Properties

Label 225.2.q.a.121.6
Level $225$
Weight $2$
Character 225.121
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
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] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.q (of order \(15\), degree \(8\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 121.6
Character \(\chi\) \(=\) 225.121
Dual form 225.2.q.a.106.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.68376 + 0.357895i) q^{2} +(-0.402409 + 1.68466i) q^{3} +(0.879882 - 0.391749i) q^{4} +(1.96791 - 1.06176i) q^{5} +(0.0746324 - 2.98058i) q^{6} +(-2.11497 - 3.66323i) q^{7} +(1.44394 - 1.04909i) q^{8} +(-2.67613 - 1.35584i) q^{9} +O(q^{10})\) \(q+(-1.68376 + 0.357895i) q^{2} +(-0.402409 + 1.68466i) q^{3} +(0.879882 - 0.391749i) q^{4} +(1.96791 - 1.06176i) q^{5} +(0.0746324 - 2.98058i) q^{6} +(-2.11497 - 3.66323i) q^{7} +(1.44394 - 1.04909i) q^{8} +(-2.67613 - 1.35584i) q^{9} +(-2.93350 + 2.49206i) q^{10} +(5.35421 - 1.13807i) q^{11} +(0.305889 + 1.63994i) q^{12} +(-2.27272 - 0.483081i) q^{13} +(4.87216 + 5.41109i) q^{14} +(0.996792 + 3.74251i) q^{15} +(-3.34474 + 3.71472i) q^{16} +(-1.13466 + 0.824379i) q^{17} +(4.99123 + 1.32515i) q^{18} +(4.74872 - 3.45015i) q^{19} +(1.31559 - 1.70515i) q^{20} +(7.02237 - 2.08888i) q^{21} +(-8.60791 + 3.83249i) q^{22} +(2.33826 + 2.59691i) q^{23} +(1.18629 + 2.85471i) q^{24} +(2.74534 - 4.17889i) q^{25} +3.99961 q^{26} +(3.36103 - 3.96276i) q^{27} +(-3.29599 - 2.39468i) q^{28} +(0.451070 - 4.29164i) q^{29} +(-3.01779 - 5.94476i) q^{30} +(0.330923 + 3.14852i) q^{31} +(2.51747 - 4.36039i) q^{32} +(-0.237324 + 9.47797i) q^{33} +(1.61546 - 1.79415i) q^{34} +(-8.05154 - 4.96333i) q^{35} +(-2.88583 - 0.144610i) q^{36} +(0.930443 + 2.86361i) q^{37} +(-6.76093 + 7.50877i) q^{38} +(1.72839 - 3.63435i) q^{39} +(1.72767 - 3.59763i) q^{40} +(-4.52265 - 0.961319i) q^{41} +(-11.0764 + 6.03045i) q^{42} +(-2.17619 - 3.76927i) q^{43} +(4.26523 - 3.09887i) q^{44} +(-6.70597 + 0.173229i) q^{45} +(-4.86650 - 3.53572i) q^{46} +(0.300021 - 2.85451i) q^{47} +(-4.91206 - 7.12958i) q^{48} +(-5.44619 + 9.43308i) q^{49} +(-3.12690 + 8.01881i) q^{50} +(-0.932197 - 2.24325i) q^{51} +(-2.18897 + 0.465280i) q^{52} +(4.61926 + 3.35609i) q^{53} +(-4.24093 + 7.87525i) q^{54} +(9.32824 - 7.92450i) q^{55} +(-6.89694 - 3.07072i) q^{56} +(3.90138 + 9.38833i) q^{57} +(0.776463 + 7.38755i) q^{58} +(11.3426 + 2.41094i) q^{59} +(2.34318 + 2.90248i) q^{60} +(-10.6036 + 2.25387i) q^{61} +(-1.68404 - 5.18293i) q^{62} +(0.693168 + 12.6709i) q^{63} +(0.411065 - 1.26513i) q^{64} +(-4.98542 + 1.46242i) q^{65} +(-2.99252 - 16.0436i) q^{66} +(-1.17916 - 11.2190i) q^{67} +(-0.675418 + 1.16986i) q^{68} +(-5.31583 + 2.89415i) q^{69} +(15.3332 + 5.47547i) q^{70} +(-5.34318 - 3.88205i) q^{71} +(-5.28658 + 0.849733i) q^{72} +(1.20170 - 3.69845i) q^{73} +(-2.59152 - 4.48864i) q^{74} +(5.93524 + 6.30658i) q^{75} +(2.82672 - 4.89603i) q^{76} +(-15.4930 - 17.2067i) q^{77} +(-1.60948 + 6.73797i) q^{78} +(0.299995 - 2.85427i) q^{79} +(-2.63803 + 10.8615i) q^{80} +(5.32338 + 7.25683i) q^{81} +7.95913 q^{82} +(6.23662 + 2.77672i) q^{83} +(5.36055 - 4.58897i) q^{84} +(-1.35762 + 2.82704i) q^{85} +(5.01319 + 5.56772i) q^{86} +(7.04843 + 2.48690i) q^{87} +(6.53724 - 7.26034i) q^{88} +(-1.41471 + 4.35403i) q^{89} +(11.2293 - 2.69171i) q^{90} +(3.03709 + 9.34720i) q^{91} +(3.07473 + 1.36896i) q^{92} +(-5.43734 - 0.709504i) q^{93} +(0.516451 + 4.91370i) q^{94} +(5.68183 - 11.8316i) q^{95} +(6.33270 + 5.99573i) q^{96} +(-1.44531 + 13.7512i) q^{97} +(5.79405 - 17.8322i) q^{98} +(-15.8716 - 4.21384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.68376 + 0.357895i −1.19060 + 0.253070i −0.760274 0.649603i \(-0.774935\pi\)
−0.430327 + 0.902673i \(0.641602\pi\)
\(3\) −0.402409 + 1.68466i −0.232331 + 0.972637i
\(4\) 0.879882 0.391749i 0.439941 0.195874i
\(5\) 1.96791 1.06176i 0.880076 0.474833i
\(6\) 0.0746324 2.98058i 0.0304686 1.21682i
\(7\) −2.11497 3.66323i −0.799383 1.38457i −0.920018 0.391876i \(-0.871826\pi\)
0.120635 0.992697i \(-0.461507\pi\)
\(8\) 1.44394 1.04909i 0.510511 0.370908i
\(9\) −2.67613 1.35584i −0.892044 0.451948i
\(10\) −2.93350 + 2.49206i −0.927654 + 0.788057i
\(11\) 5.35421 1.13807i 1.61435 0.343142i 0.689743 0.724054i \(-0.257723\pi\)
0.924611 + 0.380912i \(0.124390\pi\)
\(12\) 0.305889 + 1.63994i 0.0883026 + 0.473411i
\(13\) −2.27272 0.483081i −0.630338 0.133983i −0.118346 0.992972i \(-0.537759\pi\)
−0.511992 + 0.858990i \(0.671092\pi\)
\(14\) 4.87216 + 5.41109i 1.30214 + 1.44617i
\(15\) 0.996792 + 3.74251i 0.257371 + 0.966313i
\(16\) −3.34474 + 3.71472i −0.836186 + 0.928679i
\(17\) −1.13466 + 0.824379i −0.275195 + 0.199941i −0.716819 0.697259i \(-0.754403\pi\)
0.441624 + 0.897200i \(0.354403\pi\)
\(18\) 4.99123 + 1.32515i 1.17644 + 0.312340i
\(19\) 4.74872 3.45015i 1.08943 0.791518i 0.110128 0.993917i \(-0.464874\pi\)
0.979303 + 0.202400i \(0.0648740\pi\)
\(20\) 1.31559 1.70515i 0.294174 0.381283i
\(21\) 7.02237 2.08888i 1.53241 0.455830i
\(22\) −8.60791 + 3.83249i −1.83521 + 0.817090i
\(23\) 2.33826 + 2.59691i 0.487562 + 0.541492i 0.935851 0.352396i \(-0.114633\pi\)
−0.448289 + 0.893889i \(0.647966\pi\)
\(24\) 1.18629 + 2.85471i 0.242151 + 0.582715i
\(25\) 2.74534 4.17889i 0.549068 0.835778i
\(26\) 3.99961 0.784388
\(27\) 3.36103 3.96276i 0.646831 0.762634i
\(28\) −3.29599 2.39468i −0.622884 0.452552i
\(29\) 0.451070 4.29164i 0.0837616 0.796938i −0.869325 0.494241i \(-0.835446\pi\)
0.953087 0.302698i \(-0.0978872\pi\)
\(30\) −3.01779 5.94476i −0.550971 1.08536i
\(31\) 0.330923 + 3.14852i 0.0594355 + 0.565491i 0.983200 + 0.182531i \(0.0584289\pi\)
−0.923765 + 0.382961i \(0.874904\pi\)
\(32\) 2.51747 4.36039i 0.445030 0.770815i
\(33\) −0.237324 + 9.47797i −0.0413128 + 1.64990i
\(34\) 1.61546 1.79415i 0.277049 0.307694i
\(35\) −8.05154 4.96333i −1.36096 0.838956i
\(36\) −2.88583 0.144610i −0.480972 0.0241017i
\(37\) 0.930443 + 2.86361i 0.152964 + 0.470775i 0.997949 0.0640154i \(-0.0203907\pi\)
−0.844985 + 0.534790i \(0.820391\pi\)
\(38\) −6.76093 + 7.50877i −1.09677 + 1.21808i
\(39\) 1.72839 3.63435i 0.276764 0.581962i
\(40\) 1.72767 3.59763i 0.273169 0.568835i
\(41\) −4.52265 0.961319i −0.706319 0.150133i −0.159272 0.987235i \(-0.550915\pi\)
−0.547047 + 0.837102i \(0.684248\pi\)
\(42\) −11.0764 + 6.03045i −1.70913 + 0.930518i
\(43\) −2.17619 3.76927i −0.331866 0.574809i 0.651012 0.759068i \(-0.274345\pi\)
−0.982878 + 0.184259i \(0.941011\pi\)
\(44\) 4.26523 3.09887i 0.643008 0.467173i
\(45\) −6.70597 + 0.173229i −0.999667 + 0.0258235i
\(46\) −4.86650 3.53572i −0.717527 0.521314i
\(47\) 0.300021 2.85451i 0.0437626 0.416374i −0.950606 0.310399i \(-0.899537\pi\)
0.994369 0.105974i \(-0.0337961\pi\)
\(48\) −4.91206 7.12958i −0.708995 1.02907i
\(49\) −5.44619 + 9.43308i −0.778027 + 1.34758i
\(50\) −3.12690 + 8.01881i −0.442210 + 1.13403i
\(51\) −0.932197 2.24325i −0.130534 0.314118i
\(52\) −2.18897 + 0.465280i −0.303555 + 0.0645227i
\(53\) 4.61926 + 3.35609i 0.634504 + 0.460994i 0.857958 0.513720i \(-0.171733\pi\)
−0.223454 + 0.974715i \(0.571733\pi\)
\(54\) −4.24093 + 7.87525i −0.577118 + 1.07169i
\(55\) 9.32824 7.92450i 1.25782 1.06854i
\(56\) −6.89694 3.07072i −0.921643 0.410342i
\(57\) 3.90138 + 9.38833i 0.516750 + 1.24351i
\(58\) 0.776463 + 7.38755i 0.101955 + 0.970033i
\(59\) 11.3426 + 2.41094i 1.47668 + 0.313877i 0.874711 0.484645i \(-0.161051\pi\)
0.601966 + 0.798522i \(0.294384\pi\)
\(60\) 2.34318 + 2.90248i 0.302504 + 0.374708i
\(61\) −10.6036 + 2.25387i −1.35766 + 0.288579i −0.828521 0.559958i \(-0.810817\pi\)
−0.529136 + 0.848537i \(0.677484\pi\)
\(62\) −1.68404 5.18293i −0.213873 0.658233i
\(63\) 0.693168 + 12.6709i 0.0873309 + 1.59638i
\(64\) 0.411065 1.26513i 0.0513831 0.158141i
\(65\) −4.98542 + 1.46242i −0.618365 + 0.181390i
\(66\) −2.99252 16.0436i −0.368354 1.97483i
\(67\) −1.17916 11.2190i −0.144058 1.37062i −0.792741 0.609559i \(-0.791347\pi\)
0.648683 0.761059i \(-0.275320\pi\)
\(68\) −0.675418 + 1.16986i −0.0819064 + 0.141866i
\(69\) −5.31583 + 2.89415i −0.639951 + 0.348415i
\(70\) 15.3332 + 5.47547i 1.83267 + 0.654444i
\(71\) −5.34318 3.88205i −0.634119 0.460714i 0.223706 0.974657i \(-0.428184\pi\)
−0.857825 + 0.513942i \(0.828184\pi\)
\(72\) −5.28658 + 0.849733i −0.623030 + 0.100142i
\(73\) 1.20170 3.69845i 0.140648 0.432871i −0.855777 0.517344i \(-0.826921\pi\)
0.996426 + 0.0844731i \(0.0269207\pi\)
\(74\) −2.59152 4.48864i −0.301258 0.521794i
\(75\) 5.93524 + 6.30658i 0.685343 + 0.728221i
\(76\) 2.82672 4.89603i 0.324247 0.561613i
\(77\) −15.4930 17.2067i −1.76559 1.96089i
\(78\) −1.60948 + 6.73797i −0.182238 + 0.762925i
\(79\) 0.299995 2.85427i 0.0337521 0.321130i −0.964599 0.263722i \(-0.915050\pi\)
0.998351 0.0574078i \(-0.0182835\pi\)
\(80\) −2.63803 + 10.8615i −0.294940 + 1.21436i
\(81\) 5.32338 + 7.25683i 0.591486 + 0.806315i
\(82\) 7.95913 0.878938
\(83\) 6.23662 + 2.77672i 0.684558 + 0.304785i 0.719388 0.694608i \(-0.244422\pi\)
−0.0348298 + 0.999393i \(0.511089\pi\)
\(84\) 5.36055 4.58897i 0.584884 0.500698i
\(85\) −1.35762 + 2.82704i −0.147254 + 0.306635i
\(86\) 5.01319 + 5.56772i 0.540587 + 0.600382i
\(87\) 7.04843 + 2.48690i 0.755671 + 0.266623i
\(88\) 6.53724 7.26034i 0.696872 0.773955i
\(89\) −1.41471 + 4.35403i −0.149959 + 0.461526i −0.997615 0.0690197i \(-0.978013\pi\)
0.847656 + 0.530545i \(0.178013\pi\)
\(90\) 11.2293 2.69171i 1.18367 0.283731i
\(91\) 3.03709 + 9.34720i 0.318373 + 0.979852i
\(92\) 3.07473 + 1.36896i 0.320563 + 0.142724i
\(93\) −5.43734 0.709504i −0.563826 0.0735721i
\(94\) 0.516451 + 4.91370i 0.0532679 + 0.506810i
\(95\) 5.68183 11.8316i 0.582943 1.21389i
\(96\) 6.33270 + 5.99573i 0.646328 + 0.611937i
\(97\) −1.44531 + 13.7512i −0.146749 + 1.39623i 0.634942 + 0.772560i \(0.281024\pi\)
−0.781691 + 0.623666i \(0.785643\pi\)
\(98\) 5.79405 17.8322i 0.585287 1.80133i
\(99\) −15.8716 4.21384i −1.59516 0.423506i
\(100\) 0.778500 4.75241i 0.0778500 0.475241i
\(101\) −4.29330 7.43621i −0.427199 0.739930i 0.569424 0.822044i \(-0.307166\pi\)
−0.996623 + 0.0821135i \(0.973833\pi\)
\(102\) 2.37245 + 3.44348i 0.234907 + 0.340955i
\(103\) 0.0160907 0.00716406i 0.00158547 0.000705896i −0.405944 0.913898i \(-0.633057\pi\)
0.407529 + 0.913192i \(0.366390\pi\)
\(104\) −3.78847 + 1.68673i −0.371490 + 0.165398i
\(105\) 11.6015 11.5668i 1.13219 1.12880i
\(106\) −8.97887 3.99765i −0.872105 0.388286i
\(107\) 3.33334 0.322246 0.161123 0.986934i \(-0.448488\pi\)
0.161123 + 0.986934i \(0.448488\pi\)
\(108\) 1.40490 4.80344i 0.135187 0.462211i
\(109\) 0.885216 + 2.72442i 0.0847883 + 0.260952i 0.984458 0.175619i \(-0.0561928\pi\)
−0.899670 + 0.436571i \(0.856193\pi\)
\(110\) −12.8704 + 16.6815i −1.22715 + 1.59052i
\(111\) −5.19862 + 0.415133i −0.493431 + 0.0394027i
\(112\) 20.6819 + 4.39607i 1.95426 + 0.415390i
\(113\) 7.87550 + 1.67399i 0.740864 + 0.157476i 0.562858 0.826554i \(-0.309702\pi\)
0.178007 + 0.984029i \(0.443035\pi\)
\(114\) −9.92904 14.4114i −0.929940 1.34976i
\(115\) 7.35878 + 2.62780i 0.686210 + 0.245044i
\(116\) −1.28436 3.95285i −0.119250 0.367013i
\(117\) 5.42711 + 4.37424i 0.501737 + 0.404398i
\(118\) −19.9611 −1.83757
\(119\) 5.41966 + 2.41299i 0.496820 + 0.221198i
\(120\) 5.36553 + 4.35826i 0.489804 + 0.397852i
\(121\) 17.3233 7.71285i 1.57485 0.701168i
\(122\) 17.0474 7.58998i 1.54340 0.687165i
\(123\) 3.43945 7.23227i 0.310125 0.652111i
\(124\) 1.52460 + 2.64069i 0.136913 + 0.237141i
\(125\) 0.965608 11.1386i 0.0863666 0.996263i
\(126\) −5.70197 21.0867i −0.507972 1.87855i
\(127\) −1.46943 + 4.52243i −0.130391 + 0.401301i −0.994845 0.101411i \(-0.967664\pi\)
0.864454 + 0.502712i \(0.167664\pi\)
\(128\) −1.29194 + 12.2920i −0.114193 + 1.08647i
\(129\) 7.22565 2.14934i 0.636183 0.189239i
\(130\) 7.87087 4.24662i 0.690321 0.372453i
\(131\) 1.92495 + 18.3147i 0.168184 + 1.60016i 0.674807 + 0.737995i \(0.264227\pi\)
−0.506623 + 0.862168i \(0.669106\pi\)
\(132\) 3.50417 + 8.43247i 0.304999 + 0.733952i
\(133\) −22.6821 10.0987i −1.96679 0.875670i
\(134\) 6.00065 + 18.4681i 0.518377 + 1.59540i
\(135\) 2.40671 11.3670i 0.207137 0.978312i
\(136\) −0.773540 + 2.38071i −0.0663305 + 0.204144i
\(137\) −11.0852 + 12.3114i −0.947074 + 1.05183i 0.0515124 + 0.998672i \(0.483596\pi\)
−0.998586 + 0.0531595i \(0.983071\pi\)
\(138\) 7.91481 6.77558i 0.673753 0.576776i
\(139\) −7.23633 8.03676i −0.613778 0.681669i 0.353487 0.935440i \(-0.384996\pi\)
−0.967265 + 0.253770i \(0.918329\pi\)
\(140\) −9.02878 1.21296i −0.763071 0.102514i
\(141\) 4.68814 + 1.65412i 0.394813 + 0.139302i
\(142\) 10.3860 + 4.62415i 0.871575 + 0.388050i
\(143\) −12.7184 −1.06356
\(144\) 13.9876 5.40612i 1.16563 0.450510i
\(145\) −3.66902 8.92450i −0.304696 0.741139i
\(146\) −0.699721 + 6.65740i −0.0579094 + 0.550971i
\(147\) −13.6999 12.9709i −1.12995 1.06982i
\(148\) 1.94050 + 2.15514i 0.159508 + 0.177151i
\(149\) −4.92744 + 8.53458i −0.403672 + 0.699180i −0.994166 0.107862i \(-0.965600\pi\)
0.590494 + 0.807042i \(0.298933\pi\)
\(150\) −12.2506 8.49459i −1.00026 0.693581i
\(151\) 9.07209 + 15.7133i 0.738276 + 1.27873i 0.953271 + 0.302117i \(0.0976934\pi\)
−0.214994 + 0.976615i \(0.568973\pi\)
\(152\) 3.23738 9.96363i 0.262586 0.808157i
\(153\) 4.15423 0.667726i 0.335850 0.0539825i
\(154\) 32.2448 + 23.4272i 2.59836 + 1.88782i
\(155\) 3.99420 + 5.84465i 0.320822 + 0.469453i
\(156\) 0.0970255 3.87489i 0.00776826 0.310240i
\(157\) −1.33107 + 2.30547i −0.106231 + 0.183997i −0.914240 0.405172i \(-0.867212\pi\)
0.808010 + 0.589169i \(0.200545\pi\)
\(158\) 0.516406 + 4.91328i 0.0410831 + 0.390879i
\(159\) −7.51269 + 6.43134i −0.595795 + 0.510038i
\(160\) 0.324478 11.2538i 0.0256522 0.889691i
\(161\) 4.56772 14.0580i 0.359986 1.10792i
\(162\) −11.5605 10.3136i −0.908279 0.810312i
\(163\) 1.19215 + 3.66905i 0.0933761 + 0.287382i 0.986827 0.161779i \(-0.0517230\pi\)
−0.893451 + 0.449161i \(0.851723\pi\)
\(164\) −4.35599 + 0.925895i −0.340146 + 0.0723003i
\(165\) 9.59628 + 18.9038i 0.747070 + 1.47166i
\(166\) −11.4948 2.44329i −0.892168 0.189636i
\(167\) 1.09890 + 10.4554i 0.0850358 + 0.809061i 0.951049 + 0.309040i \(0.100008\pi\)
−0.866013 + 0.500021i \(0.833326\pi\)
\(168\) 7.94850 10.3833i 0.613240 0.801089i
\(169\) −6.94422 3.09176i −0.534170 0.237828i
\(170\) 1.27412 5.24595i 0.0977209 0.402346i
\(171\) −17.3861 + 2.79453i −1.32955 + 0.213703i
\(172\) −3.39140 2.46399i −0.258592 0.187878i
\(173\) −6.01334 + 1.27818i −0.457186 + 0.0971779i −0.430747 0.902473i \(-0.641750\pi\)
−0.0264386 + 0.999650i \(0.508417\pi\)
\(174\) −12.7579 1.66475i −0.967177 0.126204i
\(175\) −21.1146 1.21860i −1.59611 0.0921172i
\(176\) −13.6808 + 23.6959i −1.03123 + 1.78615i
\(177\) −8.62596 + 18.1381i −0.648367 + 1.36335i
\(178\) 0.823751 7.83747i 0.0617428 0.587443i
\(179\) 5.82725 + 4.23375i 0.435549 + 0.316445i 0.783864 0.620933i \(-0.213246\pi\)
−0.348315 + 0.937378i \(0.613246\pi\)
\(180\) −5.83260 + 2.77948i −0.434736 + 0.207170i
\(181\) −18.3734 + 13.3490i −1.36568 + 0.992226i −0.367622 + 0.929975i \(0.619828\pi\)
−0.998061 + 0.0622510i \(0.980172\pi\)
\(182\) −8.45906 14.6515i −0.627027 1.08604i
\(183\) 0.470004 18.7705i 0.0347437 1.38755i
\(184\) 6.10070 + 1.29674i 0.449749 + 0.0955972i
\(185\) 4.87149 + 4.64742i 0.358159 + 0.341685i
\(186\) 9.40913 0.751362i 0.689911 0.0550925i
\(187\) −5.13700 + 5.70522i −0.375655 + 0.417207i
\(188\) −0.854269 2.62917i −0.0623039 0.191752i
\(189\) −21.6250 3.93113i −1.57299 0.285948i
\(190\) −5.33240 + 21.9551i −0.386853 + 1.59279i
\(191\) −7.18086 + 7.97515i −0.519589 + 0.577062i −0.944641 0.328107i \(-0.893589\pi\)
0.425052 + 0.905169i \(0.360256\pi\)
\(192\) 1.96589 + 1.20160i 0.141876 + 0.0867182i
\(193\) 7.49531 12.9823i 0.539524 0.934483i −0.459405 0.888227i \(-0.651937\pi\)
0.998930 0.0462566i \(-0.0147292\pi\)
\(194\) −2.48793 23.6711i −0.178623 1.69949i
\(195\) −0.457490 8.98720i −0.0327615 0.643587i
\(196\) −1.09661 + 10.4335i −0.0783292 + 0.745253i
\(197\) 6.42527 + 4.66823i 0.457782 + 0.332598i 0.792660 0.609663i \(-0.208695\pi\)
−0.334879 + 0.942261i \(0.608695\pi\)
\(198\) 28.2322 + 1.41473i 2.00637 + 0.100540i
\(199\) −14.1116 −1.00034 −0.500172 0.865926i \(-0.666730\pi\)
−0.500172 + 0.865926i \(0.666730\pi\)
\(200\) −0.419902 8.91418i −0.0296916 0.630327i
\(201\) 19.3746 + 2.52814i 1.36658 + 0.178321i
\(202\) 9.89028 + 10.9843i 0.695878 + 0.772851i
\(203\) −16.6753 + 7.42432i −1.17038 + 0.521085i
\(204\) −1.69901 1.60861i −0.118955 0.112625i
\(205\) −9.92085 + 2.91017i −0.692903 + 0.203255i
\(206\) −0.0245290 + 0.0178214i −0.00170902 + 0.00124167i
\(207\) −2.73651 10.1200i −0.190201 0.703387i
\(208\) 9.39616 6.82671i 0.651507 0.473347i
\(209\) 21.4991 23.8772i 1.48712 1.65162i
\(210\) −15.3945 + 23.6279i −1.06232 + 1.63048i
\(211\) 4.89947 + 5.44141i 0.337293 + 0.374602i 0.887801 0.460228i \(-0.152232\pi\)
−0.550507 + 0.834830i \(0.685566\pi\)
\(212\) 5.37915 + 1.14337i 0.369441 + 0.0785272i
\(213\) 8.69006 7.43925i 0.595433 0.509729i
\(214\) −5.61255 + 1.19299i −0.383666 + 0.0815508i
\(215\) −8.28460 5.10700i −0.565005 0.348294i
\(216\) 0.695861 9.24801i 0.0473474 0.629247i
\(217\) 10.8339 7.87128i 0.735452 0.534337i
\(218\) −2.46555 4.27046i −0.166988 0.289232i
\(219\) 5.74705 + 3.51274i 0.388349 + 0.237369i
\(220\) 5.10334 10.6270i 0.344067 0.716469i
\(221\) 2.97700 1.32545i 0.200255 0.0891592i
\(222\) 8.60467 2.55955i 0.577508 0.171786i
\(223\) 19.8964 4.22911i 1.33236 0.283202i 0.513943 0.857825i \(-0.328184\pi\)
0.818419 + 0.574622i \(0.194851\pi\)
\(224\) −21.2975 −1.42300
\(225\) −13.0128 + 7.46102i −0.867521 + 0.497401i
\(226\) −13.8596 −0.921926
\(227\) 21.2885 4.52501i 1.41297 0.300335i 0.562689 0.826669i \(-0.309767\pi\)
0.850278 + 0.526333i \(0.176434\pi\)
\(228\) 7.11062 + 6.73226i 0.470912 + 0.445855i
\(229\) −17.1567 + 7.63866i −1.13375 + 0.504777i −0.885833 0.464005i \(-0.846412\pi\)
−0.247915 + 0.968782i \(0.579745\pi\)
\(230\) −13.3309 1.79093i −0.879015 0.118091i
\(231\) 35.2220 19.1762i 2.31744 1.26170i
\(232\) −3.85098 6.67010i −0.252830 0.437914i
\(233\) −5.17867 + 3.76252i −0.339266 + 0.246491i −0.744352 0.667787i \(-0.767242\pi\)
0.405086 + 0.914279i \(0.367242\pi\)
\(234\) −10.7035 5.42285i −0.699709 0.354503i
\(235\) −2.44039 5.93598i −0.159193 0.387220i
\(236\) 10.9246 2.32210i 0.711131 0.151156i
\(237\) 4.68773 + 1.65397i 0.304501 + 0.107437i
\(238\) −9.98903 2.12323i −0.647493 0.137629i
\(239\) −11.7685 13.0702i −0.761238 0.845440i 0.230586 0.973052i \(-0.425936\pi\)
−0.991824 + 0.127612i \(0.959269\pi\)
\(240\) −17.2364 8.81495i −1.11260 0.569003i
\(241\) 5.08374 5.64606i 0.327472 0.363695i −0.556816 0.830636i \(-0.687977\pi\)
0.884289 + 0.466941i \(0.154644\pi\)
\(242\) −26.4080 + 19.1866i −1.69757 + 1.23336i
\(243\) −14.3674 + 6.04784i −0.921672 + 0.387969i
\(244\) −8.44700 + 6.13711i −0.540764 + 0.392888i
\(245\) −0.701962 + 24.3460i −0.0448467 + 1.55541i
\(246\) −3.20283 + 13.4084i −0.204205 + 0.854888i
\(247\) −12.4592 + 5.54719i −0.792759 + 0.352959i
\(248\) 3.78091 + 4.19912i 0.240088 + 0.266644i
\(249\) −7.18750 + 9.38919i −0.455489 + 0.595016i
\(250\) 2.36058 + 19.1003i 0.149296 + 1.20801i
\(251\) 25.9812 1.63992 0.819959 0.572422i \(-0.193996\pi\)
0.819959 + 0.572422i \(0.193996\pi\)
\(252\) 5.57370 + 10.8773i 0.351110 + 0.685207i
\(253\) 15.4750 + 11.2433i 0.972906 + 0.706858i
\(254\) 0.855612 8.14061i 0.0536859 0.510787i
\(255\) −4.21627 3.42475i −0.264033 0.214466i
\(256\) −1.94583 18.5133i −0.121614 1.15708i
\(257\) 0.478674 0.829088i 0.0298589 0.0517171i −0.850710 0.525636i \(-0.823828\pi\)
0.880569 + 0.473919i \(0.157161\pi\)
\(258\) −11.3970 + 6.20501i −0.709549 + 0.386307i
\(259\) 8.52222 9.46488i 0.529545 0.588119i
\(260\) −3.81368 + 3.23978i −0.236514 + 0.200923i
\(261\) −7.02592 + 10.8734i −0.434894 + 0.673048i
\(262\) −9.79591 30.1487i −0.605193 1.86259i
\(263\) −3.53512 + 3.92615i −0.217985 + 0.242097i −0.842213 0.539146i \(-0.818747\pi\)
0.624227 + 0.781243i \(0.285414\pi\)
\(264\) 9.60053 + 13.9346i 0.590872 + 0.857617i
\(265\) 12.6536 + 1.69994i 0.777307 + 0.104427i
\(266\) 41.8056 + 8.88605i 2.56326 + 0.544838i
\(267\) −6.76574 4.13540i −0.414057 0.253082i
\(268\) −5.43255 9.40945i −0.331846 0.574774i
\(269\) 14.1657 10.2920i 0.863699 0.627514i −0.0651897 0.997873i \(-0.520765\pi\)
0.928889 + 0.370359i \(0.120765\pi\)
\(270\) 0.0158415 + 20.0006i 0.000964082 + 1.21720i
\(271\) −10.8922 7.91361i −0.661651 0.480718i 0.205569 0.978643i \(-0.434096\pi\)
−0.867220 + 0.497925i \(0.834096\pi\)
\(272\) 0.732816 6.97227i 0.0444335 0.422756i
\(273\) −16.9690 + 1.35505i −1.02701 + 0.0820113i
\(274\) 14.2587 24.6968i 0.861400 1.49199i
\(275\) 9.94324 25.4990i 0.599600 1.53765i
\(276\) −3.54353 + 4.62898i −0.213295 + 0.278632i
\(277\) 25.7950 5.48290i 1.54987 0.329436i 0.648069 0.761582i \(-0.275577\pi\)
0.901804 + 0.432146i \(0.142244\pi\)
\(278\) 15.0606 + 10.9422i 0.903274 + 0.656267i
\(279\) 3.38331 8.87454i 0.202553 0.531305i
\(280\) −16.8329 + 1.27999i −1.00596 + 0.0764942i
\(281\) 22.9358 + 10.2117i 1.36823 + 0.609176i 0.953673 0.300846i \(-0.0972690\pi\)
0.414559 + 0.910022i \(0.363936\pi\)
\(282\) −8.48573 1.10728i −0.505318 0.0659375i
\(283\) 1.50697 + 14.3378i 0.0895798 + 0.852295i 0.943385 + 0.331701i \(0.107623\pi\)
−0.853805 + 0.520593i \(0.825711\pi\)
\(284\) −6.22215 1.32256i −0.369217 0.0784795i
\(285\) 17.6457 + 14.3331i 1.04524 + 0.849017i
\(286\) 21.4148 4.55185i 1.26628 0.269156i
\(287\) 6.04373 + 18.6007i 0.356750 + 1.09796i
\(288\) −12.6491 + 8.25568i −0.745355 + 0.486471i
\(289\) −4.64544 + 14.2972i −0.273261 + 0.841011i
\(290\) 9.37180 + 13.7136i 0.550331 + 0.805292i
\(291\) −22.5845 7.96848i −1.32393 0.467120i
\(292\) −0.391510 3.72497i −0.0229114 0.217987i
\(293\) 3.34662 5.79652i 0.195512 0.338636i −0.751556 0.659669i \(-0.770697\pi\)
0.947068 + 0.321033i \(0.104030\pi\)
\(294\) 27.7096 + 16.9368i 1.61606 + 0.987777i
\(295\) 24.8810 7.29856i 1.44863 0.424939i
\(296\) 4.34768 + 3.15878i 0.252704 + 0.183600i
\(297\) 13.4858 25.0425i 0.782523 1.45312i
\(298\) 5.24217 16.1337i 0.303671 0.934602i
\(299\) −4.05970 7.03160i −0.234778 0.406648i
\(300\) 7.69291 + 3.22392i 0.444150 + 0.186133i
\(301\) −9.20515 + 15.9438i −0.530576 + 0.918985i
\(302\) −20.8990 23.2107i −1.20260 1.33562i
\(303\) 14.2551 4.24033i 0.818935 0.243601i
\(304\) −3.06694 + 29.1800i −0.175901 + 1.67359i
\(305\) −18.4739 + 15.6939i −1.05781 + 0.898631i
\(306\) −6.75577 + 2.61107i −0.386202 + 0.149265i
\(307\) 3.26128 0.186131 0.0930657 0.995660i \(-0.470333\pi\)
0.0930657 + 0.995660i \(0.470333\pi\)
\(308\) −20.3727 9.07053i −1.16084 0.516841i
\(309\) 0.00559391 + 0.0299903i 0.000318226 + 0.00170609i
\(310\) −8.81706 8.41151i −0.500775 0.477741i
\(311\) −21.5663 23.9518i −1.22291 1.35818i −0.913284 0.407324i \(-0.866462\pi\)
−0.309629 0.950858i \(-0.600205\pi\)
\(312\) −1.31705 7.06102i −0.0745634 0.399752i
\(313\) −13.7340 + 15.2532i −0.776292 + 0.862159i −0.993484 0.113969i \(-0.963643\pi\)
0.217193 + 0.976129i \(0.430310\pi\)
\(314\) 1.41608 4.35826i 0.0799142 0.245951i
\(315\) 14.8175 + 24.1992i 0.834871 + 1.36347i
\(316\) −0.854194 2.62894i −0.0480522 0.147889i
\(317\) −3.65413 1.62692i −0.205236 0.0913771i 0.301544 0.953452i \(-0.402498\pi\)
−0.506781 + 0.862075i \(0.669165\pi\)
\(318\) 10.3478 13.5176i 0.580279 0.758030i
\(319\) −2.46908 23.4917i −0.138242 1.31528i
\(320\) −0.534321 2.92611i −0.0298695 0.163575i
\(321\) −1.34137 + 5.61553i −0.0748678 + 0.313428i
\(322\) −2.65967 + 25.3051i −0.148218 + 1.41020i
\(323\) −2.54395 + 7.82948i −0.141549 + 0.435644i
\(324\) 7.52680 + 4.29973i 0.418156 + 0.238874i
\(325\) −8.25812 + 8.17121i −0.458078 + 0.453257i
\(326\) −3.32043 5.75115i −0.183902 0.318527i
\(327\) −4.94592 + 0.394954i −0.273510 + 0.0218410i
\(328\) −7.53895 + 3.35656i −0.416269 + 0.185335i
\(329\) −11.0913 + 4.93816i −0.611483 + 0.272250i
\(330\) −22.9234 28.3950i −1.26189 1.56310i
\(331\) 1.34664 + 0.599564i 0.0740181 + 0.0329550i 0.443412 0.896318i \(-0.353768\pi\)
−0.369394 + 0.929273i \(0.620435\pi\)
\(332\) 6.57527 0.360865
\(333\) 1.39262 8.92494i 0.0763149 0.489084i
\(334\) −5.59222 17.2111i −0.305993 0.941749i
\(335\) −14.2323 20.8260i −0.777596 1.13784i
\(336\) −15.7285 + 33.0729i −0.858058 + 1.80427i
\(337\) 9.11619 + 1.93771i 0.496590 + 0.105554i 0.449397 0.893332i \(-0.351639\pi\)
0.0471935 + 0.998886i \(0.484972\pi\)
\(338\) 12.7990 + 2.72050i 0.696171 + 0.147976i
\(339\) −5.98927 + 12.5939i −0.325292 + 0.684005i
\(340\) −0.0870549 + 3.01930i −0.00472122 + 0.163745i
\(341\) 5.35508 + 16.4812i 0.289994 + 0.892509i
\(342\) 28.2739 10.9277i 1.52888 0.590903i
\(343\) 16.4645 0.889001
\(344\) −7.09658 3.15960i −0.382622 0.170354i
\(345\) −7.38819 + 11.3396i −0.397767 + 0.610501i
\(346\) 9.66760 4.30429i 0.519733 0.231400i
\(347\) −6.09966 + 2.71574i −0.327447 + 0.145789i −0.563875 0.825860i \(-0.690690\pi\)
0.236428 + 0.971649i \(0.424023\pi\)
\(348\) 7.17603 0.573038i 0.384675 0.0307181i
\(349\) 2.17204 + 3.76209i 0.116267 + 0.201380i 0.918285 0.395919i \(-0.129574\pi\)
−0.802019 + 0.597299i \(0.796241\pi\)
\(350\) 35.9881 5.50497i 1.92364 0.294253i
\(351\) −9.55301 + 7.38258i −0.509902 + 0.394053i
\(352\) 8.51663 26.2115i 0.453938 1.39708i
\(353\) 0.483612 4.60126i 0.0257401 0.244900i −0.974085 0.226183i \(-0.927375\pi\)
0.999825 0.0187171i \(-0.00595818\pi\)
\(354\) 8.03253 33.6276i 0.426924 1.78728i
\(355\) −14.6367 1.96635i −0.776835 0.104363i
\(356\) 0.460907 + 4.38524i 0.0244280 + 0.232417i
\(357\) −6.24598 + 8.15926i −0.330572 + 0.431834i
\(358\) −11.3270 5.04309i −0.598648 0.266535i
\(359\) −2.78646 8.57585i −0.147064 0.452616i 0.850207 0.526449i \(-0.176477\pi\)
−0.997271 + 0.0738329i \(0.976477\pi\)
\(360\) −9.50130 + 7.28527i −0.500763 + 0.383967i
\(361\) 4.77550 14.6975i 0.251342 0.773551i
\(362\) 26.1589 29.0524i 1.37488 1.52696i
\(363\) 6.02242 + 32.2876i 0.316095 + 1.69466i
\(364\) 6.33403 + 7.03465i 0.331993 + 0.368716i
\(365\) −1.56203 8.55414i −0.0817601 0.447744i
\(366\) 5.92648 + 31.7733i 0.309782 + 1.66081i
\(367\) −8.45692 3.76527i −0.441448 0.196545i 0.173962 0.984752i \(-0.444343\pi\)
−0.615410 + 0.788207i \(0.711010\pi\)
\(368\) −17.4677 −0.910565
\(369\) 10.7998 + 8.70462i 0.562216 + 0.453144i
\(370\) −9.86573 6.08168i −0.512895 0.316171i
\(371\) 2.52455 24.0194i 0.131068 1.24703i
\(372\) −5.06217 + 1.50579i −0.262461 + 0.0780717i
\(373\) −3.62568 4.02673i −0.187731 0.208496i 0.641931 0.766762i \(-0.278133\pi\)
−0.829662 + 0.558266i \(0.811467\pi\)
\(374\) 6.60763 11.4448i 0.341673 0.591794i
\(375\) 18.3761 + 6.10898i 0.948937 + 0.315466i
\(376\) −2.56142 4.43650i −0.132095 0.228795i
\(377\) −3.09837 + 9.53579i −0.159574 + 0.491118i
\(378\) 37.8183 1.12039i 1.94516 0.0576265i
\(379\) 7.21488 + 5.24191i 0.370603 + 0.269259i 0.757461 0.652880i \(-0.226440\pi\)
−0.386858 + 0.922139i \(0.626440\pi\)
\(380\) 0.364338 12.6362i 0.0186901 0.648225i
\(381\) −7.02743 4.29535i −0.360026 0.220057i
\(382\) 9.23661 15.9983i 0.472586 0.818543i
\(383\) 1.92865 + 18.3499i 0.0985493 + 0.937634i 0.926363 + 0.376631i \(0.122918\pi\)
−0.827814 + 0.561003i \(0.810416\pi\)
\(384\) −20.1879 7.12290i −1.03021 0.363489i
\(385\) −48.7582 17.4115i −2.48495 0.887370i
\(386\) −7.97405 + 24.5416i −0.405868 + 1.24913i
\(387\) 0.713232 + 13.0376i 0.0362556 + 0.662741i
\(388\) 4.11532 + 12.6657i 0.208924 + 0.643001i
\(389\) 12.3953 2.63469i 0.628465 0.133584i 0.117341 0.993092i \(-0.462563\pi\)
0.511123 + 0.859507i \(0.329230\pi\)
\(390\) 3.98678 + 14.9686i 0.201879 + 0.757964i
\(391\) −4.79397 1.01899i −0.242441 0.0515325i
\(392\) 2.03212 + 19.3344i 0.102638 + 0.976532i
\(393\) −31.6286 4.12712i −1.59545 0.208186i
\(394\) −12.4894 5.56063i −0.629206 0.280140i
\(395\) −2.44018 5.93546i −0.122779 0.298645i
\(396\) −15.6159 + 2.51001i −0.784730 + 0.126133i
\(397\) 5.05655 + 3.67380i 0.253781 + 0.184383i 0.707401 0.706813i \(-0.249868\pi\)
−0.453620 + 0.891195i \(0.649868\pi\)
\(398\) 23.7606 5.05047i 1.19101 0.253157i
\(399\) 26.1403 34.1477i 1.30865 1.70952i
\(400\) 6.34093 + 24.1755i 0.317046 + 1.20877i
\(401\) 13.3637 23.1466i 0.667352 1.15589i −0.311290 0.950315i \(-0.600761\pi\)
0.978642 0.205572i \(-0.0659056\pi\)
\(402\) −33.5271 + 2.67729i −1.67218 + 0.133531i
\(403\) 0.768897 7.31556i 0.0383015 0.364414i
\(404\) −6.69072 4.86109i −0.332876 0.241848i
\(405\) 18.1809 + 8.62866i 0.903418 + 0.428761i
\(406\) 25.4201 18.4688i 1.26158 0.916592i
\(407\) 8.24078 + 14.2735i 0.408480 + 0.707509i
\(408\) −3.69940 2.26117i −0.183148 0.111945i
\(409\) −23.4005 4.97392i −1.15708 0.245945i −0.410893 0.911683i \(-0.634783\pi\)
−0.746185 + 0.665739i \(0.768117\pi\)
\(410\) 15.6628 8.45067i 0.773533 0.417349i
\(411\) −16.2796 23.6290i −0.803016 1.16553i
\(412\) 0.0113514 0.0126071i 0.000559246 0.000621105i
\(413\) −15.1574 46.6496i −0.745845 2.29547i
\(414\) 8.22953 + 16.0603i 0.404459 + 0.789320i
\(415\) 15.2213 1.15744i 0.747185 0.0568167i
\(416\) −7.82792 + 8.69378i −0.383795 + 0.426248i
\(417\) 16.4511 8.95666i 0.805616 0.438610i
\(418\) −27.6539 + 47.8980i −1.35260 + 2.34277i
\(419\) 1.31148 + 12.4779i 0.0640699 + 0.609584i 0.978700 + 0.205294i \(0.0658150\pi\)
−0.914631 + 0.404291i \(0.867518\pi\)
\(420\) 5.67670 14.7223i 0.276994 0.718374i
\(421\) 0.123363 1.17372i 0.00601232 0.0572034i −0.991104 0.133087i \(-0.957511\pi\)
0.997117 + 0.0758835i \(0.0241777\pi\)
\(422\) −10.1970 7.40856i −0.496382 0.360643i
\(423\) −4.67317 + 7.23228i −0.227217 + 0.351645i
\(424\) 10.1908 0.494908
\(425\) 0.329962 + 7.00482i 0.0160055 + 0.339784i
\(426\) −11.9695 + 15.6361i −0.579926 + 0.757570i
\(427\) 30.6828 + 34.0767i 1.48485 + 1.64909i
\(428\) 2.93294 1.30583i 0.141769 0.0631197i
\(429\) 5.11800 21.4261i 0.247099 1.03446i
\(430\) 15.7771 + 5.63396i 0.760839 + 0.271694i
\(431\) −20.3282 + 14.7693i −0.979174 + 0.711412i −0.957524 0.288354i \(-0.906892\pi\)
−0.0216502 + 0.999766i \(0.506892\pi\)
\(432\) 3.47873 + 25.7397i 0.167371 + 1.23840i
\(433\) 16.1875 11.7609i 0.777922 0.565193i −0.126433 0.991975i \(-0.540353\pi\)
0.904355 + 0.426782i \(0.140353\pi\)
\(434\) −15.4246 + 17.1308i −0.740405 + 0.822303i
\(435\) 16.5112 2.58974i 0.791649 0.124169i
\(436\) 1.84617 + 2.05038i 0.0884156 + 0.0981955i
\(437\) 20.0635 + 4.26462i 0.959765 + 0.204004i
\(438\) −10.9339 3.85779i −0.522440 0.184332i
\(439\) 22.1767 4.71380i 1.05844 0.224977i 0.354365 0.935107i \(-0.384697\pi\)
0.704071 + 0.710130i \(0.251364\pi\)
\(440\) 5.15597 21.2287i 0.245801 1.01204i
\(441\) 27.3645 17.8600i 1.30307 0.850476i
\(442\) −4.53820 + 3.29719i −0.215860 + 0.156832i
\(443\) 2.48298 + 4.30064i 0.117970 + 0.204330i 0.918963 0.394344i \(-0.129028\pi\)
−0.800993 + 0.598673i \(0.795695\pi\)
\(444\) −4.41154 + 2.40182i −0.209363 + 0.113985i
\(445\) 1.83890 + 10.0704i 0.0871724 + 0.477383i
\(446\) −31.9873 + 14.2416i −1.51464 + 0.674362i
\(447\) −12.3950 11.7354i −0.586263 0.555067i
\(448\) −5.50385 + 1.16988i −0.260032 + 0.0552716i
\(449\) 17.7685 0.838548 0.419274 0.907860i \(-0.362285\pi\)
0.419274 + 0.907860i \(0.362285\pi\)
\(450\) 19.2402 17.2198i 0.906994 0.811750i
\(451\) −25.3093 −1.19177
\(452\) 7.58529 1.61230i 0.356782 0.0758364i
\(453\) −30.1222 + 8.96017i −1.41527 + 0.420985i
\(454\) −34.2253 + 15.2381i −1.60627 + 0.715159i
\(455\) 15.9012 + 15.1698i 0.745459 + 0.711170i
\(456\) 15.4825 + 9.46333i 0.725036 + 0.443161i
\(457\) −10.0171 17.3501i −0.468579 0.811602i 0.530776 0.847512i \(-0.321900\pi\)
−0.999355 + 0.0359099i \(0.988567\pi\)
\(458\) 26.1540 19.0020i 1.22210 0.887906i
\(459\) −0.546812 + 7.26715i −0.0255230 + 0.339201i
\(460\) 7.50430 0.570634i 0.349890 0.0266060i
\(461\) 12.3278 2.62035i 0.574161 0.122042i 0.0883252 0.996092i \(-0.471849\pi\)
0.485836 + 0.874050i \(0.338515\pi\)
\(462\) −52.4424 + 44.8940i −2.43984 + 2.08866i
\(463\) 24.3569 + 5.17722i 1.13196 + 0.240606i 0.735552 0.677469i \(-0.236923\pi\)
0.396409 + 0.918074i \(0.370256\pi\)
\(464\) 14.4335 + 16.0300i 0.670059 + 0.744176i
\(465\) −11.4535 + 4.37691i −0.531145 + 0.202974i
\(466\) 7.37307 8.18862i 0.341551 0.379331i
\(467\) −29.6418 + 21.5361i −1.37166 + 0.996570i −0.374056 + 0.927406i \(0.622033\pi\)
−0.997605 + 0.0691640i \(0.977967\pi\)
\(468\) 6.48882 + 1.72275i 0.299946 + 0.0796341i
\(469\) −38.6039 + 28.0474i −1.78256 + 1.29511i
\(470\) 6.23350 + 9.12138i 0.287530 + 0.420738i
\(471\) −3.34830 3.17013i −0.154281 0.146072i
\(472\) 18.9073 8.41808i 0.870279 0.387473i
\(473\) −15.9415 17.7048i −0.732990 0.814068i
\(474\) −8.48499 1.10718i −0.389728 0.0508546i
\(475\) −1.38094 29.3162i −0.0633618 1.34512i
\(476\) 5.71395 0.261899
\(477\) −7.81142 15.2443i −0.357660 0.697990i
\(478\) 24.4931 + 17.7952i 1.12029 + 0.813936i
\(479\) −0.763778 + 7.26686i −0.0348979 + 0.332031i 0.963119 + 0.269078i \(0.0867188\pi\)
−0.998016 + 0.0629539i \(0.979948\pi\)
\(480\) 18.8282 + 5.07527i 0.859386 + 0.231653i
\(481\) −0.731279 6.95766i −0.0333435 0.317242i
\(482\) −6.53911 + 11.3261i −0.297849 + 0.515889i
\(483\) 21.8448 + 13.3521i 0.993972 + 0.607541i
\(484\) 12.2210 13.5728i 0.555500 0.616945i
\(485\) 11.7562 + 28.5957i 0.533823 + 1.29847i
\(486\) 22.0269 15.3252i 0.999161 0.695164i
\(487\) −7.65681 23.5652i −0.346963 1.06784i −0.960524 0.278195i \(-0.910264\pi\)
0.613561 0.789647i \(-0.289736\pi\)
\(488\) −12.9465 + 14.3786i −0.586063 + 0.650889i
\(489\) −6.66082 + 0.531897i −0.301213 + 0.0240532i
\(490\) −7.53137 41.2441i −0.340233 1.86322i
\(491\) 19.9579 + 4.24219i 0.900690 + 0.191447i 0.634910 0.772586i \(-0.281037\pi\)
0.265780 + 0.964034i \(0.414371\pi\)
\(492\) 0.193078 7.71094i 0.00870465 0.347636i
\(493\) 3.02613 + 5.24141i 0.136290 + 0.236061i
\(494\) 18.9930 13.7992i 0.854537 0.620857i
\(495\) −35.7080 + 8.55938i −1.60496 + 0.384715i
\(496\) −12.8027 9.30172i −0.574859 0.417659i
\(497\) −2.92019 + 27.7837i −0.130988 + 1.24627i
\(498\) 8.74171 18.3815i 0.391726 0.823697i
\(499\) −10.7311 + 18.5869i −0.480392 + 0.832064i −0.999747 0.0224950i \(-0.992839\pi\)
0.519355 + 0.854559i \(0.326172\pi\)
\(500\) −3.51390 10.1789i −0.157146 0.455214i
\(501\) −18.0559 2.35607i −0.806679 0.105261i
\(502\) −43.7462 + 9.29854i −1.95249 + 0.415014i
\(503\) −8.58020 6.23388i −0.382572 0.277955i 0.379833 0.925055i \(-0.375981\pi\)
−0.762405 + 0.647100i \(0.775981\pi\)
\(504\) 14.2937 + 17.5688i 0.636693 + 0.782578i
\(505\) −16.3443 10.0753i −0.727311 0.448347i
\(506\) −30.0802 13.3926i −1.33723 0.595372i
\(507\) 8.00298 10.4545i 0.355425 0.464299i
\(508\) 0.478734 + 4.55485i 0.0212404 + 0.202089i
\(509\) −4.48811 0.953978i −0.198932 0.0422843i 0.107368 0.994219i \(-0.465758\pi\)
−0.306300 + 0.951935i \(0.599091\pi\)
\(510\) 8.32490 + 4.25748i 0.368633 + 0.188524i
\(511\) −16.0899 + 3.42000i −0.711773 + 0.151292i
\(512\) 2.26343 + 6.96611i 0.100030 + 0.307861i
\(513\) 2.28849 30.4141i 0.101039 1.34281i
\(514\) −0.509248 + 1.56730i −0.0224620 + 0.0691308i
\(515\) 0.0240586 0.0311827i 0.00106015 0.00137407i
\(516\) 5.51571 4.72180i 0.242816 0.207866i
\(517\) −1.64226 15.6251i −0.0722267 0.687191i
\(518\) −10.9620 + 18.9867i −0.481641 + 0.834227i
\(519\) 0.266540 10.6448i 0.0116998 0.467253i
\(520\) −5.66446 + 7.34178i −0.248403 + 0.321958i
\(521\) 9.38013 + 6.81506i 0.410951 + 0.298573i 0.773987 0.633202i \(-0.218260\pi\)
−0.363036 + 0.931775i \(0.618260\pi\)
\(522\) 7.93844 20.8228i 0.347456 0.911391i
\(523\) −2.58596 + 7.95877i −0.113076 + 0.348013i −0.991541 0.129794i \(-0.958568\pi\)
0.878465 + 0.477807i \(0.158568\pi\)
\(524\) 8.86849 + 15.3607i 0.387422 + 0.671034i
\(525\) 10.5496 35.0804i 0.460423 1.53103i
\(526\) 4.54717 7.87592i 0.198266 0.343407i
\(527\) −2.97106 3.29970i −0.129421 0.143737i
\(528\) −34.4142 32.5830i −1.49768 1.41799i
\(529\) 1.12772 10.7295i 0.0490311 0.466500i
\(530\) −21.9141 + 1.66637i −0.951890 + 0.0723827i
\(531\) −27.0854 21.8307i −1.17541 0.947373i
\(532\) −23.9137 −1.03679
\(533\) 9.81431 + 4.36961i 0.425105 + 0.189269i
\(534\) 12.8720 + 4.54161i 0.557024 + 0.196535i
\(535\) 6.55971 3.53920i 0.283601 0.153013i
\(536\) −13.4723 14.9625i −0.581916 0.646283i
\(537\) −9.47735 + 8.11322i −0.408978 + 0.350111i
\(538\) −20.1683 + 22.3991i −0.869516 + 0.965695i
\(539\) −18.4245 + 56.7048i −0.793600 + 2.44245i
\(540\) −2.33537 10.9444i −0.100498 0.470972i
\(541\) 6.73533 + 20.7292i 0.289575 + 0.891219i 0.984990 + 0.172611i \(0.0552203\pi\)
−0.695416 + 0.718608i \(0.744780\pi\)
\(542\) 21.1721 + 9.42641i 0.909418 + 0.404899i
\(543\) −15.0949 36.3246i −0.647785 1.55884i
\(544\) 0.738137 + 7.02291i 0.0316474 + 0.301105i
\(545\) 4.63470 + 4.42152i 0.198529 + 0.189397i
\(546\) 28.0868 8.35469i 1.20200 0.357548i
\(547\) −3.48938 + 33.1992i −0.149195 + 1.41950i 0.622060 + 0.782969i \(0.286296\pi\)
−0.771255 + 0.636526i \(0.780371\pi\)
\(548\) −4.93071 + 15.1752i −0.210630 + 0.648251i
\(549\) 31.4327 + 8.34521i 1.34151 + 0.356165i
\(550\) −7.61609 + 46.4930i −0.324751 + 1.98247i
\(551\) −12.6648 21.9361i −0.539538 0.934508i
\(552\) −4.63955 + 9.75576i −0.197472 + 0.415233i
\(553\) −11.0903 + 4.93773i −0.471609 + 0.209974i
\(554\) −41.4704 + 18.4638i −1.76191 + 0.784453i
\(555\) −9.78964 + 6.33662i −0.415547 + 0.268975i
\(556\) −9.51551 4.23658i −0.403548 0.179671i
\(557\) 0.351013 0.0148729 0.00743646 0.999972i \(-0.497633\pi\)
0.00743646 + 0.999972i \(0.497633\pi\)
\(558\) −2.52054 + 16.1535i −0.106703 + 0.683833i
\(559\) 3.12500 + 9.61776i 0.132173 + 0.406788i
\(560\) 45.3677 13.3081i 1.91713 0.562370i
\(561\) −7.54416 10.9499i −0.318515 0.462306i
\(562\) −42.2731 8.98542i −1.78318 0.379027i
\(563\) −6.71206 1.42669i −0.282879 0.0601279i 0.0642869 0.997931i \(-0.479523\pi\)
−0.347166 + 0.937804i \(0.612856\pi\)
\(564\) 4.77301 0.381147i 0.200980 0.0160492i
\(565\) 17.2756 5.06762i 0.726792 0.213196i
\(566\) −7.66881 23.6022i −0.322344 0.992073i
\(567\) 15.3247 34.8488i 0.643577 1.46351i
\(568\) −11.7878 −0.494607
\(569\) 13.8450 + 6.16417i 0.580411 + 0.258416i 0.675874 0.737017i \(-0.263766\pi\)
−0.0954629 + 0.995433i \(0.530433\pi\)
\(570\) −34.8409 17.8182i −1.45933 0.746322i
\(571\) 36.1997 16.1171i 1.51491 0.674481i 0.530070 0.847954i \(-0.322166\pi\)
0.984839 + 0.173473i \(0.0554989\pi\)
\(572\) −11.1907 + 4.98241i −0.467906 + 0.208325i
\(573\) −10.5457 15.3066i −0.440555 0.639441i
\(574\) −16.8333 29.1561i −0.702609 1.21695i
\(575\) 17.2715 2.64196i 0.720272 0.110177i
\(576\) −2.81538 + 2.82831i −0.117308 + 0.117846i
\(577\) −3.56209 + 10.9630i −0.148292 + 0.456396i −0.997420 0.0717920i \(-0.977128\pi\)
0.849128 + 0.528188i \(0.177128\pi\)
\(578\) 2.70493 25.7357i 0.112510 1.07046i
\(579\) 18.8545 + 17.8512i 0.783564 + 0.741871i
\(580\) −6.72447 6.41517i −0.279218 0.266375i
\(581\) −3.01848 28.7189i −0.125228 1.19146i
\(582\) 40.8788 + 5.33416i 1.69448 + 0.221108i
\(583\) 28.5519 + 12.7121i 1.18250 + 0.526483i
\(584\) −2.14481 6.60104i −0.0887528 0.273153i
\(585\) 15.3244 + 2.84582i 0.633588 + 0.117660i
\(586\) −3.56038 + 10.9577i −0.147078 + 0.452659i
\(587\) −26.2637 + 29.1688i −1.08402 + 1.20393i −0.106228 + 0.994342i \(0.533877\pi\)
−0.977791 + 0.209583i \(0.932789\pi\)
\(588\) −17.1356 6.04596i −0.706662 0.249331i
\(589\) 12.4343 + 13.8097i 0.512347 + 0.569019i
\(590\) −39.2816 + 21.1938i −1.61720 + 0.872537i
\(591\) −10.4500 + 8.94583i −0.429854 + 0.367982i
\(592\) −13.7496 6.12171i −0.565105 0.251601i
\(593\) −2.11729 −0.0869465 −0.0434733 0.999055i \(-0.513842\pi\)
−0.0434733 + 0.999055i \(0.513842\pi\)
\(594\) −13.7442 + 46.9922i −0.563933 + 1.92811i
\(595\) 13.2274 1.00583i 0.542271 0.0412349i
\(596\) −0.992157 + 9.43975i −0.0406403 + 0.386667i
\(597\) 5.67863 23.7732i 0.232411 0.972971i
\(598\) 9.35215 + 10.3866i 0.382438 + 0.424740i
\(599\) −1.13371 + 1.96364i −0.0463219 + 0.0802320i −0.888257 0.459347i \(-0.848083\pi\)
0.841935 + 0.539579i \(0.181417\pi\)
\(600\) 15.1863 + 2.87976i 0.619978 + 0.117566i
\(601\) 17.8254 + 30.8745i 0.727113 + 1.25940i 0.958098 + 0.286440i \(0.0924718\pi\)
−0.230985 + 0.972957i \(0.574195\pi\)
\(602\) 9.79310 30.1401i 0.399137 1.22842i
\(603\) −12.0556 + 31.6223i −0.490942 + 1.28776i
\(604\) 14.1380 + 10.2719i 0.575269 + 0.417957i
\(605\) 25.9016 33.5714i 1.05305 1.36487i
\(606\) −22.4847 + 12.2416i −0.913377 + 0.497279i
\(607\) −12.5954 + 21.8159i −0.511231 + 0.885478i 0.488684 + 0.872461i \(0.337477\pi\)
−0.999915 + 0.0130175i \(0.995856\pi\)
\(608\) −3.08921 29.3919i −0.125284 1.19200i
\(609\) −5.79713 31.0798i −0.234912 1.25942i
\(610\) 25.4890 33.0366i 1.03202 1.33761i
\(611\) −2.06082 + 6.34257i −0.0833720 + 0.256593i
\(612\) 3.39365 2.21493i 0.137180 0.0895334i
\(613\) −13.2971 40.9242i −0.537063 1.65291i −0.739148 0.673543i \(-0.764772\pi\)
0.202085 0.979368i \(-0.435228\pi\)
\(614\) −5.49123 + 1.16720i −0.221608 + 0.0471043i
\(615\) −0.910393 17.8843i −0.0367106 0.721165i
\(616\) −40.4224 8.59204i −1.62866 0.346183i
\(617\) −3.34729 31.8474i −0.134757 1.28213i −0.827715 0.561149i \(-0.810360\pi\)
0.692958 0.720978i \(-0.256307\pi\)
\(618\) −0.0201522 0.0484945i −0.000810640 0.00195073i
\(619\) −11.9559 5.32313i −0.480550 0.213955i 0.152141 0.988359i \(-0.451383\pi\)
−0.632691 + 0.774404i \(0.718050\pi\)
\(620\) 5.80406 + 3.57788i 0.233096 + 0.143691i
\(621\) 18.1499 0.537700i 0.728330 0.0215771i
\(622\) 44.8848 + 32.6107i 1.79972 + 1.30757i
\(623\) 18.9419 4.02622i 0.758890 0.161307i
\(624\) 7.71956 + 18.5764i 0.309030 + 0.743653i
\(625\) −9.92623 22.9449i −0.397049 0.917797i
\(626\) 17.6658 30.5980i 0.706067 1.22294i
\(627\) 31.5734 + 45.8270i 1.26092 + 1.83015i
\(628\) −0.268015 + 2.54999i −0.0106949 + 0.101756i
\(629\) −3.41644 2.48219i −0.136222 0.0989713i
\(630\) −33.6099 35.4426i −1.33905 1.41207i
\(631\) 34.4722 25.0455i 1.37232 0.997047i 0.374765 0.927120i \(-0.377723\pi\)
0.997552 0.0699268i \(-0.0222766\pi\)
\(632\) −2.56119 4.43612i −0.101879 0.176459i
\(633\) −11.1385 + 6.06424i −0.442716 + 0.241032i
\(634\) 6.73496 + 1.43156i 0.267479 + 0.0568545i
\(635\) 1.91003 + 10.4599i 0.0757972 + 0.415089i
\(636\) −4.09081 + 8.60191i −0.162211 + 0.341088i
\(637\) 16.9346 18.8078i 0.670973 0.745191i
\(638\) 12.5649 + 38.6708i 0.497450 + 1.53099i
\(639\) 9.03561 + 17.6334i 0.357443 + 0.697566i
\(640\) 10.5087 + 25.5613i 0.415394 + 1.01040i
\(641\) −1.78356 + 1.98084i −0.0704464 + 0.0782386i −0.777338 0.629084i \(-0.783430\pi\)
0.706891 + 0.707322i \(0.250097\pi\)
\(642\) 0.248775 9.93529i 0.00981837 0.392115i
\(643\) 19.1382 33.1483i 0.754736 1.30724i −0.190769 0.981635i \(-0.561098\pi\)
0.945505 0.325607i \(-0.105569\pi\)
\(644\) −1.48815 14.1588i −0.0586412 0.557934i
\(645\) 11.9373 11.9016i 0.470032 0.468625i
\(646\) 1.48128 14.0935i 0.0582803 0.554500i
\(647\) 29.1546 + 21.1821i 1.14619 + 0.832753i 0.987969 0.154651i \(-0.0494254\pi\)
0.158217 + 0.987404i \(0.449425\pi\)
\(648\) 15.2997 + 4.89378i 0.601029 + 0.192246i
\(649\) 63.4743 2.49158
\(650\) 10.9803 16.7139i 0.430682 0.655574i
\(651\) 8.90074 + 21.4188i 0.348847 + 0.839471i
\(652\) 2.48629 + 2.76131i 0.0973708 + 0.108141i
\(653\) 25.9936 11.5731i 1.01721 0.452890i 0.170732 0.985318i \(-0.445387\pi\)
0.846476 + 0.532428i \(0.178720\pi\)
\(654\) 8.18642 2.43513i 0.320114 0.0952212i
\(655\) 23.2339 + 33.9978i 0.907824 + 1.32841i
\(656\) 18.6981 13.5850i 0.730039 0.530405i
\(657\) −8.23043 + 8.26823i −0.321100 + 0.322575i
\(658\) 16.9078 12.2842i 0.659134 0.478889i
\(659\) −21.6918 + 24.0912i −0.844993 + 0.938460i −0.998767 0.0496464i \(-0.984191\pi\)
0.153774 + 0.988106i \(0.450857\pi\)
\(660\) 15.8491 + 12.8738i 0.616926 + 0.501110i
\(661\) 31.0769 + 34.5144i 1.20875 + 1.34245i 0.923309 + 0.384059i \(0.125474\pi\)
0.285443 + 0.958396i \(0.407859\pi\)
\(662\) −2.48201 0.527567i −0.0964660 0.0205045i
\(663\) 1.03495 + 5.54860i 0.0401941 + 0.215490i
\(664\) 11.9184 2.53332i 0.462522 0.0983120i
\(665\) −55.3587 + 4.20953i −2.14672 + 0.163239i
\(666\) 0.849354 + 15.5259i 0.0329118 + 0.601617i
\(667\) 12.1997 8.86361i 0.472375 0.343200i
\(668\) 5.06279 + 8.76900i 0.195885 + 0.339283i
\(669\) −0.881903 + 35.2204i −0.0340963 + 1.36170i
\(670\) 31.4174 + 29.9723i 1.21376 + 1.15793i
\(671\) −54.2090 + 24.1354i −2.09272 + 0.931737i
\(672\) 8.57031 35.8790i 0.330607 1.38406i
\(673\) −5.72623 + 1.21715i −0.220730 + 0.0469176i −0.316949 0.948443i \(-0.602658\pi\)
0.0962191 + 0.995360i \(0.469325\pi\)
\(674\) −16.0430 −0.617953
\(675\) −7.33277 24.9245i −0.282238 0.959344i
\(676\) −7.32129 −0.281588
\(677\) −19.4462 + 4.13342i −0.747379 + 0.158860i −0.565830 0.824522i \(-0.691444\pi\)
−0.181549 + 0.983382i \(0.558111\pi\)
\(678\) 5.57723 23.3486i 0.214192 0.896699i
\(679\) 53.4307 23.7889i 2.05048 0.912934i
\(680\) 1.00548 + 5.50634i 0.0385585 + 0.211158i
\(681\) −0.943608 + 37.6847i −0.0361591 + 1.44408i
\(682\) −14.9152 25.8340i −0.571134 0.989233i
\(683\) −36.4251 + 26.4644i −1.39377 + 1.01263i −0.398328 + 0.917243i \(0.630409\pi\)
−0.995440 + 0.0953885i \(0.969591\pi\)
\(684\) −14.2029 + 9.26982i −0.543063 + 0.354441i
\(685\) −8.74299 + 35.9975i −0.334053 + 1.37539i
\(686\) −27.7224 + 5.89258i −1.05845 + 0.224980i
\(687\) −5.96450 31.9770i −0.227560 1.22000i
\(688\) 21.2806 + 4.52332i 0.811314 + 0.172450i
\(689\) −8.87700 9.85891i −0.338187 0.375595i
\(690\) 8.38160 21.7373i 0.319082 0.827526i
\(691\) 0.672969 0.747407i 0.0256009 0.0284327i −0.730208 0.683225i \(-0.760577\pi\)
0.755809 + 0.654792i \(0.227244\pi\)
\(692\) −4.79031 + 3.48036i −0.182100 + 0.132304i
\(693\) 18.1317 + 67.0536i 0.688767 + 2.54716i
\(694\) 9.29844 6.75571i 0.352964 0.256443i
\(695\) −22.7735 8.13239i −0.863850 0.308479i
\(696\) 12.7865 3.80347i 0.484671 0.144170i
\(697\) 5.92416 2.63761i 0.224394 0.0999065i
\(698\) −5.00364 5.55710i −0.189390 0.210339i
\(699\) −4.25461 10.2384i −0.160924 0.387250i
\(700\) −19.0557 + 7.19938i −0.720238 + 0.272111i
\(701\) −8.14396 −0.307593 −0.153797 0.988103i \(-0.549150\pi\)
−0.153797 + 0.988103i \(0.549150\pi\)
\(702\) 13.4428 15.8495i 0.507367 0.598201i
\(703\) 14.2983 + 10.3883i 0.539270 + 0.391803i
\(704\) 0.761121 7.24158i 0.0286858 0.272927i
\(705\) 10.9821 1.72252i 0.413610 0.0648739i
\(706\) 0.832480 + 7.92052i 0.0313308 + 0.298093i
\(707\) −18.1604 + 31.4547i −0.682992 + 1.18298i
\(708\) −0.484231 + 19.3386i −0.0181985 + 0.726791i
\(709\) 27.5012 30.5431i 1.03283 1.14707i 0.0438449 0.999038i \(-0.486039\pi\)
0.988982 0.148033i \(-0.0472941\pi\)
\(710\) 25.3485 1.92752i 0.951312 0.0723387i
\(711\) −4.67276 + 7.23165i −0.175242 + 0.271208i
\(712\) 2.52499 + 7.77112i 0.0946279 + 0.291235i
\(713\) −7.40263 + 8.22145i −0.277231 + 0.307896i
\(714\) 7.59660 15.9737i 0.284296 0.597800i
\(715\) −25.0286 + 13.5038i −0.936018 + 0.505015i
\(716\) 6.78586 + 1.44238i 0.253600 + 0.0539042i
\(717\) 26.7545 14.5662i 0.999166 0.543986i
\(718\) 7.76100 + 13.4424i 0.289638 + 0.501668i
\(719\) 39.3653 28.6006i 1.46808 1.06662i 0.486915 0.873449i \(-0.338122\pi\)
0.981165 0.193173i \(-0.0618779\pi\)
\(720\) 21.7862 25.4902i 0.811926 0.949962i
\(721\) −0.0602751 0.0437924i −0.00224476 0.00163091i
\(722\) −2.78066 + 26.4562i −0.103485 + 0.984597i
\(723\) 7.46593 + 10.8364i 0.277661 + 0.403009i
\(724\) −10.9369 + 18.9433i −0.406468 + 0.704023i
\(725\) −16.6960 13.6670i −0.620073 0.507579i
\(726\) −21.6959 52.2093i −0.805211 1.93767i
\(727\) −38.1966 + 8.11893i −1.41663 + 0.301115i −0.851703 0.524025i \(-0.824430\pi\)
−0.564929 + 0.825139i \(0.691097\pi\)
\(728\) 14.1914 + 10.3107i 0.525968 + 0.382138i
\(729\) −4.40694 26.6379i −0.163220 0.986590i
\(730\) 5.69157 + 13.8441i 0.210654 + 0.512393i
\(731\) 5.57654 + 2.48284i 0.206256 + 0.0918310i
\(732\) −6.93976 16.6999i −0.256501 0.617247i
\(733\) −0.0804066 0.765018i −0.00296989 0.0282566i 0.992937 0.118646i \(-0.0378554\pi\)
−0.995906 + 0.0903896i \(0.971189\pi\)
\(734\) 15.5870 + 3.31313i 0.575328 + 0.122290i
\(735\) −40.7321 10.9796i −1.50243 0.404989i
\(736\) 17.2100 3.65810i 0.634370 0.134839i
\(737\) −19.0815 58.7268i −0.702876 2.16323i
\(738\) −21.2997 10.7913i −0.784052 0.397234i
\(739\) 16.0888 49.5162i 0.591835 1.82148i 0.0219476 0.999759i \(-0.493013\pi\)
0.569888 0.821723i \(-0.306987\pi\)
\(740\) 6.10696 + 2.18078i 0.224496 + 0.0801672i
\(741\) −4.33141 23.2217i −0.159118 0.853070i
\(742\) 4.34570 + 41.3466i 0.159536 + 1.51788i
\(743\) 19.6551 34.0437i 0.721076 1.24894i −0.239492 0.970898i \(-0.576981\pi\)
0.960569 0.278043i \(-0.0896857\pi\)
\(744\) −8.59555 + 4.67976i −0.315128 + 0.171568i
\(745\) −0.635101 + 22.0270i −0.0232683 + 0.807008i
\(746\) 7.54594 + 5.48244i 0.276276 + 0.200727i
\(747\) −12.9252 15.8868i −0.472910 0.581266i
\(748\) −2.28494 + 7.03234i −0.0835458 + 0.257128i
\(749\) −7.04991 12.2108i −0.257598 0.446173i
\(750\) −33.1274 3.70938i −1.20964 0.135447i
\(751\) 19.8565 34.3925i 0.724575 1.25500i −0.234573 0.972098i \(-0.575369\pi\)
0.959149 0.282903i \(-0.0912973\pi\)
\(752\) 9.60021 + 10.6621i 0.350084 + 0.388807i
\(753\) −10.4551 + 43.7694i −0.381004 + 1.59504i
\(754\) 1.80410 17.1649i 0.0657016 0.625109i
\(755\) 34.5368 + 21.2900i 1.25692 + 0.774824i
\(756\) −20.5675 + 5.01264i −0.748031 + 0.182308i
\(757\) −30.6481 −1.11392 −0.556961 0.830538i \(-0.688033\pi\)
−0.556961 + 0.830538i \(0.688033\pi\)
\(758\) −14.0242 6.24398i −0.509382 0.226792i
\(759\) −25.1683 + 21.5457i −0.913552 + 0.782059i
\(760\) −4.20809 23.0448i −0.152644 0.835924i
\(761\) −12.5617 13.9511i −0.455360 0.505729i 0.471122 0.882068i \(-0.343849\pi\)
−0.926482 + 0.376340i \(0.877183\pi\)
\(762\) 13.3698 + 4.71727i 0.484337 + 0.170889i
\(763\) 8.10797 9.00481i 0.293528 0.325996i
\(764\) −3.19405 + 9.83029i −0.115557 + 0.355647i
\(765\) 7.46619 5.72481i 0.269941 0.206981i
\(766\) −9.81472 30.2066i −0.354620 1.09141i
\(767\) −24.6138 10.9588i −0.888752 0.395698i
\(768\) 31.9716 + 4.17189i 1.15368 + 0.150540i
\(769\) 3.95016 + 37.5833i 0.142446 + 1.35529i 0.799147 + 0.601136i \(0.205285\pi\)
−0.656700 + 0.754152i \(0.728048\pi\)
\(770\) 88.3289 + 11.8665i 3.18315 + 0.427638i
\(771\) 1.20411 + 1.14003i 0.0433648 + 0.0410574i
\(772\) 1.50921 14.3591i 0.0543175 0.516796i
\(773\) −8.44199 + 25.9818i −0.303637 + 0.934500i 0.676545 + 0.736401i \(0.263476\pi\)
−0.980182 + 0.198098i \(0.936524\pi\)
\(774\) −5.86702 21.6971i −0.210886 0.779885i
\(775\) 14.0658 + 7.26087i 0.505259 + 0.260818i
\(776\) 12.3393 + 21.3722i 0.442954 + 0.767219i
\(777\) 12.5157 + 18.1658i 0.448996 + 0.651693i
\(778\) −19.9278 + 8.87241i −0.714445 + 0.318091i
\(779\) −24.7935 + 11.0388i −0.888318 + 0.395505i
\(780\) −3.92326 7.72846i −0.140475 0.276723i
\(781\) −33.0265 14.7044i −1.18178 0.526164i
\(782\) 8.43660 0.301692
\(783\) −15.4907 16.2118i −0.553592 0.579364i
\(784\) −16.8251 51.7823i −0.600896 1.84937i
\(785\) −0.171562 + 5.95023i −0.00612330 + 0.212373i
\(786\) 54.7322 4.37061i 1.95223 0.155895i
\(787\) 15.6555 + 3.32767i 0.558057 + 0.118619i 0.478301 0.878196i \(-0.341253\pi\)
0.0797556 + 0.996814i \(0.474586\pi\)
\(788\) 7.48226 + 1.59040i 0.266544 + 0.0566557i
\(789\) −5.19165 7.53539i −0.184828 0.268267i
\(790\) 6.23295 + 9.12059i 0.221759 + 0.324496i
\(791\) −10.5242 32.3902i −0.374198 1.15166i
\(792\) −27.3384 + 10.5662i −0.971428 + 0.375452i
\(793\) 25.1879 0.894448
\(794\) −9.82887 4.37610i −0.348814 0.155302i
\(795\) −7.95576 + 20.6330i −0.282162 + 0.731776i
\(796\) −12.4165 + 5.52819i −0.440092 + 0.195942i
\(797\) −15.8206 + 7.04381i −0.560396 + 0.249504i −0.667331 0.744762i \(-0.732563\pi\)
0.106934 + 0.994266i \(0.465897\pi\)
\(798\) −31.7929 + 66.8522i −1.12546 + 2.36654i
\(799\) 2.01278 + 3.48623i 0.0712070 + 0.123334i
\(800\) −11.3103 22.4910i −0.399878 0.795176i
\(801\) 9.68932 9.73383i 0.342355 0.343928i
\(802\) −14.2173 + 43.7563i −0.502029 + 1.54509i
\(803\) 2.22505 21.1699i 0.0785202 0.747070i
\(804\) 18.0378 5.36552i 0.636144 0.189227i
\(805\) −5.93733 32.5147i −0.209263 1.14599i
\(806\) 1.32356 + 12.5929i 0.0466205 + 0.443565i
\(807\) 11.6381 + 28.0060i 0.409679 + 0.985857i
\(808\) −14.0005 6.23342i −0.492536 0.219291i
\(809\) 3.76845 + 11.5981i 0.132492 + 0.407767i 0.995191 0.0979492i \(-0.0312283\pi\)
−0.862700 + 0.505716i \(0.831228\pi\)
\(810\) −33.7006 8.02176i −1.18412 0.281856i
\(811\) 1.10851 3.41163i 0.0389249 0.119799i −0.929706 0.368303i \(-0.879939\pi\)
0.968631 + 0.248504i \(0.0799390\pi\)
\(812\) −11.7638 + 13.0651i −0.412829 + 0.458493i
\(813\) 17.7148 15.1650i 0.621286 0.531860i
\(814\) −18.9839 21.0838i −0.665387 0.738987i
\(815\) 6.24168 + 5.95459i 0.218637 + 0.208580i
\(816\) 11.4510 + 4.04025i 0.400865 + 0.141437i
\(817\) −23.3386 10.3910i −0.816516 0.363536i
\(818\) 41.1810 1.43986
\(819\) 4.54568 29.1322i 0.158839 1.01796i
\(820\) −7.58913 + 6.44709i −0.265024 + 0.225142i
\(821\) 0.975788 9.28401i 0.0340552 0.324014i −0.964210 0.265139i \(-0.914582\pi\)
0.998265 0.0588748i \(-0.0187513\pi\)
\(822\) 35.8678 + 33.9592i 1.25103 + 1.18446i
\(823\) −32.2029 35.7650i −1.12252 1.24669i −0.965868 0.259035i \(-0.916595\pi\)
−0.156656 0.987653i \(-0.550071\pi\)
\(824\) 0.0157184 0.0272251i 0.000547576 0.000948430i
\(825\) 38.9559 + 27.0120i 1.35627 + 0.940437i
\(826\) 42.2171 + 73.1221i 1.46892 + 2.54424i
\(827\) 8.29286 25.5228i 0.288371 0.887515i −0.696997 0.717074i \(-0.745481\pi\)
0.985368 0.170441i \(-0.0545191\pi\)
\(828\) −6.37230 7.83237i −0.221453 0.272194i
\(829\) −27.4122 19.9161i −0.952065 0.691716i −0.000770971 1.00000i \(-0.500245\pi\)
−0.951294 + 0.308284i \(0.900245\pi\)
\(830\) −25.2149 + 7.39650i −0.875221 + 0.256736i
\(831\) −1.14336 + 45.6621i −0.0396627 + 1.58400i
\(832\) −1.54539 + 2.67670i −0.0535769 + 0.0927979i
\(833\) −1.59686 15.1931i −0.0553278 0.526408i
\(834\) −24.4943 + 20.9687i −0.848169 + 0.726086i
\(835\) 13.2636 + 19.4085i 0.459007 + 0.671658i
\(836\) 9.56283 29.4314i 0.330737 1.01790i
\(837\) 13.5891 + 9.27091i 0.469707 + 0.320450i
\(838\) −6.67399 20.5404i −0.230549 0.709558i
\(839\) 17.6290 3.74715i 0.608620 0.129366i 0.106716 0.994290i \(-0.465966\pi\)
0.501904 + 0.864923i \(0.332633\pi\)
\(840\) 4.61738 28.8728i 0.159315 0.996205i
\(841\) 10.1515 + 2.15778i 0.350053 + 0.0744061i
\(842\) 0.212354 + 2.02041i 0.00731820 + 0.0696280i
\(843\) −26.4327 + 34.5296i −0.910390 + 1.18926i
\(844\) 6.44262 + 2.86844i 0.221764 + 0.0987358i
\(845\) −16.9483 + 1.28877i −0.583039 + 0.0443349i
\(846\) 5.28012 13.8500i 0.181534 0.476171i
\(847\) −64.8923 47.1470i −2.22973 1.61999i
\(848\) −27.9171 + 5.93397i −0.958679 + 0.203773i
\(849\) −24.7607 3.23095i −0.849785 0.110886i
\(850\) −3.06257 11.6764i −0.105045 0.400496i
\(851\) −5.26090 + 9.11215i −0.180341 + 0.312361i
\(852\) 4.73191 9.94998i 0.162113 0.340881i
\(853\) −4.26725 + 40.6001i −0.146108 + 1.39012i 0.638257 + 0.769823i \(0.279656\pi\)
−0.784365 + 0.620299i \(0.787011\pi\)
\(854\) −63.8586 46.3960i −2.18520 1.58764i
\(855\) −31.2471 + 23.9592i −1.06863 + 0.819387i
\(856\) 4.81315 3.49696i 0.164510 0.119524i
\(857\) −0.284511 0.492787i −0.00971870 0.0168333i 0.861125 0.508393i \(-0.169760\pi\)
−0.870844 + 0.491560i \(0.836427\pi\)
\(858\) −0.949204 + 37.9082i −0.0324053 + 1.29416i
\(859\) −34.4947 7.33208i −1.17695 0.250167i −0.422396 0.906411i \(-0.638811\pi\)
−0.754549 + 0.656244i \(0.772144\pi\)
\(860\) −9.29013 1.24807i −0.316791 0.0425590i
\(861\) −33.7678 + 2.69651i −1.15080 + 0.0918969i
\(862\) 28.9420 32.1434i 0.985769 1.09481i
\(863\) 7.48769 + 23.0447i 0.254884 + 0.784452i 0.993852 + 0.110712i \(0.0353132\pi\)
−0.738968 + 0.673740i \(0.764687\pi\)
\(864\) −8.81787 24.6315i −0.299990 0.837982i
\(865\) −10.4766 + 8.90005i −0.356215 + 0.302611i
\(866\) −23.0468 + 25.5960i −0.783161 + 0.869789i
\(867\) −22.2165 13.5793i −0.754511 0.461177i
\(868\) 6.44898 11.1700i 0.218893 0.379133i
\(869\) −1.64212 15.6237i −0.0557052 0.529999i
\(870\) −26.8740 + 10.2698i −0.911115 + 0.348178i
\(871\) −2.73977 + 26.0672i −0.0928337 + 0.883254i
\(872\) 4.13635 + 3.00523i 0.140074 + 0.101770i
\(873\) 22.5124 34.8405i 0.761928 1.17917i
\(874\) −35.3084 −1.19433
\(875\) −42.8454 + 20.0205i −1.44844 + 0.676815i
\(876\) 6.43284 + 0.839403i 0.217345 + 0.0283608i
\(877\) −32.8680 36.5036i −1.10987 1.23264i −0.970165 0.242448i \(-0.922050\pi\)
−0.139710 0.990193i \(-0.544617\pi\)
\(878\) −35.6533 + 15.8739i −1.20324 + 0.535717i
\(879\) 8.41843 + 7.97048i 0.283947 + 0.268838i
\(880\) −1.76333 + 61.1572i −0.0594419 + 2.06161i
\(881\) −9.93477 + 7.21804i −0.334711 + 0.243182i −0.742427 0.669927i \(-0.766325\pi\)
0.407716 + 0.913109i \(0.366325\pi\)
\(882\) −39.6834 + 39.8656i −1.33621 + 1.34235i
\(883\) −40.0558 + 29.1022i −1.34798 + 0.979367i −0.348874 + 0.937170i \(0.613436\pi\)
−0.999109 + 0.0421976i \(0.986564\pi\)
\(884\) 2.10017 2.33247i 0.0706363 0.0784496i
\(885\) 2.28322 + 44.8529i 0.0767495 + 1.50771i
\(886\) −5.71992 6.35262i −0.192165 0.213420i
\(887\) 46.9880 + 9.98760i 1.57770 + 0.335351i 0.911783 0.410673i \(-0.134706\pi\)
0.665919 + 0.746024i \(0.268040\pi\)
\(888\) −7.07100 + 6.05323i −0.237287 + 0.203133i
\(889\) 19.6745 4.18195i 0.659862 0.140258i
\(890\) −6.70043 16.2981i −0.224599 0.546312i
\(891\) 36.7613 + 32.7962i 1.23155 + 1.09871i
\(892\) 15.8497 11.5155i 0.530688 0.385568i
\(893\) −8.42377 14.5904i −0.281891 0.488249i
\(894\) 25.0703 + 15.3236i 0.838476 + 0.512498i
\(895\) 15.9627 + 2.14450i 0.533575 + 0.0716827i
\(896\) 47.7609 21.2645i 1.59558 0.710399i
\(897\) 13.4795 4.00961i 0.450067 0.133877i
\(898\) −29.9180 + 6.35927i −0.998376 + 0.212211i
\(899\) 13.6616 0.455640
\(900\) −8.52690 + 11.6626i −0.284230 + 0.388752i
\(901\) −8.00797 −0.266784
\(902\) 42.6148 9.05806i 1.41892 0.301600i
\(903\) −23.1556 21.9234i −0.770569 0.729567i
\(904\) 13.1279 5.84493i 0.436628 0.194399i
\(905\) −21.9837 + 45.7778i −0.730763 + 1.52171i
\(906\) 47.5120 25.8674i 1.57848 0.859387i
\(907\) −4.54408 7.87058i −0.150884 0.261338i 0.780669 0.624945i \(-0.214879\pi\)
−0.931553 + 0.363607i \(0.881545\pi\)
\(908\) 16.9587 12.3212i 0.562794 0.408894i
\(909\) 1.40710 + 25.7213i 0.0466706 + 0.853123i
\(910\) −32.2030 19.8514i −1.06752 0.658067i
\(911\) −2.29989 + 0.488856i −0.0761987 + 0.0161965i −0.245853 0.969307i \(-0.579068\pi\)
0.169655 + 0.985504i \(0.445735\pi\)
\(912\) −47.9241 16.9090i −1.58693 0.559914i
\(913\) 36.5523 + 7.76943i 1.20970 + 0.257131i
\(914\) 23.0759 + 25.6284i 0.763282 + 0.847711i
\(915\) −19.0048 37.4376i −0.628279 1.23765i
\(916\) −12.1035 + 13.4422i −0.399909 + 0.444144i
\(917\) 63.0198 45.7866i 2.08110 1.51201i
\(918\) −1.68017 12.4319i −0.0554540 0.410313i
\(919\) −35.1878 + 25.5654i −1.16074 + 0.843325i −0.989871 0.141969i \(-0.954657\pi\)
−0.170866 + 0.985294i \(0.554657\pi\)
\(920\) 13.3825 3.92559i 0.441206 0.129423i
\(921\) −1.31237 + 5.49414i −0.0432441 + 0.181038i
\(922\) −19.8192 + 8.82409i −0.652712 + 0.290606i
\(923\) 10.2682 + 11.4040i 0.337982 + 0.375367i
\(924\) 23.4789 30.6710i 0.772399 1.00900i
\(925\) 14.5211 + 3.97336i 0.477451 + 0.130643i
\(926\) −42.8642 −1.40860
\(927\) −0.0527743 0.00264455i −0.00173334 8.68583e-5i
\(928\) −17.5777 12.7709i −0.577015 0.419226i
\(929\) −5.37815 + 51.1697i −0.176451 + 1.67882i 0.445125 + 0.895469i \(0.353159\pi\)
−0.621576 + 0.783354i \(0.713507\pi\)
\(930\) 17.7186 11.4688i 0.581015 0.376078i
\(931\) 6.68307 + 63.5852i 0.219029 + 2.08392i
\(932\) −3.08265 + 5.33931i −0.100976 + 0.174895i
\(933\) 49.0290 26.6934i 1.60514 0.873901i
\(934\) 42.2022 46.8703i 1.38090 1.53364i
\(935\) −4.05159 + 16.6816i −0.132501 + 0.545547i
\(936\) 12.4254 + 0.622642i 0.406137 + 0.0203517i
\(937\) −1.71388 5.27478i −0.0559900 0.172320i 0.919151 0.393906i \(-0.128876\pi\)
−0.975141 + 0.221587i \(0.928876\pi\)
\(938\) 54.9618 61.0413i 1.79457 1.99307i
\(939\) −20.1696 29.2751i −0.658211 0.955356i
\(940\) −4.47267 4.26694i −0.145882 0.139172i
\(941\) −34.3030 7.29133i −1.11825 0.237691i −0.388527 0.921437i \(-0.627016\pi\)
−0.729720 + 0.683746i \(0.760349\pi\)
\(942\) 6.77232 + 4.13942i 0.220654 + 0.134869i
\(943\) −8.07869 13.9927i −0.263078 0.455665i
\(944\) −46.8939 + 34.0704i −1.52627 + 1.10890i
\(945\) −46.7300 + 15.2244i −1.52013 + 0.495250i
\(946\) 33.1782 + 24.1053i 1.07871 + 0.783732i
\(947\) 5.85222 55.6801i 0.190172 1.80936i −0.317984 0.948096i \(-0.603006\pi\)
0.508155 0.861265i \(-0.330328\pi\)
\(948\) 4.77260 0.381113i 0.155007 0.0123780i
\(949\) −4.51778 + 7.82502i −0.146653 + 0.254011i
\(950\) 12.8173 + 48.8673i 0.415848 + 1.58546i
\(951\) 4.21126 5.50126i 0.136559 0.178391i
\(952\) 10.3571 2.20147i 0.335676 0.0713502i
\(953\) −5.24619 3.81158i −0.169941 0.123469i 0.499564 0.866277i \(-0.333494\pi\)
−0.669505 + 0.742808i \(0.733494\pi\)
\(954\) 18.6085 + 22.8722i 0.602471 + 0.740514i
\(955\) −5.66360 + 23.3187i −0.183270 + 0.754576i
\(956\) −15.4751 6.88995i −0.500500 0.222837i
\(957\) 40.5690 + 5.29374i 1.31141 + 0.171122i
\(958\) −1.31475 12.5090i −0.0424777 0.404149i
\(959\) 68.5443 + 14.5696i 2.21341 + 0.470475i
\(960\) 5.14450 + 0.277347i 0.166038 + 0.00895132i
\(961\) 20.5189 4.36143i 0.661900 0.140691i
\(962\) 3.72141 + 11.4533i 0.119983 + 0.369270i
\(963\) −8.92045 4.51948i −0.287458 0.145638i
\(964\) 2.26125 6.95941i 0.0728300 0.224148i
\(965\) 0.966074 33.5061i 0.0310990 1.07860i
\(966\) −41.5601 14.6636i −1.33717 0.471795i
\(967\) −0.523420 4.98001i −0.0168321 0.160146i 0.982877 0.184262i \(-0.0589896\pi\)
−0.999709 + 0.0241160i \(0.992323\pi\)
\(968\) 16.9225 29.3106i 0.543909 0.942078i
\(969\) −12.1663 7.43635i −0.390837 0.238890i
\(970\) −30.0290 43.9410i −0.964173 1.41086i
\(971\) −40.8653 29.6904i −1.31143 0.952810i −0.999997 0.00254202i \(-0.999191\pi\)
−0.311434 0.950268i \(-0.600809\pi\)
\(972\) −10.2724 + 10.9498i −0.329488 + 0.351216i
\(973\) −14.1359 + 43.5059i −0.453177 + 1.39473i
\(974\) 21.3261 + 36.9380i 0.683333 + 1.18357i
\(975\) −10.4425 17.2003i −0.334429 0.550849i
\(976\) 27.0940 46.9281i 0.867257 1.50213i
\(977\) 15.9615 + 17.7270i 0.510653 + 0.567138i 0.942242 0.334933i \(-0.108714\pi\)
−0.431589 + 0.902070i \(0.642047\pi\)
\(978\) 11.0249 3.27946i 0.352537 0.104866i
\(979\) −2.61945 + 24.9224i −0.0837180 + 0.796523i
\(980\) 8.91987 + 21.6966i 0.284935 + 0.693072i
\(981\) 1.32492 8.49111i 0.0423016 0.271100i
\(982\) −35.1227 −1.12081
\(983\) 8.65772 + 3.85467i 0.276138 + 0.122945i 0.540134 0.841579i \(-0.318374\pi\)
−0.263995 + 0.964524i \(0.585040\pi\)
\(984\) −2.62090 14.0513i −0.0835513 0.447938i
\(985\) 17.6009 + 2.36458i 0.560811 + 0.0753417i
\(986\) −6.97116 7.74226i −0.222007 0.246564i
\(987\) −3.85586 20.6722i −0.122733 0.658002i
\(988\) −8.78951 + 9.76174i −0.279632 + 0.310562i
\(989\) 4.69993 14.4649i 0.149449 0.459957i
\(990\) 57.0605 27.1917i 1.81350 0.864209i
\(991\) 8.47195 + 26.0740i 0.269120 + 0.828268i 0.990715 + 0.135952i \(0.0434093\pi\)
−0.721595 + 0.692316i \(0.756591\pi\)
\(992\) 14.5619 + 6.48336i 0.462340 + 0.205847i
\(993\) −1.55196 + 2.02736i −0.0492500 + 0.0643363i
\(994\) −5.02675 47.8264i −0.159439 1.51696i
\(995\) −27.7703 + 14.9831i −0.880378 + 0.474996i
\(996\) −2.64595 + 11.0771i −0.0838402 + 0.350990i
\(997\) −2.65815 + 25.2906i −0.0841844 + 0.800961i 0.868232 + 0.496159i \(0.165257\pi\)
−0.952416 + 0.304802i \(0.901410\pi\)
\(998\) 11.4166 35.1366i 0.361385 1.11223i
\(999\) 14.4751 + 5.93756i 0.457970 + 0.187856i
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 225.2.q.a.121.6 yes 224
3.2 odd 2 675.2.r.a.496.23 224
9.2 odd 6 675.2.r.a.46.6 224
9.7 even 3 inner 225.2.q.a.196.23 yes 224
25.6 even 5 inner 225.2.q.a.31.23 224
75.56 odd 10 675.2.r.a.631.6 224
225.56 odd 30 675.2.r.a.181.23 224
225.106 even 15 inner 225.2.q.a.106.6 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.23 224 25.6 even 5 inner
225.2.q.a.106.6 yes 224 225.106 even 15 inner
225.2.q.a.121.6 yes 224 1.1 even 1 trivial
225.2.q.a.196.23 yes 224 9.7 even 3 inner
675.2.r.a.46.6 224 9.2 odd 6
675.2.r.a.181.23 224 225.56 odd 30
675.2.r.a.496.23 224 3.2 odd 2
675.2.r.a.631.6 224 75.56 odd 10