Properties

Label 187.2.p.a.4.10
Level $187$
Weight $2$
Character 187.4
Analytic conductor $1.493$
Analytic rank $0$
Dimension $128$
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] = [187,2,Mod(4,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([4, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.p (of order \(20\), 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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 4.10
Character \(\chi\) \(=\) 187.4
Dual form 187.2.p.a.47.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.201795 - 0.277747i) q^{2} +(-0.935793 - 1.83660i) q^{3} +(0.581612 + 1.79002i) q^{4} +(0.314547 - 1.98597i) q^{5} +(-0.698947 - 0.110702i) q^{6} +(0.501695 - 0.984632i) q^{7} +(1.26756 + 0.411855i) q^{8} +(-0.734024 + 1.01030i) q^{9} +O(q^{10})\) \(q+(0.201795 - 0.277747i) q^{2} +(-0.935793 - 1.83660i) q^{3} +(0.581612 + 1.79002i) q^{4} +(0.314547 - 1.98597i) q^{5} +(-0.698947 - 0.110702i) q^{6} +(0.501695 - 0.984632i) q^{7} +(1.26756 + 0.411855i) q^{8} +(-0.734024 + 1.01030i) q^{9} +(-0.488124 - 0.488124i) q^{10} +(-0.585679 - 3.26450i) q^{11} +(2.74327 - 2.74327i) q^{12} +(-2.29323 - 1.66613i) q^{13} +(-0.172239 - 0.338038i) q^{14} +(-3.94178 + 1.28076i) q^{15} +(-2.67518 + 1.94363i) q^{16} +(4.06867 + 0.667787i) q^{17} +(0.132484 + 0.407745i) q^{18} +(-3.26301 - 1.06022i) q^{19} +(3.73787 - 0.592021i) q^{20} -2.27786 q^{21} +(-1.02489 - 0.496089i) q^{22} +(6.22445 + 6.22445i) q^{23} +(-0.429761 - 2.71341i) q^{24} +(0.910132 + 0.295720i) q^{25} +(-0.925522 + 0.300720i) q^{26} +(-3.56525 - 0.564680i) q^{27} +(2.05430 + 0.325369i) q^{28} +(3.08761 + 1.57321i) q^{29} +(-0.439704 + 1.35327i) q^{30} +(-3.03403 + 0.480543i) q^{31} +3.80082i q^{32} +(-5.44750 + 4.13055i) q^{33} +(1.00651 - 0.995303i) q^{34} +(-1.79765 - 1.30607i) q^{35} +(-2.23537 - 0.726314i) q^{36} +(8.77289 + 4.47001i) q^{37} +(-0.952930 + 0.692344i) q^{38} +(-0.914018 + 5.77088i) q^{39} +(1.21664 - 2.38779i) q^{40} +(-0.965531 + 0.491963i) q^{41} +(-0.459659 + 0.632667i) q^{42} +3.73630i q^{43} +(5.50288 - 2.94705i) q^{44} +(1.77554 + 1.77554i) q^{45} +(2.98488 - 0.472759i) q^{46} +(-0.0125737 + 0.0386980i) q^{47} +(6.07308 + 3.09439i) q^{48} +(3.39669 + 4.67515i) q^{49} +(0.265795 - 0.193111i) q^{50} +(-2.58098 - 8.09741i) q^{51} +(1.64863 - 5.07395i) q^{52} +(-2.68874 + 3.70074i) q^{53} +(-0.876286 + 0.876286i) q^{54} +(-6.66744 + 0.136302i) q^{55} +(1.04145 - 1.04145i) q^{56} +(1.10631 + 6.98498i) q^{57} +(1.06002 - 0.540106i) q^{58} +(0.428824 - 0.139333i) q^{59} +(-4.58518 - 6.31095i) q^{60} +(-14.9105 - 2.36159i) q^{61} +(-0.478782 + 0.939663i) q^{62} +(0.626515 + 1.22960i) q^{63} +(-4.29470 - 3.12028i) q^{64} +(-4.03021 + 4.03021i) q^{65} +(0.0479705 + 2.34655i) q^{66} -2.31789 q^{67} +(1.17104 + 7.67138i) q^{68} +(5.60701 - 17.2566i) q^{69} +(-0.725512 + 0.235733i) q^{70} +(1.48068 - 9.34865i) q^{71} +(-1.34651 + 0.978300i) q^{72} +(2.70696 + 1.37926i) q^{73} +(3.01186 - 1.53462i) q^{74} +(-0.308577 - 1.94828i) q^{75} -6.45748i q^{76} +(-3.50817 - 1.06111i) q^{77} +(1.41840 + 1.41840i) q^{78} +(-0.675651 - 4.26589i) q^{79} +(3.01853 + 5.92420i) q^{80} +(3.45694 + 10.6394i) q^{81} +(-0.0581982 + 0.367449i) q^{82} +(-2.40062 - 3.30417i) q^{83} +(-1.32483 - 4.07740i) q^{84} +(2.60600 - 7.87022i) q^{85} +(1.03775 + 0.753967i) q^{86} -7.14289i q^{87} +(0.602119 - 4.37917i) q^{88} +1.55689 q^{89} +(0.851444 - 0.134855i) q^{90} +(-2.79102 + 1.42210i) q^{91} +(-7.52166 + 14.7621i) q^{92} +(3.72179 + 5.12260i) q^{93} +(0.00821092 + 0.0113014i) q^{94} +(-3.13193 + 6.14677i) q^{95} +(6.98057 - 3.55678i) q^{96} +(8.53858 - 1.35238i) q^{97} +1.98394 q^{98} +(3.72802 + 1.80451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 10 q^{3} + 16 q^{4} - 2 q^{5} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 10 q^{3} + 16 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{10} - 40 q^{13} + 2 q^{14} - 48 q^{16} - 18 q^{17} - 2 q^{20} + 16 q^{21} - 70 q^{22} - 16 q^{23} + 28 q^{24} - 22 q^{27} + 42 q^{28} - 2 q^{29} - 44 q^{30} - 6 q^{31} + 32 q^{33} + 44 q^{34} + 12 q^{35} + 30 q^{37} - 80 q^{38} + 78 q^{39} - 100 q^{40} - 56 q^{41} + 52 q^{44} - 68 q^{45} + 14 q^{46} - 16 q^{47} - 110 q^{48} + 84 q^{50} + 14 q^{51} - 100 q^{52} - 20 q^{54} - 84 q^{55} + 36 q^{56} - 48 q^{57} - 26 q^{58} + 28 q^{61} + 108 q^{62} - 40 q^{63} + 120 q^{64} + 28 q^{65} - 48 q^{67} + 102 q^{68} + 24 q^{69} + 2 q^{71} + 80 q^{72} - 30 q^{73} - 28 q^{74} - 80 q^{75} - 104 q^{78} + 44 q^{79} - 92 q^{80} + 140 q^{81} - 28 q^{82} - 52 q^{84} + 76 q^{85} + 12 q^{86} + 50 q^{88} - 32 q^{89} + 204 q^{90} + 42 q^{91} + 2 q^{92} + 16 q^{95} + 240 q^{96} - 34 q^{97} + 24 q^{98} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.201795 0.277747i 0.142690 0.196397i −0.731690 0.681638i \(-0.761268\pi\)
0.874380 + 0.485241i \(0.161268\pi\)
\(3\) −0.935793 1.83660i −0.540280 1.06036i −0.986242 0.165308i \(-0.947138\pi\)
0.445962 0.895052i \(-0.352862\pi\)
\(4\) 0.581612 + 1.79002i 0.290806 + 0.895009i
\(5\) 0.314547 1.98597i 0.140670 0.888154i −0.811892 0.583808i \(-0.801562\pi\)
0.952561 0.304346i \(-0.0984380\pi\)
\(6\) −0.698947 0.110702i −0.285344 0.0451940i
\(7\) 0.501695 0.984632i 0.189623 0.372156i −0.776548 0.630058i \(-0.783031\pi\)
0.966171 + 0.257902i \(0.0830311\pi\)
\(8\) 1.26756 + 0.411855i 0.448150 + 0.145613i
\(9\) −0.734024 + 1.01030i −0.244675 + 0.336766i
\(10\) −0.488124 0.488124i −0.154358 0.154358i
\(11\) −0.585679 3.26450i −0.176589 0.984285i
\(12\) 2.74327 2.74327i 0.791914 0.791914i
\(13\) −2.29323 1.66613i −0.636026 0.462100i 0.222456 0.974943i \(-0.428593\pi\)
−0.858483 + 0.512842i \(0.828593\pi\)
\(14\) −0.172239 0.338038i −0.0460328 0.0903444i
\(15\) −3.94178 + 1.28076i −1.01776 + 0.330692i
\(16\) −2.67518 + 1.94363i −0.668795 + 0.485908i
\(17\) 4.06867 + 0.667787i 0.986797 + 0.161962i
\(18\) 0.132484 + 0.407745i 0.0312269 + 0.0961065i
\(19\) −3.26301 1.06022i −0.748586 0.243230i −0.0902134 0.995922i \(-0.528755\pi\)
−0.658373 + 0.752692i \(0.728755\pi\)
\(20\) 3.73787 0.592021i 0.835813 0.132380i
\(21\) −2.27786 −0.497069
\(22\) −1.02489 0.496089i −0.218508 0.105767i
\(23\) 6.22445 + 6.22445i 1.29789 + 1.29789i 0.929786 + 0.368101i \(0.119992\pi\)
0.368101 + 0.929786i \(0.380008\pi\)
\(24\) −0.429761 2.71341i −0.0877247 0.553872i
\(25\) 0.910132 + 0.295720i 0.182026 + 0.0591439i
\(26\) −0.925522 + 0.300720i −0.181510 + 0.0589761i
\(27\) −3.56525 0.564680i −0.686132 0.108673i
\(28\) 2.05430 + 0.325369i 0.388226 + 0.0614890i
\(29\) 3.08761 + 1.57321i 0.573354 + 0.292139i 0.716527 0.697559i \(-0.245731\pi\)
−0.143173 + 0.989698i \(0.545731\pi\)
\(30\) −0.439704 + 1.35327i −0.0802785 + 0.247072i
\(31\) −3.03403 + 0.480543i −0.544928 + 0.0863081i −0.422828 0.906210i \(-0.638963\pi\)
−0.122099 + 0.992518i \(0.538963\pi\)
\(32\) 3.80082i 0.671896i
\(33\) −5.44750 + 4.13055i −0.948288 + 0.719037i
\(34\) 1.00651 0.995303i 0.172615 0.170693i
\(35\) −1.79765 1.30607i −0.303858 0.220766i
\(36\) −2.23537 0.726314i −0.372561 0.121052i
\(37\) 8.77289 + 4.47001i 1.44225 + 0.734866i 0.987774 0.155891i \(-0.0498249\pi\)
0.454481 + 0.890757i \(0.349825\pi\)
\(38\) −0.952930 + 0.692344i −0.154586 + 0.112313i
\(39\) −0.914018 + 5.77088i −0.146360 + 0.924080i
\(40\) 1.21664 2.38779i 0.192368 0.377543i
\(41\) −0.965531 + 0.491963i −0.150791 + 0.0768317i −0.527758 0.849395i \(-0.676967\pi\)
0.376967 + 0.926227i \(0.376967\pi\)
\(42\) −0.459659 + 0.632667i −0.0709270 + 0.0976226i
\(43\) 3.73630i 0.569781i 0.958560 + 0.284890i \(0.0919572\pi\)
−0.958560 + 0.284890i \(0.908043\pi\)
\(44\) 5.50288 2.94705i 0.829590 0.444284i
\(45\) 1.77554 + 1.77554i 0.264681 + 0.264681i
\(46\) 2.98488 0.472759i 0.440097 0.0697045i
\(47\) −0.0125737 + 0.0386980i −0.00183407 + 0.00564468i −0.951969 0.306193i \(-0.900945\pi\)
0.950135 + 0.311838i \(0.100945\pi\)
\(48\) 6.07308 + 3.09439i 0.876574 + 0.446637i
\(49\) 3.39669 + 4.67515i 0.485242 + 0.667878i
\(50\) 0.265795 0.193111i 0.0375891 0.0273101i
\(51\) −2.58098 8.09741i −0.361409 1.13386i
\(52\) 1.64863 5.07395i 0.228623 0.703631i
\(53\) −2.68874 + 3.70074i −0.369327 + 0.508335i −0.952718 0.303856i \(-0.901726\pi\)
0.583391 + 0.812192i \(0.301726\pi\)
\(54\) −0.876286 + 0.876286i −0.119247 + 0.119247i
\(55\) −6.66744 + 0.136302i −0.899037 + 0.0183790i
\(56\) 1.04145 1.04145i 0.139170 0.139170i
\(57\) 1.10631 + 6.98498i 0.146535 + 0.925183i
\(58\) 1.06002 0.540106i 0.139187 0.0709194i
\(59\) 0.428824 0.139333i 0.0558281 0.0181396i −0.280970 0.959717i \(-0.590656\pi\)
0.336798 + 0.941577i \(0.390656\pi\)
\(60\) −4.58518 6.31095i −0.591944 0.814741i
\(61\) −14.9105 2.36159i −1.90909 0.302371i −0.914362 0.404898i \(-0.867307\pi\)
−0.994730 + 0.102527i \(0.967307\pi\)
\(62\) −0.478782 + 0.939663i −0.0608054 + 0.119337i
\(63\) 0.626515 + 1.22960i 0.0789334 + 0.154916i
\(64\) −4.29470 3.12028i −0.536837 0.390035i
\(65\) −4.03021 + 4.03021i −0.499886 + 0.499886i
\(66\) 0.0479705 + 2.34655i 0.00590476 + 0.288840i
\(67\) −2.31789 −0.283175 −0.141588 0.989926i \(-0.545221\pi\)
−0.141588 + 0.989926i \(0.545221\pi\)
\(68\) 1.17104 + 7.67138i 0.142009 + 0.930291i
\(69\) 5.60701 17.2566i 0.675004 2.07745i
\(70\) −0.725512 + 0.235733i −0.0867152 + 0.0281755i
\(71\) 1.48068 9.34865i 0.175724 1.10948i −0.729323 0.684170i \(-0.760165\pi\)
0.905047 0.425311i \(-0.139835\pi\)
\(72\) −1.34651 + 0.978300i −0.158688 + 0.115294i
\(73\) 2.70696 + 1.37926i 0.316826 + 0.161431i 0.605170 0.796096i \(-0.293105\pi\)
−0.288345 + 0.957527i \(0.593105\pi\)
\(74\) 3.01186 1.53462i 0.350121 0.178396i
\(75\) −0.308577 1.94828i −0.0356314 0.224968i
\(76\) 6.45748i 0.740724i
\(77\) −3.50817 1.06111i −0.399793 0.120924i
\(78\) 1.41840 + 1.41840i 0.160602 + 0.160602i
\(79\) −0.675651 4.26589i −0.0760167 0.479951i −0.996100 0.0882284i \(-0.971879\pi\)
0.920084 0.391722i \(-0.128121\pi\)
\(80\) 3.01853 + 5.92420i 0.337482 + 0.662346i
\(81\) 3.45694 + 10.6394i 0.384105 + 1.18215i
\(82\) −0.0581982 + 0.367449i −0.00642691 + 0.0405779i
\(83\) −2.40062 3.30417i −0.263502 0.362679i 0.656681 0.754169i \(-0.271960\pi\)
−0.920183 + 0.391489i \(0.871960\pi\)
\(84\) −1.32483 4.07740i −0.144551 0.444881i
\(85\) 2.60600 7.87022i 0.282660 0.853645i
\(86\) 1.03775 + 0.753967i 0.111903 + 0.0813023i
\(87\) 7.14289i 0.765798i
\(88\) 0.602119 4.37917i 0.0641861 0.466821i
\(89\) 1.55689 0.165030 0.0825149 0.996590i \(-0.473705\pi\)
0.0825149 + 0.996590i \(0.473705\pi\)
\(90\) 0.851444 0.134855i 0.0897501 0.0142150i
\(91\) −2.79102 + 1.42210i −0.292579 + 0.149076i
\(92\) −7.52166 + 14.7621i −0.784187 + 1.53905i
\(93\) 3.72179 + 5.12260i 0.385931 + 0.531189i
\(94\) 0.00821092 + 0.0113014i 0.000846892 + 0.00116565i
\(95\) −3.13193 + 6.14677i −0.321330 + 0.630645i
\(96\) 6.98057 3.55678i 0.712452 0.363012i
\(97\) 8.53858 1.35238i 0.866961 0.137313i 0.292917 0.956138i \(-0.405374\pi\)
0.574044 + 0.818825i \(0.305374\pi\)
\(98\) 1.98394 0.200408
\(99\) 3.72802 + 1.80451i 0.374680 + 0.181360i
\(100\) 1.80115i 0.180115i
\(101\) 15.2750 + 11.0979i 1.51992 + 1.10428i 0.961529 + 0.274703i \(0.0885795\pi\)
0.558387 + 0.829581i \(0.311421\pi\)
\(102\) −2.76986 0.917158i −0.274257 0.0908122i
\(103\) 0.423375 + 1.30301i 0.0417164 + 0.128390i 0.969746 0.244117i \(-0.0784982\pi\)
−0.928029 + 0.372507i \(0.878498\pi\)
\(104\) −2.22060 3.05639i −0.217748 0.299704i
\(105\) −0.716493 + 4.52376i −0.0699226 + 0.441474i
\(106\) 0.485293 + 1.49358i 0.0471359 + 0.145069i
\(107\) −7.73583 15.1824i −0.747851 1.46774i −0.879224 0.476408i \(-0.841939\pi\)
0.131373 0.991333i \(-0.458061\pi\)
\(108\) −1.06280 6.71028i −0.102268 0.645697i
\(109\) −7.69383 7.69383i −0.736935 0.736935i 0.235048 0.971984i \(-0.424475\pi\)
−0.971984 + 0.235048i \(0.924475\pi\)
\(110\) −1.30760 + 1.87936i −0.124675 + 0.179190i
\(111\) 20.2953i 1.92634i
\(112\) 0.571638 + 3.60918i 0.0540147 + 0.341036i
\(113\) 7.97828 4.06514i 0.750534 0.382416i −0.0364938 0.999334i \(-0.511619\pi\)
0.787028 + 0.616918i \(0.211619\pi\)
\(114\) 2.16330 + 1.10226i 0.202612 + 0.103236i
\(115\) 14.3195 10.4037i 1.33530 0.970151i
\(116\) −1.02029 + 6.44187i −0.0947317 + 0.598113i
\(117\) 3.36656 1.09386i 0.311239 0.101128i
\(118\) 0.0478350 0.147221i 0.00440357 0.0135528i
\(119\) 2.69876 3.67112i 0.247395 0.336531i
\(120\) −5.52393 −0.504264
\(121\) −10.3140 + 3.82390i −0.937633 + 0.347627i
\(122\) −3.66478 + 3.66478i −0.331794 + 0.331794i
\(123\) 1.80707 + 1.31292i 0.162938 + 0.118382i
\(124\) −2.62481 5.15147i −0.235715 0.462616i
\(125\) 5.43783 10.6723i 0.486374 0.954563i
\(126\) 0.467946 + 0.0741154i 0.0416879 + 0.00660272i
\(127\) 5.63180 + 7.75150i 0.499741 + 0.687835i 0.982147 0.188113i \(-0.0602371\pi\)
−0.482406 + 0.875948i \(0.660237\pi\)
\(128\) −8.96288 + 2.91222i −0.792214 + 0.257406i
\(129\) 6.86208 3.49641i 0.604173 0.307841i
\(130\) 0.306102 + 1.93265i 0.0268469 + 0.169505i
\(131\) −14.1290 + 14.1290i −1.23446 + 1.23446i −0.272221 + 0.962235i \(0.587758\pi\)
−0.962235 + 0.272221i \(0.912242\pi\)
\(132\) −10.5621 7.34874i −0.919312 0.639626i
\(133\) −2.68096 + 2.68096i −0.232469 + 0.232469i
\(134\) −0.467738 + 0.643787i −0.0404064 + 0.0556147i
\(135\) −2.24288 + 6.90287i −0.193036 + 0.594104i
\(136\) 4.88225 + 2.52216i 0.418649 + 0.216273i
\(137\) 3.81103 2.76888i 0.325598 0.236561i −0.412962 0.910748i \(-0.635506\pi\)
0.738561 + 0.674187i \(0.235506\pi\)
\(138\) −3.66150 5.03962i −0.311687 0.429001i
\(139\) −9.35801 4.76815i −0.793736 0.404429i 0.00960047 0.999954i \(-0.496944\pi\)
−0.803337 + 0.595525i \(0.796944\pi\)
\(140\) 1.29235 3.97744i 0.109223 0.336155i
\(141\) 0.0828390 0.0131204i 0.00697630 0.00110494i
\(142\) −2.29776 2.29776i −0.192824 0.192824i
\(143\) −4.09598 + 8.46206i −0.342523 + 0.707633i
\(144\) 4.12940i 0.344117i
\(145\) 4.09556 5.63705i 0.340118 0.468132i
\(146\) 0.929336 0.473521i 0.0769124 0.0391888i
\(147\) 5.40776 10.6133i 0.446025 0.875372i
\(148\) −2.89898 + 18.3034i −0.238295 + 1.50453i
\(149\) −8.33164 + 6.05329i −0.682555 + 0.495905i −0.874204 0.485558i \(-0.838616\pi\)
0.191649 + 0.981463i \(0.438616\pi\)
\(150\) −0.603397 0.307446i −0.0492671 0.0251029i
\(151\) −14.5074 4.71375i −1.18060 0.383600i −0.348010 0.937491i \(-0.613142\pi\)
−0.832589 + 0.553891i \(0.813142\pi\)
\(152\) −3.69940 2.68778i −0.300061 0.218007i
\(153\) −3.66116 + 3.62039i −0.295987 + 0.292691i
\(154\) −1.00265 + 0.760256i −0.0807958 + 0.0612632i
\(155\) 6.17665i 0.496121i
\(156\) −10.8616 + 1.72030i −0.869622 + 0.137735i
\(157\) −2.41402 + 7.42959i −0.192660 + 0.592946i 0.807336 + 0.590092i \(0.200908\pi\)
−0.999996 + 0.00285405i \(0.999092\pi\)
\(158\) −1.32118 0.673175i −0.105108 0.0535549i
\(159\) 9.31287 + 1.47501i 0.738558 + 0.116976i
\(160\) 7.54833 + 1.19554i 0.596748 + 0.0945155i
\(161\) 9.25157 3.00602i 0.729126 0.236907i
\(162\) 3.65264 + 1.18682i 0.286979 + 0.0932450i
\(163\) 2.63354 + 16.6275i 0.206275 + 1.30237i 0.845759 + 0.533565i \(0.179148\pi\)
−0.639484 + 0.768804i \(0.720852\pi\)
\(164\) −1.44219 1.44219i −0.112616 0.112616i
\(165\) 6.48968 + 12.1178i 0.505221 + 0.943373i
\(166\) −1.40215 −0.108828
\(167\) 16.2545 2.57445i 1.25781 0.199217i 0.508281 0.861191i \(-0.330281\pi\)
0.749527 + 0.661974i \(0.230281\pi\)
\(168\) −2.88732 0.938146i −0.222761 0.0723796i
\(169\) −1.53431 4.72213i −0.118024 0.363241i
\(170\) −1.66005 2.31198i −0.127320 0.177320i
\(171\) 3.46626 2.51839i 0.265072 0.192586i
\(172\) −6.68805 + 2.17308i −0.509959 + 0.165696i
\(173\) 4.12476 + 8.09531i 0.313600 + 0.615475i 0.992976 0.118316i \(-0.0377495\pi\)
−0.679376 + 0.733790i \(0.737749\pi\)
\(174\) −1.98391 1.44140i −0.150400 0.109272i
\(175\) 0.747784 0.747784i 0.0565271 0.0565271i
\(176\) 7.91179 + 7.59479i 0.596374 + 0.572479i
\(177\) −0.657189 0.657189i −0.0493973 0.0493973i
\(178\) 0.314172 0.432420i 0.0235482 0.0324113i
\(179\) 3.98181 + 1.29377i 0.297614 + 0.0967008i 0.454018 0.890992i \(-0.349990\pi\)
−0.156404 + 0.987693i \(0.549990\pi\)
\(180\) −2.14557 + 4.21092i −0.159921 + 0.313863i
\(181\) 15.7999 + 2.50246i 1.17440 + 0.186006i 0.712984 0.701180i \(-0.247343\pi\)
0.461412 + 0.887186i \(0.347343\pi\)
\(182\) −0.168231 + 1.06217i −0.0124701 + 0.0787332i
\(183\) 9.61584 + 29.5945i 0.710823 + 2.18769i
\(184\) 5.32629 + 10.4534i 0.392659 + 0.770637i
\(185\) 11.6368 16.0167i 0.855556 1.17757i
\(186\) 2.17382 0.159392
\(187\) −0.202942 13.6733i −0.0148406 0.999890i
\(188\) −0.0765831 −0.00558539
\(189\) −2.34467 + 3.22716i −0.170550 + 0.234741i
\(190\) 1.07524 + 2.11027i 0.0780058 + 0.153095i
\(191\) 0.0554392 + 0.170624i 0.00401144 + 0.0123459i 0.953042 0.302838i \(-0.0979340\pi\)
−0.949031 + 0.315183i \(0.897934\pi\)
\(192\) −1.71175 + 10.8076i −0.123535 + 0.779969i
\(193\) −16.2237 2.56959i −1.16781 0.184963i −0.457735 0.889089i \(-0.651339\pi\)
−0.710075 + 0.704126i \(0.751339\pi\)
\(194\) 1.34742 2.64447i 0.0967393 0.189862i
\(195\) 11.1733 + 3.63043i 0.800138 + 0.259980i
\(196\) −6.39304 + 8.79926i −0.456646 + 0.628519i
\(197\) −4.38000 4.38000i −0.312062 0.312062i 0.533646 0.845708i \(-0.320821\pi\)
−0.845708 + 0.533646i \(0.820821\pi\)
\(198\) 1.25349 0.671304i 0.0890818 0.0477075i
\(199\) −2.03591 + 2.03591i −0.144322 + 0.144322i −0.775576 0.631254i \(-0.782540\pi\)
0.631254 + 0.775576i \(0.282540\pi\)
\(200\) 1.03185 + 0.749685i 0.0729630 + 0.0530107i
\(201\) 2.16907 + 4.25703i 0.152994 + 0.300268i
\(202\) 6.16482 2.00307i 0.433755 0.140936i
\(203\) 3.09808 2.25088i 0.217442 0.157981i
\(204\) 12.9934 9.32954i 0.909719 0.653199i
\(205\) 0.673320 + 2.07227i 0.0470267 + 0.144733i
\(206\) 0.447343 + 0.145350i 0.0311678 + 0.0101270i
\(207\) −10.8574 + 1.71965i −0.754644 + 0.119524i
\(208\) 9.37313 0.649910
\(209\) −1.55000 + 11.2731i −0.107216 + 0.779774i
\(210\) 1.11188 + 1.11188i 0.0767267 + 0.0767267i
\(211\) 0.223536 + 1.41135i 0.0153889 + 0.0971616i 0.994187 0.107664i \(-0.0343372\pi\)
−0.978798 + 0.204826i \(0.934337\pi\)
\(212\) −8.18819 2.66050i −0.562367 0.182724i
\(213\) −18.5553 + 6.02899i −1.27139 + 0.413099i
\(214\) −5.77792 0.915133i −0.394971 0.0625572i
\(215\) 7.42020 + 1.17524i 0.506053 + 0.0801510i
\(216\) −4.28660 2.18413i −0.291666 0.148611i
\(217\) −1.04900 + 3.22849i −0.0712107 + 0.219164i
\(218\) −3.68951 + 0.584361i −0.249885 + 0.0395779i
\(219\) 6.26230i 0.423167i
\(220\) −4.12185 11.8556i −0.277895 0.799302i
\(221\) −8.21776 8.31030i −0.552786 0.559011i
\(222\) −5.63695 4.09548i −0.378327 0.274871i
\(223\) −17.8276 5.79255i −1.19383 0.387898i −0.356340 0.934356i \(-0.615976\pi\)
−0.837486 + 0.546459i \(0.815976\pi\)
\(224\) 3.74241 + 1.90685i 0.250050 + 0.127407i
\(225\) −0.966823 + 0.702438i −0.0644548 + 0.0468292i
\(226\) 0.480897 3.03627i 0.0319888 0.201969i
\(227\) 5.05540 9.92178i 0.335539 0.658531i −0.660166 0.751120i \(-0.729514\pi\)
0.995704 + 0.0925884i \(0.0295141\pi\)
\(228\) −11.8598 + 6.04286i −0.785434 + 0.400198i
\(229\) −8.88135 + 12.2241i −0.586896 + 0.807793i −0.994430 0.105397i \(-0.966389\pi\)
0.407534 + 0.913190i \(0.366389\pi\)
\(230\) 6.07660i 0.400679i
\(231\) 1.33409 + 7.43607i 0.0877768 + 0.489257i
\(232\) 3.26579 + 3.26579i 0.214410 + 0.214410i
\(233\) −19.6399 + 3.11065i −1.28665 + 0.203786i −0.762026 0.647547i \(-0.775795\pi\)
−0.524627 + 0.851332i \(0.675795\pi\)
\(234\) 0.375538 1.15579i 0.0245497 0.0755562i
\(235\) 0.0728981 + 0.0371434i 0.00475535 + 0.00242297i
\(236\) 0.498818 + 0.686564i 0.0324703 + 0.0446915i
\(237\) −7.20246 + 5.23289i −0.467850 + 0.339913i
\(238\) −0.475046 1.49038i −0.0307926 0.0966072i
\(239\) 7.34542 22.6069i 0.475136 1.46232i −0.370638 0.928777i \(-0.620861\pi\)
0.845774 0.533541i \(-0.179139\pi\)
\(240\) 8.05565 11.0877i 0.519990 0.715705i
\(241\) −11.7160 + 11.7160i −0.754696 + 0.754696i −0.975352 0.220656i \(-0.929180\pi\)
0.220656 + 0.975352i \(0.429180\pi\)
\(242\) −1.01923 + 3.63631i −0.0655184 + 0.233751i
\(243\) 8.64795 8.64795i 0.554766 0.554766i
\(244\) −4.44483 28.0636i −0.284551 1.79659i
\(245\) 10.3531 5.27519i 0.661438 0.337019i
\(246\) 0.729317 0.236969i 0.0464995 0.0151086i
\(247\) 5.71637 + 7.86790i 0.363724 + 0.500623i
\(248\) −4.04373 0.640463i −0.256777 0.0406695i
\(249\) −3.82194 + 7.50098i −0.242206 + 0.475355i
\(250\) −1.86688 3.66396i −0.118072 0.231729i
\(251\) −5.79562 4.21076i −0.365816 0.265781i 0.389658 0.920960i \(-0.372593\pi\)
−0.755474 + 0.655179i \(0.772593\pi\)
\(252\) −1.83662 + 1.83662i −0.115696 + 0.115696i
\(253\) 16.6742 23.9653i 1.04830 1.50668i
\(254\) 3.28942 0.206397
\(255\) −16.8931 + 2.57873i −1.05789 + 0.161486i
\(256\) 2.28105 7.02036i 0.142566 0.438772i
\(257\) 1.10558 0.359226i 0.0689643 0.0224079i −0.274332 0.961635i \(-0.588457\pi\)
0.343296 + 0.939227i \(0.388457\pi\)
\(258\) 0.413617 2.61148i 0.0257507 0.162583i
\(259\) 8.80264 6.39549i 0.546969 0.397396i
\(260\) −9.55816 4.87013i −0.592772 0.302033i
\(261\) −3.85579 + 1.96462i −0.238667 + 0.121607i
\(262\) 1.07312 + 6.77544i 0.0662978 + 0.418588i
\(263\) 11.3845i 0.701995i −0.936376 0.350998i \(-0.885842\pi\)
0.936376 0.350998i \(-0.114158\pi\)
\(264\) −8.60622 + 2.99214i −0.529676 + 0.184154i
\(265\) 6.50383 + 6.50383i 0.399527 + 0.399527i
\(266\) 0.203624 + 1.28563i 0.0124850 + 0.0788272i
\(267\) −1.45692 2.85937i −0.0891623 0.174991i
\(268\) −1.34811 4.14906i −0.0823491 0.253444i
\(269\) 3.04015 19.1947i 0.185361 1.17032i −0.703004 0.711186i \(-0.748158\pi\)
0.888365 0.459138i \(-0.151842\pi\)
\(270\) 1.46465 + 2.01592i 0.0891357 + 0.122685i
\(271\) 7.50724 + 23.1049i 0.456033 + 1.40352i 0.869919 + 0.493195i \(0.164171\pi\)
−0.413886 + 0.910329i \(0.635829\pi\)
\(272\) −12.1824 + 6.12155i −0.738664 + 0.371173i
\(273\) 5.22364 + 3.79519i 0.316149 + 0.229696i
\(274\) 1.61725i 0.0977015i
\(275\) 0.432333 3.14432i 0.0260706 0.189610i
\(276\) 34.1507 2.05563
\(277\) 26.0806 4.13076i 1.56703 0.248194i 0.688270 0.725454i \(-0.258370\pi\)
0.878762 + 0.477261i \(0.158370\pi\)
\(278\) −3.21274 + 1.63697i −0.192687 + 0.0981790i
\(279\) 1.74156 3.41800i 0.104264 0.204630i
\(280\) −1.74071 2.39589i −0.104028 0.143182i
\(281\) 0.145242 + 0.199908i 0.00866440 + 0.0119255i 0.813327 0.581807i \(-0.197654\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(282\) 0.0130723 0.0256559i 0.000778445 0.00152779i
\(283\) −7.64336 + 3.89449i −0.454351 + 0.231503i −0.666162 0.745807i \(-0.732064\pi\)
0.211811 + 0.977311i \(0.432064\pi\)
\(284\) 17.5954 2.78684i 1.04410 0.165369i
\(285\) 14.2200 0.842318
\(286\) 1.52376 + 2.84524i 0.0901019 + 0.168243i
\(287\) 1.19751i 0.0706867i
\(288\) −3.83996 2.78989i −0.226272 0.164396i
\(289\) 16.1081 + 5.43400i 0.947537 + 0.319647i
\(290\) −0.739211 2.27506i −0.0434080 0.133596i
\(291\) −10.4741 14.4164i −0.614003 0.845103i
\(292\) −0.894508 + 5.64770i −0.0523471 + 0.330507i
\(293\) −6.45480 19.8658i −0.377093 1.16057i −0.942056 0.335457i \(-0.891109\pi\)
0.564962 0.825117i \(-0.308891\pi\)
\(294\) −1.85656 3.64370i −0.108277 0.212505i
\(295\) −0.141827 0.895459i −0.00825748 0.0521356i
\(296\) 9.27917 + 9.27917i 0.539341 + 0.539341i
\(297\) 0.244692 + 11.9695i 0.0141985 + 0.694540i
\(298\) 3.53561i 0.204812i
\(299\) −3.90335 24.6448i −0.225737 1.42524i
\(300\) 3.30798 1.68550i 0.190986 0.0973123i
\(301\) 3.67889 + 1.87449i 0.212047 + 0.108044i
\(302\) −4.23675 + 3.07818i −0.243798 + 0.177130i
\(303\) 6.08819 38.4393i 0.349757 2.20828i
\(304\) 10.7898 3.50582i 0.618838 0.201073i
\(305\) −9.38011 + 28.8690i −0.537103 + 1.65303i
\(306\) 0.266749 + 1.74745i 0.0152490 + 0.0998952i
\(307\) 18.7114 1.06791 0.533957 0.845511i \(-0.320704\pi\)
0.533957 + 0.845511i \(0.320704\pi\)
\(308\) −0.140992 6.89683i −0.00803376 0.392984i
\(309\) 1.99692 1.99692i 0.113601 0.113601i
\(310\) 1.71555 + 1.24642i 0.0974364 + 0.0707917i
\(311\) 10.0942 + 19.8110i 0.572390 + 1.12338i 0.977858 + 0.209269i \(0.0671084\pi\)
−0.405469 + 0.914109i \(0.632892\pi\)
\(312\) −3.53534 + 6.93849i −0.200149 + 0.392815i
\(313\) −10.7119 1.69660i −0.605473 0.0958975i −0.153831 0.988097i \(-0.549161\pi\)
−0.451641 + 0.892200i \(0.649161\pi\)
\(314\) 1.57641 + 2.16974i 0.0889618 + 0.122445i
\(315\) 2.63903 0.857473i 0.148693 0.0483131i
\(316\) 7.24306 3.69052i 0.407454 0.207608i
\(317\) −0.678115 4.28145i −0.0380867 0.240470i 0.961299 0.275506i \(-0.0888454\pi\)
−0.999386 + 0.0350359i \(0.988845\pi\)
\(318\) 2.28897 2.28897i 0.128359 0.128359i
\(319\) 3.32742 11.0009i 0.186300 0.615932i
\(320\) −7.54768 + 7.54768i −0.421928 + 0.421928i
\(321\) −20.6449 + 28.4152i −1.15228 + 1.58598i
\(322\) 1.03201 3.17619i 0.0575115 0.177002i
\(323\) −12.5681 6.49266i −0.699308 0.361262i
\(324\) −17.0341 + 12.3760i −0.946337 + 0.687554i
\(325\) −1.59443 2.19455i −0.0884431 0.121732i
\(326\) 5.14968 + 2.62389i 0.285214 + 0.145324i
\(327\) −6.93063 + 21.3303i −0.383265 + 1.17957i
\(328\) −1.42649 + 0.225933i −0.0787645 + 0.0124751i
\(329\) 0.0317951 + 0.0317951i 0.00175292 + 0.00175292i
\(330\) 4.67528 + 0.642833i 0.257365 + 0.0353868i
\(331\) 13.6708i 0.751415i 0.926738 + 0.375707i \(0.122600\pi\)
−0.926738 + 0.375707i \(0.877400\pi\)
\(332\) 4.51829 6.21889i 0.247973 0.341306i
\(333\) −10.9555 + 5.58213i −0.600360 + 0.305899i
\(334\) 2.56502 5.03413i 0.140352 0.275455i
\(335\) −0.729086 + 4.60327i −0.0398342 + 0.251504i
\(336\) 6.09368 4.42731i 0.332437 0.241530i
\(337\) −30.3192 15.4484i −1.65159 0.841528i −0.996281 0.0861693i \(-0.972537\pi\)
−0.655311 0.755359i \(-0.727463\pi\)
\(338\) −1.62117 0.526751i −0.0881801 0.0286515i
\(339\) −14.9320 10.8488i −0.810997 0.589224i
\(340\) 15.6035 + 0.0873648i 0.846219 + 0.00473802i
\(341\) 3.34570 + 9.62315i 0.181180 + 0.521123i
\(342\) 1.47094i 0.0795393i
\(343\) 13.9477 2.20910i 0.753106 0.119280i
\(344\) −1.53882 + 4.73599i −0.0829674 + 0.255347i
\(345\) −32.5075 16.5634i −1.75014 0.891743i
\(346\) 3.08080 + 0.487951i 0.165625 + 0.0262324i
\(347\) 7.20902 + 1.14180i 0.387001 + 0.0612949i 0.346903 0.937901i \(-0.387233\pi\)
0.0400974 + 0.999196i \(0.487233\pi\)
\(348\) 12.7859 4.15439i 0.685396 0.222699i
\(349\) 2.66339 + 0.865389i 0.142568 + 0.0463232i 0.379432 0.925220i \(-0.376119\pi\)
−0.236864 + 0.971543i \(0.576119\pi\)
\(350\) −0.0567956 0.358593i −0.00303585 0.0191676i
\(351\) 7.23509 + 7.23509i 0.386181 + 0.386181i
\(352\) 12.4078 2.22606i 0.661337 0.118649i
\(353\) −34.3129 −1.82629 −0.913147 0.407631i \(-0.866355\pi\)
−0.913147 + 0.407631i \(0.866355\pi\)
\(354\) −0.315149 + 0.0499148i −0.0167500 + 0.00265294i
\(355\) −18.1004 5.88119i −0.960671 0.312141i
\(356\) 0.905504 + 2.78686i 0.0479916 + 0.147703i
\(357\) −9.26784 1.52112i −0.490506 0.0805063i
\(358\) 1.16285 0.844859i 0.0614584 0.0446522i
\(359\) 4.75235 1.54413i 0.250820 0.0814962i −0.180909 0.983500i \(-0.557904\pi\)
0.431728 + 0.902004i \(0.357904\pi\)
\(360\) 1.51934 + 2.98186i 0.0800760 + 0.157158i
\(361\) −5.84814 4.24892i −0.307797 0.223628i
\(362\) 3.88338 3.88338i 0.204106 0.204106i
\(363\) 16.6747 + 15.3642i 0.875195 + 0.806412i
\(364\) −4.16887 4.16887i −0.218508 0.218508i
\(365\) 3.59065 4.94210i 0.187943 0.258682i
\(366\) 10.1602 + 3.30125i 0.531082 + 0.172559i
\(367\) 8.71702 17.1081i 0.455025 0.893037i −0.543535 0.839387i \(-0.682914\pi\)
0.998560 0.0536500i \(-0.0170855\pi\)
\(368\) −28.7496 4.55348i −1.49867 0.237367i
\(369\) 0.211694 1.33659i 0.0110204 0.0695799i
\(370\) −2.10034 6.46418i −0.109191 0.336056i
\(371\) 2.29494 + 4.50407i 0.119147 + 0.233839i
\(372\) −7.00491 + 9.64142i −0.363187 + 0.499885i
\(373\) 23.1982 1.20116 0.600580 0.799565i \(-0.294936\pi\)
0.600580 + 0.799565i \(0.294936\pi\)
\(374\) −3.83866 2.70283i −0.198493 0.139760i
\(375\) −24.6895 −1.27496
\(376\) −0.0318759 + 0.0438734i −0.00164387 + 0.00226260i
\(377\) −4.45941 8.75208i −0.229671 0.450755i
\(378\) 0.423191 + 1.30245i 0.0217666 + 0.0669907i
\(379\) −4.79378 + 30.2667i −0.246240 + 1.55470i 0.486190 + 0.873853i \(0.338386\pi\)
−0.732429 + 0.680843i \(0.761614\pi\)
\(380\) −12.8244 2.03118i −0.657877 0.104198i
\(381\) 8.96619 17.5971i 0.459352 0.901529i
\(382\) 0.0585776 + 0.0190330i 0.00299709 + 0.000973815i
\(383\) −10.4191 + 14.3407i −0.532393 + 0.732776i −0.987493 0.157664i \(-0.949604\pi\)
0.455100 + 0.890440i \(0.349604\pi\)
\(384\) 13.7360 + 13.7360i 0.700961 + 0.700961i
\(385\) −3.21082 + 6.63336i −0.163638 + 0.338067i
\(386\) −3.98756 + 3.98756i −0.202961 + 0.202961i
\(387\) −3.77477 2.74253i −0.191883 0.139411i
\(388\) 7.38692 + 14.4976i 0.375014 + 0.736006i
\(389\) −7.65581 + 2.48752i −0.388165 + 0.126122i −0.496597 0.867981i \(-0.665417\pi\)
0.108432 + 0.994104i \(0.465417\pi\)
\(390\) 3.26306 2.37075i 0.165231 0.120048i
\(391\) 21.1686 + 29.4818i 1.07054 + 1.49096i
\(392\) 2.38003 + 7.32497i 0.120210 + 0.369967i
\(393\) 39.1711 + 12.7274i 1.97592 + 0.642015i
\(394\) −2.10039 + 0.332669i −0.105816 + 0.0167596i
\(395\) −8.68448 −0.436963
\(396\) −1.06185 + 7.72274i −0.0533599 + 0.388083i
\(397\) −4.07733 4.07733i −0.204636 0.204636i 0.597347 0.801983i \(-0.296221\pi\)
−0.801983 + 0.597347i \(0.796221\pi\)
\(398\) 0.154631 + 0.976302i 0.00775095 + 0.0489376i
\(399\) 7.43267 + 2.41502i 0.372099 + 0.120902i
\(400\) −3.00954 + 0.977858i −0.150477 + 0.0488929i
\(401\) −28.8806 4.57423i −1.44223 0.228426i −0.614216 0.789138i \(-0.710528\pi\)
−0.828011 + 0.560712i \(0.810528\pi\)
\(402\) 1.62008 + 0.256596i 0.0808024 + 0.0127978i
\(403\) 7.75836 + 3.95308i 0.386471 + 0.196917i
\(404\) −10.9814 + 33.7971i −0.546343 + 1.68147i
\(405\) 22.2169 3.51881i 1.10397 0.174851i
\(406\) 1.31470i 0.0652473i
\(407\) 9.45427 31.2571i 0.468631 1.54936i
\(408\) 0.0634201 11.3269i 0.00313976 0.560767i
\(409\) −1.15445 0.838760i −0.0570841 0.0414740i 0.558877 0.829250i \(-0.311232\pi\)
−0.615961 + 0.787776i \(0.711232\pi\)
\(410\) 0.711437 + 0.231160i 0.0351354 + 0.0114162i
\(411\) −8.65165 4.40823i −0.426754 0.217442i
\(412\) −2.08618 + 1.51570i −0.102779 + 0.0746730i
\(413\) 0.0779467 0.492136i 0.00383551 0.0242164i
\(414\) −1.71335 + 3.36263i −0.0842064 + 0.165264i
\(415\) −7.31709 + 3.72824i −0.359182 + 0.183012i
\(416\) 6.33264 8.71614i 0.310483 0.427344i
\(417\) 21.6489i 1.06015i
\(418\) 2.81827 + 2.70535i 0.137846 + 0.132323i
\(419\) 5.08147 + 5.08147i 0.248246 + 0.248246i 0.820251 0.572004i \(-0.193834\pi\)
−0.572004 + 0.820251i \(0.693834\pi\)
\(420\) −8.51433 + 1.34854i −0.415457 + 0.0658019i
\(421\) 6.08722 18.7345i 0.296673 0.913066i −0.685981 0.727619i \(-0.740627\pi\)
0.982654 0.185447i \(-0.0593732\pi\)
\(422\) 0.437107 + 0.222717i 0.0212781 + 0.0108417i
\(423\) −0.0298670 0.0411084i −0.00145218 0.00199876i
\(424\) −4.93231 + 3.58353i −0.239534 + 0.174032i
\(425\) 3.50555 + 1.81096i 0.170044 + 0.0878444i
\(426\) −2.06983 + 6.37030i −0.100284 + 0.308642i
\(427\) −9.80582 + 13.4966i −0.474537 + 0.653144i
\(428\) 22.6776 22.6776i 1.09616 1.09616i
\(429\) 19.3744 0.396070i 0.935404 0.0191224i
\(430\) 1.82378 1.82378i 0.0879504 0.0879504i
\(431\) −0.770073 4.86205i −0.0370931 0.234197i 0.962176 0.272430i \(-0.0878272\pi\)
−0.999269 + 0.0382328i \(0.987827\pi\)
\(432\) 10.6352 5.41891i 0.511687 0.260718i
\(433\) −10.9910 + 3.57118i −0.528192 + 0.171620i −0.560960 0.827843i \(-0.689568\pi\)
0.0327681 + 0.999463i \(0.489568\pi\)
\(434\) 0.685020 + 0.942849i 0.0328820 + 0.0452582i
\(435\) −14.1856 2.24678i −0.680147 0.107725i
\(436\) 9.29727 18.2469i 0.445258 0.873869i
\(437\) −13.7112 26.9097i −0.655895 1.28727i
\(438\) −1.73933 1.26370i −0.0831085 0.0603819i
\(439\) −21.2722 + 21.2722i −1.01527 + 1.01527i −0.0153851 + 0.999882i \(0.504897\pi\)
−0.999882 + 0.0153851i \(0.995103\pi\)
\(440\) −8.50751 2.57325i −0.405580 0.122675i
\(441\) −7.21654 −0.343645
\(442\) −3.96646 + 0.605480i −0.188665 + 0.0287998i
\(443\) −11.0438 + 33.9893i −0.524706 + 1.61488i 0.240190 + 0.970726i \(0.422790\pi\)
−0.764896 + 0.644153i \(0.777210\pi\)
\(444\) 36.3289 11.8040i 1.72409 0.560192i
\(445\) 0.489715 3.09194i 0.0232147 0.146572i
\(446\) −5.20638 + 3.78266i −0.246529 + 0.179114i
\(447\) 18.9142 + 9.63724i 0.894609 + 0.455826i
\(448\) −5.22696 + 2.66327i −0.246951 + 0.125828i
\(449\) −3.51641 22.2017i −0.165950 1.04776i −0.920277 0.391267i \(-0.872037\pi\)
0.754328 0.656498i \(-0.227963\pi\)
\(450\) 0.410280i 0.0193408i
\(451\) 2.17151 + 2.86385i 0.102252 + 0.134853i
\(452\) 11.9169 + 11.9169i 0.560525 + 0.560525i
\(453\) 4.91869 + 31.0554i 0.231100 + 1.45911i
\(454\) −1.73559 3.40628i −0.0814552 0.159865i
\(455\) 1.94634 + 5.99021i 0.0912457 + 0.280826i
\(456\) −1.47448 + 9.30952i −0.0690490 + 0.435958i
\(457\) 22.0585 + 30.3609i 1.03185 + 1.42022i 0.903549 + 0.428486i \(0.140953\pi\)
0.128302 + 0.991735i \(0.459047\pi\)
\(458\) 1.60300 + 4.93353i 0.0749033 + 0.230529i
\(459\) −14.1287 4.67832i −0.659472 0.218365i
\(460\) 26.9512 + 19.5812i 1.25661 + 0.912977i
\(461\) 12.8912i 0.600403i 0.953876 + 0.300202i \(0.0970540\pi\)
−0.953876 + 0.300202i \(0.902946\pi\)
\(462\) 2.33456 + 1.13002i 0.108613 + 0.0525733i
\(463\) −39.2557 −1.82437 −0.912183 0.409783i \(-0.865605\pi\)
−0.912183 + 0.409783i \(0.865605\pi\)
\(464\) −11.3177 + 1.79254i −0.525409 + 0.0832166i
\(465\) 11.3440 5.78007i 0.526066 0.268044i
\(466\) −3.09926 + 6.08263i −0.143570 + 0.281773i
\(467\) 10.6547 + 14.6649i 0.493040 + 0.678611i 0.980945 0.194285i \(-0.0622388\pi\)
−0.487905 + 0.872897i \(0.662239\pi\)
\(468\) 3.91607 + 5.39000i 0.181020 + 0.249153i
\(469\) −1.16287 + 2.28227i −0.0536966 + 0.105385i
\(470\) 0.0250269 0.0127519i 0.00115441 0.000588199i
\(471\) 15.9042 2.51898i 0.732826 0.116068i
\(472\) 0.600944 0.0276607
\(473\) 12.1972 2.18827i 0.560827 0.100617i
\(474\) 3.05643i 0.140386i
\(475\) −2.65624 1.92987i −0.121877 0.0885486i
\(476\) 8.14099 + 2.69565i 0.373142 + 0.123555i
\(477\) −1.76524 5.43286i −0.0808249 0.248753i
\(478\) −4.79672 6.60212i −0.219397 0.301974i
\(479\) 2.68673 16.9634i 0.122760 0.775076i −0.847104 0.531428i \(-0.821656\pi\)
0.969864 0.243649i \(-0.0783443\pi\)
\(480\) −4.86795 14.9820i −0.222190 0.683832i
\(481\) −12.6706 24.8675i −0.577731 1.13386i
\(482\) 0.889855 + 5.61832i 0.0405318 + 0.255908i
\(483\) −14.1784 14.1784i −0.645139 0.645139i
\(484\) −12.8436 16.2381i −0.583799 0.738097i
\(485\) 17.3828i 0.789311i
\(486\) −0.656828 4.14705i −0.0297943 0.188114i
\(487\) −38.4935 + 19.6134i −1.74431 + 0.888769i −0.779256 + 0.626706i \(0.784403\pi\)
−0.965051 + 0.262063i \(0.915597\pi\)
\(488\) −17.9273 9.13441i −0.811531 0.413495i
\(489\) 28.0736 20.3967i 1.26953 0.922370i
\(490\) 0.624044 3.94006i 0.0281914 0.177994i
\(491\) 2.12952 0.691923i 0.0961039 0.0312261i −0.260570 0.965455i \(-0.583911\pi\)
0.356674 + 0.934229i \(0.383911\pi\)
\(492\) −1.29913 + 3.99830i −0.0585692 + 0.180257i
\(493\) 11.5119 + 8.46275i 0.518469 + 0.381143i
\(494\) 3.33882 0.150221
\(495\) 4.75635 6.83614i 0.213782 0.307262i
\(496\) 7.18258 7.18258i 0.322507 0.322507i
\(497\) −8.46213 6.14810i −0.379579 0.275780i
\(498\) 1.31212 + 2.57519i 0.0587977 + 0.115397i
\(499\) −6.35370 + 12.4698i −0.284431 + 0.558226i −0.988376 0.152027i \(-0.951420\pi\)
0.703946 + 0.710254i \(0.251420\pi\)
\(500\) 22.2664 + 3.52665i 0.995783 + 0.157717i
\(501\) −19.9390 27.4437i −0.890810 1.22609i
\(502\) −2.33905 + 0.760004i −0.104397 + 0.0339206i
\(503\) 34.2383 17.4453i 1.52661 0.777847i 0.529113 0.848551i \(-0.322525\pi\)
0.997497 + 0.0707047i \(0.0225248\pi\)
\(504\) 0.287726 + 1.81663i 0.0128163 + 0.0809191i
\(505\) 26.8449 26.8449i 1.19458 1.19458i
\(506\) −3.29150 9.46727i −0.146325 0.420871i
\(507\) −7.23685 + 7.23685i −0.321400 + 0.321400i
\(508\) −10.5998 + 14.5894i −0.470290 + 0.647299i
\(509\) −4.91800 + 15.1361i −0.217987 + 0.670894i 0.780942 + 0.624604i \(0.214740\pi\)
−0.998928 + 0.0462895i \(0.985260\pi\)
\(510\) −2.69270 + 5.21237i −0.119235 + 0.230808i
\(511\) 2.71614 1.97339i 0.120155 0.0872976i
\(512\) −12.5683 17.2988i −0.555446 0.764506i
\(513\) 11.0348 + 5.62249i 0.487197 + 0.248239i
\(514\) 0.123327 0.379562i 0.00543972 0.0167418i
\(515\) 2.72092 0.430952i 0.119898 0.0189900i
\(516\) 10.2497 + 10.2497i 0.451218 + 0.451218i
\(517\) 0.133694 + 0.0183824i 0.00587985 + 0.000808457i
\(518\) 3.73548i 0.164128i
\(519\) 11.0079 15.1511i 0.483193 0.665058i
\(520\) −6.76839 + 3.44867i −0.296814 + 0.151234i
\(521\) 10.5998 20.8034i 0.464387 0.911411i −0.533460 0.845826i \(-0.679108\pi\)
0.997847 0.0655858i \(-0.0208916\pi\)
\(522\) −0.232411 + 1.46738i −0.0101723 + 0.0642256i
\(523\) 17.7417 12.8901i 0.775788 0.563643i −0.127924 0.991784i \(-0.540831\pi\)
0.903712 + 0.428141i \(0.140831\pi\)
\(524\) −33.5087 17.0735i −1.46384 0.745861i
\(525\) −2.07315 0.673607i −0.0904796 0.0293986i
\(526\) −3.16199 2.29732i −0.137870 0.100168i
\(527\) −12.6654 0.0709140i −0.551712 0.00308906i
\(528\) 6.54477 21.6379i 0.284825 0.941670i
\(529\) 54.4875i 2.36902i
\(530\) 3.11886 0.493978i 0.135474 0.0214570i
\(531\) −0.173999 + 0.535513i −0.00755090 + 0.0232393i
\(532\) −6.35825 3.23969i −0.275665 0.140458i
\(533\) 3.03385 + 0.480515i 0.131411 + 0.0208134i
\(534\) −1.08818 0.172351i −0.0470902 0.00745836i
\(535\) −32.5852 + 10.5876i −1.40878 + 0.457741i
\(536\) −2.93806 0.954635i −0.126905 0.0412340i
\(537\) −1.35002 8.52368i −0.0582576 0.367824i
\(538\) −4.71779 4.71779i −0.203398 0.203398i
\(539\) 13.2727 13.8267i 0.571694 0.595556i
\(540\) −13.6607 −0.587865
\(541\) 26.4271 4.18564i 1.13619 0.179955i 0.440126 0.897936i \(-0.354934\pi\)
0.696062 + 0.717981i \(0.254934\pi\)
\(542\) 7.93224 + 2.57734i 0.340719 + 0.110706i
\(543\) −10.1894 31.3598i −0.437270 1.34578i
\(544\) −2.53814 + 15.4643i −0.108822 + 0.663025i
\(545\) −17.6998 + 12.8597i −0.758177 + 0.550848i
\(546\) 2.10821 0.684998i 0.0902229 0.0293152i
\(547\) 15.9274 + 31.2594i 0.681008 + 1.33655i 0.929825 + 0.368003i \(0.119958\pi\)
−0.248817 + 0.968551i \(0.580042\pi\)
\(548\) 7.17288 + 5.21140i 0.306410 + 0.222620i
\(549\) 13.3306 13.3306i 0.568934 0.568934i
\(550\) −0.786083 0.754587i −0.0335187 0.0321757i
\(551\) −8.40695 8.40695i −0.358148 0.358148i
\(552\) 14.2144 19.5645i 0.605006 0.832720i
\(553\) −4.53931 1.47491i −0.193031 0.0627196i
\(554\) 4.11563 8.07737i 0.174856 0.343175i
\(555\) −40.3059 6.38382i −1.71089 0.270978i
\(556\) 3.09233 19.5242i 0.131144 0.828011i
\(557\) 4.79316 + 14.7518i 0.203093 + 0.625055i 0.999786 + 0.0206715i \(0.00658041\pi\)
−0.796694 + 0.604383i \(0.793420\pi\)
\(558\) −0.597901 1.17345i −0.0253112 0.0496759i
\(559\) 6.22515 8.56819i 0.263296 0.362396i
\(560\) 7.34755 0.310490
\(561\) −24.9224 + 13.1681i −1.05222 + 0.555957i
\(562\) 0.0848329 0.00357846
\(563\) −22.3960 + 30.8255i −0.943879 + 1.29914i 0.0103135 + 0.999947i \(0.496717\pi\)
−0.954193 + 0.299192i \(0.903283\pi\)
\(564\) 0.0716659 + 0.140652i 0.00301768 + 0.00592253i
\(565\) −5.56371 17.1233i −0.234067 0.720384i
\(566\) −0.460710 + 2.90881i −0.0193651 + 0.122266i
\(567\) 12.2102 + 1.93391i 0.512780 + 0.0812164i
\(568\) 5.72714 11.2401i 0.240305 0.471626i
\(569\) −23.0894 7.50219i −0.967957 0.314508i −0.217966 0.975956i \(-0.569942\pi\)
−0.749991 + 0.661448i \(0.769942\pi\)
\(570\) 2.86952 3.94955i 0.120191 0.165428i
\(571\) −17.3981 17.3981i −0.728087 0.728087i 0.242151 0.970238i \(-0.422147\pi\)
−0.970238 + 0.242151i \(0.922147\pi\)
\(572\) −17.5295 2.41024i −0.732945 0.100777i
\(573\) 0.261488 0.261488i 0.0109238 0.0109238i
\(574\) 0.332604 + 0.241651i 0.0138826 + 0.0100863i
\(575\) 3.82437 + 7.50576i 0.159487 + 0.313012i
\(576\) 6.30482 2.04856i 0.262701 0.0853566i
\(577\) 37.3498 27.1362i 1.55489 1.12970i 0.614850 0.788644i \(-0.289217\pi\)
0.940044 0.341053i \(-0.110783\pi\)
\(578\) 4.75981 3.37742i 0.197982 0.140482i
\(579\) 10.4628 + 32.2011i 0.434817 + 1.33823i
\(580\) 12.4725 + 4.05255i 0.517890 + 0.168273i
\(581\) −4.45777 + 0.706041i −0.184939 + 0.0292915i
\(582\) −6.11772 −0.253588
\(583\) 13.6558 + 6.60997i 0.565566 + 0.273757i
\(584\) 2.86317 + 2.86317i 0.118479 + 0.118479i
\(585\) −1.11344 7.02998i −0.0460350 0.290654i
\(586\) −6.82021 2.21602i −0.281740 0.0915430i
\(587\) 23.4592 7.62237i 0.968266 0.314609i 0.218150 0.975915i \(-0.429998\pi\)
0.750116 + 0.661306i \(0.229998\pi\)
\(588\) 22.1433 + 3.50715i 0.913172 + 0.144632i
\(589\) 10.4095 + 1.64871i 0.428918 + 0.0679339i
\(590\) −0.277331 0.141307i −0.0114175 0.00581752i
\(591\) −3.94552 + 12.1431i −0.162297 + 0.499499i
\(592\) −32.1571 + 5.09319i −1.32165 + 0.209329i
\(593\) 12.1640i 0.499517i 0.968308 + 0.249758i \(0.0803512\pi\)
−0.968308 + 0.249758i \(0.919649\pi\)
\(594\) 3.37386 + 2.34742i 0.138431 + 0.0963157i
\(595\) −6.44186 6.51440i −0.264090 0.267064i
\(596\) −15.6813 11.3931i −0.642330 0.466680i
\(597\) 5.64433 + 1.83395i 0.231007 + 0.0750587i
\(598\) −7.63268 3.88905i −0.312124 0.159035i
\(599\) 4.54002 3.29852i 0.185500 0.134774i −0.491160 0.871070i \(-0.663427\pi\)
0.676660 + 0.736296i \(0.263427\pi\)
\(600\) 0.411268 2.59665i 0.0167900 0.106008i
\(601\) −17.3113 + 33.9753i −0.706142 + 1.38588i 0.207042 + 0.978332i \(0.433616\pi\)
−0.913183 + 0.407549i \(0.866384\pi\)
\(602\) 1.26301 0.643537i 0.0514765 0.0262286i
\(603\) 1.70139 2.34176i 0.0692858 0.0953637i
\(604\) 28.7101i 1.16820i
\(605\) 4.34994 + 21.6861i 0.176850 + 0.881663i
\(606\) −9.44783 9.44783i −0.383792 0.383792i
\(607\) −14.1884 + 2.24723i −0.575891 + 0.0912121i −0.437584 0.899177i \(-0.644166\pi\)
−0.138306 + 0.990389i \(0.544166\pi\)
\(608\) 4.02969 12.4021i 0.163426 0.502972i
\(609\) −7.03312 3.58355i −0.284996 0.145213i
\(610\) 6.12541 + 8.43091i 0.248011 + 0.341358i
\(611\) 0.0933101 0.0677937i 0.00377492 0.00274264i
\(612\) −8.60994 4.44788i −0.348036 0.179795i
\(613\) 3.25961 10.0321i 0.131655 0.405191i −0.863400 0.504520i \(-0.831670\pi\)
0.995055 + 0.0993288i \(0.0316696\pi\)
\(614\) 3.77586 5.19702i 0.152381 0.209735i
\(615\) 3.17583 3.17583i 0.128062 0.128062i
\(616\) −4.00979 2.78987i −0.161559 0.112407i
\(617\) 14.3492 14.3492i 0.577677 0.577677i −0.356586 0.934263i \(-0.616059\pi\)
0.934263 + 0.356586i \(0.116059\pi\)
\(618\) −0.151670 0.957606i −0.00610106 0.0385206i
\(619\) −21.5922 + 11.0018i −0.867863 + 0.442198i −0.830445 0.557101i \(-0.811913\pi\)
−0.0374186 + 0.999300i \(0.511913\pi\)
\(620\) −11.0563 + 3.59242i −0.444032 + 0.144275i
\(621\) −18.6769 25.7065i −0.749477 1.03157i
\(622\) 7.53939 + 1.19412i 0.302302 + 0.0478800i
\(623\) 0.781083 1.53296i 0.0312934 0.0614168i
\(624\) −8.77131 17.2147i −0.351133 0.689138i
\(625\) −15.6135 11.3439i −0.624541 0.453755i
\(626\) −2.63283 + 2.63283i −0.105229 + 0.105229i
\(627\) 22.1545 7.70251i 0.884767 0.307609i
\(628\) −14.7031 −0.586718
\(629\) 32.7090 + 24.0454i 1.30419 + 0.958754i
\(630\) 0.294382 0.906016i 0.0117285 0.0360965i
\(631\) 42.3520 13.7610i 1.68601 0.547816i 0.699944 0.714198i \(-0.253208\pi\)
0.986061 + 0.166382i \(0.0532084\pi\)
\(632\) 0.900502 5.68554i 0.0358200 0.226159i
\(633\) 2.38290 1.73128i 0.0947119 0.0688122i
\(634\) −1.32600 0.675630i −0.0526622 0.0268327i
\(635\) 17.1657 8.74638i 0.681202 0.347090i
\(636\) 2.77618 + 17.5281i 0.110083 + 0.695034i
\(637\) 16.3805i 0.649019i
\(638\) −2.38401 3.14410i −0.0943838 0.124476i
\(639\) 8.35806 + 8.35806i 0.330640 + 0.330640i
\(640\) 2.96434 + 18.7161i 0.117176 + 0.739818i
\(641\) −7.25189 14.2326i −0.286432 0.562155i 0.702294 0.711887i \(-0.252159\pi\)
−0.988727 + 0.149731i \(0.952159\pi\)
\(642\) 3.72621 + 11.4681i 0.147062 + 0.452609i
\(643\) −3.13923 + 19.8203i −0.123799 + 0.781637i 0.845178 + 0.534485i \(0.179495\pi\)
−0.968977 + 0.247151i \(0.920505\pi\)
\(644\) 10.7616 + 14.8121i 0.424068 + 0.583680i
\(645\) −4.78532 14.7277i −0.188422 0.579903i
\(646\) −4.33950 + 2.18057i −0.170735 + 0.0857932i
\(647\) −0.801890 0.582607i −0.0315256 0.0229047i 0.571911 0.820316i \(-0.306202\pi\)
−0.603436 + 0.797411i \(0.706202\pi\)
\(648\) 14.9098i 0.585712i
\(649\) −0.706007 1.31829i −0.0277132 0.0517475i
\(650\) −0.931276 −0.0365276
\(651\) 6.91108 1.09461i 0.270867 0.0429010i
\(652\) −28.2319 + 14.3849i −1.10565 + 0.563355i
\(653\) −3.20309 + 6.28641i −0.125347 + 0.246006i −0.945149 0.326640i \(-0.894083\pi\)
0.819802 + 0.572647i \(0.194083\pi\)
\(654\) 4.52585 + 6.22930i 0.176975 + 0.243585i
\(655\) 23.6156 + 32.5040i 0.922736 + 1.27004i
\(656\) 1.62678 3.19273i 0.0635149 0.124655i
\(657\) −3.38044 + 1.72242i −0.131883 + 0.0671980i
\(658\) 0.0152471 0.00241490i 0.000594392 9.41425e-5i
\(659\) 20.9428 0.815817 0.407909 0.913023i \(-0.366258\pi\)
0.407909 + 0.913023i \(0.366258\pi\)
\(660\) −17.9167 + 18.6645i −0.697406 + 0.726515i
\(661\) 38.9200i 1.51381i −0.653523 0.756906i \(-0.726710\pi\)
0.653523 0.756906i \(-0.273290\pi\)
\(662\) 3.79702 + 2.75870i 0.147575 + 0.107220i
\(663\) −7.57255 + 22.8694i −0.294093 + 0.888175i
\(664\) −1.68209 5.17693i −0.0652776 0.200904i
\(665\) 4.48103 + 6.16761i 0.173767 + 0.239170i
\(666\) −0.660354 + 4.16931i −0.0255882 + 0.161558i
\(667\) 9.42626 + 29.0110i 0.364986 + 1.12331i
\(668\) 14.0621 + 27.5984i 0.544079 + 1.06781i
\(669\) 6.04439 + 38.1628i 0.233690 + 1.47546i
\(670\) 1.13142 + 1.13142i 0.0437105 + 0.0437105i
\(671\) 1.02334 + 50.0585i 0.0395058 + 1.93249i
\(672\) 8.65772i 0.333979i
\(673\) −3.91858 24.7409i −0.151050 0.953693i −0.940479 0.339851i \(-0.889623\pi\)
0.789429 0.613842i \(-0.210377\pi\)
\(674\) −10.4090 + 5.30365i −0.400940 + 0.204289i
\(675\) −3.07786 1.56825i −0.118467 0.0603618i
\(676\) 7.56032 5.49289i 0.290781 0.211265i
\(677\) 7.24118 45.7190i 0.278301 1.75713i −0.312132 0.950039i \(-0.601043\pi\)
0.590433 0.807086i \(-0.298957\pi\)
\(678\) −6.02642 + 1.95810i −0.231443 + 0.0752004i
\(679\) 2.95217 9.08584i 0.113294 0.348683i
\(680\) 6.54464 8.90268i 0.250976 0.341402i
\(681\) −22.9531 −0.879565
\(682\) 3.34794 + 1.01264i 0.128199 + 0.0387762i
\(683\) 2.94657 2.94657i 0.112747 0.112747i −0.648482 0.761230i \(-0.724596\pi\)
0.761230 + 0.648482i \(0.224596\pi\)
\(684\) 6.52397 + 4.73994i 0.249450 + 0.181236i
\(685\) −4.30017 8.43955i −0.164301 0.322459i
\(686\) 2.20101 4.31972i 0.0840348 0.164928i
\(687\) 30.7619 + 4.87221i 1.17364 + 0.185886i
\(688\) −7.26200 9.99529i −0.276861 0.381067i
\(689\) 12.3318 4.00684i 0.469804 0.152649i
\(690\) −11.1603 + 5.68644i −0.424864 + 0.216479i
\(691\) −5.20331 32.8524i −0.197943 1.24977i −0.863857 0.503737i \(-0.831958\pi\)
0.665914 0.746029i \(-0.268042\pi\)
\(692\) −12.0917 + 12.0917i −0.459658 + 0.459658i
\(693\) 3.64711 2.76541i 0.138542 0.105049i
\(694\) 1.77187 1.77187i 0.0672594 0.0672594i
\(695\) −12.4129 + 17.0850i −0.470850 + 0.648069i
\(696\) 2.94184 9.05404i 0.111510 0.343192i
\(697\) −4.25695 + 1.35686i −0.161244 + 0.0513949i
\(698\) 0.777818 0.565118i 0.0294408 0.0213900i
\(699\) 24.0919 + 33.1597i 0.911239 + 1.25421i
\(700\) 1.77347 + 0.903626i 0.0670307 + 0.0341539i
\(701\) −0.845559 + 2.60236i −0.0319363 + 0.0982899i −0.965754 0.259459i \(-0.916456\pi\)
0.933818 + 0.357749i \(0.116456\pi\)
\(702\) 3.46953 0.549519i 0.130949 0.0207403i
\(703\) −23.8869 23.8869i −0.900910 0.900910i
\(704\) −7.67085 + 15.8475i −0.289106 + 0.597276i
\(705\) 0.168643i 0.00635146i
\(706\) −6.92417 + 9.53031i −0.260595 + 0.358678i
\(707\) 18.5907 9.47246i 0.699177 0.356248i
\(708\) 0.794151 1.55861i 0.0298460 0.0585761i
\(709\) 0.760709 4.80293i 0.0285690 0.180378i −0.969278 0.245970i \(-0.920894\pi\)
0.997847 + 0.0655921i \(0.0208936\pi\)
\(710\) −5.28605 + 3.84054i −0.198382 + 0.144133i
\(711\) 4.80576 + 2.44866i 0.180230 + 0.0918319i
\(712\) 1.97345 + 0.641212i 0.0739581 + 0.0240304i
\(713\) −21.8763 15.8940i −0.819273 0.595236i
\(714\) −2.29269 + 2.26716i −0.0858017 + 0.0848462i
\(715\) 15.5170 + 10.7962i 0.580305 + 0.403756i
\(716\) 7.87998i 0.294489i
\(717\) −48.3935 + 7.66478i −1.80729 + 0.286247i
\(718\) 0.530122 1.63155i 0.0197840 0.0608889i
\(719\) −1.32687 0.676073i −0.0494839 0.0252133i 0.429074 0.903270i \(-0.358840\pi\)
−0.478557 + 0.878056i \(0.658840\pi\)
\(720\) −8.20088 1.29889i −0.305629 0.0484068i
\(721\) 1.49539 + 0.236847i 0.0556914 + 0.00882065i
\(722\) −2.36025 + 0.766891i −0.0878394 + 0.0285407i
\(723\) 32.4814 + 10.5538i 1.20800 + 0.392502i
\(724\) 4.70996 + 29.7375i 0.175044 + 1.10519i
\(725\) 2.34490 + 2.34490i 0.0870873 + 0.0870873i
\(726\) 7.63222 1.53093i 0.283258 0.0568180i
\(727\) 17.4974 0.648942 0.324471 0.945896i \(-0.394814\pi\)
0.324471 + 0.945896i \(0.394814\pi\)
\(728\) −4.12348 + 0.653096i −0.152827 + 0.0242053i
\(729\) 7.94264 + 2.58072i 0.294172 + 0.0955822i
\(730\) −0.648079 1.99458i −0.0239865 0.0738228i
\(731\) −2.49505 + 15.2018i −0.0922829 + 0.562258i
\(732\) −47.3820 + 34.4250i −1.75129 + 1.27239i
\(733\) 26.7616 8.69537i 0.988462 0.321171i 0.230216 0.973140i \(-0.426057\pi\)
0.758246 + 0.651969i \(0.226057\pi\)
\(734\) −2.99267 5.87345i −0.110462 0.216793i
\(735\) −19.3768 14.0781i −0.714724 0.519277i
\(736\) −23.6580 + 23.6580i −0.872046 + 0.872046i
\(737\) 1.35754 + 7.56676i 0.0500056 + 0.278725i
\(738\) −0.328513 0.328513i −0.0120927 0.0120927i
\(739\) 27.7776 38.2326i 1.02182 1.40641i 0.110895 0.993832i \(-0.464628\pi\)
0.910922 0.412578i \(-0.135372\pi\)
\(740\) 35.4383 + 11.5146i 1.30274 + 0.423285i
\(741\) 9.10083 17.8614i 0.334327 0.656154i
\(742\) 1.71410 + 0.271486i 0.0629264 + 0.00996657i
\(743\) 0.220718 1.39356i 0.00809735 0.0511247i −0.983309 0.181944i \(-0.941761\pi\)
0.991406 + 0.130820i \(0.0417609\pi\)
\(744\) 2.60782 + 8.02603i 0.0956072 + 0.294249i
\(745\) 9.40099 + 18.4505i 0.344425 + 0.675973i
\(746\) 4.68129 6.44324i 0.171394 0.235904i
\(747\) 5.10030 0.186610
\(748\) 24.3574 8.31582i 0.890594 0.304056i
\(749\) −18.8301 −0.688039
\(750\) −4.98221 + 6.85742i −0.181924 + 0.250398i
\(751\) −5.92584 11.6301i −0.216237 0.424389i 0.757252 0.653123i \(-0.226541\pi\)
−0.973489 + 0.228734i \(0.926541\pi\)
\(752\) −0.0415776 0.127963i −0.00151618 0.00466632i
\(753\) −2.30998 + 14.5846i −0.0841802 + 0.531493i
\(754\) −3.33075 0.527538i −0.121299 0.0192118i
\(755\) −13.9247 + 27.3287i −0.506770 + 0.994593i
\(756\) −7.14036 2.32004i −0.259692 0.0843792i
\(757\) 6.55898 9.02767i 0.238390 0.328116i −0.673013 0.739631i \(-0.735000\pi\)
0.911403 + 0.411515i \(0.135000\pi\)
\(758\) 7.43912 + 7.43912i 0.270201 + 0.270201i
\(759\) −59.6181 8.19727i −2.16400 0.297542i
\(760\) −6.50149 + 6.50149i −0.235834 + 0.235834i
\(761\) −17.0738 12.4048i −0.618924 0.449674i 0.233622 0.972328i \(-0.424942\pi\)
−0.852545 + 0.522653i \(0.824942\pi\)
\(762\) −3.07822 6.04134i −0.111512 0.218855i
\(763\) −11.4356 + 3.71564i −0.413995 + 0.134515i
\(764\) −0.273176 + 0.198474i −0.00988317 + 0.00718054i
\(765\) 6.03839 + 8.40975i 0.218319 + 0.304055i
\(766\) 1.88056 + 5.78776i 0.0679473 + 0.209120i
\(767\) −1.21554 0.394952i −0.0438905 0.0142609i
\(768\) −15.0282 + 2.38023i −0.542282 + 0.0858890i
\(769\) −25.6798 −0.926038 −0.463019 0.886348i \(-0.653234\pi\)
−0.463019 + 0.886348i \(0.653234\pi\)
\(770\) 1.19447 + 2.23037i 0.0430456 + 0.0803770i
\(771\) −1.69435 1.69435i −0.0610205 0.0610205i
\(772\) −4.83631 30.5353i −0.174063 1.09899i
\(773\) 37.2633 + 12.1076i 1.34027 + 0.435480i 0.889408 0.457115i \(-0.151117\pi\)
0.450861 + 0.892594i \(0.351117\pi\)
\(774\) −1.52346 + 0.495002i −0.0547596 + 0.0177925i
\(775\) −2.90347 0.459865i −0.104296 0.0165188i
\(776\) 11.3801 + 1.80244i 0.408523 + 0.0647037i
\(777\) −19.9834 10.1820i −0.716900 0.365279i
\(778\) −0.854001 + 2.62835i −0.0306174 + 0.0942308i
\(779\) 3.67213 0.581608i 0.131568 0.0208383i
\(780\) 22.1119i 0.791734i
\(781\) −31.3859 + 0.641622i −1.12308 + 0.0229590i
\(782\) 12.4602 + 0.0697652i 0.445576 + 0.00249480i
\(783\) −10.1197 7.35241i −0.361649 0.262754i
\(784\) −18.1735 5.90494i −0.649055 0.210891i
\(785\) 13.9956 + 7.13114i 0.499526 + 0.254521i
\(786\) 11.4395 8.31130i 0.408034 0.296454i
\(787\) 2.67414 16.8839i 0.0953228 0.601845i −0.893069 0.449919i \(-0.851453\pi\)
0.988392 0.151925i \(-0.0485473\pi\)
\(788\) 5.29281 10.3877i 0.188549 0.370048i
\(789\) −20.9086 + 10.6535i −0.744368 + 0.379274i
\(790\) −1.75248 + 2.41208i −0.0623505 + 0.0858181i
\(791\) 9.89514i 0.351831i
\(792\) 3.98229 + 3.82273i 0.141504 + 0.135835i
\(793\) 30.2584 + 30.2584i 1.07451 + 1.07451i
\(794\) −1.95525 + 0.309681i −0.0693893 + 0.0109902i
\(795\) 5.85868 18.0311i 0.207786 0.639499i
\(796\) −4.82842 2.46020i −0.171139 0.0871995i
\(797\) 5.35541 + 7.37109i 0.189698 + 0.261097i 0.893264 0.449533i \(-0.148410\pi\)
−0.703565 + 0.710631i \(0.748410\pi\)
\(798\) 2.17064 1.57706i 0.0768397 0.0558273i
\(799\) −0.0770003 + 0.149053i −0.00272408 + 0.00527310i
\(800\) −1.12398 + 3.45925i −0.0397386 + 0.122303i
\(801\) −1.14279 + 1.57292i −0.0403786 + 0.0555763i
\(802\) −7.09843 + 7.09843i −0.250654 + 0.250654i
\(803\) 2.91720 9.64468i 0.102946 0.340353i
\(804\) −6.35860 + 6.35860i −0.224251 + 0.224251i
\(805\) −3.05981 19.3189i −0.107844 0.680902i
\(806\) 2.66355 1.35715i 0.0938196 0.0478035i
\(807\) −38.0980 + 12.3788i −1.34111 + 0.435754i
\(808\) 14.7912 + 20.3583i 0.520352 + 0.716204i
\(809\) −18.4900 2.92853i −0.650074 0.102962i −0.177316 0.984154i \(-0.556741\pi\)
−0.472758 + 0.881192i \(0.656741\pi\)
\(810\) 3.50591 6.88074i 0.123185 0.241765i
\(811\) −13.1036 25.7173i −0.460130 0.903057i −0.998189 0.0601494i \(-0.980842\pi\)
0.538059 0.842907i \(-0.319158\pi\)
\(812\) 5.83100 + 4.23647i 0.204628 + 0.148671i
\(813\) 35.4092 35.4092i 1.24185 1.24185i
\(814\) −6.77374 8.93342i −0.237420 0.313116i
\(815\) 33.8502 1.18572
\(816\) 22.6430 + 16.6456i 0.792663 + 0.582712i
\(817\) 3.96129 12.1916i 0.138588 0.426530i
\(818\) −0.465926 + 0.151389i −0.0162907 + 0.00529318i
\(819\) 0.611936 3.86361i 0.0213828 0.135006i
\(820\) −3.31778 + 2.41051i −0.115862 + 0.0841786i
\(821\) −13.6564 6.95828i −0.476611 0.242846i 0.199146 0.979970i \(-0.436183\pi\)
−0.675757 + 0.737124i \(0.736183\pi\)
\(822\) −2.97023 + 1.51341i −0.103599 + 0.0527862i
\(823\) 2.47748 + 15.6422i 0.0863595 + 0.545253i 0.992497 + 0.122269i \(0.0390171\pi\)
−0.906137 + 0.422983i \(0.860983\pi\)
\(824\) 1.82602i 0.0636123i
\(825\) −6.17943 + 2.14841i −0.215140 + 0.0747982i
\(826\) −0.120960 0.120960i −0.00420874 0.00420874i
\(827\) 6.26955 + 39.5844i 0.218014 + 1.37648i 0.817421 + 0.576040i \(0.195403\pi\)
−0.599408 + 0.800444i \(0.704597\pi\)
\(828\) −9.39301 18.4348i −0.326430 0.640654i
\(829\) 7.12527 + 21.9293i 0.247471 + 0.761637i 0.995220 + 0.0976557i \(0.0311344\pi\)
−0.747750 + 0.663981i \(0.768866\pi\)
\(830\) −0.441044 + 2.78464i −0.0153088 + 0.0966562i
\(831\) −31.9926 44.0340i −1.10981 1.52752i
\(832\) 4.64993 + 14.3110i 0.161207 + 0.496145i
\(833\) 10.6980 + 21.2899i 0.370664 + 0.737651i
\(834\) 6.01291 + 4.36863i 0.208210 + 0.151273i
\(835\) 33.0907i 1.14515i
\(836\) −21.0805 + 3.78201i −0.729083 + 0.130804i
\(837\) 11.0884 0.383272
\(838\) 2.43678 0.385948i 0.0841771 0.0133323i
\(839\) 25.7232 13.1066i 0.888064 0.452491i 0.0504327 0.998727i \(-0.483940\pi\)
0.837631 + 0.546236i \(0.183940\pi\)
\(840\) −2.77133 + 5.43904i −0.0956200 + 0.187665i
\(841\) −9.98746 13.7466i −0.344395 0.474019i
\(842\) −3.97509 5.47124i −0.136991 0.188551i
\(843\) 0.231234 0.453823i 0.00796414 0.0156305i
\(844\) −2.39634 + 1.22099i −0.0824853 + 0.0420284i
\(845\) −9.86064 + 1.56177i −0.339216 + 0.0537266i
\(846\) −0.0174447 −0.000599762
\(847\) −1.40933 + 12.0739i −0.0484251 + 0.414864i
\(848\) 15.1261i 0.519431i
\(849\) 14.3052 + 10.3933i 0.490953 + 0.356698i
\(850\) 1.21039 0.608212i 0.0415160 0.0208615i
\(851\) 26.7831 + 82.4298i 0.918111 + 2.82566i
\(852\) −21.5840 29.7078i −0.739455 1.01777i
\(853\) −3.66673 + 23.1508i −0.125547 + 0.792669i 0.841907 + 0.539622i \(0.181433\pi\)
−0.967454 + 0.253047i \(0.918567\pi\)
\(854\) 1.76986 + 5.44707i 0.0605634 + 0.186395i
\(855\) −3.91114 7.67605i −0.133758 0.262515i
\(856\) −3.55267 22.4307i −0.121428 0.766665i
\(857\) 15.4299 + 15.4299i 0.527076 + 0.527076i 0.919699 0.392624i \(-0.128432\pi\)
−0.392624 + 0.919699i \(0.628432\pi\)
\(858\) 3.79964 5.46109i 0.129718 0.186439i
\(859\) 39.8920i 1.36110i 0.732703 + 0.680549i \(0.238259\pi\)
−0.732703 + 0.680549i \(0.761741\pi\)
\(860\) 2.21197 + 13.9658i 0.0754275 + 0.476231i
\(861\) 2.19934 1.12062i 0.0749533 0.0381906i
\(862\) −1.50582 0.767251i −0.0512883 0.0261327i
\(863\) 32.8884 23.8948i 1.11954 0.813390i 0.135397 0.990791i \(-0.456769\pi\)
0.984139 + 0.177401i \(0.0567691\pi\)
\(864\) 2.14625 13.5509i 0.0730168 0.461010i
\(865\) 17.3745 5.64532i 0.590751 0.191947i
\(866\) −1.22603 + 3.77335i −0.0416624 + 0.128224i
\(867\) −5.09379 34.6692i −0.172994 1.17743i
\(868\) −6.38916 −0.216862
\(869\) −13.5303 + 4.70411i −0.458984 + 0.159576i
\(870\) −3.48661 + 3.48661i −0.118207 + 0.118207i
\(871\) 5.31545 + 3.86190i 0.180107 + 0.130855i
\(872\) −6.58365 12.9211i −0.222950 0.437565i
\(873\) −4.90121 + 9.61917i −0.165881 + 0.325560i
\(874\) −10.2409 1.62200i −0.346405 0.0548651i
\(875\) −7.78020 10.7085i −0.263019 0.362014i
\(876\) 11.2096 3.64223i 0.378738 0.123059i
\(877\) 28.9025 14.7266i 0.975968 0.497281i 0.108135 0.994136i \(-0.465512\pi\)
0.867833 + 0.496856i \(0.165512\pi\)
\(878\) 1.61566 + 10.2009i 0.0545260 + 0.344264i
\(879\) −30.4451 + 30.4451i −1.02689 + 1.02689i
\(880\) 17.5717 13.3237i 0.592342 0.449141i
\(881\) 17.0714 17.0714i 0.575151 0.575151i −0.358412 0.933563i \(-0.616682\pi\)
0.933563 + 0.358412i \(0.116682\pi\)
\(882\) −1.45626 + 2.00437i −0.0490348 + 0.0674907i
\(883\) 5.52175 16.9942i 0.185822 0.571900i −0.814140 0.580669i \(-0.802791\pi\)
0.999962 + 0.00876874i \(0.00279121\pi\)
\(884\) 10.0960 19.5433i 0.339566 0.657312i
\(885\) −1.51188 + 1.09844i −0.0508212 + 0.0369237i
\(886\) 7.21183 + 9.92624i 0.242286 + 0.333478i
\(887\) 23.6901 + 12.0707i 0.795434 + 0.405294i 0.803970 0.594669i \(-0.202717\pi\)
−0.00853583 + 0.999964i \(0.502717\pi\)
\(888\) 8.35871 25.7255i 0.280500 0.863290i
\(889\) 10.4578 1.65636i 0.350744 0.0555524i
\(890\) −0.759954 0.759954i −0.0254737 0.0254737i
\(891\) 32.7076 17.5165i 1.09575 0.586823i
\(892\) 35.2808i 1.18129i
\(893\) 0.0820564 0.112941i 0.00274591 0.00377943i
\(894\) 6.49349 3.30860i 0.217175 0.110656i
\(895\) 3.82186 7.50082i 0.127751 0.250725i
\(896\) −1.62917 + 10.2862i −0.0544268 + 0.343638i
\(897\) −41.6098 + 30.2313i −1.38931 + 1.00939i
\(898\) −6.87605 3.50352i −0.229457 0.116914i
\(899\) −10.1239 3.28945i −0.337650 0.109709i
\(900\) −1.81969 1.32208i −0.0606564 0.0440694i
\(901\) −13.4109 + 13.2616i −0.446782 + 0.441807i
\(902\) 1.23362 0.0252189i 0.0410752 0.000839699i
\(903\) 8.51076i 0.283220i
\(904\) 11.7872 1.86691i 0.392036 0.0620924i
\(905\) 9.93962 30.5910i 0.330404 1.01688i
\(906\) 9.61810 + 4.90067i 0.319540 + 0.162814i
\(907\) −17.5441 2.77872i −0.582544 0.0922658i −0.141794 0.989896i \(-0.545287\pi\)
−0.440749 + 0.897630i \(0.645287\pi\)
\(908\) 20.7004 + 3.27863i 0.686968 + 0.108805i
\(909\) −22.4244 + 7.28612i −0.743769 + 0.241665i
\(910\) 2.05652 + 0.668205i 0.0681731 + 0.0221508i
\(911\) 2.63075 + 16.6099i 0.0871606 + 0.550311i 0.992168 + 0.124914i \(0.0398654\pi\)
−0.905007 + 0.425397i \(0.860135\pi\)
\(912\) −16.5358 16.5358i −0.547556 0.547556i
\(913\) −9.38047 + 9.77200i −0.310448 + 0.323406i
\(914\) 12.8839 0.426162
\(915\) 61.7986 9.78793i 2.04300 0.323579i
\(916\) −27.0469 8.78807i −0.893655 0.290366i
\(917\) 6.82341 + 21.0003i 0.225329 + 0.693491i
\(918\) −4.15049 + 2.98015i −0.136987 + 0.0983595i
\(919\) 22.8029 16.5673i 0.752199 0.546504i −0.144309 0.989533i \(-0.546096\pi\)
0.896508 + 0.443028i \(0.146096\pi\)
\(920\) 22.4356 7.28977i 0.739680 0.240337i
\(921\) −17.5100 34.3653i −0.576973 1.13237i
\(922\) 3.58049 + 2.60138i 0.117917 + 0.0856718i
\(923\) −18.9716 + 18.9716i −0.624457 + 0.624457i
\(924\) −12.5348 + 6.71295i −0.412363 + 0.220840i
\(925\) 6.66262 + 6.66262i 0.219065 + 0.219065i
\(926\) −7.92159 + 10.9031i −0.260320 + 0.358299i
\(927\) −1.62720 0.528708i −0.0534442 0.0173651i
\(928\) −5.97950 + 11.7354i −0.196287 + 0.385235i
\(929\) −50.2653 7.96125i −1.64915 0.261200i −0.738464 0.674293i \(-0.764448\pi\)
−0.910689 + 0.413093i \(0.864448\pi\)
\(930\) 0.683770 4.31715i 0.0224217 0.141565i
\(931\) −6.12678 18.8563i −0.200797 0.617990i
\(932\) −16.9909 33.3466i −0.556556 1.09230i
\(933\) 26.9387 37.0779i 0.881934 1.21388i
\(934\) 6.22319 0.203629
\(935\) −27.2186 3.89786i −0.890144 0.127474i
\(936\) 4.71783 0.154207
\(937\) 10.6757 14.6938i 0.348758 0.480025i −0.598216 0.801335i \(-0.704123\pi\)
0.946974 + 0.321311i \(0.104123\pi\)
\(938\) 0.399231 + 0.783535i 0.0130354 + 0.0255833i
\(939\) 6.90815 + 21.2611i 0.225439 + 0.693830i
\(940\) −0.0240890 + 0.152092i −0.000785696 + 0.00496069i
\(941\) −47.8717 7.58213i −1.56057 0.247170i −0.684378 0.729128i \(-0.739926\pi\)
−0.876195 + 0.481957i \(0.839926\pi\)
\(942\) 2.50974 4.92565i 0.0817719 0.160486i
\(943\) −9.07210 2.94770i −0.295428 0.0959904i
\(944\) −0.876368 + 1.20622i −0.0285233 + 0.0392590i
\(945\) 5.67155 + 5.67155i 0.184495 + 0.184495i
\(946\) 1.85354 3.82931i 0.0602638 0.124502i
\(947\) 28.7793 28.7793i 0.935202 0.935202i −0.0628225 0.998025i \(-0.520010\pi\)
0.998025 + 0.0628225i \(0.0200102\pi\)
\(948\) −13.5560 9.84901i −0.440278 0.319881i
\(949\) −3.90964 7.67310i −0.126912 0.249079i
\(950\) −1.07203 + 0.348324i −0.0347813 + 0.0113011i
\(951\) −7.22872 + 5.25198i −0.234407 + 0.170307i
\(952\) 4.93280 3.54186i 0.159873 0.114792i
\(953\) −15.3547 47.2570i −0.497388 1.53080i −0.813202 0.581982i \(-0.802277\pi\)
0.315813 0.948821i \(-0.397723\pi\)
\(954\) −1.86517 0.606032i −0.0603873 0.0196210i
\(955\) 0.356293 0.0564313i 0.0115294 0.00182607i
\(956\) 44.7389 1.44696
\(957\) −23.3180 + 4.18344i −0.753763 + 0.135231i
\(958\) −4.16935 4.16935i −0.134706 0.134706i
\(959\) −0.814349 5.14160i −0.0262967 0.166031i
\(960\) 20.9251 + 6.79898i 0.675355 + 0.219436i
\(961\) −20.5083 + 6.66356i −0.661559 + 0.214954i
\(962\) −9.46373 1.49891i −0.305123 0.0483267i
\(963\) 21.0170 + 3.32877i 0.677265 + 0.107268i
\(964\) −27.7861 14.1577i −0.894929 0.455989i
\(965\) −10.2063 + 31.4117i −0.328551 + 1.01118i
\(966\) −6.79913 + 1.07688i −0.218758 + 0.0346479i
\(967\) 2.73503i 0.0879525i 0.999033 + 0.0439763i \(0.0140026\pi\)
−0.999033 + 0.0439763i \(0.985997\pi\)
\(968\) −14.6485 + 0.599167i −0.470819 + 0.0192579i
\(969\) −0.163259 + 29.1583i −0.00524463 + 0.936701i
\(970\) −4.82801 3.50775i −0.155018 0.112627i
\(971\) 11.9786 + 3.89208i 0.384411 + 0.124903i 0.494846 0.868981i \(-0.335224\pi\)
−0.110435 + 0.993883i \(0.535224\pi\)
\(972\) 20.5097 + 10.4502i 0.657850 + 0.335191i
\(973\) −9.38974 + 6.82205i −0.301021 + 0.218705i
\(974\) −2.32023 + 14.6493i −0.0743448 + 0.469395i
\(975\) −2.53844 + 4.98197i −0.0812951 + 0.159551i
\(976\) 44.4783 22.6628i 1.42372 0.725420i
\(977\) −21.7352 + 29.9159i −0.695370 + 0.957095i 0.304619 + 0.952474i \(0.401471\pi\)
−0.999989 + 0.00462046i \(0.998529\pi\)
\(978\) 11.9133i 0.380945i
\(979\) −0.911836 5.08246i −0.0291424 0.162436i
\(980\) 15.4642 + 15.4642i 0.493985 + 0.493985i
\(981\) 13.4205 2.12560i 0.428484 0.0678652i
\(982\) 0.237547 0.731094i 0.00758042 0.0233301i
\(983\) −5.00826 2.55184i −0.159739 0.0813910i 0.372293 0.928115i \(-0.378572\pi\)
−0.532032 + 0.846724i \(0.678572\pi\)
\(984\) 1.74984 + 2.40845i 0.0557830 + 0.0767787i
\(985\) −10.0763 + 7.32084i −0.321057 + 0.233261i
\(986\) 4.67354 1.48965i 0.148836 0.0474400i
\(987\) 0.0286411 0.0881484i 0.000911658 0.00280579i
\(988\) −10.7590 + 14.8085i −0.342289 + 0.471120i
\(989\) −23.2564 + 23.2564i −0.739511 + 0.739511i
\(990\) −0.938909 2.70056i −0.0298405 0.0858294i
\(991\) 33.0099 33.0099i 1.04859 1.04859i 0.0498359 0.998757i \(-0.484130\pi\)
0.998757 0.0498359i \(-0.0158698\pi\)
\(992\) −1.82646 11.5318i −0.0579901 0.366135i
\(993\) 25.1077 12.7930i 0.796770 0.405975i
\(994\) −3.41523 + 1.10968i −0.108325 + 0.0351968i
\(995\) 3.40287 + 4.68365i 0.107878 + 0.148482i
\(996\) −15.6498 2.47868i −0.495882 0.0785400i
\(997\) 6.37980 12.5211i 0.202050 0.396546i −0.767641 0.640880i \(-0.778569\pi\)
0.969691 + 0.244334i \(0.0785695\pi\)
\(998\) 2.18131 + 4.28107i 0.0690482 + 0.135515i
\(999\) −28.7534 20.8906i −0.909718 0.660949i
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 187.2.p.a.4.10 128
11.3 even 5 inner 187.2.p.a.157.7 yes 128
17.13 even 4 inner 187.2.p.a.81.7 yes 128
187.47 even 20 inner 187.2.p.a.47.10 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.p.a.4.10 128 1.1 even 1 trivial
187.2.p.a.47.10 yes 128 187.47 even 20 inner
187.2.p.a.81.7 yes 128 17.13 even 4 inner
187.2.p.a.157.7 yes 128 11.3 even 5 inner