Properties

Label 74.2.h.a.3.1
Level $74$
Weight $2$
Character 74.3
Analytic conductor $0.591$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,2,Mod(3,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.h (of order \(18\), degree \(6\), 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: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.1
Root \(-0.642788 + 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 74.3
Dual form 74.2.h.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.642788 + 0.766044i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.273629 - 0.751790i) q^{5} +1.87939i q^{6} +(-0.138449 - 0.0503913i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.0923963 - 0.524005i) q^{9} +O(q^{10})\) \(q+(-0.642788 + 0.766044i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.273629 - 0.751790i) q^{5} +1.87939i q^{6} +(-0.138449 - 0.0503913i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.0923963 - 0.524005i) q^{9} +(0.400019 + 0.692853i) q^{10} +(-2.40570 + 4.16679i) q^{11} +(-1.43969 - 1.20805i) q^{12} +(1.91858 - 0.338298i) q^{13} +(0.127595 - 0.0736672i) q^{14} +(-0.514255 - 1.41290i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.43779 - 0.606175i) q^{17} +(0.342020 + 0.407604i) q^{18} +(-4.33625 - 5.16775i) q^{19} +(-0.787884 - 0.138925i) q^{20} +(-0.260199 + 0.0947047i) q^{21} +(-1.64560 - 4.52124i) q^{22} +(-3.61610 + 2.08776i) q^{23} +(1.85083 - 0.326352i) q^{24} +(3.33991 + 2.80251i) q^{25} +(-0.974090 + 1.68717i) q^{26} +(2.31908 + 4.01676i) q^{27} +(-0.0255844 + 0.145096i) q^{28} +(2.63134 + 1.51921i) q^{29} +(1.41290 + 0.514255i) q^{30} -8.13740i q^{31} +(0.342020 - 0.939693i) q^{32} +(1.57021 + 8.90509i) q^{33} +(2.67412 - 2.24386i) q^{34} +(-0.0757674 + 0.0902961i) q^{35} -0.532089 q^{36} +(6.08227 - 0.0772535i) q^{37} +6.74601 q^{38} +(2.35349 - 2.80478i) q^{39} +(0.612865 - 0.514255i) q^{40} +(0.676822 + 3.83845i) q^{41} +(0.0947047 - 0.260199i) q^{42} +8.10852i q^{43} +(4.52124 + 1.64560i) q^{44} +(-0.368660 - 0.212846i) q^{45} +(0.725070 - 4.11208i) q^{46} +(-4.16911 - 7.22111i) q^{47} +(-0.939693 + 1.62760i) q^{48} +(-5.34568 - 4.48556i) q^{49} +(-4.29370 + 0.757095i) q^{50} +(-5.68164 + 3.28030i) q^{51} +(-0.666317 - 1.83069i) q^{52} +(10.2327 - 3.72440i) q^{53} +(-4.56769 - 0.805407i) q^{54} +(2.47428 + 2.94874i) q^{55} +(-0.0947047 - 0.112865i) q^{56} +(-12.4857 - 2.20157i) q^{57} +(-2.85517 + 1.03920i) q^{58} +(-2.96569 - 8.14816i) q^{59} +(-1.30214 + 0.751790i) q^{60} +(-0.346344 + 0.0610698i) q^{61} +(6.23361 + 5.23062i) q^{62} +(-0.0391975 + 0.0678921i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.270651 - 1.53494i) q^{65} +(-7.83101 - 4.52124i) q^{66} +(-2.25471 - 0.820647i) q^{67} +3.49082i q^{68} +(-2.68397 + 7.37414i) q^{69} +(-0.0204685 - 0.116082i) q^{70} +(5.34953 - 4.48879i) q^{71} +(0.342020 - 0.407604i) q^{72} +1.13399 q^{73} +(-3.85043 + 4.70895i) q^{74} +8.19401 q^{75} +(-4.33625 + 5.16775i) q^{76} +(0.543037 - 0.455662i) q^{77} +(0.635792 + 3.60576i) q^{78} +(0.646510 - 1.77627i) q^{79} +0.800038i q^{80} +(9.69119 + 3.52730i) q^{81} +(-3.37547 - 1.94883i) q^{82} +(-1.71997 + 9.75442i) q^{83} +(0.138449 + 0.239801i) q^{84} +(-1.39639 + 2.41863i) q^{85} +(-6.21149 - 5.21206i) q^{86} +(5.62359 - 0.991591i) q^{87} +(-4.16679 + 2.40570i) q^{88} +(-3.45924 - 9.50418i) q^{89} +(0.400019 - 0.145595i) q^{90} +(-0.282673 - 0.0498429i) q^{91} +(2.68397 + 3.19863i) q^{92} +(-9.83035 - 11.7154i) q^{93} +(8.21154 + 1.44792i) q^{94} +(-5.07158 + 1.84591i) q^{95} +(-0.642788 - 1.76604i) q^{96} +(5.08812 - 2.93763i) q^{97} +(6.87228 - 1.21177i) q^{98} +(1.96114 + 1.64560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 + 0.766044i −0.454519 + 0.541675i
\(3\) 1.43969 1.20805i 0.831207 0.697465i −0.124361 0.992237i \(-0.539688\pi\)
0.955568 + 0.294772i \(0.0952436\pi\)
\(4\) −0.173648 0.984808i −0.0868241 0.492404i
\(5\) 0.273629 0.751790i 0.122371 0.336211i −0.863349 0.504608i \(-0.831637\pi\)
0.985719 + 0.168397i \(0.0538592\pi\)
\(6\) 1.87939i 0.767256i
\(7\) −0.138449 0.0503913i −0.0523288 0.0190461i 0.315723 0.948851i \(-0.397753\pi\)
−0.368052 + 0.929805i \(0.619975\pi\)
\(8\) 0.866025 + 0.500000i 0.306186 + 0.176777i
\(9\) 0.0923963 0.524005i 0.0307988 0.174668i
\(10\) 0.400019 + 0.692853i 0.126497 + 0.219099i
\(11\) −2.40570 + 4.16679i −0.725346 + 1.25634i 0.233486 + 0.972360i \(0.424987\pi\)
−0.958832 + 0.283975i \(0.908347\pi\)
\(12\) −1.43969 1.20805i −0.415603 0.348733i
\(13\) 1.91858 0.338298i 0.532119 0.0938270i 0.0988686 0.995100i \(-0.468478\pi\)
0.433251 + 0.901274i \(0.357367\pi\)
\(14\) 0.127595 0.0736672i 0.0341013 0.0196884i
\(15\) −0.514255 1.41290i −0.132780 0.364810i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) −3.43779 0.606175i −0.833786 0.147019i −0.259572 0.965724i \(-0.583581\pi\)
−0.574214 + 0.818705i \(0.694692\pi\)
\(18\) 0.342020 + 0.407604i 0.0806149 + 0.0960731i
\(19\) −4.33625 5.16775i −0.994805 1.18556i −0.982619 0.185636i \(-0.940565\pi\)
−0.0121861 0.999926i \(-0.503879\pi\)
\(20\) −0.787884 0.138925i −0.176176 0.0310646i
\(21\) −0.260199 + 0.0947047i −0.0567801 + 0.0206663i
\(22\) −1.64560 4.52124i −0.350842 0.963931i
\(23\) −3.61610 + 2.08776i −0.754009 + 0.435327i −0.827141 0.561995i \(-0.810034\pi\)
0.0731316 + 0.997322i \(0.476701\pi\)
\(24\) 1.85083 0.326352i 0.377800 0.0666163i
\(25\) 3.33991 + 2.80251i 0.667981 + 0.560503i
\(26\) −0.974090 + 1.68717i −0.191035 + 0.330882i
\(27\) 2.31908 + 4.01676i 0.446307 + 0.773026i
\(28\) −0.0255844 + 0.145096i −0.00483499 + 0.0274206i
\(29\) 2.63134 + 1.51921i 0.488628 + 0.282109i 0.724005 0.689795i \(-0.242299\pi\)
−0.235377 + 0.971904i \(0.575633\pi\)
\(30\) 1.41290 + 0.514255i 0.257960 + 0.0938896i
\(31\) 8.13740i 1.46152i −0.682634 0.730760i \(-0.739166\pi\)
0.682634 0.730760i \(-0.260834\pi\)
\(32\) 0.342020 0.939693i 0.0604612 0.166116i
\(33\) 1.57021 + 8.90509i 0.273338 + 1.55018i
\(34\) 2.67412 2.24386i 0.458609 0.384818i
\(35\) −0.0757674 + 0.0902961i −0.0128070 + 0.0152628i
\(36\) −0.532089 −0.0886815
\(37\) 6.08227 0.0772535i 0.999919 0.0127004i
\(38\) 6.74601 1.09435
\(39\) 2.35349 2.80478i 0.376860 0.449124i
\(40\) 0.612865 0.514255i 0.0969024 0.0813108i
\(41\) 0.676822 + 3.83845i 0.105702 + 0.599465i 0.990938 + 0.134322i \(0.0428858\pi\)
−0.885236 + 0.465142i \(0.846003\pi\)
\(42\) 0.0947047 0.260199i 0.0146133 0.0401496i
\(43\) 8.10852i 1.23654i 0.785966 + 0.618269i \(0.212166\pi\)
−0.785966 + 0.618269i \(0.787834\pi\)
\(44\) 4.52124 + 1.64560i 0.681602 + 0.248083i
\(45\) −0.368660 0.212846i −0.0549565 0.0317292i
\(46\) 0.725070 4.11208i 0.106906 0.606293i
\(47\) −4.16911 7.22111i −0.608127 1.05331i −0.991549 0.129734i \(-0.958588\pi\)
0.383422 0.923573i \(-0.374746\pi\)
\(48\) −0.939693 + 1.62760i −0.135633 + 0.234923i
\(49\) −5.34568 4.48556i −0.763669 0.640794i
\(50\) −4.29370 + 0.757095i −0.607221 + 0.107069i
\(51\) −5.68164 + 3.28030i −0.795589 + 0.459334i
\(52\) −0.666317 1.83069i −0.0924015 0.253871i
\(53\) 10.2327 3.72440i 1.40557 0.511586i 0.475744 0.879584i \(-0.342179\pi\)
0.929827 + 0.367998i \(0.119957\pi\)
\(54\) −4.56769 0.805407i −0.621584 0.109602i
\(55\) 2.47428 + 2.94874i 0.333632 + 0.397607i
\(56\) −0.0947047 0.112865i −0.0126555 0.0150822i
\(57\) −12.4857 2.20157i −1.65378 0.291606i
\(58\) −2.85517 + 1.03920i −0.374902 + 0.136453i
\(59\) −2.96569 8.14816i −0.386100 1.06080i −0.968742 0.248072i \(-0.920203\pi\)
0.582642 0.812729i \(-0.302019\pi\)
\(60\) −1.30214 + 0.751790i −0.168105 + 0.0970557i
\(61\) −0.346344 + 0.0610698i −0.0443448 + 0.00781919i −0.195777 0.980649i \(-0.562723\pi\)
0.151432 + 0.988468i \(0.451612\pi\)
\(62\) 6.23361 + 5.23062i 0.791670 + 0.664290i
\(63\) −0.0391975 + 0.0678921i −0.00493842 + 0.00855360i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0.270651 1.53494i 0.0335702 0.190386i
\(66\) −7.83101 4.52124i −0.963931 0.556526i
\(67\) −2.25471 0.820647i −0.275457 0.100258i 0.200598 0.979674i \(-0.435711\pi\)
−0.476055 + 0.879416i \(0.657934\pi\)
\(68\) 3.49082i 0.423324i
\(69\) −2.68397 + 7.37414i −0.323112 + 0.887742i
\(70\) −0.0204685 0.116082i −0.00244645 0.0138745i
\(71\) 5.34953 4.48879i 0.634873 0.532721i −0.267566 0.963539i \(-0.586219\pi\)
0.902439 + 0.430818i \(0.141775\pi\)
\(72\) 0.342020 0.407604i 0.0403075 0.0480366i
\(73\) 1.13399 0.132724 0.0663618 0.997796i \(-0.478861\pi\)
0.0663618 + 0.997796i \(0.478861\pi\)
\(74\) −3.85043 + 4.70895i −0.447603 + 0.547404i
\(75\) 8.19401 0.946162
\(76\) −4.33625 + 5.16775i −0.497402 + 0.592781i
\(77\) 0.543037 0.455662i 0.0618848 0.0519275i
\(78\) 0.635792 + 3.60576i 0.0719893 + 0.408271i
\(79\) 0.646510 1.77627i 0.0727380 0.199846i −0.897996 0.440004i \(-0.854977\pi\)
0.970734 + 0.240158i \(0.0771992\pi\)
\(80\) 0.800038i 0.0894470i
\(81\) 9.69119 + 3.52730i 1.07680 + 0.391923i
\(82\) −3.37547 1.94883i −0.372759 0.215212i
\(83\) −1.71997 + 9.75442i −0.188791 + 1.07069i 0.732196 + 0.681094i \(0.238495\pi\)
−0.920987 + 0.389593i \(0.872616\pi\)
\(84\) 0.138449 + 0.239801i 0.0151060 + 0.0261644i
\(85\) −1.39639 + 2.41863i −0.151460 + 0.262337i
\(86\) −6.21149 5.21206i −0.669802 0.562031i
\(87\) 5.62359 0.991591i 0.602912 0.106310i
\(88\) −4.16679 + 2.40570i −0.444182 + 0.256448i
\(89\) −3.45924 9.50418i −0.366679 1.00744i −0.976616 0.214992i \(-0.931028\pi\)
0.609937 0.792450i \(-0.291195\pi\)
\(90\) 0.400019 0.145595i 0.0421657 0.0153471i
\(91\) −0.282673 0.0498429i −0.0296322 0.00522496i
\(92\) 2.68397 + 3.19863i 0.279823 + 0.333480i
\(93\) −9.83035 11.7154i −1.01936 1.21483i
\(94\) 8.21154 + 1.44792i 0.846956 + 0.149341i
\(95\) −5.07158 + 1.84591i −0.520333 + 0.189386i
\(96\) −0.642788 1.76604i −0.0656042 0.180246i
\(97\) 5.08812 2.93763i 0.516620 0.298271i −0.218930 0.975740i \(-0.570257\pi\)
0.735551 + 0.677470i \(0.236923\pi\)
\(98\) 6.87228 1.21177i 0.694205 0.122407i
\(99\) 1.96114 + 1.64560i 0.197102 + 0.165389i
\(100\) 2.17997 3.77582i 0.217997 0.377582i
\(101\) −8.50866 14.7374i −0.846643 1.46643i −0.884187 0.467134i \(-0.845287\pi\)
0.0375439 0.999295i \(-0.488047\pi\)
\(102\) 1.13924 6.46093i 0.112801 0.639727i
\(103\) 11.0391 + 6.37342i 1.08771 + 0.627992i 0.932967 0.359962i \(-0.117210\pi\)
0.154747 + 0.987954i \(0.450544\pi\)
\(104\) 1.83069 + 0.666317i 0.179514 + 0.0653377i
\(105\) 0.221529i 0.0216190i
\(106\) −3.72440 + 10.2327i −0.361746 + 0.993889i
\(107\) 2.47252 + 14.0223i 0.239027 + 1.35559i 0.833964 + 0.551819i \(0.186066\pi\)
−0.594937 + 0.803773i \(0.702823\pi\)
\(108\) 3.55303 2.98135i 0.341891 0.286880i
\(109\) −12.7198 + 15.1589i −1.21834 + 1.45196i −0.364674 + 0.931135i \(0.618819\pi\)
−0.853664 + 0.520823i \(0.825625\pi\)
\(110\) −3.84930 −0.367017
\(111\) 8.66328 7.45888i 0.822282 0.707966i
\(112\) 0.147334 0.0139218
\(113\) 5.46470 6.51257i 0.514075 0.612651i −0.445094 0.895484i \(-0.646830\pi\)
0.959169 + 0.282833i \(0.0912741\pi\)
\(114\) 9.71218 8.14949i 0.909629 0.763270i
\(115\) 0.580084 + 3.28982i 0.0540931 + 0.306777i
\(116\) 1.03920 2.85517i 0.0964871 0.265096i
\(117\) 1.03660i 0.0958342i
\(118\) 8.14816 + 2.96569i 0.750099 + 0.273014i
\(119\) 0.445413 + 0.257159i 0.0408309 + 0.0235737i
\(120\) 0.261094 1.48074i 0.0238345 0.135172i
\(121\) −6.07478 10.5218i −0.552252 0.956529i
\(122\) 0.175844 0.304570i 0.0159201 0.0275745i
\(123\) 5.61144 + 4.70855i 0.505966 + 0.424556i
\(124\) −8.01378 + 1.41305i −0.719659 + 0.126895i
\(125\) 6.48506 3.74415i 0.580042 0.334887i
\(126\) −0.0268127 0.0736672i −0.00238866 0.00656280i
\(127\) −5.19901 + 1.89229i −0.461338 + 0.167913i −0.562224 0.826985i \(-0.690054\pi\)
0.100887 + 0.994898i \(0.467832\pi\)
\(128\) −0.984808 0.173648i −0.0870455 0.0153485i
\(129\) 9.79547 + 11.6738i 0.862443 + 1.02782i
\(130\) 1.00186 + 1.19397i 0.0878690 + 0.104718i
\(131\) 0.810446 + 0.142903i 0.0708090 + 0.0124855i 0.208940 0.977928i \(-0.432999\pi\)
−0.138131 + 0.990414i \(0.544110\pi\)
\(132\) 8.49714 3.09271i 0.739581 0.269186i
\(133\) 0.339941 + 0.933979i 0.0294766 + 0.0809863i
\(134\) 2.07795 1.19971i 0.179508 0.103639i
\(135\) 3.65433 0.644357i 0.314514 0.0554574i
\(136\) −2.67412 2.24386i −0.229304 0.192409i
\(137\) −3.37116 + 5.83902i −0.288018 + 0.498861i −0.973336 0.229382i \(-0.926329\pi\)
0.685319 + 0.728243i \(0.259663\pi\)
\(138\) −3.92370 6.79605i −0.334007 0.578518i
\(139\) −2.08444 + 11.8214i −0.176800 + 1.00268i 0.759246 + 0.650804i \(0.225568\pi\)
−0.936046 + 0.351878i \(0.885543\pi\)
\(140\) 0.102081 + 0.0589366i 0.00862743 + 0.00498105i
\(141\) −14.7257 5.35970i −1.24012 0.451368i
\(142\) 6.98332i 0.586027i
\(143\) −3.20592 + 8.80818i −0.268092 + 0.736577i
\(144\) 0.0923963 + 0.524005i 0.00769969 + 0.0436671i
\(145\) 1.86213 1.56252i 0.154642 0.129760i
\(146\) −0.728915 + 0.868687i −0.0603254 + 0.0718930i
\(147\) −13.1149 −1.08170
\(148\) −1.13226 5.97645i −0.0930708 0.491261i
\(149\) −9.21354 −0.754803 −0.377401 0.926050i \(-0.623182\pi\)
−0.377401 + 0.926050i \(0.623182\pi\)
\(150\) −5.26700 + 6.27697i −0.430049 + 0.512513i
\(151\) 9.02729 7.57480i 0.734631 0.616428i −0.196759 0.980452i \(-0.563042\pi\)
0.931390 + 0.364023i \(0.118597\pi\)
\(152\) −1.17143 6.64352i −0.0950157 0.538861i
\(153\) −0.635278 + 1.74541i −0.0513591 + 0.141108i
\(154\) 0.708885i 0.0571235i
\(155\) −6.11762 2.22663i −0.491379 0.178847i
\(156\) −3.17085 1.83069i −0.253871 0.146573i
\(157\) −3.01657 + 17.1078i −0.240749 + 1.36535i 0.589414 + 0.807831i \(0.299359\pi\)
−0.830162 + 0.557522i \(0.811752\pi\)
\(158\) 0.945134 + 1.63702i 0.0751908 + 0.130234i
\(159\) 10.2327 17.7236i 0.811507 1.40557i
\(160\) −0.612865 0.514255i −0.0484512 0.0406554i
\(161\) 0.605851 0.106828i 0.0477477 0.00841921i
\(162\) −8.93145 + 5.15657i −0.701721 + 0.405139i
\(163\) 0.773358 + 2.12478i 0.0605741 + 0.166426i 0.966288 0.257464i \(-0.0828867\pi\)
−0.905714 + 0.423889i \(0.860665\pi\)
\(164\) 3.66260 1.33308i 0.286001 0.104096i
\(165\) 7.12442 + 1.25623i 0.554635 + 0.0977971i
\(166\) −6.36675 7.58759i −0.494155 0.588912i
\(167\) −10.2563 12.2230i −0.793658 0.945845i 0.205805 0.978593i \(-0.434019\pi\)
−0.999464 + 0.0327478i \(0.989574\pi\)
\(168\) −0.272691 0.0480829i −0.0210386 0.00370967i
\(169\) −8.64949 + 3.14816i −0.665345 + 0.242166i
\(170\) −0.955190 2.62436i −0.0732598 0.201280i
\(171\) −3.10858 + 1.79474i −0.237719 + 0.137247i
\(172\) 7.98534 1.40803i 0.608876 0.107361i
\(173\) −2.35572 1.97668i −0.179102 0.150284i 0.548829 0.835934i \(-0.315074\pi\)
−0.727931 + 0.685650i \(0.759518\pi\)
\(174\) −2.85517 + 4.94530i −0.216450 + 0.374902i
\(175\) −0.321185 0.556308i −0.0242793 0.0420529i
\(176\) 0.835490 4.73830i 0.0629775 0.357163i
\(177\) −14.1130 8.14816i −1.06080 0.612454i
\(178\) 9.50418 + 3.45924i 0.712368 + 0.259281i
\(179\) 10.4466i 0.780819i 0.920641 + 0.390410i \(0.127667\pi\)
−0.920641 + 0.390410i \(0.872333\pi\)
\(180\) −0.145595 + 0.400019i −0.0108520 + 0.0298157i
\(181\) 1.56392 + 8.86942i 0.116245 + 0.659259i 0.986126 + 0.165997i \(0.0530843\pi\)
−0.869881 + 0.493262i \(0.835805\pi\)
\(182\) 0.219881 0.184502i 0.0162986 0.0136762i
\(183\) −0.424854 + 0.506321i −0.0314061 + 0.0374284i
\(184\) −4.17551 −0.307823
\(185\) 1.60621 4.59373i 0.118091 0.337738i
\(186\) 15.2933 1.12136
\(187\) 10.7961 12.8663i 0.789488 0.940875i
\(188\) −6.38745 + 5.35970i −0.465852 + 0.390897i
\(189\) −0.118664 0.672978i −0.00863155 0.0489520i
\(190\) 1.84591 5.07158i 0.133916 0.367931i
\(191\) 1.00551i 0.0727558i 0.999338 + 0.0363779i \(0.0115820\pi\)
−0.999338 + 0.0363779i \(0.988418\pi\)
\(192\) 1.76604 + 0.642788i 0.127453 + 0.0463892i
\(193\) −9.52217 5.49763i −0.685421 0.395728i 0.116473 0.993194i \(-0.462841\pi\)
−0.801894 + 0.597466i \(0.796174\pi\)
\(194\) −1.02023 + 5.78600i −0.0732481 + 0.415410i
\(195\) −1.46462 2.53680i −0.104884 0.181664i
\(196\) −3.48915 + 6.04338i −0.249225 + 0.431670i
\(197\) 19.8444 + 16.6514i 1.41386 + 1.18637i 0.954537 + 0.298094i \(0.0963509\pi\)
0.459319 + 0.888271i \(0.348094\pi\)
\(198\) −2.52120 + 0.444555i −0.179174 + 0.0315932i
\(199\) −13.4873 + 7.78692i −0.956092 + 0.552000i −0.894968 0.446130i \(-0.852802\pi\)
−0.0611237 + 0.998130i \(0.519468\pi\)
\(200\) 1.49119 + 4.09700i 0.105443 + 0.289702i
\(201\) −4.23747 + 1.54231i −0.298888 + 0.108786i
\(202\) 16.7588 + 2.95503i 1.17914 + 0.207915i
\(203\) −0.287752 0.342929i −0.0201962 0.0240689i
\(204\) 4.21707 + 5.02571i 0.295254 + 0.351870i
\(205\) 3.07090 + 0.541483i 0.214481 + 0.0378188i
\(206\) −11.9781 + 4.35968i −0.834555 + 0.303753i
\(207\) 0.759881 + 2.08776i 0.0528154 + 0.145109i
\(208\) −1.68717 + 0.974090i −0.116984 + 0.0675410i
\(209\) 31.9646 5.63623i 2.21104 0.389866i
\(210\) −0.169701 0.142396i −0.0117105 0.00982627i
\(211\) 11.5871 20.0694i 0.797688 1.38164i −0.123430 0.992353i \(-0.539390\pi\)
0.921118 0.389283i \(-0.127277\pi\)
\(212\) −5.44471 9.43052i −0.373944 0.647691i
\(213\) 2.27902 12.9250i 0.156156 0.885603i
\(214\) −12.3310 7.11933i −0.842933 0.486667i
\(215\) 6.09591 + 2.21873i 0.415737 + 0.151316i
\(216\) 4.63816i 0.315587i
\(217\) −0.410055 + 1.12662i −0.0278363 + 0.0764797i
\(218\) −3.43624 19.4879i −0.232732 1.31989i
\(219\) 1.63260 1.36991i 0.110321 0.0925701i
\(220\) 2.47428 2.94874i 0.166816 0.198804i
\(221\) −6.80075 −0.457468
\(222\) 0.145189 + 11.4309i 0.00974445 + 0.767194i
\(223\) 9.91195 0.663754 0.331877 0.943323i \(-0.392318\pi\)
0.331877 + 0.943323i \(0.392318\pi\)
\(224\) −0.0947047 + 0.112865i −0.00632773 + 0.00754109i
\(225\) 1.77713 1.49119i 0.118475 0.0994125i
\(226\) 1.47628 + 8.37240i 0.0982007 + 0.556924i
\(227\) −0.684171 + 1.87974i −0.0454100 + 0.124763i −0.960325 0.278884i \(-0.910035\pi\)
0.914915 + 0.403647i \(0.132258\pi\)
\(228\) 12.6784i 0.839645i
\(229\) 8.40320 + 3.05851i 0.555299 + 0.202112i 0.604399 0.796682i \(-0.293413\pi\)
−0.0491004 + 0.998794i \(0.515635\pi\)
\(230\) −2.89302 1.67028i −0.190760 0.110135i
\(231\) 0.231346 1.31203i 0.0152214 0.0863250i
\(232\) 1.51921 + 2.63134i 0.0997407 + 0.172756i
\(233\) 10.8675 18.8230i 0.711952 1.23314i −0.252171 0.967683i \(-0.581145\pi\)
0.964123 0.265455i \(-0.0855221\pi\)
\(234\) 0.794085 + 0.666317i 0.0519110 + 0.0435585i
\(235\) −6.56955 + 1.15839i −0.428550 + 0.0755649i
\(236\) −7.50939 + 4.33555i −0.488820 + 0.282220i
\(237\) −1.21504 3.33830i −0.0789254 0.216846i
\(238\) −0.483301 + 0.175907i −0.0313278 + 0.0114024i
\(239\) −7.79702 1.37482i −0.504347 0.0889300i −0.0843148 0.996439i \(-0.526870\pi\)
−0.420032 + 0.907509i \(0.637981\pi\)
\(240\) 0.966482 + 1.15181i 0.0623862 + 0.0743489i
\(241\) 19.1413 + 22.8117i 1.23300 + 1.46943i 0.833334 + 0.552769i \(0.186429\pi\)
0.399665 + 0.916661i \(0.369127\pi\)
\(242\) 11.9650 + 2.10975i 0.769137 + 0.135620i
\(243\) 5.13816 1.87014i 0.329613 0.119969i
\(244\) 0.120284 + 0.330478i 0.00770040 + 0.0211567i
\(245\) −4.83493 + 2.79145i −0.308893 + 0.178339i
\(246\) −7.21392 + 1.27201i −0.459943 + 0.0811003i
\(247\) −10.0677 8.44780i −0.640592 0.537521i
\(248\) 4.06870 7.04720i 0.258363 0.447498i
\(249\) 9.30756 + 16.1212i 0.589843 + 1.02164i
\(250\) −1.30033 + 7.37454i −0.0822402 + 0.466407i
\(251\) 19.7765 + 11.4180i 1.24828 + 0.720695i 0.970766 0.240026i \(-0.0771560\pi\)
0.277514 + 0.960721i \(0.410489\pi\)
\(252\) 0.0736672 + 0.0268127i 0.00464060 + 0.00168904i
\(253\) 20.0901i 1.26305i
\(254\) 1.89229 5.19901i 0.118733 0.326215i
\(255\) 0.911432 + 5.16899i 0.0570761 + 0.323695i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −10.5496 + 12.5726i −0.658068 + 0.784255i −0.987107 0.160062i \(-0.948831\pi\)
0.329039 + 0.944316i \(0.393275\pi\)
\(258\) −15.2390 −0.948741
\(259\) −0.845978 0.295798i −0.0525665 0.0183800i
\(260\) −1.55862 −0.0966614
\(261\) 1.03920 1.23847i 0.0643247 0.0766592i
\(262\) −0.630415 + 0.528981i −0.0389472 + 0.0326806i
\(263\) 0.270840 + 1.53601i 0.0167007 + 0.0947145i 0.992019 0.126090i \(-0.0402428\pi\)
−0.975318 + 0.220805i \(0.929132\pi\)
\(264\) −3.09271 + 8.49714i −0.190343 + 0.522963i
\(265\) 8.71195i 0.535171i
\(266\) −0.933979 0.339941i −0.0572659 0.0208431i
\(267\) −16.4617 9.50418i −1.00744 0.581646i
\(268\) −0.416654 + 2.36296i −0.0254512 + 0.144341i
\(269\) −1.64927 2.85662i −0.100558 0.174171i 0.811357 0.584551i \(-0.198729\pi\)
−0.911915 + 0.410380i \(0.865396\pi\)
\(270\) −1.85535 + 3.21356i −0.112913 + 0.195571i
\(271\) 2.76033 + 2.31620i 0.167678 + 0.140699i 0.722766 0.691093i \(-0.242871\pi\)
−0.555087 + 0.831792i \(0.687315\pi\)
\(272\) 3.43779 0.606175i 0.208447 0.0367547i
\(273\) −0.467175 + 0.269724i −0.0282747 + 0.0163244i
\(274\) −2.30601 6.33571i −0.139311 0.382754i
\(275\) −19.7123 + 7.17469i −1.18870 + 0.432650i
\(276\) 7.72818 + 1.36269i 0.465182 + 0.0820241i
\(277\) −10.0841 12.0177i −0.605894 0.722076i 0.372683 0.927959i \(-0.378438\pi\)
−0.978577 + 0.205883i \(0.933993\pi\)
\(278\) −7.71590 9.19545i −0.462769 0.551506i
\(279\) −4.26404 0.751866i −0.255282 0.0450130i
\(280\) −0.110765 + 0.0403150i −0.00661945 + 0.00240928i
\(281\) −1.74041 4.78173i −0.103824 0.285254i 0.876894 0.480684i \(-0.159612\pi\)
−0.980718 + 0.195431i \(0.937390\pi\)
\(282\) 13.5712 7.83536i 0.808156 0.466589i
\(283\) −9.02521 + 1.59139i −0.536493 + 0.0945982i −0.435329 0.900272i \(-0.643368\pi\)
−0.101164 + 0.994870i \(0.532257\pi\)
\(284\) −5.34953 4.48879i −0.317436 0.266361i
\(285\) −5.07158 + 8.78424i −0.300415 + 0.520333i
\(286\) −4.68673 8.11766i −0.277132 0.480007i
\(287\) 0.0997192 0.565536i 0.00588624 0.0333825i
\(288\) −0.460802 0.266044i −0.0271530 0.0156768i
\(289\) −4.52384 1.64654i −0.266108 0.0968554i
\(290\) 2.43084i 0.142744i
\(291\) 3.77654 10.3760i 0.221385 0.608250i
\(292\) −0.196915 1.11676i −0.0115236 0.0653536i
\(293\) −19.3966 + 16.2757i −1.13316 + 0.950838i −0.999194 0.0401477i \(-0.987217\pi\)
−0.133970 + 0.990985i \(0.542773\pi\)
\(294\) 8.43010 10.0466i 0.491653 0.585929i
\(295\) −6.93721 −0.403900
\(296\) 5.30603 + 2.97423i 0.308407 + 0.172874i
\(297\) −22.3160 −1.29491
\(298\) 5.92235 7.05798i 0.343073 0.408858i
\(299\) −6.23150 + 5.22885i −0.360377 + 0.302392i
\(300\) −1.42287 8.06952i −0.0821497 0.465894i
\(301\) 0.408599 1.12262i 0.0235513 0.0647066i
\(302\) 11.7843i 0.678110i
\(303\) −30.0533 10.9385i −1.72652 0.628401i
\(304\) 5.84222 + 3.37301i 0.335074 + 0.193455i
\(305\) −0.0488582 + 0.277089i −0.00279761 + 0.0158660i
\(306\) −0.928714 1.60858i −0.0530910 0.0919563i
\(307\) 4.35284 7.53934i 0.248430 0.430293i −0.714661 0.699471i \(-0.753419\pi\)
0.963090 + 0.269178i \(0.0867521\pi\)
\(308\) −0.543037 0.455662i −0.0309424 0.0259638i
\(309\) 23.5923 4.15996i 1.34212 0.236652i
\(310\) 5.63803 3.25512i 0.320218 0.184878i
\(311\) 1.98686 + 5.45885i 0.112664 + 0.309543i 0.983191 0.182578i \(-0.0584441\pi\)
−0.870527 + 0.492121i \(0.836222\pi\)
\(312\) 3.44057 1.25227i 0.194784 0.0708956i
\(313\) −7.74595 1.36582i −0.437827 0.0772007i −0.0496099 0.998769i \(-0.515798\pi\)
−0.388217 + 0.921568i \(0.626909\pi\)
\(314\) −11.1663 13.3075i −0.630153 0.750987i
\(315\) 0.0403150 + 0.0480455i 0.00227149 + 0.00270706i
\(316\) −1.86155 0.328242i −0.104720 0.0184650i
\(317\) 5.26133 1.91497i 0.295506 0.107555i −0.190013 0.981782i \(-0.560853\pi\)
0.485519 + 0.874226i \(0.338631\pi\)
\(318\) 6.99959 + 19.2312i 0.392517 + 1.07843i
\(319\) −12.6604 + 7.30950i −0.708848 + 0.409253i
\(320\) 0.787884 0.138925i 0.0440440 0.00776615i
\(321\) 20.4993 + 17.2010i 1.14416 + 0.960064i
\(322\) −0.307598 + 0.532776i −0.0171418 + 0.0296905i
\(323\) 11.7746 + 20.3941i 0.655154 + 1.13476i
\(324\) 1.79086 10.1565i 0.0994922 0.564248i
\(325\) 7.35597 + 4.24697i 0.408036 + 0.235580i
\(326\) −2.12478 0.773358i −0.117681 0.0428323i
\(327\) 37.1903i 2.05663i
\(328\) −1.33308 + 3.66260i −0.0736070 + 0.202234i
\(329\) 0.213328 + 1.20984i 0.0117612 + 0.0667008i
\(330\) −5.54181 + 4.65013i −0.305067 + 0.255981i
\(331\) −11.6926 + 13.9348i −0.642686 + 0.765923i −0.984792 0.173738i \(-0.944415\pi\)
0.342106 + 0.939661i \(0.388860\pi\)
\(332\) 9.90490 0.543602
\(333\) 0.521498 3.19428i 0.0285779 0.175045i
\(334\) 15.9560 0.873074
\(335\) −1.23391 + 1.47052i −0.0674156 + 0.0803428i
\(336\) 0.212116 0.177987i 0.0115719 0.00970997i
\(337\) −5.73735 32.5381i −0.312533 1.77246i −0.585731 0.810505i \(-0.699193\pi\)
0.273198 0.961958i \(-0.411919\pi\)
\(338\) 3.14816 8.64949i 0.171237 0.470470i
\(339\) 15.9777i 0.867790i
\(340\) 2.62436 + 0.955190i 0.142326 + 0.0518025i
\(341\) 33.9069 + 19.5761i 1.83616 + 1.06011i
\(342\) 0.623306 3.53495i 0.0337045 0.191148i
\(343\) 1.02974 + 1.78357i 0.0556008 + 0.0963035i
\(344\) −4.05426 + 7.02219i −0.218591 + 0.378611i
\(345\) 4.80939 + 4.03556i 0.258929 + 0.217267i
\(346\) 3.02845 0.533998i 0.162811 0.0287079i
\(347\) 27.9743 16.1510i 1.50174 0.867029i 0.501740 0.865018i \(-0.332693\pi\)
0.999998 0.00201032i \(-0.000639905\pi\)
\(348\) −1.95305 5.36597i −0.104695 0.287646i
\(349\) −2.14851 + 0.781994i −0.115007 + 0.0418592i −0.398883 0.917002i \(-0.630602\pi\)
0.283876 + 0.958861i \(0.408380\pi\)
\(350\) 0.632610 + 0.111546i 0.0338144 + 0.00596240i
\(351\) 5.80820 + 6.92195i 0.310019 + 0.369466i
\(352\) 3.09271 + 3.68574i 0.164842 + 0.196451i
\(353\) 6.32439 + 1.11516i 0.336613 + 0.0593540i 0.339400 0.940642i \(-0.389776\pi\)
−0.00278690 + 0.999996i \(0.500887\pi\)
\(354\) 15.3135 5.57367i 0.813905 0.296237i
\(355\) −1.91084 5.24999i −0.101417 0.278640i
\(356\) −8.75910 + 5.05707i −0.464231 + 0.268024i
\(357\) 0.951917 0.167849i 0.0503808 0.00888349i
\(358\) −8.00260 6.71498i −0.422950 0.354898i
\(359\) 3.66122 6.34142i 0.193232 0.334687i −0.753088 0.657920i \(-0.771436\pi\)
0.946319 + 0.323233i \(0.104770\pi\)
\(360\) −0.212846 0.368660i −0.0112180 0.0194301i
\(361\) −4.60318 + 26.1060i −0.242273 + 1.37400i
\(362\) −7.79964 4.50312i −0.409940 0.236679i
\(363\) −21.4566 7.80958i −1.12618 0.409897i
\(364\) 0.287034i 0.0150447i
\(365\) 0.310293 0.852522i 0.0162415 0.0446231i
\(366\) −0.114774 0.650914i −0.00599932 0.0340238i
\(367\) 24.1722 20.2829i 1.26178 1.05876i 0.266288 0.963893i \(-0.414203\pi\)
0.995490 0.0948646i \(-0.0302418\pi\)
\(368\) 2.68397 3.19863i 0.139912 0.166740i
\(369\) 2.07390 0.107963
\(370\) 2.48655 + 4.18322i 0.129270 + 0.217475i
\(371\) −1.60439 −0.0832956
\(372\) −9.83035 + 11.7154i −0.509680 + 0.607413i
\(373\) −6.41137 + 5.37977i −0.331968 + 0.278554i −0.793501 0.608569i \(-0.791744\pi\)
0.461533 + 0.887123i \(0.347300\pi\)
\(374\) 2.91655 + 16.5406i 0.150811 + 0.855292i
\(375\) 4.81339 13.2247i 0.248562 0.682920i
\(376\) 8.33822i 0.430011i
\(377\) 5.56239 + 2.02454i 0.286478 + 0.104269i
\(378\) 0.591807 + 0.341680i 0.0304393 + 0.0175741i
\(379\) 4.89452 27.7582i 0.251415 1.42584i −0.553696 0.832719i \(-0.686783\pi\)
0.805111 0.593124i \(-0.202106\pi\)
\(380\) 2.69853 + 4.67400i 0.138432 + 0.239771i
\(381\) −5.19901 + 9.00496i −0.266354 + 0.461338i
\(382\) −0.770262 0.646327i −0.0394100 0.0330689i
\(383\) −8.95650 + 1.57927i −0.457656 + 0.0806970i −0.397723 0.917505i \(-0.630200\pi\)
−0.0599323 + 0.998202i \(0.519088\pi\)
\(384\) −1.62760 + 0.939693i −0.0830579 + 0.0479535i
\(385\) −0.193971 0.532932i −0.00988570 0.0271607i
\(386\) 10.3322 3.76060i 0.525893 0.191409i
\(387\) 4.24891 + 0.749197i 0.215984 + 0.0380838i
\(388\) −3.77654 4.50071i −0.191725 0.228489i
\(389\) −1.28903 1.53620i −0.0653563 0.0778886i 0.732376 0.680901i \(-0.238411\pi\)
−0.797732 + 0.603012i \(0.793967\pi\)
\(390\) 2.88474 + 0.508658i 0.146075 + 0.0257569i
\(391\) 13.6969 4.98528i 0.692684 0.252116i
\(392\) −2.38672 6.55745i −0.120547 0.331201i
\(393\) 1.33943 0.773318i 0.0675651 0.0390088i
\(394\) −25.5115 + 4.49836i −1.28525 + 0.226624i
\(395\) −1.15848 0.972079i −0.0582894 0.0489106i
\(396\) 1.28005 2.21710i 0.0643247 0.111414i
\(397\) −9.53782 16.5200i −0.478690 0.829115i 0.521012 0.853550i \(-0.325555\pi\)
−0.999701 + 0.0244346i \(0.992221\pi\)
\(398\) 2.70437 15.3372i 0.135558 0.768786i
\(399\) 1.61770 + 0.933979i 0.0809863 + 0.0467574i
\(400\) −4.09700 1.49119i −0.204850 0.0745593i
\(401\) 24.7444i 1.23568i −0.786305 0.617839i \(-0.788008\pi\)
0.786305 0.617839i \(-0.211992\pi\)
\(402\) 1.54231 4.23747i 0.0769236 0.211346i
\(403\) −2.75287 15.6123i −0.137130 0.777703i
\(404\) −13.0360 + 10.9385i −0.648566 + 0.544212i
\(405\) 5.30358 6.32056i 0.263537 0.314071i
\(406\) 0.447662 0.0222171
\(407\) −14.3102 + 25.5294i −0.709331 + 1.26545i
\(408\) −6.56060 −0.324798
\(409\) −15.8423 + 18.8801i −0.783350 + 0.933560i −0.999080 0.0428927i \(-0.986343\pi\)
0.215729 + 0.976453i \(0.430787\pi\)
\(410\) −2.38874 + 2.00439i −0.117971 + 0.0989898i
\(411\) 2.20037 + 12.4789i 0.108536 + 0.615539i
\(412\) 4.35968 11.9781i 0.214786 0.590120i
\(413\) 1.27755i 0.0628642i
\(414\) −2.08776 0.759881i −0.102608 0.0373461i
\(415\) 6.86264 + 3.96215i 0.336874 + 0.194494i
\(416\) 0.338298 1.91858i 0.0165864 0.0940663i
\(417\) 11.2799 + 19.5373i 0.552379 + 0.956748i
\(418\) −16.2289 + 28.1092i −0.793780 + 1.37487i
\(419\) −14.0011 11.7483i −0.683997 0.573942i 0.233174 0.972435i \(-0.425089\pi\)
−0.917171 + 0.398493i \(0.869533\pi\)
\(420\) 0.218164 0.0384681i 0.0106453 0.00187705i
\(421\) 32.5605 18.7988i 1.58690 0.916198i 0.593087 0.805138i \(-0.297909\pi\)
0.993814 0.111060i \(-0.0354245\pi\)
\(422\) 7.92603 + 21.7766i 0.385833 + 1.06007i
\(423\) −4.16911 + 1.51743i −0.202709 + 0.0737801i
\(424\) 10.7240 + 1.89093i 0.520803 + 0.0918316i
\(425\) −9.78308 11.6590i −0.474549 0.565545i
\(426\) 8.43617 + 10.0538i 0.408734 + 0.487110i
\(427\) 0.0510284 + 0.00899769i 0.00246944 + 0.000435429i
\(428\) 13.3800 4.86991i 0.646745 0.235396i
\(429\) 6.02515 + 16.5540i 0.290897 + 0.799233i
\(430\) −5.61802 + 3.24356i −0.270925 + 0.156419i
\(431\) −36.3170 + 6.40367i −1.74933 + 0.308454i −0.954463 0.298330i \(-0.903570\pi\)
−0.794867 + 0.606784i \(0.792459\pi\)
\(432\) −3.55303 2.98135i −0.170945 0.143440i
\(433\) −5.44689 + 9.43429i −0.261761 + 0.453383i −0.966710 0.255875i \(-0.917637\pi\)
0.704949 + 0.709258i \(0.250970\pi\)
\(434\) −0.599460 1.03829i −0.0287750 0.0498398i
\(435\) 0.793310 4.49909i 0.0380363 0.215715i
\(436\) 17.1374 + 9.89427i 0.820731 + 0.473849i
\(437\) 26.4693 + 9.63404i 1.26620 + 0.460859i
\(438\) 2.13120i 0.101833i
\(439\) 6.39195 17.5617i 0.305071 0.838176i −0.688528 0.725210i \(-0.741743\pi\)
0.993599 0.112966i \(-0.0360351\pi\)
\(440\) 0.668424 + 3.79082i 0.0318659 + 0.180720i
\(441\) −2.84438 + 2.38672i −0.135447 + 0.113653i
\(442\) 4.37144 5.20968i 0.207928 0.247799i
\(443\) 18.1659 0.863090 0.431545 0.902092i \(-0.357969\pi\)
0.431545 + 0.902092i \(0.357969\pi\)
\(444\) −8.84993 7.23644i −0.419999 0.343426i
\(445\) −8.09170 −0.383583
\(446\) −6.37128 + 7.59300i −0.301689 + 0.359539i
\(447\) −13.2647 + 11.1304i −0.627397 + 0.526449i
\(448\) −0.0255844 0.145096i −0.00120875 0.00685515i
\(449\) −5.32504 + 14.6304i −0.251304 + 0.690453i 0.748328 + 0.663329i \(0.230857\pi\)
−0.999632 + 0.0271236i \(0.991365\pi\)
\(450\) 2.31988i 0.109360i
\(451\) −17.6222 6.41397i −0.829799 0.302022i
\(452\) −7.36257 4.25078i −0.346306 0.199940i
\(453\) 3.84583 21.8108i 0.180693 1.02476i
\(454\) −1.00019 1.73238i −0.0469413 0.0813047i
\(455\) −0.114819 + 0.198872i −0.00538280 + 0.00932328i
\(456\) −9.71218 8.14949i −0.454815 0.381635i
\(457\) −10.8568 + 1.91434i −0.507858 + 0.0895491i −0.421705 0.906733i \(-0.638568\pi\)
−0.0861526 + 0.996282i \(0.527457\pi\)
\(458\) −7.74443 + 4.47125i −0.361873 + 0.208928i
\(459\) −5.53764 15.2145i −0.258475 0.710154i
\(460\) 3.13911 1.14254i 0.146362 0.0532713i
\(461\) −21.0232 3.70696i −0.979148 0.172650i −0.338903 0.940821i \(-0.610056\pi\)
−0.640245 + 0.768171i \(0.721167\pi\)
\(462\) 0.856365 + 1.02058i 0.0398417 + 0.0474815i
\(463\) 21.3348 + 25.4258i 0.991512 + 1.18164i 0.983359 + 0.181671i \(0.0581506\pi\)
0.00815253 + 0.999967i \(0.497405\pi\)
\(464\) −2.99225 0.527614i −0.138912 0.0244939i
\(465\) −11.4974 + 4.18470i −0.533177 + 0.194061i
\(466\) 7.43379 + 20.4242i 0.344364 + 0.946132i
\(467\) 12.8279 7.40621i 0.593606 0.342719i −0.172916 0.984937i \(-0.555319\pi\)
0.766522 + 0.642218i \(0.221986\pi\)
\(468\) −1.02086 + 0.180005i −0.0471891 + 0.00832071i
\(469\) 0.270809 + 0.227236i 0.0125048 + 0.0104928i
\(470\) 3.33545 5.77716i 0.153853 0.266481i
\(471\) 16.3241 + 28.2742i 0.752175 + 1.30281i
\(472\) 1.50572 8.53936i 0.0693064 0.393056i
\(473\) −33.7865 19.5067i −1.55351 0.896917i
\(474\) 3.33830 + 1.21504i 0.153333 + 0.0558087i
\(475\) 29.4122i 1.34952i
\(476\) 0.175907 0.483301i 0.00806269 0.0221521i
\(477\) −1.00614 5.70611i −0.0460681 0.261265i
\(478\) 6.06500 5.08914i 0.277407 0.232772i
\(479\) 5.78865 6.89864i 0.264490 0.315207i −0.617412 0.786640i \(-0.711819\pi\)
0.881902 + 0.471433i \(0.156263\pi\)
\(480\) −1.50358 −0.0686287
\(481\) 11.6432 2.20584i 0.530885 0.100578i
\(482\) −29.7786 −1.35638
\(483\) 0.743186 0.885694i 0.0338161 0.0403005i
\(484\) −9.30710 + 7.80958i −0.423050 + 0.354981i
\(485\) −0.816221 4.62902i −0.0370627 0.210193i
\(486\) −1.87014 + 5.13816i −0.0848311 + 0.233071i
\(487\) 3.39198i 0.153705i −0.997042 0.0768525i \(-0.975513\pi\)
0.997042 0.0768525i \(-0.0244871\pi\)
\(488\) −0.330478 0.120284i −0.0149600 0.00544500i
\(489\) 3.68023 + 2.12478i 0.166426 + 0.0960860i
\(490\) 0.969460 5.49808i 0.0437958 0.248378i
\(491\) 10.3671 + 17.9564i 0.467862 + 0.810361i 0.999326 0.0367202i \(-0.0116910\pi\)
−0.531463 + 0.847081i \(0.678358\pi\)
\(492\) 3.66260 6.34382i 0.165123 0.286001i
\(493\) −8.12509 6.81776i −0.365935 0.307056i
\(494\) 12.9428 2.28216i 0.582323 0.102679i
\(495\) 1.77377 1.02409i 0.0797249 0.0460292i
\(496\) 2.78316 + 7.64666i 0.124967 + 0.343345i
\(497\) −0.966834 + 0.351899i −0.0433684 + 0.0157848i
\(498\) −18.3323 3.23248i −0.821491 0.144851i
\(499\) 15.8653 + 18.9076i 0.710229 + 0.846418i 0.993643 0.112579i \(-0.0359113\pi\)
−0.283413 + 0.958998i \(0.591467\pi\)
\(500\) −4.81339 5.73638i −0.215261 0.256539i
\(501\) −29.5319 5.20727i −1.31939 0.232644i
\(502\) −21.4587 + 7.81034i −0.957751 + 0.348593i
\(503\) −5.69356 15.6429i −0.253863 0.697484i −0.999515 0.0311477i \(-0.990084\pi\)
0.745651 0.666336i \(-0.232138\pi\)
\(504\) −0.0678921 + 0.0391975i −0.00302415 + 0.00174600i
\(505\) −13.4077 + 2.36413i −0.596633 + 0.105203i
\(506\) 15.3899 + 12.9136i 0.684163 + 0.574081i
\(507\) −8.64949 + 14.9814i −0.384137 + 0.665345i
\(508\) 2.76634 + 4.79144i 0.122736 + 0.212586i
\(509\) 4.36442 24.7519i 0.193450 1.09711i −0.721160 0.692769i \(-0.756391\pi\)
0.914609 0.404339i \(-0.132498\pi\)
\(510\) −4.54553 2.62436i −0.201280 0.116209i
\(511\) −0.157000 0.0571433i −0.00694527 0.00252787i
\(512\) 1.00000i 0.0441942i
\(513\) 10.7015 29.4021i 0.472482 1.29813i
\(514\) −2.84997 16.1630i −0.125707 0.712918i
\(515\) 7.81209 6.55513i 0.344242 0.288853i
\(516\) 9.79547 11.6738i 0.431221 0.513910i
\(517\) 40.1185 1.76441
\(518\) 0.770379 0.457921i 0.0338485 0.0201199i
\(519\) −5.77943 −0.253689
\(520\) 1.00186 1.19397i 0.0439345 0.0523591i
\(521\) −22.0872 + 18.5334i −0.967659 + 0.811962i −0.982182 0.187932i \(-0.939821\pi\)
0.0145232 + 0.999895i \(0.495377\pi\)
\(522\) 0.280738 + 1.59214i 0.0122876 + 0.0696862i
\(523\) 1.23619 3.39641i 0.0540548 0.148514i −0.909727 0.415208i \(-0.863709\pi\)
0.963781 + 0.266693i \(0.0859311\pi\)
\(524\) 0.822948i 0.0359507i
\(525\) −1.13445 0.412907i −0.0495116 0.0180207i
\(526\) −1.35075 0.779853i −0.0588953 0.0340032i
\(527\) −4.93269 + 27.9747i −0.214871 + 1.21860i
\(528\) −4.52124 7.83101i −0.196762 0.340801i
\(529\) −2.78255 + 4.81951i −0.120980 + 0.209544i
\(530\) 6.67374 + 5.59994i 0.289889 + 0.243246i
\(531\) −4.54370 + 0.801177i −0.197180 + 0.0347681i
\(532\) 0.860760 0.496960i 0.0373187 0.0215459i
\(533\) 2.59708 + 7.13541i 0.112492 + 0.309069i
\(534\) 17.8620 6.50124i 0.772965 0.281336i
\(535\) 11.2184 + 1.97811i 0.485014 + 0.0855211i
\(536\) −1.54231 1.83806i −0.0666178 0.0793920i
\(537\) 12.6200 + 15.0400i 0.544594 + 0.649022i
\(538\) 3.24843 + 0.572786i 0.140050 + 0.0246946i
\(539\) 31.5505 11.4834i 1.35898 0.494627i
\(540\) −1.26913 3.48692i −0.0546149 0.150053i
\(541\) −9.89184 + 5.71106i −0.425284 + 0.245538i −0.697335 0.716745i \(-0.745631\pi\)
0.272052 + 0.962283i \(0.412298\pi\)
\(542\) −3.54862 + 0.625717i −0.152426 + 0.0268768i
\(543\) 12.9662 + 10.8800i 0.556434 + 0.466904i
\(544\) −1.74541 + 3.02314i −0.0748339 + 0.129616i
\(545\) 7.91579 + 13.7106i 0.339075 + 0.587295i
\(546\) 0.0936741 0.531252i 0.00400888 0.0227355i
\(547\) 28.9864 + 16.7353i 1.23937 + 0.715550i 0.968965 0.247197i \(-0.0795094\pi\)
0.270404 + 0.962747i \(0.412843\pi\)
\(548\) 6.33571 + 2.30601i 0.270648 + 0.0985078i
\(549\) 0.187129i 0.00798646i
\(550\) 7.17469 19.7123i 0.305930 0.840536i
\(551\) −3.55929 20.1858i −0.151631 0.859942i
\(552\) −6.01146 + 5.04421i −0.255865 + 0.214696i
\(553\) −0.179017 + 0.213345i −0.00761259 + 0.00907234i
\(554\) 15.6880 0.666521
\(555\) −3.23699 8.55393i −0.137402 0.363094i
\(556\) 12.0038 0.509075
\(557\) 12.5025 14.8999i 0.529747 0.631328i −0.433109 0.901341i \(-0.642584\pi\)
0.962857 + 0.270013i \(0.0870280\pi\)
\(558\) 3.31684 2.78316i 0.140413 0.117820i
\(559\) 2.74310 + 15.5569i 0.116021 + 0.657986i
\(560\) 0.0403150 0.110765i 0.00170362 0.00468066i
\(561\) 31.5656i 1.33270i
\(562\) 4.78173 + 1.74041i 0.201705 + 0.0734146i
\(563\) 16.3919 + 9.46387i 0.690837 + 0.398855i 0.803925 0.594730i \(-0.202741\pi\)
−0.113089 + 0.993585i \(0.536074\pi\)
\(564\) −2.72119 + 15.4327i −0.114583 + 0.649832i
\(565\) −3.40079 5.89033i −0.143072 0.247808i
\(566\) 4.58222 7.93663i 0.192605 0.333602i
\(567\) −1.16399 0.976704i −0.0488830 0.0410177i
\(568\) 6.87722 1.21264i 0.288562 0.0508813i
\(569\) 6.71294 3.87572i 0.281421 0.162479i −0.352645 0.935757i \(-0.614718\pi\)
0.634067 + 0.773278i \(0.281384\pi\)
\(570\) −3.46917 9.53146i −0.145307 0.399229i
\(571\) −4.66196 + 1.69681i −0.195097 + 0.0710094i −0.437721 0.899111i \(-0.644214\pi\)
0.242624 + 0.970120i \(0.421992\pi\)
\(572\) 9.23107 + 1.62769i 0.385970 + 0.0680570i
\(573\) 1.21470 + 1.44762i 0.0507447 + 0.0604752i
\(574\) 0.369127 + 0.439909i 0.0154071 + 0.0183614i
\(575\) −17.9284 3.16126i −0.747666 0.131834i
\(576\) 0.500000 0.181985i 0.0208333 0.00758271i
\(577\) 7.21587 + 19.8254i 0.300401 + 0.825344i 0.994430 + 0.105397i \(0.0336114\pi\)
−0.694030 + 0.719946i \(0.744166\pi\)
\(578\) 4.16919 2.40708i 0.173415 0.100121i
\(579\) −20.3504 + 3.58832i −0.845733 + 0.149126i
\(580\) −1.86213 1.56252i −0.0773209 0.0648800i
\(581\) 0.729667 1.26382i 0.0302717 0.0524321i
\(582\) 5.52093 + 9.56254i 0.228850 + 0.396380i
\(583\) −9.09801 + 51.5974i −0.376801 + 2.13694i
\(584\) 0.982064 + 0.566995i 0.0406381 + 0.0234624i
\(585\) −0.779309 0.283645i −0.0322205 0.0117273i
\(586\) 25.3205i 1.04598i
\(587\) −0.000238503 0 0.000655281i −9.84406e−6 0 2.70463e-5i −0.939698 0.342007i \(-0.888893\pi\)
0.939688 + 0.342034i \(0.111116\pi\)
\(588\) 2.27738 + 12.9157i 0.0939175 + 0.532633i
\(589\) −42.0520 + 35.2858i −1.73272 + 1.45393i
\(590\) 4.45915 5.31421i 0.183580 0.218783i
\(591\) 48.6855 2.00266
\(592\) −5.68904 + 2.15285i −0.233818 + 0.0884818i
\(593\) −8.38840 −0.344470 −0.172235 0.985056i \(-0.555099\pi\)
−0.172235 + 0.985056i \(0.555099\pi\)
\(594\) 14.3445 17.0951i 0.588560 0.701419i
\(595\) 0.315207 0.264490i 0.0129222 0.0108431i
\(596\) 1.59992 + 9.07357i 0.0655351 + 0.371668i
\(597\) −10.0107 + 27.5041i −0.409709 + 1.12567i
\(598\) 8.13465i 0.332651i
\(599\) −24.7128 8.99471i −1.00974 0.367514i −0.216405 0.976304i \(-0.569433\pi\)
−0.793332 + 0.608790i \(0.791655\pi\)
\(600\) 7.09622 + 4.09700i 0.289702 + 0.167259i
\(601\) 7.49727 42.5191i 0.305820 1.73439i −0.313800 0.949489i \(-0.601602\pi\)
0.619620 0.784902i \(-0.287287\pi\)
\(602\) 0.597332 + 1.03461i 0.0243454 + 0.0421676i
\(603\) −0.638350 + 1.10566i −0.0259956 + 0.0450258i
\(604\) −9.02729 7.57480i −0.367315 0.308214i
\(605\) −9.57243 + 1.68788i −0.389175 + 0.0686220i
\(606\) 27.6973 15.9910i 1.12513 0.649592i
\(607\) 11.6866 + 32.1087i 0.474345 + 1.30325i 0.914229 + 0.405197i \(0.132797\pi\)
−0.439885 + 0.898054i \(0.644981\pi\)
\(608\) −6.33918 + 2.30727i −0.257088 + 0.0935722i
\(609\) −0.828549 0.146095i −0.0335745 0.00592009i
\(610\) −0.180857 0.215537i −0.00732267 0.00872682i
\(611\) −10.4417 12.4439i −0.422425 0.503426i
\(612\) 1.82921 + 0.322539i 0.0739414 + 0.0130379i
\(613\) −38.7066 + 14.0880i −1.56334 + 0.569011i −0.971499 0.237042i \(-0.923822\pi\)
−0.591844 + 0.806052i \(0.701600\pi\)
\(614\) 2.97752 + 8.18067i 0.120163 + 0.330145i
\(615\) 5.07530 2.93022i 0.204656 0.118158i
\(616\) 0.698115 0.123097i 0.0281279 0.00495970i
\(617\) −24.5087 20.5652i −0.986681 0.827924i −0.00159734 0.999999i \(-0.500508\pi\)
−0.985084 + 0.172075i \(0.944953\pi\)
\(618\) −11.9781 + 20.7467i −0.481831 + 0.834555i
\(619\) −3.10000 5.36936i −0.124600 0.215813i 0.796977 0.604010i \(-0.206431\pi\)
−0.921576 + 0.388197i \(0.873098\pi\)
\(620\) −1.13049 + 6.41133i −0.0454016 + 0.257485i
\(621\) −16.7720 9.68334i −0.673039 0.388579i
\(622\) −5.45885 1.98686i −0.218880 0.0796657i
\(623\) 1.49016i 0.0597020i
\(624\) −1.25227 + 3.44057i −0.0501308 + 0.137733i
\(625\) 2.74516 + 15.5686i 0.109807 + 0.622744i
\(626\) 6.02528 5.05581i 0.240819 0.202071i
\(627\) 39.2104 46.7292i 1.56591 1.86618i
\(628\) 17.3717 0.693208
\(629\) −20.9564 3.42134i −0.835586 0.136418i
\(630\) −0.0627190 −0.00249878
\(631\) −23.4724 + 27.9733i −0.934421 + 1.11360i 0.0589052 + 0.998264i \(0.481239\pi\)
−0.993326 + 0.115336i \(0.963205\pi\)
\(632\) 1.44803 1.21504i 0.0575995 0.0483317i
\(633\) −7.56293 42.8915i −0.300600 1.70479i
\(634\) −1.91497 + 5.26133i −0.0760531 + 0.208954i
\(635\) 4.42635i 0.175654i
\(636\) −19.2312 6.99959i −0.762567 0.277552i
\(637\) −11.7736 6.79748i −0.466487 0.269326i
\(638\) 2.53856 14.3969i 0.100503 0.569979i
\(639\) −1.85787 3.21793i −0.0734963 0.127299i
\(640\) −0.400019 + 0.692853i −0.0158121 + 0.0273874i
\(641\) −15.2619 12.8063i −0.602810 0.505817i 0.289538 0.957167i \(-0.406498\pi\)
−0.892347 + 0.451349i \(0.850943\pi\)
\(642\) −26.3534 + 4.64681i −1.04009 + 0.183395i
\(643\) −28.9945 + 16.7400i −1.14343 + 0.660161i −0.947278 0.320412i \(-0.896179\pi\)
−0.196155 + 0.980573i \(0.562845\pi\)
\(644\) −0.210410 0.578096i −0.00829130 0.0227802i
\(645\) 11.4566 4.16985i 0.451101 0.164187i
\(646\) −23.1914 4.08926i −0.912452 0.160890i
\(647\) −7.67494 9.14664i −0.301733 0.359592i 0.593779 0.804628i \(-0.297635\pi\)
−0.895513 + 0.445036i \(0.853191\pi\)
\(648\) 6.62916 + 7.90033i 0.260418 + 0.310354i
\(649\) 41.0863 + 7.24462i 1.61278 + 0.284376i
\(650\) −7.98170 + 2.90510i −0.313068 + 0.113947i
\(651\) 0.770651 + 2.11735i 0.0302042 + 0.0829853i
\(652\) 1.95821 1.13057i 0.0766895 0.0442767i
\(653\) 13.4694 2.37501i 0.527097 0.0929414i 0.0962338 0.995359i \(-0.469320\pi\)
0.430863 + 0.902417i \(0.358209\pi\)
\(654\) −28.4894 23.9054i −1.11402 0.934777i
\(655\) 0.329195 0.570182i 0.0128627 0.0222789i
\(656\) −1.94883 3.37547i −0.0760891 0.131790i
\(657\) 0.104776 0.594217i 0.00408772 0.0231826i
\(658\) −1.06392 0.614253i −0.0414758 0.0239461i
\(659\) 31.2934 + 11.3899i 1.21902 + 0.443686i 0.869822 0.493365i \(-0.164233\pi\)
0.349194 + 0.937051i \(0.386456\pi\)
\(660\) 7.23432i 0.281596i
\(661\) −1.38912 + 3.81658i −0.0540305 + 0.148448i −0.963772 0.266728i \(-0.914058\pi\)
0.909741 + 0.415175i \(0.136280\pi\)
\(662\) −3.15875 17.9142i −0.122768 0.696254i
\(663\) −9.79099 + 8.21561i −0.380250 + 0.319068i
\(664\) −6.36675 + 7.58759i −0.247078 + 0.294456i
\(665\) 0.795174 0.0308355
\(666\) 2.11175 + 2.45273i 0.0818286 + 0.0950415i
\(667\) −12.6869 −0.491240
\(668\) −10.2563 + 12.2230i −0.396829 + 0.472923i
\(669\) 14.2702 11.9741i 0.551717 0.462945i
\(670\) −0.333339 1.89046i −0.0128780 0.0730348i
\(671\) 0.578735 1.59006i 0.0223418 0.0613836i
\(672\) 0.276898i 0.0106816i
\(673\) 17.0237 + 6.19612i 0.656216 + 0.238843i 0.648602 0.761128i \(-0.275354\pi\)
0.00761402 + 0.999971i \(0.497576\pi\)
\(674\) 28.6135 + 16.5200i 1.10215 + 0.636328i
\(675\) −3.51153 + 19.9149i −0.135159 + 0.766523i
\(676\) 4.60230 + 7.97141i 0.177011 + 0.306593i
\(677\) −10.1473 + 17.5756i −0.389991 + 0.675484i −0.992448 0.122667i \(-0.960855\pi\)
0.602457 + 0.798151i \(0.294189\pi\)
\(678\) 12.2396 + 10.2703i 0.470060 + 0.394427i
\(679\) −0.852477 + 0.150315i −0.0327150 + 0.00576855i
\(680\) −2.41863 + 1.39639i −0.0927501 + 0.0535493i
\(681\) 1.28582 + 3.53276i 0.0492728 + 0.135376i
\(682\) −36.7911 + 13.3909i −1.40880 + 0.512763i
\(683\) −23.3553 4.11816i −0.893665 0.157577i −0.292087 0.956392i \(-0.594350\pi\)
−0.601577 + 0.798814i \(0.705461\pi\)
\(684\) 2.30727 + 2.74970i 0.0882207 + 0.105137i
\(685\) 3.46727 + 4.13213i 0.132477 + 0.157881i
\(686\) −2.02820 0.357626i −0.0774369 0.0136542i
\(687\) 15.7928 5.74813i 0.602535 0.219305i
\(688\) −2.77328 7.61952i −0.105730 0.290491i
\(689\) 18.3723 10.6073i 0.699931 0.404105i
\(690\) −6.18284 + 1.09020i −0.235377 + 0.0415032i
\(691\) −2.69427 2.26076i −0.102495 0.0860034i 0.590100 0.807330i \(-0.299088\pi\)
−0.692595 + 0.721327i \(0.743533\pi\)
\(692\) −1.53759 + 2.66318i −0.0584502 + 0.101239i
\(693\) −0.188595 0.326656i −0.00716412 0.0124086i
\(694\) −5.60917 + 31.8112i −0.212921 + 1.20754i
\(695\) 8.31688 + 4.80175i 0.315477 + 0.182141i
\(696\) 5.36597 + 1.95305i 0.203396 + 0.0740303i
\(697\) 13.6060i 0.515366i
\(698\) 0.781994 2.14851i 0.0295989 0.0813224i
\(699\) −7.09324 40.2278i −0.268291 1.52155i
\(700\) −0.492083 + 0.412907i −0.0185990 + 0.0156064i
\(701\) 12.2023 14.5422i 0.460876 0.549251i −0.484688 0.874687i \(-0.661067\pi\)
0.945564 + 0.325436i \(0.105511\pi\)
\(702\) −9.03596 −0.341040
\(703\) −26.7735 31.0966i −1.00978 1.17283i
\(704\) −4.81140 −0.181336
\(705\) −8.05874 + 9.60403i −0.303510 + 0.361709i
\(706\) −4.91950 + 4.12795i −0.185148 + 0.155357i
\(707\) 0.435377 + 2.46915i 0.0163740 + 0.0928618i
\(708\) −5.57367 + 15.3135i −0.209471 + 0.575518i
\(709\) 13.0236i 0.489113i −0.969635 0.244556i \(-0.921358\pi\)
0.969635 0.244556i \(-0.0786423\pi\)
\(710\) 5.24999 + 1.91084i 0.197029 + 0.0717125i
\(711\) −0.871040 0.502895i −0.0326666 0.0188601i
\(712\) 1.75630 9.96048i 0.0658202 0.373285i
\(713\) 16.9889 + 29.4257i 0.636240 + 1.10200i
\(714\) −0.483301 + 0.837102i −0.0180871 + 0.0313278i
\(715\) 5.74467 + 4.82035i 0.214838 + 0.180271i
\(716\) 10.2879 1.81404i 0.384478 0.0677939i
\(717\) −12.8862 + 7.43983i −0.481242 + 0.277845i
\(718\) 2.50442 + 6.88084i 0.0934642 + 0.256791i
\(719\) 23.6018 8.59034i 0.880197 0.320366i 0.137908 0.990445i \(-0.455962\pi\)
0.742289 + 0.670079i \(0.233740\pi\)
\(720\) 0.419224 + 0.0739205i 0.0156236 + 0.00275486i
\(721\) −1.20719 1.43867i −0.0449580 0.0535789i
\(722\) −17.0394 20.3068i −0.634143 0.755742i
\(723\) 55.1151 + 9.71829i 2.04975 + 0.361427i
\(724\) 8.46310 3.08032i 0.314529 0.114479i
\(725\) 4.53084 + 12.4484i 0.168271 + 0.462321i
\(726\) 19.7746 11.4168i 0.733902 0.423719i
\(727\) −19.0823 + 3.36472i −0.707723 + 0.124791i −0.515913 0.856641i \(-0.672547\pi\)
−0.191811 + 0.981432i \(0.561436\pi\)
\(728\) −0.219881 0.184502i −0.00814932 0.00683810i
\(729\) −10.3316 + 17.8948i −0.382651 + 0.662770i
\(730\) 0.453618 + 0.785689i 0.0167891 + 0.0290796i
\(731\) 4.91518 27.8754i 0.181795 1.03101i
\(732\) 0.572404 + 0.330478i 0.0211567 + 0.0122148i
\(733\) 10.1457 + 3.69274i 0.374741 + 0.136395i 0.522523 0.852625i \(-0.324991\pi\)
−0.147781 + 0.989020i \(0.547213\pi\)
\(734\) 31.5546i 1.16470i
\(735\) −3.58862 + 9.85965i −0.132368 + 0.363679i
\(736\) 0.725070 + 4.11208i 0.0267264 + 0.151573i
\(737\) 8.84362 7.42068i 0.325759 0.273344i
\(738\) −1.33308 + 1.58870i −0.0490713 + 0.0584809i
\(739\) −28.0429 −1.03157 −0.515787 0.856717i \(-0.672500\pi\)
−0.515787 + 0.856717i \(0.672500\pi\)
\(740\) −4.80286 0.784114i −0.176556 0.0288246i
\(741\) −24.6997 −0.907367
\(742\) 1.03128 1.22903i 0.0378595 0.0451192i
\(743\) 13.7013 11.4967i 0.502651 0.421774i −0.355883 0.934530i \(-0.615820\pi\)
0.858534 + 0.512756i \(0.171375\pi\)
\(744\) −2.65566 15.0610i −0.0973611 0.552162i
\(745\) −2.52109 + 6.92665i −0.0923657 + 0.253773i
\(746\) 8.36944i 0.306427i
\(747\) 4.95245 + 1.80254i 0.181201 + 0.0659517i
\(748\) −14.5455 8.39787i −0.531837 0.307056i
\(749\) 0.364287 2.06597i 0.0133108 0.0754891i
\(750\) 7.03671 + 12.1879i 0.256944 + 0.445040i
\(751\) 1.32138 2.28870i 0.0482179 0.0835159i −0.840909 0.541176i \(-0.817979\pi\)
0.889127 + 0.457660i \(0.151312\pi\)
\(752\) 6.38745 + 5.35970i 0.232926 + 0.195448i
\(753\) 42.2655 7.45254i 1.54024 0.271586i
\(754\) −5.12632 + 2.95969i −0.186690 + 0.107785i
\(755\) −3.22453 8.85931i −0.117353 0.322423i
\(756\) −0.642148 + 0.233723i −0.0233547 + 0.00850042i
\(757\) 47.2794 + 8.33663i 1.71840 + 0.303000i 0.944060 0.329773i \(-0.106972\pi\)
0.774337 + 0.632773i \(0.218083\pi\)
\(758\) 18.1179 + 21.5920i 0.658071 + 0.784258i
\(759\) −24.2697 28.9235i −0.880934 1.04986i
\(760\) −5.31507 0.937191i −0.192798 0.0339955i
\(761\) 3.02398 1.10064i 0.109619 0.0398981i −0.286628 0.958042i \(-0.592534\pi\)
0.396247 + 0.918144i \(0.370312\pi\)
\(762\) −3.55633 9.77095i −0.128832 0.353964i
\(763\) 2.52492 1.45777i 0.0914084 0.0527747i
\(764\) 0.990230 0.174604i 0.0358253 0.00631696i
\(765\) 1.13835 + 0.955190i 0.0411572 + 0.0345350i
\(766\) 4.54733 7.87621i 0.164302 0.284579i
\(767\) −8.44643 14.6296i −0.304983 0.528246i
\(768\) 0.326352 1.85083i 0.0117762 0.0667862i
\(769\) 17.4613 + 10.0813i 0.629671 + 0.363541i 0.780625 0.625000i \(-0.214901\pi\)
−0.150954 + 0.988541i \(0.548234\pi\)
\(770\) 0.532932 + 0.193971i 0.0192055 + 0.00699025i
\(771\) 30.8451i 1.11086i
\(772\) −3.76060 + 10.3322i −0.135347 + 0.371863i
\(773\) −3.61493 20.5013i −0.130020 0.737380i −0.978199 0.207670i \(-0.933412\pi\)
0.848179 0.529710i \(-0.177699\pi\)
\(774\) −3.30506 + 2.77328i −0.118798 + 0.0996834i
\(775\) 22.8052 27.1782i 0.819187 0.976269i
\(776\) 5.87526 0.210909
\(777\) −1.57529 + 0.596121i −0.0565131 + 0.0213857i
\(778\) 2.00537 0.0718960
\(779\) 16.9013 20.1421i 0.605550 0.721667i
\(780\) −2.24393 + 1.88288i −0.0803456 + 0.0674180i
\(781\) 5.83450 + 33.0891i 0.208775 + 1.18402i
\(782\) −4.98528 + 13.6969i −0.178273 + 0.489801i
\(783\) 14.0926i 0.503629i
\(784\) 6.55745 + 2.38672i 0.234195 + 0.0852399i
\(785\) 12.0361 + 6.94903i 0.429586 + 0.248021i
\(786\) −0.268571 + 1.52314i −0.00957960 + 0.0543286i
\(787\) 4.71795 + 8.17173i 0.168177 + 0.291291i 0.937779 0.347233i \(-0.112879\pi\)
−0.769602 + 0.638524i \(0.779545\pi\)
\(788\) 12.9525 22.4344i 0.461414 0.799193i
\(789\) 2.24550 + 1.88420i 0.0799418 + 0.0670792i
\(790\) 1.48931 0.262606i 0.0529873 0.00934310i
\(791\) −1.08476 + 0.626286i −0.0385696 + 0.0222682i
\(792\) 0.875603 + 2.40570i 0.0311132 + 0.0854828i
\(793\) −0.643830 + 0.234335i −0.0228631 + 0.00832148i
\(794\) 18.7858 + 3.31245i 0.666685 + 0.117555i
\(795\) −10.5244 12.5425i −0.373263 0.444838i
\(796\) 10.0107 + 11.9302i 0.354819 + 0.422856i
\(797\) −44.0733 7.77131i −1.56116 0.275274i −0.674701 0.738091i \(-0.735728\pi\)
−0.886454 + 0.462817i \(0.846839\pi\)
\(798\) −1.75531 + 0.638879i −0.0621372 + 0.0226161i
\(799\) 9.95526 + 27.3519i 0.352192 + 0.967639i
\(800\) 3.77582 2.17997i 0.133495 0.0770736i
\(801\) −5.29986 + 0.934509i −0.187261 + 0.0330192i
\(802\) 18.9553 + 15.9054i 0.669336 + 0.561640i
\(803\) −2.72804 + 4.72510i −0.0962704 + 0.166745i
\(804\) 2.25471 + 3.90527i 0.0795175 + 0.137728i
\(805\) 0.0854663 0.484704i 0.00301229 0.0170836i
\(806\) 13.7292 + 7.92656i 0.483591 + 0.279201i
\(807\) −5.82538 2.12026i −0.205063 0.0746368i
\(808\) 17.0173i 0.598667i
\(809\) −7.22920 + 19.8621i −0.254165 + 0.698313i 0.745335 + 0.666691i \(0.232290\pi\)
−0.999500 + 0.0316227i \(0.989933\pi\)
\(810\) 1.43276 + 8.12556i 0.0503419 + 0.285503i
\(811\) 5.83069 4.89253i 0.204743 0.171800i −0.534651 0.845073i \(-0.679557\pi\)
0.739394 + 0.673273i \(0.235112\pi\)
\(812\) −0.287752 + 0.342929i −0.0100981 + 0.0120345i
\(813\) 6.77210 0.237508
\(814\) −10.3582 27.3723i −0.363056 0.959397i
\(815\) 1.80900 0.0633666
\(816\) 4.21707 5.02571i 0.147627 0.175935i
\(817\) 41.9028 35.1606i 1.46599 1.23011i
\(818\) −4.27977 24.2718i −0.149639 0.848643i
\(819\) −0.0522359 + 0.143517i −0.00182527 + 0.00501489i
\(820\) 3.11828i 0.108895i
\(821\) −5.77582 2.10223i −0.201577 0.0733682i 0.239258 0.970956i \(-0.423096\pi\)
−0.440836 + 0.897588i \(0.645318\pi\)
\(822\) −10.9738 6.33571i −0.382754 0.220983i
\(823\) 4.84392 27.4712i 0.168848 0.957587i −0.776159 0.630538i \(-0.782834\pi\)
0.945007 0.327050i \(-0.106054\pi\)
\(824\) 6.37342 + 11.0391i 0.222029 + 0.384565i
\(825\) −19.7123 + 34.1427i −0.686295 + 1.18870i
\(826\) −0.978661 0.821194i −0.0340520 0.0285730i
\(827\) −24.0641 + 4.24315i −0.836791 + 0.147549i −0.575593 0.817736i \(-0.695229\pi\)
−0.261198 + 0.965285i \(0.584118\pi\)
\(828\) 1.92409 1.11087i 0.0668666 0.0386055i
\(829\) 16.1603 + 44.4002i 0.561272 + 1.54208i 0.817775 + 0.575538i \(0.195207\pi\)
−0.256503 + 0.966543i \(0.582570\pi\)
\(830\) −7.44640 + 2.71027i −0.258468 + 0.0940748i
\(831\) −29.0359 5.11982i −1.00725 0.177605i
\(832\) 1.25227 + 1.49239i 0.0434145 + 0.0517394i
\(833\) 15.6583 + 18.6608i 0.542528 + 0.646559i
\(834\) −22.2170 3.91746i −0.769313 0.135651i
\(835\) −11.9956 + 4.36603i −0.415124 + 0.151093i
\(836\) −11.1012 30.5003i −0.383943 1.05488i
\(837\) 32.6860 18.8713i 1.12979 0.652287i
\(838\) 17.9994 3.17378i 0.621780 0.109637i
\(839\) −36.0502 30.2497i −1.24459 1.04434i −0.997151 0.0754333i \(-0.975966\pi\)
−0.247441 0.968903i \(-0.579590\pi\)
\(840\) −0.110765 + 0.191850i −0.00382174 + 0.00661945i
\(841\) −9.88403 17.1196i −0.340829 0.590333i
\(842\) −6.52876 + 37.0264i −0.224996 + 1.27601i
\(843\) −8.28219 4.78173i −0.285254 0.164691i
\(844\) −21.7766 7.92603i −0.749582 0.272825i
\(845\) 7.36403i 0.253330i
\(846\) 1.51743 4.16911i 0.0521704 0.143337i
\(847\) 0.310838 + 1.76285i 0.0106805 + 0.0605723i
\(848\) −8.34178 + 6.99959i −0.286458 + 0.240367i
\(849\) −11.0711 + 13.1940i −0.379958 + 0.452816i
\(850\) 15.2198 0.522034
\(851\) −21.8328 + 12.9777i −0.748419 + 0.444868i
\(852\) −13.1243 −0.449633
\(853\) 17.8441 21.2658i 0.610971 0.728127i −0.368519 0.929620i \(-0.620135\pi\)
0.979490 + 0.201493i \(0.0645794\pi\)
\(854\) −0.0396931 + 0.0333064i −0.00135827 + 0.00113972i
\(855\) 0.498669 + 2.82809i 0.0170541 + 0.0967187i
\(856\) −4.86991 + 13.3800i −0.166450 + 0.457318i
\(857\) 23.8545i 0.814853i −0.913238 0.407426i \(-0.866426\pi\)
0.913238 0.407426i \(-0.133574\pi\)
\(858\) −16.5540 6.02515i −0.565143 0.205695i
\(859\) −38.3629 22.1488i −1.30893 0.755708i −0.327008 0.945021i \(-0.606041\pi\)
−0.981917 + 0.189313i \(0.939374\pi\)
\(860\) 1.12648 6.38857i 0.0384126 0.217849i
\(861\) −0.539628 0.934663i −0.0183905 0.0318532i
\(862\) 18.4386 31.9367i 0.628023 1.08777i
\(863\) 33.1007 + 27.7748i 1.12676 + 0.945465i 0.998926 0.0463308i \(-0.0147528\pi\)
0.127835 + 0.991795i \(0.459197\pi\)
\(864\) 4.56769 0.805407i 0.155396 0.0274005i
\(865\) −2.13064 + 1.23013i −0.0724440 + 0.0418256i
\(866\) −3.72589 10.2368i −0.126611 0.347861i
\(867\) −8.50203 + 3.09449i −0.288744 + 0.105094i
\(868\) 1.18071 + 0.208190i 0.0400758 + 0.00706644i
\(869\) 5.84605 + 6.96705i 0.198314 + 0.236341i
\(870\) 2.93657 + 3.49967i 0.0995591 + 0.118650i
\(871\) −4.60347 0.811716i −0.155983 0.0275040i
\(872\) −18.5951 + 6.76808i −0.629711 + 0.229196i
\(873\) −1.06921 2.93763i −0.0361872 0.0994236i
\(874\) −24.3943 + 14.0840i −0.825148 + 0.476399i
\(875\) −1.08652 + 0.191584i −0.0367312 + 0.00647671i
\(876\) −1.63260 1.36991i −0.0551603 0.0462850i
\(877\) 20.2553 35.0832i 0.683972 1.18467i −0.289787 0.957091i \(-0.593584\pi\)
0.973759 0.227583i \(-0.0730823\pi\)
\(878\) 9.34440 + 16.1850i 0.315358 + 0.546217i
\(879\) −8.26340 + 46.8641i −0.278718 + 1.58069i
\(880\) −3.33359 1.92465i −0.112375 0.0648800i
\(881\) −22.9486 8.35260i −0.773157 0.281406i −0.0748407 0.997196i \(-0.523845\pi\)
−0.698316 + 0.715789i \(0.746067\pi\)
\(882\) 3.71307i 0.125026i
\(883\) 8.25110 22.6697i 0.277671 0.762896i −0.719954 0.694022i \(-0.755837\pi\)
0.997625 0.0688742i \(-0.0219407\pi\)
\(884\) 1.18094 + 6.69743i 0.0397192 + 0.225259i
\(885\) −9.98745 + 8.38046i −0.335724 + 0.281706i
\(886\) −11.6768 + 13.9159i −0.392291 + 0.467514i
\(887\) −4.81523 −0.161679 −0.0808397 0.996727i \(-0.525760\pi\)
−0.0808397 + 0.996727i \(0.525760\pi\)
\(888\) 11.2321 2.12794i 0.376923 0.0714091i
\(889\) 0.815153 0.0273394
\(890\) 5.20124 6.19860i 0.174346 0.207777i
\(891\) −38.0116 + 31.8955i −1.27344 + 1.06854i
\(892\) −1.72119 9.76137i −0.0576298 0.326835i
\(893\) −19.2385 + 52.8574i −0.643793 + 1.76881i
\(894\) 17.3158i 0.579127i
\(895\) 7.85369 + 2.85851i 0.262520 + 0.0955494i
\(896\) 0.127595 + 0.0736672i 0.00426266 + 0.00246105i
\(897\) −2.65476 + 15.0559i −0.0886398 + 0.502701i
\(898\) −7.78469 13.4835i −0.259778 0.449949i
\(899\) 12.3624 21.4123i 0.412309 0.714139i
\(900\) −1.77713 1.49119i −0.0592376 0.0497062i
\(901\) −37.4355 + 6.60089i −1.24716 + 0.219908i
\(902\) 16.2408 9.37660i 0.540758 0.312207i
\(903\) −0.767916 2.10983i −0.0255546 0.0702108i
\(904\) 7.98885 2.90770i 0.265705 0.0967088i
\(905\) 7.09587 + 1.25119i 0.235875 + 0.0415911i
\(906\) 14.2360 + 16.9658i 0.472958 + 0.563650i
\(907\) −3.00851 3.58540i −0.0998959 0.119051i 0.713780 0.700370i \(-0.246982\pi\)
−0.813676 + 0.581318i \(0.802537\pi\)
\(908\) 1.96999 + 0.347363i 0.0653765 + 0.0115276i
\(909\) −8.50866 + 3.09690i −0.282214 + 0.102718i
\(910\) −0.0785409 0.215789i −0.00260360 0.00715334i
\(911\) −7.63660 + 4.40899i −0.253012 + 0.146077i −0.621143 0.783698i \(-0.713331\pi\)
0.368131 + 0.929774i \(0.379998\pi\)
\(912\) 12.4857 2.20157i 0.413444 0.0729014i
\(913\) −36.5069 30.6330i −1.20820 1.01380i
\(914\) 5.51212 9.54728i 0.182325 0.315796i
\(915\) 0.264395 + 0.457945i 0.00874062 + 0.0151392i
\(916\) 1.55285 8.80664i 0.0513075 0.290980i
\(917\) −0.105004 0.0606243i −0.00346755 0.00200199i
\(918\) 15.2145 + 5.53764i 0.502155 + 0.182769i
\(919\) 8.95913i 0.295535i −0.989022 0.147767i \(-0.952791\pi\)
0.989022 0.147767i \(-0.0472087\pi\)
\(920\) −1.14254 + 3.13911i −0.0376685 + 0.103493i
\(921\) −2.84112 16.1128i −0.0936179 0.530934i
\(922\) 16.3531 13.7219i 0.538562 0.451907i
\(923\) 8.74497 10.4218i 0.287844 0.343039i
\(924\) −1.33227 −0.0438284
\(925\) 20.5307 + 16.7876i 0.675046 + 0.551974i
\(926\) −33.1910 −1.09073
\(927\) 4.35968 5.19566i 0.143191 0.170648i
\(928\) 2.32756 1.95305i 0.0764058 0.0641121i
\(929\) 6.26803 + 35.5478i 0.205647 + 1.16628i 0.896418 + 0.443210i \(0.146160\pi\)
−0.690770 + 0.723074i \(0.742729\pi\)
\(930\) 4.18470 11.4974i 0.137222 0.377013i
\(931\) 47.0756i 1.54284i
\(932\) −20.4242 7.43379i −0.669016 0.243502i
\(933\) 9.45500 + 5.45885i 0.309543 + 0.178715i
\(934\) −2.57215 + 14.5874i −0.0841633 + 0.477314i
\(935\) −6.71861 11.6370i −0.219722 0.380570i
\(936\) 0.518302 0.897726i 0.0169412 0.0293431i
\(937\) −5.84891 4.90782i −0.191076 0.160331i 0.542231 0.840229i \(-0.317580\pi\)
−0.733307 + 0.679898i \(0.762024\pi\)
\(938\) −0.348145 + 0.0613874i −0.0113674 + 0.00200437i
\(939\) −12.8018 + 7.39110i −0.417770 + 0.241199i
\(940\) 2.28158 + 6.26859i 0.0744169 + 0.204459i
\(941\) 42.2064 15.3619i 1.37589 0.500782i 0.454959 0.890512i \(-0.349654\pi\)
0.920929 + 0.389730i \(0.127432\pi\)
\(942\) −32.1522 5.66930i −1.04758 0.184716i
\(943\) −10.4612 12.4672i −0.340664 0.405987i
\(944\) 5.57367 + 6.64244i 0.181408 + 0.216193i
\(945\) −0.538408 0.0949359i −0.0175144 0.00308827i
\(946\) 36.6605 13.3433i 1.19194 0.433830i
\(947\) 2.43767 + 6.69744i 0.0792136 + 0.217638i 0.972977 0.230900i \(-0.0741671\pi\)
−0.893764 + 0.448538i \(0.851945\pi\)
\(948\) −3.07659 + 1.77627i −0.0999231 + 0.0576906i
\(949\) 2.17565 0.383626i 0.0706247 0.0124530i
\(950\) 22.5311 + 18.9058i 0.731004 + 0.613385i
\(951\) 5.26133 9.11290i 0.170610 0.295506i
\(952\) 0.257159 + 0.445413i 0.00833457 + 0.0144359i
\(953\) 1.91509 10.8610i 0.0620358 0.351823i −0.937951 0.346767i \(-0.887280\pi\)
0.999987 0.00505584i \(-0.00160933\pi\)
\(954\) 5.01787 + 2.89707i 0.162460 + 0.0937961i
\(955\) 0.755929 + 0.275136i 0.0244613 + 0.00890318i
\(956\) 7.91730i 0.256064i
\(957\) −9.39691 + 25.8178i −0.303759 + 0.834571i
\(958\) 1.56380 + 8.86872i 0.0505239 + 0.286535i
\(959\) 0.760970 0.638530i 0.0245730 0.0206192i
\(960\) 0.966482 1.15181i 0.0311931 0.0371745i
\(961\) −35.2173 −1.13604
\(962\) −5.79434 + 10.3371i −0.186817 + 0.333281i
\(963\) 7.57623 0.244141
\(964\) 19.1413 22.8117i 0.616499 0.734715i
\(965\) −6.73861 + 5.65436i −0.216923 + 0.182020i
\(966\) 0.200771 + 1.13863i 0.00645969 + 0.0366347i
\(967\) 9.23888 25.3836i 0.297102 0.816282i −0.697879 0.716216i \(-0.745872\pi\)
0.994981 0.100066i \(-0.0319053\pi\)
\(968\) 12.1496i 0.390501i
\(969\) 41.5888 + 15.1371i 1.33602 + 0.486273i
\(970\) 4.07069 + 2.35021i 0.130702 + 0.0754608i
\(971\) −8.75426 + 49.6479i −0.280937 + 1.59328i 0.438509 + 0.898727i \(0.355507\pi\)
−0.719446 + 0.694548i \(0.755604\pi\)
\(972\) −2.73396 4.73535i −0.0876917 0.151886i
\(973\) 0.884287 1.53163i 0.0283489 0.0491018i
\(974\) 2.59840 + 2.18032i 0.0832582 + 0.0698620i
\(975\) 15.7209 2.77201i 0.503471 0.0887755i
\(976\) 0.304570 0.175844i 0.00974905 0.00562862i
\(977\) 6.82658 + 18.7559i 0.218402 + 0.600054i 0.999710 0.0240919i \(-0.00766943\pi\)
−0.781308 + 0.624146i \(0.785447\pi\)
\(978\) −3.99329 + 1.45344i −0.127691 + 0.0464758i
\(979\) 47.9238 + 8.45027i 1.53165 + 0.270072i
\(980\) 3.58862 + 4.27675i 0.114634 + 0.136616i
\(981\) 6.76808 + 8.06588i 0.216088 + 0.257524i
\(982\) −20.4193 3.60047i −0.651605 0.114896i
\(983\) 10.0028 3.64071i 0.319039 0.116121i −0.177537 0.984114i \(-0.556813\pi\)
0.496576 + 0.867994i \(0.334591\pi\)
\(984\) 2.50537 + 6.88345i 0.0798683 + 0.219436i
\(985\) 17.9484 10.3625i 0.571883 0.330177i
\(986\) 10.4454 1.84181i 0.332650 0.0586551i
\(987\) 1.76867 + 1.48409i 0.0562975 + 0.0472392i
\(988\) −6.57122 + 11.3817i −0.209058 + 0.362100i
\(989\) −16.9286 29.3212i −0.538299 0.932361i
\(990\) −0.355661 + 2.01705i −0.0113037 + 0.0641062i
\(991\) −28.8161 16.6370i −0.915375 0.528492i −0.0332181 0.999448i \(-0.510576\pi\)
−0.882156 + 0.470956i \(0.843909\pi\)
\(992\) −7.64666 2.78316i −0.242782 0.0883653i
\(993\) 34.1870i 1.08489i
\(994\) 0.351899 0.966834i 0.0111616 0.0306661i
\(995\) 2.16360 + 12.2704i 0.0685906 + 0.388997i
\(996\) 14.2600 11.9656i 0.451846 0.379144i
\(997\) 8.80737 10.4962i 0.278932 0.332418i −0.608330 0.793684i \(-0.708160\pi\)
0.887262 + 0.461266i \(0.152605\pi\)
\(998\) −24.6821 −0.781297
\(999\) 14.4156 + 24.2519i 0.456088 + 0.767295i
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 74.2.h.a.3.1 12
3.2 odd 2 666.2.bj.c.595.2 12
4.3 odd 2 592.2.bq.b.225.2 12
37.5 odd 36 2738.2.a.s.1.2 6
37.25 even 18 inner 74.2.h.a.25.1 yes 12
37.32 odd 36 2738.2.a.r.1.1 6
111.62 odd 18 666.2.bj.c.469.2 12
148.99 odd 18 592.2.bq.b.321.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.h.a.3.1 12 1.1 even 1 trivial
74.2.h.a.25.1 yes 12 37.25 even 18 inner
592.2.bq.b.225.2 12 4.3 odd 2
592.2.bq.b.321.2 12 148.99 odd 18
666.2.bj.c.469.2 12 111.62 odd 18
666.2.bj.c.595.2 12 3.2 odd 2
2738.2.a.r.1.1 6 37.32 odd 36
2738.2.a.s.1.2 6 37.5 odd 36