Properties

Label 144.2.x.e.13.18
Level $144$
Weight $2$
Character 144.13
Analytic conductor $1.150$
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] = [144,2,Mod(13,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 13.18
Character \(\chi\) \(=\) 144.13
Dual form 144.2.x.e.133.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41328 - 0.0512684i) q^{2} +(0.543291 - 1.64464i) q^{3} +(1.99474 - 0.144914i) q^{4} +(0.430214 + 1.60558i) q^{5} +(0.683506 - 2.35219i) q^{6} +(-3.62762 + 2.09441i) q^{7} +(2.81171 - 0.307071i) q^{8} +(-2.40967 - 1.78703i) q^{9} +O(q^{10})\) \(q+(1.41328 - 0.0512684i) q^{2} +(0.543291 - 1.64464i) q^{3} +(1.99474 - 0.144914i) q^{4} +(0.430214 + 1.60558i) q^{5} +(0.683506 - 2.35219i) q^{6} +(-3.62762 + 2.09441i) q^{7} +(2.81171 - 0.307071i) q^{8} +(-2.40967 - 1.78703i) q^{9} +(0.690330 + 2.24708i) q^{10} +(-4.63241 - 1.24125i) q^{11} +(0.845395 - 3.35936i) q^{12} +(3.28323 - 0.879738i) q^{13} +(-5.01948 + 3.14597i) q^{14} +(2.87433 + 0.164751i) q^{15} +(3.95800 - 0.578131i) q^{16} -2.14142 q^{17} +(-3.49717 - 2.40205i) q^{18} +(1.03156 + 1.03156i) q^{19} +(1.09084 + 3.14037i) q^{20} +(1.47369 + 7.10399i) q^{21} +(-6.61055 - 1.51674i) q^{22} +(0.405884 + 0.234337i) q^{23} +(1.02255 - 4.79107i) q^{24} +(1.93733 - 1.11852i) q^{25} +(4.59503 - 1.41164i) q^{26} +(-4.24818 + 2.99216i) q^{27} +(-6.93266 + 4.70349i) q^{28} +(-1.75557 + 6.55186i) q^{29} +(4.07069 + 0.0854774i) q^{30} +(3.18054 - 5.50886i) q^{31} +(5.56414 - 1.01998i) q^{32} +(-4.55816 + 6.94428i) q^{33} +(-3.02643 + 0.109787i) q^{34} +(-4.92339 - 4.92339i) q^{35} +(-5.06564 - 3.21548i) q^{36} +(-0.728237 + 0.728237i) q^{37} +(1.51077 + 1.40500i) q^{38} +(0.336896 - 5.87767i) q^{39} +(1.70266 + 4.38232i) q^{40} +(-2.52351 - 1.45695i) q^{41} +(2.44695 + 9.96440i) q^{42} +(10.6289 + 2.84802i) q^{43} +(-9.42035 - 1.80468i) q^{44} +(1.83255 - 4.63772i) q^{45} +(0.585644 + 0.310376i) q^{46} +(-4.61716 - 7.99715i) q^{47} +(1.19953 - 6.82357i) q^{48} +(5.27308 - 9.13324i) q^{49} +(2.68065 - 1.68010i) q^{50} +(-1.16341 + 3.52186i) q^{51} +(6.42171 - 2.23063i) q^{52} +(1.17892 - 1.17892i) q^{53} +(-5.85048 + 4.44656i) q^{54} -7.97171i q^{55} +(-9.55667 + 7.00280i) q^{56} +(2.25698 - 1.13611i) q^{57} +(-2.14521 + 9.34965i) q^{58} +(0.397061 + 1.48185i) q^{59} +(5.75742 - 0.0878938i) q^{60} +(-2.01826 + 7.53224i) q^{61} +(4.21258 - 7.94865i) q^{62} +(12.4841 + 1.43585i) q^{63} +(7.81141 - 1.72679i) q^{64} +(2.82498 + 4.89300i) q^{65} +(-6.08595 + 10.0479i) q^{66} +(-9.82470 + 2.63252i) q^{67} +(-4.27158 + 0.310320i) q^{68} +(0.605914 - 0.540220i) q^{69} +(-7.21056 - 6.70573i) q^{70} +8.27863i q^{71} +(-7.32404 - 4.28468i) q^{72} -8.16641i q^{73} +(-0.991870 + 1.06654i) q^{74} +(-0.787022 - 3.79388i) q^{75} +(2.20718 + 1.90821i) q^{76} +(19.4043 - 5.19937i) q^{77} +(0.174791 - 8.32409i) q^{78} +(3.63065 + 6.28847i) q^{79} +(2.63102 + 6.10616i) q^{80} +(2.61302 + 8.61232i) q^{81} +(-3.64113 - 1.92970i) q^{82} +(2.03413 - 7.59149i) q^{83} +(3.96910 + 13.9571i) q^{84} +(-0.921267 - 3.43821i) q^{85} +(15.1677 + 3.48013i) q^{86} +(9.82166 + 6.44684i) q^{87} +(-13.4062 - 2.06756i) q^{88} -11.1968i q^{89} +(2.35215 - 6.64837i) q^{90} +(-10.0678 + 10.0678i) q^{91} +(0.843594 + 0.408625i) q^{92} +(-7.33213 - 8.22376i) q^{93} +(-6.93535 - 11.0655i) q^{94} +(-1.21246 + 2.10004i) q^{95} +(1.34544 - 9.70514i) q^{96} +(-5.67759 - 9.83387i) q^{97} +(6.98411 - 13.1782i) q^{98} +(8.94443 + 11.2693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22} - 40 q^{24} - 4 q^{26} + 8 q^{27} - 16 q^{28} + 4 q^{29} + 18 q^{30} + 28 q^{31} - 46 q^{32} - 32 q^{33} - 14 q^{34} - 16 q^{35} + 14 q^{36} + 16 q^{37} + 2 q^{38} - 10 q^{40} + 26 q^{42} - 10 q^{43} + 60 q^{44} + 40 q^{45} + 20 q^{46} - 56 q^{47} + 2 q^{48} + 4 q^{49} - 36 q^{50} - 54 q^{51} + 6 q^{52} - 8 q^{53} + 92 q^{54} + 52 q^{56} - 14 q^{58} - 14 q^{59} + 18 q^{60} - 32 q^{61} + 16 q^{62} - 108 q^{63} - 44 q^{64} - 64 q^{65} + 26 q^{66} - 18 q^{67} + 16 q^{68} + 32 q^{69} + 14 q^{70} + 114 q^{72} + 38 q^{74} + 86 q^{75} + 10 q^{76} - 36 q^{77} + 16 q^{78} + 44 q^{79} + 144 q^{80} - 44 q^{81} - 88 q^{82} + 20 q^{83} - 58 q^{84} - 8 q^{85} + 76 q^{86} - 42 q^{88} - 80 q^{91} - 68 q^{92} - 4 q^{93} + 20 q^{94} + 48 q^{95} + 94 q^{96} + 40 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41328 0.0512684i 0.999343 0.0362522i
\(3\) 0.543291 1.64464i 0.313669 0.949532i
\(4\) 1.99474 0.144914i 0.997372 0.0724568i
\(5\) 0.430214 + 1.60558i 0.192397 + 0.718037i 0.992925 + 0.118741i \(0.0378859\pi\)
−0.800528 + 0.599296i \(0.795447\pi\)
\(6\) 0.683506 2.35219i 0.279040 0.960279i
\(7\) −3.62762 + 2.09441i −1.37111 + 0.791611i −0.991068 0.133358i \(-0.957424\pi\)
−0.380043 + 0.924969i \(0.624091\pi\)
\(8\) 2.81171 0.307071i 0.994089 0.108566i
\(9\) −2.40967 1.78703i −0.803223 0.595678i
\(10\) 0.690330 + 2.24708i 0.218301 + 0.710590i
\(11\) −4.63241 1.24125i −1.39673 0.374251i −0.519557 0.854436i \(-0.673903\pi\)
−0.877168 + 0.480184i \(0.840570\pi\)
\(12\) 0.845395 3.35936i 0.244045 0.969764i
\(13\) 3.28323 0.879738i 0.910603 0.243995i 0.227039 0.973886i \(-0.427096\pi\)
0.683564 + 0.729890i \(0.260429\pi\)
\(14\) −5.01948 + 3.14597i −1.34151 + 0.840797i
\(15\) 2.87433 + 0.164751i 0.742148 + 0.0425384i
\(16\) 3.95800 0.578131i 0.989500 0.144533i
\(17\) −2.14142 −0.519370 −0.259685 0.965693i \(-0.583619\pi\)
−0.259685 + 0.965693i \(0.583619\pi\)
\(18\) −3.49717 2.40205i −0.824290 0.566168i
\(19\) 1.03156 + 1.03156i 0.236656 + 0.236656i 0.815464 0.578808i \(-0.196482\pi\)
−0.578808 + 0.815464i \(0.696482\pi\)
\(20\) 1.09084 + 3.14037i 0.243918 + 0.702209i
\(21\) 1.47369 + 7.10399i 0.321585 + 1.55022i
\(22\) −6.61055 1.51674i −1.40937 0.323371i
\(23\) 0.405884 + 0.234337i 0.0846327 + 0.0488627i 0.541719 0.840560i \(-0.317774\pi\)
−0.457086 + 0.889422i \(0.651107\pi\)
\(24\) 1.02255 4.79107i 0.208728 0.977974i
\(25\) 1.93733 1.11852i 0.387465 0.223703i
\(26\) 4.59503 1.41164i 0.901159 0.276846i
\(27\) −4.24818 + 2.99216i −0.817562 + 0.575841i
\(28\) −6.93266 + 4.70349i −1.31015 + 0.888877i
\(29\) −1.75557 + 6.55186i −0.326000 + 1.21665i 0.587302 + 0.809368i \(0.300190\pi\)
−0.913302 + 0.407282i \(0.866477\pi\)
\(30\) 4.07069 + 0.0854774i 0.743203 + 0.0156060i
\(31\) 3.18054 5.50886i 0.571242 0.989421i −0.425196 0.905101i \(-0.639795\pi\)
0.996439 0.0843198i \(-0.0268717\pi\)
\(32\) 5.56414 1.01998i 0.983610 0.180309i
\(33\) −4.55816 + 6.94428i −0.793473 + 1.20884i
\(34\) −3.02643 + 0.109787i −0.519028 + 0.0188283i
\(35\) −4.92339 4.92339i −0.832204 0.832204i
\(36\) −5.06564 3.21548i −0.844273 0.535913i
\(37\) −0.728237 + 0.728237i −0.119721 + 0.119721i −0.764429 0.644708i \(-0.776979\pi\)
0.644708 + 0.764429i \(0.276979\pi\)
\(38\) 1.51077 + 1.40500i 0.245080 + 0.227921i
\(39\) 0.336896 5.87767i 0.0539466 0.941181i
\(40\) 1.70266 + 4.38232i 0.269215 + 0.692905i
\(41\) −2.52351 1.45695i −0.394105 0.227537i 0.289832 0.957078i \(-0.406401\pi\)
−0.683937 + 0.729541i \(0.739734\pi\)
\(42\) 2.44695 + 9.96440i 0.377573 + 1.53754i
\(43\) 10.6289 + 2.84802i 1.62090 + 0.434318i 0.951265 0.308374i \(-0.0997848\pi\)
0.669633 + 0.742692i \(0.266451\pi\)
\(44\) −9.42035 1.80468i −1.42017 0.272066i
\(45\) 1.83255 4.63772i 0.273181 0.691351i
\(46\) 0.585644 + 0.310376i 0.0863485 + 0.0457625i
\(47\) −4.61716 7.99715i −0.673482 1.16650i −0.976910 0.213650i \(-0.931465\pi\)
0.303429 0.952854i \(-0.401869\pi\)
\(48\) 1.19953 6.82357i 0.173137 0.984898i
\(49\) 5.27308 9.13324i 0.753297 1.30475i
\(50\) 2.68065 1.68010i 0.379101 0.237603i
\(51\) −1.16341 + 3.52186i −0.162910 + 0.493159i
\(52\) 6.42171 2.23063i 0.890530 0.309333i
\(53\) 1.17892 1.17892i 0.161937 0.161937i −0.621487 0.783424i \(-0.713471\pi\)
0.783424 + 0.621487i \(0.213471\pi\)
\(54\) −5.85048 + 4.44656i −0.796149 + 0.605101i
\(55\) 7.97171i 1.07491i
\(56\) −9.55667 + 7.00280i −1.27706 + 0.935788i
\(57\) 2.25698 1.13611i 0.298944 0.150481i
\(58\) −2.14521 + 9.34965i −0.281680 + 1.22767i
\(59\) 0.397061 + 1.48185i 0.0516930 + 0.192921i 0.986944 0.161065i \(-0.0514928\pi\)
−0.935251 + 0.353986i \(0.884826\pi\)
\(60\) 5.75742 0.0878938i 0.743280 0.0113470i
\(61\) −2.01826 + 7.53224i −0.258411 + 0.964404i 0.707749 + 0.706464i \(0.249711\pi\)
−0.966161 + 0.257941i \(0.916956\pi\)
\(62\) 4.21258 7.94865i 0.534998 1.00948i
\(63\) 12.4841 + 1.43585i 1.57285 + 0.180900i
\(64\) 7.81141 1.72679i 0.976427 0.215849i
\(65\) 2.82498 + 4.89300i 0.350395 + 0.606902i
\(66\) −6.08595 + 10.0479i −0.749129 + 1.23682i
\(67\) −9.82470 + 2.63252i −1.20028 + 0.321614i −0.802941 0.596059i \(-0.796732\pi\)
−0.397338 + 0.917673i \(0.630066\pi\)
\(68\) −4.27158 + 0.310320i −0.518005 + 0.0376319i
\(69\) 0.605914 0.540220i 0.0729434 0.0650348i
\(70\) −7.21056 6.70573i −0.861826 0.801488i
\(71\) 8.27863i 0.982493i 0.871021 + 0.491246i \(0.163458\pi\)
−0.871021 + 0.491246i \(0.836542\pi\)
\(72\) −7.32404 4.28468i −0.863146 0.504954i
\(73\) 8.16641i 0.955806i −0.878413 0.477903i \(-0.841397\pi\)
0.878413 0.477903i \(-0.158603\pi\)
\(74\) −0.991870 + 1.06654i −0.115303 + 0.123983i
\(75\) −0.787022 3.79388i −0.0908775 0.438079i
\(76\) 2.20718 + 1.90821i 0.253181 + 0.218887i
\(77\) 19.4043 5.19937i 2.21133 0.592523i
\(78\) 0.174791 8.32409i 0.0197912 0.942518i
\(79\) 3.63065 + 6.28847i 0.408480 + 0.707508i 0.994720 0.102630i \(-0.0327257\pi\)
−0.586240 + 0.810138i \(0.699392\pi\)
\(80\) 2.63102 + 6.10616i 0.294157 + 0.682690i
\(81\) 2.61302 + 8.61232i 0.290336 + 0.956925i
\(82\) −3.64113 1.92970i −0.402095 0.213100i
\(83\) 2.03413 7.59149i 0.223275 0.833274i −0.759813 0.650142i \(-0.774710\pi\)
0.983088 0.183133i \(-0.0586238\pi\)
\(84\) 3.96910 + 13.9571i 0.433064 + 1.52284i
\(85\) −0.921267 3.43821i −0.0999254 0.372927i
\(86\) 15.1677 + 3.48013i 1.63558 + 0.375272i
\(87\) 9.82166 + 6.44684i 1.05299 + 0.691174i
\(88\) −13.4062 2.06756i −1.42910 0.220402i
\(89\) 11.1968i 1.18686i −0.804886 0.593429i \(-0.797774\pi\)
0.804886 0.593429i \(-0.202226\pi\)
\(90\) 2.35215 6.64837i 0.247938 0.700800i
\(91\) −10.0678 + 10.0678i −1.05539 + 1.05539i
\(92\) 0.843594 + 0.408625i 0.0879507 + 0.0426021i
\(93\) −7.33213 8.22376i −0.760306 0.852764i
\(94\) −6.93535 11.0655i −0.715327 1.14132i
\(95\) −1.21246 + 2.10004i −0.124396 + 0.215460i
\(96\) 1.34544 9.70514i 0.137319 0.990527i
\(97\) −5.67759 9.83387i −0.576472 0.998479i −0.995880 0.0906808i \(-0.971096\pi\)
0.419408 0.907798i \(-0.362238\pi\)
\(98\) 6.98411 13.1782i 0.705501 1.33120i
\(99\) 8.94443 + 11.2693i 0.898949 + 1.13261i
\(100\) 3.70238 2.51190i 0.370238 0.251190i
\(101\) −2.90189 0.777558i −0.288749 0.0773699i 0.111537 0.993760i \(-0.464423\pi\)
−0.400286 + 0.916390i \(0.631089\pi\)
\(102\) −1.46367 + 5.03703i −0.144925 + 0.498740i
\(103\) 1.24824 + 0.720669i 0.122992 + 0.0710096i 0.560234 0.828334i \(-0.310711\pi\)
−0.437242 + 0.899344i \(0.644045\pi\)
\(104\) 8.96133 3.48175i 0.878731 0.341414i
\(105\) −10.7720 + 5.42236i −1.05124 + 0.529168i
\(106\) 1.60570 1.72658i 0.155960 0.167701i
\(107\) 5.85602 5.85602i 0.566123 0.566123i −0.364917 0.931040i \(-0.618903\pi\)
0.931040 + 0.364917i \(0.118903\pi\)
\(108\) −8.04042 + 6.58420i −0.773689 + 0.633565i
\(109\) −2.05249 2.05249i −0.196593 0.196593i 0.601945 0.798538i \(-0.294393\pi\)
−0.798538 + 0.601945i \(0.794393\pi\)
\(110\) −0.408697 11.2663i −0.0389677 1.07420i
\(111\) 0.802042 + 1.59333i 0.0761265 + 0.151232i
\(112\) −13.1473 + 10.3869i −1.24230 + 0.981470i
\(113\) −4.12726 + 7.14862i −0.388260 + 0.672486i −0.992216 0.124532i \(-0.960257\pi\)
0.603956 + 0.797018i \(0.293590\pi\)
\(114\) 3.13151 1.72135i 0.293293 0.161219i
\(115\) −0.201630 + 0.752495i −0.0188021 + 0.0701705i
\(116\) −2.55245 + 13.3237i −0.236989 + 1.23707i
\(117\) −9.48361 3.74736i −0.876760 0.346443i
\(118\) 0.637132 + 2.07392i 0.0586528 + 0.190920i
\(119\) 7.76824 4.48500i 0.712114 0.411139i
\(120\) 8.13236 0.419392i 0.742380 0.0382851i
\(121\) 10.3923 + 5.99998i 0.944752 + 0.545453i
\(122\) −2.46621 + 10.7487i −0.223280 + 0.973138i
\(123\) −3.76715 + 3.35871i −0.339672 + 0.302845i
\(124\) 5.54606 11.4497i 0.498051 1.02821i
\(125\) 8.50616 + 8.50616i 0.760814 + 0.760814i
\(126\) 17.7172 + 1.38922i 1.57838 + 0.123762i
\(127\) −1.68483 −0.149504 −0.0747521 0.997202i \(-0.523817\pi\)
−0.0747521 + 0.997202i \(0.523817\pi\)
\(128\) 10.9512 2.84092i 0.967960 0.251104i
\(129\) 10.4586 15.9335i 0.920825 1.40286i
\(130\) 4.24335 + 6.77037i 0.372167 + 0.593801i
\(131\) −7.36461 + 1.97334i −0.643449 + 0.172412i −0.565765 0.824566i \(-0.691419\pi\)
−0.0776838 + 0.996978i \(0.524752\pi\)
\(132\) −8.08603 + 14.5126i −0.703799 + 1.26316i
\(133\) −5.90261 1.58160i −0.511821 0.137142i
\(134\) −13.7501 + 4.22420i −1.18783 + 0.364915i
\(135\) −6.63177 5.53352i −0.570772 0.476249i
\(136\) −6.02104 + 0.657567i −0.516300 + 0.0563859i
\(137\) −8.26806 + 4.77357i −0.706388 + 0.407833i −0.809722 0.586813i \(-0.800382\pi\)
0.103334 + 0.994647i \(0.467049\pi\)
\(138\) 0.828632 0.794548i 0.0705378 0.0676364i
\(139\) 3.74281 + 13.9684i 0.317461 + 1.18478i 0.921676 + 0.387960i \(0.126820\pi\)
−0.604215 + 0.796821i \(0.706513\pi\)
\(140\) −10.5344 9.10743i −0.890316 0.769718i
\(141\) −15.6609 + 3.24877i −1.31888 + 0.273596i
\(142\) 0.424432 + 11.7001i 0.0356175 + 0.981847i
\(143\) −16.3012 −1.36318
\(144\) −10.5706 5.67998i −0.880884 0.473331i
\(145\) −11.2748 −0.936321
\(146\) −0.418679 11.5415i −0.0346501 0.955178i
\(147\) −12.1561 13.6343i −1.00261 1.12454i
\(148\) −1.34711 + 1.55818i −0.110732 + 0.128081i
\(149\) 0.445462 + 1.66249i 0.0364937 + 0.136196i 0.981769 0.190077i \(-0.0608737\pi\)
−0.945276 + 0.326273i \(0.894207\pi\)
\(150\) −1.30679 5.32148i −0.106699 0.434497i
\(151\) −18.5071 + 10.6851i −1.50609 + 0.869542i −0.506115 + 0.862466i \(0.668919\pi\)
−0.999975 + 0.00707596i \(0.997748\pi\)
\(152\) 3.21721 + 2.58368i 0.260950 + 0.209564i
\(153\) 5.16011 + 3.82678i 0.417170 + 0.309377i
\(154\) 27.1572 8.34301i 2.18839 0.672299i
\(155\) 10.2132 + 2.73663i 0.820346 + 0.219811i
\(156\) −0.179733 11.7733i −0.0143901 0.942616i
\(157\) −10.2463 + 2.74550i −0.817746 + 0.219114i −0.643361 0.765563i \(-0.722461\pi\)
−0.174385 + 0.984677i \(0.555794\pi\)
\(158\) 5.45354 + 8.70125i 0.433860 + 0.692234i
\(159\) −1.29840 2.57939i −0.102970 0.204559i
\(160\) 4.03143 + 8.49485i 0.318713 + 0.671577i
\(161\) −1.96319 −0.154721
\(162\) 4.13448 + 12.0377i 0.324835 + 0.945771i
\(163\) −3.47621 3.47621i −0.272278 0.272278i 0.557739 0.830017i \(-0.311669\pi\)
−0.830017 + 0.557739i \(0.811669\pi\)
\(164\) −5.24488 2.54054i −0.409556 0.198383i
\(165\) −13.1106 4.33096i −1.02066 0.337165i
\(166\) 2.48560 10.8332i 0.192920 0.840821i
\(167\) −0.277442 0.160181i −0.0214691 0.0123952i 0.489227 0.872156i \(-0.337279\pi\)
−0.510696 + 0.859761i \(0.670612\pi\)
\(168\) 6.32502 + 19.5218i 0.487986 + 1.50614i
\(169\) −1.25270 + 0.723245i −0.0963613 + 0.0556342i
\(170\) −1.47828 4.81194i −0.113379 0.369059i
\(171\) −0.642287 4.32915i −0.0491169 0.331059i
\(172\) 21.6147 + 4.14078i 1.64811 + 0.315732i
\(173\) −3.13236 + 11.6901i −0.238149 + 0.888784i 0.738555 + 0.674193i \(0.235509\pi\)
−0.976704 + 0.214591i \(0.931158\pi\)
\(174\) 14.2113 + 8.60767i 1.07736 + 0.652546i
\(175\) −4.68525 + 8.11510i −0.354172 + 0.613444i
\(176\) −19.0527 2.23473i −1.43615 0.168449i
\(177\) 2.65283 + 0.152055i 0.199399 + 0.0114291i
\(178\) −0.574041 15.8243i −0.0430262 1.18608i
\(179\) 18.6780 + 18.6780i 1.39606 + 1.39606i 0.810958 + 0.585104i \(0.198946\pi\)
0.585104 + 0.810958i \(0.301054\pi\)
\(180\) 2.98340 9.51663i 0.222370 0.709328i
\(181\) 4.10527 4.10527i 0.305143 0.305143i −0.537879 0.843022i \(-0.680774\pi\)
0.843022 + 0.537879i \(0.180774\pi\)
\(182\) −13.7124 + 14.7448i −1.01643 + 1.09295i
\(183\) 11.2913 + 7.41150i 0.834677 + 0.547874i
\(184\) 1.21319 + 0.534253i 0.0894373 + 0.0393857i
\(185\) −1.48254 0.855945i −0.108998 0.0629303i
\(186\) −10.7840 11.2466i −0.790721 0.824641i
\(187\) 9.91993 + 2.65804i 0.725417 + 0.194375i
\(188\) −10.3689 15.2832i −0.756232 1.11464i
\(189\) 9.14397 19.7518i 0.665126 1.43673i
\(190\) −1.60588 + 3.03012i −0.116503 + 0.219828i
\(191\) 8.60099 + 14.8974i 0.622346 + 1.07793i 0.989048 + 0.147596i \(0.0471536\pi\)
−0.366702 + 0.930338i \(0.619513\pi\)
\(192\) 1.40393 13.7851i 0.101320 0.994854i
\(193\) 9.17459 15.8909i 0.660402 1.14385i −0.320108 0.947381i \(-0.603719\pi\)
0.980510 0.196468i \(-0.0629473\pi\)
\(194\) −8.52821 13.6070i −0.612290 0.976924i
\(195\) 9.58201 1.98774i 0.686182 0.142345i
\(196\) 9.19490 18.9826i 0.656779 1.35590i
\(197\) 8.80431 8.80431i 0.627281 0.627281i −0.320102 0.947383i \(-0.603717\pi\)
0.947383 + 0.320102i \(0.103717\pi\)
\(198\) 13.2188 + 15.4681i 0.939418 + 1.09927i
\(199\) 10.0277i 0.710847i −0.934705 0.355423i \(-0.884337\pi\)
0.934705 0.355423i \(-0.115663\pi\)
\(200\) 5.10373 3.73984i 0.360888 0.264446i
\(201\) −1.00813 + 17.5883i −0.0711077 + 1.24058i
\(202\) −4.14105 0.950136i −0.291364 0.0668513i
\(203\) −7.35374 27.4445i −0.516131 1.92623i
\(204\) −1.81034 + 7.19379i −0.126749 + 0.503666i
\(205\) 1.25360 4.67849i 0.0875550 0.326760i
\(206\) 1.80106 + 0.954515i 0.125486 + 0.0665042i
\(207\) −0.559278 1.29001i −0.0388725 0.0896616i
\(208\) 12.4864 5.38014i 0.865776 0.373045i
\(209\) −3.49819 6.05904i −0.241975 0.419112i
\(210\) −14.9459 + 8.21560i −1.03137 + 0.566930i
\(211\) 19.2080 5.14678i 1.32234 0.354319i 0.472483 0.881340i \(-0.343358\pi\)
0.849852 + 0.527021i \(0.176691\pi\)
\(212\) 2.18079 2.52248i 0.149778 0.173244i
\(213\) 13.6154 + 4.49770i 0.932908 + 0.308178i
\(214\) 7.97600 8.57645i 0.545228 0.586274i
\(215\) 18.2909i 1.24743i
\(216\) −11.0258 + 9.71757i −0.750213 + 0.661197i
\(217\) 26.6454i 1.80881i
\(218\) −3.00598 2.79552i −0.203591 0.189337i
\(219\) −13.4308 4.43674i −0.907569 0.299807i
\(220\) −1.15521 15.9015i −0.0778842 1.07208i
\(221\) −7.03076 + 1.88389i −0.472940 + 0.126724i
\(222\) 1.21520 + 2.21071i 0.0815589 + 0.148373i
\(223\) −6.96587 12.0652i −0.466469 0.807948i 0.532797 0.846243i \(-0.321141\pi\)
−0.999266 + 0.0382947i \(0.987807\pi\)
\(224\) −18.0483 + 15.3537i −1.20590 + 1.02586i
\(225\) −6.66714 0.766813i −0.444476 0.0511209i
\(226\) −5.46649 + 10.3146i −0.363625 + 0.686119i
\(227\) 1.96164 7.32092i 0.130198 0.485907i −0.869773 0.493452i \(-0.835735\pi\)
0.999972 + 0.00754492i \(0.00240165\pi\)
\(228\) 4.33746 2.59331i 0.287255 0.171746i
\(229\) 4.94734 + 18.4637i 0.326930 + 1.22012i 0.912358 + 0.409394i \(0.134260\pi\)
−0.585428 + 0.810724i \(0.699074\pi\)
\(230\) −0.246382 + 1.07383i −0.0162459 + 0.0708060i
\(231\) 1.99110 34.7378i 0.131005 2.28558i
\(232\) −2.92425 + 18.9610i −0.191987 + 1.24485i
\(233\) 10.7647i 0.705216i −0.935771 0.352608i \(-0.885295\pi\)
0.935771 0.352608i \(-0.114705\pi\)
\(234\) −13.5952 4.80987i −0.888743 0.314431i
\(235\) 10.8537 10.8537i 0.708017 0.708017i
\(236\) 1.00678 + 2.89838i 0.0655355 + 0.188668i
\(237\) 12.3147 2.55464i 0.799929 0.165941i
\(238\) 10.7488 6.73684i 0.696741 0.436684i
\(239\) −11.1429 + 19.3001i −0.720774 + 1.24842i 0.239916 + 0.970794i \(0.422880\pi\)
−0.960690 + 0.277624i \(0.910453\pi\)
\(240\) 11.4718 1.00965i 0.740504 0.0651729i
\(241\) 13.7285 + 23.7785i 0.884332 + 1.53171i 0.846478 + 0.532424i \(0.178719\pi\)
0.0378540 + 0.999283i \(0.487948\pi\)
\(242\) 14.9948 + 7.94688i 0.963905 + 0.510845i
\(243\) 15.5838 + 0.381525i 0.999700 + 0.0244748i
\(244\) −2.93438 + 15.3174i −0.187855 + 0.980593i
\(245\) 16.9327 + 4.53710i 1.08179 + 0.289865i
\(246\) −5.15186 + 4.93994i −0.328470 + 0.314959i
\(247\) 4.29435 + 2.47934i 0.273243 + 0.157757i
\(248\) 7.25115 16.4660i 0.460448 1.04559i
\(249\) −11.3801 7.46980i −0.721186 0.473379i
\(250\) 12.4577 + 11.5855i 0.787895 + 0.732733i
\(251\) 11.4125 11.4125i 0.720350 0.720350i −0.248326 0.968676i \(-0.579881\pi\)
0.968676 + 0.248326i \(0.0798805\pi\)
\(252\) 25.1107 + 1.05503i 1.58183 + 0.0664605i
\(253\) −1.58935 1.58935i −0.0999217 0.0999217i
\(254\) −2.38114 + 0.0863784i −0.149406 + 0.00541986i
\(255\) −6.15514 0.352800i −0.385450 0.0220932i
\(256\) 15.3315 4.57648i 0.958221 0.286030i
\(257\) −0.930384 + 1.61147i −0.0580357 + 0.100521i −0.893584 0.448897i \(-0.851817\pi\)
0.835548 + 0.549418i \(0.185150\pi\)
\(258\) 13.9640 23.0547i 0.869363 1.43532i
\(259\) 1.11654 4.16699i 0.0693785 0.258924i
\(260\) 6.34417 + 9.35091i 0.393449 + 0.579919i
\(261\) 15.9387 12.6506i 0.986583 0.783051i
\(262\) −10.3071 + 3.16646i −0.636776 + 0.195625i
\(263\) −0.0414842 + 0.0239509i −0.00255802 + 0.00147687i −0.501278 0.865286i \(-0.667137\pi\)
0.498720 + 0.866763i \(0.333803\pi\)
\(264\) −10.6838 + 20.9250i −0.657544 + 1.28784i
\(265\) 2.40003 + 1.38566i 0.147433 + 0.0851203i
\(266\) −8.42315 1.93263i −0.516457 0.118497i
\(267\) −18.4147 6.08312i −1.12696 0.372281i
\(268\) −19.2163 + 6.67493i −1.17382 + 0.407737i
\(269\) −14.5681 14.5681i −0.888235 0.888235i 0.106118 0.994354i \(-0.466158\pi\)
−0.994354 + 0.106118i \(0.966158\pi\)
\(270\) −9.65627 7.48043i −0.587662 0.455245i
\(271\) −15.7807 −0.958607 −0.479304 0.877649i \(-0.659111\pi\)
−0.479304 + 0.877649i \(0.659111\pi\)
\(272\) −8.47573 + 1.23802i −0.513917 + 0.0750659i
\(273\) 11.0881 + 22.0275i 0.671083 + 1.33317i
\(274\) −11.4404 + 7.17030i −0.691139 + 0.433174i
\(275\) −10.3629 + 2.77672i −0.624904 + 0.167442i
\(276\) 1.13036 1.16540i 0.0680395 0.0701491i
\(277\) 7.21383 + 1.93294i 0.433437 + 0.116139i 0.468939 0.883231i \(-0.344636\pi\)
−0.0355022 + 0.999370i \(0.511303\pi\)
\(278\) 6.00579 + 19.5494i 0.360203 + 1.17249i
\(279\) −17.5086 + 7.59080i −1.04821 + 0.454449i
\(280\) −15.3550 12.3313i −0.917634 0.736936i
\(281\) 5.84440 3.37427i 0.348648 0.201292i −0.315442 0.948945i \(-0.602153\pi\)
0.664089 + 0.747653i \(0.268819\pi\)
\(282\) −21.9667 + 5.39435i −1.30810 + 0.321229i
\(283\) −3.33366 12.4414i −0.198165 0.739563i −0.991425 0.130679i \(-0.958284\pi\)
0.793259 0.608884i \(-0.208383\pi\)
\(284\) 1.19969 + 16.5137i 0.0711882 + 0.979910i
\(285\) 2.79509 + 3.13499i 0.165567 + 0.185701i
\(286\) −23.0383 + 0.835738i −1.36228 + 0.0494182i
\(287\) 12.2058 0.720483
\(288\) −15.2305 7.48548i −0.897465 0.441086i
\(289\) −12.4143 −0.730255
\(290\) −15.9345 + 0.578041i −0.935706 + 0.0339437i
\(291\) −19.2577 + 3.99493i −1.12891 + 0.234187i
\(292\) −1.18342 16.2899i −0.0692546 0.953294i
\(293\) −3.71874 13.8785i −0.217251 0.810792i −0.985362 0.170475i \(-0.945470\pi\)
0.768111 0.640317i \(-0.221197\pi\)
\(294\) −17.8790 18.6459i −1.04272 1.08745i
\(295\) −2.20841 + 1.27503i −0.128579 + 0.0742349i
\(296\) −1.82397 + 2.27121i −0.106016 + 0.132011i
\(297\) 23.3933 8.58785i 1.35742 0.498318i
\(298\) 0.714797 + 2.32673i 0.0414071 + 0.134784i
\(299\) 1.53877 + 0.412311i 0.0889891 + 0.0238446i
\(300\) −2.11969 7.45377i −0.122380 0.430343i
\(301\) −44.5226 + 11.9298i −2.56624 + 0.687622i
\(302\) −25.6080 + 16.0499i −1.47358 + 0.923569i
\(303\) −2.85537 + 4.35011i −0.164037 + 0.249907i
\(304\) 4.67929 + 3.48654i 0.268376 + 0.199967i
\(305\) −12.9619 −0.742196
\(306\) 7.48889 + 5.14378i 0.428111 + 0.294050i
\(307\) 12.2394 + 12.2394i 0.698539 + 0.698539i 0.964095 0.265556i \(-0.0855556\pi\)
−0.265556 + 0.964095i \(0.585556\pi\)
\(308\) 37.9532 13.1834i 2.16258 0.751191i
\(309\) 1.86339 1.66136i 0.106005 0.0945116i
\(310\) 14.5745 + 3.34401i 0.827776 + 0.189927i
\(311\) 0.742777 + 0.428842i 0.0421190 + 0.0243174i 0.520912 0.853611i \(-0.325592\pi\)
−0.478793 + 0.877928i \(0.658925\pi\)
\(312\) −0.857609 16.6298i −0.0485526 0.941474i
\(313\) 15.8984 9.17895i 0.898631 0.518825i 0.0218755 0.999761i \(-0.493036\pi\)
0.876756 + 0.480936i \(0.159703\pi\)
\(314\) −14.3402 + 4.40548i −0.809265 + 0.248616i
\(315\) 3.06548 + 20.6620i 0.172720 + 1.16417i
\(316\) 8.15349 + 12.0177i 0.458670 + 0.676051i
\(317\) 1.07887 4.02641i 0.0605956 0.226146i −0.928987 0.370112i \(-0.879319\pi\)
0.989583 + 0.143967i \(0.0459858\pi\)
\(318\) −1.96724 3.57884i −0.110318 0.200691i
\(319\) 16.2650 28.1718i 0.910666 1.57732i
\(320\) 6.13308 + 11.7990i 0.342849 + 0.659582i
\(321\) −6.44952 12.8126i −0.359977 0.715128i
\(322\) −2.77455 + 0.100650i −0.154619 + 0.00560898i
\(323\) −2.20900 2.20900i −0.122912 0.122912i
\(324\) 6.46035 + 16.8007i 0.358908 + 0.933373i
\(325\) 5.37668 5.37668i 0.298244 0.298244i
\(326\) −5.09109 4.73465i −0.281969 0.262228i
\(327\) −4.49070 + 2.26050i −0.248336 + 0.125006i
\(328\) −7.54275 3.32161i −0.416479 0.183405i
\(329\) 33.4986 + 19.3404i 1.84684 + 1.06627i
\(330\) −18.7510 5.44871i −1.03221 0.299942i
\(331\) −4.99103 1.33734i −0.274332 0.0735070i 0.119030 0.992891i \(-0.462021\pi\)
−0.393362 + 0.919384i \(0.628688\pi\)
\(332\) 2.95746 15.4378i 0.162312 0.847262i
\(333\) 3.05620 0.453427i 0.167478 0.0248476i
\(334\) −0.400317 0.212158i −0.0219044 0.0116088i
\(335\) −8.45344 14.6418i −0.461861 0.799966i
\(336\) 9.93990 + 27.2656i 0.542266 + 1.48746i
\(337\) 1.94762 3.37338i 0.106094 0.183760i −0.808091 0.589058i \(-0.799499\pi\)
0.914185 + 0.405298i \(0.132832\pi\)
\(338\) −1.73334 + 1.08637i −0.0942811 + 0.0590910i
\(339\) 9.51459 + 10.6716i 0.516762 + 0.579603i
\(340\) −2.33593 6.72485i −0.126684 0.364706i
\(341\) −21.5715 + 21.5715i −1.16816 + 1.16816i
\(342\) −1.12968 6.08539i −0.0610862 0.329060i
\(343\) 14.8542i 0.802049i
\(344\) 30.7600 + 4.74395i 1.65847 + 0.255777i
\(345\) 1.12804 + 0.740433i 0.0607315 + 0.0398635i
\(346\) −3.82758 + 16.6821i −0.205772 + 0.896834i
\(347\) 0.816741 + 3.04812i 0.0438449 + 0.163632i 0.984377 0.176073i \(-0.0563395\pi\)
−0.940532 + 0.339705i \(0.889673\pi\)
\(348\) 20.5259 + 11.4365i 1.10030 + 0.613060i
\(349\) −0.374843 + 1.39893i −0.0200649 + 0.0748831i −0.975232 0.221183i \(-0.929008\pi\)
0.955167 + 0.296066i \(0.0956749\pi\)
\(350\) −6.20554 + 11.7091i −0.331700 + 0.625880i
\(351\) −11.3154 + 13.5612i −0.603972 + 0.723844i
\(352\) −27.0414 2.18151i −1.44131 0.116275i
\(353\) 7.73892 + 13.4042i 0.411901 + 0.713434i 0.995098 0.0988971i \(-0.0315315\pi\)
−0.583196 + 0.812331i \(0.698198\pi\)
\(354\) 3.75700 + 0.0788904i 0.199682 + 0.00419298i
\(355\) −13.2920 + 3.56158i −0.705466 + 0.189029i
\(356\) −1.62257 22.3347i −0.0859959 1.18374i
\(357\) −3.15578 15.2126i −0.167022 0.805137i
\(358\) 27.3550 + 25.4398i 1.44576 + 1.34453i
\(359\) 4.78775i 0.252688i −0.991987 0.126344i \(-0.959676\pi\)
0.991987 0.126344i \(-0.0403242\pi\)
\(360\) 3.72849 13.6027i 0.196509 0.716923i
\(361\) 16.8718i 0.887988i
\(362\) 5.59145 6.01239i 0.293880 0.316004i
\(363\) 15.5138 13.8318i 0.814264 0.725981i
\(364\) −18.6236 + 21.5416i −0.976144 + 1.12908i
\(365\) 13.1118 3.51330i 0.686304 0.183895i
\(366\) 16.3378 + 9.89567i 0.853990 + 0.517255i
\(367\) −9.93807 17.2133i −0.518763 0.898524i −0.999762 0.0218032i \(-0.993059\pi\)
0.480999 0.876721i \(-0.340274\pi\)
\(368\) 1.74197 + 0.692854i 0.0908064 + 0.0361175i
\(369\) 3.47720 + 8.02035i 0.181016 + 0.417523i
\(370\) −2.13913 1.13369i −0.111208 0.0589375i
\(371\) −1.80753 + 6.74579i −0.0938422 + 0.350224i
\(372\) −15.8174 15.3418i −0.820096 0.795433i
\(373\) 0.114573 + 0.427591i 0.00593235 + 0.0221398i 0.968829 0.247732i \(-0.0796853\pi\)
−0.962896 + 0.269872i \(0.913019\pi\)
\(374\) 14.1559 + 3.24798i 0.731987 + 0.167949i
\(375\) 18.6109 9.36823i 0.961061 0.483774i
\(376\) −15.4378 21.0679i −0.796144 1.08649i
\(377\) 23.0557i 1.18743i
\(378\) 11.9104 28.3837i 0.612604 1.45990i
\(379\) −6.18132 + 6.18132i −0.317513 + 0.317513i −0.847811 0.530298i \(-0.822080\pi\)
0.530298 + 0.847811i \(0.322080\pi\)
\(380\) −2.11422 + 4.36475i −0.108457 + 0.223907i
\(381\) −0.915351 + 2.77093i −0.0468949 + 0.141959i
\(382\) 12.9194 + 20.6132i 0.661014 + 1.05466i
\(383\) 6.46708 11.2013i 0.330452 0.572360i −0.652148 0.758091i \(-0.726132\pi\)
0.982601 + 0.185731i \(0.0594654\pi\)
\(384\) 1.27741 19.5542i 0.0651874 0.997873i
\(385\) 16.6960 + 28.9183i 0.850907 + 1.47381i
\(386\) 12.1516 22.9287i 0.618501 1.16704i
\(387\) −20.5227 25.8571i −1.04323 1.31439i
\(388\) −12.7504 18.7933i −0.647303 0.954085i
\(389\) −26.4265 7.08096i −1.33988 0.359019i −0.483489 0.875351i \(-0.660631\pi\)
−0.856389 + 0.516331i \(0.827297\pi\)
\(390\) 13.4402 3.30050i 0.680570 0.167127i
\(391\) −0.869168 0.501814i −0.0439557 0.0253778i
\(392\) 12.0218 27.2992i 0.607193 1.37882i
\(393\) −0.755693 + 13.1842i −0.0381197 + 0.665056i
\(394\) 11.9916 12.8944i 0.604128 0.649609i
\(395\) −8.53468 + 8.53468i −0.429426 + 0.429426i
\(396\) 19.4749 + 21.1832i 0.978651 + 1.06449i
\(397\) 21.9741 + 21.9741i 1.10285 + 1.10285i 0.994066 + 0.108781i \(0.0346948\pi\)
0.108781 + 0.994066i \(0.465305\pi\)
\(398\) −0.514105 14.1720i −0.0257698 0.710380i
\(399\) −5.80799 + 8.84839i −0.290763 + 0.442974i
\(400\) 7.02129 5.54711i 0.351064 0.277356i
\(401\) 13.4970 23.3775i 0.674009 1.16742i −0.302749 0.953070i \(-0.597904\pi\)
0.976758 0.214347i \(-0.0687624\pi\)
\(402\) −0.523045 + 24.9090i −0.0260871 + 1.24235i
\(403\) 5.59609 20.8849i 0.278761 1.04035i
\(404\) −5.90120 1.13051i −0.293596 0.0562448i
\(405\) −12.7036 + 7.90055i −0.631248 + 0.392581i
\(406\) −11.8000 38.4099i −0.585622 1.90625i
\(407\) 4.27742 2.46957i 0.212024 0.122412i
\(408\) −2.18972 + 10.2597i −0.108407 + 0.507930i
\(409\) −11.1537 6.43957i −0.551513 0.318416i 0.198219 0.980158i \(-0.436484\pi\)
−0.749732 + 0.661741i \(0.769818\pi\)
\(410\) 1.53183 6.67630i 0.0756517 0.329719i
\(411\) 3.35883 + 16.1914i 0.165679 + 0.798663i
\(412\) 2.59434 + 1.25666i 0.127814 + 0.0619113i
\(413\) −4.54399 4.54399i −0.223595 0.223595i
\(414\) −0.856556 1.79447i −0.0420974 0.0881934i
\(415\) 13.0638 0.641279
\(416\) 17.3710 8.24382i 0.851684 0.404186i
\(417\) 25.0063 + 1.43331i 1.22457 + 0.0701896i
\(418\) −5.25457 8.38379i −0.257009 0.410065i
\(419\) 0.203434 0.0545100i 0.00993841 0.00266299i −0.253846 0.967245i \(-0.581696\pi\)
0.263785 + 0.964582i \(0.415029\pi\)
\(420\) −20.7016 + 12.3772i −1.01014 + 0.603947i
\(421\) −34.2301 9.17194i −1.66827 0.447013i −0.703630 0.710567i \(-0.748439\pi\)
−0.964645 + 0.263554i \(0.915105\pi\)
\(422\) 26.8825 8.25862i 1.30862 0.402023i
\(423\) −3.16535 + 27.5215i −0.153905 + 1.33814i
\(424\) 2.95276 3.67678i 0.143399 0.178560i
\(425\) −4.14862 + 2.39521i −0.201238 + 0.116185i
\(426\) 19.4729 + 5.65850i 0.943467 + 0.274155i
\(427\) −8.45410 31.5511i −0.409123 1.52687i
\(428\) 10.8326 12.5299i 0.523616 0.605655i
\(429\) −8.85631 + 26.8096i −0.427587 + 1.29438i
\(430\) 0.937743 + 25.8502i 0.0452220 + 1.24661i
\(431\) 33.5339 1.61527 0.807635 0.589683i \(-0.200747\pi\)
0.807635 + 0.589683i \(0.200747\pi\)
\(432\) −15.0844 + 14.2990i −0.725750 + 0.687959i
\(433\) −28.9691 −1.39217 −0.696083 0.717962i \(-0.745075\pi\)
−0.696083 + 0.717962i \(0.745075\pi\)
\(434\) 1.36607 + 37.6575i 0.0655733 + 1.80762i
\(435\) −6.12550 + 18.5430i −0.293695 + 0.889067i
\(436\) −4.39162 3.79676i −0.210321 0.181832i
\(437\) 0.176961 + 0.660427i 0.00846519 + 0.0315925i
\(438\) −19.2090 5.58179i −0.917841 0.266708i
\(439\) 14.6656 8.46718i 0.699950 0.404116i −0.107379 0.994218i \(-0.534246\pi\)
0.807329 + 0.590102i \(0.200912\pi\)
\(440\) −2.44788 22.4141i −0.116698 1.06855i
\(441\) −29.0278 + 12.5849i −1.38227 + 0.599282i
\(442\) −9.83987 + 3.02292i −0.468035 + 0.143786i
\(443\) −3.08511 0.826654i −0.146578 0.0392755i 0.184784 0.982779i \(-0.440841\pi\)
−0.331362 + 0.943504i \(0.607508\pi\)
\(444\) 1.83076 + 3.06206i 0.0868842 + 0.145319i
\(445\) 17.9773 4.81702i 0.852208 0.228348i
\(446\) −10.4633 16.6945i −0.495452 0.790506i
\(447\) 2.97621 + 0.170590i 0.140770 + 0.00806863i
\(448\) −24.7202 + 22.6244i −1.16792 + 1.06890i
\(449\) −41.9192 −1.97829 −0.989145 0.146944i \(-0.953056\pi\)
−0.989145 + 0.146944i \(0.953056\pi\)
\(450\) −9.46188 0.741912i −0.446037 0.0349740i
\(451\) 9.88149 + 9.88149i 0.465301 + 0.465301i
\(452\) −7.19689 + 14.8578i −0.338513 + 0.698850i
\(453\) 7.51837 + 36.2427i 0.353244 + 1.70283i
\(454\) 2.39702 10.4471i 0.112498 0.490307i
\(455\) −20.4959 11.8333i −0.960862 0.554754i
\(456\) 5.99711 3.88745i 0.280840 0.182047i
\(457\) −4.93980 + 2.85199i −0.231074 + 0.133411i −0.611067 0.791579i \(-0.709260\pi\)
0.379993 + 0.924989i \(0.375926\pi\)
\(458\) 7.93860 + 25.8409i 0.370947 + 1.20746i
\(459\) 9.09712 6.40745i 0.424617 0.299074i
\(460\) −0.293154 + 1.53025i −0.0136684 + 0.0713484i
\(461\) 10.2715 38.3338i 0.478392 1.78538i −0.129743 0.991548i \(-0.541415\pi\)
0.608135 0.793834i \(-0.291918\pi\)
\(462\) 1.03304 49.1965i 0.0480614 2.28883i
\(463\) −6.28293 + 10.8824i −0.291992 + 0.505746i −0.974281 0.225337i \(-0.927652\pi\)
0.682288 + 0.731083i \(0.260985\pi\)
\(464\) −3.16070 + 26.9472i −0.146732 + 1.25099i
\(465\) 10.0495 15.3103i 0.466035 0.709997i
\(466\) −0.551886 15.2135i −0.0255656 0.704753i
\(467\) 12.1784 + 12.1784i 0.563550 + 0.563550i 0.930314 0.366764i \(-0.119534\pi\)
−0.366764 + 0.930314i \(0.619534\pi\)
\(468\) −19.4604 6.10071i −0.899558 0.282006i
\(469\) 30.1267 30.1267i 1.39112 1.39112i
\(470\) 14.7829 15.8958i 0.681884 0.733219i
\(471\) −1.05139 + 18.3431i −0.0484455 + 0.845206i
\(472\) 1.57145 + 4.04461i 0.0723321 + 0.186168i
\(473\) −45.7025 26.3864i −2.10140 1.21325i
\(474\) 17.2733 4.24178i 0.793387 0.194832i
\(475\) 3.15228 + 0.844652i 0.144637 + 0.0387553i
\(476\) 14.8457 10.0721i 0.680452 0.461656i
\(477\) −4.94756 + 0.734036i −0.226533 + 0.0336092i
\(478\) −14.7586 + 27.8478i −0.675043 + 1.27373i
\(479\) −10.6864 18.5094i −0.488275 0.845717i 0.511634 0.859204i \(-0.329040\pi\)
−0.999909 + 0.0134862i \(0.995707\pi\)
\(480\) 16.1612 2.01507i 0.737655 0.0919749i
\(481\) −1.75031 + 3.03162i −0.0798072 + 0.138230i
\(482\) 20.6214 + 32.9019i 0.939278 + 1.49864i
\(483\) −1.06658 + 3.22874i −0.0485313 + 0.146913i
\(484\) 21.5994 + 10.4624i 0.981790 + 0.475565i
\(485\) 13.3465 13.3465i 0.606033 0.606033i
\(486\) 22.0439 0.259753i 0.999931 0.0117826i
\(487\) 39.3716i 1.78410i −0.451939 0.892049i \(-0.649268\pi\)
0.451939 0.892049i \(-0.350732\pi\)
\(488\) −3.36182 + 21.7982i −0.152182 + 0.986759i
\(489\) −7.60570 + 3.82851i −0.343942 + 0.173131i
\(490\) 24.1633 + 5.54410i 1.09159 + 0.250457i
\(491\) 9.08087 + 33.8903i 0.409814 + 1.52945i 0.795001 + 0.606608i \(0.207470\pi\)
−0.385187 + 0.922839i \(0.625863\pi\)
\(492\) −7.02777 + 7.24567i −0.316836 + 0.326660i
\(493\) 3.75940 14.0303i 0.169315 0.631891i
\(494\) 6.19624 + 3.28385i 0.278782 + 0.147747i
\(495\) −14.2457 + 19.2092i −0.640297 + 0.863389i
\(496\) 9.40375 23.6428i 0.422241 1.06160i
\(497\) −17.3388 30.0317i −0.777752 1.34711i
\(498\) −16.4663 9.97351i −0.737873 0.446924i
\(499\) −12.6475 + 3.38889i −0.566181 + 0.151708i −0.530544 0.847657i \(-0.678012\pi\)
−0.0356364 + 0.999365i \(0.511346\pi\)
\(500\) 18.2003 + 15.7349i 0.813940 + 0.703688i
\(501\) −0.414172 + 0.369267i −0.0185039 + 0.0164976i
\(502\) 15.5440 16.7142i 0.693762 0.745991i
\(503\) 2.93881i 0.131035i 0.997851 + 0.0655175i \(0.0208698\pi\)
−0.997851 + 0.0655175i \(0.979130\pi\)
\(504\) 35.5427 + 0.203669i 1.58320 + 0.00907212i
\(505\) 4.99373i 0.222218i
\(506\) −2.32769 2.16472i −0.103478 0.0962337i
\(507\) 0.508897 + 2.45317i 0.0226009 + 0.108949i
\(508\) −3.36080 + 0.244154i −0.149111 + 0.0108326i
\(509\) −15.3559 + 4.11461i −0.680640 + 0.182377i −0.582543 0.812800i \(-0.697942\pi\)
−0.0980972 + 0.995177i \(0.531276\pi\)
\(510\) −8.71704 0.183043i −0.385997 0.00810527i
\(511\) 17.1038 + 29.6246i 0.756627 + 1.31052i
\(512\) 21.4332 7.25389i 0.947222 0.320580i
\(513\) −7.46884 1.29566i −0.329757 0.0572048i
\(514\) −1.23228 + 2.32517i −0.0543535 + 0.102559i
\(515\) −0.620083 + 2.31418i −0.0273241 + 0.101975i
\(516\) 18.5532 33.2987i 0.816758 1.46590i
\(517\) 11.4621 + 42.7772i 0.504103 + 1.88134i
\(518\) 1.36436 5.94638i 0.0599463 0.261269i
\(519\) 17.5243 + 11.5027i 0.769230 + 0.504914i
\(520\) 9.44551 + 12.8902i 0.414213 + 0.565274i
\(521\) 19.2119i 0.841689i −0.907133 0.420844i \(-0.861734\pi\)
0.907133 0.420844i \(-0.138266\pi\)
\(522\) 21.8774 18.6960i 0.957547 0.818302i
\(523\) −10.0495 + 10.0495i −0.439436 + 0.439436i −0.891822 0.452386i \(-0.850573\pi\)
0.452386 + 0.891822i \(0.350573\pi\)
\(524\) −14.4045 + 5.00354i −0.629265 + 0.218581i
\(525\) 10.8009 + 12.1144i 0.471392 + 0.528716i
\(526\) −0.0574010 + 0.0359762i −0.00250280 + 0.00156864i
\(527\) −6.81087 + 11.7968i −0.296686 + 0.513875i
\(528\) −14.0265 + 30.1207i −0.610424 + 1.31083i
\(529\) −11.3902 19.7284i −0.495225 0.857755i
\(530\) 3.46296 + 1.83528i 0.150422 + 0.0797196i
\(531\) 1.69133 4.28034i 0.0733976 0.185751i
\(532\) −12.0034 2.29952i −0.520413 0.0996967i
\(533\) −9.56697 2.56346i −0.414392 0.111036i
\(534\) −26.3370 7.65308i −1.13972 0.331181i
\(535\) 11.9217 + 6.88297i 0.515418 + 0.297577i
\(536\) −26.8158 + 10.4188i −1.15827 + 0.450022i
\(537\) 40.8662 20.5710i 1.76351 0.887705i
\(538\) −21.3358 19.8420i −0.919852 0.855451i
\(539\) −35.7637 + 35.7637i −1.54045 + 1.54045i
\(540\) −14.0306 10.0769i −0.603779 0.433641i
\(541\) 15.3802 + 15.3802i 0.661246 + 0.661246i 0.955674 0.294428i \(-0.0951290\pi\)
−0.294428 + 0.955674i \(0.595129\pi\)
\(542\) −22.3026 + 0.809049i −0.957977 + 0.0347516i
\(543\) −4.52133 8.98205i −0.194029 0.385457i
\(544\) −11.9151 + 2.18421i −0.510857 + 0.0936472i
\(545\) 2.41243 4.17844i 0.103337 0.178985i
\(546\) 16.8000 + 30.5627i 0.718972 + 1.30796i
\(547\) 6.19933 23.1362i 0.265064 0.989233i −0.697147 0.716928i \(-0.745548\pi\)
0.962211 0.272304i \(-0.0877858\pi\)
\(548\) −15.8009 + 10.7202i −0.674981 + 0.457944i
\(549\) 18.3237 14.5435i 0.782036 0.620702i
\(550\) −14.5033 + 4.45558i −0.618423 + 0.189986i
\(551\) −8.56961 + 4.94767i −0.365078 + 0.210778i
\(552\) 1.53777 1.70500i 0.0654517 0.0725696i
\(553\) −26.3412 15.2081i −1.12014 0.646714i
\(554\) 10.2943 + 2.36195i 0.437362 + 0.100350i
\(555\) −2.21317 + 1.97321i −0.0939438 + 0.0837583i
\(556\) 9.49015 + 27.3209i 0.402472 + 1.15866i
\(557\) 0.932077 + 0.932077i 0.0394934 + 0.0394934i 0.726578 0.687084i \(-0.241110\pi\)
−0.687084 + 0.726578i \(0.741110\pi\)
\(558\) −24.3554 + 11.6256i −1.03105 + 0.492151i
\(559\) 37.4027 1.58197
\(560\) −22.3331 16.6404i −0.943747 0.703185i
\(561\) 9.76092 14.8706i 0.412106 0.627838i
\(562\) 8.08680 5.06843i 0.341121 0.213799i
\(563\) 6.39635 1.71390i 0.269574 0.0722321i −0.121500 0.992591i \(-0.538770\pi\)
0.391074 + 0.920359i \(0.372104\pi\)
\(564\) −30.7686 + 8.74994i −1.29559 + 0.368439i
\(565\) −13.2533 3.55121i −0.557570 0.149400i
\(566\) −5.34926 17.4123i −0.224846 0.731893i
\(567\) −27.5167 25.7695i −1.15559 1.08222i
\(568\) 2.54213 + 23.2771i 0.106665 + 0.976685i
\(569\) −7.84553 + 4.52962i −0.328902 + 0.189892i −0.655353 0.755322i \(-0.727480\pi\)
0.326452 + 0.945214i \(0.394147\pi\)
\(570\) 4.11098 + 4.28733i 0.172190 + 0.179577i
\(571\) 4.79838 + 17.9078i 0.200806 + 0.749417i 0.990687 + 0.136158i \(0.0434754\pi\)
−0.789881 + 0.613260i \(0.789858\pi\)
\(572\) −32.5168 + 2.36227i −1.35959 + 0.0987714i
\(573\) 29.1736 6.05192i 1.21874 0.252823i
\(574\) 17.2502 0.625769i 0.720009 0.0261191i
\(575\) 1.04844 0.0437230
\(576\) −21.9088 9.79827i −0.912865 0.408261i
\(577\) 43.3455 1.80450 0.902248 0.431217i \(-0.141916\pi\)
0.902248 + 0.431217i \(0.141916\pi\)
\(578\) −17.5450 + 0.636463i −0.729775 + 0.0264734i
\(579\) −21.1502 23.7223i −0.878974 0.985863i
\(580\) −22.4903 + 1.63387i −0.933860 + 0.0678428i
\(581\) 8.52060 + 31.7993i 0.353494 + 1.31926i
\(582\) −27.0119 + 6.63328i −1.11968 + 0.274958i
\(583\) −6.92456 + 3.99790i −0.286786 + 0.165576i
\(584\) −2.50767 22.9616i −0.103768 0.950156i
\(585\) 1.93670 16.8389i 0.0800727 0.696201i
\(586\) −5.96717 19.4236i −0.246501 0.802383i
\(587\) 25.4359 + 6.81553i 1.04985 + 0.281307i 0.742191 0.670189i \(-0.233787\pi\)
0.307662 + 0.951496i \(0.400453\pi\)
\(588\) −26.2240 25.4354i −1.08146 1.04894i
\(589\) 8.96364 2.40180i 0.369341 0.0989645i
\(590\) −3.05574 + 1.91520i −0.125803 + 0.0788474i
\(591\) −9.69660 19.2632i −0.398865 0.792382i
\(592\) −2.46135 + 3.30338i −0.101161 + 0.135768i
\(593\) 41.9274 1.72175 0.860876 0.508814i \(-0.169916\pi\)
0.860876 + 0.508814i \(0.169916\pi\)
\(594\) 32.6211 13.3364i 1.33846 0.547200i
\(595\) 10.5430 + 10.5430i 0.432222 + 0.432222i
\(596\) 1.12950 + 3.25168i 0.0462661 + 0.133194i
\(597\) −16.4920 5.44797i −0.674972 0.222971i
\(598\) 2.19585 + 0.503823i 0.0897950 + 0.0206028i
\(599\) 21.1742 + 12.2249i 0.865154 + 0.499497i 0.865735 0.500503i \(-0.166852\pi\)
−0.000580933 1.00000i \(0.500185\pi\)
\(600\) −3.37787 10.4256i −0.137901 0.425624i
\(601\) −24.7521 + 14.2906i −1.00966 + 0.582928i −0.911092 0.412203i \(-0.864760\pi\)
−0.0985682 + 0.995130i \(0.531426\pi\)
\(602\) −62.3115 + 19.1428i −2.53963 + 0.780202i
\(603\) 28.3787 + 11.2136i 1.15567 + 0.456652i
\(604\) −35.3686 + 23.9960i −1.43913 + 0.976383i
\(605\) −5.16255 + 19.2669i −0.209887 + 0.783310i
\(606\) −3.81243 + 6.29434i −0.154869 + 0.255690i
\(607\) −9.32245 + 16.1470i −0.378387 + 0.655385i −0.990828 0.135131i \(-0.956854\pi\)
0.612441 + 0.790516i \(0.290188\pi\)
\(608\) 6.79192 + 4.68757i 0.275449 + 0.190106i
\(609\) −49.1315 2.81612i −1.99091 0.114115i
\(610\) −18.3188 + 0.664535i −0.741708 + 0.0269062i
\(611\) −22.1946 22.1946i −0.897896 0.897896i
\(612\) 10.8476 + 6.88568i 0.438490 + 0.278337i
\(613\) −13.3177 + 13.3177i −0.537896 + 0.537896i −0.922911 0.385014i \(-0.874196\pi\)
0.385014 + 0.922911i \(0.374196\pi\)
\(614\) 17.9252 + 16.6702i 0.723404 + 0.672757i
\(615\) −7.01335 4.60349i −0.282806 0.185631i
\(616\) 52.9627 20.5776i 2.13393 0.829096i
\(617\) 15.1035 + 8.72003i 0.608045 + 0.351055i 0.772200 0.635379i \(-0.219156\pi\)
−0.164155 + 0.986435i \(0.552490\pi\)
\(618\) 2.54833 2.44351i 0.102509 0.0982924i
\(619\) −21.8310 5.84959i −0.877461 0.235115i −0.208150 0.978097i \(-0.566744\pi\)
−0.669311 + 0.742982i \(0.733411\pi\)
\(620\) 20.7693 + 3.97883i 0.834117 + 0.159794i
\(621\) −2.42544 + 0.218963i −0.0973297 + 0.00878667i
\(622\) 1.07174 + 0.567995i 0.0429729 + 0.0227745i
\(623\) 23.4506 + 40.6177i 0.939530 + 1.62731i
\(624\) −2.06463 23.4586i −0.0826512 0.939095i
\(625\) −4.40527 + 7.63015i −0.176211 + 0.305206i
\(626\) 21.9984 13.7876i 0.879232 0.551061i
\(627\) −11.8655 + 2.46143i −0.473861 + 0.0983001i
\(628\) −20.0409 + 6.96139i −0.799720 + 0.277790i
\(629\) 1.55946 1.55946i 0.0621797 0.0621797i
\(630\) 5.39170 + 29.0441i 0.214810 + 1.15714i
\(631\) 19.8510i 0.790254i 0.918627 + 0.395127i \(0.129299\pi\)
−0.918627 + 0.395127i \(0.870701\pi\)
\(632\) 12.1393 + 16.5665i 0.482877 + 0.658979i
\(633\) 1.97096 34.3865i 0.0783387 1.36674i
\(634\) 1.31833 5.74578i 0.0523575 0.228194i
\(635\) −0.724836 2.70512i −0.0287642 0.107350i
\(636\) −2.96376 4.95706i −0.117521 0.196560i
\(637\) 9.27785 34.6254i 0.367602 1.37191i
\(638\) 21.5428 40.6487i 0.852886 1.60930i
\(639\) 14.7942 19.9488i 0.585249 0.789161i
\(640\) 9.27269 + 16.3608i 0.366535 + 0.646719i
\(641\) 20.5842 + 35.6529i 0.813026 + 1.40820i 0.910736 + 0.412988i \(0.135515\pi\)
−0.0977099 + 0.995215i \(0.531152\pi\)
\(642\) −9.77188 17.7771i −0.385665 0.701608i
\(643\) −25.1215 + 6.73128i −0.990694 + 0.265456i −0.717542 0.696515i \(-0.754733\pi\)
−0.273152 + 0.961971i \(0.588066\pi\)
\(644\) −3.91606 + 0.284493i −0.154314 + 0.0112106i
\(645\) 30.0818 + 9.93726i 1.18447 + 0.391279i
\(646\) −3.23520 3.00869i −0.127287 0.118375i
\(647\) 40.3426i 1.58603i −0.609201 0.793016i \(-0.708510\pi\)
0.609201 0.793016i \(-0.291490\pi\)
\(648\) 9.99165 + 23.4130i 0.392509 + 0.919748i
\(649\) 7.35741i 0.288803i
\(650\) 7.32312 7.87443i 0.287236 0.308860i
\(651\) 43.8220 + 14.4762i 1.71752 + 0.567367i
\(652\) −7.43789 6.43039i −0.291290 0.251834i
\(653\) −6.29024 + 1.68547i −0.246156 + 0.0659574i −0.379787 0.925074i \(-0.624003\pi\)
0.133631 + 0.991031i \(0.457336\pi\)
\(654\) −6.23074 + 3.42497i −0.243641 + 0.133927i
\(655\) −6.33671 10.9755i −0.247596 0.428849i
\(656\) −10.8303 4.30768i −0.422854 0.168187i
\(657\) −14.5937 + 19.6784i −0.569353 + 0.767726i
\(658\) 48.3345 + 25.6161i 1.88428 + 0.998618i
\(659\) −0.0237696 + 0.0887093i −0.000925932 + 0.00345562i −0.966387 0.257091i \(-0.917236\pi\)
0.965461 + 0.260546i \(0.0839027\pi\)
\(660\) −26.7799 6.73925i −1.04240 0.262325i
\(661\) −7.23883 27.0157i −0.281558 1.05079i −0.951318 0.308211i \(-0.900270\pi\)
0.669760 0.742578i \(-0.266397\pi\)
\(662\) −7.12231 1.63416i −0.276816 0.0635136i
\(663\) −0.721435 + 12.5865i −0.0280182 + 0.488821i
\(664\) 3.38826 21.9697i 0.131490 0.852589i
\(665\) 10.1575i 0.393892i
\(666\) 4.29603 0.797507i 0.166468 0.0309028i
\(667\) −2.24790 + 2.24790i −0.0870392 + 0.0870392i
\(668\) −0.576639 0.279316i −0.0223108 0.0108070i
\(669\) −23.6274 + 4.90140i −0.913490 + 0.189499i
\(670\) −12.6978 20.2596i −0.490558 0.782697i
\(671\) 18.6988 32.3873i 0.721859 1.25030i
\(672\) 15.4458 + 38.0245i 0.595833 + 1.46683i
\(673\) 2.48158 + 4.29822i 0.0956578 + 0.165684i 0.909883 0.414865i \(-0.136171\pi\)
−0.814225 + 0.580549i \(0.802838\pi\)
\(674\) 2.57959 4.86739i 0.0993622 0.187485i
\(675\) −4.88333 + 10.5484i −0.187959 + 0.406009i
\(676\) −2.39400 + 1.62422i −0.0920769 + 0.0624700i
\(677\) −6.63841 1.77876i −0.255135 0.0683632i 0.128985 0.991647i \(-0.458828\pi\)
−0.384119 + 0.923283i \(0.625495\pi\)
\(678\) 13.9939 + 14.5942i 0.537434 + 0.560488i
\(679\) 41.1923 + 23.7824i 1.58081 + 0.912683i
\(680\) −3.64611 9.38436i −0.139822 0.359874i
\(681\) −10.9745 7.20357i −0.420545 0.276041i
\(682\) −29.3807 + 31.5926i −1.12504 + 1.20974i
\(683\) 20.7192 20.7192i 0.792797 0.792797i −0.189151 0.981948i \(-0.560574\pi\)
0.981948 + 0.189151i \(0.0605737\pi\)
\(684\) −1.90855 8.54247i −0.0729752 0.326629i
\(685\) −11.2214 11.2214i −0.428747 0.428747i
\(686\) 0.761549 + 20.9932i 0.0290761 + 0.801522i
\(687\) 33.0540 + 1.89459i 1.26109 + 0.0722831i
\(688\) 43.7159 + 5.12753i 1.66665 + 0.195485i
\(689\) 2.83351 4.90779i 0.107948 0.186972i
\(690\) 1.63220 + 0.988609i 0.0621367 + 0.0376357i
\(691\) 1.42402 5.31450i 0.0541721 0.202173i −0.933536 0.358484i \(-0.883294\pi\)
0.987708 + 0.156311i \(0.0499603\pi\)
\(692\) −4.55420 + 23.7727i −0.173125 + 0.903704i
\(693\) −56.0494 22.1474i −2.12914 0.841310i
\(694\) 1.31056 + 4.26598i 0.0497481 + 0.161934i
\(695\) −20.8171 + 12.0188i −0.789638 + 0.455898i
\(696\) 29.5953 + 15.1107i 1.12181 + 0.572769i
\(697\) 5.40388 + 3.11993i 0.204687 + 0.118176i
\(698\) −0.458038 + 1.99631i −0.0173370 + 0.0755613i
\(699\) −17.7040 5.84834i −0.669626 0.221205i
\(700\) −8.16989 + 16.8665i −0.308793 + 0.637493i
\(701\) −1.06232 1.06232i −0.0401233 0.0401233i 0.686760 0.726884i \(-0.259032\pi\)
−0.726884 + 0.686760i \(0.759032\pi\)
\(702\) −15.2966 + 19.7460i −0.577334 + 0.745263i
\(703\) −1.50244 −0.0566656
\(704\) −38.3291 1.69673i −1.44458 0.0639478i
\(705\) −11.9537 23.7471i −0.450202 0.894368i
\(706\) 11.6245 + 18.5472i 0.437494 + 0.698033i
\(707\) 12.1555 3.25705i 0.457153 0.122494i
\(708\) 5.31375 0.0811206i 0.199703 0.00304870i
\(709\) 35.4604 + 9.50159i 1.33174 + 0.356840i 0.853365 0.521314i \(-0.174558\pi\)
0.478379 + 0.878153i \(0.341224\pi\)
\(710\) −18.6028 + 5.71498i −0.698149 + 0.214479i
\(711\) 2.48904 21.6412i 0.0933463 0.811609i
\(712\) −3.43821 31.4821i −0.128853 1.17984i
\(713\) 2.58187 1.49064i 0.0966916 0.0558249i
\(714\) −5.23994 21.3379i −0.196100 0.798552i
\(715\) −7.01301 26.1729i −0.262272 0.978812i
\(716\) 39.9646 + 34.5512i 1.49355 + 1.29124i
\(717\) 25.6878 + 28.8116i 0.959328 + 1.07599i
\(718\) −0.245460 6.76644i −0.00916048 0.252521i
\(719\) −7.37513 −0.275046 −0.137523 0.990499i \(-0.543914\pi\)
−0.137523 + 0.990499i \(0.543914\pi\)
\(720\) 4.57203 19.4156i 0.170390 0.723575i
\(721\) −6.03749 −0.224848
\(722\) −0.864988 23.8446i −0.0321915 0.887404i
\(723\) 46.5656 9.65981i 1.73179 0.359252i
\(724\) 7.59406 8.78388i 0.282231 0.326450i
\(725\) 3.92726 + 14.6567i 0.145855 + 0.544337i
\(726\) 21.2163 20.3436i 0.787411 0.755022i
\(727\) −5.80127 + 3.34936i −0.215157 + 0.124221i −0.603706 0.797207i \(-0.706310\pi\)
0.388549 + 0.921428i \(0.372977\pi\)
\(728\) −25.2161 + 31.3991i −0.934571 + 1.16373i
\(729\) 9.09400 25.4224i 0.336815 0.941571i
\(730\) 18.3506 5.63751i 0.679186 0.208654i
\(731\) −22.7610 6.09879i −0.841846 0.225572i
\(732\) 23.5973 + 13.1478i 0.872181 + 0.485956i
\(733\) 34.6439 9.28281i 1.27960 0.342868i 0.445900 0.895083i \(-0.352884\pi\)
0.833702 + 0.552214i \(0.186217\pi\)
\(734\) −14.9278 23.8177i −0.550996 0.879127i
\(735\) 16.6613 25.3832i 0.614560 0.936272i
\(736\) 2.49742 + 0.889891i 0.0920560 + 0.0328018i
\(737\) 48.7797 1.79682
\(738\) 5.32547 + 11.1568i 0.196033 + 0.410686i
\(739\) 4.01107 + 4.01107i 0.147549 + 0.147549i 0.777022 0.629473i \(-0.216729\pi\)
−0.629473 + 0.777022i \(0.716729\pi\)
\(740\) −3.08132 1.49255i −0.113272 0.0548672i
\(741\) 6.41070 5.71564i 0.235503 0.209969i
\(742\) −2.20871 + 9.62638i −0.0810841 + 0.353396i
\(743\) −19.1551 11.0592i −0.702734 0.405724i 0.105631 0.994405i \(-0.466314\pi\)
−0.808365 + 0.588682i \(0.799647\pi\)
\(744\) −23.1411 20.8713i −0.848393 0.765180i
\(745\) −2.47761 + 1.43045i −0.0907726 + 0.0524076i
\(746\) 0.183846 + 0.598434i 0.00673107 + 0.0219102i
\(747\) −18.4678 + 14.6579i −0.675703 + 0.536305i
\(748\) 20.1729 + 3.86457i 0.737594 + 0.141303i
\(749\) −8.97853 + 33.5083i −0.328068 + 1.22437i
\(750\) 25.8222 14.1941i 0.942892 0.518296i
\(751\) −6.05672 + 10.4905i −0.221013 + 0.382805i −0.955116 0.296233i \(-0.904270\pi\)
0.734103 + 0.679038i \(0.237603\pi\)
\(752\) −22.8981 28.9834i −0.835008 1.05692i
\(753\) −12.5691 24.9697i −0.458044 0.909947i
\(754\) 1.18203 + 32.5842i 0.0430469 + 1.18665i
\(755\) −25.1178 25.1178i −0.914131 0.914131i
\(756\) 15.3776 40.7249i 0.559277 1.48115i
\(757\) −19.9365 + 19.9365i −0.724604 + 0.724604i −0.969539 0.244935i \(-0.921233\pi\)
0.244935 + 0.969539i \(0.421233\pi\)
\(758\) −8.41906 + 9.05287i −0.305794 + 0.328815i
\(759\) −3.47739 + 1.75043i −0.126221 + 0.0635366i
\(760\) −2.76422 + 6.27702i −0.100269 + 0.227691i
\(761\) 37.1681 + 21.4590i 1.34734 + 0.777889i 0.987873 0.155267i \(-0.0496237\pi\)
0.359471 + 0.933156i \(0.382957\pi\)
\(762\) −1.15159 + 3.96304i −0.0417177 + 0.143566i
\(763\) 11.7444 + 3.14690i 0.425176 + 0.113925i
\(764\) 19.3156 + 28.4700i 0.698814 + 1.03001i
\(765\) −3.92426 + 9.93130i −0.141882 + 0.359067i
\(766\) 8.56555 16.1622i 0.309486 0.583964i
\(767\) 2.60728 + 4.51595i 0.0941435 + 0.163061i
\(768\) 0.802824 27.7012i 0.0289694 0.999580i
\(769\) −13.7618 + 23.8361i −0.496263 + 0.859553i −0.999991 0.00430961i \(-0.998628\pi\)
0.503728 + 0.863863i \(0.331962\pi\)
\(770\) 25.0788 + 40.0138i 0.903777 + 1.44200i
\(771\) 2.14482 + 2.40564i 0.0772438 + 0.0866371i
\(772\) 15.9982 33.0277i 0.575786 1.18869i
\(773\) −11.4688 + 11.4688i −0.412504 + 0.412504i −0.882610 0.470106i \(-0.844216\pi\)
0.470106 + 0.882610i \(0.344216\pi\)
\(774\) −30.3301 35.4912i −1.09019 1.27570i
\(775\) 14.2300i 0.511155i
\(776\) −18.9834 25.9066i −0.681465 0.929992i
\(777\) −6.24658 4.10019i −0.224095 0.147094i
\(778\) −37.7112 8.65257i −1.35201 0.310210i
\(779\) −1.10022 4.10608i −0.0394195 0.147115i
\(780\) 18.8256 5.35360i 0.674064 0.191689i
\(781\) 10.2759 38.3500i 0.367699 1.37227i
\(782\) −1.25411 0.664645i −0.0448468 0.0237677i
\(783\) −12.1462 33.0864i −0.434071 1.18241i
\(784\) 15.5906 39.1979i 0.556808 1.39992i
\(785\) −8.81622 15.2701i −0.314664 0.545015i
\(786\) −0.392075 + 18.6718i −0.0139849 + 0.666001i
\(787\) −42.8263 + 11.4753i −1.52659 + 0.409049i −0.921906 0.387414i \(-0.873368\pi\)
−0.604687 + 0.796463i \(0.706702\pi\)
\(788\) 16.2865 18.8382i 0.580181 0.671083i
\(789\) 0.0168526 + 0.0812387i 0.000599968 + 0.00289217i
\(790\) −11.6244 + 12.4995i −0.413576 + 0.444712i
\(791\) 34.5766i 1.22940i
\(792\) 28.6096 + 28.9394i 1.01660 + 1.02832i
\(793\) 26.5056i 0.941241i
\(794\) 32.1822 + 29.9290i 1.14210 + 1.06214i
\(795\) 3.58282 3.19437i 0.127070 0.113292i
\(796\) −1.45315 20.0027i −0.0515057 0.708978i
\(797\) −28.6863 + 7.68647i −1.01612 + 0.272269i −0.728185 0.685381i \(-0.759636\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(798\) −7.75470 + 12.8031i −0.274514 + 0.453223i
\(799\) 9.88726 + 17.1252i 0.349786 + 0.605847i
\(800\) 9.63868 8.19961i 0.340779 0.289900i
\(801\) −20.0091 + 26.9806i −0.706985 + 0.953312i
\(802\) 17.8766 33.7310i 0.631244 1.19108i
\(803\) −10.1366 + 37.8302i −0.357712 + 1.33500i
\(804\) 0.537831 + 35.2302i 0.0189678 + 1.24247i
\(805\) −0.844592 3.15206i −0.0297679 0.111096i
\(806\) 6.83813 29.8032i 0.240863 1.04977i
\(807\) −31.8741 + 16.0446i −1.12202 + 0.564796i
\(808\) −8.39803 1.29518i −0.295442 0.0455643i
\(809\) 16.7474i 0.588806i 0.955681 + 0.294403i \(0.0951209\pi\)
−0.955681 + 0.294403i \(0.904879\pi\)
\(810\) −17.5488 + 11.8170i −0.616601 + 0.415208i
\(811\) −7.60619 + 7.60619i −0.267090 + 0.267090i −0.827926 0.560837i \(-0.810480\pi\)
0.560837 + 0.827926i \(0.310480\pi\)
\(812\) −18.6459 53.6791i −0.654343 1.88377i
\(813\) −8.57349 + 25.9535i −0.300685 + 0.910229i
\(814\) 5.91860 3.70950i 0.207447 0.130018i
\(815\) 4.08582 7.07684i 0.143120 0.247891i
\(816\) −2.56869 + 14.6121i −0.0899223 + 0.511526i
\(817\) 8.02649 + 13.9023i 0.280811 + 0.486379i
\(818\) −16.0934 8.52912i −0.562694 0.298214i
\(819\) 42.2514 6.26855i 1.47638 0.219041i
\(820\) 1.82263 9.51404i 0.0636489 0.332245i
\(821\) 37.2860 + 9.99074i 1.30129 + 0.348679i 0.841937 0.539575i \(-0.181415\pi\)
0.459351 + 0.888255i \(0.348082\pi\)
\(822\) 5.57709 + 22.7109i 0.194523 + 0.792132i
\(823\) 23.9783 + 13.8439i 0.835831 + 0.482567i 0.855845 0.517233i \(-0.173038\pi\)
−0.0200141 + 0.999800i \(0.506371\pi\)
\(824\) 3.73097 + 1.64301i 0.129975 + 0.0572371i
\(825\) −1.06335 + 18.5517i −0.0370210 + 0.645888i
\(826\) −6.65491 6.18898i −0.231554 0.215342i
\(827\) −27.6025 + 27.6025i −0.959833 + 0.959833i −0.999224 0.0393907i \(-0.987458\pi\)
0.0393907 + 0.999224i \(0.487458\pi\)
\(828\) −1.30256 2.49218i −0.0452670 0.0866093i
\(829\) 14.8542 + 14.8542i 0.515908 + 0.515908i 0.916330 0.400423i \(-0.131137\pi\)
−0.400423 + 0.916330i \(0.631137\pi\)
\(830\) 18.4629 0.669762i 0.640858 0.0232478i
\(831\) 7.09819 10.8140i 0.246234 0.375133i
\(832\) 24.1275 12.5414i 0.836471 0.434796i
\(833\) −11.2919 + 19.5581i −0.391240 + 0.677647i
\(834\) 35.4145 + 0.743644i 1.22631 + 0.0257503i
\(835\) 0.137824 0.514368i 0.00476961 0.0178004i
\(836\) −7.85602 11.5793i −0.271706 0.400478i
\(837\) 2.97187 + 32.9193i 0.102723 + 1.13786i
\(838\) 0.284716 0.0874679i 0.00983534 0.00302153i
\(839\) 44.0413 25.4272i 1.52047 0.877846i 0.520766 0.853700i \(-0.325647\pi\)
0.999708 0.0241463i \(-0.00768676\pi\)
\(840\) −28.6227 + 18.5539i −0.987578 + 0.640169i
\(841\) −14.7301 8.50445i −0.507936 0.293257i
\(842\) −48.8471 11.2076i −1.68338 0.386240i
\(843\) −2.37424 11.4451i −0.0817731 0.394191i
\(844\) 37.5693 13.0500i 1.29319 0.449200i
\(845\) −1.70015 1.70015i −0.0584871 0.0584871i
\(846\) −3.06256 + 39.0580i −0.105293 + 1.34284i
\(847\) −50.2656 −1.72715
\(848\) 3.98458 5.34772i 0.136831 0.183641i
\(849\) −22.2727 1.27663i −0.764398 0.0438137i
\(850\) −5.74038 + 3.59780i −0.196894 + 0.123404i
\(851\) −0.466233 + 0.124927i −0.0159823 + 0.00428244i
\(852\) 27.8109 + 6.99872i 0.952786 + 0.239772i
\(853\) −13.6365 3.65390i −0.466906 0.125107i 0.0176931 0.999843i \(-0.494368\pi\)
−0.484599 + 0.874736i \(0.661034\pi\)
\(854\) −13.5656 44.1573i −0.464206 1.51103i
\(855\) 6.67448 2.89370i 0.228262 0.0989625i
\(856\) 14.6672 18.2637i 0.501315 0.624239i
\(857\) −14.7618 + 8.52275i −0.504255 + 0.291132i −0.730469 0.682946i \(-0.760698\pi\)
0.226214 + 0.974078i \(0.427365\pi\)
\(858\) −11.1420 + 38.3437i −0.380382 + 1.30903i
\(859\) −6.67877 24.9255i −0.227877 0.850448i −0.981232 0.192833i \(-0.938232\pi\)
0.753355 0.657614i \(-0.228434\pi\)
\(860\) 2.65059 + 36.4856i 0.0903845 + 1.24415i
\(861\) 6.63128 20.0741i 0.225993 0.684122i
\(862\) 47.3929 1.71923i 1.61421 0.0585571i
\(863\) −18.8217 −0.640698 −0.320349 0.947300i \(-0.603800\pi\)
−0.320349 + 0.947300i \(0.603800\pi\)
\(864\) −20.5855 + 20.9818i −0.700333 + 0.713817i
\(865\) −20.1170 −0.683999
\(866\) −40.9415 + 1.48520i −1.39125 + 0.0504691i
\(867\) −6.74459 + 20.4171i −0.229058 + 0.693401i
\(868\) 3.86128 + 53.1507i 0.131060 + 1.80405i
\(869\) −9.01309 33.6373i −0.305748 1.14107i
\(870\) −7.70640 + 26.5205i −0.261271 + 0.899130i
\(871\) −29.9408 + 17.2863i −1.01450 + 0.585725i
\(872\) −6.40126 5.14074i −0.216774 0.174088i
\(873\) −3.89235 + 33.8424i −0.131736 + 1.14539i
\(874\) 0.283955 + 0.924299i 0.00960492 + 0.0312649i
\(875\) −48.6724 13.0417i −1.64543 0.440891i
\(876\) −27.4339 6.90385i −0.926906 0.233259i
\(877\) −10.4503 + 2.80014i −0.352880 + 0.0945540i −0.430905 0.902397i \(-0.641805\pi\)
0.0780244 + 0.996951i \(0.475139\pi\)
\(878\) 20.2925 12.7184i 0.684840 0.429225i
\(879\) −24.8455 1.42409i −0.838018 0.0480335i
\(880\) −4.60869 31.5520i −0.155359 1.06362i
\(881\) 40.1658 1.35322 0.676610 0.736342i \(-0.263448\pi\)
0.676610 + 0.736342i \(0.263448\pi\)
\(882\) −40.3793 + 19.2743i −1.35964 + 0.648998i
\(883\) −16.5617 16.5617i −0.557346 0.557346i 0.371205 0.928551i \(-0.378945\pi\)
−0.928551 + 0.371205i \(0.878945\pi\)
\(884\) −13.7516 + 4.77672i −0.462515 + 0.160658i
\(885\) 0.897148 + 4.32475i 0.0301573 + 0.145375i
\(886\) −4.40252 1.01013i −0.147906 0.0339359i
\(887\) 13.1259 + 7.57822i 0.440723 + 0.254452i 0.703904 0.710295i \(-0.251438\pi\)
−0.263181 + 0.964746i \(0.584772\pi\)
\(888\) 2.74437 + 4.23370i 0.0920952 + 0.142074i
\(889\) 6.11191 3.52871i 0.204987 0.118349i
\(890\) 25.1601 7.72948i 0.843370 0.259093i
\(891\) −1.41453 43.1393i −0.0473885 1.44522i
\(892\) −15.6435 23.0576i −0.523784 0.772026i
\(893\) 3.48667 13.0124i 0.116677 0.435444i
\(894\) 4.21497 + 0.0885070i 0.140970 + 0.00296012i
\(895\) −21.9535 + 38.0246i −0.733826 + 1.27102i
\(896\) −33.7768 + 33.2421i −1.12840 + 1.11054i
\(897\) 1.51410 2.30671i 0.0505543 0.0770187i
\(898\) −59.2437 + 2.14913i −1.97699 + 0.0717174i
\(899\) 30.5097 + 30.5097i 1.01755 + 1.01755i
\(900\) −13.4104 0.563437i −0.447012 0.0187812i
\(901\) −2.52455 + 2.52455i −0.0841050 + 0.0841050i
\(902\) 14.4720 + 13.4587i 0.481863 + 0.448127i
\(903\) −4.56853 + 79.7050i −0.152031 + 2.65242i
\(904\) −9.40951 + 21.3672i −0.312956 + 0.710663i
\(905\) 8.35749 + 4.82520i 0.277812 + 0.160395i
\(906\) 12.4837 + 50.8358i 0.414743 + 1.68890i
\(907\) 9.75684 + 2.61434i 0.323971 + 0.0868077i 0.417139 0.908843i \(-0.363033\pi\)
−0.0931683 + 0.995650i \(0.529699\pi\)
\(908\) 2.85206 14.8876i 0.0946489 0.494063i
\(909\) 5.60307 + 7.05943i 0.185842 + 0.234146i
\(910\) −29.5732 15.6730i −0.980341 0.519556i
\(911\) −25.2358 43.7097i −0.836099 1.44817i −0.893132 0.449794i \(-0.851497\pi\)
0.0570332 0.998372i \(-0.481836\pi\)
\(912\) 8.27631 5.80154i 0.274056 0.192108i
\(913\) −18.8459 + 32.6420i −0.623708 + 1.08029i
\(914\) −6.83512 + 4.28393i −0.226086 + 0.141700i
\(915\) −7.04208 + 21.3176i −0.232804 + 0.704739i
\(916\) 12.5443 + 36.1135i 0.414476 + 1.19322i
\(917\) 22.5830 22.5830i 0.745757 0.745757i
\(918\) 12.5283 9.52195i 0.413496 0.314271i
\(919\) 16.7422i 0.552274i −0.961118 0.276137i \(-0.910946\pi\)
0.961118 0.276137i \(-0.0890544\pi\)
\(920\) −0.335856 + 2.17771i −0.0110729 + 0.0717970i
\(921\) 26.7789 13.4798i 0.882396 0.444175i
\(922\) 12.5512 54.7031i 0.413353 1.80155i
\(923\) 7.28302 + 27.1806i 0.239724 + 0.894661i
\(924\) −1.06224 69.5816i −0.0349453 2.28907i
\(925\) −0.596288 + 2.22538i −0.0196058 + 0.0731699i
\(926\) −8.32164 + 15.7020i −0.273466 + 0.515999i
\(927\) −1.71998 3.96721i −0.0564914 0.130300i
\(928\) −3.08543 + 38.2461i −0.101284 + 1.25549i
\(929\) 9.92665 + 17.1935i 0.325683 + 0.564099i 0.981650 0.190690i \(-0.0610725\pi\)
−0.655967 + 0.754789i \(0.727739\pi\)
\(930\) 13.4179 22.1530i 0.439990 0.726426i
\(931\) 14.8610 3.98199i 0.487049 0.130504i
\(932\) −1.55994 21.4727i −0.0510977 0.703363i
\(933\) 1.10883 0.988613i 0.0363016 0.0323657i
\(934\) 17.8359 + 16.5872i 0.583609 + 0.542749i
\(935\) 17.0708i 0.558273i
\(936\) −27.8159 7.62434i −0.909190 0.249209i
\(937\) 3.05876i 0.0999253i −0.998751 0.0499626i \(-0.984090\pi\)
0.998751 0.0499626i \(-0.0159102\pi\)
\(938\) 41.0330 44.1221i 1.33978 1.44064i
\(939\) −6.45859 31.1340i −0.210768 1.01602i
\(940\) 20.0775 23.2232i 0.654855 0.757457i
\(941\) −11.4732 + 3.07424i −0.374016 + 0.100217i −0.440930 0.897541i \(-0.645351\pi\)
0.0669140 + 0.997759i \(0.478685\pi\)
\(942\) −0.545491 + 25.9779i −0.0177731 + 0.846407i
\(943\) −0.682835 1.18270i −0.0222362 0.0385141i
\(944\) 2.42827 + 5.63562i 0.0790335 + 0.183424i
\(945\) 35.6470 + 6.18387i 1.15960 + 0.201161i
\(946\) −65.9434 34.9483i −2.14401 1.13627i
\(947\) 14.9176 55.6732i 0.484757 1.80914i −0.0963965 0.995343i \(-0.530732\pi\)
0.581153 0.813794i \(-0.302602\pi\)
\(948\) 24.1946 6.88042i 0.785803 0.223466i
\(949\) −7.18430 26.8122i −0.233212 0.870360i
\(950\) 4.49838 + 1.03212i 0.145947 + 0.0334864i
\(951\) −6.03585 3.96187i −0.195726 0.128472i
\(952\) 20.4648 14.9959i 0.663269 0.486020i
\(953\) 44.2546i 1.43355i 0.697306 + 0.716774i \(0.254382\pi\)
−0.697306 + 0.716774i \(0.745618\pi\)
\(954\) −6.95468 + 1.29105i −0.225166 + 0.0417994i
\(955\) −20.2186 + 20.2186i −0.654259 + 0.654259i
\(956\) −19.4304 + 40.1134i −0.628423 + 1.29736i
\(957\) −37.4958 42.0556i −1.21207 1.35946i
\(958\) −16.0519 25.6112i −0.518613 0.827460i
\(959\) 19.9956 34.6334i 0.645691 1.11837i
\(960\) 22.7371 3.67642i 0.733835 0.118656i
\(961\) −4.73171 8.19557i −0.152636 0.264373i
\(962\) −2.31826 + 4.37428i −0.0747436 + 0.141032i
\(963\) −24.5760 + 3.64617i −0.791951 + 0.117496i
\(964\) 30.8307 + 45.4425i 0.992990 + 1.46361i
\(965\) 29.4611 + 7.89407i 0.948386 + 0.254119i
\(966\) −1.34185 + 4.61781i −0.0431734 + 0.148576i
\(967\) −36.7930 21.2424i −1.18318 0.683110i −0.226433 0.974027i \(-0.572706\pi\)
−0.956748 + 0.290916i \(0.906040\pi\)
\(968\) 31.0625 + 13.6790i 0.998385 + 0.439661i
\(969\) −4.83314 + 2.43288i −0.155263 + 0.0781552i
\(970\) 18.1781 19.5466i 0.583664 0.627604i
\(971\) 11.1469 11.1469i 0.357720 0.357720i −0.505252 0.862972i \(-0.668600\pi\)
0.862972 + 0.505252i \(0.168600\pi\)
\(972\) 31.1409 1.49726i 0.998846 0.0480246i
\(973\) −42.8329 42.8329i −1.37316 1.37316i
\(974\) −2.01852 55.6432i −0.0646775 1.78292i
\(975\) −5.92159 11.7638i −0.189643 0.376743i
\(976\) −3.63365 + 30.9794i −0.116310 + 0.991627i
\(977\) −2.47430 + 4.28561i −0.0791598 + 0.137109i −0.902888 0.429877i \(-0.858557\pi\)
0.823728 + 0.566985i \(0.191890\pi\)
\(978\) −10.5527 + 5.80071i −0.337439 + 0.185486i
\(979\) −13.8980 + 51.8682i −0.444183 + 1.65771i
\(980\) 34.4338 + 6.59657i 1.09995 + 0.210720i
\(981\) 1.27795 + 8.61369i 0.0408019 + 0.275014i
\(982\) 14.5714 + 47.4310i 0.464991 + 1.51359i
\(983\) −41.6831 + 24.0658i −1.32948 + 0.767578i −0.985220 0.171294i \(-0.945205\pi\)
−0.344265 + 0.938873i \(0.611872\pi\)
\(984\) −9.56076 + 10.6005i −0.304786 + 0.337931i
\(985\) 17.9237 + 10.3483i 0.571098 + 0.329724i
\(986\) 4.59379 20.0215i 0.146296 0.637614i
\(987\) 50.0074 44.5856i 1.59175 1.41917i
\(988\) 8.92541 + 4.32334i 0.283955 + 0.137544i
\(989\) 3.64672 + 3.64672i 0.115959 + 0.115959i
\(990\) −19.1484 + 27.8784i −0.608577 + 0.886034i
\(991\) −8.90020 −0.282724 −0.141362 0.989958i \(-0.545148\pi\)
−0.141362 + 0.989958i \(0.545148\pi\)
\(992\) 12.0780 33.8962i 0.383478 1.07620i
\(993\) −4.91103 + 7.48188i −0.155847 + 0.237430i
\(994\) −26.0443 41.5544i −0.826076 1.31803i
\(995\) 16.1003 4.31407i 0.510414 0.136765i
\(996\) −23.7829 13.2512i −0.753590 0.419880i
\(997\) −24.8773 6.66586i −0.787873 0.211110i −0.157620 0.987500i \(-0.550382\pi\)
−0.630253 + 0.776390i \(0.717049\pi\)
\(998\) −17.7008 + 5.43789i −0.560309 + 0.172133i
\(999\) 0.914680 5.27268i 0.0289392 0.166820i
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 144.2.x.e.13.18 72
3.2 odd 2 432.2.y.e.253.1 72
4.3 odd 2 576.2.bb.e.337.8 72
9.2 odd 6 432.2.y.e.397.12 72
9.7 even 3 inner 144.2.x.e.61.7 yes 72
12.11 even 2 1728.2.bc.e.145.6 72
16.5 even 4 inner 144.2.x.e.85.7 yes 72
16.11 odd 4 576.2.bb.e.49.16 72
36.7 odd 6 576.2.bb.e.529.16 72
36.11 even 6 1728.2.bc.e.721.13 72
48.5 odd 4 432.2.y.e.37.12 72
48.11 even 4 1728.2.bc.e.1009.13 72
144.11 even 12 1728.2.bc.e.1585.6 72
144.43 odd 12 576.2.bb.e.241.8 72
144.101 odd 12 432.2.y.e.181.1 72
144.133 even 12 inner 144.2.x.e.133.18 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.18 72 1.1 even 1 trivial
144.2.x.e.61.7 yes 72 9.7 even 3 inner
144.2.x.e.85.7 yes 72 16.5 even 4 inner
144.2.x.e.133.18 yes 72 144.133 even 12 inner
432.2.y.e.37.12 72 48.5 odd 4
432.2.y.e.181.1 72 144.101 odd 12
432.2.y.e.253.1 72 3.2 odd 2
432.2.y.e.397.12 72 9.2 odd 6
576.2.bb.e.49.16 72 16.11 odd 4
576.2.bb.e.241.8 72 144.43 odd 12
576.2.bb.e.337.8 72 4.3 odd 2
576.2.bb.e.529.16 72 36.7 odd 6
1728.2.bc.e.145.6 72 12.11 even 2
1728.2.bc.e.721.13 72 36.11 even 6
1728.2.bc.e.1009.13 72 48.11 even 4
1728.2.bc.e.1585.6 72 144.11 even 12