Properties

Label 273.2.bn.c.230.23
Level $273$
Weight $2$
Character 273.230
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(146,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.146");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bn (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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 230.23
Character \(\chi\) \(=\) 273.230
Dual form 273.2.bn.c.146.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.29226 + 0.746087i) q^{2} +(-1.42689 - 0.981832i) q^{3} +(0.113292 + 0.196227i) q^{4} -2.73189 q^{5} +(-1.11138 - 2.33336i) q^{6} +(1.84288 - 1.89837i) q^{7} -2.64625i q^{8} +(1.07201 + 2.80193i) q^{9} +O(q^{10})\) \(q+(1.29226 + 0.746087i) q^{2} +(-1.42689 - 0.981832i) q^{3} +(0.113292 + 0.196227i) q^{4} -2.73189 q^{5} +(-1.11138 - 2.33336i) q^{6} +(1.84288 - 1.89837i) q^{7} -2.64625i q^{8} +(1.07201 + 2.80193i) q^{9} +(-3.53032 - 2.03823i) q^{10} +(-4.80144 - 2.77211i) q^{11} +(0.0310075 - 0.391227i) q^{12} +(-2.92207 - 2.11223i) q^{13} +(3.79783 - 1.07824i) q^{14} +(3.89810 + 2.68226i) q^{15} +(2.20091 - 3.81209i) q^{16} +(1.56754 + 2.71505i) q^{17} +(-0.705164 + 4.42063i) q^{18} +(4.83982 - 2.79427i) q^{19} +(-0.309501 - 0.536071i) q^{20} +(-4.49346 + 0.899361i) q^{21} +(-4.13648 - 7.16459i) q^{22} +(-0.778850 - 0.449669i) q^{23} +(-2.59817 + 3.77589i) q^{24} +2.46325 q^{25} +(-2.20017 - 4.90967i) q^{26} +(1.22138 - 5.05057i) q^{27} +(0.581293 + 0.146553i) q^{28} +(5.87835 + 3.39386i) q^{29} +(3.03616 + 6.37451i) q^{30} +2.36359i q^{31} +(1.10487 - 0.637899i) q^{32} +(4.12936 + 8.66970i) q^{33} +4.67808i q^{34} +(-5.03455 + 5.18614i) q^{35} +(-0.428363 + 0.527792i) q^{36} +(-1.46680 + 2.54056i) q^{37} +8.33908 q^{38} +(2.09561 + 5.88289i) q^{39} +7.22927i q^{40} +(-1.12250 + 1.94422i) q^{41} +(-6.47772 - 2.19030i) q^{42} +(0.910699 + 1.57738i) q^{43} -1.25623i q^{44} +(-2.92862 - 7.65457i) q^{45} +(-0.670985 - 1.16218i) q^{46} -1.03761 q^{47} +(-6.88329 + 3.27850i) q^{48} +(-0.207608 - 6.99692i) q^{49} +(3.18316 + 1.83780i) q^{50} +(0.429030 - 5.41313i) q^{51} +(0.0834302 - 0.812686i) q^{52} -8.97651i q^{53} +(5.34651 - 5.61539i) q^{54} +(13.1170 + 7.57312i) q^{55} +(-5.02355 - 4.87671i) q^{56} +(-9.64938 - 0.764783i) q^{57} +(5.06424 + 8.77151i) q^{58} +(-1.59559 - 2.76364i) q^{59} +(-0.0847093 + 1.06879i) q^{60} +(1.62596 - 0.938746i) q^{61} +(-1.76344 + 3.05438i) q^{62} +(7.29467 + 3.12853i) q^{63} -6.89994 q^{64} +(7.98278 + 5.77039i) q^{65} +(-1.13214 + 14.2844i) q^{66} +(6.70479 - 11.6130i) q^{67} +(-0.355178 + 0.615186i) q^{68} +(0.669831 + 1.40633i) q^{69} +(-10.3753 + 2.94564i) q^{70} +(3.21113 - 1.85394i) q^{71} +(7.41459 - 2.83680i) q^{72} -7.46851i q^{73} +(-3.79096 + 2.18871i) q^{74} +(-3.51477 - 2.41850i) q^{75} +(1.09662 + 0.633135i) q^{76} +(-14.1110 + 4.00624i) q^{77} +(-1.68108 + 9.16574i) q^{78} +12.5967 q^{79} +(-6.01266 + 10.4142i) q^{80} +(-6.70159 + 6.00739i) q^{81} +(-2.90112 + 1.67496i) q^{82} +6.48224 q^{83} +(-0.685549 - 0.779846i) q^{84} +(-4.28235 - 7.41724i) q^{85} +2.71784i q^{86} +(-5.05553 - 10.6142i) q^{87} +(-7.33570 + 12.7058i) q^{88} +(5.08611 - 8.80940i) q^{89} +(1.92643 - 12.0767i) q^{90} +(-9.39480 + 1.65459i) q^{91} -0.203775i q^{92} +(2.32065 - 3.37258i) q^{93} +(-1.34086 - 0.774148i) q^{94} +(-13.2219 + 7.63365i) q^{95} +(-2.20284 - 0.174591i) q^{96} +(-7.68183 + 4.43511i) q^{97} +(4.95203 - 9.19674i) q^{98} +(2.62006 - 16.4250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9} - 18 q^{15} - 16 q^{16} + 8 q^{18} - 44 q^{21} - 32 q^{22} + 48 q^{25} + 40 q^{28} - 40 q^{30} - 6 q^{36} + 12 q^{37} - 12 q^{42} + 40 q^{43} - 36 q^{46} - 24 q^{49} - 28 q^{51} - 68 q^{57} - 116 q^{60} + 4 q^{63} - 48 q^{64} - 28 q^{67} - 64 q^{70} + 62 q^{72} - 2 q^{78} + 56 q^{79} + 10 q^{81} + 28 q^{85} + 80 q^{88} - 16 q^{91} + 46 q^{93} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29226 + 0.746087i 0.913766 + 0.527563i 0.881641 0.471921i \(-0.156439\pi\)
0.0321252 + 0.999484i \(0.489772\pi\)
\(3\) −1.42689 0.981832i −0.823813 0.566861i
\(4\) 0.113292 + 0.196227i 0.0566458 + 0.0981134i
\(5\) −2.73189 −1.22174 −0.610870 0.791731i \(-0.709180\pi\)
−0.610870 + 0.791731i \(0.709180\pi\)
\(6\) −1.11138 2.33336i −0.453718 0.952592i
\(7\) 1.84288 1.89837i 0.696542 0.717516i
\(8\) 2.64625i 0.935589i
\(9\) 1.07201 + 2.80193i 0.357337 + 0.933976i
\(10\) −3.53032 2.03823i −1.11639 0.644545i
\(11\) −4.80144 2.77211i −1.44769 0.835824i −0.449346 0.893358i \(-0.648343\pi\)
−0.998344 + 0.0575343i \(0.981676\pi\)
\(12\) 0.0310075 0.391227i 0.00895110 0.112937i
\(13\) −2.92207 2.11223i −0.810436 0.585827i
\(14\) 3.79783 1.07824i 1.01501 0.288172i
\(15\) 3.89810 + 2.68226i 1.00649 + 0.692557i
\(16\) 2.20091 3.81209i 0.550228 0.953023i
\(17\) 1.56754 + 2.71505i 0.380184 + 0.658497i 0.991088 0.133207i \(-0.0425274\pi\)
−0.610905 + 0.791704i \(0.709194\pi\)
\(18\) −0.705164 + 4.42063i −0.166209 + 1.04195i
\(19\) 4.83982 2.79427i 1.11033 0.641050i 0.171416 0.985199i \(-0.445166\pi\)
0.938915 + 0.344149i \(0.111833\pi\)
\(20\) −0.309501 0.536071i −0.0692064 0.119869i
\(21\) −4.49346 + 0.899361i −0.980553 + 0.196257i
\(22\) −4.13648 7.16459i −0.881900 1.52749i
\(23\) −0.778850 0.449669i −0.162401 0.0937625i 0.416597 0.909091i \(-0.363223\pi\)
−0.578998 + 0.815329i \(0.696556\pi\)
\(24\) −2.59817 + 3.77589i −0.530349 + 0.770751i
\(25\) 2.46325 0.492649
\(26\) −2.20017 4.90967i −0.431488 0.962865i
\(27\) 1.22138 5.05057i 0.235055 0.971982i
\(28\) 0.581293 + 0.146553i 0.109854 + 0.0276958i
\(29\) 5.87835 + 3.39386i 1.09158 + 0.630225i 0.933997 0.357281i \(-0.116296\pi\)
0.157584 + 0.987506i \(0.449629\pi\)
\(30\) 3.03616 + 6.37451i 0.554325 + 1.16382i
\(31\) 2.36359i 0.424513i 0.977214 + 0.212257i \(0.0680813\pi\)
−0.977214 + 0.212257i \(0.931919\pi\)
\(32\) 1.10487 0.637899i 0.195316 0.112766i
\(33\) 4.12936 + 8.66970i 0.718830 + 1.50920i
\(34\) 4.67808i 0.802284i
\(35\) −5.03455 + 5.18614i −0.850994 + 0.876618i
\(36\) −0.428363 + 0.527792i −0.0713939 + 0.0879653i
\(37\) −1.46680 + 2.54056i −0.241140 + 0.417666i −0.961039 0.276412i \(-0.910855\pi\)
0.719900 + 0.694078i \(0.244188\pi\)
\(38\) 8.33908 1.35278
\(39\) 2.09561 + 5.88289i 0.335566 + 0.942017i
\(40\) 7.22927i 1.14305i
\(41\) −1.12250 + 1.94422i −0.175305 + 0.303637i −0.940267 0.340439i \(-0.889424\pi\)
0.764962 + 0.644075i \(0.222758\pi\)
\(42\) −6.47772 2.19030i −0.999534 0.337971i
\(43\) 0.910699 + 1.57738i 0.138880 + 0.240548i 0.927073 0.374881i \(-0.122316\pi\)
−0.788193 + 0.615428i \(0.788983\pi\)
\(44\) 1.25623i 0.189384i
\(45\) −2.92862 7.65457i −0.436573 1.14108i
\(46\) −0.670985 1.16218i −0.0989313 0.171354i
\(47\) −1.03761 −0.151351 −0.0756756 0.997132i \(-0.524111\pi\)
−0.0756756 + 0.997132i \(0.524111\pi\)
\(48\) −6.88329 + 3.27850i −0.993517 + 0.473210i
\(49\) −0.207608 6.99692i −0.0296583 0.999560i
\(50\) 3.18316 + 1.83780i 0.450166 + 0.259904i
\(51\) 0.429030 5.41313i 0.0600762 0.757990i
\(52\) 0.0834302 0.812686i 0.0115697 0.112699i
\(53\) 8.97651i 1.23302i −0.787348 0.616509i \(-0.788546\pi\)
0.787348 0.616509i \(-0.211454\pi\)
\(54\) 5.34651 5.61539i 0.727568 0.764158i
\(55\) 13.1170 + 7.57312i 1.76870 + 1.02116i
\(56\) −5.02355 4.87671i −0.671300 0.651677i
\(57\) −9.64938 0.764783i −1.27809 0.101298i
\(58\) 5.06424 + 8.77151i 0.664967 + 1.15176i
\(59\) −1.59559 2.76364i −0.207728 0.359795i 0.743271 0.668991i \(-0.233274\pi\)
−0.950998 + 0.309196i \(0.899940\pi\)
\(60\) −0.0847093 + 1.06879i −0.0109359 + 0.137980i
\(61\) 1.62596 0.938746i 0.208182 0.120194i −0.392284 0.919844i \(-0.628315\pi\)
0.600466 + 0.799650i \(0.294982\pi\)
\(62\) −1.76344 + 3.05438i −0.223958 + 0.387906i
\(63\) 7.29467 + 3.12853i 0.919043 + 0.394158i
\(64\) −6.89994 −0.862493
\(65\) 7.98278 + 5.77039i 0.990142 + 0.715729i
\(66\) −1.13214 + 14.2844i −0.139357 + 1.75829i
\(67\) 6.70479 11.6130i 0.819120 1.41876i −0.0872108 0.996190i \(-0.527795\pi\)
0.906331 0.422568i \(-0.138871\pi\)
\(68\) −0.355178 + 0.615186i −0.0430716 + 0.0746022i
\(69\) 0.669831 + 1.40633i 0.0806381 + 0.169302i
\(70\) −10.3753 + 2.94564i −1.24008 + 0.352071i
\(71\) 3.21113 1.85394i 0.381091 0.220023i −0.297202 0.954815i \(-0.596054\pi\)
0.678293 + 0.734792i \(0.262720\pi\)
\(72\) 7.41459 2.83680i 0.873818 0.334321i
\(73\) 7.46851i 0.874123i −0.899432 0.437062i \(-0.856019\pi\)
0.899432 0.437062i \(-0.143981\pi\)
\(74\) −3.79096 + 2.18871i −0.440691 + 0.254433i
\(75\) −3.51477 2.41850i −0.405851 0.279264i
\(76\) 1.09662 + 0.633135i 0.125791 + 0.0726255i
\(77\) −14.1110 + 4.00624i −1.60809 + 0.456554i
\(78\) −1.68108 + 9.16574i −0.190345 + 1.03782i
\(79\) 12.5967 1.41724 0.708620 0.705590i \(-0.249318\pi\)
0.708620 + 0.705590i \(0.249318\pi\)
\(80\) −6.01266 + 10.4142i −0.672236 + 1.16435i
\(81\) −6.70159 + 6.00739i −0.744621 + 0.667488i
\(82\) −2.90112 + 1.67496i −0.320375 + 0.184969i
\(83\) 6.48224 0.711518 0.355759 0.934578i \(-0.384222\pi\)
0.355759 + 0.934578i \(0.384222\pi\)
\(84\) −0.685549 0.779846i −0.0747996 0.0850882i
\(85\) −4.28235 7.41724i −0.464486 0.804513i
\(86\) 2.71784i 0.293073i
\(87\) −5.05553 10.6142i −0.542009 1.13796i
\(88\) −7.33570 + 12.7058i −0.781988 + 1.35444i
\(89\) 5.08611 8.80940i 0.539127 0.933795i −0.459825 0.888010i \(-0.652088\pi\)
0.998951 0.0457849i \(-0.0145789\pi\)
\(90\) 1.92643 12.0767i 0.203064 1.27300i
\(91\) −9.39480 + 1.65459i −0.984843 + 0.173448i
\(92\) 0.203775i 0.0212450i
\(93\) 2.32065 3.37258i 0.240640 0.349720i
\(94\) −1.34086 0.774148i −0.138300 0.0798473i
\(95\) −13.2219 + 7.63365i −1.35654 + 0.783196i
\(96\) −2.20284 0.174591i −0.224826 0.0178191i
\(97\) −7.68183 + 4.43511i −0.779972 + 0.450317i −0.836420 0.548089i \(-0.815356\pi\)
0.0564485 + 0.998406i \(0.482022\pi\)
\(98\) 4.95203 9.19674i 0.500230 0.929011i
\(99\) 2.62006 16.4250i 0.263326 1.65078i
\(100\) 0.279065 + 0.483355i 0.0279065 + 0.0483355i
\(101\) 4.29061 7.43156i 0.426932 0.739468i −0.569667 0.821876i \(-0.692928\pi\)
0.996599 + 0.0824081i \(0.0262611\pi\)
\(102\) 4.59309 6.67509i 0.454783 0.660932i
\(103\) 2.58413i 0.254622i 0.991863 + 0.127311i \(0.0406346\pi\)
−0.991863 + 0.127311i \(0.959365\pi\)
\(104\) −5.58948 + 7.73251i −0.548094 + 0.758235i
\(105\) 12.2756 2.45696i 1.19798 0.239775i
\(106\) 6.69725 11.6000i 0.650495 1.12669i
\(107\) 6.21163 + 3.58629i 0.600501 + 0.346699i 0.769239 0.638962i \(-0.220636\pi\)
−0.168738 + 0.985661i \(0.553969\pi\)
\(108\) 1.12943 0.332518i 0.108679 0.0319966i
\(109\) −4.98533 −0.477508 −0.238754 0.971080i \(-0.576739\pi\)
−0.238754 + 0.971080i \(0.576739\pi\)
\(110\) 11.3004 + 19.5729i 1.07745 + 1.86620i
\(111\) 4.58736 2.18495i 0.435413 0.207386i
\(112\) −3.18075 11.2034i −0.300552 1.05862i
\(113\) −16.6455 + 9.61026i −1.56587 + 0.904057i −0.569230 + 0.822178i \(0.692759\pi\)
−0.996642 + 0.0818789i \(0.973908\pi\)
\(114\) −11.8989 8.18757i −1.11444 0.766837i
\(115\) 2.12774 + 1.22845i 0.198412 + 0.114553i
\(116\) 1.53799i 0.142798i
\(117\) 2.78582 10.4518i 0.257549 0.966265i
\(118\) 4.76179i 0.438358i
\(119\) 8.04295 + 2.02775i 0.737296 + 0.185883i
\(120\) 7.09793 10.3153i 0.647949 0.941658i
\(121\) 9.86923 + 17.0940i 0.897202 + 1.55400i
\(122\) 2.80154 0.253640
\(123\) 3.51058 1.67208i 0.316538 0.150767i
\(124\) −0.463800 + 0.267775i −0.0416505 + 0.0240469i
\(125\) 6.93014 0.619851
\(126\) 7.09246 + 9.48534i 0.631847 + 0.845022i
\(127\) −5.59291 + 9.68721i −0.496291 + 0.859601i −0.999991 0.00427785i \(-0.998638\pi\)
0.503700 + 0.863879i \(0.331972\pi\)
\(128\) −11.1263 6.42375i −0.983432 0.567785i
\(129\) 0.249255 3.14489i 0.0219457 0.276892i
\(130\) 6.01063 + 13.4127i 0.527167 + 1.17637i
\(131\) −13.2568 −1.15825 −0.579126 0.815238i \(-0.696606\pi\)
−0.579126 + 0.815238i \(0.696606\pi\)
\(132\) −1.23341 + 1.79250i −0.107354 + 0.156017i
\(133\) 3.61464 14.3373i 0.313429 1.24320i
\(134\) 17.3287 10.0047i 1.49697 0.864275i
\(135\) −3.33669 + 13.7976i −0.287177 + 1.18751i
\(136\) 7.18470 4.14809i 0.616083 0.355696i
\(137\) 14.7843 8.53574i 1.26311 0.729257i 0.289435 0.957198i \(-0.406532\pi\)
0.973675 + 0.227940i \(0.0731991\pi\)
\(138\) −0.183646 + 2.31709i −0.0156330 + 0.197244i
\(139\) −1.21033 + 0.698786i −0.102659 + 0.0592702i −0.550451 0.834868i \(-0.685544\pi\)
0.447791 + 0.894138i \(0.352211\pi\)
\(140\) −1.58803 0.400366i −0.134213 0.0338371i
\(141\) 1.48055 + 1.01876i 0.124685 + 0.0857951i
\(142\) 5.53282 0.464304
\(143\) 8.17480 + 18.2421i 0.683611 + 1.52548i
\(144\) 13.0406 + 2.08019i 1.08672 + 0.173349i
\(145\) −16.0590 9.27168i −1.33363 0.769971i
\(146\) 5.57216 9.65126i 0.461155 0.798744i
\(147\) −6.57357 + 10.1876i −0.542179 + 0.840263i
\(148\) −0.664702 −0.0546382
\(149\) −15.3595 + 8.86783i −1.25830 + 0.726481i −0.972744 0.231880i \(-0.925512\pi\)
−0.285558 + 0.958361i \(0.592179\pi\)
\(150\) −2.73760 5.74765i −0.223524 0.469294i
\(151\) 2.09610 0.170578 0.0852891 0.996356i \(-0.472819\pi\)
0.0852891 + 0.996356i \(0.472819\pi\)
\(152\) −7.39433 12.8074i −0.599759 1.03881i
\(153\) −5.92697 + 7.30269i −0.479167 + 0.590388i
\(154\) −21.2240 5.35090i −1.71028 0.431187i
\(155\) 6.45708i 0.518645i
\(156\) −0.916967 + 1.07770i −0.0734161 + 0.0862848i
\(157\) 10.7453i 0.857571i −0.903406 0.428786i \(-0.858942\pi\)
0.903406 0.428786i \(-0.141058\pi\)
\(158\) 16.2782 + 9.39824i 1.29503 + 0.747684i
\(159\) −8.81342 + 12.8085i −0.698950 + 1.01578i
\(160\) −3.01840 + 1.74267i −0.238625 + 0.137770i
\(161\) −2.28896 + 0.649859i −0.180395 + 0.0512161i
\(162\) −13.1422 + 2.76315i −1.03255 + 0.217093i
\(163\) 2.58939 + 4.48495i 0.202817 + 0.351289i 0.949435 0.313964i \(-0.101657\pi\)
−0.746618 + 0.665253i \(0.768324\pi\)
\(164\) −0.508678 −0.0397211
\(165\) −11.2810 23.6847i −0.878223 1.84385i
\(166\) 8.37674 + 4.83631i 0.650161 + 0.375371i
\(167\) 10.2389 17.7342i 0.792307 1.37232i −0.132228 0.991219i \(-0.542213\pi\)
0.924535 0.381097i \(-0.124454\pi\)
\(168\) 2.37993 + 11.8908i 0.183616 + 0.917395i
\(169\) 4.07697 + 12.3442i 0.313613 + 0.949551i
\(170\) 12.7800i 0.980182i
\(171\) 13.0177 + 10.5653i 0.995487 + 0.807951i
\(172\) −0.206349 + 0.357407i −0.0157340 + 0.0272520i
\(173\) −0.888921 1.53966i −0.0675834 0.117058i 0.830254 0.557386i \(-0.188196\pi\)
−0.897837 + 0.440328i \(0.854862\pi\)
\(174\) 1.38607 17.4882i 0.105077 1.32578i
\(175\) 4.53946 4.67615i 0.343151 0.353484i
\(176\) −21.1351 + 12.2024i −1.59312 + 0.919788i
\(177\) −0.436707 + 5.51000i −0.0328249 + 0.414157i
\(178\) 13.1452 7.58936i 0.985271 0.568847i
\(179\) 10.8509 + 6.26477i 0.811035 + 0.468251i 0.847315 0.531091i \(-0.178218\pi\)
−0.0362804 + 0.999342i \(0.511551\pi\)
\(180\) 1.17024 1.44187i 0.0872248 0.107471i
\(181\) 20.7938i 1.54559i 0.634656 + 0.772795i \(0.281142\pi\)
−0.634656 + 0.772795i \(0.718858\pi\)
\(182\) −13.3750 4.87119i −0.991421 0.361076i
\(183\) −3.24175 0.256932i −0.239637 0.0189929i
\(184\) −1.18994 + 2.06103i −0.0877232 + 0.151941i
\(185\) 4.00713 6.94055i 0.294610 0.510280i
\(186\) 5.51512 2.62684i 0.404388 0.192609i
\(187\) 17.3816i 1.27107i
\(188\) −0.117553 0.203607i −0.00857341 0.0148496i
\(189\) −7.33698 11.6262i −0.533687 0.845682i
\(190\) −22.7815 −1.65274
\(191\) 16.9894 9.80886i 1.22931 0.709744i 0.262427 0.964952i \(-0.415477\pi\)
0.966886 + 0.255207i \(0.0821437\pi\)
\(192\) 9.84543 + 6.77458i 0.710533 + 0.488913i
\(193\) 3.49255 6.04928i 0.251399 0.435437i −0.712512 0.701660i \(-0.752443\pi\)
0.963911 + 0.266223i \(0.0857759\pi\)
\(194\) −13.2359 −0.950282
\(195\) −5.72497 16.0714i −0.409974 1.15090i
\(196\) 1.34946 0.833430i 0.0963902 0.0595307i
\(197\) −18.7335 10.8158i −1.33471 0.770594i −0.348691 0.937238i \(-0.613374\pi\)
−0.986017 + 0.166644i \(0.946707\pi\)
\(198\) 15.6403 19.2706i 1.11151 1.36950i
\(199\) −12.5873 + 7.26731i −0.892294 + 0.515166i −0.874692 0.484679i \(-0.838936\pi\)
−0.0176015 + 0.999845i \(0.505603\pi\)
\(200\) 6.51836i 0.460918i
\(201\) −20.9690 + 9.98751i −1.47904 + 0.704464i
\(202\) 11.0892 6.40234i 0.780232 0.450467i
\(203\) 17.2759 4.90479i 1.21253 0.344249i
\(204\) 1.11081 0.529075i 0.0777721 0.0370427i
\(205\) 3.06655 5.31141i 0.214177 0.370965i
\(206\) −1.92798 + 3.33937i −0.134329 + 0.232665i
\(207\) 0.425005 2.66433i 0.0295399 0.185184i
\(208\) −14.4832 + 6.49037i −1.00423 + 0.450026i
\(209\) −30.9841 −2.14322
\(210\) 17.6964 + 5.98367i 1.22117 + 0.412913i
\(211\) −6.98629 + 12.1006i −0.480956 + 0.833040i −0.999761 0.0218526i \(-0.993044\pi\)
0.518805 + 0.854892i \(0.326377\pi\)
\(212\) 1.76143 1.01696i 0.120976 0.0698453i
\(213\) −6.40218 0.507419i −0.438670 0.0347678i
\(214\) 5.35136 + 9.26883i 0.365812 + 0.633605i
\(215\) −2.48793 4.30923i −0.169676 0.293887i
\(216\) −13.3650 3.23208i −0.909376 0.219915i
\(217\) 4.48697 + 4.35581i 0.304595 + 0.295691i
\(218\) −6.44234 3.71949i −0.436331 0.251916i
\(219\) −7.33283 + 10.6567i −0.495506 + 0.720114i
\(220\) 3.43188i 0.231378i
\(221\) 1.15437 11.2446i 0.0776510 0.756392i
\(222\) 7.55823 + 0.599044i 0.507275 + 0.0402052i
\(223\) 16.2803 + 9.39944i 1.09021 + 0.629433i 0.933632 0.358233i \(-0.116621\pi\)
0.156577 + 0.987666i \(0.449954\pi\)
\(224\) 0.825178 3.27303i 0.0551346 0.218688i
\(225\) 2.64063 + 6.90184i 0.176042 + 0.460123i
\(226\) −28.6804 −1.90779
\(227\) 2.91196 + 5.04367i 0.193274 + 0.334760i 0.946333 0.323193i \(-0.104756\pi\)
−0.753060 + 0.657952i \(0.771423\pi\)
\(228\) −0.943122 1.98011i −0.0624598 0.131136i
\(229\) 17.2490i 1.13984i 0.821699 + 0.569922i \(0.193027\pi\)
−0.821699 + 0.569922i \(0.806973\pi\)
\(230\) 1.83306 + 3.17495i 0.120868 + 0.209350i
\(231\) 24.0682 + 8.13814i 1.58357 + 0.535451i
\(232\) 8.98100 15.5556i 0.589632 1.02127i
\(233\) 15.1362i 0.991603i −0.868436 0.495802i \(-0.834874\pi\)
0.868436 0.495802i \(-0.165126\pi\)
\(234\) 11.3979 11.4279i 0.745106 0.747067i
\(235\) 2.83464 0.184912
\(236\) 0.361533 0.626194i 0.0235338 0.0407618i
\(237\) −17.9741 12.3679i −1.16754 0.803378i
\(238\) 8.88072 + 8.62112i 0.575651 + 0.558824i
\(239\) 9.13875i 0.591136i 0.955322 + 0.295568i \(0.0955090\pi\)
−0.955322 + 0.295568i \(0.904491\pi\)
\(240\) 18.8044 8.95651i 1.21382 0.578140i
\(241\) −16.2277 + 9.36906i −1.04532 + 0.603514i −0.921335 0.388770i \(-0.872900\pi\)
−0.123982 + 0.992284i \(0.539567\pi\)
\(242\) 29.4532i 1.89332i
\(243\) 15.4607 1.99203i 0.991801 0.127789i
\(244\) 0.368414 + 0.212704i 0.0235853 + 0.0136170i
\(245\) 0.567163 + 19.1148i 0.0362347 + 1.22120i
\(246\) 5.78410 + 0.458432i 0.368781 + 0.0292285i
\(247\) −20.0444 2.05776i −1.27540 0.130932i
\(248\) 6.25464 0.397170
\(249\) −9.24942 6.36447i −0.586158 0.403332i
\(250\) 8.95555 + 5.17049i 0.566399 + 0.327010i
\(251\) 5.72137 + 9.90971i 0.361130 + 0.625495i 0.988147 0.153510i \(-0.0490578\pi\)
−0.627017 + 0.779005i \(0.715724\pi\)
\(252\) 0.212523 + 1.78585i 0.0133877 + 0.112498i
\(253\) 2.49307 + 4.31812i 0.156738 + 0.271478i
\(254\) −14.4550 + 8.34560i −0.906987 + 0.523649i
\(255\) −1.17206 + 14.7881i −0.0733975 + 0.926067i
\(256\) −2.68542 4.65128i −0.167839 0.290705i
\(257\) 6.64490 11.5093i 0.414498 0.717931i −0.580878 0.813991i \(-0.697291\pi\)
0.995376 + 0.0960597i \(0.0306240\pi\)
\(258\) 2.66847 3.87805i 0.166131 0.241437i
\(259\) 2.11980 + 7.46647i 0.131718 + 0.463944i
\(260\) −0.227922 + 2.22017i −0.0141351 + 0.137689i
\(261\) −3.20771 + 20.1090i −0.198552 + 1.24471i
\(262\) −17.1312 9.89073i −1.05837 0.611051i
\(263\) −9.59512 5.53975i −0.591661 0.341595i 0.174093 0.984729i \(-0.444301\pi\)
−0.765754 + 0.643134i \(0.777634\pi\)
\(264\) 22.9422 10.9273i 1.41199 0.672529i
\(265\) 24.5229i 1.50643i
\(266\) 15.3679 15.8306i 0.942266 0.970639i
\(267\) −15.9067 + 7.57631i −0.973472 + 0.463663i
\(268\) 3.03838 0.185599
\(269\) 12.8859 + 22.3191i 0.785668 + 1.36082i 0.928599 + 0.371085i \(0.121014\pi\)
−0.142931 + 0.989733i \(0.545653\pi\)
\(270\) −14.6061 + 15.3407i −0.888899 + 0.933602i
\(271\) 23.0734 + 13.3214i 1.40161 + 0.809218i 0.994558 0.104188i \(-0.0332245\pi\)
0.407049 + 0.913406i \(0.366558\pi\)
\(272\) 13.8001 0.836751
\(273\) 15.0298 + 6.86322i 0.909648 + 0.415381i
\(274\) 25.4736 1.53892
\(275\) −11.8271 6.82840i −0.713203 0.411768i
\(276\) −0.200073 + 0.290764i −0.0120430 + 0.0175019i
\(277\) 5.64884 + 9.78407i 0.339406 + 0.587868i 0.984321 0.176386i \(-0.0564407\pi\)
−0.644915 + 0.764254i \(0.723107\pi\)
\(278\) −2.08542 −0.125075
\(279\) −6.62261 + 2.53379i −0.396485 + 0.151694i
\(280\) 13.7238 + 13.3226i 0.820155 + 0.796181i
\(281\) 13.4298i 0.801153i −0.916263 0.400576i \(-0.868810\pi\)
0.916263 0.400576i \(-0.131190\pi\)
\(282\) 1.15318 + 2.42113i 0.0686707 + 0.144176i
\(283\) −1.72819 0.997772i −0.102730 0.0593114i 0.447755 0.894156i \(-0.352224\pi\)
−0.550485 + 0.834845i \(0.685557\pi\)
\(284\) 0.727587 + 0.420073i 0.0431744 + 0.0249267i
\(285\) 26.3611 + 2.08931i 1.56150 + 0.123760i
\(286\) −3.04618 + 29.6726i −0.180125 + 1.75458i
\(287\) 1.62223 + 5.71388i 0.0957570 + 0.337280i
\(288\) 2.97178 + 2.41194i 0.175114 + 0.142125i
\(289\) 3.58565 6.21053i 0.210921 0.365325i
\(290\) −13.8350 23.9629i −0.812417 1.40715i
\(291\) 15.3156 + 1.21387i 0.897818 + 0.0711586i
\(292\) 1.46552 0.846120i 0.0857632 0.0495154i
\(293\) 13.4902 + 23.3658i 0.788109 + 1.36504i 0.927124 + 0.374754i \(0.122273\pi\)
−0.139016 + 0.990290i \(0.544394\pi\)
\(294\) −16.0956 + 8.26064i −0.938717 + 0.481770i
\(295\) 4.35898 + 7.54997i 0.253790 + 0.439576i
\(296\) 6.72296 + 3.88150i 0.390764 + 0.225608i
\(297\) −19.8651 + 20.8642i −1.15269 + 1.21066i
\(298\) −26.4647 −1.53306
\(299\) 1.32605 + 2.95907i 0.0766874 + 0.171128i
\(300\) 0.0763792 0.963688i 0.00440976 0.0556386i
\(301\) 4.67275 + 1.17807i 0.269333 + 0.0679028i
\(302\) 2.70871 + 1.56387i 0.155869 + 0.0899908i
\(303\) −13.4188 + 6.39133i −0.770888 + 0.367172i
\(304\) 24.5998i 1.41089i
\(305\) −4.44194 + 2.56456i −0.254345 + 0.146846i
\(306\) −13.1076 + 5.01495i −0.749313 + 0.286686i
\(307\) 22.9472i 1.30966i −0.755775 0.654832i \(-0.772739\pi\)
0.755775 0.654832i \(-0.227261\pi\)
\(308\) −2.38478 2.31507i −0.135886 0.131914i
\(309\) 2.53718 3.68726i 0.144335 0.209761i
\(310\) 4.81754 8.34423i 0.273618 0.473920i
\(311\) −14.0205 −0.795030 −0.397515 0.917596i \(-0.630127\pi\)
−0.397515 + 0.917596i \(0.630127\pi\)
\(312\) 15.5676 5.54549i 0.881341 0.313952i
\(313\) 0.982717i 0.0555465i 0.999614 + 0.0277732i \(0.00884163\pi\)
−0.999614 + 0.0277732i \(0.991158\pi\)
\(314\) 8.01696 13.8858i 0.452423 0.783620i
\(315\) −19.9283 8.54683i −1.12283 0.481559i
\(316\) 1.42710 + 2.47181i 0.0802807 + 0.139050i
\(317\) 9.12747i 0.512650i −0.966591 0.256325i \(-0.917488\pi\)
0.966591 0.256325i \(-0.0825117\pi\)
\(318\) −20.9455 + 9.97628i −1.17456 + 0.559442i
\(319\) −18.8164 32.5909i −1.05351 1.82474i
\(320\) 18.8499 1.05374
\(321\) −5.34216 11.2160i −0.298170 0.626016i
\(322\) −3.44279 0.867978i −0.191859 0.0483705i
\(323\) 15.1732 + 8.76025i 0.844259 + 0.487433i
\(324\) −1.93804 0.634444i −0.107669 0.0352469i
\(325\) −7.19778 5.20294i −0.399261 0.288607i
\(326\) 7.72764i 0.427994i
\(327\) 7.11350 + 4.89476i 0.393377 + 0.270681i
\(328\) 5.14489 + 2.97041i 0.284079 + 0.164013i
\(329\) −1.91219 + 1.96977i −0.105422 + 0.108597i
\(330\) 3.09289 39.0234i 0.170258 2.14817i
\(331\) −14.4100 24.9588i −0.792043 1.37186i −0.924700 0.380697i \(-0.875684\pi\)
0.132657 0.991162i \(-0.457649\pi\)
\(332\) 0.734383 + 1.27199i 0.0403045 + 0.0698095i
\(333\) −8.69090 1.38634i −0.476258 0.0759710i
\(334\) 26.4626 15.2782i 1.44797 0.835984i
\(335\) −18.3168 + 31.7256i −1.00075 + 1.73335i
\(336\) −6.46126 + 19.1089i −0.352491 + 1.04248i
\(337\) 11.4930 0.626066 0.313033 0.949742i \(-0.398655\pi\)
0.313033 + 0.949742i \(0.398655\pi\)
\(338\) −3.94131 + 18.9936i −0.214379 + 1.03312i
\(339\) 33.1868 + 2.63030i 1.80246 + 0.142858i
\(340\) 0.970308 1.68062i 0.0526223 0.0911445i
\(341\) 6.55214 11.3486i 0.354818 0.614563i
\(342\) 8.93958 + 23.3655i 0.483397 + 1.26346i
\(343\) −13.6653 12.5003i −0.737859 0.674955i
\(344\) 4.17413 2.40993i 0.225054 0.129935i
\(345\) −1.82991 3.84194i −0.0985189 0.206843i
\(346\) 2.65285i 0.142618i
\(347\) 19.8548 11.4631i 1.06586 0.615374i 0.138812 0.990319i \(-0.455672\pi\)
0.927047 + 0.374945i \(0.122338\pi\)
\(348\) 1.51004 2.19453i 0.0809468 0.117639i
\(349\) −18.2528 10.5383i −0.977052 0.564101i −0.0756733 0.997133i \(-0.524111\pi\)
−0.901379 + 0.433031i \(0.857444\pi\)
\(350\) 9.35498 2.65597i 0.500045 0.141968i
\(351\) −14.2369 + 12.1783i −0.759911 + 0.650027i
\(352\) −7.07331 −0.377009
\(353\) 8.26451 14.3146i 0.439876 0.761887i −0.557804 0.829973i \(-0.688356\pi\)
0.997679 + 0.0680859i \(0.0216892\pi\)
\(354\) −4.67528 + 6.79454i −0.248488 + 0.361126i
\(355\) −8.77246 + 5.06478i −0.465594 + 0.268811i
\(356\) 2.30485 0.122157
\(357\) −9.48547 10.7902i −0.502025 0.571078i
\(358\) 9.34813 + 16.1914i 0.494064 + 0.855744i
\(359\) 4.77131i 0.251820i 0.992042 + 0.125910i \(0.0401851\pi\)
−0.992042 + 0.125910i \(0.959815\pi\)
\(360\) −20.2559 + 7.74985i −1.06758 + 0.408453i
\(361\) 6.11590 10.5930i 0.321889 0.557529i
\(362\) −15.5140 + 26.8710i −0.815396 + 1.41231i
\(363\) 2.70118 34.0811i 0.141775 1.78880i
\(364\) −1.38903 1.65606i −0.0728048 0.0868012i
\(365\) 20.4032i 1.06795i
\(366\) −3.99749 2.75065i −0.208952 0.143779i
\(367\) 0.192629 + 0.111214i 0.0100551 + 0.00580533i 0.505019 0.863108i \(-0.331485\pi\)
−0.494964 + 0.868913i \(0.664819\pi\)
\(368\) −3.42836 + 1.97937i −0.178716 + 0.103182i
\(369\) −6.65090 1.06093i −0.346232 0.0552297i
\(370\) 10.3565 5.97934i 0.538410 0.310851i
\(371\) −17.0407 16.5426i −0.884710 0.858849i
\(372\) 0.924700 + 0.0732891i 0.0479435 + 0.00379986i
\(373\) −1.16748 2.02213i −0.0604496 0.104702i 0.834217 0.551436i \(-0.185920\pi\)
−0.894666 + 0.446735i \(0.852587\pi\)
\(374\) 12.9682 22.4615i 0.670568 1.16146i
\(375\) −9.88852 6.80424i −0.510641 0.351369i
\(376\) 2.74577i 0.141603i
\(377\) −10.0083 22.3335i −0.515454 1.15023i
\(378\) −0.807121 20.4981i −0.0415138 1.05431i
\(379\) −1.58669 + 2.74823i −0.0815030 + 0.141167i −0.903896 0.427753i \(-0.859305\pi\)
0.822393 + 0.568920i \(0.192639\pi\)
\(380\) −2.99585 1.72966i −0.153684 0.0887295i
\(381\) 17.4917 8.33125i 0.896125 0.426823i
\(382\) 29.2731 1.49774
\(383\) −11.5345 19.9784i −0.589386 1.02085i −0.994313 0.106498i \(-0.966036\pi\)
0.404927 0.914349i \(-0.367297\pi\)
\(384\) 9.56887 + 20.0901i 0.488310 + 1.02522i
\(385\) 38.5497 10.9446i 1.96467 0.557790i
\(386\) 9.02658 5.21150i 0.459441 0.265258i
\(387\) −3.44342 + 4.24268i −0.175039 + 0.215667i
\(388\) −1.74057 1.00492i −0.0883642 0.0510171i
\(389\) 36.7393i 1.86276i 0.364051 + 0.931379i \(0.381393\pi\)
−0.364051 + 0.931379i \(0.618607\pi\)
\(390\) 4.59254 25.0398i 0.232552 1.26794i
\(391\) 2.81949i 0.142588i
\(392\) −18.5156 + 0.549382i −0.935178 + 0.0277480i
\(393\) 18.9160 + 13.0160i 0.954184 + 0.656568i
\(394\) −16.1391 27.9537i −0.813074 1.40829i
\(395\) −34.4129 −1.73150
\(396\) 3.51986 1.34669i 0.176880 0.0676737i
\(397\) −9.72327 + 5.61373i −0.487997 + 0.281745i −0.723743 0.690070i \(-0.757580\pi\)
0.235746 + 0.971815i \(0.424247\pi\)
\(398\) −21.6882 −1.08713
\(399\) −19.2345 + 16.9087i −0.962927 + 0.846493i
\(400\) 5.42139 9.39013i 0.271070 0.469506i
\(401\) 12.8082 + 7.39483i 0.639612 + 0.369280i 0.784465 0.620173i \(-0.212938\pi\)
−0.144853 + 0.989453i \(0.546271\pi\)
\(402\) −34.5490 2.73826i −1.72315 0.136572i
\(403\) 4.99245 6.90658i 0.248691 0.344041i
\(404\) 1.94436 0.0967356
\(405\) 18.3080 16.4116i 0.909733 0.815497i
\(406\) 25.9843 + 6.55104i 1.28958 + 0.325122i
\(407\) 14.0855 8.13225i 0.698191 0.403101i
\(408\) −14.3245 1.13532i −0.709168 0.0562067i
\(409\) 10.3595 5.98106i 0.512244 0.295744i −0.221512 0.975158i \(-0.571099\pi\)
0.733756 + 0.679413i \(0.237766\pi\)
\(410\) 7.92555 4.57582i 0.391415 0.225984i
\(411\) −29.4762 2.33620i −1.45395 0.115236i
\(412\) −0.507075 + 0.292760i −0.0249818 + 0.0144232i
\(413\) −8.18688 2.06403i −0.402850 0.101564i
\(414\) 2.53704 3.12592i 0.124689 0.153631i
\(415\) −17.7088 −0.869291
\(416\) −4.57591 0.469761i −0.224352 0.0230319i
\(417\) 2.41310 + 0.191255i 0.118170 + 0.00936581i
\(418\) −40.0396 23.1169i −1.95840 1.13068i
\(419\) −5.08405 + 8.80583i −0.248372 + 0.430193i −0.963074 0.269236i \(-0.913229\pi\)
0.714702 + 0.699429i \(0.246562\pi\)
\(420\) 1.87285 + 2.13046i 0.0913857 + 0.103956i
\(421\) 1.53126 0.0746289 0.0373145 0.999304i \(-0.488120\pi\)
0.0373145 + 0.999304i \(0.488120\pi\)
\(422\) −18.0562 + 10.4248i −0.878962 + 0.507469i
\(423\) −1.11233 2.90731i −0.0540834 0.141358i
\(424\) −23.7540 −1.15360
\(425\) 3.86123 + 6.68785i 0.187297 + 0.324408i
\(426\) −7.89470 5.43230i −0.382500 0.263196i
\(427\) 1.21435 4.81666i 0.0587665 0.233094i
\(428\) 1.62518i 0.0785563i
\(429\) 6.24612 34.0556i 0.301565 1.64422i
\(430\) 7.42486i 0.358059i
\(431\) −26.7372 15.4367i −1.28788 0.743560i −0.309607 0.950865i \(-0.600198\pi\)
−0.978276 + 0.207305i \(0.933531\pi\)
\(432\) −16.5651 15.7719i −0.796987 0.758825i
\(433\) −7.30929 + 4.22002i −0.351262 + 0.202801i −0.665241 0.746629i \(-0.731671\pi\)
0.313979 + 0.949430i \(0.398338\pi\)
\(434\) 2.54852 + 8.97651i 0.122333 + 0.430886i
\(435\) 13.8112 + 28.9969i 0.662195 + 1.39029i
\(436\) −0.564796 0.978255i −0.0270488 0.0468499i
\(437\) −5.02599 −0.240426
\(438\) −17.4268 + 8.30033i −0.832683 + 0.396605i
\(439\) 15.2471 + 8.80294i 0.727706 + 0.420142i 0.817583 0.575811i \(-0.195314\pi\)
−0.0898761 + 0.995953i \(0.528647\pi\)
\(440\) 20.0403 34.7109i 0.955386 1.65478i
\(441\) 19.3823 8.08248i 0.922967 0.384880i
\(442\) 9.88117 13.6697i 0.469999 0.650200i
\(443\) 14.0924i 0.669551i 0.942298 + 0.334776i \(0.108661\pi\)
−0.942298 + 0.334776i \(0.891339\pi\)
\(444\) 0.948455 + 0.652626i 0.0450117 + 0.0309723i
\(445\) −13.8947 + 24.0664i −0.658673 + 1.14085i
\(446\) 14.0256 + 24.2930i 0.664131 + 1.15031i
\(447\) 30.6230 + 2.42710i 1.44842 + 0.114798i
\(448\) −12.7157 + 13.0986i −0.600762 + 0.618852i
\(449\) 17.2357 9.95103i 0.813402 0.469618i −0.0347338 0.999397i \(-0.511058\pi\)
0.848136 + 0.529779i \(0.177725\pi\)
\(450\) −1.73699 + 10.8891i −0.0818826 + 0.513318i
\(451\) 10.7792 6.22338i 0.507573 0.293048i
\(452\) −3.77158 2.17752i −0.177400 0.102422i
\(453\) −2.99090 2.05802i −0.140525 0.0966942i
\(454\) 8.69031i 0.407856i
\(455\) 25.6656 4.52015i 1.20322 0.211908i
\(456\) −2.02380 + 25.5346i −0.0947733 + 1.19577i
\(457\) 12.3601 21.4083i 0.578181 1.00144i −0.417507 0.908674i \(-0.637096\pi\)
0.995688 0.0927651i \(-0.0295706\pi\)
\(458\) −12.8692 + 22.2902i −0.601340 + 1.04155i
\(459\) 15.6271 4.60083i 0.729412 0.214748i
\(460\) 0.556692i 0.0259559i
\(461\) 13.0742 + 22.6451i 0.608925 + 1.05469i 0.991418 + 0.130730i \(0.0417322\pi\)
−0.382493 + 0.923958i \(0.624934\pi\)
\(462\) 25.0306 + 28.4736i 1.16453 + 1.32471i
\(463\) 22.7832 1.05883 0.529413 0.848364i \(-0.322412\pi\)
0.529413 + 0.848364i \(0.322412\pi\)
\(464\) 25.8755 14.9392i 1.20124 0.693535i
\(465\) −6.33977 + 9.21352i −0.294000 + 0.427267i
\(466\) 11.2929 19.5599i 0.523133 0.906094i
\(467\) 11.7468 0.543578 0.271789 0.962357i \(-0.412385\pi\)
0.271789 + 0.962357i \(0.412385\pi\)
\(468\) 2.36652 0.637443i 0.109393 0.0294658i
\(469\) −9.68972 34.1296i −0.447430 1.57596i
\(470\) 3.66310 + 2.11489i 0.168966 + 0.0975527i
\(471\) −10.5501 + 15.3324i −0.486124 + 0.706479i
\(472\) −7.31327 + 4.22232i −0.336621 + 0.194348i
\(473\) 10.0982i 0.464318i
\(474\) −13.9997 29.3927i −0.643027 1.35005i
\(475\) 11.9217 6.88298i 0.547004 0.315813i
\(476\) 0.513301 + 1.80797i 0.0235271 + 0.0828681i
\(477\) 25.1515 9.62291i 1.15161 0.440603i
\(478\) −6.81830 + 11.8096i −0.311862 + 0.540161i
\(479\) 3.81589 6.60932i 0.174353 0.301988i −0.765584 0.643335i \(-0.777550\pi\)
0.939937 + 0.341348i \(0.110883\pi\)
\(480\) 6.01792 + 0.476964i 0.274679 + 0.0217703i
\(481\) 9.65233 4.32550i 0.440108 0.197226i
\(482\) −27.9605 −1.27357
\(483\) 3.90414 + 1.32010i 0.177645 + 0.0600667i
\(484\) −2.23620 + 3.87321i −0.101645 + 0.176055i
\(485\) 20.9860 12.1162i 0.952923 0.550170i
\(486\) 21.4654 + 8.96077i 0.973691 + 0.406469i
\(487\) 10.7128 + 18.5552i 0.485446 + 0.840816i 0.999860 0.0167253i \(-0.00532408\pi\)
−0.514415 + 0.857542i \(0.671991\pi\)
\(488\) −2.48415 4.30268i −0.112452 0.194773i
\(489\) 0.708707 8.94186i 0.0320488 0.404365i
\(490\) −13.5284 + 25.1245i −0.611152 + 1.13501i
\(491\) −2.74421 1.58437i −0.123845 0.0715017i 0.436798 0.899560i \(-0.356112\pi\)
−0.560643 + 0.828058i \(0.689446\pi\)
\(492\) 0.725826 + 0.499437i 0.0327228 + 0.0225163i
\(493\) 21.2800i 0.958405i
\(494\) −24.3674 17.6140i −1.09634 0.792493i
\(495\) −7.15773 + 44.8714i −0.321716 + 2.01682i
\(496\) 9.01023 + 5.20206i 0.404571 + 0.233579i
\(497\) 2.39824 9.51249i 0.107576 0.426694i
\(498\) −7.20421 15.1254i −0.322828 0.677787i
\(499\) 1.64154 0.0734852 0.0367426 0.999325i \(-0.488302\pi\)
0.0367426 + 0.999325i \(0.488302\pi\)
\(500\) 0.785127 + 1.35988i 0.0351119 + 0.0608156i
\(501\) −32.0217 + 15.2519i −1.43063 + 0.681404i
\(502\) 17.0746i 0.762075i
\(503\) −11.4570 19.8441i −0.510843 0.884805i −0.999921 0.0125654i \(-0.996000\pi\)
0.489079 0.872240i \(-0.337333\pi\)
\(504\) 8.27887 19.3035i 0.368770 0.859846i
\(505\) −11.7215 + 20.3022i −0.521600 + 0.903437i
\(506\) 7.44018i 0.330756i
\(507\) 6.30252 21.6166i 0.279905 0.960028i
\(508\) −2.53452 −0.112451
\(509\) −13.5701 + 23.5041i −0.601485 + 1.04180i 0.391112 + 0.920343i \(0.372091\pi\)
−0.992596 + 0.121459i \(0.961243\pi\)
\(510\) −12.5478 + 18.2356i −0.555627 + 0.807487i
\(511\) −14.1780 13.7636i −0.627197 0.608864i
\(512\) 17.6808i 0.781388i
\(513\) −8.20137 27.8567i −0.362099 1.22990i
\(514\) 17.1739 9.91535i 0.757508 0.437347i
\(515\) 7.05956i 0.311082i
\(516\) 0.645351 0.307379i 0.0284100 0.0135316i
\(517\) 4.98203 + 2.87638i 0.219109 + 0.126503i
\(518\) −2.83129 + 11.2302i −0.124400 + 0.493426i
\(519\) −0.243295 + 3.06969i −0.0106795 + 0.134744i
\(520\) 15.2699 21.1244i 0.669628 0.926367i
\(521\) 29.5173 1.29318 0.646588 0.762839i \(-0.276195\pi\)
0.646588 + 0.762839i \(0.276195\pi\)
\(522\) −19.1482 + 23.5928i −0.838095 + 1.03263i
\(523\) −22.2430 12.8420i −0.972619 0.561542i −0.0725853 0.997362i \(-0.523125\pi\)
−0.900034 + 0.435820i \(0.856458\pi\)
\(524\) −1.50188 2.60134i −0.0656101 0.113640i
\(525\) −11.0685 + 2.21535i −0.483069 + 0.0966857i
\(526\) −8.26627 14.3176i −0.360426 0.624277i
\(527\) −6.41728 + 3.70502i −0.279541 + 0.161393i
\(528\) 42.1381 + 3.33975i 1.83382 + 0.145344i
\(529\) −11.0956 19.2181i −0.482417 0.835571i
\(530\) −18.2962 + 31.6899i −0.794736 + 1.37652i
\(531\) 6.03303 7.43337i 0.261811 0.322581i
\(532\) 3.22286 0.915002i 0.139729 0.0396704i
\(533\) 7.38666 3.31018i 0.319952 0.143380i
\(534\) −26.2081 2.07718i −1.13414 0.0898885i
\(535\) −16.9695 9.79736i −0.733656 0.423577i
\(536\) −30.7310 17.7425i −1.32737 0.766360i
\(537\) −9.33205 19.5929i −0.402708 0.845495i
\(538\) 38.4561i 1.65796i
\(539\) −18.3994 + 34.1708i −0.792520 + 1.47184i
\(540\) −3.08548 + 0.908405i −0.132778 + 0.0390915i
\(541\) 8.86441 0.381111 0.190555 0.981676i \(-0.438971\pi\)
0.190555 + 0.981676i \(0.438971\pi\)
\(542\) 19.8779 + 34.4295i 0.853827 + 1.47887i
\(543\) 20.4160 29.6704i 0.876135 1.27328i
\(544\) 3.46386 + 1.99986i 0.148512 + 0.0857433i
\(545\) 13.6194 0.583391
\(546\) 14.3019 + 20.0826i 0.612066 + 0.859457i
\(547\) −9.77953 −0.418143 −0.209071 0.977900i \(-0.567044\pi\)
−0.209071 + 0.977900i \(0.567044\pi\)
\(548\) 3.34988 + 1.93405i 0.143100 + 0.0826187i
\(549\) 4.37334 + 3.54946i 0.186650 + 0.151487i
\(550\) −10.1892 17.6481i −0.434467 0.752520i
\(551\) 37.9335 1.61602
\(552\) 3.72149 1.77254i 0.158397 0.0754442i
\(553\) 23.2142 23.9132i 0.987168 1.01689i
\(554\) 16.8581i 0.716232i
\(555\) −12.5322 + 5.96905i −0.531961 + 0.253372i
\(556\) −0.274241 0.158333i −0.0116304 0.00671482i
\(557\) 2.45545 + 1.41766i 0.104041 + 0.0600680i 0.551118 0.834428i \(-0.314202\pi\)
−0.447077 + 0.894496i \(0.647535\pi\)
\(558\) −10.4486 1.66672i −0.442323 0.0705578i
\(559\) 0.670657 6.53281i 0.0283658 0.276308i
\(560\) 8.68946 + 30.6064i 0.367197 + 1.29336i
\(561\) −17.0658 + 24.8015i −0.720518 + 1.04712i
\(562\) 10.0198 17.3548i 0.422659 0.732066i
\(563\) −15.0972 26.1492i −0.636273 1.10206i −0.986244 0.165296i \(-0.947142\pi\)
0.349971 0.936761i \(-0.386191\pi\)
\(564\) −0.0321738 + 0.405941i −0.00135476 + 0.0170932i
\(565\) 45.4736 26.2542i 1.91309 1.10452i
\(566\) −1.48885 2.57876i −0.0625810 0.108393i
\(567\) −0.945955 + 23.7930i −0.0397264 + 0.999211i
\(568\) −4.90599 8.49743i −0.205851 0.356544i
\(569\) 6.05199 + 3.49412i 0.253712 + 0.146481i 0.621463 0.783444i \(-0.286539\pi\)
−0.367750 + 0.929924i \(0.619872\pi\)
\(570\) 32.5066 + 22.3676i 1.36155 + 0.936875i
\(571\) −0.691674 −0.0289457 −0.0144728 0.999895i \(-0.504607\pi\)
−0.0144728 + 0.999895i \(0.504607\pi\)
\(572\) −2.65344 + 3.67079i −0.110946 + 0.153483i
\(573\) −33.8727 2.68465i −1.41505 0.112153i
\(574\) −2.16671 + 8.59414i −0.0904368 + 0.358713i
\(575\) −1.91850 1.10765i −0.0800070 0.0461920i
\(576\) −7.39681 19.3331i −0.308200 0.805547i
\(577\) 28.5220i 1.18739i 0.804691 + 0.593693i \(0.202331\pi\)
−0.804691 + 0.593693i \(0.797669\pi\)
\(578\) 9.26720 5.35042i 0.385465 0.222548i
\(579\) −10.9229 + 5.20253i −0.453938 + 0.216210i
\(580\) 4.20161i 0.174462i
\(581\) 11.9460 12.3057i 0.495602 0.510526i
\(582\) 18.8861 + 12.9954i 0.782855 + 0.538678i
\(583\) −24.8839 + 43.1002i −1.03059 + 1.78503i
\(584\) −19.7635 −0.817820
\(585\) −7.61057 + 28.5531i −0.314658 + 1.18053i
\(586\) 40.2596i 1.66311i
\(587\) 7.10897 12.3131i 0.293418 0.508216i −0.681197 0.732100i \(-0.738540\pi\)
0.974616 + 0.223884i \(0.0718738\pi\)
\(588\) −2.74382 0.135736i −0.113153 0.00559764i
\(589\) 6.60451 + 11.4394i 0.272134 + 0.471350i
\(590\) 13.0087i 0.535560i
\(591\) 16.1113 + 33.8261i 0.662731 + 1.39142i
\(592\) 6.45658 + 11.1831i 0.265364 + 0.459624i
\(593\) 11.0169 0.452412 0.226206 0.974080i \(-0.427368\pi\)
0.226206 + 0.974080i \(0.427368\pi\)
\(594\) −41.2374 + 12.1408i −1.69199 + 0.498144i
\(595\) −21.9725 5.53959i −0.900785 0.227101i
\(596\) −3.48021 2.00930i −0.142555 0.0823042i
\(597\) 25.0960 + 1.98904i 1.02711 + 0.0814059i
\(598\) −0.494126 + 4.81324i −0.0202063 + 0.196828i
\(599\) 9.21125i 0.376362i −0.982134 0.188181i \(-0.939741\pi\)
0.982134 0.188181i \(-0.0602591\pi\)
\(600\) −6.39994 + 9.30096i −0.261276 + 0.379710i
\(601\) 14.6701 + 8.46981i 0.598407 + 0.345491i 0.768415 0.639952i \(-0.221046\pi\)
−0.170007 + 0.985443i \(0.554379\pi\)
\(602\) 5.15947 + 5.00865i 0.210284 + 0.204137i
\(603\) 39.7265 + 6.33703i 1.61779 + 0.258064i
\(604\) 0.237471 + 0.411311i 0.00966254 + 0.0167360i
\(605\) −26.9617 46.6990i −1.09615 1.89858i
\(606\) −22.1090 1.75230i −0.898118 0.0711823i
\(607\) 19.8418 11.4557i 0.805354 0.464971i −0.0399857 0.999200i \(-0.512731\pi\)
0.845340 + 0.534229i \(0.179398\pi\)
\(608\) 3.56492 6.17463i 0.144577 0.250414i
\(609\) −29.4664 9.96343i −1.19404 0.403739i
\(610\) −7.65353 −0.309882
\(611\) 3.03197 + 2.19167i 0.122660 + 0.0886656i
\(612\) −2.10446 0.335696i −0.0850677 0.0135697i
\(613\) −20.3388 + 35.2278i −0.821477 + 1.42284i 0.0831059 + 0.996541i \(0.473516\pi\)
−0.904583 + 0.426299i \(0.859817\pi\)
\(614\) 17.1206 29.6537i 0.690930 1.19673i
\(615\) −9.59053 + 4.56795i −0.386727 + 0.184198i
\(616\) 10.6015 + 37.3411i 0.427147 + 1.50451i
\(617\) 18.7586 10.8303i 0.755195 0.436012i −0.0723732 0.997378i \(-0.523057\pi\)
0.827568 + 0.561366i \(0.189724\pi\)
\(618\) 6.02971 2.87194i 0.242551 0.115526i
\(619\) 13.0520i 0.524605i 0.964986 + 0.262302i \(0.0844817\pi\)
−0.964986 + 0.262302i \(0.915518\pi\)
\(620\) 1.26705 0.731533i 0.0508860 0.0293791i
\(621\) −3.22236 + 3.38441i −0.129309 + 0.135812i
\(622\) −18.1181 10.4605i −0.726471 0.419428i
\(623\) −7.35042 25.8900i −0.294488 1.03726i
\(624\) 27.0384 + 4.95909i 1.08240 + 0.198523i
\(625\) −31.2486 −1.24995
\(626\) −0.733193 + 1.26993i −0.0293043 + 0.0507565i
\(627\) 44.2109 + 30.4212i 1.76561 + 1.21491i
\(628\) 2.10852 1.21736i 0.0841392 0.0485778i
\(629\) −9.19703 −0.366709
\(630\) −19.3759 25.9130i −0.771953 1.03240i
\(631\) −3.42275 5.92838i −0.136258 0.236005i 0.789820 0.613339i \(-0.210174\pi\)
−0.926077 + 0.377334i \(0.876841\pi\)
\(632\) 33.3340i 1.32596i
\(633\) 21.8494 10.4068i 0.868436 0.413634i
\(634\) 6.80989 11.7951i 0.270455 0.468442i
\(635\) 15.2792 26.4644i 0.606338 1.05021i
\(636\) −3.51185 0.278339i −0.139254 0.0110369i
\(637\) −14.1725 + 20.8840i −0.561533 + 0.827454i
\(638\) 56.1546i 2.22318i
\(639\) 8.63698 + 7.00989i 0.341674 + 0.277307i
\(640\) 30.3958 + 17.5490i 1.20150 + 0.693686i
\(641\) −32.2373 + 18.6122i −1.27330 + 0.735138i −0.975607 0.219525i \(-0.929549\pi\)
−0.297690 + 0.954663i \(0.596216\pi\)
\(642\) 1.46465 18.4797i 0.0578052 0.729336i
\(643\) 25.6103 14.7861i 1.00997 0.583107i 0.0987882 0.995108i \(-0.468503\pi\)
0.911183 + 0.412001i \(0.135170\pi\)
\(644\) −0.386840 0.375532i −0.0152436 0.0147980i
\(645\) −0.680939 + 8.59151i −0.0268120 + 0.338290i
\(646\) 13.0718 + 22.6410i 0.514304 + 0.890800i
\(647\) 12.1062 20.9686i 0.475944 0.824360i −0.523676 0.851918i \(-0.675440\pi\)
0.999620 + 0.0275577i \(0.00877300\pi\)
\(648\) 15.8970 + 17.7340i 0.624495 + 0.696659i
\(649\) 17.6926i 0.694496i
\(650\) −5.41956 12.0937i −0.212573 0.474355i
\(651\) −2.12572 10.6207i −0.0833136 0.416258i
\(652\) −0.586712 + 1.01621i −0.0229774 + 0.0397980i
\(653\) −13.1479 7.59096i −0.514518 0.297057i 0.220171 0.975461i \(-0.429339\pi\)
−0.734689 + 0.678404i \(0.762672\pi\)
\(654\) 5.54058 + 11.6326i 0.216654 + 0.454870i
\(655\) 36.2162 1.41508
\(656\) 4.94104 + 8.55813i 0.192915 + 0.334139i
\(657\) 20.9262 8.00633i 0.816410 0.312357i
\(658\) −3.94067 + 1.11879i −0.153623 + 0.0436151i
\(659\) −15.5162 + 8.95828i −0.604425 + 0.348965i −0.770780 0.637101i \(-0.780133\pi\)
0.166355 + 0.986066i \(0.446800\pi\)
\(660\) 3.36953 4.89691i 0.131159 0.190612i
\(661\) −8.15101 4.70599i −0.317037 0.183042i 0.333034 0.942915i \(-0.391928\pi\)
−0.650071 + 0.759873i \(0.725261\pi\)
\(662\) 43.0043i 1.67141i
\(663\) −12.6874 + 14.9113i −0.492739 + 0.579108i
\(664\) 17.1536i 0.665689i
\(665\) −9.87480 + 39.1679i −0.382928 + 1.51887i
\(666\) −10.1966 8.27568i −0.395109 0.320676i
\(667\) −3.05223 5.28662i −0.118183 0.204699i
\(668\) 4.63991 0.179523
\(669\) −14.0015 29.3965i −0.541328 1.13653i
\(670\) −47.3401 + 27.3318i −1.82891 + 1.05592i
\(671\) −10.4092 −0.401844
\(672\) −4.39100 + 3.86005i −0.169386 + 0.148905i
\(673\) −4.30087 + 7.44933i −0.165786 + 0.287151i −0.936934 0.349506i \(-0.886350\pi\)
0.771148 + 0.636656i \(0.219683\pi\)
\(674\) 14.8520 + 8.57481i 0.572078 + 0.330289i
\(675\) 3.00857 12.4408i 0.115800 0.478846i
\(676\) −1.96037 + 2.19850i −0.0753988 + 0.0845577i
\(677\) −0.179419 −0.00689562 −0.00344781 0.999994i \(-0.501097\pi\)
−0.00344781 + 0.999994i \(0.501097\pi\)
\(678\) 40.9236 + 28.1593i 1.57166 + 1.08145i
\(679\) −5.73720 + 22.7563i −0.220174 + 0.873307i
\(680\) −19.6279 + 11.3321i −0.752694 + 0.434568i
\(681\) 0.796994 10.0558i 0.0305409 0.385339i
\(682\) 16.9342 9.77694i 0.648442 0.374378i
\(683\) 7.02462 4.05566i 0.268789 0.155186i −0.359548 0.933127i \(-0.617069\pi\)
0.628337 + 0.777941i \(0.283736\pi\)
\(684\) −0.598407 + 3.75138i −0.0228807 + 0.143438i
\(685\) −40.3892 + 23.3187i −1.54319 + 0.890963i
\(686\) −8.33282 26.3492i −0.318149 1.00602i
\(687\) 16.9356 24.6123i 0.646134 0.939019i
\(688\) 8.01748 0.305664
\(689\) −18.9604 + 26.2300i −0.722335 + 0.999282i
\(690\) 0.501702 6.33005i 0.0190995 0.240981i
\(691\) −39.8678 23.0177i −1.51664 0.875633i −0.999809 0.0195462i \(-0.993778\pi\)
−0.516832 0.856087i \(-0.672889\pi\)
\(692\) 0.201415 0.348860i 0.00765664 0.0132617i
\(693\) −26.3523 35.2431i −1.00104 1.33878i
\(694\) 34.2100 1.29859
\(695\) 3.30650 1.90901i 0.125423 0.0724128i
\(696\) −28.0878 + 13.3782i −1.06467 + 0.507098i
\(697\) −7.03823 −0.266592
\(698\) −15.7250 27.2364i −0.595198 1.03091i
\(699\) −14.8612 + 21.5976i −0.562101 + 0.816896i
\(700\) 1.43187 + 0.360995i 0.0541196 + 0.0136443i
\(701\) 13.7239i 0.518344i −0.965831 0.259172i \(-0.916550\pi\)
0.965831 0.259172i \(-0.0834497\pi\)
\(702\) −27.4839 + 5.11550i −1.03731 + 0.193072i
\(703\) 16.3945i 0.618330i
\(704\) 33.1297 + 19.1274i 1.24862 + 0.720892i
\(705\) −4.04472 2.78315i −0.152333 0.104819i
\(706\) 21.3598 12.3321i 0.803887 0.464124i
\(707\) −6.20077 21.8406i −0.233204 0.821401i
\(708\) −1.13069 + 0.538543i −0.0424937 + 0.0202397i
\(709\) 19.8771 + 34.4282i 0.746502 + 1.29298i 0.949490 + 0.313798i \(0.101601\pi\)
−0.202988 + 0.979181i \(0.565065\pi\)
\(710\) −15.1151 −0.567258
\(711\) 13.5038 + 35.2951i 0.506432 + 1.32367i
\(712\) −23.3118 13.4591i −0.873648 0.504401i
\(713\) 1.06283 1.84088i 0.0398034 0.0689416i
\(714\) −4.20728 21.0207i −0.157453 0.786681i
\(715\) −22.3327 49.8354i −0.835196 1.86374i
\(716\) 2.83898i 0.106098i
\(717\) 8.97272 13.0400i 0.335092 0.486986i
\(718\) −3.55982 + 6.16578i −0.132851 + 0.230105i
\(719\) −1.45563 2.52122i −0.0542858 0.0940258i 0.837605 0.546276i \(-0.183955\pi\)
−0.891891 + 0.452250i \(0.850622\pi\)
\(720\) −35.6256 5.68286i −1.32769 0.211788i
\(721\) 4.90563 + 4.76223i 0.182695 + 0.177355i
\(722\) 15.8067 9.12598i 0.588263 0.339634i
\(723\) 32.3539 + 2.56428i 1.20325 + 0.0953666i
\(724\) −4.08030 + 2.35576i −0.151643 + 0.0875512i
\(725\) 14.4798 + 8.35993i 0.537767 + 0.310480i
\(726\) 28.9181 42.0264i 1.07325 1.55975i
\(727\) 16.3030i 0.604645i 0.953206 + 0.302322i \(0.0977619\pi\)
−0.953206 + 0.302322i \(0.902238\pi\)
\(728\) 4.37844 + 24.8610i 0.162276 + 0.921409i
\(729\) −24.0164 12.3374i −0.889498 0.456939i
\(730\) −15.2226 + 26.3662i −0.563412 + 0.975858i
\(731\) −2.85511 + 4.94520i −0.105600 + 0.182905i
\(732\) −0.316846 0.665226i −0.0117110 0.0245874i
\(733\) 1.06305i 0.0392646i 0.999807 + 0.0196323i \(0.00624956\pi\)
−0.999807 + 0.0196323i \(0.993750\pi\)
\(734\) 0.165951 + 0.287435i 0.00612536 + 0.0106094i
\(735\) 17.9583 27.8316i 0.662402 1.02658i
\(736\) −1.14737 −0.0422928
\(737\) −64.3853 + 37.1729i −2.37166 + 1.36928i
\(738\) −7.80315 6.33315i −0.287238 0.233126i
\(739\) 14.5653 25.2279i 0.535794 0.928022i −0.463331 0.886186i \(-0.653346\pi\)
0.999124 0.0418368i \(-0.0133209\pi\)
\(740\) 1.81590 0.0667537
\(741\) 26.5808 + 22.6164i 0.976468 + 0.830836i
\(742\) −9.67883 34.0912i −0.355321 1.25153i
\(743\) 4.35485 + 2.51427i 0.159764 + 0.0922397i 0.577750 0.816214i \(-0.303931\pi\)
−0.417987 + 0.908453i \(0.637264\pi\)
\(744\) −8.92467 6.14101i −0.327194 0.225140i
\(745\) 41.9606 24.2260i 1.53732 0.887572i
\(746\) 3.48415i 0.127564i
\(747\) 6.94903 + 18.1628i 0.254252 + 0.664541i
\(748\) 3.41073 1.96919i 0.124709 0.0720005i
\(749\) 18.2554 5.18288i 0.667037 0.189378i
\(750\) −7.70200 16.1705i −0.281237 0.590465i
\(751\) 21.4022 37.0697i 0.780977 1.35269i −0.150396 0.988626i \(-0.548055\pi\)
0.931373 0.364066i \(-0.118612\pi\)
\(752\) −2.28369 + 3.95547i −0.0832777 + 0.144241i
\(753\) 1.56592 19.7575i 0.0570653 0.720002i
\(754\) 3.72940 36.3278i 0.135817 1.32298i
\(755\) −5.72633 −0.208402
\(756\) 1.45016 2.75686i 0.0527417 0.100266i
\(757\) −12.1617 + 21.0646i −0.442024 + 0.765607i −0.997840 0.0656980i \(-0.979073\pi\)
0.555816 + 0.831305i \(0.312406\pi\)
\(758\) −4.10084 + 2.36762i −0.148949 + 0.0859959i
\(759\) 0.682345 8.60924i 0.0247675 0.312496i
\(760\) 20.2005 + 34.9883i 0.732750 + 1.26916i
\(761\) 20.5036 + 35.5132i 0.743253 + 1.28735i 0.951006 + 0.309171i \(0.100052\pi\)
−0.207753 + 0.978181i \(0.566615\pi\)
\(762\) 28.8196 + 2.28416i 1.04402 + 0.0827465i
\(763\) −9.18735 + 9.46399i −0.332604 + 0.342620i
\(764\) 3.84952 + 2.22252i 0.139271 + 0.0804081i
\(765\) 16.1918 19.9502i 0.585417 0.721300i
\(766\) 34.4230i 1.24375i
\(767\) −1.17502 + 11.4458i −0.0424276 + 0.413284i
\(768\) −0.734990 + 9.27348i −0.0265217 + 0.334628i
\(769\) −19.8423 11.4560i −0.715533 0.413113i 0.0975737 0.995228i \(-0.468892\pi\)
−0.813106 + 0.582115i \(0.802225\pi\)
\(770\) 57.9818 + 14.6181i 2.08952 + 0.526799i
\(771\) −20.7817 + 9.89830i −0.748436 + 0.356479i
\(772\) 1.58271 0.0569629
\(773\) −19.7617 34.2283i −0.710780 1.23111i −0.964565 0.263847i \(-0.915009\pi\)
0.253784 0.967261i \(-0.418325\pi\)
\(774\) −7.61520 + 2.91356i −0.273723 + 0.104726i
\(775\) 5.82211i 0.209136i
\(776\) 11.7364 + 20.3280i 0.421312 + 0.729733i
\(777\) 4.30610 12.7351i 0.154480 0.456869i
\(778\) −27.4107 + 47.4768i −0.982722 + 1.70213i
\(779\) 12.5463i 0.449516i
\(780\) 2.50506 2.94415i 0.0896954 0.105418i
\(781\) −20.5574 −0.735601
\(782\) 2.10359 3.64352i 0.0752241 0.130292i
\(783\) 24.3207 25.5438i 0.869149 0.912860i
\(784\) −27.1298 14.6082i −0.968923 0.521721i
\(785\) 29.3551i 1.04773i
\(786\) 14.7333 + 30.9329i 0.525520 + 1.10334i
\(787\) 1.33472 0.770603i 0.0475778 0.0274690i −0.476022 0.879433i \(-0.657922\pi\)
0.523600 + 0.851964i \(0.324589\pi\)
\(788\) 4.90136i 0.174604i
\(789\) 8.25205 + 17.3254i 0.293781 + 0.616800i
\(790\) −44.4704 25.6750i −1.58219 0.913476i
\(791\) −12.4317 + 49.3097i −0.442021 + 1.75325i
\(792\) −43.4647 6.93333i −1.54445 0.246365i
\(793\) −6.73400 0.691311i −0.239131 0.0245492i
\(794\) −16.7533 −0.594553
\(795\) 24.0773 34.9914i 0.853935 1.24102i
\(796\) −2.85208 1.64665i −0.101089 0.0583640i
\(797\) 24.6129 + 42.6309i 0.871835 + 1.51006i 0.860096 + 0.510132i \(0.170403\pi\)
0.0117386 + 0.999931i \(0.496263\pi\)
\(798\) −37.4713 + 7.49984i −1.32647 + 0.265491i
\(799\) −1.62649 2.81717i −0.0575412 0.0996643i
\(800\) 2.72158 1.57130i 0.0962223 0.0555539i
\(801\) 30.1357 + 4.80713i 1.06479 + 0.169852i
\(802\) 11.0344 + 19.1121i 0.389637 + 0.674872i
\(803\) −20.7036 + 35.8596i −0.730613 + 1.26546i
\(804\) −4.33543 2.98318i −0.152899 0.105209i
\(805\) 6.25320 1.77535i 0.220396 0.0625727i
\(806\) 11.6044 5.20030i 0.408749 0.183173i
\(807\) 3.52683 44.4986i 0.124150 1.56642i
\(808\) −19.6657 11.3540i −0.691838 0.399433i
\(809\) 27.9253 + 16.1227i 0.981801 + 0.566843i 0.902813 0.430033i \(-0.141498\pi\)
0.0789874 + 0.996876i \(0.474831\pi\)
\(810\) 35.9032 7.54863i 1.26151 0.265232i
\(811\) 46.2744i 1.62492i −0.583020 0.812458i \(-0.698129\pi\)
0.583020 0.812458i \(-0.301871\pi\)
\(812\) 2.91966 + 2.83432i 0.102460 + 0.0994650i
\(813\) −19.8437 41.6623i −0.695948 1.46116i
\(814\) 24.2695 0.850644
\(815\) −7.07394 12.2524i −0.247789 0.429183i
\(816\) −19.6911 13.5493i −0.689327 0.474322i
\(817\) 8.81524 + 5.08948i 0.308406 + 0.178058i
\(818\) 17.8496 0.624095
\(819\) −14.7074 24.5498i −0.513917 0.857840i
\(820\) 1.38966 0.0485289
\(821\) 13.4915 + 7.78933i 0.470857 + 0.271849i 0.716598 0.697486i \(-0.245698\pi\)
−0.245741 + 0.969335i \(0.579031\pi\)
\(822\) −36.3479 25.0108i −1.26778 0.872352i
\(823\) −11.0357 19.1143i −0.384679 0.666283i 0.607046 0.794667i \(-0.292354\pi\)
−0.991725 + 0.128384i \(0.959021\pi\)
\(824\) 6.83824 0.238221
\(825\) 10.1716 + 21.3556i 0.354131 + 0.743507i
\(826\) −9.03964 8.77540i −0.314529 0.305335i
\(827\) 43.0278i 1.49622i 0.663573 + 0.748112i \(0.269039\pi\)
−0.663573 + 0.748112i \(0.730961\pi\)
\(828\) 0.570962 0.218449i 0.0198423 0.00759162i
\(829\) 10.0663 + 5.81180i 0.349618 + 0.201852i 0.664517 0.747273i \(-0.268637\pi\)
−0.314899 + 0.949125i \(0.601971\pi\)
\(830\) −22.8844 13.2123i −0.794328 0.458606i
\(831\) 1.54607 19.5070i 0.0536325 0.676690i
\(832\) 20.1621 + 14.5743i 0.698995 + 0.505271i
\(833\) 18.6716 11.5316i 0.646932 0.399546i
\(834\) 2.97566 + 2.04753i 0.103039 + 0.0709002i
\(835\) −27.9715 + 48.4481i −0.967994 + 1.67661i
\(836\) −3.51024 6.07992i −0.121404 0.210278i
\(837\) 11.9375 + 2.88685i 0.412619 + 0.0997842i
\(838\) −13.1398 + 7.58628i −0.453908 + 0.262064i
\(839\) 20.5689 + 35.6264i 0.710117 + 1.22996i 0.964813 + 0.262938i \(0.0846915\pi\)
−0.254695 + 0.967021i \(0.581975\pi\)
\(840\) −6.50172 32.4844i −0.224331 1.12082i
\(841\) 8.53663 + 14.7859i 0.294367 + 0.509858i
\(842\) 1.97878 + 1.14245i 0.0681934 + 0.0393715i
\(843\) −13.1858 + 19.1628i −0.454142 + 0.660000i
\(844\) −3.16595 −0.108976
\(845\) −11.1379 33.7229i −0.383154 1.16010i
\(846\) 0.731686 4.58690i 0.0251559 0.157701i
\(847\) 50.6385 + 12.7667i 1.73996 + 0.438669i
\(848\) −34.2193 19.7565i −1.17509 0.678441i
\(849\) 1.48629 + 3.12050i 0.0510093 + 0.107095i
\(850\) 11.5233i 0.395245i
\(851\) 2.28483 1.31915i 0.0783229 0.0452197i
\(852\) −0.625744 1.31376i −0.0214376 0.0450088i
\(853\) 23.2038i 0.794482i −0.917714 0.397241i \(-0.869968\pi\)
0.917714 0.397241i \(-0.130032\pi\)
\(854\) 5.16290 5.31837i 0.176671 0.181991i
\(855\) −35.5629 28.8634i −1.21623 0.987106i
\(856\) 9.49020 16.4375i 0.324368 0.561822i
\(857\) 17.3181 0.591575 0.295788 0.955254i \(-0.404418\pi\)
0.295788 + 0.955254i \(0.404418\pi\)
\(858\) 33.4801 39.3486i 1.14299 1.34334i
\(859\) 1.05148i 0.0358759i −0.999839 0.0179379i \(-0.994290\pi\)
0.999839 0.0179379i \(-0.00571013\pi\)
\(860\) 0.563724 0.976398i 0.0192228 0.0332949i
\(861\) 3.29534 9.74581i 0.112305 0.332136i
\(862\) −23.0343 39.8965i −0.784550 1.35888i
\(863\) 18.0952i 0.615968i −0.951392 0.307984i \(-0.900346\pi\)
0.951392 0.307984i \(-0.0996543\pi\)
\(864\) −1.87228 6.35936i −0.0636961 0.216350i
\(865\) 2.42844 + 4.20618i 0.0825694 + 0.143014i
\(866\) −12.5940 −0.427962
\(867\) −11.2140 + 5.34122i −0.380848 + 0.181397i
\(868\) −0.346390 + 1.37394i −0.0117573 + 0.0466345i
\(869\) −60.4824 34.9195i −2.05172 1.18456i
\(870\) −3.78658 + 47.7759i −0.128377 + 1.61975i
\(871\) −44.1212 + 19.7720i −1.49499 + 0.669950i
\(872\) 13.1924i 0.446751i
\(873\) −20.6619 16.7694i −0.699298 0.567560i
\(874\) −6.49489 3.74983i −0.219693 0.126840i
\(875\) 12.7714 13.1560i 0.431752 0.444753i
\(876\) −2.92188 0.231580i −0.0987212 0.00782437i
\(877\) 2.08989 + 3.61980i 0.0705707 + 0.122232i 0.899152 0.437637i \(-0.144185\pi\)
−0.828581 + 0.559869i \(0.810851\pi\)
\(878\) 13.1355 + 22.7514i 0.443302 + 0.767822i
\(879\) 3.69224 46.5855i 0.124536 1.57129i
\(880\) 57.7389 33.3356i 1.94638 1.12374i
\(881\) 22.0623 38.2129i 0.743296 1.28743i −0.207690 0.978195i \(-0.566595\pi\)
0.950987 0.309232i \(-0.100072\pi\)
\(882\) 31.0772 + 4.01622i 1.04642 + 0.135233i
\(883\) 15.3513 0.516612 0.258306 0.966063i \(-0.416836\pi\)
0.258306 + 0.966063i \(0.416836\pi\)
\(884\) 2.33727 1.04740i 0.0786108 0.0352278i
\(885\) 1.19304 15.0527i 0.0401035 0.505992i
\(886\) −10.5142 + 18.2111i −0.353231 + 0.611813i
\(887\) −16.8966 + 29.2658i −0.567333 + 0.982650i 0.429495 + 0.903069i \(0.358692\pi\)
−0.996828 + 0.0795811i \(0.974642\pi\)
\(888\) −5.78192 12.1393i −0.194028 0.407368i
\(889\) 8.08284 + 28.4697i 0.271090 + 0.954845i
\(890\) −35.9112 + 20.7333i −1.20375 + 0.694983i
\(891\) 48.8304 10.2666i 1.63588 0.343943i
\(892\) 4.25951i 0.142619i
\(893\) −5.02185 + 2.89937i −0.168050 + 0.0970236i
\(894\) 37.7621 + 25.9839i 1.26295 + 0.869032i
\(895\) −29.6435 17.1147i −0.990874 0.572081i
\(896\) −32.6990 + 9.28357i −1.09240 + 0.310142i
\(897\) 1.01319 5.52422i 0.0338295 0.184448i
\(898\) 29.6973 0.991013
\(899\) −8.02171 + 13.8940i −0.267539 + 0.463391i
\(900\) −1.05516 + 1.30008i −0.0351722 + 0.0433361i
\(901\) 24.3717 14.0710i 0.811939 0.468773i
\(902\) 18.5727 0.618405
\(903\) −5.51082 6.26883i −0.183389 0.208614i
\(904\) 25.4311 + 44.0480i 0.845826 + 1.46501i
\(905\) 56.8064i 1.88831i
\(906\) −2.32956 4.89097i −0.0773944 0.162492i
\(907\) −0.313363 + 0.542760i −0.0104050 + 0.0180220i −0.871181 0.490962i \(-0.836645\pi\)
0.860776 + 0.508984i \(0.169979\pi\)
\(908\) −0.659801 + 1.14281i −0.0218963 + 0.0379255i
\(909\) 25.4223 + 4.05527i 0.843203 + 0.134505i
\(910\) 36.5391 + 13.3076i 1.21126 + 0.441142i
\(911\) 7.90527i 0.261913i 0.991388 + 0.130957i \(0.0418049\pi\)
−0.991388 + 0.130957i \(0.958195\pi\)
\(912\) −24.1529 + 35.1011i −0.799781 + 1.16231i
\(913\) −31.1241 17.9695i −1.03006 0.594704i
\(914\) 31.9449 18.4434i 1.05664 0.610054i
\(915\) 8.85611 + 0.701910i 0.292774 + 0.0232044i
\(916\) −3.38471 + 1.95416i −0.111834 + 0.0645674i
\(917\) −24.4307 + 25.1663i −0.806771 + 0.831064i
\(918\) 23.6269 + 5.71373i 0.779805 + 0.188581i
\(919\) 8.11060 + 14.0480i 0.267544 + 0.463400i 0.968227 0.250073i \(-0.0804546\pi\)
−0.700683 + 0.713473i \(0.747121\pi\)
\(920\) 3.25078 5.63051i 0.107175 0.185632i
\(921\) −22.5303 + 32.7430i −0.742397 + 1.07892i
\(922\) 39.0179i 1.28499i
\(923\) −13.2991 1.36528i −0.437745 0.0449388i
\(924\) 1.12980 + 5.64481i 0.0371678 + 0.185701i
\(925\) −3.61308 + 6.25804i −0.118797 + 0.205763i
\(926\) 29.4419 + 16.9983i 0.967520 + 0.558598i
\(927\) −7.24054 + 2.77021i −0.237810 + 0.0909857i
\(928\) 8.65977 0.284271
\(929\) −12.4689 21.5967i −0.409091 0.708566i 0.585697 0.810530i \(-0.300821\pi\)
−0.994788 + 0.101964i \(0.967487\pi\)
\(930\) −15.0667 + 7.17625i −0.494057 + 0.235319i
\(931\) −20.5561 33.2837i −0.673698 1.09083i
\(932\) 2.97012 1.71480i 0.0972896 0.0561701i
\(933\) 20.0057 + 13.7658i 0.654956 + 0.450671i
\(934\) 15.1799 + 8.76414i 0.496703 + 0.286772i
\(935\) 47.4846i 1.55291i
\(936\) −27.6579 7.37197i −0.904027 0.240960i
\(937\) 17.5533i 0.573440i −0.958014 0.286720i \(-0.907435\pi\)
0.958014 0.286720i \(-0.0925649\pi\)
\(938\) 12.9420 51.3337i 0.422570 1.67610i
\(939\) 0.964864 1.40223i 0.0314871 0.0457599i
\(940\) 0.321141 + 0.556233i 0.0104745 + 0.0181423i
\(941\) −16.1819 −0.527514 −0.263757 0.964589i \(-0.584962\pi\)
−0.263757 + 0.964589i \(0.584962\pi\)
\(942\) −25.0728 + 11.9421i −0.816916 + 0.389095i
\(943\) 1.74851 1.00951i 0.0569395 0.0328740i
\(944\) −14.0470 −0.457191
\(945\) 20.0438 + 31.7616i 0.652026 + 1.03320i
\(946\) 7.53417 13.0496i 0.244957 0.424278i
\(947\) −4.78591 2.76314i −0.155521 0.0897901i 0.420220 0.907422i \(-0.361953\pi\)
−0.575741 + 0.817632i \(0.695286\pi\)
\(948\) 0.390593 4.92817i 0.0126859 0.160059i
\(949\) −15.7752 + 21.8235i −0.512085 + 0.708421i
\(950\) 20.5412 0.666445
\(951\) −8.96165 + 13.0239i −0.290601 + 0.422328i
\(952\) 5.36592 21.2836i 0.173910 0.689807i
\(953\) −38.2971 + 22.1108i −1.24056 + 0.716240i −0.969209 0.246239i \(-0.920805\pi\)
−0.271355 + 0.962479i \(0.587472\pi\)
\(954\) 39.6818 + 6.32991i 1.28475 + 0.204938i
\(955\) −46.4134 + 26.7968i −1.50190 + 0.867123i
\(956\) −1.79327 + 1.03534i −0.0579984 + 0.0334854i
\(957\) −5.14998 + 64.9780i −0.166475 + 2.10044i
\(958\) 9.86225 5.69398i 0.318635 0.183964i
\(959\) 11.0417 43.7964i 0.356556 1.41426i
\(960\) −26.8967 18.5074i −0.868087 0.597325i
\(961\) 25.4134 0.819788
\(962\) 15.7005 + 1.61181i 0.506205 + 0.0519669i
\(963\) −3.38958 + 21.2491i −0.109228 + 0.684742i
\(964\) −3.67692 2.12287i −0.118426 0.0683731i
\(965\) −9.54129 + 16.5260i −0.307145 + 0.531991i
\(966\) 4.06026 + 4.61875i 0.130637 + 0.148606i
\(967\) −44.0147 −1.41542 −0.707709 0.706504i \(-0.750271\pi\)
−0.707709 + 0.706504i \(0.750271\pi\)
\(968\) 45.2349 26.1164i 1.45391 0.839413i
\(969\) −13.0493 27.3974i −0.419205 0.880132i
\(970\) 36.1591 1.16100
\(971\) −1.59883 2.76926i −0.0513090 0.0888698i 0.839230 0.543776i \(-0.183006\pi\)
−0.890539 + 0.454907i \(0.849673\pi\)
\(972\) 2.14245 + 2.80811i 0.0687192 + 0.0900703i
\(973\) −0.903941 + 3.58543i −0.0289790 + 0.114944i
\(974\) 31.9709i 1.02441i
\(975\) 5.16200 + 14.4910i 0.165316 + 0.464084i
\(976\) 8.26439i 0.264537i
\(977\) 43.7474 + 25.2576i 1.39960 + 0.808061i 0.994351 0.106144i \(-0.0338503\pi\)
0.405252 + 0.914205i \(0.367184\pi\)
\(978\) 7.58724 11.0265i 0.242613 0.352587i
\(979\) −48.8413 + 28.1985i −1.56098 + 0.901229i
\(980\) −3.68659 + 2.27684i −0.117764 + 0.0727311i
\(981\) −5.34433 13.9685i −0.170631 0.445981i
\(982\) −2.36416 4.09484i −0.0754433 0.130672i
\(983\) −23.2037 −0.740083 −0.370041 0.929015i \(-0.620657\pi\)
−0.370041 + 0.929015i \(0.620657\pi\)
\(984\) −4.42474 9.28986i −0.141056 0.296150i
\(985\) 51.1780 + 29.5476i 1.63067 + 0.941466i
\(986\) −15.8768 + 27.4994i −0.505619 + 0.875758i
\(987\) 4.66246 0.933187i 0.148408 0.0297037i
\(988\) −1.86708 4.16638i −0.0593997 0.132550i
\(989\) 1.63805i 0.0520871i
\(990\) −42.7276 + 52.6453i −1.35797 + 1.67318i
\(991\) −2.83645 + 4.91288i −0.0901029 + 0.156063i −0.907554 0.419935i \(-0.862053\pi\)
0.817451 + 0.575998i \(0.195386\pi\)
\(992\) 1.50773 + 2.61147i 0.0478705 + 0.0829142i
\(993\) −3.94396 + 49.7615i −0.125158 + 1.57913i
\(994\) 10.1963 10.5033i 0.323407 0.333145i
\(995\) 34.3873 19.8535i 1.09015 0.629399i
\(996\) 0.200998 2.53603i 0.00636887 0.0803570i
\(997\) −2.89159 + 1.66946i −0.0915777 + 0.0528724i −0.545089 0.838378i \(-0.683504\pi\)
0.453512 + 0.891250i \(0.350171\pi\)
\(998\) 2.12129 + 1.22473i 0.0671483 + 0.0387681i
\(999\) 11.0398 + 10.5112i 0.349283 + 0.332558i
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 273.2.bn.c.230.23 yes 64
3.2 odd 2 inner 273.2.bn.c.230.9 yes 64
7.6 odd 2 inner 273.2.bn.c.230.24 yes 64
13.3 even 3 inner 273.2.bn.c.146.10 yes 64
21.20 even 2 inner 273.2.bn.c.230.10 yes 64
39.29 odd 6 inner 273.2.bn.c.146.24 yes 64
91.55 odd 6 inner 273.2.bn.c.146.9 64
273.146 even 6 inner 273.2.bn.c.146.23 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bn.c.146.9 64 91.55 odd 6 inner
273.2.bn.c.146.10 yes 64 13.3 even 3 inner
273.2.bn.c.146.23 yes 64 273.146 even 6 inner
273.2.bn.c.146.24 yes 64 39.29 odd 6 inner
273.2.bn.c.230.9 yes 64 3.2 odd 2 inner
273.2.bn.c.230.10 yes 64 21.20 even 2 inner
273.2.bn.c.230.23 yes 64 1.1 even 1 trivial
273.2.bn.c.230.24 yes 64 7.6 odd 2 inner