Properties

Label 126.4.m.a.41.6
Level $126$
Weight $4$
Character 126.41
Analytic conductor $7.434$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,4,Mod(41,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.41");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.m (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: \(7.43424066072\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.6
Character \(\chi\) \(=\) 126.41
Dual form 126.4.m.a.83.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(-0.111457 + 5.19496i) q^{3} +(2.00000 - 3.46410i) q^{4} +(8.24952 - 14.2886i) q^{5} +(-5.00191 - 9.10939i) q^{6} +(-17.4194 + 6.29008i) q^{7} +8.00000i q^{8} +(-26.9752 - 1.15803i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{2} +(-0.111457 + 5.19496i) q^{3} +(2.00000 - 3.46410i) q^{4} +(8.24952 - 14.2886i) q^{5} +(-5.00191 - 9.10939i) q^{6} +(-17.4194 + 6.29008i) q^{7} +8.00000i q^{8} +(-26.9752 - 1.15803i) q^{9} +32.9981i q^{10} +(-36.5379 + 21.0952i) q^{11} +(17.7729 + 10.7760i) q^{12} +(-39.5847 - 22.8542i) q^{13} +(23.8812 - 28.3141i) q^{14} +(73.3091 + 44.4485i) q^{15} +(-8.00000 - 13.8564i) q^{16} -65.3440 q^{17} +(47.8804 - 24.9694i) q^{18} -161.794i q^{19} +(-32.9981 - 57.1544i) q^{20} +(-30.7352 - 91.1940i) q^{21} +(42.1903 - 73.0758i) q^{22} +(147.699 + 85.2741i) q^{23} +(-41.5597 - 0.891656i) q^{24} +(-73.6092 - 127.495i) q^{25} +91.4169 q^{26} +(9.02248 - 140.006i) q^{27} +(-13.0493 + 72.9227i) q^{28} +(-171.860 + 99.2232i) q^{29} +(-171.424 - 3.67787i) q^{30} +(-48.4789 - 27.9893i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-105.516 - 192.164i) q^{33} +(113.179 - 65.3440i) q^{34} +(-53.8252 + 300.789i) q^{35} +(-57.9618 + 91.1286i) q^{36} -133.655 q^{37} +(161.794 + 280.236i) q^{38} +(123.139 - 203.093i) q^{39} +(114.309 + 65.9962i) q^{40} +(-9.23461 + 15.9948i) q^{41} +(144.429 + 127.217i) q^{42} +(12.1938 + 21.1202i) q^{43} +168.761i q^{44} +(-239.079 + 375.884i) q^{45} -341.096 q^{46} +(61.6110 + 106.713i) q^{47} +(72.8751 - 40.0153i) q^{48} +(263.870 - 219.139i) q^{49} +(254.990 + 147.218i) q^{50} +(7.28305 - 339.460i) q^{51} +(-158.339 + 91.4169i) q^{52} -400.837i q^{53} +(124.378 + 251.519i) q^{54} +696.100i q^{55} +(-50.3207 - 139.355i) q^{56} +(840.514 + 18.0331i) q^{57} +(198.446 - 343.719i) q^{58} +(114.190 - 197.783i) q^{59} +(300.592 - 165.053i) q^{60} +(-212.887 + 122.910i) q^{61} +111.957 q^{62} +(477.175 - 149.504i) q^{63} -64.0000 q^{64} +(-653.109 + 377.073i) q^{65} +(374.923 + 227.322i) q^{66} +(-466.625 + 808.218i) q^{67} +(-130.688 + 226.358i) q^{68} +(-459.457 + 757.786i) q^{69} +(-207.561 - 574.806i) q^{70} +808.476i q^{71} +(9.26423 - 215.801i) q^{72} -98.0777i q^{73} +(231.498 - 133.655i) q^{74} +(670.535 - 368.186i) q^{75} +(-560.472 - 323.589i) q^{76} +(503.777 - 597.291i) q^{77} +(-10.1891 + 474.907i) q^{78} +(-450.095 - 779.587i) q^{79} -263.985 q^{80} +(726.318 + 62.4760i) q^{81} -36.9384i q^{82} +(605.681 + 1049.07i) q^{83} +(-377.376 - 75.9182i) q^{84} +(-539.057 + 933.674i) q^{85} +(-42.2405 - 24.3875i) q^{86} +(-496.305 - 903.863i) q^{87} +(-168.761 - 292.303i) q^{88} -678.302 q^{89} +(38.2127 - 890.128i) q^{90} +(833.296 + 149.116i) q^{91} +(590.796 - 341.096i) q^{92} +(150.807 - 248.726i) q^{93} +(-213.427 - 123.222i) q^{94} +(-2311.81 - 1334.73i) q^{95} +(-86.2081 + 142.184i) q^{96} +(749.281 - 432.598i) q^{97} +(-237.897 + 643.429i) q^{98} +(1010.04 - 526.734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.00000i −0.612372 + 0.353553i
\(3\) −0.111457 + 5.19496i −0.0214499 + 0.999770i
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 8.24952 14.2886i 0.737860 1.27801i −0.215598 0.976482i \(-0.569170\pi\)
0.953457 0.301528i \(-0.0974967\pi\)
\(6\) −5.00191 9.10939i −0.340337 0.619815i
\(7\) −17.4194 + 6.29008i −0.940558 + 0.339633i
\(8\) 8.00000i 0.353553i
\(9\) −26.9752 1.15803i −0.999080 0.0428899i
\(10\) 32.9981i 1.04349i
\(11\) −36.5379 + 21.0952i −1.00151 + 0.578221i −0.908694 0.417462i \(-0.862920\pi\)
−0.0928143 + 0.995683i \(0.529586\pi\)
\(12\) 17.7729 + 10.7760i 0.427551 + 0.259231i
\(13\) −39.5847 22.8542i −0.844524 0.487586i 0.0142753 0.999898i \(-0.495456\pi\)
−0.858800 + 0.512312i \(0.828789\pi\)
\(14\) 23.8812 28.3141i 0.455894 0.540519i
\(15\) 73.3091 + 44.4485i 1.26189 + 0.765103i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −65.3440 −0.932251 −0.466125 0.884719i \(-0.654350\pi\)
−0.466125 + 0.884719i \(0.654350\pi\)
\(18\) 47.8804 24.9694i 0.626973 0.326963i
\(19\) 161.794i 1.95359i −0.214183 0.976794i \(-0.568709\pi\)
0.214183 0.976794i \(-0.431291\pi\)
\(20\) −32.9981 57.1544i −0.368930 0.639005i
\(21\) −30.7352 91.1940i −0.319379 0.947627i
\(22\) 42.1903 73.0758i 0.408864 0.708174i
\(23\) 147.699 + 85.2741i 1.33902 + 0.773081i 0.986662 0.162785i \(-0.0520477\pi\)
0.352355 + 0.935867i \(0.385381\pi\)
\(24\) −41.5597 0.891656i −0.353472 0.00758369i
\(25\) −73.6092 127.495i −0.588874 1.01996i
\(26\) 91.4169 0.689551
\(27\) 9.02248 140.006i 0.0643102 0.997930i
\(28\) −13.0493 + 72.9227i −0.0880744 + 0.492182i
\(29\) −171.860 + 99.2232i −1.10047 + 0.635355i −0.936344 0.351085i \(-0.885813\pi\)
−0.164123 + 0.986440i \(0.552480\pi\)
\(30\) −171.424 3.67787i −1.04325 0.0223828i
\(31\) −48.4789 27.9893i −0.280873 0.162162i 0.352945 0.935644i \(-0.385180\pi\)
−0.633819 + 0.773482i \(0.718513\pi\)
\(32\) 27.7128 + 16.0000i 0.153093 + 0.0883883i
\(33\) −105.516 192.164i −0.556606 1.01368i
\(34\) 113.179 65.3440i 0.570885 0.329600i
\(35\) −53.8252 + 300.789i −0.259946 + 1.45264i
\(36\) −57.9618 + 91.1286i −0.268342 + 0.421892i
\(37\) −133.655 −0.593859 −0.296929 0.954899i \(-0.595963\pi\)
−0.296929 + 0.954899i \(0.595963\pi\)
\(38\) 161.794 + 280.236i 0.690697 + 1.19632i
\(39\) 123.139 203.093i 0.505589 0.833871i
\(40\) 114.309 + 65.9962i 0.451845 + 0.260873i
\(41\) −9.23461 + 15.9948i −0.0351757 + 0.0609261i −0.883077 0.469228i \(-0.844532\pi\)
0.847902 + 0.530154i \(0.177866\pi\)
\(42\) 144.429 + 127.217i 0.530616 + 0.467383i
\(43\) 12.1938 + 21.1202i 0.0432450 + 0.0749025i 0.886838 0.462081i \(-0.152897\pi\)
−0.843593 + 0.536983i \(0.819564\pi\)
\(44\) 168.761i 0.578221i
\(45\) −239.079 + 375.884i −0.791994 + 1.24519i
\(46\) −341.096 −1.09330
\(47\) 61.6110 + 106.713i 0.191210 + 0.331186i 0.945652 0.325181i \(-0.105425\pi\)
−0.754441 + 0.656368i \(0.772092\pi\)
\(48\) 72.8751 40.0153i 0.219138 0.120327i
\(49\) 263.870 219.139i 0.769300 0.638888i
\(50\) 254.990 + 147.218i 0.721220 + 0.416397i
\(51\) 7.28305 339.460i 0.0199967 0.932036i
\(52\) −158.339 + 91.4169i −0.422262 + 0.243793i
\(53\) 400.837i 1.03885i −0.854515 0.519427i \(-0.826146\pi\)
0.854515 0.519427i \(-0.173854\pi\)
\(54\) 124.378 + 251.519i 0.313440 + 0.633842i
\(55\) 696.100i 1.70658i
\(56\) −50.3207 139.355i −0.120078 0.332538i
\(57\) 840.514 + 18.0331i 1.95314 + 0.0419043i
\(58\) 198.446 343.719i 0.449264 0.778148i
\(59\) 114.190 197.783i 0.251971 0.436426i −0.712098 0.702080i \(-0.752255\pi\)
0.964068 + 0.265655i \(0.0855881\pi\)
\(60\) 300.592 165.053i 0.646772 0.355138i
\(61\) −212.887 + 122.910i −0.446842 + 0.257984i −0.706496 0.707718i \(-0.749725\pi\)
0.259654 + 0.965702i \(0.416392\pi\)
\(62\) 111.957 0.229332
\(63\) 477.175 149.504i 0.954260 0.298979i
\(64\) −64.0000 −0.125000
\(65\) −653.109 + 377.073i −1.24628 + 0.719540i
\(66\) 374.923 + 227.322i 0.699241 + 0.423960i
\(67\) −466.625 + 808.218i −0.850856 + 1.47373i 0.0295817 + 0.999562i \(0.490582\pi\)
−0.880437 + 0.474163i \(0.842751\pi\)
\(68\) −130.688 + 226.358i −0.233063 + 0.403676i
\(69\) −459.457 + 757.786i −0.801625 + 1.32213i
\(70\) −207.561 574.806i −0.354403 0.981464i
\(71\) 808.476i 1.35139i 0.737183 + 0.675693i \(0.236156\pi\)
−0.737183 + 0.675693i \(0.763844\pi\)
\(72\) 9.26423 215.801i 0.0151639 0.353228i
\(73\) 98.0777i 0.157248i −0.996904 0.0786241i \(-0.974947\pi\)
0.996904 0.0786241i \(-0.0250527\pi\)
\(74\) 231.498 133.655i 0.363663 0.209961i
\(75\) 670.535 368.186i 1.03236 0.566860i
\(76\) −560.472 323.589i −0.845928 0.488397i
\(77\) 503.777 597.291i 0.745594 0.883996i
\(78\) −10.1891 + 474.907i −0.0147908 + 0.689392i
\(79\) −450.095 779.587i −0.641008 1.11026i −0.985208 0.171362i \(-0.945183\pi\)
0.344200 0.938896i \(-0.388150\pi\)
\(80\) −263.985 −0.368930
\(81\) 726.318 + 62.4760i 0.996321 + 0.0857009i
\(82\) 36.9384i 0.0497459i
\(83\) 605.681 + 1049.07i 0.800989 + 1.38735i 0.918966 + 0.394338i \(0.129026\pi\)
−0.117976 + 0.993016i \(0.537641\pi\)
\(84\) −377.376 75.9182i −0.490179 0.0986114i
\(85\) −539.057 + 933.674i −0.687870 + 1.19143i
\(86\) −42.2405 24.3875i −0.0529640 0.0305788i
\(87\) −496.305 903.863i −0.611604 1.11384i
\(88\) −168.761 292.303i −0.204432 0.354087i
\(89\) −678.302 −0.807864 −0.403932 0.914789i \(-0.632357\pi\)
−0.403932 + 0.914789i \(0.632357\pi\)
\(90\) 38.2127 890.128i 0.0447553 1.04253i
\(91\) 833.296 + 149.116i 0.959924 + 0.171775i
\(92\) 590.796 341.096i 0.669508 0.386541i
\(93\) 150.807 248.726i 0.168150 0.277330i
\(94\) −213.427 123.222i −0.234184 0.135206i
\(95\) −2311.81 1334.73i −2.49670 1.44147i
\(96\) −86.2081 + 142.184i −0.0916518 + 0.151162i
\(97\) 749.281 432.598i 0.784309 0.452821i −0.0536461 0.998560i \(-0.517084\pi\)
0.837955 + 0.545739i \(0.183751\pi\)
\(98\) −237.897 + 643.429i −0.245217 + 0.663226i
\(99\) 1010.04 526.734i 1.02539 0.534735i
\(100\) −588.874 −0.588874
\(101\) −85.8176 148.640i −0.0845463 0.146438i 0.820652 0.571429i \(-0.193611\pi\)
−0.905198 + 0.424991i \(0.860277\pi\)
\(102\) 326.845 + 595.244i 0.317279 + 0.577823i
\(103\) −480.335 277.322i −0.459503 0.265294i 0.252332 0.967641i \(-0.418802\pi\)
−0.711835 + 0.702346i \(0.752136\pi\)
\(104\) 182.834 316.677i 0.172388 0.298584i
\(105\) −1556.58 313.144i −1.44673 0.291045i
\(106\) 400.837 + 694.271i 0.367290 + 0.636165i
\(107\) 379.663i 0.343022i −0.985182 0.171511i \(-0.945135\pi\)
0.985182 0.171511i \(-0.0548649\pi\)
\(108\) −466.949 311.266i −0.416039 0.277330i
\(109\) −701.227 −0.616196 −0.308098 0.951355i \(-0.599693\pi\)
−0.308098 + 0.951355i \(0.599693\pi\)
\(110\) −696.100 1205.68i −0.603369 1.04507i
\(111\) 14.8968 694.333i 0.0127382 0.593722i
\(112\) 226.513 + 191.049i 0.191102 + 0.161183i
\(113\) 844.466 + 487.553i 0.703015 + 0.405886i 0.808469 0.588538i \(-0.200296\pi\)
−0.105454 + 0.994424i \(0.533630\pi\)
\(114\) −1473.85 + 809.280i −1.21086 + 0.664877i
\(115\) 2436.89 1406.94i 1.97601 1.14085i
\(116\) 793.786i 0.635355i
\(117\) 1041.34 + 662.336i 0.822835 + 0.523359i
\(118\) 456.760i 0.356340i
\(119\) 1138.25 411.019i 0.876836 0.316623i
\(120\) −355.588 + 586.473i −0.270505 + 0.446145i
\(121\) 224.513 388.867i 0.168680 0.292162i
\(122\) 245.820 425.774i 0.182422 0.315965i
\(123\) −82.0631 49.7561i −0.0601575 0.0364745i
\(124\) −193.916 + 111.957i −0.140437 + 0.0810811i
\(125\) −366.583 −0.262305
\(126\) −676.987 + 736.123i −0.478657 + 0.520468i
\(127\) 1119.91 0.782490 0.391245 0.920286i \(-0.372044\pi\)
0.391245 + 0.920286i \(0.372044\pi\)
\(128\) 110.851 64.0000i 0.0765466 0.0441942i
\(129\) −111.078 + 60.9921i −0.0758128 + 0.0416284i
\(130\) 754.146 1306.22i 0.508792 0.881253i
\(131\) −810.040 + 1403.03i −0.540256 + 0.935751i 0.458633 + 0.888626i \(0.348339\pi\)
−0.998889 + 0.0471250i \(0.984994\pi\)
\(132\) −876.708 18.8096i −0.578088 0.0124028i
\(133\) 1017.70 + 2818.36i 0.663502 + 1.83746i
\(134\) 1866.50i 1.20329i
\(135\) −1926.05 1283.90i −1.22791 0.818521i
\(136\) 522.752i 0.329600i
\(137\) 821.304 474.180i 0.512181 0.295708i −0.221549 0.975149i \(-0.571111\pi\)
0.733730 + 0.679442i \(0.237778\pi\)
\(138\) 38.0176 1771.98i 0.0234512 1.09305i
\(139\) −2707.36 1563.10i −1.65206 0.953814i −0.976226 0.216756i \(-0.930452\pi\)
−0.675829 0.737058i \(-0.736214\pi\)
\(140\) 934.312 + 788.033i 0.564027 + 0.475721i
\(141\) −561.238 + 308.173i −0.335211 + 0.184062i
\(142\) −808.476 1400.32i −0.477787 0.827552i
\(143\) 1928.46 1.12773
\(144\) 199.755 + 383.043i 0.115599 + 0.221668i
\(145\) 3274.18i 1.87521i
\(146\) 98.0777 + 169.875i 0.0555956 + 0.0962945i
\(147\) 1109.01 + 1395.22i 0.622240 + 0.782827i
\(148\) −267.310 + 462.995i −0.148465 + 0.257148i
\(149\) −1674.91 967.009i −0.920898 0.531681i −0.0369767 0.999316i \(-0.511773\pi\)
−0.883922 + 0.467635i \(0.845106\pi\)
\(150\) −793.214 + 1308.25i −0.431771 + 0.712122i
\(151\) 1160.63 + 2010.27i 0.625501 + 1.08340i 0.988444 + 0.151588i \(0.0484387\pi\)
−0.362943 + 0.931811i \(0.618228\pi\)
\(152\) 1294.35 0.690697
\(153\) 1762.67 + 75.6703i 0.931393 + 0.0399842i
\(154\) −275.277 + 1538.32i −0.144042 + 0.804942i
\(155\) −799.855 + 461.797i −0.414490 + 0.239306i
\(156\) −457.259 832.752i −0.234680 0.427394i
\(157\) −991.971 572.715i −0.504254 0.291131i 0.226214 0.974078i \(-0.427365\pi\)
−0.730469 + 0.682946i \(0.760698\pi\)
\(158\) 1559.17 + 900.190i 0.785071 + 0.453261i
\(159\) 2082.33 + 44.6761i 1.03861 + 0.0222833i
\(160\) 457.235 263.985i 0.225922 0.130436i
\(161\) −3109.21 556.383i −1.52199 0.272355i
\(162\) −1320.50 + 618.106i −0.640419 + 0.299772i
\(163\) 1808.95 0.869250 0.434625 0.900611i \(-0.356881\pi\)
0.434625 + 0.900611i \(0.356881\pi\)
\(164\) 36.9384 + 63.9792i 0.0175878 + 0.0304630i
\(165\) −3616.21 77.5852i −1.70619 0.0366061i
\(166\) −2098.14 1211.36i −0.981008 0.566385i
\(167\) 1152.46 1996.12i 0.534013 0.924938i −0.465197 0.885207i \(-0.654017\pi\)
0.999210 0.0397312i \(-0.0126502\pi\)
\(168\) 729.552 245.882i 0.335037 0.112918i
\(169\) −53.8688 93.3034i −0.0245192 0.0424686i
\(170\) 2156.23i 0.972795i
\(171\) −187.362 + 4364.43i −0.0837892 + 1.95179i
\(172\) 97.5502 0.0432450
\(173\) −585.924 1014.85i −0.257497 0.445998i 0.708074 0.706139i \(-0.249564\pi\)
−0.965571 + 0.260140i \(0.916231\pi\)
\(174\) 1763.49 + 1069.23i 0.768332 + 0.465852i
\(175\) 2084.18 + 1757.87i 0.900281 + 0.759330i
\(176\) 584.607 + 337.523i 0.250377 + 0.144555i
\(177\) 1014.75 + 615.256i 0.430921 + 0.261274i
\(178\) 1174.85 678.302i 0.494714 0.285623i
\(179\) 534.622i 0.223238i −0.993751 0.111619i \(-0.964396\pi\)
0.993751 0.111619i \(-0.0356036\pi\)
\(180\) 823.942 + 1579.96i 0.341183 + 0.654241i
\(181\) 238.167i 0.0978058i −0.998804 0.0489029i \(-0.984428\pi\)
0.998804 0.0489029i \(-0.0155725\pi\)
\(182\) −1592.43 + 575.020i −0.648563 + 0.234194i
\(183\) −614.786 1119.64i −0.248340 0.452273i
\(184\) −682.193 + 1181.59i −0.273326 + 0.473414i
\(185\) −1102.59 + 1909.74i −0.438185 + 0.758958i
\(186\) −12.4784 + 581.613i −0.00491915 + 0.229279i
\(187\) 2387.54 1378.44i 0.933657 0.539047i
\(188\) 492.888 0.191210
\(189\) 723.481 + 2495.56i 0.278442 + 0.960453i
\(190\) 5338.90 2.03855
\(191\) −273.555 + 157.937i −0.103632 + 0.0598321i −0.550920 0.834558i \(-0.685723\pi\)
0.447288 + 0.894390i \(0.352390\pi\)
\(192\) 7.13325 332.477i 0.00268124 0.124971i
\(193\) 680.432 1178.54i 0.253775 0.439551i −0.710787 0.703407i \(-0.751661\pi\)
0.964562 + 0.263856i \(0.0849944\pi\)
\(194\) −865.195 + 1498.56i −0.320193 + 0.554590i
\(195\) −1886.08 3434.90i −0.692642 1.26143i
\(196\) −231.379 1352.35i −0.0843219 0.492839i
\(197\) 706.051i 0.255350i −0.991816 0.127675i \(-0.959249\pi\)
0.991816 0.127675i \(-0.0407515\pi\)
\(198\) −1222.72 + 1922.37i −0.438861 + 0.689986i
\(199\) 24.9282i 0.00887998i 0.999990 + 0.00443999i \(0.00141330\pi\)
−0.999990 + 0.00443999i \(0.998587\pi\)
\(200\) 1019.96 588.874i 0.360610 0.208198i
\(201\) −4146.65 2514.18i −1.45514 0.882271i
\(202\) 297.281 + 171.635i 0.103548 + 0.0597832i
\(203\) 2369.57 2809.42i 0.819266 0.971343i
\(204\) −1161.36 704.148i −0.398584 0.241668i
\(205\) 152.362 + 263.899i 0.0519094 + 0.0899098i
\(206\) 1109.29 0.375183
\(207\) −3885.45 2471.32i −1.30463 0.829800i
\(208\) 731.335i 0.243793i
\(209\) 3413.08 + 5911.63i 1.12961 + 1.95653i
\(210\) 3009.23 1014.20i 0.988840 0.333270i
\(211\) 1612.49 2792.92i 0.526107 0.911243i −0.473431 0.880831i \(-0.656985\pi\)
0.999537 0.0304125i \(-0.00968208\pi\)
\(212\) −1388.54 801.675i −0.449837 0.259713i
\(213\) −4200.00 90.1103i −1.35108 0.0289871i
\(214\) 379.663 + 657.595i 0.121277 + 0.210057i
\(215\) 402.371 0.127635
\(216\) 1120.05 + 72.1798i 0.352822 + 0.0227371i
\(217\) 1020.53 + 182.620i 0.319253 + 0.0571293i
\(218\) 1214.56 701.227i 0.377342 0.217858i
\(219\) 509.509 + 10.9314i 0.157212 + 0.00337296i
\(220\) 2411.36 + 1392.20i 0.738973 + 0.426646i
\(221\) 2586.62 + 1493.39i 0.787308 + 0.454553i
\(222\) 668.531 + 1217.52i 0.202112 + 0.368083i
\(223\) −3385.12 + 1954.40i −1.01652 + 0.586890i −0.913095 0.407747i \(-0.866314\pi\)
−0.103428 + 0.994637i \(0.532981\pi\)
\(224\) −583.381 104.394i −0.174013 0.0311390i
\(225\) 1837.98 + 3524.44i 0.544586 + 1.04428i
\(226\) −1950.21 −0.574009
\(227\) −943.561 1634.30i −0.275887 0.477850i 0.694471 0.719520i \(-0.255638\pi\)
−0.970359 + 0.241670i \(0.922305\pi\)
\(228\) 1743.50 2875.56i 0.506429 0.835257i
\(229\) −1330.72 768.290i −0.384001 0.221703i 0.295557 0.955325i \(-0.404495\pi\)
−0.679558 + 0.733622i \(0.737828\pi\)
\(230\) −2813.88 + 4873.78i −0.806704 + 1.39725i
\(231\) 3046.75 + 2683.67i 0.867799 + 0.764385i
\(232\) −793.786 1374.88i −0.224632 0.389074i
\(233\) 4906.62i 1.37959i −0.724007 0.689793i \(-0.757702\pi\)
0.724007 0.689793i \(-0.242298\pi\)
\(234\) −2465.99 105.863i −0.688917 0.0295748i
\(235\) 2033.05 0.564346
\(236\) −456.760 791.131i −0.125985 0.218213i
\(237\) 4100.09 2251.33i 1.12375 0.617046i
\(238\) −1560.49 + 1850.16i −0.425007 + 0.503899i
\(239\) −2270.06 1310.62i −0.614384 0.354715i 0.160295 0.987069i \(-0.448755\pi\)
−0.774679 + 0.632354i \(0.782089\pi\)
\(240\) 29.4229 1371.39i 0.00791351 0.368845i
\(241\) 3017.49 1742.15i 0.806530 0.465650i −0.0392193 0.999231i \(-0.512487\pi\)
0.845749 + 0.533580i \(0.179154\pi\)
\(242\) 898.051i 0.238549i
\(243\) −405.513 + 3766.23i −0.107052 + 0.994253i
\(244\) 983.282i 0.257984i
\(245\) −954.384 5578.12i −0.248871 1.45458i
\(246\) 191.894 + 4.11704i 0.0497345 + 0.00106705i
\(247\) −3697.68 + 6404.58i −0.952542 + 1.64985i
\(248\) 223.914 387.831i 0.0573330 0.0993037i
\(249\) −5517.38 + 3029.56i −1.40422 + 0.771046i
\(250\) 634.940 366.583i 0.160628 0.0927389i
\(251\) −2998.70 −0.754089 −0.377045 0.926195i \(-0.623060\pi\)
−0.377045 + 0.926195i \(0.623060\pi\)
\(252\) 436.453 1951.99i 0.109103 0.487951i
\(253\) −7195.49 −1.78805
\(254\) −1939.75 + 1119.91i −0.479176 + 0.276652i
\(255\) −4790.32 2904.44i −1.17640 0.713268i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −9.14903 + 15.8466i −0.00222063 + 0.00384624i −0.867134 0.498076i \(-0.834040\pi\)
0.864913 + 0.501922i \(0.167374\pi\)
\(258\) 131.400 216.719i 0.0317078 0.0522959i
\(259\) 2328.19 840.702i 0.558559 0.201694i
\(260\) 3016.58i 0.719540i
\(261\) 4750.84 2477.54i 1.12670 0.587571i
\(262\) 3240.16i 0.764037i
\(263\) −5374.18 + 3102.78i −1.26002 + 0.727475i −0.973079 0.230473i \(-0.925973\pi\)
−0.286944 + 0.957947i \(0.592639\pi\)
\(264\) 1537.31 844.129i 0.358390 0.196790i
\(265\) −5727.40 3306.72i −1.32767 0.766528i
\(266\) −4581.06 3863.84i −1.05595 0.890628i
\(267\) 75.6015 3523.75i 0.0173286 0.807678i
\(268\) 1866.50 + 3232.87i 0.425428 + 0.736863i
\(269\) 330.596 0.0749323 0.0374661 0.999298i \(-0.488071\pi\)
0.0374661 + 0.999298i \(0.488071\pi\)
\(270\) 4619.92 + 297.724i 1.04133 + 0.0671072i
\(271\) 1365.01i 0.305971i 0.988228 + 0.152986i \(0.0488888\pi\)
−0.988228 + 0.152986i \(0.951111\pi\)
\(272\) 522.752 + 905.434i 0.116531 + 0.201838i
\(273\) −867.526 + 4312.31i −0.192326 + 0.956019i
\(274\) −948.361 + 1642.61i −0.209097 + 0.362167i
\(275\) 5379.05 + 3105.60i 1.17952 + 0.680999i
\(276\) 1706.13 + 3107.18i 0.372091 + 0.677645i
\(277\) −2448.77 4241.40i −0.531165 0.920004i −0.999338 0.0363677i \(-0.988421\pi\)
0.468174 0.883636i \(-0.344912\pi\)
\(278\) 6252.39 1.34890
\(279\) 1275.31 + 811.156i 0.273660 + 0.174060i
\(280\) −2406.31 430.601i −0.513587 0.0919048i
\(281\) 2204.08 1272.53i 0.467917 0.270152i −0.247450 0.968901i \(-0.579593\pi\)
0.715367 + 0.698749i \(0.246259\pi\)
\(282\) 663.921 1095.01i 0.140198 0.231230i
\(283\) 540.515 + 312.067i 0.113535 + 0.0655492i 0.555692 0.831388i \(-0.312453\pi\)
−0.442157 + 0.896937i \(0.645787\pi\)
\(284\) 2800.64 + 1616.95i 0.585168 + 0.337847i
\(285\) 7191.51 11861.0i 1.49470 2.46521i
\(286\) −3340.18 + 1928.46i −0.690591 + 0.398713i
\(287\) 60.2525 336.706i 0.0123923 0.0692513i
\(288\) −729.029 463.695i −0.149161 0.0948732i
\(289\) −643.156 −0.130909
\(290\) −3274.18 5671.04i −0.662987 1.14833i
\(291\) 2163.81 + 3940.70i 0.435894 + 0.793842i
\(292\) −339.751 196.155i −0.0680905 0.0393121i
\(293\) −845.058 + 1463.68i −0.168494 + 0.291841i −0.937891 0.346931i \(-0.887224\pi\)
0.769396 + 0.638772i \(0.220557\pi\)
\(294\) −3316.07 1307.58i −0.657814 0.259386i
\(295\) −1884.02 3263.23i −0.371838 0.644042i
\(296\) 1069.24i 0.209961i
\(297\) 2623.78 + 5305.85i 0.512617 + 1.03662i
\(298\) 3868.04 0.751910
\(299\) −3897.75 6751.09i −0.753888 1.30577i
\(300\) 65.6341 3059.17i 0.0126313 0.588738i
\(301\) −345.256 291.202i −0.0661137 0.0557627i
\(302\) −4020.54 2321.26i −0.766079 0.442296i
\(303\) 781.746 429.252i 0.148218 0.0813857i
\(304\) −2241.89 + 1294.35i −0.422964 + 0.244198i
\(305\) 4055.80i 0.761425i
\(306\) −3128.70 + 1631.60i −0.584496 + 0.304812i
\(307\) 6791.33i 1.26255i −0.775561 0.631273i \(-0.782533\pi\)
0.775561 0.631273i \(-0.217467\pi\)
\(308\) −1061.52 2939.72i −0.196383 0.543851i
\(309\) 1494.21 2464.41i 0.275089 0.453707i
\(310\) 923.594 1599.71i 0.169215 0.293089i
\(311\) 2070.08 3585.49i 0.377440 0.653744i −0.613249 0.789889i \(-0.710138\pi\)
0.990689 + 0.136145i \(0.0434713\pi\)
\(312\) 1624.75 + 985.110i 0.294818 + 0.178753i
\(313\) −6079.07 + 3509.75i −1.09779 + 0.633811i −0.935641 0.352954i \(-0.885177\pi\)
−0.162153 + 0.986766i \(0.551844\pi\)
\(314\) 2290.86 0.411722
\(315\) 1800.26 8051.49i 0.322011 1.44016i
\(316\) −3600.76 −0.641008
\(317\) 4218.89 2435.78i 0.747497 0.431567i −0.0772920 0.997008i \(-0.524627\pi\)
0.824789 + 0.565441i \(0.191294\pi\)
\(318\) −3651.38 + 2004.95i −0.643897 + 0.353560i
\(319\) 4186.26 7250.82i 0.734751 1.27263i
\(320\) −527.969 + 914.470i −0.0922325 + 0.159751i
\(321\) 1972.33 + 42.3160i 0.342943 + 0.00735779i
\(322\) 5941.69 2145.52i 1.02831 0.371321i
\(323\) 10572.3i 1.82123i
\(324\) 1669.06 2391.09i 0.286190 0.409994i
\(325\) 6729.13i 1.14851i
\(326\) −3133.19 + 1808.95i −0.532305 + 0.307326i
\(327\) 78.1567 3642.85i 0.0132174 0.616054i
\(328\) −127.958 73.8768i −0.0215406 0.0124365i
\(329\) −1744.46 1471.34i −0.292326 0.246559i
\(330\) 6341.05 3481.83i 1.05777 0.580813i
\(331\) −3117.40 5399.50i −0.517667 0.896626i −0.999789 0.0205218i \(-0.993467\pi\)
0.482122 0.876104i \(-0.339866\pi\)
\(332\) 4845.45 0.800989
\(333\) 3605.37 + 154.777i 0.593312 + 0.0254706i
\(334\) 4609.85i 0.755209i
\(335\) 7698.87 + 13334.8i 1.25562 + 2.17480i
\(336\) −1017.74 + 1155.43i −0.165245 + 0.187601i
\(337\) −1295.87 + 2244.51i −0.209467 + 0.362808i −0.951547 0.307504i \(-0.900506\pi\)
0.742080 + 0.670312i \(0.233840\pi\)
\(338\) 186.607 + 107.738i 0.0300298 + 0.0173377i
\(339\) −2626.94 + 4332.62i −0.420872 + 0.694147i
\(340\) 2156.23 + 3734.70i 0.343935 + 0.595713i
\(341\) 2361.76 0.375063
\(342\) −4039.90 7746.77i −0.638752 1.22485i
\(343\) −3218.05 + 5477.02i −0.506584 + 0.862191i
\(344\) −168.962 + 97.5502i −0.0264820 + 0.0152894i
\(345\) 7037.39 + 12816.4i 1.09820 + 2.00003i
\(346\) 2029.70 + 1171.85i 0.315368 + 0.182078i
\(347\) −552.196 318.811i −0.0854278 0.0493218i 0.456678 0.889632i \(-0.349039\pi\)
−0.542105 + 0.840311i \(0.682373\pi\)
\(348\) −4123.68 88.4730i −0.635209 0.0136283i
\(349\) −2436.50 + 1406.71i −0.373704 + 0.215758i −0.675076 0.737749i \(-0.735889\pi\)
0.301371 + 0.953507i \(0.402556\pi\)
\(350\) −5367.78 960.547i −0.819771 0.146695i
\(351\) −3556.87 + 5335.88i −0.540889 + 0.811419i
\(352\) −1350.09 −0.204432
\(353\) 920.770 + 1594.82i 0.138832 + 0.240464i 0.927055 0.374926i \(-0.122332\pi\)
−0.788223 + 0.615390i \(0.788999\pi\)
\(354\) −2372.85 50.9090i −0.356258 0.00764346i
\(355\) 11552.0 + 6669.54i 1.72709 + 0.997134i
\(356\) −1356.60 + 2349.71i −0.201966 + 0.349815i
\(357\) 2008.36 + 5958.99i 0.297742 + 0.883426i
\(358\) 534.622 + 925.993i 0.0789264 + 0.136705i
\(359\) 13045.6i 1.91789i 0.283599 + 0.958943i \(0.408471\pi\)
−0.283599 + 0.958943i \(0.591529\pi\)
\(360\) −3007.07 1912.63i −0.440240 0.280012i
\(361\) −19318.4 −2.81650
\(362\) 238.167 + 412.518i 0.0345796 + 0.0598936i
\(363\) 1995.13 + 1209.68i 0.288476 + 0.174908i
\(364\) 2183.14 2588.39i 0.314362 0.372716i
\(365\) −1401.39 809.094i −0.200965 0.116027i
\(366\) 2184.48 + 1324.48i 0.311979 + 0.189158i
\(367\) 6006.43 3467.82i 0.854314 0.493238i −0.00779004 0.999970i \(-0.502480\pi\)
0.862104 + 0.506731i \(0.169146\pi\)
\(368\) 2728.77i 0.386541i
\(369\) 267.627 420.768i 0.0377564 0.0593613i
\(370\) 4410.37i 0.619687i
\(371\) 2521.30 + 6982.34i 0.352828 + 0.977102i
\(372\) −560.000 1019.86i −0.0780501 0.142143i
\(373\) 5686.57 9849.43i 0.789382 1.36725i −0.136964 0.990576i \(-0.543735\pi\)
0.926346 0.376674i \(-0.122932\pi\)
\(374\) −2756.89 + 4775.07i −0.381164 + 0.660195i
\(375\) 40.8582 1904.38i 0.00562642 0.262245i
\(376\) −853.707 + 492.888i −0.117092 + 0.0676031i
\(377\) 9070.68 1.23916
\(378\) −3748.67 3598.96i −0.510082 0.489711i
\(379\) 9779.96 1.32549 0.662747 0.748843i \(-0.269390\pi\)
0.662747 + 0.748843i \(0.269390\pi\)
\(380\) −9247.25 + 5338.90i −1.24835 + 0.720737i
\(381\) −124.822 + 5817.90i −0.0167843 + 0.782310i
\(382\) 315.874 547.111i 0.0423077 0.0732791i
\(383\) −4830.39 + 8366.47i −0.644442 + 1.11621i 0.339988 + 0.940430i \(0.389577\pi\)
−0.984430 + 0.175776i \(0.943756\pi\)
\(384\) 320.122 + 583.001i 0.0425421 + 0.0774769i
\(385\) −4378.53 12125.6i −0.579612 1.60514i
\(386\) 2721.73i 0.358892i
\(387\) −304.471 583.842i −0.0399926 0.0766883i
\(388\) 3460.78i 0.452821i
\(389\) 5033.86 2906.30i 0.656110 0.378805i −0.134683 0.990889i \(-0.543002\pi\)
0.790793 + 0.612083i \(0.209668\pi\)
\(390\) 6701.69 + 4063.34i 0.870137 + 0.527578i
\(391\) −9651.25 5572.15i −1.24830 0.720706i
\(392\) 1753.11 + 2110.96i 0.225881 + 0.271988i
\(393\) −7198.40 4364.50i −0.923947 0.560203i
\(394\) 706.051 + 1222.92i 0.0902800 + 0.156370i
\(395\) −14852.3 −1.89190
\(396\) 195.430 4552.36i 0.0247999 0.577689i
\(397\) 6603.43i 0.834803i −0.908722 0.417402i \(-0.862941\pi\)
0.908722 0.417402i \(-0.137059\pi\)
\(398\) −24.9282 43.1770i −0.00313955 0.00543786i
\(399\) −14754.7 + 4972.78i −1.85127 + 0.623936i
\(400\) −1177.75 + 2039.92i −0.147218 + 0.254990i
\(401\) 12295.6 + 7098.88i 1.53121 + 0.884042i 0.999307 + 0.0372347i \(0.0118549\pi\)
0.531899 + 0.846808i \(0.321478\pi\)
\(402\) 9696.39 + 208.034i 1.20301 + 0.0258105i
\(403\) 1279.35 + 2215.90i 0.158136 + 0.273900i
\(404\) −686.541 −0.0845463
\(405\) 6884.47 9862.66i 0.844672 1.21007i
\(406\) −1294.79 + 7235.62i −0.158274 + 0.884478i
\(407\) 4883.48 2819.48i 0.594755 0.343382i
\(408\) 2715.68 + 58.2644i 0.329525 + 0.00706990i
\(409\) 12573.0 + 7259.05i 1.52004 + 0.877597i 0.999721 + 0.0236262i \(0.00752116\pi\)
0.520321 + 0.853971i \(0.325812\pi\)
\(410\) −527.798 304.724i −0.0635758 0.0367055i
\(411\) 2371.81 + 4319.49i 0.284653 + 0.518406i
\(412\) −1921.34 + 1109.29i −0.229751 + 0.132647i
\(413\) −745.048 + 4163.52i −0.0887686 + 0.496061i
\(414\) 9201.12 + 394.999i 1.09230 + 0.0468917i
\(415\) 19986.3 2.36407
\(416\) −731.335 1266.71i −0.0861939 0.149292i
\(417\) 8421.98 13890.4i 0.989031 1.63122i
\(418\) −11823.3 6826.16i −1.38348 0.798752i
\(419\) 709.447 1228.80i 0.0827178 0.143271i −0.821699 0.569922i \(-0.806973\pi\)
0.904416 + 0.426651i \(0.140307\pi\)
\(420\) −4197.93 + 4765.88i −0.487710 + 0.553693i
\(421\) −2315.86 4011.18i −0.268095 0.464354i 0.700275 0.713873i \(-0.253061\pi\)
−0.968370 + 0.249519i \(0.919727\pi\)
\(422\) 6449.97i 0.744027i
\(423\) −1538.39 2949.96i −0.176830 0.339082i
\(424\) 3206.70 0.367290
\(425\) 4809.92 + 8331.03i 0.548978 + 0.950857i
\(426\) 7364.72 4043.92i 0.837610 0.459927i
\(427\) 2935.24 3480.10i 0.332661 0.394411i
\(428\) −1315.19 759.325i −0.148533 0.0857555i
\(429\) −214.940 + 10018.2i −0.0241897 + 1.12747i
\(430\) −696.927 + 402.371i −0.0781601 + 0.0451257i
\(431\) 7638.31i 0.853653i −0.904333 0.426827i \(-0.859631\pi\)
0.904333 0.426827i \(-0.140369\pi\)
\(432\) −2012.16 + 995.026i −0.224097 + 0.110818i
\(433\) 930.244i 0.103244i 0.998667 + 0.0516220i \(0.0164391\pi\)
−0.998667 + 0.0516220i \(0.983561\pi\)
\(434\) −1950.23 + 704.220i −0.215700 + 0.0778886i
\(435\) −17009.2 364.930i −1.87478 0.0402231i
\(436\) −1402.45 + 2429.12i −0.154049 + 0.266821i
\(437\) 13796.9 23896.9i 1.51028 2.61588i
\(438\) −893.427 + 490.575i −0.0974648 + 0.0535173i
\(439\) −14238.8 + 8220.78i −1.54802 + 0.893751i −0.549728 + 0.835343i \(0.685269\pi\)
−0.998293 + 0.0584071i \(0.981398\pi\)
\(440\) −5568.80 −0.603369
\(441\) −7371.70 + 5605.73i −0.795993 + 0.605305i
\(442\) −5973.55 −0.642834
\(443\) −6731.30 + 3886.32i −0.721927 + 0.416805i −0.815462 0.578811i \(-0.803517\pi\)
0.0935343 + 0.995616i \(0.470184\pi\)
\(444\) −2375.45 1440.27i −0.253905 0.153946i
\(445\) −5595.67 + 9691.98i −0.596090 + 1.03246i
\(446\) 3908.80 6770.25i 0.414994 0.718790i
\(447\) 5210.25 8593.30i 0.551312 0.909282i
\(448\) 1114.84 402.565i 0.117570 0.0424541i
\(449\) 12669.0i 1.33160i −0.746130 0.665800i \(-0.768090\pi\)
0.746130 0.665800i \(-0.231910\pi\)
\(450\) −6707.91 4266.52i −0.702697 0.446946i
\(451\) 779.222i 0.0813573i
\(452\) 3377.87 1950.21i 0.351508 0.202943i
\(453\) −10572.6 + 5805.36i −1.09657 + 0.602118i
\(454\) 3268.59 + 1887.12i 0.337891 + 0.195082i
\(455\) 9004.94 10676.5i 0.927820 1.10005i
\(456\) −144.265 + 6724.11i −0.0148154 + 0.690538i
\(457\) 3159.06 + 5471.65i 0.323358 + 0.560072i 0.981179 0.193102i \(-0.0618550\pi\)
−0.657821 + 0.753174i \(0.728522\pi\)
\(458\) 3073.16 0.313535
\(459\) −589.565 + 9148.54i −0.0599533 + 0.930321i
\(460\) 11255.5i 1.14085i
\(461\) −1951.76 3380.55i −0.197186 0.341535i 0.750429 0.660951i \(-0.229847\pi\)
−0.947615 + 0.319415i \(0.896513\pi\)
\(462\) −7960.81 1601.51i −0.801667 0.161275i
\(463\) −1503.35 + 2603.89i −0.150900 + 0.261367i −0.931559 0.363591i \(-0.881551\pi\)
0.780658 + 0.624958i \(0.214884\pi\)
\(464\) 2749.76 + 1587.57i 0.275117 + 0.158839i
\(465\) −2309.86 4206.68i −0.230360 0.419528i
\(466\) 4906.62 + 8498.52i 0.487757 + 0.844820i
\(467\) −5666.92 −0.561528 −0.280764 0.959777i \(-0.590588\pi\)
−0.280764 + 0.959777i \(0.590588\pi\)
\(468\) 4377.07 2282.62i 0.432330 0.225458i
\(469\) 3044.56 17013.8i 0.299754 1.67510i
\(470\) −3521.34 + 2033.05i −0.345590 + 0.199526i
\(471\) 3085.79 5089.41i 0.301881 0.497894i
\(472\) 1582.26 + 913.519i 0.154300 + 0.0890850i
\(473\) −891.070 514.460i −0.0866204 0.0500103i
\(474\) −4850.23 + 7999.51i −0.469996 + 0.775168i
\(475\) −20627.9 + 11909.5i −1.99258 + 1.15042i
\(476\) 852.693 4765.06i 0.0821074 0.458837i
\(477\) −464.181 + 10812.6i −0.0445564 + 1.03790i
\(478\) 5242.47 0.501643
\(479\) −7177.17 12431.2i −0.684621 1.18580i −0.973556 0.228450i \(-0.926634\pi\)
0.288935 0.957349i \(-0.406699\pi\)
\(480\) 1320.43 + 2404.74i 0.125560 + 0.228668i
\(481\) 5290.70 + 3054.59i 0.501528 + 0.289557i
\(482\) −3484.30 + 6034.98i −0.329265 + 0.570303i
\(483\) 3236.93 16090.2i 0.304938 1.51579i
\(484\) −898.051 1555.47i −0.0843399 0.146081i
\(485\) 14274.9i 1.33647i
\(486\) −3063.86 6928.81i −0.285966 0.646702i
\(487\) −3209.55 −0.298642 −0.149321 0.988789i \(-0.547709\pi\)
−0.149321 + 0.988789i \(0.547709\pi\)
\(488\) −983.282 1703.09i −0.0912112 0.157982i
\(489\) −201.620 + 9397.41i −0.0186453 + 0.869050i
\(490\) 7231.16 + 8707.20i 0.666674 + 0.802757i
\(491\) −11741.8 6779.15i −1.07923 0.623093i −0.148541 0.988906i \(-0.547458\pi\)
−0.930688 + 0.365813i \(0.880791\pi\)
\(492\) −336.486 + 184.763i −0.0308333 + 0.0169304i
\(493\) 11230.0 6483.65i 1.02591 0.592310i
\(494\) 14790.7i 1.34710i
\(495\) 806.104 18777.4i 0.0731953 1.70501i
\(496\) 895.658i 0.0810811i
\(497\) −5085.38 14083.2i −0.458975 1.27106i
\(498\) 6526.82 10764.7i 0.587297 0.968633i
\(499\) −8097.41 + 14025.1i −0.726432 + 1.25822i 0.231949 + 0.972728i \(0.425490\pi\)
−0.958382 + 0.285490i \(0.907844\pi\)
\(500\) −733.165 + 1269.88i −0.0655763 + 0.113581i
\(501\) 10241.3 + 6209.48i 0.913271 + 0.553730i
\(502\) 5193.90 2998.70i 0.461783 0.266611i
\(503\) 3233.66 0.286644 0.143322 0.989676i \(-0.454222\pi\)
0.143322 + 0.989676i \(0.454222\pi\)
\(504\) 1196.03 + 3817.40i 0.105705 + 0.337382i
\(505\) −2831.82 −0.249533
\(506\) 12462.9 7195.49i 1.09495 0.632171i
\(507\) 490.711 269.447i 0.0429847 0.0236027i
\(508\) 2239.83 3879.49i 0.195623 0.338828i
\(509\) −3720.92 + 6444.82i −0.324021 + 0.561221i −0.981314 0.192414i \(-0.938368\pi\)
0.657292 + 0.753636i \(0.271702\pi\)
\(510\) 11201.5 + 240.327i 0.972571 + 0.0208664i
\(511\) 616.916 + 1708.45i 0.0534066 + 0.147901i
\(512\) 512.000i 0.0441942i
\(513\) −22652.1 1459.79i −1.94954 0.125636i
\(514\) 36.5961i 0.00314044i
\(515\) −7925.07 + 4575.54i −0.678097 + 0.391500i
\(516\) −10.8726 + 506.769i −0.000927600 + 0.0432350i
\(517\) −4502.27 2599.39i −0.382998 0.221124i
\(518\) −3191.84 + 3784.33i −0.270737 + 0.320992i
\(519\) 5337.41 2930.74i 0.451419 0.247871i
\(520\) −3016.58 5224.87i −0.254396 0.440627i
\(521\) −15082.0 −1.26824 −0.634121 0.773234i \(-0.718638\pi\)
−0.634121 + 0.773234i \(0.718638\pi\)
\(522\) −5751.16 + 9042.08i −0.482225 + 0.758163i
\(523\) 16623.1i 1.38983i −0.719093 0.694913i \(-0.755443\pi\)
0.719093 0.694913i \(-0.244557\pi\)
\(524\) 3240.16 + 5612.12i 0.270128 + 0.467875i
\(525\) −9364.38 + 10631.3i −0.778467 + 0.883787i
\(526\) 6205.57 10748.4i 0.514402 0.890971i
\(527\) 3167.81 + 1828.93i 0.261844 + 0.151176i
\(528\) −1818.57 + 2999.39i −0.149893 + 0.247219i
\(529\) 8459.83 + 14652.9i 0.695310 + 1.20431i
\(530\) 13226.9 1.08403
\(531\) −3309.33 + 5202.98i −0.270457 + 0.425217i
\(532\) 11798.5 + 2111.30i 0.961520 + 0.172061i
\(533\) 731.098 422.100i 0.0594134 0.0343024i
\(534\) 3392.81 + 6178.92i 0.274946 + 0.500726i
\(535\) −5424.84 3132.04i −0.438386 0.253102i
\(536\) −6465.75 3733.00i −0.521040 0.300823i
\(537\) 2777.34 + 59.5874i 0.223186 + 0.00478843i
\(538\) −572.609 + 330.596i −0.0458865 + 0.0264926i
\(539\) −5018.48 + 13573.2i −0.401041 + 1.08468i
\(540\) −8299.66 + 4104.25i −0.661408 + 0.327072i
\(541\) 1812.75 0.144060 0.0720299 0.997402i \(-0.477052\pi\)
0.0720299 + 0.997402i \(0.477052\pi\)
\(542\) −1365.01 2364.26i −0.108177 0.187368i
\(543\) 1237.27 + 26.5454i 0.0977833 + 0.00209792i
\(544\) −1810.87 1045.50i −0.142721 0.0824001i
\(545\) −5784.79 + 10019.5i −0.454666 + 0.787505i
\(546\) −2809.72 8336.67i −0.220228 0.653437i
\(547\) 8331.58 + 14430.7i 0.651248 + 1.12800i 0.982820 + 0.184565i \(0.0590877\pi\)
−0.331572 + 0.943430i \(0.607579\pi\)
\(548\) 3793.44i 0.295708i
\(549\) 5884.99 3068.99i 0.457496 0.238582i
\(550\) −12422.4 −0.963077
\(551\) 16053.8 + 27805.9i 1.24122 + 2.14986i
\(552\) −6062.29 3675.66i −0.467442 0.283417i
\(553\) 12744.0 + 10748.8i 0.979985 + 0.826555i
\(554\) 8482.80 + 4897.55i 0.650541 + 0.375590i
\(555\) −9798.15 5940.77i −0.749384 0.454363i
\(556\) −10829.5 + 6252.39i −0.826028 + 0.476907i
\(557\) 5558.97i 0.422875i −0.977392 0.211437i \(-0.932186\pi\)
0.977392 0.211437i \(-0.0678144\pi\)
\(558\) −3020.06 129.650i −0.229121 0.00983603i
\(559\) 1114.72i 0.0843426i
\(560\) 4598.45 1660.49i 0.347000 0.125301i
\(561\) 6894.85 + 12556.8i 0.518896 + 0.945005i
\(562\) −2545.06 + 4408.17i −0.191026 + 0.330867i
\(563\) −9704.90 + 16809.4i −0.726488 + 1.25831i 0.231870 + 0.972747i \(0.425516\pi\)
−0.958359 + 0.285568i \(0.907818\pi\)
\(564\) −54.9358 + 2560.53i −0.00410144 + 0.191166i
\(565\) 13932.9 8044.16i 1.03745 0.598974i
\(566\) −1248.27 −0.0927006
\(567\) −13045.0 + 3480.31i −0.966205 + 0.257776i
\(568\) −6467.81 −0.477787
\(569\) 8339.85 4815.01i 0.614454 0.354755i −0.160252 0.987076i \(-0.551231\pi\)
0.774707 + 0.632321i \(0.217897\pi\)
\(570\) −595.058 + 27735.4i −0.0437267 + 2.03808i
\(571\) 11113.4 19249.0i 0.814504 1.41076i −0.0951799 0.995460i \(-0.530343\pi\)
0.909684 0.415302i \(-0.136324\pi\)
\(572\) 3856.91 6680.37i 0.281933 0.488322i
\(573\) −789.988 1438.71i −0.0575955 0.104892i
\(574\) 232.346 + 643.445i 0.0168953 + 0.0467889i
\(575\) 25107.8i 1.82099i
\(576\) 1726.41 + 74.1138i 0.124885 + 0.00536124i
\(577\) 13671.2i 0.986378i 0.869922 + 0.493189i \(0.164169\pi\)
−0.869922 + 0.493189i \(0.835831\pi\)
\(578\) 1113.98 643.156i 0.0801650 0.0462833i
\(579\) 6046.64 + 3666.17i 0.434007 + 0.263145i
\(580\) 11342.1 + 6548.35i 0.811990 + 0.468803i
\(581\) −17149.3 14464.4i −1.22457 1.03285i
\(582\) −7688.54 4661.68i −0.547595 0.332015i
\(583\) 8455.73 + 14645.8i 0.600687 + 1.04042i
\(584\) 784.621 0.0555956
\(585\) 18054.4 9415.28i 1.27599 0.665425i
\(586\) 3380.23i 0.238287i
\(587\) 6314.02 + 10936.2i 0.443965 + 0.768970i 0.997979 0.0635372i \(-0.0202382\pi\)
−0.554015 + 0.832507i \(0.686905\pi\)
\(588\) 7051.18 1051.28i 0.494534 0.0737311i
\(589\) −4528.51 + 7843.61i −0.316798 + 0.548710i
\(590\) 6526.45 + 3768.05i 0.455406 + 0.262929i
\(591\) 3667.90 + 78.6943i 0.255292 + 0.00547724i
\(592\) 1069.24 + 1851.98i 0.0742324 + 0.128574i
\(593\) −26058.7 −1.80456 −0.902280 0.431150i \(-0.858108\pi\)
−0.902280 + 0.431150i \(0.858108\pi\)
\(594\) −9850.37 6566.21i −0.680413 0.453561i
\(595\) 3517.15 19654.7i 0.242335 1.35423i
\(596\) −6699.63 + 3868.04i −0.460449 + 0.265840i
\(597\) −129.501 2.77843i −0.00887794 0.000190475i
\(598\) 13502.2 + 7795.49i 0.923320 + 0.533079i
\(599\) −6925.41 3998.39i −0.472395 0.272737i 0.244847 0.969562i \(-0.421262\pi\)
−0.717242 + 0.696824i \(0.754596\pi\)
\(600\) 2945.49 + 5364.28i 0.200415 + 0.364993i
\(601\) −8015.01 + 4627.47i −0.543992 + 0.314074i −0.746695 0.665166i \(-0.768361\pi\)
0.202703 + 0.979240i \(0.435027\pi\)
\(602\) 889.203 + 159.120i 0.0602013 + 0.0107728i
\(603\) 13523.2 21261.4i 0.913281 1.43588i
\(604\) 9285.03 0.625501
\(605\) −3704.25 6415.94i −0.248924 0.431149i
\(606\) −924.772 + 1525.23i −0.0619906 + 0.102241i
\(607\) 4856.01 + 2803.62i 0.324710 + 0.187472i 0.653490 0.756935i \(-0.273304\pi\)
−0.328780 + 0.944407i \(0.606637\pi\)
\(608\) 2588.71 4483.77i 0.172674 0.299081i
\(609\) 14330.7 + 12622.9i 0.953546 + 0.839913i
\(610\) −4055.80 7024.86i −0.269204 0.466276i
\(611\) 5632.29i 0.372926i
\(612\) 3787.46 5954.71i 0.250162 0.393309i
\(613\) 86.2923 0.00568566 0.00284283 0.999996i \(-0.499095\pi\)
0.00284283 + 0.999996i \(0.499095\pi\)
\(614\) 6791.33 + 11762.9i 0.446378 + 0.773149i
\(615\) −1387.93 + 762.101i −0.0910025 + 0.0499689i
\(616\) 4778.33 + 4030.22i 0.312540 + 0.263607i
\(617\) −312.162 180.227i −0.0203682 0.0117596i 0.489781 0.871845i \(-0.337077\pi\)
−0.510150 + 0.860086i \(0.670410\pi\)
\(618\) −123.638 + 5762.69i −0.00804763 + 0.375096i
\(619\) −7320.65 + 4226.58i −0.475350 + 0.274444i −0.718477 0.695551i \(-0.755160\pi\)
0.243127 + 0.969995i \(0.421827\pi\)
\(620\) 3694.37i 0.239306i
\(621\) 13271.5 19909.3i 0.857594 1.28653i
\(622\) 8280.34i 0.533780i
\(623\) 11815.6 4266.58i 0.759843 0.274377i
\(624\) −3799.25 81.5124i −0.243737 0.00522934i
\(625\) 6177.02 10698.9i 0.395329 0.684730i
\(626\) 7019.51 12158.1i 0.448172 0.776257i
\(627\) −31091.1 + 17071.9i −1.98031 + 1.08738i
\(628\) −3967.88 + 2290.86i −0.252127 + 0.145566i
\(629\) 8733.57 0.553625
\(630\) 4933.34 + 15745.8i 0.311982 + 0.995761i
\(631\) 6541.89 0.412723 0.206362 0.978476i \(-0.433838\pi\)
0.206362 + 0.978476i \(0.433838\pi\)
\(632\) 6236.70 3600.76i 0.392536 0.226631i
\(633\) 14329.4 + 8688.12i 0.899749 + 0.545532i
\(634\) −4871.55 + 8437.78i −0.305164 + 0.528560i
\(635\) 9238.75 16002.0i 0.577368 1.00003i
\(636\) 4319.43 7124.06i 0.269303 0.444162i
\(637\) −15453.4 + 2644.00i −0.961205 + 0.164457i
\(638\) 16745.1i 1.03910i
\(639\) 936.238 21808.8i 0.0579609 1.35014i
\(640\) 2111.88i 0.130436i
\(641\) 11151.5 6438.30i 0.687139 0.396720i −0.115400 0.993319i \(-0.536815\pi\)
0.802539 + 0.596599i \(0.203482\pi\)
\(642\) −3458.49 + 1899.04i −0.212610 + 0.116743i
\(643\) −3396.70 1961.09i −0.208325 0.120276i 0.392208 0.919877i \(-0.371711\pi\)
−0.600533 + 0.799600i \(0.705045\pi\)
\(644\) −8145.78 + 9657.84i −0.498430 + 0.590951i
\(645\) −44.8471 + 2090.30i −0.00273775 + 0.127605i
\(646\) −10572.3 18311.7i −0.643903 1.11527i
\(647\) 1398.46 0.0849755 0.0424877 0.999097i \(-0.486472\pi\)
0.0424877 + 0.999097i \(0.486472\pi\)
\(648\) −499.808 + 5810.54i −0.0302999 + 0.352253i
\(649\) 9635.42i 0.582779i
\(650\) −6729.13 11655.2i −0.406058 0.703314i
\(651\) −1062.45 + 5281.24i −0.0639641 + 0.317954i
\(652\) 3617.90 6266.38i 0.217313 0.376396i
\(653\) −20232.9 11681.5i −1.21252 0.700049i −0.249212 0.968449i \(-0.580172\pi\)
−0.963307 + 0.268400i \(0.913505\pi\)
\(654\) 3507.47 + 6387.75i 0.209714 + 0.381928i
\(655\) 13364.9 + 23148.7i 0.797266 + 1.38091i
\(656\) 295.507 0.0175878
\(657\) −113.577 + 2645.66i −0.00674437 + 0.157104i
\(658\) 4492.84 + 803.979i 0.266184 + 0.0476328i
\(659\) 4429.36 2557.29i 0.261826 0.151165i −0.363341 0.931656i \(-0.618364\pi\)
0.625167 + 0.780491i \(0.285031\pi\)
\(660\) −7501.19 + 12371.8i −0.442399 + 0.729651i
\(661\) 10826.3 + 6250.57i 0.637057 + 0.367805i 0.783480 0.621417i \(-0.213443\pi\)
−0.146423 + 0.989222i \(0.546776\pi\)
\(662\) 10799.0 + 6234.80i 0.634010 + 0.366046i
\(663\) −8046.38 + 13270.9i −0.471336 + 0.777377i
\(664\) −8392.56 + 4845.45i −0.490504 + 0.283192i
\(665\) 48665.9 + 8708.60i 2.83787 + 0.507827i
\(666\) −6399.46 + 3337.29i −0.372333 + 0.194170i
\(667\) −33844.7 −1.96472
\(668\) −4609.85 7984.50i −0.267007 0.462469i
\(669\) −9775.74 17803.4i −0.564950 1.02888i
\(670\) −26669.7 15397.7i −1.53782 0.887860i
\(671\) 5185.63 8981.77i 0.298344 0.516747i
\(672\) 607.346 3019.01i 0.0348644 0.173305i
\(673\) 7226.37 + 12516.4i 0.413902 + 0.716899i 0.995312 0.0967113i \(-0.0308323\pi\)
−0.581411 + 0.813610i \(0.697499\pi\)
\(674\) 5183.47i 0.296231i
\(675\) −18514.1 + 9155.39i −1.05572 + 0.522061i
\(676\) −430.950 −0.0245192
\(677\) −7473.87 12945.1i −0.424290 0.734891i 0.572064 0.820209i \(-0.306143\pi\)
−0.996354 + 0.0853175i \(0.972810\pi\)
\(678\) 217.365 10131.3i 0.0123124 0.573877i
\(679\) −10330.9 + 12248.6i −0.583896 + 0.692281i
\(680\) −7469.39 4312.46i −0.421233 0.243199i
\(681\) 8595.26 4719.61i 0.483658 0.265574i
\(682\) −4090.68 + 2361.76i −0.229678 + 0.132605i
\(683\) 31786.1i 1.78077i 0.455213 + 0.890383i \(0.349563\pi\)
−0.455213 + 0.890383i \(0.650437\pi\)
\(684\) 14744.1 + 9377.89i 0.824202 + 0.524229i
\(685\) 15647.0i 0.872763i
\(686\) 96.7988 12704.5i 0.00538746 0.707086i
\(687\) 4139.55 6827.38i 0.229889 0.379157i
\(688\) 195.100 337.924i 0.0108112 0.0187256i
\(689\) −9160.83 + 15867.0i −0.506531 + 0.877337i
\(690\) −25005.5 15161.2i −1.37963 0.836489i
\(691\) 10608.4 6124.78i 0.584029 0.337189i −0.178704 0.983903i \(-0.557191\pi\)
0.762733 + 0.646714i \(0.223857\pi\)
\(692\) −4687.40 −0.257497
\(693\) −14281.2 + 15528.6i −0.782823 + 0.851204i
\(694\) 1275.24 0.0697515
\(695\) −44668.9 + 25789.6i −2.43797 + 1.40756i
\(696\) 7230.90 3970.44i 0.393803 0.216235i
\(697\) 603.427 1045.17i 0.0327926 0.0567984i
\(698\) 2813.43 4873.00i 0.152564 0.264249i
\(699\) 25489.7 + 546.877i 1.37927 + 0.0295920i
\(700\) 10257.8 3704.06i 0.553870 0.200001i
\(701\) 35354.1i 1.90486i 0.304757 + 0.952430i \(0.401425\pi\)
−0.304757 + 0.952430i \(0.598575\pi\)
\(702\) 824.807 12798.9i 0.0443452 0.688124i
\(703\) 21624.6i 1.16016i
\(704\) 2338.43 1350.09i 0.125189 0.0722777i
\(705\) −226.597 + 10561.6i −0.0121052 + 0.564216i
\(706\) −3189.64 1841.54i −0.170034 0.0981689i
\(707\) 2429.85 + 2049.43i 0.129256 + 0.109019i
\(708\) 4160.80 2284.67i 0.220865 0.121276i
\(709\) −15616.4 27048.4i −0.827203 1.43276i −0.900224 0.435427i \(-0.856597\pi\)
0.0730207 0.997330i \(-0.476736\pi\)
\(710\) −26678.2 −1.41016
\(711\) 11238.6 + 21550.7i 0.592799 + 1.13673i
\(712\) 5426.42i 0.285623i
\(713\) −4773.52 8267.99i −0.250729 0.434276i
\(714\) −9437.57 8312.90i −0.494667 0.435718i
\(715\) 15908.8 27554.9i 0.832107 1.44125i
\(716\) −1851.99 1069.24i −0.0966647 0.0558094i
\(717\) 7061.62 11646.8i 0.367812 0.606634i
\(718\) −13045.6 22595.7i −0.678075 1.17446i
\(719\) −17546.8 −0.910132 −0.455066 0.890458i \(-0.650384\pi\)
−0.455066 + 0.890458i \(0.650384\pi\)
\(720\) 7121.03 + 305.702i 0.368590 + 0.0158234i
\(721\) 10111.5 + 1809.42i 0.522292 + 0.0934625i
\(722\) 33460.4 19318.4i 1.72475 0.995784i
\(723\) 8714.07 + 15869.9i 0.448243 + 0.816333i
\(724\) −825.036 476.335i −0.0423511 0.0244514i
\(725\) 25300.9 + 14607.5i 1.29607 + 0.748288i
\(726\) −4665.34 100.094i −0.238494 0.00511686i
\(727\) 27922.8 16121.3i 1.42449 0.822427i 0.427807 0.903870i \(-0.359286\pi\)
0.996678 + 0.0814430i \(0.0259529\pi\)
\(728\) −1192.92 + 6666.36i −0.0607318 + 0.339385i
\(729\) −19520.2 2526.40i −0.991728 0.128354i
\(730\) 3236.37 0.164087
\(731\) −796.791 1380.08i −0.0403151 0.0698279i
\(732\) −5108.11 109.594i −0.257925 0.00553374i
\(733\) 7458.32 + 4306.06i 0.375825 + 0.216982i 0.676000 0.736902i \(-0.263712\pi\)
−0.300175 + 0.953884i \(0.597045\pi\)
\(734\) −6935.63 + 12012.9i −0.348772 + 0.604091i
\(735\) 29084.4 4336.26i 1.45959 0.217613i
\(736\) 2728.77 + 4726.37i 0.136663 + 0.236707i
\(737\) 39374.1i 1.96793i
\(738\) −42.7757 + 996.420i −0.00213360 + 0.0497002i
\(739\) 20330.4 1.01200 0.505999 0.862534i \(-0.331124\pi\)
0.505999 + 0.862534i \(0.331124\pi\)
\(740\) 4410.37 + 7638.98i 0.219092 + 0.379479i
\(741\) −32859.4 19923.1i −1.62904 0.987712i
\(742\) −11349.4 9572.46i −0.561520 0.473607i
\(743\) 15779.3 + 9110.20i 0.779122 + 0.449826i 0.836119 0.548548i \(-0.184819\pi\)
−0.0569970 + 0.998374i \(0.518153\pi\)
\(744\) 1989.81 + 1206.45i 0.0980510 + 0.0594499i
\(745\) −27634.4 + 15954.7i −1.35899 + 0.784612i
\(746\) 22746.3i 1.11635i
\(747\) −15123.5 29000.2i −0.740749 1.42043i
\(748\) 11027.6i 0.539047i
\(749\) 2388.11 + 6613.49i 0.116501 + 0.322632i
\(750\) 1833.61 + 3339.34i 0.0892721 + 0.162581i
\(751\) −9944.27 + 17224.0i −0.483184 + 0.836900i −0.999814 0.0193093i \(-0.993853\pi\)
0.516629 + 0.856209i \(0.327187\pi\)
\(752\) 985.776 1707.41i 0.0478026 0.0827965i
\(753\) 334.226 15578.1i 0.0161751 0.753916i
\(754\) −15710.9 + 9070.68i −0.758828 + 0.438110i
\(755\) 38298.5 1.84613
\(756\) 10091.9 + 2484.92i 0.485499 + 0.119544i
\(757\) −18149.2 −0.871394 −0.435697 0.900093i \(-0.643498\pi\)
−0.435697 + 0.900093i \(0.643498\pi\)
\(758\) −16939.4 + 9779.96i −0.811697 + 0.468633i
\(759\) 801.987 37380.2i 0.0383535 1.78764i
\(760\) 10677.8 18494.5i 0.509638 0.882718i
\(761\) −4020.37 + 6963.48i −0.191509 + 0.331703i −0.945750 0.324894i \(-0.894671\pi\)
0.754242 + 0.656597i \(0.228005\pi\)
\(762\) −5601.71 10201.7i −0.266310 0.484999i
\(763\) 12214.9 4410.78i 0.579568 0.209280i
\(764\) 1263.50i 0.0598321i
\(765\) 15622.4 24561.8i 0.738337 1.16083i
\(766\) 19321.5i 0.911378i
\(767\) −9040.34 + 5219.44i −0.425590 + 0.245715i
\(768\) −1137.47 689.665i −0.0534438 0.0324038i
\(769\) −15453.5 8922.08i −0.724665 0.418385i 0.0918025 0.995777i \(-0.470737\pi\)
−0.816467 + 0.577392i \(0.804071\pi\)
\(770\) 19709.5 + 16623.7i 0.922442 + 0.778021i
\(771\) −81.3026 49.2950i −0.00379772 0.00230262i
\(772\) −2721.73 4714.17i −0.126888 0.219776i
\(773\) 9883.75 0.459889 0.229944 0.973204i \(-0.426146\pi\)
0.229944 + 0.973204i \(0.426146\pi\)
\(774\) 1111.20 + 706.774i 0.0516038 + 0.0328223i
\(775\) 8241.08i 0.381972i
\(776\) 3460.78 + 5994.25i 0.160096 + 0.277295i
\(777\) 4107.92 + 12188.6i 0.189666 + 0.562757i
\(778\) −5812.60 + 10067.7i −0.267856 + 0.463940i
\(779\) 2587.87 + 1494.11i 0.119024 + 0.0687188i
\(780\) −15671.0 336.219i −0.719375 0.0154341i
\(781\) −17054.9 29540.0i −0.781401 1.35343i
\(782\) 22288.6 1.01923
\(783\) 12341.2 + 24956.6i 0.563268 + 1.13905i
\(784\) −5147.43 1903.18i −0.234486 0.0866972i
\(785\) −16366.6 + 9449.25i −0.744138 + 0.429628i
\(786\) 16832.5 + 361.138i 0.763862 + 0.0163885i
\(787\) 7760.64 + 4480.61i 0.351508 + 0.202943i 0.665349 0.746532i \(-0.268283\pi\)
−0.313841 + 0.949475i \(0.601616\pi\)
\(788\) −2445.83 1412.10i −0.110570 0.0638376i
\(789\) −15519.8 28264.5i −0.700280 1.27534i
\(790\) 25724.9 14852.3i 1.15854 0.668886i
\(791\) −17776.8 3181.11i −0.799079 0.142993i
\(792\) 4213.87 + 8080.36i 0.189057 + 0.362529i
\(793\) 11236.1 0.503158
\(794\) 6603.43 + 11437.5i 0.295147 + 0.511210i
\(795\) 17816.6 29385.0i 0.794830 1.31092i
\(796\) 86.3540 + 49.8565i 0.00384514 + 0.00222000i
\(797\) −15480.1 + 26812.3i −0.687995 + 1.19164i 0.284491 + 0.958679i \(0.408176\pi\)
−0.972486 + 0.232963i \(0.925158\pi\)
\(798\) 20583.1 23367.8i 0.913073 1.03660i
\(799\) −4025.91 6973.08i −0.178256 0.308748i
\(800\) 4710.99i 0.208198i
\(801\) 18297.3 + 785.493i 0.807121 + 0.0346492i
\(802\) −28395.5 −1.25022
\(803\) 2068.97 + 3583.55i 0.0909243 + 0.157485i
\(804\) −17002.7 + 9336.06i −0.745818 + 0.409524i
\(805\) −33599.4 + 39836.3i −1.47108 + 1.74415i
\(806\) −4431.79 2558.70i −0.193676 0.111819i
\(807\) −36.8472 + 1717.43i −0.00160729 + 0.0749151i
\(808\) 1189.12 686.541i 0.0517738 0.0298916i
\(809\) 11260.0i 0.489345i 0.969606 + 0.244673i \(0.0786805\pi\)
−0.969606 + 0.244673i \(0.921320\pi\)
\(810\) −2061.59 + 23967.1i −0.0894282 + 1.03965i
\(811\) 26285.2i 1.13810i 0.822304 + 0.569049i \(0.192688\pi\)
−0.822304 + 0.569049i \(0.807312\pi\)
\(812\) −4992.98 13827.3i −0.215787 0.597588i
\(813\) −7091.15 152.139i −0.305901 0.00656305i
\(814\) −5638.96 + 9766.96i −0.242808 + 0.420555i
\(815\) 14923.0 25847.3i 0.641385 1.11091i
\(816\) −4761.95 + 2614.76i −0.204291 + 0.112175i
\(817\) 3417.13 1972.88i 0.146328 0.0844828i
\(818\) −29036.2 −1.24111
\(819\) −22305.6 4987.40i −0.951674 0.212788i
\(820\) 1218.90 0.0519094
\(821\) −25195.4 + 14546.6i −1.07104 + 0.618367i −0.928466 0.371417i \(-0.878872\pi\)
−0.142576 + 0.989784i \(0.545539\pi\)
\(822\) −8427.58 5109.77i −0.357598 0.216817i
\(823\) 21484.0 37211.4i 0.909946 1.57607i 0.0958090 0.995400i \(-0.469456\pi\)
0.814137 0.580673i \(-0.197210\pi\)
\(824\) 2218.57 3842.68i 0.0937957 0.162459i
\(825\) −16733.0 + 27597.8i −0.706143 + 1.16465i
\(826\) −2873.06 7956.47i −0.121025 0.335159i
\(827\) 18283.1i 0.768762i 0.923175 + 0.384381i \(0.125585\pi\)
−0.923175 + 0.384381i \(0.874415\pi\)
\(828\) −16331.8 + 8516.97i −0.685471 + 0.357470i
\(829\) 28273.8i 1.18455i −0.805737 0.592273i \(-0.798231\pi\)
0.805737 0.592273i \(-0.201769\pi\)
\(830\) −34617.3 + 19986.3i −1.44769 + 0.835825i
\(831\) 22306.8 12248.5i 0.931186 0.511308i
\(832\) 2533.42 + 1462.67i 0.105566 + 0.0609483i
\(833\) −17242.3 + 14319.4i −0.717180 + 0.595604i
\(834\) −696.872 + 32480.9i −0.0289337 + 1.34859i
\(835\) −19014.5 32934.1i −0.788054 1.36495i
\(836\) 27304.6 1.12961
\(837\) −4356.06 + 6534.79i −0.179890 + 0.269863i
\(838\) 2837.79i 0.116981i
\(839\) −22654.6 39238.8i −0.932208 1.61463i −0.779539 0.626354i \(-0.784547\pi\)
−0.152669 0.988277i \(-0.548787\pi\)
\(840\) 2505.15 12452.7i 0.102900 0.511498i
\(841\) 7496.00 12983.5i 0.307352 0.532349i
\(842\) 8022.36 + 4631.71i 0.328348 + 0.189572i
\(843\) 6365.07 + 11592.0i 0.260053 + 0.473604i
\(844\) −6449.97 11171.7i −0.263053 0.455622i
\(845\) −1777.57 −0.0723670
\(846\) 5614.53 + 3571.09i 0.228169 + 0.145126i
\(847\) −1464.86 + 8186.03i −0.0594254 + 0.332084i
\(848\) −5554.16 + 3206.70i −0.224918 + 0.129857i
\(849\) −1681.42 + 2773.17i −0.0679694 + 0.112102i
\(850\) −16662.1 9619.85i −0.672358 0.388186i
\(851\) −19740.7 11397.3i −0.795187 0.459101i
\(852\) −8712.15 + 14369.0i −0.350321 + 0.577786i
\(853\) −9129.40 + 5270.86i −0.366453 + 0.211572i −0.671908 0.740635i \(-0.734525\pi\)
0.305454 + 0.952207i \(0.401192\pi\)
\(854\) −1603.89 + 8962.94i −0.0642670 + 0.359140i
\(855\) 60815.8 + 38681.6i 2.43258 + 1.54723i
\(856\) 3037.30 0.121277
\(857\) −3669.34 6355.49i −0.146257 0.253325i 0.783584 0.621286i \(-0.213389\pi\)
−0.929841 + 0.367961i \(0.880056\pi\)
\(858\) −9645.96 17567.0i −0.383808 0.698985i
\(859\) 18600.0 + 10738.7i 0.738796 + 0.426544i 0.821631 0.570019i \(-0.193064\pi\)
−0.0828357 + 0.996563i \(0.526398\pi\)
\(860\) 804.742 1393.85i 0.0319087 0.0552675i
\(861\) 1742.46 + 350.537i 0.0689696 + 0.0138749i
\(862\) 7638.31 + 13229.9i 0.301812 + 0.522754i
\(863\) 1403.26i 0.0553507i 0.999617 + 0.0276754i \(0.00881047\pi\)
−0.999617 + 0.0276754i \(0.991190\pi\)
\(864\) 2490.13 3735.59i 0.0980508 0.147092i
\(865\) −19334.4 −0.759987
\(866\) −930.244 1611.23i −0.0365023 0.0632238i
\(867\) 71.6842 3341.17i 0.00280798 0.130879i
\(868\) 2673.67 3169.97i 0.104551 0.123958i
\(869\) 32891.1 + 18989.7i 1.28395 + 0.741289i
\(870\) 29825.7 16377.1i 1.16228 0.638203i
\(871\) 36942.4 21328.7i 1.43714 0.829731i
\(872\) 5609.82i 0.217858i
\(873\) −20712.9 + 10801.7i −0.803009 + 0.418765i
\(874\) 55187.4i 2.13586i
\(875\) 6385.64 2305.83i 0.246713 0.0890874i
\(876\) 1056.89 1743.13i 0.0407635 0.0672316i
\(877\) −13024.4 + 22559.0i −0.501487 + 0.868600i 0.498512 + 0.866883i \(0.333880\pi\)
−0.999999 + 0.00171749i \(0.999453\pi\)
\(878\) 16441.6 28477.6i 0.631977 1.09462i
\(879\) −7509.58 4553.18i −0.288159 0.174715i
\(880\) 9645.45 5568.80i 0.369486 0.213323i
\(881\) 25474.5 0.974187 0.487093 0.873350i \(-0.338057\pi\)
0.487093 + 0.873350i \(0.338057\pi\)
\(882\) 7162.42 17081.1i 0.273437 0.652098i
\(883\) 16202.6 0.617508 0.308754 0.951142i \(-0.400088\pi\)
0.308754 + 0.951142i \(0.400088\pi\)
\(884\) 10346.5 5973.55i 0.393654 0.227276i
\(885\) 17162.3 9423.72i 0.651870 0.357938i
\(886\) 7772.64 13462.6i 0.294726 0.510480i
\(887\) −9778.12 + 16936.2i −0.370144 + 0.641107i −0.989587 0.143934i \(-0.954025\pi\)
0.619444 + 0.785041i \(0.287358\pi\)
\(888\) 5554.66 + 119.174i 0.209913 + 0.00450364i
\(889\) −19508.2 + 7044.35i −0.735978 + 0.265759i
\(890\) 22382.7i 0.842999i
\(891\) −27856.1 + 13039.1i −1.04738 + 0.490264i
\(892\) 15635.2i 0.586890i
\(893\) 17265.6 9968.31i 0.647001 0.373546i
\(894\) −431.119 + 20094.3i −0.0161284 + 0.751737i
\(895\) −7639.00 4410.38i −0.285300 0.164718i
\(896\) −1528.40 + 1812.10i −0.0569867 + 0.0675649i
\(897\) 35506.1 19496.2i 1.32164 0.725706i
\(898\) 12669.0 + 21943.4i 0.470792 + 0.815435i
\(899\) 11108.8 0.412122
\(900\) 15885.0 + 681.932i 0.588332 + 0.0252568i
\(901\) 26192.3i 0.968472i
\(902\) 779.222 + 1349.65i 0.0287642 + 0.0498210i
\(903\) 1551.26 1761.13i 0.0571680 0.0649024i
\(904\) −3900.42 + 6755.73i −0.143502 + 0.248553i
\(905\) −3403.08 1964.77i −0.124997 0.0721669i
\(906\) 12507.0 20627.8i 0.458626 0.756416i
\(907\) 17714.3 + 30682.1i 0.648504 + 1.12324i 0.983480 + 0.181016i \(0.0579385\pi\)
−0.334976 + 0.942227i \(0.608728\pi\)
\(908\) −7548.49 −0.275887
\(909\) 2142.81 + 4108.98i 0.0781877 + 0.149930i
\(910\) −4920.53 + 27497.2i −0.179246 + 1.00167i
\(911\) −8301.17 + 4792.68i −0.301899 + 0.174301i −0.643296 0.765618i \(-0.722433\pi\)
0.341397 + 0.939919i \(0.389100\pi\)
\(912\) −6474.24 11790.8i −0.235070 0.428105i
\(913\) −44260.6 25553.9i −1.60440 0.926298i
\(914\) −10943.3 6318.11i −0.396031 0.228648i
\(915\) −21069.7 452.047i −0.761250 0.0163325i
\(916\) −5322.87 + 3073.16i −0.192000 + 0.110852i
\(917\) 5285.22 29535.1i 0.190331 1.06362i
\(918\) −8127.38 16435.3i −0.292204 0.590899i
\(919\) −49145.6 −1.76405 −0.882026 0.471202i \(-0.843820\pi\)
−0.882026 + 0.471202i \(0.843820\pi\)
\(920\) 11255.5 + 19495.1i 0.403352 + 0.698626i
\(921\) 35280.7 + 756.941i 1.26226 + 0.0270815i
\(922\) 6761.10 + 3903.52i 0.241502 + 0.139431i
\(923\) 18477.1 32003.3i 0.658918 1.14128i
\(924\) 15390.0 5186.91i 0.547938 0.184672i
\(925\) 9838.25 + 17040.4i 0.349708 + 0.605712i
\(926\) 6013.42i 0.213405i
\(927\) 12636.0 + 8037.03i 0.447702 + 0.284758i
\(928\) −6350.29 −0.224632
\(929\) 1073.78 + 1859.84i 0.0379220 + 0.0656828i 0.884363 0.466799i \(-0.154593\pi\)
−0.846441 + 0.532482i \(0.821260\pi\)
\(930\) 8207.49 + 4976.33i 0.289392 + 0.175463i
\(931\) −35455.4 42692.6i −1.24812 1.50289i
\(932\) −16997.0 9813.24i −0.597378 0.344896i
\(933\) 18395.7 + 11153.6i 0.645498 + 0.391375i
\(934\) 9815.39 5666.92i 0.343864 0.198530i
\(935\) 45486.0i 1.59096i
\(936\) −5298.69 + 8330.70i −0.185035 + 0.290916i
\(937\) 304.033i 0.0106001i −0.999986 0.00530007i \(-0.998313\pi\)
0.999986 0.00530007i \(-0.00168707\pi\)
\(938\) 11740.4 + 32513.3i 0.408677 + 1.13177i
\(939\) −17555.5 31971.7i −0.610118 1.11114i
\(940\) 4066.09 7042.68i 0.141086 0.244369i
\(941\) −26628.9 + 46122.6i −0.922505 + 1.59783i −0.126980 + 0.991905i \(0.540528\pi\)
−0.795525 + 0.605921i \(0.792805\pi\)
\(942\) −255.332 + 11900.9i −0.00883139 + 0.411627i
\(943\) −2727.88 + 1574.94i −0.0942016 + 0.0543873i
\(944\) −3654.08 −0.125985
\(945\) 41626.5 + 10249.7i 1.43292 + 0.352828i
\(946\) 2057.84 0.0707253
\(947\) 31983.1 18465.5i 1.09748 0.633629i 0.161921 0.986804i \(-0.448231\pi\)
0.935558 + 0.353174i \(0.114898\pi\)
\(948\) 401.330 18705.8i 0.0137496 0.640860i
\(949\) −2241.49 + 3882.37i −0.0766721 + 0.132800i
\(950\) 23819.1 41255.9i 0.813467 1.40897i
\(951\) 12183.5 + 22188.4i 0.415434 + 0.756582i
\(952\) 3288.16 + 9106.02i 0.111943 + 0.310008i
\(953\) 34392.3i 1.16902i 0.811386 + 0.584510i \(0.198713\pi\)
−0.811386 + 0.584510i \(0.801287\pi\)
\(954\) −10008.7 19192.2i −0.339667 0.651333i
\(955\) 5211.63i 0.176591i
\(956\) −9080.23 + 5242.47i −0.307192 + 0.177357i
\(957\) 37201.1 + 22555.6i 1.25657 + 0.761880i
\(958\) 24862.5 + 14354.3i 0.838486 + 0.484100i
\(959\) −11324.0 + 13426.0i −0.381304 + 0.452084i
\(960\) −4691.79 2844.70i −0.157736 0.0956379i
\(961\) −13328.7 23086.0i −0.447407 0.774931i
\(962\) −12218.3 −0.409496
\(963\) −439.660 + 10241.5i −0.0147122 + 0.342707i
\(964\) 13937.2i 0.465650i
\(965\) −11226.5 19444.8i −0.374501 0.648654i
\(966\) 10483.7 + 31105.9i 0.349178 + 1.03604i
\(967\) −20065.3 + 34754.1i −0.667277 + 1.15576i 0.311385 + 0.950284i \(0.399207\pi\)
−0.978663 + 0.205474i \(0.934126\pi\)
\(968\) 3110.94 + 1796.10i 0.103295 + 0.0596373i
\(969\) −54922.6 1178.36i −1.82081 0.0390653i
\(970\) 14274.9 + 24724.8i 0.472515 + 0.818420i
\(971\) 3583.78 0.118444 0.0592219 0.998245i \(-0.481138\pi\)
0.0592219 + 0.998245i \(0.481138\pi\)
\(972\) 12235.6 + 8937.19i 0.403761 + 0.294918i
\(973\) 56992.6 + 10198.6i 1.87780 + 0.336026i
\(974\) 5559.10 3209.55i 0.182880 0.105586i
\(975\) −34957.5 750.008i −1.14824 0.0246354i
\(976\) 3406.19 + 1966.56i 0.111710 + 0.0644961i
\(977\) 16070.4 + 9278.23i 0.526240 + 0.303825i 0.739484 0.673174i \(-0.235070\pi\)
−0.213244 + 0.976999i \(0.568403\pi\)
\(978\) −9048.20 16478.4i −0.295838 0.538775i
\(979\) 24783.7 14308.9i 0.809083 0.467124i
\(980\) −21231.9 7850.15i −0.692070 0.255881i
\(981\) 18915.7 + 812.041i 0.615629 + 0.0264286i
\(982\) 27116.6 0.881187
\(983\) 24784.7 + 42928.3i 0.804180 + 1.39288i 0.916844 + 0.399247i \(0.130728\pi\)
−0.112664 + 0.993633i \(0.535938\pi\)
\(984\) 398.049 656.505i 0.0128957 0.0212689i
\(985\) −10088.5 5824.58i −0.326340 0.188413i
\(986\) −12967.3 + 22460.0i −0.418826 + 0.725429i
\(987\) 7838.00 8898.41i 0.252772 0.286970i
\(988\) 14790.7 + 25618.3i 0.476271 + 0.824926i
\(989\) 4159.25i 0.133727i
\(990\) 17381.2 + 33329.5i 0.557991 + 1.06998i
\(991\) −36296.8 −1.16348 −0.581739 0.813375i \(-0.697628\pi\)
−0.581739 + 0.813375i \(0.697628\pi\)
\(992\) −895.658 1551.32i −0.0286665 0.0496518i
\(993\) 28397.6 15592.9i 0.907523 0.498315i
\(994\) 22891.3 + 19307.4i 0.730451 + 0.616089i
\(995\) 356.189 + 205.646i 0.0113487 + 0.00655218i
\(996\) −540.059 + 25171.9i −0.0171811 + 0.800805i
\(997\) 925.524 534.352i 0.0293998 0.0169740i −0.485228 0.874388i \(-0.661263\pi\)
0.514628 + 0.857414i \(0.327930\pi\)
\(998\) 32389.6i 1.02733i
\(999\) −1205.90 + 18712.5i −0.0381912 + 0.592630i
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 126.4.m.a.41.6 48
3.2 odd 2 378.4.m.a.125.23 48
7.6 odd 2 inner 126.4.m.a.41.7 yes 48
9.2 odd 6 inner 126.4.m.a.83.7 yes 48
9.4 even 3 1134.4.d.b.1133.41 48
9.5 odd 6 1134.4.d.b.1133.8 48
9.7 even 3 378.4.m.a.251.24 48
21.20 even 2 378.4.m.a.125.24 48
63.13 odd 6 1134.4.d.b.1133.7 48
63.20 even 6 inner 126.4.m.a.83.6 yes 48
63.34 odd 6 378.4.m.a.251.23 48
63.41 even 6 1134.4.d.b.1133.42 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.4.m.a.41.6 48 1.1 even 1 trivial
126.4.m.a.41.7 yes 48 7.6 odd 2 inner
126.4.m.a.83.6 yes 48 63.20 even 6 inner
126.4.m.a.83.7 yes 48 9.2 odd 6 inner
378.4.m.a.125.23 48 3.2 odd 2
378.4.m.a.125.24 48 21.20 even 2
378.4.m.a.251.23 48 63.34 odd 6
378.4.m.a.251.24 48 9.7 even 3
1134.4.d.b.1133.7 48 63.13 odd 6
1134.4.d.b.1133.8 48 9.5 odd 6
1134.4.d.b.1133.41 48 9.4 even 3
1134.4.d.b.1133.42 48 63.41 even 6