Properties

Label 260.2.o.a.27.35
Level $260$
Weight $2$
Character 260.27
Analytic conductor $2.076$
Analytic rank $0$
Dimension $72$
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] = [260,2,Mod(27,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.o (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 27.35
Character \(\chi\) \(=\) 260.27
Dual form 260.2.o.a.183.35

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.38346 + 0.293307i) q^{2} +(-1.30064 - 1.30064i) q^{3} +(1.82794 + 0.811558i) q^{4} +(-2.07556 - 0.831896i) q^{5} +(-1.41790 - 2.18087i) q^{6} +(2.44850 - 2.44850i) q^{7} +(2.29086 + 1.65891i) q^{8} +0.383307i q^{9} +O(q^{10})\) \(q+(1.38346 + 0.293307i) q^{2} +(-1.30064 - 1.30064i) q^{3} +(1.82794 + 0.811558i) q^{4} +(-2.07556 - 0.831896i) q^{5} +(-1.41790 - 2.18087i) q^{6} +(2.44850 - 2.44850i) q^{7} +(2.29086 + 1.65891i) q^{8} +0.383307i q^{9} +(-2.62746 - 1.75967i) q^{10} -4.04492i q^{11} +(-1.32195 - 3.43303i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(4.10558 - 2.66925i) q^{14} +(1.61755 + 3.78154i) q^{15} +(2.68275 + 2.96696i) q^{16} +(5.07945 + 5.07945i) q^{17} +(-0.112426 + 0.530291i) q^{18} -3.28931 q^{19} +(-3.11887 - 3.20510i) q^{20} -6.36922 q^{21} +(1.18640 - 5.59600i) q^{22} +(-1.98605 - 1.98605i) q^{23} +(-0.821932 - 5.13721i) q^{24} +(3.61590 + 3.45330i) q^{25} +(-1.18566 + 0.770857i) q^{26} +(-3.40336 + 3.40336i) q^{27} +(6.46282 - 2.48862i) q^{28} -5.17756i q^{29} +(1.12868 + 5.70606i) q^{30} +5.36907i q^{31} +(2.84125 + 4.89155i) q^{32} +(-5.26096 + 5.26096i) q^{33} +(5.53740 + 8.51707i) q^{34} +(-7.11891 + 3.04511i) q^{35} +(-0.311076 + 0.700662i) q^{36} +(5.53799 + 5.53799i) q^{37} +(-4.55063 - 0.964776i) q^{38} +1.83938 q^{39} +(-3.37477 - 5.34892i) q^{40} -9.24262 q^{41} +(-8.81158 - 1.86814i) q^{42} +(6.42292 + 6.42292i) q^{43} +(3.28269 - 7.39388i) q^{44} +(0.318871 - 0.795576i) q^{45} +(-2.16511 - 3.33016i) q^{46} +(1.30528 - 1.30528i) q^{47} +(0.369664 - 7.34821i) q^{48} -4.99032i q^{49} +(3.98959 + 5.83808i) q^{50} -13.2130i q^{51} +(-1.86641 + 0.718692i) q^{52} +(-3.32666 + 3.32666i) q^{53} +(-5.70666 + 3.71020i) q^{54} +(-3.36495 + 8.39547i) q^{55} +(9.67101 - 1.54732i) q^{56} +(4.27819 + 4.27819i) q^{57} +(1.51861 - 7.16297i) q^{58} +4.58583 q^{59} +(-0.112145 + 8.22518i) q^{60} +6.40427 q^{61} +(-1.57478 + 7.42791i) q^{62} +(0.938527 + 0.938527i) q^{63} +(2.49604 + 7.60064i) q^{64} +(2.05588 - 0.879404i) q^{65} +(-8.82143 + 5.73528i) q^{66} +(-3.98978 + 3.98978i) q^{67} +(5.16267 + 13.4072i) q^{68} +5.16627i q^{69} +(-10.7419 + 2.12478i) q^{70} -8.66139i q^{71} +(-0.635871 + 0.878100i) q^{72} +(8.05408 - 8.05408i) q^{73} +(6.03728 + 9.28593i) q^{74} +(-0.211484 - 9.19445i) q^{75} +(-6.01266 - 2.66946i) q^{76} +(-9.90399 - 9.90399i) q^{77} +(2.54471 + 0.539502i) q^{78} +1.43474 q^{79} +(-3.10000 - 8.38988i) q^{80} +10.0030 q^{81} +(-12.7868 - 2.71092i) q^{82} +(-5.26584 - 5.26584i) q^{83} +(-11.6426 - 5.16899i) q^{84} +(-6.31713 - 14.7683i) q^{85} +(7.00199 + 10.7698i) q^{86} +(-6.73412 + 6.73412i) q^{87} +(6.71015 - 9.26632i) q^{88} +8.95535i q^{89} +(0.674494 - 1.00712i) q^{90} +3.46270i q^{91} +(-2.01859 - 5.24219i) q^{92} +(6.98320 - 6.98320i) q^{93} +(2.18865 - 1.42296i) q^{94} +(6.82715 + 2.73636i) q^{95} +(2.66670 - 10.0576i) q^{96} +(0.869405 + 0.869405i) q^{97} +(1.46370 - 6.90393i) q^{98} +1.55044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38346 + 0.293307i 0.978256 + 0.207399i
\(3\) −1.30064 1.30064i −0.750922 0.750922i 0.223729 0.974651i \(-0.428177\pi\)
−0.974651 + 0.223729i \(0.928177\pi\)
\(4\) 1.82794 + 0.811558i 0.913971 + 0.405779i
\(5\) −2.07556 0.831896i −0.928219 0.372035i
\(6\) −1.41790 2.18087i −0.578854 0.890335i
\(7\) 2.44850 2.44850i 0.925447 0.925447i −0.0719607 0.997407i \(-0.522926\pi\)
0.997407 + 0.0719607i \(0.0229256\pi\)
\(8\) 2.29086 + 1.65891i 0.809940 + 0.586513i
\(9\) 0.383307i 0.127769i
\(10\) −2.62746 1.75967i −0.830876 0.556457i
\(11\) 4.04492i 1.21959i −0.792560 0.609794i \(-0.791252\pi\)
0.792560 0.609794i \(-0.208748\pi\)
\(12\) −1.32195 3.43303i −0.381613 0.991030i
\(13\) −0.707107 + 0.707107i −0.196116 + 0.196116i
\(14\) 4.10558 2.66925i 1.09726 0.713387i
\(15\) 1.61755 + 3.78154i 0.417651 + 0.976390i
\(16\) 2.68275 + 2.96696i 0.670686 + 0.741741i
\(17\) 5.07945 + 5.07945i 1.23195 + 1.23195i 0.963215 + 0.268734i \(0.0866051\pi\)
0.268734 + 0.963215i \(0.413395\pi\)
\(18\) −0.112426 + 0.530291i −0.0264992 + 0.124991i
\(19\) −3.28931 −0.754618 −0.377309 0.926087i \(-0.623151\pi\)
−0.377309 + 0.926087i \(0.623151\pi\)
\(20\) −3.11887 3.20510i −0.697401 0.716681i
\(21\) −6.36922 −1.38988
\(22\) 1.18640 5.59600i 0.252942 1.19307i
\(23\) −1.98605 1.98605i −0.414121 0.414121i 0.469050 0.883171i \(-0.344596\pi\)
−0.883171 + 0.469050i \(0.844596\pi\)
\(24\) −0.821932 5.13721i −0.167776 1.04863i
\(25\) 3.61590 + 3.45330i 0.723180 + 0.690660i
\(26\) −1.18566 + 0.770857i −0.232526 + 0.151178i
\(27\) −3.40336 + 3.40336i −0.654978 + 0.654978i
\(28\) 6.46282 2.48862i 1.22136 0.470305i
\(29\) 5.17756i 0.961449i −0.876872 0.480725i \(-0.840374\pi\)
0.876872 0.480725i \(-0.159626\pi\)
\(30\) 1.12868 + 5.70606i 0.206067 + 1.04178i
\(31\) 5.36907i 0.964313i 0.876085 + 0.482156i \(0.160146\pi\)
−0.876085 + 0.482156i \(0.839854\pi\)
\(32\) 2.84125 + 4.89155i 0.502267 + 0.864713i
\(33\) −5.26096 + 5.26096i −0.915816 + 0.915816i
\(34\) 5.53740 + 8.51707i 0.949656 + 1.46067i
\(35\) −7.11891 + 3.04511i −1.20332 + 0.514718i
\(36\) −0.311076 + 0.700662i −0.0518460 + 0.116777i
\(37\) 5.53799 + 5.53799i 0.910440 + 0.910440i 0.996307 0.0858669i \(-0.0273660\pi\)
−0.0858669 + 0.996307i \(0.527366\pi\)
\(38\) −4.55063 0.964776i −0.738210 0.156507i
\(39\) 1.83938 0.294536
\(40\) −3.37477 5.34892i −0.533598 0.845738i
\(41\) −9.24262 −1.44345 −0.721727 0.692178i \(-0.756652\pi\)
−0.721727 + 0.692178i \(0.756652\pi\)
\(42\) −8.81158 1.86814i −1.35966 0.288259i
\(43\) 6.42292 + 6.42292i 0.979487 + 0.979487i 0.999794 0.0203072i \(-0.00646443\pi\)
−0.0203072 + 0.999794i \(0.506464\pi\)
\(44\) 3.28269 7.39388i 0.494884 1.11467i
\(45\) 0.318871 0.795576i 0.0475345 0.118597i
\(46\) −2.16511 3.33016i −0.319228 0.491005i
\(47\) 1.30528 1.30528i 0.190394 0.190394i −0.605472 0.795867i \(-0.707016\pi\)
0.795867 + 0.605472i \(0.207016\pi\)
\(48\) 0.369664 7.34821i 0.0533565 1.06062i
\(49\) 4.99032i 0.712903i
\(50\) 3.98959 + 5.83808i 0.564213 + 0.825629i
\(51\) 13.2130i 1.85019i
\(52\) −1.86641 + 0.718692i −0.258824 + 0.0996646i
\(53\) −3.32666 + 3.32666i −0.456951 + 0.456951i −0.897653 0.440702i \(-0.854729\pi\)
0.440702 + 0.897653i \(0.354729\pi\)
\(54\) −5.70666 + 3.71020i −0.776578 + 0.504894i
\(55\) −3.36495 + 8.39547i −0.453730 + 1.13204i
\(56\) 9.67101 1.54732i 1.29234 0.206770i
\(57\) 4.27819 + 4.27819i 0.566660 + 0.566660i
\(58\) 1.51861 7.16297i 0.199404 0.940544i
\(59\) 4.58583 0.597024 0.298512 0.954406i \(-0.403510\pi\)
0.298512 + 0.954406i \(0.403510\pi\)
\(60\) −0.112145 + 8.22518i −0.0144779 + 1.06187i
\(61\) 6.40427 0.819983 0.409991 0.912089i \(-0.365532\pi\)
0.409991 + 0.912089i \(0.365532\pi\)
\(62\) −1.57478 + 7.42791i −0.199998 + 0.943345i
\(63\) 0.938527 + 0.938527i 0.118243 + 0.118243i
\(64\) 2.49604 + 7.60064i 0.312005 + 0.950080i
\(65\) 2.05588 0.879404i 0.255001 0.109077i
\(66\) −8.82143 + 5.73528i −1.08584 + 0.705964i
\(67\) −3.98978 + 3.98978i −0.487429 + 0.487429i −0.907494 0.420065i \(-0.862007\pi\)
0.420065 + 0.907494i \(0.362007\pi\)
\(68\) 5.16267 + 13.4072i 0.626066 + 1.62586i
\(69\) 5.16627i 0.621945i
\(70\) −10.7419 + 2.12478i −1.28390 + 0.253960i
\(71\) 8.66139i 1.02792i −0.857815 0.513959i \(-0.828178\pi\)
0.857815 0.513959i \(-0.171822\pi\)
\(72\) −0.635871 + 0.878100i −0.0749381 + 0.103485i
\(73\) 8.05408 8.05408i 0.942658 0.942658i −0.0557846 0.998443i \(-0.517766\pi\)
0.998443 + 0.0557846i \(0.0177660\pi\)
\(74\) 6.03728 + 9.28593i 0.701819 + 1.07947i
\(75\) −0.211484 9.19445i −0.0244201 1.06168i
\(76\) −6.01266 2.66946i −0.689699 0.306208i
\(77\) −9.90399 9.90399i −1.12866 1.12866i
\(78\) 2.54471 + 0.539502i 0.288132 + 0.0610865i
\(79\) 1.43474 0.161421 0.0807105 0.996738i \(-0.474281\pi\)
0.0807105 + 0.996738i \(0.474281\pi\)
\(80\) −3.10000 8.38988i −0.346590 0.938017i
\(81\) 10.0030 1.11144
\(82\) −12.7868 2.71092i −1.41207 0.299371i
\(83\) −5.26584 5.26584i −0.578001 0.578001i 0.356351 0.934352i \(-0.384021\pi\)
−0.934352 + 0.356351i \(0.884021\pi\)
\(84\) −11.6426 5.16899i −1.27031 0.563983i
\(85\) −6.31713 14.7683i −0.685189 1.60185i
\(86\) 7.00199 + 10.7698i 0.755044 + 1.16133i
\(87\) −6.73412 + 6.73412i −0.721974 + 0.721974i
\(88\) 6.71015 9.26632i 0.715305 0.987793i
\(89\) 8.95535i 0.949266i 0.880184 + 0.474633i \(0.157419\pi\)
−0.880184 + 0.474633i \(0.842581\pi\)
\(90\) 0.674494 1.00712i 0.0710980 0.106160i
\(91\) 3.46270i 0.362990i
\(92\) −2.01859 5.24219i −0.210453 0.546536i
\(93\) 6.98320 6.98320i 0.724124 0.724124i
\(94\) 2.18865 1.42296i 0.225742 0.146767i
\(95\) 6.82715 + 2.73636i 0.700451 + 0.280744i
\(96\) 2.66670 10.0576i 0.272169 1.02650i
\(97\) 0.869405 + 0.869405i 0.0882747 + 0.0882747i 0.749865 0.661591i \(-0.230118\pi\)
−0.661591 + 0.749865i \(0.730118\pi\)
\(98\) 1.46370 6.90393i 0.147856 0.697402i
\(99\) 1.55044 0.155825
\(100\) 3.80710 + 9.24694i 0.380710 + 0.924694i
\(101\) −6.55124 −0.651872 −0.325936 0.945392i \(-0.605679\pi\)
−0.325936 + 0.945392i \(0.605679\pi\)
\(102\) 3.87547 18.2797i 0.383729 1.80996i
\(103\) −5.55670 5.55670i −0.547518 0.547518i 0.378204 0.925722i \(-0.376542\pi\)
−0.925722 + 0.378204i \(0.876542\pi\)
\(104\) −2.79291 + 0.446854i −0.273867 + 0.0438176i
\(105\) 13.2197 + 5.29853i 1.29011 + 0.517083i
\(106\) −5.57804 + 3.62658i −0.541787 + 0.352244i
\(107\) −1.32934 + 1.32934i −0.128512 + 0.128512i −0.768437 0.639925i \(-0.778965\pi\)
0.639925 + 0.768437i \(0.278965\pi\)
\(108\) −8.98318 + 3.45912i −0.864407 + 0.332854i
\(109\) 13.9365i 1.33488i −0.744664 0.667439i \(-0.767390\pi\)
0.744664 0.667439i \(-0.232610\pi\)
\(110\) −7.11773 + 10.6279i −0.678649 + 1.01333i
\(111\) 14.4058i 1.36734i
\(112\) 13.8333 + 0.695909i 1.30713 + 0.0657572i
\(113\) −4.38056 + 4.38056i −0.412089 + 0.412089i −0.882466 0.470377i \(-0.844118\pi\)
0.470377 + 0.882466i \(0.344118\pi\)
\(114\) 4.66390 + 7.17354i 0.436814 + 0.671863i
\(115\) 2.46999 + 5.77437i 0.230327 + 0.538462i
\(116\) 4.20190 9.46429i 0.390136 0.878737i
\(117\) −0.271039 0.271039i −0.0250575 0.0250575i
\(118\) 6.34433 + 1.34506i 0.584043 + 0.123822i
\(119\) 24.8741 2.28020
\(120\) −2.56765 + 11.3463i −0.234393 + 1.03577i
\(121\) −5.36136 −0.487396
\(122\) 8.86007 + 1.87842i 0.802153 + 0.170064i
\(123\) 12.0213 + 12.0213i 1.08392 + 1.08392i
\(124\) −4.35731 + 9.81434i −0.391298 + 0.881354i
\(125\) −4.63223 10.1756i −0.414319 0.910132i
\(126\) 1.02314 + 1.57369i 0.0911487 + 0.140196i
\(127\) −5.18321 + 5.18321i −0.459935 + 0.459935i −0.898634 0.438699i \(-0.855439\pi\)
0.438699 + 0.898634i \(0.355439\pi\)
\(128\) 1.22386 + 11.2473i 0.108175 + 0.994132i
\(129\) 16.7078i 1.47104i
\(130\) 3.10217 0.613619i 0.272078 0.0538179i
\(131\) 4.49467i 0.392701i 0.980534 + 0.196350i \(0.0629090\pi\)
−0.980534 + 0.196350i \(0.937091\pi\)
\(132\) −13.8863 + 5.34716i −1.20865 + 0.465410i
\(133\) −8.05387 + 8.05387i −0.698359 + 0.698359i
\(134\) −6.68994 + 4.34948i −0.577923 + 0.375738i
\(135\) 9.89513 4.23264i 0.851637 0.364288i
\(136\) 3.20994 + 20.0626i 0.275250 + 1.72036i
\(137\) 3.56651 + 3.56651i 0.304707 + 0.304707i 0.842852 0.538145i \(-0.180875\pi\)
−0.538145 + 0.842852i \(0.680875\pi\)
\(138\) −1.51530 + 7.14734i −0.128991 + 0.608422i
\(139\) −7.66785 −0.650378 −0.325189 0.945649i \(-0.605428\pi\)
−0.325189 + 0.945649i \(0.605428\pi\)
\(140\) −15.4842 0.211118i −1.30866 0.0178428i
\(141\) −3.39538 −0.285943
\(142\) 2.54044 11.9827i 0.213189 1.00557i
\(143\) 2.86019 + 2.86019i 0.239181 + 0.239181i
\(144\) −1.13726 + 1.02831i −0.0947714 + 0.0856929i
\(145\) −4.30719 + 10.7463i −0.357693 + 0.892435i
\(146\) 13.5048 8.78020i 1.11767 0.726655i
\(147\) −6.49059 + 6.49059i −0.535335 + 0.535335i
\(148\) 5.62872 + 14.6175i 0.462678 + 1.20155i
\(149\) 6.55325i 0.536863i −0.963299 0.268432i \(-0.913495\pi\)
0.963299 0.268432i \(-0.0865053\pi\)
\(150\) 2.40421 12.7822i 0.196303 1.04366i
\(151\) 4.41532i 0.359313i −0.983729 0.179657i \(-0.942501\pi\)
0.983729 0.179657i \(-0.0574987\pi\)
\(152\) −7.53532 5.45666i −0.611195 0.442593i
\(153\) −1.94699 + 1.94699i −0.157405 + 0.157405i
\(154\) −10.7969 16.6067i −0.870039 1.33821i
\(155\) 4.46650 11.1438i 0.358758 0.895093i
\(156\) 3.36227 + 1.49276i 0.269197 + 0.119517i
\(157\) 5.29541 + 5.29541i 0.422620 + 0.422620i 0.886105 0.463485i \(-0.153401\pi\)
−0.463485 + 0.886105i \(0.653401\pi\)
\(158\) 1.98491 + 0.420819i 0.157911 + 0.0334786i
\(159\) 8.65353 0.686270
\(160\) −1.82792 12.5163i −0.144510 0.989503i
\(161\) −9.72572 −0.766494
\(162\) 13.8388 + 2.93395i 1.08728 + 0.230513i
\(163\) 13.9615 + 13.9615i 1.09355 + 1.09355i 0.995147 + 0.0984035i \(0.0313736\pi\)
0.0984035 + 0.995147i \(0.468626\pi\)
\(164\) −16.8950 7.50093i −1.31928 0.585724i
\(165\) 15.2960 6.54287i 1.19079 0.509362i
\(166\) −5.74059 8.82960i −0.445556 0.685310i
\(167\) −0.479622 + 0.479622i −0.0371143 + 0.0371143i −0.725420 0.688306i \(-0.758355\pi\)
0.688306 + 0.725420i \(0.258355\pi\)
\(168\) −14.5910 10.5660i −1.12572 0.815181i
\(169\) 1.00000i 0.0769231i
\(170\) −4.40789 22.2842i −0.338069 1.70912i
\(171\) 1.26081i 0.0964168i
\(172\) 6.52815 + 16.9533i 0.497767 + 1.29268i
\(173\) 7.85353 7.85353i 0.597093 0.597093i −0.342445 0.939538i \(-0.611255\pi\)
0.939538 + 0.342445i \(0.111255\pi\)
\(174\) −11.2916 + 7.34125i −0.856012 + 0.556539i
\(175\) 17.3089 0.398128i 1.30843 0.0300956i
\(176\) 12.0011 10.8515i 0.904619 0.817962i
\(177\) −5.96450 5.96450i −0.448319 0.448319i
\(178\) −2.62667 + 12.3894i −0.196877 + 0.928625i
\(179\) −8.22537 −0.614793 −0.307397 0.951582i \(-0.599458\pi\)
−0.307397 + 0.951582i \(0.599458\pi\)
\(180\) 1.22853 1.19548i 0.0915696 0.0891062i
\(181\) −12.1292 −0.901555 −0.450778 0.892636i \(-0.648853\pi\)
−0.450778 + 0.892636i \(0.648853\pi\)
\(182\) −1.01563 + 4.79053i −0.0752839 + 0.355097i
\(183\) −8.32962 8.32962i −0.615743 0.615743i
\(184\) −1.25508 7.84445i −0.0925257 0.578300i
\(185\) −6.88740 16.1015i −0.506372 1.18380i
\(186\) 11.7092 7.61278i 0.858562 0.558196i
\(187\) 20.5460 20.5460i 1.50247 1.50247i
\(188\) 3.44528 1.32666i 0.251273 0.0967569i
\(189\) 16.6663i 1.21229i
\(190\) 8.64252 + 5.78810i 0.626994 + 0.419913i
\(191\) 7.58940i 0.549150i 0.961566 + 0.274575i \(0.0885371\pi\)
−0.961566 + 0.274575i \(0.911463\pi\)
\(192\) 6.63923 13.1321i 0.479145 0.947728i
\(193\) 1.87226 1.87226i 0.134769 0.134769i −0.636504 0.771273i \(-0.719620\pi\)
0.771273 + 0.636504i \(0.219620\pi\)
\(194\) 0.947788 + 1.45779i 0.0680472 + 0.104663i
\(195\) −3.81774 1.53017i −0.273394 0.109578i
\(196\) 4.04994 9.12202i 0.289281 0.651573i
\(197\) 1.75492 + 1.75492i 0.125033 + 0.125033i 0.766854 0.641821i \(-0.221821\pi\)
−0.641821 + 0.766854i \(0.721821\pi\)
\(198\) 2.14498 + 0.454756i 0.152437 + 0.0323181i
\(199\) −17.3332 −1.22871 −0.614357 0.789028i \(-0.710585\pi\)
−0.614357 + 0.789028i \(0.710585\pi\)
\(200\) 2.55479 + 13.9095i 0.180651 + 0.983547i
\(201\) 10.3785 0.732043
\(202\) −9.06340 1.92152i −0.637698 0.135198i
\(203\) −12.6773 12.6773i −0.889770 0.889770i
\(204\) 10.7231 24.1527i 0.750771 1.69102i
\(205\) 19.1836 + 7.68889i 1.33984 + 0.537016i
\(206\) −6.05767 9.31731i −0.422058 0.649168i
\(207\) 0.761268 0.761268i 0.0529118 0.0529118i
\(208\) −3.99495 0.200973i −0.277000 0.0139349i
\(209\) 13.3050i 0.920324i
\(210\) 16.7349 + 11.2077i 1.15482 + 0.773408i
\(211\) 23.7012i 1.63166i 0.578293 + 0.815829i \(0.303719\pi\)
−0.578293 + 0.815829i \(0.696281\pi\)
\(212\) −8.78071 + 3.38116i −0.603062 + 0.232219i
\(213\) −11.2653 + 11.2653i −0.771887 + 0.771887i
\(214\) −2.22900 + 1.44919i −0.152371 + 0.0990645i
\(215\) −7.98796 18.6744i −0.544774 1.27358i
\(216\) −13.4425 + 2.15074i −0.914646 + 0.146340i
\(217\) 13.1462 + 13.1462i 0.892420 + 0.892420i
\(218\) 4.08768 19.2807i 0.276853 1.30585i
\(219\) −20.9508 −1.41573
\(220\) −12.9643 + 12.6156i −0.874056 + 0.850542i
\(221\) −7.18343 −0.483210
\(222\) 4.22532 19.9299i 0.283585 1.33761i
\(223\) −19.9355 19.9355i −1.33498 1.33498i −0.900848 0.434134i \(-0.857055\pi\)
−0.434134 0.900848i \(-0.642945\pi\)
\(224\) 18.9338 + 5.02017i 1.26507 + 0.335424i
\(225\) −1.32367 + 1.38600i −0.0882448 + 0.0923999i
\(226\) −7.34520 + 4.77550i −0.488595 + 0.317662i
\(227\) −20.7704 + 20.7704i −1.37858 + 1.37858i −0.531552 + 0.847026i \(0.678391\pi\)
−0.847026 + 0.531552i \(0.821609\pi\)
\(228\) 4.34828 + 11.2923i 0.287972 + 0.747850i
\(229\) 17.0966i 1.12977i −0.825168 0.564887i \(-0.808920\pi\)
0.825168 0.564887i \(-0.191080\pi\)
\(230\) 1.72347 + 8.71309i 0.113642 + 0.574524i
\(231\) 25.7630i 1.69508i
\(232\) 8.58911 11.8611i 0.563903 0.778716i
\(233\) −10.6350 + 10.6350i −0.696720 + 0.696720i −0.963702 0.266982i \(-0.913974\pi\)
0.266982 + 0.963702i \(0.413974\pi\)
\(234\) −0.295475 0.454470i −0.0193158 0.0297096i
\(235\) −3.79504 + 1.62333i −0.247561 + 0.105894i
\(236\) 8.38264 + 3.72167i 0.545663 + 0.242260i
\(237\) −1.86607 1.86607i −0.121215 0.121215i
\(238\) 34.4124 + 7.29574i 2.23062 + 0.472913i
\(239\) −10.4291 −0.674601 −0.337301 0.941397i \(-0.609514\pi\)
−0.337301 + 0.941397i \(0.609514\pi\)
\(240\) −6.88021 + 14.9441i −0.444116 + 0.964640i
\(241\) −0.787159 −0.0507054 −0.0253527 0.999679i \(-0.508071\pi\)
−0.0253527 + 0.999679i \(0.508071\pi\)
\(242\) −7.41724 1.57252i −0.476799 0.101086i
\(243\) −2.80016 2.80016i −0.179630 0.179630i
\(244\) 11.7066 + 5.19744i 0.749440 + 0.332732i
\(245\) −4.15143 + 10.3577i −0.265225 + 0.661730i
\(246\) 13.1051 + 20.1569i 0.835549 + 1.28516i
\(247\) 2.32589 2.32589i 0.147993 0.147993i
\(248\) −8.90680 + 12.2998i −0.565582 + 0.781035i
\(249\) 13.6979i 0.868067i
\(250\) −3.42396 15.4362i −0.216550 0.976272i
\(251\) 1.87578i 0.118398i 0.998246 + 0.0591990i \(0.0188546\pi\)
−0.998246 + 0.0591990i \(0.981145\pi\)
\(252\) 0.953904 + 2.47724i 0.0600903 + 0.156052i
\(253\) −8.03343 + 8.03343i −0.505057 + 0.505057i
\(254\) −8.69105 + 5.65051i −0.545325 + 0.354544i
\(255\) −10.9919 + 27.4244i −0.688337 + 1.71739i
\(256\) −1.60575 + 15.9192i −0.100359 + 0.994951i
\(257\) 18.7433 + 18.7433i 1.16917 + 1.16917i 0.982404 + 0.186771i \(0.0598022\pi\)
0.186771 + 0.982404i \(0.440198\pi\)
\(258\) 4.90050 23.1146i 0.305092 1.43905i
\(259\) 27.1196 1.68513
\(260\) 4.47172 + 0.0609692i 0.277324 + 0.00378115i
\(261\) 1.98459 0.122843
\(262\) −1.31832 + 6.21821i −0.0814458 + 0.384162i
\(263\) −17.1908 17.1908i −1.06003 1.06003i −0.998079 0.0619500i \(-0.980268\pi\)
−0.0619500 0.998079i \(-0.519732\pi\)
\(264\) −20.7796 + 3.32465i −1.27889 + 0.204618i
\(265\) 9.67210 4.13724i 0.594153 0.254149i
\(266\) −13.5045 + 8.77998i −0.828013 + 0.538335i
\(267\) 11.6477 11.6477i 0.712825 0.712825i
\(268\) −10.5310 + 4.05515i −0.643285 + 0.247708i
\(269\) 1.97488i 0.120410i −0.998186 0.0602052i \(-0.980825\pi\)
0.998186 0.0602052i \(-0.0191755\pi\)
\(270\) 14.9310 2.95340i 0.908673 0.179738i
\(271\) 7.20848i 0.437884i 0.975738 + 0.218942i \(0.0702605\pi\)
−0.975738 + 0.218942i \(0.929739\pi\)
\(272\) −1.44367 + 28.6974i −0.0875355 + 1.74004i
\(273\) 4.50372 4.50372i 0.272577 0.272577i
\(274\) 3.88805 + 5.98022i 0.234886 + 0.361278i
\(275\) 13.9683 14.6260i 0.842321 0.881982i
\(276\) −4.19273 + 9.44364i −0.252373 + 0.568440i
\(277\) −3.84054 3.84054i −0.230756 0.230756i 0.582252 0.813008i \(-0.302172\pi\)
−0.813008 + 0.582252i \(0.802172\pi\)
\(278\) −10.6082 2.24903i −0.636237 0.134888i
\(279\) −2.05800 −0.123209
\(280\) −21.3600 4.83371i −1.27650 0.288869i
\(281\) −20.4586 −1.22046 −0.610229 0.792225i \(-0.708923\pi\)
−0.610229 + 0.792225i \(0.708923\pi\)
\(282\) −4.69739 0.995889i −0.279725 0.0593043i
\(283\) 6.85477 + 6.85477i 0.407474 + 0.407474i 0.880857 0.473383i \(-0.156967\pi\)
−0.473383 + 0.880857i \(0.656967\pi\)
\(284\) 7.02922 15.8325i 0.417108 0.939487i
\(285\) −5.32063 12.4386i −0.315167 0.736802i
\(286\) 3.11805 + 4.79588i 0.184374 + 0.283586i
\(287\) −22.6306 + 22.6306i −1.33584 + 1.33584i
\(288\) −1.87497 + 1.08907i −0.110483 + 0.0641741i
\(289\) 34.6017i 2.03539i
\(290\) −9.11082 + 13.6038i −0.535006 + 0.798845i
\(291\) 2.26156i 0.132575i
\(292\) 21.2587 8.18603i 1.24407 0.479051i
\(293\) −0.877370 + 0.877370i −0.0512565 + 0.0512565i −0.732270 0.681014i \(-0.761539\pi\)
0.681014 + 0.732270i \(0.261539\pi\)
\(294\) −10.8832 + 7.07576i −0.634723 + 0.412667i
\(295\) −9.51817 3.81493i −0.554169 0.222114i
\(296\) 3.49971 + 21.8738i 0.203417 + 1.27139i
\(297\) 13.7663 + 13.7663i 0.798804 + 0.798804i
\(298\) 1.92211 9.06618i 0.111345 0.525190i
\(299\) 2.80871 0.162432
\(300\) 7.07525 16.9786i 0.408490 0.980258i
\(301\) 31.4531 1.81293
\(302\) 1.29504 6.10843i 0.0745213 0.351501i
\(303\) 8.52077 + 8.52077i 0.489506 + 0.489506i
\(304\) −8.82437 9.75925i −0.506112 0.559731i
\(305\) −13.2924 5.32768i −0.761123 0.305062i
\(306\) −3.26465 + 2.12252i −0.186628 + 0.121337i
\(307\) 20.5875 20.5875i 1.17499 1.17499i 0.193990 0.981004i \(-0.437857\pi\)
0.981004 0.193990i \(-0.0621428\pi\)
\(308\) −10.0663 26.1416i −0.573578 1.48956i
\(309\) 14.4545i 0.822287i
\(310\) 9.44780 14.1070i 0.536599 0.801225i
\(311\) 9.63704i 0.546467i −0.961948 0.273233i \(-0.911907\pi\)
0.961948 0.273233i \(-0.0880931\pi\)
\(312\) 4.21375 + 3.05136i 0.238556 + 0.172749i
\(313\) 8.99972 8.99972i 0.508694 0.508694i −0.405431 0.914126i \(-0.632879\pi\)
0.914126 + 0.405431i \(0.132879\pi\)
\(314\) 5.77283 + 8.87919i 0.325780 + 0.501082i
\(315\) −1.16721 2.72873i −0.0657650 0.153746i
\(316\) 2.62262 + 1.16438i 0.147534 + 0.0655013i
\(317\) −20.0235 20.0235i −1.12463 1.12463i −0.991036 0.133596i \(-0.957348\pi\)
−0.133596 0.991036i \(-0.542652\pi\)
\(318\) 11.9718 + 2.53814i 0.671348 + 0.142332i
\(319\) −20.9428 −1.17257
\(320\) 1.14226 17.8520i 0.0638544 0.997959i
\(321\) 3.45798 0.193005
\(322\) −13.4552 2.85262i −0.749827 0.158970i
\(323\) −16.7079 16.7079i −0.929651 0.929651i
\(324\) 18.2849 + 8.11802i 1.01583 + 0.451001i
\(325\) −4.99868 + 0.114976i −0.277277 + 0.00637772i
\(326\) 15.2202 + 23.4103i 0.842971 + 1.29657i
\(327\) −18.1264 + 18.1264i −1.00239 + 1.00239i
\(328\) −21.1735 15.3327i −1.16911 0.846605i
\(329\) 6.39195i 0.352400i
\(330\) 23.0806 4.56540i 1.27054 0.251317i
\(331\) 5.51957i 0.303383i −0.988428 0.151691i \(-0.951528\pi\)
0.988428 0.151691i \(-0.0484720\pi\)
\(332\) −5.35211 13.8992i −0.293735 0.762816i
\(333\) −2.12275 + 2.12275i −0.116326 + 0.116326i
\(334\) −0.804216 + 0.522863i −0.0440047 + 0.0286098i
\(335\) 11.6001 4.96195i 0.633782 0.271100i
\(336\) −17.0870 18.8972i −0.932172 1.03093i
\(337\) −16.1027 16.1027i −0.877168 0.877168i 0.116073 0.993241i \(-0.462969\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(338\) 0.293307 1.38346i 0.0159538 0.0752505i
\(339\) 11.3950 0.618893
\(340\) 0.437968 32.1223i 0.0237521 1.74208i
\(341\) 21.7174 1.17607
\(342\) 0.369805 1.74429i 0.0199968 0.0943203i
\(343\) 4.92070 + 4.92070i 0.265693 + 0.265693i
\(344\) 4.05894 + 25.3690i 0.218844 + 1.36781i
\(345\) 4.29779 10.7229i 0.231385 0.577301i
\(346\) 13.1686 8.56158i 0.707946 0.460273i
\(347\) 17.6205 17.6205i 0.945919 0.945919i −0.0526918 0.998611i \(-0.516780\pi\)
0.998611 + 0.0526918i \(0.0167801\pi\)
\(348\) −17.7747 + 6.84446i −0.952825 + 0.366901i
\(349\) 2.32443i 0.124424i −0.998063 0.0622120i \(-0.980185\pi\)
0.998063 0.0622120i \(-0.0198155\pi\)
\(350\) 24.0631 + 4.52604i 1.28623 + 0.241927i
\(351\) 4.81308i 0.256903i
\(352\) 19.7859 11.4926i 1.05459 0.612559i
\(353\) 12.1932 12.1932i 0.648976 0.648976i −0.303769 0.952746i \(-0.598245\pi\)
0.952746 + 0.303769i \(0.0982452\pi\)
\(354\) −6.50224 10.0011i −0.345590 0.531552i
\(355\) −7.20537 + 17.9772i −0.382421 + 0.954133i
\(356\) −7.26779 + 16.3699i −0.385192 + 0.867601i
\(357\) −32.3521 32.3521i −1.71226 1.71226i
\(358\) −11.3795 2.41256i −0.601425 0.127508i
\(359\) 27.6037 1.45687 0.728433 0.685117i \(-0.240249\pi\)
0.728433 + 0.685117i \(0.240249\pi\)
\(360\) 2.05028 1.29357i 0.108059 0.0681772i
\(361\) −8.18047 −0.430551
\(362\) −16.7803 3.55757i −0.881952 0.186982i
\(363\) 6.97317 + 6.97317i 0.365997 + 0.365997i
\(364\) −2.81019 + 6.32962i −0.147294 + 0.331762i
\(365\) −23.4169 + 10.0166i −1.22569 + 0.524291i
\(366\) −9.08059 13.9669i −0.474650 0.730060i
\(367\) 7.66039 7.66039i 0.399869 0.399869i −0.478318 0.878187i \(-0.658753\pi\)
0.878187 + 0.478318i \(0.158753\pi\)
\(368\) 0.564473 11.2206i 0.0294252 0.584916i
\(369\) 3.54276i 0.184429i
\(370\) −4.80580 24.2959i −0.249842 1.26308i
\(371\) 16.2906i 0.845768i
\(372\) 18.4322 7.09761i 0.955663 0.367994i
\(373\) −23.0212 + 23.0212i −1.19199 + 1.19199i −0.215488 + 0.976506i \(0.569134\pi\)
−0.976506 + 0.215488i \(0.930866\pi\)
\(374\) 34.4509 22.3983i 1.78141 1.15819i
\(375\) −7.20988 + 19.2596i −0.372316 + 0.994560i
\(376\) 5.15554 0.824866i 0.265877 0.0425392i
\(377\) 3.66109 + 3.66109i 0.188556 + 0.188556i
\(378\) −4.88834 + 23.0572i −0.251429 + 1.18593i
\(379\) −27.4799 −1.41155 −0.705774 0.708437i \(-0.749401\pi\)
−0.705774 + 0.708437i \(0.749401\pi\)
\(380\) 10.2589 + 10.5425i 0.526272 + 0.540821i
\(381\) 13.4829 0.690751
\(382\) −2.22602 + 10.4997i −0.113893 + 0.537209i
\(383\) 2.40431 + 2.40431i 0.122855 + 0.122855i 0.765861 0.643006i \(-0.222313\pi\)
−0.643006 + 0.765861i \(0.722313\pi\)
\(384\) 13.0369 16.2205i 0.665285 0.827747i
\(385\) 12.3172 + 28.7954i 0.627745 + 1.46755i
\(386\) 3.13936 2.04106i 0.159789 0.103887i
\(387\) −2.46195 + 2.46195i −0.125148 + 0.125148i
\(388\) 0.883649 + 2.29480i 0.0448605 + 0.116501i
\(389\) 3.40359i 0.172569i 0.996271 + 0.0862845i \(0.0274994\pi\)
−0.996271 + 0.0862845i \(0.972501\pi\)
\(390\) −4.83289 3.23670i −0.244723 0.163897i
\(391\) 20.1761i 1.02035i
\(392\) 8.27850 11.4321i 0.418127 0.577409i
\(393\) 5.84592 5.84592i 0.294888 0.294888i
\(394\) 1.91314 + 2.94260i 0.0963825 + 0.148246i
\(395\) −2.97789 1.19355i −0.149834 0.0600542i
\(396\) 2.83412 + 1.25828i 0.142420 + 0.0632307i
\(397\) −1.08718 1.08718i −0.0545638 0.0545638i 0.679298 0.733862i \(-0.262284\pi\)
−0.733862 + 0.679298i \(0.762284\pi\)
\(398\) −23.9798 5.08393i −1.20200 0.254834i
\(399\) 20.9503 1.04883
\(400\) −0.545274 + 19.9926i −0.0272637 + 0.999628i
\(401\) 16.5439 0.826162 0.413081 0.910694i \(-0.364453\pi\)
0.413081 + 0.910694i \(0.364453\pi\)
\(402\) 14.3583 + 3.04408i 0.716126 + 0.151825i
\(403\) −3.79650 3.79650i −0.189117 0.189117i
\(404\) −11.9753 5.31671i −0.595792 0.264516i
\(405\) −20.7618 8.32145i −1.03166 0.413496i
\(406\) −13.8202 21.2569i −0.685886 1.05496i
\(407\) 22.4007 22.4007i 1.11036 1.11036i
\(408\) 21.9192 30.2692i 1.08516 1.49855i
\(409\) 1.14078i 0.0564082i −0.999602 0.0282041i \(-0.991021\pi\)
0.999602 0.0282041i \(-0.00897883\pi\)
\(410\) 24.2846 + 16.2640i 1.19933 + 0.803221i
\(411\) 9.27746i 0.457623i
\(412\) −5.64774 14.6669i −0.278244 0.722587i
\(413\) 11.2284 11.2284i 0.552514 0.552514i
\(414\) 1.27647 0.829901i 0.0627351 0.0407874i
\(415\) 6.54893 + 15.3102i 0.321474 + 0.751547i
\(416\) −5.46792 1.44978i −0.268087 0.0710815i
\(417\) 9.97308 + 9.97308i 0.488384 + 0.488384i
\(418\) −3.90244 + 18.4069i −0.190874 + 0.900313i
\(419\) 22.1193 1.08060 0.540300 0.841473i \(-0.318311\pi\)
0.540300 + 0.841473i \(0.318311\pi\)
\(420\) 19.8648 + 20.4140i 0.969302 + 0.996099i
\(421\) −6.48977 −0.316292 −0.158146 0.987416i \(-0.550552\pi\)
−0.158146 + 0.987416i \(0.550552\pi\)
\(422\) −6.95173 + 32.7898i −0.338405 + 1.59618i
\(423\) 0.500322 + 0.500322i 0.0243265 + 0.0243265i
\(424\) −13.1395 + 2.10227i −0.638111 + 0.102095i
\(425\) 0.825922 + 35.9077i 0.0400631 + 1.74178i
\(426\) −18.8893 + 12.2810i −0.915192 + 0.595014i
\(427\) 15.6809 15.6809i 0.758850 0.758850i
\(428\) −3.50880 + 1.35112i −0.169604 + 0.0653089i
\(429\) 7.44013i 0.359213i
\(430\) −5.57373 28.1782i −0.268789 1.35887i
\(431\) 3.21316i 0.154773i −0.997001 0.0773863i \(-0.975343\pi\)
0.997001 0.0773863i \(-0.0246575\pi\)
\(432\) −19.2280 0.967298i −0.925109 0.0465392i
\(433\) −8.29376 + 8.29376i −0.398573 + 0.398573i −0.877729 0.479157i \(-0.840943\pi\)
0.479157 + 0.877729i \(0.340943\pi\)
\(434\) 14.3314 + 22.0431i 0.687929 + 1.05810i
\(435\) 19.5792 8.37499i 0.938749 0.401550i
\(436\) 11.3103 25.4752i 0.541666 1.22004i
\(437\) 6.53274 + 6.53274i 0.312503 + 0.312503i
\(438\) −28.9847 6.14502i −1.38494 0.293621i
\(439\) 2.29089 0.109338 0.0546690 0.998505i \(-0.482590\pi\)
0.0546690 + 0.998505i \(0.482590\pi\)
\(440\) −21.6359 + 13.6507i −1.03145 + 0.650770i
\(441\) 1.91282 0.0910869
\(442\) −9.93801 2.10695i −0.472703 0.100217i
\(443\) 18.0983 + 18.0983i 0.859874 + 0.859874i 0.991323 0.131449i \(-0.0419630\pi\)
−0.131449 + 0.991323i \(0.541963\pi\)
\(444\) 11.6912 26.3330i 0.554838 1.24971i
\(445\) 7.44992 18.5874i 0.353160 0.881126i
\(446\) −21.7329 33.4273i −1.02908 1.58283i
\(447\) −8.52339 + 8.52339i −0.403143 + 0.403143i
\(448\) 24.7217 + 12.4986i 1.16799 + 0.590505i
\(449\) 28.9770i 1.36751i −0.729712 0.683755i \(-0.760346\pi\)
0.729712 0.683755i \(-0.239654\pi\)
\(450\) −2.23778 + 1.52924i −0.105490 + 0.0720889i
\(451\) 37.3856i 1.76042i
\(452\) −11.5625 + 4.45233i −0.543854 + 0.209420i
\(453\) −5.74272 + 5.74272i −0.269816 + 0.269816i
\(454\) −34.8271 + 22.6430i −1.63452 + 1.06269i
\(455\) 2.88061 7.18705i 0.135045 0.336934i
\(456\) 2.70359 + 16.8978i 0.126607 + 0.791314i
\(457\) −18.3539 18.3539i −0.858557 0.858557i 0.132611 0.991168i \(-0.457664\pi\)
−0.991168 + 0.132611i \(0.957664\pi\)
\(458\) 5.01454 23.6525i 0.234314 1.10521i
\(459\) −34.5745 −1.61380
\(460\) −0.171244 + 12.5597i −0.00798431 + 0.585601i
\(461\) 23.9354 1.11478 0.557392 0.830249i \(-0.311802\pi\)
0.557392 + 0.830249i \(0.311802\pi\)
\(462\) −7.55645 + 35.6421i −0.351558 + 1.65822i
\(463\) 2.34220 + 2.34220i 0.108851 + 0.108851i 0.759435 0.650583i \(-0.225476\pi\)
−0.650583 + 0.759435i \(0.725476\pi\)
\(464\) 15.3616 13.8901i 0.713146 0.644831i
\(465\) −20.3033 + 8.68476i −0.941545 + 0.402746i
\(466\) −17.8324 + 11.5938i −0.826070 + 0.537072i
\(467\) 21.3761 21.3761i 0.989168 0.989168i −0.0107738 0.999942i \(-0.503429\pi\)
0.999942 + 0.0107738i \(0.00342948\pi\)
\(468\) −0.275479 0.715407i −0.0127340 0.0330697i
\(469\) 19.5380i 0.902179i
\(470\) −5.72643 + 1.13270i −0.264140 + 0.0522478i
\(471\) 13.7748i 0.634710i
\(472\) 10.5055 + 7.60748i 0.483554 + 0.350163i
\(473\) 25.9802 25.9802i 1.19457 1.19457i
\(474\) −2.03431 3.12898i −0.0934391 0.143719i
\(475\) −11.8938 11.3590i −0.545725 0.521185i
\(476\) 45.4684 + 20.1868i 2.08404 + 0.925260i
\(477\) −1.27513 1.27513i −0.0583842 0.0583842i
\(478\) −14.4283 3.05892i −0.659933 0.139912i
\(479\) −31.6109 −1.44434 −0.722169 0.691716i \(-0.756855\pi\)
−0.722169 + 0.691716i \(0.756855\pi\)
\(480\) −13.9017 + 18.6567i −0.634524 + 0.851556i
\(481\) −7.83190 −0.357104
\(482\) −1.08901 0.230879i −0.0496028 0.0105163i
\(483\) 12.6496 + 12.6496i 0.575577 + 0.575577i
\(484\) −9.80025 4.35106i −0.445466 0.197775i
\(485\) −1.08125 2.52776i −0.0490970 0.114780i
\(486\) −3.05261 4.69522i −0.138469 0.212980i
\(487\) 16.0980 16.0980i 0.729470 0.729470i −0.241044 0.970514i \(-0.577490\pi\)
0.970514 + 0.241044i \(0.0774898\pi\)
\(488\) 14.6713 + 10.6241i 0.664137 + 0.480931i
\(489\) 36.3177i 1.64234i
\(490\) −8.78134 + 13.1119i −0.396700 + 0.592334i
\(491\) 4.44534i 0.200615i 0.994956 + 0.100308i \(0.0319827\pi\)
−0.994956 + 0.100308i \(0.968017\pi\)
\(492\) 12.2182 + 31.7302i 0.550841 + 1.43051i
\(493\) 26.2992 26.2992i 1.18446 1.18446i
\(494\) 3.89998 2.53558i 0.175469 0.114081i
\(495\) −3.21804 1.28981i −0.144640 0.0579725i
\(496\) −15.9298 + 14.4038i −0.715270 + 0.646752i
\(497\) −21.2074 21.2074i −0.951283 0.951283i
\(498\) −4.01768 + 18.9505i −0.180036 + 0.849192i
\(499\) 1.10569 0.0494976 0.0247488 0.999694i \(-0.492121\pi\)
0.0247488 + 0.999694i \(0.492121\pi\)
\(500\) −0.209375 22.3597i −0.00936354 0.999956i
\(501\) 1.24763 0.0557399
\(502\) −0.550178 + 2.59507i −0.0245556 + 0.115824i
\(503\) 11.9973 + 11.9973i 0.534933 + 0.534933i 0.922036 0.387104i \(-0.126524\pi\)
−0.387104 + 0.922036i \(0.626524\pi\)
\(504\) 0.593099 + 3.70696i 0.0264187 + 0.165121i
\(505\) 13.5975 + 5.44994i 0.605080 + 0.242519i
\(506\) −13.4702 + 8.75769i −0.598824 + 0.389327i
\(507\) −1.30064 + 1.30064i −0.0577633 + 0.0577633i
\(508\) −13.6811 + 5.26813i −0.607000 + 0.233735i
\(509\) 0.850066i 0.0376785i −0.999823 0.0188393i \(-0.994003\pi\)
0.999823 0.0188393i \(-0.00599708\pi\)
\(510\) −23.2506 + 34.7167i −1.02955 + 1.53728i
\(511\) 39.4408i 1.74476i
\(512\) −6.89071 + 21.5527i −0.304529 + 0.952503i
\(513\) 11.1947 11.1947i 0.494258 0.494258i
\(514\) 20.4331 + 31.4282i 0.901266 + 1.38624i
\(515\) 6.91067 + 16.1559i 0.304520 + 0.711912i
\(516\) 13.5593 30.5408i 0.596916 1.34449i
\(517\) −5.27974 5.27974i −0.232203 0.232203i
\(518\) 37.5189 + 7.95435i 1.64849 + 0.349494i
\(519\) −20.4292 −0.896740
\(520\) 6.16858 + 1.39593i 0.270510 + 0.0612158i
\(521\) 31.9059 1.39782 0.698910 0.715209i \(-0.253669\pi\)
0.698910 + 0.715209i \(0.253669\pi\)
\(522\) 2.74561 + 0.582095i 0.120172 + 0.0254776i
\(523\) −19.7168 19.7168i −0.862155 0.862155i 0.129433 0.991588i \(-0.458684\pi\)
−0.991588 + 0.129433i \(0.958684\pi\)
\(524\) −3.64768 + 8.21599i −0.159350 + 0.358917i
\(525\) −23.0305 21.9948i −1.00513 0.959932i
\(526\) −18.7406 28.8250i −0.817131 1.25683i
\(527\) −27.2719 + 27.2719i −1.18798 + 1.18798i
\(528\) −29.7229 1.49526i −1.29352 0.0650729i
\(529\) 15.1112i 0.657008i
\(530\) 14.5945 2.88683i 0.633944 0.125396i
\(531\) 1.75778i 0.0762811i
\(532\) −21.2582 + 8.18582i −0.921660 + 0.354900i
\(533\) 6.53552 6.53552i 0.283085 0.283085i
\(534\) 19.5304 12.6978i 0.845165 0.549486i
\(535\) 3.86500 1.65325i 0.167098 0.0714764i
\(536\) −15.7587 + 2.52133i −0.680672 + 0.108905i
\(537\) 10.6982 + 10.6982i 0.461662 + 0.461662i
\(538\) 0.579244 2.73217i 0.0249730 0.117792i
\(539\) −20.1854 −0.869449
\(540\) 21.5228 + 0.293450i 0.926193 + 0.0126281i
\(541\) 23.7553 1.02132 0.510659 0.859783i \(-0.329401\pi\)
0.510659 + 0.859783i \(0.329401\pi\)
\(542\) −2.11430 + 9.97267i −0.0908168 + 0.428363i
\(543\) 15.7757 + 15.7757i 0.676998 + 0.676998i
\(544\) −10.4144 + 39.2784i −0.446515 + 1.68405i
\(545\) −11.5937 + 28.9261i −0.496622 + 1.23906i
\(546\) 7.55170 4.90976i 0.323183 0.210118i
\(547\) −25.4126 + 25.4126i −1.08657 + 1.08657i −0.0906855 + 0.995880i \(0.528906\pi\)
−0.995880 + 0.0906855i \(0.971094\pi\)
\(548\) 3.62494 + 9.41381i 0.154850 + 0.402138i
\(549\) 2.45480i 0.104768i
\(550\) 23.6146 16.1376i 1.00693 0.688108i
\(551\) 17.0306i 0.725527i
\(552\) −8.57037 + 11.8352i −0.364779 + 0.503738i
\(553\) 3.51297 3.51297i 0.149386 0.149386i
\(554\) −4.18679 6.43971i −0.177880 0.273597i
\(555\) −11.9841 + 29.9001i −0.508698 + 1.26919i
\(556\) −14.0164 6.22291i −0.594427 0.263910i
\(557\) 4.98781 + 4.98781i 0.211340 + 0.211340i 0.804837 0.593496i \(-0.202253\pi\)
−0.593496 + 0.804837i \(0.702253\pi\)
\(558\) −2.84717 0.603625i −0.120530 0.0255535i
\(559\) −9.08338 −0.384186
\(560\) −28.1330 12.9523i −1.18884 0.547334i
\(561\) −53.4456 −2.25648
\(562\) −28.3037 6.00065i −1.19392 0.253122i
\(563\) 16.6885 + 16.6885i 0.703337 + 0.703337i 0.965125 0.261788i \(-0.0843122\pi\)
−0.261788 + 0.965125i \(0.584312\pi\)
\(564\) −6.20656 2.75555i −0.261343 0.116030i
\(565\) 12.7363 5.44795i 0.535820 0.229197i
\(566\) 7.47277 + 11.4939i 0.314104 + 0.483124i
\(567\) 24.4924 24.4924i 1.02858 1.02858i
\(568\) 14.3685 19.8420i 0.602887 0.832552i
\(569\) 30.7533i 1.28925i −0.764501 0.644623i \(-0.777014\pi\)
0.764501 0.644623i \(-0.222986\pi\)
\(570\) −3.71256 18.7690i −0.155502 0.786146i
\(571\) 30.5271i 1.27752i 0.769407 + 0.638759i \(0.220552\pi\)
−0.769407 + 0.638759i \(0.779448\pi\)
\(572\) 2.90705 + 7.54947i 0.121550 + 0.315659i
\(573\) 9.87104 9.87104i 0.412369 0.412369i
\(574\) −37.9463 + 24.6709i −1.58385 + 1.02974i
\(575\) −0.322934 14.0398i −0.0134673 0.585501i
\(576\) −2.91338 + 0.956749i −0.121391 + 0.0398645i
\(577\) 9.01226 + 9.01226i 0.375185 + 0.375185i 0.869362 0.494176i \(-0.164530\pi\)
−0.494176 + 0.869362i \(0.664530\pi\)
\(578\) −10.1489 + 47.8701i −0.422139 + 1.99114i
\(579\) −4.87027 −0.202401
\(580\) −16.5946 + 16.1482i −0.689053 + 0.670516i
\(581\) −25.7868 −1.06982
\(582\) 0.663331 3.12878i 0.0274959 0.129692i
\(583\) 13.4560 + 13.4560i 0.557292 + 0.557292i
\(584\) 31.8117 5.08974i 1.31638 0.210615i
\(585\) 0.337081 + 0.788033i 0.0139366 + 0.0325812i
\(586\) −1.47115 + 0.956470i −0.0607725 + 0.0395114i
\(587\) −10.4686 + 10.4686i −0.432086 + 0.432086i −0.889337 0.457252i \(-0.848834\pi\)
0.457252 + 0.889337i \(0.348834\pi\)
\(588\) −17.1319 + 6.59693i −0.706509 + 0.272053i
\(589\) 17.6605i 0.727688i
\(590\) −12.0491 8.06956i −0.496053 0.332219i
\(591\) 4.56502i 0.187780i
\(592\) −1.57400 + 31.2880i −0.0646909 + 1.28593i
\(593\) −25.3945 + 25.3945i −1.04283 + 1.04283i −0.0437878 + 0.999041i \(0.513943\pi\)
−0.999041 + 0.0437878i \(0.986057\pi\)
\(594\) 15.0075 + 23.0830i 0.615763 + 0.947106i
\(595\) −51.6277 20.6927i −2.11653 0.848316i
\(596\) 5.31835 11.9790i 0.217848 0.490677i
\(597\) 22.5441 + 22.5441i 0.922669 + 0.922669i
\(598\) 3.88574 + 0.823812i 0.158900 + 0.0336882i
\(599\) 19.7377 0.806462 0.403231 0.915098i \(-0.367887\pi\)
0.403231 + 0.915098i \(0.367887\pi\)
\(600\) 14.7683 21.4140i 0.602913 0.874223i
\(601\) −13.2207 −0.539282 −0.269641 0.962961i \(-0.586905\pi\)
−0.269641 + 0.962961i \(0.586905\pi\)
\(602\) 43.5142 + 9.22540i 1.77351 + 0.375999i
\(603\) −1.52931 1.52931i −0.0622783 0.0622783i
\(604\) 3.58329 8.07094i 0.145802 0.328402i
\(605\) 11.1278 + 4.46009i 0.452410 + 0.181328i
\(606\) 9.28898 + 14.2874i 0.377339 + 0.580385i
\(607\) 13.8113 13.8113i 0.560582 0.560582i −0.368890 0.929473i \(-0.620262\pi\)
0.929473 + 0.368890i \(0.120262\pi\)
\(608\) −9.34574 16.0898i −0.379020 0.652528i
\(609\) 32.9770i 1.33630i
\(610\) −16.8270 11.2694i −0.681304 0.456285i
\(611\) 1.84594i 0.0746788i
\(612\) −5.13908 + 1.97889i −0.207735 + 0.0799918i
\(613\) 3.80362 3.80362i 0.153627 0.153627i −0.626109 0.779736i \(-0.715354\pi\)
0.779736 + 0.626109i \(0.215354\pi\)
\(614\) 34.5206 22.4436i 1.39314 0.905752i
\(615\) −14.9504 34.9513i −0.602860 1.40937i
\(616\) −6.25879 39.1184i −0.252174 1.57613i
\(617\) −6.05214 6.05214i −0.243650 0.243650i 0.574708 0.818358i \(-0.305115\pi\)
−0.818358 + 0.574708i \(0.805115\pi\)
\(618\) −4.23960 + 19.9972i −0.170542 + 0.804407i
\(619\) 26.1152 1.04966 0.524829 0.851207i \(-0.324129\pi\)
0.524829 + 0.851207i \(0.324129\pi\)
\(620\) 17.2084 16.7454i 0.691105 0.672513i
\(621\) 13.5185 0.542480
\(622\) 2.82661 13.3325i 0.113337 0.534584i
\(623\) 21.9272 + 21.9272i 0.878495 + 0.878495i
\(624\) 4.93458 + 5.45736i 0.197541 + 0.218469i
\(625\) 1.14946 + 24.9736i 0.0459782 + 0.998942i
\(626\) 15.0905 9.81110i 0.603136 0.392131i
\(627\) 17.3049 17.3049i 0.691092 0.691092i
\(628\) 5.38217 + 13.9772i 0.214772 + 0.557753i
\(629\) 56.2599i 2.24323i
\(630\) −0.814442 4.11744i −0.0324482 0.164043i
\(631\) 30.5634i 1.21671i 0.793665 + 0.608355i \(0.208170\pi\)
−0.793665 + 0.608355i \(0.791830\pi\)
\(632\) 3.28678 + 2.38010i 0.130741 + 0.0946755i
\(633\) 30.8266 30.8266i 1.22525 1.22525i
\(634\) −21.8288 33.5748i −0.866930 1.33343i
\(635\) 15.0699 6.44617i 0.598032 0.255808i
\(636\) 15.8182 + 7.02285i 0.627231 + 0.278474i
\(637\) 3.52869 + 3.52869i 0.139812 + 0.139812i
\(638\) −28.9736 6.14267i −1.14708 0.243191i
\(639\) 3.31997 0.131336
\(640\) 6.81640 24.3626i 0.269442 0.963017i
\(641\) −31.0791 −1.22755 −0.613775 0.789481i \(-0.710350\pi\)
−0.613775 + 0.789481i \(0.710350\pi\)
\(642\) 4.78398 + 1.01425i 0.188809 + 0.0400292i
\(643\) −24.4247 24.4247i −0.963214 0.963214i 0.0361326 0.999347i \(-0.488496\pi\)
−0.999347 + 0.0361326i \(0.988496\pi\)
\(644\) −17.7780 7.89299i −0.700553 0.311027i
\(645\) −13.8991 + 34.6780i −0.547277 + 1.36544i
\(646\) −18.2142 28.0153i −0.716628 1.10225i
\(647\) 11.3024 11.3024i 0.444343 0.444343i −0.449126 0.893469i \(-0.648264\pi\)
0.893469 + 0.449126i \(0.148264\pi\)
\(648\) 22.9154 + 16.5941i 0.900203 + 0.651876i
\(649\) 18.5493i 0.728124i
\(650\) −6.94921 1.30708i −0.272570 0.0512679i
\(651\) 34.1968i 1.34028i
\(652\) 14.1903 + 36.8514i 0.555733 + 1.44321i
\(653\) −32.6706 + 32.6706i −1.27850 + 1.27850i −0.336991 + 0.941508i \(0.609409\pi\)
−0.941508 + 0.336991i \(0.890591\pi\)
\(654\) −30.3937 + 19.7606i −1.18849 + 0.772700i
\(655\) 3.73909 9.32895i 0.146098 0.364512i
\(656\) −24.7956 27.4225i −0.968105 1.07067i
\(657\) 3.08718 + 3.08718i 0.120442 + 0.120442i
\(658\) 1.87480 8.84303i 0.0730874 0.344737i
\(659\) −23.7796 −0.926321 −0.463161 0.886274i \(-0.653285\pi\)
−0.463161 + 0.886274i \(0.653285\pi\)
\(660\) 33.2702 + 0.453618i 1.29504 + 0.0176571i
\(661\) 40.2359 1.56499 0.782497 0.622654i \(-0.213946\pi\)
0.782497 + 0.622654i \(0.213946\pi\)
\(662\) 1.61893 7.63612i 0.0629213 0.296786i
\(663\) 9.34303 + 9.34303i 0.362853 + 0.362853i
\(664\) −3.32773 20.7988i −0.129141 0.807150i
\(665\) 23.4163 10.0163i 0.908044 0.388416i
\(666\) −3.55936 + 2.31413i −0.137922 + 0.0896706i
\(667\) −10.2829 + 10.2829i −0.398156 + 0.398156i
\(668\) −1.26596 + 0.487480i −0.0489816 + 0.0188612i
\(669\) 51.8577i 2.00494i
\(670\) 17.5037 3.46228i 0.676227 0.133760i
\(671\) 25.9047i 1.00004i
\(672\) −18.0965 31.1554i −0.698089 1.20184i
\(673\) −22.3504 + 22.3504i −0.861545 + 0.861545i −0.991518 0.129973i \(-0.958511\pi\)
0.129973 + 0.991518i \(0.458511\pi\)
\(674\) −17.5544 27.0005i −0.676171 1.04002i
\(675\) −24.0591 + 0.553389i −0.926034 + 0.0213000i
\(676\) 0.811558 1.82794i 0.0312138 0.0703055i
\(677\) −21.3069 21.3069i −0.818891 0.818891i 0.167056 0.985947i \(-0.446574\pi\)
−0.985947 + 0.167056i \(0.946574\pi\)
\(678\) 15.7646 + 3.34224i 0.605436 + 0.128358i
\(679\) 4.25748 0.163387
\(680\) 10.0276 44.3116i 0.384541 1.69927i
\(681\) 54.0294 2.07041
\(682\) 30.0453 + 6.36987i 1.15049 + 0.243915i
\(683\) 22.2168 + 22.2168i 0.850101 + 0.850101i 0.990145 0.140044i \(-0.0447245\pi\)
−0.140044 + 0.990145i \(0.544725\pi\)
\(684\) 1.02322 2.30469i 0.0391239 0.0881221i
\(685\) −4.43554 10.3695i −0.169473 0.396197i
\(686\) 5.36433 + 8.25088i 0.204811 + 0.315020i
\(687\) −22.2364 + 22.2364i −0.848372 + 0.848372i
\(688\) −1.82551 + 36.2877i −0.0695970 + 1.38345i
\(689\) 4.70460i 0.179231i
\(690\) 9.09094 13.5742i 0.346086 0.516760i
\(691\) 29.8285i 1.13473i −0.823467 0.567364i \(-0.807963\pi\)
0.823467 0.567364i \(-0.192037\pi\)
\(692\) 20.7294 7.98220i 0.788013 0.303438i
\(693\) 3.79627 3.79627i 0.144208 0.144208i
\(694\) 29.5456 19.2091i 1.12153 0.729168i
\(695\) 15.9151 + 6.37885i 0.603693 + 0.241964i
\(696\) −26.5982 + 4.25561i −1.00820 + 0.161308i
\(697\) −46.9474 46.9474i −1.77826 1.77826i
\(698\) 0.681771 3.21577i 0.0258054 0.121719i
\(699\) 27.6644 1.04637
\(700\) 31.9629 + 13.3195i 1.20808 + 0.503429i
\(701\) −11.6474 −0.439915 −0.219958 0.975509i \(-0.570592\pi\)
−0.219958 + 0.975509i \(0.570592\pi\)
\(702\) 1.41171 6.65873i 0.0532816 0.251317i
\(703\) −18.2161 18.2161i −0.687035 0.687035i
\(704\) 30.7440 10.0963i 1.15871 0.380518i
\(705\) 7.04732 + 2.82460i 0.265417 + 0.106381i
\(706\) 20.4451 13.2925i 0.769463 0.500268i
\(707\) −16.0407 + 16.0407i −0.603273 + 0.603273i
\(708\) −6.06222 15.7433i −0.227832 0.591669i
\(709\) 1.13943i 0.0427923i 0.999771 + 0.0213962i \(0.00681113\pi\)
−0.999771 + 0.0213962i \(0.993189\pi\)
\(710\) −15.2412 + 22.7575i −0.571993 + 0.854072i
\(711\) 0.549946i 0.0206246i
\(712\) −14.8561 + 20.5154i −0.556757 + 0.768848i
\(713\) 10.6633 10.6633i 0.399342 0.399342i
\(714\) −35.2689 54.2471i −1.31991 2.03015i
\(715\) −3.55712 8.31587i −0.133029 0.310996i
\(716\) −15.0355 6.67537i −0.561903 0.249470i
\(717\) 13.5644 + 13.5644i 0.506573 + 0.506573i
\(718\) 38.1887 + 8.09634i 1.42519 + 0.302153i
\(719\) −0.753679 −0.0281075 −0.0140537 0.999901i \(-0.504474\pi\)
−0.0140537 + 0.999901i \(0.504474\pi\)
\(720\) 3.21590 1.18825i 0.119849 0.0442834i
\(721\) −27.2112 −1.01340
\(722\) −11.3174 2.39939i −0.421189 0.0892960i
\(723\) 1.02381 + 1.02381i 0.0380758 + 0.0380758i
\(724\) −22.1714 9.84354i −0.823995 0.365832i
\(725\) 17.8797 18.7215i 0.664034 0.695301i
\(726\) 7.60185 + 11.6924i 0.282131 + 0.433946i
\(727\) −30.7685 + 30.7685i −1.14114 + 1.14114i −0.152898 + 0.988242i \(0.548861\pi\)
−0.988242 + 0.152898i \(0.951139\pi\)
\(728\) −5.74431 + 7.93256i −0.212898 + 0.294000i
\(729\) 22.7250i 0.841667i
\(730\) −35.3343 + 6.98923i −1.30778 + 0.258683i
\(731\) 65.2499i 2.41335i
\(732\) −8.46609 21.9860i −0.312916 0.812628i
\(733\) −32.7186 + 32.7186i −1.20849 + 1.20849i −0.236971 + 0.971517i \(0.576155\pi\)
−0.971517 + 0.236971i \(0.923845\pi\)
\(734\) 12.8447 8.35102i 0.474107 0.308242i
\(735\) 18.8711 8.07212i 0.696072 0.297745i
\(736\) 4.07201 15.3578i 0.150096 0.566095i
\(737\) 16.1383 + 16.1383i 0.594463 + 0.594463i
\(738\) 1.03911 4.90128i 0.0382503 0.180418i
\(739\) 23.2546 0.855435 0.427718 0.903912i \(-0.359318\pi\)
0.427718 + 0.903912i \(0.359318\pi\)
\(740\) 0.477504 35.0221i 0.0175534 1.28744i
\(741\) −6.05027 −0.222262
\(742\) −4.77816 + 22.5375i −0.175412 + 0.827378i
\(743\) 17.0992 + 17.0992i 0.627310 + 0.627310i 0.947391 0.320080i \(-0.103710\pi\)
−0.320080 + 0.947391i \(0.603710\pi\)
\(744\) 27.5820 4.41301i 1.01121 0.161789i
\(745\) −5.45162 + 13.6017i −0.199732 + 0.498326i
\(746\) −38.6013 + 25.0968i −1.41330 + 0.918858i
\(747\) 2.01843 2.01843i 0.0738505 0.0738505i
\(748\) 54.2311 20.8826i 1.98289 0.763543i
\(749\) 6.50979i 0.237862i
\(750\) −15.6236 + 24.5302i −0.570492 + 0.895716i
\(751\) 30.0382i 1.09611i −0.836443 0.548054i \(-0.815369\pi\)
0.836443 0.548054i \(-0.184631\pi\)
\(752\) 7.37444 + 0.370984i 0.268918 + 0.0135284i
\(753\) 2.43970 2.43970i 0.0889077 0.0889077i
\(754\) 3.99116 + 6.13881i 0.145350 + 0.223562i
\(755\) −3.67308 + 9.16425i −0.133677 + 0.333521i
\(756\) −13.5257 + 30.4650i −0.491924 + 1.10800i
\(757\) −9.63522 9.63522i −0.350198 0.350198i 0.509985 0.860183i \(-0.329651\pi\)
−0.860183 + 0.509985i \(0.829651\pi\)
\(758\) −38.0175 8.06005i −1.38086 0.292754i
\(759\) 20.8971 0.758518
\(760\) 11.1006 + 17.5942i 0.402663 + 0.638210i
\(761\) −24.2327 −0.878435 −0.439218 0.898381i \(-0.644744\pi\)
−0.439218 + 0.898381i \(0.644744\pi\)
\(762\) 18.6531 + 3.95463i 0.675732 + 0.143261i
\(763\) −34.1236 34.1236i −1.23536 1.23536i
\(764\) −6.15924 + 13.8730i −0.222833 + 0.501907i
\(765\) 5.66078 2.42140i 0.204666 0.0875459i
\(766\) 2.62107 + 4.03148i 0.0947033 + 0.145663i
\(767\) −3.24267 + 3.24267i −0.117086 + 0.117086i
\(768\) 22.7936 18.6166i 0.822493 0.671769i
\(769\) 5.49796i 0.198261i −0.995074 0.0991307i \(-0.968394\pi\)
0.995074 0.0991307i \(-0.0316062\pi\)
\(770\) 8.59456 + 43.4501i 0.309726 + 1.56583i
\(771\) 48.7564i 1.75592i
\(772\) 4.94184 1.90294i 0.177861 0.0684883i
\(773\) 10.0820 10.0820i 0.362625 0.362625i −0.502153 0.864779i \(-0.667459\pi\)
0.864779 + 0.502153i \(0.167459\pi\)
\(774\) −4.12812 + 2.68391i −0.148382 + 0.0964712i
\(775\) −18.5410 + 19.4140i −0.666012 + 0.697372i
\(776\) 0.549417 + 3.43395i 0.0197229 + 0.123271i
\(777\) −35.2727 35.2727i −1.26540 1.26540i
\(778\) −0.998297 + 4.70875i −0.0357907 + 0.168817i
\(779\) 30.4018 1.08926
\(780\) −5.73678 5.89538i −0.205410 0.211088i
\(781\) −35.0346 −1.25364
\(782\) 5.91780 27.9129i 0.211620 0.998165i
\(783\) 17.6211 + 17.6211i 0.629728 + 0.629728i
\(784\) 14.8061 13.3878i 0.528790 0.478135i
\(785\) −6.58572 15.3962i −0.235054 0.549513i
\(786\) 9.80227 6.37297i 0.349635 0.227316i
\(787\) 12.8322 12.8322i 0.457420 0.457420i −0.440388 0.897808i \(-0.645159\pi\)
0.897808 + 0.440388i \(0.145159\pi\)
\(788\) 1.78367 + 4.63211i 0.0635407 + 0.165012i
\(789\) 44.7179i 1.59200i
\(790\) −3.76972 2.52467i −0.134121 0.0898239i
\(791\) 21.4516i 0.762733i
\(792\) 3.55184 + 2.57205i 0.126209 + 0.0913937i
\(793\) −4.52850 + 4.52850i −0.160812 + 0.160812i
\(794\) −1.18519 1.82294i −0.0420609 0.0646939i
\(795\) −17.9609 7.19884i −0.637008 0.255316i
\(796\) −31.6840 14.0669i −1.12301 0.498587i
\(797\) 30.4077 + 30.4077i 1.07709 + 1.07709i 0.996769 + 0.0803258i \(0.0255961\pi\)
0.0803258 + 0.996769i \(0.474404\pi\)
\(798\) 28.9840 + 6.14487i 1.02602 + 0.217526i
\(799\) 13.2602 0.469112
\(800\) −6.61832 + 27.4991i −0.233993 + 0.972238i
\(801\) −3.43265 −0.121287
\(802\) 22.8878 + 4.85243i 0.808198 + 0.171345i
\(803\) −32.5781 32.5781i −1.14966 1.14966i
\(804\) 18.9713 + 8.42276i 0.669066 + 0.297048i
\(805\) 20.1863 + 8.09078i 0.711474 + 0.285163i
\(806\) −4.13878 6.36586i −0.145782 0.224228i
\(807\) −2.56859 + 2.56859i −0.0904188 + 0.0904188i
\(808\) −15.0079 10.8679i −0.527977 0.382332i
\(809\) 13.2474i 0.465752i 0.972506 + 0.232876i \(0.0748137\pi\)
−0.972506 + 0.232876i \(0.925186\pi\)
\(810\) −26.2825 17.6020i −0.923472 0.618471i
\(811\) 4.19848i 0.147428i 0.997279 + 0.0737142i \(0.0234853\pi\)
−0.997279 + 0.0737142i \(0.976515\pi\)
\(812\) −12.8850 33.4617i −0.452174 1.17427i
\(813\) 9.37561 9.37561i 0.328817 0.328817i
\(814\) 37.5608 24.4203i 1.31651 0.855930i
\(815\) −17.3634 40.5925i −0.608215 1.42189i
\(816\) 39.2026 35.4472i 1.37237 1.24090i
\(817\) −21.1270 21.1270i −0.739139 0.739139i
\(818\) 0.334600 1.57823i 0.0116990 0.0551816i
\(819\) −1.32728 −0.0463788
\(820\) 28.8265 + 29.6235i 1.00667 + 1.03450i
\(821\) 34.5644 1.20631 0.603153 0.797626i \(-0.293911\pi\)
0.603153 + 0.797626i \(0.293911\pi\)
\(822\) 2.72114 12.8350i 0.0949107 0.447673i
\(823\) 33.9394 + 33.9394i 1.18305 + 1.18305i 0.978949 + 0.204106i \(0.0654287\pi\)
0.204106 + 0.978949i \(0.434571\pi\)
\(824\) −3.51154 21.9477i −0.122330 0.764583i
\(825\) −37.1908 + 0.855436i −1.29482 + 0.0297825i
\(826\) 18.8275 12.2407i 0.655092 0.425910i
\(827\) −33.9719 + 33.9719i −1.18132 + 1.18132i −0.201915 + 0.979403i \(0.564717\pi\)
−0.979403 + 0.201915i \(0.935283\pi\)
\(828\) 2.00937 0.773740i 0.0698303 0.0268893i
\(829\) 17.7964i 0.618093i 0.951047 + 0.309047i \(0.100010\pi\)
−0.951047 + 0.309047i \(0.899990\pi\)
\(830\) 4.56963 + 23.1019i 0.158614 + 0.801880i
\(831\) 9.99030i 0.346560i
\(832\) −7.13943 3.60950i −0.247515 0.125137i
\(833\) 25.3481 25.3481i 0.878260 0.878260i
\(834\) 10.8722 + 16.7226i 0.376474 + 0.579055i
\(835\) 1.39448 0.596489i 0.0482580 0.0206424i
\(836\) −10.7978 + 24.3207i −0.373448 + 0.841149i
\(837\) −18.2729 18.2729i −0.631604 0.631604i
\(838\) 30.6013 + 6.48775i 1.05710 + 0.224115i
\(839\) −53.3406 −1.84152 −0.920762 0.390126i \(-0.872431\pi\)
−0.920762 + 0.390126i \(0.872431\pi\)
\(840\) 21.4946 + 34.0684i 0.741636 + 1.17547i
\(841\) 2.19283 0.0756149
\(842\) −8.97836 1.90349i −0.309415 0.0655987i
\(843\) 26.6092 + 26.6092i 0.916470 + 0.916470i
\(844\) −19.2349 + 43.3244i −0.662093 + 1.49129i
\(845\) −0.831896 + 2.07556i −0.0286181 + 0.0714014i
\(846\) 0.545429 + 0.838925i 0.0187522 + 0.0288428i
\(847\) −13.1273 + 13.1273i −0.451059 + 0.451059i
\(848\) −18.7946 0.945496i −0.645410 0.0324685i
\(849\) 17.8311i 0.611962i
\(850\) −9.38933 + 49.9192i −0.322051 + 1.71221i
\(851\) 21.9975i 0.754064i
\(852\) −29.7348 + 11.4499i −1.01870 + 0.392266i
\(853\) 24.9385 24.9385i 0.853877 0.853877i −0.136731 0.990608i \(-0.543660\pi\)
0.990608 + 0.136731i \(0.0436595\pi\)
\(854\) 26.2932 17.0946i 0.899735 0.584965i
\(855\) −1.04886 + 2.61689i −0.0358704 + 0.0894958i
\(856\) −5.25058 + 0.840072i −0.179461 + 0.0287131i
\(857\) 34.0706 + 34.0706i 1.16383 + 1.16383i 0.983630 + 0.180201i \(0.0576747\pi\)
0.180201 + 0.983630i \(0.442325\pi\)
\(858\) 2.18224 10.2931i 0.0745004 0.351402i
\(859\) −18.3484 −0.626039 −0.313019 0.949747i \(-0.601340\pi\)
−0.313019 + 0.949747i \(0.601340\pi\)
\(860\) 0.553807 40.6184i 0.0188846 1.38507i
\(861\) 58.8683 2.00622
\(862\) 0.942442 4.44529i 0.0320997 0.151407i
\(863\) −12.3725 12.3725i −0.421166 0.421166i 0.464439 0.885605i \(-0.346256\pi\)
−0.885605 + 0.464439i \(0.846256\pi\)
\(864\) −26.3176 6.97793i −0.895341 0.237394i
\(865\) −22.8338 + 9.76715i −0.776372 + 0.332093i
\(866\) −13.9067 + 9.04150i −0.472570 + 0.307243i
\(867\) 45.0042 45.0042i 1.52842 1.52842i
\(868\) 13.3616 + 34.6993i 0.453521 + 1.17777i
\(869\) 5.80341i 0.196867i
\(870\) 29.5435 5.84379i 1.00162 0.198123i
\(871\) 5.64240i 0.191185i
\(872\) 23.1195 31.9266i 0.782924 1.08117i
\(873\) −0.333249 + 0.333249i −0.0112788 + 0.0112788i
\(874\) 7.12171 + 10.9539i 0.240895 + 0.370521i
\(875\) −36.2570 13.5729i −1.22571 0.458848i
\(876\) −38.2969 17.0028i −1.29393 0.574472i
\(877\) 4.05376 + 4.05376i 0.136886 + 0.136886i 0.772230 0.635344i \(-0.219142\pi\)
−0.635344 + 0.772230i \(0.719142\pi\)
\(878\) 3.16936 + 0.671933i 0.106961 + 0.0226766i
\(879\) 2.28228 0.0769793
\(880\) −33.9364 + 12.5392i −1.14399 + 0.422697i
\(881\) −18.6698 −0.629002 −0.314501 0.949257i \(-0.601837\pi\)
−0.314501 + 0.949257i \(0.601837\pi\)
\(882\) 2.64632 + 0.561044i 0.0891063 + 0.0188913i
\(883\) −30.3858 30.3858i −1.02256 1.02256i −0.999739 0.0228255i \(-0.992734\pi\)
−0.0228255 0.999739i \(-0.507266\pi\)
\(884\) −13.1309 5.82977i −0.441640 0.196077i
\(885\) 7.41783 + 17.3415i 0.249348 + 0.582928i
\(886\) 19.7299 + 30.3466i 0.662840 + 1.01951i
\(887\) 23.9673 23.9673i 0.804743 0.804743i −0.179090 0.983833i \(-0.557315\pi\)
0.983833 + 0.179090i \(0.0573152\pi\)
\(888\) 23.8979 33.0016i 0.801962 1.10746i
\(889\) 25.3822i 0.851291i
\(890\) 15.7585 23.5298i 0.528226 0.788722i
\(891\) 40.4613i 1.35550i
\(892\) −20.2622 52.6199i −0.678427 1.76184i
\(893\) −4.29346 + 4.29346i −0.143675 + 0.143675i
\(894\) −14.2918 + 9.29183i −0.477988 + 0.310765i
\(895\) 17.0723 + 6.84265i 0.570662 + 0.228725i
\(896\) 30.5357 + 24.5425i 1.02013 + 0.819906i
\(897\) −3.65310 3.65310i −0.121974 0.121974i
\(898\) 8.49916 40.0887i 0.283621 1.33778i
\(899\) 27.7987 0.927138
\(900\) −3.54442 + 1.45929i −0.118147 + 0.0486429i
\(901\) −33.7952 −1.12588
\(902\) −10.9655 + 51.7217i −0.365110 + 1.72214i
\(903\) −40.9090 40.9090i −1.36137 1.36137i
\(904\) −17.3022 + 2.76828i −0.575463 + 0.0920717i
\(905\) 25.1749 + 10.0902i 0.836840 + 0.335410i
\(906\) −9.62922 + 6.26046i −0.319909 + 0.207990i
\(907\) 8.59846 8.59846i 0.285507 0.285507i −0.549793 0.835301i \(-0.685294\pi\)
0.835301 + 0.549793i \(0.185294\pi\)
\(908\) −54.8234 + 21.1107i −1.81938 + 0.700582i
\(909\) 2.51113i 0.0832890i
\(910\) 6.09323 9.09812i 0.201989 0.301600i
\(911\) 2.86336i 0.0948674i 0.998874 + 0.0474337i \(0.0151043\pi\)
−0.998874 + 0.0474337i \(0.984896\pi\)
\(912\) −1.21594 + 24.1705i −0.0402638 + 0.800366i
\(913\) −21.2999 + 21.2999i −0.704923 + 0.704923i
\(914\) −20.0086 30.7752i −0.661825 1.01795i
\(915\) 10.3593 + 24.2180i 0.342466 + 0.800623i
\(916\) 13.8749 31.2516i 0.458439 1.03258i
\(917\) 11.0052 + 11.0052i 0.363424 + 0.363424i
\(918\) −47.8325 10.1409i −1.57871 0.334700i
\(919\) 43.9157 1.44865 0.724323 0.689461i \(-0.242153\pi\)
0.724323 + 0.689461i \(0.242153\pi\)
\(920\) −3.92077 + 17.3257i −0.129264 + 0.571212i
\(921\) −53.5538 −1.76466
\(922\) 33.1138 + 7.02043i 1.09054 + 0.231205i
\(923\) 6.12453 + 6.12453i 0.201591 + 0.201591i
\(924\) −20.9082 + 47.0932i −0.687828 + 1.54925i
\(925\) 0.900480 + 39.1491i 0.0296076 + 1.28722i
\(926\) 2.55337 + 3.92733i 0.0839088 + 0.129060i
\(927\) 2.12992 2.12992i 0.0699558 0.0699558i
\(928\) 25.3263 14.7108i 0.831378 0.482904i
\(929\) 16.0663i 0.527118i −0.964643 0.263559i \(-0.915104\pi\)
0.964643 0.263559i \(-0.0848964\pi\)
\(930\) −30.6362 + 6.05994i −1.00460 + 0.198713i
\(931\) 16.4147i 0.537970i
\(932\) −28.0710 + 10.8092i −0.919496 + 0.354067i
\(933\) −12.5343 + 12.5343i −0.410354 + 0.410354i
\(934\) 35.8428 23.3033i 1.17281 0.762507i
\(935\) −59.7365 + 25.5523i −1.95359 + 0.835649i
\(936\) −0.171282 1.07054i −0.00559853 0.0349917i
\(937\) 5.64650 + 5.64650i 0.184463 + 0.184463i 0.793297 0.608834i \(-0.208363\pi\)
−0.608834 + 0.793297i \(0.708363\pi\)
\(938\) −5.73062 + 27.0301i −0.187111 + 0.882563i
\(939\) −23.4107 −0.763980
\(940\) −8.25454 0.112546i −0.269233 0.00367083i
\(941\) 53.0796 1.73034 0.865172 0.501475i \(-0.167209\pi\)
0.865172 + 0.501475i \(0.167209\pi\)
\(942\) 4.04024 19.0569i 0.131638 0.620909i
\(943\) 18.3563 + 18.3563i 0.597765 + 0.597765i
\(944\) 12.3026 + 13.6060i 0.400416 + 0.442837i
\(945\) 13.8646 34.5919i 0.451016 1.12527i
\(946\) 43.5628 28.3225i 1.41635 0.920843i
\(947\) −27.3732 + 27.3732i −0.889508 + 0.889508i −0.994476 0.104967i \(-0.966526\pi\)
0.104967 + 0.994476i \(0.466526\pi\)
\(948\) −1.89665 4.92551i −0.0616003 0.159973i
\(949\) 11.3902i 0.369741i
\(950\) −13.1230 19.2032i −0.425766 0.623035i
\(951\) 52.0866i 1.68902i
\(952\) 56.9830 + 41.2639i 1.84683 + 1.33737i
\(953\) 32.6767 32.6767i 1.05850 1.05850i 0.0603242 0.998179i \(-0.480787\pi\)
0.998179 0.0603242i \(-0.0192135\pi\)
\(954\) −1.39009 2.13810i −0.0450058 0.0692235i
\(955\) 6.31359 15.7523i 0.204303 0.509731i
\(956\) −19.0638 8.46381i −0.616566 0.273739i
\(957\) 27.2390 + 27.2390i 0.880511 + 0.880511i
\(958\) −43.7325 9.27169i −1.41293 0.299555i
\(959\) 17.4652 0.563981
\(960\) −24.7047 + 21.7333i −0.797340 + 0.701440i
\(961\) 2.17312 0.0701006
\(962\) −10.8351 2.29715i −0.349339 0.0740631i
\(963\) −0.509545 0.509545i −0.0164199 0.0164199i
\(964\) −1.43888 0.638825i −0.0463432 0.0205752i
\(965\) −5.44353 + 2.32847i −0.175233 + 0.0749561i
\(966\) 13.7901 + 21.2105i 0.443688 + 0.682437i
\(967\) 8.08950 8.08950i 0.260141 0.260141i −0.564970 0.825111i \(-0.691112\pi\)
0.825111 + 0.564970i \(0.191112\pi\)
\(968\) −12.2821 8.89401i −0.394762 0.285864i
\(969\) 43.4617i 1.39619i
\(970\) −0.754459 3.81420i −0.0242242 0.122466i
\(971\) 20.1023i 0.645115i −0.946550 0.322558i \(-0.895457\pi\)
0.946550 0.322558i \(-0.104543\pi\)
\(972\) −2.84604 7.39102i −0.0912867 0.237067i
\(973\) −18.7747 + 18.7747i −0.601891 + 0.601891i
\(974\) 26.9927 17.5493i 0.864900 0.562317i
\(975\) 6.65100 + 6.35192i 0.213003 + 0.203424i
\(976\) 17.1810 + 19.0012i 0.549951 + 0.608215i
\(977\) 1.38681 + 1.38681i 0.0443679 + 0.0443679i 0.728943 0.684575i \(-0.240012\pi\)
−0.684575 + 0.728943i \(0.740012\pi\)
\(978\) 10.6522 50.2442i 0.340621 1.60663i
\(979\) 36.2237 1.15771
\(980\) −15.9945 + 15.5642i −0.510924 + 0.497180i
\(981\) 5.34197 0.170556
\(982\) −1.30385 + 6.14996i −0.0416075 + 0.196253i
\(983\) −29.9544 29.9544i −0.955397 0.955397i 0.0436496 0.999047i \(-0.486101\pi\)
−0.999047 + 0.0436496i \(0.986101\pi\)
\(984\) 7.59680 + 47.4812i 0.242177 + 1.51365i
\(985\) −2.18253 5.10235i −0.0695412 0.162574i
\(986\) 44.0977 28.6702i 1.40436 0.913046i
\(987\) −8.31360 + 8.31360i −0.264625 + 0.264625i
\(988\) 6.13919 2.36400i 0.195314 0.0752088i
\(989\) 25.5125i 0.811252i
\(990\) −4.07373 2.72827i −0.129472 0.0867103i
\(991\) 5.41262i 0.171937i −0.996298 0.0859687i \(-0.972601\pi\)
0.996298 0.0859687i \(-0.0273985\pi\)
\(992\) −26.2631 + 15.2549i −0.833854 + 0.484342i
\(993\) −7.17894 + 7.17894i −0.227817 + 0.227817i
\(994\) −23.1194 35.5600i −0.733304 1.12789i
\(995\) 35.9760 + 14.4194i 1.14052 + 0.457125i
\(996\) −11.1166 + 25.0389i −0.352244 + 0.793388i
\(997\) −10.8817 10.8817i −0.344626 0.344626i 0.513477 0.858103i \(-0.328357\pi\)
−0.858103 + 0.513477i \(0.828357\pi\)
\(998\) 1.52968 + 0.324307i 0.0484213 + 0.0102658i
\(999\) −37.6956 −1.19264
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 260.2.o.a.27.35 yes 72
4.3 odd 2 inner 260.2.o.a.27.21 72
5.3 odd 4 inner 260.2.o.a.183.21 yes 72
20.3 even 4 inner 260.2.o.a.183.35 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.o.a.27.21 72 4.3 odd 2 inner
260.2.o.a.27.35 yes 72 1.1 even 1 trivial
260.2.o.a.183.21 yes 72 5.3 odd 4 inner
260.2.o.a.183.35 yes 72 20.3 even 4 inner