Properties

Label 315.3.ca.b.298.5
Level $315$
Weight $3$
Character 315.298
Analytic conductor $8.583$
Analytic rank $0$
Dimension $64$
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] = [315,3,Mod(37,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), 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: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 298.5
Character \(\chi\) \(=\) 315.298
Dual form 315.3.ca.b.37.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.13226 - 0.571337i) q^{2} +(0.756006 + 0.436480i) q^{4} +(-2.78563 + 4.15214i) q^{5} +(2.73668 + 6.44287i) q^{7} +(4.88107 + 4.88107i) q^{8} +O(q^{10})\) \(q+(-2.13226 - 0.571337i) q^{2} +(0.756006 + 0.436480i) q^{4} +(-2.78563 + 4.15214i) q^{5} +(2.73668 + 6.44287i) q^{7} +(4.88107 + 4.88107i) q^{8} +(8.31195 - 7.26192i) q^{10} +(4.69282 - 8.12820i) q^{11} +(-0.405222 - 0.405222i) q^{13} +(-2.15427 - 15.3014i) q^{14} +(-9.36489 - 16.2205i) q^{16} +(-2.82961 - 10.5602i) q^{17} +(-23.8500 + 13.7698i) q^{19} +(-3.91828 + 1.92317i) q^{20} +(-14.6503 + 14.6503i) q^{22} +(-1.02354 + 3.81990i) q^{23} +(-9.48058 - 23.1326i) q^{25} +(0.632520 + 1.09556i) q^{26} +(-0.743235 + 6.06535i) q^{28} +34.6601i q^{29} +(-11.8284 + 20.4874i) q^{31} +(3.55465 + 13.2661i) q^{32} +24.1338i q^{34} +(-34.3751 - 6.58431i) q^{35} +(25.6130 + 6.86297i) q^{37} +(58.7215 - 15.7344i) q^{38} +(-33.8637 + 6.67007i) q^{40} -54.6731 q^{41} +(-47.3942 - 47.3942i) q^{43} +(7.09560 - 4.09664i) q^{44} +(4.36491 - 7.56024i) q^{46} +(16.9830 + 4.55058i) q^{47} +(-34.0211 + 35.2642i) q^{49} +(6.99854 + 54.7414i) q^{50} +(-0.129479 - 0.483221i) q^{52} +(-14.7503 + 3.95234i) q^{53} +(20.6770 + 42.1274i) q^{55} +(-18.0901 + 44.8060i) q^{56} +(19.8026 - 73.9044i) q^{58} +(-90.3630 - 52.1711i) q^{59} +(-12.5803 - 21.7897i) q^{61} +(36.9264 - 36.9264i) q^{62} +44.6014i q^{64} +(2.81133 - 0.553743i) q^{65} +(0.364564 + 1.36057i) q^{67} +(2.47014 - 9.21867i) q^{68} +(69.5348 + 33.6792i) q^{70} -86.5935 q^{71} +(-84.9471 + 22.7615i) q^{73} +(-50.6924 - 29.2673i) q^{74} -24.0409 q^{76} +(65.2117 + 7.99089i) q^{77} +(128.353 - 74.1049i) q^{79} +(93.4368 + 6.29977i) q^{80} +(116.577 + 31.2368i) q^{82} +(-35.5711 - 35.5711i) q^{83} +(51.7299 + 17.6679i) q^{85} +(73.9787 + 128.135i) q^{86} +(62.5803 - 16.7683i) q^{88} +(-130.143 + 75.1382i) q^{89} +(1.50183 - 3.71975i) q^{91} +(-2.44111 + 2.44111i) q^{92} +(-33.6122 - 19.4060i) q^{94} +(9.26295 - 137.386i) q^{95} +(74.8462 - 74.8462i) q^{97} +(92.6896 - 55.7549i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13226 0.571337i −1.06613 0.285669i −0.317228 0.948349i \(-0.602752\pi\)
−0.748902 + 0.662681i \(0.769419\pi\)
\(3\) 0 0
\(4\) 0.756006 + 0.436480i 0.189001 + 0.109120i
\(5\) −2.78563 + 4.15214i −0.557125 + 0.830429i
\(6\) 0 0
\(7\) 2.73668 + 6.44287i 0.390955 + 0.920410i
\(8\) 4.88107 + 4.88107i 0.610133 + 0.610133i
\(9\) 0 0
\(10\) 8.31195 7.26192i 0.831195 0.726192i
\(11\) 4.69282 8.12820i 0.426620 0.738927i −0.569950 0.821679i \(-0.693038\pi\)
0.996570 + 0.0827519i \(0.0263709\pi\)
\(12\) 0 0
\(13\) −0.405222 0.405222i −0.0311709 0.0311709i 0.691350 0.722520i \(-0.257016\pi\)
−0.722520 + 0.691350i \(0.757016\pi\)
\(14\) −2.15427 15.3014i −0.153877 1.09296i
\(15\) 0 0
\(16\) −9.36489 16.2205i −0.585306 1.01378i
\(17\) −2.82961 10.5602i −0.166448 0.621191i −0.997851 0.0655217i \(-0.979129\pi\)
0.831404 0.555669i \(-0.187538\pi\)
\(18\) 0 0
\(19\) −23.8500 + 13.7698i −1.25526 + 0.724725i −0.972149 0.234362i \(-0.924700\pi\)
−0.283111 + 0.959087i \(0.591367\pi\)
\(20\) −3.91828 + 1.92317i −0.195914 + 0.0961587i
\(21\) 0 0
\(22\) −14.6503 + 14.6503i −0.665921 + 0.665921i
\(23\) −1.02354 + 3.81990i −0.0445017 + 0.166083i −0.984601 0.174819i \(-0.944066\pi\)
0.940099 + 0.340902i \(0.110732\pi\)
\(24\) 0 0
\(25\) −9.48058 23.1326i −0.379223 0.925305i
\(26\) 0.632520 + 1.09556i 0.0243277 + 0.0421368i
\(27\) 0 0
\(28\) −0.743235 + 6.06535i −0.0265441 + 0.216620i
\(29\) 34.6601i 1.19518i 0.801803 + 0.597588i \(0.203874\pi\)
−0.801803 + 0.597588i \(0.796126\pi\)
\(30\) 0 0
\(31\) −11.8284 + 20.4874i −0.381561 + 0.660883i −0.991286 0.131730i \(-0.957947\pi\)
0.609724 + 0.792613i \(0.291280\pi\)
\(32\) 3.55465 + 13.2661i 0.111083 + 0.414566i
\(33\) 0 0
\(34\) 24.1338i 0.709819i
\(35\) −34.3751 6.58431i −0.982145 0.188123i
\(36\) 0 0
\(37\) 25.6130 + 6.86297i 0.692242 + 0.185486i 0.587753 0.809040i \(-0.300013\pi\)
0.104489 + 0.994526i \(0.466679\pi\)
\(38\) 58.7215 15.7344i 1.54530 0.414063i
\(39\) 0 0
\(40\) −33.8637 + 6.67007i −0.846593 + 0.166752i
\(41\) −54.6731 −1.33349 −0.666745 0.745286i \(-0.732313\pi\)
−0.666745 + 0.745286i \(0.732313\pi\)
\(42\) 0 0
\(43\) −47.3942 47.3942i −1.10219 1.10219i −0.994146 0.108044i \(-0.965541\pi\)
−0.108044 0.994146i \(-0.534459\pi\)
\(44\) 7.09560 4.09664i 0.161264 0.0931055i
\(45\) 0 0
\(46\) 4.36491 7.56024i 0.0948893 0.164353i
\(47\) 16.9830 + 4.55058i 0.361340 + 0.0968208i 0.434921 0.900468i \(-0.356776\pi\)
−0.0735811 + 0.997289i \(0.523443\pi\)
\(48\) 0 0
\(49\) −34.0211 + 35.2642i −0.694308 + 0.719678i
\(50\) 6.99854 + 54.7414i 0.139971 + 1.09483i
\(51\) 0 0
\(52\) −0.129479 0.483221i −0.00248997 0.00929271i
\(53\) −14.7503 + 3.95234i −0.278308 + 0.0745725i −0.395273 0.918564i \(-0.629350\pi\)
0.116965 + 0.993136i \(0.462683\pi\)
\(54\) 0 0
\(55\) 20.6770 + 42.1274i 0.375946 + 0.765952i
\(56\) −18.0901 + 44.8060i −0.323038 + 0.800108i
\(57\) 0 0
\(58\) 19.8026 73.9044i 0.341424 1.27421i
\(59\) −90.3630 52.1711i −1.53158 0.884256i −0.999289 0.0376927i \(-0.987999\pi\)
−0.532288 0.846564i \(-0.678667\pi\)
\(60\) 0 0
\(61\) −12.5803 21.7897i −0.206235 0.357209i 0.744291 0.667856i \(-0.232788\pi\)
−0.950525 + 0.310647i \(0.899454\pi\)
\(62\) 36.9264 36.9264i 0.595587 0.595587i
\(63\) 0 0
\(64\) 44.6014i 0.696897i
\(65\) 2.81133 0.553743i 0.0432513 0.00851912i
\(66\) 0 0
\(67\) 0.364564 + 1.36057i 0.00544126 + 0.0203071i 0.968593 0.248651i \(-0.0799873\pi\)
−0.963152 + 0.268958i \(0.913321\pi\)
\(68\) 2.47014 9.21867i 0.0363255 0.135569i
\(69\) 0 0
\(70\) 69.5348 + 33.6792i 0.993354 + 0.481132i
\(71\) −86.5935 −1.21963 −0.609813 0.792545i \(-0.708756\pi\)
−0.609813 + 0.792545i \(0.708756\pi\)
\(72\) 0 0
\(73\) −84.9471 + 22.7615i −1.16366 + 0.311802i −0.788427 0.615129i \(-0.789104\pi\)
−0.375233 + 0.926931i \(0.622437\pi\)
\(74\) −50.6924 29.2673i −0.685033 0.395504i
\(75\) 0 0
\(76\) −24.0409 −0.316328
\(77\) 65.2117 + 7.99089i 0.846905 + 0.103778i
\(78\) 0 0
\(79\) 128.353 74.1049i 1.62473 0.938036i 0.639095 0.769128i \(-0.279309\pi\)
0.985632 0.168909i \(-0.0540243\pi\)
\(80\) 93.4368 + 6.29977i 1.16796 + 0.0787472i
\(81\) 0 0
\(82\) 116.577 + 31.2368i 1.42167 + 0.380936i
\(83\) −35.5711 35.5711i −0.428567 0.428567i 0.459573 0.888140i \(-0.348002\pi\)
−0.888140 + 0.459573i \(0.848002\pi\)
\(84\) 0 0
\(85\) 51.7299 + 17.6679i 0.608587 + 0.207858i
\(86\) 73.9787 + 128.135i 0.860217 + 1.48994i
\(87\) 0 0
\(88\) 62.5803 16.7683i 0.711139 0.190549i
\(89\) −130.143 + 75.1382i −1.46228 + 0.844250i −0.999117 0.0420218i \(-0.986620\pi\)
−0.463166 + 0.886271i \(0.653287\pi\)
\(90\) 0 0
\(91\) 1.50183 3.71975i 0.0165036 0.0408764i
\(92\) −2.44111 + 2.44111i −0.0265338 + 0.0265338i
\(93\) 0 0
\(94\) −33.6122 19.4060i −0.357577 0.206447i
\(95\) 9.26295 137.386i 0.0975047 1.44617i
\(96\) 0 0
\(97\) 74.8462 74.8462i 0.771610 0.771610i −0.206778 0.978388i \(-0.566298\pi\)
0.978388 + 0.206778i \(0.0662977\pi\)
\(98\) 92.6896 55.7549i 0.945812 0.568928i
\(99\) 0 0
\(100\) 2.92956 21.6265i 0.0292956 0.216265i
\(101\) 65.3840 113.248i 0.647366 1.12127i −0.336384 0.941725i \(-0.609204\pi\)
0.983750 0.179546i \(-0.0574628\pi\)
\(102\) 0 0
\(103\) 9.95292 37.1448i 0.0966303 0.360629i −0.900631 0.434584i \(-0.856895\pi\)
0.997262 + 0.0739549i \(0.0235621\pi\)
\(104\) 3.95583i 0.0380368i
\(105\) 0 0
\(106\) 33.7097 0.318016
\(107\) 193.691 + 51.8993i 1.81019 + 0.485040i 0.995492 0.0948408i \(-0.0302342\pi\)
0.814701 + 0.579881i \(0.196901\pi\)
\(108\) 0 0
\(109\) −126.264 72.8985i −1.15838 0.668793i −0.207468 0.978242i \(-0.566522\pi\)
−0.950916 + 0.309449i \(0.899856\pi\)
\(110\) −20.0198 101.640i −0.181998 0.924001i
\(111\) 0 0
\(112\) 78.8776 104.727i 0.704264 0.935063i
\(113\) 50.0612 + 50.0612i 0.443020 + 0.443020i 0.893026 0.450006i \(-0.148578\pi\)
−0.450006 + 0.893026i \(0.648578\pi\)
\(114\) 0 0
\(115\) −13.0096 14.8907i −0.113127 0.129484i
\(116\) −15.1284 + 26.2032i −0.130418 + 0.225890i
\(117\) 0 0
\(118\) 162.870 + 162.870i 1.38026 + 1.38026i
\(119\) 60.2945 47.1308i 0.506677 0.396058i
\(120\) 0 0
\(121\) 16.4549 + 28.5007i 0.135991 + 0.235543i
\(122\) 14.3752 + 53.6490i 0.117830 + 0.439746i
\(123\) 0 0
\(124\) −17.8847 + 10.3257i −0.144231 + 0.0832719i
\(125\) 122.459 + 25.0741i 0.979675 + 0.200593i
\(126\) 0 0
\(127\) −120.362 + 120.362i −0.947736 + 0.947736i −0.998700 0.0509644i \(-0.983771\pi\)
0.0509644 + 0.998700i \(0.483771\pi\)
\(128\) 39.7010 148.166i 0.310164 1.15755i
\(129\) 0 0
\(130\) −6.31087 0.425497i −0.0485451 0.00327305i
\(131\) 61.7290 + 106.918i 0.471214 + 0.816166i 0.999458 0.0329263i \(-0.0104827\pi\)
−0.528244 + 0.849093i \(0.677149\pi\)
\(132\) 0 0
\(133\) −153.987 115.979i −1.15779 0.872019i
\(134\) 3.10939i 0.0232044i
\(135\) 0 0
\(136\) 37.7337 65.3568i 0.277454 0.480564i
\(137\) 38.7216 + 144.511i 0.282639 + 1.05482i 0.950547 + 0.310581i \(0.100523\pi\)
−0.667908 + 0.744244i \(0.732810\pi\)
\(138\) 0 0
\(139\) 86.7413i 0.624038i 0.950076 + 0.312019i \(0.101005\pi\)
−0.950076 + 0.312019i \(0.898995\pi\)
\(140\) −23.1138 19.9818i −0.165099 0.142727i
\(141\) 0 0
\(142\) 184.640 + 49.4741i 1.30028 + 0.348409i
\(143\) −5.19535 + 1.39209i −0.0363311 + 0.00973490i
\(144\) 0 0
\(145\) −143.914 96.5501i −0.992508 0.665863i
\(146\) 194.134 1.32968
\(147\) 0 0
\(148\) 16.3680 + 16.3680i 0.110595 + 0.110595i
\(149\) 21.7762 12.5725i 0.146149 0.0843791i −0.425142 0.905126i \(-0.639776\pi\)
0.571291 + 0.820747i \(0.306443\pi\)
\(150\) 0 0
\(151\) −100.832 + 174.647i −0.667765 + 1.15660i 0.310763 + 0.950487i \(0.399415\pi\)
−0.978528 + 0.206115i \(0.933918\pi\)
\(152\) −183.624 49.2020i −1.20806 0.323697i
\(153\) 0 0
\(154\) −134.483 54.2965i −0.873265 0.352575i
\(155\) −52.1171 106.183i −0.336239 0.685054i
\(156\) 0 0
\(157\) 7.52733 + 28.0924i 0.0479448 + 0.178932i 0.985746 0.168240i \(-0.0538084\pi\)
−0.937801 + 0.347173i \(0.887142\pi\)
\(158\) −316.022 + 84.6778i −2.00014 + 0.535935i
\(159\) 0 0
\(160\) −64.9847 22.1950i −0.406155 0.138719i
\(161\) −27.4122 + 3.85934i −0.170262 + 0.0239710i
\(162\) 0 0
\(163\) −21.9253 + 81.8264i −0.134511 + 0.502003i 0.865488 + 0.500929i \(0.167008\pi\)
−0.999999 + 0.00107335i \(0.999658\pi\)
\(164\) −41.3332 23.8637i −0.252032 0.145510i
\(165\) 0 0
\(166\) 55.5237 + 96.1699i 0.334480 + 0.579336i
\(167\) −147.643 + 147.643i −0.884091 + 0.884091i −0.993947 0.109856i \(-0.964961\pi\)
0.109856 + 0.993947i \(0.464961\pi\)
\(168\) 0 0
\(169\) 168.672i 0.998057i
\(170\) −100.207 67.2279i −0.589454 0.395458i
\(171\) 0 0
\(172\) −15.1437 56.5169i −0.0880445 0.328587i
\(173\) 18.0662 67.4239i 0.104429 0.389733i −0.893851 0.448364i \(-0.852007\pi\)
0.998280 + 0.0586307i \(0.0186734\pi\)
\(174\) 0 0
\(175\) 123.095 124.389i 0.703401 0.710794i
\(176\) −175.791 −0.998812
\(177\) 0 0
\(178\) 320.428 85.8585i 1.80016 0.482351i
\(179\) 10.7449 + 6.20357i 0.0600273 + 0.0346568i 0.529713 0.848177i \(-0.322300\pi\)
−0.469686 + 0.882834i \(0.655633\pi\)
\(180\) 0 0
\(181\) −163.979 −0.905964 −0.452982 0.891520i \(-0.649640\pi\)
−0.452982 + 0.891520i \(0.649640\pi\)
\(182\) −5.32752 + 7.07343i −0.0292721 + 0.0388650i
\(183\) 0 0
\(184\) −23.6412 + 13.6492i −0.128485 + 0.0741806i
\(185\) −99.8441 + 87.2310i −0.539698 + 0.471519i
\(186\) 0 0
\(187\) −99.1146 26.5577i −0.530025 0.142020i
\(188\) 10.8530 + 10.8530i 0.0577287 + 0.0577287i
\(189\) 0 0
\(190\) −98.2447 + 287.650i −0.517077 + 1.51395i
\(191\) −63.0093 109.135i −0.329892 0.571389i 0.652598 0.757704i \(-0.273679\pi\)
−0.982490 + 0.186315i \(0.940346\pi\)
\(192\) 0 0
\(193\) 53.1737 14.2479i 0.275512 0.0738231i −0.118418 0.992964i \(-0.537782\pi\)
0.393929 + 0.919141i \(0.371115\pi\)
\(194\) −202.354 + 116.829i −1.04306 + 0.602212i
\(195\) 0 0
\(196\) −41.1123 + 11.8104i −0.209757 + 0.0602571i
\(197\) −62.0394 + 62.0394i −0.314921 + 0.314921i −0.846812 0.531892i \(-0.821481\pi\)
0.531892 + 0.846812i \(0.321481\pi\)
\(198\) 0 0
\(199\) 242.793 + 140.177i 1.22007 + 0.704405i 0.964932 0.262501i \(-0.0845472\pi\)
0.255134 + 0.966906i \(0.417880\pi\)
\(200\) 66.6366 159.187i 0.333183 0.795937i
\(201\) 0 0
\(202\) −204.119 + 204.119i −1.01049 + 1.01049i
\(203\) −223.311 + 94.8538i −1.10005 + 0.467260i
\(204\) 0 0
\(205\) 152.299 227.011i 0.742921 1.10737i
\(206\) −42.4444 + 73.5159i −0.206041 + 0.356873i
\(207\) 0 0
\(208\) −2.77803 + 10.3677i −0.0133559 + 0.0498449i
\(209\) 258.476i 1.23673i
\(210\) 0 0
\(211\) 215.254 1.02016 0.510081 0.860126i \(-0.329615\pi\)
0.510081 + 0.860126i \(0.329615\pi\)
\(212\) −12.8765 3.45024i −0.0607380 0.0162747i
\(213\) 0 0
\(214\) −383.347 221.326i −1.79134 1.03423i
\(215\) 328.810 64.7650i 1.52935 0.301233i
\(216\) 0 0
\(217\) −164.368 20.1413i −0.757457 0.0928170i
\(218\) 227.578 + 227.578i 1.04393 + 1.04393i
\(219\) 0 0
\(220\) −2.75582 + 40.8736i −0.0125264 + 0.185789i
\(221\) −3.13262 + 5.42586i −0.0141747 + 0.0245514i
\(222\) 0 0
\(223\) 129.293 + 129.293i 0.579788 + 0.579788i 0.934845 0.355057i \(-0.115538\pi\)
−0.355057 + 0.934845i \(0.615538\pi\)
\(224\) −75.7439 + 59.2073i −0.338142 + 0.264318i
\(225\) 0 0
\(226\) −78.1417 135.345i −0.345760 0.598874i
\(227\) 12.3978 + 46.2690i 0.0546156 + 0.203828i 0.987842 0.155460i \(-0.0496860\pi\)
−0.933227 + 0.359289i \(0.883019\pi\)
\(228\) 0 0
\(229\) −275.307 + 158.949i −1.20221 + 0.694099i −0.961047 0.276384i \(-0.910864\pi\)
−0.241168 + 0.970483i \(0.577530\pi\)
\(230\) 19.2322 + 39.1837i 0.0836183 + 0.170364i
\(231\) 0 0
\(232\) −169.178 + 169.178i −0.729217 + 0.729217i
\(233\) 70.2155 262.048i 0.301354 1.12467i −0.634685 0.772771i \(-0.718870\pi\)
0.936039 0.351897i \(-0.114463\pi\)
\(234\) 0 0
\(235\) −66.2029 + 57.8396i −0.281715 + 0.246126i
\(236\) −45.5433 78.8833i −0.192980 0.334251i
\(237\) 0 0
\(238\) −155.491 + 66.0467i −0.653324 + 0.277507i
\(239\) 18.7596i 0.0784918i −0.999230 0.0392459i \(-0.987504\pi\)
0.999230 0.0392459i \(-0.0124956\pi\)
\(240\) 0 0
\(241\) −39.4000 + 68.2427i −0.163485 + 0.283165i −0.936116 0.351690i \(-0.885607\pi\)
0.772631 + 0.634855i \(0.218940\pi\)
\(242\) −18.8026 70.1723i −0.0776968 0.289968i
\(243\) 0 0
\(244\) 21.9642i 0.0900173i
\(245\) −51.6519 239.493i −0.210824 0.977524i
\(246\) 0 0
\(247\) 15.2443 + 4.08470i 0.0617179 + 0.0165373i
\(248\) −157.735 + 42.2651i −0.636030 + 0.170424i
\(249\) 0 0
\(250\) −246.789 123.430i −0.987158 0.493720i
\(251\) 86.2825 0.343755 0.171877 0.985118i \(-0.445017\pi\)
0.171877 + 0.985118i \(0.445017\pi\)
\(252\) 0 0
\(253\) 26.2456 + 26.2456i 0.103738 + 0.103738i
\(254\) 325.412 187.877i 1.28115 0.739671i
\(255\) 0 0
\(256\) −80.1031 + 138.743i −0.312903 + 0.541963i
\(257\) 241.586 + 64.7328i 0.940024 + 0.251879i 0.696124 0.717922i \(-0.254906\pi\)
0.243900 + 0.969800i \(0.421573\pi\)
\(258\) 0 0
\(259\) 25.8774 + 183.803i 0.0999126 + 0.709663i
\(260\) 2.36708 + 0.808459i 0.00910416 + 0.00310946i
\(261\) 0 0
\(262\) −70.5362 263.245i −0.269222 1.00475i
\(263\) 350.527 93.9235i 1.33280 0.357123i 0.479043 0.877791i \(-0.340984\pi\)
0.853759 + 0.520668i \(0.174317\pi\)
\(264\) 0 0
\(265\) 24.6782 72.2553i 0.0931254 0.272661i
\(266\) 262.077 + 335.275i 0.985251 + 1.26043i
\(267\) 0 0
\(268\) −0.318250 + 1.18773i −0.00118750 + 0.00443181i
\(269\) −255.637 147.592i −0.950323 0.548669i −0.0571419 0.998366i \(-0.518199\pi\)
−0.893181 + 0.449697i \(0.851532\pi\)
\(270\) 0 0
\(271\) 208.489 + 361.113i 0.769332 + 1.33252i 0.937926 + 0.346836i \(0.112744\pi\)
−0.168594 + 0.985686i \(0.553923\pi\)
\(272\) −144.793 + 144.793i −0.532328 + 0.532328i
\(273\) 0 0
\(274\) 330.258i 1.20532i
\(275\) −232.517 31.4971i −0.845517 0.114535i
\(276\) 0 0
\(277\) −65.5326 244.571i −0.236580 0.882927i −0.977430 0.211258i \(-0.932244\pi\)
0.740851 0.671670i \(-0.234423\pi\)
\(278\) 49.5586 184.955i 0.178268 0.665306i
\(279\) 0 0
\(280\) −135.649 199.926i −0.484460 0.714020i
\(281\) −235.018 −0.836363 −0.418181 0.908363i \(-0.637332\pi\)
−0.418181 + 0.908363i \(0.637332\pi\)
\(282\) 0 0
\(283\) 45.4761 12.1853i 0.160693 0.0430576i −0.177576 0.984107i \(-0.556825\pi\)
0.338269 + 0.941050i \(0.390159\pi\)
\(284\) −65.4652 37.7963i −0.230511 0.133086i
\(285\) 0 0
\(286\) 11.8732 0.0415147
\(287\) −149.623 352.252i −0.521335 1.22736i
\(288\) 0 0
\(289\) 146.769 84.7373i 0.507852 0.293209i
\(290\) 251.699 + 288.093i 0.867927 + 0.993425i
\(291\) 0 0
\(292\) −74.1555 19.8699i −0.253957 0.0680476i
\(293\) 12.1766 + 12.1766i 0.0415584 + 0.0415584i 0.727581 0.686022i \(-0.240645\pi\)
−0.686022 + 0.727581i \(0.740645\pi\)
\(294\) 0 0
\(295\) 468.340 229.871i 1.58759 0.779224i
\(296\) 91.5200 + 158.517i 0.309189 + 0.535531i
\(297\) 0 0
\(298\) −53.6156 + 14.3663i −0.179918 + 0.0482089i
\(299\) 1.96267 1.13315i 0.00656410 0.00378979i
\(300\) 0 0
\(301\) 175.652 435.058i 0.583560 1.44537i
\(302\) 314.783 314.783i 1.04233 1.04233i
\(303\) 0 0
\(304\) 446.704 + 257.905i 1.46942 + 0.848371i
\(305\) 125.518 + 8.46279i 0.411535 + 0.0277468i
\(306\) 0 0
\(307\) −104.260 + 104.260i −0.339609 + 0.339609i −0.856220 0.516611i \(-0.827193\pi\)
0.516611 + 0.856220i \(0.327193\pi\)
\(308\) 45.8125 + 34.5048i 0.148742 + 0.112028i
\(309\) 0 0
\(310\) 50.4606 + 256.187i 0.162776 + 0.826410i
\(311\) 16.5632 28.6884i 0.0532580 0.0922455i −0.838167 0.545413i \(-0.816373\pi\)
0.891425 + 0.453168i \(0.149706\pi\)
\(312\) 0 0
\(313\) −112.285 + 419.052i −0.358737 + 1.33882i 0.516980 + 0.855998i \(0.327056\pi\)
−0.875716 + 0.482826i \(0.839610\pi\)
\(314\) 64.2009i 0.204462i
\(315\) 0 0
\(316\) 129.381 0.409434
\(317\) −270.012 72.3496i −0.851774 0.228232i −0.193584 0.981084i \(-0.562011\pi\)
−0.658190 + 0.752852i \(0.728678\pi\)
\(318\) 0 0
\(319\) 281.724 + 162.654i 0.883148 + 0.509886i
\(320\) −185.191 124.243i −0.578723 0.388259i
\(321\) 0 0
\(322\) 60.6550 + 7.43252i 0.188370 + 0.0230824i
\(323\) 212.898 + 212.898i 0.659128 + 0.659128i
\(324\) 0 0
\(325\) −5.53210 + 13.2156i −0.0170219 + 0.0406633i
\(326\) 93.5010 161.948i 0.286813 0.496774i
\(327\) 0 0
\(328\) −266.863 266.863i −0.813607 0.813607i
\(329\) 17.1583 + 121.873i 0.0521529 + 0.370434i
\(330\) 0 0
\(331\) −125.181 216.820i −0.378191 0.655047i 0.612608 0.790387i \(-0.290121\pi\)
−0.990799 + 0.135340i \(0.956787\pi\)
\(332\) −11.3659 42.4180i −0.0342345 0.127765i
\(333\) 0 0
\(334\) 399.168 230.460i 1.19511 0.689999i
\(335\) −6.66483 2.27632i −0.0198950 0.00679499i
\(336\) 0 0
\(337\) −7.57759 + 7.57759i −0.0224854 + 0.0224854i −0.718260 0.695775i \(-0.755061\pi\)
0.695775 + 0.718260i \(0.255061\pi\)
\(338\) −96.3684 + 359.652i −0.285114 + 1.06406i
\(339\) 0 0
\(340\) 31.3964 + 35.9361i 0.0923423 + 0.105694i
\(341\) 111.017 + 192.287i 0.325563 + 0.563892i
\(342\) 0 0
\(343\) −320.308 122.687i −0.933842 0.357687i
\(344\) 462.669i 1.34497i
\(345\) 0 0
\(346\) −77.0436 + 133.443i −0.222669 + 0.385675i
\(347\) 80.6472 + 300.979i 0.232413 + 0.867376i 0.979298 + 0.202423i \(0.0648817\pi\)
−0.746885 + 0.664953i \(0.768452\pi\)
\(348\) 0 0
\(349\) 396.973i 1.13746i 0.822525 + 0.568729i \(0.192565\pi\)
−0.822525 + 0.568729i \(0.807435\pi\)
\(350\) −333.539 + 194.901i −0.952968 + 0.556859i
\(351\) 0 0
\(352\) 124.511 + 33.3626i 0.353724 + 0.0947802i
\(353\) 127.946 34.2831i 0.362454 0.0971193i −0.0729959 0.997332i \(-0.523256\pi\)
0.435450 + 0.900213i \(0.356589\pi\)
\(354\) 0 0
\(355\) 241.217 359.548i 0.679484 1.01281i
\(356\) −131.185 −0.368498
\(357\) 0 0
\(358\) −19.3666 19.3666i −0.0540966 0.0540966i
\(359\) 66.6339 38.4711i 0.185610 0.107162i −0.404316 0.914619i \(-0.632490\pi\)
0.589926 + 0.807458i \(0.299157\pi\)
\(360\) 0 0
\(361\) 198.713 344.182i 0.550453 0.953412i
\(362\) 349.647 + 93.6876i 0.965875 + 0.258805i
\(363\) 0 0
\(364\) 2.75899 2.15664i 0.00757963 0.00592483i
\(365\) 142.122 416.118i 0.389375 1.14005i
\(366\) 0 0
\(367\) 60.6221 + 226.245i 0.165183 + 0.616471i 0.998017 + 0.0629479i \(0.0200502\pi\)
−0.832834 + 0.553523i \(0.813283\pi\)
\(368\) 71.5459 19.1707i 0.194418 0.0520942i
\(369\) 0 0
\(370\) 262.732 128.955i 0.710087 0.348526i
\(371\) −65.8315 84.2182i −0.177443 0.227003i
\(372\) 0 0
\(373\) −98.3605 + 367.087i −0.263701 + 0.984146i 0.699339 + 0.714790i \(0.253478\pi\)
−0.963041 + 0.269356i \(0.913189\pi\)
\(374\) 196.165 + 113.256i 0.524505 + 0.302823i
\(375\) 0 0
\(376\) 60.6835 + 105.107i 0.161392 + 0.279539i
\(377\) 14.0450 14.0450i 0.0372547 0.0372547i
\(378\) 0 0
\(379\) 369.290i 0.974379i −0.873296 0.487190i \(-0.838022\pi\)
0.873296 0.487190i \(-0.161978\pi\)
\(380\) 66.9690 99.8214i 0.176234 0.262688i
\(381\) 0 0
\(382\) 71.9991 + 268.704i 0.188479 + 0.703415i
\(383\) −187.821 + 700.956i −0.490393 + 1.83017i 0.0640459 + 0.997947i \(0.479600\pi\)
−0.554439 + 0.832224i \(0.687067\pi\)
\(384\) 0 0
\(385\) −214.835 + 248.509i −0.558012 + 0.645477i
\(386\) −121.521 −0.314820
\(387\) 0 0
\(388\) 89.2530 23.9153i 0.230034 0.0616373i
\(389\) −135.464 78.2101i −0.348236 0.201054i 0.315672 0.948868i \(-0.397770\pi\)
−0.663908 + 0.747814i \(0.731103\pi\)
\(390\) 0 0
\(391\) 43.2353 0.110576
\(392\) −338.186 + 6.06760i −0.862720 + 0.0154786i
\(393\) 0 0
\(394\) 167.730 96.8387i 0.425710 0.245784i
\(395\) −49.8504 + 739.370i −0.126204 + 1.87182i
\(396\) 0 0
\(397\) 608.327 + 163.001i 1.53231 + 0.410581i 0.923772 0.382944i \(-0.125090\pi\)
0.608538 + 0.793525i \(0.291756\pi\)
\(398\) −437.610 437.610i −1.09952 1.09952i
\(399\) 0 0
\(400\) −286.437 + 370.414i −0.716093 + 0.926035i
\(401\) −175.823 304.535i −0.438463 0.759439i 0.559109 0.829094i \(-0.311143\pi\)
−0.997571 + 0.0696551i \(0.977810\pi\)
\(402\) 0 0
\(403\) 13.0950 3.50881i 0.0324939 0.00870672i
\(404\) 98.8613 57.0776i 0.244706 0.141281i
\(405\) 0 0
\(406\) 530.350 74.6673i 1.30628 0.183910i
\(407\) 175.981 175.981i 0.432385 0.432385i
\(408\) 0 0
\(409\) 63.4064 + 36.6077i 0.155028 + 0.0895055i 0.575507 0.817797i \(-0.304805\pi\)
−0.420479 + 0.907302i \(0.638138\pi\)
\(410\) −454.440 + 397.032i −1.10839 + 0.968370i
\(411\) 0 0
\(412\) 23.7374 23.7374i 0.0576151 0.0576151i
\(413\) 88.8365 724.973i 0.215101 1.75538i
\(414\) 0 0
\(415\) 246.784 48.6085i 0.594660 0.117129i
\(416\) 3.93530 6.81614i 0.00945985 0.0163849i
\(417\) 0 0
\(418\) 147.677 551.139i 0.353295 1.31851i
\(419\) 19.8543i 0.0473849i 0.999719 + 0.0236925i \(0.00754225\pi\)
−0.999719 + 0.0236925i \(0.992458\pi\)
\(420\) 0 0
\(421\) −19.3162 −0.0458817 −0.0229408 0.999737i \(-0.507303\pi\)
−0.0229408 + 0.999737i \(0.507303\pi\)
\(422\) −458.978 122.983i −1.08763 0.291429i
\(423\) 0 0
\(424\) −91.2891 52.7058i −0.215304 0.124306i
\(425\) −217.460 + 165.574i −0.511670 + 0.389585i
\(426\) 0 0
\(427\) 105.960 140.685i 0.248150 0.329473i
\(428\) 123.778 + 123.778i 0.289202 + 0.289202i
\(429\) 0 0
\(430\) −738.111 49.7655i −1.71654 0.115734i
\(431\) 129.158 223.709i 0.299671 0.519046i −0.676389 0.736544i \(-0.736456\pi\)
0.976061 + 0.217498i \(0.0697897\pi\)
\(432\) 0 0
\(433\) −307.927 307.927i −0.711147 0.711147i 0.255628 0.966775i \(-0.417718\pi\)
−0.966775 + 0.255628i \(0.917718\pi\)
\(434\) 338.968 + 136.856i 0.781032 + 0.315337i
\(435\) 0 0
\(436\) −63.6375 110.223i −0.145957 0.252806i
\(437\) −28.1878 105.198i −0.0645030 0.240729i
\(438\) 0 0
\(439\) −544.482 + 314.357i −1.24028 + 0.716074i −0.969151 0.246469i \(-0.920730\pi\)
−0.271127 + 0.962544i \(0.587396\pi\)
\(440\) −104.701 + 306.552i −0.237956 + 0.696710i
\(441\) 0 0
\(442\) 9.77955 9.77955i 0.0221257 0.0221257i
\(443\) −173.821 + 648.708i −0.392372 + 1.46435i 0.433839 + 0.900990i \(0.357159\pi\)
−0.826211 + 0.563361i \(0.809508\pi\)
\(444\) 0 0
\(445\) 50.5456 749.680i 0.113586 1.68467i
\(446\) −201.816 349.556i −0.452502 0.783757i
\(447\) 0 0
\(448\) −287.361 + 122.060i −0.641431 + 0.272455i
\(449\) 36.1975i 0.0806181i −0.999187 0.0403091i \(-0.987166\pi\)
0.999187 0.0403091i \(-0.0128342\pi\)
\(450\) 0 0
\(451\) −256.571 + 444.394i −0.568893 + 0.985352i
\(452\) 15.9958 + 59.6973i 0.0353890 + 0.132074i
\(453\) 0 0
\(454\) 105.741i 0.232910i
\(455\) 11.2614 + 16.5976i 0.0247504 + 0.0364783i
\(456\) 0 0
\(457\) −628.547 168.419i −1.37538 0.368531i −0.505937 0.862570i \(-0.668853\pi\)
−0.869440 + 0.494039i \(0.835520\pi\)
\(458\) 677.840 181.627i 1.48000 0.396565i
\(459\) 0 0
\(460\) −3.33582 16.9359i −0.00725179 0.0368171i
\(461\) 224.604 0.487210 0.243605 0.969875i \(-0.421670\pi\)
0.243605 + 0.969875i \(0.421670\pi\)
\(462\) 0 0
\(463\) 36.7738 + 36.7738i 0.0794250 + 0.0794250i 0.745703 0.666278i \(-0.232114\pi\)
−0.666278 + 0.745703i \(0.732114\pi\)
\(464\) 562.203 324.588i 1.21164 0.699543i
\(465\) 0 0
\(466\) −299.435 + 518.637i −0.642565 + 1.11296i
\(467\) 249.401 + 66.8267i 0.534049 + 0.143098i 0.515757 0.856735i \(-0.327511\pi\)
0.0182915 + 0.999833i \(0.494177\pi\)
\(468\) 0 0
\(469\) −7.76830 + 6.07230i −0.0165635 + 0.0129473i
\(470\) 174.208 85.5049i 0.370655 0.181925i
\(471\) 0 0
\(472\) −186.417 695.719i −0.394952 1.47398i
\(473\) −607.642 + 162.817i −1.28465 + 0.344222i
\(474\) 0 0
\(475\) 544.643 + 421.167i 1.14662 + 0.886666i
\(476\) 66.1547 9.31384i 0.138980 0.0195669i
\(477\) 0 0
\(478\) −10.7180 + 40.0002i −0.0224227 + 0.0836825i
\(479\) 633.380 + 365.682i 1.32230 + 0.763429i 0.984095 0.177645i \(-0.0568478\pi\)
0.338202 + 0.941073i \(0.390181\pi\)
\(480\) 0 0
\(481\) −7.59790 13.1599i −0.0157960 0.0273596i
\(482\) 123.001 123.001i 0.255188 0.255188i
\(483\) 0 0
\(484\) 28.7290i 0.0593574i
\(485\) 102.279 + 519.266i 0.210884 + 1.07065i
\(486\) 0 0
\(487\) 194.148 + 724.570i 0.398661 + 1.48782i 0.815454 + 0.578823i \(0.196488\pi\)
−0.416792 + 0.909002i \(0.636846\pi\)
\(488\) 44.9518 167.762i 0.0921144 0.343776i
\(489\) 0 0
\(490\) −26.6961 + 540.173i −0.0544819 + 1.10239i
\(491\) 114.225 0.232638 0.116319 0.993212i \(-0.462891\pi\)
0.116319 + 0.993212i \(0.462891\pi\)
\(492\) 0 0
\(493\) 366.019 98.0745i 0.742432 0.198934i
\(494\) −30.1711 17.4193i −0.0610751 0.0352618i
\(495\) 0 0
\(496\) 443.087 0.893320
\(497\) −236.979 557.910i −0.476819 1.12256i
\(498\) 0 0
\(499\) −326.723 + 188.633i −0.654755 + 0.378023i −0.790275 0.612752i \(-0.790063\pi\)
0.135521 + 0.990775i \(0.456729\pi\)
\(500\) 81.6356 + 72.4072i 0.163271 + 0.144814i
\(501\) 0 0
\(502\) −183.977 49.2964i −0.366487 0.0982000i
\(503\) 29.7057 + 29.7057i 0.0590572 + 0.0590572i 0.736019 0.676961i \(-0.236704\pi\)
−0.676961 + 0.736019i \(0.736704\pi\)
\(504\) 0 0
\(505\) 288.088 + 586.951i 0.570472 + 1.16228i
\(506\) −40.9674 70.9576i −0.0809633 0.140233i
\(507\) 0 0
\(508\) −143.531 + 38.4589i −0.282540 + 0.0757065i
\(509\) 147.952 85.4202i 0.290672 0.167820i −0.347573 0.937653i \(-0.612994\pi\)
0.638245 + 0.769833i \(0.279661\pi\)
\(510\) 0 0
\(511\) −379.123 485.012i −0.741924 0.949143i
\(512\) −183.792 + 183.792i −0.358968 + 0.358968i
\(513\) 0 0
\(514\) −478.141 276.055i −0.930234 0.537071i
\(515\) 126.505 + 144.797i 0.245642 + 0.281160i
\(516\) 0 0
\(517\) 116.686 116.686i 0.225699 0.225699i
\(518\) 49.8361 406.700i 0.0962087 0.785135i
\(519\) 0 0
\(520\) 16.4252 + 11.0195i 0.0315869 + 0.0211913i
\(521\) 75.4299 130.648i 0.144779 0.250765i −0.784511 0.620114i \(-0.787086\pi\)
0.929291 + 0.369350i \(0.120420\pi\)
\(522\) 0 0
\(523\) 210.608 786.001i 0.402693 1.50287i −0.405579 0.914060i \(-0.632930\pi\)
0.808271 0.588810i \(-0.200403\pi\)
\(524\) 107.774i 0.205676i
\(525\) 0 0
\(526\) −801.077 −1.52296
\(527\) 249.821 + 66.9395i 0.474044 + 0.127020i
\(528\) 0 0
\(529\) 444.583 + 256.680i 0.840422 + 0.485218i
\(530\) −93.9026 + 139.967i −0.177175 + 0.264090i
\(531\) 0 0
\(532\) −65.7925 154.893i −0.123670 0.291151i
\(533\) 22.1547 + 22.1547i 0.0415661 + 0.0415661i
\(534\) 0 0
\(535\) −755.043 + 659.660i −1.41130 + 1.23301i
\(536\) −4.86159 + 8.42051i −0.00907012 + 0.0157099i
\(537\) 0 0
\(538\) 460.760 + 460.760i 0.856431 + 0.856431i
\(539\) 126.980 + 442.019i 0.235584 + 0.820072i
\(540\) 0 0
\(541\) −525.462 910.127i −0.971280 1.68231i −0.691702 0.722183i \(-0.743139\pi\)
−0.279577 0.960123i \(-0.590194\pi\)
\(542\) −238.235 889.105i −0.439548 1.64042i
\(543\) 0 0
\(544\) 130.035 75.0758i 0.239035 0.138007i
\(545\) 654.409 321.198i 1.20075 0.589354i
\(546\) 0 0
\(547\) 332.845 332.845i 0.608492 0.608492i −0.334060 0.942552i \(-0.608419\pi\)
0.942552 + 0.334060i \(0.108419\pi\)
\(548\) −33.8024 + 126.152i −0.0616833 + 0.230205i
\(549\) 0 0
\(550\) 477.792 + 200.006i 0.868712 + 0.363647i
\(551\) −477.262 826.642i −0.866174 1.50026i
\(552\) 0 0
\(553\) 828.711 + 624.163i 1.49857 + 1.12868i
\(554\) 558.930i 1.00890i
\(555\) 0 0
\(556\) −37.8609 + 65.5769i −0.0680951 + 0.117944i
\(557\) −177.542 662.596i −0.318747 1.18958i −0.920450 0.390860i \(-0.872177\pi\)
0.601703 0.798720i \(-0.294489\pi\)
\(558\) 0 0
\(559\) 38.4103i 0.0687125i
\(560\) 215.118 + 619.241i 0.384140 + 1.10579i
\(561\) 0 0
\(562\) 501.120 + 134.275i 0.891672 + 0.238923i
\(563\) −451.611 + 121.009i −0.802152 + 0.214936i −0.636528 0.771253i \(-0.719630\pi\)
−0.165623 + 0.986189i \(0.552964\pi\)
\(564\) 0 0
\(565\) −347.313 + 68.4096i −0.614714 + 0.121079i
\(566\) −103.929 −0.183620
\(567\) 0 0
\(568\) −422.669 422.669i −0.744135 0.744135i
\(569\) −492.294 + 284.226i −0.865192 + 0.499519i −0.865747 0.500481i \(-0.833156\pi\)
0.000555696 1.00000i \(0.499823\pi\)
\(570\) 0 0
\(571\) 377.172 653.280i 0.660546 1.14410i −0.319927 0.947442i \(-0.603658\pi\)
0.980472 0.196657i \(-0.0630084\pi\)
\(572\) −4.53534 1.21524i −0.00792891 0.00212455i
\(573\) 0 0
\(574\) 117.781 + 836.577i 0.205193 + 1.45745i
\(575\) 98.0681 12.5377i 0.170553 0.0218048i
\(576\) 0 0
\(577\) −146.947 548.414i −0.254675 0.950458i −0.968271 0.249902i \(-0.919602\pi\)
0.713597 0.700557i \(-0.247065\pi\)
\(578\) −361.364 + 96.8272i −0.625197 + 0.167521i
\(579\) 0 0
\(580\) −66.6574 135.808i −0.114927 0.234152i
\(581\) 131.833 326.527i 0.226907 0.562008i
\(582\) 0 0
\(583\) −37.0953 + 138.441i −0.0636282 + 0.237464i
\(584\) −525.733 303.532i −0.900228 0.519747i
\(585\) 0 0
\(586\) −19.0067 32.9206i −0.0324347 0.0561786i
\(587\) −191.752 + 191.752i −0.326665 + 0.326665i −0.851317 0.524652i \(-0.824195\pi\)
0.524652 + 0.851317i \(0.324195\pi\)
\(588\) 0 0
\(589\) 651.497i 1.10611i
\(590\) −1129.96 + 222.565i −1.91518 + 0.377229i
\(591\) 0 0
\(592\) −128.542 479.725i −0.217132 0.810346i
\(593\) −158.838 + 592.793i −0.267856 + 0.999651i 0.692623 + 0.721299i \(0.256455\pi\)
−0.960479 + 0.278352i \(0.910212\pi\)
\(594\) 0 0
\(595\) 27.7361 + 381.640i 0.0466154 + 0.641412i
\(596\) 21.9506 0.0368298
\(597\) 0 0
\(598\) −4.83233 + 1.29482i −0.00808081 + 0.00216525i
\(599\) 649.805 + 375.165i 1.08482 + 0.626319i 0.932192 0.361965i \(-0.117894\pi\)
0.152625 + 0.988284i \(0.451227\pi\)
\(600\) 0 0
\(601\) −592.685 −0.986165 −0.493083 0.869982i \(-0.664130\pi\)
−0.493083 + 0.869982i \(0.664130\pi\)
\(602\) −623.100 + 827.300i −1.03505 + 1.37425i
\(603\) 0 0
\(604\) −152.460 + 88.0227i −0.252417 + 0.145733i
\(605\) −164.176 11.0692i −0.271366 0.0182963i
\(606\) 0 0
\(607\) 387.642 + 103.868i 0.638619 + 0.171117i 0.563578 0.826063i \(-0.309425\pi\)
0.0750410 + 0.997180i \(0.476091\pi\)
\(608\) −267.450 267.450i −0.439884 0.439884i
\(609\) 0 0
\(610\) −262.802 89.7581i −0.430823 0.147144i
\(611\) −5.03788 8.72587i −0.00824531 0.0142813i
\(612\) 0 0
\(613\) −212.730 + 57.0009i −0.347031 + 0.0929868i −0.428125 0.903720i \(-0.640826\pi\)
0.0810932 + 0.996707i \(0.474159\pi\)
\(614\) 281.877 162.742i 0.459084 0.265052i
\(615\) 0 0
\(616\) 279.299 + 357.307i 0.453407 + 0.580043i
\(617\) −338.020 + 338.020i −0.547844 + 0.547844i −0.925817 0.377973i \(-0.876621\pi\)
0.377973 + 0.925817i \(0.376621\pi\)
\(618\) 0 0
\(619\) 266.400 + 153.806i 0.430371 + 0.248475i 0.699505 0.714628i \(-0.253404\pi\)
−0.269134 + 0.963103i \(0.586737\pi\)
\(620\) 6.94612 103.023i 0.0112034 0.166167i
\(621\) 0 0
\(622\) −51.7078 + 51.7078i −0.0831316 + 0.0831316i
\(623\) −840.266 632.866i −1.34874 1.01584i
\(624\) 0 0
\(625\) −445.237 + 438.622i −0.712379 + 0.701795i
\(626\) 478.840 829.375i 0.764920 1.32488i
\(627\) 0 0
\(628\) −6.57106 + 24.5235i −0.0104635 + 0.0390502i
\(629\) 289.899i 0.460888i
\(630\) 0 0
\(631\) −219.545 −0.347931 −0.173966 0.984752i \(-0.555658\pi\)
−0.173966 + 0.984752i \(0.555658\pi\)
\(632\) 988.213 + 264.791i 1.56363 + 0.418973i
\(633\) 0 0
\(634\) 534.401 + 308.536i 0.842903 + 0.486650i
\(635\) −164.477 835.047i −0.259020 1.31503i
\(636\) 0 0
\(637\) 28.0759 0.503726i 0.0440752 0.000790779i
\(638\) −507.779 507.779i −0.795892 0.795892i
\(639\) 0 0
\(640\) 504.615 + 577.580i 0.788462 + 0.902469i
\(641\) −417.537 + 723.194i −0.651383 + 1.12823i 0.331404 + 0.943489i \(0.392478\pi\)
−0.982787 + 0.184740i \(0.940856\pi\)
\(642\) 0 0
\(643\) −649.916 649.916i −1.01076 1.01076i −0.999942 0.0108149i \(-0.996557\pi\)
−0.0108149 0.999942i \(-0.503443\pi\)
\(644\) −22.4083 9.04721i −0.0347955 0.0140485i
\(645\) 0 0
\(646\) −332.318 575.591i −0.514424 0.891008i
\(647\) −95.3328 355.787i −0.147346 0.549902i −0.999640 0.0268391i \(-0.991456\pi\)
0.852294 0.523063i \(-0.175211\pi\)
\(648\) 0 0
\(649\) −848.115 + 489.659i −1.30680 + 0.754483i
\(650\) 19.3464 25.0184i 0.0297637 0.0384898i
\(651\) 0 0
\(652\) −52.2913 + 52.2913i −0.0802014 + 0.0802014i
\(653\) −117.038 + 436.792i −0.179232 + 0.668901i 0.816561 + 0.577260i \(0.195878\pi\)
−0.995792 + 0.0916414i \(0.970789\pi\)
\(654\) 0 0
\(655\) −615.892 41.5252i −0.940293 0.0633972i
\(656\) 512.008 + 886.823i 0.780499 + 1.35186i
\(657\) 0 0
\(658\) 33.0444 269.668i 0.0502195 0.409829i
\(659\) 395.881i 0.600730i 0.953824 + 0.300365i \(0.0971085\pi\)
−0.953824 + 0.300365i \(0.902892\pi\)
\(660\) 0 0
\(661\) −41.2693 + 71.4804i −0.0624346 + 0.108140i −0.895553 0.444955i \(-0.853220\pi\)
0.833119 + 0.553094i \(0.186553\pi\)
\(662\) 143.042 + 533.838i 0.216075 + 0.806403i
\(663\) 0 0
\(664\) 347.250i 0.522966i
\(665\) 910.509 316.302i 1.36919 0.475642i
\(666\) 0 0
\(667\) −132.398 35.4760i −0.198498 0.0531874i
\(668\) −176.062 + 47.1758i −0.263567 + 0.0706225i
\(669\) 0 0
\(670\) 12.9106 + 8.66158i 0.0192696 + 0.0129277i
\(671\) −236.148 −0.351935
\(672\) 0 0
\(673\) 923.540 + 923.540i 1.37227 + 1.37227i 0.857066 + 0.515207i \(0.172285\pi\)
0.515207 + 0.857066i \(0.327715\pi\)
\(674\) 20.4868 11.8280i 0.0303958 0.0175490i
\(675\) 0 0
\(676\) 73.6218 127.517i 0.108908 0.188634i
\(677\) 242.099 + 64.8703i 0.357606 + 0.0958203i 0.433149 0.901322i \(-0.357402\pi\)
−0.0755429 + 0.997143i \(0.524069\pi\)
\(678\) 0 0
\(679\) 687.055 + 277.394i 1.01186 + 0.408533i
\(680\) 166.259 + 338.735i 0.244498 + 0.498140i
\(681\) 0 0
\(682\) −126.856 473.434i −0.186006 0.694185i
\(683\) 1283.82 344.000i 1.87968 0.503660i 0.880101 0.474787i \(-0.157475\pi\)
0.999583 0.0288723i \(-0.00919162\pi\)
\(684\) 0 0
\(685\) −707.894 241.776i −1.03342 0.352957i
\(686\) 612.884 + 444.603i 0.893417 + 0.648110i
\(687\) 0 0
\(688\) −324.914 + 1212.60i −0.472259 + 1.76250i
\(689\) 7.57873 + 4.37558i 0.0109996 + 0.00635063i
\(690\) 0 0
\(691\) 161.274 + 279.335i 0.233392 + 0.404247i 0.958804 0.284068i \(-0.0916840\pi\)
−0.725412 + 0.688315i \(0.758351\pi\)
\(692\) 43.0873 43.0873i 0.0622649 0.0622649i
\(693\) 0 0
\(694\) 687.843i 0.991129i
\(695\) −360.162 241.629i −0.518219 0.347667i
\(696\) 0 0
\(697\) 154.703 + 577.361i 0.221956 + 0.828352i
\(698\) 226.805 846.449i 0.324936 1.21268i
\(699\) 0 0
\(700\) 147.354 40.3101i 0.210506 0.0575859i
\(701\) −993.695 −1.41754 −0.708769 0.705440i \(-0.750749\pi\)
−0.708769 + 0.705440i \(0.750749\pi\)
\(702\) 0 0
\(703\) −705.369 + 189.003i −1.00337 + 0.268852i
\(704\) 362.529 + 209.306i 0.514956 + 0.297310i
\(705\) 0 0
\(706\) −292.402 −0.414167
\(707\) 908.580 + 111.335i 1.28512 + 0.157476i
\(708\) 0 0
\(709\) 594.099 343.003i 0.837940 0.483785i −0.0186238 0.999827i \(-0.505928\pi\)
0.856563 + 0.516042i \(0.172595\pi\)
\(710\) −719.761 + 628.835i −1.01375 + 0.885683i
\(711\) 0 0
\(712\) −1001.99 268.483i −1.40729 0.377083i
\(713\) −66.1530 66.1530i −0.0927811 0.0927811i
\(714\) 0 0
\(715\) 8.69215 25.4497i 0.0121568 0.0355940i
\(716\) 5.41547 + 9.37986i 0.00756350 + 0.0131004i
\(717\) 0 0
\(718\) −164.061 + 43.9599i −0.228497 + 0.0612255i
\(719\) −258.622 + 149.315i −0.359696 + 0.207671i −0.668948 0.743310i \(-0.733255\pi\)
0.309251 + 0.950980i \(0.399922\pi\)
\(720\) 0 0
\(721\) 266.557 37.5282i 0.369705 0.0520503i
\(722\) −620.353 + 620.353i −0.859214 + 0.859214i
\(723\) 0 0
\(724\) −123.969 71.5738i −0.171228 0.0988588i
\(725\) 801.779 328.598i 1.10590 0.453239i
\(726\) 0 0
\(727\) 427.959 427.959i 0.588665 0.588665i −0.348605 0.937270i \(-0.613344\pi\)
0.937270 + 0.348605i \(0.113344\pi\)
\(728\) 25.4869 10.8259i 0.0350094 0.0148707i
\(729\) 0 0
\(730\) −540.784 + 806.072i −0.740800 + 1.10421i
\(731\) −366.387 + 634.601i −0.501214 + 0.868127i
\(732\) 0 0
\(733\) 112.025 418.082i 0.152830 0.570370i −0.846451 0.532466i \(-0.821265\pi\)
0.999281 0.0379039i \(-0.0120681\pi\)
\(734\) 517.048i 0.704426i
\(735\) 0 0
\(736\) −54.3136 −0.0737956
\(737\) 12.7698 + 3.42167i 0.0173268 + 0.00464270i
\(738\) 0 0
\(739\) −160.126 92.4489i −0.216680 0.125100i 0.387732 0.921772i \(-0.373259\pi\)
−0.604412 + 0.796672i \(0.706592\pi\)
\(740\) −113.557 + 22.3672i −0.153456 + 0.0302259i
\(741\) 0 0
\(742\) 92.2528 + 217.187i 0.124330 + 0.292705i
\(743\) 576.263 + 576.263i 0.775589 + 0.775589i 0.979077 0.203488i \(-0.0652278\pi\)
−0.203488 + 0.979077i \(0.565228\pi\)
\(744\) 0 0
\(745\) −8.45753 + 125.440i −0.0113524 + 0.168376i
\(746\) 419.461 726.527i 0.562280 0.973897i
\(747\) 0 0
\(748\) −63.3393 63.3393i −0.0846782 0.0846782i
\(749\) 195.690 + 1389.96i 0.261269 + 1.85575i
\(750\) 0 0
\(751\) 710.061 + 1229.86i 0.945487 + 1.63763i 0.754772 + 0.655987i \(0.227747\pi\)
0.190715 + 0.981645i \(0.438919\pi\)
\(752\) −85.2314 318.088i −0.113340 0.422989i
\(753\) 0 0
\(754\) −37.9721 + 21.9232i −0.0503609 + 0.0290759i
\(755\) −444.278 905.172i −0.588447 1.19890i
\(756\) 0 0
\(757\) −316.057 + 316.057i −0.417512 + 0.417512i −0.884345 0.466833i \(-0.845395\pi\)
0.466833 + 0.884345i \(0.345395\pi\)
\(758\) −210.989 + 787.422i −0.278350 + 1.03882i
\(759\) 0 0
\(760\) 715.803 625.377i 0.941846 0.822864i
\(761\) −393.410 681.407i −0.516965 0.895409i −0.999806 0.0197013i \(-0.993728\pi\)
0.482841 0.875708i \(-0.339605\pi\)
\(762\) 0 0
\(763\) 124.131 1013.00i 0.162688 1.32766i
\(764\) 110.009i 0.143991i
\(765\) 0 0
\(766\) 800.964 1387.31i 1.04565 1.81111i
\(767\) 15.4762 + 57.7579i 0.0201776 + 0.0753037i
\(768\) 0 0
\(769\) 1512.03i 1.96622i −0.183008 0.983111i \(-0.558583\pi\)
0.183008 0.983111i \(-0.441417\pi\)
\(770\) 600.066 407.142i 0.779306 0.528756i
\(771\) 0 0
\(772\) 46.4186 + 12.4378i 0.0601277 + 0.0161112i
\(773\) 228.469 61.2182i 0.295562 0.0791956i −0.107991 0.994152i \(-0.534442\pi\)
0.403553 + 0.914956i \(0.367775\pi\)
\(774\) 0 0
\(775\) 586.067 + 79.3895i 0.756216 + 0.102438i
\(776\) 730.659 0.941570
\(777\) 0 0
\(778\) 244.160 + 244.160i 0.313830 + 0.313830i
\(779\) 1303.95 752.836i 1.67388 0.966414i
\(780\) 0 0
\(781\) −406.367 + 703.849i −0.520317 + 0.901215i
\(782\) −92.1889 24.7019i −0.117889 0.0315882i
\(783\) 0 0
\(784\) 890.606 + 221.593i 1.13598 + 0.282644i
\(785\) −137.612 47.0003i −0.175302 0.0598730i
\(786\) 0 0
\(787\) −154.380 576.154i −0.196163 0.732090i −0.991963 0.126530i \(-0.959616\pi\)
0.795800 0.605560i \(-0.207051\pi\)
\(788\) −73.9811 + 19.8232i −0.0938847 + 0.0251563i
\(789\) 0 0
\(790\) 528.724 1548.05i 0.669271 1.95955i
\(791\) −185.536 + 459.540i −0.234559 + 0.580961i
\(792\) 0 0
\(793\) −3.73186 + 13.9275i −0.00470600 + 0.0175630i
\(794\) −1203.98 695.120i −1.51635 0.875466i
\(795\) 0 0
\(796\) 122.369 + 211.949i 0.153729 + 0.266267i
\(797\) −650.745 + 650.745i −0.816493 + 0.816493i −0.985598 0.169105i \(-0.945912\pi\)
0.169105 + 0.985598i \(0.445912\pi\)
\(798\) 0 0
\(799\) 192.221i 0.240577i
\(800\) 273.180 207.999i 0.341475 0.259999i
\(801\) 0 0
\(802\) 200.909 + 749.803i 0.250510 + 0.934916i
\(803\) −213.631 + 797.283i −0.266041 + 0.992880i
\(804\) 0 0
\(805\) 60.3357 124.570i 0.0749512 0.154746i
\(806\) −29.9268 −0.0371300
\(807\) 0 0
\(808\) 871.917 233.629i 1.07910 0.289145i
\(809\) −1022.42 590.294i −1.26381 0.729659i −0.289998 0.957027i \(-0.593655\pi\)
−0.973809 + 0.227368i \(0.926988\pi\)
\(810\) 0 0
\(811\) 919.216 1.13344 0.566718 0.823912i \(-0.308213\pi\)
0.566718 + 0.823912i \(0.308213\pi\)
\(812\) −210.226 25.7606i −0.258899 0.0317249i
\(813\) 0 0
\(814\) −475.781 + 274.692i −0.584497 + 0.337460i
\(815\) −278.679 318.975i −0.341938 0.391380i
\(816\) 0 0
\(817\) 1782.96 + 477.742i 2.18232 + 0.584751i
\(818\) −114.284 114.284i −0.139711 0.139711i
\(819\) 0 0
\(820\) 214.224 105.146i 0.261249 0.128227i
\(821\) −390.979 677.195i −0.476222 0.824842i 0.523406 0.852083i \(-0.324661\pi\)
−0.999629 + 0.0272416i \(0.991328\pi\)
\(822\) 0 0
\(823\) 343.971 92.1667i 0.417947 0.111989i −0.0437157 0.999044i \(-0.513920\pi\)
0.461663 + 0.887055i \(0.347253\pi\)
\(824\) 229.887 132.725i 0.278989 0.161074i
\(825\) 0 0
\(826\) −603.627 + 1495.08i −0.730783 + 1.81002i
\(827\) 953.358 953.358i 1.15279 1.15279i 0.166800 0.985991i \(-0.446656\pi\)
0.985991 0.166800i \(-0.0533435\pi\)
\(828\) 0 0
\(829\) −230.809 133.258i −0.278419 0.160745i 0.354288 0.935136i \(-0.384723\pi\)
−0.632708 + 0.774391i \(0.718056\pi\)
\(830\) −553.979 37.3509i −0.667445 0.0450010i
\(831\) 0 0
\(832\) 18.0735 18.0735i 0.0217229 0.0217229i
\(833\) 468.665 + 259.487i 0.562623 + 0.311509i
\(834\) 0 0
\(835\) −201.757 1024.31i −0.241625 1.22672i
\(836\) −112.820 + 195.410i −0.134952 + 0.233743i
\(837\) 0 0
\(838\) 11.3435 42.3345i 0.0135364 0.0505185i
\(839\) 709.681i 0.845866i −0.906161 0.422933i \(-0.861001\pi\)
0.906161 0.422933i \(-0.138999\pi\)
\(840\) 0 0
\(841\) −360.323 −0.428446
\(842\) 41.1871 + 11.0361i 0.0489158 + 0.0131070i
\(843\) 0 0
\(844\) 162.734 + 93.9543i 0.192812 + 0.111320i
\(845\) 700.349 + 469.856i 0.828815 + 0.556042i
\(846\) 0 0
\(847\) −138.595 + 184.014i −0.163630 + 0.217254i
\(848\) 202.244 + 202.244i 0.238496 + 0.238496i
\(849\) 0 0
\(850\) 558.279 228.803i 0.656799 0.269180i
\(851\) −52.4318 + 90.8145i −0.0616119 + 0.106715i
\(852\) 0 0
\(853\) −2.10021 2.10021i −0.00246214 0.00246214i 0.705875 0.708337i \(-0.250554\pi\)
−0.708337 + 0.705875i \(0.750554\pi\)
\(854\) −306.313 + 239.438i −0.358680 + 0.280372i
\(855\) 0 0
\(856\) 692.094 + 1198.74i 0.808521 + 1.40040i
\(857\) −9.61382 35.8793i −0.0112180 0.0418661i 0.960090 0.279691i \(-0.0902321\pi\)
−0.971308 + 0.237825i \(0.923565\pi\)
\(858\) 0 0
\(859\) 83.8106 48.3881i 0.0975677 0.0563307i −0.450422 0.892816i \(-0.648727\pi\)
0.547990 + 0.836485i \(0.315393\pi\)
\(860\) 276.851 + 94.5563i 0.321920 + 0.109949i
\(861\) 0 0
\(862\) −403.212 + 403.212i −0.467764 + 0.467764i
\(863\) 33.9627 126.751i 0.0393543 0.146872i −0.943453 0.331506i \(-0.892443\pi\)
0.982807 + 0.184634i \(0.0591099\pi\)
\(864\) 0 0
\(865\) 229.628 + 262.831i 0.265466 + 0.303851i
\(866\) 480.650 + 832.510i 0.555023 + 0.961328i
\(867\) 0 0
\(868\) −115.472 86.9703i −0.133032 0.100196i
\(869\) 1391.04i 1.60074i
\(870\) 0 0
\(871\) 0.403604 0.699063i 0.000463380 0.000802598i
\(872\) −260.480 972.125i −0.298716 1.11482i
\(873\) 0 0
\(874\) 240.415i 0.275074i
\(875\) 173.584 + 857.609i 0.198381 + 0.980125i
\(876\) 0 0
\(877\) −636.168 170.461i −0.725391 0.194368i −0.122815 0.992430i \(-0.539192\pi\)
−0.602576 + 0.798062i \(0.705859\pi\)
\(878\) 1340.58 359.207i 1.52686 0.409120i
\(879\) 0 0
\(880\) 489.688 729.909i 0.556463 0.829442i
\(881\) 1005.81 1.14167 0.570834 0.821066i \(-0.306620\pi\)
0.570834 + 0.821066i \(0.306620\pi\)
\(882\) 0 0
\(883\) 571.004 + 571.004i 0.646664 + 0.646664i 0.952185 0.305522i \(-0.0988308\pi\)
−0.305522 + 0.952185i \(0.598831\pi\)
\(884\) −4.73656 + 2.73465i −0.00535810 + 0.00309350i
\(885\) 0 0
\(886\) 741.262 1283.90i 0.836639 1.44910i
\(887\) −708.127 189.742i −0.798339 0.213914i −0.163484 0.986546i \(-0.552273\pi\)
−0.634855 + 0.772632i \(0.718940\pi\)
\(888\) 0 0
\(889\) −1104.87 446.085i −1.24283 0.501783i
\(890\) −536.097 + 1569.63i −0.602356 + 1.76363i
\(891\) 0 0
\(892\) 41.3123 + 154.180i 0.0463143 + 0.172847i
\(893\) −467.704 + 125.321i −0.523745 + 0.140337i
\(894\) 0 0
\(895\) −55.6893 + 27.3335i −0.0622227 + 0.0305402i
\(896\) 1063.27 149.696i 1.18668 0.167071i
\(897\) 0 0
\(898\) −20.6810 + 77.1826i −0.0230301 + 0.0859494i
\(899\) −710.095 409.973i −0.789872 0.456033i
\(900\) 0 0
\(901\) 83.4754 + 144.584i 0.0926475 + 0.160470i
\(902\) 800.975 800.975i 0.887999 0.887999i
\(903\) 0 0
\(904\) 488.705i 0.540602i
\(905\) 456.785 680.866i 0.504735 0.752338i
\(906\) 0 0
\(907\) 63.8934 + 238.454i 0.0704448 + 0.262904i 0.992162 0.124959i \(-0.0398800\pi\)
−0.921717 + 0.387863i \(0.873213\pi\)
\(908\) −10.8227 + 40.3910i −0.0119193 + 0.0444835i
\(909\) 0 0
\(910\) −14.5294 41.8245i −0.0159664 0.0459610i
\(911\) 322.782 0.354316 0.177158 0.984182i \(-0.443310\pi\)
0.177158 + 0.984182i \(0.443310\pi\)
\(912\) 0 0
\(913\) −456.057 + 122.200i −0.499515 + 0.133845i
\(914\) 1244.00 + 718.225i 1.36105 + 0.785804i
\(915\) 0 0
\(916\) −277.512 −0.302960
\(917\) −519.924 + 690.312i −0.566984 + 0.752794i
\(918\) 0 0
\(919\) −355.096 + 205.015i −0.386394 + 0.223084i −0.680596 0.732659i \(-0.738279\pi\)
0.294203 + 0.955743i \(0.404946\pi\)
\(920\) 9.18186 136.183i 0.00998028 0.148025i
\(921\) 0 0
\(922\) −478.914 128.325i −0.519429 0.139181i
\(923\) 35.0895 + 35.0895i 0.0380168 + 0.0380168i
\(924\) 0 0
\(925\) −84.0672 657.560i −0.0908835 0.710876i
\(926\) −57.4010 99.4215i −0.0619881 0.107367i
\(927\) 0 0
\(928\) −459.805 + 123.204i −0.495480 + 0.132763i
\(929\) −392.860 + 226.818i −0.422884 + 0.244152i −0.696311 0.717741i \(-0.745176\pi\)
0.273426 + 0.961893i \(0.411843\pi\)
\(930\) 0 0
\(931\) 325.822 1309.51i 0.349970 1.40657i
\(932\) 167.462 167.462i 0.179680 0.179680i
\(933\) 0 0
\(934\) −493.607 284.984i −0.528487 0.305122i
\(935\) 386.367 337.558i 0.413227 0.361025i
\(936\) 0 0
\(937\) −699.175 + 699.175i −0.746184 + 0.746184i −0.973760 0.227576i \(-0.926920\pi\)
0.227576 + 0.973760i \(0.426920\pi\)
\(938\) 20.0334 8.50941i 0.0213575 0.00907186i
\(939\) 0 0
\(940\) −75.2956 + 14.8308i −0.0801017 + 0.0157775i
\(941\) −401.325 + 695.115i −0.426488 + 0.738698i −0.996558 0.0828975i \(-0.973583\pi\)
0.570070 + 0.821596i \(0.306916\pi\)
\(942\) 0 0
\(943\) 55.9601 208.846i 0.0593426 0.221470i
\(944\) 1954.31i 2.07024i
\(945\) 0 0
\(946\) 1388.67 1.46794
\(947\) 110.716 + 29.6662i 0.116912 + 0.0313265i 0.316801 0.948492i \(-0.397391\pi\)
−0.199889 + 0.979819i \(0.564058\pi\)
\(948\) 0 0
\(949\) 43.6459 + 25.1990i 0.0459914 + 0.0265532i
\(950\) −920.692 1209.21i −0.969149 1.27285i
\(951\) 0 0
\(952\) 524.350 + 64.2527i 0.550788 + 0.0674923i
\(953\) −45.8367 45.8367i −0.0480973 0.0480973i 0.682649 0.730746i \(-0.260828\pi\)
−0.730746 + 0.682649i \(0.760828\pi\)
\(954\) 0 0
\(955\) 628.666 + 42.3864i 0.658289 + 0.0443837i
\(956\) 8.18817 14.1823i 0.00856503 0.0148351i
\(957\) 0 0
\(958\) −1141.60 1141.60i −1.19165 1.19165i
\(959\) −825.097 + 644.959i −0.860372 + 0.672533i
\(960\) 0 0
\(961\) 200.678 + 347.585i 0.208822 + 0.361691i
\(962\) 8.68193 + 32.4014i 0.00902487 + 0.0336813i
\(963\) 0 0
\(964\) −59.5732 + 34.3946i −0.0617979 + 0.0356790i
\(965\) −88.9629 + 260.474i −0.0921896 + 0.269921i
\(966\) 0 0
\(967\) −464.416 + 464.416i −0.480265 + 0.480265i −0.905216 0.424951i \(-0.860291\pi\)
0.424951 + 0.905216i \(0.360291\pi\)
\(968\) −58.7965 + 219.432i −0.0607402 + 0.226686i
\(969\) 0 0
\(970\) 78.5911 1165.64i 0.0810218 1.20170i
\(971\) 515.699 + 893.217i 0.531101 + 0.919894i 0.999341 + 0.0362930i \(0.0115550\pi\)
−0.468240 + 0.883601i \(0.655112\pi\)
\(972\) 0 0
\(973\) −558.863 + 237.384i −0.574371 + 0.243971i
\(974\) 1655.90i 1.70010i
\(975\) 0 0
\(976\) −235.626 + 408.117i −0.241421 + 0.418153i
\(977\) 36.2844 + 135.415i 0.0371386 + 0.138603i 0.982006 0.188850i \(-0.0604761\pi\)
−0.944867 + 0.327454i \(0.893809\pi\)
\(978\) 0 0
\(979\) 1410.44i 1.44069i
\(980\) 65.4849 203.603i 0.0668214 0.207759i
\(981\) 0 0
\(982\) −243.558 65.2611i −0.248022 0.0664574i
\(983\) 456.919 122.431i 0.464821 0.124549i −0.0188048 0.999823i \(-0.505986\pi\)
0.483626 + 0.875275i \(0.339319\pi\)
\(984\) 0 0
\(985\) −84.7780 430.415i −0.0860690 0.436970i
\(986\) −836.482 −0.848359
\(987\) 0 0
\(988\) 9.74190 + 9.74190i 0.00986023 + 0.00986023i
\(989\) 229.551 132.531i 0.232104 0.134005i
\(990\) 0 0
\(991\) −423.672 + 733.822i −0.427520 + 0.740486i −0.996652 0.0817597i \(-0.973946\pi\)
0.569132 + 0.822246i \(0.307279\pi\)
\(992\) −313.834 84.0915i −0.316365 0.0847697i
\(993\) 0 0
\(994\) 186.546 + 1325.00i 0.187672 + 1.33300i
\(995\) −1258.36 + 617.632i −1.26469 + 0.620736i
\(996\) 0 0
\(997\) −62.9660 234.992i −0.0631554 0.235699i 0.927132 0.374735i \(-0.122266\pi\)
−0.990287 + 0.139036i \(0.955600\pi\)
\(998\) 804.431 215.547i 0.806043 0.215979i
\(999\) 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 315.3.ca.b.298.5 64
3.2 odd 2 105.3.v.a.88.12 yes 64
5.2 odd 4 inner 315.3.ca.b.172.12 64
7.2 even 3 inner 315.3.ca.b.163.12 64
15.2 even 4 105.3.v.a.67.5 yes 64
21.2 odd 6 105.3.v.a.58.5 yes 64
35.2 odd 12 inner 315.3.ca.b.37.5 64
105.2 even 12 105.3.v.a.37.12 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.v.a.37.12 64 105.2 even 12
105.3.v.a.58.5 yes 64 21.2 odd 6
105.3.v.a.67.5 yes 64 15.2 even 4
105.3.v.a.88.12 yes 64 3.2 odd 2
315.3.ca.b.37.5 64 35.2 odd 12 inner
315.3.ca.b.163.12 64 7.2 even 3 inner
315.3.ca.b.172.12 64 5.2 odd 4 inner
315.3.ca.b.298.5 64 1.1 even 1 trivial