Properties

Label 99.2.j.a.62.1
Level $99$
Weight $2$
Character 99.62
Analytic conductor $0.791$
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] = [99,2,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), 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: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 62.1
Root \(-0.0783900 + 1.17295i\) of defining polynomial
Character \(\chi\) \(=\) 99.62
Dual form 99.2.j.a.8.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.97102 - 1.43203i) q^{2} +(1.21618 + 3.74302i) q^{4} +(2.23109 + 3.07083i) q^{5} +(-0.349790 + 0.113654i) q^{7} +(1.45728 - 4.48505i) q^{8} +O(q^{10})\) \(q+(-1.97102 - 1.43203i) q^{2} +(1.21618 + 3.74302i) q^{4} +(2.23109 + 3.07083i) q^{5} +(-0.349790 + 0.113654i) q^{7} +(1.45728 - 4.48505i) q^{8} -9.24768i q^{10} +(2.97756 - 1.46086i) q^{11} +(-0.557375 + 0.767161i) q^{13} +(0.852201 + 0.276897i) q^{14} +(-2.92705 + 2.12663i) q^{16} +(-2.77873 + 2.01886i) q^{17} +(4.05368 + 1.31712i) q^{19} +(-8.78079 + 12.0857i) q^{20} +(-7.96085 - 1.38457i) q^{22} -4.96800i q^{23} +(-2.90717 + 8.94734i) q^{25} +(2.19720 - 0.713913i) q^{26} +(-0.850818 - 1.17105i) q^{28} +(0.767418 + 2.36187i) q^{29} +(-2.84281 - 2.06543i) q^{31} -0.617031 q^{32} +8.36801 q^{34} +(-1.12943 - 0.820576i) q^{35} +(-2.21947 - 6.83082i) q^{37} +(-6.10374 - 8.40108i) q^{38} +(17.0242 - 5.53148i) q^{40} +(0.840249 - 2.58602i) q^{41} -1.88749i q^{43} +(9.08931 + 9.36841i) q^{44} +(-7.11434 + 9.79205i) q^{46} +(-0.0195991 - 0.00636813i) q^{47} +(-5.55368 + 4.03499i) q^{49} +(18.5430 - 13.4723i) q^{50} +(-3.54937 - 1.15326i) q^{52} +(3.25941 - 4.48619i) q^{53} +(11.1293 + 5.88428i) q^{55} +1.73445i q^{56} +(1.86968 - 5.75427i) q^{58} +(-6.29998 + 2.04699i) q^{59} +(-5.73238 - 7.88994i) q^{61} +(2.64550 + 8.14200i) q^{62} +(7.07028 + 5.13686i) q^{64} -3.59938 q^{65} +4.46351 q^{67} +(-10.9361 - 7.94554i) q^{68} +(1.05103 + 3.23475i) q^{70} +(-6.06985 - 8.35443i) q^{71} +(-4.18072 + 1.35840i) q^{73} +(-5.40733 + 16.6420i) q^{74} +16.7749i q^{76} +(-0.875490 + 0.849407i) q^{77} +(6.42867 - 8.84831i) q^{79} +(-13.0610 - 4.24379i) q^{80} +(-5.35942 + 3.89384i) q^{82} +(-7.42940 + 5.39778i) q^{83} +(-12.3992 - 4.02874i) q^{85} +(-2.70294 + 3.72028i) q^{86} +(-2.21290 - 15.4834i) q^{88} +3.04837i q^{89} +(0.107774 - 0.331693i) q^{91} +(18.5954 - 6.04200i) q^{92} +(0.0295109 + 0.0406183i) q^{94} +(4.99948 + 15.3868i) q^{95} +(12.2055 + 8.86782i) q^{97} +16.7247 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70} - 20 q^{73} - 12 q^{82} - 100 q^{85} - 12 q^{88} - 72 q^{91} - 80 q^{94} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97102 1.43203i −1.39372 1.01260i −0.995445 0.0953352i \(-0.969608\pi\)
−0.398279 0.917264i \(-0.630392\pi\)
\(3\) 0 0
\(4\) 1.21618 + 3.74302i 0.608091 + 1.87151i
\(5\) 2.23109 + 3.07083i 0.997774 + 1.37332i 0.926681 + 0.375849i \(0.122649\pi\)
0.0710932 + 0.997470i \(0.477351\pi\)
\(6\) 0 0
\(7\) −0.349790 + 0.113654i −0.132208 + 0.0429571i −0.374374 0.927278i \(-0.622142\pi\)
0.242165 + 0.970235i \(0.422142\pi\)
\(8\) 1.45728 4.48505i 0.515226 1.58570i
\(9\) 0 0
\(10\) 9.24768i 2.92437i
\(11\) 2.97756 1.46086i 0.897769 0.440467i
\(12\) 0 0
\(13\) −0.557375 + 0.767161i −0.154588 + 0.212772i −0.879286 0.476295i \(-0.841979\pi\)
0.724698 + 0.689067i \(0.241979\pi\)
\(14\) 0.852201 + 0.276897i 0.227760 + 0.0740038i
\(15\) 0 0
\(16\) −2.92705 + 2.12663i −0.731763 + 0.531657i
\(17\) −2.77873 + 2.01886i −0.673940 + 0.489646i −0.871342 0.490676i \(-0.836750\pi\)
0.197402 + 0.980323i \(0.436750\pi\)
\(18\) 0 0
\(19\) 4.05368 + 1.31712i 0.929979 + 0.302168i 0.734554 0.678550i \(-0.237391\pi\)
0.195425 + 0.980719i \(0.437391\pi\)
\(20\) −8.78079 + 12.0857i −1.96344 + 2.70245i
\(21\) 0 0
\(22\) −7.96085 1.38457i −1.69726 0.295191i
\(23\) 4.96800i 1.03590i −0.855411 0.517950i \(-0.826695\pi\)
0.855411 0.517950i \(-0.173305\pi\)
\(24\) 0 0
\(25\) −2.90717 + 8.94734i −0.581433 + 1.78947i
\(26\) 2.19720 0.713913i 0.430906 0.140010i
\(27\) 0 0
\(28\) −0.850818 1.17105i −0.160789 0.221308i
\(29\) 0.767418 + 2.36187i 0.142506 + 0.438588i 0.996682 0.0813958i \(-0.0259378\pi\)
−0.854176 + 0.519984i \(0.825938\pi\)
\(30\) 0 0
\(31\) −2.84281 2.06543i −0.510585 0.370961i 0.302461 0.953162i \(-0.402192\pi\)
−0.813045 + 0.582200i \(0.802192\pi\)
\(32\) −0.617031 −0.109077
\(33\) 0 0
\(34\) 8.36801 1.43510
\(35\) −1.12943 0.820576i −0.190908 0.138703i
\(36\) 0 0
\(37\) −2.21947 6.83082i −0.364878 1.12298i −0.950057 0.312075i \(-0.898976\pi\)
0.585179 0.810904i \(-0.301024\pi\)
\(38\) −6.10374 8.40108i −0.990158 1.36284i
\(39\) 0 0
\(40\) 17.0242 5.53148i 2.69176 0.874604i
\(41\) 0.840249 2.58602i 0.131225 0.403869i −0.863759 0.503905i \(-0.831896\pi\)
0.994984 + 0.100037i \(0.0318960\pi\)
\(42\) 0 0
\(43\) 1.88749i 0.287839i −0.989589 0.143919i \(-0.954029\pi\)
0.989589 0.143919i \(-0.0459706\pi\)
\(44\) 9.08931 + 9.36841i 1.37026 + 1.41234i
\(45\) 0 0
\(46\) −7.11434 + 9.79205i −1.04895 + 1.44376i
\(47\) −0.0195991 0.00636813i −0.00285882 0.000928888i 0.307587 0.951520i \(-0.400478\pi\)
−0.310446 + 0.950591i \(0.600478\pi\)
\(48\) 0 0
\(49\) −5.55368 + 4.03499i −0.793383 + 0.576427i
\(50\) 18.5430 13.4723i 2.62237 1.90526i
\(51\) 0 0
\(52\) −3.54937 1.15326i −0.492209 0.159928i
\(53\) 3.25941 4.48619i 0.447714 0.616226i −0.524190 0.851601i \(-0.675632\pi\)
0.971905 + 0.235375i \(0.0756319\pi\)
\(54\) 0 0
\(55\) 11.1293 + 5.88428i 1.50067 + 0.793436i
\(56\) 1.73445i 0.231776i
\(57\) 0 0
\(58\) 1.86968 5.75427i 0.245500 0.755573i
\(59\) −6.29998 + 2.04699i −0.820187 + 0.266495i −0.688906 0.724850i \(-0.741909\pi\)
−0.131281 + 0.991345i \(0.541909\pi\)
\(60\) 0 0
\(61\) −5.73238 7.88994i −0.733956 1.01020i −0.998944 0.0459514i \(-0.985368\pi\)
0.264988 0.964252i \(-0.414632\pi\)
\(62\) 2.64550 + 8.14200i 0.335978 + 1.03404i
\(63\) 0 0
\(64\) 7.07028 + 5.13686i 0.883786 + 0.642108i
\(65\) −3.59938 −0.446448
\(66\) 0 0
\(67\) 4.46351 0.545305 0.272652 0.962113i \(-0.412099\pi\)
0.272652 + 0.962113i \(0.412099\pi\)
\(68\) −10.9361 7.94554i −1.32620 0.963538i
\(69\) 0 0
\(70\) 1.05103 + 3.23475i 0.125623 + 0.386626i
\(71\) −6.06985 8.35443i −0.720359 0.991489i −0.999512 0.0312420i \(-0.990054\pi\)
0.279153 0.960247i \(-0.409946\pi\)
\(72\) 0 0
\(73\) −4.18072 + 1.35840i −0.489317 + 0.158989i −0.543275 0.839555i \(-0.682816\pi\)
0.0539588 + 0.998543i \(0.482816\pi\)
\(74\) −5.40733 + 16.6420i −0.628589 + 1.93460i
\(75\) 0 0
\(76\) 16.7749i 1.92421i
\(77\) −0.875490 + 0.849407i −0.0997714 + 0.0967989i
\(78\) 0 0
\(79\) 6.42867 8.84831i 0.723282 0.995513i −0.276126 0.961121i \(-0.589051\pi\)
0.999408 0.0343911i \(-0.0109492\pi\)
\(80\) −13.0610 4.24379i −1.46027 0.474470i
\(81\) 0 0
\(82\) −5.35942 + 3.89384i −0.591848 + 0.430003i
\(83\) −7.42940 + 5.39778i −0.815483 + 0.592483i −0.915415 0.402511i \(-0.868137\pi\)
0.0999323 + 0.994994i \(0.468137\pi\)
\(84\) 0 0
\(85\) −12.3992 4.02874i −1.34488 0.436978i
\(86\) −2.70294 + 3.72028i −0.291466 + 0.401168i
\(87\) 0 0
\(88\) −2.21290 15.4834i −0.235896 1.65054i
\(89\) 3.04837i 0.323127i 0.986862 + 0.161563i \(0.0516536\pi\)
−0.986862 + 0.161563i \(0.948346\pi\)
\(90\) 0 0
\(91\) 0.107774 0.331693i 0.0112978 0.0347709i
\(92\) 18.5954 6.04200i 1.93870 0.629922i
\(93\) 0 0
\(94\) 0.0295109 + 0.0406183i 0.00304382 + 0.00418946i
\(95\) 4.99948 + 15.3868i 0.512935 + 1.57865i
\(96\) 0 0
\(97\) 12.2055 + 8.86782i 1.23928 + 0.900391i 0.997550 0.0699519i \(-0.0222846\pi\)
0.241732 + 0.970343i \(0.422285\pi\)
\(98\) 16.7247 1.68945
\(99\) 0 0
\(100\) −37.0257 −3.70257
\(101\) 14.1253 + 10.2626i 1.40552 + 1.02117i 0.993955 + 0.109787i \(0.0350168\pi\)
0.411562 + 0.911382i \(0.364983\pi\)
\(102\) 0 0
\(103\) −2.87868 8.85967i −0.283645 0.872969i −0.986802 0.161934i \(-0.948227\pi\)
0.703157 0.711035i \(-0.251773\pi\)
\(104\) 2.62850 + 3.61782i 0.257746 + 0.354757i
\(105\) 0 0
\(106\) −12.8487 + 4.17481i −1.24798 + 0.405493i
\(107\) 4.76675 14.6705i 0.460819 1.41825i −0.403347 0.915047i \(-0.632153\pi\)
0.864166 0.503207i \(-0.167847\pi\)
\(108\) 0 0
\(109\) 10.6286i 1.01803i −0.860757 0.509016i \(-0.830009\pi\)
0.860757 0.509016i \(-0.169991\pi\)
\(110\) −13.5096 27.5355i −1.28809 2.62541i
\(111\) 0 0
\(112\) 0.782155 1.07654i 0.0739067 0.101724i
\(113\) 0.995774 + 0.323547i 0.0936746 + 0.0304367i 0.355479 0.934684i \(-0.384318\pi\)
−0.261805 + 0.965121i \(0.584318\pi\)
\(114\) 0 0
\(115\) 15.2559 11.0841i 1.42262 1.03359i
\(116\) −7.90722 + 5.74493i −0.734167 + 0.533404i
\(117\) 0 0
\(118\) 15.3487 + 4.98711i 1.41297 + 0.459101i
\(119\) 0.742521 1.02199i 0.0680668 0.0936859i
\(120\) 0 0
\(121\) 6.73176 8.69962i 0.611978 0.790875i
\(122\) 23.7602i 2.15115i
\(123\) 0 0
\(124\) 4.27356 13.1527i 0.383777 1.18114i
\(125\) −15.9120 + 5.17013i −1.42321 + 0.462430i
\(126\) 0 0
\(127\) 10.3127 + 14.1942i 0.915101 + 1.25953i 0.965394 + 0.260794i \(0.0839845\pi\)
−0.0502930 + 0.998735i \(0.516016\pi\)
\(128\) −6.19820 19.0761i −0.547848 1.68610i
\(129\) 0 0
\(130\) 7.09446 + 5.15442i 0.622225 + 0.452073i
\(131\) 13.8890 1.21349 0.606744 0.794897i \(-0.292475\pi\)
0.606744 + 0.794897i \(0.292475\pi\)
\(132\) 0 0
\(133\) −1.56764 −0.135931
\(134\) −8.79769 6.39189i −0.760004 0.552176i
\(135\) 0 0
\(136\) 5.00531 + 15.4048i 0.429202 + 1.32095i
\(137\) 0.609963 + 0.839541i 0.0521126 + 0.0717269i 0.834278 0.551344i \(-0.185885\pi\)
−0.782165 + 0.623071i \(0.785885\pi\)
\(138\) 0 0
\(139\) −18.8643 + 6.12938i −1.60005 + 0.519887i −0.967119 0.254324i \(-0.918147\pi\)
−0.632928 + 0.774210i \(0.718147\pi\)
\(140\) 1.69785 5.22544i 0.143494 0.441630i
\(141\) 0 0
\(142\) 25.1590i 2.11130i
\(143\) −0.538902 + 3.09852i −0.0450652 + 0.259111i
\(144\) 0 0
\(145\) −5.54073 + 7.62616i −0.460133 + 0.633318i
\(146\) 10.1856 + 3.30949i 0.842964 + 0.273896i
\(147\) 0 0
\(148\) 22.8686 16.6150i 1.87979 1.36575i
\(149\) −6.50125 + 4.72344i −0.532603 + 0.386959i −0.821331 0.570452i \(-0.806768\pi\)
0.288727 + 0.957411i \(0.406768\pi\)
\(150\) 0 0
\(151\) −9.58050 3.11289i −0.779650 0.253324i −0.107959 0.994155i \(-0.534432\pi\)
−0.671691 + 0.740832i \(0.734432\pi\)
\(152\) 11.8147 16.2615i 0.958299 1.31899i
\(153\) 0 0
\(154\) 2.94199 0.420471i 0.237072 0.0338826i
\(155\) 13.3380i 1.07133i
\(156\) 0 0
\(157\) −5.00062 + 15.3903i −0.399093 + 1.22828i 0.526635 + 0.850091i \(0.323453\pi\)
−0.925728 + 0.378190i \(0.876547\pi\)
\(158\) −25.3421 + 8.23416i −2.01611 + 0.655074i
\(159\) 0 0
\(160\) −1.37665 1.89480i −0.108834 0.149797i
\(161\) 0.564633 + 1.73776i 0.0444993 + 0.136955i
\(162\) 0 0
\(163\) −3.45923 2.51328i −0.270948 0.196855i 0.444012 0.896021i \(-0.353555\pi\)
−0.714959 + 0.699166i \(0.753555\pi\)
\(164\) 10.7014 0.835642
\(165\) 0 0
\(166\) 22.3733 1.73651
\(167\) −14.8478 10.7875i −1.14896 0.834765i −0.160614 0.987017i \(-0.551347\pi\)
−0.988342 + 0.152252i \(0.951347\pi\)
\(168\) 0 0
\(169\) 3.73935 + 11.5085i 0.287642 + 0.885272i
\(170\) 18.6698 + 25.6968i 1.43191 + 1.97085i
\(171\) 0 0
\(172\) 7.06490 2.29553i 0.538694 0.175032i
\(173\) −1.91046 + 5.87980i −0.145250 + 0.447033i −0.997043 0.0768452i \(-0.975515\pi\)
0.851793 + 0.523878i \(0.175515\pi\)
\(174\) 0 0
\(175\) 3.46010i 0.261559i
\(176\) −5.60877 + 10.6082i −0.422777 + 0.799622i
\(177\) 0 0
\(178\) 4.36536 6.00841i 0.327198 0.450349i
\(179\) −8.77414 2.85089i −0.655810 0.213086i −0.0378357 0.999284i \(-0.512046\pi\)
−0.617974 + 0.786198i \(0.712046\pi\)
\(180\) 0 0
\(181\) 3.38790 2.46145i 0.251821 0.182958i −0.454713 0.890638i \(-0.650258\pi\)
0.706533 + 0.707680i \(0.250258\pi\)
\(182\) −0.687420 + 0.499440i −0.0509550 + 0.0370209i
\(183\) 0 0
\(184\) −22.2817 7.23977i −1.64263 0.533723i
\(185\) 16.0245 22.0558i 1.17814 1.62157i
\(186\) 0 0
\(187\) −5.32455 + 10.0706i −0.389370 + 0.736438i
\(188\) 0.0811047i 0.00591517i
\(189\) 0 0
\(190\) 12.1803 37.4872i 0.883653 2.71960i
\(191\) 19.1951 6.23688i 1.38891 0.451285i 0.483323 0.875442i \(-0.339430\pi\)
0.905589 + 0.424157i \(0.139430\pi\)
\(192\) 0 0
\(193\) 4.71049 + 6.48343i 0.339068 + 0.466687i 0.944169 0.329462i \(-0.106867\pi\)
−0.605101 + 0.796149i \(0.706867\pi\)
\(194\) −11.3583 34.9574i −0.815481 2.50979i
\(195\) 0 0
\(196\) −21.8573 15.8803i −1.56124 1.13431i
\(197\) −21.1710 −1.50837 −0.754187 0.656659i \(-0.771969\pi\)
−0.754187 + 0.656659i \(0.771969\pi\)
\(198\) 0 0
\(199\) −10.5160 −0.745457 −0.372729 0.927940i \(-0.621578\pi\)
−0.372729 + 0.927940i \(0.621578\pi\)
\(200\) 35.8927 + 26.0775i 2.53799 + 1.84396i
\(201\) 0 0
\(202\) −13.1449 40.4557i −0.924869 2.84645i
\(203\) −0.536871 0.738940i −0.0376810 0.0518634i
\(204\) 0 0
\(205\) 9.81591 3.18938i 0.685573 0.222756i
\(206\) −7.01339 + 21.5850i −0.488646 + 1.50390i
\(207\) 0 0
\(208\) 3.43085i 0.237886i
\(209\) 13.9942 2.00007i 0.968001 0.138347i
\(210\) 0 0
\(211\) −2.17376 + 2.99193i −0.149648 + 0.205973i −0.877259 0.480017i \(-0.840631\pi\)
0.727611 + 0.685990i \(0.240631\pi\)
\(212\) 20.7560 + 6.74402i 1.42553 + 0.463181i
\(213\) 0 0
\(214\) −30.4041 + 22.0898i −2.07838 + 1.51003i
\(215\) 5.79615 4.21115i 0.395294 0.287198i
\(216\) 0 0
\(217\) 1.22913 + 0.399369i 0.0834390 + 0.0271110i
\(218\) −15.2205 + 20.9492i −1.03086 + 1.41886i
\(219\) 0 0
\(220\) −8.48976 + 48.8135i −0.572380 + 3.29101i
\(221\) 3.25699i 0.219089i
\(222\) 0 0
\(223\) −5.53051 + 17.0212i −0.370351 + 1.13982i 0.576212 + 0.817301i \(0.304530\pi\)
−0.946562 + 0.322521i \(0.895470\pi\)
\(224\) 0.215832 0.0701279i 0.0144209 0.00468562i
\(225\) 0 0
\(226\) −1.49936 2.06370i −0.0997363 0.137275i
\(227\) 5.37022 + 16.5278i 0.356434 + 1.09699i 0.955173 + 0.296047i \(0.0956684\pi\)
−0.598740 + 0.800944i \(0.704332\pi\)
\(228\) 0 0
\(229\) −3.45989 2.51375i −0.228636 0.166114i 0.467570 0.883956i \(-0.345130\pi\)
−0.696205 + 0.717843i \(0.745130\pi\)
\(230\) −45.9425 −3.02936
\(231\) 0 0
\(232\) 11.7114 0.768894
\(233\) 18.9171 + 13.7441i 1.23930 + 0.900404i 0.997552 0.0699355i \(-0.0222793\pi\)
0.241748 + 0.970339i \(0.422279\pi\)
\(234\) 0 0
\(235\) −0.0241719 0.0743935i −0.00157680 0.00485289i
\(236\) −15.3238 21.0915i −0.997497 1.37294i
\(237\) 0 0
\(238\) −2.92705 + 0.951057i −0.189733 + 0.0616478i
\(239\) −6.17902 + 19.0171i −0.399687 + 1.23011i 0.525563 + 0.850754i \(0.323855\pi\)
−0.925251 + 0.379356i \(0.876145\pi\)
\(240\) 0 0
\(241\) 2.32570i 0.149811i −0.997191 0.0749057i \(-0.976134\pi\)
0.997191 0.0749057i \(-0.0238656\pi\)
\(242\) −25.7266 + 7.50707i −1.65377 + 0.482573i
\(243\) 0 0
\(244\) 22.5606 31.0520i 1.44430 1.98790i
\(245\) −24.7815 8.05201i −1.58323 0.514424i
\(246\) 0 0
\(247\) −3.26987 + 2.37570i −0.208057 + 0.151162i
\(248\) −13.4063 + 9.74025i −0.851301 + 0.618507i
\(249\) 0 0
\(250\) 38.7668 + 12.5961i 2.45182 + 0.796646i
\(251\) −1.88681 + 2.59698i −0.119095 + 0.163920i −0.864402 0.502801i \(-0.832303\pi\)
0.745307 + 0.666721i \(0.232303\pi\)
\(252\) 0 0
\(253\) −7.25758 14.7925i −0.456280 0.929999i
\(254\) 42.7451i 2.68207i
\(255\) 0 0
\(256\) −9.69957 + 29.8522i −0.606223 + 1.86576i
\(257\) 17.1597 5.57552i 1.07039 0.347792i 0.279752 0.960072i \(-0.409748\pi\)
0.790641 + 0.612281i \(0.209748\pi\)
\(258\) 0 0
\(259\) 1.55270 + 2.13710i 0.0964798 + 0.132793i
\(260\) −4.37750 13.4726i −0.271481 0.835533i
\(261\) 0 0
\(262\) −27.3756 19.8895i −1.69127 1.22878i
\(263\) −2.05966 −0.127004 −0.0635019 0.997982i \(-0.520227\pi\)
−0.0635019 + 0.997982i \(0.520227\pi\)
\(264\) 0 0
\(265\) 21.0484 1.29299
\(266\) 3.08985 + 2.24490i 0.189451 + 0.137644i
\(267\) 0 0
\(268\) 5.42845 + 16.7070i 0.331595 + 1.02054i
\(269\) −1.69280 2.32994i −0.103212 0.142059i 0.754287 0.656545i \(-0.227983\pi\)
−0.857499 + 0.514486i \(0.827983\pi\)
\(270\) 0 0
\(271\) 9.67272 3.14286i 0.587576 0.190915i −0.000115761 1.00000i \(-0.500037\pi\)
0.587692 + 0.809085i \(0.300037\pi\)
\(272\) 3.84011 11.8186i 0.232841 0.716610i
\(273\) 0 0
\(274\) 2.52824i 0.152737i
\(275\) 4.41457 + 30.8882i 0.266208 + 1.86263i
\(276\) 0 0
\(277\) 4.29714 5.91450i 0.258190 0.355368i −0.660169 0.751117i \(-0.729515\pi\)
0.918358 + 0.395750i \(0.129515\pi\)
\(278\) 45.9594 + 14.9331i 2.75646 + 0.895629i
\(279\) 0 0
\(280\) −5.32621 + 3.86972i −0.318302 + 0.231260i
\(281\) 1.86513 1.35510i 0.111264 0.0808384i −0.530762 0.847521i \(-0.678094\pi\)
0.642026 + 0.766683i \(0.278094\pi\)
\(282\) 0 0
\(283\) 23.2370 + 7.55016i 1.38130 + 0.448810i 0.903095 0.429441i \(-0.141289\pi\)
0.478200 + 0.878251i \(0.341289\pi\)
\(284\) 23.8888 32.8801i 1.41754 1.95108i
\(285\) 0 0
\(286\) 5.49936 5.33553i 0.325184 0.315496i
\(287\) 1.00006i 0.0590318i
\(288\) 0 0
\(289\) −1.60777 + 4.94822i −0.0945749 + 0.291072i
\(290\) 21.8418 7.09684i 1.28260 0.416741i
\(291\) 0 0
\(292\) −10.1690 13.9965i −0.595098 0.819082i
\(293\) −3.29456 10.1396i −0.192470 0.592362i −0.999997 0.00253112i \(-0.999194\pi\)
0.807527 0.589831i \(-0.200806\pi\)
\(294\) 0 0
\(295\) −20.3418 14.7792i −1.18434 0.860476i
\(296\) −33.8709 −1.96871
\(297\) 0 0
\(298\) 19.5782 1.13414
\(299\) 3.81126 + 2.76904i 0.220411 + 0.160138i
\(300\) 0 0
\(301\) 0.214520 + 0.660224i 0.0123647 + 0.0380547i
\(302\) 14.4256 + 19.8552i 0.830102 + 1.14254i
\(303\) 0 0
\(304\) −14.6664 + 4.76539i −0.841174 + 0.273314i
\(305\) 11.4392 35.2063i 0.655009 2.01591i
\(306\) 0 0
\(307\) 4.56848i 0.260737i −0.991466 0.130369i \(-0.958384\pi\)
0.991466 0.130369i \(-0.0416160\pi\)
\(308\) −4.24411 2.24395i −0.241830 0.127861i
\(309\) 0 0
\(310\) −19.1004 + 26.2894i −1.08483 + 1.49314i
\(311\) 8.92302 + 2.89926i 0.505978 + 0.164402i 0.550872 0.834590i \(-0.314295\pi\)
−0.0448944 + 0.998992i \(0.514295\pi\)
\(312\) 0 0
\(313\) 4.05804 2.94834i 0.229374 0.166650i −0.467162 0.884172i \(-0.654724\pi\)
0.696536 + 0.717522i \(0.254724\pi\)
\(314\) 31.8958 23.1736i 1.79998 1.30776i
\(315\) 0 0
\(316\) 40.9379 + 13.3015i 2.30294 + 0.748269i
\(317\) −6.86310 + 9.44624i −0.385470 + 0.530554i −0.957023 0.290011i \(-0.906341\pi\)
0.571553 + 0.820565i \(0.306341\pi\)
\(318\) 0 0
\(319\) 5.73541 + 5.91153i 0.321121 + 0.330982i
\(320\) 33.1725i 1.85440i
\(321\) 0 0
\(322\) 1.37562 4.23374i 0.0766606 0.235937i
\(323\) −13.9232 + 4.52391i −0.774706 + 0.251717i
\(324\) 0 0
\(325\) −5.24366 7.21728i −0.290866 0.400343i
\(326\) 3.21912 + 9.90745i 0.178291 + 0.548723i
\(327\) 0 0
\(328\) −10.3739 7.53711i −0.572805 0.416167i
\(329\) 0.00757934 0.000417863
\(330\) 0 0
\(331\) −29.0516 −1.59682 −0.798411 0.602113i \(-0.794326\pi\)
−0.798411 + 0.602113i \(0.794326\pi\)
\(332\) −29.2395 21.2438i −1.60473 1.16590i
\(333\) 0 0
\(334\) 13.8172 + 42.5250i 0.756044 + 2.32686i
\(335\) 9.95850 + 13.7067i 0.544091 + 0.748877i
\(336\) 0 0
\(337\) 27.4668 8.92451i 1.49621 0.486149i 0.557302 0.830310i \(-0.311837\pi\)
0.938911 + 0.344161i \(0.111837\pi\)
\(338\) 9.11025 28.0385i 0.495532 1.52509i
\(339\) 0 0
\(340\) 51.3101i 2.78268i
\(341\) −11.4820 1.99697i −0.621783 0.108142i
\(342\) 0 0
\(343\) 2.99731 4.12544i 0.161840 0.222753i
\(344\) −8.46546 2.75060i −0.456427 0.148302i
\(345\) 0 0
\(346\) 12.1856 8.85338i 0.655103 0.475961i
\(347\) −17.9141 + 13.0153i −0.961678 + 0.698700i −0.953540 0.301267i \(-0.902590\pi\)
−0.00813801 + 0.999967i \(0.502590\pi\)
\(348\) 0 0
\(349\) −14.8959 4.83997i −0.797359 0.259078i −0.118125 0.992999i \(-0.537688\pi\)
−0.679235 + 0.733921i \(0.737688\pi\)
\(350\) −4.95498 + 6.81994i −0.264855 + 0.364541i
\(351\) 0 0
\(352\) −1.83725 + 0.901398i −0.0979257 + 0.0480447i
\(353\) 11.1636i 0.594180i 0.954850 + 0.297090i \(0.0960161\pi\)
−0.954850 + 0.297090i \(0.903984\pi\)
\(354\) 0 0
\(355\) 12.1127 37.2790i 0.642874 1.97856i
\(356\) −11.4101 + 3.70737i −0.604735 + 0.196490i
\(357\) 0 0
\(358\) 13.2115 + 18.1840i 0.698248 + 0.961055i
\(359\) −5.11867 15.7536i −0.270153 0.831445i −0.990461 0.137791i \(-0.956000\pi\)
0.720308 0.693654i \(-0.244000\pi\)
\(360\) 0 0
\(361\) −0.673787 0.489535i −0.0354625 0.0257650i
\(362\) −10.2025 −0.536232
\(363\) 0 0
\(364\) 1.37261 0.0719442
\(365\) −13.4990 9.80759i −0.706569 0.513353i
\(366\) 0 0
\(367\) 3.03154 + 9.33012i 0.158245 + 0.487028i 0.998475 0.0552016i \(-0.0175801\pi\)
−0.840230 + 0.542230i \(0.817580\pi\)
\(368\) 10.5651 + 14.5416i 0.550743 + 0.758033i
\(369\) 0 0
\(370\) −63.1692 + 20.5249i −3.28401 + 1.06704i
\(371\) −0.630238 + 1.93967i −0.0327203 + 0.100703i
\(372\) 0 0
\(373\) 12.6350i 0.654216i 0.944987 + 0.327108i \(0.106074\pi\)
−0.944987 + 0.327108i \(0.893926\pi\)
\(374\) 24.9163 12.2245i 1.28839 0.632115i
\(375\) 0 0
\(376\) −0.0571228 + 0.0786227i −0.00294588 + 0.00405466i
\(377\) −2.23967 0.727714i −0.115349 0.0374792i
\(378\) 0 0
\(379\) −28.3981 + 20.6325i −1.45871 + 1.05982i −0.475019 + 0.879975i \(0.657559\pi\)
−0.983695 + 0.179843i \(0.942441\pi\)
\(380\) −51.5129 + 37.4263i −2.64256 + 1.91993i
\(381\) 0 0
\(382\) −46.7655 15.1950i −2.39273 0.777445i
\(383\) −13.2760 + 18.2729i −0.678374 + 0.933701i −0.999913 0.0131951i \(-0.995800\pi\)
0.321539 + 0.946896i \(0.395800\pi\)
\(384\) 0 0
\(385\) −4.56169 0.793379i −0.232485 0.0404344i
\(386\) 19.5246i 0.993774i
\(387\) 0 0
\(388\) −18.3484 + 56.4704i −0.931497 + 2.86685i
\(389\) −6.99867 + 2.27401i −0.354847 + 0.115297i −0.481015 0.876712i \(-0.659732\pi\)
0.126169 + 0.992009i \(0.459732\pi\)
\(390\) 0 0
\(391\) 10.0297 + 13.8047i 0.507225 + 0.698135i
\(392\) 10.0038 + 30.7886i 0.505270 + 1.55506i
\(393\) 0 0
\(394\) 41.7286 + 30.3176i 2.10226 + 1.52738i
\(395\) 41.5146 2.08883
\(396\) 0 0
\(397\) 16.7327 0.839790 0.419895 0.907573i \(-0.362067\pi\)
0.419895 + 0.907573i \(0.362067\pi\)
\(398\) 20.7272 + 15.0592i 1.03896 + 0.754850i
\(399\) 0 0
\(400\) −10.5182 32.3718i −0.525911 1.61859i
\(401\) 2.98209 + 4.10449i 0.148918 + 0.204968i 0.876959 0.480566i \(-0.159569\pi\)
−0.728040 + 0.685534i \(0.759569\pi\)
\(402\) 0 0
\(403\) 3.16903 1.02968i 0.157860 0.0512920i
\(404\) −21.2343 + 65.3525i −1.05645 + 3.25141i
\(405\) 0 0
\(406\) 2.22528i 0.110439i
\(407\) −16.5875 17.0968i −0.822211 0.847459i
\(408\) 0 0
\(409\) 19.0135 26.1698i 0.940156 1.29401i −0.0156071 0.999878i \(-0.504968\pi\)
0.955764 0.294136i \(-0.0950319\pi\)
\(410\) −23.9147 7.77035i −1.18106 0.383750i
\(411\) 0 0
\(412\) 29.6610 21.5500i 1.46129 1.06169i
\(413\) 1.97102 1.43203i 0.0969877 0.0704657i
\(414\) 0 0
\(415\) −33.1513 10.7715i −1.62734 0.528753i
\(416\) 0.343918 0.473362i 0.0168619 0.0232085i
\(417\) 0 0
\(418\) −30.4471 16.0980i −1.48922 0.787379i
\(419\) 27.9075i 1.36337i −0.731645 0.681686i \(-0.761247\pi\)
0.731645 0.681686i \(-0.238753\pi\)
\(420\) 0 0
\(421\) 8.25960 25.4204i 0.402549 1.23892i −0.520376 0.853937i \(-0.674208\pi\)
0.922925 0.384980i \(-0.125792\pi\)
\(422\) 8.56907 2.78426i 0.417136 0.135536i
\(423\) 0 0
\(424\) −15.3709 21.1562i −0.746478 1.02744i
\(425\) −9.98523 30.7314i −0.484355 1.49069i
\(426\) 0 0
\(427\) 2.90185 + 2.10832i 0.140430 + 0.102029i
\(428\) 60.7094 2.93450
\(429\) 0 0
\(430\) −17.4549 −0.841748
\(431\) 0.579760 + 0.421220i 0.0279260 + 0.0202895i 0.601661 0.798752i \(-0.294506\pi\)
−0.573735 + 0.819041i \(0.694506\pi\)
\(432\) 0 0
\(433\) 3.53281 + 10.8729i 0.169776 + 0.522517i 0.999356 0.0358703i \(-0.0114203\pi\)
−0.829580 + 0.558387i \(0.811420\pi\)
\(434\) −1.85074 2.54732i −0.0888383 0.122275i
\(435\) 0 0
\(436\) 39.7830 12.9263i 1.90526 0.619056i
\(437\) 6.54346 20.1387i 0.313016 0.963365i
\(438\) 0 0
\(439\) 8.57525i 0.409274i −0.978838 0.204637i \(-0.934399\pi\)
0.978838 0.204637i \(-0.0656015\pi\)
\(440\) 42.6097 41.3403i 2.03134 1.97082i
\(441\) 0 0
\(442\) −4.66412 + 6.41961i −0.221850 + 0.305350i
\(443\) −13.2928 4.31910i −0.631561 0.205207i −0.0242947 0.999705i \(-0.507734\pi\)
−0.607267 + 0.794498i \(0.707734\pi\)
\(444\) 0 0
\(445\) −9.36104 + 6.80119i −0.443756 + 0.322407i
\(446\) 35.2756 25.6292i 1.67035 1.21358i
\(447\) 0 0
\(448\) −3.05694 0.993261i −0.144427 0.0469271i
\(449\) −12.7008 + 17.4811i −0.599388 + 0.824986i −0.995652 0.0931501i \(-0.970306\pi\)
0.396264 + 0.918136i \(0.370306\pi\)
\(450\) 0 0
\(451\) −1.27593 8.92753i −0.0600811 0.420381i
\(452\) 4.12070i 0.193821i
\(453\) 0 0
\(454\) 13.0836 40.2671i 0.614042 1.88983i
\(455\) 1.25903 0.409083i 0.0590241 0.0191781i
\(456\) 0 0
\(457\) 5.76327 + 7.93246i 0.269594 + 0.371065i 0.922253 0.386587i \(-0.126346\pi\)
−0.652658 + 0.757652i \(0.726346\pi\)
\(458\) 3.21974 + 9.90934i 0.150449 + 0.463033i
\(459\) 0 0
\(460\) 60.0419 + 43.6230i 2.79947 + 2.03393i
\(461\) 12.3585 0.575595 0.287797 0.957691i \(-0.407077\pi\)
0.287797 + 0.957691i \(0.407077\pi\)
\(462\) 0 0
\(463\) −33.8717 −1.57415 −0.787076 0.616856i \(-0.788406\pi\)
−0.787076 + 0.616856i \(0.788406\pi\)
\(464\) −7.26909 5.28130i −0.337459 0.245178i
\(465\) 0 0
\(466\) −17.6041 54.1797i −0.815493 2.50983i
\(467\) −9.24994 12.7315i −0.428036 0.589142i 0.539465 0.842008i \(-0.318627\pi\)
−0.967501 + 0.252867i \(0.918627\pi\)
\(468\) 0 0
\(469\) −1.56129 + 0.507295i −0.0720939 + 0.0234247i
\(470\) −0.0588904 + 0.181246i −0.00271641 + 0.00836026i
\(471\) 0 0
\(472\) 31.2387i 1.43788i
\(473\) −2.75736 5.62011i −0.126783 0.258413i
\(474\) 0 0
\(475\) −23.5695 + 32.4406i −1.08144 + 1.48848i
\(476\) 4.72838 + 1.53634i 0.216725 + 0.0704182i
\(477\) 0 0
\(478\) 39.4120 28.6345i 1.80266 1.30971i
\(479\) −10.0877 + 7.32913i −0.460918 + 0.334877i −0.793891 0.608060i \(-0.791948\pi\)
0.332973 + 0.942936i \(0.391948\pi\)
\(480\) 0 0
\(481\) 6.47741 + 2.10464i 0.295344 + 0.0959632i
\(482\) −3.33048 + 4.58401i −0.151699 + 0.208796i
\(483\) 0 0
\(484\) 40.7499 + 14.6168i 1.85227 + 0.664400i
\(485\) 57.2660i 2.60032i
\(486\) 0 0
\(487\) −2.14955 + 6.61563i −0.0974054 + 0.299783i −0.987873 0.155263i \(-0.950377\pi\)
0.890468 + 0.455046i \(0.150377\pi\)
\(488\) −43.7404 + 14.2121i −1.98004 + 0.643353i
\(489\) 0 0
\(490\) 37.3143 + 51.3587i 1.68569 + 2.32015i
\(491\) −0.0932984 0.287143i −0.00421050 0.0129586i 0.948929 0.315489i \(-0.102169\pi\)
−0.953140 + 0.302531i \(0.902169\pi\)
\(492\) 0 0
\(493\) −6.90074 5.01368i −0.310794 0.225805i
\(494\) 9.84705 0.443040
\(495\) 0 0
\(496\) 12.7135 0.570851
\(497\) 3.07269 + 2.23244i 0.137829 + 0.100139i
\(498\) 0 0
\(499\) 2.04468 + 6.29287i 0.0915323 + 0.281707i 0.986334 0.164755i \(-0.0526835\pi\)
−0.894802 + 0.446463i \(0.852683\pi\)
\(500\) −38.7038 53.2713i −1.73089 2.38236i
\(501\) 0 0
\(502\) 7.43791 2.41672i 0.331970 0.107864i
\(503\) 3.19188 9.82361i 0.142319 0.438013i −0.854337 0.519719i \(-0.826037\pi\)
0.996657 + 0.0817056i \(0.0260367\pi\)
\(504\) 0 0
\(505\) 66.2732i 2.94912i
\(506\) −6.87855 + 39.5495i −0.305789 + 1.75819i
\(507\) 0 0
\(508\) −40.5870 + 55.8633i −1.80076 + 2.47853i
\(509\) −19.3302 6.28078i −0.856798 0.278390i −0.152507 0.988302i \(-0.548735\pi\)
−0.704291 + 0.709912i \(0.748735\pi\)
\(510\) 0 0
\(511\) 1.30799 0.950310i 0.0578621 0.0420392i
\(512\) 29.4132 21.3699i 1.29989 0.944427i
\(513\) 0 0
\(514\) −41.8065 13.5838i −1.84401 0.599154i
\(515\) 20.7840 28.6067i 0.915851 1.26056i
\(516\) 0 0
\(517\) −0.0676605 + 0.00967009i −0.00297571 + 0.000425290i
\(518\) 6.43579i 0.282772i
\(519\) 0 0
\(520\) −5.24530 + 16.1434i −0.230022 + 0.707934i
\(521\) −11.4110 + 3.70764i −0.499923 + 0.162435i −0.548115 0.836403i \(-0.684654\pi\)
0.0481915 + 0.998838i \(0.484654\pi\)
\(522\) 0 0
\(523\) −22.2395 30.6101i −0.972466 1.33848i −0.940791 0.338986i \(-0.889916\pi\)
−0.0316743 0.999498i \(-0.510084\pi\)
\(524\) 16.8916 + 51.9869i 0.737912 + 2.27106i
\(525\) 0 0
\(526\) 4.05963 + 2.94949i 0.177008 + 0.128604i
\(527\) 12.0692 0.525743
\(528\) 0 0
\(529\) −1.68106 −0.0730898
\(530\) −41.4869 30.1420i −1.80207 1.30928i
\(531\) 0 0
\(532\) −1.90653 5.86770i −0.0826586 0.254397i
\(533\) 1.51556 + 2.08599i 0.0656462 + 0.0903542i
\(534\) 0 0
\(535\) 55.6858 18.0934i 2.40751 0.782247i
\(536\) 6.50459 20.0191i 0.280955 0.864692i
\(537\) 0 0
\(538\) 7.01652i 0.302504i
\(539\) −10.6419 + 20.1276i −0.458378 + 0.866957i
\(540\) 0 0
\(541\) 21.6491 29.7975i 0.930769 1.28109i −0.0287904 0.999585i \(-0.509166\pi\)
0.959559 0.281508i \(-0.0908345\pi\)
\(542\) −23.5658 7.65700i −1.01224 0.328896i
\(543\) 0 0
\(544\) 1.71456 1.24570i 0.0735112 0.0534090i
\(545\) 32.6386 23.7133i 1.39808 1.01577i
\(546\) 0 0
\(547\) 34.8795 + 11.3330i 1.49134 + 0.484565i 0.937478 0.348044i \(-0.113154\pi\)
0.553860 + 0.832610i \(0.313154\pi\)
\(548\) −2.40060 + 3.30414i −0.102548 + 0.141146i
\(549\) 0 0
\(550\) 35.5317 67.2032i 1.51508 2.86555i
\(551\) 10.5851i 0.450939i
\(552\) 0 0
\(553\) −1.24304 + 3.82570i −0.0528596 + 0.162685i
\(554\) −16.9395 + 5.50398i −0.719691 + 0.233842i
\(555\) 0 0
\(556\) −45.8848 63.1550i −1.94595 2.67837i
\(557\) 2.30765 + 7.10223i 0.0977784 + 0.300931i 0.987968 0.154660i \(-0.0494281\pi\)
−0.890189 + 0.455591i \(0.849428\pi\)
\(558\) 0 0
\(559\) 1.44800 + 1.05204i 0.0612441 + 0.0444964i
\(560\) 5.05095 0.213441
\(561\) 0 0
\(562\) −5.61676 −0.236929
\(563\) −3.16715 2.30107i −0.133479 0.0969784i 0.519042 0.854749i \(-0.326289\pi\)
−0.652521 + 0.757770i \(0.726289\pi\)
\(564\) 0 0
\(565\) 1.22811 + 3.77972i 0.0516668 + 0.159014i
\(566\) −34.9886 48.1576i −1.47068 2.02422i
\(567\) 0 0
\(568\) −46.3155 + 15.0488i −1.94335 + 0.631434i
\(569\) −11.6410 + 35.8274i −0.488017 + 1.50196i 0.339546 + 0.940590i \(0.389727\pi\)
−0.827563 + 0.561373i \(0.810273\pi\)
\(570\) 0 0
\(571\) 30.3411i 1.26974i 0.772621 + 0.634868i \(0.218946\pi\)
−0.772621 + 0.634868i \(0.781054\pi\)
\(572\) −12.2532 + 1.75124i −0.512333 + 0.0732231i
\(573\) 0 0
\(574\) 1.43212 1.97115i 0.0597756 0.0822741i
\(575\) 44.4504 + 14.4428i 1.85371 + 0.602307i
\(576\) 0 0
\(577\) 2.68563 1.95122i 0.111804 0.0812305i −0.530478 0.847699i \(-0.677988\pi\)
0.642282 + 0.766468i \(0.277988\pi\)
\(578\) 10.2550 7.45067i 0.426550 0.309907i
\(579\) 0 0
\(580\) −35.2835 11.4643i −1.46507 0.476029i
\(581\) 1.98526 2.73247i 0.0823623 0.113362i
\(582\) 0 0
\(583\) 3.15138 18.1195i 0.130517 0.750432i
\(584\) 20.7303i 0.857826i
\(585\) 0 0
\(586\) −8.02659 + 24.7033i −0.331576 + 1.02048i
\(587\) 38.9053 12.6411i 1.60579 0.521754i 0.637263 0.770647i \(-0.280067\pi\)
0.968531 + 0.248893i \(0.0800666\pi\)
\(588\) 0 0
\(589\) −8.80345 12.1169i −0.362740 0.499269i
\(590\) 18.9299 + 58.2601i 0.779330 + 2.39853i
\(591\) 0 0
\(592\) 21.0231 + 15.2742i 0.864044 + 0.627764i
\(593\) −4.62924 −0.190100 −0.0950500 0.995472i \(-0.530301\pi\)
−0.0950500 + 0.995472i \(0.530301\pi\)
\(594\) 0 0
\(595\) 4.79500 0.196576
\(596\) −25.5866 18.5898i −1.04807 0.761467i
\(597\) 0 0
\(598\) −3.54672 10.9157i −0.145036 0.446376i
\(599\) 17.9738 + 24.7388i 0.734390 + 1.01080i 0.998922 + 0.0464237i \(0.0147824\pi\)
−0.264532 + 0.964377i \(0.585218\pi\)
\(600\) 0 0
\(601\) −29.7015 + 9.65061i −1.21155 + 0.393657i −0.843998 0.536346i \(-0.819804\pi\)
−0.367552 + 0.930003i \(0.619804\pi\)
\(602\) 0.522639 1.60852i 0.0213012 0.0655583i
\(603\) 0 0
\(604\) 39.6459i 1.61317i
\(605\) 41.7343 + 1.26245i 1.69674 + 0.0513259i
\(606\) 0 0
\(607\) −18.0842 + 24.8908i −0.734016 + 1.01029i 0.264925 + 0.964269i \(0.414653\pi\)
−0.998941 + 0.0460167i \(0.985347\pi\)
\(608\) −2.50125 0.812705i −0.101439 0.0329595i
\(609\) 0 0
\(610\) −72.9636 + 53.0112i −2.95421 + 2.14636i
\(611\) 0.0158094 0.0114862i 0.000639581 0.000464683i
\(612\) 0 0
\(613\) 24.2244 + 7.87097i 0.978413 + 0.317906i 0.754207 0.656636i \(-0.228021\pi\)
0.224205 + 0.974542i \(0.428021\pi\)
\(614\) −6.54221 + 9.00458i −0.264022 + 0.363395i
\(615\) 0 0
\(616\) 2.53380 + 5.16444i 0.102090 + 0.208081i
\(617\) 4.20930i 0.169460i −0.996404 0.0847300i \(-0.972997\pi\)
0.996404 0.0847300i \(-0.0270028\pi\)
\(618\) 0 0
\(619\) 11.8981 36.6187i 0.478227 1.47183i −0.363329 0.931661i \(-0.618360\pi\)
0.841556 0.540170i \(-0.181640\pi\)
\(620\) 49.9243 16.2214i 2.00501 0.651467i
\(621\) 0 0
\(622\) −13.4356 18.4926i −0.538720 0.741484i
\(623\) −0.346459 1.06629i −0.0138806 0.0427200i
\(624\) 0 0
\(625\) −13.3225 9.67935i −0.532899 0.387174i
\(626\) −12.2206 −0.488433
\(627\) 0 0
\(628\) −63.6880 −2.54143
\(629\) 19.9578 + 14.5002i 0.795769 + 0.578160i
\(630\) 0 0
\(631\) −3.65655 11.2537i −0.145565 0.448003i 0.851518 0.524325i \(-0.175682\pi\)
−0.997083 + 0.0763220i \(0.975682\pi\)
\(632\) −30.3167 41.7274i −1.20593 1.65983i
\(633\) 0 0
\(634\) 27.0547 8.79059i 1.07448 0.349119i
\(635\) −20.5794 + 63.3370i −0.816670 + 2.51345i
\(636\) 0 0
\(637\) 6.50957i 0.257918i
\(638\) −2.83913 19.8650i −0.112402 0.786465i
\(639\) 0 0
\(640\) 44.7507 61.5941i 1.76893 2.43472i
\(641\) −34.1810 11.1061i −1.35007 0.438664i −0.457354 0.889285i \(-0.651203\pi\)
−0.892716 + 0.450620i \(0.851203\pi\)
\(642\) 0 0
\(643\) −2.63357 + 1.91340i −0.103858 + 0.0754571i −0.638502 0.769620i \(-0.720446\pi\)
0.534644 + 0.845077i \(0.320446\pi\)
\(644\) −5.81778 + 4.22687i −0.229253 + 0.166562i
\(645\) 0 0
\(646\) 33.9213 + 11.0217i 1.33461 + 0.433643i
\(647\) −7.14454 + 9.83361i −0.280881 + 0.386599i −0.926025 0.377461i \(-0.876797\pi\)
0.645145 + 0.764060i \(0.276797\pi\)
\(648\) 0 0
\(649\) −15.7682 + 15.2984i −0.618956 + 0.600516i
\(650\) 21.7345i 0.852498i
\(651\) 0 0
\(652\) 5.20020 16.0046i 0.203656 0.626787i
\(653\) 24.2713 7.88623i 0.949811 0.308612i 0.207172 0.978305i \(-0.433574\pi\)
0.742639 + 0.669692i \(0.233574\pi\)
\(654\) 0 0
\(655\) 30.9877 + 42.6508i 1.21079 + 1.66651i
\(656\) 3.04005 + 9.35631i 0.118694 + 0.365303i
\(657\) 0 0
\(658\) −0.0149391 0.0108539i −0.000582385 0.000423127i
\(659\) −27.9441 −1.08855 −0.544273 0.838908i \(-0.683194\pi\)
−0.544273 + 0.838908i \(0.683194\pi\)
\(660\) 0 0
\(661\) −27.3798 −1.06495 −0.532475 0.846446i \(-0.678738\pi\)
−0.532475 + 0.846446i \(0.678738\pi\)
\(662\) 57.2615 + 41.6029i 2.22553 + 1.61694i
\(663\) 0 0
\(664\) 13.3826 + 41.1873i 0.519344 + 1.59838i
\(665\) −3.49754 4.81395i −0.135629 0.186677i
\(666\) 0 0
\(667\) 11.7338 3.81254i 0.454334 0.147622i
\(668\) 22.3204 68.6952i 0.863603 2.65790i
\(669\) 0 0
\(670\) 41.2771i 1.59467i
\(671\) −28.5946 15.1186i −1.10388 0.583646i
\(672\) 0 0
\(673\) −7.96377 + 10.9612i −0.306981 + 0.422523i −0.934437 0.356129i \(-0.884096\pi\)
0.627456 + 0.778652i \(0.284096\pi\)
\(674\) −66.9179 21.7429i −2.57758 0.837507i
\(675\) 0 0
\(676\) −38.5290 + 27.9930i −1.48189 + 1.07665i
\(677\) 29.6885 21.5700i 1.14102 0.829001i 0.153760 0.988108i \(-0.450862\pi\)
0.987261 + 0.159107i \(0.0508616\pi\)
\(678\) 0 0
\(679\) −5.27723 1.71468i −0.202522 0.0658033i
\(680\) −36.1382 + 49.7399i −1.38584 + 1.90744i
\(681\) 0 0
\(682\) 19.7715 + 20.3786i 0.757089 + 0.780337i
\(683\) 30.8347i 1.17986i −0.807455 0.589929i \(-0.799156\pi\)
0.807455 0.589929i \(-0.200844\pi\)
\(684\) 0 0
\(685\) −1.21721 + 3.74619i −0.0465072 + 0.143134i
\(686\) −11.8155 + 3.83910i −0.451119 + 0.146578i
\(687\) 0 0
\(688\) 4.01398 + 5.52477i 0.153031 + 0.210630i
\(689\) 1.62492 + 5.00098i 0.0619045 + 0.190522i
\(690\) 0 0
\(691\) 38.6062 + 28.0491i 1.46865 + 1.06704i 0.981002 + 0.193997i \(0.0621452\pi\)
0.487649 + 0.873040i \(0.337855\pi\)
\(692\) −24.3317 −0.924953
\(693\) 0 0
\(694\) 53.9474 2.04782
\(695\) −60.9102 44.2539i −2.31046 1.67864i
\(696\) 0 0
\(697\) 2.88600 + 8.88220i 0.109315 + 0.336437i
\(698\) 22.4292 + 30.8711i 0.848957 + 1.16849i
\(699\) 0 0
\(700\) 12.9512 4.20812i 0.489511 0.159052i
\(701\) 4.34678 13.3780i 0.164176 0.505281i −0.834799 0.550555i \(-0.814416\pi\)
0.998975 + 0.0452742i \(0.0144162\pi\)
\(702\) 0 0
\(703\) 30.6133i 1.15460i
\(704\) 28.5565 + 4.96661i 1.07626 + 0.187186i
\(705\) 0 0
\(706\) 15.9867 22.0038i 0.601666 0.828122i
\(707\) −6.10727 1.98437i −0.229688 0.0746300i
\(708\) 0 0
\(709\) 7.34115 5.33366i 0.275703 0.200310i −0.441338 0.897341i \(-0.645496\pi\)
0.717041 + 0.697031i \(0.245496\pi\)
\(710\) −77.2591 + 56.1320i −2.89948 + 2.10660i
\(711\) 0 0
\(712\) 13.6721 + 4.44233i 0.512383 + 0.166483i
\(713\) −10.2610 + 14.1231i −0.384279 + 0.528915i
\(714\) 0 0
\(715\) −10.7174 + 5.25820i −0.400807 + 0.196645i
\(716\) 36.3090i 1.35693i
\(717\) 0 0
\(718\) −12.4707 + 38.3809i −0.465402 + 1.43236i
\(719\) 32.2802 10.4885i 1.20385 0.391155i 0.362674 0.931916i \(-0.381864\pi\)
0.841176 + 0.540761i \(0.181864\pi\)
\(720\) 0 0
\(721\) 2.01387 + 2.77186i 0.0750005 + 0.103229i
\(722\) 0.627020 + 1.92977i 0.0233353 + 0.0718186i
\(723\) 0 0
\(724\) 13.3336 + 9.68741i 0.495539 + 0.360030i
\(725\) −23.3635 −0.867697
\(726\) 0 0
\(727\) 30.8992 1.14599 0.572993 0.819560i \(-0.305782\pi\)
0.572993 + 0.819560i \(0.305782\pi\)
\(728\) −1.33060 0.966740i −0.0493154 0.0358298i
\(729\) 0 0
\(730\) 12.5620 + 38.6620i 0.464942 + 1.43094i
\(731\) 3.81058 + 5.24481i 0.140939 + 0.193986i
\(732\) 0 0
\(733\) −39.5648 + 12.8554i −1.46136 + 0.474825i −0.928485 0.371369i \(-0.878889\pi\)
−0.532876 + 0.846194i \(0.678889\pi\)
\(734\) 7.38580 22.7312i 0.272615 0.839022i
\(735\) 0 0
\(736\) 3.06541i 0.112993i
\(737\) 13.2904 6.52058i 0.489558 0.240189i
\(738\) 0 0
\(739\) −8.44687 + 11.6261i −0.310723 + 0.427674i −0.935607 0.353044i \(-0.885146\pi\)
0.624883 + 0.780718i \(0.285146\pi\)
\(740\) 102.044 + 33.1561i 3.75121 + 1.21884i
\(741\) 0 0
\(742\) 4.01989 2.92062i 0.147575 0.107219i
\(743\) −10.8649 + 7.89384i −0.398596 + 0.289597i −0.768969 0.639286i \(-0.779230\pi\)
0.370373 + 0.928883i \(0.379230\pi\)
\(744\) 0 0
\(745\) −29.0098 9.42585i −1.06284 0.345336i
\(746\) 18.0937 24.9039i 0.662459 0.911796i
\(747\) 0 0
\(748\) −44.1703 7.68220i −1.61502 0.280889i
\(749\) 5.67337i 0.207301i
\(750\) 0 0
\(751\) −11.2373 + 34.5847i −0.410054 + 1.26202i 0.506547 + 0.862212i \(0.330922\pi\)
−0.916601 + 0.399803i \(0.869078\pi\)
\(752\) 0.0709102 0.0230401i 0.00258583 0.000840187i
\(753\) 0 0
\(754\) 3.37234 + 4.64163i 0.122813 + 0.169038i
\(755\) −11.8158 36.3653i −0.430021 1.32347i
\(756\) 0 0
\(757\) −32.2811 23.4536i −1.17328 0.852435i −0.181878 0.983321i \(-0.558218\pi\)
−0.991397 + 0.130887i \(0.958218\pi\)
\(758\) 85.5197 3.10622
\(759\) 0 0
\(760\) 76.2962 2.76755
\(761\) −2.75887 2.00443i −0.100009 0.0726607i 0.536657 0.843801i \(-0.319687\pi\)
−0.636666 + 0.771140i \(0.719687\pi\)
\(762\) 0 0
\(763\) 1.20798 + 3.71777i 0.0437317 + 0.134592i
\(764\) 46.6896 + 64.2627i 1.68917 + 2.32494i
\(765\) 0 0
\(766\) 52.3347 17.0046i 1.89093 0.614401i
\(767\) 1.94108 5.97403i 0.0700884 0.215710i
\(768\) 0 0
\(769\) 21.4154i 0.772260i −0.922444 0.386130i \(-0.873812\pi\)
0.922444 0.386130i \(-0.126188\pi\)
\(770\) 7.85505 + 8.09625i 0.283076 + 0.291769i
\(771\) 0 0
\(772\) −18.5388 + 25.5165i −0.667227 + 0.918359i
\(773\) 34.1302 + 11.0896i 1.22758 + 0.398864i 0.849836 0.527048i \(-0.176701\pi\)
0.377741 + 0.925911i \(0.376701\pi\)
\(774\) 0 0
\(775\) 26.7446 19.4311i 0.960694 0.697985i
\(776\) 57.5595 41.8194i 2.06626 1.50123i
\(777\) 0 0
\(778\) 17.0510 + 5.54020i 0.611308 + 0.198626i
\(779\) 6.81221 9.37620i 0.244073 0.335937i
\(780\) 0 0
\(781\) −30.2780 16.0086i −1.08343 0.572833i
\(782\) 41.5723i 1.48662i
\(783\) 0 0
\(784\) 7.67500 23.6212i 0.274107 0.843615i
\(785\) −58.4180 + 18.9811i −2.08503 + 0.677466i
\(786\) 0 0
\(787\) −28.2510 38.8842i −1.00704 1.38607i −0.920905 0.389787i \(-0.872549\pi\)
−0.0861340 0.996284i \(-0.527451\pi\)
\(788\) −25.7479 79.2437i −0.917229 2.82294i
\(789\) 0 0
\(790\) −81.8263 59.4503i −2.91125 2.11515i
\(791\) −0.385085 −0.0136920
\(792\) 0 0
\(793\) 9.24793 0.328404
\(794\) −32.9805 23.9618i −1.17044 0.850371i
\(795\) 0 0
\(796\) −12.7893 39.3615i −0.453306 1.39513i
\(797\) −3.55363 4.89115i −0.125876 0.173253i 0.741428 0.671033i \(-0.234149\pi\)
−0.867304 + 0.497779i \(0.834149\pi\)
\(798\) 0 0
\(799\) 0.0673169 0.0218726i 0.00238150 0.000773797i
\(800\) 1.79381 5.52078i 0.0634208 0.195189i
\(801\) 0 0
\(802\) 12.3605i 0.436464i
\(803\) −10.4639 + 10.1522i −0.369264 + 0.358263i
\(804\) 0 0
\(805\) −4.07663 + 5.61099i −0.143682 + 0.197762i
\(806\) −7.72076 2.50863i −0.271952 0.0883626i
\(807\) 0 0
\(808\) 66.6128 48.3970i 2.34343 1.70260i
\(809\) 6.01444 4.36974i 0.211456 0.153632i −0.477016 0.878895i \(-0.658282\pi\)
0.688472 + 0.725263i \(0.258282\pi\)
\(810\) 0 0
\(811\) 27.7357 + 9.01188i 0.973933 + 0.316450i 0.752402 0.658704i \(-0.228895\pi\)
0.221530 + 0.975154i \(0.428895\pi\)
\(812\) 2.11294 2.90821i 0.0741495 0.102058i
\(813\) 0 0
\(814\) 8.21110 + 57.4521i 0.287799 + 2.01369i
\(815\) 16.2301i 0.568514i
\(816\) 0 0
\(817\) 2.48605 7.65127i 0.0869758 0.267684i
\(818\) −74.9521 + 24.3534i −2.62064 + 0.851497i
\(819\) 0 0
\(820\) 23.8759 + 32.8623i 0.833782 + 1.14760i
\(821\) 0.331389 + 1.01991i 0.0115656 + 0.0355952i 0.956673 0.291165i \(-0.0940430\pi\)
−0.945107 + 0.326760i \(0.894043\pi\)
\(822\) 0 0
\(823\) 7.23762 + 5.25844i 0.252288 + 0.183298i 0.706740 0.707473i \(-0.250165\pi\)
−0.454452 + 0.890771i \(0.650165\pi\)
\(824\) −43.9311 −1.53041
\(825\) 0 0
\(826\) −5.93565 −0.206528
\(827\) 28.5608 + 20.7507i 0.993157 + 0.721571i 0.960610 0.277899i \(-0.0896381\pi\)
0.0325471 + 0.999470i \(0.489638\pi\)
\(828\) 0 0
\(829\) 8.36614 + 25.7483i 0.290568 + 0.894276i 0.984674 + 0.174404i \(0.0557998\pi\)
−0.694106 + 0.719873i \(0.744200\pi\)
\(830\) 49.9169 + 68.7047i 1.73264 + 2.38478i
\(831\) 0 0
\(832\) −7.88160 + 2.56089i −0.273245 + 0.0887828i
\(833\) 7.28608 22.4243i 0.252448 0.776954i
\(834\) 0 0
\(835\) 69.6630i 2.41079i
\(836\) 24.5058 + 49.9483i 0.847552 + 1.72750i
\(837\) 0 0
\(838\) −39.9645 + 55.0064i −1.38055 + 1.90016i
\(839\) 35.4106 + 11.5056i 1.22251 + 0.397218i 0.847996 0.530003i \(-0.177809\pi\)
0.374515 + 0.927221i \(0.377809\pi\)
\(840\) 0 0
\(841\) 18.4720 13.4207i 0.636965 0.462782i
\(842\) −52.6828 + 38.2763i −1.81557 + 1.31909i
\(843\) 0 0
\(844\) −13.8425 4.49772i −0.476480 0.154818i
\(845\) −26.9980 + 37.1595i −0.928759 + 1.27833i
\(846\) 0 0
\(847\) −1.36596 + 3.80813i −0.0469349 + 0.130849i
\(848\) 20.0629i 0.688962i
\(849\) 0 0
\(850\) −24.3272 + 74.8714i −0.834416 + 2.56807i
\(851\) −33.9355 + 11.0263i −1.16329 + 0.377977i
\(852\) 0 0
\(853\) 20.6424 + 28.4118i 0.706782 + 0.972802i 0.999860 + 0.0167139i \(0.00532045\pi\)
−0.293078 + 0.956089i \(0.594680\pi\)
\(854\) −2.70044 8.31109i −0.0924070 0.284400i
\(855\) 0 0
\(856\) −58.8516 42.7582i −2.01151 1.46144i
\(857\) −29.9637 −1.02354 −0.511770 0.859122i \(-0.671010\pi\)
−0.511770 + 0.859122i \(0.671010\pi\)
\(858\) 0 0
\(859\) 17.2684 0.589189 0.294595 0.955622i \(-0.404815\pi\)
0.294595 + 0.955622i \(0.404815\pi\)
\(860\) 22.8116 + 16.5736i 0.777870 + 0.565156i
\(861\) 0 0
\(862\) −0.539519 1.66047i −0.0183761 0.0565558i
\(863\) −20.4637 28.1659i −0.696593 0.958778i −0.999983 0.00591175i \(-0.998118\pi\)
0.303389 0.952867i \(-0.401882\pi\)
\(864\) 0 0
\(865\) −22.3183 + 7.25166i −0.758845 + 0.246564i
\(866\) 8.60705 26.4898i 0.292480 0.900159i
\(867\) 0 0
\(868\) 5.08638i 0.172643i
\(869\) 6.21560 35.7378i 0.210850 1.21232i
\(870\) 0 0
\(871\) −2.48785 + 3.42423i −0.0842976 + 0.116026i
\(872\) −47.6696 15.4888i −1.61430 0.524517i
\(873\) 0 0
\(874\) −41.7366 + 30.3234i −1.41176 + 1.02570i
\(875\) 4.97827 3.61692i 0.168296 0.122274i
\(876\) 0 0
\(877\) −1.88584 0.612748i −0.0636804 0.0206910i 0.277004 0.960869i \(-0.410659\pi\)
−0.340684 + 0.940178i \(0.610659\pi\)
\(878\) −12.2800 + 16.9020i −0.414431 + 0.570416i
\(879\) 0 0
\(880\) −45.0896 + 6.44424i −1.51997 + 0.217235i
\(881\) 48.9571i 1.64941i 0.565566 + 0.824703i \(0.308658\pi\)
−0.565566 + 0.824703i \(0.691342\pi\)
\(882\) 0 0
\(883\) 10.7400 33.0542i 0.361429 1.11236i −0.590758 0.806848i \(-0.701171\pi\)
0.952187 0.305515i \(-0.0988286\pi\)
\(884\) 12.1910 3.96110i 0.410028 0.133226i
\(885\) 0 0
\(886\) 20.0154 + 27.5488i 0.672430 + 0.925520i
\(887\) −4.47860 13.7837i −0.150377 0.462812i 0.847287 0.531136i \(-0.178235\pi\)
−0.997663 + 0.0683244i \(0.978235\pi\)
\(888\) 0 0
\(889\) −5.22049 3.79291i −0.175090 0.127210i
\(890\) 28.1903 0.944943
\(891\) 0 0
\(892\) −70.4368 −2.35840
\(893\) −0.0710609 0.0516288i −0.00237796 0.00172769i
\(894\) 0 0
\(895\) −10.8213 33.3045i −0.361716 1.11325i
\(896\) 4.33614 + 5.96818i 0.144860 + 0.199383i
\(897\) 0 0
\(898\) 50.0671 16.2678i 1.67076 0.542863i
\(899\) 2.69664 8.29941i 0.0899380 0.276801i
\(900\) 0 0
\(901\) 19.0462i 0.634521i
\(902\) −10.2696 + 19.4235i −0.341941 + 0.646733i
\(903\) 0 0
\(904\) 2.90224 3.99460i 0.0965272 0.132858i
\(905\) 15.1174 + 4.91195i 0.502520 + 0.163279i
\(906\) 0 0
\(907\) −18.4206 + 13.3834i −0.611647 + 0.444387i −0.849994 0.526793i \(-0.823394\pi\)
0.238347 + 0.971180i \(0.423394\pi\)
\(908\) −55.3329 + 40.2017i −1.83629 + 1.33414i
\(909\) 0 0
\(910\) −3.06739 0.996656i −0.101683 0.0330388i
\(911\) 13.3395 18.3602i 0.441956 0.608300i −0.528689 0.848815i \(-0.677316\pi\)
0.970645 + 0.240515i \(0.0773164\pi\)
\(912\) 0 0
\(913\) −14.2361 + 26.9256i −0.471146 + 0.891106i
\(914\) 23.8883i 0.790153i
\(915\) 0 0
\(916\) 5.20119 16.0076i 0.171852 0.528907i
\(917\) −4.85824 + 1.57854i −0.160433 + 0.0521280i
\(918\) 0 0
\(919\) −0.737746 1.01542i −0.0243360 0.0334956i 0.796676 0.604407i \(-0.206590\pi\)
−0.821012 + 0.570911i \(0.806590\pi\)
\(920\) −27.4804 84.5761i −0.906003 2.78839i
\(921\) 0 0
\(922\) −24.3590 17.6978i −0.802220 0.582847i
\(923\) 9.79237 0.322320
\(924\) 0 0
\(925\) 67.5699 2.22169
\(926\) 66.7619 + 48.5054i 2.19393 + 1.59399i
\(927\) 0 0
\(928\) −0.473521 1.45735i −0.0155441 0.0478398i
\(929\) 1.68995 + 2.32602i 0.0554456 + 0.0763143i 0.835839 0.548974i \(-0.184981\pi\)
−0.780394 + 0.625288i \(0.784981\pi\)
\(930\) 0 0
\(931\) −27.8274 + 9.04168i −0.912007 + 0.296329i
\(932\) −28.4377 + 87.5224i −0.931509 + 2.86689i
\(933\) 0 0
\(934\) 38.3402i 1.25453i
\(935\) −42.8048 + 6.11769i −1.39987 + 0.200070i
\(936\) 0 0
\(937\) 18.1303 24.9542i 0.592291 0.815219i −0.402684 0.915339i \(-0.631923\pi\)
0.994975 + 0.100120i \(0.0319227\pi\)
\(938\) 3.80381 + 1.23593i 0.124199 + 0.0403546i
\(939\) 0 0
\(940\) 0.249059 0.180952i 0.00812341 0.00590200i
\(941\) −5.29167 + 3.84462i −0.172503 + 0.125331i −0.670687 0.741741i \(-0.734001\pi\)
0.498184 + 0.867072i \(0.334001\pi\)
\(942\) 0 0
\(943\) −12.8474 4.17436i −0.418368 0.135936i
\(944\) 14.0872 19.3893i 0.458498 0.631069i
\(945\) 0 0
\(946\) −2.61336 + 15.0260i −0.0849675 + 0.488537i
\(947\) 33.2579i 1.08074i −0.841429 0.540368i \(-0.818285\pi\)
0.841429 0.540368i \(-0.181715\pi\)
\(948\) 0 0
\(949\) 1.28812 3.96442i 0.0418141 0.128691i
\(950\) 92.9119 30.1889i 3.01446 0.979457i
\(951\) 0 0
\(952\) −3.50162 4.81957i −0.113488 0.156203i
\(953\) 16.9820 + 52.2651i 0.550100 + 1.69303i 0.708545 + 0.705666i \(0.249352\pi\)
−0.158445 + 0.987368i \(0.550648\pi\)
\(954\) 0 0
\(955\) 61.9785 + 45.0300i 2.00558 + 1.45714i
\(956\) −78.6961 −2.54521
\(957\) 0 0
\(958\) 30.3786 0.981488
\(959\) −0.308776 0.224339i −0.00997090 0.00724428i
\(960\) 0 0
\(961\) −5.76392 17.7395i −0.185933 0.572242i
\(962\) −9.75321 13.4241i −0.314456 0.432812i
\(963\) 0 0
\(964\) 8.70515 2.82847i 0.280374 0.0910990i
\(965\) −9.40000 + 28.9302i −0.302597 + 0.931297i
\(966\) 0 0
\(967\) 34.0395i 1.09464i −0.836925 0.547318i \(-0.815649\pi\)
0.836925 0.547318i \(-0.184351\pi\)
\(968\) −29.2082 42.8700i −0.938786 1.37790i
\(969\) 0 0
\(970\) 82.0068 112.873i 2.63308 3.62412i
\(971\) 36.2008 + 11.7624i 1.16174 + 0.377472i 0.825554 0.564323i \(-0.190863\pi\)
0.336186 + 0.941796i \(0.390863\pi\)
\(972\) 0 0
\(973\) 5.90192 4.28799i 0.189207 0.137467i
\(974\) 13.7106 9.96134i 0.439316 0.319182i
\(975\) 0 0
\(976\) 33.5579 + 10.9036i 1.07416 + 0.349017i
\(977\) −18.8682 + 25.9699i −0.603648 + 0.830850i −0.996036 0.0889499i \(-0.971649\pi\)
0.392388 + 0.919800i \(0.371649\pi\)
\(978\) 0 0
\(979\) 4.45325 + 9.07671i 0.142327 + 0.290093i
\(980\) 102.551i 3.27586i
\(981\) 0 0
\(982\) −0.227305 + 0.699572i −0.00725358 + 0.0223242i
\(983\) 20.3816 6.62238i 0.650071 0.211221i 0.0346258 0.999400i \(-0.488976\pi\)
0.615446 + 0.788179i \(0.288976\pi\)
\(984\) 0 0
\(985\) −47.2345 65.0128i −1.50502 2.07148i
\(986\) 6.42177 + 19.7642i 0.204511 + 0.629419i
\(987\) 0 0
\(988\) −12.8690 9.34991i −0.409419 0.297460i
\(989\) −9.37704 −0.298172
\(990\) 0 0
\(991\) −29.3068 −0.930962 −0.465481 0.885058i \(-0.654119\pi\)
−0.465481 + 0.885058i \(0.654119\pi\)
\(992\) 1.75410 + 1.27443i 0.0556929 + 0.0404632i
\(993\) 0 0
\(994\) −2.85942 8.80038i −0.0906952 0.279131i
\(995\) −23.4621 32.2928i −0.743798 1.02375i
\(996\) 0 0
\(997\) −31.1587 + 10.1241i −0.986807 + 0.320633i −0.757582 0.652740i \(-0.773619\pi\)
−0.229225 + 0.973373i \(0.573619\pi\)
\(998\) 4.98148 15.3314i 0.157686 0.485308i
\(999\) 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 99.2.j.a.62.1 yes 16
3.2 odd 2 inner 99.2.j.a.62.4 yes 16
4.3 odd 2 1584.2.cd.c.161.4 16
9.2 odd 6 891.2.u.c.458.4 32
9.4 even 3 891.2.u.c.755.4 32
9.5 odd 6 891.2.u.c.755.1 32
9.7 even 3 891.2.u.c.458.1 32
11.5 even 5 1089.2.d.g.1088.15 16
11.6 odd 10 1089.2.d.g.1088.1 16
11.8 odd 10 inner 99.2.j.a.8.4 yes 16
12.11 even 2 1584.2.cd.c.161.1 16
33.5 odd 10 1089.2.d.g.1088.2 16
33.8 even 10 inner 99.2.j.a.8.1 16
33.17 even 10 1089.2.d.g.1088.16 16
44.19 even 10 1584.2.cd.c.305.1 16
99.41 even 30 891.2.u.c.107.1 32
99.52 odd 30 891.2.u.c.701.1 32
99.74 even 30 891.2.u.c.701.4 32
99.85 odd 30 891.2.u.c.107.4 32
132.107 odd 10 1584.2.cd.c.305.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.j.a.8.1 16 33.8 even 10 inner
99.2.j.a.8.4 yes 16 11.8 odd 10 inner
99.2.j.a.62.1 yes 16 1.1 even 1 trivial
99.2.j.a.62.4 yes 16 3.2 odd 2 inner
891.2.u.c.107.1 32 99.41 even 30
891.2.u.c.107.4 32 99.85 odd 30
891.2.u.c.458.1 32 9.7 even 3
891.2.u.c.458.4 32 9.2 odd 6
891.2.u.c.701.1 32 99.52 odd 30
891.2.u.c.701.4 32 99.74 even 30
891.2.u.c.755.1 32 9.5 odd 6
891.2.u.c.755.4 32 9.4 even 3
1089.2.d.g.1088.1 16 11.6 odd 10
1089.2.d.g.1088.2 16 33.5 odd 10
1089.2.d.g.1088.15 16 11.5 even 5
1089.2.d.g.1088.16 16 33.17 even 10
1584.2.cd.c.161.1 16 12.11 even 2
1584.2.cd.c.161.4 16 4.3 odd 2
1584.2.cd.c.305.1 16 44.19 even 10
1584.2.cd.c.305.4 16 132.107 odd 10