Properties

Label 15.4.e.a.8.2
Level $15$
Weight $4$
Character 15.8
Analytic conductor $0.885$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,4,Mod(2,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 15.e (of order \(4\), 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: \(0.885028650086\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.28356903014400.8
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 209x^{4} + 1600 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.2
Root \(-1.18766 + 1.18766i\) of defining polynomial
Character \(\chi\) \(=\) 15.8
Dual form 15.4.e.a.2.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18766 - 1.18766i) q^{2} +(5.11173 - 0.932827i) q^{3} -5.17891i q^{4} +(-2.48157 + 10.9015i) q^{5} +(-7.17891 - 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(-15.6521 + 15.6521i) q^{8} +(25.2597 - 9.53673i) q^{9} +O(q^{10})\) \(q+(-1.18766 - 1.18766i) q^{2} +(5.11173 - 0.932827i) q^{3} -5.17891i q^{4} +(-2.48157 + 10.9015i) q^{5} +(-7.17891 - 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(-15.6521 + 15.6521i) q^{8} +(25.2597 - 9.53673i) q^{9} +(15.8945 - 10.0000i) q^{10} -28.7164i q^{11} +(-4.83102 - 26.4732i) q^{12} +(14.1789 + 14.1789i) q^{13} +31.7292 q^{14} +(-2.51595 + 58.0402i) q^{15} -4.25236 q^{16} +(-18.5587 - 18.5587i) q^{17} +(-41.3264 - 18.6736i) q^{18} -49.0735i q^{19} +(56.4577 + 12.8518i) q^{20} +(-55.8211 + 80.7421i) q^{21} +(-34.1055 + 34.1055i) q^{22} +(37.7738 - 37.7738i) q^{23} +(-65.4088 + 94.6102i) q^{24} +(-112.684 - 54.1055i) q^{25} -33.6796i q^{26} +(120.225 - 72.3121i) q^{27} +(69.1789 + 69.1789i) q^{28} -125.854 q^{29} +(71.9204 - 65.9442i) q^{30} +247.367 q^{31} +(130.267 + 130.267i) q^{32} +(-26.7874 - 146.791i) q^{33} +44.0829i q^{34} +(-112.471 - 178.768i) q^{35} +(-49.3898 - 130.818i) q^{36} +(-127.463 + 127.463i) q^{37} +(-58.2828 + 58.2828i) q^{38} +(85.7053 + 59.2524i) q^{39} +(-131.789 - 209.473i) q^{40} +390.328i q^{41} +(162.191 - 29.5978i) q^{42} +(-39.3993 - 39.3993i) q^{43} -148.720 q^{44} +(41.2806 + 299.033i) q^{45} -89.7251 q^{46} +(-124.560 - 124.560i) q^{47} +(-21.7369 + 3.96671i) q^{48} -13.8625i q^{49} +(69.5712 + 198.089i) q^{50} +(-112.179 - 77.5549i) q^{51} +(73.4313 - 73.4313i) q^{52} +(160.441 - 160.441i) q^{53} +(-228.669 - 56.9040i) q^{54} +(313.051 + 71.2618i) q^{55} -418.156i q^{56} +(-45.7770 - 250.850i) q^{57} +(149.473 + 149.473i) q^{58} +729.423 q^{59} +(300.585 + 13.0299i) q^{60} +2.00000 q^{61} +(-293.789 - 293.789i) q^{62} +(-210.024 + 464.804i) q^{63} -275.409i q^{64} +(-189.757 + 119.385i) q^{65} +(-142.524 + 206.153i) q^{66} +(-329.987 + 329.987i) q^{67} +(-96.1136 + 96.1136i) q^{68} +(157.853 - 228.326i) q^{69} +(-78.7382 + 345.895i) q^{70} -171.760i q^{71} +(-246.097 + 544.637i) q^{72} +(-279.927 - 279.927i) q^{73} +302.767 q^{74} +(-626.480 - 171.458i) q^{75} -254.147 q^{76} +(383.589 + 383.589i) q^{77} +(-31.4172 - 172.161i) q^{78} -48.0189i q^{79} +(10.5525 - 46.3569i) q^{80} +(547.102 - 481.789i) q^{81} +(463.578 - 463.578i) q^{82} +(-144.451 + 144.451i) q^{83} +(418.156 + 289.092i) q^{84} +(248.371 - 156.262i) q^{85} +93.5862i q^{86} +(-643.334 + 117.400i) q^{87} +(449.473 + 449.473i) q^{88} -1417.21 q^{89} +(306.124 - 404.179i) q^{90} -378.799 q^{91} +(-195.627 - 195.627i) q^{92} +(1264.48 - 230.751i) q^{93} +295.872i q^{94} +(534.972 + 121.779i) q^{95} +(787.409 + 544.375i) q^{96} +(908.111 - 908.111i) q^{97} +(-16.4640 + 16.4640i) q^{98} +(-273.861 - 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18766 1.18766i −0.419903 0.419903i 0.465267 0.885170i \(-0.345958\pi\)
−0.885170 + 0.465267i \(0.845958\pi\)
\(3\) 5.11173 0.932827i 0.983754 0.179523i
\(4\) 5.17891i 0.647364i
\(5\) −2.48157 + 10.9015i −0.221958 + 0.975056i
\(6\) −7.17891 4.96314i −0.488463 0.337699i
\(7\) −13.3578 + 13.3578i −0.721254 + 0.721254i −0.968861 0.247606i \(-0.920356\pi\)
0.247606 + 0.968861i \(0.420356\pi\)
\(8\) −15.6521 + 15.6521i −0.691732 + 0.691732i
\(9\) 25.2597 9.53673i 0.935543 0.353212i
\(10\) 15.8945 10.0000i 0.502630 0.316228i
\(11\) 28.7164i 0.787121i −0.919299 0.393560i \(-0.871243\pi\)
0.919299 0.393560i \(-0.128757\pi\)
\(12\) −4.83102 26.4732i −0.116216 0.636846i
\(13\) 14.1789 + 14.1789i 0.302502 + 0.302502i 0.841992 0.539490i \(-0.181383\pi\)
−0.539490 + 0.841992i \(0.681383\pi\)
\(14\) 31.7292 0.605713
\(15\) −2.51595 + 58.0402i −0.0433078 + 0.999062i
\(16\) −4.25236 −0.0664431
\(17\) −18.5587 18.5587i −0.264773 0.264773i 0.562217 0.826990i \(-0.309949\pi\)
−0.826990 + 0.562217i \(0.809949\pi\)
\(18\) −41.3264 18.6736i −0.541152 0.244522i
\(19\) 49.0735i 0.592538i −0.955105 0.296269i \(-0.904258\pi\)
0.955105 0.296269i \(-0.0957425\pi\)
\(20\) 56.4577 + 12.8518i 0.631216 + 0.143688i
\(21\) −55.8211 + 80.7421i −0.580055 + 0.839018i
\(22\) −34.1055 + 34.1055i −0.330514 + 0.330514i
\(23\) 37.7738 37.7738i 0.342451 0.342451i −0.514837 0.857288i \(-0.672148\pi\)
0.857288 + 0.514837i \(0.172148\pi\)
\(24\) −65.4088 + 94.6102i −0.556313 + 0.804676i
\(25\) −112.684 54.1055i −0.901469 0.432844i
\(26\) 33.6796i 0.254042i
\(27\) 120.225 72.3121i 0.856935 0.515425i
\(28\) 69.1789 + 69.1789i 0.466914 + 0.466914i
\(29\) −125.854 −0.805882 −0.402941 0.915226i \(-0.632012\pi\)
−0.402941 + 0.915226i \(0.632012\pi\)
\(30\) 71.9204 65.9442i 0.437694 0.401324i
\(31\) 247.367 1.43318 0.716588 0.697496i \(-0.245703\pi\)
0.716588 + 0.697496i \(0.245703\pi\)
\(32\) 130.267 + 130.267i 0.719632 + 0.719632i
\(33\) −26.7874 146.791i −0.141306 0.774333i
\(34\) 44.0829i 0.222357i
\(35\) −112.471 178.768i −0.543175 0.863352i
\(36\) −49.3898 130.818i −0.228657 0.605637i
\(37\) −127.463 + 127.463i −0.566347 + 0.566347i −0.931103 0.364756i \(-0.881152\pi\)
0.364756 + 0.931103i \(0.381152\pi\)
\(38\) −58.2828 + 58.2828i −0.248808 + 0.248808i
\(39\) 85.7053 + 59.2524i 0.351893 + 0.243281i
\(40\) −131.789 209.473i −0.520942 0.828014i
\(41\) 390.328i 1.48680i 0.668845 + 0.743402i \(0.266789\pi\)
−0.668845 + 0.743402i \(0.733211\pi\)
\(42\) 162.191 29.5978i 0.595873 0.108739i
\(43\) −39.3993 39.3993i −0.139729 0.139729i 0.633783 0.773511i \(-0.281501\pi\)
−0.773511 + 0.633783i \(0.781501\pi\)
\(44\) −148.720 −0.509553
\(45\) 41.2806 + 299.033i 0.136750 + 0.990606i
\(46\) −89.7251 −0.287592
\(47\) −124.560 124.560i −0.386575 0.386575i 0.486889 0.873464i \(-0.338132\pi\)
−0.873464 + 0.486889i \(0.838132\pi\)
\(48\) −21.7369 + 3.96671i −0.0653637 + 0.0119280i
\(49\) 13.8625i 0.0404155i
\(50\) 69.5712 + 198.089i 0.196777 + 0.560281i
\(51\) −112.179 77.5549i −0.308004 0.212938i
\(52\) 73.4313 73.4313i 0.195829 0.195829i
\(53\) 160.441 160.441i 0.415816 0.415816i −0.467943 0.883759i \(-0.655005\pi\)
0.883759 + 0.467943i \(0.155005\pi\)
\(54\) −228.669 56.9040i −0.576257 0.143401i
\(55\) 313.051 + 71.2618i 0.767487 + 0.174708i
\(56\) 418.156i 0.997830i
\(57\) −45.7770 250.850i −0.106374 0.582912i
\(58\) 149.473 + 149.473i 0.338392 + 0.338392i
\(59\) 729.423 1.60954 0.804769 0.593588i \(-0.202289\pi\)
0.804769 + 0.593588i \(0.202289\pi\)
\(60\) 300.585 + 13.0299i 0.646756 + 0.0280359i
\(61\) 2.00000 0.00419793 0.00209897 0.999998i \(-0.499332\pi\)
0.00209897 + 0.999998i \(0.499332\pi\)
\(62\) −293.789 293.789i −0.601795 0.601795i
\(63\) −210.024 + 464.804i −0.420009 + 0.929520i
\(64\) 275.409i 0.537908i
\(65\) −189.757 + 119.385i −0.362099 + 0.227813i
\(66\) −142.524 + 206.153i −0.265810 + 0.384479i
\(67\) −329.987 + 329.987i −0.601706 + 0.601706i −0.940765 0.339059i \(-0.889891\pi\)
0.339059 + 0.940765i \(0.389891\pi\)
\(68\) −96.1136 + 96.1136i −0.171404 + 0.171404i
\(69\) 157.853 228.326i 0.275410 0.398365i
\(70\) −78.7382 + 345.895i −0.134443 + 0.590604i
\(71\) 171.760i 0.287100i −0.989643 0.143550i \(-0.954148\pi\)
0.989643 0.143550i \(-0.0458518\pi\)
\(72\) −246.097 + 544.637i −0.402817 + 0.891474i
\(73\) −279.927 279.927i −0.448807 0.448807i 0.446151 0.894958i \(-0.352795\pi\)
−0.894958 + 0.446151i \(0.852795\pi\)
\(74\) 302.767 0.475621
\(75\) −626.480 171.458i −0.964529 0.263978i
\(76\) −254.147 −0.383587
\(77\) 383.589 + 383.589i 0.567714 + 0.567714i
\(78\) −31.4172 172.161i −0.0456064 0.249915i
\(79\) 48.0189i 0.0683866i −0.999415 0.0341933i \(-0.989114\pi\)
0.999415 0.0341933i \(-0.0108862\pi\)
\(80\) 10.5525 46.3569i 0.0147476 0.0647858i
\(81\) 547.102 481.789i 0.750483 0.660890i
\(82\) 463.578 463.578i 0.624313 0.624313i
\(83\) −144.451 + 144.451i −0.191031 + 0.191031i −0.796141 0.605111i \(-0.793129\pi\)
0.605111 + 0.796141i \(0.293129\pi\)
\(84\) 418.156 + 289.092i 0.543150 + 0.375507i
\(85\) 248.371 156.262i 0.316937 0.199400i
\(86\) 93.5862i 0.117345i
\(87\) −643.334 + 117.400i −0.792789 + 0.144674i
\(88\) 449.473 + 449.473i 0.544477 + 0.544477i
\(89\) −1417.21 −1.68790 −0.843952 0.536419i \(-0.819777\pi\)
−0.843952 + 0.536419i \(0.819777\pi\)
\(90\) 306.124 404.179i 0.358536 0.473380i
\(91\) −378.799 −0.436361
\(92\) −195.627 195.627i −0.221690 0.221690i
\(93\) 1264.48 230.751i 1.40989 0.257288i
\(94\) 295.872i 0.324647i
\(95\) 534.972 + 121.779i 0.577758 + 0.131519i
\(96\) 787.409 + 544.375i 0.837131 + 0.578751i
\(97\) 908.111 908.111i 0.950564 0.950564i −0.0482702 0.998834i \(-0.515371\pi\)
0.998834 + 0.0482702i \(0.0153708\pi\)
\(98\) −16.4640 + 16.4640i −0.0169706 + 0.0169706i
\(99\) −273.861 725.367i −0.278020 0.736385i
\(100\) −280.207 + 583.578i −0.280207 + 0.583578i
\(101\) 337.668i 0.332665i 0.986070 + 0.166333i \(0.0531926\pi\)
−0.986070 + 0.166333i \(0.946807\pi\)
\(102\) 41.1217 + 225.340i 0.0399182 + 0.218745i
\(103\) −933.505 933.505i −0.893019 0.893019i 0.101787 0.994806i \(-0.467544\pi\)
−0.994806 + 0.101787i \(0.967544\pi\)
\(104\) −443.860 −0.418500
\(105\) −741.683 808.899i −0.689342 0.751814i
\(106\) −381.100 −0.349205
\(107\) 596.188 + 596.188i 0.538651 + 0.538651i 0.923133 0.384481i \(-0.125620\pi\)
−0.384481 + 0.923133i \(0.625620\pi\)
\(108\) −374.498 622.632i −0.333667 0.554748i
\(109\) 2074.60i 1.82303i 0.411264 + 0.911516i \(0.365087\pi\)
−0.411264 + 0.911516i \(0.634913\pi\)
\(110\) −287.164 456.434i −0.248909 0.395630i
\(111\) −532.657 + 770.460i −0.455474 + 0.658818i
\(112\) 56.8022 56.8022i 0.0479224 0.0479224i
\(113\) −271.193 + 271.193i −0.225767 + 0.225767i −0.810922 0.585154i \(-0.801034\pi\)
0.585154 + 0.810922i \(0.301034\pi\)
\(114\) −243.558 + 352.294i −0.200099 + 0.289433i
\(115\) 318.051 + 505.527i 0.257899 + 0.409919i
\(116\) 651.788i 0.521698i
\(117\) 493.375 + 222.934i 0.389851 + 0.176156i
\(118\) −866.309 866.309i −0.675849 0.675849i
\(119\) 495.806 0.381937
\(120\) −869.073 947.833i −0.661126 0.721041i
\(121\) 506.367 0.380441
\(122\) −2.37533 2.37533i −0.00176272 0.00176272i
\(123\) 364.108 + 1995.25i 0.266915 + 1.46265i
\(124\) 1281.09i 0.927786i
\(125\) 869.461 1094.15i 0.622135 0.782910i
\(126\) 801.469 302.593i 0.566671 0.213945i
\(127\) 105.588 105.588i 0.0737747 0.0737747i −0.669257 0.743031i \(-0.733387\pi\)
0.743031 + 0.669257i \(0.233387\pi\)
\(128\) 715.045 715.045i 0.493763 0.493763i
\(129\) −238.151 164.646i −0.162543 0.112374i
\(130\) 367.156 + 83.5782i 0.247706 + 0.0563868i
\(131\) 1979.28i 1.32008i −0.751231 0.660039i \(-0.770540\pi\)
0.751231 0.660039i \(-0.229460\pi\)
\(132\) −760.216 + 138.730i −0.501275 + 0.0914763i
\(133\) 655.514 + 655.514i 0.427371 + 0.427371i
\(134\) 783.827 0.505316
\(135\) 489.962 + 1490.07i 0.312364 + 0.949962i
\(136\) 580.964 0.366304
\(137\) −507.451 507.451i −0.316456 0.316456i 0.530948 0.847404i \(-0.321836\pi\)
−0.847404 + 0.530948i \(0.821836\pi\)
\(138\) −458.651 + 83.6979i −0.282920 + 0.0516293i
\(139\) 68.4333i 0.0417585i −0.999782 0.0208793i \(-0.993353\pi\)
0.999782 0.0208793i \(-0.00664656\pi\)
\(140\) −925.823 + 582.479i −0.558903 + 0.351632i
\(141\) −752.913 520.527i −0.449693 0.310895i
\(142\) −203.993 + 203.993i −0.120554 + 0.120554i
\(143\) 407.167 407.167i 0.238105 0.238105i
\(144\) −107.413 + 40.5536i −0.0621604 + 0.0234685i
\(145\) 312.316 1372.00i 0.178872 0.785780i
\(146\) 664.917i 0.376911i
\(147\) −12.9313 70.8616i −0.00725550 0.0397590i
\(148\) 660.121 + 660.121i 0.366632 + 0.366632i
\(149\) −363.356 −0.199780 −0.0998902 0.994998i \(-0.531849\pi\)
−0.0998902 + 0.994998i \(0.531849\pi\)
\(150\) 540.413 + 947.683i 0.294163 + 0.515853i
\(151\) −2083.14 −1.12267 −0.561337 0.827588i \(-0.689713\pi\)
−0.561337 + 0.827588i \(0.689713\pi\)
\(152\) 768.103 + 768.103i 0.409878 + 0.409878i
\(153\) −645.774 291.797i −0.341227 0.154185i
\(154\) 911.149i 0.476769i
\(155\) −613.859 + 2696.66i −0.318105 + 1.39743i
\(156\) 306.863 443.860i 0.157491 0.227803i
\(157\) −1208.52 + 1208.52i −0.614333 + 0.614333i −0.944072 0.329739i \(-0.893039\pi\)
0.329739 + 0.944072i \(0.393039\pi\)
\(158\) −57.0303 + 57.0303i −0.0287157 + 0.0287157i
\(159\) 670.468 969.795i 0.334412 0.483709i
\(160\) −1743.37 + 1096.84i −0.861410 + 0.541953i
\(161\) 1009.15i 0.493989i
\(162\) −1221.98 77.5696i −0.592639 0.0376200i
\(163\) 626.062 + 626.062i 0.300840 + 0.300840i 0.841343 0.540502i \(-0.181766\pi\)
−0.540502 + 0.841343i \(0.681766\pi\)
\(164\) 2021.47 0.962502
\(165\) 1666.71 + 72.2492i 0.786382 + 0.0340884i
\(166\) 343.119 0.160429
\(167\) −3009.65 3009.65i −1.39457 1.39457i −0.814724 0.579848i \(-0.803112\pi\)
−0.579848 0.814724i \(-0.696888\pi\)
\(168\) −390.067 2137.50i −0.179133 0.981619i
\(169\) 1794.92i 0.816985i
\(170\) −480.568 109.395i −0.216811 0.0493541i
\(171\) −468.000 1239.58i −0.209292 0.554345i
\(172\) −204.045 + 204.045i −0.0904552 + 0.0904552i
\(173\) −1839.23 + 1839.23i −0.808288 + 0.808288i −0.984375 0.176086i \(-0.943656\pi\)
0.176086 + 0.984375i \(0.443656\pi\)
\(174\) 903.497 + 624.633i 0.393643 + 0.272145i
\(175\) 2227.94 782.476i 0.962379 0.337998i
\(176\) 122.113i 0.0522987i
\(177\) 3728.61 680.425i 1.58339 0.288948i
\(178\) 1683.16 + 1683.16i 0.708755 + 0.708755i
\(179\) 821.582 0.343061 0.171530 0.985179i \(-0.445129\pi\)
0.171530 + 0.985179i \(0.445129\pi\)
\(180\) 1548.67 213.788i 0.641282 0.0885269i
\(181\) 2314.20 0.950350 0.475175 0.879891i \(-0.342385\pi\)
0.475175 + 0.879891i \(0.342385\pi\)
\(182\) 449.885 + 449.885i 0.183229 + 0.183229i
\(183\) 10.2235 1.86565i 0.00412973 0.000753623i
\(184\) 1182.48i 0.473769i
\(185\) −1073.23 1705.84i −0.426515 0.677925i
\(186\) −1775.83 1227.72i −0.700053 0.483982i
\(187\) −532.938 + 532.938i −0.208408 + 0.208408i
\(188\) −645.087 + 645.087i −0.250254 + 0.250254i
\(189\) −640.007 + 2571.87i −0.246316 + 0.989820i
\(190\) −490.735 780.000i −0.187377 0.297827i
\(191\) 931.167i 0.352758i −0.984322 0.176379i \(-0.943562\pi\)
0.984322 0.176379i \(-0.0564385\pi\)
\(192\) −256.909 1407.82i −0.0965666 0.529169i
\(193\) −2623.28 2623.28i −0.978382 0.978382i 0.0213891 0.999771i \(-0.493191\pi\)
−0.999771 + 0.0213891i \(0.993191\pi\)
\(194\) −2157.06 −0.798289
\(195\) −858.621 + 787.274i −0.315319 + 0.289117i
\(196\) −71.7928 −0.0261636
\(197\) 2995.05 + 2995.05i 1.08319 + 1.08319i 0.996210 + 0.0869796i \(0.0277215\pi\)
0.0869796 + 0.996210i \(0.472279\pi\)
\(198\) −536.238 + 1186.75i −0.192469 + 0.425952i
\(199\) 109.458i 0.0389912i 0.999810 + 0.0194956i \(0.00620603\pi\)
−0.999810 + 0.0194956i \(0.993794\pi\)
\(200\) 2610.60 916.872i 0.922987 0.324163i
\(201\) −1378.98 + 1994.63i −0.483911 + 0.699951i
\(202\) 401.036 401.036i 0.139687 0.139687i
\(203\) 1681.14 1681.14i 0.581246 0.581246i
\(204\) −401.650 + 580.964i −0.137849 + 0.199390i
\(205\) −4255.14 968.625i −1.44972 0.330008i
\(206\) 2217.38i 0.749962i
\(207\) 593.915 1314.39i 0.199420 0.441336i
\(208\) −60.2938 60.2938i −0.0200991 0.0200991i
\(209\) −1409.21 −0.466399
\(210\) −79.8292 + 1841.57i −0.0262321 + 0.605145i
\(211\) 2714.94 0.885801 0.442901 0.896571i \(-0.353949\pi\)
0.442901 + 0.896571i \(0.353949\pi\)
\(212\) −830.909 830.909i −0.269184 0.269184i
\(213\) −160.222 877.989i −0.0515409 0.282436i
\(214\) 1416.14i 0.452362i
\(215\) 527.281 331.737i 0.167257 0.105229i
\(216\) −749.932 + 3013.61i −0.236233 + 0.949305i
\(217\) −3304.29 + 3304.29i −1.03368 + 1.03368i
\(218\) 2463.93 2463.93i 0.765496 0.765496i
\(219\) −1692.03 1169.79i −0.522087 0.360945i
\(220\) 369.058 1621.26i 0.113100 0.496843i
\(221\) 526.283i 0.160188i
\(222\) 1547.67 282.429i 0.467894 0.0853847i
\(223\) 2830.49 + 2830.49i 0.849971 + 0.849971i 0.990129 0.140158i \(-0.0447612\pi\)
−0.140158 + 0.990129i \(0.544761\pi\)
\(224\) −3480.17 −1.03808
\(225\) −3362.34 292.053i −0.996249 0.0865343i
\(226\) 644.173 0.189601
\(227\) 1398.96 + 1398.96i 0.409042 + 0.409042i 0.881404 0.472362i \(-0.156599\pi\)
−0.472362 + 0.881404i \(0.656599\pi\)
\(228\) −1299.13 + 237.075i −0.377356 + 0.0688626i
\(229\) 3930.38i 1.13418i 0.823656 + 0.567089i \(0.191931\pi\)
−0.823656 + 0.567089i \(0.808069\pi\)
\(230\) 222.659 978.134i 0.0638335 0.280419i
\(231\) 2318.63 + 1602.98i 0.660408 + 0.456573i
\(232\) 1969.89 1969.89i 0.557454 0.557454i
\(233\) 1980.71 1980.71i 0.556912 0.556912i −0.371515 0.928427i \(-0.621162\pi\)
0.928427 + 0.371515i \(0.121162\pi\)
\(234\) −321.193 850.735i −0.0897309 0.237668i
\(235\) 1667.00 1048.79i 0.462736 0.291129i
\(236\) 3777.61i 1.04196i
\(237\) −44.7933 245.460i −0.0122769 0.0672756i
\(238\) −588.851 588.851i −0.160376 0.160376i
\(239\) 2976.20 0.805500 0.402750 0.915310i \(-0.368054\pi\)
0.402750 + 0.915310i \(0.368054\pi\)
\(240\) 10.6987 246.808i 0.00287750 0.0663808i
\(241\) 1835.45 0.490587 0.245294 0.969449i \(-0.421116\pi\)
0.245294 + 0.969449i \(0.421116\pi\)
\(242\) −601.394 601.394i −0.159748 0.159748i
\(243\) 2347.21 2973.13i 0.619645 0.784882i
\(244\) 10.3578i 0.00271759i
\(245\) 151.122 + 34.4008i 0.0394074 + 0.00897057i
\(246\) 1937.25 2802.13i 0.502092 0.726248i
\(247\) 695.808 695.808i 0.179244 0.179244i
\(248\) −3871.82 + 3871.82i −0.991374 + 0.991374i
\(249\) −603.648 + 873.143i −0.153633 + 0.222222i
\(250\) −2332.11 + 266.855i −0.589982 + 0.0675095i
\(251\) 1542.14i 0.387805i 0.981021 + 0.193902i \(0.0621145\pi\)
−0.981021 + 0.193902i \(0.937885\pi\)
\(252\) 2407.18 + 1087.70i 0.601738 + 0.271898i
\(253\) −1084.73 1084.73i −0.269550 0.269550i
\(254\) −250.805 −0.0619564
\(255\) 1123.84 1030.46i 0.275991 0.253057i
\(256\) −3901.74 −0.952572
\(257\) 428.853 + 428.853i 0.104090 + 0.104090i 0.757234 0.653144i \(-0.226550\pi\)
−0.653144 + 0.757234i \(0.726550\pi\)
\(258\) 87.2997 + 478.388i 0.0210660 + 0.115438i
\(259\) 3405.26i 0.816960i
\(260\) 618.283 + 982.733i 0.147478 + 0.234410i
\(261\) −3179.04 + 1200.24i −0.753937 + 0.284647i
\(262\) −2350.72 + 2350.72i −0.554304 + 0.554304i
\(263\) −5256.99 + 5256.99i −1.23255 + 1.23255i −0.269565 + 0.962982i \(0.586880\pi\)
−0.962982 + 0.269565i \(0.913120\pi\)
\(264\) 2716.87 + 1878.31i 0.633377 + 0.437885i
\(265\) 1350.89 + 2147.18i 0.313150 + 0.497738i
\(266\) 1557.06i 0.358908i
\(267\) −7244.38 + 1322.01i −1.66048 + 0.303017i
\(268\) 1708.97 + 1708.97i 0.389523 + 0.389523i
\(269\) 1930.34 0.437528 0.218764 0.975778i \(-0.429797\pi\)
0.218764 + 0.975778i \(0.429797\pi\)
\(270\) 1187.79 2351.61i 0.267729 0.530054i
\(271\) −3261.67 −0.731116 −0.365558 0.930789i \(-0.619122\pi\)
−0.365558 + 0.930789i \(0.619122\pi\)
\(272\) 78.9180 + 78.9180i 0.0175923 + 0.0175923i
\(273\) −1936.32 + 353.353i −0.429272 + 0.0783367i
\(274\) 1205.36i 0.265762i
\(275\) −1553.72 + 3235.87i −0.340700 + 0.709565i
\(276\) −1182.48 817.507i −0.257887 0.178290i
\(277\) 4865.57 4865.57i 1.05539 1.05539i 0.0570194 0.998373i \(-0.481840\pi\)
0.998373 0.0570194i \(-0.0181597\pi\)
\(278\) −81.2758 + 81.2758i −0.0175345 + 0.0175345i
\(279\) 6248.41 2359.07i 1.34080 0.506215i
\(280\) 4558.51 + 1037.68i 0.972940 + 0.221477i
\(281\) 3981.96i 0.845351i 0.906281 + 0.422676i \(0.138909\pi\)
−0.906281 + 0.422676i \(0.861091\pi\)
\(282\) 275.997 + 1512.42i 0.0582815 + 0.319373i
\(283\) −4092.66 4092.66i −0.859658 0.859658i 0.131640 0.991298i \(-0.457976\pi\)
−0.991298 + 0.131640i \(0.957976\pi\)
\(284\) −889.527 −0.185858
\(285\) 2848.24 + 123.467i 0.591982 + 0.0256615i
\(286\) −967.156 −0.199962
\(287\) −5213.93 5213.93i −1.07236 1.07236i
\(288\) 4532.83 + 2048.19i 0.927429 + 0.419064i
\(289\) 4224.15i 0.859791i
\(290\) −2000.40 + 1258.54i −0.405060 + 0.254842i
\(291\) 3794.91 5489.13i 0.764473 1.10577i
\(292\) −1449.71 + 1449.71i −0.290541 + 0.290541i
\(293\) 4515.35 4515.35i 0.900305 0.900305i −0.0951570 0.995462i \(-0.530335\pi\)
0.995462 + 0.0951570i \(0.0303353\pi\)
\(294\) −68.8017 + 99.5179i −0.0136483 + 0.0197415i
\(295\) −1810.11 + 7951.77i −0.357250 + 1.56939i
\(296\) 3990.14i 0.783521i
\(297\) −2076.54 3452.42i −0.405701 0.674511i
\(298\) 431.545 + 431.545i 0.0838883 + 0.0838883i
\(299\) 1071.18 0.207184
\(300\) −887.968 + 3244.48i −0.170889 + 0.624401i
\(301\) 1052.58 0.201560
\(302\) 2474.07 + 2474.07i 0.471413 + 0.471413i
\(303\) 314.986 + 1726.07i 0.0597210 + 0.327261i
\(304\) 208.678i 0.0393701i
\(305\) −4.96314 + 21.8029i −0.000931766 + 0.00409322i
\(306\) 420.406 + 1113.52i 0.0785393 + 0.208025i
\(307\) 1831.07 1831.07i 0.340406 0.340406i −0.516114 0.856520i \(-0.672622\pi\)
0.856520 + 0.516114i \(0.172622\pi\)
\(308\) 1986.57 1986.57i 0.367517 0.367517i
\(309\) −5642.63 3901.03i −1.03883 0.718194i
\(310\) 3931.79 2473.67i 0.720357 0.453210i
\(311\) 4010.21i 0.731184i 0.930775 + 0.365592i \(0.119134\pi\)
−0.930775 + 0.365592i \(0.880866\pi\)
\(312\) −2268.89 + 414.044i −0.411701 + 0.0751303i
\(313\) 6072.69 + 6072.69i 1.09664 + 1.09664i 0.994801 + 0.101841i \(0.0324733\pi\)
0.101841 + 0.994801i \(0.467527\pi\)
\(314\) 2870.63 0.515920
\(315\) −4545.85 3443.01i −0.813110 0.615847i
\(316\) −248.685 −0.0442710
\(317\) −3112.10 3112.10i −0.551397 0.551397i 0.375447 0.926844i \(-0.377489\pi\)
−0.926844 + 0.375447i \(0.877489\pi\)
\(318\) −1948.08 + 355.500i −0.343531 + 0.0626901i
\(319\) 3614.09i 0.634326i
\(320\) 3002.36 + 683.446i 0.524490 + 0.119393i
\(321\) 3603.70 + 2491.42i 0.626600 + 0.433200i
\(322\) 1198.53 1198.53i 0.207427 0.207427i
\(323\) −910.737 + 910.737i −0.156888 + 0.156888i
\(324\) −2495.14 2833.39i −0.427836 0.485835i
\(325\) −830.574 2364.89i −0.141760 0.403632i
\(326\) 1487.10i 0.252647i
\(327\) 1935.24 + 10604.8i 0.327275 + 1.79342i
\(328\) −6109.45 6109.45i −1.02847 1.02847i
\(329\) 3327.71 0.557637
\(330\) −1893.68 2065.30i −0.315890 0.344518i
\(331\) −9589.47 −1.59240 −0.796201 0.605033i \(-0.793160\pi\)
−0.796201 + 0.605033i \(0.793160\pi\)
\(332\) 748.099 + 748.099i 0.123666 + 0.123666i
\(333\) −2004.10 + 4435.26i −0.329801 + 0.729883i
\(334\) 7148.90i 1.17117i
\(335\) −2778.45 4416.22i −0.453144 0.720251i
\(336\) 237.371 343.345i 0.0385407 0.0557470i
\(337\) −2561.34 + 2561.34i −0.414021 + 0.414021i −0.883137 0.469115i \(-0.844573\pi\)
0.469115 + 0.883137i \(0.344573\pi\)
\(338\) −2131.76 + 2131.76i −0.343054 + 0.343054i
\(339\) −1133.29 + 1639.24i −0.181569 + 0.262630i
\(340\) −809.265 1286.29i −0.129084 0.205173i
\(341\) 7103.50i 1.12808i
\(342\) −916.377 + 2028.03i −0.144889 + 0.320653i
\(343\) −4396.56 4396.56i −0.692104 0.692104i
\(344\) 1233.36 0.193310
\(345\) 2097.36 + 2287.44i 0.327299 + 0.356960i
\(346\) 4368.77 0.678805
\(347\) 8177.44 + 8177.44i 1.26509 + 1.26509i 0.948592 + 0.316503i \(0.102509\pi\)
0.316503 + 0.948592i \(0.397491\pi\)
\(348\) 608.005 + 3331.77i 0.0936566 + 0.513223i
\(349\) 2766.04i 0.424249i −0.977243 0.212124i \(-0.931962\pi\)
0.977243 0.212124i \(-0.0680382\pi\)
\(350\) −3575.36 1716.72i −0.546032 0.262179i
\(351\) 2729.96 + 679.347i 0.415141 + 0.103307i
\(352\) 3740.81 3740.81i 0.566437 0.566437i
\(353\) 6338.53 6338.53i 0.955711 0.955711i −0.0433491 0.999060i \(-0.513803\pi\)
0.999060 + 0.0433491i \(0.0138028\pi\)
\(354\) −5236.46 3620.23i −0.786199 0.543539i
\(355\) 1872.43 + 426.233i 0.279939 + 0.0637242i
\(356\) 7339.58i 1.09269i
\(357\) 2534.43 462.501i 0.375732 0.0685663i
\(358\) −975.763 975.763i −0.144052 0.144052i
\(359\) −8827.47 −1.29776 −0.648880 0.760890i \(-0.724762\pi\)
−0.648880 + 0.760890i \(0.724762\pi\)
\(360\) −5326.63 4034.38i −0.779828 0.590640i
\(361\) 4450.80 0.648899
\(362\) −2748.50 2748.50i −0.399055 0.399055i
\(363\) 2588.42 472.353i 0.374261 0.0682978i
\(364\) 1961.76i 0.282484i
\(365\) 3746.27 2356.95i 0.537229 0.337996i
\(366\) −14.3578 9.92628i −0.00205053 0.00141764i
\(367\) 6191.27 6191.27i 0.880605 0.880605i −0.112991 0.993596i \(-0.536043\pi\)
0.993596 + 0.112991i \(0.0360432\pi\)
\(368\) −160.628 + 160.628i −0.0227535 + 0.0227535i
\(369\) 3722.45 + 9859.55i 0.525157 + 1.39097i
\(370\) −751.338 + 3300.60i −0.105568 + 0.463757i
\(371\) 4286.28i 0.599818i
\(372\) −1195.04 6548.60i −0.166559 0.912713i
\(373\) 3584.46 + 3584.46i 0.497577 + 0.497577i 0.910683 0.413106i \(-0.135556\pi\)
−0.413106 + 0.910683i \(0.635556\pi\)
\(374\) 1265.90 0.175022
\(375\) 3423.80 6404.06i 0.471478 0.881878i
\(376\) 3899.27 0.534812
\(377\) −1784.48 1784.48i −0.243781 0.243781i
\(378\) 3814.63 2294.40i 0.519057 0.312200i
\(379\) 7110.48i 0.963695i 0.876255 + 0.481848i \(0.160034\pi\)
−0.876255 + 0.481848i \(0.839966\pi\)
\(380\) 630.683 2770.57i 0.0851404 0.374019i
\(381\) 441.241 638.231i 0.0593319 0.0858203i
\(382\) −1105.91 + 1105.91i −0.148124 + 0.148124i
\(383\) −1695.77 + 1695.77i −0.226240 + 0.226240i −0.811120 0.584880i \(-0.801142\pi\)
0.584880 + 0.811120i \(0.301142\pi\)
\(384\) 2988.11 4322.14i 0.397100 0.574383i
\(385\) −5133.58 + 3229.77i −0.679562 + 0.427544i
\(386\) 6231.15i 0.821650i
\(387\) −1370.95 619.472i −0.180076 0.0813683i
\(388\) −4703.02 4703.02i −0.615361 0.615361i
\(389\) −12362.2 −1.61128 −0.805640 0.592405i \(-0.798178\pi\)
−0.805640 + 0.592405i \(0.798178\pi\)
\(390\) 1954.77 + 84.7362i 0.253804 + 0.0110020i
\(391\) −1402.06 −0.181343
\(392\) 216.978 + 216.978i 0.0279567 + 0.0279567i
\(393\) −1846.32 10117.5i −0.236984 1.29863i
\(394\) 7114.22i 0.909668i
\(395\) 523.476 + 119.162i 0.0666808 + 0.0151790i
\(396\) −3756.61 + 1418.30i −0.476709 + 0.179980i
\(397\) −1340.12 + 1340.12i −0.169417 + 0.169417i −0.786723 0.617306i \(-0.788224\pi\)
0.617306 + 0.786723i \(0.288224\pi\)
\(398\) 129.999 129.999i 0.0163725 0.0163725i
\(399\) 3962.30 + 2739.33i 0.497150 + 0.343705i
\(400\) 479.171 + 230.076i 0.0598964 + 0.0287595i
\(401\) 2281.30i 0.284096i −0.989860 0.142048i \(-0.954631\pi\)
0.989860 0.142048i \(-0.0453688\pi\)
\(402\) 4006.72 731.175i 0.497107 0.0907156i
\(403\) 3507.40 + 3507.40i 0.433538 + 0.433538i
\(404\) 1748.75 0.215356
\(405\) 3894.53 + 7159.80i 0.477829 + 0.878453i
\(406\) −3993.26 −0.488133
\(407\) 3660.29 + 3660.29i 0.445783 + 0.445783i
\(408\) 2969.74 541.939i 0.360352 0.0657597i
\(409\) 4614.82i 0.557917i −0.960303 0.278959i \(-0.910011\pi\)
0.960303 0.278959i \(-0.0899892\pi\)
\(410\) 3903.28 + 6204.08i 0.470169 + 0.747311i
\(411\) −3067.32 2120.59i −0.368126 0.254504i
\(412\) −4834.54 + 4834.54i −0.578108 + 0.578108i
\(413\) −9743.49 + 9743.49i −1.16089 + 1.16089i
\(414\) −2266.43 + 855.683i −0.269055 + 0.101581i
\(415\) −1216.26 1933.19i −0.143865 0.228667i
\(416\) 3694.10i 0.435380i
\(417\) −63.8364 349.813i −0.00749660 0.0410801i
\(418\) 1673.67 + 1673.67i 0.195842 + 0.195842i
\(419\) −2142.28 −0.249779 −0.124889 0.992171i \(-0.539858\pi\)
−0.124889 + 0.992171i \(0.539858\pi\)
\(420\) −4189.21 + 3841.11i −0.486697 + 0.446255i
\(421\) −8889.30 −1.02907 −0.514534 0.857470i \(-0.672035\pi\)
−0.514534 + 0.857470i \(0.672035\pi\)
\(422\) −3224.43 3224.43i −0.371950 0.371950i
\(423\) −4334.26 1958.46i −0.498200 0.225115i
\(424\) 5022.48i 0.575267i
\(425\) 1087.13 + 3095.38i 0.124079 + 0.353289i
\(426\) −852.466 + 1233.05i −0.0969534 + 0.140238i
\(427\) −26.7156 + 26.7156i −0.00302778 + 0.00302778i
\(428\) 3087.60 3087.60i 0.348703 0.348703i
\(429\) 1701.52 2461.15i 0.191492 0.276982i
\(430\) −1020.23 232.241i −0.114418 0.0260457i
\(431\) 15707.3i 1.75543i −0.479179 0.877717i \(-0.659065\pi\)
0.479179 0.877717i \(-0.340935\pi\)
\(432\) −511.238 + 307.497i −0.0569374 + 0.0342464i
\(433\) 5430.81 + 5430.81i 0.602744 + 0.602744i 0.941040 0.338296i \(-0.109851\pi\)
−0.338296 + 0.941040i \(0.609851\pi\)
\(434\) 7848.76 0.868094
\(435\) 316.644 7304.62i 0.0349009 0.805126i
\(436\) 10744.2 1.18016
\(437\) −1853.69 1853.69i −0.202915 0.202915i
\(438\) 620.253 + 3398.88i 0.0676640 + 0.370787i
\(439\) 8221.92i 0.893874i −0.894565 0.446937i \(-0.852515\pi\)
0.894565 0.446937i \(-0.147485\pi\)
\(440\) −6015.31 + 3784.51i −0.651747 + 0.410044i
\(441\) −132.203 350.163i −0.0142753 0.0378105i
\(442\) −625.047 + 625.047i −0.0672635 + 0.0672635i
\(443\) −1960.53 + 1960.53i −0.210265 + 0.210265i −0.804380 0.594115i \(-0.797502\pi\)
0.594115 + 0.804380i \(0.297502\pi\)
\(444\) 3990.14 + 2758.58i 0.426495 + 0.294857i
\(445\) 3516.89 15449.6i 0.374644 1.64580i
\(446\) 6723.34i 0.713810i
\(447\) −1857.38 + 338.948i −0.196535 + 0.0358651i
\(448\) 3678.86 + 3678.86i 0.387968 + 0.387968i
\(449\) 17849.2 1.87607 0.938036 0.346537i \(-0.112643\pi\)
0.938036 + 0.346537i \(0.112643\pi\)
\(450\) 3646.47 + 4340.19i 0.381992 + 0.454664i
\(451\) 11208.8 1.17029
\(452\) 1404.49 + 1404.49i 0.146154 + 0.146154i
\(453\) −10648.5 + 1943.21i −1.10443 + 0.201545i
\(454\) 3323.00i 0.343516i
\(455\) 940.015 4129.46i 0.0968540 0.425477i
\(456\) 4642.85 + 3209.83i 0.476801 + 0.329636i
\(457\) −6346.80 + 6346.80i −0.649652 + 0.649652i −0.952909 0.303257i \(-0.901926\pi\)
0.303257 + 0.952909i \(0.401926\pi\)
\(458\) 4667.97 4667.97i 0.476245 0.476245i
\(459\) −3573.22 889.192i −0.363363 0.0904225i
\(460\) 2618.08 1647.16i 0.265366 0.166954i
\(461\) 8848.20i 0.893930i −0.894552 0.446965i \(-0.852505\pi\)
0.894552 0.446965i \(-0.147495\pi\)
\(462\) −849.944 4657.55i −0.0855908 0.469024i
\(463\) 1329.43 + 1329.43i 0.133443 + 0.133443i 0.770673 0.637230i \(-0.219920\pi\)
−0.637230 + 0.770673i \(0.719920\pi\)
\(464\) 535.178 0.0535453
\(465\) −622.365 + 14357.3i −0.0620677 + 1.43183i
\(466\) −4704.83 −0.467697
\(467\) −1479.96 1479.96i −0.146647 0.146647i 0.629971 0.776618i \(-0.283067\pi\)
−0.776618 + 0.629971i \(0.783067\pi\)
\(468\) 1154.56 2555.14i 0.114037 0.252375i
\(469\) 8815.81i 0.867966i
\(470\) −3225.44 734.227i −0.316550 0.0720582i
\(471\) −5050.29 + 7304.96i −0.494066 + 0.714639i
\(472\) −11417.0 + 11417.0i −1.11337 + 1.11337i
\(473\) −1131.41 + 1131.41i −0.109983 + 0.109983i
\(474\) −238.324 + 344.723i −0.0230941 + 0.0334043i
\(475\) −2655.14 + 5529.77i −0.256476 + 0.534155i
\(476\) 2567.73i 0.247252i
\(477\) 2522.60 5582.76i 0.242143 0.535885i
\(478\) −3534.73 3534.73i −0.338231 0.338231i
\(479\) −5039.60 −0.480720 −0.240360 0.970684i \(-0.577266\pi\)
−0.240360 + 0.970684i \(0.577266\pi\)
\(480\) −7888.49 + 7233.00i −0.750122 + 0.687791i
\(481\) −3614.58 −0.342642
\(482\) −2179.89 2179.89i −0.205999 0.205999i
\(483\) 941.362 + 5158.51i 0.0886821 + 0.485963i
\(484\) 2622.43i 0.246284i
\(485\) 7646.20 + 12153.3i 0.715868 + 1.13784i
\(486\) −6318.78 + 743.377i −0.589765 + 0.0693833i
\(487\) 1292.93 1292.93i 0.120305 0.120305i −0.644391 0.764696i \(-0.722889\pi\)
0.764696 + 0.644391i \(0.222889\pi\)
\(488\) −31.3042 + 31.3042i −0.00290384 + 0.00290384i
\(489\) 3784.27 + 2616.26i 0.349961 + 0.241945i
\(490\) −138.625 220.339i −0.0127805 0.0203140i
\(491\) 13865.7i 1.27444i 0.770681 + 0.637221i \(0.219916\pi\)
−0.770681 + 0.637221i \(0.780084\pi\)
\(492\) 10333.2 1885.68i 0.946865 0.172791i
\(493\) 2335.69 + 2335.69i 0.213375 + 0.213375i
\(494\) −1652.77 −0.150530
\(495\) 8587.17 1185.43i 0.779726 0.107639i
\(496\) −1051.89 −0.0952247
\(497\) 2294.33 + 2294.33i 0.207072 + 0.207072i
\(498\) 1753.93 320.070i 0.157822 0.0288006i
\(499\) 10884.3i 0.976453i 0.872717 + 0.488226i \(0.162356\pi\)
−0.872717 + 0.488226i \(0.837644\pi\)
\(500\) −5666.50 4502.86i −0.506827 0.402748i
\(501\) −18192.0 12577.0i −1.62227 1.12156i
\(502\) 1831.54 1831.54i 0.162840 0.162840i
\(503\) 7880.86 7880.86i 0.698589 0.698589i −0.265517 0.964106i \(-0.585543\pi\)
0.964106 + 0.265517i \(0.0855427\pi\)
\(504\) −3987.84 10562.5i −0.352445 0.933513i
\(505\) −3681.07 837.946i −0.324368 0.0738379i
\(506\) 2576.58i 0.226370i
\(507\) −1674.35 9175.14i −0.146667 0.803713i
\(508\) −546.829 546.829i −0.0477590 0.0477590i
\(509\) −1788.46 −0.155741 −0.0778704 0.996963i \(-0.524812\pi\)
−0.0778704 + 0.996963i \(0.524812\pi\)
\(510\) −2558.58 110.911i −0.222149 0.00962981i
\(511\) 7478.42 0.647408
\(512\) −1086.41 1086.41i −0.0937754 0.0937754i
\(513\) −3548.60 5899.84i −0.305409 0.507766i
\(514\) 1018.67i 0.0874153i
\(515\) 12493.1 7860.01i 1.06896 0.672531i
\(516\) −852.686 + 1233.36i −0.0727469 + 0.105224i
\(517\) −3576.93 + 3576.93i −0.304281 + 0.304281i
\(518\) −4044.31 + 4044.31i −0.343044 + 0.343044i
\(519\) −7685.96 + 11117.3i −0.650051 + 0.940263i
\(520\) 1101.47 4838.72i 0.0928896 0.408061i
\(521\) 18251.6i 1.53478i 0.641183 + 0.767388i \(0.278444\pi\)
−0.641183 + 0.767388i \(0.721556\pi\)
\(522\) 5201.11 + 2350.15i 0.436104 + 0.197056i
\(523\) −2125.69 2125.69i −0.177725 0.177725i 0.612639 0.790363i \(-0.290108\pi\)
−0.790363 + 0.612639i \(0.790108\pi\)
\(524\) −10250.5 −0.854570
\(525\) 10658.7 6078.09i 0.886066 0.505276i
\(526\) 12487.1 1.03510
\(527\) −4590.80 4590.80i −0.379466 0.379466i
\(528\) 113.910 + 624.207i 0.00938880 + 0.0514491i
\(529\) 9313.29i 0.765455i
\(530\) 945.725 4154.54i 0.0775088 0.340494i
\(531\) 18425.0 6956.30i 1.50579 0.568508i
\(532\) 3394.85 3394.85i 0.276664 0.276664i
\(533\) −5534.42 + 5534.42i −0.449761 + 0.449761i
\(534\) 10174.0 + 7033.79i 0.824478 + 0.570003i
\(535\) −7978.81 + 5019.84i −0.644774 + 0.405657i
\(536\) 10330.0i 0.832439i
\(537\) 4199.71 766.393i 0.337488 0.0615872i
\(538\) −2292.60 2292.60i −0.183719 0.183719i
\(539\) −398.082 −0.0318119
\(540\) 7716.94 2537.47i 0.614971 0.202213i
\(541\) −2214.16 −0.175960 −0.0879798 0.996122i \(-0.528041\pi\)
−0.0879798 + 0.996122i \(0.528041\pi\)
\(542\) 3873.77 + 3873.77i 0.306998 + 0.306998i
\(543\) 11829.6 2158.75i 0.934911 0.170609i
\(544\) 4835.17i 0.381078i
\(545\) −22616.2 5148.26i −1.77756 0.404637i
\(546\) 2719.36 + 1880.03i 0.213146 + 0.147359i
\(547\) 12385.1 12385.1i 0.968098 0.968098i −0.0314090 0.999507i \(-0.509999\pi\)
0.999507 + 0.0314090i \(0.00999944\pi\)
\(548\) −2628.04 + 2628.04i −0.204862 + 0.204862i
\(549\) 50.5193 19.0735i 0.00392735 0.00148276i
\(550\) 5688.42 1997.84i 0.441009 0.154887i
\(551\) 6176.11i 0.477516i
\(552\) 1103.05 + 6044.52i 0.0850522 + 0.466072i
\(553\) 641.427 + 641.427i 0.0493242 + 0.0493242i
\(554\) −11557.3 −0.886324
\(555\) −7077.31 7718.69i −0.541288 0.590343i
\(556\) −354.410 −0.0270329
\(557\) 8716.96 + 8716.96i 0.663105 + 0.663105i 0.956111 0.293006i \(-0.0946555\pi\)
−0.293006 + 0.956111i \(0.594656\pi\)
\(558\) −10222.8 4619.23i −0.775566 0.350444i
\(559\) 1117.28i 0.0845363i
\(560\) 478.268 + 760.186i 0.0360902 + 0.0573638i
\(561\) −2227.10 + 3221.38i −0.167608 + 0.242436i
\(562\) 4729.23 4729.23i 0.354965 0.354965i
\(563\) 11697.0 11697.0i 0.875615 0.875615i −0.117462 0.993077i \(-0.537476\pi\)
0.993077 + 0.117462i \(0.0374759\pi\)
\(564\) −2695.76 + 3899.27i −0.201262 + 0.291115i
\(565\) −2283.42 3629.39i −0.170025 0.270247i
\(566\) 9721.40i 0.721945i
\(567\) −872.435 + 13743.7i −0.0646188 + 1.01796i
\(568\) 2688.40 + 2688.40i 0.198596 + 0.198596i
\(569\) 11517.5 0.848576 0.424288 0.905527i \(-0.360524\pi\)
0.424288 + 0.905527i \(0.360524\pi\)
\(570\) −3236.11 3529.38i −0.237799 0.259350i
\(571\) −11093.9 −0.813072 −0.406536 0.913635i \(-0.633263\pi\)
−0.406536 + 0.913635i \(0.633263\pi\)
\(572\) −2108.68 2108.68i −0.154141 0.154141i
\(573\) −868.617 4759.88i −0.0633281 0.347027i
\(574\) 12384.8i 0.900577i
\(575\) −6300.25 + 2212.72i −0.456937 + 0.160481i
\(576\) −2626.50 6956.73i −0.189995 0.503236i
\(577\) −14119.4 + 14119.4i −1.01871 + 1.01871i −0.0188920 + 0.999822i \(0.506014\pi\)
−0.999822 + 0.0188920i \(0.993986\pi\)
\(578\) −5016.87 + 5016.87i −0.361028 + 0.361028i
\(579\) −15856.6 10962.4i −1.13813 0.786846i
\(580\) −7105.44 1617.46i −0.508685 0.115795i
\(581\) 3859.10i 0.275564i
\(582\) −11026.3 + 2012.16i −0.785320 + 0.143311i
\(583\) −4607.29 4607.29i −0.327297 0.327297i
\(584\) 8762.89 0.620909
\(585\) −3654.65 + 4825.28i −0.258293 + 0.341027i
\(586\) −10725.4 −0.756081
\(587\) 8524.33 + 8524.33i 0.599381 + 0.599381i 0.940148 0.340767i \(-0.110687\pi\)
−0.340767 + 0.940148i \(0.610687\pi\)
\(588\) −366.986 + 66.9702i −0.0257385 + 0.00469695i
\(589\) 12139.2i 0.849211i
\(590\) 11593.8 7294.23i 0.809001 0.508981i
\(591\) 18103.8 + 12516.0i 1.26005 + 0.871135i
\(592\) 542.020 542.020i 0.0376298 0.0376298i
\(593\) −4580.53 + 4580.53i −0.317200 + 0.317200i −0.847691 0.530491i \(-0.822008\pi\)
0.530491 + 0.847691i \(0.322008\pi\)
\(594\) −1634.08 + 6566.55i −0.112874 + 0.453584i
\(595\) −1230.38 + 5405.01i −0.0847740 + 0.372410i
\(596\) 1881.79i 0.129331i
\(597\) 102.105 + 559.518i 0.00699979 + 0.0383577i
\(598\) −1272.20 1272.20i −0.0869971 0.0869971i
\(599\) −10195.8 −0.695477 −0.347738 0.937592i \(-0.613050\pi\)
−0.347738 + 0.937592i \(0.613050\pi\)
\(600\) 12489.4 7122.05i 0.849798 0.484594i
\(601\) 18915.8 1.28385 0.641923 0.766769i \(-0.278137\pi\)
0.641923 + 0.766769i \(0.278137\pi\)
\(602\) −1250.11 1250.11i −0.0846355 0.0846355i
\(603\) −5188.36 + 11482.4i −0.350392 + 0.775452i
\(604\) 10788.4i 0.726778i
\(605\) −1256.59 + 5520.14i −0.0844421 + 0.370952i
\(606\) 1675.89 2424.09i 0.112341 0.162495i
\(607\) 12758.2 12758.2i 0.853113 0.853113i −0.137402 0.990515i \(-0.543875\pi\)
0.990515 + 0.137402i \(0.0438753\pi\)
\(608\) 6392.67 6392.67i 0.426409 0.426409i
\(609\) 7025.33 10161.8i 0.467456 0.676149i
\(610\) 31.7891 20.0000i 0.00211000 0.00132750i
\(611\) 3532.26i 0.233879i
\(612\) −1511.19 + 3344.41i −0.0998140 + 0.220898i
\(613\) 7340.02 + 7340.02i 0.483622 + 0.483622i 0.906286 0.422664i \(-0.138905\pi\)
−0.422664 + 0.906286i \(0.638905\pi\)
\(614\) −4349.39 −0.285875
\(615\) −22654.7 982.047i −1.48541 0.0643902i
\(616\) −12007.9 −0.785412
\(617\) −17118.9 17118.9i −1.11698 1.11698i −0.992182 0.124803i \(-0.960170\pi\)
−0.124803 0.992182i \(-0.539830\pi\)
\(618\) 2068.43 + 11334.7i 0.134635 + 0.737778i
\(619\) 3176.16i 0.206237i −0.994669 0.103118i \(-0.967118\pi\)
0.994669 0.103118i \(-0.0328820\pi\)
\(620\) 13965.8 + 3179.12i 0.904644 + 0.205930i
\(621\) 1809.84 7272.84i 0.116950 0.469966i
\(622\) 4762.79 4762.79i 0.307026 0.307026i
\(623\) 18930.8 18930.8i 1.21741 1.21741i
\(624\) −364.450 251.962i −0.0233809 0.0161644i
\(625\) 9770.20 + 12193.6i 0.625293 + 0.780390i
\(626\) 14424.6i 0.920965i
\(627\) −7203.53 + 1314.55i −0.458822 + 0.0837291i
\(628\) 6258.80 + 6258.80i 0.397697 + 0.397697i
\(629\) 4731.09 0.299906
\(630\) 1309.80 + 9488.09i 0.0828312 + 0.600023i
\(631\) −11467.2 −0.723459 −0.361729 0.932283i \(-0.617814\pi\)
−0.361729 + 0.932283i \(0.617814\pi\)
\(632\) 751.597 + 751.597i 0.0473052 + 0.0473052i
\(633\) 13878.0 2532.57i 0.871410 0.159021i
\(634\) 7392.26i 0.463066i
\(635\) 889.036 + 1413.08i 0.0555596 + 0.0883094i
\(636\) −5022.48 3472.29i −0.313136 0.216486i
\(637\) 196.556 196.556i 0.0122258 0.0122258i
\(638\) 4292.32 4292.32i 0.266355 0.266355i
\(639\) −1638.02 4338.59i −0.101407 0.268595i
\(640\) 6020.60 + 9569.47i 0.371852 + 0.591042i
\(641\) 12383.2i 0.763035i −0.924362 0.381518i \(-0.875402\pi\)
0.924362 0.381518i \(-0.124598\pi\)
\(642\) −1321.02 7238.95i −0.0812092 0.445013i
\(643\) −11142.9 11142.9i −0.683413 0.683413i 0.277354 0.960768i \(-0.410542\pi\)
−0.960768 + 0.277354i \(0.910542\pi\)
\(644\) 5226.29 0.319790
\(645\) 2385.87 2187.62i 0.145649 0.133546i
\(646\) 2163.30 0.131755
\(647\) −2391.21 2391.21i −0.145299 0.145299i 0.630716 0.776014i \(-0.282761\pi\)
−0.776014 + 0.630716i \(0.782761\pi\)
\(648\) −1022.28 + 16104.3i −0.0619738 + 0.976292i
\(649\) 20946.4i 1.26690i
\(650\) −1822.25 + 3795.13i −0.109961 + 0.229011i
\(651\) −13808.3 + 19973.0i −0.831322 + 1.20246i
\(652\) 3242.32 3242.32i 0.194753 0.194753i
\(653\) −16623.3 + 16623.3i −0.996201 + 0.996201i −0.999993 0.00379136i \(-0.998793\pi\)
0.00379136 + 0.999993i \(0.498793\pi\)
\(654\) 10296.5 14893.4i 0.615636 0.890484i
\(655\) 21577.0 + 4911.71i 1.28715 + 0.293002i
\(656\) 1659.81i 0.0987878i
\(657\) −9740.43 4401.27i −0.578403 0.261354i
\(658\) −3952.20 3952.20i −0.234153 0.234153i
\(659\) 20089.8 1.18754 0.593768 0.804636i \(-0.297640\pi\)
0.593768 + 0.804636i \(0.297640\pi\)
\(660\) 374.172 8631.73i 0.0220676 0.509075i
\(661\) 541.434 0.0318598 0.0159299 0.999873i \(-0.494929\pi\)
0.0159299 + 0.999873i \(0.494929\pi\)
\(662\) 11389.1 + 11389.1i 0.668654 + 0.668654i
\(663\) −490.931 2690.22i −0.0287574 0.157586i
\(664\) 4521.93i 0.264284i
\(665\) −8772.76 + 5519.36i −0.511569 + 0.321852i
\(666\) 7647.80 2887.41i 0.444964 0.167995i
\(667\) −4753.99 + 4753.99i −0.275975 + 0.275975i
\(668\) −15586.7 + 15586.7i −0.902796 + 0.902796i
\(669\) 17109.1 + 11828.3i 0.988751 + 0.683573i
\(670\) −1945.12 + 8544.86i −0.112159 + 0.492711i
\(671\) 57.4328i 0.00330428i
\(672\) −17789.7 + 3246.40i −1.02121 + 0.186358i
\(673\) −24314.3 24314.3i −1.39264 1.39264i −0.819354 0.573288i \(-0.805668\pi\)
−0.573288 0.819354i \(-0.694332\pi\)
\(674\) 6084.03 0.347697
\(675\) −17459.8 + 1643.58i −0.995599 + 0.0937207i
\(676\) −9295.71 −0.528887
\(677\) −14662.4 14662.4i −0.832380 0.832380i 0.155462 0.987842i \(-0.450313\pi\)
−0.987842 + 0.155462i \(0.950313\pi\)
\(678\) 3292.84 600.902i 0.186520 0.0340376i
\(679\) 24260.8i 1.37120i
\(680\) −1441.70 + 6333.36i −0.0813041 + 0.357166i
\(681\) 8456.13 + 5846.14i 0.475829 + 0.328964i
\(682\) −8436.57 + 8436.57i −0.473685 + 0.473685i
\(683\) −15981.2 + 15981.2i −0.895320 + 0.895320i −0.995018 0.0996976i \(-0.968212\pi\)
0.0996976 + 0.995018i \(0.468212\pi\)
\(684\) −6419.67 + 2423.73i −0.358863 + 0.135488i
\(685\) 6791.23 4272.68i 0.378803 0.238322i
\(686\) 10443.3i 0.581233i
\(687\) 3666.36 + 20091.1i 0.203611 + 1.11575i
\(688\) 167.540 + 167.540i 0.00928400 + 0.00928400i
\(689\) 4549.75 0.251570
\(690\) 225.744 5207.66i 0.0124550 0.287322i
\(691\) −16714.9 −0.920209 −0.460105 0.887865i \(-0.652188\pi\)
−0.460105 + 0.887865i \(0.652188\pi\)
\(692\) 9525.19 + 9525.19i 0.523256 + 0.523256i
\(693\) 13347.5 + 6031.14i 0.731645 + 0.330598i
\(694\) 19424.1i 1.06243i
\(695\) 746.023 + 169.822i 0.0407169 + 0.00926865i
\(696\) 8231.98 11907.1i 0.448322 0.648474i
\(697\) 7243.96 7243.96i 0.393665 0.393665i
\(698\) −3285.13 + 3285.13i −0.178143 + 0.178143i
\(699\) 8277.19 11972.5i 0.447886 0.647842i
\(700\) −4052.37 11538.3i −0.218808 0.623009i
\(701\) 6990.49i 0.376643i −0.982107 0.188322i \(-0.939695\pi\)
0.982107 0.188322i \(-0.0603048\pi\)
\(702\) −2435.44 4049.11i −0.130940 0.217698i
\(703\) 6255.06 + 6255.06i 0.335582 + 0.335582i
\(704\) −7908.75 −0.423398
\(705\) 7542.91 6916.13i 0.402954 0.369470i
\(706\) −15056.1 −0.802611
\(707\) −4510.51 4510.51i −0.239936 0.239936i
\(708\) −3523.86 19310.2i −0.187055 1.02503i
\(709\) 28175.0i 1.49243i 0.665705 + 0.746215i \(0.268131\pi\)
−0.665705 + 0.746215i \(0.731869\pi\)
\(710\) −1717.60 2730.04i −0.0907890 0.144305i
\(711\) −457.943 1212.94i −0.0241550 0.0639787i
\(712\) 22182.3 22182.3i 1.16758 1.16758i
\(713\) 9343.99 9343.99i 0.490793 0.490793i
\(714\) −3559.35 2460.75i −0.186562 0.128980i
\(715\) 3428.31 + 5449.13i 0.179317 + 0.285015i
\(716\) 4254.90i 0.222085i
\(717\) 15213.6 2776.28i 0.792414 0.144605i
\(718\) 10484.1 + 10484.1i 0.544933 + 0.544933i
\(719\) −20143.8 −1.04484 −0.522418 0.852690i \(-0.674970\pi\)
−0.522418 + 0.852690i \(0.674970\pi\)
\(720\) −175.540 1271.60i −0.00908609 0.0658189i
\(721\) 24939.2 1.28819
\(722\) −5286.05 5286.05i −0.272474 0.272474i
\(723\) 9382.32 1712.15i 0.482617 0.0880715i
\(724\) 11985.0i 0.615222i
\(725\) 14181.7 + 6809.41i 0.726477 + 0.348821i
\(726\) −3635.16 2513.17i −0.185831 0.128475i
\(727\) −9805.90 + 9805.90i −0.500249 + 0.500249i −0.911515 0.411267i \(-0.865087\pi\)
0.411267 + 0.911515i \(0.365087\pi\)
\(728\) 5929.00 5929.00i 0.301845 0.301845i
\(729\) 9224.92 17387.4i 0.468674 0.883371i
\(730\) −7248.57 1650.04i −0.367509 0.0836585i
\(731\) 1462.39i 0.0739926i
\(732\) −9.66205 52.9464i −0.000487868 0.00267344i
\(733\) 16533.1 + 16533.1i 0.833100 + 0.833100i 0.987940 0.154840i \(-0.0494861\pi\)
−0.154840 + 0.987940i \(0.549486\pi\)
\(734\) −14706.3 −0.739536
\(735\) 804.585 + 34.8775i 0.0403776 + 0.00175031i
\(736\) 9841.37 0.492877
\(737\) 9476.04 + 9476.04i 0.473615 + 0.473615i
\(738\) 7288.81 16130.8i 0.363557 0.804586i
\(739\) 15250.1i 0.759114i 0.925168 + 0.379557i \(0.123924\pi\)
−0.925168 + 0.379557i \(0.876076\pi\)
\(740\) −8834.41 + 5558.14i −0.438864 + 0.276110i
\(741\) 2907.72 4205.85i 0.144153 0.208510i
\(742\) 5090.66 5090.66i 0.251865 0.251865i
\(743\) −5438.49 + 5438.49i −0.268531 + 0.268531i −0.828508 0.559977i \(-0.810810\pi\)
0.559977 + 0.828508i \(0.310810\pi\)
\(744\) −16180.0 + 23403.5i −0.797294 + 1.15324i
\(745\) 901.693 3961.11i 0.0443429 0.194797i
\(746\) 8514.27i 0.417868i
\(747\) −2271.20 + 5026.38i −0.111243 + 0.246192i
\(748\) 2760.04 + 2760.04i 0.134916 + 0.134916i
\(749\) −15927.5 −0.777009
\(750\) −11672.2 + 3539.54i −0.568278 + 0.172328i
\(751\) 2087.82 0.101446 0.0507228 0.998713i \(-0.483848\pi\)
0.0507228 + 0.998713i \(0.483848\pi\)
\(752\) 529.676 + 529.676i 0.0256852 + 0.0256852i
\(753\) 1438.55 + 7883.01i 0.0696197 + 0.381505i
\(754\) 4238.72i 0.204728i
\(755\) 5169.46 22709.3i 0.249187 1.09467i
\(756\) 13319.5 + 3314.54i 0.640774 + 0.159456i
\(757\) −10258.6 + 10258.6i −0.492546 + 0.492546i −0.909107 0.416562i \(-0.863235\pi\)
0.416562 + 0.909107i \(0.363235\pi\)
\(758\) 8444.86 8444.86i 0.404658 0.404658i
\(759\) −6556.70 4532.98i −0.313561 0.216781i
\(760\) −10279.5 + 6467.35i −0.490629 + 0.308678i
\(761\) 26879.5i 1.28040i 0.768210 + 0.640198i \(0.221148\pi\)
−0.768210 + 0.640198i \(0.778852\pi\)
\(762\) −1282.05 + 233.958i −0.0609498 + 0.0111226i
\(763\) −27712.1 27712.1i −1.31487 1.31487i
\(764\) −4822.43 −0.228363
\(765\) 4783.54 6315.77i 0.226078 0.298493i
\(766\) 4028.02 0.189998
\(767\) 10342.4 + 10342.4i 0.486888 + 0.486888i
\(768\) −19944.6 + 3639.64i −0.937097 + 0.171008i
\(769\) 25180.9i 1.18082i −0.807105 0.590408i \(-0.798967\pi\)
0.807105 0.590408i \(-0.201033\pi\)
\(770\) 9932.85 + 2261.08i 0.464877 + 0.105823i
\(771\) 2592.23 + 1792.14i 0.121085 + 0.0837124i
\(772\) −13585.7 + 13585.7i −0.633369 + 0.633369i
\(773\) 18871.2 18871.2i 0.878072 0.878072i −0.115263 0.993335i \(-0.536771\pi\)
0.993335 + 0.115263i \(0.0367711\pi\)
\(774\) 892.506 + 2363.96i 0.0414476 + 0.109781i
\(775\) −27874.2 13383.9i −1.29196 0.620341i
\(776\) 28427.7i 1.31507i
\(777\) −3176.52 17406.8i −0.146663 0.803688i
\(778\) 14682.1 + 14682.1i 0.676581 + 0.676581i
\(779\) 19154.7 0.880988
\(780\) 4077.22 + 4446.72i 0.187164 + 0.204126i
\(781\) −4932.32 −0.225982
\(782\) 1665.18 + 1665.18i 0.0761465 + 0.0761465i
\(783\) −15130.8 + 9100.79i −0.690588 + 0.415371i
\(784\) 58.9485i 0.00268533i
\(785\) −10175.6 16173.6i −0.462653 0.735365i
\(786\) −9823.43 + 14209.0i −0.445789 + 0.644809i
\(787\) 14716.0 14716.0i 0.666542 0.666542i −0.290372 0.956914i \(-0.593779\pi\)
0.956914 + 0.290372i \(0.0937789\pi\)
\(788\) 15511.1 15511.1i 0.701217 0.701217i
\(789\) −21968.5 + 31776.2i −0.991253 + 1.43379i
\(790\) −480.189 763.238i −0.0216258 0.0343731i
\(791\) 7245.10i 0.325672i
\(792\) 15640.0 + 7067.03i 0.701697 + 0.317066i
\(793\) 28.3578 + 28.3578i 0.00126988 + 0.00126988i
\(794\) 3183.22 0.142277
\(795\) 8908.37 + 9715.69i 0.397418 + 0.433434i
\(796\) 566.871 0.0252415
\(797\) 17463.9 + 17463.9i 0.776163 + 0.776163i 0.979176 0.203013i \(-0.0650735\pi\)
−0.203013 + 0.979176i \(0.565073\pi\)
\(798\) −1452.47 7959.28i −0.0644321 0.353077i
\(799\) 4623.35i 0.204709i
\(800\) −7630.82 21727.2i −0.337238 0.960214i
\(801\) −35798.1 + 13515.5i −1.57911 + 0.596188i
\(802\) −2709.42 + 2709.42i −0.119293 + 0.119293i
\(803\) −8038.49 + 8038.49i −0.353265 + 0.353265i
\(804\) 10330.0 + 7141.64i 0.453122 + 0.313266i
\(805\) −11001.2 2504.28i −0.481667 0.109645i
\(806\) 8331.22i 0.364088i
\(807\) 9867.40 1800.68i 0.430420 0.0785462i
\(808\) −5285.22 5285.22i −0.230115 0.230115i
\(809\) −24097.9 −1.04727 −0.523633 0.851944i \(-0.675424\pi\)
−0.523633 + 0.851944i \(0.675424\pi\)
\(810\) 3878.04 13128.8i 0.168223 0.569506i
\(811\) 25302.7 1.09556 0.547780 0.836622i \(-0.315473\pi\)
0.547780 + 0.836622i \(0.315473\pi\)
\(812\) −8706.47 8706.47i −0.376277 0.376277i
\(813\) −16672.8 + 3042.57i −0.719238 + 0.131252i
\(814\) 8694.39i 0.374371i
\(815\) −8378.61 + 5271.38i −0.360110 + 0.226562i
\(816\) 477.025 + 329.791i 0.0204647 + 0.0141483i
\(817\) −1933.46 + 1933.46i −0.0827945 + 0.0827945i
\(818\) −5480.85 + 5480.85i −0.234271 + 0.234271i
\(819\) −9568.33 + 3612.50i −0.408235 + 0.154128i
\(820\) −5016.42 + 22037.0i −0.213635 + 0.938494i
\(821\) 27925.3i 1.18709i −0.804802 0.593544i \(-0.797728\pi\)
0.804802 0.593544i \(-0.202272\pi\)
\(822\) 1124.39 + 6161.50i 0.0477102 + 0.261444i
\(823\) 997.907 + 997.907i 0.0422659 + 0.0422659i 0.727924 0.685658i \(-0.240485\pi\)
−0.685658 + 0.727924i \(0.740485\pi\)
\(824\) 29222.6 1.23546
\(825\) −4923.67 + 17990.3i −0.207782 + 0.759200i
\(826\) 23144.0 0.974918
\(827\) −18683.3 18683.3i −0.785590 0.785590i 0.195178 0.980768i \(-0.437471\pi\)
−0.980768 + 0.195178i \(0.937471\pi\)
\(828\) −6807.11 3075.83i −0.285705 0.129097i
\(829\) 21146.9i 0.885962i 0.896531 + 0.442981i \(0.146079\pi\)
−0.896531 + 0.442981i \(0.853921\pi\)
\(830\) −851.473 + 3740.49i −0.0356085 + 0.156427i
\(831\) 20332.8 29410.2i 0.848780 1.22771i
\(832\) 3904.99 3904.99i 0.162718 0.162718i
\(833\) −257.270 + 257.270i −0.0107009 + 0.0107009i
\(834\) −339.644 + 491.276i −0.0141018 + 0.0203975i
\(835\) 40278.2 25340.9i 1.66932 1.05025i
\(836\) 7298.19i 0.301930i
\(837\) 29739.6 17887.6i 1.22814 0.738695i
\(838\) 2544.31 + 2544.31i 0.104883 + 0.104883i
\(839\) 30903.4 1.27164 0.635820 0.771838i \(-0.280662\pi\)
0.635820 + 0.771838i \(0.280662\pi\)
\(840\) 24269.9 + 1052.06i 0.996894 + 0.0432138i
\(841\) −8549.68 −0.350555
\(842\) 10557.5 + 10557.5i 0.432109 + 0.432109i
\(843\) 3714.48 + 20354.7i 0.151760 + 0.831618i
\(844\) 14060.4i 0.573435i
\(845\) 19567.2 + 4454.21i 0.796607 + 0.181337i
\(846\) 2821.65 + 7473.63i 0.114669 + 0.303722i
\(847\) −6763.96 + 6763.96i −0.274395 + 0.274395i
\(848\) −682.252 + 682.252i −0.0276281 + 0.0276281i
\(849\) −24738.3 17102.8i −1.00002 0.691364i
\(850\) 2385.12 4967.42i 0.0962460 0.200448i
\(851\) 9629.53i 0.387892i
\(852\) −4547.02 + 829.774i −0.182839 + 0.0333657i
\(853\) 181.224 + 181.224i 0.00727432 + 0.00727432i 0.710735 0.703460i \(-0.248363\pi\)
−0.703460 + 0.710735i \(0.748363\pi\)
\(854\) 63.4584 0.00254274
\(855\) 14674.6 2025.78i 0.586971 0.0810295i
\(856\) −18663.2 −0.745205
\(857\) −13852.9 13852.9i −0.552167 0.552167i 0.374899 0.927066i \(-0.377677\pi\)
−0.927066 + 0.374899i \(0.877677\pi\)
\(858\) −4943.85 + 902.189i −0.196713 + 0.0358977i
\(859\) 8910.47i 0.353925i −0.984218 0.176962i \(-0.943373\pi\)
0.984218 0.176962i \(-0.0566271\pi\)
\(860\) −1718.04 2730.74i −0.0681216 0.108276i
\(861\) −31515.9 21788.5i −1.24746 0.862428i
\(862\) −18655.0 + 18655.0i −0.737112 + 0.737112i
\(863\) −6487.75 + 6487.75i −0.255905 + 0.255905i −0.823386 0.567481i \(-0.807918\pi\)
0.567481 + 0.823386i \(0.307918\pi\)
\(864\) 25081.2 + 6241.43i 0.987594 + 0.245761i
\(865\) −15486.1 24614.4i −0.608720 0.967533i
\(866\) 12900.0i 0.506187i
\(867\) −3940.40 21592.8i −0.154352 0.845823i
\(868\) 17112.6 + 17112.6i 0.669170 + 0.669170i
\(869\) −1378.93 −0.0538285
\(870\) −9051.50 + 8299.37i −0.352729 + 0.323419i
\(871\) −9357.71 −0.364034
\(872\) −32471.9 32471.9i −1.26105 1.26105i
\(873\) 14278.2 31599.0i 0.553543 1.22504i
\(874\) 4403.12i 0.170409i
\(875\) 3001.35 + 26229.5i 0.115959 + 1.01339i
\(876\) −6058.22 + 8762.89i −0.233662 + 0.337980i
\(877\) −20231.6 + 20231.6i −0.778987 + 0.778987i −0.979659 0.200672i \(-0.935688\pi\)
0.200672 + 0.979659i \(0.435688\pi\)
\(878\) −9764.88 + 9764.88i −0.375340 + 0.375340i
\(879\) 18869.2 27293.3i 0.724054 1.04730i
\(880\) −1331.20 303.031i −0.0509942 0.0116081i
\(881\) 33209.0i 1.26996i 0.772527 + 0.634982i \(0.218993\pi\)
−0.772527 + 0.634982i \(0.781007\pi\)
\(882\) −258.863 + 572.889i −0.00988251 + 0.0218709i
\(883\) 26984.3 + 26984.3i 1.02842 + 1.02842i 0.999584 + 0.0288331i \(0.00917914\pi\)
0.0288331 + 0.999584i \(0.490821\pi\)
\(884\) −2725.57 −0.103700
\(885\) −1835.19 + 42335.9i −0.0697055 + 1.60803i
\(886\) 4656.90 0.176582
\(887\) 24008.9 + 24008.9i 0.908838 + 0.908838i 0.996179 0.0873406i \(-0.0278369\pi\)
−0.0873406 + 0.996179i \(0.527837\pi\)
\(888\) −3722.11 20396.5i −0.140660 0.770792i
\(889\) 2820.84i 0.106421i
\(890\) −22525.8 + 14172.1i −0.848390 + 0.533762i
\(891\) −13835.3 15710.8i −0.520200 0.590720i
\(892\) 14658.8 14658.8i 0.550240 0.550240i
\(893\) −6112.61 + 6112.61i −0.229060 + 0.229060i
\(894\) 2608.50 + 1803.39i 0.0975853 + 0.0674656i
\(895\) −2038.81 + 8956.44i −0.0761452 + 0.334504i
\(896\) 19102.9i 0.712258i
\(897\) 5475.59 999.226i 0.203818 0.0371942i
\(898\) −21198.9 21198.9i −0.787768 0.787768i
\(899\) −31132.2 −1.15497
\(900\) −1512.52 + 17413.3i −0.0560191 + 0.644935i
\(901\) −5955.13 −0.220193
\(902\) −13312.3 13312.3i −0.491409 0.491409i
\(903\) 5380.49 981.871i 0.198285 0.0361845i
\(904\) 8489.50i 0.312341i
\(905\) −5742.86 + 25228.2i −0.210938 + 0.926645i
\(906\) 14954.7 + 10338.9i 0.548384 + 0.379125i
\(907\) −23026.7 + 23026.7i −0.842989 + 0.842989i −0.989246 0.146258i \(-0.953277\pi\)
0.146258 + 0.989246i \(0.453277\pi\)
\(908\) 7245.11 7245.11i 0.264799 0.264799i
\(909\) 3220.25 + 8529.38i 0.117501 + 0.311223i
\(910\) −6020.83 + 3787.99i −0.219328 + 0.137990i
\(911\) 33422.1i 1.21550i −0.794127 0.607752i \(-0.792071\pi\)
0.794127 0.607752i \(-0.207929\pi\)
\(912\) 194.660 + 1066.71i 0.00706781 + 0.0387304i
\(913\) 4148.12 + 4148.12i 0.150364 + 0.150364i
\(914\) 15075.7 0.545581
\(915\) −5.03191 + 116.080i −0.000181803 + 0.00419399i
\(916\) 20355.1 0.734226
\(917\) 26438.8 + 26438.8i 0.952112 + 0.952112i
\(918\) 3187.73 + 5299.85i 0.114609 + 0.190546i
\(919\) 42542.2i 1.52703i −0.645792 0.763513i \(-0.723473\pi\)
0.645792 0.763513i \(-0.276527\pi\)
\(920\) −12890.7 2934.40i −0.461951 0.105157i
\(921\) 7651.86 11068.0i 0.273765 0.395986i
\(922\) −10508.7 + 10508.7i −0.375363 + 0.375363i
\(923\) 2435.36 2435.36i 0.0868482 0.0868482i
\(924\) 8301.70 12007.9i 0.295569 0.427524i
\(925\) 21259.5 7466.56i 0.755684 0.265404i
\(926\) 3157.84i 0.112066i
\(927\) −32482.6 14677.4i −1.15088 0.520033i
\(928\) −16394.7 16394.7i −0.579938 0.579938i
\(929\) 5721.21 0.202053 0.101026 0.994884i \(-0.467787\pi\)
0.101026 + 0.994884i \(0.467787\pi\)
\(930\) 17790.8 16312.4i 0.627292 0.575168i
\(931\) −680.282 −0.0239477
\(932\) −10257.9 10257.9i −0.360524 0.360524i
\(933\) 3740.83 + 20499.1i 0.131264 + 0.719305i
\(934\) 3515.38i 0.123155i
\(935\) −4487.28 7132.32i −0.156952 0.249467i
\(936\) −11211.8 + 4232.97i −0.391525 + 0.147819i
\(937\) 1344.01 1344.01i 0.0468589 0.0468589i −0.683289 0.730148i \(-0.739451\pi\)
0.730148 + 0.683289i \(0.239451\pi\)
\(938\) −10470.2 + 10470.2i −0.364461 + 0.364461i
\(939\) 36706.8 + 25377.2i 1.27570 + 0.881953i
\(940\) −5431.56 8633.22i −0.188466 0.299558i
\(941\) 9625.77i 0.333466i −0.986002 0.166733i \(-0.946678\pi\)
0.986002 0.166733i \(-0.0533217\pi\)
\(942\) 14673.9 2677.80i 0.507538 0.0926192i
\(943\) 14744.1 + 14744.1i 0.509157 + 0.509157i
\(944\) −3101.77 −0.106943
\(945\) −26448.9 13359.3i −0.910459 0.459870i
\(946\) 2687.46 0.0923645
\(947\) −2234.24 2234.24i −0.0766664 0.0766664i 0.667734 0.744400i \(-0.267264\pi\)
−0.744400 + 0.667734i \(0.767264\pi\)
\(948\) −1271.21 + 231.980i −0.0435518 + 0.00794765i
\(949\) 7938.11i 0.271530i
\(950\) 9720.93 3414.10i 0.331988 0.116598i
\(951\) −18811.3 13005.2i −0.641427 0.443451i
\(952\) −7760.41 + 7760.41i −0.264198 + 0.264198i
\(953\) 6457.14 6457.14i 0.219483 0.219483i −0.588798 0.808281i \(-0.700398\pi\)
0.808281 + 0.588798i \(0.200398\pi\)
\(954\) −9626.45 + 3634.44i −0.326696 + 0.123343i
\(955\) 10151.1 + 2310.75i 0.343959 + 0.0782977i
\(956\) 15413.5i 0.521451i
\(957\) 3371.32 + 18474.3i 0.113876 + 0.624021i
\(958\) 5985.35 + 5985.35i 0.201856 + 0.201856i
\(959\) 13556.9 0.456491
\(960\) 15984.8 + 692.916i 0.537403 + 0.0232956i
\(961\) 31399.6 1.05399
\(962\) 4292.91 + 4292.91i 0.143876 + 0.143876i
\(963\) 20745.2 + 9373.84i 0.694190 + 0.313674i
\(964\) 9505.61i 0.317588i
\(965\) 35107.4 22087.7i 1.17114 0.736817i
\(966\) 5008.55 7244.59i 0.166819 0.241295i
\(967\) 13166.9 13166.9i 0.437869 0.437869i −0.453425 0.891294i \(-0.649798\pi\)
0.891294 + 0.453425i \(0.149798\pi\)
\(968\) −7925.72 + 7925.72i −0.263163 + 0.263163i
\(969\) −3805.89 + 5505.01i −0.126174 + 0.182504i
\(970\) 5352.90 23515.1i 0.177187 0.778376i
\(971\) 21504.3i 0.710716i −0.934730 0.355358i \(-0.884359\pi\)
0.934730 0.355358i \(-0.115641\pi\)
\(972\) −15397.6 12156.0i −0.508104 0.401136i
\(973\) 914.119 + 914.119i 0.0301185 + 0.0301185i
\(974\) −3071.14 −0.101032
\(975\) −6451.71 11313.9i −0.211918 0.371625i
\(976\) −8.50472 −0.000278924
\(977\) −8996.19 8996.19i −0.294589 0.294589i 0.544301 0.838890i \(-0.316795\pi\)
−0.838890 + 0.544301i \(0.816795\pi\)
\(978\) −1387.21 7601.68i −0.0453559 0.248543i
\(979\) 40697.1i 1.32858i
\(980\) 178.159 782.646i 0.00580722 0.0255109i
\(981\) 19784.9 + 52403.7i 0.643917 + 1.70553i
\(982\) 16467.8 16467.8i 0.535142 0.535142i
\(983\) −16337.3 + 16337.3i −0.530090 + 0.530090i −0.920599 0.390509i \(-0.872299\pi\)
0.390509 + 0.920599i \(0.372299\pi\)
\(984\) −36929.0 25530.8i −1.19639 0.827128i
\(985\) −40082.8 + 25218.0i −1.29659 + 0.815748i
\(986\) 5548.02i 0.179194i
\(987\) 17010.4 3104.18i 0.548578 0.100108i
\(988\) −3603.53 3603.53i −0.116036 0.116036i
\(989\) −2976.52 −0.0957004
\(990\) −11606.6 8790.77i −0.372607 0.282211i
\(991\) −18296.9 −0.586500 −0.293250 0.956036i \(-0.594737\pi\)
−0.293250 + 0.956036i \(0.594737\pi\)
\(992\) 32223.9 + 32223.9i 1.03136 + 1.03136i
\(993\) −49018.8 + 8945.31i −1.56653 + 0.285872i
\(994\) 5449.79i 0.173900i
\(995\) −1193.25 271.627i −0.0380186 0.00865441i
\(996\) 4521.93 + 3126.24i 0.143858 + 0.0994564i
\(997\) 20406.0 20406.0i 0.648210 0.648210i −0.304350 0.952560i \(-0.598439\pi\)
0.952560 + 0.304350i \(0.0984393\pi\)
\(998\) 12926.9 12926.9i 0.410015 0.410015i
\(999\) −6107.09 + 24541.4i −0.193413 + 0.777232i
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 15.4.e.a.8.2 yes 8
3.2 odd 2 inner 15.4.e.a.8.3 yes 8
4.3 odd 2 240.4.v.c.113.1 8
5.2 odd 4 inner 15.4.e.a.2.3 yes 8
5.3 odd 4 75.4.e.c.32.2 8
5.4 even 2 75.4.e.c.68.3 8
12.11 even 2 240.4.v.c.113.2 8
15.2 even 4 inner 15.4.e.a.2.2 8
15.8 even 4 75.4.e.c.32.3 8
15.14 odd 2 75.4.e.c.68.2 8
20.7 even 4 240.4.v.c.17.2 8
60.47 odd 4 240.4.v.c.17.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.4.e.a.2.2 8 15.2 even 4 inner
15.4.e.a.2.3 yes 8 5.2 odd 4 inner
15.4.e.a.8.2 yes 8 1.1 even 1 trivial
15.4.e.a.8.3 yes 8 3.2 odd 2 inner
75.4.e.c.32.2 8 5.3 odd 4
75.4.e.c.32.3 8 15.8 even 4
75.4.e.c.68.2 8 15.14 odd 2
75.4.e.c.68.3 8 5.4 even 2
240.4.v.c.17.1 8 60.47 odd 4
240.4.v.c.17.2 8 20.7 even 4
240.4.v.c.113.1 8 4.3 odd 2
240.4.v.c.113.2 8 12.11 even 2