Properties

Label 336.2.bq.b.109.19
Level $336$
Weight $2$
Character 336.109
Analytic conductor $2.683$
Analytic rank $0$
Dimension $120$
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] = [336,2,Mod(37,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bq (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(30\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 109.19
Character \(\chi\) \(=\) 336.109
Dual form 336.2.bq.b.37.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.426746 - 1.34829i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.63577 - 1.15076i) q^{4} +(-3.88430 - 1.04080i) q^{5} +(0.0632421 - 1.41280i) q^{6} +(-0.638884 + 2.56746i) q^{7} +(-2.24962 + 1.71442i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.426746 - 1.34829i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.63577 - 1.15076i) q^{4} +(-3.88430 - 1.04080i) q^{5} +(0.0632421 - 1.41280i) q^{6} +(-0.638884 + 2.56746i) q^{7} +(-2.24962 + 1.71442i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-3.06091 + 4.79301i) q^{10} +(-0.993411 - 3.70746i) q^{11} +(-1.87787 - 0.688176i) q^{12} +(-4.53157 - 4.53157i) q^{13} +(3.18903 + 1.95705i) q^{14} -4.02132 q^{15} +(1.35152 + 3.76476i) q^{16} +(1.26445 - 2.19010i) q^{17} +(-0.304572 - 1.38103i) q^{18} +(-1.08273 + 4.04080i) q^{19} +(5.15614 + 6.17239i) q^{20} +(0.0473917 + 2.64533i) q^{21} +(-5.42267 - 0.242739i) q^{22} +(2.54337 - 1.46841i) q^{23} +(-1.72924 + 2.23824i) q^{24} +(9.67441 + 5.58552i) q^{25} +(-8.04371 + 4.17604i) q^{26} +(0.707107 - 0.707107i) q^{27} +(3.99959 - 3.46458i) q^{28} +(-3.12009 - 3.12009i) q^{29} +(-1.71609 + 5.42191i) q^{30} +(2.63521 - 4.56432i) q^{31} +(5.65274 - 0.215644i) q^{32} +(-1.91912 - 3.32402i) q^{33} +(-2.41329 - 2.63947i) q^{34} +(5.15381 - 9.30782i) q^{35} +(-1.99200 - 0.178697i) q^{36} +(2.82212 + 0.756186i) q^{37} +(4.98612 + 3.18423i) q^{38} +(-5.55002 - 3.20430i) q^{39} +(10.5225 - 4.31793i) q^{40} +2.08157i q^{41} +(3.58689 + 1.06499i) q^{42} +(2.65257 - 2.65257i) q^{43} +(-2.64139 + 7.20775i) q^{44} +(-3.88430 + 1.04080i) q^{45} +(-0.894475 - 4.05584i) q^{46} +(-3.11058 - 5.38768i) q^{47} +(2.27986 + 3.28668i) q^{48} +(-6.18365 - 3.28061i) q^{49} +(11.6594 - 10.6603i) q^{50} +(0.654529 - 2.44273i) q^{51} +(2.19790 + 12.6274i) q^{52} +(1.24836 + 4.65894i) q^{53} +(-0.651630 - 1.25514i) q^{54} +15.4348i q^{55} +(-2.96445 - 6.87110i) q^{56} +4.18334i q^{57} +(-5.53828 + 2.87530i) q^{58} +(-3.15101 - 11.7597i) q^{59} +(6.57798 + 4.62756i) q^{60} +(-2.48072 + 9.25819i) q^{61} +(-5.02946 - 5.50083i) q^{62} +(0.730438 + 2.54292i) q^{63} +(2.12154 - 7.71356i) q^{64} +(12.8855 + 22.3184i) q^{65} +(-5.30072 + 1.16902i) q^{66} +(-1.23853 + 0.331863i) q^{67} +(-4.58863 + 2.12743i) q^{68} +(2.07665 - 2.07665i) q^{69} +(-10.3503 - 10.9209i) q^{70} -3.96281i q^{71} +(-1.09101 + 2.60954i) q^{72} +(-10.8844 - 6.28413i) q^{73} +(2.22389 - 3.48234i) q^{74} +(10.7904 + 2.89128i) q^{75} +(6.42108 - 5.36388i) q^{76} +(10.1534 - 0.181901i) q^{77} +(-6.68878 + 6.11561i) q^{78} +(-1.77968 - 3.08249i) q^{79} +(-1.33137 - 16.0301i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.80656 + 0.888303i) q^{82} +(-1.10495 - 1.10495i) q^{83} +(2.96660 - 4.38170i) q^{84} +(-7.19095 + 7.19095i) q^{85} +(-2.44446 - 4.70840i) q^{86} +(-3.82131 - 2.20624i) q^{87} +(8.59093 + 6.63724i) q^{88} +(-2.08687 + 1.20486i) q^{89} +(-0.254317 + 5.68132i) q^{90} +(14.5298 - 8.73946i) q^{91} +(-5.85016 - 0.524802i) q^{92} +(1.36408 - 5.09083i) q^{93} +(-8.59159 + 1.89479i) q^{94} +(8.41129 - 14.5688i) q^{95} +(5.40432 - 1.67133i) q^{96} +3.77428 q^{97} +(-7.06207 + 6.93737i) q^{98} +(-2.71405 - 2.71405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.426746 1.34829i 0.301755 0.953385i
\(3\) 0.965926 0.258819i 0.557678 0.149429i
\(4\) −1.63577 1.15076i −0.817887 0.575378i
\(5\) −3.88430 1.04080i −1.73711 0.465458i −0.755310 0.655367i \(-0.772514\pi\)
−0.981802 + 0.189910i \(0.939181\pi\)
\(6\) 0.0632421 1.41280i 0.0258185 0.576773i
\(7\) −0.638884 + 2.56746i −0.241475 + 0.970407i
\(8\) −2.24962 + 1.71442i −0.795359 + 0.606139i
\(9\) 0.866025 0.500000i 0.288675 0.166667i
\(10\) −3.06091 + 4.79301i −0.967943 + 1.51568i
\(11\) −0.993411 3.70746i −0.299525 1.11784i −0.937557 0.347832i \(-0.886918\pi\)
0.638032 0.770010i \(-0.279749\pi\)
\(12\) −1.87787 0.688176i −0.542096 0.198659i
\(13\) −4.53157 4.53157i −1.25683 1.25683i −0.952597 0.304235i \(-0.901599\pi\)
−0.304235 0.952597i \(-0.598401\pi\)
\(14\) 3.18903 + 1.95705i 0.852305 + 0.523045i
\(15\) −4.02132 −1.03830
\(16\) 1.35152 + 3.76476i 0.337880 + 0.941189i
\(17\) 1.26445 2.19010i 0.306675 0.531176i −0.670958 0.741495i \(-0.734117\pi\)
0.977633 + 0.210319i \(0.0674503\pi\)
\(18\) −0.304572 1.38103i −0.0717883 0.325511i
\(19\) −1.08273 + 4.04080i −0.248395 + 0.927023i 0.723251 + 0.690585i \(0.242647\pi\)
−0.971647 + 0.236438i \(0.924020\pi\)
\(20\) 5.15614 + 6.17239i 1.15295 + 1.38019i
\(21\) 0.0473917 + 2.64533i 0.0103417 + 0.577258i
\(22\) −5.42267 0.242739i −1.15612 0.0517521i
\(23\) 2.54337 1.46841i 0.530329 0.306185i −0.210822 0.977525i \(-0.567614\pi\)
0.741150 + 0.671339i \(0.234281\pi\)
\(24\) −1.72924 + 2.23824i −0.352979 + 0.456880i
\(25\) 9.67441 + 5.58552i 1.93488 + 1.11710i
\(26\) −8.04371 + 4.17604i −1.57750 + 0.818989i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 3.99959 3.46458i 0.755851 0.654744i
\(29\) −3.12009 3.12009i −0.579386 0.579386i 0.355348 0.934734i \(-0.384362\pi\)
−0.934734 + 0.355348i \(0.884362\pi\)
\(30\) −1.71609 + 5.42191i −0.313313 + 0.989901i
\(31\) 2.63521 4.56432i 0.473298 0.819775i −0.526235 0.850339i \(-0.676397\pi\)
0.999533 + 0.0305636i \(0.00973022\pi\)
\(32\) 5.65274 0.215644i 0.999273 0.0381208i
\(33\) −1.91912 3.32402i −0.334076 0.578637i
\(34\) −2.41329 2.63947i −0.413875 0.452665i
\(35\) 5.15381 9.30782i 0.871153 1.57331i
\(36\) −1.99200 0.178697i −0.332000 0.0297828i
\(37\) 2.82212 + 0.756186i 0.463954 + 0.124316i 0.483221 0.875498i \(-0.339467\pi\)
−0.0192671 + 0.999814i \(0.506133\pi\)
\(38\) 4.98612 + 3.18423i 0.808856 + 0.516550i
\(39\) −5.55002 3.20430i −0.888714 0.513099i
\(40\) 10.5225 4.31793i 1.66376 0.682724i
\(41\) 2.08157i 0.325087i 0.986701 + 0.162543i \(0.0519697\pi\)
−0.986701 + 0.162543i \(0.948030\pi\)
\(42\) 3.58689 + 1.06499i 0.553470 + 0.164331i
\(43\) 2.65257 2.65257i 0.404513 0.404513i −0.475307 0.879820i \(-0.657663\pi\)
0.879820 + 0.475307i \(0.157663\pi\)
\(44\) −2.64139 + 7.20775i −0.398204 + 1.08661i
\(45\) −3.88430 + 1.04080i −0.579037 + 0.155153i
\(46\) −0.894475 4.05584i −0.131883 0.598000i
\(47\) −3.11058 5.38768i −0.453725 0.785874i 0.544889 0.838508i \(-0.316572\pi\)
−0.998614 + 0.0526337i \(0.983238\pi\)
\(48\) 2.27986 + 3.28668i 0.329069 + 0.474391i
\(49\) −6.18365 3.28061i −0.883379 0.468659i
\(50\) 11.6594 10.6603i 1.64889 1.50760i
\(51\) 0.654529 2.44273i 0.0916524 0.342051i
\(52\) 2.19790 + 12.6274i 0.304793 + 1.75110i
\(53\) 1.24836 + 4.65894i 0.171475 + 0.639955i 0.997125 + 0.0757721i \(0.0241422\pi\)
−0.825650 + 0.564183i \(0.809191\pi\)
\(54\) −0.651630 1.25514i −0.0886756 0.170803i
\(55\) 15.4348i 2.08123i
\(56\) −2.96445 6.87110i −0.396141 0.918190i
\(57\) 4.18334i 0.554097i
\(58\) −5.53828 + 2.87530i −0.727211 + 0.377545i
\(59\) −3.15101 11.7597i −0.410226 1.53099i −0.794209 0.607645i \(-0.792114\pi\)
0.383982 0.923340i \(-0.374552\pi\)
\(60\) 6.57798 + 4.62756i 0.849214 + 0.597416i
\(61\) −2.48072 + 9.25819i −0.317624 + 1.18539i 0.603897 + 0.797062i \(0.293614\pi\)
−0.921521 + 0.388328i \(0.873053\pi\)
\(62\) −5.02946 5.50083i −0.638742 0.698607i
\(63\) 0.730438 + 2.54292i 0.0920265 + 0.320378i
\(64\) 2.12154 7.71356i 0.265192 0.964196i
\(65\) 12.8855 + 22.3184i 1.59826 + 2.76826i
\(66\) −5.30072 + 1.16902i −0.652474 + 0.143897i
\(67\) −1.23853 + 0.331863i −0.151311 + 0.0405436i −0.333679 0.942687i \(-0.608290\pi\)
0.182369 + 0.983230i \(0.441624\pi\)
\(68\) −4.58863 + 2.12743i −0.556453 + 0.257988i
\(69\) 2.07665 2.07665i 0.249999 0.249999i
\(70\) −10.3503 10.9209i −1.23709 1.30530i
\(71\) 3.96281i 0.470299i −0.971959 0.235149i \(-0.924442\pi\)
0.971959 0.235149i \(-0.0755579\pi\)
\(72\) −1.09101 + 2.60954i −0.128577 + 0.307537i
\(73\) −10.8844 6.28413i −1.27393 0.735502i −0.298202 0.954503i \(-0.596387\pi\)
−0.975725 + 0.219001i \(0.929720\pi\)
\(74\) 2.22389 3.48234i 0.258522 0.404814i
\(75\) 10.7904 + 2.89128i 1.24597 + 0.333856i
\(76\) 6.42108 5.36388i 0.736548 0.615279i
\(77\) 10.1534 0.181901i 1.15709 0.0207295i
\(78\) −6.68878 + 6.11561i −0.757356 + 0.692457i
\(79\) −1.77968 3.08249i −0.200230 0.346808i 0.748373 0.663278i \(-0.230835\pi\)
−0.948602 + 0.316471i \(0.897502\pi\)
\(80\) −1.33137 16.0301i −0.148851 1.79222i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 2.80656 + 0.888303i 0.309933 + 0.0980966i
\(83\) −1.10495 1.10495i −0.121284 0.121284i 0.643859 0.765144i \(-0.277332\pi\)
−0.765144 + 0.643859i \(0.777332\pi\)
\(84\) 2.96660 4.38170i 0.323683 0.478082i
\(85\) −7.19095 + 7.19095i −0.779969 + 0.779969i
\(86\) −2.44446 4.70840i −0.263593 0.507720i
\(87\) −3.82131 2.20624i −0.409688 0.236533i
\(88\) 8.59093 + 6.63724i 0.915797 + 0.707532i
\(89\) −2.08687 + 1.20486i −0.221208 + 0.127715i −0.606510 0.795076i \(-0.707431\pi\)
0.385301 + 0.922791i \(0.374097\pi\)
\(90\) −0.254317 + 5.68132i −0.0268074 + 0.598864i
\(91\) 14.5298 8.73946i 1.52313 0.916144i
\(92\) −5.85016 0.524802i −0.609921 0.0547143i
\(93\) 1.36408 5.09083i 0.141449 0.527895i
\(94\) −8.59159 + 1.89479i −0.886155 + 0.195433i
\(95\) 8.41129 14.5688i 0.862980 1.49473i
\(96\) 5.40432 1.67133i 0.551576 0.170580i
\(97\) 3.77428 0.383220 0.191610 0.981471i \(-0.438629\pi\)
0.191610 + 0.981471i \(0.438629\pi\)
\(98\) −7.06207 + 6.93737i −0.713377 + 0.700780i
\(99\) −2.71405 2.71405i −0.272772 0.272772i
\(100\) −9.39758 20.2695i −0.939758 2.02695i
\(101\) 2.95739 + 11.0371i 0.294272 + 1.09824i 0.941794 + 0.336191i \(0.109139\pi\)
−0.647522 + 0.762047i \(0.724195\pi\)
\(102\) −3.01420 1.92492i −0.298450 0.190596i
\(103\) −5.48477 + 3.16663i −0.540430 + 0.312017i −0.745253 0.666782i \(-0.767671\pi\)
0.204823 + 0.978799i \(0.434338\pi\)
\(104\) 17.9633 + 2.42528i 1.76145 + 0.237818i
\(105\) 2.56916 10.3246i 0.250724 1.00757i
\(106\) 6.81434 + 0.305035i 0.661868 + 0.0296277i
\(107\) 8.41748 + 2.25546i 0.813748 + 0.218043i 0.641611 0.767030i \(-0.278266\pi\)
0.172137 + 0.985073i \(0.444933\pi\)
\(108\) −1.97038 + 0.342960i −0.189599 + 0.0330013i
\(109\) 3.89270 1.04305i 0.372853 0.0999057i −0.0675262 0.997717i \(-0.521511\pi\)
0.440379 + 0.897812i \(0.354844\pi\)
\(110\) 20.8106 + 6.58676i 1.98422 + 0.628023i
\(111\) 2.92168 0.277313
\(112\) −10.5293 + 1.06472i −0.994926 + 0.100607i
\(113\) −5.68947 −0.535221 −0.267610 0.963527i \(-0.586234\pi\)
−0.267610 + 0.963527i \(0.586234\pi\)
\(114\) 5.64036 + 1.78523i 0.528268 + 0.167202i
\(115\) −11.4075 + 3.05663i −1.06376 + 0.285033i
\(116\) 1.51330 + 8.69423i 0.140507 + 0.807239i
\(117\) −6.19024 1.65867i −0.572288 0.153344i
\(118\) −17.2002 0.769945i −1.58341 0.0708792i
\(119\) 4.81513 + 4.64564i 0.441403 + 0.425865i
\(120\) 9.04643 6.89423i 0.825822 0.629354i
\(121\) −3.23212 + 1.86607i −0.293829 + 0.169642i
\(122\) 11.4241 + 7.29564i 1.03429 + 0.660516i
\(123\) 0.538750 + 2.01064i 0.0485774 + 0.181294i
\(124\) −9.56303 + 4.43371i −0.858785 + 0.398159i
\(125\) −17.5474 17.5474i −1.56949 1.56949i
\(126\) 3.74031 + 0.100341i 0.333213 + 0.00893911i
\(127\) 19.9556 1.77077 0.885385 0.464858i \(-0.153895\pi\)
0.885385 + 0.464858i \(0.153895\pi\)
\(128\) −9.49477 6.15218i −0.839227 0.543781i
\(129\) 1.87565 3.24872i 0.165142 0.286034i
\(130\) 35.5906 7.84915i 3.12150 0.688416i
\(131\) −1.95603 + 7.30000i −0.170899 + 0.637804i 0.826315 + 0.563208i \(0.190433\pi\)
−0.997214 + 0.0745954i \(0.976233\pi\)
\(132\) −0.685882 + 7.64579i −0.0596984 + 0.665481i
\(133\) −9.68283 5.36146i −0.839608 0.464898i
\(134\) −0.0810904 + 1.81152i −0.00700515 + 0.156492i
\(135\) −3.48257 + 2.01066i −0.299732 + 0.173050i
\(136\) 0.910210 + 7.09467i 0.0780499 + 0.608363i
\(137\) 0.476286 + 0.274984i 0.0406918 + 0.0234934i 0.520208 0.854040i \(-0.325854\pi\)
−0.479516 + 0.877533i \(0.659188\pi\)
\(138\) −1.91372 3.68613i −0.162907 0.313784i
\(139\) −1.08821 + 1.08821i −0.0923008 + 0.0923008i −0.751750 0.659449i \(-0.770790\pi\)
0.659449 + 0.751750i \(0.270790\pi\)
\(140\) −19.1415 + 9.29472i −1.61775 + 0.785547i
\(141\) −4.39903 4.39903i −0.370465 0.370465i
\(142\) −5.34301 1.69111i −0.448376 0.141915i
\(143\) −12.2989 + 21.3023i −1.02849 + 1.78139i
\(144\) 3.05283 + 2.58462i 0.254402 + 0.215385i
\(145\) 8.87199 + 15.3667i 0.736779 + 1.27614i
\(146\) −13.1177 + 11.9936i −1.08563 + 0.992601i
\(147\) −6.82204 1.56838i −0.562672 0.129358i
\(148\) −3.74617 4.48453i −0.307934 0.368626i
\(149\) −6.77583 1.81558i −0.555098 0.148738i −0.0296445 0.999561i \(-0.509438\pi\)
−0.525453 + 0.850823i \(0.676104\pi\)
\(150\) 8.50305 13.3148i 0.694271 1.08714i
\(151\) −1.76080 1.01660i −0.143292 0.0827297i 0.426640 0.904422i \(-0.359697\pi\)
−0.569932 + 0.821692i \(0.693030\pi\)
\(152\) −4.49190 10.9465i −0.364341 0.887878i
\(153\) 2.52890i 0.204450i
\(154\) 4.08768 13.7674i 0.329395 1.10941i
\(155\) −14.9865 + 14.9865i −1.20374 + 1.20374i
\(156\) 5.39121 + 11.6282i 0.431642 + 0.931004i
\(157\) 21.7807 5.83613i 1.73829 0.465774i 0.756225 0.654312i \(-0.227042\pi\)
0.982066 + 0.188538i \(0.0603750\pi\)
\(158\) −4.91557 + 1.08408i −0.391062 + 0.0862448i
\(159\) 2.41165 + 4.17710i 0.191256 + 0.331265i
\(160\) −22.1814 5.04572i −1.75359 0.398899i
\(161\) 2.14517 + 7.46812i 0.169063 + 0.588571i
\(162\) −0.954281 1.04372i −0.0749754 0.0820023i
\(163\) 0.777413 2.90135i 0.0608917 0.227251i −0.928774 0.370648i \(-0.879136\pi\)
0.989665 + 0.143397i \(0.0458025\pi\)
\(164\) 2.39538 3.40498i 0.187048 0.265884i
\(165\) 3.99483 + 14.9089i 0.310997 + 1.16066i
\(166\) −1.96133 + 1.01826i −0.152229 + 0.0790325i
\(167\) 1.58111i 0.122350i 0.998127 + 0.0611749i \(0.0194848\pi\)
−0.998127 + 0.0611749i \(0.980515\pi\)
\(168\) −4.64181 5.86972i −0.358123 0.452859i
\(169\) 28.0703i 2.15925i
\(170\) 6.62678 + 12.7642i 0.508251 + 0.978970i
\(171\) 1.08273 + 4.04080i 0.0827984 + 0.309008i
\(172\) −7.39146 + 1.28654i −0.563594 + 0.0980981i
\(173\) −2.51559 + 9.38832i −0.191257 + 0.713781i 0.801947 + 0.597395i \(0.203798\pi\)
−0.993204 + 0.116386i \(0.962869\pi\)
\(174\) −4.60538 + 4.21074i −0.349133 + 0.319215i
\(175\) −20.5214 + 21.2701i −1.55127 + 1.60787i
\(176\) 12.6151 8.75066i 0.950897 0.659606i
\(177\) −6.08728 10.5435i −0.457548 0.792496i
\(178\) 0.733931 + 3.32788i 0.0550105 + 0.249435i
\(179\) −3.15648 + 0.845775i −0.235926 + 0.0632162i −0.374845 0.927088i \(-0.622304\pi\)
0.138919 + 0.990304i \(0.455637\pi\)
\(180\) 7.55154 + 2.76738i 0.562859 + 0.206268i
\(181\) 7.83598 7.83598i 0.582444 0.582444i −0.353130 0.935574i \(-0.614883\pi\)
0.935574 + 0.353130i \(0.114883\pi\)
\(182\) −5.58281 23.3199i −0.413825 1.72858i
\(183\) 9.58478i 0.708528i
\(184\) −3.20412 + 7.66376i −0.236211 + 0.564980i
\(185\) −10.1749 5.87451i −0.748077 0.431902i
\(186\) −6.28180 4.01168i −0.460604 0.294150i
\(187\) −9.37582 2.51224i −0.685628 0.183713i
\(188\) −1.11170 + 12.3926i −0.0810792 + 0.903820i
\(189\) 1.36371 + 2.26722i 0.0991950 + 0.164916i
\(190\) −16.0535 17.5580i −1.16464 1.27379i
\(191\) −5.64673 9.78043i −0.408583 0.707687i 0.586148 0.810204i \(-0.300644\pi\)
−0.994731 + 0.102517i \(0.967310\pi\)
\(192\) 0.0528300 7.99983i 0.00381268 0.577338i
\(193\) 7.11865 12.3299i 0.512412 0.887523i −0.487485 0.873132i \(-0.662085\pi\)
0.999896 0.0143917i \(-0.00458118\pi\)
\(194\) 1.61066 5.08882i 0.115639 0.365356i
\(195\) 18.2229 + 18.2229i 1.30497 + 1.30497i
\(196\) 6.33988 + 12.4822i 0.452849 + 0.891587i
\(197\) 11.5300 11.5300i 0.821480 0.821480i −0.164840 0.986320i \(-0.552711\pi\)
0.986320 + 0.164840i \(0.0527109\pi\)
\(198\) −4.81754 + 2.50112i −0.342368 + 0.177747i
\(199\) 4.94931 + 2.85748i 0.350847 + 0.202562i 0.665058 0.746792i \(-0.268407\pi\)
−0.314211 + 0.949353i \(0.601740\pi\)
\(200\) −31.3396 + 4.02071i −2.21605 + 0.284307i
\(201\) −1.11044 + 0.641111i −0.0783241 + 0.0452205i
\(202\) 16.1433 + 0.722636i 1.13584 + 0.0508445i
\(203\) 10.0041 6.01732i 0.702148 0.422333i
\(204\) −3.88165 + 3.24256i −0.271770 + 0.227025i
\(205\) 2.16649 8.08544i 0.151314 0.564712i
\(206\) 1.92893 + 8.74641i 0.134395 + 0.609391i
\(207\) 1.46841 2.54337i 0.102062 0.176776i
\(208\) 10.9358 23.1848i 0.758258 1.60757i
\(209\) 16.0567 1.11067
\(210\) −12.8241 7.86995i −0.884950 0.543078i
\(211\) −10.2662 10.2662i −0.706752 0.706752i 0.259099 0.965851i \(-0.416574\pi\)
−0.965851 + 0.259099i \(0.916574\pi\)
\(212\) 3.31927 9.05754i 0.227969 0.622075i
\(213\) −1.02565 3.82778i −0.0702764 0.262275i
\(214\) 6.63314 10.3867i 0.453432 0.710020i
\(215\) −13.0641 + 7.54259i −0.890967 + 0.514400i
\(216\) −0.378441 + 2.80300i −0.0257497 + 0.190720i
\(217\) 10.0351 + 9.68185i 0.681226 + 0.657247i
\(218\) 0.254867 5.69361i 0.0172618 0.385620i
\(219\) −12.1400 3.25291i −0.820346 0.219811i
\(220\) 17.7617 25.2479i 1.19750 1.70221i
\(221\) −15.6545 + 4.19462i −1.05304 + 0.282161i
\(222\) 1.24682 3.93927i 0.0836808 0.264387i
\(223\) 5.71071 0.382418 0.191209 0.981549i \(-0.438759\pi\)
0.191209 + 0.981549i \(0.438759\pi\)
\(224\) −3.05779 + 14.6509i −0.204307 + 0.978907i
\(225\) 11.1710 0.744736
\(226\) −2.42796 + 7.67106i −0.161506 + 0.510272i
\(227\) 11.5885 3.10513i 0.769157 0.206095i 0.147158 0.989113i \(-0.452987\pi\)
0.621999 + 0.783018i \(0.286321\pi\)
\(228\) 4.81401 6.84301i 0.318816 0.453189i
\(229\) −2.70340 0.724374i −0.178646 0.0478680i 0.168387 0.985721i \(-0.446144\pi\)
−0.347033 + 0.937853i \(0.612811\pi\)
\(230\) −0.746885 + 16.6851i −0.0492482 + 1.10018i
\(231\) 9.76037 2.80360i 0.642185 0.184463i
\(232\) 12.3681 + 1.66986i 0.812008 + 0.109632i
\(233\) −16.2767 + 9.39735i −1.06632 + 0.615641i −0.927174 0.374631i \(-0.877769\pi\)
−0.139147 + 0.990272i \(0.544436\pi\)
\(234\) −4.87803 + 7.63841i −0.318887 + 0.499339i
\(235\) 6.47495 + 24.1649i 0.422379 + 1.57634i
\(236\) −8.37824 + 22.8623i −0.545377 + 1.48821i
\(237\) −2.51685 2.51685i −0.163487 0.163487i
\(238\) 8.31852 4.50969i 0.539209 0.292320i
\(239\) −15.0892 −0.976040 −0.488020 0.872832i \(-0.662281\pi\)
−0.488020 + 0.872832i \(0.662281\pi\)
\(240\) −5.43490 15.1393i −0.350821 0.977238i
\(241\) −11.2008 + 19.4003i −0.721505 + 1.24968i 0.238892 + 0.971046i \(0.423216\pi\)
−0.960397 + 0.278637i \(0.910117\pi\)
\(242\) 1.13670 + 5.15418i 0.0730701 + 0.331323i
\(243\) 0.258819 0.965926i 0.0166032 0.0619642i
\(244\) 14.7118 12.2896i 0.941828 0.786761i
\(245\) 20.6047 + 19.1788i 1.31639 + 1.22529i
\(246\) 2.94084 + 0.131643i 0.187501 + 0.00839325i
\(247\) 23.2176 13.4047i 1.47730 0.852921i
\(248\) 1.89694 + 14.7858i 0.120456 + 0.938900i
\(249\) −1.35329 0.781320i −0.0857610 0.0495141i
\(250\) −31.1473 + 16.1707i −1.96993 + 1.02272i
\(251\) 11.4516 11.4516i 0.722816 0.722816i −0.246362 0.969178i \(-0.579235\pi\)
0.969178 + 0.246362i \(0.0792351\pi\)
\(252\) 1.73145 5.00021i 0.109071 0.314983i
\(253\) −7.97069 7.97069i −0.501113 0.501113i
\(254\) 8.51597 26.9059i 0.534340 1.68823i
\(255\) −5.08477 + 8.80708i −0.318421 + 0.551521i
\(256\) −12.3468 + 10.1763i −0.771674 + 0.636018i
\(257\) −5.49728 9.52156i −0.342911 0.593939i 0.642061 0.766653i \(-0.278080\pi\)
−0.984972 + 0.172715i \(0.944746\pi\)
\(258\) −3.57979 3.91530i −0.222868 0.243756i
\(259\) −3.74448 + 6.76256i −0.232671 + 0.420205i
\(260\) 4.60521 51.3360i 0.285603 3.18373i
\(261\) −4.26212 1.14203i −0.263819 0.0706900i
\(262\) 9.00779 + 5.75254i 0.556503 + 0.355393i
\(263\) −20.0628 11.5833i −1.23713 0.714255i −0.268620 0.963246i \(-0.586567\pi\)
−0.968506 + 0.248992i \(0.919901\pi\)
\(264\) 10.0160 + 4.18758i 0.616445 + 0.257728i
\(265\) 19.3960i 1.19149i
\(266\) −11.3609 + 10.7673i −0.696583 + 0.660185i
\(267\) −1.70392 + 1.70392i −0.104279 + 0.104279i
\(268\) 2.40785 + 0.882394i 0.147083 + 0.0539008i
\(269\) −24.2452 + 6.49649i −1.47826 + 0.396098i −0.905754 0.423803i \(-0.860695\pi\)
−0.572504 + 0.819902i \(0.694028\pi\)
\(270\) 1.22478 + 5.55356i 0.0745379 + 0.337979i
\(271\) −5.08157 8.80154i −0.308684 0.534656i 0.669391 0.742910i \(-0.266555\pi\)
−0.978075 + 0.208255i \(0.933222\pi\)
\(272\) 9.95411 + 1.80040i 0.603557 + 0.109165i
\(273\) 11.7727 12.2022i 0.712518 0.738514i
\(274\) 0.574011 0.524823i 0.0346773 0.0317057i
\(275\) 11.0974 41.4162i 0.669201 2.49749i
\(276\) −5.78665 + 1.00721i −0.348315 + 0.0606271i
\(277\) −6.02122 22.4715i −0.361780 1.35018i −0.871734 0.489979i \(-0.837004\pi\)
0.509954 0.860202i \(-0.329662\pi\)
\(278\) 1.00283 + 1.93161i 0.0601460 + 0.115851i
\(279\) 5.27042i 0.315532i
\(280\) 4.36341 + 29.7748i 0.260763 + 1.77939i
\(281\) 17.6828i 1.05487i −0.849596 0.527434i \(-0.823154\pi\)
0.849596 0.527434i \(-0.176846\pi\)
\(282\) −7.80843 + 4.05390i −0.464985 + 0.241406i
\(283\) −7.95895 29.7032i −0.473110 1.76567i −0.628491 0.777817i \(-0.716327\pi\)
0.155380 0.987855i \(-0.450340\pi\)
\(284\) −4.56022 + 6.48226i −0.270600 + 0.384651i
\(285\) 4.35400 16.2494i 0.257909 0.962529i
\(286\) 23.4732 + 25.6732i 1.38800 + 1.51809i
\(287\) −5.34434 1.32988i −0.315466 0.0785005i
\(288\) 4.78760 3.01312i 0.282112 0.177550i
\(289\) 5.30232 + 9.18389i 0.311901 + 0.540229i
\(290\) 24.5049 5.40432i 1.43898 0.317353i
\(291\) 3.64567 0.976855i 0.213713 0.0572643i
\(292\) 10.5730 + 22.8048i 0.618737 + 1.33455i
\(293\) −4.87935 + 4.87935i −0.285055 + 0.285055i −0.835121 0.550066i \(-0.814602\pi\)
0.550066 + 0.835121i \(0.314602\pi\)
\(294\) −5.02591 + 8.52879i −0.293117 + 0.497409i
\(295\) 48.9579i 2.85044i
\(296\) −7.64511 + 3.13718i −0.444363 + 0.182345i
\(297\) −3.32402 1.91912i −0.192879 0.111359i
\(298\) −5.33949 + 8.36100i −0.309308 + 0.484340i
\(299\) −18.1797 4.87123i −1.05136 0.281710i
\(300\) −14.3235 17.1466i −0.826968 0.989960i
\(301\) 5.11566 + 8.50503i 0.294862 + 0.490222i
\(302\) −2.12209 + 1.94024i −0.122112 + 0.111648i
\(303\) 5.71325 + 9.89564i 0.328218 + 0.568489i
\(304\) −16.6760 + 1.38501i −0.956432 + 0.0794356i
\(305\) 19.2718 33.3797i 1.10350 1.91131i
\(306\) −3.40970 1.07920i −0.194920 0.0616938i
\(307\) −5.50837 5.50837i −0.314379 0.314379i 0.532224 0.846604i \(-0.321356\pi\)
−0.846604 + 0.532224i \(0.821356\pi\)
\(308\) −16.8180 11.3866i −0.958296 0.648809i
\(309\) −4.47829 + 4.47829i −0.254761 + 0.254761i
\(310\) 13.8107 + 26.6015i 0.784394 + 1.51087i
\(311\) 26.4649 + 15.2795i 1.50069 + 0.866421i 1.00000 0.000792710i \(0.000252327\pi\)
0.500686 + 0.865629i \(0.333081\pi\)
\(312\) 17.9789 2.30660i 1.01786 0.130586i
\(313\) 25.4306 14.6823i 1.43742 0.829895i 0.439750 0.898120i \(-0.355067\pi\)
0.997670 + 0.0682256i \(0.0217338\pi\)
\(314\) 1.42605 31.8573i 0.0804767 1.79781i
\(315\) −0.190577 10.6377i −0.0107378 0.599367i
\(316\) −0.636046 + 7.09024i −0.0357804 + 0.398857i
\(317\) −3.66874 + 13.6919i −0.206057 + 0.769016i 0.783068 + 0.621937i \(0.213654\pi\)
−0.989125 + 0.147079i \(0.953013\pi\)
\(318\) 6.66110 1.46904i 0.373536 0.0823797i
\(319\) −8.46808 + 14.6671i −0.474121 + 0.821202i
\(320\) −16.2689 + 27.7537i −0.909461 + 1.55148i
\(321\) 8.71441 0.486391
\(322\) 10.9846 + 0.294685i 0.612150 + 0.0164221i
\(323\) 7.48068 + 7.48068i 0.416236 + 0.416236i
\(324\) −1.81447 + 0.841244i −0.100804 + 0.0467358i
\(325\) −18.5291 69.1515i −1.02781 3.83583i
\(326\) −3.58010 2.28632i −0.198283 0.126627i
\(327\) 3.49010 2.01501i 0.193003 0.111430i
\(328\) −3.56868 4.68273i −0.197048 0.258561i
\(329\) 15.8199 4.54417i 0.872181 0.250528i
\(330\) 21.8063 + 0.976132i 1.20040 + 0.0537343i
\(331\) 13.2086 + 3.53924i 0.726011 + 0.194534i 0.602852 0.797853i \(-0.294031\pi\)
0.123159 + 0.992387i \(0.460698\pi\)
\(332\) 0.535923 + 3.07899i 0.0294126 + 0.168981i
\(333\) 2.82212 0.756186i 0.154651 0.0414387i
\(334\) 2.13179 + 0.674733i 0.116647 + 0.0369197i
\(335\) 5.15623 0.281715
\(336\) −9.89496 + 3.75363i −0.539814 + 0.204777i
\(337\) −7.46365 −0.406571 −0.203285 0.979120i \(-0.565162\pi\)
−0.203285 + 0.979120i \(0.565162\pi\)
\(338\) 37.8469 + 11.9789i 2.05860 + 0.651566i
\(339\) −5.49561 + 1.47254i −0.298481 + 0.0799776i
\(340\) 20.0378 3.48775i 1.08670 0.189150i
\(341\) −19.5399 5.23569i −1.05814 0.283529i
\(342\) 5.91022 + 0.264564i 0.319588 + 0.0143060i
\(343\) 12.3735 13.7803i 0.668104 0.744068i
\(344\) −1.41964 + 10.5149i −0.0765421 + 0.566923i
\(345\) −10.2277 + 5.90496i −0.550641 + 0.317913i
\(346\) 11.5847 + 7.39818i 0.622795 + 0.397729i
\(347\) 8.97232 + 33.4852i 0.481659 + 1.79758i 0.594654 + 0.803982i \(0.297289\pi\)
−0.112995 + 0.993596i \(0.536044\pi\)
\(348\) 3.71197 + 8.00631i 0.198982 + 0.429183i
\(349\) −9.29390 9.29390i −0.497491 0.497491i 0.413165 0.910656i \(-0.364423\pi\)
−0.910656 + 0.413165i \(0.864423\pi\)
\(350\) 19.9209 + 36.7458i 1.06481 + 1.96414i
\(351\) −6.40861 −0.342066
\(352\) −6.41499 20.7431i −0.341920 1.10561i
\(353\) 2.51157 4.35017i 0.133678 0.231536i −0.791414 0.611281i \(-0.790655\pi\)
0.925092 + 0.379744i \(0.123988\pi\)
\(354\) −16.8134 + 3.70803i −0.893622 + 0.197080i
\(355\) −4.12447 + 15.3927i −0.218904 + 0.816961i
\(356\) 4.80015 + 0.430608i 0.254408 + 0.0228222i
\(357\) 5.85344 + 3.24110i 0.309797 + 0.171537i
\(358\) −0.206664 + 4.61678i −0.0109225 + 0.244004i
\(359\) 8.39455 4.84660i 0.443047 0.255794i −0.261842 0.965111i \(-0.584330\pi\)
0.704889 + 0.709317i \(0.250997\pi\)
\(360\) 6.95382 9.00071i 0.366499 0.474379i
\(361\) 1.29872 + 0.749817i 0.0683538 + 0.0394641i
\(362\) −7.22120 13.9091i −0.379538 0.731049i
\(363\) −2.63902 + 2.63902i −0.138512 + 0.138512i
\(364\) −33.8244 2.42442i −1.77288 0.127074i
\(365\) 35.7379 + 35.7379i 1.87061 + 1.87061i
\(366\) 12.9231 + 4.09027i 0.675500 + 0.213802i
\(367\) 15.2674 26.4439i 0.796951 1.38036i −0.124642 0.992202i \(-0.539778\pi\)
0.921593 0.388158i \(-0.126889\pi\)
\(368\) 8.96563 + 7.59057i 0.467366 + 0.395686i
\(369\) 1.04079 + 1.80269i 0.0541811 + 0.0938444i
\(370\) −12.2627 + 11.2119i −0.637505 + 0.582877i
\(371\) −12.7592 + 0.228584i −0.662424 + 0.0118675i
\(372\) −8.08964 + 6.75773i −0.419429 + 0.350372i
\(373\) 33.5787 + 8.99740i 1.73864 + 0.465867i 0.982144 0.188130i \(-0.0602425\pi\)
0.756497 + 0.653997i \(0.226909\pi\)
\(374\) −7.38833 + 11.5692i −0.382041 + 0.598231i
\(375\) −21.4911 12.4079i −1.10979 0.640740i
\(376\) 16.2344 + 6.78738i 0.837223 + 0.350032i
\(377\) 28.2778i 1.45638i
\(378\) 3.63883 0.871142i 0.187161 0.0448067i
\(379\) 6.01103 6.01103i 0.308766 0.308766i −0.535665 0.844431i \(-0.679939\pi\)
0.844431 + 0.535665i \(0.179939\pi\)
\(380\) −30.5241 + 14.1519i −1.56585 + 0.725977i
\(381\) 19.2756 5.16488i 0.987519 0.264605i
\(382\) −15.5966 + 3.43967i −0.797991 + 0.175989i
\(383\) 4.96173 + 8.59397i 0.253533 + 0.439132i 0.964496 0.264098i \(-0.0850741\pi\)
−0.710963 + 0.703229i \(0.751741\pi\)
\(384\) −10.7635 3.48513i −0.549275 0.177850i
\(385\) −39.6282 9.86107i −2.01964 0.502567i
\(386\) −13.5864 14.8597i −0.691529 0.756341i
\(387\) 0.970907 3.62347i 0.0493540 0.184192i
\(388\) −6.17387 4.34328i −0.313431 0.220496i
\(389\) 2.85837 + 10.6676i 0.144925 + 0.540869i 0.999759 + 0.0219662i \(0.00699261\pi\)
−0.854833 + 0.518903i \(0.826341\pi\)
\(390\) 32.3463 16.7932i 1.63792 0.850358i
\(391\) 7.42695i 0.375597i
\(392\) 19.5352 3.22126i 0.986676 0.162698i
\(393\) 7.55752i 0.381226i
\(394\) −10.6254 20.4662i −0.535301 1.03107i
\(395\) 3.70456 + 13.8256i 0.186397 + 0.695642i
\(396\) 1.31636 + 7.56279i 0.0661498 + 0.380044i
\(397\) 9.60625 35.8510i 0.482124 1.79931i −0.110552 0.993870i \(-0.535262\pi\)
0.592676 0.805441i \(-0.298071\pi\)
\(398\) 5.96482 5.45368i 0.298989 0.273368i
\(399\) −10.7405 2.67267i −0.537700 0.133801i
\(400\) −7.95298 + 43.9707i −0.397649 + 2.19854i
\(401\) −13.8724 24.0278i −0.692756 1.19989i −0.970931 0.239359i \(-0.923063\pi\)
0.278175 0.960530i \(-0.410270\pi\)
\(402\) 0.390529 + 1.77078i 0.0194778 + 0.0883186i
\(403\) −32.6252 + 8.74189i −1.62518 + 0.435464i
\(404\) 7.86344 21.4575i 0.391221 1.06755i
\(405\) −2.84351 + 2.84351i −0.141295 + 0.141295i
\(406\) −3.84389 16.0563i −0.190769 0.796859i
\(407\) 11.2141i 0.555863i
\(408\) 2.71543 + 6.61735i 0.134434 + 0.327608i
\(409\) 0.188170 + 0.108640i 0.00930442 + 0.00537191i 0.504645 0.863327i \(-0.331623\pi\)
−0.495341 + 0.868699i \(0.664957\pi\)
\(410\) −9.97699 6.37149i −0.492728 0.314665i
\(411\) 0.531228 + 0.142342i 0.0262035 + 0.00702122i
\(412\) 12.6159 + 1.13173i 0.621539 + 0.0557565i
\(413\) 32.2057 0.576973i 1.58474 0.0283910i
\(414\) −2.80256 3.06522i −0.137738 0.150647i
\(415\) 3.14194 + 5.44200i 0.154232 + 0.267137i
\(416\) −26.5930 24.6386i −1.30383 1.20801i
\(417\) −0.769481 + 1.33278i −0.0376817 + 0.0652665i
\(418\) 6.85214 21.6491i 0.335149 1.05889i
\(419\) 15.2324 + 15.2324i 0.744152 + 0.744152i 0.973374 0.229222i \(-0.0736181\pi\)
−0.229222 + 0.973374i \(0.573618\pi\)
\(420\) −16.0836 + 13.9322i −0.784801 + 0.679821i
\(421\) −0.698740 + 0.698740i −0.0340545 + 0.0340545i −0.723929 0.689874i \(-0.757666\pi\)
0.689874 + 0.723929i \(0.257666\pi\)
\(422\) −18.2228 + 9.46072i −0.887073 + 0.460541i
\(423\) −5.38768 3.11058i −0.261958 0.151242i
\(424\) −10.7957 8.34062i −0.524286 0.405056i
\(425\) 24.4657 14.1253i 1.18676 0.685175i
\(426\) −5.59865 0.250616i −0.271255 0.0121424i
\(427\) −22.1851 12.2841i −1.07361 0.594467i
\(428\) −11.1736 13.3759i −0.540097 0.646548i
\(429\) −6.36638 + 23.7597i −0.307372 + 1.14713i
\(430\) 4.59452 + 20.8330i 0.221568 + 1.00466i
\(431\) 1.51849 2.63011i 0.0731433 0.126688i −0.827134 0.562005i \(-0.810030\pi\)
0.900277 + 0.435317i \(0.143364\pi\)
\(432\) 3.61775 + 1.70642i 0.174059 + 0.0821000i
\(433\) −20.7669 −0.997996 −0.498998 0.866603i \(-0.666298\pi\)
−0.498998 + 0.866603i \(0.666298\pi\)
\(434\) 17.3364 9.39851i 0.832173 0.451143i
\(435\) 12.5469 + 12.5469i 0.601577 + 0.601577i
\(436\) −7.56787 2.77336i −0.362435 0.132820i
\(437\) 3.17979 + 11.8671i 0.152110 + 0.567682i
\(438\) −9.56657 + 14.9801i −0.457108 + 0.715776i
\(439\) 31.8434 18.3848i 1.51980 0.877458i 0.520074 0.854121i \(-0.325904\pi\)
0.999728 0.0233372i \(-0.00742914\pi\)
\(440\) −26.4618 34.7224i −1.26151 1.65533i
\(441\) −6.99551 + 0.250733i −0.333119 + 0.0119397i
\(442\) −1.02495 + 22.8969i −0.0487519 + 1.08909i
\(443\) 22.7956 + 6.10805i 1.08305 + 0.290202i 0.755845 0.654751i \(-0.227227\pi\)
0.327205 + 0.944953i \(0.393893\pi\)
\(444\) −4.77921 3.36214i −0.226811 0.159560i
\(445\) 9.36005 2.50802i 0.443709 0.118891i
\(446\) 2.43703 7.69970i 0.115397 0.364591i
\(447\) −7.01486 −0.331791
\(448\) 18.4488 + 10.3750i 0.871625 + 0.490174i
\(449\) −21.2018 −1.00057 −0.500287 0.865860i \(-0.666772\pi\)
−0.500287 + 0.865860i \(0.666772\pi\)
\(450\) 4.76720 15.0618i 0.224728 0.710021i
\(451\) 7.71734 2.06786i 0.363395 0.0973715i
\(452\) 9.30670 + 6.54720i 0.437750 + 0.307954i
\(453\) −1.96392 0.526230i −0.0922729 0.0247245i
\(454\) 0.758736 16.9498i 0.0356092 0.795493i
\(455\) −65.5339 + 18.8242i −3.07228 + 0.882491i
\(456\) −7.17200 9.41091i −0.335860 0.440706i
\(457\) −19.8896 + 11.4833i −0.930397 + 0.537165i −0.886937 0.461890i \(-0.847171\pi\)
−0.0434598 + 0.999055i \(0.513838\pi\)
\(458\) −2.13033 + 3.33585i −0.0995439 + 0.155874i
\(459\) −0.654529 2.44273i −0.0305508 0.114017i
\(460\) 22.1776 + 8.12731i 1.03403 + 0.378938i
\(461\) 4.17593 + 4.17593i 0.194493 + 0.194493i 0.797634 0.603142i \(-0.206085\pi\)
−0.603142 + 0.797634i \(0.706085\pi\)
\(462\) 0.385134 14.3562i 0.0179181 0.667913i
\(463\) −1.33807 −0.0621854 −0.0310927 0.999517i \(-0.509899\pi\)
−0.0310927 + 0.999517i \(0.509899\pi\)
\(464\) 7.52952 15.9632i 0.349549 0.741075i
\(465\) −10.5970 + 18.3546i −0.491425 + 0.851174i
\(466\) 5.72434 + 25.9560i 0.265175 + 1.20239i
\(467\) −0.0511596 + 0.190930i −0.00236738 + 0.00883520i −0.967099 0.254399i \(-0.918122\pi\)
0.964732 + 0.263234i \(0.0847891\pi\)
\(468\) 8.21712 + 9.83667i 0.379836 + 0.454700i
\(469\) −0.0607666 3.39189i −0.00280594 0.156623i
\(470\) 35.3444 + 1.58215i 1.63032 + 0.0729790i
\(471\) 19.5281 11.2745i 0.899805 0.519503i
\(472\) 27.2496 + 21.0527i 1.25427 + 0.969029i
\(473\) −12.4694 7.19920i −0.573343 0.331019i
\(474\) −4.46750 + 2.31938i −0.205199 + 0.106533i
\(475\) −33.0447 + 33.0447i −1.51620 + 1.51620i
\(476\) −2.53047 13.1403i −0.115984 0.602283i
\(477\) 3.41058 + 3.41058i 0.156160 + 0.156160i
\(478\) −6.43927 + 20.3447i −0.294525 + 0.930543i
\(479\) 7.78319 13.4809i 0.355623 0.615957i −0.631601 0.775293i \(-0.717602\pi\)
0.987224 + 0.159336i \(0.0509354\pi\)
\(480\) −22.7315 + 0.867174i −1.03755 + 0.0395809i
\(481\) −9.36195 16.2154i −0.426868 0.739357i
\(482\) 21.3774 + 23.3809i 0.973712 + 1.06497i
\(483\) 4.00497 + 6.65844i 0.182232 + 0.302970i
\(484\) 7.43441 + 0.666920i 0.337928 + 0.0303146i
\(485\) −14.6604 3.92825i −0.665696 0.178373i
\(486\) −1.19190 0.761169i −0.0540656 0.0345273i
\(487\) −0.00792057 0.00457294i −0.000358915 0.000207220i 0.499821 0.866129i \(-0.333399\pi\)
−0.500179 + 0.865922i \(0.666733\pi\)
\(488\) −10.2917 25.0804i −0.465885 1.13533i
\(489\) 3.00369i 0.135832i
\(490\) 34.6516 19.5967i 1.56540 0.885287i
\(491\) −8.63759 + 8.63759i −0.389809 + 0.389809i −0.874619 0.484810i \(-0.838889\pi\)
0.484810 + 0.874619i \(0.338889\pi\)
\(492\) 1.43249 3.90893i 0.0645814 0.176228i
\(493\) −10.7785 + 2.88809i −0.485439 + 0.130073i
\(494\) −8.16540 37.0245i −0.367379 1.66581i
\(495\) 7.71742 + 13.3670i 0.346872 + 0.600800i
\(496\) 20.7451 + 3.75216i 0.931481 + 0.168477i
\(497\) 10.1743 + 2.53177i 0.456381 + 0.113566i
\(498\) −1.63096 + 1.49120i −0.0730849 + 0.0668221i
\(499\) −1.77590 + 6.62773i −0.0795000 + 0.296698i −0.994216 0.107399i \(-0.965748\pi\)
0.914716 + 0.404097i \(0.132414\pi\)
\(500\) 8.51081 + 48.8964i 0.380615 + 2.18671i
\(501\) 0.409221 + 1.52723i 0.0182826 + 0.0682318i
\(502\) −10.5531 20.3270i −0.471009 0.907236i
\(503\) 41.8322i 1.86520i −0.360906 0.932602i \(-0.617533\pi\)
0.360906 0.932602i \(-0.382467\pi\)
\(504\) −6.00284 4.46832i −0.267388 0.199035i
\(505\) 45.9496i 2.04473i
\(506\) −14.1483 + 7.34535i −0.628968 + 0.326540i
\(507\) 7.26512 + 27.1138i 0.322655 + 1.20417i
\(508\) −32.6428 22.9640i −1.44829 1.01886i
\(509\) −1.74449 + 6.51052i −0.0773231 + 0.288574i −0.993750 0.111628i \(-0.964393\pi\)
0.916427 + 0.400202i \(0.131060\pi\)
\(510\) 9.70460 + 10.6141i 0.429727 + 0.470002i
\(511\) 23.0881 23.9305i 1.02136 1.05862i
\(512\) 8.45164 + 20.9898i 0.373513 + 0.927625i
\(513\) 2.09167 + 3.62288i 0.0923496 + 0.159954i
\(514\) −15.1838 + 3.34863i −0.669728 + 0.147702i
\(515\) 24.6003 6.59163i 1.08402 0.290462i
\(516\) −6.80662 + 3.15576i −0.299645 + 0.138924i
\(517\) −16.8845 + 16.8845i −0.742581 + 0.742581i
\(518\) 7.51995 + 7.93455i 0.330408 + 0.348624i
\(519\) 9.71951i 0.426639i
\(520\) −67.2506 28.1166i −2.94914 1.23300i
\(521\) −16.2403 9.37632i −0.711499 0.410784i 0.100117 0.994976i \(-0.468078\pi\)
−0.811616 + 0.584192i \(0.801412\pi\)
\(522\) −3.35864 + 5.25922i −0.147004 + 0.230190i
\(523\) −5.86363 1.57115i −0.256398 0.0687018i 0.128330 0.991732i \(-0.459038\pi\)
−0.384729 + 0.923030i \(0.625705\pi\)
\(524\) 11.6001 9.69024i 0.506755 0.423320i
\(525\) −14.3170 + 25.8567i −0.624847 + 1.12848i
\(526\) −24.1793 + 22.1074i −1.05427 + 0.963927i
\(527\) −6.66419 11.5427i −0.290297 0.502809i
\(528\) 9.92039 11.7175i 0.431730 0.509939i
\(529\) −7.18753 + 12.4492i −0.312501 + 0.541268i
\(530\) −26.1515 8.27719i −1.13595 0.359538i
\(531\) −8.60872 8.60872i −0.373586 0.373586i
\(532\) 9.66920 + 19.9127i 0.419213 + 0.863326i
\(533\) 9.43278 9.43278i 0.408579 0.408579i
\(534\) 1.57024 + 3.02453i 0.0679510 + 0.130884i
\(535\) −30.3485 17.5217i −1.31208 0.757531i
\(536\) 2.21726 2.86992i 0.0957713 0.123962i
\(537\) −2.83002 + 1.63391i −0.122124 + 0.0705085i
\(538\) −1.58741 + 35.4620i −0.0684381 + 1.52887i
\(539\) −6.01983 + 26.1847i −0.259293 + 1.12785i
\(540\) 8.01048 + 0.718598i 0.344716 + 0.0309235i
\(541\) −7.83661 + 29.2466i −0.336922 + 1.25741i 0.564848 + 0.825195i \(0.308935\pi\)
−0.901770 + 0.432216i \(0.857732\pi\)
\(542\) −14.0356 + 3.09541i −0.602880 + 0.132959i
\(543\) 5.54087 9.59707i 0.237782 0.411850i
\(544\) 6.67534 12.6527i 0.286203 0.542481i
\(545\) −16.2060 −0.694189
\(546\) −11.4282 21.0803i −0.489082 0.902155i
\(547\) −11.8928 11.8928i −0.508499 0.508499i 0.405567 0.914065i \(-0.367074\pi\)
−0.914065 + 0.405567i \(0.867074\pi\)
\(548\) −0.462657 0.997900i −0.0197637 0.0426282i
\(549\) 2.48072 + 9.25819i 0.105875 + 0.395130i
\(550\) −51.1053 32.6368i −2.17914 1.39164i
\(551\) 15.9859 9.22945i 0.681021 0.393188i
\(552\) −1.11142 + 8.23191i −0.0473050 + 0.350373i
\(553\) 9.05118 2.59989i 0.384895 0.110559i
\(554\) −32.8676 1.47128i −1.39641 0.0625086i
\(555\) −11.3487 3.04087i −0.481724 0.129078i
\(556\) 3.03233 0.527802i 0.128600 0.0223838i
\(557\) −32.2841 + 8.65050i −1.36792 + 0.366533i −0.866719 0.498797i \(-0.833775\pi\)
−0.501202 + 0.865330i \(0.667109\pi\)
\(558\) −7.10606 2.24913i −0.300823 0.0952134i
\(559\) −24.0406 −1.01681
\(560\) 42.0072 + 6.82315i 1.77513 + 0.288331i
\(561\) −9.70656 −0.409811
\(562\) −23.8416 7.54608i −1.00570 0.318312i
\(563\) −0.208812 + 0.0559511i −0.00880039 + 0.00235806i −0.263217 0.964737i \(-0.584783\pi\)
0.254416 + 0.967095i \(0.418117\pi\)
\(564\) 2.13361 + 12.2580i 0.0898411 + 0.516156i
\(565\) 22.0996 + 5.92158i 0.929738 + 0.249123i
\(566\) −43.4450 1.94476i −1.82613 0.0817444i
\(567\) 1.90404 + 1.83702i 0.0799621 + 0.0771475i
\(568\) 6.79391 + 8.91479i 0.285066 + 0.374056i
\(569\) 1.41592 0.817484i 0.0593586 0.0342707i −0.470027 0.882652i \(-0.655756\pi\)
0.529386 + 0.848381i \(0.322422\pi\)
\(570\) −20.0508 12.8048i −0.839836 0.536335i
\(571\) 4.44776 + 16.5993i 0.186133 + 0.694657i 0.994385 + 0.105821i \(0.0337471\pi\)
−0.808252 + 0.588836i \(0.799586\pi\)
\(572\) 44.6321 20.6928i 1.86616 0.865209i
\(573\) −7.98569 7.98569i −0.333607 0.333607i
\(574\) −4.07374 + 6.63820i −0.170035 + 0.277073i
\(575\) 32.8074 1.36816
\(576\) −2.01948 7.74091i −0.0841449 0.322538i
\(577\) −10.1753 + 17.6242i −0.423605 + 0.733705i −0.996289 0.0860708i \(-0.972569\pi\)
0.572684 + 0.819776i \(0.305902\pi\)
\(578\) 14.6453 3.22988i 0.609164 0.134345i
\(579\) 3.68489 13.7522i 0.153139 0.571521i
\(580\) 3.17079 35.3460i 0.131660 1.46766i
\(581\) 3.54285 2.13098i 0.146982 0.0884080i
\(582\) 0.238693 5.33230i 0.00989416 0.221031i
\(583\) 16.0327 9.25650i 0.664007 0.383365i
\(584\) 35.2594 4.52360i 1.45905 0.187188i
\(585\) 22.3184 + 12.8855i 0.922753 + 0.532752i
\(586\) 4.49653 + 8.66102i 0.185750 + 0.357784i
\(587\) 22.3449 22.3449i 0.922271 0.922271i −0.0749186 0.997190i \(-0.523870\pi\)
0.997190 + 0.0749186i \(0.0238697\pi\)
\(588\) 9.35449 + 10.4160i 0.385773 + 0.429549i
\(589\) 15.5903 + 15.5903i 0.642386 + 0.642386i
\(590\) 66.0094 + 20.8926i 2.71756 + 0.860134i
\(591\) 8.15296 14.1213i 0.335368 0.580874i
\(592\) 0.967299 + 11.6466i 0.0397557 + 0.478673i
\(593\) 13.9250 + 24.1189i 0.571833 + 0.990443i 0.996378 + 0.0850365i \(0.0271007\pi\)
−0.424545 + 0.905407i \(0.639566\pi\)
\(594\) −4.00605 + 3.66276i −0.164370 + 0.150285i
\(595\) −13.8683 23.0566i −0.568544 0.945230i
\(596\) 8.99445 + 10.7672i 0.368427 + 0.441042i
\(597\) 5.52023 + 1.47914i 0.225928 + 0.0605372i
\(598\) −14.3259 + 22.4327i −0.585831 + 0.917341i
\(599\) −27.8898 16.1022i −1.13955 0.657917i −0.193228 0.981154i \(-0.561896\pi\)
−0.946318 + 0.323237i \(0.895229\pi\)
\(600\) −29.2311 + 11.9950i −1.19336 + 0.489694i
\(601\) 0.114559i 0.00467296i 0.999997 + 0.00233648i \(0.000743725\pi\)
−0.999997 + 0.00233648i \(0.999256\pi\)
\(602\) 13.6503 3.26791i 0.556346 0.133190i
\(603\) −0.906667 + 0.906667i −0.0369224 + 0.0369224i
\(604\) 1.71042 + 3.68918i 0.0695959 + 0.150111i
\(605\) 14.4967 3.88439i 0.589376 0.157923i
\(606\) 15.7803 3.48019i 0.641031 0.141373i
\(607\) 9.42723 + 16.3284i 0.382639 + 0.662751i 0.991439 0.130573i \(-0.0416819\pi\)
−0.608799 + 0.793324i \(0.708349\pi\)
\(608\) −5.24901 + 23.0751i −0.212876 + 0.935818i
\(609\) 8.10579 8.40152i 0.328463 0.340447i
\(610\) −36.7813 40.2286i −1.48923 1.62881i
\(611\) −10.3189 + 38.5105i −0.417456 + 1.55797i
\(612\) −2.91015 + 4.13672i −0.117636 + 0.167217i
\(613\) 10.1503 + 37.8813i 0.409965 + 1.53001i 0.794711 + 0.606988i \(0.207622\pi\)
−0.384746 + 0.923022i \(0.625711\pi\)
\(614\) −9.77757 + 5.07621i −0.394590 + 0.204859i
\(615\) 8.37067i 0.337538i
\(616\) −22.5294 + 17.8164i −0.907736 + 0.717844i
\(617\) 16.4957i 0.664093i −0.943263 0.332046i \(-0.892261\pi\)
0.943263 0.332046i \(-0.107739\pi\)
\(618\) 4.12694 + 7.94913i 0.166010 + 0.319761i
\(619\) 0.161946 + 0.604390i 0.00650915 + 0.0242925i 0.969104 0.246652i \(-0.0793306\pi\)
−0.962595 + 0.270945i \(0.912664\pi\)
\(620\) 41.7602 7.26871i 1.67713 0.291918i
\(621\) 0.760107 2.83676i 0.0305020 0.113835i
\(622\) 31.8950 29.1619i 1.27887 1.16928i
\(623\) −1.76015 6.12772i −0.0705188 0.245502i
\(624\) 4.56247 25.2252i 0.182645 1.00981i
\(625\) 21.9685 + 38.0506i 0.878740 + 1.52202i
\(626\) −8.94366 40.5534i −0.357460 1.62084i
\(627\) 15.5096 4.15578i 0.619393 0.165966i
\(628\) −42.3443 15.5177i −1.68972 0.619224i
\(629\) 5.22456 5.22456i 0.208317 0.208317i
\(630\) −14.4241 4.28265i −0.574668 0.170625i
\(631\) 6.27661i 0.249868i 0.992165 + 0.124934i \(0.0398719\pi\)
−0.992165 + 0.124934i \(0.960128\pi\)
\(632\) 9.28828 + 3.88331i 0.369468 + 0.154470i
\(633\) −12.5734 7.25927i −0.499749 0.288530i
\(634\) 16.8951 + 10.7895i 0.670990 + 0.428507i
\(635\) −77.5134 20.7697i −3.07603 0.824219i
\(636\) 0.861907 9.60801i 0.0341769 0.380982i
\(637\) 13.1553 + 42.8880i 0.521233 + 1.69928i
\(638\) 16.1619 + 17.6766i 0.639854 + 0.699823i
\(639\) −1.98140 3.43189i −0.0783831 0.135764i
\(640\) 30.4774 + 33.7790i 1.20472 + 1.33523i
\(641\) −9.59100 + 16.6121i −0.378822 + 0.656138i −0.990891 0.134666i \(-0.957004\pi\)
0.612069 + 0.790804i \(0.290337\pi\)
\(642\) 3.71884 11.7496i 0.146771 0.463718i
\(643\) 14.4014 + 14.4014i 0.567936 + 0.567936i 0.931550 0.363614i \(-0.118457\pi\)
−0.363614 + 0.931550i \(0.618457\pi\)
\(644\) 5.08498 14.6847i 0.200376 0.578660i
\(645\) −10.6668 + 10.6668i −0.420006 + 0.420006i
\(646\) 13.2785 6.89378i 0.522435 0.271232i
\(647\) 35.0536 + 20.2382i 1.37810 + 0.795645i 0.991930 0.126784i \(-0.0404654\pi\)
0.386167 + 0.922429i \(0.373799\pi\)
\(648\) 0.359923 + 2.80543i 0.0141391 + 0.110208i
\(649\) −40.4685 + 23.3645i −1.58853 + 0.917136i
\(650\) −101.143 4.52756i −3.96717 0.177585i
\(651\) 12.1990 + 6.75468i 0.478116 + 0.264737i
\(652\) −4.61042 + 3.85134i −0.180558 + 0.150830i
\(653\) 11.2852 42.1170i 0.441625 1.64817i −0.283073 0.959098i \(-0.591354\pi\)
0.724698 0.689067i \(-0.241979\pi\)
\(654\) −1.22743 5.56557i −0.0479964 0.217631i
\(655\) 15.1956 26.3196i 0.593742 1.02839i
\(656\) −7.83661 + 2.81328i −0.305968 + 0.109840i
\(657\) −12.5683 −0.490335
\(658\) 0.624239 23.2691i 0.0243354 0.907123i
\(659\) 29.8986 + 29.8986i 1.16468 + 1.16468i 0.983438 + 0.181246i \(0.0580129\pi\)
0.181246 + 0.983438i \(0.441987\pi\)
\(660\) 10.6219 28.9847i 0.413456 1.12823i
\(661\) 11.4172 + 42.6096i 0.444078 + 1.65732i 0.718360 + 0.695671i \(0.244893\pi\)
−0.274282 + 0.961649i \(0.588440\pi\)
\(662\) 10.4086 16.2987i 0.404543 0.633466i
\(663\) −14.0355 + 8.10338i −0.545092 + 0.314709i
\(664\) 4.38007 + 0.591367i 0.169980 + 0.0229495i
\(665\) 32.0309 + 30.9034i 1.24210 + 1.19838i
\(666\) 0.184773 4.12774i 0.00715981 0.159947i
\(667\) −12.5171 3.35395i −0.484665 0.129865i
\(668\) 1.81947 2.58634i 0.0703975 0.100068i
\(669\) 5.51612 1.47804i 0.213266 0.0571444i
\(670\) 2.20040 6.95209i 0.0850089 0.268583i
\(671\) 36.7888 1.42021
\(672\) 0.838342 + 14.9431i 0.0323397 + 0.576444i
\(673\) 2.70465 0.104257 0.0521284 0.998640i \(-0.483400\pi\)
0.0521284 + 0.998640i \(0.483400\pi\)
\(674\) −3.18509 + 10.0632i −0.122685 + 0.387619i
\(675\) 10.7904 2.89128i 0.415323 0.111285i
\(676\) 32.3021 45.9167i 1.24239 1.76603i
\(677\) 44.5491 + 11.9369i 1.71216 + 0.458772i 0.975953 0.217983i \(-0.0699477\pi\)
0.736208 + 0.676755i \(0.236614\pi\)
\(678\) −0.359815 + 8.03808i −0.0138186 + 0.308701i
\(679\) −2.41133 + 9.69029i −0.0925382 + 0.371879i
\(680\) 3.84857 28.5052i 0.147586 1.09312i
\(681\) 10.3900 5.99866i 0.398145 0.229869i
\(682\) −15.3978 + 24.1111i −0.589612 + 0.923262i
\(683\) −4.68057 17.4681i −0.179097 0.668399i −0.995817 0.0913654i \(-0.970877\pi\)
0.816720 0.577034i \(-0.195790\pi\)
\(684\) 2.87888 7.85580i 0.110077 0.300374i
\(685\) −1.56384 1.56384i −0.0597511 0.0597511i
\(686\) −13.2995 22.5637i −0.507779 0.861487i
\(687\) −2.79877 −0.106780
\(688\) 13.5713 + 6.40127i 0.517400 + 0.244046i
\(689\) 15.4553 26.7694i 0.588800 1.01983i
\(690\) 3.59697 + 16.3098i 0.136934 + 0.620905i
\(691\) −0.979749 + 3.65647i −0.0372714 + 0.139099i −0.982054 0.188598i \(-0.939606\pi\)
0.944783 + 0.327697i \(0.106272\pi\)
\(692\) 14.9186 12.4623i 0.567121 0.473747i
\(693\) 8.70217 5.23424i 0.330568 0.198832i
\(694\) 48.9766 + 2.19238i 1.85913 + 0.0832215i
\(695\) 5.35954 3.09433i 0.203299 0.117375i
\(696\) 12.3789 1.58815i 0.469221 0.0601986i
\(697\) 4.55884 + 2.63205i 0.172678 + 0.0996959i
\(698\) −16.4970 + 8.56474i −0.624421 + 0.324180i
\(699\) −13.2899 + 13.2899i −0.502669 + 0.502669i
\(700\) 58.0451 11.1780i 2.19390 0.422488i
\(701\) 2.35208 + 2.35208i 0.0888369 + 0.0888369i 0.750129 0.661292i \(-0.229992\pi\)
−0.661292 + 0.750129i \(0.729992\pi\)
\(702\) −2.73485 + 8.64067i −0.103220 + 0.326121i
\(703\) −6.11119 + 10.5849i −0.230488 + 0.399217i
\(704\) −30.7053 0.202775i −1.15725 0.00764235i
\(705\) 12.5087 + 21.6656i 0.471103 + 0.815975i
\(706\) −4.79349 5.24275i −0.180405 0.197314i
\(707\) −30.2268 + 0.541521i −1.13680 + 0.0203660i
\(708\) −2.17556 + 24.2517i −0.0817624 + 0.911436i
\(709\) −37.5067 10.0499i −1.40859 0.377432i −0.527171 0.849759i \(-0.676747\pi\)
−0.881423 + 0.472327i \(0.843414\pi\)
\(710\) 18.9938 + 12.1298i 0.712823 + 0.455222i
\(711\) −3.08249 1.77968i −0.115603 0.0667432i
\(712\) 2.62903 6.28824i 0.0985272 0.235662i
\(713\) 15.4783i 0.579667i
\(714\) 6.86788 6.50902i 0.257024 0.243594i
\(715\) 69.9440 69.9440i 2.61576 2.61576i
\(716\) 6.13656 + 2.24884i 0.229334 + 0.0840430i
\(717\) −14.5751 + 3.90538i −0.544316 + 0.145849i
\(718\) −2.95227 13.3866i −0.110178 0.499582i
\(719\) 15.0657 + 26.0946i 0.561857 + 0.973164i 0.997335 + 0.0729649i \(0.0232461\pi\)
−0.435478 + 0.900199i \(0.643421\pi\)
\(720\) −9.16805 13.2168i −0.341673 0.492561i
\(721\) −4.62605 16.1050i −0.172283 0.599782i
\(722\) 1.56520 1.43107i 0.0582506 0.0532590i
\(723\) −5.79794 + 21.6382i −0.215628 + 0.804734i
\(724\) −21.8352 + 3.80059i −0.811499 + 0.141248i
\(725\) −12.7577 47.6124i −0.473809 1.76828i
\(726\) 2.43197 + 4.68435i 0.0902589 + 0.173853i
\(727\) 12.8325i 0.475931i 0.971274 + 0.237965i \(0.0764804\pi\)
−0.971274 + 0.237965i \(0.923520\pi\)
\(728\) −17.7033 + 44.5705i −0.656127 + 1.65189i
\(729\) 1.00000i 0.0370370i
\(730\) 63.4361 32.9341i 2.34788 1.21894i
\(731\) −2.45533 9.16342i −0.0908137 0.338921i
\(732\) 11.0298 15.6785i 0.407671 0.579496i
\(733\) −0.425989 + 1.58981i −0.0157343 + 0.0587211i −0.973347 0.229339i \(-0.926344\pi\)
0.957612 + 0.288060i \(0.0930103\pi\)
\(734\) −29.1387 31.8697i −1.07553 1.17633i
\(735\) 24.8665 + 13.1924i 0.917214 + 0.486609i
\(736\) 14.0603 8.84902i 0.518271 0.326179i
\(737\) 2.46074 + 4.26213i 0.0906425 + 0.156997i
\(738\) 2.87470 0.633988i 0.105819 0.0233374i
\(739\) −18.7079 + 5.01277i −0.688182 + 0.184398i −0.585931 0.810361i \(-0.699271\pi\)
−0.102251 + 0.994759i \(0.532604\pi\)
\(740\) 9.88379 + 21.3183i 0.363335 + 0.783675i
\(741\) 18.9571 18.9571i 0.696407 0.696407i
\(742\) −5.13674 + 17.3006i −0.188576 + 0.635127i
\(743\) 29.1865i 1.07075i −0.844615 0.535374i \(-0.820171\pi\)
0.844615 0.535374i \(-0.179829\pi\)
\(744\) 5.65915 + 13.7910i 0.207475 + 0.505604i
\(745\) 24.4297 + 14.1045i 0.895036 + 0.516749i
\(746\) 26.4607 41.4343i 0.968795 1.51702i
\(747\) −1.50939 0.404441i −0.0552258 0.0147977i
\(748\) 12.4457 + 14.8987i 0.455062 + 0.544752i
\(749\) −11.1686 + 20.1705i −0.408091 + 0.737015i
\(750\) −25.9007 + 23.6812i −0.945759 + 0.864715i
\(751\) 3.22740 + 5.59002i 0.117770 + 0.203983i 0.918883 0.394529i \(-0.129092\pi\)
−0.801114 + 0.598512i \(0.795759\pi\)
\(752\) 16.0793 18.9921i 0.586352 0.692572i
\(753\) 8.09748 14.0252i 0.295089 0.511108i
\(754\) 38.1267 + 12.0675i 1.38849 + 0.439471i
\(755\) 5.78141 + 5.78141i 0.210407 + 0.210407i
\(756\) 0.378307 5.27796i 0.0137589 0.191958i
\(757\) 23.4259 23.4259i 0.851430 0.851430i −0.138880 0.990309i \(-0.544350\pi\)
0.990309 + 0.138880i \(0.0443501\pi\)
\(758\) −5.53943 10.6698i −0.201201 0.387545i
\(759\) −9.76207 5.63613i −0.354341 0.204579i
\(760\) 6.05483 + 47.1946i 0.219632 + 1.71193i
\(761\) −28.6262 + 16.5273i −1.03770 + 0.599115i −0.919180 0.393837i \(-0.871148\pi\)
−0.118518 + 0.992952i \(0.537814\pi\)
\(762\) 1.26203 28.1932i 0.0457186 1.02133i
\(763\) 0.190989 + 10.6607i 0.00691428 + 0.385944i
\(764\) −2.01811 + 22.4966i −0.0730126 + 0.813898i
\(765\) −2.63207 + 9.82303i −0.0951628 + 0.355152i
\(766\) 13.7046 3.02241i 0.495166 0.109204i
\(767\) −39.0110 + 67.5690i −1.40861 + 2.43978i
\(768\) −9.29227 + 13.0251i −0.335306 + 0.470004i
\(769\) −21.4351 −0.772971 −0.386486 0.922295i \(-0.626311\pi\)
−0.386486 + 0.922295i \(0.626311\pi\)
\(770\) −30.2068 + 49.2222i −1.08858 + 1.77385i
\(771\) −7.77432 7.77432i −0.279985 0.279985i
\(772\) −25.8332 + 11.9771i −0.929757 + 0.431064i
\(773\) 6.66560 + 24.8764i 0.239745 + 0.894740i 0.975952 + 0.217984i \(0.0699482\pi\)
−0.736207 + 0.676756i \(0.763385\pi\)
\(774\) −4.47116 2.85537i −0.160713 0.102634i
\(775\) 50.9882 29.4380i 1.83155 1.05745i
\(776\) −8.49067 + 6.47069i −0.304797 + 0.232284i
\(777\) −1.86661 + 7.50128i −0.0669644 + 0.269107i
\(778\) 15.6028 + 0.698441i 0.559388 + 0.0250403i
\(779\) −8.41121 2.25378i −0.301363 0.0807499i
\(780\) −8.83845 50.7787i −0.316467 1.81817i
\(781\) −14.6919 + 3.93670i −0.525719 + 0.140866i
\(782\) −10.0137 3.16943i −0.358089 0.113338i
\(783\) −4.41247 −0.157689
\(784\) 3.99338 27.7138i 0.142621 0.989777i
\(785\) −90.6771 −3.23640
\(786\) 10.1897 + 3.22514i 0.363456 + 0.115037i
\(787\) 46.7511 12.5269i 1.66650 0.446537i 0.702335 0.711846i \(-0.252141\pi\)
0.964163 + 0.265310i \(0.0854742\pi\)
\(788\) −32.1288 + 5.59227i −1.14454 + 0.199216i
\(789\) −22.3771 5.99594i −0.796647 0.213461i
\(790\) 20.2219 + 0.905206i 0.719461 + 0.0322058i
\(791\) 3.63491 14.6075i 0.129243 0.519382i
\(792\) 10.7586 + 1.45255i 0.382290 + 0.0516141i
\(793\) 53.1957 30.7126i 1.88904 1.09064i
\(794\) −44.2382 28.2513i −1.56995 1.00260i
\(795\) −5.02006 18.7351i −0.178043 0.664466i
\(796\) −4.80768 10.3696i −0.170404 0.367542i
\(797\) −4.34951 4.34951i −0.154068 0.154068i 0.625864 0.779932i \(-0.284746\pi\)
−0.779932 + 0.625864i \(0.784746\pi\)
\(798\) −8.18703 + 13.3408i −0.289818 + 0.472260i
\(799\) −15.7327 −0.556584
\(800\) 55.8914 + 29.4873i 1.97606 + 1.04253i
\(801\) −1.20486 + 2.08687i −0.0425715 + 0.0737360i
\(802\) −38.3164 + 8.45031i −1.35300 + 0.298391i
\(803\) −12.4855 + 46.5963i −0.440602 + 1.64435i
\(804\) 2.55419 + 0.229129i 0.0900792 + 0.00808075i
\(805\) −0.559692 31.2411i −0.0197266 1.10110i
\(806\) −2.13607 + 47.7188i −0.0752399 + 1.68082i
\(807\) −21.7377 + 12.5503i −0.765203 + 0.441790i
\(808\) −25.5753 19.7591i −0.899736 0.695123i
\(809\) 6.02555 + 3.47885i 0.211847 + 0.122310i 0.602170 0.798368i \(-0.294303\pi\)
−0.390322 + 0.920678i \(0.627636\pi\)
\(810\) 2.62042 + 5.04733i 0.0920720 + 0.177345i
\(811\) −16.3080 + 16.3080i −0.572653 + 0.572653i −0.932869 0.360216i \(-0.882703\pi\)
0.360216 + 0.932869i \(0.382703\pi\)
\(812\) −23.2889 1.66927i −0.817279 0.0585799i
\(813\) −7.18643 7.18643i −0.252039 0.252039i
\(814\) −15.1199 4.78559i −0.529952 0.167735i
\(815\) −6.03941 + 10.4606i −0.211551 + 0.366418i
\(816\) 10.0809 0.837261i 0.352902 0.0293100i
\(817\) 7.84648 + 13.5905i 0.274514 + 0.475471i
\(818\) 0.226780 0.207346i 0.00792916 0.00724970i
\(819\) 8.21341 14.8335i 0.287000 0.518323i
\(820\) −12.8483 + 10.7329i −0.448681 + 0.374808i
\(821\) −34.1696 9.15571i −1.19253 0.319537i −0.392643 0.919691i \(-0.628439\pi\)
−0.799884 + 0.600154i \(0.795106\pi\)
\(822\) 0.418618 0.655505i 0.0146010 0.0228634i
\(823\) −37.7926 21.8196i −1.31737 0.760582i −0.334062 0.942551i \(-0.608420\pi\)
−0.983304 + 0.181969i \(0.941753\pi\)
\(824\) 6.90968 16.5269i 0.240710 0.575741i
\(825\) 42.8772i 1.49279i
\(826\) 12.9657 43.6689i 0.451136 1.51943i
\(827\) −2.43200 + 2.43200i −0.0845689 + 0.0845689i −0.748126 0.663557i \(-0.769046\pi\)
0.663557 + 0.748126i \(0.269046\pi\)
\(828\) −5.32879 + 2.47059i −0.185188 + 0.0858589i
\(829\) −16.2793 + 4.36202i −0.565402 + 0.151499i −0.530187 0.847881i \(-0.677878\pi\)
−0.0352152 + 0.999380i \(0.511212\pi\)
\(830\) 8.67821 1.91389i 0.301225 0.0664322i
\(831\) −11.6321 20.1474i −0.403513 0.698905i
\(832\) −44.5685 + 25.3407i −1.54513 + 0.878530i
\(833\) −15.0038 + 9.39462i −0.519851 + 0.325504i
\(834\) 1.46860 + 1.60624i 0.0508535 + 0.0556197i
\(835\) 1.64561 6.14150i 0.0569487 0.212535i
\(836\) −26.2652 18.4774i −0.908399 0.639053i
\(837\) −1.36408 5.09083i −0.0471497 0.175965i
\(838\) 27.0381 14.0373i 0.934016 0.484912i
\(839\) 30.8652i 1.06558i 0.846246 + 0.532792i \(0.178857\pi\)
−0.846246 + 0.532792i \(0.821143\pi\)
\(840\) 11.9210 + 27.6309i 0.411314 + 0.953357i
\(841\) 9.53008i 0.328623i
\(842\) 0.643920 + 1.24029i 0.0221910 + 0.0427432i
\(843\) −4.57665 17.0803i −0.157628 0.588276i
\(844\) 4.97928 + 28.6070i 0.171394 + 0.984693i
\(845\) 29.2154 109.033i 1.00504 3.75086i
\(846\) −6.49314 + 5.93673i −0.223239 + 0.204109i
\(847\) −2.72609 9.49053i −0.0936696 0.326098i
\(848\) −15.8526 + 10.9964i −0.544381 + 0.377619i
\(849\) −15.3755 26.6312i −0.527686 0.913979i
\(850\) −8.60431 39.0147i −0.295126 1.33819i
\(851\) 8.28809 2.22079i 0.284112 0.0761276i
\(852\) −2.72711 + 7.44165i −0.0934291 + 0.254947i
\(853\) 28.8385 28.8385i 0.987412 0.987412i −0.0125101 0.999922i \(-0.503982\pi\)
0.999922 + 0.0125101i \(0.00398219\pi\)
\(854\) −26.0299 + 24.6698i −0.890725 + 0.844182i
\(855\) 16.8226i 0.575320i
\(856\) −22.8029 + 9.35717i −0.779386 + 0.319822i
\(857\) 47.4775 + 27.4111i 1.62180 + 0.936346i 0.986439 + 0.164130i \(0.0524818\pi\)
0.635360 + 0.772216i \(0.280852\pi\)
\(858\) 29.3181 + 18.7231i 1.00090 + 0.639196i
\(859\) −28.0614 7.51903i −0.957443 0.256546i −0.253925 0.967224i \(-0.581722\pi\)
−0.703518 + 0.710678i \(0.748388\pi\)
\(860\) 30.0497 + 2.69567i 1.02469 + 0.0919217i
\(861\) −5.50643 + 0.0986491i −0.187659 + 0.00336195i
\(862\) −2.89814 3.16976i −0.0987110 0.107962i
\(863\) 4.75785 + 8.24083i 0.161959 + 0.280521i 0.935571 0.353138i \(-0.114885\pi\)
−0.773612 + 0.633659i \(0.781552\pi\)
\(864\) 3.84461 4.14958i 0.130796 0.141171i
\(865\) 19.5426 33.8488i 0.664470 1.15090i
\(866\) −8.86222 + 27.9999i −0.301150 + 0.951474i
\(867\) 7.49861 + 7.49861i 0.254666 + 0.254666i
\(868\) −5.27369 27.3853i −0.179001 0.929517i
\(869\) −9.66028 + 9.66028i −0.327702 + 0.327702i
\(870\) 22.2712 11.5625i 0.755064 0.392006i
\(871\) 7.11635 + 4.10863i 0.241128 + 0.139216i
\(872\) −6.96886 + 9.02017i −0.235995 + 0.305462i
\(873\) 3.26862 1.88714i 0.110626 0.0638700i
\(874\) 17.3573 + 0.776977i 0.587119 + 0.0262817i
\(875\) 56.2629 33.8414i 1.90203 1.14405i
\(876\) 16.1150 + 19.2912i 0.544476 + 0.651790i
\(877\) −9.58952 + 35.7886i −0.323815 + 1.20849i 0.591683 + 0.806171i \(0.298464\pi\)
−0.915498 + 0.402323i \(0.868203\pi\)
\(878\) −11.1990 50.7798i −0.377947 1.71373i
\(879\) −3.45022 + 5.97596i −0.116373 + 0.201564i
\(880\) −58.1084 + 20.8605i −1.95883 + 0.703206i
\(881\) 30.0725 1.01317 0.506583 0.862191i \(-0.330908\pi\)
0.506583 + 0.862191i \(0.330908\pi\)
\(882\) −2.64725 + 9.53898i −0.0891375 + 0.321194i
\(883\) −13.8875 13.8875i −0.467352 0.467352i 0.433704 0.901056i \(-0.357206\pi\)
−0.901056 + 0.433704i \(0.857206\pi\)
\(884\) 30.4343 + 11.1531i 1.02362 + 0.375119i
\(885\) 12.6712 + 47.2897i 0.425939 + 1.58962i
\(886\) 17.9634 28.1285i 0.603491 0.944994i
\(887\) 26.4423 15.2665i 0.887847 0.512599i 0.0146094 0.999893i \(-0.495350\pi\)
0.873238 + 0.487294i \(0.162016\pi\)
\(888\) −6.57265 + 5.00898i −0.220564 + 0.168090i
\(889\) −12.7493 + 51.2350i −0.427598 + 1.71837i
\(890\) 0.612831 13.6904i 0.0205422 0.458902i
\(891\) −3.70746 0.993411i −0.124205 0.0332805i
\(892\) −9.34144 6.57164i −0.312775 0.220035i
\(893\) 25.1385 6.73583i 0.841227 0.225406i
\(894\) −2.99357 + 9.45806i −0.100120 + 0.316325i
\(895\) 13.1410 0.439254
\(896\) 21.8615 20.4469i 0.730342 0.683082i
\(897\) −18.8210 −0.628414
\(898\) −9.04779 + 28.5862i −0.301929 + 0.953933i
\(899\) −22.4632 + 6.01899i −0.749189 + 0.200744i
\(900\) −18.2733 12.8552i −0.609110 0.428505i
\(901\) 11.7820 + 3.15699i 0.392516 + 0.105174i
\(902\) 0.505278 11.2877i 0.0168239 0.375838i
\(903\) 7.14262 + 6.89120i 0.237691 + 0.229325i
\(904\) 12.7991 9.75414i 0.425693 0.324418i
\(905\) −38.5929 + 22.2816i −1.28287 + 0.740667i
\(906\) −1.54761 + 2.42337i −0.0514158 + 0.0805109i
\(907\) −13.6828 51.0650i −0.454331 1.69559i −0.690047 0.723765i \(-0.742410\pi\)
0.235716 0.971822i \(-0.424257\pi\)
\(908\) −22.5295 8.25626i −0.747666 0.273994i
\(909\) 8.07975 + 8.07975i 0.267988 + 0.267988i
\(910\) −2.58590 + 96.3919i −0.0857218 + 3.19536i
\(911\) −32.7905 −1.08640 −0.543199 0.839604i \(-0.682787\pi\)
−0.543199 + 0.839604i \(0.682787\pi\)
\(912\) −15.7493 + 5.65387i −0.521511 + 0.187218i
\(913\) −2.99890 + 5.19424i −0.0992490 + 0.171904i
\(914\) 6.99497 + 31.7174i 0.231373 + 1.04912i
\(915\) 9.97580 37.2302i 0.329790 1.23079i
\(916\) 3.58858 + 4.29587i 0.118570 + 0.141940i
\(917\) −17.4927 9.68587i −0.577661 0.319856i
\(918\) −3.57283 0.159933i −0.117921 0.00527859i
\(919\) −22.8540 + 13.1948i −0.753883 + 0.435255i −0.827095 0.562062i \(-0.810008\pi\)
0.0732120 + 0.997316i \(0.476675\pi\)
\(920\) 20.4222 26.4335i 0.673299 0.871487i
\(921\) −6.74635 3.89501i −0.222300 0.128345i
\(922\) 7.41244 3.84831i 0.244116 0.126737i
\(923\) −17.9577 + 17.9577i −0.591086 + 0.591086i
\(924\) −19.1920 6.64575i −0.631371 0.218629i
\(925\) 23.0787 + 23.0787i 0.758823 + 0.758823i
\(926\) −0.571016 + 1.80411i −0.0187648 + 0.0592866i
\(927\) −3.16663 + 5.48477i −0.104006 + 0.180143i
\(928\) −18.3099 16.9642i −0.601052 0.556878i
\(929\) 5.10708 + 8.84572i 0.167558 + 0.290219i 0.937561 0.347822i \(-0.113079\pi\)
−0.770003 + 0.638040i \(0.779745\pi\)
\(930\) 20.2251 + 22.1206i 0.663206 + 0.725364i
\(931\) 19.9515 21.4349i 0.653885 0.702500i
\(932\) 37.4391 + 3.35855i 1.22636 + 0.110013i
\(933\) 29.5177 + 7.90926i 0.966368 + 0.258937i
\(934\) 0.235597 + 0.150457i 0.00770898 + 0.00492310i
\(935\) 33.8038 + 19.5166i 1.10550 + 0.638261i
\(936\) 16.7693 6.88130i 0.548122 0.224922i
\(937\) 35.6178i 1.16358i 0.813338 + 0.581791i \(0.197648\pi\)
−0.813338 + 0.581791i \(0.802352\pi\)
\(938\) −4.59919 1.36555i −0.150169 0.0445867i
\(939\) 20.7640 20.7640i 0.677606 0.677606i
\(940\) 17.2163 46.9794i 0.561534 1.53230i
\(941\) −32.1629 + 8.61802i −1.04848 + 0.280939i −0.741624 0.670816i \(-0.765944\pi\)
−0.306857 + 0.951756i \(0.599277\pi\)
\(942\) −6.86781 31.1409i −0.223765 1.01462i
\(943\) 3.05660 + 5.29419i 0.0995367 + 0.172403i
\(944\) 40.0139 27.7563i 1.30234 0.903390i
\(945\) −2.93733 10.2259i −0.0955513 0.332649i
\(946\) −15.0279 + 13.7401i −0.488598 + 0.446730i
\(947\) 10.4381 38.9555i 0.339192 1.26588i −0.560060 0.828452i \(-0.689222\pi\)
0.899252 0.437430i \(-0.144111\pi\)
\(948\) 1.22072 + 7.01327i 0.0396470 + 0.227780i
\(949\) 20.8466 + 77.8006i 0.676709 + 2.52551i
\(950\) 30.4522 + 58.6556i 0.987999 + 1.90304i
\(951\) 14.1749i 0.459654i
\(952\) −18.7968 2.19575i −0.609207 0.0711647i
\(953\) 27.8613i 0.902516i −0.892394 0.451258i \(-0.850975\pi\)
0.892394 0.451258i \(-0.149025\pi\)
\(954\) 6.05391 3.14300i 0.196003 0.101759i
\(955\) 11.7542 + 43.8672i 0.380357 + 1.41951i
\(956\) 24.6826 + 17.3640i 0.798291 + 0.561592i
\(957\) −4.38340 + 16.3591i −0.141695 + 0.528814i
\(958\) −14.8547 16.2469i −0.479933 0.524914i
\(959\) −1.01030 + 1.04716i −0.0326243 + 0.0338146i
\(960\) −8.53139 + 31.0187i −0.275349 + 1.00113i
\(961\) 1.61135 + 2.79093i 0.0519789 + 0.0900301i
\(962\) −25.8582 + 5.70277i −0.833702 + 0.183865i
\(963\) 8.41748 2.25546i 0.271249 0.0726811i
\(964\) 40.6470 18.8452i 1.30915 0.606962i
\(965\) −40.4838 + 40.4838i −1.30322 + 1.30322i
\(966\) 10.6866 2.55839i 0.343836 0.0823149i
\(967\) 10.9745i 0.352917i 0.984308 + 0.176459i \(0.0564642\pi\)
−0.984308 + 0.176459i \(0.943536\pi\)
\(968\) 4.07181 9.73914i 0.130873 0.313028i
\(969\) 9.16192 + 5.28964i 0.294323 + 0.169928i
\(970\) −11.5527 + 18.0902i −0.370935 + 0.580840i
\(971\) −6.09982 1.63444i −0.195752 0.0524517i 0.159611 0.987180i \(-0.448976\pi\)
−0.355363 + 0.934728i \(0.615643\pi\)
\(972\) −1.53492 + 1.28220i −0.0492324 + 0.0411266i
\(973\) −2.09869 3.48917i −0.0672810 0.111858i
\(974\) −0.00954573 + 0.00872774i −0.000305865 + 0.000279655i
\(975\) −35.7954 61.9995i −1.14637 1.98557i
\(976\) −38.2076 + 3.17330i −1.22299 + 0.101575i
\(977\) 19.5861 33.9242i 0.626616 1.08533i −0.361610 0.932329i \(-0.617773\pi\)
0.988226 0.153001i \(-0.0488937\pi\)
\(978\) −4.04985 1.28182i −0.129500 0.0409879i
\(979\) 6.54008 + 6.54008i 0.209022 + 0.209022i
\(980\) −11.6346 55.0832i −0.371652 1.75957i
\(981\) 2.84965 2.84965i 0.0909825 0.0909825i
\(982\) 7.95992 + 15.3320i 0.254011 + 0.489265i
\(983\) 9.11870 + 5.26468i 0.290841 + 0.167917i 0.638321 0.769770i \(-0.279629\pi\)
−0.347480 + 0.937687i \(0.612963\pi\)
\(984\) −4.65906 3.59953i −0.148526 0.114749i
\(985\) −56.7865 + 32.7857i −1.80937 + 1.04464i
\(986\) −0.705702 + 15.7650i −0.0224741 + 0.502061i
\(987\) 14.1048 8.48383i 0.448960 0.270043i
\(988\) −53.4044 4.79076i −1.69902 0.152414i
\(989\) 2.85138 10.6415i 0.0906688 0.338380i
\(990\) 21.3159 4.70102i 0.677464 0.149408i
\(991\) 25.5186 44.1996i 0.810626 1.40405i −0.101800 0.994805i \(-0.532460\pi\)
0.912426 0.409241i \(-0.134207\pi\)
\(992\) 13.9119 26.3692i 0.441703 0.837222i
\(993\) 13.6746 0.433949
\(994\) 7.75543 12.6375i 0.245987 0.400838i
\(995\) −16.2505 16.2505i −0.515177 0.515177i
\(996\) 1.31456 + 2.83537i 0.0416535 + 0.0898420i
\(997\) −13.4313 50.1265i −0.425375 1.58752i −0.763103 0.646277i \(-0.776325\pi\)
0.337728 0.941244i \(-0.390342\pi\)
\(998\) 8.17825 + 5.22278i 0.258878 + 0.165324i
\(999\) 2.53025 1.46084i 0.0800535 0.0462189i
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 336.2.bq.b.109.19 yes 120
7.2 even 3 inner 336.2.bq.b.205.3 yes 120
16.5 even 4 inner 336.2.bq.b.277.3 yes 120
112.37 even 12 inner 336.2.bq.b.37.19 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bq.b.37.19 120 112.37 even 12 inner
336.2.bq.b.109.19 yes 120 1.1 even 1 trivial
336.2.bq.b.205.3 yes 120 7.2 even 3 inner
336.2.bq.b.277.3 yes 120 16.5 even 4 inner