Properties

Label 322.2.g.b.229.3
Level $322$
Weight $2$
Character 322.229
Analytic conductor $2.571$
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] = [322,2,Mod(45,322)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(322, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("322.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 229.3
Root \(-0.452119 + 1.67200i\) of defining polynomial
Character \(\chi\) \(=\) 322.229
Dual form 322.2.g.b.45.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.07743 + 0.622057i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.668984 + 1.15871i) q^{5} +1.24411i q^{6} +(-2.09536 - 1.61539i) q^{7} -1.00000 q^{8} +(-0.726090 + 1.25762i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.07743 + 0.622057i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.668984 + 1.15871i) q^{5} +1.24411i q^{6} +(-2.09536 - 1.61539i) q^{7} -1.00000 q^{8} +(-0.726090 + 1.25762i) q^{9} +(0.668984 + 1.15871i) q^{10} +(-5.22660 + 3.01758i) q^{11} +(1.07743 + 0.622057i) q^{12} -6.52207i q^{13} +(-2.44664 + 1.00694i) q^{14} -1.66459i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.568151 - 0.984066i) q^{17} +(0.726090 + 1.25762i) q^{18} +(-1.77489 + 3.07420i) q^{19} +1.33797 q^{20} +(3.26247 + 0.437039i) q^{21} +6.03516i q^{22} +(-1.35675 + 4.59992i) q^{23} +(1.07743 - 0.622057i) q^{24} +(1.60492 + 2.77980i) q^{25} +(-5.64828 - 3.26103i) q^{26} -5.53902i q^{27} +(-0.351285 + 2.62233i) q^{28} -3.18236 q^{29} +(-1.44157 - 0.832293i) q^{30} +(2.80352 - 1.61862i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.75422 - 6.50249i) q^{33} -1.13630 q^{34} +(3.27353 - 1.34726i) q^{35} +1.45218 q^{36} +(-5.10738 - 2.94875i) q^{37} +(1.77489 + 3.07420i) q^{38} +(4.05710 + 7.02710i) q^{39} +(0.668984 - 1.15871i) q^{40} +0.928266i q^{41} +(2.00972 - 2.60687i) q^{42} +0.303546i q^{43} +(5.22660 + 3.01758i) q^{44} +(-0.971485 - 1.68266i) q^{45} +(3.30527 + 3.47494i) q^{46} +(-0.243918 - 0.140826i) q^{47} -1.24411i q^{48} +(1.78106 + 6.76962i) q^{49} +3.20984 q^{50} +(1.22429 + 0.706844i) q^{51} +(-5.64828 + 3.26103i) q^{52} +(11.3667 - 6.56256i) q^{53} +(-4.79693 - 2.76951i) q^{54} -8.07486i q^{55} +(2.09536 + 1.61539i) q^{56} -4.41633i q^{57} +(-1.59118 + 2.75600i) q^{58} +(-1.10083 + 0.635567i) q^{59} +(-1.44157 + 0.832293i) q^{60} +(7.00107 - 12.1262i) q^{61} -3.23723i q^{62} +(3.55297 - 1.46226i) q^{63} +1.00000 q^{64} +(7.55722 + 4.36316i) q^{65} +(-3.75422 - 6.50249i) q^{66} +(-3.57337 + 2.06308i) q^{67} +(-0.568151 + 0.984066i) q^{68} +(-1.39960 - 5.80009i) q^{69} +(0.470008 - 3.50859i) q^{70} -4.02749 q^{71} +(0.726090 - 1.25762i) q^{72} +(-11.1001 + 6.40863i) q^{73} +(-5.10738 + 2.94875i) q^{74} +(-3.45839 - 1.99670i) q^{75} +3.54978 q^{76} +(15.8262 + 2.12006i) q^{77} +8.11420 q^{78} +(-10.6180 - 6.13032i) q^{79} +(-0.668984 - 1.15871i) q^{80} +(1.26732 + 2.19506i) q^{81} +(0.803902 + 0.464133i) q^{82} +5.99365 q^{83} +(-1.25275 - 3.04391i) q^{84} +1.52033 q^{85} +(0.262878 + 0.151773i) q^{86} +(3.42878 - 1.97961i) q^{87} +(5.22660 - 3.01758i) q^{88} +(-4.71966 + 8.17470i) q^{89} -1.94297 q^{90} +(-10.5357 + 13.6661i) q^{91} +(4.66202 - 1.12497i) q^{92} +(-2.01374 + 3.48790i) q^{93} +(-0.243918 + 0.140826i) q^{94} +(-2.37474 - 4.11318i) q^{95} +(-1.07743 - 0.622057i) q^{96} +14.1845 q^{97} +(6.75320 + 1.84237i) q^{98} -8.76414i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −1.07743 + 0.622057i −0.622057 + 0.359145i −0.777670 0.628673i \(-0.783598\pi\)
0.155612 + 0.987818i \(0.450265\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.668984 + 1.15871i −0.299179 + 0.518193i −0.975948 0.218002i \(-0.930046\pi\)
0.676769 + 0.736195i \(0.263379\pi\)
\(6\) 1.24411i 0.507908i
\(7\) −2.09536 1.61539i −0.791971 0.610558i
\(8\) −1.00000 −0.353553
\(9\) −0.726090 + 1.25762i −0.242030 + 0.419208i
\(10\) 0.668984 + 1.15871i 0.211551 + 0.366418i
\(11\) −5.22660 + 3.01758i −1.57588 + 0.909835i −0.580455 + 0.814292i \(0.697125\pi\)
−0.995425 + 0.0955426i \(0.969541\pi\)
\(12\) 1.07743 + 0.622057i 0.311029 + 0.179572i
\(13\) 6.52207i 1.80890i −0.426583 0.904448i \(-0.640283\pi\)
0.426583 0.904448i \(-0.359717\pi\)
\(14\) −2.44664 + 1.00694i −0.653893 + 0.269117i
\(15\) 1.66459i 0.429794i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.568151 0.984066i −0.137797 0.238671i 0.788866 0.614566i \(-0.210669\pi\)
−0.926662 + 0.375895i \(0.877335\pi\)
\(18\) 0.726090 + 1.25762i 0.171141 + 0.296425i
\(19\) −1.77489 + 3.07420i −0.407187 + 0.705269i −0.994573 0.104038i \(-0.966824\pi\)
0.587386 + 0.809307i \(0.300157\pi\)
\(20\) 1.33797 0.299179
\(21\) 3.26247 + 0.437039i 0.711930 + 0.0953697i
\(22\) 6.03516i 1.28670i
\(23\) −1.35675 + 4.59992i −0.282903 + 0.959149i
\(24\) 1.07743 0.622057i 0.219930 0.126977i
\(25\) 1.60492 + 2.77980i 0.320984 + 0.555961i
\(26\) −5.64828 3.26103i −1.10772 0.639541i
\(27\) 5.53902i 1.06598i
\(28\) −0.351285 + 2.62233i −0.0663866 + 0.495573i
\(29\) −3.18236 −0.590948 −0.295474 0.955351i \(-0.595478\pi\)
−0.295474 + 0.955351i \(0.595478\pi\)
\(30\) −1.44157 0.832293i −0.263194 0.151955i
\(31\) 2.80352 1.61862i 0.503528 0.290712i −0.226641 0.973978i \(-0.572775\pi\)
0.730169 + 0.683266i \(0.239441\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 3.75422 6.50249i 0.653525 1.13194i
\(34\) −1.13630 −0.194874
\(35\) 3.27353 1.34726i 0.553328 0.227728i
\(36\) 1.45218 0.242030
\(37\) −5.10738 2.94875i −0.839649 0.484771i 0.0174962 0.999847i \(-0.494431\pi\)
−0.857145 + 0.515076i \(0.827764\pi\)
\(38\) 1.77489 + 3.07420i 0.287925 + 0.498701i
\(39\) 4.05710 + 7.02710i 0.649656 + 1.12524i
\(40\) 0.668984 1.15871i 0.105776 0.183209i
\(41\) 0.928266i 0.144971i 0.997369 + 0.0724854i \(0.0230931\pi\)
−0.997369 + 0.0724854i \(0.976907\pi\)
\(42\) 2.00972 2.60687i 0.310107 0.402248i
\(43\) 0.303546i 0.0462903i 0.999732 + 0.0231451i \(0.00736798\pi\)
−0.999732 + 0.0231451i \(0.992632\pi\)
\(44\) 5.22660 + 3.01758i 0.787940 + 0.454917i
\(45\) −0.971485 1.68266i −0.144820 0.250836i
\(46\) 3.30527 + 3.47494i 0.487335 + 0.512352i
\(47\) −0.243918 0.140826i −0.0355792 0.0205416i 0.482105 0.876113i \(-0.339872\pi\)
−0.517684 + 0.855572i \(0.673206\pi\)
\(48\) 1.24411i 0.179572i
\(49\) 1.78106 + 6.76962i 0.254437 + 0.967089i
\(50\) 3.20984 0.453940
\(51\) 1.22429 + 0.706844i 0.171435 + 0.0989780i
\(52\) −5.64828 + 3.26103i −0.783275 + 0.452224i
\(53\) 11.3667 6.56256i 1.56133 0.901437i 0.564211 0.825630i \(-0.309180\pi\)
0.997123 0.0758061i \(-0.0241530\pi\)
\(54\) −4.79693 2.76951i −0.652780 0.376883i
\(55\) 8.07486i 1.08881i
\(56\) 2.09536 + 1.61539i 0.280004 + 0.215865i
\(57\) 4.41633i 0.584957i
\(58\) −1.59118 + 2.75600i −0.208932 + 0.361881i
\(59\) −1.10083 + 0.635567i −0.143316 + 0.0827438i −0.569944 0.821684i \(-0.693035\pi\)
0.426627 + 0.904428i \(0.359702\pi\)
\(60\) −1.44157 + 0.832293i −0.186106 + 0.107449i
\(61\) 7.00107 12.1262i 0.896396 1.55260i 0.0643281 0.997929i \(-0.479510\pi\)
0.832068 0.554674i \(-0.187157\pi\)
\(62\) 3.23723i 0.411129i
\(63\) 3.55297 1.46226i 0.447632 0.184227i
\(64\) 1.00000 0.125000
\(65\) 7.55722 + 4.36316i 0.937357 + 0.541183i
\(66\) −3.75422 6.50249i −0.462112 0.800402i
\(67\) −3.57337 + 2.06308i −0.436556 + 0.252046i −0.702136 0.712043i \(-0.747770\pi\)
0.265580 + 0.964089i \(0.414437\pi\)
\(68\) −0.568151 + 0.984066i −0.0688984 + 0.119335i
\(69\) −1.39960 5.80009i −0.168492 0.698248i
\(70\) 0.470008 3.50859i 0.0561767 0.419357i
\(71\) −4.02749 −0.477975 −0.238987 0.971023i \(-0.576815\pi\)
−0.238987 + 0.971023i \(0.576815\pi\)
\(72\) 0.726090 1.25762i 0.0855705 0.148212i
\(73\) −11.1001 + 6.40863i −1.29917 + 0.750074i −0.980260 0.197713i \(-0.936649\pi\)
−0.318906 + 0.947786i \(0.603315\pi\)
\(74\) −5.10738 + 2.94875i −0.593721 + 0.342785i
\(75\) −3.45839 1.99670i −0.399341 0.230560i
\(76\) 3.54978 0.407187
\(77\) 15.8262 + 2.12006i 1.80356 + 0.241603i
\(78\) 8.11420 0.918752
\(79\) −10.6180 6.13032i −1.19462 0.689715i −0.235270 0.971930i \(-0.575597\pi\)
−0.959351 + 0.282215i \(0.908931\pi\)
\(80\) −0.668984 1.15871i −0.0747947 0.129548i
\(81\) 1.26732 + 2.19506i 0.140813 + 0.243896i
\(82\) 0.803902 + 0.464133i 0.0887761 + 0.0512549i
\(83\) 5.99365 0.657889 0.328944 0.944349i \(-0.393307\pi\)
0.328944 + 0.944349i \(0.393307\pi\)
\(84\) −1.25275 3.04391i −0.136686 0.332117i
\(85\) 1.52033 0.164903
\(86\) 0.262878 + 0.151773i 0.0283469 + 0.0163661i
\(87\) 3.42878 1.97961i 0.367604 0.212236i
\(88\) 5.22660 3.01758i 0.557158 0.321675i
\(89\) −4.71966 + 8.17470i −0.500283 + 0.866516i 0.499717 + 0.866189i \(0.333438\pi\)
−1.00000 0.000327275i \(0.999896\pi\)
\(90\) −1.94297 −0.204807
\(91\) −10.5357 + 13.6661i −1.10444 + 1.43259i
\(92\) 4.66202 1.12497i 0.486049 0.117287i
\(93\) −2.01374 + 3.48790i −0.208815 + 0.361679i
\(94\) −0.243918 + 0.140826i −0.0251583 + 0.0145251i
\(95\) −2.37474 4.11318i −0.243644 0.422003i
\(96\) −1.07743 0.622057i −0.109965 0.0634884i
\(97\) 14.1845 1.44022 0.720109 0.693861i \(-0.244092\pi\)
0.720109 + 0.693861i \(0.244092\pi\)
\(98\) 6.75320 + 1.84237i 0.682176 + 0.186107i
\(99\) 8.76414i 0.880829i
\(100\) 1.60492 2.77980i 0.160492 0.277980i
\(101\) −8.86258 + 5.11681i −0.881860 + 0.509142i −0.871271 0.490802i \(-0.836704\pi\)
−0.0105887 + 0.999944i \(0.503371\pi\)
\(102\) 1.22429 0.706844i 0.121223 0.0699880i
\(103\) −6.03001 + 10.4443i −0.594154 + 1.02911i 0.399511 + 0.916728i \(0.369180\pi\)
−0.993666 + 0.112377i \(0.964154\pi\)
\(104\) 6.52207i 0.639541i
\(105\) −2.68895 + 3.48790i −0.262414 + 0.340385i
\(106\) 13.1251i 1.27482i
\(107\) −7.66359 4.42458i −0.740867 0.427740i 0.0815172 0.996672i \(-0.474023\pi\)
−0.822385 + 0.568932i \(0.807357\pi\)
\(108\) −4.79693 + 2.76951i −0.461585 + 0.266496i
\(109\) −6.67380 + 3.85312i −0.639234 + 0.369062i −0.784319 0.620357i \(-0.786988\pi\)
0.145086 + 0.989419i \(0.453654\pi\)
\(110\) −6.99303 4.03743i −0.666759 0.384954i
\(111\) 7.33716 0.696413
\(112\) 2.44664 1.00694i 0.231186 0.0951471i
\(113\) 8.89491i 0.836762i 0.908272 + 0.418381i \(0.137402\pi\)
−0.908272 + 0.418381i \(0.862598\pi\)
\(114\) −3.82465 2.20816i −0.358212 0.206814i
\(115\) −4.42234 4.64936i −0.412386 0.433555i
\(116\) 1.59118 + 2.75600i 0.147737 + 0.255888i
\(117\) 8.20231 + 4.73561i 0.758304 + 0.437807i
\(118\) 1.27113i 0.117017i
\(119\) −0.399166 + 2.97975i −0.0365914 + 0.273154i
\(120\) 1.66459i 0.151955i
\(121\) 12.7116 22.0171i 1.15560 2.00156i
\(122\) −7.00107 12.1262i −0.633848 1.09786i
\(123\) −0.577435 1.00015i −0.0520655 0.0901801i
\(124\) −2.80352 1.61862i −0.251764 0.145356i
\(125\) −10.9845 −0.982484
\(126\) 0.510129 3.80809i 0.0454459 0.339252i
\(127\) −11.4514 −1.01615 −0.508075 0.861313i \(-0.669643\pi\)
−0.508075 + 0.861313i \(0.669643\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −0.188823 0.327051i −0.0166249 0.0287952i
\(130\) 7.55722 4.36316i 0.662812 0.382675i
\(131\) −6.21988 3.59105i −0.543433 0.313751i 0.203036 0.979171i \(-0.434919\pi\)
−0.746469 + 0.665420i \(0.768252\pi\)
\(132\) −7.50843 −0.653525
\(133\) 8.68504 3.57442i 0.753089 0.309941i
\(134\) 4.12617i 0.356447i
\(135\) 6.41814 + 3.70552i 0.552386 + 0.318920i
\(136\) 0.568151 + 0.984066i 0.0487185 + 0.0843829i
\(137\) −3.87856 + 2.23929i −0.331368 + 0.191315i −0.656448 0.754371i \(-0.727942\pi\)
0.325080 + 0.945686i \(0.394609\pi\)
\(138\) −5.72282 1.68796i −0.487159 0.143688i
\(139\) 9.07132i 0.769419i −0.923038 0.384709i \(-0.874302\pi\)
0.923038 0.384709i \(-0.125698\pi\)
\(140\) −2.80352 2.16133i −0.236941 0.182666i
\(141\) 0.350408 0.0295097
\(142\) −2.01374 + 3.48790i −0.168990 + 0.292698i
\(143\) 19.6809 + 34.0883i 1.64580 + 2.85060i
\(144\) −0.726090 1.25762i −0.0605075 0.104802i
\(145\) 2.12895 3.68744i 0.176799 0.306225i
\(146\) 12.8173i 1.06076i
\(147\) −6.13007 6.18591i −0.505600 0.510205i
\(148\) 5.89750i 0.484771i
\(149\) 15.4017 + 8.89220i 1.26176 + 0.728478i 0.973415 0.229049i \(-0.0735616\pi\)
0.288345 + 0.957526i \(0.406895\pi\)
\(150\) −3.45839 + 1.99670i −0.282377 + 0.163030i
\(151\) 9.74158 + 16.8729i 0.792759 + 1.37310i 0.924253 + 0.381782i \(0.124689\pi\)
−0.131494 + 0.991317i \(0.541977\pi\)
\(152\) 1.77489 3.07420i 0.143962 0.249350i
\(153\) 1.65011 0.133404
\(154\) 9.74911 12.6458i 0.785606 1.01903i
\(155\) 4.33131i 0.347899i
\(156\) 4.05710 7.02710i 0.324828 0.562619i
\(157\) −4.10550 7.11094i −0.327655 0.567515i 0.654391 0.756156i \(-0.272925\pi\)
−0.982046 + 0.188642i \(0.939592\pi\)
\(158\) −10.6180 + 6.13032i −0.844725 + 0.487702i
\(159\) −8.16457 + 14.1415i −0.647493 + 1.12149i
\(160\) −1.33797 −0.105776
\(161\) 10.2735 7.44680i 0.809667 0.586890i
\(162\) 2.53464 0.199140
\(163\) −7.48801 + 12.9696i −0.586506 + 1.01586i 0.408180 + 0.912902i \(0.366164\pi\)
−0.994686 + 0.102957i \(0.967170\pi\)
\(164\) 0.803902 0.464133i 0.0627742 0.0362427i
\(165\) 5.02302 + 8.70013i 0.391042 + 0.677304i
\(166\) 2.99683 5.19065i 0.232599 0.402873i
\(167\) 14.5565i 1.12642i 0.826315 + 0.563208i \(0.190433\pi\)
−0.826315 + 0.563208i \(0.809567\pi\)
\(168\) −3.26247 0.437039i −0.251705 0.0337183i
\(169\) −29.5374 −2.27211
\(170\) 0.760167 1.31665i 0.0583022 0.100982i
\(171\) −2.57746 4.46429i −0.197103 0.341392i
\(172\) 0.262878 0.151773i 0.0200443 0.0115726i
\(173\) 0.143633 + 0.0829263i 0.0109202 + 0.00630477i 0.505450 0.862856i \(-0.331326\pi\)
−0.494530 + 0.869161i \(0.664660\pi\)
\(174\) 3.95921i 0.300147i
\(175\) 1.12757 8.41725i 0.0852362 0.636284i
\(176\) 6.03516i 0.454917i
\(177\) 0.790718 1.36956i 0.0594340 0.102943i
\(178\) 4.71966 + 8.17470i 0.353754 + 0.612720i
\(179\) −4.07122 7.05156i −0.304297 0.527058i 0.672807 0.739818i \(-0.265088\pi\)
−0.977105 + 0.212759i \(0.931755\pi\)
\(180\) −0.971485 + 1.68266i −0.0724102 + 0.125418i
\(181\) −16.7773 −1.24705 −0.623524 0.781804i \(-0.714300\pi\)
−0.623524 + 0.781804i \(0.714300\pi\)
\(182\) 6.56734 + 15.9572i 0.486804 + 1.18283i
\(183\) 17.4203i 1.28774i
\(184\) 1.35675 4.59992i 0.100021 0.339110i
\(185\) 6.83352 3.94533i 0.502410 0.290067i
\(186\) 2.01374 + 3.48790i 0.147655 + 0.255746i
\(187\) 5.93900 + 3.42888i 0.434302 + 0.250745i
\(188\) 0.281653i 0.0205416i
\(189\) −8.94765 + 11.6062i −0.650846 + 0.844230i
\(190\) −4.74949 −0.344564
\(191\) 3.11889 + 1.80069i 0.225675 + 0.130294i 0.608575 0.793496i \(-0.291741\pi\)
−0.382900 + 0.923790i \(0.625075\pi\)
\(192\) −1.07743 + 0.622057i −0.0777571 + 0.0448931i
\(193\) 7.15236 + 12.3883i 0.514838 + 0.891726i 0.999852 + 0.0172195i \(0.00548140\pi\)
−0.485013 + 0.874507i \(0.661185\pi\)
\(194\) 7.09225 12.2841i 0.509194 0.881950i
\(195\) −10.8565 −0.777453
\(196\) 4.97214 4.92726i 0.355153 0.351947i
\(197\) −12.0468 −0.858299 −0.429149 0.903233i \(-0.641187\pi\)
−0.429149 + 0.903233i \(0.641187\pi\)
\(198\) −7.58997 4.38207i −0.539395 0.311420i
\(199\) −9.74098 16.8719i −0.690520 1.19602i −0.971668 0.236351i \(-0.924048\pi\)
0.281148 0.959664i \(-0.409285\pi\)
\(200\) −1.60492 2.77980i −0.113485 0.196562i
\(201\) 2.56671 4.44568i 0.181042 0.313574i
\(202\) 10.2336i 0.720036i
\(203\) 6.66818 + 5.14073i 0.468014 + 0.360808i
\(204\) 1.41369i 0.0989780i
\(205\) −1.07560 0.620995i −0.0751229 0.0433722i
\(206\) 6.03001 + 10.4443i 0.420131 + 0.727687i
\(207\) −4.79984 5.04624i −0.333612 0.350738i
\(208\) 5.64828 + 3.26103i 0.391638 + 0.226112i
\(209\) 21.4235i 1.48189i
\(210\) 1.67614 + 4.07265i 0.115665 + 0.281039i
\(211\) 12.1866 0.838961 0.419480 0.907764i \(-0.362212\pi\)
0.419480 + 0.907764i \(0.362212\pi\)
\(212\) −11.3667 6.56256i −0.780667 0.450718i
\(213\) 4.33935 2.50533i 0.297328 0.171662i
\(214\) −7.66359 + 4.42458i −0.523872 + 0.302458i
\(215\) −0.351723 0.203067i −0.0239873 0.0138491i
\(216\) 5.53902i 0.376883i
\(217\) −8.48908 1.13719i −0.576276 0.0771975i
\(218\) 7.70624i 0.521932i
\(219\) 7.97307 13.8098i 0.538770 0.933178i
\(220\) −6.99303 + 4.03743i −0.471470 + 0.272203i
\(221\) −6.41814 + 3.70552i −0.431731 + 0.249260i
\(222\) 3.66858 6.35417i 0.246219 0.426464i
\(223\) 16.5496i 1.10824i −0.832436 0.554122i \(-0.813054\pi\)
0.832436 0.554122i \(-0.186946\pi\)
\(224\) 0.351285 2.62233i 0.0234712 0.175212i
\(225\) −4.66126 −0.310751
\(226\) 7.70322 + 4.44745i 0.512410 + 0.295840i
\(227\) −8.69075 15.0528i −0.576825 0.999090i −0.995841 0.0911113i \(-0.970958\pi\)
0.419016 0.907979i \(-0.362375\pi\)
\(228\) −3.82465 + 2.20816i −0.253294 + 0.146239i
\(229\) 0.486122 0.841988i 0.0321239 0.0556402i −0.849517 0.527562i \(-0.823106\pi\)
0.881640 + 0.471922i \(0.156440\pi\)
\(230\) −6.23764 + 1.50518i −0.411297 + 0.0992486i
\(231\) −18.3705 + 7.56055i −1.20869 + 0.497448i
\(232\) 3.18236 0.208932
\(233\) 3.41466 5.91436i 0.223702 0.387463i −0.732227 0.681060i \(-0.761519\pi\)
0.955929 + 0.293597i \(0.0948525\pi\)
\(234\) 8.20231 4.73561i 0.536202 0.309576i
\(235\) 0.326355 0.188421i 0.0212891 0.0122912i
\(236\) 1.10083 + 0.635567i 0.0716582 + 0.0413719i
\(237\) 15.2536 0.990830
\(238\) 2.38096 + 1.83556i 0.154335 + 0.118982i
\(239\) 14.7894 0.956647 0.478324 0.878184i \(-0.341245\pi\)
0.478324 + 0.878184i \(0.341245\pi\)
\(240\) 1.44157 + 0.832293i 0.0930532 + 0.0537243i
\(241\) −6.60378 11.4381i −0.425387 0.736791i 0.571070 0.820902i \(-0.306529\pi\)
−0.996456 + 0.0841102i \(0.973195\pi\)
\(242\) −12.7116 22.0171i −0.817132 1.41531i
\(243\) 11.6599 + 6.73184i 0.747982 + 0.431848i
\(244\) −14.0021 −0.896396
\(245\) −9.03556 2.46503i −0.577261 0.157485i
\(246\) −1.15487 −0.0736318
\(247\) 20.0501 + 11.5759i 1.27576 + 0.736560i
\(248\) −2.80352 + 1.61862i −0.178024 + 0.102782i
\(249\) −6.45777 + 3.72839i −0.409244 + 0.236277i
\(250\) −5.49225 + 9.51286i −0.347361 + 0.601646i
\(251\) −9.65778 −0.609593 −0.304797 0.952417i \(-0.598589\pi\)
−0.304797 + 0.952417i \(0.598589\pi\)
\(252\) −3.04284 2.34583i −0.191681 0.147773i
\(253\) −6.78940 28.1360i −0.426846 1.76890i
\(254\) −5.72571 + 9.91722i −0.359263 + 0.622262i
\(255\) −1.63806 + 0.945735i −0.102579 + 0.0592242i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.82152 3.36106i −0.363137 0.209657i 0.307319 0.951607i \(-0.400568\pi\)
−0.670456 + 0.741949i \(0.733901\pi\)
\(258\) −0.377645 −0.0235112
\(259\) 5.93844 + 14.4291i 0.368996 + 0.896579i
\(260\) 8.72632i 0.541183i
\(261\) 2.31068 4.00221i 0.143027 0.247730i
\(262\) −6.21988 + 3.59105i −0.384265 + 0.221856i
\(263\) 22.1864 12.8094i 1.36808 0.789859i 0.377393 0.926053i \(-0.376821\pi\)
0.990682 + 0.136195i \(0.0434873\pi\)
\(264\) −3.75422 + 6.50249i −0.231056 + 0.400201i
\(265\) 17.5610i 1.07876i
\(266\) 1.24698 9.30868i 0.0764575 0.570752i
\(267\) 11.7436i 0.718697i
\(268\) 3.57337 + 2.06308i 0.218278 + 0.126023i
\(269\) −19.4220 + 11.2133i −1.18418 + 0.683686i −0.956978 0.290162i \(-0.906291\pi\)
−0.227201 + 0.973848i \(0.572958\pi\)
\(270\) 6.41814 3.70552i 0.390596 0.225511i
\(271\) 0.355990 + 0.205531i 0.0216248 + 0.0124851i 0.510773 0.859715i \(-0.329359\pi\)
−0.489149 + 0.872200i \(0.662692\pi\)
\(272\) 1.13630 0.0688984
\(273\) 2.85040 21.2781i 0.172514 1.28781i
\(274\) 4.47858i 0.270561i
\(275\) −16.7766 9.68595i −1.01166 0.584085i
\(276\) −4.32322 + 4.11213i −0.260227 + 0.247521i
\(277\) −2.30603 3.99416i −0.138556 0.239986i 0.788394 0.615170i \(-0.210913\pi\)
−0.926950 + 0.375184i \(0.877579\pi\)
\(278\) −7.85599 4.53566i −0.471171 0.272031i
\(279\) 4.70104i 0.281444i
\(280\) −3.27353 + 1.34726i −0.195631 + 0.0805140i
\(281\) 20.5915i 1.22839i 0.789156 + 0.614193i \(0.210518\pi\)
−0.789156 + 0.614193i \(0.789482\pi\)
\(282\) 0.175204 0.303462i 0.0104333 0.0180709i
\(283\) −0.174471 0.302193i −0.0103712 0.0179635i 0.860793 0.508955i \(-0.169968\pi\)
−0.871164 + 0.490991i \(0.836635\pi\)
\(284\) 2.01374 + 3.48790i 0.119494 + 0.206969i
\(285\) 5.11726 + 2.95445i 0.303121 + 0.175007i
\(286\) 39.3617 2.32751
\(287\) 1.49951 1.94505i 0.0885131 0.114813i
\(288\) −1.45218 −0.0855705
\(289\) 7.85441 13.6042i 0.462024 0.800249i
\(290\) −2.12895 3.68744i −0.125016 0.216534i
\(291\) −15.2829 + 8.82357i −0.895898 + 0.517247i
\(292\) 11.1001 + 6.40863i 0.649583 + 0.375037i
\(293\) 25.1643 1.47011 0.735057 0.678005i \(-0.237155\pi\)
0.735057 + 0.678005i \(0.237155\pi\)
\(294\) −8.42219 + 2.21584i −0.491192 + 0.129231i
\(295\) 1.70074i 0.0990208i
\(296\) 5.10738 + 2.94875i 0.296861 + 0.171393i
\(297\) 16.7144 + 28.9503i 0.969870 + 1.67986i
\(298\) 15.4017 8.89220i 0.892199 0.515111i
\(299\) 30.0010 + 8.84884i 1.73500 + 0.511742i
\(300\) 3.99341i 0.230560i
\(301\) 0.490343 0.636037i 0.0282629 0.0366606i
\(302\) 19.4832 1.12113
\(303\) 6.36590 11.0261i 0.365712 0.633431i
\(304\) −1.77489 3.07420i −0.101797 0.176317i
\(305\) 9.36722 + 16.2245i 0.536365 + 0.929012i
\(306\) 0.825057 1.42904i 0.0471653 0.0816928i
\(307\) 12.9274i 0.737806i −0.929468 0.368903i \(-0.879734\pi\)
0.929468 0.368903i \(-0.120266\pi\)
\(308\) −6.07706 14.7659i −0.346272 0.841365i
\(309\) 15.0040i 0.853550i
\(310\) 3.75103 + 2.16566i 0.213044 + 0.123001i
\(311\) 3.10046 1.79005i 0.175811 0.101504i −0.409512 0.912305i \(-0.634301\pi\)
0.585323 + 0.810800i \(0.300968\pi\)
\(312\) −4.05710 7.02710i −0.229688 0.397831i
\(313\) 2.70313 4.68196i 0.152790 0.264640i −0.779462 0.626449i \(-0.784507\pi\)
0.932252 + 0.361809i \(0.117841\pi\)
\(314\) −8.21100 −0.463374
\(315\) −0.682536 + 5.09510i −0.0384566 + 0.287077i
\(316\) 12.2606i 0.689715i
\(317\) −13.5155 + 23.4095i −0.759106 + 1.31481i 0.184201 + 0.982889i \(0.441030\pi\)
−0.943307 + 0.331921i \(0.892303\pi\)
\(318\) 8.16457 + 14.1415i 0.457846 + 0.793013i
\(319\) 16.6329 9.60301i 0.931264 0.537666i
\(320\) −0.668984 + 1.15871i −0.0373974 + 0.0647741i
\(321\) 11.0094 0.614483
\(322\) −1.31235 12.6205i −0.0731346 0.703315i
\(323\) 4.03362 0.224436
\(324\) 1.26732 2.19506i 0.0704066 0.121948i
\(325\) 18.1301 10.4674i 1.00568 0.580627i
\(326\) 7.48801 + 12.9696i 0.414722 + 0.718320i
\(327\) 4.79372 8.30297i 0.265093 0.459155i
\(328\) 0.928266i 0.0512549i
\(329\) 0.283608 + 0.689104i 0.0156358 + 0.0379915i
\(330\) 10.0460 0.553017
\(331\) 3.64113 6.30662i 0.200134 0.346643i −0.748437 0.663206i \(-0.769195\pi\)
0.948572 + 0.316563i \(0.102529\pi\)
\(332\) −2.99683 5.19065i −0.164472 0.284874i
\(333\) 7.41684 4.28211i 0.406440 0.234658i
\(334\) 12.6063 + 7.27825i 0.689786 + 0.398248i
\(335\) 5.52068i 0.301627i
\(336\) −2.00972 + 2.60687i −0.109639 + 0.142216i
\(337\) 19.2503i 1.04863i −0.851524 0.524316i \(-0.824321\pi\)
0.851524 0.524316i \(-0.175679\pi\)
\(338\) −14.7687 + 25.5801i −0.803311 + 1.39138i
\(339\) −5.53314 9.58368i −0.300519 0.520514i
\(340\) −0.760167 1.31665i −0.0412259 0.0714053i
\(341\) −9.76861 + 16.9197i −0.529000 + 0.916254i
\(342\) −5.15491 −0.278746
\(343\) 7.20359 17.0619i 0.388957 0.921256i
\(344\) 0.303546i 0.0163661i
\(345\) 7.65695 + 2.25843i 0.412236 + 0.121590i
\(346\) 0.143633 0.0829263i 0.00772173 0.00445814i
\(347\) −14.4944 25.1050i −0.778100 1.34771i −0.933035 0.359785i \(-0.882850\pi\)
0.154935 0.987925i \(-0.450483\pi\)
\(348\) −3.42878 1.97961i −0.183802 0.106118i
\(349\) 12.4174i 0.664687i −0.943159 0.332343i \(-0.892161\pi\)
0.943159 0.332343i \(-0.107839\pi\)
\(350\) −6.72577 5.18513i −0.359508 0.277157i
\(351\) −36.1259 −1.92826
\(352\) −5.22660 3.01758i −0.278579 0.160838i
\(353\) 6.43499 3.71525i 0.342500 0.197743i −0.318877 0.947796i \(-0.603306\pi\)
0.661377 + 0.750054i \(0.269972\pi\)
\(354\) −0.790718 1.36956i −0.0420262 0.0727915i
\(355\) 2.69432 4.66671i 0.143000 0.247683i
\(356\) 9.43933 0.500283
\(357\) −1.42350 3.45879i −0.0753397 0.183059i
\(358\) −8.14244 −0.430341
\(359\) −17.2194 9.94165i −0.908808 0.524700i −0.0287603 0.999586i \(-0.509156\pi\)
−0.880047 + 0.474886i \(0.842489\pi\)
\(360\) 0.971485 + 1.68266i 0.0512018 + 0.0886840i
\(361\) 3.19954 + 5.54177i 0.168397 + 0.291672i
\(362\) −8.38866 + 14.5296i −0.440898 + 0.763658i
\(363\) 31.6293i 1.66011i
\(364\) 17.1030 + 2.29110i 0.896441 + 0.120087i
\(365\) 17.1491i 0.897625i
\(366\) 15.0864 + 8.71014i 0.788579 + 0.455286i
\(367\) 10.8893 + 18.8608i 0.568416 + 0.984525i 0.996723 + 0.0808918i \(0.0257768\pi\)
−0.428307 + 0.903633i \(0.640890\pi\)
\(368\) −3.30527 3.47494i −0.172299 0.181144i
\(369\) −1.16741 0.674005i −0.0607729 0.0350873i
\(370\) 7.89066i 0.410216i
\(371\) −34.4183 4.61066i −1.78691 0.239373i
\(372\) 4.02749 0.208815
\(373\) 17.5547 + 10.1352i 0.908948 + 0.524781i 0.880092 0.474802i \(-0.157480\pi\)
0.0288554 + 0.999584i \(0.490814\pi\)
\(374\) 5.93900 3.42888i 0.307098 0.177303i
\(375\) 11.8351 6.83299i 0.611161 0.352854i
\(376\) 0.243918 + 0.140826i 0.0125791 + 0.00726257i
\(377\) 20.7555i 1.06896i
\(378\) 5.57747 + 13.5520i 0.286874 + 0.697040i
\(379\) 17.4861i 0.898200i 0.893481 + 0.449100i \(0.148255\pi\)
−0.893481 + 0.449100i \(0.851745\pi\)
\(380\) −2.37474 + 4.11318i −0.121822 + 0.211002i
\(381\) 12.3382 7.12344i 0.632103 0.364945i
\(382\) 3.11889 1.80069i 0.159576 0.0921315i
\(383\) 8.88242 15.3848i 0.453870 0.786126i −0.544752 0.838597i \(-0.683376\pi\)
0.998622 + 0.0524707i \(0.0167096\pi\)
\(384\) 1.24411i 0.0634884i
\(385\) −13.0440 + 16.9197i −0.664784 + 0.862309i
\(386\) 14.3047 0.728091
\(387\) −0.381746 0.220401i −0.0194053 0.0112036i
\(388\) −7.09225 12.2841i −0.360055 0.623633i
\(389\) −13.9506 + 8.05439i −0.707324 + 0.408374i −0.810069 0.586334i \(-0.800571\pi\)
0.102746 + 0.994708i \(0.467237\pi\)
\(390\) −5.42827 + 9.40204i −0.274871 + 0.476091i
\(391\) 5.29746 1.27831i 0.267904 0.0646469i
\(392\) −1.78106 6.76962i −0.0899572 0.341918i
\(393\) 8.93535 0.450729
\(394\) −6.02340 + 10.4328i −0.303454 + 0.525599i
\(395\) 14.2066 8.20217i 0.714811 0.412696i
\(396\) −7.58997 + 4.38207i −0.381410 + 0.220207i
\(397\) −5.91641 3.41584i −0.296936 0.171436i 0.344130 0.938922i \(-0.388174\pi\)
−0.641066 + 0.767486i \(0.721507\pi\)
\(398\) −19.4820 −0.976543
\(399\) −7.13407 + 9.25380i −0.357150 + 0.463269i
\(400\) −3.20984 −0.160492
\(401\) −16.3143 9.41906i −0.814697 0.470365i 0.0338876 0.999426i \(-0.489211\pi\)
−0.848584 + 0.529060i \(0.822545\pi\)
\(402\) −2.56671 4.44568i −0.128016 0.221730i
\(403\) −10.5567 18.2848i −0.525868 0.910830i
\(404\) 8.86258 + 5.11681i 0.440930 + 0.254571i
\(405\) −3.39126 −0.168513
\(406\) 7.78609 3.20445i 0.386417 0.159034i
\(407\) 35.5924 1.76425
\(408\) −1.22429 0.706844i −0.0606114 0.0349940i
\(409\) 5.12526 2.95907i 0.253428 0.146316i −0.367905 0.929863i \(-0.619925\pi\)
0.621333 + 0.783547i \(0.286592\pi\)
\(410\) −1.07560 + 0.620995i −0.0531199 + 0.0306688i
\(411\) 2.78593 4.82538i 0.137420 0.238018i
\(412\) 12.0600 0.594154
\(413\) 3.33333 + 0.446530i 0.164022 + 0.0219723i
\(414\) −6.77009 + 1.63366i −0.332732 + 0.0802902i
\(415\) −4.00966 + 6.94493i −0.196826 + 0.340913i
\(416\) 5.64828 3.26103i 0.276930 0.159885i
\(417\) 5.64288 + 9.77375i 0.276333 + 0.478623i
\(418\) −18.5533 10.7117i −0.907471 0.523928i
\(419\) −4.13562 −0.202038 −0.101019 0.994884i \(-0.532210\pi\)
−0.101019 + 0.994884i \(0.532210\pi\)
\(420\) 4.36509 + 0.584744i 0.212994 + 0.0285326i
\(421\) 29.2892i 1.42747i 0.700416 + 0.713735i \(0.252998\pi\)
−0.700416 + 0.713735i \(0.747002\pi\)
\(422\) 6.09331 10.5539i 0.296617 0.513757i
\(423\) 0.354213 0.204505i 0.0172224 0.00994338i
\(424\) −11.3667 + 6.56256i −0.552015 + 0.318706i
\(425\) 1.82367 3.15869i 0.0884611 0.153219i
\(426\) 5.01065i 0.242767i
\(427\) −34.2583 + 14.0993i −1.65787 + 0.682315i
\(428\) 8.84915i 0.427740i
\(429\) −42.4097 24.4853i −2.04756 1.18216i
\(430\) −0.351723 + 0.203067i −0.0169616 + 0.00979277i
\(431\) −4.57492 + 2.64133i −0.220366 + 0.127228i −0.606120 0.795373i \(-0.707275\pi\)
0.385754 + 0.922602i \(0.373941\pi\)
\(432\) 4.79693 + 2.76951i 0.230793 + 0.133248i
\(433\) −29.0430 −1.39572 −0.697860 0.716235i \(-0.745864\pi\)
−0.697860 + 0.716235i \(0.745864\pi\)
\(434\) −5.22938 + 6.78316i −0.251018 + 0.325602i
\(435\) 5.29730i 0.253986i
\(436\) 6.67380 + 3.85312i 0.319617 + 0.184531i
\(437\) −11.7330 12.3353i −0.561264 0.590076i
\(438\) −7.97307 13.8098i −0.380968 0.659856i
\(439\) 29.6005 + 17.0899i 1.41276 + 0.815655i 0.995647 0.0932020i \(-0.0297102\pi\)
0.417108 + 0.908857i \(0.363044\pi\)
\(440\) 8.07486i 0.384954i
\(441\) −9.80685 2.67545i −0.466993 0.127402i
\(442\) 7.41103i 0.352507i
\(443\) 0.874186 1.51413i 0.0415338 0.0719387i −0.844511 0.535538i \(-0.820109\pi\)
0.886045 + 0.463599i \(0.153442\pi\)
\(444\) −3.66858 6.35417i −0.174103 0.301555i
\(445\) −6.31476 10.9375i −0.299348 0.518487i
\(446\) −14.3324 8.27481i −0.678658 0.391823i
\(447\) −22.1258 −1.04652
\(448\) −2.09536 1.61539i −0.0989964 0.0763198i
\(449\) 20.7363 0.978607 0.489303 0.872114i \(-0.337251\pi\)
0.489303 + 0.872114i \(0.337251\pi\)
\(450\) −2.33063 + 4.03677i −0.109867 + 0.190295i
\(451\) −2.80112 4.85168i −0.131900 0.228457i
\(452\) 7.70322 4.44745i 0.362329 0.209191i
\(453\) −20.9918 12.1196i −0.986283 0.569431i
\(454\) −17.3815 −0.815754
\(455\) −8.78690 21.3502i −0.411936 1.00091i
\(456\) 4.41633i 0.206814i
\(457\) −10.3635 5.98335i −0.484782 0.279889i 0.237625 0.971357i \(-0.423631\pi\)
−0.722407 + 0.691468i \(0.756964\pi\)
\(458\) −0.486122 0.841988i −0.0227150 0.0393435i
\(459\) −5.45076 + 3.14700i −0.254420 + 0.146889i
\(460\) −1.81529 + 6.15454i −0.0846385 + 0.286957i
\(461\) 14.9676i 0.697109i 0.937289 + 0.348554i \(0.113327\pi\)
−0.937289 + 0.348554i \(0.886673\pi\)
\(462\) −2.63760 + 19.6896i −0.122712 + 0.916041i
\(463\) 8.01243 0.372369 0.186185 0.982515i \(-0.440388\pi\)
0.186185 + 0.982515i \(0.440388\pi\)
\(464\) 1.59118 2.75600i 0.0738686 0.127944i
\(465\) −2.69432 4.66671i −0.124946 0.216413i
\(466\) −3.41466 5.91436i −0.158181 0.273978i
\(467\) 0.207210 0.358899i 0.00958855 0.0166078i −0.861191 0.508281i \(-0.830281\pi\)
0.870780 + 0.491673i \(0.163614\pi\)
\(468\) 9.47121i 0.437807i
\(469\) 10.8202 + 1.44946i 0.499629 + 0.0669299i
\(470\) 0.376843i 0.0173824i
\(471\) 8.84682 + 5.10771i 0.407640 + 0.235351i
\(472\) 1.10083 0.635567i 0.0506700 0.0292543i
\(473\) −0.915973 1.58651i −0.0421165 0.0729479i
\(474\) 7.62682 13.2100i 0.350311 0.606757i
\(475\) −11.3942 −0.522803
\(476\) 2.78012 1.14419i 0.127427 0.0524438i
\(477\) 19.0600i 0.872698i
\(478\) 7.39470 12.8080i 0.338226 0.585824i
\(479\) 10.3395 + 17.9086i 0.472425 + 0.818264i 0.999502 0.0315532i \(-0.0100454\pi\)
−0.527077 + 0.849818i \(0.676712\pi\)
\(480\) 1.44157 0.832293i 0.0657985 0.0379888i
\(481\) −19.2319 + 33.3107i −0.876901 + 1.51884i
\(482\) −13.2076 −0.601588
\(483\) −6.43672 + 14.4142i −0.292881 + 0.655867i
\(484\) −25.4232 −1.15560
\(485\) −9.48921 + 16.4358i −0.430883 + 0.746311i
\(486\) 11.6599 6.73184i 0.528903 0.305363i
\(487\) −3.26073 5.64774i −0.147758 0.255924i 0.782641 0.622474i \(-0.213872\pi\)
−0.930398 + 0.366550i \(0.880539\pi\)
\(488\) −7.00107 + 12.1262i −0.316924 + 0.548928i
\(489\) 18.6319i 0.842563i
\(490\) −6.65256 + 6.59251i −0.300532 + 0.297819i
\(491\) 14.6314 0.660306 0.330153 0.943927i \(-0.392900\pi\)
0.330153 + 0.943927i \(0.392900\pi\)
\(492\) −0.577435 + 1.00015i −0.0260328 + 0.0450901i
\(493\) 1.80806 + 3.13165i 0.0814308 + 0.141042i
\(494\) 20.0501 11.5759i 0.902098 0.520826i
\(495\) 10.1551 + 5.86307i 0.456439 + 0.263525i
\(496\) 3.23723i 0.145356i
\(497\) 8.43903 + 6.50594i 0.378542 + 0.291831i
\(498\) 7.45679i 0.334147i
\(499\) −8.69163 + 15.0544i −0.389091 + 0.673925i −0.992328 0.123637i \(-0.960544\pi\)
0.603237 + 0.797562i \(0.293877\pi\)
\(500\) 5.49225 + 9.51286i 0.245621 + 0.425428i
\(501\) −9.05497 15.6837i −0.404546 0.700695i
\(502\) −4.82889 + 8.36388i −0.215524 + 0.373298i
\(503\) 17.7000 0.789206 0.394603 0.918852i \(-0.370882\pi\)
0.394603 + 0.918852i \(0.370882\pi\)
\(504\) −3.55297 + 1.46226i −0.158262 + 0.0651342i
\(505\) 13.6923i 0.609298i
\(506\) −27.7612 8.18823i −1.23414 0.364011i
\(507\) 31.8246 18.3739i 1.41338 0.816015i
\(508\) 5.72571 + 9.91722i 0.254037 + 0.440006i
\(509\) −24.1180 13.9245i −1.06901 0.617193i −0.141099 0.989995i \(-0.545064\pi\)
−0.927911 + 0.372802i \(0.878397\pi\)
\(510\) 1.89147i 0.0837557i
\(511\) 33.6111 + 4.50251i 1.48687 + 0.199179i
\(512\) −1.00000 −0.0441942
\(513\) 17.0280 + 9.83114i 0.751806 + 0.434056i
\(514\) −5.82152 + 3.36106i −0.256776 + 0.148250i
\(515\) −8.06796 13.9741i −0.355517 0.615773i
\(516\) −0.188823 + 0.327051i −0.00831246 + 0.0143976i
\(517\) 1.69982 0.0747580
\(518\) 15.4652 + 2.07170i 0.679500 + 0.0910254i
\(519\) −0.206340 −0.00905730
\(520\) −7.55722 4.36316i −0.331406 0.191337i
\(521\) 6.81914 + 11.8111i 0.298752 + 0.517453i 0.975851 0.218439i \(-0.0700964\pi\)
−0.677099 + 0.735892i \(0.736763\pi\)
\(522\) −2.31068 4.00221i −0.101136 0.175172i
\(523\) −16.1015 + 27.8887i −0.704071 + 1.21949i 0.262954 + 0.964808i \(0.415303\pi\)
−0.967026 + 0.254679i \(0.918030\pi\)
\(524\) 7.18209i 0.313751i
\(525\) 4.02113 + 9.77045i 0.175497 + 0.426417i
\(526\) 25.6187i 1.11703i
\(527\) −3.18565 1.83923i −0.138769 0.0801183i
\(528\) 3.75422 + 6.50249i 0.163381 + 0.282985i
\(529\) −19.3184 12.4819i −0.839932 0.542691i
\(530\) 15.2083 + 8.78049i 0.660605 + 0.381400i
\(531\) 1.84591i 0.0801059i
\(532\) −7.43806 5.73426i −0.322481 0.248612i
\(533\) 6.05422 0.262237
\(534\) −10.1703 5.87180i −0.440110 0.254098i
\(535\) 10.2536 5.91994i 0.443304 0.255942i
\(536\) 3.57337 2.06308i 0.154346 0.0891117i
\(537\) 8.77295 + 5.06506i 0.378581 + 0.218574i
\(538\) 22.4266i 0.966878i
\(539\) −29.7368 30.0077i −1.28085 1.29252i
\(540\) 7.41103i 0.318920i
\(541\) −4.06544 + 7.04155i −0.174787 + 0.302740i −0.940088 0.340933i \(-0.889257\pi\)
0.765301 + 0.643673i \(0.222590\pi\)
\(542\) 0.355990 0.205531i 0.0152911 0.00882830i
\(543\) 18.0765 10.4365i 0.775736 0.447871i
\(544\) 0.568151 0.984066i 0.0243593 0.0421915i
\(545\) 10.3107i 0.441662i
\(546\) −17.0022 13.1076i −0.727625 0.560952i
\(547\) 23.6938 1.01307 0.506536 0.862219i \(-0.330926\pi\)
0.506536 + 0.862219i \(0.330926\pi\)
\(548\) 3.87856 + 2.23929i 0.165684 + 0.0956577i
\(549\) 10.1668 + 17.6094i 0.433909 + 0.751553i
\(550\) −16.7766 + 9.68595i −0.715355 + 0.413011i
\(551\) 5.64833 9.78319i 0.240627 0.416778i
\(552\) 1.39960 + 5.80009i 0.0595708 + 0.246868i
\(553\) 12.3457 + 29.9974i 0.524995 + 1.27562i
\(554\) −4.61206 −0.195948
\(555\) −4.90844 + 8.50168i −0.208352 + 0.360876i
\(556\) −7.85599 + 4.53566i −0.333168 + 0.192355i
\(557\) 19.8469 11.4586i 0.840942 0.485518i −0.0166424 0.999862i \(-0.505298\pi\)
0.857584 + 0.514343i \(0.171964\pi\)
\(558\) 4.07122 + 2.35052i 0.172349 + 0.0995055i
\(559\) 1.97975 0.0837343
\(560\) −0.470008 + 3.50859i −0.0198615 + 0.148265i
\(561\) −8.53184 −0.360215
\(562\) 17.8328 + 10.2958i 0.752230 + 0.434300i
\(563\) −11.0559 19.1493i −0.465949 0.807048i 0.533295 0.845930i \(-0.320954\pi\)
−0.999244 + 0.0388818i \(0.987620\pi\)
\(564\) −0.175204 0.303462i −0.00737743 0.0127781i
\(565\) −10.3067 5.95055i −0.433604 0.250342i
\(566\) −0.348943 −0.0146672
\(567\) 0.890380 6.64665i 0.0373924 0.279133i
\(568\) 4.02749 0.168990
\(569\) 11.4658 + 6.61980i 0.480673 + 0.277517i 0.720697 0.693250i \(-0.243822\pi\)
−0.240024 + 0.970767i \(0.577155\pi\)
\(570\) 5.11726 2.95445i 0.214339 0.123748i
\(571\) −17.6182 + 10.1719i −0.737298 + 0.425679i −0.821086 0.570805i \(-0.806631\pi\)
0.0837883 + 0.996484i \(0.473298\pi\)
\(572\) 19.6809 34.0883i 0.822899 1.42530i
\(573\) −4.48054 −0.187177
\(574\) −0.934710 2.27114i −0.0390140 0.0947954i
\(575\) −14.9643 + 3.61099i −0.624056 + 0.150589i
\(576\) −0.726090 + 1.25762i −0.0302537 + 0.0524010i
\(577\) −14.5048 + 8.37436i −0.603843 + 0.348629i −0.770552 0.637377i \(-0.780019\pi\)
0.166709 + 0.986006i \(0.446686\pi\)
\(578\) −7.85441 13.6042i −0.326700 0.565862i
\(579\) −15.4124 8.89836i −0.640518 0.369803i
\(580\) −4.25789 −0.176799
\(581\) −12.5589 9.68205i −0.521029 0.401679i
\(582\) 17.6471i 0.731498i
\(583\) −39.6061 + 68.5998i −1.64032 + 2.84111i
\(584\) 11.1001 6.40863i 0.459325 0.265191i
\(585\) −10.9744 + 6.33609i −0.453737 + 0.261965i
\(586\) 12.5822 21.7929i 0.519764 0.900258i
\(587\) 39.7788i 1.64185i 0.571037 + 0.820924i \(0.306541\pi\)
−0.571037 + 0.820924i \(0.693459\pi\)
\(588\) −2.29212 + 8.40175i −0.0945253 + 0.346482i
\(589\) 11.4914i 0.473497i
\(590\) −1.47288 0.850369i −0.0606376 0.0350091i
\(591\) 12.9796 7.49380i 0.533911 0.308254i
\(592\) 5.10738 2.94875i 0.209912 0.121193i
\(593\) −10.8382 6.25742i −0.445070 0.256961i 0.260676 0.965426i \(-0.416055\pi\)
−0.705746 + 0.708465i \(0.749388\pi\)
\(594\) 33.4289 1.37160
\(595\) −3.18565 2.45593i −0.130599 0.100683i
\(596\) 17.7844i 0.728478i
\(597\) 20.9905 + 12.1189i 0.859086 + 0.495993i
\(598\) 22.6638 21.5572i 0.926792 0.881539i
\(599\) −19.3086 33.4435i −0.788928 1.36646i −0.926624 0.375989i \(-0.877303\pi\)
0.137696 0.990475i \(-0.456030\pi\)
\(600\) 3.45839 + 1.99670i 0.141188 + 0.0815151i
\(601\) 4.35612i 0.177690i −0.996045 0.0888449i \(-0.971682\pi\)
0.996045 0.0888449i \(-0.0283176\pi\)
\(602\) −0.305653 0.742668i −0.0124575 0.0302689i
\(603\) 5.99194i 0.244011i
\(604\) 9.74158 16.8729i 0.396379 0.686549i
\(605\) 17.0077 + 29.4582i 0.691462 + 1.19765i
\(606\) −6.36590 11.0261i −0.258597 0.447903i
\(607\) −36.2312 20.9181i −1.47058 0.849039i −0.471123 0.882067i \(-0.656151\pi\)
−0.999454 + 0.0330288i \(0.989485\pi\)
\(608\) −3.54978 −0.143962
\(609\) −10.3824 1.39081i −0.420714 0.0563586i
\(610\) 18.7344 0.758535
\(611\) −0.918479 + 1.59085i −0.0371577 + 0.0643590i
\(612\) −0.825057 1.42904i −0.0333509 0.0577655i
\(613\) −16.0219 + 9.25027i −0.647120 + 0.373615i −0.787352 0.616504i \(-0.788548\pi\)
0.140232 + 0.990119i \(0.455215\pi\)
\(614\) −11.1955 6.46370i −0.451812 0.260854i
\(615\) 1.54518 0.0623076
\(616\) −15.8262 2.12006i −0.637655 0.0854197i
\(617\) 10.0161i 0.403233i 0.979465 + 0.201616i \(0.0646194\pi\)
−0.979465 + 0.201616i \(0.935381\pi\)
\(618\) −12.9939 7.50202i −0.522690 0.301775i
\(619\) 9.18249 + 15.9045i 0.369075 + 0.639257i 0.989421 0.145071i \(-0.0463411\pi\)
−0.620346 + 0.784328i \(0.713008\pi\)
\(620\) 3.75103 2.16566i 0.150645 0.0869749i
\(621\) 25.4790 + 7.51509i 1.02244 + 0.301570i
\(622\) 3.58010i 0.143549i
\(623\) 23.0947 9.50485i 0.925269 0.380804i
\(624\) −8.11420 −0.324828
\(625\) −0.676141 + 1.17111i −0.0270456 + 0.0468444i
\(626\) −2.70313 4.68196i −0.108039 0.187129i
\(627\) 13.3266 + 23.0824i 0.532214 + 0.921822i
\(628\) −4.10550 + 7.11094i −0.163827 + 0.283757i
\(629\) 6.70133i 0.267200i
\(630\) 4.07122 + 3.13865i 0.162201 + 0.125047i
\(631\) 3.02292i 0.120341i −0.998188 0.0601703i \(-0.980836\pi\)
0.998188 0.0601703i \(-0.0191644\pi\)
\(632\) 10.6180 + 6.13032i 0.422362 + 0.243851i
\(633\) −13.1303 + 7.58077i −0.521882 + 0.301309i
\(634\) 13.5155 + 23.4095i 0.536769 + 0.929711i
\(635\) 7.66082 13.2689i 0.304010 0.526561i
\(636\) 16.3291 0.647493
\(637\) 44.1520 11.6162i 1.74936 0.460251i
\(638\) 19.2060i 0.760374i
\(639\) 2.92432 5.06506i 0.115684 0.200371i
\(640\) 0.668984 + 1.15871i 0.0264439 + 0.0458022i
\(641\) 0.850505 0.491039i 0.0335929 0.0193949i −0.483109 0.875560i \(-0.660493\pi\)
0.516702 + 0.856165i \(0.327159\pi\)
\(642\) 5.50468 9.53439i 0.217252 0.376292i
\(643\) 42.9115 1.69227 0.846133 0.532972i \(-0.178925\pi\)
0.846133 + 0.532972i \(0.178925\pi\)
\(644\) −11.5859 5.17373i −0.456547 0.203874i
\(645\) 0.505278 0.0198953
\(646\) 2.01681 3.49321i 0.0793502 0.137439i
\(647\) 24.5410 14.1688i 0.964807 0.557032i 0.0671579 0.997742i \(-0.478607\pi\)
0.897649 + 0.440711i \(0.145274\pi\)
\(648\) −1.26732 2.19506i −0.0497850 0.0862301i
\(649\) 3.83575 6.64371i 0.150566 0.260789i
\(650\) 20.9348i 0.821131i
\(651\) 9.85382 4.05544i 0.386202 0.158945i
\(652\) 14.9760 0.586506
\(653\) 14.4667 25.0571i 0.566127 0.980561i −0.430817 0.902439i \(-0.641774\pi\)
0.996944 0.0781215i \(-0.0248922\pi\)
\(654\) −4.79372 8.30297i −0.187449 0.324672i
\(655\) 8.32200 4.80471i 0.325167 0.187735i
\(656\) −0.803902 0.464133i −0.0313871 0.0181214i
\(657\) 18.6130i 0.726161i
\(658\) 0.738586 + 0.0989404i 0.0287931 + 0.00385710i
\(659\) 31.7305i 1.23605i −0.786160 0.618023i \(-0.787934\pi\)
0.786160 0.618023i \(-0.212066\pi\)
\(660\) 5.02302 8.70013i 0.195521 0.338652i
\(661\) 13.8069 + 23.9142i 0.537025 + 0.930154i 0.999062 + 0.0432937i \(0.0137851\pi\)
−0.462038 + 0.886860i \(0.652882\pi\)
\(662\) −3.64113 6.30662i −0.141516 0.245114i
\(663\) 4.61009 7.98490i 0.179041 0.310108i
\(664\) −5.99365 −0.232599
\(665\) −1.66842 + 12.4547i −0.0646987 + 0.482973i
\(666\) 8.56422i 0.331857i
\(667\) 4.31767 14.6386i 0.167181 0.566807i
\(668\) 12.6063 7.27825i 0.487752 0.281604i
\(669\) 10.2948 + 17.8311i 0.398020 + 0.689391i
\(670\) −4.78105 2.76034i −0.184708 0.106641i
\(671\) 84.5052i 3.26229i
\(672\) 1.25275 + 3.04391i 0.0483259 + 0.117421i
\(673\) 5.70731 0.220001 0.110000 0.993932i \(-0.464915\pi\)
0.110000 + 0.993932i \(0.464915\pi\)
\(674\) −16.6713 9.62517i −0.642154 0.370748i
\(675\) 15.3974 8.88969i 0.592646 0.342164i
\(676\) 14.7687 + 25.5801i 0.568027 + 0.983851i
\(677\) −20.5855 + 35.6550i −0.791163 + 1.37033i 0.134084 + 0.990970i \(0.457191\pi\)
−0.925247 + 0.379365i \(0.876143\pi\)
\(678\) −11.0663 −0.424998
\(679\) −29.7216 22.9134i −1.14061 0.879337i
\(680\) −1.52033 −0.0583022
\(681\) 18.7274 + 10.8123i 0.717636 + 0.414328i
\(682\) 9.76861 + 16.9197i 0.374059 + 0.647890i
\(683\) −2.95142 5.11202i −0.112933 0.195606i 0.804019 0.594604i \(-0.202691\pi\)
−0.916952 + 0.398998i \(0.869358\pi\)
\(684\) −2.57746 + 4.46429i −0.0985515 + 0.170696i
\(685\) 5.99220i 0.228950i
\(686\) −11.1742 14.7694i −0.426635 0.563900i
\(687\) 1.20958i 0.0461485i
\(688\) −0.262878 0.151773i −0.0100221 0.00578628i
\(689\) −42.8014 74.1343i −1.63061 2.82429i
\(690\) 5.78434 5.50190i 0.220206 0.209454i
\(691\) 12.6557 + 7.30676i 0.481445 + 0.277962i 0.721018 0.692916i \(-0.243674\pi\)
−0.239574 + 0.970878i \(0.577008\pi\)
\(692\) 0.165853i 0.00630477i
\(693\) −14.1575 + 18.3640i −0.537797 + 0.697591i
\(694\) −28.9888 −1.10040
\(695\) 10.5111 + 6.06857i 0.398707 + 0.230194i
\(696\) −3.42878 + 1.97961i −0.129968 + 0.0750368i
\(697\) 0.913475 0.527395i 0.0346003 0.0199765i
\(698\) −10.7538 6.20868i −0.407036 0.235002i
\(699\) 8.49645i 0.321365i
\(700\) −7.85334 + 3.23212i −0.296828 + 0.122163i
\(701\) 15.3358i 0.579225i 0.957144 + 0.289613i \(0.0935265\pi\)
−0.957144 + 0.289613i \(0.906474\pi\)
\(702\) −18.0629 + 31.2859i −0.681742 + 1.18081i
\(703\) 18.1301 10.4674i 0.683789 0.394786i
\(704\) −5.22660 + 3.01758i −0.196985 + 0.113729i
\(705\) −0.234418 + 0.406023i −0.00882868 + 0.0152917i
\(706\) 7.43049i 0.279650i
\(707\) 26.8359 + 3.59492i 1.00927 + 0.135201i
\(708\) −1.58144 −0.0594340
\(709\) −6.16233 3.55782i −0.231431 0.133617i 0.379801 0.925068i \(-0.375992\pi\)
−0.611232 + 0.791451i \(0.709326\pi\)
\(710\) −2.69432 4.66671i −0.101116 0.175138i
\(711\) 15.4193 8.90232i 0.578268 0.333863i
\(712\) 4.71966 8.17470i 0.176877 0.306360i
\(713\) 3.64180 + 15.0920i 0.136387 + 0.565201i
\(714\) −3.70715 0.496608i −0.138737 0.0185851i
\(715\) −52.6648 −1.96955
\(716\) −4.07122 + 7.05156i −0.152149 + 0.263529i
\(717\) −15.9346 + 9.19985i −0.595089 + 0.343575i
\(718\) −17.2194 + 9.94165i −0.642624 + 0.371019i
\(719\) −11.2974 6.52254i −0.421321 0.243250i 0.274321 0.961638i \(-0.411547\pi\)
−0.695642 + 0.718388i \(0.744880\pi\)
\(720\) 1.94297 0.0724102
\(721\) 29.5066 12.1437i 1.09888 0.452256i
\(722\) 6.39908 0.238149
\(723\) 14.2303 + 8.21585i 0.529230 + 0.305551i
\(724\) 8.38866 + 14.5296i 0.311762 + 0.539988i
\(725\) −5.10743 8.84632i −0.189685 0.328544i
\(726\) 27.3918 + 15.8147i 1.01661 + 0.586938i
\(727\) −10.9061 −0.404485 −0.202242 0.979336i \(-0.564823\pi\)
−0.202242 + 0.979336i \(0.564823\pi\)
\(728\) 10.5357 13.6661i 0.390477 0.506499i
\(729\) −24.3543 −0.902010
\(730\) −14.8516 8.57455i −0.549681 0.317358i
\(731\) 0.298709 0.172460i 0.0110481 0.00637865i
\(732\) 15.0864 8.71014i 0.557609 0.321936i
\(733\) 20.8868 36.1769i 0.771470 1.33623i −0.165287 0.986246i \(-0.552855\pi\)
0.936757 0.349980i \(-0.113812\pi\)
\(734\) 21.7786 0.803861
\(735\) 11.2686 2.96473i 0.415649 0.109356i
\(736\) −4.66202 + 1.12497i −0.171844 + 0.0414671i
\(737\) 12.4510 21.5658i 0.458640 0.794388i
\(738\) −1.16741 + 0.674005i −0.0429730 + 0.0248104i
\(739\) −2.88980 5.00528i −0.106303 0.184122i 0.807967 0.589228i \(-0.200568\pi\)
−0.914270 + 0.405106i \(0.867235\pi\)
\(740\) −6.83352 3.94533i −0.251205 0.145033i
\(741\) −28.8036 −1.05813
\(742\) −21.2021 + 27.5018i −0.778354 + 1.00962i
\(743\) 2.74633i 0.100753i −0.998730 0.0503766i \(-0.983958\pi\)
0.998730 0.0503766i \(-0.0160422\pi\)
\(744\) 2.01374 3.48790i 0.0738274 0.127873i
\(745\) −20.6070 + 11.8975i −0.754984 + 0.435890i
\(746\) 17.5547 10.1352i 0.642723 0.371076i
\(747\) −4.35193 + 7.53776i −0.159229 + 0.275792i
\(748\) 6.85776i 0.250745i
\(749\) 8.91058 + 21.6507i 0.325586 + 0.791101i
\(750\) 13.6660i 0.499011i
\(751\) 38.7452 + 22.3695i 1.41383 + 0.816275i 0.995747 0.0921329i \(-0.0293685\pi\)
0.418084 + 0.908408i \(0.362702\pi\)
\(752\) 0.243918 0.140826i 0.00889479 0.00513541i
\(753\) 10.4056 6.00769i 0.379202 0.218932i
\(754\) 17.9748 + 10.3778i 0.654604 + 0.377936i
\(755\) −26.0679 −0.948707
\(756\) 14.5251 + 1.94577i 0.528274 + 0.0707671i
\(757\) 12.3037i 0.447185i 0.974683 + 0.223593i \(0.0717785\pi\)
−0.974683 + 0.223593i \(0.928222\pi\)
\(758\) 15.1434 + 8.74305i 0.550033 + 0.317562i
\(759\) 24.8174 + 26.0914i 0.900813 + 0.947056i
\(760\) 2.37474 + 4.11318i 0.0861410 + 0.149201i
\(761\) 19.1725 + 11.0692i 0.695002 + 0.401260i 0.805483 0.592618i \(-0.201906\pi\)
−0.110481 + 0.993878i \(0.535239\pi\)
\(762\) 14.2469i 0.516110i
\(763\) 20.2083 + 2.70709i 0.731589 + 0.0980031i
\(764\) 3.60139i 0.130294i
\(765\) −1.10390 + 1.91201i −0.0399116 + 0.0691289i
\(766\) −8.88242 15.3848i −0.320935 0.555875i
\(767\) 4.14521 + 7.17972i 0.149675 + 0.259245i
\(768\) 1.07743 + 0.622057i 0.0388786 + 0.0224466i
\(769\) −0.436260 −0.0157320 −0.00786598 0.999969i \(-0.502504\pi\)
−0.00786598 + 0.999969i \(0.502504\pi\)
\(770\) 8.13091 + 19.7563i 0.293018 + 0.711968i
\(771\) 8.36308 0.301189
\(772\) 7.15236 12.3883i 0.257419 0.445863i
\(773\) −13.4233 23.2498i −0.482801 0.836236i 0.517004 0.855983i \(-0.327047\pi\)
−0.999805 + 0.0197472i \(0.993714\pi\)
\(774\) −0.381746 + 0.220401i −0.0137216 + 0.00792216i
\(775\) 8.99887 + 5.19550i 0.323249 + 0.186628i
\(776\) −14.1845 −0.509194
\(777\) −15.3740 11.8523i −0.551539 0.425200i
\(778\) 16.1088i 0.577527i
\(779\) −2.85367 1.64757i −0.102243 0.0590303i
\(780\) 5.42827 + 9.40204i 0.194363 + 0.336647i
\(781\) 21.0501 12.1533i 0.753231 0.434878i
\(782\) 1.54168 5.22689i 0.0551304 0.186913i
\(783\) 17.6271i 0.629942i
\(784\) −6.75320 1.84237i −0.241186 0.0657989i
\(785\) 10.9861 0.392109
\(786\) 4.46767 7.73824i 0.159357 0.276014i
\(787\) 10.3912 + 17.9982i 0.370408 + 0.641565i 0.989628 0.143652i \(-0.0458847\pi\)
−0.619221 + 0.785217i \(0.712551\pi\)
\(788\) 6.02340 + 10.4328i 0.214575 + 0.371654i
\(789\) −15.9363 + 27.6025i −0.567347 + 0.982674i
\(790\) 16.4043i 0.583640i
\(791\) 14.3687 18.6380i 0.510892 0.662692i
\(792\) 8.76414i 0.311420i
\(793\) −79.0880 45.6615i −2.80850 1.62149i
\(794\) −5.91641 + 3.41584i −0.209966 + 0.121224i
\(795\) −10.9239 18.9208i −0.387432 0.671052i
\(796\) −9.74098 + 16.8719i −0.345260 + 0.598008i
\(797\) −15.7307 −0.557209 −0.278605 0.960406i \(-0.589872\pi\)
−0.278605 + 0.960406i \(0.589872\pi\)
\(798\) 4.44699 + 10.8052i 0.157422 + 0.382499i
\(799\) 0.320042i 0.0113223i
\(800\) −1.60492 + 2.77980i −0.0567425 + 0.0982809i
\(801\) −6.85380 11.8711i −0.242167 0.419446i
\(802\) −16.3143 + 9.41906i −0.576077 + 0.332598i
\(803\) 38.6771 66.9908i 1.36489 2.36405i
\(804\) −5.13342 −0.181042
\(805\) 1.75589 + 16.8859i 0.0618869 + 0.595149i
\(806\) −21.1134 −0.743689
\(807\) 13.9506 24.1632i 0.491085 0.850584i
\(808\) 8.86258 5.11681i 0.311785 0.180009i
\(809\) −5.87066 10.1683i −0.206401 0.357498i 0.744177 0.667983i \(-0.232842\pi\)
−0.950578 + 0.310485i \(0.899509\pi\)
\(810\) −1.69563 + 2.93692i −0.0595784 + 0.103193i
\(811\) 32.1592i 1.12926i −0.825343 0.564631i \(-0.809018\pi\)
0.825343 0.564631i \(-0.190982\pi\)
\(812\) 1.11791 8.34518i 0.0392311 0.292858i
\(813\) −0.511408 −0.0179358
\(814\) 17.7962 30.8239i 0.623756 1.08038i
\(815\) −10.0187 17.3529i −0.350940 0.607847i
\(816\) −1.22429 + 0.706844i −0.0428587 + 0.0247445i
\(817\) −0.933159 0.538760i −0.0326471 0.0188488i
\(818\) 5.91813i 0.206923i
\(819\) −9.53696 23.1727i −0.333248 0.809719i
\(820\) 1.24199i 0.0433722i
\(821\) −1.84632 + 3.19792i −0.0644371 + 0.111608i −0.896444 0.443157i \(-0.853859\pi\)
0.832007 + 0.554765i \(0.187192\pi\)
\(822\) −2.78593 4.82538i −0.0971705 0.168304i
\(823\) −9.19610 15.9281i −0.320556 0.555219i 0.660047 0.751224i \(-0.270536\pi\)
−0.980603 + 0.196005i \(0.937203\pi\)
\(824\) 6.03001 10.4443i 0.210065 0.363844i
\(825\) 24.1009 0.839085
\(826\) 2.05337 2.66348i 0.0714459 0.0926744i
\(827\) 2.41961i 0.0841382i 0.999115 + 0.0420691i \(0.0133950\pi\)
−0.999115 + 0.0420691i \(0.986605\pi\)
\(828\) −1.97025 + 6.67990i −0.0684709 + 0.232143i
\(829\) −9.79002 + 5.65227i −0.340021 + 0.196311i −0.660282 0.751018i \(-0.729563\pi\)
0.320260 + 0.947330i \(0.396230\pi\)
\(830\) 4.00966 + 6.94493i 0.139177 + 0.241062i
\(831\) 4.96919 + 2.86897i 0.172379 + 0.0995233i
\(832\) 6.52207i 0.226112i
\(833\) 5.64984 5.59885i 0.195755 0.193989i
\(834\) 11.2858 0.390794
\(835\) −16.8668 9.73806i −0.583700 0.337000i
\(836\) −18.5533 + 10.7117i −0.641679 + 0.370473i
\(837\) −8.96554 15.5288i −0.309895 0.536753i
\(838\) −2.06781 + 3.58155i −0.0714313 + 0.123723i
\(839\) 28.2187 0.974219 0.487110 0.873341i \(-0.338051\pi\)
0.487110 + 0.873341i \(0.338051\pi\)
\(840\) 2.68895 3.48790i 0.0927775 0.120344i
\(841\) −18.8726 −0.650780
\(842\) 25.3652 + 14.6446i 0.874143 + 0.504687i
\(843\) −12.8091 22.1860i −0.441169 0.764126i
\(844\) −6.09331 10.5539i −0.209740 0.363281i
\(845\) 19.7600 34.2254i 0.679766 1.17739i
\(846\) 0.409010i 0.0140621i
\(847\) −62.2015 + 25.5997i −2.13727 + 0.879615i
\(848\) 13.1251i 0.450718i
\(849\) 0.375963 + 0.217062i 0.0129030 + 0.00744956i
\(850\) −1.82367 3.15869i −0.0625515 0.108342i
\(851\) 20.4935 19.4928i 0.702507 0.668205i
\(852\) −4.33935 2.50533i −0.148664 0.0858311i
\(853\) 44.0603i 1.50860i −0.656532 0.754298i \(-0.727977\pi\)
0.656532 0.754298i \(-0.272023\pi\)
\(854\) −4.91874 + 36.7182i −0.168316 + 1.25647i
\(855\) 6.89711 0.235876
\(856\) 7.66359 + 4.42458i 0.261936 + 0.151229i
\(857\) −47.2791 + 27.2966i −1.61502 + 0.932434i −0.626842 + 0.779147i \(0.715653\pi\)
−0.988182 + 0.153287i \(0.951014\pi\)
\(858\) −42.4097 + 24.4853i −1.44784 + 0.835913i
\(859\) 2.15309 + 1.24309i 0.0734626 + 0.0424136i 0.536281 0.844039i \(-0.319829\pi\)
−0.462819 + 0.886453i \(0.653162\pi\)
\(860\) 0.406134i 0.0138491i
\(861\) −0.405688 + 3.02844i −0.0138258 + 0.103209i
\(862\) 5.28266i 0.179928i
\(863\) −21.9157 + 37.9590i −0.746018 + 1.29214i 0.203700 + 0.979033i \(0.434703\pi\)
−0.949718 + 0.313107i \(0.898630\pi\)
\(864\) 4.79693 2.76951i 0.163195 0.0942207i
\(865\) −0.192176 + 0.110953i −0.00653417 + 0.00377251i
\(866\) −14.5215 + 25.1520i −0.493461 + 0.854700i
\(867\) 19.5436i 0.663734i
\(868\) 3.25970 + 7.92035i 0.110642 + 0.268834i
\(869\) 73.9949 2.51011
\(870\) 4.58760 + 2.64865i 0.155534 + 0.0897977i
\(871\) 13.4556 + 23.3057i 0.455925 + 0.789685i
\(872\) 6.67380 3.85312i 0.226003 0.130483i
\(873\) −10.2992 + 17.8388i −0.348576 + 0.603751i
\(874\) −16.5491 + 3.99341i −0.559783 + 0.135079i
\(875\) 23.0165 + 17.7442i 0.778099 + 0.599864i
\(876\) −15.9461 −0.538770
\(877\) 2.75727 4.77574i 0.0931065 0.161265i −0.815710 0.578461i \(-0.803654\pi\)
0.908817 + 0.417195i \(0.136987\pi\)
\(878\) 29.6005 17.0899i 0.998969 0.576755i
\(879\) −27.1129 + 15.6536i −0.914495 + 0.527984i
\(880\) 6.99303 + 4.03743i 0.235735 + 0.136102i
\(881\) −51.6788 −1.74110 −0.870552 0.492076i \(-0.836238\pi\)
−0.870552 + 0.492076i \(0.836238\pi\)
\(882\) −7.22043 + 7.15526i −0.243125 + 0.240930i
\(883\) 53.5374 1.80168 0.900838 0.434155i \(-0.142953\pi\)
0.900838 + 0.434155i \(0.142953\pi\)
\(884\) 6.41814 + 3.70552i 0.215866 + 0.124630i
\(885\) 1.05796 + 1.83243i 0.0355628 + 0.0615966i
\(886\) −0.874186 1.51413i −0.0293688 0.0508683i
\(887\) 23.7721 + 13.7248i 0.798190 + 0.460835i 0.842838 0.538167i \(-0.180883\pi\)
−0.0446478 + 0.999003i \(0.514217\pi\)
\(888\) −7.33716 −0.246219
\(889\) 23.9948 + 18.4985i 0.804761 + 0.620418i
\(890\) −12.6295 −0.423343
\(891\) −13.2475 7.64847i −0.443809 0.256233i
\(892\) −14.3324 + 8.27481i −0.479884 + 0.277061i
\(893\) 0.865856 0.499902i 0.0289748 0.0167286i
\(894\) −11.0629 + 19.1615i −0.369999 + 0.640858i
\(895\) 10.8943 0.364157
\(896\) −2.44664 + 1.00694i −0.0817366 + 0.0336396i
\(897\) −37.8286 + 9.12827i −1.26306 + 0.304784i
\(898\) 10.3682 17.9582i 0.345990 0.599272i
\(899\) −8.92181 + 5.15101i −0.297559 + 0.171796i
\(900\) 2.33063 + 4.03677i 0.0776877 + 0.134559i
\(901\) −12.9160 7.45704i −0.430293 0.248430i
\(902\) −5.60224 −0.186534
\(903\) −0.132661 + 0.990310i −0.00441469 + 0.0329554i
\(904\) 8.89491i 0.295840i
\(905\) 11.2238 19.4401i 0.373091 0.646212i
\(906\) −20.9918 + 12.1196i −0.697407 + 0.402648i
\(907\) −7.07108 + 4.08249i −0.234791 + 0.135557i −0.612781 0.790253i \(-0.709949\pi\)
0.377989 + 0.925810i \(0.376616\pi\)
\(908\) −8.69075 + 15.0528i −0.288413 + 0.499545i
\(909\) 14.8611i 0.492910i
\(910\) −22.8833 3.06543i −0.758573 0.101618i
\(911\) 5.20076i 0.172309i −0.996282 0.0861544i \(-0.972542\pi\)
0.996282 0.0861544i \(-0.0274578\pi\)
\(912\) 3.82465 + 2.20816i 0.126647 + 0.0731196i
\(913\) −31.3264 + 18.0863i −1.03675 + 0.598570i
\(914\) −10.3635 + 5.98335i −0.342793 + 0.197912i
\(915\) −20.1851 11.6539i −0.667300 0.385266i
\(916\) −0.972244 −0.0321239
\(917\) 7.23195 + 17.5720i 0.238820 + 0.580279i
\(918\) 6.29399i 0.207733i
\(919\) 13.2238 + 7.63479i 0.436214 + 0.251848i 0.701990 0.712186i \(-0.252295\pi\)
−0.265776 + 0.964035i \(0.585628\pi\)
\(920\) 4.42234 + 4.64936i 0.145800 + 0.153285i
\(921\) 8.04158 + 13.9284i 0.264979 + 0.458957i
\(922\) 12.9623 + 7.48378i 0.426890 + 0.246465i
\(923\) 26.2675i 0.864607i
\(924\) 15.7329 + 12.1290i 0.517573 + 0.399015i
\(925\) 18.9300i 0.622415i
\(926\) 4.00621 6.93897i 0.131652 0.228029i
\(927\) −8.75665 15.1670i −0.287606 0.498149i
\(928\) −1.59118 2.75600i −0.0522330 0.0904701i
\(929\) −9.12023 5.26557i −0.299225 0.172758i 0.342870 0.939383i \(-0.388601\pi\)
−0.642095 + 0.766625i \(0.721934\pi\)
\(930\) −5.38865 −0.176701
\(931\) −23.9723 6.54000i −0.785662 0.214340i
\(932\) −6.82932 −0.223702
\(933\) −2.22703 + 3.85732i −0.0729096 + 0.126283i
\(934\) −0.207210 0.358899i −0.00678013 0.0117435i
\(935\) −7.94619 + 4.58773i −0.259868 + 0.150035i
\(936\) −8.20231 4.73561i −0.268101 0.154788i
\(937\) 30.4361 0.994304 0.497152 0.867663i \(-0.334379\pi\)
0.497152 + 0.867663i \(0.334379\pi\)
\(938\) 6.66535 8.64580i 0.217631 0.282296i
\(939\) 6.72601i 0.219495i
\(940\) −0.326355 0.188421i −0.0106445 0.00614562i
\(941\) −8.00849 13.8711i −0.261069 0.452185i 0.705457 0.708753i \(-0.250742\pi\)
−0.966526 + 0.256567i \(0.917408\pi\)
\(942\) 8.84682 5.10771i 0.288245 0.166418i
\(943\) −4.26995 1.25943i −0.139049 0.0410126i
\(944\) 1.27113i 0.0413719i
\(945\) −7.46248 18.1322i −0.242754 0.589839i
\(946\) −1.83195 −0.0595617
\(947\) 26.9028 46.5971i 0.874225 1.51420i 0.0166392 0.999862i \(-0.494703\pi\)
0.857586 0.514341i \(-0.171963\pi\)
\(948\) −7.62682 13.2100i −0.247708 0.429042i
\(949\) 41.7975 + 72.3955i 1.35681 + 2.35006i
\(950\) −5.69711 + 9.86768i −0.184839 + 0.320150i
\(951\) 33.6296i 1.09052i
\(952\) 0.399166 2.97975i 0.0129370 0.0965743i
\(953\) 21.2679i 0.688936i 0.938798 + 0.344468i \(0.111941\pi\)
−0.938798 + 0.344468i \(0.888059\pi\)
\(954\) 16.5065 + 9.53001i 0.534416 + 0.308545i
\(955\) −4.17298 + 2.40927i −0.135034 + 0.0779622i
\(956\) −7.39470 12.8080i −0.239162 0.414240i
\(957\) −11.9472 + 20.6932i −0.386200 + 0.668917i
\(958\) 20.6791 0.668110
\(959\) 11.7443 + 1.57326i 0.379243 + 0.0508031i
\(960\) 1.66459i 0.0537243i
\(961\) −10.2602 + 17.7711i −0.330973 + 0.573262i
\(962\) 19.2319 + 33.3107i 0.620063 + 1.07398i
\(963\) 11.1289 6.42528i 0.358624 0.207052i
\(964\) −6.60378 + 11.4381i −0.212693 + 0.368396i
\(965\) −19.1393 −0.616115
\(966\) 9.26467 + 12.7814i 0.298086 + 0.411236i
\(967\) −23.6682 −0.761116 −0.380558 0.924757i \(-0.624268\pi\)
−0.380558 + 0.924757i \(0.624268\pi\)
\(968\) −12.7116 + 22.0171i −0.408566 + 0.707657i
\(969\) −4.34596 + 2.50914i −0.139612 + 0.0806052i
\(970\) 9.48921 + 16.4358i 0.304680 + 0.527722i
\(971\) −28.3288 + 49.0669i −0.909114 + 1.57463i −0.0938170 + 0.995589i \(0.529907\pi\)
−0.815297 + 0.579043i \(0.803426\pi\)
\(972\) 13.4637i 0.431848i
\(973\) −14.6537 + 19.0077i −0.469775 + 0.609358i
\(974\) −6.52145 −0.208961
\(975\) −13.0226 + 22.5559i −0.417058 + 0.722366i
\(976\) 7.00107 + 12.1262i 0.224099 + 0.388151i
\(977\) −31.5941 + 18.2409i −1.01079 + 0.583577i −0.911422 0.411474i \(-0.865014\pi\)
−0.0993638 + 0.995051i \(0.531681\pi\)
\(978\) −16.1357 9.31594i −0.515962 0.297891i
\(979\) 56.9679i 1.82070i
\(980\) 2.38300 + 9.05754i 0.0761223 + 0.289333i
\(981\) 11.1908i 0.357296i
\(982\) 7.31570 12.6712i 0.233453 0.404353i
\(983\) −10.0238 17.3617i −0.319708 0.553751i 0.660719 0.750633i \(-0.270252\pi\)
−0.980427 + 0.196883i \(0.936918\pi\)
\(984\) 0.577435 + 1.00015i 0.0184079 + 0.0318835i
\(985\) 8.05912 13.9588i 0.256785 0.444764i
\(986\) 3.61611 0.115161
\(987\) −0.734231 0.566044i −0.0233708 0.0180174i
\(988\) 23.1519i 0.736560i
\(989\) −1.39628 0.411837i −0.0443992 0.0130956i
\(990\) 10.1551 5.86307i 0.322751 0.186341i
\(991\) 2.86853 + 4.96844i 0.0911219 + 0.157828i 0.907983 0.419006i \(-0.137621\pi\)
−0.816862 + 0.576834i \(0.804288\pi\)
\(992\) 2.80352 + 1.61862i 0.0890120 + 0.0513911i
\(993\) 9.05996i 0.287509i
\(994\) 9.85382 4.05544i 0.312544 0.128631i
\(995\) 26.0663 0.826356
\(996\) 6.45777 + 3.72839i 0.204622 + 0.118139i
\(997\) 2.57381 1.48599i 0.0815134 0.0470618i −0.458689 0.888597i \(-0.651681\pi\)
0.540203 + 0.841535i \(0.318348\pi\)
\(998\) 8.69163 + 15.0544i 0.275129 + 0.476537i
\(999\) −16.3332 + 28.2899i −0.516759 + 0.895053i
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 322.2.g.b.229.3 yes 16
7.2 even 3 2254.2.c.b.2253.6 16
7.3 odd 6 inner 322.2.g.b.45.4 yes 16
7.5 odd 6 2254.2.c.b.2253.11 16
23.22 odd 2 inner 322.2.g.b.229.4 yes 16
161.45 even 6 inner 322.2.g.b.45.3 16
161.68 even 6 2254.2.c.b.2253.12 16
161.114 odd 6 2254.2.c.b.2253.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.2.g.b.45.3 16 161.45 even 6 inner
322.2.g.b.45.4 yes 16 7.3 odd 6 inner
322.2.g.b.229.3 yes 16 1.1 even 1 trivial
322.2.g.b.229.4 yes 16 23.22 odd 2 inner
2254.2.c.b.2253.5 16 161.114 odd 6
2254.2.c.b.2253.6 16 7.2 even 3
2254.2.c.b.2253.11 16 7.5 odd 6
2254.2.c.b.2253.12 16 161.68 even 6