Properties

Label 750.2.o.a.469.8
Level $750$
Weight $2$
Character 750.469
Analytic conductor $5.989$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [750,2,Mod(19,750)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(750, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("750.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.o (of order \(50\), degree \(20\), 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: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{50})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label 469.8
Character \(\chi\) \(=\) 750.469
Dual form 750.2.o.a.379.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.43594 - 1.71408i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(1.49962 + 2.06405i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\) \(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.43594 - 1.71408i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(1.49962 + 2.06405i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.54074 - 1.62053i) q^{10} +(-0.289561 - 4.60244i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(2.46349 + 2.03798i) q^{13} +(1.62626 + 1.96581i) q^{14} +(2.02910 + 0.939549i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.389358 - 3.08208i) q^{17} +(0.587785 - 0.809017i) q^{18} +(1.05471 - 2.24137i) q^{19} +(-1.63945 - 1.52059i) q^{20} +(-2.23573 - 1.22910i) q^{21} +(-0.577980 - 4.57518i) q^{22} +(0.146045 + 0.368869i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.876126 + 4.92264i) q^{25} +(2.58660 + 1.87927i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(1.74649 + 1.85982i) q^{28} +(5.99115 - 5.62606i) q^{29} +(2.08409 + 0.810286i) q^{30} +(8.06219 + 1.01849i) q^{31} +(0.951057 - 0.309017i) q^{32} +(2.22163 + 4.04113i) q^{33} +(0.195064 - 3.10045i) q^{34} +(1.38457 - 5.53433i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.74014 - 6.77739i) q^{37} +(0.911892 - 2.30318i) q^{38} +(-3.09677 - 0.795115i) q^{39} +(-1.73170 - 1.41465i) q^{40} +(-2.24812 - 0.890093i) q^{41} +(-2.30849 - 1.08629i) q^{42} +(0.383833 + 0.124715i) q^{43} +(-0.864117 - 4.52986i) q^{44} +(-2.23603 + 0.0138199i) q^{45} +(0.168919 + 0.358970i) q^{46} +(9.21716 + 1.75827i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(0.151678 - 0.466818i) q^{49} +(-0.565302 + 4.96794i) q^{50} +(0.959986 + 2.95453i) q^{51} +(2.69950 + 1.71315i) q^{52} +(-4.36007 + 7.93094i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(-7.47315 + 7.10518i) q^{55} +(1.85982 + 1.74649i) q^{56} +2.47713i q^{57} +(5.62606 - 5.99115i) q^{58} +(-3.29531 - 5.19258i) q^{59} +(2.13086 + 0.677826i) q^{60} +(-9.34956 + 3.70175i) q^{61} +(8.11024 + 0.510253i) q^{62} +(2.54627 + 0.160198i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-0.0441852 - 7.14905i) q^{65} +(2.47099 + 3.89365i) q^{66} +(0.826201 - 0.879815i) q^{67} -3.10658i q^{68} +(-0.289202 - 0.271579i) q^{69} +(1.03434 - 5.61034i) q^{70} +(-1.40168 + 7.34789i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-4.07345 - 2.58509i) q^{73} +(-2.16226 - 6.65475i) q^{74} +(-1.30322 - 4.82718i) q^{75} +(0.765475 - 2.35589i) q^{76} +(9.06544 - 7.49958i) q^{77} +(-3.14058 - 0.599098i) q^{78} +(-2.40112 - 5.10264i) q^{79} +(-1.81711 - 1.30312i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-2.29957 - 0.747176i) q^{82} +(7.44716 + 3.50437i) q^{83} +(-2.37214 - 0.939198i) q^{84} +(-5.84203 + 3.75831i) q^{85} +(0.390906 + 0.100368i) q^{86} +(-3.02549 + 7.64152i) q^{87} +(-1.14684 - 4.46666i) q^{88} +(-9.37710 + 14.7759i) q^{89} +(-2.23075 + 0.154194i) q^{90} +(-0.512186 + 8.14097i) q^{91} +(0.191125 + 0.347656i) q^{92} +(-7.72854 + 2.51116i) q^{93} +(9.30937 + 1.17605i) q^{94} +(-5.35639 + 1.41063i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(2.14846 + 2.28788i) q^{97} +(0.122067 - 0.475420i) q^{98} +(-3.73082 - 2.71060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{49}{50}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.998027 0.0627905i 0.705711 0.0443996i
\(3\) −0.904827 + 0.425779i −0.522402 + 0.245824i
\(4\) 0.992115 0.125333i 0.496057 0.0626666i
\(5\) −1.43594 1.71408i −0.642174 0.766559i
\(6\) −0.876307 + 0.481754i −0.357751 + 0.196675i
\(7\) 1.49962 + 2.06405i 0.566803 + 0.780137i 0.992171 0.124883i \(-0.0398555\pi\)
−0.425369 + 0.905020i \(0.639856\pi\)
\(8\) 0.982287 0.187381i 0.347291 0.0662493i
\(9\) 0.637424 0.770513i 0.212475 0.256838i
\(10\) −1.54074 1.62053i −0.487224 0.512457i
\(11\) −0.289561 4.60244i −0.0873060 1.38769i −0.761035 0.648711i \(-0.775309\pi\)
0.673729 0.738978i \(-0.264691\pi\)
\(12\) −0.844328 + 0.535827i −0.243736 + 0.154680i
\(13\) 2.46349 + 2.03798i 0.683251 + 0.565234i 0.912972 0.408022i \(-0.133781\pi\)
−0.229721 + 0.973256i \(0.573781\pi\)
\(14\) 1.62626 + 1.96581i 0.434637 + 0.525386i
\(15\) 2.02910 + 0.939549i 0.523911 + 0.242590i
\(16\) 0.968583 0.248690i 0.242146 0.0621725i
\(17\) 0.389358 3.08208i 0.0944331 0.747515i −0.871803 0.489857i \(-0.837049\pi\)
0.966236 0.257658i \(-0.0829509\pi\)
\(18\) 0.587785 0.809017i 0.138542 0.190687i
\(19\) 1.05471 2.24137i 0.241967 0.514206i −0.746547 0.665332i \(-0.768290\pi\)
0.988515 + 0.151126i \(0.0482899\pi\)
\(20\) −1.63945 1.52059i −0.366593 0.340014i
\(21\) −2.23573 1.22910i −0.487875 0.268212i
\(22\) −0.577980 4.57518i −0.123226 0.975432i
\(23\) 0.146045 + 0.368869i 0.0304526 + 0.0769144i 0.944207 0.329352i \(-0.106830\pi\)
−0.913755 + 0.406267i \(0.866830\pi\)
\(24\) −0.809017 + 0.587785i −0.165140 + 0.119981i
\(25\) −0.876126 + 4.92264i −0.175225 + 0.984528i
\(26\) 2.58660 + 1.87927i 0.507274 + 0.368556i
\(27\) −0.248690 + 0.968583i −0.0478604 + 0.186404i
\(28\) 1.74649 + 1.85982i 0.330055 + 0.351473i
\(29\) 5.99115 5.62606i 1.11253 1.04473i 0.113842 0.993499i \(-0.463684\pi\)
0.998687 0.0512350i \(-0.0163157\pi\)
\(30\) 2.08409 + 0.810286i 0.380501 + 0.147937i
\(31\) 8.06219 + 1.01849i 1.44801 + 0.182927i 0.809697 0.586848i \(-0.199631\pi\)
0.638316 + 0.769775i \(0.279631\pi\)
\(32\) 0.951057 0.309017i 0.168125 0.0546270i
\(33\) 2.22163 + 4.04113i 0.386736 + 0.703470i
\(34\) 0.195064 3.10045i 0.0334532 0.531723i
\(35\) 1.38457 5.53433i 0.234035 0.935472i
\(36\) 0.535827 0.844328i 0.0893045 0.140721i
\(37\) −1.74014 6.77739i −0.286077 1.11420i −0.935374 0.353661i \(-0.884937\pi\)
0.649297 0.760535i \(-0.275063\pi\)
\(38\) 0.911892 2.30318i 0.147928 0.373625i
\(39\) −3.09677 0.795115i −0.495880 0.127320i
\(40\) −1.73170 1.41465i −0.273805 0.223675i
\(41\) −2.24812 0.890093i −0.351097 0.139009i 0.185955 0.982558i \(-0.440462\pi\)
−0.537052 + 0.843549i \(0.680462\pi\)
\(42\) −2.30849 1.08629i −0.356208 0.167619i
\(43\) 0.383833 + 0.124715i 0.0585340 + 0.0190188i 0.338138 0.941097i \(-0.390203\pi\)
−0.279604 + 0.960116i \(0.590203\pi\)
\(44\) −0.864117 4.52986i −0.130271 0.682902i
\(45\) −2.23603 + 0.0138199i −0.333327 + 0.00206015i
\(46\) 0.168919 + 0.358970i 0.0249057 + 0.0529273i
\(47\) 9.21716 + 1.75827i 1.34446 + 0.256470i 0.808860 0.588002i \(-0.200085\pi\)
0.535601 + 0.844471i \(0.320085\pi\)
\(48\) −0.770513 + 0.637424i −0.111214 + 0.0920042i
\(49\) 0.151678 0.466818i 0.0216683 0.0666882i
\(50\) −0.565302 + 4.96794i −0.0799458 + 0.702573i
\(51\) 0.959986 + 2.95453i 0.134425 + 0.413717i
\(52\) 2.69950 + 1.71315i 0.374353 + 0.237571i
\(53\) −4.36007 + 7.93094i −0.598902 + 1.08940i 0.387001 + 0.922079i \(0.373511\pi\)
−0.985903 + 0.167319i \(0.946489\pi\)
\(54\) −0.187381 + 0.982287i −0.0254994 + 0.133672i
\(55\) −7.47315 + 7.10518i −1.00768 + 0.958063i
\(56\) 1.85982 + 1.74649i 0.248529 + 0.233384i
\(57\) 2.47713i 0.328104i
\(58\) 5.62606 5.99115i 0.738738 0.786676i
\(59\) −3.29531 5.19258i −0.429013 0.676016i 0.559212 0.829025i \(-0.311104\pi\)
−0.988225 + 0.153008i \(0.951104\pi\)
\(60\) 2.13086 + 0.677826i 0.275092 + 0.0875070i
\(61\) −9.34956 + 3.70175i −1.19709 + 0.473961i −0.880246 0.474518i \(-0.842622\pi\)
−0.316842 + 0.948478i \(0.602622\pi\)
\(62\) 8.11024 + 0.510253i 1.03000 + 0.0648022i
\(63\) 2.54627 + 0.160198i 0.320800 + 0.0201830i
\(64\) 0.929776 0.368125i 0.116222 0.0460156i
\(65\) −0.0441852 7.14905i −0.00548050 0.886730i
\(66\) 2.47099 + 3.89365i 0.304158 + 0.479276i
\(67\) 0.826201 0.879815i 0.100937 0.107486i −0.676517 0.736427i \(-0.736511\pi\)
0.777453 + 0.628941i \(0.216511\pi\)
\(68\) 3.10658i 0.376728i
\(69\) −0.289202 0.271579i −0.0348159 0.0326943i
\(70\) 1.03434 5.61034i 0.123627 0.670564i
\(71\) −1.40168 + 7.34789i −0.166349 + 0.872034i 0.797040 + 0.603927i \(0.206398\pi\)
−0.963389 + 0.268107i \(0.913602\pi\)
\(72\) 0.481754 0.876307i 0.0567752 0.103274i
\(73\) −4.07345 2.58509i −0.476761 0.302562i 0.275647 0.961259i \(-0.411108\pi\)
−0.752408 + 0.658697i \(0.771108\pi\)
\(74\) −2.16226 6.65475i −0.251358 0.773600i
\(75\) −1.30322 4.82718i −0.150482 0.557394i
\(76\) 0.765475 2.35589i 0.0878060 0.270239i
\(77\) 9.06544 7.49958i 1.03310 0.854657i
\(78\) −3.14058 0.599098i −0.355601 0.0678345i
\(79\) −2.40112 5.10264i −0.270147 0.574091i 0.723016 0.690832i \(-0.242755\pi\)
−0.993162 + 0.116740i \(0.962755\pi\)
\(80\) −1.81711 1.30312i −0.203159 0.145693i
\(81\) −0.187381 0.982287i −0.0208201 0.109143i
\(82\) −2.29957 0.747176i −0.253945 0.0825118i
\(83\) 7.44716 + 3.50437i 0.817432 + 0.384654i 0.788582 0.614930i \(-0.210816\pi\)
0.0288497 + 0.999584i \(0.490816\pi\)
\(84\) −2.37214 0.939198i −0.258822 0.102475i
\(85\) −5.84203 + 3.75831i −0.633657 + 0.407646i
\(86\) 0.390906 + 0.100368i 0.0421525 + 0.0108229i
\(87\) −3.02549 + 7.64152i −0.324367 + 0.819257i
\(88\) −1.14684 4.46666i −0.122254 0.476148i
\(89\) −9.37710 + 14.7759i −0.993970 + 1.56625i −0.181379 + 0.983413i \(0.558056\pi\)
−0.812592 + 0.582833i \(0.801944\pi\)
\(90\) −2.23075 + 0.154194i −0.235141 + 0.0162535i
\(91\) −0.512186 + 8.14097i −0.0536917 + 0.853406i
\(92\) 0.191125 + 0.347656i 0.0199262 + 0.0362456i
\(93\) −7.72854 + 2.51116i −0.801413 + 0.260395i
\(94\) 9.30937 + 1.17605i 0.960188 + 0.121300i
\(95\) −5.35639 + 1.41063i −0.549555 + 0.144728i
\(96\) −0.728969 + 0.684547i −0.0744000 + 0.0698663i
\(97\) 2.14846 + 2.28788i 0.218143 + 0.232299i 0.828727 0.559652i \(-0.189065\pi\)
−0.610584 + 0.791951i \(0.709065\pi\)
\(98\) 0.122067 0.475420i 0.0123306 0.0480247i
\(99\) −3.73082 2.71060i −0.374961 0.272425i
\(100\) −0.252247 + 4.99363i −0.0252247 + 0.499363i
\(101\) −14.0725 + 10.2243i −1.40027 + 1.01735i −0.405619 + 0.914042i \(0.632944\pi\)
−0.994649 + 0.103312i \(0.967056\pi\)
\(102\) 1.14361 + 2.88843i 0.113234 + 0.285997i
\(103\) 1.58723 + 12.5642i 0.156394 + 1.23799i 0.853527 + 0.521048i \(0.174459\pi\)
−0.697133 + 0.716942i \(0.745541\pi\)
\(104\) 2.80174 + 1.54027i 0.274733 + 0.151036i
\(105\) 1.10360 + 5.59713i 0.107701 + 0.546224i
\(106\) −3.85348 + 8.18907i −0.374283 + 0.795392i
\(107\) 5.73106 7.88813i 0.554043 0.762575i −0.436511 0.899699i \(-0.643786\pi\)
0.990554 + 0.137124i \(0.0437860\pi\)
\(108\) −0.125333 + 0.992115i −0.0120602 + 0.0954663i
\(109\) 3.07718 0.790086i 0.294741 0.0756765i −0.0984241 0.995145i \(-0.531380\pi\)
0.393165 + 0.919468i \(0.371380\pi\)
\(110\) −7.01227 + 7.56041i −0.668594 + 0.720856i
\(111\) 4.46020 + 5.39145i 0.423343 + 0.511734i
\(112\) 1.96581 + 1.62626i 0.185752 + 0.153667i
\(113\) −0.139915 + 0.0887930i −0.0131621 + 0.00835294i −0.542392 0.840126i \(-0.682481\pi\)
0.529229 + 0.848479i \(0.322481\pi\)
\(114\) 0.155540 + 2.47224i 0.0145677 + 0.231547i
\(115\) 0.422556 0.780008i 0.0394036 0.0727361i
\(116\) 5.23877 6.33259i 0.486408 0.587966i
\(117\) 3.14058 0.599098i 0.290347 0.0553866i
\(118\) −3.61485 4.97542i −0.332774 0.458024i
\(119\) 6.94546 3.81830i 0.636690 0.350023i
\(120\) 2.16921 + 0.542691i 0.198021 + 0.0495407i
\(121\) −10.1854 + 1.28671i −0.925943 + 0.116974i
\(122\) −9.09867 + 4.28151i −0.823755 + 0.387630i
\(123\) 2.41314 0.151822i 0.217586 0.0136893i
\(124\) 8.12627 0.729761
\(125\) 9.69586 5.56689i 0.867224 0.497918i
\(126\) 2.55131 0.227288
\(127\) −0.190928 + 0.0120121i −0.0169421 + 0.00106591i −0.0712593 0.997458i \(-0.522702\pi\)
0.0543172 + 0.998524i \(0.482702\pi\)
\(128\) 0.904827 0.425779i 0.0799762 0.0376339i
\(129\) −0.400403 + 0.0505827i −0.0352536 + 0.00445356i
\(130\) −0.492990 7.13217i −0.0432381 0.625532i
\(131\) −11.0792 + 6.09084i −0.967994 + 0.532159i −0.885604 0.464441i \(-0.846255\pi\)
−0.0823896 + 0.996600i \(0.526255\pi\)
\(132\) 2.71060 + 3.73082i 0.235927 + 0.324726i
\(133\) 6.20797 1.18423i 0.538299 0.102686i
\(134\) 0.769327 0.929956i 0.0664597 0.0803360i
\(135\) 2.01733 0.964558i 0.173624 0.0830159i
\(136\) −0.195064 3.10045i −0.0167266 0.265861i
\(137\) −10.9295 + 6.93606i −0.933768 + 0.592587i −0.913337 0.407204i \(-0.866504\pi\)
−0.0204308 + 0.999791i \(0.506504\pi\)
\(138\) −0.305684 0.252884i −0.0260216 0.0215269i
\(139\) −6.03257 7.29212i −0.511676 0.618510i 0.449890 0.893084i \(-0.351463\pi\)
−0.961566 + 0.274574i \(0.911463\pi\)
\(140\) 0.680018 5.66422i 0.0574720 0.478714i
\(141\) −9.08857 + 2.33355i −0.765395 + 0.196520i
\(142\) −0.937541 + 7.42140i −0.0786767 + 0.622790i
\(143\) 8.66636 11.9282i 0.724717 0.997488i
\(144\) 0.425779 0.904827i 0.0354816 0.0754023i
\(145\) −18.2465 2.19058i −1.51529 0.181918i
\(146\) −4.22773 2.32422i −0.349890 0.192353i
\(147\) 0.0615187 + 0.486971i 0.00507398 + 0.0401647i
\(148\) −2.57585 6.50585i −0.211734 0.534778i
\(149\) −5.52669 + 4.01538i −0.452764 + 0.328953i −0.790686 0.612222i \(-0.790276\pi\)
0.337922 + 0.941174i \(0.390276\pi\)
\(150\) −1.60375 4.73582i −0.130945 0.386678i
\(151\) −6.26861 4.55441i −0.510132 0.370633i 0.302741 0.953073i \(-0.402098\pi\)
−0.812874 + 0.582440i \(0.802098\pi\)
\(152\) 0.616037 2.39931i 0.0499672 0.194609i
\(153\) −2.12660 2.26460i −0.171925 0.183082i
\(154\) 8.57665 8.05401i 0.691126 0.649010i
\(155\) −9.83109 15.2817i −0.789652 1.22746i
\(156\) −3.17200 0.400717i −0.253963 0.0320830i
\(157\) −4.94949 + 1.60819i −0.395012 + 0.128347i −0.499786 0.866149i \(-0.666588\pi\)
0.104774 + 0.994496i \(0.466588\pi\)
\(158\) −2.71678 4.94180i −0.216135 0.393148i
\(159\) 0.568281 9.03256i 0.0450676 0.716329i
\(160\) −1.89534 1.18645i −0.149840 0.0937974i
\(161\) −0.542350 + 0.854607i −0.0427432 + 0.0673525i
\(162\) −0.248690 0.968583i −0.0195389 0.0760991i
\(163\) −3.96292 + 10.0092i −0.310400 + 0.783981i 0.687906 + 0.725800i \(0.258530\pi\)
−0.998306 + 0.0581810i \(0.981470\pi\)
\(164\) −2.34195 0.601311i −0.182876 0.0469545i
\(165\) 3.73667 9.61088i 0.290899 0.748206i
\(166\) 7.65250 + 3.02984i 0.593949 + 0.235161i
\(167\) 16.6075 + 7.81490i 1.28513 + 0.604735i 0.942333 0.334676i \(-0.108627\pi\)
0.342794 + 0.939411i \(0.388627\pi\)
\(168\) −2.42644 0.788397i −0.187204 0.0608261i
\(169\) −0.520513 2.72863i −0.0400395 0.209894i
\(170\) −5.59451 + 4.11772i −0.429080 + 0.315815i
\(171\) −1.05471 2.24137i −0.0806557 0.171402i
\(172\) 0.396437 + 0.0756244i 0.0302280 + 0.00576631i
\(173\) 12.3727 10.2356i 0.940680 0.778198i −0.0345474 0.999403i \(-0.510999\pi\)
0.975227 + 0.221205i \(0.0709990\pi\)
\(174\) −2.53971 + 7.81642i −0.192535 + 0.592561i
\(175\) −11.4744 + 5.57372i −0.867386 + 0.421334i
\(176\) −1.42505 4.38584i −0.107417 0.330595i
\(177\) 5.19258 + 3.29531i 0.390298 + 0.247691i
\(178\) −8.43080 + 15.3356i −0.631916 + 1.14945i
\(179\) 2.44081 12.7952i 0.182435 0.956358i −0.766823 0.641859i \(-0.778164\pi\)
0.949258 0.314499i \(-0.101836\pi\)
\(180\) −2.21666 + 0.293959i −0.165220 + 0.0219104i
\(181\) 16.6896 + 15.6726i 1.24053 + 1.16494i 0.979898 + 0.199497i \(0.0639309\pi\)
0.260632 + 0.965438i \(0.416069\pi\)
\(182\) 8.15707i 0.604642i
\(183\) 6.88360 7.33029i 0.508850 0.541871i
\(184\) 0.212578 + 0.334969i 0.0156714 + 0.0246942i
\(185\) −9.11824 + 12.7147i −0.670386 + 0.934803i
\(186\) −7.55562 + 2.99148i −0.554005 + 0.219346i
\(187\) −14.2979 0.899545i −1.04556 0.0657813i
\(188\) 9.36485 + 0.589186i 0.683002 + 0.0429708i
\(189\) −2.37214 + 0.939198i −0.172548 + 0.0683166i
\(190\) −5.25725 + 1.74418i −0.381401 + 0.126536i
\(191\) −10.7613 16.9571i −0.778663 1.22698i −0.969437 0.245342i \(-0.921100\pi\)
0.190774 0.981634i \(-0.438900\pi\)
\(192\) −0.684547 + 0.728969i −0.0494029 + 0.0526088i
\(193\) 2.35157i 0.169270i 0.996412 + 0.0846348i \(0.0269724\pi\)
−0.996412 + 0.0846348i \(0.973028\pi\)
\(194\) 2.28788 + 2.14846i 0.164260 + 0.154250i
\(195\) 3.08390 + 6.44984i 0.220842 + 0.461883i
\(196\) 0.0919744 0.482147i 0.00656960 0.0344391i
\(197\) −3.47871 + 6.32774i −0.247848 + 0.450833i −0.970742 0.240126i \(-0.922811\pi\)
0.722894 + 0.690959i \(0.242811\pi\)
\(198\) −3.89365 2.47099i −0.276710 0.175605i
\(199\) −0.240182 0.739203i −0.0170260 0.0524007i 0.942183 0.335100i \(-0.108770\pi\)
−0.959209 + 0.282699i \(0.908770\pi\)
\(200\) 0.0618033 + 4.99962i 0.00437015 + 0.353526i
\(201\) −0.372962 + 1.14786i −0.0263067 + 0.0809637i
\(202\) −13.4028 + 11.0877i −0.943015 + 0.780130i
\(203\) 20.5969 + 3.92907i 1.44562 + 0.275767i
\(204\) 1.32272 + 2.81092i 0.0926088 + 0.196804i
\(205\) 1.70249 + 5.13158i 0.118907 + 0.358405i
\(206\) 2.37301 + 12.4398i 0.165336 + 0.866720i
\(207\) 0.377311 + 0.122596i 0.0262249 + 0.00852099i
\(208\) 2.89292 + 1.36131i 0.200588 + 0.0943897i
\(209\) −10.6212 4.20523i −0.734684 0.290882i
\(210\) 1.45287 + 5.51679i 0.100258 + 0.380695i
\(211\) 18.8283 + 4.83429i 1.29619 + 0.332806i 0.832913 0.553405i \(-0.186672\pi\)
0.463282 + 0.886211i \(0.346672\pi\)
\(212\) −3.33168 + 8.41487i −0.228821 + 0.577936i
\(213\) −1.86030 7.24537i −0.127465 0.496445i
\(214\) 5.22446 8.23242i 0.357136 0.562757i
\(215\) −0.337392 0.837003i −0.0230099 0.0570831i
\(216\) −0.0627905 + 0.998027i −0.00427235 + 0.0679071i
\(217\) 9.98801 + 18.1681i 0.678030 + 1.23333i
\(218\) 3.02150 0.981745i 0.204642 0.0664922i
\(219\) 4.78645 + 0.604669i 0.323438 + 0.0408597i
\(220\) −6.52371 + 7.98579i −0.439828 + 0.538402i
\(221\) 7.24041 6.79920i 0.487043 0.457363i
\(222\) 4.78993 + 5.10076i 0.321479 + 0.342340i
\(223\) −5.61536 + 21.8704i −0.376033 + 1.46455i 0.445961 + 0.895053i \(0.352862\pi\)
−0.821993 + 0.569497i \(0.807138\pi\)
\(224\) 2.06405 + 1.49962i 0.137910 + 0.100198i
\(225\) 3.23450 + 3.81288i 0.215633 + 0.254192i
\(226\) −0.134064 + 0.0974032i −0.00891780 + 0.00647916i
\(227\) −6.86721 17.3446i −0.455793 1.15120i −0.958080 0.286500i \(-0.907508\pi\)
0.502287 0.864701i \(-0.332492\pi\)
\(228\) 0.310467 + 2.45760i 0.0205612 + 0.162758i
\(229\) 9.42358 + 5.18066i 0.622728 + 0.342348i 0.761682 0.647951i \(-0.224374\pi\)
−0.138954 + 0.990299i \(0.544374\pi\)
\(230\) 0.372745 0.805001i 0.0245781 0.0530802i
\(231\) −5.00949 + 10.6457i −0.329600 + 0.700436i
\(232\) 4.83081 6.64904i 0.317158 0.436531i
\(233\) −0.253980 + 2.01046i −0.0166388 + 0.131710i −0.998246 0.0592020i \(-0.981144\pi\)
0.981607 + 0.190912i \(0.0611444\pi\)
\(234\) 3.09677 0.795115i 0.202442 0.0519783i
\(235\) −10.2215 18.3237i −0.666779 1.19531i
\(236\) −3.92013 4.73862i −0.255179 0.308458i
\(237\) 4.34519 + 3.59466i 0.282251 + 0.233498i
\(238\) 6.69200 4.24688i 0.433778 0.275284i
\(239\) −1.17874 18.7355i −0.0762463 1.21190i −0.831144 0.556058i \(-0.812313\pi\)
0.754898 0.655843i \(-0.227687\pi\)
\(240\) 2.19901 + 0.405414i 0.141945 + 0.0261694i
\(241\) −19.4142 + 23.4678i −1.25058 + 1.51169i −0.475668 + 0.879625i \(0.657794\pi\)
−0.774913 + 0.632068i \(0.782206\pi\)
\(242\) −10.0845 + 1.92372i −0.648255 + 0.123661i
\(243\) 0.587785 + 0.809017i 0.0377064 + 0.0518985i
\(244\) −8.81188 + 4.84437i −0.564123 + 0.310129i
\(245\) −1.01796 + 0.410336i −0.0650353 + 0.0262154i
\(246\) 2.39885 0.303045i 0.152945 0.0193214i
\(247\) 7.16615 3.37213i 0.455971 0.214564i
\(248\) 8.11024 0.510253i 0.515000 0.0324011i
\(249\) −8.23048 −0.521585
\(250\) 9.32718 6.16471i 0.589903 0.389891i
\(251\) 22.3364 1.40986 0.704931 0.709275i \(-0.250978\pi\)
0.704931 + 0.709275i \(0.250978\pi\)
\(252\) 2.54627 0.160198i 0.160400 0.0100915i
\(253\) 1.65541 0.778976i 0.104075 0.0489738i
\(254\) −0.189797 + 0.0239769i −0.0119089 + 0.00150444i
\(255\) 3.68581 5.88804i 0.230815 0.368723i
\(256\) 0.876307 0.481754i 0.0547692 0.0301096i
\(257\) 1.65676 + 2.28034i 0.103346 + 0.142244i 0.857558 0.514388i \(-0.171981\pi\)
−0.754212 + 0.656631i \(0.771981\pi\)
\(258\) −0.396437 + 0.0756244i −0.0246811 + 0.00470817i
\(259\) 11.3793 13.7552i 0.707077 0.854709i
\(260\) −0.939850 7.08714i −0.0582870 0.439526i
\(261\) −0.516054 8.20245i −0.0319430 0.507719i
\(262\) −10.6749 + 6.77449i −0.659497 + 0.418529i
\(263\) −14.4816 11.9802i −0.892975 0.738733i 0.0730102 0.997331i \(-0.476739\pi\)
−0.965985 + 0.258598i \(0.916739\pi\)
\(264\) 2.93951 + 3.55326i 0.180914 + 0.218688i
\(265\) 19.8551 3.91489i 1.21969 0.240490i
\(266\) 6.12136 1.57170i 0.375325 0.0963670i
\(267\) 2.19336 17.3622i 0.134232 1.06255i
\(268\) 0.709416 0.976427i 0.0433345 0.0596448i
\(269\) −11.1739 + 23.7457i −0.681285 + 1.44780i 0.202200 + 0.979344i \(0.435191\pi\)
−0.883485 + 0.468460i \(0.844809\pi\)
\(270\) 1.95279 1.08932i 0.118843 0.0662941i
\(271\) 22.4122 + 12.3212i 1.36144 + 0.748460i 0.984100 0.177613i \(-0.0568376\pi\)
0.377344 + 0.926073i \(0.376838\pi\)
\(272\) −0.389358 3.08208i −0.0236083 0.186879i
\(273\) −3.00282 7.58425i −0.181739 0.459020i
\(274\) −10.4724 + 7.60864i −0.632660 + 0.459655i
\(275\) 22.9099 + 2.60692i 1.38152 + 0.157203i
\(276\) −0.320960 0.233191i −0.0193195 0.0140364i
\(277\) 3.23009 12.5804i 0.194077 0.755881i −0.794765 0.606917i \(-0.792406\pi\)
0.988843 0.148964i \(-0.0475940\pi\)
\(278\) −6.47854 6.89895i −0.388557 0.413771i
\(279\) 5.92380 5.56282i 0.354648 0.333037i
\(280\) 0.323017 5.69574i 0.0193040 0.340386i
\(281\) 0.998720 + 0.126168i 0.0595786 + 0.00752653i 0.155066 0.987904i \(-0.450441\pi\)
−0.0954874 + 0.995431i \(0.530441\pi\)
\(282\) −8.92411 + 2.89962i −0.531423 + 0.172670i
\(283\) −11.4279 20.7873i −0.679318 1.23568i −0.961101 0.276197i \(-0.910926\pi\)
0.281783 0.959478i \(-0.409074\pi\)
\(284\) −0.469697 + 7.46562i −0.0278714 + 0.443003i
\(285\) 4.24599 3.55702i 0.251511 0.210700i
\(286\) 7.90028 12.4488i 0.467153 0.736116i
\(287\) −1.53413 5.97503i −0.0905567 0.352695i
\(288\) 0.368125 0.929776i 0.0216919 0.0547876i
\(289\) 7.11827 + 1.82766i 0.418722 + 0.107509i
\(290\) −18.3480 1.04055i −1.07743 0.0611034i
\(291\) −2.91812 1.15536i −0.171063 0.0677286i
\(292\) −4.36533 2.05417i −0.255462 0.120211i
\(293\) 20.0338 + 6.50937i 1.17039 + 0.380281i 0.828787 0.559564i \(-0.189032\pi\)
0.341599 + 0.939846i \(0.389032\pi\)
\(294\) 0.0919744 + 0.482147i 0.00536406 + 0.0281194i
\(295\) −4.16860 + 13.1047i −0.242705 + 0.762984i
\(296\) −2.97927 6.33128i −0.173167 0.367998i
\(297\) 4.52986 + 0.864117i 0.262849 + 0.0501412i
\(298\) −5.26366 + 4.35448i −0.304916 + 0.252248i
\(299\) −0.391965 + 1.20634i −0.0226679 + 0.0697646i
\(300\) −1.89795 4.62578i −0.109578 0.267069i
\(301\) 0.318186 + 0.979275i 0.0183399 + 0.0564445i
\(302\) −6.54222 4.15182i −0.376462 0.238910i
\(303\) 8.37991 15.2430i 0.481413 0.875687i
\(304\) 0.464168 2.43325i 0.0266218 0.139557i
\(305\) 19.7705 + 10.7104i 1.13206 + 0.613273i
\(306\) −2.26460 2.12660i −0.129459 0.121570i
\(307\) 8.35714i 0.476967i 0.971147 + 0.238484i \(0.0766503\pi\)
−0.971147 + 0.238484i \(0.923350\pi\)
\(308\) 8.05401 8.57665i 0.458920 0.488700i
\(309\) −6.78576 10.6926i −0.386028 0.608283i
\(310\) −10.7712 14.6343i −0.611765 0.831171i
\(311\) −1.21908 + 0.482667i −0.0691275 + 0.0273695i −0.402434 0.915449i \(-0.631836\pi\)
0.333306 + 0.942819i \(0.391836\pi\)
\(312\) −3.19090 0.200755i −0.180649 0.0113655i
\(313\) 6.17937 + 0.388773i 0.349278 + 0.0219747i 0.236461 0.971641i \(-0.424012\pi\)
0.112817 + 0.993616i \(0.464012\pi\)
\(314\) −4.83874 + 1.91579i −0.273066 + 0.108115i
\(315\) −3.38171 4.59454i −0.190538 0.258873i
\(316\) −3.02171 4.76146i −0.169985 0.267853i
\(317\) 11.6286 12.3832i 0.653127 0.695509i −0.314110 0.949387i \(-0.601706\pi\)
0.967236 + 0.253878i \(0.0817060\pi\)
\(318\) 9.05042i 0.507522i
\(319\) −27.6284 25.9448i −1.54690 1.45263i
\(320\) −1.96610 1.06510i −0.109908 0.0595411i
\(321\) −1.82702 + 9.57756i −0.101974 + 0.534568i
\(322\) −0.487619 + 0.886976i −0.0271739 + 0.0494292i
\(323\) −6.49744 4.12340i −0.361527 0.229432i
\(324\) −0.309017 0.951057i −0.0171676 0.0528365i
\(325\) −12.1906 + 10.3414i −0.676212 + 0.573636i
\(326\) −3.32662 + 10.2383i −0.184244 + 0.567046i
\(327\) −2.44792 + 2.02509i −0.135370 + 0.111988i
\(328\) −2.37509 0.453072i −0.131142 0.0250167i
\(329\) 10.1931 + 21.6614i 0.561963 + 1.19423i
\(330\) 3.12583 9.82654i 0.172071 0.540933i
\(331\) 2.82739 + 14.8217i 0.155408 + 0.814675i 0.971552 + 0.236827i \(0.0761075\pi\)
−0.816144 + 0.577848i \(0.803893\pi\)
\(332\) 7.82765 + 2.54336i 0.429598 + 0.139585i
\(333\) −6.33128 2.97927i −0.346952 0.163263i
\(334\) 17.0654 + 6.75668i 0.933779 + 0.369709i
\(335\) −2.69445 0.152808i −0.147213 0.00834878i
\(336\) −2.47115 0.634484i −0.134812 0.0346139i
\(337\) −6.87890 + 17.3741i −0.374717 + 0.946428i 0.612987 + 0.790093i \(0.289968\pi\)
−0.987704 + 0.156335i \(0.950032\pi\)
\(338\) −0.690818 2.69056i −0.0375755 0.146347i
\(339\) 0.0887930 0.139915i 0.00482257 0.00759916i
\(340\) −5.32492 + 4.46088i −0.288784 + 0.241925i
\(341\) 2.35305 37.4007i 0.127425 2.02536i
\(342\) −1.19337 2.17073i −0.0645299 0.117379i
\(343\) 18.1760 5.90575i 0.981414 0.318881i
\(344\) 0.400403 + 0.0505827i 0.0215883 + 0.00272724i
\(345\) −0.0502292 + 0.885688i −0.00270425 + 0.0476838i
\(346\) 11.7056 10.9923i 0.629297 0.590949i
\(347\) 8.94237 + 9.52265i 0.480051 + 0.511203i 0.922714 0.385485i \(-0.125966\pi\)
−0.442663 + 0.896688i \(0.645966\pi\)
\(348\) −2.04390 + 7.96046i −0.109564 + 0.426726i
\(349\) −16.8515 12.2434i −0.902042 0.655372i 0.0369479 0.999317i \(-0.488236\pi\)
−0.938990 + 0.343946i \(0.888236\pi\)
\(350\) −11.1018 + 6.28321i −0.593417 + 0.335852i
\(351\) −2.58660 + 1.87927i −0.138062 + 0.100308i
\(352\) −1.69762 4.28770i −0.0904836 0.228535i
\(353\) 4.01448 + 31.7778i 0.213669 + 1.69136i 0.625596 + 0.780147i \(0.284856\pi\)
−0.411927 + 0.911217i \(0.635144\pi\)
\(354\) 5.38925 + 2.96276i 0.286435 + 0.157469i
\(355\) 14.6076 8.14856i 0.775290 0.432481i
\(356\) −7.45124 + 15.8347i −0.394915 + 0.839237i
\(357\) −4.65869 + 6.41214i −0.246564 + 0.339366i
\(358\) 1.63258 12.9232i 0.0862846 0.683013i
\(359\) 1.86563 0.479013i 0.0984644 0.0252814i −0.199136 0.979972i \(-0.563814\pi\)
0.297601 + 0.954690i \(0.403814\pi\)
\(360\) −2.19383 + 0.432564i −0.115625 + 0.0227981i
\(361\) 8.19971 + 9.91175i 0.431564 + 0.521671i
\(362\) 17.6408 + 14.5937i 0.927179 + 0.767029i
\(363\) 8.66815 5.50097i 0.454960 0.288726i
\(364\) 0.512186 + 8.14097i 0.0268459 + 0.426703i
\(365\) 1.41820 + 10.6943i 0.0742322 + 0.559763i
\(366\) 6.40975 7.74805i 0.335043 0.404997i
\(367\) 25.5869 4.88097i 1.33563 0.254784i 0.530398 0.847749i \(-0.322043\pi\)
0.805229 + 0.592964i \(0.202043\pi\)
\(368\) 0.233191 + 0.320960i 0.0121559 + 0.0167312i
\(369\) −2.11883 + 1.16484i −0.110302 + 0.0606391i
\(370\) −8.30188 + 13.2621i −0.431594 + 0.689466i
\(371\) −22.9083 + 2.89399i −1.18934 + 0.150249i
\(372\) −7.35287 + 3.46000i −0.381229 + 0.179393i
\(373\) −15.6725 + 0.986029i −0.811490 + 0.0510546i −0.463112 0.886300i \(-0.653267\pi\)
−0.348378 + 0.937354i \(0.613267\pi\)
\(374\) −14.3261 −0.740787
\(375\) −6.40281 + 9.16537i −0.330640 + 0.473298i
\(376\) 9.38336 0.483910
\(377\) 26.2250 1.64994i 1.35065 0.0849760i
\(378\) −2.30849 + 1.08629i −0.118736 + 0.0558729i
\(379\) 16.7591 2.11717i 0.860859 0.108752i 0.317506 0.948256i \(-0.397155\pi\)
0.543353 + 0.839504i \(0.317155\pi\)
\(380\) −5.13736 + 2.07084i −0.263541 + 0.106232i
\(381\) 0.167642 0.0921619i 0.00858855 0.00472160i
\(382\) −11.8048 16.2480i −0.603989 0.831319i
\(383\) −18.4003 + 3.51005i −0.940214 + 0.179355i −0.634635 0.772812i \(-0.718850\pi\)
−0.305578 + 0.952167i \(0.598850\pi\)
\(384\) −0.637424 + 0.770513i −0.0325284 + 0.0393201i
\(385\) −25.8723 4.76988i −1.31858 0.243096i
\(386\) 0.147656 + 2.34693i 0.00751550 + 0.119456i
\(387\) 0.340759 0.216252i 0.0173217 0.0109927i
\(388\) 2.41827 + 2.00056i 0.122769 + 0.101563i
\(389\) −22.4573 27.1462i −1.13863 1.37637i −0.915860 0.401499i \(-0.868489\pi\)
−0.222772 0.974871i \(-0.571511\pi\)
\(390\) 3.48280 + 6.24347i 0.176358 + 0.316151i
\(391\) 1.19375 0.306502i 0.0603704 0.0155005i
\(392\) 0.0615187 0.486971i 0.00310716 0.0245957i
\(393\) 7.43140 10.2284i 0.374865 0.515957i
\(394\) −3.07452 + 6.53369i −0.154892 + 0.329162i
\(395\) −5.29844 + 11.4428i −0.266594 + 0.575750i
\(396\) −4.04113 2.22163i −0.203074 0.111641i
\(397\) −2.39997 18.9978i −0.120451 0.953470i −0.930292 0.366820i \(-0.880446\pi\)
0.809841 0.586650i \(-0.199554\pi\)
\(398\) −0.286122 0.722663i −0.0143420 0.0362238i
\(399\) −5.11292 + 3.71475i −0.255966 + 0.185970i
\(400\) 0.375610 + 4.98587i 0.0187805 + 0.249294i
\(401\) −16.8058 12.2102i −0.839244 0.609746i 0.0829154 0.996557i \(-0.473577\pi\)
−0.922159 + 0.386810i \(0.873577\pi\)
\(402\) −0.300151 + 1.16901i −0.0149702 + 0.0583051i
\(403\) 17.7855 + 18.9396i 0.885959 + 0.943451i
\(404\) −12.6801 + 11.9074i −0.630859 + 0.592416i
\(405\) −1.41465 + 1.73170i −0.0702944 + 0.0860487i
\(406\) 20.8030 + 2.62803i 1.03243 + 0.130427i
\(407\) −30.6887 + 9.97136i −1.52118 + 0.494262i
\(408\) 1.49661 + 2.72232i 0.0740931 + 0.134775i
\(409\) 2.45768 39.0637i 0.121525 1.93158i −0.190853 0.981619i \(-0.561125\pi\)
0.312377 0.949958i \(-0.398875\pi\)
\(410\) 2.02134 + 5.01455i 0.0998269 + 0.247651i
\(411\) 6.93606 10.9295i 0.342130 0.539111i
\(412\) 3.14943 + 12.2662i 0.155161 + 0.604313i
\(413\) 5.77603 14.5886i 0.284220 0.717857i
\(414\) 0.384264 + 0.0986623i 0.0188856 + 0.00484899i
\(415\) −4.68695 17.7971i −0.230073 0.873625i
\(416\) 2.97269 + 1.17697i 0.145748 + 0.0577058i
\(417\) 8.56327 + 4.02957i 0.419345 + 0.197329i
\(418\) −10.8643 3.53002i −0.531390 0.172659i
\(419\) 3.53333 + 18.5224i 0.172615 + 0.904877i 0.958195 + 0.286117i \(0.0923647\pi\)
−0.785580 + 0.618760i \(0.787635\pi\)
\(420\) 1.79641 + 5.41468i 0.0876557 + 0.264209i
\(421\) −14.5819 30.9882i −0.710680 1.51027i −0.853820 0.520568i \(-0.825720\pi\)
0.143140 0.989702i \(-0.454280\pi\)
\(422\) 19.0947 + 3.64251i 0.929516 + 0.177315i
\(423\) 7.23001 5.98118i 0.351535 0.290815i
\(424\) −2.79673 + 8.60746i −0.135821 + 0.418015i
\(425\) 14.8309 + 4.61696i 0.719403 + 0.223956i
\(426\) −2.31157 7.11427i −0.111996 0.344687i
\(427\) −21.6614 13.7467i −1.04827 0.665251i
\(428\) 4.69723 8.54423i 0.227049 0.413001i
\(429\) −2.76277 + 14.4829i −0.133388 + 0.699242i
\(430\) −0.389282 0.814166i −0.0187728 0.0392626i
\(431\) −23.4853 22.0542i −1.13125 1.06231i −0.997455 0.0713045i \(-0.977284\pi\)
−0.133794 0.991009i \(-0.542716\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 2.53643 2.70102i 0.121893 0.129803i −0.665127 0.746730i \(-0.731623\pi\)
0.787020 + 0.616927i \(0.211623\pi\)
\(434\) 11.1091 + 17.5051i 0.533253 + 0.840272i
\(435\) 17.4426 5.78687i 0.836309 0.277459i
\(436\) 2.95389 1.16953i 0.141466 0.0560103i
\(437\) 0.980808 + 0.0617072i 0.0469184 + 0.00295186i
\(438\) 4.81497 + 0.302932i 0.230068 + 0.0144747i
\(439\) −3.55587 + 1.40787i −0.169712 + 0.0671939i −0.451444 0.892299i \(-0.649091\pi\)
0.281732 + 0.959493i \(0.409091\pi\)
\(440\) −6.00940 + 8.37966i −0.286487 + 0.399485i
\(441\) −0.263006 0.414431i −0.0125241 0.0197348i
\(442\) 6.79920 7.24041i 0.323405 0.344391i
\(443\) 12.1737i 0.578391i −0.957270 0.289196i \(-0.906612\pi\)
0.957270 0.289196i \(-0.0933878\pi\)
\(444\) 5.10076 + 4.78993i 0.242071 + 0.227320i
\(445\) 38.7921 5.14436i 1.83892 0.243866i
\(446\) −4.23103 + 22.1798i −0.200345 + 1.05025i
\(447\) 3.29104 5.98637i 0.155661 0.283146i
\(448\) 2.15414 + 1.36706i 0.101773 + 0.0645874i
\(449\) 11.4842 + 35.3448i 0.541973 + 1.66802i 0.728080 + 0.685492i \(0.240413\pi\)
−0.186107 + 0.982530i \(0.559587\pi\)
\(450\) 3.46753 + 3.60226i 0.163461 + 0.169812i
\(451\) −3.44564 + 10.6046i −0.162249 + 0.499350i
\(452\) −0.127683 + 0.105629i −0.00600572 + 0.00496837i
\(453\) 7.61119 + 1.45191i 0.357605 + 0.0682167i
\(454\) −7.94274 16.8792i −0.372771 0.792179i
\(455\) 14.6897 10.8121i 0.688665 0.506877i
\(456\) 0.464168 + 2.43325i 0.0217366 + 0.113947i
\(457\) −28.7502 9.34150i −1.34488 0.436977i −0.453911 0.891047i \(-0.649971\pi\)
−0.890966 + 0.454070i \(0.849971\pi\)
\(458\) 9.73029 + 4.57872i 0.454666 + 0.213950i
\(459\) 2.88843 + 1.14361i 0.134820 + 0.0533791i
\(460\) 0.321463 0.826818i 0.0149883 0.0385506i
\(461\) −11.2574 2.89042i −0.524311 0.134620i −0.0227479 0.999741i \(-0.507242\pi\)
−0.501563 + 0.865121i \(0.667242\pi\)
\(462\) −4.33115 + 10.9392i −0.201503 + 0.508940i
\(463\) 5.58424 + 21.7492i 0.259522 + 1.01077i 0.956041 + 0.293232i \(0.0947308\pi\)
−0.696520 + 0.717538i \(0.745269\pi\)
\(464\) 4.40378 6.93925i 0.204440 0.322147i
\(465\) 15.4021 + 9.64144i 0.714254 + 0.447111i
\(466\) −0.127241 + 2.02244i −0.00589433 + 0.0936877i
\(467\) 12.3614 + 22.4854i 0.572019 + 1.04050i 0.991172 + 0.132583i \(0.0423270\pi\)
−0.419153 + 0.907916i \(0.637673\pi\)
\(468\) 3.04073 0.987993i 0.140558 0.0456700i
\(469\) 3.05497 + 0.385932i 0.141065 + 0.0178207i
\(470\) −11.3519 17.6457i −0.523624 0.813937i
\(471\) 3.79370 3.56252i 0.174804 0.164152i
\(472\) −4.20993 4.48313i −0.193778 0.206353i
\(473\) 0.462850 1.80268i 0.0212819 0.0828874i
\(474\) 4.56233 + 3.31473i 0.209555 + 0.152250i
\(475\) 10.1094 + 7.15569i 0.463852 + 0.328325i
\(476\) 6.41214 4.65869i 0.293900 0.213531i
\(477\) 3.33168 + 8.41487i 0.152547 + 0.385290i
\(478\) −2.35283 18.6245i −0.107616 0.851867i
\(479\) 35.3023 + 19.4076i 1.61300 + 0.886755i 0.994923 + 0.100639i \(0.0320888\pi\)
0.618079 + 0.786116i \(0.287911\pi\)
\(480\) 2.22013 + 0.266537i 0.101334 + 0.0121657i
\(481\) 9.52537 20.2424i 0.434319 0.922976i
\(482\) −17.9024 + 24.6405i −0.815431 + 1.12234i
\(483\) 0.126859 1.00419i 0.00577229 0.0456924i
\(484\) −9.94379 + 2.55313i −0.451991 + 0.116051i
\(485\) 0.836531 6.96789i 0.0379849 0.316396i
\(486\) 0.637424 + 0.770513i 0.0289141 + 0.0349512i
\(487\) 15.9957 + 13.2328i 0.724836 + 0.599636i 0.924929 0.380141i \(-0.124124\pi\)
−0.200093 + 0.979777i \(0.564124\pi\)
\(488\) −8.49031 + 5.38811i −0.384338 + 0.243908i
\(489\) −0.675950 10.7439i −0.0305675 0.485857i
\(490\) −0.990189 + 0.473445i −0.0447322 + 0.0213880i
\(491\) −1.25634 + 1.51865i −0.0566978 + 0.0685358i −0.798100 0.602525i \(-0.794161\pi\)
0.741402 + 0.671061i \(0.234161\pi\)
\(492\) 2.37509 0.453072i 0.107077 0.0204261i
\(493\) −15.0073 20.6558i −0.675895 0.930290i
\(494\) 6.94027 3.81545i 0.312258 0.171665i
\(495\) 0.711071 + 10.2872i 0.0319603 + 0.462374i
\(496\) 8.06219 1.01849i 0.362003 0.0457316i
\(497\) −17.2684 + 8.12589i −0.774593 + 0.364496i
\(498\) −8.21424 + 0.516796i −0.368089 + 0.0231582i
\(499\) 7.54980 0.337975 0.168988 0.985618i \(-0.445950\pi\)
0.168988 + 0.985618i \(0.445950\pi\)
\(500\) 8.92169 6.73821i 0.398990 0.301342i
\(501\) −18.3543 −0.820011
\(502\) 22.2924 1.40252i 0.994956 0.0625974i
\(503\) −31.3591 + 14.7565i −1.39823 + 0.657959i −0.969414 0.245431i \(-0.921071\pi\)
−0.428820 + 0.903390i \(0.641071\pi\)
\(504\) 2.53119 0.319763i 0.112748 0.0142434i
\(505\) 37.7326 + 9.43989i 1.67908 + 0.420070i
\(506\) 1.60323 0.881382i 0.0712722 0.0391822i
\(507\) 1.63277 + 2.24731i 0.0725137 + 0.0998066i
\(508\) −0.187916 + 0.0358470i −0.00833745 + 0.00159045i
\(509\) −14.0878 + 17.0293i −0.624432 + 0.754809i −0.983972 0.178321i \(-0.942934\pi\)
0.359540 + 0.933130i \(0.382934\pi\)
\(510\) 3.30883 6.10785i 0.146517 0.270460i
\(511\) −0.772873 12.2845i −0.0341899 0.543432i
\(512\) 0.844328 0.535827i 0.0373144 0.0236804i
\(513\) 1.90866 + 1.57898i 0.0842694 + 0.0697137i
\(514\) 1.79668 + 2.17181i 0.0792481 + 0.0957944i
\(515\) 19.2569 20.7622i 0.848560 0.914890i
\(516\) −0.390906 + 0.100368i −0.0172087 + 0.00441844i
\(517\) 5.42339 42.9306i 0.238521 1.88808i
\(518\) 10.4932 14.4426i 0.461044 0.634572i
\(519\) −6.83706 + 14.5295i −0.300114 + 0.637774i
\(520\) −1.38300 7.01414i −0.0606486 0.307590i
\(521\) −19.7689 10.8680i −0.866090 0.476137i −0.0142253 0.999899i \(-0.504528\pi\)
−0.851865 + 0.523762i \(0.824528\pi\)
\(522\) −1.03007 8.15386i −0.0450850 0.356885i
\(523\) 10.4441 + 26.3788i 0.456688 + 1.15346i 0.957635 + 0.287985i \(0.0929852\pi\)
−0.500947 + 0.865478i \(0.667015\pi\)
\(524\) −10.2284 + 7.43140i −0.446832 + 0.324642i
\(525\) 8.00920 9.92883i 0.349550 0.433330i
\(526\) −15.2053 11.0473i −0.662982 0.481685i
\(527\) 6.27816 24.4518i 0.273481 1.06514i
\(528\) 3.15682 + 3.36167i 0.137383 + 0.146298i
\(529\) 16.6515 15.6368i 0.723980 0.679863i
\(530\) 19.5701 5.15388i 0.850070 0.223870i
\(531\) −6.10146 0.770794i −0.264781 0.0334496i
\(532\) 6.01060 1.95296i 0.260592 0.0846716i
\(533\) −3.72424 6.77436i −0.161315 0.293430i
\(534\) 1.09885 17.4657i 0.0475519 0.755815i
\(535\) −21.7504 + 1.50343i −0.940350 + 0.0649990i
\(536\) 0.646706 1.01905i 0.0279334 0.0440161i
\(537\) 3.23941 + 12.6167i 0.139791 + 0.544450i
\(538\) −9.66084 + 24.4005i −0.416509 + 1.05198i
\(539\) −2.19242 0.562918i −0.0944343 0.0242466i
\(540\) 1.88053 1.20979i 0.0809253 0.0520611i
\(541\) 4.40413 + 1.74372i 0.189348 + 0.0749684i 0.460885 0.887460i \(-0.347532\pi\)
−0.271537 + 0.962428i \(0.587532\pi\)
\(542\) 23.1416 + 10.8896i 0.994018 + 0.467749i
\(543\) −21.7743 7.07490i −0.934425 0.303613i
\(544\) −0.582115 3.05155i −0.0249580 0.130834i
\(545\) −5.77293 4.14001i −0.247285 0.177339i
\(546\) −3.47311 7.38073i −0.148635 0.315866i
\(547\) −1.62875 0.310701i −0.0696405 0.0132846i 0.152443 0.988312i \(-0.451286\pi\)
−0.222084 + 0.975028i \(0.571286\pi\)
\(548\) −9.97397 + 8.25119i −0.426067 + 0.352473i
\(549\) −3.10738 + 9.56354i −0.132620 + 0.408162i
\(550\) 23.0284 + 1.16325i 0.981932 + 0.0496011i
\(551\) −6.29118 19.3623i −0.268013 0.824861i
\(552\) −0.334969 0.212578i −0.0142572 0.00904790i
\(553\) 6.93133 12.6080i 0.294750 0.536148i
\(554\) 2.43379 12.7584i 0.103402 0.542051i
\(555\) 2.83677 15.3870i 0.120414 0.653140i
\(556\) −6.89895 6.47854i −0.292581 0.274751i
\(557\) 1.73647i 0.0735766i −0.999323 0.0367883i \(-0.988287\pi\)
0.999323 0.0367883i \(-0.0117127\pi\)
\(558\) 5.56282 5.92380i 0.235493 0.250774i
\(559\) 0.691404 + 1.08948i 0.0292433 + 0.0460800i
\(560\) −0.0352588 5.70478i −0.00148996 0.241071i
\(561\) 13.3201 5.27380i 0.562375 0.222660i
\(562\) 1.00467 + 0.0632085i 0.0423795 + 0.00266629i
\(563\) 23.1692 + 1.45768i 0.976465 + 0.0614340i 0.542997 0.839735i \(-0.317290\pi\)
0.433468 + 0.901169i \(0.357290\pi\)
\(564\) −8.72443 + 3.45425i −0.367365 + 0.145450i
\(565\) 0.353109 + 0.112324i 0.0148554 + 0.00472551i
\(566\) −12.7106 20.0287i −0.534266 0.841869i
\(567\) 1.74649 1.85982i 0.0733456 0.0781052i
\(568\) 7.48038i 0.313870i
\(569\) −5.29539 4.97270i −0.221994 0.208466i 0.565568 0.824702i \(-0.308657\pi\)
−0.787562 + 0.616235i \(0.788657\pi\)
\(570\) 4.01427 3.81661i 0.168139 0.159860i
\(571\) −6.14310 + 32.2032i −0.257081 + 1.34766i 0.586189 + 0.810174i \(0.300627\pi\)
−0.843270 + 0.537490i \(0.819373\pi\)
\(572\) 7.10302 12.9203i 0.296992 0.540227i
\(573\) 16.9571 + 10.7613i 0.708395 + 0.449561i
\(574\) −1.90627 5.86691i −0.0795664 0.244880i
\(575\) −1.94376 + 0.395754i −0.0810605 + 0.0165041i
\(576\) 0.309017 0.951057i 0.0128757 0.0396274i
\(577\) −3.50107 + 2.89634i −0.145751 + 0.120576i −0.707442 0.706771i \(-0.750151\pi\)
0.561691 + 0.827347i \(0.310151\pi\)
\(578\) 7.21898 + 1.37709i 0.300270 + 0.0572796i
\(579\) −1.00125 2.12776i −0.0416105 0.0884268i
\(580\) −18.3771 + 0.113581i −0.763069 + 0.00471620i
\(581\) 3.93472 + 20.6265i 0.163240 + 0.855732i
\(582\) −2.98490 0.969854i −0.123728 0.0402017i
\(583\) 37.7642 + 17.7705i 1.56403 + 0.735979i
\(584\) −4.48570 1.77601i −0.185619 0.0734920i
\(585\) −5.53660 4.52293i −0.228910 0.187000i
\(586\) 20.4030 + 5.23859i 0.842839 + 0.216404i
\(587\) −2.93018 + 7.40078i −0.120941 + 0.305463i −0.977617 0.210393i \(-0.932526\pi\)
0.856676 + 0.515855i \(0.172526\pi\)
\(588\) 0.122067 + 0.475420i 0.00503397 + 0.0196060i
\(589\) 10.7861 16.9962i 0.444434 0.700315i
\(590\) −3.33753 + 13.3406i −0.137404 + 0.549222i
\(591\) 0.453405 7.20667i 0.0186506 0.296443i
\(592\) −3.37094 6.13171i −0.138545 0.252012i
\(593\) −36.7893 + 11.9536i −1.51075 + 0.490874i −0.943133 0.332416i \(-0.892136\pi\)
−0.567622 + 0.823290i \(0.692136\pi\)
\(594\) 4.57518 + 0.577980i 0.187722 + 0.0237148i
\(595\) −16.5182 6.42220i −0.677179 0.263284i
\(596\) −4.97985 + 4.67639i −0.203983 + 0.191553i
\(597\) 0.532060 + 0.566586i 0.0217758 + 0.0231888i
\(598\) −0.315444 + 1.22857i −0.0128995 + 0.0502402i
\(599\) 10.2116 + 7.41919i 0.417237 + 0.303140i 0.776525 0.630086i \(-0.216981\pi\)
−0.359288 + 0.933227i \(0.616981\pi\)
\(600\) −2.18466 4.49748i −0.0891882 0.183609i
\(601\) 11.2395 8.16595i 0.458467 0.333096i −0.334463 0.942409i \(-0.608555\pi\)
0.792930 + 0.609313i \(0.208555\pi\)
\(602\) 0.379047 + 0.957363i 0.0154488 + 0.0390192i
\(603\) −0.151269 1.19741i −0.00616013 0.0487625i
\(604\) −6.79000 3.73284i −0.276281 0.151887i
\(605\) 16.8312 + 15.6109i 0.684284 + 0.634673i
\(606\) 7.40626 15.7391i 0.300859 0.639357i
\(607\) 11.0500 15.2091i 0.448507 0.617317i −0.523569 0.851983i \(-0.675400\pi\)
0.972076 + 0.234667i \(0.0753998\pi\)
\(608\) 0.310467 2.45760i 0.0125911 0.0996687i
\(609\) −20.3096 + 5.21461i −0.822985 + 0.211307i
\(610\) 20.4040 + 9.44782i 0.826135 + 0.382531i
\(611\) 19.1231 + 23.1159i 0.773638 + 0.935168i
\(612\) −2.39366 1.98021i −0.0967580 0.0800452i
\(613\) 16.4274 10.4251i 0.663495 0.421067i −0.160986 0.986957i \(-0.551467\pi\)
0.824481 + 0.565890i \(0.191467\pi\)
\(614\) 0.524749 + 8.34065i 0.0211772 + 0.336601i
\(615\) −3.72537 3.91831i −0.150222 0.158001i
\(616\) 7.49958 9.06544i 0.302167 0.365257i
\(617\) −35.4705 + 6.76635i −1.42799 + 0.272403i −0.842683 0.538411i \(-0.819025\pi\)
−0.585304 + 0.810814i \(0.699025\pi\)
\(618\) −7.44376 10.2455i −0.299432 0.412133i
\(619\) −0.783807 + 0.430902i −0.0315039 + 0.0173194i −0.497428 0.867505i \(-0.665722\pi\)
0.465924 + 0.884825i \(0.345722\pi\)
\(620\) −11.6689 13.9291i −0.468633 0.559405i
\(621\) −0.393600 + 0.0497232i −0.0157946 + 0.00199532i
\(622\) −1.18636 + 0.558261i −0.0475689 + 0.0223842i
\(623\) −44.5604 + 2.80350i −1.78527 + 0.112320i
\(624\) −3.19721 −0.127991
\(625\) −23.4648 8.62571i −0.938592 0.345029i
\(626\) 6.19158 0.247465
\(627\) 11.4008 0.717281i 0.455306 0.0286454i
\(628\) −4.70890 + 2.21584i −0.187906 + 0.0884217i
\(629\) −21.5660 + 2.72442i −0.859894 + 0.108630i
\(630\) −3.66353 4.37314i −0.145959 0.174230i
\(631\) −12.0851 + 6.64384i −0.481100 + 0.264487i −0.703798 0.710401i \(-0.748514\pi\)
0.222697 + 0.974888i \(0.428514\pi\)
\(632\) −3.31473 4.56233i −0.131853 0.181480i
\(633\) −19.0947 + 3.64251i −0.758947 + 0.144777i
\(634\) 10.8281 13.0889i 0.430039 0.519827i
\(635\) 0.294751 + 0.310016i 0.0116968 + 0.0123026i
\(636\) −0.568281 9.03256i −0.0225338 0.358164i
\(637\) 1.32502 0.840885i 0.0524993 0.0333171i
\(638\) −29.2030 24.1588i −1.15616 0.956457i
\(639\) 4.76818 + 5.76373i 0.188626 + 0.228010i
\(640\) −2.02910 0.939549i −0.0802072 0.0371389i
\(641\) 8.09332 2.07801i 0.319667 0.0820765i −0.0854470 0.996343i \(-0.527232\pi\)
0.405114 + 0.914266i \(0.367232\pi\)
\(642\) −1.22203 + 9.67338i −0.0482298 + 0.381778i
\(643\) −24.8963 + 34.2668i −0.981815 + 1.35135i −0.0459692 + 0.998943i \(0.514638\pi\)
−0.935846 + 0.352410i \(0.885362\pi\)
\(644\) −0.430963 + 0.915843i −0.0169823 + 0.0360893i
\(645\) 0.661660 + 0.613689i 0.0260528 + 0.0241640i
\(646\) −6.74353 3.70729i −0.265321 0.145861i
\(647\) −0.605824 4.79559i −0.0238174 0.188534i 0.975717 0.219033i \(-0.0702903\pi\)
−0.999535 + 0.0304992i \(0.990290\pi\)
\(648\) −0.368125 0.929776i −0.0144613 0.0365251i
\(649\) −22.9444 + 16.6701i −0.900645 + 0.654357i
\(650\) −11.5172 + 11.0864i −0.451741 + 0.434845i
\(651\) −16.7730 12.1863i −0.657387 0.477619i
\(652\) −2.67719 + 10.4270i −0.104847 + 0.408351i
\(653\) 26.0522 + 27.7427i 1.01950 + 1.08566i 0.996302 + 0.0859261i \(0.0273849\pi\)
0.0231983 + 0.999731i \(0.492615\pi\)
\(654\) −2.31593 + 2.17480i −0.0905600 + 0.0850415i
\(655\) 26.3493 + 10.2445i 1.02955 + 0.400286i
\(656\) −2.39885 0.303045i −0.0936593 0.0118319i
\(657\) −4.58836 + 1.49085i −0.179009 + 0.0581636i
\(658\) 11.5331 + 20.9786i 0.449607 + 0.817832i
\(659\) −1.45111 + 23.0648i −0.0565274 + 0.898477i 0.862939 + 0.505308i \(0.168621\pi\)
−0.919466 + 0.393169i \(0.871379\pi\)
\(660\) 2.50264 10.0034i 0.0974153 0.389383i
\(661\) 20.7477 32.6931i 0.806992 1.27162i −0.152056 0.988372i \(-0.548589\pi\)
0.959048 0.283244i \(-0.0914106\pi\)
\(662\) 3.75248 + 14.6149i 0.145844 + 0.568026i
\(663\) −3.65636 + 9.23491i −0.142001 + 0.358654i
\(664\) 7.97190 + 2.04684i 0.309370 + 0.0794326i
\(665\) −10.9442 8.94045i −0.424397 0.346696i
\(666\) −6.50585 2.57585i −0.252097 0.0998121i
\(667\) 2.95026 + 1.38829i 0.114234 + 0.0537547i
\(668\) 17.4560 + 5.67180i 0.675393 + 0.219449i
\(669\) −4.23103 22.1798i −0.163581 0.857522i
\(670\) −2.69873 + 0.0166797i −0.104261 + 0.000644392i
\(671\) 19.7444 + 41.9589i 0.762223 + 1.61981i
\(672\) −2.50611 0.478067i −0.0966755 0.0184418i
\(673\) −19.4813 + 16.1163i −0.750949 + 0.621239i −0.932094 0.362218i \(-0.882020\pi\)
0.181145 + 0.983456i \(0.442020\pi\)
\(674\) −5.77439 + 17.7718i −0.222421 + 0.684542i
\(675\) −4.55010 2.07281i −0.175134 0.0797826i
\(676\) −0.858396 2.64187i −0.0330152 0.101610i
\(677\) 5.37302 + 3.40982i 0.206502 + 0.131050i 0.635056 0.772466i \(-0.280977\pi\)
−0.428554 + 0.903516i \(0.640977\pi\)
\(678\) 0.0798324 0.145215i 0.00306595 0.00557694i
\(679\) −1.50042 + 7.86547i −0.0575808 + 0.301849i
\(680\) −5.03431 + 4.78643i −0.193057 + 0.183551i
\(681\) 13.5986 + 12.7699i 0.521100 + 0.489345i
\(682\) 37.4746i 1.43498i
\(683\) −3.47753 + 3.70319i −0.133064 + 0.141699i −0.792049 0.610457i \(-0.790986\pi\)
0.658986 + 0.752156i \(0.270986\pi\)
\(684\) −1.32731 2.09151i −0.0507511 0.0799709i
\(685\) 27.5831 + 8.77418i 1.05389 + 0.335244i
\(686\) 17.7694 7.03538i 0.678437 0.268612i
\(687\) −10.7325 0.675234i −0.409472 0.0257618i
\(688\) 0.402789 + 0.0253414i 0.0153562 + 0.000966130i
\(689\) −26.9041 + 10.6521i −1.02497 + 0.405813i
\(690\) 0.00548275 + 0.887094i 0.000208725 + 0.0337711i
\(691\) −5.22786 8.23778i −0.198877 0.313380i 0.730223 0.683209i \(-0.239416\pi\)
−0.929100 + 0.369829i \(0.879416\pi\)
\(692\) 10.9923 11.7056i 0.417864 0.444980i
\(693\) 11.7655i 0.446933i
\(694\) 9.52265 + 8.94237i 0.361475 + 0.339448i
\(695\) −3.83683 + 20.8114i −0.145539 + 0.789421i
\(696\) −1.54002 + 8.07309i −0.0583745 + 0.306010i
\(697\) −3.61867 + 6.58233i −0.137067 + 0.249323i
\(698\) −17.5870 11.1611i −0.665679 0.422453i
\(699\) −0.626204 1.92726i −0.0236852 0.0728956i
\(700\) −10.6854 + 6.96790i −0.403869 + 0.263362i
\(701\) −11.9989 + 36.9289i −0.453193 + 1.39479i 0.420050 + 0.907501i \(0.362013\pi\)
−0.873243 + 0.487285i \(0.837987\pi\)
\(702\) −2.46349 + 2.03798i −0.0929786 + 0.0769186i
\(703\) −17.0260 3.24789i −0.642148 0.122496i
\(704\) −1.96350 4.17265i −0.0740022 0.157263i
\(705\) 17.0506 + 12.2277i 0.642161 + 0.460521i
\(706\) 6.00190 + 31.4631i 0.225885 + 1.18413i
\(707\) −42.2069 13.7138i −1.58735 0.515762i
\(708\) 5.56465 + 2.61852i 0.209132 + 0.0984102i
\(709\) −26.2466 10.3918i −0.985711 0.390271i −0.180705 0.983537i \(-0.557838\pi\)
−0.805006 + 0.593266i \(0.797838\pi\)
\(710\) 14.0671 9.04970i 0.527929 0.339629i
\(711\) −5.46218 1.40245i −0.204848 0.0525960i
\(712\) −6.44227 + 16.2713i −0.241434 + 0.609793i
\(713\) 0.801757 + 3.12264i 0.0300260 + 0.116944i
\(714\) −4.24688 + 6.69200i −0.158935 + 0.250442i
\(715\) −32.8903 + 2.27345i −1.23003 + 0.0850221i
\(716\) 0.817904 13.0002i 0.0305665 0.485841i
\(717\) 9.04375 + 16.4505i 0.337745 + 0.614356i
\(718\) 1.83187 0.595212i 0.0683650 0.0222131i
\(719\) −28.4717 3.59682i −1.06182 0.134139i −0.425031 0.905179i \(-0.639737\pi\)
−0.636786 + 0.771040i \(0.719737\pi\)
\(720\) −2.16234 + 0.569463i −0.0805856 + 0.0212226i
\(721\) −23.5529 + 22.1177i −0.877157 + 0.823705i
\(722\) 8.80590 + 9.37733i 0.327722 + 0.348988i
\(723\) 7.57443 29.5005i 0.281696 1.09713i
\(724\) 18.5223 + 13.4573i 0.688377 + 0.500135i
\(725\) 22.4461 + 34.4214i 0.833627 + 1.27838i
\(726\) 8.30564 6.03440i 0.308251 0.223957i
\(727\) −18.9582 47.8830i −0.703121 1.77588i −0.627324 0.778759i \(-0.715850\pi\)
−0.0757975 0.997123i \(-0.524150\pi\)
\(728\) 1.02235 + 8.09275i 0.0378909 + 0.299937i
\(729\) −0.876307 0.481754i −0.0324558 0.0178427i
\(730\) 2.08690 + 10.5841i 0.0772397 + 0.391735i
\(731\) 0.533830 1.13445i 0.0197444 0.0419590i
\(732\) 5.91059 8.13523i 0.218462 0.300687i
\(733\) −1.78044 + 14.0936i −0.0657619 + 0.520559i 0.924483 + 0.381223i \(0.124497\pi\)
−0.990245 + 0.139336i \(0.955503\pi\)
\(734\) 25.2300 6.47795i 0.931255 0.239106i
\(735\) 0.746368 0.804711i 0.0275302 0.0296822i
\(736\) 0.252884 + 0.305684i 0.00932143 + 0.0112677i
\(737\) −4.28853 3.54778i −0.157970 0.130684i
\(738\) −2.04151 + 1.29558i −0.0751491 + 0.0476911i
\(739\) 1.71283 + 27.2247i 0.0630076 + 1.00148i 0.894822 + 0.446423i \(0.147302\pi\)
−0.831814 + 0.555054i \(0.812698\pi\)
\(740\) −7.45276 + 13.7573i −0.273969 + 0.505727i
\(741\) −5.04834 + 6.10240i −0.185455 + 0.224177i
\(742\) −22.6814 + 4.32671i −0.832660 + 0.158838i
\(743\) 7.61654 + 10.4833i 0.279424 + 0.384594i 0.925543 0.378643i \(-0.123609\pi\)
−0.646119 + 0.763237i \(0.723609\pi\)
\(744\) −7.12111 + 3.91486i −0.261072 + 0.143526i
\(745\) 14.8187 + 3.70732i 0.542915 + 0.135826i
\(746\) −15.5796 + 1.96817i −0.570411 + 0.0720597i
\(747\) 7.44716 3.50437i 0.272477 0.128218i
\(748\) −14.2979 + 0.899545i −0.522782 + 0.0328906i
\(749\) 24.8759 0.908946
\(750\) −5.81468 + 9.54932i −0.212322 + 0.348692i
\(751\) −31.1341 −1.13610 −0.568049 0.822995i \(-0.692302\pi\)
−0.568049 + 0.822995i \(0.692302\pi\)
\(752\) 9.36485 0.589186i 0.341501 0.0214854i
\(753\) −20.2106 + 9.51039i −0.736515 + 0.346578i
\(754\) 26.0696 3.29336i 0.949400 0.119937i
\(755\) 1.19476 + 17.2848i 0.0434818 + 0.629057i
\(756\) −2.23573 + 1.22910i −0.0813126 + 0.0447020i
\(757\) −11.4622 15.7764i −0.416601 0.573402i 0.548212 0.836339i \(-0.315309\pi\)
−0.964813 + 0.262938i \(0.915309\pi\)
\(758\) 16.5931 3.16531i 0.602690 0.114969i
\(759\) −1.16619 + 1.40968i −0.0423299 + 0.0511680i
\(760\) −4.99719 + 2.38933i −0.181267 + 0.0866703i
\(761\) −0.787628 12.5190i −0.0285515 0.453813i −0.986166 0.165760i \(-0.946992\pi\)
0.957615 0.288053i \(-0.0930078\pi\)
\(762\) 0.161524 0.102506i 0.00585140 0.00371341i
\(763\) 6.24538 + 5.16663i 0.226098 + 0.187045i
\(764\) −12.8018 15.4747i −0.463152 0.559854i
\(765\) −0.828020 + 6.89700i −0.0299371 + 0.249362i
\(766\) −18.1436 + 4.65849i −0.655556 + 0.168318i
\(767\) 2.46439 19.5077i 0.0889840 0.704381i
\(768\) −0.587785 + 0.809017i −0.0212099 + 0.0291929i
\(769\) −8.54023 + 18.1489i −0.307968 + 0.654466i −0.997566 0.0697264i \(-0.977787\pi\)
0.689598 + 0.724193i \(0.257787\pi\)
\(770\) −26.1208 3.13593i −0.941328 0.113011i
\(771\) −2.47001 1.35790i −0.0889551 0.0489035i
\(772\) 0.294730 + 2.33303i 0.0106076 + 0.0839674i
\(773\) −7.03440 17.7669i −0.253010 0.639029i 0.746647 0.665220i \(-0.231662\pi\)
−0.999657 + 0.0261907i \(0.991662\pi\)
\(774\) 0.326508 0.237222i 0.0117361 0.00852676i
\(775\) −12.0772 + 38.7950i −0.433825 + 1.39356i
\(776\) 2.53911 + 1.84477i 0.0911487 + 0.0662234i
\(777\) −4.43962 + 17.2912i −0.159271 + 0.620318i
\(778\) −24.1175 25.6826i −0.864656 0.920765i
\(779\) −4.36615 + 4.10008i −0.156433 + 0.146901i
\(780\) 3.86796 + 6.01247i 0.138495 + 0.215281i
\(781\) 34.2241 + 4.32351i 1.22463 + 0.154707i
\(782\) 1.17215 0.380854i 0.0419159 0.0136193i
\(783\) 3.95937 + 7.20207i 0.141496 + 0.257381i
\(784\) 0.0308202 0.489872i 0.00110072 0.0174954i
\(785\) 9.86375 + 6.17454i 0.352052 + 0.220379i
\(786\) 6.77449 10.6749i 0.241638 0.380760i
\(787\) −3.89580 15.1731i −0.138870 0.540864i −0.999500 0.0316320i \(-0.989930\pi\)
0.860629 0.509232i \(-0.170070\pi\)
\(788\) −2.65820 + 6.71384i −0.0946944 + 0.239171i
\(789\) 18.2043 + 4.67407i 0.648090 + 0.166401i
\(790\) −4.56949 + 11.7529i −0.162575 + 0.418150i
\(791\) −0.393093 0.155637i −0.0139768 0.00553380i
\(792\) −4.17265 1.96350i −0.148269 0.0697699i
\(793\) −30.5767 9.93496i −1.08581 0.352801i
\(794\) −3.58812 18.8096i −0.127338 0.667527i
\(795\) −16.2985 + 11.9962i −0.578049 + 0.425461i
\(796\) −0.330934 0.703271i −0.0117297 0.0249268i
\(797\) −29.2076 5.57164i −1.03459 0.197358i −0.358000 0.933722i \(-0.616541\pi\)
−0.676586 + 0.736364i \(0.736541\pi\)
\(798\) −4.86958 + 4.02846i −0.172381 + 0.142606i
\(799\) 9.00790 27.7235i 0.318677 0.980786i
\(800\) 0.687934 + 4.95245i 0.0243221 + 0.175095i
\(801\) 5.40787 + 16.6437i 0.191078 + 0.588077i
\(802\) −17.5394 11.1308i −0.619337 0.393043i
\(803\) −10.7182 + 19.4964i −0.378238 + 0.688012i
\(804\) −0.226156 + 1.18555i −0.00797592 + 0.0418112i
\(805\) 2.24365 0.297538i 0.0790782 0.0104868i
\(806\) 18.9396 + 17.7855i 0.667120 + 0.626468i
\(807\) 26.2434i 0.923812i
\(808\) −11.9074 + 12.6801i −0.418901 + 0.446085i
\(809\) 10.3157 + 16.2549i 0.362681 + 0.571493i 0.975846 0.218462i \(-0.0701039\pi\)
−0.613165 + 0.789955i \(0.710104\pi\)
\(810\) −1.30312 + 1.81711i −0.0457870 + 0.0638466i
\(811\) 12.1750 4.82041i 0.427521 0.169268i −0.144503 0.989504i \(-0.546158\pi\)
0.572024 + 0.820237i \(0.306158\pi\)
\(812\) 20.9270 + 1.31661i 0.734392 + 0.0462040i
\(813\) −25.5253 1.60591i −0.895210 0.0563219i
\(814\) −30.0020 + 11.8786i −1.05157 + 0.416346i
\(815\) 22.8471 7.57989i 0.800298 0.265512i
\(816\) 1.66459 + 2.62297i 0.0582723 + 0.0918224i
\(817\) 0.684365 0.728775i 0.0239429 0.0254966i
\(818\) 39.1410i 1.36853i
\(819\) 5.94625 + 5.58390i 0.207779 + 0.195117i
\(820\) 2.33222 + 4.87773i 0.0814446 + 0.170338i
\(821\) 4.31246 22.6067i 0.150506 0.788979i −0.824339 0.566096i \(-0.808453\pi\)
0.974845 0.222883i \(-0.0715468\pi\)
\(822\) 6.23610 11.3434i 0.217509 0.395647i
\(823\) −34.0722 21.6229i −1.18768 0.753725i −0.212940 0.977065i \(-0.568304\pi\)
−0.974741 + 0.223340i \(0.928304\pi\)
\(824\) 3.91342 + 12.0443i 0.136330 + 0.419582i
\(825\) −21.8394 + 7.39574i −0.760352 + 0.257487i
\(826\) 4.84861 14.9225i 0.168705 0.519219i
\(827\) −33.3621 + 27.5996i −1.16011 + 0.959731i −0.999627 0.0273072i \(-0.991307\pi\)
−0.160488 + 0.987038i \(0.551307\pi\)
\(828\) 0.389701 + 0.0743395i 0.0135430 + 0.00258347i
\(829\) 17.3910 + 36.9578i 0.604014 + 1.28360i 0.939822 + 0.341665i \(0.110991\pi\)
−0.335807 + 0.941931i \(0.609009\pi\)
\(830\) −5.79519 17.4677i −0.201154 0.606312i
\(831\) 2.43379 + 12.7584i 0.0844272 + 0.442583i
\(832\) 3.04073 + 0.987993i 0.105418 + 0.0342525i
\(833\) −1.37971 0.649244i −0.0478043 0.0224950i
\(834\) 8.79939 + 3.48392i 0.304698 + 0.120638i
\(835\) −10.4521 39.6883i −0.361710 1.37347i
\(836\) −11.0645 2.84088i −0.382674 0.0982539i
\(837\) −2.99148 + 7.55562i −0.103401 + 0.261160i
\(838\) 4.68939 + 18.2640i 0.161992 + 0.630918i
\(839\) 23.9949 37.8100i 0.828397 1.30534i −0.121440 0.992599i \(-0.538751\pi\)
0.949837 0.312746i \(-0.101249\pi\)
\(840\) 2.13285 + 5.29119i 0.0735904 + 0.182564i
\(841\) 2.42035 38.4704i 0.0834604 1.32657i
\(842\) −16.4989 30.0114i −0.568590 1.03426i
\(843\) −0.957388 + 0.311074i −0.0329742 + 0.0107140i
\(844\) 19.2857 + 2.43636i 0.663843 + 0.0838629i
\(845\) −3.92965 + 4.81036i −0.135184 + 0.165481i
\(846\) 6.84018 6.42335i 0.235170 0.220839i
\(847\) −17.9300 19.0935i −0.616083 0.656062i
\(848\) −2.25075 + 8.76608i −0.0772910 + 0.301029i
\(849\) 19.1911 + 13.9431i 0.658636 + 0.478527i
\(850\) 15.0915 + 3.67662i 0.517634 + 0.126107i
\(851\) 2.24583 1.63169i 0.0769860 0.0559336i
\(852\) −2.75371 6.95508i −0.0943406 0.238277i
\(853\) 5.31947 + 42.1079i 0.182135 + 1.44175i 0.772707 + 0.634763i \(0.218902\pi\)
−0.590572 + 0.806985i \(0.701098\pi\)
\(854\) −22.4818 12.3595i −0.769311 0.422932i
\(855\) −2.32738 + 5.02634i −0.0795948 + 0.171897i
\(856\) 4.15146 8.82231i 0.141894 0.301540i
\(857\) −13.2716 + 18.2667i −0.453348 + 0.623980i −0.973113 0.230330i \(-0.926020\pi\)
0.519765 + 0.854309i \(0.326020\pi\)
\(858\) −1.84792 + 14.6278i −0.0630871 + 0.499386i
\(859\) 21.4732 5.51338i 0.732656 0.188114i 0.136111 0.990694i \(-0.456540\pi\)
0.596545 + 0.802580i \(0.296540\pi\)
\(860\) −0.439636 0.788117i −0.0149914 0.0268746i
\(861\) 3.93216 + 4.75317i 0.134008 + 0.161988i
\(862\) −24.8238 20.5360i −0.845502 0.699460i
\(863\) −24.6996 + 15.6748i −0.840783 + 0.533577i −0.885079 0.465442i \(-0.845896\pi\)
0.0442960 + 0.999018i \(0.485896\pi\)
\(864\) 0.0627905 + 0.998027i 0.00213618 + 0.0339536i
\(865\) −35.3111 6.51004i −1.20061 0.221348i
\(866\) 2.36183 2.85496i 0.0802581 0.0970154i
\(867\) −7.21898 + 1.37709i −0.245169 + 0.0467686i
\(868\) 12.1863 + 16.7730i 0.413631 + 0.569314i
\(869\) −22.7893 + 12.5285i −0.773075 + 0.425001i
\(870\) 17.0448 6.87068i 0.577874 0.232938i
\(871\) 3.82839 0.483638i 0.129720 0.0163874i
\(872\) 2.87463 1.35270i 0.0973473 0.0458081i
\(873\) 3.13232 0.197069i 0.106013 0.00666977i
\(874\) 0.982747 0.0332419
\(875\) 26.0304 + 11.6645i 0.879990 + 0.394333i
\(876\) 4.82449 0.163004
\(877\) 29.0999 1.83081i 0.982635 0.0618222i 0.436663 0.899625i \(-0.356160\pi\)
0.545972 + 0.837803i \(0.316160\pi\)
\(878\) −3.46045 + 1.62837i −0.116785 + 0.0549547i
\(879\) −20.8987 + 2.64011i −0.704894 + 0.0890489i
\(880\) −5.47138 + 8.74046i −0.184440 + 0.294641i
\(881\) 9.39837 5.16680i 0.316639 0.174074i −0.315506 0.948923i \(-0.602174\pi\)
0.632146 + 0.774850i \(0.282174\pi\)
\(882\) −0.288509 0.397099i −0.00971461 0.0133710i
\(883\) −26.3245 + 5.02167i −0.885890 + 0.168993i −0.610194 0.792252i \(-0.708908\pi\)
−0.275696 + 0.961245i \(0.588908\pi\)
\(884\) 6.33115 7.65305i 0.212940 0.257400i
\(885\) −1.80784 13.6324i −0.0607698 0.458247i
\(886\) −0.764395 12.1497i −0.0256803 0.408177i
\(887\) 24.0418 15.2574i 0.807243 0.512292i −0.0670159 0.997752i \(-0.521348\pi\)
0.874259 + 0.485460i \(0.161348\pi\)
\(888\) 5.39145 + 4.46020i 0.180925 + 0.149674i
\(889\) −0.311112 0.376070i −0.0104344 0.0126130i
\(890\) 38.3925 7.56998i 1.28692 0.253746i
\(891\) −4.46666 + 1.14684i −0.149639 + 0.0384207i
\(892\) −2.83000 + 22.4017i −0.0947553 + 0.750065i
\(893\) 13.6624 18.8046i 0.457194 0.629273i
\(894\) 2.90866 6.18121i 0.0972800 0.206731i
\(895\) −25.4368 + 14.1894i −0.850260 + 0.474301i
\(896\) 2.23573 + 1.22910i 0.0746904 + 0.0410614i
\(897\) −0.158976 1.25842i −0.00530805 0.0420175i
\(898\) 13.6809 + 34.5539i 0.456536 + 1.15308i
\(899\) 54.0319 39.2565i 1.80206 1.30928i
\(900\) 3.68687 + 3.37742i 0.122896 + 0.112581i
\(901\) 22.7462 + 16.5261i 0.757786 + 0.550564i
\(902\) −2.77297 + 10.8000i −0.0923298 + 0.359601i
\(903\) −0.704858 0.750598i −0.0234562 0.0249783i
\(904\) −0.120799 + 0.113438i −0.00401771 + 0.00377288i
\(905\) 2.89868 51.1123i 0.0963555 1.69903i
\(906\) 7.68733 + 0.971136i 0.255395 + 0.0322638i
\(907\) −25.4386 + 8.26550i −0.844675 + 0.274452i −0.699214 0.714912i \(-0.746467\pi\)
−0.145461 + 0.989364i \(0.546467\pi\)
\(908\) −8.98692 16.3471i −0.298241 0.542499i
\(909\) −1.09222 + 17.3603i −0.0362265 + 0.575804i
\(910\) 13.9818 11.7131i 0.463494 0.388285i
\(911\) 8.99213 14.1693i 0.297923 0.469451i −0.662083 0.749430i \(-0.730328\pi\)
0.960006 + 0.279979i \(0.0903276\pi\)
\(912\) 0.616037 + 2.39931i 0.0203990 + 0.0794490i
\(913\) 13.9722 35.2898i 0.462414 1.16792i
\(914\) −29.2800 7.51783i −0.968496 0.248668i
\(915\) −22.4492 1.27314i −0.742146 0.0420886i
\(916\) 9.99859 + 3.95872i 0.330363 + 0.130800i
\(917\) −29.1864 13.7341i −0.963819 0.453539i
\(918\) 2.95453 + 0.959986i 0.0975141 + 0.0316843i
\(919\) 0.489920 + 2.56825i 0.0161610 + 0.0847188i 0.989454 0.144848i \(-0.0462692\pi\)
−0.973293 + 0.229566i \(0.926269\pi\)
\(920\) 0.268913 0.845371i 0.00886579 0.0278711i
\(921\) −3.55830 7.56177i −0.117250 0.249169i
\(922\) −11.4167 2.17785i −0.375989 0.0717238i
\(923\) −18.4279 + 15.2449i −0.606561 + 0.501791i
\(924\) −3.63573 + 11.1896i −0.119607 + 0.368111i
\(925\) 34.8873 2.62823i 1.14709 0.0864156i
\(926\) 6.93886 + 21.3556i 0.228025 + 0.701789i
\(927\) 10.6926 + 6.78576i 0.351192 + 0.222873i
\(928\) 3.95937 7.20207i 0.129973 0.236420i
\(929\) 5.50853 28.8767i 0.180729 0.947415i −0.770152 0.637860i \(-0.779820\pi\)
0.950881 0.309555i \(-0.100180\pi\)
\(930\) 15.9771 + 8.65532i 0.523909 + 0.283819i
\(931\) −0.886336 0.832325i −0.0290485 0.0272783i
\(932\) 2.02644i 0.0663782i
\(933\) 0.897544 0.955787i 0.0293843 0.0312911i
\(934\) 13.7489 + 21.6648i 0.449878 + 0.708894i
\(935\) 18.9890 + 25.7993i 0.621008 + 0.843729i
\(936\) 2.97269 1.17697i 0.0971655 0.0384706i
\(937\) 4.81064 + 0.302660i 0.157157 + 0.00988746i 0.141174 0.989985i \(-0.454912\pi\)
0.0159827 + 0.999872i \(0.494912\pi\)
\(938\) 3.07317 + 0.193348i 0.100343 + 0.00631302i
\(939\) −5.75679 + 2.27927i −0.187866 + 0.0743813i
\(940\) −12.4375 16.8981i −0.405666 0.551156i
\(941\) −17.8400 28.1114i −0.581569 0.916405i −0.999967 0.00814175i \(-0.997408\pi\)
0.418398 0.908264i \(-0.362592\pi\)
\(942\) 3.56252 3.79370i 0.116073 0.123605i
\(943\) 0.959254i 0.0312376i
\(944\) −4.48313 4.20993i −0.145913 0.137022i
\(945\) 5.01613 + 2.71740i 0.163175 + 0.0883971i
\(946\) 0.348745 1.82819i 0.0113387 0.0594395i
\(947\) 7.21448 13.1231i 0.234439 0.426443i −0.732751 0.680497i \(-0.761764\pi\)
0.967190 + 0.254054i \(0.0817640\pi\)
\(948\) 4.76146 + 3.02171i 0.154645 + 0.0981407i
\(949\) −4.76656 14.6700i −0.154729 0.476207i
\(950\) 10.5388 + 6.50679i 0.341923 + 0.211108i
\(951\) −5.24936 + 16.1559i −0.170222 + 0.523890i
\(952\) 6.10696 5.05212i 0.197928 0.163740i
\(953\) 5.06336 + 0.965887i 0.164018 + 0.0312881i 0.268736 0.963214i \(-0.413394\pi\)
−0.104718 + 0.994502i \(0.533394\pi\)
\(954\) 3.85348 + 8.18907i 0.124761 + 0.265131i
\(955\) −13.6132 + 42.7953i −0.440513 + 1.38482i
\(956\) −3.51763 18.4401i −0.113768 0.596394i
\(957\) 36.0457 + 11.7120i 1.16519 + 0.378594i
\(958\) 36.4512 + 17.1526i 1.17769 + 0.554177i
\(959\) −30.7064 12.1575i −0.991562 0.392587i
\(960\) 2.23248 + 0.126609i 0.0720530 + 0.00408627i
\(961\) 33.9356 + 8.71317i 1.09470 + 0.281070i
\(962\) 8.23554 20.8006i 0.265524 0.670638i
\(963\) −2.42479 9.44395i −0.0781379 0.304327i
\(964\) −16.3199 + 25.7160i −0.525627 + 0.828256i
\(965\) 4.03077 3.37672i 0.129755 0.108701i
\(966\) 0.0635550 1.01018i 0.00204485 0.0325019i
\(967\) 12.6303 + 22.9745i 0.406165 + 0.738811i 0.997723 0.0674518i \(-0.0214869\pi\)
−0.591558 + 0.806262i \(0.701487\pi\)
\(968\) −9.76386 + 3.17247i −0.313822 + 0.101967i
\(969\) 7.63472 + 0.964490i 0.245263 + 0.0309839i
\(970\) 0.397363 7.00667i 0.0127585 0.224971i
\(971\) 29.8902 28.0688i 0.959222 0.900769i −0.0359066 0.999355i \(-0.511432\pi\)
0.995129 + 0.0985858i \(0.0314319\pi\)
\(972\) 0.684547 + 0.728969i 0.0219569 + 0.0233817i
\(973\) 6.00474 23.3869i 0.192503 0.749751i
\(974\) 16.7951 + 12.2023i 0.538148 + 0.390988i
\(975\) 6.62722 14.5477i 0.212241 0.465898i
\(976\) −8.13523 + 5.91059i −0.260402 + 0.189193i
\(977\) −9.19808 23.2317i −0.294273 0.743248i −0.999416 0.0341826i \(-0.989117\pi\)
0.705143 0.709065i \(-0.250883\pi\)
\(978\) −1.34923 10.6803i −0.0431437 0.341518i
\(979\) 70.7207 + 38.8790i 2.26024 + 1.24258i
\(980\) −0.958507 + 0.534685i −0.0306184 + 0.0170799i
\(981\) 1.35270 2.87463i 0.0431883 0.0917799i
\(982\) −1.15850 + 1.59454i −0.0369693 + 0.0508839i
\(983\) −1.99119 + 15.7619i −0.0635090 + 0.502725i 0.927989 + 0.372607i \(0.121536\pi\)
−0.991498 + 0.130119i \(0.958464\pi\)
\(984\) 2.34195 0.601311i 0.0746586 0.0191691i
\(985\) 15.8415 3.12351i 0.504751 0.0995234i
\(986\) −16.2747 19.6727i −0.518291 0.626507i
\(987\) −18.4460 15.2598i −0.587141 0.485725i
\(988\) 6.68700 4.24370i 0.212742 0.135010i
\(989\) 0.0100536 + 0.159798i 0.000319687 + 0.00508128i
\(990\) 1.35561 + 10.2222i 0.0430840 + 0.324884i
\(991\) 4.20570 5.08382i 0.133598 0.161493i −0.699471 0.714661i \(-0.746581\pi\)
0.833070 + 0.553168i \(0.186581\pi\)
\(992\) 7.98233 1.52271i 0.253439 0.0483461i
\(993\) −8.86908 12.2072i −0.281452 0.387385i
\(994\) −16.7241 + 9.19414i −0.530456 + 0.291621i
\(995\) −0.922164 + 1.47314i −0.0292346 + 0.0467018i
\(996\) −8.16558 + 1.03155i −0.258736 + 0.0326860i
\(997\) −36.4655 + 17.1594i −1.15487 + 0.543443i −0.905241 0.424898i \(-0.860310\pi\)
−0.249633 + 0.968340i \(0.580310\pi\)
\(998\) 7.53490 0.474056i 0.238513 0.0150060i
\(999\) 6.99722 0.221382
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 750.2.o.a.469.8 yes 240
125.4 even 50 inner 750.2.o.a.379.8 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
750.2.o.a.379.8 240 125.4 even 50 inner
750.2.o.a.469.8 yes 240 1.1 even 1 trivial