Properties

Label 115.3.c.c.114.17
Level $115$
Weight $3$
Character 115.114
Analytic conductor $3.134$
Analytic rank $0$
Dimension $20$
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] = [115,3,Mod(114,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, 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("115.114");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 115.c (of order \(2\), degree \(1\), 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: \(3.13352304014\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 6 x^{18} - 827 x^{16} - 12720 x^{14} + 346250 x^{12} + 9668500 x^{10} + 216406250 x^{8} - 4968750000 x^{6} - 201904296875 x^{4} + \cdots + 95367431640625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 114.17
Root \(4.94294 - 0.753214i\) of defining polynomial
Character \(\chi\) \(=\) 115.114
Dual form 115.3.c.c.114.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.38977i q^{2} -3.81595i q^{3} -7.49055 q^{4} +(-4.94294 - 0.753214i) q^{5} +12.9352 q^{6} -7.85531 q^{7} -11.8322i q^{8} -5.56149 q^{9} +O(q^{10})\) \(q+3.38977i q^{2} -3.81595i q^{3} -7.49055 q^{4} +(-4.94294 - 0.753214i) q^{5} +12.9352 q^{6} -7.85531 q^{7} -11.8322i q^{8} -5.56149 q^{9} +(2.55323 - 16.7554i) q^{10} -14.6318i q^{11} +28.5836i q^{12} -7.02001i q^{13} -26.6277i q^{14} +(-2.87423 + 18.8620i) q^{15} +10.1462 q^{16} -15.0008 q^{17} -18.8522i q^{18} +19.6736i q^{19} +(37.0254 + 5.64199i) q^{20} +29.9755i q^{21} +49.5984 q^{22} +(3.89296 + 22.6681i) q^{23} -45.1511 q^{24} +(23.8653 + 7.44619i) q^{25} +23.7962 q^{26} -13.1212i q^{27} +58.8406 q^{28} -36.8947 q^{29} +(-63.9380 - 9.74299i) q^{30} -12.6964 q^{31} -12.9355i q^{32} -55.8341 q^{33} -50.8494i q^{34} +(38.8283 + 5.91673i) q^{35} +41.6587 q^{36} -1.40335 q^{37} -66.6890 q^{38} -26.7880 q^{39} +(-8.91217 + 58.4858i) q^{40} +5.88082 q^{41} -101.610 q^{42} +81.8367 q^{43} +109.600i q^{44} +(27.4901 + 4.18900i) q^{45} +(-76.8398 + 13.1962i) q^{46} -65.3796i q^{47} -38.7174i q^{48} +12.7059 q^{49} +(-25.2409 + 80.8980i) q^{50} +57.2425i q^{51} +52.5838i q^{52} -59.2189 q^{53} +44.4778 q^{54} +(-11.0209 + 72.3240i) q^{55} +92.9454i q^{56} +75.0735 q^{57} -125.065i q^{58} -16.2369 q^{59} +(21.5296 - 141.287i) q^{60} -108.080i q^{61} -43.0381i q^{62} +43.6872 q^{63} +84.4330 q^{64} +(-5.28757 + 34.6995i) q^{65} -189.265i q^{66} +95.6533 q^{67} +112.365 q^{68} +(86.5006 - 14.8554i) q^{69} +(-20.0564 + 131.619i) q^{70} -89.4921 q^{71} +65.8046i q^{72} -58.6284i q^{73} -4.75703i q^{74} +(28.4143 - 91.0690i) q^{75} -147.366i q^{76} +114.937i q^{77} -90.8053i q^{78} +42.3986i q^{79} +(-50.1520 - 7.64226i) q^{80} -100.123 q^{81} +19.9346i q^{82} +57.2277 q^{83} -224.533i q^{84} +(74.1482 + 11.2988i) q^{85} +277.408i q^{86} +140.788i q^{87} -173.126 q^{88} -21.1091i q^{89} +(-14.1997 + 93.1853i) q^{90} +55.1443i q^{91} +(-29.1604 - 169.797i) q^{92} +48.4490i q^{93} +221.622 q^{94} +(14.8184 - 97.2455i) q^{95} -49.3611 q^{96} -101.231 q^{97} +43.0699i q^{98} +81.3745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 56 q^{59} - 28 q^{64} + 376 q^{69} - 636 q^{70} - 196 q^{71} + 428 q^{75} - 988 q^{81} - 284 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.38977i 1.69489i 0.530886 + 0.847443i \(0.321859\pi\)
−0.530886 + 0.847443i \(0.678141\pi\)
\(3\) 3.81595i 1.27198i −0.771696 0.635992i \(-0.780591\pi\)
0.771696 0.635992i \(-0.219409\pi\)
\(4\) −7.49055 −1.87264
\(5\) −4.94294 0.753214i −0.988588 0.150643i
\(6\) 12.9352 2.15587
\(7\) −7.85531 −1.12219 −0.561093 0.827753i \(-0.689619\pi\)
−0.561093 + 0.827753i \(0.689619\pi\)
\(8\) 11.8322i 1.47902i
\(9\) −5.56149 −0.617944
\(10\) 2.55323 16.7554i 0.255323 1.67554i
\(11\) 14.6318i 1.33016i −0.746772 0.665080i \(-0.768397\pi\)
0.746772 0.665080i \(-0.231603\pi\)
\(12\) 28.5836i 2.38197i
\(13\) 7.02001i 0.540001i −0.962860 0.270000i \(-0.912976\pi\)
0.962860 0.270000i \(-0.0870238\pi\)
\(14\) 26.6277i 1.90198i
\(15\) −2.87423 + 18.8620i −0.191615 + 1.25747i
\(16\) 10.1462 0.634137
\(17\) −15.0008 −0.882402 −0.441201 0.897408i \(-0.645447\pi\)
−0.441201 + 0.897408i \(0.645447\pi\)
\(18\) 18.8522i 1.04734i
\(19\) 19.6736i 1.03545i 0.855546 + 0.517726i \(0.173221\pi\)
−0.855546 + 0.517726i \(0.826779\pi\)
\(20\) 37.0254 + 5.64199i 1.85127 + 0.282100i
\(21\) 29.9755i 1.42740i
\(22\) 49.5984 2.25447
\(23\) 3.89296 + 22.6681i 0.169259 + 0.985572i
\(24\) −45.1511 −1.88129
\(25\) 23.8653 + 7.44619i 0.954613 + 0.297848i
\(26\) 23.7962 0.915240
\(27\) 13.1212i 0.485970i
\(28\) 58.8406 2.10145
\(29\) −36.8947 −1.27223 −0.636115 0.771594i \(-0.719460\pi\)
−0.636115 + 0.771594i \(0.719460\pi\)
\(30\) −63.9380 9.74299i −2.13127 0.324766i
\(31\) −12.6964 −0.409563 −0.204781 0.978808i \(-0.565648\pi\)
−0.204781 + 0.978808i \(0.565648\pi\)
\(32\) 12.9355i 0.404233i
\(33\) −55.8341 −1.69194
\(34\) 50.8494i 1.49557i
\(35\) 38.8283 + 5.91673i 1.10938 + 0.169049i
\(36\) 41.6587 1.15719
\(37\) −1.40335 −0.0379283 −0.0189642 0.999820i \(-0.506037\pi\)
−0.0189642 + 0.999820i \(0.506037\pi\)
\(38\) −66.6890 −1.75497
\(39\) −26.7880 −0.686872
\(40\) −8.91217 + 58.4858i −0.222804 + 1.46214i
\(41\) 5.88082 0.143435 0.0717173 0.997425i \(-0.477152\pi\)
0.0717173 + 0.997425i \(0.477152\pi\)
\(42\) −101.610 −2.41929
\(43\) 81.8367 1.90318 0.951589 0.307373i \(-0.0994499\pi\)
0.951589 + 0.307373i \(0.0994499\pi\)
\(44\) 109.600i 2.49091i
\(45\) 27.4901 + 4.18900i 0.610892 + 0.0930888i
\(46\) −76.8398 + 13.1962i −1.67043 + 0.286875i
\(47\) 65.3796i 1.39106i −0.718499 0.695528i \(-0.755171\pi\)
0.718499 0.695528i \(-0.244829\pi\)
\(48\) 38.7174i 0.806612i
\(49\) 12.7059 0.259303
\(50\) −25.2409 + 80.8980i −0.504818 + 1.61796i
\(51\) 57.2425i 1.12240i
\(52\) 52.5838i 1.01123i
\(53\) −59.2189 −1.11734 −0.558668 0.829391i \(-0.688688\pi\)
−0.558668 + 0.829391i \(0.688688\pi\)
\(54\) 44.4778 0.823663
\(55\) −11.0209 + 72.3240i −0.200379 + 1.31498i
\(56\) 92.9454i 1.65974i
\(57\) 75.0735 1.31708
\(58\) 125.065i 2.15629i
\(59\) −16.2369 −0.275202 −0.137601 0.990488i \(-0.543939\pi\)
−0.137601 + 0.990488i \(0.543939\pi\)
\(60\) 21.5296 141.287i 0.358826 2.35478i
\(61\) 108.080i 1.77181i −0.463870 0.885903i \(-0.653539\pi\)
0.463870 0.885903i \(-0.346461\pi\)
\(62\) 43.0381i 0.694162i
\(63\) 43.6872 0.693448
\(64\) 84.4330 1.31927
\(65\) −5.28757 + 34.6995i −0.0813473 + 0.533838i
\(66\) 189.265i 2.86765i
\(67\) 95.6533 1.42766 0.713830 0.700319i \(-0.246959\pi\)
0.713830 + 0.700319i \(0.246959\pi\)
\(68\) 112.365 1.65242
\(69\) 86.5006 14.8554i 1.25363 0.215295i
\(70\) −20.0564 + 131.619i −0.286520 + 1.88027i
\(71\) −89.4921 −1.26045 −0.630226 0.776412i \(-0.717038\pi\)
−0.630226 + 0.776412i \(0.717038\pi\)
\(72\) 65.8046i 0.913953i
\(73\) 58.6284i 0.803129i −0.915831 0.401564i \(-0.868467\pi\)
0.915831 0.401564i \(-0.131533\pi\)
\(74\) 4.75703i 0.0642842i
\(75\) 28.4143 91.0690i 0.378857 1.21425i
\(76\) 147.366i 1.93903i
\(77\) 114.937i 1.49269i
\(78\) 90.8053i 1.16417i
\(79\) 42.3986i 0.536691i 0.963323 + 0.268345i \(0.0864768\pi\)
−0.963323 + 0.268345i \(0.913523\pi\)
\(80\) −50.1520 7.64226i −0.626900 0.0955282i
\(81\) −100.123 −1.23609
\(82\) 19.9346i 0.243105i
\(83\) 57.2277 0.689490 0.344745 0.938696i \(-0.387965\pi\)
0.344745 + 0.938696i \(0.387965\pi\)
\(84\) 224.533i 2.67301i
\(85\) 74.1482 + 11.2988i 0.872332 + 0.132928i
\(86\) 277.408i 3.22567i
\(87\) 140.788i 1.61826i
\(88\) −173.126 −1.96734
\(89\) 21.1091i 0.237181i −0.992943 0.118591i \(-0.962162\pi\)
0.992943 0.118591i \(-0.0378376\pi\)
\(90\) −14.1997 + 93.1853i −0.157775 + 1.03539i
\(91\) 55.1443i 0.605982i
\(92\) −29.1604 169.797i −0.316961 1.84562i
\(93\) 48.4490i 0.520957i
\(94\) 221.622 2.35768
\(95\) 14.8184 97.2455i 0.155984 1.02364i
\(96\) −49.3611 −0.514178
\(97\) −101.231 −1.04362 −0.521811 0.853061i \(-0.674743\pi\)
−0.521811 + 0.853061i \(0.674743\pi\)
\(98\) 43.0699i 0.439489i
\(99\) 81.3745i 0.821964i
\(100\) −178.765 55.7761i −1.78765 0.557761i
\(101\) 10.8200 0.107129 0.0535644 0.998564i \(-0.482942\pi\)
0.0535644 + 0.998564i \(0.482942\pi\)
\(102\) −194.039 −1.90234
\(103\) −78.3852 −0.761021 −0.380511 0.924777i \(-0.624252\pi\)
−0.380511 + 0.924777i \(0.624252\pi\)
\(104\) −83.0620 −0.798674
\(105\) 22.5780 148.167i 0.215028 1.41111i
\(106\) 200.738i 1.89376i
\(107\) −129.231 −1.20776 −0.603881 0.797074i \(-0.706380\pi\)
−0.603881 + 0.797074i \(0.706380\pi\)
\(108\) 98.2849i 0.910045i
\(109\) 0.761552i 0.00698671i 0.999994 + 0.00349336i \(0.00111197\pi\)
−0.999994 + 0.00349336i \(0.998888\pi\)
\(110\) −245.162 37.3582i −2.22874 0.339620i
\(111\) 5.35511i 0.0482442i
\(112\) −79.7015 −0.711620
\(113\) 82.8256 0.732970 0.366485 0.930424i \(-0.380561\pi\)
0.366485 + 0.930424i \(0.380561\pi\)
\(114\) 254.482i 2.23230i
\(115\) −2.16870 114.980i −0.0188582 0.999822i
\(116\) 276.362 2.38243
\(117\) 39.0417i 0.333690i
\(118\) 55.0395i 0.466436i
\(119\) 117.836 0.990220
\(120\) 223.179 + 34.0084i 1.85983 + 0.283404i
\(121\) −93.0886 −0.769327
\(122\) 366.367 3.00301
\(123\) 22.4409i 0.182447i
\(124\) 95.1034 0.766963
\(125\) −112.356 54.7818i −0.898851 0.438254i
\(126\) 148.090i 1.17532i
\(127\) 202.484i 1.59436i 0.603739 + 0.797182i \(0.293677\pi\)
−0.603739 + 0.797182i \(0.706323\pi\)
\(128\) 234.467i 1.83177i
\(129\) 312.285i 2.42081i
\(130\) −117.623 17.9237i −0.904795 0.137874i
\(131\) 161.376 1.23188 0.615938 0.787795i \(-0.288777\pi\)
0.615938 + 0.787795i \(0.288777\pi\)
\(132\) 418.229 3.16840
\(133\) 154.542i 1.16197i
\(134\) 324.243i 2.41972i
\(135\) −9.88306 + 64.8572i −0.0732079 + 0.480424i
\(136\) 177.493i 1.30509i
\(137\) −207.622 −1.51549 −0.757745 0.652551i \(-0.773699\pi\)
−0.757745 + 0.652551i \(0.773699\pi\)
\(138\) 50.3563 + 293.217i 0.364900 + 2.12476i
\(139\) −139.793 −1.00570 −0.502852 0.864372i \(-0.667716\pi\)
−0.502852 + 0.864372i \(0.667716\pi\)
\(140\) −290.846 44.3196i −2.07747 0.316569i
\(141\) −249.485 −1.76940
\(142\) 303.358i 2.13632i
\(143\) −102.715 −0.718288
\(144\) −56.4280 −0.391861
\(145\) 182.368 + 27.7896i 1.25771 + 0.191652i
\(146\) 198.737 1.36121
\(147\) 48.4849i 0.329829i
\(148\) 10.5118 0.0710260
\(149\) 153.810i 1.03228i −0.856504 0.516140i \(-0.827368\pi\)
0.856504 0.516140i \(-0.172632\pi\)
\(150\) 308.703 + 96.3180i 2.05802 + 0.642120i
\(151\) 89.8082 0.594756 0.297378 0.954760i \(-0.403888\pi\)
0.297378 + 0.954760i \(0.403888\pi\)
\(152\) 232.782 1.53146
\(153\) 83.4270 0.545275
\(154\) −389.610 −2.52994
\(155\) 62.7578 + 9.56315i 0.404889 + 0.0616977i
\(156\) 200.657 1.28626
\(157\) 98.8554 0.629652 0.314826 0.949149i \(-0.398054\pi\)
0.314826 + 0.949149i \(0.398054\pi\)
\(158\) −143.721 −0.909629
\(159\) 225.976i 1.42123i
\(160\) −9.74318 + 63.9392i −0.0608949 + 0.399620i
\(161\) −30.5804 178.065i −0.189940 1.10600i
\(162\) 339.395i 2.09503i
\(163\) 64.0772i 0.393112i 0.980493 + 0.196556i \(0.0629757\pi\)
−0.980493 + 0.196556i \(0.937024\pi\)
\(164\) −44.0506 −0.268601
\(165\) 275.985 + 42.0551i 1.67264 + 0.254879i
\(166\) 193.989i 1.16861i
\(167\) 154.332i 0.924143i −0.886843 0.462072i \(-0.847106\pi\)
0.886843 0.462072i \(-0.152894\pi\)
\(168\) 354.675 2.11116
\(169\) 119.719 0.708399
\(170\) −38.3005 + 251.346i −0.225297 + 1.47850i
\(171\) 109.415i 0.639852i
\(172\) −613.002 −3.56397
\(173\) 115.869i 0.669761i −0.942261 0.334880i \(-0.891304\pi\)
0.942261 0.334880i \(-0.108696\pi\)
\(174\) −477.241 −2.74276
\(175\) −187.470 58.4921i −1.07125 0.334241i
\(176\) 148.457i 0.843504i
\(177\) 61.9593i 0.350053i
\(178\) 71.5551 0.401995
\(179\) −69.9062 −0.390538 −0.195269 0.980750i \(-0.562558\pi\)
−0.195269 + 0.980750i \(0.562558\pi\)
\(180\) −205.916 31.3779i −1.14398 0.174322i
\(181\) 198.065i 1.09428i 0.837041 + 0.547141i \(0.184284\pi\)
−0.837041 + 0.547141i \(0.815716\pi\)
\(182\) −186.927 −1.02707
\(183\) −412.429 −2.25371
\(184\) 268.214 46.0622i 1.45768 0.250338i
\(185\) 6.93666 + 1.05702i 0.0374955 + 0.00571363i
\(186\) −164.231 −0.882964
\(187\) 219.489i 1.17374i
\(188\) 489.729i 2.60494i
\(189\) 103.071i 0.545349i
\(190\) 329.640 + 50.2311i 1.73495 + 0.264374i
\(191\) 54.6601i 0.286179i 0.989710 + 0.143089i \(0.0457036\pi\)
−0.989710 + 0.143089i \(0.954296\pi\)
\(192\) 322.192i 1.67809i
\(193\) 234.294i 1.21396i −0.794718 0.606979i \(-0.792381\pi\)
0.794718 0.606979i \(-0.207619\pi\)
\(194\) 343.151i 1.76882i
\(195\) 132.412 + 20.1771i 0.679034 + 0.103472i
\(196\) −95.1739 −0.485581
\(197\) 103.313i 0.524430i 0.965009 + 0.262215i \(0.0844530\pi\)
−0.965009 + 0.262215i \(0.915547\pi\)
\(198\) −275.841 −1.39314
\(199\) 104.822i 0.526743i 0.964694 + 0.263372i \(0.0848345\pi\)
−0.964694 + 0.263372i \(0.915165\pi\)
\(200\) 88.1047 282.379i 0.440523 1.41190i
\(201\) 365.008i 1.81596i
\(202\) 36.6774i 0.181571i
\(203\) 289.819 1.42768
\(204\) 428.778i 2.10185i
\(205\) −29.0685 4.42952i −0.141798 0.0216074i
\(206\) 265.708i 1.28984i
\(207\) −21.6507 126.069i −0.104593 0.609028i
\(208\) 71.2264i 0.342434i
\(209\) 287.860 1.37732
\(210\) 502.252 + 76.5341i 2.39168 + 0.364448i
\(211\) −325.637 −1.54330 −0.771651 0.636046i \(-0.780569\pi\)
−0.771651 + 0.636046i \(0.780569\pi\)
\(212\) 443.582 2.09237
\(213\) 341.497i 1.60327i
\(214\) 438.062i 2.04702i
\(215\) −404.514 61.6406i −1.88146 0.286700i
\(216\) −155.252 −0.718760
\(217\) 99.7345 0.459606
\(218\) −2.58149 −0.0118417
\(219\) −223.723 −1.02157
\(220\) 82.5523 541.747i 0.375238 2.46248i
\(221\) 105.306i 0.476498i
\(222\) −18.1526 −0.0817684
\(223\) 83.1916i 0.373056i −0.982450 0.186528i \(-0.940276\pi\)
0.982450 0.186528i \(-0.0597236\pi\)
\(224\) 101.612i 0.453625i
\(225\) −132.727 41.4119i −0.589897 0.184053i
\(226\) 280.760i 1.24230i
\(227\) 20.1827 0.0889106 0.0444553 0.999011i \(-0.485845\pi\)
0.0444553 + 0.999011i \(0.485845\pi\)
\(228\) −562.342 −2.46641
\(229\) 31.8770i 0.139201i −0.997575 0.0696004i \(-0.977828\pi\)
0.997575 0.0696004i \(-0.0221724\pi\)
\(230\) 389.754 7.35139i 1.69458 0.0319626i
\(231\) 438.594 1.89868
\(232\) 436.545i 1.88166i
\(233\) 70.1772i 0.301190i −0.988596 0.150595i \(-0.951881\pi\)
0.988596 0.150595i \(-0.0481189\pi\)
\(234\) −132.343 −0.565567
\(235\) −49.2449 + 323.168i −0.209553 + 1.37518i
\(236\) 121.624 0.515354
\(237\) 161.791 0.682662
\(238\) 399.438i 1.67831i
\(239\) 102.474 0.428763 0.214382 0.976750i \(-0.431226\pi\)
0.214382 + 0.976750i \(0.431226\pi\)
\(240\) −29.1625 + 191.378i −0.121510 + 0.797407i
\(241\) 146.746i 0.608903i −0.952528 0.304452i \(-0.901527\pi\)
0.952528 0.304452i \(-0.0984732\pi\)
\(242\) 315.549i 1.30392i
\(243\) 263.975i 1.08632i
\(244\) 809.581i 3.31795i
\(245\) −62.8043 9.57023i −0.256344 0.0390622i
\(246\) 76.0696 0.309226
\(247\) 138.109 0.559145
\(248\) 150.227i 0.605753i
\(249\) 218.378i 0.877020i
\(250\) 185.698 380.863i 0.742791 1.52345i
\(251\) 244.758i 0.975133i 0.873086 + 0.487566i \(0.162115\pi\)
−0.873086 + 0.487566i \(0.837885\pi\)
\(252\) −327.242 −1.29858
\(253\) 331.675 56.9609i 1.31097 0.225142i
\(254\) −686.375 −2.70226
\(255\) 43.1158 282.946i 0.169082 1.10959i
\(256\) −457.057 −1.78538
\(257\) 102.219i 0.397738i 0.980026 + 0.198869i \(0.0637268\pi\)
−0.980026 + 0.198869i \(0.936273\pi\)
\(258\) 1058.57 4.10300
\(259\) 11.0237 0.0425626
\(260\) 39.6068 259.918i 0.152334 0.999686i
\(261\) 205.190 0.786167
\(262\) 547.027i 2.08789i
\(263\) −331.315 −1.25975 −0.629876 0.776696i \(-0.716894\pi\)
−0.629876 + 0.776696i \(0.716894\pi\)
\(264\) 660.640i 2.50242i
\(265\) 292.715 + 44.6045i 1.10459 + 0.168319i
\(266\) 523.863 1.96941
\(267\) −80.5514 −0.301691
\(268\) −716.496 −2.67349
\(269\) −45.6414 −0.169671 −0.0848353 0.996395i \(-0.527036\pi\)
−0.0848353 + 0.996395i \(0.527036\pi\)
\(270\) −219.851 33.5013i −0.814264 0.124079i
\(271\) 272.196 1.00441 0.502206 0.864748i \(-0.332522\pi\)
0.502206 + 0.864748i \(0.332522\pi\)
\(272\) −152.201 −0.559564
\(273\) 210.428 0.770799
\(274\) 703.791i 2.56858i
\(275\) 108.951 349.192i 0.396185 1.26979i
\(276\) −647.937 + 111.275i −2.34760 + 0.403170i
\(277\) 347.550i 1.25469i 0.778740 + 0.627347i \(0.215859\pi\)
−0.778740 + 0.627347i \(0.784141\pi\)
\(278\) 473.866i 1.70455i
\(279\) 70.6112 0.253087
\(280\) 70.0079 459.424i 0.250028 1.64080i
\(281\) 339.063i 1.20663i −0.797503 0.603316i \(-0.793846\pi\)
0.797503 0.603316i \(-0.206154\pi\)
\(282\) 845.699i 2.99893i
\(283\) 214.943 0.759517 0.379758 0.925086i \(-0.376007\pi\)
0.379758 + 0.925086i \(0.376007\pi\)
\(284\) 670.345 2.36037
\(285\) −371.084 56.5465i −1.30205 0.198409i
\(286\) 348.181i 1.21742i
\(287\) −46.1956 −0.160960
\(288\) 71.9405i 0.249793i
\(289\) −63.9751 −0.221367
\(290\) −94.2005 + 618.187i −0.324829 + 2.13168i
\(291\) 386.294i 1.32747i
\(292\) 439.159i 1.50397i
\(293\) −164.482 −0.561371 −0.280686 0.959800i \(-0.590562\pi\)
−0.280686 + 0.959800i \(0.590562\pi\)
\(294\) 164.353 0.559023
\(295\) 80.2581 + 12.2299i 0.272062 + 0.0414572i
\(296\) 16.6047i 0.0560968i
\(297\) −191.986 −0.646418
\(298\) 521.380 1.74960
\(299\) 159.131 27.3286i 0.532209 0.0914000i
\(300\) −212.839 + 682.157i −0.709463 + 2.27386i
\(301\) −642.852 −2.13572
\(302\) 304.429i 1.00804i
\(303\) 41.2887i 0.136266i
\(304\) 199.612i 0.656619i
\(305\) −81.4076 + 534.234i −0.266910 + 1.75159i
\(306\) 282.799i 0.924178i
\(307\) 485.528i 1.58152i −0.612124 0.790762i \(-0.709685\pi\)
0.612124 0.790762i \(-0.290315\pi\)
\(308\) 860.942i 2.79527i
\(309\) 299.114i 0.968007i
\(310\) −32.4169 + 212.735i −0.104571 + 0.686241i
\(311\) −239.365 −0.769663 −0.384832 0.922987i \(-0.625741\pi\)
−0.384832 + 0.922987i \(0.625741\pi\)
\(312\) 316.961i 1.01590i
\(313\) −72.9249 −0.232987 −0.116493 0.993191i \(-0.537165\pi\)
−0.116493 + 0.993191i \(0.537165\pi\)
\(314\) 335.097i 1.06719i
\(315\) −215.943 32.9059i −0.685535 0.104463i
\(316\) 317.589i 1.00503i
\(317\) 151.052i 0.476503i −0.971203 0.238252i \(-0.923426\pi\)
0.971203 0.238252i \(-0.0765743\pi\)
\(318\) −766.008 −2.40883
\(319\) 539.834i 1.69227i
\(320\) −417.348 63.5962i −1.30421 0.198738i
\(321\) 493.138i 1.53625i
\(322\) 603.601 103.661i 1.87454 0.321927i
\(323\) 295.120i 0.913685i
\(324\) 749.979 2.31475
\(325\) 52.2723 167.535i 0.160838 0.515492i
\(326\) −217.207 −0.666279
\(327\) 2.90605 0.00888699
\(328\) 69.5829i 0.212143i
\(329\) 513.577i 1.56102i
\(330\) −142.557 + 935.526i −0.431991 + 2.83493i
\(331\) 544.555 1.64518 0.822590 0.568634i \(-0.192528\pi\)
0.822590 + 0.568634i \(0.192528\pi\)
\(332\) −428.667 −1.29117
\(333\) 7.80471 0.0234376
\(334\) 523.150 1.56632
\(335\) −472.808 72.0474i −1.41137 0.215067i
\(336\) 304.137i 0.905170i
\(337\) 90.1232 0.267428 0.133714 0.991020i \(-0.457310\pi\)
0.133714 + 0.991020i \(0.457310\pi\)
\(338\) 405.822i 1.20066i
\(339\) 316.059i 0.932326i
\(340\) −555.411 84.6346i −1.63356 0.248925i
\(341\) 185.771i 0.544784i
\(342\) 370.891 1.08448
\(343\) 285.102 0.831200
\(344\) 968.307i 2.81484i
\(345\) −438.756 + 8.27565i −1.27176 + 0.0239874i
\(346\) 392.768 1.13517
\(347\) 435.423i 1.25482i 0.778689 + 0.627411i \(0.215885\pi\)
−0.778689 + 0.627411i \(0.784115\pi\)
\(348\) 1054.58i 3.03041i
\(349\) 191.631 0.549085 0.274543 0.961575i \(-0.411474\pi\)
0.274543 + 0.961575i \(0.411474\pi\)
\(350\) 198.275 635.479i 0.566500 1.81565i
\(351\) −92.1108 −0.262424
\(352\) −189.269 −0.537695
\(353\) 174.369i 0.493962i 0.969020 + 0.246981i \(0.0794386\pi\)
−0.969020 + 0.246981i \(0.920561\pi\)
\(354\) −210.028 −0.593299
\(355\) 442.354 + 67.4067i 1.24607 + 0.189878i
\(356\) 158.119i 0.444155i
\(357\) 449.657i 1.25954i
\(358\) 236.966i 0.661917i
\(359\) 490.103i 1.36519i −0.730797 0.682594i \(-0.760852\pi\)
0.730797 0.682594i \(-0.239148\pi\)
\(360\) 49.5650 325.268i 0.137681 0.903523i
\(361\) −26.0507 −0.0721626
\(362\) −671.395 −1.85468
\(363\) 355.222i 0.978572i
\(364\) 413.062i 1.13478i
\(365\) −44.1598 + 289.797i −0.120986 + 0.793964i
\(366\) 1398.04i 3.81978i
\(367\) 443.384 1.20813 0.604065 0.796935i \(-0.293547\pi\)
0.604065 + 0.796935i \(0.293547\pi\)
\(368\) 39.4987 + 229.995i 0.107333 + 0.624987i
\(369\) −32.7061 −0.0886345
\(370\) −3.58306 + 23.5137i −0.00968395 + 0.0635506i
\(371\) 465.182 1.25386
\(372\) 362.910i 0.975565i
\(373\) −379.967 −1.01868 −0.509339 0.860566i \(-0.670110\pi\)
−0.509339 + 0.860566i \(0.670110\pi\)
\(374\) −744.016 −1.98935
\(375\) −209.045 + 428.747i −0.557453 + 1.14332i
\(376\) −773.584 −2.05740
\(377\) 259.001i 0.687005i
\(378\) −349.387 −0.924304
\(379\) 219.444i 0.579008i −0.957177 0.289504i \(-0.906510\pi\)
0.957177 0.289504i \(-0.0934904\pi\)
\(380\) −110.998 + 728.422i −0.292101 + 1.91690i
\(381\) 772.670 2.02801
\(382\) −185.285 −0.485040
\(383\) 188.650 0.492558 0.246279 0.969199i \(-0.420792\pi\)
0.246279 + 0.969199i \(0.420792\pi\)
\(384\) 894.715 2.32999
\(385\) 86.5722 568.127i 0.224863 1.47565i
\(386\) 794.202 2.05752
\(387\) −455.134 −1.17606
\(388\) 758.279 1.95433
\(389\) 139.634i 0.358955i 0.983762 + 0.179478i \(0.0574408\pi\)
−0.983762 + 0.179478i \(0.942559\pi\)
\(390\) −68.3958 + 448.845i −0.175374 + 1.15089i
\(391\) −58.3976 340.041i −0.149355 0.869670i
\(392\) 150.338i 0.383515i
\(393\) 615.802i 1.56693i
\(394\) −350.207 −0.888850
\(395\) 31.9352 209.574i 0.0808486 0.530566i
\(396\) 609.540i 1.53924i
\(397\) 572.066i 1.44097i −0.693470 0.720486i \(-0.743919\pi\)
0.693470 0.720486i \(-0.256081\pi\)
\(398\) −355.322 −0.892769
\(399\) −589.726 −1.47801
\(400\) 242.142 + 75.5505i 0.605356 + 0.188876i
\(401\) 401.445i 1.00111i −0.865705 0.500555i \(-0.833129\pi\)
0.865705 0.500555i \(-0.166871\pi\)
\(402\) 1237.30 3.07785
\(403\) 89.1292i 0.221164i
\(404\) −81.0479 −0.200614
\(405\) 494.903 + 75.4143i 1.22198 + 0.186208i
\(406\) 982.421i 2.41976i
\(407\) 20.5334i 0.0504507i
\(408\) 677.303 1.66006
\(409\) −106.927 −0.261436 −0.130718 0.991420i \(-0.541728\pi\)
−0.130718 + 0.991420i \(0.541728\pi\)
\(410\) 15.0151 98.5357i 0.0366221 0.240331i
\(411\) 792.276i 1.92768i
\(412\) 587.148 1.42512
\(413\) 127.546 0.308828
\(414\) 427.344 73.3908i 1.03223 0.177273i
\(415\) −282.873 43.1047i −0.681622 0.103867i
\(416\) −90.8071 −0.218286
\(417\) 533.443i 1.27924i
\(418\) 975.778i 2.33440i
\(419\) 704.907i 1.68236i −0.540758 0.841178i \(-0.681863\pi\)
0.540758 0.841178i \(-0.318137\pi\)
\(420\) −169.121 + 1109.85i −0.402670 + 2.64251i
\(421\) 579.217i 1.37581i 0.725800 + 0.687906i \(0.241470\pi\)
−0.725800 + 0.687906i \(0.758530\pi\)
\(422\) 1103.83i 2.61572i
\(423\) 363.608i 0.859594i
\(424\) 700.688i 1.65257i
\(425\) −358.000 111.699i −0.842353 0.262821i
\(426\) −1157.60 −2.71737
\(427\) 849.003i 1.98830i
\(428\) 968.009 2.26170
\(429\) 391.956i 0.913650i
\(430\) 208.947 1371.21i 0.485924 3.18886i
\(431\) 366.876i 0.851220i −0.904907 0.425610i \(-0.860060\pi\)
0.904907 0.425610i \(-0.139940\pi\)
\(432\) 133.130i 0.308171i
\(433\) −684.534 −1.58091 −0.790455 0.612520i \(-0.790156\pi\)
−0.790455 + 0.612520i \(0.790156\pi\)
\(434\) 338.077i 0.778980i
\(435\) 106.044 695.909i 0.243779 1.59979i
\(436\) 5.70445i 0.0130836i
\(437\) −445.964 + 76.5886i −1.02051 + 0.175260i
\(438\) 758.371i 1.73144i
\(439\) 354.150 0.806720 0.403360 0.915041i \(-0.367842\pi\)
0.403360 + 0.915041i \(0.367842\pi\)
\(440\) 855.750 + 130.401i 1.94489 + 0.296365i
\(441\) −70.6635 −0.160235
\(442\) −356.963 −0.807609
\(443\) 269.078i 0.607399i 0.952768 + 0.303700i \(0.0982220\pi\)
−0.952768 + 0.303700i \(0.901778\pi\)
\(444\) 40.1127i 0.0903440i
\(445\) −15.8997 + 104.341i −0.0357297 + 0.234474i
\(446\) 282.001 0.632288
\(447\) −586.931 −1.31304
\(448\) −663.247 −1.48046
\(449\) 101.610 0.226303 0.113152 0.993578i \(-0.463905\pi\)
0.113152 + 0.993578i \(0.463905\pi\)
\(450\) 140.377 449.914i 0.311949 0.999809i
\(451\) 86.0468i 0.190791i
\(452\) −620.410 −1.37259
\(453\) 342.704i 0.756520i
\(454\) 68.4148i 0.150693i
\(455\) 41.5355 272.575i 0.0912868 0.599066i
\(456\) 888.284i 1.94799i
\(457\) −486.800 −1.06521 −0.532604 0.846364i \(-0.678787\pi\)
−0.532604 + 0.846364i \(0.678787\pi\)
\(458\) 108.056 0.235929
\(459\) 196.829i 0.428820i
\(460\) 16.2447 + 861.261i 0.0353147 + 1.87231i
\(461\) −110.762 −0.240264 −0.120132 0.992758i \(-0.538332\pi\)
−0.120132 + 0.992758i \(0.538332\pi\)
\(462\) 1486.73i 3.21804i
\(463\) 110.728i 0.239154i 0.992825 + 0.119577i \(0.0381539\pi\)
−0.992825 + 0.119577i \(0.961846\pi\)
\(464\) −374.341 −0.806768
\(465\) 36.4925 239.481i 0.0784785 0.515012i
\(466\) 237.885 0.510482
\(467\) 559.817 1.19875 0.599376 0.800468i \(-0.295416\pi\)
0.599376 + 0.800468i \(0.295416\pi\)
\(468\) 292.444i 0.624881i
\(469\) −751.386 −1.60210
\(470\) −1095.46 166.929i −2.33078 0.355168i
\(471\) 377.228i 0.800908i
\(472\) 192.118i 0.407030i
\(473\) 1197.41i 2.53153i
\(474\) 548.434i 1.15703i
\(475\) −146.493 + 469.517i −0.308407 + 0.988457i
\(476\) −882.658 −1.85432
\(477\) 329.345 0.690451
\(478\) 347.365i 0.726705i
\(479\) 389.448i 0.813044i −0.913641 0.406522i \(-0.866741\pi\)
0.913641 0.406522i \(-0.133259\pi\)
\(480\) 243.989 + 37.1795i 0.508311 + 0.0774573i
\(481\) 9.85151i 0.0204813i
\(482\) 497.434 1.03202
\(483\) −679.489 + 116.693i −1.40681 + 0.241601i
\(484\) 697.285 1.44067
\(485\) 500.381 + 76.2489i 1.03171 + 0.157214i
\(486\) −894.815 −1.84118
\(487\) 303.721i 0.623657i 0.950138 + 0.311828i \(0.100941\pi\)
−0.950138 + 0.311828i \(0.899059\pi\)
\(488\) −1278.83 −2.62054
\(489\) 244.515 0.500032
\(490\) 32.4409 212.892i 0.0662059 0.434474i
\(491\) 893.361 1.81947 0.909736 0.415187i \(-0.136284\pi\)
0.909736 + 0.415187i \(0.136284\pi\)
\(492\) 168.095i 0.341656i
\(493\) 553.451 1.12262
\(494\) 468.158i 0.947687i
\(495\) 61.2924 402.229i 0.123823 0.812584i
\(496\) −128.821 −0.259719
\(497\) 702.988 1.41446
\(498\) 740.252 1.48645
\(499\) −373.121 −0.747737 −0.373868 0.927482i \(-0.621969\pi\)
−0.373868 + 0.927482i \(0.621969\pi\)
\(500\) 841.612 + 410.346i 1.68322 + 0.820692i
\(501\) −588.923 −1.17550
\(502\) −829.675 −1.65274
\(503\) −572.051 −1.13728 −0.568639 0.822587i \(-0.692530\pi\)
−0.568639 + 0.822587i \(0.692530\pi\)
\(504\) 516.915i 1.02563i
\(505\) −53.4827 8.14979i −0.105906 0.0161382i
\(506\) 193.084 + 1124.30i 0.381590 + 2.22194i
\(507\) 456.844i 0.901073i
\(508\) 1516.72i 2.98567i
\(509\) −172.246 −0.338400 −0.169200 0.985582i \(-0.554118\pi\)
−0.169200 + 0.985582i \(0.554118\pi\)
\(510\) 959.123 + 146.153i 1.88063 + 0.286574i
\(511\) 460.544i 0.901261i
\(512\) 611.452i 1.19424i
\(513\) 258.141 0.503199
\(514\) −346.498 −0.674120
\(515\) 387.453 + 59.0408i 0.752337 + 0.114642i
\(516\) 2339.19i 4.53331i
\(517\) −956.619 −1.85033
\(518\) 37.3679i 0.0721388i
\(519\) −442.149 −0.851925
\(520\) 410.571 + 62.5635i 0.789559 + 0.120314i
\(521\) 190.011i 0.364704i −0.983233 0.182352i \(-0.941629\pi\)
0.983233 0.182352i \(-0.0583711\pi\)
\(522\) 695.546i 1.33246i
\(523\) 255.175 0.487906 0.243953 0.969787i \(-0.421556\pi\)
0.243953 + 0.969787i \(0.421556\pi\)
\(524\) −1208.79 −2.30686
\(525\) −223.203 + 715.375i −0.425149 + 1.36262i
\(526\) 1123.08i 2.13513i
\(527\) 190.457 0.361399
\(528\) −566.504 −1.07292
\(529\) −498.690 + 176.492i −0.942703 + 0.333634i
\(530\) −151.199 + 992.238i −0.285281 + 1.87215i
\(531\) 90.3015 0.170059
\(532\) 1157.61i 2.17595i
\(533\) 41.2834i 0.0774548i
\(534\) 273.051i 0.511331i
\(535\) 638.779 + 97.3383i 1.19398 + 0.181941i
\(536\) 1131.79i 2.11154i
\(537\) 266.759i 0.496758i
\(538\) 154.714i 0.287572i
\(539\) 185.909i 0.344915i
\(540\) 74.0296 485.817i 0.137092 0.899660i
\(541\) 275.118 0.508537 0.254268 0.967134i \(-0.418165\pi\)
0.254268 + 0.967134i \(0.418165\pi\)
\(542\) 922.681i 1.70236i
\(543\) 755.806 1.39191
\(544\) 194.043i 0.356696i
\(545\) 0.573612 3.76431i 0.00105250 0.00690698i
\(546\) 713.303i 1.30642i
\(547\) 310.599i 0.567823i −0.958850 0.283912i \(-0.908368\pi\)
0.958850 0.283912i \(-0.0916323\pi\)
\(548\) 1555.20 2.83796
\(549\) 601.087i 1.09488i
\(550\) 1183.68 + 369.319i 2.15215 + 0.671489i
\(551\) 725.851i 1.31733i
\(552\) −175.771 1023.49i −0.318426 1.85415i
\(553\) 333.054i 0.602267i
\(554\) −1178.12 −2.12656
\(555\) 4.03354 26.4700i 0.00726765 0.0476937i
\(556\) 1047.13 1.88332
\(557\) 99.9420 0.179429 0.0897146 0.995968i \(-0.471405\pi\)
0.0897146 + 0.995968i \(0.471405\pi\)
\(558\) 239.356i 0.428953i
\(559\) 574.494i 1.02772i
\(560\) 393.960 + 60.0323i 0.703499 + 0.107201i
\(561\) 837.558 1.49297
\(562\) 1149.35 2.04510
\(563\) 469.692 0.834266 0.417133 0.908846i \(-0.363035\pi\)
0.417133 + 0.908846i \(0.363035\pi\)
\(564\) 1868.78 3.31345
\(565\) −409.402 62.3854i −0.724606 0.110417i
\(566\) 728.609i 1.28729i
\(567\) 786.499 1.38712
\(568\) 1058.89i 1.86424i
\(569\) 299.605i 0.526547i −0.964721 0.263274i \(-0.915198\pi\)
0.964721 0.263274i \(-0.0848022\pi\)
\(570\) 191.680 1257.89i 0.336280 2.20683i
\(571\) 833.584i 1.45987i −0.683518 0.729933i \(-0.739551\pi\)
0.683518 0.729933i \(-0.260449\pi\)
\(572\) 769.393 1.34509
\(573\) 208.580 0.364015
\(574\) 156.593i 0.272810i
\(575\) −75.8845 + 569.971i −0.131973 + 0.991253i
\(576\) −469.574 −0.815232
\(577\) 372.711i 0.645947i 0.946408 + 0.322974i \(0.104682\pi\)
−0.946408 + 0.322974i \(0.895318\pi\)
\(578\) 216.861i 0.375192i
\(579\) −894.054 −1.54413
\(580\) −1366.04 208.160i −2.35524 0.358896i
\(581\) −449.541 −0.773736
\(582\) −1309.45 −2.24991
\(583\) 866.476i 1.48624i
\(584\) −693.702 −1.18785
\(585\) 29.4068 192.981i 0.0502680 0.329882i
\(586\) 557.556i 0.951460i
\(587\) 478.228i 0.814698i −0.913273 0.407349i \(-0.866453\pi\)
0.913273 0.407349i \(-0.133547\pi\)
\(588\) 363.179i 0.617651i
\(589\) 249.785i 0.424083i
\(590\) −41.4565 + 272.057i −0.0702653 + 0.461113i
\(591\) 394.237 0.667067
\(592\) −14.2386 −0.0240517
\(593\) 685.488i 1.15597i 0.816049 + 0.577983i \(0.196160\pi\)
−0.816049 + 0.577983i \(0.803840\pi\)
\(594\) 650.789i 1.09560i
\(595\) −582.457 88.7559i −0.978919 0.149170i
\(596\) 1152.12i 1.93309i
\(597\) 399.995 0.670009
\(598\) 92.6378 + 539.416i 0.154913 + 0.902034i
\(599\) 806.008 1.34559 0.672795 0.739829i \(-0.265094\pi\)
0.672795 + 0.739829i \(0.265094\pi\)
\(600\) −1077.55 336.203i −1.79591 0.560339i
\(601\) −162.773 −0.270836 −0.135418 0.990789i \(-0.543238\pi\)
−0.135418 + 0.990789i \(0.543238\pi\)
\(602\) 2179.12i 3.61980i
\(603\) −531.975 −0.882214
\(604\) −672.713 −1.11376
\(605\) 460.131 + 70.1156i 0.760548 + 0.115894i
\(606\) 139.959 0.230956
\(607\) 862.711i 1.42127i −0.703561 0.710635i \(-0.748408\pi\)
0.703561 0.710635i \(-0.251592\pi\)
\(608\) 254.487 0.418564
\(609\) 1105.94i 1.81599i
\(610\) −1810.93 275.953i −2.96874 0.452382i
\(611\) −458.965 −0.751171
\(612\) −624.915 −1.02110
\(613\) 31.4095 0.0512390 0.0256195 0.999672i \(-0.491844\pi\)
0.0256195 + 0.999672i \(0.491844\pi\)
\(614\) 1645.83 2.68050
\(615\) −16.9028 + 110.924i −0.0274843 + 0.180364i
\(616\) 1359.96 2.20772
\(617\) 356.586 0.577935 0.288968 0.957339i \(-0.406688\pi\)
0.288968 + 0.957339i \(0.406688\pi\)
\(618\) −1013.93 −1.64066
\(619\) 150.564i 0.243238i 0.992577 + 0.121619i \(0.0388086\pi\)
−0.992577 + 0.121619i \(0.961191\pi\)
\(620\) −470.091 71.6333i −0.758211 0.115538i
\(621\) 297.433 51.0802i 0.478958 0.0822548i
\(622\) 811.394i 1.30449i
\(623\) 165.819i 0.266162i
\(624\) −271.796 −0.435571
\(625\) 514.109 + 355.412i 0.822574 + 0.568659i
\(626\) 247.199i 0.394886i
\(627\) 1098.46i 1.75193i
\(628\) −740.482 −1.17911
\(629\) 21.0514 0.0334680
\(630\) 111.543 731.999i 0.177053 1.16190i
\(631\) 251.228i 0.398143i −0.979985 0.199072i \(-0.936207\pi\)
0.979985 0.199072i \(-0.0637927\pi\)
\(632\) 501.668 0.793778
\(633\) 1242.61i 1.96306i
\(634\) 512.030 0.807619
\(635\) 152.514 1000.87i 0.240180 1.57617i
\(636\) 1692.69i 2.66146i
\(637\) 89.1952i 0.140024i
\(638\) −1829.92 −2.86821
\(639\) 497.710 0.778888
\(640\) 176.604 1158.96i 0.275944 1.81087i
\(641\) 601.005i 0.937605i 0.883303 + 0.468803i \(0.155314\pi\)
−0.883303 + 0.468803i \(0.844686\pi\)
\(642\) −1671.62 −2.60378
\(643\) −532.541 −0.828214 −0.414107 0.910228i \(-0.635906\pi\)
−0.414107 + 0.910228i \(0.635906\pi\)
\(644\) 229.064 + 1333.81i 0.355690 + 2.07113i
\(645\) −235.217 + 1543.61i −0.364678 + 2.39319i
\(646\) 1000.39 1.54859
\(647\) 627.608i 0.970028i −0.874506 0.485014i \(-0.838815\pi\)
0.874506 0.485014i \(-0.161185\pi\)
\(648\) 1184.68i 1.82820i
\(649\) 237.575i 0.366063i
\(650\) 567.905 + 177.191i 0.873700 + 0.272602i
\(651\) 380.582i 0.584612i
\(652\) 479.974i 0.736156i
\(653\) 243.613i 0.373068i 0.982449 + 0.186534i \(0.0597254\pi\)
−0.982449 + 0.186534i \(0.940275\pi\)
\(654\) 9.85083i 0.0150624i
\(655\) −797.670 121.550i −1.21782 0.185573i
\(656\) 59.6679 0.0909572
\(657\) 326.061i 0.496288i
\(658\) −1740.91 −2.64576
\(659\) 568.999i 0.863427i 0.902011 + 0.431714i \(0.142091\pi\)
−0.902011 + 0.431714i \(0.857909\pi\)
\(660\) −2067.28 315.016i −3.13224 0.477297i
\(661\) 165.702i 0.250683i −0.992114 0.125342i \(-0.959997\pi\)
0.992114 0.125342i \(-0.0400027\pi\)
\(662\) 1845.92i 2.78839i
\(663\) 401.843 0.606097
\(664\) 677.128i 1.01977i
\(665\) −116.403 + 763.893i −0.175043 + 1.14871i
\(666\) 26.4562i 0.0397240i
\(667\) −143.630 836.334i −0.215337 1.25387i
\(668\) 1156.03i 1.73059i
\(669\) −317.455 −0.474522
\(670\) 244.224 1602.71i 0.364514 2.39211i
\(671\) −1581.40 −2.35679
\(672\) 387.747 0.577004
\(673\) 787.294i 1.16983i −0.811095 0.584914i \(-0.801128\pi\)
0.811095 0.584914i \(-0.198872\pi\)
\(674\) 305.497i 0.453260i
\(675\) 97.7028 313.141i 0.144745 0.463913i
\(676\) −896.765 −1.32658
\(677\) 640.320 0.945820 0.472910 0.881111i \(-0.343204\pi\)
0.472910 + 0.881111i \(0.343204\pi\)
\(678\) 1071.37 1.58019
\(679\) 795.203 1.17114
\(680\) 133.690 877.335i 0.196603 1.29020i
\(681\) 77.0162i 0.113093i
\(682\) −629.723 −0.923347
\(683\) 1135.46i 1.66246i 0.555930 + 0.831229i \(0.312362\pi\)
−0.555930 + 0.831229i \(0.687638\pi\)
\(684\) 819.576i 1.19821i
\(685\) 1026.26 + 156.384i 1.49819 + 0.228298i
\(686\) 966.430i 1.40879i
\(687\) −121.641 −0.177061
\(688\) 830.330 1.20688
\(689\) 415.717i 0.603363i
\(690\) −28.0526 1487.28i −0.0406559 2.15548i
\(691\) −584.766 −0.846261 −0.423131 0.906069i \(-0.639069\pi\)
−0.423131 + 0.906069i \(0.639069\pi\)
\(692\) 867.920i 1.25422i
\(693\) 639.221i 0.922397i
\(694\) −1475.98 −2.12678
\(695\) 690.988 + 105.294i 0.994228 + 0.151502i
\(696\) 1665.83 2.39344
\(697\) −88.2172 −0.126567
\(698\) 649.585i 0.930637i
\(699\) −267.793 −0.383109
\(700\) 1404.25 + 438.138i 2.00607 + 0.625912i
\(701\) 789.534i 1.12630i 0.826356 + 0.563148i \(0.190410\pi\)
−0.826356 + 0.563148i \(0.809590\pi\)
\(702\) 312.235i 0.444779i
\(703\) 27.6089i 0.0392730i
\(704\) 1235.40i 1.75484i
\(705\) 1233.19 + 187.916i 1.74921 + 0.266548i
\(706\) −591.070 −0.837210
\(707\) −84.9946 −0.120219
\(708\) 464.110i 0.655522i
\(709\) 1356.27i 1.91294i 0.291836 + 0.956468i \(0.405734\pi\)
−0.291836 + 0.956468i \(0.594266\pi\)
\(710\) −228.493 + 1499.48i −0.321822 + 2.11194i
\(711\) 235.799i 0.331645i
\(712\) −249.767 −0.350796
\(713\) −49.4268 287.805i −0.0693223 0.403654i
\(714\) 1524.23 2.13478
\(715\) 507.715 + 77.3665i 0.710091 + 0.108205i
\(716\) 523.637 0.731336
\(717\) 391.038i 0.545380i
\(718\) 1661.34 2.31384
\(719\) 1205.36 1.67644 0.838221 0.545330i \(-0.183596\pi\)
0.838221 + 0.545330i \(0.183596\pi\)
\(720\) 278.920 + 42.5024i 0.387389 + 0.0590311i
\(721\) 615.740 0.854008
\(722\) 88.3059i 0.122307i
\(723\) −559.974 −0.774515
\(724\) 1483.62i 2.04919i
\(725\) −880.504 274.725i −1.21449 0.378931i
\(726\) −1204.12 −1.65857
\(727\) −949.180 −1.30561 −0.652806 0.757525i \(-0.726408\pi\)
−0.652806 + 0.757525i \(0.726408\pi\)
\(728\) 652.478 0.896261
\(729\) 106.207 0.145688
\(730\) −982.345 149.692i −1.34568 0.205057i
\(731\) −1227.62 −1.67937
\(732\) 3089.32 4.22039
\(733\) −24.1006 −0.0328794 −0.0164397 0.999865i \(-0.505233\pi\)
−0.0164397 + 0.999865i \(0.505233\pi\)
\(734\) 1502.97i 2.04764i
\(735\) −36.5195 + 239.658i −0.0496865 + 0.326066i
\(736\) 293.223 50.3572i 0.398401 0.0684202i
\(737\) 1399.58i 1.89902i
\(738\) 110.866i 0.150225i
\(739\) −49.6986 −0.0672512 −0.0336256 0.999435i \(-0.510705\pi\)
−0.0336256 + 0.999435i \(0.510705\pi\)
\(740\) −51.9595 7.91768i −0.0702155 0.0106996i
\(741\) 527.017i 0.711224i
\(742\) 1576.86i 2.12515i
\(743\) 728.213 0.980099 0.490049 0.871695i \(-0.336979\pi\)
0.490049 + 0.871695i \(0.336979\pi\)
\(744\) 573.258 0.770508
\(745\) −115.852 + 760.272i −0.155506 + 1.02050i
\(746\) 1288.00i 1.72654i
\(747\) −318.271 −0.426066
\(748\) 1644.09i 2.19798i
\(749\) 1015.15 1.35533
\(750\) −1453.35 708.614i −1.93780 0.944819i
\(751\) 832.335i 1.10830i 0.832416 + 0.554151i \(0.186957\pi\)
−0.832416 + 0.554151i \(0.813043\pi\)
\(752\) 663.354i 0.882120i
\(753\) 933.986 1.24035
\(754\) −877.955 −1.16440
\(755\) −443.917 67.6448i −0.587969 0.0895958i
\(756\) 772.058i 1.02124i
\(757\) −83.6711 −0.110530 −0.0552649 0.998472i \(-0.517600\pi\)
−0.0552649 + 0.998472i \(0.517600\pi\)
\(758\) 743.865 0.981353
\(759\) −217.360 1265.66i −0.286377 1.66753i
\(760\) −1150.63 175.335i −1.51398 0.230703i
\(761\) −1113.77 −1.46356 −0.731782 0.681539i \(-0.761311\pi\)
−0.731782 + 0.681539i \(0.761311\pi\)
\(762\) 2619.18i 3.43724i
\(763\) 5.98222i 0.00784040i
\(764\) 409.434i 0.535909i
\(765\) −412.375 62.8384i −0.539052 0.0821417i
\(766\) 639.480i 0.834830i
\(767\) 113.983i 0.148609i
\(768\) 1744.11i 2.27097i
\(769\) 945.642i 1.22970i −0.788643 0.614852i \(-0.789216\pi\)
0.788643 0.614852i \(-0.210784\pi\)
\(770\) 1925.82 + 293.460i 2.50107 + 0.381117i
\(771\) 390.061 0.505916
\(772\) 1754.99i 2.27330i
\(773\) −966.297 −1.25006 −0.625030 0.780601i \(-0.714913\pi\)
−0.625030 + 0.780601i \(0.714913\pi\)
\(774\) 1542.80i 1.99328i
\(775\) −303.005 94.5402i −0.390974 0.121987i
\(776\) 1197.79i 1.54354i
\(777\) 42.0660i 0.0541390i
\(778\) −473.326 −0.608388
\(779\) 115.697i 0.148520i
\(780\) −991.836 151.138i −1.27159 0.193766i
\(781\) 1309.43i 1.67660i
\(782\) 1152.66 197.955i 1.47399 0.253139i
\(783\) 484.102i 0.618265i
\(784\) 128.916 0.164434
\(785\) −488.636 74.4593i −0.622467 0.0948526i
\(786\) 2087.43 2.65576
\(787\) −156.202 −0.198477 −0.0992386 0.995064i \(-0.531641\pi\)
−0.0992386 + 0.995064i \(0.531641\pi\)
\(788\) 773.870i 0.982069i
\(789\) 1264.28i 1.60238i
\(790\) 710.407 + 108.253i 0.899249 + 0.137029i
\(791\) −650.621 −0.822529
\(792\) 962.838 1.21570
\(793\) −758.724 −0.956777
\(794\) 1939.17 2.44228
\(795\) 170.209 1116.99i 0.214099 1.40502i
\(796\) 785.174i 0.986399i
\(797\) 559.866 0.702467 0.351233 0.936288i \(-0.385762\pi\)
0.351233 + 0.936288i \(0.385762\pi\)
\(798\) 1999.04i 2.50506i
\(799\) 980.748i 1.22747i
\(800\) 96.3199 308.709i 0.120400 0.385886i
\(801\) 117.398i 0.146565i
\(802\) 1360.81 1.69677
\(803\) −857.837 −1.06829
\(804\) 2734.11i 3.40064i
\(805\) 17.0358 + 903.200i 0.0211625 + 1.12199i
\(806\) −302.128 −0.374848
\(807\) 174.165i 0.215818i
\(808\) 128.024i 0.158446i
\(809\) 1289.52 1.59396 0.796981 0.604004i \(-0.206429\pi\)
0.796981 + 0.604004i \(0.206429\pi\)
\(810\) −255.637 + 1677.61i −0.315601 + 2.07112i
\(811\) −1091.91 −1.34637 −0.673185 0.739474i \(-0.735074\pi\)
−0.673185 + 0.739474i \(0.735074\pi\)
\(812\) −2170.91 −2.67353
\(813\) 1038.69i 1.27760i
\(814\) −69.6037 −0.0855082
\(815\) 48.2639 316.730i 0.0592195 0.388625i
\(816\) 580.793i 0.711756i
\(817\) 1610.02i 1.97065i
\(818\) 362.459i 0.443104i
\(819\) 306.685i 0.374463i
\(820\) 217.739 + 33.1795i 0.265536 + 0.0404629i
\(821\) −950.992 −1.15833 −0.579167 0.815209i \(-0.696622\pi\)
−0.579167 + 0.815209i \(0.696622\pi\)
\(822\) −2685.63 −3.26719
\(823\) 472.254i 0.573820i −0.957957 0.286910i \(-0.907372\pi\)
0.957957 0.286910i \(-0.0926281\pi\)
\(824\) 927.468i 1.12557i
\(825\) −1332.50 415.751i −1.61515 0.503941i
\(826\) 432.352i 0.523428i
\(827\) −1539.15 −1.86113 −0.930565 0.366126i \(-0.880684\pi\)
−0.930565 + 0.366126i \(0.880684\pi\)
\(828\) 162.176 + 944.325i 0.195864 + 1.14049i
\(829\) −175.844 −0.212116 −0.106058 0.994360i \(-0.533823\pi\)
−0.106058 + 0.994360i \(0.533823\pi\)
\(830\) 146.115 958.875i 0.176042 1.15527i
\(831\) 1326.23 1.59595
\(832\) 592.721i 0.712405i
\(833\) −190.598 −0.228810
\(834\) −1808.25 −2.16817
\(835\) −116.245 + 762.854i −0.139216 + 0.913597i
\(836\) −2156.23 −2.57922
\(837\) 166.592i 0.199035i
\(838\) 2389.47 2.85140
\(839\) 1603.02i 1.91063i 0.295596 + 0.955313i \(0.404482\pi\)
−0.295596 + 0.955313i \(0.595518\pi\)
\(840\) −1753.14 267.147i −2.08707 0.318032i
\(841\) 520.218 0.618571
\(842\) −1963.41 −2.33185
\(843\) −1293.85 −1.53482
\(844\) 2439.20 2.89005
\(845\) −591.766 90.1744i −0.700315 0.106715i
\(846\) −1232.55 −1.45691
\(847\) 731.239 0.863329
\(848\) −600.846 −0.708545
\(849\) 820.213i 0.966093i
\(850\) 378.634 1213.54i 0.445452 1.42769i
\(851\) −5.46317 31.8113i −0.00641971 0.0373811i
\(852\) 2558.01i 3.00235i
\(853\) 480.409i 0.563200i −0.959532 0.281600i \(-0.909135\pi\)
0.959532 0.281600i \(-0.0908651\pi\)
\(854\) −2877.93 −3.36994
\(855\) −82.4127 + 540.830i −0.0963891 + 0.632550i
\(856\) 1529.08i 1.78631i
\(857\) 30.1380i 0.0351669i 0.999845 + 0.0175834i \(0.00559727\pi\)
−0.999845 + 0.0175834i \(0.994403\pi\)
\(858\) −1328.64 −1.54853
\(859\) −548.892 −0.638990 −0.319495 0.947588i \(-0.603513\pi\)
−0.319495 + 0.947588i \(0.603513\pi\)
\(860\) 3030.03 + 461.722i 3.52329 + 0.536886i
\(861\) 176.280i 0.204739i
\(862\) 1243.62 1.44272
\(863\) 514.023i 0.595624i 0.954625 + 0.297812i \(0.0962569\pi\)
−0.954625 + 0.297812i \(0.903743\pi\)
\(864\) −169.729 −0.196445
\(865\) −87.2739 + 572.732i −0.100895 + 0.662118i
\(866\) 2320.41i 2.67946i
\(867\) 244.126i 0.281576i
\(868\) −747.067 −0.860676
\(869\) 620.366 0.713885
\(870\) 2358.97 + 359.464i 2.71146 + 0.413178i
\(871\) 671.487i 0.770938i
\(872\) 9.01082 0.0103335
\(873\) 562.997 0.644900
\(874\) −259.618 1511.72i −0.297045 1.72965i
\(875\) 882.594 + 430.328i 1.00868 + 0.491803i
\(876\) 1675.81 1.91303
\(877\) 474.355i 0.540883i −0.962736 0.270442i \(-0.912830\pi\)
0.962736 0.270442i \(-0.0871697\pi\)
\(878\) 1200.49i 1.36730i
\(879\) 627.655i 0.714055i
\(880\) −111.820 + 733.813i −0.127068 + 0.833878i
\(881\) 884.227i 1.00366i −0.864966 0.501831i \(-0.832660\pi\)
0.864966 0.501831i \(-0.167340\pi\)
\(882\) 239.533i 0.271580i
\(883\) 1166.30i 1.32083i −0.750899 0.660417i \(-0.770380\pi\)
0.750899 0.660417i \(-0.229620\pi\)
\(884\) 788.800i 0.892308i
\(885\) 46.6687 306.261i 0.0527329 0.346058i
\(886\) −912.113 −1.02947
\(887\) 40.5530i 0.0457193i −0.999739 0.0228596i \(-0.992723\pi\)
0.999739 0.0228596i \(-0.00727708\pi\)
\(888\) 63.3626 0.0713543
\(889\) 1590.58i 1.78917i
\(890\) −353.693 53.8963i −0.397408 0.0605577i
\(891\) 1464.98i 1.64420i
\(892\) 623.151i 0.698600i
\(893\) 1286.25 1.44037
\(894\) 1989.56i 2.22546i
\(895\) 345.542 + 52.6544i 0.386081 + 0.0588317i
\(896\) 1841.81i 2.05559i
\(897\) −104.285 607.235i −0.116259 0.676962i
\(898\) 344.435i 0.383558i
\(899\) 468.432 0.521058
\(900\) 994.198 + 310.198i 1.10466 + 0.344665i
\(901\) 888.332 0.985940
\(902\) 291.679 0.323369
\(903\) 2453.09i 2.71660i
\(904\) 980.008i 1.08408i
\(905\) 149.185 979.023i 0.164846 1.08179i
\(906\) 1161.69 1.28222
\(907\) 699.890 0.771654 0.385827 0.922571i \(-0.373916\pi\)
0.385827 + 0.922571i \(0.373916\pi\)
\(908\) −151.180 −0.166497
\(909\) −60.1755 −0.0661996
\(910\) 923.968 + 140.796i 1.01535 + 0.154721i
\(911\) 1678.86i 1.84287i −0.388531 0.921436i \(-0.627017\pi\)
0.388531 0.921436i \(-0.372983\pi\)
\(912\) 761.710 0.835209
\(913\) 837.342i 0.917132i
\(914\) 1650.14i 1.80541i
\(915\) 2038.61 + 310.647i 2.22799 + 0.339505i
\(916\) 238.776i 0.260673i
\(917\) −1267.66 −1.38239
\(918\) −667.204 −0.726802
\(919\) 392.082i 0.426640i 0.976982 + 0.213320i \(0.0684277\pi\)
−0.976982 + 0.213320i \(0.931572\pi\)
\(920\) −1360.46 + 25.6604i −1.47876 + 0.0278918i
\(921\) −1852.75 −2.01167
\(922\) 375.458i 0.407221i
\(923\) 628.235i 0.680645i
\(924\) −3285.31 −3.55553
\(925\) −33.4914 10.4496i −0.0362069 0.0112969i
\(926\) −375.344 −0.405339
\(927\) 435.939 0.470268
\(928\) 477.250i 0.514278i
\(929\) −1172.07 −1.26165 −0.630823 0.775927i \(-0.717282\pi\)
−0.630823 + 0.775927i \(0.717282\pi\)
\(930\) 811.785 + 123.701i 0.872887 + 0.133012i
\(931\) 249.970i 0.268496i
\(932\) 525.666i 0.564020i
\(933\) 913.407i 0.979000i
\(934\) 1897.65i 2.03175i
\(935\) 165.322 1084.92i 0.176815 1.16034i
\(936\) 461.949 0.493535
\(937\) −183.235 −0.195555 −0.0977773 0.995208i \(-0.531173\pi\)
−0.0977773 + 0.995208i \(0.531173\pi\)
\(938\) 2547.03i 2.71538i
\(939\) 278.278i 0.296356i
\(940\) 368.871 2420.70i 0.392416 2.57522i
\(941\) 808.527i 0.859221i 0.903014 + 0.429611i \(0.141349\pi\)
−0.903014 + 0.429611i \(0.858651\pi\)
\(942\) 1278.72 1.35745
\(943\) 22.8938 + 133.307i 0.0242776 + 0.141365i
\(944\) −164.743 −0.174516
\(945\) 77.6345 509.473i 0.0821529 0.539125i
\(946\) 4058.96 4.29066
\(947\) 171.842i 0.181460i 0.995876 + 0.0907298i \(0.0289199\pi\)
−0.995876 + 0.0907298i \(0.971080\pi\)
\(948\) −1211.90 −1.27838
\(949\) −411.572 −0.433690
\(950\) −1591.56 496.579i −1.67532 0.522715i
\(951\) −576.405 −0.606104
\(952\) 1394.26i 1.46456i
\(953\) −500.502 −0.525185 −0.262593 0.964907i \(-0.584578\pi\)
−0.262593 + 0.964907i \(0.584578\pi\)
\(954\) 1116.41i 1.17024i
\(955\) 41.1708 270.182i 0.0431108 0.282913i
\(956\) −767.591 −0.802919
\(957\) 2059.98 2.15254
\(958\) 1320.14 1.37802
\(959\) 1630.93 1.70066
\(960\) −242.680 + 1592.58i −0.252792 + 1.65894i
\(961\) −799.800 −0.832258
\(962\) −33.3944 −0.0347135
\(963\) 718.715 0.746329
\(964\) 1099.21i 1.14026i
\(965\) −176.473 + 1158.10i −0.182874 + 1.20010i
\(966\) −395.564 2303.31i −0.409486 2.38438i
\(967\) 881.587i 0.911672i 0.890064 + 0.455836i \(0.150660\pi\)
−0.890064 + 0.455836i \(0.849340\pi\)
\(968\) 1101.44i 1.13785i
\(969\) −1126.17 −1.16219
\(970\) −258.466 + 1696.18i −0.266460 + 1.74864i
\(971\) 918.528i 0.945961i 0.881073 + 0.472980i \(0.156822\pi\)
−0.881073 + 0.472980i \(0.843178\pi\)
\(972\) 1977.32i 2.03428i
\(973\) 1098.12 1.12859
\(974\) −1029.54 −1.05703
\(975\) −639.305 199.469i −0.655698 0.204583i
\(976\) 1096.60i 1.12357i
\(977\) 410.684 0.420352 0.210176 0.977664i \(-0.432596\pi\)
0.210176 + 0.977664i \(0.432596\pi\)
\(978\) 828.852i 0.847497i
\(979\) −308.864 −0.315489
\(980\) 470.439 + 71.6863i 0.480040 + 0.0731493i
\(981\) 4.23537i 0.00431740i
\(982\) 3028.29i 3.08380i
\(983\) 1275.13 1.29719 0.648594 0.761135i \(-0.275358\pi\)
0.648594 + 0.761135i \(0.275358\pi\)
\(984\) −265.525 −0.269843
\(985\) 77.8167 510.669i 0.0790017 0.518446i
\(986\) 1876.07i 1.90271i
\(987\) 1959.78 1.98560
\(988\) −1034.51 −1.04708
\(989\) 318.587 + 1855.09i 0.322130 + 1.87572i
\(990\) 1363.47 + 207.767i 1.37724 + 0.209866i
\(991\) −1260.06 −1.27151 −0.635754 0.771892i \(-0.719311\pi\)
−0.635754 + 0.771892i \(0.719311\pi\)
\(992\) 164.234i 0.165559i
\(993\) 2078.00i 2.09264i
\(994\) 2382.97i 2.39735i
\(995\) 78.9533 518.128i 0.0793501 0.520732i
\(996\) 1635.77i 1.64234i
\(997\) 951.919i 0.954783i −0.878691 0.477392i \(-0.841582\pi\)
0.878691 0.477392i \(-0.158418\pi\)
\(998\) 1264.79i 1.26733i
\(999\) 18.4136i 0.0184320i
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 115.3.c.c.114.17 yes 20
5.2 odd 4 575.3.d.i.551.3 20
5.3 odd 4 575.3.d.i.551.18 20
5.4 even 2 inner 115.3.c.c.114.4 yes 20
23.22 odd 2 inner 115.3.c.c.114.18 yes 20
115.22 even 4 575.3.d.i.551.4 20
115.68 even 4 575.3.d.i.551.17 20
115.114 odd 2 inner 115.3.c.c.114.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.3.c.c.114.3 20 115.114 odd 2 inner
115.3.c.c.114.4 yes 20 5.4 even 2 inner
115.3.c.c.114.17 yes 20 1.1 even 1 trivial
115.3.c.c.114.18 yes 20 23.22 odd 2 inner
575.3.d.i.551.3 20 5.2 odd 4
575.3.d.i.551.4 20 115.22 even 4
575.3.d.i.551.17 20 115.68 even 4
575.3.d.i.551.18 20 5.3 odd 4