Properties

Label 100.3.d.b.99.4
Level $100$
Weight $3$
Character 100.99
Analytic conductor $2.725$
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] = [100,3,Mod(99,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.99");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 100.d (of order \(2\), degree \(1\), not 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: \(2.72480264360\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.4
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 100.99
Dual form 100.3.d.b.99.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17557 + 1.61803i) q^{2} +3.80423 q^{3} +(-1.23607 - 3.80423i) q^{4} +(-4.47214 + 6.15537i) q^{6} +8.50651 q^{7} +(7.60845 + 2.47214i) q^{8} +5.47214 q^{9} +O(q^{10})\) \(q+(-1.17557 + 1.61803i) q^{2} +3.80423 q^{3} +(-1.23607 - 3.80423i) q^{4} +(-4.47214 + 6.15537i) q^{6} +8.50651 q^{7} +(7.60845 + 2.47214i) q^{8} +5.47214 q^{9} -1.79611i q^{11} +(-4.70228 - 14.4721i) q^{12} +0.472136i q^{13} +(-10.0000 + 13.7638i) q^{14} +(-12.9443 + 9.40456i) q^{16} +23.8885i q^{17} +(-6.43288 + 8.85410i) q^{18} -9.40456i q^{19} +32.3607 q^{21} +(2.90617 + 2.11146i) q^{22} -16.1150 q^{23} +(28.9443 + 9.40456i) q^{24} +(-0.763932 - 0.555029i) q^{26} -13.4208 q^{27} +(-10.5146 - 32.3607i) q^{28} -6.94427 q^{29} -47.4468i q^{31} -32.0000i q^{32} -6.83282i q^{33} +(-38.6525 - 28.0827i) q^{34} +(-6.76393 - 20.8172i) q^{36} -26.3607i q^{37} +(15.2169 + 11.0557i) q^{38} +1.79611i q^{39} -41.4164 q^{41} +(-38.0423 + 52.3607i) q^{42} -2.00811 q^{43} +(-6.83282 + 2.22012i) q^{44} +(18.9443 - 26.0746i) q^{46} +35.3481 q^{47} +(-49.2429 + 35.7771i) q^{48} +23.3607 q^{49} +90.8774i q^{51} +(1.79611 - 0.583592i) q^{52} -21.6393i q^{53} +(15.7771 - 21.7153i) q^{54} +(64.7214 + 21.0292i) q^{56} -35.7771i q^{57} +(8.16348 - 11.2361i) q^{58} +73.8644i q^{59} -26.1378 q^{61} +(76.7706 + 55.7771i) q^{62} +46.5488 q^{63} +(51.7771 + 37.6183i) q^{64} +(11.0557 + 8.03246i) q^{66} -88.8693 q^{67} +(90.8774 - 29.5279i) q^{68} -61.3050 q^{69} +39.4144i q^{71} +(41.6345 + 13.5279i) q^{72} +137.554i q^{73} +(42.6525 + 30.9888i) q^{74} +(-35.7771 + 11.6247i) q^{76} -15.2786i q^{77} +(-2.90617 - 2.11146i) q^{78} -113.703i q^{79} -100.305 q^{81} +(48.6879 - 67.0132i) q^{82} +21.2412 q^{83} +(-40.0000 - 123.107i) q^{84} +(2.36068 - 3.24920i) q^{86} -26.4176 q^{87} +(4.44023 - 13.6656i) q^{88} -67.4427 q^{89} +4.01623i q^{91} +(19.9192 + 61.3050i) q^{92} -180.498i q^{93} +(-41.5542 + 57.1944i) q^{94} -121.735i q^{96} +39.1672i q^{97} +(-27.4621 + 37.7984i) q^{98} -9.82857i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 8 q^{9} - 80 q^{14} - 32 q^{16} + 80 q^{21} + 160 q^{24} - 24 q^{26} + 16 q^{29} - 184 q^{34} - 72 q^{36} - 224 q^{41} + 160 q^{44} + 80 q^{46} + 8 q^{49} - 160 q^{54} + 160 q^{56} + 256 q^{61} + 128 q^{64} + 160 q^{66} - 240 q^{69} + 216 q^{74} - 552 q^{81} - 320 q^{84} - 160 q^{86} + 176 q^{89} + 240 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17557 + 1.61803i −0.587785 + 0.809017i
\(3\) 3.80423 1.26808 0.634038 0.773302i \(-0.281396\pi\)
0.634038 + 0.773302i \(0.281396\pi\)
\(4\) −1.23607 3.80423i −0.309017 0.951057i
\(5\) 0 0
\(6\) −4.47214 + 6.15537i −0.745356 + 1.02589i
\(7\) 8.50651 1.21522 0.607608 0.794237i \(-0.292129\pi\)
0.607608 + 0.794237i \(0.292129\pi\)
\(8\) 7.60845 + 2.47214i 0.951057 + 0.309017i
\(9\) 5.47214 0.608015
\(10\) 0 0
\(11\) 1.79611i 0.163283i −0.996662 0.0816415i \(-0.973984\pi\)
0.996662 0.0816415i \(-0.0260162\pi\)
\(12\) −4.70228 14.4721i −0.391857 1.20601i
\(13\) 0.472136i 0.0363182i 0.999835 + 0.0181591i \(0.00578053\pi\)
−0.999835 + 0.0181591i \(0.994219\pi\)
\(14\) −10.0000 + 13.7638i −0.714286 + 0.983130i
\(15\) 0 0
\(16\) −12.9443 + 9.40456i −0.809017 + 0.587785i
\(17\) 23.8885i 1.40521i 0.711581 + 0.702604i \(0.247980\pi\)
−0.711581 + 0.702604i \(0.752020\pi\)
\(18\) −6.43288 + 8.85410i −0.357382 + 0.491895i
\(19\) 9.40456i 0.494977i −0.968891 0.247489i \(-0.920395\pi\)
0.968891 0.247489i \(-0.0796053\pi\)
\(20\) 0 0
\(21\) 32.3607 1.54098
\(22\) 2.90617 + 2.11146i 0.132099 + 0.0959753i
\(23\) −16.1150 −0.700650 −0.350325 0.936628i \(-0.613929\pi\)
−0.350325 + 0.936628i \(0.613929\pi\)
\(24\) 28.9443 + 9.40456i 1.20601 + 0.391857i
\(25\) 0 0
\(26\) −0.763932 0.555029i −0.0293820 0.0213473i
\(27\) −13.4208 −0.497066
\(28\) −10.5146 32.3607i −0.375522 1.15574i
\(29\) −6.94427 −0.239458 −0.119729 0.992807i \(-0.538203\pi\)
−0.119729 + 0.992807i \(0.538203\pi\)
\(30\) 0 0
\(31\) 47.4468i 1.53054i −0.643708 0.765271i \(-0.722605\pi\)
0.643708 0.765271i \(-0.277395\pi\)
\(32\) 32.0000i 1.00000i
\(33\) 6.83282i 0.207055i
\(34\) −38.6525 28.0827i −1.13684 0.825961i
\(35\) 0 0
\(36\) −6.76393 20.8172i −0.187887 0.578257i
\(37\) 26.3607i 0.712451i −0.934400 0.356225i \(-0.884064\pi\)
0.934400 0.356225i \(-0.115936\pi\)
\(38\) 15.2169 + 11.0557i 0.400445 + 0.290940i
\(39\) 1.79611i 0.0460542i
\(40\) 0 0
\(41\) −41.4164 −1.01016 −0.505078 0.863074i \(-0.668536\pi\)
−0.505078 + 0.863074i \(0.668536\pi\)
\(42\) −38.0423 + 52.3607i −0.905768 + 1.24668i
\(43\) −2.00811 −0.0467003 −0.0233502 0.999727i \(-0.507433\pi\)
−0.0233502 + 0.999727i \(0.507433\pi\)
\(44\) −6.83282 + 2.22012i −0.155291 + 0.0504572i
\(45\) 0 0
\(46\) 18.9443 26.0746i 0.411832 0.566838i
\(47\) 35.3481 0.752087 0.376044 0.926602i \(-0.377284\pi\)
0.376044 + 0.926602i \(0.377284\pi\)
\(48\) −49.2429 + 35.7771i −1.02589 + 0.745356i
\(49\) 23.3607 0.476749
\(50\) 0 0
\(51\) 90.8774i 1.78191i
\(52\) 1.79611 0.583592i 0.0345406 0.0112229i
\(53\) 21.6393i 0.408289i −0.978941 0.204145i \(-0.934559\pi\)
0.978941 0.204145i \(-0.0654413\pi\)
\(54\) 15.7771 21.7153i 0.292168 0.402135i
\(55\) 0 0
\(56\) 64.7214 + 21.0292i 1.15574 + 0.375522i
\(57\) 35.7771i 0.627668i
\(58\) 8.16348 11.2361i 0.140750 0.193725i
\(59\) 73.8644i 1.25194i 0.779848 + 0.625970i \(0.215297\pi\)
−0.779848 + 0.625970i \(0.784703\pi\)
\(60\) 0 0
\(61\) −26.1378 −0.428488 −0.214244 0.976780i \(-0.568729\pi\)
−0.214244 + 0.976780i \(0.568729\pi\)
\(62\) 76.7706 + 55.7771i 1.23824 + 0.899630i
\(63\) 46.5488 0.738869
\(64\) 51.7771 + 37.6183i 0.809017 + 0.587785i
\(65\) 0 0
\(66\) 11.0557 + 8.03246i 0.167511 + 0.121704i
\(67\) −88.8693 −1.32641 −0.663204 0.748439i \(-0.730804\pi\)
−0.663204 + 0.748439i \(0.730804\pi\)
\(68\) 90.8774 29.5279i 1.33643 0.434233i
\(69\) −61.3050 −0.888478
\(70\) 0 0
\(71\) 39.4144i 0.555132i 0.960707 + 0.277566i \(0.0895277\pi\)
−0.960707 + 0.277566i \(0.910472\pi\)
\(72\) 41.6345 + 13.5279i 0.578257 + 0.187887i
\(73\) 137.554i 1.88430i 0.335186 + 0.942152i \(0.391201\pi\)
−0.335186 + 0.942152i \(0.608799\pi\)
\(74\) 42.6525 + 30.9888i 0.576385 + 0.418768i
\(75\) 0 0
\(76\) −35.7771 + 11.6247i −0.470751 + 0.152956i
\(77\) 15.2786i 0.198424i
\(78\) −2.90617 2.11146i −0.0372586 0.0270700i
\(79\) 113.703i 1.43928i −0.694350 0.719638i \(-0.744308\pi\)
0.694350 0.719638i \(-0.255692\pi\)
\(80\) 0 0
\(81\) −100.305 −1.23833
\(82\) 48.6879 67.0132i 0.593755 0.817234i
\(83\) 21.2412 0.255919 0.127959 0.991779i \(-0.459157\pi\)
0.127959 + 0.991779i \(0.459157\pi\)
\(84\) −40.0000 123.107i −0.476190 1.46556i
\(85\) 0 0
\(86\) 2.36068 3.24920i 0.0274498 0.0377814i
\(87\) −26.4176 −0.303650
\(88\) 4.44023 13.6656i 0.0504572 0.155291i
\(89\) −67.4427 −0.757783 −0.378892 0.925441i \(-0.623695\pi\)
−0.378892 + 0.925441i \(0.623695\pi\)
\(90\) 0 0
\(91\) 4.01623i 0.0441344i
\(92\) 19.9192 + 61.3050i 0.216513 + 0.666358i
\(93\) 180.498i 1.94084i
\(94\) −41.5542 + 57.1944i −0.442066 + 0.608451i
\(95\) 0 0
\(96\) 121.735i 1.26808i
\(97\) 39.1672i 0.403785i 0.979408 + 0.201893i \(0.0647092\pi\)
−0.979408 + 0.201893i \(0.935291\pi\)
\(98\) −27.4621 + 37.7984i −0.280226 + 0.385698i
\(99\) 9.82857i 0.0992785i
\(100\) 0 0
\(101\) 99.8885 0.988995 0.494498 0.869179i \(-0.335352\pi\)
0.494498 + 0.869179i \(0.335352\pi\)
\(102\) −147.043 106.833i −1.44160 1.04738i
\(103\) −35.7721 −0.347302 −0.173651 0.984807i \(-0.555556\pi\)
−0.173651 + 0.984807i \(0.555556\pi\)
\(104\) −1.16718 + 3.59222i −0.0112229 + 0.0345406i
\(105\) 0 0
\(106\) 35.0132 + 25.4385i 0.330313 + 0.239986i
\(107\) 121.099 1.13177 0.565884 0.824485i \(-0.308535\pi\)
0.565884 + 0.824485i \(0.308535\pi\)
\(108\) 16.5890 + 51.0557i 0.153602 + 0.472738i
\(109\) 197.469 1.81164 0.905821 0.423660i \(-0.139255\pi\)
0.905821 + 0.423660i \(0.139255\pi\)
\(110\) 0 0
\(111\) 100.282i 0.903441i
\(112\) −110.111 + 80.0000i −0.983130 + 0.714286i
\(113\) 81.2786i 0.719280i 0.933091 + 0.359640i \(0.117100\pi\)
−0.933091 + 0.359640i \(0.882900\pi\)
\(114\) 57.8885 + 42.0585i 0.507794 + 0.368934i
\(115\) 0 0
\(116\) 8.58359 + 26.4176i 0.0739965 + 0.227738i
\(117\) 2.58359i 0.0220820i
\(118\) −119.515 86.8328i −1.01284 0.735871i
\(119\) 203.208i 1.70763i
\(120\) 0 0
\(121\) 117.774 0.973339
\(122\) 30.7268 42.2918i 0.251859 0.346654i
\(123\) −157.557 −1.28095
\(124\) −180.498 + 58.6475i −1.45563 + 0.472964i
\(125\) 0 0
\(126\) −54.7214 + 75.3175i −0.434297 + 0.597758i
\(127\) 1.84616 0.0145367 0.00726834 0.999974i \(-0.497686\pi\)
0.00726834 + 0.999974i \(0.497686\pi\)
\(128\) −121.735 + 39.5542i −0.951057 + 0.309017i
\(129\) −7.63932 −0.0592195
\(130\) 0 0
\(131\) 225.609i 1.72221i −0.508428 0.861105i \(-0.669773\pi\)
0.508428 0.861105i \(-0.330227\pi\)
\(132\) −25.9936 + 8.44582i −0.196921 + 0.0639835i
\(133\) 80.0000i 0.601504i
\(134\) 104.472 143.794i 0.779643 1.07309i
\(135\) 0 0
\(136\) −59.0557 + 181.755i −0.434233 + 1.33643i
\(137\) 52.8328i 0.385641i 0.981234 + 0.192820i \(0.0617635\pi\)
−0.981234 + 0.192820i \(0.938236\pi\)
\(138\) 72.0683 99.1935i 0.522234 0.718793i
\(139\) 125.852i 0.905407i −0.891661 0.452703i \(-0.850460\pi\)
0.891661 0.452703i \(-0.149540\pi\)
\(140\) 0 0
\(141\) 134.472 0.953703
\(142\) −63.7738 46.3344i −0.449111 0.326298i
\(143\) 0.848009 0.00593013
\(144\) −70.8328 + 51.4631i −0.491895 + 0.357382i
\(145\) 0 0
\(146\) −222.567 161.705i −1.52443 1.10757i
\(147\) 88.8693 0.604553
\(148\) −100.282 + 32.5836i −0.677581 + 0.220159i
\(149\) −132.971 −0.892420 −0.446210 0.894928i \(-0.647227\pi\)
−0.446210 + 0.894928i \(0.647227\pi\)
\(150\) 0 0
\(151\) 151.221i 1.00146i 0.865603 + 0.500732i \(0.166936\pi\)
−0.865603 + 0.500732i \(0.833064\pi\)
\(152\) 23.2494 71.5542i 0.152956 0.470751i
\(153\) 130.721i 0.854388i
\(154\) 24.7214 + 17.9611i 0.160528 + 0.116631i
\(155\) 0 0
\(156\) 6.83282 2.22012i 0.0438001 0.0142315i
\(157\) 36.7477i 0.234062i 0.993128 + 0.117031i \(0.0373376\pi\)
−0.993128 + 0.117031i \(0.962662\pi\)
\(158\) 183.975 + 133.666i 1.16440 + 0.845985i
\(159\) 82.3209i 0.517741i
\(160\) 0 0
\(161\) −137.082 −0.851441
\(162\) 117.916 162.297i 0.727874 1.00183i
\(163\) 302.854 1.85800 0.929000 0.370079i \(-0.120669\pi\)
0.929000 + 0.370079i \(0.120669\pi\)
\(164\) 51.1935 + 157.557i 0.312155 + 0.960716i
\(165\) 0 0
\(166\) −24.9706 + 34.3691i −0.150425 + 0.207043i
\(167\) −99.3839 −0.595113 −0.297557 0.954704i \(-0.596172\pi\)
−0.297557 + 0.954704i \(0.596172\pi\)
\(168\) 246.215 + 80.0000i 1.46556 + 0.476190i
\(169\) 168.777 0.998681
\(170\) 0 0
\(171\) 51.4631i 0.300954i
\(172\) 2.48217 + 7.63932i 0.0144312 + 0.0444147i
\(173\) 181.639i 1.04994i −0.851121 0.524969i \(-0.824077\pi\)
0.851121 0.524969i \(-0.175923\pi\)
\(174\) 31.0557 42.7445i 0.178481 0.245658i
\(175\) 0 0
\(176\) 16.8916 + 23.2494i 0.0959753 + 0.132099i
\(177\) 280.997i 1.58755i
\(178\) 79.2837 109.125i 0.445414 0.613060i
\(179\) 260.907i 1.45758i −0.684735 0.728792i \(-0.740082\pi\)
0.684735 0.728792i \(-0.259918\pi\)
\(180\) 0 0
\(181\) 157.777 0.871697 0.435848 0.900020i \(-0.356448\pi\)
0.435848 + 0.900020i \(0.356448\pi\)
\(182\) −6.49839 4.72136i −0.0357055 0.0259415i
\(183\) −99.4340 −0.543355
\(184\) −122.610 39.8384i −0.666358 0.216513i
\(185\) 0 0
\(186\) 292.053 + 212.189i 1.57018 + 1.14080i
\(187\) 42.9065 0.229447
\(188\) −43.6926 134.472i −0.232408 0.715277i
\(189\) −114.164 −0.604043
\(190\) 0 0
\(191\) 324.095i 1.69683i 0.529328 + 0.848417i \(0.322444\pi\)
−0.529328 + 0.848417i \(0.677556\pi\)
\(192\) 196.972 + 143.108i 1.02589 + 0.745356i
\(193\) 181.777i 0.941850i 0.882173 + 0.470925i \(0.156080\pi\)
−0.882173 + 0.470925i \(0.843920\pi\)
\(194\) −63.3738 46.0438i −0.326669 0.237339i
\(195\) 0 0
\(196\) −28.8754 88.8693i −0.147323 0.453415i
\(197\) 140.525i 0.713324i −0.934234 0.356662i \(-0.883915\pi\)
0.934234 0.356662i \(-0.116085\pi\)
\(198\) 15.9030 + 11.5542i 0.0803180 + 0.0583544i
\(199\) 168.234i 0.845397i 0.906270 + 0.422698i \(0.138917\pi\)
−0.906270 + 0.422698i \(0.861083\pi\)
\(200\) 0 0
\(201\) −338.079 −1.68198
\(202\) −117.426 + 161.623i −0.581317 + 0.800114i
\(203\) −59.0715 −0.290993
\(204\) 345.718 112.331i 1.69470 0.550641i
\(205\) 0 0
\(206\) 42.0526 57.8805i 0.204139 0.280973i
\(207\) −88.1833 −0.426006
\(208\) −4.44023 6.11146i −0.0213473 0.0293820i
\(209\) −16.8916 −0.0808213
\(210\) 0 0
\(211\) 93.9455i 0.445240i −0.974905 0.222620i \(-0.928539\pi\)
0.974905 0.222620i \(-0.0714608\pi\)
\(212\) −82.3209 + 26.7477i −0.388306 + 0.126168i
\(213\) 149.941i 0.703949i
\(214\) −142.361 + 195.943i −0.665237 + 0.915620i
\(215\) 0 0
\(216\) −102.111 33.1780i −0.472738 0.153602i
\(217\) 403.607i 1.85994i
\(218\) −232.139 + 319.512i −1.06486 + 1.46565i
\(219\) 523.287i 2.38944i
\(220\) 0 0
\(221\) −11.2786 −0.0510346
\(222\) 162.260 + 117.889i 0.730899 + 0.531029i
\(223\) 214.035 0.959797 0.479899 0.877324i \(-0.340673\pi\)
0.479899 + 0.877324i \(0.340673\pi\)
\(224\) 272.208i 1.21522i
\(225\) 0 0
\(226\) −131.512 95.5488i −0.581910 0.422782i
\(227\) 41.4225 0.182478 0.0912389 0.995829i \(-0.470917\pi\)
0.0912389 + 0.995829i \(0.470917\pi\)
\(228\) −136.104 + 44.2229i −0.596948 + 0.193960i
\(229\) −73.2786 −0.319994 −0.159997 0.987117i \(-0.551148\pi\)
−0.159997 + 0.987117i \(0.551148\pi\)
\(230\) 0 0
\(231\) 58.1234i 0.251616i
\(232\) −52.8352 17.1672i −0.227738 0.0739965i
\(233\) 307.050i 1.31781i −0.752227 0.658905i \(-0.771020\pi\)
0.752227 0.658905i \(-0.228980\pi\)
\(234\) −4.18034 3.03719i −0.0178647 0.0129795i
\(235\) 0 0
\(236\) 280.997 91.3014i 1.19066 0.386870i
\(237\) 432.551i 1.82511i
\(238\) −328.798 238.885i −1.38150 1.00372i
\(239\) 42.9065i 0.179525i −0.995963 0.0897625i \(-0.971389\pi\)
0.995963 0.0897625i \(-0.0286108\pi\)
\(240\) 0 0
\(241\) −135.082 −0.560506 −0.280253 0.959926i \(-0.590418\pi\)
−0.280253 + 0.959926i \(0.590418\pi\)
\(242\) −138.452 + 190.562i −0.572114 + 0.787448i
\(243\) −260.796 −1.07323
\(244\) 32.3081 + 99.4340i 0.132410 + 0.407516i
\(245\) 0 0
\(246\) 185.220 254.933i 0.752926 1.03631i
\(247\) 4.44023 0.0179767
\(248\) 117.295 360.997i 0.472964 1.45563i
\(249\) 80.8065 0.324524
\(250\) 0 0
\(251\) 221.169i 0.881152i 0.897715 + 0.440576i \(0.145226\pi\)
−0.897715 + 0.440576i \(0.854774\pi\)
\(252\) −57.5374 177.082i −0.228323 0.702707i
\(253\) 28.9443i 0.114404i
\(254\) −2.17029 + 2.98715i −0.00854445 + 0.0117604i
\(255\) 0 0
\(256\) 79.1084 243.470i 0.309017 0.951057i
\(257\) 257.056i 1.00022i 0.865963 + 0.500108i \(0.166707\pi\)
−0.865963 + 0.500108i \(0.833293\pi\)
\(258\) 8.98056 12.3607i 0.0348084 0.0479096i
\(259\) 224.237i 0.865781i
\(260\) 0 0
\(261\) −38.0000 −0.145594
\(262\) 365.044 + 265.220i 1.39330 + 1.01229i
\(263\) −164.168 −0.624212 −0.312106 0.950047i \(-0.601034\pi\)
−0.312106 + 0.950047i \(0.601034\pi\)
\(264\) 16.8916 51.9872i 0.0639835 0.196921i
\(265\) 0 0
\(266\) 129.443 + 94.0456i 0.486627 + 0.353555i
\(267\) −256.567 −0.960926
\(268\) 109.849 + 338.079i 0.409882 + 1.26149i
\(269\) 35.4752 0.131878 0.0659391 0.997824i \(-0.478996\pi\)
0.0659391 + 0.997824i \(0.478996\pi\)
\(270\) 0 0
\(271\) 298.950i 1.10314i −0.834130 0.551568i \(-0.814030\pi\)
0.834130 0.551568i \(-0.185970\pi\)
\(272\) −224.661 309.220i −0.825961 1.13684i
\(273\) 15.2786i 0.0559657i
\(274\) −85.4853 62.1087i −0.311990 0.226674i
\(275\) 0 0
\(276\) 75.7771 + 233.218i 0.274555 + 0.844992i
\(277\) 457.246i 1.65071i 0.564616 + 0.825354i \(0.309024\pi\)
−0.564616 + 0.825354i \(0.690976\pi\)
\(278\) 203.632 + 147.947i 0.732490 + 0.532185i
\(279\) 259.635i 0.930593i
\(280\) 0 0
\(281\) −5.63932 −0.0200688 −0.0100344 0.999950i \(-0.503194\pi\)
−0.0100344 + 0.999950i \(0.503194\pi\)
\(282\) −158.081 + 217.580i −0.560573 + 0.771562i
\(283\) −169.918 −0.600418 −0.300209 0.953874i \(-0.597056\pi\)
−0.300209 + 0.953874i \(0.597056\pi\)
\(284\) 149.941 48.7188i 0.527962 0.171545i
\(285\) 0 0
\(286\) −0.996894 + 1.37211i −0.00348564 + 0.00479758i
\(287\) −352.309 −1.22756
\(288\) 175.108i 0.608015i
\(289\) −281.663 −0.974611
\(290\) 0 0
\(291\) 149.001i 0.512030i
\(292\) 523.287 170.026i 1.79208 0.582282i
\(293\) 26.8591i 0.0916694i −0.998949 0.0458347i \(-0.985405\pi\)
0.998949 0.0458347i \(-0.0145947\pi\)
\(294\) −104.472 + 143.794i −0.355347 + 0.489094i
\(295\) 0 0
\(296\) 65.1672 200.564i 0.220159 0.677581i
\(297\) 24.1052i 0.0811624i
\(298\) 156.316 215.151i 0.524551 0.721983i
\(299\) 7.60845i 0.0254463i
\(300\) 0 0
\(301\) −17.0820 −0.0567510
\(302\) −244.681 177.771i −0.810201 0.588645i
\(303\) 379.999 1.25412
\(304\) 88.4458 + 121.735i 0.290940 + 0.400445i
\(305\) 0 0
\(306\) −211.512 153.672i −0.691214 0.502197i
\(307\) 118.031 0.384466 0.192233 0.981349i \(-0.438427\pi\)
0.192233 + 0.981349i \(0.438427\pi\)
\(308\) −58.1234 + 18.8854i −0.188712 + 0.0613164i
\(309\) −136.085 −0.440405
\(310\) 0 0
\(311\) 121.835i 0.391753i −0.980629 0.195877i \(-0.937245\pi\)
0.980629 0.195877i \(-0.0627552\pi\)
\(312\) −4.44023 + 13.6656i −0.0142315 + 0.0438001i
\(313\) 219.548i 0.701431i 0.936482 + 0.350716i \(0.114062\pi\)
−0.936482 + 0.350716i \(0.885938\pi\)
\(314\) −59.4590 43.1995i −0.189360 0.137578i
\(315\) 0 0
\(316\) −432.551 + 140.544i −1.36883 + 0.444761i
\(317\) 366.859i 1.15728i −0.815582 0.578642i \(-0.803583\pi\)
0.815582 0.578642i \(-0.196417\pi\)
\(318\) 133.198 + 96.7740i 0.418862 + 0.304321i
\(319\) 12.4727i 0.0390993i
\(320\) 0 0
\(321\) 460.689 1.43517
\(322\) 161.150 221.803i 0.500465 0.688830i
\(323\) 224.661 0.695546
\(324\) 123.984 + 381.583i 0.382666 + 1.17772i
\(325\) 0 0
\(326\) −356.026 + 490.028i −1.09211 + 1.50315i
\(327\) 751.217 2.29730
\(328\) −315.115 102.387i −0.960716 0.312155i
\(329\) 300.689 0.913948
\(330\) 0 0
\(331\) 162.846i 0.491981i 0.969272 + 0.245990i \(0.0791132\pi\)
−0.969272 + 0.245990i \(0.920887\pi\)
\(332\) −26.2556 80.8065i −0.0790832 0.243393i
\(333\) 144.249i 0.433181i
\(334\) 116.833 160.807i 0.349799 0.481457i
\(335\) 0 0
\(336\) −418.885 + 304.338i −1.24668 + 0.905768i
\(337\) 17.1084i 0.0507666i −0.999678 0.0253833i \(-0.991919\pi\)
0.999678 0.0253833i \(-0.00808063\pi\)
\(338\) −198.409 + 273.087i −0.587010 + 0.807950i
\(339\) 309.202i 0.912101i
\(340\) 0 0
\(341\) −85.2198 −0.249911
\(342\) 83.2690 + 60.4984i 0.243477 + 0.176896i
\(343\) −218.101 −0.635863
\(344\) −15.2786 4.96433i −0.0444147 0.0144312i
\(345\) 0 0
\(346\) 293.899 + 213.530i 0.849418 + 0.617138i
\(347\) −167.498 −0.482703 −0.241351 0.970438i \(-0.577591\pi\)
−0.241351 + 0.970438i \(0.577591\pi\)
\(348\) 32.6539 + 100.498i 0.0938331 + 0.288789i
\(349\) 483.495 1.38537 0.692687 0.721239i \(-0.256427\pi\)
0.692687 + 0.721239i \(0.256427\pi\)
\(350\) 0 0
\(351\) 6.33644i 0.0180525i
\(352\) −57.4756 −0.163283
\(353\) 307.994i 0.872504i 0.899825 + 0.436252i \(0.143694\pi\)
−0.899825 + 0.436252i \(0.856306\pi\)
\(354\) −454.663 330.332i −1.28436 0.933140i
\(355\) 0 0
\(356\) 83.3638 + 256.567i 0.234168 + 0.720695i
\(357\) 773.050i 2.16540i
\(358\) 422.157 + 306.715i 1.17921 + 0.856746i
\(359\) 23.2494i 0.0647615i −0.999476 0.0323807i \(-0.989691\pi\)
0.999476 0.0323807i \(-0.0103089\pi\)
\(360\) 0 0
\(361\) 272.554 0.754998
\(362\) −185.478 + 255.289i −0.512370 + 0.705217i
\(363\) 448.039 1.23427
\(364\) 15.2786 4.96433i 0.0419743 0.0136383i
\(365\) 0 0
\(366\) 116.892 160.888i 0.319376 0.439583i
\(367\) 517.325 1.40960 0.704802 0.709404i \(-0.251036\pi\)
0.704802 + 0.709404i \(0.251036\pi\)
\(368\) 208.596 151.554i 0.566838 0.411832i
\(369\) −226.636 −0.614190
\(370\) 0 0
\(371\) 184.075i 0.496159i
\(372\) −686.657 + 223.108i −1.84585 + 0.599754i
\(373\) 88.3545i 0.236875i −0.992961 0.118438i \(-0.962211\pi\)
0.992961 0.118438i \(-0.0377886\pi\)
\(374\) −50.4396 + 69.4242i −0.134865 + 0.185626i
\(375\) 0 0
\(376\) 268.944 + 87.3853i 0.715277 + 0.232408i
\(377\) 3.27864i 0.00869666i
\(378\) 134.208 184.721i 0.355047 0.488681i
\(379\) 19.3332i 0.0510112i 0.999675 + 0.0255056i \(0.00811956\pi\)
−0.999675 + 0.0255056i \(0.991880\pi\)
\(380\) 0 0
\(381\) 7.02321 0.0184336
\(382\) −524.397 380.997i −1.37277 0.997374i
\(383\) −431.612 −1.12692 −0.563462 0.826142i \(-0.690531\pi\)
−0.563462 + 0.826142i \(0.690531\pi\)
\(384\) −463.108 + 150.473i −1.20601 + 0.391857i
\(385\) 0 0
\(386\) −294.122 213.692i −0.761973 0.553606i
\(387\) −10.9887 −0.0283945
\(388\) 149.001 48.4133i 0.384023 0.124777i
\(389\) 296.354 0.761837 0.380918 0.924609i \(-0.375608\pi\)
0.380918 + 0.924609i \(0.375608\pi\)
\(390\) 0 0
\(391\) 384.963i 0.984560i
\(392\) 177.739 + 57.7508i 0.453415 + 0.147323i
\(393\) 858.269i 2.18389i
\(394\) 227.374 + 165.197i 0.577091 + 0.419281i
\(395\) 0 0
\(396\) −37.3901 + 12.1488i −0.0944194 + 0.0306787i
\(397\) 86.1904i 0.217104i 0.994091 + 0.108552i \(0.0346214\pi\)
−0.994091 + 0.108552i \(0.965379\pi\)
\(398\) −272.208 197.771i −0.683940 0.496912i
\(399\) 304.338i 0.762752i
\(400\) 0 0
\(401\) 442.997 1.10473 0.552365 0.833602i \(-0.313725\pi\)
0.552365 + 0.833602i \(0.313725\pi\)
\(402\) 397.436 547.023i 0.988646 1.36075i
\(403\) 22.4014 0.0555865
\(404\) −123.469 379.999i −0.305616 0.940591i
\(405\) 0 0
\(406\) 69.4427 95.5797i 0.171041 0.235418i
\(407\) −47.3467 −0.116331
\(408\) −224.661 + 691.437i −0.550641 + 1.69470i
\(409\) −63.4102 −0.155037 −0.0775186 0.996991i \(-0.524700\pi\)
−0.0775186 + 0.996991i \(0.524700\pi\)
\(410\) 0 0
\(411\) 200.988i 0.489022i
\(412\) 44.2167 + 136.085i 0.107322 + 0.330304i
\(413\) 628.328i 1.52138i
\(414\) 103.666 142.684i 0.250400 0.344646i
\(415\) 0 0
\(416\) 15.1084 0.0363182
\(417\) 478.768i 1.14812i
\(418\) 19.8573 27.3313i 0.0475056 0.0653858i
\(419\) 435.678i 1.03980i −0.854226 0.519902i \(-0.825968\pi\)
0.854226 0.519902i \(-0.174032\pi\)
\(420\) 0 0
\(421\) −582.912 −1.38459 −0.692294 0.721615i \(-0.743400\pi\)
−0.692294 + 0.721615i \(0.743400\pi\)
\(422\) 152.007 + 110.440i 0.360206 + 0.261705i
\(423\) 193.430 0.457280
\(424\) 53.4953 164.642i 0.126168 0.388306i
\(425\) 0 0
\(426\) −242.610 176.266i −0.569507 0.413771i
\(427\) −222.341 −0.520705
\(428\) −149.687 460.689i −0.349736 1.07638i
\(429\) 3.22602 0.00751986
\(430\) 0 0
\(431\) 375.882i 0.872117i −0.899918 0.436058i \(-0.856374\pi\)
0.899918 0.436058i \(-0.143626\pi\)
\(432\) 173.722 126.217i 0.402135 0.292168i
\(433\) 368.164i 0.850263i −0.905131 0.425132i \(-0.860228\pi\)
0.905131 0.425132i \(-0.139772\pi\)
\(434\) 653.050 + 474.468i 1.50472 + 1.09324i
\(435\) 0 0
\(436\) −244.085 751.217i −0.559828 1.72297i
\(437\) 151.554i 0.346806i
\(438\) −846.696 615.161i −1.93310 1.40448i
\(439\) 483.549i 1.10148i 0.834677 + 0.550739i \(0.185654\pi\)
−0.834677 + 0.550739i \(0.814346\pi\)
\(440\) 0 0
\(441\) 127.833 0.289870
\(442\) 13.2588 18.2492i 0.0299974 0.0412878i
\(443\) −279.181 −0.630205 −0.315102 0.949058i \(-0.602039\pi\)
−0.315102 + 0.949058i \(0.602039\pi\)
\(444\) −381.495 + 123.955i −0.859224 + 0.279179i
\(445\) 0 0
\(446\) −251.613 + 346.316i −0.564155 + 0.776492i
\(447\) −505.850 −1.13166
\(448\) 440.442 + 320.000i 0.983130 + 0.714286i
\(449\) −756.079 −1.68392 −0.841959 0.539542i \(-0.818597\pi\)
−0.841959 + 0.539542i \(0.818597\pi\)
\(450\) 0 0
\(451\) 74.3885i 0.164941i
\(452\) 309.202 100.466i 0.684076 0.222270i
\(453\) 575.279i 1.26993i
\(454\) −48.6950 + 67.0230i −0.107258 + 0.147628i
\(455\) 0 0
\(456\) 88.4458 272.208i 0.193960 0.596948i
\(457\) 285.672i 0.625103i −0.949901 0.312551i \(-0.898816\pi\)
0.949901 0.312551i \(-0.101184\pi\)
\(458\) 86.1442 118.567i 0.188088 0.258881i
\(459\) 320.603i 0.698482i
\(460\) 0 0
\(461\) −99.1146 −0.214999 −0.107500 0.994205i \(-0.534284\pi\)
−0.107500 + 0.994205i \(0.534284\pi\)
\(462\) 94.0456 + 68.3282i 0.203562 + 0.147896i
\(463\) −630.603 −1.36199 −0.680997 0.732286i \(-0.738453\pi\)
−0.680997 + 0.732286i \(0.738453\pi\)
\(464\) 89.8885 65.3078i 0.193725 0.140750i
\(465\) 0 0
\(466\) 496.817 + 360.958i 1.06613 + 0.774589i
\(467\) −496.010 −1.06212 −0.531060 0.847334i \(-0.678206\pi\)
−0.531060 + 0.847334i \(0.678206\pi\)
\(468\) 9.82857 3.19350i 0.0210012 0.00682371i
\(469\) −755.967 −1.61187
\(470\) 0 0
\(471\) 139.796i 0.296808i
\(472\) −182.603 + 561.994i −0.386870 + 1.19066i
\(473\) 3.60680i 0.00762537i
\(474\) 699.882 + 508.494i 1.47655 + 1.07277i
\(475\) 0 0
\(476\) 773.050 251.179i 1.62405 0.527687i
\(477\) 118.413i 0.248246i
\(478\) 69.4242 + 50.4396i 0.145239 + 0.105522i
\(479\) 579.090i 1.20896i 0.796621 + 0.604478i \(0.206618\pi\)
−0.796621 + 0.604478i \(0.793382\pi\)
\(480\) 0 0
\(481\) 12.4458 0.0258749
\(482\) 158.798 218.567i 0.329457 0.453459i
\(483\) −521.491 −1.07969
\(484\) −145.577 448.039i −0.300778 0.925700i
\(485\) 0 0
\(486\) 306.584 421.976i 0.630830 0.868264i
\(487\) −626.363 −1.28617 −0.643084 0.765796i \(-0.722345\pi\)
−0.643084 + 0.765796i \(0.722345\pi\)
\(488\) −198.868 64.6161i −0.407516 0.132410i
\(489\) 1152.13 2.35608
\(490\) 0 0
\(491\) 22.3013i 0.0454201i −0.999742 0.0227100i \(-0.992771\pi\)
0.999742 0.0227100i \(-0.00722945\pi\)
\(492\) 194.752 + 599.384i 0.395837 + 1.21826i
\(493\) 165.889i 0.336488i
\(494\) −5.21981 + 7.18445i −0.0105664 + 0.0145434i
\(495\) 0 0
\(496\) 446.217 + 614.165i 0.899630 + 1.23824i
\(497\) 335.279i 0.674605i
\(498\) −94.9937 + 130.748i −0.190750 + 0.262546i
\(499\) 627.362i 1.25724i 0.777714 + 0.628619i \(0.216379\pi\)
−0.777714 + 0.628619i \(0.783621\pi\)
\(500\) 0 0
\(501\) −378.079 −0.754649
\(502\) −357.859 260.000i −0.712867 0.517928i
\(503\) 780.853 1.55239 0.776196 0.630492i \(-0.217147\pi\)
0.776196 + 0.630492i \(0.217147\pi\)
\(504\) 354.164 + 115.075i 0.702707 + 0.228323i
\(505\) 0 0
\(506\) −46.8328 34.0260i −0.0925550 0.0672451i
\(507\) 642.066 1.26640
\(508\) −2.28198 7.02321i −0.00449208 0.0138252i
\(509\) 288.950 0.567683 0.283841 0.958871i \(-0.408391\pi\)
0.283841 + 0.958871i \(0.408391\pi\)
\(510\) 0 0
\(511\) 1170.11i 2.28984i
\(512\) 300.946 + 414.217i 0.587785 + 0.809017i
\(513\) 126.217i 0.246036i
\(514\) −415.925 302.187i −0.809192 0.587913i
\(515\) 0 0
\(516\) 9.44272 + 29.0617i 0.0182998 + 0.0563211i
\(517\) 63.4891i 0.122803i
\(518\) 362.824 + 263.607i 0.700432 + 0.508893i
\(519\) 690.997i 1.33140i
\(520\) 0 0
\(521\) −602.984 −1.15736 −0.578680 0.815555i \(-0.696432\pi\)
−0.578680 + 0.815555i \(0.696432\pi\)
\(522\) 44.6717 61.4853i 0.0855779 0.117788i
\(523\) 367.962 0.703560 0.351780 0.936083i \(-0.385577\pi\)
0.351780 + 0.936083i \(0.385577\pi\)
\(524\) −858.269 + 278.869i −1.63792 + 0.532192i
\(525\) 0 0
\(526\) 192.991 265.629i 0.366902 0.504998i
\(527\) 1133.44 2.15073
\(528\) 64.2597 + 88.4458i 0.121704 + 0.167511i
\(529\) −269.308 −0.509089
\(530\) 0 0
\(531\) 404.196i 0.761198i
\(532\) −304.338 + 98.8854i −0.572064 + 0.185875i
\(533\) 19.5542i 0.0366870i
\(534\) 301.613 415.135i 0.564818 0.777406i
\(535\) 0 0
\(536\) −676.158 219.697i −1.26149 0.409882i
\(537\) 992.551i 1.84833i
\(538\) −41.7036 + 57.4001i −0.0775161 + 0.106692i
\(539\) 41.9584i 0.0778449i
\(540\) 0 0
\(541\) −616.885 −1.14027 −0.570134 0.821551i \(-0.693109\pi\)
−0.570134 + 0.821551i \(0.693109\pi\)
\(542\) 483.711 + 351.437i 0.892455 + 0.648407i
\(543\) 600.220 1.10538
\(544\) 764.433 1.40521
\(545\) 0 0
\(546\) −24.7214 17.9611i −0.0452772 0.0328958i
\(547\) 97.8499 0.178885 0.0894423 0.995992i \(-0.471492\pi\)
0.0894423 + 0.995992i \(0.471492\pi\)
\(548\) 200.988 65.3050i 0.366766 0.119170i
\(549\) −143.029 −0.260527
\(550\) 0 0
\(551\) 65.3078i 0.118526i
\(552\) −466.436 151.554i −0.844992 0.274555i
\(553\) 967.214i 1.74903i
\(554\) −739.840 537.525i −1.33545 0.970262i
\(555\) 0 0
\(556\) −478.768 + 155.561i −0.861093 + 0.279786i
\(557\) 896.302i 1.60916i −0.593845 0.804580i \(-0.702391\pi\)
0.593845 0.804580i \(-0.297609\pi\)
\(558\) 420.099 + 305.220i 0.752866 + 0.546989i
\(559\) 0.948103i 0.00169607i
\(560\) 0 0
\(561\) 163.226 0.290955
\(562\) 6.62942 9.12461i 0.0117961 0.0162360i
\(563\) 771.186 1.36978 0.684890 0.728647i \(-0.259850\pi\)
0.684890 + 0.728647i \(0.259850\pi\)
\(564\) −166.217 511.562i −0.294710 0.907026i
\(565\) 0 0
\(566\) 199.751 274.933i 0.352917 0.485748i
\(567\) −853.245 −1.50484
\(568\) −97.4377 + 299.882i −0.171545 + 0.527962i
\(569\) −8.74767 −0.0153738 −0.00768688 0.999970i \(-0.502447\pi\)
−0.00768688 + 0.999970i \(0.502447\pi\)
\(570\) 0 0
\(571\) 511.138i 0.895164i −0.894243 0.447582i \(-0.852285\pi\)
0.894243 0.447582i \(-0.147715\pi\)
\(572\) −1.04820 3.22602i −0.00183251 0.00563989i
\(573\) 1232.93i 2.15171i
\(574\) 414.164 570.048i 0.721540 0.993115i
\(575\) 0 0
\(576\) 283.331 + 205.852i 0.491895 + 0.357382i
\(577\) 713.712i 1.23694i 0.785810 + 0.618468i \(0.212246\pi\)
−0.785810 + 0.618468i \(0.787754\pi\)
\(578\) 331.114 455.740i 0.572862 0.788477i
\(579\) 691.521i 1.19434i
\(580\) 0 0
\(581\) 180.689 0.310996
\(582\) −241.088 175.161i −0.414241 0.300964i
\(583\) −38.8666 −0.0666666
\(584\) −340.053 + 1046.57i −0.582282 + 1.79208i
\(585\) 0 0
\(586\) 43.4590 + 31.5748i 0.0741621 + 0.0538819i
\(587\) 422.169 0.719198 0.359599 0.933107i \(-0.382914\pi\)
0.359599 + 0.933107i \(0.382914\pi\)
\(588\) −109.849 338.079i −0.186817 0.574964i
\(589\) −446.217 −0.757584
\(590\) 0 0
\(591\) 534.588i 0.904548i
\(592\) 247.911 + 341.220i 0.418768 + 0.576385i
\(593\) 308.663i 0.520510i −0.965540 0.260255i \(-0.916193\pi\)
0.965540 0.260255i \(-0.0838067\pi\)
\(594\) −39.0031 28.3374i −0.0656618 0.0477061i
\(595\) 0 0
\(596\) 164.361 + 505.850i 0.275773 + 0.848742i
\(597\) 640.000i 1.07203i
\(598\) 12.3107 + 8.94427i 0.0205865 + 0.0149570i
\(599\) 462.196i 0.771612i −0.922580 0.385806i \(-0.873923\pi\)
0.922580 0.385806i \(-0.126077\pi\)
\(600\) 0 0
\(601\) 355.358 0.591277 0.295639 0.955300i \(-0.404468\pi\)
0.295639 + 0.955300i \(0.404468\pi\)
\(602\) 20.0811 27.6393i 0.0333574 0.0459125i
\(603\) −486.305 −0.806476
\(604\) 575.279 186.919i 0.952448 0.309469i
\(605\) 0 0
\(606\) −446.715 + 614.851i −0.737154 + 1.01461i
\(607\) −630.403 −1.03856 −0.519278 0.854605i \(-0.673799\pi\)
−0.519278 + 0.854605i \(0.673799\pi\)
\(608\) −300.946 −0.494977
\(609\) −224.721 −0.369001
\(610\) 0 0
\(611\) 16.6891i 0.0273144i
\(612\) 497.294 161.580i 0.812571 0.264020i
\(613\) 812.525i 1.32549i 0.748846 + 0.662745i \(0.230608\pi\)
−0.748846 + 0.662745i \(0.769392\pi\)
\(614\) −138.754 + 190.978i −0.225984 + 0.311040i
\(615\) 0 0
\(616\) 37.7709 116.247i 0.0613164 0.188712i
\(617\) 437.935i 0.709781i 0.934908 + 0.354891i \(0.115482\pi\)
−0.934908 + 0.354891i \(0.884518\pi\)
\(618\) 159.978 220.190i 0.258864 0.356295i
\(619\) 770.250i 1.24435i −0.782880 0.622173i \(-0.786250\pi\)
0.782880 0.622173i \(-0.213750\pi\)
\(620\) 0 0
\(621\) 216.276 0.348270
\(622\) 197.134 + 143.226i 0.316935 + 0.230267i
\(623\) −573.702 −0.920870
\(624\) −16.8916 23.2494i −0.0270700 0.0372586i
\(625\) 0 0
\(626\) −355.236 258.094i −0.567470 0.412291i
\(627\) −64.2597 −0.102487
\(628\) 139.796 45.4226i 0.222606 0.0723290i
\(629\) 629.718 1.00114
\(630\) 0 0
\(631\) 875.496i 1.38747i 0.720228 + 0.693737i \(0.244037\pi\)
−0.720228 + 0.693737i \(0.755963\pi\)
\(632\) 281.089 865.102i 0.444761 1.36883i
\(633\) 357.390i 0.564597i
\(634\) 593.591 + 431.269i 0.936263 + 0.680235i
\(635\) 0 0
\(636\) −313.167 + 101.754i −0.492401 + 0.159991i
\(637\) 11.0294i 0.0173146i
\(638\) −20.1812 14.6625i −0.0316320 0.0229820i
\(639\) 215.681i 0.337529i
\(640\) 0 0
\(641\) 842.571 1.31446 0.657232 0.753689i \(-0.271727\pi\)
0.657232 + 0.753689i \(0.271727\pi\)
\(642\) −541.572 + 745.410i −0.843570 + 1.16108i
\(643\) −1153.20 −1.79348 −0.896738 0.442563i \(-0.854069\pi\)
−0.896738 + 0.442563i \(0.854069\pi\)
\(644\) 169.443 + 521.491i 0.263110 + 0.809769i
\(645\) 0 0
\(646\) −264.105 + 363.510i −0.408832 + 0.562708i
\(647\) 355.751 0.549847 0.274924 0.961466i \(-0.411347\pi\)
0.274924 + 0.961466i \(0.411347\pi\)
\(648\) −763.165 247.967i −1.17772 0.382666i
\(649\) 132.669 0.204420
\(650\) 0 0
\(651\) 1535.41i 2.35854i
\(652\) −374.348 1152.13i −0.574154 1.76706i
\(653\) 557.915i 0.854387i −0.904160 0.427194i \(-0.859502\pi\)
0.904160 0.427194i \(-0.140498\pi\)
\(654\) −883.108 + 1215.49i −1.35032 + 1.85855i
\(655\) 0 0
\(656\) 536.105 389.503i 0.817234 0.593755i
\(657\) 752.715i 1.14569i
\(658\) −353.481 + 486.525i −0.537205 + 0.739399i
\(659\) 284.157i 0.431194i 0.976482 + 0.215597i \(0.0691697\pi\)
−0.976482 + 0.215597i \(0.930830\pi\)
\(660\) 0 0
\(661\) 716.735 1.08432 0.542160 0.840275i \(-0.317607\pi\)
0.542160 + 0.840275i \(0.317607\pi\)
\(662\) −263.490 191.437i −0.398021 0.289179i
\(663\) −42.9065 −0.0647157
\(664\) 161.613 + 52.5112i 0.243393 + 0.0790832i
\(665\) 0 0
\(666\) 233.400 + 169.575i 0.350451 + 0.254617i
\(667\) 111.907 0.167776
\(668\) 122.845 + 378.079i 0.183900 + 0.565986i
\(669\) 814.237 1.21710
\(670\) 0 0
\(671\) 46.9464i 0.0699648i
\(672\) 1035.54i 1.54098i
\(673\) 695.378i 1.03325i −0.856212 0.516625i \(-0.827188\pi\)
0.856212 0.516625i \(-0.172812\pi\)
\(674\) 27.6819 + 20.1121i 0.0410711 + 0.0298399i
\(675\) 0 0
\(676\) −208.620 642.066i −0.308609 0.949802i
\(677\) 820.237i 1.21158i 0.795626 + 0.605788i \(0.207142\pi\)
−0.795626 + 0.605788i \(0.792858\pi\)
\(678\) −500.300 363.489i −0.737905 0.536120i
\(679\) 333.176i 0.490686i
\(680\) 0 0
\(681\) 157.580 0.231396
\(682\) 100.182 137.889i 0.146894 0.202183i
\(683\) 335.508 0.491227 0.245613 0.969368i \(-0.421011\pi\)
0.245613 + 0.969368i \(0.421011\pi\)
\(684\) −195.777 + 63.6118i −0.286224 + 0.0929998i
\(685\) 0 0
\(686\) 256.393 352.895i 0.373751 0.514424i
\(687\) −278.769 −0.405777
\(688\) 25.9936 18.8854i 0.0377814 0.0274498i
\(689\) 10.2167 0.0148283
\(690\) 0 0
\(691\) 336.568i 0.487074i −0.969892 0.243537i \(-0.921692\pi\)
0.969892 0.243537i \(-0.0783077\pi\)
\(692\) −690.997 + 224.519i −0.998551 + 0.324449i
\(693\) 83.6068i 0.120645i
\(694\) 196.906 271.017i 0.283726 0.390515i
\(695\) 0 0
\(696\) −200.997 65.3078i −0.288789 0.0938331i
\(697\) 989.378i 1.41948i
\(698\) −568.383 + 782.312i −0.814302 + 1.12079i
\(699\) 1168.09i 1.67108i
\(700\) 0 0
\(701\) −429.364 −0.612502 −0.306251 0.951951i \(-0.599075\pi\)
−0.306251 + 0.951951i \(0.599075\pi\)
\(702\) 10.2526 + 7.44893i 0.0146048 + 0.0106110i
\(703\) −247.911 −0.352647
\(704\) 67.5666 92.9974i 0.0959753 0.132099i
\(705\) 0 0
\(706\) −498.344 362.068i −0.705870 0.512845i
\(707\) 849.703 1.20184
\(708\) 1068.98 347.331i 1.50985 0.490581i
\(709\) −1224.60 −1.72722 −0.863609 0.504162i \(-0.831801\pi\)
−0.863609 + 0.504162i \(0.831801\pi\)
\(710\) 0 0
\(711\) 622.197i 0.875101i
\(712\) −513.135 166.728i −0.720695 0.234168i
\(713\) 764.604i 1.07238i
\(714\) −1250.82 908.774i −1.75185 1.27279i
\(715\) 0 0
\(716\) −992.551 + 322.499i −1.38624 + 0.450418i
\(717\) 163.226i 0.227651i
\(718\) 37.6183 + 27.3313i 0.0523931 + 0.0380658i
\(719\) 496.022i 0.689877i 0.938625 + 0.344939i \(0.112100\pi\)
−0.938625 + 0.344939i \(0.887900\pi\)
\(720\) 0 0
\(721\) −304.296 −0.422047
\(722\) −320.407 + 441.002i −0.443777 + 0.610806i
\(723\) −513.883 −0.710764
\(724\) −195.023 600.220i −0.269369 0.829033i
\(725\) 0 0
\(726\) −526.701 + 724.942i −0.725484 + 0.998543i
\(727\) 152.843 0.210238 0.105119 0.994460i \(-0.466478\pi\)
0.105119 + 0.994460i \(0.466478\pi\)
\(728\) −9.92866 + 30.5573i −0.0136383 + 0.0419743i
\(729\) −89.3808 −0.122607
\(730\) 0 0
\(731\) 47.9709i 0.0656237i
\(732\) 122.907 + 378.269i 0.167906 + 0.516761i
\(733\) 761.286i 1.03859i −0.854595 0.519295i \(-0.826195\pi\)
0.854595 0.519295i \(-0.173805\pi\)
\(734\) −608.152 + 837.049i −0.828544 + 1.14039i
\(735\) 0 0
\(736\) 515.679i 0.700650i
\(737\) 159.619i 0.216580i
\(738\) 266.427 366.705i 0.361012 0.496890i
\(739\) 183.975i 0.248951i −0.992223 0.124476i \(-0.960275\pi\)
0.992223 0.124476i \(-0.0397249\pi\)
\(740\) 0 0
\(741\) 16.8916 0.0227957
\(742\) 297.840 + 216.393i 0.401401 + 0.291635i
\(743\) 495.247 0.666551 0.333275 0.942830i \(-0.391846\pi\)
0.333275 + 0.942830i \(0.391846\pi\)
\(744\) 446.217 1373.31i 0.599754 1.84585i
\(745\) 0 0
\(746\) 142.961 + 103.867i 0.191636 + 0.139232i
\(747\) 116.235 0.155602
\(748\) −53.0353 163.226i −0.0709029 0.218217i
\(749\) 1030.13 1.37534
\(750\) 0 0
\(751\) 800.059i 1.06533i −0.846328 0.532663i \(-0.821191\pi\)
0.846328 0.532663i \(-0.178809\pi\)
\(752\) −457.555 + 332.433i −0.608451 + 0.442066i
\(753\) 841.378i 1.11737i
\(754\) 5.30495 + 3.85427i 0.00703574 + 0.00511177i
\(755\) 0 0
\(756\) 141.115 + 434.306i 0.186659 + 0.574479i
\(757\) 276.367i 0.365082i 0.983198 + 0.182541i \(0.0584322\pi\)
−0.983198 + 0.182541i \(0.941568\pi\)
\(758\) −31.2818 22.7276i −0.0412689 0.0299836i
\(759\) 110.111i 0.145073i
\(760\) 0 0
\(761\) 891.207 1.17110 0.585550 0.810636i \(-0.300879\pi\)
0.585550 + 0.810636i \(0.300879\pi\)
\(762\) −8.25627 + 11.3638i −0.0108350 + 0.0149131i
\(763\) 1679.77 2.20154
\(764\) 1232.93 400.604i 1.61379 0.524351i
\(765\) 0 0
\(766\) 507.390 698.363i 0.662389 0.911700i
\(767\) −34.8740 −0.0454681
\(768\) 300.946 926.217i 0.391857 1.20601i
\(769\) 835.430 1.08639 0.543193 0.839608i \(-0.317215\pi\)
0.543193 + 0.839608i \(0.317215\pi\)
\(770\) 0 0
\(771\) 977.898i 1.26835i
\(772\) 691.521 224.689i 0.895753 0.291048i
\(773\) 213.522i 0.276225i 0.990417 + 0.138112i \(0.0441035\pi\)
−0.990417 + 0.138112i \(0.955897\pi\)
\(774\) 12.9180 17.7800i 0.0166899 0.0229716i
\(775\) 0 0
\(776\) −96.8266 + 298.002i −0.124777 + 0.384023i
\(777\) 853.050i 1.09788i
\(778\) −348.386 + 479.512i −0.447796 + 0.616339i
\(779\) 389.503i 0.500004i
\(780\) 0 0
\(781\) 70.7926 0.0906436
\(782\) 622.883 + 452.551i 0.796526 + 0.578710i
\(783\) 93.1976 0.119026
\(784\) −302.387 + 219.697i −0.385698 + 0.280226i
\(785\) 0 0
\(786\) 1388.71 + 1008.96i 1.76681 + 1.28366i
\(787\) 370.182 0.470371 0.235185 0.971951i \(-0.424430\pi\)
0.235185 + 0.971951i \(0.424430\pi\)
\(788\) −534.588 + 173.698i −0.678411 + 0.220429i
\(789\) −624.531 −0.791547
\(790\) 0 0
\(791\) 691.397i 0.874080i
\(792\) 24.2976 74.7802i 0.0306787 0.0944194i
\(793\) 12.3406i 0.0155619i
\(794\) −139.459 101.323i −0.175641 0.127611i
\(795\) 0 0
\(796\) 640.000 207.949i 0.804020 0.261242i
\(797\) 274.426i 0.344323i −0.985069 0.172162i \(-0.944925\pi\)
0.985069 0.172162i \(-0.0550752\pi\)
\(798\) 492.429 + 357.771i 0.617079 + 0.448334i
\(799\) 844.414i 1.05684i
\(800\) 0 0
\(801\) −369.056 −0.460744
\(802\) −520.774 + 716.784i −0.649344 + 0.893746i
\(803\) 247.063 0.307675
\(804\) 417.889 + 1286.13i 0.519762 + 1.59966i
\(805\) 0 0
\(806\) −26.3344 + 36.2461i −0.0326729 + 0.0449704i
\(807\) 134.956 0.167232
\(808\) 759.997 + 246.938i 0.940591 + 0.305616i
\(809\) −665.214 −0.822266 −0.411133 0.911575i \(-0.634867\pi\)
−0.411133 + 0.911575i \(0.634867\pi\)
\(810\) 0 0
\(811\) 360.665i 0.444717i 0.974965 + 0.222358i \(0.0713755\pi\)
−0.974965 + 0.222358i \(0.928624\pi\)
\(812\) 73.0164 + 224.721i 0.0899217 + 0.276750i
\(813\) 1137.27i 1.39886i
\(814\) 55.6594 76.6086i 0.0683777 0.0941138i
\(815\) 0 0
\(816\) −854.663 1176.34i −1.04738 1.44160i
\(817\) 18.8854i 0.0231156i
\(818\) 74.5432 102.600i 0.0911286 0.125428i
\(819\) 21.9773i 0.0268344i
\(820\) 0 0
\(821\) −666.899 −0.812301 −0.406151 0.913806i \(-0.633129\pi\)
−0.406151 + 0.913806i \(0.633129\pi\)
\(822\) −325.205 236.276i −0.395627 0.287440i
\(823\) −122.433 −0.148764 −0.0743822 0.997230i \(-0.523698\pi\)
−0.0743822 + 0.997230i \(0.523698\pi\)
\(824\) −272.170 88.4335i −0.330304 0.107322i
\(825\) 0 0
\(826\) −1016.66 738.644i −1.23082 0.894242i
\(827\) −1532.98 −1.85366 −0.926832 0.375477i \(-0.877479\pi\)
−0.926832 + 0.375477i \(0.877479\pi\)
\(828\) 109.000 + 335.469i 0.131643 + 0.405156i
\(829\) 195.475 0.235796 0.117898 0.993026i \(-0.462384\pi\)
0.117898 + 0.993026i \(0.462384\pi\)
\(830\) 0 0
\(831\) 1739.47i 2.09322i
\(832\) −17.7609 + 24.4458i −0.0213473 + 0.0293820i
\(833\) 558.053i 0.669931i
\(834\) 774.663 + 562.825i 0.928852 + 0.674850i
\(835\) 0 0
\(836\) 20.8792 + 64.2597i 0.0249752 + 0.0768656i
\(837\) 636.774i 0.760781i
\(838\) 704.942 + 512.170i 0.841219 + 0.611182i
\(839\) 1325.97i 1.58041i −0.612840 0.790207i \(-0.709973\pi\)
0.612840 0.790207i \(-0.290027\pi\)
\(840\) 0 0
\(841\) −792.777 −0.942660
\(842\) 685.254 943.171i 0.813841 1.12016i
\(843\) −21.4532 −0.0254487
\(844\) −357.390 + 116.123i −0.423448 + 0.137587i
\(845\) 0 0
\(846\) −227.390 + 312.976i −0.268783 + 0.369948i
\(847\) 1001.85 1.18282
\(848\) 203.508 + 280.105i 0.239986 + 0.330313i
\(849\) −646.407 −0.761375
\(850\) 0 0
\(851\) 424.801i 0.499179i
\(852\) 570.410 185.337i 0.669495 0.217532i
\(853\) 1055.28i 1.23714i 0.785730 + 0.618570i \(0.212288\pi\)
−0.785730 + 0.618570i \(0.787712\pi\)
\(854\) 261.378 359.756i 0.306063 0.421259i
\(855\) 0 0
\(856\) 921.378 + 299.374i 1.07638 + 0.349736i
\(857\) 155.378i 0.181304i −0.995883 0.0906521i \(-0.971105\pi\)
0.995883 0.0906521i \(-0.0288951\pi\)
\(858\) −3.79241 + 5.21981i −0.00442006 + 0.00608369i
\(859\) 226.033i 0.263136i 0.991307 + 0.131568i \(0.0420011\pi\)
−0.991307 + 0.131568i \(0.957999\pi\)
\(860\) 0 0
\(861\) −1340.26 −1.55664
\(862\) 608.190 + 441.876i 0.705557 + 0.512617i
\(863\) −930.702 −1.07845 −0.539225 0.842162i \(-0.681283\pi\)
−0.539225 + 0.842162i \(0.681283\pi\)
\(864\) 429.465i 0.497066i
\(865\) 0 0
\(866\) 595.702 + 432.803i 0.687878 + 0.499772i
\(867\) −1071.51 −1.23588
\(868\) −1535.41 + 498.885i −1.76891 + 0.574753i
\(869\) −204.223 −0.235009
\(870\) 0 0
\(871\) 41.9584i 0.0481727i
\(872\) 1502.43 + 488.170i 1.72297 + 0.559828i
\(873\) 214.328i 0.245508i
\(874\) −245.220 178.163i −0.280572 0.203847i
\(875\) 0 0
\(876\) 1990.70 646.819i 2.27249 0.738377i
\(877\) 33.5217i 0.0382231i 0.999817 + 0.0191115i \(0.00608376\pi\)
−0.999817 + 0.0191115i \(0.993916\pi\)
\(878\) −782.399 568.446i −0.891115 0.647433i
\(879\) 102.178i 0.116244i
\(880\) 0 0
\(881\) −933.850 −1.05999 −0.529994 0.848001i \(-0.677806\pi\)
−0.529994 + 0.848001i \(0.677806\pi\)
\(882\) −150.276 + 206.838i −0.170382 + 0.234510i
\(883\) −542.308 −0.614166 −0.307083 0.951683i \(-0.599353\pi\)
−0.307083 + 0.951683i \(0.599353\pi\)
\(884\) 13.9412 + 42.9065i 0.0157706 + 0.0485368i
\(885\) 0 0
\(886\) 328.197 451.724i 0.370425 0.509846i
\(887\) −714.720 −0.805773 −0.402886 0.915250i \(-0.631993\pi\)
−0.402886 + 0.915250i \(0.631993\pi\)
\(888\) 247.911 762.991i 0.279179 0.859224i
\(889\) 15.7044 0.0176652
\(890\) 0 0
\(891\) 180.159i 0.202199i
\(892\) −264.562 814.237i −0.296594 0.912822i
\(893\) 332.433i 0.372266i
\(894\) 594.663 818.483i 0.665171 0.915529i
\(895\) 0 0
\(896\) −1035.54 + 336.468i −1.15574 + 0.375522i
\(897\) 28.9443i 0.0322679i
\(898\) 888.824 1223.36i 0.989782 1.36232i
\(899\) 329.484i 0.366500i
\(900\) 0 0
\(901\) 516.932 0.573731
\(902\) −120.363 87.4489i −0.133440 0.0969500i
\(903\) −64.9839 −0.0719645
\(904\) −200.932 + 618.405i −0.222270 + 0.684076i
\(905\) 0 0
\(906\) −930.820 676.281i −1.02740 0.746447i
\(907\) −347.233 −0.382837 −0.191418 0.981509i \(-0.561309\pi\)
−0.191418 + 0.981509i \(0.561309\pi\)
\(908\) −51.2010 157.580i −0.0563888 0.173547i
\(909\) 546.604 0.601324
\(910\) 0 0
\(911\) 1427.54i 1.56701i −0.621386 0.783504i \(-0.713430\pi\)
0.621386 0.783504i \(-0.286570\pi\)
\(912\) 336.468 + 463.108i 0.368934 + 0.507794i
\(913\) 38.1517i 0.0417871i
\(914\) 462.227 + 335.827i 0.505719 + 0.367426i
\(915\) 0 0
\(916\) 90.5774 + 278.769i 0.0988836 + 0.304332i
\(917\) 1919.15i 2.09286i
\(918\) 518.747 + 376.892i 0.565084 + 0.410557i
\(919\) 569.162i 0.619327i −0.950846 0.309664i \(-0.899784\pi\)
0.950846 0.309664i \(-0.100216\pi\)
\(920\) 0 0
\(921\) 449.017 0.487532
\(922\) 116.516 160.371i 0.126373 0.173938i
\(923\) −18.6089 −0.0201614
\(924\) −221.115 + 71.8445i −0.239301 + 0.0777538i
\(925\) 0 0
\(926\) 741.319 1020.34i 0.800560 1.10188i
\(927\) −195.750 −0.211165
\(928\) 222.217i 0.239458i
\(929\) −1535.96 −1.65335 −0.826675 0.562680i \(-0.809770\pi\)
−0.826675 + 0.562680i \(0.809770\pi\)
\(930\) 0 0
\(931\) 219.697i 0.235980i
\(932\) −1168.09 + 379.534i −1.25331 + 0.407225i
\(933\) 463.489i 0.496773i
\(934\) 583.094 802.561i 0.624298 0.859273i
\(935\) 0 0
\(936\) −6.38699 + 19.6571i −0.00682371 + 0.0210012i
\(937\) 338.721i 0.361496i −0.983529 0.180748i \(-0.942148\pi\)
0.983529 0.180748i \(-0.0578518\pi\)
\(938\) 888.693 1223.18i 0.947434 1.30403i
\(939\) 835.210i 0.889468i
\(940\) 0 0
\(941\) 1439.77 1.53004 0.765022 0.644004i \(-0.222728\pi\)
0.765022 + 0.644004i \(0.222728\pi\)
\(942\) −226.195 164.341i −0.240123 0.174459i
\(943\) 667.424 0.707766
\(944\) −694.663 956.121i −0.735871 1.01284i
\(945\) 0 0
\(946\) −5.83592 4.24005i −0.00616905 0.00448208i
\(947\) −656.135 −0.692856 −0.346428 0.938077i \(-0.612606\pi\)
−0.346428 + 0.938077i \(0.612606\pi\)
\(948\) −1645.52 + 534.663i −1.73578 + 0.563990i
\(949\) −64.9443 −0.0684344
\(950\) 0 0
\(951\) 1395.62i 1.46752i
\(952\) −502.358 + 1546.10i −0.527687 + 1.62405i
\(953\) 436.675i 0.458211i 0.973402 + 0.229105i \(0.0735801\pi\)
−0.973402 + 0.229105i \(0.926420\pi\)
\(954\) 191.597 + 139.203i 0.200835 + 0.145915i
\(955\) 0 0
\(956\) −163.226 + 53.0353i −0.170739 + 0.0554763i
\(957\) 47.4489i 0.0495809i
\(958\) −936.988 680.762i −0.978067 0.710607i
\(959\) 449.423i 0.468637i
\(960\) 0 0
\(961\) −1290.20 −1.34256
\(962\) −14.6309 + 20.1378i −0.0152089 + 0.0209332i
\(963\) 662.671 0.688132
\(964\) 166.971 + 513.883i 0.173206 + 0.533073i
\(965\) 0 0
\(966\) 613.050 843.790i 0.634627 0.873489i
\(967\) 903.436 0.934267 0.467133 0.884187i \(-0.345287\pi\)
0.467133 + 0.884187i \(0.345287\pi\)
\(968\) 896.078 + 291.153i 0.925700 + 0.300778i
\(969\) 854.663 0.882005
\(970\) 0 0
\(971\) 1866.89i 1.92265i 0.275420 + 0.961324i \(0.411183\pi\)
−0.275420 + 0.961324i \(0.588817\pi\)
\(972\) 322.361 + 992.125i 0.331647 + 1.02071i
\(973\) 1070.56i 1.10026i
\(974\) 736.334 1013.48i 0.755990 1.04053i
\(975\) 0 0
\(976\) 338.334 245.814i 0.346654 0.251859i
\(977\) 1073.95i 1.09923i 0.835418 + 0.549615i \(0.185226\pi\)
−0.835418 + 0.549615i \(0.814774\pi\)
\(978\) −1354.40 + 1864.18i −1.38487 + 1.90611i
\(979\) 121.135i 0.123733i
\(980\) 0 0
\(981\) 1080.58 1.10151
\(982\) 36.0842 + 26.2167i 0.0367456 + 0.0266973i
\(983\) 534.114 0.543351 0.271675 0.962389i \(-0.412422\pi\)
0.271675 + 0.962389i \(0.412422\pi\)
\(984\) −1198.77 389.503i −1.21826 0.395837i
\(985\) 0 0
\(986\) 268.413 + 195.014i 0.272224 + 0.197783i
\(987\) 1143.89 1.15895
\(988\) −5.48843 16.8916i −0.00555509 0.0170968i
\(989\) 32.3607 0.0327206
\(990\) 0 0
\(991\) 520.419i 0.525146i −0.964912 0.262573i \(-0.915429\pi\)
0.964912 0.262573i \(-0.0845710\pi\)
\(992\) −1518.30 −1.53054
\(993\) 619.502i 0.623869i
\(994\) −542.492 394.144i −0.545767 0.396523i
\(995\) 0 0
\(996\) −99.8823 307.406i −0.100283 0.308641i
\(997\) 457.680i 0.459057i −0.973302 0.229528i \(-0.926282\pi\)
0.973302 0.229528i \(-0.0737184\pi\)
\(998\) −1015.09 737.508i −1.01713 0.738986i
\(999\) 353.781i 0.354135i
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 100.3.d.b.99.4 8
3.2 odd 2 900.3.f.e.199.5 8
4.3 odd 2 inner 100.3.d.b.99.6 8
5.2 odd 4 20.3.b.a.11.1 4
5.3 odd 4 100.3.b.f.51.4 4
5.4 even 2 inner 100.3.d.b.99.5 8
8.3 odd 2 1600.3.h.n.1599.7 8
8.5 even 2 1600.3.h.n.1599.2 8
12.11 even 2 900.3.f.e.199.3 8
15.2 even 4 180.3.c.a.91.4 4
15.8 even 4 900.3.c.k.451.1 4
15.14 odd 2 900.3.f.e.199.4 8
20.3 even 4 100.3.b.f.51.3 4
20.7 even 4 20.3.b.a.11.2 yes 4
20.19 odd 2 inner 100.3.d.b.99.3 8
40.3 even 4 1600.3.b.s.1151.4 4
40.13 odd 4 1600.3.b.s.1151.1 4
40.19 odd 2 1600.3.h.n.1599.1 8
40.27 even 4 320.3.b.c.191.1 4
40.29 even 2 1600.3.h.n.1599.8 8
40.37 odd 4 320.3.b.c.191.4 4
60.23 odd 4 900.3.c.k.451.2 4
60.47 odd 4 180.3.c.a.91.3 4
60.59 even 2 900.3.f.e.199.6 8
80.27 even 4 1280.3.g.e.1151.8 8
80.37 odd 4 1280.3.g.e.1151.2 8
80.67 even 4 1280.3.g.e.1151.1 8
80.77 odd 4 1280.3.g.e.1151.7 8
120.77 even 4 2880.3.e.e.2431.4 4
120.107 odd 4 2880.3.e.e.2431.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.3.b.a.11.1 4 5.2 odd 4
20.3.b.a.11.2 yes 4 20.7 even 4
100.3.b.f.51.3 4 20.3 even 4
100.3.b.f.51.4 4 5.3 odd 4
100.3.d.b.99.3 8 20.19 odd 2 inner
100.3.d.b.99.4 8 1.1 even 1 trivial
100.3.d.b.99.5 8 5.4 even 2 inner
100.3.d.b.99.6 8 4.3 odd 2 inner
180.3.c.a.91.3 4 60.47 odd 4
180.3.c.a.91.4 4 15.2 even 4
320.3.b.c.191.1 4 40.27 even 4
320.3.b.c.191.4 4 40.37 odd 4
900.3.c.k.451.1 4 15.8 even 4
900.3.c.k.451.2 4 60.23 odd 4
900.3.f.e.199.3 8 12.11 even 2
900.3.f.e.199.4 8 15.14 odd 2
900.3.f.e.199.5 8 3.2 odd 2
900.3.f.e.199.6 8 60.59 even 2
1280.3.g.e.1151.1 8 80.67 even 4
1280.3.g.e.1151.2 8 80.37 odd 4
1280.3.g.e.1151.7 8 80.77 odd 4
1280.3.g.e.1151.8 8 80.27 even 4
1600.3.b.s.1151.1 4 40.13 odd 4
1600.3.b.s.1151.4 4 40.3 even 4
1600.3.h.n.1599.1 8 40.19 odd 2
1600.3.h.n.1599.2 8 8.5 even 2
1600.3.h.n.1599.7 8 8.3 odd 2
1600.3.h.n.1599.8 8 40.29 even 2
2880.3.e.e.2431.3 4 120.107 odd 4
2880.3.e.e.2431.4 4 120.77 even 4