.948026 + 1.64203i
\(530\) 5170.59 8955.72i 0.423766 0.733984i
\(531\) −4894.06 7483.75i −0.399970 0.611614i
\(532\) 17146.1 + 9460.81i 1.39733 + 0.771012i
\(533\) 10791.4i 0.876977i
\(534\) 8109.40 + 13186.0i 0.657168 + 1.06857i
\(535\) −1874.40 + 1082.18i −0.151472 + 0.0874522i
\(536\) −983.158 + 567.626i −0.0792275 + 0.0457420i
\(537\) 3007.89 + 4890.88i 0.241713 + 0.393030i
\(538\) 20585.1i 1.64960i
\(539\) −4538.85 2390.80i −0.362713 0.191056i
\(540\) 389.616 + 4664.70i 0.0310489 + 0.371735i
\(541\) −4421.27 + 7657.86i −0.351359 + 0.608571i −0.986488 0.163835i \(-0.947614\pi\)
0.635129 + 0.772406i \(0.280947\pi\)
\(542\) 8422.35 + 14587.9i 0.667474 + 1.15610i
\(543\) −15185.1 + 421.903i −1.20010 + 0.0333436i
\(544\) 4543.32 + 2623.08i 0.358076 + 0.206735i
\(545\) −3896.52 −0.306254
\(546\) 19810.1 12719.2i 1.55274 0.996943i
\(547\) 14918.7 1.16614 0.583068 0.812423i \(-0.301852\pi\)
0.583068 + 0.812423i \(0.301852\pi\)
\(548\) −18158.9 10484.1i −1.41553 0.817256i
\(549\) 432.949 + 218.859i 0.0336572 + 0.0170140i
\(550\) −716.133 1240.38i −0.0555200 0.0961635i
\(551\) −14228.7 + 24644.8i −1.10012 + 1.90546i
\(552\) 4361.10 + 2358.87i 0.336269 + 0.181885i
\(553\) −1684.27 2790.82i −0.129516 0.214607i
\(554\) 10622.5i 0.814636i
\(555\) 8099.01 4980.89i 0.619430 0.380949i
\(556\) −13868.3 + 8006.84i −1.05781 + 0.610730i
\(557\) −15459.3 + 8925.46i −1.17600 + 0.678966i −0.955087 0.296327i \(-0.904238\pi\)
−0.220916 + 0.975293i \(0.570905\pi\)
\(558\) −7643.08 + 425.040i −0.579852 + 0.0322462i
\(559\) 3859.05i 0.291987i
\(560\) −6745.23 + 130.830i −0.508996 + 0.00987249i
\(561\) 813.600 1504.19i 0.0612304 0.113203i
\(562\) 5054.03 8753.84i 0.379344 0.657043i
\(563\) −2584.61 4476.68i −0.193478 0.335114i 0.752922 0.658109i \(-0.228644\pi\)
−0.946401 + 0.322995i \(0.895310\pi\)
\(564\) −9.72713 350.097i −0.000726216 0.0261378i
\(565\) −2120.18 1224.09i −0.157870 0.0911463i
\(566\) −29032.9 −2.15609
\(567\) 5171.68 12471.5i 0.383051 0.923727i
\(568\) 2862.38 0.211449
\(569\) 16171.2 + 9336.43i 1.19144 + 0.687880i 0.958634 0.284643i \(-0.0918749\pi\)
0.232809 + 0.972522i \(0.425208\pi\)
\(570\) −437.981 15763.7i −0.0321842 1.15837i
\(571\) 1206.49 + 2089.71i 0.0884242 + 0.153155i 0.906845 0.421464i \(-0.138484\pi\)
−0.818421 + 0.574619i \(0.805150\pi\)
\(572\) −3186.88 + 5519.84i −0.232955 + 0.403490i
\(573\) −2376.21 + 4393.15i −0.173242 + 0.320291i
\(574\) −10263.4 + 6193.99i −0.746314 + 0.450404i
\(575\) 4692.83i 0.340356i
\(576\) −8906.68 + 495.310i −0.644291 + 0.0358297i
\(577\) −13459.4 + 7770.80i −0.971097 + 0.560663i −0.899570 0.436776i \(-0.856120\pi\)
−0.0715262 + 0.997439i \(0.522787\pi\)
\(578\) 14691.7 8482.29i 1.05726 0.610409i
\(579\) −5230.15 + 3216.54i −0.375402 + 0.230872i
\(580\) 5991.95i 0.428969i
\(581\) 5681.64 10297.0i 0.405704 0.735271i
\(582\) −18070.2 9773.97i −1.28700 0.696124i
\(583\) 4037.72 6993.53i 0.286836 0.496814i
\(584\) −1541.30 2669.61i −0.109211 0.189159i
\(585\) −7694.35 3889.56i −0.543799 0.274895i
\(586\) 386.302 + 223.032i 0.0272321 + 0.0157224i
\(587\) 998.851 0.0702334 0.0351167 0.999383i \(-0.488820\pi\)
0.0351167 + 0.999383i \(0.488820\pi\)
\(588\) −10672.4 5248.28i −0.748509 0.368088i
\(589\) 11728.2 0.820464
\(590\) 5493.23 + 3171.52i 0.383310 + 0.221304i
\(591\) −19360.6 + 537.918i −1.34753 + 0.0374399i
\(592\) 13331.3 + 23090.4i 0.925526 + 1.60306i
\(593\) 1608.16 2785.42i 0.111365 0.192889i −0.804956 0.593334i \(-0.797811\pi\)
0.916321 + 0.400445i \(0.131145\pi\)
\(594\) 669.010 + 8009.76i 0.0462118 + 0.553274i
\(595\) 984.433 1784.12i 0.0678282 0.122927i
\(596\) 5298.50i 0.364153i
\(597\) 7007.92 + 11395.0i 0.480427 + 0.781183i
\(598\) 39768.3 22960.3i 2.71948 1.57009i
\(599\) 14726.7 8502.49i 1.00454 0.579970i 0.0949504 0.995482i \(-0.469731\pi\)
0.909588 + 0.415512i \(0.136397\pi\)
\(600\) 345.925 + 562.479i 0.0235372 + 0.0382719i
\(601\) 19431.1i 1.31882i −0.751782 0.659412i \(-0.770805\pi\)
0.751782 0.659412i \(-0.229195\pi\)
\(602\) −3670.21 + 2214.99i −0.248483 + 0.149961i
\(603\) 3300.27 + 5046.60i 0.222881 + 0.340818i
\(604\) 1927.49 3338.51i 0.129848 0.224904i
\(605\) 2768.27 + 4794.79i 0.186027 + 0.322208i
\(606\) −657.735 + 18.2746i −0.0440902 + 0.00122501i
\(607\) −6767.31 3907.11i −0.452515 0.261260i 0.256377 0.966577i \(-0.417471\pi\)
−0.708892 + 0.705317i \(0.750805\pi\)
\(608\) 37777.8 2.51989
\(609\) 7925.94 15358.0i 0.527381 1.02190i
\(610\) −344.125 −0.0228413
\(611\) 558.650 + 322.537i 0.0369894 + 0.0213559i
\(612\) 1788.61 3538.25i 0.118138 0.233701i
\(613\) −9304.17 16115.3i −0.613038 1.06181i −0.990725 0.135879i \(-0.956614\pi\)
0.377688 0.925933i \(-0.376719\pi\)
\(614\) 15102.7 26158.6i 0.992663 1.71934i
\(615\) 3861.46 + 2088.63i 0.253186 + 0.136946i
\(616\) −1407.78 + 27.3053i −0.0920797 + 0.00178598i
\(617\) 25699.5i 1.67686i −0.545011 0.838429i \(-0.683475\pi\)
0.545011 0.838429i \(-0.316525\pi\)
\(618\) −15951.7 + 9810.30i −1.03830 + 0.638557i
\(619\) 2647.00 1528.25i 0.171877 0.0992334i −0.411593 0.911368i \(-0.635028\pi\)
0.583471 + 0.812134i \(0.301694\pi\)
\(620\) 2138.63 1234.74i 0.138531 0.0799811i
\(621\) 11223.7 23824.0i 0.725267 1.53949i
\(622\) 37744.4i 2.43314i
\(623\) 7442.50 + 12332.1i 0.478615 + 0.793060i
\(624\) 11502.2 21265.3i 0.737909 1.36425i
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 9250.04 + 16021.5i 0.590585 + 1.02292i
\(627\) −342.020 12309.9i −0.0217846 0.784068i
\(628\) −8198.51 4733.41i −0.520949 0.300770i
\(629\) −8053.06 −0.510488
\(630\) 717.117 + 9550.34i 0.0453502 + 0.603960i
\(631\) 4012.52 0.253147 0.126574 0.991957i \(-0.459602\pi\)
0.126574 + 0.991957i \(0.459602\pi\)
\(632\) −774.822 447.344i −0.0487670 0.0281557i
\(633\) 189.061 + 6804.67i 0.0118713 + 0.427269i
\(634\) 3300.74 + 5717.04i 0.206765 + 0.358127i
\(635\) 1088.06 1884.57i 0.0679971 0.117774i
\(636\) 8906.85 16467.0i 0.555314 1.02667i
\(637\) 18531.5 11680.0i 1.15266 0.726496i
\(638\) 10288.8i 0.638458i
\(639\) −844.186 15180.2i −0.0522621 0.939778i
\(640\) −2778.68 + 1604.27i −0.171620 + 0.0990850i
\(641\) 15938.5 9202.09i 0.982110 0.567021i 0.0792033 0.996858i \(-0.474762\pi\)
0.902906 + 0.429837i \(0.141429\pi\)
\(642\) −7339.09 + 4513.54i −0.451169 + 0.277469i
\(643\) 18685.2i 1.14599i −0.819558 0.572996i \(-0.805781\pi\)
0.819558 0.572996i \(-0.194219\pi\)
\(644\) −20311.7 11207.5i −1.24284 0.685771i
\(645\) 1380.87 + 746.900i 0.0842974 + 0.0455956i
\(646\) −6678.30 + 11567.2i −0.406740 + 0.704495i
\(647\) 106.007 + 183.609i 0.00644134 + 0.0111567i 0.869228 0.494411i \(-0.164616\pi\)
−0.862787 + 0.505568i \(0.831283\pi\)
\(648\) −410.887 3682.87i −0.0249092 0.223266i
\(649\) 4289.67 + 2476.64i 0.259452 + 0.149795i
\(650\) 6115.78 0.369047
\(651\) −7114.79 + 335.858i −0.428342 + 0.0202201i
\(652\) 14154.7 0.850216
\(653\) 888.276 + 512.847i 0.0532327 + 0.0307339i 0.526380 0.850249i \(-0.323549\pi\)
−0.473147 + 0.880983i \(0.656882\pi\)
\(654\) −15505.3 + 430.800i −0.927071 + 0.0257578i
\(655\) 84.8790 + 147.015i 0.00506335 + 0.00876998i
\(656\) −6155.41 + 10661.5i −0.366354 + 0.634544i
\(657\) −13703.2 + 8961.34i −0.813720 + 0.532139i
\(658\) −13.8961 716.440i −0.000823291 0.0424464i
\(659\) 16866.8i 0.997024i −0.866883 0.498512i \(-0.833880\pi\)
0.866883 0.498512i \(-0.166120\pi\)
\(660\) −1358.34 2208.69i −0.0801113 0.130262i
\(661\) 1890.14 1091.27i 0.111222 0.0642141i −0.443357 0.896345i \(-0.646213\pi\)
0.554579 + 0.832131i \(0.312879\pi\)
\(662\) −19624.2 + 11330.0i −1.15214 + 0.665188i
\(663\) 3825.35 + 6220.09i 0.224079 + 0.364356i
\(664\) 3227.93i 0.188656i
\(665\) −284.553 14670.7i −0.0165932 0.855497i
\(666\) 31677.4 20715.7i 1.84306 1.20528i
\(667\) 16855.6 29194.8i 0.978489 1.69479i
\(668\) −7668.14 13281.6i −0.444146 0.769283i
\(669\) −7711.17 + 214.248i −0.445637 + 0.0123816i
\(670\) −3704.31 2138.68i −0.213597 0.123320i
\(671\) −268.728 −0.0154607
\(672\) −22917.5 + 1081.83i −1.31557 + 0.0621020i
\(673\) 15734.2 0.901203 0.450601 0.892725i \(-0.351210\pi\)
0.450601 + 0.892725i \(0.351210\pi\)
\(674\) 33523.9 + 19355.0i 1.91586 + 1.10612i
\(675\) 2880.99 2000.44i 0.164281 0.114070i
\(676\) −6277.77 10873.4i −0.357178 0.618651i
\(677\) −12363.2 + 21413.8i −0.701858 + 1.21565i 0.265955 + 0.963985i \(0.414313\pi\)
−0.967813 + 0.251669i \(0.919021\pi\)
\(678\) −8572.09 4636.56i −0.485559 0.262634i
\(679\) −16737.1 9235.10i −0.945964 0.521960i
\(680\) 559.289i 0.0315408i
\(681\) 12285.0 7555.24i 0.691278 0.425136i
\(682\) 3672.24 2120.17i 0.206184 0.119040i
\(683\) 561.677 324.284i 0.0314670 0.0181675i −0.484184 0.874966i \(-0.660883\pi\)
0.515651 + 0.856799i \(0.327550\pi\)
\(684\) −1585.22 28505.4i −0.0886144 1.59347i
\(685\) 15711.3i 0.876345i
\(686\) −21745.0 10920.7i −1.21025 0.607803i
\(687\) −9302.73 + 17198.9i −0.516625 + 0.955139i
\(688\) −2201.20 + 3812.58i −0.121976 + 0.211269i
\(689\) 17241.1 + 29862.4i 0.953313 + 1.65119i
\(690\) 518.841 + 18674.0i 0.0286260 + 1.03030i
\(691\) 5917.06 + 3416.22i 0.325754 + 0.188074i 0.653954 0.756534i \(-0.273109\pi\)
−0.328201 + 0.944608i \(0.606442\pi\)
\(692\) 8038.92 0.441610
\(693\) 559.997 + 7457.87i 0.0306963 + 0.408804i
\(694\) 33289.7 1.82084
\(695\) 10391.4 + 5999.47i 0.567148 + 0.327443i
\(696\) −131.745 4741.75i −0.00717499 0.258241i
\(697\) −1859.16 3220.16i −0.101034 0.174996i
\(698\) −2737.33 + 4741.20i −0.148438 + 0.257102i
\(699\) −8940.59 + 16529.4i −0.483783 + 0.894421i
\(700\) −1596.41 2645.23i −0.0861979 0.142829i
\(701\) 18697.9i 1.00743i 0.863869 + 0.503717i \(0.168035\pi\)
−0.863869 + 0.503717i \(0.831965\pi\)
\(702\) −31047.9 14626.9i −1.66927 0.786406i
\(703\) −50221.1 + 28995.2i −2.69434 + 1.55558i
\(704\) 4279.35 2470.69i 0.229097 0.132269i
\(705\) −223.536 + 137.475i −0.0119416 + 0.00734411i
\(706\) 31659.2i 1.68769i
\(707\) −612.130 + 11.8729i −0.0325622 + 0.000631577i
\(708\) 10100.5 + 5463.25i 0.536158 + 0.290002i
\(709\) −6566.08 + 11372.8i −0.347806 + 0.602417i −0.985859 0.167575i \(-0.946406\pi\)
0.638054 + 0.769992i \(0.279740\pi\)
\(710\) 5392.40 + 9339.91i 0.285032 + 0.493691i
\(711\) −2143.90 + 4241.07i −0.113084 + 0.223703i
\(712\) 3423.80 + 1976.73i 0.180214 + 0.104047i
\(713\) −13893.5 −0.729755
\(714\) 3720.07 7208.32i 0.194986 0.377822i
\(715\) 4775.82 0.249798
\(716\) −6385.77 3686.83i −0.333307 0.192435i
\(717\) 24493.5 680.530i 1.27577 0.0354461i
\(718\) −566.745 981.631i −0.0294578 0.0510225i
\(719\) 9575.52 16585.3i 0.496671 0.860259i −0.503322 0.864099i \(-0.667889\pi\)
0.999993 + 0.00383968i \(0.00122221\pi\)
\(720\) 5383.10 + 8231.57i 0.278634 + 0.426073i
\(721\) −14918.7 + 9003.53i −0.770600 + 0.465061i
\(722\) 69907.6i 3.60345i
\(723\) −19899.0 32356.0i −1.02358 1.66436i
\(724\) 16894.7 9754.17i 0.867248 0.500706i
\(725\) 3888.22 2244.86i 0.199179 0.114996i
\(726\) 11545.8 + 18773.7i 0.590227 + 0.959720i
\(727\) 21313.6i 1.08731i 0.839307 + 0.543657i \(0.182961\pi\)
−0.839307 + 0.543657i \(0.817039\pi\)
\(728\) 2904.64 5264.17i 0.147875 0.267999i
\(729\) −19410.3 + 3265.24i −0.986144 + 0.165891i
\(730\) 5807.25 10058.5i 0.294433 0.509973i
\(731\) −664.842 1151.54i −0.0336390 0.0582644i
\(732\) −622.759 + 17.3028i −0.0314451 + 0.000873675i
\(733\) 15935.6 + 9200.45i 0.802996 + 0.463610i 0.844518 0.535528i \(-0.179887\pi\)
−0.0415215 + 0.999138i \(0.513221\pi\)
\(734\) −10493.2 −0.527672
\(735\) 592.741 + 8891.67i 0.0297464 + 0.446223i
\(736\) −44752.4 −2.24130
\(737\) −2892.70 1670.10i −0.144578 0.0834721i
\(738\) 15596.7 + 7884.27i 0.777944 + 0.393258i
\(739\) 1609.97 + 2788.55i 0.0801404 + 0.138807i 0.903310 0.428988i \(-0.141130\pi\)
−0.823170 + 0.567795i \(0.807796\pi\)
\(740\) −6105.17 + 10574.5i −0.303285 + 0.525304i
\(741\) 46251.4 + 25016.9i 2.29297 + 1.24024i
\(742\) 18505.2 33537.6i 0.915564 1.65931i
\(743\) 36940.2i 1.82396i −0.410229 0.911982i \(-0.634551\pi\)
0.410229 0.911982i \(-0.365449\pi\)
\(744\) −1665.26 + 1024.14i −0.0820585 + 0.0504660i
\(745\) −3438.24 + 1985.07i −0.169084 + 0.0976204i
\(746\) 24277.4 14016.6i 1.19150 0.687913i
\(747\) −17118.8 + 951.993i −0.838478 + 0.0466287i
\(748\) 2196.16i 0.107352i
\(749\) −6863.83 + 4142.35i −0.334845 + 0.202080i
\(750\) −1183.68 + 2188.39i −0.0576291 + 0.106545i
\(751\) 568.670 984.966i 0.0276313 0.0478587i −0.851879 0.523738i \(-0.824537\pi\)
0.879510 + 0.475880i \(0.157870\pi\)
\(752\) −367.949 637.306i −0.0178427 0.0309044i
\(753\) 406.538 + 14632.0i 0.0196747 + 0.708128i
\(754\) −38047.2 21966.6i −1.83766 1.06097i
\(755\) −2888.51 −0.139236
\(756\) 1777.95 + 17247.1i 0.0855338 + 0.829722i
\(757\) −24998.2 −1.20023 −0.600117 0.799912i \(-0.704879\pi\)
−0.600117 + 0.799912i \(0.704879\pi\)
\(758\) 20618.8 + 11904.2i 0.988004 + 0.570424i
\(759\) 405.163 + 14582.6i 0.0193762 + 0.697383i
\(760\) −2013.73 3487.88i −0.0961125 0.166472i
\(761\) −16387.5 + 28383.9i −0.780611 + 1.35206i 0.150976 + 0.988537i \(0.451758\pi\)
−0.931586 + 0.363520i \(0.881575\pi\)
\(762\) 4121.30 7619.49i 0.195931 0.362238i
\(763\) −14430.2 + 279.888i −0.684676 + 0.0132800i
\(764\) 6414.14i 0.303737i
\(765\) −2966.09 + 164.948i −0.140182 + 0.00779568i
\(766\) −22457.5 + 12965.9i −1.05930 + 0.611587i
\(767\) −18316.9 + 10575.3i −0.862301 + 0.497850i
\(768\) −22578.4 + 13885.7i −1.06084 + 0.652417i
\(769\) 15999.0i 0.750244i −0.926976 0.375122i \(-0.877601\pi\)
0.926976 0.375122i \(-0.122399\pi\)
\(770\) −2741.19 4542.12i −0.128293 0.212580i
\(771\) 14474.3 + 7829.03i 0.676110 + 0.365701i
\(772\) 3942.58 6828.75i 0.183804 0.318357i
\(773\) 2048.20 + 3547.59i 0.0953024 + 0.165069i 0.909735 0.415190i \(-0.136285\pi\)
−0.814432 + 0.580259i \(0.802952\pi\)
\(774\) 5577.44 + 2819.44i 0.259014 + 0.130934i
\(775\) −1602.46 925.181i −0.0742736 0.0428819i
\(776\) −5246.77 −0.242716
\(777\) 29635.7 19027.7i 1.36831 0.878528i
\(778\) −30178.6 −1.39069
\(779\) −23188.5 13387.9i −1.06651 0.615751i
\(780\) 11067.7 307.505i 0.508059 0.0141159i
\(781\) 4210.93 + 7293.54i 0.192931 + 0.334166i
\(782\) 7911.25 13702.7i 0.361772 0.626607i
\(783\) −25108.2 + 2097.15i −1.14597 + 0.0957163i
\(784\) −24970.6 + 969.023i −1.13751 + 0.0441428i
\(785\) 7093.43i 0.322516i
\(786\) 354.010 + 575.626i 0.0160650 + 0.0261220i
\(787\) 36383.7 21006.2i 1.64795 0.951447i 0.670071 0.742297i \(-0.266264\pi\)
0.977884 0.209149i \(-0.0670695\pi\)
\(788\) 21540.4 12436.4i 0.973789 0.562218i
\(789\) −13456.2 21880.1i −0.607167 0.987264i
\(790\) 3370.97i 0.151815i
\(791\) −7939.70 4380.93i −0.356894 0.196925i
\(792\) 1123.49 + 1717.99i 0.0504061 + 0.0770784i
\(793\) 573.734 993.737i 0.0256922 0.0445002i
\(794\) −14615.9 25315.5i −0.653273 1.13150i
\(795\) −14022.5 + 389.602i −0.625568 + 0.0173808i
\(796\) −14877.9 8589.75i −0.662478 0.382482i
\(797\) 5478.00 0.243464 0.121732 0.992563i \(-0.461155\pi\)
0.121732 + 0.992563i \(0.461155\pi\)
\(798\) −2754.31 58347.2i −0.122182 2.58831i
\(799\) 222.268 0.00984140
\(800\) −5161.69 2980.10i −0.228116 0.131703i
\(801\) 9473.50 18740.5i 0.417890 0.826671i
\(802\) −29544.1 51171.8i −1.30079 2.25304i
\(803\) 4534.89 7854.66i 0.199294 0.345187i
\(804\) −6811.18 3684.10i −0.298771 0.161602i
\(805\) 337.087 + 17379.2i 0.0147587 + 0.760916i
\(806\) 18106.3i 0.791273i
\(807\) 23785.7 14628.2i 1.03754 0.638089i
\(808\) −145.530 + 84.0219i −0.00633631 + 0.00365827i
\(809\) 6862.81 3962.25i 0.298249 0.172194i −0.343407 0.939187i \(-0.611581\pi\)
0.641656 + 0.766992i \(0.278248\pi\)
\(810\) 11243.1 8278.81i 0.487705 0.359121i
\(811\) 17180.9i 0.743899i 0.928253 + 0.371949i \(0.121311\pi\)
−0.928253 + 0.371949i \(0.878689\pi\)
\(812\) 430.403 + 22190.3i 0.0186012 + 0.959024i
\(813\) 10871.0 20098.4i 0.468958 0.867012i
\(814\) −10483.2 + 18157.4i −0.451395 + 0.781839i
\(815\) −5303.01 9185.08i −0.227922 0.394772i
\(816\) −231.363 8327.16i −0.00992563 0.357241i
\(817\) −8292.27 4787.55i −0.355092 0.205012i
\(818\) 696.327 0.0297635
\(819\) −28774.3 13851.7i −1.22766 0.590988i
\(820\) −5637.85 −0.240100
\(821\) 14693.9 + 8483.55i 0.624631 + 0.360631i 0.778670 0.627434i \(-0.215895\pi\)
−0.154039 + 0.988065i \(0.549228\pi\)
\(822\) 1737.04 + 62519.3i 0.0737060 + 2.65281i
\(823\) −12711.3 22016.6i −0.538381 0.932504i −0.998991 0.0449014i \(-0.985703\pi\)
0.460610 0.887603i \(-0.347631\pi\)
\(824\) −2391.34 + 4141.93i −0.101100 + 0.175110i
\(825\) −924.336 + 1708.92i −0.0390076 + 0.0721174i
\(826\) 20571.2 + 11350.7i 0.866541 + 0.478136i
\(827\) 1688.52i 0.0709984i 0.999370 + 0.0354992i \(0.0113021\pi\)
−0.999370 + 0.0354992i \(0.988698\pi\)
\(828\) 1877.88 + 33768.1i 0.0788175 + 1.41730i
\(829\) 2085.14 1203.86i 0.0873582 0.0504363i −0.455685 0.890141i \(-0.650605\pi\)
0.543043 + 0.839705i \(0.317272\pi\)
\(830\) 10532.7 6081.04i 0.440475 0.254308i
\(831\) 12274.1 7548.60i 0.512377 0.315112i
\(832\) 21099.7i 0.879206i
\(833\) 3517.55 6677.94i 0.146310 0.277763i
\(834\) 42013.4 + 22724.6i 1.74437 + 0.943513i
\(835\) −5745.69 + 9951.83i −0.238129 + 0.412452i
\(836\) 7907.31 + 13695.9i 0.327129 + 0.566604i
\(837\) 5922.46 + 8529.40i 0.244576 + 0.352233i
\(838\) 24812.4 + 14325.4i 1.02283 + 0.590530i
\(839\) −12915.1 −0.531442 −0.265721 0.964050i \(-0.585610\pi\)
−0.265721 + 0.964050i \(0.585610\pi\)
\(840\) 1321.48 + 2058.21i 0.0542804 + 0.0845418i
\(841\) −7863.23 −0.322409
\(842\) −30086.8 17370.6i −1.23142 0.710962i
\(843\) −13706.4 + 380.820i −0.559992 + 0.0155589i
\(844\) −4371.00 7570.79i −0.178265 0.308765i
\(845\) −4703.89 + 8147.38i −0.191501 + 0.331690i
\(846\) −874.311 + 571.763i −0.0355312 + 0.0232359i
\(847\) 10596.3 + 17558.0i 0.429862 + 0.712277i
\(848\) 39337.1i 1.59297i
\(849\) 20631.4 + 33547.0i 0.834002 + 1.35610i
\(850\) 1824.95 1053.63i 0.0736415 0.0425169i
\(851\) 59492.9 34348.3i 2.39646 1.38360i
\(852\) 10228.2 + 16631.2i 0.411281 + 0.668750i
\(853\) 16815.4i 0.674968i 0.941331 + 0.337484i \(0.109576\pi\)
−0.941331 + 0.337484i \(0.890424\pi\)
\(854\) −1274.42 + 24.7186i −0.0510652 + 0.000990461i
\(855\) −17903.5 + 11708.1i −0.716123 + 0.468315i
\(856\) −1100.21 + 1905.62i −0.0439304 + 0.0760897i
\(857\) −11067.3 19169.2i −0.441135 0.764069i 0.556639 0.830755i \(-0.312091\pi\)
−0.997774 + 0.0666857i \(0.978758\pi\)
\(858\) 19004.3 528.016i 0.756171 0.0210095i
\(859\) 27724.8 + 16006.9i 1.10123 + 0.635798i 0.936545 0.350548i \(-0.114005\pi\)
0.164689 + 0.986346i \(0.447338\pi\)
\(860\) −2016.12 −0.0799407
\(861\) 14450.4 + 7457.55i 0.571972 + 0.295183i
\(862\) 32105.0 1.26856
\(863\) 3035.49 + 1752.54i 0.119733 + 0.0691277i 0.558670 0.829390i \(-0.311312\pi\)
−0.438938 + 0.898518i \(0.644645\pi\)
\(864\) 19076.9 + 27474.1i 0.751166 + 1.08181i
\(865\) −3011.75 5216.51i −0.118385 0.205048i
\(866\) 10803.4 18712.0i 0.423918 0.734248i
\(867\) −20241.4 10948.4i −0.792888 0.428865i
\(868\) 7831.41 4726.29i 0.306239 0.184817i
\(869\) 2632.40i 0.102759i
\(870\) 15224.1 9362.79i 0.593269 0.364860i
\(871\) 12351.8 7131.34i 0.480512 0.277424i
\(872\) −3430.69 + 1980.71i −0.133232 + 0.0769213i
\(873\) 1547.40 + 27825.3i 0.0599902 + 1.07875i
\(874\) 113938.i 4.40963i
\(875\) −1118.42 + 2026.95i −0.0432108 + 0.0783124i
\(876\) 10003.6 18494.7i 0.385832 0.713329i
\(877\) −22418.6 + 38830.1i −0.863194 + 1.49510i 0.00563608 + 0.999984i \(0.498206\pi\)
−0.868830 + 0.495111i \(0.835127\pi\)
\(878\) 4042.95 + 7002.59i 0.155402 + 0.269164i
\(879\) −16.8054 604.856i −0.000644859 0.0232096i
\(880\) −4718.31 2724.12i −0.180744 0.104352i
\(881\) −34786.1 −1.33028 −0.665138 0.746720i \(-0.731627\pi\)
−0.665138 + 0.746720i \(0.731627\pi\)
\(882\) 3341.74 + 35316.8i 0.127576 + 1.34827i
\(883\) 41449.1 1.57970 0.789848 0.613302i \(-0.210159\pi\)
0.789848 + 0.613302i \(0.210159\pi\)
\(884\) −8121.26 4688.81i −0.308990 0.178396i
\(885\) −238.973 8601.07i −0.00907682 0.326691i
\(886\) −1826.74 3164.01i −0.0692671 0.119974i
\(887\) −5361.62 + 9286.60i −0.202960 + 0.351537i −0.949481 0.313825i \(-0.898389\pi\)
0.746521 + 0.665362i \(0.231723\pi\)
\(888\) 4598.85 8502.39i 0.173792 0.321308i
\(889\) 3894.09 7057.37i 0.146910 0.266251i
\(890\) 14895.7i 0.561018i
\(891\) 8779.72 6464.93i 0.330114 0.243079i
\(892\) 8579.35 4953.29i 0.322038 0.185929i
\(893\) 1386.12 800.279i 0.0519428 0.0299892i
\(894\) −13462.2 + 8279.24i −0.503628 + 0.309731i
\(895\) 5525.03i 0.206348i
\(896\) −10175.2 + 6140.78i −0.379386 + 0.228961i
\(897\) −54790.4 29635.6i −2.03946 1.10312i
\(898\) −7021.56 + 12161.7i −0.260927 + 0.451939i
\(899\) 6646.09 + 11511.4i 0.246562 + 0.427059i
\(900\) −2032.06 + 4019.82i −0.0752613 + 0.148882i
\(901\) 10289.5 + 5940.63i 0.380457 + 0.219657i
\(902\) −9680.76 −0.357355
\(903\) 5167.51 + 2666.85i 0.190436 + 0.0982803i
\(904\) −2488.95 −0.0915722
\(905\) −12659.1 7308.74i −0.464975 0.268454i
\(906\) −11494.1 + 319.354i −0.421487 + 0.0117106i
\(907\) 18339.4 + 31764.8i 0.671389 + 1.16288i 0.977510 + 0.210887i \(0.0676353\pi\)
−0.306122 + 0.951992i \(0.599031\pi\)
\(908\) −9260.61 + 16039.9i −0.338463 + 0.586235i
\(909\) 488.516 + 747.015i 0.0178252 + 0.0272573i
\(910\) 22648.9 439.298i 0.825060 0.0160029i
\(911\) 13062.2i 0.475051i −0.971381 0.237525i \(-0.923664\pi\)
0.971381 0.237525i \(-0.0763363\pi\)
\(912\) −31424.9 51097.4i −1.14099 1.85527i
\(913\) 8224.97 4748.69i 0.298146 0.172134i
\(914\) −28616.9 + 16521.9i −1.03563 + 0.597918i
\(915\) 244.543 + 397.630i 0.00883533 + 0.0143664i
\(916\) 25111.0i 0.905775i
\(917\) 324.897 + 538.351i 0.0117002 + 0.0193870i
\(918\) −11784.6 + 984.303i −0.423694 + 0.0353887i
\(919\) −19593.8 + 33937.5i −0.703309 + 1.21817i 0.263990 + 0.964525i \(0.414961\pi\)
−0.967299 + 0.253641i \(0.918372\pi\)
\(920\) 2385.50 + 4131.81i 0.0854866 + 0.148067i
\(921\) −40958.1 + 1137.98i −1.46538 + 0.0407143i
\(922\) 23849.3 + 13769.4i 0.851880 + 0.491833i
\(923\) −35961.4 −1.28243
\(924\) −5189.08 8082.00i −0.184749 0.287747i
\(925\) 9149.13 0.325213
\(926\) −7571.52 4371.42i −0.268699 0.155134i
\(927\) 22671.3 + 11460.5i 0.803260 + 0.406055i
\(928\) 21407.7 + 37079.3i 0.757267 + 1.31162i
\(929\) 15873.1 27493.1i 0.560582 0.970956i −0.436864 0.899528i \(-0.643911\pi\)
0.997446 0.0714285i \(-0.0227558\pi\)
\(930\) −6478.91 3504.37i −0.228443 0.123562i
\(931\) −2107.60 54310.4i −0.0741932 1.91187i
\(932\) 24133.5i 0.848195i
\(933\) 43613.0 26822.0i 1.53036 0.941170i
\(934\) 21420.5 12367.1i 0.750427 0.433259i
\(935\) 1425.10 822.785i 0.0498459 0.0287785i
\(936\) −8751.67 + 486.690i −0.305617 + 0.0169957i
\(937\) 16884.3i 0.588674i 0.955702 + 0.294337i \(0.0950988\pi\)
−0.955702 + 0.294337i \(0.904901\pi\)
\(938\) −13872.0 7654.23i −0.482875 0.266439i
\(939\) 11939.3 22073.5i 0.414936 0.767137i
\(940\) 168.505 291.860i 0.00584685 0.0101270i
\(941\) −22301.8 38627.9i −0.772603 1.33819i −0.936132 0.351649i \(-0.885621\pi\)
0.163529 0.986539i \(-0.447712\pi\)
\(942\) 784.252 + 28226.6i 0.0271256 + 0.976299i
\(943\) 27469.5 + 15859.5i 0.948601 + 0.547675i
\(944\) 24128.5 0.831901
\(945\) 10525.6 7615.29i 0.362327 0.262143i
\(946\) −3461.87 −0.118980
\(947\) 47658.4 + 27515.6i 1.63537 + 0.944179i 0.982400 + 0.186791i \(0.0598088\pi\)
0.652966 + 0.757387i \(0.273524\pi\)
\(948\) −169.494 6100.41i −0.00580688 0.209000i
\(949\) 19364.0 + 33539.4i 0.662362 + 1.14725i
\(950\) 7587.25 13141.5i 0.259119 0.448807i
\(951\) 4260.37 7876.59i 0.145270 0.268576i
\(952\) −40.1739 2071.24i −0.00136769 0.0705141i
\(953\) 44397.5i 1.50910i 0.656240 + 0.754552i \(0.272146\pi\)
−0.656240 + 0.754552i \(0.727854\pi\)
\(954\) −55756.2 + 3100.66i −1.89222 + 0.105228i
\(955\) −4162.18 + 2403.03i −0.141031 + 0.0814245i
\(956\) −27251.2 + 15733.5i −0.921932 + 0.532278i
\(957\) 11888.5 7311.42i 0.401568 0.246964i
\(958\) 52721.3i 1.77803i
\(959\) 1128.54 + 58184.4i 0.0380006 + 1.95920i
\(960\) −7550.03 4083.73i −0.253829 0.137294i
\(961\) −12156.4 + 21055.6i −0.408057 + 0.706776i
\(962\) −44763.3 77532.3i −1.50023 2.59848i
\(963\) 10430.6 + 5272.77i 0.349036 + 0.176441i
\(964\) 42245.7 + 24390.6i 1.41145 + 0.814903i
\(965\) −5908.30 −0.197093
\(966\) 3262.81 + 69119.3i 0.108674 + 2.30215i
\(967\) −42649.0 −1.41830 −0.709151 0.705057i \(-0.750922\pi\)
−0.709151 + 0.705057i \(0.750922\pi\)
\(968\) 4874.66 + 2814.38i 0.161857 + 0.0934481i
\(969\) 18111.4 503.208i 0.600435 0.0166825i
\(970\) −9884.30 17120.1i −0.327181 0.566694i
\(971\) 6546.89 11339.6i 0.216375 0.374772i −0.737322 0.675541i \(-0.763910\pi\)
0.953697 + 0.300769i \(0.0972434\pi\)
\(972\) 19930.2 15547.4i 0.657676 0.513048i
\(973\) 38914.0 + 21471.8i 1.28214 + 0.707454i
\(974\) 25402.2i 0.835668i
\(975\) −4346.00 7066.67i −0.142752 0.232118i
\(976\) −1133.65 + 654.514i −0.0371796 + 0.0214657i
\(977\) 13101.1 7563.95i 0.429010 0.247689i −0.269915 0.962884i \(-0.586996\pi\)
0.698925 + 0.715195i \(0.253662\pi\)
\(978\) −22117.6 35963.6i −0.723152 1.17586i
\(979\) 11632.1i 0.379738i
\(980\) −6102.07 9681.55i −0.198902 0.315577i
\(981\) 11516.2 + 17609.9i 0.374804 + 0.573131i
\(982\) −3540.50 + 6132.33i −0.115053 + 0.199277i
\(983\) −9102.04 15765.2i −0.295330 0.511527i 0.679731 0.733461i \(-0.262096\pi\)
−0.975062 + 0.221934i \(0.928763\pi\)
\(984\) 4461.54 123.960i 0.144541 0.00401595i
\(985\) −16140.1 9318.49i −0.522098 0.301433i
\(986\) −15137.7 −0.488928
\(987\) −817.959 + 525.174i −0.0263788 + 0.0169367i
\(988\) −67528.5 −2.17446
\(989\) 9823.20 + 5671.43i 0.315834 + 0.182347i
\(990\) −3489.24 + 6902.43i −0.112016 + 0.221590i
\(991\) −22984.4 39810.1i −0.736754 1.27610i −0.953950 0.299967i \(-0.903024\pi\)
0.217196 0.976128i \(-0.430309\pi\)
\(992\) 8822.83 15281.6i 0.282384 0.489104i
\(993\) 27037.0 + 14624.0i 0.864042 + 0.467351i
\(994\) 20640.9 + 34201.7i 0.658640 + 1.09136i
\(995\) 12872.5i 0.410136i
\(996\) 18755.1 11534.4i 0.596664 0.366948i
\(997\) 23332.0 13470.8i 0.741156 0.427907i −0.0813334 0.996687i \(-0.525918\pi\)
0.822490 + 0.568780i \(0.192585\pi\)
\(998\) 42822.7 24723.7i 1.35825 0.784184i
\(999\) −46447.3 21881.7i −1.47100 0.692998i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 105.4.s.b.26.14 yes 32
3.2 odd 2 105.4.s.a.26.3 32
7.3 odd 6 105.4.s.a.101.3 yes 32
21.17 even 6 inner 105.4.s.b.101.14 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.s.a.26.3 32 3.2 odd 2
105.4.s.a.101.3 yes 32 7.3 odd 6
105.4.s.b.26.14 yes 32 1.1 even 1 trivial
105.4.s.b.101.14 yes 32 21.17 even 6 inner