Properties

Label 144.3.m.b.91.3
Level $144$
Weight $3$
Character 144.91
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
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] = [144,3,Mod(19,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 91.3
Root \(-1.66730 + 1.10459i\) of defining polynomial
Character \(\chi\) \(=\) 144.91
Dual form 144.3.m.b.19.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10459 - 1.66730i) q^{2} +(-1.55976 + 3.68336i) q^{4} +(-4.23991 - 4.23991i) q^{5} -0.262225 q^{7} +(7.86415 - 1.46802i) q^{8} +O(q^{10})\) \(q+(-1.10459 - 1.66730i) q^{2} +(-1.55976 + 3.68336i) q^{4} +(-4.23991 - 4.23991i) q^{5} -0.262225 q^{7} +(7.86415 - 1.46802i) q^{8} +(-2.38583 + 11.7525i) q^{10} +(-8.60531 + 8.60531i) q^{11} +(-15.9957 + 15.9957i) q^{13} +(0.289652 + 0.437208i) q^{14} +(-11.1343 - 11.4903i) q^{16} -3.51534 q^{17} +(10.7566 + 10.7566i) q^{19} +(22.2304 - 9.00387i) q^{20} +(23.8530 + 4.84227i) q^{22} -16.4968 q^{23} +10.9536i q^{25} +(44.3382 + 9.00087i) q^{26} +(0.409009 - 0.965871i) q^{28} +(-25.9522 + 25.9522i) q^{29} -46.2072i q^{31} +(-6.85895 + 31.2563i) q^{32} +(3.88301 + 5.86112i) q^{34} +(1.11181 + 1.11181i) q^{35} +(-2.99313 - 2.99313i) q^{37} +(6.05283 - 29.8162i) q^{38} +(-39.5676 - 27.1190i) q^{40} +21.9026i q^{41} +(48.7016 - 48.7016i) q^{43} +(-18.2742 - 45.1187i) q^{44} +(18.2222 + 27.5051i) q^{46} -70.7760i q^{47} -48.9312 q^{49} +(18.2630 - 12.0993i) q^{50} +(-33.9684 - 83.8672i) q^{52} +(-52.8193 - 52.8193i) q^{53} +72.9715 q^{55} +(-2.06218 + 0.384952i) q^{56} +(71.9366 + 14.6035i) q^{58} +(-61.7726 + 61.7726i) q^{59} +(-22.9004 + 22.9004i) q^{61} +(-77.0411 + 51.0400i) q^{62} +(59.6898 - 23.0895i) q^{64} +135.640 q^{65} +(-54.9939 - 54.9939i) q^{67} +(5.48309 - 12.9483i) q^{68} +(0.625624 - 3.08182i) q^{70} +84.2532 q^{71} +78.0341i q^{73} +(-1.68426 + 8.29663i) q^{74} +(-56.3983 + 22.8428i) q^{76} +(2.25653 - 2.25653i) q^{77} +59.2887i q^{79} +(-1.50953 + 95.9263i) q^{80} +(36.5181 - 24.1934i) q^{82} +(111.661 + 111.661i) q^{83} +(14.9047 + 14.9047i) q^{85} +(-134.995 - 27.4047i) q^{86} +(-55.0407 + 80.3063i) q^{88} -34.5426i q^{89} +(4.19447 - 4.19447i) q^{91} +(25.7311 - 60.7637i) q^{92} +(-118.005 + 78.1784i) q^{94} -91.2142i q^{95} -66.0805 q^{97} +(54.0490 + 81.5829i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10459 1.66730i −0.552295 0.833649i
\(3\) 0 0
\(4\) −1.55976 + 3.68336i −0.389940 + 0.920840i
\(5\) −4.23991 4.23991i −0.847982 0.847982i 0.141900 0.989881i \(-0.454679\pi\)
−0.989881 + 0.141900i \(0.954679\pi\)
\(6\) 0 0
\(7\) −0.262225 −0.0374608 −0.0187304 0.999825i \(-0.505962\pi\)
−0.0187304 + 0.999825i \(0.505962\pi\)
\(8\) 7.86415 1.46802i 0.983019 0.183503i
\(9\) 0 0
\(10\) −2.38583 + 11.7525i −0.238583 + 1.17525i
\(11\) −8.60531 + 8.60531i −0.782301 + 0.782301i −0.980219 0.197917i \(-0.936582\pi\)
0.197917 + 0.980219i \(0.436582\pi\)
\(12\) 0 0
\(13\) −15.9957 + 15.9957i −1.23044 + 1.23044i −0.266640 + 0.963796i \(0.585913\pi\)
−0.963796 + 0.266640i \(0.914087\pi\)
\(14\) 0.289652 + 0.437208i 0.0206894 + 0.0312291i
\(15\) 0 0
\(16\) −11.1343 11.4903i −0.695893 0.718145i
\(17\) −3.51534 −0.206785 −0.103392 0.994641i \(-0.532970\pi\)
−0.103392 + 0.994641i \(0.532970\pi\)
\(18\) 0 0
\(19\) 10.7566 + 10.7566i 0.566138 + 0.566138i 0.931044 0.364906i \(-0.118899\pi\)
−0.364906 + 0.931044i \(0.618899\pi\)
\(20\) 22.2304 9.00387i 1.11152 0.450193i
\(21\) 0 0
\(22\) 23.8530 + 4.84227i 1.08423 + 0.220103i
\(23\) −16.4968 −0.717253 −0.358626 0.933481i \(-0.616755\pi\)
−0.358626 + 0.933481i \(0.616755\pi\)
\(24\) 0 0
\(25\) 10.9536i 0.438145i
\(26\) 44.3382 + 9.00087i 1.70532 + 0.346187i
\(27\) 0 0
\(28\) 0.409009 0.965871i 0.0146075 0.0344954i
\(29\) −25.9522 + 25.9522i −0.894903 + 0.894903i −0.994980 0.100077i \(-0.968091\pi\)
0.100077 + 0.994980i \(0.468091\pi\)
\(30\) 0 0
\(31\) 46.2072i 1.49055i −0.666755 0.745277i \(-0.732317\pi\)
0.666755 0.745277i \(-0.267683\pi\)
\(32\) −6.85895 + 31.2563i −0.214342 + 0.976759i
\(33\) 0 0
\(34\) 3.88301 + 5.86112i 0.114206 + 0.172386i
\(35\) 1.11181 + 1.11181i 0.0317660 + 0.0317660i
\(36\) 0 0
\(37\) −2.99313 2.99313i −0.0808955 0.0808955i 0.665501 0.746397i \(-0.268218\pi\)
−0.746397 + 0.665501i \(0.768218\pi\)
\(38\) 6.05283 29.8162i 0.159285 0.784636i
\(39\) 0 0
\(40\) −39.5676 27.1190i −0.989189 0.677975i
\(41\) 21.9026i 0.534210i 0.963667 + 0.267105i \(0.0860670\pi\)
−0.963667 + 0.267105i \(0.913933\pi\)
\(42\) 0 0
\(43\) 48.7016 48.7016i 1.13260 1.13260i 0.142851 0.989744i \(-0.454373\pi\)
0.989744 0.142851i \(-0.0456270\pi\)
\(44\) −18.2742 45.1187i −0.415324 1.02543i
\(45\) 0 0
\(46\) 18.2222 + 27.5051i 0.396135 + 0.597937i
\(47\) 70.7760i 1.50587i −0.658094 0.752936i \(-0.728637\pi\)
0.658094 0.752936i \(-0.271363\pi\)
\(48\) 0 0
\(49\) −48.9312 −0.998597
\(50\) 18.2630 12.0993i 0.365259 0.241986i
\(51\) 0 0
\(52\) −33.9684 83.8672i −0.653239 1.61283i
\(53\) −52.8193 52.8193i −0.996590 0.996590i 0.00340427 0.999994i \(-0.498916\pi\)
−0.999994 + 0.00340427i \(0.998916\pi\)
\(54\) 0 0
\(55\) 72.9715 1.32675
\(56\) −2.06218 + 0.384952i −0.0368247 + 0.00687415i
\(57\) 0 0
\(58\) 71.9366 + 14.6035i 1.24029 + 0.251784i
\(59\) −61.7726 + 61.7726i −1.04699 + 1.04699i −0.0481541 + 0.998840i \(0.515334\pi\)
−0.998840 + 0.0481541i \(0.984666\pi\)
\(60\) 0 0
\(61\) −22.9004 + 22.9004i −0.375416 + 0.375416i −0.869445 0.494029i \(-0.835524\pi\)
0.494029 + 0.869445i \(0.335524\pi\)
\(62\) −77.0411 + 51.0400i −1.24260 + 0.823226i
\(63\) 0 0
\(64\) 59.6898 23.0895i 0.932654 0.360773i
\(65\) 135.640 2.08677
\(66\) 0 0
\(67\) −54.9939 54.9939i −0.820804 0.820804i 0.165419 0.986223i \(-0.447102\pi\)
−0.986223 + 0.165419i \(0.947102\pi\)
\(68\) 5.48309 12.9483i 0.0806337 0.190416i
\(69\) 0 0
\(70\) 0.625624 3.08182i 0.00893749 0.0440260i
\(71\) 84.2532 1.18666 0.593332 0.804958i \(-0.297812\pi\)
0.593332 + 0.804958i \(0.297812\pi\)
\(72\) 0 0
\(73\) 78.0341i 1.06896i 0.845181 + 0.534480i \(0.179493\pi\)
−0.845181 + 0.534480i \(0.820507\pi\)
\(74\) −1.68426 + 8.29663i −0.0227602 + 0.112117i
\(75\) 0 0
\(76\) −56.3983 + 22.8428i −0.742083 + 0.300563i
\(77\) 2.25653 2.25653i 0.0293056 0.0293056i
\(78\) 0 0
\(79\) 59.2887i 0.750490i 0.926926 + 0.375245i \(0.122441\pi\)
−0.926926 + 0.375245i \(0.877559\pi\)
\(80\) −1.50953 + 95.9263i −0.0188691 + 1.19908i
\(81\) 0 0
\(82\) 36.5181 24.1934i 0.445343 0.295041i
\(83\) 111.661 + 111.661i 1.34531 + 1.34531i 0.890676 + 0.454638i \(0.150231\pi\)
0.454638 + 0.890676i \(0.349769\pi\)
\(84\) 0 0
\(85\) 14.9047 + 14.9047i 0.175350 + 0.175350i
\(86\) −134.995 27.4047i −1.56971 0.318660i
\(87\) 0 0
\(88\) −55.0407 + 80.3063i −0.625463 + 0.912571i
\(89\) 34.5426i 0.388119i −0.980990 0.194060i \(-0.937834\pi\)
0.980990 0.194060i \(-0.0621655\pi\)
\(90\) 0 0
\(91\) 4.19447 4.19447i 0.0460931 0.0460931i
\(92\) 25.7311 60.7637i 0.279686 0.660475i
\(93\) 0 0
\(94\) −118.005 + 78.1784i −1.25537 + 0.831686i
\(95\) 91.2142i 0.960150i
\(96\) 0 0
\(97\) −66.0805 −0.681242 −0.340621 0.940201i \(-0.610637\pi\)
−0.340621 + 0.940201i \(0.610637\pi\)
\(98\) 54.0490 + 81.5829i 0.551520 + 0.832479i
\(99\) 0 0
\(100\) −40.3462 17.0850i −0.403462 0.170850i
\(101\) −25.5254 25.5254i −0.252727 0.252727i 0.569361 0.822088i \(-0.307191\pi\)
−0.822088 + 0.569361i \(0.807191\pi\)
\(102\) 0 0
\(103\) −14.2072 −0.137934 −0.0689670 0.997619i \(-0.521970\pi\)
−0.0689670 + 0.997619i \(0.521970\pi\)
\(104\) −102.310 + 149.274i −0.983754 + 1.43533i
\(105\) 0 0
\(106\) −29.7218 + 146.409i −0.280394 + 1.38122i
\(107\) 21.8489 21.8489i 0.204195 0.204195i −0.597600 0.801795i \(-0.703879\pi\)
0.801795 + 0.597600i \(0.203879\pi\)
\(108\) 0 0
\(109\) 17.8979 17.8979i 0.164201 0.164201i −0.620224 0.784425i \(-0.712958\pi\)
0.784425 + 0.620224i \(0.212958\pi\)
\(110\) −80.6036 121.665i −0.732760 1.10605i
\(111\) 0 0
\(112\) 2.91970 + 3.01305i 0.0260687 + 0.0269023i
\(113\) 174.546 1.54465 0.772325 0.635227i \(-0.219093\pi\)
0.772325 + 0.635227i \(0.219093\pi\)
\(114\) 0 0
\(115\) 69.9450 + 69.9450i 0.608217 + 0.608217i
\(116\) −55.1121 136.070i −0.475104 1.17302i
\(117\) 0 0
\(118\) 171.227 + 34.7599i 1.45107 + 0.294575i
\(119\) 0.921813 0.00774632
\(120\) 0 0
\(121\) 27.1029i 0.223991i
\(122\) 63.4773 + 12.8862i 0.520306 + 0.105625i
\(123\) 0 0
\(124\) 170.198 + 72.0722i 1.37256 + 0.581227i
\(125\) −59.5553 + 59.5553i −0.476442 + 0.476442i
\(126\) 0 0
\(127\) 45.3438i 0.357037i −0.983937 0.178519i \(-0.942869\pi\)
0.983937 0.178519i \(-0.0571305\pi\)
\(128\) −104.430 74.0163i −0.815858 0.578252i
\(129\) 0 0
\(130\) −149.827 226.153i −1.15252 1.73964i
\(131\) −32.6213 32.6213i −0.249017 0.249017i 0.571550 0.820567i \(-0.306342\pi\)
−0.820567 + 0.571550i \(0.806342\pi\)
\(132\) 0 0
\(133\) −2.82066 2.82066i −0.0212080 0.0212080i
\(134\) −30.9454 + 152.437i −0.230936 + 1.13759i
\(135\) 0 0
\(136\) −27.6452 + 5.16059i −0.203274 + 0.0379455i
\(137\) 115.159i 0.840577i 0.907390 + 0.420289i \(0.138071\pi\)
−0.907390 + 0.420289i \(0.861929\pi\)
\(138\) 0 0
\(139\) −122.841 + 122.841i −0.883748 + 0.883748i −0.993913 0.110165i \(-0.964862\pi\)
0.110165 + 0.993913i \(0.464862\pi\)
\(140\) −5.82936 + 2.36104i −0.0416383 + 0.0168646i
\(141\) 0 0
\(142\) −93.0652 140.475i −0.655389 0.989261i
\(143\) 275.296i 1.92514i
\(144\) 0 0
\(145\) 220.070 1.51772
\(146\) 130.106 86.1957i 0.891137 0.590382i
\(147\) 0 0
\(148\) 15.6934 6.35622i 0.106036 0.0429474i
\(149\) −99.9710 99.9710i −0.670946 0.670946i 0.286988 0.957934i \(-0.407346\pi\)
−0.957934 + 0.286988i \(0.907346\pi\)
\(150\) 0 0
\(151\) −222.762 −1.47525 −0.737623 0.675212i \(-0.764052\pi\)
−0.737623 + 0.675212i \(0.764052\pi\)
\(152\) 100.383 + 68.8008i 0.660413 + 0.452637i
\(153\) 0 0
\(154\) −6.25485 1.26977i −0.0406159 0.00824524i
\(155\) −195.914 + 195.914i −1.26396 + 1.26396i
\(156\) 0 0
\(157\) 45.9080 45.9080i 0.292408 0.292408i −0.545623 0.838031i \(-0.683707\pi\)
0.838031 + 0.545623i \(0.183707\pi\)
\(158\) 98.8519 65.4898i 0.625645 0.414492i
\(159\) 0 0
\(160\) 161.605 103.442i 1.01003 0.646515i
\(161\) 4.32588 0.0268689
\(162\) 0 0
\(163\) 37.3289 + 37.3289i 0.229012 + 0.229012i 0.812280 0.583268i \(-0.198226\pi\)
−0.583268 + 0.812280i \(0.698226\pi\)
\(164\) −80.6752 34.1628i −0.491922 0.208310i
\(165\) 0 0
\(166\) 62.8325 309.512i 0.378509 1.86453i
\(167\) 71.6232 0.428882 0.214441 0.976737i \(-0.431207\pi\)
0.214441 + 0.976737i \(0.431207\pi\)
\(168\) 0 0
\(169\) 342.723i 2.02795i
\(170\) 8.38700 41.3142i 0.0493353 0.243025i
\(171\) 0 0
\(172\) 103.423 + 255.348i 0.601295 + 1.48458i
\(173\) −100.398 + 100.398i −0.580334 + 0.580334i −0.934995 0.354661i \(-0.884596\pi\)
0.354661 + 0.934995i \(0.384596\pi\)
\(174\) 0 0
\(175\) 2.87232i 0.0164133i
\(176\) 194.692 + 3.06373i 1.10620 + 0.0174076i
\(177\) 0 0
\(178\) −57.5928 + 38.1554i −0.323555 + 0.214356i
\(179\) 64.4199 + 64.4199i 0.359888 + 0.359888i 0.863771 0.503884i \(-0.168096\pi\)
−0.503884 + 0.863771i \(0.668096\pi\)
\(180\) 0 0
\(181\) −79.0033 79.0033i −0.436482 0.436482i 0.454344 0.890826i \(-0.349874\pi\)
−0.890826 + 0.454344i \(0.849874\pi\)
\(182\) −11.6266 2.36026i −0.0638824 0.0129685i
\(183\) 0 0
\(184\) −129.733 + 24.2177i −0.705073 + 0.131618i
\(185\) 25.3812i 0.137196i
\(186\) 0 0
\(187\) 30.2506 30.2506i 0.161768 0.161768i
\(188\) 260.693 + 110.394i 1.38667 + 0.587200i
\(189\) 0 0
\(190\) −152.081 + 100.754i −0.800427 + 0.530286i
\(191\) 304.422i 1.59383i 0.604089 + 0.796917i \(0.293537\pi\)
−0.604089 + 0.796917i \(0.706463\pi\)
\(192\) 0 0
\(193\) 253.689 1.31445 0.657225 0.753695i \(-0.271730\pi\)
0.657225 + 0.753695i \(0.271730\pi\)
\(194\) 72.9919 + 110.176i 0.376247 + 0.567917i
\(195\) 0 0
\(196\) 76.3210 180.231i 0.389393 0.919548i
\(197\) −89.4218 89.4218i −0.453918 0.453918i 0.442735 0.896653i \(-0.354008\pi\)
−0.896653 + 0.442735i \(0.854008\pi\)
\(198\) 0 0
\(199\) 117.278 0.589339 0.294670 0.955599i \(-0.404790\pi\)
0.294670 + 0.955599i \(0.404790\pi\)
\(200\) 16.0802 + 86.1411i 0.0804008 + 0.430705i
\(201\) 0 0
\(202\) −14.3633 + 70.7536i −0.0711056 + 0.350265i
\(203\) 6.80533 6.80533i 0.0335238 0.0335238i
\(204\) 0 0
\(205\) 92.8650 92.8650i 0.453000 0.453000i
\(206\) 15.6931 + 23.6876i 0.0761802 + 0.114988i
\(207\) 0 0
\(208\) 361.896 + 5.69491i 1.73988 + 0.0273794i
\(209\) −185.128 −0.885781
\(210\) 0 0
\(211\) −80.8941 80.8941i −0.383384 0.383384i 0.488936 0.872320i \(-0.337385\pi\)
−0.872320 + 0.488936i \(0.837385\pi\)
\(212\) 276.938 112.167i 1.30631 0.529090i
\(213\) 0 0
\(214\) −60.5626 12.2945i −0.283003 0.0574510i
\(215\) −412.981 −1.92084
\(216\) 0 0
\(217\) 12.1167i 0.0558373i
\(218\) −49.6109 10.0713i −0.227573 0.0461984i
\(219\) 0 0
\(220\) −113.818 + 268.780i −0.517355 + 1.22173i
\(221\) 56.2303 56.2303i 0.254436 0.254436i
\(222\) 0 0
\(223\) 263.109i 1.17986i 0.807453 + 0.589931i \(0.200845\pi\)
−0.807453 + 0.589931i \(0.799155\pi\)
\(224\) 1.79859 8.19619i 0.00802943 0.0365901i
\(225\) 0 0
\(226\) −192.801 291.019i −0.853103 1.28770i
\(227\) −112.085 112.085i −0.493765 0.493765i 0.415725 0.909490i \(-0.363528\pi\)
−0.909490 + 0.415725i \(0.863528\pi\)
\(228\) 0 0
\(229\) 100.869 + 100.869i 0.440477 + 0.440477i 0.892172 0.451695i \(-0.149180\pi\)
−0.451695 + 0.892172i \(0.649180\pi\)
\(230\) 39.3585 193.880i 0.171124 0.842955i
\(231\) 0 0
\(232\) −165.994 + 242.190i −0.715490 + 1.04392i
\(233\) 325.669i 1.39772i −0.715259 0.698860i \(-0.753691\pi\)
0.715259 0.698860i \(-0.246309\pi\)
\(234\) 0 0
\(235\) −300.084 + 300.084i −1.27695 + 1.27695i
\(236\) −131.180 323.881i −0.555849 1.37238i
\(237\) 0 0
\(238\) −1.01823 1.53694i −0.00427826 0.00645771i
\(239\) 25.2269i 0.105552i 0.998606 + 0.0527760i \(0.0168069\pi\)
−0.998606 + 0.0527760i \(0.983193\pi\)
\(240\) 0 0
\(241\) −305.987 −1.26966 −0.634828 0.772653i \(-0.718929\pi\)
−0.634828 + 0.772653i \(0.718929\pi\)
\(242\) −45.1885 + 29.9376i −0.186730 + 0.123709i
\(243\) 0 0
\(244\) −48.6313 120.070i −0.199309 0.492088i
\(245\) 207.464 + 207.464i 0.846792 + 0.846792i
\(246\) 0 0
\(247\) −344.119 −1.39319
\(248\) −67.8331 363.381i −0.273521 1.46524i
\(249\) 0 0
\(250\) 165.081 + 33.5122i 0.660322 + 0.134049i
\(251\) 99.5293 99.5293i 0.396531 0.396531i −0.480476 0.877008i \(-0.659536\pi\)
0.877008 + 0.480476i \(0.159536\pi\)
\(252\) 0 0
\(253\) 141.960 141.960i 0.561108 0.561108i
\(254\) −75.6015 + 50.0863i −0.297644 + 0.197190i
\(255\) 0 0
\(256\) −8.05500 + 255.873i −0.0314648 + 0.999505i
\(257\) −265.635 −1.03360 −0.516799 0.856107i \(-0.672876\pi\)
−0.516799 + 0.856107i \(0.672876\pi\)
\(258\) 0 0
\(259\) 0.784876 + 0.784876i 0.00303041 + 0.00303041i
\(260\) −211.566 + 499.612i −0.813717 + 1.92159i
\(261\) 0 0
\(262\) −18.3562 + 90.4225i −0.0700619 + 0.345124i
\(263\) 206.692 0.785901 0.392950 0.919560i \(-0.371454\pi\)
0.392950 + 0.919560i \(0.371454\pi\)
\(264\) 0 0
\(265\) 447.898i 1.69018i
\(266\) −1.58721 + 7.81856i −0.00596694 + 0.0293931i
\(267\) 0 0
\(268\) 288.340 116.785i 1.07589 0.435765i
\(269\) 8.03470 8.03470i 0.0298688 0.0298688i −0.692015 0.721883i \(-0.743277\pi\)
0.721883 + 0.692015i \(0.243277\pi\)
\(270\) 0 0
\(271\) 216.666i 0.799507i 0.916623 + 0.399754i \(0.130904\pi\)
−0.916623 + 0.399754i \(0.869096\pi\)
\(272\) 39.1409 + 40.3924i 0.143900 + 0.148502i
\(273\) 0 0
\(274\) 192.004 127.204i 0.700746 0.464247i
\(275\) −94.2595 94.2595i −0.342762 0.342762i
\(276\) 0 0
\(277\) 65.0909 + 65.0909i 0.234985 + 0.234985i 0.814770 0.579785i \(-0.196863\pi\)
−0.579785 + 0.814770i \(0.696863\pi\)
\(278\) 340.502 + 69.1235i 1.22483 + 0.248646i
\(279\) 0 0
\(280\) 10.3756 + 7.11130i 0.0370558 + 0.0253975i
\(281\) 403.952i 1.43755i 0.695242 + 0.718776i \(0.255297\pi\)
−0.695242 + 0.718776i \(0.744703\pi\)
\(282\) 0 0
\(283\) 245.705 245.705i 0.868214 0.868214i −0.124061 0.992275i \(-0.539592\pi\)
0.992275 + 0.124061i \(0.0395917\pi\)
\(284\) −131.415 + 310.335i −0.462728 + 1.09273i
\(285\) 0 0
\(286\) −458.999 + 304.089i −1.60489 + 1.06325i
\(287\) 5.74342i 0.0200119i
\(288\) 0 0
\(289\) −276.642 −0.957240
\(290\) −243.087 366.922i −0.838231 1.26525i
\(291\) 0 0
\(292\) −287.428 121.715i −0.984342 0.416831i
\(293\) 67.6849 + 67.6849i 0.231007 + 0.231007i 0.813113 0.582106i \(-0.197771\pi\)
−0.582106 + 0.813113i \(0.697771\pi\)
\(294\) 0 0
\(295\) 523.821 1.77566
\(296\) −27.9324 19.1445i −0.0943664 0.0646773i
\(297\) 0 0
\(298\) −56.2544 + 277.108i −0.188773 + 0.929894i
\(299\) 263.878 263.878i 0.882534 0.882534i
\(300\) 0 0
\(301\) −12.7708 + 12.7708i −0.0424279 + 0.0424279i
\(302\) 246.061 + 371.411i 0.814772 + 1.22984i
\(303\) 0 0
\(304\) 3.82966 243.365i 0.0125976 0.800541i
\(305\) 194.191 0.636692
\(306\) 0 0
\(307\) −4.98162 4.98162i −0.0162268 0.0162268i 0.698947 0.715174i \(-0.253652\pi\)
−0.715174 + 0.698947i \(0.753652\pi\)
\(308\) 4.79197 + 11.8313i 0.0155584 + 0.0384132i
\(309\) 0 0
\(310\) 543.052 + 110.242i 1.75178 + 0.355620i
\(311\) 380.390 1.22312 0.611560 0.791198i \(-0.290542\pi\)
0.611560 + 0.791198i \(0.290542\pi\)
\(312\) 0 0
\(313\) 145.761i 0.465691i −0.972514 0.232845i \(-0.925196\pi\)
0.972514 0.232845i \(-0.0748036\pi\)
\(314\) −127.252 25.8328i −0.405261 0.0822699i
\(315\) 0 0
\(316\) −218.382 92.4762i −0.691082 0.292646i
\(317\) 283.175 283.175i 0.893295 0.893295i −0.101537 0.994832i \(-0.532376\pi\)
0.994832 + 0.101537i \(0.0323759\pi\)
\(318\) 0 0
\(319\) 446.654i 1.40017i
\(320\) −350.977 155.182i −1.09680 0.484944i
\(321\) 0 0
\(322\) −4.77833 7.21254i −0.0148395 0.0223992i
\(323\) −37.8132 37.8132i −0.117069 0.117069i
\(324\) 0 0
\(325\) −175.211 175.211i −0.539110 0.539110i
\(326\) 21.0052 103.472i 0.0644333 0.317397i
\(327\) 0 0
\(328\) 32.1535 + 172.245i 0.0980288 + 0.525139i
\(329\) 18.5593i 0.0564111i
\(330\) 0 0
\(331\) 105.963 105.963i 0.320131 0.320131i −0.528687 0.848817i \(-0.677315\pi\)
0.848817 + 0.528687i \(0.177315\pi\)
\(332\) −585.453 + 237.124i −1.76341 + 0.714227i
\(333\) 0 0
\(334\) −79.1143 119.417i −0.236869 0.357537i
\(335\) 466.338i 1.39205i
\(336\) 0 0
\(337\) 249.581 0.740595 0.370298 0.928913i \(-0.379256\pi\)
0.370298 + 0.928913i \(0.379256\pi\)
\(338\) −571.421 + 378.568i −1.69059 + 1.12002i
\(339\) 0 0
\(340\) −78.1473 + 31.6517i −0.229845 + 0.0930932i
\(341\) 397.627 + 397.627i 1.16606 + 1.16606i
\(342\) 0 0
\(343\) 25.6801 0.0748690
\(344\) 311.502 454.492i 0.905529 1.32120i
\(345\) 0 0
\(346\) 278.291 + 56.4945i 0.804310 + 0.163279i
\(347\) 297.586 297.586i 0.857597 0.857597i −0.133458 0.991054i \(-0.542608\pi\)
0.991054 + 0.133458i \(0.0426081\pi\)
\(348\) 0 0
\(349\) −288.797 + 288.797i −0.827498 + 0.827498i −0.987170 0.159672i \(-0.948956\pi\)
0.159672 + 0.987170i \(0.448956\pi\)
\(350\) −4.78901 + 3.17274i −0.0136829 + 0.00906497i
\(351\) 0 0
\(352\) −209.947 327.994i −0.596439 0.931800i
\(353\) −255.362 −0.723404 −0.361702 0.932294i \(-0.617804\pi\)
−0.361702 + 0.932294i \(0.617804\pi\)
\(354\) 0 0
\(355\) −357.226 357.226i −1.00627 1.00627i
\(356\) 127.233 + 53.8782i 0.357396 + 0.151343i
\(357\) 0 0
\(358\) 36.2495 178.565i 0.101256 0.498784i
\(359\) −381.798 −1.06350 −0.531752 0.846900i \(-0.678466\pi\)
−0.531752 + 0.846900i \(0.678466\pi\)
\(360\) 0 0
\(361\) 129.590i 0.358975i
\(362\) −44.4557 + 218.988i −0.122806 + 0.604940i
\(363\) 0 0
\(364\) 8.90738 + 21.9921i 0.0244708 + 0.0604179i
\(365\) 330.857 330.857i 0.906459 0.906459i
\(366\) 0 0
\(367\) 18.6026i 0.0506884i 0.999679 + 0.0253442i \(0.00806817\pi\)
−0.999679 + 0.0253442i \(0.991932\pi\)
\(368\) 183.680 + 189.554i 0.499131 + 0.515092i
\(369\) 0 0
\(370\) 42.3180 28.0358i 0.114373 0.0757726i
\(371\) 13.8506 + 13.8506i 0.0373330 + 0.0373330i
\(372\) 0 0
\(373\) 150.079 + 150.079i 0.402357 + 0.402357i 0.879063 0.476706i \(-0.158169\pi\)
−0.476706 + 0.879063i \(0.658169\pi\)
\(374\) −83.8514 17.0222i −0.224202 0.0455140i
\(375\) 0 0
\(376\) −103.901 556.593i −0.276331 1.48030i
\(377\) 830.245i 2.20224i
\(378\) 0 0
\(379\) 379.359 379.359i 1.00095 1.00095i 0.000948851 1.00000i \(-0.499698\pi\)
1.00000 0.000948851i \(-0.000302029\pi\)
\(380\) 335.975 + 142.272i 0.884144 + 0.374401i
\(381\) 0 0
\(382\) 507.562 336.262i 1.32870 0.880267i
\(383\) 427.421i 1.11598i 0.829847 + 0.557991i \(0.188428\pi\)
−0.829847 + 0.557991i \(0.811572\pi\)
\(384\) 0 0
\(385\) −19.1350 −0.0497012
\(386\) −280.222 422.975i −0.725964 1.09579i
\(387\) 0 0
\(388\) 103.070 243.398i 0.265644 0.627315i
\(389\) 236.247 + 236.247i 0.607318 + 0.607318i 0.942244 0.334926i \(-0.108711\pi\)
−0.334926 + 0.942244i \(0.608711\pi\)
\(390\) 0 0
\(391\) 57.9920 0.148317
\(392\) −384.803 + 71.8320i −0.981640 + 0.183245i
\(393\) 0 0
\(394\) −50.3183 + 247.867i −0.127711 + 0.629105i
\(395\) 251.379 251.379i 0.636402 0.636402i
\(396\) 0 0
\(397\) −427.593 + 427.593i −1.07706 + 1.07706i −0.0802895 + 0.996772i \(0.525584\pi\)
−0.996772 + 0.0802895i \(0.974416\pi\)
\(398\) −129.545 195.538i −0.325489 0.491302i
\(399\) 0 0
\(400\) 125.861 121.961i 0.314652 0.304902i
\(401\) −638.396 −1.59201 −0.796005 0.605290i \(-0.793057\pi\)
−0.796005 + 0.605290i \(0.793057\pi\)
\(402\) 0 0
\(403\) 739.115 + 739.115i 1.83403 + 1.83403i
\(404\) 133.833 54.2058i 0.331270 0.134173i
\(405\) 0 0
\(406\) −18.8636 3.82940i −0.0464621 0.00943203i
\(407\) 51.5137 0.126569
\(408\) 0 0
\(409\) 273.582i 0.668905i 0.942413 + 0.334453i \(0.108551\pi\)
−0.942413 + 0.334453i \(0.891449\pi\)
\(410\) −257.411 52.2558i −0.627833 0.127453i
\(411\) 0 0
\(412\) 22.1598 52.3302i 0.0537860 0.127015i
\(413\) 16.1984 16.1984i 0.0392212 0.0392212i
\(414\) 0 0
\(415\) 946.865i 2.28160i
\(416\) −390.252 609.679i −0.938105 1.46557i
\(417\) 0 0
\(418\) 204.491 + 308.664i 0.489213 + 0.738430i
\(419\) −150.314 150.314i −0.358745 0.358745i 0.504606 0.863350i \(-0.331638\pi\)
−0.863350 + 0.504606i \(0.831638\pi\)
\(420\) 0 0
\(421\) −220.826 220.826i −0.524527 0.524527i 0.394408 0.918935i \(-0.370950\pi\)
−0.918935 + 0.394408i \(0.870950\pi\)
\(422\) −45.5196 + 224.229i −0.107866 + 0.531349i
\(423\) 0 0
\(424\) −492.919 337.839i −1.16254 0.796790i
\(425\) 38.5058i 0.0906018i
\(426\) 0 0
\(427\) 6.00507 6.00507i 0.0140634 0.0140634i
\(428\) 46.3983 + 114.556i 0.108407 + 0.267655i
\(429\) 0 0
\(430\) 456.174 + 688.561i 1.06087 + 1.60131i
\(431\) 463.722i 1.07592i 0.842970 + 0.537960i \(0.180805\pi\)
−0.842970 + 0.537960i \(0.819195\pi\)
\(432\) 0 0
\(433\) −310.114 −0.716199 −0.358099 0.933683i \(-0.616575\pi\)
−0.358099 + 0.933683i \(0.616575\pi\)
\(434\) 20.2021 13.3840i 0.0465487 0.0308387i
\(435\) 0 0
\(436\) 38.0079 + 93.8407i 0.0871741 + 0.215231i
\(437\) −177.450 177.450i −0.406064 0.406064i
\(438\) 0 0
\(439\) 89.9103 0.204807 0.102404 0.994743i \(-0.467347\pi\)
0.102404 + 0.994743i \(0.467347\pi\)
\(440\) 573.859 107.124i 1.30422 0.243463i
\(441\) 0 0
\(442\) −155.864 31.6412i −0.352633 0.0715864i
\(443\) 78.9267 78.9267i 0.178164 0.178164i −0.612391 0.790555i \(-0.709792\pi\)
0.790555 + 0.612391i \(0.209792\pi\)
\(444\) 0 0
\(445\) −146.458 + 146.458i −0.329118 + 0.329118i
\(446\) 438.682 290.628i 0.983591 0.651632i
\(447\) 0 0
\(448\) −15.6522 + 6.05465i −0.0349379 + 0.0135148i
\(449\) −187.048 −0.416587 −0.208294 0.978066i \(-0.566791\pi\)
−0.208294 + 0.978066i \(0.566791\pi\)
\(450\) 0 0
\(451\) −188.479 188.479i −0.417913 0.417913i
\(452\) −272.249 + 642.914i −0.602321 + 1.42238i
\(453\) 0 0
\(454\) −63.0709 + 310.686i −0.138923 + 0.684331i
\(455\) −35.5683 −0.0781722
\(456\) 0 0
\(457\) 153.318i 0.335489i 0.985831 + 0.167744i \(0.0536483\pi\)
−0.985831 + 0.167744i \(0.946352\pi\)
\(458\) 56.7599 279.598i 0.123930 0.610477i
\(459\) 0 0
\(460\) −366.730 + 148.535i −0.797239 + 0.322903i
\(461\) −99.6025 + 99.6025i −0.216057 + 0.216057i −0.806835 0.590777i \(-0.798821\pi\)
0.590777 + 0.806835i \(0.298821\pi\)
\(462\) 0 0
\(463\) 255.682i 0.552229i 0.961125 + 0.276114i \(0.0890469\pi\)
−0.961125 + 0.276114i \(0.910953\pi\)
\(464\) 587.158 + 9.23971i 1.26543 + 0.0199132i
\(465\) 0 0
\(466\) −542.986 + 359.730i −1.16521 + 0.771954i
\(467\) −285.533 285.533i −0.611420 0.611420i 0.331896 0.943316i \(-0.392312\pi\)
−0.943316 + 0.331896i \(0.892312\pi\)
\(468\) 0 0
\(469\) 14.4208 + 14.4208i 0.0307480 + 0.0307480i
\(470\) 831.798 + 168.859i 1.76978 + 0.359275i
\(471\) 0 0
\(472\) −395.106 + 576.473i −0.837089 + 1.22134i
\(473\) 838.185i 1.77206i
\(474\) 0 0
\(475\) −117.824 + 117.824i −0.248051 + 0.248051i
\(476\) −1.43781 + 3.39537i −0.00302060 + 0.00713313i
\(477\) 0 0
\(478\) 42.0608 27.8654i 0.0879933 0.0582959i
\(479\) 418.575i 0.873852i −0.899498 0.436926i \(-0.856067\pi\)
0.899498 0.436926i \(-0.143933\pi\)
\(480\) 0 0
\(481\) 95.7543 0.199073
\(482\) 337.991 + 510.172i 0.701225 + 1.05845i
\(483\) 0 0
\(484\) 99.8297 + 42.2740i 0.206260 + 0.0873430i
\(485\) 280.175 + 280.175i 0.577681 + 0.577681i
\(486\) 0 0
\(487\) −162.560 −0.333800 −0.166900 0.985974i \(-0.553376\pi\)
−0.166900 + 0.985974i \(0.553376\pi\)
\(488\) −146.474 + 213.711i −0.300152 + 0.437931i
\(489\) 0 0
\(490\) 116.741 575.067i 0.238248 1.17361i
\(491\) −559.393 + 559.393i −1.13929 + 1.13929i −0.150715 + 0.988577i \(0.548158\pi\)
−0.988577 + 0.150715i \(0.951842\pi\)
\(492\) 0 0
\(493\) 91.2309 91.2309i 0.185052 0.185052i
\(494\) 380.110 + 573.748i 0.769454 + 1.16143i
\(495\) 0 0
\(496\) −530.936 + 514.485i −1.07043 + 1.03727i
\(497\) −22.0933 −0.0444534
\(498\) 0 0
\(499\) 247.957 + 247.957i 0.496908 + 0.496908i 0.910474 0.413566i \(-0.135717\pi\)
−0.413566 + 0.910474i \(0.635717\pi\)
\(500\) −126.472 312.256i −0.252943 0.624511i
\(501\) 0 0
\(502\) −275.884 56.0059i −0.549570 0.111565i
\(503\) −260.971 −0.518829 −0.259415 0.965766i \(-0.583530\pi\)
−0.259415 + 0.965766i \(0.583530\pi\)
\(504\) 0 0
\(505\) 216.451i 0.428616i
\(506\) −393.498 79.8820i −0.777664 0.157870i
\(507\) 0 0
\(508\) 167.017 + 70.7254i 0.328774 + 0.139223i
\(509\) −149.941 + 149.941i −0.294580 + 0.294580i −0.838886 0.544306i \(-0.816793\pi\)
0.544306 + 0.838886i \(0.316793\pi\)
\(510\) 0 0
\(511\) 20.4625i 0.0400441i
\(512\) 435.514 269.205i 0.850614 0.525791i
\(513\) 0 0
\(514\) 293.417 + 442.892i 0.570851 + 0.861657i
\(515\) 60.2372 + 60.2372i 0.116965 + 0.116965i
\(516\) 0 0
\(517\) 609.049 + 609.049i 1.17805 + 1.17805i
\(518\) 0.441655 2.17559i 0.000852616 0.00419998i
\(519\) 0 0
\(520\) 1066.70 199.123i 2.05134 0.382928i
\(521\) 391.686i 0.751797i 0.926661 + 0.375899i \(0.122666\pi\)
−0.926661 + 0.375899i \(0.877334\pi\)
\(522\) 0 0
\(523\) −128.962 + 128.962i −0.246582 + 0.246582i −0.819566 0.572985i \(-0.805786\pi\)
0.572985 + 0.819566i \(0.305786\pi\)
\(524\) 171.037 69.2745i 0.326407 0.132203i
\(525\) 0 0
\(526\) −228.310 344.617i −0.434049 0.655165i
\(527\) 162.434i 0.308224i
\(528\) 0 0
\(529\) −256.855 −0.485548
\(530\) 746.779 494.743i 1.40902 0.933478i
\(531\) 0 0
\(532\) 14.7891 5.98996i 0.0277990 0.0112593i
\(533\) −350.347 350.347i −0.657311 0.657311i
\(534\) 0 0
\(535\) −185.274 −0.346307
\(536\) −513.212 351.748i −0.957486 0.656247i
\(537\) 0 0
\(538\) −22.2713 4.52118i −0.0413965 0.00840369i
\(539\) 421.069 421.069i 0.781204 0.781204i
\(540\) 0 0
\(541\) 71.0166 71.0166i 0.131269 0.131269i −0.638420 0.769689i \(-0.720411\pi\)
0.769689 + 0.638420i \(0.220411\pi\)
\(542\) 361.247 239.328i 0.666508 0.441564i
\(543\) 0 0
\(544\) 24.1116 109.877i 0.0443227 0.201979i
\(545\) −151.771 −0.278478
\(546\) 0 0
\(547\) −672.846 672.846i −1.23007 1.23007i −0.963938 0.266128i \(-0.914255\pi\)
−0.266128 0.963938i \(-0.585745\pi\)
\(548\) −424.172 179.621i −0.774037 0.327775i
\(549\) 0 0
\(550\) −53.0405 + 261.277i −0.0964372 + 0.475048i
\(551\) −558.316 −1.01328
\(552\) 0 0
\(553\) 15.5470i 0.0281140i
\(554\) 36.6271 180.425i 0.0661139 0.325676i
\(555\) 0 0
\(556\) −260.865 644.070i −0.469182 1.15840i
\(557\) −294.546 + 294.546i −0.528809 + 0.528809i −0.920217 0.391408i \(-0.871988\pi\)
0.391408 + 0.920217i \(0.371988\pi\)
\(558\) 0 0
\(559\) 1558.03i 2.78717i
\(560\) 0.395836 25.1543i 0.000706850 0.0449184i
\(561\) 0 0
\(562\) 673.508 446.201i 1.19841 0.793953i
\(563\) −613.943 613.943i −1.09048 1.09048i −0.995477 0.0950080i \(-0.969712\pi\)
−0.0950080 0.995477i \(-0.530288\pi\)
\(564\) 0 0
\(565\) −740.057 740.057i −1.30984 1.30984i
\(566\) −681.065 138.260i −1.20330 0.244275i
\(567\) 0 0
\(568\) 662.580 123.685i 1.16651 0.217756i
\(569\) 1044.74i 1.83610i −0.396460 0.918052i \(-0.629761\pi\)
0.396460 0.918052i \(-0.370239\pi\)
\(570\) 0 0
\(571\) 131.781 131.781i 0.230789 0.230789i −0.582233 0.813022i \(-0.697821\pi\)
0.813022 + 0.582233i \(0.197821\pi\)
\(572\) 1014.01 + 429.395i 1.77275 + 0.750691i
\(573\) 0 0
\(574\) −9.57599 + 6.34413i −0.0166829 + 0.0110525i
\(575\) 180.700i 0.314261i
\(576\) 0 0
\(577\) −114.453 −0.198359 −0.0991794 0.995070i \(-0.531622\pi\)
−0.0991794 + 0.995070i \(0.531622\pi\)
\(578\) 305.576 + 461.245i 0.528679 + 0.798002i
\(579\) 0 0
\(580\) −343.256 + 810.596i −0.591821 + 1.39758i
\(581\) −29.2804 29.2804i −0.0503965 0.0503965i
\(582\) 0 0
\(583\) 909.053 1.55927
\(584\) 114.556 + 613.672i 0.196157 + 1.05081i
\(585\) 0 0
\(586\) 38.0868 187.615i 0.0649945 0.320162i
\(587\) −308.249 + 308.249i −0.525125 + 0.525125i −0.919115 0.393990i \(-0.871095\pi\)
0.393990 + 0.919115i \(0.371095\pi\)
\(588\) 0 0
\(589\) 497.034 497.034i 0.843860 0.843860i
\(590\) −578.607 873.365i −0.980690 1.48028i
\(591\) 0 0
\(592\) −1.06564 + 67.7185i −0.00180007 + 0.114389i
\(593\) −646.173 −1.08967 −0.544834 0.838544i \(-0.683407\pi\)
−0.544834 + 0.838544i \(0.683407\pi\)
\(594\) 0 0
\(595\) −3.90840 3.90840i −0.00656874 0.00656874i
\(596\) 524.160 212.298i 0.879463 0.356205i
\(597\) 0 0
\(598\) −731.439 148.486i −1.22314 0.248304i
\(599\) 528.055 0.881561 0.440780 0.897615i \(-0.354702\pi\)
0.440780 + 0.897615i \(0.354702\pi\)
\(600\) 0 0
\(601\) 280.764i 0.467161i −0.972338 0.233580i \(-0.924956\pi\)
0.972338 0.233580i \(-0.0750442\pi\)
\(602\) 35.3992 + 7.18622i 0.0588027 + 0.0119372i
\(603\) 0 0
\(604\) 347.456 820.514i 0.575258 1.35847i
\(605\) −114.914 + 114.914i −0.189940 + 0.189940i
\(606\) 0 0
\(607\) 662.871i 1.09204i −0.837771 0.546022i \(-0.816141\pi\)
0.837771 0.546022i \(-0.183859\pi\)
\(608\) −409.991 + 262.433i −0.674328 + 0.431633i
\(609\) 0 0
\(610\) −214.502 323.774i −0.351642 0.530778i
\(611\) 1132.11 + 1132.11i 1.85288 + 1.85288i
\(612\) 0 0
\(613\) 128.389 + 128.389i 0.209443 + 0.209443i 0.804031 0.594588i \(-0.202685\pi\)
−0.594588 + 0.804031i \(0.702685\pi\)
\(614\) −2.80319 + 13.8085i −0.00456546 + 0.0224894i
\(615\) 0 0
\(616\) 14.4331 21.0584i 0.0234303 0.0341856i
\(617\) 20.8646i 0.0338162i −0.999857 0.0169081i \(-0.994618\pi\)
0.999857 0.0169081i \(-0.00538228\pi\)
\(618\) 0 0
\(619\) −472.367 + 472.367i −0.763113 + 0.763113i −0.976884 0.213771i \(-0.931425\pi\)
0.213771 + 0.976884i \(0.431425\pi\)
\(620\) −416.044 1027.20i −0.671038 1.65678i
\(621\) 0 0
\(622\) −420.175 634.224i −0.675523 1.01965i
\(623\) 9.05795i 0.0145393i
\(624\) 0 0
\(625\) 778.859 1.24617
\(626\) −243.027 + 161.006i −0.388222 + 0.257199i
\(627\) 0 0
\(628\) 97.4903 + 240.701i 0.155239 + 0.383282i
\(629\) 10.5219 + 10.5219i 0.0167280 + 0.0167280i
\(630\) 0 0
\(631\) −906.653 −1.43685 −0.718426 0.695604i \(-0.755137\pi\)
−0.718426 + 0.695604i \(0.755137\pi\)
\(632\) 87.0370 + 466.256i 0.137717 + 0.737746i
\(633\) 0 0
\(634\) −784.928 159.344i −1.23806 0.251332i
\(635\) −192.253 + 192.253i −0.302761 + 0.302761i
\(636\) 0 0
\(637\) 782.688 782.688i 1.22871 1.22871i
\(638\) −744.704 + 493.369i −1.16725 + 0.773306i
\(639\) 0 0
\(640\) 128.951 + 756.595i 0.201485 + 1.18218i
\(641\) 1125.11 1.75524 0.877622 0.479353i \(-0.159129\pi\)
0.877622 + 0.479353i \(0.159129\pi\)
\(642\) 0 0
\(643\) −607.794 607.794i −0.945247 0.945247i 0.0533302 0.998577i \(-0.483016\pi\)
−0.998577 + 0.0533302i \(0.983016\pi\)
\(644\) −6.74734 + 15.9338i −0.0104772 + 0.0247419i
\(645\) 0 0
\(646\) −21.2778 + 104.814i −0.0329377 + 0.162251i
\(647\) −383.377 −0.592545 −0.296273 0.955103i \(-0.595744\pi\)
−0.296273 + 0.955103i \(0.595744\pi\)
\(648\) 0 0
\(649\) 1063.15i 1.63813i
\(650\) −98.5923 + 485.664i −0.151680 + 0.747176i
\(651\) 0 0
\(652\) −195.720 + 79.2717i −0.300184 + 0.121582i
\(653\) 755.121 755.121i 1.15639 1.15639i 0.171141 0.985246i \(-0.445254\pi\)
0.985246 0.171141i \(-0.0547455\pi\)
\(654\) 0 0
\(655\) 276.622i 0.422324i
\(656\) 251.668 243.870i 0.383640 0.371753i
\(657\) 0 0
\(658\) 30.9438 20.5004i 0.0470271 0.0311556i
\(659\) 31.8233 + 31.8233i 0.0482902 + 0.0482902i 0.730840 0.682549i \(-0.239129\pi\)
−0.682549 + 0.730840i \(0.739129\pi\)
\(660\) 0 0
\(661\) 579.890 + 579.890i 0.877292 + 0.877292i 0.993254 0.115961i \(-0.0369949\pi\)
−0.115961 + 0.993254i \(0.536995\pi\)
\(662\) −293.718 59.6263i −0.443683 0.0900699i
\(663\) 0 0
\(664\) 1042.04 + 714.199i 1.56934 + 1.07560i
\(665\) 23.9187i 0.0359680i
\(666\) 0 0
\(667\) 428.129 428.129i 0.641872 0.641872i
\(668\) −111.715 + 263.814i −0.167238 + 0.394931i
\(669\) 0 0
\(670\) 777.524 515.112i 1.16048 0.768824i
\(671\) 394.130i 0.587377i
\(672\) 0 0
\(673\) 262.375 0.389859 0.194930 0.980817i \(-0.437552\pi\)
0.194930 + 0.980817i \(0.437552\pi\)
\(674\) −275.684 416.125i −0.409027 0.617396i
\(675\) 0 0
\(676\) 1262.37 + 534.566i 1.86741 + 0.790777i
\(677\) −574.436 574.436i −0.848502 0.848502i 0.141444 0.989946i \(-0.454825\pi\)
−0.989946 + 0.141444i \(0.954825\pi\)
\(678\) 0 0
\(679\) 17.3280 0.0255199
\(680\) 139.094 + 95.3327i 0.204549 + 0.140195i
\(681\) 0 0
\(682\) 223.748 1102.18i 0.328076 1.61610i
\(683\) −253.790 + 253.790i −0.371582 + 0.371582i −0.868053 0.496471i \(-0.834629\pi\)
0.496471 + 0.868053i \(0.334629\pi\)
\(684\) 0 0
\(685\) 488.264 488.264i 0.712794 0.712794i
\(686\) −28.3659 42.8163i −0.0413498 0.0624144i
\(687\) 0 0
\(688\) −1101.85 17.3391i −1.60153 0.0252022i
\(689\) 1689.76 2.45248
\(690\) 0 0
\(691\) 734.512 + 734.512i 1.06297 + 1.06297i 0.997879 + 0.0650902i \(0.0207335\pi\)
0.0650902 + 0.997879i \(0.479266\pi\)
\(692\) −213.205 526.398i −0.308099 0.760690i
\(693\) 0 0
\(694\) −824.875 167.454i −1.18858 0.241288i
\(695\) 1041.67 1.49880
\(696\) 0 0
\(697\) 76.9952i 0.110467i
\(698\) 800.513 + 162.508i 1.14687 + 0.232820i
\(699\) 0 0
\(700\) 10.5798 + 4.48013i 0.0151140 + 0.00640019i
\(701\) −745.410 + 745.410i −1.06335 + 1.06335i −0.0655005 + 0.997853i \(0.520864\pi\)
−0.997853 + 0.0655005i \(0.979136\pi\)
\(702\) 0 0
\(703\) 64.3920i 0.0915961i
\(704\) −314.958 + 712.342i −0.447383 + 1.01185i
\(705\) 0 0
\(706\) 282.070 + 425.764i 0.399533 + 0.603065i
\(707\) 6.69342 + 6.69342i 0.00946735 + 0.00946735i
\(708\) 0 0
\(709\) −809.881 809.881i −1.14229 1.14229i −0.988031 0.154255i \(-0.950702\pi\)
−0.154255 0.988031i \(-0.549298\pi\)
\(710\) −201.013 + 990.189i −0.283117 + 1.39463i
\(711\) 0 0
\(712\) −50.7093 271.648i −0.0712209 0.381529i
\(713\) 762.272i 1.06910i
\(714\) 0 0
\(715\) −1167.23 + 1167.23i −1.63249 + 1.63249i
\(716\) −337.761 + 136.802i −0.471734 + 0.191064i
\(717\) 0 0
\(718\) 421.730 + 636.570i 0.587368 + 0.886588i
\(719\) 662.400i 0.921280i −0.887587 0.460640i \(-0.847620\pi\)
0.887587 0.460640i \(-0.152380\pi\)
\(720\) 0 0
\(721\) 3.72549 0.00516711
\(722\) −216.065 + 143.144i −0.299259 + 0.198260i
\(723\) 0 0
\(724\) 414.224 167.771i 0.572132 0.231728i
\(725\) −284.271 284.271i −0.392098 0.392098i
\(726\) 0 0
\(727\) −1253.93 −1.72481 −0.862403 0.506222i \(-0.831042\pi\)
−0.862403 + 0.506222i \(0.831042\pi\)
\(728\) 26.8284 39.1435i 0.0368522 0.0537686i
\(729\) 0 0
\(730\) −917.100 186.176i −1.25630 0.255035i
\(731\) −171.203 + 171.203i −0.234204 + 0.234204i
\(732\) 0 0
\(733\) −509.300 + 509.300i −0.694816 + 0.694816i −0.963288 0.268472i \(-0.913481\pi\)
0.268472 + 0.963288i \(0.413481\pi\)
\(734\) 31.0161 20.5483i 0.0422563 0.0279949i
\(735\) 0 0
\(736\) 113.151 515.629i 0.153738 0.700583i
\(737\) 946.479 1.28423
\(738\) 0 0
\(739\) 818.847 + 818.847i 1.10805 + 1.10805i 0.993407 + 0.114640i \(0.0365716\pi\)
0.114640 + 0.993407i \(0.463428\pi\)
\(740\) −93.4882 39.5886i −0.126335 0.0534981i
\(741\) 0 0
\(742\) 7.79381 38.3922i 0.0105038 0.0517415i
\(743\) 1110.03 1.49398 0.746991 0.664834i \(-0.231498\pi\)
0.746991 + 0.664834i \(0.231498\pi\)
\(744\) 0 0
\(745\) 847.736i 1.13790i
\(746\) 84.4506 416.002i 0.113205 0.557644i
\(747\) 0 0
\(748\) 64.2403 + 158.608i 0.0858827 + 0.212042i
\(749\) −5.72933 + 5.72933i −0.00764931 + 0.00764931i
\(750\) 0 0
\(751\) 34.0597i 0.0453525i 0.999743 + 0.0226762i \(0.00721869\pi\)
−0.999743 + 0.0226762i \(0.992781\pi\)
\(752\) −813.239 + 788.040i −1.08143 + 1.04793i
\(753\) 0 0
\(754\) −1384.27 + 917.081i −1.83590 + 1.21629i
\(755\) 944.491 + 944.491i 1.25098 + 1.25098i
\(756\) 0 0
\(757\) 398.543 + 398.543i 0.526477 + 0.526477i 0.919520 0.393043i \(-0.128578\pi\)
−0.393043 + 0.919520i \(0.628578\pi\)
\(758\) −1051.54 213.468i −1.38726 0.281620i
\(759\) 0 0
\(760\) −133.904 717.323i −0.176190 0.943845i
\(761\) 903.338i 1.18704i 0.804819 + 0.593520i \(0.202262\pi\)
−0.804819 + 0.593520i \(0.797738\pi\)
\(762\) 0 0
\(763\) −4.69328 + 4.69328i −0.00615108 + 0.00615108i
\(764\) −1121.30 474.826i −1.46767 0.621500i
\(765\) 0 0
\(766\) 712.638 472.125i 0.930337 0.616352i
\(767\) 1976.19i 2.57652i
\(768\) 0 0
\(769\) −98.9621 −0.128689 −0.0643447 0.997928i \(-0.520496\pi\)
−0.0643447 + 0.997928i \(0.520496\pi\)
\(770\) 21.1363 + 31.9037i 0.0274498 + 0.0414334i
\(771\) 0 0
\(772\) −395.694 + 934.427i −0.512557 + 1.21040i
\(773\) 111.945 + 111.945i 0.144818 + 0.144818i 0.775799 0.630980i \(-0.217347\pi\)
−0.630980 + 0.775799i \(0.717347\pi\)
\(774\) 0 0
\(775\) 506.137 0.653080
\(776\) −519.667 + 97.0075i −0.669674 + 0.125010i
\(777\) 0 0
\(778\) 132.938 654.849i 0.170871 0.841709i
\(779\) −235.598 + 235.598i −0.302437 + 0.302437i
\(780\) 0 0
\(781\) −725.025 + 725.025i −0.928329 + 0.928329i
\(782\) −64.0574 96.6899i −0.0819148 0.123644i
\(783\) 0 0
\(784\) 544.815 + 562.236i 0.694917 + 0.717137i
\(785\) −389.291 −0.495913
\(786\) 0 0
\(787\) −163.931 163.931i −0.208299 0.208299i 0.595245 0.803544i \(-0.297055\pi\)
−0.803544 + 0.595245i \(0.797055\pi\)
\(788\) 468.850 189.896i 0.594987 0.240985i
\(789\) 0 0
\(790\) −696.794 141.453i −0.882017 0.179054i
\(791\) −45.7703 −0.0578638
\(792\) 0 0
\(793\) 732.614i 0.923852i
\(794\) 1185.24 + 240.610i 1.49275 + 0.303035i
\(795\) 0 0
\(796\) −182.926 + 431.979i −0.229807 + 0.542687i
\(797\) 271.277 271.277i 0.340373 0.340373i −0.516135 0.856507i \(-0.672630\pi\)
0.856507 + 0.516135i \(0.172630\pi\)
\(798\) 0 0
\(799\) 248.802i 0.311392i
\(800\) −342.370 75.1304i −0.427962 0.0939130i
\(801\) 0 0
\(802\) 705.166 + 1064.40i 0.879260 + 1.32718i
\(803\) −671.508 671.508i −0.836249 0.836249i
\(804\) 0 0
\(805\) −18.3414 18.3414i −0.0227843 0.0227843i
\(806\) 415.905 2048.74i 0.516011 2.54187i
\(807\) 0 0
\(808\) −238.208 163.264i −0.294811 0.202059i
\(809\) 1505.90i 1.86144i −0.365736 0.930718i \(-0.619183\pi\)
0.365736 0.930718i \(-0.380817\pi\)
\(810\) 0 0
\(811\) −492.677 + 492.677i −0.607493 + 0.607493i −0.942290 0.334797i \(-0.891332\pi\)
0.334797 + 0.942290i \(0.391332\pi\)
\(812\) 14.4518 + 35.6811i 0.0177978 + 0.0439423i
\(813\) 0 0
\(814\) −56.9015 85.8887i −0.0699036 0.105514i
\(815\) 316.542i 0.388396i
\(816\) 0 0
\(817\) 1047.73 1.28241
\(818\) 456.143 302.196i 0.557632 0.369433i
\(819\) 0 0
\(820\) 197.208 + 486.903i 0.240498 + 0.593784i
\(821\) −139.500 139.500i −0.169914 0.169914i 0.617027 0.786942i \(-0.288337\pi\)
−0.786942 + 0.617027i \(0.788337\pi\)
\(822\) 0 0
\(823\) −1262.09 −1.53353 −0.766763 0.641931i \(-0.778134\pi\)
−0.766763 + 0.641931i \(0.778134\pi\)
\(824\) −111.728 + 20.8564i −0.135592 + 0.0253112i
\(825\) 0 0
\(826\) −44.9000 9.11493i −0.0543584 0.0110350i
\(827\) 179.936 179.936i 0.217577 0.217577i −0.589900 0.807477i \(-0.700833\pi\)
0.807477 + 0.589900i \(0.200833\pi\)
\(828\) 0 0
\(829\) −144.901 + 144.901i −0.174790 + 0.174790i −0.789080 0.614290i \(-0.789443\pi\)
0.614290 + 0.789080i \(0.289443\pi\)
\(830\) −1578.71 + 1045.90i −1.90206 + 1.26012i
\(831\) 0 0
\(832\) −585.447 + 1324.11i −0.703663 + 1.59148i
\(833\) 172.010 0.206495
\(834\) 0 0
\(835\) −303.676 303.676i −0.363684 0.363684i
\(836\) 288.756 681.894i 0.345402 0.815663i
\(837\) 0 0
\(838\) −84.5827 + 416.653i −0.100934 + 0.497200i
\(839\) −1006.03 −1.19908 −0.599540 0.800345i \(-0.704650\pi\)
−0.599540 + 0.800345i \(0.704650\pi\)
\(840\) 0 0
\(841\) 506.033i 0.601703i
\(842\) −124.260 + 612.105i −0.147578 + 0.726965i
\(843\) 0 0
\(844\) 424.137 171.787i 0.502532 0.203539i
\(845\) −1453.11 + 1453.11i −1.71966 + 1.71966i
\(846\) 0 0
\(847\) 7.10706i 0.00839087i
\(848\) −18.8051 + 1195.02i −0.0221759 + 1.40922i
\(849\) 0 0
\(850\) −64.2006 + 42.5331i −0.0755301 + 0.0500390i
\(851\) 49.3772 + 49.3772i 0.0580225 + 0.0580225i
\(852\) 0 0
\(853\) 77.4150 + 77.4150i 0.0907561 + 0.0907561i 0.751027 0.660271i \(-0.229559\pi\)
−0.660271 + 0.751027i \(0.729559\pi\)
\(854\) −16.6454 3.37909i −0.0194911 0.00395678i
\(855\) 0 0
\(856\) 139.748 203.898i 0.163257 0.238198i
\(857\) 175.567i 0.204863i 0.994740 + 0.102431i \(0.0326622\pi\)
−0.994740 + 0.102431i \(0.967338\pi\)
\(858\) 0 0
\(859\) 1058.18 1058.18i 1.23188 1.23188i 0.268634 0.963242i \(-0.413428\pi\)
0.963242 0.268634i \(-0.0865722\pi\)
\(860\) 644.151 1521.16i 0.749013 1.76879i
\(861\) 0 0
\(862\) 773.162 512.222i 0.896939 0.594225i
\(863\) 569.219i 0.659581i 0.944054 + 0.329791i \(0.106978\pi\)
−0.944054 + 0.329791i \(0.893022\pi\)
\(864\) 0 0
\(865\) 851.355 0.984225
\(866\) 342.549 + 517.052i 0.395553 + 0.597058i
\(867\) 0 0
\(868\) −44.6302 18.8992i −0.0514173 0.0217732i
\(869\) −510.198 510.198i −0.587110 0.587110i
\(870\) 0 0
\(871\) 1759.33 2.01989
\(872\) 114.477 167.026i 0.131281 0.191544i
\(873\) 0 0
\(874\) −99.8524 + 491.872i −0.114248 + 0.562782i
\(875\) 15.6169 15.6169i 0.0178479 0.0178479i
\(876\) 0 0
\(877\) −166.695 + 166.695i −0.190074 + 0.190074i −0.795728 0.605654i \(-0.792912\pi\)
0.605654 + 0.795728i \(0.292912\pi\)
\(878\) −99.3141 149.907i −0.113114 0.170737i
\(879\) 0 0
\(880\) −812.486 838.466i −0.923279 0.952802i
\(881\) 1495.53 1.69754 0.848771 0.528761i \(-0.177343\pi\)
0.848771 + 0.528761i \(0.177343\pi\)
\(882\) 0 0
\(883\) 134.367 + 134.367i 0.152171 + 0.152171i 0.779087 0.626916i \(-0.215683\pi\)
−0.626916 + 0.779087i \(0.715683\pi\)
\(884\) 119.411 + 294.822i 0.135080 + 0.333509i
\(885\) 0 0
\(886\) −218.776 44.4126i −0.246926 0.0501271i
\(887\) −414.255 −0.467030 −0.233515 0.972353i \(-0.575023\pi\)
−0.233515 + 0.972353i \(0.575023\pi\)
\(888\) 0 0
\(889\) 11.8903i 0.0133749i
\(890\) 405.964 + 82.4127i 0.456139 + 0.0925985i
\(891\) 0 0
\(892\) −969.127 410.388i −1.08646 0.460076i
\(893\) 761.311 761.311i 0.852531 0.852531i
\(894\) 0 0
\(895\) 546.269i 0.610356i
\(896\) 27.3842 + 19.4090i 0.0305627 + 0.0216618i
\(897\) 0 0
\(898\) 206.611 + 311.864i 0.230079 + 0.347287i
\(899\) 1199.18 + 1199.18i 1.33390 + 1.33390i
\(900\) 0 0
\(901\) 185.678 + 185.678i 0.206080 + 0.206080i
\(902\) −106.058 + 522.442i −0.117581 + 0.579204i
\(903\) 0 0
\(904\) 1372.65 256.236i 1.51842 0.283447i
\(905\) 669.933i 0.740258i
\(906\) 0 0
\(907\) −312.683 + 312.683i −0.344744 + 0.344744i −0.858148 0.513403i \(-0.828385\pi\)
0.513403 + 0.858148i \(0.328385\pi\)
\(908\) 587.674 238.023i 0.647218 0.262140i
\(909\) 0 0
\(910\) 39.2884 + 59.3030i 0.0431741 + 0.0651681i
\(911\) 391.366i 0.429601i 0.976658 + 0.214800i \(0.0689101\pi\)
−0.976658 + 0.214800i \(0.931090\pi\)
\(912\) 0 0
\(913\) −1921.76 −2.10488
\(914\) 255.627 169.354i 0.279680 0.185289i
\(915\) 0 0
\(916\) −528.870 + 214.206i −0.577369 + 0.233850i
\(917\) 8.55413 + 8.55413i 0.00932838 + 0.00932838i
\(918\) 0 0
\(919\) 294.161 0.320088 0.160044 0.987110i \(-0.448836\pi\)
0.160044 + 0.987110i \(0.448836\pi\)
\(920\) 652.739 + 447.377i 0.709499 + 0.486280i
\(921\) 0 0
\(922\) 276.087 + 56.0470i 0.299443 + 0.0607885i
\(923\) −1347.69 + 1347.69i −1.46011 + 1.46011i
\(924\) 0 0
\(925\) 32.7857 32.7857i 0.0354440 0.0354440i
\(926\) 426.298 282.424i 0.460365 0.304993i
\(927\) 0 0
\(928\) −633.164 989.174i −0.682289 1.06592i
\(929\) −1015.40 −1.09300 −0.546501 0.837458i \(-0.684041\pi\)
−0.546501 + 0.837458i \(0.684041\pi\)
\(930\) 0 0
\(931\) −526.335 526.335i −0.565344 0.565344i
\(932\) 1199.55 + 507.965i 1.28708 + 0.545027i
\(933\) 0 0
\(934\) −160.672 + 791.466i −0.172025 + 0.847394i
\(935\) −256.520 −0.274353
\(936\) 0 0
\(937\) 1582.09i 1.68846i 0.535977 + 0.844232i \(0.319943\pi\)
−0.535977 + 0.844232i \(0.680057\pi\)
\(938\) 8.11468 39.9728i 0.00865105 0.0426149i
\(939\) 0 0
\(940\) −637.257 1573.37i −0.677933 1.67380i
\(941\) −113.842 + 113.842i −0.120980 + 0.120980i −0.765005 0.644025i \(-0.777263\pi\)
0.644025 + 0.765005i \(0.277263\pi\)
\(942\) 0 0
\(943\) 361.323i 0.383163i
\(944\) 1397.58 + 21.9928i 1.48049 + 0.0232974i
\(945\) 0 0
\(946\) 1397.50 925.851i 1.47728 0.978701i
\(947\) −388.664 388.664i −0.410416 0.410416i 0.471467 0.881884i \(-0.343725\pi\)
−0.881884 + 0.471467i \(0.843725\pi\)
\(948\) 0 0
\(949\) −1248.21 1248.21i −1.31529 1.31529i
\(950\) 326.595 + 66.3005i 0.343785 + 0.0697900i
\(951\) 0 0
\(952\) 7.24928 1.35324i 0.00761479 0.00142147i
\(953\) 211.977i 0.222431i −0.993796 0.111215i \(-0.964526\pi\)
0.993796 0.111215i \(-0.0354744\pi\)
\(954\) 0 0
\(955\) 1290.72 1290.72i 1.35154 1.35154i
\(956\) −92.9199 39.3480i −0.0971966 0.0411590i
\(957\) 0 0
\(958\) −697.889 + 462.354i −0.728485 + 0.482624i
\(959\) 30.1976i 0.0314887i
\(960\) 0 0
\(961\) −1174.11 −1.22175
\(962\) −105.769 159.651i −0.109947 0.165957i
\(963\) 0 0
\(964\) 477.267 1127.06i 0.495090 1.16915i
\(965\) −1075.62 1075.62i −1.11463 1.11463i
\(966\) 0 0
\(967\) 516.501 0.534127 0.267063 0.963679i \(-0.413947\pi\)
0.267063 + 0.963679i \(0.413947\pi\)
\(968\) −39.7876 213.141i −0.0411029 0.220187i
\(969\) 0 0
\(970\) 157.657 776.614i 0.162532 0.800633i
\(971\) −795.556 + 795.556i −0.819316 + 0.819316i −0.986009 0.166693i \(-0.946691\pi\)
0.166693 + 0.986009i \(0.446691\pi\)
\(972\) 0 0
\(973\) 32.2120 32.2120i 0.0331059 0.0331059i
\(974\) 179.563 + 271.037i 0.184356 + 0.278272i
\(975\) 0 0
\(976\) 518.113 + 8.15318i 0.530853 + 0.00835367i
\(977\) −512.430 −0.524493 −0.262246 0.965001i \(-0.584463\pi\)
−0.262246 + 0.965001i \(0.584463\pi\)
\(978\) 0 0
\(979\) 297.250 + 297.250i 0.303626 + 0.303626i
\(980\) −1087.76 + 440.570i −1.10996 + 0.449562i
\(981\) 0 0
\(982\) 1550.57 + 314.774i 1.57900 + 0.320544i
\(983\) 722.200 0.734690 0.367345 0.930085i \(-0.380267\pi\)
0.367345 + 0.930085i \(0.380267\pi\)
\(984\) 0 0
\(985\) 758.281i 0.769828i
\(986\) −252.882 51.3363i −0.256472 0.0520652i
\(987\) 0 0
\(988\) 536.743 1267.51i 0.543262 1.28291i
\(989\) −803.421 + 803.421i −0.812357 + 0.812357i
\(990\) 0 0
\(991\) 794.715i 0.801932i −0.916093 0.400966i \(-0.868675\pi\)
0.916093 0.400966i \(-0.131325\pi\)
\(992\) 1444.26 + 316.933i 1.45591 + 0.319489i
\(993\) 0 0
\(994\) 24.4041 + 36.8361i 0.0245514 + 0.0370585i
\(995\) −497.250 497.250i −0.499749 0.499749i
\(996\) 0 0
\(997\) 1080.18 + 1080.18i 1.08343 + 1.08343i 0.996187 + 0.0872401i \(0.0278047\pi\)
0.0872401 + 0.996187i \(0.472195\pi\)
\(998\) 139.527 687.310i 0.139807 0.688687i
\(999\) 0 0
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 144.3.m.b.91.3 yes 16
3.2 odd 2 inner 144.3.m.b.91.6 yes 16
4.3 odd 2 576.3.m.b.271.2 16
8.3 odd 2 1152.3.m.d.415.7 16
8.5 even 2 1152.3.m.e.415.7 16
12.11 even 2 576.3.m.b.271.7 16
16.3 odd 4 inner 144.3.m.b.19.3 16
16.5 even 4 1152.3.m.d.991.7 16
16.11 odd 4 1152.3.m.e.991.7 16
16.13 even 4 576.3.m.b.559.2 16
24.5 odd 2 1152.3.m.e.415.2 16
24.11 even 2 1152.3.m.d.415.2 16
48.5 odd 4 1152.3.m.d.991.2 16
48.11 even 4 1152.3.m.e.991.2 16
48.29 odd 4 576.3.m.b.559.7 16
48.35 even 4 inner 144.3.m.b.19.6 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.3.m.b.19.3 16 16.3 odd 4 inner
144.3.m.b.19.6 yes 16 48.35 even 4 inner
144.3.m.b.91.3 yes 16 1.1 even 1 trivial
144.3.m.b.91.6 yes 16 3.2 odd 2 inner
576.3.m.b.271.2 16 4.3 odd 2
576.3.m.b.271.7 16 12.11 even 2
576.3.m.b.559.2 16 16.13 even 4
576.3.m.b.559.7 16 48.29 odd 4
1152.3.m.d.415.2 16 24.11 even 2
1152.3.m.d.415.7 16 8.3 odd 2
1152.3.m.d.991.2 16 48.5 odd 4
1152.3.m.d.991.7 16 16.5 even 4
1152.3.m.e.415.2 16 24.5 odd 2
1152.3.m.e.415.7 16 8.5 even 2
1152.3.m.e.991.2 16 48.11 even 4
1152.3.m.e.991.7 16 16.11 odd 4