Properties

Label 75.4.e.c.68.2
Level $75$
Weight $4$
Character 75.68
Analytic conductor $4.425$
Analytic rank $0$
Dimension $8$
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] = [75,4,Mod(32,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, 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("75.32");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 75.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: \(4.42514325043\)
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: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 68.2
Root \(-1.18766 + 1.18766i\) of defining polynomial
Character \(\chi\) \(=\) 75.68
Dual form 75.4.e.c.32.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18766 - 1.18766i) q^{2} +(0.932827 - 5.11173i) q^{3} -5.17891i q^{4} +(-7.17891 + 4.96314i) q^{6} +(13.3578 - 13.3578i) q^{7} +(-15.6521 + 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +O(q^{10})\) \(q+(-1.18766 - 1.18766i) q^{2} +(0.932827 - 5.11173i) q^{3} -5.17891i q^{4} +(-7.17891 + 4.96314i) q^{6} +(13.3578 - 13.3578i) q^{7} +(-15.6521 + 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +28.7164i q^{11} +(-26.4732 - 4.83102i) q^{12} +(-14.1789 - 14.1789i) q^{13} -31.7292 q^{14} -4.25236 q^{16} +(-18.5587 - 18.5587i) q^{17} +(18.6736 + 41.3264i) q^{18} -49.0735i q^{19} +(-55.8211 - 80.7421i) q^{21} +(34.1055 - 34.1055i) q^{22} +(37.7738 - 37.7738i) q^{23} +(65.4088 + 94.6102i) q^{24} +33.6796i q^{26} +(-72.3121 + 120.225i) q^{27} +(-69.1789 - 69.1789i) q^{28} +125.854 q^{29} +247.367 q^{31} +(130.267 + 130.267i) q^{32} +(146.791 + 26.7874i) q^{33} +44.0829i q^{34} +(-49.3898 + 130.818i) q^{36} +(127.463 - 127.463i) q^{37} +(-58.2828 + 58.2828i) q^{38} +(-85.7053 + 59.2524i) q^{39} -390.328i q^{41} +(-29.5978 + 162.191i) q^{42} +(39.3993 + 39.3993i) q^{43} +148.720 q^{44} -89.7251 q^{46} +(-124.560 - 124.560i) q^{47} +(-3.96671 + 21.7369i) q^{48} -13.8625i q^{49} +(-112.179 + 77.5549i) q^{51} +(-73.4313 + 73.4313i) q^{52} +(160.441 - 160.441i) q^{53} +(228.669 - 56.9040i) q^{54} +418.156i q^{56} +(-250.850 - 45.7770i) q^{57} +(-149.473 - 149.473i) q^{58} -729.423 q^{59} +2.00000 q^{61} +(-293.789 - 293.789i) q^{62} +(-464.804 + 210.024i) q^{63} -275.409i q^{64} +(-142.524 - 206.153i) q^{66} +(329.987 - 329.987i) q^{67} +(-96.1136 + 96.1136i) q^{68} +(-157.853 - 228.326i) q^{69} +171.760i q^{71} +(544.637 - 246.097i) q^{72} +(279.927 + 279.927i) q^{73} -302.767 q^{74} -254.147 q^{76} +(383.589 + 383.589i) q^{77} +(172.161 + 31.4172i) q^{78} -48.0189i q^{79} +(547.102 + 481.789i) q^{81} +(-463.578 + 463.578i) q^{82} +(-144.451 + 144.451i) q^{83} +(-418.156 + 289.092i) q^{84} -93.5862i q^{86} +(117.400 - 643.334i) q^{87} +(-449.473 - 449.473i) q^{88} +1417.21 q^{89} -378.799 q^{91} +(-195.627 - 195.627i) q^{92} +(230.751 - 1264.48i) q^{93} +295.872i q^{94} +(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 \( 8 q + 6 q^{3} - 12 q^{6} + 16 q^{7} - 132 q^{12} - 68 q^{13} + 284 q^{16} + 240 q^{18} - 492 q^{21} + 500 q^{22} - 702 q^{27} - 508 q^{28} + 616 q^{31} + 240 q^{33} - 804 q^{36} + 1156 q^{37} - 540 q^{42} - 548 q^{43} + 736 q^{46} + 1116 q^{48} - 852 q^{51} - 224 q^{52} - 684 q^{57} - 60 q^{58} + 16 q^{61} - 1428 q^{63} + 2040 q^{66} - 404 q^{67} + 1800 q^{72} + 2512 q^{73} - 1488 q^{76} + 360 q^{78} + 288 q^{81} - 2800 q^{82} + 1680 q^{87} - 2460 q^{88} - 1304 q^{91} - 3408 q^{93} + 4164 q^{96} - 1904 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 \(0.845958\pi\)
\(3\) 0.932827 5.11173i 0.179523 0.983754i
\(4\) 5.17891i 0.647364i
\(5\) 0 0
\(6\) −7.17891 + 4.96314i −0.488463 + 0.337699i
\(7\) 13.3578 13.3578i 0.721254 0.721254i −0.247606 0.968861i \(-0.579644\pi\)
0.968861 + 0.247606i \(0.0796440\pi\)
\(8\) −15.6521 + 15.6521i −0.691732 + 0.691732i
\(9\) −25.2597 9.53673i −0.935543 0.353212i
\(10\) 0 0
\(11\) 28.7164i 0.787121i 0.919299 + 0.393560i \(0.128757\pi\)
−0.919299 + 0.393560i \(0.871243\pi\)
\(12\) −26.4732 4.83102i −0.636846 0.116216i
\(13\) −14.1789 14.1789i −0.302502 0.302502i 0.539490 0.841992i \(-0.318617\pi\)
−0.841992 + 0.539490i \(0.818617\pi\)
\(14\) −31.7292 −0.605713
\(15\) 0 0
\(16\) −4.25236 −0.0664431
\(17\) −18.5587 18.5587i −0.264773 0.264773i 0.562217 0.826990i \(-0.309949\pi\)
−0.826990 + 0.562217i \(0.809949\pi\)
\(18\) 18.6736 + 41.3264i 0.244522 + 0.541152i
\(19\) 49.0735i 0.592538i −0.955105 0.296269i \(-0.904258\pi\)
0.955105 0.296269i \(-0.0957425\pi\)
\(20\) 0 0
\(21\) −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
\(25\) 0 0
\(26\) 33.6796i 0.254042i
\(27\) −72.3121 + 120.225i −0.515425 + 0.856935i
\(28\) −69.1789 69.1789i −0.466914 0.466914i
\(29\) 125.854 0.805882 0.402941 0.915226i \(-0.367988\pi\)
0.402941 + 0.915226i \(0.367988\pi\)
\(30\) 0 0
\(31\) 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
\(33\) 146.791 + 26.7874i 0.774333 + 0.141306i
\(34\) 44.0829i 0.222357i
\(35\) 0 0
\(36\) −49.3898 + 130.818i −0.228657 + 0.605637i
\(37\) 127.463 127.463i 0.566347 0.566347i −0.364756 0.931103i \(-0.618848\pi\)
0.931103 + 0.364756i \(0.118848\pi\)
\(38\) −58.2828 + 58.2828i −0.248808 + 0.248808i
\(39\) −85.7053 + 59.2524i −0.351893 + 0.243281i
\(40\) 0 0
\(41\) 390.328i 1.48680i −0.668845 0.743402i \(-0.733211\pi\)
0.668845 0.743402i \(-0.266789\pi\)
\(42\) −29.5978 + 162.191i −0.108739 + 0.595873i
\(43\) 39.3993 + 39.3993i 0.139729 + 0.139729i 0.773511 0.633783i \(-0.218499\pi\)
−0.633783 + 0.773511i \(0.718499\pi\)
\(44\) 148.720 0.509553
\(45\) 0 0
\(46\) −89.7251 −0.287592
\(47\) −124.560 124.560i −0.386575 0.386575i 0.486889 0.873464i \(-0.338132\pi\)
−0.873464 + 0.486889i \(0.838132\pi\)
\(48\) −3.96671 + 21.7369i −0.0119280 + 0.0653637i
\(49\) 13.8625i 0.0404155i
\(50\) 0 0
\(51\) −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
\(55\) 0 0
\(56\) 418.156i 0.997830i
\(57\) −250.850 45.7770i −0.582912 0.106374i
\(58\) −149.473 149.473i −0.338392 0.338392i
\(59\) −729.423 −1.60954 −0.804769 0.593588i \(-0.797711\pi\)
−0.804769 + 0.593588i \(0.797711\pi\)
\(60\) 0 0
\(61\) 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
\(63\) −464.804 + 210.024i −0.929520 + 0.420009i
\(64\) 275.409i 0.537908i
\(65\) 0 0
\(66\) −142.524 206.153i −0.265810 0.384479i
\(67\) 329.987 329.987i 0.601706 0.601706i −0.339059 0.940765i \(-0.610109\pi\)
0.940765 + 0.339059i \(0.110109\pi\)
\(68\) −96.1136 + 96.1136i −0.171404 + 0.171404i
\(69\) −157.853 228.326i −0.275410 0.398365i
\(70\) 0 0
\(71\) 171.760i 0.287100i 0.989643 + 0.143550i \(0.0458518\pi\)
−0.989643 + 0.143550i \(0.954148\pi\)
\(72\) 544.637 246.097i 0.891474 0.402817i
\(73\) 279.927 + 279.927i 0.448807 + 0.448807i 0.894958 0.446151i \(-0.147205\pi\)
−0.446151 + 0.894958i \(0.647205\pi\)
\(74\) −302.767 −0.475621
\(75\) 0 0
\(76\) −254.147 −0.383587
\(77\) 383.589 + 383.589i 0.567714 + 0.567714i
\(78\) 172.161 + 31.4172i 0.249915 + 0.0456064i
\(79\) 48.0189i 0.0683866i −0.999415 0.0341933i \(-0.989114\pi\)
0.999415 0.0341933i \(-0.0108862\pi\)
\(80\) 0 0
\(81\) 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
\(85\) 0 0
\(86\) 93.5862i 0.117345i
\(87\) 117.400 643.334i 0.144674 0.792789i
\(88\) −449.473 449.473i −0.544477 0.544477i
\(89\) 1417.21 1.68790 0.843952 0.536419i \(-0.180223\pi\)
0.843952 + 0.536419i \(0.180223\pi\)
\(90\) 0 0
\(91\) −378.799 −0.436361
\(92\) −195.627 195.627i −0.221690 0.221690i
\(93\) 230.751 1264.48i 0.257288 1.40989i
\(94\) 295.872i 0.324647i
\(95\) 0 0
\(96\) 787.409 544.375i 0.837131 0.578751i
\(97\) −908.111 + 908.111i −0.950564 + 0.950564i −0.998834 0.0482702i \(-0.984629\pi\)
0.0482702 + 0.998834i \(0.484629\pi\)
\(98\) −16.4640 + 16.4640i −0.0169706 + 0.0169706i
\(99\) 273.861 725.367i 0.278020 0.736385i
\(100\) 0 0
\(101\) 337.668i 0.332665i −0.986070 0.166333i \(-0.946807\pi\)
0.986070 0.166333i \(-0.0531926\pi\)
\(102\) 225.340 + 41.1217i 0.218745 + 0.0399182i
\(103\) 933.505 + 933.505i 0.893019 + 0.893019i 0.994806 0.101787i \(-0.0324561\pi\)
−0.101787 + 0.994806i \(0.532456\pi\)
\(104\) 443.860 0.418500
\(105\) 0 0
\(106\) −381.100 −0.349205
\(107\) 596.188 + 596.188i 0.538651 + 0.538651i 0.923133 0.384481i \(-0.125620\pi\)
−0.384481 + 0.923133i \(0.625620\pi\)
\(108\) 622.632 + 374.498i 0.554748 + 0.333667i
\(109\) 2074.60i 1.82303i 0.411264 + 0.911516i \(0.365087\pi\)
−0.411264 + 0.911516i \(0.634913\pi\)
\(110\) 0 0
\(111\) −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
\(115\) 0 0
\(116\) 651.788i 0.521698i
\(117\) 222.934 + 493.375i 0.176156 + 0.389851i
\(118\) 866.309 + 866.309i 0.675849 + 0.675849i
\(119\) −495.806 −0.381937
\(120\) 0 0
\(121\) 506.367 0.380441
\(122\) −2.37533 2.37533i −0.00176272 0.00176272i
\(123\) −1995.25 364.108i −1.46265 0.266915i
\(124\) 1281.09i 0.927786i
\(125\) 0 0
\(126\) 801.469 + 302.593i 0.566671 + 0.213945i
\(127\) −105.588 + 105.588i −0.0737747 + 0.0737747i −0.743031 0.669257i \(-0.766613\pi\)
0.669257 + 0.743031i \(0.266613\pi\)
\(128\) 715.045 715.045i 0.493763 0.493763i
\(129\) 238.151 164.646i 0.162543 0.112374i
\(130\) 0 0
\(131\) 1979.28i 1.32008i 0.751231 + 0.660039i \(0.229460\pi\)
−0.751231 + 0.660039i \(0.770540\pi\)
\(132\) 138.730 760.216i 0.0914763 0.501275i
\(133\) −655.514 655.514i −0.427371 0.427371i
\(134\) −783.827 −0.505316
\(135\) 0 0
\(136\) 580.964 0.366304
\(137\) −507.451 507.451i −0.316456 0.316456i 0.530948 0.847404i \(-0.321836\pi\)
−0.847404 + 0.530948i \(0.821836\pi\)
\(138\) −83.6979 + 458.651i −0.0516293 + 0.282920i
\(139\) 68.4333i 0.0417585i −0.999782 0.0208793i \(-0.993353\pi\)
0.999782 0.0208793i \(-0.00664656\pi\)
\(140\) 0 0
\(141\) −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
\(145\) 0 0
\(146\) 664.917i 0.376911i
\(147\) −70.8616 12.9313i −0.0397590 0.00725550i
\(148\) −660.121 660.121i −0.366632 0.366632i
\(149\) 363.356 0.199780 0.0998902 0.994998i \(-0.468151\pi\)
0.0998902 + 0.994998i \(0.468151\pi\)
\(150\) 0 0
\(151\) −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
\(153\) 291.797 + 645.774i 0.154185 + 0.341227i
\(154\) 911.149i 0.476769i
\(155\) 0 0
\(156\) 306.863 + 443.860i 0.157491 + 0.227803i
\(157\) 1208.52 1208.52i 0.614333 0.614333i −0.329739 0.944072i \(-0.606961\pi\)
0.944072 + 0.329739i \(0.106961\pi\)
\(158\) −57.0303 + 57.0303i −0.0287157 + 0.0287157i
\(159\) −670.468 969.795i −0.334412 0.483709i
\(160\) 0 0
\(161\) 1009.15i 0.493989i
\(162\) −77.5696 1221.98i −0.0376200 0.592639i
\(163\) −626.062 626.062i −0.300840 0.300840i 0.540502 0.841343i \(-0.318234\pi\)
−0.841343 + 0.540502i \(0.818234\pi\)
\(164\) −2021.47 −0.962502
\(165\) 0 0
\(166\) 343.119 0.160429
\(167\) −3009.65 3009.65i −1.39457 1.39457i −0.814724 0.579848i \(-0.803112\pi\)
−0.579848 0.814724i \(-0.696888\pi\)
\(168\) 2137.50 + 390.067i 0.981619 + 0.179133i
\(169\) 1794.92i 0.816985i
\(170\) 0 0
\(171\) −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
\(175\) 0 0
\(176\) 122.113i 0.0522987i
\(177\) −680.425 + 3728.61i −0.288948 + 1.58339i
\(178\) −1683.16 1683.16i −0.708755 0.708755i
\(179\) −821.582 −0.343061 −0.171530 0.985179i \(-0.554871\pi\)
−0.171530 + 0.985179i \(0.554871\pi\)
\(180\) 0 0
\(181\) 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
\(183\) 1.86565 10.2235i 0.000753623 0.00412973i
\(184\) 1182.48i 0.473769i
\(185\) 0 0
\(186\) −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
\(190\) 0 0
\(191\) 931.167i 0.352758i 0.984322 + 0.176379i \(0.0564385\pi\)
−0.984322 + 0.176379i \(0.943562\pi\)
\(192\) −1407.82 256.909i −0.529169 0.0965666i
\(193\) 2623.28 + 2623.28i 0.978382 + 0.978382i 0.999771 0.0213891i \(-0.00680888\pi\)
−0.0213891 + 0.999771i \(0.506809\pi\)
\(194\) 2157.06 0.798289
\(195\) 0 0
\(196\) −71.7928 −0.0261636
\(197\) 2995.05 + 2995.05i 1.08319 + 1.08319i 0.996210 + 0.0869796i \(0.0277215\pi\)
0.0869796 + 0.996210i \(0.472279\pi\)
\(198\) −1186.75 + 536.238i −0.425952 + 0.192469i
\(199\) 109.458i 0.0389912i 0.999810 + 0.0194956i \(0.00620603\pi\)
−0.999810 + 0.0194956i \(0.993794\pi\)
\(200\) 0 0
\(201\) −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
\(205\) 0 0
\(206\) 2217.38i 0.749962i
\(207\) −1314.39 + 593.915i −0.441336 + 0.199420i
\(208\) 60.2938 + 60.2938i 0.0200991 + 0.0200991i
\(209\) 1409.21 0.466399
\(210\) 0 0
\(211\) 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
\(213\) 877.989 + 160.222i 0.282436 + 0.0515409i
\(214\) 1416.14i 0.452362i
\(215\) 0 0
\(216\) −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
\(220\) 0 0
\(221\) 526.283i 0.160188i
\(222\) −282.429 + 1547.67i −0.0853847 + 0.467894i
\(223\) −2830.49 2830.49i −0.849971 0.849971i 0.140158 0.990129i \(-0.455239\pi\)
−0.990129 + 0.140158i \(0.955239\pi\)
\(224\) 3480.17 1.03808
\(225\) 0 0
\(226\) 644.173 0.189601
\(227\) 1398.96 + 1398.96i 0.409042 + 0.409042i 0.881404 0.472362i \(-0.156599\pi\)
−0.472362 + 0.881404i \(0.656599\pi\)
\(228\) −237.075 + 1299.13i −0.0688626 + 0.377356i
\(229\) 3930.38i 1.13418i 0.823656 + 0.567089i \(0.191931\pi\)
−0.823656 + 0.567089i \(0.808069\pi\)
\(230\) 0 0
\(231\) 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
\(235\) 0 0
\(236\) 3777.61i 1.04196i
\(237\) −245.460 44.7933i −0.0672756 0.0122769i
\(238\) 588.851 + 588.851i 0.160376 + 0.160376i
\(239\) −2976.20 −0.805500 −0.402750 0.915310i \(-0.631946\pi\)
−0.402750 + 0.915310i \(0.631946\pi\)
\(240\) 0 0
\(241\) 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
\(243\) 2973.13 2347.21i 0.784882 0.619645i
\(244\) 10.3578i 0.00271759i
\(245\) 0 0
\(246\) 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
\(250\) 0 0
\(251\) 1542.14i 0.387805i −0.981021 0.193902i \(-0.937885\pi\)
0.981021 0.193902i \(-0.0621145\pi\)
\(252\) 1087.70 + 2407.18i 0.271898 + 0.601738i
\(253\) 1084.73 + 1084.73i 0.269550 + 0.269550i
\(254\) 250.805 0.0619564
\(255\) 0 0
\(256\) −3901.74 −0.952572
\(257\) 428.853 + 428.853i 0.104090 + 0.104090i 0.757234 0.653144i \(-0.226550\pi\)
−0.653144 + 0.757234i \(0.726550\pi\)
\(258\) −478.388 87.2997i −0.115438 0.0210660i
\(259\) 3405.26i 0.816960i
\(260\) 0 0
\(261\) −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
\(265\) 0 0
\(266\) 1557.06i 0.358908i
\(267\) 1322.01 7244.38i 0.303017 1.66048i
\(268\) −1708.97 1708.97i −0.389523 0.389523i
\(269\) −1930.34 −0.437528 −0.218764 0.975778i \(-0.570203\pi\)
−0.218764 + 0.975778i \(0.570203\pi\)
\(270\) 0 0
\(271\) −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
\(273\) −353.353 + 1936.32i −0.0783367 + 0.429272i
\(274\) 1205.36i 0.265762i
\(275\) 0 0
\(276\) −1182.48 + 817.507i −0.257887 + 0.178290i
\(277\) −4865.57 + 4865.57i −1.05539 + 1.05539i −0.0570194 + 0.998373i \(0.518160\pi\)
−0.998373 + 0.0570194i \(0.981840\pi\)
\(278\) −81.2758 + 81.2758i −0.0175345 + 0.0175345i
\(279\) −6248.41 2359.07i −1.34080 0.506215i
\(280\) 0 0
\(281\) 3981.96i 0.845351i −0.906281 0.422676i \(-0.861091\pi\)
0.906281 0.422676i \(-0.138909\pi\)
\(282\) 1512.42 + 275.997i 0.319373 + 0.0582815i
\(283\) 4092.66 + 4092.66i 0.859658 + 0.859658i 0.991298 0.131640i \(-0.0420242\pi\)
−0.131640 + 0.991298i \(0.542024\pi\)
\(284\) 889.527 0.185858
\(285\) 0 0
\(286\) −967.156 −0.199962
\(287\) −5213.93 5213.93i −1.07236 1.07236i
\(288\) −2048.19 4532.83i −0.419064 0.927429i
\(289\) 4224.15i 0.859791i
\(290\) 0 0
\(291\) 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
\(295\) 0 0
\(296\) 3990.14i 0.783521i
\(297\) −3452.42 2076.54i −0.674511 0.405701i
\(298\) −431.545 431.545i −0.0838883 0.0838883i
\(299\) −1071.18 −0.207184
\(300\) 0 0
\(301\) 1052.58 0.201560
\(302\) 2474.07 + 2474.07i 0.471413 + 0.471413i
\(303\) −1726.07 314.986i −0.327261 0.0597210i
\(304\) 208.678i 0.0393701i
\(305\) 0 0
\(306\) 420.406 1113.52i 0.0785393 0.208025i
\(307\) −1831.07 + 1831.07i −0.340406 + 0.340406i −0.856520 0.516114i \(-0.827378\pi\)
0.516114 + 0.856520i \(0.327378\pi\)
\(308\) 1986.57 1986.57i 0.367517 0.367517i
\(309\) 5642.63 3901.03i 1.03883 0.718194i
\(310\) 0 0
\(311\) 4010.21i 0.731184i −0.930775 0.365592i \(-0.880866\pi\)
0.930775 0.365592i \(-0.119134\pi\)
\(312\) 414.044 2268.89i 0.0751303 0.411701i
\(313\) −6072.69 6072.69i −1.09664 1.09664i −0.994801 0.101841i \(-0.967527\pi\)
−0.101841 0.994801i \(-0.532473\pi\)
\(314\) −2870.63 −0.515920
\(315\) 0 0
\(316\) −248.685 −0.0442710
\(317\) −3112.10 3112.10i −0.551397 0.551397i 0.375447 0.926844i \(-0.377489\pi\)
−0.926844 + 0.375447i \(0.877489\pi\)
\(318\) −355.500 + 1948.08i −0.0626901 + 0.343531i
\(319\) 3614.09i 0.634326i
\(320\) 0 0
\(321\) 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
\(325\) 0 0
\(326\) 1487.10i 0.252647i
\(327\) 10604.8 + 1935.24i 1.79342 + 0.327275i
\(328\) 6109.45 + 6109.45i 1.02847 + 1.02847i
\(329\) −3327.71 −0.557637
\(330\) 0 0
\(331\) −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
\(333\) −4435.26 + 2004.10i −0.729883 + 0.329801i
\(334\) 7148.90i 1.17117i
\(335\) 0 0
\(336\) 237.371 + 343.345i 0.0385407 + 0.0557470i
\(337\) 2561.34 2561.34i 0.414021 0.414021i −0.469115 0.883137i \(-0.655427\pi\)
0.883137 + 0.469115i \(0.155427\pi\)
\(338\) −2131.76 + 2131.76i −0.343054 + 0.343054i
\(339\) 1133.29 + 1639.24i 0.181569 + 0.262630i
\(340\) 0 0
\(341\) 7103.50i 1.12808i
\(342\) 2028.03 916.377i 0.320653 0.144889i
\(343\) 4396.56 + 4396.56i 0.692104 + 0.692104i
\(344\) −1233.36 −0.193310
\(345\) 0 0
\(346\) 4368.77 0.678805
\(347\) 8177.44 + 8177.44i 1.26509 + 1.26509i 0.948592 + 0.316503i \(0.102509\pi\)
0.316503 + 0.948592i \(0.397491\pi\)
\(348\) −3331.77 608.005i −0.513223 0.0936566i
\(349\) 2766.04i 0.424249i −0.977243 0.212124i \(-0.931962\pi\)
0.977243 0.212124i \(-0.0680382\pi\)
\(350\) 0 0
\(351\) 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
\(355\) 0 0
\(356\) 7339.58i 1.09269i
\(357\) −462.501 + 2534.43i −0.0685663 + 0.375732i
\(358\) 975.763 + 975.763i 0.144052 + 0.144052i
\(359\) 8827.47 1.29776 0.648880 0.760890i \(-0.275238\pi\)
0.648880 + 0.760890i \(0.275238\pi\)
\(360\) 0 0
\(361\) 4450.80 0.648899
\(362\) −2748.50 2748.50i −0.399055 0.399055i
\(363\) 472.353 2588.42i 0.0682978 0.374261i
\(364\) 1961.76i 0.282484i
\(365\) 0 0
\(366\) −14.3578 + 9.92628i −0.00205053 + 0.00141764i
\(367\) −6191.27 + 6191.27i −0.880605 + 0.880605i −0.993596 0.112991i \(-0.963957\pi\)
0.112991 + 0.993596i \(0.463957\pi\)
\(368\) −160.628 + 160.628i −0.0227535 + 0.0227535i
\(369\) −3722.45 + 9859.55i −0.525157 + 1.39097i
\(370\) 0 0
\(371\) 4286.28i 0.599818i
\(372\) −6548.60 1195.04i −0.912713 0.166559i
\(373\) −3584.46 3584.46i −0.497577 0.497577i 0.413106 0.910683i \(-0.364444\pi\)
−0.910683 + 0.413106i \(0.864444\pi\)
\(374\) −1265.90 −0.175022
\(375\) 0 0
\(376\) 3899.27 0.534812
\(377\) −1784.48 1784.48i −0.243781 0.243781i
\(378\) 2294.40 3814.63i 0.312200 0.519057i
\(379\) 7110.48i 0.963695i 0.876255 + 0.481848i \(0.160034\pi\)
−0.876255 + 0.481848i \(0.839966\pi\)
\(380\) 0 0
\(381\) 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
\(385\) 0 0
\(386\) 6231.15i 0.821650i
\(387\) −619.472 1370.95i −0.0813683 0.180076i
\(388\) 4703.02 + 4703.02i 0.615361 + 0.615361i
\(389\) 12362.2 1.61128 0.805640 0.592405i \(-0.201822\pi\)
0.805640 + 0.592405i \(0.201822\pi\)
\(390\) 0 0
\(391\) −1402.06 −0.181343
\(392\) 216.978 + 216.978i 0.0279567 + 0.0279567i
\(393\) 10117.5 + 1846.32i 1.29863 + 0.236984i
\(394\) 7114.22i 0.909668i
\(395\) 0 0
\(396\) −3756.61 1418.30i −0.476709 0.179980i
\(397\) 1340.12 1340.12i 0.169417 0.169417i −0.617306 0.786723i \(-0.711776\pi\)
0.786723 + 0.617306i \(0.211776\pi\)
\(398\) 129.999 129.999i 0.0163725 0.0163725i
\(399\) −3962.30 + 2739.33i −0.497150 + 0.343705i
\(400\) 0 0
\(401\) 2281.30i 0.284096i 0.989860 + 0.142048i \(0.0453688\pi\)
−0.989860 + 0.142048i \(0.954631\pi\)
\(402\) −731.175 + 4006.72i −0.0907156 + 0.497107i
\(403\) −3507.40 3507.40i −0.433538 0.433538i
\(404\) −1748.75 −0.215356
\(405\) 0 0
\(406\) −3993.26 −0.488133
\(407\) 3660.29 + 3660.29i 0.445783 + 0.445783i
\(408\) 541.939 2969.74i 0.0657597 0.360352i
\(409\) 4614.82i 0.557917i −0.960303 0.278959i \(-0.910011\pi\)
0.960303 0.278959i \(-0.0899892\pi\)
\(410\) 0 0
\(411\) −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
\(415\) 0 0
\(416\) 3694.10i 0.435380i
\(417\) −349.813 63.8364i −0.0410801 0.00749660i
\(418\) −1673.67 1673.67i −0.195842 0.195842i
\(419\) 2142.28 0.249779 0.124889 0.992171i \(-0.460142\pi\)
0.124889 + 0.992171i \(0.460142\pi\)
\(420\) 0 0
\(421\) −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
\(423\) 1958.46 + 4334.26i 0.225115 + 0.498200i
\(424\) 5022.48i 0.575267i
\(425\) 0 0
\(426\) −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
\(430\) 0 0
\(431\) 15707.3i 1.75543i 0.479179 + 0.877717i \(0.340935\pi\)
−0.479179 + 0.877717i \(0.659065\pi\)
\(432\) 307.497 511.238i 0.0342464 0.0569374i
\(433\) −5430.81 5430.81i −0.602744 0.602744i 0.338296 0.941040i \(-0.390149\pi\)
−0.941040 + 0.338296i \(0.890149\pi\)
\(434\) −7848.76 −0.868094
\(435\) 0 0
\(436\) 10744.2 1.18016
\(437\) −1853.69 1853.69i −0.202915 0.202915i
\(438\) −3398.88 620.253i −0.370787 0.0676640i
\(439\) 8221.92i 0.893874i −0.894565 0.446937i \(-0.852515\pi\)
0.894565 0.446937i \(-0.147485\pi\)
\(440\) 0 0
\(441\) −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
\(445\) 0 0
\(446\) 6723.34i 0.713810i
\(447\) 338.948 1857.38i 0.0358651 0.196535i
\(448\) −3678.86 3678.86i −0.387968 0.387968i
\(449\) −17849.2 −1.87607 −0.938036 0.346537i \(-0.887357\pi\)
−0.938036 + 0.346537i \(0.887357\pi\)
\(450\) 0 0
\(451\) 11208.8 1.17029
\(452\) 1404.49 + 1404.49i 0.146154 + 0.146154i
\(453\) −1943.21 + 10648.5i −0.201545 + 1.10443i
\(454\) 3323.00i 0.343516i
\(455\) 0 0
\(456\) 4642.85 3209.83i 0.476801 0.329636i
\(457\) 6346.80 6346.80i 0.649652 0.649652i −0.303257 0.952909i \(-0.598074\pi\)
0.952909 + 0.303257i \(0.0980740\pi\)
\(458\) 4667.97 4667.97i 0.476245 0.476245i
\(459\) 3573.22 889.192i 0.363363 0.0904225i
\(460\) 0 0
\(461\) 8848.20i 0.893930i 0.894552 + 0.446965i \(0.147495\pi\)
−0.894552 + 0.446965i \(0.852505\pi\)
\(462\) −4657.55 849.944i −0.469024 0.0855908i
\(463\) −1329.43 1329.43i −0.133443 0.133443i 0.637230 0.770673i \(-0.280080\pi\)
−0.770673 + 0.637230i \(0.780080\pi\)
\(464\) −535.178 −0.0535453
\(465\) 0 0
\(466\) −4704.83 −0.467697
\(467\) −1479.96 1479.96i −0.146647 0.146647i 0.629971 0.776618i \(-0.283067\pi\)
−0.776618 + 0.629971i \(0.783067\pi\)
\(468\) 2555.14 1154.56i 0.252375 0.114037i
\(469\) 8815.81i 0.867966i
\(470\) 0 0
\(471\) −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
\(475\) 0 0
\(476\) 2567.73i 0.247252i
\(477\) −5582.76 + 2522.60i −0.535885 + 0.242143i
\(478\) 3534.73 + 3534.73i 0.338231 + 0.338231i
\(479\) 5039.60 0.480720 0.240360 0.970684i \(-0.422734\pi\)
0.240360 + 0.970684i \(0.422734\pi\)
\(480\) 0 0
\(481\) −3614.58 −0.342642
\(482\) −2179.89 2179.89i −0.205999 0.205999i
\(483\) −5158.51 941.362i −0.485963 0.0886821i
\(484\) 2622.43i 0.246284i
\(485\) 0 0
\(486\) −6318.78 743.377i −0.589765 0.0693833i
\(487\) −1292.93 + 1292.93i −0.120305 + 0.120305i −0.764696 0.644391i \(-0.777111\pi\)
0.644391 + 0.764696i \(0.277111\pi\)
\(488\) −31.3042 + 31.3042i −0.00290384 + 0.00290384i
\(489\) −3784.27 + 2616.26i −0.349961 + 0.241945i
\(490\) 0 0
\(491\) 13865.7i 1.27444i −0.770681 0.637221i \(-0.780084\pi\)
0.770681 0.637221i \(-0.219916\pi\)
\(492\) −1885.68 + 10333.2i −0.172791 + 0.946865i
\(493\) −2335.69 2335.69i −0.213375 0.213375i
\(494\) 1652.77 0.150530
\(495\) 0 0
\(496\) −1051.89 −0.0952247
\(497\) 2294.33 + 2294.33i 0.207072 + 0.207072i
\(498\) 320.070 1753.93i 0.0288006 0.157822i
\(499\) 10884.3i 0.976453i 0.872717 + 0.488226i \(0.162356\pi\)
−0.872717 + 0.488226i \(0.837644\pi\)
\(500\) 0 0
\(501\) −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
\(505\) 0 0
\(506\) 2576.58i 0.226370i
\(507\) −9175.14 1674.35i −0.803713 0.146667i
\(508\) 546.829 + 546.829i 0.0477590 + 0.0477590i
\(509\) 1788.46 0.155741 0.0778704 0.996963i \(-0.475188\pi\)
0.0778704 + 0.996963i \(0.475188\pi\)
\(510\) 0 0
\(511\) 7478.42 0.647408
\(512\) −1086.41 1086.41i −0.0937754 0.0937754i
\(513\) 5899.84 + 3548.60i 0.507766 + 0.305409i
\(514\) 1018.67i 0.0874153i
\(515\) 0 0
\(516\) −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
\(520\) 0 0
\(521\) 18251.6i 1.53478i −0.641183 0.767388i \(-0.721556\pi\)
0.641183 0.767388i \(-0.278444\pi\)
\(522\) 2350.15 + 5201.11i 0.197056 + 0.436104i
\(523\) 2125.69 + 2125.69i 0.177725 + 0.177725i 0.790363 0.612639i \(-0.209892\pi\)
−0.612639 + 0.790363i \(0.709892\pi\)
\(524\) 10250.5 0.854570
\(525\) 0 0
\(526\) 12487.1 1.03510
\(527\) −4590.80 4590.80i −0.379466 0.379466i
\(528\) −624.207 113.910i −0.0514491 0.00938880i
\(529\) 9313.29i 0.765455i
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) 10330.0i 0.832439i
\(537\) −766.393 + 4199.71i −0.0615872 + 0.337488i
\(538\) 2292.60 + 2292.60i 0.183719 + 0.183719i
\(539\) 398.082 0.0318119
\(540\) 0 0
\(541\) −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
\(543\) 2158.75 11829.6i 0.170609 0.934911i
\(544\) 4835.17i 0.381078i
\(545\) 0 0
\(546\) 2719.36 1880.03i 0.213146 0.147359i
\(547\) −12385.1 + 12385.1i −0.968098 + 0.968098i −0.999507 0.0314090i \(-0.990001\pi\)
0.0314090 + 0.999507i \(0.490001\pi\)
\(548\) −2628.04 + 2628.04i −0.204862 + 0.204862i
\(549\) −50.5193 19.0735i −0.00392735 0.00148276i
\(550\) 0 0
\(551\) 6176.11i 0.477516i
\(552\) 6044.52 + 1103.05i 0.466072 + 0.0850522i
\(553\) −641.427 641.427i −0.0493242 0.0493242i
\(554\) 11557.3 0.886324
\(555\) 0 0
\(556\) −354.410 −0.0270329
\(557\) 8716.96 + 8716.96i 0.663105 + 0.663105i 0.956111 0.293006i \(-0.0946555\pi\)
−0.293006 + 0.956111i \(0.594656\pi\)
\(558\) 4619.23 + 10222.8i 0.350444 + 0.775566i
\(559\) 1117.28i 0.0845363i
\(560\) 0 0
\(561\) −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
\(565\) 0 0
\(566\) 9721.40i 0.721945i
\(567\) 13743.7 872.435i 1.01796 0.0646188i
\(568\) −2688.40 2688.40i −0.198596 0.198596i
\(569\) −11517.5 −0.848576 −0.424288 0.905527i \(-0.639476\pi\)
−0.424288 + 0.905527i \(0.639476\pi\)
\(570\) 0 0
\(571\) −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
\(573\) 4759.88 + 868.617i 0.347027 + 0.0633281i
\(574\) 12384.8i 0.900577i
\(575\) 0 0
\(576\) −2626.50 + 6956.73i −0.189995 + 0.503236i
\(577\) 14119.4 14119.4i 1.01871 1.01871i 0.0188920 0.999822i \(-0.493986\pi\)
0.999822 0.0188920i \(-0.00601387\pi\)
\(578\) −5016.87 + 5016.87i −0.361028 + 0.361028i
\(579\) 15856.6 10962.4i 1.13813 0.786846i
\(580\) 0 0
\(581\) 3859.10i 0.275564i
\(582\) 2012.16 11026.3i 0.143311 0.785320i
\(583\) 4607.29 + 4607.29i 0.327297 + 0.327297i
\(584\) −8762.89 −0.620909
\(585\) 0 0
\(586\) −10725.4 −0.756081
\(587\) 8524.33 + 8524.33i 0.599381 + 0.599381i 0.940148 0.340767i \(-0.110687\pi\)
−0.340767 + 0.940148i \(0.610687\pi\)
\(588\) −66.9702 + 366.986i −0.00469695 + 0.0257385i
\(589\) 12139.2i 0.849211i
\(590\) 0 0
\(591\) 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
\(595\) 0 0
\(596\) 1881.79i 0.129331i
\(597\) 559.518 + 102.105i 0.0383577 + 0.00699979i
\(598\) 1272.20 + 1272.20i 0.0869971 + 0.0869971i
\(599\) 10195.8 0.695477 0.347738 0.937592i \(-0.386950\pi\)
0.347738 + 0.937592i \(0.386950\pi\)
\(600\) 0 0
\(601\) 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
\(603\) −11482.4 + 5188.36i −0.775452 + 0.350392i
\(604\) 10788.4i 0.726778i
\(605\) 0 0
\(606\) 1675.89 + 2424.09i 0.112341 + 0.162495i
\(607\) −12758.2 + 12758.2i −0.853113 + 0.853113i −0.990515 0.137402i \(-0.956125\pi\)
0.137402 + 0.990515i \(0.456125\pi\)
\(608\) 6392.67 6392.67i 0.426409 0.426409i
\(609\) −7025.33 10161.8i −0.467456 0.676149i
\(610\) 0 0
\(611\) 3532.26i 0.233879i
\(612\) 3344.41 1511.19i 0.220898 0.0998140i
\(613\) −7340.02 7340.02i −0.483622 0.483622i 0.422664 0.906286i \(-0.361095\pi\)
−0.906286 + 0.422664i \(0.861095\pi\)
\(614\) 4349.39 0.285875
\(615\) 0 0
\(616\) −12007.9 −0.785412
\(617\) −17118.9 17118.9i −1.11698 1.11698i −0.992182 0.124803i \(-0.960170\pi\)
−0.124803 0.992182i \(-0.539830\pi\)
\(618\) −11334.7 2068.43i −0.737778 0.134635i
\(619\) 3176.16i 0.206237i −0.994669 0.103118i \(-0.967118\pi\)
0.994669 0.103118i \(-0.0328820\pi\)
\(620\) 0 0
\(621\) 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
\(625\) 0 0
\(626\) 14424.6i 0.920965i
\(627\) 1314.55 7203.53i 0.0837291 0.458822i
\(628\) −6258.80 6258.80i −0.397697 0.397697i
\(629\) −4731.09 −0.299906
\(630\) 0 0
\(631\) −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
\(633\) 2532.57 13878.0i 0.159021 0.871410i
\(634\) 7392.26i 0.463066i
\(635\) 0 0
\(636\) −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
\(640\) 0 0
\(641\) 12383.2i 0.763035i 0.924362 + 0.381518i \(0.124598\pi\)
−0.924362 + 0.381518i \(0.875402\pi\)
\(642\) −7238.95 1321.02i −0.445013 0.0812092i
\(643\) 11142.9 + 11142.9i 0.683413 + 0.683413i 0.960768 0.277354i \(-0.0894576\pi\)
−0.277354 + 0.960768i \(0.589458\pi\)
\(644\) −5226.29 −0.319790
\(645\) 0 0
\(646\) 2163.30 0.131755
\(647\) −2391.21 2391.21i −0.145299 0.145299i 0.630716 0.776014i \(-0.282761\pi\)
−0.776014 + 0.630716i \(0.782761\pi\)
\(648\) −16104.3 + 1022.28i −0.976292 + 0.0619738i
\(649\) 20946.4i 1.26690i
\(650\) 0 0
\(651\) −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
\(655\) 0 0
\(656\) 1659.81i 0.0987878i
\(657\) −4401.27 9740.43i −0.261354 0.578403i
\(658\) 3952.20 + 3952.20i 0.234153 + 0.234153i
\(659\) −20089.8 −1.18754 −0.593768 0.804636i \(-0.702360\pi\)
−0.593768 + 0.804636i \(0.702360\pi\)
\(660\) 0 0
\(661\) 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
\(663\) 2690.22 + 490.931i 0.157586 + 0.0287574i
\(664\) 4521.93i 0.264284i
\(665\) 0 0
\(666\) 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
\(670\) 0 0
\(671\) 57.4328i 0.00330428i
\(672\) 3246.40 17789.7i 0.186358 1.02121i
\(673\) 24314.3 + 24314.3i 1.39264 + 1.39264i 0.819354 + 0.573288i \(0.194332\pi\)
0.573288 + 0.819354i \(0.305668\pi\)
\(674\) −6084.03 −0.347697
\(675\) 0 0
\(676\) −9295.71 −0.528887
\(677\) −14662.4 14662.4i −0.832380 0.832380i 0.155462 0.987842i \(-0.450313\pi\)
−0.987842 + 0.155462i \(0.950313\pi\)
\(678\) 600.902 3292.84i 0.0340376 0.186520i
\(679\) 24260.8i 1.37120i
\(680\) 0 0
\(681\) 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
\(685\) 0 0
\(686\) 10443.3i 0.581233i
\(687\) 20091.1 + 3666.36i 1.11575 + 0.203611i
\(688\) −167.540 167.540i −0.00928400 0.00928400i
\(689\) −4549.75 −0.251570
\(690\) 0 0
\(691\) −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
\(693\) −6031.14 13347.5i −0.330598 0.731645i
\(694\) 19424.1i 1.06243i
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) 6990.49i 0.376643i 0.982107 + 0.188322i \(0.0603048\pi\)
−0.982107 + 0.188322i \(0.939695\pi\)
\(702\) −4049.11 2435.44i −0.217698 0.130940i
\(703\) −6255.06 6255.06i −0.335582 0.335582i
\(704\) 7908.75 0.423398
\(705\) 0 0
\(706\) −15056.1 −0.802611
\(707\) −4510.51 4510.51i −0.239936 0.239936i
\(708\) 19310.2 + 3523.86i 1.02503 + 0.187055i
\(709\) 28175.0i 1.49243i 0.665705 + 0.746215i \(0.268131\pi\)
−0.665705 + 0.746215i \(0.731869\pi\)
\(710\) 0 0
\(711\) −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
\(715\) 0 0
\(716\) 4254.90i 0.222085i
\(717\) −2776.28 + 15213.6i −0.144605 + 0.792414i
\(718\) −10484.1 10484.1i −0.544933 0.544933i
\(719\) 20143.8 1.04484 0.522418 0.852690i \(-0.325030\pi\)
0.522418 + 0.852690i \(0.325030\pi\)
\(720\) 0 0
\(721\) 24939.2 1.28819
\(722\) −5286.05 5286.05i −0.272474 0.272474i
\(723\) 1712.15 9382.32i 0.0880715 0.482617i
\(724\) 11985.0i 0.615222i
\(725\) 0 0
\(726\) −3635.16 + 2513.17i −0.185831 + 0.128475i
\(727\) 9805.90 9805.90i 0.500249 0.500249i −0.411267 0.911515i \(-0.634913\pi\)
0.911515 + 0.411267i \(0.134913\pi\)
\(728\) 5929.00 5929.00i 0.301845 0.301845i
\(729\) −9224.92 17387.4i −0.468674 0.883371i
\(730\) 0 0
\(731\) 1462.39i 0.0739926i
\(732\) −52.9464 9.66205i −0.00267344 0.000487868i
\(733\) −16533.1 16533.1i −0.833100 0.833100i 0.154840 0.987940i \(-0.450514\pi\)
−0.987940 + 0.154840i \(0.950514\pi\)
\(734\) 14706.3 0.739536
\(735\) 0 0
\(736\) 9841.37 0.492877
\(737\) 9476.04 + 9476.04i 0.473615 + 0.473615i
\(738\) 16130.8 7288.81i 0.804586 0.363557i
\(739\) 15250.1i 0.759114i 0.925168 + 0.379557i \(0.123924\pi\)
−0.925168 + 0.379557i \(0.876076\pi\)
\(740\) 0 0
\(741\) 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
\(745\) 0 0
\(746\) 8514.27i 0.417868i
\(747\) 5026.38 2271.20i 0.246192 0.111243i
\(748\) −2760.04 2760.04i −0.134916 0.134916i
\(749\) 15927.5 0.777009
\(750\) 0 0
\(751\) 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
\(753\) −7883.01 1438.55i −0.381505 0.0696197i
\(754\) 4238.72i 0.204728i
\(755\) 0 0
\(756\) 13319.5 3314.54i 0.640774 0.159456i
\(757\) 10258.6 10258.6i 0.492546 0.492546i −0.416562 0.909107i \(-0.636765\pi\)
0.909107 + 0.416562i \(0.136765\pi\)
\(758\) 8444.86 8444.86i 0.404658 0.404658i
\(759\) 6556.70 4532.98i 0.313561 0.216781i
\(760\) 0 0
\(761\) 26879.5i 1.28040i −0.768210 0.640198i \(-0.778852\pi\)
0.768210 0.640198i \(-0.221148\pi\)
\(762\) 233.958 1282.05i 0.0111226 0.0609498i
\(763\) 27712.1 + 27712.1i 1.31487 + 1.31487i
\(764\) 4822.43 0.228363
\(765\) 0 0
\(766\) 4028.02 0.189998
\(767\) 10342.4 + 10342.4i 0.486888 + 0.486888i
\(768\) −3639.64 + 19944.6i −0.171008 + 0.937097i
\(769\) 25180.9i 1.18082i −0.807105 0.590408i \(-0.798967\pi\)
0.807105 0.590408i \(-0.201033\pi\)
\(770\) 0 0
\(771\) 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
\(775\) 0 0
\(776\) 28427.7i 1.31507i
\(777\) −17406.8 3176.52i −0.803688 0.146663i
\(778\) −14682.1 14682.1i −0.676581 0.676581i
\(779\) −19154.7 −0.880988
\(780\) 0 0
\(781\) −4932.32 −0.225982
\(782\) 1665.18 + 1665.18i 0.0761465 + 0.0761465i
\(783\) −9100.79 + 15130.8i −0.415371 + 0.690588i
\(784\) 58.9485i 0.00268533i
\(785\) 0 0
\(786\) −9823.43 14209.0i −0.445789 0.644809i
\(787\) −14716.0 + 14716.0i −0.666542 + 0.666542i −0.956914 0.290372i \(-0.906221\pi\)
0.290372 + 0.956914i \(0.406221\pi\)
\(788\) 15511.1 15511.1i 0.701217 0.701217i
\(789\) 21968.5 + 31776.2i 0.991253 + 1.43379i
\(790\) 0 0
\(791\) 7245.10i 0.325672i
\(792\) 7067.03 + 15640.0i 0.317066 + 0.701697i
\(793\) −28.3578 28.3578i −0.00126988 0.00126988i
\(794\) −3183.22 −0.142277
\(795\) 0 0
\(796\) 566.871 0.0252415
\(797\) 17463.9 + 17463.9i 0.776163 + 0.776163i 0.979176 0.203013i \(-0.0650735\pi\)
−0.203013 + 0.979176i \(0.565073\pi\)
\(798\) 7959.28 + 1452.47i 0.353077 + 0.0644321i
\(799\) 4623.35i 0.204709i
\(800\) 0 0
\(801\) −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
\(805\) 0 0
\(806\) 8331.22i 0.364088i
\(807\) −1800.68 + 9867.40i −0.0785462 + 0.430420i
\(808\) 5285.22 + 5285.22i 0.230115 + 0.230115i
\(809\) 24097.9 1.04727 0.523633 0.851944i \(-0.324576\pi\)
0.523633 + 0.851944i \(0.324576\pi\)
\(810\) 0 0
\(811\) 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
\(813\) −3042.57 + 16672.8i −0.131252 + 0.719238i
\(814\) 8694.39i 0.374371i
\(815\) 0 0
\(816\) 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
\(820\) 0 0
\(821\) 27925.3i 1.18709i 0.804802 + 0.593544i \(0.202272\pi\)
−0.804802 + 0.593544i \(0.797728\pi\)
\(822\) 6161.50 + 1124.39i 0.261444 + 0.0477102i
\(823\) −997.907 997.907i −0.0422659 0.0422659i 0.685658 0.727924i \(-0.259515\pi\)
−0.727924 + 0.685658i \(0.759515\pi\)
\(824\) −29222.6 −1.23546
\(825\) 0 0
\(826\) 23144.0 0.974918
\(827\) −18683.3 18683.3i −0.785590 0.785590i 0.195178 0.980768i \(-0.437471\pi\)
−0.980768 + 0.195178i \(0.937471\pi\)
\(828\) 3075.83 + 6807.11i 0.129097 + 0.285705i
\(829\) 21146.9i 0.885962i 0.896531 + 0.442981i \(0.146079\pi\)
−0.896531 + 0.442981i \(0.853921\pi\)
\(830\) 0 0
\(831\) 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
\(835\) 0 0
\(836\) 7298.19i 0.301930i
\(837\) −17887.6 + 29739.6i −0.738695 + 1.22814i
\(838\) −2544.31 2544.31i −0.104883 0.104883i
\(839\) −30903.4 −1.27164 −0.635820 0.771838i \(-0.719338\pi\)
−0.635820 + 0.771838i \(0.719338\pi\)
\(840\) 0 0
\(841\) −8549.68 −0.350555
\(842\) 10557.5 + 10557.5i 0.432109 + 0.432109i
\(843\) −20354.7 3714.48i −0.831618 0.151760i
\(844\) 14060.4i 0.573435i
\(845\) 0 0
\(846\) 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
\(850\) 0 0
\(851\) 9629.53i 0.387892i
\(852\) 829.774 4547.02i 0.0333657 0.182839i
\(853\) −181.224 181.224i −0.00727432 0.00727432i 0.703460 0.710735i \(-0.251637\pi\)
−0.710735 + 0.703460i \(0.751637\pi\)
\(854\) −63.4584 −0.00254274
\(855\) 0 0
\(856\) −18663.2 −0.745205
\(857\) −13852.9 13852.9i −0.552167 0.552167i 0.374899 0.927066i \(-0.377677\pi\)
−0.927066 + 0.374899i \(0.877677\pi\)
\(858\) −902.189 + 4943.85i −0.0358977 + 0.196713i
\(859\) 8910.47i 0.353925i −0.984218 0.176962i \(-0.943373\pi\)
0.984218 0.176962i \(-0.0566271\pi\)
\(860\) 0 0
\(861\) −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
\(865\) 0 0
\(866\) 12900.0i 0.506187i
\(867\) −21592.8 3940.40i −0.845823 0.154352i
\(868\) −17112.6 17112.6i −0.669170 0.669170i
\(869\) 1378.93 0.0538285
\(870\) 0 0
\(871\) −9357.71 −0.364034
\(872\) −32471.9 32471.9i −1.26105 1.26105i
\(873\) 31599.0 14278.2i 1.22504 0.553543i
\(874\) 4403.12i 0.170409i
\(875\) 0 0
\(876\) −6058.22 8762.89i −0.233662 0.337980i
\(877\) 20231.6 20231.6i 0.778987 0.778987i −0.200672 0.979659i \(-0.564312\pi\)
0.979659 + 0.200672i \(0.0643124\pi\)
\(878\) −9764.88 + 9764.88i −0.375340 + 0.375340i
\(879\) −18869.2 27293.3i −0.724054 1.04730i
\(880\) 0 0
\(881\) 33209.0i 1.26996i −0.772527 0.634982i \(-0.781007\pi\)
0.772527 0.634982i \(-0.218993\pi\)
\(882\) 572.889 258.863i 0.0218709 0.00988251i
\(883\) −26984.3 26984.3i −1.02842 1.02842i −0.999584 0.0288331i \(-0.990821\pi\)
−0.0288331 0.999584i \(-0.509179\pi\)
\(884\) 2725.57 0.103700
\(885\) 0 0
\(886\) 4656.90 0.176582
\(887\) 24008.9 + 24008.9i 0.908838 + 0.908838i 0.996179 0.0873406i \(-0.0278369\pi\)
−0.0873406 + 0.996179i \(0.527837\pi\)
\(888\) 20396.5 + 3722.11i 0.770792 + 0.140660i
\(889\) 2820.84i 0.106421i
\(890\) 0 0
\(891\) −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
\(895\) 0 0
\(896\) 19102.9i 0.712258i
\(897\) −999.226 + 5475.59i −0.0371942 + 0.203818i
\(898\) 21198.9 + 21198.9i 0.787768 + 0.787768i
\(899\) 31132.2 1.15497
\(900\) 0 0
\(901\) −5955.13 −0.220193
\(902\) −13312.3 13312.3i −0.491409 0.491409i
\(903\) 981.871 5380.49i 0.0361845 0.198285i
\(904\) 8489.50i 0.312341i
\(905\) 0 0
\(906\) 14954.7 10338.9i 0.548384 0.379125i
\(907\) 23026.7 23026.7i 0.842989 0.842989i −0.146258 0.989246i \(-0.546723\pi\)
0.989246 + 0.146258i \(0.0467229\pi\)
\(908\) 7245.11 7245.11i 0.264799 0.264799i
\(909\) −3220.25 + 8529.38i −0.117501 + 0.311223i
\(910\) 0 0
\(911\) 33422.1i 1.21550i 0.794127 + 0.607752i \(0.207929\pi\)
−0.794127 + 0.607752i \(0.792071\pi\)
\(912\) 1066.71 + 194.660i 0.0387304 + 0.00706781i
\(913\) −4148.12 4148.12i −0.150364 0.150364i
\(914\) −15075.7 −0.545581
\(915\) 0 0
\(916\) 20355.1 0.734226
\(917\) 26438.8 + 26438.8i 0.952112 + 0.952112i
\(918\) −5299.85 3187.73i −0.190546 0.114609i
\(919\) 42542.2i 1.52703i −0.645792 0.763513i \(-0.723473\pi\)
0.645792 0.763513i \(-0.276527\pi\)
\(920\) 0 0
\(921\) 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
\(925\) 0 0
\(926\) 3157.84i 0.112066i
\(927\) −14677.4 32482.6i −0.520033 1.15088i
\(928\) 16394.7 + 16394.7i 0.579938 + 0.579938i
\(929\) −5721.21 −0.202053 −0.101026 0.994884i \(-0.532213\pi\)
−0.101026 + 0.994884i \(0.532213\pi\)
\(930\) 0 0
\(931\) −680.282 −0.0239477
\(932\) −10257.9 10257.9i −0.360524 0.360524i
\(933\) −20499.1 3740.83i −0.719305 0.131264i
\(934\) 3515.38i 0.123155i
\(935\) 0 0
\(936\) −11211.8 4232.97i −0.391525 0.147819i
\(937\) −1344.01 + 1344.01i −0.0468589 + 0.0468589i −0.730148 0.683289i \(-0.760549\pi\)
0.683289 + 0.730148i \(0.260549\pi\)
\(938\) −10470.2 + 10470.2i −0.364461 + 0.364461i
\(939\) −36706.8 + 25377.2i −1.27570 + 0.881953i
\(940\) 0 0
\(941\) 9625.77i 0.333466i 0.986002 + 0.166733i \(0.0533217\pi\)
−0.986002 + 0.166733i \(0.946678\pi\)
\(942\) −2677.80 + 14673.9i −0.0926192 + 0.507538i
\(943\) −14744.1 14744.1i −0.509157 0.509157i
\(944\) 3101.77 0.106943
\(945\) 0 0
\(946\) 2687.46 0.0923645
\(947\) −2234.24 2234.24i −0.0766664 0.0766664i 0.667734 0.744400i \(-0.267264\pi\)
−0.744400 + 0.667734i \(0.767264\pi\)
\(948\) −231.980 + 1271.21i −0.00794765 + 0.0435518i
\(949\) 7938.11i 0.271530i
\(950\) 0 0
\(951\) −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
\(955\) 0 0
\(956\) 15413.5i 0.521451i
\(957\) 18474.3 + 3371.32i 0.624021 + 0.113876i
\(958\) −5985.35 5985.35i −0.201856 0.201856i
\(959\) −13556.9 −0.456491
\(960\) 0 0
\(961\) 31399.6 1.05399
\(962\) 4292.91 + 4292.91i 0.143876 + 0.143876i
\(963\) −9373.84 20745.2i −0.313674 0.694190i
\(964\) 9505.61i 0.317588i
\(965\) 0 0
\(966\) 5008.55 + 7244.59i 0.166819 + 0.241295i
\(967\) −13166.9 + 13166.9i −0.437869 + 0.437869i −0.891294 0.453425i \(-0.850202\pi\)
0.453425 + 0.891294i \(0.350202\pi\)
\(968\) −7925.72 + 7925.72i −0.263163 + 0.263163i
\(969\) 3805.89 + 5505.01i 0.126174 + 0.182504i
\(970\) 0 0
\(971\) 21504.3i 0.710716i 0.934730 + 0.355358i \(0.115641\pi\)
−0.934730 + 0.355358i \(0.884359\pi\)
\(972\) −12156.0 15397.6i −0.401136 0.508104i
\(973\) −914.119 914.119i −0.0301185 0.0301185i
\(974\) 3071.14 0.101032
\(975\) 0 0
\(976\) −8.50472 −0.000278924
\(977\) −8996.19 8996.19i −0.294589 0.294589i 0.544301 0.838890i \(-0.316795\pi\)
−0.838890 + 0.544301i \(0.816795\pi\)
\(978\) 7601.68 + 1387.21i 0.248543 + 0.0453559i
\(979\) 40697.1i 1.32858i
\(980\) 0 0
\(981\) 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
\(985\) 0 0
\(986\) 5548.02i 0.179194i
\(987\) −3104.18 + 17010.4i −0.100108 + 0.548578i
\(988\) 3603.53 + 3603.53i 0.116036 + 0.116036i
\(989\) 2976.52 0.0957004
\(990\) 0 0
\(991\) −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
\(993\) −8945.31 + 49018.8i −0.285872 + 1.56653i
\(994\) 5449.79i 0.173900i
\(995\) 0 0
\(996\) 4521.93 3126.24i 0.143858 0.0994564i
\(997\) −20406.0 + 20406.0i −0.648210 + 0.648210i −0.952560 0.304350i \(-0.901561\pi\)
0.304350 + 0.952560i \(0.401561\pi\)
\(998\) 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 75.4.e.c.68.2 8
3.2 odd 2 inner 75.4.e.c.68.3 8
5.2 odd 4 inner 75.4.e.c.32.3 8
5.3 odd 4 15.4.e.a.2.2 8
5.4 even 2 15.4.e.a.8.3 yes 8
15.2 even 4 inner 75.4.e.c.32.2 8
15.8 even 4 15.4.e.a.2.3 yes 8
15.14 odd 2 15.4.e.a.8.2 yes 8
20.3 even 4 240.4.v.c.17.1 8
20.19 odd 2 240.4.v.c.113.2 8
60.23 odd 4 240.4.v.c.17.2 8
60.59 even 2 240.4.v.c.113.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.4.e.a.2.2 8 5.3 odd 4
15.4.e.a.2.3 yes 8 15.8 even 4
15.4.e.a.8.2 yes 8 15.14 odd 2
15.4.e.a.8.3 yes 8 5.4 even 2
75.4.e.c.32.2 8 15.2 even 4 inner
75.4.e.c.32.3 8 5.2 odd 4 inner
75.4.e.c.68.2 8 1.1 even 1 trivial
75.4.e.c.68.3 8 3.2 odd 2 inner
240.4.v.c.17.1 8 20.3 even 4
240.4.v.c.17.2 8 60.23 odd 4
240.4.v.c.113.1 8 60.59 even 2
240.4.v.c.113.2 8 20.19 odd 2